LMFDB - Embedded newform 75.12.e.d.32.5

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			32.5
Character	$\chi$	$=$	75.32
Dual form			75.12.e.d.68.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-37.4902 + 37.4902i) q^{2} +(-201.005 + 369.789i) q^{3} -763.031i q^{4} +(-6327.78 - 21399.2i) q^{6} +(46363.7 + 46363.7i) q^{7} +(-48173.8 - 48173.8i) q^{8} +(-96341.3 - 148659. i) q^{9} +O(q^{10})$	\(q+(-37.4902 + 37.4902i) q^{2} +(-201.005 + 369.789i) q^{3} -763.031i q^{4} +(-6327.78 - 21399.2i) q^{6} +(46363.7 + 46363.7i) q^{7} +(-48173.8 - 48173.8i) q^{8} +(-96341.3 - 148659. i) q^{9} -55617.1i q^{11} +(282161. + 153373. i) q^{12} +(-631358. + 631358. i) q^{13} -3.47637e6 q^{14} +5.17478e6 q^{16} +(2.79681e6 - 2.79681e6i) q^{17} +(9.18510e6 + 1.96139e6i) q^{18} -1.01926e7i q^{19} +(-2.64641e7 + 7.82549e6i) q^{21} +(2.08510e6 + 2.08510e6i) q^{22} +(1.26689e7 + 1.26689e7i) q^{23} +(2.74973e7 - 8.13100e6i) q^{24} -4.73395e7i q^{26} +(7.43374e7 - 5.74493e6i) q^{27} +(3.53770e7 - 3.53770e7i) q^{28} +1.48130e8 q^{29} +2.61818e8 q^{31} +(-9.53435e7 + 9.53435e7i) q^{32} +(2.05666e7 + 1.11793e7i) q^{33} +2.09706e8i q^{34} +(-1.13431e8 + 7.35114e7i) q^{36} +(3.41740e8 + 3.41740e8i) q^{37} +(3.82124e8 + 3.82124e8i) q^{38} +(-1.06564e8 - 3.60375e8i) q^{39} -1.32229e9i q^{41} +(6.98767e8 - 1.28553e9i) q^{42} +(6.29639e7 - 6.29639e7i) q^{43} -4.24376e7 q^{44} -9.49916e8 q^{46} +(1.38825e9 - 1.38825e9i) q^{47} +(-1.04015e9 + 1.91358e9i) q^{48} +2.32187e9i q^{49} +(4.72059e8 + 1.59640e9i) q^{51} +(4.81746e8 + 4.81746e8i) q^{52} +(-4.62211e8 - 4.62211e8i) q^{53} +(-2.57155e9 + 3.00230e9i) q^{54} -4.46703e9i q^{56} +(3.76912e9 + 2.04876e9i) q^{57} +(-5.55343e9 + 5.55343e9i) q^{58} +6.47821e9 q^{59} -6.68237e9 q^{61} +(-9.81560e9 + 9.81560e9i) q^{62} +(2.42563e9 - 1.13591e10i) q^{63} +3.44904e9i q^{64} +(-1.19016e9 + 3.51933e8i) q^{66} +(-3.32538e9 - 3.32538e9i) q^{67} +(-2.13405e9 - 2.13405e9i) q^{68} +(-7.23131e9 + 2.13831e9i) q^{69} +7.73190e9i q^{71} +(-2.52032e9 + 1.18026e10i) q^{72} +(-1.89044e9 + 1.89044e9i) q^{73} -2.56238e10 q^{74} -7.77729e9 q^{76} +(2.57862e9 - 2.57862e9i) q^{77} +(1.75056e10 + 9.51545e9i) q^{78} +2.39607e10i q^{79} +(-1.28178e10 + 2.86440e10i) q^{81} +(4.95730e10 + 4.95730e10i) q^{82} +(-2.08763e10 - 2.08763e10i) q^{83} +(5.97110e9 + 2.01930e10i) q^{84} +4.72106e9i q^{86} +(-2.97748e10 + 5.47769e10i) q^{87} +(-2.67928e9 + 2.67928e9i) q^{88} -1.75952e10 q^{89} -5.85443e10 q^{91} +(9.66673e9 - 9.66673e9i) q^{92} +(-5.26266e10 + 9.68174e10i) q^{93} +1.04092e11i q^{94} +(-1.60925e10 - 5.44215e10i) q^{96} +(-4.63107e10 - 4.63107e10i) q^{97} +(-8.70472e10 - 8.70472e10i) q^{98} +(-8.26796e9 + 5.35823e9i) 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 $

$2$	−37.4902	+	37.4902i	−0.828424	+	0.828424i	−0.987299	−	0.158874i	$-0.949213\pi$
$2$	−37.4902	+	37.4902i	−0.828424	+	0.828424i	0.158874	+	0.987299i	$0.449213\pi$
$3$	−201.005	+	369.789i	−0.477572	+	0.878593i
$3$	−201.005	+	369.789i	−0.477572	+	0.878593i
$4$		−	763.031i		−	0.372574i
$5$		0			0
$5$		0			0
$6$	−6327.78	−	21399.2i	−0.332215	−	1.12348i
$7$	46363.7	+	46363.7i	1.04265	+	1.04265i	0.999049	+	0.0436027i	$0.0138836\pi$
$7$	46363.7	+	46363.7i	1.04265	+	1.04265i	0.0436027	+	0.999049i	$0.486116\pi$
$8$	−48173.8	−	48173.8i	−0.519775	−	0.519775i
$9$	−96341.3	−	148659.i	−0.543850	−	0.839183i
$10$		0			0
$11$		−	55617.1i		−	0.104123i	−0.998644	−	0.0520617i	$-0.983421\pi$
$11$		−	55617.1i		−	0.104123i	0.998644	−	0.0520617i	$-0.0165793\pi$
$12$	282161.	+	153373.i	0.327341	+	0.177931i
$13$	−631358.	+	631358.i	−0.471615	+	0.471615i	−0.902437	−	0.430822i	$-0.858224\pi$
$13$	−631358.	+	631358.i	−0.471615	+	0.471615i	0.430822	+	0.902437i	$0.358224\pi$
$14$	−3.47637e6			−1.72752
$15$		0			0
$16$	5.17478e6			1.23376
$17$	2.79681e6	−	2.79681e6i	0.477743	−	0.477743i	−0.426666	−	0.904409i	$-0.640312\pi$
$17$	2.79681e6	−	2.79681e6i	0.477743	−	0.477743i	0.904409	+	0.426666i	$0.140312\pi$
$18$	9.18510e6	+	1.96139e6i	1.14574	+	0.244661i
$19$		−	1.01926e7i		−	0.944368i	−0.881500	−	0.472184i	$-0.843466\pi$
$19$		−	1.01926e7i		−	0.944368i	0.881500	−	0.472184i	$-0.156534\pi$
$20$		0			0
$21$	−2.64641e7	+	7.82549e6i	−1.41401	+	0.418125i
$22$	2.08510e6	+	2.08510e6i	0.0862584	+	0.0862584i
$23$	1.26689e7	+	1.26689e7i	0.410426	+	0.410426i	0.881887	−	0.471461i	$-0.156273\pi$
$23$	1.26689e7	+	1.26689e7i	0.410426	+	0.410426i	−0.471461	+	0.881887i	$0.656273\pi$
$24$	2.74973e7	−	8.13100e6i	0.704901	−	0.208440i
$25$		0			0
$26$		−	4.73395e7i		−	0.781394i
$27$	7.43374e7	−	5.74493e6i	0.997027	−	0.0770520i
$28$	3.53770e7	−	3.53770e7i	0.388465	−	0.388465i
$29$	1.48130e8			1.34108			0.670539	−	0.741874i	$-0.266063\pi$
$29$	1.48130e8			1.34108			0.670539	+	0.741874i	$0.266063\pi$
$30$		0			0
$31$	2.61818e8			1.64252			0.821258	−	0.570557i	$-0.193273\pi$
$31$	2.61818e8			1.64252			0.821258	+	0.570557i	$0.193273\pi$
$32$	−9.53435e7	+	9.53435e7i	−0.502304	+	0.502304i
$33$	2.05666e7	+	1.11793e7i	0.0914821	+	0.0497265i
$34$			2.09706e8i			0.791548i
$35$		0			0
$36$	−1.13431e8	+	7.35114e7i	−0.312657	+	0.202624i
$37$	3.41740e8	+	3.41740e8i	0.810189	+	0.810189i	0.984662	−	0.174473i	$-0.0558222\pi$
$37$	3.41740e8	+	3.41740e8i	0.810189	+	0.810189i	−0.174473	+	0.984662i	$0.555822\pi$
$38$	3.82124e8	+	3.82124e8i	0.782337	+	0.782337i
$39$	−1.06564e8	−	3.60375e8i	−0.189127	−	0.639587i
$40$		0			0
$41$		−	1.32229e9i		−	1.78244i	−0.453567	−	0.891222i	$-0.649849\pi$
$41$		−	1.32229e9i		−	1.78244i	0.453567	−	0.891222i	$-0.350151\pi$
$42$	6.98767e8	−	1.28553e9i	0.825014	−	1.51778i
$43$	6.29639e7	−	6.29639e7i	0.0653153	−	0.0653153i	−0.673695	−	0.739010i	$-0.735294\pi$
$43$	6.29639e7	−	6.29639e7i	0.0653153	−	0.0653153i	0.739010	+	0.673695i	$0.235294\pi$
$44$	−4.24376e7			−0.0387937
$45$		0			0
$46$	−9.49916e8			−0.680013
$47$	1.38825e9	−	1.38825e9i	0.882939	−	0.882939i	−0.110894	−	0.993832i	$-0.535371\pi$
$47$	1.38825e9	−	1.38825e9i	0.882939	−	0.882939i	0.993832	+	0.110894i	$0.0353713\pi$
$48$	−1.04015e9	+	1.91358e9i	−0.589211	+	1.08397i
$49$			2.32187e9i			1.17425i
$50$		0			0
$51$	4.72059e8	+	1.59640e9i	0.191585	+	0.647898i
$52$	4.81746e8	+	4.81746e8i	0.175711	+	0.175711i
$53$	−4.62211e8	−	4.62211e8i	−0.151818	−	0.151818i	0.627112	−	0.778929i	$-0.284237\pi$
$53$	−4.62211e8	−	4.62211e8i	−0.151818	−	0.151818i	−0.778929	+	0.627112i	$0.784237\pi$
$54$	−2.57155e9	+	3.00230e9i	−0.762130	+	0.889793i
$55$		0			0
$56$		−	4.46703e9i		−	1.08389i
$57$	3.76912e9	+	2.04876e9i	0.829715	+	0.451004i
$58$	−5.55343e9	+	5.55343e9i	−1.11098	+	1.11098i
$59$	6.47821e9			1.17969			0.589847	−	0.807515i	$-0.299188\pi$
$59$	6.47821e9			1.17969			0.589847	+	0.807515i	$0.299188\pi$
$60$		0			0
$61$	−6.68237e9			−1.01302			−0.506508	−	0.862235i	$-0.669064\pi$
$61$	−6.68237e9			−1.01302			−0.506508	+	0.862235i	$0.669064\pi$
$62$	−9.81560e9	+	9.81560e9i	−1.36070	+	1.36070i
$63$	2.42563e9	−	1.13591e10i	0.307929	−	1.44202i
$64$			3.44904e9i			0.401521i
$65$		0			0
$66$	−1.19016e9	+	3.51933e8i	−0.116981	+	0.0345914i
$67$	−3.32538e9	−	3.32538e9i	−0.300905	−	0.300905i	0.540463	−	0.841368i	$-0.318249\pi$
$67$	−3.32538e9	−	3.32538e9i	−0.300905	−	0.300905i	−0.841368	+	0.540463i	$0.818249\pi$
$68$	−2.13405e9	−	2.13405e9i	−0.177994	−	0.177994i
$69$	−7.23131e9	+	2.13831e9i	−0.556605	+	0.164589i
$70$		0			0
$71$			7.73190e9i			0.508587i	0.967127	+	0.254293i	$0.0818429\pi$
$71$			7.73190e9i			0.508587i	−0.967127	+	0.254293i	$0.918157\pi$
$72$	−2.52032e9	+	1.18026e10i	−0.153507	+	0.718866i
$73$	−1.89044e9	+	1.89044e9i	−0.106730	+	0.106730i	−0.758455	−	0.651725i	$-0.774046\pi$
$73$	−1.89044e9	+	1.89044e9i	−0.106730	+	0.106730i	0.651725	+	0.758455i	$0.274046\pi$
$74$	−2.56238e10			−1.34236
$75$		0			0
$76$	−7.77729e9			−0.351847
$77$	2.57862e9	−	2.57862e9i	0.108564	−	0.108564i
$78$	1.75056e10	+	9.51545e9i	0.686527	+	0.373172i
$79$			2.39607e10i			0.876094i	0.898952	+	0.438047i	$0.144330\pi$
$79$			2.39607e10i			0.876094i	−0.898952	+	0.438047i	$0.855670\pi$
$80$		0			0
$81$	−1.28178e10	+	2.86440e10i	−0.408455	+	0.912778i
$82$	4.95730e10	+	4.95730e10i	1.47662	+	1.47662i
