LMFDB - Embedded newform 750.2.g.e.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(151,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("750.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$750 = 2 \cdot 3 \cdot 5^{3}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	750.g (of order $5$ , degree $4$ , not 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{6} + x^{4} - x^{2} + 1$ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$5$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			451.2
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	750.451
Dual form			750.2.g.e.301.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.309017 + 0.951057i) q^{6} +1.72654 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(1.97599 + 1.43564i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(-2.40211 + 1.74524i) q^{13} +(1.39680 + 1.01484i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-1.03353 + 3.18088i) q^{17} -1.00000 q^{18} +(0.694265 - 2.13673i) q^{19} +(0.533531 + 1.64204i) q^{21} +(0.754763 + 2.32292i) q^{22} +(7.37660 + 5.35941i) q^{23} -1.00000 q^{24} -2.96917 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.533531 + 1.64204i) q^{28} +(-2.89825 - 8.91991i) q^{29} +(-1.89294 + 5.82588i) q^{31} -1.00000 q^{32} +(-0.754763 + 2.32292i) q^{33} +(-2.70582 + 1.96589i) q^{34} +(-0.809017 - 0.587785i) q^{36} +(2.67078 - 1.94043i) q^{37} +(1.81761 - 1.32057i) q^{38} +(-2.40211 - 1.74524i) q^{39} +(4.95730 - 3.60169i) q^{41} +(-0.533531 + 1.64204i) q^{42} -7.06997 q^{43} +(-0.754763 + 2.32292i) q^{44} +(2.81761 + 8.67171i) q^{46} +(1.54270 + 4.74794i) q^{47} +(-0.809017 - 0.587785i) q^{48} -4.01905 q^{49} -3.34458 q^{51} +(-2.40211 - 1.74524i) q^{52} +(2.11710 + 6.51577i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-0.533531 + 1.64204i) q^{56} +2.24669 q^{57} +(2.89825 - 8.91991i) q^{58} +(0.147763 - 0.107356i) q^{59} +(-4.16750 - 3.02786i) q^{61} +(-4.95579 + 3.60059i) q^{62} +(-1.39680 + 1.01484i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.97599 + 1.43564i) q^{66} +(3.67432 - 11.3084i) q^{67} -3.34458 q^{68} +(-2.81761 + 8.67171i) q^{69} +(-3.51098 - 10.8057i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(5.44095 + 3.95309i) q^{73} +3.30127 q^{74} +2.24669 q^{76} +(3.41164 + 2.47870i) q^{77} +(-0.917526 - 2.82385i) q^{78} +(-3.50953 - 10.8012i) q^{79} +(0.309017 - 0.951057i) q^{81} +6.12756 q^{82} +(2.82417 - 8.69192i) q^{83} +(-1.39680 + 1.01484i) q^{84} +(-5.71972 - 4.15562i) q^{86} +(7.58773 - 5.51281i) q^{87} +(-1.97599 + 1.43564i) q^{88} +(6.56674 + 4.77102i) q^{89} +(-4.14735 + 3.01323i) q^{91} +(-2.81761 + 8.67171i) q^{92} -6.12569 q^{93} +(-1.54270 + 4.74794i) q^{94} +(-0.309017 - 0.951057i) q^{96} +(3.05493 + 9.40211i) q^{97} +(-3.25148 - 2.36234i) q^{98} -2.44246 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} + 2 q^{8} - 2 q^{9} + 10 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} - 2 q^{16} - 2 q^{17} - 8 q^{18} + 8 q^{19} - 2 q^{21} + 10 q^{23} - 8 q^{24} + 4 q^{26}+ \cdots - 20 q^{99}+O(q^{100})$ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 + 8 * q^7 + 2 * q^8 - 2 * q^9 + 10 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^14 - 2 * q^16 - 2 * q^17 - 8 * q^18 + 8 * q^19 - 2 * q^21 + 10 * q^23 - 8 * q^24 + 4 * q^26 - 2 * q^27 - 2 * q^28 + 22 * q^29 + 24 * q^31 - 8 * q^32 - 8 * q^34 - 2 * q^36 - 14 * q^37 + 2 * q^38 - 4 * q^39 + 22 * q^41 + 2 * q^42 + 28 * q^43 + 10 * q^46 + 30 * q^47 - 2 * q^48 - 8 * q^49 - 12 * q^51 - 4 * q^52 + 12 * q^53 + 2 * q^54 + 2 * q^56 - 12 * q^57 - 22 * q^58 + 20 * q^59 + 6 * q^62 - 2 * q^63 - 2 * q^64 - 10 * q^66 + 18 * q^67 - 12 * q^68 - 10 * q^69 + 20 * q^71 + 2 * q^72 + 16 * q^73 + 4 * q^74 - 12 * q^76 - 6 * q^78 - 16 * q^79 - 2 * q^81 + 28 * q^82 + 6 * q^83 - 2 * q^84 - 18 * q^86 - 8 * q^87 - 10 * q^88 + 34 * q^89 - 24 * q^91 - 10 * q^92 - 36 * q^93 - 30 * q^94 + 2 * q^96 - 4 * q^97 - 22 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$ .

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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

)

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.309017	+	0.951057i	−0.126156	+	0.388267i
$7$	1.72654			0.652572			0.326286	−	0.945271i	$-0.394203\pi$
$7$	1.72654			0.652572			0.326286	+	0.945271i	$0.394203\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	1.97599	+	1.43564i	0.595785	+	0.432863i	0.844380	−	0.535744i	$-0.179969\pi$
$11$	1.97599	+	1.43564i	0.595785	+	0.432863i	−0.248595	+	0.968607i	$0.579969\pi$
$12$	−0.809017	+	0.587785i	−0.233543	+	0.169679i
$13$	−2.40211	+	1.74524i	−0.666226	+	0.484042i	−0.868760	−	0.495234i	$-0.835082\pi$
$13$	−2.40211	+	1.74524i	−0.666226	+	0.484042i	0.202534	+	0.979275i	$0.435082\pi$
$14$	1.39680	+	1.01484i	0.373311	+	0.271226i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.03353	+	3.18088i	−0.250668	+	0.771477i	0.743984	+	0.668197i	$0.232934\pi$
$17$	−1.03353	+	3.18088i	−0.250668	+	0.771477i	−0.994652	+	0.103280i	$0.967066\pi$
$18$	−1.00000			−0.235702
$19$	0.694265	−	2.13673i	0.159275	−	0.490199i	−0.839294	−	0.543678i	$-0.817031\pi$
$19$	0.694265	−	2.13673i	0.159275	−	0.490199i	0.998569	+	0.0534793i	$0.0170311\pi$
$20$		0			0
$21$	0.533531	+	1.64204i	0.116426	+	0.358322i
$22$	0.754763	+	2.32292i	0.160916	+	0.495248i
$23$	7.37660	+	5.35941i	1.53813	+	1.11751i	0.951496	+	0.307660i	$0.0995461\pi$
$23$	7.37660	+	5.35941i	1.53813	+	1.11751i	0.586631	+	0.809854i	$0.300454\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$	−2.96917			−0.582303
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.533531	+	1.64204i	0.100828	+	0.310316i
$29$	−2.89825	−	8.91991i	−0.538192	−	1.65639i	−0.736648	−	0.676276i	$-0.763593\pi$
$29$	−2.89825	−	8.91991i	−0.538192	−	1.65639i	0.198456	−	0.980110i	$-0.436407\pi$
$30$		0			0
$31$	−1.89294	+	5.82588i	−0.339983	+	1.04636i	0.624233	+	0.781239i	$0.285412\pi$
$31$	−1.89294	+	5.82588i	−0.339983	+	1.04636i	−0.964215	+	0.265121i	$0.914588\pi$
$32$	−1.00000			−0.176777
$33$	−0.754763	+	2.32292i	−0.131387	+	0.404369i
$34$	−2.70582	+	1.96589i	−0.464044	+	0.337148i
$35$		0			0
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	2.67078	−	1.94043i	0.439073	−	0.319006i	−0.346193	−	0.938163i	$-0.612526\pi$
$37$	2.67078	−	1.94043i	0.439073	−	0.319006i	0.785267	+	0.619158i	$0.212526\pi$
$38$	1.81761	−	1.32057i	0.294855	−	0.214225i
$39$	−2.40211	−	1.74524i	−0.384646	−	0.279462i
$40$		0			0
$41$	4.95730	−	3.60169i	0.774200	−	0.562489i	−0.129033	−	0.991640i	$-0.541187\pi$
$41$	4.95730	−	3.60169i	0.774200	−	0.562489i	0.903233	+	0.429151i	$0.141187\pi$
$42$	−0.533531	+	1.64204i	−0.0823256	+	0.253372i
$43$	−7.06997			−1.07816			−0.539080	−	0.842255i	$-0.681228\pi$
$43$	−7.06997			−1.07816			−0.539080	+	0.842255i	$0.681228\pi$
$44$	−0.754763	+	2.32292i	−0.113785	+	0.350193i
$45$		0			0
$46$	2.81761	+	8.67171i	0.415434	+	1.27857i
$47$	1.54270	+	4.74794i	0.225026	+	0.692559i	0.998289	+	0.0584733i	$0.0186232\pi$
$47$	1.54270	+	4.74794i	0.225026	+	0.692559i	−0.773263	+	0.634085i	$0.781377\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	−4.01905			−0.574150
$50$		0			0
$51$	−3.34458			−0.468334
$52$	−2.40211	−	1.74524i	−0.333113	−	0.242021i
$53$	2.11710	+	6.51577i	0.290806	+	0.895010i	0.984598	+	0.174834i	$0.0559388\pi$
$53$	2.11710	+	6.51577i	0.290806	+	0.895010i	−0.693792	+	0.720176i	$0.744061\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$		0			0
$56$	−0.533531	+	1.64204i	−0.0712961	+	0.219427i
$57$	2.24669			0.297581
$58$	2.89825	−	8.91991i	0.380559	−	1.17124i
$59$	0.147763	−	0.107356i	0.0192371	−	0.0139766i	−0.578125	−	0.815948i	$-0.696215\pi$
$59$	0.147763	−	0.107356i	0.0192371	−	0.0139766i	0.597362	+	0.801972i	$0.296215\pi$
$60$		0			0
