LMFDB - Embedded newform 75.12.e.d.32.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,12,Mod(32,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	75.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:	$57.6257385420$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.4
Character	$\chi$	$=$	75.32
Dual form			75.12.e.d.68.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-43.6110 + 43.6110i) q^{2} +(-46.3532 - 418.328i) q^{3} -1755.85i q^{4} +(20265.2 + 16222.2i) q^{6} +(-35410.1 - 35410.1i) q^{7} +(-12741.2 - 12741.2i) q^{8} +(-172850. + 38781.7i) q^{9} +O(q^{10})$	\(q+(-43.6110 + 43.6110i) q^{2} +(-46.3532 - 418.328i) q^{3} -1755.85i q^{4} +(20265.2 + 16222.2i) q^{6} +(-35410.1 - 35410.1i) q^{7} +(-12741.2 - 12741.2i) q^{8} +(-172850. + 38781.7i) q^{9} +524649. i q^{11} +(-734519. + 81389.0i) q^{12} +(409234. - 409234. i) q^{13} +3.08854e6 q^{14} +4.70728e6 q^{16} +(-4.40971e6 + 4.40971e6i) q^{17} +(5.84685e6 - 9.22947e6i) q^{18} +9.09734e6i q^{19} +(-1.31717e7 + 1.64544e7i) q^{21} +(-2.28805e7 - 2.28805e7i) q^{22} +(3.10110e7 + 3.10110e7i) q^{23} +(-4.73939e6 + 5.92058e6i) q^{24} +3.56942e7i q^{26} +(2.42356e7 + 7.05103e7i) q^{27} +(-6.21747e7 + 6.21747e7i) q^{28} +1.53459e7 q^{29} -1.36758e8 q^{31} +(-1.79196e8 + 1.79196e8i) q^{32} +(2.19475e8 - 2.43191e7i) q^{33} -3.84624e8i q^{34} +(6.80946e7 + 3.03497e8i) q^{36} +(-5.28154e8 - 5.28154e8i) q^{37} +(-3.96744e8 - 3.96744e8i) q^{38} +(-1.90163e8 - 1.52225e8i) q^{39} -1.17968e8i q^{41} +(-1.43164e8 - 1.29202e9i) q^{42} +(6.42326e8 - 6.42326e8i) q^{43} +9.21202e8 q^{44} -2.70484e9 q^{46} +(-1.78057e9 + 1.78057e9i) q^{47} +(-2.18197e8 - 1.96919e9i) q^{48} +5.30426e8i q^{49} +(2.04911e9 + 1.64030e9i) q^{51} +(-7.18552e8 - 7.18552e8i) q^{52} +(-6.96556e8 - 6.96556e8i) q^{53} +(-4.13196e9 - 2.01809e9i) q^{54} +9.02332e8i q^{56} +(3.80567e9 - 4.21690e8i) q^{57} +(-6.69250e8 + 6.69250e8i) q^{58} +2.53786e9 q^{59} +1.20966e10 q^{61} +(5.96414e9 - 5.96414e9i) q^{62} +(7.49389e9 + 4.74737e9i) q^{63} -5.98930e9i q^{64} +(-8.51096e9 + 1.06321e10i) q^{66} +(-4.84703e9 - 4.84703e9i) q^{67} +(7.74277e9 + 7.74277e9i) q^{68} +(1.15353e10 - 1.44102e10i) q^{69} -1.33743e10i q^{71} +(2.69643e9 + 1.70818e9i) q^{72} +(-1.02228e10 + 1.02228e10i) q^{73} +4.60666e10 q^{74} +1.59735e10 q^{76} +(1.85779e10 - 1.85779e10i) q^{77} +(1.49319e10 - 1.65454e9i) q^{78} +2.79769e10i q^{79} +(2.83730e10 - 1.34068e10i) q^{81} +(5.14472e9 + 5.14472e9i) q^{82} +(6.76670e9 + 6.76670e9i) q^{83} +(2.88914e10 + 2.31274e10i) q^{84} +5.60250e10i q^{86} +(-7.11330e8 - 6.41962e9i) q^{87} +(6.68463e9 - 6.68463e9i) q^{88} +1.37523e9 q^{89} -2.89820e10 q^{91} +(5.44505e10 - 5.44505e10i) q^{92} +(6.33914e9 + 5.72095e10i) q^{93} -1.55305e11i q^{94} +(8.32688e10 + 6.66563e10i) q^{96} +(2.33049e9 + 2.33049e9i) q^{97} +(-2.31324e10 - 2.31324e10i) q^{98} +(-2.03467e10 - 9.06854e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7}+O(q^{10}) $ 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7	$ 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7} + 1714188 q^{12} + 3448472 q^{13} - 43202180 q^{16} - 3729120 q^{18} + 33570840 q^{21} + 21743260 q^{22} - 113282712 q^{27} - 253355948 q^{28} + 67990880 q^{31} + 563443560 q^{33} + 1116103980 q^{36} - 1292573224 q^{37} + 5132304780 q^{42} - 4012128208 q^{43} - 8170829920 q^{46} + 13847034876 q^{48} + 5424535440 q^{51} - 10287332704 q^{52} + 10576855656 q^{57} - 56277468420 q^{58} - 24994982320 q^{61} + 50371112832 q^{63} + 56311074600 q^{66} - 37314988144 q^{67} + 92983114440 q^{72} - 51361482568 q^{73} - 121004023440 q^{76} + 104085843000 q^{78} - 22936122360 q^{81} + 56747065840 q^{82} - 84564024000 q^{87} - 148338843420 q^{88} + 230876677280 q^{91} - 38932525008 q^{93} - 437860137180 q^{96} + 294950050616 q^{97}+O(q^{100}) $ 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7 + 1714188 * q^12 + 3448472 * q^13 - 43202180 * q^16 - 3729120 * q^18 + 33570840 * q^21 + 21743260 * q^22 - 113282712 * q^27 - 253355948 * q^28 + 67990880 * q^31 + 563443560 * q^33 + 1116103980 * q^36 - 1292573224 * q^37 + 5132304780 * q^42 - 4012128208 * q^43 - 8170829920 * q^46 + 13847034876 * q^48 + 5424535440 * q^51 - 10287332704 * q^52 + 10576855656 * q^57 - 56277468420 * q^58 - 24994982320 * q^61 + 50371112832 * q^63 + 56311074600 * q^66 - 37314988144 * q^67 + 92983114440 * q^72 - 51361482568 * q^73 - 121004023440 * q^76 + 104085843000 * q^78 - 22936122360 * q^81 + 56747065840 * q^82 - 84564024000 * q^87 - 148338843420 * q^88 + 230876677280 * q^91 - 38932525008 * q^93 - 437860137180 * q^96 + 294950050616 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−43.6110	+	43.6110i	−0.963677	+	0.963677i	−0.999363	−	0.0356861i	$-0.988638\pi$
$2$	−43.6110	+	43.6110i	−0.963677	+	0.963677i	0.0356861	+	0.999363i	$0.488638\pi$
$3$	−46.3532	−	418.328i	−0.110132	−	0.993917i
$3$	−46.3532	−	418.328i	−0.110132	−	0.993917i
$4$		−	1755.85i		−	0.857346i
$5$		0			0
$5$		0			0
$6$	20265.2	+	16222.2i	1.06395	+	0.851683i
$7$	−35410.1	−	35410.1i	−0.796321	−	0.796321i	0.186192	−	0.982513i	$-0.440385\pi$
$7$	−35410.1	−	35410.1i	−0.796321	−	0.796321i	−0.982513	+	0.186192i	$0.940385\pi$
$8$	−12741.2	−	12741.2i	−0.137472	−	0.137472i
$9$	−172850.	+	38781.7i	−0.975742	+	0.218924i
$10$		0			0
$11$			524649.i			0.982220i	0.871098	+	0.491110i	$0.163409\pi$
$11$			524649.i			0.982220i	−0.871098	+	0.491110i	$0.836591\pi$
$12$	−734519.	+	81389.0i	−0.852131	+	0.0944210i
$13$	409234.	−	409234.i	0.305691	−	0.305691i	−0.537544	−	0.843236i	$-0.680648\pi$
$13$	409234.	−	409234.i	0.305691	−	0.305691i	0.843236	+	0.537544i	$0.180648\pi$
$14$	3.08854e6			1.53479
$15$		0			0
$16$	4.70728e6			1.12230
$17$	−4.40971e6	+	4.40971e6i	−0.753253	+	0.753253i	−0.975085	−	0.221832i	$-0.928796\pi$
$17$	−4.40971e6	+	4.40971e6i	−0.753253	+	0.753253i	0.221832	+	0.975085i	$0.428796\pi$
$18$	5.84685e6	−	9.22947e6i	0.729328	−	1.15127i
$19$			9.09734e6i			0.842888i	0.906855	+	0.421444i	$0.138477\pi$
$19$			9.09734e6i			0.842888i	−0.906855	+	0.421444i	$0.861523\pi$
$20$		0			0
$21$	−1.31717e7	+	1.64544e7i	−0.703777	+	0.879177i
$22$	−2.28805e7	−	2.28805e7i	−0.946543	−	0.946543i
$23$	3.10110e7	+	3.10110e7i	1.00464	+	1.00464i	0.999989	+	0.00465491i	$0.00148171\pi$
$23$	3.10110e7	+	3.10110e7i	1.00464	+	1.00464i	0.00465491	+	0.999989i	$0.498518\pi$
$24$	−4.73939e6	+	5.92058e6i	−0.121496	+	0.151776i
$25$		0			0
$26$			3.56942e7i			0.589175i
$27$	2.42356e7	+	7.05103e7i	0.325052	+	0.945696i
$28$	−6.21747e7	+	6.21747e7i	−0.682723	+	0.682723i
$29$	1.53459e7			0.138932			0.0694661	−	0.997584i	$-0.477870\pi$
$29$	1.53459e7			0.138932			0.0694661	+	0.997584i	$0.477870\pi$
$30$		0			0
$31$	−1.36758e8			−0.857950			−0.428975	−	0.903316i	$-0.641125\pi$
$31$	−1.36758e8			−0.857950			−0.428975	+	0.903316i	$0.641125\pi$
$32$	−1.79196e8	+	1.79196e8i	−0.944066	+	0.944066i
$33$	2.19475e8	−	2.43191e7i	0.976245	−	0.108174i
$34$		−	3.84624e8i		−	1.45179i
$35$		0			0
$36$	6.80946e7	+	3.03497e8i	0.187693	+	0.836549i
$37$	−5.28154e8	−	5.28154e8i	−1.25213	−	1.25213i	−0.954762	−	0.297372i	$-0.903890\pi$
$37$	−5.28154e8	−	5.28154e8i	−1.25213	−	1.25213i	−0.297372	−	0.954762i	$-0.596110\pi$
$38$	−3.96744e8	−	3.96744e8i	−0.812271	−	0.812271i
$39$	−1.90163e8	−	1.52225e8i	−0.337498	−	0.270166i
$40$		0			0
$41$		−	1.17968e8i		−	0.159021i	−0.996834	−	0.0795104i	$-0.974664\pi$
$41$		−	1.17968e8i		−	0.159021i	0.996834	−	0.0795104i	$-0.0253357\pi$
$42$	−1.43164e8	−	1.29202e9i	−0.169029	−	1.52546i
$43$	6.42326e8	−	6.42326e8i	0.666315	−	0.666315i	−0.290546	−	0.956861i	$-0.593837\pi$
$43$	6.42326e8	−	6.42326e8i	0.666315	−	0.666315i	0.956861	+	0.290546i	$0.0938371\pi$
$44$	9.21202e8			0.842103
$45$		0			0
$46$	−2.70484e9			−1.93630
$47$	−1.78057e9	+	1.78057e9i	−1.13246	+	1.13246i	−0.142688	+	0.989768i	$0.545574\pi$
$47$	−1.78057e9	+	1.78057e9i	−1.13246	+	1.13246i	−0.989768	+	0.142688i	$0.954426\pi$
$48$	−2.18197e8	−	1.96919e9i	−0.123601	−	1.11548i
$49$			5.30426e8i			0.268254i
$50$		0			0
$51$	2.04911e9	+	1.64030e9i	0.831628	+	0.665714i
$52$	−7.18552e8	−	7.18552e8i	−0.262083	−	0.262083i
$53$	−6.96556e8	−	6.96556e8i	−0.228791	−	0.228791i	0.583397	−	0.812187i	$-0.301723\pi$
$53$	−6.96556e8	−	6.96556e8i	−0.228791	−	0.228791i	−0.812187	+	0.583397i	$0.801723\pi$
$54$	−4.13196e9	−	2.01809e9i	−1.22459	−	0.598100i
$55$		0			0
$56$			9.02332e8i			0.218944i
$57$	3.80567e9	−	4.21690e8i	0.837760	−	0.0928286i
$58$	−6.69250e8	+	6.69250e8i	−0.133886	+	0.133886i
$59$	2.53786e9			0.462149			0.231074	−	0.972936i	$-0.425776\pi$
$59$	2.53786e9			0.462149			0.231074	+	0.972936i	$0.425776\pi$
