LMFDB - Embedded newform 75.10.e.g.32.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,10,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, 10, names="a")

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

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
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:	$38.6276877123$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.14
Character	$\chi$	$=$	75.32
Dual form			75.10.e.g.68.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.26503 - 3.26503i) q^{2} +(-38.9302 - 134.787i) q^{3} +490.679i q^{4} +(-567.190 - 312.974i) q^{6} +(-2739.43 - 2739.43i) q^{7} +(3273.77 + 3273.77i) q^{8} +(-16651.9 + 10494.6i) q^{9} +O(q^{10})$	\(q+(3.26503 - 3.26503i) q^{2} +(-38.9302 - 134.787i) q^{3} +490.679i q^{4} +(-567.190 - 312.974i) q^{6} +(-2739.43 - 2739.43i) q^{7} +(3273.77 + 3273.77i) q^{8} +(-16651.9 + 10494.6i) q^{9} +6978.29i q^{11} +(66137.0 - 19102.3i) q^{12} +(-22060.3 + 22060.3i) q^{13} -17888.6 q^{14} -229850. q^{16} +(369918. - 369918. i) q^{17} +(-20103.8 + 88633.8i) q^{18} +406484. i q^{19} +(-262592. + 475885. i) q^{21} +(22784.3 + 22784.3i) q^{22} +(723815. + 723815. i) q^{23} +(313812. - 568710. i) q^{24} +144055. i q^{26} +(2.06279e6 + 1.83589e6i) q^{27} +(1.34418e6 - 1.34418e6i) q^{28} +3.65106e6 q^{29} +2.01886e6 q^{31} +(-2.42664e6 + 2.42664e6i) q^{32} +(940580. - 271667. i) q^{33} -2.41558e6i q^{34} +(-5.14946e6 - 8.17073e6i) q^{36} +(-9.47109e6 - 9.47109e6i) q^{37} +(1.32718e6 + 1.32718e6i) q^{38} +(3.83224e6 + 2.11462e6i) q^{39} -3.22659e7i q^{41} +(696408. + 2.41115e6i) q^{42} +(2.26407e7 - 2.26407e7i) q^{43} -3.42410e6 q^{44} +4.72655e6 q^{46} +(1.27263e7 - 1.27263e7i) q^{47} +(8.94811e6 + 3.09807e7i) q^{48} -2.53447e7i q^{49} +(-6.42610e7 - 3.54590e7i) q^{51} +(-1.08245e7 - 1.08245e7i) q^{52} +(6.38680e7 + 6.38680e7i) q^{53} +(1.27293e7 - 740810. i) q^{54} -1.79365e7i q^{56} +(5.47887e7 - 1.58245e7i) q^{57} +(1.19208e7 - 1.19208e7i) q^{58} +1.73925e8 q^{59} -8.75702e7 q^{61} +(6.59164e6 - 6.59164e6i) q^{62} +(7.43657e7 + 1.68675e7i) q^{63} -1.01837e8i q^{64} +(2.18402e6 - 3.95802e6i) q^{66} +(3.71805e7 + 3.71805e7i) q^{67} +(1.81511e8 + 1.81511e8i) q^{68} +(6.93823e7 - 1.25739e8i) q^{69} -2.72704e8i q^{71} +(-8.88712e7 - 2.01577e7i) q^{72} +(1.26813e8 - 1.26813e8i) q^{73} -6.18467e7 q^{74} -1.99453e8 q^{76} +(1.91165e7 - 1.91165e7i) q^{77} +(1.94167e7 - 5.60809e6i) q^{78} +3.95223e8i q^{79} +(1.67149e8 - 3.49508e8i) q^{81} +(-1.05349e8 - 1.05349e8i) q^{82} +(-2.69488e8 - 2.69488e8i) q^{83} +(-2.33507e8 - 1.28848e8i) q^{84} -1.47845e8i q^{86} +(-1.42137e8 - 4.92114e8i) q^{87} +(-2.28453e7 + 2.28453e7i) q^{88} +1.56645e8 q^{89} +1.20865e8 q^{91} +(-3.55161e8 + 3.55161e8i) q^{92} +(-7.85949e7 - 2.72116e8i) q^{93} -8.31036e7i q^{94} +(4.21548e8 + 2.32609e8i) q^{96} +(8.99507e8 + 8.99507e8i) q^{97} +(-8.27509e7 - 8.27509e7i) q^{98} +(-7.32340e7 - 1.16202e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 10788 q^{6}+O(q^{10}) $ 48 * q + 10788 * q^6	$ 48 q + 10788 q^{6} - 3683496 q^{16} + 2202288 q^{21} - 50381304 q^{31} + 225716076 q^{36} - 336695184 q^{46} + 673842108 q^{51} + 69620856 q^{61} - 445930020 q^{66} + 4632842472 q^{76} - 4102516332 q^{81} + 11717060616 q^{91} - 14562582156 q^{96}+O(q^{100}) $ 48 * q + 10788 * q^6 - 3683496 * q^16 + 2202288 * q^21 - 50381304 * q^31 + 225716076 * q^36 - 336695184 * q^46 + 673842108 * q^51 + 69620856 * q^61 - 445930020 * q^66 + 4632842472 * q^76 - 4102516332 * q^81 + 11717060616 * q^91 - 14562582156 * q^96

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 $

$2$	3.26503	−	3.26503i	0.144295	−	0.144295i	−0.631269	−	0.775564i	$-0.717466\pi$
$2$	3.26503	−	3.26503i	0.144295	−	0.144295i	0.775564	+	0.631269i	$0.217466\pi$
$3$	−38.9302	−	134.787i	−0.277486	−	0.960730i
$3$	−38.9302	−	134.787i	−0.277486	−	0.960730i
$4$			490.679i			0.958358i
$5$		0			0
$5$		0			0
$6$	−567.190	−	312.974i	−0.178668	−	0.0985887i
$7$	−2739.43	−	2739.43i	−0.431240	−	0.431240i	0.457810	−	0.889050i	$-0.348634\pi$
$7$	−2739.43	−	2739.43i	−0.431240	−	0.431240i	−0.889050	+	0.457810i	$0.848634\pi$
$8$	3273.77	+	3273.77i	0.282581	+	0.282581i
$9$	−16651.9	+	10494.6i	−0.846003	+	0.533179i
$10$		0			0
$11$			6978.29i			0.143708i	0.997415	+	0.0718542i	$0.0228916\pi$
$11$			6978.29i			0.143708i	−0.997415	+	0.0718542i	$0.977108\pi$
$12$	66137.0	−	19102.3i	0.920723	−	0.265931i
$13$	−22060.3	+	22060.3i	−0.214223	+	0.214223i	−0.806059	−	0.591836i	$-0.798403\pi$
$13$	−22060.3	+	22060.3i	−0.214223	+	0.214223i	0.591836	+	0.806059i	$0.298403\pi$
$14$	−17888.6			−0.124452
$15$		0			0
$16$	−229850.			−0.876808
$17$	369918.	−	369918.i	1.07420	−	1.07420i	0.0771839	−	0.997017i	$-0.475407\pi$
$17$	369918.	−	369918.i	1.07420	−	1.07420i	0.997017	−	0.0771839i	$-0.0245928\pi$
$18$	−20103.8	+	88633.8i	−0.0451390	+	0.199009i
$19$			406484.i			0.715571i	0.933804	+	0.357786i	$0.116468\pi$
$19$			406484.i			0.715571i	−0.933804	+	0.357786i	$0.883532\pi$
$20$		0			0
$21$	−262592.	+	475885.i	−0.294642	+	0.533968i
$22$	22784.3	+	22784.3i	0.0207364	+	0.0207364i
$23$	723815.	+	723815.i	0.539328	+	0.539328i	0.923331	−	0.384004i	$-0.125455\pi$
$23$	723815.	+	723815.i	0.539328	+	0.539328i	−0.384004	+	0.923331i	$0.625455\pi$
$24$	313812.	−	568710.i	0.193072	−	0.349897i
$25$		0			0
$26$			144055.i			0.0618226i
$27$	2.06279e6	+	1.83589e6i	0.746995	+	0.664830i
$28$	1.34418e6	−	1.34418e6i	0.413282	−	0.413282i
$29$	3.65106e6			0.958579			0.479290	−	0.877657i	$-0.340894\pi$
$29$	3.65106e6			0.958579			0.479290	+	0.877657i	$0.340894\pi$
$30$		0			0
$31$	2.01886e6			0.392626			0.196313	−	0.980541i	$-0.437103\pi$
$31$	2.01886e6			0.392626			0.196313	+	0.980541i	$0.437103\pi$
$32$	−2.42664e6	+	2.42664e6i	−0.409100	+	0.409100i
$33$	940580.	−	271667.i	0.138065	−	0.0398771i
$34$		−	2.41558e6i		−	0.310004i
$35$		0			0
$36$	−5.14946e6	−	8.17073e6i	−0.510976	−	0.810773i
$37$	−9.47109e6	−	9.47109e6i	−0.830792	−	0.830792i	0.156833	−	0.987625i	$-0.449872\pi$
$37$	−9.47109e6	−	9.47109e6i	−0.830792	−	0.830792i	−0.987625	+	0.156833i	$0.949872\pi$
$38$	1.32718e6	+	1.32718e6i	0.103253	+	0.103253i
$39$	3.83224e6	+	2.11462e6i	0.265254	+	0.146366i
$40$		0			0
$41$		−	3.22659e7i		−	1.78327i	−0.452756	−	0.891634i	$-0.649559\pi$
$41$		−	3.22659e7i		−	1.78327i	0.452756	−	0.891634i	$-0.350441\pi$
$42$	696408.	+	2.41115e6i	0.0345336	+	0.119564i
$43$	2.26407e7	−	2.26407e7i	1.00991	−	1.00991i	0.00995875	−	0.999950i	$-0.496830\pi$
$43$	2.26407e7	−	2.26407e7i	1.00991	−	1.00991i	0.999950	−	0.00995875i	$-0.00317002\pi$
$44$	−3.42410e6			−0.137724
$45$		0			0
$46$	4.72655e6			0.155645
$47$	1.27263e7	−	1.27263e7i	0.380419	−	0.380419i	−0.490834	−	0.871253i	$-0.663308\pi$
$47$	1.27263e7	−	1.27263e7i	0.380419	−	0.380419i	0.871253	+	0.490834i	$0.163308\pi$
$48$	8.94811e6	+	3.09807e7i	0.243302	+	0.842375i
$49$		−	2.53447e7i		−	0.628064i
$50$		0			0
$51$	−6.42610e7	−	3.54590e7i	−1.33009	−	0.733941i
$52$	−1.08245e7	−	1.08245e7i	−0.205302	−	0.205302i
$53$	6.38680e7	+	6.38680e7i	1.11184	+	1.11184i	0.992902	+	0.118938i	$0.0379490\pi$
$53$	6.38680e7	+	6.38680e7i	1.11184	+	1.11184i	0.118938	+	0.992902i	$0.462051\pi$
$54$	1.27293e7	−	740810.i	0.203719	−	0.0118559i
$55$		0			0
$56$		−	1.79365e7i		−	0.243721i
$57$	5.47887e7	−	1.58245e7i	0.687470	−	0.198561i
$58$	1.19208e7	−	1.19208e7i	0.138318	−	0.138318i
$59$	1.73925e8			1.86865			0.934326	−	0.356418i	$-0.116002\pi$
$59$	1.73925e8			1.86865			0.934326	+	0.356418i	$0.116002\pi$
$60$		0			0
$61$	−8.75702e7			−0.809790			−0.404895	−	0.914363i	$-0.632692\pi$
$61$	−8.75702e7			−0.809790			−0.404895	+	0.914363i	$0.632692\pi$
$62$	6.59164e6	−	6.59164e6i	0.0566541	−	0.0566541i
$63$	7.43657e7	+	1.68675e7i	0.594758	+	0.134902i
$64$		−	1.01837e8i		−	0.758745i
$65$		0			0
$66$	2.18402e6	−	3.95802e6i	0.0141680	−	0.0256761i
$67$	3.71805e7	+	3.71805e7i	0.225413	+	0.225413i	0.810773	−	0.585360i	$-0.199047\pi$
$67$	3.71805e7	+	3.71805e7i	0.225413	+	0.225413i	−0.585360	+	0.810773i	$0.699047\pi$
$68$	1.81511e8	+	1.81511e8i	1.02947	+	1.02947i
$69$	6.93823e7	−	1.25739e8i	0.368492	−	0.667804i
$70$		0			0
$71$		−	2.72704e8i		−	1.27359i	−0.771035	−	0.636793i	$-0.780261\pi$
$71$		−	2.72704e8i		−	1.27359i	0.771035	−	0.636793i	$-0.219739\pi$
$72$	−8.88712e7	−	2.01577e7i	−0.389731	−	0.0883983i
