LMFDB - Embedded newform 35.10.k.a.3.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,10,Mod(3,35)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("35.3");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	35.k (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.0262542657$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$34$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			3.14
Character	$\chi$	$=$	35.3
Dual form			35.10.k.a.12.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-10.2381 - 2.74328i) q^{2} +(-21.6326 - 80.7338i) q^{3} +(-346.113 - 199.828i) q^{4} +(1190.45 - 732.094i) q^{5} +885.901i q^{6} +(5772.19 + 2652.45i) q^{7} +(6832.66 + 6832.66i) q^{8} +(10996.0 - 6348.54i) q^{9} +(-14196.2 + 4229.50i) q^{10} +(1932.11 - 3346.52i) q^{11} +(-8645.59 + 32265.8i) q^{12} +(12774.8 - 12774.8i) q^{13} +(-51819.6 - 42990.6i) q^{14} +(-84857.1 - 80272.2i) q^{15} +(51102.8 + 88512.6i) q^{16} +(372544. - 99822.8i) q^{17} +(-129994. + 34831.7i) q^{18} +(-318593. - 551820. i) q^{19} +(-558322. + 15502.3i) q^{20} +(89275.0 - 523390. i) q^{21} +(-28961.5 + 28961.5i) q^{22} +(-294437. + 1.09885e6i) q^{23} +(403819. - 699435. i) q^{24} +(881201. - 1.74304e6i) q^{25} +(-165834. + 95744.3i) q^{26} +(-1.91370e6 - 1.91370e6i) q^{27} +(-1.46779e6 - 2.07149e6i) q^{28} -6.05925e6i q^{29} +(648563. + 1.05462e6i) q^{30} +(449698. + 259633. i) q^{31} +(-1.56085e6 - 5.82519e6i) q^{32} +(-311974. - 83593.1i) q^{33} -4.08797e6 q^{34} +(8.81332e6 - 1.06819e6i) q^{35} -5.07448e6 q^{36} +(-6.89807e6 - 1.84833e6i) q^{37} +(1.74798e6 + 6.52355e6i) q^{38} +(-1.30771e6 - 755007. i) q^{39} +(1.31361e7 + 3.13177e6i) q^{40} +2.94020e7i q^{41} +(-2.34981e6 + 5.11359e6i) q^{42} +(-9.27815e6 - 9.27815e6i) q^{43} +(-1.33746e6 + 772182. i) q^{44} +(8.44242e6 - 1.56077e7i) q^{45} +(6.02893e6 - 1.04424e7i) q^{46} +(-4.11403e6 + 1.53538e7i) q^{47} +(6.04048e6 - 6.04048e6i) q^{48} +(2.62827e7 + 3.06208e7i) q^{49} +(-1.38034e7 + 1.54279e7i) q^{50} +(-1.61181e7 - 2.79174e7i) q^{51} +(-6.97429e6 + 1.86876e6i) q^{52} +(5.95461e7 - 1.59553e7i) q^{53} +(1.43428e7 + 2.48424e7i) q^{54} +(-149889. - 5.39834e6i) q^{55} +(2.13161e7 + 5.75627e7i) q^{56} +(-3.76585e7 + 3.76585e7i) q^{57} +(-1.66222e7 + 6.20350e7i) q^{58} +(-1.85075e7 + 3.20559e7i) q^{59} +(1.33295e7 + 4.47401e7i) q^{60} +(-3.68156e7 + 2.12555e7i) q^{61} +(-3.89178e6 - 3.89178e6i) q^{62} +(8.03101e7 - 7.47867e6i) q^{63} +1.15912e7i q^{64} +(5.85536e6 - 2.45601e7i) q^{65} +(2.96468e6 + 1.71166e6i) q^{66} +(-5.85014e7 - 2.18330e8i) q^{67} +(-1.48890e8 - 3.98948e7i) q^{68} +9.50841e7 q^{69} +(-9.31616e7 - 1.32412e7i) q^{70} +9.71371e7 q^{71} +(1.18509e8 + 3.17545e7i) q^{72} +(-6.89296e7 - 2.57249e8i) q^{73} +(6.55523e7 + 3.78466e7i) q^{74} +(-1.59785e8 - 3.34363e7i) q^{75} +2.54656e8i q^{76} +(2.00290e7 - 1.41919e7i) q^{77} +(1.13172e7 + 1.13172e7i) q^{78} +(-2.78581e8 + 1.60839e8i) q^{79} +(1.25635e8 + 6.79575e7i) q^{80} +(1.18562e7 - 2.05355e7i) q^{81} +(8.06578e7 - 3.01019e8i) q^{82} +(4.06253e8 - 4.06253e8i) q^{83} +(-1.35487e8 + 1.63312e8i) q^{84} +(3.70414e8 - 3.91571e8i) q^{85} +(6.95377e7 + 1.20443e8i) q^{86} +(-4.89186e8 + 1.31077e8i) q^{87} +(3.60671e7 - 9.66415e6i) q^{88} +(-3.62942e8 - 6.28634e8i) q^{89} +(-1.29250e8 + 1.36633e8i) q^{90} +(1.07623e8 - 3.98540e7i) q^{91} +(3.21491e8 - 3.21491e8i) q^{92} +(1.12331e7 - 4.19223e7i) q^{93} +(8.42394e7 - 1.45907e8i) q^{94} +(-7.83252e8 - 4.23672e8i) q^{95} +(-4.36524e8 + 2.52027e8i) q^{96} +(3.74959e8 + 3.74959e8i) q^{97} +(-1.85082e8 - 3.85599e8i) q^{98} -4.90644e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{2} - 6 q^{3} - 1710 q^{5} + 5940 q^{7} - 3484 q^{8} + 153786 q^{10} - 87752 q^{11} + 3066 q^{12} - 318872 q^{15} + 3132804 q^{16} - 1578678 q^{17} - 239036 q^{18} - 5745396 q^{21} + 2132088 q^{22}+ \cdots + 5117393178 q^{98}+O(q^{100}) $ 136 * q - 2 * q^2 - 6 * q^3 - 1710 * q^5 + 5940 * q^7 - 3484 * q^8 + 153786 * q^10 - 87752 * q^11 + 3066 * q^12 - 318872 * q^15 + 3132804 * q^16 - 1578678 * q^17 - 239036 * q^18 - 5745396 * q^21 + 2132088 * q^22 + 312550 * q^23 + 4308518 * q^25 + 2294580 * q^26 - 9559382 * q^28 + 21412708 * q^30 + 8900220 * q^31 + 17154282 * q^32 - 13729410 * q^33 + 6034552 * q^35 - 114903056 * q^36 + 26817310 * q^37 - 20958672 * q^38 + 143985558 * q^40 - 38052106 * q^42 + 46427728 * q^43 - 96332286 * q^45 + 2421124 * q^46 + 147698754 * q^47 - 11742092 * q^50 - 138178540 * q^51 - 126665976 * q^52 - 16288570 * q^53 + 501495076 * q^56 - 71567164 * q^57 - 681848346 * q^58 + 254653694 * q^60 - 575844240 * q^61 + 491512776 * q^63 + 833960586 * q^65 + 260439612 * q^66 + 22092746 * q^67 - 2824755312 * q^68 - 1044240840 * q^70 + 355056144 * q^71 + 98662792 * q^72 + 1852831146 * q^73 + 2937834474 * q^75 + 1226263510 * q^77 + 2595615712 * q^78 - 3778385244 * q^80 + 1504403888 * q^81 - 3707543946 * q^82 - 1726556112 * q^85 + 1771746456 * q^86 + 30331668 * q^87 - 1182712628 * q^88 - 4378590056 * q^91 + 2593806924 * q^92 - 4305536726 * q^93 + 861804818 * q^95 + 15624596040 * q^96 + 5117393178 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−10.2381	−	2.74328i	−0.452462	−	0.121237i	0.0253889	−	0.999678i	$-0.491918\pi$
$2$	−10.2381	−	2.74328i	−0.452462	−	0.121237i	−0.477851	+	0.878441i	$0.658584\pi$
$3$	−21.6326	−	80.7338i	−0.154192	−	0.575453i	−0.999173	−	0.0406565i	$-0.987055\pi$
$3$	−21.6326	−	80.7338i	−0.154192	−	0.575453i	0.844981	−	0.534796i	$-0.179612\pi$
$4$	−346.113	−	199.828i	−0.676002	−	0.390290i
$5$	1190.45	−	732.094i	0.851814	−	0.523844i
$5$	1190.45	−	732.094i	0.851814	−	0.523844i
$6$			885.901i			0.279065i
$7$	5772.19	+	2652.45i	0.908655	+	0.417547i
$7$	5772.19	+	2652.45i	0.908655	+	0.417547i
$8$	6832.66	+	6832.66i	0.589773	+	0.589773i
$9$	10996.0	−	6348.54i	0.558655	−	0.322539i
$10$	−14196.2	+	4229.50i	−0.448923	+	0.133748i
$11$	1932.11	−	3346.52i	0.0397892	−	0.0689169i	−0.845445	−	0.534063i	$-0.820665\pi$
$11$	1932.11	−	3346.52i	0.0397892	−	0.0689169i	0.885234	+	0.465146i	$0.153998\pi$
$12$	−8645.59	+	32265.8i	−0.120359	+	0.449186i
$13$	12774.8	−	12774.8i	0.124054	−	0.124054i	−0.642354	−	0.766408i	$-0.722042\pi$
$13$	12774.8	−	12774.8i	0.124054	−	0.124054i	0.766408	+	0.642354i	$0.222042\pi$
$14$	−51819.6	−	42990.6i	−0.360510	−	0.299087i
$15$	−84857.1	−	80272.2i	−0.432790	−	0.409406i
$16$	51102.8	+	88512.6i	0.194942	+	0.337649i
$17$	372544.	−	99822.8i	1.08183	−	0.289874i	0.326482	−	0.945203i	$-0.394137\pi$
$17$	372544.	−	99822.8i	1.08183	−	0.289874i	0.755343	+	0.655329i	$0.227470\pi$
$18$	−129994.	+	34831.7i	−0.291874	+	0.0782074i
$19$	−318593.	−	551820.i	−0.560848	−	0.971418i	−0.997423	−	0.0717496i	$-0.977142\pi$
$19$	−318593.	−	551820.i	−0.560848	−	0.971418i	0.436574	−	0.899668i	$-0.356192\pi$
$20$	−558322.	+	15502.3i	−0.780279	+	0.0216651i
$21$	89275.0	−	523390.i	0.100171	−	0.587271i
$22$	−28961.5	+	28961.5i	−0.0263584	+	0.0263584i
$23$	−294437.	+	1.09885e6i	−0.219390	+	0.818775i	0.765185	+	0.643811i	$0.222648\pi$
$23$	−294437.	+	1.09885e6i	−0.219390	+	0.818775i	−0.984575	+	0.174964i	$0.944019\pi$
$24$	403819.	−	699435.i	0.248448	−	0.430325i
$25$	881201.	−	1.74304e6i	0.451175	−	0.892436i
$26$	−165834.	+	95744.3i	−0.0711694	+	0.0410897i
$27$	−1.91370e6	−	1.91370e6i	−0.693007	−	0.693007i
$28$	−1.46779e6	−	2.07149e6i	−0.451288	−	0.636901i
$29$		−	6.05925e6i		−	1.59085i	−0.606055	−	0.795423i	$-0.707249\pi$
$29$		−	6.05925e6i		−	1.59085i	0.606055	−	0.795423i	$-0.292751\pi$
$30$	648563.	+	1.05462e6i	0.146186	+	0.237711i
$31$	449698.	+	259633.i	0.0874567	+	0.0504931i	0.543091	−	0.839674i	$-0.317254\pi$
$31$	449698.	+	259633.i	0.0874567	+	0.0504931i	−0.455634	+	0.890167i	$0.650587\pi$
$32$	−1.56085e6	−	5.82519e6i	−0.263140	−	0.982053i
$33$	−311974.	−	83593.1i	−0.0457936	−	0.0122704i
$34$	−4.08797e6			−0.524629
$35$	8.81332e6	−	1.06819e6i	0.992735	−	0.120321i
$36$	−5.07448e6			−0.503535
$37$	−6.89807e6	−	1.84833e6i	−0.605090	−	0.162133i	−0.0567491	−	0.998388i	$-0.518074\pi$
$37$	−6.89807e6	−	1.84833e6i	−0.605090	−	0.162133i	−0.548340	+	0.836255i	$0.684740\pi$
$38$	1.74798e6	+	6.52355e6i	0.135991	+	0.507526i
$39$	−1.30771e6	−	755007.i	−0.0905150	−	0.0522589i
$40$	1.31361e7	+	3.13177e6i	0.811327	+	0.193428i
$41$			2.94020e7i			1.62498i	0.582973	+	0.812492i	$0.301889\pi$
$41$			2.94020e7i			1.62498i	−0.582973	+	0.812492i	$0.698111\pi$
$42$	−2.34981e6	+	5.11359e6i	−0.116523	+	0.253573i
$43$	−9.27815e6	−	9.27815e6i	−0.413860	−	0.413860i	0.469221	−	0.883081i	$-0.344535\pi$
$43$	−9.27815e6	−	9.27815e6i	−0.413860	−	0.413860i	−0.883081	+	0.469221i	$0.844535\pi$
$44$	−1.33746e6	+	772182.i	−0.0537951	+	0.0310586i
$45$	8.44242e6	−	1.56077e7i	0.306910	−	0.567392i
$46$	6.02893e6	−	1.04424e7i	0.198532	−	0.343867i
$47$	−4.11403e6	+	1.53538e7i	−0.122978	+	0.458960i	−0.999760	−	0.0219289i	$-0.993019\pi$
$47$	−4.11403e6	+	1.53538e7i	−0.122978	+	0.458960i	0.876782	+	0.480889i	$0.159686\pi$
$48$	6.04048e6	−	6.04048e6i	0.164243	−	0.164243i
$49$	2.62827e7	+	3.06208e7i	0.651309	+	0.758813i
$50$	−1.38034e7	+	1.54279e7i	−0.312336	+	0.349095i
$51$	−1.61181e7	−	2.79174e7i	−0.333618	−	0.577843i
$52$	−6.97429e6	+	1.86876e6i	−0.132277	+	0.0354436i
$53$	5.95461e7	−	1.59553e7i	1.03660	−	0.277757i	0.299898	−	0.953971i	$-0.403047\pi$
$53$	5.95461e7	−	1.59553e7i	1.03660	−	0.277757i	0.736705	+	0.676215i	$0.236381\pi$
$54$	1.43428e7	+	2.48424e7i	0.229542	+	0.397578i
$55$	−149889.	−	5.39834e6i	−0.00220871	−	0.0795478i
$56$	2.13161e7	+	5.75627e7i	0.289642	+	0.782159i
$57$	−3.76585e7	+	3.76585e7i	−0.472527	+	0.472527i
$58$	−1.66222e7	+	6.20350e7i	−0.192869	+	0.719798i
$59$	−1.85075e7	+	3.20559e7i	−0.198845	+	0.344409i	−0.948154	−	0.317811i	$-0.897052\pi$
$59$	−1.85075e7	+	3.20559e7i	−0.198845	+	0.344409i	0.749310	+	0.662220i	$0.230386\pi$
$60$	1.33295e7	+	4.47401e7i	0.132780	+	0.445673i
$61$	−3.68156e7	+	2.12555e7i	−0.340446	+	0.196556i	−0.660469	−	0.750853i	$-0.729643\pi$
$61$	−3.68156e7	+	2.12555e7i	−0.340446	+	0.196556i	0.320023	+	0.947410i	$0.396309\pi$
$62$	−3.89178e6	−	3.89178e6i	−0.0334492	−	0.0334492i
$63$	8.03101e7	−	7.47867e6i	0.642300	−	0.0598125i
$64$			1.15912e7i			0.0863611i
$65$	5.85536e6	−	2.45601e7i	0.0406859	−	0.170655i
$66$	2.96468e6	+	1.71166e6i	0.0192323	+	0.0111038i