$60$		0			0
$61$	1.20966e10			1.83379			0.916894	−	0.399132i	$-0.130688\pi$
$61$	1.20966e10			1.83379			0.916894	+	0.399132i	$0.130688\pi$
$62$	5.96414e9	−	5.96414e9i	0.826787	−	0.826787i
$63$	7.49389e9	+	4.74737e9i	0.951337	+	0.602670i
$64$		−	5.98930e9i		−	0.697246i
$65$		0			0
$66$	−8.51096e9	+	1.06321e10i	−0.836541	+	1.04503i
$67$	−4.84703e9	−	4.84703e9i	−0.438595	−	0.438595i	0.452944	−	0.891539i	$-0.350374\pi$
$67$	−4.84703e9	−	4.84703e9i	−0.438595	−	0.438595i	−0.891539	+	0.452944i	$0.850374\pi$
$68$	7.74277e9	+	7.74277e9i	0.645799	+	0.645799i
$69$	1.15353e10	−	1.44102e10i	0.887890	−	1.10918i
$70$		0			0
$71$		−	1.33743e10i		−	0.879733i	−0.898063	−	0.439866i	$-0.855026\pi$
$71$		−	1.33743e10i		−	0.879733i	0.898063	−	0.439866i	$-0.144974\pi$
$72$	2.69643e9	+	1.70818e9i	0.164233	+	0.104041i
$73$	−1.02228e10	+	1.02228e10i	−0.577155	+	0.577155i	−0.934118	−	0.356963i	$-0.883812\pi$
$73$	−1.02228e10	+	1.02228e10i	−0.577155	+	0.577155i	0.356963	+	0.934118i	$0.383812\pi$
$74$	4.60666e10			2.41330
$75$		0			0
$76$	1.59735e10			0.722647
$77$	1.85779e10	−	1.85779e10i	0.782163	−	0.782163i
$78$	1.49319e10	−	1.65454e9i	0.585592	−	0.0648869i
$79$			2.79769e10i			1.02294i	0.859301	+	0.511470i	$0.170899\pi$
$79$			2.79769e10i			1.02294i	−0.859301	+	0.511470i	$0.829101\pi$
$80$		0			0
$81$	2.83730e10	−	1.34068e10i	0.904145	−	0.427226i
$82$	5.14472e9	+	5.14472e9i	0.153245	+	0.153245i
$83$	6.76670e9	+	6.76670e9i	0.188559	+	0.188559i	0.795073	−	0.606514i	$-0.207433\pi$
$83$	6.76670e9	+	6.76670e9i	0.188559	+	0.188559i	−0.606514	+	0.795073i	$0.707433\pi$
$84$	2.88914e10	+	2.31274e10i	0.753759	+	0.603381i
$85$		0			0
$86$			5.60250e10i			1.28422i
$87$	−7.11330e8	−	6.41962e9i	−0.0153008	−	0.138087i
$88$	6.68463e9	−	6.68463e9i	0.135028	−	0.135028i
$89$	1.37523e9			0.0261054			0.0130527	−	0.999915i	$-0.495845\pi$
$89$	1.37523e9			0.0261054			0.0130527	+	0.999915i	$0.495845\pi$
$90$		0			0
$91$	−2.89820e10			−0.486857
$92$	5.44505e10	−	5.44505e10i	0.861328	−	0.861328i
$93$	6.33914e9	+	5.72095e10i	0.0944875	+	0.852731i
$94$		−	1.55305e11i		−	2.18264i
$95$		0			0
$96$	8.32688e10	+	6.66563e10i	1.04229	+	0.834352i
$97$	2.33049e9	+	2.33049e9i	0.0275551	+	0.0275551i	0.720750	−	0.693195i	$-0.243798\pi$
$97$	2.33049e9	+	2.33049e9i	0.0275551	+	0.0275551i	−0.693195	+	0.720750i	$0.743798\pi$
$98$	−2.31324e10	−	2.31324e10i	−0.258510	−	0.258510i
$99$	−2.03467e10	−	9.06854e10i	−0.215031	−	0.958393i
$100$		0			0
$101$		−	9.60815e10i		−	0.909646i	−0.890582	−	0.454823i	$-0.849703\pi$
$101$		−	9.60815e10i		−	0.909646i	0.890582	−	0.454823i	$-0.150297\pi$
$102$	−1.60899e11	+	1.78285e10i	−1.44295	+	0.159888i
$103$	1.06495e11	−	1.06495e11i	0.905162	−	0.905162i	−0.0907153	−	0.995877i	$-0.528915\pi$
$103$	1.06495e11	−	1.06495e11i	0.905162	−	0.905162i	0.995877	+	0.0907153i	$0.0289153\pi$
$104$	−1.04282e10			−0.0840480
$105$		0			0
$106$	6.07550e10			0.440961
$107$	1.75132e11	−	1.75132e11i	1.20713	−	1.20713i	0.235181	−	0.971952i	$-0.424432\pi$
$107$	1.75132e11	−	1.75132e11i	1.20713	−	1.20713i	0.971952	−	0.235181i	$-0.0755684\pi$
$108$	1.23805e11	−	4.25539e10i	0.810789	−	0.278682i
$109$		−	4.46073e10i		−	0.277690i	−0.990314	−	0.138845i	$-0.955661\pi$
$109$		−	4.46073e10i		−	0.277690i	0.990314	−	0.138845i	$-0.0443390\pi$
$110$		0			0
$111$	−1.96460e11	+	2.45423e11i	−1.10662	+	1.38242i
$112$	−1.66685e11	−	1.66685e11i	−0.893714	−	0.893714i
$113$	−1.89887e11	−	1.89887e11i	−0.969533	−	0.969533i	0.0300160	−	0.999549i	$-0.490444\pi$
$113$	−1.89887e11	−	1.89887e11i	−0.969533	−	0.969533i	−0.999549	+	0.0300160i	$0.990444\pi$
$114$	−1.47579e11	+	1.84360e11i	−0.717873	+	0.896787i
$115$		0			0
$116$		−	2.69450e10i		−	0.119113i
$117$	−5.48652e10	+	8.66068e10i	−0.231353	+	0.365199i
$118$	−1.10679e11	+	1.10679e11i	−0.445362	+	0.445362i
$119$	3.12297e11			1.19966
$120$		0			0
$121$	1.00554e10			0.0352436
$122$	−5.27545e11	+	5.27545e11i	−1.76718	+	1.76718i
$123$	−4.93494e10	+	5.46820e9i	−0.158053	+	0.0175132i
$124$			2.40125e11i			0.735560i
$125$		0			0
$126$	−5.33854e11	+	1.19779e11i	−1.49756	+	0.336002i
$127$	1.55054e11	+	1.55054e11i	0.416451	+	0.416451i	0.883978	−	0.467528i	$-0.154855\pi$
$127$	1.55054e11	+	1.55054e11i	0.416451	+	0.416451i	−0.467528	+	0.883978i	$0.654855\pi$
$128$	−1.05793e11	−	1.05793e11i	−0.272146	−	0.272146i
$129$	−2.98477e11	−	2.38929e11i	−0.735644	−	0.588879i
$130$		0			0
$131$		−	6.50357e11i		−	1.47286i	−0.676516	−	0.736428i	$-0.736511\pi$
$131$		−	6.50357e11i		−	1.47286i	0.676516	−	0.736428i	$-0.263489\pi$
$132$	−4.27006e10	−	3.85365e11i	−0.0927422	−	0.836980i
$133$	3.22138e11	−	3.22138e11i	0.671209	−	0.671209i
$134$	4.22768e11			0.845328
$135$		0			0
$136$	1.12370e11			0.207102
$137$	1.92236e11	−	1.92236e11i	0.340308	−	0.340308i	−0.516175	−	0.856483i	$-0.672645\pi$
$137$	1.92236e11	−	1.92236e11i	0.340308	−	0.340308i	0.856483	+	0.516175i	$0.172645\pi$
$138$	1.25378e11	+	1.13151e12i	0.213249	+	1.92453i
$139$		−	2.69329e10i		−	0.0440252i	−0.999758	−	0.0220126i	$-0.992993\pi$
$139$		−	2.69329e10i		−	0.0440252i	0.999758	−	0.0220126i	$-0.00700739\pi$
$140$		0			0
$141$	8.27398e11	+	6.62328e11i	1.25029	+	1.00085i
$142$	5.83268e11	+	5.83268e11i	0.847778	+	0.847778i
$143$	2.14704e11	+	2.14704e11i	0.300256	+	0.300256i
$144$	−8.13653e11	+	1.82556e11i	−1.09508	+	0.245699i
$145$		0			0
$146$		−	8.91651e11i		−	1.11238i
$147$	2.21892e11	−	2.45869e10i	0.266623	−	0.0295433i
$148$	−9.27356e11	+	9.27356e11i	−1.07351	+	1.07351i
$149$	−9.46891e11			−1.05627			−0.528136	−	0.849160i	$-0.677109\pi$
$149$	−9.46891e11			−1.05627			−0.528136	+	0.849160i	$0.677109\pi$
$150$		0			0
$151$	3.02676e10			0.0313766			0.0156883	−	0.999877i	$-0.495006\pi$
$151$	3.02676e10			0.0313766			0.0156883	+	0.999877i	$0.495006\pi$
$152$	1.15911e11	−	1.15911e11i	0.115873	−	0.115873i
$153$	5.91202e11	−	9.33233e11i	0.570076	−	0.899886i
$154$			1.62040e12i			1.50750i
$155$		0			0
$156$	−2.67283e11	+	3.33897e11i	−0.231625	+	0.289353i
$157$	1.66536e12	+	1.66536e12i	1.39335	+	1.39335i	0.817689	+	0.575660i	$0.195255\pi$
$157$	1.66536e12	+	1.66536e12i	1.39335	+	1.39335i	0.575660	+	0.817689i	$0.304745\pi$
$158$	−1.22010e12	−	1.22010e12i	−0.985784	−	0.985784i
$159$	−2.59101e11	+	3.23676e11i	−0.202202	+	0.252596i
$160$		0			0
$161$		−	2.19620e12i		−	1.60004i
$162$	−6.52693e11	+	1.82206e12i	−0.459596	+	1.28301i
$163$	−9.84088e11	+	9.84088e11i	−0.669888	+	0.669888i	−0.957690	−	0.287802i	$-0.907076\pi$
$163$	−9.84088e11	+	9.84088e11i	−0.669888	+	0.669888i	0.287802	+	0.957690i	$0.407076\pi$
$164$	−2.07134e11			−0.136336
$165$		0			0
$166$	−5.90205e11			−0.363420
$167$	2.63049e11	−	2.63049e11i	0.156710	−	0.156710i	−0.624397	−	0.781107i	$-0.714655\pi$
$167$	2.63049e11	−	2.63049e11i	0.156710	−	0.156710i	0.781107	+	0.624397i	$0.214655\pi$
$168$	3.77471e11	−	4.18259e10i	0.217612	−	0.0241126i
$169$			1.45722e12i			0.813106i
$170$		0			0
$171$	−3.52810e11	−	1.57247e12i	−0.184528	−	0.822441i
$172$	−1.12783e12	−	1.12783e12i	−0.571262	−	0.571262i
$173$	−7.49313e11	−	7.49313e11i	−0.367629	−	0.367629i	0.498983	−	0.866612i	$-0.333707\pi$
$173$	−7.49313e11	−	7.49313e11i	−0.367629	−	0.367629i	−0.866612	+	0.498983i	$0.833707\pi$
$174$	3.10988e11	+	2.48944e11i	0.147816	+	0.118326i
$175$		0			0
$176$			2.46967e12i			1.10235i
$177$	−1.17638e11	−	1.06166e12i	−0.0508972	−	0.459338i
$178$	−5.99752e10	+	5.99752e10i	−0.0251572	+	0.0251572i
$179$	−1.18450e12			−0.481773			−0.240887	−	0.970553i	$-0.577438\pi$
$179$	−1.18450e12			−0.481773			−0.240887	+	0.970553i	$0.577438\pi$
$180$		0			0
$181$	1.00633e12			0.385044			0.192522	−	0.981293i	$-0.438333\pi$
$181$	1.00633e12			0.385044			0.192522	+	0.981293i	$0.438333\pi$
$182$	1.26394e12	−	1.26394e12i	0.469173	−	0.469173i
$183$	−5.60715e11	−	5.06034e12i	−0.201958	−	1.82263i
$184$		−	7.90231e11i		−	0.276221i
$185$		0			0
$186$	−2.77142e12	−	2.21851e12i	−0.912813	−	0.730702i
$187$	−2.31355e12	−	2.31355e12i	−0.739860	−	0.739860i
$188$	3.12641e12	+	3.12641e12i	0.970907	+	0.970907i
$189$	1.63859e12	−	3.35496e12i	0.494232	−	1.01192i
$190$		0			0
$191$			2.04814e12i			0.583009i	0.956569	+	0.291505i	$0.0941559\pi$
$191$			2.04814e12i			0.583009i	−0.956569	+	0.291505i	$0.905844\pi$
$192$	−2.50549e12	+	2.77623e11i	−0.693005	+	0.0767889i
$193$	−2.05616e12	+	2.05616e12i	−0.552702	+	0.552702i	−0.927220	−	0.374518i	$-0.877808\pi$
$193$	−2.05616e12	+	2.05616e12i	−0.552702	+	0.552702i	0.374518	+	0.927220i	$0.377808\pi$
$194$	−2.03270e11			−0.0531084
$195$		0			0
$196$	9.31347e11			0.229987
$197$	−3.24306e12	+	3.24306e12i	−0.778736	+	0.778736i	−0.979616	−	0.200880i	$-0.935620\pi$
