LMFDB - Embedded newform 429.2.m.a.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(109,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("429.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.m (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	429.109
Dual form			429.2.m.a.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67111 - 1.67111i) q^{2} -1.00000 q^{3} +3.58521i q^{4} +(2.12568 - 2.12568i) q^{5} +(1.67111 + 1.67111i) q^{6} +(-1.37191 + 1.37191i) q^{7} +(2.64907 - 2.64907i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.67111 - 1.67111i) q^{2} -1.00000 q^{3} +3.58521i q^{4} +(2.12568 - 2.12568i) q^{5} +(1.67111 + 1.67111i) q^{6} +(-1.37191 + 1.37191i) q^{7} +(2.64907 - 2.64907i) q^{8} +1.00000 q^{9} -7.10448 q^{10} +(2.22009 + 2.46398i) q^{11} -3.58521i q^{12} +(-0.554044 - 3.56273i) q^{13} +4.58521 q^{14} +(-2.12568 + 2.12568i) q^{15} -1.68333 q^{16} +6.69098 q^{17} +(-1.67111 - 1.67111i) q^{18} +(2.46045 + 2.46045i) q^{19} +(7.62101 + 7.62101i) q^{20} +(1.37191 - 1.37191i) q^{21} +(0.407572 - 7.82759i) q^{22} -3.28445i q^{23} +(-2.64907 + 2.64907i) q^{24} -4.03701i q^{25} +(-5.02784 + 6.87958i) q^{26} -1.00000 q^{27} +(-4.91858 - 4.91858i) q^{28} -3.36320i q^{29} +7.10448 q^{30} +(0.273940 - 0.273940i) q^{31} +(-2.48510 - 2.48510i) q^{32} +(-2.22009 - 2.46398i) q^{33} +(-11.1814 - 11.1814i) q^{34} +5.83246i q^{35} +3.58521i q^{36} +(-5.74595 - 5.74595i) q^{37} -8.22335i q^{38} +(0.554044 + 3.56273i) q^{39} -11.2621i q^{40} +(-0.977956 - 0.977956i) q^{41} -4.58521 q^{42} +2.55799 q^{43} +(-8.83390 + 7.95949i) q^{44} +(2.12568 - 2.12568i) q^{45} +(-5.48868 + 5.48868i) q^{46} +(-5.10855 - 5.10855i) q^{47} +1.68333 q^{48} +3.23574i q^{49} +(-6.74629 + 6.74629i) q^{50} -6.69098 q^{51} +(12.7731 - 1.98637i) q^{52} +9.35644 q^{53} +(1.67111 + 1.67111i) q^{54} +(9.95682 + 0.518439i) q^{55} +7.26854i q^{56} +(-2.46045 - 2.46045i) q^{57} +(-5.62027 + 5.62027i) q^{58} +(-2.90188 - 2.90188i) q^{59} +(-7.62101 - 7.62101i) q^{60} -6.86934i q^{61} -0.915567 q^{62} +(-1.37191 + 1.37191i) q^{63} +11.6724i q^{64} +(-8.75093 - 6.39549i) q^{65} +(-0.407572 + 7.82759i) q^{66} +(-5.85989 + 5.85989i) q^{67} +23.9886i q^{68} +3.28445i q^{69} +(9.74669 - 9.74669i) q^{70} +(11.6156 - 11.6156i) q^{71} +(2.64907 - 2.64907i) q^{72} +(2.50097 - 2.50097i) q^{73} +19.2042i q^{74} +4.03701i q^{75} +(-8.82122 + 8.82122i) q^{76} +(-6.42611 - 0.334599i) q^{77} +(5.02784 - 6.87958i) q^{78} -0.392524i q^{79} +(-3.57822 + 3.57822i) q^{80} +1.00000 q^{81} +3.26854i q^{82} +(11.1055 + 11.1055i) q^{83} +(4.91858 + 4.91858i) q^{84} +(14.2229 - 14.2229i) q^{85} +(-4.27468 - 4.27468i) q^{86} +3.36320i q^{87} +(12.4084 + 0.646089i) q^{88} +(-5.52141 - 5.52141i) q^{89} -7.10448 q^{90} +(5.64783 + 4.12763i) q^{91} +11.7755 q^{92} +(-0.273940 + 0.273940i) q^{93} +17.0739i q^{94} +10.4602 q^{95} +(2.48510 + 2.48510i) q^{96} +(-8.21511 + 8.21511i) q^{97} +(5.40728 - 5.40728i) q^{98} +(2.22009 + 2.46398i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9}+O(q^{10}) $ 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9	$ 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9} + 4 q^{11} + 48 q^{14} - 4 q^{15} - 52 q^{16} - 8 q^{20} - 32 q^{22} - 4 q^{26} - 28 q^{27} + 24 q^{31} - 4 q^{33} + 16 q^{34} - 12 q^{37} - 48 q^{42} - 24 q^{44} + 4 q^{45} - 8 q^{47} + 52 q^{48} - 8 q^{53} + 48 q^{55} - 64 q^{58} + 4 q^{59} + 8 q^{60} + 32 q^{66} + 28 q^{67} - 4 q^{70} + 12 q^{71} + 4 q^{78} + 56 q^{80} + 28 q^{81} - 8 q^{86} - 104 q^{89} - 76 q^{91} - 24 q^{93} - 8 q^{97} + 4 q^{99}+O(q^{100}) $ 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9 + 4 * q^11 + 48 * q^14 - 4 * q^15 - 52 * q^16 - 8 * q^20 - 32 * q^22 - 4 * q^26 - 28 * q^27 + 24 * q^31 - 4 * q^33 + 16 * q^34 - 12 * q^37 - 48 * q^42 - 24 * q^44 + 4 * q^45 - 8 * q^47 + 52 * q^48 - 8 * q^53 + 48 * q^55 - 64 * q^58 + 4 * q^59 + 8 * q^60 + 32 * q^66 + 28 * q^67 - 4 * q^70 + 12 * q^71 + 4 * q^78 + 56 * q^80 + 28 * q^81 - 8 * q^86 - 104 * q^89 - 76 * q^91 - 24 * q^93 - 8 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.67111	−	1.67111i	−1.18165	−	1.18165i	−0.979316	−	0.202337i	$-0.935146\pi$
$2$	−1.67111	−	1.67111i	−1.18165	−	1.18165i	−0.202337	−	0.979316i	$-0.564854\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$			3.58521i			1.79261i
$5$	2.12568	−	2.12568i	0.950632	−	0.950632i	−0.0482055	−	0.998837i	$-0.515350\pi$
$5$	2.12568	−	2.12568i	0.950632	−	0.950632i	0.998837	+	0.0482055i	$0.0153502\pi$
$6$	1.67111	+	1.67111i	0.682228	+	0.682228i
$7$	−1.37191	+	1.37191i	−0.518532	+	0.518532i	−0.917127	−	0.398595i	$-0.869498\pi$
$7$	−1.37191	+	1.37191i	−0.518532	+	0.518532i	0.398595	+	0.917127i	$0.369498\pi$
$8$	2.64907	−	2.64907i	0.936586	−	0.936586i
$9$	1.00000			0.333333
$10$	−7.10448			−2.24663
$11$	2.22009	+	2.46398i	0.669382	+	0.742918i
$11$	2.22009	+	2.46398i	0.669382	+	0.742918i
$12$		−	3.58521i		−	1.03496i
$13$	−0.554044	−	3.56273i	−0.153664	−	0.988123i
$13$	−0.554044	−	3.56273i	−0.153664	−	0.988123i
$14$	4.58521			1.22545
$15$	−2.12568	+	2.12568i	−0.548848	+	0.548848i
$16$	−1.68333			−0.420832
$17$	6.69098			1.62280			0.811400	−	0.584491i	$-0.198706\pi$
$17$	6.69098			1.62280			0.811400	+	0.584491i	$0.198706\pi$
$18$	−1.67111	−	1.67111i	−0.393884	−	0.393884i
$19$	2.46045	+	2.46045i	0.564465	+	0.564465i	0.930573	−	0.366108i	$-0.119310\pi$
$19$	2.46045	+	2.46045i	0.564465	+	0.564465i	−0.366108	+	0.930573i	$0.619310\pi$
$20$	7.62101	+	7.62101i	1.70411	+	1.70411i
$21$	1.37191	−	1.37191i	0.299375	−	0.299375i
$22$	0.407572	−	7.82759i	0.0868947	−	1.66885i
$23$		−	3.28445i		−	0.684856i	−0.939544	−	0.342428i	$-0.888751\pi$
$23$		−	3.28445i		−	0.684856i	0.939544	−	0.342428i	$-0.111249\pi$
$24$	−2.64907	+	2.64907i	−0.540738	+	0.540738i
$25$		−	4.03701i		−	0.807402i
$26$	−5.02784	+	6.87958i	−0.986041	+	1.34920i
$27$	−1.00000			−0.192450
$28$	−4.91858	−	4.91858i	−0.929524	−	0.929524i
$29$		−	3.36320i		−	0.624530i	−0.949995	−	0.312265i	$-0.898912\pi$
$29$		−	3.36320i		−	0.624530i	0.949995	−	0.312265i	$-0.101088\pi$
$30$	7.10448			1.29709
$31$	0.273940	−	0.273940i	0.0492011	−	0.0492011i	−0.682078	−	0.731279i	$-0.738924\pi$
$31$	0.273940	−	0.273940i	0.0492011	−	0.0492011i	0.731279	+	0.682078i	$0.238924\pi$
$32$	−2.48510	−	2.48510i	−0.439308	−	0.439308i
$33$	−2.22009	−	2.46398i	−0.386468	−	0.428924i
$34$	−11.1814	−	11.1814i	−1.91759	−	1.91759i
$35$			5.83246i			0.985866i
$36$			3.58521i			0.597536i
$37$	−5.74595	−	5.74595i	−0.944628	−	0.944628i	0.0539177	−	0.998545i	$-0.482829\pi$
$37$	−5.74595	−	5.74595i	−0.944628	−	0.944628i	−0.998545	+	0.0539177i	$0.982829\pi$
$38$		−	8.22335i		−	1.33400i
$39$	0.554044	+	3.56273i	0.0887181	+	0.570493i
$40$		−	11.2621i		−	1.78070i
$41$	−0.977956	−	0.977956i	−0.152731	−	0.152731i	0.626606	−	0.779337i	$-0.284444\pi$
$41$	−0.977956	−	0.977956i	−0.152731	−	0.152731i	−0.779337	+	0.626606i	$0.784444\pi$
$42$	−4.58521			−0.707514
$43$	2.55799			0.390090			0.195045	−	0.980794i	$-0.437515\pi$
$43$	2.55799			0.390090			0.195045	+	0.980794i	$0.437515\pi$
$44$	−8.83390	+	7.95949i	−1.33176	+	1.19994i
$45$	2.12568	−	2.12568i	0.316877	−	0.316877i
$46$	−5.48868	+	5.48868i	−0.809262	+	0.809262i
$47$	−5.10855	−	5.10855i	−0.745159	−	0.745159i	0.228407	−	0.973566i	$-0.426648\pi$
$47$	−5.10855	−	5.10855i	−0.745159	−	0.745159i	−0.973566	+	0.228407i	$0.926648\pi$
$48$	1.68333			0.242968
$49$			3.23574i			0.462249i
$50$	−6.74629	+	6.74629i	−0.954069	+	0.954069i
$51$	−6.69098			−0.936925
$52$	12.7731	−	1.98637i	1.77132	−	0.275460i
$53$	9.35644			1.28521			0.642603	−	0.766199i	$-0.277854\pi$
$53$	9.35644			1.28521			0.642603	+	0.766199i	$0.277854\pi$
$54$	1.67111	+	1.67111i	0.227409	+	0.227409i
$55$	9.95682	+	0.518439i	1.34258	+	0.0699062i
$56$			7.26854i			0.971300i
$57$	−2.46045	−	2.46045i	−0.325894	−	0.325894i
$58$	−5.62027	+	5.62027i	−0.737977	+	0.737977i
$59$	−2.90188	−	2.90188i	−0.377793	−	0.377793i	0.492512	−	0.870305i	$-0.336079\pi$
$59$	−2.90188	−	2.90188i	−0.377793	−	0.377793i	−0.870305	+	0.492512i	$0.836079\pi$
$60$	−7.62101	−	7.62101i	−0.983868	−	0.983868i
$61$		−	6.86934i		−	0.879529i	−0.898113	−	0.439765i	$-0.855062\pi$
$61$		−	6.86934i		−	0.879529i	0.898113	−	0.439765i	$-0.144938\pi$
$62$	−0.915567			−0.116277
$63$	−1.37191	+	1.37191i	−0.172844	+	0.172844i
