LMFDB - Embedded newform 605.2.s.b.416.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(16,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(110))

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("605.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.s (of order $55$, degree $40$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$880$
Relative dimension:	$22$ over $\Q(\zeta_{55})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{55}]$

Embedding invariants

Embedding label			416.4
Character	$\chi$	$=$	605.416
Dual form			605.2.s.b.16.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80070 + 0.206611i) q^{2} +(-1.29126 + 0.938155i) q^{3} +(1.25182 - 0.291098i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(2.13134 - 1.95613i) q^{6} +(-0.0685099 + 0.0704951i) q^{7} +(1.22021 - 0.435369i) q^{8} +(-0.139834 + 0.430365i) q^{9} +O(q^{10})$	\(q+(-1.80070 + 0.206611i) q^{2} +(-1.29126 + 0.938155i) q^{3} +(1.25182 - 0.291098i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(2.13134 - 1.95613i) q^{6} +(-0.0685099 + 0.0704951i) q^{7} +(1.22021 - 0.435369i) q^{8} +(-0.139834 + 0.430365i) q^{9} +(1.18695 + 1.36981i) q^{10} +(-0.376086 + 3.29523i) q^{11} +(-1.34333 + 1.55029i) q^{12} +(-2.20746 - 3.66065i) q^{13} +(0.108801 - 0.141096i) q^{14} +(1.50326 + 0.536363i) q^{15} +(-4.41399 + 2.17021i) q^{16} +(-3.22476 - 2.63687i) q^{17} +(0.162881 - 0.803851i) q^{18} +(-0.263287 + 0.0150553i) q^{19} +(-0.946875 - 0.869034i) q^{20} +(0.0223288 - 0.155300i) q^{21} +(-0.00361276 - 6.01144i) q^{22} +(0.379754 + 2.64125i) q^{23} +(-1.16716 + 1.70692i) q^{24} +(-0.362808 + 0.931864i) q^{25} +(4.73131 + 6.13567i) q^{26} +(-1.70284 - 5.24080i) q^{27} +(-0.0652411 + 0.108190i) q^{28} +(-0.892183 - 2.29155i) q^{29} +(-2.81775 - 0.655240i) q^{30} +(5.76378 - 2.43580i) q^{31} +(5.32012 - 3.41903i) q^{32} +(-2.60581 - 4.60783i) q^{33} +(6.35164 + 4.08195i) q^{34} +(0.0968617 + 0.0167626i) q^{35} +(-0.0497686 + 0.579445i) q^{36} +(-0.824959 - 9.60482i) q^{37} +(0.470990 - 0.0815081i) q^{38} +(6.28466 + 2.65592i) q^{39} +(-1.04812 - 0.761505i) q^{40} +(5.23917 + 2.95869i) q^{41} +(-0.00812075 + 0.284263i) q^{42} +(4.86190 + 1.42758i) q^{43} +(0.488444 + 4.23452i) q^{44} +(0.434182 - 0.127487i) q^{45} +(-1.22954 - 4.67764i) q^{46} +(2.13115 + 10.5176i) q^{47} +(3.66361 - 6.94331i) q^{48} +(0.199616 + 6.98749i) q^{49} +(0.460775 - 1.75297i) q^{50} +(6.63779 + 0.379563i) q^{51} +(-3.82895 - 3.93989i) q^{52} +(6.05615 + 2.97761i) q^{53} +(4.14912 + 9.08530i) q^{54} +(2.93240 - 1.54952i) q^{55} +(-0.0529049 + 0.115846i) q^{56} +(0.325847 - 0.266444i) q^{57} +(2.08002 + 3.94207i) q^{58} +(4.92121 - 2.77914i) q^{59} +(2.03795 + 0.233833i) q^{60} +(7.14248 + 0.819523i) q^{61} +(-9.87560 + 5.57701i) q^{62} +(-0.0207586 - 0.0393419i) q^{63} +(-1.25808 + 1.02873i) q^{64} +(-1.77578 + 3.88842i) q^{65} +(5.64433 + 7.75894i) q^{66} +(-6.40855 - 14.0328i) q^{67} +(-4.80440 - 2.36217i) q^{68} +(-2.96826 - 3.05427i) q^{69} +(-0.177882 - 0.0101717i) q^{70} +(2.93646 - 11.1715i) q^{71} +(0.0167411 + 0.586014i) q^{72} +(4.39767 - 8.33451i) q^{73} +(3.46997 + 17.1250i) q^{74} +(-0.405754 - 1.54365i) q^{75} +(-0.325205 + 0.0954888i) q^{76} +(-0.206532 - 0.252268i) q^{77} +(-11.8656 - 3.48404i) q^{78} +(0.439528 - 15.3855i) q^{79} +(4.28289 + 2.41866i) q^{80} +(6.01722 + 4.37177i) q^{81} +(-10.0455 - 4.24526i) q^{82} +(14.7312 - 2.54934i) q^{83} +(-0.0172560 - 0.200908i) q^{84} +(-0.356470 + 4.15031i) q^{85} +(-9.04979 - 1.56613i) q^{86} +(3.30187 + 2.12199i) q^{87} +(0.975739 + 4.18460i) q^{88} +(-8.67057 + 5.57224i) q^{89} +(-0.755493 + 0.319274i) q^{90} +(0.409291 + 0.0951765i) q^{91} +(1.24425 + 3.19582i) q^{92} +(-5.15739 + 8.55257i) q^{93} +(-6.01062 - 18.4988i) q^{94} +(0.161038 + 0.208838i) q^{95} +(-3.66207 + 9.40596i) q^{96} +(4.94458 - 7.23122i) q^{97} +(-1.80314 - 12.5411i) q^{98} +(-1.36556 - 0.622640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9}+O(q^{10}) $ 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9	\( 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9} - 6 q^{10} + 5 q^{11} - 5 q^{12} - 26 q^{13} - 108 q^{14} - 12 q^{15} + 34 q^{16} - q^{17} - 14 q^{18} + q^{19} + 19 q^{20} - 10 q^{21} + 275 q^{22} - 51 q^{23} + 283 q^{24} + 22 q^{25} - 16 q^{27} - 4 q^{28} - 19 q^{29} + q^{30} - 34 q^{31} - 122 q^{32} + 19 q^{33} + 52 q^{34} + 8 q^{35} - 21 q^{36} - 109 q^{37} - 10 q^{38} - 9 q^{39} - 64 q^{40} + 4 q^{41} - 49 q^{42} - 97 q^{43} + 17 q^{44} - 80 q^{45} - 91 q^{46} + 166 q^{47} - 159 q^{48} + 175 q^{49} + 4 q^{50} - 112 q^{51} - 128 q^{52} - 141 q^{53} - 37 q^{54} - 5 q^{55} + 79 q^{56} - 204 q^{57} - 190 q^{58} + 9 q^{59} - 22 q^{60} + 2 q^{61} - 105 q^{62} - q^{63} - 176 q^{64} - 14 q^{65} - 112 q^{66} - 13 q^{67} - 35 q^{68} - 53 q^{69} + 24 q^{70} - 50 q^{71} + 705 q^{72} + q^{73} + 40 q^{74} - q^{75} - 148 q^{76} - 104 q^{77} - 187 q^{78} - 83 q^{79} - q^{80} - 238 q^{81} - 54 q^{82} - 151 q^{83} + 4 q^{84} - 29 q^{85} - 39 q^{86} - 74 q^{87} - 143 q^{88} - 52 q^{89} - 28 q^{90} - 188 q^{91} - 253 q^{92} + 122 q^{93} - 187 q^{94} + 122 q^{95} - 155 q^{96} + 283 q^{97} - 92 q^{98} + 172 q^{99}+O(q^{100}) \) 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9 - 6 * q^10 + 5 * q^11 - 5 * q^12 - 26 * q^13 - 108 * q^14 - 12 * q^15 + 34 * q^16 - q^17 - 14 * q^18 + q^19 + 19 * q^20 - 10 * q^21 + 275 * q^22 - 51 * q^23 + 283 * q^24 + 22 * q^25 - 16 * q^27 - 4 * q^28 - 19 * q^29 + q^30 - 34 * q^31 - 122 * q^32 + 19 * q^33 + 52 * q^34 + 8 * q^35 - 21 * q^36 - 109 * q^37 - 10 * q^38 - 9 * q^39 - 64 * q^40 + 4 * q^41 - 49 * q^42 - 97 * q^43 + 17 * q^44 - 80 * q^45 - 91 * q^46 + 166 * q^47 - 159 * q^48 + 175 * q^49 + 4 * q^50 - 112 * q^51 - 128 * q^52 - 141 * q^53 - 37 * q^54 - 5 * q^55 + 79 * q^56 - 204 * q^57 - 190 * q^58 + 9 * q^59 - 22 * q^60 + 2 * q^61 - 105 * q^62 - q^63 - 176 * q^64 - 14 * q^65 - 112 * q^66 - 13 * q^67 - 35 * q^68 - 53 * q^69 + 24 * q^70 - 50 * q^71 + 705 * q^72 + q^73 + 40 * q^74 - q^75 - 148 * q^76 - 104 * q^77 - 187 * q^78 - 83 * q^79 - q^80 - 238 * q^81 - 54 * q^82 - 151 * q^83 + 4 * q^84 - 29 * q^85 - 39 * q^86 - 74 * q^87 - 143 * q^88 - 52 * q^89 - 28 * q^90 - 188 * q^91 - 253 * q^92 + 122 * q^93 - 187 * q^94 + 122 * q^95 - 155 * q^96 + 283 * q^97 - 92 * q^98 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{53}{55}\right)$

Coefficient data

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

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

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

$2$	−1.80070	+	0.206611i	−1.27329	+	0.146096i	−0.724155	−	0.689637i	$-0.757770\pi$
$2$	−1.80070	+	0.206611i	−1.27329	+	0.146096i	−0.549135	+	0.835734i	$0.685043\pi$
$3$	−1.29126	+	0.938155i	−0.745509	+	0.541644i	−0.894432	−	0.447205i	$-0.852420\pi$
$3$	−1.29126	+	0.938155i	−0.745509	+	0.541644i	0.148922	+	0.988849i	$0.452420\pi$
$4$	1.25182	−	0.291098i	0.625910	−	0.145549i
$5$	−0.564443	−	0.825472i	−0.252427	−	0.369162i
$5$	−0.564443	−	0.825472i	−0.252427	−	0.369162i
$6$	2.13134	−	1.95613i	0.870117	−	0.798586i
$7$	−0.0685099	+	0.0704951i	−0.0258943	+	0.0266446i	−0.729955	−	0.683495i	$-0.760459\pi$
$7$	−0.0685099	+	0.0704951i	−0.0258943	+	0.0266446i	0.704061	+	0.710140i	$0.251368\pi$
$8$	1.22021	−	0.435369i	0.431408	−	0.153926i
$9$	−0.139834	+	0.430365i	−0.0466113	+	0.143455i
$10$	1.18695	+	1.36981i	0.375346	+	0.433172i
$11$	−0.376086	+	3.29523i	−0.113394	+	0.993550i
$11$	−0.376086	+	3.29523i	−0.113394	+	0.993550i
$12$	−1.34333	+	1.55029i	−0.387786	+	0.447529i
$13$	−2.20746	−	3.66065i	−0.612238	−	1.01528i	−0.995781	−	0.0917599i	$-0.970751\pi$
$13$	−2.20746	−	3.66065i	−0.612238	−	1.01528i	0.383543	−	0.923523i	$-0.374704\pi$
$14$	0.108801	−	0.141096i	0.0290783	−	0.0377094i
$15$	1.50326	+	0.536363i	0.388141	+	0.138488i
$16$	−4.41399	+	2.17021i	−1.10350	+	0.542553i
$17$	−3.22476	−	2.63687i	−0.782118	−	0.639535i	0.155250	−	0.987875i	$-0.450382\pi$
$17$	−3.22476	−	2.63687i	−0.782118	−	0.639535i	−0.937368	+	0.348340i	$0.886745\pi$
$18$	0.162881	−	0.803851i	0.0383915	−	0.189469i
$19$	−0.263287	+	0.0150553i	−0.0604021	+	0.00345392i	−0.0872637	−	0.996185i	$-0.527812\pi$
$19$	−0.263287	+	0.0150553i	−0.0604021	+	0.00345392i	0.0268616	+	0.999639i	$0.491449\pi$
$20$	−0.946875	−	0.869034i	−0.211728	−	0.194322i
$21$	0.0223288	−	0.155300i	0.00487255	−	0.0338893i
$22$	−0.00361276	−	6.01144i	−0.000770243	−	1.28164i
$23$	0.379754	+	2.64125i	0.0791842	+	0.550738i	0.990338	+	0.138673i	$0.0442835\pi$
$23$	0.379754	+	2.64125i	0.0791842	+	0.550738i	−0.911154	+	0.412066i	$0.864807\pi$
$24$	−1.16716	+	1.70692i	−0.238246	+	0.348423i
$25$	−0.362808	+	0.931864i	−0.0725615	+	0.186373i
$26$	4.73131	+	6.13567i	0.927886	+	1.20330i
$27$	−1.70284	−	5.24080i	−0.327712	−	1.00859i
$28$	−0.0652411	+	0.108190i	−0.0123294	+	0.0204460i
$29$	−0.892183	−	2.29155i	−0.165674	−	0.425531i	0.824412	−	0.565990i	$-0.191506\pi$
$29$	−0.892183	−	2.29155i	−0.165674	−	0.425531i	−0.990087	+	0.140459i	$0.955142\pi$
$30$	−2.81775	−	0.655240i	−0.514449	−	0.119630i
$31$	5.76378	−	2.43580i	1.03521	−	0.437482i	0.195604	−	0.980683i	$-0.437333\pi$
$31$	5.76378	−	2.43580i	1.03521	−	0.437482i	0.839603	+	0.543201i	$0.182788\pi$
$32$	5.32012	−	3.41903i	0.940473	−	0.604405i
$33$	−2.60581	−	4.60783i	−0.453614	−	0.802120i
$34$	6.35164	+	4.08195i	1.08930	+	0.700049i
$35$	0.0968617	+	0.0167626i	0.0163726	+	0.00283339i
$36$	−0.0497686	+	0.579445i	−0.00829476	+	0.0965741i
$37$	−0.824959	−	9.60482i	−0.135622	−	1.57902i	−0.675552	−	0.737312i	$-0.736095\pi$
$37$	−0.824959	−	9.60482i	−0.135622	−	1.57902i	0.539930	−	0.841710i	$-0.318451\pi$
$38$	0.470990	−	0.0815081i	0.0764047	−	0.0132224i
$39$	6.28466	+	2.65592i	1.00635	+	0.425288i
$40$	−1.04812	−	0.761505i	−0.165723	−	0.120405i
$41$	5.23917	+	2.95869i	0.818220	+	0.462070i	0.843189	−	0.537618i	$-0.180676\pi$
$41$	5.23917	+	2.95869i	0.818220	+	0.462070i	−0.0249682	+	0.999688i	$0.507948\pi$
$42$	−0.00812075	+	0.284263i	−0.00125306	+	0.0438628i
$43$	4.86190	+	1.42758i	0.741433	+	0.217704i	0.630571	−	0.776132i	$-0.282821\pi$
$43$	4.86190	+	1.42758i	0.741433	+	0.217704i	0.110862	+	0.993836i	$0.464639\pi$