$197$	−3.24306e12	+	3.24306e12i	−0.778736	+	0.778736i	0.200880	+	0.979616i	$0.435620\pi$
$198$	4.84223e12	+	3.06754e12i	1.13080	+	0.716361i
$199$		−	6.74004e12i		−	1.53098i	−0.643446	−	0.765491i	$-0.722496\pi$
$199$		−	6.74004e12i		−	1.53098i	0.643446	−	0.765491i	$-0.277504\pi$
$200$		0			0
$201$	−1.80297e12	+	2.25232e12i	−0.387624	+	0.484231i
$202$	4.19022e12	+	4.19022e12i	0.876605	+	0.876605i
$203$	−5.43400e11	−	5.43400e11i	−0.110635	−	0.110635i
$204$	2.88012e12	−	3.59792e12i	0.570748	−	0.712993i
$205$		0			0
$206$			9.28875e12i			1.74457i
$207$	−6.56290e12	−	4.15758e12i	−1.20021	−	0.760333i
$208$	1.92638e12	−	1.92638e12i	0.343079	−	0.343079i
$209$	−4.77291e12			−0.827901
$210$		0			0
$211$	3.08005e11			0.0506996			0.0253498	−	0.999679i	$-0.491930\pi$
$211$	3.08005e11			0.0506996			0.0253498	+	0.999679i	$0.491930\pi$
$212$	−1.22304e12	+	1.22304e12i	−0.196153	+	0.196153i
$213$	−5.59485e12	+	6.19942e11i	−0.874381	+	0.0968865i
$214$			1.52754e13i			2.32657i
$215$		0			0
$216$	5.89593e11	−	1.20717e12i	0.0853212	−	0.174692i
$217$	4.84260e12	+	4.84260e12i	0.683204	+	0.683204i
$218$	1.94537e12	+	1.94537e12i	0.267604	+	0.267604i
$219$	4.75033e12	+	3.80261e12i	0.637208	+	0.510081i
$220$		0			0
$221$			3.60921e12i			0.460526i
$222$	−2.13533e12	−	1.92710e13i	−0.265781	−	2.39862i
$223$	1.09568e13	−	1.09568e13i	1.33048	−	1.33048i	0.425541	−	0.904939i	$-0.360084\pi$
$223$	1.09568e13	−	1.09568e13i	1.33048	−	1.33048i	0.904939	−	0.425541i	$-0.139916\pi$
$224$	1.26907e13			1.50356
$225$		0			0
$226$	1.65623e13			1.86863
$227$	3.27175e12	−	3.27175e12i	0.360278	−	0.360278i	−0.503637	−	0.863915i	$-0.668005\pi$
$227$	3.27175e12	−	3.27175e12i	0.360278	−	0.360278i	0.863915	+	0.503637i	$0.168005\pi$
$228$	−7.40423e11	−	6.68217e12i	−0.0795863	−	0.718251i
$229$		−	1.21950e13i		−	1.27964i	−0.768524	−	0.639821i	$-0.779009\pi$
$229$		−	1.21950e13i		−	1.27964i	0.768524	−	0.639821i	$-0.220991\pi$
$230$		0			0
$231$	−8.63279e12	−	6.91050e12i	−0.863546	−	0.691264i
$232$	−1.95524e11	−	1.95524e11i	−0.0190993	−	0.0190993i
$233$	8.14531e12	+	8.14531e12i	0.777052	+	0.777052i	0.979329	−	0.202276i	$-0.0648339\pi$
$233$	8.14531e12	+	8.14531e12i	0.777052	+	0.777052i	−0.202276	+	0.979329i	$0.564834\pi$
$234$	−1.38428e12	−	6.16974e12i	−0.128984	−	0.574883i
$235$		0			0
$236$		−	4.45609e12i		−	0.396222i
$237$	1.17035e13	−	1.29682e12i	1.01672	−	0.112658i
$238$	−1.36196e13	+	1.36196e13i	−1.15609	+	1.15609i
$239$	8.97959e12			0.744849			0.372424	−	0.928063i	$-0.378527\pi$
$239$	8.97959e12			0.744849			0.372424	+	0.928063i	$0.378527\pi$
$240$		0			0
$241$	2.36577e12			0.187447			0.0937237	−	0.995598i	$-0.470123\pi$
$241$	2.36577e12			0.187447			0.0937237	+	0.995598i	$0.470123\pi$
$242$	−4.38527e11	+	4.38527e11i	−0.0339635	+	0.0339635i
$243$	−6.92362e12	−	1.12478e13i	−0.524202	−	0.851594i
$244$		−	2.12397e13i		−	1.57219i
$245$		0			0
$246$	1.91371e12	−	2.39065e12i	0.135435	−	0.169190i
$247$	3.72294e12	+	3.72294e12i	0.257663	+	0.257663i
$248$	1.74245e12	+	1.74245e12i	0.117944	+	0.117944i
$249$	2.51704e12	−	3.14436e12i	0.166646	−	0.208178i
$250$		0			0
$251$		−	9.49671e12i		−	0.601683i	−0.953674	−	0.300841i	$-0.902732\pi$
$251$		−	9.49671e12i		−	0.601683i	0.953674	−	0.300841i	$-0.0972675\pi$
$252$	8.33564e12	−	1.31581e13i	0.516697	−	0.815626i
$253$	−1.62699e13	+	1.62699e13i	−0.986782	+	0.986782i
$254$	−1.35242e13			−0.802648
$255$		0			0
$256$	2.14936e13			1.22177
$257$	1.01861e13	−	1.01861e13i	0.566728	−	0.566728i	−0.364482	−	0.931210i	$-0.618754\pi$
$257$	1.01861e13	−	1.01861e13i	0.566728	−	0.566728i	0.931210	+	0.364482i	$0.118754\pi$
$258$	2.34368e13	−	2.59694e12i	1.27641	−	0.141434i
$259$			3.74040e13i			1.99420i
$260$		0			0
$261$	−2.65253e12	+	5.95139e11i	−0.135562	+	0.0304155i
$262$	2.83628e13	+	2.83628e13i	1.41936	+	1.41936i
$263$	−4.58647e10	−	4.58647e10i	−0.00224761	−	0.00224761i	0.705982	−	0.708230i	$-0.250506\pi$
$263$	−4.58647e10	−	4.58647e10i	−0.00224761	−	0.00224761i	−0.708230	+	0.705982i	$0.750506\pi$
$264$	−3.10622e12	−	2.48652e12i	−0.149077	−	0.119336i
$265$		0			0
$266$			2.80975e13i			1.29366i
$267$	−6.37462e10	−	5.75297e11i	−0.00287503	−	0.0259466i
$268$	−8.51063e12	+	8.51063e12i	−0.376028	+	0.376028i
$269$	−3.13380e12			−0.135654			−0.0678272	−	0.997697i	$-0.521607\pi$
$269$	−3.13380e12			−0.135654			−0.0678272	+	0.997697i	$0.521607\pi$
$270$		0			0
$271$	−1.44504e12			−0.0600549			−0.0300274	−	0.999549i	$-0.509559\pi$
$271$	−1.44504e12			−0.0600549			−0.0300274	+	0.999549i	$0.509559\pi$
$272$	−2.07577e13	+	2.07577e13i	−0.845379	+	0.845379i
$273$	1.34341e12	+	1.21240e13i	0.0536184	+	0.483895i
$274$			1.67673e13i			0.655894i
$275$		0			0
$276$	−2.53021e13	−	2.02542e13i	−0.950948	−	0.761229i
$277$	−1.18058e13	−	1.18058e13i	−0.434968	−	0.434968i	0.455346	−	0.890314i	$-0.349515\pi$
$277$	−1.18058e13	−	1.18058e13i	−0.434968	−	0.434968i	−0.890314	+	0.455346i	$0.849515\pi$
$278$	1.17457e12	+	1.17457e12i	0.0424260	+	0.0424260i
$279$	2.36385e13	−	5.30368e12i	0.837138	−	0.187826i
$280$		0			0
$281$		−	1.53930e12i		−	0.0524130i	−0.999657	−	0.0262065i	$-0.991657\pi$
$281$		−	1.53930e12i		−	0.0524130i	0.999657	−	0.0262065i	$-0.00834275\pi$
$282$	−6.49685e13	+	7.19888e12i	−2.16937	+	0.240378i
$283$	−7.71006e11	+	7.71006e11i	−0.0252483	+	0.0252483i	−0.719618	−	0.694370i	$-0.755683\pi$
$283$	−7.71006e11	+	7.71006e11i	−0.0252483	+	0.0252483i	0.694370	+	0.719618i	$0.255683\pi$
$284$	−2.34832e13			−0.754236
$285$		0			0
$286$	−1.87269e13			−0.578700
$287$	−4.17727e12	+	4.17727e12i	−0.126632	+	0.126632i
$288$	2.40244e13	−	3.79234e13i	0.714487	−	1.12784i
$289$		−	4.61919e12i		−	0.134781i
$290$		0			0
$291$	8.66882e11	−	1.08293e12i	0.0243528	−	0.0304222i
$292$	1.79496e13	+	1.79496e13i	0.494822	+	0.494822i
$293$	−8.16396e11	−	8.16396e11i	−0.0220866	−	0.0220866i	0.695977	−	0.718064i	$-0.254971\pi$
$293$	−8.16396e11	−	8.16396e11i	−0.0220866	−	0.0220866i	−0.718064	+	0.695977i	$0.754971\pi$
$294$	−8.60469e12	+	1.07492e13i	−0.228468	+	0.285408i
$295$		0			0
$296$			1.34586e13i			0.344267i
$297$	−3.69931e13	+	1.27152e13i	−0.928882	+	0.319273i
$298$	4.12949e13	−	4.12949e13i	1.01790	−	1.01790i
$299$	2.53815e13			0.614222
$300$		0			0
$301$	−4.54897e13			−1.06120
$302$	−1.32000e12	+	1.32000e12i	−0.0302369	+	0.0302369i
$303$	−4.01936e13	+	4.45368e12i	−0.904112	+	0.100181i
$304$			4.28237e13i			0.945976i
$305$		0			0
$306$	1.49164e13	+	6.64822e13i	0.317830	+	1.41657i
$307$	−4.17893e13	−	4.17893e13i	−0.874589	−	0.874589i	0.118379	−	0.992968i	$-0.462230\pi$
$307$	−4.17893e13	−	4.17893e13i	−0.874589	−	0.874589i	−0.992968	+	0.118379i	$0.962230\pi$
$308$	−3.26199e13	−	3.26199e13i	−0.670584	−	0.670584i
$309$	−4.94864e13	−	3.96136e13i	−0.999342	−	0.799968i
$310$		0			0
$311$		−	5.25247e13i		−	1.02372i	−0.859069	−	0.511860i	$-0.828957\pi$
$311$		−	5.25247e13i		−	1.02372i	0.859069	−	0.511860i	$-0.171043\pi$
$312$	4.83381e11	+	4.36242e12i	0.00925635	+	0.0835367i
$313$	−6.89998e13	+	6.89998e13i	−1.29824	+	1.29824i	−0.368680	+	0.929556i	$0.620190\pi$
$313$	−6.89998e13	+	6.89998e13i	−1.29824	+	1.29824i	−0.929556	+	0.368680i	$0.879810\pi$
$314$	−1.45256e14			−2.68548
$315$		0			0
$316$	4.91231e13			0.877014
$317$	1.10255e13	−	1.10255e13i	0.193451	−	0.193451i	−0.603735	−	0.797185i	$-0.706321\pi$
$317$	1.10255e13	−	1.10255e13i	0.193451	−	0.193451i	0.797185	+	0.603735i	$0.206321\pi$
$318$	−2.81619e12	−	2.54155e13i	−0.0485638	−	0.438279i
$319$			8.05120e12i			0.136462i
$320$		0			0
$321$	−8.13806e13	−	6.51448e13i	−1.33273	−	1.06685i
$322$	9.57787e13	+	9.57787e13i	1.54192	+	1.54192i
$323$	−4.01166e13	−	4.01166e13i	−0.634908	−	0.634908i
$324$	−2.35403e13	−	4.98187e13i	−0.366281	−	0.775165i
$325$		0			0
$326$		−	8.58342e13i		−	1.29111i
$327$	−1.86605e13	+	2.06769e12i	−0.276001	+	0.0305825i
$328$	−1.50305e12	+	1.50305e12i	−0.0218609	+	0.0218609i
$329$	1.26100e14			1.80360
$330$		0			0
$331$	−2.20341e12			−0.0304819			−0.0152410	−	0.999884i	$-0.504852\pi$
$331$	−2.20341e12			−0.0304819			−0.0152410	+	0.999884i	$0.504852\pi$
$332$	1.18813e13	−	1.18813e13i	0.161660	−	0.161660i
$333$	1.11774e14	+	7.08086e13i	1.49588	+	0.947638i
$334$			2.29437e13i			0.302035i
$335$		0			0
$336$	−6.20028e13	+	7.74556e13i	−0.789851	+	0.986704i
$337$	1.38530e13	+	1.38530e13i	0.173611	+	0.173611i	0.788564	−	0.614953i	$-0.210825\pi$
$337$	1.38530e13	+	1.38530e13i	0.173611	+	0.173611i	−0.614953	+	0.788564i	$0.710825\pi$
$338$	−6.35507e13	−	6.35507e13i	−0.783571	−	0.783571i
$339$	−7.06330e13	+	8.82367e13i	−0.856859	+	1.07041i
$340$		0			0
$341$		−	7.17497e13i		−	0.842696i