$64$			11.6724i			1.45905i
$65$	−8.75093	−	6.39549i	−1.08542	−	0.793263i
$66$	−0.407572	+	7.82759i	−0.0501687	+	0.963510i
$67$	−5.85989	+	5.85989i	−0.715900	+	0.715900i	−0.967763	−	0.251863i	$-0.918957\pi$
$67$	−5.85989	+	5.85989i	−0.715900	+	0.715900i	0.251863	+	0.967763i	$0.418957\pi$
$68$			23.9886i			2.90904i
$69$			3.28445i			0.395402i
$70$	9.74669	−	9.74669i	1.16495	−	1.16495i
$71$	11.6156	−	11.6156i	1.37852	−	1.37852i	0.531396	−	0.847124i	$-0.321668\pi$
$71$	11.6156	−	11.6156i	1.37852	−	1.37852i	0.847124	−	0.531396i	$-0.178332\pi$
$72$	2.64907	−	2.64907i	0.312195	−	0.312195i
$73$	2.50097	−	2.50097i	0.292717	−	0.292717i	−0.545436	−	0.838153i	$-0.683636\pi$
$73$	2.50097	−	2.50097i	0.292717	−	0.292717i	0.838153	+	0.545436i	$0.183636\pi$
$74$			19.2042i			2.23244i
$75$			4.03701i			0.466154i
$76$	−8.82122	+	8.82122i	−1.01186	+	1.01186i
$77$	−6.42611	−	0.334599i	−0.732323	−	0.0381311i
$78$	5.02784	−	6.87958i	0.569291	−	0.778959i
$79$		−	0.392524i		−	0.0441624i	−0.999756	−	0.0220812i	$-0.992971\pi$
$79$		−	0.392524i		−	0.0441624i	0.999756	−	0.0220812i	$-0.00702924\pi$
$80$	−3.57822	+	3.57822i	−0.400057	+	0.400057i
$81$	1.00000			0.111111
$82$			3.26854i			0.360950i
$83$	11.1055	+	11.1055i	1.21899	+	1.21899i	0.967986	+	0.251003i	$0.0807604\pi$
$83$	11.1055	+	11.1055i	1.21899	+	1.21899i	0.251003	+	0.967986i	$0.419240\pi$
$84$	4.91858	+	4.91858i	0.536661	+	0.536661i
$85$	14.2229	−	14.2229i	1.54269	−	1.54269i
$86$	−4.27468	−	4.27468i	−0.460951	−	0.460951i
$87$			3.36320i			0.360572i
$88$	12.4084	+	0.646089i	1.32274	+	0.0688734i
$89$	−5.52141	−	5.52141i	−0.585268	−	0.585268i	0.351078	−	0.936346i	$-0.385815\pi$
$89$	−5.52141	−	5.52141i	−0.585268	−	0.585268i	−0.936346	+	0.351078i	$0.885815\pi$
$90$	−7.10448			−0.748878
$91$	5.64783	+	4.12763i	0.592053	+	0.432694i
$92$	11.7755			1.22768
$93$	−0.273940	+	0.273940i	−0.0284063	+	0.0284063i
$94$			17.0739i			1.76104i
$95$	10.4602			1.07320
$96$	2.48510	+	2.48510i	0.253635	+	0.253635i
$97$	−8.21511	+	8.21511i	−0.834119	+	0.834119i	−0.988077	−	0.153959i	$-0.950798\pi$
$97$	−8.21511	+	8.21511i	−0.834119	+	0.834119i	0.153959	+	0.988077i	$0.450798\pi$
$98$	5.40728	−	5.40728i	0.546218	−	0.546218i
$99$	2.22009	+	2.46398i	0.223127	+	0.247639i
$100$	14.4735			1.44735
$101$	6.28207			0.625089			0.312545	−	0.949903i	$-0.398819\pi$
$101$	6.28207			0.625089			0.312545	+	0.949903i	$0.398819\pi$
$102$	11.1814	+	11.1814i	1.10712	+	1.10712i
$103$		−	11.5572i		−	1.13877i	−0.822072	−	0.569384i	$-0.807182\pi$
$103$		−	11.5572i		−	1.13877i	0.822072	−	0.569384i	$-0.192818\pi$
$104$	−10.9056	−	7.97020i	−1.06938	−	0.781543i
$105$		−	5.83246i		−	0.569190i
$106$	−15.6356	−	15.6356i	−1.51867	−	1.51867i
$107$		−	9.56070i		−	0.924267i	−0.886810	−	0.462134i	$-0.847084\pi$
$107$		−	9.56070i		−	0.924267i	0.886810	−	0.462134i	$-0.152916\pi$
$108$		−	3.58521i		−	0.344987i
$109$	12.7836	+	12.7836i	1.22445	+	1.22445i	0.966035	+	0.258411i	$0.0831987\pi$
$109$	12.7836	+	12.7836i	1.22445	+	1.22445i	0.258411	+	0.966035i	$0.416801\pi$
$110$	−15.7726	−	17.5053i	−1.50386	−	1.66907i
$111$	5.74595	+	5.74595i	0.545381	+	0.545381i
$112$	2.30937	−	2.30937i	0.218215	−	0.218215i
$113$	14.7052			1.38335			0.691674	−	0.722210i	$-0.256873\pi$
$113$	14.7052			1.38335			0.691674	+	0.722210i	$0.256873\pi$
$114$			8.22335i			0.770187i
$115$	−6.98169	−	6.98169i	−0.651046	−	0.651046i
$116$	12.0578			1.11954
$117$	−0.554044	−	3.56273i	−0.0512214	−	0.329374i
$118$			9.69873i			0.892841i
$119$	−9.17940	+	9.17940i	−0.841474	+	0.841474i
$120$			11.2621i			1.02809i
$121$	−1.14241	+	10.9405i	−0.103856	+	0.994592i
$122$	−11.4794	+	11.4794i	−1.03930	+	1.03930i
$123$	0.977956	+	0.977956i	0.0881793	+	0.0881793i
$124$	0.982133	+	0.982133i	0.0881982	+	0.0881982i
$125$	2.04700	+	2.04700i	0.183089	+	0.183089i
$126$	4.58521			0.408483
$127$	3.77210			0.334720			0.167360	−	0.985896i	$-0.446476\pi$
$127$	3.77210			0.334720			0.167360	+	0.985896i	$0.446476\pi$
$128$	14.5357	−	14.5357i	1.28478	−	1.28478i
$129$	−2.55799			−0.225218
$130$	3.93620	+	25.3113i	0.345227	+	2.21995i
$131$			21.8690i			1.91071i	0.295465	+	0.955354i	$0.404525\pi$
$131$			21.8690i			1.91071i	−0.295465	+	0.955354i	$0.595475\pi$
$132$	8.83390	−	7.95949i	0.768892	−	0.692785i
$133$	−6.75101			−0.585386
$134$	19.5851			1.69189
$135$	−2.12568	+	2.12568i	−0.182949	+	0.182949i
$136$	17.7248	−	17.7248i	1.51989	−	1.51989i
$137$	−8.09074	−	8.09074i	−0.691238	−	0.691238i	0.271266	−	0.962504i	$-0.412558\pi$
$137$	−8.09074	−	8.09074i	−0.691238	−	0.691238i	−0.962504	+	0.271266i	$0.912558\pi$
$138$	5.48868	−	5.48868i	0.467227	−	0.467227i
$139$		−	3.08211i		−	0.261421i	−0.991421	−	0.130711i	$-0.958274\pi$
$139$		−	3.08211i		−	0.261421i	0.991421	−	0.130711i	$-0.0417259\pi$
$140$	−20.9106			−1.76727
$141$	5.10855	+	5.10855i	0.430218	+	0.430218i
$142$	−38.8219			−3.25786
$143$	7.54847	−	9.27473i	0.631235	−	0.775592i
$144$	−1.68333			−0.140277
$145$	−7.14907	−	7.14907i	−0.593698	−	0.593698i
$146$	−8.35880			−0.691779
$147$		−	3.23574i		−	0.266880i
$148$	20.6004	−	20.6004i	1.69335	−	1.69335i
$149$	−13.7526	−	13.7526i	−1.12666	−	1.12666i	−0.990717	−	0.135942i	$-0.956594\pi$
$149$	−13.7526	−	13.7526i	−1.12666	−	1.12666i	−0.135942	−	0.990717i	$-0.543406\pi$
$150$	6.74629	−	6.74629i	0.550832	−	0.550832i
$151$	−4.90414	+	4.90414i	−0.399094	+	0.399094i	−0.877913	−	0.478820i	$-0.841065\pi$
$151$	−4.90414	+	4.90414i	−0.399094	+	0.399094i	0.478820	+	0.877913i	$0.341065\pi$
$152$	13.0358			1.05734
$153$	6.69098			0.540934
$154$	10.1796	+	11.2979i	0.820294	+	0.910409i
$155$		−	1.16462i		−	0.0935442i
$156$	−12.7731	+	1.98637i	−1.02267	+	0.159037i
$157$	6.61674			0.528073			0.264037	−	0.964513i	$-0.414946\pi$
$157$	6.61674			0.528073			0.264037	+	0.964513i	$0.414946\pi$
$158$	−0.655951	+	0.655951i	−0.0521847	+	0.0521847i
$159$	−9.35644			−0.742014
$160$	−10.5651			−0.835241
$161$	4.50596	+	4.50596i	0.355120	+	0.355120i
$162$	−1.67111	−	1.67111i	−0.131295	−	0.131295i
$163$	7.31951	+	7.31951i	0.573308	+	0.573308i	0.933051	−	0.359743i	$-0.117136\pi$
$163$	7.31951	+	7.31951i	0.573308	+	0.573308i	−0.359743	+	0.933051i	$0.617136\pi$
$164$	3.50618	−	3.50618i	0.273787	−	0.273787i
$165$	−9.95682	−	0.518439i	−0.775138	−	0.0403604i
$166$		−	37.1171i		−	2.88084i
$167$	−3.21549	+	3.21549i	−0.248822	+	0.248822i	−0.820487	−	0.571665i	$-0.806298\pi$
$167$	−3.21549	+	3.21549i	−0.248822	+	0.248822i	0.571665	+	0.820487i	$0.306298\pi$
$168$		−	7.26854i		−	0.560780i
$169$	−12.3861	+	3.94782i	−0.952775	+	0.303678i
$170$	−47.5359			−3.64584
$171$	2.46045	+	2.46045i	0.188155	+	0.188155i
$172$			9.17094i			0.699278i
$173$	−23.6361			−1.79702			−0.898509	−	0.438955i	$-0.855349\pi$
$173$	−23.6361			−1.79702			−0.898509	+	0.438955i	$0.855349\pi$
$174$	5.62027	−	5.62027i	0.426071	−	0.426071i
$175$	5.53840	+	5.53840i	0.418664	+	0.418664i
$176$	−3.73714	−	4.14769i	−0.281698	−	0.312644i
$177$	2.90188	+	2.90188i	0.218119	+	0.218119i
$178$			18.4538i			1.38317i
$179$			7.35371i			0.549642i	0.961495	+	0.274821i	$0.0886186\pi$
$179$			7.35371i			0.549642i	−0.961495	+	0.274821i	$0.911381\pi$
$180$	7.62101	+	7.62101i	0.568036	+	0.568036i
$181$			21.8269i			1.62238i	0.584780	+	0.811192i	$0.301181\pi$
$181$			21.8269i			1.62238i	−0.584780	+	0.811192i	$0.698819\pi$
$182$	−2.54041	−	16.3359i	−0.188308	−	1.21090i
$183$			6.86934i			0.507796i
$184$	−8.70073	−	8.70073i	−0.641426	−	0.641426i
$185$	−24.4281			−1.79599
$186$	0.915567			0.0671327
$187$	14.8546	+	16.4865i	1.08627	+	1.20561i
$188$	18.3153	−	18.3153i	1.33578	−	1.33578i
$189$	1.37191	−	1.37191i	0.0997916	−	0.0997916i
$190$	−17.4802	−	17.4802i	−1.26815	−	1.26815i
$191$	−6.84281			−0.495129			−0.247564	−	0.968871i	$-0.579630\pi$
$191$	−6.84281			−0.495129			−0.247564	+	0.968871i	$0.579630\pi$
$192$		−	11.6724i		−	0.842384i
$193$	0.448878	−	0.448878i	0.0323109	−	0.0323109i	−0.690767	−	0.723078i	$-0.742727\pi$
$193$	0.448878	−	0.448878i	0.0323109	−	0.0323109i	0.723078	+	0.690767i	$0.242727\pi$
$194$	27.4567			1.97128
$195$	8.75093	+	6.39549i	0.626667	+	0.457991i
$196$	−11.6008			−0.828630
$197$	−5.93703	−	5.93703i	−0.422996	−	0.422996i	0.463238	−	0.886234i	$-0.346687\pi$
$197$	−5.93703	−	5.93703i	−0.422996	−	0.422996i	−0.886234	+	0.463238i	$0.846687\pi$
$198$	0.407572	−	7.82759i	0.0289649	−	0.556283i