$44$	0.488444	+	4.23452i	0.0736357	+	0.638377i
$45$	0.434182	−	0.127487i	0.0647241	−	0.0190047i
$46$	−1.22954	−	4.67764i	−0.181285	−	0.689681i
$47$	2.13115	+	10.5176i	0.310860	+	1.53415i	0.765475	+	0.643465i	$0.222504\pi$
$47$	2.13115	+	10.5176i	0.310860	+	1.53415i	−0.454616	+	0.890688i	$0.650223\pi$
$48$	3.66361	−	6.94331i	0.528797	−	1.00218i
$49$	0.199616	+	6.98749i	0.0285166	+	0.998212i
$50$	0.460775	−	1.75297i	0.0651635	−	0.247908i
$51$	6.63779	+	0.379563i	0.929477	+	0.0531494i
$52$	−3.82895	−	3.93989i	−0.530980	−	0.546365i
$53$	6.05615	+	2.97761i	0.831876	+	0.409006i	0.806904	−	0.590682i	$-0.201141\pi$
$53$	6.05615	+	2.97761i	0.831876	+	0.409006i	0.0249715	+	0.999688i	$0.492051\pi$
$54$	4.14912	+	9.08530i	0.564623	+	1.23635i
$55$	2.93240	−	1.54952i	0.395405	−	0.208938i
$56$	−0.0529049	+	0.115846i	−0.00706972	+	0.0154805i
$57$	0.325847	−	0.266444i	0.0431595	−	0.0352914i
$58$	2.08002	+	3.94207i	0.273120	+	0.517620i
$59$	4.92121	−	2.77914i	0.640687	−	0.361813i	−0.136902	−	0.990585i	$-0.543715\pi$
$59$	4.92121	−	2.77914i	0.640687	−	0.361813i	0.777590	+	0.628772i	$0.216442\pi$
$60$	2.03795	+	0.233833i	0.263098	+	0.0301877i
$61$	7.14248	+	0.819523i	0.914500	+	0.104929i	0.558450	−	0.829538i	$-0.311396\pi$
$61$	7.14248	+	0.819523i	0.914500	+	0.104929i	0.356050	+	0.934467i	$0.384123\pi$
$62$	−9.87560	+	5.57701i	−1.25420	+	0.708281i
$63$	−0.0207586	−	0.0393419i	−0.00261533	−	0.00495661i
$64$	−1.25808	+	1.02873i	−0.157260	+	0.128591i
$65$	−1.77578	+	3.88842i	−0.220259	+	0.482300i
$66$	5.64433	+	7.75894i	0.694769	+	0.955060i
$67$	−6.40855	−	14.0328i	−0.782929	−	1.71437i	−0.695866	−	0.718172i	$-0.744979\pi$
$67$	−6.40855	−	14.0328i	−0.782929	−	1.71437i	−0.0870630	−	0.996203i	$-0.527748\pi$
$68$	−4.80440	−	2.36217i	−0.582620	−	0.286455i
$69$	−2.96826	−	3.05427i	−0.357337	−	0.367691i
$70$	−0.177882	−	0.0101717i	−0.0212610	−	0.00121575i
$71$	2.93646	−	11.1715i	0.348494	−	1.32581i	−0.529976	−	0.848012i	$-0.677799\pi$
$71$	2.93646	−	11.1715i	0.348494	−	1.32581i	0.878470	−	0.477797i	$-0.158564\pi$
$72$	0.0167411	+	0.586014i	0.00197295	+	0.0690624i
$73$	4.39767	−	8.33451i	0.514708	−	0.975480i	−0.480434	−	0.877031i	$-0.659521\pi$
$73$	4.39767	−	8.33451i	0.514708	−	0.975480i	0.995142	−	0.0984493i	$-0.0313882\pi$
$74$	3.46997	+	17.1250i	0.403376	+	1.99074i
$75$	−0.405754	−	1.54365i	−0.0468524	−	0.178245i
$76$	−0.325205	+	0.0954888i	−0.0373036	+	0.0109533i
$77$	−0.206532	−	0.252268i	−0.0235365	−	0.0287487i
$78$	−11.8656	−	3.48404i	−1.34351	−	0.394490i
$79$	0.439528	−	15.3855i	0.0494508	−	1.73100i	−0.475366	−	0.879788i	$-0.657684\pi$
$79$	0.439528	−	15.3855i	0.0494508	−	1.73100i	0.524817	−	0.851215i	$-0.324134\pi$
$80$	4.28289	+	2.41866i	0.478842	+	0.270415i
$81$	6.01722	+	4.37177i	0.668580	+	0.485752i
$82$	−10.0455	−	4.24526i	−1.10934	−	0.468810i
$83$	14.7312	−	2.54934i	1.61696	−	0.279826i	0.711002	−	0.703190i	$-0.248242\pi$
$83$	14.7312	−	2.54934i	1.61696	−	0.279826i	0.905960	+	0.423364i	$0.139151\pi$
$84$	−0.0172560	−	0.200908i	−0.00188278	−	0.0219209i
$85$	−0.356470	+	4.15031i	−0.0386646	+	0.450164i
$86$	−9.04979	−	1.56613i	−0.975864	−	0.168880i
$87$	3.30187	+	2.12199i	0.353998	+	0.227501i
$88$	0.975739	+	4.18460i	0.104014	+	0.446080i
$89$	−8.67057	+	5.57224i	−0.919079	+	0.590656i	−0.912390	−	0.409322i	$-0.865765\pi$
$89$	−8.67057	+	5.57224i	−0.919079	+	0.590656i	−0.00668857	+	0.999978i	$0.502129\pi$
$90$	−0.755493	+	0.319274i	−0.0796360	+	0.0336545i
$91$	0.409291	+	0.0951765i	0.0429053	+	0.00997721i
$92$	1.24425	+	3.19582i	0.129722	+	0.333187i
$93$	−5.15739	+	8.55257i	−0.534796	+	0.886860i
$94$	−6.01062	−	18.4988i	−0.619948	−	1.90801i
$95$	0.161038	+	0.208838i	0.0165222	+	0.0214263i
$96$	−3.66207	+	9.40596i	−0.373759	+	0.959992i
$97$	4.94458	−	7.23122i	0.502046	−	0.734219i	−0.488324	−	0.872662i	$-0.662392\pi$
$97$	4.94458	−	7.23122i	0.502046	−	0.734219i	0.990370	+	0.138443i	$0.0442099\pi$
$98$	−1.80314	−	12.5411i	−0.182145	−	1.26685i
$99$	−1.36556	−	0.622640i	−0.137244	−	0.0625777i
$100$	−0.182906	+	1.27214i	−0.0182906	+	0.127214i
$101$	0.208736	+	0.191576i	0.0207700	+	0.0190625i	0.686493	−	0.727137i	$-0.259149\pi$
$101$	0.208736	+	0.191576i	0.0207700	+	0.0190625i	−0.665723	+	0.746199i	$0.731877\pi$
$102$	−12.0311	+	0.687964i	−1.19126	+	0.0681186i
$103$	−1.83204	+	9.04149i	−0.180517	+	0.890884i	0.782750	+	0.622337i	$0.213816\pi$
$103$	−1.83204	+	9.04149i	−0.180517	+	0.890884i	−0.963266	+	0.268548i	$0.913456\pi$
$104$	−4.28729	−	3.50570i	−0.420403	−	0.343762i
$105$	−0.140799	+	0.0692264i	−0.0137406	+	0.00675581i
$106$	−11.5205	−	4.11052i	−1.11897	−	0.399249i
$107$	−2.08371	+	2.70220i	−0.201439	+	0.261231i	−0.881776	−	0.471669i	$-0.843652\pi$
$107$	−2.08371	+	2.70220i	−0.201439	+	0.261231i	0.680336	+	0.732900i	$0.261834\pi$
$108$	−3.65724	−	6.06485i	−0.351918	−	0.583590i
$109$	7.17490	−	8.28028i	0.687231	−	0.793107i	−0.299737	−	0.954022i	$-0.596899\pi$
$109$	7.17490	−	8.28028i	0.687231	−	0.793107i	0.986968	+	0.160915i	$0.0514445\pi$
$110$	−4.96024	+	3.39610i	−0.472940	+	0.323805i
$111$	10.0760	+	11.6284i	0.956376	+	1.10372i
$112$	0.149413	−	0.459845i	0.0141182	−	0.0434513i
$113$	−7.80481	+	2.78475i	−0.734215	+	0.261967i	−0.676579	−	0.736370i	$-0.736538\pi$
$113$	−7.80481	+	2.78475i	−0.734215	+	0.261967i	−0.0576362	+	0.998338i	$0.518356\pi$
$114$	−0.531704	+	0.547110i	−0.0497986	+	0.0512416i
$115$	1.96593	−	1.80431i	0.183324	−	0.168253i
$116$	−1.78392	−	2.60890i	−0.165633	−	0.242230i
$117$	1.88409	−	0.438127i	0.174185	−	0.0405049i
$118$	−8.28744	+	6.02118i	−0.762921	+	0.554295i
$119$	0.406814	−	0.0466776i	0.0372926	−	0.00427893i
$120$	2.06781			0.188764
$121$	−10.7171	−	2.47858i	−0.974283	−	0.225326i
$122$	−13.0308			−1.17975
$123$	−9.54084	+	1.09471i	−0.860269	+	0.0987066i
$124$	6.50617	−	4.72701i	0.584271	−	0.424498i
$125$	0.974012	−	0.226497i	0.0871183	−	0.0202585i
$126$	0.0455085	+	0.0665541i	0.00405422	+	0.00592911i
$127$	0.448785	−	0.411891i	0.0398232	−	0.0365494i	−0.656016	−	0.754747i	$-0.727760\pi$
$127$	0.448785	−	0.411891i	0.0398232	−	0.0365494i	0.695840	+	0.718197i	$0.255032\pi$
$128$	−6.76203	+	6.95797i	−0.597685	+	0.615003i
$129$	−7.61727	+	2.71784i	−0.670663	+	0.239292i
$130$	2.39427	−	7.36880i	0.209991	−	0.646286i
$131$	8.76183	+	10.1117i	0.765525	+	0.883463i	0.995976	−	0.0896213i	$-0.0285657\pi$
$131$	8.76183	+	10.1117i	0.765525	+	0.883463i	−0.230451	+	0.973084i	$0.574020\pi$
$132$	−4.60334	−	5.00963i	−0.400670	−	0.436032i
$133$	0.0169764	−	0.0195918i	0.00147204	−	0.00169883i
$134$	14.4392	+	23.9448i	1.24736	+	2.06851i
$135$	−3.36498	+	4.36378i	−0.289611	+	0.375574i
$136$	−5.08288	−	1.81357i	−0.435853	−	0.155512i
$137$	−17.9084	+	8.80497i	−1.53002	+	0.752259i	−0.995666	−	0.0930033i	$-0.970353\pi$
$137$	−17.9084	+	8.80497i	−1.53002	+	0.752259i	−0.534352	+	0.845262i	$0.679444\pi$
$138$	5.97601	+	4.88656i	0.508712	+	0.415971i
$139$	1.76518	−	8.71151i	0.149721	−	0.738901i	−0.832922	−	0.553391i	$-0.813334\pi$
$139$	1.76518	−	8.71151i	0.149721	−	0.738901i	0.982642	−	0.185510i	$-0.0593937\pi$
$140$	0.126133	−	0.00721254i	0.0106602	−	0.000609571i
$141$	−12.6190	−	11.5816i	−1.06271	−	0.975350i
$142$	−2.97955	+	20.7232i	−0.250038	+	1.73905i
$143$	12.8929	−	5.89736i	1.07816	−	0.493162i
$144$	−0.316757	−	2.20309i	−0.0263964	−	0.183591i
$145$	−1.38803	+	2.02992i	−0.115269	+	0.168576i
$146$	−6.19689	+	15.9166i	−0.512858	+	1.31727i
$147$	−6.81310	−	8.83539i	−0.561935	−	0.728731i
$148$	−3.82865	−	11.7834i	−0.314713	−	0.968586i
$149$	3.59950	−	5.96910i	0.294883	−	0.489008i	−0.673261	−	0.739405i	$-0.735107\pi$
$149$	3.59950	−	5.96910i	0.294883	−	0.489008i	0.968143	+	0.250397i	$0.0805613\pi$
$150$	1.04958	+	2.69582i	0.0856977	+	0.220113i
$151$	6.99438	+	1.62647i	0.569195	+	0.132361i	0.501210	−	0.865326i	$-0.332889\pi$
$151$	6.99438	+	1.62647i	0.569195	+	0.132361i	0.0679848	+	0.997686i	$0.478343\pi$
$152$	−0.314709	+	0.132997i	−0.0255263	+	0.0107875i
$153$	1.58575	−	1.01910i	0.128200	−	0.0823892i
$154$	0.424024	+	0.411589i	0.0341689	+	0.0331668i
$155$	−5.26401	−	3.38297i	−0.422815	−	0.271727i
$156$	8.64040	+	1.49528i	0.691786	+	0.119718i
$157$	−0.619479	+	7.21246i	−0.0494398	+	0.575617i	0.929137	+	0.369735i	$0.120552\pi$
$157$	−0.619479	+	7.21246i	−0.0494398	+	0.575617i	−0.978577	+	0.205882i	$0.933994\pi$
$158$	2.38736	+	27.7955i	0.189928	+	2.21129i
$159$	−10.6135	+	1.83674i	−0.841707	+	0.145663i
$160$	−5.82522	−	2.46176i	−0.460524	−	0.194619i
$161$	−0.212212	−	0.154181i	−0.0167246	−	0.0121512i
$162$	−11.7385	−	6.62903i	−0.922263	−	0.520826i
$163$	−0.149437	+	5.23098i	−0.0117048	+	0.409722i	0.972522	+	0.232811i	$0.0747923\pi$
$163$	−0.149437	+	5.23098i	−0.0117048	+	0.409722i	−0.984227	+	0.176911i	$0.943389\pi$
$164$	7.41976	+	2.17864i	0.579386	+	0.170123i
$165$	−2.33280	+	4.75188i	−0.181608	+	0.369934i
$166$	−25.9998	+	7.63424i	−2.01798	+	0.592532i
$167$	−6.51061	−	24.7689i	−0.503806	−	1.91668i	−0.382130	−	0.924108i	$-0.624809\pi$
$167$	−6.51061	−	24.7689i	−0.503806	−	1.91668i	−0.121676	−	0.992570i	$-0.538827\pi$
$168$	−0.0403672	−	0.199220i	−0.00311440	−	0.0153701i
$169$	−2.46086	+	4.66384i	−0.189297	+	0.358757i
$170$	−0.215604	−	7.54713i	−0.0165361	−	0.578838i
$171$	0.0303372	−	0.115415i	0.00231994	−	0.00882597i
$172$	6.50179	+	0.371786i	0.495757	+	0.0283484i
$173$	14.6135	+	15.0369i	1.11104	+	1.14324i	0.988569	+	0.150766i	$0.0481741\pi$
$173$	14.6135	+	15.0369i	1.11104	+	1.14324i	0.122475	+	0.992472i	$0.460917\pi$
$174$	−6.38412	−	3.13886i	−0.483979	−	0.237957i
$175$	−0.0408359	−	0.0894181i	−0.00308690	−	0.00675937i
$176$	−5.49131	−	15.3613i	−0.413923	−	1.15790i
$177$	−3.74730	+	8.20545i	−0.281665	+	0.616760i
$178$	14.4618	−	11.8254i	1.08396	−	0.886350i
$179$	−6.99269	−	13.2526i	−0.522658	−	0.990548i	−0.994081	−	0.108640i	$-0.965350\pi$
$179$	−6.99269	−	13.2526i	−0.522658	−	0.990548i	0.471423	−	0.881907i	$-0.343741\pi$
$180$	0.506407	−	0.285981i	0.0377453	−	0.0213158i
$181$	−0.638744	−	0.0732890i	−0.0474775	−	0.00544753i	0.0902201	−	0.995922i	$-0.471243\pi$
$181$	−0.638744	−	0.0732890i	−0.0474775	−	0.00544753i	−0.137698	+	0.990474i	$0.543970\pi$
$182$	−0.756676	−	0.0868205i	−0.0560885	−	0.00643556i
$183$	−9.99163	+	5.64253i	−0.738603	+	0.417108i