$83$	−2.08763e10	−	2.08763e10i	−0.581733	−	0.581733i	0.353647	−	0.935379i	$-0.384942\pi$
$83$	−2.08763e10	−	2.08763e10i	−0.581733	−	0.581733i	−0.935379	+	0.353647i	$0.884942\pi$
$84$	5.97110e9	+	2.01930e10i	0.155782	+	0.526822i
$85$		0			0
$86$			4.72106e9i			0.108218i
$87$	−2.97748e10	+	5.47769e10i	−0.640462	+	1.17826i
$88$	−2.67928e9	+	2.67928e9i	−0.0541208	+	0.0541208i
$89$	−1.75952e10			−0.334001			−0.167001	−	0.985957i	$-0.553408\pi$
$89$	−1.75952e10			−0.334001			−0.167001	+	0.985957i	$0.553408\pi$
$90$		0			0
$91$	−5.85443e10			−0.983460
$92$	9.66673e9	−	9.66673e9i	0.152914	−	0.152914i
$93$	−5.26266e10	+	9.68174e10i	−0.784420	+	1.44310i
$94$			1.04092e11i			1.46290i
$95$		0			0
$96$	−1.60925e10	−	5.44215e10i	−0.201434	−	0.681207i
$97$	−4.63107e10	−	4.63107e10i	−0.547566	−	0.547566i	0.378170	−	0.925736i	$-0.376553\pi$
$97$	−4.63107e10	−	4.63107e10i	−0.547566	−	0.547566i	−0.925736	+	0.378170i	$0.876553\pi$
$98$	−8.70472e10	−	8.70472e10i	−0.972773	−	0.972773i
$99$	−8.26796e9	+	5.35823e9i	−0.0873786	+	0.0566275i
$100$		0			0
$101$		−	1.36284e11i		−	1.29026i	−0.764073	−	0.645129i	$-0.776803\pi$
$101$		−	1.36284e11i		−	1.29026i	0.764073	−	0.645129i	$-0.223197\pi$
$102$	−7.75471e10	−	4.21519e10i	−0.695448	−	0.378021i
$103$	4.19193e9	−	4.19193e9i	0.0356295	−	0.0356295i	−0.689068	−	0.724697i	$-0.741980\pi$
$103$	4.19193e9	−	4.19193e9i	0.0356295	−	0.0356295i	0.724697	+	0.689068i	$0.241980\pi$
$104$	6.08298e10			0.490267
$105$		0			0
$106$	3.46568e10			0.251539
$107$	1.14858e11	−	1.14858e11i	0.791681	−	0.791681i	−0.190086	−	0.981767i	$-0.560877\pi$
$107$	1.14858e11	−	1.14858e11i	0.791681	−	0.791681i	0.981767	+	0.190086i	$0.0608767\pi$
$108$	−4.38356e9	−	5.67218e10i	−0.0287075	−	0.371466i
$109$			7.06110e10i			0.439568i	0.975549	+	0.219784i	$0.0705353\pi$
$109$			7.06110e10i			0.439568i	−0.975549	+	0.219784i	$0.929465\pi$
$110$		0			0
$111$	−1.95063e11	+	5.76805e10i	−1.09875	+	0.324902i
$112$	2.39922e11	+	2.39922e11i	1.28638	+	1.28638i
$113$	1.87895e11	+	1.87895e11i	0.959366	+	0.959366i	0.999206	−	0.0398404i	$-0.0126850\pi$
$113$	1.87895e11	+	1.87895e11i	0.959366	+	0.959366i	−0.0398404	+	0.999206i	$0.512685\pi$
$114$	−2.18114e11	+	6.44967e10i	−1.06098	+	0.313733i
$115$		0			0
$116$		−	1.13028e11i		−	0.499651i
$117$	1.54683e11	+	3.30310e10i	0.652258	+	0.139283i
$118$	−2.42870e11	+	2.42870e11i	−0.977287	+	0.977287i
$119$	2.59341e11			0.996239
$120$		0			0
$121$	2.82218e11			0.989158
$122$	2.50524e11	−	2.50524e11i	0.839208	−	0.839208i
$123$	4.88969e11	+	2.65787e11i	1.56604	+	0.851246i
$124$		−	1.99775e11i		−	0.611959i
$125$		0			0
$126$	3.34918e11	+	5.16793e11i	0.939509	+	1.44970i
$127$	−2.27468e11	−	2.27468e11i	−0.610941	−	0.610941i	0.332250	−	0.943191i	$-0.392192\pi$
$127$	−2.27468e11	−	2.27468e11i	−0.610941	−	0.610941i	−0.943191	+	0.332250i	$0.892192\pi$
$128$	−3.24569e11	−	3.24569e11i	−0.834934	−	0.834934i
$129$	1.06274e10	+	3.59394e10i	0.0261928	+	0.0885784i
$130$		0			0
$131$		−	6.52427e11i		−	1.47754i	−0.673957	−	0.738771i	$-0.735407\pi$
$131$		−	6.52427e11i		−	1.47754i	0.673957	−	0.738771i	$-0.264593\pi$
$132$	8.53014e9	−	1.56930e10i	0.0185268	−	0.0340838i
$133$	4.72568e11	−	4.72568e11i	0.984647	−	0.984647i
$134$	2.49338e11			0.498555
$135$		0			0
$136$	−2.69466e11			−0.496638
$137$	−6.39965e11	+	6.39965e11i	−1.13290	+	1.13290i	−0.143212	+	0.989692i	$0.545743\pi$
$137$	−6.39965e11	+	6.39965e11i	−1.13290	+	1.13290i	−0.989692	+	0.143212i	$0.954257\pi$
$138$	1.90937e11	−	3.51269e11i	0.324755	−	0.597454i
$139$		−	9.51431e11i		−	1.55523i	−0.628738	−	0.777617i	$-0.716428\pi$
$139$		−	9.51431e11i		−	1.55523i	0.628738	−	0.777617i	$-0.283572\pi$
$140$		0			0
$141$	2.34316e11	+	7.92407e11i	0.354076	+	1.19741i
$142$	−2.89870e11	−	2.89870e11i	−0.421326	−	0.421326i
$143$	3.51143e10	+	3.51143e10i	0.0491061	+	0.0491061i
$144$	−4.98545e11	−	7.69275e11i	−0.670981	−	1.03535i
$145$		0			0
$146$		−	1.41746e11i		−	0.176836i
$147$	−8.58601e11	−	4.66706e11i	−1.03168	−	0.560787i
$148$	2.60758e11	−	2.60758e11i	0.301855	−	0.301855i
$149$	7.48036e11			0.834446			0.417223	−	0.908804i	$-0.363003\pi$
$149$	7.48036e11			0.834446			0.417223	+	0.908804i	$0.363003\pi$
$150$		0			0
$151$	4.28642e11			0.444346			0.222173	−	0.975007i	$-0.428685\pi$
$151$	4.28642e11			0.444346			0.222173	+	0.975007i	$0.428685\pi$
$152$	−4.91017e11	+	4.91017e11i	−0.490859	+	0.490859i
$153$	−6.85219e11	−	1.46322e11i	−0.660734	−	0.141093i
$154$			1.93346e11i			0.179875i
$155$		0			0
$156$	−2.74978e11	+	8.13114e10i	−0.238293	+	0.0704638i
$157$	1.71815e11	+	1.71815e11i	0.143752	+	0.143752i	0.775320	−	0.631568i	$-0.217589\pi$
$157$	1.71815e11	+	1.71815e11i	0.143752	+	0.143752i	−0.631568	+	0.775320i	$0.717589\pi$
$158$	−8.98292e11	−	8.98292e11i	−0.725778	−	0.725778i
$159$	2.63827e11	−	7.80142e10i	0.205890	−	0.0608821i
$160$		0			0
$161$			1.17475e12i			0.855862i
$162$	−5.93328e11	−	1.55441e12i	−0.417794	−	1.09454i
$163$	−1.17074e12	+	1.17074e12i	−0.796947	+	0.796947i	−0.982613	−	0.185666i	$-0.940556\pi$
$163$	−1.17074e12	+	1.17074e12i	−0.796947	+	0.796947i	0.185666	+	0.982613i	$0.440556\pi$
$164$	−1.00895e12			−0.664092
$165$		0			0
$166$	1.56531e12			0.963843
$167$	1.53598e12	−	1.53598e12i	0.915051	−	0.915051i	−0.0816127	−	0.996664i	$-0.526007\pi$
$167$	1.53598e12	−	1.53598e12i	0.915051	−	0.915051i	0.996664	+	0.0816127i	$0.0260071\pi$
$168$	1.65186e12	+	8.97893e11i	0.952297	+	0.517635i
$169$			9.94934e11i			0.555159i
$170$		0			0
$171$	−1.51522e12	+	9.81971e11i	−0.792497	+	0.513594i
$172$	−4.80434e10	−	4.80434e10i	−0.0243348	−	0.0243348i
$173$	6.87025e11	+	6.87025e11i	0.337069	+	0.337069i	0.855263	−	0.518194i	$-0.173395\pi$
$173$	6.87025e11	+	6.87025e11i	0.337069	+	0.337069i	−0.518194	+	0.855263i	$0.673395\pi$
$174$	−9.37334e11	−	3.16986e12i	−0.445527	−	1.50668i
$175$		0			0
$176$		−	2.87806e11i		−	0.128464i
$177$	−1.30215e12	+	2.39557e12i	−0.563389	+	1.03647i
$178$	6.59647e11	−	6.59647e11i	0.276695	−	0.276695i
$179$	−1.31234e12			−0.533769			−0.266884	−	0.963729i	$-0.585994\pi$
$179$	−1.31234e12			−0.533769			−0.266884	+	0.963729i	$0.585994\pi$
$180$		0			0
$181$	2.03204e12			0.777498			0.388749	−	0.921344i	$-0.372907\pi$
$181$	2.03204e12			0.777498			0.388749	+	0.921344i	$0.372907\pi$
$182$	2.19484e12	−	2.19484e12i	0.814722	−	0.814722i
$183$	1.34319e12	−	2.47107e12i	0.483789	−	0.890029i
$184$		−	1.22061e12i		−	0.426658i
$185$		0			0
$186$	−1.65672e12	−	5.60268e12i	−0.545669	−	1.84533i
$187$	−1.55551e11	−	1.55551e11i	−0.0497442	−	0.0497442i
$188$	−1.05928e12	−	1.05928e12i	−0.328960	−	0.328960i
$189$	3.71292e12	+	3.18021e12i	1.11989	+	0.959214i
$190$		0			0
$191$			1.22025e12i			0.347350i	0.984803	+	0.173675i	$0.0555642\pi$
$191$			1.22025e12i			0.347350i	−0.984803	+	0.173675i	$0.944436\pi$
$192$	−1.27542e12	−	6.93273e11i	−0.352774	−	0.191755i
$193$	−1.22556e12	+	1.22556e12i	−0.329435	+	0.329435i	−0.852372	−	0.522936i	$-0.824837\pi$
$193$	−1.22556e12	+	1.22556e12i	−0.329435	+	0.329435i	0.522936	+	0.852372i	$0.324837\pi$
$194$	3.47239e12			0.907234
$195$		0			0
$196$	1.77166e12			0.437493
$197$	−1.43636e12	+	1.43636e12i	−0.344904	+	0.344904i	−0.858207	−	0.513304i	$-0.828421\pi$
$197$	−1.43636e12	+	1.43636e12i	−0.344904	+	0.344904i	0.513304	+	0.858207i	$0.328421\pi$
$198$	1.09087e11	−	5.10849e11i	0.0254750	−	0.119298i
$199$			1.44198e12i			0.327543i	0.986498	+	0.163771i	$0.0523660\pi$
$199$			1.44198e12i			0.327543i	−0.986498	+	0.163771i	$0.947634\pi$
$200$		0			0
$201$	1.89811e12	−	5.61274e11i	0.408077	−	0.120669i
$202$	5.10931e12	+	5.10931e12i	1.06888	+	1.06888i
$203$	6.86787e12	+	6.86787e12i	1.39828	+	1.39828i
$204$	1.21811e12	−	3.60196e11i	0.241390	−	0.0713794i
$205$		0			0
$206$			3.14313e11i			0.0590327i
$207$	6.62801e11	−	3.10387e12i	0.121212	−	0.567632i
$208$	−3.26714e12	+	3.26714e12i	−0.581861	+	0.581861i
$209$	−5.66884e11			−0.0983309
$210$		0			0
$211$	−3.21613e12			−0.529395			−0.264698	−	0.964331i	$-0.585272\pi$
$211$	−3.21613e12			−0.529395			−0.264698	+	0.964331i	$0.585272\pi$
$212$	−3.52682e11	+	3.52682e11i	−0.0565634	+	0.0565634i
$213$	−2.85917e12	−	1.55415e12i	−0.446841	−	0.242887i
$214$			8.61210e12i			1.31170i