$73$	1.26813e8	−	1.26813e8i	0.522649	−	0.522649i	−0.395721	−	0.918371i	$-0.629505\pi$
$73$	1.26813e8	−	1.26813e8i	0.522649	−	0.522649i	0.918371	+	0.395721i	$0.129505\pi$
$74$	−6.18467e7			−0.239758
$75$		0			0
$76$	−1.99453e8			−0.685773
$77$	1.91165e7	−	1.91165e7i	0.0619728	−	0.0619728i
$78$	1.94167e7	−	5.60809e6i	0.0593948	−	0.0171549i
$79$			3.95223e8i			1.14162i	0.821083	+	0.570809i	$0.193370\pi$
$79$			3.95223e8i			1.14162i	−0.821083	+	0.570809i	$0.806630\pi$
$80$		0			0
$81$	1.67149e8	−	3.49508e8i	0.431441	−	0.902141i
$82$	−1.05349e8	−	1.05349e8i	−0.257317	−	0.257317i
$83$	−2.69488e8	−	2.69488e8i	−0.623286	−	0.623286i	0.323084	−	0.946370i	$-0.395280\pi$
$83$	−2.69488e8	−	2.69488e8i	−0.623286	−	0.623286i	−0.946370	+	0.323084i	$0.895280\pi$
$84$	−2.33507e8	−	1.28848e8i	−0.511733	−	0.282372i
$85$		0			0
$86$		−	1.47845e8i		−	0.291450i
$87$	−1.42137e8	−	4.92114e8i	−0.265993	−	0.920936i
$88$	−2.28453e7	+	2.28453e7i	−0.0406093	+	0.0406093i
$89$	1.56645e8			0.264643			0.132321	−	0.991207i	$-0.457757\pi$
$89$	1.56645e8			0.264643			0.132321	+	0.991207i	$0.457757\pi$
$90$		0			0
$91$	1.20865e8			0.184763
$92$	−3.55161e8	+	3.55161e8i	−0.516869	+	0.516869i
$93$	−7.85949e7	−	2.72116e8i	−0.108948	−	0.377208i
$94$		−	8.31036e7i		−	0.109785i
$95$		0			0
$96$	4.21548e8	+	2.32609e8i	0.506555	+	0.279515i
$97$	8.99507e8	+	8.99507e8i	1.03165	+	1.03165i	0.999483	+	0.0321658i	$0.0102405\pi$
$97$	8.99507e8	+	8.99507e8i	1.03165	+	1.03165i	0.0321658	+	0.999483i	$0.489760\pi$
$98$	−8.27509e7	−	8.27509e7i	−0.0906266	−	0.0906266i
$99$	−7.32340e7	−	1.16202e8i	−0.0766222	−	0.121578i
$100$		0			0
$101$			1.80640e9i			1.72730i	0.504092	+	0.863650i	$0.331827\pi$
$101$			1.80640e9i			1.72730i	−0.504092	+	0.863650i	$0.668173\pi$
$102$	−3.25588e8	+	9.40393e7i	−0.297830	+	0.0860218i
$103$	−2.06609e8	+	2.06609e8i	−0.180877	+	0.180877i	−0.791738	−	0.610861i	$-0.790823\pi$
$103$	−2.06609e8	+	2.06609e8i	−0.180877	+	0.180877i	0.610861	+	0.791738i	$0.290823\pi$
$104$	−1.44441e8			−0.121071
$105$		0			0
$106$	4.17062e8			0.320866
$107$	2.98620e8	−	2.98620e8i	0.220238	−	0.220238i	−0.588361	−	0.808599i	$-0.700226\pi$
$107$	2.98620e8	−	2.98620e8i	0.220238	−	0.220238i	0.808599	+	0.588361i	$0.200226\pi$
$108$	−9.00835e8	+	1.01217e9i	−0.637145	+	0.715888i
$109$			1.33793e9i			0.907851i	0.891040	+	0.453926i	$0.149977\pi$
$109$			1.33793e9i			0.907851i	−0.891040	+	0.453926i	$0.850023\pi$
$110$		0			0
$111$	−9.07865e8	+	1.64529e9i	−0.567633	+	1.02870i
$112$	6.29658e8	+	6.29658e8i	0.378114	+	0.378114i
$113$	−7.24249e8	−	7.24249e8i	−0.417864	−	0.417864i	0.466603	−	0.884467i	$-0.345478\pi$
$113$	−7.24249e8	−	7.24249e8i	−0.417864	−	0.417864i	−0.884467	+	0.466603i	$0.845478\pi$
$114$	1.27219e8	−	2.30554e8i	0.0705472	−	0.127850i
$115$		0			0
$116$			1.79150e9i			0.918662i
$117$	1.35832e8	−	5.98858e8i	0.0670141	−	0.295452i
$118$	5.67870e8	−	5.67870e8i	0.269637	−	0.269637i
$119$	−2.02673e9			−0.926477
$120$		0			0
$121$	2.30925e9			0.979348
$122$	−2.85919e8	+	2.85919e8i	−0.116849	+	0.116849i
$123$	−4.34901e9	+	1.25612e9i	−1.71324	+	0.494832i
$124$			9.90615e8i			0.376277i
$125$		0			0
$126$	2.97879e8	−	1.87733e8i	0.105286	−	0.0663549i
$127$	−1.35392e9	−	1.35392e9i	−0.461823	−	0.461823i	0.437430	−	0.899253i	$-0.355889\pi$
$127$	−1.35392e9	−	1.35392e9i	−0.461823	−	0.461823i	−0.899253	+	0.437430i	$0.855889\pi$
$128$	−1.57494e9	−	1.57494e9i	−0.518584	−	0.518584i
$129$	−3.93308e9	−	2.17026e9i	−1.25049	−	0.690014i
$130$		0			0
$131$		−	8.69854e8i		−	0.258063i	−0.991641	−	0.129031i	$-0.958813\pi$
$131$		−	8.69854e8i		−	0.258063i	0.991641	−	0.129031i	$-0.0411868\pi$
$132$	1.33301e8	+	4.61523e8i	0.0382165	+	0.132316i
$133$	1.11354e9	−	1.11354e9i	0.308583	−	0.308583i
$134$	2.42791e8			0.0650520
$135$		0			0
$136$	2.42206e9			0.607098
$137$	−1.07632e9	+	1.07632e9i	−0.261036	+	0.261036i	−0.825475	−	0.564439i	$-0.809093\pi$
$137$	−1.07632e9	+	1.07632e9i	−0.261036	+	0.261036i	0.564439	+	0.825475i	$0.309093\pi$
$138$	−1.84006e8	−	6.37076e8i	−0.0431892	−	0.149532i
$139$			5.29894e9i			1.20399i	0.798500	+	0.601995i	$0.205627\pi$
$139$			5.29894e9i			1.20399i	−0.798500	+	0.601995i	$0.794373\pi$
$140$		0			0
$141$	−2.21078e9	−	1.21990e9i	−0.471041	−	0.259919i
$142$	−8.90384e8	−	8.90384e8i	−0.183772	−	0.183772i
$143$	−1.53943e8	−	1.53943e8i	−0.0307856	−	0.0307856i
$144$	3.82743e9	−	2.41217e9i	0.741782	−	0.467495i
$145$		0			0
$146$		−	8.28094e8i		−	0.150831i
$147$	−3.41612e9	+	9.86674e8i	−0.603400	+	0.174279i
$148$	4.64727e9	−	4.64727e9i	0.796196	−	0.796196i
$149$	−3.60253e9			−0.598782			−0.299391	−	0.954130i	$-0.596784\pi$
$149$	−3.60253e9			−0.598782			−0.299391	+	0.954130i	$0.596784\pi$
$150$		0			0
$151$	7.07390e8			0.110729			0.0553646	−	0.998466i	$-0.482368\pi$
$151$	7.07390e8			0.110729			0.0553646	+	0.998466i	$0.482368\pi$
$152$	−1.33074e9	+	1.33074e9i	−0.202207	+	0.202207i
$153$	−2.27770e9	+	1.00420e10i	−0.336036	+	1.48152i
$154$		−	1.24832e8i		−	0.0178847i
$155$		0			0
$156$	−1.03760e9	+	1.88040e9i	−0.140271	+	0.254208i
$157$	4.94554e9	+	4.94554e9i	0.649629	+	0.649629i	0.952903	−	0.303274i	$-0.0980798\pi$
$157$	4.94554e9	+	4.94554e9i	0.649629	+	0.649629i	−0.303274	+	0.952903i	$0.598080\pi$
$158$	1.29041e9	+	1.29041e9i	0.164730	+	0.164730i
$159$	6.12216e9	−	1.10950e10i	0.759657	−	1.37670i
$160$		0			0
$161$		−	3.96568e9i		−	0.465159i
$162$	−5.95406e8	−	1.68690e9i	−0.0679196	−	0.192429i
$163$	9.64519e9	−	9.64519e9i	1.07020	−	1.07020i	0.0728623	−	0.997342i	$-0.476787\pi$
$163$	9.64519e9	−	9.64519e9i	1.07020	−	1.07020i	0.997342	−	0.0728623i	$-0.0232134\pi$
$164$	1.58322e10			1.70901
$165$		0			0
$166$	−1.75977e9			−0.179874
$167$	8.66151e9	−	8.66151e9i	0.861727	−	0.861727i	−0.129812	−	0.991539i	$-0.541437\pi$
$167$	8.66151e9	−	8.66151e9i	0.861727	−	0.861727i	0.991539	+	0.129812i	$0.0414373\pi$
$168$	−2.41761e9	+	6.98274e8i	−0.234150	+	0.0676292i
$169$			9.63119e9i			0.908217i
$170$		0			0
$171$	−4.26587e9	−	6.76873e9i	−0.381527	−	0.605375i
$172$	1.11093e10	+	1.11093e10i	0.967854	+	0.967854i
$173$	1.16537e10	+	1.16537e10i	0.989134	+	0.989134i	0.999942	−	0.0108074i	$-0.00344017\pi$
$173$	1.16537e10	+	1.16537e10i	0.989134	+	0.989134i	−0.0108074	+	0.999942i	$0.503440\pi$
$174$	−2.07084e9	−	1.14269e9i	−0.171268	−	0.0945051i
$175$		0			0
$176$		−	1.60396e9i		−	0.126005i
$177$	−6.77095e9	−	2.34428e10i	−0.518525	−	1.79527i
$178$	5.11448e8	−	5.11448e8i	0.0381867	−	0.0381867i
$179$	−8.77063e9			−0.638546			−0.319273	−	0.947663i	$-0.603439\pi$
$179$	−8.77063e9			−0.638546			−0.319273	+	0.947663i	$0.603439\pi$
$180$		0			0
$181$	−2.45454e10			−1.69987			−0.849936	−	0.526885i	$-0.823360\pi$
$181$	−2.45454e10			−1.69987			−0.849936	+	0.526885i	$0.823360\pi$
$182$	3.94628e8	−	3.94628e8i	0.0266604	−	0.0266604i
$183$	3.40913e9	+	1.18033e10i	0.224706	+	0.777989i
$184$			4.73921e9i			0.304808i
$185$		0			0
$186$	−1.14508e9	−	6.31851e8i	−0.0701500	−	0.0387085i
$187$	2.58140e9	+	2.58140e9i	0.154372	+	0.154372i
$188$	6.24454e9	+	6.24454e9i	0.364578	+	0.364578i
$189$	−6.21556e8	−	1.06802e10i	−0.0354325	−	0.608835i
$190$		0			0
$191$		−	3.11754e10i		−	1.69497i	−0.530822	−	0.847483i	$-0.678117\pi$
$191$		−	3.11754e10i		−	1.69497i	0.530822	−	0.847483i	$-0.321883\pi$
$192$	−1.37263e10	+	3.96454e9i	−0.728949	+	0.210541i
$193$	1.66423e10	−	1.66423e10i	0.863389	−	0.863389i	−0.128341	−	0.991730i	$-0.540965\pi$
$193$	1.66423e10	−	1.66423e10i	0.863389	−	0.863389i	0.991730	+	0.128341i	$0.0409652\pi$
$194$	5.87383e9			0.297724
$195$		0			0
$196$	1.24361e10			0.601910
$197$	9.24438e9	−	9.24438e9i	0.437301	−	0.437301i	−0.453802	−	0.891103i	$-0.649933\pi$
$197$	9.24438e9	−	9.24438e9i	0.437301	−	0.437301i	0.891103	+	0.453802i	$0.149933\pi$
$198$	−6.18512e8	−	1.40290e8i	−0.0285993	−	0.00648685i
$199$			1.17707e10i			0.532064i	0.963964	+	0.266032i	$0.0857127\pi$
$199$			1.17707e10i			0.532064i	−0.963964	+	0.266032i	$0.914287\pi$
$200$		0			0
$201$	3.56399e9	−	6.45889e9i	0.154012	−	0.279110i
$202$	5.89794e9	+	5.89794e9i	0.249241	+	0.249241i
$203$	−1.00018e10	−	1.00018e10i	−0.413378	−	0.413378i
$204$	1.73990e10	−	3.15315e10i	0.703378	−	1.27470i
$205$		0			0
$206$			1.34917e9i			0.0521992i
$207$	−1.96490e10	−	4.45676e9i	−0.743830	−	0.168715i
$208$	5.07055e9	−	5.07055e9i	0.187832	−	0.187832i