$184$	1.61330	+	3.05754i	0.118934	+	0.225405i
$185$	−7.46287	+	6.10236i	−0.548681	+	0.448654i
$186$	7.51987	−	16.4662i	0.551384	−	1.20736i
$187$	9.90189	−	9.63463i	0.724098	−	0.704554i
$188$	5.72947	+	12.5458i	0.417865	+	0.914996i
$189$	0.486112	+	0.239005i	0.0353594	+	0.0173851i
$190$	−0.333130	−	0.342783i	−0.0241678	−	0.0248681i
$191$	−8.66844	−	0.495679i	−0.627226	−	0.0358661i	−0.259414	−	0.965766i	$-0.583529\pi$
$191$	−8.66844	−	0.495679i	−0.627226	−	0.0358661i	−0.367812	+	0.929900i	$0.619893\pi$
$192$	0.659404	−	2.50863i	0.0475884	−	0.181045i
$193$	−0.271233	−	9.49441i	−0.0195238	−	0.683423i	−0.949133	−	0.314876i	$-0.898037\pi$
$193$	−0.271233	−	9.49441i	−0.0195238	−	0.683423i	0.929609	−	0.368547i	$-0.120145\pi$
$194$	−7.40967	+	14.0429i	−0.531983	+	1.00822i
$195$	−1.35495	−	6.68693i	−0.0970298	−	0.478861i
$196$	2.28393	+	8.68897i	0.163138	+	0.620641i
$197$	−2.97086	+	0.872323i	−0.211665	+	0.0621504i	−0.385846	−	0.922563i	$-0.626090\pi$
$197$	−2.97086	+	0.872323i	−0.211665	+	0.0621504i	0.174181	+	0.984714i	$0.444272\pi$
$198$	2.58762	+	0.839049i	0.183894	+	0.0596286i
$199$	8.73506	+	2.56484i	0.619212	+	0.181817i	0.576268	−	0.817261i	$-0.304508\pi$
$199$	8.73506	+	2.56484i	0.619212	+	0.181817i	0.0429433	+	0.999078i	$0.486327\pi$
$200$	−0.0369958	+	1.29502i	−0.00261600	+	0.0915719i
$201$	21.4400	+	12.1077i	1.51226	+	0.854013i
$202$	−0.415453	−	0.301844i	−0.0292312	−	0.0212377i
$203$	0.222667	+	0.0940997i	0.0156281	+	0.00660451i
$204$	8.41981	−	1.45711i	0.589505	−	0.102018i
$205$	−0.514894	−	5.99480i	−0.0359617	−	0.418695i
$206$	1.43089	−	16.6596i	0.0996949	−	1.16073i
$207$	−1.18980	−	0.205904i	−0.0826970	−	0.0143113i
$208$	17.6881	+	11.3674i	1.22645	+	0.788190i
$209$	0.0494079	−	0.873253i	0.00341761	−	0.0604041i
$210$	0.239235	−	0.153747i	0.0165088	−	0.0106096i
$211$	−5.55155	+	2.34610i	−0.382184	+	0.161512i	−0.571893	−	0.820328i	$-0.693791\pi$
$211$	−5.55155	+	2.34610i	−0.382184	+	0.161512i	0.189709	+	0.981840i	$0.439245\pi$
$212$	8.44798	+	1.96449i	0.580210	+	0.134922i
$213$	6.68883	+	17.1801i	0.458311	+	1.17716i
$214$	3.19383	−	5.29637i	0.218326	−	0.362053i
$215$	−1.56584	−	4.81915i	−0.106789	−	0.328663i
$216$	−4.35950	−	5.65350i	−0.296626	−	0.384672i
$217$	−0.223165	+	0.573195i	−0.0151494	+	0.0389110i
$218$	−11.2091	+	16.3927i	−0.759174	+	1.11026i
$219$	2.14053	+	14.8877i	0.144644	+	1.00602i
$220$	3.21978	−	2.79334i	0.217077	−	0.188327i
$221$	−2.53416	+	17.6255i	−0.170466	+	1.18562i
$222$	−20.5465	−	18.8574i	−1.37899	−	1.26563i
$223$	6.06223	−	0.346651i	0.405957	−	0.0232135i	0.147082	−	0.989124i	$-0.453012\pi$
$223$	6.06223	−	0.346651i	0.405957	−	0.0232135i	0.258875	+	0.965911i	$0.416648\pi$
$224$	−0.123456	+	0.609280i	−0.00824876	+	0.0407092i
$225$	−0.350309	−	0.286446i	−0.0233539	−	0.0190964i
$226$	13.4788	−	6.62707i	0.896596	−	0.440826i
$227$	20.6334	+	7.36199i	1.36949	+	0.488632i	0.915479	−	0.402365i	$-0.131812\pi$
$227$	20.6334	+	7.36199i	1.36949	+	0.488632i	0.454009	+	0.890997i	$0.349993\pi$
$228$	0.330341	−	0.428393i	0.0218773	−	0.0283710i
$229$	−3.94933	−	6.54923i	−0.260979	−	0.432785i	0.698068	−	0.716031i	$-0.254043\pi$
$229$	−3.94933	−	6.54923i	−0.260979	−	0.432785i	−0.959047	+	0.283246i	$0.908589\pi$
$230$	−3.16726	+	3.65521i	−0.208843	+	0.241018i
$231$	0.503353	+	0.131985i	0.0331182	+	0.00868398i
$232$	−2.08632	−	2.40774i	−0.136974	−	0.158076i
$233$	6.11746	−	18.8276i	0.400768	−	1.23344i	−0.523610	−	0.851958i	$-0.675415\pi$
$233$	6.11746	−	18.8276i	0.400768	−	1.23344i	0.924378	−	0.381478i	$-0.124585\pi$
$234$	−3.30217	+	1.17821i	−0.215870	+	0.0770222i
$235$	7.47909	−	7.69580i	0.487882	−	0.502019i
$236$	5.35147	−	4.91154i	0.348351	−	0.319714i
$237$	13.8664	+	20.2790i	0.900722	+	1.31726i
$238$	−0.722908	+	0.168105i	−0.0468591	+	0.0108966i
$239$	−1.92707	+	1.40010i	−0.124652	+	0.0905651i	−0.648364	−	0.761330i	$-0.724547\pi$
$239$	−1.92707	+	1.40010i	−0.124652	+	0.0905651i	0.523712	+	0.851895i	$0.324547\pi$
$240$	−7.79941	+	0.894899i	−0.503450	+	0.0577655i
$241$	−21.6560			−1.39498			−0.697492	−	0.716593i	$-0.745701\pi$
$241$	−21.6560			−1.39498			−0.697492	+	0.716593i	$0.745701\pi$
$242$	19.8105	+	2.24892i	1.27346	+	0.144566i
$243$	4.66032			0.298959
$244$	9.17966	−	1.05327i	0.587667	−	0.0674285i
$245$	5.65530	−	4.10882i	0.361304	−	0.262503i
$246$	16.9540	−	3.94249i	1.08095	−	0.251364i
$247$	0.636306	+	0.930567i	0.0404872	+	0.0592106i
$248$	5.97254	−	5.48155i	0.379257	−	0.348079i
$249$	−16.6302	+	17.1120i	−1.05389	+	1.08443i
$250$	−1.70711	+	0.609095i	−0.107967	+	0.0385226i
$251$	6.49148	−	19.9787i	0.409738	−	1.26104i	−0.507135	−	0.861867i	$-0.669295\pi$
$251$	6.49148	−	19.9787i	0.409738	−	1.26104i	0.916873	−	0.399178i	$-0.130705\pi$
$252$	−0.0374384	−	0.0432062i	−0.00235840	−	0.00272173i
$253$	−8.84635	+	0.258041i	−0.556165	+	0.0162229i
$254$	−0.723027	+	0.834417i	−0.0453667	+	0.0523560i
$255$	−3.43334	−	5.69355i	−0.215004	−	0.356544i
$256$	12.7236	−	16.5002i	0.795224	−	1.03127i
$257$	−13.8058	−	4.92591i	−0.861183	−	0.307270i	−0.131718	−	0.991287i	$-0.542049\pi$
$257$	−13.8058	−	4.92591i	−0.861183	−	0.307270i	−0.729465	+	0.684018i	$0.760231\pi$
$258$	13.1549	−	6.46783i	0.818989	−	0.402670i
$259$	0.733610	+	0.599870i	0.0455843	+	0.0372741i
$260$	−1.09105	+	5.38454i	−0.0676640	+	0.333935i
$261$	1.11096	−	0.0635271i	0.0687668	−	0.00393223i
$262$	−17.8666	−	16.3979i	−1.10381	−	1.01306i
$263$	0.371273	−	2.58226i	0.0228937	−	0.159229i	−0.975168	−	0.221468i	$-0.928915\pi$
$263$	0.371273	−	2.58226i	0.0228937	−	0.159229i	0.998061	+	0.0622392i	$0.0198242\pi$
$264$	−5.18574	−	4.48801i	−0.319160	−	0.276218i
$265$	−0.960420	−	6.67987i	−0.0589981	−	0.410341i
$266$	−0.0265216	+	0.0387866i	−0.00162614	+	0.00237816i
$267$	5.96834	−	15.3296i	0.365256	−	0.938153i
$268$	−12.1073	−	15.7010i	−0.739569	−	0.959090i
$269$	4.60780	+	14.1814i	0.280943	+	0.864653i	0.987585	+	0.157082i	$0.0502089\pi$
$269$	4.60780	+	14.1814i	0.280943	+	0.864653i	−0.706643	+	0.707571i	$0.749791\pi$
$270$	5.15772	−	8.55312i	0.313889	−	0.520526i
$271$	2.76886	+	7.11176i	0.168196	+	0.432009i	0.990582	−	0.136922i	$-0.0437209\pi$
$271$	2.76886	+	7.11176i	0.168196	+	0.432009i	−0.822386	+	0.568931i	$0.807357\pi$
$272$	19.9566	+	4.64071i	1.21005	+	0.281384i
$273$	−0.617791	+	0.261081i	−0.0373904	+	0.0158013i
$274$	30.4285	−	19.5552i	1.83825	−	1.18137i
$275$	−2.93426	−	1.54600i	−0.176943	−	0.0932271i
$276$	−4.60482	−	2.95934i	−0.277178	−	0.178131i
$277$	13.0231	+	2.25373i	0.782482	+	0.135414i	0.547745	−	0.836645i	$-0.315486\pi$
$277$	13.0231	+	2.25373i	0.782482	+	0.135414i	0.234737	+	0.972059i	$0.424577\pi$
$278$	−1.37867	+	16.0516i	−0.0826871	+	0.962708i
$279$	0.242308	+	2.82114i	0.0145066	+	0.168897i
$280$	0.125489	−	0.0217168i	0.00749941	−	0.00129782i
$281$	−3.49462	−	1.47684i	−0.208472	−	0.0881009i	0.282534	−	0.959257i	$-0.408825\pi$
$281$	−3.49462	−	1.47684i	−0.208472	−	0.0881009i	−0.491006	+	0.871156i	$0.663371\pi$
$282$	25.1160	+	18.2479i	1.49564	+	1.08664i
$283$	8.58845	+	4.85012i	0.510531	+	0.288310i	0.725394	−	0.688334i	$-0.241658\pi$
$283$	8.58845	+	4.85012i	0.510531	+	0.288310i	−0.214863	+	0.976644i	$0.568931\pi$
$284$	0.423929	−	14.8395i	0.0251556	−	0.880560i
$285$	−0.403864	−	0.118585i	−0.0239229	−	0.00702438i
$286$	−21.9978	+	13.2832i	−1.30076	+	0.785453i
$287$	−0.567508	+	0.166635i	−0.0334990	+	0.00983618i
$288$	0.727498	+	2.76769i	0.0428682	+	0.163088i
$289$	0.0699314	+	0.345125i	0.00411361	+	0.0203015i
$290$	2.08002	−	3.94207i	0.122143	−	0.231487i
$291$	0.399267	+	13.9762i	0.0234054	+	0.819297i
$292$	3.07893	−	11.7135i	0.180181	−	0.685478i
$293$	−15.2227	−	0.870467i	−0.889321	−	0.0508532i	−0.393547	−	0.919305i	$-0.628752\pi$
$293$	−15.2227	−	0.870467i	−0.889321	−	0.0508532i	−0.495774	+	0.868451i	$0.665116\pi$
$294$	14.0939	+	14.5023i	0.821971	+	0.845788i
$295$	−5.07185	−	2.49366i	−0.295294	−	0.145186i
$296$	−5.18826	−	11.3607i	−0.301562	−	0.660328i
$297$	17.9101	−	3.64026i	1.03925	−	0.211229i
$298$	−5.24835	+	11.4923i	−0.304029	+	0.665730i
$299$	8.83041	−	7.22059i	0.510676	−	0.417577i
$300$	−0.957285	−	1.81426i	−0.0552689	−	0.104746i
$301$	−0.433726	+	0.244936i	−0.0249995	+	0.0141179i
$302$	−12.9309	−	1.48368i	−0.744087	−	0.0853760i
$303$	−0.449260	−	0.0515478i	−0.0258093	−	0.00296134i
$304$	1.12947	−	0.637841i	0.0647796	−	0.0365827i
$305$	−3.35503	−	6.35849i	−0.192108	−	0.364086i
$306$	−2.64490	+	2.16273i	−0.151199	+	0.123635i
$307$	3.41970	−	7.48811i	0.195173	−	0.427369i	−0.786591	−	0.617475i	$-0.788156\pi$
$307$	3.41970	−	7.48811i	0.195173	−	0.427369i	0.981764	+	0.190106i	$0.0608831\pi$
$308$	−0.331976	−	0.255674i	−0.0189161	−	0.0145684i
$309$	−6.11668	−	13.3937i	−0.347966	−	0.761938i
$310$	10.1779	+	5.00413i	0.578065	+	0.284215i
$311$	10.3644	+	10.6647i	0.587712	+	0.604741i	0.944125	−	0.329587i	$-0.106910\pi$
$311$	10.3644	+	10.6647i	0.587712	+	0.604741i	−0.356414	+	0.934328i	$0.616001\pi$
$312$	8.82489	+	0.504626i	0.499611	+	0.0285688i
$313$	−0.100331	+	0.381699i	−0.00567105	+	0.0215749i	−0.969922	−	0.243415i	$-0.921732\pi$
$313$	−0.100331	+	0.381699i	−0.00567105	+	0.0215749i	0.964251	+	0.264990i	$0.0853687\pi$
$314$	−0.374680	−	13.1155i	−0.0211444	−	0.740150i
$315$	−0.0207586	+	0.0393419i	−0.00116961	+	0.00221666i
$316$	−3.92848	−	19.3878i	−0.220994	−	1.09065i
$317$	−3.81430	−	14.5111i	−0.214232	−	0.815025i	−0.984218	−	0.176963i	$-0.943373\pi$
$317$	−3.81430	−	14.5111i	−0.214232	−	0.815025i	0.769985	−	0.638062i	$-0.220264\pi$
$318$	18.7323	−	5.50030i	1.05046	−	0.308441i
$319$	7.88674	−	2.07813i	0.441573	−	0.116353i
$320$	1.55930	+	0.457853i	0.0871677	+	0.0255948i
$321$	0.155525	−	5.44408i	0.00868055	−	0.303859i
$322$	0.413986	+	0.233789i	0.0230706	+	0.0130285i
$323$	0.888734	+	0.645703i	0.0494505	+	0.0359279i
$324$	8.80509	+	3.72106i	0.489172	+	0.206726i
$325$	4.21211	−	0.728935i	0.233646	−	0.0404340i
$326$	−0.811689	−	9.45032i	−0.0449553	−	0.523405i
$327$	−1.49648	+	17.4232i	−0.0827553	+	0.963503i
$328$	7.68099	+	1.32925i	0.424112	+	0.0733954i
$329$	−0.887445	−	0.570326i	−0.0489264	−	0.0314431i
$330$	3.21889	−	9.03872i	0.177194	−	0.497565i
$331$	9.18509	−	5.90290i	0.504858	−	0.324453i	−0.263299	−	0.964714i	$-0.584810\pi$
