LMFDB - Embedded newform 930.2.j.d.497.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.3
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	930.497
Dual form			930.2.j.d.683.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.22474 + 1.22474i) q^{3} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +1.73205i q^{6} +(-3.44949 - 3.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.22474 + 1.22474i) q^{3} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +1.73205i q^{6} +(-3.44949 - 3.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +(2.00000 - 1.00000i) q^{10} +6.29253i q^{11} +(1.22474 + 1.22474i) q^{12} +(-4.44949 + 4.44949i) q^{13} -4.87832 q^{14} +(-3.46410 + 1.73205i) q^{15} -1.00000 q^{16} +(0.317837 - 0.317837i) q^{17} +(-2.12132 - 2.12132i) q^{18} +4.89898i q^{19} +(0.707107 - 2.12132i) q^{20} +8.44949 q^{21} +(4.44949 + 4.44949i) q^{22} +(-1.73205 - 1.73205i) q^{23} +1.73205 q^{24} +(4.00000 + 3.00000i) q^{25} +6.29253i q^{26} +(3.67423 + 3.67423i) q^{27} +(-3.44949 + 3.44949i) q^{28} +2.82843 q^{29} +(-1.22474 + 3.67423i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-7.70674 - 7.70674i) q^{33} -0.449490i q^{34} +(-4.87832 - 9.75663i) q^{35} -3.00000 q^{36} +(3.46410 + 3.46410i) q^{38} -10.8990i q^{39} +(-1.00000 - 2.00000i) q^{40} +2.82843i q^{41} +(5.97469 - 5.97469i) q^{42} +(-2.44949 + 2.44949i) q^{43} +6.29253 q^{44} +(2.12132 - 6.36396i) q^{45} -2.44949 q^{46} +(-5.65685 + 5.65685i) q^{47} +(1.22474 - 1.22474i) q^{48} +16.7980i q^{49} +(4.94975 - 0.707107i) q^{50} +0.778539i q^{51} +(4.44949 + 4.44949i) q^{52} +(4.24264 + 4.24264i) q^{53} +5.19615 q^{54} +(-4.44949 + 13.3485i) q^{55} +4.87832i q^{56} +(-6.00000 - 6.00000i) q^{57} +(2.00000 - 2.00000i) q^{58} -10.5352 q^{59} +(1.73205 + 3.46410i) q^{60} +0.449490 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-10.3485 + 10.3485i) q^{63} +1.00000i q^{64} +(-12.5851 + 6.29253i) q^{65} -10.8990 q^{66} +(-3.55051 - 3.55051i) q^{67} +(-0.317837 - 0.317837i) q^{68} +4.24264 q^{69} +(-10.3485 - 3.44949i) q^{70} +2.19275i q^{71} +(-2.12132 + 2.12132i) q^{72} +(4.89898 - 4.89898i) q^{73} +(-8.57321 + 1.22474i) q^{75} +4.89898 q^{76} +(21.7060 - 21.7060i) q^{77} +(-7.70674 - 7.70674i) q^{78} -0.898979i q^{79} +(-2.12132 - 0.707107i) q^{80} -9.00000 q^{81} +(2.00000 + 2.00000i) q^{82} +(-6.29253 - 6.29253i) q^{83} -8.44949i q^{84} +(0.898979 - 0.449490i) q^{85} +3.46410i q^{86} +(-3.46410 + 3.46410i) q^{87} +(4.44949 - 4.44949i) q^{88} -4.38551 q^{89} +(-3.00000 - 6.00000i) q^{90} +30.6969 q^{91} +(-1.73205 + 1.73205i) q^{92} +(1.22474 - 1.22474i) q^{93} +8.00000i q^{94} +(-3.46410 + 10.3923i) q^{95} -1.73205i q^{96} +(-3.00000 - 3.00000i) q^{97} +(11.8780 + 11.8780i) q^{98} +18.8776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7}+O(q^{10}) $ 8 * q - 8 * q^7	$ 8 q - 8 q^{7} + 16 q^{10} - 16 q^{13} - 8 q^{16} + 48 q^{21} + 16 q^{22} + 32 q^{25} - 8 q^{28} - 8 q^{31} - 24 q^{36} - 8 q^{40} + 16 q^{52} - 16 q^{55} - 48 q^{57} + 16 q^{58} - 16 q^{61} - 24 q^{63} - 48 q^{66} - 48 q^{67} - 24 q^{70} - 72 q^{81} + 16 q^{82} - 32 q^{85} + 16 q^{88} - 24 q^{90} + 128 q^{91} - 24 q^{97}+O(q^{100}) $ 8 * q - 8 * q^7 + 16 * q^10 - 16 * q^13 - 8 * q^16 + 48 * q^21 + 16 * q^22 + 32 * q^25 - 8 * q^28 - 8 * q^31 - 24 * q^36 - 8 * q^40 + 16 * q^52 - 16 * q^55 - 48 * q^57 + 16 * q^58 - 16 * q^61 - 24 * q^63 - 48 * q^66 - 48 * q^67 - 24 * q^70 - 72 * q^81 + 16 * q^82 - 32 * q^85 + 16 * q^88 - 24 * q^90 + 128 * q^91 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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
$3$	−1.22474	+	1.22474i	−0.707107	+	0.707107i
$3$	−1.22474	+	1.22474i	−0.707107	+	0.707107i
$4$		−	1.00000i		−	0.500000i
$5$	2.12132	+	0.707107i	0.948683	+	0.316228i
$5$	2.12132	+	0.707107i	0.948683	+	0.316228i
$6$			1.73205i			0.707107i
$7$	−3.44949	−	3.44949i	−1.30378	−	1.30378i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$	−3.44949	−	3.44949i	−1.30378	−	1.30378i	−0.377964	−	0.925820i	$-0.623376\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		−	3.00000i		−	1.00000i
$10$	2.00000	−	1.00000i	0.632456	−	0.316228i
$11$			6.29253i			1.89727i	0.316374	+	0.948634i	$0.397534\pi$
$11$			6.29253i			1.89727i	−0.316374	+	0.948634i	$0.602466\pi$
$12$	1.22474	+	1.22474i	0.353553	+	0.353553i
$13$	−4.44949	+	4.44949i	−1.23407	+	1.23407i	−0.271678	+	0.962388i	$0.587579\pi$
$13$	−4.44949	+	4.44949i	−1.23407	+	1.23407i	−0.962388	+	0.271678i	$0.912421\pi$
$14$	−4.87832			−1.30378
$15$	−3.46410	+	1.73205i	−0.894427	+	0.447214i
$16$	−1.00000			−0.250000
$17$	0.317837	−	0.317837i	0.0770869	−	0.0770869i	−0.667512	−	0.744599i	$-0.732641\pi$
$17$	0.317837	−	0.317837i	0.0770869	−	0.0770869i	0.744599	+	0.667512i	$0.232641\pi$
$18$	−2.12132	−	2.12132i	−0.500000	−	0.500000i
$19$			4.89898i			1.12390i	0.827170	+	0.561951i	$0.189949\pi$
$19$			4.89898i			1.12390i	−0.827170	+	0.561951i	$0.810051\pi$
$20$	0.707107	−	2.12132i	0.158114	−	0.474342i
$21$	8.44949			1.84383
$22$	4.44949	+	4.44949i	0.948634	+	0.948634i
$23$	−1.73205	−	1.73205i	−0.361158	−	0.361158i	0.503081	−	0.864239i	$-0.332200\pi$
$23$	−1.73205	−	1.73205i	−0.361158	−	0.361158i	−0.864239	+	0.503081i	$0.832200\pi$
$24$	1.73205			0.353553
$25$	4.00000	+	3.00000i	0.800000	+	0.600000i
$26$			6.29253i			1.23407i
$27$	3.67423	+	3.67423i	0.707107	+	0.707107i
$28$	−3.44949	+	3.44949i	−0.651892	+	0.651892i
$29$	2.82843			0.525226			0.262613	−	0.964901i	$-0.415416\pi$
$29$	2.82843			0.525226			0.262613	+	0.964901i	$0.415416\pi$
$30$	−1.22474	+	3.67423i	−0.223607	+	0.670820i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−7.70674	−	7.70674i	−1.34157	−	1.34157i
$34$		−	0.449490i		−	0.0770869i
$35$	−4.87832	−	9.75663i	−0.824586	−	1.64917i
$36$	−3.00000			−0.500000
$37$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$37$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$38$	3.46410	+	3.46410i	0.561951	+	0.561951i
$39$		−	10.8990i		−	1.74523i
$40$	−1.00000	−	2.00000i	−0.158114	−	0.316228i
$41$			2.82843i			0.441726i	0.975305	+	0.220863i	$0.0708874\pi$
$41$			2.82843i			0.441726i	−0.975305	+	0.220863i	$0.929113\pi$
$42$	5.97469	−	5.97469i	0.921915	−	0.921915i
$43$	−2.44949	+	2.44949i	−0.373544	+	0.373544i	−0.868766	−	0.495222i	$-0.835087\pi$
$43$	−2.44949	+	2.44949i	−0.373544	+	0.373544i	0.495222	+	0.868766i	$0.335087\pi$
$44$	6.29253			0.948634
$45$	2.12132	−	6.36396i	0.316228	−	0.948683i
$46$	−2.44949			−0.361158
$47$	−5.65685	+	5.65685i	−0.825137	+	0.825137i	−0.986840	−	0.161703i	$-0.948301\pi$
$47$	−5.65685	+	5.65685i	−0.825137	+	0.825137i	0.161703	+	0.986840i	$0.448301\pi$
$48$	1.22474	−	1.22474i	0.176777	−	0.176777i
$49$			16.7980i			2.39971i
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$			0.778539i			0.109017i
$52$	4.44949	+	4.44949i	0.617033	+	0.617033i
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	0.935664	−	0.352892i	$-0.114802\pi$
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	−0.352892	+	0.935664i	$0.614802\pi$
$54$	5.19615			0.707107
$55$	−4.44949	+	13.3485i	−0.599969	+	1.79991i
$56$			4.87832i			0.651892i
$57$	−6.00000	−	6.00000i	−0.794719	−	0.794719i
$58$	2.00000	−	2.00000i	0.262613	−	0.262613i
$59$	−10.5352			−1.37156			−0.685781	−	0.727808i	$-0.740539\pi$
$59$	−10.5352			−1.37156			−0.685781	+	0.727808i	$0.740539\pi$
$60$	1.73205	+	3.46410i	0.223607	+	0.447214i
$61$	0.449490			0.0575513			0.0287756	−	0.999586i	$-0.490839\pi$
$61$	0.449490			0.0575513			0.0287756	+	0.999586i	$0.490839\pi$
$62$	−0.707107	+	0.707107i	−0.0898027	+	0.0898027i
$63$	−10.3485	+	10.3485i	−1.30378	+	1.30378i
$64$			1.00000i			0.125000i
$65$	−12.5851	+	6.29253i	−1.56098	+	0.780492i
$66$	−10.8990			−1.34157
$67$	−3.55051	−	3.55051i	−0.433764	−	0.433764i	0.456143	−	0.889907i	$-0.349231\pi$
$67$	−3.55051	−	3.55051i	−0.433764	−	0.433764i	−0.889907	+	0.456143i	$0.849231\pi$
$68$	−0.317837	−	0.317837i	−0.0385434	−	0.0385434i
$69$	4.24264			0.510754
$70$	−10.3485	−	3.44949i	−1.23688	−	0.412293i
$71$			2.19275i			0.260232i	0.991499	+	0.130116i	$0.0415350\pi$
$71$			2.19275i			0.260232i	−0.991499	+	0.130116i	$0.958465\pi$
