LMFDB - Embedded newform 35.10.k.a.3.7

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			3.7
Character	$\chi$	$=$	35.3
Dual form			35.10.k.a.12.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-27.8720 - 7.46827i) q^{2} +(30.2294 + 112.818i) q^{3} +(277.667 + 160.311i) q^{4} +(211.406 + 1381.46i) q^{5} -3370.21i q^{6} +(3847.43 + 5054.79i) q^{7} +(3904.82 + 3904.82i) q^{8} +(5231.97 - 3020.68i) q^{9} +(4424.83 - 40082.9i) q^{10} +(-16070.5 + 27834.9i) q^{11} +(-9692.22 + 36171.8i) q^{12} +(113925. - 113925. i) q^{13} +(-69485.0 - 169621. i) q^{14} +(-149462. + 65611.0i) q^{15} +(-161752. - 280163. i) q^{16} +(178620. - 47861.0i) q^{17} +(-168385. + 45118.5i) q^{18} +(398832. + 690796. i) q^{19} +(-162763. + 417477. i) q^{20} +(-453964. + 586862. i) q^{21} +(655794. - 655794. i) q^{22} +(-283178. + 1.05683e6i) q^{23} +(-322492. + 558573. i) q^{24} +(-1.86374e6 + 584097. i) q^{25} +(-4.02615e6 + 2.32450e6i) q^{26} +(2.12453e6 + 2.12453e6i) q^{27} +(257967. + 2.02033e6i) q^{28} +1.92791e6i q^{29} +(4.65582e6 - 712482. i) q^{30} +(5.39281e6 + 3.11354e6i) q^{31} +(1.68423e6 + 6.28565e6i) q^{32} +(-3.62607e6 - 971601. i) q^{33} -5.33593e6 q^{34} +(-6.16962e6 + 6.38369e6i) q^{35} +1.93699e6 q^{36} +(-1.49786e7 - 4.01351e6i) q^{37} +(-5.95717e6 - 2.22324e7i) q^{38} +(1.62967e7 + 9.40889e6i) q^{39} +(-4.56885e6 + 6.21985e6i) q^{40} -1.99948e7i q^{41} +(1.70357e7 - 1.29667e7i) q^{42} +(-2.11886e7 - 2.11886e7i) q^{43} +(-8.92448e6 + 5.15255e6i) q^{44} +(5.27901e6 + 6.58917e6i) q^{45} +(1.57854e7 - 2.73412e7i) q^{46} +(-3.89633e6 + 1.45413e7i) q^{47} +(2.67176e7 - 2.67176e7i) q^{48} +(-1.07481e7 + 3.88959e7i) q^{49} +(5.63083e7 - 2.36101e6i) q^{50} +(1.07991e7 + 1.87047e7i) q^{51} +(4.98968e7 - 1.33698e7i) q^{52} +(3.60954e7 - 9.67172e6i) q^{53} +(-4.33483e7 - 7.50814e7i) q^{54} +(-4.18502e7 - 1.63163e7i) q^{55} +(-4.71449e6 + 3.47615e7i) q^{56} +(-6.58776e7 + 6.58776e7i) q^{57} +(1.43982e7 - 5.37347e7i) q^{58} +(-5.81237e7 + 1.00673e8i) q^{59} +(-5.20190e7 - 5.74249e6i) q^{60} +(8.40056e7 - 4.85006e7i) q^{61} +(-1.27056e8 - 1.27056e8i) q^{62} +(3.53985e7 + 1.48246e7i) q^{63} -2.21377e7i q^{64} +(1.81468e8 + 1.33299e8i) q^{65} +(9.38094e7 + 5.41609e7i) q^{66} +(-44818.6 - 167265. i) q^{67} +(5.72695e7 + 1.53453e7i) q^{68} -1.27790e8 q^{69} +(2.19635e8 - 1.31850e8i) q^{70} -3.87720e8 q^{71} +(3.22251e7 + 8.63468e6i) q^{72} +(-7.64135e7 - 2.85179e8i) q^{73} +(3.87510e8 + 2.23729e8i) q^{74} +(-1.22236e8 - 1.92606e8i) q^{75} +2.55748e8i q^{76} +(-2.02529e8 + 2.58600e7i) q^{77} +(-3.83953e8 - 3.83953e8i) q^{78} +(-1.45334e7 + 8.39084e6i) q^{79} +(3.52838e8 - 2.82682e8i) q^{80} +(-1.16005e8 + 2.00927e8i) q^{81} +(-1.49326e8 + 5.57294e8i) q^{82} +(1.73477e8 - 1.73477e8i) q^{83} +(-2.20131e8 + 9.01767e7i) q^{84} +(1.03879e8 + 2.36638e8i) q^{85} +(4.32326e8 + 7.48811e8i) q^{86} +(-2.17502e8 + 5.82796e7i) q^{87} +(-1.71442e8 + 4.59378e7i) q^{88} +(1.94079e8 + 3.36154e8i) q^{89} +(-9.79268e7 - 2.23078e8i) q^{90} +(1.01419e9 + 1.37548e8i) q^{91} +(-2.48051e8 + 2.48051e8i) q^{92} +(-1.88241e8 + 7.02525e8i) q^{93} +(2.17197e8 - 3.76196e8i) q^{94} +(-8.69993e8 + 6.97008e8i) q^{95} +(-6.58219e8 + 3.80023e8i) q^{96} +(-1.03254e9 - 1.03254e9i) q^{97} +(5.90057e8 - 1.00384e9i) q^{98} +1.94175e8i 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 $

$2$	−27.8720	−	7.46827i	−1.23178	−	0.330054i	−0.416507	−	0.909132i	$-0.636746\pi$
$2$	−27.8720	−	7.46827i	−1.23178	−	0.330054i	−0.815272	+	0.579078i	$0.803413\pi$
$3$	30.2294	+	112.818i	0.215469	+	0.804140i	0.986001	+	0.166739i	$0.0533237\pi$
$3$	30.2294	+	112.818i	0.215469	+	0.804140i	−0.770533	+	0.637401i	$0.780010\pi$
$4$	277.667	+	160.311i	0.542318	+	0.313108i
$5$	211.406	+	1381.46i	0.151269	+	0.988493i
$5$	211.406	+	1381.46i	0.151269	+	0.988493i
$6$		−	3370.21i		−	1.06164i
$7$	3847.43	+	5054.79i	0.605661	+	0.795722i
$7$	3847.43	+	5054.79i	0.605661	+	0.795722i
$8$	3904.82	+	3904.82i	0.337051	+	0.337051i
$9$	5231.97	−	3020.68i	0.265812	−	0.153466i
$10$	4424.83	−	40082.9i	0.139926	−	1.26753i
$11$	−16070.5	+	27834.9i	−0.330949	+	0.573221i	−0.982698	−	0.185214i	$-0.940702\pi$
$11$	−16070.5	+	27834.9i	−0.330949	+	0.573221i	0.651749	+	0.758435i	$0.274036\pi$
$12$	−9692.22	+	36171.8i	−0.134930	+	0.503564i
$13$	113925.	−	113925.i	1.10631	−	1.10631i	0.112674	−	0.993632i	$-0.464059\pi$
$13$	113925.	−	113925.i	1.10631	−	1.10631i	0.993632	−	0.112674i	$-0.0359414\pi$
$14$	−69485.0	−	169621.i	−0.483409	−	1.18006i
$15$	−149462.	+	65611.0i	−0.762292	+	0.334631i
$16$	−161752.	−	280163.i	−0.617035	−	1.06874i
$17$	178620.	−	47861.0i	0.518692	−	0.138983i	0.0100305	−	0.999950i	$-0.496807\pi$
$17$	178620.	−	47861.0i	0.518692	−	0.138983i	0.508662	+	0.860967i	$0.330140\pi$
$18$	−168385.	+	45118.5i	−0.378073	+	0.101304i
$19$	398832.	+	690796.i	0.702099	+	1.21607i	0.967728	+	0.251996i	$0.0810869\pi$
$19$	398832.	+	690796.i	0.702099	+	1.21607i	−0.265629	+	0.964075i	$0.585580\pi$
$20$	−162763.	+	417477.i	−0.227468	+	0.583441i
$21$	−453964.	+	586862.i	−0.509371	+	0.658490i
$22$	655794.	−	655794.i	0.596850	−	0.596850i
$23$	−283178.	+	1.05683e6i	−0.211001	+	0.787465i	0.776536	+	0.630073i	$0.216975\pi$
$23$	−283178.	+	1.05683e6i	−0.211001	+	0.787465i	−0.987536	+	0.157392i	$0.949692\pi$
$24$	−322492.	+	558573.i	−0.198412	+	0.343660i
$25$	−1.86374e6	+	584097.i	−0.954235	+	0.299057i
$26$	−4.02615e6	+	2.32450e6i	−1.72786	+	0.997583i
$27$	2.12453e6	+	2.12453e6i	0.769353	+	0.769353i
$28$	257967.	+	2.02033e6i	0.0793145	+	0.621172i
$29$			1.92791e6i			0.506169i	0.967444	+	0.253085i	$0.0814452\pi$
$29$			1.92791e6i			0.506169i	−0.967444	+	0.253085i	$0.918555\pi$
$30$	4.65582e6	−	712482.i	1.04942	−	0.160594i
$31$	5.39281e6	+	3.11354e6i	1.04879	+	0.605518i	0.922310	−	0.386452i	$-0.126299\pi$
$31$	5.39281e6	+	3.11354e6i	1.04879	+	0.605518i	0.126478	+	0.991969i	$0.459633\pi$
$32$	1.68423e6	+	6.28565e6i	0.283941	+	1.05968i
$33$	−3.62607e6	−	971601.i	−0.532259	−	0.142618i
$34$	−5.33593e6			−0.684786
$35$	−6.16962e6	+	6.38369e6i	−0.694948	+	0.719060i
$36$	1.93699e6			0.192206
$37$	−1.49786e7	−	4.01351e6i	−1.31391	−	0.352060i	−0.467214	−	0.884144i	$-0.654742\pi$
$37$	−1.49786e7	−	4.01351e6i	−1.31391	−	0.352060i	−0.846691	+	0.532084i	$0.821409\pi$
$38$	−5.95717e6	−	2.22324e7i	−0.463461	−	1.72966i
$39$	1.62967e7	+	9.40889e6i	1.12800	+	0.651250i
$40$	−4.56885e6	+	6.21985e6i	−0.282187	+	0.384158i
$41$		−	1.99948e7i		−	1.10507i	−0.833490	−	0.552534i	$-0.813661\pi$
$41$		−	1.99948e7i		−	1.10507i	0.833490	−	0.552534i	$-0.186339\pi$
$42$	1.70357e7	−	1.29667e7i	0.844770	−	0.642994i
$43$	−2.11886e7	−	2.11886e7i	−0.945136	−	0.945136i	0.0534354	−	0.998571i	$-0.482983\pi$
$43$	−2.11886e7	−	2.11886e7i	−0.945136	−	0.945136i	−0.998571	+	0.0534354i	$0.982983\pi$
$44$	−8.92448e6	+	5.15255e6i	−0.358960	+	0.207245i
$45$	5.27901e6	+	6.58917e6i	0.191910	+	0.239538i
$46$	1.57854e7	−	2.73412e7i	0.519812	−	0.900341i
$47$	−3.89633e6	+	1.45413e7i	−0.116470	+	0.434673i	−0.999393	−	0.0348458i	$-0.988906\pi$
$47$	−3.89633e6	+	1.45413e7i	−0.116470	+	0.434673i	0.882922	+	0.469519i	$0.155573\pi$
$48$	2.67176e7	−	2.67176e7i	0.726461	−	0.726461i
$49$	−1.07481e7	+	3.88959e7i	−0.266349	+	0.963877i
$50$	5.63083e7	−	2.36101e6i	1.27411	−	0.0534234i
$51$	1.07991e7	+	1.87047e7i	0.223524	+	0.387154i
$52$	4.98968e7	−	1.33698e7i	0.946362	−	0.253577i
$53$	3.60954e7	−	9.67172e6i	0.628362	−	0.168369i	0.0694357	−	0.997586i	$-0.477880\pi$
$53$	3.60954e7	−	9.67172e6i	0.628362	−	0.168369i	0.558926	+	0.829217i	$0.311213\pi$
$54$	−4.33483e7	−	7.50814e7i	−0.693745	−	1.20160i
$55$	−4.18502e7	−	1.63163e7i	−0.616687	−	0.240430i
$56$	−4.71449e6	+	3.47615e7i	−0.0640603	+	0.472338i
$57$	−6.58776e7	+	6.58776e7i	−0.826611	+	0.826611i
$58$	1.43982e7	−	5.37347e7i	0.167063	−	0.623489i
$59$	−5.81237e7	+	1.00673e8i	−0.624480	+	1.08163i	0.364161	+	0.931336i	$0.381356\pi$
$59$	−5.81237e7	+	1.00673e8i	−0.624480	+	1.08163i	−0.988641	+	0.150296i	$0.951977\pi$
$60$	−5.20190e7	−	5.74249e6i	−0.518180	−	0.0572031i
$61$	8.40056e7	−	4.85006e7i	0.776826	−	0.448501i	−0.0584781	−	0.998289i	$-0.518625\pi$
$61$	8.40056e7	−	4.85006e7i	0.776826	−	0.448501i	0.835304	+	0.549788i	$0.185291\pi$
$62$	−1.27056e8	−	1.27056e8i	−1.09202	−	1.09202i
$63$	3.53985e7	+	1.48246e7i	0.283108	+	0.118564i
$64$		−	2.21377e7i		−	0.164939i
$65$	1.81468e8	+	1.33299e8i	1.26093	+	0.926225i
$66$	9.38094e7	+	5.41609e7i	0.608554	+	0.351349i
$67$	−44818.6	−	167265.i	−0.000271720	−	0.00101407i	0.965790	−	0.259326i	$-0.0835004\pi$
$67$	−44818.6	−	167265.i	−0.000271720	−	0.00101407i	−0.966062	+	0.258312i	$0.916834\pi$
$68$	5.72695e7	+	1.53453e7i	0.324813	+	0.0870333i
$69$	−1.27790e8			−0.678696
$70$	2.19635e8	−	1.31850e8i	1.09335	−	0.656353i
$71$	−3.87720e8			−1.81074			−0.905368	−	0.424627i	$-0.860405\pi$
$71$	−3.87720e8			−1.81074			−0.905368	+	0.424627i	$0.860405\pi$
$72$	3.22251e7	+	8.63468e6i	0.141318	+	0.0378661i
$73$	−7.64135e7	−	2.85179e8i	−0.314932	−	1.17534i	−0.924052	−	0.382266i	$-0.875144\pi$
$73$	−7.64135e7	−	2.85179e8i	−0.314932	−	1.17534i	0.609120	−	0.793078i	$-0.291523\pi$
$74$	3.87510e8	+	2.23729e8i	1.50224	+	0.867320i
$75$	−1.22236e8	−	1.92606e8i	−0.446092	−	0.702901i
$76$			2.55748e8i			0.879330i
$77$	−2.02529e8	+	2.58600e7i	−0.656568	+	0.0838340i
$78$	−3.83953e8	−	3.83953e8i	−1.17450	−	1.17450i
$79$	−1.45334e7	+	8.39084e6i	−0.0419802	+	0.0242373i	−0.520843	−	0.853652i	$-0.674382\pi$
$79$	−1.45334e7	+	8.39084e6i	−0.0419802	+	0.0242373i	0.478863	+	0.877890i	$0.341049\pi$
$80$	3.52838e8	−	2.82682e8i	0.963099	−	0.771601i
$81$	−1.16005e8	+	2.00927e8i	−0.299430	+	0.518628i
$82$	−1.49326e8	+	5.57294e8i	−0.364732	+	1.36120i
$83$	1.73477e8	−	1.73477e8i	0.401227	−	0.401227i	−0.477438	−	0.878665i	$-0.658434\pi$
$83$	1.73477e8	−	1.73477e8i	0.401227	−	0.401227i	0.878665	+	0.477438i	$0.158434\pi$