$331$	9.18509	−	5.90290i	0.504858	−	0.324453i	0.768157	+	0.640262i	$0.221174\pi$
$332$	17.6987	−	7.47954i	0.971344	−	0.410493i
$333$	4.24893	+	0.988047i	0.232840	+	0.0541447i
$334$	16.8412	+	43.2563i	0.921511	+	2.36688i
$335$	−7.96639	+	13.2108i	−0.435250	+	0.721782i
$336$	0.238476	+	0.733952i	0.0130099	+	0.0400404i
$337$	5.26945	+	6.83354i	0.287045	+	0.372247i	0.913241	−	0.407419i	$-0.133571\pi$
$337$	5.26945	+	6.83354i	0.287045	+	0.372247i	−0.626196	+	0.779665i	$0.715389\pi$
$338$	3.46767	−	8.90663i	0.188616	−	0.484457i
$339$	7.46551	−	10.9180i	0.405471	−	0.592982i
$340$	0.761911	+	5.29921i	0.0413204	+	0.287390i
$341$	5.85883	+	19.9091i	0.317274	+	1.07814i
$342$	−0.0307823	+	0.214095i	−0.00166451	+	0.0115769i
$343$	−1.01322	−	0.929923i	−0.0547086	−	0.0502111i
$344$	6.55405	−	0.374774i	0.353371	−	0.0202065i
$345$	−0.845798	+	4.17418i	−0.0455363	+	0.224730i
$346$	−29.4214	−	24.0578i	−1.58170	−	1.29335i
$347$	−27.1666	+	13.3569i	−1.45838	+	0.717038i	−0.986368	−	0.164554i	$-0.947381\pi$
$347$	−27.1666	+	13.3569i	−1.45838	+	0.717038i	−0.472013	+	0.881592i	$0.656472\pi$
$348$	4.75106	+	1.69517i	0.254684	+	0.0908709i
$349$	−6.06433	+	7.86436i	−0.324616	+	0.420970i	−0.925725	−	0.378198i	$-0.876544\pi$
$349$	−6.06433	+	7.86436i	−0.324616	+	0.420970i	0.601109	+	0.799167i	$0.294726\pi$
$350$	0.0920081	+	0.152578i	0.00491804	+	0.00815565i
$351$	−15.4258	+	17.8023i	−0.823369	+	0.950219i
$352$	9.26569	+	18.8169i	0.493863	+	1.00294i
$353$	−23.9002	−	27.5823i	−1.27208	−	1.46806i	−0.815922	−	0.578162i	$-0.803770\pi$
$353$	−23.9002	−	27.5823i	−1.27208	−	1.46806i	−0.456160	−	0.889898i	$-0.650775\pi$
$354$	5.05244	−	15.5498i	0.268534	−	0.826464i
$355$	−10.8792	+	3.88169i	−0.577408	+	0.206019i
$356$	−9.23193	+	9.49943i	−0.489291	+	0.503469i
$357$	−0.481512	+	0.441928i	−0.0254843	+	0.0233893i
$358$	15.3299	+	22.4193i	0.810211	+	1.18490i
$359$	13.5945	−	3.16128i	0.717493	−	0.166846i	0.148172	−	0.988962i	$-0.452661\pi$
$359$	13.5945	−	3.16128i	0.717493	−	0.166846i	0.569320	+	0.822116i	$0.307206\pi$
$360$	0.474288	−	0.344591i	0.0249972	−	0.0181615i
$361$	−18.8071	+	2.15791i	−0.989845	+	0.113574i
$362$	1.16533			0.0612484
$363$	16.1639	−	6.85382i	0.848384	−	0.359732i
$364$	0.540064			0.0283071
$365$	−9.36213	+	1.07420i	−0.490036	+	0.0562264i
$366$	16.8262	−	12.2249i	0.879517	−	0.639007i
$367$	−16.4503	+	3.82535i	−0.858698	+	0.199682i	−0.632653	−	0.774435i	$-0.718034\pi$
$367$	−16.4503	+	3.82535i	−0.858698	+	0.199682i	−0.226045	+	0.974117i	$0.572580\pi$
$368$	−7.40830	−	10.8343i	−0.386184	−	0.564777i
$369$	−2.00593	+	1.84103i	−0.104425	+	0.0958400i
$370$	12.1776	−	12.5304i	0.633083	−	0.651427i
$371$	−0.624813	+	0.222933i	−0.0324387	+	0.0115741i
$372$	−3.96649	+	12.2076i	−0.205653	+	0.632934i
$373$	−13.3631	−	15.4218i	−0.691915	−	0.798512i	0.295721	−	0.955274i	$-0.404440\pi$
$373$	−13.3631	−	15.4218i	−0.691915	−	0.798512i	−0.987636	+	0.156762i	$0.949895\pi$
$374$	−15.8397	+	19.3950i	−0.819053	+	1.00289i
$375$	−1.04521	+	1.20624i	−0.0539746	+	0.0622900i
$376$	7.17948	+	11.9058i	0.370254	+	0.613997i
$377$	−6.41913	+	8.32448i	−0.330602	+	0.428733i
$378$	−0.924725	−	0.329941i	−0.0475627	−	0.0169703i
$379$	−27.0861	+	13.3173i	−1.39132	+	0.684066i	−0.974388	−	0.224872i	$-0.927804\pi$
$379$	−27.0861	+	13.3173i	−1.39132	+	0.684066i	−0.416932	+	0.908938i	$0.636895\pi$
$380$	0.262383	+	0.214549i	0.0134600	+	0.0110062i
$381$	−0.193080	+	0.952888i	−0.00989179	+	0.0488179i
$382$	15.7117	−	0.898427i	0.803880	−	0.0459675i
$383$	5.95985	+	5.46990i	0.304534	+	0.279499i	0.813843	−	0.581085i	$-0.197372\pi$
$383$	5.95985	+	5.46990i	0.304534	+	0.279499i	−0.509309	+	0.860584i	$0.670099\pi$
$384$	2.20389	−	15.3284i	0.112467	−	0.782223i
$385$	−0.0916649	+	0.312878i	−0.00467168	+	0.0159457i
$386$	2.45006	+	17.0406i	0.124705	+	0.867342i
$387$	−1.29424	+	1.89277i	−0.0657899	+	0.0962147i
$388$	4.08473	−	10.4915i	0.207371	−	0.532627i
$389$	−11.7171	−	15.1950i	−0.594079	−	0.770415i	0.394860	−	0.918741i	$-0.370793\pi$
$389$	−11.7171	−	15.1950i	−0.594079	−	0.770415i	−0.988938	+	0.148326i	$0.952611\pi$
$390$	3.82145	+	11.7612i	0.193507	+	0.595553i
$391$	5.74001	−	9.51875i	0.290285	−	0.481384i
$392$	3.28571	+	8.43927i	0.165953	+	0.426248i
$393$	−20.8001	−	4.83687i	−1.04923	−	0.243988i
$394$	5.16940	−	2.18461i	0.260431	−	0.110059i
$395$	−12.9484	+	8.32142i	−0.651504	+	0.418696i
$396$	−1.89069	−	0.381920i	−0.0950107	−	0.0191922i
$397$	21.9492	+	14.1059i	1.10160	+	0.707956i	0.959447	−	0.281889i	$-0.0909610\pi$
$397$	21.9492	+	14.1059i	1.10160	+	0.707956i	0.142153	+	0.989845i	$0.454597\pi$
$398$	−16.2592	−	2.81376i	−0.814998	−	0.141041i
$399$	−0.00354079	+	0.0412247i	−0.000177261	+	0.00206382i
$400$	−0.420913	−	4.90061i	−0.0210457	−	0.245030i
$401$	28.8050	−	4.98489i	1.43845	−	0.248934i	0.602667	−	0.797993i	$-0.294105\pi$
$401$	28.8050	−	4.98489i	1.43845	−	0.248934i	0.835784	+	0.549059i	$0.185014\pi$
$402$	−41.1087	−	17.3727i	−2.05032	−	0.866470i
$403$	−21.6399	−	15.7223i	−1.07796	−	0.783184i
$404$	0.317067	+	0.179056i	0.0157747	+	0.00890837i
$405$	0.212391	−	7.43466i	0.0105538	−	0.369431i
$406$	−0.420399	−	0.123440i	−0.0208640	−	0.00612624i
$407$	31.9604	+	0.893811i	1.58422	+	0.0443046i
$408$	8.26473	−	2.42674i	0.409165	−	0.120142i
$409$	2.10325	+	8.00158i	0.103999	+	0.395652i	0.998698	−	0.0510172i	$-0.0162463\pi$
$409$	2.10325	+	8.00158i	0.103999	+	0.395652i	−0.894699	+	0.446670i	$0.852610\pi$
$410$	2.16577	+	10.6885i	0.106960	+	0.527866i
$411$	14.8640	−	28.1704i	0.733186	−	1.38954i
$412$	0.338574	+	11.8516i	0.0166803	+	0.583888i
$413$	−0.141237	+	0.537320i	−0.00694980	+	0.0264398i
$414$	2.18502	+	0.124944i	0.107388	+	0.00614067i
$415$	−10.4193	−	10.7213i	−0.511465	−	0.526285i
$416$	−24.2598	−	11.9278i	−1.18944	−	0.584806i
$417$	5.89344	+	12.9048i	0.288603	+	0.631953i
$418$	0.0914550	+	1.58268i	0.00447321	+	0.0774113i
$419$	11.0155	−	24.1207i	0.538144	−	1.17837i	−0.423958	−	0.905682i	$-0.639359\pi$
$419$	11.0155	−	24.1207i	0.538144	−	1.17837i	0.962102	−	0.272690i	$-0.0879132\pi$
$420$	−0.156104	+	0.127646i	−0.00761709	+	0.00622847i
$421$	−7.86751	−	14.9106i	−0.383439	−	0.726698i	0.614630	−	0.788816i	$-0.289305\pi$
$421$	−7.86751	−	14.9106i	−0.383439	−	0.726698i	−0.998069	+	0.0621179i	$0.980215\pi$
$422$	9.51196	−	5.37165i	0.463035	−	0.261488i
$423$	−4.82442	−	0.553551i	−0.234571	−	0.0269146i
$424$	8.68611	+	0.996638i	0.421835	+	0.0484010i
$425$	3.62717	−	2.04836i	0.175944	−	0.0993599i
$426$	−15.5942	−	29.5543i	−0.755542	−	1.43191i
$427$	−0.547103	+	0.447364i	−0.0264762	+	0.0216495i
$428$	−1.82182	+	3.98923i	−0.0880610	+	0.192827i
$429$	−11.1155	+	19.7106i	−0.536659	+	0.951635i
$430$	3.81530	+	8.35434i	0.183990	+	0.402882i
$431$	21.4751	+	10.5586i	1.03442	+	0.508589i	0.877779	−	0.479067i	$-0.159025\pi$
$431$	21.4751	+	10.5586i	1.03442	+	0.508589i	0.156640	+	0.987656i	$0.449934\pi$
$432$	18.8900	+	19.4373i	0.908844	+	0.935178i
$433$	−30.1585	−	1.72452i	−1.44932	−	0.0828754i	−0.685393	−	0.728173i	$-0.740370\pi$
$433$	−30.1585	−	1.72452i	−1.44932	−	0.0828754i	−0.763931	+	0.645298i	$0.776733\pi$
$434$	0.283425	−	1.07826i	0.0136049	−	0.0517582i
$435$	−0.112081	−	3.92335i	−0.00537387	−	0.188110i
$436$	6.57131	−	12.4540i	0.314709	−	0.596439i
$437$	−0.139749	−	0.689688i	−0.00668510	−	0.0329922i
$438$	−6.93043	−	26.3661i	−0.331149	−	1.25982i
$439$	12.2592	−	3.59963i	0.585100	−	0.171801i	0.0242323	−	0.999706i	$-0.492286\pi$
$439$	12.2592	−	3.59963i	0.585100	−	0.171801i	0.560868	+	0.827906i	$0.310468\pi$
$440$	2.90352	−	3.16742i	0.138420	−	0.151001i
$441$	−3.03508	−	0.891180i	−0.144528	−	0.0424372i
$442$	0.921648	−	32.2619i	0.0438383	−	1.53454i
$443$	18.4614	+	10.4256i	0.877127	+	0.495337i	0.863372	−	0.504569i	$-0.168348\pi$
$443$	18.4614	+	10.4256i	0.877127	+	0.495337i	0.0137559	+	0.999905i	$0.495621\pi$
$444$	15.9984	+	11.6235i	0.759251	+	0.551628i
$445$	9.49377	+	4.01210i	0.450048	+	0.190192i
$446$	−10.8447	+	1.87674i	−0.513509	+	0.0888663i
$447$	0.952053	+	11.0846i	0.0450306	+	0.524281i
$448$	0.0136709	−	0.159167i	0.000645887	−	0.00751993i
$449$	10.9735	+	1.89904i	0.517871	+	0.0896211i	0.423465	−	0.905913i	$-0.360814\pi$
$449$	10.9735	+	1.89904i	0.517871	+	0.0896211i	0.0944065	+	0.995534i	$0.469905\pi$
$450$	0.689985	+	0.443426i	0.0325262	+	0.0209033i
$451$	−11.7200	+	16.1515i	−0.551872	+	0.760547i
$452$	−8.95958	+	5.75797i	−0.421423	+	0.270832i
$453$	−10.5574	+	4.46161i	−0.496032	+	0.209625i
$454$	−38.6757	−	8.99366i	−1.81514	−	0.422093i
$455$	−0.152456	−	0.391580i	−0.00714724	−	0.0183575i
$456$	0.281600	−	0.466980i	0.0131871	−	0.0218684i
$457$	10.2282	+	31.4792i	0.478455	+	1.47253i	0.841241	+	0.540661i	$0.181826\pi$
$457$	10.2282	+	31.4792i	0.478455	+	1.47253i	−0.362786	+	0.931873i	$0.618174\pi$
$458$	8.46472	+	10.9772i	0.395530	+	0.512933i
$459$	−8.32807	+	21.3905i	−0.388721	+	0.998422i
$460$	1.93575	−	2.83095i	0.0902550	−	0.131994i
$461$	−3.10535	−	21.5982i	−0.144631	−	1.00593i	−0.924826	−	0.380392i	$-0.875789\pi$
$461$	−3.10535	−	21.5982i	−0.144631	−	1.00593i	0.780195	−	0.625537i	$-0.215120\pi$
$462$	−0.933660	−	0.133667i	−0.0434378	−	0.00621877i
$463$	−0.863202	+	6.00370i	−0.0401164	+	0.279016i	−0.999999	−	0.00138635i	$-0.999559\pi$
$463$	−0.863202	+	6.00370i	−0.0401164	+	0.279016i	0.959883	+	0.280402i	$0.0904678\pi$
$464$	8.91125	+	8.17867i	0.413694	+	0.379685i
$465$	9.97096	−	0.570160i	0.462392	−	0.0264405i
$466$	−7.12573	+	35.1668i	−0.330093	+	1.62907i
$467$	13.3351	+	10.9041i	0.617075	+	0.504580i	0.889101	−	0.457710i	$-0.151330\pi$
$467$	13.3351	+	10.9041i	0.617075	+	0.504580i	−0.272027	+	0.962290i	$0.587694\pi$
$468$	2.23101	−	1.09691i	0.103128	−	0.0507048i
$469$	1.42829	+	0.509613i	0.0659523	+	0.0235317i
$470$	−11.8776	+	15.4031i	−0.547872	+	0.710493i
$471$	−5.96650	−	9.89433i	−0.274922	−	0.455907i
$472$	4.79495	−	5.53367i	0.220705	−	0.254708i
$473$	−6.53271	+	15.4842i	−0.300374	+	0.711964i
$474$	−29.1592	−	33.6515i	−1.33933	−	1.54567i
$475$	0.0814929	−	0.250809i	0.00373915	−	0.0115079i
$476$	0.495670	−	0.176855i	0.0227190	−	0.00810613i
$477$	−2.12831	+	2.18998i	−0.0974487	+	0.100272i
$478$	3.18081	−	2.91932i	0.145487	−	0.133527i