$342$	8.39636e13	+	5.31908e13i	0.970393	+	0.614742i
$343$	−5.12349e13	+	5.12349e13i	−0.582704	+	0.582704i
$344$	−1.63680e13			−0.183199
$345$		0			0
$346$	6.53567e13			0.708551
$347$	2.89299e13	−	2.89299e13i	0.308699	−	0.308699i	−0.535706	−	0.844405i	$-0.679954\pi$
$347$	2.89299e13	−	2.89299e13i	0.308699	−	0.308699i	0.844405	+	0.535706i	$0.179954\pi$
$348$	−1.12719e13	+	1.24899e12i	−0.118389	+	0.0131181i
$349$		−	3.69871e13i		−	0.382394i	−0.981552	−	0.191197i	$-0.938763\pi$
$349$		−	3.69871e13i		−	0.382394i	0.981552	−	0.191197i	$-0.0612369\pi$
$350$		0			0
$351$	3.87732e13	+	1.89372e13i	0.388457	+	0.189726i
$352$	−9.40147e13	−	9.40147e13i	−0.927281	−	0.927281i
$353$	4.86573e13	+	4.86573e13i	0.472484	+	0.472484i	0.902717	−	0.430234i	$-0.141569\pi$
$353$	4.86573e13	+	4.86573e13i	0.472484	+	0.472484i	−0.430234	+	0.902717i	$0.641569\pi$
$354$	5.14303e13	+	4.11697e13i	0.491701	+	0.393605i
$355$		0			0
$356$		−	2.41469e12i		−	0.0223814i
$357$	−1.44759e13	−	1.30642e14i	−0.132121	−	1.19237i
$358$	5.16572e13	−	5.16572e13i	0.464274	−	0.464274i
$359$	1.26269e14			1.11758			0.558790	−	0.829309i	$-0.311266\pi$
$359$	1.26269e14			1.11758			0.558790	+	0.829309i	$0.311266\pi$
$360$		0			0
$361$	3.37287e13			0.289541
$362$	−4.38873e13	+	4.38873e13i	−0.371058	+	0.371058i
$363$	−4.66101e11	−	4.20647e12i	−0.00388144	−	0.0350293i
$364$			5.08880e13i			0.417405i
$365$		0			0
$366$	2.45140e14	+	1.96234e14i	1.95105	+	1.56181i
$367$	1.15683e14	+	1.15683e14i	0.907000	+	0.907000i	0.996029	−	0.0890292i	$-0.0283764\pi$
$367$	1.15683e14	+	1.15683e14i	0.907000	+	0.907000i	−0.0890292	+	0.996029i	$0.528376\pi$
$368$	1.45977e14	+	1.45977e14i	1.12752	+	1.12752i
$369$	4.57500e12	+	2.03908e13i	0.0348134	+	0.155163i
$370$		0			0
$371$			4.93303e13i			0.364382i
$372$	1.00451e14	−	1.11306e13i	0.731086	−	0.0810085i
$373$	1.04829e14	−	1.04829e14i	0.751766	−	0.751766i	−0.223043	−	0.974809i	$-0.571599\pi$
$373$	1.04829e14	−	1.04829e14i	0.751766	−	0.751766i	0.974809	+	0.223043i	$0.0715990\pi$
$374$	2.01793e14			1.42597
$375$		0			0
$376$	4.53731e13			0.311362
$377$	6.28006e12	−	6.28006e12i	0.0424704	−	0.0424704i
$378$	7.48527e13	+	2.17774e14i	0.498887	+	1.45145i
$379$		−	1.55567e14i		−	1.02188i	−0.859615	−	0.510942i	$-0.829297\pi$
$379$		−	1.55567e14i		−	1.02188i	0.859615	−	0.510942i	$-0.170703\pi$
$380$		0			0
$381$	5.76764e13	−	7.20509e13i	0.368053	−	0.459782i
$382$	−8.93214e13	−	8.93214e13i	−0.561833	−	0.561833i
$383$	−1.84591e14	−	1.84591e14i	−1.14450	−	1.14450i	−0.987617	−	0.156887i	$-0.949854\pi$
$383$	−1.84591e14	−	1.84591e14i	−1.14450	−	1.14450i	−0.156887	−	0.987617i	$-0.550146\pi$
$384$	−3.93524e13	+	4.91601e13i	−0.240519	+	0.300463i
$385$		0			0
$386$		−	1.79342e14i		−	1.06525i
$387$	−8.61155e13	+	1.35936e14i	−0.504279	+	0.796023i
$388$	4.09197e12	−	4.09197e12i	0.0236243	−	0.0236243i
$389$	1.77987e14			1.01313			0.506565	−	0.862202i	$-0.330915\pi$
$389$	1.77987e14			1.01313			0.506565	+	0.862202i	$0.330915\pi$
$390$		0			0
$391$	−2.73499e14			−1.51350
$392$	6.75825e12	−	6.75825e12i	0.0368774	−	0.0368774i
$393$	−2.72063e14	+	3.01461e13i	−1.46390	+	0.162208i
$394$		−	2.82866e14i		−	1.50090i
$395$		0			0
$396$	−1.59230e14	+	3.57257e13i	−0.821675	+	0.184356i
$397$	3.44281e13	+	3.44281e13i	0.175213	+	0.175213i	0.789265	−	0.614052i	$-0.210462\pi$
$397$	3.44281e13	+	3.44281e13i	0.175213	+	0.175213i	−0.614052	+	0.789265i	$0.710462\pi$
$398$	2.93940e14	+	2.93940e14i	1.47537	+	1.47537i
$399$	−1.49691e14	−	1.19827e14i	−0.741048	−	0.593205i
$400$		0			0
$401$			3.46217e14i			1.66746i	0.552174	+	0.833729i	$0.313798\pi$
$401$			3.46217e14i			1.66746i	−0.552174	+	0.833729i	$0.686202\pi$
$402$	−1.95966e13	−	1.76856e14i	−0.0930975	−	0.840186i
$403$	−5.59658e13	+	5.59658e13i	−0.262268	+	0.262268i
$404$	−1.68704e14			−0.779882
$405$		0			0
$406$	4.73965e13			0.213232
$407$	2.77095e14	−	2.77095e14i	1.22987	−	1.22987i
$408$	−5.20869e12	−	4.70074e13i	−0.0228085	−	0.205843i
$409$			8.06958e13i			0.348637i	0.984689	+	0.174318i	$0.0557721\pi$
$409$			8.06958e13i			0.348637i	−0.984689	+	0.174318i	$0.944228\pi$
$410$		0			0
$411$	−8.93287e13	−	7.15071e13i	−0.375717	−	0.300759i
$412$	−1.86989e14	−	1.86989e14i	−0.776037	−	0.776037i
$413$	−8.98660e13	−	8.98660e13i	−0.368019	−	0.368019i
$414$	4.67531e14	−	1.04898e14i	1.88933	−	0.423903i
$415$		0			0
$416$			1.46666e14i			0.577186i
$417$	−1.12668e13	+	1.24842e12i	−0.0437574	+	0.00484857i
$418$	2.08151e14	−	2.08151e14i	0.797829	−	0.797829i
$419$	−2.61478e14			−0.989141			−0.494570	−	0.869138i	$-0.664675\pi$
$419$	−2.61478e14			−0.989141			−0.494570	+	0.869138i	$0.664675\pi$
$420$		0			0
$421$	9.14555e13			0.337022			0.168511	−	0.985700i	$-0.446104\pi$
$421$	9.14555e13			0.337022			0.168511	+	0.985700i	$0.446104\pi$
$422$	−1.34324e13	+	1.34324e13i	−0.0488581	+	0.0488581i
$423$	2.38718e14	−	3.76825e14i	0.857063	−	1.35291i
$424$			1.77499e13i			0.0629046i
$425$		0			0
$426$	2.16961e14	−	2.71034e14i	0.749254	−	0.935988i
$427$	−4.28342e14	−	4.28342e14i	−1.46028	−	1.46028i
$428$	−3.07505e14	−	3.07505e14i	−1.03493	−	1.03493i
$429$	7.98645e13	−	9.97689e13i	0.265362	−	0.331498i
$430$		0			0
$431$		−	9.83391e13i		−	0.318494i	−0.987239	−	0.159247i	$-0.949093\pi$
$431$		−	9.83391e13i		−	0.318494i	0.987239	−	0.159247i	$-0.0509066\pi$
$432$	1.14084e14	+	3.31912e14i	0.364807	+	1.06136i
$433$	2.84348e14	−	2.84348e14i	0.897772	−	0.897772i	−0.0974667	−	0.995239i	$-0.531074\pi$
$433$	2.84348e14	−	2.84348e14i	0.897772	−	0.897772i	0.995239	+	0.0974667i	$0.0310739\pi$
$434$	−4.22382e14			−1.31678
$435$		0			0
$436$	−7.83236e13			−0.238077
$437$	−2.82117e14	+	2.82117e14i	−0.846802	+	0.846802i
$438$	−3.73003e14	+	4.13308e13i	−1.10562	+	0.122509i
$439$		−	2.55151e14i		−	0.746866i	−0.927657	−	0.373433i	$-0.878181\pi$
$439$		−	2.55151e14i		−	0.746866i	0.927657	−	0.373433i	$-0.121819\pi$
$440$		0			0
$441$	−2.05708e13	−	9.16841e13i	−0.0587272	−	0.261747i
$442$	−1.57401e14	−	1.57401e14i	−0.443798	−	0.443798i
$443$	−2.85465e13	−	2.85465e13i	−0.0794935	−	0.0794935i	0.666242	−	0.745736i	$-0.267902\pi$
$443$	−2.85465e13	−	2.85465e13i	−0.0794935	−	0.0794935i	−0.745736	+	0.666242i	$0.767902\pi$
$444$	4.30925e14	+	3.44953e14i	1.18521	+	0.948754i
$445$		0			0
$446$			9.55678e14i			2.56431i
$447$	4.38914e13	+	3.96111e14i	0.116329	+	1.04985i
$448$	−2.12082e14	+	2.12082e14i	−0.555232	+	0.555232i
$449$	2.81157e13			0.0727100			0.0363550	−	0.999339i	$-0.488425\pi$
$449$	2.81157e13			0.0727100			0.0363550	+	0.999339i	$0.488425\pi$
$450$		0			0
$451$	6.18919e13			0.156193
$452$	−3.33411e14	+	3.33411e14i	−0.831226	+	0.831226i
$453$	−1.40300e12	−	1.26618e13i	−0.00345555	−	0.0311857i
$454$			2.85369e14i			0.694383i
$455$		0			0
$456$	−5.38615e13	−	4.31159e13i	−0.127930	−	0.102407i
$457$	2.53401e13	+	2.53401e13i	0.0594661	+	0.0594661i	0.736214	−	0.676748i	$-0.236611\pi$
$457$	2.53401e13	+	2.53401e13i	0.0594661	+	0.0594661i	−0.676748	+	0.736214i	$0.736611\pi$
$458$	5.31839e14	+	5.31839e14i	1.23316	+	1.23316i
$459$	−4.17802e14	−	2.04058e14i	−0.957195	−	0.467502i
$460$		0			0
$461$		−	1.23789e14i		−	0.276903i	−0.990369	−	0.138452i	$-0.955787\pi$
$461$		−	1.23789e14i		−	0.276903i	0.990369	−	0.138452i	$-0.0442125\pi$
$462$	6.77859e14	−	7.51107e13i	1.49833	−	0.166024i
$463$	−3.20134e13	+	3.20134e13i	−0.0699257	+	0.0699257i	−0.741205	−	0.671279i	$-0.765745\pi$
$463$	−3.20134e13	+	3.20134e13i	−0.0699257	+	0.0699257i	0.671279	+	0.741205i	$0.265745\pi$
$464$	7.22374e13			0.155924
$465$		0			0
$466$	−7.10451e14			−1.49765
$467$	4.74080e14	−	4.74080e14i	0.987662	−	0.987662i	−0.0122624	−	0.999925i	$-0.503903\pi$
$467$	4.74080e14	−	4.74080e14i	0.987662	−	0.987662i	0.999925	+	0.0122624i	$0.00390333\pi$
$468$	1.52068e14	+	9.63349e13i	0.313102	+	0.198350i
$469$			3.43268e14i			0.698525i
$470$		0			0
$471$	6.19472e14	−	7.73861e14i	1.23142	−	1.53833i
$472$	−3.23353e13	−	3.23353e13i	−0.0635325	−	0.0635325i
$473$	3.36996e14	+	3.36996e14i	0.654468	+	0.654468i
$474$	−4.53847e14	+	5.66958e14i	−0.871221	+	1.08835i
$475$		0			0
$476$		−	5.48345e14i		−	1.02853i
$477$	1.47413e14	+	9.33859e13i	0.273329	+	0.173153i
$478$	−3.91609e14	+	3.91609e14i	−0.717793	+	0.717793i
$479$	−2.24349e14			−0.406517			−0.203259	−	0.979125i	$-0.565153\pi$
$479$	−2.24349e14			−0.406517			−0.203259	+	0.979125i	$0.565153\pi$
$480$		0			0
$481$	−4.32277e14			−0.765533
$482$	−1.03174e14	+	1.03174e14i	−0.180639	+	0.180639i
$483$	−9.18734e14	+	1.01801e14i	−1.59031	+	0.176215i
$484$		−	1.76558e13i		−	0.0302160i
$485$		0			0
$486$	7.92474e14	+	1.88581e14i	1.32582	+	0.315500i
$487$	7.05283e14	+	7.05283e14i	1.16669	+	1.16669i	0.982981	+	0.183705i	$0.0588092\pi$