$61$	−4.16750	−	3.02786i	−0.533593	−	0.387678i	0.288107	−	0.957598i	$-0.406974\pi$
$61$	−4.16750	−	3.02786i	−0.533593	−	0.387678i	−0.821700	+	0.569920i	$0.806974\pi$
$62$	−4.95579	+	3.60059i	−0.629386	+	0.457276i
$63$	−1.39680	+	1.01484i	−0.175981	+	0.127857i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$		0			0
$66$	−1.97599	+	1.43564i	−0.243228	+	0.176716i
$67$	3.67432	−	11.3084i	0.448889	−	1.38154i	−0.429272	−	0.903175i	$-0.641230\pi$
$67$	3.67432	−	11.3084i	0.448889	−	1.38154i	0.878162	−	0.478364i	$-0.158770\pi$
$68$	−3.34458			−0.405589
$69$	−2.81761	+	8.67171i	−0.339200	+	1.04395i
$70$		0			0
$71$	−3.51098	−	10.8057i	−0.416676	−	1.28240i	−0.910743	−	0.412974i	$-0.864490\pi$
$71$	−3.51098	−	10.8057i	−0.416676	−	1.28240i	0.494066	−	0.869424i	$-0.335510\pi$
$72$	−0.309017	−	0.951057i	−0.0364180	−	0.112083i
$73$	5.44095	+	3.95309i	0.636816	+	0.462674i	0.858755	−	0.512387i	$-0.171239\pi$
$73$	5.44095	+	3.95309i	0.636816	+	0.462674i	−0.221939	+	0.975061i	$0.571239\pi$
$74$	3.30127			0.383764
$75$		0			0
$76$	2.24669			0.257713
$77$	3.41164	+	2.47870i	0.388792	+	0.282474i
$78$	−0.917526	−	2.82385i	−0.103889	−	0.319738i
$79$	−3.50953	−	10.8012i	−0.394852	−	1.21523i	−0.929076	−	0.369888i	$-0.879396\pi$
$79$	−3.50953	−	10.8012i	−0.394852	−	1.21523i	0.534224	−	0.845343i	$-0.320604\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	6.12756			0.676676
$83$	2.82417	−	8.69192i	0.309993	−	0.954062i	−0.667773	−	0.744365i	$-0.732752\pi$
$83$	2.82417	−	8.69192i	0.309993	−	0.954062i	0.977766	−	0.209697i	$-0.0672477\pi$
$84$	−1.39680	+	1.01484i	−0.152404	+	0.110728i
$85$		0			0
$86$	−5.71972	−	4.15562i	−0.616774	−	0.448112i
$87$	7.58773	−	5.51281i	0.813490	−	0.591035i
$88$	−1.97599	+	1.43564i	−0.210642	+	0.153040i
$89$	6.56674	+	4.77102i	0.696073	+	0.505727i	0.878651	−	0.477465i	$-0.158444\pi$
$89$	6.56674	+	4.77102i	0.696073	+	0.505727i	−0.182578	+	0.983191i	$0.558444\pi$
$90$		0			0
$91$	−4.14735	+	3.01323i	−0.434760	+	0.315872i
$92$	−2.81761	+	8.67171i	−0.293756	+	0.904088i
$93$	−6.12569			−0.635205
$94$	−1.54270	+	4.74794i	−0.159117	+	0.489713i
$95$		0			0
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	3.05493	+	9.40211i	0.310181	+	0.954640i	0.977693	+	0.210040i	$0.0673595\pi$
$97$	3.05493	+	9.40211i	0.310181	+	0.954640i	−0.667511	+	0.744600i	$0.732640\pi$
$98$	−3.25148	−	2.36234i	−0.328449	−	0.238632i
$99$	−2.44246			−0.245477
$100$		0			0
$101$	6.28885			0.625764			0.312882	−	0.949792i	$-0.398706\pi$
$101$	6.28885			0.625764			0.312882	+	0.949792i	$0.398706\pi$
$102$	−2.70582	−	1.96589i	−0.267916	−	0.194652i
$103$	−2.65121	−	8.15958i	−0.261231	−	0.803987i	−0.992538	−	0.121938i	$-0.961089\pi$
$103$	−2.65121	−	8.15958i	−0.261231	−	0.803987i	0.731306	−	0.682049i	$-0.238911\pi$
$104$	−0.917526	−	2.82385i	−0.0899708	−	0.276902i
$105$		0			0
$106$	−2.11710	+	6.51577i	−0.205631	+	0.632867i
$107$	9.09673			0.879415			0.439707	−	0.898141i	$-0.355082\pi$
$107$	9.09673			0.879415			0.439707	+	0.898141i	$0.355082\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	11.0110	−	7.99994i	1.05466	−	0.766256i	0.0815673	−	0.996668i	$-0.474007\pi$
$109$	11.0110	−	7.99994i	1.05466	−	0.766256i	0.973093	+	0.230412i	$0.0740075\pi$
$110$		0			0
$111$	2.67078	+	1.94043i	0.253499	+	0.184178i
$112$	−1.39680	+	1.01484i	−0.131985	+	0.0958930i
$113$	6.68863	−	4.85958i	0.629214	−	0.457150i	−0.226914	−	0.973915i	$-0.572864\pi$
$113$	6.68863	−	4.85958i	0.629214	−	0.457150i	0.856128	+	0.516764i	$0.172864\pi$
$114$	1.81761	+	1.32057i	0.170235	+	0.123683i
$115$		0			0
$116$	7.58773	−	5.51281i	0.704503	−	0.511851i
$117$	0.917526	−	2.82385i	0.0848253	−	0.261065i
$118$	0.182645			0.0168138
$119$	−1.78444	+	5.49193i	−0.163579	+	0.503444i
$120$		0			0
$121$	−1.55571	−	4.78797i	−0.141428	−	0.435270i
$122$	−1.59184	−	4.89919i	−0.144119	−	0.443552i
$123$	4.95730	+	3.60169i	0.446985	+	0.324753i
$124$	−6.12569			−0.550104
$125$		0			0
$126$	−1.72654			−0.153813
$127$	−14.4107	−	10.4700i	−1.27875	−	0.929064i	−0.279232	−	0.960224i	$-0.590080\pi$
$127$	−14.4107	−	10.4700i	−1.27875	−	0.929064i	−0.999514	+	0.0311599i	$0.990080\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−2.18474	−	6.72394i	−0.192356	−	0.592010i
$130$		0			0
$131$	3.19446	−	9.83155i	0.279102	−	0.858986i	−0.709003	−	0.705205i	$-0.750855\pi$
$131$	3.19446	−	9.83155i	0.279102	−	0.858986i	0.988105	−	0.153781i	$-0.0491451\pi$
$132$	−2.44246			−0.212589
$133$	1.19868	−	3.68915i	0.103939	−	0.319890i
$134$	9.61949	−	6.98897i	0.830997	−	0.603755i
$135$		0			0
$136$	−2.70582	−	1.96589i	−0.232022	−	0.168574i
$137$	−13.0103	+	9.45254i	−1.11155	+	0.807585i	−0.982906	−	0.184106i	$-0.941061\pi$
$137$	−13.0103	+	9.45254i	−1.11155	+	0.807585i	−0.128639	+	0.991691i	$0.541061\pi$
$138$	−7.37660	+	5.35941i	−0.627938	+	0.456224i
$139$	13.3564	+	9.70399i	1.13287	+	0.823082i	0.986111	−	0.166090i	$-0.0531142\pi$
$139$	13.3564	+	9.70399i	1.13287	+	0.823082i	0.146764	+	0.989172i	$0.453114\pi$
$140$		0			0
$141$	−4.03884	+	2.93439i	−0.340132	+	0.247120i
$142$	3.51098	−	10.8057i	0.294635	−	0.906792i
$143$	−7.25210			−0.606451
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$		0			0
$146$	2.07826	+	6.39623i	0.171998	+	0.529355i
$147$	−1.24196	−	3.82234i	−0.102435	−	0.315262i
$148$	2.67078	+	1.94043i	0.219537	+	0.159503i
$149$	20.5325			1.68209			0.841045	−	0.540965i	$-0.181941\pi$
$149$	20.5325			1.68209			0.841045	+	0.540965i	$0.181941\pi$
$150$		0			0
$151$	2.78808			0.226891			0.113445	−	0.993544i	$-0.463811\pi$
$151$	2.78808			0.226891			0.113445	+	0.993544i	$0.463811\pi$
$152$	1.81761	+	1.32057i	0.147428	+	0.107112i
$153$	−1.03353	−	3.18088i	−0.0835560	−	0.257159i
$154$	1.30313	+	4.01062i	0.105009	+	0.323185i
$155$		0			0
$156$	0.917526	−	2.82385i	0.0734608	−	0.226089i
$157$	−14.3416			−1.14458			−0.572291	−	0.820051i	$-0.693945\pi$
$157$	−14.3416			−1.14458			−0.572291	+	0.820051i	$0.693945\pi$
$158$	3.50953	−	10.8012i	0.279203	−	0.859298i
$159$	−5.54264	+	4.02697i	−0.439560	+	0.319359i
$160$		0			0
$161$	12.7360	+	9.25325i	1.00374	+	0.729259i
$162$	0.809017	−	0.587785i	0.0635624	−	0.0461808i
$163$	−4.77575	+	3.46979i	−0.374066	+	0.271775i	−0.758895	−	0.651213i	$-0.774260\pi$
$163$	−4.77575	+	3.46979i	−0.374066	+	0.271775i	0.384829	+	0.922988i	$0.374260\pi$
$164$	4.95730	+	3.60169i	0.387100	+	0.281245i
$165$		0			0
$166$	7.39378	−	5.37190i	0.573869	−	0.416940i
$167$	2.76393	−	8.50651i	0.213879	−	0.658253i	−0.785352	−	0.619050i	$-0.787518\pi$
$167$	2.76393	−	8.50651i	0.213879	−	0.658253i	0.999231	−	0.0392036i	$-0.0124821\pi$
$168$	−1.72654			−0.133206
$169$	−1.29293	+	3.97922i	−0.0994559	+	0.306094i
$170$		0			0
$171$	0.694265	+	2.13673i	0.0530918	+	0.163400i
$172$	−2.18474	−	6.72394i	−0.166585	−	0.512695i
$173$	20.9658	+	15.2325i	1.59400	+	1.15811i	0.897935	+	0.440128i	$0.145067\pi$
$173$	20.9658	+	15.2325i	1.59400	+	1.15811i	0.696064	+	0.717980i	$0.254933\pi$
$174$	9.37895			0.711016
$175$		0			0
$176$	−2.44246			−0.184108
$177$	0.147763	+	0.107356i	0.0111065	+	0.00806937i
$178$	2.50827	+	7.71967i	0.188003	+	0.578613i
$179$	0.0148362	+	0.0456612i	0.00110891	+	0.00341288i	0.951609	−	0.307310i	$-0.0994289\pi$
$179$	0.0148362	+	0.0456612i	0.00110891	+	0.00341288i	−0.950501	+	0.310723i	$0.899429\pi$
$180$		0			0
$181$	6.34558	−	19.5297i	0.471663	−	1.45163i	−0.378743	−	0.925502i	$-0.623644\pi$
$181$	6.34558	−	19.5297i	0.471663	−	1.45163i	0.850406	−	0.526127i	$-0.176356\pi$
$182$	−5.12641			−0.379995
$183$	1.59184	−	4.89919i	0.117672	−	0.362158i
$184$	−7.37660	+	5.35941i	−0.543810	+	0.395101i
$185$		0			0
$186$	−4.95579	−	3.60059i	−0.363376	−	0.264008i
$187$	−6.60886	+	4.80162i	−0.483288	+	0.351129i
$188$	−4.03884	+	2.93439i	−0.294563	+	0.214012i
$189$	−1.39680	−	1.01484i	−0.101602	−	0.0738185i
$190$		0			0