$84$	−2.20131e8	+	9.01767e7i	−0.482419	+	0.197623i
$85$	1.03879e8	+	2.36638e8i	0.215846	+	0.491699i
$86$	4.32326e8	+	7.48811e8i	0.852253	+	1.47614i
$87$	−2.17502e8	+	5.82796e7i	−0.407031	+	0.109064i
$88$	−1.71442e8	+	4.59378e7i	−0.304752	+	0.0816579i
$89$	1.94079e8	+	3.36154e8i	0.327886	+	0.567915i	0.982092	−	0.188401i	$-0.0603306\pi$
$89$	1.94079e8	+	3.36154e8i	0.327886	+	0.567915i	−0.654206	+	0.756316i	$0.726997\pi$
$90$	−9.79268e7	−	2.23078e8i	−0.157330	−	0.358398i
$91$	1.01419e9	+	1.37548e8i	1.55036	+	0.210266i
$92$	−2.48051e8	+	2.48051e8i	−0.360991	+	0.360991i
$93$	−1.88241e8	+	7.02525e8i	−0.260940	+	0.973842i
$94$	2.17197e8	−	3.76196e8i	0.286931	−	0.496980i
$95$	−8.69993e8	+	6.97008e8i	−1.09587	+	0.877974i
$96$	−6.58219e8	+	3.80023e8i	−0.790951	+	0.456656i
$97$	−1.03254e9	−	1.03254e9i	−1.18423	−	1.18423i	−0.978638	−	0.205589i	$-0.934089\pi$
$97$	−1.03254e9	−	1.03254e9i	−1.18423	−	1.18423i	−0.205589	−	0.978638i	$-0.565911\pi$
$98$	5.90057e8	−	1.00384e9i	0.646214	−	1.09937i
$99$			1.94175e8i			0.203158i
$100$	−6.11136e8	−	1.36594e8i	−0.611136	−	0.136594i
$101$	1.28616e9	+	7.42565e8i	1.22984	+	0.710049i	0.966997	−	0.254789i	$-0.0820061\pi$
$101$	1.28616e9	+	7.42565e8i	1.22984	+	0.710049i	0.262844	+	0.964838i	$0.415339\pi$
$102$	−1.61302e8	−	6.01987e8i	−0.147550	−	0.550664i
$103$	−4.15181e8	−	1.11247e8i	−0.363471	−	0.0973919i	0.0724611	−	0.997371i	$-0.476915\pi$
$103$	−4.15181e8	−	1.11247e8i	−0.363471	−	0.0973919i	−0.435932	+	0.899979i	$0.643581\pi$
$104$	8.89715e8			0.745763
$105$	−9.06696e8	−	5.03067e8i	−0.727964	−	0.403900i
$106$	−1.07828e9			−0.829574
$107$	1.19745e9	+	3.20855e8i	0.883138	+	0.236636i	0.671761	−	0.740768i	$-0.265538\pi$
$107$	1.19745e9	+	3.20855e8i	0.883138	+	0.236636i	0.211378	+	0.977404i	$0.432205\pi$
$108$	2.49326e8	+	9.30498e8i	0.176344	+	0.658125i
$109$	−1.01825e9	−	5.87887e8i	−0.690931	−	0.398909i	0.113029	−	0.993592i	$-0.463945\pi$
$109$	−1.01825e9	−	5.87887e8i	−0.690931	−	0.398909i	−0.803961	+	0.594682i	$0.797278\pi$
$110$	1.04459e9	+	7.67315e8i	0.680267	+	0.499697i
$111$		−	1.81118e9i		−	1.13242i
$112$	7.93833e8	−	1.89553e9i	0.476703	−	1.13828i
$113$	9.99500e8	+	9.99500e8i	0.576673	+	0.576673i	0.933985	−	0.357312i	$-0.116307\pi$
$113$	9.99500e8	+	9.99500e8i	0.576673	+	0.576673i	−0.357312	+	0.933985i	$0.616307\pi$
$114$	2.32813e9	−	1.34415e9i	1.29103	−	0.745375i
$115$	−1.51984e9	−	1.67778e8i	−0.810321	−	0.0894531i
$116$	−3.09066e8	+	5.35317e8i	−0.158486	+	0.274505i
$117$	2.51922e8	−	9.40185e8i	0.124288	−	0.463849i
$118$	2.37188e9	−	2.37188e9i	1.12622	−	1.12622i
$119$	9.29155e8	+	7.18743e8i	0.424744	+	0.328558i
$120$	−8.39822e8	−	3.27425e8i	−0.369719	−	0.144144i
$121$	6.62454e8	+	1.14740e9i	0.280945	+	0.486611i
$122$	−2.70362e9	+	7.24432e8i	−1.10491	+	0.296059i
$123$	2.25576e9	−	6.04430e8i	0.888629	−	0.238108i
$124$	9.98270e8	+	1.72905e9i	0.379184	+	0.656767i
$125$	−1.20091e9	−	2.45120e9i	−0.439963	−	0.898016i
$126$	−8.75913e8	−	6.77557e8i	−0.309595	−	0.239485i
$127$	2.22075e9	−	2.22075e9i	0.757501	−	0.757501i	−0.218366	−	0.975867i	$-0.570073\pi$
$127$	2.22075e9	−	2.22075e9i	0.757501	−	0.757501i	0.975867	+	0.218366i	$0.0700726\pi$
$128$	6.96997e8	−	2.60123e9i	0.229502	−	0.856513i
$129$	1.74993e9	−	3.03097e9i	0.556374	−	0.963668i
$130$	−4.06235e9	−	5.07055e9i	−1.24748	−	1.55708i
$131$	−4.29311e9	+	2.47863e9i	−1.27365	+	0.735345i	−0.975674	−	0.219227i	$-0.929646\pi$
$131$	−4.29311e9	+	2.47863e9i	−1.27365	+	0.735345i	−0.297980	+	0.954572i	$0.596313\pi$
$132$	−8.51080e8	−	8.51080e8i	−0.243999	−	0.243999i
$133$	−1.95735e9	+	4.67380e9i	−0.542421	+	1.29520i
$134$			4.99673e6i			0.00133880i
$135$	−2.48582e9	+	3.38409e9i	−0.644121	+	0.876880i
$136$	8.84366e8	+	5.10589e8i	0.221670	+	0.127981i
$137$	3.57546e8	+	1.33438e9i	0.0867140	+	0.323621i	0.995633	−	0.0933512i	$-0.0297579\pi$
$137$	3.57546e8	+	1.33438e9i	0.0867140	+	0.323621i	−0.908919	+	0.416972i	$0.863091\pi$
$138$	3.56175e9	+	9.54369e8i	0.836003	+	0.224006i
$139$	−1.52308e9			−0.346065			−0.173032	−	0.984916i	$-0.555357\pi$
$139$	−1.52308e9			−0.346065			−0.173032	+	0.984916i	$0.555357\pi$
$140$	−2.73647e9	+	7.83480e8i	−0.602026	+	0.172366i
$141$	−1.75830e9			−0.374634
$142$	1.08065e10	+	2.89560e9i	2.23043	+	0.597641i
$143$	1.34026e9	+	5.00193e9i	0.268027	+	1.00029i
$144$	−1.69256e9	−	9.77201e8i	−0.328030	−	0.189388i
$145$	−2.66333e9	+	4.07571e8i	−0.500345	+	0.0765680i
$146$			8.51919e9i			1.55171i
$147$	−4.71305e9	−	3.67786e7i	−0.832481	−	0.00649631i
$148$	−3.51566e9	−	3.51566e9i	−0.602322	−	0.602322i
$149$	2.32473e9	−	1.34218e9i	0.386397	−	0.223087i	−0.294201	−	0.955744i	$-0.595053\pi$
$149$	2.32473e9	−	1.34218e9i	0.386397	−	0.223087i	0.680598	+	0.732657i	$0.261720\pi$
$150$	1.96853e9	+	6.28120e9i	0.317491	+	1.01305i
$151$	3.84418e7	−	6.65831e7i	0.00601738	−	0.0104224i	−0.863001	−	0.505202i	$-0.831418\pi$
$151$	3.84418e7	−	6.65831e7i	0.00601738	−	0.0104224i	0.869018	+	0.494780i	$0.164751\pi$
$152$	−1.14007e9	+	4.25480e9i	−0.173235	+	0.646521i
$153$	7.89961e8	−	7.89961e8i	0.116545	−	0.116545i
$154$	5.83802e9	+	7.91775e8i	0.836416	+	0.113438i
$155$	−3.16116e9	+	8.10817e9i	−0.439900	+	1.12832i
$156$	3.01670e9	+	5.22508e9i	0.407823	+	0.706370i
$157$	−3.57964e9	+	9.59162e8i	−0.470209	+	0.125992i	−0.486140	−	0.873881i	$-0.661596\pi$
$157$	−3.57964e9	+	9.59162e8i	−0.470209	+	0.125992i	0.0159308	+	0.999873i	$0.494929\pi$
$158$	4.67739e8	−	1.25330e8i	0.0597099	−	0.0159992i
$159$	2.18228e9	+	3.77982e9i	0.270784	+	0.469012i
$160$	−8.32732e9	+	3.65552e9i	−1.00454	+	0.440971i
$161$	−6.43157e9	+	2.63469e9i	−0.754398	+	0.309039i
$162$	4.73387e9	−	4.73387e9i	0.540007	−	0.540007i
$163$	2.85643e9	−	1.06603e10i	0.316941	−	1.18284i	−0.605227	−	0.796053i	$-0.706918\pi$
$163$	2.85643e9	−	1.06603e10i	0.316941	−	1.18284i	0.922169	−	0.386788i	$-0.126415\pi$
$164$	3.20538e9	−	5.55189e9i	0.346005	−	0.599299i
$165$	5.75658e8	−	5.21467e9i	0.0604626	−	0.547708i
$166$	−6.13072e9	+	3.53957e9i	−0.626650	+	0.361797i
$167$	7.44429e9	+	7.44429e9i	0.740626	+	0.740626i	0.972699	−	0.232072i	$-0.0745505\pi$
$167$	7.44429e9	+	7.44429e9i	0.740626	+	0.740626i	−0.232072	+	0.972699i	$0.574551\pi$
$168$	−4.06423e9	+	5.18942e8i	−0.393629	+	0.0502605i
$169$		−	1.53535e10i		−	1.44782i
$170$	−1.12804e9	−	7.37137e9i	−0.103587	−	0.676906i
$171$	4.17335e9	+	2.40948e9i	0.373252	+	0.215497i
$172$	−2.48661e9	−	9.28014e9i	−0.216635	−	0.808494i
$173$	7.93112e9	+	2.12514e9i	0.673173	+	0.180376i	0.579184	−	0.815197i	$-0.303371\pi$
$173$	7.93112e9	+	2.12514e9i	0.673173	+	0.180376i	0.0939895	+	0.995573i	$0.470038\pi$
$174$	6.49747e9			0.537369
$175$	−1.01231e10	−	7.17354e9i	−0.815910	−	0.578179i
$176$	1.03977e10			0.816829
$177$	−1.31148e10	−	3.51409e9i	−1.00434	−	0.269112i
$178$	−2.89886e9	−	1.08187e10i	−0.216440	−	0.807765i
$179$	−2.95856e9	−	1.70813e9i	−0.215398	−	0.124360i	0.388419	−	0.921483i	$-0.373021\pi$
$179$	−2.95856e9	−	1.70813e9i	−0.215398	−	0.124360i	−0.603818	+	0.797122i	$0.706355\pi$
$180$	4.09491e8	+	2.67588e9i	0.0290749	+	0.189994i
$181$			1.64802e9i			0.114133i	0.998370	+	0.0570663i	$0.0181747\pi$
$181$			1.64802e9i			0.114133i	−0.998370	+	0.0570663i	$0.981825\pi$
$182$	−2.72402e10	−	1.14080e10i	−1.84030	−	0.770703i
$183$	8.01117e9	+	8.01117e9i	0.528039	+	0.528039i
$184$	−5.23250e9	+	3.02098e9i	−0.336534	+	0.194298i
$185$	2.37794e9	−	2.15408e10i	0.149255	−	1.35204i
$186$	1.04933e10	−	1.81749e10i	0.642841	−	1.11343i
$187$	−1.53830e9	+	5.74101e9i	−0.0919927	+	0.343322i
$188$	−3.41301e9	+	3.41301e9i	−0.199264	+	0.199264i
$189$	−2.56506e9	+	1.89130e10i	−0.146224	+	1.07816i
$190$	2.94539e10	−	1.29296e10i	1.63965	−	0.719773i
$191$	7.06347e9	+	1.22343e10i	0.384033	+	0.665164i	0.991634	−	0.129078i	$-0.0412017\pi$
$191$	7.06347e9	+	1.22343e10i	0.384033	+	0.665164i	−0.607602	+	0.794242i	$0.707868\pi$
$192$	2.49752e9	−	6.69209e8i	0.132634	−	0.0355391i
$193$	1.95288e10	−	5.23273e9i	1.01314	−	0.271469i	0.286198	−	0.958171i	$-0.407609\pi$
$193$	1.95288e10	−	5.23273e9i	1.01314	−	0.271469i	0.726940	+	0.686701i	$0.240942\pi$
$194$	2.10677e10	+	3.64903e10i	1.06785	+	1.84957i
$195$	−9.55281e9	+	2.45023e10i	−0.473124	+	1.21353i
$196$	−9.21984e9	+	9.07706e9i	−0.446243	+	0.439332i
$197$	1.76914e10	−	1.76914e10i	0.836882	−	0.836882i	−0.151565	−	0.988447i	$-0.548431\pi$
$197$	1.76914e10	−	1.76914e10i	0.836882	−	0.836882i	0.988447	+	0.151565i	$0.0484314\pi$
$198$	1.45015e9	−	5.41204e9i	0.0670532	−	0.250246i
$199$	−1.72880e9	+	2.99437e9i	−0.0781459	+	0.135353i	−0.902450	−	0.430795i	$-0.858233\pi$
$199$	−1.72880e9	+	2.99437e9i	−0.0781459	+	0.135353i	0.824304	+	0.566147i	$0.191567\pi$
$200$	−9.55835e9	−	4.99677e9i	−0.422424	−	0.220828i
$201$	1.75156e7	−	1.01127e7i	0.000756909	−	0.000437001i
$202$	−3.03021e10	−	3.03021e10i	−1.28054	−	1.28054i
$203$	−9.74518e9	+	7.41751e9i	−0.402770	+	0.306567i
$204$			6.92489e9i			0.279948i
$205$	2.76220e10	−	4.22701e9i	1.09235	−	0.167163i
$206$	1.07411e10	+	6.20137e9i	0.415572	+	0.239930i
$207$	1.71078e9	+	6.38470e9i	0.0647630	+	0.241699i
$208$	−5.03453e10	−	1.34900e10i	−1.86498	−	0.499719i
$209$	−2.56376e10			−0.929436
$210$	2.15144e10	+	2.07929e10i	0.763382	+	0.737783i
$211$	1.97828e10			0.687095			0.343548	−	0.939135i	$-0.388371\pi$
$211$	1.97828e10			0.687095			0.343548	+	0.939135i	$0.388371\pi$
$212$	1.15730e10	+	3.10097e9i	0.393490	+	0.105435i
$213$	−1.17205e10	−	4.37416e10i	−0.390157	−	1.45609i
$214$	−3.09789e10	−	1.78857e10i	−1.00973	−	0.582967i
$215$	2.47918e10	−	3.37506e10i	0.791290	−	1.07723i
$216$			1.65918e10i			0.518623i
$217$	5.01019e9	+	3.92386e10i	0.153386	+	1.20128i
$218$	2.39901e10	+	2.39901e10i	0.719413	+	0.719413i
$219$	2.98633e10	−	1.72416e10i	0.877283	−	0.506499i
$220$	−9.00472e9	−	1.12395e10i	−0.259160	−	0.323479i
