LMFDB - Embedded newform 1218.2.m.a.307.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(307,1218)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1218.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1218 = 2 \cdot 3 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1218.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.13
Character	$\chi$	$=$	1218.307
Dual form			1218.2.m.a.853.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +1.77140 q^{5} -1.00000 q^{6} +(-1.44420 - 2.21682i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(1.25257 - 1.25257i) q^{10} +(2.65105 - 2.65105i) q^{11} +(-0.707107 + 0.707107i) q^{12} +6.25822 q^{13} +(-2.58873 - 0.546323i) q^{14} +(-1.25257 - 1.25257i) q^{15} -1.00000 q^{16} +(5.28024 + 5.28024i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-1.07898 - 1.07898i) q^{19} -1.77140i q^{20} +(-0.546323 + 2.58873i) q^{21} -3.74916i q^{22} +0.212711 q^{23} +1.00000i q^{24} -1.86213 q^{25} +(4.42523 - 4.42523i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.21682 + 1.44420i) q^{28} +(-3.80292 - 3.81285i) q^{29} -1.77140 q^{30} +(-2.50464 - 2.50464i) q^{31} +(-0.707107 + 0.707107i) q^{32} -3.74916 q^{33} +7.46738 q^{34} +(-2.55826 - 3.92688i) q^{35} +1.00000 q^{36} +(-4.32333 - 4.32333i) q^{37} -1.52590 q^{38} +(-4.42523 - 4.42523i) q^{39} +(-1.25257 - 1.25257i) q^{40} +(-3.16605 + 3.16605i) q^{41} +(1.44420 + 2.21682i) q^{42} +(0.313944 - 0.313944i) q^{43} +(-2.65105 - 2.65105i) q^{44} +1.77140i q^{45} +(0.150409 - 0.150409i) q^{46} +(2.82583 - 2.82583i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-2.82857 + 6.40306i) q^{49} +(-1.31672 + 1.31672i) q^{50} -7.46738i q^{51} -6.25822i q^{52} -1.80816 q^{53} -1.00000i q^{54} +(4.69609 - 4.69609i) q^{55} +(-0.546323 + 2.58873i) q^{56} +1.52590i q^{57} +(-5.38516 - 0.00702541i) q^{58} -13.9548i q^{59} +(-1.25257 + 1.25257i) q^{60} +(5.59790 + 5.59790i) q^{61} -3.54209 q^{62} +(2.21682 - 1.44420i) q^{63} +1.00000i q^{64} +11.0858 q^{65} +(-2.65105 + 2.65105i) q^{66} -7.40715i q^{67} +(5.28024 - 5.28024i) q^{68} +(-0.150409 - 0.150409i) q^{69} +(-4.58569 - 0.967759i) q^{70} +12.8883i q^{71} +(0.707107 - 0.707107i) q^{72} +(4.51463 - 4.51463i) q^{73} -6.11411 q^{74} +(1.31672 + 1.31672i) q^{75} +(-1.07898 + 1.07898i) q^{76} +(-9.70556 - 2.04825i) q^{77} -6.25822 q^{78} +(1.08096 - 1.08096i) q^{79} -1.77140 q^{80} -1.00000 q^{81} +4.47747i q^{82} +2.33957i q^{83} +(2.58873 + 0.546323i) q^{84} +(9.35344 + 9.35344i) q^{85} -0.443984i q^{86} +(-0.00702541 + 5.38516i) q^{87} -3.74916 q^{88} +(0.425839 + 0.425839i) q^{89} +(1.25257 + 1.25257i) q^{90} +(-9.03813 - 13.8733i) q^{91} -0.212711i q^{92} +3.54209i q^{93} -3.99632i q^{94} +(-1.91130 - 1.91130i) q^{95} +1.00000 q^{96} +(3.18914 - 3.18914i) q^{97} +(2.52755 + 6.52775i) q^{98} +(2.65105 + 2.65105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{6} + 4 q^{10} + 4 q^{14} - 4 q^{15} - 40 q^{16} + 8 q^{19} - 4 q^{21} + 24 q^{25} - 12 q^{28} + 8 q^{29} - 24 q^{31} - 12 q^{35} + 40 q^{36} - 16 q^{37} - 4 q^{40} + 16 q^{41} - 20 q^{43} + 4 q^{46}+ \cdots - 8 q^{98}+O(q^{100}) $ 40 * q - 40 * q^6 + 4 * q^10 + 4 * q^14 - 4 * q^15 - 40 * q^16 + 8 * q^19 - 4 * q^21 + 24 * q^25 - 12 * q^28 + 8 * q^29 - 24 * q^31 - 12 * q^35 + 40 * q^36 - 16 * q^37 - 4 * q^40 + 16 * q^41 - 20 * q^43 + 4 * q^46 - 16 * q^47 + 28 * q^49 + 32 * q^50 + 16 * q^53 - 24 * q^55 - 4 * q^56 - 20 * q^58 - 4 * q^60 - 44 * q^61 + 12 * q^63 - 4 * q^69 - 28 * q^70 - 52 * q^73 - 32 * q^75 + 8 * q^76 + 44 * q^77 + 4 * q^79 - 40 * q^81 - 4 * q^84 - 24 * q^85 - 12 * q^87 + 24 * q^89 + 4 * q^90 - 16 * q^95 + 40 * q^96 - 68 * q^97 - 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1218\mathbb{Z}\right)^\times$.

$n$	$379$	$407$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	1.77140			0.792196			0.396098	−	0.918208i	$-0.370364\pi$
$5$	1.77140			0.792196			0.396098	+	0.918208i	$0.370364\pi$
$6$	−1.00000			−0.408248
$7$	−1.44420	−	2.21682i	−0.545857	−	0.837879i
$7$	−1.44420	−	2.21682i	−0.545857	−	0.837879i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	1.25257	−	1.25257i	0.396098	−	0.396098i
$11$	2.65105	−	2.65105i	0.799323	−	0.799323i	−0.183666	−	0.982989i	$-0.558796\pi$
$11$	2.65105	−	2.65105i	0.799323	−	0.799323i	0.982989	+	0.183666i	$0.0587965\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	6.25822			1.73572			0.867860	−	0.496810i	$-0.165495\pi$
$13$	6.25822			1.73572			0.867860	+	0.496810i	$0.165495\pi$
$14$	−2.58873	−	0.546323i	−0.691868	−	0.146011i
$15$	−1.25257	−	1.25257i	−0.323413	−	0.323413i
$16$	−1.00000			−0.250000
$17$	5.28024	+	5.28024i	1.28065	+	1.28065i	0.940300	+	0.340345i	$0.110544\pi$
$17$	5.28024	+	5.28024i	1.28065	+	1.28065i	0.340345	+	0.940300i	$0.389456\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−1.07898	−	1.07898i	−0.247534	−	0.247534i	0.572424	−	0.819958i	$-0.306003\pi$
$19$	−1.07898	−	1.07898i	−0.247534	−	0.247534i	−0.819958	+	0.572424i	$0.806003\pi$
$20$		−	1.77140i		−	0.396098i
$21$	−0.546323	+	2.58873i	−0.119217	+	0.564908i
$22$		−	3.74916i		−	0.799323i
$23$	0.212711			0.0443533			0.0221766	−	0.999754i	$-0.492940\pi$
$23$	0.212711			0.0443533			0.0221766	+	0.999754i	$0.492940\pi$
$24$			1.00000i			0.204124i
$25$	−1.86213			−0.372425
$26$	4.42523	−	4.42523i	0.867860	−	0.867860i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−2.21682	+	1.44420i	−0.418939	+	0.272928i
$29$	−3.80292	−	3.81285i	−0.706184	−	0.708029i
$29$	−3.80292	−	3.81285i	−0.706184	−	0.708029i
$30$	−1.77140			−0.323413
$31$	−2.50464	−	2.50464i	−0.449846	−	0.449846i	0.445457	−	0.895303i	$-0.353041\pi$
$31$	−2.50464	−	2.50464i	−0.449846	−	0.449846i	−0.895303	+	0.445457i	$0.853041\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−3.74916			−0.652644
$34$	7.46738			1.28065
$35$	−2.55826	−	3.92688i	−0.432425	−	0.663764i
$36$	1.00000			0.166667
$37$	−4.32333	−	4.32333i	−0.710751	−	0.710751i	0.255942	−	0.966692i	$-0.417614\pi$
$37$	−4.32333	−	4.32333i	−0.710751	−	0.710751i	−0.966692	+	0.255942i	$0.917614\pi$
$38$	−1.52590			−0.247534
$39$	−4.42523	−	4.42523i	−0.708604	−	0.708604i
$40$	−1.25257	−	1.25257i	−0.198049	−	0.198049i
$41$	−3.16605	+	3.16605i	−0.494454	+	0.494454i	−0.909706	−	0.415252i	$-0.863693\pi$
$41$	−3.16605	+	3.16605i	−0.494454	+	0.494454i	0.415252	+	0.909706i	$0.363693\pi$
$42$	1.44420	+	2.21682i	0.222845	+	0.342062i
$43$	0.313944	−	0.313944i	0.0478761	−	0.0478761i	−0.682763	−	0.730640i	$-0.739222\pi$
$43$	0.313944	−	0.313944i	0.0478761	−	0.0478761i	0.730640	+	0.682763i	$0.239222\pi$
$44$	−2.65105	−	2.65105i	−0.399661	−	0.399661i
$45$			1.77140i			0.264065i
$46$	0.150409	−	0.150409i	0.0221766	−	0.0221766i
$47$	2.82583	−	2.82583i	0.412189	−	0.412189i	−0.470311	−	0.882500i	$-0.655858\pi$
$47$	2.82583	−	2.82583i	0.412189	−	0.412189i	0.882500	+	0.470311i	$0.155858\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$	−2.82857	+	6.40306i	−0.404081	+	0.914723i
$50$	−1.31672	+	1.31672i	−0.186213	+	0.186213i
$51$		−	7.46738i		−	1.04564i
$52$		−	6.25822i		−	0.867860i
$53$	−1.80816			−0.248370			−0.124185	−	0.992259i	$-0.539632\pi$
$53$	−1.80816			−0.248370			−0.124185	+	0.992259i	$0.539632\pi$
$54$		−	1.00000i		−	0.136083i
$55$	4.69609	−	4.69609i	0.633220	−	0.633220i
$56$	−0.546323	+	2.58873i	−0.0730055	+	0.345934i
$57$			1.52590i			0.202111i
$58$	−5.38516	−	0.00702541i	−0.707106	−	0.000922481i
$59$		−	13.9548i		−	1.81677i	−0.418139	−	0.908383i	$-0.637317\pi$
$59$		−	13.9548i		−	1.81677i	0.418139	−	0.908383i	$-0.362683\pi$
$60$	−1.25257	+	1.25257i	−0.161706	+	0.161706i
$61$	5.59790	+	5.59790i	0.716738	+	0.716738i	0.967936	−	0.251198i	$-0.0808245\pi$
$61$	5.59790	+	5.59790i	0.716738	+	0.716738i	−0.251198	+	0.967936i	$0.580824\pi$
$62$	−3.54209			−0.449846
$63$	2.21682	−	1.44420i	0.279293	−	0.181952i
$64$			1.00000i			0.125000i
$65$	11.0858			1.37503
$66$	−2.65105	+	2.65105i	−0.326322	+	0.326322i
$67$		−	7.40715i		−	0.904928i	−0.891783	−	0.452464i	$-0.850545\pi$
$67$		−	7.40715i		−	0.904928i	0.891783	−	0.452464i	$-0.149455\pi$
$68$	5.28024	−	5.28024i	0.640323	−	0.640323i
$69$	−0.150409	−	0.150409i	−0.0181072	−	0.0181072i
$70$	−4.58569	−	0.967759i	−0.548095	−	0.115669i
$71$			12.8883i			1.52955i	0.644295	+	0.764777i	$0.277151\pi$