$72$	−2.12132	+	2.12132i	−0.250000	+	0.250000i
$73$	4.89898	−	4.89898i	0.573382	−	0.573382i	−0.359690	−	0.933072i	$-0.617117\pi$
$73$	4.89898	−	4.89898i	0.573382	−	0.573382i	0.933072	+	0.359690i	$0.117117\pi$
$74$		0			0
$75$	−8.57321	+	1.22474i	−0.989949	+	0.141421i
$76$	4.89898			0.561951
$77$	21.7060	−	21.7060i	2.47363	−	2.47363i
$78$	−7.70674	−	7.70674i	−0.872617	−	0.872617i
$79$		−	0.898979i		−	0.101143i	−0.998720	−	0.0505715i	$-0.983896\pi$
$79$		−	0.898979i		−	0.101143i	0.998720	−	0.0505715i	$-0.0161043\pi$
$80$	−2.12132	−	0.707107i	−0.237171	−	0.0790569i
$81$	−9.00000			−1.00000
$82$	2.00000	+	2.00000i	0.220863	+	0.220863i
$83$	−6.29253	−	6.29253i	−0.690695	−	0.690695i	0.271690	−	0.962385i	$-0.412417\pi$
$83$	−6.29253	−	6.29253i	−0.690695	−	0.690695i	−0.962385	+	0.271690i	$0.912417\pi$
$84$		−	8.44949i		−	0.921915i
$85$	0.898979	−	0.449490i	0.0975080	−	0.0487540i
$86$			3.46410i			0.373544i
$87$	−3.46410	+	3.46410i	−0.371391	+	0.371391i
$88$	4.44949	−	4.44949i	0.474317	−	0.474317i
$89$	−4.38551			−0.464863			−0.232431	−	0.972613i	$-0.574668\pi$
$89$	−4.38551			−0.464863			−0.232431	+	0.972613i	$0.574668\pi$
$90$	−3.00000	−	6.00000i	−0.316228	−	0.632456i
$91$	30.6969			3.21791
$92$	−1.73205	+	1.73205i	−0.180579	+	0.180579i
$93$	1.22474	−	1.22474i	0.127000	−	0.127000i
$94$			8.00000i			0.825137i
$95$	−3.46410	+	10.3923i	−0.355409	+	1.06623i
$96$		−	1.73205i		−	0.176777i
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	0.538208	−	0.842812i	$-0.319101\pi$
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	−0.842812	+	0.538208i	$0.819101\pi$
$98$	11.8780	+	11.8780i	1.19985	+	1.19985i
$99$	18.8776			1.89727
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$		−	9.89949i		−	0.985037i	−0.870302	−	0.492518i	$-0.836076\pi$
$101$		−	9.89949i		−	0.985037i	0.870302	−	0.492518i	$-0.163924\pi$
$102$	0.550510	+	0.550510i	0.0545086	+	0.0545086i
$103$	−1.44949	+	1.44949i	−0.142822	+	0.142822i	−0.774903	−	0.632080i	$-0.782201\pi$
$103$	−1.44949	+	1.44949i	−0.142822	+	0.142822i	0.632080	+	0.774903i	$0.282201\pi$
$104$	6.29253			0.617033
$105$	17.9241	+	5.97469i	1.74921	+	0.583070i
$106$	6.00000			0.582772
$107$	7.70674	−	7.70674i	0.745039	−	0.745039i	−0.228504	−	0.973543i	$-0.573383\pi$
$107$	7.70674	−	7.70674i	0.745039	−	0.745039i	0.973543	+	0.228504i	$0.0733834\pi$
$108$	3.67423	−	3.67423i	0.353553	−	0.353553i
$109$		−	2.89898i		−	0.277672i	−0.990315	−	0.138836i	$-0.955664\pi$
$109$		−	2.89898i		−	0.277672i	0.990315	−	0.138836i	$-0.0443361\pi$
$110$	6.29253	+	12.5851i	0.599969	+	1.19994i
$111$		0			0
$112$	3.44949	+	3.44949i	0.325946	+	0.325946i
$113$	−8.34242	−	8.34242i	−0.784789	−	0.784789i	0.195846	−	0.980635i	$-0.437255\pi$
$113$	−8.34242	−	8.34242i	−0.784789	−	0.784789i	−0.980635	+	0.195846i	$0.937255\pi$
$114$	−8.48528			−0.794719
$115$	−2.44949	−	4.89898i	−0.228416	−	0.456832i
$116$		−	2.82843i		−	0.262613i
$117$	13.3485	+	13.3485i	1.23407	+	1.23407i
$118$	−7.44949	+	7.44949i	−0.685781	+	0.685781i
$119$	−2.19275			−0.201009
$120$	3.67423	+	1.22474i	0.335410	+	0.111803i
$121$	−28.5959			−2.59963
$122$	0.317837	−	0.317837i	0.0287756	−	0.0287756i
$123$	−3.46410	−	3.46410i	−0.312348	−	0.312348i
$124$			1.00000i			0.0898027i
$125$	6.36396	+	9.19239i	0.569210	+	0.822192i
$126$			14.6349i			1.30378i
$127$	10.4495	+	10.4495i	0.927242	+	0.927242i	0.997527	−	0.0702847i	$-0.0223908\pi$
$127$	10.4495	+	10.4495i	0.927242	+	0.927242i	−0.0702847	+	0.997527i	$0.522391\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		−	6.00000i		−	0.528271i
$130$	−4.44949	+	13.3485i	−0.390246	+	1.17074i
$131$		−	3.60697i		−	0.315142i	−0.987508	−	0.157571i	$-0.949634\pi$
$131$		−	3.60697i		−	0.315142i	0.987508	−	0.157571i	$-0.0503663\pi$
$132$	−7.70674	+	7.70674i	−0.670786	+	0.670786i
$133$	16.8990	−	16.8990i	1.46533	−	1.46533i
$134$	−5.02118			−0.433764
$135$	5.19615	+	10.3923i	0.447214	+	0.894427i
$136$	−0.449490			−0.0385434
$137$	10.7101	−	10.7101i	0.915029	−	0.915029i	−0.0816332	−	0.996662i	$-0.526014\pi$
$137$	10.7101	−	10.7101i	0.915029	−	0.915029i	0.996662	+	0.0816332i	$0.0260136\pi$
$138$	3.00000	−	3.00000i	0.255377	−	0.255377i
$139$			18.4495i			1.56487i	0.622735	+	0.782433i	$0.286021\pi$
$139$			18.4495i			1.56487i	−0.622735	+	0.782433i	$0.713979\pi$
$140$	−9.75663	+	4.87832i	−0.824586	+	0.412293i
$141$		−	13.8564i		−	1.16692i
$142$	1.55051	+	1.55051i	0.130116	+	0.130116i
$143$	−27.9985	−	27.9985i	−2.34136	−	2.34136i
$144$			3.00000i			0.250000i
$145$	6.00000	+	2.00000i	0.498273	+	0.166091i
$146$		−	6.92820i		−	0.573382i
$147$	−20.5732	−	20.5732i	−1.69685	−	1.69685i
$148$		0			0
$149$	20.9275			1.71445			0.857223	−	0.514946i	$-0.172188\pi$
$149$	20.9275			1.71445			0.857223	+	0.514946i	$0.172188\pi$
$150$	−5.19615	+	6.92820i	−0.424264	+	0.565685i
$151$	16.8990			1.37522			0.687610	−	0.726080i	$-0.258660\pi$
$151$	16.8990			1.37522			0.687610	+	0.726080i	$0.258660\pi$
$152$	3.46410	−	3.46410i	0.280976	−	0.280976i
$153$	−0.953512	−	0.953512i	−0.0770869	−	0.0770869i
$154$		−	30.6969i		−	2.47363i
$155$	−2.12132	−	0.707107i	−0.170389	−	0.0567962i
$156$	−10.8990			−0.872617
$157$	7.10102	+	7.10102i	0.566723	+	0.566723i	0.931209	−	0.364486i	$-0.118755\pi$
$157$	7.10102	+	7.10102i	0.566723	+	0.566723i	−0.364486	+	0.931209i	$0.618755\pi$
$158$	−0.635674	−	0.635674i	−0.0505715	−	0.0505715i
$159$	−10.3923			−0.824163
$160$	−2.00000	+	1.00000i	−0.158114	+	0.0790569i
$161$			11.9494i			0.941743i
$162$	−6.36396	+	6.36396i	−0.500000	+	0.500000i
$163$	2.65153	−	2.65153i	0.207684	−	0.207684i	−0.595598	−	0.803282i	$-0.703085\pi$
$163$	2.65153	−	2.65153i	0.207684	−	0.207684i	0.803282	+	0.595598i	$0.203085\pi$
$164$	2.82843			0.220863
$165$	−10.8990	−	21.7980i	−0.848484	−	1.69697i
$166$	−8.89898			−0.690695
$167$	−12.1244	+	12.1244i	−0.938211	+	0.938211i	−0.998199	−	0.0599883i	$-0.980894\pi$
$167$	−12.1244	+	12.1244i	−0.938211	+	0.938211i	0.0599883	+	0.998199i	$0.480894\pi$
$168$	−5.97469	−	5.97469i	−0.460957	−	0.460957i
$169$		−	26.5959i		−	2.04584i
$170$	0.317837	−	0.953512i	0.0243770	−	0.0731310i
$171$	14.6969			1.12390
$172$	2.44949	+	2.44949i	0.186772	+	0.186772i
$173$	13.9993	+	13.9993i	1.06434	+	1.06434i	0.997782	+	0.0665626i	$0.0212032\pi$
$173$	13.9993	+	13.9993i	1.06434	+	1.06434i	0.0665626	+	0.997782i	$0.478797\pi$
$174$			4.89898i			0.371391i
$175$	−3.44949	−	24.1464i	−0.260757	−	1.82530i
$176$		−	6.29253i		−	0.474317i
$177$	12.9029	−	12.9029i	0.969841	−	0.969841i
$178$	−3.10102	+	3.10102i	−0.232431	+	0.232431i
$179$	−24.5344			−1.83379			−0.916895	−	0.399128i	$-0.869313\pi$
$179$	−24.5344			−1.83379			−0.916895	+	0.399128i	$0.869313\pi$
$180$	−6.36396	−	2.12132i	−0.474342	−	0.158114i
$181$	−8.44949			−0.628046			−0.314023	−	0.949415i	$-0.601677\pi$
$181$	−8.44949			−0.628046			−0.314023	+	0.949415i	$0.601677\pi$
$182$	21.7060	−	21.7060i	1.60896	−	1.60896i
$183$	−0.550510	+	0.550510i	−0.0406949	+	0.0406949i
$184$			2.44949i			0.180579i
$185$		0			0
$186$		−	1.73205i		−	0.127000i
$187$	2.00000	+	2.00000i	0.146254	+	0.146254i
$188$	5.65685	+	5.65685i	0.412568	+	0.412568i
$189$		−	25.3485i		−	1.84383i
$190$	4.89898	+	9.79796i	0.355409	+	0.710819i
$191$		−	0.921404i		−	0.0666704i	−0.999444	−	0.0333352i	$-0.989387\pi$
$191$		−	0.921404i		−	0.0666704i	0.999444	−	0.0333352i	$-0.0106129\pi$
$192$	−1.22474	−	1.22474i	−0.0883883	−	0.0883883i
$193$	−7.00000	+	7.00000i	−0.503871	+	0.503871i	−0.912639	−	0.408768i	$-0.865959\pi$
$193$	−7.00000	+	7.00000i	−0.503871	+	0.503871i	0.408768	+	0.912639i	$0.365959\pi$
$194$	−4.24264			−0.304604
$195$	7.70674	−	23.1202i	0.551891	−	1.65567i
$196$	16.7980			1.19985
$197$	−2.04989	+	2.04989i	−0.146048	+	0.146048i	−0.776350	−	0.630302i	$-0.782931\pi$
$197$	−2.04989	+	2.04989i	−0.146048	+	0.146048i	0.630302	+	0.776350i	$0.282931\pi$
$198$	13.3485	−	13.3485i	0.948634	−	0.948634i
$199$		−	18.6969i		−	1.32539i	−0.748889	−	0.662695i	$-0.769412\pi$
$199$		−	18.6969i		−	1.32539i	0.748889	−	0.662695i	$-0.230588\pi$
$200$	−0.707107	−	4.94975i	−0.0500000	−	0.350000i
$201$	8.69694			0.613435
$202$	−7.00000	−	7.00000i	−0.492518	−	0.492518i