$199$			24.1066i			1.70887i	0.519557	+	0.854436i	$0.326097\pi$
$199$			24.1066i			1.70887i	−0.519557	+	0.854436i	$0.673903\pi$
$200$	−10.6943	−	10.6943i	−0.756202	−	0.756202i
$201$	5.85989	−	5.85989i	0.413325	−	0.413325i
$202$	−10.4980	−	10.4980i	−0.738639	−	0.738639i
$203$	4.61399	+	4.61399i	0.323839	+	0.323839i
$204$		−	23.9886i		−	1.67954i
$205$	−4.15764			−0.290382
$206$	−19.3134	+	19.3134i	−1.34563	+	1.34563i
$207$		−	3.28445i		−	0.228285i
$208$	0.932639	+	5.99725i	0.0646669	+	0.415834i
$209$	−0.600086	+	11.5249i	−0.0415088	+	0.797194i
$210$	−9.74669	+	9.74669i	−0.672585	+	0.672585i
$211$		−	7.75020i		−	0.533546i	−0.963759	−	0.266773i	$-0.914043\pi$
$211$		−	7.75020i		−	0.533546i	0.963759	−	0.266773i	$-0.0859573\pi$
$212$			33.5448i			2.30387i
$213$	−11.6156	+	11.6156i	−0.795889	+	0.795889i
$214$	−15.9770	+	15.9770i	−1.09216	+	1.09216i
$215$	5.43746	−	5.43746i	0.370832	−	0.370832i
$216$	−2.64907	+	2.64907i	−0.180246	+	0.180246i
$217$			0.751640i			0.0510247i
$218$		−	42.7256i		−	2.89374i
$219$	−2.50097	+	2.50097i	−0.169000	+	0.169000i
$220$	−1.85871	+	35.6973i	−0.125314	+	2.40671i
$221$	−3.70710	−	23.8381i	−0.249367	−	1.60353i
$222$		−	19.2042i		−	1.28890i
$223$	6.78100	−	6.78100i	0.454089	−	0.454089i	−0.442620	−	0.896709i	$-0.645951\pi$
$223$	6.78100	−	6.78100i	0.454089	−	0.454089i	0.896709	+	0.442620i	$0.145951\pi$
$224$	6.81866			0.455591
$225$		−	4.03701i		−	0.269134i
$226$	−24.5740	−	24.5740i	−1.63464	−	1.63464i
$227$	−0.583085	−	0.583085i	−0.0387007	−	0.0387007i	0.687492	−	0.726192i	$-0.258712\pi$
$227$	−0.583085	−	0.583085i	−0.0387007	−	0.0387007i	−0.726192	+	0.687492i	$0.758712\pi$
$228$	8.82122	−	8.82122i	0.584200	−	0.584200i
$229$	4.76299	+	4.76299i	0.314748	+	0.314748i	0.846746	−	0.531998i	$-0.178559\pi$
$229$	4.76299	+	4.76299i	0.314748	+	0.314748i	−0.531998	+	0.846746i	$0.678559\pi$
$230$			23.3343i			1.53862i
$231$	6.42611	+	0.334599i	0.422807	+	0.0220150i
$232$	−8.90933	−	8.90933i	−0.584926	−	0.584926i
$233$	11.5756			0.758343			0.379172	−	0.925326i	$-0.376209\pi$
$233$	11.5756			0.758343			0.379172	+	0.925326i	$0.376209\pi$
$234$	−5.02784	+	6.87958i	−0.328680	+	0.449732i
$235$	−21.7183			−1.41674
$236$	10.4039	−	10.4039i	0.677235	−	0.677235i
$237$			0.392524i			0.0254972i
$238$	30.6796			1.98866
$239$	−16.0412	−	16.0412i	−1.03762	−	1.03762i	−0.999264	−	0.0383573i	$-0.987787\pi$
$239$	−16.0412	−	16.0412i	−1.03762	−	1.03762i	−0.0383573	−	0.999264i	$-0.512213\pi$
$240$	3.57822	−	3.57822i	0.230973	−	0.230973i
$241$	16.0481	−	16.0481i	1.03375	−	1.03375i	0.0343356	−	0.999410i	$-0.489069\pi$
$241$	16.0481	−	16.0481i	1.03375	−	1.03375i	0.999410	−	0.0343356i	$-0.0109315\pi$
$242$	20.1919	−	16.3737i	1.29798	−	1.05254i
$243$	−1.00000			−0.0641500
$244$	24.6281			1.57665
$245$	6.87815	+	6.87815i	0.439429	+	0.439429i
$246$		−	3.26854i		−	0.208395i
$247$	7.40270	−	10.1291i	0.471023	−	0.644499i
$248$		−	1.45137i		−	0.0921621i
$249$	−11.1055	−	11.1055i	−0.703784	−	0.703784i
$250$		−	6.84153i		−	0.432696i
$251$		−	13.8730i		−	0.875657i	−0.899058	−	0.437829i	$-0.855748\pi$
$251$		−	13.8730i		−	0.875657i	0.899058	−	0.437829i	$-0.144252\pi$
$252$	−4.91858	−	4.91858i	−0.309841	−	0.309841i
$253$	8.09283	−	7.29178i	0.508792	−	0.458430i
$254$	−6.30360	−	6.30360i	−0.395523	−	0.395523i
$255$	−14.2229	+	14.2229i	−0.890670	+	0.890670i
$256$	−25.2366			−1.57729
$257$			14.3028i			0.892186i	0.894987	+	0.446093i	$0.147185\pi$
$257$			14.3028i			0.892186i	−0.894987	+	0.446093i	$0.852815\pi$
$258$	4.27468	+	4.27468i	0.266130	+	0.266130i
$259$	15.7658			0.979640
$260$	22.9292	−	31.3740i	1.42201	−	1.94573i
$261$		−	3.36320i		−	0.208177i
$262$	36.5456	−	36.5456i	2.25779	−	2.25779i
$263$		−	11.5120i		−	0.709859i	−0.934893	−	0.354930i	$-0.884505\pi$
$263$		−	11.5120i		−	0.709859i	0.934893	−	0.354930i	$-0.115495\pi$
$264$	−12.4084	−	0.646089i	−0.763685	−	0.0397641i
$265$	19.8888	−	19.8888i	1.22176	−	1.22176i
$266$	11.2817	+	11.2817i	0.691724	+	0.691724i
$267$	5.52141	+	5.52141i	0.337905	+	0.337905i
$268$	−21.0090	−	21.0090i	−1.28333	−	1.28333i
$269$	20.2722			1.23602			0.618010	−	0.786170i	$-0.287939\pi$
$269$	20.2722			1.23602			0.618010	+	0.786170i	$0.287939\pi$
$270$	7.10448			0.432365
$271$	1.35380	−	1.35380i	0.0822374	−	0.0822374i	−0.664792	−	0.747029i	$-0.731480\pi$
$271$	1.35380	−	1.35380i	0.0822374	−	0.0822374i	0.747029	+	0.664792i	$0.231480\pi$
$272$	−11.2631			−0.682927
$273$	−5.64783	−	4.12763i	−0.341822	−	0.249816i
$274$			27.0410i			1.63361i
$275$	9.94712	−	8.96252i	0.599834	−	0.540461i
$276$	−11.7755			−0.708800
$277$	17.7086			1.06400			0.532002	−	0.846743i	$-0.321440\pi$
$277$	17.7086			1.06400			0.532002	+	0.846743i	$0.321440\pi$
$278$	−5.15054	+	5.15054i	−0.308909	+	0.308909i
$279$	0.273940	−	0.273940i	0.0164004	−	0.0164004i
$280$	15.4506	+	15.4506i	0.923349	+	0.923349i
$281$	−11.6127	+	11.6127i	−0.692757	+	0.692757i	−0.962838	−	0.270081i	$-0.912950\pi$
$281$	−11.6127	+	11.6127i	−0.692757	+	0.692757i	0.270081	+	0.962838i	$0.412950\pi$
$282$		−	17.0739i		−	1.01674i
$283$	−18.8088			−1.11807			−0.559034	−	0.829145i	$-0.688828\pi$
$283$	−18.8088			−1.11807			−0.559034	+	0.829145i	$0.688828\pi$
$284$	41.6445	+	41.6445i	2.47114	+	2.47114i
$285$	−10.4602			−0.619611
$286$	−28.1134	+	2.88477i	−1.66238	+	0.170580i
$287$	2.68333			0.158392
$288$	−2.48510	−	2.48510i	−0.146436	−	0.146436i
$289$	27.7692			1.63348
$290$			23.8938i			1.40309i
$291$	8.21511	−	8.21511i	0.481579	−	0.481579i
$292$	8.96652	+	8.96652i	0.524726	+	0.524726i
$293$	−22.4031	+	22.4031i	−1.30881	+	1.30881i	−0.386528	+	0.922278i	$0.626326\pi$
$293$	−22.4031	+	22.4031i	−1.30881	+	1.30881i	−0.922278	+	0.386528i	$0.873674\pi$
$294$	−5.40728	+	5.40728i	−0.315359	+	0.315359i
$295$	−12.3369			−0.718284
$296$	−30.4428			−1.76945
$297$	−2.22009	−	2.46398i	−0.128823	−	0.142975i
$298$			45.9643i			2.66264i
$299$	−11.7016	+	1.81973i	−0.676722	+	0.105238i
$300$	−14.4735			−0.835631
$301$	−3.50932	+	3.50932i	−0.202274	+	0.202274i
$302$	16.3907			0.943180
$303$	−6.28207			−0.360896
$304$	−4.14174	−	4.14174i	−0.237545	−	0.237545i
$305$	−14.6020	−	14.6020i	−0.836108	−	0.836108i
$306$	−11.1814	−	11.1814i	−0.639196	−	0.639196i
$307$	−13.3054	+	13.3054i	−0.759377	+	0.759377i	−0.976209	−	0.216832i	$-0.930428\pi$
$307$	−13.3054	+	13.3054i	−0.759377	+	0.759377i	0.216832	+	0.976209i	$0.430428\pi$
$308$	1.19961	−	23.0390i	0.0683540	−	1.31277i
$309$			11.5572i			0.657468i
$310$	−1.94620	+	1.94620i	−0.110537	+	0.110537i
$311$			13.0705i			0.741160i	0.928801	+	0.370580i	$0.120841\pi$
$311$			13.0705i			0.741160i	−0.928801	+	0.370580i	$0.879159\pi$
$312$	10.9056	+	7.97020i	0.617408	+	0.451224i
$313$	−11.5886			−0.655026			−0.327513	−	0.944847i	$-0.606211\pi$
$313$	−11.5886			−0.655026			−0.327513	+	0.944847i	$0.606211\pi$
$314$	−11.0573	−	11.0573i	−0.623999	−	0.623999i
$315$			5.83246i			0.328622i
$316$	1.40728			0.0791659
$317$	−17.1628	+	17.1628i	−0.963956	+	0.963956i	−0.999373	−	0.0354165i	$-0.988724\pi$
$317$	−17.1628	+	17.1628i	−0.963956	+	0.963956i	0.0354165	+	0.999373i	$0.488724\pi$
$318$	15.6356	+	15.6356i	0.876803	+	0.876803i
$319$	8.28685	−	7.46659i	0.463975	−	0.418049i
$320$	24.8118	+	24.8118i	1.38702	+	1.38702i
$321$			9.56070i			0.533626i
$322$		−	15.0599i		−	0.839256i
$323$	16.4628	+	16.4628i	0.916014	+	0.916014i
$324$			3.58521i			0.199179i
$325$	−14.3828	+	2.23668i	−0.797813	+	0.124069i
$326$		−	24.4634i		−	1.35490i
$327$	−12.7836	−	12.7836i	−0.706934	−	0.706934i
$328$	−5.18134			−0.286092
$329$	14.0169			0.772778
$330$	15.7726	+	17.5053i	0.868252	+	0.963636i
$331$	13.0175	−	13.0175i	0.715504	−	0.715504i	−0.252177	−	0.967681i	$-0.581147\pi$
$331$	13.0175	−	13.0175i	0.715504	−	0.715504i	0.967681	+	0.252177i	$0.0811466\pi$
$332$	−39.8157	+	39.8157i	−2.18517	+	2.18517i
$333$	−5.74595	−	5.74595i	−0.314876	−	0.314876i
$334$	10.7469			0.588042
$335$			24.9125i			1.36111i
$336$	−2.30937	+	2.30937i	−0.125987	+	0.125987i
$337$	−3.45615			−0.188268			−0.0941342	−	0.995560i	$-0.530008\pi$
$337$	−3.45615			−0.188268			−0.0941342	+	0.995560i	$0.530008\pi$
$338$	27.2957	+	14.1012i	1.48469	+	0.767006i
$339$	−14.7052			−0.798676
$340$	50.9920	+	50.9920i	2.76543	+	2.76543i
$341$	1.28315	+	0.0668121i	0.0694867	+	0.00361808i
$342$		−	8.22335i		−	0.444668i
$343$	−14.0425	−	14.0425i	−0.758223	−	0.758223i