$71$			12.8883i			1.52955i	−0.644295	+	0.764777i	$0.722849\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	4.51463	−	4.51463i	0.528397	−	0.528397i	−0.391697	−	0.920094i	$-0.628112\pi$
$73$	4.51463	−	4.51463i	0.528397	−	0.528397i	0.920094	+	0.391697i	$0.128112\pi$
$74$	−6.11411			−0.710751
$75$	1.31672	+	1.31672i	0.152042	+	0.152042i
$76$	−1.07898	+	1.07898i	−0.123767	+	0.123767i
$77$	−9.70556	−	2.04825i	−1.10605	−	0.233420i
$78$	−6.25822			−0.708604
$79$	1.08096	−	1.08096i	0.121617	−	0.121617i	−0.643679	−	0.765296i	$-0.722593\pi$
$79$	1.08096	−	1.08096i	0.121617	−	0.121617i	0.765296	+	0.643679i	$0.222593\pi$
$80$	−1.77140			−0.198049
$81$	−1.00000			−0.111111
$82$			4.47747i			0.494454i
$83$			2.33957i			0.256802i	0.991722	+	0.128401i	$0.0409844\pi$
$83$			2.33957i			0.256802i	−0.991722	+	0.128401i	$0.959016\pi$
$84$	2.58873	+	0.546323i	0.282454	+	0.0596087i
$85$	9.35344	+	9.35344i	1.01452	+	1.01452i
$86$		−	0.443984i		−	0.0478761i
$87$	−0.00702541	+	5.38516i	−0.000753203	+	0.577350i
$88$	−3.74916			−0.399661
$89$	0.425839	+	0.425839i	0.0451388	+	0.0451388i	0.729316	−	0.684177i	$-0.239838\pi$
$89$	0.425839	+	0.425839i	0.0451388	+	0.0451388i	−0.684177	+	0.729316i	$0.739838\pi$
$90$	1.25257	+	1.25257i	0.132033	+	0.132033i
$91$	−9.03813	−	13.8733i	−0.947454	−	1.45432i
$92$		−	0.212711i		−	0.0221766i
$93$			3.54209i			0.367298i
$94$		−	3.99632i		−	0.412189i
$95$	−1.91130	−	1.91130i	−0.196096	−	0.196096i
$96$	1.00000			0.102062
$97$	3.18914	−	3.18914i	0.323809	−	0.323809i	−0.526418	−	0.850226i	$-0.676465\pi$
$97$	3.18914	−	3.18914i	0.323809	−	0.323809i	0.850226	+	0.526418i	$0.176465\pi$
$98$	2.52755	+	6.52775i	0.255321	+	0.659402i
$99$	2.65105	+	2.65105i	0.266441	+	0.266441i
$100$			1.86213i			0.186213i
$101$	−4.68494	−	4.68494i	−0.466169	−	0.466169i	0.434502	−	0.900671i	$-0.356924\pi$
$101$	−4.68494	−	4.68494i	−0.466169	−	0.466169i	−0.900671	+	0.434502i	$0.856924\pi$
$102$	−5.28024	−	5.28024i	−0.522822	−	0.522822i
$103$			12.8517i			1.26631i	0.774024	+	0.633156i	$0.218241\pi$
$103$			12.8517i			1.26631i	−0.774024	+	0.633156i	$0.781759\pi$
$104$	−4.42523	−	4.42523i	−0.433930	−	0.433930i
$105$	−0.967759	+	4.58569i	−0.0944436	+	0.447518i
$106$	−1.27856	+	1.27856i	−0.124185	+	0.124185i
$107$	3.34698			0.323565			0.161782	−	0.986826i	$-0.448276\pi$
$107$	3.34698			0.323565			0.161782	+	0.986826i	$0.448276\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$			11.0821i			1.06147i	0.847537	+	0.530737i	$0.178085\pi$
$109$			11.0821i			1.06147i	−0.847537	+	0.530737i	$0.821915\pi$
$110$		−	6.64127i		−	0.633220i
$111$			6.11411i			0.580325i
$112$	1.44420	+	2.21682i	0.136464	+	0.209470i
$113$	5.75260	+	5.75260i	0.541159	+	0.541159i	0.923869	−	0.382710i	$-0.125009\pi$
$113$	5.75260	+	5.75260i	0.541159	+	0.541159i	−0.382710	+	0.923869i	$0.625009\pi$
$114$	1.07898	+	1.07898i	0.101055	+	0.101055i
$115$	0.376797			0.0351365
$116$	−3.81285	+	3.80292i	−0.354014	+	0.353092i
$117$			6.25822i			0.578573i
$118$	−9.86757	−	9.86757i	−0.908383	−	0.908383i
$119$	4.07960	−	19.3311i	0.373977	−	1.77207i
$120$			1.77140i			0.161706i
$121$		−	3.05617i		−	0.277834i
$122$	7.91663			0.716738
$123$	4.47747			0.403720
$124$	−2.50464	+	2.50464i	−0.224923	+	0.224923i
$125$	−12.1556			−1.08723
$126$	0.546323	−	2.58873i	0.0486703	−	0.230623i
$127$	−14.8159	+	14.8159i	−1.31469	+	1.31469i	−0.396782	+	0.917913i	$0.629873\pi$
$127$	−14.8159	+	14.8159i	−1.31469	+	1.31469i	−0.917913	+	0.396782i	$0.870127\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−0.443984			−0.0390906
$130$	7.83888	−	7.83888i	0.687515	−	0.687515i
$131$	−8.00174	+	8.00174i	−0.699115	+	0.699115i	−0.964220	−	0.265104i	$-0.914594\pi$
$131$	−8.00174	+	8.00174i	−0.699115	+	0.699115i	0.265104	+	0.964220i	$0.414594\pi$
$132$			3.74916i			0.326322i
$133$	−0.833636	+	3.95016i	−0.0722854	+	0.342522i
$134$	−5.23765	−	5.23765i	−0.452464	−	0.452464i
$135$	1.25257	−	1.25257i	0.107804	−	0.107804i
$136$		−	7.46738i		−	0.640323i
$137$	11.4407	−	11.4407i	0.977443	−	0.977443i	−0.0223080	−	0.999751i	$-0.507101\pi$
$137$	11.4407	−	11.4407i	0.977443	−	0.977443i	0.999751	+	0.0223080i	$0.00710146\pi$
$138$	−0.212711			−0.0181072
$139$			13.9456i			1.18285i	0.806361	+	0.591424i	$0.201434\pi$
$139$			13.9456i			1.18285i	−0.806361	+	0.591424i	$0.798566\pi$
$140$	−3.92688	+	2.55826i	−0.331882	+	0.216213i
$141$	−3.99632			−0.336551
$142$	9.11337	+	9.11337i	0.764777	+	0.764777i
$143$	16.5909	−	16.5909i	1.38740	−	1.38740i
$144$		−	1.00000i		−	0.0833333i
$145$	−6.73650	−	6.75410i	−0.559436	−	0.560898i
$146$		−	6.38465i		−	0.528397i
$147$	6.52775	−	2.52755i	0.538400	−	0.208469i
$148$	−4.32333	+	4.32333i	−0.355375	+	0.355375i
$149$		−	17.8178i		−	1.45969i	−0.683611	−	0.729847i	$-0.739591\pi$
$149$		−	17.8178i		−	1.45969i	0.683611	−	0.729847i	$-0.260409\pi$
$150$	1.86213			0.152042
$151$			6.26978i			0.510227i	0.966911	+	0.255114i	$0.0821128\pi$
$151$			6.26978i			0.510227i	−0.966911	+	0.255114i	$0.917887\pi$
$152$			1.52590i			0.123767i
$153$	−5.28024	+	5.28024i	−0.426882	+	0.426882i
$154$	−8.31120	+	5.41453i	−0.669735	+	0.436316i
$155$	−4.43672	−	4.43672i	−0.356366	−	0.356366i
$156$	−4.42523	+	4.42523i	−0.354302	+	0.354302i
$157$	2.23270	−	2.23270i	0.178189	−	0.178189i	−0.612377	−	0.790566i	$-0.709786\pi$
$157$	2.23270	−	2.23270i	0.178189	−	0.178189i	0.790566	+	0.612377i	$0.209786\pi$
$158$		−	1.52871i		−	0.121617i
$159$	1.27856	+	1.27856i	0.101397	+	0.101397i
$160$	−1.25257	+	1.25257i	−0.0990245	+	0.0990245i
$161$	−0.307197	−	0.471542i	−0.0242105	−	0.0371627i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	0.336379	+	0.336379i	0.0263472	+	0.0263472i	0.720158	−	0.693810i	$-0.244069\pi$
$163$	0.336379	+	0.336379i	0.0263472	+	0.0263472i	−0.693810	+	0.720158i	$0.744069\pi$
$164$	3.16605	+	3.16605i	0.247227	+	0.247227i
$165$	−6.64127			−0.517022
$166$	1.65433	+	1.65433i	0.128401	+	0.128401i
$167$	6.79715			0.525979			0.262990	−	0.964799i	$-0.415292\pi$
$167$	6.79715			0.525979			0.262990	+	0.964799i	$0.415292\pi$
$168$	2.21682	−	1.44420i	0.171031	−	0.111423i
$169$	26.1654			2.01272
$170$	13.2278			1.01452
$171$	1.07898	−	1.07898i	0.0825114	−	0.0825114i
$172$	−0.313944	−	0.313944i	−0.0239380	−	0.0239380i
$173$	−1.30807			−0.0994507			−0.0497253	−	0.998763i	$-0.515835\pi$
$173$	−1.30807			−0.0994507			−0.0497253	+	0.998763i	$0.515835\pi$
$174$	3.80292	+	3.81285i	0.288298	+	0.289051i
$175$	2.68929	+	4.12800i	0.203291	+	0.312047i
$176$	−2.65105	+	2.65105i	−0.199831	+	0.199831i
$177$	−9.86757	+	9.86757i	−0.741692	+	0.741692i
$178$	0.602227			0.0451388
$179$			1.07302i			0.0802015i	0.999196	+	0.0401008i	$0.0127679\pi$
$179$			1.07302i			0.0802015i	−0.999196	+	0.0401008i	$0.987232\pi$
$180$	1.77140			0.132033
$181$			1.98060i			0.147217i	0.997287	+	0.0736083i	$0.0234515\pi$
$181$			1.98060i			0.147217i	−0.997287	+	0.0736083i	$0.976549\pi$
$182$	−16.2009	−	3.41901i	−1.20089	−	0.253434i
$183$		−	7.91663i		−	0.585214i
$184$	−0.150409	−	0.150409i	−0.0110883	−	0.0110883i
$185$	−7.65836	−	7.65836i	−0.563054	−	0.563054i
$186$	2.50464	+	2.50464i	0.183649	+	0.183649i
$187$	27.9964			2.04730
$188$	−2.82583	−	2.82583i	−0.206094	−	0.206094i
$189$	−2.58873	−	0.546323i	−0.188303	−	0.0397392i
$190$	−2.70299			−0.196096
$191$	13.3495	−	13.3495i	0.965938	−	0.965938i	−0.0335003	−	0.999439i	$-0.510665\pi$
$191$	13.3495	−	13.3495i	0.965938	−	0.965938i	0.999439	+	0.0335003i	$0.0106655\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−12.6253	+	12.6253i	−0.908788	+	0.908788i	−0.996175	−	0.0873863i	$-0.972149\pi$
$193$	−12.6253	+	12.6253i	−0.908788	+	0.908788i	0.0873863	+	0.996175i	$0.472149\pi$
$194$		−	4.51013i		−	0.323809i
$195$	−7.83888	−	7.83888i	−0.561354	−	0.561354i
$196$	6.40306	+	2.82857i	0.457362	+	0.202041i
$197$	−18.9073			−1.34709			−0.673545	−	0.739146i	$-0.735229\pi$
$197$	−18.9073			−1.34709			−0.673545	+	0.739146i	$0.735229\pi$
$198$	3.74916			0.266441
$199$			16.7240i			1.18553i	0.805374	+	0.592767i	$0.201965\pi$
$199$			16.7240i			1.18553i	−0.805374	+	0.592767i	$0.798035\pi$
$200$	1.31672	+	1.31672i	0.0931064	+	0.0931064i
$201$	−5.23765	+	5.23765i	−0.369435	+	0.369435i
$202$	−6.62551			−0.466169
$203$	−2.96022	+	13.9369i	−0.207767	+	0.978178i
$204$	−7.46738			−0.522822
