LMFDB - Embedded newform 16.10.e.a.5.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,10,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, degree $2$, 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:	$8.24057337862$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.12
Character	$\chi$	$=$	16.5
Dual form			16.10.e.a.13.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.74072 + 20.8710i) q^{2} +(-8.26401 + 8.26401i) q^{3} +(-359.200 + 364.856i) q^{4} +(-1313.02 - 1313.02i) q^{5} +(-244.712 - 100.245i) q^{6} -3840.19i q^{7} +(-10754.6 - 4307.77i) q^{8} +19546.4i q^{9} +O(q^{10})$	\(q+(8.74072 + 20.8710i) q^{2} +(-8.26401 + 8.26401i) q^{3} +(-359.200 + 364.856i) q^{4} +(-1313.02 - 1313.02i) q^{5} +(-244.712 - 100.245i) q^{6} -3840.19i q^{7} +(-10754.6 - 4307.77i) q^{8} +19546.4i q^{9} +(15927.3 - 38880.8i) q^{10} +(-40800.5 - 40800.5i) q^{11} +(-46.7403 - 5983.60i) q^{12} +(61875.1 - 61875.1i) q^{13} +(80148.8 - 33566.0i) q^{14} +21701.6 q^{15} +(-4095.18 - 262112. i) q^{16} -438489. q^{17} +(-407954. + 170850. i) q^{18} +(-390530. + 390530. i) q^{19} +(950699. - 7426.30i) q^{20} +(31735.4 + 31735.4i) q^{21} +(494923. - 1.20817e6i) q^{22} +2.06658e6i q^{23} +(124475. - 53276.5i) q^{24} +1.49492e6i q^{25} +(1.83223e6 + 750564. i) q^{26} +(-324192. - 324192. i) q^{27} +(1.40112e6 + 1.37940e6i) q^{28} +(-300464. + 300464. i) q^{29} +(189688. + 452935. i) q^{30} -3.48723e6 q^{31} +(5.43475e6 - 2.37652e6i) q^{32} +674352. q^{33} +(-3.83271e6 - 9.15172e6i) q^{34} +(-5.04225e6 + 5.04225e6i) q^{35} +(-7.13162e6 - 7.02107e6i) q^{36} +(-3.11267e6 - 3.11267e6i) q^{37} +(-1.15643e7 - 4.73725e6i) q^{38} +1.02267e6i q^{39} +(8.46479e6 + 1.97772e7i) q^{40} -3.29270e7i q^{41} +(-384960. + 939741. i) q^{42} +(1.67806e7 + 1.67806e7i) q^{43} +(2.95418e7 - 230763. i) q^{44} +(2.56648e7 - 2.56648e7i) q^{45} +(-4.31316e7 + 1.80634e7i) q^{46} -1.07902e7 q^{47} +(2.19994e6 + 2.13225e6i) q^{48} +2.56065e7 q^{49} +(-3.12005e7 + 1.30667e7i) q^{50} +(3.62368e6 - 3.62368e6i) q^{51} +(349959. + 4.48010e7i) q^{52} +(1.22567e7 + 1.22567e7i) q^{53} +(3.93255e6 - 9.59990e6i) q^{54} +1.07144e8i q^{55} +(-1.65427e7 + 4.12996e7i) q^{56} -6.45469e6i q^{57} +(-8.89725e6 - 3.64472e6i) q^{58} +(-7.95943e7 - 7.95943e7i) q^{59} +(-7.79522e6 + 7.91796e6i) q^{60} +(1.24768e8 - 1.24768e8i) q^{61} +(-3.04809e7 - 7.27820e7i) q^{62} +7.50620e7 q^{63} +(9.71040e7 + 9.26564e7i) q^{64} -1.62486e8 q^{65} +(5.89432e6 + 1.40744e7i) q^{66} +(-4.18062e7 + 4.18062e7i) q^{67} +(1.57505e8 - 1.59985e8i) q^{68} +(-1.70782e7 - 1.70782e7i) q^{69} +(-1.49310e8 - 6.11641e7i) q^{70} +2.39067e8i q^{71} +(8.42014e7 - 2.10213e8i) q^{72} -6.87647e7i q^{73} +(3.77577e7 - 9.21716e7i) q^{74} +(-1.23540e7 - 1.23540e7i) q^{75} +(-2.20879e6 - 2.82765e8i) q^{76} +(-1.56682e8 + 1.56682e8i) q^{77} +(-2.13442e7 + 8.93890e6i) q^{78} -4.52979e8 q^{79} +(-3.38781e8 + 3.49535e8i) q^{80} -3.79374e8 q^{81} +(6.87220e8 - 2.87806e8i) q^{82} +(3.47281e8 - 3.47281e8i) q^{83} +(-2.29782e7 + 179492. i) q^{84} +(5.75745e8 + 5.75745e8i) q^{85} +(-2.03554e8 + 4.96904e8i) q^{86} -4.96607e6i q^{87} +(2.63033e8 + 6.14551e8i) q^{88} +5.59113e8i q^{89} +(7.59981e8 + 3.11322e8i) q^{90} +(-2.37612e8 - 2.37612e8i) q^{91} +(-7.54002e8 - 7.42314e8i) q^{92} +(2.88185e7 - 2.88185e7i) q^{93} +(-9.43138e7 - 2.25202e8i) q^{94} +1.02555e9 q^{95} +(-2.52733e7 + 6.45524e7i) q^{96} -6.64755e8 q^{97} +(2.23819e8 + 5.34435e8i) q^{98} +(7.97504e8 - 7.97504e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 2 q^{2} - 2 q^{3} + 168 q^{4} - 2 q^{5} - 2192 q^{6} - 716 q^{8}+O(q^{10}) $ 34 * q - 2 * q^2 - 2 * q^3 + 168 * q^4 - 2 * q^5 - 2192 * q^6 - 716 * q^8	\( 34 q - 2 q^{2} - 2 q^{3} + 168 q^{4} - 2 q^{5} - 2192 q^{6} - 716 q^{8} + 4684 q^{10} + 65858 q^{11} + 217156 q^{12} - 2 q^{13} - 133540 q^{14} + 404996 q^{15} - 817256 q^{16} - 4 q^{17} + 2179902 q^{18} - 480890 q^{19} - 3277988 q^{20} + 39364 q^{21} - 34300 q^{22} + 1863856 q^{24} - 6347768 q^{26} + 6364408 q^{27} + 3629528 q^{28} - 633402 q^{29} - 4677804 q^{30} - 11082256 q^{31} - 1655992 q^{32} - 4 q^{33} - 4528204 q^{34} + 23026556 q^{35} + 23564140 q^{36} - 1214778 q^{37} - 14996352 q^{38} - 11751288 q^{40} + 105399160 q^{42} - 34881078 q^{43} - 94223356 q^{44} + 3866882 q^{45} + 15432396 q^{46} + 97593616 q^{47} + 7831528 q^{48} - 126825626 q^{49} - 6289530 q^{50} - 27382140 q^{51} - 28284428 q^{52} - 74907850 q^{53} + 105311008 q^{54} + 26511256 q^{56} - 178271784 q^{58} + 94503354 q^{59} + 229034112 q^{60} - 90121106 q^{61} - 136788944 q^{62} - 153644796 q^{63} - 349292928 q^{64} + 62806084 q^{65} + 192273844 q^{66} + 406167670 q^{67} - 285757488 q^{68} + 382399540 q^{69} + 606051200 q^{70} + 882075684 q^{72} + 123910860 q^{74} - 1038797114 q^{75} - 453269100 q^{76} + 286751428 q^{77} - 1735024804 q^{78} + 1913565952 q^{79} - 700272856 q^{80} - 774840982 q^{81} - 674287584 q^{82} - 1637053442 q^{83} + 1281919912 q^{84} + 425303748 q^{85} + 243980676 q^{86} + 1781147128 q^{88} + 3084087192 q^{90} + 2019528196 q^{91} - 3131634504 q^{92} + 1071927184 q^{93} - 2068460272 q^{94} - 5087413260 q^{95} - 3896483152 q^{96} - 4 q^{97} - 3100632102 q^{98} + 3713751422 q^{99}+O(q^{100}) \) 34 * q - 2 * q^2 - 2 * q^3 + 168 * q^4 - 2 * q^5 - 2192 * q^6 - 716 * q^8 + 4684 * q^10 + 65858 * q^11 + 217156 * q^12 - 2 * q^13 - 133540 * q^14 + 404996 * q^15 - 817256 * q^16 - 4 * q^17 + 2179902 * q^18 - 480890 * q^19 - 3277988 * q^20 + 39364 * q^21 - 34300 * q^22 + 1863856 * q^24 - 6347768 * q^26 + 6364408 * q^27 + 3629528 * q^28 - 633402 * q^29 - 4677804 * q^30 - 11082256 * q^31 - 1655992 * q^32 - 4 * q^33 - 4528204 * q^34 + 23026556 * q^35 + 23564140 * q^36 - 1214778 * q^37 - 14996352 * q^38 - 11751288 * q^40 + 105399160 * q^42 - 34881078 * q^43 - 94223356 * q^44 + 3866882 * q^45 + 15432396 * q^46 + 97593616 * q^47 + 7831528 * q^48 - 126825626 * q^49 - 6289530 * q^50 - 27382140 * q^51 - 28284428 * q^52 - 74907850 * q^53 + 105311008 * q^54 + 26511256 * q^56 - 178271784 * q^58 + 94503354 * q^59 + 229034112 * q^60 - 90121106 * q^61 - 136788944 * q^62 - 153644796 * q^63 - 349292928 * q^64 + 62806084 * q^65 + 192273844 * q^66 + 406167670 * q^67 - 285757488 * q^68 + 382399540 * q^69 + 606051200 * q^70 + 882075684 * q^72 + 123910860 * q^74 - 1038797114 * q^75 - 453269100 * q^76 + 286751428 * q^77 - 1735024804 * q^78 + 1913565952 * q^79 - 700272856 * q^80 - 774840982 * q^81 - 674287584 * q^82 - 1637053442 * q^83 + 1281919912 * q^84 + 425303748 * q^85 + 243980676 * q^86 + 1781147128 * q^88 + 3084087192 * q^90 + 2019528196 * q^91 - 3131634504 * q^92 + 1071927184 * q^93 - 2068460272 * q^94 - 5087413260 * q^95 - 3896483152 * q^96 - 4 * q^97 - 3100632102 * q^98 + 3713751422 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	8.74072	+	20.8710i	0.386289	+	0.922378i
$2$	8.74072	+	20.8710i	0.386289	+	0.922378i
$3$	−8.26401	+	8.26401i	−0.0589041	+	0.0589041i	−0.735945	−	0.677041i	$-0.763262\pi$
$3$	−8.26401	+	8.26401i	−0.0589041	+	0.0589041i	0.677041	+	0.735945i	$0.263262\pi$
$4$	−359.200	+	364.856i	−0.701562	+	0.712609i
$5$	−1313.02	−	1313.02i	−0.939521	−	0.939521i	0.0587518	−	0.998273i	$-0.481288\pi$
$5$	−1313.02	−	1313.02i	−0.939521	−	0.939521i	−0.998273	+	0.0587518i	$0.981288\pi$
$6$	−244.712	−	100.245i	−0.0770858	−	0.0315778i
$7$		−	3840.19i		−	0.604522i	−0.953225	−	0.302261i	$-0.902259\pi$
$7$		−	3840.19i		−	0.604522i	0.953225	−	0.302261i	$-0.0977413\pi$
$8$	−10754.6	−	4307.77i	−0.928300	−	0.371832i
$9$			19546.4i			0.993061i
$10$	15927.3	−	38880.8i	0.503667	−	1.22952i
$11$	−40800.5	−	40800.5i	−0.840231	−	0.840231i	0.148658	−	0.988889i	$-0.452505\pi$
$11$	−40800.5	−	40800.5i	−0.840231	−	0.840231i	−0.988889	+	0.148658i	$0.952505\pi$
$12$	−46.7403	−	5983.60i	−0.000650693	−	0.0833004i
$13$	61875.1	−	61875.1i	0.600856	−	0.600856i	−0.339683	−	0.940540i	$-0.610320\pi$
$13$	61875.1	−	61875.1i	0.600856	−	0.600856i	0.940540	+	0.339683i	$0.110320\pi$
$14$	80148.8	−	33566.0i	0.557597	−	0.233520i
$15$	21701.6			0.110683
$16$	−4095.18	−	262112.i	−0.0156219	−	0.999878i
$17$	−438489.			−1.27332			−0.636662	−	0.771143i	$-0.719685\pi$
$17$	−438489.			−1.27332			−0.636662	+	0.771143i	$0.719685\pi$
$18$	−407954.	+	170850.i	−0.915977	+	0.383608i
$19$	−390530.	+	390530.i	−0.687485	+	0.687485i	−0.961675	−	0.274190i	$-0.911590\pi$
$19$	−390530.	+	390530.i	−0.687485	+	0.687485i	0.274190	+	0.961675i	$0.411590\pi$
$20$	950699.	−	7426.30i	1.32864	−	0.0103786i
$21$	31735.4	+	31735.4i	0.0356088	+	0.0356088i
$22$	494923.	−	1.20817e6i	0.450439	−	1.09958i
$23$			2.06658e6i			1.53984i	0.638138	+	0.769922i	$0.279705\pi$
$23$			2.06658e6i			1.53984i	−0.638138	+	0.769922i	$0.720295\pi$
$24$	124475.	−	53276.5i	0.0765831	−	0.0327782i
$25$			1.49492e6i			0.765399i
$26$	1.83223e6	+	750564.i	0.786321	+	0.322112i
$27$	−324192.	−	324192.i	−0.117399	−	0.117399i
$28$	1.40112e6	+	1.37940e6i	0.430787	+	0.424109i
$29$	−300464.	+	300464.i	−0.0788861	+	0.0788861i	−0.745449	−	0.666563i	$-0.767765\pi$
$29$	−300464.	+	300464.i	−0.0788861	+	0.0788861i	0.666563	+	0.745449i	$0.267765\pi$
$30$	189688.	+	452935.i	0.0427557	+	0.102092i
$31$	−3.48723e6			−0.678192			−0.339096	−	0.940752i	$-0.610121\pi$
$31$	−3.48723e6			−0.678192			−0.339096	+	0.940752i	$0.610121\pi$
$32$	5.43475e6	−	2.37652e6i	0.916231	−	0.400651i
$33$	674352.			0.0989861
$34$	−3.83271e6	−	9.15172e6i	−0.491871	−	1.17449i
$35$	−5.04225e6	+	5.04225e6i	−0.567961	+	0.567961i
$36$	−7.13162e6	−	7.02107e6i	−0.707663	−	0.696693i
$37$	−3.11267e6	−	3.11267e6i	−0.273040	−	0.273040i	0.557283	−	0.830323i	$-0.311844\pi$
$37$	−3.11267e6	−	3.11267e6i	−0.273040	−	0.273040i	−0.830323	+	0.557283i	$0.811844\pi$
$38$	−1.15643e7	−	4.73725e6i	−0.899689	−	0.368553i
$39$			1.02267e6i			0.0707858i
$40$	8.46479e6	+	1.97772e7i	0.522813	+	1.22150i
$41$		−	3.29270e7i		−	1.81980i	−0.414823	−	0.909902i	$-0.636157\pi$
$41$		−	3.29270e7i		−	1.81980i	0.414823	−	0.909902i	$-0.363843\pi$
$42$	−384960.	+	939741.i	−0.0190895	+	0.0466000i
$43$	1.67806e7	+	1.67806e7i	0.748514	+	0.748514i	0.974200	−	0.225686i	$-0.0724623\pi$
$43$	1.67806e7	+	1.67806e7i	0.748514	+	0.748514i	−0.225686	+	0.974200i	$0.572462\pi$