$209$	−2.83657e9			−0.102834
$210$		0			0
$211$	1.85382e10			0.643868			0.321934	−	0.946762i	$-0.395667\pi$
$211$	1.85382e10			0.643868			0.321934	+	0.946762i	$0.395667\pi$
$212$	−3.13387e10	+	3.13387e10i	−1.06554	+	1.06554i
$213$	−3.67568e10	+	1.06164e10i	−1.22357	+	0.353403i
$214$		−	1.95001e9i		−	0.0635585i
$215$		0			0
$216$	7.42794e8	+	1.27634e10i	0.0232181	+	0.398955i
$217$	−5.53054e9	−	5.53054e9i	−0.169316	−	0.169316i
$218$	4.36838e9	+	4.36838e9i	0.130998	+	0.130998i
$219$	−2.20295e10	−	1.21558e10i	−0.647153	−	0.357097i
$220$		0			0
$221$			1.63210e10i			0.460237i
$222$	2.40771e9	+	8.33611e9i	0.0665297	+	0.230343i
$223$	9.83728e9	−	9.83728e9i	0.266381	−	0.266381i	−0.561259	−	0.827640i	$-0.689683\pi$
$223$	9.83728e9	−	9.83728e9i	0.266381	−	0.266381i	0.827640	+	0.561259i	$0.189683\pi$
$224$	1.32952e10			0.352841
$225$		0			0
$226$	−4.72938e9			−0.120591
$227$	2.69088e9	−	2.69088e9i	0.0672632	−	0.0672632i	−0.672675	−	0.739938i	$-0.734855\pi$
$227$	2.69088e9	−	2.69088e9i	0.0672632	−	0.0672632i	0.739938	+	0.672675i	$0.234855\pi$
$228$	7.76477e9	+	2.68837e10i	0.190293	+	0.658843i
$229$			6.85964e10i			1.64832i	0.566357	+	0.824160i	$0.308352\pi$
$229$			6.85964e10i			1.64832i	−0.566357	+	0.824160i	$0.691648\pi$
$230$		0			0
$231$	−3.32087e9	−	1.83244e9i	−0.0767357	−	0.0423425i
$232$	1.19527e10	+	1.19527e10i	0.270877	+	0.270877i
$233$	−3.42053e10	−	3.42053e10i	−0.760312	−	0.760312i	0.216066	−	0.976379i	$-0.430677\pi$
$233$	−3.42053e10	−	3.42053e10i	−0.760312	−	0.760312i	−0.976379	+	0.216066i	$0.930677\pi$
$234$	−1.51179e9	−	2.39878e9i	−0.0329625	−	0.0523021i
$235$		0			0
$236$			8.53415e10i			1.79084i
$237$	5.32708e10	−	1.53861e10i	1.09679	−	0.316783i
$238$	−6.61732e9	+	6.61732e9i	−0.133686	+	0.133686i
$239$	−5.82035e10			−1.15388			−0.576938	−	0.816788i	$-0.695752\pi$
$239$	−5.82035e10			−1.15388			−0.576938	+	0.816788i	$0.695752\pi$
$240$		0			0
$241$	3.65269e10			0.697487			0.348744	−	0.937218i	$-0.386608\pi$
$241$	3.65269e10			0.697487			0.348744	+	0.937218i	$0.386608\pi$
$242$	7.53976e9	−	7.53976e9i	0.141315	−	0.141315i
$243$	−5.36162e10	−	8.92305e9i	−0.986433	−	0.164167i
$244$		−	4.29689e10i		−	0.776068i
$245$		0			0
$246$	−1.00984e10	+	1.83009e10i	−0.175810	+	0.318614i
$247$	−8.96716e9	−	8.96716e9i	−0.153292	−	0.153292i
$248$	6.60930e9	+	6.60930e9i	0.110949	+	0.110949i
$249$	−2.58321e10	+	4.68146e10i	−0.425856	+	0.771763i
$250$		0			0
$251$			1.79221e10i			0.285008i	0.989794	+	0.142504i	$0.0455154\pi$
$251$			1.79221e10i			0.285008i	−0.989794	+	0.142504i	$0.954485\pi$
$252$	−8.27655e9	+	3.64897e10i	−0.129285	+	0.569991i
$253$	−5.05099e9	+	5.05099e9i	−0.0775059	+	0.0775059i
$254$	−8.84115e9			−0.133278
$255$		0			0
$256$	4.18561e10			0.609087
$257$	6.36170e10	−	6.36170e10i	0.909649	−	0.909649i	−0.0865943	−	0.996244i	$-0.527598\pi$
$257$	6.36170e10	−	6.36170e10i	0.909649	−	0.909649i	0.996244	+	0.0865943i	$0.0275984\pi$
$258$	−1.99275e10	+	5.75564e9i	−0.280005	+	0.0808733i
$259$			5.18908e10i			0.716541i
$260$		0			0
$261$	−6.07970e10	+	3.83162e10i	−0.810961	+	0.511094i
$262$	−2.84009e9	−	2.84009e9i	−0.0372372	−	0.0372372i
$263$	−6.53223e10	−	6.53223e10i	−0.841900	−	0.841900i	0.147206	−	0.989106i	$-0.452972\pi$
$263$	−6.53223e10	−	6.53223e10i	−0.841900	−	0.841900i	−0.989106	+	0.147206i	$0.952972\pi$
$264$	3.96862e9	+	2.18987e9i	0.0502831	+	0.0277460i
$265$		0			0
$266$		−	7.27144e9i		−	0.0890540i
$267$	−6.09821e9	−	2.11136e10i	−0.0734348	−	0.254250i
$268$	−1.82437e10	+	1.82437e10i	−0.216026	+	0.216026i
$269$	−2.68352e10			−0.312478			−0.156239	−	0.987719i	$-0.549937\pi$
$269$	−2.68352e10			−0.312478			−0.156239	+	0.987719i	$0.549937\pi$
$270$		0			0
$271$	3.33398e10			0.375493			0.187746	−	0.982218i	$-0.439882\pi$
$271$	3.33398e10			0.375493			0.187746	+	0.982218i	$0.439882\pi$
$272$	−8.50256e10	+	8.50256e10i	−0.941867	+	0.941867i
$273$	−4.70531e9	−	1.62910e10i	−0.0512692	−	0.177507i
$274$			7.02845e9i			0.0753324i
$275$		0			0
$276$	6.16975e10	+	3.40445e10i	0.639995	+	0.353147i
$277$	−3.50925e9	−	3.50925e9i	−0.0358142	−	0.0358142i	0.688973	−	0.724787i	$-0.258062\pi$
$277$	−3.50925e9	−	3.50925e9i	−0.0358142	−	0.0358142i	−0.724787	+	0.688973i	$0.758062\pi$
$278$	1.73012e10	+	1.73012e10i	0.173730	+	0.173730i
$279$	−3.36179e10	+	2.11871e10i	−0.332163	+	0.209340i
$280$		0			0
$281$			3.04362e10i			0.291214i	0.989342	+	0.145607i	$0.0465135\pi$
$281$			3.04362e10i			0.291214i	−0.989342	+	0.145607i	$0.953486\pi$
$282$	−1.12012e10	+	3.23524e9i	−0.105474	+	0.0304639i
$283$	1.07190e10	−	1.07190e10i	0.0993382	−	0.0993382i	−0.655691	−	0.755029i	$-0.727623\pi$
$283$	1.07190e10	−	1.07190e10i	0.0993382	−	0.0993382i	0.755029	+	0.655691i	$0.227623\pi$
$284$	1.33810e11			1.22055
$285$		0			0
$286$	−1.00526e9			−0.00888443
$287$	−8.83902e10	+	8.83902e10i	−0.769017	+	0.769017i
$288$	1.49416e10	−	6.58745e10i	0.127977	−	0.564224i
$289$		−	1.55091e11i		−	1.30781i
$290$		0			0
$291$	8.62235e10	−	1.56260e11i	0.704867	−	1.27740i
$292$	6.22244e10	+	6.22244e10i	0.500885	+	0.500885i
$293$	5.03438e10	+	5.03438e10i	0.399063	+	0.399063i	0.877903	−	0.478839i	$-0.158942\pi$
$293$	5.03438e10	+	5.03438e10i	0.399063	+	0.399063i	−0.478839	+	0.877903i	$0.658942\pi$
$294$	−7.93221e9	+	1.43752e10i	−0.0619200	+	0.112215i
$295$		0			0
$296$		−	6.20124e10i		−	0.469533i
$297$	−1.28114e10	+	1.43947e10i	−0.0955416	+	0.107349i
$298$	−1.17623e10	+	1.17623e10i	−0.0864013	+	0.0864013i
$299$	−3.19351e10			−0.231073
$300$		0			0
$301$	−1.24045e11			−0.871026
$302$	2.30964e9	−	2.30964e9i	0.0159777	−	0.0159777i
$303$	2.43479e11	−	7.03236e10i	1.65947	−	0.479302i
$304$		−	9.34304e10i		−	0.627418i
$305$		0			0
$306$	2.53505e10	+	4.02240e10i	0.165287	+	0.262264i
$307$	−1.79306e11	−	1.79306e11i	−1.15205	−	1.15205i	−0.986141	−	0.165910i	$-0.946944\pi$
$307$	−1.79306e11	−	1.79306e11i	−1.15205	−	1.15205i	−0.165910	−	0.986141i	$-0.553056\pi$
$308$	9.38009e9	+	9.38009e9i	0.0593921	+	0.0593921i
$309$	3.58915e10	+	1.98048e10i	0.223964	+	0.123583i
$310$		0			0
$311$		−	1.79126e11i		−	1.08577i	−0.839808	−	0.542883i	$-0.817333\pi$
$311$		−	1.79126e11i		−	1.08577i	0.839808	−	0.542883i	$-0.182667\pi$
$312$	5.62311e9	+	1.94687e10i	0.0335955	+	0.116316i
$313$	−2.15424e11	+	2.15424e11i	−1.26866	+	1.26866i	−0.321878	+	0.946781i	$0.604314\pi$
$313$	−2.15424e11	+	2.15424e11i	−1.26866	+	1.26866i	−0.946781	+	0.321878i	$0.895686\pi$
$314$	3.22946e10			0.187477
$315$		0			0
$316$	−1.93928e11			−1.09408
$317$	1.87228e11	−	1.87228e11i	1.04137	−	1.04137i	0.0422596	−	0.999107i	$-0.486544\pi$
$317$	1.87228e11	−	1.87228e11i	1.04137	−	1.04137i	0.999107	−	0.0422596i	$-0.0134557\pi$
$318$	−1.62363e10	−	5.62143e10i	−0.0890359	−	0.308265i
$319$			2.54782e10i			0.137756i
$320$		0			0
$321$	−5.18754e10	−	2.86247e10i	−0.272702	−	0.150476i
$322$	−1.29481e10	−	1.29481e10i	−0.0671202	−	0.0671202i
$323$	1.50366e11	+	1.50366e11i	0.768667	+	0.768667i
$324$	1.71496e11	+	8.20167e10i	0.864574	+	0.413475i
$325$		0			0
$326$		−	6.29836e10i		−	0.308850i
$327$	1.80335e11	−	5.20860e10i	0.872200	−	0.251916i
$328$	1.05631e11	−	1.05631e11i	0.503919	−	0.503919i
$329$	−6.97258e10			−0.328104
$330$		0			0
$331$	−2.64891e11			−1.21295			−0.606473	−	0.795104i	$-0.707416\pi$
$331$	−2.64891e11			−1.21295			−0.606473	+	0.795104i	$0.707416\pi$
$332$	1.32232e11	−	1.32232e11i	0.597331	−	0.597331i
$333$	2.57106e11	+	5.83165e10i	1.14581	+	0.259892i
$334$		−	5.65601e10i		−	0.248686i
$335$		0			0
$336$	6.03567e10	−	1.09382e11i	0.258344	−	0.468187i
$337$	1.00996e11	+	1.00996e11i	0.426548	+	0.426548i	0.887451	−	0.460902i	$-0.152474\pi$
$337$	1.00996e11	+	1.00996e11i	0.426548	+	0.426548i	−0.460902	+	0.887451i	$0.652474\pi$
$338$	3.14461e10	+	3.14461e10i	0.131051	+	0.131051i
$339$	−6.94239e10	+	1.25814e11i	−0.285503	+	0.517406i
$340$		0			0
$341$			1.40882e10i			0.0564237i
$342$	−3.60282e10	−	8.17188e9i	−0.142405	−	0.0323002i
$343$	−1.79976e11	+	1.79976e11i	−0.702086	+	0.702086i
$344$	1.48241e11			0.570763
$345$		0			0
$346$	7.60990e10			0.285454
$347$	−1.27916e11	+	1.27916e11i	−0.473633	+	0.473633i	−0.903088	−	0.429455i	$-0.858706\pi$
$347$	−1.27916e11	+	1.27916e11i	−0.473633	+	0.473633i	0.429455	+	0.903088i	$0.358706\pi$
$348$	2.41470e11	−	6.97435e10i	0.882586	−	0.254916i
$349$		−	4.24124e11i		−	1.53031i	−0.643849	−	0.765153i	$-0.722663\pi$
