LMFDB - Embedded newform 840.2.j.f.589.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [840,2,Mod(589,840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(840, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("840.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.j (of order $2$, degree $1$, 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.14
Character	$\chi$	$=$	840.589
Dual form			840.2.j.f.589.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.150941 + 1.40614i) q^{2} +1.00000 q^{3} +(-1.95443 - 0.424487i) q^{4} +(-2.20890 + 0.347530i) q^{5} +(-0.150941 + 1.40614i) q^{6} -1.00000i q^{7} +(0.891891 - 2.68413i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.150941 + 1.40614i) q^{2} +1.00000 q^{3} +(-1.95443 - 0.424487i) q^{4} +(-2.20890 + 0.347530i) q^{5} +(-0.150941 + 1.40614i) q^{6} -1.00000i q^{7} +(0.891891 - 2.68413i) q^{8} +1.00000 q^{9} +(-0.155261 - 3.15846i) q^{10} -1.02458i q^{11} +(-1.95443 - 0.424487i) q^{12} -0.301914 q^{13} +(1.40614 + 0.150941i) q^{14} +(-2.20890 + 0.347530i) q^{15} +(3.63962 + 1.65927i) q^{16} -4.15362i q^{17} +(-0.150941 + 1.40614i) q^{18} +2.92290i q^{19} +(4.46466 + 0.258424i) q^{20} -1.00000i q^{21} +(1.44069 + 0.154651i) q^{22} -8.22770i q^{23} +(0.891891 - 2.68413i) q^{24} +(4.75845 - 1.53532i) q^{25} +(0.0455712 - 0.424532i) q^{26} +1.00000 q^{27} +(-0.424487 + 1.95443i) q^{28} -7.23543i q^{29} +(-0.155261 - 3.15846i) q^{30} +6.43162 q^{31} +(-2.88252 + 4.86735i) q^{32} -1.02458i q^{33} +(5.84055 + 0.626952i) q^{34} +(0.347530 + 2.20890i) q^{35} +(-1.95443 - 0.424487i) q^{36} -9.18883 q^{37} +(-4.10999 - 0.441186i) q^{38} -0.301914 q^{39} +(-1.03728 + 6.23891i) q^{40} +10.4006 q^{41} +(1.40614 + 0.150941i) q^{42} +8.63817 q^{43} +(-0.434920 + 2.00247i) q^{44} +(-2.20890 + 0.347530i) q^{45} +(11.5693 + 1.24190i) q^{46} +1.71255i q^{47} +(3.63962 + 1.65927i) q^{48} -1.00000 q^{49} +(1.44062 + 6.92276i) q^{50} -4.15362i q^{51} +(0.590070 + 0.128159i) q^{52} +1.80258 q^{53} +(-0.150941 + 1.40614i) q^{54} +(0.356072 + 2.26318i) q^{55} +(-2.68413 - 0.891891i) q^{56} +2.92290i q^{57} +(10.1740 + 1.09212i) q^{58} -7.16525i q^{59} +(4.46466 + 0.258424i) q^{60} +3.32514i q^{61} +(-0.970796 + 9.04373i) q^{62} -1.00000i q^{63} +(-6.40906 - 4.78790i) q^{64} +(0.666896 - 0.104924i) q^{65} +(1.44069 + 0.154651i) q^{66} -3.42576 q^{67} +(-1.76316 + 8.11797i) q^{68} -8.22770i q^{69} +(-3.15846 + 0.155261i) q^{70} -10.5849 q^{71} +(0.891891 - 2.68413i) q^{72} -6.04378i q^{73} +(1.38697 - 12.9207i) q^{74} +(4.75845 - 1.53532i) q^{75} +(1.24073 - 5.71261i) q^{76} -1.02458 q^{77} +(0.0455712 - 0.424532i) q^{78} -4.47042 q^{79} +(-8.61619 - 2.40027i) q^{80} +1.00000 q^{81} +(-1.56989 + 14.6247i) q^{82} -5.42745 q^{83} +(-0.424487 + 1.95443i) q^{84} +(1.44351 + 9.17491i) q^{85} +(-1.30385 + 12.1464i) q^{86} -7.23543i q^{87} +(-2.75009 - 0.913811i) q^{88} +4.53265 q^{89} +(-0.155261 - 3.15846i) q^{90} +0.301914i q^{91} +(-3.49256 + 16.0805i) q^{92} +6.43162 q^{93} +(-2.40807 - 0.258494i) q^{94} +(-1.01580 - 6.45638i) q^{95} +(-2.88252 + 4.86735i) q^{96} -4.47010i q^{97} +(0.150941 - 1.40614i) q^{98} -1.02458i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 32 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 + 32 * q^3 - 2 * q^4 + 2 * q^6 + 2 * q^8 + 32 * q^9	$ 32 q + 2 q^{2} + 32 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{8} + 32 q^{9} - 8 q^{10} - 2 q^{12} + 32 q^{13} + 6 q^{16} + 2 q^{18} + 24 q^{20} + 2 q^{24} - 16 q^{25} + 12 q^{26} + 32 q^{27} + 8 q^{28} - 8 q^{30} + 32 q^{31} + 22 q^{32} + 4 q^{35} - 2 q^{36} - 8 q^{37} - 32 q^{38} + 32 q^{39} - 24 q^{40} + 24 q^{41} - 8 q^{43} - 24 q^{44} + 12 q^{46} + 6 q^{48} - 32 q^{49} - 26 q^{50} - 16 q^{52} - 24 q^{53} + 2 q^{54} + 24 q^{55} - 12 q^{56} - 16 q^{58} + 24 q^{60} - 48 q^{62} + 22 q^{64} + 8 q^{65} + 24 q^{67} + 4 q^{68} + 6 q^{70} + 40 q^{71} + 2 q^{72} - 20 q^{74} - 16 q^{75} - 52 q^{76} - 16 q^{77} + 12 q^{78} - 24 q^{79} - 44 q^{80} + 32 q^{81} + 24 q^{82} + 8 q^{84} - 8 q^{85} - 76 q^{86} + 56 q^{88} + 24 q^{89} - 8 q^{90} - 96 q^{92} + 32 q^{93} + 32 q^{94} - 48 q^{95} + 22 q^{96} - 2 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 32 * q^3 - 2 * q^4 + 2 * q^6 + 2 * q^8 + 32 * q^9 - 8 * q^10 - 2 * q^12 + 32 * q^13 + 6 * q^16 + 2 * q^18 + 24 * q^20 + 2 * q^24 - 16 * q^25 + 12 * q^26 + 32 * q^27 + 8 * q^28 - 8 * q^30 + 32 * q^31 + 22 * q^32 + 4 * q^35 - 2 * q^36 - 8 * q^37 - 32 * q^38 + 32 * q^39 - 24 * q^40 + 24 * q^41 - 8 * q^43 - 24 * q^44 + 12 * q^46 + 6 * q^48 - 32 * q^49 - 26 * q^50 - 16 * q^52 - 24 * q^53 + 2 * q^54 + 24 * q^55 - 12 * q^56 - 16 * q^58 + 24 * q^60 - 48 * q^62 + 22 * q^64 + 8 * q^65 + 24 * q^67 + 4 * q^68 + 6 * q^70 + 40 * q^71 + 2 * q^72 - 20 * q^74 - 16 * q^75 - 52 * q^76 - 16 * q^77 + 12 * q^78 - 24 * q^79 - 44 * q^80 + 32 * q^81 + 24 * q^82 + 8 * q^84 - 8 * q^85 - 76 * q^86 + 56 * q^88 + 24 * q^89 - 8 * q^90 - 96 * q^92 + 32 * q^93 + 32 * q^94 - 48 * q^95 + 22 * q^96 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$1$	$1$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.150941	+	1.40614i	−0.106732	+	0.994288i
$2$	−0.150941	+	1.40614i	−0.106732	+	0.994288i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.95443	−	0.424487i	−0.977217	−	0.212244i
$5$	−2.20890	+	0.347530i	−0.987848	+	0.155420i
$5$	−2.20890	+	0.347530i	−0.987848	+	0.155420i
$6$	−0.150941	+	1.40614i	−0.0616215	+	0.574052i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.891891	−	2.68413i	0.315331	−	0.948982i
$9$	1.00000			0.333333
$10$	−0.155261	−	3.15846i	−0.0490980	−	0.998794i
$11$		−	1.02458i		−	0.308922i	−0.987999	−	0.154461i	$-0.950636\pi$
$11$		−	1.02458i		−	0.308922i	0.987999	−	0.154461i	$-0.0493640\pi$
$12$	−1.95443	−	0.424487i	−0.564196	−	0.122539i
$13$	−0.301914			−0.0837358			−0.0418679	−	0.999123i	$-0.513331\pi$
$13$	−0.301914			−0.0837358			−0.0418679	+	0.999123i	$0.513331\pi$
$14$	1.40614	+	0.150941i	0.375805	+	0.0403407i
$15$	−2.20890	+	0.347530i	−0.570335	+	0.0897320i
$16$	3.63962	+	1.65927i	0.909905	+	0.414816i
$17$		−	4.15362i		−	1.00740i	−0.863879	−	0.503700i	$-0.831972\pi$
$17$		−	4.15362i		−	1.00740i	0.863879	−	0.503700i	$-0.168028\pi$
$18$	−0.150941	+	1.40614i	−0.0355772	+	0.331429i
$19$			2.92290i			0.670559i	0.942119	+	0.335280i	$0.108831\pi$
$19$			2.92290i			0.670559i	−0.942119	+	0.335280i	$0.891169\pi$
$20$	4.46466	+	0.258424i	0.998329	+	0.0577853i
$21$		−	1.00000i		−	0.218218i
$22$	1.44069	+	0.154651i	0.307157	+	0.0329717i
$23$		−	8.22770i		−	1.71559i	−0.513988	−	0.857797i	$-0.671832\pi$
$23$		−	8.22770i		−	1.71559i	0.513988	−	0.857797i	$-0.328168\pi$
$24$	0.891891	−	2.68413i	0.182057	−	0.547895i
$25$	4.75845	−	1.53532i	0.951689	−	0.307063i
$26$	0.0455712	−	0.424532i	0.00893725	−	0.0832575i
$27$	1.00000			0.192450
$28$	−0.424487	+	1.95443i	−0.0802206	+	0.369353i
$29$		−	7.23543i		−	1.34358i	−0.740739	−	0.671792i	$-0.765525\pi$
$29$		−	7.23543i		−	1.34358i	0.740739	−	0.671792i	$-0.234475\pi$
$30$	−0.155261	−	3.15846i	−0.0283467	−	0.576654i
$31$	6.43162			1.15515			0.577576	−	0.816337i	$-0.303999\pi$
$31$	6.43162			1.15515			0.577576	+	0.816337i	$0.303999\pi$
$32$	−2.88252	+	4.86735i	−0.509562	+	0.860434i
$33$		−	1.02458i		−	0.178356i
$34$	5.84055	+	0.626952i	1.00165	+	0.107521i
$35$	0.347530	+	2.20890i	0.0587434	+	0.373372i
$36$	−1.95443	−	0.424487i	−0.325739	−	0.0707479i
$37$	−9.18883			−1.51063			−0.755317	−	0.655360i	$-0.772517\pi$
$37$	−9.18883			−1.51063			−0.755317	+	0.655360i	$0.772517\pi$
$38$	−4.10999	−	0.441186i	−0.666729	−	0.0715698i
$39$	−0.301914			−0.0483449
$40$	−1.03728	+	6.23891i	−0.164008	+	0.986459i
$41$	10.4006			1.62431			0.812154	−	0.583443i	$-0.198295\pi$
$41$	10.4006			1.62431			0.812154	+	0.583443i	$0.198295\pi$
$42$	1.40614	+	0.150941i	0.216971	+	0.0232907i
$43$	8.63817			1.31731			0.658654	−	0.752446i	$-0.271126\pi$
$43$	8.63817			1.31731			0.658654	+	0.752446i	$0.271126\pi$
$44$	−0.434920	+	2.00247i	−0.0655667	+	0.301883i
$45$	−2.20890	+	0.347530i	−0.329283	+	0.0518068i
$46$	11.5693	+	1.24190i	1.70579	+	0.183108i
$47$			1.71255i			0.249801i	0.992169	+	0.124900i	$0.0398611\pi$
$47$			1.71255i			0.249801i	−0.992169	+	0.124900i	$0.960139\pi$
$48$	3.63962	+	1.65927i	0.525334	+	0.239494i
$49$	−1.00000			−0.142857
$50$	1.44062	+	6.92276i	0.203734	+	0.979026i
$51$		−	4.15362i		−	0.581623i
$52$	0.590070	+	0.128159i	0.0818280	+	0.0177724i
$53$	1.80258			0.247604			0.123802	−	0.992307i	$-0.460491\pi$
$53$	1.80258			0.247604			0.123802	+	0.992307i	$0.460491\pi$