$44$	2.95418e7	−	230763.i	1.18823	−	0.00928174i
$45$	2.56648e7	−	2.56648e7i	0.933001	−	0.933001i
$46$	−4.31316e7	+	1.80634e7i	−1.42032	+	0.594824i
$47$	−1.07902e7			−0.322543			−0.161271	−	0.986910i	$-0.551559\pi$
$47$	−1.07902e7			−0.322543			−0.161271	+	0.986910i	$0.551559\pi$
$48$	2.19994e6	+	2.13225e6i	0.0598171	+	0.0579767i
$49$	2.56065e7			0.634554
$50$	−3.12005e7	+	1.30667e7i	−0.705987	+	0.295665i
$51$	3.62368e6	−	3.62368e6i	0.0750039	−	0.0750039i
$52$	349959.	+	4.48010e7i	0.00663745	+	0.849713i
$53$	1.22567e7	+	1.22567e7i	0.213369	+	0.213369i	0.805697	−	0.592328i	$-0.201791\pi$
$53$	1.22567e7	+	1.22567e7i	0.213369	+	0.213369i	−0.592328	+	0.805697i	$0.701791\pi$
$54$	3.93255e6	−	9.59990e6i	0.0629365	−	0.153637i
$55$			1.07144e8i			1.57883i
$56$	−1.65427e7	+	4.12996e7i	−0.224781	+	0.561177i
$57$		−	6.45469e6i		−	0.0809914i
$58$	−8.89725e6	−	3.64472e6i	−0.103236	−	0.0422900i
$59$	−7.95943e7	−	7.95943e7i	−0.855161	−	0.855161i	0.135602	−	0.990763i	$-0.456703\pi$
$59$	−7.95943e7	−	7.95943e7i	−0.855161	−	0.855161i	−0.990763	+	0.135602i	$0.956703\pi$
$60$	−7.79522e6	+	7.91796e6i	−0.0776511	+	0.0788738i
$61$	1.24768e8	−	1.24768e8i	1.15377	−	1.15377i	0.167984	−	0.985790i	$-0.446274\pi$
$61$	1.24768e8	−	1.24768e8i	1.15377	−	1.15377i	0.985790	−	0.167984i	$-0.0537257\pi$
$62$	−3.04809e7	−	7.27820e7i	−0.261978	−	0.625549i
$63$	7.50620e7			0.600327
$64$	9.71040e7	+	9.26564e7i	0.723481	+	0.690344i
$65$	−1.62486e8			−1.12903
$66$	5.89432e6	+	1.40744e7i	0.0382372	+	0.0913026i
$67$	−4.18062e7	+	4.18062e7i	−0.253457	+	0.253457i	−0.822386	−	0.568929i	$-0.807358\pi$
$67$	−4.18062e7	+	4.18062e7i	−0.253457	+	0.253457i	0.568929	+	0.822386i	$0.307358\pi$
$68$	1.57505e8	−	1.59985e8i	0.893315	−	0.907381i
$69$	−1.70782e7	−	1.70782e7i	−0.0907031	−	0.0907031i
$70$	−1.49310e8	−	6.11641e7i	−0.743271	−	0.304477i
$71$			2.39067e8i			1.11650i	0.829674	+	0.558248i	$0.188526\pi$
$71$			2.39067e8i			1.11650i	−0.829674	+	0.558248i	$0.811474\pi$
$72$	8.42014e7	−	2.10213e8i	0.369252	−	0.921858i
$73$		−	6.87647e7i		−	0.283409i	−0.989909	−	0.141704i	$-0.954742\pi$
$73$		−	6.87647e7i		−	0.283409i	0.989909	−	0.141704i	$-0.0452582\pi$
$74$	3.77577e7	−	9.21716e7i	0.146373	−	0.357318i
$75$	−1.23540e7	−	1.23540e7i	−0.0450851	−	0.0450851i
$76$	−2.20879e6	−	2.82765e8i	−0.00759441	−	0.972221i
$77$	−1.56682e8	+	1.56682e8i	−0.507938	+	0.507938i
$78$	−2.13442e7	+	8.93890e6i	−0.0652912	+	0.0273438i
$79$	−4.52979e8			−1.30845			−0.654223	−	0.756302i	$-0.727004\pi$
$79$	−4.52979e8			−1.30845			−0.654223	+	0.756302i	$0.727004\pi$
$80$	−3.38781e8	+	3.49535e8i	−0.924729	+	0.954083i
$81$	−3.79374e8			−0.979230
$82$	6.87220e8	−	2.87806e8i	1.67855	−	0.702970i
$83$	3.47281e8	−	3.47281e8i	0.803210	−	0.803210i	−0.180386	−	0.983596i	$-0.557735\pi$
$83$	3.47281e8	−	3.47281e8i	0.803210	−	0.803210i	0.983596	+	0.180386i	$0.0577347\pi$
$84$	−2.29782e7	+	179492.i	−0.0503569	+	0.000393358i
$85$	5.75745e8	+	5.75745e8i	1.19631	+	1.19631i
$86$	−2.03554e8	+	4.96904e8i	−0.401270	+	0.979556i
$87$		−	4.96607e6i		−	0.00929343i
$88$	2.63033e8	+	6.14551e8i	0.467561	+	1.09241i
$89$			5.59113e8i			0.944592i	0.881440	+	0.472296i	$0.156575\pi$
$89$			5.59113e8i			0.944592i	−0.881440	+	0.472296i	$0.843425\pi$
$90$	7.59981e8	+	3.11322e8i	1.22099	+	0.500172i
$91$	−2.37612e8	−	2.37612e8i	−0.363231	−	0.363231i
$92$	−7.54002e8	−	7.42314e8i	−1.09731	−	1.08030i
$93$	2.88185e7	−	2.88185e7i	0.0399483	−	0.0399483i
$94$	−9.43138e7	−	2.25202e8i	−0.124595	−	0.297506i
$95$	1.02555e9			1.29181
$96$	−2.52733e7	+	6.45524e7i	−0.0303698	+	0.0775697i
$97$	−6.64755e8			−0.762410			−0.381205	−	0.924490i	$-0.624491\pi$
$97$	−6.64755e8			−0.762410			−0.381205	+	0.924490i	$0.624491\pi$
$98$	2.23819e8	+	5.34435e8i	0.245121	+	0.585298i
$99$	7.97504e8	−	7.97504e8i	0.834400	−	0.834400i
$100$	−5.45430e8	−	5.36974e8i	−0.545430	−	0.536974i
$101$	1.08534e8	+	1.08534e8i	0.103782	+	0.103782i	0.757091	−	0.653309i	$-0.226620\pi$
$101$	1.08534e8	+	1.08534e8i	0.103782	+	0.103782i	−0.653309	+	0.757091i	$0.726620\pi$
$102$	1.07304e8	+	4.39564e7i	0.0981552	+	0.0402088i
$103$			5.30049e8i			0.464032i	0.972712	+	0.232016i	$0.0745322\pi$
$103$			5.30049e8i			0.464032i	−0.972712	+	0.232016i	$0.925468\pi$
$104$	−9.31983e8	+	3.98897e8i	−0.781193	+	0.334357i
$105$		−	8.33384e7i		−	0.0669104i
$106$	−1.48677e8	+	3.62942e8i	−0.114385	+	0.279229i
$107$	−1.72739e9	−	1.72739e9i	−1.27398	−	1.27398i	−0.943982	−	0.329998i	$-0.892952\pi$
$107$	−1.72739e9	−	1.72739e9i	−1.27398	−	1.27398i	−0.329998	−	0.943982i	$-0.607048\pi$
$108$	2.34733e8	−	1.83360e6i	0.166023	−	0.00129687i
$109$	1.68795e9	−	1.68795e9i	1.14536	−	1.14536i	0.157904	−	0.987454i	$-0.449526\pi$
$109$	1.68795e9	−	1.68795e9i	1.14536	−	1.14536i	0.987454	−	0.157904i	$-0.0504737\pi$
$110$	−2.23620e9	+	9.36514e8i	−1.45628	+	0.609884i
$111$	5.14463e7			0.0321663
$112$	−1.00656e9	+	1.57263e7i	−0.604448	+	0.00944375i
$113$	−2.54077e9			−1.46593			−0.732965	−	0.680267i	$-0.761864\pi$
$113$	−2.54077e9			−1.46593			−0.732965	+	0.680267i	$0.761864\pi$
$114$	1.34716e8	−	5.64186e7i	0.0747046	−	0.0312861i
$115$	2.71346e9	−	2.71346e9i	1.44671	−	1.44671i
$116$	−1.69939e6	−	2.17552e8i	−0.000871428	−	0.111558i
$117$	1.20944e9	+	1.20944e9i	0.596687	+	0.596687i
$118$	9.65503e8	−	2.35693e9i	0.458442	−	1.11912i
$119$			1.68388e9i			0.769751i
$120$	−2.33392e8	−	9.34856e7i	−0.102747	−	0.0411556i
$121$			9.71418e8i			0.411976i
$122$	3.69461e9	+	1.51348e9i	1.50991	+	0.618525i
$123$	2.72109e8	+	2.72109e8i	0.107194	+	0.107194i
$124$	1.25261e9	−	1.27233e9i	0.475794	−	0.483285i
$125$	−6.01634e8	+	6.01634e8i	−0.220413	+	0.220413i
$126$	6.56096e8	+	1.56662e9i	0.231899	+	0.553728i
$127$	2.38701e8			0.0814212			0.0407106	−	0.999171i	$-0.487038\pi$
$127$	2.38701e8			0.0814212			0.0407106	+	0.999171i	$0.487038\pi$
$128$	−1.08508e9	+	2.83654e9i	−0.357285	+	0.933995i
$129$	−2.77351e8			−0.0881811
$130$	−1.42025e9	−	3.39126e9i	−0.436133	−	1.04140i
$131$	−4.37584e9	+	4.37584e9i	−1.29820	+	1.29820i	−0.368614	+	0.929582i	$0.620168\pi$
$131$	−4.37584e9	+	4.37584e9i	−1.29820	+	1.29820i	−0.929582	+	0.368614i	$0.879832\pi$
$132$	−2.42227e8	+	2.46041e8i	−0.0694448	+	0.0705383i
$133$	1.49971e9	+	1.49971e9i	0.415600	+	0.415600i
$134$	−1.23796e9	−	5.07123e8i	−0.331691	−	0.135876i
$135$			8.51342e8i			0.220598i
$136$	4.71576e9	+	1.88891e9i	1.18203	+	0.473463i
$137$		−	9.62548e8i		−	0.233442i	−0.993165	−	0.116721i	$-0.962762\pi$
$137$		−	9.62548e8i		−	0.233442i	0.993165	−	0.116721i	$-0.0372384\pi$
$138$	2.07164e8	−	5.05716e8i	0.0486249	−	0.118700i
$139$	3.99963e8	+	3.99963e8i	0.0908769	+	0.0908769i	0.751084	−	0.660207i	$-0.229531\pi$
$139$	3.99963e8	+	3.99963e8i	0.0908769	+	0.0908769i	−0.660207	+	0.751084i	$0.729531\pi$
$140$	−2.85184e7	−	3.65087e9i	−0.00627407	−	0.803193i
$141$	8.91700e7	−	8.91700e7i	0.0189991	−	0.0189991i
$142$	−4.98958e9	+	2.08962e9i	−1.02983	+	0.431290i
$143$	−5.04907e9			−1.00972
$144$	5.12335e9	−	8.00460e7i	0.992939	−	0.0155135i
$145$	7.89029e8			0.148230
$146$	1.43519e9	−	6.01053e8i	0.261410	−	0.109478i
$147$	−2.11613e8	+	2.11613e8i	−0.0373778	+	0.0373778i
$148$	2.25375e9	−	1.76049e7i	0.386124	−	0.00301617i
$149$	−5.31070e9	−	5.31070e9i	−0.882701	−	0.882701i	0.111107	−	0.993808i	$-0.464560\pi$
$149$	−5.31070e9	−	5.31070e9i	−0.882701	−	0.882701i	−0.993808	+	0.111107i	$0.964560\pi$
$150$	1.49858e8	−	3.65824e8i	0.0241696	−	0.0590014i
$151$			1.01725e10i			1.59232i	0.605088	+	0.796158i	$0.293138\pi$
$151$			1.01725e10i			1.59232i	−0.605088	+	0.796158i	$0.706862\pi$
$152$	5.88230e9	−	2.51767e9i	0.893822	−	0.382563i
$153$		−	8.57089e9i		−	1.26449i
$154$	−4.63962e9	−	1.90060e9i	−0.664721	−	0.272300i
$155$	4.57880e9	+	4.57880e9i	0.637176	+	0.637176i
$156$	−3.73128e8	−	3.67344e8i	−0.0504426	−	0.0496606i
$157$	6.31237e8	−	6.31237e8i	0.0829170	−	0.0829170i	−0.664432	−	0.747349i	$-0.731326\pi$
$157$	6.31237e8	−	6.31237e8i	0.0829170	−	0.0829170i	0.747349	+	0.664432i	$0.231326\pi$
$158$	−3.95936e9	−	9.45413e9i	−0.505438	−	1.20688i
$159$	−2.02579e8			−0.0251366
$160$	−1.02564e10	−	4.01552e9i	−1.23724	−	0.484398i
$161$	7.93606e9			0.930868
$162$	−3.31600e9	−	7.91792e9i	−0.378266	−	0.903220i
$163$	−1.79948e9	+	1.79948e9i	−0.199665	+	0.199665i	−0.799856	−	0.600191i	$-0.795091\pi$
$163$	−1.79948e9	+	1.79948e9i	−0.199665	+	0.199665i	0.600191	+	0.799856i	$0.295091\pi$
$164$	1.20136e10	+	1.18274e10i	1.29681	+	1.27671i
$165$	−8.85438e8	−	8.85438e8i	−0.0929995	−	0.0929995i
$166$	1.02836e10	+	4.21262e9i	1.05113	+	0.430592i
$167$		−	1.86360e10i		−	1.85408i	−0.374959	−	0.927041i	$-0.622343\pi$
$167$		−	1.86360e10i		−	1.85408i	0.374959	−	0.927041i	$-0.377657\pi$
$168$	−2.04592e8	−	4.78009e8i	−0.0198151	−	0.0462961i
$169$			2.94745e9i			0.277943i
$170$	−6.98397e9	+	1.70488e10i	−0.641331	+	1.56558i
$171$	−7.63346e9	−	7.63346e9i	−0.682714	−	0.682714i
$172$	−1.21501e10	+	9.49094e7i	−1.05853	+	0.00826858i
$173$	5.44187e9	−	5.44187e9i	0.461892	−	0.461892i	−0.437383	−	0.899275i	$-0.644095\pi$
$173$	5.44187e9	−	5.44187e9i	0.461892	−	0.461892i	0.899275	+	0.437383i	$0.144095\pi$
$174$	1.03647e8	−	4.34070e7i	0.00857206	−	0.00358995i
$175$	5.74078e9			0.462700
$176$	−1.05272e10	+	1.08614e10i	−0.827002	+	0.853254i
$177$	1.31554e9			0.100745
$178$	−1.16693e10	+	4.88705e9i	−0.871271	+	0.364885i
$179$	−5.16149e9	+	5.16149e9i	−0.375782	+	0.375782i	−0.869578	−	0.493796i	$-0.835609\pi$
$179$	−5.16149e9	+	5.16149e9i	−0.375782	+	0.375782i	0.493796	+	0.869578i	$0.335609\pi$
$180$	1.45157e8	+	1.85828e10i	0.0103065	+	1.31942i
$181$	4.03566e9	+	4.03566e9i	0.279486	+	0.279486i	0.832904	−	0.553418i	$-0.186677\pi$
$181$	4.03566e9	+	4.03566e9i	0.279486	+	0.279486i	−0.553418	+	0.832904i	$0.686677\pi$
$182$	2.88231e9	−	7.03611e9i	0.194724	−	0.475348i
$183$			2.06218e9i			0.135924i
$184$	8.90234e9	−	2.22252e10i	0.572564	−	1.42944i
$185$			8.17400e9i			0.513053i
$186$	8.53366e8	+	3.49577e8i	0.0522790	+	0.0214158i
$187$	1.78906e10	+	1.78906e10i	1.06989	+	1.06989i
$188$	3.87582e9	−	3.93685e9i	0.226284	−	0.229847i
$189$	−1.24496e9	+	1.24496e9i	−0.0709705	+	0.0709705i
$190$	8.96402e9	+	2.14042e10i	0.499013	+	1.19154i
$191$	2.06898e10			1.12488			0.562441	−	0.826838i	$-0.309862\pi$