$349$		−	4.24124e11i		−	1.53031i	0.643849	−	0.765153i	$-0.277337\pi$
$350$		0			0
$351$	−8.60060e10	+	5.00531e9i	−0.302445	+	0.0176015i
$352$	−1.69338e10	−	1.69338e10i	−0.0587911	−	0.0587911i
$353$	1.70829e11	+	1.70829e11i	0.585565	+	0.585565i	0.936427	−	0.350862i	$-0.114111\pi$
$353$	1.70829e11	+	1.70829e11i	0.585565	+	0.585565i	−0.350862	+	0.936427i	$0.614111\pi$
$354$	−9.86487e10	−	5.44340e10i	−0.333869	−	0.184228i
$355$		0			0
$356$			7.68622e10i			0.253623i
$357$	7.89011e10	+	2.73176e11i	0.257084	+	0.890093i
$358$	−2.86363e10	+	2.86363e10i	−0.0921390	+	0.0921390i
$359$	2.18580e11			0.694522			0.347261	−	0.937769i	$-0.387112\pi$
$359$	2.18580e11			0.694522			0.347261	+	0.937769i	$0.387112\pi$
$360$		0			0
$361$	1.57458e11			0.487958
$362$	−8.01413e10	+	8.01413e10i	−0.245283	+	0.245283i
$363$	−8.98997e10	−	3.11256e11i	−0.271756	−	0.940889i
$364$			5.93060e10i			0.177069i
$365$		0			0
$366$	4.96690e10	+	2.74072e10i	0.144684	+	0.0798361i
$367$	−3.23965e11	−	3.23965e11i	−0.932182	−	0.932182i	0.0656598	−	0.997842i	$-0.479085\pi$
$367$	−3.23965e11	−	3.23965e11i	−0.932182	−	0.932182i	−0.997842	+	0.0656598i	$0.979085\pi$
$368$	−1.66369e11	−	1.66369e11i	−0.472886	−	0.472886i
$369$	3.38616e11	+	5.37288e11i	0.950800	+	1.50865i
$370$		0			0
$371$		−	3.49924e11i		−	0.958939i
$372$	1.33522e11	−	3.85649e10i	0.361500	−	0.104412i
$373$	2.23497e11	−	2.23497e11i	0.597836	−	0.597836i	−0.341900	−	0.939736i	$-0.611070\pi$
$373$	2.23497e11	−	2.23497e11i	0.597836	−	0.597836i	0.939736	+	0.341900i	$0.111070\pi$
$374$	1.68566e10			0.0445501
$375$		0			0
$376$	8.33262e10			0.214999
$377$	−8.05434e10	+	8.05434e10i	−0.205350	+	0.205350i
$378$	−3.69004e10	−	3.28416e10i	−0.0929647	−	0.0827392i
$379$		−	5.15379e11i		−	1.28307i	−0.767093	−	0.641535i	$-0.778298\pi$
$379$		−	5.15379e11i		−	1.28307i	0.767093	−	0.641535i	$-0.221702\pi$
$380$		0			0
$381$	−1.29782e11	+	2.35198e11i	−0.315537	+	0.571836i
$382$	−1.01788e11	−	1.01788e11i	−0.244575	−	0.244575i
$383$	−3.01545e11	−	3.01545e11i	−0.716074	−	0.716074i	0.251725	−	0.967799i	$-0.419002\pi$
$383$	−3.01545e11	−	3.01545e11i	−0.716074	−	0.716074i	−0.967799	+	0.251725i	$0.919002\pi$
$384$	−1.50968e11	+	2.73593e11i	−0.354319	+	0.642119i
$385$		0			0
$386$		−	1.08675e11i		−	0.249166i
$387$	−1.39406e11	+	6.14615e11i	−0.315924	+	1.39285i
$388$	−4.41369e11	+	4.41369e11i	−0.988688	+	0.988688i
$389$	−3.71561e11			−0.822730			−0.411365	−	0.911471i	$-0.634948\pi$
$389$	−3.71561e11			−0.822730			−0.411365	+	0.911471i	$0.634948\pi$
$390$		0			0
$391$	5.35505e11			1.15869
$392$	8.29727e10	−	8.29727e10i	0.177479	−	0.177479i
$393$	−1.17245e11	+	3.38636e10i	−0.247929	+	0.0716089i
$394$		−	6.03663e10i		−	0.126201i
$395$		0			0
$396$	5.70177e10	−	3.59344e10i	0.116515	−	0.0734315i
$397$	−1.05515e11	−	1.05515e11i	−0.213185	−	0.213185i	0.592434	−	0.805619i	$-0.298167\pi$
$397$	−1.05515e11	−	1.05515e11i	−0.213185	−	0.213185i	−0.805619	+	0.592434i	$0.798167\pi$
$398$	3.84317e10	+	3.84317e10i	0.0767742	+	0.0767742i
$399$	−1.93440e11	−	1.06740e11i	−0.382092	−	0.210837i
$400$		0			0
$401$			8.36433e11i			1.61540i	0.589591	+	0.807702i	$0.299289\pi$
$401$			8.36433e11i			1.61540i	−0.589591	+	0.807702i	$0.700711\pi$
$402$	−9.45190e9	−	3.27249e10i	−0.0180510	−	0.0624974i
$403$	−4.45367e10	+	4.45367e10i	−0.0841096	+	0.0841096i
$404$	−8.86363e11			−1.65537
$405$		0			0
$406$	−6.53124e10			−0.119297
$407$	6.60920e10	−	6.60920e10i	0.119392	−	0.119392i
$408$	−9.42912e10	−	3.26461e11i	−0.168461	−	0.583257i
$409$			6.29414e11i			1.11220i	0.831116	+	0.556099i	$0.187702\pi$
$409$			6.29414e11i			1.11220i	−0.831116	+	0.556099i	$0.812298\pi$
$410$		0			0
$411$	1.86976e11	+	1.03173e11i	0.323219	+	0.178351i
$412$	−1.01379e11	−	1.01379e11i	−0.173344	−	0.173344i
$413$	−4.76456e11	−	4.76456e11i	−0.805838	−	0.805838i
$414$	−7.87059e10	+	4.96030e10i	−0.131676	+	0.0829864i
$415$		0			0
$416$		−	1.07065e11i		−	0.175277i
$417$	7.14227e11	−	2.06289e11i	1.15671	−	0.334090i
$418$	−9.26146e9	+	9.26146e9i	−0.0148384	+	0.0148384i
$419$	1.99350e11			0.315976			0.157988	−	0.987441i	$-0.449499\pi$
$419$	1.99350e11			0.315976			0.157988	+	0.987441i	$0.449499\pi$
$420$		0			0
$421$	1.38083e11			0.214225			0.107113	−	0.994247i	$-0.465839\pi$
$421$	1.38083e11			0.214225			0.107113	+	0.994247i	$0.465839\pi$
$422$	6.05277e10	−	6.05277e10i	0.0929070	−	0.0929070i
$423$	−7.83601e10	+	3.45474e11i	−0.119004	+	0.524667i
$424$			4.18179e11i			0.628370i
$425$		0			0
$426$	−8.53490e10	+	1.54675e11i	−0.125561	+	0.227550i
$427$	2.39893e11	+	2.39893e11i	0.349214	+	0.349214i
$428$	1.46527e11	+	1.46527e11i	0.211067	+	0.211067i
$429$	−1.47564e10	+	2.67425e10i	−0.0210341	+	0.0381192i
$430$		0			0
$431$			1.27164e12i			1.77507i	0.460736	+	0.887537i	$0.347586\pi$
$431$			1.27164e12i			1.77507i	−0.460736	+	0.887537i	$0.652414\pi$
$432$	−4.74131e11	−	4.21980e11i	−0.654970	−	0.582928i
$433$	−6.41747e11	+	6.41747e11i	−0.877340	+	0.877340i	−0.993259	−	0.115918i	$-0.963019\pi$
$433$	−6.41747e11	+	6.41747e11i	−0.877340	+	0.877340i	0.115918	+	0.993259i	$0.463019\pi$
$434$	−3.61147e10			−0.0488630
$435$		0			0
$436$	−6.56495e11			−0.870046
$437$	−2.94220e11	+	2.94220e11i	−0.385927	+	0.385927i
$438$	−1.11616e11	+	3.22379e10i	−0.144908	+	0.0418537i
$439$		−	3.81169e11i		−	0.489809i	−0.969547	−	0.244905i	$-0.921243\pi$
$439$		−	3.81169e11i		−	0.489809i	0.969547	−	0.244905i	$-0.0787567\pi$
$440$		0			0
$441$	2.65981e11	+	4.22036e11i	0.334870	+	0.531344i
$442$	5.32884e10	+	5.32884e10i	0.0664099	+	0.0664099i
$443$	−2.04361e11	−	2.04361e11i	−0.252104	−	0.252104i	0.569729	−	0.821833i	$-0.307048\pi$
$443$	−2.04361e11	−	2.04361e11i	−0.252104	−	0.252104i	−0.821833	+	0.569729i	$0.807048\pi$
$444$	−8.07309e11	−	4.45470e11i	−0.985863	−	0.543996i
$445$		0			0
$446$		−	6.42380e10i		−	0.0768750i
$447$	1.40247e11	+	4.85572e11i	0.166154	+	0.575268i
$448$	−2.78975e11	+	2.78975e11i	−0.327201	+	0.327201i
$449$	8.98753e11			1.04359			0.521797	−	0.853070i	$-0.325262\pi$
$449$	8.98753e11			1.04359			0.521797	+	0.853070i	$0.325262\pi$
$450$		0			0
$451$	2.25161e11			0.256271
$452$	3.55374e11	−	3.55374e11i	0.400463	−	0.400463i
$453$	−2.75388e10	−	9.53467e10i	−0.0307258	−	0.106381i
$454$		−	1.75716e10i		−	0.0194115i
$455$		0			0
$456$	2.31172e11	+	1.27560e11i	0.250376	+	0.138157i
$457$	4.44151e11	+	4.44151e11i	0.476330	+	0.476330i	0.903956	−	0.427626i	$-0.140650\pi$
$457$	4.44151e11	+	4.44151e11i	0.476330	+	0.476330i	−0.427626	+	0.903956i	$0.640650\pi$
$458$	2.23969e11	+	2.23969e11i	0.237844	+	0.237844i
$459$	1.44219e12	−	8.39316e10i	1.51658	−	0.0882610i
$460$		0			0
$461$			2.28416e11i			0.235544i	0.993041	+	0.117772i	$0.0375752\pi$
$461$			2.28416e11i			0.235544i	−0.993041	+	0.117772i	$0.962425\pi$
$462$	−1.68257e10	+	4.85974e9i	−0.0171824	+	0.00496277i
$463$	1.10117e12	−	1.10117e12i	1.11362	−	1.11362i	0.120967	−	0.992657i	$-0.461400\pi$
$463$	1.10117e12	−	1.10117e12i	1.11362	−	1.11362i	0.992657	−	0.120967i	$-0.0385995\pi$
$464$	−8.39196e11			−0.840490
$465$		0			0
$466$	−2.23362e11			−0.219419
$467$	−4.86949e11	+	4.86949e11i	−0.473759	+	0.473759i	−0.903129	−	0.429370i	$-0.858736\pi$
$467$	−4.86949e11	+	4.86949e11i	−0.473759	+	0.473759i	0.429370	+	0.903129i	$0.358736\pi$
$468$	2.93847e11	+	6.66500e10i	0.283149	+	0.0642235i
$469$		−	2.03707e11i		−	0.194414i
$470$		0			0
$471$	4.74062e11	−	8.59124e11i	0.443855	−	0.804381i
$472$	5.69392e11	+	5.69392e11i	0.528047	+	0.528047i
$473$	1.57994e11	+	1.57994e11i	0.145132	+	0.145132i
$474$	1.23694e11	−	2.24167e11i	0.112551	−	0.203971i
$475$		0			0
$476$		−	9.94474e11i		−	0.887896i
$477$	−1.73379e12	−	3.93256e11i	−1.53343	−	0.347810i
$478$	−1.90036e11	+	1.90036e11i	−0.166499	+	0.166499i
$479$	5.26724e11			0.457166			0.228583	−	0.973524i	$-0.426591\pi$
$479$	5.26724e11			0.457166			0.228583	+	0.973524i	$0.426591\pi$
$480$		0			0
$481$	4.17870e11			0.355949
$482$	1.19261e11	−	1.19261e11i	0.100644	−	0.100644i
$483$	−5.34521e11	+	1.54385e11i	−0.446892	+	0.129075i
$484$			1.13310e12i			0.938566i
$485$		0			0
$486$	−2.04192e11	+	1.45924e11i	−0.166026	+	0.118649i
$487$	−8.18404e10	−	8.18404e10i	−0.0659306	−	0.0659306i	0.673373	−	0.739303i	$-0.264845\pi$
$487$	−8.18404e10	−	8.18404e10i	−0.0659306	−	0.0659306i	−0.739303	+	0.673373i	$0.764845\pi$
$488$	−2.86685e11	−	2.86685e11i	−0.228832	−	0.228832i