$203$	−9.75663	−	9.75663i	−0.684781	−	0.684781i
$204$	0.778539			0.0545086
$205$	−2.00000	+	6.00000i	−0.139686	+	0.419058i
$206$			2.04989i			0.142822i
$207$	−5.19615	+	5.19615i	−0.361158	+	0.361158i
$208$	4.44949	−	4.44949i	0.308517	−	0.308517i
$209$	−30.8270			−2.13235
$210$	16.8990	−	8.44949i	1.16614	−	0.583070i
$211$	6.69694			0.461036			0.230518	−	0.973068i	$-0.425958\pi$
$211$	6.69694			0.461036			0.230518	+	0.973068i	$0.425958\pi$
$212$	4.24264	−	4.24264i	0.291386	−	0.291386i
$213$	−2.68556	−	2.68556i	−0.184012	−	0.184012i
$214$		−	10.8990i		−	0.745039i
$215$	−6.92820	+	3.46410i	−0.472500	+	0.236250i
$216$		−	5.19615i		−	0.353553i
$217$	3.44949	+	3.44949i	0.234167	+	0.234167i
$218$	−2.04989	−	2.04989i	−0.138836	−	0.138836i
$219$			12.0000i			0.810885i
$220$	13.3485	+	4.44949i	0.899954	+	0.299985i
$221$			2.82843i			0.190261i
$222$		0			0
$223$	3.55051	−	3.55051i	0.237760	−	0.237760i	−0.578162	−	0.815922i	$-0.696230\pi$
$223$	3.55051	−	3.55051i	0.237760	−	0.237760i	0.815922	+	0.578162i	$0.196230\pi$
$224$	4.87832			0.325946
$225$	9.00000	−	12.0000i	0.600000	−	0.800000i
$226$	−11.7980			−0.784789
$227$	6.43539	−	6.43539i	0.427132	−	0.427132i	−0.460518	−	0.887650i	$-0.652336\pi$
$227$	6.43539	−	6.43539i	0.427132	−	0.427132i	0.887650	+	0.460518i	$0.152336\pi$
$228$	−6.00000	+	6.00000i	−0.397360	+	0.397360i
$229$			16.4495i			1.08701i	0.839405	+	0.543506i	$0.182904\pi$
$229$			16.4495i			1.08701i	−0.839405	+	0.543506i	$0.817096\pi$
$230$	−5.19615	−	1.73205i	−0.342624	−	0.114208i
$231$			53.1687i			3.49824i
$232$	−2.00000	−	2.00000i	−0.131306	−	0.131306i
$233$	7.70674	+	7.70674i	0.504885	+	0.504885i	0.912952	−	0.408067i	$-0.133797\pi$
$233$	7.70674	+	7.70674i	0.504885	+	0.504885i	−0.408067	+	0.912952i	$0.633797\pi$
$234$	18.8776			1.23407
$235$	−16.0000	+	8.00000i	−1.04372	+	0.521862i
$236$			10.5352i			0.685781i
$237$	1.10102	+	1.10102i	0.0715190	+	0.0715190i
$238$	−1.55051	+	1.55051i	−0.100505	+	0.100505i
$239$	28.6342			1.85219			0.926097	−	0.377286i	$-0.123143\pi$
$239$	28.6342			1.85219			0.926097	+	0.377286i	$0.123143\pi$
$240$	3.46410	−	1.73205i	0.223607	−	0.111803i
$241$	13.1010			0.843911			0.421955	−	0.906617i	$-0.361344\pi$
$241$	13.1010			0.843911			0.421955	+	0.906617i	$0.361344\pi$
$242$	−20.2204	+	20.2204i	−1.29981	+	1.29981i
$243$	11.0227	−	11.0227i	0.707107	−	0.707107i
$244$		−	0.449490i		−	0.0287756i
$245$	−11.8780	+	35.6339i	−0.758854	+	2.27656i
$246$	−4.89898			−0.312348
$247$	−21.7980	−	21.7980i	−1.38697	−	1.38697i
$248$	0.707107	+	0.707107i	0.0449013	+	0.0449013i
$249$	15.4135			0.976790
$250$	11.0000	+	2.00000i	0.695701	+	0.126491i
$251$			1.90702i			0.120370i	0.998187	+	0.0601851i	$0.0191691\pi$
$251$			1.90702i			0.120370i	−0.998187	+	0.0601851i	$0.980831\pi$
$252$	10.3485	+	10.3485i	0.651892	+	0.651892i
$253$	10.8990	−	10.8990i	0.685213	−	0.685213i
$254$	14.7778			0.927242
$255$	−0.550510	+	1.65153i	−0.0344743	+	0.103423i
$256$	1.00000			0.0625000
$257$	−6.43539	+	6.43539i	−0.401429	+	0.401429i	−0.878736	−	0.477308i	$-0.841613\pi$
$257$	−6.43539	+	6.43539i	−0.401429	+	0.401429i	0.477308	+	0.878736i	$0.341613\pi$
$258$	−4.24264	−	4.24264i	−0.264135	−	0.264135i
$259$		0			0
$260$	6.29253	+	12.5851i	0.390246	+	0.780492i
$261$		−	8.48528i		−	0.525226i
$262$	−2.55051	−	2.55051i	−0.157571	−	0.157571i
$263$	2.65345	+	2.65345i	0.163619	+	0.163619i	0.784168	−	0.620549i	$-0.213090\pi$
$263$	2.65345	+	2.65345i	0.163619	+	0.163619i	−0.620549	+	0.784168i	$0.713090\pi$
$264$			10.8990i			0.670786i
$265$	6.00000	+	12.0000i	0.368577	+	0.737154i
$266$		−	23.8988i		−	1.46533i
$267$	5.37113	−	5.37113i	0.328708	−	0.328708i
$268$	−3.55051	+	3.55051i	−0.216882	+	0.216882i
$269$	−5.65685			−0.344904			−0.172452	−	0.985018i	$-0.555169\pi$
$269$	−5.65685			−0.344904			−0.172452	+	0.985018i	$0.555169\pi$
$270$	11.0227	+	3.67423i	0.670820	+	0.223607i
$271$	5.79796			0.352201			0.176100	−	0.984372i	$-0.443652\pi$
$271$	5.79796			0.352201			0.176100	+	0.984372i	$0.443652\pi$
$272$	−0.317837	+	0.317837i	−0.0192717	+	0.0192717i
$273$	−37.5959	+	37.5959i	−2.27541	+	2.27541i
$274$		−	15.1464i		−	0.915029i
$275$	−18.8776	+	25.1701i	−1.13836	+	1.51782i
$276$		−	4.24264i		−	0.255377i
$277$	−2.65153	−	2.65153i	−0.159315	−	0.159315i	0.622948	−	0.782263i	$-0.285935\pi$
$277$	−2.65153	−	2.65153i	−0.159315	−	0.159315i	−0.782263	+	0.622948i	$0.785935\pi$
$278$	13.0458	+	13.0458i	0.782433	+	0.782433i
$279$			3.00000i			0.179605i
$280$	−3.44949	+	10.3485i	−0.206146	+	0.618439i
$281$		−	5.65685i		−	0.337460i	−0.985662	−	0.168730i	$-0.946033\pi$
$281$		−	5.65685i		−	0.337460i	0.985662	−	0.168730i	$-0.0539665\pi$
$282$	−9.79796	−	9.79796i	−0.583460	−	0.583460i
$283$	−18.2474	+	18.2474i	−1.08470	+	1.08470i	−0.0886340	+	0.996064i	$0.528250\pi$
$283$	−18.2474	+	18.2474i	−1.08470	+	1.08470i	−0.996064	+	0.0886340i	$0.971750\pi$
$284$	2.19275			0.130116
$285$	−8.48528	−	16.9706i	−0.502625	−	1.00525i
$286$	−39.5959			−2.34136
$287$	9.75663	−	9.75663i	0.575916	−	0.575916i
$288$	2.12132	+	2.12132i	0.125000	+	0.125000i
$289$			16.7980i			0.988115i
$290$	5.65685	−	2.82843i	0.332182	−	0.166091i
$291$	7.34847			0.430775
$292$	−4.89898	−	4.89898i	−0.286691	−	0.286691i
$293$	−12.7279	−	12.7279i	−0.743573	−	0.743573i	0.229691	−	0.973264i	$-0.426229\pi$
$293$	−12.7279	−	12.7279i	−0.743573	−	0.743573i	−0.973264	+	0.229691i	$0.926229\pi$
$294$	−29.0949			−1.69685
$295$	−22.3485	−	7.44949i	−1.30118	−	0.433726i
$296$		0			0
$297$	−23.1202	+	23.1202i	−1.34157	+	1.34157i
$298$	14.7980	−	14.7980i	0.857223	−	0.857223i
$299$	15.4135			0.891385
$300$	1.22474	+	8.57321i	0.0707107	+	0.494975i
$301$	16.8990			0.974041
$302$	11.9494	−	11.9494i	0.687610	−	0.687610i
$303$	12.1244	+	12.1244i	0.696526	+	0.696526i
$304$		−	4.89898i		−	0.280976i
$305$	0.953512	+	0.317837i	0.0545979	+	0.0181993i
$306$	−1.34847			−0.0770869
$307$	−11.3485	−	11.3485i	−0.647691	−	0.647691i	0.304743	−	0.952435i	$-0.401429\pi$
$307$	−11.3485	−	11.3485i	−0.647691	−	0.647691i	−0.952435	+	0.304743i	$0.901429\pi$
$308$	−21.7060	−	21.7060i	−1.23681	−	1.23681i
$309$		−	3.55051i		−	0.201981i
$310$	−2.00000	+	1.00000i	−0.113592	+	0.0567962i
$311$		−	19.1633i		−	1.08665i	−0.839522	−	0.543326i	$-0.817165\pi$
$311$		−	19.1633i		−	1.08665i	0.839522	−	0.543326i	$-0.182835\pi$
$312$	−7.70674	+	7.70674i	−0.436308	+	0.436308i
$313$	−5.10102	+	5.10102i	−0.288327	+	0.288327i	−0.836418	−	0.548092i	$-0.815355\pi$
$313$	−5.10102	+	5.10102i	−0.288327	+	0.288327i	0.548092	+	0.836418i	$0.315355\pi$
$314$	10.0424			0.566723
$315$	−29.2699	+	14.6349i	−1.64917	+	0.824586i
$316$	−0.898979			−0.0505715
$317$	2.68556	−	2.68556i	0.150836	−	0.150836i	−0.627655	−	0.778491i	$-0.715985\pi$
$317$	2.68556	−	2.68556i	0.150836	−	0.150836i	0.778491	+	0.627655i	$0.215985\pi$
$318$	−7.34847	+	7.34847i	−0.412082	+	0.412082i
$319$			17.7980i			0.996494i
$320$	−0.707107	+	2.12132i	−0.0395285	+	0.118585i
$321$			18.8776i			1.05364i
$322$	8.44949	+	8.44949i	0.470872	+	0.470872i
$323$	1.55708	+	1.55708i	0.0866381	+	0.0866381i
$324$			9.00000i			0.500000i
$325$	−31.1464	+	4.44949i	−1.72769	+	0.246813i
$326$		−	3.74983i		−	0.207684i
$327$	3.55051	+	3.55051i	0.196344	+	0.196344i
$328$	2.00000	−	2.00000i	0.110432	−	0.110432i
$329$	39.0265			2.15160
$330$	−23.1202	−	7.70674i	−1.27273	−	0.424242i
$331$	20.2474			1.11290			0.556450	−	0.830881i	$-0.312163\pi$
$331$	20.2474			1.11290			0.556450	+	0.830881i	$0.312163\pi$
$332$	−6.29253	+	6.29253i	−0.345347	+	0.345347i
$333$		0			0
$334$			17.1464i			0.938211i
$335$	−5.02118	−	10.0424i	−0.274336	−	0.548673i
$336$	−8.44949			−0.460957
$337$	−4.89898	−	4.89898i	−0.266864	−	0.266864i	0.560971	−	0.827835i	$-0.310428\pi$
$337$	−4.89898	−	4.89898i	−0.266864	−	0.266864i	−0.827835	+	0.560971i	$0.810428\pi$
$338$	−18.8062	−	18.8062i	−1.02292	−	1.02292i
$339$	20.4347			1.10986
$340$	−0.449490	−	0.898979i	−0.0243770	−	0.0487540i
$341$		−	6.29253i		−	0.340760i
$342$	10.3923	−	10.3923i	0.561951	−	0.561951i
$343$	33.7980	−	33.7980i	1.82492	−	1.82492i
$344$	3.46410			0.186772
$345$	9.00000	+	3.00000i	0.484544	+	0.161515i