$54$	−0.150941	+	1.40614i	−0.0205405	+	0.191351i
$55$	0.356072	+	2.26318i	0.0480127	+	0.305168i
$56$	−2.68413	−	0.891891i	−0.358681	−	0.119184i
$57$			2.92290i			0.387148i
$58$	10.1740	+	1.09212i	1.33591	+	0.143403i
$59$		−	7.16525i		−	0.932836i	−0.884565	−	0.466418i	$-0.845544\pi$
$59$		−	7.16525i		−	0.932836i	0.884565	−	0.466418i	$-0.154456\pi$
$60$	4.46466	+	0.258424i	0.576386	+	0.0333623i
$61$			3.32514i			0.425740i	0.977081	+	0.212870i	$0.0682811\pi$
$61$			3.32514i			0.425740i	−0.977081	+	0.212870i	$0.931719\pi$
$62$	−0.970796	+	9.04373i	−0.123291	+	1.14855i
$63$		−	1.00000i		−	0.125988i
$64$	−6.40906	−	4.78790i	−0.801132	−	0.598487i
$65$	0.666896	−	0.104924i	0.0827183	−	0.0130142i
$66$	1.44069	+	0.154651i	0.177337	+	0.0190362i
$67$	−3.42576			−0.418524			−0.209262	−	0.977860i	$-0.567106\pi$
$67$	−3.42576			−0.418524			−0.209262	+	0.977860i	$0.567106\pi$
$68$	−1.76316	+	8.11797i	−0.213814	+	0.984448i
$69$		−	8.22770i		−	0.990499i
$70$	−3.15846	+	0.155261i	−0.377509	+	0.0185573i
$71$	−10.5849			−1.25620			−0.628099	−	0.778133i	$-0.716167\pi$
$71$	−10.5849			−1.25620			−0.628099	+	0.778133i	$0.716167\pi$
$72$	0.891891	−	2.68413i	0.105110	−	0.316327i
$73$		−	6.04378i		−	0.707371i	−0.935364	−	0.353686i	$-0.884928\pi$
$73$		−	6.04378i		−	0.707371i	0.935364	−	0.353686i	$-0.115072\pi$
$74$	1.38697	−	12.9207i	0.161232	−	1.50200i
$75$	4.75845	−	1.53532i	0.549458	−	0.177283i
$76$	1.24073	−	5.71261i	0.142322	−	0.655282i
$77$	−1.02458			−0.116761
$78$	0.0455712	−	0.424532i	0.00515992	−	0.0480687i
$79$	−4.47042			−0.502962			−0.251481	−	0.967862i	$-0.580918\pi$
$79$	−4.47042			−0.502962			−0.251481	+	0.967862i	$0.580918\pi$
$80$	−8.61619	−	2.40027i	−0.963319	−	0.268358i
$81$	1.00000			0.111111
$82$	−1.56989	+	14.6247i	−0.173365	+	1.61503i
$83$	−5.42745			−0.595740			−0.297870	−	0.954606i	$-0.596276\pi$
$83$	−5.42745			−0.595740			−0.297870	+	0.954606i	$0.596276\pi$
$84$	−0.424487	+	1.95443i	−0.0463154	+	0.213246i
$85$	1.44351	+	9.17491i	0.156570	+	0.995159i
$86$	−1.30385	+	12.1464i	−0.140598	+	1.30978i
$87$		−	7.23543i		−	0.775719i
$88$	−2.75009	−	0.913811i	−0.293161	−	0.0974126i
$89$	4.53265			0.480459			0.240230	−	0.970716i	$-0.422777\pi$
$89$	4.53265			0.480459			0.240230	+	0.970716i	$0.422777\pi$
$90$	−0.155261	−	3.15846i	−0.0163660	−	0.332931i
$91$			0.301914i			0.0316492i
$92$	−3.49256	+	16.0805i	−0.364124	+	1.67651i
$93$	6.43162			0.666928
$94$	−2.40807	−	0.258494i	−0.248374	−	0.0266616i
$95$	−1.01580	−	6.45638i	−0.104219	−	0.662411i
$96$	−2.88252	+	4.86735i	−0.294196	+	0.496772i
$97$		−	4.47010i		−	0.453870i	−0.973910	−	0.226935i	$-0.927129\pi$
$97$		−	4.47010i		−	0.453870i	0.973910	−	0.226935i	$-0.0728705\pi$
$98$	0.150941	−	1.40614i	0.0152474	−	0.142041i
$99$		−	1.02458i		−	0.102974i
$100$	−9.95179	+	0.980776i	−0.995179	+	0.0980776i
$101$		−	17.3542i		−	1.72681i	−0.504513	−	0.863404i	$-0.668328\pi$
$101$		−	17.3542i		−	1.72681i	0.504513	−	0.863404i	$-0.331672\pi$
$102$	5.84055	+	0.626952i	0.578301	+	0.0620775i
$103$		−	0.359677i		−	0.0354400i	−0.999843	−	0.0177200i	$-0.994359\pi$
$103$		−	0.359677i		−	0.0354400i	0.999843	−	0.0177200i	$-0.00564075\pi$
$104$	−0.269274	+	0.810375i	−0.0264045	+	0.0794638i
$105$	0.347530	+	2.20890i	0.0339155	+	0.215566i
$106$	−0.272084	+	2.53467i	−0.0264271	+	0.246189i
$107$	−17.6014			−1.70159			−0.850795	−	0.525499i	$-0.823879\pi$
$107$	−17.6014			−1.70159			−0.850795	+	0.525499i	$0.823879\pi$
$108$	−1.95443	−	0.424487i	−0.188065	−	0.0408463i
$109$			13.9927i			1.34025i	0.742247	+	0.670127i	$0.233760\pi$
$109$			13.9927i			1.34025i	−0.742247	+	0.670127i	$0.766240\pi$
$110$	−3.23609	+	0.159077i	−0.308549	+	0.0151674i
$111$	−9.18883			−0.872165
$112$	1.65927	−	3.63962i	0.156786	−	0.343912i
$113$			7.55485i			0.710700i	0.934733	+	0.355350i	$0.115638\pi$
$113$			7.55485i			0.710700i	−0.934733	+	0.355350i	$0.884362\pi$
$114$	−4.10999	−	0.441186i	−0.384936	−	0.0413209i
$115$	2.85938	+	18.1741i	0.266638	+	1.69475i
$116$	−3.07135	+	14.1412i	−0.285167	+	1.31297i
$117$	−0.301914			−0.0279119
$118$	10.0753	+	1.08153i	0.927507	+	0.0995630i
$119$	−4.15362			−0.380762
$120$	−1.03728	+	6.23891i	−0.0946903	+	0.569532i
$121$	9.95024			0.904567
$122$	−4.67559	−	0.501900i	−0.423308	−	0.0454399i
$123$	10.4006			0.937795
$124$	−12.5702	−	2.73014i	−1.12883	−	0.245174i
$125$	−9.97734	+	5.04506i	−0.892401	+	0.451244i
$126$	1.40614	+	0.150941i	0.125268	+	0.0134469i
$127$		−	17.3725i		−	1.54156i	−0.637103	−	0.770778i	$-0.719868\pi$
$127$		−	17.3725i		−	1.54156i	0.637103	−	0.770778i	$-0.280132\pi$
$128$	7.69982	−	8.28932i	0.680575	−	0.732679i
$129$	8.63817			0.760548
$130$	0.0468756	+	0.953584i	0.00411126	+	0.0836348i
$131$		−	0.00846755i		−	0.000739813i	−1.00000		0.000369907i	$-0.999882\pi$
$131$		−	0.00846755i		−	0.000739813i	1.00000		0.000369907i	$-0.000117745\pi$
$132$	−0.434920	+	2.00247i	−0.0378549	+	0.174292i
$133$	2.92290			0.253448
$134$	0.517089	−	4.81709i	0.0446697	−	0.416133i
$135$	−2.20890	+	0.347530i	−0.190112	+	0.0299107i
$136$	−11.1488	−	3.70458i	−0.956004	−	0.317665i
$137$		−	5.55173i		−	0.474317i	−0.971471	−	0.237158i	$-0.923784\pi$
$137$		−	5.55173i		−	0.474317i	0.971471	−	0.237158i	$-0.0762160\pi$
$138$	11.5693	+	1.24190i	0.984841	+	0.105717i
$139$			4.35224i			0.369152i	0.982818	+	0.184576i	$0.0590912\pi$
$139$			4.35224i			0.369152i	−0.982818	+	0.184576i	$0.940909\pi$
$140$	0.258424	−	4.46466i	0.0218408	−	0.377333i
$141$			1.71255i			0.144223i
$142$	1.59770	−	14.8838i	0.134076	−	1.24902i
$143$			0.309334i			0.0258678i
$144$	3.63962	+	1.65927i	0.303302	+	0.138272i
$145$	2.51453	+	15.9823i	0.208820	+	1.32726i
$146$	8.49838	+	0.912256i	0.703331	+	0.0754988i
$147$	−1.00000			−0.0824786
$148$	17.9589	+	3.90054i	1.47622	+	0.320622i
$149$			15.4696i			1.26731i	0.773614	+	0.633657i	$0.218447\pi$
$149$			15.4696i			1.26731i	−0.773614	+	0.633657i	$0.781553\pi$
$150$	1.44062	+	6.92276i	0.117626	+	0.565241i
$151$	−11.2519			−0.915669			−0.457834	−	0.889038i	$-0.651375\pi$
$151$	−11.2519			−0.915669			−0.457834	+	0.889038i	$0.651375\pi$
$152$	7.84543	+	2.60691i	0.636348	+	0.211448i
$153$		−	4.15362i		−	0.335800i
$154$	0.154651	−	1.44069i	0.0124621	−	0.116094i
$155$	−14.2068	+	2.23518i	−1.14112	+	0.179534i
$156$	0.590070	+	0.128159i	0.0472434	+	0.0102609i
$157$	23.9531			1.91166			0.955832	−	0.293913i	$-0.0949576\pi$
$157$	23.9531			1.91166			0.955832	+	0.293913i	$0.0949576\pi$
$158$	0.674771	−	6.28602i	0.0536819	−	0.500089i
$159$	1.80258			0.142954
$160$	4.67564	−	11.7532i	0.369641	−	0.929174i
$161$	−8.22770			−0.648434
$162$	−0.150941	+	1.40614i	−0.0118591	+	0.110476i
$163$	2.69940			0.211433			0.105717	−	0.994396i	$-0.466286\pi$
$163$	2.69940			0.211433			0.105717	+	0.994396i	$0.466286\pi$
$164$	−20.3274	−	4.41494i	−1.58730	−	0.344749i
$165$	0.356072	+	2.26318i	0.0277201	+	0.176189i
$166$	0.819225	−	7.63172i	0.0635842	−	0.592337i
$167$			18.7605i			1.45173i	0.687837	+	0.725865i	$0.258560\pi$
$167$			18.7605i			1.45173i	−0.687837	+	0.725865i	$0.741440\pi$
$168$	−2.68413	−	0.891891i	−0.207085	−	0.0688109i
$169$	−12.9088			−0.992988
$170$	−13.1191	+	0.644897i	−1.00619	+	0.0494613i
$171$			2.92290i			0.223520i
$172$	−16.8827	−	3.66679i	−1.28730	−	0.279590i
$173$	10.1052			0.768284			0.384142	−	0.923274i	$-0.374497\pi$
$173$	10.1052			0.768284			0.384142	+	0.923274i	$0.374497\pi$
$174$	10.1740	+	1.09212i	0.771288	+	0.0827937i
$175$	−1.53532	−	4.75845i	−0.116059	−	0.359705i
$176$	1.70004	−	3.72907i	0.128146	−	0.281089i
$177$		−	7.16525i		−	0.538573i
$178$	−0.684163	+	6.37351i	−0.0512802	+	0.477715i
$179$		−	4.85789i		−	0.363095i	−0.983382	−	0.181548i	$-0.941889\pi$
$179$		−	4.85789i		−	0.363095i	0.983382	−	0.181548i	$-0.0581107\pi$
$180$	4.46466	+	0.258424i	0.332776	+	0.0192618i
$181$		−	13.8496i		−	1.02943i	−0.857361	−	0.514715i	$-0.827898\pi$
$181$		−	13.8496i		−	1.02943i	0.857361	−	0.514715i	$-0.172102\pi$
$182$	−0.424532	−	0.0455712i	−0.0314684	−	0.00337796i
$183$			3.32514i			0.245801i
$184$	−22.0842	−	7.33822i	−1.62807	−	0.540981i
$185$	20.2972	−	3.19340i	1.49228	−	0.234783i
$186$	−0.970796	+	9.04373i	−0.0711822	+	0.663118i
$187$	−4.25570			−0.311208
$188$	0.726955	−	3.34706i	0.0530186	−	0.244109i
$189$		−	1.00000i		−	0.0727393i
$190$	9.23187	−	0.453814i	0.669751	−	0.0329231i
$191$	−9.71830			−0.703192			−0.351596	−	0.936152i	$-0.614361\pi$
$191$	−9.71830			−0.703192			−0.351596	+	0.936152i	$0.614361\pi$
$192$	−6.40906	−	4.78790i	−0.462534	−	0.345537i