$487$	7.05283e14	+	7.05283e14i	1.16669	+	1.16669i	0.183705	+	0.982981i	$0.441191\pi$
$488$	−1.54125e14	−	1.54125e14i	−0.252094	−	0.252094i
$489$	4.57287e14	+	3.66056e14i	0.739589	+	0.592037i
$490$		0			0
$491$		−	1.74499e13i		−	0.0275959i	−0.999905	−	0.0137980i	$-0.995608\pi$
$491$		−	1.74499e13i		−	0.0275959i	0.999905	−	0.0137980i	$-0.00439217\pi$
$492$	9.60131e12	+	8.66499e13i	0.0150149	+	0.135507i
$493$	−6.76709e13	+	6.76709e13i	−0.104651	+	0.104651i
$494$	−3.24723e14			−0.496609
$495$		0			0
$496$	−6.43756e14			−0.962880
$497$	−4.73586e14	+	4.73586e14i	−0.700550	+	0.700550i
$498$	2.73579e13	+	2.46900e14i	0.0400241	+	0.361209i
$499$		−	8.00087e14i		−	1.15767i	−0.815445	−	0.578834i	$-0.803508\pi$
$499$		−	8.00087e14i		−	1.15767i	0.815445	−	0.578834i	$-0.196492\pi$
$500$		0			0
$501$	−1.22234e14	−	9.78476e13i	−0.173015	−	0.138498i
$502$	4.14161e14	+	4.14161e14i	0.579828	+	0.579828i
$503$	7.05829e14	+	7.05829e14i	0.977407	+	0.977407i	0.999750	−	0.0223432i	$-0.00711265\pi$
$503$	7.05829e14	+	7.05829e14i	0.977407	+	0.977407i	−0.0223432	+	0.999750i	$0.507113\pi$
$504$	−3.49939e13	−	1.55968e14i	−0.0479319	−	0.213632i
$505$		0			0
$506$		−	1.41909e15i		−	1.90188i
$507$	6.09594e14	−	6.75465e13i	0.808159	−	0.0895487i
$508$	2.72252e14	−	2.72252e14i	0.357043	−	0.357043i
$509$	9.96639e14			1.29298			0.646488	−	0.762925i	$-0.276237\pi$
$509$	9.96639e14			1.29298			0.646488	+	0.762925i	$0.276237\pi$
$510$		0			0
$511$	7.23979e14			0.919202
$512$	−7.20693e14	+	7.20693e14i	−0.905243	+	0.905243i
$513$	−6.41456e14	+	2.20479e14i	−0.797116	+	0.273982i
$514$			8.88451e14i			1.09229i
$515$		0			0
$516$	−4.19523e14	+	5.24080e14i	−0.504873	+	0.630701i
$517$	−9.34174e14	−	9.34174e14i	−1.11232	−	1.11232i
$518$	−1.63123e15	−	1.63123e15i	−1.92177	−	1.92177i
$519$	−2.78726e14	+	3.48192e14i	−0.324905	+	0.405881i
$520$		0			0
$521$			7.12040e14i			0.812637i	0.913731	+	0.406319i	$0.133188\pi$
$521$			7.12040e14i			0.812637i	−0.913731	+	0.406319i	$0.866812\pi$
$522$	8.97251e13	−	1.41634e14i	0.101327	−	0.159949i
$523$	3.57233e14	−	3.57233e14i	0.399202	−	0.399202i	−0.478749	−	0.877952i	$-0.658910\pi$
$523$	3.57233e14	−	3.57233e14i	0.399202	−	0.399202i	0.877952	+	0.478749i	$0.158910\pi$
$524$	−1.14193e15			−1.26275
$525$		0			0
$526$	4.00041e12			0.00433195
$527$	6.03061e14	−	6.03061e14i	0.646254	−	0.646254i
$528$	1.03313e15	−	1.14477e14i	1.09564	−	0.121404i
$529$			9.70551e14i			1.01862i
$530$		0			0
$531$	−4.38669e14	+	9.84225e13i	−0.450938	+	0.101175i
$532$	−5.65624e14	−	5.65624e14i	−0.575459	−	0.575459i
$533$	−4.82766e13	−	4.82766e13i	−0.0486113	−	0.0486113i
$534$	2.78693e13	+	2.23093e13i	0.0277747	+	0.0222335i
$535$		0			0
$536$			1.23513e14i			0.120589i
$537$	5.49052e13	+	4.95509e14i	0.0530585	+	0.478843i
$538$	1.36668e14	−	1.36668e14i	0.130727	−	0.130727i
$539$	−2.78288e14			−0.263485
$540$		0			0
$541$	1.09682e15			1.01754			0.508769	−	0.860903i	$-0.330101\pi$
$541$	1.09682e15			1.01754			0.508769	+	0.860903i	$0.330101\pi$
$542$	6.30196e13	−	6.30196e13i	0.0578735	−	0.0578735i
$543$	−4.66467e13	−	4.20978e14i	−0.0424055	−	0.382701i
$544$		−	1.58040e15i		−	1.42224i
$545$		0			0
$546$	−5.87328e14	−	4.70153e14i	−0.517990	−	0.414648i
$547$	−4.89786e13	−	4.89786e13i	−0.0427638	−	0.0427638i	0.685402	−	0.728165i	$-0.259627\pi$
$547$	−4.89786e13	−	4.89786e13i	−0.0427638	−	0.0427638i	−0.728165	+	0.685402i	$0.759627\pi$
$548$	−3.37537e14	−	3.37537e14i	−0.291762	−	0.291762i
$549$	−2.09089e15	+	4.69126e14i	−1.78930	+	0.401459i
$550$		0			0
$551$			1.39607e14i			0.117104i
$552$	−3.30576e14	+	3.66297e13i	−0.274540	+	0.0304207i
$553$	9.90665e14	−	9.90665e14i	0.814589	−	0.814589i
$554$	1.02973e15			0.838337
$555$		0			0
$556$	−4.72899e13			−0.0377448
$557$	−3.29530e14	+	3.29530e14i	−0.260430	+	0.260430i	−0.825229	−	0.564799i	$-0.808954\pi$
$557$	−3.29530e14	+	3.29530e14i	−0.260430	+	0.260430i	0.564799	+	0.825229i	$0.308954\pi$
$558$	−7.99601e14	+	1.26220e15i	−0.625727	+	0.987734i
$559$		−	5.25724e14i		−	0.407373i
$560$		0			0
$561$	−8.60582e14	+	1.07506e15i	−0.653878	+	0.816842i
$562$	6.71306e13	+	6.71306e13i	0.0505092	+	0.0505092i
$563$	2.49095e14	+	2.49095e14i	0.185596	+	0.185596i	0.793789	−	0.608193i	$-0.208105\pi$
$563$	2.49095e14	+	2.49095e14i	0.185596	+	0.185596i	−0.608193	+	0.793789i	$0.708105\pi$
$564$	1.16295e15	−	1.45278e15i	0.858073	−	1.07193i
$565$		0			0
$566$		−	6.72488e13i		−	0.0486625i
$567$	−1.47943e15	−	5.29956e14i	−1.06020	−	0.379781i
$568$	−1.70404e14	+	1.70404e14i	−0.120939	+	0.120939i
$569$	−4.22881e14			−0.297235			−0.148618	−	0.988895i	$-0.547482\pi$
$569$	−4.22881e14			−0.297235			−0.148618	+	0.988895i	$0.547482\pi$
$570$		0			0
$571$	−1.29378e15			−0.891991			−0.445995	−	0.895035i	$-0.647150\pi$
$571$	−1.29378e15			−0.891991			−0.445995	+	0.895035i	$0.647150\pi$
$572$	3.76987e14	−	3.76987e14i	0.257424	−	0.257424i
$573$	8.56793e14	−	9.49376e13i	0.579463	−	0.0642078i
$574$		−	3.64350e14i		−	0.244064i
$575$		0			0
$576$	2.32275e14	+	1.03525e15i	0.152644	+	0.680332i
$577$	1.67279e15	+	1.67279e15i	1.08887	+	1.08887i	0.995645	+	0.0932237i	$0.0297172\pi$
$577$	1.67279e15	+	1.67279e15i	1.08887	+	1.08887i	0.0932237	+	0.995645i	$0.470283\pi$
$578$	2.01448e14	+	2.01448e14i	0.129885	+	0.129885i
$579$	9.55457e14	+	7.64839e14i	0.610210	+	0.488470i
$580$		0			0
$581$		−	4.79219e14i		−	0.300307i
$582$	9.42220e12	+	8.50335e13i	0.00584892	+	0.0527854i
$583$	3.65447e14	−	3.65447e14i	0.224723	−	0.224723i
$584$	2.60500e14			0.158685
$585$		0			0
$586$	7.12077e13			0.0425687
$587$	9.50478e14	−	9.50478e14i	0.562902	−	0.562902i	−0.367229	−	0.930131i	$-0.619693\pi$
$587$	9.50478e14	−	9.50478e14i	0.562902	−	0.562902i	0.930131	+	0.367229i	$0.119693\pi$
$588$	−4.31709e13	−	3.89609e14i	−0.0253288	−	0.228588i
$589$		−	1.24413e15i		−	0.723155i
$590$		0			0
$591$	1.50699e15	+	1.20634e15i	0.859763	+	0.688236i
$592$	−2.48617e15	−	2.48617e15i	−1.40527	−	1.40527i
$593$	1.14157e15	+	1.14157e15i	0.639298	+	0.639298i	0.950382	−	0.311084i	$-0.100692\pi$
$593$	1.14157e15	+	1.14157e15i	0.639298	+	0.639298i	−0.311084	+	0.950382i	$0.600692\pi$
$594$	1.05879e15	−	2.16783e15i	0.587466	−	1.20282i
$595$		0			0
$596$			1.66259e15i			0.905590i
$597$	−2.81955e15	+	3.12422e14i	−1.52167	+	0.168610i
$598$	−1.10691e15	+	1.10691e15i	−0.591912	+	0.591912i
$599$	1.03710e15			0.549509			0.274755	−	0.961514i	$-0.411403\pi$
$599$	1.03710e15			0.549509			0.274755	+	0.961514i	$0.411403\pi$
$600$		0			0
$601$	1.37246e15			0.713985			0.356993	−	0.934107i	$-0.383802\pi$
$601$	1.37246e15			0.713985			0.356993	+	0.934107i	$0.383802\pi$
$602$	1.98385e15	−	1.98385e15i	1.02265	−	1.02265i
$603$	1.02578e15	+	6.49832e14i	0.523975	+	0.331937i
$604$		−	5.31453e13i		−	0.0269006i
$605$		0			0
$606$	1.55866e15	−	1.94711e15i	0.774730	−	0.967814i
$607$	−4.62201e14	−	4.62201e14i	−0.227663	−	0.227663i	0.584053	−	0.811716i	$-0.301466\pi$
$607$	−4.62201e14	−	4.62201e14i	−0.227663	−	0.227663i	−0.811716	+	0.584053i	$0.801466\pi$
$608$	−1.63020e15	−	1.63020e15i	−0.795742	−	0.795742i
$609$	−2.02131e14	+	2.52508e14i	−0.0977773	+	0.122146i
$610$		0			0
$611$			1.45734e15i			0.692364i
$612$	−1.63861e15	−	1.03806e15i	−0.771514	−	0.488753i
$613$	−1.83647e15	+	1.83647e15i	−0.856942	+	0.856942i	−0.990977	−	0.134035i	$-0.957207\pi$
$613$	−1.83647e15	+	1.83647e15i	−0.856942	+	0.856942i	0.134035	+	0.990977i	$0.457207\pi$
$614$	3.64495e15			1.68564
$615$		0			0
$616$	−4.73407e14			−0.215051
$617$	9.64469e14	−	9.64469e14i	0.434230	−	0.434230i	−0.455834	−	0.890065i	$-0.650659\pi$
$617$	9.64469e14	−	9.64469e14i	0.434230	−	0.434230i	0.890065	+	0.455834i	$0.150659\pi$
$618$	3.88574e15	−	4.30563e14i	1.73395	−	0.192132i
$619$			1.94681e15i			0.861042i	0.902581	+	0.430521i	$0.141670\pi$
$619$			1.94681e15i			0.861042i	−0.902581	+	0.430521i	$0.858330\pi$
$620$		0			0
$621$	−1.43502e15	+	2.93816e15i	−0.623526	+	1.27665i
$622$	2.29066e15	+	2.29066e15i	0.986536	+	0.986536i
$623$	−4.86970e13	−	4.86970e13i	−0.0207883	−	0.0207883i
$624$	−8.95152e14	−	7.16565e14i	−0.378775	−	0.303208i
$625$		0			0
$626$		−	6.01830e15i		−	2.50216i
$627$	2.21239e14	+	1.99664e15i	0.0911782	+	0.822865i
$628$	2.92411e15	−	2.92411e15i	1.19458	−	1.19458i
$629$	4.65801e15			1.88635
$630$		0			0
$631$	−1.00138e15			−0.398507			−0.199253	−	0.979948i	$-0.563852\pi$
$631$	−1.00138e15			−0.398507			−0.199253	+	0.979948i	$0.563852\pi$
$632$	3.56458e14	−	3.56458e14i	0.140626	−	0.140626i
$633$	−1.42770e13	−	1.28847e14i	−0.00558364	−	0.0503912i
$634$			9.61664e14i			0.372848i
$635$		0			0
$636$	5.68326e14	+	4.54942e14i	0.216562	+	0.173357i