$205$	−5.60835	+	5.60835i	−0.391704	+	0.391704i
$206$	9.08749	+	9.08749i	0.633156	+	0.633156i
$207$			0.212711i			0.0147844i
$208$	−6.25822			−0.433930
$209$	−5.72085			−0.395720
$210$	2.55826	+	3.92688i	0.176537	+	0.270981i
$211$	15.3466	+	15.3466i	1.05650	+	1.05650i	0.998305	+	0.0581989i	$0.0185357\pi$
$211$	15.3466	+	15.3466i	1.05650	+	1.05650i	0.0581989	+	0.998305i	$0.481464\pi$
$212$			1.80816i			0.124185i
$213$	9.11337	−	9.11337i	0.624438	−	0.624438i
$214$	2.36667	−	2.36667i	0.161782	−	0.161782i
$215$	0.556122	−	0.556122i	0.0379272	−	0.0379272i
$216$	−1.00000			−0.0680414
$217$	−1.93512	+	9.16952i	−0.131365	+	0.622467i
$218$	7.83624	+	7.83624i	0.530737	+	0.530737i
$219$	−6.38465			−0.431434
$220$	−4.69609	−	4.69609i	−0.316610	−	0.316610i
$221$	33.0449	+	33.0449i	2.22284	+	2.22284i
$222$	4.32333	+	4.32333i	0.290163	+	0.290163i
$223$			13.3595i			0.894616i	0.894380	+	0.447308i	$0.147617\pi$
$223$			13.3595i			0.894616i	−0.894380	+	0.447308i	$0.852383\pi$
$224$	2.58873	+	0.546323i	0.172967	+	0.0365027i
$225$		−	1.86213i		−	0.124142i
$226$	8.13540			0.541159
$227$		−	12.8118i		−	0.850352i	−0.905111	−	0.425176i	$-0.860212\pi$
$227$		−	12.8118i		−	0.850352i	0.905111	−	0.425176i	$-0.139788\pi$
$228$	1.52590			0.101055
$229$	−0.586795	+	0.586795i	−0.0387765	+	0.0387765i	−0.726229	−	0.687453i	$-0.758729\pi$
$229$	−0.586795	+	0.586795i	−0.0387765	+	0.0387765i	0.687453	+	0.726229i	$0.258729\pi$
$230$	0.266436	−	0.266436i	0.0175683	−	0.0175683i
$231$	5.41453	+	8.31120i	0.356250	+	0.546837i
$232$	−0.00702541	+	5.38516i	−0.000461241	+	0.353553i
$233$	5.20556			0.341028			0.170514	−	0.985355i	$-0.445457\pi$
$233$	5.20556			0.341028			0.170514	+	0.985355i	$0.445457\pi$
$234$	4.42523	+	4.42523i	0.289287	+	0.289287i
$235$	5.00568	−	5.00568i	0.326534	−	0.326534i
$236$	−13.9548			−0.908383
$237$	−1.52871			−0.0993001
$238$	−10.7844	−	16.5538i	−0.699049	−	1.07303i
$239$	12.8131			0.828809			0.414405	−	0.910093i	$-0.363990\pi$
$239$	12.8131			0.828809			0.414405	+	0.910093i	$0.363990\pi$
$240$	1.25257	+	1.25257i	0.0808532	+	0.0808532i
$241$	27.6897			1.78365			0.891826	−	0.452379i	$-0.149425\pi$
$241$	27.6897			1.78365			0.891826	+	0.452379i	$0.149425\pi$
$242$	−2.16104	−	2.16104i	−0.138917	−	0.138917i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	5.59790	−	5.59790i	0.358369	−	0.358369i
$245$	−5.01054	+	11.3424i	−0.320111	+	0.724640i
$246$	3.16605	−	3.16605i	0.201860	−	0.201860i
$247$	−6.75248	−	6.75248i	−0.429650	−	0.429650i
$248$			3.54209i			0.224923i
$249$	1.65433	−	1.65433i	0.104839	−	0.104839i
$250$	−8.59531	+	8.59531i	−0.543615	+	0.543615i
$251$	−2.94742	−	2.94742i	−0.186040	−	0.186040i	0.607942	−	0.793982i	$-0.291995\pi$
$251$	−2.94742	−	2.94742i	−0.186040	−	0.186040i	−0.793982	+	0.607942i	$0.791995\pi$
$252$	−1.44420	−	2.21682i	−0.0909761	−	0.139646i
$253$	0.563908	−	0.563908i	0.0354526	−	0.0354526i
$254$			20.9528i			1.31469i
$255$		−	13.2278i		−	0.828354i
$256$	1.00000			0.0625000
$257$			27.9351i			1.74254i	0.490802	+	0.871271i	$0.336704\pi$
$257$			27.9351i			1.74254i	−0.490802	+	0.871271i	$0.663296\pi$
$258$	−0.313944	+	0.313944i	−0.0195453	+	0.0195453i
$259$	−3.34028	+	15.8278i	−0.207555	+	0.983491i
$260$		−	11.0858i		−	0.687515i
$261$	3.81285	−	3.80292i	0.236010	−	0.235395i
$262$			11.3162i			0.699115i
$263$	−0.396506	+	0.396506i	−0.0244496	+	0.0244496i	−0.719226	−	0.694776i	$-0.755503\pi$
$263$	−0.396506	+	0.396506i	−0.0244496	+	0.0244496i	0.694776	+	0.719226i	$0.255503\pi$
$264$	2.65105	+	2.65105i	0.163161	+	0.163161i
$265$	−3.20299			−0.196758
$266$	2.20371	+	3.38265i	0.135118	+	0.207404i
$267$		−	0.602227i		−	0.0368557i
$268$	−7.40715			−0.452464
$269$	21.5599	−	21.5599i	1.31453	−	1.31453i	0.396497	−	0.918036i	$-0.370226\pi$
$269$	21.5599	−	21.5599i	1.31453	−	1.31453i	0.918036	−	0.396497i	$-0.129774\pi$
$270$		−	1.77140i		−	0.107804i
$271$	8.09274	−	8.09274i	0.491599	−	0.491599i	−0.417211	−	0.908810i	$-0.636992\pi$
$271$	8.09274	−	8.09274i	0.491599	−	0.491599i	0.908810	+	0.417211i	$0.136992\pi$
$272$	−5.28024	−	5.28024i	−0.320161	−	0.320161i
$273$	−3.41901	+	16.2009i	−0.206928	+	0.980521i
$274$		−	16.1796i		−	0.977443i
$275$	−4.93660	+	4.93660i	−0.297688	+	0.297688i
$276$	−0.150409	+	0.150409i	−0.00905358	+	0.00905358i
$277$	5.90076			0.354542			0.177271	−	0.984162i	$-0.443273\pi$
$277$	5.90076			0.354542			0.177271	+	0.984162i	$0.443273\pi$
$278$	9.86100	+	9.86100i	0.591424	+	0.591424i
$279$	2.50464	−	2.50464i	0.149949	−	0.149949i
$280$	−0.967759	+	4.58569i	−0.0578347	+	0.274047i
$281$	6.89258			0.411177			0.205588	−	0.978639i	$-0.434089\pi$
$281$	6.89258			0.411177			0.205588	+	0.978639i	$0.434089\pi$
$282$	−2.82583	+	2.82583i	−0.168275	+	0.168275i
$283$	−11.4632			−0.681415			−0.340707	−	0.940169i	$-0.610667\pi$
$283$	−11.4632			−0.681415			−0.340707	+	0.940169i	$0.610667\pi$
$284$	12.8883			0.764777
$285$			2.70299i			0.160111i
$286$		−	23.4631i		−	1.38740i
$287$	11.5910	+	2.44614i	0.684193	+	0.144391i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$			38.7618i			2.28011i
$290$	−9.53930	−	0.0124448i	−0.560167	−	0.000730786i
$291$	−4.51013			−0.264389
$292$	−4.51463	−	4.51463i	−0.264199	−	0.264199i
$293$	10.3162	+	10.3162i	0.602679	+	0.602679i	0.941023	−	0.338344i	$-0.109867\pi$
$293$	10.3162	+	10.3162i	0.602679	+	0.602679i	−0.338344	+	0.941023i	$0.609867\pi$
$294$	2.82857	−	6.40306i	0.164965	−	0.373434i
$295$		−	24.7197i		−	1.43923i
$296$			6.11411i			0.355375i
$297$		−	3.74916i		−	0.217548i
$298$	−12.5991	−	12.5991i	−0.729847	−	0.729847i
$299$	1.33119			0.0769849
$300$	1.31672	−	1.31672i	0.0760210	−	0.0760210i
$301$	−1.14936	−	0.242559i	−0.0662478	−	0.0139809i
$302$	4.43340	+	4.43340i	0.255114	+	0.255114i
$303$			6.62551i			0.380625i
$304$	1.07898	+	1.07898i	0.0618836	+	0.0618836i
$305$	9.91615	+	9.91615i	0.567797	+	0.567797i
$306$			7.46738i			0.426882i
$307$	7.44335	+	7.44335i	0.424814	+	0.424814i	0.886858	−	0.462043i	$-0.152883\pi$
$307$	7.44335	+	7.44335i	0.424814	+	0.424814i	−0.462043	+	0.886858i	$0.652883\pi$
$308$	−2.04825	+	9.70556i	−0.116710	+	0.553025i
$309$	9.08749	−	9.08749i	0.516969	−	0.516969i
$310$	−6.27447			−0.356366
$311$	0.377853	+	0.377853i	0.0214261	+	0.0214261i	0.717739	−	0.696313i	$-0.245177\pi$
$311$	0.377853	+	0.377853i	0.0214261	+	0.0214261i	−0.696313	+	0.717739i	$0.745177\pi$
$312$			6.25822i			0.354302i
$313$			7.28551i			0.411802i	0.978573	+	0.205901i	$0.0660124\pi$
$313$			7.28551i			0.411802i	−0.978573	+	0.205901i	$0.933988\pi$
$314$		−	3.15752i		−	0.178189i
$315$	3.92688	−	2.55826i	0.221255	−	0.144142i
$316$	−1.08096	−	1.08096i	−0.0608086	−	0.0608086i
$317$	−12.6924	−	12.6924i	−0.712877	−	0.712877i	0.254259	−	0.967136i	$-0.418168\pi$
$317$	−12.6924	−	12.6924i	−0.712877	−	0.712877i	−0.967136	+	0.254259i	$0.918168\pi$
$318$	1.80816			0.101397
$319$	−20.1898	−	0.0263394i	−1.13041	−	0.00147472i
$320$			1.77140i			0.0990245i
$321$	−2.36667	−	2.36667i	−0.132095	−	0.132095i
$322$	−0.550652	−	0.116209i	−0.0306866	−	0.00647607i
$323$		−	11.3945i		−	0.634008i
$324$			1.00000i			0.0555556i
$325$	−11.6536			−0.646426
$326$	0.475712			0.0263472
$327$	7.83624	−	7.83624i	0.433345	−	0.433345i
$328$	4.47747			0.247227
$329$	−10.3454	−	2.18328i	−0.570360	−	0.120368i
$330$	−4.69609	+	4.69609i	−0.258511	+	0.258511i
$331$	−11.1472	−	11.1472i	−0.612703	−	0.612703i	0.330946	−	0.943650i	$-0.392632\pi$
$331$	−11.1472	−	11.1472i	−0.612703	−	0.612703i	−0.943650	+	0.330946i	$0.892632\pi$
$332$	2.33957			0.128401
$333$	4.32333	−	4.32333i	0.236917	−	0.236917i
$334$	4.80631	−	4.80631i	0.262990	−	0.262990i
$335$		−	13.1211i		−	0.716880i
$336$	0.546323	−	2.58873i	0.0298044	−	0.141227i
$337$	−16.5902	−	16.5902i	−0.903723	−	0.903723i	0.0920325	−	0.995756i	$-0.470664\pi$
$337$	−16.5902	−	16.5902i	−0.903723	−	0.903723i	−0.995756	+	0.0920325i	$0.970664\pi$
$338$	18.5017	−	18.5017i	1.00636	−	1.00636i
$339$		−	8.13540i		−	0.441854i
$340$	9.35344	−	9.35344i	0.507261	−	0.507261i
$341$	−13.2798			−0.719144
$342$		−	1.52590i		−	0.0825114i
$343$	18.2794	−	2.97689i	0.986997	−	0.160737i
$344$	−0.443984			−0.0239380
$345$	−0.266436	−	0.266436i	−0.0143444	−	0.0143444i
$346$	−0.924945	+	0.924945i	−0.0497253	+	0.0497253i
$347$		−	31.7175i		−	1.70269i	−0.524609	−	0.851343i	$-0.675788\pi$