$191$	2.06898e10			1.12488			0.562441	+	0.826838i	$0.309862\pi$
$192$	−1.56818e9	+	3.67551e7i	−0.0832801	+	0.00195192i
$193$	1.19176e10			0.618276			0.309138	−	0.951017i	$-0.399960\pi$
$193$	1.19176e10			0.618276			0.309138	+	0.951017i	$0.399960\pi$
$194$	−5.81043e9	−	1.38741e10i	−0.294511	−	0.703230i
$195$	1.34279e9	−	1.34279e9i	0.0665047	−	0.0665047i
$196$	−9.19786e9	+	9.34269e9i	−0.445179	+	0.452188i
$197$	−2.11946e10	−	2.11946e10i	−1.00260	−	1.00260i	−0.999997	−	0.00260455i	$-0.999171\pi$
$197$	−2.11946e10	−	2.11946e10i	−1.00260	−	1.00260i	−0.00260455	−	0.999997i	$-0.500829\pi$
$198$	2.36155e10	+	9.67397e9i	1.09195	+	0.447313i
$199$		−	2.99119e10i		−	1.35209i	−0.736862	−	0.676044i	$-0.763693\pi$
$199$		−	2.99119e10i		−	1.35209i	0.736862	−	0.676044i	$-0.236307\pi$
$200$	6.43976e9	−	1.60772e10i	0.284600	−	0.710519i
$201$		−	6.90975e8i		−	0.0298593i
$202$	−1.31656e9	+	3.21389e9i	−0.0556363	+	0.135816i
$203$	1.15384e9	+	1.15384e9i	0.0476884	+	0.0476884i
$204$	2.04951e7	+	2.62374e9i	0.000828543	+	0.106068i
$205$	−4.32338e10	+	4.32338e10i	−1.70974	+	1.70974i
$206$	−1.10627e10	+	4.63301e9i	−0.428013	+	0.179250i
$207$	−4.03942e10			−1.52916
$208$	−1.64716e10	−	1.59648e10i	−0.610169	−	0.591396i
$209$	3.18677e10			1.15529
$210$	1.73936e9	−	7.28438e8i	0.0617167	−	0.0258467i
$211$	1.77839e9	−	1.77839e9i	0.0617669	−	0.0617669i	−0.675549	−	0.737315i	$-0.736093\pi$
$211$	1.77839e9	−	1.77839e9i	0.0617669	−	0.0617669i	0.737315	+	0.675549i	$0.236093\pi$
$212$	−8.87452e9	+	6.93225e7i	−0.301740	+	0.00235702i
$213$	−1.97565e9	−	1.97565e9i	−0.0657662	−	0.0657662i
$214$	2.09537e10	−	5.11509e10i	0.682966	−	1.66721i
$215$		−	4.40666e10i		−	1.40649i
$216$	2.09001e9	+	4.88310e9i	0.0653289	+	0.152635i
$217$			1.33916e10i			0.409982i
$218$	4.99833e10	+	2.04754e10i	1.49889	+	0.614014i
$219$	5.68273e8	+	5.68273e8i	0.0166939	+	0.0166939i
$220$	−3.90920e10	−	3.84860e10i	−1.12509	−	1.10765i
$221$	−2.71315e10	+	2.71315e10i	−0.765084	+	0.765084i
$222$	4.49678e8	+	1.07374e9i	0.0124255	+	0.0296695i
$223$	−3.83210e9			−0.103768			−0.0518842	−	0.998653i	$-0.516523\pi$
$223$	−3.83210e9			−0.103768			−0.0518842	+	0.998653i	$0.516523\pi$
$224$	−9.12628e9	−	2.08705e10i	−0.242202	−	0.553881i
$225$	−2.92203e10			−0.760087
$226$	−2.22082e10	−	5.30286e10i	−0.566272	−	1.35214i
$227$	−1.77347e10	+	1.77347e10i	−0.443310	+	0.443310i	−0.893123	−	0.449813i	$-0.851491\pi$
$227$	−1.77347e10	+	1.77347e10i	−0.443310	+	0.443310i	0.449813	+	0.893123i	$0.351491\pi$
$228$	2.35503e9	+	2.31852e9i	0.0577151	+	0.0568205i
$229$	2.70249e10	+	2.70249e10i	0.649389	+	0.649389i	0.952845	−	0.303456i	$-0.0981406\pi$
$229$	2.70249e10	+	2.70249e10i	0.649389	+	0.649389i	−0.303456	+	0.952845i	$0.598141\pi$
$230$	8.03503e10	+	3.29151e10i	1.89327	+	0.775568i
$231$		−	2.58964e9i		−	0.0598392i
$232$	4.52568e9	−	1.93703e9i	0.102562	−	0.0438976i
$233$			1.82890e10i			0.406527i	0.979124	+	0.203264i	$0.0651548\pi$
$233$			1.82890e10i			0.406527i	−0.979124	+	0.203264i	$0.934845\pi$
$234$	−1.46708e10	+	3.58135e10i	−0.319877	+	0.780864i
$235$	1.41677e10	+	1.41677e10i	0.303036	+	0.303036i
$236$	5.76307e10	−	4.50176e8i	1.20934	−	0.00944667i
$237$	3.74342e9	−	3.74342e9i	0.0770728	−	0.0770728i
$238$	−3.51444e10	+	1.47183e10i	−0.710002	+	0.297346i
$239$	5.82893e10			1.15558			0.577788	−	0.816187i	$-0.303916\pi$
$239$	5.82893e10			1.15558			0.577788	+	0.816187i	$0.303916\pi$
$240$	−8.88720e7	−	5.68826e9i	−0.00172908	−	0.110670i
$241$	1.77620e10			0.339168			0.169584	−	0.985516i	$-0.445758\pi$
$241$	1.77620e10			0.339168			0.169584	+	0.985516i	$0.445758\pi$
$242$	−2.02745e10	+	8.49089e9i	−0.379998	+	0.159142i
$243$	9.51623e9	−	9.51623e9i	0.175080	−	0.175080i
$244$	7.05677e8	+	9.03393e10i	0.0127453	+	1.63163i
$245$	−3.36219e10	−	3.36219e10i	−0.596176	−	0.596176i
$246$	−3.30077e9	+	8.05763e9i	−0.0574655	+	0.140281i
$247$			4.83282e10i			0.826160i
$248$	3.75037e10	+	1.50222e10i	0.629566	+	0.252174i
$249$			5.73986e9i			0.0946247i
$250$	−1.78154e10	−	7.29800e9i	−0.288447	−	0.118161i
$251$	−2.71646e10	−	2.71646e10i	−0.431988	−	0.431988i	0.457316	−	0.889304i	$-0.348811\pi$
$251$	−2.71646e10	−	2.71646e10i	−0.431988	−	0.431988i	−0.889304	+	0.457316i	$0.848811\pi$
$252$	−2.69622e10	+	2.73868e10i	−0.421166	+	0.427798i
$253$	8.43175e10	−	8.43175e10i	1.29382	−	1.29382i
$254$	2.08642e9	+	4.98193e9i	0.0314521	+	0.0751011i
$255$	−9.51593e9			−0.140936
$256$	−6.86859e10	+	2.14679e9i	−0.999512	+	0.0312399i
$257$	−3.49312e10			−0.499475			−0.249738	−	0.968314i	$-0.580344\pi$
$257$	−3.49312e10			−0.499475			−0.249738	+	0.968314i	$0.580344\pi$
$258$	−2.42424e9	−	5.78859e9i	−0.0340634	−	0.0813363i
$259$	−1.19533e10	+	1.19533e10i	−0.165058	+	0.165058i
$260$	5.83651e10	−	5.92841e10i	0.792087	−	0.804559i
$261$	−5.87298e9	−	5.87298e9i	−0.0783387	−	0.0783387i
$262$	−1.29576e11	−	5.30803e10i	−1.69891	−	0.695949i
$263$			7.94121e10i			1.02350i	0.859136	+	0.511748i	$0.171002\pi$
$263$			7.94121e10i			1.02350i	−0.859136	+	0.511748i	$0.828998\pi$
$264$	−7.25237e9	−	2.90495e9i	−0.0918888	−	0.0368062i
$265$		−	3.21866e10i		−	0.400930i
$266$	−1.81920e10	+	4.44091e10i	−0.222798	+	0.543881i
$267$	−4.62051e9	−	4.62051e9i	−0.0556403	−	0.0556403i
$268$	−2.36451e8	−	3.02700e10i	−0.00279985	−	0.358432i
$269$	4.53335e10	−	4.53335e10i	0.527879	−	0.527879i	−0.392061	−	0.919939i	$-0.628238\pi$
$269$	4.53335e10	−	4.53335e10i	0.527879	−	0.527879i	0.919939	+	0.392061i	$0.128238\pi$
$270$	−1.77684e10	+	7.44134e9i	−0.203475	+	0.0852147i
$271$	1.12684e10			0.126911			0.0634557	−	0.997985i	$-0.479788\pi$
$271$	1.12684e10			0.126911			0.0634557	+	0.997985i	$0.479788\pi$
$272$	1.79569e9	+	1.14933e11i	0.0198917	+	1.27317i
$273$	3.92726e9			0.0427915
$274$	2.00894e10	−	8.41336e9i	0.215322	−	0.0901762i
$275$	6.09935e10	−	6.09935e10i	0.643112	−	0.643112i
$276$	1.23656e10	−	9.65926e7i	0.128270	−	0.00100197i
$277$	6.68057e10	+	6.68057e10i	0.681796	+	0.681796i	0.960405	−	0.278609i	$-0.0898733\pi$
$277$	6.68057e10	+	6.68057e10i	0.681796	+	0.681796i	−0.278609	+	0.960405i	$0.589873\pi$
$278$	−4.85168e9	+	1.18436e10i	−0.0487181	+	0.118928i
$279$		−	6.81628e10i		−	0.673486i
$280$	7.59481e10	−	3.25064e10i	0.738424	−	0.316052i
$281$		−	1.83235e11i		−	1.75319i	−0.481227	−	0.876596i	$-0.659809\pi$
$281$		−	1.83235e11i		−	1.75319i	0.481227	−	0.876596i	$-0.340191\pi$
$282$	2.64048e9	+	1.08166e9i	0.0248635	+	0.0101852i
$283$	−6.18515e10	−	6.18515e10i	−0.573207	−	0.573207i	0.359816	−	0.933023i	$-0.382839\pi$
$283$	−6.18515e10	−	6.18515e10i	−0.573207	−	0.573207i	−0.933023	+	0.359816i	$0.882839\pi$
$284$	−8.72249e10	−	8.58728e10i	−0.795625	−	0.783291i
$285$	−8.47514e9	+	8.47514e9i	−0.0760931	+	0.0760931i
$286$	−4.41325e10	−	1.05379e11i	−0.390042	−	0.931340i
$287$	−1.26446e11			−1.10011
$288$	4.64524e10	+	1.06230e11i	0.397871	+	0.909873i
$289$	7.36849e10			0.621352
$290$	6.89668e9	+	1.64679e10i	0.0572597	+	0.136724i
$291$	5.49354e9	−	5.49354e9i	0.0449091	−	0.0449091i
$292$	2.50892e10	+	2.47003e10i	0.201959	+	0.198829i
$293$	2.16042e9	+	2.16042e9i	0.0171251	+	0.0171251i	0.715618	−	0.698492i	$-0.246145\pi$
$293$	2.16042e9	+	2.16042e9i	0.0171251	+	0.0171251i	−0.698492	+	0.715618i	$0.746145\pi$
$294$	−6.26622e9	−	2.56693e9i	−0.0489151	−	0.0200378i
$295$			2.09018e11i			1.60688i
$296$	2.00668e10	+	4.68841e10i	0.151938	+	0.354987i
$297$			2.64544e10i			0.197285i
$298$	6.44205e10	−	1.57259e11i	0.473206	−	1.15516i
$299$	1.27870e11	+	1.27870e11i	0.925225	+	0.925225i
$300$	8.94500e9	−	6.98730e7i	0.0637580	−	0.000498040i
$301$	6.44408e10	−	6.44408e10i	0.452493	−	0.452493i
$302$	−2.12310e11	+	8.89146e10i	−1.46872	+	0.615094i
$303$	−1.79386e9			−0.0122263
$304$	1.03962e11	+	1.00763e11i	0.698141	+	0.676661i
$305$	−3.27647e11			−2.16799
$306$	1.78883e11	−	7.49157e10i	1.16634	−	0.488457i
$307$	−1.32910e11	+	1.32910e11i	−0.853955	+	0.853955i	−0.990618	−	0.136663i	$-0.956362\pi$
$307$	−1.32910e11	+	1.32910e11i	−0.853955	+	0.853955i	0.136663	+	0.990618i	$0.456362\pi$
$308$	−8.86175e8	−	1.13446e11i	−0.00561101	−	0.718310i
$309$	−4.38033e9	−	4.38033e9i	−0.0273334	−	0.0273334i
$310$	−5.55423e10	+	1.35586e11i	−0.341583	+	0.833850i
$311$			1.82864e11i			1.10842i	0.832376	+	0.554212i	$0.186980\pi$
$311$			1.82864e11i			1.10842i	−0.832376	+	0.554212i	$0.813020\pi$
$312$	4.40544e9	−	1.09984e10i	0.0263204	−	0.0657104i
$313$			1.89355e11i			1.11513i	0.830133	+	0.557566i	$0.188265\pi$
$313$			1.89355e11i			1.11513i	−0.830133	+	0.557566i	$0.811735\pi$
$314$	1.86920e10	+	7.65710e9i	0.108511	+	0.0444509i
$315$	−9.85579e10	−	9.85579e10i	−0.564019	−	0.564019i
$316$	1.62710e11	−	1.65272e11i	0.917956	−	0.932410i
$317$	−3.98041e10	+	3.98041e10i	−0.221392	+	0.221392i	−0.809084	−	0.587693i	$-0.800036\pi$
$317$	−3.98041e10	+	3.98041e10i	−0.221392	+	0.221392i	0.587693	+	0.809084i	$0.300036\pi$
$318$	−1.77069e9	−	4.22803e9i	−0.00971000	−	0.0231855i
$319$	2.45181e10			0.132565
$320$	−5.83980e9	−	2.49159e11i	−0.0311332	−	1.32832i
$321$	2.85503e10			0.150085
$322$	6.93668e10	+	1.65634e11i	0.359584	+	0.858612i
$323$	1.71243e11	−	1.71243e11i	0.875391	−	0.875391i
$324$	1.36271e11	−	1.38417e11i	0.686990	−	0.697808i
$325$	9.24982e10	+	9.24982e10i	0.459895	+	0.459895i
$326$	−5.32857e10	−	2.18282e10i	−0.261295	−	0.107038i
$327$			2.78986e10i			0.134933i
$328$	−1.41842e11	+	3.54116e11i	−0.676662	+	1.68932i
$329$			4.14363e10i			0.194984i
$330$	1.07406e10	−	2.62194e10i	0.0498560	−	0.121705i
$331$	−1.32177e11	−	1.32177e11i	−0.605242	−	0.605242i	0.336457	−	0.941699i	$-0.390771\pi$
$331$	−1.32177e11	−	1.32177e11i	−0.605242	−	0.605242i	−0.941699	+	0.336457i	$0.890771\pi$
$332$	1.96418e9	+	2.51450e11i	0.00887278	+	1.13588i
$333$	6.08416e10	−	6.08416e10i	0.271145	−	0.271145i
$334$	3.88953e11	−	1.62892e11i	1.71017	−	0.716212i
$335$	1.09785e11			0.476256
$336$	8.18827e9	−	8.44819e9i	0.0350482	−	0.0361607i
$337$	−1.58205e11			−0.668170			−0.334085	−	0.942543i	$-0.608427\pi$
$337$	−1.58205e11			−0.668170			−0.334085	+	0.942543i	$0.608427\pi$
$338$	−6.15163e10	+	2.57628e10i	−0.256369	+	0.107366i
$339$	2.09970e10	−	2.09970e10i	0.0863492	−	0.0863492i
$340$	−4.16871e11	+	3.25635e9i	−1.69179	+	0.0132153i
$341$	1.42281e11	+	1.42281e11i	0.569838	+	0.569838i