$637$	2.17068e14	+	2.17068e14i	0.0820030	+	0.0820030i
$638$	−3.51121e14	−	3.51121e14i	−0.131505	−	0.131505i
$639$	5.18678e14	+	2.31175e15i	0.192594	+	0.858392i
$640$		0			0
$641$		−	4.09876e14i		−	0.149601i	−0.997199	−	0.0748004i	$-0.976168\pi$
$641$		−	4.09876e14i		−	0.149601i	0.997199	−	0.0748004i	$-0.0238320\pi$
$642$	6.39012e15	−	7.08062e14i	2.31242	−	0.256229i
$643$	−2.45331e15	+	2.45331e15i	−0.880221	+	0.880221i	−0.993557	−	0.113336i	$-0.963846\pi$
$643$	−2.45331e15	+	2.45331e15i	−0.880221	+	0.880221i	0.113336	+	0.993557i	$0.463846\pi$
$644$	−3.85620e15			−1.37179
$645$		0			0
$646$	3.49906e15			1.22369
$647$	−1.26128e15	+	1.26128e15i	−0.437358	+	0.437358i	−0.891122	−	0.453764i	$-0.850081\pi$
$647$	−1.26128e15	+	1.26128e15i	−0.437358	+	0.437358i	0.453764	+	0.891122i	$0.350081\pi$
$648$	−5.32323e14	−	1.90687e14i	−0.183026	−	0.0655630i
$649$			1.33149e15i			0.453932i
$650$		0			0
$651$	1.80133e15	−	2.25027e15i	0.603805	−	0.754290i
$652$	1.72791e15	+	1.72791e15i	0.574326	+	0.574326i
$653$	2.15668e15	+	2.15668e15i	0.710827	+	0.710827i	0.966708	−	0.255881i	$-0.0823656\pi$
$653$	2.15668e15	+	2.15668e15i	0.710827	+	0.710827i	−0.255881	+	0.966708i	$0.582366\pi$
$654$	7.23630e14	−	9.03978e14i	0.236504	−	0.295447i
$655$		0			0
$656$		−	5.55310e14i		−	0.178470i
$657$	1.37055e15	−	2.16346e15i	0.436802	−	0.689508i
$658$	−5.49937e15	+	5.49937e15i	−1.73808	+	1.73808i
$659$	−4.17629e15			−1.30894			−0.654471	−	0.756087i	$-0.727109\pi$
$659$	−4.17629e15			−1.30894			−0.654471	+	0.756087i	$0.727109\pi$
$660$		0			0
$661$	4.79966e15			1.47946			0.739729	−	0.672905i	$-0.234954\pi$
$661$	4.79966e15			1.47946			0.739729	+	0.672905i	$0.234954\pi$
$662$	9.60932e13	−	9.60932e13i	0.0293747	−	0.0293747i
$663$	1.50983e15	−	1.67298e14i	0.457725	−	0.0507185i
$664$		−	1.72431e14i		−	0.0518431i
$665$		0			0
$666$	−7.96261e15	+	1.78654e15i	−2.35476	+	0.528329i
$667$	4.75891e14	+	4.75891e14i	0.139577	+	0.139577i
$668$	−4.61873e14	−	4.61873e14i	−0.134354	−	0.134354i
$669$	−5.09144e15	−	4.07567e15i	−1.46892	−	1.17586i
$670$		0			0
$671$			6.34646e15i			1.80118i
$672$	−5.88253e14	−	5.30886e15i	−0.165590	−	1.49441i
$673$	−1.24138e14	+	1.24138e14i	−0.0346596	+	0.0346596i	−0.724224	−	0.689565i	$-0.757802\pi$
$673$	−1.24138e14	+	1.24138e14i	−0.0346596	+	0.0346596i	0.689565	+	0.724224i	$0.257802\pi$
$674$	−1.20828e15			−0.334611
$675$		0			0
$676$	2.55865e15			0.697113
$677$	−2.60495e15	+	2.60495e15i	−0.703982	+	0.703982i	−0.965263	−	0.261281i	$-0.915855\pi$
$677$	−2.60495e15	+	2.60495e15i	−0.703982	+	0.703982i	0.261281	+	0.965263i	$0.415855\pi$
$678$	−7.67715e14	−	6.92848e15i	−0.205796	−	1.85727i
$679$		−	1.65046e14i		−	0.0438854i
$680$		0			0
$681$	−1.52032e15	−	1.21701e15i	−0.397764	−	0.318408i
$682$	3.12908e15	+	3.12908e15i	0.812087	+	0.812087i
$683$	−1.58495e15	−	1.58495e15i	−0.408038	−	0.408038i	0.473016	−	0.881054i	$-0.343165\pi$
$683$	−1.58495e15	−	1.58495e15i	−0.408038	−	0.408038i	−0.881054	+	0.473016i	$0.843165\pi$
$684$	−2.76102e15	+	6.19480e14i	−0.705117	+	0.158204i
$685$		0			0
$686$		−	4.46882e15i		−	1.12308i
$687$	−5.10153e15	+	5.65279e14i	−1.27186	+	0.140929i
$688$	3.02361e15	−	3.02361e15i	0.747807	−	0.747807i
$689$	−5.70109e14			−0.139879
$690$		0			0
$691$	1.60272e14			0.0387016			0.0193508	−	0.999813i	$-0.493840\pi$
$691$	1.60272e14			0.0387016			0.0193508	+	0.999813i	$0.493840\pi$
$692$	−1.31568e15	+	1.31568e15i	−0.315186	+	0.315186i
$693$	−2.49070e15	+	3.93166e15i	−0.591955	+	0.934423i
$694$			2.52333e15i			0.594972i
$695$		0			0
$696$	−7.27302e13	+	9.08566e13i	−0.0168797	+	0.0210865i
$697$	5.20206e14	+	5.20206e14i	0.119783	+	0.119783i
$698$	1.61305e15	+	1.61305e15i	0.368504	+	0.368504i
$699$	3.02985e15	−	3.78497e15i	0.686747	−	0.857904i
$700$		0			0
$701$		−	3.89618e15i		−	0.869341i	−0.900590	−	0.434670i	$-0.856865\pi$
$701$		−	3.89618e15i		−	0.869341i	0.900590	−	0.434670i	$-0.143135\pi$
$702$	−2.51681e15	+	8.65071e14i	−0.557181	+	0.191513i
$703$	4.80479e15	−	4.80479e15i	1.05541	−	1.05541i
$704$	3.14228e15			0.684849
$705$		0			0
$706$	−4.24399e15			−0.910643
$707$	−3.40226e15	+	3.40226e15i	−0.724370	+	0.724370i
$708$	−1.86411e15	+	2.06554e14i	−0.393811	+	0.0436366i
$709$			3.29111e15i			0.689903i	0.938621	+	0.344951i	$0.112105\pi$
$709$			3.29111e15i			0.689903i	−0.938621	+	0.344951i	$0.887895\pi$
$710$		0			0
$711$	−1.08499e15	−	4.83580e15i	−0.223946	−	0.998126i
$712$	−1.75220e13	−	1.75220e13i	−0.00358876	−	0.00358876i
$713$	−4.24098e15	−	4.24098e15i	−0.861935	−	0.861935i
$714$	6.32877e15	+	5.06614e15i	1.27638	+	1.02173i
$715$		0			0
$716$			2.07980e15i			0.413047i
$717$	−4.16232e14	−	3.75641e15i	−0.0820314	−	0.740318i
$718$	−5.50674e15	+	5.50674e15i	−1.07699	+	1.07699i
$719$	1.04637e15			0.203085			0.101542	−	0.994831i	$-0.467622\pi$
$719$	1.04637e15			0.203085			0.101542	+	0.994831i	$0.467622\pi$
$720$		0			0
$721$	−7.54203e15			−1.44160
$722$	−1.47094e15	+	1.47094e15i	−0.279024	+	0.279024i
$723$	−1.09661e14	−	9.89669e14i	−0.0206439	−	0.186307i
$724$		−	1.76697e15i		−	0.330116i
$725$		0			0
$726$	2.03775e14	+	1.63121e14i	0.0374973	+	0.0300164i
$727$	−3.80599e14	−	3.80599e14i	−0.0695070	−	0.0695070i	0.671499	−	0.741006i	$-0.265651\pi$
$727$	−3.80599e14	−	3.80599e14i	−0.0695070	−	0.0695070i	−0.741006	+	0.671499i	$0.765651\pi$
$728$	3.69265e14	+	3.69265e14i	0.0669292	+	0.0669292i
$729$	−4.38433e15	+	3.41772e15i	−0.788682	+	0.614801i
$730$		0			0
$731$			5.66495e15i			1.00381i
$732$	−8.88518e15	+	9.84529e14i	−1.56263	+	0.173148i
$733$	6.61123e15	−	6.61123e15i	1.15401	−	1.15401i	0.168272	−	0.985741i	$-0.446181\pi$
$733$	6.61123e15	−	6.61123e15i	1.15401	−	1.15401i	0.985741	−	0.168272i	$-0.0538186\pi$
$734$	−1.00901e16			−1.74811
$735$		0			0
$736$	−1.11141e16			−1.89690
$737$	2.54299e15	−	2.54299e15i	0.430797	−	0.430797i
$738$	−1.08878e15	−	6.89742e14i	−0.183076	−	0.115978i
$739$			3.70884e15i			0.619004i	0.950899	+	0.309502i	$0.100162\pi$
$739$			3.70884e15i			0.619004i	−0.950899	+	0.309502i	$0.899838\pi$
$740$		0			0
$741$	1.38484e15	−	1.72998e15i	0.227719	−	0.284473i
$742$	−2.15134e15	−	2.15134e15i	−0.351146	−	0.351146i
$743$	3.37013e15	+	3.37013e15i	0.546020	+	0.546020i	0.925287	−	0.379268i	$-0.123824\pi$
$743$	3.37013e15	+	3.37013e15i	0.546020	+	0.546020i	−0.379268	+	0.925287i	$0.623824\pi$
$744$	6.48148e14	−	8.09684e14i	0.104237	−	0.130216i
$745$		0			0
$746$			9.14340e15i			1.44892i
$747$	−1.43205e15	−	9.07198e14i	−0.225265	−	0.142705i
$748$	−4.06223e15	+	4.06223e15i	−0.634317	+	0.634317i
$749$	−1.24029e16			−1.92253
$750$		0			0
$751$	8.69107e15			1.32756			0.663779	−	0.747929i	$-0.268952\pi$
$751$	8.69107e15			1.32756			0.663779	+	0.747929i	$0.268952\pi$
$752$	−8.38165e15	+	8.38165e15i	−1.27096	+	1.27096i
$753$	−3.97274e15	+	4.40202e14i	−0.598023	+	0.0662644i
$754$			5.47760e14i			0.0818555i
$755$		0			0
$756$	−5.89079e15	−	2.87711e15i	−0.867569	−	0.423728i
$757$	7.61805e15	+	7.61805e15i	1.11382	+	1.11382i	0.992629	+	0.121195i	$0.0386726\pi$
$757$	7.61805e15	+	7.61805e15i	1.11382	+	1.11382i	0.121195	+	0.992629i	$0.461327\pi$
$758$	6.78444e15	+	6.78444e15i	0.984767	+	0.984767i
$759$	7.56030e15	+	6.05198e15i	1.08945	+	0.872103i
$760$		0			0
$761$		−	1.45627e15i		−	0.206836i	−0.994638	−	0.103418i	$-0.967022\pi$
$761$		−	1.45627e15i		−	0.206836i	0.994638	−	0.103418i	$-0.0329779\pi$
$762$	6.26888e14	+	5.65754e15i	0.0883970	+	0.797766i
$763$	−1.57955e15	+	1.57955e15i	−0.221131	+	0.221131i
$764$	3.59621e15			0.499841
$765$		0			0
$766$	1.61004e16			2.20586
$767$	1.03858e15	−	1.03858e15i	0.141275	−	0.141275i
$768$	−9.96295e14	−	8.99136e15i	−0.134555	−	1.21434i
$769$		−	7.74566e15i		−	1.03864i	−0.854581	−	0.519318i	$-0.826186\pi$
$769$		−	7.74566e15i		−	1.03864i	0.854581	−	0.519318i	$-0.173814\pi$
$770$		0			0
$771$	−4.73328e15	−	3.78897e15i	−0.625695	−	0.500866i
$772$	3.61029e15	+	3.61029e15i	0.473857	+	0.473857i
$773$	−2.38412e15	−	2.38412e15i	−0.310699	−	0.310699i	0.534481	−	0.845180i	$-0.320507\pi$
$773$	−2.38412e15	−	2.38412e15i	−0.310699	−	0.310699i	−0.845180	+	0.534481i	$0.820507\pi$
$774$	−2.17274e15	−	9.68392e15i	−0.281147	−	1.25307i
$775$		0			0
$776$		−	5.93862e13i		−	0.00757610i
$777$	1.56471e16	−	1.73379e15i	1.98207	−	0.219625i
$778$	−7.76219e15	+	7.76219e15i	−0.976330	+	0.976330i
$779$	1.07320e15			0.134037
$780$		0			0
$781$	7.01682e15			0.864091
$782$	1.19276e16	−	1.19276e16i	1.45853	−	1.45853i
$783$	3.71917e14	+	1.08204e15i	0.0451602	+	0.131388i
$784$			2.49687e15i			0.301063i
$785$		0			0
$786$	1.05502e16	−	1.31796e16i	1.25441	−	1.56704i