$67$	−5.85014e7	−	2.18330e8i	−0.354674	−	1.32366i	−0.880894	−	0.473314i	$-0.843058\pi$
$67$	−5.85014e7	−	2.18330e8i	−0.354674	−	1.32366i	0.526220	−	0.850349i	$-0.323609\pi$
$68$	−1.48890e8	−	3.98948e7i	−0.844451	−	0.226270i
$69$	9.50841e7			0.504995
$70$	−9.31616e7	−	1.32412e7i	−0.463763	−	0.0659155i
$71$	9.71371e7			0.453652			0.226826	−	0.973935i	$-0.427165\pi$
$71$	9.71371e7			0.453652			0.226826	+	0.973935i	$0.427165\pi$
$72$	1.18509e8	+	3.17545e7i	0.519705	+	0.139254i
$73$	−6.89296e7	−	2.57249e8i	−0.284088	−	1.06023i	−0.949503	−	0.313758i	$-0.898412\pi$
$73$	−6.89296e7	−	2.57249e8i	−0.284088	−	1.06023i	0.665415	−	0.746474i	$-0.268255\pi$
$74$	6.55523e7	+	3.78466e7i	0.254124	+	0.146718i
$75$	−1.59785e8	−	3.34363e7i	−0.583122	−	0.122023i
$76$			2.54656e8i			0.875573i
$77$	2.00290e7	−	1.41919e7i	0.0649308	−	0.0460079i
$78$	1.13172e7	+	1.13172e7i	0.0346189	+	0.0346189i
$79$	−2.78581e8	+	1.60839e8i	−0.804692	+	0.464589i	−0.845109	−	0.534594i	$-0.820465\pi$
$79$	−2.78581e8	+	1.60839e8i	−0.804692	+	0.464589i	0.0404172	+	0.999183i	$0.487131\pi$
$80$	1.25635e8	+	6.79575e7i	0.342929	+	0.185495i
$81$	1.18562e7	−	2.05355e7i	0.0306029	−	0.0530058i
$82$	8.06578e7	−	3.01019e8i	0.197008	−	0.735244i
$83$	4.06253e8	−	4.06253e8i	0.939606	−	0.939606i	−0.0586716	−	0.998277i	$-0.518686\pi$
$83$	4.06253e8	−	4.06253e8i	0.939606	−	0.939606i	0.998277	+	0.0586716i	$0.0186865\pi$
$84$	−1.35487e8	+	1.63312e8i	−0.296922	+	0.357900i
$85$	3.70414e8	−	3.91571e8i	0.769665	−	0.813627i
$86$	6.95377e7	+	1.20443e8i	0.137081	+	0.237431i
$87$	−4.89186e8	+	1.31077e8i	−0.915456	+	0.245296i
$88$	3.60671e7	−	9.66415e6i	0.0641120	−	0.0171788i
$89$	−3.62942e8	−	6.28634e8i	−0.613172	−	1.06204i	−0.990702	−	0.136048i	$-0.956560\pi$
$89$	−3.62942e8	−	6.28634e8i	−0.613172	−	1.06204i	0.377530	−	0.925997i	$-0.376773\pi$
$90$	−1.29250e8	+	1.36633e8i	−0.207654	+	0.219515i
$91$	1.07623e8	−	3.98540e7i	0.164520	−	0.0609237i
$92$	3.21491e8	−	3.21491e8i	0.467868	−	0.467868i
$93$	1.12331e7	−	4.19223e7i	0.0155713	−	0.0581128i
$94$	8.42394e7	−	1.45907e8i	0.111286	−	0.192753i
$95$	−7.83252e8	−	4.23672e8i	−0.986610	−	0.533670i
$96$	−4.36524e8	+	2.52027e8i	−0.524551	+	0.302850i
$97$	3.74959e8	+	3.74959e8i	0.430042	+	0.430042i	0.888643	−	0.458600i	$-0.151649\pi$
$97$	3.74959e8	+	3.74959e8i	0.430042	+	0.430042i	−0.458600	+	0.888643i	$0.651649\pi$
$98$	−1.85082e8	−	3.85599e8i	−0.202697	−	0.422297i
$99$		−	4.90644e7i		−	0.0513344i
$100$	−6.53303e8	+	4.27199e8i	−0.653303	+	0.427199i
$101$	−8.00738e8	−	4.62306e8i	−0.765675	−	0.442063i	0.0656546	−	0.997842i	$-0.479086\pi$
$101$	−8.00738e8	−	4.62306e8i	−0.765675	−	0.442063i	−0.831330	+	0.555780i	$0.812420\pi$
$102$	8.84332e7	+	3.30037e8i	0.0808936	+	0.301899i
$103$	1.69925e9	+	4.55312e8i	1.48761	+	0.398604i	0.908929	−	0.416951i	$-0.136901\pi$
$103$	1.69925e9	+	4.55312e8i	1.48761	+	0.398604i	0.578680	+	0.815555i	$0.303568\pi$
$104$	1.74572e8			0.146327
$105$	−2.76893e8	−	6.88425e8i	−0.222311	−	0.552720i
$106$	−6.53407e8			−0.502698
$107$	−1.06280e9	−	2.84777e8i	−0.783837	−	0.210028i	−0.155361	−	0.987858i	$-0.549654\pi$
$107$	−1.06280e9	−	2.84777e8i	−0.783837	−	0.210028i	−0.628476	+	0.777829i	$0.716321\pi$
$108$	2.79945e8	+	1.04477e9i	0.198000	+	0.738947i
$109$	2.31872e9	+	1.33871e9i	1.57336	+	0.908381i	0.995753	+	0.0920683i	$0.0293478\pi$
$109$	2.31872e9	+	1.33871e9i	1.57336	+	0.908381i	0.577610	+	0.816313i	$0.303986\pi$
$110$	−1.32746e7	+	5.56797e7i	−0.00864477	+	0.0362602i
$111$			5.96891e8i			0.373200i
$112$	6.01997e7	+	6.46459e8i	0.0361504	+	0.388204i
$113$	2.38195e8	+	2.38195e8i	0.137429	+	0.137429i	0.772475	−	0.635046i	$-0.219019\pi$
$113$	2.38195e8	+	2.38195e8i	0.137429	+	0.137429i	−0.635046	+	0.772475i	$0.719019\pi$
$114$	4.88858e8	−	2.82242e8i	0.271088	−	0.156513i
$115$	4.53953e8	+	1.52368e9i	0.242031	+	0.812371i
$116$	−1.21081e9	+	2.09718e9i	−0.620890	+	1.07541i
$117$	5.93703e7	−	2.21573e8i	0.0292909	−	0.109315i
$118$	2.77419e8	−	2.77419e8i	0.131725	−	0.131725i
$119$	2.41517e9	+	4.11957e8i	1.10404	+	0.188317i
$120$	−3.13274e7	−	1.12827e9i	−0.0137914	−	0.496705i
$121$	1.17151e9	+	2.02911e9i	0.496834	+	0.860541i
$122$	4.35230e8	−	1.16620e8i	0.177869	−	0.0476598i
$123$	2.37373e9	−	6.36039e8i	0.935101	−	0.250560i
$124$	−1.03764e8	−	1.79725e8i	−0.0394139	−	0.0682669i
$125$	−2.27045e8	−	2.72012e9i	−0.0831798	−	0.996535i
$126$	−8.42736e8	−	1.43746e8i	−0.297868	−	0.0508076i
$127$	−4.78836e8	+	4.78836e8i	−0.163331	+	0.163331i	−0.784041	−	0.620709i	$-0.786845\pi$
$127$	−4.78836e8	+	4.78836e8i	−0.163331	+	0.163331i	0.620709	+	0.784041i	$0.286845\pi$
$128$	−7.67359e8	+	2.86382e9i	−0.252670	+	0.942978i
$129$	−5.48350e8	+	9.49771e8i	−0.174343	+	0.301971i
$130$	−1.27323e8	+	2.35385e8i	−0.0390985	+	0.0722825i
$131$	−4.51190e9	+	2.60495e9i	−1.33856	+	0.772820i	−0.986594	−	0.163192i	$-0.947821\pi$
$131$	−4.51190e9	+	2.60495e9i	−1.33856	+	0.772820i	−0.351969	+	0.936012i	$0.614488\pi$
$132$	9.12738e7	+	9.12738e7i	0.0261676	+	0.0261676i
$133$	−3.75307e8	−	4.03026e9i	−0.104005	−	1.11686i
$134$			2.39576e9i			0.641907i
$135$	−3.67917e9	−	8.77150e8i	−0.953341	−	0.227286i
$136$	3.22752e9	+	1.86341e9i	0.808992	+	0.467072i
$137$	−1.78645e9	−	6.66711e9i	−0.433259	−	1.61694i	−0.745199	−	0.666842i	$-0.767646\pi$
$137$	−1.78645e9	−	6.66711e9i	−0.433259	−	1.61694i	0.311940	−	0.950102i	$-0.399021\pi$
$138$	−9.73476e8	−	2.60842e8i	−0.228491	−	0.0612240i
$139$	2.89309e9			0.657349			0.328674	−	0.944443i	$-0.393398\pi$
$139$	2.89309e9			0.657349			0.328674	+	0.944443i	$0.393398\pi$
$140$	−3.26386e9	−	1.39144e9i	−0.718050	−	0.306117i
$141$	1.32856e9			0.283072
$142$	−9.94495e8	−	2.66474e8i	−0.205260	−	0.0549994i
$143$	−1.80687e7	−	6.74335e7i	−0.00361340	−	0.0134854i
$144$	1.12385e9	+	6.48857e8i	0.217810	+	0.125753i
$145$	−4.43594e9	−	7.21321e9i	−0.833355	−	1.35510i
$146$			2.82282e9i			0.514157i
$147$	1.90358e9	−	2.78431e9i	0.336234	−	0.491800i
$148$	2.01816e9	+	2.01816e9i	0.345763	+	0.345763i
$149$	−5.39244e8	+	3.11333e8i	−0.0896287	+	0.0517472i	−0.544144	−	0.838992i	$-0.683146\pi$
$149$	−5.39244e8	+	3.11333e8i	−0.0896287	+	0.0517472i	0.454516	+	0.890739i	$0.349812\pi$
$150$	1.54416e9	+	7.80657e8i	0.249047	+	0.125907i
$151$	1.15507e9	−	2.00065e9i	0.180806	−	0.313165i	−0.761349	−	0.648342i	$-0.775463\pi$
$151$	1.15507e9	−	2.00065e9i	0.180806	−	0.313165i	0.942155	+	0.335177i	$0.108796\pi$
$152$	1.59356e9	−	5.94724e9i	0.242143	−	0.903690i
$153$	3.46276e9	−	3.46276e9i	0.510871	−	0.510871i
$154$	−2.43990e8	+	9.03524e7i	−0.0349566	+	0.0129448i
$155$	7.25417e8	−	2.01418e7i	0.100947	−	0.00280288i
$156$	3.01743e8	+	5.22635e8i	0.0407922	+	0.0706541i
$157$	8.59720e8	−	2.30361e8i	0.112930	−	0.0302595i	−0.201912	−	0.979404i	$-0.564715\pi$
$157$	8.59720e8	−	2.30361e8i	0.112930	−	0.0302595i	0.314841	+	0.949144i	$0.398049\pi$
$158$	3.29335e9	−	8.82452e8i	0.420418	−	0.112651i
$159$	−2.57627e9	−	4.46223e9i	−0.319672	−	0.553688i
$160$	−6.12270e9	−	5.79188e9i	−0.738589	−	0.698682i
$161$	−4.61420e9	+	5.56181e9i	−0.541227	+	0.652379i
$162$	−1.77719e8	+	1.77719e8i	−0.0202729	+	0.0202729i
$163$	−1.93714e9	+	7.22950e9i	−0.214940	+	0.802166i	0.771248	+	0.636535i	$0.219633\pi$
$163$	−1.93714e9	+	7.22950e9i	−0.214940	+	0.802166i	−0.986188	+	0.165631i	$0.947034\pi$
$164$	5.87534e9	−	1.01764e10i	0.634214	−	1.09849i
$165$	−4.32586e8	+	1.28881e8i	−0.0454354	+	0.0135366i
$166$	−5.27371e9	+	3.04478e9i	−0.539051	+	0.311221i
$167$	−1.75389e9	−	1.75389e9i	−0.174493	−	0.174493i	0.614457	−	0.788950i	$-0.289375\pi$
$167$	−1.75389e9	−	1.75389e9i	−0.174493	−	0.174493i	−0.788950	+	0.614457i	$0.789375\pi$
$168$	4.18613e9	−	2.96616e9i	0.405435	−	0.287278i
$169$			1.02781e10i			0.969221i
$170$	−4.86651e9	+	2.99278e9i	−0.446886	+	0.274824i
$171$	−7.00650e9	−	4.04521e9i	−0.626641	−	0.361791i
$172$	1.35725e9	+	5.06533e9i	0.118245	+	0.441295i
$173$	−9.29831e9	−	2.49148e9i	−0.789218	−	0.211470i	−0.158373	−	0.987379i	$-0.550625\pi$
$173$	−9.29831e9	−	2.49148e9i	−0.789218	−	0.211470i	−0.630845	+	0.775909i	$0.717291\pi$
$174$	5.36790e9			0.443948
$175$	9.70977e9	−	7.72380e9i	0.782596	−	0.622529i
$176$	3.94945e8			0.0310263
$177$	2.98836e9	+	8.00729e8i	0.228851	+	0.0613205i
$178$	1.99130e9	+	7.43164e9i	0.148678	+	0.554875i
$179$	1.71643e10	+	9.90979e9i	1.24964	+	0.721483i	0.971039	−	0.238923i	$-0.0767942\pi$
$179$	1.71643e10	+	9.90979e9i	1.24964	+	0.721483i	0.278606	+	0.960405i	$0.410128\pi$
$180$	−6.04089e9	+	3.71499e9i	−0.428919	+	0.263774i
$181$			9.29447e9i			0.643681i	0.946794	+	0.321841i	$0.104302\pi$
$181$			9.29447e9i			0.643681i	−0.946794	+	0.321841i	$0.895698\pi$
$182$	−1.21118e9	+	1.12788e8i	−0.0818254	+	0.00761977i
$183$	2.51245e9	+	2.51245e9i	0.165603	+	0.165603i
$184$	−9.51989e9	+	5.49631e9i	−0.612282	+	0.353501i
$185$	−9.56493e9	+	2.84970e9i	−0.600356	+	0.178865i
$186$	−2.30009e8	+	3.98388e8i	−0.0140908	+	0.0244061i
$187$	3.85738e8	−	1.43959e9i	0.0230677	−	0.0860900i
$188$	4.49204e9	−	4.49204e9i	0.262261	−	0.262261i
$189$	−5.97025e9	−	1.61222e10i	−0.340341	−	0.919068i
$190$	6.85673e9	+	6.48625e9i	0.381703	+	0.361079i
$191$	9.75213e9	+	1.68912e10i	0.530212	+	0.918354i	0.999379	+	0.0352444i	$0.0112210\pi$
$191$	9.75213e9	+	1.68912e10i	0.530212	+	0.918354i	−0.469167	+	0.883110i	$0.655446\pi$
$192$	9.35801e8	−	2.50747e8i	0.0496967	−	0.0133162i
$193$	2.64390e10	−	7.08432e9i	1.37163	−	0.367528i	0.503558	−	0.863962i	$-0.332024\pi$
$193$	2.64390e10	−	7.08432e9i	1.37163	−	0.367528i	0.868075	+	0.496434i	$0.165357\pi$
$194$	−2.81024e9	−	4.86747e9i	−0.142441	−	0.246715i
$195$	−2.10949e9	+	5.85718e7i	−0.104477	+	0.00290090i
$196$	−2.97785e9	−	1.58503e10i	−0.144129	−	0.767158i
$197$	−2.19522e10	+	2.19522e10i	−1.03844	+	1.03844i	−0.0392070	+	0.999231i	$0.512483\pi$
$197$	−2.19522e10	+	2.19522e10i	−1.03844	+	1.03844i	−0.999231	+	0.0392070i	$0.987517\pi$
$198$	−1.34597e8	+	5.02324e8i	−0.00622362	+	0.0232269i
$199$	−1.10686e10	+	1.91713e10i	−0.500326	+	0.866590i	0.499674	+	0.866214i	$0.333453\pi$
$199$	−1.10686e10	+	1.91713e10i	−0.500326	+	0.866590i	−1.00000		0.000376564i	$0.999880\pi$
$200$	1.79305e10	−	5.88864e9i	0.792426	−	0.260244i
$201$	−1.63611e10	+	9.44608e9i	−0.707017	+	0.408197i
$202$	6.92977e9	+	6.92977e9i	0.292845	+	0.292845i