$342$	9.25963e10	−	2.26040e11i	0.365996	−	0.893446i
$343$		−	2.53300e11i		−	0.988123i
$344$	−1.08181e11	−	2.52756e11i	−0.416524	−	0.973168i
$345$			4.48481e10i			0.170435i
$346$	1.61143e11	+	6.60116e10i	0.604463	+	0.247615i
$347$	−1.68202e11	−	1.68202e11i	−0.622800	−	0.622800i	0.323446	−	0.946247i	$-0.395159\pi$
$347$	−1.68202e11	−	1.68202e11i	−0.622800	−	0.622800i	−0.946247	+	0.323446i	$0.895159\pi$
$348$	1.81190e9	+	1.78381e9i	0.00662258	+	0.00651992i
$349$	−4.25447e10	+	4.25447e10i	−0.153508	+	0.153508i	−0.779683	−	0.626175i	$-0.784620\pi$
$349$	−4.25447e10	+	4.25447e10i	−0.153508	+	0.153508i	0.626175	+	0.779683i	$0.284620\pi$
$350$	5.01785e10	+	1.19816e11i	0.178736	+	0.426784i
$351$	−4.01189e10			−0.141080
$352$	−3.18704e11	−	1.24778e11i	−1.10648	−	0.433206i
$353$	−3.23705e11			−1.10959			−0.554795	−	0.831987i	$-0.687203\pi$
$353$	−3.23705e11			−1.10959			−0.554795	+	0.831987i	$0.687203\pi$
$354$	1.14987e10	+	2.74566e10i	0.0389166	+	0.0929249i
$355$	3.13900e11	−	3.13900e11i	1.04897	−	1.04897i
$356$	−2.03995e11	−	2.00833e11i	−0.673124	−	0.662690i
$357$	−1.39156e10	−	1.39156e10i	−0.0453415	−	0.0453415i
$358$	−1.52841e11	−	6.26104e10i	−0.491773	−	0.201453i
$359$		−	3.68764e10i		−	0.117172i	−0.998282	−	0.0585860i	$-0.981341\pi$
$359$		−	3.68764e10i		−	0.117172i	0.998282	−	0.0585860i	$-0.0186592\pi$
$360$	−3.86572e11	+	1.65456e11i	−1.21302	+	0.519185i
$361$			1.76602e10i			0.0547284i
$362$	−4.89538e10	+	1.19503e11i	−0.149830	+	0.365755i
$363$	−8.02781e9	−	8.02781e9i	−0.0242671	−	0.0242671i
$364$	1.72044e11	−	1.34391e9i	0.513670	−	0.00401248i
$365$	−9.02895e10	+	9.02895e10i	−0.266268	+	0.266268i
$366$	−4.30398e10	+	1.80249e10i	−0.125373	+	0.0525059i
$367$	3.03452e11			0.873158			0.436579	−	0.899666i	$-0.356190\pi$
$367$	3.03452e11			0.873158			0.436579	+	0.899666i	$0.356190\pi$
$368$	5.41675e11	−	8.46300e9i	1.53966	−	0.0240552i
$369$	6.43605e11			1.80718
$370$	−1.70600e11	+	7.14466e10i	−0.473228	+	0.198186i
$371$	4.70680e10	−	4.70680e10i	0.128986	−	0.128986i
$372$	1.62994e8	+	2.08662e10i	0.000441295	+	0.0564937i
$373$	−2.87485e11	−	2.87485e11i	−0.769000	−	0.769000i	0.208931	−	0.977930i	$-0.433002\pi$
$373$	−2.87485e11	−	2.87485e11i	−0.769000	−	0.769000i	−0.977930	+	0.208931i	$0.933002\pi$
$374$	−2.17018e11	+	5.29772e11i	−0.573554	+	1.40012i
$375$		−	9.94382e9i		−	0.0259664i
$376$	1.16044e11	+	4.64815e10i	0.299417	+	0.119932i
$377$			3.71824e10i			0.0947985i
$378$	−3.68655e10	−	1.51018e10i	−0.0928767	−	0.0380465i
$379$	2.04877e11	+	2.04877e11i	0.510054	+	0.510054i	0.914543	−	0.404489i	$-0.132551\pi$
$379$	2.04877e11	+	2.04877e11i	0.510054	+	0.510054i	−0.404489	+	0.914543i	$0.632551\pi$
$380$	−3.68376e11	+	3.74177e11i	−0.906287	+	0.920557i
$381$	−1.97263e9	+	1.97263e9i	−0.00479604	+	0.00479604i
$382$	1.80844e11	+	4.31818e11i	0.434529	+	1.03757i
$383$	−6.09105e10			−0.144643			−0.0723215	−	0.997381i	$-0.523041\pi$
$383$	−6.09105e10			−0.144643			−0.0723215	+	0.997381i	$0.523041\pi$
$384$	−1.44742e10	−	3.24083e10i	−0.0339706	−	0.0760617i
$385$	4.11453e11			0.954436
$386$	1.04169e11	+	2.48733e11i	0.238833	+	0.570284i
$387$	−3.28001e11	+	3.28001e11i	−0.743320	+	0.743320i
$388$	2.38780e11	−	2.42540e11i	0.534878	−	0.543300i
$389$	−9.36986e10	−	9.36986e10i	−0.207472	−	0.207472i	0.595720	−	0.803192i	$-0.296867\pi$
$389$	−9.36986e10	−	9.36986e10i	−0.207472	−	0.207472i	−0.803192	+	0.595720i	$0.796867\pi$
$390$	3.97624e10	+	1.62885e10i	0.0870325	+	0.0356524i
$391$		−	9.06172e11i		−	1.96072i
$392$	−2.75387e11	−	1.10307e11i	−0.589056	−	0.235948i
$393$		−	7.23240e10i		−	0.152938i
$394$	2.57098e11	−	6.27611e11i	0.537483	−	1.31207i
$395$	5.94770e11	+	5.94770e11i	1.22931	+	1.22931i
$396$	4.51059e9	+	5.77437e11i	0.00921733	+	1.17998i
$397$	−2.80144e11	+	2.80144e11i	−0.566010	+	0.566010i	−0.931008	−	0.364998i	$-0.881070\pi$
$397$	−2.80144e11	+	2.80144e11i	−0.566010	+	0.566010i	0.364998	+	0.931008i	$0.381070\pi$
$398$	6.24292e11	−	2.61451e11i	1.24714	−	0.522296i
$399$	−2.47873e10			−0.0489610
$400$	3.91836e11	−	6.12196e9i	0.765305	−	0.0119569i
$401$	−1.10199e11			−0.212828			−0.106414	−	0.994322i	$-0.533937\pi$
$401$	−1.10199e11			−0.212828			−0.106414	+	0.994322i	$0.533937\pi$
$402$	1.44214e10	−	6.03962e9i	0.0275416	−	0.0115343i
$403$	−2.15772e11	+	2.15772e11i	−0.407496	+	0.407496i
$404$	−7.85849e10	+	6.13859e8i	−0.146765	+	0.00114644i
$405$	4.98125e11	+	4.98125e11i	0.920007	+	0.920007i
$406$	−1.39964e10	+	3.41671e10i	−0.0255652	+	0.0624082i
$407$			2.53997e11i			0.458832i
$408$	−5.45811e10	+	2.33612e10i	−0.0975150	+	0.0417373i
$409$		−	1.58401e10i		−	0.0279900i	−0.999902	−	0.0139950i	$-0.995545\pi$
$409$		−	1.58401e10i		−	0.0279900i	0.999902	−	0.0139950i	$-0.00445490\pi$
$410$	−1.28023e12	−	5.24439e11i	−2.23748	−	0.916575i
$411$	7.95451e9	+	7.95451e9i	0.0137507	+	0.0137507i
$412$	−1.93391e11	−	1.90393e11i	−0.330673	−	0.325547i
$413$	−3.05657e11	+	3.05657e11i	−0.516963	+	0.516963i
$414$	−3.53074e11	−	8.43068e11i	−0.590697	−	1.41046i
$415$	−9.11973e11			−1.50926
$416$	1.89228e11	−	4.83323e11i	0.309789	−	0.791257i
$417$	−6.61060e9			−0.0107060
$418$	2.78546e11	+	6.65111e11i	0.446277	+	1.06562i
$419$	−4.32067e11	+	4.32067e11i	−0.684838	+	0.684838i	−0.961086	−	0.276248i	$-0.910909\pi$
$419$	−4.32067e11	+	4.32067e11i	−0.684838	+	0.684838i	0.276248	+	0.961086i	$0.410909\pi$
$420$	3.04065e10	+	2.99351e10i	0.0476809	+	0.0469418i
$421$	−6.16787e11	−	6.16787e11i	−0.956898	−	0.956898i	0.0422110	−	0.999109i	$-0.486560\pi$
$421$	−6.16787e11	−	6.16787e11i	−0.956898	−	0.956898i	−0.999109	+	0.0422110i	$0.986560\pi$
$422$	5.26612e10	+	2.15724e10i	0.0808323	+	0.0331126i
$423$		−	2.10909e11i		−	0.320305i
$424$	−7.90165e10	−	1.84614e11i	−0.118733	−	0.277408i
$425$		−	6.55506e11i		−	0.974600i
$426$	2.39653e10	−	5.85025e10i	0.0352565	−	0.0860660i
$427$	−4.79135e11	−	4.79135e11i	−0.697481	−	0.697481i
$428$	1.25072e12	−	9.76990e9i	1.80162	−	0.0140732i
$429$	4.17256e10	−	4.17256e10i	0.0594764	−	0.0594764i
$430$	9.19715e11	−	3.85174e11i	1.29731	−	0.543311i
$431$	4.84710e11			0.676603			0.338301	−	0.941038i	$-0.390148\pi$
$431$	4.84710e11			0.676603			0.338301	+	0.941038i	$0.390148\pi$
$432$	−8.36471e10	+	8.63023e10i	−0.115551	+	0.119219i
$433$	5.47297e11			0.748217			0.374109	−	0.927385i	$-0.377949\pi$
$433$	5.47297e11			0.748217			0.374109	+	0.927385i	$0.377949\pi$
$434$	−2.79497e11	+	1.17052e11i	−0.378158	+	0.158371i
$435$	−6.52055e9	+	6.52055e9i	−0.00873137	+	0.00873137i
$436$	9.54688e9	+	1.22217e12i	0.0126524	+	1.61973i
$437$	−8.07061e11	−	8.07061e11i	−1.05862	−	1.05862i
$438$	−6.89333e9	+	1.68276e10i	−0.00894943	+	0.0218468i
$439$			4.68387e11i			0.601886i	0.953642	+	0.300943i	$0.0973013\pi$
$439$			4.68387e11i			0.601886i	−0.953642	+	0.300943i	$0.902699\pi$
$440$	4.61551e11	−	1.15229e12i	0.587060	−	1.46563i
$441$			5.00516e11i			0.630150i
$442$	−8.03413e11	−	3.29114e11i	−1.00124	−	0.410153i
$443$	6.80072e11	+	6.80072e11i	0.838954	+	0.838954i	0.988721	−	0.149767i	$-0.0478524\pi$
$443$	6.80072e11	+	6.80072e11i	0.838954	+	0.838954i	−0.149767	+	0.988721i	$0.547852\pi$
$444$	−1.84795e10	+	1.87705e10i	−0.0225666	+	0.0229220i
$445$	7.34126e11	−	7.34126e11i	0.887464	−	0.887464i
$446$	−3.34953e10	−	7.99799e10i	−0.0400846	−	0.0957137i
$447$	8.77754e10			0.103989
$448$	3.55818e11	−	3.72898e11i	0.417328	−	0.437360i
$449$	6.82844e11			0.792890			0.396445	−	0.918059i	$-0.370244\pi$
$449$	6.82844e11			0.792890			0.396445	+	0.918059i	$0.370244\pi$
$450$	−2.55406e11	−	6.09858e11i	−0.293613	−	0.701088i
$451$	−1.34344e12	+	1.34344e12i	−1.52906	+	1.52906i
$452$	9.12645e11	−	9.27016e11i	1.02844	−	1.04463i
$453$	−8.40653e10	−	8.40653e10i	−0.0937940	−	0.0937940i
$454$	−5.25155e11	−	2.15127e11i	−0.580145	−	0.237653i
$455$			6.23979e11i			0.682525i
$456$	−2.78053e10	+	6.94175e10i	−0.0301152	+	0.0751843i
$457$			5.28969e11i			0.567293i	0.958929	+	0.283646i	$0.0915442\pi$
$457$			5.28969e11i			0.567293i	−0.958929	+	0.283646i	$0.908456\pi$
$458$	−3.27821e11	+	8.00256e11i	−0.348130	+	0.849834i
$459$	1.42155e11	+	1.42155e11i	0.149487	+	0.149487i
$460$	1.53470e10	+	1.96469e12i	0.0159814	+	2.04590i
$461$	−1.30782e11	+	1.30782e11i	−0.134863	+	0.134863i	−0.771316	−	0.636453i	$-0.780401\pi$
$461$	−1.30782e11	+	1.30782e11i	−0.134863	+	0.134863i	0.636453	+	0.771316i	$0.280401\pi$
$462$	5.40485e10	−	2.26353e10i	0.0551944	−	0.0231152i
$463$	−4.99288e11			−0.504936			−0.252468	−	0.967605i	$-0.581242\pi$
$463$	−4.99288e11			−0.504936			−0.252468	+	0.967605i	$0.581242\pi$
$464$	7.99855e10	+	7.75246e10i	0.0801089	+	0.0776442i
$465$	−7.56785e10			−0.0750645
$466$	−3.81711e11	+	1.59859e11i	−0.374972	+	0.157037i
$467$	9.26317e11	−	9.26317e11i	0.901226	−	0.901226i	−0.0943161	−	0.995542i	$-0.530066\pi$
$467$	9.26317e11	−	9.26317e11i	0.901226	−	0.901226i	0.995542	+	0.0943161i	$0.0300664\pi$
$468$	−8.75698e11	+	6.84043e9i	−0.843817	+	0.00659139i
$469$	1.60544e11	+	1.60544e11i	0.153220	+	0.153220i
$470$	−1.71859e11	+	4.19530e11i	−0.162454	+	0.396573i
$471$			1.04331e10i			0.00976830i
$472$	5.13129e11	+	1.19888e12i	0.475869	+	1.11182i
$473$		−	1.36932e12i		−	1.25785i
$474$	1.10849e11	+	4.54089e10i	0.100863	+	0.0413179i
$475$	−5.83811e11	−	5.83811e11i	−0.526200	−	0.526200i
$476$	−6.14374e11	−	6.04850e11i	−0.548531	−	0.540028i
$477$	−2.39574e11	+	2.39574e11i	−0.211889	+	0.211889i
$478$	5.09490e11	+	1.21656e12i	0.446386	+	1.06588i
$479$	2.03414e12			1.76551			0.882756	−	0.469831i	$-0.155685\pi$
$479$	2.03414e12			1.76551			0.882756	+	0.469831i	$0.155685\pi$
$480$	1.17943e11	−	5.15743e10i	0.101411	−	0.0443453i
$481$	−3.85194e11			−0.328115
$482$	1.55253e11	+	3.70711e11i	0.131017	+	0.312841i
$483$	−6.55837e10	+	6.55837e10i	−0.0548320	+	0.0548320i
$484$	−3.54427e11	−	3.48933e11i	−0.293578	−	0.289027i
$485$	8.72837e11	+	8.72837e11i	0.716300	+	0.716300i
$486$	2.81792e11	+	1.15435e11i	0.229121	+	0.0938585i
$487$		−	1.98422e12i		−	1.59849i	−0.601007	−	0.799244i	$-0.705234\pi$
$487$		−	1.98422e12i		−	1.59849i	0.601007	−	0.799244i	$-0.294766\pi$
$488$	−1.87931e12	+	8.04358e11i	−1.50006	+	0.642038i
$489$		−	2.97418e10i		−	0.0235222i
$490$	4.07844e11	−	9.95603e11i	0.319604	−	0.780196i
$491$	1.04778e12	+	1.04778e12i	0.813583	+	0.813583i	0.985169	−	0.171586i	$-0.0548891\pi$