$346$	19.7980			1.06434
$347$	−17.6062	+	17.6062i	−0.945152	+	0.945152i	−0.998572	−	0.0534198i	$-0.982988\pi$
$347$	−17.6062	+	17.6062i	−0.945152	+	0.945152i	0.0534198	+	0.998572i	$0.482988\pi$
$348$	3.46410	+	3.46410i	0.185695	+	0.185695i
$349$			27.3939i			1.46636i	0.680034	+	0.733180i	$0.261965\pi$
$349$			27.3939i			1.46636i	−0.680034	+	0.733180i	$0.738035\pi$
$350$	−19.5133	−	14.6349i	−1.04303	−	0.782271i
$351$	−32.6969			−1.74523
$352$	−4.44949	−	4.44949i	−0.237159	−	0.237159i
$353$	−13.5386	−	13.5386i	−0.720585	−	0.720585i	0.248139	−	0.968724i	$-0.420181\pi$
$353$	−13.5386	−	13.5386i	−0.720585	−	0.720585i	−0.968724	+	0.248139i	$0.920181\pi$
$354$		−	18.2474i		−	0.969841i
$355$	−1.55051	+	4.65153i	−0.0822925	+	0.246878i
$356$			4.38551i			0.232431i
$357$	2.68556	−	2.68556i	0.142135	−	0.142135i
$358$	−17.3485	+	17.3485i	−0.916895	+	0.916895i
$359$	24.5344			1.29488			0.647439	−	0.762117i	$-0.275840\pi$
$359$	24.5344			1.29488			0.647439	+	0.762117i	$0.275840\pi$
$360$	−6.00000	+	3.00000i	−0.316228	+	0.158114i
$361$	−5.00000			−0.263158
$362$	−5.97469	+	5.97469i	−0.314023	+	0.314023i
$363$	35.0227	−	35.0227i	1.83822	−	1.83822i
$364$		−	30.6969i		−	1.60896i
$365$	13.8564	−	6.92820i	0.725277	−	0.362639i
$366$			0.778539i			0.0406949i
$367$	8.44949	+	8.44949i	0.441060	+	0.441060i	0.892368	−	0.451308i	$-0.149043\pi$
$367$	8.44949	+	8.44949i	0.441060	+	0.441060i	−0.451308	+	0.892368i	$0.649043\pi$
$368$	1.73205	+	1.73205i	0.0902894	+	0.0902894i
$369$	8.48528			0.441726
$370$		0			0
$371$		−	29.2699i		−	1.51962i
$372$	−1.22474	−	1.22474i	−0.0635001	−	0.0635001i
$373$	−10.0000	+	10.0000i	−0.517780	+	0.517780i	−0.916899	−	0.399119i	$-0.869316\pi$
$373$	−10.0000	+	10.0000i	−0.517780	+	0.517780i	0.399119	+	0.916899i	$0.369316\pi$
$374$	2.82843			0.146254
$375$	−19.0526	−	3.46410i	−0.983870	−	0.178885i
$376$	8.00000			0.412568
$377$	−12.5851	+	12.5851i	−0.648163	+	0.648163i
$378$	−17.9241	−	17.9241i	−0.921915	−	0.921915i
$379$		−	12.0000i		−	0.616399i	−0.951322	−	0.308199i	$-0.900274\pi$
$379$		−	12.0000i		−	0.616399i	0.951322	−	0.308199i	$-0.0997264\pi$
$380$	10.3923	+	3.46410i	0.533114	+	0.177705i
$381$	−25.5959			−1.31132
$382$	−0.651531	−	0.651531i	−0.0333352	−	0.0333352i
$383$	16.5099	+	16.5099i	0.843614	+	0.843614i	0.989327	−	0.145712i	$-0.0465474\pi$
$383$	16.5099	+	16.5099i	0.843614	+	0.843614i	−0.145712	+	0.989327i	$0.546547\pi$
$384$	−1.73205			−0.0883883
$385$	61.3939	−	30.6969i	3.12892	−	1.56446i
$386$			9.89949i			0.503871i
$387$	7.34847	+	7.34847i	0.373544	+	0.373544i
$388$	−3.00000	+	3.00000i	−0.152302	+	0.152302i
$389$	−7.21393			−0.365761			−0.182880	−	0.983135i	$-0.558542\pi$
$389$	−7.21393			−0.365761			−0.182880	+	0.983135i	$0.558542\pi$
$390$	−10.8990	−	21.7980i	−0.551891	−	1.10378i
$391$	−1.10102			−0.0556810
$392$	11.8780	−	11.8780i	0.599927	−	0.599927i
$393$	4.41761	+	4.41761i	0.222839	+	0.222839i
$394$			2.89898i			0.146048i
$395$	0.635674	−	1.90702i	0.0319843	−	0.0959528i
$396$		−	18.8776i		−	0.948634i
$397$	12.6969	+	12.6969i	0.637241	+	0.637241i	0.949874	−	0.312633i	$-0.101211\pi$
$397$	12.6969	+	12.6969i	0.637241	+	0.637241i	−0.312633	+	0.949874i	$0.601211\pi$
$398$	−13.2207	−	13.2207i	−0.662695	−	0.662695i
$399$			41.3939i			2.07229i
$400$	−4.00000	−	3.00000i	−0.200000	−	0.150000i
$401$			18.2419i			0.910958i	0.890247	+	0.455479i	$0.150532\pi$
$401$			18.2419i			0.910958i	−0.890247	+	0.455479i	$0.849468\pi$
$402$	6.14966	−	6.14966i	0.306717	−	0.306717i
$403$	4.44949	−	4.44949i	0.221645	−	0.221645i
$404$	−9.89949			−0.492518
$405$	−19.0919	−	6.36396i	−0.948683	−	0.316228i
$406$	−13.7980			−0.684781
$407$		0			0
$408$	0.550510	−	0.550510i	0.0272543	−	0.0272543i
$409$			27.3939i			1.35454i	0.735735	+	0.677270i	$0.236837\pi$
$409$			27.3939i			1.35454i	−0.735735	+	0.677270i	$0.763163\pi$
$410$	2.82843	+	5.65685i	0.139686	+	0.279372i
$411$			26.2344i			1.29405i
$412$	1.44949	+	1.44949i	0.0714112	+	0.0714112i
$413$	36.3410	+	36.3410i	1.78822	+	1.78822i
$414$			7.34847i			0.361158i
$415$	−8.89898	−	17.7980i	−0.436834	−	0.873667i
$416$		−	6.29253i		−	0.308517i
$417$	−22.5959	−	22.5959i	−1.10653	−	1.10653i
$418$	−21.7980	+	21.7980i	−1.06617	+	1.06617i
$419$	29.0628			1.41981			0.709906	−	0.704297i	$-0.248738\pi$
$419$	29.0628			1.41981			0.709906	+	0.704297i	$0.248738\pi$
$420$	5.97469	−	17.9241i	0.291535	−	0.874605i
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$	4.73545	−	4.73545i	0.230518	−	0.230518i
$423$	16.9706	+	16.9706i	0.825137	+	0.825137i
$424$		−	6.00000i		−	0.291386i
$425$	2.22486	−	0.317837i	0.107922	−	0.0154174i
$426$	−3.79796			−0.184012
$427$	−1.55051	−	1.55051i	−0.0750345	−	0.0750345i
$428$	−7.70674	−	7.70674i	−0.372519	−	0.372519i
$429$	68.5821			3.31118
$430$	−2.44949	+	7.34847i	−0.118125	+	0.354375i
$431$		−	34.5768i		−	1.66551i	−0.553645	−	0.832753i	$-0.686763\pi$
$431$		−	34.5768i		−	1.66551i	0.553645	−	0.832753i	$-0.313237\pi$
$432$	−3.67423	−	3.67423i	−0.176777	−	0.176777i
$433$	−9.79796	+	9.79796i	−0.470860	+	0.470860i	−0.902193	−	0.431333i	$-0.858043\pi$
$433$	−9.79796	+	9.79796i	−0.470860	+	0.470860i	0.431333	+	0.902193i	$0.358043\pi$
$434$	4.87832			0.234167
$435$	−9.79796	+	4.89898i	−0.469776	+	0.234888i
$436$	−2.89898			−0.138836
$437$	8.48528	−	8.48528i	0.405906	−	0.405906i
$438$	8.48528	+	8.48528i	0.405442	+	0.405442i
$439$			2.89898i			0.138361i	0.997604	+	0.0691804i	$0.0220384\pi$
$439$			2.89898i			0.138361i	−0.997604	+	0.0691804i	$0.977962\pi$
$440$	12.5851	−	6.29253i	0.599969	−	0.299985i
$441$	50.3939			2.39971
$442$	2.00000	+	2.00000i	0.0951303	+	0.0951303i
$443$	−19.0205	−	19.0205i	−0.903689	−	0.903689i	0.0920642	−	0.995753i	$-0.470654\pi$
$443$	−19.0205	−	19.0205i	−0.903689	−	0.903689i	−0.995753	+	0.0920642i	$0.970654\pi$
$444$		0			0
$445$	−9.30306	−	3.10102i	−0.441007	−	0.147002i
$446$		−	5.02118i		−	0.237760i
$447$	−25.6308	+	25.6308i	−1.21230	+	1.21230i
$448$	3.44949	−	3.44949i	0.162973	−	0.162973i
$449$	−23.8988			−1.12785			−0.563926	−	0.825825i	$-0.690710\pi$
$449$	−23.8988			−1.12785			−0.563926	+	0.825825i	$0.690710\pi$
$450$	−2.12132	−	14.8492i	−0.100000	−	0.700000i
$451$	−17.7980			−0.838073
$452$	−8.34242	+	8.34242i	−0.392394	+	0.392394i
$453$	−20.6969	+	20.6969i	−0.972427	+	0.972427i
$454$		−	9.10102i		−	0.427132i
$455$	65.1180	+	21.7060i	3.05278	+	1.01759i
$456$			8.48528i			0.397360i
$457$	7.10102	+	7.10102i	0.332172	+	0.332172i	0.853411	−	0.521239i	$-0.174530\pi$
$457$	7.10102	+	7.10102i	0.332172	+	0.332172i	−0.521239	+	0.853411i	$0.674530\pi$
$458$	11.6315	+	11.6315i	0.543506	+	0.543506i
$459$	2.33562			0.109017
$460$	−4.89898	+	2.44949i	−0.228416	+	0.114208i
$461$		−	30.8270i		−	1.43576i	−0.696169	−	0.717878i	$-0.745114\pi$
$461$		−	30.8270i		−	1.43576i	0.696169	−	0.717878i	$-0.254886\pi$
$462$	37.5959	+	37.5959i	1.74912	+	1.74912i
$463$	−3.34847	+	3.34847i	−0.155617	+	0.155617i	−0.780621	−	0.625005i	$-0.785097\pi$
$463$	−3.34847	+	3.34847i	−0.155617	+	0.155617i	0.625005	+	0.780621i	$0.285097\pi$
$464$	−2.82843			−0.131306
$465$	3.46410	−	1.73205i	0.160644	−	0.0803219i
$466$	10.8990			0.504885
$467$	−20.0061	+	20.0061i	−0.925771	+	0.925771i	−0.997429	−	0.0716587i	$-0.977171\pi$
$467$	−20.0061	+	20.0061i	−0.925771	+	0.925771i	0.0716587	+	0.997429i	$0.477171\pi$
$468$	13.3485	−	13.3485i	0.617033	−	0.617033i
$469$			24.4949i			1.13107i
$470$	−5.65685	+	16.9706i	−0.260931	+	0.782794i
$471$	−17.3939			−0.801468
$472$	7.44949	+	7.44949i	0.342891	+	0.342891i
$473$	−15.4135	−	15.4135i	−0.708713	−	0.708713i
$474$	1.55708			0.0715190
$475$	−14.6969	+	19.5959i	−0.674342	+	0.899122i
$476$			2.19275i			0.100505i
$477$	12.7279	−	12.7279i	0.582772	−	0.582772i
$478$	20.2474	−	20.2474i	0.926097	−	0.926097i
$479$	−19.1633			−0.875594			−0.437797	−	0.899074i	$-0.644241\pi$
$479$	−19.1633			−0.875594			−0.437797	+	0.899074i	$0.644241\pi$
$480$	1.22474	−	3.67423i	0.0559017	−	0.167705i
$481$		0			0
$482$	9.26382	−	9.26382i	0.421955	−	0.421955i
$483$	−14.6349	−	14.6349i	−0.665913	−	0.665913i
$484$			28.5959i			1.29981i
$485$	−4.24264	−	8.48528i	−0.192648	−	0.385297i
$486$		−	15.5885i		−	0.707107i