$221$	1.48967e10	−	2.58019e10i	0.420074	−	0.727590i
$222$	−1.35264e10	+	5.04811e10i	−0.373760	+	1.39489i
$223$	2.01267e10	−	2.01267e10i	0.545005	−	0.545005i	−0.379987	−	0.924992i	$-0.624072\pi$
$223$	2.01267e10	−	2.01267e10i	0.545005	−	0.545005i	0.924992	+	0.379987i	$0.124072\pi$
$224$	−2.52926e10	+	3.26970e10i	−0.671240	+	0.867746i
$225$	−7.98666e9	+	8.68573e9i	−0.207751	+	0.225936i
$226$	−2.03935e10	−	3.53226e10i	−0.520001	−	0.900668i
$227$	−2.99499e10	+	8.02504e9i	−0.748650	+	0.200600i	−0.612919	−	0.790146i	$-0.710005\pi$
$227$	−2.99499e10	+	8.02504e9i	−0.748650	+	0.200600i	−0.135731	+	0.990746i	$0.543338\pi$
$228$	−2.88529e10	+	7.73112e9i	−0.707104	+	0.189468i
$229$	−3.24544e9	−	5.62127e9i	−0.0779855	−	0.135075i	0.824395	−	0.566015i	$-0.191515\pi$
$229$	−3.24544e9	−	5.62127e9i	−0.0779855	−	0.135075i	−0.902381	+	0.430940i	$0.858182\pi$
$230$	4.11079e10	+	1.60269e10i	0.968612	+	0.377636i
$231$	−9.03981e9	−	2.20672e10i	−0.208884	−	0.509909i
$232$	−7.52814e9	+	7.52814e9i	−0.170605	+	0.170605i
$233$	−3.05343e9	+	1.13956e10i	−0.0678713	+	0.253299i	−0.991523	−	0.129935i	$-0.958523\pi$
$233$	−3.05343e9	+	1.13956e10i	−0.0678713	+	0.253299i	0.923651	+	0.383234i	$0.125190\pi$
$234$	−1.40431e10	+	2.43234e10i	−0.306191	+	0.530338i
$235$	−2.09119e10	−	2.30851e9i	−0.447290	−	0.0493773i
$236$	−3.22780e10	+	1.86357e10i	−0.677334	+	0.391059i
$237$	−1.38597e9	−	1.38597e9i	−0.0285355	−	0.0285355i
$238$	−2.05296e10	−	2.69720e10i	−0.414748	−	0.544900i
$239$		−	8.24519e10i		−	1.63459i	−0.576216	−	0.817297i	$-0.695471\pi$
$239$		−	8.24519e10i		−	1.63459i	0.576216	−	0.817297i	$-0.304529\pi$
$240$	4.25576e10	+	3.12611e10i	0.827993	+	0.608210i
$241$	4.02639e10	+	2.32463e10i	0.768845	+	0.443893i	0.832462	−	0.554082i	$-0.186930\pi$
$241$	4.02639e10	+	2.32463e10i	0.768845	+	0.443893i	−0.0636176	+	0.997974i	$0.520264\pi$
$242$	−9.89477e9	−	3.69278e10i	−0.185454	−	0.692125i
$243$	3.09484e10	+	8.29259e9i	0.569390	+	0.152567i
$244$	3.11008e10			0.561716
$245$	−5.60054e10	−	6.62530e9i	−0.993075	−	0.117478i
$246$	−6.73867e10			−1.17318
$247$	1.24136e11	+	3.32622e10i	2.12208	+	0.568610i
$248$	8.90013e9	+	3.32157e10i	0.149405	+	0.557585i
$249$	2.48154e10	+	1.43272e10i	0.409095	+	0.236191i
$250$	1.51655e10	+	7.72886e10i	0.245543	+	1.25137i
$251$		−	8.82907e10i		−	1.40405i	−0.712151	−	0.702026i	$-0.752279\pi$
$251$		−	8.82907e10i		−	1.40405i	0.712151	−	0.702026i	$-0.247721\pi$
$252$	7.45245e9	+	9.79109e9i	0.116412	+	0.152943i
$253$	−2.48660e10	−	2.48660e10i	−0.381561	−	0.381561i
$254$	−7.84819e10	+	4.53116e10i	−1.18309	+	0.683058i
$255$	−2.35568e10	+	1.88729e10i	−0.348887	+	0.279516i
$256$	−4.45206e10	+	7.71120e10i	−0.647861	+	1.12213i
$257$	−1.44808e10	+	5.40431e10i	−0.207059	+	0.772754i	0.781753	+	0.623588i	$0.214326\pi$
$257$	−1.44808e10	+	5.40431e10i	−0.207059	+	0.772754i	−0.988812	+	0.149166i	$0.952341\pi$
$258$	−7.14101e10	+	7.14101e10i	−1.00339	+	1.00339i
$259$	−3.73418e10	−	9.11554e10i	−0.515640	−	1.25873i
$260$	2.90183e10	+	6.61040e10i	0.393815	+	0.897114i
$261$	5.82360e9	+	1.00868e10i	0.0776800	+	0.134546i
$262$	1.38169e11	−	3.70222e10i	1.81156	−	0.485407i
$263$	−2.14102e10	+	5.73686e9i	−0.275944	+	0.0739390i	−0.394137	−	0.919052i	$-0.628956\pi$
$263$	−2.14102e10	+	5.73686e9i	−0.275944	+	0.0739390i	0.118193	+	0.992991i	$0.462290\pi$
$264$	−1.03652e10	−	1.79530e10i	−0.131329	−	0.227468i
$265$	2.09919e10	+	4.78196e10i	0.261484	+	0.595662i
$266$	8.94605e10	−	1.15650e11i	1.09563	−	1.41638i
$267$	−3.20572e10	+	3.20572e10i	−0.386034	+	0.386034i
$268$	1.43698e7	−	5.36289e7i	0.000170155	−	0.000635027i
$269$	−5.58211e10	+	9.66849e10i	−0.649999	+	1.12583i	0.333123	+	0.942883i	$0.391897\pi$
$269$	−5.58211e10	+	9.66849e10i	−0.649999	+	1.12583i	−0.983123	+	0.182948i	$0.941436\pi$
$270$	9.45579e10	−	7.57566e10i	1.08283	−	0.867528i
$271$	3.64919e10	−	2.10686e10i	0.410993	−	0.237287i	−0.280223	−	0.959935i	$-0.590408\pi$
$271$	3.64919e10	−	2.10686e10i	0.410993	−	0.237287i	0.691216	+	0.722648i	$0.257075\pi$
$272$	−4.23010e10	−	4.23010e10i	−0.468587	−	0.468587i
$273$	1.51404e10	+	1.18576e11i	0.164971	+	1.29201i
$274$		−	3.98620e10i		−	0.427250i
$275$	1.36929e10	−	6.12637e10i	0.144377	−	0.645960i
$276$	−3.54830e10	−	2.04861e10i	−0.368069	−	0.212505i
$277$	1.06778e10	+	3.98502e10i	0.108974	+	0.406697i	0.998766	−	0.0496702i	$-0.0158170\pi$
$277$	1.06778e10	+	3.98502e10i	0.108974	+	0.406697i	−0.889792	+	0.456367i	$0.849150\pi$
$278$	4.24514e10	+	1.13748e10i	0.426275	+	0.114220i
$279$	3.76200e10			0.371706
$280$	−4.90183e10	+	8.35893e8i	−0.476593	+	0.00812717i
$281$	−1.21048e11			−1.15818			−0.579092	−	0.815262i	$-0.696593\pi$
$281$	−1.21048e11			−1.15818			−0.579092	+	0.815262i	$0.696593\pi$
$282$	4.90073e10	+	1.31315e10i	0.461466	+	0.123649i
$283$	2.22094e10	+	8.28867e10i	0.205825	+	0.768150i	0.989196	+	0.146596i	$0.0468317\pi$
$283$	2.22094e10	+	8.28867e10i	0.205825	+	0.768150i	−0.783371	+	0.621554i	$0.786502\pi$
$284$	−1.07657e11	−	6.21558e10i	−0.981996	−	0.566956i
$285$	−1.04934e11	−	7.70804e10i	−0.942139	−	0.692057i
$286$		−	1.49423e11i		−	1.32060i
$287$	1.01069e11	−	7.69286e10i	0.879328	−	0.669297i
$288$	2.77988e10	+	2.77988e10i	0.238100	+	0.238100i
$289$	−7.30857e10	+	4.21961e10i	−0.616300	+	0.355821i
$290$	7.72762e10	+	8.53069e9i	0.641586	+	0.0708260i
$291$	8.52759e10	−	1.47702e11i	0.697121	−	1.20745i
$292$	2.44999e10	−	9.14348e10i	0.197215	−	0.736018i
$293$	6.38396e10	−	6.38396e10i	0.506042	−	0.506042i	−0.407267	−	0.913309i	$-0.633518\pi$
$293$	6.38396e10	−	6.38396e10i	0.506042	−	0.506042i	0.913309	+	0.407267i	$0.133518\pi$
$294$	1.31087e11	+	3.62235e10i	1.02329	+	0.282766i
$295$	−1.51364e11	−	5.90127e10i	−1.16365	−	0.453676i
$296$	−4.28167e10	−	7.41608e10i	−0.324191	−	0.561515i
$297$	−9.32782e10	+	2.49938e10i	−0.695627	+	0.186393i
$298$	−7.48186e10	+	2.00476e10i	−0.549587	+	0.147261i
$299$	8.81389e10	+	1.52661e11i	0.637746	+	1.10461i
$300$	−3.06408e9	−	7.30761e10i	−0.0218401	−	0.520871i
$301$	2.55821e10	−	1.88626e11i	0.179634	−	1.32450i
$302$	−1.56871e9	+	1.56871e9i	−0.0108520	+	0.0108520i
$303$	−4.48946e10	+	1.67549e11i	−0.305986	+	1.14196i
$304$	1.29024e11	−	2.23475e11i	0.866439	−	1.50072i
$305$	8.47610e10	+	1.05797e11i	0.560850	+	0.700042i
$306$	−2.79174e10	+	1.61181e10i	−0.182024	+	0.105092i
$307$	−1.08979e11	−	1.08979e11i	−0.700194	−	0.700194i	0.264258	−	0.964452i	$-0.414873\pi$
$307$	−1.08979e11	−	1.08979e11i	−0.700194	−	0.700194i	−0.964452	+	0.264258i	$0.914873\pi$
$308$	−6.03814e10	−	2.52872e10i	−0.382318	−	0.160112i
$309$		−	5.02027e10i		−	0.313267i
$310$	1.48662e11	−	2.02382e11i	0.914265	−	1.24464i
$311$	3.79317e10	+	2.18999e10i	0.229922	+	0.132746i	0.610536	−	0.791988i	$-0.290954\pi$
$311$	3.79317e10	+	2.18999e10i	0.229922	+	0.132746i	−0.380614	+	0.924734i	$0.624287\pi$
$312$	2.68955e10	+	1.00376e11i	0.160688	+	0.599698i
$313$	5.67795e10	+	1.52140e10i	0.334381	+	0.0895972i	0.422103	−	0.906548i	$-0.361292\pi$
$313$	5.67795e10	+	1.52140e10i	0.334381	+	0.0895972i	−0.0877218	+	0.996145i	$0.527959\pi$
$314$	1.06935e11			0.620778
$315$	−1.29962e10	+	5.20357e10i	−0.0743735	+	0.297786i
$316$	−5.38058e9			−0.0303555
$317$	−3.38860e8	−	9.07974e7i	−0.00188475	−	0.000505018i	0.257877	−	0.966178i	$-0.416977\pi$
$317$	−3.38860e8	−	9.07974e7i	−0.00188475	−	0.000505018i	−0.259761	+	0.965673i	$0.583644\pi$
$318$	−3.25958e10	−	1.21649e11i	−0.178747	−	0.667093i
$319$	−5.36631e10	−	3.09824e10i	−0.290147	−	0.167516i
$320$	3.05824e10	−	4.68003e9i	0.163041	−	0.0249502i
$321$			1.44792e11i			0.761154i
$322$	1.98937e11	−	2.54013e10i	1.03125	−	0.131676i
$323$	1.04301e11	+	1.04301e11i	0.533186	+	0.533186i
$324$	−6.44216e10	+	3.71939e10i	−0.324773	+	0.187508i
$325$	−1.45784e11	+	2.78871e11i	−0.724827	+	1.38652i
$326$	−1.59228e11	+	2.75792e11i	−0.780803	+	1.35239i
$327$	3.55429e10	−	1.32648e11i	0.171905	−	0.641558i
$328$	7.80759e10	−	7.80759e10i	0.372464	−	0.372464i
$329$	−8.84940e10	+	3.62516e10i	−0.416421	+	0.170587i
$330$	−5.49893e10	+	1.41044e11i	−0.255250	+	0.654699i
$331$	1.08723e11	+	1.88313e11i	0.497845	+	0.862293i	0.999997	−	0.00248676i	$-0.000791560\pi$
$331$	1.08723e11	+	1.88313e11i	0.497845	+	0.862293i	−0.502152	+	0.864779i	$0.667458\pi$
$332$	7.59792e10	−	2.03586e10i	0.343220	−	0.0919656i
$333$	−9.04912e10	+	2.42470e10i	−0.403280	+	0.108059i
$334$	−1.51891e11	−	2.63083e11i	−0.667841	−	1.15673i
$335$	2.21595e8	−	9.72759e7i	0.000961300	−	0.000421991i
$336$	2.37846e11	+	3.22576e10i	1.01805	+	0.138072i
$337$	−3.11169e11	+	3.11169e11i	−1.31420	+	1.31420i	−0.395917	+	0.918286i	$0.629573\pi$
$337$	−3.11169e11	+	3.11169e11i	−1.31420	+	1.31420i	−0.918286	+	0.395917i	$0.870427\pi$
$338$	−1.14664e11	+	4.27931e11i	−0.477861	+	1.78340i
$339$	−8.25470e10	+	1.42976e11i	−0.339471	+	0.587981i
$340$	−9.09186e9	+	8.23596e10i	−0.0368975	+	0.334241i
$341$	−1.73330e11	+	1.00072e11i	−0.694191	+	0.400791i
$342$	−9.83248e10	−	9.83248e10i	−0.388638	−	0.388638i
$343$	−2.37963e11	+	9.53199e10i	−0.928295	+	0.371843i
$344$		−	1.65475e11i		−	0.637118i
$345$	−2.70155e10	−	1.76536e11i	−0.102666	−	0.670886i
$346$	−2.05185e11	−	1.18464e11i	−0.769667	−	0.444367i
$347$	7.18181e10	+	2.68029e11i	0.265920	+	0.992428i	0.961685	+	0.274158i	$0.0883991\pi$
$347$	7.18181e10	+	2.68029e11i	0.265920	+	0.992428i	−0.695764	+	0.718270i	$0.744934\pi$
$348$	−6.97361e10	−	1.86857e10i	−0.254889	−	0.0682973i
$349$	−6.41238e10			−0.231369			−0.115684	−	0.993286i	$-0.536906\pi$
$349$	−6.41238e10			−0.231369			−0.115684	+	0.993286i	$0.536906\pi$
$350$	2.28577e11	+	2.75543e11i	0.814191	+	0.981483i
$351$	4.84075e11			1.70228
$352$	−2.02027e11	−	5.41329e10i	−0.701401	−	0.187940i
$353$	−1.29012e11	−	4.81480e11i	−0.442226	−	1.65041i	−0.723158	−	0.690683i	$-0.757310\pi$
$353$	−1.29012e11	−	4.81480e11i	−0.442226	−	1.65041i	0.280931	−	0.959728i	$-0.409357\pi$