$203$	1.60718e10	−	3.49751e10i	0.664253	−	1.44553i
$204$			1.28834e10i			0.520830i
$205$	2.15250e10	+	3.50015e10i	0.851238	+	1.38418i
$206$	−1.61479e10	−	9.32301e9i	−0.624762	−	0.360706i
$207$	3.73849e9	+	1.39522e10i	0.141524	+	0.528175i
$208$	1.78356e9	+	4.77903e8i	0.0660697	+	0.0177033i
$209$	−2.46223e9			−0.0892629
$210$	9.46309e8	+	7.80773e9i	0.0335773	+	0.277037i
$211$	3.88771e10			1.35028			0.675139	−	0.737691i	$-0.264084\pi$
$211$	3.88771e10			1.35028			0.675139	+	0.737691i	$0.264084\pi$
$212$	−2.37980e10	−	6.37666e9i	−0.809150	−	0.216811i
$213$	−2.10132e9	−	7.84225e9i	−0.0699495	−	0.261055i
$214$	1.00998e10	+	5.83113e9i	0.329194	+	0.190060i
$215$	−1.78376e10	−	4.25266e9i	−0.569330	−	0.135734i
$216$		−	2.61514e10i		−	0.817434i
$217$	1.90708e9	+	2.69145e9i	0.0583847	+	0.0823981i
$218$	−2.00667e10	−	2.00667e10i	−0.601758	−	0.601758i
$219$	−1.92776e10	+	1.11299e10i	−0.566309	+	0.326959i
$220$	−1.02686e9	+	1.89839e9i	−0.0295536	+	0.0546365i
$221$	3.48396e9	−	6.03439e9i	0.0982443	−	0.170164i
$222$	1.63744e9	−	6.11101e9i	0.0452456	−	0.168859i
$223$	−4.65121e10	+	4.65121e10i	−1.25949	+	1.25949i	−0.308150	+	0.951338i	$0.599710\pi$
$223$	−4.65121e10	+	4.65121e10i	−1.25949	+	1.25949i	−0.951338	+	0.308150i	$0.900290\pi$
$224$	6.44146e9	−	3.77641e10i	0.170950	−	1.00222i
$225$	−1.37607e9	−	2.47608e10i	−0.0357947	−	0.644085i
$226$	−1.78522e9	−	3.09208e9i	−0.0455200	−	0.0788430i
$227$	1.58304e9	−	4.24175e8i	0.0395709	−	0.0106030i	−0.238979	−	0.971025i	$-0.576813\pi$
$227$	1.58304e9	−	4.24175e8i	0.0395709	−	0.0106030i	0.278550	+	0.960422i	$0.410146\pi$
$228$	2.05593e10	−	5.50886e9i	0.503851	−	0.135006i
$229$	−2.78781e10	−	4.82863e10i	−0.669890	−	1.16028i	−0.977934	−	0.208912i	$-0.933008\pi$
$229$	−2.78781e10	−	4.82863e10i	−0.669890	−	1.16028i	0.308044	−	0.951372i	$-0.400326\pi$
$230$	−4.67711e8	−	1.68449e10i	−0.0110205	−	0.396910i
$231$	−1.57904e9	−	1.31001e9i	−0.0364872	−	0.0302705i
$232$	4.14008e10	−	4.14008e10i	0.938238	−	0.938238i
$233$	−1.09736e10	+	4.09540e10i	−0.243920	+	0.910322i	0.730003	+	0.683444i	$0.239519\pi$
$233$	−1.09736e10	+	4.09540e10i	−0.243920	+	0.910322i	−0.973923	+	0.226878i	$0.927148\pi$
$234$	−1.21567e9	+	2.10561e9i	−0.0265061	+	0.0459099i
$235$	6.34287e9	+	2.12897e10i	0.135669	+	0.455370i
$236$	1.28114e10	−	7.39664e9i	0.268838	−	0.155214i
$237$	1.90115e10	+	1.90115e10i	0.391426	+	0.391426i
$238$	−2.35965e10	−	1.08431e10i	−0.476707	−	0.219057i
$239$			4.80069e10i			0.951728i	0.879519	+	0.475864i	$0.157865\pi$
$239$			4.80069e10i			0.951728i	−0.879519	+	0.475864i	$0.842135\pi$
$240$	2.76867e9	−	1.16131e10i	0.0538667	−	0.225942i
$241$	7.18409e10	+	4.14774e10i	1.37181	+	0.792017i	0.991156	−	0.132699i	$-0.0423643\pi$
$241$	7.18409e10	+	4.14774e10i	1.37181	+	0.792017i	0.380658	+	0.924716i	$0.375698\pi$
$242$	−6.42755e9	−	2.39879e10i	−0.120469	−	0.449597i
$243$	−5.33690e10	−	1.43002e10i	−0.981886	−	0.263096i
$244$	1.69898e10			0.306856
$245$	5.37054e10	+	1.72111e10i	0.952294	+	0.305183i
$246$	−2.60472e10			−0.453475
$247$	−1.11194e10	−	2.97942e9i	−0.190083	−	0.0509326i
$248$	1.29865e9	+	4.84662e9i	0.0218001	+	0.0813591i
$249$	−4.15867e10	−	2.40101e10i	−0.685578	−	0.395819i
$250$	−5.13753e9	+	2.84716e10i	−0.0831811	+	0.460979i
$251$		−	6.15075e10i		−	0.978129i	−0.872248	−	0.489064i	$-0.837338\pi$
$251$		−	6.15075e10i		−	0.978129i	0.872248	−	0.489064i	$-0.162662\pi$
$252$	−2.92908e10	−	1.34598e10i	−0.457540	−	0.210250i
$253$	3.10845e9	+	3.10845e9i	0.0476981	+	0.0476981i
$254$	6.21593e9	−	3.58877e9i	0.0937031	−	0.0540995i
$255$	−3.96260e10	−	2.14342e10i	−0.586880	−	0.317451i
$256$	1.86799e10	−	3.23545e10i	0.271828	−	0.470820i
$257$	1.41269e10	−	5.27222e10i	0.201998	−	0.753867i	−0.788346	−	0.615233i	$-0.789062\pi$
$257$	1.41269e10	−	5.27222e10i	0.201998	−	0.753867i	0.990344	−	0.138634i	$-0.0442713\pi$
$258$	8.21953e9	−	8.21953e9i	0.115494	−	0.115494i
$259$	−3.49143e10	−	2.89657e10i	−0.482120	−	0.399977i
$260$	−6.93441e9	+	7.33049e9i	−0.0941087	+	0.0994839i
$261$	−3.84674e10	−	6.66275e10i	−0.513110	−	0.888733i
$262$	5.33392e10	−	1.42922e10i	0.699344	−	0.187389i
$263$	−6.00181e10	+	1.60818e10i	−0.773538	+	0.207269i	−0.623934	−	0.781477i	$-0.714466\pi$
$263$	−6.00181e10	+	1.60818e10i	−0.773538	+	0.207269i	−0.149604	+	0.988746i	$0.547800\pi$
$264$	−1.56045e9	−	2.70277e9i	−0.0197711	−	0.0342446i
$265$	5.92057e10	−	6.25874e10i	0.737491	−	0.779615i
$266$	−7.21371e9	+	4.22916e10i	−0.0883469	+	0.517949i
$267$	−4.29006e10	+	4.29006e10i	−0.516610	+	0.516610i
$268$	−2.33805e10	+	8.72571e10i	−0.276851	+	1.03322i
$269$	1.74477e10	−	3.02203e10i	0.203167	−	0.351895i	−0.746380	−	0.665520i	$-0.768210\pi$
$269$	1.74477e10	−	3.02203e10i	0.203167	−	0.351895i	0.949547	+	0.313624i	$0.101543\pi$
$270$	3.52613e10	+	1.90733e10i	0.403796	+	0.218418i
$271$	4.60621e10	−	2.65940e10i	0.518778	−	0.299517i	−0.217656	−	0.976025i	$-0.569841\pi$
$271$	4.60621e10	−	2.65940e10i	0.518778	−	0.299517i	0.736435	+	0.676509i	$0.236508\pi$
$272$	2.78736e10	+	2.78736e10i	0.308769	+	0.308769i
$273$	−5.54573e9	−	7.82667e9i	−0.0604264	−	0.0852796i
$274$			7.31590e10i			0.784133i
$275$	−4.13053e9	−	6.31670e9i	−0.0435520	−	0.0666029i
$276$	−3.29098e10	−	1.90005e10i	−0.341377	−	0.197094i
$277$	1.62284e10	+	6.05651e10i	0.165621	+	0.618107i	0.997960	+	0.0638400i	$0.0203347\pi$
$277$	1.62284e10	+	6.05651e10i	0.165621	+	0.618107i	−0.832339	+	0.554267i	$0.812999\pi$
$278$	−2.96197e10	−	7.93657e9i	−0.297426	−	0.0796950i
$279$	6.59317e9			0.0651441
$280$	6.75170e10	+	5.29199e10i	0.656451	+	0.514527i
$281$	1.07128e11			1.02501			0.512503	−	0.858686i	$-0.328719\pi$
$281$	1.07128e11			1.02501			0.512503	+	0.858686i	$0.328719\pi$
$282$	−1.36019e10	−	3.64462e9i	−0.128079	−	0.0343188i
$283$	2.22388e10	+	8.29965e10i	0.206098	+	0.769167i	0.989112	+	0.147164i	$0.0470144\pi$
$283$	2.22388e10	+	8.29965e10i	0.206098	+	0.769167i	−0.783014	+	0.622003i	$0.786319\pi$
$284$	−3.36204e10	−	1.94107e10i	−0.306669	−	0.177056i
$285$	−1.72609e10	+	7.24000e10i	−0.154975	+	0.650035i
$286$			7.39955e8i			0.00653971i
$287$	−7.79871e10	+	1.69714e11i	−0.678507	+	1.47655i
$288$	−5.41446e10	−	5.41446e10i	−0.463755	−	0.463755i
$289$	2.61242e10	−	1.50828e10i	0.220294	−	0.127187i
$290$	2.56276e10	+	8.60183e10i	0.212773	+	0.714167i
$291$	2.21606e10	−	3.83832e10i	0.181160	−	0.313778i
$292$	−2.75482e10	+	1.02811e11i	−0.221753	+	0.827595i
$293$	7.27727e10	−	7.27727e10i	0.576851	−	0.576851i	−0.357183	−	0.934034i	$-0.616263\pi$
$293$	7.27727e10	−	7.27727e10i	0.576851	−	0.576851i	0.934034	+	0.357183i	$0.116263\pi$
$294$	−2.71270e10	+	2.32838e10i	−0.211758	+	0.181757i
$295$	1.43577e9	+	5.17101e10i	0.0110379	+	0.397536i
$296$	−3.45031e10	−	5.97612e10i	−0.261244	−	0.452488i
$297$	−1.01017e10	+	2.70675e9i	−0.0753341	+	0.0201857i
$298$	6.37488e9	−	1.70815e9i	0.0468273	−	0.0125473i
$299$	1.02763e10	+	1.77990e10i	0.0743558	+	0.128788i
$300$	4.86220e10	+	4.35022e10i	0.346567	+	0.310074i
$301$	−2.89454e10	−	7.81651e10i	−0.203250	−	0.548862i
$302$	−1.73140e10	+	1.73140e10i	−0.119775	+	0.119775i
$303$	−2.00017e10	+	7.46475e10i	−0.136325	+	0.508772i
$304$	3.25620e10	−	5.63991e10i	0.218665	−	0.378740i
$305$	−2.82660e10	+	5.22560e10i	−0.187032	+	0.345770i
$306$	−4.49513e10	+	2.59526e10i	−0.293086	+	0.169214i
$307$	7.45205e10	+	7.45205e10i	0.478799	+	0.478799i	0.904747	−	0.425949i	$-0.140060\pi$
$307$	7.45205e10	+	7.45205e10i	0.478799	+	0.478799i	−0.425949	+	0.904747i	$0.640060\pi$
$308$	−9.76823e9	+	9.09640e8i	−0.0618497	+	0.00575959i
$309$		−	1.47036e11i		−	0.917510i
$310$	−7.48211e9	−	1.78381e9i	−0.0460147	−	0.0109704i
$311$	−1.01416e11	−	5.85524e10i	−0.614729	−	0.354914i	0.160085	−	0.987103i	$-0.448823\pi$
$311$	−1.01416e11	−	5.85524e10i	−0.614729	−	0.354914i	−0.774814	+	0.632190i	$0.782156\pi$
$312$	−3.77643e9	−	1.40938e10i	−0.0225625	−	0.0842042i
$313$	2.03038e11	+	5.44038e10i	1.19571	+	0.320391i	0.801142	−	0.598474i	$-0.204226\pi$
$313$	2.03038e11	+	5.44038e10i	1.19571	+	0.320391i	0.394572	+	0.918865i	$0.370893\pi$
$314$	−9.43381e9			−0.0547651
$315$	9.01298e10	−	6.76975e10i	0.515788	−	0.387414i
$316$	1.28561e11			0.725297
$317$	1.71798e11	+	4.60332e10i	0.955547	+	0.256038i	0.702715	−	0.711472i	$-0.251971\pi$
$317$	1.71798e11	+	4.60332e10i	0.955547	+	0.256038i	0.252833	+	0.967510i	$0.418638\pi$
$318$	1.41349e10	+	5.27520e10i	0.0775121	+	0.289279i
$319$	−2.02774e10	−	1.17072e10i	−0.109636	−	0.0632985i
$320$	8.48584e9	+	1.37987e10i	0.0452397	+	0.0735636i
$321$			9.19646e10i			0.483446i
$322$	6.24980e10	−	4.42841e10i	0.323977	−	0.229560i
$323$	−1.73774e11	−	1.73774e11i	−0.888329	−	0.888329i
$324$	−8.20716e9	+	4.73840e9i	−0.0413752	+	0.0238880i
$325$	−1.10098e10	−	3.35241e10i	−0.0547399	−	0.166680i
$326$	3.96651e10	−	6.87020e10i	0.194504	−	0.336891i
$327$	5.79195e10	−	2.16159e11i	0.280130	−	1.04546i
$328$	−2.00894e11	+	2.00894e11i	−0.958372	+	0.958372i
$329$	−6.44720e10	+	7.77126e10i	−0.303382	+	0.365687i
$330$	4.78240e9	−	1.32787e8i	0.0221990	−	0.000616372i
$331$	−1.13854e11	−	1.97201e11i	−0.521343	−	0.902992i	−0.999692	−	0.0248222i	$-0.992098\pi$
$331$	−1.13854e11	−	1.97201e11i	−0.521343	−	0.902992i	0.478349	−	0.878170i	$-0.341235\pi$
$332$	−2.21790e11	+	5.94286e10i	−1.00189	+	0.268456i
$333$	−8.75854e10	+	2.34684e10i	−0.390331	+	0.104589i
$334$	1.31450e10	+	2.27678e10i	0.0577966	+	0.100107i
$335$	−2.29481e11	−	2.17082e11i	−0.995509	−	0.941720i
$336$	5.08888e10	−	1.88447e10i	0.217819	−	0.0806608i
$337$	1.91956e11	−	1.91956e11i	0.810712	−	0.810712i	−0.174028	−	0.984741i	$-0.555678\pi$
$337$	1.91956e11	−	1.91956e11i	0.810712	−	0.810712i	0.984741	+	0.174028i	$0.0556784\pi$
$338$	2.81957e10	−	1.05228e11i	0.117505	−	0.438536i
$339$	1.40776e10	−	2.43831e10i	0.0578935	−	0.100274i
$340$	−2.06452e11	+	6.15085e10i	−0.837845	+	0.249620i
$341$	1.73773e9	−	1.00328e9i	0.00695967	−	0.00401816i
$342$	6.06359e10	+	6.06359e10i	0.239669	+	0.239669i
$343$	7.04882e10	+	2.46463e11i	0.274975	+	0.961451i
$344$		−	1.26789e11i		−	0.488167i
$345$	1.13192e11	−	6.96105e10i	0.430162	−	0.264538i
$346$	8.83619e10	+	5.10157e10i	0.331453	+	0.191365i
$347$	−1.56023e10	−	5.82284e10i	−0.0577703	−	0.215602i	0.931006	−	0.365003i	$-0.118932\pi$
$347$	−1.56023e10	−	5.82284e10i	−0.0577703	−	0.215602i	−0.988777	+	0.149401i	$0.952265\pi$