$191$	−1.95814	+	1.42267i	−0.141686	+	0.102941i	−0.656370	−	0.754439i	$-0.727909\pi$
$191$	−1.95814	+	1.42267i	−0.141686	+	0.102941i	0.514684	+	0.857380i	$0.327909\pi$
$192$	0.309017	−	0.951057i	0.0223014	−	0.0686366i
$193$	−13.3764			−0.962857			−0.481429	−	0.876485i	$-0.659882\pi$
$193$	−13.3764			−0.962857			−0.481429	+	0.876485i	$0.659882\pi$
$194$	−3.05493	+	9.40211i	−0.219331	+	0.675032i
$195$		0			0
$196$	−1.24196	−	3.82234i	−0.0887111	−	0.273025i
$197$	−5.84770	−	17.9974i	−0.416631	−	1.28226i	−0.910783	−	0.412884i	$-0.864521\pi$
$197$	−5.84770	−	17.9974i	−0.416631	−	1.28226i	0.494152	−	0.869376i	$-0.335479\pi$
$198$	−1.97599	−	1.43564i	−0.140428	−	0.102027i
$199$	−22.6784			−1.60763			−0.803815	−	0.594879i	$-0.797200\pi$
$199$	−22.6784			−1.60763			−0.803815	+	0.594879i	$0.797200\pi$
$200$		0			0
$201$	11.8903			0.838680
$202$	5.08779	+	3.69649i	0.357975	+	0.260084i
$203$	−5.00396	−	15.4006i	−0.351209	−	1.08091i
$204$	−1.03353	−	3.18088i	−0.0723616	−	0.222706i
$205$		0			0
$206$	2.65121	−	8.15958i	0.184718	−	0.568505i
$207$	−9.11798			−0.633743
$208$	0.917526	−	2.82385i	0.0636189	−	0.195799i
$209$	4.43945	−	3.22545i	0.307083	−	0.223109i
$210$		0			0
$211$	−2.07008	−	1.50400i	−0.142510	−	0.103540i	0.514246	−	0.857643i	$-0.328072\pi$
$211$	−2.07008	−	1.50400i	−0.142510	−	0.103540i	−0.656756	+	0.754103i	$0.728072\pi$
$212$	−5.54264	+	4.02697i	−0.380670	+	0.276573i
$213$	9.19186	−	6.67828i	0.629816	−	0.457588i
$214$	7.35941	+	5.34693i	0.503079	+	0.365508i
$215$		0			0
$216$	0.809017	−	0.587785i	0.0550466	−	0.0399937i
$217$	−3.26825	+	10.0586i	−0.221863	+	0.682824i
$218$	13.6103			0.921807
$219$	−2.07826	+	6.39623i	−0.140436	+	0.432217i
$220$		0			0
$221$	−3.06873	−	9.44459i	−0.206425	−	0.635312i
$222$	1.02015	+	3.13969i	0.0684678	+	0.210722i
$223$	−15.0916	−	10.9647i	−1.01061	−	0.734251i	−0.0462729	−	0.998929i	$-0.514734\pi$
$223$	−15.0916	−	10.9647i	−1.01061	−	0.734251i	−0.964337	+	0.264678i	$0.914734\pi$
$224$	−1.72654			−0.115359
$225$		0			0
$226$	8.26761			0.549953
$227$	8.94897	+	6.50181i	0.593964	+	0.431540i	0.843731	−	0.536766i	$-0.180354\pi$
$227$	8.94897	+	6.50181i	0.593964	+	0.431540i	−0.249767	+	0.968306i	$0.580354\pi$
$228$	0.694265	+	2.13673i	0.0459788	+	0.141508i
$229$	8.35868	+	25.7254i	0.552357	+	1.69998i	0.702823	+	0.711365i	$0.251923\pi$
$229$	8.35868	+	25.7254i	0.552357	+	1.69998i	−0.150466	+	0.988615i	$0.548077\pi$
$230$		0			0
$231$	−1.30313	+	4.01062i	−0.0857397	+	0.263880i
$232$	9.37895			0.615758
$233$	5.64803	−	17.3828i	0.370015	−	1.13879i	−0.576766	−	0.816909i	$-0.695686\pi$
$233$	5.64803	−	17.3828i	0.370015	−	1.13879i	0.946781	−	0.321879i	$-0.104314\pi$
$234$	2.40211	−	1.74524i	0.157031	−	0.114090i
$235$		0			0
$236$	0.147763	+	0.107356i	0.00961854	+	0.00698828i
$237$	9.18806	−	6.67551i	0.596828	−	0.433621i
$238$	−4.67171	+	3.39420i	−0.302822	+	0.220013i
$239$	2.07768	+	1.50953i	0.134394	+	0.0976431i	0.652951	−	0.757400i	$-0.273531\pi$
$239$	2.07768	+	1.50953i	0.134394	+	0.0976431i	−0.518557	+	0.855043i	$0.673531\pi$
$240$		0			0
$241$	−10.7918	+	7.84068i	−0.695159	+	0.505063i	−0.878352	−	0.478014i	$-0.841357\pi$
$241$	−10.7918	+	7.84068i	−0.695159	+	0.505063i	0.183193	+	0.983077i	$0.441357\pi$
$242$	1.55571	−	4.78797i	0.100005	−	0.307783i
$243$	1.00000			0.0641500
$244$	1.59184	−	4.89919i	0.101907	−	0.313638i
$245$		0			0
$246$	1.89352	+	5.82766i	0.120726	+	0.371558i
$247$	2.06140	+	6.34432i	0.131163	+	0.403680i
$248$	−4.95579	−	3.60059i	−0.314693	−	0.228638i
$249$	9.13922			0.579175
$250$		0			0
$251$	−14.3409			−0.905191			−0.452595	−	0.891716i	$-0.649502\pi$
$251$	−14.3409			−0.905191			−0.452595	+	0.891716i	$0.649502\pi$
$252$	−1.39680	−	1.01484i	−0.0879903	−	0.0639287i
$253$	6.88191	+	21.1803i	0.432662	+	1.33160i
$254$	−5.50441	−	16.9408i	−0.345378	−	1.06296i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−16.0010			−0.998117			−0.499059	−	0.866568i	$-0.666321\pi$
$257$	−16.0010			−0.998117			−0.499059	+	0.866568i	$0.666321\pi$
$258$	2.18474	−	6.72394i	0.136016	−	0.418614i
$259$	4.61121	−	3.35024i	0.286527	−	0.208174i
$260$		0			0
$261$	7.58773	+	5.51281i	0.469669	+	0.341234i
$262$	8.36321	−	6.07623i	0.516681	−	0.375391i
$263$	−16.0658	+	11.6725i	−0.990657	+	0.719754i	−0.960065	−	0.279778i	$-0.909739\pi$
$263$	−16.0658	+	11.6725i	−0.990657	+	0.719754i	−0.0305919	+	0.999532i	$0.509739\pi$
$264$	−1.97599	−	1.43564i	−0.121614	−	0.0883578i
$265$		0			0
$266$	3.13818	−	2.28002i	0.192414	−	0.139797i
$267$	−2.50827	+	7.71967i	−0.153504	+	0.472436i
$268$	11.8903			0.726318
$269$	−0.822243	+	2.53060i	−0.0501331	+	0.154294i	−0.972989	−	0.230852i	$-0.925849\pi$
$269$	−0.822243	+	2.53060i	−0.0501331	+	0.154294i	0.922856	+	0.385146i	$0.125849\pi$
$270$		0			0
$271$	−4.15958	−	12.8019i	−0.252677	−	0.777659i	−0.994279	−	0.106818i	$-0.965934\pi$
$271$	−4.15958	−	12.8019i	−0.252677	−	0.777659i	0.741602	−	0.670840i	$-0.234066\pi$
$272$	−1.03353	−	3.18088i	−0.0626670	−	0.192869i
$273$	−4.14735	−	3.01323i	−0.251009	−	0.182369i
$274$	−16.0816			−0.971527
$275$		0			0
$276$	−9.11798			−0.548838
$277$	−4.32620	−	3.14317i	−0.259936	−	0.188855i	0.450183	−	0.892936i	$-0.351359\pi$
$277$	−4.32620	−	3.14317i	−0.259936	−	0.188855i	−0.710119	+	0.704082i	$0.751359\pi$
$278$	5.10169	+	15.7014i	0.305979	+	0.941706i
$279$	−1.89294	−	5.82588i	−0.113328	−	0.348786i
$280$		0			0
$281$	−5.16582	+	15.8988i	−0.308167	+	0.948441i	0.670309	+	0.742082i	$0.266162\pi$
$281$	−5.16582	+	15.8988i	−0.308167	+	0.948441i	−0.978476	+	0.206359i	$0.933838\pi$
$282$	−4.99228			−0.297286
$283$	4.37660	−	13.4698i	0.260162	−	0.800696i	−0.732607	−	0.680652i	$-0.761697\pi$
$283$	4.37660	−	13.4698i	0.260162	−	0.800696i	0.992769	−	0.120044i	$-0.0383034\pi$
$284$	9.19186	−	6.67828i	0.545436	−	0.396283i
$285$		0			0
$286$	−5.86707	−	4.26268i	−0.346927	−	0.252057i
$287$	8.55899	−	6.21847i	0.505221	−	0.367065i
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	4.70347	+	3.41727i	0.276675	+	0.201016i
$290$		0			0
$291$	−7.99792	+	5.81083i	−0.468846	+	0.340637i
$292$	−2.07826	+	6.39623i	−0.121621	+	0.374311i
$293$	−12.4643			−0.728175			−0.364088	−	0.931365i	$-0.618619\pi$
$293$	−12.4643			−0.728175			−0.364088	+	0.931365i	$0.618619\pi$
$294$	1.24196	−	3.82234i	0.0724323	−	0.222924i
$295$		0			0
$296$	1.02015	+	3.13969i	0.0592948	+	0.182491i
$297$	−0.754763	−	2.32292i	−0.0437958	−	0.134790i
$298$	16.6112	+	12.0687i	0.962259	+	0.699122i
$299$	−27.0729			−1.56566
$300$		0			0
$301$	−12.2066			−0.703577
$302$	2.25560	+	1.63879i	0.129795	+	0.0943019i
$303$	1.94336	+	5.98105i	0.111643	+	0.343602i
$304$	0.694265	+	2.13673i	0.0398188	+	0.122550i
$305$		0			0
$306$	1.03353	−	3.18088i	0.0590830	−	0.181839i
$307$	23.9974			1.36960			0.684801	−	0.728730i	$-0.259889\pi$
$307$	23.9974			1.36960			0.684801	+	0.728730i	$0.259889\pi$
$308$	−1.30313	+	4.01062i	−0.0742527	+	0.228526i
$309$	6.94095	−	5.04290i	0.394857	−	0.286880i
$310$		0			0
$311$	11.2931	+	8.20494i	0.640375	+	0.465260i	0.859979	−	0.510329i	$-0.170477\pi$
$311$	11.2931	+	8.20494i	0.640375	+	0.465260i	−0.219604	+	0.975589i	$0.570477\pi$
$312$	2.40211	−	1.74524i	0.135993	−	0.0988046i
$313$	7.78872	−	5.65884i	0.440245	−	0.319856i	−0.345488	−	0.938423i	$-0.612286\pi$
$313$	7.78872	−	5.65884i	0.440245	−	0.319856i	0.785732	+	0.618567i	$0.212286\pi$
$314$	−11.6026	−	8.42976i	−0.654771	−	0.475719i
$315$		0			0
$316$	9.18806	−	6.67551i	0.516869	−	0.375527i
$317$	0.171911	−	0.529086i	0.00965546	−	0.0297164i	−0.946113	−	0.323838i	$-0.895027\pi$
$317$	0.171911	−	0.529086i	0.00965546	−	0.0297164i	0.955768	+	0.294121i	$0.0950269\pi$
$318$	−6.85108			−0.384190
$319$	7.07888	−	21.7866i	0.396341	−	1.21981i
$320$		0			0
$321$	2.81105	+	8.65151i	0.156897	+	0.482880i
$322$	4.86472	+	14.9721i	0.271100	+	0.834361i