$215$		0			0
$216$	−3.85787e12	−	3.30436e12i	−0.558280	−	0.478180i
$217$	1.21388e13	+	1.21388e13i	1.71257	+	1.71257i
$218$	−2.64722e12	−	2.64722e12i	−0.364149	−	0.364149i
$219$	−3.19077e11	−	1.07905e12i	−0.0428009	−	0.144744i
$220$		0			0
$221$			3.53158e12i			0.450621i
$222$	5.15050e12	−	9.47541e12i	0.641074	−	1.17939i
$223$	−9.25140e11	+	9.25140e11i	−0.112339	+	0.112339i	−0.761042	−	0.648703i	$-0.775312\pi$
$223$	−9.25140e11	+	9.25140e11i	−0.112339	+	0.112339i	0.648703	+	0.761042i	$0.275312\pi$
$224$	−8.84097e12			−1.04746
$225$		0			0
$226$	−1.40885e13			−1.58952
$227$	−4.50902e12	+	4.50902e12i	−0.496523	+	0.496523i	−0.910354	−	0.413830i	$-0.864191\pi$
$227$	−4.50902e12	+	4.50902e12i	−0.496523	+	0.496523i	0.413830	+	0.910354i	$0.364191\pi$
$228$	1.56327e12	−	2.87596e12i	0.168032	−	0.309130i
$229$			4.57505e12i			0.480066i	0.970765	+	0.240033i	$0.0771582\pi$
$229$			4.57505e12i			0.480066i	−0.970765	+	0.240033i	$0.922842\pi$
$230$		0			0
$231$	4.35231e11	+	1.47186e12i	0.0435366	+	0.147231i
$232$	−7.13598e12	−	7.13598e12i	−0.697060	−	0.697060i
$233$	2.74585e12	+	2.74585e12i	0.261950	+	0.261950i	0.825846	−	0.563896i	$-0.190698\pi$
$233$	2.74585e12	+	2.74585e12i	0.261950	+	0.261950i	−0.563896	+	0.825846i	$0.690698\pi$
$234$	−7.03743e12	+	4.56075e12i	−0.655732	+	0.424961i
$235$		0			0
$236$		−	4.94308e12i		−	0.439523i
$237$	−8.86042e12	−	4.81621e12i	−0.769730	−	0.418398i
$238$	−9.72276e12	+	9.72276e12i	−0.825308	+	0.825308i
$239$	−1.86895e13			−1.55028			−0.775138	−	0.631792i	$-0.782320\pi$
$239$	−1.86895e13			−1.55028			−0.775138	+	0.631792i	$0.782320\pi$
$240$		0			0
$241$	2.13946e13			1.69516			0.847579	−	0.530669i	$-0.178059\pi$
$241$	2.13946e13			1.69516			0.847579	+	0.530669i	$0.178059\pi$
$242$	−1.05804e13	+	1.05804e13i	−0.819443	+	0.819443i
$243$	−8.01580e12	−	1.04974e13i	−0.606894	−	0.794783i
$244$			5.09886e12i			0.377423i
$245$		0			0
$246$	−2.82959e13	+	8.36716e12i	−2.00254	+	0.592155i
$247$	6.43520e12	+	6.43520e12i	0.445378	+	0.445378i
$248$	−1.26127e13	−	1.26127e13i	−0.853739	−	0.853739i
$249$	1.19160e13	−	3.52360e12i	0.788925	−	0.233287i
$250$		0			0
$251$			3.63600e12i			0.230366i	0.993344	+	0.115183i	$0.0367454\pi$
$251$			3.63600e12i			0.230366i	−0.993344	+	0.115183i	$0.963255\pi$
$252$	−8.66736e12	−	1.85083e12i	−0.537259	−	0.114726i
$253$	7.04605e11	−	7.04605e11i	0.0427349	−	0.0427349i
$254$	1.70556e13			1.01224
$255$		0			0
$256$	1.72727e13			0.981838
$257$	−1.95072e13	+	1.95072e13i	−1.08533	+	1.08533i	−0.0893287	+	0.996002i	$0.528472\pi$
$257$	−1.95072e13	+	1.95072e13i	−1.08533	+	1.08533i	−0.996002	+	0.0893287i	$0.971528\pi$
$258$	−1.74580e12	−	9.48955e11i	−0.0950792	−	0.0516817i
$259$			3.16887e13i			1.68949i
$260$		0			0
$261$	−1.42711e13	−	2.20208e13i	−0.729345	−	1.12541i
$262$	2.44596e13	+	2.44596e13i	1.22403	+	1.22403i
$263$	5.04148e12	+	5.04148e12i	0.247059	+	0.247059i	0.819763	−	0.572703i	$-0.194105\pi$
$263$	5.04148e12	+	5.04148e12i	0.247059	+	0.247059i	−0.572703	+	0.819763i	$0.694105\pi$
$264$	−4.52222e11	−	1.52932e12i	−0.0217035	−	0.0733967i
$265$		0			0
$266$			3.54334e13i			1.63141i
$267$	3.53671e12	−	6.50651e12i	0.159510	−	0.293451i
$268$	−2.53737e12	+	2.53737e12i	−0.112109	+	0.112109i
$269$	8.15175e12			0.352869			0.176434	−	0.984312i	$-0.443544\pi$
$269$	8.15175e12			0.352869			0.176434	+	0.984312i	$0.443544\pi$
$270$		0			0
$271$	1.26813e13			0.527027			0.263513	−	0.964656i	$-0.415119\pi$
$271$	1.26813e13			0.527027			0.263513	+	0.964656i	$0.415119\pi$
$272$	1.44729e13	−	1.44729e13i	0.589421	−	0.589421i
$273$	1.17677e13	−	2.16490e13i	0.469673	−	0.864060i
$274$		−	4.79849e13i		−	1.87705i
$275$		0			0
$276$	1.63160e12	+	5.51771e12i	0.0613215	+	0.207376i
$277$	−1.01118e13	−	1.01118e13i	−0.372554	−	0.372554i	0.495853	−	0.868407i	$-0.334856\pi$
$277$	−1.01118e13	−	1.01118e13i	−0.372554	−	0.372554i	−0.868407	+	0.495853i	$0.834856\pi$
$278$	3.56693e13	+	3.56693e13i	1.28839	+	1.28839i
$279$	−2.52239e13	−	3.89215e13i	−0.893282	−	1.37837i
$280$		0			0
$281$		−	1.28758e13i		−	0.438418i	−0.975678	−	0.219209i	$-0.929652\pi$
$281$		−	1.28758e13i		−	0.438418i	0.975678	−	0.219209i	$-0.0703477\pi$
$282$	−3.84920e13	−	2.09229e13i	−1.28529	−	0.698638i
$283$	1.06470e13	−	1.06470e13i	0.348661	−	0.348661i	−0.510950	−	0.859611i	$-0.670706\pi$
$283$	1.06470e13	−	1.06470e13i	0.348661	−	0.348661i	0.859611	+	0.510950i	$0.170706\pi$
$284$	5.89968e12			0.189486
$285$		0			0
$286$	−2.63289e12			−0.0813615
$287$	6.13064e13	−	6.13064e13i	1.85847	−	1.85847i
$288$	2.33592e13	+	4.98812e12i	0.694702	+	0.148347i
$289$			1.86276e13i			0.543524i
$290$		0			0
$291$	2.64338e13	−	7.81654e12i	0.742590	−	0.219585i
$292$	1.44246e12	+	1.44246e12i	0.0397648	+	0.0397648i
$293$	−2.44636e13	−	2.44636e13i	−0.661834	−	0.661834i	0.293978	−	0.955812i	$-0.405021\pi$
$293$	−2.44636e13	−	2.44636e13i	−0.661834	−	0.661834i	−0.955812	+	0.293978i	$0.905021\pi$
$294$	4.96860e13	−	1.46923e13i	1.31924	−	0.390102i
$295$		0			0
$296$		−	3.29258e13i		−	0.842232i
$297$	−3.19516e11	−	4.13443e12i	−0.00802292	−	0.103814i
$298$	−2.80440e13	+	2.80440e13i	−0.691275	+	0.691275i
$299$	−1.59972e13			−0.387125
$300$		0			0
$301$	5.83848e12			0.136202
$302$	−1.60699e13	+	1.60699e13i	−0.368107	+	0.368107i
$303$	5.03963e13	+	2.73937e13i	1.13361	+	0.616192i
$304$		−	5.27445e13i		−	1.16513i
$305$		0			0
$306$	3.11746e13	−	2.02034e13i	0.664253	−	0.430483i
$307$	2.31565e13	+	2.31565e13i	0.484632	+	0.484632i	0.906607	−	0.421976i	$-0.138663\pi$
$307$	2.31565e13	+	2.31565e13i	0.484632	+	0.484632i	−0.421976	+	0.906607i	$0.638663\pi$
$308$	−1.96756e12	−	1.96756e12i	−0.0404483	−	0.0404483i
$309$	7.07534e11	+	2.39273e12i	0.0142881	+	0.0483194i
$310$		0			0
$311$			2.95317e13i			0.575581i	0.957693	+	0.287790i	$0.0929206\pi$
$311$			2.95317e13i			0.575581i	−0.957693	+	0.287790i	$0.907079\pi$
$312$	−1.22271e13	+	2.24942e13i	−0.234138	+	0.430745i
$313$	3.21868e13	−	3.21868e13i	0.605597	−	0.605597i	−0.336195	−	0.941792i	$-0.609140\pi$
$313$	3.21868e13	−	3.21868e13i	0.605597	−	0.605597i	0.941792	+	0.336195i	$0.109140\pi$
$314$	−1.28828e13			−0.238175
$315$		0			0
$316$	1.82828e13			0.326410
$317$	3.70619e13	−	3.70619e13i	0.650282	−	0.650282i	−0.302779	−	0.953061i	$-0.597914\pi$
$317$	3.70619e13	−	3.70619e13i	0.650282	−	0.650282i	0.953061	+	0.302779i	$0.0979143\pi$
$318$	−6.96617e12	+	1.28157e13i	−0.120128	+	0.221001i
$319$		−	8.23857e12i		−	0.139638i
$320$		0			0
$321$	1.93863e13	+	6.55602e13i	0.317480	+	1.07365i
$322$	−4.40417e13	−	4.40417e13i	−0.709017	−	0.709017i
$323$	−2.85069e13	−	2.85069e13i	−0.451165	−	0.451165i
$324$	2.18562e13	+	9.78034e12i	0.340077	+	0.152180i
$325$		0			0
$326$		−	8.77827e13i		−	1.32042i
$327$	−2.61112e13	−	1.41931e13i	−0.386201	−	0.209926i
$328$	−6.36997e13	+	6.36997e13i	−0.926470	+	0.926470i
$329$	1.28729e14			1.84120
$330$		0			0
$331$	9.26878e13			1.28224			0.641119	−	0.767441i	$-0.278470\pi$
$331$	9.26878e13			1.28224			0.641119	+	0.767441i	$0.278470\pi$
$332$	−1.59292e13	+	1.59292e13i	−0.216738	+	0.216738i
$333$	1.78789e13	−	8.37263e13i	0.239276	−	1.12052i
$334$			1.15169e14i			1.51610i
$335$		0			0
$336$	−1.36946e14	+	4.04952e13i	−1.74455	+	0.515866i
$337$	−3.00431e13	−	3.00431e13i	−0.376513	−	0.376513i	0.493330	−	0.869842i	$-0.335780\pi$
$337$	−3.00431e13	−	3.00431e13i	−0.376513	−	0.376513i	−0.869842	+	0.493330i	$0.835780\pi$
$338$	−3.73003e13	−	3.73003e13i	−0.459907	−	0.459907i
$339$	−1.07249e14	+	3.17138e13i	−1.30106	+	0.384725i
$340$		0			0
$341$		−	1.45615e13i		−	0.171024i
$342$	1.99917e13	−	9.36203e13i	0.231050	−	1.08200i
$343$	−1.59741e13	+	1.59741e13i	−0.181677	+	0.181677i
$344$	−6.06642e12			−0.0678986
$345$		0			0
$346$	−5.15134e13			−0.558473
$347$	−2.84539e13	+	2.84539e13i	−0.303619	+	0.303619i	−0.842428	−	0.538809i	$-0.818874\pi$
$347$	−2.84539e13	+	2.84539e13i	−0.303619	+	0.303619i	0.538809	+	0.842428i	$0.318874\pi$
$348$	4.17965e13	+	2.27191e13i	0.438989	+	0.238619i
$349$		−	1.78493e14i		−	1.84536i	−0.385571	−	0.922678i	$-0.625996\pi$
$349$		−	1.78493e14i		−	1.84536i	0.385571	−	0.922678i	$-0.374004\pi$
$350$		0			0
$351$	−4.33064e13	+	5.05607e13i	−0.433874	+	0.506551i