$348$	1.95506e11	+	5.23858e10i	0.714586	+	0.191473i
$349$	−4.59776e11			−1.65894			−0.829472	−	0.558549i	$-0.811358\pi$
$349$	−4.59776e11			−1.65894			−0.829472	+	0.558549i	$0.811358\pi$
$350$	−1.20598e11	+	5.24401e10i	−0.429569	+	0.186792i
$351$	−4.88944e10			−0.171940
$352$	−2.25098e10	−	6.03149e9i	−0.0781502	−	0.0209403i
$353$	−1.08153e11	−	4.03633e11i	−0.370726	−	1.38357i	−0.859491	−	0.511152i	$-0.829219\pi$
$353$	−1.08153e11	−	4.03633e11i	−0.370726	−	1.38357i	0.488765	−	0.872416i	$-0.337448\pi$
$354$	−2.83984e10	−	1.63958e10i	−0.0961123	−	0.0554905i
$355$	1.15637e11	−	7.11135e10i	0.386427	−	0.237643i
$356$			2.90104e11i			0.957259i
$357$	−1.89874e10	−	2.03897e11i	−0.0618669	−	0.664361i
$358$	−1.48543e11	−	1.48543e11i	−0.477947	−	0.477947i
$359$	3.00801e11	−	1.73667e11i	0.955770	−	0.551814i	0.0609017	−	0.998144i	$-0.480602\pi$
$359$	3.00801e11	−	1.73667e11i	0.955770	−	0.551814i	0.894869	+	0.446329i	$0.147269\pi$
$360$	1.64326e11	−	4.89580e10i	0.515640	−	0.153625i
$361$	−4.16595e10	+	7.21564e10i	−0.129102	+	0.223611i
$362$	2.54973e10	−	9.51573e10i	0.0780380	−	0.291242i
$363$	1.38475e11	−	1.38475e11i	0.418593	−	0.418593i
$364$	−4.52137e10	−	7.71213e9i	−0.134994	−	0.0230260i
$365$	−2.70388e11	−	2.55778e11i	−0.797386	−	0.754302i
$366$	−1.88303e10	−	3.26150e10i	−0.0548519	−	0.0950063i
$367$	−1.83786e11	+	4.92453e10i	−0.528829	+	0.141699i	−0.513347	−	0.858181i	$-0.671595\pi$
$367$	−1.83786e11	+	4.92453e10i	−0.528829	+	0.141699i	−0.0154815	+	0.999880i	$0.504928\pi$
$368$	−1.12309e11	+	3.00931e10i	−0.319227	+	0.0855366i
$369$	1.86660e11	+	3.23304e11i	0.524121	+	0.907805i
$370$	1.05744e11	−	2.93606e9i	0.293324	−	0.00814437i
$371$	3.86032e11	+	6.58458e10i	1.05789	+	0.180445i
$372$	−1.22652e10	+	1.22652e10i	−0.0332070	+	0.0332070i
$373$	1.10968e11	−	4.14138e11i	0.296830	−	1.10778i	−0.642923	−	0.765930i	$-0.722279\pi$
$373$	1.10968e11	−	4.14138e11i	0.296830	−	1.10778i	0.939753	−	0.341854i	$-0.111055\pi$
$374$	−7.89841e9	+	1.36805e10i	−0.0208746	+	0.0361558i
$375$	−2.14694e11	+	7.71733e10i	−0.560633	+	0.201524i
$376$	−1.33017e11	+	7.67974e10i	−0.343211	+	0.198153i
$377$	−7.74057e10	−	7.74057e10i	−0.197350	−	0.197350i
$378$	1.68960e10	+	1.81439e11i	0.0425667	+	0.457106i
$379$			7.56215e11i			1.88265i	0.337507	+	0.941323i	$0.390416\pi$
$379$			7.56215e11i			1.88265i	−0.337507	+	0.941323i	$0.609584\pi$
$380$	1.86432e11	+	3.03154e11i	0.458664	+	0.745826i
$381$	4.90167e10	+	2.82998e10i	0.119174	+	0.0688051i
$382$	−5.35057e10	−	1.99686e11i	−0.128563	−	0.479802i
$383$	4.99086e11	+	1.33730e11i	1.18517	+	0.317566i	0.796976	−	0.604011i	$-0.206432\pi$
$383$	4.99086e11	+	1.33730e11i	1.18517	+	0.317566i	0.388196	+	0.921577i	$0.373099\pi$
$384$	2.47807e11			0.581599
$385$	1.34536e10	−	3.15578e10i	0.0312080	−	0.0732037i
$386$	−2.90119e11			−0.665170
$387$	−1.60925e11	−	4.31198e10i	−0.364691	−	0.0977187i
$388$	−5.48507e10	−	2.04706e11i	−0.122868	−	0.458550i
$389$	1.46659e11	+	8.46733e10i	0.324739	+	0.187488i	0.653503	−	0.756924i	$-0.273299\pi$
$389$	1.46659e11	+	8.46733e10i	0.324739	+	0.187488i	−0.328764	+	0.944412i	$0.606632\pi$
$390$	2.17578e10	+	5.18727e9i	0.0476238	+	0.0113540i
$391$			4.38763e11i			0.949368i
$392$	−2.96413e10	+	3.88802e11i	−0.0634031	+	0.831652i
$393$	3.07911e11	+	3.07911e11i	0.651117	+	0.651117i
$394$	2.84969e11	−	1.64527e11i	0.595751	−	0.343957i
$395$	−2.13887e11	+	3.95418e11i	−0.442076	+	0.817277i
$396$	−9.80446e9	+	1.69818e10i	−0.0200353	+	0.0347021i
$397$	−1.38222e11	+	5.15852e11i	−0.279267	+	1.04224i	0.673660	+	0.739042i	$0.264721\pi$
$397$	−1.38222e11	+	5.15852e11i	−0.279267	+	1.04224i	−0.952927	+	0.303199i	$0.901945\pi$
$398$	1.65913e11	−	1.65913e11i	0.331442	−	0.331442i
$399$	−3.17259e11	+	1.17485e11i	−0.626666	+	0.232062i
$400$	1.99313e11	−	1.10767e10i	0.389283	−	0.0216342i
$401$	2.61779e11	+	4.53415e11i	0.505575	+	0.875681i	0.999979	+	0.00644926i	$0.00205288\pi$
$401$	2.61779e11	+	4.53415e11i	0.505575	+	0.875681i	−0.494404	+	0.869232i	$0.664614\pi$
$402$	1.93419e11	−	5.18265e10i	0.369387	−	0.0989770i
$403$	9.06156e9	−	2.42804e9i	0.0171132	−	0.00458546i
$404$	1.84764e11	+	3.20020e11i	0.345065	+	0.597670i
$405$	−9.19778e8	−	3.31263e10i	−0.00169877	−	0.0611822i
$406$	−2.60491e11	+	3.13988e11i	−0.475801	+	0.573516i
$407$	−1.95133e10	+	1.95133e10i	−0.0352498	+	0.0352498i
$408$	8.06207e10	−	3.00880e11i	0.144038	−	0.537555i
$409$	3.34585e11	−	5.79517e11i	0.591223	−	1.02403i	−0.402845	−	0.915268i	$-0.631979\pi$
$409$	3.34585e11	−	5.79517e11i	0.591223	−	1.02403i	0.994068	−	0.108760i	$-0.0346879\pi$
$410$	−1.24355e11	−	4.17396e11i	−0.217339	−	0.729493i
$411$	−4.99615e11	+	2.88453e11i	−0.863670	+	0.498640i
$412$	−4.97147e11	−	4.97147e11i	−0.850055	−	0.850055i
$413$	−1.91855e11	+	1.35943e11i	−0.324488	+	0.229922i
$414$		−	1.53100e11i		−	0.256137i
$415$	1.86207e11	−	7.81039e11i	0.308163	−	1.29258i
$416$	−9.43552e10	−	5.44760e10i	−0.154471	−	0.0891836i
$417$	−6.25850e10	−	2.33570e11i	−0.101358	−	0.378273i
$418$	2.52085e10	+	6.75459e9i	0.0403881	+	0.0108220i
$419$	−3.95834e11			−0.627408			−0.313704	−	0.949521i	$-0.601570\pi$
$419$	−3.95834e11			−0.627408			−0.313704	+	0.949521i	$0.601570\pi$
$420$	−4.17305e10	+	2.93604e11i	−0.0654382	+	0.460405i
$421$	−1.99334e11			−0.309251			−0.154626	−	0.987973i	$-0.549417\pi$
$421$	−1.99334e11			−0.309251			−0.154626	+	0.987973i	$0.549417\pi$
$422$	−3.98026e11	−	1.06651e11i	−0.610950	−	0.163703i
$423$	5.22362e10	+	1.94948e11i	0.0793305	+	0.296065i
$424$	5.15876e11	+	2.97841e11i	0.775174	+	0.447547i
$425$	1.54291e11	−	7.37322e11i	0.229398	−	1.09624i
$426$			8.60539e10i			0.126598i
$427$	−2.68886e11	+	2.50393e10i	−0.391419	+	0.0364499i
$428$	3.10943e11	+	3.10943e11i	0.447903	+	0.447903i
$429$	−5.05329e9	+	2.91752e9i	−0.00720304	+	0.00415868i
$430$	1.70956e11	+	9.24726e10i	0.241145	+	0.130438i
$431$	−5.97272e11	+	1.03451e12i	−0.833728	+	1.44406i	0.0613342	+	0.998117i	$0.480464\pi$
$431$	−5.97272e11	+	1.03451e12i	−0.833728	+	1.44406i	−0.895062	+	0.445942i	$0.852869\pi$
$432$	7.15913e10	−	2.67182e11i	0.0988971	−	0.369089i
$433$	4.08237e11	−	4.08237e11i	0.558106	−	0.558106i	−0.370662	−	0.928768i	$-0.620869\pi$
$433$	4.08237e11	−	4.08237e11i	0.558106	−	0.558106i	0.928768	+	0.370662i	$0.120869\pi$
$434$	−1.21414e10	−	3.27869e10i	−0.0164272	−	0.0443605i
$435$	−4.86389e11	+	5.14171e11i	−0.651302	+	0.688503i
$436$	−5.35025e11	−	9.26691e11i	−0.709064	−	1.22813i
$437$	7.00175e11	−	1.87611e11i	0.918417	−	0.246089i
$438$	2.27897e11	−	6.10649e10i	0.295873	−	0.0792789i
$439$	6.29233e11	+	1.08986e12i	0.808576	+	1.40049i	0.913850	+	0.406051i	$0.133095\pi$
$439$	6.29233e11	+	1.08986e12i	0.808576	+	1.40049i	−0.105274	+	0.994443i	$0.533572\pi$
$440$	3.58609e10	−	3.79092e10i	0.0456125	−	0.0482178i
$441$	4.83402e11	+	1.69850e11i	0.608604	+	0.213842i
$442$	−5.22230e10	+	5.22230e10i	−0.0650821	+	0.0650821i
$443$	−1.22359e11	+	4.56650e11i	−0.150945	+	0.563335i	0.848473	+	0.529238i	$0.177522\pi$
$443$	−1.22359e11	+	4.56650e11i	−0.150945	+	0.563335i	−0.999419	+	0.0340970i	$0.989144\pi$
$444$	1.19276e11	−	2.06592e11i	0.145656	−	0.252284i
$445$	−8.92283e11	−	4.82647e11i	−1.07865	−	0.583459i
$446$	6.03789e11	−	3.48598e11i	0.722567	−	0.417174i
$447$	3.68003e10	+	3.68003e10i	0.0435981	+	0.0435981i
$448$	−3.07450e10	+	6.69065e10i	−0.0360598	+	0.0784725i
$449$		−	8.25468e11i		−	0.958499i	−0.877679	−	0.479250i	$-0.840909\pi$
$449$		−	8.25468e11i		−	0.958499i	0.877679	−	0.479250i	$-0.159091\pi$
$450$	−5.38375e10	+	2.57277e11i	−0.0618912	+	0.295764i
$451$	9.83942e10	+	5.68079e10i	0.111989	+	0.0646568i
$452$	−3.48442e10	−	1.30040e11i	−0.0392651	−	0.146539i
$453$	−1.86507e11	−	4.99744e10i	−0.208091	−	0.0557578i
$454$	−1.73709e10			−0.0191898
$455$	9.89425e10	−	1.26234e11i	0.108226	−	0.138079i
$456$	−5.14616e11			−0.557367
$457$	1.13112e12	+	3.03083e11i	1.21307	+	0.325041i	0.807966	−	0.589230i	$-0.200569\pi$
$457$	1.13112e12	+	3.03083e11i	1.21307	+	0.325041i	0.405104	+	0.914271i	$0.367235\pi$
$458$	1.52955e11	+	5.70836e11i	0.162431	+	0.606201i
$459$	−9.03969e11	−	5.21907e11i	−0.950598	−	0.548828i
$460$	1.47356e11	−	6.18079e11i	0.153447	−	0.643626i
$461$			5.50285e11i			0.567457i	0.958905	+	0.283729i	$0.0915715\pi$
$461$			5.50285e11i			0.567457i	−0.958905	+	0.283729i	$0.908428\pi$
$462$	1.25726e10	+	1.77437e10i	0.0128392	+	0.0181199i
$463$	−2.84402e11	−	2.84402e11i	−0.287620	−	0.287620i	0.548519	−	0.836138i	$-0.315192\pi$
$463$	−2.84402e11	−	2.84402e11i	−0.287620	−	0.287620i	−0.836138	+	0.548519i	$0.815192\pi$
$464$	5.36320e11	−	3.09645e11i	0.537147	−	0.310122i
$465$	−1.73187e10	−	5.81299e10i	−0.0171782	−	0.0576583i
$466$	2.24697e11	−	3.89186e11i	0.220729	−	0.382314i
$467$	1.06381e11	−	3.97020e11i	0.103500	−	0.386266i	−0.894671	−	0.446726i	$-0.852590\pi$
$467$	1.06381e11	−	3.97020e11i	0.103500	−	0.386266i	0.998171	+	0.0604598i	$0.0192567\pi$
$468$	−6.48254e10	+	6.48254e10i	−0.0624653	+	0.0624653i
$469$	2.41428e11	−	1.41541e12i	0.230415	−	1.35085i
$470$	−6.53511e9	−	2.35365e11i	−0.00617750	−	0.222486i
$471$	−3.71959e10	−	6.44252e10i	−0.0348258	−	0.0603200i
$472$	−3.45483e11	+	9.25719e10i	−0.320396	+	0.0858499i
$473$	−4.89760e10	+	1.31231e10i	−0.0449891	+	0.0120548i
$474$	−1.42487e11	−	2.46795e11i	−0.129650	−	0.224561i
$475$	−1.24259e12	+	6.90561e10i	−1.11997	+	0.0622416i
$476$	−7.53599e11	−	6.25202e11i	−0.672836	−	0.558199i
$477$	5.53476e11	−	5.53476e11i	0.489515	−	0.489515i
$478$	1.31696e11	−	4.91497e11i	0.115385	−	0.430621i
$479$	−8.29971e11	+	1.43755e12i	−0.720366	+	1.24771i	0.240488	+	0.970652i	$0.422693\pi$
$479$	−8.29971e11	+	1.43755e12i	−0.720366	+	1.24771i	−0.960853	+	0.277058i	$0.910641\pi$
$480$	−3.35151e11	+	6.19602e11i	−0.288174	+	0.532754i
$481$	−1.11734e11	+	6.45094e10i	−0.0951767	+	0.0549503i
$482$	−6.21727e11	−	6.21727e11i	−0.524673	−	0.524673i
$483$	5.48843e11	+	2.52205e11i	0.458866	+	0.210859i
$484$		−	9.36402e11i		−	0.775636i
$485$	7.20875e11	+	1.71863e11i	0.591591	+	0.141041i
$486$	5.07166e11	+	2.92812e11i	0.412370	+	0.238082i
$487$	3.64505e11	+	1.36035e12i	0.293645	+	1.09590i	0.942287	+	0.334805i	$0.108670\pi$
$487$	3.64505e11	+	1.36035e12i	0.293645	+	1.09590i	−0.648642	+	0.761093i	$0.724663\pi$
$488$	−3.96780e11	−	1.06317e11i	−0.316710	−	0.0848621i