$491$	1.04778e12	+	1.04778e12i	0.813583	+	0.813583i	−0.171586	+	0.985169i	$0.554889\pi$
$492$	−1.97022e11	+	1.53902e9i	−0.151590	+	0.00118413i
$493$	1.31750e11	−	1.31750e11i	0.100448	−	0.100448i
$494$	−1.00866e12	+	4.22423e11i	−0.762031	+	0.319136i
$495$	−2.09428e12			−1.56787
$496$	1.42808e10	+	9.14044e11i	0.0105946	+	0.678109i
$497$	9.18063e11			0.674946
$498$	−1.19797e11	+	5.01705e10i	−0.0872797	+	0.0365525i
$499$	8.52448e11	−	8.52448e11i	0.615482	−	0.615482i	−0.328887	−	0.944369i	$-0.606674\pi$
$499$	8.52448e11	−	8.52448e11i	0.615482	−	0.615482i	0.944369	+	0.328887i	$0.106674\pi$
$500$	−3.40277e9	−	4.35616e11i	−0.00243483	−	0.311701i
$501$	1.54008e11	+	1.54008e11i	0.109213	+	0.109213i
$502$	3.29515e11	−	8.04392e11i	0.231584	−	0.565329i
$503$		−	1.05588e12i		−	0.735461i	−0.929932	−	0.367730i	$-0.880135\pi$
$503$		−	1.05588e12i		−	0.735461i	0.929932	−	0.367730i	$-0.119865\pi$
$504$	−8.07260e11	−	3.23350e11i	−0.557283	−	0.223221i
$505$		−	2.85016e11i		−	0.195010i
$506$	2.49679e12	+	1.02280e12i	1.69318	+	0.693605i
$507$	−2.43578e10	−	2.43578e10i	−0.0163720	−	0.0163720i
$508$	−8.57413e10	+	8.70914e10i	−0.0571220	+	0.0580214i
$509$	−6.93104e11	+	6.93104e11i	−0.457687	+	0.457687i	−0.897896	−	0.440208i	$-0.854905\pi$
$509$	−6.93104e11	+	6.93104e11i	−0.457687	+	0.457687i	0.440208	+	0.897896i	$0.354905\pi$
$510$	−8.31761e10	−	1.98607e11i	−0.0544418	−	0.129996i
$511$	−2.64070e11			−0.171327
$512$	−6.45170e11	−	1.41478e12i	−0.414915	−	0.909860i
$513$	2.53214e11			0.161421
$514$	−3.05324e11	−	7.29050e11i	−0.192942	−	0.460705i
$515$	6.95965e11	−	6.95965e11i	0.435968	−	0.435968i
$516$	9.96243e10	−	1.01193e11i	0.0618645	−	0.0628386i
$517$	4.40244e11	+	4.40244e11i	0.271011	+	0.271011i
$518$	−3.53957e11	−	1.44997e11i	−0.216006	−	0.0884859i
$519$			8.99434e10i			0.0544147i
$520$	1.74747e12	+	6.99954e11i	1.04808	+	0.419811i
$521$			1.54199e12i			0.916876i	0.888726	+	0.458438i	$0.151591\pi$
$521$			1.54199e12i			0.916876i	−0.888726	+	0.458438i	$0.848409\pi$
$522$	7.12411e10	−	1.73909e11i	0.0419965	−	0.102519i
$523$	−1.67885e12	−	1.67885e12i	−0.981193	−	0.981193i	0.0186337	−	0.999826i	$-0.494068\pi$
$523$	−1.67885e12	−	1.67885e12i	−0.981193	−	0.981193i	−0.999826	+	0.0186337i	$0.994068\pi$
$524$	−2.47493e10	−	3.16835e12i	−0.0143407	−	1.83587i
$525$	−4.74419e10	+	4.74419e10i	−0.0272549	+	0.0272549i
$526$	−1.65741e12	+	6.94119e11i	−0.944049	+	0.395365i
$527$	1.52911e12			0.863558
$528$	−2.76159e9	−	1.76756e11i	−0.00154635	−	0.0989740i
$529$	−2.46959e12			−1.37112
$530$	6.71767e11	−	2.81334e11i	0.369809	−	0.154875i
$531$	1.55578e12	−	1.55578e12i	0.849227	−	0.849227i
$532$	−1.08587e12	+	8.48220e9i	−0.587729	+	0.00459099i
$533$	−2.03736e12	−	2.03736e12i	−1.09344	−	1.09344i
$534$	5.60483e10	−	1.36822e11i	0.0298282	−	0.0728146i
$535$			4.53619e12i			2.39386i
$536$	6.29700e11	−	2.69517e11i	0.329528	−	0.141041i
$537$		−	8.53092e10i		−	0.0442702i
$538$	1.34240e12	+	5.49909e11i	0.690817	+	0.282990i
$539$	−1.04476e12	−	1.04476e12i	−0.533172	−	0.533172i
$540$	−3.10617e11	−	3.05802e11i	−0.157200	−	0.154763i
$541$	3.71704e11	−	3.71704e11i	0.186556	−	0.186556i	−0.607649	−	0.794205i	$-0.707887\pi$
$541$	3.71704e11	−	3.71704e11i	0.186556	−	0.186556i	0.794205	+	0.607649i	$0.207887\pi$
$542$	9.84940e10	+	2.35183e11i	0.0490245	+	0.117060i
$543$	−6.67015e10			−0.0329258
$544$	−2.38308e12	+	1.04208e12i	−1.16666	+	0.510158i
$545$	−4.43264e12			−2.15218
$546$	3.43271e10	+	8.19660e10i	0.0165299	+	0.0394700i
$547$	−6.36269e11	+	6.36269e11i	−0.303877	+	0.303877i	−0.842529	−	0.538652i	$-0.818934\pi$
$547$	−6.36269e11	+	6.36269e11i	−0.303877	+	0.303877i	0.538652	+	0.842529i	$0.318934\pi$
$548$	3.51191e11	+	3.45747e11i	0.166353	+	0.163774i
$549$	2.43878e12	+	2.43878e12i	1.14577	+	1.14577i
$550$	1.80612e12	+	7.39870e11i	0.841619	+	0.344765i
$551$		−	2.34680e11i		−	0.108466i
$552$	1.10100e11	+	2.57238e11i	0.0504733	+	0.117926i
$553$			1.73953e12i			0.790984i
$554$	−8.10373e11	+	1.97823e12i	−0.365503	+	0.892244i
$555$	−6.75501e10	−	6.75501e10i	−0.0302209	−	0.0302209i
$556$	−2.89595e11	+	2.26215e9i	−0.128515	+	0.00100389i
$557$	7.19543e11	−	7.19543e11i	0.316744	−	0.316744i	−0.530771	−	0.847515i	$-0.678098\pi$
$557$	7.19543e11	−	7.19543e11i	0.316744	−	0.316744i	0.847515	+	0.530771i	$0.178098\pi$
$558$	1.42263e12	−	5.95792e11i	0.621208	−	0.260160i
$559$	2.07660e12			0.899499
$560$	1.34228e12	+	1.30099e12i	0.576764	+	0.559019i
$561$	−2.95696e11			−0.126041
$562$	3.82430e12	−	1.60160e12i	1.61711	−	0.677239i
$563$	−2.69649e11	+	2.69649e11i	−0.113113	+	0.113113i	−0.761398	−	0.648285i	$-0.775486\pi$
$563$	−2.69649e11	+	2.69649e11i	−0.113113	+	0.113113i	0.648285	+	0.761398i	$0.275486\pi$
$564$	5.04336e8	+	6.45640e10i	0.000209877	+	0.0268680i
$565$	3.33609e12	+	3.33609e12i	1.37727	+	1.37727i
$566$	7.50278e11	−	1.83153e12i	0.307290	−	0.750137i
$567$			1.45687e12i			0.591966i
$568$	1.02985e12	−	2.57106e12i	0.415149	−	1.03644i
$569$			4.51686e12i			1.80647i	0.429144	+	0.903236i	$0.358815\pi$
$569$			4.51686e12i			1.80647i	−0.429144	+	0.903236i	$0.641185\pi$
$570$	−2.50964e11	−	1.02806e11i	−0.0995805	−	0.0407927i
$571$	−2.35053e12	−	2.35053e12i	−0.925344	−	0.925344i	0.0720570	−	0.997401i	$-0.477044\pi$
$571$	−2.35053e12	−	2.35053e12i	−0.925344	−	0.925344i	−0.997401	+	0.0720570i	$0.977044\pi$
$572$	1.81362e12	−	1.84218e12i	0.708378	−	0.719532i
$573$	−1.70981e11	+	1.70981e11i	−0.0662601	+	0.0662601i
$574$	−1.10523e12	−	2.63906e12i	−0.424961	−	1.01472i
$575$	−3.08937e12			−1.17859
$576$	−1.81110e12	+	1.89804e12i	−0.685553	+	0.718461i
$577$	1.98023e12			0.743745			0.371872	−	0.928284i	$-0.378716\pi$
$577$	1.98023e12			0.743745			0.371872	+	0.928284i	$0.378716\pi$
$578$	6.44059e11	+	1.53788e12i	0.240021	+	0.573122i
$579$	−9.84875e10	+	9.84875e10i	−0.0364190	+	0.0364190i
$580$	−2.83419e11	+	2.87882e11i	−0.103993	+	0.105630i
$581$	−1.33362e12	−	1.33362e12i	−0.485558	−	0.485558i
$582$	1.62673e11	+	6.66384e10i	0.0587710	+	0.0240753i
$583$		−	1.00016e12i		−	0.358559i
$584$	−2.96223e11	+	7.39536e11i	−0.105381	+	0.263088i
$585$		−	3.17603e12i		−	1.12120i
$586$	−2.62066e10	+	6.39738e10i	−0.00918060	+	0.0224111i
$587$	1.99501e12	+	1.99501e12i	0.693545	+	0.693545i	0.963010	−	0.269465i	$-0.0868469\pi$
$587$	1.99501e12	+	1.99501e12i	0.693545	+	0.693545i	−0.269465	+	0.963010i	$0.586847\pi$
$588$	−1.19686e9	−	1.53219e11i	−0.000412900	−	0.0528586i
$589$	1.36187e12	−	1.36187e12i	0.466247	−	0.466247i
$590$	−4.36242e12	+	1.82697e12i	−1.48215	+	0.620721i
$591$	3.50306e11			0.118115
$592$	−8.03122e11	+	8.28615e11i	−0.268741	+	0.277272i
$593$	−3.31891e12			−1.10217			−0.551087	−	0.834448i	$-0.685787\pi$
$593$	−3.31891e12			−1.10217			−0.551087	+	0.834448i	$0.685787\pi$
$594$	−5.52131e11	+	2.31231e11i	−0.181972	+	0.0762091i
$595$	2.21097e12	−	2.21097e12i	0.723197	−	0.723197i
$596$	3.84524e12	−	3.00367e10i	1.24829	−	0.00975090i
$597$	2.47192e11	+	2.47192e11i	0.0796435	+	0.0796435i
$598$	−1.55110e12	+	3.78644e12i	−0.496003	+	1.21081i
$599$			3.12151e12i			0.990704i	0.868692	+	0.495352i	$0.164961\pi$
$599$			3.12151e12i			0.990704i	−0.868692	+	0.495352i	$0.835039\pi$
$600$	7.96441e10	+	1.86081e11i	0.0250884	+	0.0586166i
$601$		−	3.75771e12i		−	1.17487i	−0.809272	−	0.587433i	$-0.800138\pi$
$601$		−	3.75771e12i		−	1.17487i	0.809272	−	0.587433i	$-0.199862\pi$
$602$	1.90821e12	+	7.81687e11i	0.592163	+	0.242577i
$603$	−8.17162e11	−	8.17162e11i	−0.251698	−	0.251698i
$604$	−3.71148e12	−	3.65394e12i	−1.13470	−	1.11711i
$605$	1.27549e12	−	1.27549e12i	0.387060	−	0.387060i
$606$	−1.56796e10	−	3.74397e10i	−0.00472290	−	0.0112773i
$607$	−1.75568e12			−0.524924			−0.262462	−	0.964942i	$-0.584534\pi$
$607$	−1.75568e12			−0.524924			−0.262462	+	0.964942i	$0.584534\pi$
$608$	−1.19433e12	+	3.05054e12i	−0.354453	+	0.905337i
$609$	−1.90707e10			−0.00561808
$610$	−2.86387e12	−	6.83833e12i	−0.837470	−	1.99970i
$611$	−6.67642e11	+	6.67642e11i	−0.193802	+	0.193802i
$612$	3.12714e12	+	3.07866e12i	0.901084	+	0.887116i
$613$	−3.75115e12	−	3.75115e12i	−1.07298	−	1.07298i	−0.997118	−	0.0758623i	$-0.975829\pi$
$613$	−3.75115e12	−	3.75115e12i	−1.07298	−	1.07298i	−0.0758623	−	0.997118i	$-0.524171\pi$
$614$	−3.93570e12	−	1.61224e12i	−1.11754	−	0.457796i
$615$		−	7.14569e11i		−	0.201422i
$616$	2.36000e12	−	1.01010e12i	0.660386	−	0.282651i
$617$		−	6.69612e12i		−	1.86012i	−0.367413	−	0.930058i	$-0.619756\pi$
$617$		−	6.69612e12i		−	1.86012i	0.367413	−	0.930058i	$-0.380244\pi$
$618$	5.31347e10	−	1.29709e11i	0.0146531	−	0.0357703i
$619$	3.18356e12	+	3.18356e12i	0.871575	+	0.871575i	0.992644	−	0.121069i	$-0.0386322\pi$
$619$	3.18356e12	+	3.18356e12i	0.871575	+	0.871575i	−0.121069	+	0.992644i	$0.538632\pi$
$620$	−3.31530e12	+	2.58972e10i	−0.901075	+	0.00703866i
$621$	6.69969e11	−	6.69969e11i	0.180777	−	0.180777i
$622$	−3.81655e12	+	1.59836e12i	−1.02239	+	0.428172i
$623$	2.14710e12			0.571026
$624$	2.68055e11	−	4.18803e9i	0.0707771	−	0.00110581i
$625$	4.49968e12			1.17956
$626$	−3.95202e12	+	1.65509e12i	−1.02857	+	0.430763i
$627$	−2.63355e11	+	2.63355e11i	−0.0680514	+	0.0680514i
$628$	3.57020e9	+	4.57050e11i	0.000915956	+	0.117259i
$629$	1.36487e12	+	1.36487e12i	0.347668	+	0.347668i
$630$	1.19554e12	−	2.91847e12i	0.302365	−	0.738113i
$631$		−	6.31897e11i		−	0.158677i	−0.996848	−	0.0793385i	$-0.974719\pi$
$631$		−	6.31897e11i		−	0.158677i	0.996848	−	0.0793385i	$-0.0252808\pi$
$632$	4.87159e12	+	1.95133e12i	1.21463	+	0.486523i
$633$			2.93933e10i			0.00727664i
$634$	−1.17867e12	−	4.82836e11i	−0.289728	−	0.118686i
$635$	−3.13419e11	−	3.13419e11i	−0.0764969	−	0.0764969i
$636$	7.27663e10	−	7.39120e10i	0.0176349	−	0.0179126i
$637$	1.58441e12	−	1.58441e12i	0.381276	−	0.381276i
$638$	2.14306e11	+	5.11719e11i	0.0512084	+	0.122275i
$639$	−4.67290e12			−1.10875
$640$	5.14917e12	−	2.29971e12i	1.21318	−	0.541831i
$641$	5.17619e12			1.21101			0.605507	−	0.795840i	$-0.292970\pi$
$641$	5.17619e12			1.21101			0.605507	+	0.795840i	$0.292970\pi$
$642$	2.49550e11	+	5.95874e11i	0.0579762	+	0.138435i
$643$	−2.60400e12	+	2.60400e12i	−0.600747	+	0.600747i	−0.940511	−	0.339764i	$-0.889653\pi$