$347$		−	31.7175i		−	1.70269i	0.524609	−	0.851343i	$-0.324212\pi$
$348$	5.38516	+	0.00702541i	0.288675	+	0.000376601i
$349$			23.9454i			1.28177i	0.767637	+	0.640885i	$0.221432\pi$
$349$			23.9454i			1.28177i	−0.767637	+	0.640885i	$0.778568\pi$
$350$	4.82055	+	1.01732i	0.257669	+	0.0543782i
$351$	4.42523	−	4.42523i	0.236201	−	0.236201i
$352$			3.74916i			0.199831i
$353$	−23.0797			−1.22841			−0.614205	−	0.789147i	$-0.710523\pi$
$353$	−23.0797			−1.22841			−0.614205	+	0.789147i	$0.710523\pi$
$354$			13.9548i			0.741692i
$355$			22.8303i			1.21171i
$356$	0.425839	−	0.425839i	0.0225694	−	0.0225694i
$357$	−16.5538	+	10.7844i	−0.876122	+	0.570771i
$358$	0.758742	+	0.758742i	0.0401008	+	0.0401008i
$359$	−25.6638	+	25.6638i	−1.35448	+	1.35448i	−0.473906	+	0.880576i	$0.657156\pi$
$359$	−25.6638	+	25.6638i	−1.35448	+	1.35448i	−0.880576	+	0.473906i	$0.842844\pi$
$360$	1.25257	−	1.25257i	0.0660163	−	0.0660163i
$361$		−	16.6716i		−	0.877454i
$362$	1.40049	+	1.40049i	0.0736083	+	0.0736083i
$363$	−2.16104	+	2.16104i	−0.113425	+	0.113425i
$364$	−13.8733	+	9.03813i	−0.727161	+	0.473727i
$365$	7.99723	−	7.99723i	0.418594	−	0.418594i
$366$	−5.59790	−	5.59790i	−0.292607	−	0.292607i
$367$	−13.6921	−	13.6921i	−0.714722	−	0.714722i	0.252797	−	0.967519i	$-0.418649\pi$
$367$	−13.6921	−	13.6921i	−0.714722	−	0.714722i	−0.967519	+	0.252797i	$0.918649\pi$
$368$	−0.212711			−0.0110883
$369$	−3.16605	−	3.16605i	−0.164818	−	0.164818i
$370$	−10.8306			−0.563054
$371$	2.61135	+	4.00837i	0.135575	+	0.208104i
$372$	3.54209			0.183649
$373$	−11.1283			−0.576202			−0.288101	−	0.957600i	$-0.593024\pi$
$373$	−11.1283			−0.576202			−0.288101	+	0.957600i	$0.593024\pi$
$374$	19.7964	−	19.7964i	1.02365	−	1.02365i
$375$	8.59531	+	8.59531i	0.443860	+	0.443860i
$376$	−3.99632			−0.206094
$377$	−23.7995	−	23.8617i	−1.22574	−	1.22894i
$378$	−2.21682	+	1.44420i	−0.114021	+	0.0742817i
$379$	15.7720	−	15.7720i	0.810155	−	0.810155i	−0.174501	−	0.984657i	$-0.555831\pi$
$379$	15.7720	−	15.7720i	0.810155	−	0.810155i	0.984657	+	0.174501i	$0.0558314\pi$
$380$	−1.91130	+	1.91130i	−0.0980478	+	0.0980478i
$381$	20.9528			1.07344
$382$		−	18.8791i		−	0.965938i
$383$	−10.2175			−0.522091			−0.261045	−	0.965327i	$-0.584067\pi$
$383$	−10.2175			−0.522091			−0.261045	+	0.965327i	$0.584067\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−17.1925	−	3.62828i	−0.876209	−	0.184914i
$386$			17.8549i			0.908788i
$387$	0.313944	+	0.313944i	0.0159587	+	0.0159587i
$388$	−3.18914	−	3.18914i	−0.161904	−	0.161904i
$389$	−6.04000	−	6.04000i	−0.306240	−	0.306240i	0.537209	−	0.843449i	$-0.319479\pi$
$389$	−6.04000	−	6.04000i	−0.306240	−	0.306240i	−0.843449	+	0.537209i	$0.819479\pi$
$390$	−11.0858			−0.561354
$391$	1.12316	+	1.12316i	0.0568009	+	0.0568009i
$392$	6.52775	−	2.52755i	0.329701	−	0.127661i
$393$	11.3162			0.570825
$394$	−13.3695	+	13.3695i	−0.673545	+	0.673545i
$395$	1.91481	−	1.91481i	0.0963447	−	0.0963447i
$396$	2.65105	−	2.65105i	0.133220	−	0.133220i
$397$		−	3.99158i		−	0.200332i	−0.994971	−	0.100166i	$-0.968063\pi$
$397$		−	3.99158i		−	0.200332i	0.994971	−	0.100166i	$-0.0319373\pi$
$398$	11.8257	+	11.8257i	0.592767	+	0.592767i
$399$	3.38265	−	2.20371i	0.169344	−	0.110324i
$400$	1.86213			0.0931064
$401$	25.1175			1.25431			0.627154	−	0.778896i	$-0.284220\pi$
$401$	25.1175			1.25431			0.627154	+	0.778896i	$0.284220\pi$
$402$			7.40715i			0.369435i
$403$	−15.6746	−	15.6746i	−0.780806	−	0.780806i
$404$	−4.68494	+	4.68494i	−0.233084	+	0.233084i
$405$	−1.77140			−0.0880218
$406$	7.76168	+	11.9481i	0.385206	+	0.592973i
$407$	−22.9227			−1.13624
$408$	−5.28024	+	5.28024i	−0.261411	+	0.261411i
$409$	−0.199703	−	0.199703i	−0.00987467	−	0.00987467i	0.702152	−	0.712027i	$-0.252223\pi$
$409$	−0.199703	−	0.199703i	−0.00987467	−	0.00987467i	−0.712027	+	0.702152i	$0.752223\pi$
$410$			7.93141i			0.391704i
$411$	−16.1796			−0.798079
$412$	12.8517			0.633156
$413$	−30.9354	+	20.1536i	−1.52223	+	0.991694i
$414$	0.150409	+	0.150409i	0.00739222	+	0.00739222i
$415$			4.14433i			0.203437i
$416$	−4.42523	+	4.42523i	−0.216965	+	0.216965i
$417$	9.86100	−	9.86100i	0.482895	−	0.482895i
$418$	−4.04525	+	4.04525i	−0.197860	+	0.197860i
$419$	34.3570			1.67845			0.839224	−	0.543785i	$-0.183009\pi$
$419$	34.3570			1.67845			0.839224	+	0.543785i	$0.183009\pi$
$420$	4.58569	+	0.967759i	0.223759	+	0.0472218i
$421$	26.1995	+	26.1995i	1.27689	+	1.27689i	0.942401	+	0.334485i	$0.108562\pi$
$421$	26.1995	+	26.1995i	1.27689	+	1.27689i	0.334485	+	0.942401i	$0.391438\pi$
$422$	21.7034			1.05650
$423$	2.82583	+	2.82583i	0.137396	+	0.137396i
$424$	1.27856	+	1.27856i	0.0620925	+	0.0620925i
$425$	−9.83248	−	9.83248i	−0.476945	−	0.476945i
$426$		−	12.8883i		−	0.624438i
$427$	4.32504	−	20.4940i	0.209303	−	0.991775i
$428$		−	3.34698i		−	0.161782i
$429$	−23.4631			−1.13281
$430$		−	0.786476i		−	0.0379272i
$431$	3.55210			0.171099			0.0855493	−	0.996334i	$-0.472735\pi$
$431$	3.55210			0.171099			0.0855493	+	0.996334i	$0.472735\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	−5.39204	+	5.39204i	−0.259125	+	0.259125i	−0.824698	−	0.565573i	$-0.808655\pi$
$433$	−5.39204	+	5.39204i	−0.259125	+	0.259125i	0.565573	+	0.824698i	$0.308655\pi$
$434$	5.11549	+	7.85217i	0.245551	+	0.376916i
$435$	−0.0124448	+	9.53930i	−0.000596684	+	0.457374i
$436$	11.0821			0.530737
$437$	−0.229510	−	0.229510i	−0.0109790	−	0.0109790i
$438$	−4.51463	+	4.51463i	−0.215717	+	0.215717i
$439$	23.7523			1.13364			0.566819	−	0.823842i	$-0.308174\pi$
$439$	23.7523			1.13364			0.566819	+	0.823842i	$0.308174\pi$
$440$	−6.64127			−0.316610
$441$	−6.40306	−	2.82857i	−0.304908	−	0.134694i
$442$	46.7326			2.22284
$443$	−6.66754	−	6.66754i	−0.316784	−	0.316784i	0.530746	−	0.847531i	$-0.321912\pi$
$443$	−6.66754	−	6.66754i	−0.316784	−	0.316784i	−0.847531	+	0.530746i	$0.821912\pi$
$444$	6.11411			0.290163
$445$	0.754333	+	0.754333i	0.0357588	+	0.0357588i
$446$	9.44657	+	9.44657i	0.447308	+	0.447308i
$447$	−12.5991	+	12.5991i	−0.595918	+	0.595918i
$448$	2.21682	−	1.44420i	0.104735	−	0.0682321i
$449$	−12.2300	+	12.2300i	−0.577167	+	0.577167i	−0.934122	−	0.356954i	$-0.883815\pi$
$449$	−12.2300	+	12.2300i	−0.577167	+	0.577167i	0.356954	+	0.934122i	$0.383815\pi$
$450$	−1.31672	−	1.31672i	−0.0620709	−	0.0620709i
$451$			16.7867i			0.790456i
$452$	5.75260	−	5.75260i	0.270579	−	0.270579i
$453$	4.43340	−	4.43340i	0.208299	−	0.208299i
$454$	−9.05934	−	9.05934i	−0.425176	−	0.425176i
$455$	−16.0102	−	24.5753i	−0.750569	−	1.15211i
$456$	1.07898	−	1.07898i	0.0505277	−	0.0505277i
$457$			10.3099i			0.482275i	0.970491	+	0.241137i	$0.0775205\pi$
$457$			10.3099i			0.482275i	−0.970491	+	0.241137i	$0.922480\pi$
$458$			0.829853i			0.0387765i
$459$	7.46738			0.348548
$460$		−	0.376797i		−	0.0175683i
$461$	−1.38174	+	1.38174i	−0.0643538	+	0.0643538i	−0.738551	−	0.674197i	$-0.764490\pi$
$461$	−1.38174	+	1.38174i	−0.0643538	+	0.0643538i	0.674197	+	0.738551i	$0.264490\pi$
$462$	9.70556	+	2.04825i	0.451543	+	0.0952932i
$463$			11.0458i			0.513343i	0.966499	+	0.256672i	$0.0826259\pi$
$463$			11.0458i			0.513343i	−0.966499	+	0.256672i	$0.917374\pi$
$464$	3.80292	+	3.81285i	0.176546	+	0.177007i
$465$			6.27447i			0.290972i
$466$	3.68089	−	3.68089i	0.170514	−	0.170514i
$467$	−11.2760	−	11.2760i	−0.521790	−	0.521790i	0.396322	−	0.918112i	$-0.370286\pi$
$467$	−11.2760	−	11.2760i	−0.521790	−	0.521790i	−0.918112	+	0.396322i	$0.870286\pi$
$468$	6.25822			0.289287
$469$	−16.4203	+	10.6974i	−0.758220	+	0.493961i
$470$		−	7.07910i		−	0.326534i
$471$	−3.15752			−0.145491
$472$	−9.86757	+	9.86757i	−0.454192	+	0.454192i
$473$		−	1.66457i		−	0.0765368i
$474$	−1.08096	+	1.08096i	−0.0496501	+	0.0496501i
$475$	2.00919	+	2.00919i	0.0921881	+	0.0921881i
$476$	−19.3311	−	4.07960i	−0.886037	−	0.186988i
$477$		−	1.80816i		−	0.0827901i
$478$	9.06022	−	9.06022i	0.414405	−	0.414405i
$479$	19.6737	−	19.6737i	0.898914	−	0.898914i	−0.0964260	−	0.995340i	$-0.530741\pi$
$479$	19.6737	−	19.6737i	0.898914	−	0.898914i	0.995340	+	0.0964260i	$0.0307411\pi$
$480$	1.77140			0.0808532
$481$	−27.0563	−	27.0563i	−1.23366	−	1.23366i
$482$	19.5796	−	19.5796i	0.891826	−	0.891826i
$483$	−0.116209	+	0.550652i	−0.00528769	+	0.0250555i
$484$	−3.05617			−0.138917