$487$	−17.1464	−	17.1464i	−0.776979	−	0.776979i	0.202337	−	0.979316i	$-0.435146\pi$
$487$	−17.1464	−	17.1464i	−0.776979	−	0.776979i	−0.979316	+	0.202337i	$0.935146\pi$
$488$	−0.317837	−	0.317837i	−0.0143878	−	0.0143878i
$489$			6.49490i			0.293709i
$490$	16.7980	+	33.5959i	0.758854	+	1.51771i
$491$			29.9056i			1.34962i	0.737992	+	0.674810i	$0.235774\pi$
$491$			29.9056i			1.34962i	−0.737992	+	0.674810i	$0.764226\pi$
$492$	−3.46410	+	3.46410i	−0.156174	+	0.156174i
$493$	0.898979	−	0.898979i	0.0404880	−	0.0404880i
$494$	−30.8270			−1.38697
$495$	40.0454	+	13.3485i	1.79991	+	0.599969i
$496$	1.00000			0.0449013
$497$	7.56388	−	7.56388i	0.339286	−	0.339286i
$498$	10.8990	−	10.8990i	0.488395	−	0.488395i
$499$			10.4495i			0.467783i	0.972263	+	0.233892i	$0.0751461\pi$
$499$			10.4495i			0.467783i	−0.972263	+	0.233892i	$0.924854\pi$
$500$	9.19239	−	6.36396i	0.411096	−	0.284605i
$501$		−	29.6985i		−	1.32683i
$502$	1.34847	+	1.34847i	0.0601851	+	0.0601851i
$503$	24.2487	+	24.2487i	1.08120	+	1.08120i	0.996398	+	0.0847985i	$0.0270246\pi$
$503$	24.2487	+	24.2487i	1.08120	+	1.08120i	0.0847985	+	0.996398i	$0.472975\pi$
$504$	14.6349			0.651892
$505$	7.00000	−	21.0000i	0.311496	−	0.934488i
$506$		−	15.4135i		−	0.685213i
$507$	32.5732	+	32.5732i	1.44663	+	1.44663i
$508$	10.4495	−	10.4495i	0.463621	−	0.463621i
$509$	23.6130			1.04663			0.523315	−	0.852139i	$-0.324695\pi$
$509$	23.6130			1.04663			0.523315	+	0.852139i	$0.324695\pi$
$510$	0.778539	+	1.55708i	0.0344743	+	0.0689486i
$511$	−33.7980			−1.49513
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−18.0000	+	18.0000i	−0.794719	+	0.794719i
$514$			9.10102i			0.401429i
$515$	−4.09978	+	2.04989i	−0.180658	+	0.0903289i
$516$	−6.00000			−0.264135
$517$	−35.5959	−	35.5959i	−1.56551	−	1.56551i
$518$		0			0
$519$	−34.2911			−1.50521
$520$	13.3485	+	4.44949i	0.585369	+	0.195123i
$521$		−	2.54270i		−	0.111398i	−0.998448	−	0.0556988i	$-0.982261\pi$
$521$		−	2.54270i		−	0.111398i	0.998448	−	0.0556988i	$-0.0177387\pi$
$522$	−6.00000	−	6.00000i	−0.262613	−	0.262613i
$523$	−7.59592	+	7.59592i	−0.332146	+	0.332146i	−0.853401	−	0.521255i	$-0.825464\pi$
$523$	−7.59592	+	7.59592i	−0.332146	+	0.332146i	0.521255	+	0.853401i	$0.325464\pi$
$524$	−3.60697			−0.157571
$525$	33.7980	+	25.3485i	1.47506	+	1.10630i
$526$	3.75255			0.163619
$527$	−0.317837	+	0.317837i	−0.0138452	+	0.0138452i
$528$	7.70674	+	7.70674i	0.335393	+	0.335393i
$529$		−	17.0000i		−	0.739130i
$530$	12.7279	+	4.24264i	0.552866	+	0.184289i
$531$			31.6055i			1.37156i
$532$	−16.8990	−	16.8990i	−0.732664	−	0.732664i
$533$	−12.5851	−	12.5851i	−0.545119	−	0.545119i
$534$		−	7.59592i		−	0.328708i
$535$	21.7980	−	10.8990i	0.942408	−	0.471204i
$536$			5.02118i			0.216882i
$537$	30.0484	−	30.0484i	1.29669	−	1.29669i
$538$	−4.00000	+	4.00000i	−0.172452	+	0.172452i
$539$	−105.702			−4.55289
$540$	10.3923	−	5.19615i	0.447214	−	0.223607i
$541$	−4.69694			−0.201937			−0.100969	−	0.994890i	$-0.532194\pi$
$541$	−4.69694			−0.201937			−0.100969	+	0.994890i	$0.532194\pi$
$542$	4.09978	−	4.09978i	0.176100	−	0.176100i
$543$	10.3485	−	10.3485i	0.444095	−	0.444095i
$544$			0.449490i			0.0192717i
$545$	2.04989	−	6.14966i	0.0878076	−	0.263423i
$546$			53.1687i			2.27541i
$547$	16.2474	+	16.2474i	0.694691	+	0.694691i	0.963260	−	0.268570i	$-0.0865509\pi$
$547$	16.2474	+	16.2474i	0.694691	+	0.694691i	−0.268570	+	0.963260i	$0.586551\pi$
$548$	−10.7101	−	10.7101i	−0.457515	−	0.457515i
$549$		−	1.34847i		−	0.0575513i
$550$	4.44949	+	31.1464i	0.189727	+	1.32809i
$551$			13.8564i			0.590303i
$552$	−3.00000	−	3.00000i	−0.127688	−	0.127688i
$553$	−3.10102	+	3.10102i	−0.131869	+	0.131869i
$554$	−3.74983			−0.159315
$555$		0			0
$556$	18.4495			0.782433
$557$	24.6773	−	24.6773i	1.04561	−	1.04561i	0.0467021	−	0.998909i	$-0.485129\pi$
$557$	24.6773	−	24.6773i	1.04561	−	1.04561i	0.998909	−	0.0467021i	$-0.0148712\pi$
$558$	2.12132	+	2.12132i	0.0898027	+	0.0898027i
$559$		−	21.7980i		−	0.921955i
$560$	4.87832	+	9.75663i	0.206146	+	0.412293i
$561$	−4.89898			−0.206835
$562$	−4.00000	−	4.00000i	−0.168730	−	0.168730i
$563$	8.48528	+	8.48528i	0.357612	+	0.357612i	0.862932	−	0.505320i	$-0.168626\pi$
$563$	8.48528	+	8.48528i	0.357612	+	0.357612i	−0.505320	+	0.862932i	$0.668626\pi$
$564$	−13.8564			−0.583460
$565$	−11.7980	−	23.5959i	−0.496344	−	0.992688i
$566$			25.8058i			1.08470i
$567$	31.0454	+	31.0454i	1.30378	+	1.30378i
$568$	1.55051	−	1.55051i	0.0650580	−	0.0650580i
$569$	−27.6486			−1.15909			−0.579545	−	0.814940i	$-0.696770\pi$
$569$	−27.6486			−1.15909			−0.579545	+	0.814940i	$0.696770\pi$
$570$	−18.0000	−	6.00000i	−0.753937	−	0.251312i
$571$	34.9444			1.46238			0.731189	−	0.682175i	$-0.238966\pi$
$571$	34.9444			1.46238			0.731189	+	0.682175i	$0.238966\pi$
$572$	−27.9985	+	27.9985i	−1.17068	+	1.17068i
$573$	1.12848	+	1.12848i	0.0471431	+	0.0471431i
$574$		−	13.7980i		−	0.575916i
$575$	−1.73205	−	12.1244i	−0.0722315	−	0.505621i
$576$	3.00000			0.125000
$577$	8.79796	+	8.79796i	0.366264	+	0.366264i	0.866113	−	0.499849i	$-0.166611\pi$
$577$	8.79796	+	8.79796i	0.366264	+	0.366264i	−0.499849	+	0.866113i	$0.666611\pi$
$578$	11.8780	+	11.8780i	0.494058	+	0.494058i
$579$		−	17.1464i		−	0.712581i
$580$	2.00000	−	6.00000i	0.0830455	−	0.249136i
$581$			43.4120i			1.80103i
$582$	5.19615	−	5.19615i	0.215387	−	0.215387i
$583$	−26.6969	+	26.6969i	−1.10567	+	1.10567i
$584$	−6.92820			−0.286691
$585$	18.8776	+	37.7552i	0.780492	+	1.56098i
$586$	−18.0000			−0.743573
$587$	10.6780	−	10.6780i	0.440730	−	0.440730i	−0.451528	−	0.892257i	$-0.649121\pi$
$587$	10.6780	−	10.6780i	0.440730	−	0.440730i	0.892257	+	0.451528i	$0.149121\pi$
$588$	−20.5732	+	20.5732i	−0.848425	+	0.848425i
$589$		−	4.89898i		−	0.201859i
$590$	−21.0703	+	10.5352i	−0.867452	+	0.433726i
$591$		−	5.02118i		−	0.206544i
$592$		0			0
$593$	13.0779	+	13.0779i	0.537044	+	0.537044i	0.922659	−	0.385616i	$-0.126011\pi$
$593$	13.0779	+	13.0779i	0.537044	+	0.537044i	−0.385616	+	0.922659i	$0.626011\pi$
$594$			32.6969i			1.34157i
$595$	−4.65153	−	1.55051i	−0.190694	−	0.0635647i
$596$		−	20.9275i		−	0.857223i
$597$	22.8990	+	22.8990i	0.937193	+	0.937193i
$598$	10.8990	−	10.8990i	0.445692	−	0.445692i
$599$	−23.2631			−0.950504			−0.475252	−	0.879850i	$-0.657643\pi$
$599$	−23.2631			−0.950504			−0.475252	+	0.879850i	$0.657643\pi$
$600$	6.92820	+	5.19615i	0.282843	+	0.212132i
$601$	−14.8990			−0.607742			−0.303871	−	0.952713i	$-0.598279\pi$
$601$	−14.8990			−0.607742			−0.303871	+	0.952713i	$0.598279\pi$
$602$	11.9494	−	11.9494i	0.487020	−	0.487020i
$603$	−10.6515	+	10.6515i	−0.433764	+	0.433764i
$604$		−	16.8990i		−	0.687610i
$605$	−60.6611	−	20.2204i	−2.46622	−	0.822075i
$606$	17.1464			0.696526
$607$	3.44949	+	3.44949i	0.140010	+	0.140010i	0.773638	−	0.633628i	$-0.218435\pi$
$607$	3.44949	+	3.44949i	0.140010	+	0.140010i	−0.633628	+	0.773638i	$0.718435\pi$
$608$	−3.46410	−	3.46410i	−0.140488	−	0.140488i
$609$	23.8988			0.968427
$610$	0.898979	−	0.449490i	0.0363986	−	0.0181993i
$611$		−	50.3402i		−	2.03655i
$612$	−0.953512	+	0.953512i	−0.0385434	+	0.0385434i
$613$	−16.0454	+	16.0454i	−0.648068	+	0.648068i	−0.952526	−	0.304458i	$-0.901525\pi$
$613$	−16.0454	+	16.0454i	−0.648068	+	0.648068i	0.304458	+	0.952526i	$0.401525\pi$
$614$	−16.0492			−0.647691
$615$	−4.89898	−	9.79796i	−0.197546	−	0.395092i
$616$	−30.6969			−1.23681
$617$	−15.9063	+	15.9063i	−0.640363	+	0.640363i	−0.950645	−	0.310281i	$-0.899577\pi$
$617$	−15.9063	+	15.9063i	−0.640363	+	0.640363i	0.310281	+	0.950645i	$0.399577\pi$
$618$	−2.51059	−	2.51059i	−0.100991	−	0.100991i
$619$			42.9444i			1.72608i	0.505135	+	0.863040i	$0.331443\pi$
$619$			42.9444i			1.72608i	−0.505135	+	0.863040i	$0.668557\pi$
$620$	−0.707107	+	2.12132i	−0.0283981	+	0.0851943i
$621$		−	12.7279i		−	0.510754i
$622$	−13.5505	−	13.5505i	−0.543326	−	0.543326i
$623$	15.1278	+	15.1278i	0.606081	+	0.606081i
$624$			10.8990i			0.436308i
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$			7.21393i			0.288327i
$627$	37.7552	−	37.7552i	1.50780	−	1.50780i
$628$	7.10102	−	7.10102i	0.283362	−	0.283362i
$629$		0			0