$344$	6.77628	−	6.77628i	0.365353	−	0.365353i
$345$	6.98169	+	6.98169i	0.375881	+	0.375881i
$346$	39.4985	+	39.4985i	2.12345	+	2.12345i
$347$			16.8397i			0.904005i	0.892017	+	0.452002i	$0.149290\pi$
$347$			16.8397i			0.904005i	−0.892017	+	0.452002i	$0.850710\pi$
$348$	−12.0578			−0.646365
$349$	−15.2709	+	15.2709i	−0.817433	+	0.817433i	−0.985735	−	0.168302i	$-0.946172\pi$
$349$	−15.2709	+	15.2709i	−0.817433	+	0.817433i	0.168302	+	0.985735i	$0.446172\pi$
$350$		−	18.5106i		−	0.989431i
$351$	0.554044	+	3.56273i	0.0295727	+	0.190164i
$352$	0.606100	−	11.6404i	0.0323052	−	0.620435i
$353$	2.12218	−	2.12218i	0.112952	−	0.112952i	−0.648372	−	0.761324i	$-0.724550\pi$
$353$	2.12218	−	2.12218i	0.112952	−	0.112952i	0.761324	+	0.648372i	$0.224550\pi$
$354$		−	9.69873i		−	0.515482i
$355$		−	49.3821i		−	2.62093i
$356$	19.7954	−	19.7954i	1.04916	−	1.04916i
$357$	9.17940	−	9.17940i	0.485825	−	0.485825i
$358$	12.2889	−	12.2889i	0.649486	−	0.649486i
$359$	−6.07486	+	6.07486i	−0.320619	+	0.320619i	−0.849005	−	0.528386i	$-0.822798\pi$
$359$	−6.07486	+	6.07486i	−0.320619	+	0.320619i	0.528386	+	0.849005i	$0.322798\pi$
$360$		−	11.2621i		−	0.593566i
$361$		−	6.89241i		−	0.362759i
$362$	36.4752	−	36.4752i	1.91709	−	1.91709i
$363$	1.14241	−	10.9405i	0.0599612	−	0.574228i
$364$	−14.7985	+	20.2487i	−0.775650	+	1.06132i
$365$		−	10.6325i		−	0.556532i
$366$	11.4794	−	11.4794i	0.600039	−	0.600039i
$367$	−21.3852			−1.11630			−0.558150	−	0.829740i	$-0.688489\pi$
$367$	−21.3852			−1.11630			−0.558150	+	0.829740i	$0.688489\pi$
$368$			5.52882i			0.288210i
$369$	−0.977956	−	0.977956i	−0.0509104	−	0.0509104i
$370$	40.8220	+	40.8220i	2.12223	+	2.12223i
$371$	−12.8362	+	12.8362i	−0.666421	+	0.666421i
$372$	−0.982133	−	0.982133i	−0.0509212	−	0.0509212i
$373$			20.2050i			1.04618i	0.852278	+	0.523089i	$0.175220\pi$
$373$			20.2050i			1.04618i	−0.852278	+	0.523089i	$0.824780\pi$
$374$	2.72706	−	52.3743i	0.141013	−	2.70821i
$375$	−2.04700	−	2.04700i	−0.105707	−	0.105707i
$376$	−27.0658			−1.39581
$377$	−11.9822	+	1.86336i	−0.617112	+	0.0959679i
$378$	−4.58521			−0.235838
$379$	−19.6483	+	19.6483i	−1.00926	+	1.00926i	−0.00930684	+	0.999957i	$0.502963\pi$
$379$	−19.6483	+	19.6483i	−1.00926	+	1.00926i	−0.999957	+	0.00930684i	$0.997037\pi$
$380$			37.5022i			1.92382i
$381$	−3.77210			−0.193251
$382$	11.4351	+	11.4351i	0.585070	+	0.585070i
$383$	−12.0548	+	12.0548i	−0.615972	+	0.615972i	−0.944496	−	0.328524i	$-0.893449\pi$
$383$	−12.0548	+	12.0548i	−0.615972	+	0.615972i	0.328524	+	0.944496i	$0.393449\pi$
$384$	−14.5357	+	14.5357i	−0.741771	+	0.741771i
$385$	−14.3711	+	12.9486i	−0.732418	+	0.659921i
$386$	−1.50025			−0.0763606
$387$	2.55799			0.130030
$388$	−29.4529	−	29.4529i	−1.49525	−	1.49525i
$389$		−	2.80700i		−	0.142321i	−0.997465	−	0.0711604i	$-0.977330\pi$
$389$		−	2.80700i		−	0.142321i	0.997465	−	0.0711604i	$-0.0226702\pi$
$390$	−3.93620	−	25.3113i	−0.199317	−	1.28169i
$391$		−	21.9762i		−	1.11138i
$392$	8.57169	+	8.57169i	0.432936	+	0.432936i
$393$		−	21.8690i		−	1.10315i
$394$			19.8428i			0.999668i
$395$	−0.834380	−	0.834380i	−0.0419822	−	0.0419822i
$396$	−8.83390	+	7.95949i	−0.443920	+	0.399980i
$397$	−4.30770	−	4.30770i	−0.216197	−	0.216197i	0.590697	−	0.806894i	$-0.298853\pi$
$397$	−4.30770	−	4.30770i	−0.216197	−	0.216197i	−0.806894	+	0.590697i	$0.798853\pi$
$398$	40.2848	−	40.2848i	2.01929	−	2.01929i
$399$	6.75101			0.337973
$400$			6.79562i			0.339781i
$401$	−0.575718	−	0.575718i	−0.0287500	−	0.0287500i	0.692586	−	0.721336i	$-0.256471\pi$
$401$	−0.575718	−	0.575718i	−0.0287500	−	0.0287500i	−0.721336	+	0.692586i	$0.756471\pi$
$402$	−19.5851			−0.976814
$403$	−1.12775	−	0.824199i	−0.0561772	−	0.0410563i
$404$			22.5226i			1.12054i
$405$	2.12568	−	2.12568i	0.105626	−	0.105626i
$406$		−	15.4210i		−	0.765330i
$407$	1.40140	−	26.9144i	0.0694647	−	1.33410i
$408$	−17.7248	+	17.7248i	−0.877510	+	0.877510i
$409$	−6.90171	−	6.90171i	−0.341268	−	0.341268i	0.515576	−	0.856844i	$-0.327578\pi$
$409$	−6.90171	−	6.90171i	−0.341268	−	0.341268i	−0.856844	+	0.515576i	$0.827578\pi$
$410$	6.94787	+	6.94787i	0.343131	+	0.343131i
$411$	8.09074	+	8.09074i	0.399087	+	0.399087i
$412$	41.4351			2.04136
$413$	7.96223			0.391796
$414$	−5.48868	+	5.48868i	−0.269754	+	0.269754i
$415$	47.2135			2.31762
$416$	−7.47689	+	10.2306i	−0.366585	+	0.501597i
$417$			3.08211i			0.150932i
$418$	20.2622	−	18.2566i	0.991056	−	0.892958i
$419$	0.159209			0.00777788			0.00388894	−	0.999992i	$-0.498762\pi$
$419$	0.159209			0.00777788			0.00388894	+	0.999992i	$0.498762\pi$
$420$	20.9106			1.02033
$421$	1.88602	−	1.88602i	0.0919190	−	0.0919190i	−0.659652	−	0.751571i	$-0.729296\pi$
$421$	1.88602	−	1.88602i	0.0919190	−	0.0919190i	0.751571	+	0.659652i	$0.229296\pi$
$422$	−12.9514	+	12.9514i	−0.630466	+	0.630466i
$423$	−5.10855	−	5.10855i	−0.248386	−	0.248386i
$424$	24.7858	−	24.7858i	1.20371	−	1.20371i
$425$		−	27.0116i		−	1.31025i
$426$	38.8219			1.88093
$427$	9.42410	+	9.42410i	0.456064	+	0.456064i
$428$	34.2771			1.65685
$429$	−7.54847	+	9.27473i	−0.364444	+	0.447788i
$430$	−18.1732			−0.876389
$431$	17.4987	+	17.4987i	0.842883	+	0.842883i	0.989233	−	0.146350i	$-0.0467526\pi$
$431$	17.4987	+	17.4987i	0.842883	+	0.842883i	−0.146350	+	0.989233i	$0.546753\pi$
$432$	1.68333			0.0809892
$433$		−	0.335335i		−	0.0161152i	−0.999968	−	0.00805758i	$-0.997435\pi$
$433$		−	0.335335i		−	0.0161152i	0.999968	−	0.00805758i	$-0.00256483\pi$
$434$	1.25607	−	1.25607i	0.0602935	−	0.0602935i
$435$	7.14907	+	7.14907i	0.342772	+	0.342772i
$436$	−45.8319	+	45.8319i	−2.19495	+	2.19495i
$437$	8.08122	−	8.08122i	0.386577	−	0.386577i
$438$	8.35880			0.399399
$439$	−18.6067			−0.888051			−0.444025	−	0.896014i	$-0.646450\pi$
$439$	−18.6067			−0.888051			−0.444025	+	0.896014i	$0.646450\pi$
$440$	27.7497	−	25.0029i	1.32291	−	1.19197i
$441$			3.23574i			0.154083i
$442$	−33.6412	+	46.0311i	−1.60015	+	2.18948i
$443$	25.0591			1.19059			0.595296	−	0.803506i	$-0.297035\pi$
$443$	25.0591			1.19059			0.595296	+	0.803506i	$0.297035\pi$
$444$	−20.6004	+	20.6004i	−0.977654	+	0.977654i
$445$	−23.4735			−1.11275
$446$	−22.6636			−1.07315
$447$	13.7526	+	13.7526i	0.650477	+	0.650477i
$448$	−16.0135	−	16.0135i	−0.756565	−	0.756565i
$449$	−12.9682	−	12.9682i	−0.612008	−	0.612008i	0.331461	−	0.943469i	$-0.392458\pi$
$449$	−12.9682	−	12.9682i	−0.612008	−	0.612008i	−0.943469	+	0.331461i	$0.892458\pi$
$450$	−6.74629	+	6.74629i	−0.318023	+	0.318023i
$451$	0.238517	−	4.58082i	0.0112313	−	0.215702i
$452$			52.7213i			2.47980i
$453$	4.90414	−	4.90414i	0.230417	−	0.230417i
$454$			1.94880i			0.0914615i
$455$	20.7795	−	3.23144i	0.974157	−	0.151492i
$456$	−13.0358			−0.610456
$457$	12.4301	+	12.4301i	0.581456	+	0.581456i	0.935303	−	0.353847i	$-0.115127\pi$
$457$	12.4301	+	12.4301i	0.581456	+	0.581456i	−0.353847	+	0.935303i	$0.615127\pi$
$458$		−	15.9190i		−	0.743845i
$459$	−6.69098			−0.312308
$460$	25.0308	−	25.0308i	1.16707	−	1.16707i
$461$	−19.9560	−	19.9560i	−0.929444	−	0.929444i	0.0682257	−	0.997670i	$-0.478266\pi$
$461$	−19.9560	−	19.9560i	−0.929444	−	0.929444i	−0.997670	+	0.0682257i	$0.978266\pi$
$462$	−10.1796	−	11.2979i	−0.473597	−	0.525625i
$463$	0.914773	+	0.914773i	0.0425131	+	0.0425131i	0.728044	−	0.685531i	$-0.240430\pi$
$463$	0.914773	+	0.914773i	0.0425131	+	0.0425131i	−0.685531	+	0.728044i	$0.740430\pi$
$464$			5.66137i			0.262822i
$465$			1.16462i			0.0540078i
$466$	−19.3441	−	19.3441i	−0.896099	−	0.896099i
$467$		−	10.9958i		−	0.508823i	−0.967096	−	0.254412i	$-0.918118\pi$
$467$		−	10.9958i		−	0.508823i	0.967096	−	0.254412i	$-0.0818818\pi$
$468$	12.7731	−	1.98637i	0.590439	−	0.0918199i
$469$		−	16.0785i		−	0.742434i
$470$	36.2936	+	36.2936i	1.67410	+	1.67410i
$471$	−6.61674			−0.304883
$472$	−15.3746			−0.707672
$473$	5.67896	+	6.30284i	0.261119	+	0.289805i
$474$	0.655951	−	0.655951i	0.0301288	−	0.0301288i
$475$	9.93285	−	9.93285i	0.455750	−	0.455750i
$476$	−32.9101	−	32.9101i	−1.50843	−	1.50843i
$477$	9.35644			0.428402
$478$			53.6133i			2.45222i
$479$	1.37957	−	1.37957i	0.0630344	−	0.0630344i	−0.674887	−	0.737921i	$-0.735808\pi$
$479$	1.37957	−	1.37957i	0.0630344	−	0.0630344i	0.737921	+	0.674887i	$0.235808\pi$
$480$	10.5651			0.482227
$481$	−17.2877	+	23.6548i	−0.788253	+	1.07856i
$482$	−53.6361			−2.44306
$483$	−4.50596	−	4.50596i	−0.205028	−	0.205028i