$354$	3.39290e11	+	1.95889e11i	1.14830	+	0.662973i
$355$	−8.19661e10	−	5.35619e11i	−0.273909	−	1.78990i
$356$			1.24452e11i			0.410654i
$357$	−5.29991e10	+	1.26552e11i	−0.172688	+	0.412347i
$358$	6.97042e10	+	6.97042e10i	0.224277	+	0.224277i
$359$	−2.57349e11	+	1.48581e11i	−0.817706	+	0.472103i	−0.849625	−	0.527387i	$-0.823172\pi$
$359$	−2.57349e11	+	1.48581e11i	−0.817706	+	0.472103i	0.0319185	+	0.999490i	$0.489838\pi$
$360$	−5.11591e9	+	4.63431e10i	−0.0160532	+	0.145420i
$361$	−1.56789e11	+	2.71567e11i	−0.485886	+	0.841579i
$362$	1.23079e10	−	4.59337e10i	0.0376700	−	0.140586i
$363$	−1.09422e11	+	1.09422e11i	−0.330769	+	0.330769i
$364$	2.59556e11	+	2.00778e11i	0.774952	+	0.599460i
$365$	3.77810e11	−	1.65851e11i	1.11418	−	0.489102i
$366$	−1.63458e11	−	2.83117e11i	−0.476146	−	0.824709i
$367$	−2.15592e10	+	5.77677e9i	−0.0620348	+	0.0166222i	−0.289703	−	0.957117i	$-0.593557\pi$
$367$	−2.15592e10	+	5.77677e9i	−0.0620348	+	0.0166222i	0.227668	+	0.973739i	$0.426890\pi$
$368$	3.41890e11	−	9.16091e10i	0.971786	−	0.260389i
$369$	−6.03978e10	−	1.04612e11i	−0.169591	−	0.293740i
$370$	−2.27151e11	+	5.82627e11i	−0.630096	+	1.61615i
$371$	1.87763e11	+	1.45243e11i	0.514550	+	0.398027i
$372$	−1.64891e11	+	1.64891e11i	−0.446430	+	0.446430i
$373$	1.79225e11	−	6.68877e11i	0.479412	−	1.78919i	−0.124591	−	0.992208i	$-0.539762\pi$
$373$	1.79225e11	−	6.68877e11i	0.479412	−	1.78919i	0.604003	−	0.796982i	$-0.293571\pi$
$374$	8.57509e10	−	1.48525e11i	0.226629	−	0.392534i
$375$	2.40236e11	−	2.09582e11i	0.627332	−	0.547286i
$376$	−7.19956e10	+	4.15667e10i	−0.185764	+	0.107251i
$377$	2.19638e11	+	2.19638e11i	0.559978	+	0.559978i
$378$	2.12741e11	−	5.07987e11i	0.535967	−	1.27979i
$379$			3.22702e10i			0.0803388i	0.999193	+	0.0401694i	$0.0127898\pi$
$379$			3.22702e10i			0.0803388i	−0.999193	+	0.0401694i	$0.987210\pi$
$380$	−3.53306e11	+	5.40666e10i	−0.869211	+	0.133016i
$381$	3.17672e11	+	1.83408e11i	0.772355	+	0.445919i
$382$	−1.05504e11	−	3.93746e11i	−0.253503	−	0.946087i
$383$	2.75580e11	+	7.38414e10i	0.654414	+	0.175350i	0.570724	−	0.821142i	$-0.306663\pi$
$383$	2.75580e11	+	7.38414e10i	0.654414	+	0.175350i	0.0836904	+	0.996492i	$0.473329\pi$
$384$	3.14535e11			0.738206
$385$	−7.85404e10	−	2.74319e11i	−0.182188	−	0.636331i
$386$	−5.83386e11			−1.33756
$387$	−1.74862e11	−	4.68541e10i	−0.396275	−	0.106181i
$388$	−1.21175e11	−	4.52231e11i	−0.271438	−	1.01302i
$389$	3.42646e11	+	1.97827e11i	0.758705	+	0.438038i	0.828830	−	0.559500i	$-0.189007\pi$
$389$	3.42646e11	+	1.97827e11i	0.758705	+	0.438038i	−0.0701258	+	0.997538i	$0.522340\pi$
$390$	4.49246e11	−	6.11585e11i	0.983316	−	1.33865i
$391$			2.02325e11i			0.437777i
$392$	−1.93851e11	+	1.09912e11i	−0.414649	+	0.235103i
$393$	−4.09412e11	−	4.09412e11i	−0.865752	−	0.865752i
$394$	−6.25219e11	+	3.60970e11i	−1.30707	+	0.754637i
$395$	−1.46640e10	−	1.83034e10i	−0.0303087	−	0.0378307i
$396$	−3.11284e10	+	5.39159e10i	−0.0636104	+	0.110176i
$397$	1.28182e11	−	4.78382e11i	0.258982	−	0.966535i	−0.706849	−	0.707364i	$-0.749884\pi$
$397$	1.28182e11	−	4.78382e11i	0.258982	−	0.966535i	0.965831	−	0.259171i	$-0.0834493\pi$
$398$	7.05479e10	−	7.05479e10i	0.140932	−	0.140932i
$399$	−5.86457e11	−	7.95376e10i	−1.15840	−	0.157107i
$400$	4.65106e11	+	4.27672e11i	0.908410	+	0.835296i
$401$	−4.88809e11	−	8.46642e11i	−0.944038	−	1.63512i	−0.757666	−	0.652642i	$-0.773661\pi$
$401$	−4.88809e11	−	8.46642e11i	−0.944038	−	1.63512i	−0.186371	−	0.982479i	$-0.559673\pi$
$402$	−5.63719e8	+	1.51048e8i	−0.00107658	+	0.000288468i
$403$	9.69089e11	−	2.59667e11i	1.83017	−	0.490392i
$404$	2.38083e11	+	4.12372e11i	0.444643	+	0.770145i
$405$	−3.02097e11	−	1.17780e11i	−0.557954	−	0.217532i
$406$	3.27013e11	−	1.33961e11i	0.597308	−	0.244687i
$407$	3.52429e11	−	3.52429e11i	0.636644	−	0.636644i
$408$	−3.08696e10	+	1.15207e11i	−0.0551519	+	0.205830i
$409$	−2.12824e11	+	3.68622e11i	−0.376068	+	0.651369i	−0.990486	−	0.137612i	$-0.956057\pi$
$409$	−2.12824e11	+	3.68622e11i	−0.376068	+	0.651369i	0.614418	+	0.788980i	$0.289391\pi$
$410$	−8.01448e11	−	8.84736e10i	−1.40071	−	0.154627i
$411$	−1.39733e11	+	8.06750e10i	−0.241552	+	0.139460i
$412$	−9.74479e10	−	9.74479e10i	−0.166623	−	0.166623i
$413$	−7.32508e11	+	9.35304e10i	−1.23890	+	0.158190i
$414$		−	1.90731e11i		−	0.319095i
$415$	2.76326e11	+	2.02978e11i	0.457304	+	0.335917i
$416$	9.07971e11	+	5.24217e11i	1.48646	+	0.858206i
$417$	−4.60419e10	−	1.71831e11i	−0.0745661	−	0.278284i
$418$	7.14572e11	+	1.91469e11i	1.14486	+	0.306764i
$419$	9.52921e11			1.51041			0.755203	−	0.655491i	$-0.227538\pi$
$419$	9.52921e11			1.51041			0.755203	+	0.655491i	$0.227538\pi$
$420$	−1.71112e11	−	2.85039e11i	−0.268324	−	0.446974i
$421$	7.30083e11			1.13267			0.566334	−	0.824176i	$-0.308361\pi$
$421$	7.30083e11			1.13267			0.566334	+	0.824176i	$0.308361\pi$
$422$	−5.51386e11	−	1.47743e11i	−0.846349	−	0.226779i
$423$	2.35391e10	+	8.78492e10i	0.0357486	+	0.133415i
$424$	1.78712e11	+	1.03179e11i	0.268539	+	0.155041i
$425$	−3.04946e11	+	1.93532e11i	−0.453390	+	0.287741i
$426$			1.30670e12i			1.92235i
$427$	5.68366e11	+	2.38027e11i	0.827376	+	0.346498i
$428$	2.81054e11	+	2.81054e11i	0.404849	+	0.404849i
$429$	−5.23791e11	+	3.02411e11i	−0.746620	+	0.431062i
$430$	−9.43056e11	+	7.55544e11i	−1.33024	+	1.06574i
$431$	1.08482e11	−	1.87896e11i	0.151429	−	0.262283i	−0.780324	−	0.625376i	$-0.784946\pi$
$431$	1.08482e11	−	1.87896e11i	0.151429	−	0.262283i	0.931753	+	0.363093i	$0.118279\pi$
$432$	2.51567e11	−	9.38861e11i	0.347518	−	1.29695i
$433$	−6.98441e10	+	6.98441e10i	−0.0954848	+	0.0954848i	−0.753236	−	0.657751i	$-0.771508\pi$
$433$	−6.98441e10	+	6.98441e10i	−0.0954848	+	0.0954848i	0.657751	+	0.753236i	$0.271508\pi$
$434$	1.53401e11	−	1.13108e12i	0.207551	−	1.53034i
$435$	−1.26492e11	−	2.88150e11i	−0.169380	−	0.385849i
$436$	−1.88489e11	−	3.26473e11i	−0.249803	−	0.432672i
$437$	−8.42997e11	+	2.25880e11i	−1.10576	+	0.296286i
$438$	−9.61115e11	+	2.57530e11i	−1.24779	+	0.334344i
$439$	2.07474e10	+	3.59355e10i	0.0266608	+	0.0461778i	0.879048	−	0.476733i	$-0.158179\pi$
$439$	2.07474e10	+	3.59355e10i	0.0266608	+	0.0461778i	−0.852387	+	0.522911i	$0.824846\pi$
$440$	−9.97051e10	−	2.27129e11i	−0.126818	−	0.288892i
$441$	6.12582e10	+	2.35969e11i	0.0771241	+	0.297085i
$442$	−6.07897e11	+	6.07897e11i	−0.757583	+	0.757583i
$443$	1.79352e11	−	6.69351e11i	0.221253	−	0.825728i	−0.762618	−	0.646849i	$-0.776086\pi$
$443$	1.79352e11	−	6.69351e11i	0.221253	−	0.825728i	0.983871	−	0.178879i	$-0.0572470\pi$
$444$	2.90352e11	−	5.02905e11i	0.354570	−	0.614133i
$445$	−4.23354e11	+	3.39177e11i	−0.511780	+	0.410021i
$446$	−7.11282e11	+	4.10659e11i	−0.851207	+	0.491444i
$447$	2.21697e11	+	2.21697e11i	0.262649	+	0.262649i
$448$	1.11901e11	−	8.51733e10i	0.131245	−	0.0998970i
$449$		−	5.19684e10i		−	0.0603436i	−0.999545	−	0.0301718i	$-0.990395\pi$
$449$		−	5.19684e10i		−	0.0603436i	0.999545	−	0.0301718i	$-0.00960544\pi$
$450$	2.87472e11	−	1.82442e11i	0.330475	−	0.209734i
$451$	5.56552e11	+	3.21325e11i	0.633448	+	0.365722i
$452$	1.17297e11	+	4.37759e11i	0.132180	+	0.493301i
$453$	8.67382e9	+	2.32414e9i	0.00967762	+	0.00259311i
$454$	8.94695e11			0.988380
$455$	2.43877e10	+	1.43014e12i	0.0266759	+	1.56433i
$456$	−5.14480e11			−0.557220
$457$	1.02088e12	+	2.73544e11i	1.09484	+	0.293362i	0.760663	−	0.649147i	$-0.224874\pi$
$457$	1.02088e12	+	2.73544e11i	1.09484	+	0.293362i	0.334179	+	0.942509i	$0.391541\pi$
$458$	4.84757e10	+	1.80914e11i	0.0514789	+	0.192122i
$459$	4.81165e11	+	2.77801e11i	0.505985	+	0.292130i
$460$	−3.95112e11	−	2.90233e11i	−0.411443	−	0.302230i
$461$			7.16379e11i			0.738735i	0.929283	+	0.369367i	$0.120426\pi$
$461$			7.16379e11i			0.738735i	−0.929283	+	0.369367i	$0.879574\pi$
$462$	8.71537e10	+	6.82567e11i	0.0890014	+	0.697038i
$463$	6.24878e10	+	6.24878e10i	0.0631947	+	0.0631947i	0.737998	−	0.674803i	$-0.235771\pi$
$463$	6.24878e10	+	6.24878e10i	0.0631947	+	0.0631947i	−0.674803	+	0.737998i	$0.735771\pi$
$464$	5.40129e11	−	3.11843e11i	0.540961	−	0.312324i
$465$	−1.01031e12	−	1.11530e11i	−1.00211	−	0.110625i
$466$	1.70210e11	−	2.94813e11i	0.167205	−	0.289608i
$467$	4.59700e11	−	1.71562e12i	0.447248	−	1.66915i	−0.262684	−	0.964882i	$-0.584608\pi$
$467$	4.59700e11	−	1.71562e12i	0.447248	−	1.66915i	0.709932	−	0.704270i	$-0.248726\pi$
$468$	2.20673e11	−	2.20673e11i	0.212638	−	0.212638i
$469$	6.73053e8	−	8.70090e8i	0.000642350	−	0.000830398i
$470$	5.65616e11	+	2.20519e11i	0.534665	+	0.208452i
$471$	−2.16421e11	−	3.74852e11i	−0.202631	−	0.350967i
$472$	−6.20072e11	+	1.66148e11i	−0.575047	+	0.154083i
$473$	9.30293e11	−	2.49271e11i	0.854564	−	0.228980i
$474$	2.82789e10	+	4.89805e10i	0.0257312	+	0.0445678i
$475$	−1.14681e12	−	1.05451e12i	−1.03364	−	0.950450i
$476$	1.42773e11	+	3.48525e11i	0.127472	+	0.311174i
$477$	1.59635e11	−	1.59635e11i	0.141187	−	0.141187i
$478$	−6.15773e11	+	2.29810e12i	−0.539505	+	2.01346i
$479$	3.78303e11	−	6.55239e11i	0.328344	−	0.568709i	−0.653839	−	0.756634i	$-0.726843\pi$
$479$	3.78303e11	−	6.55239e11i	0.328344	−	0.568709i	0.982183	+	0.187924i	$0.0601760\pi$
$480$	−6.64137e11	−	8.28964e11i	−0.571048	−	0.712771i
$481$	−2.16368e12	+	1.24920e12i	−1.84307	+	1.06410i
$482$	−9.48623e11	−	9.48623e11i	−0.800538	−	0.800538i
$483$	−4.91662e11	−	6.45950e11i	−0.411060	−	0.540053i
$484$			4.24795e11i			0.351864i
$485$	1.20813e12	−	1.64470e12i	0.991463	−	1.34974i
$486$	−8.00661e11	−	4.62262e11i	−0.651007	−	0.375859i
$487$	5.75700e11	+	2.14854e12i	0.463784	+	1.73087i	0.660889	+	0.750484i	$0.270180\pi$
$487$	5.75700e11	+	2.14854e12i	0.463784	+	1.73087i	−0.197104	+	0.980382i	$0.563154\pi$
$488$	5.17412e11	+	1.38640e11i	0.412998	+	0.110662i
$489$	1.28902e12			1.01946
$490$	1.51150e12	+	6.02924e11i	1.18448	+	0.472476i
$491$	1.29738e11			0.100740			0.0503698	−	0.998731i	$-0.483960\pi$