$630$	−10.3485	+	31.0454i	−0.412293	+	1.23688i
$631$	−28.0000			−1.11466			−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000			−1.11466			−0.557331	+	0.830290i	$0.688175\pi$
$632$	−0.635674	+	0.635674i	−0.0252858	+	0.0252858i
$633$	−8.20204	+	8.20204i	−0.326002	+	0.326002i
$634$		−	3.79796i		−	0.150836i
$635$	14.7778	+	29.5556i	0.586440	+	1.17288i
$636$			10.3923i			0.412082i
$637$	−74.7423	−	74.7423i	−2.96140	−	2.96140i
$638$	12.5851	+	12.5851i	0.498247	+	0.498247i
$639$	6.57826			0.260232
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$		−	7.56388i		−	0.298755i	−0.988780	−	0.149378i	$-0.952273\pi$
$641$		−	7.56388i		−	0.298755i	0.988780	−	0.149378i	$-0.0477270\pi$
$642$	13.3485	+	13.3485i	0.526822	+	0.526822i
$643$	−12.0000	+	12.0000i	−0.473234	+	0.473234i	−0.902959	−	0.429726i	$-0.858610\pi$
$643$	−12.0000	+	12.0000i	−0.473234	+	0.473234i	0.429726	+	0.902959i	$0.358610\pi$
$644$	11.9494			0.470872
$645$	4.24264	−	12.7279i	0.167054	−	0.501161i
$646$	2.20204			0.0866381
$647$	21.2453	−	21.2453i	0.835239	−	0.835239i	−0.152989	−	0.988228i	$-0.548890\pi$
$647$	21.2453	−	21.2453i	0.835239	−	0.835239i	0.988228	+	0.152989i	$0.0488898\pi$
$648$	6.36396	+	6.36396i	0.250000	+	0.250000i
$649$		−	66.2929i		−	2.60222i
$650$	−18.8776	+	25.1701i	−0.740440	+	0.987253i
$651$	−8.44949			−0.331162
$652$	−2.65153	−	2.65153i	−0.103842	−	0.103842i
$653$	3.11416	+	3.11416i	0.121866	+	0.121866i	0.765410	−	0.643543i	$-0.222536\pi$
$653$	3.11416	+	3.11416i	0.121866	+	0.121866i	−0.643543	+	0.765410i	$0.722536\pi$
$654$	5.02118			0.196344
$655$	2.55051	−	7.65153i	0.0996567	−	0.298970i
$656$		−	2.82843i		−	0.110432i
$657$	−14.6969	−	14.6969i	−0.573382	−	0.573382i
$658$	27.5959	−	27.5959i	1.07580	−	1.07580i
$659$	−3.32124			−0.129377			−0.0646885	−	0.997906i	$-0.520605\pi$
$659$	−3.32124			−0.129377			−0.0646885	+	0.997906i	$0.520605\pi$
$660$	−21.7980	+	10.8990i	−0.848484	+	0.424242i
$661$	−2.00000			−0.0777910			−0.0388955	−	0.999243i	$-0.512384\pi$
$661$	−2.00000			−0.0777910			−0.0388955	+	0.999243i	$0.512384\pi$
$662$	14.3171	−	14.3171i	0.556450	−	0.556450i
$663$	−3.46410	−	3.46410i	−0.134535	−	0.134535i
$664$			8.89898i			0.345347i
$665$	47.7975	−	23.8988i	1.85351	−	0.926754i
$666$		0			0
$667$	−4.89898	−	4.89898i	−0.189689	−	0.189689i
$668$	12.1244	+	12.1244i	0.469105	+	0.469105i
$669$			8.69694i			0.336243i
$670$	−10.6515	−	3.55051i	−0.411505	−	0.137168i
$671$			2.82843i			0.109190i
$672$	−5.97469	+	5.97469i	−0.230479	+	0.230479i
$673$	−3.79796	+	3.79796i	−0.146401	+	0.146401i	−0.776508	−	0.630107i	$-0.783011\pi$
$673$	−3.79796	+	3.79796i	−0.146401	+	0.146401i	0.630107	+	0.776508i	$0.283011\pi$
$674$	−6.92820			−0.266864
$675$	3.67423	+	25.7196i	0.141421	+	0.989949i
$676$	−26.5959			−1.02292
$677$	−12.7279	+	12.7279i	−0.489174	+	0.489174i	−0.908045	−	0.418872i	$-0.862426\pi$
$677$	−12.7279	+	12.7279i	−0.489174	+	0.489174i	0.418872	+	0.908045i	$0.362426\pi$
$678$	14.4495	−	14.4495i	0.554929	−	0.554929i
$679$			20.6969i			0.794276i
$680$	−0.953512	−	0.317837i	−0.0365655	−	0.0121885i
$681$			15.7634i			0.604056i
$682$	−4.44949	−	4.44949i	−0.170380	−	0.170380i
$683$	16.1920	+	16.1920i	0.619571	+	0.619571i	0.945421	−	0.325851i	$-0.105651\pi$
$683$	16.1920	+	16.1920i	0.619571	+	0.619571i	−0.325851	+	0.945421i	$0.605651\pi$
$684$		−	14.6969i		−	0.561951i
$685$	30.2929	−	15.1464i	1.15743	−	0.578715i
$686$		−	47.7975i		−	1.82492i
$687$	−20.1464	−	20.1464i	−0.768634	−	0.768634i
$688$	2.44949	−	2.44949i	0.0933859	−	0.0933859i
$689$	−37.7552			−1.43836
$690$	8.48528	−	4.24264i	0.323029	−	0.161515i
$691$	20.4949			0.779663			0.389831	−	0.920886i	$-0.372533\pi$
$691$	20.4949			0.779663			0.389831	+	0.920886i	$0.372533\pi$
$692$	13.9993	−	13.9993i	0.532172	−	0.532172i
$693$	−65.1180	−	65.1180i	−2.47363	−	2.47363i
$694$			24.8990i			0.945152i
$695$	−13.0458	+	39.1373i	−0.494854	+	1.48456i
$696$	4.89898			0.185695
$697$	0.898979	+	0.898979i	0.0340513	+	0.0340513i
$698$	19.3704	+	19.3704i	0.733180	+	0.733180i
$699$	−18.8776			−0.714016
$700$	−24.1464	+	3.44949i	−0.912649	+	0.130378i
$701$		−	29.4128i		−	1.11090i	−0.831548	−	0.555452i	$-0.812545\pi$
$701$		−	29.4128i		−	1.11090i	0.831548	−	0.555452i	$-0.187455\pi$
$702$	−23.1202	+	23.1202i	−0.872617	+	0.872617i
$703$		0			0
$704$	−6.29253			−0.237159
$705$	9.79796	−	29.3939i	0.369012	−	1.10704i
$706$	−19.1464			−0.720585
$707$	−34.1482	+	34.1482i	−1.28428	+	1.28428i
$708$	−12.9029	−	12.9029i	−0.484920	−	0.484920i
$709$			12.0454i			0.452375i	0.974084	+	0.226187i	$0.0726262\pi$
$709$			12.0454i			0.452375i	−0.974084	+	0.226187i	$0.927374\pi$
$710$	2.19275	+	4.38551i	0.0822925	+	0.164585i
$711$	−2.69694			−0.101143
$712$	3.10102	+	3.10102i	0.116216	+	0.116216i
$713$	1.73205	+	1.73205i	0.0648658	+	0.0648658i
$714$		−	3.79796i		−	0.142135i
$715$	−39.5959	−	79.1918i	−1.48080	−	2.96161i
$716$			24.5344i			0.916895i
$717$	−35.0696	+	35.0696i	−1.30970	+	1.30970i
$718$	17.3485	−	17.3485i	0.647439	−	0.647439i
$719$	21.7060			0.809498			0.404749	−	0.914428i	$-0.367359\pi$
$719$	21.7060			0.809498			0.404749	+	0.914428i	$0.367359\pi$
$720$	−2.12132	+	6.36396i	−0.0790569	+	0.237171i
$721$	10.0000			0.372419
$722$	−3.53553	+	3.53553i	−0.131579	+	0.131579i
$723$	−16.0454	+	16.0454i	−0.596735	+	0.596735i
$724$			8.44949i			0.314023i
$725$	11.3137	+	8.48528i	0.420181	+	0.315135i
$726$		−	49.5296i		−	1.83822i
$727$	−14.1464	−	14.1464i	−0.524662	−	0.524662i	0.394314	−	0.918976i	$-0.370982\pi$
$727$	−14.1464	−	14.1464i	−0.524662	−	0.524662i	−0.918976	+	0.394314i	$0.870982\pi$
$728$	−21.7060	−	21.7060i	−0.804478	−	0.804478i
$729$			27.0000i			1.00000i
$730$	4.89898	−	14.6969i	0.181319	−	0.543958i
$731$			1.55708i			0.0575906i
$732$	0.550510	+	0.550510i	0.0203474	+	0.0203474i
$733$	31.3939	−	31.3939i	1.15956	−	1.15956i	0.174989	−	0.984570i	$-0.444011\pi$
$733$	31.3939	−	31.3939i	1.15956	−	1.15956i	0.984570	−	0.174989i	$-0.0559890\pi$
$734$	11.9494			0.441060
$735$	−29.0949	−	58.1898i	−1.07318	−	2.14636i
$736$	2.44949			0.0902894
$737$	22.3417	−	22.3417i	0.822967	−	0.822967i
$738$	6.00000	−	6.00000i	0.220863	−	0.220863i
$739$		−	10.9444i		−	0.402596i	−0.979530	−	0.201298i	$-0.935484\pi$
$739$		−	10.9444i		−	0.402596i	0.979530	−	0.201298i	$-0.0645159\pi$
$740$		0			0
$741$	53.3939			1.96147
$742$	−20.6969	−	20.6969i	−0.759809	−	0.759809i
$743$	−7.38891	−	7.38891i	−0.271073	−	0.271073i	0.558459	−	0.829532i	$-0.311393\pi$
$743$	−7.38891	−	7.38891i	−0.271073	−	0.271073i	−0.829532	+	0.558459i	$0.811393\pi$
$744$	−1.73205			−0.0635001
$745$	44.3939	+	14.7980i	1.62647	+	0.542155i
$746$			14.1421i			0.517780i
$747$	−18.8776	+	18.8776i	−0.690695	+	0.690695i
$748$	2.00000	−	2.00000i	0.0731272	−	0.0731272i
$749$	−53.1687			−1.94274
$750$	−15.9217	+	11.0227i	−0.581378	+	0.402492i
$751$	−3.30306			−0.120530			−0.0602652	−	0.998182i	$-0.519195\pi$
$751$	−3.30306			−0.120530			−0.0602652	+	0.998182i	$0.519195\pi$
$752$	5.65685	−	5.65685i	0.206284	−	0.206284i
$753$	−2.33562	−	2.33562i	−0.0851146	−	0.0851146i
$754$			17.7980i			0.648163i
$755$	35.8481	+	11.9494i	1.30465	+	0.434883i
$756$	−25.3485			−0.921915
$757$	−1.34847	−	1.34847i	−0.0490109	−	0.0490109i	0.682177	−	0.731187i	$-0.261034\pi$
$757$	−1.34847	−	1.34847i	−0.0490109	−	0.0490109i	−0.731187	+	0.682177i	$0.761034\pi$
$758$	−8.48528	−	8.48528i	−0.308199	−	0.308199i
$759$			26.6969i			0.969037i
$760$	9.79796	−	4.89898i	0.355409	−	0.177705i
$761$			7.49966i			0.271863i	0.990718	+	0.135931i	$0.0434026\pi$
$761$			7.49966i			0.271863i	−0.990718	+	0.135931i	$0.956597\pi$
$762$	−18.0990	+	18.0990i	−0.655659	+	0.655659i
$763$	−10.0000	+	10.0000i	−0.362024	+	0.362024i
$764$	−0.921404			−0.0333352
$765$	−1.34847	−	2.69694i	−0.0487540	−	0.0975080i
$766$	23.3485			0.843614
$767$	46.8761	−	46.8761i	1.69260	−	1.69260i
$768$	−1.22474	+	1.22474i	−0.0441942	+	0.0441942i
$769$			11.5959i			0.418159i	0.977899	+	0.209080i	$0.0670468\pi$
$769$			11.5959i			0.418159i	−0.977899	+	0.209080i	$0.932953\pi$
$770$	21.7060	−	65.1180i	0.782230	−	2.34669i
$771$		−	15.7634i		−	0.567706i
$772$	7.00000	+	7.00000i	0.251936	+	0.251936i