$323$	6.07914	+	4.41675i	0.338252	+	0.245755i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−5.90315			−0.326945
$327$	11.0110	+	7.99994i	0.608908	+	0.442398i
$328$	1.89352	+	5.82766i	0.104552	+	0.321778i
$329$	2.66354	+	8.19753i	0.146846	+	0.451944i
$330$		0			0
$331$	−3.57383	+	10.9991i	−0.196435	+	0.604565i	0.803522	+	0.595276i	$0.202957\pi$
$331$	−3.57383	+	10.9991i	−0.196435	+	0.604565i	−0.999957	+	0.00928983i	$0.997043\pi$
$332$	9.13922			0.501580
$333$	−1.02015	+	3.13969i	−0.0559037	+	0.172054i
$334$	7.23607	−	5.25731i	0.395940	−	0.287667i
$335$		0			0
$336$	−1.39680	−	1.01484i	−0.0762018	−	0.0553639i
$337$	−24.1708	+	17.5611i	−1.31667	+	0.956613i	−0.316698	+	0.948526i	$0.602574\pi$
$337$	−24.1708	+	17.5611i	−1.31667	+	0.956613i	−0.999967	+	0.00808669i	$0.997426\pi$
$338$	−3.38493	+	2.45929i	−0.184116	+	0.133768i
$339$	6.68863	+	4.85958i	0.363277	+	0.263936i
$340$		0			0
$341$	−12.1043	+	8.79432i	−0.655487	+	0.476239i
$342$	−0.694265	+	2.13673i	−0.0375416	+	0.115541i
$343$	−19.0249			−1.02725
$344$	2.18474	−	6.72394i	0.117793	−	0.362530i
$345$		0			0
$346$	8.00822	+	24.6468i	0.430524	+	1.32502i
$347$	−1.31230	−	4.03884i	−0.0704479	−	0.216816i	0.909634	−	0.415411i	$-0.136362\pi$
$347$	−1.31230	−	4.03884i	−0.0704479	−	0.216816i	−0.980082	+	0.198595i	$0.936362\pi$
$348$	7.58773	+	5.51281i	0.406745	+	0.295518i
$349$	−19.3711			−1.03691			−0.518456	−	0.855104i	$-0.673493\pi$
$349$	−19.3711			−1.03691			−0.518456	+	0.855104i	$0.673493\pi$
$350$		0			0
$351$	2.96917			0.158483
$352$	−1.97599	−	1.43564i	−0.105321	−	0.0765201i
$353$	−0.0751761	−	0.231368i	−0.00400122	−	0.0123145i	0.949036	−	0.315168i	$-0.102061\pi$
$353$	−0.0751761	−	0.231368i	−0.00400122	−	0.0123145i	−0.953037	+	0.302853i	$0.902061\pi$
$354$	0.0564404	+	0.173706i	0.00299977	+	0.00923235i
$355$		0			0
$356$	−2.50827	+	7.71967i	−0.132938	+	0.409142i
$357$	−5.77455			−0.305622
$358$	−0.0148362	+	0.0456612i	−0.000784119	+	0.00241327i
$359$	−17.0243	+	12.3689i	−0.898508	+	0.652805i	−0.938082	−	0.346412i	$-0.887400\pi$
$359$	−17.0243	+	12.3689i	−0.898508	+	0.652805i	0.0395740	+	0.999217i	$0.487400\pi$
$360$		0			0
$361$	11.2877	+	8.20101i	0.594090	+	0.431632i
$362$	16.6129	−	12.0700i	0.873156	−	0.634385i
$363$	4.07289	−	2.95913i	0.213771	−	0.155314i
$364$	−4.14735	−	3.01323i	−0.217380	−	0.157936i
$365$		0			0
$366$	4.16750	−	3.02786i	0.217839	−	0.158269i
$367$	−2.42065	+	7.45000i	−0.126357	+	0.388887i	−0.994146	−	0.108046i	$-0.965541\pi$
$367$	−2.42065	+	7.45000i	−0.126357	+	0.388887i	0.867789	+	0.496933i	$0.165541\pi$
$368$	−9.11798			−0.475307
$369$	−1.89352	+	5.82766i	−0.0985727	+	0.303376i
$370$		0			0
$371$	3.65527	+	11.2498i	0.189772	+	0.584058i
$372$	−1.89294	−	5.82588i	−0.0981446	−	0.302058i
$373$	12.5604	+	9.12569i	0.650355	+	0.472511i	0.863392	−	0.504534i	$-0.168336\pi$
$373$	12.5604	+	9.12569i	0.650355	+	0.472511i	−0.213037	+	0.977044i	$0.568336\pi$
$374$	−8.16901			−0.422409
$375$		0			0
$376$	−4.99228			−0.257457
$377$	22.5293	+	16.3685i	1.16032	+	0.843020i
$378$	−0.533531	−	1.64204i	−0.0274419	−	0.0844574i
$379$	−3.35706	−	10.3320i	−0.172441	−	0.530718i	0.827067	−	0.562104i	$-0.190008\pi$
$379$	−3.35706	−	10.3320i	−0.172441	−	0.530718i	−0.999507	+	0.0313859i	$0.990008\pi$
$380$		0			0
$381$	5.50441	−	16.9408i	0.282000	−	0.867906i
$382$	−2.42040			−0.123838
$383$	−2.96537	+	9.12648i	−0.151523	+	0.466341i	−0.997792	−	0.0664152i	$-0.978844\pi$
$383$	−2.96537	+	9.12648i	−0.151523	+	0.466341i	0.846269	+	0.532756i	$0.178844\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$		0			0
$386$	−10.8218	−	7.86247i	−0.550814	−	0.400189i
$387$	5.71972	−	4.15562i	0.290750	−	0.211242i
$388$	−7.99792	+	5.81083i	−0.406033	+	0.295000i
$389$	−28.1716	−	20.4679i	−1.42836	−	1.03776i	−0.990320	−	0.138805i	$-0.955674\pi$
$389$	−28.1716	−	20.4679i	−1.42836	−	1.03776i	−0.438037	−	0.898957i	$-0.644326\pi$
$390$		0			0
$391$	−24.6716	+	17.9250i	−1.24770	+	0.906504i
$392$	1.24196	−	3.82234i	0.0627282	−	0.193058i
$393$	10.3375			0.521458
$394$	5.84770	−	17.9974i	0.294603	−	0.906695i
$395$		0			0
$396$	−0.754763	−	2.32292i	−0.0379283	−	0.116731i
$397$	4.94607	+	15.2224i	0.248236	+	0.763992i	0.995087	+	0.0990008i	$0.0315646\pi$
$397$	4.94607	+	15.2224i	0.248236	+	0.763992i	−0.746851	+	0.664991i	$0.768435\pi$
$398$	−18.3472	−	13.3300i	−0.919663	−	0.668175i
$399$	3.87901			0.194193
$400$		0			0
$401$	11.5284			0.575701			0.287850	−	0.957675i	$-0.407059\pi$
$401$	11.5284			0.575701			0.287850	+	0.957675i	$0.407059\pi$
$402$	9.61949	+	6.98897i	0.479776	+	0.348578i
$403$	−5.62048	−	17.2981i	−0.279976	−	0.861678i
$404$	1.94336	+	5.98105i	0.0966858	+	0.297568i
$405$		0			0
$406$	5.00396	−	15.4006i	0.248342	−	0.764319i
$407$	8.06322			0.399679
$408$	1.03353	−	3.18088i	0.0511674	−	0.157477i
$409$	11.8041	−	8.57616i	0.583674	−	0.424064i	−0.256373	−	0.966578i	$-0.582527\pi$
$409$	11.8041	−	8.57616i	0.583674	−	0.424064i	0.840047	+	0.542514i	$0.182527\pi$
$410$		0			0
$411$	−13.0103	−	9.45254i	−0.641751	−	0.466260i
$412$	6.94095	−	5.04290i	0.341956	−	0.248446i
$413$	0.255119	−	0.185355i	0.0125536	−	0.00912071i
$414$	−7.37660	−	5.35941i	−0.362540	−	0.263401i
$415$		0			0
$416$	2.40211	−	1.74524i	0.117773	−	0.0855673i
$417$	−5.10169	+	15.7014i	−0.249831	+	0.768900i
$418$	5.48746			0.268400
$419$	−4.35926	+	13.4164i	−0.212964	+	0.655434i	0.786328	+	0.617809i	$0.211979\pi$
$419$	−4.35926	+	13.4164i	−0.212964	+	0.655434i	−0.999292	+	0.0376256i	$0.988021\pi$
$420$		0			0
$421$	−3.98266	−	12.2574i	−0.194103	−	0.597388i	−0.999986	−	0.00531260i	$-0.998309\pi$
$421$	−3.98266	−	12.2574i	−0.194103	−	0.597388i	0.805883	−	0.592075i	$-0.201691\pi$
$422$	−0.790700	−	2.43352i	−0.0384907	−	0.118462i
$423$	−4.03884	−	2.93439i	−0.196375	−	0.142675i
$424$	−6.85108			−0.332718
$425$		0			0
$426$	11.3618			0.550479
$427$	−7.19536	−	5.22774i	−0.348208	−	0.252988i
$428$	2.81105	+	8.65151i	0.135877	+	0.418186i
$429$	−2.24102	−	6.89716i	−0.108198	−	0.332998i
$430$		0			0
$431$	−7.15141	+	22.0098i	−0.344471	+	1.06017i	0.617395	+	0.786653i	$0.288188\pi$
$431$	−7.15141	+	22.0098i	−0.344471	+	1.06017i	−0.961866	+	0.273520i	$0.911812\pi$
$432$	1.00000			0.0481125
$433$	−7.26516	+	22.3599i	−0.349142	+	1.07455i	0.610188	+	0.792257i	$0.291094\pi$
$433$	−7.26516	+	22.3599i	−0.349142	+	1.07455i	−0.959329	+	0.282290i	$0.908906\pi$
$434$	−8.55638	+	6.21658i	−0.410720	+	0.298405i
$435$		0			0
$436$	11.0110	+	7.99994i	0.527330	+	0.383128i
$437$	16.5729	−	12.0409i	0.792791	−	0.575996i
$438$	−5.44095	+	3.95309i	−0.259979	+	0.188886i
$439$	−1.61188	−	1.17110i	−0.0769309	−	0.0558936i	0.548655	−	0.836049i	$-0.315140\pi$
$439$	−1.61188	−	1.17110i	−0.0769309	−	0.0558936i	−0.625586	+	0.780155i	$0.715140\pi$
$440$		0			0
$441$	3.25148	−	2.36234i	0.154832	−	0.112492i
$442$	3.06873	−	9.44459i	0.145965	−	0.449233i
$443$	−13.0327			−0.619202			−0.309601	−	0.950867i	$-0.600195\pi$
$443$	−13.0327			−0.619202			−0.309601	+	0.950867i	$0.600195\pi$
$444$	−1.02015	+	3.13969i	−0.0484140	+	0.149003i
$445$		0			0
$446$	−5.76449	−	17.7413i	−0.272956	−	0.840073i
$447$	6.34490	+	19.5276i	0.300103	+	0.923623i
$448$	−1.39680	−	1.01484i	−0.0659927	−	0.0479465i
$449$	12.0846			0.570310			0.285155	−	0.958481i	$-0.407955\pi$
$449$	12.0846			0.570310			0.285155	+	0.958481i	$0.407955\pi$
$450$		0			0
$451$	14.9663			0.704737
$452$	6.68863	+	4.85958i	0.314607	+	0.228575i
$453$	0.861564	+	2.65162i	0.0404798	+	0.124584i
$454$	3.41820	+	10.5201i	0.160424	+	0.493735i
$455$		0			0
$456$	−0.694265	+	2.13673i	−0.0325119	+	0.100061i
$457$	5.62762			0.263249			0.131624	−	0.991300i	$-0.457981\pi$
$457$	5.62762			0.263249			0.131624	+	0.991300i	$0.457981\pi$
$458$	−8.35868	+	25.7254i	−0.390575	+	1.20207i
$459$	2.70582	−	1.96589i	0.126297	−	0.0917600i