$479$	11.0536	+	16.1654i	0.505053	+	0.738617i	0.990778	−	0.135495i	$-0.0432625\pi$
$479$	11.0536	+	16.1654i	0.505053	+	0.738617i	−0.485725	+	0.874112i	$0.661444\pi$
$480$	9.83139	−	2.28619i	0.448739	−	0.104350i
$481$	−33.3389	+	24.2221i	−1.52012	+	1.10443i
$482$	38.9960	−	4.47437i	1.77622	−	0.203802i
$483$	0.418666			0.0190500
$484$	−14.1374	+	0.0169926i	−0.642610	+	0.000772392i
$485$	−8.76010			−0.397776
$486$	−8.39185	+	0.962875i	−0.380662	+	0.0436769i
$487$	16.2194	−	11.7841i	0.734970	−	0.533987i	−0.156162	−	0.987731i	$-0.549912\pi$
$487$	16.2194	−	11.7841i	0.734970	−	0.533987i	0.891132	+	0.453745i	$0.149912\pi$
$488$	9.07209	−	2.10962i	0.410674	−	0.0954982i
$489$	−4.71451	−	6.89475i	−0.213198	−	0.311791i
$490$	−9.33459	+	8.56721i	−0.421694	+	0.387027i
$491$	13.1911	−	13.5734i	0.595308	−	0.612557i	−0.350784	−	0.936456i	$-0.614085\pi$
$491$	13.1911	−	13.5734i	0.595308	−	0.612557i	0.946092	+	0.323899i	$0.104994\pi$
$492$	−11.6247	+	4.14770i	−0.524084	+	0.186993i
$493$	−3.16546	+	9.74228i	−0.142565	+	0.438770i
$494$	−1.33806	−	1.54421i	−0.0602023	−	0.0694772i
$495$	0.256811	+	1.47868i	0.0115428	+	0.0664617i
$496$	−20.1551	+	23.2602i	−0.904990	+	1.04441i
$497$	0.586356	+	0.972363i	0.0263017	+	0.0436164i
$498$	26.4104	−	34.2497i	1.18348	−	1.53476i
$499$	−35.4506	−	12.6488i	−1.58699	−	0.566236i	−0.612460	−	0.790502i	$-0.709820\pi$
$499$	−35.4506	−	12.6488i	−1.58699	−	0.566236i	−0.974528	+	0.224266i	$0.928002\pi$
$500$	1.15335	−	0.567066i	0.0515796	−	0.0253600i
$501$	31.6440	+	25.8752i	1.41375	+	1.15602i
$502$	−7.56139	+	37.3169i	−0.337481	+	1.66554i
$503$	−28.3789	+	1.62276i	−1.26535	+	0.0723555i	−0.676839	−	0.736132i	$-0.736650\pi$
$503$	−28.3789	+	1.62276i	−1.26535	+	0.0723555i	−0.588514	+	0.808487i	$0.700287\pi$
$504$	−0.0424580	−	0.0389676i	−0.00189123	−	0.00173575i
$505$	0.0403211	−	0.280439i	0.00179426	−	0.0124794i
$506$	15.8763	−	2.29241i	0.705789	−	0.101910i
$507$	−1.19780	−	8.33090i	−0.0531963	−	0.369988i
$508$	0.441897	−	0.646254i	0.0196060	−	0.0286729i
$509$	1.36200	−	3.49828i	0.0603698	−	0.155059i	−0.898448	−	0.439079i	$-0.855305\pi$
$509$	1.36200	−	3.49828i	0.0603698	−	0.155059i	0.958818	+	0.284021i	$0.0916684\pi$
$510$	7.35878	+	9.54303i	0.325852	+	0.422573i
$511$	0.286258	+	0.881010i	0.0126633	+	0.0389736i
$512$	−9.48158	+	15.7234i	−0.419031	+	0.694884i
$513$	0.527236	+	1.35420i	0.0232781	+	0.0597892i
$514$	25.8779	+	6.01765i	1.14143	+	0.265427i
$515$	8.49758	−	3.59111i	0.374448	−	0.158243i
$516$	−8.74429	+	5.61962i	−0.384946	+	0.247390i
$517$	−35.4595	+	3.06709i	−1.55951	+	0.134890i
$518$	−1.44495	−	0.928616i	−0.0634877	−	0.0408010i
$519$	−32.9768	−	5.70687i	−1.44752	−	0.250504i
$520$	−0.473925	+	5.51780i	−0.0207830	+	0.241972i
$521$	−0.658656	−	7.66859i	−0.0288562	−	0.335967i	−0.996497	−	0.0836335i	$-0.973347\pi$
$521$	−0.658656	−	7.66859i	−0.0288562	−	0.335967i	0.967640	−	0.252333i	$-0.0811980\pi$
$522$	−1.98739	+	0.343931i	−0.0869856	+	0.0150535i
$523$	−11.0217	−	4.65782i	−0.481947	−	0.203672i	0.134740	−	0.990881i	$-0.456980\pi$
$523$	−11.0217	−	4.65782i	−0.481947	−	0.203672i	−0.616687	+	0.787209i	$0.711525\pi$
$524$	13.9117	+	10.1075i	0.607737	+	0.441547i
$525$	0.136618	+	0.0771516i	0.00596249	+	0.00336717i
$526$	−0.135028	+	4.72660i	−0.00588750	+	0.206089i
$527$	−25.0097	−	7.34350i	−1.08944	−	0.319888i
$528$	21.5020	+	14.6837i	0.935754	+	0.639028i
$529$	15.2364	−	4.47380i	0.662450	−	0.194513i
$530$	3.10957	+	11.8300i	0.135071	+	0.513863i
$531$	0.507890	+	2.50654i	0.0220405	+	0.108774i
$532$	0.0155483	−	0.0294673i	0.000674103	−	0.00127757i
$533$	−0.734475	−	25.7100i	−0.0318136	−	1.11362i
$534$	−7.57994	+	28.8371i	−0.328016	+	1.24790i
$535$	3.40672	+	0.194803i	0.147285	+	0.00842208i
$536$	−13.9292	−	14.3328i	−0.601649	−	0.619082i
$537$	21.4624	+	10.5524i	0.926171	+	0.455368i
$538$	−11.2273	−	24.5844i	−0.484044	−	1.05991i
$539$	−23.1005	−	1.97012i	−0.995008	−	0.0848589i
$540$	−2.94206	+	6.44221i	−0.126606	+	0.277228i
$541$	11.7536	−	9.61091i	0.505329	−	0.413205i	−0.345683	−	0.938351i	$-0.612353\pi$
$541$	11.7536	−	9.61091i	0.505329	−	0.413205i	0.851012	+	0.525146i	$0.175989\pi$
$542$	−6.45527	−	12.2341i	−0.277277	−	0.525499i
$543$	0.893541	−	0.504606i	0.0383455	−	0.0216547i
$544$	−26.1716	−	3.00292i	−1.12210	−	0.128749i
$545$	−10.8850	−	1.24893i	−0.466260	−	0.0534984i
$546$	1.05852	−	0.597772i	0.0453003	−	0.0255823i
$547$	5.04202	+	9.55570i	0.215581	+	0.408572i	0.968307	−	0.249762i	$-0.0803524\pi$
$547$	5.04202	+	9.55570i	0.215581	+	0.408572i	−0.752726	+	0.658334i	$0.771261\pi$
$548$	−19.8550	+	16.2353i	−0.848163	+	0.693539i
$549$	−1.35145	+	2.95927i	−0.0576787	+	0.126299i
$550$	5.60316	+	2.17763i	0.238919	+	0.0928545i
$551$	0.269400	+	0.589903i	0.0114768	+	0.0251307i
$552$	−4.95163	−	2.43455i	−0.210755	−	0.103621i
$553$	1.05449	+	1.08504i	0.0448415	+	0.0461408i
$554$	−23.9164	−	1.36759i	−1.01611	−	0.0581032i
$555$	3.91154	−	14.8811i	0.166036	−	0.631666i
$556$	−0.326217	−	11.4191i	−0.0138347	−	0.484277i
$557$	5.24547	−	9.94127i	0.222258	−	0.421225i	−0.747861	−	0.663855i	$-0.768919\pi$
$557$	5.24547	−	9.94127i	0.222258	−	0.421225i	0.970119	+	0.242630i	$0.0780101\pi$
$558$	−1.01920	−	5.02997i	−0.0431463	−	0.212936i
$559$	−5.50654	−	20.9491i	−0.232902	−	0.886051i
$560$	−0.463925	+	0.136221i	−0.0196044	+	0.00575637i
$561$	−3.74713	+	21.7303i	−0.158204	+	0.917455i
$562$	6.59791	+	1.93732i	0.278316	+	0.0817210i
$563$	1.18649	−	41.5325i	0.0500045	−	1.75039i	−0.457927	−	0.888990i	$-0.651408\pi$
$563$	1.18649	−	41.5325i	0.0500045	−	1.75039i	0.507932	−	0.861397i	$-0.330410\pi$
$564$	−19.1681	−	10.8247i	−0.807125	−	0.455804i
$565$	6.70411	+	4.87082i	0.282044	+	0.204917i
$566$	−16.4673	−	6.95916i	−0.692174	−	0.292515i
$567$	−0.720428	+	0.124675i	−0.0302551	+	0.00523585i
$568$	−1.28062	−	14.9099i	−0.0537335	−	0.625607i
$569$	2.76833	−	32.2311i	0.116054	−	1.35120i	−0.674259	−	0.738495i	$-0.735537\pi$
$569$	2.76833	−	32.2311i	0.116054	−	1.35120i	0.790313	−	0.612703i	$-0.209918\pi$
$570$	0.751741	+	0.130094i	0.0314870	+	0.00544903i
$571$	−28.1293	−	18.0776i	−1.17718	−	0.756525i	−0.202310	−	0.979321i	$-0.564845\pi$
$571$	−28.1293	−	18.0776i	−1.17718	−	0.756525i	−0.974865	+	0.222797i	$0.928481\pi$
$572$	14.4229	−	11.1355i	0.603051	−	0.465600i
$573$	11.6582	−	7.49229i	0.487029	−	0.312995i
$574$	0.987485	−	0.417315i	0.0412168	−	0.0174184i
$575$	−2.59906	−	0.604386i	−0.108388	−	0.0252046i
$576$	−0.266806	−	0.685286i	−0.0111169	−	0.0285536i
$577$	−18.0071	+	29.8615i	−0.749646	+	1.24315i	0.214226	+	0.976784i	$0.431277\pi$
$577$	−18.0071	+	29.8615i	−0.749646	+	1.24315i	−0.963872	+	0.266365i	$0.914177\pi$
$578$	−0.197233	−	0.607020i	−0.00820380	−	0.0252487i
$579$	9.25746	+	12.0053i	0.384727	+	0.498923i
$580$	−1.14665	+	2.94515i	−0.0476122	+	0.122291i
$581$	−0.829519	+	1.21313i	−0.0344143	+	0.0503292i
$582$	−3.60660	−	25.0844i	−0.149498	−	1.03978i
$583$	−12.0895	+	18.8366i	−0.500698	+	0.780131i
$584$	1.73748	−	12.0844i	0.0718974	−	0.500057i
$585$	−1.42513	−	1.30797i	−0.0589217	−	0.0540779i
$586$	27.5915	−	1.57774i	1.13979	−	0.0651757i
$587$	−3.55191	+	17.5294i	−0.146603	+	0.723514i	0.837574	+	0.546324i	$0.183973\pi$
$587$	−3.55191	+	17.5294i	−0.146603	+	0.723514i	−0.984177	+	0.177190i	$0.943299\pi$
$588$	−11.1007	−	9.07704i	−0.457787	−	0.374331i
$589$	−1.48086	+	0.728088i	−0.0610176	+	0.0300003i
$590$	9.64811	+	3.44244i	0.397206	+	0.141723i
$591$	3.01778	−	3.91352i	0.124135	−	0.160981i
$592$	24.4859	+	40.6052i	1.00636	+	1.66886i
$593$	−26.8291	+	30.9624i	−1.10174	+	1.27147i	−0.142216	+	0.989836i	$0.545423\pi$
$593$	−26.8291	+	30.9624i	−1.10174	+	1.27147i	−0.959521	+	0.281637i	$0.909123\pi$
$594$	−31.4986	+	10.2555i	−1.29240	+	0.420786i
$595$	−0.268155	−	0.309467i	−0.0109933	−	0.0126869i
$596$	2.76833	−	8.52005i	0.113395	−	0.348995i
$597$	−13.6854	+	4.88296i	−0.560108	+	0.199846i
$598$	−14.4091	+	14.8266i	−0.589231	+	0.606305i
$599$	−13.3297	+	12.2339i	−0.544637	+	0.499863i	−0.900607	−	0.434634i	$-0.856878\pi$
$599$	−13.3297	+	12.2339i	−0.544637	+	0.499863i	0.355970	+	0.934497i	$0.384150\pi$
$600$	−1.16716	−	1.70692i	−0.0476491	−	0.0696846i
$601$	24.9539	−	5.80279i	1.01789	−	0.236701i	0.315829	−	0.948816i	$-0.397717\pi$
$601$	24.9539	−	5.80279i	1.01789	−	0.236701i	0.702062	+	0.712115i	$0.252263\pi$
$602$	0.730405	−	0.530670i	0.0297691	−	0.0216285i
$603$	6.93534	−	0.795756i	0.282429	−	0.0324057i
$604$	9.22917			0.375530
$605$	4.00320	+	10.2457i	0.162753	+	0.416547i
$606$	0.819634			0.0332954
$607$	−24.0870	+	2.76372i	−0.977659	+	0.112176i	−0.588068	−	0.808812i	$-0.700111\pi$
$607$	−24.0870	+	2.76372i	−0.977659	+	0.112176i	−0.389592	+	0.920988i	$0.627384\pi$
$608$	−1.34924	+	0.980281i	−0.0547190	+	0.0397557i
$609$	−0.375801	+	0.0873887i	−0.0152282	+	0.00354117i
$610$	7.35515	+	10.7566i	0.297801	+	0.435520i
$611$	33.7970	−	31.0186i	1.36728	−	1.25488i
$612$	1.68841	−	1.73734i	0.0682500	−	0.0702276i
$613$	−15.7384	+	5.61545i	−0.635668	+	0.226806i	−0.634171	−	0.773193i	$-0.718658\pi$
$613$	−15.7384	+	5.61545i	−0.635668	+	0.226806i	−0.00149698	+	0.999999i	$0.500477\pi$
$614$	−4.61074	+	14.1904i	−0.186074	+	0.572678i
$615$	6.28891	+	7.25779i	0.253593	+	0.292662i
$616$	−0.361842	−	0.217902i	−0.0145790	−	0.00877952i
$617$	15.2307	−	17.5771i	0.613163	−	0.707628i	−0.361230	−	0.932477i	$-0.617643\pi$
$617$	15.2307	−	17.5771i	0.613163	−	0.707628i	0.974394	+	0.224848i	$0.0721886\pi$
$618$	13.7816	+	22.8542i	0.554377	+	0.919332i
$619$	27.6360	−	35.8390i	1.11078	−	1.44049i	0.226219	−	0.974077i	$-0.427364\pi$
$619$	27.6360	−	35.8390i	1.11078	−	1.44049i	0.884566	−	0.466415i	$-0.154455\pi$
$620$	−7.57437	−	2.70253i	−0.304194	−	0.108536i
$621$	13.1956	−	6.48784i	0.529521	−	0.260348i
$622$	−20.8667	−	17.0626i	−0.836677	−	0.684148i
$623$	0.201205	−	0.992986i	0.00806111	−	0.0397832i
$624$	−33.5043	+	1.91585i	−1.34125	+	0.0766953i
$625$	−0.736741	−	0.676175i	−0.0294696	−	0.0270470i
$626$	0.101803	−	0.708057i	0.00406887	−	0.0282996i
$627$	0.755448	+	1.17395i	0.0301697	+	0.0468830i
$628$	1.32406	+	9.20903i	0.0528357	+	0.367480i
$629$	−22.6664	+	33.1485i	−0.903767	+	1.32172i
$630$	0.0292516	−	0.0751320i	0.00116541	−	0.00299333i
$631$	4.12005	+	5.34298i	0.164017	+	0.212701i	0.866737	−	0.498766i	$-0.166213\pi$