$773$	24.3916	+	24.3916i	0.877304	+	0.877304i	0.993255	−	0.115951i	$-0.0369915\pi$
$773$	24.3916	+	24.3916i	0.877304	+	0.877304i	−0.115951	+	0.993255i	$0.536992\pi$
$774$	10.3923			0.373544
$775$	−4.00000	−	3.00000i	−0.143684	−	0.107763i
$776$			4.24264i			0.152302i
$777$		0			0
$778$	−5.10102	+	5.10102i	−0.182880	+	0.182880i
$779$	−13.8564			−0.496457
$780$	−23.1202	−	7.70674i	−0.827837	−	0.275946i
$781$	−13.7980			−0.493730
$782$	−0.778539	+	0.778539i	−0.0278405	+	0.0278405i
$783$	10.3923	+	10.3923i	0.371391	+	0.371391i
$784$		−	16.7980i		−	0.599927i
$785$	10.0424	+	20.0847i	0.358427	+	0.716854i
$786$	6.24745			0.222839
$787$	23.3485	+	23.3485i	0.832283	+	0.832283i	0.987829	−	0.155546i	$-0.0497136\pi$
$787$	23.3485	+	23.3485i	0.832283	+	0.832283i	−0.155546	+	0.987829i	$0.549714\pi$
$788$	2.04989	+	2.04989i	0.0730242	+	0.0730242i
$789$	−6.49961			−0.231392
$790$	−0.898979	−	1.79796i	−0.0319843	−	0.0639685i
$791$			57.5542i			2.04639i
$792$	−13.3485	−	13.3485i	−0.474317	−	0.474317i
$793$	−2.00000	+	2.00000i	−0.0710221	+	0.0710221i
$794$	17.9562			0.637241
$795$	−22.0454	−	7.34847i	−0.781870	−	0.260623i
$796$	−18.6969			−0.662695
$797$	−37.2624	+	37.2624i	−1.31990	+	1.31990i	−0.406050	+	0.913851i	$0.633094\pi$
$797$	−37.2624	+	37.2624i	−1.31990	+	1.31990i	−0.913851	+	0.406050i	$0.866906\pi$
$798$	29.2699	+	29.2699i	1.03614	+	1.03614i
$799$			3.59592i			0.127214i
$800$	−4.94975	+	0.707107i	−0.175000	+	0.0250000i
$801$			13.1565i			0.464863i
$802$	12.8990	+	12.8990i	0.455479	+	0.455479i
$803$	30.8270	+	30.8270i	1.08786	+	1.08786i
$804$		−	8.69694i		−	0.306717i
$805$	−8.44949	+	25.3485i	−0.297805	+	0.893416i
$806$		−	6.29253i		−	0.221645i
$807$	6.92820	−	6.92820i	0.243884	−	0.243884i
$808$	−7.00000	+	7.00000i	−0.246259	+	0.246259i
$809$	−34.6410			−1.21791			−0.608957	−	0.793204i	$-0.708412\pi$
$809$	−34.6410			−1.21791			−0.608957	+	0.793204i	$0.708412\pi$
$810$	−18.0000	+	9.00000i	−0.632456	+	0.316228i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$	−9.75663	+	9.75663i	−0.342391	+	0.342391i
$813$	−7.10102	+	7.10102i	−0.249044	+	0.249044i
$814$		0			0
$815$	7.49966	−	3.74983i	0.262702	−	0.131351i
$816$		−	0.778539i		−	0.0272543i
$817$	−12.0000	−	12.0000i	−0.419827	−	0.419827i
$818$	19.3704	+	19.3704i	0.677270	+	0.677270i
$819$		−	92.0908i		−	3.21791i
$820$	6.00000	+	2.00000i	0.209529	+	0.0698430i
$821$			23.3273i			0.814129i	0.913399	+	0.407064i	$0.133448\pi$
$821$			23.3273i			0.814129i	−0.913399	+	0.407064i	$0.866552\pi$
$822$	18.5505	+	18.5505i	0.647023	+	0.647023i
$823$	9.14643	−	9.14643i	0.318824	−	0.318824i	−0.529491	−	0.848316i	$-0.677617\pi$
$823$	9.14643	−	9.14643i	0.318824	−	0.318824i	0.848316	+	0.529491i	$0.177617\pi$
$824$	2.04989			0.0714112
$825$	−7.70674	−	53.9472i	−0.268314	−	1.87820i
$826$	51.3939			1.78822
$827$	2.47848	−	2.47848i	0.0861853	−	0.0861853i	−0.662700	−	0.748885i	$-0.730589\pi$
$827$	2.47848	−	2.47848i	0.0861853	−	0.0861853i	0.748885	+	0.662700i	$0.230589\pi$
$828$	5.19615	+	5.19615i	0.180579	+	0.180579i
$829$			45.3485i			1.57502i	0.616304	+	0.787509i	$0.288629\pi$
$829$			45.3485i			1.57502i	−0.616304	+	0.787509i	$0.711371\pi$
$830$	−18.8776	−	6.29253i	−0.655251	−	0.218417i
$831$	6.49490			0.225305
$832$	−4.44949	−	4.44949i	−0.154258	−	0.154258i
$833$	5.33902	+	5.33902i	0.184986	+	0.184986i
$834$	−31.9555			−1.10653
$835$	−34.2929	+	17.1464i	−1.18675	+	0.593377i
$836$			30.8270i			1.06617i
$837$	−3.67423	−	3.67423i	−0.127000	−	0.127000i
$838$	20.5505	−	20.5505i	0.709906	−	0.709906i
$839$	40.2337			1.38902			0.694510	−	0.719483i	$-0.255621\pi$
$839$	40.2337			1.38902			0.694510	+	0.719483i	$0.255621\pi$
$840$	−8.44949	−	16.8990i	−0.291535	−	0.583070i
$841$	−21.0000			−0.724138
$842$	−1.41421	+	1.41421i	−0.0487370	+	0.0487370i
$843$	6.92820	+	6.92820i	0.238620	+	0.238620i
$844$		−	6.69694i		−	0.230518i
$845$	18.8062	−	56.4185i	0.646951	−	1.94085i
$846$	24.0000			0.825137
$847$	98.6413	+	98.6413i	3.38936	+	3.38936i
$848$	−4.24264	−	4.24264i	−0.145693	−	0.145693i
$849$		−	44.6969i		−	1.53399i
$850$	1.34847	−	1.79796i	0.0462521	−	0.0616695i
$851$		0			0
$852$	−2.68556	+	2.68556i	−0.0920059	+	0.0920059i
$853$	20.0000	−	20.0000i	0.684787	−	0.684787i	−0.276288	−	0.961075i	$-0.589104\pi$
$853$	20.0000	−	20.0000i	0.684787	−	0.684787i	0.961075	+	0.276288i	$0.0891043\pi$
$854$	−2.19275			−0.0750345
$855$	31.1769	+	10.3923i	1.06623	+	0.355409i
$856$	−10.8990			−0.372519
$857$	−2.68556	+	2.68556i	−0.0917371	+	0.0917371i	−0.751486	−	0.659749i	$-0.770663\pi$
$857$	−2.68556	+	2.68556i	−0.0917371	+	0.0917371i	0.659749	+	0.751486i	$0.270663\pi$
$858$	48.4949	−	48.4949i	1.65559	−	1.65559i
$859$		−	23.8434i		−	0.813525i	−0.913534	−	0.406763i	$-0.866658\pi$
$859$		−	23.8434i		−	0.813525i	0.913534	−	0.406763i	$-0.133342\pi$
$860$	3.46410	+	6.92820i	0.118125	+	0.236250i
$861$			23.8988i			0.814468i
$862$	−24.4495	−	24.4495i	−0.832753	−	0.832753i
$863$	5.54610	+	5.54610i	0.188791	+	0.188791i	0.795173	−	0.606382i	$-0.207380\pi$
$863$	5.54610	+	5.54610i	0.188791	+	0.188791i	−0.606382	+	0.795173i	$0.707380\pi$
$864$	−5.19615			−0.176777
$865$	19.7980	+	39.5959i	0.673151	+	1.34630i
$866$			13.8564i			0.470860i
$867$	−20.5732	−	20.5732i	−0.698703	−	0.698703i
$868$	3.44949	−	3.44949i	0.117083	−	0.117083i
$869$	5.65685			0.191896
$870$	−3.46410	+	10.3923i	−0.117444	+	0.352332i
$871$	31.5959			1.07059
$872$	−2.04989	+	2.04989i	−0.0694180	+	0.0694180i
$873$	−9.00000	+	9.00000i	−0.304604	+	0.304604i
$874$		−	12.0000i		−	0.405906i
$875$	9.75663	−	53.6615i	0.329834	−	1.81409i
$876$	12.0000			0.405442
$877$	11.1010	+	11.1010i	0.374855	+	0.374855i	0.869242	−	0.494387i	$-0.164607\pi$
$877$	11.1010	+	11.1010i	0.374855	+	0.374855i	−0.494387	+	0.869242i	$0.664607\pi$
$878$	2.04989	+	2.04989i	0.0691804	+	0.0691804i
$879$	31.1769			1.05157
$880$	4.44949	−	13.3485i	0.149992	−	0.449977i
$881$		−	11.9494i		−	0.402585i	−0.979531	−	0.201292i	$-0.935486\pi$
$881$		−	11.9494i		−	0.402585i	0.979531	−	0.201292i	$-0.0645142\pi$
$882$	35.6339	−	35.6339i	1.19985	−	1.19985i
$883$	28.8990	−	28.8990i	0.972528	−	0.972528i	−0.0271045	−	0.999633i	$-0.508629\pi$
$883$	28.8990	−	28.8990i	0.972528	−	0.972528i	0.999633	+	0.0271045i	$0.00862869\pi$
$884$	2.82843			0.0951303
$885$	36.4949	−	18.2474i	1.22676	−	0.613381i
$886$	−26.8990			−0.903689
$887$	10.0424	−	10.0424i	0.337189	−	0.337189i	−0.518119	−	0.855309i	$-0.673368\pi$
$887$	10.0424	−	10.0424i	0.337189	−	0.337189i	0.855309	+	0.518119i	$0.173368\pi$
$888$		0			0
$889$		−	72.0908i		−	2.41785i
$890$	−8.77101	+	4.38551i	−0.294005	+	0.147002i
$891$		−	56.6328i		−	1.89727i
$892$	−3.55051	−	3.55051i	−0.118880	−	0.118880i
$893$	−27.7128	−	27.7128i	−0.927374	−	0.927374i
$894$			36.2474i			1.21230i
$895$	−52.0454	−	17.3485i	−1.73969	−	0.579895i
$896$		−	4.87832i		−	0.162973i
$897$	−18.8776	+	18.8776i	−0.630304	+	0.630304i
$898$	−16.8990	+	16.8990i	−0.563926	+	0.563926i
$899$	−2.82843			−0.0943333
$900$	−12.0000	−	9.00000i	−0.400000	−	0.300000i
$901$	2.69694			0.0898480
$902$	−12.5851	+	12.5851i	−0.419037	+	0.419037i
$903$	−20.6969	+	20.6969i	−0.688751	+	0.688751i
$904$			11.7980i			0.392394i
$905$	−17.9241	−	5.97469i	−0.595816	−	0.198605i
$906$			29.2699i			0.972427i
$907$	26.9444	+	26.9444i	0.894674	+	0.894674i	0.994959	−	0.100285i	$-0.0319755\pi$
$907$	26.9444	+	26.9444i	0.894674	+	0.894674i	−0.100285	+	0.994959i	$0.531975\pi$
$908$	−6.43539	−	6.43539i	−0.213566	−	0.213566i
$909$	−29.6985			−0.985037
$910$	61.3939	−	30.6969i	2.03519	−	1.01759i
$911$			22.6274i			0.749680i	0.927090	+	0.374840i	$0.122302\pi$
$911$			22.6274i			0.749680i	−0.927090	+	0.374840i	$0.877698\pi$
$912$	6.00000	+	6.00000i	0.198680	+	0.198680i
$913$	39.5959	−	39.5959i	1.31043	−	1.31043i
$914$	10.0424			0.332172
$915$	−1.55708	+	0.778539i	−0.0514754	+	0.0257377i
$916$	16.4495			0.543506
$917$	−12.4422	+	12.4422i	−0.410877	+	0.410877i
$918$	1.65153	−	1.65153i	0.0545086	−	0.0545086i
$919$		−	31.1918i		−	1.02892i	−0.857513	−	0.514462i	$-0.827992\pi$
$919$		−	31.1918i		−	1.02892i	0.857513	−	0.514462i	$-0.172008\pi$
$920$	−1.73205	+	5.19615i	−0.0571040	+	0.171312i