$489$	6.25570e11			0.494751
$490$	−5.02624e11	−	3.23537e11i	−0.393878	−	0.253537i
$491$	1.07303e12			0.833193			0.416597	−	0.909091i	$-0.363223\pi$
$491$	1.07303e12			0.833193			0.416597	+	0.909091i	$0.363223\pi$
$492$	−9.48677e11	−	2.54197e11i	−0.729921	−	0.195582i
$493$	−6.04851e11	−	2.25734e12i	−0.461145	−	1.72102i
$494$	1.05667e11	+	6.10070e10i	0.0798305	+	0.0460902i
$495$	−3.59198e10	−	5.84086e10i	−0.0268912	−	0.0437273i
$496$			5.30719e10i			0.0393729i
$497$	5.60693e11	+	2.57651e11i	0.412213	+	0.189421i
$498$	3.59900e11	+	3.59900e11i	0.262211	+	0.262211i
$499$	−2.30566e12	+	1.33118e12i	−1.66473	+	0.961132i	−0.694320	+	0.719666i	$0.744295\pi$
$499$	−2.30566e12	+	1.33118e12i	−1.66473	+	0.961132i	−0.970409	+	0.241466i	$0.922372\pi$
$500$	−4.64973e11	+	9.86837e11i	−0.332707	+	0.706123i
$501$	−1.03657e11	+	1.79539e11i	−0.0735071	+	0.127318i
$502$	−1.68732e11	+	6.29717e11i	−0.118585	+	0.442567i
$503$	−6.93308e10	+	6.93308e10i	−0.0482914	+	0.0482914i	−0.730840	−	0.682549i	$-0.760872\pi$
$503$	−6.93308e10	+	6.93308e10i	−0.0482914	+	0.0482914i	0.682549	+	0.730840i	$0.260872\pi$
$504$	5.99831e11	+	4.97633e11i	0.414087	+	0.343536i
$505$	−1.29169e12	+	3.58648e10i	−0.883785	+	0.0245390i
$506$	−2.32971e10	−	4.03518e10i	−0.0157988	−	0.0273644i
$507$	8.29791e11	−	2.22342e11i	0.557741	−	0.149446i
$508$	2.61416e11	−	7.00462e10i	0.174159	−	0.0466657i
$509$	4.02433e11	+	6.97035e11i	0.265744	+	0.460282i	0.967758	−	0.251881i	$-0.0810490\pi$
$509$	4.02433e11	+	6.97035e11i	0.265744	+	0.460282i	−0.702014	+	0.712163i	$0.747716\pi$
$510$	3.46893e11	+	3.28150e11i	0.227054	+	0.214786i
$511$	2.84464e11	−	1.66772e12i	0.184558	−	1.08201i
$512$	7.93387e11	−	7.93387e11i	0.510235	−	0.510235i
$513$	−4.46326e11	+	1.66571e12i	−0.284528	+	1.06187i
$514$	−2.89264e11	+	5.01019e11i	−0.182793	+	0.316607i
$515$	2.35619e12	−	7.01984e11i	1.47597	−	0.439739i
$516$	3.79582e11	−	2.19152e11i	0.235712	−	0.136089i
$517$	4.34329e10	+	4.34329e10i	0.0267369	+	0.0267369i
$518$	2.77994e11	+	3.92332e11i	0.169649	+	0.239425i
$519$			8.04585e11i			0.486764i
$520$	2.07818e11	−	1.27803e11i	0.124643	−	0.0766525i
$521$	−1.78655e11	−	1.03147e11i	−0.106230	−	0.0613317i	0.445944	−	0.895061i	$-0.352868\pi$
$521$	−1.78655e11	−	1.03147e11i	−0.106230	−	0.0613317i	−0.552174	+	0.833729i	$0.686201\pi$
$522$	2.11054e11	+	7.87663e11i	0.124416	+	0.464326i
$523$	−1.16244e12	−	3.11476e11i	−0.679383	−	0.182040i	−0.0974051	−	0.995245i	$-0.531054\pi$
$523$	−1.16244e12	−	3.11476e11i	−0.679383	−	0.182040i	−0.581978	+	0.813205i	$0.697721\pi$
$524$	2.08217e12			1.20649
$525$	−8.33619e11	−	6.16821e11i	−0.478906	−	0.354358i
$526$	6.58586e11			0.375125
$527$	1.93449e11	+	5.18346e10i	0.109250	+	0.0292733i
$528$	−8.54368e9	−	3.18854e10i	−0.00478401	−	0.0178542i
$529$	4.39057e11	+	2.53490e11i	0.243764	+	0.140737i
$530$	−7.77846e11	+	4.78355e11i	−0.428205	+	0.263335i
$531$			4.69983e11i			0.256541i
$532$	−6.75461e11	+	1.46992e12i	−0.365593	+	0.795594i
$533$	3.75604e11	+	3.75604e11i	0.201585	+	0.201585i
$534$	5.56908e11	−	3.21531e11i	0.296379	−	0.171115i
$535$	−1.47369e12	+	4.39060e11i	−0.777706	+	0.231703i
$536$	1.09206e12	−	1.89150e12i	0.571483	−	0.989838i
$537$	4.28748e11	−	1.60011e12i	0.222494	−	0.830359i
$538$	−2.61533e11	+	2.61533e11i	−0.134588	+	0.134588i
$539$	1.53254e11	−	2.87925e10i	0.0782101	−	0.0146936i
$540$	1.09813e12	+	1.03880e12i	0.555753	+	0.525724i
$541$	2.11974e11	+	3.67150e11i	0.106389	+	0.184271i	0.914305	−	0.405027i	$-0.132738\pi$
$541$	2.11974e11	+	3.67150e11i	0.106389	+	0.184271i	−0.807916	+	0.589298i	$0.799405\pi$
$542$	−5.44541e11	+	1.45909e11i	−0.271040	+	0.0726250i
$543$	7.50377e11	−	2.01063e11i	0.370408	−	0.0992506i
$544$	−1.16297e12	−	2.01433e12i	−0.569344	−	0.986132i
$545$	3.74037e12	−	1.03854e11i	1.81606	−	0.0504244i
$546$	3.53067e10	+	9.53434e10i	0.0170016	+	0.0459117i
$547$	−1.45969e12	+	1.45969e12i	−0.697139	+	0.697139i	−0.963792	−	0.266654i	$-0.914082\pi$
$547$	−1.45969e12	+	1.45969e12i	−0.697139	+	0.697139i	0.266654	+	0.963792i	$0.414082\pi$
$548$	−7.13965e11	+	2.66455e12i	−0.338193	+	1.26215i
$549$	−2.69883e11	+	4.67451e11i	−0.126794	+	0.219614i
$550$	2.49601e10	+	7.60019e10i	0.0116309	+	0.0354154i
$551$	−3.34361e12	+	1.93044e12i	−1.54538	+	0.892223i
$552$	6.49677e11	+	6.49677e11i	0.297832	+	0.297832i
$553$	−2.03464e12	+	1.89470e11i	−0.925175	+	0.0861545i
$554$		−	6.64588e11i		−	0.299750i
$555$	4.36981e11	+	7.10567e11i	0.195499	+	0.317897i
$556$	−1.00134e12	−	5.78122e11i	−0.444369	−	0.256556i
$557$	5.66917e11	+	2.11576e12i	0.249558	+	0.931363i	0.971038	+	0.238927i	$0.0767957\pi$
$557$	5.66917e11	+	2.11576e12i	0.249558	+	0.931363i	−0.721480	+	0.692436i	$0.756538\pi$
$558$	−6.75012e10	−	1.80869e10i	−0.0294753	−	0.00789787i
$559$	−2.37053e11			−0.102682
$560$	5.44933e11	+	7.25503e11i	0.234152	+	0.311740i
$561$	−1.24568e11			−0.0530976
$562$	−1.09679e12	−	2.93883e11i	−0.463776	−	0.124269i
$563$	−1.56177e11	−	5.82861e11i	−0.0655133	−	0.244499i	0.925402	−	0.378987i	$-0.123728\pi$
$563$	−1.56177e11	−	5.82861e11i	−0.0655133	−	0.244499i	−0.990915	+	0.134488i	$0.957061\pi$
$564$	−4.59833e11	−	2.65485e11i	−0.191357	−	0.110480i
$565$	4.57939e11	+	1.09177e11i	0.189056	+	0.0450727i
$566$		−	9.10730e11i		−	0.373006i
$567$	1.22905e11	−	8.70869e10i	0.0499399	−	0.0353858i
$568$	6.63705e11	+	6.63705e11i	0.267552	+	0.267552i
$569$	−3.42539e12	+	1.97765e12i	−1.36995	+	0.790941i	−0.990921	−	0.134444i	$-0.957075\pi$
$569$	−3.42539e12	+	1.97765e12i	−1.36995	+	0.790941i	−0.379029	+	0.925385i	$0.623742\pi$
$570$	3.75331e11	−	6.93884e11i	0.148929	−	0.275328i
$571$	1.37171e12	−	2.37586e12i	0.540006	−	0.935317i	−0.458897	−	0.888489i	$-0.651755\pi$
$571$	1.37171e12	−	2.37586e12i	0.540006	−	0.935317i	0.998903	−	0.0468281i	$-0.0149113\pi$
$572$	−7.22129e9	+	2.69502e10i	−0.00282054	+	0.0105264i
$573$	1.15273e12	−	1.15273e12i	0.446715	−	0.446715i
$574$	1.26401e12	−	1.52360e12i	0.486011	−	0.585823i
$575$	1.65589e12	+	1.48153e12i	0.631721	+	0.565202i
$576$	7.35872e10	+	1.27457e11i	0.0278549	+	0.0482460i
$577$	9.28828e11	−	2.48879e11i	0.348854	−	0.0934752i	−0.0801369	−	0.996784i	$-0.525536\pi$
$577$	9.28828e11	−	2.48879e11i	0.348854	−	0.0934752i	0.428991	+	0.903309i	$0.358869\pi$
$578$	−3.08837e11	+	8.27527e10i	−0.115094	+	0.0308395i
$579$	−1.14389e12	−	1.98127e12i	−0.422990	−	0.732640i
$580$	9.39320e10	+	3.38301e12i	0.0344658	+	1.24130i
$581$	3.42254e12	−	1.26740e12i	1.24611	−	0.461448i
$582$	−3.32177e11	+	3.32177e11i	−0.120010	+	0.120010i
$583$	6.16550e10	−	2.30100e11i	0.0221035	−	0.0824912i
$584$	1.28672e12	−	2.22867e12i	0.457749	−	0.792844i
$585$	−9.15352e10	−	3.07236e11i	−0.0323137	−	0.108460i
$586$	−9.44686e11	+	5.45415e11i	−0.330939	+	0.191068i
$587$	−3.00692e12	−	3.00692e12i	−1.04532	−	1.04532i	−0.998923	−	0.0464010i	$-0.985225\pi$
$587$	−3.00692e12	−	3.00692e12i	−1.04532	−	1.04532i	−0.0464010	−	0.998923i	$-0.514775\pi$
$588$	−1.21523e12	+	5.83295e11i	−0.419239	+	0.201229i
$589$		−	3.30869e11i		−	0.113276i
$590$	1.27156e11	−	5.33350e11i	0.0432018	−	0.181208i
$591$	2.24717e12	+	1.29740e12i	0.757691	+	0.437453i
$592$	−1.88910e11	−	7.05021e11i	−0.0632131	−	0.235914i
$593$	−3.30272e12	−	8.84961e11i	−1.09680	−	0.293885i	−0.335336	−	0.942099i	$-0.608850\pi$
$593$	−3.30272e12	−	8.84961e11i	−1.09680	−	0.293885i	−0.761459	+	0.648213i	$0.775517\pi$
$594$	1.10847e11			0.0365331
$595$	3.17672e12	−	1.27772e12i	1.03909	−	0.417935i
$596$	2.48852e11			0.0807855
$597$	1.78722e12	+	4.78883e11i	0.575828	+	0.154293i
$598$	−5.63813e10	−	2.10418e11i	−0.0180294	−	0.0672865i
$599$	−1.51961e12	−	8.77349e11i	−0.482295	−	0.278453i	0.239078	−	0.971000i	$-0.423155\pi$
$599$	−1.51961e12	−	8.77349e11i	−0.482295	−	0.278453i	−0.721372	+	0.692548i	$0.756488\pi$
$600$	−8.63296e11	−	1.32021e12i	−0.271944	−	0.415876i
$601$		−	3.24074e12i		−	1.01323i	−0.862171	−	0.506617i	$-0.830896\pi$
$601$		−	3.24074e12i		−	1.01323i	0.862171	−	0.506617i	$-0.169104\pi$
$602$	8.19163e10	+	8.79664e11i	0.0254206	+	0.272981i
$603$	−2.02936e12	−	2.02936e12i	−0.625074	−	0.625074i
$604$	−7.99571e11	+	4.61633e11i	−0.244450	+	0.141134i
$605$	2.88012e12	+	1.55789e12i	0.873999	+	0.472758i
$606$	4.09558e11	−	7.09375e11i	0.123364	−	0.213673i
$607$	4.37568e11	−	1.63303e12i	0.130827	−	0.488252i	−0.869153	−	0.494543i	$-0.835336\pi$
$607$	4.37568e11	−	1.63303e12i	0.130827	−	0.488252i	0.999980	+	0.00629029i	$0.00200228\pi$
$608$	−2.71718e12	+	2.71718e12i	−0.806402	+	0.806402i
$609$	−3.17135e12	−	5.40939e11i	−0.934257	−	0.159357i
$610$	4.32742e11	−	4.57459e11i	0.126545	−	0.133773i
$611$	1.43585e11	+	2.48697e11i	0.0416797	+	0.0721914i
$612$	−1.89046e12	+	5.06548e11i	−0.544737	+	0.145962i
$613$	4.93390e12	−	1.32203e12i	1.41130	−	0.378156i	0.528908	−	0.848679i	$-0.322602\pi$
$613$	4.93390e12	−	1.32203e12i	1.41130	−	0.378156i	0.882387	+	0.470524i	$0.155935\pi$
$614$	−5.58514e11	−	9.67375e11i	−0.158590	−	0.274686i
$615$	2.36016e12	−	2.49497e12i	0.665278	−	0.703277i
$616$	2.33820e11	+	3.98828e10i	0.0654286	+	0.0111602i
$617$	−1.65308e12	+	1.65308e12i	−0.459209	+	0.459209i	−0.898396	−	0.439187i	$-0.855267\pi$
$617$	−1.65308e12	+	1.65308e12i	−0.459209	+	0.459209i	0.439187	+	0.898396i	$0.355267\pi$
$618$	−4.03361e11	+	1.50536e12i	−0.111236	+	0.415139i
$619$	−1.52270e12	+	2.63739e12i	−0.416875	+	0.722048i	−0.995623	−	0.0934579i	$-0.970208\pi$
$619$	−1.52270e12	+	2.63739e12i	−0.416875	+	0.722048i	0.578749	+	0.815506i	$0.303541\pi$
$620$	−2.55101e11	−	1.37987e11i	−0.0693345	−	0.0375040i
$621$	2.66635e12	−	1.53942e12i	0.719456	−	0.415378i
$622$	8.77674e11	+	8.77674e11i	0.235113	+	0.235113i
$623$	−4.27550e11	−	4.59128e12i	−0.113708	−	1.22106i
$624$		−	1.54332e11i		−	0.0407497i
$625$	−2.26167e12	−	3.07193e12i	−0.592882	−	0.805289i
$626$	−1.92947e12	−	1.11398e12i	−0.502173	−	0.289929i
$627$	5.32644e10	+	1.98785e11i	0.0137636	+	0.0513666i
$628$	−3.43593e11	−	9.20654e10i	−0.0881507	−	0.0236199i
$629$	−2.75434e12			−0.701600
$630$	−1.10847e12	+	4.45840e11i	−0.280344	+	0.112758i
$631$	−1.62153e12			−0.407185			−0.203593	−	0.979056i	$-0.565262\pi$
$631$	−1.62153e12			−0.407185			−0.203593	+	0.979056i	$0.565262\pi$
$632$	−3.00241e12	−	8.04493e11i	−0.748588	−	0.200584i
$633$	−8.41011e11	−	3.13870e12i	−0.208202	−	0.777021i