$193$		−	15.6000i		−	1.12291i	−0.827507	−	0.561456i	$-0.810241\pi$
$193$		−	15.6000i		−	1.12291i	0.827507	−	0.561456i	$-0.189759\pi$
$194$	6.28557	+	0.674723i	0.451278	+	0.0484423i
$195$	0.666896	−	0.104924i	0.0477574	−	0.00751378i
$196$	1.95443	+	0.424487i	0.139602	+	0.0303205i
$197$	20.6643			1.47227			0.736137	−	0.676833i	$-0.236648\pi$
$197$	20.6643			1.47227			0.736137	+	0.676833i	$0.236648\pi$
$198$	1.44069	+	0.154651i	0.102386	+	0.0109906i
$199$	−1.69565			−0.120201			−0.0601006	−	0.998192i	$-0.519142\pi$
$199$	−1.69565			−0.120201			−0.0601006	+	0.998192i	$0.519142\pi$
$200$	0.123031	−	14.1416i	0.00869962	−	0.999962i
$201$	−3.42576			−0.241635
$202$	24.4024	+	2.61947i	1.71694	+	0.184305i
$203$	−7.23543			−0.507827
$204$	−1.76316	+	8.11797i	−0.123446	+	0.568372i
$205$	−22.9739	+	3.61454i	−1.60457	+	0.252450i
$206$	0.505754	+	0.0542900i	0.0352376	+	0.00378257i
$207$		−	8.22770i		−	0.571865i
$208$	−1.09885	−	0.500955i	−0.0761917	−	0.0347350i
$209$	2.99474			0.207150
$210$	−3.15846	+	0.155261i	−0.217955	+	0.0107141i
$211$			11.9624i			0.823524i	0.911291	+	0.411762i	$0.135086\pi$
$211$			11.9624i			0.823524i	−0.911291	+	0.411762i	$0.864914\pi$
$212$	−3.52303	−	0.765173i	−0.241962	−	0.0525523i
$213$	−10.5849			−0.725267
$214$	2.65677	−	24.7499i	0.181613	−	1.69187i
$215$	−19.0808	+	3.00203i	−1.30130	+	0.204736i
$216$	0.891891	−	2.68413i	0.0606855	−	0.182632i
$217$		−	6.43162i		−	0.436607i
$218$	−19.6756	−	2.11207i	−1.33260	−	0.143047i
$219$		−	6.04378i		−	0.408401i
$220$	0.264775	−	4.57439i	0.0178511	−	0.308405i
$221$			1.25403i			0.0843555i
$222$	1.38697	−	12.9207i	0.0930875	−	0.867183i
$223$			3.72092i			0.249171i	0.992209	+	0.124586i	$0.0397601\pi$
$223$			3.72092i			0.249171i	−0.992209	+	0.124586i	$0.960240\pi$
$224$	4.86735	+	2.88252i	0.325213	+	0.192596i
$225$	4.75845	−	1.53532i	0.317230	−	0.102354i
$226$	−10.6231	−	1.14034i	−0.706641	−	0.0758541i
$227$	−15.1069			−1.00268			−0.501341	−	0.865250i	$-0.667160\pi$
$227$	−15.1069			−1.00268			−0.501341	+	0.865250i	$0.667160\pi$
$228$	1.24073	−	5.71261i	0.0821696	−	0.378327i
$229$			2.17339i			0.143621i	0.997418	+	0.0718107i	$0.0228777\pi$
$229$			2.17339i			0.143621i	−0.997418	+	0.0718107i	$0.977122\pi$
$230$	−25.9869	+	1.27745i	−1.71353	+	0.0842323i
$231$	−1.02458			−0.0674122
$232$	−19.4208	−	6.45321i	−1.27504	−	0.423674i
$233$			3.91693i			0.256606i	0.991735	+	0.128303i	$0.0409531\pi$
$233$			3.91693i			0.256606i	−0.991735	+	0.128303i	$0.959047\pi$
$234$	0.0455712	−	0.424532i	0.00297908	−	0.0277525i
$235$	−0.595162	−	3.78284i	−0.0388241	−	0.246765i
$236$	−3.04156	+	14.0040i	−0.197989	+	0.911583i
$237$	−4.47042			−0.290385
$238$	0.626952	−	5.84055i	0.0406393	−	0.378587i
$239$	−16.6158			−1.07479			−0.537393	−	0.843332i	$-0.680591\pi$
$239$	−16.6158			−1.07479			−0.537393	+	0.843332i	$0.680591\pi$
$240$	−8.61619	−	2.40027i	−0.556173	−	0.154936i
$241$	24.1578			1.55614			0.778071	−	0.628177i	$-0.216198\pi$
$241$	24.1578			1.55614			0.778071	+	0.628177i	$0.216198\pi$
$242$	−1.50190	+	13.9914i	−0.0965459	+	0.899400i
$243$	1.00000			0.0641500
$244$	1.41148	−	6.49876i	0.0903606	−	0.416040i
$245$	2.20890	−	0.347530i	0.141121	−	0.0222029i
$246$	−1.56989	+	14.6247i	−0.100092	+	0.932438i
$247$		−	0.882464i		−	0.0561498i
$248$	5.73630	−	17.2633i	0.364256	−	1.09622i
$249$	−5.42745			−0.343950
$250$	−5.58805	−	14.7910i	−0.353419	−	0.935465i
$251$		−	18.0430i		−	1.13887i	−0.822038	−	0.569433i	$-0.807163\pi$
$251$		−	18.0430i		−	1.13887i	0.822038	−	0.569433i	$-0.192837\pi$
$252$	−0.424487	+	1.95443i	−0.0267402	+	0.123118i
$253$	−8.42992			−0.529984
$254$	24.4280	+	2.62222i	1.53275	+	0.164533i
$255$	1.44351	+	9.17491i	0.0903960	+	0.574555i
$256$	10.4937	+	12.0782i	0.655855	+	0.754887i
$257$			16.8090i			1.04852i	0.851559	+	0.524258i	$0.175657\pi$
$257$			16.8090i			1.04852i	−0.851559	+	0.524258i	$0.824343\pi$
$258$	−1.30385	+	12.1464i	−0.0811745	+	0.756204i
$259$			9.18883i			0.570966i
$260$	−1.34794	−	0.0780216i	−0.0835959	−	0.00483870i
$261$		−	7.23543i		−	0.447862i
$262$	0.0119065	+	0.00127810i	0.000735588	+	7.89614e-5i
$263$			5.18982i			0.320018i	0.987116	+	0.160009i	$0.0511524\pi$
$263$			5.18982i			0.320018i	−0.987116	+	0.160009i	$0.948848\pi$
$264$	−2.75009	−	0.913811i	−0.169257	−	0.0562412i
$265$	−3.98171	+	0.626452i	−0.244595	+	0.0384826i
$266$	−0.441186	+	4.10999i	−0.0270508	+	0.252000i
$267$	4.53265			0.277393
$268$	6.69543	+	1.45419i	0.408988	+	0.0888290i
$269$		−	1.81394i		−	0.110598i	−0.998470	−	0.0552990i	$-0.982389\pi$
$269$		−	1.81394i		−	0.110598i	0.998470	−	0.0552990i	$-0.0176112\pi$
$270$	−0.155261	−	3.15846i	−0.00944891	−	0.192218i
$271$	−3.23107			−0.196274			−0.0981369	−	0.995173i	$-0.531288\pi$
$271$	−3.23107			−0.196274			−0.0981369	+	0.995173i	$0.531288\pi$
$272$	6.89195	−	15.1176i	0.417886	−	0.916639i
$273$			0.301914i			0.0182727i
$274$	7.80649	+	0.837985i	0.471607	+	0.0506245i
$275$	−1.57305	−	4.87539i	−0.0948585	−	0.293997i
$276$	−3.49256	+	16.0805i	−0.210227	+	0.967932i
$277$	−13.5526			−0.814299			−0.407149	−	0.913362i	$-0.633477\pi$
$277$	−13.5526			−0.814299			−0.407149	+	0.913362i	$0.633477\pi$
$278$	−6.11984	−	0.656932i	−0.367043	−	0.0394002i
$279$	6.43162			0.385051
$280$	6.23891	+	1.03728i	0.372846	+	0.0619893i
$281$	−23.9254			−1.42727			−0.713636	−	0.700516i	$-0.752953\pi$
$281$	−23.9254			−1.42727			−0.713636	+	0.700516i	$0.752953\pi$
$282$	−2.40807	−	0.258494i	−0.143399	−	0.0153931i
$283$	14.1251			0.839648			0.419824	−	0.907606i	$-0.362092\pi$
$283$	14.1251			0.839648			0.419824	+	0.907606i	$0.362092\pi$
$284$	20.6875	+	4.49316i	1.22758	+	0.266620i
$285$	−1.01580	−	6.45638i	−0.0601706	−	0.382443i
$286$	−0.434965	−	0.0466912i	−0.0257200	−	0.00276091i
$287$		−	10.4006i		−	0.613931i
$288$	−2.88252	+	4.86735i	−0.169854	+	0.286811i
$289$	−0.252541			−0.0148553
$290$	−22.8528	+	1.12338i	−1.34196	+	0.0659673i
$291$		−	4.47010i		−	0.262042i
$292$	−2.56551	+	11.8122i	−0.150135	+	0.691255i
$293$	23.1137			1.35032			0.675158	−	0.737673i	$-0.264075\pi$
$293$	23.1137			1.35032			0.675158	+	0.737673i	$0.264075\pi$
$294$	0.150941	−	1.40614i	0.00880307	−	0.0820075i
$295$	2.49014	+	15.8273i	0.144982	+	0.921500i
$296$	−8.19543	+	24.6640i	−0.476350	+	1.43356i
$297$		−	1.02458i		−	0.0594520i
$298$	−21.7523	−	2.33499i	−1.26008	−	0.135262i
$299$			2.48406i			0.143657i
$300$	−9.95179	+	0.980776i	−0.574567	+	0.0566251i
$301$		−	8.63817i		−	0.497896i
$302$	1.69838	−	15.8217i	0.0977307	−	0.910438i
$303$		−	17.3542i		−	0.996973i
$304$	−4.84987	+	10.6382i	−0.278159	+	0.610145i
$305$	−1.15559	−	7.34488i	−0.0661687	−	0.420567i
$306$	5.84055	+	0.626952i	0.333882	+	0.0358405i
$307$	−10.5228			−0.600567			−0.300283	−	0.953850i	$-0.597081\pi$
$307$	−10.5228			−0.600567			−0.300283	+	0.953850i	$0.597081\pi$
$308$	2.00247	+	0.434920i	0.114101	+	0.0247819i
$309$		−	0.359677i		−	0.0204613i
$310$	−0.998583	−	20.3140i	−0.0567157	−	1.15376i
$311$	7.69672			0.436441			0.218220	−	0.975899i	$-0.429975\pi$
$311$	7.69672			0.436441			0.218220	+	0.975899i	$0.429975\pi$
$312$	−0.269274	+	0.810375i	−0.0152447	+	0.0458784i
$313$			32.2218i			1.82128i	0.413198	+	0.910641i	$0.364412\pi$
$313$			32.2218i			1.82128i	−0.413198	+	0.910641i	$0.635588\pi$
$314$	−3.61551	+	33.6813i	−0.204035	+	1.90074i
$315$	0.347530	+	2.20890i	0.0195811	+	0.124457i
$316$	8.73714	+	1.89764i	0.491503	+	0.106751i
$317$	20.2834			1.13923			0.569615	−	0.821911i	$-0.307092\pi$
$317$	20.2834			1.13923			0.569615	+	0.821911i	$0.307092\pi$
$318$	−0.272084	+	2.53467i	−0.0152577	+	0.142137i
$319$	−7.41325			−0.415062
$320$	15.8209	+	8.34862i	0.884415	+	0.466702i
$321$	−17.6014			−0.982413
$322$	1.24190	−	11.5693i	0.0692083	−	0.644730i
$323$	12.1406			0.675522
$324$	−1.95443	−	0.424487i	−0.108580	−	0.0235826i
$325$	−1.43664	+	0.463534i	−0.0796905	+	0.0257122i
$326$	−0.407450	+	3.79572i	−0.0225666	+	0.210225i
$327$			13.9927i			0.773796i
$328$	9.27625	−	27.9166i	0.512195	−	1.54144i
$329$	1.71255			0.0944158
$330$	−3.23609	+	0.159077i	−0.178141	+	0.00875692i
$331$		−	29.7725i		−	1.63644i	−0.574902	−	0.818222i	$-0.694960\pi$
$331$		−	29.7725i		−	1.63644i	0.574902	−	0.818222i	$-0.305040\pi$
$332$	10.6076	+	2.30388i	0.582167	+	0.126442i
$333$	−9.18883			−0.503545
$334$	−26.3798	−	2.83173i	−1.44344	−	0.154945i
$335$	7.56716	−	1.19056i	0.413438	−	0.0650471i
$336$	1.65927	−	3.63962i	0.0905203	−	0.198558i
$337$			15.4404i			0.841091i	0.907271	+	0.420546i	$0.138161\pi$
$337$			15.4404i			0.841091i	−0.907271	+	0.420546i	$0.861839\pi$
$338$	1.94848	−	18.1516i	0.105983	−	0.987316i