$460$		0			0
$461$	3.74321	+	2.71960i	0.174339	+	0.126664i	0.671533	−	0.740975i	$-0.265636\pi$
$461$	3.74321	+	2.71960i	0.174339	+	0.126664i	−0.497194	+	0.867639i	$0.665636\pi$
$462$	−3.41164	+	2.47870i	−0.158724	+	0.115320i
$463$	4.65923	−	3.38513i	0.216533	−	0.157320i	−0.474232	−	0.880400i	$-0.657274\pi$
$463$	4.65923	−	3.38513i	0.216533	−	0.157320i	0.690764	+	0.723080i	$0.257274\pi$
$464$	7.58773	+	5.51281i	0.352251	+	0.255926i
$465$		0			0
$466$	14.7867	−	10.7432i	0.684982	−	0.497669i
$467$	−7.59619	+	23.3787i	−0.351510	+	1.08184i	0.606496	+	0.795087i	$0.292575\pi$
$467$	−7.59619	+	23.3787i	−0.351510	+	1.08184i	−0.958006	+	0.286749i	$0.907425\pi$
$468$	2.96917			0.137250
$469$	6.34386	−	19.5244i	0.292932	−	0.901553i
$470$		0			0
$471$	−4.43179	−	13.6396i	−0.204206	−	0.628481i
$472$	0.0564404	+	0.173706i	0.00259788	+	0.00799545i
$473$	−13.9702	−	10.1500i	−0.642351	−	0.466695i
$474$	11.3571			0.521647
$475$		0			0
$476$	−5.77455			−0.264676
$477$	−5.54264	−	4.02697i	−0.253780	−	0.184382i
$478$	0.793604	+	2.44246i	0.0362986	+	0.111716i
$479$	−1.80512	−	5.55560i	−0.0824782	−	0.253842i	0.901310	−	0.433174i	$-0.142606\pi$
$479$	−1.80512	−	5.55560i	−0.0824782	−	0.253842i	−0.983789	+	0.179332i	$0.942606\pi$
$480$		0			0
$481$	−3.02900	+	9.32229i	−0.138110	+	0.425060i
$482$	−13.3394			−0.607592
$483$	−4.86472	+	14.9721i	−0.221353	+	0.681253i
$484$	4.07289	−	2.95913i	0.185131	−	0.134506i
$485$		0			0
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	4.12901	−	2.99990i	0.187103	−	0.135939i	−0.490290	−	0.871559i	$-0.663109\pi$
$487$	4.12901	−	2.99990i	0.187103	−	0.135939i	0.677394	+	0.735621i	$0.263109\pi$
$488$	4.16750	−	3.02786i	0.188654	−	0.137065i
$489$	−4.77575	−	3.46979i	−0.215967	−	0.156909i
$490$		0			0
$491$	−31.6198	+	22.9731i	−1.42698	+	1.03676i	−0.436412	+	0.899747i	$0.643751\pi$
$491$	−31.6198	+	22.9731i	−1.42698	+	1.03676i	−0.990569	+	0.137015i	$0.956249\pi$
$492$	−1.89352	+	5.82766i	−0.0853665	+	0.262731i
$493$	31.3686			1.41277
$494$	−2.06140	+	6.34432i	−0.0927465	+	0.285445i
$495$		0			0
$496$	−1.89294	−	5.82588i	−0.0849957	−	0.261590i
$497$	−6.06185	−	18.6565i	−0.271911	−	0.836857i
$498$	7.39378	+	5.37190i	0.331323	+	0.240721i
$499$	−12.0527			−0.539553			−0.269777	−	0.962923i	$-0.586950\pi$
$499$	−12.0527			−0.539553			−0.269777	+	0.962923i	$0.586950\pi$
$500$		0			0
$501$	8.94427			0.399601
$502$	−11.6020	−	8.42938i	−0.517825	−	0.376222i
$503$	−3.05342	−	9.39747i	−0.136145	−	0.419012i	0.859621	−	0.510932i	$-0.170700\pi$
$503$	−3.05342	−	9.39747i	−0.136145	−	0.419012i	−0.995766	+	0.0919197i	$0.970700\pi$
$504$	−0.533531	−	1.64204i	−0.0237654	−	0.0731423i
$505$		0			0
$506$	−6.88191	+	21.1803i	−0.305938	+	0.941581i
$507$	−4.18400			−0.185818
$508$	5.50441	−	16.9408i	0.244219	−	0.751628i
$509$	−16.1886	+	11.7617i	−0.717546	+	0.521328i	−0.885599	−	0.464450i	$-0.846252\pi$
$509$	−16.1886	+	11.7617i	−0.717546	+	0.521328i	0.168053	+	0.985778i	$0.446252\pi$
$510$		0			0
$511$	9.39404	+	6.82517i	0.415568	+	0.301928i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−1.81761	+	1.32057i	−0.0802494	+	0.0583046i
$514$	−12.9451	−	9.40518i	−0.570984	−	0.414844i
$515$		0			0
$516$	5.71972	−	4.15562i	0.251797	−	0.182941i
$517$	−3.76799	+	11.5967i	−0.165716	+	0.510021i
$518$	5.69977			0.250434
$519$	−8.00822	+	24.6468i	−0.351522	+	1.08187i
$520$		0			0
$521$	3.33077	+	10.2511i	0.145924	+	0.449107i	0.997129	−	0.0757262i	$-0.0241275\pi$
$521$	3.33077	+	10.2511i	0.145924	+	0.449107i	−0.851205	+	0.524834i	$0.824128\pi$
$522$	2.89825	+	8.91991i	0.126853	+	0.390414i
$523$	21.4025	+	15.5498i	0.935865	+	0.679945i	0.947422	−	0.319988i	$-0.103679\pi$
$523$	21.4025	+	15.5498i	0.935865	+	0.679945i	−0.0115570	+	0.999933i	$0.503679\pi$
$524$	10.3375			0.451596
$525$		0			0
$526$	−19.8584			−0.865866
$527$	−16.5750	−	12.0425i	−0.722019	−	0.524578i
$528$	−0.754763	−	2.32292i	−0.0328468	−	0.101092i
$529$	18.5835	+	57.1942i	0.807979	+	2.48670i
$530$		0			0
$531$	−0.0564404	+	0.173706i	−0.00244930	+	0.00753818i
$532$	3.87901			0.168176
$533$	−5.62219	+	17.3033i	−0.243524	+	0.749490i
$534$	−6.56674	+	4.77102i	−0.284171	+	0.206462i
$535$		0			0
$536$	9.61949	+	6.98897i	0.415499	+	0.301877i
$537$	−0.0388418	+	0.0282202i	−0.00167615	+	0.00121779i
$538$	−2.15266	+	1.56400i	−0.0928078	+	0.0674288i
$539$	−7.94162	−	5.76993i	−0.342070	−	0.248528i
$540$		0			0
$541$	22.7282	−	16.5130i	0.977161	−	0.709949i	0.0200887	−	0.999798i	$-0.493605\pi$
$541$	22.7282	−	16.5130i	0.977161	−	0.709949i	0.957072	+	0.289849i	$0.0936051\pi$
$542$	4.15958	−	12.8019i	0.178669	−	0.549888i
$543$	20.5347			0.881229
$544$	1.03353	−	3.18088i	0.0443123	−	0.136379i
$545$		0			0
$546$	−1.58415	−	4.87550i	−0.0677952	−	0.208652i
$547$	−2.27977	−	7.01640i	−0.0974758	−	0.300000i	0.890415	−	0.455149i	$-0.150414\pi$
$547$	−2.27977	−	7.01640i	−0.0974758	−	0.300000i	−0.987891	+	0.155150i	$0.950414\pi$
$548$	−13.0103	−	9.45254i	−0.555773	−	0.403793i
$549$	5.15131			0.219853
$550$		0			0
$551$	−21.0716			−0.897680
$552$	−7.37660	−	5.35941i	−0.313969	−	0.228112i
$553$	−6.05934	−	18.6487i	−0.257670	−	0.793025i
$554$	−1.65246	−	5.08576i	−0.0702064	−	0.216073i
$555$		0			0
$556$	−5.10169	+	15.7014i	−0.216360	+	0.665887i
$557$	−17.2189			−0.729587			−0.364794	−	0.931088i	$-0.618860\pi$
$557$	−17.2189			−0.729587			−0.364794	+	0.931088i	$0.618860\pi$
$558$	1.89294	−	5.82588i	0.0801347	−	0.246629i
$559$	16.9829	−	12.3388i	0.718298	−	0.521874i
$560$		0			0
$561$	−6.60886	−	4.80162i	−0.279026	−	0.202725i
$562$	−13.5243	+	9.82598i	−0.570488	+	0.414484i
$563$	0.161402	−	0.117265i	0.00680228	−	0.00494214i	−0.584379	−	0.811481i	$-0.698662\pi$
$563$	0.161402	−	0.117265i	0.00680228	−	0.00494214i	0.591181	+	0.806539i	$0.298662\pi$
$564$	−4.03884	−	2.93439i	−0.170066	−	0.123560i
$565$		0			0
$566$	11.4581	−	8.32479i	0.481619	−	0.349917i
$567$	0.533531	−	1.64204i	0.0224062	−	0.0689592i
$568$	11.3618			0.476729
$569$	−5.82382	+	17.9239i	−0.244147	+	0.751408i	0.751628	+	0.659587i	$0.229269\pi$
$569$	−5.82382	+	17.9239i	−0.244147	+	0.751408i	−0.995776	+	0.0918209i	$0.970731\pi$
$570$		0			0
$571$	5.61672	+	17.2865i	0.235053	+	0.723417i	0.997114	+	0.0759132i	$0.0241872\pi$
$571$	5.61672	+	17.2865i	0.235053	+	0.723417i	−0.762062	+	0.647504i	$0.775813\pi$
$572$	−2.24102	−	6.89716i	−0.0937019	−	0.288385i
$573$	−1.95814	−	1.42267i	−0.0818025	−	0.0594330i
$574$	10.5795			0.441579
$575$		0			0
$576$	1.00000			0.0416667
$577$	−0.307187	−	0.223184i	−0.0127884	−	0.00929129i	0.581373	−	0.813637i	$-0.302516\pi$
$577$	−0.307187	−	0.223184i	−0.0127884	−	0.00929129i	−0.594161	+	0.804346i	$0.702516\pi$
$578$	1.79657	+	5.52926i	0.0747273	+	0.229987i
$579$	−4.13355	−	12.7218i	−0.171784	−	0.528698i
$580$		0			0
$581$	4.87606	−	15.0070i	0.202293	−	0.622594i
$582$	−9.88597			−0.409787
$583$	−5.17094	+	15.9145i	−0.214159	+	0.659112i
$584$	−5.44095	+	3.95309i	−0.225148	+	0.163580i
$585$		0			0
$586$	−10.0839	−	7.32636i	−0.416561	−	0.302649i
$587$	−12.5658	+	9.12959i	−0.518646	+	0.376819i	−0.816094	−	0.577920i	$-0.803865\pi$
$587$	−12.5658	+	9.12959i	−0.518646	+	0.376819i	0.297447	+	0.954738i	$0.403865\pi$
$588$	3.25148	−	2.36234i	0.134089	−	0.0974212i
$589$	11.1341	+	8.08941i	0.458774	+	0.333319i
$590$		0			0
$591$	15.3095	−	11.1230i	0.629748	−	0.457539i
$592$	−1.02015	+	3.13969i	−0.0419278	+	0.129040i
$593$	4.62686			0.190002			0.0950012	−	0.995477i	$-0.469715\pi$
$593$	4.62686			0.190002			0.0950012	+	0.995477i	$0.469715\pi$
$594$	0.754763	−	2.32292i	0.0309683	−	0.0953106i
$595$		0			0
$596$	6.34490	+	19.5276i	0.259897	+	0.799881i
$597$	−7.00802	−	21.5685i	−0.286819	−	0.882738i
$598$	−21.9024	−	15.9130i	−0.895656	−	0.650732i
$599$	28.6517			1.17067			0.585337	−	0.810790i	$-0.300962\pi$