$787$	−1.08462e15	−	1.08462e15i	−0.128061	−	0.128061i	0.640171	−	0.768232i	$-0.278863\pi$
$787$	−1.08462e15	−	1.08462e15i	−0.128061	−	0.128061i	−0.768232	+	0.640171i	$0.778863\pi$
$788$	5.69431e15	+	5.69431e15i	0.667647	+	0.667647i
$789$	−1.70605e13	+	2.13125e13i	−0.00198641	+	0.00248148i
$790$		0			0
$791$			1.34478e16i			1.54412i
$792$	−8.96196e14	+	1.41468e15i	−0.102191	+	0.161313i
$793$	4.95034e15	−	4.95034e15i	0.560573	−	0.560573i
$794$	−3.00289e15			−0.337697
$795$		0			0
$796$	−1.18345e16			−1.31258
$797$	2.91353e15	−	2.91353e15i	0.320921	−	0.320921i	−0.528199	−	0.849120i	$-0.677133\pi$
$797$	2.91353e15	−	2.91353e15i	0.320921	−	0.320921i	0.849120	+	0.528199i	$0.177133\pi$
$798$	1.17540e16	−	1.30241e15i	1.28579	−	0.142473i
$799$		−	1.57036e16i		−	1.70605i
$800$		0			0
$801$	−2.37708e14	+	5.33337e13i	−0.0254721	+	0.00571508i
$802$	−1.50989e16	−	1.50989e16i	−1.60689	−	1.60689i
$803$	−5.36336e15	−	5.36336e15i	−0.566894	−	0.566894i
$804$	3.95473e15	+	3.16574e15i	0.415153	+	0.332328i
$805$		0			0
$806$		−	4.88146e15i		−	0.505483i
$807$	1.45262e14	+	1.31096e15i	0.0149399	+	0.134829i
$808$	−1.22419e15	+	1.22419e15i	−0.125051	+	0.125051i
$809$	7.90345e15			0.801862			0.400931	−	0.916108i	$-0.368687\pi$
$809$	7.90345e15			0.801862			0.400931	+	0.916108i	$0.368687\pi$
$810$		0			0
$811$	5.61796e14			0.0562295			0.0281147	−	0.999605i	$-0.491050\pi$
$811$	5.61796e14			0.0562295			0.0281147	+	0.999605i	$0.491050\pi$
$812$	−9.54126e14	+	9.54126e14i	−0.0948523	+	0.0948523i
$813$	6.69821e13	+	6.04500e14i	0.00661395	+	0.0596896i
$814$			2.41688e16i			2.37040i
$815$		0			0
$816$	9.64574e15	+	7.72136e15i	0.933339	+	0.747133i
$817$	5.84346e15	+	5.84346e15i	0.561628	+	0.561628i
$818$	−3.51923e15	−	3.51923e15i	−0.335973	−	0.335973i
$819$	5.00954e15	−	1.12397e15i	0.475047	−	0.106584i
$820$		0			0
$821$		−	2.05944e16i		−	1.92691i	−0.267863	−	0.963457i	$-0.586317\pi$
$821$		−	2.05944e16i		−	1.92691i	0.267863	−	0.963457i	$-0.413683\pi$
$822$	7.01422e15	−	7.77215e14i	0.651905	−	0.0722348i
$823$	−6.78977e14	+	6.78977e14i	−0.0626839	+	0.0626839i	−0.737754	−	0.675070i	$-0.764113\pi$
$823$	−6.78977e14	+	6.78977e14i	−0.0626839	+	0.0626839i	0.675070	+	0.737754i	$0.264113\pi$
$824$	−2.71375e15			−0.248869
$825$		0			0
$826$	7.83830e15			0.709302
$827$	1.41696e16	−	1.41696e16i	1.27373	−	1.27373i	0.329610	−	0.944117i	$-0.393083\pi$
$827$	1.41696e16	−	1.41696e16i	1.27373	−	1.27373i	0.944117	−	0.329610i	$-0.106917\pi$
$828$	−7.30007e15	+	1.15234e16i	−0.651869	+	1.02900i
$829$		−	6.83571e15i		−	0.606365i	−0.952933	−	0.303182i	$-0.901951\pi$
$829$		−	6.83571e15i		−	0.606365i	0.952933	−	0.303182i	$-0.0980491\pi$
$830$		0			0
$831$	−4.39147e15	+	5.48594e15i	−0.384418	+	0.480226i
$832$	−2.45102e15	−	2.45102e15i	−0.213142	−	0.213142i
$833$	−2.33903e15	−	2.33903e15i	−0.202063	−	0.202063i
$834$	4.36910e14	−	5.45801e14i	0.0374955	−	0.0468404i
$835$		0			0
$836$			8.38049e15i			0.709798i
$837$	−3.31440e15	−	9.64281e15i	−0.278878	−	0.811360i
$838$	1.14033e16	−	1.14033e16i	0.953212	−	0.953212i
$839$	1.62429e16			1.34888			0.674439	−	0.738330i	$-0.264385\pi$
$839$	1.62429e16			1.34888			0.674439	+	0.738330i	$0.264385\pi$
$840$		0			0
$841$	−1.19650e16			−0.980698
$842$	−3.98847e15	+	3.98847e15i	−0.324780	+	0.324780i
$843$	−6.43933e14	+	7.13515e13i	−0.0520942	+	0.00577234i
$844$		−	5.40810e14i		−	0.0434672i
$845$		0			0
$846$	6.02299e15	+	2.68445e16i	0.477832	+	2.12970i
$847$	−3.56064e14	−	3.56064e14i	−0.0280653	−	0.0280653i
$848$	−3.27888e15	−	3.27888e15i	−0.256773	−	0.256773i
$849$	3.58272e14	+	2.86795e14i	0.0278754	+	0.0223141i
$850$		0			0
$851$		−	3.27571e16i		−	2.51590i
$852$	1.08852e15	+	9.82370e15i	0.0830653	+	0.749648i
$853$	−1.05949e16	+	1.05949e16i	−0.803299	+	0.803299i	−0.983610	−	0.180311i	$-0.942290\pi$
$853$	−1.05949e16	+	1.05949e16i	−0.803299	+	0.803299i	0.180311	+	0.983610i	$0.442290\pi$
$854$	3.73609e16			2.81448
$855$		0			0
$856$	−4.46277e15			−0.331894
$857$	−1.56110e16	+	1.56110e16i	−1.15355	+	1.15355i	−0.167712	+	0.985836i	$0.553638\pi$
$857$	−1.56110e16	+	1.56110e16i	−1.15355	+	1.15355i	−0.985836	+	0.167712i	$0.946362\pi$
$858$	8.68052e14	+	7.83400e15i	0.0637332	+	0.575180i
$859$			3.62241e15i			0.264262i	0.991232	+	0.132131i	$0.0421820\pi$
$859$			3.62241e15i			0.264262i	−0.991232	+	0.132131i	$0.957818\pi$
$860$		0			0
$861$	1.94110e15	+	1.55384e15i	0.139807	+	0.111915i
$862$	4.28867e15	+	4.28867e15i	0.306925	+	0.306925i
$863$	1.31884e16	+	1.31884e16i	0.937851	+	0.937851i	0.998179	−	0.0603272i	$-0.0192144\pi$
$863$	1.31884e16	+	1.31884e16i	0.937851	+	0.937851i	−0.0603272	+	0.998179i	$0.519214\pi$
$864$	−1.69780e16	−	8.29222e15i	−1.19967	−	0.585929i
$865$		0			0
$866$			2.48014e16i			1.73032i
$867$	−1.93234e15	+	2.14114e14i	−0.133961	+	0.0148436i
$868$	8.50286e15	−	8.50286e15i	0.585742	−	0.585742i
$869$	−1.46780e16			−1.00475
$870$		0			0
$871$	−3.96714e15			−0.268150
$872$	−5.68349e14	+	5.68349e14i	−0.0381746	+	0.0381746i
$873$	−4.93204e14	−	3.12444e14i	−0.0329191	−	0.0208542i
$874$		−	2.46069e16i		−	1.63209i
$875$		0			0
$876$	6.67680e15	−	8.34084e15i	0.437317	−	0.546308i
$877$	−1.16123e16	−	1.16123e16i	−0.755823	−	0.755823i	0.219736	−	0.975559i	$-0.429480\pi$
$877$	−1.16123e16	−	1.16123e16i	−0.755823	−	0.755823i	−0.975559	+	0.219736i	$0.929480\pi$
$878$	1.11274e16	+	1.11274e16i	0.719738	+	0.719738i
$879$	−3.03679e14	+	3.79364e14i	−0.0195198	+	0.0243847i
$880$		0			0
$881$			1.32482e16i			0.840986i	0.907296	+	0.420493i	$0.138143\pi$
$881$			1.32482e16i			0.840986i	−0.907296	+	0.420493i	$0.861857\pi$
$882$	4.89555e15	+	3.10132e15i	0.308834	+	0.195646i
$883$	1.65974e16	−	1.65974e16i	1.04053	−	1.04053i	0.0413890	−	0.999143i	$-0.486822\pi$
$883$	1.65974e16	−	1.65974e16i	1.04053	−	1.04053i	0.999143	−	0.0413890i	$-0.0131783\pi$
$884$	6.33721e15			0.394830
$885$		0			0
$886$	2.48988e15			0.153212
$887$	7.50237e15	−	7.50237e15i	0.458795	−	0.458795i	−0.439465	−	0.898260i	$-0.644832\pi$
$887$	7.50237e15	−	7.50237e15i	0.458795	−	0.458795i	0.898260	+	0.439465i	$0.144832\pi$
$888$	5.63010e15	−	6.23848e14i	0.342172	−	0.0379147i
$889$		−	1.09810e16i		−	0.663257i
$890$		0			0
$891$	7.03386e15	+	1.48859e16i	0.419630	+	0.888069i
$892$	−1.92385e16	−	1.92385e16i	−1.14068	−	1.14068i
$893$	−1.61985e16	−	1.61985e16i	−0.954533	−	0.954533i
$894$	−1.91890e16	−	1.53607e16i	−1.12382	−	0.899609i
$895$		0			0
$896$			7.49229e15i			0.433432i
$897$	−1.17651e15	−	1.06178e16i	−0.0676453	−	0.610486i
$898$	−1.22615e15	+	1.22615e15i	−0.0700689	+	0.0700689i
$899$	−2.09867e15			−0.119197
$900$		0			0
$901$	6.14322e15			0.344675
$902$	−2.69917e15	+	2.69917e15i	−0.150520	+	0.150520i
$903$	2.10859e15	+	1.90296e16i	0.116872	+	1.05475i
$904$			4.83875e15i			0.266567i
$905$		0			0
$906$	6.13381e14	+	4.91008e14i	0.0333830	+	0.0267229i
$907$	−1.85347e16	−	1.85347e16i	−1.00264	−	1.00264i	−0.999997	−	0.00264257i	$-0.999159\pi$
$907$	−1.85347e16	−	1.85347e16i	−1.00264	−	1.00264i	−0.00264257	−	0.999997i	$-0.500841\pi$
$908$	−5.74468e15	−	5.74468e15i	−0.308883	−	0.308883i
$909$	3.72620e15	+	1.66077e16i	0.199143	+	0.887580i
$910$		0			0
$911$		−	1.51583e16i		−	0.800385i	−0.916431	−	0.400193i	$-0.868943\pi$
$911$		−	1.51583e16i		−	0.800385i	0.916431	−	0.400193i	$-0.131057\pi$
$912$	1.79144e16	−	1.98502e15i	0.940221	−	0.104182i
$913$	−3.55014e15	+	3.55014e15i	−0.185206	+	0.185206i
$914$	−2.21022e15			−0.114612
$915$		0			0
$916$	−2.14126e16			−1.09710
$917$	−2.30292e16	+	2.30292e16i	−1.17287	+	1.17287i
$918$	2.71199e16	−	9.32159e15i	1.37295	−	0.471906i
$919$		−	3.09647e16i		−	1.55823i	−0.626883	−	0.779114i	$-0.715669\pi$
$919$		−	3.09647e16i		−	1.55823i	0.626883	−	0.779114i	$-0.284331\pi$
$920$		0			0
$921$	−1.55446e16	+	1.94187e16i	−0.772949	+	0.965589i
$922$	5.39858e15	+	5.39858e15i	0.266845	+	0.266845i
$923$	−5.47322e15	−	5.47322e15i	−0.268927	−	0.268927i
$924$	−1.21338e16	+	1.51578e16i	−0.592652	+	0.740358i
$925$		0			0
$926$		−	2.79228e15i		−	0.134772i
$927$	−1.42776e16	+	2.25378e16i	−0.685043	+	1.08137i
$928$	−2.74992e15	+	2.74992e15i	−0.131161	+	0.131161i
$929$	−1.82161e16			−0.863710			−0.431855	−	0.901943i	$-0.642141\pi$
$929$	−1.82161e16			−0.863710			−0.431855	+	0.901943i	$0.642141\pi$
$930$		0			0
$931$	−4.82547e15			−0.226108
$932$	1.43019e16	−	1.43019e16i	0.666203	−	0.666203i
$933$	−2.19726e16	+	2.43468e15i	−1.01749	+	0.112744i
$934$			4.13502e16i			1.90358i
$935$		0			0
$936$	1.80252e15	−	4.04424e14i	0.0820091	−	0.0184001i
$937$	−2.78714e15	−	2.78714e15i	−0.126064	−	0.126064i	0.641260	−	0.767324i	$-0.278412\pi$
$937$	−2.78714e15	−	2.78714e15i	−0.126064	−	0.126064i	−0.767324	+	0.641260i	$0.778412\pi$