$631$	4.12005	+	5.34298i	0.164017	+	0.212701i	−0.702720	+	0.711466i	$0.748031\pi$
$632$	−6.16205	−	18.9648i	−0.245113	−	0.754381i
$633$	4.96748	−	8.23764i	0.197440	−	0.327417i
$634$	9.86658	+	25.3421i	0.391852	+	1.00646i
$635$	−0.593318	−	0.137970i	−0.0235451	−	0.00547518i
$636$	−12.7515	+	5.38885i	−0.505631	+	0.213682i
$637$	25.1381	−	16.1553i	0.996009	−	0.640096i
$638$	−13.7723	+	5.37159i	−0.545251	+	0.212663i
$639$	4.39719	+	2.82590i	0.173950	+	0.111791i
$640$	9.56039	+	1.65449i	0.377908	+	0.0653995i
$641$	−2.71215	+	31.5769i	−0.107123	+	1.24721i	0.723478	+	0.690347i	$0.242542\pi$
$641$	−2.71215	+	31.5769i	−0.107123	+	1.24721i	−0.830602	+	0.556867i	$0.812003\pi$
$642$	0.844755	+	9.83530i	0.0333398	+	0.388168i
$643$	9.74049	−	1.68566i	0.384127	−	0.0664759i	0.0248122	−	0.999692i	$-0.492101\pi$
$643$	9.74049	−	1.68566i	0.384127	−	0.0664759i	0.359315	+	0.933216i	$0.383010\pi$
$644$	−0.310533	−	0.131232i	−0.0122367	−	0.00517128i
$645$	6.54301	+	4.75378i	0.257631	+	0.187180i
$646$	−1.73376	−	0.979097i	−0.0682137	−	0.0385220i
$647$	−0.209424	+	7.33081i	−0.00823332	+	0.288204i	0.985034	+	0.172360i	$0.0551391\pi$
$647$	−0.209424	+	7.33081i	−0.00823332	+	0.288204i	−0.993267	+	0.115844i	$0.963043\pi$
$648$	9.24559	+	2.71475i	0.363201	+	0.106645i
$649$	7.30710	+	17.2617i	0.286829	+	0.677583i
$650$	−7.43416	+	2.18287i	−0.291592	+	0.0856191i
$651$	−0.249582	−	0.949507i	−0.00978187	−	0.0372141i
$652$	1.33566	+	6.59175i	0.0523085	+	0.258153i
$653$	−9.12600	+	17.2957i	−0.357128	+	0.676833i	−0.995691	−	0.0927369i	$-0.970438\pi$
$653$	−9.12600	+	17.2957i	−0.357128	+	0.676833i	0.638563	+	0.769570i	$0.279529\pi$
$654$	−0.905114	−	31.6831i	−0.0353928	−	1.23891i
$655$	3.40136	−	12.9401i	0.132902	−	0.505612i
$656$	−29.5466	−	1.68954i	−1.15360	−	0.0659653i
$657$	2.97193	+	3.05805i	0.115946	+	0.119306i
$658$	1.71586	+	0.843632i	0.0668912	+	0.0328882i
$659$	−10.8884	−	23.8422i	−0.424151	−	0.928760i	−0.994240	−	0.107178i	$-0.965819\pi$
$659$	−10.8884	−	23.8422i	−0.424151	−	0.928760i	0.570089	−	0.821583i	$-0.306909\pi$
$660$	−1.53698	+	6.62758i	−0.0598269	+	0.257978i
$661$	−12.1415	+	26.5861i	−0.472248	+	1.03408i	0.512274	+	0.858822i	$0.328803\pi$
$661$	−12.1415	+	26.5861i	−0.472248	+	1.03408i	−0.984523	+	0.175258i	$0.943924\pi$
$662$	−15.3200	+	12.5271i	−0.595429	+	0.486880i
$663$	−13.2632	−	25.1365i	−0.515100	−	0.976222i
$664$	16.8652	−	9.52423i	0.654498	−	0.369612i
$665$	−0.0257547	−	0.00295508i	−0.000998726	−	0.000114593i
$666$	−7.85521	−	0.901302i	−0.304383	−	0.0349247i
$667$	5.71375	−	3.22671i	0.221237	−	0.124939i
$668$	−15.3603	−	29.1110i	−0.594308	−	1.12634i
$669$	−7.50270	+	6.13493i	−0.290071	+	0.237190i
$670$	11.6156	−	25.4346i	0.448750	−	0.982625i
$671$	−5.38671	+	23.2279i	−0.207951	+	0.896703i
$672$	−0.412185	−	0.902560i	−0.0159004	−	0.0348170i
$673$	−3.69909	−	1.81872i	−0.142589	−	0.0701065i	0.368532	−	0.929615i	$-0.379861\pi$
$673$	−3.69909	−	1.81872i	−0.142589	−	0.0701065i	−0.511121	+	0.859509i	$0.670770\pi$
$674$	−10.9006	−	11.2164i	−0.419875	−	0.432041i
$675$	5.50152	+	0.314588i	0.211753	+	0.0121085i
$676$	−1.72291	+	6.55464i	−0.0662659	+	0.252102i
$677$	−1.07593	−	37.6623i	−0.0413512	−	1.44748i	−0.710157	−	0.704044i	$-0.751376\pi$
$677$	−1.07593	−	37.6623i	−0.0413512	−	1.44748i	0.668806	−	0.743437i	$-0.266806\pi$
$678$	−11.1874	+	21.2025i	−0.429649	+	0.814276i
$679$	0.171012	+	0.843979i	0.00656285	+	0.0323889i
$680$	1.37195	+	5.21943i	0.0526118	+	0.200156i
$681$	−33.5498	+	9.85111i	−1.28563	+	0.377495i
$682$	−14.6635	−	34.6398i	−0.561493	−	1.32643i
$683$	30.3463	+	8.91049i	1.16117	+	0.340950i	0.804887	−	0.593428i	$-0.202226\pi$
$683$	30.3463	+	8.91049i	1.16117	+	0.340950i	0.356283	+	0.934378i	$0.384044\pi$
$684$	0.00437969	−	0.153309i	0.000167462	−	0.00586193i
$685$	17.3765	+	9.81297i	0.663923	+	0.374934i
$686$	2.01664	+	1.46517i	0.0769956	+	0.0559406i
$687$	11.2438	+	4.75167i	0.428978	+	0.181288i
$688$	−24.5585	+	4.25002i	−0.936285	+	0.162030i
$689$	−2.46869	−	28.7424i	−0.0940495	−	1.09500i
$690$	0.660599	−	7.69121i	0.0251486	−	0.292799i
$691$	−4.39047	−	0.759800i	−0.167021	−	0.0289042i	0.0863981	−	0.996261i	$-0.472464\pi$
$691$	−4.39047	−	0.759800i	−0.167021	−	0.0289042i	−0.253419	+	0.967357i	$0.581555\pi$
$692$	22.6707	+	14.5696i	0.861811	+	0.553853i
$693$	0.137448	−	0.0536084i	0.00522121	−	0.00203641i
$694$	46.1593	−	29.6648i	1.75218	−	1.12606i
$695$	−8.18745	+	3.46005i	−0.310568	+	0.131247i
$696$	4.95282	+	1.15173i	0.187736	+	0.0436561i
$697$	−9.09335	−	23.3561i	−0.344435	−	0.884674i
$698$	9.29519	−	15.4143i	0.351828	−	0.583441i
$699$	9.76398	+	30.0504i	0.369308	+	1.13661i
$700$	−0.0771486	−	0.100048i	−0.00291594	−	0.00378146i
$701$	15.5787	−	40.0135i	0.588398	−	1.51129i	−0.251120	−	0.967956i	$-0.580799\pi$
$701$	15.5787	−	40.0135i	0.588398	−	1.51129i	0.839518	−	0.543332i	$-0.182837\pi$
$702$	24.0992	−	35.2439i	0.909564	−	1.33019i
$703$	0.361804	+	2.51640i	0.0136457	+	0.0949078i
$704$	−2.91675	−	4.53257i	−0.109929	−	0.170828i
$705$	−2.43759	+	16.9538i	−0.0918050	+	0.638518i
$706$	48.7361	+	44.7296i	1.83421	+	1.68342i
$707$	−0.0278056	+	0.00158998i	−0.00104574	+	5.97975e-5i
$708$	−2.30236	+	11.3626i	−0.0865279	+	0.427032i
$709$	11.4660	+	9.37570i	0.430615	+	0.352112i	0.823344	−	0.567542i	$-0.192106\pi$
$709$	11.4660	+	9.37570i	0.430615	+	0.352112i	−0.392730	+	0.919654i	$0.628469\pi$
$710$	18.7882	−	9.23754i	0.705109	−	0.346679i
$711$	6.55992	+	2.34057i	0.246016	+	0.0877784i
$712$	−8.15391	+	10.5742i	−0.305581	+	0.396284i
$713$	8.62236	+	14.2986i	0.322910	+	0.535486i
$714$	0.775753	−	0.895267i	0.0290318	−	0.0335045i
$715$	−12.1454	−	7.31401i	−0.454213	−	0.273528i
$716$	−12.6114	−	14.5543i	−0.471311	−	0.543921i
$717$	1.17484	−	3.61579i	0.0438753	−	0.135034i
$718$	−23.8266	+	8.50131i	−0.889200	+	0.317266i
$719$	−18.0151	+	18.5371i	−0.671849	+	0.691316i	−0.964254	−	0.264978i	$-0.914635\pi$
$719$	−18.0151	+	18.5371i	−0.671849	+	0.691316i	0.292405	+	0.956294i	$0.405544\pi$
$720$	−1.63980	+	1.50500i	−0.0611118	+	0.0560879i
$721$	−0.511867	−	0.748582i	−0.0190629	−	0.0278786i
$722$	33.4201	−	7.77151i	1.24377	−	0.289226i
$723$	27.9635	−	20.3167i	1.03997	−	0.755585i
$724$	−0.820927	+	0.0941926i	−0.0305095	+	0.00350064i
$725$	2.45911			0.0913290
$726$	−27.6903	+	15.6813i	−1.02768	+	0.581989i
$727$	33.0416			1.22545			0.612723	−	0.790298i	$-0.290074\pi$
$727$	33.0416			1.22545			0.612723	+	0.790298i	$0.290074\pi$
$728$	0.540856	−	0.0620575i	0.0200455	−	0.00230000i
$729$	−24.0693	+	17.4874i	−0.891457	+	0.647682i
$730$	16.6365	−	3.86865i	0.615744	−	0.143185i
$731$	−11.9141	−	17.4238i	−0.440658	−	0.644443i
$732$	−10.8652	+	9.97198i	−0.401589	+	0.368575i
$733$	13.6795	−	14.0759i	0.505264	−	0.519904i	−0.415726	−	0.909490i	$-0.636473\pi$
$733$	13.6795	−	14.0759i	0.505264	−	0.519904i	0.920990	+	0.389586i	$0.127382\pi$
$734$	28.8317	−	10.2871i	1.06420	−	0.379705i
$735$	−3.44776	+	10.6111i	−0.127172	+	0.391396i
$736$	11.0509	+	12.7534i	0.407340	+	0.470095i
$737$	48.6514	−	15.8401i	1.79210	−	0.583479i
$738$	3.23171	−	3.72959i	0.118961	−	0.137288i
$739$	19.9661	+	33.1101i	0.734466	+	1.21798i	0.969286	+	0.245936i	$0.0790954\pi$
$739$	19.9661	+	33.1101i	0.734466	+	1.21798i	−0.234820	+	0.972039i	$0.575450\pi$
$740$	−7.56578	+	9.81148i	−0.278124	+	0.360677i
$741$	−1.69465	−	0.604651i	−0.0622546	−	0.0222124i
$742$	1.07904	−	0.530529i	0.0396129	−	0.0194763i
$743$	8.30113	+	6.78780i	0.304539	+	0.249020i	0.772916	−	0.634509i	$-0.218797\pi$
$743$	8.30113	+	6.78780i	0.304539	+	0.249020i	−0.468377	+	0.883529i	$0.655161\pi$
$744$	−2.56956	+	12.6813i	−0.0942046	+	0.464918i
$745$	−6.95904	+	0.397932i	−0.254960	+	0.0145791i
$746$	27.2493	+	25.0092i	0.997668	+	0.915651i
$747$	−0.962780	+	6.69628i	−0.0352263	+	0.245004i
$748$	9.59076	−	14.9432i	0.350673	−	0.546379i
$749$	−0.0477370	−	0.332018i	−0.00174427	−	0.0121317i
$750$	1.63290	−	2.38803i	0.0596249	−	0.0871987i
$751$	6.22903	−	15.9991i	0.227301	−	0.583817i	−0.771313	−	0.636456i	$-0.780400\pi$
$751$	6.22903	−	15.9991i	0.227301	−	0.583817i	0.998614	+	0.0526391i	$0.0167633\pi$
$752$	−32.2323	−	41.7996i	−1.17539	−	1.52428i
$753$	10.3609	+	31.8877i	0.377574	+	1.16205i
$754$	9.83902	−	16.3162i	0.358316	−	0.594201i
$755$	−2.60532	−	6.69172i	−0.0948174	−	0.243536i
$756$	0.678099	+	0.157685i	0.0246622	+	0.00573495i
$757$	43.8440	−	18.5286i	1.59354	−	0.673435i	0.601443	−	0.798916i	$-0.294593\pi$
$757$	43.8440	−	18.5286i	1.59354	−	0.673435i	0.992096	+	0.125481i	$0.0400473\pi$
$758$	46.0225	−	29.5769i	1.67161	−	1.07428i
$759$	11.1809	−	8.63245i	0.405839	−	0.313338i
$760$	0.287421	+	0.184714i	0.0104259	+	0.00670029i
$761$	3.76729	+	0.651954i	0.136564	+	0.0236333i	0.238394	−	0.971168i	$-0.423379\pi$
$761$	3.76729	+	0.651954i	0.136564	+	0.0236333i	−0.101830	+	0.994802i	$0.532470\pi$
$762$	0.150802	−	1.75576i	0.00546300	−	0.0636045i
$763$	0.0921666	+	1.07308i	0.00333665	+	0.0388480i
$764$	−10.9956	+	1.90287i	−0.397807	+	0.0688433i
$765$	−1.73630	−	0.733767i	−0.0627761	−	0.0265294i
$766$	−11.8621	−	8.61830i	−0.428594	−	0.311392i
$767$	−21.0368	−	11.8800i	−0.759596	−	0.428963i
$768$	−0.949670	+	33.2428i	−0.0342683	+	1.19955i
$769$	41.0116	+	12.0421i	1.47892	+	0.434249i	0.918986	−	0.394291i	$-0.129010\pi$
$769$	41.0116	+	12.0421i	1.47892	+	0.434249i	0.559930	+	0.828540i	$0.310828\pi$
$770$	0.100417	−	0.582339i	0.00361879	−	0.0209860i
$771$	22.4482	−	6.59137i	0.808451	−	0.237383i
$772$	−3.10334	−	11.8063i	−0.111692	−	0.424919i
$773$	0.600459	+	2.96338i	0.0215970	+	0.106585i	0.989431	−	0.145004i	$-0.0463195\pi$
$773$	0.600459	+	2.96338i	0.0215970	+	0.106585i	−0.967834	+	0.251589i	$0.919047\pi$
$774$	1.93948	−	3.67571i	0.0697130	−	0.132121i
$775$	0.178685	+	6.25479i	0.00641855	+	0.224679i
$776$	2.88516	−	10.9763i	0.103571	−	0.394026i
$777$	−1.51005	−	0.0863479i	−0.0541728	−	0.00309772i
$778$	24.2384	+	24.9407i	0.868989	+	0.894169i
$779$	−1.42395	−	0.700107i	−0.0510182	−	0.0250839i
$780$	−3.64270	−	7.97641i	−0.130430	−	0.285601i
$781$	35.7082	+	13.8778i	1.27774	+	0.496586i
$782$	−8.36938	+	18.3264i	−0.299288	+	0.655350i
$783$	−10.4903	+	8.57790i	−0.374894	+	0.306549i
$784$	−16.0454	−	30.4095i	−0.573051	−	1.08605i