$485$	5.64926	−	5.64926i	0.256520	−	0.256520i
$486$	1.00000			0.0453609
$487$	−28.7993			−1.30502			−0.652511	−	0.757779i	$-0.726285\pi$
$487$	−28.7993			−1.30502			−0.652511	+	0.757779i	$0.726285\pi$
$488$		−	7.91663i		−	0.358369i
$489$		−	0.475712i		−	0.0215124i
$490$	4.47731	+	11.5633i	0.202264	+	0.522376i
$491$	−11.8275	−	11.8275i	−0.533768	−	0.533768i	0.387923	−	0.921692i	$-0.373192\pi$
$491$	−11.8275	−	11.8275i	−0.533768	−	0.533768i	−0.921692	+	0.387923i	$0.873192\pi$
$492$		−	4.47747i		−	0.201860i
$493$	0.0524614	−	40.2131i	0.00236274	−	1.81111i
$494$	−9.54945			−0.429650
$495$	4.69609	+	4.69609i	0.211073	+	0.211073i
$496$	2.50464	+	2.50464i	0.112461	+	0.112461i
$497$	28.5709	−	18.6132i	1.28158	−	0.834917i
$498$		−	2.33957i		−	0.104839i
$499$			19.0996i			0.855017i	0.904011	+	0.427509i	$0.140609\pi$
$499$			19.0996i			0.855017i	−0.904011	+	0.427509i	$0.859391\pi$
$500$			12.1556i			0.543615i
$501$	−4.80631	−	4.80631i	−0.214730	−	0.214730i
$502$	−4.16829			−0.186040
$503$	−1.34934	+	1.34934i	−0.0601642	+	0.0601642i	−0.736549	−	0.676385i	$-0.763546\pi$
$503$	−1.34934	+	1.34934i	−0.0601642	+	0.0601642i	0.676385	+	0.736549i	$0.263546\pi$
$504$	−2.58873	−	0.546323i	−0.115311	−	0.0243352i
$505$	−8.29892	−	8.29892i	−0.369297	−	0.369297i
$506$		−	0.797487i		−	0.0354526i
$507$	−18.5017	−	18.5017i	−0.821690	−	0.821690i
$508$	14.8159	+	14.8159i	0.657347	+	0.657347i
$509$			10.8673i			0.481686i	0.970564	+	0.240843i	$0.0774238\pi$
$509$			10.8673i			0.481686i	−0.970564	+	0.240843i	$0.922576\pi$
$510$	−9.35344	−	9.35344i	−0.414177	−	0.414177i
$511$	−16.5281	−	3.48808i	−0.731162	−	0.154304i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.52590			−0.0673703
$514$	19.7531	+	19.7531i	0.871271	+	0.871271i
$515$			22.7655i			1.00317i
$516$			0.443984i			0.0195453i
$517$		−	14.9828i		−	0.658944i
$518$	8.83000	+	13.5539i	0.387968	+	0.595523i
$519$	0.924945	+	0.924945i	0.0406006	+	0.0406006i
$520$	−7.83888	−	7.83888i	−0.343757	−	0.343757i
$521$	25.7076			1.12627			0.563134	−	0.826365i	$-0.309595\pi$
$521$	25.7076			1.12627			0.563134	+	0.826365i	$0.309595\pi$
$522$	0.00702541	−	5.38516i	0.000307494	−	0.235702i
$523$			32.5533i			1.42346i	0.702455	+	0.711729i	$0.252087\pi$
$523$			32.5533i			1.42346i	−0.702455	+	0.711729i	$0.747913\pi$
$524$	8.00174	+	8.00174i	0.349558	+	0.349558i
$525$	1.01732	−	4.82055i	0.0443996	−	0.210386i
$526$			0.560744i			0.0244496i
$527$		−	26.4501i		−	1.15219i
$528$	3.74916			0.163161
$529$	−22.9548			−0.998033
$530$	−2.26485	+	2.26485i	−0.0983789	+	0.0983789i
$531$	13.9548			0.605589
$532$	3.95016	+	0.833636i	0.171261	+	0.0361427i
$533$	−19.8138	+	19.8138i	−0.858233	+	0.858233i
$534$	−0.425839	−	0.425839i	−0.0184278	−	0.0184278i
$535$	5.92886			0.256327
$536$	−5.23765	+	5.23765i	−0.226232	+	0.226232i
$537$	0.758742	−	0.758742i	0.0327421	−	0.0327421i
$538$		−	30.4904i		−	1.31453i
$539$	9.47618	+	24.4735i	0.408168	+	1.05415i
$540$	−1.25257	−	1.25257i	−0.0539021	−	0.0539021i
$541$	23.8786	−	23.8786i	1.02662	−	1.02662i	0.0269839	−	0.999636i	$-0.491410\pi$
$541$	23.8786	−	23.8786i	1.02662	−	1.02662i	0.999636	−	0.0269839i	$-0.00859027\pi$
$542$		−	11.4449i		−	0.491599i
$543$	1.40049	−	1.40049i	0.0601009	−	0.0601009i
$544$	−7.46738			−0.320161
$545$			19.6309i			0.840896i
$546$	9.03813	+	13.8733i	0.386796	+	0.593724i
$547$	−36.9831			−1.58128			−0.790642	−	0.612278i	$-0.790253\pi$
$547$	−36.9831			−1.58128			−0.790642	+	0.612278i	$0.790253\pi$
$548$	−11.4407	−	11.4407i	−0.488722	−	0.488722i
$549$	−5.59790	+	5.59790i	−0.238913	+	0.238913i
$550$			6.98140i			0.297688i
$551$	−0.0107201	+	8.21724i	−0.000456692	+	0.350066i
$552$			0.212711i			0.00905358i
$553$	−3.95741	−	0.835167i	−0.168286	−	0.0355149i
$554$	4.17247	−	4.17247i	0.177271	−	0.177271i
$555$			10.8306i			0.459731i
$556$	13.9456			0.591424
$557$			26.1803i			1.10929i	0.832086	+	0.554647i	$0.187147\pi$
$557$			26.1803i			1.10929i	−0.832086	+	0.554647i	$0.812853\pi$
$558$		−	3.54209i		−	0.149949i
$559$	1.96473	−	1.96473i	0.0830994	−	0.0830994i
$560$	2.55826	+	3.92688i	0.108106	+	0.165941i
$561$	−19.7964	−	19.7964i	−0.835806	−	0.835806i
$562$	4.87379	−	4.87379i	0.205588	−	0.205588i
$563$	−4.30463	+	4.30463i	−0.181419	+	0.181419i	−0.791974	−	0.610555i	$-0.790946\pi$
$563$	−4.30463	+	4.30463i	−0.181419	+	0.181419i	0.610555	+	0.791974i	$0.290946\pi$
$564$			3.99632i			0.168275i
$565$	10.1902	+	10.1902i	0.428704	+	0.428704i
$566$	−8.10568	+	8.10568i	−0.340707	+	0.340707i
$567$	1.44420	+	2.21682i	0.0606507	+	0.0930976i
$568$	9.11337	−	9.11337i	0.382389	−	0.382389i
$569$	29.4715	+	29.4715i	1.23551	+	1.23551i	0.961817	+	0.273692i	$0.0882448\pi$
$569$	29.4715	+	29.4715i	1.23551	+	1.23551i	0.273692	+	0.961817i	$0.411755\pi$
$570$	1.91130	+	1.91130i	0.0800557	+	0.0800557i
$571$	−28.7188			−1.20185			−0.600923	−	0.799307i	$-0.705200\pi$
$571$	−28.7188			−1.20185			−0.600923	+	0.799307i	$0.705200\pi$
$572$	−16.5909	−	16.5909i	−0.693700	−	0.693700i
$573$	−18.8791			−0.788685
$574$	9.92574	−	6.46637i	0.414292	−	0.269901i
$575$	−0.396095			−0.0165183
$576$	−1.00000			−0.0416667
$577$	20.9754	−	20.9754i	0.873217	−	0.873217i	−0.119605	−	0.992822i	$-0.538163\pi$
$577$	20.9754	−	20.9754i	0.873217	−	0.873217i	0.992822	+	0.119605i	$0.0381628\pi$
$578$	27.4088	+	27.4088i	1.14005	+	1.14005i
$579$	17.8549			0.742022
$580$	−6.75410	+	6.73650i	−0.280449	+	0.279718i
$581$	5.18641	−	3.37881i	0.215169	−	0.140177i
$582$	−3.18914	+	3.18914i	−0.132194	+	0.132194i
$583$	−4.79353	+	4.79353i	−0.198528	+	0.198528i
$584$	−6.38465			−0.264199
$585$			11.0858i			0.458343i
$586$	14.5893			0.602679
$587$			10.9396i			0.451526i	0.974182	+	0.225763i	$0.0724875\pi$
$587$			10.9396i			0.451526i	−0.974182	+	0.225763i	$0.927513\pi$
$588$	−2.52755	−	6.52775i	−0.104234	−	0.269200i
$589$			5.40489i			0.222705i
$590$	−17.4794	−	17.4794i	−0.719617	−	0.719617i
$591$	13.3695	+	13.3695i	0.549947	+	0.549947i
$592$	4.32333	+	4.32333i	0.177688	+	0.177688i
$593$	3.34604			0.137405			0.0687027	−	0.997637i	$-0.478114\pi$
$593$	3.34604			0.137405			0.0687027	+	0.997637i	$0.478114\pi$
$594$	−2.65105	−	2.65105i	−0.108774	−	0.108774i
$595$	7.22663	−	34.2431i	0.296263	−	1.40383i
$596$	−17.8178			−0.729847
$597$	11.8257	−	11.8257i	0.483992	−	0.483992i
$598$	0.941296	−	0.941296i	0.0384924	−	0.0384924i
$599$	−28.9241	+	28.9241i	−1.18181	+	1.18181i	−0.202531	+	0.979276i	$0.564917\pi$
$599$	−28.9241	+	28.9241i	−1.18181	+	1.18181i	−0.979276	+	0.202531i	$0.935083\pi$
$600$		−	1.86213i		−	0.0760210i
$601$	24.3904	+	24.3904i	0.994903	+	0.994903i	0.999987	−	0.00508391i	$-0.00161826\pi$
$601$	24.3904	+	24.3904i	0.994903	+	0.994903i	−0.00508391	+	0.999987i	$0.501618\pi$
$602$	−0.984233	+	0.641203i	−0.0401143	+	0.0261335i
$603$	7.40715			0.301643
$604$	6.26978			0.255114
$605$		−	5.41371i		−	0.220099i
$606$	4.68494	+	4.68494i	0.190313	+	0.190313i
$607$	5.41664	−	5.41664i	0.219854	−	0.219854i	−0.588583	−	0.808437i	$-0.700314\pi$
$607$	5.41664	−	5.41664i	0.219854	−	0.219854i	0.808437	+	0.588583i	$0.200314\pi$
$608$	1.52590			0.0618836
$609$	11.9481	−	7.76168i	0.484160	−	0.314519i
$610$	14.0235			0.567797
$611$	17.6846	−	17.6846i	0.715444	−	0.715444i
$612$	5.28024	+	5.28024i	0.213441	+	0.213441i
$613$			7.68465i			0.310380i	0.987885	+	0.155190i	$0.0495990\pi$
$613$			7.68465i			0.310380i	−0.987885	+	0.155190i	$0.950401\pi$
$614$	10.5265			0.424814
$615$	7.93141			0.319825
$616$	5.41453	+	8.31120i	0.218158	+	0.334868i
$617$	−30.8424	−	30.8424i	−1.24167	−	1.24167i	−0.959309	−	0.282359i	$-0.908883\pi$
$617$	−30.8424	−	30.8424i	−1.24167	−	1.24167i	−0.282359	−	0.959309i	$-0.591117\pi$
$618$		−	12.8517i		−	0.516969i
$619$	30.2202	−	30.2202i	1.21465	−	1.21465i	0.245175	−	0.969479i	$-0.421155\pi$
$619$	30.2202	−	30.2202i	1.21465	−	1.21465i	0.969479	−	0.245175i	$-0.0788454\pi$
$620$	−4.43672	+	4.43672i	−0.178183	+	0.178183i
$621$	0.150409	−	0.150409i	0.00603572	−	0.00603572i
$622$	0.534365			0.0214261
$623$	0.329010	−	1.55900i	0.0131815	−	0.0624602i
$624$	4.42523	+	4.42523i	0.177151	+	0.177151i
$625$	−12.2218			−0.488874
$626$	5.15164	+	5.15164i	0.205901	+	0.205901i
$627$	4.04525	+	4.04525i	0.161552	+	0.161552i
$628$	−2.23270	−	2.23270i	−0.0890946	−	0.0890946i
$629$		−	45.6564i		−	1.82044i