$339$			7.55485i			0.410323i
$340$	1.07339	−	18.5445i	0.0582129	−	1.00572i
$341$		−	6.58969i		−	0.356852i
$342$	−4.10999	−	0.441186i	−0.222243	−	0.0238566i
$343$			1.00000i			0.0539949i
$344$	7.70430	−	23.1859i	0.415388	−	1.25010i
$345$	2.85938	+	18.1741i	0.153944	+	0.978463i
$346$	−1.52529	+	14.2093i	−0.0820001	+	0.763896i
$347$	−1.41233			−0.0758178			−0.0379089	−	0.999281i	$-0.512070\pi$
$347$	−1.41233			−0.0758178			−0.0379089	+	0.999281i	$0.512070\pi$
$348$	−3.07135	+	14.1412i	−0.164642	+	0.758046i
$349$			16.2491i			0.869797i	0.900479	+	0.434898i	$0.143216\pi$
$349$			16.2491i			0.869797i	−0.900479	+	0.434898i	$0.856784\pi$
$350$	6.92276	−	1.44062i	0.370037	−	0.0770043i
$351$	−0.301914			−0.0161150
$352$	4.98697	+	2.95336i	0.265807	+	0.157415i
$353$			19.4895i			1.03732i	0.854980	+	0.518660i	$0.173569\pi$
$353$			19.4895i			1.03732i	−0.854980	+	0.518660i	$0.826431\pi$
$354$	10.0753	+	1.08153i	0.535497	+	0.0574827i
$355$	23.3810	−	3.67858i	1.24093	−	0.195239i
$356$	−8.85875	−	1.92405i	−0.469513	−	0.101974i
$357$	−4.15362			−0.219833
$358$	6.83084	+	0.733255i	0.361021	+	0.0387537i
$359$	34.2909			1.80980			0.904901	−	0.425622i	$-0.139945\pi$
$359$	34.2909			1.80980			0.904901	+	0.425622i	$0.139945\pi$
$360$	−1.03728	+	6.23891i	−0.0546695	+	0.328820i
$361$	10.4567			0.550350
$362$	19.4744	+	2.09047i	1.02355	+	0.109873i
$363$	9.95024			0.522252
$364$	0.128159	−	0.590070i	0.00671734	−	0.0309281i
$365$	2.10040	+	13.3501i	0.109940	+	0.698775i
$366$	−4.67559	−	0.501900i	−0.244397	−	0.0262347i
$367$			25.2416i			1.31760i	0.752317	+	0.658802i	$0.228936\pi$
$367$			25.2416i			1.31760i	−0.752317	+	0.658802i	$0.771064\pi$
$368$	13.6519	−	29.9457i	0.711657	−	1.56103i
$369$	10.4006			0.541436
$370$	1.42667	+	29.0226i	0.0741691	+	1.50881i
$371$		−	1.80258i		−	0.0935854i
$372$	−12.5702	−	2.73014i	−0.651733	−	0.141551i
$373$	2.77058			0.143455			0.0717277	−	0.997424i	$-0.477149\pi$
$373$	2.77058			0.143455			0.0717277	+	0.997424i	$0.477149\pi$
$374$	0.642361	−	5.98409i	0.0332157	−	0.309430i
$375$	−9.97734	+	5.04506i	−0.515228	+	0.260526i
$376$	4.59669	+	1.52741i	0.237056	+	0.0787700i
$377$			2.18447i			0.112506i
$378$	1.40614	+	0.150941i	0.0723238	+	0.00776358i
$379$			17.0485i			0.875722i	0.899043	+	0.437861i	$0.144264\pi$
$379$			17.0485i			0.875722i	−0.899043	+	0.437861i	$0.855736\pi$
$380$	−0.755346	+	13.0498i	−0.0387484	+	0.669439i
$381$		−	17.3725i		−	0.890018i
$382$	1.46689	−	13.6653i	0.0750527	−	0.699175i
$383$			15.2557i			0.779532i	0.920914	+	0.389766i	$0.127444\pi$
$383$			15.2557i			0.779532i	−0.920914	+	0.389766i	$0.872556\pi$
$384$	7.69982	−	8.28932i	0.392930	−	0.423012i
$385$	2.26318	−	0.356072i	0.115343	−	0.0181471i
$386$	21.9357	+	2.35468i	1.11650	+	0.119850i
$387$	8.63817			0.439103
$388$	−1.89750	+	8.73652i	−0.0963311	+	0.443530i
$389$		−	24.5266i		−	1.24355i	−0.783197	−	0.621773i	$-0.786413\pi$
$389$		−	24.5266i		−	1.24355i	0.783197	−	0.621773i	$-0.213587\pi$
$390$	0.0468756	+	0.953584i	0.00237364	+	0.0482866i
$391$	−34.1747			−1.72829
$392$	−0.891891	+	2.68413i	−0.0450473	+	0.135569i
$393$		−	0.00846755i		−	0.000427131i
$394$	−3.11910	+	29.0569i	−0.157138	+	1.46386i
$395$	9.87470	−	1.55361i	0.496850	−	0.0781705i
$396$	−0.434920	+	2.00247i	−0.0218556	+	0.100628i
$397$	1.88981			0.0948466			0.0474233	−	0.998875i	$-0.484899\pi$
$397$	1.88981			0.0948466			0.0474233	+	0.998875i	$0.484899\pi$
$398$	0.255943	−	2.38431i	0.0128293	−	0.119515i
$399$	2.92290			0.146328
$400$	19.8664	+	2.30755i	0.993322	+	0.115377i
$401$	9.58031			0.478418			0.239209	−	0.970968i	$-0.423112\pi$
$401$	9.58031			0.478418			0.239209	+	0.970968i	$0.423112\pi$
$402$	0.517089	−	4.81709i	0.0257901	−	0.240255i
$403$	−1.94179			−0.0967277
$404$	−7.36665	+	33.9177i	−0.366504	+	1.68747i
$405$	−2.20890	+	0.347530i	−0.109761	+	0.0172689i
$406$	1.09212	−	10.1740i	0.0542012	−	0.504927i
$407$			9.41466i			0.466667i
$408$	−11.1488	−	3.70458i	−0.551949	−	0.183404i
$409$	10.5903			0.523657			0.261829	−	0.965114i	$-0.415674\pi$
$409$	10.5903			0.523657			0.261829	+	0.965114i	$0.415674\pi$
$410$	−1.61482	−	32.8501i	−0.0797503	−	1.62235i
$411$		−	5.55173i		−	0.273847i
$412$	−0.152678	+	0.702964i	−0.00752192	+	0.0346326i
$413$	−7.16525			−0.352579
$414$	11.5693	+	1.24190i	0.568598	+	0.0610360i
$415$	11.9887	−	1.88620i	0.588500	−	0.0925901i
$416$	0.870273	−	1.46952i	0.0426686	−	0.0720491i
$417$			4.35224i			0.213130i
$418$	−0.452029	+	4.21100i	−0.0221095	+	0.205967i
$419$			30.2179i			1.47624i	0.674669	+	0.738121i	$0.264286\pi$
$419$			30.2179i			1.47624i	−0.674669	+	0.738121i	$0.735714\pi$
$420$	0.258424	−	4.46466i	0.0126098	−	0.217853i
$421$		−	10.4041i		−	0.507066i	−0.967327	−	0.253533i	$-0.918407\pi$
$421$		−	10.4041i		−	0.507066i	0.967327	−	0.253533i	$-0.0815926\pi$
$422$	−16.8207	−	1.80561i	−0.818820	−	0.0878959i
$423$			1.71255i			0.0832669i
$424$	1.60771	−	4.83835i	0.0780771	−	0.234971i
$425$	−6.37712	−	19.7648i	−0.309336	−	0.958732i
$426$	1.59770	−	14.8838i	0.0774088	−	0.721124i
$427$	3.32514			0.160915
$428$	34.4007	+	7.47156i	1.66282	+	0.361152i
$429$			0.309334i			0.0149348i
$430$	−1.34117	−	27.2833i	−0.0646772	−	1.31572i
$431$	4.75821			0.229195			0.114598	−	0.993412i	$-0.463442\pi$
$431$	4.75821			0.229195			0.114598	+	0.993412i	$0.463442\pi$
$432$	3.63962	+	1.65927i	0.175111	+	0.0798314i
$433$		−	28.3237i		−	1.36115i	−0.732679	−	0.680575i	$-0.761730\pi$
$433$		−	28.3237i		−	1.36115i	0.732679	−	0.680575i	$-0.238270\pi$
$434$	9.04373	+	0.970796i	0.434113	+	0.0465997i
$435$	2.51453	+	15.9823i	0.120563	+	0.766293i
$436$	5.93971	−	27.3477i	0.284460	−	1.30972i
$437$	24.0488			1.15041
$438$	8.49838	+	0.912256i	0.406068	+	0.0435893i
$439$	18.1847			0.867909			0.433954	−	0.900935i	$-0.357118\pi$
$439$	18.1847			0.867909			0.433954	+	0.900935i	$0.357118\pi$
$440$	6.39225	+	1.06277i	0.304738	+	0.0506657i
$441$	−1.00000			−0.0476190
$442$	−1.76334	−	0.189285i	−0.0838736	−	0.00900339i
$443$	34.8499			1.65577			0.827884	−	0.560900i	$-0.189545\pi$
$443$	34.8499			1.65577			0.827884	+	0.560900i	$0.189545\pi$
$444$	17.9589	+	3.90054i	0.852294	+	0.185111i
$445$	−10.0121	+	1.57523i	−0.474621	+	0.0746732i
$446$	−5.23212	−	0.561640i	−0.247748	−	0.0265944i
$447$			15.4696i			0.731685i
$448$	−4.78790	+	6.40906i	−0.226207	+	0.302800i
$449$	4.49487			0.212126			0.106063	−	0.994359i	$-0.466175\pi$
$449$	4.49487			0.212126			0.106063	+	0.994359i	$0.466175\pi$
$450$	1.44062	+	6.92276i	0.0679114	+	0.326342i
$451$		−	10.6563i		−	0.501784i
$452$	3.20694	−	14.7654i	0.150842	−	0.694508i
$453$	−11.2519			−0.528662
$454$	2.28026	−	21.2424i	0.107018	−	0.996954i
$455$	−0.104924	−	0.666896i	−0.00491892	−	0.0312646i
$456$	7.84543	+	2.60691i	0.367396	+	0.122080i
$457$			30.4030i			1.42219i	0.703094	+	0.711097i	$0.251801\pi$
$457$			30.4030i			1.42219i	−0.703094	+	0.711097i	$0.748199\pi$
$458$	−3.05608	−	0.328053i	−0.142801	−	0.0153289i
$459$		−	4.15362i		−	0.193874i
$460$	2.12623	−	36.7339i	0.0991361	−	1.71273i
$461$			3.09587i			0.144189i	0.997398	+	0.0720946i	$0.0229683\pi$
$461$			3.09587i			0.144189i	−0.997398	+	0.0720946i	$0.977032\pi$
$462$	0.154651	−	1.44069i	0.00719501	−	0.0670272i
$463$		−	19.3315i		−	0.898410i	−0.893429	−	0.449205i	$-0.851707\pi$
$463$		−	19.3315i		−	0.898410i	0.893429	−	0.449205i	$-0.148293\pi$
$464$	12.0055	−	26.3342i	0.557341	−	1.22253i
$465$	−14.2068	+	2.23518i	−0.658824	+	0.103654i
$466$	−5.50773	−	0.591226i	−0.255141	−	0.0273880i
$467$	−33.2290			−1.53766			−0.768828	−	0.639456i	$-0.779160\pi$
$467$	−33.2290			−1.53766			−0.768828	+	0.639456i	$0.779160\pi$
$468$	0.590070	+	0.128159i	0.0272760	+	0.00592413i
$469$			3.42576i			0.158187i
$470$	5.40902	−	0.265893i	0.249499	−	0.0122647i
$471$	23.9531			1.10370
$472$	−19.2324	−	6.39062i	−0.885244	−	0.294152i
$473$		−	8.85047i		−	0.406945i
$474$	0.674771	−	6.28602i	0.0309933	−	0.288726i
$475$	4.48758	+	13.9085i	0.205904	+	0.638164i
$476$	8.11797	+	1.76316i	0.372087	+	0.0808142i
$477$	1.80258			0.0825345
$478$	2.50801	−	23.3641i	0.114714	−	1.06865i
$479$	35.4373			1.61917			0.809587	−	0.587000i	$-0.199691\pi$
$479$	35.4373			1.61917			0.809587	+	0.587000i	$0.199691\pi$
$480$	4.67564	−	11.7532i	0.213413	−	0.536459i
$481$	2.77423			0.126494
$482$	−3.64641	+	33.9692i	−0.166089	+	1.54725i
$483$	−8.22770			−0.374373
$484$	−19.4471	−	4.22375i	−0.883958	−	0.191989i
$485$	1.55350	+	9.87399i	0.0705407	+	0.448355i
$486$	−0.150941	+	1.40614i	−0.00684683	+	0.0637836i
$487$			26.2747i			1.19062i	0.803497	+	0.595309i	$0.202970\pi$