$785$	6.30335	−	3.55966i	0.224976	−	0.127050i
$786$	38.4542	+	4.41221i	1.37162	+	0.157378i
$787$	−13.9835	−	1.60446i	−0.498460	−	0.0571929i	−0.138884	−	0.990309i	$-0.544351\pi$
$787$	−13.9835	−	1.60446i	−0.498460	−	0.0571929i	−0.359576	+	0.933116i	$0.617079\pi$
$788$	−3.46505	+	1.95680i	−0.123437	+	0.0697082i
$789$	1.94315	+	3.68268i	0.0691780	+	0.131107i
$790$	21.5969	−	17.6597i	0.768383	−	0.628304i
$791$	0.338396	−	0.740984i	0.0120320	−	0.0263464i
$792$	−1.93735	−	0.165226i	−0.0688406	−	0.00587105i
$793$	−12.7667	−	27.9552i	−0.453359	−	0.992718i
$794$	−42.4385	−	20.8656i	−1.50609	−	0.740493i
$795$	7.50690	+	7.72442i	0.266242	+	0.273957i
$796$	11.6813	+	0.667963i	0.414034	+	0.0236753i
$797$	−8.00212	+	30.4432i	−0.283450	+	1.07835i	0.661183	+	0.750225i	$0.270055\pi$
$797$	−8.00212	+	30.4432i	−0.283450	+	1.07835i	−0.944633	+	0.328130i	$0.893582\pi$
$798$	−0.00214158	−	0.0749650i	−7.58110e−5	−	0.00265373i
$799$	20.8612	−	39.5363i	0.738015	−	1.39869i
$800$	1.25589	+	6.19808i	0.0444025	+	0.219135i
$801$	−1.18565	−	4.51070i	−0.0418930	−	0.159378i
$802$	−50.8392	+	14.9277i	−1.79520	+	0.527117i
$803$	25.8102	+	17.6258i	0.910823	+	0.622002i
$804$	30.3636	+	8.91555i	1.07084	+	0.314427i
$805$	−0.00749049	+	0.262201i	−0.000264005	+	0.00924138i
$806$	42.2155	+	23.8402i	1.48698	+	0.839734i
$807$	−19.2542	−	13.9890i	−0.677780	−	0.492436i
$808$	0.338107	+	0.142885i	0.0118946	+	0.00502668i
$809$	−33.1941	+	5.74447i	−1.16704	+	0.201965i	−0.720927	−	0.693011i	$-0.756284\pi$
$809$	−33.1941	+	5.74447i	−1.16704	+	0.201965i	−0.446116	+	0.894975i	$0.647193\pi$
$810$	1.15363	+	13.4315i	0.0405345	+	0.471935i
$811$	−1.10837	+	12.9045i	−0.0389201	+	0.453139i	0.950768	+	0.309902i	$0.100296\pi$
$811$	−1.10837	+	12.9045i	−0.0389201	+	0.453139i	−0.989689	+	0.143236i	$0.954249\pi$
$812$	0.306131	+	0.0529780i	0.0107431	+	0.00185917i
$813$	−10.2473	−	6.58551i	−0.359387	−	0.230964i
$814$	−57.7358	+	4.99389i	−2.02364	+	0.175036i
$815$	4.40238	−	2.82924i	0.154209	−	0.0991038i
$816$	−30.1229	+	12.7300i	−1.05451	+	0.445640i
$817$	−1.30157	−	0.302666i	−0.0455360	−	0.0105889i
$818$	−5.44054	−	13.9739i	−0.190224	−	0.488586i
$819$	−0.0981934	+	0.162835i	−0.00343115	+	0.00568993i
$820$	−2.38963	−	7.35453i	−0.0834495	−	0.256831i
$821$	10.2729	+	13.3221i	0.358525	+	0.464943i	0.936274	−	0.351271i	$-0.114250\pi$
$821$	10.2729	+	13.3221i	0.358525	+	0.464943i	−0.577749	+	0.816215i	$0.696069\pi$
$822$	−20.9453	+	53.7975i	−0.730551	+	1.87640i
$823$	7.84167	−	11.4681i	0.273343	−	0.399752i	−0.664236	−	0.747523i	$-0.731243\pi$
$823$	7.84167	−	11.4681i	0.273343	−	0.399752i	0.937580	+	0.347771i	$0.113061\pi$
$824$	1.70091	+	11.8301i	0.0592541	+	0.412121i
$825$	5.23928	−	0.756509i	0.182408	−	0.0263383i
$826$	0.143309	−	0.996735i	0.00498635	−	0.0346808i
$827$	−12.6710	−	11.6294i	−0.440614	−	0.404392i	0.424929	−	0.905227i	$-0.360299\pi$
$827$	−12.6710	−	11.6294i	−0.440614	−	0.404392i	−0.865543	+	0.500835i	$0.833026\pi$
$828$	−1.54936	+	0.0885955i	−0.0538439	+	0.00307891i
$829$	4.42828	−	21.8544i	0.153800	−	0.759035i	−0.826719	−	0.562615i	$-0.809796\pi$
$829$	4.42828	−	21.8544i	0.153800	−	0.759035i	0.980520	−	0.196421i	$-0.0629318\pi$
$830$	20.9773	+	17.1530i	0.728132	+	0.595391i
$831$	−18.9305	+	9.30752i	−0.656693	+	0.322874i
$832$	6.54299	+	2.33453i	0.226837	+	0.0809354i
$833$	17.7814	−	23.0593i	0.616088	−	0.798958i
$834$	−13.2786	−	22.0201i	−0.459801	−	0.762495i
$835$	−16.7712	+	19.3550i	−0.580391	+	0.669807i
$836$	−0.192353	−	1.10754i	−0.00665265	−	0.0383050i
$837$	−22.5803	−	26.0591i	−0.780490	−	0.900733i
$838$	−14.8521	+	45.7101i	−0.513058	+	1.57903i
$839$	12.2627	−	4.37531i	0.423355	−	0.151053i	−0.115775	−	0.993275i	$-0.536935\pi$
$839$	12.2627	−	4.37531i	0.423355	−	0.151053i	0.539130	+	0.842223i	$0.318753\pi$
$840$	−0.141665	+	0.145770i	−0.00488792	+	0.00502955i
$841$	16.9103	−	15.5201i	0.583112	−	0.535176i
$842$	17.2478	+	25.2240i	0.594397	+	0.869278i
$843$	5.89797	−	1.37152i	0.203137	−	0.0472375i
$844$	−6.26659	+	4.55294i	−0.215705	+	0.156719i
$845$	5.23888	−	0.601106i	0.180223	−	0.0206787i
$846$	8.80172			0.302609
$847$	0.908957	−	0.585696i	0.0312321	−	0.0201248i
$848$	−33.1938			−1.13988
$849$	−15.6401	+	1.79453i	−0.536767	+	0.0615882i
$850$	−6.10824	+	4.43790i	−0.209511	+	0.152219i
$851$	25.0554	−	5.82639i	0.858889	−	0.199726i
$852$	13.3743	+	19.5593i	0.458197	+	0.670091i
$853$	15.3244	−	14.0646i	0.524699	−	0.481564i	−0.369502	−	0.929230i	$-0.620472\pi$
$853$	15.3244	−	14.0646i	0.524699	−	0.481564i	0.894201	+	0.447666i	$0.147744\pi$
$854$	0.892739	−	0.918607i	0.0305489	−	0.0314341i
$855$	−0.112395	+	0.0401025i	−0.00384383	+	0.00137148i
$856$	−1.36610	+	4.20442i	−0.0466923	+	0.143704i
$857$	8.06374	+	9.30605i	0.275452	+	0.317889i	0.876573	−	0.481270i	$-0.159824\pi$
$857$	8.06374	+	9.30605i	0.275452	+	0.317889i	−0.601120	+	0.799158i	$0.705279\pi$
$858$	15.9432	−	37.7895i	0.544292	−	1.29011i
$859$	3.97514	−	4.58756i	0.135630	−	0.156526i	−0.683871	−	0.729603i	$-0.739705\pi$
$859$	3.97514	−	4.58756i	0.135630	−	0.156526i	0.819501	+	0.573077i	$0.194250\pi$
$860$	−3.36299	−	5.57690i	−0.114677	−	0.190171i
$861$	0.576471	−	0.747581i	0.0196461	−	0.0254775i
$862$	−40.8518	−	14.5759i	−1.39142	−	0.496457i
$863$	−24.0833	+	11.8410i	−0.819805	+	0.403071i	−0.802407	−	0.596778i	$-0.796447\pi$
$863$	−24.0833	+	11.8410i	−0.819805	+	0.403071i	−0.0173982	+	0.999849i	$0.505538\pi$
$864$	−26.9778	−	22.0596i	−0.917803	−	0.750484i
$865$	4.16408	−	20.5505i	0.141583	−	0.698740i
$866$	54.6628	−	3.12573i	1.85752	−	0.106217i
$867$	−0.414081	−	0.380040i	−0.0140629	−	0.0129068i
$868$	−0.112506	+	0.782499i	−0.00381872	+	0.0265598i
$869$	50.5335	+	7.23462i	1.71423	+	0.245418i
$870$	1.01243	+	7.04162i	0.0343247	+	0.238733i
$871$	−37.2225	+	54.4362i	−1.26124	+	1.84450i
$872$	5.14989	−	13.2274i	0.174397	−	0.447936i
$873$	2.42064	+	3.13914i	0.0819263	+	0.106244i
$874$	0.394144	+	1.21305i	0.0133321	+	0.0410320i
$875$	−0.0507626	+	0.0841803i	−0.00171609	+	0.00284581i
$876$	7.01334	+	18.0136i	0.236959	+	0.608624i
$877$	−30.2636	−	7.03750i	−1.02193	−	0.237639i	−0.318136	−	0.948045i	$-0.603057\pi$
$877$	−30.2636	−	7.03750i	−1.02193	−	0.237639i	−0.703793	+	0.710406i	$0.748512\pi$
$878$	−21.3315	+	9.01475i	−0.719902	+	0.304233i
$879$	20.4731	−	13.1573i	0.690542	−	0.443784i
$880$	−9.58079	+	13.2035i	−0.322968	+	0.445090i
$881$	−11.2766	−	7.24704i	−0.379919	−	0.244159i	0.336718	−	0.941606i	$-0.390683\pi$
$881$	−11.2766	−	7.24704i	−0.379919	−	0.244159i	−0.716637	+	0.697447i	$0.754319\pi$
$882$	5.64941	+	0.977669i	0.190226	+	0.0329198i
$883$	1.35173	−	15.7379i	0.0454894	−	0.529624i	−0.937751	−	0.347309i	$-0.887095\pi$
$883$	1.35173	−	15.7379i	0.0454894	−	0.529624i	0.983240	−	0.182315i	$-0.0583591\pi$
$884$	1.95843	+	22.8016i	0.0658693	+	0.766902i
$885$	8.88851	−	1.53822i	0.298784	−	0.0517066i
$886$	−35.3976	−	14.9591i	−1.18920	−	0.502562i
$887$	−11.7268	−	8.52003i	−0.393748	−	0.286075i	0.373242	−	0.927734i	$-0.378246\pi$
$887$	−11.7268	−	8.52003i	−0.393748	−	0.286075i	−0.766990	+	0.641660i	$0.778246\pi$
$888$	17.3575	+	9.80223i	0.582480	+	0.328941i
$889$	−0.00170994	+	0.0598557i	−5.73496e−5	+	0.00200750i
$890$	−17.9244	−	5.26308i	−0.600828	−	0.176419i
$891$	−16.6690	+	18.1840i	−0.558432	+	0.609186i
$892$	7.48791	−	2.19865i	0.250714	−	0.0736162i
$893$	−0.719448	−	2.73706i	−0.0240754	−	0.0915923i
$894$	−4.00456	−	19.7633i	−0.133933	−	0.660983i
$895$	−6.99269	+	13.2526i	−0.233740	+	0.442986i
$896$	−0.0272359	−	0.953380i	−0.000909887	−	0.0318502i
$897$	−4.62832	+	17.6080i	−0.154535	+	0.587912i
$898$	−20.1524	−	1.15235i	−0.672493	−	0.0384546i
$899$	−10.7241	−	11.0349i	−0.357669	−	0.368033i
$900$	−0.521907	−	0.256605i	−0.0173969	−	0.00855349i
$901$	−11.6780	−	25.5713i	−0.389052	−	0.851904i
$902$	17.7671	−	31.5056i	0.591579	−	1.04902i
$903$	0.330265	−	0.723179i	0.0109905	−	0.0240659i
$904$	−8.31109	+	6.79594i	−0.276423	+	0.226030i
$905$	0.300037	+	0.568633i	0.00997355	+	0.0189020i
$906$	18.0890	−	10.2153i	0.600967	−	0.339382i
$907$	6.98104	+	0.801000i	0.231802	+	0.0265968i	0.229114	−	0.973400i	$-0.426417\pi$
$907$	6.98104	+	0.801000i	0.231802	+	0.0265968i	0.00268775	+	0.999996i	$0.499144\pi$
$908$	27.9724	+	3.20953i	0.928297	+	0.106512i
$909$	−0.111636	+	0.0630437i	−0.00370273	+	0.00209103i
$910$	0.355433	+	0.673620i	0.0117825	+	0.0223303i
$911$	−17.3611	+	14.1961i	−0.575198	+	0.470337i	−0.875307	−	0.483568i	$-0.839341\pi$
$911$	−17.3611	+	14.1961i	−0.575198	+	0.470337i	0.300109	+	0.953905i	$0.402977\pi$
$912$	−0.860046	+	1.88324i	−0.0284790	+	0.0623602i
$913$	2.86045	+	49.5016i	0.0946671	+	1.63826i
$914$	−24.9219	−	54.5714i	−0.824343	−	1.80506i
$915$	10.2975	+	5.06292i	0.340424	+	0.167375i
$916$	−6.85032	−	7.04882i	−0.226341	−	0.232899i
$917$	−1.31310	−	0.0750856i	−0.0433623	−	0.00247954i
$918$	10.5769	−	40.2386i	0.349089	−	1.32807i
$919$	−0.564128	−	19.7471i	−0.0186089	−	0.651395i	−0.954347	−	0.298700i	$-0.903447\pi$
$919$	−0.564128	−	19.7471i	−0.0186089	−	0.651395i	0.935738	−	0.352695i	$-0.114735\pi$
$920$	1.61330	−	3.05754i	0.0531888	−	0.100804i
$921$	2.60928	+	12.8773i	0.0859787	+	0.424322i
$922$	10.0542	+	38.2503i	0.331119	+	1.25971i
$923$	−47.3770	+	13.9111i	−1.55943	+	0.457891i
$924$	0.668529	+	0.0186962i	0.0219930	+	0.000615061i
$925$	9.24969	+	2.71595i	0.304128	+	0.0893000i
$926$	0.313937	−	10.9892i	0.0103166	−	0.361129i
$927$	−3.63496	−	2.05275i	−0.119388	−	0.0674213i
$928$	−12.5814	−	9.14094i	−0.413005	−	0.300066i
$929$	−11.3363	−	4.79077i	−0.371933	−	0.157180i	0.195288	−	0.980746i	$-0.437436\pi$
$929$	−11.3363	−	4.79077i	−0.371933	−	0.157180i	−0.567221	+	0.823566i	$0.691981\pi$
$930$	−17.8369	+	3.08680i	−0.584896	+	0.101220i
$931$	−0.157755	−	1.83671i	−0.00517020	−	0.0601956i
$932$	2.17727	−	25.3495i	0.0713190	−	0.830352i
$933$	−23.3883	−	4.04751i	−0.765699	−	0.132509i
$934$	−26.2655	−	16.8798i	−0.859432	−	0.552324i
$935$	−13.5422	−	2.73553i	−0.442876	−	0.0894613i
$936$	2.10824	−	1.35488i	0.0689099	−	0.0442857i
$937$	52.9182	−	22.3634i	1.72876	−	0.730581i	0.729868	−	0.683588i	$-0.239581\pi$
$937$	52.9182	−	22.3634i	1.72876	−	0.730581i	0.998895	−	0.0469936i	$-0.0149640\pi$
$938$	−2.67722	−	0.622560i	−0.0874143	−	0.0203273i