$599$	28.6517			1.17067			0.585337	+	0.810790i	$0.300962\pi$
$600$		0			0
$601$	7.54545			0.307785			0.153893	−	0.988088i	$-0.450819\pi$
$601$	7.54545			0.307785			0.153893	+	0.988088i	$0.450819\pi$
$602$	−9.87535	−	7.17486i	−0.402489	−	0.292425i
$603$	3.67432	+	11.3084i	0.149630	+	0.460513i
$604$	0.861564	+	2.65162i	0.0350565	+	0.107893i
$605$		0			0
$606$	−1.94336	+	5.98105i	−0.0789436	+	0.242964i
$607$	0.971865			0.0394468			0.0197234	−	0.999805i	$-0.493721\pi$
$607$	0.971865			0.0394468			0.0197234	+	0.999805i	$0.493721\pi$
$608$	−0.694265	+	2.13673i	−0.0281562	+	0.0866558i
$609$	13.1005	−	9.51810i	0.530861	−	0.385693i
$610$		0			0
$611$	−11.9920	−	8.71272i	−0.485146	−	0.352479i
$612$	2.70582	−	1.96589i	0.109376	−	0.0794665i
$613$	33.2284	−	24.1418i	1.34208	−	0.975080i	0.342717	−	0.939439i	$-0.388653\pi$
$613$	33.2284	−	24.1418i	1.34208	−	0.975080i	0.999365	−	0.0356409i	$-0.0113473\pi$
$614$	19.4143	+	14.1053i	0.783497	+	0.569244i
$615$		0			0
$616$	−3.41164	+	2.47870i	−0.137459	+	0.0998697i
$617$	2.53661	−	7.80690i	0.102120	−	0.314294i	−0.886924	−	0.461916i	$-0.847162\pi$
$617$	2.53661	−	7.80690i	0.102120	−	0.314294i	0.989044	+	0.147622i	$0.0471620\pi$
$618$	8.57949			0.345118
$619$	14.0919	−	43.3705i	0.566402	−	1.74321i	−0.0973461	−	0.995251i	$-0.531035\pi$
$619$	14.0919	−	43.3705i	0.566402	−	1.74321i	0.663748	−	0.747956i	$-0.268965\pi$
$620$		0			0
$621$	−2.81761	−	8.67171i	−0.113067	−	0.347984i
$622$	4.31359	+	13.2759i	0.172959	+	0.532314i
$623$	11.3378	+	8.23736i	0.454238	+	0.330023i
$624$	2.96917			0.118862
$625$		0			0
$626$	9.62739			0.384788
$627$	4.43945	+	3.22545i	0.177294	+	0.128812i
$628$	−4.43179	−	13.6396i	−0.176847	−	0.544281i
$629$	3.41196	+	10.5009i	0.136044	+	0.418700i
$630$		0			0
$631$	10.5472	−	32.4610i	0.419878	−	1.29225i	−0.487936	−	0.872879i	$-0.662250\pi$
$631$	10.5472	−	32.4610i	0.419878	−	1.29225i	0.907814	−	0.419372i	$-0.137750\pi$
$632$	11.3571			0.451760
$633$	0.790700	−	2.43352i	0.0314275	−	0.0967239i
$634$	0.450068	−	0.326993i	0.0178745	−	0.0129866i
$635$		0			0
$636$	−5.54264	−	4.02697i	−0.219780	−	0.159680i
$637$	9.65421	−	7.01420i	0.382514	−	0.277913i
$638$	18.5328	−	13.4648i	0.733719	−	0.533078i
$639$	9.19186	+	6.67828i	0.363624	+	0.264189i
$640$		0			0
$641$	27.8267	−	20.2173i	1.09909	−	0.798535i	0.118178	−	0.992992i	$-0.462295\pi$
$641$	27.8267	−	20.2173i	1.09909	−	0.798535i	0.980911	+	0.194458i	$0.0622946\pi$
$642$	−2.81105	+	8.65151i	−0.110943	+	0.341448i
$643$	−2.71413			−0.107035			−0.0535173	−	0.998567i	$-0.517043\pi$
$643$	−2.71413			−0.107035			−0.0535173	+	0.998567i	$0.517043\pi$
$644$	−4.86472	+	14.9721i	−0.191697	+	0.589983i
$645$		0			0
$646$	2.32202	+	7.14645i	0.0913588	+	0.281173i
$647$	−8.83917	−	27.2042i	−0.347504	−	1.06951i	−0.960230	−	0.279211i	$-0.909927\pi$
$647$	−8.83917	−	27.2042i	−0.347504	−	1.06951i	0.612726	−	0.790295i	$-0.290073\pi$
$648$	0.809017	+	0.587785i	0.0317812	+	0.0230904i
$649$	0.446104			0.0175111
$650$		0			0
$651$	−10.5763			−0.414517
$652$	−4.77575	−	3.46979i	−0.187033	−	0.135887i
$653$	−10.5937	−	32.6040i	−0.414562	−	1.27589i	−0.912642	−	0.408760i	$-0.865961\pi$
$653$	−10.5937	−	32.6040i	−0.414562	−	1.27589i	0.498079	−	0.867132i	$-0.334039\pi$
$654$	4.20582	+	12.9442i	0.164461	+	0.506158i
$655$		0			0
$656$	−1.89352	+	5.82766i	−0.0739295	+	0.227532i
$657$	−6.72539			−0.262382
$658$	−2.66354	+	8.19753i	−0.103836	+	0.319573i
$659$	−14.9714	+	10.8774i	−0.583203	+	0.423722i	−0.839878	−	0.542776i	$-0.817373\pi$
$659$	−14.9714	+	10.8774i	−0.583203	+	0.423722i	0.256674	+	0.966498i	$0.417373\pi$
$660$		0			0
$661$	−10.7699	−	7.82476i	−0.418899	−	0.304348i	0.358296	−	0.933608i	$-0.383358\pi$
$661$	−10.7699	−	7.82476i	−0.418899	−	0.304348i	−0.777195	+	0.629260i	$0.783358\pi$
$662$	−9.35640	+	6.79782i	−0.363647	+	0.264205i
$663$	8.03405	−	5.83708i	0.312017	−	0.226693i
$664$	7.39378	+	5.37190i	0.286935	+	0.208470i
$665$		0			0
$666$	−2.67078	+	1.94043i	−0.103491	+	0.0751903i
$667$	26.4262	−	81.3315i	1.02323	−	3.14917i
$668$	8.94427			0.346064
$669$	5.76449	−	17.7413i	0.222868	−	0.685917i
$670$		0			0
$671$	−3.88802	−	11.9661i	−0.150095	−	0.461946i
$672$	−0.533531	−	1.64204i	−0.0205814	−	0.0633430i
$673$	−29.0908	−	21.1357i	−1.12137	−	0.814722i	−0.136952	−	0.990578i	$-0.543731\pi$
$673$	−29.0908	−	21.1357i	−1.12137	−	0.814722i	−0.984416	+	0.175856i	$0.943731\pi$
$674$	−29.8767			−1.15081
$675$		0			0
$676$	−4.18400			−0.160923
$677$	4.95116	+	3.59723i	0.190289	+	0.138253i	0.678851	−	0.734276i	$-0.262478\pi$
$677$	4.95116	+	3.59723i	0.190289	+	0.138253i	−0.488562	+	0.872529i	$0.662478\pi$
$678$	2.55483	+	7.86296i	0.0981177	+	0.301975i
$679$	5.27447	+	16.2331i	0.202416	+	0.622971i
$680$		0			0
$681$	−3.41820	+	10.5201i	−0.130986	+	0.403133i
$682$	−14.9618			−0.572916
$683$	−2.28659	+	7.03739i	−0.0874938	+	0.269278i	−0.985225	−	0.171266i	$-0.945214\pi$
$683$	−2.28659	+	7.03739i	−0.0874938	+	0.269278i	0.897731	+	0.440544i	$0.145214\pi$
$684$	−1.81761	+	1.32057i	−0.0694981	+	0.0504933i
$685$		0			0
$686$	−15.3914	−	11.1825i	−0.587648	−	0.426951i
$687$	−21.8833	+	15.8992i	−0.834900	+	0.606590i
$688$	5.71972	−	4.15562i	0.218062	−	0.158432i
$689$	−16.4571	−	11.9568i	−0.626965	−	0.455517i
$690$		0			0
$691$	26.4101	−	19.1880i	1.00469	−	0.729947i	0.0415986	−	0.999134i	$-0.486755\pi$
$691$	26.4101	−	19.1880i	1.00469	−	0.729947i	0.963088	+	0.269187i	$0.0867549\pi$
$692$	−8.00822	+	24.6468i	−0.304427	+	0.936929i
$693$	−4.21702			−0.160191
$694$	1.31230	−	4.03884i	0.0498142	−	0.153312i
$695$		0			0
$696$	2.89825	+	8.91991i	0.109858	+	0.338108i
$697$	6.33302	+	19.4910i	0.239880	+	0.738276i
$698$	−15.6716	−	11.3861i	−0.593177	−	0.430969i
$699$	18.2774			0.691315
$700$		0			0
$701$	15.4733			0.584418			0.292209	−	0.956354i	$-0.405610\pi$
$701$	15.4733			0.584418			0.292209	+	0.956354i	$0.405610\pi$
$702$	2.40211	+	1.74524i	0.0906619	+	0.0658697i
$703$	−2.29195	−	7.05391i	−0.0864427	−	0.266043i
$704$	−0.754763	−	2.32292i	−0.0284462	−	0.0875484i
$705$		0			0
$706$	0.0751761	−	0.231368i	0.00282929	−	0.00870766i
$707$	10.8580			0.408356
$708$	−0.0564404	+	0.173706i	−0.00212116	+	0.00652826i
$709$	−5.10700	+	3.71045i	−0.191797	+	0.139349i	−0.679540	−	0.733639i	$-0.737821\pi$
$709$	−5.10700	+	3.71045i	−0.191797	+	0.139349i	0.487742	+	0.872988i	$0.337821\pi$
$710$		0			0
$711$	9.18806	+	6.67551i	0.344579	+	0.250351i
$712$	−6.56674	+	4.77102i	−0.246099	+	0.178801i
$713$	−45.1868	+	32.8301i	−1.69226	+	1.22950i
$714$	−4.67171	−	3.39420i	−0.174834	−	0.127025i
$715$		0			0
$716$	−0.0388418	+	0.0282202i	−0.00145159	+	0.00105464i
$717$	−0.793604	+	2.44246i	−0.0296377	+	0.0912155i
$718$	−21.0432			−0.785325
$719$	9.20729	−	28.3371i	0.343374	−	1.05680i	−0.619074	−	0.785332i	$-0.712492\pi$
$719$	9.20729	−	28.3371i	0.343374	−	1.05680i	0.962448	−	0.271464i	$-0.0875079\pi$
$720$		0			0
$721$	−4.57742	−	14.0879i	−0.170472	−	0.524660i
$722$	4.31152	+	13.2695i	0.160458	+	0.493840i
$723$	−10.7918	−	7.84068i	−0.401350	−	0.291598i
$724$	20.5347			0.763167
$725$		0			0
$726$	5.03437			0.186843
$727$	−7.83431	−	5.69196i	−0.290559	−	0.211103i	0.432951	−	0.901417i	$-0.357472\pi$
$727$	−7.83431	−	5.69196i	−0.290559	−	0.211103i	−0.723510	+	0.690314i	$0.757472\pi$
$728$	−1.58415	−	4.87550i	−0.0587124	−	0.180698i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	7.30703	−	22.4887i	0.270260	−	0.831776i
$732$	5.15131			0.190398
$733$	−10.7283	+	33.0184i	−0.396260	+	1.21956i	0.531716	+	0.846923i	$0.321548\pi$
$733$	−10.7283	+	33.0184i	−0.396260	+	1.21956i	−0.927976	+	0.372640i	$0.878452\pi$
$734$	−6.33734	+	4.60435i	−0.233916	+	0.169950i
$735$		0			0
$736$	−7.37660	−	5.35941i	−0.271905	−	0.197551i
$737$	23.4952	−	17.0703i	0.865458	−	0.628792i
$738$	−4.95730	+	3.60169i	−0.182481	+	0.132580i