$489$	−1.67553e12	−	9.24553e11i	−1.32514	−	0.731210i
$490$		0			0
$491$		−	2.37936e12i		−	1.84754i	−0.382946	−	0.923771i	$-0.625090\pi$
$491$		−	2.37936e12i		−	1.84754i	0.382946	−	0.923771i	$-0.374910\pi$
$492$	−6.16352e11	−	2.13397e12i	−0.474227	−	1.64190i
$493$	1.35059e12	−	1.35059e12i	1.02971	−	1.02971i
$494$	−5.85560e10			−0.0442385
$495$		0			0
$496$	−4.64036e11			−0.344258
$497$	−7.47052e11	+	7.47052e11i	−0.549221	+	0.549221i
$498$	6.85082e10	+	2.37193e11i	0.0499127	+	0.172811i
$499$			1.15174e12i			0.831573i	0.909462	+	0.415786i	$0.136494\pi$
$499$			1.15174e12i			0.831573i	−0.909462	+	0.415786i	$0.863506\pi$
$500$		0			0
$501$	−1.50465e12	−	8.30261e11i	−1.06700	−	0.588769i
$502$	5.85162e10	+	5.85162e10i	0.0411253	+	0.0411253i
$503$	1.39360e12	+	1.39360e12i	0.970692	+	0.970692i	0.999583	−	0.0288902i	$-0.00919733\pi$
$503$	1.39360e12	+	1.39360e12i	0.970692	+	0.970692i	−0.0288902	+	0.999583i	$0.509197\pi$
$504$	1.88236e11	+	2.98677e11i	0.129947	+	0.206188i
$505$		0			0
$506$			3.29832e10i			0.0223674i
$507$	1.29816e12	−	3.74944e11i	0.872551	−	0.252018i
$508$	6.64339e11	−	6.64339e11i	0.442592	−	0.442592i
$509$	1.67339e12			1.10501			0.552507	−	0.833508i	$-0.313671\pi$
$509$	1.67339e12			1.10501			0.552507	+	0.833508i	$0.313671\pi$
$510$		0			0
$511$	−6.94790e11			−0.450775
$512$	9.43030e11	−	9.43030e11i	0.606472	−	0.606472i
$513$	−7.46263e11	+	8.38491e11i	−0.475733	+	0.534528i
$514$		−	4.15422e11i		−	0.262516i
$515$		0			0
$516$	1.06490e12	−	1.92988e12i	0.661280	−	1.19841i
$517$	8.88080e10	+	8.88080e10i	0.0546695	+	0.0546695i
$518$	1.69425e11	+	1.69425e11i	0.103393	+	0.103393i
$519$	1.11708e12	−	2.02444e12i	0.675819	−	1.22476i
$520$		0			0
$521$		−	5.44464e11i		−	0.323742i	−0.986812	−	0.161871i	$-0.948247\pi$
$521$		−	5.44464e11i		−	0.323742i	0.986812	−	0.161871i	$-0.0517529\pi$
$522$	−7.34002e10	+	3.23607e11i	−0.0432693	+	0.190766i
$523$	1.24062e12	−	1.24062e12i	0.725070	−	0.725070i	−0.244563	−	0.969633i	$-0.578645\pi$
$523$	1.24062e12	−	1.24062e12i	0.725070	−	0.725070i	0.969633	+	0.244563i	$0.0786447\pi$
$524$	4.26819e11			0.247317
$525$		0			0
$526$	−4.26558e11			−0.242964
$527$	7.46814e11	−	7.46814e11i	0.421760	−	0.421760i
$528$	−2.16192e11	+	6.24425e10i	−0.121056	+	0.0349645i
$529$		−	7.53335e11i		−	0.418252i
$530$		0			0
$531$	−2.89618e12	+	1.82527e12i	−1.58089	+	0.996326i
$532$	5.46389e11	+	5.46389e11i	0.295733	+	0.295733i
$533$	7.11795e11	+	7.11795e11i	0.382017	+	0.382017i
$534$	−8.88472e10	−	4.90256e10i	−0.0472833	−	0.0260908i
$535$		0			0
$536$			2.43441e11i			0.127395i
$537$	3.41443e11	+	1.18216e12i	0.177188	+	0.613470i
$538$	−8.76175e10	+	8.76175e10i	−0.0450890	+	0.0450890i
$539$	1.76862e11			0.0902581
$540$		0			0
$541$	2.67240e12			1.34126			0.670631	−	0.741791i	$-0.266023\pi$
$541$	2.67240e12			1.34126			0.670631	+	0.741791i	$0.266023\pi$
$542$	1.08855e11	−	1.08855e11i	0.0541817	−	0.0541817i
$543$	9.55558e11	+	3.30839e12i	0.471691	+	1.63312i
$544$			1.79531e12i			0.878912i
$545$		0			0
$546$	−6.85535e10	−	3.78276e10i	−0.0330113	−	0.0182155i
$547$	−2.01587e11	−	2.01587e11i	−0.0962764	−	0.0962764i	0.657328	−	0.753605i	$-0.271687\pi$
$547$	−2.01587e11	−	2.01587e11i	−0.0962764	−	0.0962764i	−0.753605	+	0.657328i	$0.771687\pi$
$548$	−5.28130e11	−	5.28130e11i	−0.250166	−	0.250166i
$549$	1.45821e12	−	9.19011e11i	0.685084	−	0.431763i
$550$		0			0
$551$			1.48410e12i			0.685932i
$552$	6.38783e11	−	1.84499e11i	0.292838	−	0.0845800i
$553$	1.08269e12	−	1.08269e12i	0.492311	−	0.492311i
$554$	−2.29156e10			−0.0103356
$555$		0			0
$556$	−2.60008e12			−1.15385
$557$	−8.30184e11	+	8.30184e11i	−0.365448	+	0.365448i	−0.865814	−	0.500366i	$-0.833199\pi$
$557$	−8.30184e11	+	8.30184e11i	−0.365448	+	0.365448i	0.500366	+	0.865814i	$0.333199\pi$
$558$	−4.05868e10	+	1.78940e11i	−0.0177228	+	0.0781362i
$559$			9.98921e11i			0.432691i
$560$		0			0
$561$	2.47443e11	−	4.48432e11i	0.105473	−	0.191145i
$562$	9.93751e10	+	9.93751e10i	0.0420208	+	0.0420208i
$563$	1.55742e12	+	1.55742e12i	0.653308	+	0.653308i	0.953788	−	0.300480i	$-0.0971470\pi$
$563$	1.55742e12	+	1.55742e12i	0.653308	+	0.653308i	−0.300480	+	0.953788i	$0.597147\pi$
$564$	5.98580e11	−	1.08478e12i	0.249095	−	0.451426i
$565$		0			0
$566$		−	6.99958e10i		−	0.0286680i
$567$	−1.41535e12	+	4.99559e11i	−0.575094	+	0.202984i
$568$	8.92770e11	−	8.92770e11i	0.359892	−	0.359892i
$569$	−1.02493e12			−0.409909			−0.204954	−	0.978772i	$-0.565705\pi$
$569$	−1.02493e12			−0.409909			−0.204954	+	0.978772i	$0.565705\pi$
$570$		0			0
$571$	1.51100e12			0.594842			0.297421	−	0.954746i	$-0.403874\pi$
$571$	1.51100e12			0.594842			0.297421	+	0.954746i	$0.403874\pi$
$572$	7.55367e10	−	7.55367e10i	0.0295036	−	0.0295036i
$573$	−4.20202e12	+	1.21366e12i	−1.62840	+	0.470330i
$574$			5.77193e11i			0.221931i
$575$		0			0
$576$	1.06873e12	+	1.69578e12i	0.404547	+	0.641901i
$577$	−1.15445e12	−	1.15445e12i	−0.433593	−	0.433593i	0.456256	−	0.889849i	$-0.349190\pi$
$577$	−1.15445e12	−	1.15445e12i	−0.433593	−	0.433593i	−0.889849	+	0.456256i	$0.849190\pi$
$578$	−5.06376e11	−	5.06376e11i	−0.188711	−	0.188711i
$579$	−2.89106e12	−	1.59528e12i	−1.06906	−	0.589905i
$580$		0			0
$581$			1.47649e12i			0.537572i
$582$	−2.28669e11	−	7.91713e11i	−0.0826142	−	0.286032i
$583$	−4.45690e11	+	4.45690e11i	−0.159781	+	0.159781i
$584$	8.30313e11			0.295382
$585$		0			0
$586$	3.28748e11			0.115166
$587$	6.71898e10	−	6.71898e10i	0.0233578	−	0.0233578i	−0.695331	−	0.718689i	$-0.744742\pi$
$587$	6.71898e10	−	6.71898e10i	0.0233578	−	0.0233578i	0.718689	+	0.695331i	$0.244742\pi$
$588$	−4.84140e11	−	1.67622e12i	−0.167022	−	0.578273i
$589$			8.20637e11i			0.280952i
$590$		0			0
$591$	−1.60591e12	−	8.86133e11i	−0.541472	−	0.298783i
$592$	2.17693e12	+	2.17693e12i	0.728445	+	0.728445i
$593$	−3.69715e12	−	3.69715e12i	−1.22778	−	1.22778i	−0.964801	−	0.262979i	$-0.915295\pi$
$593$	−3.69715e12	−	3.69715e12i	−1.22778	−	1.22778i	−0.262979	−	0.964801i	$-0.584705\pi$
$594$	5.16959e9	+	8.88287e10i	0.00170379	+	0.0292762i
$595$		0			0
$596$		−	1.76768e12i		−	0.573848i
$597$	1.58653e12	−	4.58237e11i	0.511170	−	0.147640i
$598$	−1.04269e11	+	1.04269e11i	−0.0333426	+	0.0333426i
$599$	−2.60751e12			−0.827571			−0.413785	−	0.910374i	$-0.635794\pi$
$599$	−2.60751e12			−0.827571			−0.413785	+	0.910374i	$0.635794\pi$
$600$		0			0
$601$	4.64986e12			1.45380			0.726901	−	0.686743i	$-0.240960\pi$
$601$	4.64986e12			1.45380			0.726901	+	0.686743i	$0.240960\pi$
$602$	−4.05011e11	+	4.05011e11i	−0.125685	+	0.125685i
$603$	−1.00932e12	−	2.28932e11i	−0.310885	−	0.0705147i
$604$			3.47101e11i			0.106118i
$605$		0			0
$606$	5.65355e11	−	1.02457e12i	0.170292	−	0.308614i
$607$	−9.03435e11	−	9.03435e11i	−0.270114	−	0.270114i	0.559032	−	0.829146i	$-0.311173\pi$
$607$	−9.03435e11	−	9.03435e11i	−0.270114	−	0.270114i	−0.829146	+	0.559032i	$0.811173\pi$
$608$	−9.86390e11	−	9.86390e11i	−0.292740	−	0.292740i
$609$	−9.58739e11	+	1.73749e12i	−0.282438	+	0.511851i
$610$		0			0
$611$			5.61493e11i			0.162989i
$612$	−4.92738e12	−	1.11762e12i	−1.41982	−	0.322043i
$613$	1.10973e11	−	1.10973e11i	0.0317428	−	0.0317428i	−0.691057	−	0.722800i	$-0.742855\pi$
$613$	1.10973e11	−	1.10973e11i	0.0317428	−	0.0317428i	0.722800	+	0.691057i	$0.242855\pi$
$614$	−1.17088e12			−0.332471
$615$		0			0
$616$	1.25166e11			0.0350247
$617$	−8.90409e11	+	8.90409e11i	−0.247347	+	0.247347i	−0.819881	−	0.572534i	$-0.805960\pi$
$617$	−8.90409e11	+	8.90409e11i	−0.247347	+	0.247347i	0.572534	+	0.819881i	$0.305960\pi$
$618$	1.81850e11	−	5.25235e10i	0.0501493	−	0.0144846i
$619$			1.79885e12i			0.492480i	0.969209	+	0.246240i	$0.0791951\pi$
$619$			1.79885e12i			0.492480i	−0.969209	+	0.246240i	$0.920805\pi$
$620$		0			0
$621$	1.64228e11	+	2.82193e12i	0.0443135	+	0.761436i
$622$	−5.84850e11	−	5.84850e11i	−0.156671	−	0.156671i
$623$	−4.29117e11	−	4.29117e11i	−0.114125	−	0.114125i
$624$	−8.80840e11	−	4.86045e11i	−0.232577	−	0.128335i
$625$		0			0
$626$			1.40673e12i			0.366123i
$627$	1.10428e11	+	3.82331e11i	0.0285349	+	0.0987952i
$628$	−2.42667e12	+	2.42667e12i	−0.622577	+	0.622577i
$629$	−7.00706e12			−1.78487
$630$		0			0
$631$	−2.75410e12			−0.691588			−0.345794	−	0.938311i	$-0.612390\pi$
$631$	−2.75410e12			−0.691588			−0.345794	+	0.938311i	$0.612390\pi$