$630$	0.967759	−	4.58569i	0.0385564	−	0.182698i
$631$			15.1104i			0.601535i	0.953697	+	0.300768i	$0.0972428\pi$
$631$			15.1104i			0.601535i	−0.953697	+	0.300768i	$0.902757\pi$
$632$	−1.52871			−0.0608086
$633$		−	21.7034i		−	0.862632i
$634$	−17.9498			−0.712877
$635$	−26.2449	+	26.2449i	−1.04150	+	1.04150i
$636$	1.27856	−	1.27856i	0.0506983	−	0.0506983i
$637$	−17.7018	+	40.0718i	−0.701371	+	1.58770i
$638$	−14.2950	+	14.2577i	−0.565943	+	0.564469i
$639$	−12.8883			−0.509851
$640$	1.25257	+	1.25257i	0.0495123	+	0.0495123i
$641$	−7.98301	+	7.98301i	−0.315310	+	0.315310i	−0.846963	−	0.531653i	$-0.821571\pi$
$641$	−7.98301	+	7.98301i	−0.315310	+	0.315310i	0.531653	+	0.846963i	$0.321571\pi$
$642$	−3.34698			−0.132095
$643$	1.09891			0.0433369			0.0216684	−	0.999765i	$-0.493102\pi$
$643$	1.09891			0.0433369			0.0216684	+	0.999765i	$0.493102\pi$
$644$	−0.471542	+	0.307197i	−0.0185813	+	0.0121053i
$645$	−0.786476			−0.0309674
$646$	−8.05714	−	8.05714i	−0.317004	−	0.317004i
$647$	−42.3555			−1.66517			−0.832583	−	0.553900i	$-0.813139\pi$
$647$	−42.3555			−1.66517			−0.832583	+	0.553900i	$0.813139\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	−36.9950	−	36.9950i	−1.45218	−	1.45218i
$650$	−8.24035	+	8.24035i	−0.323213	+	0.323213i
$651$	7.85217	−	5.11549i	0.307751	−	0.200492i
$652$	0.336379	−	0.336379i	0.0131736	−	0.0131736i
$653$	21.4298	+	21.4298i	0.838613	+	0.838613i	0.988676	−	0.150063i	$-0.0479478\pi$
$653$	21.4298	+	21.4298i	0.838613	+	0.838613i	−0.150063	+	0.988676i	$0.547948\pi$
$654$		−	11.0821i		−	0.433345i
$655$	−14.1743	+	14.1743i	−0.553836	+	0.553836i
$656$	3.16605	−	3.16605i	0.123613	−	0.123613i
$657$	4.51463	+	4.51463i	0.176132	+	0.176132i
$658$	−8.85912	+	5.77149i	−0.345364	+	0.224996i
$659$	−11.2796	+	11.2796i	−0.439390	+	0.439390i	−0.891807	−	0.452417i	$-0.850562\pi$
$659$	−11.2796	+	11.2796i	−0.439390	+	0.439390i	0.452417	+	0.891807i	$0.350562\pi$
$660$			6.64127i			0.258511i
$661$		−	32.1711i		−	1.25131i	−0.780099	−	0.625656i	$-0.784832\pi$
$661$		−	32.1711i		−	1.25131i	0.780099	−	0.625656i	$-0.215168\pi$
$662$	−15.7645			−0.612703
$663$		−	46.7326i		−	1.81494i
$664$	1.65433	−	1.65433i	0.0642004	−	0.0642004i
$665$	−1.47671	+	6.99732i	−0.0572642	+	0.271345i
$666$		−	6.11411i		−	0.236917i
$667$	−0.808922	−	0.811035i	−0.0313216	−	0.0314034i
$668$		−	6.79715i		−	0.262990i
$669$	9.44657	−	9.44657i	0.365226	−	0.365226i
$670$	−9.27799	−	9.27799i	−0.358440	−	0.358440i
$671$	29.6807			1.14581
$672$	−1.44420	−	2.21682i	−0.0557113	−	0.0855156i
$673$			33.0712i			1.27480i	0.770533	+	0.637400i	$0.219990\pi$
$673$			33.0712i			1.27480i	−0.770533	+	0.637400i	$0.780010\pi$
$674$	−23.4620			−0.903723
$675$	−1.31672	+	1.31672i	−0.0506807	+	0.0506807i
$676$		−	26.1654i		−	1.00636i
$677$	−21.9256	+	21.9256i	−0.842669	+	0.842669i	−0.989205	−	0.146536i	$-0.953188\pi$
$677$	−21.9256	+	21.9256i	−0.842669	+	0.842669i	0.146536	+	0.989205i	$0.453188\pi$
$678$	−5.75260	−	5.75260i	−0.220927	−	0.220927i
$679$	−11.6755	−	2.46399i	−0.448065	−	0.0945592i
$680$		−	13.2278i		−	0.507261i
$681$	−9.05934	+	9.05934i	−0.347155	+	0.347155i
$682$	−9.39027	+	9.39027i	−0.359572	+	0.359572i
$683$	33.8910			1.29680			0.648401	−	0.761299i	$-0.275438\pi$
$683$	33.8910			1.29680			0.648401	+	0.761299i	$0.275438\pi$
$684$	−1.07898	−	1.07898i	−0.0412557	−	0.0412557i
$685$	20.2661	−	20.2661i	0.774327	−	0.774327i
$686$	10.8205	−	15.0305i	0.413130	−	0.573867i
$687$	0.829853			0.0316609
$688$	−0.313944	+	0.313944i	−0.0119690	+	0.0119690i
$689$	−11.3159			−0.431101
$690$	−0.376797			−0.0143444
$691$			24.5578i			0.934221i	0.884199	+	0.467111i	$0.154705\pi$
$691$			24.5578i			0.934221i	−0.884199	+	0.467111i	$0.845295\pi$
$692$			1.30807i			0.0497253i
$693$	2.04825	−	9.70556i	0.0778066	−	0.368684i
$694$	−22.4277	−	22.4277i	−0.851343	−	0.851343i
$695$			24.7032i			0.937047i
$696$	3.81285	−	3.80292i	0.144526	−	0.144149i
$697$	−33.4350			−1.26644
$698$	16.9320	+	16.9320i	0.640885	+	0.640885i
$699$	−3.68089	−	3.68089i	−0.139224	−	0.139224i
$700$	4.12800	−	2.68929i	0.156024	−	0.101645i
$701$		−	13.9533i		−	0.527007i	−0.964658	−	0.263504i	$-0.915122\pi$
$701$		−	13.9533i		−	0.527007i	0.964658	−	0.263504i	$-0.0848781\pi$
$702$		−	6.25822i		−	0.236201i
$703$			9.32954i			0.351870i
$704$	2.65105	+	2.65105i	0.0999153	+	0.0999153i
$705$	−7.07910			−0.266614
$706$	−16.3198	+	16.3198i	−0.614205	+	0.614205i
$707$	−3.61967	+	17.1517i	−0.136132	+	0.645054i
$708$	9.86757	+	9.86757i	0.370846	+	0.370846i
$709$		−	36.5548i		−	1.37284i	−0.727203	−	0.686422i	$-0.759180\pi$
$709$		−	36.5548i		−	1.37284i	0.727203	−	0.686422i	$-0.240820\pi$
$710$	16.1435	+	16.1435i	0.605853	+	0.605853i
$711$	1.08096	+	1.08096i	0.0405391	+	0.0405391i
$712$		−	0.602227i		−	0.0225694i
$713$	−0.532763	−	0.532763i	−0.0199521	−	0.0199521i
$714$	−4.07960	+	19.3311i	−0.152675	+	0.723447i
$715$	29.3892	−	29.3892i	1.09909	−	1.09909i
$716$	1.07302			0.0401008
$717$	−9.06022	−	9.06022i	−0.338360	−	0.338360i
$718$			36.2940i			1.35448i
$719$			8.65885i			0.322921i	0.986879	+	0.161460i	$0.0516204\pi$
$719$			8.65885i			0.322921i	−0.986879	+	0.161460i	$0.948380\pi$
$720$		−	1.77140i		−	0.0660163i
$721$	28.4898	−	18.5604i	1.06102	−	0.691224i
$722$	−11.7886	−	11.7886i	−0.438727	−	0.438727i
$723$	−19.5796	−	19.5796i	−0.728173	−	0.728173i
$724$	1.98060			0.0736083
$725$	7.08151	+	7.10001i	0.263001	+	0.263688i
$726$			3.05617i			0.113425i
$727$	−36.6881	−	36.6881i	−1.36069	−	1.36069i	−0.873042	−	0.487645i	$-0.837856\pi$
$727$	−36.6881	−	36.6881i	−1.36069	−	1.36069i	−0.487645	−	0.873042i	$-0.662144\pi$
$728$	−3.41901	+	16.2009i	−0.126717	+	0.600444i
$729$		−	1.00000i		−	0.0370370i
$730$		−	11.3098i		−	0.418594i
$731$	3.31540			0.122625
$732$	−7.91663			−0.292607
$733$	−34.1573	+	34.1573i	−1.26163	+	1.26163i	−0.311323	+	0.950304i	$0.600772\pi$
$733$	−34.1573	+	34.1573i	−1.26163	+	1.26163i	−0.950304	+	0.311323i	$0.899228\pi$
$734$	−19.3636			−0.714722
$735$	11.5633	−	4.47731i	0.426518	−	0.165148i
$736$	−0.150409	+	0.150409i	−0.00554416	+	0.00554416i
$737$	−19.6368	−	19.6368i	−0.723329	−	0.723329i
$738$	−4.47747			−0.164818
$739$	3.68225	−	3.68225i	0.135454	−	0.135454i	−0.636129	−	0.771583i	$-0.719465\pi$
$739$	3.68225	−	3.68225i	0.135454	−	0.135454i	0.771583	+	0.636129i	$0.219465\pi$
$740$	−7.65836	+	7.65836i	−0.281527	+	0.281527i
$741$			9.54945i			0.350808i
$742$	4.68085	+	0.987841i	0.171839	+	0.0362648i
$743$	−25.3145	−	25.3145i	−0.928698	−	0.928698i	0.0689238	−	0.997622i	$-0.478043\pi$
$743$	−25.3145	−	25.3145i	−0.928698	−	0.928698i	−0.997622	+	0.0689238i	$0.978043\pi$
$744$	2.50464	−	2.50464i	0.0918244	−	0.0918244i
$745$		−	31.5626i		−	1.15636i
$746$	−7.86890	+	7.86890i	−0.288101	+	0.288101i
$747$	−2.33957			−0.0856005
$748$		−	27.9964i		−	1.02365i
$749$	−4.83371	−	7.41965i	−0.176620	−	0.271108i
$750$	12.1556			0.443860
$751$	−31.9097	−	31.9097i	−1.16440	−	1.16440i	−0.983501	−	0.180900i	$-0.942099\pi$
$751$	−31.9097	−	31.9097i	−1.16440	−	1.16440i	−0.180900	−	0.983501i	$-0.557901\pi$
$752$	−2.82583	+	2.82583i	−0.103047	+	0.103047i
$753$			4.16829i			0.151901i
$754$	−33.7015	−	0.0439666i	−1.22734	−	0.00160117i
$755$			11.1063i			0.404200i
$756$	−0.546323	+	2.58873i	−0.0198696	+	0.0941513i
$757$	2.25680	−	2.25680i	0.0820249	−	0.0820249i	−0.664904	−	0.746929i	$-0.731528\pi$
$757$	2.25680	−	2.25680i	0.0820249	−	0.0820249i	0.746929	+	0.664904i	$0.231528\pi$
$758$		−	22.3050i		−	0.810155i
$759$	−0.797487			−0.0289469
$760$			2.70299i			0.0980478i
$761$			11.1308i			0.403490i	0.979438	+	0.201745i	$0.0646613\pi$
$761$			11.1308i			0.403490i	−0.979438	+	0.201745i	$0.935339\pi$
$762$	14.8159	−	14.8159i	0.536722	−	0.536722i
$763$	24.5670	−	16.0048i	0.889386	−	0.579413i
$764$	−13.3495	−	13.3495i	−0.482969	−	0.482969i
$765$	−9.35344	+	9.35344i	−0.338174	+	0.338174i
$766$	−7.22488	+	7.22488i	−0.261045	+	0.261045i
$767$		−	87.3326i		−	3.15340i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−23.3556	+	23.3556i	−0.842224	+	0.842224i	−0.989148	−	0.146924i	$-0.953063\pi$
$769$	−23.3556	+	23.3556i	−0.842224	+	0.842224i	0.146924	+	0.989148i	$0.453063\pi$
$770$	−14.7225	+	9.59133i	−0.530562	+	0.345648i
$771$	19.7531	−	19.7531i	0.711390	−	0.711390i