$491$	1.29738e11			0.100740			0.0503698	+	0.998731i	$0.483960\pi$
$492$	7.23248e11	+	1.93794e11i	0.556473	+	0.149107i
$493$	9.22718e10	+	3.44363e11i	0.0703490	+	0.262546i
$494$	−3.21151e12	−	1.85417e12i	−2.42626	−	1.40080i
$495$	−2.68245e11	+	4.10496e10i	−0.200820	+	0.0307316i
$496$		−	2.01449e12i		−	1.49450i
$497$	−1.49173e12	−	1.95984e12i	−1.09669	−	1.44084i
$498$	−5.84655e11	−	5.84655e11i	−0.425959	−	0.425959i
$499$	−4.99006e11	+	2.88101e11i	−0.360291	+	0.208014i	−0.669208	−	0.743075i	$-0.733367\pi$
$499$	−4.99006e11	+	2.88101e11i	−0.360291	+	0.208014i	0.308917	+	0.951089i	$0.400033\pi$
$500$	5.95015e10	−	8.73137e11i	0.0425758	−	0.624766i
$501$	−6.14811e11	+	1.06488e12i	−0.435985	+	0.755149i
$502$	−6.59379e11	+	2.46084e12i	−0.463413	+	1.72948i
$503$	−1.09667e12	+	1.09667e12i	−0.763874	+	0.763874i	−0.977020	−	0.213146i	$-0.931629\pi$
$503$	−1.09667e12	+	1.09667e12i	−0.763874	+	0.763874i	0.213146	+	0.977020i	$0.431629\pi$
$504$	8.03373e10	+	1.96112e11i	0.0554600	+	0.135384i
$505$	−7.53923e11	+	1.93376e12i	−0.515841	+	1.32310i
$506$	5.07359e11	+	8.78771e11i	0.344063	+	0.595934i
$507$	1.73214e12	−	4.64126e11i	1.16425	−	0.311961i
$508$	9.72641e11	−	2.60618e11i	0.647986	−	0.173627i
$509$	6.46829e11	+	1.12034e12i	0.427129	+	0.739809i	0.996617	−	0.0821906i	$-0.0261916\pi$
$509$	6.46829e11	+	1.12034e12i	0.427129	+	0.739809i	−0.569487	+	0.822000i	$0.692858\pi$
$510$	7.97521e11	−	3.50096e11i	0.522007	−	0.229151i
$511$	1.14752e12	−	1.48346e12i	0.744505	−	0.962459i
$512$	8.41805e11	−	8.41805e11i	0.541373	−	0.541373i
$513$	−6.20288e11	+	2.31495e12i	−0.395426	+	1.47575i
$514$	8.07218e11	−	1.39814e12i	0.510101	−	0.883522i
$515$	6.59124e10	−	5.97075e11i	0.0412890	−	0.374021i
$516$	9.71796e11	−	5.61066e11i	0.603464	−	0.348410i
$517$	−3.42139e11	−	3.42139e11i	−0.210618	−	0.210618i
$518$	3.60016e11	+	2.81956e12i	0.219704	+	1.72067i
$519$			9.59012e11i			0.580191i
$520$	1.88091e11	+	1.22911e12i	0.112811	+	0.737181i
$521$	1.12344e12	+	6.48618e11i	0.668005	+	0.385673i	0.795320	−	0.606189i	$-0.207303\pi$
$521$	1.12344e12	+	6.48618e11i	0.668005	+	0.385673i	−0.127315	+	0.991862i	$0.540636\pi$
$522$	−8.69845e10	−	3.24630e11i	−0.0512772	−	0.191369i
$523$	2.33103e12	+	6.24596e11i	1.36235	+	0.365041i	0.864680	−	0.502324i	$-0.167521\pi$
$523$	2.33103e12	+	6.24596e11i	1.36235	+	0.365041i	0.497673	+	0.867365i	$0.334188\pi$
$524$	−1.58941e12			−0.920968
$525$	5.03286e11	−	1.35892e12i	0.289133	−	0.780685i
$526$	6.39590e11			0.364306
$527$	1.11228e12	+	2.98035e11i	0.628155	+	0.168313i
$528$	3.14317e11	+	1.17305e12i	0.176001	+	0.656845i
$529$	5.23137e11	+	3.02034e11i	0.290446	+	0.167689i
$530$	−2.27954e11	−	1.48960e12i	−0.125489	−	0.820028i
$531$			7.02291e11i			0.383347i
$532$	−1.29275e12	+	9.83975e11i	−0.699703	+	0.532576i
$533$	−2.27791e12	−	2.27791e12i	−1.22254	−	1.22254i
$534$	1.13291e12	−	6.54086e11i	0.602920	−	0.348096i
$535$	−1.90101e11	+	1.72205e12i	−0.100321	+	0.908771i
$536$	4.78131e8	−	8.28148e8i	0.000250211	−	0.000433378i
$537$	1.03271e11	−	3.85414e11i	0.0535915	−	0.200006i
$538$	2.27791e12	−	2.27791e12i	1.17224	−	1.17224i
$539$	−9.09935e11	−	9.24248e11i	−0.464367	−	0.471671i
$540$	−1.23274e12	+	5.41146e11i	−0.623876	+	0.273869i
$541$	−1.89653e12	−	3.28489e12i	−0.951858	−	1.64867i	−0.741401	−	0.671063i	$-0.765838\pi$
$541$	−1.89653e12	−	3.28489e12i	−0.951858	−	1.64867i	−0.210457	−	0.977603i	$-0.567495\pi$
$542$	−1.17445e12	+	3.14692e11i	−0.584571	+	0.156635i
$543$	−1.85926e11	+	4.98188e10i	−0.0917786	+	0.0245920i
$544$	6.01675e11	+	1.04213e12i	0.294556	+	0.510185i
$545$	5.96878e11	−	1.53095e12i	0.289802	−	0.743323i
$546$	4.63566e11	−	3.41803e12i	0.223226	−	1.64592i
$547$	2.22980e12	−	2.22980e12i	1.06493	−	1.06493i	0.0671940	−	0.997740i	$-0.478595\pi$
$547$	2.22980e12	−	2.22980e12i	1.06493	−	1.06493i	0.997740	−	0.0671940i	$-0.0214046\pi$
$548$	−1.14637e11	+	4.27831e11i	−0.0543016	+	0.202656i
$549$	2.93010e11	−	5.07508e11i	0.137660	−	0.238433i
$550$	−8.39183e11	+	1.60528e12i	−0.391043	+	0.748028i
$551$	−1.33179e12	+	7.68912e11i	−0.615538	+	0.355381i
$552$	−4.98995e11	−	4.98995e11i	−0.228755	−	0.228755i
$553$	−9.83300e10	−	4.11798e10i	−0.0447119	−	0.0187250i
$554$		−	1.19045e12i		−	0.536928i
$555$	2.50207e12	−	3.82893e11i	1.11939	−	0.171301i
$556$	−4.22910e11	−	2.44167e11i	−0.187677	−	0.108355i
$557$	−6.29355e11	−	2.34879e12i	−0.277043	−	1.03394i	−0.954460	−	0.298340i	$-0.903567\pi$
$557$	−6.29355e11	−	2.34879e12i	−0.277043	−	1.03394i	0.677416	−	0.735600i	$-0.263100\pi$
$558$	−1.04854e12	−	2.80957e11i	−0.457860	−	0.122683i
$559$	−4.82784e12			−2.09122
$560$	2.78642e12	+	6.95923e11i	1.19729	+	0.299030i
$561$	−6.94189e11			−0.295900
$562$	3.37384e12	+	9.04017e11i	1.42663	+	0.382264i
$563$	−1.11393e12	−	4.15723e12i	−0.467270	−	1.74388i	−0.649251	−	0.760575i	$-0.724917\pi$
$563$	−1.11393e12	−	4.15723e12i	−0.467270	−	1.74388i	0.181980	−	0.983302i	$-0.441749\pi$
$564$	−4.88222e11	−	2.81875e11i	−0.203171	−	0.117301i
$565$	−1.16947e12	+	1.59207e12i	−0.482804	+	0.657271i
$566$		−	2.47608e12i		−	1.01412i
$567$	−1.46197e12	+	1.86671e11i	−0.594037	+	0.0758497i
$568$	−1.51397e12	−	1.51397e12i	−0.610311	−	0.610311i
$569$	−6.98867e11	+	4.03491e11i	−0.279505	+	0.161372i	−0.633199	−	0.773989i	$-0.718259\pi$
$569$	−6.98867e11	+	4.03491e11i	−0.279505	+	0.161372i	0.353694	+	0.935361i	$0.384925\pi$
$570$	2.34907e12	+	2.93206e12i	0.932091	+	1.16342i
$571$	1.90984e12	−	3.30795e12i	0.751857	−	1.30225i	−0.195064	−	0.980790i	$-0.562492\pi$
$571$	1.90984e12	−	3.30795e12i	0.751857	−	1.30225i	0.946922	−	0.321464i	$-0.104175\pi$
$572$	−4.29718e11	+	1.60373e12i	−0.167842	+	0.626396i
$573$	−1.16672e12	+	1.16672e12i	−0.452138	+	0.452138i
$574$	−3.39153e12	+	1.38934e12i	−1.30404	+	0.534200i
$575$	−8.95232e10	−	2.13507e12i	−0.0341531	−	0.814528i
$576$	−6.68709e10	−	1.15824e11i	−0.0253125	−	0.0438426i
$577$	3.30129e12	−	8.84577e11i	1.23992	−	0.332234i	0.421482	−	0.906837i	$-0.361510\pi$
$577$	3.30129e12	−	8.84577e11i	1.23992	−	0.332234i	0.818433	+	0.574602i	$0.194843\pi$
$578$	2.35218e12	−	6.30264e11i	0.876586	−	0.234880i
$579$	1.18069e12	+	2.04501e12i	0.436598	+	0.756211i
$580$	−8.04858e11	−	3.13793e11i	−0.295320	−	0.115138i
$581$	1.54433e12	+	2.09448e11i	0.562274	+	0.0762577i
$582$	−3.47989e12	+	3.47989e12i	−1.25722	+	1.25722i
$583$	−3.10858e11	+	1.16014e12i	−0.111443	+	0.415912i
$584$	8.15192e11	−	1.41195e12i	0.290003	−	0.502299i
$585$	1.35209e12	+	1.49260e11i	0.477313	+	0.0526916i
$586$	−2.25611e12	+	1.30257e12i	−0.790352	+	0.456310i
$587$	5.39920e11	+	5.39920e11i	0.187697	+	0.187697i	0.794700	−	0.607003i	$-0.207628\pi$
$587$	5.39920e11	+	5.39920e11i	0.187697	+	0.187697i	−0.607003	+	0.794700i	$0.707628\pi$
$588$	−1.30276e12	−	7.65767e11i	−0.449436	−	0.264179i
$589$			4.96711e12i			1.70053i
$590$	3.77808e12	+	2.77522e12i	1.28362	+	0.942897i
$591$	2.53070e12	+	1.46110e12i	0.853292	+	0.492648i
$592$	1.29839e12	+	4.84564e12i	0.434466	+	1.62145i
$593$	−1.01171e12	−	2.71086e11i	−0.335976	−	0.0900244i	0.0868870	−	0.996218i	$-0.472308\pi$
$593$	−1.01171e12	−	2.71086e11i	−0.335976	−	0.0900244i	−0.422863	+	0.906194i	$0.638975\pi$
$594$	2.78651e12			0.918378
$595$	−7.96487e11	+	1.43554e12i	−0.260527	+	0.469557i
$596$	8.60668e11			0.279401
$597$	−3.90079e11	−	1.04521e11i	−0.125681	−	0.0336760i
$598$	−1.31649e12	−	4.91321e12i	−0.420981	−	1.57112i
$599$	−4.54697e11	−	2.62519e11i	−0.144312	−	0.0833184i	0.426106	−	0.904673i	$-0.359885\pi$
$599$	−4.54697e11	−	2.62519e11i	−0.144312	−	0.0833184i	−0.570417	+	0.821355i	$0.693219\pi$
$600$	2.74781e11	−	1.22940e12i	0.0865578	−	0.387269i
$601$			3.10406e12i			0.970500i	0.874376	+	0.485250i	$0.161271\pi$
$601$			3.10406e12i			0.970500i	−0.874376	+	0.485250i	$0.838729\pi$
$602$	−2.12173e12	+	5.06631e12i	−0.658425	+	1.57220i
$603$	−7.39744e8	−	7.39744e8i	−0.000227852	−	0.000227852i
$604$	2.13480e10	−	1.23253e10i	0.00652667	−	0.00376817i
$605$	−1.44505e12	+	1.15772e12i	−0.438513	+	0.351322i
$606$	2.50260e12	−	4.33463e12i	0.753815	−	1.30565i
$607$	6.19968e11	−	2.31375e12i	0.185362	−	0.691779i	−0.809191	−	0.587546i	$-0.800094\pi$
$607$	6.19968e11	−	2.31375e12i	0.185362	−	0.691779i	0.994553	−	0.104234i	$-0.0332390\pi$
$608$	−3.67038e12	+	3.67038e12i	−1.08929	+	1.08929i
$609$	−1.13142e12	−	8.75201e11i	−0.333307	−	0.257828i
$610$	−1.57233e12	−	3.58179e12i	−0.459791	−	1.04741i
$611$	1.21273e12	+	2.10051e12i	0.352030	+	0.609733i
$612$	3.45985e11	−	9.27065e10i	0.0996957	−	0.0267134i
$613$	−4.41578e12	+	1.18321e12i	−1.26309	+	0.338445i	−0.827381	−	0.561641i	$-0.810170\pi$
$613$	−4.41578e12	+	1.18321e12i	−1.26309	+	0.338445i	−0.435713	+	0.900086i	$0.643504\pi$
$614$	2.22357e12	+	3.85133e12i	0.631382	+	1.09359i
$615$	1.31188e12	+	2.98847e12i	0.369790	+	0.842385i
$616$	−8.91818e11	−	6.89861e11i	−0.249553	−	0.193041i
$617$	−5.72709e10	+	5.72709e10i	−0.0159093	+	0.0159093i	−0.715017	−	0.699107i	$-0.753581\pi$
$617$	−5.72709e10	+	5.72709e10i	−0.0159093	+	0.0159093i	0.699107	+	0.715017i	$0.253581\pi$
$618$	−3.74928e11	+	1.39925e12i	−0.103395	+	0.385875i
$619$	−3.11787e12	+	5.40031e12i	−0.853592	+	1.47846i	0.0243532	+	0.999703i	$0.492247\pi$
$619$	−3.11787e12	+	5.40031e12i	−0.853592	+	1.47846i	−0.877945	+	0.478761i	$0.841086\pi$
$620$	−2.17758e12	+	1.74460e12i	−0.591850	+	0.474170i
$621$	−2.84689e12	+	1.64365e12i	−0.768173	+	0.443505i
$622$	−8.93677e11	−	8.93677e11i	−0.239400	−	0.239400i
$623$	−9.52482e11	+	2.27436e12i	−0.253315	+	0.604870i
$624$		−	6.08763e12i		−	1.60738i
$625$	3.13236e12	−	2.17721e12i	0.821129	−	0.570742i
$626$	−1.46893e12	−	8.48090e11i	−0.382312	−	0.220728i
$627$	−7.75010e11	−	2.89238e12i	−0.200264	−	0.747397i
$628$	−1.14771e12	−	3.07529e11i	−0.294452	−	0.0788982i
$629$	−2.86757e12			−0.730443
$630$	7.50846e11	−	1.35328e12i	0.189897	−	0.342259i