$632$	−1.29387e12	+	1.29387e12i	−0.322600	+	0.322600i
$633$	−7.21697e11	−	2.49870e12i	−0.178664	−	0.618583i
$634$		−	1.22261e12i		−	0.300528i
$635$		0			0
$636$	5.44406e12	+	3.00402e12i	1.31937	+	0.728023i
$637$	5.59110e11	+	5.59110e11i	0.134546	+	0.134546i
$638$	8.31868e10	+	8.31868e10i	0.0198775	+	0.0198775i
$639$	2.86190e12	+	4.54103e12i	0.679049	+	1.07746i
$640$		0			0
$641$			4.27294e11i			0.0999690i	0.998750	+	0.0499845i	$0.0159172\pi$
$641$			4.27294e11i			0.0999690i	−0.998750	+	0.0499845i	$0.984083\pi$
$642$	−2.62835e11	+	7.59142e10i	−0.0610626	+	0.0176366i
$643$	−1.46468e12	+	1.46468e12i	−0.337905	+	0.337905i	−0.855578	−	0.517673i	$-0.826798\pi$
$643$	−1.46468e12	+	1.46468e12i	−0.337905	+	0.337905i	0.517673	+	0.855578i	$0.326798\pi$
$644$	1.94588e12			0.445789
$645$		0			0
$646$	9.81897e11			0.221830
$647$	3.63395e12	−	3.63395e12i	0.815286	−	0.815286i	−0.170135	−	0.985421i	$-0.554420\pi$
$647$	3.63395e12	−	3.63395e12i	0.815286	−	0.815286i	0.985421	+	0.170135i	$0.0544204\pi$
$648$	1.69142e12	−	5.97001e11i	0.376846	−	0.133011i
$649$			1.21370e12i			0.268541i
$650$		0			0
$651$	−5.30137e11	+	9.60747e11i	−0.115684	+	0.209650i
$652$	4.73270e12	+	4.73270e12i	1.02564	+	1.02564i
$653$	−4.23316e12	−	4.23316e12i	−0.911077	−	0.911077i	0.0852803	−	0.996357i	$-0.472821\pi$
$653$	−4.23316e12	−	4.23316e12i	−0.911077	−	0.911077i	−0.996357	+	0.0852803i	$0.972821\pi$
$654$	4.18737e11	−	7.58861e11i	0.0895038	−	0.162204i
$655$		0			0
$656$			7.41632e12i			1.56358i
$657$	−7.80827e11	+	3.44252e12i	−0.163497	+	0.720828i
$658$	−2.27656e11	+	2.27656e11i	−0.0473438	+	0.0473438i
$659$	7.19985e12			1.48710			0.743548	−	0.668682i	$-0.233141\pi$
$659$	7.19985e12			1.48710			0.743548	+	0.668682i	$0.233141\pi$
$660$		0			0
$661$	−9.83708e9			−0.00200429			−0.00100214	−	0.999999i	$-0.500319\pi$
$661$	−9.83708e9			−0.00200429			−0.00100214	+	0.999999i	$0.500319\pi$
$662$	−8.64876e11	+	8.64876e11i	−0.175022	+	0.175022i
$663$	2.19985e12	−	6.35380e11i	0.442163	−	0.127709i
$664$		−	1.76448e12i		−	0.352258i
$665$		0			0
$666$	1.02986e12	−	6.49054e11i	0.202836	−	0.127834i
$667$	2.64269e12	+	2.64269e12i	0.516988	+	0.516988i
$668$	4.25002e12	+	4.25002e12i	0.825843	+	0.825843i
$669$	−1.70890e12	−	9.42967e11i	−0.329837	−	0.182003i
$670$		0			0
$671$		−	6.11091e11i		−	0.116374i
$672$	−5.17585e11	−	1.79202e12i	−0.0979085	−	0.338985i
$673$	−8.37012e11	+	8.37012e11i	−0.157277	+	0.157277i	−0.781359	−	0.624082i	$-0.785473\pi$
$673$	−8.37012e11	+	8.37012e11i	−0.157277	+	0.157277i	0.624082	+	0.781359i	$0.285473\pi$
$674$	6.59507e11			0.123098
$675$		0			0
$676$	−4.72582e12			−0.870397
$677$	2.48682e12	−	2.48682e12i	0.454984	−	0.454984i	−0.442021	−	0.897005i	$-0.645738\pi$
$677$	2.48682e12	−	2.48682e12i	0.454984	−	0.454984i	0.897005	+	0.442021i	$0.145738\pi$
$678$	1.84116e11	+	6.37458e11i	0.0334625	+	0.115856i
$679$		−	4.92827e12i		−	0.889776i
$680$		0			0
$681$	−4.67451e11	−	2.57938e11i	−0.0832864	−	0.0459572i
$682$	4.59984e10	+	4.59984e10i	0.00814166	+	0.00814166i
$683$	2.35648e12	+	2.35648e12i	0.414353	+	0.414353i	0.883252	−	0.468899i	$-0.155349\pi$
$683$	2.35648e12	+	2.35648e12i	0.414353	+	0.414353i	−0.468899	+	0.883252i	$0.655349\pi$
$684$	3.32127e12	−	2.09318e12i	0.580166	−	0.365639i
$685$		0			0
$686$			1.17525e12i			0.202615i
$687$	9.24587e12	−	2.67047e12i	1.58359	−	0.457386i
$688$	−5.20397e12	+	5.20397e12i	−0.885496	+	0.885496i
$689$	−2.81789e12			−0.476363
$690$		0			0
$691$	−3.87331e12			−0.646295			−0.323148	−	0.946349i	$-0.604741\pi$
$691$	−3.87331e12			−0.646295			−0.323148	+	0.946349i	$0.604741\pi$
$692$	−5.71821e12	+	5.71821e12i	−0.947945	+	0.947945i
$693$	−1.17707e11	+	5.18946e11i	−0.0193866	+	0.0854717i
$694$			8.35298e11i			0.136686i
$695$		0			0
$696$	1.14575e12	−	2.07639e12i	0.185075	−	0.335404i
$697$	−1.19357e13	−	1.19357e13i	−1.91559	−	1.91559i
$698$	−1.38477e12	−	1.38477e12i	−0.220816	−	0.220816i
$699$	−3.27880e12	+	5.94204e12i	−0.519478	+	0.941431i
$700$		0			0
$701$		−	5.30397e12i		−	0.829603i	−0.909912	−	0.414801i	$-0.863851\pi$
$701$		−	5.30397e12i		−	0.829603i	0.909912	−	0.414801i	$-0.136149\pi$
$702$	−2.64469e11	+	2.97154e11i	−0.0411015	+	0.0461812i
$703$	3.84985e12	−	3.84985e12i	0.594491	−	0.594491i
$704$	7.10649e11			0.109038
$705$		0			0
$706$	1.11552e12			0.168988
$707$	4.94851e12	−	4.94851e12i	0.744881	−	0.744881i
$708$	1.15029e13	−	3.32237e12i	1.72051	−	0.496933i
$709$			4.74942e12i			0.705882i	0.935646	+	0.352941i	$0.114818\pi$
$709$			4.74942e12i			0.705882i	−0.935646	+	0.352941i	$0.885182\pi$
$710$		0			0
$711$	−4.14769e12	−	6.58121e12i	−0.608686	−	0.965812i
$712$	5.12819e11	+	5.12819e11i	0.0747832	+	0.0747832i
$713$	1.46129e12	+	1.46129e12i	0.211754	+	0.211754i
$714$	1.14954e12	+	6.34313e11i	0.165532	+	0.0913401i
$715$		0			0
$716$		−	4.30357e12i		−	0.611956i
$717$	2.26588e12	+	7.84506e12i	0.320184	+	1.10856i
$718$	7.13670e11	−	7.13670e11i	0.100216	−	0.100216i
$719$	8.22096e11			0.114721			0.0573605	−	0.998354i	$-0.481732\pi$
$719$	8.22096e11			0.114721			0.0573605	+	0.998354i	$0.481732\pi$
$720$		0			0
$721$	1.13198e12			0.156002
$722$	5.14105e11	−	5.14105e11i	0.0704100	−	0.0704100i
$723$	−1.42200e12	−	4.92334e12i	−0.193543	−	0.670097i
$724$		−	1.20439e13i		−	1.62909i
$725$		0			0
$726$	−1.30978e12	−	7.22734e11i	−0.174979	−	0.0965526i
$727$	−6.43823e12	−	6.43823e12i	−0.854794	−	0.854794i	0.135925	−	0.990719i	$-0.456599\pi$
$727$	−6.43823e12	−	6.43823e12i	−0.854794	−	0.854794i	−0.990719	+	0.135925i	$0.956599\pi$
$728$	3.95685e11	+	3.95685e11i	0.0522106	+	0.0522106i
$729$	8.84582e11	+	7.57412e12i	0.116002	+	0.993249i
$730$		0			0
$731$		−	1.67504e13i		−	2.16969i
$732$	−5.79163e12	+	1.67279e12i	−0.745592	+	0.215348i
$733$	−4.31349e12	+	4.31349e12i	−0.551901	+	0.551901i	−0.926989	−	0.375088i	$-0.877612\pi$
$733$	−4.31349e12	+	4.31349e12i	−0.551901	+	0.551901i	0.375088	+	0.926989i	$0.377612\pi$
$734$	−2.11551e12			−0.269019
$735$		0			0
$736$	−3.51287e12			−0.441278
$737$	−2.59457e11	+	2.59457e11i	−0.0323937	+	0.0323937i
$738$	2.85985e12	+	6.48668e11i	0.354887	+	0.0804950i
$739$		−	1.23965e13i		−	1.52897i	−0.644643	−	0.764484i	$-0.722994\pi$
$739$		−	1.23965e13i		−	1.52897i	0.644643	−	0.764484i	$-0.277006\pi$
$740$		0			0
$741$	−8.59560e11	+	1.55775e12i	−0.104736	+	0.189808i
$742$	−1.14251e12	−	1.14251e12i	−0.138370	−	0.138370i
$743$	1.03279e13	+	1.03279e13i	1.24326	+	1.24326i	0.958639	+	0.284626i	$0.0918693\pi$
$743$	1.03279e13	+	1.03279e13i	1.24326	+	1.24326i	0.284626	+	0.958639i	$0.408131\pi$
$744$	6.33544e11	−	1.14815e12i	0.0758051	−	0.137379i
$745$		0			0
$746$		−	1.45945e12i		−	0.172530i
$747$	7.31563e12	+	1.65932e12i	0.859625	+	0.194979i
$748$	−1.26664e12	+	1.26664e12i	−0.147943	+	0.147943i
$749$	−1.63610e12			−0.189951
$750$		0			0
$751$	4.34098e12			0.497976			0.248988	−	0.968507i	$-0.419902\pi$
$751$	4.34098e12			0.497976			0.248988	+	0.968507i	$0.419902\pi$
$752$	−2.92514e12	+	2.92514e12i	−0.333555	+	0.333555i
$753$	2.41566e12	−	6.97712e11i	0.273816	−	0.0790859i
$754$			5.25953e11i			0.0592619i
$755$		0			0
$756$	5.24053e12	−	3.04985e11i	0.583482	−	0.0339570i
$757$	−4.77574e12	−	4.77574e12i	−0.528578	−	0.528578i	0.391570	−	0.920148i	$-0.371932\pi$
$757$	−4.77574e12	−	4.77574e12i	−0.528578	−	0.528578i	−0.920148	+	0.391570i	$0.871932\pi$
$758$	−1.68273e12	−	1.68273e12i	−0.185141	−	0.185141i
$759$	8.77443e11	+	4.84170e11i	0.0959690	+	0.0529554i
$760$		0			0
$761$			1.54764e12i			0.167278i	0.996496	+	0.0836392i	$0.0266543\pi$
$761$			1.54764e12i			0.167278i	−0.996496	+	0.0836392i	$0.973346\pi$
$762$	3.44188e11	+	1.19167e12i	0.0369827	+	0.128044i
$763$	3.66517e12	−	3.66517e12i	0.391502	−	0.391502i
$764$	1.52971e13			1.62438
$765$		0			0
$766$	−1.96910e12			−0.206652
$767$	−3.83684e12	+	3.83684e12i	−0.400308	+	0.400308i
$768$	−1.62947e12	−	5.64165e12i	−0.169013	−	0.585168i
$769$		−	1.00560e13i		−	1.03694i	−0.855095	−	0.518471i	$-0.826501\pi$
$769$		−	1.00560e13i		−	1.03694i	0.855095	−	0.518471i	$-0.173499\pi$
$770$		0			0
$771$	−1.10513e13	−	6.09809e12i	−1.12634	−	0.621512i
$772$	8.16605e12	+	8.16605e12i	0.827436	+	0.827436i
$773$	−3.81956e12	−	3.81956e12i	−0.384774	−	0.384774i	0.488045	−	0.872819i	$-0.337710\pi$
$773$	−3.81956e12	−	3.81956e12i	−0.384774	−	0.384774i	−0.872819	+	0.488045i	$0.837710\pi$