$643$	−2.60400e12	+	2.60400e12i	−0.600747	+	0.600747i	0.339764	+	0.940511i	$0.389653\pi$
$644$	−2.85063e12	+	2.89551e12i	−0.653062	+	0.663345i
$645$	3.64167e11	+	3.64167e11i	0.0828480	+	0.0828480i
$646$	5.07081e12	+	2.07723e12i	1.14559	+	0.469287i
$647$		−	8.68210e11i		−	0.194785i	−0.995246	−	0.0973925i	$-0.968950\pi$
$647$		−	8.68210e11i		−	0.194785i	0.995246	−	0.0973925i	$-0.0310502\pi$
$648$	4.08000e12	+	1.63425e12i	0.909019	+	0.364109i
$649$			6.49498e12i			1.43707i
$650$	−1.12203e12	+	2.73903e12i	−0.246544	+	0.601849i
$651$	−1.10669e11	−	1.10669e11i	−0.0241496	−	0.0241496i
$652$	−1.01776e10	−	1.30292e12i	−0.00220563	−	0.282361i
$653$	−2.40547e12	+	2.40547e12i	−0.517716	+	0.517716i	−0.916880	−	0.399164i	$-0.869300\pi$
$653$	−2.40547e12	+	2.40547e12i	−0.517716	+	0.517716i	0.399164	+	0.916880i	$0.369300\pi$
$654$	−5.82272e11	+	2.43853e11i	−0.124459	+	0.0521230i
$655$	1.14911e13			2.43937
$656$	−8.63056e12	+	1.34842e11i	−1.81958	+	0.0284287i
$657$	1.34410e12			0.281442
$658$	−8.64818e11	+	3.62183e11i	−0.179849	+	0.0753202i
$659$	−2.01027e12	+	2.01027e12i	−0.415213	+	0.415213i	−0.883550	−	0.468337i	$-0.844853\pi$
$659$	−2.01027e12	+	2.01027e12i	−0.415213	+	0.415213i	0.468337	+	0.883550i	$0.344853\pi$
$660$	6.41106e11	−	5.00794e9i	0.131517	−	0.00102733i
$661$	−1.23987e12	−	1.23987e12i	−0.252622	−	0.252622i	0.569423	−	0.822045i	$-0.307167\pi$
$661$	−1.23987e12	−	1.23987e12i	−0.252622	−	0.252622i	−0.822045	+	0.569423i	$0.807167\pi$
$662$	1.60334e12	−	3.91398e12i	0.324464	−	0.792060i
$663$		−	4.48431e11i		−	0.0901332i
$664$	−5.23086e12	+	2.23885e12i	−1.04428	+	0.446960i
$665$		−	3.93830e12i		−	0.780929i
$666$	1.80162e12	+	7.38027e11i	0.354838	+	0.145358i
$667$	−6.20931e11	−	6.20931e11i	−0.121472	−	0.121472i
$668$	6.79946e12	+	6.69405e12i	1.32124	+	1.30075i
$669$	3.16686e10	−	3.16686e10i	0.00611239	−	0.00611239i
$670$	9.59599e11	+	2.29132e12i	0.183973	+	0.439288i
$671$	−1.01812e13			−1.93887
$672$	2.47894e11	+	9.70543e10i	0.0468926	+	0.0183592i
$673$	−4.49295e12			−0.844235			−0.422118	−	0.906541i	$-0.638713\pi$
$673$	−4.49295e12			−0.844235			−0.422118	+	0.906541i	$0.638713\pi$
$674$	−1.38283e12	−	3.30191e12i	−0.258106	−	0.616305i
$675$	4.84641e11	−	4.84641e11i	0.0898573	−	0.0898573i
$676$	−1.07539e12	−	1.05872e12i	−0.198065	−	0.194994i
$677$	3.89555e11	+	3.89555e11i	0.0712722	+	0.0712722i	0.741844	−	0.670572i	$-0.233951\pi$
$677$	3.89555e11	+	3.89555e11i	0.0712722	+	0.0712722i	−0.670572	+	0.741844i	$0.733951\pi$
$678$	6.21758e11	+	2.54700e11i	0.113002	+	0.0462909i
$679$			2.55279e12i			0.460893i
$680$	−3.71172e12	−	8.67207e12i	−0.665710	−	1.55537i
$681$		−	2.93119e11i		−	0.0522255i
$682$	−1.72591e12	+	4.21318e12i	−0.305484	+	0.745728i
$683$	1.39189e12	+	1.39189e12i	0.244744	+	0.244744i	0.818810	−	0.574065i	$-0.194634\pi$
$683$	1.39189e12	+	1.39189e12i	0.244744	+	0.244744i	−0.574065	+	0.818810i	$0.694634\pi$
$684$	5.52705e12	−	4.31740e10i	0.965475	−	0.00754171i
$685$	−1.26385e12	+	1.26385e12i	−0.219324	+	0.219324i
$686$	5.28662e12	−	2.21402e12i	0.911423	−	0.381701i
$687$	−4.46669e11			−0.0765034
$688$	4.32968e12	−	4.46712e12i	0.736730	−	0.760116i
$689$	1.51677e12			0.256408
$690$	−9.36026e11	+	3.92005e11i	−0.157205	+	0.0658371i
$691$	−2.94050e12	+	2.94050e12i	−0.490649	+	0.490649i	−0.908511	−	0.417862i	$-0.862780\pi$
$691$	−2.94050e12	+	2.94050e12i	−0.490649	+	0.490649i	0.417862	+	0.908511i	$0.362780\pi$
$692$	3.07786e10	+	3.94022e12i	0.00510237	+	0.653194i
$693$	−3.06257e12	−	3.06257e12i	−0.504413	−	0.504413i
$694$	2.04034e12	−	4.98076e12i	0.333876	−	0.815038i
$695$		−	1.05032e12i		−	0.170761i
$696$	−2.13927e10	+	5.34080e10i	−0.00345560	+	0.00862709i
$697$			1.44381e13i			2.31720i
$698$	−1.25982e12	−	5.16081e11i	−0.200891	−	0.0822940i
$699$	−1.51141e11	−	1.51141e11i	−0.0239461	−	0.0239461i
$700$	−2.06209e12	+	2.09455e12i	−0.324613	+	0.329724i
$701$	−5.22777e12	+	5.22777e12i	−0.817684	+	0.817684i	−0.985772	−	0.168088i	$-0.946241\pi$
$701$	−5.22777e12	+	5.22777e12i	−0.817684	+	0.817684i	0.168088	+	0.985772i	$0.446241\pi$
$702$	−3.50668e11	−	8.37322e11i	−0.0544978	−	0.130129i
$703$	2.43118e12			0.375421
$704$	−1.81465e11	−	7.74232e12i	−0.0278430	−	1.18794i
$705$	−2.34164e11			−0.0357001
$706$	−2.82941e12	−	6.75605e12i	−0.428622	−	1.02346i
$707$	4.16793e11	−	4.16793e11i	0.0627383	−	0.0627383i
$708$	−4.72540e11	+	4.79981e11i	−0.0706788	+	0.0717917i
$709$	−1.68131e12	−	1.68131e12i	−0.249885	−	0.249885i	0.571039	−	0.820923i	$-0.306541\pi$
$709$	−1.68131e12	−	1.68131e12i	−0.249885	−	0.249885i	−0.820923	+	0.571039i	$0.806541\pi$
$710$	9.29512e12	+	3.80770e12i	1.37275	+	0.562342i
$711$		−	8.85411e12i		−	1.29937i
$712$	2.40853e12	−	6.01302e12i	0.351230	−	0.876865i
$713$		−	7.20663e12i		−	1.04431i
$714$	1.68801e11	−	4.12066e11i	0.0243071	−	0.0593369i
$715$	6.62953e12	+	6.62953e12i	0.948649	+	0.948649i
$716$	−2.91928e10	−	3.73720e12i	−0.00415114	−	0.531420i
$717$	−4.81704e11	+	4.81704e11i	−0.0680681	+	0.0680681i
$718$	7.69648e11	−	3.22326e11i	0.108077	−	0.0452622i
$719$	1.24541e12			0.173793			0.0868965	−	0.996217i	$-0.472305\pi$
$719$	1.24541e12			0.173793			0.0868965	+	0.996217i	$0.472305\pi$
$720$	−6.83216e12	−	6.62196e12i	−0.947462	−	0.918312i
$721$	2.03549e12			0.280517
$722$	−3.68586e11	+	1.54363e11i	−0.0504803	+	0.0211410i
$723$	−1.46786e11	+	1.46786e11i	−0.0199784	+	0.0199784i
$724$	−2.92204e12	+	2.28252e10i	−0.395241	+	0.00308739i
$725$	−4.49169e11	−	4.49169e11i	−0.0603793	−	0.0603793i
$726$	9.73798e10	−	2.37718e11i	0.0130093	−	0.0317575i
$727$		−	7.92895e12i		−	1.05272i	−0.850263	−	0.526358i	$-0.823557\pi$
$727$		−	7.92895e12i		−	1.05272i	0.850263	−	0.526358i	$-0.176443\pi$
$728$	1.53184e12	+	3.57900e12i	0.202126	+	0.472248i
$729$		−	7.30993e12i		−	0.958604i
$730$	−2.67363e12	−	1.09524e12i	−0.348456	−	0.142743i
$731$	−7.35812e12	−	7.35812e12i	−0.953101	−	0.953101i
$732$	−7.52397e11	−	7.40733e11i	−0.0968606	−	0.0953591i
$733$	−1.05764e12	+	1.05764e12i	−0.135322	+	0.135322i	−0.771523	−	0.636201i	$-0.780505\pi$
$733$	−1.05764e12	+	1.05764e12i	−0.135322	+	0.135322i	0.636201	+	0.771523i	$0.280505\pi$
$734$	2.65239e12	+	6.33336e12i	0.337291	+	0.805381i
$735$	5.55704e11			0.0702344
$736$	4.91126e12	+	1.12313e13i	0.616940	+	1.41085i
$737$	3.41143e12			0.425925
$738$	5.62557e12	+	1.34327e13i	0.698092	+	1.66690i
$739$	−7.05822e12	+	7.05822e12i	−0.870553	+	0.870553i	−0.992533	−	0.121979i	$-0.961076\pi$
$739$	−7.05822e12	+	7.05822e12i	−0.870553	+	0.870553i	0.121979	+	0.992533i	$0.461076\pi$
$740$	−2.98233e12	−	2.93610e12i	−0.365606	−	0.359938i
$741$	−3.99385e11	−	3.99385e11i	−0.0486642	−	0.0486642i
$742$	1.39377e12	+	5.70950e11i	0.168800	+	0.0691481i
$743$		−	1.14907e13i		−	1.38323i	−0.722264	−	0.691617i	$-0.756899\pi$
$743$		−	1.14907e13i		−	1.38323i	0.722264	−	0.691617i	$-0.243101\pi$
$744$	−4.34074e11	+	1.85787e11i	−0.0519381	+	0.0222299i
$745$			1.39461e13i			1.65863i
$746$	3.48729e12	−	8.51295e12i	0.412252	−	1.00636i
$747$	6.78809e12	+	6.78809e12i	0.797636	+	0.797636i
$748$	−1.29538e13	+	1.01187e11i	−1.51300	+	0.0118187i
$749$	−6.63349e12	+	6.63349e12i	−0.770148	+	0.770148i
$750$	2.07538e11	−	8.69161e10i	0.0239509	−	0.0100305i
$751$	7.14477e12			0.819612			0.409806	−	0.912173i	$-0.365596\pi$
$751$	7.14477e12			0.819612			0.409806	+	0.912173i	$0.365596\pi$
$752$	4.41876e10	+	2.82823e12i	0.00503872	+	0.322504i
$753$	4.48978e11			0.0508918
$754$	−7.76035e11	+	3.25001e11i	−0.0874400	+	0.0366196i
$755$	1.33566e13	−	1.33566e13i	1.49601	−	1.49601i
$756$	−7.04136e9	−	9.01421e11i	−0.000783987	−	0.100364i
$757$	−2.88410e12	−	2.88410e12i	−0.319212	−	0.319212i	0.529252	−	0.848464i	$-0.322472\pi$
$757$	−2.88410e12	−	2.88410e12i	−0.319212	−	0.319212i	−0.848464	+	0.529252i	$0.822472\pi$
$758$	−2.48522e12	+	6.06675e12i	−0.273434	+	0.667490i
$759$			1.39360e12i			0.152423i
$760$	−1.10293e13	−	4.41782e12i	−1.19919	−	0.480338i
$761$			1.92737e12i			0.208322i	0.994560	+	0.104161i	$0.0332156\pi$
$761$			1.92737e12i			0.208322i	−0.994560	+	0.104161i	$0.966784\pi$
$762$	−5.84130e10	−	2.39286e10i	−0.00627642	−	0.00257110i
$763$	−6.48207e12	−	6.48207e12i	−0.692394	−	0.692394i
$764$	−7.43178e12	+	7.54880e12i	−0.789174	+	0.801600i
$765$	−1.12538e13	+	1.12538e13i	−1.18801	+	1.18801i
$766$	−5.32401e11	−	1.27126e12i	−0.0558740	−	0.133416i
$767$	−9.84980e12			−1.02766
$768$	5.49880e11	−	5.85363e11i	0.0570352	−	0.0607155i
$769$	1.76009e13			1.81496			0.907478	−	0.420100i	$-0.138005\pi$
$769$	1.76009e13			1.81496			0.907478	+	0.420100i	$0.138005\pi$
$770$	3.59639e12	+	8.58744e12i	0.368688	+	0.880351i
$771$	2.88672e11	−	2.88672e11i	0.0294211	−	0.0294211i
$772$	−4.28081e12	+	4.34822e12i	−0.433759	+	0.440589i
$773$	9.09471e12	+	9.09471e12i	0.916181	+	0.916181i	0.996749	−	0.0805684i	$-0.0256735\pi$
$773$	9.09471e12	+	9.09471e12i	0.916181	+	0.916181i	−0.0805684	+	0.996749i	$0.525674\pi$
$774$	−9.71268e12	−	3.97875e12i	−0.972758	−	0.398486i
$775$		−	5.21312e12i		−	0.519087i
$776$	7.14916e12	+	2.86361e12i	0.707745	+	0.283489i
$777$		−	1.97564e11i		−	0.0194452i
$778$	1.13659e12	−	2.77458e12i	0.111224	−	0.271512i
$779$	1.28590e13	+	1.28590e13i	1.25109	+	1.25109i
$780$	7.59467e9	+	9.72254e11i	0.000734655	+	0.0940490i
$781$	9.75406e12	−	9.75406e12i	0.938114	−	0.938114i
$782$	1.89127e13	−	7.92059e12i	1.80852	−	0.757404i
$783$	1.94816e11			0.0185224
$784$	−1.04863e11	−	6.71178e12i	−0.00991291	−	0.634476i
$785$	−1.65765e12			−0.155805
$786$	1.50948e12	−	6.32164e11i	0.141067	−	0.0590783i
$787$	3.53115e12	−	3.53115e12i	0.328118	−	0.328118i	−0.523753	−	0.851870i	$-0.675468\pi$
$787$	3.53115e12	−	3.53115e12i	0.328118	−	0.328118i	0.851870	+	0.523753i	$0.175468\pi$
$788$	1.53461e13	−	1.19875e11i	1.41785	−	0.0110754i
$789$	−6.56263e11	−	6.56263e11i	−0.0602880	−	0.0602880i
$790$	−7.21475e12	+	1.76122e13i	−0.659021	+	1.60876i
$791$			9.75706e12i			0.886186i
$792$	−1.20123e13	+	5.14135e12i	−1.08483	+	0.464317i
$793$		−	1.54401e13i		−	1.38650i
$794$	−8.29556e12	−	3.39823e12i	−0.740719	−	0.303432i
$795$	2.65990e11	+	2.65990e11i	0.0236164	+	0.0236164i
$796$	1.09135e13	+	1.07443e13i	0.963509	+	0.948573i
$797$	1.07752e13	−	1.07752e13i	0.945934	−	0.945934i	−0.0526772	−	0.998612i	$-0.516775\pi$