$938$	−1.49703e16	−	1.49703e16i	−0.673153	−	0.673153i
$939$	3.20629e16	+	2.56662e16i	1.43332	+	1.14736i
$940$		0			0
$941$		−	4.44952e16i		−	1.96594i	−0.183771	−	0.982969i	$-0.558831\pi$
$941$		−	4.44952e16i		−	1.96594i	0.183771	−	0.982969i	$-0.441169\pi$
$942$	6.73308e15	+	6.07647e16i	0.295756	+	2.66914i
$943$	3.65831e15	−	3.65831e15i	0.159759	−	0.159759i
$944$	1.19464e16			0.518671
$945$		0			0
$946$	−2.93935e16			−1.26139
$947$	1.25087e16	−	1.25087e16i	0.533689	−	0.533689i	−0.387979	−	0.921668i	$-0.626827\pi$
$947$	1.25087e16	−	1.25087e16i	0.533689	−	0.533689i	0.921668	+	0.387979i	$0.126827\pi$
$948$	−2.27701e15	−	2.05496e16i	−0.0965871	−	0.871679i
$949$			8.36701e15i			0.352863i
$950$		0			0
$951$	−5.12332e15	−	4.10119e15i	−0.213579	−	0.170969i
$952$	−3.97902e15	−	3.97902e15i	−0.164920	−	0.164920i
$953$	−2.79601e16	−	2.79601e16i	−1.15220	−	1.15220i	−0.986111	−	0.166089i	$-0.946886\pi$
$953$	−2.79601e16	−	2.79601e16i	−1.15220	−	1.15220i	−0.166089	−	0.986111i	$-0.553114\pi$
$954$	−1.05015e16	+	2.35618e15i	−0.430264	+	0.0965367i
$955$		0			0
$956$		−	1.57668e16i		−	0.638593i
$957$	3.36804e15	−	3.73199e14i	0.135632	−	0.0150288i
$958$	9.78409e15	−	9.78409e15i	0.391751	−	0.391751i
$959$	−1.36142e16			−0.541989
$960$		0			0
$961$	−6.70585e15			−0.263922
$962$	1.88520e16	−	1.88520e16i	0.737726	−	0.737726i
$963$	−2.34796e16	+	3.70635e16i	−0.913580	+	1.44212i
$964$		−	4.15393e15i		−	0.160707i
$965$		0			0
$966$	3.56273e16	−	4.45066e16i	1.36273	−	1.70235i
$967$	3.03053e16	+	3.03053e16i	1.15259	+	1.15259i	0.986033	+	0.166553i	$0.0532636\pi$
$967$	3.03053e16	+	3.03053e16i	1.15259	+	1.15259i	0.166553	+	0.986033i	$0.446736\pi$
$968$	−1.28118e14	−	1.28118e14i	−0.00484501	−	0.00484501i
$969$	−1.49224e16	+	1.86414e16i	−0.561122	+	0.700969i
$970$		0			0
$971$			3.03744e16i			1.12928i	0.825337	+	0.564640i	$0.190985\pi$
$971$			3.03744e16i			1.12928i	−0.825337	+	0.564640i	$0.809015\pi$
$972$	−1.97494e16	+	1.21568e16i	−0.730111	+	0.449423i
$973$	−9.53696e14	+	9.53696e14i	−0.0350582	+	0.0350582i
$974$	−6.15163e16			−2.24862
$975$		0			0
$976$	5.69421e16			2.05807
$977$	−9.89543e15	+	9.89543e15i	−0.355643	+	0.355643i	−0.862204	−	0.506561i	$-0.830916\pi$
$977$	−9.89543e15	+	9.89543e15i	−0.355643	+	0.355643i	0.506561	+	0.862204i	$0.330916\pi$
$978$	−3.59069e16	+	3.97869e15i	−1.28326	+	0.142192i
$979$			7.21512e14i			0.0256412i
$980$		0			0
$981$	1.72995e15	+	7.71037e15i	0.0607929	+	0.270954i
$982$	7.61009e14	+	7.61009e14i	0.0265936	+	0.0265936i
$983$	1.66606e16	+	1.66606e16i	0.578956	+	0.578956i	0.934616	−	0.355660i	$-0.115744\pi$
$983$	1.66606e16	+	1.66606e16i	0.578956	+	0.578956i	−0.355660	+	0.934616i	$0.615744\pi$
$984$	6.98440e14	+	5.59098e14i	0.0241355	+	0.0193203i
$985$		0			0
$986$		−	5.90240e15i		−	0.201700i
$987$	−5.84515e15	−	5.27514e16i	−0.198633	−	1.79262i
$988$	6.53691e15	−	6.53691e15i	0.220907	−	0.220907i
$989$	3.98383e16			1.33882
$990$		0			0
$991$	−1.41406e16			−0.469963			−0.234981	−	0.972000i	$-0.575503\pi$
$991$	−1.41406e16			−0.469963			−0.234981	+	0.972000i	$0.575503\pi$
$992$	2.45063e16	−	2.45063e16i	0.809962	−	0.809962i
$993$	1.02135e14	+	9.21750e14i	0.00335703	+	0.0302965i
$994$		−	4.13072e16i		−	1.35021i
$995$		0			0
$996$	−5.52101e15	−	4.41954e15i	−0.178481	−	0.142873i
$997$	6.58117e15	+	6.58117e15i	0.211583	+	0.211583i	0.804940	−	0.593357i	$-0.202198\pi$
$997$	6.58117e15	+	6.58117e15i	0.211583	+	0.211583i	−0.593357	+	0.804940i	$0.702198\pi$
$998$	3.48926e16	+	3.48926e16i	1.11562	+	1.11562i
$999$	2.44401e16	−	5.00404e16i	0.777129	−	1.59115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.12.e.d.32.4		40
3.2	odd	2	inner	75.12.e.d.32.17		40
5.2	odd	4		15.12.e.a.8.4	yes	40
5.3	odd	4	inner	75.12.e.d.68.17		40
5.4	even	2		15.12.e.a.2.17	yes	40
15.2	even	4		15.12.e.a.8.17	yes	40
15.8	even	4	inner	75.12.e.d.68.4		40
15.14	odd	2		15.12.e.a.2.4	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.12.e.a.2.4	✓	40	15.14	odd	2
15.12.e.a.2.17	yes	40	5.4	even	2
15.12.e.a.8.4	yes	40	5.2	odd	4
15.12.e.a.8.17	yes	40	15.2	even	4
75.12.e.d.32.4		40	1.1	even	1	trivial
75.12.e.d.32.17		40	3.2	odd	2	inner
75.12.e.d.68.4		40	15.8	even	4	inner
75.12.e.d.68.17		40	5.3	odd	4	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-43.6110 + 43.6110i) q^{2} +(-46.3532 - 418.328i) q^{3} -1755.85i q^{4} +(20265.2 + 16222.2i) q^{6} +(-35410.1 - 35410.1i) q^{7} +(-12741.2 - 12741.2i) q^{8} +(-172850. + 38781.7i) q^{9} +O(q^{10})\)	\(q+(-43.6110 + 43.6110i) q^{2} +(-46.3532 - 418.328i) q^{3} -1755.85i q^{4} +(20265.2 + 16222.2i) q^{6} +(-35410.1 - 35410.1i) q^{7} +(-12741.2 - 12741.2i) q^{8} +(-172850. + 38781.7i) q^{9} +524649. i q^{11} +(-734519. + 81389.0i) q^{12} +(409234. - 409234. i) q^{13} +3.08854e6 q^{14} +4.70728e6 q^{16} +(-4.40971e6 + 4.40971e6i) q^{17} +(5.84685e6 - 9.22947e6i) q^{18} +9.09734e6i q^{19} +(-1.31717e7 + 1.64544e7i) q^{21} +(-2.28805e7 - 2.28805e7i) q^{22} +(3.10110e7 + 3.10110e7i) q^{23} +(-4.73939e6 + 5.92058e6i) q^{24} +3.56942e7i q^{26} +(2.42356e7 + 7.05103e7i) q^{27} +(-6.21747e7 + 6.21747e7i) q^{28} +1.53459e7 q^{29} -1.36758e8 q^{31} +(-1.79196e8 + 1.79196e8i) q^{32} +(2.19475e8 - 2.43191e7i) q^{33} -3.84624e8i q^{34} +(6.80946e7 + 3.03497e8i) q^{36} +(-5.28154e8 - 5.28154e8i) q^{37} +(-3.96744e8 - 3.96744e8i) q^{38} +(-1.90163e8 - 1.52225e8i) q^{39} -1.17968e8i q^{41} +(-1.43164e8 - 1.29202e9i) q^{42} +(6.42326e8 - 6.42326e8i) q^{43} +9.21202e8 q^{44} -2.70484e9 q^{46} +(-1.78057e9 + 1.78057e9i) q^{47} +(-2.18197e8 - 1.96919e9i) q^{48} +5.30426e8i q^{49} +(2.04911e9 + 1.64030e9i) q^{51} +(-7.18552e8 - 7.18552e8i) q^{52} +(-6.96556e8 - 6.96556e8i) q^{53} +(-4.13196e9 - 2.01809e9i) q^{54} +9.02332e8i q^{56} +(3.80567e9 - 4.21690e8i) q^{57} +(-6.69250e8 + 6.69250e8i) q^{58} +2.53786e9 q^{59} +1.20966e10 q^{61} +(5.96414e9 - 5.96414e9i) q^{62} +(7.49389e9 + 4.74737e9i) q^{63} -5.98930e9i q^{64} +(-8.51096e9 + 1.06321e10i) q^{66} +(-4.84703e9 - 4.84703e9i) q^{67} +(7.74277e9 + 7.74277e9i) q^{68} +(1.15353e10 - 1.44102e10i) q^{69} -1.33743e10i q^{71} +(2.69643e9 + 1.70818e9i) q^{72} +(-1.02228e10 + 1.02228e10i) q^{73} +4.60666e10 q^{74} +1.59735e10 q^{76} +(1.85779e10 - 1.85779e10i) q^{77} +(1.49319e10 - 1.65454e9i) q^{78} +2.79769e10i q^{79} +(2.83730e10 - 1.34068e10i) q^{81} +(5.14472e9 + 5.14472e9i) q^{82} +(6.76670e9 + 6.76670e9i) q^{83} +(2.88914e10 + 2.31274e10i) q^{84} +5.60250e10i q^{86} +(-7.11330e8 - 6.41962e9i) q^{87} +(6.68463e9 - 6.68463e9i) q^{88} +1.37523e9 q^{89} -2.89820e10 q^{91} +(5.44505e10 - 5.44505e10i) q^{92} +(6.33914e9 + 5.72095e10i) q^{93} -1.55305e11i q^{94} +(8.32688e10 + 6.66563e10i) q^{96} +(2.33049e9 + 2.33049e9i) q^{97} +(-2.31324e10 - 2.31324e10i) q^{98} +(-2.03467e10 - 9.06854e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7}+O(q^{10}) \) 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7	\( 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7} + 1714188 q^{12} + 3448472 q^{13} - 43202180 q^{16} - 3729120 q^{18} + 33570840 q^{21} + 21743260 q^{22} - 113282712 q^{27} - 253355948 q^{28} + 67990880 q^{31} + 563443560 q^{33} + 1116103980 q^{36} - 1292573224 q^{37} + 5132304780 q^{42} - 4012128208 q^{43} - 8170829920 q^{46} + 13847034876 q^{48} + 5424535440 q^{51} - 10287332704 q^{52} + 10576855656 q^{57} - 56277468420 q^{58} - 24994982320 q^{61} + 50371112832 q^{63} + 56311074600 q^{66} - 37314988144 q^{67} + 92983114440 q^{72} - 51361482568 q^{73} - 121004023440 q^{76} + 104085843000 q^{78} - 22936122360 q^{81} + 56747065840 q^{82} - 84564024000 q^{87} - 148338843420 q^{88} + 230876677280 q^{91} - 38932525008 q^{93} - 437860137180 q^{96} + 294950050616 q^{97}+O(q^{100}) \) 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7 + 1714188 * q^12 + 3448472 * q^13 - 43202180 * q^16 - 3729120 * q^18 + 33570840 * q^21 + 21743260 * q^22 - 113282712 * q^27 - 253355948 * q^28 + 67990880 * q^31 + 563443560 * q^33 + 1116103980 * q^36 - 1292573224 * q^37 + 5132304780 * q^42 - 4012128208 * q^43 - 8170829920 * q^46 + 13847034876 * q^48 + 5424535440 * q^51 - 10287332704 * q^52 + 10576855656 * q^57 - 56277468420 * q^58 - 24994982320 * q^61 + 50371112832 * q^63 + 56311074600 * q^66 - 37314988144 * q^67 + 92983114440 * q^72 - 51361482568 * q^73 - 121004023440 * q^76 + 104085843000 * q^78 - 22936122360 * q^81 + 56747065840 * q^82 - 84564024000 * q^87 - 148338843420 * q^88 + 230876677280 * q^91 - 38932525008 * q^93 - 437860137180 * q^96 + 294950050616 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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