$352$	5.30273e12	+	5.30273e12i	0.0523016	+	0.0523016i
$353$	9.49048e12	+	9.49048e12i	0.0921568	+	0.0921568i	0.751682	−	0.659525i	$-0.229243\pi$
$353$	9.49048e12	+	9.49048e12i	0.0921568	+	0.0921568i	−0.659525	+	0.751682i	$0.729243\pi$
$354$	−4.09927e13	−	1.38628e14i	−0.391912	−	1.32536i
$355$		0			0
$356$			1.34257e13i			0.124440i
$357$	−5.21288e13	+	9.59017e13i	−0.475776	+	0.875288i
$358$	4.91997e13	−	4.91997e13i	0.442187	−	0.442187i
$359$	−7.78654e13			−0.689168			−0.344584	−	0.938756i	$-0.611980\pi$
$359$	−7.78654e13			−0.689168			−0.344584	+	0.938756i	$0.611980\pi$
$360$		0			0
$361$	1.26006e13			0.108169
$362$	−7.61814e13	+	7.61814e13i	−0.644098	+	0.644098i
$363$	−5.67272e13	+	1.04361e14i	−0.472394	+	0.869067i
$364$			4.46711e13i			0.366411i
$365$		0			0
$366$	4.22846e13	+	1.42997e14i	0.336539	+	1.13810i
$367$	1.49313e14	+	1.49313e14i	1.17067	+	1.17067i	0.982050	+	0.188622i	$0.0604021\pi$
$367$	1.49313e14	+	1.49313e14i	1.17067	+	1.17067i	0.188622	+	0.982050i	$0.439598\pi$
$368$	6.55585e13	+	6.55585e13i	0.506368	+	0.506368i
$369$	−1.96570e14	+	1.27391e14i	−1.49580	+	0.969382i
$370$		0			0
$371$		−	4.28597e13i		−	0.316587i
$372$	7.38747e13	+	4.01557e13i	0.537662	+	0.292254i
$373$	1.72842e14	−	1.72842e14i	1.23951	−	1.23951i	0.279308	−	0.960201i	$-0.409895\pi$
$373$	1.72842e14	−	1.72842e14i	1.23951	−	1.23951i	0.960201	−	0.279308i	$-0.0901052\pi$
$374$	1.16632e13			0.0824187
$375$		0			0
$376$	−1.33755e14			−0.917859
$377$	−9.35232e13	+	9.35232e13i	−0.632473	+	0.632473i
$378$	−2.58425e14	+	1.99715e13i	−1.72238	+	0.133109i
$379$			2.55919e14i			1.68107i	0.541754	+	0.840537i	$0.317760\pi$
$379$			2.55919e14i			1.68107i	−0.541754	+	0.840537i	$0.682240\pi$
$380$		0			0
$381$	1.29837e14	−	3.83931e13i	0.828537	−	0.245000i
$382$	−4.57476e13	−	4.57476e13i	−0.287753	−	0.287753i
$383$	−1.56911e14	−	1.56911e14i	−0.972883	−	0.972883i	0.0267587	−	0.999642i	$-0.491481\pi$
$383$	−1.56911e14	−	1.56911e14i	−0.972883	−	0.972883i	−0.999642	+	0.0267587i	$0.991481\pi$
$384$	1.85262e14	−	5.47823e13i	1.13231	−	0.334825i
$385$		0			0
$386$		−	9.18932e13i		−	0.545825i
$387$	−1.54262e13	−	3.29411e12i	−0.0903332	−	0.0192898i
$388$	−3.53365e13	+	3.53365e13i	−0.204009	+	0.204009i
$389$	1.06415e14			0.605730			0.302865	−	0.953033i	$-0.402057\pi$
$389$	1.06415e14			0.605730			0.302865	+	0.953033i	$0.402057\pi$
$390$		0			0
$391$	7.08648e13			0.392156
$392$	1.11853e14	−	1.11853e14i	0.610343	−	0.610343i
$393$	2.41260e14	+	1.31141e14i	1.29816	+	0.705633i
$394$		−	1.07699e14i		−	0.571453i
$395$		0			0
$396$	4.08849e12	+	6.30871e12i	0.0210979	+	0.0325550i
$397$	4.67234e13	+	4.67234e13i	0.237786	+	0.237786i	0.815933	−	0.578147i	$-0.196224\pi$
$397$	4.67234e13	+	4.67234e13i	0.237786	+	0.237786i	−0.578147	+	0.815933i	$0.696224\pi$
$398$	−5.40603e13	−	5.40603e13i	−0.271345	−	0.271345i
$399$	7.97623e13	+	2.69739e14i	0.394863	+	1.33534i
$400$		0			0
$401$			1.16339e14i			0.560313i	0.959954	+	0.280157i	$0.0903864\pi$
$401$			1.16339e14i			0.560313i	−0.959954	+	0.280157i	$0.909614\pi$
$402$	−5.01181e13	+	9.22027e13i	−0.238096	+	0.438026i
$403$	−1.65301e14	+	1.65301e14i	−0.774635	+	0.774635i
$404$	−1.03989e14			−0.480717
$405$		0			0
$406$	−5.14955e14			−2.31674
$407$	1.90066e13	−	1.90066e13i	0.0843597	−	0.0843597i
$408$	5.41639e13	−	9.96456e13i	0.237180	−	0.436342i
$409$			1.31811e14i			0.569472i	0.958606	+	0.284736i	$0.0919059\pi$
$409$			1.31811e14i			0.569472i	−0.958606	+	0.284736i	$0.908094\pi$
$410$		0			0
$411$	−1.08016e14	−	3.65288e14i	−0.454318	−	1.53640i
$412$	−3.19857e12	−	3.19857e12i	−0.0132746	−	0.0132746i
$413$	3.00354e14	+	3.00354e14i	1.23001	+	1.23001i
$414$	9.15162e13	+	1.41213e14i	0.369825	+	0.570655i
$415$		0			0
$416$		−	1.20392e14i		−	0.473788i
$417$	3.51829e14	+	1.91242e14i	1.36642	+	0.742737i
$418$	2.12526e13	−	2.12526e13i	0.0814597	−	0.0814597i
$419$	2.41692e14			0.914293			0.457146	−	0.889391i	$-0.348872\pi$
$419$	2.41692e14			0.914293			0.457146	+	0.889391i	$0.348872\pi$
$420$		0			0
$421$	1.15430e14			0.425372			0.212686	−	0.977121i	$-0.431779\pi$
$421$	1.15430e14			0.425372			0.212686	+	0.977121i	$0.431779\pi$
$422$	1.20573e14	−	1.20573e14i	0.438564	−	0.438564i
$423$	−3.40122e14	−	7.26297e13i	−1.22113	−	0.260761i
$424$			4.45329e13i			0.157822i
$425$		0			0
$426$	1.65456e14	−	4.89257e13i	0.571387	−	0.168960i
$427$	−3.09820e14	−	3.09820e14i	−1.05622	−	1.05622i
$428$	−8.76402e13	−	8.76402e13i	−0.294960	−	0.294960i
$429$	−2.00430e13	+	5.92676e12i	−0.0665960	+	0.0196926i
$430$		0			0
$431$			2.25269e14i			0.729587i	0.931089	+	0.364793i	$0.118860\pi$
$431$			2.25269e14i			0.729587i	−0.931089	+	0.364793i	$0.881140\pi$
$432$	3.84680e14	−	2.97287e13i	1.23009	−	0.0950638i
$433$	−1.67103e14	+	1.67103e14i	−0.527597	+	0.527597i	−0.919855	−	0.392258i	$-0.871694\pi$
$433$	−1.67103e14	+	1.67103e14i	−0.527597	+	0.527597i	0.392258	+	0.919855i	$0.371694\pi$
$434$	−9.10176e14			−2.83747
$435$		0			0
$436$	5.38784e13			0.163772
$437$	1.29129e14	−	1.29129e14i	0.387593	−	0.387593i
$438$	5.24161e13	+	2.84916e13i	0.155366	+	0.0844518i
$439$		−	1.10282e14i		−	0.322812i	−0.986888	−	0.161406i	$-0.948397\pi$
$439$		−	1.10282e14i		−	0.322812i	0.986888	−	0.161406i	$-0.0516029\pi$
$440$		0			0
$441$	3.45166e14	−	2.23692e14i	0.985406	−	0.638613i
$442$	−1.32400e14	−	1.32400e14i	−0.373306	−	0.373306i
$443$	2.12623e14	+	2.12623e14i	0.592093	+	0.592093i	0.938196	−	0.346104i	$-0.112495\pi$
$443$	2.12623e14	+	2.12623e14i	0.592093	+	0.592093i	−0.346104	+	0.938196i	$0.612495\pi$
$444$	4.40120e13	+	1.48839e14i	0.121050	+	0.409365i
$445$		0			0
$446$		−	6.93674e13i		−	0.186129i
$447$	−1.50359e14	+	2.76616e14i	−0.398508	+	0.733138i
$448$	−1.59910e14	+	1.59910e14i	−0.418647	+	0.418647i
$449$	−2.09893e14			−0.542803			−0.271402	−	0.962466i	$-0.587487\pi$
$449$	−2.09893e14			−0.542803			−0.271402	+	0.962466i	$0.587487\pi$
$450$		0			0
$451$	−7.35420e13			−0.185594
$452$	1.43370e14	−	1.43370e14i	0.357434	−	0.357434i
$453$	−8.61589e13	+	1.58507e14i	−0.212207	+	0.390399i
$454$		−	3.38088e14i		−	0.822664i
$455$		0			0
$456$	−8.28762e13	−	2.80270e14i	−0.196844	−	0.665686i
$457$	3.40714e13	+	3.40714e13i	0.0799561	+	0.0799561i	0.745954	−	0.665998i	$-0.231994\pi$
$457$	3.40714e13	+	3.40714e13i	0.0799561	+	0.0799561i	−0.665998	+	0.745954i	$0.731994\pi$
$458$	−1.71520e14	−	1.71520e14i	−0.397698	−	0.397698i
$459$	1.91840e14	−	2.23975e14i	0.439512	−	0.513134i
$460$		0			0
$461$			8.31120e14i			1.85913i	0.368663	+	0.929563i	$0.379816\pi$
$461$			8.31120e14i			1.85913i	−0.368663	+	0.929563i	$0.620184\pi$
$462$	−7.14972e13	−	3.88634e13i	−0.158037	−	0.0859033i
$463$	5.49396e14	−	5.49396e14i	1.20002	−	1.20002i	0.225865	−	0.974159i	$-0.427479\pi$
$463$	5.49396e14	−	5.49396e14i	1.20002	−	1.20002i	0.974159	−	0.225865i	$-0.0725208\pi$
$464$	7.66540e14			1.65457
$465$		0			0
$466$	−2.05885e14			−0.434012
$467$	−1.39727e14	+	1.39727e14i	−0.291097	+	0.291097i	−0.837514	−	0.546416i	$-0.815992\pi$
$467$	−1.39727e14	+	1.39727e14i	−0.291097	+	0.291097i	0.546416	+	0.837514i	$0.315992\pi$
$468$	2.52037e13	−	1.18028e14i	0.0518933	−	0.243014i
$469$		−	3.08354e14i		−	0.627479i
$470$		0			0
$471$	−9.80709e13	+	2.89997e13i	−0.194951	+	0.0576473i
$472$	−3.12080e14	−	3.12080e14i	−0.613175	−	0.613175i
$473$	−3.50187e12	−	3.50187e12i	−0.00680086	−	0.00680086i
$474$	5.12740e14	−	1.51618e14i	0.984274	−	0.291052i
$475$		0			0
$476$		−	1.97885e14i		−	0.371172i
$477$	−2.41817e13	+	1.13242e14i	−0.0448369	+	0.209969i
$478$	7.00673e14	−	7.00673e14i	1.28429	−	1.28429i
$479$	4.58603e14			0.830981			0.415491	−	0.909597i	$-0.363610\pi$
$479$	4.58603e14			0.830981			0.415491	+	0.909597i	$0.363610\pi$
$480$		0			0
$481$	−4.31521e14			−0.764194
$482$	−8.02088e14	+	8.02088e14i	−1.40431	+	1.40431i
$483$	−4.34410e14	−	2.36130e14i	−0.751954	−	0.408736i
$484$		−	2.15341e14i		−	0.368534i
$485$		0			0
$486$	6.94065e14	+	9.30369e13i	1.16118	+	0.155652i
$487$	−3.32018e14	−	3.32018e14i	−0.549228	−	0.549228i	0.376990	−	0.926217i	$-0.376959\pi$
$487$	−3.32018e14	−	3.32018e14i	−0.549228	−	0.549228i	−0.926217	+	0.376990i	$0.876959\pi$
$488$	3.21915e14	+	3.21915e14i	0.526541	+	0.526541i