$484$	−39.2241	−	4.09580i	−1.78291	−	0.186173i
$485$			34.9254i			1.58588i
$486$	1.67111	+	1.67111i	0.0758031	+	0.0758031i
$487$	3.04720	−	3.04720i	0.138082	−	0.138082i	−0.634687	−	0.772769i	$-0.718871\pi$
$487$	3.04720	−	3.04720i	0.138082	−	0.138082i	0.772769	+	0.634687i	$0.218871\pi$
$488$	−18.1973	−	18.1973i	−0.823755	−	0.823755i
$489$	−7.31951	−	7.31951i	−0.331000	−	0.331000i
$490$		−	22.9883i		−	1.03850i
$491$	7.62513			0.344117			0.172059	−	0.985087i	$-0.444958\pi$
$491$	7.62513			0.344117			0.172059	+	0.985087i	$0.444958\pi$
$492$	−3.50618	+	3.50618i	−0.158071	+	0.158071i
$493$		−	22.5031i		−	1.01349i
$494$	−29.2976	+	4.55610i	−1.31816	+	0.204989i
$495$	9.95682	+	0.518439i	0.447526	+	0.0233021i
$496$	−0.461131	+	0.461131i	−0.0207054	+	0.0207054i
$497$			31.8711i			1.42961i
$498$			37.1171i			1.66326i
$499$	−0.181339	+	0.181339i	−0.00811785	+	0.00811785i	−0.711154	−	0.703036i	$-0.751827\pi$
$499$	−0.181339	+	0.181339i	−0.00811785	+	0.00811785i	0.703036	+	0.711154i	$0.251827\pi$
$500$	−7.33894	+	7.33894i	−0.328207	+	0.328207i
$501$	3.21549	−	3.21549i	0.143657	−	0.143657i
$502$	−23.1833	+	23.1833i	−1.03472	+	1.03472i
$503$			25.2385i			1.12533i	0.826685	+	0.562665i	$0.190224\pi$
$503$			25.2385i			1.12533i	−0.826685	+	0.562665i	$0.809776\pi$
$504$			7.26854i			0.323767i
$505$	13.3537	−	13.3537i	0.594230	−	0.594230i
$506$	−25.7094	−	1.33865i	−1.14292	−	0.0595104i
$507$	12.3861	−	3.94782i	0.550085	−	0.175329i
$508$			13.5238i			0.600021i
$509$	25.1988	−	25.1988i	1.11692	−	1.11692i	0.124724	−	0.992191i	$-0.460195\pi$
$509$	25.1988	−	25.1988i	1.11692	−	1.11692i	0.992191	−	0.124724i	$-0.0398046\pi$
$510$	47.5359			2.10493
$511$			6.86220i			0.303566i
$512$	13.1017	+	13.1017i	0.579021	+	0.579021i
$513$	−2.46045	−	2.46045i	−0.108631	−	0.108631i
$514$	23.9016	−	23.9016i	1.05425	−	1.05425i
$515$	−24.5670	−	24.5670i	−1.08255	−	1.08255i
$516$		−	9.17094i		−	0.403728i
$517$	1.24594	−	23.9288i	0.0547964	−	1.05239i
$518$	−26.3464	−	26.3464i	−1.15759	−	1.15759i
$519$	23.6361			1.03751
$520$	−40.1239	+	6.23971i	−1.75955	+	0.273630i
$521$	33.5718			1.47081			0.735404	−	0.677629i	$-0.236993\pi$
$521$	33.5718			1.47081			0.735404	+	0.677629i	$0.236993\pi$
$522$	−5.62027	+	5.62027i	−0.245992	+	0.245992i
$523$			4.69450i			0.205276i	0.994719	+	0.102638i	$0.0327283\pi$
$523$			4.69450i			0.205276i	−0.994719	+	0.102638i	$0.967272\pi$
$524$	−78.4052			−3.42515
$525$	−5.53840	−	5.53840i	−0.241716	−	0.241716i
$526$	−19.2378	+	19.2378i	−0.838807	+	0.838807i
$527$	1.83293	−	1.83293i	0.0798435	−	0.0798435i
$528$	3.73714	+	4.14769i	0.162638	+	0.180505i
$529$	12.2124			0.530973
$530$	−66.4727			−2.88739
$531$	−2.90188	−	2.90188i	−0.125931	−	0.125931i
$532$		−	24.2038i		−	1.04937i
$533$	−2.94236	+	4.02602i	−0.127448	+	0.174386i
$534$		−	18.4538i		−	0.798573i
$535$	−20.3230	−	20.3230i	−0.878638	−	0.878638i
$536$			31.0465i			1.34100i
$537$		−	7.35371i		−	0.317336i
$538$	−33.8771	−	33.8771i	−1.46055	−	1.46055i
$539$	−7.97281	+	7.18363i	−0.343413	+	0.309421i
$540$	−7.62101	−	7.62101i	−0.327956	−	0.327956i
$541$	−20.0958	+	20.0958i	−0.863987	+	0.863987i	−0.991798	−	0.127812i	$-0.959205\pi$
$541$	−20.0958	+	20.0958i	−0.863987	+	0.863987i	0.127812	+	0.991798i	$0.459205\pi$
$542$	−4.52469			−0.194352
$543$		−	21.8269i		−	0.936683i
$544$	−16.6278	−	16.6278i	−0.712910	−	0.712910i
$545$	54.3476			2.32799
$546$	2.54041	+	16.3359i	0.108720	+	0.699111i
$547$		−	9.45282i		−	0.404173i	−0.979368	−	0.202087i	$-0.935228\pi$
$547$		−	9.45282i		−	0.404173i	0.979368	−	0.202087i	$-0.0647723\pi$
$548$	29.0070	−	29.0070i	1.23912	−	1.23912i
$549$		−	6.86934i		−	0.293176i
$550$	−31.6001	−	1.64537i	−1.34743	−	0.0701590i
$551$	8.27496	−	8.27496i	0.352525	−	0.352525i
$552$	8.70073	+	8.70073i	0.370328	+	0.370328i
$553$	0.538507	+	0.538507i	0.0228996	+	0.0228996i
$554$	−29.5930	−	29.5930i	−1.25728	−	1.25728i
$555$	24.4281			1.03691
$556$	11.0500			0.468625
$557$	−25.1768	+	25.1768i	−1.06678	+	1.06678i	−0.0691713	+	0.997605i	$0.522036\pi$
$557$	−25.1768	+	25.1768i	−1.06678	+	1.06678i	−0.997605	+	0.0691713i	$0.977964\pi$
$558$	−0.915567			−0.0387591
$559$	−1.41724	−	9.11342i	−0.0599429	−	0.385457i
$560$		−	9.81796i		−	0.414885i
$561$	−14.8546	−	16.4865i	−0.627160	−	0.696059i
$562$	38.8123			1.63720
$563$	−16.3670			−0.689787			−0.344894	−	0.938642i	$-0.612085\pi$
$563$	−16.3670			−0.689787			−0.344894	+	0.938642i	$0.612085\pi$
$564$	−18.3153	+	18.3153i	−0.771211	+	0.771211i
$565$	31.2585	−	31.2585i	1.31506	−	1.31506i
$566$	31.4316	+	31.4316i	1.32117	+	1.32117i
$567$	−1.37191	+	1.37191i	−0.0576147	+	0.0576147i
$568$		−	61.5410i		−	2.58220i
$569$	33.0118			1.38393			0.691963	−	0.721933i	$-0.256746\pi$
$569$	33.0118			1.38393			0.691963	+	0.721933i	$0.256746\pi$
$570$	17.4802	+	17.4802i	0.732165	+	0.732165i
$571$	−38.8441			−1.62557			−0.812787	−	0.582561i	$-0.802051\pi$
$571$	−38.8441			−1.62557			−0.812787	+	0.582561i	$0.802051\pi$
$572$	33.2519	+	27.0629i	1.39033	+	1.13156i
$573$	6.84281			0.285863
$574$	−4.48414	−	4.48414i	−0.187164	−	0.187164i
$575$	−13.2594			−0.552954
$576$			11.6724i			0.486351i
$577$	−28.5709	+	28.5709i	−1.18942	+	1.18942i	−0.212194	+	0.977227i	$0.568061\pi$
$577$	−28.5709	+	28.5709i	−1.18942	+	1.18942i	−0.977227	+	0.212194i	$0.931939\pi$
$578$	−46.4054	−	46.4054i	−1.93021	−	1.93021i
$579$	−0.448878	+	0.448878i	−0.0186547	+	0.0186547i
$580$	25.6309	−	25.6309i	1.06427	−	1.06427i
$581$	−30.4715			−1.26417
$582$	−27.4567			−1.13812
$583$	20.7721	+	23.0541i	0.860294	+	0.954803i
$584$		−	13.2505i		−	0.548309i
$585$	−8.75093	−	6.39549i	−0.361807	−	0.264421i
$586$	74.8762			3.09311
$587$	−28.9300	+	28.9300i	−1.19407	+	1.19407i	−0.218156	+	0.975914i	$0.570004\pi$
$587$	−28.9300	+	28.9300i	−1.19407	+	1.19407i	−0.975914	+	0.218156i	$0.929996\pi$
$588$	11.6008			0.478410
$589$	1.34803			0.0555446
$590$	20.6164	+	20.6164i	0.848763	+	0.848763i
$591$	5.93703	+	5.93703i	0.244217	+	0.244217i
$592$	9.67232	+	9.67232i	0.397530	+	0.397530i
$593$	14.1603	−	14.1603i	0.581496	−	0.581496i	−0.353818	−	0.935314i	$-0.615117\pi$
$593$	14.1603	−	14.1603i	0.581496	−	0.581496i	0.935314	+	0.353818i	$0.115117\pi$
$594$	−0.407572	+	7.82759i	−0.0167229	+	0.321170i
$595$			39.0249i			1.59986i
$596$	49.3061	−	49.3061i	2.01966	−	2.01966i
$597$		−	24.1066i		−	0.986617i
$598$	22.5956	+	16.5137i	0.924005	+	0.675296i
$599$	−38.3843			−1.56834			−0.784171	−	0.620545i	$-0.786911\pi$
$599$	−38.3843			−1.56834			−0.784171	+	0.620545i	$0.786911\pi$
$600$	10.6943	+	10.6943i	0.436593	+	0.436593i
$601$		−	44.6167i		−	1.81995i	−0.414660	−	0.909976i	$-0.636100\pi$
$601$		−	44.6167i		−	1.81995i	0.414660	−	0.909976i	$-0.363900\pi$
$602$	11.7289			0.478035
$603$	−5.85989	+	5.85989i	−0.238633	+	0.238633i
$604$	−17.5824	−	17.5824i	−0.715418	−	0.715418i
$605$	20.8276	+	25.6844i	0.846763	+	1.04422i
$606$	10.4980	+	10.4980i	0.426453	+	0.426453i
$607$			32.2248i			1.30797i	0.756509	+	0.653983i	$0.226903\pi$
$607$			32.2248i			1.30797i	−0.756509	+	0.653983i	$0.773097\pi$
$608$		−	12.2289i		−	0.495948i
$609$	−4.61399	−	4.61399i	−0.186968	−	0.186968i
$610$			48.8031i			1.97598i
$611$	−15.3700	+	21.0307i	−0.621804	+	0.850813i
$612$			23.9886i			0.969681i
$613$	18.6007	+	18.6007i	0.751276	+	0.751276i	0.974717	−	0.223442i	$-0.0717292\pi$
$613$	18.6007	+	18.6007i	0.751276	+	0.751276i	−0.223442	+	0.974717i	$0.571729\pi$
$614$	44.4694			1.79464
$615$	4.15764			0.167652
$616$	−17.9096	+	16.1368i	−0.721597	+	0.650171i
$617$	7.05413	−	7.05413i	0.283989	−	0.283989i	−0.550709	−	0.834697i	$-0.685643\pi$
$617$	7.05413	−	7.05413i	0.283989	−	0.283989i	0.834697	+	0.550709i	$0.185643\pi$
$618$	19.3134	−	19.3134i	0.776899	−	0.776899i
$619$	5.06137	+	5.06137i	0.203434	+	0.203434i	0.801469	−	0.598036i	$-0.204052\pi$
$619$	5.06137	+	5.06137i	0.203434	+	0.203434i	−0.598036	+	0.801469i	$0.704052\pi$
$620$	4.17540			0.167688
$621$			3.28445i			0.131801i
$622$	21.8422	−	21.8422i	0.875794	−	0.875794i
$623$	15.1497			0.606961
$624$	−0.932639	−	5.99725i	−0.0373355	−	0.240082i
$625$	28.8876			1.15550
$626$	19.3658	+	19.3658i	0.774014	+	0.774014i
$627$	0.600086	−	11.5249i	0.0239651	−	0.460260i
$628$			23.7224i			0.946627i
$629$	−38.4460	−	38.4460i	−1.53294	−	1.53294i
$630$	9.74669	−	9.74669i	0.388317	−	0.388317i