$739$	18.3619	+	13.3407i	0.675454	+	0.490746i	0.871846	−	0.489780i	$-0.162923\pi$
$739$	18.3619	+	13.3407i	0.675454	+	0.490746i	−0.196393	+	0.980525i	$0.562923\pi$
$740$		0			0
$741$	−5.39680	+	3.92101i	−0.198256	+	0.144042i
$742$	−3.65527	+	11.2498i	−0.134189	+	0.412991i
$743$	9.53920			0.349959			0.174980	−	0.984572i	$-0.444014\pi$
$743$	9.53920			0.349959			0.174980	+	0.984572i	$0.444014\pi$
$744$	1.89294	−	5.82588i	0.0693987	−	0.213587i
$745$		0			0
$746$	4.79766	+	14.7657i	0.175655	+	0.540610i
$747$	2.82417	+	8.69192i	0.103331	+	0.318021i
$748$	−6.60886	−	4.80162i	−0.241644	−	0.175565i
$749$	15.7059			0.573881
$750$		0			0
$751$	22.5289			0.822090			0.411045	−	0.911615i	$-0.365164\pi$
$751$	22.5289			0.822090			0.411045	+	0.911615i	$0.365164\pi$
$752$	−4.03884	−	2.93439i	−0.147281	−	0.107006i
$753$	−4.43159	−	13.6390i	−0.161496	−	0.497034i
$754$	8.60542	+	26.4848i	0.313391	+	0.964519i
$755$		0			0
$756$	0.533531	−	1.64204i	0.0194043	−	0.0597204i
$757$	38.3200			1.39276			0.696382	−	0.717672i	$-0.254792\pi$
$757$	38.3200			1.39276			0.696382	+	0.717672i	$0.254792\pi$
$758$	3.35706	−	10.3320i	0.121934	−	0.375274i
$759$	−18.0171	+	13.0902i	−0.653978	+	0.475143i
$760$		0			0
$761$	−16.5112	−	11.9961i	−0.598530	−	0.434857i	0.246827	−	0.969060i	$-0.420612\pi$
$761$	−16.5112	−	11.9961i	−0.598530	−	0.434857i	−0.845357	+	0.534202i	$0.820612\pi$
$762$	14.4107	−	10.4700i	0.522046	−	0.379289i
$763$	19.0109	−	13.8122i	0.688242	−	0.500037i
$764$	−1.95814	−	1.42267i	−0.0708431	−	0.0514705i
$765$		0			0
$766$	−7.76345	+	5.64047i	−0.280505	+	0.203799i
$767$	−0.167581	+	0.515763i	−0.00605101	+	0.0186231i
$768$	1.00000			0.0360844
$769$	−9.28293	+	28.5699i	−0.334751	+	1.03026i	0.632094	+	0.774892i	$0.282196\pi$
$769$	−9.28293	+	28.5699i	−0.334751	+	1.03026i	−0.966845	+	0.255365i	$0.917804\pi$
$770$		0			0
$771$	−4.94459	−	15.2179i	−0.178075	−	0.548059i
$772$	−4.13355	−	12.7218i	−0.148770	−	0.457866i
$773$	−17.5936	−	12.7825i	−0.632796	−	0.459753i	0.224572	−	0.974458i	$-0.427902\pi$
$773$	−17.5936	−	12.7825i	−0.632796	−	0.459753i	−0.857368	+	0.514704i	$0.827902\pi$
$774$	7.06997			0.254125
$775$		0			0
$776$	−9.88597			−0.354886
$777$	4.61121	+	3.35024i	0.165426	+	0.120189i
$778$	−10.7606	−	33.1177i	−0.385786	−	1.18733i
$779$	−4.25415	−	13.0929i	−0.152421	−	0.469103i
$780$		0			0
$781$	8.57543	−	26.3925i	0.306853	−	0.944397i
$782$	−30.4958			−1.09053
$783$	−2.89825	+	8.91991i	−0.103575	+	0.318772i
$784$	3.25148	−	2.36234i	0.116124	−	0.0843692i
$785$		0			0
$786$	8.36321	+	6.07623i	0.298306	+	0.216732i
$787$	−10.6763	+	7.75679i	−0.380569	+	0.276500i	−0.761580	−	0.648071i	$-0.775576\pi$
$787$	−10.6763	+	7.75679i	−0.380569	+	0.276500i	0.381011	+	0.924571i	$0.375576\pi$
$788$	15.3095	−	11.1230i	0.545378	−	0.396240i
$789$	−16.0658	−	11.6725i	−0.571956	−	0.415550i
$790$		0			0
$791$	11.5482	−	8.39027i	0.410607	−	0.298323i
$792$	0.754763	−	2.32292i	0.0268193	−	0.0825414i
$793$	15.2951			0.543146
$794$	−4.94607	+	15.2224i	−0.175529	+	0.540224i
$795$		0			0
$796$	−7.00802	−	21.5685i	−0.248393	−	0.764474i
$797$	−5.15230	−	15.8571i	−0.182504	−	0.561689i	0.817393	−	0.576081i	$-0.195419\pi$
$797$	−5.15230	−	15.8571i	−0.182504	−	0.561689i	−0.999896	+	0.0143921i	$0.995419\pi$
$798$	3.13818	+	2.28002i	0.111090	+	0.0807119i
$799$	−16.6971			−0.590700
$800$		0			0
$801$	−8.11694			−0.286798
$802$	9.32667	+	6.77622i	0.329336	+	0.239277i
$803$	5.07607	+	15.6225i	0.179131	+	0.551308i
$804$	3.67432	+	11.3084i	0.129583	+	0.398816i
$805$		0			0
$806$	5.62048	−	17.2981i	0.197973	−	0.609298i
$807$	−2.66084			−0.0936658
$808$	−1.94336	+	5.98105i	−0.0683672	+	0.210413i
$809$	22.2409	−	16.1590i	0.781949	−	0.568119i	−0.123614	−	0.992330i	$-0.539449\pi$
$809$	22.2409	−	16.1590i	0.781949	−	0.568119i	0.905563	+	0.424211i	$0.139449\pi$
$810$		0			0
$811$	20.9090	+	15.1913i	0.734213	+	0.533437i	0.890894	−	0.454212i	$-0.150079\pi$
$811$	20.9090	+	15.1913i	0.734213	+	0.533437i	−0.156680	+	0.987649i	$0.550079\pi$
$812$	13.1005	−	9.51810i	0.459739	−	0.334020i
$813$	10.8899	−	7.91199i	0.381926	−	0.277486i
$814$	6.52328	+	4.73944i	0.228641	+	0.166117i
$815$		0			0
$816$	2.70582	−	1.96589i	0.0947226	−	0.0688200i
$817$	−4.90843	+	15.1066i	−0.171724	+	0.528513i
$818$	14.5906			0.510150
$819$	1.58415	−	4.87550i	0.0553546	−	0.170364i
$820$		0			0
$821$	−10.0931	−	31.0634i	−0.352252	−	1.08412i	−0.957586	−	0.288149i	$-0.906960\pi$
$821$	−10.0931	−	31.0634i	−0.352252	−	1.08412i	0.605333	−	0.795972i	$-0.293040\pi$
$822$	−4.96950	−	15.2945i	−0.173331	−	0.533458i
$823$	−39.6567	−	28.8122i	−1.38234	−	1.00433i	−0.996657	−	0.0817020i	$-0.973964\pi$
$823$	−39.6567	−	28.8122i	−1.38234	−	1.00433i	−0.385687	−	0.922630i	$-0.626036\pi$
$824$	8.57949			0.298881
$825$		0			0
$826$	0.315344			0.0109722
$827$	−7.66109	−	5.56611i	−0.266402	−	0.193553i	0.446563	−	0.894752i	$-0.352648\pi$
$827$	−7.66109	−	5.56611i	−0.266402	−	0.193553i	−0.712965	+	0.701200i	$0.752648\pi$
$828$	−2.81761	−	8.67171i	−0.0979187	−	0.301363i
$829$	−17.1806	−	52.8765i	−0.596707	−	1.83648i	−0.546039	−	0.837760i	$-0.683865\pi$
$829$	−17.1806	−	52.8765i	−0.596707	−	1.83648i	−0.0506676	−	0.998716i	$-0.516135\pi$
$830$		0			0
$831$	1.65246	−	5.08576i	0.0573233	−	0.176423i
$832$	2.96917			0.102938
$833$	4.15381	−	12.7841i	0.143921	−	0.442944i
$834$	−13.3564	+	9.70399i	−0.462494	+	0.336022i
$835$		0			0
$836$	4.43945	+	3.22545i	0.153541	+	0.111554i
$837$	4.95579	−	3.60059i	0.171297	−	0.124455i
$838$	−11.4127	+	8.29180i	−0.394244	+	0.286435i
$839$	4.96116	+	3.60449i	0.171278	+	0.124441i	0.670122	−	0.742251i	$-0.266242\pi$
$839$	4.96116	+	3.60449i	0.171278	+	0.124441i	−0.498844	+	0.866692i	$0.666242\pi$
$840$		0			0
$841$	−47.7034	+	34.6586i	−1.64495	+	1.19512i
$842$	3.98266	−	12.2574i	0.137252	−	0.422417i
$843$	−16.7170			−0.575763
$844$	0.790700	−	2.43352i	0.0272170	−	0.0837654i
$845$		0			0
$846$	−1.54270	−	4.74794i	−0.0530391	−	0.163238i
$847$	−2.68599	−	8.26664i	−0.0922918	−	0.284045i
$848$	−5.54264	−	4.02697i	−0.190335	−	0.138287i
$849$	14.1630			0.486072
$850$		0			0
$851$	30.1009			1.03184
$852$	9.19186	+	6.67828i	0.314908	+	0.228794i
$853$	9.41798	+	28.9856i	0.322465	+	0.992447i	0.972572	+	0.232603i	$0.0747244\pi$
$853$	9.41798	+	28.9856i	0.322465	+	0.992447i	−0.650106	+	0.759843i	$0.725276\pi$
$854$	−2.74838	−	8.45865i	−0.0940477	−	0.289449i
$855$		0			0
$856$	−2.81105	+	8.65151i	−0.0960796	+	0.295702i
$857$	−7.53137			−0.257267			−0.128633	−	0.991692i	$-0.541059\pi$
$857$	−7.53137			−0.257267			−0.128633	+	0.991692i	$0.541059\pi$
$858$	2.24102	−	6.89716i	0.0765073	−	0.235465i
$859$	−39.9169	+	29.0013i	−1.36195	+	0.989512i	−0.363628	+	0.931544i	$0.618462\pi$
$859$	−39.9169	+	29.0013i	−1.36195	+	0.989512i	−0.998318	+	0.0579677i	$0.981538\pi$
$860$		0			0
$861$	8.55899	+	6.21847i	0.291690	+	0.211925i
$862$	−18.7226	+	13.6028i	−0.637695	+	0.463313i
$863$	25.4736	−	18.5076i	0.867131	−	0.630008i	−0.0626845	−	0.998033i	$-0.519966\pi$
$863$	25.4736	−	18.5076i	0.867131	−	0.630008i	0.929816	+	0.368026i	$0.119966\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$		0			0
$866$	−19.0204	+	13.8192i	−0.646341	+	0.469594i
$867$	−1.79657	+	5.52926i	−0.0610146	+	0.187784i
$868$	−10.5763			−0.358982
$869$	8.57189	−	26.3816i	0.290781	−	0.894933i
$870$		0			0
$871$	10.9097	+	33.5766i	0.369661	+	1.13770i
$872$	4.20582	+	12.9442i	0.142427	+	0.438345i
$873$	−7.99792	−	5.81083i	−0.270688	−	0.196667i
$874$	20.4853			0.692924
$875$		0			0
$876$	−6.72539			−0.227230
$877$	−6.37431	−	4.63120i	−0.215245	−	0.156385i	0.474939	−	0.880019i	$-0.342470\pi$
$877$	−6.37431	−	4.63120i	−0.215245	−	0.156385i	−0.690184	+	0.723634i	$0.742470\pi$
$878$	−0.615684	−	1.89488i	−0.0207783	−	0.0639491i
$879$	−3.85170	−	11.8543i	−0.129914	−	0.399836i