$921$	27.7980			0.915974
$922$	−21.7980	−	21.7980i	−0.717878	−	0.717878i
$923$	−9.75663	−	9.75663i	−0.321143	−	0.321143i
$924$	53.1687			1.74912
$925$		0			0
$926$			4.73545i			0.155617i
$927$	4.34847	+	4.34847i	0.142822	+	0.142822i
$928$	−2.00000	+	2.00000i	−0.0656532	+	0.0656532i
$929$	14.4921			0.475470			0.237735	−	0.971330i	$-0.423595\pi$
$929$	14.4921			0.475470			0.237735	+	0.971330i	$0.423595\pi$
$930$	1.22474	−	3.67423i	0.0401610	−	0.120483i
$931$	−82.2929			−2.69704
$932$	7.70674	−	7.70674i	0.252443	−	0.252443i
$933$	23.4702	+	23.4702i	0.768379	+	0.768379i
$934$			28.2929i			0.925771i
$935$	2.82843	+	5.65685i	0.0924995	+	0.184999i
$936$		−	18.8776i		−	0.617033i
$937$	−28.5959	−	28.5959i	−0.934188	−	0.934188i	0.0637763	−	0.997964i	$-0.479686\pi$
$937$	−28.5959	−	28.5959i	−0.934188	−	0.934188i	−0.997964	+	0.0637763i	$0.979686\pi$
$938$	17.3205	+	17.3205i	0.565535	+	0.565535i
$939$		−	12.4949i		−	0.407756i
$940$	8.00000	+	16.0000i	0.260931	+	0.521862i
$941$		−	33.0839i		−	1.07851i	−0.842144	−	0.539253i	$-0.818707\pi$
$941$		−	33.0839i		−	1.07851i	0.842144	−	0.539253i	$-0.181293\pi$
$942$	−12.2993	+	12.2993i	−0.400734	+	0.400734i
$943$	4.89898	−	4.89898i	0.159533	−	0.159533i
$944$	10.5352			0.342891
$945$	17.9241	−	53.7722i	0.583070	−	1.74921i
$946$	−21.7980			−0.708713
$947$	−3.11416	+	3.11416i	−0.101196	+	0.101196i	−0.755892	−	0.654696i	$-0.772797\pi$
$947$	−3.11416	+	3.11416i	−0.101196	+	0.101196i	0.654696	+	0.755892i	$0.272797\pi$
$948$	1.10102	−	1.10102i	0.0357595	−	0.0357595i
$949$			43.5959i			1.41518i
$950$	3.46410	+	24.2487i	0.112390	+	0.786732i
$951$			6.57826i			0.213315i
$952$	1.55051	+	1.55051i	0.0502523	+	0.0502523i
$953$	22.9453	+	22.9453i	0.743270	+	0.743270i	0.973206	−	0.229936i	$-0.0738517\pi$
$953$	22.9453	+	22.9453i	0.743270	+	0.743270i	−0.229936	+	0.973206i	$0.573852\pi$
$954$		−	18.0000i		−	0.582772i
$955$	0.651531	−	1.95459i	0.0210830	−	0.0632491i
$956$		−	28.6342i		−	0.926097i
$957$	−21.7980	−	21.7980i	−0.704628	−	0.704628i
$958$	−13.5505	+	13.5505i	−0.437797	+	0.437797i
$959$	−73.8891			−2.38600
$960$	−1.73205	−	3.46410i	−0.0559017	−	0.111803i
$961$	1.00000			0.0322581
$962$		0			0
$963$	−23.1202	−	23.1202i	−0.745039	−	0.745039i
$964$		−	13.1010i		−	0.421955i
$965$	−19.7990	+	9.89949i	−0.637352	+	0.318676i
$966$	−20.6969			−0.665913
$967$	37.8434	+	37.8434i	1.21696	+	1.21696i	0.968691	+	0.248270i	$0.0798619\pi$
$967$	37.8434	+	37.8434i	1.21696	+	1.21696i	0.248270	+	0.968691i	$0.420138\pi$
$968$	20.2204	+	20.2204i	0.649907	+	0.649907i
$969$	−3.81405			−0.122525
$970$	−9.00000	−	3.00000i	−0.288973	−	0.0963242i
$971$		−	43.9048i		−	1.40897i	−0.709717	−	0.704487i	$-0.751177\pi$
$971$		−	43.9048i		−	1.40897i	0.709717	−	0.704487i	$-0.248823\pi$
$972$	−11.0227	−	11.0227i	−0.353553	−	0.353553i
$973$	63.6413	−	63.6413i	2.04025	−	2.04025i
$974$	−24.2487			−0.776979
$975$	32.6969	−	43.5959i	1.04714	−	1.39619i
$976$	−0.449490			−0.0143878
$977$	26.9343	−	26.9343i	0.861704	−	0.861704i	−0.129832	−	0.991536i	$-0.541444\pi$
$977$	26.9343	−	26.9343i	0.861704	−	0.861704i	0.991536	+	0.129832i	$0.0414439\pi$
$978$	4.59259	+	4.59259i	0.146855	+	0.146855i
$979$		−	27.5959i		−	0.881969i
$980$	35.6339	+	11.8780i	1.13828	+	0.379427i
$981$	−8.69694			−0.277672
$982$	21.1464	+	21.1464i	0.674810	+	0.674810i
$983$	1.73205	+	1.73205i	0.0552438	+	0.0552438i	0.734189	−	0.678945i	$-0.237563\pi$
$983$	1.73205	+	1.73205i	0.0552438	+	0.0552438i	−0.678945	+	0.734189i	$0.737563\pi$
$984$			4.89898i			0.156174i
$985$	−5.79796	+	2.89898i	−0.184738	+	0.0923692i
$986$		−	1.27135i		−	0.0404880i
$987$	−47.7975	+	47.7975i	−1.52141	+	1.52141i
$988$	−21.7980	+	21.7980i	−0.693485	+	0.693485i
$989$	8.48528			0.269816
$990$	37.7552	−	18.8776i	1.19994	−	0.599969i
$991$	44.8990			1.42626			0.713132	−	0.701030i	$-0.247276\pi$
$991$	44.8990			1.42626			0.713132	+	0.701030i	$0.247276\pi$
$992$	0.707107	−	0.707107i	0.0224507	−	0.0224507i
$993$	−24.7980	+	24.7980i	−0.786939	+	0.786939i
$994$		−	10.6969i		−	0.339286i
$995$	13.2207	−	39.6622i	0.419125	−	1.25738i
$996$		−	15.4135i		−	0.488395i
$997$	32.6969	+	32.6969i	1.03552	+	1.03552i	0.999345	+	0.0361770i	$0.0115180\pi$
$997$	32.6969	+	32.6969i	1.03552	+	1.03552i	0.0361770	+	0.999345i	$0.488482\pi$
$998$	7.38891	+	7.38891i	0.233892	+	0.233892i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.d.497.3	yes	8
3.2	odd	2	inner	930.2.j.d.497.1	✓	8
5.3	odd	4	inner	930.2.j.d.683.1	yes	8
15.8	even	4	inner	930.2.j.d.683.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.d.497.1	✓	8	3.2	odd	2	inner
930.2.j.d.497.3	yes	8	1.1	even	1	trivial
930.2.j.d.683.1	yes	8	5.3	odd	4	inner
930.2.j.d.683.3	yes	8	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.22474 + 1.22474i) q^{3} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +1.73205i q^{6} +(-3.44949 - 3.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.22474 + 1.22474i) q^{3} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +1.73205i q^{6} +(-3.44949 - 3.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} -3.00000i q^{9} +(2.00000 - 1.00000i) q^{10} +6.29253i q^{11} +(1.22474 + 1.22474i) q^{12} +(-4.44949 + 4.44949i) q^{13} -4.87832 q^{14} +(-3.46410 + 1.73205i) q^{15} -1.00000 q^{16} +(0.317837 - 0.317837i) q^{17} +(-2.12132 - 2.12132i) q^{18} +4.89898i q^{19} +(0.707107 - 2.12132i) q^{20} +8.44949 q^{21} +(4.44949 + 4.44949i) q^{22} +(-1.73205 - 1.73205i) q^{23} +1.73205 q^{24} +(4.00000 + 3.00000i) q^{25} +6.29253i q^{26} +(3.67423 + 3.67423i) q^{27} +(-3.44949 + 3.44949i) q^{28} +2.82843 q^{29} +(-1.22474 + 3.67423i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-7.70674 - 7.70674i) q^{33} -0.449490i q^{34} +(-4.87832 - 9.75663i) q^{35} -3.00000 q^{36} +(3.46410 + 3.46410i) q^{38} -10.8990i q^{39} +(-1.00000 - 2.00000i) q^{40} +2.82843i q^{41} +(5.97469 - 5.97469i) q^{42} +(-2.44949 + 2.44949i) q^{43} +6.29253 q^{44} +(2.12132 - 6.36396i) q^{45} -2.44949 q^{46} +(-5.65685 + 5.65685i) q^{47} +(1.22474 - 1.22474i) q^{48} +16.7980i q^{49} +(4.94975 - 0.707107i) q^{50} +0.778539i q^{51} +(4.44949 + 4.44949i) q^{52} +(4.24264 + 4.24264i) q^{53} +5.19615 q^{54} +(-4.44949 + 13.3485i) q^{55} +4.87832i q^{56} +(-6.00000 - 6.00000i) q^{57} +(2.00000 - 2.00000i) q^{58} -10.5352 q^{59} +(1.73205 + 3.46410i) q^{60} +0.449490 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-10.3485 + 10.3485i) q^{63} +1.00000i q^{64} +(-12.5851 + 6.29253i) q^{65} -10.8990 q^{66} +(-3.55051 - 3.55051i) q^{67} +(-0.317837 - 0.317837i) q^{68} +4.24264 q^{69} +(-10.3485 - 3.44949i) q^{70} +2.19275i q^{71} +(-2.12132 + 2.12132i) q^{72} +(4.89898 - 4.89898i) q^{73} +(-8.57321 + 1.22474i) q^{75} +4.89898 q^{76} +(21.7060 - 21.7060i) q^{77} +(-7.70674 - 7.70674i) q^{78} -0.898979i q^{79} +(-2.12132 - 0.707107i) q^{80} -9.00000 q^{81} +(2.00000 + 2.00000i) q^{82} +(-6.29253 - 6.29253i) q^{83} -8.44949i q^{84} +(0.898979 - 0.449490i) q^{85} +3.46410i q^{86} +(-3.46410 + 3.46410i) q^{87} +(4.44949 - 4.44949i) q^{88} -4.38551 q^{89} +(-3.00000 - 6.00000i) q^{90} +30.6969 q^{91} +(-1.73205 + 1.73205i) q^{92} +(1.22474 - 1.22474i) q^{93} +8.00000i q^{94} +(-3.46410 + 10.3923i) q^{95} -1.73205i q^{96} +(-3.00000 - 3.00000i) q^{97} +(11.8780 + 11.8780i) q^{98} +18.8776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7}+O(q^{10}) \) 8 * q - 8 * q^7	\( 8 q - 8 q^{7} + 16 q^{10} - 16 q^{13} - 8 q^{16} + 48 q^{21} + 16 q^{22} + 32 q^{25} - 8 q^{28} - 8 q^{31} - 24 q^{36} - 8 q^{40} + 16 q^{52} - 16 q^{55} - 48 q^{57} + 16 q^{58} - 16 q^{61} - 24 q^{63} - 48 q^{66} - 48 q^{67} - 24 q^{70} - 72 q^{81} + 16 q^{82} - 32 q^{85} + 16 q^{88} - 24 q^{90} + 128 q^{91} - 24 q^{97}+O(q^{100}) \) 8 * q - 8 * q^7 + 16 * q^10 - 16 * q^13 - 8 * q^16 + 48 * q^21 + 16 * q^22 + 32 * q^25 - 8 * q^28 - 8 * q^31 - 24 * q^36 - 8 * q^40 + 16 * q^52 - 16 * q^55 - 48 * q^57 + 16 * q^58 - 16 * q^61 - 24 * q^63 - 48 * q^66 - 48 * q^67 - 24 * q^70 - 72 * q^81 + 16 * q^82 - 32 * q^85 + 16 * q^88 - 24 * q^90 + 128 * q^91 - 24 * q^97

Introduction

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