$631$	4.99620e12			1.25461			0.627303	−	0.778775i	$-0.284159\pi$
$631$	4.99620e12			1.25461			0.627303	+	0.778775i	$0.284159\pi$
$632$	−8.95148e10	−	2.39854e10i	−0.0223187	−	0.00598026i
$633$	5.98022e11	+	2.23185e12i	0.148047	+	0.552520i
$634$	8.76661e9	+	5.06140e9i	0.00215491	+	0.00124414i
$635$	3.53736e12	+	2.59840e12i	0.863371	+	0.634198i
$636$			1.39938e12i			0.339139i
$637$	3.20674e12	+	5.65571e12i	0.771679	+	1.36101i
$638$	1.26431e12	+	1.26431e12i	0.302107	+	0.302107i
$639$	−2.02854e12	+	1.17118e12i	−0.481315	+	0.277887i
$640$	3.74085e12	+	4.12960e11i	0.881373	+	0.0972967i
$641$	−5.63605e11	+	9.76192e11i	−0.131860	+	0.228389i	−0.924394	−	0.381440i	$-0.875428\pi$
$641$	−5.63605e11	+	9.76192e11i	−0.131860	+	0.228389i	0.792533	+	0.609828i	$0.208762\pi$
$642$	1.08135e12	−	4.03565e12i	0.251222	−	0.937574i
$643$	4.17318e12	−	4.17318e12i	0.962760	−	0.962760i	−0.0365714	−	0.999331i	$-0.511644\pi$
$643$	4.17318e12	−	4.17318e12i	0.962760	−	0.962760i	0.999331	+	0.0365714i	$0.0116436\pi$
$644$	−2.20821e12	−	2.99485e11i	−0.505886	−	0.0686103i
$645$	4.55711e12	+	1.77670e12i	1.03674	+	0.404198i
$646$	−2.12814e12	−	3.68604e12i	−0.480787	−	0.832748i
$647$	−4.18198e12	+	1.12056e12i	−0.938238	+	0.251400i	−0.695364	−	0.718658i	$-0.744757\pi$
$647$	−4.18198e12	+	1.12056e12i	−0.938238	+	0.251400i	−0.242874	+	0.970058i	$0.578090\pi$
$648$	−1.23756e12	+	3.31604e11i	−0.275727	+	0.0738809i
$649$	−1.86815e12	−	3.23573e12i	−0.413343	−	0.715931i
$650$	6.14596e12	−	6.68392e12i	1.35045	−	1.46866i
$651$	−4.27536e12	+	1.75140e12i	−0.932949	+	0.382182i
$652$	2.50210e12	−	2.50210e12i	0.542239	−	0.542239i
$653$	2.00705e12	−	7.49042e12i	0.431966	−	1.61212i	−0.316258	−	0.948673i	$-0.602427\pi$
$653$	2.00705e12	−	7.49042e12i	0.431966	−	1.61212i	0.748224	−	0.663446i	$-0.230907\pi$
$654$	−1.98130e12	+	3.43172e12i	−0.423498	+	0.733519i
$655$	−4.33172e12	−	5.40677e12i	−0.919548	−	1.14776i
$656$	−5.60179e12	+	3.23419e12i	−1.18103	+	0.681866i
$657$	−1.26123e12	−	1.26123e12i	−0.264088	−	0.264088i
$658$	2.73724e12	−	3.49505e11i	0.569241	−	0.0726837i
$659$			2.14788e12i			0.443636i	0.975088	+	0.221818i	$0.0711990\pi$
$659$			2.14788e12i			0.443636i	−0.975088	+	0.221818i	$0.928801\pi$
$660$	9.95810e11	−	1.35566e12i	0.204281	−	0.278101i
$661$	−4.89940e12	−	2.82867e12i	−0.998243	−	0.576336i	−0.0905154	−	0.995895i	$-0.528851\pi$
$661$	−4.89940e12	−	2.82867e12i	−0.998243	−	0.576336i	−0.907728	+	0.419559i	$0.862185\pi$
$662$	−1.62394e12	−	6.06063e12i	−0.328632	−	1.22647i
$663$	3.36123e12	+	9.00639e11i	0.675597	+	0.181026i
$664$	1.35479e12			0.270468
$665$	−6.87047e12	−	1.71594e12i	−1.36235	−	0.340254i
$666$	2.70325e12			0.532418
$667$	−2.03748e12	−	5.45941e11i	−0.398591	−	0.106802i
$668$	8.73631e11	+	3.26044e12i	0.169759	+	0.633551i
$669$	2.87906e12	+	1.66223e12i	0.555691	+	0.320829i
$670$	−6.90278e9	+	1.05634e9i	−0.00132339	+	0.000202519i
$671$			3.11771e12i			0.593724i
$672$	−4.45339e12	−	1.86504e12i	−0.842420	−	0.352799i
$673$	7.14222e12	+	7.14222e12i	1.34204	+	1.34204i	0.894027	+	0.448013i	$0.147868\pi$
$673$	7.14222e12	+	7.14222e12i	1.34204	+	1.34204i	0.448013	+	0.894027i	$0.352132\pi$
$674$	1.09968e13	−	6.34901e12i	2.05257	−	1.18505i
$675$	−5.20050e12	−	2.71864e12i	−0.964225	−	0.504063i
$676$	2.46133e12	−	4.26315e12i	0.453325	−	0.785182i
$677$	−1.22613e12	+	4.57596e12i	−0.224329	+	0.837209i	0.758343	+	0.651856i	$0.226009\pi$
$677$	−1.22613e12	+	4.57596e12i	−0.224329	+	0.837209i	−0.982672	+	0.185353i	$0.940657\pi$
$678$	3.36853e12	−	3.36853e12i	0.612219	−	0.612219i
$679$	1.24664e12	−	9.19192e12i	0.225076	−	1.65956i
$680$	−5.18399e11	+	1.32966e12i	−0.0929766	+	0.238479i
$681$	−1.81073e12	−	3.13628e12i	−0.322621	−	0.558796i
$682$	5.57841e12	−	1.49473e12i	0.987373	−	0.264566i
$683$	−3.61325e12	+	9.68166e11i	−0.635337	+	0.170238i	−0.562091	−	0.827076i	$-0.690003\pi$
$683$	−3.61325e12	+	9.68166e11i	−0.635337	+	0.170238i	−0.0732468	+	0.997314i	$0.523336\pi$
$684$	7.72534e11	+	1.33807e12i	0.134948	+	0.233736i
$685$	−1.76780e12	+	7.76030e11i	−0.306780	+	0.134670i
$686$	7.34438e12	−	8.79580e11i	1.26618	−	0.151641i
$687$	5.36071e11	−	5.36071e11i	0.0918157	−	0.0918157i
$688$	−2.50896e12	+	9.36355e12i	−0.426919	+	1.59328i
$689$	3.01032e12	−	5.21403e12i	0.508893	−	0.881428i
$690$	−5.65448e11	+	5.12218e12i	−0.0949669	+	0.860268i
$691$	8.13046e12	−	4.69413e12i	1.35664	−	0.783256i	0.367469	−	0.930036i	$-0.380224\pi$
$691$	8.13046e12	−	4.69413e12i	1.35664	−	0.783256i	0.989169	+	0.146780i	$0.0468910\pi$
$692$	1.86153e12	+	1.86153e12i	0.308597	+	0.308597i
$693$	−9.81512e11	+	7.47075e11i	−0.161658	+	0.123045i
$694$		−	8.00685e12i		−	1.31022i
$695$	−3.21988e11	−	2.10408e12i	−0.0523490	−	0.342082i
$696$	−1.07688e12	−	6.21736e11i	−0.173950	−	0.100430i
$697$	−9.56971e11	−	3.57146e12i	−0.153586	−	0.573190i
$698$	1.78726e12	+	4.78894e11i	0.284995	+	0.0763643i
$699$	−1.37792e12			−0.218312
$700$	−1.66085e12	−	3.61470e12i	−0.261451	−	0.569025i
$701$	6.18771e12			0.967830			0.483915	−	0.875115i	$-0.339214\pi$
$701$	6.18771e12			0.967830			0.483915	+	0.875115i	$0.339214\pi$
$702$	−1.34921e13	−	3.61521e12i	−2.09683	−	0.561845i
$703$	−3.20143e12	−	1.19479e13i	−0.494362	−	1.84498i
$704$	6.16200e11	+	3.55763e11i	0.0945463	+	0.0545863i
$705$	−3.71714e11	−	2.42902e12i	−0.0566706	−	0.370323i
$706$			1.43833e13i			2.17890i
$707$	1.19491e12	+	9.35823e12i	0.179865	+	1.40866i
$708$	−3.07819e12	−	3.07819e12i	−0.460410	−	0.460410i
$709$	−4.93279e12	+	2.84795e12i	−0.733136	+	0.423276i	−0.819568	−	0.572981i	$-0.805787\pi$
$709$	−4.93279e12	+	2.84795e12i	−0.733136	+	0.423276i	0.0864321	+	0.996258i	$0.472453\pi$
$710$	−1.71560e12	+	1.55409e13i	−0.253368	+	2.29517i
$711$	−5.06921e10	+	8.78012e10i	−0.00743921	+	0.0128851i
$712$	−5.54778e11	+	2.07046e12i	−0.0809020	+	0.301930i
$713$	−4.81762e12	+	4.81762e12i	−0.698119	+	0.698119i
$714$	2.42232e12	−	3.13145e12i	0.348810	−	0.450924i
$715$	−6.62663e12	+	2.90896e12i	−0.948234	+	0.416255i
$716$	−5.47664e11	−	9.48581e11i	−0.0778763	−	0.134886i
$717$	9.30203e12	−	2.49247e12i	1.31444	−	0.352204i
$718$	8.28246e12	−	2.21928e12i	1.16305	−	0.311639i
$719$	2.84902e12	+	4.93464e12i	0.397571	+	0.688613i	0.993426	−	0.114479i	$-0.0365199\pi$
$719$	2.84902e12	+	4.93464e12i	0.397571	+	0.688613i	−0.595855	+	0.803092i	$0.703187\pi$
$720$	9.92148e11	−	2.54479e12i	0.137588	−	0.352904i
$721$	−1.03505e12	−	2.52667e12i	−0.142644	−	0.348209i
$722$	6.39817e12	−	6.39817e12i	0.876270	−	0.876270i
$723$	−1.40545e12	+	5.24520e12i	−0.191290	+	0.713903i
$724$	−2.64197e11	+	4.57602e11i	−0.0357358	+	0.0618962i
$725$	−1.12609e12	−	3.59313e12i	−0.151374	−	0.483005i
$726$	3.86700e12	−	2.23261e12i	0.516605	−	0.298262i
$727$	2.63835e12	+	2.63835e12i	0.350290	+	0.350290i	0.860217	−	0.509928i	$-0.170328\pi$
$727$	2.63835e12	+	2.63835e12i	0.350290	+	0.350290i	−0.509928	+	0.860217i	$0.670328\pi$
$728$	3.42312e12	+	4.49732e12i	0.451680	+	0.593420i
$729$			8.30887e12i			1.08960i
$730$	−1.17689e13	+	1.80100e12i	−1.53385	+	0.234726i
$731$	−4.79881e12	−	2.77060e12i	−0.621592	−	0.358877i
$732$	9.40158e11	+	3.50872e12i	0.121032	+	0.451698i
$733$	−4.62527e12	−	1.23934e12i	−0.591792	−	0.158570i	−0.0495201	−	0.998773i	$-0.515769\pi$
$733$	−4.62527e12	−	1.23934e12i	−0.591792	−	0.158570i	−0.542272	+	0.840203i	$0.682436\pi$
$734$	6.44040e11			0.0818993
$735$	−9.45558e11	−	6.51867e12i	−0.119507	−	0.823884i
$736$	−7.11982e12			−0.894373
$737$	5.37606e9	+	1.44051e9i	0.000671213	+	0.000179851i
$738$	9.02134e11	+	3.36681e12i	0.111948	+	0.417797i
$739$	−8.54581e11	−	4.93392e11i	−0.105403	−	0.0608545i	0.446372	−	0.894848i	$-0.352716\pi$
$739$	−8.54581e11	−	4.93392e11i	−0.105403	−	0.0608545i	−0.551775	+	0.833993i	$0.686049\pi$
$740$	4.11351e12	−	5.59997e12i	0.504278	−	0.686504i
$741$			1.50103e13i			1.82897i
$742$	−4.14861e12	−	5.45047e12i	−0.502441	−	0.660111i
$743$	5.27756e12	+	5.27756e12i	0.635307	+	0.635307i	0.949394	−	0.314087i	$-0.101698\pi$
$743$	5.27756e12	+	5.27756e12i	0.635307	+	0.635307i	−0.314087	+	0.949394i	$0.601698\pi$
$744$	−3.47828e12	+	2.00818e12i	−0.416184	+	0.240284i
$745$	2.34563e12	+	2.92778e12i	0.278970	+	0.348205i
$746$	−9.99071e12	+	1.73044e13i	−1.18106	+	2.04565i
$747$	3.83608e11	−	1.43164e12i	0.0450760	−	0.168226i
$748$	−1.34748e12	+	1.34748e12i	−0.157386	+	0.157386i
$749$	2.98524e12	+	7.28730e12i	0.346586	+	0.846054i
$750$	−8.26107e12	+	4.04733e12i	−0.953369	+	0.467081i
$751$	1.89262e11	+	3.27811e11i	0.0217112	+	0.0376049i	0.876677	−	0.481080i	$-0.159755\pi$
$751$	1.89262e11	+	3.27811e11i	0.0217112	+	0.0376049i	−0.854966	+	0.518685i	$0.826422\pi$
$752$	4.70417e12	−	1.26048e12i	0.536417	−	0.143733i
$753$	9.96076e12	−	2.66898e12i	1.12905	−	0.302529i
$754$	−4.48143e12	−	7.76206e12i	−0.504946	−	0.874592i
$755$	1.00109e11	+	3.90298e10i	0.0112127	+	0.00437154i
$756$	−3.74420e12	+	4.84032e12i	−0.416880	+	0.538922i
$757$	1.98920e12	−	1.98920e12i	0.220165	−	0.220165i	−0.588403	−	0.808568i	$-0.700243\pi$
$757$	1.98920e12	−	1.98920e12i	0.220165	−	0.220165i	0.808568	+	0.588403i	$0.200243\pi$
$758$	2.41003e11	−	8.99434e11i	0.0265162	−	0.0989596i
$759$	2.05364e12	−	3.55701e12i	0.224614	−	0.389043i
$760$	−6.11885e12	−	6.75473e11i	−0.665286	−	0.0734424i
$761$	4.69871e12	−	2.71280e12i	0.507864	−	0.293216i	−0.224091	−	0.974568i	$-0.571941\pi$
$761$	4.69871e12	−	2.71280e12i	0.507864	−	0.293216i	0.731955	+	0.681353i	$0.238608\pi$
$762$	−7.48441e12	−	7.48441e12i	−0.804193	−	0.804193i
$763$	−9.46005e11	−	7.40889e12i	−0.101049	−	0.791394i
$764$			4.52941e12i			0.480974i
$765$	1.25830e12	+	9.24297e11i	0.132834	+	0.0975742i
$766$	−7.12948e12	−	4.11621e12i	−0.748219	−	0.431984i
$767$	4.84746e12	+	1.80910e13i	0.505749	+	1.88748i
$768$	−1.00454e13	−	2.69167e12i	−1.04194	−	0.279187i
$769$	1.51290e13			1.56006			0.780028	−	0.625744i	$-0.215205\pi$