$880$		0			0
$881$	−10.2217	+	31.4592i	−0.344378	+	1.05989i	0.617537	+	0.786542i	$0.288130\pi$
$881$	−10.2217	+	31.4592i	−0.344378	+	1.05989i	−0.961916	+	0.273346i	$0.911870\pi$
$882$	4.01905			0.135328
$883$	−2.41489	+	7.43225i	−0.0812674	+	0.250115i	−0.983432	−	0.181276i	$-0.941977\pi$
$883$	−2.41489	+	7.43225i	−0.0812674	+	0.250115i	0.902165	+	0.431391i	$0.141977\pi$
$884$	8.03405	−	5.83708i	0.270214	−	0.196322i
$885$		0			0
$886$	−10.5437	−	7.66042i	−0.354221	−	0.257357i
$887$	−8.18071	+	5.94363i	−0.274681	+	0.199568i	−0.716594	−	0.697490i	$-0.754300\pi$
$887$	−8.18071	+	5.94363i	−0.274681	+	0.199568i	0.441913	+	0.897058i	$0.354300\pi$
$888$	−2.67078	+	1.94043i	−0.0896255	+	0.0651167i
$889$	−24.8808	−	18.0769i	−0.834474	−	0.606281i
$890$		0			0
$891$	1.97599	−	1.43564i	0.0661983	−	0.0480959i
$892$	5.76449	−	17.7413i	0.193009	−	0.594022i
$893$	11.2161			0.375333
$894$	−6.34490	+	19.5276i	−0.212205	+	0.653100i
$895$		0			0
$896$	−0.533531	−	1.64204i	−0.0178240	−	0.0548567i
$897$	−8.36598	−	25.7478i	−0.279332	−	0.859695i
$898$	9.77668	+	7.10318i	0.326252	+	0.237036i
$899$	57.4526			1.91615
$900$		0			0
$901$	−22.9140			−0.763375
$902$	12.1080	+	8.79699i	0.403153	+	0.292908i
$903$	−3.77205	−	11.6092i	−0.125526	−	0.386329i
$904$	2.55483	+	7.86296i	0.0849724	+	0.261518i
$905$		0			0
$906$	−0.861564	+	2.65162i	−0.0286235	+	0.0880942i
$907$	−10.2207			−0.339373			−0.169686	−	0.985498i	$-0.554275\pi$
$907$	−10.2207			−0.339373			−0.169686	+	0.985498i	$0.554275\pi$
$908$	−3.41820	+	10.5201i	−0.113437	+	0.349123i
$909$	−5.08779	+	3.69649i	−0.168751	+	0.122605i
$910$		0			0
$911$	−34.3471	−	24.9546i	−1.13797	−	0.826784i	−0.151135	−	0.988513i	$-0.548293\pi$
$911$	−34.3471	−	24.9546i	−1.13797	−	0.826784i	−0.986835	+	0.161729i	$0.948293\pi$
$912$	−1.81761	+	1.32057i	−0.0601871	+	0.0437285i
$913$	18.0590	−	13.1207i	0.597667	−	0.434231i
$914$	4.55284	+	3.30783i	0.150594	+	0.109413i
$915$		0			0
$916$	−21.8833	+	15.8992i	−0.723045	+	0.525323i
$917$	5.51538	−	16.9746i	0.182134	−	0.560550i
$918$	3.34458			0.110387
$919$	16.0903	−	49.5209i	0.530770	−	1.63354i	−0.221844	−	0.975082i	$-0.571208\pi$
$919$	16.0903	−	49.5209i	0.530770	−	1.63354i	0.752615	−	0.658461i	$-0.228792\pi$
$920$		0			0
$921$	7.41560	+	22.8229i	0.244352	+	0.752039i
$922$	1.42978	+	4.40041i	0.0470872	+	0.144920i
$923$	27.2922	+	19.8290i	0.898335	+	0.652679i
$924$	−4.21702			−0.138730
$925$		0			0
$926$	5.75912			0.189256
$927$	6.94095	+	5.04290i	0.227971	+	0.165631i
$928$	2.89825	+	8.91991i	0.0951399	+	0.292810i
$929$	8.13402	+	25.0339i	0.266869	+	0.821337i	0.991257	+	0.131945i	$0.0421223\pi$
$929$	8.13402	+	25.0339i	0.266869	+	0.821337i	−0.724388	+	0.689392i	$0.757878\pi$
$930$		0			0
$931$	−2.79029	+	8.58762i	−0.0914480	+	0.281448i
$932$	18.2774			0.598696
$933$	−4.31359	+	13.2759i	−0.141221	+	0.434633i
$934$	−19.8871	+	14.4488i	−0.650726	+	0.472780i
$935$		0			0
$936$	2.40211	+	1.74524i	0.0785155	+	0.0570449i
$937$	8.14485	−	5.91758i	0.266081	−	0.193319i	−0.446743	−	0.894662i	$-0.647416\pi$
$937$	8.14485	−	5.91758i	0.266081	−	0.193319i	0.712823	+	0.701343i	$0.247416\pi$
$938$	16.6085	−	12.0667i	0.542285	−	0.393993i
$939$	7.78872	+	5.65884i	0.254175	+	0.184669i
$940$		0			0
$941$	−8.08466	+	5.87385i	−0.263552	+	0.191482i	−0.711712	−	0.702472i	$-0.752080\pi$
$941$	−8.08466	+	5.87385i	−0.263552	+	0.191482i	0.448159	+	0.893954i	$0.352080\pi$
$942$	4.43179	−	13.6396i	0.144395	−	0.444403i
$943$	55.8709			1.81941
$944$	−0.0564404	+	0.173706i	−0.00183698	+	0.00565364i
$945$		0			0
$946$	−5.33615	−	16.4230i	−0.173493	−	0.533957i
$947$	17.1336	+	52.7319i	0.556768	+	1.71356i	0.691228	+	0.722637i	$0.257070\pi$
$947$	17.1336	+	52.7319i	0.556768	+	1.71356i	−0.134460	+	0.990919i	$0.542930\pi$
$948$	9.18806	+	6.67551i	0.298414	+	0.216811i
$949$	−19.9689			−0.648217
$950$		0			0
$951$	0.556314			0.0180397
$952$	−4.67171	−	3.39420i	−0.151411	−	0.110007i
$953$	3.74063	+	11.5125i	0.121171	+	0.372925i	0.993184	−	0.116557i	$-0.0371858\pi$
$953$	3.74063	+	11.5125i	0.121171	+	0.372925i	−0.872013	+	0.489482i	$0.837186\pi$
$954$	−2.11710	−	6.51577i	−0.0685437	−	0.210956i
$955$		0			0
$956$	−0.793604	+	2.44246i	−0.0256670	+	0.0789949i
$957$	22.9077			0.740502
$958$	1.80512	−	5.55560i	0.0583209	−	0.179493i
$959$	−22.4629	+	16.3202i	−0.725363	+	0.527007i
$960$		0			0
$961$	−5.27814	−	3.83479i	−0.170262	−	0.123703i
$962$	−7.93001	+	5.76149i	−0.255674	+	0.185758i
$963$	−7.35941	+	5.34693i	−0.237154	+	0.172302i
$964$	−10.7918	−	7.84068i	−0.347580	−	0.252531i
$965$		0			0
$966$	−12.7360	+	9.25325i	−0.409774	+	0.297719i
$967$	0.900961	−	2.77287i	0.0289729	−	0.0891695i	−0.935524	−	0.353262i	$-0.885072\pi$
$967$	0.900961	−	2.77287i	0.0289729	−	0.0891695i	0.964497	+	0.264092i	$0.0850724\pi$
$968$	5.03437			0.161811
$969$	−2.32202	+	7.14645i	−0.0745941	+	0.229577i
$970$		0			0
$971$	3.50206	+	10.7782i	0.112387	+	0.345890i	0.991393	−	0.130920i	$-0.0417930\pi$
$971$	3.50206	+	10.7782i	0.112387	+	0.345890i	−0.879006	+	0.476810i	$0.841793\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	23.0604	+	16.7544i	0.739282	+	0.537120i
$974$	5.10374			0.163534
$975$		0			0
$976$	5.15131			0.164889
$977$	−3.88577	−	2.82318i	−0.124317	−	0.0903214i	0.523889	−	0.851786i	$-0.324481\pi$
$977$	−3.88577	−	2.82318i	−0.124317	−	0.0903214i	−0.648206	+	0.761465i	$0.724481\pi$
$978$	−1.82417	−	5.61423i	−0.0583307	−	0.179523i
$979$	6.12636	+	18.8550i	0.195799	+	0.602609i
$980$		0			0
$981$	−4.20582	+	12.9442i	−0.134281	+	0.413276i
$982$	−39.0842			−1.24723
$983$	−2.39810	+	7.38058i	−0.0764874	+	0.235404i	−0.981989	−	0.188939i	$-0.939495\pi$
$983$	−2.39810	+	7.38058i	−0.0764874	+	0.235404i	0.905501	+	0.424343i	$0.139495\pi$
$984$	−4.95730	+	3.60169i	−0.158033	+	0.114818i
$985$		0			0
$986$	25.3777	+	18.4380i	0.808192	+	0.587186i
$987$	−6.97323	+	5.06635i	−0.221960	+	0.161264i
$988$	−5.39680	+	3.92101i	−0.171695	+	0.124744i
$989$	−52.1523	−	37.8909i	−1.65835	−	1.20486i
$990$		0			0
$991$	36.2536	−	26.3398i	1.15163	−	0.836711i	0.162937	−	0.986636i	$-0.447903\pi$
$991$	36.2536	−	26.3398i	1.15163	−	0.836711i	0.988697	+	0.149925i	$0.0479033\pi$
$992$	1.89294	−	5.82588i	0.0601010	−	0.184972i
$993$	−11.5651			−0.367009
$994$	6.06185	−	18.6565i	0.192270	−	0.591747i
$995$		0			0
$996$	2.82417	+	8.69192i	0.0894874	+	0.275414i
$997$	1.23356	+	3.79651i	0.0390673	+	0.120237i	0.968688	−	0.248281i	$-0.0798655\pi$
$997$	1.23356	+	3.79651i	0.0390673	+	0.120237i	−0.929621	+	0.368517i	$0.879866\pi$
$998$	−9.75085	−	7.08441i	−0.308658	−	0.224253i
$999$	−3.30127			−0.104447

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.g.e.451.2		8
5.2	odd	4		750.2.h.c.49.1		8
5.3	odd	4		150.2.h.a.109.2	✓	8
5.4	even	2		750.2.g.c.451.1		8
15.8	even	4		450.2.l.a.109.1		8
25.2	odd	20		150.2.h.a.139.2	yes	8
25.6	even	5		3750.2.a.m.1.3		4
25.8	odd	20		3750.2.c.e.1249.6		8
25.11	even	5	inner	750.2.g.e.301.2		8
25.14	even	10		750.2.g.c.301.1		8
25.17	odd	20		3750.2.c.e.1249.3		8
25.19	even	10		3750.2.a.o.1.2		4
25.23	odd	20		750.2.h.c.199.1		8
75.2	even	20		450.2.l.a.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.a.109.2	✓	8	5.3	odd	4
150.2.h.a.139.2	yes	8	25.2	odd	20
450.2.l.a.109.1		8	15.8	even	4
450.2.l.a.289.1		8	75.2	even	20
750.2.g.c.301.1		8	25.14	even	10
750.2.g.c.451.1		8	5.4	even	2
750.2.g.e.301.2		8	25.11	even	5	inner
750.2.g.e.451.2		8	1.1	even	1	trivial
750.2.h.c.49.1		8	5.2	odd	4
750.2.h.c.199.1		8	25.23	odd	20
3750.2.a.m.1.3		4	25.6	even	5
3750.2.a.o.1.2		4	25.19	even	10
3750.2.c.e.1249.3		8	25.17	odd	20
3750.2.c.e.1249.6		8	25.8	odd	20

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	750.2.g.e.451.2

Level	$750$
Weight	$2$
Character	750.451
Analytic conductor	$5.989$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$