$634$	−1.63260e12	−	9.42581e11i	−0.401308	−	0.231695i
$635$	−2.19475e11	+	9.20581e11i	−0.0535678	+	0.224688i
$636$			2.05925e12i			0.499058i
$637$	7.26931e11	+	5.54194e10i	0.174931	+	0.0133363i
$638$	1.75485e11	+	1.75485e11i	0.0419321	+	0.0419321i
$639$	1.06812e12	−	6.16679e11i	0.253435	−	0.146321i
$640$	1.18309e12	+	3.97101e12i	0.278745	+	0.935602i
$641$	6.13202e11	−	1.06210e12i	0.143464	−	0.248487i	−0.785335	−	0.619071i	$-0.787509\pi$
$641$	6.13202e11	−	1.06210e12i	0.143464	−	0.248487i	0.928799	+	0.370584i	$0.120843\pi$
$642$	2.52284e11	−	9.41538e11i	0.0586115	−	0.218741i
$643$	−1.31181e12	+	1.31181e12i	−0.302637	+	0.302637i	−0.842045	−	0.539408i	$-0.818648\pi$
$643$	−1.31181e12	+	1.31181e12i	−0.302637	+	0.302637i	0.539408	+	0.842045i	$0.318648\pi$
$644$	2.70844e12	−	1.00297e12i	0.620487	−	0.229774i
$645$	4.25399e10	+	1.53210e12i	0.00967782	+	0.348552i
$646$	1.30240e12	+	2.25582e12i	0.294237	+	0.509634i
$647$	6.42847e12	−	1.72250e12i	1.44224	−	0.386448i	0.548924	−	0.835872i	$-0.315038\pi$
$647$	6.42847e12	−	1.72250e12i	1.44224	−	0.386448i	0.893318	+	0.449425i	$0.148371\pi$
$648$	2.21322e11	−	5.93030e10i	0.0493102	−	0.0132126i
$649$	7.15171e10	+	1.23871e11i	0.0158237	+	0.0274075i
$650$	2.07529e10	+	3.73425e11i	0.00456004	+	0.0820528i
$651$	1.76036e11	−	2.12188e11i	0.0384138	−	0.0463028i
$652$	2.11513e12	−	2.11513e12i	0.458377	−	0.458377i
$653$	−1.22234e12	+	4.56185e12i	−0.263078	+	0.981819i	0.700339	+	0.713811i	$0.253032\pi$
$653$	−1.22234e12	+	4.56185e12i	−0.263078	+	0.981819i	−0.963416	+	0.268009i	$0.913634\pi$
$654$	−1.18597e12	+	2.05416e12i	−0.253497	+	0.439070i
$655$	−3.46411e12	+	6.40419e12i	−0.735370	+	1.35950i
$656$	−2.60244e12	+	1.50252e12i	−0.548674	+	0.316777i
$657$	−2.39111e12	−	2.39111e12i	−0.500674	−	0.500674i
$658$	8.73255e11	−	6.18761e11i	0.181604	−	0.128679i
$659$			9.36491e11i			0.193428i	0.995312	+	0.0967140i	$0.0308332\pi$
$659$			9.36491e11i			0.193428i	−0.995312	+	0.0967140i	$0.969167\pi$
$660$	1.75478e11	+	4.18355e10i	0.0359976	+	0.00858218i
$661$	1.64940e12	+	9.52279e11i	0.336061	+	0.194025i	0.658529	−	0.752555i	$-0.271179\pi$
$661$	1.64940e12	+	9.52279e11i	0.336061	+	0.194025i	−0.322468	+	0.946580i	$0.604512\pi$
$662$	6.24668e11	+	2.33129e12i	0.126412	+	0.471776i
$663$	−5.62546e11	−	1.50734e11i	−0.113070	−	0.0302970i
$664$	5.55159e12			1.10831
$665$	−3.39731e12	−	4.52305e12i	−0.673656	−	0.896879i
$666$	9.61085e11			0.189290
$667$	6.65823e12	+	1.78407e12i	1.30254	+	0.349016i
$668$	2.56567e11	+	9.57521e11i	0.0498548	+	0.186061i
$669$	4.76127e12	+	2.74892e12i	0.918979	+	0.530573i
$670$	1.75392e12	+	2.85203e12i	0.336259	+	0.546786i
$671$			1.64272e11i			0.0312833i
$672$	−3.18819e12	+	2.96891e11i	−0.603090	+	0.0561611i
$673$	2.14359e12	+	2.14359e12i	0.402786	+	0.402786i	0.879214	−	0.476427i	$-0.158069\pi$
$673$	2.14359e12	+	2.14359e12i	0.402786	+	0.402786i	−0.476427	+	0.879214i	$0.658069\pi$
$674$	−2.49184e12	+	1.43867e12i	−0.465105	+	0.268529i
$675$	−5.02201e12	+	1.64930e12i	−0.931131	+	0.305797i
$676$	2.05386e12	−	3.55738e12i	0.378277	−	0.655195i
$677$	−1.33911e12	+	4.99762e12i	−0.245000	+	0.914354i	0.728383	+	0.685170i	$0.240272\pi$
$677$	−1.33911e12	+	4.99762e12i	−0.245000	+	0.914354i	−0.973383	+	0.229184i	$0.926394\pi$
$678$	−2.11017e11	+	2.11017e11i	−0.0383516	+	0.0383516i
$679$	1.16978e12	+	3.15889e12i	0.211197	+	0.570323i
$680$	5.20639e12	−	1.44559e11i	0.933783	−	0.0259272i
$681$	−6.84905e10	−	1.18629e11i	−0.0122030	−	0.0211363i
$682$	−2.05433e10	+	5.50456e9i	−0.00363614	+	0.000974300i
$683$	5.35950e12	−	1.43607e12i	0.942391	−	0.252513i	0.245260	−	0.969457i	$-0.421127\pi$
$683$	5.35950e12	−	1.43607e12i	0.942391	−	0.252513i	0.697130	+	0.716944i	$0.254460\pi$
$684$	1.61669e12	+	2.80020e12i	0.282407	+	0.489143i
$685$	−7.00762e12	−	6.62899e12i	−1.21608	−	1.15038i
$686$	−4.55469e10	−	2.71667e12i	−0.00785237	−	0.468358i
$687$	−3.29526e12	+	3.29526e12i	−0.564397	+	0.564397i
$688$	3.47094e11	−	1.29537e12i	0.0590608	−	0.220418i
$689$	5.56864e11	−	9.64517e11i	0.0941375	−	0.163051i
$690$	−1.34983e12	+	4.02158e11i	−0.226704	+	0.0675422i
$691$	−6.21215e11	+	3.58659e11i	−0.103655	+	0.0598454i	−0.550931	−	0.834551i	$-0.685727\pi$
$691$	−6.21215e11	+	3.58659e11i	−0.103655	+	0.0598454i	0.447276	+	0.894396i	$0.352394\pi$
$692$	2.72040e12	+	2.72040e12i	0.450978	+	0.450978i
$693$	1.30141e11	−	2.83209e11i	0.0214345	−	0.0466452i
$694$			6.38947e11i			0.104556i
$695$	3.44407e12	−	2.11802e12i	0.559939	−	0.344348i
$696$	−4.23805e12	−	2.44684e12i	−0.684580	−	0.395243i
$697$	2.93499e12	+	1.09535e13i	0.471041	+	1.75795i
$698$	4.70721e12	+	1.26129e12i	0.750610	+	0.201125i
$699$	3.54376e12			0.561458
$700$	−4.90411e12	+	7.33019e11i	−0.772003	+	0.115392i
$701$	−6.24032e12			−0.976059			−0.488030	−	0.872827i	$-0.662284\pi$
$701$	−6.24032e12			−0.976059			−0.488030	+	0.872827i	$0.662284\pi$
$702$	5.00583e11	+	1.34131e11i	0.0777964	+	0.0208455i
$703$	1.17773e12	+	4.39536e12i	0.181864	+	0.678727i
$704$	3.87901e10	+	2.23955e10i	0.00595174	+	0.00343624i
$705$	1.58159e12	−	9.72635e11i	0.241125	−	0.148286i
$706$			4.42911e12i			0.670958i
$707$	−3.39577e12	−	4.79243e12i	−0.511153	−	0.721388i
$708$	−8.74302e11	−	8.74302e11i	−0.130771	−	0.130771i
$709$	8.44136e11	−	4.87362e11i	0.125460	−	0.0724342i	−0.435957	−	0.899968i	$-0.643590\pi$
$709$	8.44136e11	−	4.87362e11i	0.125460	−	0.0724342i	0.561416	+	0.827533i	$0.310257\pi$
$710$	−1.37898e12	+	4.10841e11i	−0.203655	+	0.0606752i
$711$	−2.04218e12	+	3.53717e12i	−0.299697	+	0.519090i
$712$	1.81538e12	−	6.77511e12i	0.264733	−	0.987998i
$713$	−4.17706e11	+	4.17706e11i	−0.0605297	+	0.0605297i
$714$	−3.64953e11	+	2.13960e12i	−0.0525527	+	0.308099i
$715$	−7.08775e10	−	6.70479e10i	−0.0101422	−	0.00959418i
$716$	−3.96051e12	−	6.85981e12i	−0.563175	−	0.975447i
$717$	3.87578e12	−	1.03851e12i	0.547674	−	0.146749i
$718$	−3.55603e12	+	9.52836e11i	−0.499351	+	0.133801i
$719$	−1.20788e12	−	2.09210e12i	−0.168555	−	0.291946i	0.769357	−	0.638819i	$-0.220577\pi$
$719$	−1.20788e12	−	2.09210e12i	−0.168555	−	0.291946i	−0.937912	+	0.346873i	$0.887244\pi$
$720$	1.81291e12	−	5.03369e10i	0.251409	−	0.00698056i
$721$	8.60068e12	+	7.13531e12i	1.18529	+	0.983340i
$722$	6.24458e11	−	6.24458e11i	0.0855235	−	0.0855235i
$723$	1.79452e12	−	6.69725e12i	0.244246	−	0.911537i
$724$	1.85730e12	−	3.21693e12i	0.251222	−	0.435130i
$725$	−1.05615e13	−	5.33942e12i	−1.41973	−	0.717749i
$726$	−1.79759e12	+	1.03784e12i	−0.240147	+	0.138649i
$727$	−7.40934e12	−	7.40934e12i	−0.983727	−	0.983727i	0.0161430	−	0.999870i	$-0.494861\pi$
$727$	−7.40934e12	−	7.40934e12i	−0.983727	−	0.983727i	−0.999870	+	0.0161430i	$0.994861\pi$
$728$	1.00766e12	+	4.63043e11i	0.132961	+	0.0610984i
$729$			4.15130e12i			0.544391i
$730$	2.06657e12	+	3.36042e12i	0.269338	+	0.437966i
$731$	−4.38269e12	−	2.53035e12i	−0.567692	−	0.327757i
$732$	−3.67533e11	−	1.37165e12i	−0.0473147	−	0.176581i
$733$	8.40665e12	+	2.25255e12i	1.07561	+	0.288209i	0.752796	−	0.658254i	$-0.228705\pi$
$733$	8.40665e12	+	2.25255e12i	1.07561	+	0.288209i	0.322814	+	0.946462i	$0.395371\pi$
$734$	2.01671e12			0.256454
$735$	2.27731e11	−	4.70816e12i	0.0287825	−	0.595057i
$736$	6.86060e12			0.861811
$737$	−8.43677e11	−	2.26063e11i	−0.105335	−	0.0282244i
$738$	−1.02412e12	−	3.82206e12i	−0.127086	−	0.474290i
$739$	−7.63289e12	−	4.40685e12i	−0.941432	−	0.543536i	−0.0510233	−	0.998697i	$-0.516248\pi$
$739$	−7.63289e12	−	4.40685e12i	−0.941432	−	0.543536i	−0.890409	+	0.455161i	$0.849582\pi$
$740$	3.88000e12	+	9.25028e11i	0.475651	+	0.113400i
$741$			9.62160e11i			0.117237i
$742$	−3.77159e12	−	1.73313e12i	−0.456779	−	0.209900i
$743$	−4.38483e12	−	4.38483e12i	−0.527841	−	0.527841i	0.392087	−	0.919928i	$-0.371753\pi$
$743$	−4.38483e12	−	4.38483e12i	−0.527841	−	0.527841i	−0.919928	+	0.392087i	$0.871753\pi$
$744$	3.63193e11	−	2.09689e11i	0.0434569	−	0.0250899i
$745$	−4.14016e11	+	7.65402e11i	−0.0492396	+	0.0910304i
$746$	−2.27219e12	+	3.93555e12i	−0.268609	+	0.465244i
$747$	1.88805e12	−	7.04628e12i	0.221855	−	0.827975i
$748$	−4.21180e11	+	4.21180e11i	−0.0491939	+	0.0491939i
$749$	−5.37934e12	−	4.46282e12i	−0.624541	−	0.518132i
$750$	2.40975e12	−	2.01140e11i	0.278097	−	0.0232125i
$751$	6.53815e12	+	1.13244e13i	0.750024	+	1.29908i	0.947810	+	0.318835i	$0.103292\pi$
$751$	6.53815e12	+	1.13244e13i	0.750024	+	1.29908i	−0.197786	+	0.980245i	$0.563375\pi$
$752$	−1.56924e12	+	4.20477e11i	−0.178941	+	0.0479470i
$753$	−4.96573e12	+	1.33056e12i	−0.562867	+	0.150820i
$754$	5.80139e11	+	1.00483e12i	0.0653673	+	0.113220i
$755$	−8.96081e10	−	3.22728e12i	−0.0100366	−	0.361473i
$756$	−1.15530e12	+	6.77314e12i	−0.128631	+	0.754123i
$757$	1.59890e12	−	1.59890e12i	0.176966	−	0.176966i	−0.613066	−	0.790032i	$-0.710064\pi$
$757$	1.59890e12	−	1.59890e12i	0.176966	−	0.176966i	0.790032	+	0.613066i	$0.210064\pi$
$758$	2.07451e12	−	7.74217e12i	0.228246	−	0.851827i
$759$	1.83713e11	−	3.18201e11i	0.0200933	−	0.0348027i
$760$	−2.45689e12	−	8.24651e12i	−0.267132	−	0.896621i
$761$	−1.08972e13	+	6.29150e12i	−1.17783	+	0.680023i	−0.955512	−	0.294951i	$-0.904697\pi$
$761$	−1.08972e13	+	6.29150e12i	−1.17783	+	0.680023i	−0.222321	+	0.974973i	$0.571363\pi$
$762$	−4.24201e11	−	4.24201e11i	−0.0455800	−	0.0455800i
$763$	9.83321e12	+	1.38776e13i	1.05035	+	1.48236i
$764$		−	7.79501e12i		−	0.827745i
$765$	1.58717e12	−	6.65730e12i	0.167550	−	0.702784i
$766$	−4.74282e12	−	2.73827e12i	−0.497745	−	0.287373i
$767$	1.73079e11	+	6.45938e11i	0.0180578	+	0.0673925i
$768$	−3.01620e12	−	8.08187e11i	−0.312848	−	0.0838275i
$769$	7.26428e12			0.749073			0.374536	−	0.927212i	$-0.377802\pi$
$769$	7.26428e12			0.749073			0.374536	+	0.927212i	$0.377802\pi$
$770$	−2.24311e11	+	2.86183e11i	−0.0229954	+	0.0293384i
$771$	−4.56207e12			−0.464961
$772$	−1.05665e13	−	2.83129e12i	−1.07067	−	0.286885i
$773$	3.07560e11	+	1.14783e12i	0.0309829	+	0.115630i	0.979686	−	0.200540i	$-0.0642697\pi$
$773$	3.07560e11	+	1.14783e12i	0.0309829	+	0.115630i	−0.948703	+	0.316170i	$0.897603\pi$
$774$	1.52927e12	+	8.82927e11i	0.153162	+	0.0884281i
$775$	8.48824e11	−	5.55051e11i	0.0845201	−	0.0552682i
$776$			5.12394e12i			0.507255i
$777$	−1.58322e12	+	3.44537e12i	−0.155829	+	0.339110i
$778$	−1.26922e12	−	1.26922e12i	−0.124202	−	0.124202i