$489$	−1.97603e14	−	6.68252e14i	−0.319592	−	1.08079i
$490$		0			0
$491$			6.44188e14i			1.01874i	0.860547	+	0.509372i	$0.170122\pi$
$491$			6.44188e14i			1.01874i	−0.860547	+	0.509372i	$0.829878\pi$
$492$	2.02803e14	−	3.73099e14i	0.317152	−	0.583466i
$493$	4.14292e14	−	4.14292e14i	0.640691	−	0.640691i
$494$	−4.82514e14			−0.737924
$495$		0			0
$496$	1.35485e15			2.02648
$497$	−3.58480e14	+	3.58480e14i	−0.530279	+	0.530279i
$498$	−3.14635e14	+	5.78835e14i	−0.460304	+	0.846825i
$499$			3.35306e14i			0.485164i	0.970131	+	0.242582i	$0.0779944\pi$
$499$			3.35306e14i			0.485164i	−0.970131	+	0.242582i	$0.922006\pi$
$500$		0			0
$501$	2.59250e14	+	8.76729e14i	0.366954	+	1.24096i
$502$	−1.36314e14	−	1.36314e14i	−0.190841	−	0.190841i
$503$	4.24232e14	+	4.24232e14i	0.587461	+	0.587461i	0.936943	−	0.349482i	$-0.113642\pi$
$503$	4.24232e14	+	4.24232e14i	0.587461	+	0.587461i	−0.349482	+	0.936943i	$0.613642\pi$
$504$	−6.64063e14	+	4.30360e14i	−0.909581	+	0.589473i
$505$		0			0
$506$			5.28316e13i			0.0708053i
$507$	−3.67916e14	−	1.99986e14i	−0.487759	−	0.265129i
$508$	−1.73565e14	+	1.73565e14i	−0.227621	+	0.227621i
$509$	1.01770e14			0.132030			0.0660149	−	0.997819i	$-0.478971\pi$
$509$	1.01770e14			0.132030			0.0660149	+	0.997819i	$0.478971\pi$
$510$		0			0
$511$	−1.75296e14			−0.222565
$512$	1.71611e13	−	1.71611e13i	0.0215556	−	0.0215556i
$513$	−5.85559e13	−	7.57694e14i	−0.0727654	−	0.941560i
$514$		−	1.46266e15i		−	1.79823i
$515$		0			0
$516$	2.74229e13	−	8.10900e12i	0.0330020	−	0.00975874i
$517$	−7.72106e13	−	7.72106e13i	−0.0919346	−	0.0919346i
$518$	−1.18802e15	−	1.18802e15i	−1.39961	−	1.39961i
$519$	−3.92150e14	+	1.15959e14i	−0.457121	+	0.135172i
$520$		0			0
$521$		−	1.19954e15i		−	1.36901i	−0.729008	−	0.684505i	$-0.760019\pi$
$521$		−	1.19954e15i		−	1.36901i	0.729008	−	0.684505i	$-0.239981\pi$
$522$	1.36059e15	+	2.90541e14i	1.53652	+	0.328110i
$523$	−1.65527e14	+	1.65527e14i	−0.184973	+	0.184973i	−0.793519	−	0.608546i	$-0.791753\pi$
$523$	−1.65527e14	+	1.65527e14i	−0.184973	+	0.184973i	0.608546	+	0.793519i	$0.291753\pi$
$524$	−4.97822e14			−0.550493
$525$		0			0
$526$	−3.78012e14			−0.409340
$527$	7.32255e14	−	7.32255e14i	0.784700	−	0.784700i
$528$	1.06428e14	+	5.78503e13i	0.112867	+	0.0613506i
$529$		−	6.31810e14i		−	0.663102i
$530$		0			0
$531$	−6.24120e14	−	9.63043e14i	−0.641576	−	0.989978i
$532$	−3.60584e14	−	3.60584e14i	−0.366854	−	0.366854i
$533$	8.34839e14	+	8.34839e14i	0.840627	+	0.840627i
$534$	1.11338e14	+	3.76522e14i	0.110960	+	0.375244i
$535$		0			0
$536$			3.20392e14i			0.312806i
$537$	2.63785e14	−	4.85288e14i	0.254913	−	0.468965i
$538$	−3.05611e14	+	3.05611e14i	−0.292325	+	0.292325i
$539$	1.29135e14			0.122266
$540$		0			0
$541$	−4.90173e14			−0.454742			−0.227371	−	0.973808i	$-0.573013\pi$
$541$	−4.90173e14			−0.454742			−0.227371	+	0.973808i	$0.573013\pi$
$542$	−4.75425e14	+	4.75425e14i	−0.436602	+	0.436602i
$543$	−4.08448e14	+	7.51425e14i	−0.371311	+	0.683104i
$544$			5.33316e14i			0.479944i
$545$		0			0
$546$	3.70455e14	+	1.25280e15i	0.326720	+	1.10490i
$547$	−7.74424e14	−	7.74424e14i	−0.676159	−	0.676159i	0.282970	−	0.959129i	$-0.408680\pi$
$547$	−7.74424e14	−	7.74424e14i	−0.676159	−	0.676159i	−0.959129	+	0.282970i	$0.908680\pi$
$548$	4.88313e14	+	4.88313e14i	0.422090	+	0.422090i
$549$	6.43789e14	+	9.93393e14i	0.550929	+	0.850106i
$550$		0			0
$551$		−	1.50983e15i		−	1.26647i
$552$	4.51370e14	+	2.45349e14i	0.374859	+	0.203760i
$553$	−1.11091e15	+	1.11091e15i	−0.913461	+	0.913461i
$554$	7.58186e14			0.617266
$555$		0			0
$556$	−7.25971e14			−0.579440
$557$	1.65220e15	−	1.65220e15i	1.30575	−	1.30575i	0.381293	−	0.924454i	$-0.375479\pi$
$557$	1.65220e15	−	1.65220e15i	1.30575	−	1.30575i	0.924454	−	0.381293i	$-0.124521\pi$
$558$	2.40482e15	+	5.13526e14i	1.88189	+	0.401860i
$559$			7.95056e13i			0.0616074i
$560$		0			0
$561$	8.87873e13	−	2.62546e13i	0.0674614	−	0.0199485i
$562$	4.82715e14	+	4.82715e14i	0.363196	+	0.363196i
$563$	−1.34187e15	−	1.34187e15i	−0.999803	−	0.999803i	0.000197220	−	1.00000i	$-0.499937\pi$
$563$	−1.34187e15	−	1.34187e15i	−0.999803	−	0.999803i	−1.00000		0.000197220i	$0.999937\pi$
$564$	6.04631e14	−	1.78790e14i	0.446124	−	0.131920i
$565$		0			0
$566$			7.98319e14i			0.577678i
$567$	−1.92232e15	+	7.33762e14i	−1.37759	+	0.525834i
$568$	3.72474e14	−	3.72474e14i	0.264351	−	0.264351i
$569$	7.18460e14			0.504993			0.252496	−	0.967598i	$-0.418748\pi$
$569$	7.18460e14			0.504993			0.252496	+	0.967598i	$0.418748\pi$
$570$		0			0
$571$	−3.57104e14			−0.246205			−0.123102	−	0.992394i	$-0.539284\pi$
$571$	−3.57104e14			−0.246205			−0.123102	+	0.992394i	$0.539284\pi$
$572$	2.67933e13	−	2.67933e13i	0.0182957	−	0.0182957i
$573$	−4.51237e14	−	2.45277e14i	−0.305179	−	0.165885i
$574$			4.59678e15i			3.07920i
$575$		0			0
$576$	5.12730e14	−	3.32285e14i	0.336950	−	0.218367i
$577$	1.43625e15	+	1.43625e15i	0.934899	+	0.934899i	0.998007	−	0.0631080i	$-0.0201013\pi$
$577$	1.43625e15	+	1.43625e15i	0.934899	+	0.934899i	−0.0631080	+	0.998007i	$0.520101\pi$
$578$	−6.98352e14	−	6.98352e14i	−0.450268	−	0.450268i
$579$	−2.06856e14	−	6.99544e14i	−0.132110	−	0.446769i
$580$		0			0
$581$		−	1.93580e15i		−	1.21309i
$582$	−6.97967e14	+	1.28405e15i	−0.433270	+	0.797089i
$583$	−2.57068e13	+	2.57068e13i	−0.0158078	+	0.0158078i
$584$	1.82139e14			0.110951
$585$		0			0
$586$	1.83429e15			1.09656
$587$	8.41064e14	−	8.41064e14i	0.498103	−	0.498103i	−0.412744	−	0.910847i	$-0.635430\pi$
$587$	8.41064e14	−	8.41064e14i	0.498103	−	0.498103i	0.910847	+	0.412744i	$0.135430\pi$
$588$	−3.56111e14	+	6.55140e14i	−0.208934	+	0.384378i
$589$		−	2.66861e15i		−	1.55114i
$590$		0			0
$591$	−2.42435e14	−	8.19863e14i	−0.138313	−	0.467746i
$592$	1.76843e15	+	1.76843e15i	0.999581	+	0.999581i
$593$	2.40054e14	+	2.40054e14i	0.134434	+	0.134434i	0.771122	−	0.636688i	$-0.219696\pi$
$593$	2.40054e14	+	2.40054e14i	0.134434	+	0.134434i	−0.636688	+	0.771122i	$0.719696\pi$
$594$	1.66979e14	+	1.43022e14i	0.0926483	+	0.0793556i
$595$		0			0
$596$		−	5.70775e14i		−	0.310893i
$597$	−5.33230e14	−	2.89845e14i	−0.287777	−	0.156425i
$598$	5.99737e14	−	5.99737e14i	0.320704	−	0.320704i
$599$	−7.78763e14			−0.412627			−0.206314	−	0.978486i	$-0.566147\pi$
$599$	−7.78763e14			−0.412627			−0.206314	+	0.978486i	$0.566147\pi$
$600$		0			0
$601$	−8.50292e14			−0.442342			−0.221171	−	0.975235i	$-0.570988\pi$
$601$	−8.50292e14			−0.442342			−0.221171	+	0.975235i	$0.570988\pi$
$602$	−2.18886e14	+	2.18886e14i	−0.112833	+	0.112833i
$603$	−1.73975e14	+	8.14718e14i	−0.0888673	+	0.416162i
$604$		−	3.27067e14i		−	0.165552i
$605$		0			0
$606$	−2.91636e15	+	8.62374e14i	−1.44958	+	0.428643i
$607$	1.93561e15	+	1.93561e15i	0.953409	+	0.953409i	0.998962	−	0.0455530i	$-0.0145050\pi$
$607$	1.93561e15	+	1.93561e15i	0.953409	+	0.953409i	−0.0455530	+	0.998962i	$0.514505\pi$
$608$	9.71801e14	+	9.71801e14i	0.474360	+	0.474360i
$609$	−3.92014e15	+	1.15919e15i	−1.89630	+	0.560738i
$610$		0			0
$611$			1.75297e15i			0.832814i
$612$	−1.11648e14	+	5.22843e14i	−0.0525676	+	0.246172i
$613$	2.12061e14	−	2.12061e14i	0.0989527	−	0.0989527i	−0.655897	−	0.754850i	$-0.727710\pi$
$613$	2.12061e14	−	2.12061e14i	0.0989527	−	0.0989527i	0.754850	+	0.655897i	$0.227710\pi$
$614$	−1.73628e15			−0.802961
$615$		0			0
$616$	−2.48443e14			−0.112858
$617$	−1.80161e15	+	1.80161e15i	−0.811134	+	0.811134i	−0.984804	−	0.173670i	$-0.944437\pi$
$617$	−1.80161e15	+	1.80161e15i	−0.811134	+	0.811134i	0.173670	+	0.984804i	$0.444437\pi$
$618$	−1.16230e14	−	6.31783e13i	−0.0518656	−	0.0281924i
$619$			2.75526e15i			1.21861i	0.792937	+	0.609303i	$0.208551\pi$
$619$			2.75526e15i			1.21861i	−0.792937	+	0.609303i	$0.791449\pi$
$620$		0			0
$621$	1.01455e15	+	8.68989e14i	0.440829	+	0.377581i
$622$	−1.10715e15	−	1.10715e15i	−0.476825	−	0.476825i
$623$	−8.15778e14	−	8.15778e14i	−0.348247	−	0.348247i
$624$	−5.51443e14	−	1.86486e15i	−0.233338	−	0.789099i
$625$		0			0
$626$			2.41338e15i			1.00338i
$627$	1.13946e14	−	2.09628e14i	0.0469601	−	0.0863928i
$628$	1.31100e14	−	1.31100e14i	0.0535581	−	0.0535581i
$629$	1.91156e15			0.774124
$630$		0			0