$774$	1.55157e12	+	2.46190e12i	0.155395	+	0.246567i
$775$		0			0
$776$			5.88956e12i			0.583049i
$777$	6.99418e12	−	2.02012e12i	0.688403	−	0.198830i
$778$	−1.21316e12	+	1.21316e12i	−0.118716	+	0.118716i
$779$	1.31156e13			1.27606
$780$		0			0
$781$	1.90300e12			0.183025
$782$	1.74844e12	−	1.74844e12i	0.167194	−	0.167194i
$783$	7.53136e12	+	6.70296e12i	0.716054	+	0.637293i
$784$			5.82547e12i			0.550692i
$785$		0			0
$786$	−2.72241e11	+	4.93372e11i	−0.0254421	+	0.0461077i
$787$	−9.17194e12	−	9.17194e12i	−0.852265	−	0.852265i	0.138147	−	0.990412i	$-0.455885\pi$
$787$	−9.17194e12	−	9.17194e12i	−0.852265	−	0.852265i	−0.990412	+	0.138147i	$0.955885\pi$
$788$	4.53603e12	+	4.53603e12i	0.419090	+	0.419090i
$789$	−6.26156e12	+	1.13476e13i	−0.575223	+	1.04245i
$790$		0			0
$791$			3.96806e12i			0.360399i
$792$	1.40666e11	−	6.20169e11i	0.0127036	−	0.0560076i
$793$	1.93182e12	−	1.93182e12i	0.173476	−	0.173476i
$794$	−6.89016e11			−0.0615230
$795$		0			0
$796$	−5.77564e12			−0.509908
$797$	−3.87015e11	+	3.87015e11i	−0.0339754	+	0.0339754i	−0.723890	−	0.689915i	$-0.757648\pi$
$797$	−3.87015e11	+	3.87015e11i	−0.0339754	+	0.0339754i	0.689915	+	0.723890i	$0.257648\pi$
$798$	−9.80093e11	+	2.83079e11i	−0.0855568	+	0.0247112i
$799$		−	9.41540e12i		−	0.817294i
$800$		0			0
$801$	−2.60842e12	+	1.64391e12i	−0.223889	+	0.141102i
$802$	2.73097e12	+	2.73097e12i	0.233095	+	0.233095i
$803$	8.84937e11	+	8.84937e11i	0.0751091	+	0.0751091i
$804$	3.16924e12	+	1.74878e12i	0.267487	+	0.147599i
$805$		0			0
$806$			2.90827e11i			0.0242732i
$807$	1.04470e12	+	3.61702e12i	0.0867082	+	0.300206i
$808$	−5.91374e12	+	5.91374e12i	−0.488103	+	0.488103i
$809$	−1.77665e13			−1.45825			−0.729126	−	0.684380i	$-0.760073\pi$
$809$	−1.77665e13			−1.45825			−0.729126	+	0.684380i	$0.760073\pi$
$810$		0			0
$811$	2.96258e12			0.240479			0.120239	−	0.992745i	$-0.461634\pi$
$811$	2.96258e12			0.240479			0.120239	+	0.992745i	$0.461634\pi$
$812$	4.90769e12	−	4.90769e12i	0.396164	−	0.396164i
$813$	−1.29793e12	−	4.49376e12i	−0.104194	−	0.360747i
$814$		−	4.31584e11i		−	0.0344553i
$815$		0			0
$816$	1.47704e13	+	8.15025e12i	1.16624	+	0.643525i
$817$	9.20310e12	+	9.20310e12i	0.722662	+	0.722662i
$818$	2.05505e12	+	2.05505e12i	0.160485	+	0.160485i
$819$	−2.01263e12	+	1.26843e12i	−0.156310	+	0.0985116i
$820$		0			0
$821$			2.07501e13i			1.59396i	0.604008	+	0.796978i	$0.293570\pi$
$821$			2.07501e13i			1.59396i	−0.604008	+	0.796978i	$0.706430\pi$
$822$	9.47341e11	−	2.73619e11i	0.0723741	−	0.0209037i
$823$	−1.00242e13	+	1.00242e13i	−0.761639	+	0.761639i	−0.976619	−	0.214979i	$-0.931032\pi$
$823$	−1.00242e13	+	1.00242e13i	−0.761639	+	0.761639i	0.214979	+	0.976619i	$0.431032\pi$
$824$	−1.35278e12			−0.102225
$825$		0			0
$826$	−3.11128e12			−0.232557
$827$	5.24278e12	−	5.24278e12i	0.389751	−	0.389751i	−0.484848	−	0.874598i	$-0.661125\pi$
$827$	5.24278e12	−	5.24278e12i	0.389751	−	0.389751i	0.874598	+	0.484848i	$0.161125\pi$
$828$	2.18684e12	−	9.64136e12i	0.161689	−	0.712856i
$829$			1.36975e13i			1.00727i	0.863917	+	0.503633i	$0.168004\pi$
$829$			1.36975e13i			1.00727i	−0.863917	+	0.503633i	$0.831996\pi$
$830$		0			0
$831$	−3.36384e11	+	6.09616e11i	−0.0244698	+	0.0443457i
$832$	2.24655e12	+	2.24655e12i	0.162541	+	0.162541i
$833$	−9.37545e12	−	9.37545e12i	−0.674667	−	0.674667i
$834$	1.65843e12	−	3.00551e12i	0.118700	−	0.215115i
$835$		0			0
$836$		−	1.39184e12i		−	0.0985513i
$837$	4.16449e12	+	3.70642e12i	0.293290	+	0.261030i
$838$	6.50883e11	−	6.50883e11i	0.0455937	−	0.0455937i
$839$	−1.61698e13			−1.12662			−0.563309	−	0.826246i	$-0.690472\pi$
$839$	−1.61698e13			−1.12662			−0.563309	+	0.826246i	$0.690472\pi$
$840$		0			0
$841$	−1.17690e12			−0.0811256
$842$	4.50845e11	−	4.50845e11i	0.0309117	−	0.0309117i
$843$	4.10240e12	−	1.18489e12i	0.279778	−	0.0808079i
$844$			9.09632e12i			0.617056i
$845$		0			0
$846$	8.72135e11	+	1.38383e12i	0.0585352	+	0.0928787i
$847$	−6.32603e12	−	6.32603e12i	−0.422334	−	0.422334i
$848$	−1.46801e13	−	1.46801e13i	−0.974870	−	0.974870i
$849$	−1.86208e12	−	1.02749e12i	−0.123002	−	0.0678722i
$850$		0			0
$851$		−	1.37106e13i		−	0.896138i
$852$	−5.20925e12	−	1.80358e13i	−0.338686	−	1.17262i
$853$	−1.56626e13	+	1.56626e13i	−1.01297	+	1.01297i	−0.0130504	+	0.999915i	$0.504154\pi$
$853$	−1.56626e13	+	1.56626e13i	−1.01297	+	1.01297i	−0.999915	+	0.0130504i	$0.995846\pi$
$854$	1.56651e12			0.100780
$855$		0			0
$856$	1.95523e12			0.124470
$857$	−3.62087e12	+	3.62087e12i	−0.229297	+	0.229297i	−0.812399	−	0.583102i	$-0.801839\pi$
$857$	−3.62087e12	+	3.62087e12i	−0.229297	+	0.229297i	0.583102	+	0.812399i	$0.301839\pi$
$858$	3.91349e10	+	1.35495e11i	0.00246531	+	0.00853553i
$859$			4.55193e12i			0.285250i	0.989777	+	0.142625i	$0.0455543\pi$
$859$			4.55193e12i			0.285250i	−0.989777	+	0.142625i	$0.954446\pi$
$860$		0			0
$861$	1.53549e13	+	8.47277e12i	0.952208	+	0.525425i
$862$	4.15194e12	+	4.15194e12i	0.256135	+	0.256135i
$863$	−9.13849e12	−	9.13849e12i	−0.560823	−	0.560823i	0.368718	−	0.929541i	$-0.379797\pi$
$863$	−9.13849e12	−	9.13849e12i	−0.560823	−	0.560823i	−0.929541	+	0.368718i	$0.879797\pi$
$864$	−9.46068e12	+	5.50586e11i	−0.577578	+	0.0336135i
$865$		0			0
$866$			4.19064e12i			0.253192i
$867$	−2.09042e13	+	6.03773e12i	−1.25646	+	0.362901i
$868$	2.71372e12	−	2.71372e12i	0.162265	−	0.162265i
$869$	−2.75798e12			−0.164060
$870$		0			0
$871$	−1.64043e12			−0.0965773
$872$	−4.38008e12	+	4.38008e12i	−0.256542	+	0.256542i
$873$	−2.44184e13	−	5.53855e12i	−1.42283	−	0.322725i
$874$			1.92127e12i			0.111375i
$875$		0			0
$876$	5.96461e12	−	1.08094e13i	0.342226	−	0.620204i
$877$	−6.40067e12	−	6.40067e12i	−0.365365	−	0.365365i	0.500418	−	0.865784i	$-0.333180\pi$
$877$	−6.40067e12	−	6.40067e12i	−0.365365	−	0.365365i	−0.865784	+	0.500418i	$0.833180\pi$
$878$	−1.24453e12	−	1.24453e12i	−0.0706771	−	0.0706771i
$879$	4.82578e12	−	8.74557e12i	0.272657	−	0.494127i
$880$		0			0
$881$			2.69914e13i			1.50950i	0.656010	+	0.754752i	$0.272243\pi$
$881$			2.69914e13i			1.50950i	−0.656010	+	0.754752i	$0.727757\pi$
$882$	2.24639e12	+	5.09524e11i	0.124990	+	0.0283502i
$883$	1.59651e13	−	1.59651e13i	0.883788	−	0.883788i	−0.110129	−	0.993917i	$-0.535127\pi$
$883$	1.59651e13	−	1.59651e13i	0.883788	−	0.883788i	0.993917	+	0.110129i	$0.0351265\pi$
$884$	−8.00837e12			−0.441072
$885$		0			0
$886$	−1.33448e12			−0.0727548
$887$	−2.00890e13	+	2.00890e13i	−1.08969	+	1.08969i	−0.0941302	+	0.995560i	$0.530007\pi$
$887$	−2.00890e13	+	2.00890e13i	−1.08969	+	1.08969i	−0.995560	+	0.0941302i	$0.969993\pi$
$888$	−8.35844e12	+	2.41416e12i	−0.451094	+	0.130289i
$889$			7.41792e12i			0.398313i
$890$		0			0
$891$	2.43897e12	+	1.16642e12i	0.129645	+	0.0620017i
$892$	4.82695e12	+	4.82695e12i	0.255288	+	0.255288i
$893$	5.17305e12	+	5.17305e12i	0.272217	+	0.272217i
$894$	2.04332e12	+	1.12750e12i	0.106983	+	0.0590331i
$895$		0			0
$896$			8.62887e12i			0.447268i
$897$	1.24324e12	+	4.30443e12i	0.0641195	+	0.221998i
$898$	2.93445e12	−	2.93445e12i	0.150586	−	0.150586i
$899$	7.37100e12			0.376364
$900$		0			0
$901$	4.72519e13			2.38868
$902$	7.35156e11	−	7.35156e11i	0.0369786	−	0.0369786i
$903$	4.82912e12	+	1.67197e13i	0.241698	+	0.836821i
$904$		−	4.74205e12i		−	0.236161i
$905$		0			0
$906$	−4.01224e11	−	2.21394e11i	−0.0197838	−	0.0109166i
$907$	1.21043e13	+	1.21043e13i	0.593891	+	0.593891i	0.938680	−	0.344789i	$-0.112050\pi$
$907$	1.21043e13	+	1.21043e13i	0.593891	+	0.593891i	−0.344789	+	0.938680i	$0.612050\pi$
$908$	1.32036e12	+	1.32036e12i	0.0644623	+	0.0644623i
$909$	−1.89574e13	−	3.00799e13i	−0.920959	−	1.46130i
$910$		0			0
$911$		−	2.70661e13i		−	1.30195i	−0.759100	−	0.650974i	$-0.774361\pi$
$911$		−	2.70661e13i		−	1.30195i	0.759100	−	0.650974i	$-0.225639\pi$
$912$	−1.25932e13	+	3.63727e12i	−0.602779	+	0.174100i
$913$	1.88056e12	−	1.88056e12i	0.0895715	−	0.0895715i
$914$	2.90033e12			0.137464
$915$		0			0
$916$	−3.36588e13			−1.57968
$917$	−2.38290e12	+	2.38290e12i	−0.111287	+	0.111287i
$918$	4.43476e12	−	4.98283e12i	0.206100	−	0.231571i
$919$			1.03582e12i			0.0479031i	0.999713	+	0.0239515i	$0.00762474\pi$
$919$			1.03582e12i			0.0479031i	−0.999713	+	0.0239515i	$0.992375\pi$
$920$		0			0
$921$	−1.71876e13	+	3.11484e13i	−0.787131	+	1.42649i
$922$	7.45783e11	+	7.45783e11i	0.0339878	+	0.0339878i
$923$	6.01592e12	+	6.01592e12i	0.272831	+	0.272831i