$779$	1.62246e13	−	9.36727e12i	1.57854	−	0.911369i
$780$	7.41827e11	+	4.01264e11i	0.0717591	+	0.0388155i
$781$	1.87680e11	−	3.25071e11i	0.0180504	−	0.0312643i
$782$	1.20365e12	−	4.49208e12i	0.115098	−	0.429553i
$783$	−1.15956e13	+	1.15956e13i	−1.10247	+	1.10247i
$784$	−1.36721e12	+	3.89116e12i	−0.129245	+	0.367838i
$785$	8.54805e11	−	9.03629e11i	0.0803440	−	0.0849331i
$786$	−2.30773e12	−	3.99710e12i	−0.215667	−	0.373546i
$787$	1.92551e13	−	5.15939e12i	1.78920	−	0.479416i	0.796993	−	0.603988i	$-0.206423\pi$
$787$	1.92551e13	−	5.15939e12i	1.78920	−	0.479416i	0.992211	+	0.124572i	$0.0397559\pi$
$788$	1.19846e13	−	3.21127e12i	1.10728	−	0.296694i
$789$	2.59669e12	+	4.49760e12i	0.238547	+	0.413175i
$790$	3.27452e12	−	3.46156e12i	0.299107	−	0.316191i
$791$	7.43105e11	+	2.00670e12i	0.0674926	+	0.182259i
$792$	3.35241e11	−	3.35241e11i	0.0302756	−	0.0302756i
$793$	−1.98777e11	+	7.41847e11i	−0.0178500	+	0.0666170i
$794$	2.83025e12	−	4.90214e12i	0.252716	−	0.437717i
$795$	−6.33369e12	−	3.42597e12i	−0.562347	−	0.304181i
$796$	7.66196e12	−	4.42363e12i	0.676442	−	0.390544i
$797$	−5.49407e12	−	5.49407e12i	−0.482316	−	0.482316i	0.423555	−	0.905871i	$-0.360782\pi$
$797$	−5.49407e12	−	5.49407e12i	−0.482316	−	0.482316i	−0.905871	+	0.423555i	$0.860782\pi$
$798$	3.57041e12	−	3.32485e11i	0.311677	−	0.0290241i
$799$			6.13063e12i			0.532163i
$800$	−1.15289e13	−	2.41253e12i	−0.995141	−	0.208242i
$801$	−7.98182e12	−	4.60831e12i	−0.685103	−	0.395544i
$802$	−1.43627e12	−	5.36022e12i	−0.122589	−	0.457507i
$803$	−9.94068e11	−	2.66360e11i	−0.0843716	−	0.0226073i
$804$	7.55038e12			0.637260
$805$	−1.42119e12	+	9.99907e12i	−0.119280	+	0.839224i
$806$	−9.94335e10			−0.00829899
$807$	−2.81724e12	−	7.54876e11i	−0.233826	−	0.0626534i
$808$	−2.31239e12	−	8.62996e12i	−0.190858	−	0.712291i
$809$	−7.67737e12	−	4.43253e12i	−0.630151	−	0.363818i	0.150660	−	0.988586i	$-0.451860\pi$
$809$	−7.67737e12	−	4.43253e12i	−0.630151	−	0.363818i	−0.780810	+	0.624768i	$0.785194\pi$
$810$	−8.14579e10	+	3.41672e11i	−0.00664891	+	0.0278886i
$811$			1.40381e13i			1.13950i	0.821817	+	0.569752i	$0.192961\pi$
$811$			1.40381e13i			1.13950i	−0.821817	+	0.569752i	$0.807039\pi$
$812$	−1.25517e13	+	8.89373e12i	−1.01321	+	0.717929i
$813$	−3.14347e12	−	3.14347e12i	−0.252349	−	0.252349i
$814$	2.53309e11	−	1.46248e11i	0.0202228	−	0.0116756i
$815$	2.98662e12	+	1.00245e13i	0.237121	+	0.795891i
$816$	1.64736e12	−	2.85332e12i	0.130072	−	0.225291i
$817$	−2.16391e12	+	8.07583e12i	−0.169918	+	0.634144i
$818$	−5.01527e12	+	5.01527e12i	−0.391656	+	0.391656i
$819$	9.30408e11	−	1.12148e12i	0.0722596	−	0.0870995i
$820$	−4.55797e11	−	1.64158e13i	−0.0352054	−	1.26794i
$821$	8.50703e12	+	1.47346e13i	0.653482	+	1.13186i	0.982272	+	0.187461i	$0.0600258\pi$
$821$	8.50703e12	+	1.47346e13i	0.653482	+	1.13186i	−0.328790	+	0.944403i	$0.606641\pi$
$822$	5.90640e12	−	1.58261e12i	0.451232	−	0.120907i
$823$	1.03008e13	−	2.76008e12i	0.782654	−	0.209712i	0.154700	−	0.987962i	$-0.450559\pi$
$823$	1.03008e13	−	2.76008e12i	0.782654	−	0.209712i	0.627955	+	0.778250i	$0.283892\pi$
$824$	8.49939e12	+	1.47214e13i	0.642266	+	1.11244i
$825$	−4.20617e11	+	4.70120e11i	−0.0316114	+	0.0353318i
$826$	2.33715e12	−	8.65475e11i	0.174694	−	0.0646911i
$827$	1.67816e12	−	1.67816e12i	0.124756	−	0.124756i	−0.641972	−	0.766728i	$-0.721884\pi$
$827$	1.67816e12	−	1.67816e12i	0.124756	−	0.124756i	0.766728	+	0.641972i	$0.221884\pi$
$828$	1.49411e12	−	5.57611e12i	0.110471	−	0.412282i
$829$	−1.00219e13	+	1.73585e13i	−0.736980	+	1.27649i	0.216869	+	0.976201i	$0.430416\pi$
$829$	−1.00219e13	+	1.73585e13i	−0.736980	+	1.27649i	−0.953849	+	0.300286i	$0.902918\pi$
$830$	−4.04901e12	+	7.48550e12i	−0.296140	+	0.547482i
$831$	4.53859e12	−	2.62036e12i	0.330154	−	0.190614i
$832$	1.48075e11	+	1.48075e11i	0.0107134	+	0.0107134i
$833$	1.28481e13	+	8.78399e12i	0.924563	+	0.632105i
$834$			2.56300e12i			0.183443i
$835$	−3.37193e12	−	8.03900e11i	−0.240043	−	0.0572286i
$836$	8.52210e11	+	4.92024e11i	0.0603418	+	0.0348384i
$837$	−3.63727e11	−	1.35745e12i	−0.0256160	−	0.0956002i
$838$	4.05257e12	+	1.08588e12i	0.283879	+	0.0760650i
$839$	−2.54379e12			−0.177236			−0.0886181	−	0.996066i	$-0.528245\pi$
$839$	−2.54379e12			−0.177236			−0.0886181	+	0.996066i	$0.528245\pi$
$840$	2.81186e12	−	6.59570e12i	0.194866	−	0.457092i
$841$	−2.22074e13			−1.53079
$842$	2.04079e12	+	5.46828e11i	0.139925	+	0.0374927i
$843$	−2.31746e12	−	8.64888e12i	−0.158048	−	0.589842i
$844$	−1.34559e13	−	7.76875e12i	−0.912789	−	0.526999i
$845$	7.52454e12	+	1.22355e13i	0.507721	+	0.825597i
$846$		−	2.13919e12i		−	0.143576i
$847$	1.38005e12	+	1.48198e13i	0.0921340	+	0.989387i
$848$	4.45522e12	+	4.45522e12i	0.295861	+	0.295861i
$849$	6.21954e12	−	3.59085e12i	0.410841	−	0.237199i
$850$	−3.60232e12	+	7.12548e12i	−0.236699	+	0.468197i
$851$	4.06209e12	−	7.03575e12i	0.265501	−	0.459862i
$852$	−8.39808e11	+	3.13421e12i	−0.0546011	+	0.203774i
$853$	2.36913e12	−	2.36913e12i	0.153221	−	0.153221i	−0.626334	−	0.779555i	$-0.715445\pi$
$853$	2.36913e12	−	2.36913e12i	0.153221	−	0.153221i	0.779555	+	0.626334i	$0.215445\pi$
$854$	2.82156e12	+	4.81275e11i	0.181522	+	0.0309623i
$855$	−1.13023e13	+	3.13819e11i	−0.723304	+	0.0200831i
$856$	−5.31599e12	−	9.20756e12i	−0.338417	−	0.586155i
$857$	−7.12367e12	+	1.90878e12i	−0.451118	+	0.120877i	−0.477222	−	0.878783i	$-0.658356\pi$
$857$	−7.12367e12	+	1.90878e12i	−0.451118	+	0.120877i	0.0261045	+	0.999659i	$0.491690\pi$
$858$	5.97394e10	−	1.60071e10i	0.00376329	−	0.00100837i
$859$	1.10027e13	+	1.90572e13i	0.689492	+	1.19424i	0.972002	+	0.234971i	$0.0754995\pi$
$859$	1.10027e13	+	1.90572e13i	0.689492	+	1.19424i	−0.282510	+	0.959264i	$0.591167\pi$
$860$	5.32403e12	+	5.03636e12i	0.331892	+	0.313960i
$861$	1.53887e13	+	2.62486e12i	0.954305	+	0.162777i
$862$	8.95284e12	−	8.95284e12i	0.552304	−	0.552304i
$863$	2.59786e12	−	9.69533e12i	0.159429	−	0.594996i	−0.839257	−	0.543735i	$-0.817010\pi$
$863$	2.59786e12	−	9.69533e12i	0.159429	−	0.594996i	0.998685	−	0.0512603i	$-0.0163238\pi$
$864$	−8.16067e12	+	1.41347e13i	−0.498211	+	0.862928i
$865$	−1.28931e13	+	3.84127e12i	−0.783044	+	0.233294i
$866$	−5.29946e12	+	3.05964e12i	−0.320185	+	0.184859i
$867$	−1.78282e12	−	1.78282e12i	−0.107157	−	0.107157i
$868$	−1.22235e11	−	1.31263e12i	−0.00730900	−	0.0784882i
$869$			1.24304e12i			0.0739425i
$870$	6.39019e12	−	3.92981e12i	0.378162	−	0.232560i
$871$	−3.53647e12	−	2.04178e12i	−0.208204	−	0.120206i
$872$	6.69605e12	+	2.49900e13i	0.392188	+	1.46367i
$873$	6.50350e12	+	1.74261e12i	0.378951	+	0.101540i
$874$	−7.68310e12			−0.445385
$875$	5.90442e12	−	1.63032e13i	0.340518	−	0.940238i
$876$	8.89628e12			0.510434
$877$	−1.21742e13	−	3.26206e12i	−0.694931	−	0.186206i	−0.105972	−	0.994369i	$-0.533795\pi$
$877$	−1.21742e13	−	3.26206e12i	−0.694931	−	0.186206i	−0.588959	+	0.808163i	$0.700462\pi$
$878$	−3.45232e12	−	1.28842e13i	−0.196059	−	0.731701i
$879$	−7.44947e12	−	4.30095e12i	−0.420897	−	0.243005i
$880$	4.70161e11	−	2.89137e11i	0.0264286	−	0.0162529i
$881$		−	1.00961e13i		−	0.564625i	−0.959322	−	0.282312i	$-0.908898\pi$
$881$		−	1.00961e13i		−	0.564625i	0.959322	−	0.282312i	$-0.0911015\pi$
$882$	−4.48315e12	−	3.06504e12i	−0.249445	−	0.170541i
$883$	−2.06841e13	−	2.06841e13i	−1.14502	−	1.14502i	−0.987519	−	0.157503i	$-0.949656\pi$
$883$	−2.06841e13	−	2.06841e13i	−1.14502	−	1.14502i	−0.157503	−	0.987519i	$-0.550344\pi$
$884$	−2.41168e12	+	1.39239e12i	−0.132827	+	0.0766875i
$885$	4.14369e12	−	1.23454e12i	0.227061	−	0.0676487i
$886$	2.50544e12	−	4.33955e12i	0.136594	−	0.236588i
$887$	2.72804e12	−	1.01812e13i	0.147977	−	0.552258i	−0.851628	−	0.524147i	$-0.824384\pi$
$887$	2.72804e12	−	1.01812e13i	0.147977	−	0.552258i	0.999605	−	0.0281107i	$-0.00894908\pi$
$888$	−4.07836e12	+	4.07836e12i	−0.220103	+	0.220103i
$889$	−4.03401e12	+	1.49384e12i	−0.216611	+	0.0802134i
$890$	7.81120e12	+	7.38915e12i	0.417314	+	0.394766i
$891$	−4.58150e10	−	7.93539e10i	−0.00243533	−	0.00421812i
$892$	2.53929e13	−	6.80399e12i	1.34298	−	0.359851i
$893$	9.78322e12	−	2.62140e12i	0.514814	−	0.137944i
$894$	−2.75810e11	−	4.77717e11i	−0.0144408	−	0.0250122i
$895$	2.76880e13	−	7.68781e11i	1.44241	−	0.0400497i
$896$	−1.20255e13	+	1.44951e13i	−0.623328	+	0.751340i
$897$	1.21468e12	−	1.21468e12i	0.0626464	−	0.0626464i
$898$	−2.26449e12	+	8.45119e12i	−0.116206	+	0.433685i
$899$	1.57318e12	−	2.72483e12i	0.0803268	−	0.139130i
$900$	−4.47163e12	+	8.84500e12i	−0.227182	+	0.449373i
$901$	2.05908e13	−	1.18881e13i	1.04091	−	0.600969i
$902$	−8.51525e11	−	8.51525e11i	−0.0428320	−	0.0428320i
$903$	−5.68440e12	+	4.02778e12i	−0.284505	+	0.201591i
$904$			3.25501e12i			0.162104i
$905$	6.80443e12	+	1.10646e13i	0.337189	+	0.548297i
$906$	1.77237e12	+	1.02328e12i	0.0873934	+	0.0504566i
$907$	6.37717e12	+	2.37999e13i	0.312893	+	1.16773i	0.925936	+	0.377681i	$0.123279\pi$
$907$	6.37717e12	+	2.37999e13i	0.312893	+	1.16773i	−0.613043	+	0.790050i	$0.710055\pi$
$908$	−6.32673e11	−	1.69524e11i	−0.0308882	−	0.00827648i
$909$	−1.17399e13			−0.570331
$910$	−1.35928e12	+	1.02097e12i	−0.0657084	+	0.0493544i
$911$	1.44127e13			0.693285			0.346642	−	0.937997i	$-0.387322\pi$
$911$	1.44127e13			0.693285			0.346642	+	0.937997i	$0.387322\pi$
$912$	−5.25771e12	−	1.40880e12i	−0.251663	−	0.0674330i
$913$	−5.74607e11	−	2.14446e12i	−0.0273686	−	0.102141i
$914$	−1.07490e13	−	6.20596e12i	−0.509462	−	0.294138i
$915$	4.83029e12	+	1.15159e12i	0.227813	+	0.0543128i
$916$			2.22833e13i			1.04581i
$917$	−3.29530e13	+	3.06866e12i	−1.53898	+	0.143314i
$918$	7.82315e12	+	7.82315e12i	0.363572	+	0.363572i
$919$	2.54958e13	−	1.47200e13i	1.17909	−	0.680751i	0.223290	−	0.974752i	$-0.428320\pi$
$919$	2.54958e13	−	1.47200e13i	1.17909	−	0.680751i	0.955805	+	0.294001i	$0.0949870\pi$
$920$	−7.30910e12	+	1.35125e13i	−0.336371	+	0.621858i
$921$	4.40425e12	−	7.62839e12i	0.201699	−	0.349353i
$922$	1.50958e12	−	5.63385e12i	0.0687968	−	0.256753i
$923$	1.24091e12	−	1.24091e12i	0.0562771	−	0.0562771i
$924$	2.84750e11	+	7.68948e11i	0.0128511	+	0.0347035i
$925$	−9.30030e12	+	1.03948e13i	−0.417695	+	0.466853i
$926$	2.13153e12	+	3.69192e12i	0.0952671	+	0.165007i
$927$	2.15755e13	−	5.78113e12i	0.959625	−	0.257131i
$928$	−3.52963e13	+	9.45760e12i	−1.56229	+	0.418615i