$631$	28.6267	+	28.6267i	1.13961	+	1.13961i	0.988520	+	0.151092i	$0.0482789\pi$
$631$	28.6267	+	28.6267i	1.13961	+	1.13961i	0.151092	+	0.988520i	$0.451721\pi$
$632$	−1.03982	−	1.03982i	−0.0413619	−	0.0413619i
$633$			7.75020i			0.308043i
$634$	57.3617			2.27812
$635$	8.01828	−	8.01828i	0.318196	−	0.318196i
$636$		−	33.5448i		−	1.33014i
$637$	11.5281	−	1.79274i	0.456759	−	0.0710311i
$638$	−26.3257	−	1.37075i	−1.04225	−	0.0542683i
$639$	11.6156	−	11.6156i	0.459507	−	0.459507i
$640$		−	61.7963i		−	2.44272i
$641$			15.0769i			0.595503i	0.954643	+	0.297751i	$0.0962366\pi$
$641$			15.0769i			0.595503i	−0.954643	+	0.297751i	$0.903763\pi$
$642$	15.9770	−	15.9770i	0.630561	−	0.630561i
$643$	9.61392	−	9.61392i	0.379136	−	0.379136i	−0.491655	−	0.870790i	$-0.663608\pi$
$643$	9.61392	−	9.61392i	0.379136	−	0.379136i	0.870790	+	0.491655i	$0.163608\pi$
$644$	−16.1548	+	16.1548i	−0.636590	+	0.636590i
$645$	−5.43746	+	5.43746i	−0.214100	+	0.214100i
$646$		−	55.0223i		−	2.16482i
$647$			19.7013i			0.774536i	0.921967	+	0.387268i	$0.126581\pi$
$647$			19.7013i			0.774536i	−0.921967	+	0.387268i	$0.873419\pi$
$648$	2.64907	−	2.64907i	0.104065	−	0.104065i
$649$	0.707750	−	13.5926i	0.0277816	−	0.533557i
$650$	27.7729	+	20.2975i	1.08934	+	0.796132i
$651$		−	0.751640i		−	0.0294591i
$652$	−26.2420	+	26.2420i	−1.02772	+	1.02772i
$653$	−43.2375			−1.69201			−0.846007	−	0.533172i	$-0.821000\pi$
$653$	−43.2375			−1.69201			−0.846007	+	0.533172i	$0.821000\pi$
$654$			42.7256i			1.67070i
$655$	46.4865	+	46.4865i	1.81638	+	1.81638i
$656$	1.64622	+	1.64622i	0.0642742	+	0.0642742i
$657$	2.50097	−	2.50097i	0.0975722	−	0.0975722i
$658$	−23.4238	−	23.4238i	−0.913155	−	0.913155i
$659$			18.1385i			0.706575i	0.935515	+	0.353287i	$0.114936\pi$
$659$			18.1385i			0.706575i	−0.935515	+	0.353287i	$0.885064\pi$
$660$	1.85871	−	35.6973i	0.0723503	−	1.38952i
$661$	−4.09800	−	4.09800i	−0.159394	−	0.159394i	0.622904	−	0.782298i	$-0.285953\pi$
$661$	−4.09800	−	4.09800i	−0.159394	−	0.159394i	−0.782298	+	0.622904i	$0.785953\pi$
$662$	−43.5072			−1.69095
$663$	3.70710	+	23.8381i	0.143972	+	0.925797i
$664$	58.8385			2.28338
$665$	−14.3505	+	14.3505i	−0.556487	+	0.556487i
$666$			19.2042i			0.744148i
$667$	−11.0463			−0.427713
$668$	−11.5282	−	11.5282i	−0.446040	−	0.446040i
$669$	−6.78100	+	6.78100i	−0.262169	+	0.262169i
$670$	41.6315	−	41.6315i	1.60837	−	1.60837i
$671$	16.9259	−	15.2505i	0.653418	−	0.588741i
$672$	−6.81866			−0.263036
$673$	32.5180			1.25348			0.626738	−	0.779230i	$-0.284390\pi$
$673$	32.5180			1.25348			0.626738	+	0.779230i	$0.284390\pi$
$674$	5.77560	+	5.77560i	0.222468	+	0.222468i
$675$			4.03701i			0.155385i
$676$	−14.1538	−	44.4067i	−0.544376	−	1.70795i
$677$		−	7.87815i		−	0.302782i	−0.988474	−	0.151391i	$-0.951625\pi$
$677$		−	7.87815i		−	0.302782i	0.988474	−	0.151391i	$-0.0483752\pi$
$678$	24.5740	+	24.5740i	0.943758	+	0.943758i
$679$		−	22.5407i		−	0.865035i
$680$		−	75.3546i		−	2.88972i
$681$	0.583085	+	0.583085i	0.0223438	+	0.0223438i
$682$	−2.03264	−	2.25594i	−0.0778338	−	0.0863845i
$683$	−15.2941	−	15.2941i	−0.585214	−	0.585214i	0.351117	−	0.936332i	$-0.385802\pi$
$683$	−15.2941	−	15.2941i	−0.585214	−	0.585214i	−0.936332	+	0.351117i	$0.885802\pi$
$684$	−8.82122	+	8.82122i	−0.337288	+	0.337288i
$685$	−34.3966			−1.31423
$686$			46.9331i			1.79191i
$687$	−4.76299	−	4.76299i	−0.181720	−	0.181720i
$688$	−4.30594			−0.164162
$689$	−5.18388	−	33.3345i	−0.197490	−	1.26994i
$690$		−	23.3343i		−	0.888323i
$691$	20.8412	−	20.8412i	0.792835	−	0.792835i	−0.189119	−	0.981954i	$-0.560563\pi$
$691$	20.8412	−	20.8412i	0.792835	−	0.792835i	0.981954	+	0.189119i	$0.0605632\pi$
$692$		−	84.7404i		−	3.22135i
$693$	−6.42611	−	0.334599i	−0.244108	−	0.0127104i
$694$	28.1410	−	28.1410i	1.06822	−	1.06822i
$695$	−6.55157	−	6.55157i	−0.248515	−	0.248515i
$696$	8.90933	+	8.90933i	0.337707	+	0.337707i
$697$	−6.54348	−	6.54348i	−0.247852	−	0.247852i
$698$	51.0387			1.93184
$699$	−11.5756			−0.437830
$700$	−19.8564	+	19.8564i	−0.750500	+	0.750500i
$701$	21.6055			0.816028			0.408014	−	0.912976i	$-0.366222\pi$
$701$	21.6055			0.816028			0.408014	+	0.912976i	$0.366222\pi$
$702$	5.02784	−	6.87958i	0.189764	−	0.259653i
$703$		−	28.2752i		−	1.06642i
$704$	−28.7606	+	25.9138i	−1.08396	+	0.976663i
$705$	21.7183			0.817957
$706$	−7.09280			−0.266941
$707$	−8.61842	+	8.61842i	−0.324129	+	0.324129i
$708$	−10.4039	+	10.4039i	−0.391002	+	0.391002i
$709$	9.65076	+	9.65076i	0.362442	+	0.362442i	0.864711	−	0.502269i	$-0.167501\pi$
$709$	9.65076	+	9.65076i	0.362442	+	0.362442i	−0.502269	+	0.864711i	$0.667501\pi$
$710$	−82.5229	+	82.5229i	−3.09703	+	3.09703i
$711$		−	0.392524i		−	0.0147208i
$712$	−29.2532			−1.09631
$713$	−0.899743	−	0.899743i	−0.0336956	−	0.0336956i
$714$	−30.6796			−1.14815
$715$	−3.66947	−	35.7607i	−0.137230	−	1.33737i
$716$	−26.3646			−0.985292
$717$	16.0412	+	16.0412i	0.599071	+	0.599071i
$718$	20.3035			0.757721
$719$			9.46044i			0.352815i	0.984317	+	0.176407i	$0.0564476\pi$
$719$			9.46044i			0.352815i	−0.984317	+	0.176407i	$0.943552\pi$
$720$	−3.57822	+	3.57822i	−0.133352	+	0.133352i
$721$	15.8554	+	15.8554i	0.590488	+	0.590488i
$722$	−11.5180	+	11.5180i	−0.428655	+	0.428655i
$723$	−16.0481	+	16.0481i	−0.596833	+	0.596833i
$724$	−78.2542			−2.90830
$725$	−13.5773			−0.504247
$726$	−20.1919	+	16.3737i	−0.749392	+	0.607685i
$727$		−	34.6624i		−	1.28556i	−0.766052	−	0.642778i	$-0.777782\pi$
$727$		−	34.6624i		−	1.28556i	0.766052	−	0.642778i	$-0.222218\pi$
$728$	25.8958	−	4.02710i	0.959764	−	0.149254i
$729$	1.00000			0.0370370
$730$	−17.7681	+	17.7681i	−0.657627	+	0.657627i
$731$	17.1155			0.633038
$732$	−24.6281			−0.910279
$733$	−0.126504	−	0.126504i	−0.00467254	−	0.00467254i	0.704767	−	0.709439i	$-0.251052\pi$
$733$	−0.126504	−	0.126504i	−0.00467254	−	0.00467254i	−0.709439	+	0.704767i	$0.751052\pi$
$734$	35.7371	+	35.7371i	1.31908	+	1.31908i
$735$	−6.87815	−	6.87815i	−0.253704	−	0.253704i
$736$	−8.16220	+	8.16220i	−0.300863	+	0.300863i
$737$	−27.4482	−	1.42919i	−1.01107	−	0.0526449i
$738$			3.26854i			0.120317i
$739$	12.8617	−	12.8617i	0.473125	−	0.473125i	−0.429799	−	0.902925i	$-0.641416\pi$
$739$	12.8617	−	12.8617i	0.473125	−	0.473125i	0.902925	+	0.429799i	$0.141416\pi$
$740$		−	87.5798i		−	3.21950i
$741$	−7.40270	+	10.1291i	−0.271945	+	0.372102i
$742$	42.9013			1.57496
$743$	30.3980	+	30.3980i	1.11519	+	1.11519i	0.992437	+	0.122757i	$0.0391735\pi$
$743$	30.3980	+	30.3980i	1.11519	+	1.11519i	0.122757	+	0.992437i	$0.460827\pi$
$744$			1.45137i			0.0532098i
$745$	−58.4673			−2.14208
$746$	33.7648	−	33.7648i	1.23622	−	1.23622i
$747$	11.1055	+	11.1055i	0.406330	+	0.406330i
$748$	−59.1075	+	53.2568i	−2.16118	+	1.94726i
$749$	13.1164	+	13.1164i	0.479262	+	0.479262i
$750$			6.84153i			0.249817i
$751$			18.0117i			0.657256i	0.944459	+	0.328628i	$0.106586\pi$
$751$			18.0117i			0.657256i	−0.944459	+	0.328628i	$0.893414\pi$
$752$	8.59938	+	8.59938i	0.313587	+	0.313587i
$753$			13.8730i			0.505561i
$754$	23.1374	+	16.9096i	0.842613	+	0.615812i
$755$			20.8493i			0.758782i
$756$	4.91858	+	4.91858i	0.178887	+	0.178887i
$757$	−18.3639			−0.667448			−0.333724	−	0.942671i	$-0.608305\pi$
$757$	−18.3639			−0.667448			−0.333724	+	0.942671i	$0.608305\pi$
$758$	65.6688			2.38520
$759$	−8.09283	+	7.29178i	−0.293751	+	0.264675i
$760$	27.7098	−	27.7098i	1.00514	−	1.00514i
$761$	27.6011	−	27.6011i	1.00054	−	1.00054i	0.000539050	−	1.00000i	$-0.499828\pi$
$761$	27.6011	−	27.6011i	1.00054	−	1.00054i	1.00000		0.000539050i	$-0.000171585\pi$
$762$	6.30360	+	6.30360i	0.228355	+	0.228355i
$763$	−35.0758			−1.26983
$764$		−	24.5329i		−	0.887571i
$765$	14.2229	−	14.2229i	0.514229	−	0.514229i
$766$	40.2898			1.45573
$767$	−8.73085	+	11.9464i	−0.315253	+	0.431359i
$768$	25.2366			0.910647
$769$	5.30817	+	5.30817i	0.191417	+	0.191417i	0.796308	−	0.604891i	$-0.206783\pi$
$769$	5.30817	+	5.30817i	0.191417	+	0.191417i	−0.604891	+	0.796308i	$0.706783\pi$
$770$	45.6542	+	2.37715i	1.64526	+	0.0856666i
$771$		−	14.3028i		−	0.515104i
$772$	1.60932	+	1.60932i	0.0579208	+	0.0579208i
$773$	−12.0100	+	12.0100i	−0.431969	+	0.431969i	−0.889298	−	0.457329i	$-0.848806\pi$
$773$	−12.0100	+	12.0100i	−0.431969	+	0.431969i	0.457329	+	0.889298i	$0.348806\pi$
$774$	−4.27468	−	4.27468i	−0.153650	−	0.153650i
$775$	−1.10590	−	1.10590i	−0.0397251	−	0.0397251i