$631$	−7.08725e13			−0.0282043			−0.0141022	−	0.999901i	$-0.504489\pi$
$631$	−7.08725e13			−0.0282043			−0.0141022	+	0.999901i	$0.504489\pi$
$632$	1.15428e15	−	1.15428e15i	0.455372	−	0.455372i
$633$	6.46457e14	−	1.18929e15i	0.252824	−	0.465123i
$634$			2.77892e15i			1.07742i
$635$		0			0
$636$	−5.95273e13	−	2.01308e14i	−0.0226831	−	0.0767093i
$637$	−1.46593e15	−	1.46593e15i	−0.553791	−	0.553791i
$638$	3.08866e14	+	3.08866e14i	0.115679	+	0.115679i
$639$	1.14941e15	−	7.44901e14i	0.426797	−	0.276595i
$640$		0			0
$641$			4.19967e14i			0.153284i	0.997059	+	0.0766418i	$0.0244198\pi$
$641$			4.19967e14i			0.153284i	−0.997059	+	0.0766418i	$0.975580\pi$
$642$	−3.18466e15	−	1.73107e15i	−1.15245	−	0.626430i
$643$	−1.15949e15	+	1.15949e15i	−0.416013	+	0.416013i	−0.883827	−	0.467814i	$-0.845042\pi$
$643$	−1.15949e15	+	1.15949e15i	−0.416013	+	0.416013i	0.467814	+	0.883827i	$0.345042\pi$
$644$	8.96372e14			0.318872
$645$		0			0
$646$	2.13746e15			0.747512
$647$	3.26531e14	−	3.26531e14i	0.113227	−	0.113227i	−0.648223	−	0.761450i	$-0.724488\pi$
$647$	3.26531e14	−	3.26531e14i	0.113227	−	0.113227i	0.761450	+	0.648223i	$0.224488\pi$
$648$	1.99737e15	−	7.62407e14i	0.686744	−	0.262135i
$649$		−	3.60299e14i		−	0.122834i
$650$		0			0
$651$	−6.92878e15	+	2.04885e15i	−2.32253	+	0.686776i
$652$	8.93312e14	+	8.93312e14i	0.296921	+	0.296921i
$653$	−3.10191e15	−	3.10191e15i	−1.02237	−	1.02237i	−0.999744	−	0.0226233i	$-0.992798\pi$
$653$	−3.10191e15	−	3.10191e15i	−1.02237	−	1.02237i	−0.0226233	−	0.999744i	$-0.507202\pi$
$654$	1.51102e15	−	4.46810e14i	0.493846	−	0.146031i
$655$		0			0
$656$		−	6.84256e15i		−	2.19911i
$657$	4.63157e14	+	9.89027e13i	0.147611	+	0.0315209i
$658$	−4.82609e15	+	4.82609e15i	−1.52529	+	1.52529i
$659$	−3.56536e15			−1.11747			−0.558733	−	0.829348i	$-0.688712\pi$
$659$	−3.56536e15			−1.11747			−0.558733	+	0.829348i	$0.688712\pi$
$660$		0			0
$661$	−1.39665e15			−0.430507			−0.215254	−	0.976558i	$-0.569058\pi$
$661$	−1.39665e15			−0.430507			−0.215254	+	0.976558i	$0.569058\pi$
$662$	−3.47489e15	+	3.47489e15i	−1.06224	+	1.06224i
$663$	−1.30594e15	−	7.09864e14i	−0.395912	−	0.215204i
$664$			2.01138e15i			0.604740i
$665$		0			0
$666$	2.46863e15	+	3.80920e15i	0.730042	+	1.12649i
$667$	1.87664e15	+	1.87664e15i	0.550413	+	0.550413i
$668$	−1.17200e15	−	1.17200e15i	−0.340924	−	0.340924i
$669$	−1.56150e14	−	5.28064e14i	−0.0450502	−	0.152350i
$670$		0			0
$671$			3.71654e14i			0.105479i
$672$	1.77707e15	−	3.26930e15i	0.500236	−	0.920287i
$673$	−1.04662e15	+	1.04662e15i	−0.292216	+	0.292216i	−0.837955	−	0.545739i	$-0.816249\pi$
$673$	−1.04662e15	+	1.04662e15i	−0.292216	+	0.292216i	0.545739	+	0.837955i	$0.316249\pi$
$674$	2.25264e15			0.623825
$675$		0			0
$676$	7.59166e14			0.206838
$677$	−2.97438e15	+	2.97438e15i	−0.803820	+	0.803820i	−0.983690	−	0.179871i	$-0.942432\pi$
$677$	−2.97438e15	+	2.97438e15i	−0.803820	+	0.803820i	0.179871	+	0.983690i	$0.442432\pi$
$678$	2.83184e15	−	5.20976e15i	0.759112	−	1.39654i
$679$		−	4.29427e15i		−	1.14184i
$680$		0			0
$681$	−7.61054e14	−	2.57372e15i	−0.199116	−	0.673368i
$682$	5.45915e14	+	5.45915e14i	0.141681	+	0.141681i
$683$	−8.63475e14	−	8.63475e14i	−0.222298	−	0.222298i	0.587167	−	0.809466i	$-0.300243\pi$
$683$	−8.63475e14	−	8.63475e14i	−0.222298	−	0.222298i	−0.809466	+	0.587167i	$0.800243\pi$
$684$	7.49275e14	+	1.15616e15i	0.191352	+	0.295264i
$685$		0			0
$686$		−	1.19775e15i		−	0.301011i
$687$	−1.69180e15	−	9.19606e14i	−0.421782	−	0.229266i
$688$	3.25824e14	−	3.25824e14i	0.0805836	−	0.0805836i
$689$	5.83642e14			0.143199
$690$		0			0
$691$	6.92420e15			1.67201			0.836007	−	0.548718i	$-0.184884\pi$
$691$	6.92420e15			1.67201			0.836007	+	0.548718i	$0.184884\pi$
$692$	5.24221e14	−	5.24221e14i	0.125583	−	0.125583i
$693$	−6.31761e14	−	1.34906e14i	−0.150148	−	0.0320627i
$694$		−	2.13348e15i		−	0.503051i
$695$		0			0
$696$	4.07318e15	−	1.20445e15i	0.945328	−	0.279535i
$697$	−3.69820e15	−	3.69820e15i	−0.851550	−	0.851550i
$698$	6.69172e15	+	6.69172e15i	1.52874	+	1.52874i
$699$	−1.56731e15	+	4.63458e14i	−0.355248	+	0.105047i
$700$		0			0
$701$			5.35981e15i			1.19591i	0.801528	+	0.597957i	$0.204021\pi$
$701$			5.35981e15i			1.19591i	−0.801528	+	0.597957i	$0.795979\pi$
$702$	−2.71962e14	−	3.51910e15i	−0.0602080	−	0.779071i
$703$	3.48323e15	−	3.48323e15i	0.765117	−	0.765117i
$704$	1.91826e14			0.0418078
$705$		0			0
$706$	−7.11600e14			−0.152690
$707$	6.31863e15	−	6.31863e15i	1.34529	−	1.34529i
$708$	1.82790e15	+	9.93581e14i	0.386161	+	0.209904i
$709$		−	2.97820e15i		−	0.624310i	−0.950031	−	0.312155i	$-0.898949\pi$
$709$		−	2.97820e15i		−	0.624310i	0.950031	−	0.312155i	$-0.101051\pi$
$710$		0			0
$711$	3.56197e15	−	2.30841e15i	0.735203	−	0.476464i
$712$	8.47625e14	+	8.47625e14i	0.173606	+	0.173606i
$713$	3.31693e15	+	3.31693e15i	0.674131	+	0.674131i
$714$	−1.64105e15	−	5.54969e15i	−0.330966	−	1.11925i
$715$		0			0
$716$			1.00135e15i			0.198868i
$717$	3.75667e15	−	6.91117e15i	0.740369	−	1.36206i
$718$	2.91919e15	−	2.91919e15i	0.570923	−	0.570923i
$719$	5.08231e15			0.986398			0.493199	−	0.869916i	$-0.335827\pi$
$719$	5.08231e15			0.986398			0.493199	+	0.869916i	$0.335827\pi$
$720$		0			0
$721$	3.88707e14			0.0742983
$722$	−4.72401e14	+	4.72401e14i	−0.0896099	+	0.0896099i
$723$	−4.30041e15	+	7.91149e15i	−0.809561	+	1.48935i
$724$		−	1.55051e15i		−	0.289675i
$725$		0			0
$726$	−1.78582e15	−	6.03924e15i	−0.328613	−	1.11130i
$727$	5.23725e15	+	5.23725e15i	0.956454	+	0.956454i	0.999091	−	0.0426365i	$-0.0135757\pi$
$727$	5.23725e15	+	5.23725e15i	0.956454	+	0.956454i	−0.0426365	+	0.999091i	$0.513576\pi$
$728$	2.82030e15	+	2.82030e15i	0.511178	+	0.511178i
$729$	5.49305e15	−	8.54126e14i	0.988126	−	0.153646i
$730$		0			0
$731$		−	3.52196e14i		−	0.0624079i
$732$	−1.88550e15	−	1.02489e15i	−0.331601	−	0.180247i
$733$	1.65063e15	−	1.65063e15i	0.288123	−	0.288123i	−0.548215	−	0.836337i	$-0.684692\pi$
$733$	1.65063e15	−	1.65063e15i	0.288123	−	0.288123i	0.836337	+	0.548215i	$0.184692\pi$
$734$	−1.11956e16			−1.93963
$735$		0			0
$736$	−2.41579e15			−0.412317
$737$	−1.84948e14	+	1.84948e14i	−0.0313313	+	0.0313313i
$738$	2.59353e15	−	1.21454e16i	0.436095	−	2.04221i
$739$			1.89093e14i			0.0315596i	0.999875	+	0.0157798i	$0.00502308\pi$
$739$			1.89093e14i			0.0315596i	−0.999875	+	0.0157798i	$0.994977\pi$
$740$		0			0
$741$	−3.67317e15	+	1.08616e15i	−0.604006	+	0.178606i
$742$	1.60682e15	+	1.60682e15i	0.262268	+	0.262268i
$743$	6.46972e15	+	6.46972e15i	1.04821	+	1.04821i	0.998778	+	0.0494294i	$0.0157403\pi$
$743$	6.46972e15	+	6.46972e15i	1.04821	+	1.04821i	0.0494294	+	0.998778i	$0.484260\pi$
$744$	7.19928e15	−	2.12884e15i	1.15781	−	0.342367i
$745$		0			0
$746$			1.29597e16i			2.05368i
$747$	−1.09219e15	+	5.11469e15i	−0.171805	+	0.804555i
$748$	−1.18690e14	+	1.18690e14i	−0.0185334	+	0.0185334i
$749$	1.06505e16			1.65090
$750$		0			0
$751$	4.99169e15			0.762479			0.381239	−	0.924476i	$-0.375497\pi$
$751$	4.99169e15			0.762479			0.381239	+	0.924476i	$0.375497\pi$
$752$	7.18390e15	−	7.18390e15i	1.08934	−	1.08934i
$753$	−1.34455e15	−	7.30852e14i	−0.202398	−	0.110016i
$754$		−	7.01240e15i		−	1.04791i
$755$		0			0
$756$	2.42660e15	−	2.83307e15i	0.357378	−	0.417242i
$757$	−2.11962e15	−	2.11962e15i	−0.309907	−	0.309907i	0.534967	−	0.844873i	$-0.320324\pi$
$757$	−2.11962e15	−	2.11962e15i	−0.309907	−	0.309907i	−0.844873	+	0.534967i	$0.820324\pi$
$758$	−9.59446e15	−	9.59446e15i	−1.39264	−	1.39264i
$759$	1.18927e14	+	4.02184e14i	0.0171376	+	0.0579556i
$760$		0			0
$761$		−	9.13233e15i		−	1.29708i	−0.761182	−	0.648539i	$-0.775380\pi$
$761$		−	9.13233e15i		−	1.29708i	0.761182	−	0.648539i	$-0.224620\pi$
$762$	−3.42826e15	+	6.30699e15i	−0.483416	+	0.889344i
$763$	−3.27379e15	+	3.27379e15i	−0.458317	+	0.458317i
$764$	9.31092e14			0.129413
$765$		0			0
$766$	1.17653e16			1.61192
$767$	−4.09007e15	+	4.09007e15i	−0.556361	+	0.556361i
$768$	−3.47189e15	+	6.38725e15i	−0.468898	+	0.862635i
$769$			8.83397e15i			1.18457i	0.805728	+	0.592285i	$0.201774\pi$
$769$			8.83397e15i			1.18457i	−0.805728	+	0.592285i	$0.798226\pi$
$770$		0			0
$771$	−3.29251e15	−	1.11346e16i	−0.435240	−	1.47189i