$487$			26.2747i			1.19062i	−0.803497	+	0.595309i	$0.797030\pi$
$488$	8.92508	+	2.96566i	0.404019	+	0.134249i
$489$	2.69940			0.122071
$490$	0.155261	+	3.15846i	0.00701400	+	0.142685i
$491$		−	38.4357i		−	1.73458i	−0.497806	−	0.867289i	$-0.665861\pi$
$491$		−	38.4357i		−	1.73458i	0.497806	−	0.867289i	$-0.334139\pi$
$492$	−20.3274	−	4.41494i	−0.916429	−	0.199041i
$493$	−30.0532			−1.35353
$494$	1.24086	+	0.133200i	0.0558291	+	0.00599296i
$495$	0.356072	+	2.26318i	0.0160042	+	0.101723i
$496$	23.4087	+	10.6718i	1.05108	+	0.479176i
$497$			10.5849i			0.474798i
$498$	0.819225	−	7.63172i	0.0367104	−	0.341986i
$499$			13.8004i			0.617789i	0.951096	+	0.308894i	$0.0999589\pi$
$499$			13.8004i			0.617789i	−0.951096	+	0.308894i	$0.900041\pi$
$500$	21.6416	−	5.62498i	0.967843	−	0.251557i
$501$			18.7605i			0.838156i
$502$	25.3710	+	2.72344i	1.13236	+	0.121553i
$503$			40.9495i			1.82585i	0.408132	+	0.912923i	$0.366180\pi$
$503$			40.9495i			1.82585i	−0.408132	+	0.912923i	$0.633820\pi$
$504$	−2.68413	−	0.891891i	−0.119560	−	0.0397280i
$505$	6.03112	+	38.3337i	0.268381	+	1.70583i
$506$	1.27242	−	11.8536i	0.0565660	−	0.526957i
$507$	−12.9088			−0.573302
$508$	−7.37439	+	33.9533i	−0.327186	+	1.50643i
$509$			9.38948i			0.416181i	0.978110	+	0.208091i	$0.0667249\pi$
$509$			9.38948i			0.416181i	−0.978110	+	0.208091i	$0.933275\pi$
$510$	−13.1191	+	0.644897i	−0.580921	+	0.0285565i
$511$	−6.04378			−0.267361
$512$	−18.5675	+	12.9324i	−0.820575	+	0.571538i
$513$			2.92290i			0.129049i
$514$	−23.6357	−	2.53717i	−1.04253	−	0.111910i
$515$	0.124999	+	0.794489i	0.00550810	+	0.0350093i
$516$	−16.8827	−	3.66679i	−0.743220	−	0.161422i
$517$	1.75464			0.0771688
$518$	−12.9207	−	1.38697i	−0.567704	−	0.0609401i
$519$	10.1052			0.443569
$520$	0.313169	−	1.88361i	0.0137334	−	0.0826019i
$521$	−4.53997			−0.198900			−0.0994498	−	0.995043i	$-0.531708\pi$
$521$	−4.53997			−0.198900			−0.0994498	+	0.995043i	$0.531708\pi$
$522$	10.1740	+	1.09212i	0.445303	+	0.0478010i
$523$	−1.71593			−0.0750325			−0.0375163	−	0.999296i	$-0.511945\pi$
$523$	−1.71593			−0.0750325			−0.0375163	+	0.999296i	$0.511945\pi$
$524$	−0.00359437	+	0.0165493i	−0.000157021	+	0.000722958i
$525$	−1.53532	−	4.75845i	−0.0670067	−	0.207676i
$526$	−7.29759	−	0.783358i	−0.318190	−	0.0341560i
$527$		−	26.7145i		−	1.16370i
$528$	1.70004	−	3.72907i	0.0739850	−	0.162287i
$529$	−44.6951			−1.94326
$530$	−0.279871	−	5.69339i	−0.0121568	−	0.247305i
$531$		−	7.16525i		−	0.310945i
$532$	−5.71261	−	1.24073i	−0.247673	−	0.0537927i
$533$	−3.14010			−0.136013
$534$	−0.684163	+	6.37351i	−0.0296066	+	0.275809i
$535$	38.8796	−	6.11701i	1.68091	−	0.264462i
$536$	−3.05541	+	9.19518i	−0.131974	+	0.397171i
$537$		−	4.85789i		−	0.209633i
$538$	2.55065	+	0.273799i	0.109966	+	0.0118043i
$539$			1.02458i			0.0441317i
$540$	4.46466	+	0.258424i	0.192129	+	0.0111208i
$541$			22.8888i			0.984068i	0.870576	+	0.492034i	$0.163746\pi$
$541$			22.8888i			0.984068i	−0.870576	+	0.492034i	$0.836254\pi$
$542$	0.487702	−	4.54333i	0.0209486	−	0.195153i
$543$		−	13.8496i		−	0.594342i
$544$	20.2171	+	11.9729i	0.866801	+	0.513333i
$545$	−4.86288	−	30.9083i	−0.208303	−	1.32397i
$546$	−0.424532	−	0.0455712i	−0.0181683	−	0.00195027i
$547$	−6.87767			−0.294068			−0.147034	−	0.989131i	$-0.546973\pi$
$547$	−6.87767			−0.294068			−0.147034	+	0.989131i	$0.546973\pi$
$548$	−2.35664	+	10.8505i	−0.100671	+	0.463510i
$549$			3.32514i			0.141913i
$550$	7.09290	−	1.47603i	0.302442	−	0.0629379i
$551$	21.1484			0.900953
$552$	−22.0842	−	7.33822i	−0.939965	−	0.312335i
$553$			4.47042i			0.190102i
$554$	2.04565	−	19.0568i	0.0869114	−	0.809647i
$555$	20.2972	−	3.19340i	0.861567	−	0.135552i
$556$	1.84747	−	8.50616i	0.0783502	−	0.360742i
$557$	44.0344			1.86580			0.932898	−	0.360141i	$-0.117271\pi$
$557$	44.0344			1.86580			0.932898	+	0.360141i	$0.117271\pi$
$558$	−0.970796	+	9.04373i	−0.0410971	+	0.382851i
$559$	−2.60798			−0.110306
$560$	−2.40027	+	8.61619i	−0.101430	+	0.364100i
$561$	−4.25570			−0.179676
$562$	3.61134	−	33.6424i	0.152335	−	1.41912i
$563$	−31.2793			−1.31826			−0.659132	−	0.752028i	$-0.729076\pi$
$563$	−31.2793			−1.31826			−0.659132	+	0.752028i	$0.729076\pi$
$564$	0.726955	−	3.34706i	0.0306103	−	0.140937i
$565$	−2.62554	−	16.6879i	−0.110457	−	0.702064i
$566$	−2.13205	+	19.8618i	−0.0896169	+	0.834852i
$567$		−	1.00000i		−	0.0419961i
$568$	−9.44060	+	28.4112i	−0.396119	+	1.19211i
$569$	−3.77928			−0.158436			−0.0792178	−	0.996857i	$-0.525242\pi$
$569$	−3.77928			−0.158436			−0.0792178	+	0.996857i	$0.525242\pi$
$570$	9.23187	−	0.453814i	0.386681	−	0.0190082i
$571$			22.3461i			0.935155i	0.883952	+	0.467578i	$0.154873\pi$
$571$			22.3461i			0.935155i	−0.883952	+	0.467578i	$0.845127\pi$
$572$	0.131308	−	0.604573i	0.00549028	−	0.0252784i
$573$	−9.71830			−0.405988
$574$	14.6247	+	1.56989i	0.610424	+	0.0655258i
$575$	−12.6321	−	39.1511i	−0.526796	−	1.63271i
$576$	−6.40906	−	4.78790i	−0.267044	−	0.199496i
$577$		−	13.7253i		−	0.571394i	−0.958320	−	0.285697i	$-0.907775\pi$
$577$		−	13.7253i		−	0.571394i	0.958320	−	0.285697i	$-0.0922250\pi$
$578$	0.0381188	−	0.355106i	0.00158553	−	0.0147705i
$579$		−	15.6000i		−	0.648313i
$580$	1.86980	−	32.3037i	0.0776394	−	1.34134i
$581$			5.42745i			0.225168i
$582$	6.28557	+	0.674723i	0.260545	+	0.0279682i
$583$		−	1.84688i		−	0.0764901i
$584$	−16.2223	−	5.39040i	−0.671282	−	0.223056i
$585$	0.666896	−	0.104924i	0.0275728	−	0.00433808i
$586$	−3.48881	+	32.5010i	−0.144121	+	1.34260i
$587$	−12.6409			−0.521745			−0.260872	−	0.965373i	$-0.584010\pi$
$587$	−12.6409			−0.521745			−0.260872	+	0.965373i	$0.584010\pi$
$588$	1.95443	+	0.424487i	0.0805995	+	0.0175056i
$589$			18.7990i			0.774598i
$590$	−22.6312	+	1.11249i	−0.931711	+	0.0458004i
$591$	20.6643			0.850018
$592$	−33.4438	−	15.2467i	−1.37453	−	0.626635i
$593$			20.6510i			0.848035i	0.905654	+	0.424018i	$0.139381\pi$
$593$			20.6510i			0.848035i	−0.905654	+	0.424018i	$0.860619\pi$
$594$	1.44069	+	0.154651i	0.0591124	+	0.00634540i
$595$	9.17491	−	1.44351i	0.376135	−	0.0591781i
$596$	6.56663	−	30.2342i	0.268980	−	1.23844i
$597$	−1.69565			−0.0693982
$598$	−3.49292	−	0.374946i	−0.142836	−	0.0153327i
$599$	−32.0115			−1.30796			−0.653978	−	0.756514i	$-0.726901\pi$
$599$	−32.0115			−1.30796			−0.653978	+	0.756514i	$0.726901\pi$
$600$	0.123031	−	14.1416i	0.00502273	−	0.577328i
$601$	−10.3278			−0.421278			−0.210639	−	0.977564i	$-0.567554\pi$
$601$	−10.3278			−0.421278			−0.210639	+	0.977564i	$0.567554\pi$
$602$	12.1464	+	1.30385i	0.495052	+	0.0531412i
$603$	−3.42576			−0.139508
$604$	21.9911	+	4.77630i	0.894807	+	0.194345i
$605$	−21.9791	+	3.45801i	−0.893576	+	0.140588i
$606$	24.4024	+	2.61947i	0.991279	+	0.106408i
$607$		−	26.8494i		−	1.08978i	−0.838507	−	0.544891i	$-0.816571\pi$
$607$		−	26.8494i		−	1.08978i	0.838507	−	0.544891i	$-0.183429\pi$
$608$	−14.2268	−	8.42532i	−0.576972	−	0.341692i
$609$	−7.23543			−0.293194
$610$	10.5023	−	0.516266i	0.425227	−	0.0209030i
$611$		−	0.517042i		−	0.0209173i
$612$	−1.76316	+	8.11797i	−0.0712715	+	0.328149i
$613$	−24.1414			−0.975060			−0.487530	−	0.873106i	$-0.662102\pi$
$613$	−24.1414			−0.975060			−0.487530	+	0.873106i	$0.662102\pi$
$614$	1.58832	−	14.7965i	0.0640994	−	0.597136i
$615$	−22.9739	+	3.61454i	−0.926399	+	0.145752i
$616$	−0.913811	+	2.75009i	−0.0368185	+	0.110804i
$617$		−	18.7729i		−	0.755770i	−0.925852	−	0.377885i	$-0.876651\pi$
$617$		−	18.7729i		−	0.755770i	0.925852	−	0.377885i	$-0.123349\pi$
$618$	0.505754	+	0.0542900i	0.0203444	+	0.00218387i
$619$			24.0861i			0.968103i	0.875040	+	0.484051i	$0.160835\pi$
$619$			24.0861i			0.968103i	−0.875040	+	0.484051i	$0.839165\pi$
$620$	28.7150	+	1.66208i	1.15322	+	0.0667508i
$621$		−	8.22770i		−	0.330166i
$622$	−1.16175	+	10.8226i	−0.0465820	+	0.433948i
$623$		−	4.53265i		−	0.181597i
$624$	−1.09885	−	0.500955i	−0.0439893	−	0.0200542i
$625$	20.2856	−	14.6114i	0.811424	−	0.584458i
$626$	−45.3082	−	4.86359i	−1.81088	−	0.194388i
$627$	2.99474			0.119598
$628$	−46.8147	−	10.1678i	−1.86811	−	0.405739i
$629$			38.1669i			1.52181i
$630$	−3.15846	+	0.155261i	−0.125836	+	0.00618577i
$631$	−8.28239			−0.329717			−0.164858	−	0.986317i	$-0.552717\pi$
$631$	−8.28239			−0.329717			−0.164858	+	0.986317i	$0.552717\pi$
$632$	−3.98713	+	11.9992i	−0.158600	+	0.477302i
$633$			11.9624i			0.475462i
$634$	−3.06160	+	28.5212i	−0.121592	+	1.13272i
$635$	6.03746	+	38.3740i	0.239589	+	1.52282i
$636$	−3.52303	−	0.765173i	−0.139697	−	0.0303411i
$637$	0.301914			0.0119623