$772$	12.6253	+	12.6253i	0.454394	+	0.454394i
$773$	35.3652	+	35.3652i	1.27200	+	1.27200i	0.945037	+	0.326962i	$0.106025\pi$
$773$	35.3652	+	35.3652i	1.27200	+	1.27200i	0.326962	+	0.945037i	$0.393975\pi$
$774$	0.443984			0.0159587
$775$	4.66395	+	4.66395i	0.167534	+	0.167534i
$776$	−4.51013			−0.161904
$777$	13.5539	−	8.83000i	0.486242	−	0.316774i
$778$	−8.54185			−0.306240
$779$	6.83219			0.244789
$780$	−7.83888	+	7.83888i	−0.280677	+	0.280677i
$781$	34.1675	+	34.1675i	1.22261	+	1.22261i
$782$	1.58839			0.0568009
$783$	−5.38516	−	0.00702541i	−0.192450	−	0.000251068i
$784$	2.82857	−	6.40306i	0.101020	−	0.228681i
$785$	3.95502	−	3.95502i	0.141161	−	0.141161i
$786$	8.00174	−	8.00174i	0.285413	−	0.285413i
$787$	17.8708			0.637025			0.318512	−	0.947919i	$-0.396817\pi$
$787$	17.8708			0.637025			0.318512	+	0.947919i	$0.396817\pi$
$788$			18.9073i			0.673545i
$789$	0.560744			0.0199630
$790$		−	2.70796i		−	0.0963447i
$791$	4.44456	−	21.0604i	0.158030	−	0.748820i
$792$		−	3.74916i		−	0.133220i
$793$	35.0329	+	35.0329i	1.24406	+	1.24406i
$794$	−2.82247	−	2.82247i	−0.100166	−	0.100166i
$795$	2.26485	+	2.26485i	0.0803261	+	0.0803261i
$796$	16.7240			0.592767
$797$	7.00288	+	7.00288i	0.248055	+	0.248055i	0.820172	−	0.572117i	$-0.193878\pi$
$797$	7.00288	+	7.00288i	0.248055	+	0.248055i	−0.572117	+	0.820172i	$0.693878\pi$
$798$	0.833636	−	3.95016i	0.0295104	−	0.139834i
$799$	29.8421			1.05574
$800$	1.31672	−	1.31672i	0.0465532	−	0.0465532i
$801$	−0.425839	+	0.425839i	−0.0150463	+	0.0150463i
$802$	17.7607	−	17.7607i	0.627154	−	0.627154i
$803$		−	23.9370i		−	0.844720i
$804$	5.23765	+	5.23765i	0.184718	+	0.184718i
$805$	−0.544171	−	0.835291i	−0.0191795	−	0.0294401i
$806$	−22.1672			−0.780806
$807$	−30.4904			−1.07331
$808$			6.62551i			0.233084i
$809$	−26.8998	−	26.8998i	−0.945748	−	0.945748i	0.0528544	−	0.998602i	$-0.483168\pi$
$809$	−26.8998	−	26.8998i	−0.945748	−	0.945748i	−0.998602	+	0.0528544i	$0.983168\pi$
$810$	−1.25257	+	1.25257i	−0.0440109	+	0.0440109i
$811$	−21.8894			−0.768639			−0.384320	−	0.923200i	$-0.625564\pi$
$811$	−21.8894			−0.768639			−0.384320	+	0.923200i	$0.625564\pi$
$812$	13.9369	+	2.96022i	0.489089	+	0.103883i
$813$	−11.4449			−0.401389
$814$	−16.2088	+	16.2088i	−0.568119	+	0.568119i
$815$	0.595863	+	0.595863i	0.0208722	+	0.0208722i
$816$			7.46738i			0.261411i
$817$	−0.677477			−0.0237019
$818$	−0.282422			−0.00987467
$819$	13.8733	−	9.03813i	0.484774	−	0.315818i
$820$	5.60835	+	5.60835i	0.195852	+	0.195852i
$821$		−	22.7930i		−	0.795481i	−0.917498	−	0.397740i	$-0.869794\pi$
$821$		−	22.7930i		−	0.795481i	0.917498	−	0.397740i	$-0.130206\pi$
$822$	−11.4407	+	11.4407i	−0.399039	+	0.399039i
$823$	34.3796	−	34.3796i	1.19840	−	1.19840i	0.223752	−	0.974646i	$-0.428169\pi$
$823$	34.3796	−	34.3796i	1.19840	−	1.19840i	0.974646	−	0.223752i	$-0.0718306\pi$
$824$	9.08749	−	9.08749i	0.316578	−	0.316578i
$825$	6.98140			0.243061
$826$	−7.62385	+	36.1254i	−0.265268	+	1.25696i
$827$	−1.04334	−	1.04334i	−0.0362806	−	0.0362806i	0.688734	−	0.725014i	$-0.258167\pi$
$827$	−1.04334	−	1.04334i	−0.0362806	−	0.0362806i	−0.725014	+	0.688734i	$0.758167\pi$
$828$	0.212711			0.00739222
$829$	17.4499	+	17.4499i	0.606059	+	0.606059i	0.941914	−	0.335855i	$-0.109025\pi$
$829$	17.4499	+	17.4499i	0.606059	+	0.606059i	−0.335855	+	0.941914i	$0.609025\pi$
$830$	2.93048	+	2.93048i	0.101719	+	0.101719i
$831$	−4.17247	−	4.17247i	−0.144741	−	0.144741i
$832$			6.25822i			0.216965i
$833$	−48.7452	+	18.8742i	−1.68892	+	0.653952i
$834$		−	13.9456i		−	0.482895i
$835$	12.0405			0.416679
$836$			5.72085i			0.197860i
$837$	−3.54209			−0.122433
$838$	24.2941	−	24.2941i	0.839224	−	0.839224i
$839$	−0.729922	+	0.729922i	−0.0251997	+	0.0251997i	−0.719594	−	0.694395i	$-0.755672\pi$
$839$	−0.729922	+	0.729922i	−0.0251997	+	0.0251997i	0.694395	+	0.719594i	$0.255672\pi$
$840$	3.92688	−	2.55826i	0.135490	−	0.0882685i
$841$	−0.0756659	+	28.9999i	−0.00260917	+	0.999997i
$842$	37.0517			1.27689
$843$	−4.87379	−	4.87379i	−0.167862	−	0.167862i
$844$	15.3466	−	15.3466i	0.528252	−	0.528252i
$845$	46.3495			1.59447
$846$	3.99632			0.137396
$847$	−6.77497	+	4.41372i	−0.232791	+	0.151657i
$848$	1.80816			0.0620925
$849$	8.10568	+	8.10568i	0.278186	+	0.278186i
$850$	−13.9052			−0.476945
$851$	−0.919619	−	0.919619i	−0.0315241	−	0.0315241i
$852$	−9.11337	−	9.11337i	−0.312219	−	0.312219i
$853$	40.3203	−	40.3203i	1.38054	−	1.38054i	0.536889	−	0.843653i	$-0.319600\pi$
$853$	40.3203	−	40.3203i	1.38054	−	1.38054i	0.843653	−	0.536889i	$-0.180400\pi$
$854$	−11.4332	−	17.5497i	−0.391236	−	0.600539i
$855$	1.91130	−	1.91130i	0.0653652	−	0.0653652i
$856$	−2.36667	−	2.36667i	−0.0808912	−	0.0808912i
$857$			11.4895i			0.392474i	0.980556	+	0.196237i	$0.0628723\pi$
$857$			11.4895i			0.392474i	−0.980556	+	0.196237i	$0.937128\pi$
$858$	−16.5909	+	16.5909i	−0.566404	+	0.566404i
$859$	−18.3189	+	18.3189i	−0.625032	+	0.625032i	−0.946814	−	0.321782i	$-0.895718\pi$
$859$	−18.3189	+	18.3189i	−0.625032	+	0.625032i	0.321782	+	0.946814i	$0.395718\pi$
$860$	−0.556122	−	0.556122i	−0.0189636	−	0.0189636i
$861$	−6.46637	−	9.92574i	−0.220373	−	0.338268i
$862$	2.51171	−	2.51171i	0.0855493	−	0.0855493i
$863$			0.920279i			0.0313267i	0.999877	+	0.0156633i	$0.00498600\pi$
$863$			0.920279i			0.0313267i	−0.999877	+	0.0156633i	$0.995014\pi$
$864$			1.00000i			0.0340207i
$865$	−2.31712			−0.0787844
$866$			7.62549i			0.259125i
$867$	27.4088	−	27.4088i	0.930850	−	0.930850i
$868$	9.16952	+	1.93512i	0.311234	+	0.0656824i
$869$		−	5.73136i		−	0.194423i
$870$	6.73650	+	6.75410i	0.228389	+	0.228985i
$871$		−	46.3556i		−	1.57070i
$872$	7.83624	−	7.83624i	0.265369	−	0.265369i
$873$	3.18914	+	3.18914i	0.107936	+	0.107936i
$874$	−0.324576			−0.0109790
$875$	17.5551	+	26.9468i	0.593472	+	0.910967i
$876$			6.38465i			0.215717i
$877$	10.4200			0.351857			0.175929	−	0.984403i	$-0.443707\pi$
$877$	10.4200			0.351857			0.175929	+	0.984403i	$0.443707\pi$
$878$	16.7954	−	16.7954i	0.566819	−	0.566819i
$879$		−	14.5893i		−	0.492085i
$880$	−4.69609	+	4.69609i	−0.158305	+	0.158305i
$881$	12.2681	+	12.2681i	0.413324	+	0.413324i	0.882895	−	0.469571i	$-0.155591\pi$
$881$	12.2681	+	12.2681i	0.413324	+	0.413324i	−0.469571	+	0.882895i	$0.655591\pi$
$882$	−6.52775	+	2.52755i	−0.219801	+	0.0851070i
$883$			44.5394i			1.49887i	0.662078	+	0.749435i	$0.269675\pi$
$883$			44.5394i			1.49887i	−0.662078	+	0.749435i	$0.730325\pi$
$884$	33.0449	−	33.0449i	1.11142	−	1.11142i
$885$	−17.4794	+	17.4794i	−0.587565	+	0.587565i
$886$	−9.42932			−0.316784
$887$	6.04195	+	6.04195i	0.202869	+	0.202869i	0.801228	−	0.598359i	$-0.204180\pi$
$887$	6.04195	+	6.04195i	0.202869	+	0.202869i	−0.598359	+	0.801228i	$0.704180\pi$
$888$	4.32333	−	4.32333i	0.145081	−	0.145081i
$889$	54.2411	+	11.4470i	1.81919	+	0.383920i
$890$	1.06679			0.0357588
$891$	−2.65105	+	2.65105i	−0.0888136	+	0.0888136i
$892$	13.3595			0.447308
$893$	−6.09800			−0.204062
$894$			17.8178i			0.595918i
$895$			1.90076i			0.0635354i
$896$	0.546323	−	2.58873i	0.0182514	−	0.0864835i
$897$	−0.941296	−	0.941296i	−0.0314289	−	0.0314289i
$898$			17.2958i			0.577167i
$899$	−0.0248846	+	19.0747i	−0.000829949	+	0.636177i
$900$	−1.86213			−0.0620709
$901$	−9.54753	−	9.54753i	−0.318074	−	0.318074i
$902$	11.8700	+	11.8700i	0.395228	+	0.395228i
$903$	0.641203	+	0.984233i	0.0213379	+	0.0327532i
$904$		−	8.13540i		−	0.270579i
$905$			3.50844i			0.116624i
$906$		−	6.26978i		−	0.208299i
$907$	10.8633	+	10.8633i	0.360709	+	0.360709i	0.864074	−	0.503365i	$-0.167905\pi$
$907$	10.8633	+	10.8633i	0.360709	+	0.360709i	−0.503365	+	0.864074i	$0.667905\pi$
$908$	−12.8118			−0.425176
$909$	4.68494	−	4.68494i	0.155390	−	0.155390i
$910$	−28.6983	−	6.05645i	−0.951339	−	0.200769i
$911$	−6.42874	−	6.42874i	−0.212994	−	0.212994i	0.592544	−	0.805538i	$-0.298124\pi$
$911$	−6.42874	−	6.42874i	−0.212994	−	0.212994i	−0.805538	+	0.592544i	$0.798124\pi$
$912$		−	1.52590i		−	0.0505277i
$913$	6.20233	+	6.20233i	0.205267	+	0.205267i
$914$	7.29017	+	7.29017i	0.241137	+	0.241137i
$915$		−	14.0235i		−	0.463604i
$916$	0.586795	+	0.586795i	0.0193882	+	0.0193882i
$917$	29.2945	+	6.18228i	0.967391	+	0.204157i
$918$	5.28024	−	5.28024i	0.174274	−	0.174274i
$919$	−31.9688			−1.05455			−0.527277	−	0.849693i	$-0.676787\pi$