$776$			43.5248i			1.56245i
$777$	−15.7658			−0.565595
$778$	−4.69081	+	4.69081i	−0.168174	+	0.168174i
$779$		−	4.81242i		−	0.172423i
$780$	−22.9292	+	31.3740i	−0.820997	+	1.12337i
$781$	54.4083	+	2.83297i	1.94688	+	0.101372i
$782$	−36.7246	+	36.7246i	−1.31327	+	1.31327i
$783$			3.36320i			0.120191i
$784$		−	5.44682i		−	0.194529i
$785$	14.0650	−	14.0650i	0.502003	−	0.502003i
$786$	−36.5456	+	36.5456i	−1.30354	+	1.30354i
$787$	−23.4689	+	23.4689i	−0.836576	+	0.836576i	−0.988407	−	0.151830i	$-0.951483\pi$
$787$	−23.4689	+	23.4689i	−0.836576	+	0.836576i	0.151830	+	0.988407i	$0.451483\pi$
$788$	21.2855	−	21.2855i	0.758265	−	0.758265i
$789$			11.5120i			0.409838i
$790$			2.78868i			0.0992168i
$791$	−20.1742	+	20.1742i	−0.717310	+	0.717310i
$792$	12.4084	+	0.646089i	0.440914	+	0.0229578i
$793$	−24.4736	+	3.80592i	−0.869083	+	0.135152i
$794$			14.3973i			0.510940i
$795$	−19.8888	+	19.8888i	−0.705382	+	0.705382i
$796$	−86.4273			−3.06333
$797$			10.8428i			0.384072i	0.981388	+	0.192036i	$0.0615091\pi$
$797$			10.8428i			0.384072i	−0.981388	+	0.192036i	$0.938491\pi$
$798$	−11.2817	−	11.2817i	−0.399367	−	0.399367i
$799$	−34.1812	−	34.1812i	−1.20924	−	1.20924i
$800$	−10.0324	+	10.0324i	−0.354699	+	0.354699i
$801$	−5.52141	−	5.52141i	−0.195089	−	0.195089i
$802$			1.92418i			0.0679450i
$803$	11.7147	+	0.609970i	0.413404	+	0.0215254i
$804$	21.0090	+	21.0090i	0.740929	+	0.740929i
$805$	19.1565			0.675176
$806$	0.507265	+	3.26192i	0.0178676	+	0.114896i
$807$	−20.2722			−0.713616
$808$	16.6416	−	16.6416i	0.585450	−	0.585450i
$809$		−	53.1019i		−	1.86696i	−0.358627	−	0.933481i	$-0.616755\pi$
$809$		−	53.1019i		−	1.86696i	0.358627	−	0.933481i	$-0.383245\pi$
$810$	−7.10448			−0.249626
$811$	−26.2176	−	26.2176i	−0.920623	−	0.920623i	0.0764500	−	0.997073i	$-0.475641\pi$
$811$	−26.2176	−	26.2176i	−0.920623	−	0.920623i	−0.997073	+	0.0764500i	$0.975641\pi$
$812$	−16.5421	+	16.5421i	−0.580516	+	0.580516i
$813$	−1.35380	+	1.35380i	−0.0474798	+	0.0474798i
$814$	−47.3188	+	42.6350i	−1.65852	+	1.49436i
$815$	31.1178			1.09001
$816$	11.2631			0.394288
$817$	6.29379	+	6.29379i	0.220192	+	0.220192i
$818$			23.0670i			0.806520i
$819$	5.64783	+	4.12763i	0.197351	+	0.144231i
$820$		−	14.9060i		−	0.520541i
$821$	−24.6705	−	24.6705i	−0.861007	−	0.861007i	0.130448	−	0.991455i	$-0.458358\pi$
$821$	−24.6705	−	24.6705i	−0.861007	−	0.861007i	−0.991455	+	0.130448i	$0.958358\pi$
$822$		−	27.0410i		−	0.943164i
$823$		−	0.0943442i		−	0.00328863i	−0.999999	−	0.00164432i	$-0.999477\pi$
$823$		−	0.0943442i		−	0.00328863i	0.999999	−	0.00164432i	$-0.000523402\pi$
$824$	−30.6159	−	30.6159i	−1.06655	−	1.06655i
$825$	−9.94712	+	8.96252i	−0.346314	+	0.312035i
$826$	−13.3058	−	13.3058i	−0.462967	−	0.462967i
$827$	−19.5041	+	19.5041i	−0.678225	+	0.678225i	−0.959598	−	0.281373i	$-0.909210\pi$
$827$	−19.5041	+	19.5041i	−0.678225	+	0.678225i	0.281373	+	0.959598i	$0.409210\pi$
$828$	11.7755			0.409226
$829$			0.226343i			0.00786123i	0.999992	+	0.00393061i	$0.00125116\pi$
$829$			0.226343i			0.00786123i	−0.999992	+	0.00393061i	$0.998749\pi$
$830$	−78.8990	−	78.8990i	−2.73862	−	2.73862i
$831$	−17.7086			−0.614303
$832$	41.5857	−	6.46704i	1.44172	−	0.224204i
$833$			21.6503i			0.750138i
$834$	5.15054	−	5.15054i	0.178349	−	0.178349i
$835$			13.6702i			0.473076i
$836$	−41.3192	−	2.15144i	−1.42906	−	0.0744090i
$837$	−0.273940	+	0.273940i	−0.00946875	+	0.00946875i
$838$	−0.266056	−	0.266056i	−0.00919075	−	0.00919075i
$839$	−38.0409	−	38.0409i	−1.31332	−	1.31332i	−0.918954	−	0.394365i	$-0.870965\pi$
$839$	−38.0409	−	38.0409i	−1.31332	−	1.31332i	−0.394365	−	0.918954i	$-0.629035\pi$
$840$	−15.4506	−	15.4506i	−0.533096	−	0.533096i
$841$	17.6889			0.609963
$842$	−6.30349			−0.217233
$843$	11.6127	−	11.6127i	0.399964	−	0.399964i
$844$	27.7861			0.956437
$845$	−17.9370	+	34.7206i	−0.617052	+	1.19442i
$846$			17.0739i			0.587013i
$847$	−13.4421	−	16.5767i	−0.461876	−	0.569581i
$848$	−15.7500			−0.540856
$849$	18.8088			0.645517
$850$	−45.1393	+	45.1393i	−1.54826	+	1.54826i
$851$	−18.8723	+	18.8723i	−0.646934	+	0.646934i
$852$	−41.6445	−	41.6445i	−1.42672	−	1.42672i
$853$	17.6673	−	17.6673i	0.604915	−	0.604915i	−0.336698	−	0.941613i	$-0.609310\pi$
$853$	17.6673	−	17.6673i	0.604915	−	0.604915i	0.941613	+	0.336698i	$0.109310\pi$
$854$		−	31.4974i		−	1.07782i
$855$	10.4602			0.357732
$856$	−25.3269	−	25.3269i	−0.865656	−	0.865656i
$857$	10.0523			0.343380			0.171690	−	0.985151i	$-0.445077\pi$
$857$	10.0523			0.343380			0.171690	+	0.985151i	$0.445077\pi$
$858$	28.1134	−	2.88477i	0.959776	−	0.0984843i
$859$	−26.5447			−0.905692			−0.452846	−	0.891589i	$-0.649591\pi$
$859$	−26.5447			−0.905692			−0.452846	+	0.891589i	$0.649591\pi$
$860$	19.4945	+	19.4945i	0.664756	+	0.664756i
$861$	−2.68333			−0.0914476
$862$		−	58.4845i		−	1.99199i
$863$	2.19810	−	2.19810i	0.0748241	−	0.0748241i	−0.668704	−	0.743528i	$-0.733151\pi$
$863$	2.19810	−	2.19810i	0.0748241	−	0.0748241i	0.743528	+	0.668704i	$0.233151\pi$
$864$	2.48510	+	2.48510i	0.0845449	+	0.0845449i
$865$	−50.2427	+	50.2427i	−1.70830	+	1.70830i
$866$	−0.560381	+	0.560381i	−0.0190425	+	0.0190425i
$867$	−27.7692			−0.943092
$868$	−2.69479			−0.0914672
$869$	0.967173	−	0.871439i	0.0328091	−	0.0295615i
$870$		−	23.8938i		−	0.810074i
$871$	24.1239	+	17.6306i	0.817406	+	0.597389i
$872$	67.7291			2.29360
$873$	−8.21511	+	8.21511i	−0.278040	+	0.278040i
$874$	−27.0092			−0.913600
$875$	−5.61660			−0.189876
$876$	−8.96652	−	8.96652i	−0.302951	−	0.302951i
$877$	26.2528	+	26.2528i	0.886495	+	0.886495i	0.994185	−	0.107689i	$-0.0343452\pi$
$877$	26.2528	+	26.2528i	0.886495	+	0.886495i	−0.107689	+	0.994185i	$0.534345\pi$
$878$	31.0939	+	31.0939i	1.04937	+	1.04937i
$879$	22.4031	−	22.4031i	0.755639	−	0.755639i
$880$	−16.7606	−	0.872703i	−0.565000	−	0.0294188i
$881$			11.9563i			0.402817i	0.979507	+	0.201409i	$0.0645519\pi$
$881$			11.9563i			0.402817i	−0.979507	+	0.201409i	$0.935448\pi$
$882$	5.40728	−	5.40728i	0.182073	−	0.182073i
$883$		−	18.2558i		−	0.614358i	−0.951652	−	0.307179i	$-0.900615\pi$
$883$		−	18.2558i		−	0.614358i	0.951652	−	0.307179i	$-0.0993851\pi$
$884$	85.4648	−	13.2907i	2.87449	−	0.447016i
$885$	12.3369			0.414702
$886$	−41.8764	−	41.8764i	−1.40687	−	1.40687i
$887$		−	10.9503i		−	0.367675i	−0.982957	−	0.183837i	$-0.941148\pi$
$887$		−	10.9503i		−	0.367675i	0.982957	−	0.183837i	$-0.0588520\pi$
$888$	30.4428			1.02159
$889$	−5.17498	+	5.17498i	−0.173563	+	0.173563i
$890$	39.2268	+	39.2268i	1.31488	+	1.31488i
$891$	2.22009	+	2.46398i	0.0743758	+	0.0825465i
$892$	24.3113	+	24.3113i	0.814004	+	0.814004i
$893$		−	25.1386i		−	0.841232i
$894$		−	45.9643i		−	1.53728i
$895$	15.6316	+	15.6316i	0.522507	+	0.522507i
$896$			39.8832i			1.33240i
$897$	11.7016	−	1.81973i	0.390706	−	0.0607591i
$898$			43.3426i			1.44636i
$899$	−0.921314	−	0.921314i	−0.0307275	−	0.0307275i
$900$	14.4735			0.482452
$901$	62.6038			2.08563
$902$	−8.05363	+	7.25646i	−0.268157	+	0.241614i
$903$	3.50932	−	3.50932i	0.116783	−	0.116783i
$904$	38.9550	−	38.9550i	1.29562	−	1.29562i
$905$	46.3970	+	46.3970i	1.54229	+	1.54229i
$906$	−16.3907			−0.544545
$907$			14.9510i			0.496440i	0.968704	+	0.248220i	$0.0798455\pi$
$907$			14.9510i			0.496440i	−0.968704	+	0.248220i	$0.920154\pi$
$908$	2.09048	−	2.09048i	0.0693751	−	0.0693751i
$909$	6.28207			0.208363
$910$	−40.1249	−	29.3247i	−1.33013	−	0.972104i
$911$	55.6492			1.84374			0.921870	−	0.387500i	$-0.126661\pi$
$911$	55.6492			1.84374			0.921870	+	0.387500i	$0.126661\pi$
$912$	4.14174	+	4.14174i	0.137147	+	0.137147i
$913$	−2.70856	+	52.0190i	−0.0896403	+	1.72158i
$914$		−	41.5442i		−	1.37416i
$915$	14.6020	+	14.6020i	0.482727	+	0.482727i
$916$	−17.0764	+	17.0764i	−0.564219	+	0.564219i
$917$	−30.0023	−	30.0023i	−0.990763	−	0.990763i
$918$	11.1814	+	11.1814i	0.369040	+	0.369040i
$919$		−	38.7745i		−	1.27905i	−0.768770	−	0.639526i	$-0.779131\pi$
$919$		−	38.7745i		−	1.27905i	0.768770	−	0.639526i	$-0.220869\pi$
$920$	−36.9899			−1.21952
$921$	13.3054	−	13.3054i	0.438427	−	0.438427i
$922$			66.6974i			2.19656i
$923$	−47.8188	−	34.9477i	−1.57398	−	1.15032i
$924$	−1.19961	+	23.0390i	−0.0394642	+	0.757927i
$925$	−23.1965	+	23.1965i	−0.762695	+	0.762695i
$926$		−	3.05737i		−	0.100472i
$927$		−	11.5572i		−	0.379589i
$928$	−8.35789	+	8.35789i	−0.274361	+	0.274361i