$797$	1.07752e13	−	1.07752e13i	0.945934	−	0.945934i	0.998612	+	0.0526772i	$0.0167754\pi$
$798$	−2.16658e11	−	5.17336e11i	−0.0189131	−	0.0451606i
$799$	4.73137e12			0.410701
$800$	3.55270e12	+	8.12452e12i	0.306658	+	0.701282i
$801$	−1.09286e13			−0.938037
$802$	−9.63219e11	−	2.29997e12i	−0.0822130	−	0.196308i
$803$	−2.80564e12	+	2.80564e12i	−0.238129	+	0.238129i
$804$	2.52106e11	+	2.48198e11i	0.0212780	+	0.0209482i
$805$	−1.04202e13	−	1.04202e13i	−0.874570	−	0.874570i
$806$	−6.38940e12	−	2.61739e12i	−0.533276	−	0.218454i
$807$			7.49273e11i			0.0621884i
$808$	−6.99700e11	−	1.63478e12i	−0.0577512	−	0.134930i
$809$		−	3.77277e12i		−	0.309665i	−0.987941	−	0.154832i	$-0.950516\pi$
$809$		−	3.77277e12i		−	0.309665i	0.987941	−	0.154832i	$-0.0494837\pi$
$810$	−6.04242e12	+	1.47504e13i	−0.493206	+	1.20398i
$811$	−7.82330e12	−	7.82330e12i	−0.635033	−	0.635033i	0.314293	−	0.949326i	$-0.398233\pi$
$811$	−7.82330e12	−	7.82330e12i	−0.635033	−	0.635033i	−0.949326	+	0.314293i	$0.898233\pi$
$812$	−8.35442e11	+	6.52598e9i	−0.0674395	+	0.000526797i
$813$	−9.31223e10	+	9.31223e10i	−0.00747560	+	0.00747560i
$814$	−5.30118e12	+	2.22012e12i	−0.423217	+	0.177242i
$815$	4.72550e12			0.375179
$816$	−9.64650e11	−	9.34971e11i	−0.0761665	−	0.0738231i
$817$	−1.31067e13			−1.02918
$818$	3.30599e11	−	1.38454e11i	0.0258174	−	0.0108122i
$819$	4.64447e12	−	4.64447e12i	0.360710	−	0.360710i
$820$	−2.44526e11	−	3.13037e13i	−0.0188870	−	2.41787i
$821$	1.01563e13	+	1.01563e13i	0.780177	+	0.780177i	0.979861	−	0.199683i	$-0.0639913\pi$
$821$	1.01563e13	+	1.01563e13i	0.780177	+	0.780177i	−0.199683	+	0.979861i	$0.563991\pi$
$822$	−9.64907e10	+	2.35547e11i	−0.00737161	+	0.0179951i
$823$			2.41428e13i			1.83438i	0.398451	+	0.917189i	$0.369548\pi$
$823$			2.41428e13i			1.83438i	−0.398451	+	0.917189i	$0.630452\pi$
$824$	2.28333e12	−	5.70045e12i	0.172542	−	0.430761i
$825$			1.00810e12i			0.0757638i
$826$	−9.05105e12	−	3.70772e12i	−0.676532	−	0.277138i
$827$	−1.58368e13	−	1.58368e13i	−1.17731	−	1.17731i	−0.980426	−	0.196888i	$-0.936916\pi$
$827$	−1.58368e13	−	1.58368e13i	−1.17731	−	1.17731i	−0.196888	−	0.980426i	$-0.563084\pi$
$828$	1.45096e13	−	1.47380e13i	1.07280	−	1.08969i
$829$	1.39560e13	−	1.39560e13i	1.02628	−	1.02628i	0.0266360	−	0.999645i	$-0.491520\pi$
$829$	1.39560e13	−	1.39560e13i	1.02628	−	1.02628i	0.999645	−	0.0266360i	$-0.00847951\pi$
$830$	−7.97130e12	−	1.90338e13i	−0.583012	−	1.39211i
$831$	−1.10417e12			−0.0803211
$832$	1.17414e13	−	2.75196e11i	0.849506	−	0.0199107i
$833$	−1.12282e13			−0.807992
$834$	−5.77814e10	−	1.37970e11i	−0.00413562	−	0.00987501i
$835$	−2.44695e13	+	2.44695e13i	−1.74195	+	1.74195i
$836$	−1.14469e13	+	1.16271e13i	−0.810509	+	0.823271i
$837$	1.13053e12	+	1.13053e12i	0.0796193	+	0.0796193i
$838$	−1.27943e13	−	5.24111e12i	−0.896225	−	0.367134i
$839$		−	4.34316e12i		−	0.302605i	−0.988487	−	0.151303i	$-0.951653\pi$
$839$		−	4.34316e12i		−	0.302605i	0.988487	−	0.151303i	$-0.0483468\pi$
$840$	−3.59003e11	+	8.96270e11i	−0.0248795	+	0.0621129i
$841$			1.43266e13i			0.987554i
$842$	7.48181e12	−	1.82641e13i	0.512982	−	1.25226i
$843$	1.51426e12	+	1.51426e12i	0.103270	+	0.103270i
$844$	1.00584e10	+	1.28765e12i	0.000682318	+	0.0873489i
$845$	3.87006e12	−	3.87006e12i	0.261134	−	0.261134i
$846$	4.40189e12	−	1.84350e12i	0.295442	−	0.123730i
$847$	3.73043e12			0.249048
$848$	3.16243e12	−	3.26282e12i	0.210010	−	0.216676i
$849$	1.02228e12			0.0675285
$850$	1.36811e13	−	5.72959e12i	0.898949	−	0.376477i
$851$	6.43258e12	−	6.43258e12i	0.420438	−	0.420438i
$852$	1.43048e12	−	1.11741e10i	0.0930046	−	0.000726496i
$853$	−8.52989e12	−	8.52989e12i	−0.551662	−	0.551662i	0.375258	−	0.926920i	$-0.377554\pi$
$853$	−8.52989e12	−	8.52989e12i	−0.551662	−	0.551662i	−0.926920	+	0.375258i	$0.877554\pi$
$854$	5.81206e12	−	1.41880e13i	0.373912	−	0.912770i
$855$			2.00458e13i			1.28285i
$856$	1.11361e13	+	2.60185e13i	0.708928	+	1.65634i
$857$		−	6.23374e11i		−	0.0394762i	−0.999805	−	0.0197381i	$-0.993717\pi$
$857$		−	6.23374e11i		−	0.0394762i	0.999805	−	0.0197381i	$-0.00628324\pi$
$858$	1.23557e12	+	5.06144e11i	0.0778348	+	0.0318846i
$859$	−3.35049e12	−	3.35049e12i	−0.209961	−	0.209961i	0.594290	−	0.804251i	$-0.297433\pi$
$859$	−3.35049e12	−	3.35049e12i	−0.209961	−	0.209961i	−0.804251	+	0.594290i	$0.797433\pi$
$860$	1.60779e13	+	1.58287e13i	1.00228	+	0.986739i
$861$	1.04495e12	−	1.04495e12i	0.0648010	−	0.0648010i
$862$	4.23671e12	+	1.01164e13i	0.261364	+	0.624084i
$863$	−2.61039e13			−1.60198			−0.800989	−	0.598679i	$-0.795692\pi$
$863$	−2.61039e13			−1.60198			−0.800989	+	0.598679i	$0.795692\pi$
$864$	−2.53235e12	−	9.91456e11i	−0.154601	−	0.0605288i
$865$	−1.42906e13			−0.867915
$866$	4.78377e12	+	1.14227e13i	0.289028	+	0.690139i
$867$	−6.08933e11	+	6.08933e11i	−0.0366002	+	0.0366002i
$868$	−4.88601e12	−	4.81027e12i	−0.292156	−	0.287628i
$869$	1.84818e13	+	1.84818e13i	1.09940	+	1.09940i
$870$	−1.93085e11	−	7.90963e10i	−0.0114265	−	0.00468079i
$871$			5.17353e12i			0.304583i
$872$	−2.54245e13	+	1.08819e13i	−1.48912	+	0.637355i
$873$		−	1.29936e13i		−	0.757120i
$874$	9.78990e12	−	2.38985e13i	0.567514	−	1.38538i
$875$	2.31039e12	+	2.31039e12i	0.133244	+	0.133244i
$876$	−4.11461e11	+	3.21409e9i	−0.0236081	+	0.000184412i
$877$	−9.75430e12	+	9.75430e12i	−0.556799	+	0.556799i	−0.928395	−	0.371596i	$-0.878811\pi$
$877$	−9.75430e12	+	9.75430e12i	−0.556799	+	0.556799i	0.371596	+	0.928395i	$0.378811\pi$
$878$	−9.77571e12	+	4.09403e12i	−0.555166	+	0.232502i
$879$	−3.57075e10			−0.00201748
$880$	2.80837e13	−	4.38773e11i	1.57864	−	0.0246642i
$881$	2.24072e13			1.25313			0.626566	−	0.779369i	$-0.284460\pi$
$881$	2.24072e13			1.25313			0.626566	+	0.779369i	$0.284460\pi$
$882$	−1.04463e13	+	4.37487e12i	−0.581237	+	0.243420i
$883$	1.88138e13	−	1.88138e13i	1.04149	−	1.04149i	0.0423846	−	0.999101i	$-0.486505\pi$
$883$	1.88138e13	−	1.88138e13i	1.04149	−	1.04149i	0.999101	−	0.0423846i	$-0.0134955\pi$
$884$	−1.53453e11	−	1.96447e13i	−0.00845163	−	1.08196i
$885$	−1.72733e12	−	1.72733e12i	−0.0946520	−	0.0946520i
$886$	−8.24949e12	+	2.01381e13i	−0.449754	+	1.09791i
$887$			3.34858e13i			1.81637i	0.418569	+	0.908185i	$0.362532\pi$
$887$			3.34858e13i			1.81637i	−0.418569	+	0.908185i	$0.637468\pi$
$888$	−5.53283e11	−	2.21619e11i	−0.0298600	−	0.0119605i
$889$		−	9.16658e11i		−	0.0492209i
$890$	2.17388e13	+	8.90518e12i	1.16139	+	0.475760i
$891$	1.54786e13	+	1.54786e13i	0.822779	+	0.822779i
$892$	1.37649e12	−	1.39816e12i	0.0728000	−	0.0739463i
$893$	4.21388e12	−	4.21388e12i	0.221743	−	0.221743i
$894$	7.67220e11	+	1.83196e12i	0.0401699	+	0.0959175i
$895$	1.35543e13			0.706110
$896$	1.08929e13	+	4.16690e12i	0.564620	+	0.215987i
$897$	−2.11343e12			−0.108999
$898$	5.96854e12	+	1.42516e13i	0.306284	+	0.731344i
$899$	1.04778e12	−	1.04778e12i	0.0535000	−	0.0535000i
$900$	1.04959e13	−	1.06612e13i	0.533248	−	0.541645i
$901$	−5.37443e12	−	5.37443e12i	−0.271688	−	0.271688i
$902$	−3.97816e13	−	1.62963e13i	−2.00102	−	0.819710i
$903$			1.06508e12i			0.0533074i
$904$	2.73249e13	+	1.09451e13i	1.36082	+	0.545080i
$905$		−	1.05978e13i		−	0.525167i
$906$	1.01974e12	−	2.48932e12i	0.0502819	−	0.122745i
$907$	−1.61680e13	−	1.61680e13i	−0.793273	−	0.793273i	0.188752	−	0.982025i	$-0.439556\pi$
$907$	−1.61680e13	−	1.61680e13i	−0.793273	−	0.793273i	−0.982025	+	0.188752i	$0.939556\pi$
$908$	−1.00305e11	−	1.28409e13i	−0.00489709	−	0.626915i
$909$	−2.12146e12	+	2.12146e12i	−0.103062	+	0.103062i
$910$	−1.30231e13	+	5.45403e12i	−0.629546	+	0.263652i
$911$	−2.43991e13			−1.17366			−0.586828	−	0.809711i	$-0.699624\pi$
$911$	−2.43991e13			−1.17366			−0.586828	+	0.809711i	$0.699624\pi$
$912$	−1.69185e12	+	2.64331e10i	−0.0809815	+	0.00126524i
$913$	−2.83385e13			−1.34976
$914$	−1.10401e13	+	4.62357e12i	−0.523258	+	0.219139i
$915$	2.70768e12	−	2.70768e12i	0.127703	−	0.127703i
$916$	−1.95676e13	+	1.52850e11i	−0.918347	+	0.00717358i
$917$	1.68041e13	+	1.68041e13i	0.784788	+	0.784788i
$918$	−1.72438e12	+	4.20945e12i	−0.0801386	+	0.195629i
$919$		−	1.13796e13i		−	0.526267i	−0.964759	−	0.263134i	$-0.915244\pi$
$919$		−	1.13796e13i		−	0.526267i	0.964759	−	0.263134i	$-0.0847560\pi$
$920$	−4.08710e13	+	1.74931e13i	−1.88092	+	0.805050i
$921$		−	2.19674e12i		−	0.100603i
$922$	−3.87267e12	−	1.58642e12i	−0.176491	−	0.0722986i
$923$	1.47923e13	+	1.47923e13i	0.670854	+	0.670854i
$924$	9.44845e11	+	9.30199e11i	0.0426419	+	0.0419809i
$925$	4.65319e12	−	4.65319e12i	0.208984	−	0.208984i
$926$	−4.36413e12	−	1.04206e13i	−0.195051	−	0.465742i
$927$	−1.03605e13			−0.460812
$928$	−9.18888e11	+	2.34700e12i	−0.0406721	+	0.103884i
$929$	4.95411e12			0.218220			0.109110	−	0.994030i	$-0.465200\pi$
$929$	4.95411e12			0.218220			0.109110	+	0.994030i	$0.465200\pi$
$930$	−6.61485e11	−	1.57949e12i	−0.0289966	−	0.0692378i
$931$	−1.00001e13	+	1.00001e13i	−0.436246	+	0.436246i
$932$	−6.67286e12	−	6.56942e12i	−0.289695	−	0.285204i
$933$	−1.51119e12	−	1.51119e12i	−0.0652907	−	0.0652907i
$934$	2.74299e13	+	1.12365e13i	1.17940	+	0.483138i
$935$		−	4.69814e13i		−	2.01036i
$936$	−7.79700e12	−	1.82169e13i	−0.332037	−	0.775772i
$937$		−	1.05650e13i		−	0.447757i	−0.974617	−	0.223878i	$-0.928128\pi$
$937$		−	1.05650e13i		−	0.447757i	0.974617	−	0.223878i	$-0.0718719\pi$
$938$	−1.94745e12	+	4.75399e12i	−0.0821397	+	0.200514i
$939$	−1.56483e12	−	1.56483e12i	−0.0656858	−	0.0656858i
$940$	−1.02582e13	+	8.01309e10i	−0.428544	+	0.00334753i
$941$	1.76834e13	−	1.76834e13i	0.735213	−	0.735213i	−0.236434	−	0.971647i	$-0.575979\pi$
$941$	1.76834e13	−	1.76834e13i	0.735213	−	0.735213i	0.971647	+	0.236434i	$0.0759788\pi$
$942$	−2.17749e11	+	9.11928e10i	−0.00901007	+	0.00377339i
$943$	6.80462e13			2.80221
$944$	−2.05367e13	+	2.11886e13i	−0.841697	+	0.868416i
$945$	3.26932e12			0.133356
$946$	2.85791e13	−	1.19688e13i	1.16021	−	0.485893i
$947$	4.62889e12	−	4.62889e12i	0.187026	−	0.187026i	−0.607383	−	0.794409i	$-0.707781\pi$
$947$	4.62889e12	−	4.62889e12i	0.187026	−	0.187026i	0.794409	+	0.607383i	$0.207781\pi$
$948$	2.11724e10	+	2.71044e12i	0.000851397	+	0.108994i
$949$	−4.25482e12	−	4.25482e12i	−0.170288	−	0.170288i
$950$	7.08181e12	−	1.72877e13i	0.282090	−	0.688621i
$951$		−	6.57883e11i		−	0.0260817i
$952$	7.25377e12	−	1.81094e13i	0.286219	−	0.714560i