$924$	8.99141e11	−	1.62948e12i	0.0405793	−	0.0735402i
$925$		0			0
$926$		−	7.19067e12i		−	0.321381i
$927$	1.27216e12	−	5.60870e12i	0.0565826	−	0.249461i
$928$	−8.85980e12	+	8.85980e12i	−0.392155	+	0.392155i
$929$	2.27257e13			1.00103			0.500514	−	0.865729i	$-0.333144\pi$
$929$	2.27257e13			1.00103			0.500514	+	0.865729i	$0.333144\pi$
$930$		0			0
$931$	1.03022e13			0.449425
$932$	1.67838e13	−	1.67838e13i	0.728651	−	0.728651i
$933$	−2.41437e13	+	6.97341e12i	−1.04313	+	0.301285i
$934$			3.17980e12i			0.136722i
$935$		0			0
$936$	2.40521e12	−	1.51584e12i	0.102426	−	0.0645524i
$937$	1.36582e13	+	1.36582e13i	0.578848	+	0.578848i	0.934586	−	0.355738i	$-0.115770\pi$
$937$	1.36582e13	+	1.36582e13i	0.578848	+	0.578848i	−0.355738	+	0.934586i	$0.615770\pi$
$938$	−6.65108e11	−	6.65108e11i	−0.0280530	−	0.0280530i
$939$	3.74228e13	+	2.06498e13i	1.57087	+	0.866803i
$940$		0			0
$941$			3.14251e13i			1.30654i	0.757124	+	0.653271i	$0.226604\pi$
$941$			3.14251e13i			1.30654i	−0.757124	+	0.653271i	$0.773396\pi$
$942$	−1.25724e12	−	4.35288e12i	−0.0520222	−	0.180114i
$943$	2.33546e13	−	2.33546e13i	0.961766	−	0.961766i
$944$	−3.99767e13			−1.63845
$945$		0			0
$946$	1.03171e12			0.0418838
$947$	2.12526e13	−	2.12526e13i	0.858693	−	0.858693i	−0.132491	−	0.991184i	$-0.542298\pi$
$947$	2.12526e13	−	2.12526e13i	0.858693	−	0.858693i	0.991184	+	0.132491i	$0.0422976\pi$
$948$	7.54966e12	+	2.61389e13i	0.303592	+	1.05111i
$949$			5.59505e12i			0.223927i
$950$		0			0
$951$	−3.25246e13	−	1.79470e13i	−1.28944	−	0.711507i
$952$	−6.63505e12	−	6.63505e12i	−0.261805	−	0.261805i
$953$	−7.87915e11	−	7.87915e11i	−0.0309429	−	0.0309429i	0.691466	−	0.722409i	$-0.256965\pi$
$953$	−7.87915e11	−	7.87915e11i	−0.0309429	−	0.0309429i	−0.722409	+	0.691466i	$0.756965\pi$
$954$	−6.94486e12	+	4.37687e12i	−0.271454	+	0.171079i
$955$		0			0
$956$		−	2.85593e13i		−	1.10583i
$957$	3.43412e12	−	9.91871e11i	0.132346	−	0.0382254i
$958$	1.71977e12	−	1.71977e12i	0.0659668	−	0.0659668i
$959$	5.89703e12			0.225138
$960$		0			0
$961$	−2.23638e13			−0.845845
$962$	1.36436e12	−	1.36436e12i	0.0513617	−	0.0513617i
$963$	−1.83870e12	+	8.10647e12i	−0.0688958	+	0.303748i
$964$			1.79230e13i			0.668442i
$965$		0			0
$966$	−1.24115e12	+	2.24930e12i	−0.0458594	+	0.0831093i
$967$	−1.08232e13	−	1.08232e13i	−0.398051	−	0.398051i	0.479494	−	0.877545i	$-0.340820\pi$
$967$	−1.08232e13	−	1.08232e13i	−0.398051	−	0.398051i	−0.877545	+	0.479494i	$0.840820\pi$
$968$	7.55996e12	+	7.55996e12i	0.276746	+	0.276746i
$969$	1.44135e13	−	2.61211e13i	0.525187	−	0.951776i
$970$		0			0
$971$		−	1.85785e13i		−	0.670693i	−0.942095	−	0.335347i	$-0.891147\pi$
$971$		−	1.85785e13i		−	0.670693i	0.942095	−	0.335347i	$-0.108853\pi$
$972$	4.37836e12	−	2.63083e13i	0.157331	−	0.945355i
$973$	1.45161e13	−	1.45161e13i	0.519208	−	0.519208i
$974$	−5.34422e11			−0.0190269
$975$		0			0
$976$	2.01280e13			0.710030
$977$	1.75329e13	−	1.75329e13i	0.615642	−	0.615642i	−0.328769	−	0.944410i	$-0.606634\pi$
$977$	1.75329e13	−	1.75329e13i	0.615642	−	0.615642i	0.944410	+	0.328769i	$0.106634\pi$
$978$	−8.48935e12	+	2.45197e12i	−0.296722	+	0.0857018i
$979$			1.09311e12i			0.0380314i
$980$		0			0
$981$	−1.40410e13	−	2.22791e13i	−0.484047	−	0.768045i
$982$	−7.76868e12	−	7.76868e12i	−0.266591	−	0.266591i
$983$	3.05862e13	+	3.05862e13i	1.04480	+	1.04480i	0.998948	+	0.0458554i	$0.0146014\pi$
$983$	3.05862e13	+	3.05862e13i	1.04480	+	1.04480i	0.0458554	+	0.998948i	$0.485399\pi$
$984$	−1.83499e13	−	1.01254e13i	−0.623960	−	0.344299i
$985$		0			0
$986$		−	8.81944e12i		−	0.297163i
$987$	2.71444e12	+	9.39810e12i	0.0910444	+	0.315219i
$988$	4.40000e12	−	4.40000e12i	0.146908	−	0.146908i
$989$	3.27754e13			1.08934
$990$		0			0
$991$	−9.34871e12			−0.307907			−0.153954	−	0.988078i	$-0.549201\pi$
$991$	−9.34871e12			−0.307907			−0.153954	+	0.988078i	$0.549201\pi$
$992$	−4.89905e12	+	4.89905e12i	−0.160624	+	0.160624i
$993$	1.03123e13	+	3.57038e13i	0.336576	+	1.16531i
$994$			4.87829e12i			0.158500i
$995$		0			0
$996$	−2.29709e13	−	1.26753e13i	−0.739625	−	0.408123i
$997$	2.79784e13	+	2.79784e13i	0.896797	+	0.896797i	0.995151	−	0.0983543i	$-0.0313579\pi$
$997$	2.79784e13	+	2.79784e13i	0.896797	+	0.896797i	−0.0983543	+	0.995151i	$0.531358\pi$
$998$	3.76045e12	+	3.76045e12i	0.119992	+	0.119992i
$999$	−2.14892e12	−	3.69248e13i	−0.0682615	−	1.17293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.e.g.32.14	yes	48
3.2	odd	2	inner	75.10.e.g.32.12	yes	48
5.2	odd	4	inner	75.10.e.g.68.13	yes	48
5.3	odd	4	inner	75.10.e.g.68.12	yes	48
5.4	even	2	inner	75.10.e.g.32.11	✓	48
15.2	even	4	inner	75.10.e.g.68.11	yes	48
15.8	even	4	inner	75.10.e.g.68.14	yes	48
15.14	odd	2	inner	75.10.e.g.32.13	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.10.e.g.32.11	✓	48	5.4	even	2	inner
75.10.e.g.32.12	yes	48	3.2	odd	2	inner
75.10.e.g.32.13	yes	48	15.14	odd	2	inner
75.10.e.g.32.14	yes	48	1.1	even	1	trivial
75.10.e.g.68.11	yes	48	15.2	even	4	inner
75.10.e.g.68.12	yes	48	5.3	odd	4	inner
75.10.e.g.68.13	yes	48	5.2	odd	4	inner
75.10.e.g.68.14	yes	48	15.8	even	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.26503 - 3.26503i) q^{2} +(-38.9302 - 134.787i) q^{3} +490.679i q^{4} +(-567.190 - 312.974i) q^{6} +(-2739.43 - 2739.43i) q^{7} +(3273.77 + 3273.77i) q^{8} +(-16651.9 + 10494.6i) q^{9} +O(q^{10})\)	\(q+(3.26503 - 3.26503i) q^{2} +(-38.9302 - 134.787i) q^{3} +490.679i q^{4} +(-567.190 - 312.974i) q^{6} +(-2739.43 - 2739.43i) q^{7} +(3273.77 + 3273.77i) q^{8} +(-16651.9 + 10494.6i) q^{9} +6978.29i q^{11} +(66137.0 - 19102.3i) q^{12} +(-22060.3 + 22060.3i) q^{13} -17888.6 q^{14} -229850. q^{16} +(369918. - 369918. i) q^{17} +(-20103.8 + 88633.8i) q^{18} +406484. i q^{19} +(-262592. + 475885. i) q^{21} +(22784.3 + 22784.3i) q^{22} +(723815. + 723815. i) q^{23} +(313812. - 568710. i) q^{24} +144055. i q^{26} +(2.06279e6 + 1.83589e6i) q^{27} +(1.34418e6 - 1.34418e6i) q^{28} +3.65106e6 q^{29} +2.01886e6 q^{31} +(-2.42664e6 + 2.42664e6i) q^{32} +(940580. - 271667. i) q^{33} -2.41558e6i q^{34} +(-5.14946e6 - 8.17073e6i) q^{36} +(-9.47109e6 - 9.47109e6i) q^{37} +(1.32718e6 + 1.32718e6i) q^{38} +(3.83224e6 + 2.11462e6i) q^{39} -3.22659e7i q^{41} +(696408. + 2.41115e6i) q^{42} +(2.26407e7 - 2.26407e7i) q^{43} -3.42410e6 q^{44} +4.72655e6 q^{46} +(1.27263e7 - 1.27263e7i) q^{47} +(8.94811e6 + 3.09807e7i) q^{48} -2.53447e7i q^{49} +(-6.42610e7 - 3.54590e7i) q^{51} +(-1.08245e7 - 1.08245e7i) q^{52} +(6.38680e7 + 6.38680e7i) q^{53} +(1.27293e7 - 740810. i) q^{54} -1.79365e7i q^{56} +(5.47887e7 - 1.58245e7i) q^{57} +(1.19208e7 - 1.19208e7i) q^{58} +1.73925e8 q^{59} -8.75702e7 q^{61} +(6.59164e6 - 6.59164e6i) q^{62} +(7.43657e7 + 1.68675e7i) q^{63} -1.01837e8i q^{64} +(2.18402e6 - 3.95802e6i) q^{66} +(3.71805e7 + 3.71805e7i) q^{67} +(1.81511e8 + 1.81511e8i) q^{68} +(6.93823e7 - 1.25739e8i) q^{69} -2.72704e8i q^{71} +(-8.88712e7 - 2.01577e7i) q^{72} +(1.26813e8 - 1.26813e8i) q^{73} -6.18467e7 q^{74} -1.99453e8 q^{76} +(1.91165e7 - 1.91165e7i) q^{77} +(1.94167e7 - 5.60809e6i) q^{78} +3.95223e8i q^{79} +(1.67149e8 - 3.49508e8i) q^{81} +(-1.05349e8 - 1.05349e8i) q^{82} +(-2.69488e8 - 2.69488e8i) q^{83} +(-2.33507e8 - 1.28848e8i) q^{84} -1.47845e8i q^{86} +(-1.42137e8 - 4.92114e8i) q^{87} +(-2.28453e7 + 2.28453e7i) q^{88} +1.56645e8 q^{89} +1.20865e8 q^{91} +(-3.55161e8 + 3.55161e8i) q^{92} +(-7.85949e7 - 2.72116e8i) q^{93} -8.31036e7i q^{94} +(4.21548e8 + 2.32609e8i) q^{96} +(8.99507e8 + 8.99507e8i) q^{97} +(-8.27509e7 - 8.27509e7i) q^{98} +(-7.32340e7 - 1.16202e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 10788 q^{6}+O(q^{10}) \) 48 * q + 10788 * q^6	\( 48 q + 10788 q^{6} - 3683496 q^{16} + 2202288 q^{21} - 50381304 q^{31} + 225716076 q^{36} - 336695184 q^{46} + 673842108 q^{51} + 69620856 q^{61} - 445930020 q^{66} + 4632842472 q^{76} - 4102516332 q^{81} + 11717060616 q^{91} - 14562582156 q^{96}+O(q^{100}) \) 48 * q + 10788 * q^6 - 3683496 * q^16 + 2202288 * q^21 - 50381304 * q^31 + 225716076 * q^36 - 336695184 * q^46 + 673842108 * q^51 + 69620856 * q^61 - 445930020 * q^66 + 4632842472 * q^76 - 4102516332 * q^81 + 11717060616 * q^91 - 14562582156 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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