$939$	−0.228540	−	0.586999i	−0.00745811	−	0.0191560i
$940$	7.12224	−	11.8109i	0.232302	−	0.385229i
$941$	−12.9165	−	39.7530i	−0.421067	−	1.29591i	−0.906711	−	0.421753i	$-0.861415\pi$
$941$	−12.9165	−	39.7530i	−0.421067	−	1.29591i	0.485644	−	0.874157i	$-0.338585\pi$
$942$	12.7882	+	16.5840i	0.416661	+	0.540336i
$943$	−5.82505	+	14.9615i	−0.189690	+	0.487214i
$944$	−15.6909	+	22.9472i	−0.510694	+	0.746866i
$945$	−0.0770906	−	0.536177i	−0.00250776	−	0.0174418i
$946$	8.56426	−	29.2322i	0.278448	−	0.950420i
$947$	−7.29894	+	50.7653i	−0.237184	+	1.64965i	0.428593	+	0.903498i	$0.359010\pi$
$947$	−7.29894	+	50.7653i	−0.237184	+	1.64965i	−0.665776	+	0.746151i	$0.731900\pi$
$948$	23.2615	+	21.3492i	0.755498	+	0.693389i
$949$	−40.2174	+	2.29971i	−1.30551	+	0.0746519i
$950$	−0.0949245	+	0.468471i	−0.00307976	+	0.0151992i
$951$	18.5389	+	15.1592i	0.601166	+	0.491571i
$952$	0.476076	−	0.234071i	0.0154297	−	0.00758627i
$953$	−36.4844	−	13.0176i	−1.18185	−	0.421682i	−0.329246	−	0.944244i	$-0.606794\pi$
$953$	−36.4844	−	13.0176i	−1.18185	−	0.421682i	−0.852601	+	0.522562i	$0.824976\pi$
$954$	3.37998	−	4.38324i	0.109431	−	0.141913i
$955$	4.48367	+	7.43533i	0.145088	+	0.240602i
$956$	−2.00478	+	2.31364i	−0.0648393	+	0.0748286i
$957$	−8.23423	+	10.0824i	−0.266175	+	0.325918i
$958$	−23.2443	−	26.8253i	−0.750988	−	0.866686i
$959$	0.606197	−	1.86568i	0.0195751	−	0.0602460i
$960$	−2.44300	+	0.871662i	−0.0788476	+	0.0281328i
$961$	5.68305	−	5.84772i	0.183324	−	0.188636i
$962$	55.0288	−	50.5050i	1.77420	−	1.62835i
$963$	−0.871558	−	1.27461i	−0.0280856	−	0.0410738i
$964$	−27.1094	+	6.30402i	−0.873135	+	0.203039i
$965$	−7.68427	+	5.58295i	−0.247365	+	0.179722i
$966$	−0.753894	+	0.0865013i	−0.0242561	+	0.00278313i
$967$	30.6163			0.984555			0.492277	−	0.870438i	$-0.336165\pi$
$967$	30.6163			0.984555			0.492277	+	0.870438i	$0.336165\pi$
$968$	−14.1562	+	1.64151i	−0.454997	+	0.0527603i
$969$	−1.75336			−0.0563259
$970$	15.7743	−	1.80994i	0.506484	−	0.0581136i
$971$	22.5275	−	16.3672i	0.722943	−	0.525249i	−0.164380	−	0.986397i	$-0.552562\pi$
$971$	22.5275	−	16.3672i	0.722943	−	0.525249i	0.887323	+	0.461148i	$0.152562\pi$
$972$	5.83388	−	1.35661i	0.187122	−	0.0435133i
$973$	0.493186	+	0.721262i	0.0158108	+	0.0231226i
$974$	−26.7715	+	24.5707i	−0.857816	+	0.787296i
$975$	−4.75508	+	4.89286i	−0.152284	+	0.156697i
$976$	−33.3053	+	11.8833i	−1.06608	+	0.380376i
$977$	−10.5511	+	32.4728i	−0.337558	+	1.03890i	0.627890	+	0.778302i	$0.283919\pi$
$977$	−10.5511	+	32.4728i	−0.337558	+	1.03890i	−0.965448	+	0.260595i	$0.916081\pi$
$978$	9.91397	+	11.4413i	0.317014	+	0.365853i
$979$	−15.1009	−	30.6672i	−0.482628	−	0.980128i
$980$	5.88335	−	6.78975i	0.187937	−	0.216891i
$981$	2.56024	+	4.24569i	0.0817423	+	0.135554i
$982$	−20.9489	+	27.1670i	−0.668507	+	0.866935i
$983$	34.6010	+	12.3456i	1.10360	+	0.393764i	0.824136	−	0.566392i	$-0.191661\pi$
$983$	34.6010	+	12.3456i	1.10360	+	0.393764i	0.279464	+	0.960156i	$0.409843\pi$
$984$	−11.1652	+	5.48956i	−0.355933	+	0.175001i
$985$	2.39696	+	1.95998i	0.0763734	+	0.0624503i
$986$	3.68718	−	18.1970i	0.117424	−	0.579510i
$987$	1.68098	−	0.0961217i	0.0535061	−	0.00305959i
$988$	1.06743	+	0.979675i	0.0339594	+	0.0311676i
$989$	−1.92427	+	13.3836i	−0.0611883	+	0.425574i
$990$	−0.767952	−	2.60960i	−0.0244071	−	0.0829386i
$991$	8.51702	+	59.2372i	0.270552	+	1.88173i	0.442714	+	0.896663i	$0.354016\pi$
$991$	8.51702	+	59.2372i	0.270552	+	1.88173i	−0.172162	+	0.985069i	$0.555075\pi$
$992$	22.3360	−	32.6653i	0.709167	−	1.03712i
$993$	−6.32250	+	16.2392i	−0.200639	+	0.515336i
$994$	−1.25675	−	1.62979i	−0.0398618	−	0.0516938i
$995$	−2.81324	−	8.65825i	−0.0891856	−	0.274485i
$996$	−15.8367	+	26.2622i	−0.501805	+	0.832149i
$997$	19.5086	+	50.1074i	0.617843	+	1.58692i	0.797587	+	0.603204i	$0.206109\pi$
$997$	19.5086	+	50.1074i	0.617843	+	1.58692i	−0.179744	+	0.983713i	$0.557527\pi$
$998$	66.4494	+	15.4522i	2.10342	+	0.489129i
$999$	−48.9322	+	20.6789i	−1.54815	+	0.654252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.s.b.416.4	yes	880
121.16	even	55	inner	605.2.s.b.16.4	✓	880

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.s.b.16.4	✓	880	121.16	even	55	inner
605.2.s.b.416.4	yes	880	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.s (of order \(55\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80070 + 0.206611i) q^{2} +(-1.29126 + 0.938155i) q^{3} +(1.25182 - 0.291098i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(2.13134 - 1.95613i) q^{6} +(-0.0685099 + 0.0704951i) q^{7} +(1.22021 - 0.435369i) q^{8} +(-0.139834 + 0.430365i) q^{9} +O(q^{10})\)	\(q+(-1.80070 + 0.206611i) q^{2} +(-1.29126 + 0.938155i) q^{3} +(1.25182 - 0.291098i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(2.13134 - 1.95613i) q^{6} +(-0.0685099 + 0.0704951i) q^{7} +(1.22021 - 0.435369i) q^{8} +(-0.139834 + 0.430365i) q^{9} +(1.18695 + 1.36981i) q^{10} +(-0.376086 + 3.29523i) q^{11} +(-1.34333 + 1.55029i) q^{12} +(-2.20746 - 3.66065i) q^{13} +(0.108801 - 0.141096i) q^{14} +(1.50326 + 0.536363i) q^{15} +(-4.41399 + 2.17021i) q^{16} +(-3.22476 - 2.63687i) q^{17} +(0.162881 - 0.803851i) q^{18} +(-0.263287 + 0.0150553i) q^{19} +(-0.946875 - 0.869034i) q^{20} +(0.0223288 - 0.155300i) q^{21} +(-0.00361276 - 6.01144i) q^{22} +(0.379754 + 2.64125i) q^{23} +(-1.16716 + 1.70692i) q^{24} +(-0.362808 + 0.931864i) q^{25} +(4.73131 + 6.13567i) q^{26} +(-1.70284 - 5.24080i) q^{27} +(-0.0652411 + 0.108190i) q^{28} +(-0.892183 - 2.29155i) q^{29} +(-2.81775 - 0.655240i) q^{30} +(5.76378 - 2.43580i) q^{31} +(5.32012 - 3.41903i) q^{32} +(-2.60581 - 4.60783i) q^{33} +(6.35164 + 4.08195i) q^{34} +(0.0968617 + 0.0167626i) q^{35} +(-0.0497686 + 0.579445i) q^{36} +(-0.824959 - 9.60482i) q^{37} +(0.470990 - 0.0815081i) q^{38} +(6.28466 + 2.65592i) q^{39} +(-1.04812 - 0.761505i) q^{40} +(5.23917 + 2.95869i) q^{41} +(-0.00812075 + 0.284263i) q^{42} +(4.86190 + 1.42758i) q^{43} +(0.488444 + 4.23452i) q^{44} +(0.434182 - 0.127487i) q^{45} +(-1.22954 - 4.67764i) q^{46} +(2.13115 + 10.5176i) q^{47} +(3.66361 - 6.94331i) q^{48} +(0.199616 + 6.98749i) q^{49} +(0.460775 - 1.75297i) q^{50} +(6.63779 + 0.379563i) q^{51} +(-3.82895 - 3.93989i) q^{52} +(6.05615 + 2.97761i) q^{53} +(4.14912 + 9.08530i) q^{54} +(2.93240 - 1.54952i) q^{55} +(-0.0529049 + 0.115846i) q^{56} +(0.325847 - 0.266444i) q^{57} +(2.08002 + 3.94207i) q^{58} +(4.92121 - 2.77914i) q^{59} +(2.03795 + 0.233833i) q^{60} +(7.14248 + 0.819523i) q^{61} +(-9.87560 + 5.57701i) q^{62} +(-0.0207586 - 0.0393419i) q^{63} +(-1.25808 + 1.02873i) q^{64} +(-1.77578 + 3.88842i) q^{65} +(5.64433 + 7.75894i) q^{66} +(-6.40855 - 14.0328i) q^{67} +(-4.80440 - 2.36217i) q^{68} +(-2.96826 - 3.05427i) q^{69} +(-0.177882 - 0.0101717i) q^{70} +(2.93646 - 11.1715i) q^{71} +(0.0167411 + 0.586014i) q^{72} +(4.39767 - 8.33451i) q^{73} +(3.46997 + 17.1250i) q^{74} +(-0.405754 - 1.54365i) q^{75} +(-0.325205 + 0.0954888i) q^{76} +(-0.206532 - 0.252268i) q^{77} +(-11.8656 - 3.48404i) q^{78} +(0.439528 - 15.3855i) q^{79} +(4.28289 + 2.41866i) q^{80} +(6.01722 + 4.37177i) q^{81} +(-10.0455 - 4.24526i) q^{82} +(14.7312 - 2.54934i) q^{83} +(-0.0172560 - 0.200908i) q^{84} +(-0.356470 + 4.15031i) q^{85} +(-9.04979 - 1.56613i) q^{86} +(3.30187 + 2.12199i) q^{87} +(0.975739 + 4.18460i) q^{88} +(-8.67057 + 5.57224i) q^{89} +(-0.755493 + 0.319274i) q^{90} +(0.409291 + 0.0951765i) q^{91} +(1.24425 + 3.19582i) q^{92} +(-5.15739 + 8.55257i) q^{93} +(-6.01062 - 18.4988i) q^{94} +(0.161038 + 0.208838i) q^{95} +(-3.66207 + 9.40596i) q^{96} +(4.94458 - 7.23122i) q^{97} +(-1.80314 - 12.5411i) q^{98} +(-1.36556 - 0.622640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9}+O(q^{10}) \) 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9	\( 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9} - 6 q^{10} + 5 q^{11} - 5 q^{12} - 26 q^{13} - 108 q^{14} - 12 q^{15} + 34 q^{16} - q^{17} - 14 q^{18} + q^{19} + 19 q^{20} - 10 q^{21} + 275 q^{22} - 51 q^{23} + 283 q^{24} + 22 q^{25} - 16 q^{27} - 4 q^{28} - 19 q^{29} + q^{30} - 34 q^{31} - 122 q^{32} + 19 q^{33} + 52 q^{34} + 8 q^{35} - 21 q^{36} - 109 q^{37} - 10 q^{38} - 9 q^{39} - 64 q^{40} + 4 q^{41} - 49 q^{42} - 97 q^{43} + 17 q^{44} - 80 q^{45} - 91 q^{46} + 166 q^{47} - 159 q^{48} + 175 q^{49} + 4 q^{50} - 112 q^{51} - 128 q^{52} - 141 q^{53} - 37 q^{54} - 5 q^{55} + 79 q^{56} - 204 q^{57} - 190 q^{58} + 9 q^{59} - 22 q^{60} + 2 q^{61} - 105 q^{62} - q^{63} - 176 q^{64} - 14 q^{65} - 112 q^{66} - 13 q^{67} - 35 q^{68} - 53 q^{69} + 24 q^{70} - 50 q^{71} + 705 q^{72} + q^{73} + 40 q^{74} - q^{75} - 148 q^{76} - 104 q^{77} - 187 q^{78} - 83 q^{79} - q^{80} - 238 q^{81} - 54 q^{82} - 151 q^{83} + 4 q^{84} - 29 q^{85} - 39 q^{86} - 74 q^{87} - 143 q^{88} - 52 q^{89} - 28 q^{90} - 188 q^{91} - 253 q^{92} + 122 q^{93} - 187 q^{94} + 122 q^{95} - 155 q^{96} + 283 q^{97} - 92 q^{98} + 172 q^{99}+O(q^{100}) \) 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9 - 6 * q^10 + 5 * q^11 - 5 * q^12 - 26 * q^13 - 108 * q^14 - 12 * q^15 + 34 * q^16 - q^17 - 14 * q^18 + q^19 + 19 * q^20 - 10 * q^21 + 275 * q^22 - 51 * q^23 + 283 * q^24 + 22 * q^25 - 16 * q^27 - 4 * q^28 - 19 * q^29 + q^30 - 34 * q^31 - 122 * q^32 + 19 * q^33 + 52 * q^34 + 8 * q^35 - 21 * q^36 - 109 * q^37 - 10 * q^38 - 9 * q^39 - 64 * q^40 + 4 * q^41 - 49 * q^42 - 97 * q^43 + 17 * q^44 - 80 * q^45 - 91 * q^46 + 166 * q^47 - 159 * q^48 + 175 * q^49 + 4 * q^50 - 112 * q^51 - 128 * q^52 - 141 * q^53 - 37 * q^54 - 5 * q^55 + 79 * q^56 - 204 * q^57 - 190 * q^58 + 9 * q^59 - 22 * q^60 + 2 * q^61 - 105 * q^62 - q^63 - 176 * q^64 - 14 * q^65 - 112 * q^66 - 13 * q^67 - 35 * q^68 - 53 * q^69 + 24 * q^70 - 50 * q^71 + 705 * q^72 + q^73 + 40 * q^74 - q^75 - 148 * q^76 - 104 * q^77 - 187 * q^78 - 83 * q^79 - q^80 - 238 * q^81 - 54 * q^82 - 151 * q^83 + 4 * q^84 - 29 * q^85 - 39 * q^86 - 74 * q^87 - 143 * q^88 - 52 * q^89 - 28 * q^90 - 188 * q^91 - 253 * q^92 + 122 * q^93 - 187 * q^94 + 122 * q^95 - 155 * q^96 + 283 * q^97 - 92 * q^98 + 172 * q^99

Introduction

L-functions

Modular forms

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