$769$	1.51290e13			1.56006			0.780028	+	0.625744i	$0.215205\pi$
$770$	1.40384e11	+	8.23238e12i	0.0143916	+	0.843951i
$771$	−6.53476e12			−0.666017
$772$	6.26137e12	+	1.67773e12i	0.634442	+	0.169998i
$773$	−1.33538e12	−	4.98371e12i	−0.134523	−	0.502047i	−0.999999	−	0.00109740i	$-0.999651\pi$
$773$	−1.33538e12	−	4.98371e12i	−0.134523	−	0.502047i	0.865476	−	0.500950i	$-0.167016\pi$
$774$	4.52383e12	+	2.61184e12i	0.453077	+	0.261584i
$775$	−1.18694e13	−	2.65291e12i	−1.18187	−	0.264159i
$776$		−	8.06378e12i		−	0.798290i
$777$	9.15512e12	−	6.96839e12i	0.901093	−	0.685864i
$778$	−8.07280e12	−	8.07280e12i	−0.789980	−	0.789980i
$779$	1.38123e13	−	7.97455e12i	1.34384	−	0.775867i
$780$	−6.58049e12	+	5.27206e12i	−0.636550	+	0.509982i
$781$	6.23084e12	−	1.07921e13i	0.599262	−	1.03795i
$782$	1.51102e12	−	5.63919e12i	0.144490	−	0.539245i
$783$	−4.09590e12	+	4.09590e12i	−0.389423	+	0.389423i
$784$	1.26357e13	−	3.28027e12i	1.19448	−	0.310089i
$785$	−2.08180e12	−	4.74236e12i	−0.195671	−	0.445740i
$786$	8.35351e12	+	1.44687e13i	0.780670	+	1.35216i
$787$	−4.00453e12	+	1.07301e12i	−0.372105	+	0.0997053i	−0.440025	−	0.897986i	$-0.645030\pi$
$787$	−4.00453e12	+	1.07301e12i	−0.372105	+	0.0997053i	0.0679199	+	0.997691i	$0.478364\pi$
$788$	7.74845e12	−	2.07619e12i	0.715891	−	0.191822i
$789$	−1.29444e12	−	2.24203e12i	−0.118914	−	0.205966i
$790$	2.72021e11	+	6.19667e11i	0.0248474	+	0.0566026i
$791$	−1.20675e12	+	8.89777e12i	−0.109603	+	0.808141i
$792$	−7.58217e11	+	7.58217e11i	−0.0684747	+	0.0684747i
$793$	4.04491e12	−	1.50958e13i	0.363228	−	1.35559i
$794$	−7.14538e12	+	1.23762e13i	−0.638018	+	1.10508i
$795$	−4.76033e12	+	3.81381e12i	−0.422654	+	0.338616i
$796$	−9.60062e11	+	5.54292e11i	−0.0847599	+	0.0489362i
$797$	−1.19936e13	−	1.19936e13i	−1.05290	−	1.05290i	−0.998520	−	0.0543802i	$-0.982682\pi$
$797$	−1.19936e13	−	1.19936e13i	−1.05290	−	1.05290i	−0.0543802	−	0.998520i	$-0.517318\pi$
$798$	1.57517e13	+	6.59669e12i	1.37504	+	0.575855i
$799$			2.78385e12i			0.241649i
$800$	−6.81040e12	−	1.07311e13i	−0.587852	−	0.926270i
$801$	2.03083e12	+	1.17250e12i	0.174312	+	0.100639i
$802$	7.30112e12	+	2.72481e13i	0.623167	+	2.32569i
$803$	9.16593e12	+	2.45600e12i	0.777958	+	0.208453i
$804$	6.48468e9			0.000547314
$805$	−4.99939e12	−	8.32797e12i	−0.419600	−	0.698969i
$806$	−2.89497e13			−2.41622
$807$	−1.25952e13	−	3.37487e12i	−1.04538	−	0.280109i
$808$	2.12264e12	+	7.92180e12i	0.175196	+	0.653842i
$809$	−1.13878e13	−	6.57474e12i	−0.934696	−	0.539647i	−0.0464025	−	0.998923i	$-0.514776\pi$
$809$	−1.13878e13	−	6.57474e12i	−0.934696	−	0.539647i	−0.888294	+	0.459276i	$0.848109\pi$
$810$	7.54042e12	+	5.53889e12i	0.615479	+	0.452106i
$811$		−	1.31963e13i		−	1.07117i	−0.844482	−	0.535584i	$-0.820092\pi$
$811$		−	1.31963e13i		−	1.07117i	0.844482	−	0.535584i	$-0.179908\pi$
$812$	−3.89502e12	+	4.97337e11i	−0.314418	+	0.0401466i
$813$	3.48004e12	+	3.48004e12i	0.279368	+	0.279368i
$814$	−1.24549e13	+	7.19086e12i	−0.994332	+	0.574078i
$815$	1.53307e13	+	1.69239e12i	1.21717	+	0.134366i
$816$	3.49357e12	−	6.05103e12i	0.275844	−	0.477775i
$817$	6.18633e12	−	2.30877e13i	0.485773	−	1.81293i
$818$	8.68481e12	−	8.68481e12i	0.678219	−	0.678219i
$819$	5.72169e12	−	2.34389e12i	0.444372	−	0.182037i
$820$	8.34735e12	+	3.25441e12i	0.644742	+	0.251368i
$821$	1.18730e13	+	2.05647e13i	0.912049	+	1.57971i	0.811166	+	0.584816i	$0.198833\pi$
$821$	1.18730e13	+	2.05647e13i	0.912049	+	1.57971i	0.100883	+	0.994898i	$0.467833\pi$
$822$	4.49714e12	−	1.20501e12i	0.343568	−	0.0920589i
$823$	−4.34196e11	+	1.16342e11i	−0.0329903	+	0.00883973i	−0.275276	−	0.961365i	$-0.588769\pi$
$823$	−4.34196e11	+	1.16342e11i	−0.0329903	+	0.00883973i	0.242286	+	0.970205i	$0.422103\pi$
$824$	−1.18681e12	−	2.05561e12i	−0.0896824	−	0.155334i
$825$	7.32555e12	−	3.07160e11i	0.550551	−	0.0230846i
$826$	2.11150e13	+	2.86369e12i	1.57827	+	0.214050i
$827$	−4.03833e12	+	4.03833e12i	−0.300211	+	0.300211i	−0.841096	−	0.540885i	$-0.818089\pi$
$827$	−4.03833e12	+	4.03833e12i	−0.300211	+	0.300211i	0.540885	+	0.841096i	$0.318089\pi$
$828$	−5.48513e11	+	2.04708e12i	−0.0405556	+	0.151355i
$829$	4.85602e12	−	8.41087e12i	0.357096	−	0.618508i	−0.630378	−	0.776288i	$-0.717100\pi$
$829$	4.85602e12	−	8.41087e12i	0.357096	−	0.618508i	0.987474	+	0.157780i	$0.0504336\pi$
$830$	−6.18585e12	−	7.72107e12i	−0.452426	−	0.564710i
$831$	−4.17302e12	+	2.40929e12i	−0.303561	+	0.175261i
$832$	−2.52204e12	−	2.52204e12i	−0.182473	−	0.182473i
$833$	−5.82301e10	+	7.46200e12i	−0.00419030	+	0.536973i
$834$			5.13312e12i			0.367396i
$835$	−8.71023e12	+	1.18578e13i	−0.620070	+	0.844138i
$836$	−7.11872e12	−	4.11000e12i	−0.504050	−	0.291014i
$837$	4.84238e12	+	1.80720e13i	0.341031	+	1.27275i
$838$	−2.65598e13	−	7.11667e12i	−1.86049	−	0.498516i
$839$	−2.67824e13			−1.86604			−0.933020	−	0.359825i	$-0.882836\pi$
$839$	−2.67824e13			−1.86604			−0.933020	+	0.359825i	$0.882836\pi$
$840$	−1.57610e12	−	5.50487e12i	−0.109226	−	0.381496i
$841$	1.07903e13			0.743792
$842$	−2.03489e13	−	5.45246e12i	−1.39520	−	0.373842i
$843$	−3.65920e12	−	1.36563e13i	−0.249552	−	0.931342i
$844$	5.49303e12	+	3.17140e12i	0.372624	+	0.215135i
$845$	2.12102e13	−	3.24580e12i	1.43116	−	0.219012i
$846$		−	2.62433e12i		−	0.176137i
$847$	−3.25113e12	+	7.76312e12i	−0.217050	+	0.518276i
$848$	−8.54815e12	−	8.54815e12i	−0.567663	−	0.567663i
$849$	−8.67971e12	+	5.01123e12i	−0.573351	+	0.331024i
$850$	9.94478e12	−	3.11670e12i	0.653447	−	0.204790i
$851$	8.48322e12	−	1.46934e13i	0.554469	−	0.960369i
$852$	3.75786e12	−	1.40245e13i	0.244322	−	0.911823i
$853$	−5.19492e11	+	5.19492e11i	−0.0335976	+	0.0335976i	−0.723706	−	0.690108i	$-0.757563\pi$
$853$	−5.19492e11	+	5.19492e11i	−0.0335976	+	0.0335976i	0.690108	+	0.723706i	$0.257563\pi$
$854$	−1.40638e13	−	1.08790e13i	−0.904781	−	0.699888i
$855$	−2.44634e12	+	6.27469e12i	−0.156556	+	0.401555i
$856$	3.42293e12	+	5.92868e12i	0.217904	+	0.377421i
$857$	7.47838e12	−	2.00383e12i	0.473581	−	0.126896i	−0.0141312	−	0.999900i	$-0.504498\pi$
$857$	7.47838e12	−	2.00383e12i	0.473581	−	0.126896i	0.487712	+	0.873005i	$0.337832\pi$
$858$	1.68576e13	−	4.51697e12i	1.06195	−	0.284547i
$859$	−1.92792e11	−	3.33925e11i	−0.0120814	−	0.0209257i	0.859921	−	0.510426i	$-0.170512\pi$
$859$	−1.92792e11	−	3.33925e11i	−0.0120814	−	0.0209257i	−0.872003	+	0.489501i	$0.837179\pi$
$860$	1.22945e13	−	5.39702e12i	0.766420	−	0.336443i
$861$	1.17342e13	+	9.07690e12i	0.727676	+	0.562890i
$862$	−4.42686e12	+	4.42686e12i	−0.273095	+	0.273095i
$863$	5.37341e12	−	2.00538e13i	0.329763	−	1.23069i	−0.579674	−	0.814848i	$-0.696820\pi$
$863$	5.37341e12	−	2.00538e13i	0.329763	−	1.23069i	0.909437	−	0.415842i	$-0.136513\pi$
$864$	−9.77584e12	+	1.69323e13i	−0.596818	+	1.03372i
$865$	−1.25911e12	+	1.14058e13i	−0.0764700	+	0.692712i
$866$	2.46831e12	−	1.42508e12i	0.149131	−	0.0861010i
$867$	−6.96980e12	−	6.96980e12i	−0.418923	−	0.418923i
$868$	−4.89922e12	+	1.16985e13i	−0.292947	+	0.699504i
$869$		−	5.39379e11i		−	0.0320852i
$870$	1.37360e12	+	8.97600e12i	0.0812875	+	0.531185i
$871$	−2.41617e10	−	1.39498e10i	−0.00142248	−	0.000821269i
$872$	−1.68049e12	−	6.27167e12i	−0.0984263	−	0.367332i
$873$	−8.52121e12	−	2.28325e12i	−0.496520	−	0.133042i
$874$	2.51829e13			1.45984
$875$	7.76988e12	−	1.55012e13i	0.448103	−	0.893982i
$876$	1.10561e13			0.634355
$877$	−2.09705e13	−	5.61903e12i	−1.19705	−	0.320747i	−0.395379	−	0.918518i	$-0.629387\pi$
$877$	−2.09705e13	−	5.61903e12i	−1.19705	−	0.320747i	−0.801667	+	0.597771i	$0.796053\pi$
$878$	−3.09894e11	−	1.15654e12i	−0.0175990	−	0.0656803i
$879$	9.13207e12	+	5.27241e12i	0.515964	+	0.297892i
$880$	2.19814e12	+	1.43640e13i	0.123561	+	0.807429i
$881$		−	2.20109e12i		−	0.123097i	−0.998104	−	0.0615485i	$-0.980396\pi$
$881$		−	2.20109e12i		−	0.123097i	0.998104	−	0.0615485i	$-0.0196039\pi$
$882$	5.48934e10	−	7.03441e12i	0.00305430	−	0.391398i
$883$	−4.03058e12	−	4.03058e12i	−0.223123	−	0.223123i	0.586689	−	0.809812i	$-0.300431\pi$
$883$	−4.03058e12	−	4.03058e12i	−0.223123	−	0.223123i	−0.809812	+	0.586689i	$0.800431\pi$
$884$	8.27266e12	−	4.77622e12i	0.455628	−	0.263057i
$885$	2.08204e12	−	1.88604e13i	0.114089	−	1.03349i
$886$	−9.99779e12	+	1.73167e13i	−0.545070	+	0.944089i
$887$	−8.43206e12	+	3.14689e13i	−0.457380	+	1.70697i	0.223614	+	0.974678i	$0.428214\pi$
$887$	−8.43206e12	+	3.14689e13i	−0.457380	+	1.70697i	−0.680994	+	0.732289i	$0.738452\pi$
$888$	7.07232e12	−	7.07232e12i	0.381684	−	0.381684i
$889$	1.97696e13	+	2.68123e12i	1.06155	+	0.143972i
$890$	1.43328e13	−	6.29180e12i	0.765729	−	0.336140i
$891$	−3.72852e12	−	6.45798e12i	−0.198192	−	0.343279i
$892$	8.81504e12	−	2.36198e12i	0.466211	−	0.124921i
$893$	−1.15991e13	+	3.10796e12i	−0.610367	+	0.163547i
$894$	−4.52344e12	−	7.83483e12i	−0.236837	−	0.410214i
$895$	1.73425e12	−	4.44825e12i	0.0903460	−	0.231732i
$896$	1.58303e13	−	6.48488e12i	0.820547	−	0.336137i
$897$	−1.45585e13	+	1.45585e13i	−0.750845	+	0.750845i
$898$	−3.88114e11	+	1.44846e12i	−0.0199166	+	0.0743299i
$899$	−6.00263e12	+	1.03969e13i	−0.306495	+	0.530864i
$900$	−3.61005e12	+	1.13139e12i	−0.183410	+	0.0574806i
$901$	5.98445e12	−	3.45512e12i	0.302526	−	0.174663i
$902$	−1.31125e13	−	1.31125e13i	−0.659560	−	0.659560i
$903$	2.20536e13	−	2.81592e12i	1.10379	−	0.140937i
$904$			7.80573e12i			0.388737i
$905$	−2.27668e12	+	3.48401e11i	−0.112819	+	0.0172648i
$906$	−2.24399e11	−	1.29557e11i	−0.0110648	−	0.00638828i
$907$	7.66702e12	+	2.86137e13i	0.376178	+	1.40392i	0.851616	+	0.524167i	$0.175623\pi$
$907$	7.66702e12	+	2.86137e13i	0.376178	+	1.40392i	−0.475437	+	0.879750i	$0.657710\pi$
$908$	−9.60259e12	−	2.57301e12i	−0.468816	−	0.125619i
$909$	8.97220e12			0.435874
$910$	1.00009e13	−	4.00429e13i	0.483453	−	1.93571i
$911$	−2.45928e13			−1.18297			−0.591487	−	0.806315i	$-0.701459\pi$