$638$	1.11896	−	10.4240i	0.0443002	−	0.412691i
$639$	−10.5849			−0.418733
$640$	−14.1273	+	20.9862i	−0.558431	+	0.829551i
$641$	−21.3808			−0.844490			−0.422245	−	0.906482i	$-0.638758\pi$
$641$	−21.3808			−0.844490			−0.422245	+	0.906482i	$0.638758\pi$
$642$	2.65677	−	24.7499i	0.104854	−	0.976801i
$643$	37.4739			1.47783			0.738913	−	0.673801i	$-0.235339\pi$
$643$	37.4739			1.47783			0.738913	+	0.673801i	$0.235339\pi$
$644$	16.0805	+	3.49256i	0.633660	+	0.137626i
$645$	−19.0808	+	3.00203i	−0.751306	+	0.118205i
$646$	−1.83252	+	17.0713i	−0.0720995	+	0.671663i
$647$			6.43510i			0.252990i	0.991967	+	0.126495i	$0.0403727\pi$
$647$			6.43510i			0.252990i	−0.991967	+	0.126495i	$0.959627\pi$
$648$	0.891891	−	2.68413i	0.0350368	−	0.105442i
$649$	−7.34135			−0.288173
$650$	−0.434943	−	2.09008i	−0.0170599	−	0.0819796i
$651$		−	6.43162i		−	0.252075i
$652$	−5.27579	−	1.14586i	−0.206616	−	0.0448754i
$653$	29.0491			1.13678			0.568390	−	0.822759i	$-0.307567\pi$
$653$	29.0491			1.13678			0.568390	+	0.822759i	$0.307567\pi$
$654$	−19.6756	−	2.11207i	−0.769376	−	0.0825884i
$655$	0.00294273	+	0.0187039i	0.000114982	+	0.000730824i
$656$	37.8544	+	17.2574i	1.47797	+	0.673789i
$657$		−	6.04378i		−	0.235790i
$658$	−0.258494	+	2.40807i	−0.0100771	+	0.0938765i
$659$		−	45.3226i		−	1.76552i	−0.469828	−	0.882758i	$-0.655684\pi$
$659$		−	45.3226i		−	1.76552i	0.469828	−	0.882758i	$-0.344316\pi$
$660$	0.264775	−	4.57439i	0.0103063	−	0.178058i
$661$		−	25.8232i		−	1.00441i	−0.864749	−	0.502204i	$-0.832523\pi$
$661$		−	25.8232i		−	1.00441i	0.864749	−	0.502204i	$-0.167477\pi$
$662$	41.8642	+	4.49390i	1.62710	+	0.174660i
$663$			1.25403i			0.0487027i
$664$	−4.84069	+	14.5679i	−0.187855	+	0.565346i
$665$	−6.45638	+	1.01580i	−0.250368	+	0.0393909i
$666$	1.38697	−	12.9207i	0.0537441	−	0.500668i
$667$	−59.5309			−2.30505
$668$	7.96359	−	36.6661i	0.308120	−	1.41865i
$669$			3.72092i			0.143859i
$670$	0.531889	+	10.8202i	0.0205487	+	0.418019i
$671$	3.40686			0.131520
$672$	4.86735	+	2.88252i	0.187762	+	0.111196i
$673$		−	6.78492i		−	0.261540i	−0.991413	−	0.130770i	$-0.958255\pi$
$673$		−	6.78492i		−	0.261540i	0.991413	−	0.130770i	$-0.0417449\pi$
$674$	−21.7113	−	2.33059i	−0.836287	−	0.0897710i
$675$	4.75845	−	1.53532i	0.183153	−	0.0590944i
$676$	25.2295	+	5.47964i	0.970365	+	0.210756i
$677$	22.0422			0.847151			0.423576	−	0.905861i	$-0.360775\pi$
$677$	22.0422			0.847151			0.423576	+	0.905861i	$0.360775\pi$
$678$	−10.6231	−	1.14034i	−0.407979	−	0.0437944i
$679$	−4.47010			−0.171547
$680$	25.9141	+	4.30846i	0.993759	+	0.165222i
$681$	−15.1069			−0.578898
$682$	9.26599	+	0.994655i	0.354813	+	0.0380873i
$683$	−24.9567			−0.954941			−0.477471	−	0.878648i	$-0.658446\pi$
$683$	−24.9567			−0.954941			−0.477471	+	0.878648i	$0.658446\pi$
$684$	1.24073	−	5.71261i	0.0474407	−	0.218427i
$685$	1.92940	+	12.2632i	0.0737185	+	0.468553i
$686$	−1.40614	−	0.150941i	−0.0536865	−	0.00576296i
$687$			2.17339i			0.0829199i
$688$	31.4396	+	14.3330i	1.19863	+	0.546441i
$689$	−0.544224			−0.0207333
$690$	−25.9869	+	1.27745i	−0.989304	+	0.0486315i
$691$		−	7.04928i		−	0.268167i	−0.990970	−	0.134084i	$-0.957191\pi$
$691$		−	7.04928i		−	0.268167i	0.990970	−	0.134084i	$-0.0428091\pi$
$692$	−19.7499	−	4.28953i	−0.750780	−	0.163063i
$693$	−1.02458			−0.0389205
$694$	0.213179	−	1.98593i	0.00809215	−	0.0753847i
$695$	−1.51254	−	9.61364i	−0.0573737	−	0.364666i
$696$	−19.4208	−	6.45321i	−0.736143	−	0.244608i
$697$		−	43.2003i		−	1.63633i
$698$	−22.8485	−	2.45267i	−0.864829	−	0.0928348i
$699$			3.91693i			0.148152i
$700$	0.980776	+	9.95179i	0.0370698	+	0.376142i
$701$		−	34.2690i		−	1.29432i	−0.762353	−	0.647162i	$-0.775956\pi$
$701$		−	34.2690i		−	1.29432i	0.762353	−	0.647162i	$-0.224044\pi$
$702$	0.0455712	−	0.424532i	0.00171997	−	0.0160229i
$703$		−	26.8580i		−	1.01297i
$704$	−4.90557	+	6.56658i	−0.184886	+	0.247487i
$705$	−0.595162	−	3.78284i	−0.0224151	−	0.142470i
$706$	−27.4049	−	2.94177i	−1.03140	−	0.110715i
$707$	−17.3542			−0.652672
$708$	−3.04156	+	14.0040i	−0.114309	+	0.526303i
$709$		−	41.3292i		−	1.55215i	−0.630640	−	0.776076i	$-0.717207\pi$
$709$		−	41.3292i		−	1.55215i	0.630640	−	0.776076i	$-0.282793\pi$
$710$	1.64343	+	33.4321i	0.0616768	+	1.25468i
$711$	−4.47042			−0.167654
$712$	4.04263	−	12.1662i	0.151504	−	0.455947i
$713$		−	52.9174i		−	1.98177i
$714$	0.626952	−	5.84055i	0.0234631	−	0.218577i
$715$	−0.107503	−	0.683287i	−0.00402038	−	0.0255535i
$716$	−2.06211	+	9.49441i	−0.0770647	+	0.354823i
$717$	−16.6158			−0.620528
$718$	−5.17590	+	48.2176i	−0.193163	+	1.79946i
$719$	49.8123			1.85768			0.928842	−	0.370475i	$-0.120805\pi$
$719$	49.8123			1.85768			0.928842	+	0.370475i	$0.120805\pi$
$720$	−8.61619	−	2.40027i	−0.321106	−	0.0894526i
$721$	−0.359677			−0.0133951
$722$	−1.57834	+	14.7035i	−0.0587397	+	0.547207i
$723$	24.1578			0.898439
$724$	−5.87897	+	27.0680i	−0.218490	+	1.00598i
$725$	−11.1087	−	34.4294i	−0.412566	−	1.27868i
$726$	−1.50190	+	13.9914i	−0.0557408	+	0.519269i
$727$			38.6661i			1.43404i	0.697050	+	0.717022i	$0.254496\pi$
$727$			38.6661i			1.43404i	−0.697050	+	0.717022i	$0.745504\pi$
$728$	0.810375	+	0.269274i	0.0300345	+	0.00997997i
$729$	1.00000			0.0370370
$730$	−19.0891	+	0.938367i	−0.706518	+	0.0347305i
$731$		−	35.8796i		−	1.32706i
$732$	1.41148	−	6.49876i	0.0521697	−	0.240201i
$733$	6.64450			0.245420			0.122710	−	0.992443i	$-0.460841\pi$
$733$	6.64450			0.245420			0.122710	+	0.992443i	$0.460841\pi$
$734$	−35.4932	−	3.81000i	−1.31008	−	0.140630i
$735$	2.20890	−	0.347530i	0.0814764	−	0.0128189i
$736$	40.0471	+	23.7165i	1.47616	+	0.874202i
$737$			3.50996i			0.129291i
$738$	−1.56989	+	14.6247i	−0.0577883	+	0.538343i
$739$		−	24.8892i		−	0.915562i	−0.889065	−	0.457781i	$-0.848644\pi$
$739$		−	24.8892i		−	0.915562i	0.889065	−	0.457781i	$-0.151356\pi$
$740$	−41.0250	−	2.37461i	−1.50811	−	0.0872924i
$741$		−	0.882464i		−	0.0324181i
$742$	2.53467	+	0.272084i	0.0930508	+	0.00998851i
$743$			7.85701i			0.288246i	0.989560	+	0.144123i	$0.0460361\pi$
$743$			7.85701i			0.288246i	−0.989560	+	0.144123i	$0.953964\pi$
$744$	5.73630	−	17.2633i	0.210303	−	0.632902i
$745$	−5.37614	−	34.1706i	−0.196967	−	1.25192i
$746$	−0.418195	+	3.89582i	−0.0153112	+	0.142636i
$747$	−5.42745			−0.198580
$748$	8.31749	+	1.80649i	0.304117	+	0.0660519i
$749$			17.6014i			0.643140i
$750$	−5.58805	−	14.7910i	−0.204047	−	0.540091i
$751$	40.4814			1.47719			0.738593	−	0.674151i	$-0.235491\pi$
$751$	40.4814			1.47719			0.738593	+	0.674151i	$0.235491\pi$
$752$	−2.84157	+	6.23302i	−0.103621	+	0.227295i
$753$		−	18.0430i		−	0.657525i
$754$	−3.07167	−	0.329727i	−0.111864	−	0.0120080i
$755$	24.8543	−	3.91039i	0.904542	−	0.142314i
$756$	−0.424487	+	1.95443i	−0.0154385	+	0.0710821i
$757$	31.2485			1.13575			0.567873	−	0.823116i	$-0.307766\pi$
$757$	31.2485			1.13575			0.567873	+	0.823116i	$0.307766\pi$
$758$	−23.9725	−	2.57332i	−0.870720	−	0.0934672i
$759$	−8.42992			−0.305987
$760$	−18.2357	−	3.03187i	−0.661479	−	0.109977i
$761$	−7.70845			−0.279431			−0.139716	−	0.990192i	$-0.544619\pi$
$761$	−7.70845			−0.279431			−0.139716	+	0.990192i	$0.544619\pi$
$762$	24.4280	+	2.62222i	0.884934	+	0.0949930i
$763$	13.9927			0.506568
$764$	18.9938	+	4.12530i	0.687171	+	0.149248i
$765$	1.44351	+	9.17491i	0.0521902	+	0.331720i
$766$	−21.4516	−	2.30272i	−0.775079	−	0.0832006i
$767$			2.16329i			0.0781118i
$768$	10.4937	+	12.0782i	0.378658	+	0.435834i
$769$	−19.6982			−0.710335			−0.355167	−	0.934803i	$-0.615576\pi$
$769$	−19.6982			−0.710335			−0.355167	+	0.934803i	$0.615576\pi$
$770$	0.159077	+	3.23609i	0.00573275	+	0.116621i
$771$			16.8090i			0.605361i
$772$	−6.62200	+	30.4891i	−0.238331	+	1.09733i
$773$	−8.07370			−0.290391			−0.145195	−	0.989403i	$-0.546381\pi$
$773$	−8.07370			−0.290391			−0.145195	+	0.989403i	$0.546381\pi$
$774$	−1.30385	+	12.1464i	−0.0468661	+	0.436594i
$775$	30.6045	−	9.87458i	1.09935	−	0.354705i
$776$	−11.9983	−	3.98685i	−0.430715	−	0.143119i
$777$			9.18883i			0.329647i
$778$	34.4877	+	3.70207i	1.23644	+	0.132726i
$779$			30.4000i			1.08919i
$780$	−1.34794	−	0.0780216i	−0.0482641	−	0.00279362i
$781$			10.8451i			0.388067i
$782$	5.15837	−	48.0543i	0.184463	−	1.71842i
$783$		−	7.23543i		−	0.258573i
$784$	−3.63962	−	1.65927i	−0.129986	−	0.0592595i
$785$	−52.9099	+	8.32443i	−1.88843	+	0.297112i
$786$	0.0119065	+	0.00127810i	0.000424692	+	4.55884e-5i
$787$	39.6114			1.41200			0.705998	−	0.708214i	$-0.250499\pi$
$787$	39.6114			1.41200			0.705998	+	0.708214i	$0.250499\pi$
$788$	−40.3871	−	8.77176i	−1.43873	−	0.312481i