$929$	−2.09278e13	−	3.62480e13i	−0.921835	−	1.59666i	−0.796574	−	0.604541i	$-0.793357\pi$
$929$	−2.09278e13	−	3.62480e13i	−0.921835	−	1.59666i	−0.125261	−	0.992124i	$-0.539977\pi$
$930$	1.78436e10	+	6.42648e11i	0.000782186	+	0.0281708i
$931$	8.52371e12	−	2.42589e13i	0.371839	−	1.05827i
$932$	1.19819e13	−	1.19819e13i	0.520180	−	0.520180i
$933$	−2.53327e12	+	9.45431e12i	−0.109450	+	0.408472i
$934$	−2.17827e12	+	3.77288e12i	−0.0936594	+	0.162223i
$935$	−5.94718e11	−	1.99616e12i	−0.0254483	−	0.0854166i
$936$	1.91959e12	−	1.10828e12i	0.0817462	−	0.0471962i
$937$	−2.21670e13	−	2.21670e13i	−0.939461	−	0.939461i	0.0588085	−	0.998269i	$-0.481270\pi$
$937$	−2.21670e13	−	2.21670e13i	−0.939461	−	0.939461i	−0.998269	+	0.0588085i	$0.981270\pi$
$938$	−6.35463e12	+	1.38288e13i	−0.268027	+	0.583272i
$939$		−	1.75689e13i		−	0.737479i
$940$	2.05894e12	−	8.63612e12i	0.0860136	−	0.360781i
$941$	−3.88943e13	−	2.24557e13i	−1.61709	−	0.933625i	−0.987669	−	0.156557i	$-0.949960\pi$
$941$	−3.88943e13	−	2.24557e13i	−1.61709	−	0.933625i	−0.629417	−	0.777068i	$-0.716706\pi$
$942$	2.04077e11	+	7.61627e11i	0.00844434	+	0.0315147i
$943$	−3.23085e13	−	8.65703e12i	−1.33050	−	0.356505i
$944$	−3.78314e12			−0.155052
$945$	−1.89103e13	−	1.48219e13i	−0.771356	−	0.604589i
$946$	5.37419e11			0.0218174
$947$	−2.58859e12	−	6.93610e11i	−0.104589	−	0.0280247i	0.206145	−	0.978522i	$-0.433908\pi$
$947$	−2.58859e12	−	6.93610e11i	−0.104589	−	0.0280247i	−0.310734	+	0.950497i	$0.600575\pi$
$948$	−2.78109e12	−	1.03792e13i	−0.111835	−	0.417374i
$949$	−4.16687e12	−	2.40574e12i	−0.166768	−	0.0962833i
$950$	1.29111e13	+	2.70176e12i	0.514290	+	0.107620i
$951$		−	1.48657e13i		−	0.589351i
$952$	1.36873e13	+	1.93168e13i	0.540070	+	0.762199i
$953$	1.46092e13	+	1.46092e13i	0.573732	+	0.573732i	0.933169	−	0.359437i	$-0.117031\pi$
$953$	1.46092e13	+	1.46092e13i	0.573732	+	0.573732i	−0.359437	+	0.933169i	$0.617031\pi$
$954$	−7.18486e12	+	4.14818e12i	−0.280835	+	0.162140i
$955$	2.39753e13	+	1.29686e13i	0.932716	+	0.504519i
$956$	9.59313e12	−	1.66158e13i	0.371450	−	0.643369i
$957$	−5.06511e11	+	1.89033e12i	−0.0195203	+	0.0728506i
$958$	1.24409e13	−	1.24409e13i	0.477207	−	0.477207i
$959$	7.37245e12	−	4.32222e13i	0.281467	−	1.65015i
$960$	9.30450e11	−	9.83595e11i	0.0353568	−	0.0373763i
$961$	−1.30850e13	−	2.26639e13i	−0.494901	−	0.857193i
$962$	1.32090e12	−	3.53934e11i	0.0497259	−	0.0133240i
$963$	−1.34945e13	+	3.61584e12i	−0.505637	+	0.135485i
$964$	−1.65767e13	−	2.87117e13i	−0.618232	−	1.07081i
$965$	2.62879e13	−	2.77894e13i	0.975849	−	1.03159i
$966$	−4.92722e12	−	4.08772e12i	−0.182056	−	0.151037i
$967$	−8.19929e12	+	8.19929e12i	−0.301548	+	0.301548i	−0.841619	−	0.540071i	$-0.818397\pi$
$967$	−8.19929e12	+	8.19929e12i	−0.301548	+	0.301548i	0.540071	+	0.841619i	$0.318397\pi$
$968$	−5.85971e12	+	2.18688e13i	−0.214505	+	0.800543i
$969$	−1.02703e13	+	1.77886e13i	−0.374218	+	0.648165i
$970$	−6.90889e12	−	3.73711e12i	−0.250574	−	0.135539i
$971$	3.39424e11	−	1.95967e11i	0.0122534	−	0.00707450i	−0.493861	−	0.869541i	$-0.664415\pi$
$971$	3.39424e11	−	1.95967e11i	0.0122534	−	0.00707450i	0.506114	+	0.862466i	$0.331081\pi$
$972$	1.56141e13	+	1.56141e13i	0.561073	+	0.561073i
$973$	1.66995e13	+	7.67378e12i	0.597304	+	0.274474i
$974$		−	1.49273e13i		−	0.531454i
$975$	−2.46836e12	+	1.61408e12i	−0.0874758	+	0.0572009i
$976$	−3.76276e12	−	2.17243e12i	−0.132734	−	0.0766341i
$977$	9.04598e12	+	3.37601e13i	0.317636	+	1.18544i	0.921510	+	0.388355i	$0.126957\pi$
$977$	9.04598e12	+	3.37601e13i	0.317636	+	1.18544i	−0.603873	+	0.797080i	$0.706377\pi$
$978$	−6.40463e12	−	1.71611e12i	−0.223856	−	0.0599821i
$979$	−2.80498e12			−0.0975905
$980$	−1.51489e13	−	1.66888e13i	−0.524642	−	0.577975i
$981$	3.39955e13			1.17196
$982$	−1.09858e13	−	2.94363e12i	−0.376989	−	0.101014i
$983$	3.62481e12	+	1.35280e13i	0.123821	+	0.462106i	0.999795	−	0.0202524i	$-0.00644697\pi$
$983$	3.62481e12	+	1.35280e13i	0.123821	+	0.462106i	−0.875974	+	0.482358i	$0.839780\pi$
$984$	2.05648e13	+	1.18731e13i	0.699271	+	0.403724i
$985$	−1.00619e13	+	4.22041e13i	−0.340577	+	1.42854i
$986$			2.47700e13i			0.834603i
$987$	7.66872e12	+	3.52395e12i	0.257215	+	0.118196i
$988$	3.25318e12	+	3.25318e12i	0.108618	+	0.108618i
$989$	1.29272e13	−	7.46351e12i	0.429655	−	0.248062i
$990$	2.07518e11	+	6.96528e11i	0.00686589	+	0.0230452i
$991$	2.10828e13	−	3.65165e13i	0.694381	−	1.20270i	−0.276008	−	0.961155i	$-0.589012\pi$
$991$	2.10828e13	−	3.65165e13i	0.694381	−	1.20270i	0.970389	−	0.241547i	$-0.0776549\pi$
$992$	8.10499e11	−	3.02482e12i	0.0265736	−	0.0991739i
$993$	−1.34578e13	+	1.34578e13i	−0.439242	+	0.439242i
$994$	−5.03360e12	−	4.17598e12i	−0.163546	−	0.135681i
$995$	8.58677e11	+	3.09257e13i	0.0277732	+	1.00027i
$996$	9.59579e12	+	1.66204e13i	0.308968	+	0.535148i
$997$	1.39184e13	−	3.72942e12i	0.446129	−	0.119540i	−0.0287584	−	0.999586i	$-0.509155\pi$
$997$	1.39184e13	−	3.72942e12i	0.446129	−	0.119540i	0.474888	+	0.880046i	$0.342489\pi$
$998$	2.72573e13	−	7.30358e12i	0.869752	−	0.233049i
$999$	9.66369e12	+	1.67380e13i	0.306972	+	0.531691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.k.a.3.14	✓	136
5.2	odd	4	inner	35.10.k.a.17.21	yes	136
7.5	odd	6	inner	35.10.k.a.33.21	yes	136
35.12	even	12	inner	35.10.k.a.12.14	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.14	✓	136	1.1	even	1	trivial
35.10.k.a.12.14	yes	136	35.12	even	12	inner
35.10.k.a.17.21	yes	136	5.2	odd	4	inner
35.10.k.a.33.21	yes	136	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	35.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.2381 - 2.74328i) q^{2} +(-21.6326 - 80.7338i) q^{3} +(-346.113 - 199.828i) q^{4} +(1190.45 - 732.094i) q^{5} +885.901i q^{6} +(5772.19 + 2652.45i) q^{7} +(6832.66 + 6832.66i) q^{8} +(10996.0 - 6348.54i) q^{9} +(-14196.2 + 4229.50i) q^{10} +(1932.11 - 3346.52i) q^{11} +(-8645.59 + 32265.8i) q^{12} +(12774.8 - 12774.8i) q^{13} +(-51819.6 - 42990.6i) q^{14} +(-84857.1 - 80272.2i) q^{15} +(51102.8 + 88512.6i) q^{16} +(372544. - 99822.8i) q^{17} +(-129994. + 34831.7i) q^{18} +(-318593. - 551820. i) q^{19} +(-558322. + 15502.3i) q^{20} +(89275.0 - 523390. i) q^{21} +(-28961.5 + 28961.5i) q^{22} +(-294437. + 1.09885e6i) q^{23} +(403819. - 699435. i) q^{24} +(881201. - 1.74304e6i) q^{25} +(-165834. + 95744.3i) q^{26} +(-1.91370e6 - 1.91370e6i) q^{27} +(-1.46779e6 - 2.07149e6i) q^{28} -6.05925e6i q^{29} +(648563. + 1.05462e6i) q^{30} +(449698. + 259633. i) q^{31} +(-1.56085e6 - 5.82519e6i) q^{32} +(-311974. - 83593.1i) q^{33} -4.08797e6 q^{34} +(8.81332e6 - 1.06819e6i) q^{35} -5.07448e6 q^{36} +(-6.89807e6 - 1.84833e6i) q^{37} +(1.74798e6 + 6.52355e6i) q^{38} +(-1.30771e6 - 755007. i) q^{39} +(1.31361e7 + 3.13177e6i) q^{40} +2.94020e7i q^{41} +(-2.34981e6 + 5.11359e6i) q^{42} +(-9.27815e6 - 9.27815e6i) q^{43} +(-1.33746e6 + 772182. i) q^{44} +(8.44242e6 - 1.56077e7i) q^{45} +(6.02893e6 - 1.04424e7i) q^{46} +(-4.11403e6 + 1.53538e7i) q^{47} +(6.04048e6 - 6.04048e6i) q^{48} +(2.62827e7 + 3.06208e7i) q^{49} +(-1.38034e7 + 1.54279e7i) q^{50} +(-1.61181e7 - 2.79174e7i) q^{51} +(-6.97429e6 + 1.86876e6i) q^{52} +(5.95461e7 - 1.59553e7i) q^{53} +(1.43428e7 + 2.48424e7i) q^{54} +(-149889. - 5.39834e6i) q^{55} +(2.13161e7 + 5.75627e7i) q^{56} +(-3.76585e7 + 3.76585e7i) q^{57} +(-1.66222e7 + 6.20350e7i) q^{58} +(-1.85075e7 + 3.20559e7i) q^{59} +(1.33295e7 + 4.47401e7i) q^{60} +(-3.68156e7 + 2.12555e7i) q^{61} +(-3.89178e6 - 3.89178e6i) q^{62} +(8.03101e7 - 7.47867e6i) q^{63} +1.15912e7i q^{64} +(5.85536e6 - 2.45601e7i) q^{65} +(2.96468e6 + 1.71166e6i) q^{66} +(-5.85014e7 - 2.18330e8i) q^{67} +(-1.48890e8 - 3.98948e7i) q^{68} +9.50841e7 q^{69} +(-9.31616e7 - 1.32412e7i) q^{70} +9.71371e7 q^{71} +(1.18509e8 + 3.17545e7i) q^{72} +(-6.89296e7 - 2.57249e8i) q^{73} +(6.55523e7 + 3.78466e7i) q^{74} +(-1.59785e8 - 3.34363e7i) q^{75} +2.54656e8i q^{76} +(2.00290e7 - 1.41919e7i) q^{77} +(1.13172e7 + 1.13172e7i) q^{78} +(-2.78581e8 + 1.60839e8i) q^{79} +(1.25635e8 + 6.79575e7i) q^{80} +(1.18562e7 - 2.05355e7i) q^{81} +(8.06578e7 - 3.01019e8i) q^{82} +(4.06253e8 - 4.06253e8i) q^{83} +(-1.35487e8 + 1.63312e8i) q^{84} +(3.70414e8 - 3.91571e8i) q^{85} +(6.95377e7 + 1.20443e8i) q^{86} +(-4.89186e8 + 1.31077e8i) q^{87} +(3.60671e7 - 9.66415e6i) q^{88} +(-3.62942e8 - 6.28634e8i) q^{89} +(-1.29250e8 + 1.36633e8i) q^{90} +(1.07623e8 - 3.98540e7i) q^{91} +(3.21491e8 - 3.21491e8i) q^{92} +(1.12331e7 - 4.19223e7i) q^{93} +(8.42394e7 - 1.45907e8i) q^{94} +(-7.83252e8 - 4.23672e8i) q^{95} +(-4.36524e8 + 2.52027e8i) q^{96} +(3.74959e8 + 3.74959e8i) q^{97} +(-1.85082e8 - 3.85599e8i) q^{98} -4.90644e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{2} - 6 q^{3} - 1710 q^{5} + 5940 q^{7} - 3484 q^{8} + 153786 q^{10} - 87752 q^{11} + 3066 q^{12} - 318872 q^{15} + 3132804 q^{16} - 1578678 q^{17} - 239036 q^{18} - 5745396 q^{21} + 2132088 q^{22}+ \cdots + 5117393178 q^{98}+O(q^{100}) \) 136 * q - 2 * q^2 - 6 * q^3 - 1710 * q^5 + 5940 * q^7 - 3484 * q^8 + 153786 * q^10 - 87752 * q^11 + 3066 * q^12 - 318872 * q^15 + 3132804 * q^16 - 1578678 * q^17 - 239036 * q^18 - 5745396 * q^21 + 2132088 * q^22 + 312550 * q^23 + 4308518 * q^25 + 2294580 * q^26 - 9559382 * q^28 + 21412708 * q^30 + 8900220 * q^31 + 17154282 * q^32 - 13729410 * q^33 + 6034552 * q^35 - 114903056 * q^36 + 26817310 * q^37 - 20958672 * q^38 + 143985558 * q^40 - 38052106 * q^42 + 46427728 * q^43 - 96332286 * q^45 + 2421124 * q^46 + 147698754 * q^47 - 11742092 * q^50 - 138178540 * q^51 - 126665976 * q^52 - 16288570 * q^53 + 501495076 * q^56 - 71567164 * q^57 - 681848346 * q^58 + 254653694 * q^60 - 575844240 * q^61 + 491512776 * q^63 + 833960586 * q^65 + 260439612 * q^66 + 22092746 * q^67 - 2824755312 * q^68 - 1044240840 * q^70 + 355056144 * q^71 + 98662792 * q^72 + 1852831146 * q^73 + 2937834474 * q^75 + 1226263510 * q^77 + 2595615712 * q^78 - 3778385244 * q^80 + 1504403888 * q^81 - 3707543946 * q^82 - 1726556112 * q^85 + 1771746456 * q^86 + 30331668 * q^87 - 1182712628 * q^88 - 4378590056 * q^91 + 2593806924 * q^92 - 4305536726 * q^93 + 861804818 * q^95 + 15624596040 * q^96 + 5117393178 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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