$953$			2.50198e13i			0.982575i	0.870997	+	0.491288i	$0.163474\pi$
$953$			2.50198e13i			0.982575i	−0.870997	+	0.491288i	$0.836526\pi$
$954$	−7.09421e12	−	2.90611e12i	−0.277292	−	0.113591i
$955$	−2.71662e13	−	2.71662e13i	−1.05685	−	1.05685i
$956$	−2.09375e13	+	2.12672e13i	−0.810708	+	0.823473i
$957$	−2.02618e11	+	2.02618e11i	−0.00780863	+	0.00780863i
$958$	1.77798e13	+	4.24546e13i	0.681998	+	1.62847i
$959$	−3.69637e12			−0.141121
$960$	2.10732e12	+	2.01080e12i	0.0800772	+	0.0764095i
$961$	−1.42789e13			−0.540056
$962$	−3.36687e12	−	8.03938e12i	−0.126747	−	0.302646i
$963$	3.37642e13	−	3.37642e13i	1.26514	−	1.26514i
$964$	−6.38011e12	+	6.48057e12i	−0.237948	+	0.241694i
$965$	−1.56481e13	−	1.56481e13i	−0.580883	−	0.580883i
$966$	−1.94205e12	−	7.95550e11i	−0.0717567	−	0.0293948i
$967$		−	1.82224e13i		−	0.670171i	−0.942188	−	0.335085i	$-0.891235\pi$
$967$		−	1.82224e13i		−	0.670171i	0.942188	−	0.335085i	$-0.108765\pi$
$968$	4.18464e12	−	1.04472e13i	0.153186	−	0.382437i
$969$			2.83031e12i			0.103128i
$970$	−1.05878e13	+	2.58462e13i	−0.384001	+	0.937398i
$971$	−1.83810e13	−	1.83810e13i	−0.663563	−	0.663563i	0.292655	−	0.956218i	$-0.405461\pi$
$971$	−1.83810e13	−	1.83810e13i	−0.663563	−	0.663563i	−0.956218	+	0.292655i	$0.905461\pi$
$972$	5.38227e10	+	6.89028e12i	0.00193405	+	0.247593i
$973$	1.53594e12	−	1.53594e12i	0.0549370	−	0.0549370i
$974$	4.14127e13	−	1.73435e13i	1.47441	−	0.617478i
$975$	−1.52881e12			−0.0541793
$976$	−3.32143e13	−	3.21924e13i	−1.17166	−	1.13561i
$977$	9.39015e12			0.329721			0.164861	−	0.986317i	$-0.447283\pi$
$977$	9.39015e12			0.329721			0.164861	+	0.986317i	$0.447283\pi$
$978$	6.20742e11	−	2.59965e11i	0.0216963	−	0.00908636i
$979$	2.28121e13	−	2.28121e13i	0.793675	−	0.793675i
$980$	2.43441e13	−	1.90162e11i	0.843095	−	0.00658576i
$981$	3.29935e13	+	3.29935e13i	1.13741	+	1.13741i
$982$	−1.27099e13	+	3.10265e13i	−0.436153	+	1.06471i
$983$			2.61280e13i			0.892514i	0.894905	+	0.446257i	$0.147243\pi$
$983$			2.61280e13i			0.892514i	−0.894905	+	0.446257i	$0.852757\pi$
$984$	−1.75423e12	−	4.09860e12i	−0.0596499	−	0.139366i
$985$			5.56580e13i			1.88393i
$986$	3.90135e12	+	1.59817e12i	0.131452	+	0.0538488i
$987$	−3.42430e11	−	3.42430e11i	−0.0114854	−	0.0114854i
$988$	−1.76328e13	−	1.73595e13i	−0.588728	−	0.579602i
$989$	−3.46785e13	+	3.46785e13i	−1.15259	+	1.15259i
$990$	−1.83055e13	−	4.37097e13i	−0.605652	−	1.44617i
$991$	−1.21437e13			−0.399963			−0.199981	−	0.979800i	$-0.564088\pi$
$991$	−1.21437e13			−0.399963			−0.199981	+	0.979800i	$0.564088\pi$
$992$	−1.89522e13	+	8.28746e12i	−0.621380	+	0.271718i
$993$	2.18462e12			0.0713024
$994$	8.02453e12	+	1.91609e13i	0.260724	+	0.622555i
$995$	−3.92749e13	+	3.92749e13i	−1.27031	+	1.27031i
$996$	−2.09422e12	−	2.06176e12i	−0.0674304	−	0.0663851i
$997$	−6.12347e12	−	6.12347e12i	−0.196277	−	0.196277i	0.602125	−	0.798402i	$-0.294321\pi$
$997$	−6.12347e12	−	6.12347e12i	−0.196277	−	0.196277i	−0.798402	+	0.602125i	$0.794321\pi$
$998$	2.52425e13	+	1.03405e13i	0.805461	+	0.329953i
$999$			2.01821e12i			0.0641094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.10.e.a.5.12	✓	34
4.3	odd	2		64.10.e.a.49.10		34
8.3	odd	2		128.10.e.a.97.8		34
8.5	even	2		128.10.e.b.97.10		34
16.3	odd	4		64.10.e.a.17.10		34
16.5	even	4		128.10.e.b.33.10		34
16.11	odd	4		128.10.e.a.33.8		34
16.13	even	4	inner	16.10.e.a.13.12	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.10.e.a.5.12	✓	34	1.1	even	1	trivial
16.10.e.a.13.12	yes	34	16.13	even	4	inner
64.10.e.a.17.10		34	16.3	odd	4
64.10.e.a.49.10		34	4.3	odd	2
128.10.e.a.33.8		34	16.11	odd	4
128.10.e.a.97.8		34	8.3	odd	2
128.10.e.b.33.10		34	16.5	even	4
128.10.e.b.97.10		34	8.5	even	2

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.74072 + 20.8710i) q^{2} +(-8.26401 + 8.26401i) q^{3} +(-359.200 + 364.856i) q^{4} +(-1313.02 - 1313.02i) q^{5} +(-244.712 - 100.245i) q^{6} -3840.19i q^{7} +(-10754.6 - 4307.77i) q^{8} +19546.4i q^{9} +O(q^{10})\)	\(q+(8.74072 + 20.8710i) q^{2} +(-8.26401 + 8.26401i) q^{3} +(-359.200 + 364.856i) q^{4} +(-1313.02 - 1313.02i) q^{5} +(-244.712 - 100.245i) q^{6} -3840.19i q^{7} +(-10754.6 - 4307.77i) q^{8} +19546.4i q^{9} +(15927.3 - 38880.8i) q^{10} +(-40800.5 - 40800.5i) q^{11} +(-46.7403 - 5983.60i) q^{12} +(61875.1 - 61875.1i) q^{13} +(80148.8 - 33566.0i) q^{14} +21701.6 q^{15} +(-4095.18 - 262112. i) q^{16} -438489. q^{17} +(-407954. + 170850. i) q^{18} +(-390530. + 390530. i) q^{19} +(950699. - 7426.30i) q^{20} +(31735.4 + 31735.4i) q^{21} +(494923. - 1.20817e6i) q^{22} +2.06658e6i q^{23} +(124475. - 53276.5i) q^{24} +1.49492e6i q^{25} +(1.83223e6 + 750564. i) q^{26} +(-324192. - 324192. i) q^{27} +(1.40112e6 + 1.37940e6i) q^{28} +(-300464. + 300464. i) q^{29} +(189688. + 452935. i) q^{30} -3.48723e6 q^{31} +(5.43475e6 - 2.37652e6i) q^{32} +674352. q^{33} +(-3.83271e6 - 9.15172e6i) q^{34} +(-5.04225e6 + 5.04225e6i) q^{35} +(-7.13162e6 - 7.02107e6i) q^{36} +(-3.11267e6 - 3.11267e6i) q^{37} +(-1.15643e7 - 4.73725e6i) q^{38} +1.02267e6i q^{39} +(8.46479e6 + 1.97772e7i) q^{40} -3.29270e7i q^{41} +(-384960. + 939741. i) q^{42} +(1.67806e7 + 1.67806e7i) q^{43} +(2.95418e7 - 230763. i) q^{44} +(2.56648e7 - 2.56648e7i) q^{45} +(-4.31316e7 + 1.80634e7i) q^{46} -1.07902e7 q^{47} +(2.19994e6 + 2.13225e6i) q^{48} +2.56065e7 q^{49} +(-3.12005e7 + 1.30667e7i) q^{50} +(3.62368e6 - 3.62368e6i) q^{51} +(349959. + 4.48010e7i) q^{52} +(1.22567e7 + 1.22567e7i) q^{53} +(3.93255e6 - 9.59990e6i) q^{54} +1.07144e8i q^{55} +(-1.65427e7 + 4.12996e7i) q^{56} -6.45469e6i q^{57} +(-8.89725e6 - 3.64472e6i) q^{58} +(-7.95943e7 - 7.95943e7i) q^{59} +(-7.79522e6 + 7.91796e6i) q^{60} +(1.24768e8 - 1.24768e8i) q^{61} +(-3.04809e7 - 7.27820e7i) q^{62} +7.50620e7 q^{63} +(9.71040e7 + 9.26564e7i) q^{64} -1.62486e8 q^{65} +(5.89432e6 + 1.40744e7i) q^{66} +(-4.18062e7 + 4.18062e7i) q^{67} +(1.57505e8 - 1.59985e8i) q^{68} +(-1.70782e7 - 1.70782e7i) q^{69} +(-1.49310e8 - 6.11641e7i) q^{70} +2.39067e8i q^{71} +(8.42014e7 - 2.10213e8i) q^{72} -6.87647e7i q^{73} +(3.77577e7 - 9.21716e7i) q^{74} +(-1.23540e7 - 1.23540e7i) q^{75} +(-2.20879e6 - 2.82765e8i) q^{76} +(-1.56682e8 + 1.56682e8i) q^{77} +(-2.13442e7 + 8.93890e6i) q^{78} -4.52979e8 q^{79} +(-3.38781e8 + 3.49535e8i) q^{80} -3.79374e8 q^{81} +(6.87220e8 - 2.87806e8i) q^{82} +(3.47281e8 - 3.47281e8i) q^{83} +(-2.29782e7 + 179492. i) q^{84} +(5.75745e8 + 5.75745e8i) q^{85} +(-2.03554e8 + 4.96904e8i) q^{86} -4.96607e6i q^{87} +(2.63033e8 + 6.14551e8i) q^{88} +5.59113e8i q^{89} +(7.59981e8 + 3.11322e8i) q^{90} +(-2.37612e8 - 2.37612e8i) q^{91} +(-7.54002e8 - 7.42314e8i) q^{92} +(2.88185e7 - 2.88185e7i) q^{93} +(-9.43138e7 - 2.25202e8i) q^{94} +1.02555e9 q^{95} +(-2.52733e7 + 6.45524e7i) q^{96} -6.64755e8 q^{97} +(2.23819e8 + 5.34435e8i) q^{98} +(7.97504e8 - 7.97504e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 2 q^{2} - 2 q^{3} + 168 q^{4} - 2 q^{5} - 2192 q^{6} - 716 q^{8}+O(q^{10}) \) 34 * q - 2 * q^2 - 2 * q^3 + 168 * q^4 - 2 * q^5 - 2192 * q^6 - 716 * q^8	\( 34 q - 2 q^{2} - 2 q^{3} + 168 q^{4} - 2 q^{5} - 2192 q^{6} - 716 q^{8} + 4684 q^{10} + 65858 q^{11} + 217156 q^{12} - 2 q^{13} - 133540 q^{14} + 404996 q^{15} - 817256 q^{16} - 4 q^{17} + 2179902 q^{18} - 480890 q^{19} - 3277988 q^{20} + 39364 q^{21} - 34300 q^{22} + 1863856 q^{24} - 6347768 q^{26} + 6364408 q^{27} + 3629528 q^{28} - 633402 q^{29} - 4677804 q^{30} - 11082256 q^{31} - 1655992 q^{32} - 4 q^{33} - 4528204 q^{34} + 23026556 q^{35} + 23564140 q^{36} - 1214778 q^{37} - 14996352 q^{38} - 11751288 q^{40} + 105399160 q^{42} - 34881078 q^{43} - 94223356 q^{44} + 3866882 q^{45} + 15432396 q^{46} + 97593616 q^{47} + 7831528 q^{48} - 126825626 q^{49} - 6289530 q^{50} - 27382140 q^{51} - 28284428 q^{52} - 74907850 q^{53} + 105311008 q^{54} + 26511256 q^{56} - 178271784 q^{58} + 94503354 q^{59} + 229034112 q^{60} - 90121106 q^{61} - 136788944 q^{62} - 153644796 q^{63} - 349292928 q^{64} + 62806084 q^{65} + 192273844 q^{66} + 406167670 q^{67} - 285757488 q^{68} + 382399540 q^{69} + 606051200 q^{70} + 882075684 q^{72} + 123910860 q^{74} - 1038797114 q^{75} - 453269100 q^{76} + 286751428 q^{77} - 1735024804 q^{78} + 1913565952 q^{79} - 700272856 q^{80} - 774840982 q^{81} - 674287584 q^{82} - 1637053442 q^{83} + 1281919912 q^{84} + 425303748 q^{85} + 243980676 q^{86} + 1781147128 q^{88} + 3084087192 q^{90} + 2019528196 q^{91} - 3131634504 q^{92} + 1071927184 q^{93} - 2068460272 q^{94} - 5087413260 q^{95} - 3896483152 q^{96} - 4 q^{97} - 3100632102 q^{98} + 3713751422 q^{99}+O(q^{100}) \) 34 * q - 2 * q^2 - 2 * q^3 + 168 * q^4 - 2 * q^5 - 2192 * q^6 - 716 * q^8 + 4684 * q^10 + 65858 * q^11 + 217156 * q^12 - 2 * q^13 - 133540 * q^14 + 404996 * q^15 - 817256 * q^16 - 4 * q^17 + 2179902 * q^18 - 480890 * q^19 - 3277988 * q^20 + 39364 * q^21 - 34300 * q^22 + 1863856 * q^24 - 6347768 * q^26 + 6364408 * q^27 + 3629528 * q^28 - 633402 * q^29 - 4677804 * q^30 - 11082256 * q^31 - 1655992 * q^32 - 4 * q^33 - 4528204 * q^34 + 23026556 * q^35 + 23564140 * q^36 - 1214778 * q^37 - 14996352 * q^38 - 11751288 * q^40 + 105399160 * q^42 - 34881078 * q^43 - 94223356 * q^44 + 3866882 * q^45 + 15432396 * q^46 + 97593616 * q^47 + 7831528 * q^48 - 126825626 * q^49 - 6289530 * q^50 - 27382140 * q^51 - 28284428 * q^52 - 74907850 * q^53 + 105311008 * q^54 + 26511256 * q^56 - 178271784 * q^58 + 94503354 * q^59 + 229034112 * q^60 - 90121106 * q^61 - 136788944 * q^62 - 153644796 * q^63 - 349292928 * q^64 + 62806084 * q^65 + 192273844 * q^66 + 406167670 * q^67 - 285757488 * q^68 + 382399540 * q^69 + 606051200 * q^70 + 882075684 * q^72 + 123910860 * q^74 - 1038797114 * q^75 - 453269100 * q^76 + 286751428 * q^77 - 1735024804 * q^78 + 1913565952 * q^79 - 700272856 * q^80 - 774840982 * q^81 - 674287584 * q^82 - 1637053442 * q^83 + 1281919912 * q^84 + 425303748 * q^85 + 243980676 * q^86 + 1781147128 * q^88 + 3084087192 * q^90 + 2019528196 * q^91 - 3131634504 * q^92 + 1071927184 * q^93 - 2068460272 * q^94 - 5087413260 * q^95 - 3896483152 * q^96 - 4 * q^97 - 3100632102 * q^98 + 3713751422 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more