$772$	9.35142e14	+	9.35142e14i	0.122739	+	0.122739i
$773$	−5.04041e15	−	5.04041e15i	−0.656869	−	0.656869i	0.297769	−	0.954638i	$-0.403758\pi$
$773$	−5.04041e15	−	5.04041e15i	−0.656869	−	0.656869i	−0.954638	+	0.297769i	$0.903758\pi$
$774$	7.01827e14	−	4.54833e14i	0.0908144	−	0.0588541i
$775$		0			0
$776$			4.46192e15i			0.569222i
$777$	−1.17181e16	−	6.36957e15i	−1.48437	−	0.806853i
$778$	−3.98951e15	+	3.98951e15i	−0.501802	+	0.501802i
$779$	−1.34776e16			−1.68328
$780$		0			0
$781$	4.30026e14			0.0529558
$782$	−2.65674e15	+	2.65674e15i	−0.324871	+	0.324871i
$783$	1.10116e16	−	8.50997e14i	1.33709	−	0.103333i
$784$			1.20151e16i			1.44874i
$785$		0			0
$786$	−1.39614e16	+	4.12841e15i	−1.65999	+	0.490861i
$787$	−2.36821e15	−	2.36821e15i	−0.279614	−	0.279614i	0.553341	−	0.832955i	$-0.313353\pi$
$787$	−2.36821e15	−	2.36821e15i	−0.279614	−	0.279614i	−0.832955	+	0.553341i	$0.813353\pi$
$788$	1.09598e15	+	1.09598e15i	0.128502	+	0.128502i
$789$	−2.87764e15	+	8.50925e14i	−0.335053	+	0.0990758i
$790$		0			0
$791$			1.74230e16i			2.00057i
$792$	6.56425e14	+	1.40173e14i	0.0748508	+	0.0159837i
$793$	4.21897e15	−	4.21897e15i	0.477754	−	0.477754i
$794$	−3.50334e15			−0.393975
$795$		0			0
$796$	1.10028e15			0.122034
$797$	−8.64980e15	+	8.64980e15i	−0.952764	+	0.952764i	−0.998934	−	0.0461696i	$-0.985299\pi$
$797$	−8.64980e15	+	8.64980e15i	−0.952764	+	0.952764i	0.0461696	+	0.998934i	$0.485299\pi$
$798$	−1.31029e16	−	7.12227e15i	−1.43335	−	0.779116i
$799$		−	7.76537e15i		−	0.843635i
$800$		0			0
$801$	1.69514e15	+	2.61567e15i	0.181647	+	0.280288i
$802$	−4.36157e15	−	4.36157e15i	−0.464177	−	0.464177i
$803$	1.05141e14	+	1.05141e14i	0.0111131	+	0.0111131i
$804$	−4.28269e14	−	1.44831e15i	−0.0449582	−	0.152039i
$805$		0			0
$806$		−	1.23943e16i		−	1.28345i
$807$	−1.63854e15	+	3.01443e15i	−0.168520	+	0.310028i
$808$	−6.56530e15	+	6.56530e15i	−0.670645	+	0.670645i
$809$	−3.82178e15			−0.387747			−0.193874	−	0.981027i	$-0.562105\pi$
$809$	−3.82178e15			−0.387747			−0.193874	+	0.981027i	$0.562105\pi$
$810$		0			0
$811$	−1.93944e16			−1.94116			−0.970581	−	0.240776i	$-0.922598\pi$
$811$	−1.93944e16			−1.94116			−0.970581	+	0.240776i	$0.922598\pi$
$812$	5.24040e15	−	5.24040e15i	0.520962	−	0.520962i
$813$	−2.54900e15	+	4.68941e15i	−0.251693	+	0.463042i
$814$			1.42512e15i			0.139771i
$815$		0			0
$816$	2.44280e15	+	8.26103e15i	0.236370	+	0.799352i
$817$	−6.41768e14	−	6.41768e14i	−0.0616817	−	0.0616817i
$818$	−4.94161e15	−	4.94161e15i	−0.471764	−	0.471764i
$819$	5.64023e15	+	8.70311e15i	0.534854	+	0.825302i
$820$		0			0
$821$		−	6.91983e15i		−	0.647453i	−0.946151	−	0.323727i	$-0.895064\pi$
$821$		−	6.91983e15i		−	0.647453i	0.946151	−	0.323727i	$-0.104936\pi$
$822$	1.77443e16	+	9.64517e15i	1.64916	+	0.896427i
$823$	9.24390e15	−	9.24390e15i	0.853407	−	0.853407i	−0.137144	−	0.990551i	$-0.543792\pi$
$823$	9.24390e15	−	9.24390e15i	0.853407	−	0.853407i	0.990551	+	0.137144i	$0.0437923\pi$
$824$	−4.03882e14			−0.0370386
$825$		0			0
$826$	−2.25207e16			−2.03794
$827$	1.10814e14	−	1.10814e14i	0.00996130	−	0.00996130i	−0.702109	−	0.712070i	$-0.747758\pi$
$827$	1.10814e14	−	1.10814e14i	0.00996130	−	0.00996130i	0.712070	+	0.702109i	$0.247758\pi$
$828$	−2.36835e15	−	5.05738e14i	−0.211485	−	0.0451605i
$829$			6.85619e14i			0.0608181i	0.999538	+	0.0304091i	$0.00968100\pi$
$829$			6.85619e14i			0.0608181i	−0.999538	+	0.0304091i	$0.990319\pi$
$830$		0			0
$831$	5.77175e15	−	1.70672e15i	0.505245	−	0.149402i
$832$	−2.17758e15	−	2.17758e15i	−0.189363	−	0.189363i
$833$	6.49382e15	+	6.49382e15i	0.560987	+	0.560987i
$834$	−2.03598e16	+	6.02044e15i	−1.74727	+	0.516672i
$835$		0			0
$836$			4.32550e14i			0.0366355i
$837$	1.94629e16	−	1.50412e15i	1.63763	−	0.126559i
$838$	−9.06108e15	+	9.06108e15i	−0.757422	+	0.757422i
$839$	−9.59629e15			−0.796916			−0.398458	−	0.917187i	$-0.630454\pi$
$839$	−9.59629e15			−0.796916			−0.398458	+	0.917187i	$0.630454\pi$
$840$		0			0
$841$	9.74202e15			0.798493
$842$	−4.32751e15	+	4.32751e15i	−0.352388	+	0.352388i
$843$	4.76132e15	+	2.58809e15i	0.385191	+	0.209376i
$844$			2.45401e15i			0.197239i
$845$		0			0
$846$	1.54742e16	−	1.00283e16i	1.22764	−	0.795595i
$847$	1.30847e16	+	1.30847e16i	1.03135	+	1.03135i
$848$	−2.39184e15	−	2.39184e15i	−0.187307	−	0.187307i
$849$	1.79706e15	+	6.07726e15i	0.139820	+	0.472842i
$850$		0			0
$851$			8.65891e15i			0.665044i
$852$	−1.18586e15	+	2.18164e15i	−0.0904933	+	0.166481i
$853$	−5.31904e15	+	5.31904e15i	−0.403286	+	0.403286i	−0.879389	−	0.476103i	$-0.842049\pi$
$853$	−5.31904e15	+	5.31904e15i	−0.403286	+	0.403286i	0.476103	+	0.879389i	$0.342049\pi$
$854$	2.32304e16			1.75000
$855$		0			0
$856$	−1.10663e16			−0.822993
$857$	−9.41959e15	+	9.41959e15i	−0.696045	+	0.696045i	−0.963555	−	0.267510i	$-0.913799\pi$
$857$	−9.41959e15	+	9.41959e15i	−0.696045	+	0.696045i	0.267510	+	0.963555i	$0.413799\pi$
$858$	5.29222e14	−	9.73613e14i	0.0388560	−	0.0714836i
$859$			1.25705e16i			0.917045i	0.888683	+	0.458523i	$0.151621\pi$
$859$			1.25705e16i			0.917045i	−0.888683	+	0.458523i	$0.848379\pi$
$860$		0			0
$861$	1.03476e16	+	3.49933e16i	0.745284	+	2.52039i
$862$	−8.44539e15	−	8.44539e15i	−0.604407	−	0.604407i
$863$	3.67056e14	+	3.67056e14i	0.0261019	+	0.0261019i	0.720037	−	0.693935i	$-0.244125\pi$
$863$	3.67056e14	+	3.67056e14i	0.0261019	+	0.0261019i	−0.693935	+	0.720037i	$0.744125\pi$
$864$	−6.53985e15	+	7.63534e15i	−0.462107	+	0.539514i
$865$		0			0
$866$		−	1.25295e16i		−	0.874148i
$867$	−6.88828e15	−	3.74423e15i	−0.477536	−	0.259572i
$868$	9.26232e15	−	9.26232e15i	0.638060	−	0.638060i
$869$	1.33263e15			0.0912220
$870$		0			0
$871$	4.19901e15			0.283823
$872$	3.40160e15	−	3.40160e15i	0.228477	−	0.228477i
$873$	−2.42285e15	+	1.13461e16i	−0.161714	+	0.757302i
$874$			9.68214e15i			0.642182i
$875$		0			0
$876$	−8.23349e14	+	2.43466e14i	−0.0539277	+	0.0159465i
$877$	7.08696e15	+	7.08696e15i	0.461278	+	0.461278i	0.899074	−	0.437797i	$-0.144241\pi$
$877$	7.08696e15	+	7.08696e15i	0.461278	+	0.461278i	−0.437797	+	0.899074i	$0.644241\pi$
$878$	4.13450e15	+	4.13450e15i	0.267426	+	0.267426i
$879$	1.39637e16	−	4.12909e15i	0.897556	−	0.265409i
$880$		0			0
$881$		−	2.86234e16i		−	1.81700i	−0.417887	−	0.908499i	$-0.637229\pi$
$881$		−	2.86234e16i		−	1.81700i	0.417887	−	0.908499i	$-0.362771\pi$
$882$	−4.55408e15	+	2.13266e16i	−0.287292	+	1.34538i
$883$	5.81145e15	−	5.81145e15i	0.364335	−	0.364335i	−0.501071	−	0.865406i	$-0.667061\pi$
$883$	5.81145e15	−	5.81145e15i	0.364335	−	0.364335i	0.865406	+	0.501071i	$0.167061\pi$
$884$	2.69471e15			0.167890
$885$		0			0
$886$	−1.59426e16			−0.981008
$887$	1.32618e15	−	1.32618e15i	0.0811005	−	0.0811005i	−0.665393	−	0.746493i	$-0.731736\pi$
$887$	1.32618e15	−	1.32618e15i	0.0811005	−	0.0811005i	0.746493	+	0.665393i	$0.231736\pi$
$888$	1.21756e16	+	6.61823e15i	0.739979	+	0.402227i
$889$		−	2.10925e16i		−	1.27400i
$890$		0			0
$891$	1.59309e15	+	7.12886e14i	0.0950416	+	0.0425297i
$892$	7.05910e14	+	7.05910e14i	0.0418546	+	0.0418546i
$893$	−1.41499e16	−	1.41499e16i	−0.833819	−	0.833819i
$894$	−4.73341e15	−	1.60074e16i	−0.277215	−	0.937483i
$895$		0			0
$896$		−	3.00965e16i		−	1.74109i
$897$	3.21550e15	−	5.91558e15i	0.184880	−	0.340125i
$898$	7.86892e15	−	7.86892e15i	0.449671	−	0.449671i
$899$	3.87831e16			2.20274
$900$		0			0
$901$	−2.58544e15			−0.145060
$902$	2.75710e15	−	2.75710e15i	0.153751	−	0.153751i
$903$	−1.17356e15	+	2.15901e15i	−0.0650464	+	0.119666i
$904$		−	1.81032e16i		−	0.997309i
$905$		0			0
$906$	−2.71235e15	−	9.17258e15i	−0.147618	−	0.499214i
$907$	−7.63881e15	−	7.63881e15i	−0.413224	−	0.413224i	0.469636	−	0.882860i	$-0.344385\pi$
$907$	−7.63881e15	−	7.63881e15i	−0.413224	−	0.413224i	−0.882860	+	0.469636i	$0.844385\pi$
$908$	3.44052e15	+	3.44052e15i	0.184992	+	0.184992i
$909$	−2.02598e16	+	1.31298e16i	−1.08276	+	0.701707i
$910$		0			0
$911$		−	1.10415e16i		−	0.583009i	−0.956569	−	0.291504i	$-0.905844\pi$
$911$		−	1.10415e16i		−	0.583009i	0.956569	−	0.291504i	$-0.0941558\pi$
$912$	1.95044e16	+	1.06019e16i	1.02367	+	0.556432i
$913$	−1.16108e15	+	1.16108e15i	−0.0605720	+	0.0605720i
$914$	−2.55469e15			−0.132475