$911$	−2.45928e13			−1.18297			−0.591487	+	0.806315i	$0.701459\pi$
$912$	2.91123e13	+	7.80061e12i	1.39348	+	0.373381i
$913$	2.04085e12	+	7.61657e12i	0.0972061	+	0.362778i
$914$	−2.64110e13	−	1.52484e13i	−1.25178	−	0.722714i
$915$	−9.37351e12	+	1.27607e13i	−0.442086	+	0.601839i
$916$		−	2.08112e12i		−	0.0976715i
$917$	−2.90464e13	−	1.21644e13i	−1.35653	−	0.568105i
$918$	−1.13363e13	−	1.13363e13i	−0.526842	−	0.526842i
$919$	3.31395e12	−	1.91331e12i	0.153259	−	0.0884842i	−0.421409	−	0.906871i	$-0.638464\pi$
$919$	3.31395e12	−	1.91331e12i	0.153259	−	0.0884842i	0.574668	+	0.818386i	$0.305131\pi$
$920$	−5.27955e12	−	6.58983e12i	−0.242969	−	0.303270i
$921$	9.00035e12	−	1.55891e13i	0.412184	−	0.713924i
$922$	5.35011e12	−	1.99669e13i	0.243823	−	0.909958i
$923$	−4.41711e13	+	4.41711e13i	−2.00323	+	2.00323i
$924$	1.02755e12	−	7.57650e12i	0.0463747	−	0.341936i
$925$	3.02605e13	−	1.26882e12i	1.35906	−	0.0569853i
$926$	−1.27498e12	−	2.20833e12i	−0.0569842	−	0.0986996i
$927$	−2.50826e12	+	6.72086e11i	−0.111561	+	0.0298927i
$928$	−1.21182e13	+	3.24705e12i	−0.536378	+	0.143722i
$929$	−7.13239e12	−	1.23537e13i	−0.314170	−	0.544158i	0.665091	−	0.746762i	$-0.268393\pi$
$929$	−7.13239e12	−	1.23537e13i	−0.314170	−	0.544158i	−0.979261	+	0.202605i	$0.935059\pi$
$930$	2.73263e13	+	1.06538e13i	1.19786	+	0.467015i
$931$	−3.11558e13	+	8.08815e12i	−1.35915	+	0.352838i
$932$	−2.67467e12	+	2.67467e12i	−0.116118	+	0.116118i
$933$	−1.32404e12	+	4.94139e12i	−0.0572050	+	0.213492i
$934$	−2.56255e13	+	4.43846e13i	−1.10182	+	1.90841i
$935$	−8.25618e12	−	9.11418e11i	−0.353286	−	0.0390001i
$936$	4.65496e12	−	2.68754e12i	0.198232	−	0.114450i
$937$	7.70176e12	+	7.70176e12i	0.326409	+	0.326409i	0.851219	−	0.524810i	$-0.175864\pi$
$937$	7.70176e12	+	7.70176e12i	0.326409	+	0.326409i	−0.524810	+	0.851219i	$0.675864\pi$
$938$	−2.52574e10	+	1.92246e10i	−0.00106531	+	0.000810857i
$939$			6.86564e12i			0.288195i
$940$	−5.43647e12	−	3.99341e12i	−0.227113	−	0.166828i
$941$	−1.57528e13	−	9.09489e12i	−0.654945	−	0.378133i	0.135403	−	0.990791i	$-0.456767\pi$
$941$	−1.57528e13	−	9.09489e12i	−0.654945	−	0.378133i	−0.790348	+	0.612658i	$0.790100\pi$
$942$	3.23258e12	+	1.20642e13i	0.133758	+	0.499192i
$943$	2.11311e13	+	5.66207e12i	0.870202	+	0.233170i
$944$	3.76065e13			1.54130
$945$	−2.66699e13	+	4.54792e11i	−1.08787	+	0.0185511i
$946$	−2.77907e13			−1.12821
$947$	2.19374e13	+	5.87812e12i	0.886362	+	0.237500i	0.673150	−	0.739506i	$-0.264941\pi$
$947$	2.19374e13	+	5.87812e12i	0.886362	+	0.237500i	0.213212	+	0.977006i	$0.431608\pi$
$948$	−1.62652e11	−	6.07024e11i	−0.00654065	−	0.0244100i
$949$	−4.11946e13	−	2.37837e13i	−1.64870	−	0.951878i
$950$	2.40885e13	+	3.79559e13i	0.959519	+	1.51190i
$951$		−	4.09742e10i		−	0.00162442i
$952$	8.21621e11	+	6.43474e12i	0.0324194	+	0.253901i
$953$	2.62694e13	+	2.62694e13i	1.03165	+	1.03165i	0.999482	+	0.0321680i	$0.0102412\pi$
$953$	2.62694e13	+	2.62694e13i	1.03165	+	1.03165i	0.0321680	+	0.999482i	$0.489759\pi$
$954$	−5.64153e12	+	3.25714e12i	−0.220510	+	0.127312i
$955$	−1.54079e13	+	1.23443e13i	−0.599417	+	0.480232i
$956$	1.32180e13	−	2.28942e13i	0.511804	−	0.886471i
$957$	1.87316e12	−	6.99073e12i	0.0721891	−	0.269413i
$958$	−1.54375e13	+	1.54375e13i	−0.592152	+	0.592152i
$959$	−5.36937e12	+	6.94125e12i	−0.204993	+	0.265005i
$960$	1.45248e12	+	3.30876e12i	0.0551936	+	0.125731i
$961$	6.16846e12	+	1.06841e13i	0.233304	+	0.404094i
$962$	6.96356e13	−	1.86588e13i	2.62146	−	0.702418i
$963$	7.23419e12	−	1.93840e12i	0.271064	−	0.0726314i
$964$	7.45329e12	+	1.29095e13i	0.277972	+	0.481462i
$965$	1.13573e13	+	2.58721e13i	0.421602	+	0.960414i
$966$	8.87947e12	+	2.16758e13i	0.328088	+	0.800898i
$967$	1.58324e13	−	1.58324e13i	0.582274	−	0.582274i	−0.353253	−	0.935528i	$-0.614925\pi$
$967$	1.58324e13	−	1.58324e13i	0.582274	−	0.582274i	0.935528	+	0.353253i	$0.114925\pi$
$968$	−1.89364e12	+	7.06716e12i	−0.0693200	+	0.258706i
$969$	−8.61408e12	+	1.49200e13i	−0.313871	+	0.543641i
$970$	−4.59561e13	+	3.68184e13i	−1.66675	+	1.33534i
$971$	1.28518e13	−	7.42000e12i	0.463957	−	0.267866i	−0.249749	−	0.968310i	$-0.580348\pi$
$971$	1.28518e13	−	7.42000e12i	0.463957	−	0.267866i	0.713707	+	0.700445i	$0.247015\pi$
$972$	7.26395e12	+	7.26395e12i	0.261020	+	0.261020i
$973$	−5.85996e12	−	7.69886e12i	−0.209598	−	0.275371i
$974$		−	6.41836e13i		−	2.28512i
$975$	−3.58685e13	−	8.01690e12i	−1.27114	−	0.284109i
$976$	−2.71761e13	−	1.56902e13i	−0.958658	−	0.553481i
$977$	−3.51254e11	−	1.31090e12i	−0.0123338	−	0.0460302i	0.959485	−	0.281761i	$-0.0909184\pi$
$977$	−3.51254e11	−	1.31090e12i	−0.0123338	−	0.0460302i	−0.971818	+	0.235730i	$0.924252\pi$
$978$	−3.59276e13	−	9.62676e12i	−1.25575	−	0.336477i
$979$	−1.24757e13			−0.434054
$980$	−1.44887e13	−	1.08179e13i	−0.501780	−	0.374650i
$981$	−7.10326e12			−0.244877
$982$	−3.61605e12	−	9.68918e11i	−0.124089	−	0.0332495i
$983$	7.10748e12	+	2.65255e13i	0.242787	+	0.906092i	0.974483	+	0.224461i	$0.0720622\pi$
$983$	7.10748e12	+	2.65255e13i	0.242787	+	0.906092i	−0.731697	+	0.681631i	$0.761271\pi$
$984$	1.11685e13	+	6.44816e12i	0.379768	+	0.219259i
$985$	2.81800e13	+	2.06999e13i	0.953846	+	0.700657i
$986$		−	1.02872e13i		−	0.346618i
$987$	−6.76494e12	−	8.88783e12i	−0.226901	−	0.298104i
$988$	2.91362e13	+	2.91362e13i	0.972808	+	0.972808i
$989$	2.83930e13	−	1.63927e13i	0.943685	−	0.544837i
$990$	7.78308e12	+	8.59192e11i	0.257510	+	0.0284270i
$991$	2.55166e13	−	4.41960e13i	0.840409	−	1.45563i	−0.0491406	−	0.998792i	$-0.515648\pi$
$991$	2.55166e13	−	4.41960e13i	0.840409	−	1.45563i	0.889549	−	0.456839i	$-0.151018\pi$
$992$	−1.04879e13	+	3.91412e13i	−0.343862	+	1.28331i
$993$	−1.79584e13	+	1.79584e13i	−0.586134	+	0.586134i
$994$	2.69407e13	+	6.57652e13i	0.875327	+	2.13677i
$995$	−4.50209e12	−	1.75524e12i	−0.145616	−	0.0567719i
$996$	4.59361e12	+	7.95636e12i	0.147906	+	0.256181i
$997$	1.76849e12	−	4.73866e11i	0.0566859	−	0.0151889i	−0.230365	−	0.973104i	$-0.573992\pi$
$997$	1.76849e12	−	4.73866e11i	0.0566859	−	0.0151889i	0.287051	+	0.957915i	$0.407325\pi$
$998$	1.60599e13	−	4.30324e12i	0.512455	−	0.137312i
$999$	−2.32957e13	−	4.03493e13i	−0.739999	−	1.28172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.k.a.3.7	✓	136
5.2	odd	4	inner	35.10.k.a.17.28	yes	136
7.5	odd	6	inner	35.10.k.a.33.28	yes	136
35.12	even	12	inner	35.10.k.a.12.7	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.7	✓	136	1.1	even	1	trivial
35.10.k.a.12.7	yes	136	35.12	even	12	inner
35.10.k.a.17.28	yes	136	5.2	odd	4	inner
35.10.k.a.33.28	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+(-27.8720 - 7.46827i) q^{2} +(30.2294 + 112.818i) q^{3} +(277.667 + 160.311i) q^{4} +(211.406 + 1381.46i) q^{5} -3370.21i q^{6} +(3847.43 + 5054.79i) q^{7} +(3904.82 + 3904.82i) q^{8} +(5231.97 - 3020.68i) q^{9} +(4424.83 - 40082.9i) q^{10} +(-16070.5 + 27834.9i) q^{11} +(-9692.22 + 36171.8i) q^{12} +(113925. - 113925. i) q^{13} +(-69485.0 - 169621. i) q^{14} +(-149462. + 65611.0i) q^{15} +(-161752. - 280163. i) q^{16} +(178620. - 47861.0i) q^{17} +(-168385. + 45118.5i) q^{18} +(398832. + 690796. i) q^{19} +(-162763. + 417477. i) q^{20} +(-453964. + 586862. i) q^{21} +(655794. - 655794. i) q^{22} +(-283178. + 1.05683e6i) q^{23} +(-322492. + 558573. i) q^{24} +(-1.86374e6 + 584097. i) q^{25} +(-4.02615e6 + 2.32450e6i) q^{26} +(2.12453e6 + 2.12453e6i) q^{27} +(257967. + 2.02033e6i) q^{28} +1.92791e6i q^{29} +(4.65582e6 - 712482. i) q^{30} +(5.39281e6 + 3.11354e6i) q^{31} +(1.68423e6 + 6.28565e6i) q^{32} +(-3.62607e6 - 971601. i) q^{33} -5.33593e6 q^{34} +(-6.16962e6 + 6.38369e6i) q^{35} +1.93699e6 q^{36} +(-1.49786e7 - 4.01351e6i) q^{37} +(-5.95717e6 - 2.22324e7i) q^{38} +(1.62967e7 + 9.40889e6i) q^{39} +(-4.56885e6 + 6.21985e6i) q^{40} -1.99948e7i q^{41} +(1.70357e7 - 1.29667e7i) q^{42} +(-2.11886e7 - 2.11886e7i) q^{43} +(-8.92448e6 + 5.15255e6i) q^{44} +(5.27901e6 + 6.58917e6i) q^{45} +(1.57854e7 - 2.73412e7i) q^{46} +(-3.89633e6 + 1.45413e7i) q^{47} +(2.67176e7 - 2.67176e7i) q^{48} +(-1.07481e7 + 3.88959e7i) q^{49} +(5.63083e7 - 2.36101e6i) q^{50} +(1.07991e7 + 1.87047e7i) q^{51} +(4.98968e7 - 1.33698e7i) q^{52} +(3.60954e7 - 9.67172e6i) q^{53} +(-4.33483e7 - 7.50814e7i) q^{54} +(-4.18502e7 - 1.63163e7i) q^{55} +(-4.71449e6 + 3.47615e7i) q^{56} +(-6.58776e7 + 6.58776e7i) q^{57} +(1.43982e7 - 5.37347e7i) q^{58} +(-5.81237e7 + 1.00673e8i) q^{59} +(-5.20190e7 - 5.74249e6i) q^{60} +(8.40056e7 - 4.85006e7i) q^{61} +(-1.27056e8 - 1.27056e8i) q^{62} +(3.53985e7 + 1.48246e7i) q^{63} -2.21377e7i q^{64} +(1.81468e8 + 1.33299e8i) q^{65} +(9.38094e7 + 5.41609e7i) q^{66} +(-44818.6 - 167265. i) q^{67} +(5.72695e7 + 1.53453e7i) q^{68} -1.27790e8 q^{69} +(2.19635e8 - 1.31850e8i) q^{70} -3.87720e8 q^{71} +(3.22251e7 + 8.63468e6i) q^{72} +(-7.64135e7 - 2.85179e8i) q^{73} +(3.87510e8 + 2.23729e8i) q^{74} +(-1.22236e8 - 1.92606e8i) q^{75} +2.55748e8i q^{76} +(-2.02529e8 + 2.58600e7i) q^{77} +(-3.83953e8 - 3.83953e8i) q^{78} +(-1.45334e7 + 8.39084e6i) q^{79} +(3.52838e8 - 2.82682e8i) q^{80} +(-1.16005e8 + 2.00927e8i) q^{81} +(-1.49326e8 + 5.57294e8i) q^{82} +(1.73477e8 - 1.73477e8i) q^{83} +(-2.20131e8 + 9.01767e7i) q^{84} +(1.03879e8 + 2.36638e8i) q^{85} +(4.32326e8 + 7.48811e8i) q^{86} +(-2.17502e8 + 5.82796e7i) q^{87} +(-1.71442e8 + 4.59378e7i) q^{88} +(1.94079e8 + 3.36154e8i) q^{89} +(-9.79268e7 - 2.23078e8i) q^{90} +(1.01419e9 + 1.37548e8i) q^{91} +(-2.48051e8 + 2.48051e8i) q^{92} +(-1.88241e8 + 7.02525e8i) q^{93} +(2.17197e8 - 3.76196e8i) q^{94} +(-8.69993e8 + 6.97008e8i) q^{95} +(-6.58219e8 + 3.80023e8i) q^{96} +(-1.03254e9 - 1.03254e9i) q^{97} +(5.90057e8 - 1.00384e9i) q^{98} +1.94175e8i 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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