$789$			5.18982i			0.184763i
$790$	0.694085	+	14.1197i	0.0246944	+	0.502355i
$791$	7.55485			0.268619
$792$	−2.75009	−	0.913811i	−0.0977203	−	0.0324709i
$793$		−	1.00390i		−	0.0356497i
$794$	−0.285249	+	2.65732i	−0.0101231	+	0.0943048i
$795$	−3.98171	+	0.626452i	−0.141217	+	0.0222180i
$796$	3.31403	+	0.719781i	0.117463	+	0.0255119i
$797$	−4.35953			−0.154423			−0.0772113	−	0.997015i	$-0.524602\pi$
$797$	−4.35953			−0.154423			−0.0772113	+	0.997015i	$0.524602\pi$
$798$	−0.441186	+	4.10999i	−0.0156178	+	0.145492i
$799$	7.11327			0.251649
$800$	−6.24339	+	27.5866i	−0.220737	+	0.975333i
$801$	4.53265			0.160153
$802$	−1.44606	+	13.4712i	−0.0510623	+	0.475685i
$803$	−6.19232			−0.218522
$804$	6.69543	+	1.45419i	0.236130	+	0.0512855i
$805$	18.1741	−	2.85938i	0.640554	−	0.100780i
$806$	0.293097	−	2.73043i	0.0103239	−	0.0961751i
$807$		−	1.81394i		−	0.0638538i
$808$	−46.5809	−	15.4781i	−1.63871	−	0.544517i
$809$	−15.2086			−0.534705			−0.267352	−	0.963599i	$-0.586149\pi$
$809$	−15.2086			−0.534705			−0.267352	+	0.963599i	$0.586149\pi$
$810$	−0.155261	−	3.15846i	−0.00545533	−	0.110977i
$811$		−	29.7710i		−	1.04540i	−0.852516	−	0.522701i	$-0.824924\pi$
$811$		−	29.7710i		−	1.04540i	0.852516	−	0.522701i	$-0.175076\pi$
$812$	14.1412	+	3.07135i	0.496257	+	0.107783i
$813$	−3.23107			−0.113319
$814$	−13.2383	−	1.42106i	−0.464002	−	0.0498081i
$815$	−5.96269	+	0.938123i	−0.208864	+	0.0328610i
$816$	6.89195	−	15.1176i	0.241267	−	0.529222i
$817$			25.2485i			0.883333i
$818$	−1.59851	+	14.8914i	−0.0558907	+	0.520666i
$819$			0.301914i			0.0105497i
$820$	46.4354	+	2.68777i	1.62159	+	0.0938611i
$821$			23.3742i			0.815764i	0.913035	+	0.407882i	$0.133733\pi$
$821$			23.3742i			0.815764i	−0.913035	+	0.407882i	$0.866267\pi$
$822$	7.80649	+	0.837985i	0.272283	+	0.0292281i
$823$			53.9345i			1.88004i	0.341122	+	0.940019i	$0.389193\pi$
$823$			53.9345i			1.88004i	−0.341122	+	0.940019i	$0.610807\pi$
$824$	−0.965417	−	0.320793i	−0.0336319	−	0.0111753i
$825$	−1.57305	−	4.87539i	−0.0547666	−	0.169739i
$826$	1.08153	−	10.0753i	0.0376313	−	0.350565i
$827$	9.98196			0.347107			0.173553	−	0.984824i	$-0.444475\pi$
$827$	9.98196			0.347107			0.173553	+	0.984824i	$0.444475\pi$
$828$	−3.49256	+	16.0805i	−0.121375	+	0.558836i
$829$			8.29991i			0.288268i	0.989558	+	0.144134i	$0.0460396\pi$
$829$			8.29991i			0.288268i	−0.989558	+	0.144134i	$0.953960\pi$
$830$	0.842673	+	17.1424i	0.0292496	+	0.595021i
$831$	−13.5526			−0.470136
$832$	1.93498	+	1.44553i	0.0670835	+	0.0501148i
$833$			4.15362i			0.143914i
$834$	−6.11984	−	0.656932i	−0.211913	−	0.0227477i
$835$	−6.51984	−	41.4400i	−0.225628	−	1.43409i
$836$	−5.85301	−	1.27123i	−0.202431	−	0.0439663i
$837$	6.43162			0.222309
$838$	−42.4905	−	4.56113i	−1.46781	−	0.157561i
$839$	−36.9779			−1.27662			−0.638309	−	0.769780i	$-0.720366\pi$
$839$	−36.9779			−1.27662			−0.638309	+	0.769780i	$0.720366\pi$
$840$	6.23891	+	1.03728i	0.215263	+	0.0357896i
$841$	−23.3514			−0.805220
$842$	14.6296	+	1.57041i	0.504169	+	0.0541199i
$843$	−23.9254			−0.824036
$844$	5.07788	−	23.3797i	0.174788	−	0.804761i
$845$	28.5143	−	4.48622i	0.980922	−	0.154331i
$846$	−2.40807	−	0.258494i	−0.0827913	−	0.00888720i
$847$		−	9.95024i		−	0.341894i
$848$	6.56071	+	2.99096i	0.225296	+	0.102710i
$849$	14.1251			0.484771
$850$	28.7545	−	5.98378i	0.986271	−	0.205242i
$851$			75.6029i			2.59163i
$852$	20.6875	+	4.49316i	0.708743	+	0.153933i
$853$	−39.5811			−1.35523			−0.677616	−	0.735416i	$-0.736987\pi$
$853$	−39.5811			−1.35523			−0.677616	+	0.735416i	$0.736987\pi$
$854$	−0.501900	+	4.67559i	−0.0171747	+	0.159995i
$855$	−1.01580	−	6.45638i	−0.0347395	−	0.220804i
$856$	−15.6985	+	47.2443i	−0.536564	+	1.61478i
$857$		−	30.2970i		−	1.03493i	−0.855705	−	0.517463i	$-0.826876\pi$
$857$		−	30.2970i		−	1.03493i	0.855705	−	0.517463i	$-0.173124\pi$
$858$	−0.434965	−	0.0466912i	−0.0148495	−	0.00159401i
$859$		−	27.2250i		−	0.928906i	−0.885598	−	0.464453i	$-0.846251\pi$
$859$		−	27.2250i		−	0.928906i	0.885598	−	0.464453i	$-0.153749\pi$
$860$	38.5665	+	2.23231i	1.31511	+	0.0761210i
$861$		−	10.4006i		−	0.354453i
$862$	−0.718210	+	6.69069i	−0.0244623	+	0.227886i
$863$		−	29.2760i		−	0.996568i	−0.867014	−	0.498284i	$-0.833964\pi$
$863$		−	29.2760i		−	0.996568i	0.867014	−	0.498284i	$-0.166036\pi$
$864$	−2.88252	+	4.86735i	−0.0980653	+	0.165591i
$865$	−22.3213	+	3.51186i	−0.758948	+	0.119407i
$866$	39.8269	+	4.27521i	1.35337	+	0.145278i
$867$	−0.252541			−0.00857673
$868$	−2.73014	+	12.5702i	−0.0926670	+	0.426659i
$869$			4.58029i			0.155376i
$870$	−22.8528	+	1.12338i	−0.774784	+	0.0380863i
$871$	1.03429			0.0350454
$872$	37.5581	+	12.4799i	1.27188	+	0.422624i
$873$		−	4.47010i		−	0.151290i
$874$	−3.62995	+	33.8158i	−0.122785	+	1.14384i
$875$	5.04506	+	9.97734i	0.170554	+	0.337296i
$876$	−2.56551	+	11.8122i	−0.0866805	+	0.399096i
$877$	−11.0964			−0.374700			−0.187350	−	0.982293i	$-0.559990\pi$
$877$	−11.0964			−0.374700			−0.187350	+	0.982293i	$0.559990\pi$
$878$	−2.74482	+	25.5702i	−0.0926332	+	0.862951i
$879$	23.1137			0.779605
$880$	−2.45926	+	8.82795i	−0.0829015	+	0.297590i
$881$	−24.9501			−0.840590			−0.420295	−	0.907388i	$-0.638073\pi$
$881$	−24.9501			−0.840590			−0.420295	+	0.907388i	$0.638073\pi$
$882$	0.150941	−	1.40614i	0.00508245	−	0.0473470i
$883$	−43.2304			−1.45482			−0.727409	−	0.686204i	$-0.759276\pi$
$883$	−43.2304			−1.45482			−0.727409	+	0.686204i	$0.759276\pi$
$884$	0.532322	−	2.45093i	0.0179039	−	0.0824336i
$885$	2.49014	+	15.8273i	0.0837052	+	0.532028i
$886$	−5.26028	+	49.0036i	−0.176723	+	1.64631i
$887$		−	15.6827i		−	0.526572i	−0.964718	−	0.263286i	$-0.915194\pi$
$887$		−	15.6827i		−	0.526572i	0.964718	−	0.263286i	$-0.0848063\pi$
$888$	−8.19543	+	24.6640i	−0.275021	+	0.827668i
$889$	−17.3725			−0.582654
$890$	−0.703745	−	14.3162i	−0.0235896	−	0.479880i
$891$		−	1.02458i		−	0.0343246i
$892$	1.57948	−	7.27229i	0.0528850	−	0.243494i
$893$	−5.00561			−0.167506
$894$	−21.7523	−	2.33499i	−0.727505	−	0.0780938i
$895$	1.68826	+	10.7306i	0.0564324	+	0.358683i
$896$	−8.28932	−	7.69982i	−0.276927	−	0.257233i
$897$			2.48406i			0.0829402i
$898$	−0.678462	+	6.32040i	−0.0226406	+	0.210915i
$899$		−	46.5355i		−	1.55205i
$900$	−9.95179	+	0.980776i	−0.331726	+	0.0326925i
$901$		−	7.48723i		−	0.249436i
$902$	14.9841	+	1.60847i	0.498918	+	0.0535561i
$903$		−	8.63817i		−	0.287460i
$904$	20.2782	+	6.73810i	0.674442	+	0.224106i
$905$	4.81314	+	30.5922i	0.159994	+	1.01692i
$906$	1.69838	−	15.8217i	0.0564249	−	0.525642i
$907$	25.1640			0.835558			0.417779	−	0.908549i	$-0.362809\pi$
$907$	25.1640			0.835558			0.417779	+	0.908549i	$0.362809\pi$
$908$	29.5255	+	6.41270i	0.979837	+	0.212813i
$909$		−	17.3542i		−	0.575603i
$910$	0.953584	−	0.0468756i	0.0316110	−	0.00155391i
$911$	24.2806			0.804453			0.402226	−	0.915540i	$-0.368236\pi$
$911$	24.2806			0.804453			0.402226	+	0.915540i	$0.368236\pi$
$912$	−4.84987	+	10.6382i	−0.160595	+	0.352268i
$913$			5.56084i			0.184037i
$914$	−42.7508	−	4.58907i	−1.41407	−	0.151793i
$915$	−1.15559	−	7.34488i	−0.0382025	−	0.242814i
$916$	0.922575	−	4.24774i	0.0304827	−	0.140349i
$917$	−0.00846755			−0.000279623
$918$	5.84055	+	0.626952i	0.192767	+	0.0206925i
$919$	−15.7280			−0.518820			−0.259410	−	0.965767i	$-0.583528\pi$
$919$	−15.7280			−0.518820			−0.259410	+	0.965767i	$0.583528\pi$
$920$	51.3319	+	8.53443i	1.69236	+	0.281372i
$921$	−10.5228			−0.346738
$922$	−4.35321	−	0.467294i	−0.143365	−	0.0153895i
$923$	3.19573			0.105189
$924$	2.00247	+	0.434920i	0.0658763	+	0.0143078i
$925$	−43.7245	+	14.1078i	−1.43765	+	0.463860i
$926$	27.1827	+	2.91792i	0.893278	+	0.0958887i
$927$		−	0.359677i		−	0.0118133i
$928$	35.2173	+	20.8563i	1.15607	+	0.684640i
$929$	31.3064			1.02713			0.513565	−	0.858051i	$-0.328325\pi$
$929$	31.3064			1.02713			0.513565	+	0.858051i	$0.328325\pi$
$930$	−0.998583	−	20.3140i	−0.0327448	−	0.666123i
$931$		−	2.92290i		−	0.0957942i
$932$	1.66269	−	7.65537i	0.0544631	−	0.250760i
$933$	7.69672			0.251979
$934$	5.01563	−	46.7245i	0.164116	−	1.52887i
$935$	9.40040	−	1.47899i	0.307426	−	0.0483680i
$936$	−0.269274	+	0.810375i	−0.00880151	+	0.0264879i
$937$		−	36.0757i		−	1.17854i	−0.807936	−	0.589270i	$-0.799415\pi$
$937$		−	36.0757i		−	1.17854i	0.807936	−	0.589270i	$-0.200585\pi$
$938$	−4.81709	−	0.517089i	−0.157284	−	0.0168836i
$939$			32.2218i			1.05152i
$940$	−0.442563	+	7.64595i	−0.0144348	+	0.249383i
$941$			16.0847i			0.524347i	0.965021	+	0.262173i	$0.0844392\pi$
$941$			16.0847i			0.524347i	−0.965021	+	0.262173i	$0.915561\pi$