$915$		0			0
$916$	3.49090e15			0.178860
$917$	3.02489e16	−	3.02489e16i	1.54056	−	1.54056i
$918$	1.20475e15	+	1.55890e16i	0.0609903	+	0.789194i
$919$			1.55832e16i			0.784192i	0.919924	+	0.392096i	$0.128250\pi$
$919$			1.55832e16i			0.784192i	−0.919924	+	0.392096i	$0.871750\pi$
$920$		0			0
$921$	−1.32176e16	+	3.90846e15i	−0.657240	+	0.194347i
$922$	−3.11589e16	−	3.11589e16i	−1.54015	−	1.54015i
$923$	−4.88160e15	−	4.88160e15i	−0.239857	−	0.239857i
$924$	1.12307e15	−	3.32095e14i	0.0548545	−	0.0162206i
$925$		0			0
$926$			4.11939e16i			1.98826i
$927$	−1.02702e15	−	2.19311e14i	−0.0492767	−	0.0105226i
$928$	−1.41233e16	+	1.41233e16i	−0.673629	+	0.673629i
$929$	−3.49192e16			−1.65569			−0.827843	−	0.560961i	$-0.810432\pi$
$929$	−3.49192e16			−1.65569			−0.827843	+	0.560961i	$0.810432\pi$
$930$		0			0
$931$	2.36659e16			1.10892
$932$	2.09517e15	−	2.09517e15i	0.0975959	−	0.0975959i
$933$	−1.09205e16	−	5.93601e15i	−0.505701	−	0.274881i
$934$		−	1.04768e16i		−	0.482304i
$935$		0			0
$936$	−5.86042e15	−	9.04288e15i	−0.266632	−	0.411424i
$937$	7.08661e15	+	7.08661e15i	0.320532	+	0.320532i	0.848971	−	0.528439i	$-0.177223\pi$
$937$	7.08661e15	+	7.08661e15i	0.320532	+	0.320532i	−0.528439	+	0.848971i	$0.677223\pi$
$938$	1.15603e16	+	1.15603e16i	0.519819	+	0.519819i
$939$	5.43264e15	+	1.83720e16i	0.242857	+	0.821289i
$940$		0			0
$941$			9.27144e15i			0.409642i	0.978799	+	0.204821i	$0.0656612\pi$
$941$			9.27144e15i			0.409642i	−0.978799	+	0.204821i	$0.934339\pi$
$942$	2.58949e15	−	4.76390e15i	0.113746	−	0.209258i
$943$	1.67519e16	−	1.67519e16i	0.731560	−	0.731560i
$944$	3.35233e16			1.45546
$945$		0			0
$946$	2.62572e14			0.0112680
$947$	−2.29673e15	+	2.29673e15i	−0.0979906	+	0.0979906i	−0.754403	−	0.656412i	$-0.772073\pi$
$947$	−2.29673e15	+	2.29673e15i	−0.0979906	+	0.0979906i	0.656412	+	0.754403i	$0.272073\pi$
$948$	−3.67492e15	+	6.76078e15i	−0.155884	+	0.286781i
$949$		−	2.38709e15i		−	0.100671i
$950$		0			0
$951$	6.25549e15	+	2.11547e16i	0.260776	+	0.881890i
$952$	−1.24934e16	−	1.24934e16i	−0.517820	−	0.517820i
$953$	1.33125e16	+	1.33125e16i	0.548590	+	0.548590i	0.926033	−	0.377443i	$-0.123196\pi$
$953$	1.33125e16	+	1.33125e16i	0.548590	+	0.548590i	−0.377443	+	0.926033i	$0.623196\pi$
$954$	−3.33888e15	−	5.15203e15i	−0.136800	−	0.211088i
$955$		0			0
$956$			1.42607e16i			0.577592i
$957$	3.04653e15	+	1.65599e15i	0.122685	+	0.0666871i
$958$	−1.71931e16	+	1.71931e16i	−0.688405	+	0.688405i
$959$	−5.93424e16			−2.36245
$960$		0			0
$961$	4.31400e16			1.69786
$962$	1.61778e16	−	1.61778e16i	0.633077	−	0.633077i
$963$	−2.81402e16	−	6.00907e15i	−1.09492	−	0.233810i
$964$		−	1.63247e16i		−	0.631572i
$965$		0			0
$966$	2.51387e16	−	7.43356e15i	0.961543	−	0.284330i
$967$	1.60974e16	+	1.60974e16i	0.612225	+	0.612225i	0.943525	−	0.331300i	$-0.107487\pi$
$967$	1.60974e16	+	1.60974e16i	0.612225	+	0.612225i	−0.331300	+	0.943525i	$0.607487\pi$
$968$	−1.35955e16	−	1.35955e16i	−0.514140	−	0.514140i
$969$	1.62715e16	−	4.81152e15i	0.611854	−	0.180926i
$970$		0			0
$971$		−	1.94286e16i		−	0.722330i	−0.932502	−	0.361165i	$-0.882379\pi$
$971$		−	1.94286e16i		−	0.722330i	0.932502	−	0.361165i	$-0.117621\pi$
$972$	−8.00987e15	+	6.11631e15i	−0.296115	+	0.226113i
$973$	4.41119e16	−	4.41119e16i	1.62157	−	1.62157i
$974$	2.48949e16			0.909987
$975$		0			0
$976$	−3.45798e16			−1.24982
$977$	−1.62065e16	+	1.62065e16i	−0.582464	+	0.582464i	−0.935580	−	0.353116i	$-0.885122\pi$
$977$	−1.62065e16	+	1.62065e16i	−0.582464	+	0.582464i	0.353116	+	0.935580i	$0.385122\pi$
$978$	3.24611e16	+	1.76447e16i	1.16011	+	0.630596i
$979$			9.78592e14i			0.0347774i
$980$		0			0
$981$	1.04969e16	−	6.80276e15i	0.368878	−	0.239059i
$982$	−2.41508e16	−	2.41508e16i	−0.843952	−	0.843952i
$983$	−2.73690e16	−	2.73690e16i	−0.951074	−	0.951074i	0.0477837	−	0.998858i	$-0.484784\pi$
$983$	−2.73690e16	−	2.73690e16i	−0.951074	−	0.951074i	−0.998858	+	0.0477837i	$0.984784\pi$
$984$	−1.07515e16	−	3.63594e16i	−0.371533	−	1.25645i
$985$		0			0
$986$			3.10638e16i			1.06153i
$987$	−2.58752e16	+	4.76027e16i	−0.879303	+	1.61766i
$988$	4.91026e15	−	4.91026e15i	0.165936	−	0.165936i
$989$	1.59536e15			0.0536142
$990$		0			0
$991$	−3.79251e16			−1.26044			−0.630219	−	0.776417i	$-0.717035\pi$
$991$	−3.79251e16			−1.26044			−0.630219	+	0.776417i	$0.717035\pi$
$992$	−2.49626e16	+	2.49626e16i	−0.825042	+	0.825042i
$993$	−1.86307e16	+	3.42750e16i	−0.612361	+	1.12656i
$994$		−	2.68790e16i		−	0.878592i
$995$		0			0
$996$	−2.68861e15	−	9.09231e15i	−0.0869165	−	0.293933i
$997$	−2.46526e16	−	2.46526e16i	−0.792574	−	0.792574i	0.189338	−	0.981912i	$-0.439366\pi$
$997$	−2.46526e16	−	2.46526e16i	−0.792574	−	0.792574i	−0.981912	+	0.189338i	$0.939366\pi$
$998$	−1.25707e16	−	1.25707e16i	−0.401922	−	0.401922i
$999$	2.73674e16	+	2.34408e16i	0.870207	+	0.745354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.12.e.d.32.5		40
3.2	odd	2	inner	75.12.e.d.32.16		40
5.2	odd	4		15.12.e.a.8.5	yes	40
5.3	odd	4	inner	75.12.e.d.68.16		40
5.4	even	2		15.12.e.a.2.16	yes	40
15.2	even	4		15.12.e.a.8.16	yes	40
15.8	even	4	inner	75.12.e.d.68.5		40
15.14	odd	2		15.12.e.a.2.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.12.e.a.2.5	✓	40	15.14	odd	2
15.12.e.a.2.16	yes	40	5.4	even	2
15.12.e.a.8.5	yes	40	5.2	odd	4
15.12.e.a.8.16	yes	40	15.2	even	4
75.12.e.d.32.5		40	1.1	even	1	trivial
75.12.e.d.32.16		40	3.2	odd	2	inner
75.12.e.d.68.5		40	15.8	even	4	inner
75.12.e.d.68.16		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)

\(f(q)\)	\(=\)	\(q+(-37.4902 + 37.4902i) q^{2} +(-201.005 + 369.789i) q^{3} -763.031i q^{4} +(-6327.78 - 21399.2i) q^{6} +(46363.7 + 46363.7i) q^{7} +(-48173.8 - 48173.8i) q^{8} +(-96341.3 - 148659. i) q^{9} +O(q^{10})\)	\(q+(-37.4902 + 37.4902i) q^{2} +(-201.005 + 369.789i) q^{3} -763.031i q^{4} +(-6327.78 - 21399.2i) q^{6} +(46363.7 + 46363.7i) q^{7} +(-48173.8 - 48173.8i) q^{8} +(-96341.3 - 148659. i) q^{9} -55617.1i q^{11} +(282161. + 153373. i) q^{12} +(-631358. + 631358. i) q^{13} -3.47637e6 q^{14} +5.17478e6 q^{16} +(2.79681e6 - 2.79681e6i) q^{17} +(9.18510e6 + 1.96139e6i) q^{18} -1.01926e7i q^{19} +(-2.64641e7 + 7.82549e6i) q^{21} +(2.08510e6 + 2.08510e6i) q^{22} +(1.26689e7 + 1.26689e7i) q^{23} +(2.74973e7 - 8.13100e6i) q^{24} -4.73395e7i q^{26} +(7.43374e7 - 5.74493e6i) q^{27} +(3.53770e7 - 3.53770e7i) q^{28} +1.48130e8 q^{29} +2.61818e8 q^{31} +(-9.53435e7 + 9.53435e7i) q^{32} +(2.05666e7 + 1.11793e7i) q^{33} +2.09706e8i q^{34} +(-1.13431e8 + 7.35114e7i) q^{36} +(3.41740e8 + 3.41740e8i) q^{37} +(3.82124e8 + 3.82124e8i) q^{38} +(-1.06564e8 - 3.60375e8i) q^{39} -1.32229e9i q^{41} +(6.98767e8 - 1.28553e9i) q^{42} +(6.29639e7 - 6.29639e7i) q^{43} -4.24376e7 q^{44} -9.49916e8 q^{46} +(1.38825e9 - 1.38825e9i) q^{47} +(-1.04015e9 + 1.91358e9i) q^{48} +2.32187e9i q^{49} +(4.72059e8 + 1.59640e9i) q^{51} +(4.81746e8 + 4.81746e8i) q^{52} +(-4.62211e8 - 4.62211e8i) q^{53} +(-2.57155e9 + 3.00230e9i) q^{54} -4.46703e9i q^{56} +(3.76912e9 + 2.04876e9i) q^{57} +(-5.55343e9 + 5.55343e9i) q^{58} +6.47821e9 q^{59} -6.68237e9 q^{61} +(-9.81560e9 + 9.81560e9i) q^{62} +(2.42563e9 - 1.13591e10i) q^{63} +3.44904e9i q^{64} +(-1.19016e9 + 3.51933e8i) q^{66} +(-3.32538e9 - 3.32538e9i) q^{67} +(-2.13405e9 - 2.13405e9i) q^{68} +(-7.23131e9 + 2.13831e9i) q^{69} +7.73190e9i q^{71} +(-2.52032e9 + 1.18026e10i) q^{72} +(-1.89044e9 + 1.89044e9i) q^{73} -2.56238e10 q^{74} -7.77729e9 q^{76} +(2.57862e9 - 2.57862e9i) q^{77} +(1.75056e10 + 9.51545e9i) q^{78} +2.39607e10i q^{79} +(-1.28178e10 + 2.86440e10i) q^{81} +(4.95730e10 + 4.95730e10i) q^{82} +(-2.08763e10 - 2.08763e10i) q^{83} +(5.97110e9 + 2.01930e10i) q^{84} +4.72106e9i q^{86} +(-2.97748e10 + 5.47769e10i) q^{87} +(-2.67928e9 + 2.67928e9i) q^{88} -1.75952e10 q^{89} -5.85443e10 q^{91} +(9.66673e9 - 9.66673e9i) q^{92} +(-5.26266e10 + 9.68174e10i) q^{93} +1.04092e11i q^{94} +(-1.60925e10 - 5.44215e10i) q^{96} +(-4.63107e10 - 4.63107e10i) q^{97} +(-8.70472e10 - 8.70472e10i) q^{98} +(-8.26796e9 + 5.35823e9i) 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

Properties

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