$929$	29.6889	−	29.6889i	0.974063	−	0.974063i	−0.0256095	−	0.999672i	$-0.508153\pi$
$929$	29.6889	−	29.6889i	0.974063	−	0.974063i	0.999672	+	0.0256095i	$0.00815265\pi$
$930$	1.94620	−	1.94620i	0.0638185	−	0.0638185i
$931$	−7.96137	+	7.96137i	−0.260923	+	0.260923i
$932$			41.5010i			1.35941i
$933$		−	13.0705i		−	0.427909i
$934$	−18.3751	+	18.3751i	−0.601253	+	0.601253i
$935$	66.6209	+	3.46886i	2.17874	+	0.113444i
$936$	−10.9056	−	7.97020i	−0.356461	−	0.260514i
$937$			14.2474i			0.465442i	0.972544	+	0.232721i	$0.0747629\pi$
$937$			14.2474i			0.465442i	−0.972544	+	0.232721i	$0.925237\pi$
$938$	−26.8689	+	26.8689i	−0.877300	+	0.877300i
$939$	11.5886			0.378180
$940$		−	77.8646i		−	2.53966i
$941$	26.8870	+	26.8870i	0.876492	+	0.876492i	0.993170	−	0.116678i	$-0.0372244\pi$
$941$	26.8870	+	26.8870i	0.876492	+	0.876492i	−0.116678	+	0.993170i	$0.537224\pi$
$942$	11.0573	+	11.0573i	0.360266	+	0.360266i
$943$	−3.21205	+	3.21205i	−0.104599	+	0.104599i
$944$	4.88483	+	4.88483i	0.158988	+	0.158988i
$945$		−	5.83246i		−	0.189730i
$946$	1.04257	−	20.0229i	0.0338967	−	0.651001i
$947$	27.0448	+	27.0448i	0.878839	+	0.878839i	0.993415	−	0.114576i	$-0.0365509\pi$
$947$	27.0448	+	27.0448i	0.878839	+	0.878839i	−0.114576	+	0.993415i	$0.536551\pi$
$948$	−1.40728			−0.0457064
$949$	−10.2959	−	7.52464i	−0.334220	−	0.244260i
$950$	−33.1978			−1.07708
$951$	17.1628	−	17.1628i	0.556540	−	0.556540i
$952$			48.6337i			1.57623i
$953$	23.3736			0.757146			0.378573	−	0.925571i	$-0.376415\pi$
$953$	23.3736			0.757146			0.378573	+	0.925571i	$0.376415\pi$
$954$	−15.6356	−	15.6356i	−0.506222	−	0.506222i
$955$	−14.5456	+	14.5456i	−0.470685	+	0.470685i
$956$	57.5113	−	57.5113i	1.86005	−	1.86005i
$957$	−8.28685	+	7.46659i	−0.267876	+	0.241361i
$958$	−4.61084			−0.148969
$959$	22.1995			0.716858
$960$	−24.8118	−	24.8118i	−0.800797	−	0.800797i
$961$			30.8499i			0.995159i
$962$	68.4194	−	10.6400i	2.20593	−	0.343047i
$963$		−	9.56070i		−	0.308089i
$964$	57.5357	+	57.5357i	1.85310	+	1.85310i
$965$		−	1.90834i		−	0.0614316i
$966$			15.0599i			0.484545i
$967$	−18.7976	−	18.7976i	−0.604490	−	0.604490i	0.337011	−	0.941501i	$-0.390584\pi$
$967$	−18.7976	−	18.7976i	−0.604490	−	0.604490i	−0.941501	+	0.337011i	$0.890584\pi$
$968$	25.9558	+	32.0085i	0.834252	+	1.02879i
$969$	−16.4628	−	16.4628i	−0.528861	−	0.528861i
$970$	58.3641	−	58.3641i	1.87396	−	1.87396i
$971$	−19.8860			−0.638171			−0.319086	−	0.947726i	$-0.603376\pi$
$971$	−19.8860			−0.638171			−0.319086	+	0.947726i	$0.603376\pi$
$972$		−	3.58521i		−	0.114996i
$973$	4.22837	+	4.22837i	0.135555	+	0.135555i
$974$	−10.1844			−0.326329
$975$	14.3828	−	2.23668i	0.460617	−	0.0716312i
$976$			11.5634i			0.370134i
$977$	8.66382	−	8.66382i	0.277180	−	0.277180i	−0.554802	−	0.831982i	$-0.687206\pi$
$977$	8.66382	−	8.66382i	0.277180	−	0.277180i	0.831982	+	0.554802i	$0.187206\pi$
$978$			24.4634i			0.782253i
$979$	1.34664	−	25.8627i	0.0430386	−	0.826575i
$980$	−24.6596	+	24.6596i	−0.787723	+	0.787723i
$981$	12.7836	+	12.7836i	0.408149	+	0.408149i
$982$	−12.7424	−	12.7424i	−0.406627	−	0.406627i
$983$	−32.0373	−	32.0373i	−1.02183	−	1.02183i	−0.999756	−	0.0220744i	$-0.992973\pi$
$983$	−32.0373	−	32.0373i	−1.02183	−	1.02183i	−0.0220744	−	0.999756i	$-0.507027\pi$
$984$	5.18134			0.165175
$985$	−25.2404			−0.804226
$986$	−37.6051	+	37.6051i	−1.19759	+	1.19759i
$987$	−14.0169			−0.446163
$988$	36.3150	+	26.5403i	1.15533	+	0.844359i
$989$		−	8.40160i		−	0.267155i
$990$	−15.7726	−	17.5053i	−0.501285	−	0.556355i
$991$	−55.8304			−1.77351			−0.886755	−	0.462239i	$-0.847046\pi$
$991$	−55.8304			−1.77351			−0.886755	+	0.462239i	$0.847046\pi$
$992$	−1.36154			−0.0432289
$993$	−13.0175	+	13.0175i	−0.413096	+	0.413096i
$994$	53.2601	−	53.2601i	1.68931	−	1.68931i
$995$	51.2429	+	51.2429i	1.62451	+	1.62451i
$996$	39.8157	−	39.8157i	1.26161	−	1.26161i
$997$			21.2850i			0.674103i	0.941486	+	0.337052i	$0.109430\pi$
$997$			21.2850i			0.674103i	−0.941486	+	0.337052i	$0.890570\pi$
$998$	0.606074			0.0191850
$999$	5.74595	+	5.74595i	0.181794	+	0.181794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.m.a.109.2	✓	28
11.10	odd	2	inner	429.2.m.a.109.13	yes	28
13.8	odd	4	inner	429.2.m.a.307.13	yes	28
143.21	even	4	inner	429.2.m.a.307.2	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.m.a.109.2	✓	28	1.1	even	1	trivial
429.2.m.a.109.13	yes	28	11.10	odd	2	inner
429.2.m.a.307.2	yes	28	143.21	even	4	inner
429.2.m.a.307.13	yes	28	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67111 - 1.67111i) q^{2} -1.00000 q^{3} +3.58521i q^{4} +(2.12568 - 2.12568i) q^{5} +(1.67111 + 1.67111i) q^{6} +(-1.37191 + 1.37191i) q^{7} +(2.64907 - 2.64907i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.67111 - 1.67111i) q^{2} -1.00000 q^{3} +3.58521i q^{4} +(2.12568 - 2.12568i) q^{5} +(1.67111 + 1.67111i) q^{6} +(-1.37191 + 1.37191i) q^{7} +(2.64907 - 2.64907i) q^{8} +1.00000 q^{9} -7.10448 q^{10} +(2.22009 + 2.46398i) q^{11} -3.58521i q^{12} +(-0.554044 - 3.56273i) q^{13} +4.58521 q^{14} +(-2.12568 + 2.12568i) q^{15} -1.68333 q^{16} +6.69098 q^{17} +(-1.67111 - 1.67111i) q^{18} +(2.46045 + 2.46045i) q^{19} +(7.62101 + 7.62101i) q^{20} +(1.37191 - 1.37191i) q^{21} +(0.407572 - 7.82759i) q^{22} -3.28445i q^{23} +(-2.64907 + 2.64907i) q^{24} -4.03701i q^{25} +(-5.02784 + 6.87958i) q^{26} -1.00000 q^{27} +(-4.91858 - 4.91858i) q^{28} -3.36320i q^{29} +7.10448 q^{30} +(0.273940 - 0.273940i) q^{31} +(-2.48510 - 2.48510i) q^{32} +(-2.22009 - 2.46398i) q^{33} +(-11.1814 - 11.1814i) q^{34} +5.83246i q^{35} +3.58521i q^{36} +(-5.74595 - 5.74595i) q^{37} -8.22335i q^{38} +(0.554044 + 3.56273i) q^{39} -11.2621i q^{40} +(-0.977956 - 0.977956i) q^{41} -4.58521 q^{42} +2.55799 q^{43} +(-8.83390 + 7.95949i) q^{44} +(2.12568 - 2.12568i) q^{45} +(-5.48868 + 5.48868i) q^{46} +(-5.10855 - 5.10855i) q^{47} +1.68333 q^{48} +3.23574i q^{49} +(-6.74629 + 6.74629i) q^{50} -6.69098 q^{51} +(12.7731 - 1.98637i) q^{52} +9.35644 q^{53} +(1.67111 + 1.67111i) q^{54} +(9.95682 + 0.518439i) q^{55} +7.26854i q^{56} +(-2.46045 - 2.46045i) q^{57} +(-5.62027 + 5.62027i) q^{58} +(-2.90188 - 2.90188i) q^{59} +(-7.62101 - 7.62101i) q^{60} -6.86934i q^{61} -0.915567 q^{62} +(-1.37191 + 1.37191i) q^{63} +11.6724i q^{64} +(-8.75093 - 6.39549i) q^{65} +(-0.407572 + 7.82759i) q^{66} +(-5.85989 + 5.85989i) q^{67} +23.9886i q^{68} +3.28445i q^{69} +(9.74669 - 9.74669i) q^{70} +(11.6156 - 11.6156i) q^{71} +(2.64907 - 2.64907i) q^{72} +(2.50097 - 2.50097i) q^{73} +19.2042i q^{74} +4.03701i q^{75} +(-8.82122 + 8.82122i) q^{76} +(-6.42611 - 0.334599i) q^{77} +(5.02784 - 6.87958i) q^{78} -0.392524i q^{79} +(-3.57822 + 3.57822i) q^{80} +1.00000 q^{81} +3.26854i q^{82} +(11.1055 + 11.1055i) q^{83} +(4.91858 + 4.91858i) q^{84} +(14.2229 - 14.2229i) q^{85} +(-4.27468 - 4.27468i) q^{86} +3.36320i q^{87} +(12.4084 + 0.646089i) q^{88} +(-5.52141 - 5.52141i) q^{89} -7.10448 q^{90} +(5.64783 + 4.12763i) q^{91} +11.7755 q^{92} +(-0.273940 + 0.273940i) q^{93} +17.0739i q^{94} +10.4602 q^{95} +(2.48510 + 2.48510i) q^{96} +(-8.21511 + 8.21511i) q^{97} +(5.40728 - 5.40728i) q^{98} +(2.22009 + 2.46398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9}+O(q^{10}) \) 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9	\( 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9} + 4 q^{11} + 48 q^{14} - 4 q^{15} - 52 q^{16} - 8 q^{20} - 32 q^{22} - 4 q^{26} - 28 q^{27} + 24 q^{31} - 4 q^{33} + 16 q^{34} - 12 q^{37} - 48 q^{42} - 24 q^{44} + 4 q^{45} - 8 q^{47} + 52 q^{48} - 8 q^{53} + 48 q^{55} - 64 q^{58} + 4 q^{59} + 8 q^{60} + 32 q^{66} + 28 q^{67} - 4 q^{70} + 12 q^{71} + 4 q^{78} + 56 q^{80} + 28 q^{81} - 8 q^{86} - 104 q^{89} - 76 q^{91} - 24 q^{93} - 8 q^{97} + 4 q^{99}+O(q^{100}) \) 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9 + 4 * q^11 + 48 * q^14 - 4 * q^15 - 52 * q^16 - 8 * q^20 - 32 * q^22 - 4 * q^26 - 28 * q^27 + 24 * q^31 - 4 * q^33 + 16 * q^34 - 12 * q^37 - 48 * q^42 - 24 * q^44 + 4 * q^45 - 8 * q^47 + 52 * q^48 - 8 * q^53 + 48 * q^55 - 64 * q^58 + 4 * q^59 + 8 * q^60 + 32 * q^66 + 28 * q^67 - 4 * q^70 + 12 * q^71 + 4 * q^78 + 56 * q^80 + 28 * q^81 - 8 * q^86 - 104 * q^89 - 76 * q^91 - 24 * q^93 - 8 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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