$942$	−3.61551	+	33.6813i	−0.117800	+	1.09740i
$943$		−	85.5734i		−	2.78665i
$944$	11.8890	−	26.0788i	0.386955	−	0.848792i
$945$	0.347530	+	2.20890i	0.0113052	+	0.0718554i
$946$	12.4450	+	1.33590i	0.404620	+	0.0434338i
$947$	−5.29847			−0.172177			−0.0860886	−	0.996287i	$-0.527437\pi$
$947$	−5.29847			−0.172177			−0.0860886	+	0.996287i	$0.527437\pi$
$948$	8.73714	+	1.89764i	0.283769	+	0.0616324i
$949$			1.82470i			0.0592323i
$950$	−20.2345	+	4.21079i	−0.656495	+	0.136616i
$951$	20.2834			0.657735
$952$	−3.70458	+	11.1488i	−0.120066	+	0.361336i
$953$			30.2929i			0.981284i	0.871361	+	0.490642i	$0.163238\pi$
$953$			30.2929i			0.981284i	−0.871361	+	0.490642i	$0.836762\pi$
$954$	−0.272084	+	2.53467i	−0.00880904	+	0.0820631i
$955$	21.4667	−	3.37741i	0.694647	−	0.109290i
$956$	32.4745	+	7.05320i	1.05030	+	0.228117i
$957$	−7.41325			−0.239636
$958$	−5.34895	+	49.8297i	−0.172817	+	1.60992i
$959$	−5.55173			−0.179275
$960$	15.8209	+	8.34862i	0.510617	+	0.269451i
$961$	10.3657			0.334378
$962$	−0.418746	+	3.90095i	−0.0135009	+	0.125772i
$963$	−17.6014			−0.567196
$964$	−47.2148	−	10.2547i	−1.52069	−	0.330281i
$965$	5.42147	+	34.4587i	0.174523	+	1.10927i
$966$	1.24190	−	11.5693i	0.0399574	−	0.372235i
$967$		−	43.0466i		−	1.38429i	−0.721760	−	0.692143i	$-0.756667\pi$
$967$		−	43.0466i		−	1.38429i	0.721760	−	0.692143i	$-0.243333\pi$
$968$	8.87453	−	26.7077i	0.285238	−	0.858418i
$969$	12.1406			0.390013
$970$	−14.1187	+	0.694035i	−0.453323	+	0.0222841i
$971$			48.3929i			1.55300i	0.630117	+	0.776500i	$0.283007\pi$
$971$			48.3929i			1.55300i	−0.630117	+	0.776500i	$0.716993\pi$
$972$	−1.95443	−	0.424487i	−0.0626885	−	0.0136154i
$973$	4.35224			0.139526
$974$	−36.9457	−	3.96593i	−1.18382	−	0.127077i
$975$	−1.43664	+	0.463534i	−0.0460093	+	0.0148450i
$976$	−5.51728	+	12.1022i	−0.176604	+	0.387383i
$977$		−	4.57680i		−	0.146425i	−0.997316	−	0.0732124i	$-0.976675\pi$
$977$		−	4.57680i		−	0.146425i	0.997316	−	0.0732124i	$-0.0233251\pi$
$978$	−0.407450	+	3.79572i	−0.0130288	+	0.121374i
$979$		−	4.64404i		−	0.148424i
$980$	−4.46466	−	0.258424i	−0.142618	−	0.00825504i
$981$			13.9927i			0.446751i
$982$	54.0457	+	5.80152i	1.72467	+	0.185134i
$983$			42.5565i			1.35734i	0.734443	+	0.678671i	$0.237444\pi$
$983$			42.5565i			1.35734i	−0.734443	+	0.678671i	$0.762556\pi$
$984$	9.27625	−	27.9166i	0.295716	−	0.889950i
$985$	−45.6454	+	7.18149i	−1.45438	+	0.228821i
$986$	4.53626	−	42.2589i	0.144464	−	1.34580i
$987$	1.71255			0.0545110
$988$	−0.374595	+	1.72472i	−0.0119174	+	0.0548706i
$989$		−	71.0723i		−	2.25997i
$990$	−3.23609	+	0.159077i	−0.102850	+	0.00505581i
$991$	−10.2413			−0.325324			−0.162662	−	0.986682i	$-0.552008\pi$
$991$	−10.2413			−0.325324			−0.162662	+	0.986682i	$0.552008\pi$
$992$	−18.5393	+	31.3049i	−0.588622	+	0.993932i
$993$		−	29.7725i		−	0.944802i
$994$	−14.8838	−	1.59770i	−0.472086	−	0.0506760i
$995$	3.74551	−	0.589289i	0.118741	−	0.0186817i
$996$	10.6076	+	2.30388i	0.336114	+	0.0730013i
$997$	38.6808			1.22503			0.612516	−	0.790458i	$-0.290157\pi$
$997$	38.6808			1.22503			0.612516	+	0.790458i	$0.290157\pi$
$998$	−19.4052	−	2.08304i	−0.614260	−	0.0659375i
$999$	−9.18883			−0.290722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.j.f.589.14	yes	32
4.3	odd	2		3360.2.j.e.1009.2		32
5.4	even	2		840.2.j.e.589.19	✓	32
8.3	odd	2		3360.2.j.f.1009.31		32
8.5	even	2		840.2.j.e.589.20	yes	32
20.19	odd	2		3360.2.j.f.1009.32		32
40.19	odd	2		3360.2.j.e.1009.1		32
40.29	even	2	inner	840.2.j.f.589.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.j.e.589.19	✓	32	5.4	even	2
840.2.j.e.589.20	yes	32	8.5	even	2
840.2.j.f.589.13	yes	32	40.29	even	2	inner
840.2.j.f.589.14	yes	32	1.1	even	1	trivial
3360.2.j.e.1009.1		32	40.19	odd	2
3360.2.j.e.1009.2		32	4.3	odd	2
3360.2.j.f.1009.31		32	8.3	odd	2
3360.2.j.f.1009.32		32	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.150941 + 1.40614i) q^{2} +1.00000 q^{3} +(-1.95443 - 0.424487i) q^{4} +(-2.20890 + 0.347530i) q^{5} +(-0.150941 + 1.40614i) q^{6} -1.00000i q^{7} +(0.891891 - 2.68413i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.150941 + 1.40614i) q^{2} +1.00000 q^{3} +(-1.95443 - 0.424487i) q^{4} +(-2.20890 + 0.347530i) q^{5} +(-0.150941 + 1.40614i) q^{6} -1.00000i q^{7} +(0.891891 - 2.68413i) q^{8} +1.00000 q^{9} +(-0.155261 - 3.15846i) q^{10} -1.02458i q^{11} +(-1.95443 - 0.424487i) q^{12} -0.301914 q^{13} +(1.40614 + 0.150941i) q^{14} +(-2.20890 + 0.347530i) q^{15} +(3.63962 + 1.65927i) q^{16} -4.15362i q^{17} +(-0.150941 + 1.40614i) q^{18} +2.92290i q^{19} +(4.46466 + 0.258424i) q^{20} -1.00000i q^{21} +(1.44069 + 0.154651i) q^{22} -8.22770i q^{23} +(0.891891 - 2.68413i) q^{24} +(4.75845 - 1.53532i) q^{25} +(0.0455712 - 0.424532i) q^{26} +1.00000 q^{27} +(-0.424487 + 1.95443i) q^{28} -7.23543i q^{29} +(-0.155261 - 3.15846i) q^{30} +6.43162 q^{31} +(-2.88252 + 4.86735i) q^{32} -1.02458i q^{33} +(5.84055 + 0.626952i) q^{34} +(0.347530 + 2.20890i) q^{35} +(-1.95443 - 0.424487i) q^{36} -9.18883 q^{37} +(-4.10999 - 0.441186i) q^{38} -0.301914 q^{39} +(-1.03728 + 6.23891i) q^{40} +10.4006 q^{41} +(1.40614 + 0.150941i) q^{42} +8.63817 q^{43} +(-0.434920 + 2.00247i) q^{44} +(-2.20890 + 0.347530i) q^{45} +(11.5693 + 1.24190i) q^{46} +1.71255i q^{47} +(3.63962 + 1.65927i) q^{48} -1.00000 q^{49} +(1.44062 + 6.92276i) q^{50} -4.15362i q^{51} +(0.590070 + 0.128159i) q^{52} +1.80258 q^{53} +(-0.150941 + 1.40614i) q^{54} +(0.356072 + 2.26318i) q^{55} +(-2.68413 - 0.891891i) q^{56} +2.92290i q^{57} +(10.1740 + 1.09212i) q^{58} -7.16525i q^{59} +(4.46466 + 0.258424i) q^{60} +3.32514i q^{61} +(-0.970796 + 9.04373i) q^{62} -1.00000i q^{63} +(-6.40906 - 4.78790i) q^{64} +(0.666896 - 0.104924i) q^{65} +(1.44069 + 0.154651i) q^{66} -3.42576 q^{67} +(-1.76316 + 8.11797i) q^{68} -8.22770i q^{69} +(-3.15846 + 0.155261i) q^{70} -10.5849 q^{71} +(0.891891 - 2.68413i) q^{72} -6.04378i q^{73} +(1.38697 - 12.9207i) q^{74} +(4.75845 - 1.53532i) q^{75} +(1.24073 - 5.71261i) q^{76} -1.02458 q^{77} +(0.0455712 - 0.424532i) q^{78} -4.47042 q^{79} +(-8.61619 - 2.40027i) q^{80} +1.00000 q^{81} +(-1.56989 + 14.6247i) q^{82} -5.42745 q^{83} +(-0.424487 + 1.95443i) q^{84} +(1.44351 + 9.17491i) q^{85} +(-1.30385 + 12.1464i) q^{86} -7.23543i q^{87} +(-2.75009 - 0.913811i) q^{88} +4.53265 q^{89} +(-0.155261 - 3.15846i) q^{90} +0.301914i q^{91} +(-3.49256 + 16.0805i) q^{92} +6.43162 q^{93} +(-2.40807 - 0.258494i) q^{94} +(-1.01580 - 6.45638i) q^{95} +(-2.88252 + 4.86735i) q^{96} -4.47010i q^{97} +(0.150941 - 1.40614i) q^{98} -1.02458i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 32 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 + 32 * q^3 - 2 * q^4 + 2 * q^6 + 2 * q^8 + 32 * q^9	\( 32 q + 2 q^{2} + 32 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{8} + 32 q^{9} - 8 q^{10} - 2 q^{12} + 32 q^{13} + 6 q^{16} + 2 q^{18} + 24 q^{20} + 2 q^{24} - 16 q^{25} + 12 q^{26} + 32 q^{27} + 8 q^{28} - 8 q^{30} + 32 q^{31} + 22 q^{32} + 4 q^{35} - 2 q^{36} - 8 q^{37} - 32 q^{38} + 32 q^{39} - 24 q^{40} + 24 q^{41} - 8 q^{43} - 24 q^{44} + 12 q^{46} + 6 q^{48} - 32 q^{49} - 26 q^{50} - 16 q^{52} - 24 q^{53} + 2 q^{54} + 24 q^{55} - 12 q^{56} - 16 q^{58} + 24 q^{60} - 48 q^{62} + 22 q^{64} + 8 q^{65} + 24 q^{67} + 4 q^{68} + 6 q^{70} + 40 q^{71} + 2 q^{72} - 20 q^{74} - 16 q^{75} - 52 q^{76} - 16 q^{77} + 12 q^{78} - 24 q^{79} - 44 q^{80} + 32 q^{81} + 24 q^{82} + 8 q^{84} - 8 q^{85} - 76 q^{86} + 56 q^{88} + 24 q^{89} - 8 q^{90} - 96 q^{92} + 32 q^{93} + 32 q^{94} - 48 q^{95} + 22 q^{96} - 2 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 32 * q^3 - 2 * q^4 + 2 * q^6 + 2 * q^8 + 32 * q^9 - 8 * q^10 - 2 * q^12 + 32 * q^13 + 6 * q^16 + 2 * q^18 + 24 * q^20 + 2 * q^24 - 16 * q^25 + 12 * q^26 + 32 * q^27 + 8 * q^28 - 8 * q^30 + 32 * q^31 + 22 * q^32 + 4 * q^35 - 2 * q^36 - 8 * q^37 - 32 * q^38 + 32 * q^39 - 24 * q^40 + 24 * q^41 - 8 * q^43 - 24 * q^44 + 12 * q^46 + 6 * q^48 - 32 * q^49 - 26 * q^50 - 16 * q^52 - 24 * q^53 + 2 * q^54 + 24 * q^55 - 12 * q^56 - 16 * q^58 + 24 * q^60 - 48 * q^62 + 22 * q^64 + 8 * q^65 + 24 * q^67 + 4 * q^68 + 6 * q^70 + 40 * q^71 + 2 * q^72 - 20 * q^74 - 16 * q^75 - 52 * q^76 - 16 * q^77 + 12 * q^78 - 24 * q^79 - 44 * q^80 + 32 * q^81 + 24 * q^82 + 8 * q^84 - 8 * q^85 - 76 * q^86 + 56 * q^88 + 24 * q^89 - 8 * q^90 - 96 * q^92 + 32 * q^93 + 32 * q^94 - 48 * q^95 + 22 * q^96 - 2 * q^98

Introduction

L-functions

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