$919$	−31.9688			−1.05455			−0.527277	+	0.849693i	$0.676787\pi$
$920$	−0.266436	−	0.266436i	−0.00878413	−	0.00878413i
$921$		−	10.5265i		−	0.346860i
$922$			1.95407i			0.0643538i
$923$			80.6576i			2.65488i
$924$	8.31120	−	5.41453i	0.273418	−	0.178125i
$925$	8.05058	+	8.05058i	0.264702	+	0.264702i
$926$	7.81058	+	7.81058i	0.256672	+	0.256672i
$927$	−12.8517			−0.422104
$928$	5.38516	+	0.00702541i	0.176777	+	0.000230620i
$929$		−	12.0813i		−	0.396375i	−0.980164	−	0.198188i	$-0.936494\pi$
$929$		−	12.0813i		−	0.396375i	0.980164	−	0.198188i	$-0.0635055\pi$
$930$	4.43672	+	4.43672i	0.145486	+	0.145486i
$931$	9.96072	−	3.85680i	0.326449	−	0.126401i
$932$		−	5.20556i		−	0.170514i
$933$		−	0.534365i		−	0.0174943i
$934$	−15.9466			−0.521790
$935$	49.5929			1.62186
$936$	4.42523	−	4.42523i	0.144643	−	0.144643i
$937$	44.9724			1.46918			0.734592	−	0.678509i	$-0.237374\pi$
$937$	44.9724			1.46918			0.734592	+	0.678509i	$0.237374\pi$
$938$	−4.04670	+	19.1751i	−0.132129	+	0.626090i
$939$	5.15164	−	5.15164i	0.168117	−	0.168117i
$940$	−5.00568	−	5.00568i	−0.163267	−	0.163267i
$941$	−55.5130			−1.80967			−0.904835	−	0.425762i	$-0.860006\pi$
$941$	−55.5130			−1.80967			−0.904835	+	0.425762i	$0.860006\pi$
$942$	−2.23270	+	2.23270i	−0.0727454	+	0.0727454i
$943$	−0.673453	+	0.673453i	−0.0219307	+	0.0219307i
$944$			13.9548i			0.454192i
$945$	−4.58569	−	0.967759i	−0.149173	−	0.0314812i
$946$	−1.17703	−	1.17703i	−0.0382684	−	0.0382684i
$947$	12.0347	−	12.0347i	0.391075	−	0.391075i	−0.483996	−	0.875070i	$-0.660815\pi$
$947$	12.0347	−	12.0347i	0.391075	−	0.391075i	0.875070	+	0.483996i	$0.160815\pi$
$948$			1.52871i			0.0496501i
$949$	28.2536	−	28.2536i	0.917149	−	0.917149i
$950$	2.84143			0.0921881
$951$			17.9498i			0.582062i
$952$	−16.5538	+	10.7844i	−0.536513	+	0.349525i
$953$	−46.2921			−1.49955			−0.749773	−	0.661695i	$-0.769838\pi$
$953$	−46.2921			−1.49955			−0.749773	+	0.661695i	$0.769838\pi$
$954$	−1.27856	−	1.27856i	−0.0413950	−	0.0413950i
$955$	23.6474	−	23.6474i	0.765213	−	0.765213i
$956$		−	12.8131i		−	0.414405i
$957$	14.2577	+	14.2950i	0.460887	+	0.462091i
$958$		−	27.8228i		−	0.898914i
$959$	−41.8845	−	8.83927i	−1.35252	−	0.285435i
$960$	1.25257	−	1.25257i	0.0404266	−	0.0404266i
$961$		−	18.4536i		−	0.595278i
$962$	−38.2635			−1.23366
$963$			3.34698i			0.107855i
$964$		−	27.6897i		−	0.891826i
$965$	−22.3645	+	22.3645i	−0.719938	+	0.719938i
$966$	0.307197	+	0.471542i	0.00988391	+	0.0151716i
$967$	−40.2645	−	40.2645i	−1.29482	−	1.29482i	−0.931770	−	0.363050i	$-0.881735\pi$
$967$	−40.2645	−	40.2645i	−1.29482	−	1.29482i	−0.363050	−	0.931770i	$-0.618265\pi$
$968$	−2.16104	+	2.16104i	−0.0694584	+	0.0694584i
$969$	−8.05714	+	8.05714i	−0.258833	+	0.258833i
$970$		−	7.98927i		−	0.256520i
$971$	13.7244	+	13.7244i	0.440436	+	0.440436i	0.892159	−	0.451722i	$-0.149190\pi$
$971$	13.7244	+	13.7244i	0.440436	+	0.440436i	−0.451722	+	0.892159i	$0.649190\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	30.9148	−	20.1402i	0.991083	−	0.645665i
$974$	−20.3642	+	20.3642i	−0.652511	+	0.652511i
$975$	8.24035	+	8.24035i	0.263902	+	0.263902i
$976$	−5.59790	−	5.59790i	−0.179184	−	0.179184i
$977$	−40.3911			−1.29223			−0.646113	−	0.763242i	$-0.723606\pi$
$977$	−40.3911			−1.29223			−0.646113	+	0.763242i	$0.723606\pi$
$978$	−0.336379	−	0.336379i	−0.0107562	−	0.0107562i
$979$	2.25784			0.0721610
$980$	11.3424	+	5.01054i	0.362320	+	0.160056i
$981$	−11.0821			−0.353825
$982$	−16.7266			−0.533768
$983$	−13.9382	+	13.9382i	−0.444561	+	0.444561i	−0.893541	−	0.448981i	$-0.851787\pi$
$983$	−13.9382	+	13.9382i	−0.444561	+	0.444561i	0.448981	+	0.893541i	$0.351787\pi$
$984$	−3.16605	−	3.16605i	−0.100930	−	0.100930i
$985$	−33.4925			−1.06716
$986$	−28.3978	−	28.4720i	−0.904371	−	0.906734i
$987$	5.77149	+	8.85912i	0.183709	+	0.281989i
$988$	−6.75248	+	6.75248i	−0.214825	+	0.214825i
$989$	0.0667794	−	0.0667794i	0.00212346	−	0.00212346i
$990$	6.64127			0.211073
$991$			52.2709i			1.66044i	0.557437	+	0.830219i	$0.311785\pi$
$991$			52.2709i			1.66044i	−0.557437	+	0.830219i	$0.688215\pi$
$992$	3.54209			0.112461
$993$			15.7645i			0.500270i
$994$	7.04115	−	33.3642i	0.223332	−	1.05825i
$995$			29.6250i			0.939176i
$996$	−1.65433	−	1.65433i	−0.0524194	−	0.0524194i
$997$	−1.58925	−	1.58925i	−0.0503322	−	0.0503322i	0.681493	−	0.731825i	$-0.261331\pi$
$997$	−1.58925	−	1.58925i	−0.0503322	−	0.0503322i	−0.731825	+	0.681493i	$0.761331\pi$
$998$	13.5055	+	13.5055i	0.427509	+	0.427509i
$999$	−6.11411			−0.193442

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.m.a.307.13	✓	40
7.6	odd	2		1218.2.m.b.307.13	yes	40
29.12	odd	4		1218.2.m.b.853.13	yes	40
203.41	even	4	inner	1218.2.m.a.853.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.m.a.307.13	✓	40	1.1	even	1	trivial
1218.2.m.a.853.13	yes	40	203.41	even	4	inner
1218.2.m.b.307.13	yes	40	7.6	odd	2
1218.2.m.b.853.13	yes	40	29.12	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +1.77140 q^{5} -1.00000 q^{6} +(-1.44420 - 2.21682i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(1.25257 - 1.25257i) q^{10} +(2.65105 - 2.65105i) q^{11} +(-0.707107 + 0.707107i) q^{12} +6.25822 q^{13} +(-2.58873 - 0.546323i) q^{14} +(-1.25257 - 1.25257i) q^{15} -1.00000 q^{16} +(5.28024 + 5.28024i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-1.07898 - 1.07898i) q^{19} -1.77140i q^{20} +(-0.546323 + 2.58873i) q^{21} -3.74916i q^{22} +0.212711 q^{23} +1.00000i q^{24} -1.86213 q^{25} +(4.42523 - 4.42523i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.21682 + 1.44420i) q^{28} +(-3.80292 - 3.81285i) q^{29} -1.77140 q^{30} +(-2.50464 - 2.50464i) q^{31} +(-0.707107 + 0.707107i) q^{32} -3.74916 q^{33} +7.46738 q^{34} +(-2.55826 - 3.92688i) q^{35} +1.00000 q^{36} +(-4.32333 - 4.32333i) q^{37} -1.52590 q^{38} +(-4.42523 - 4.42523i) q^{39} +(-1.25257 - 1.25257i) q^{40} +(-3.16605 + 3.16605i) q^{41} +(1.44420 + 2.21682i) q^{42} +(0.313944 - 0.313944i) q^{43} +(-2.65105 - 2.65105i) q^{44} +1.77140i q^{45} +(0.150409 - 0.150409i) q^{46} +(2.82583 - 2.82583i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-2.82857 + 6.40306i) q^{49} +(-1.31672 + 1.31672i) q^{50} -7.46738i q^{51} -6.25822i q^{52} -1.80816 q^{53} -1.00000i q^{54} +(4.69609 - 4.69609i) q^{55} +(-0.546323 + 2.58873i) q^{56} +1.52590i q^{57} +(-5.38516 - 0.00702541i) q^{58} -13.9548i q^{59} +(-1.25257 + 1.25257i) q^{60} +(5.59790 + 5.59790i) q^{61} -3.54209 q^{62} +(2.21682 - 1.44420i) q^{63} +1.00000i q^{64} +11.0858 q^{65} +(-2.65105 + 2.65105i) q^{66} -7.40715i q^{67} +(5.28024 - 5.28024i) q^{68} +(-0.150409 - 0.150409i) q^{69} +(-4.58569 - 0.967759i) q^{70} +12.8883i q^{71} +(0.707107 - 0.707107i) q^{72} +(4.51463 - 4.51463i) q^{73} -6.11411 q^{74} +(1.31672 + 1.31672i) q^{75} +(-1.07898 + 1.07898i) q^{76} +(-9.70556 - 2.04825i) q^{77} -6.25822 q^{78} +(1.08096 - 1.08096i) q^{79} -1.77140 q^{80} -1.00000 q^{81} +4.47747i q^{82} +2.33957i q^{83} +(2.58873 + 0.546323i) q^{84} +(9.35344 + 9.35344i) q^{85} -0.443984i q^{86} +(-0.00702541 + 5.38516i) q^{87} -3.74916 q^{88} +(0.425839 + 0.425839i) q^{89} +(1.25257 + 1.25257i) q^{90} +(-9.03813 - 13.8733i) q^{91} -0.212711i q^{92} +3.54209i q^{93} -3.99632i q^{94} +(-1.91130 - 1.91130i) q^{95} +1.00000 q^{96} +(3.18914 - 3.18914i) q^{97} +(2.52755 + 6.52775i) q^{98} +(2.65105 + 2.65105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{6} + 4 q^{10} + 4 q^{14} - 4 q^{15} - 40 q^{16} + 8 q^{19} - 4 q^{21} + 24 q^{25} - 12 q^{28} + 8 q^{29} - 24 q^{31} - 12 q^{35} + 40 q^{36} - 16 q^{37} - 4 q^{40} + 16 q^{41} - 20 q^{43} + 4 q^{46}+ \cdots - 8 q^{98}+O(q^{100}) \) 40 * q - 40 * q^6 + 4 * q^10 + 4 * q^14 - 4 * q^15 - 40 * q^16 + 8 * q^19 - 4 * q^21 + 24 * q^25 - 12 * q^28 + 8 * q^29 - 24 * q^31 - 12 * q^35 + 40 * q^36 - 16 * q^37 - 4 * q^40 + 16 * q^41 - 20 * q^43 + 4 * q^46 - 16 * q^47 + 28 * q^49 + 32 * q^50 + 16 * q^53 - 24 * q^55 - 4 * q^56 - 20 * q^58 - 4 * q^60 - 44 * q^61 + 12 * q^63 - 4 * q^69 - 28 * q^70 - 52 * q^73 - 32 * q^75 + 8 * q^76 + 44 * q^77 + 4 * q^79 - 40 * q^81 - 4 * q^84 - 24 * q^85 - 12 * q^87 + 24 * q^89 + 4 * q^90 - 16 * q^95 + 40 * q^96 - 68 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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