LMFDB - Embedded newform 225.2.q.a.106.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			106.27
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.43022 + 0.516560i) q^{2} +(0.810393 - 1.53077i) q^{3} +(3.81206 + 1.69724i) q^{4} +(-2.22233 + 0.247525i) q^{5} +(2.76017 - 3.30150i) q^{6} +(-0.644527 + 1.11635i) q^{7} +(4.36740 + 3.17310i) q^{8} +(-1.68652 - 2.48105i) q^{9} +(-5.52861 - 0.546422i) q^{10} +(0.502326 + 0.106773i) q^{11} +(5.68735 - 4.45996i) q^{12} +(-4.87743 + 1.03673i) q^{13} +(-2.14301 + 2.38005i) q^{14} +(-1.42205 + 3.60247i) q^{15} +(3.39033 + 3.76535i) q^{16} +(5.60571 + 4.07278i) q^{17} +(-2.81702 - 6.90071i) q^{18} +(-4.21905 - 3.06532i) q^{19} +(-8.89175 - 2.82823i) q^{20} +(1.18656 + 1.89131i) q^{21} +(1.16561 + 0.518963i) q^{22} +(2.78826 - 3.09668i) q^{23} +(8.39660 - 4.11403i) q^{24} +(4.87746 - 1.10016i) q^{25} -12.3888 q^{26} +(-5.16468 + 0.571054i) q^{27} +(-4.35169 + 3.16169i) q^{28} +(0.724325 + 6.89149i) q^{29} +(-5.31680 + 8.02022i) q^{30} +(0.160665 - 1.52862i) q^{31} +(0.895838 + 1.55164i) q^{32} +(0.570526 - 0.682419i) q^{33} +(11.5193 + 12.7935i) q^{34} +(1.15602 - 2.64044i) q^{35} +(-2.21819 - 12.3204i) q^{36} +(2.27325 - 6.99635i) q^{37} +(-8.66982 - 9.62881i) q^{38} +(-2.36564 + 8.30640i) q^{39} +(-10.4912 - 5.97062i) q^{40} +(-3.98547 + 0.847138i) q^{41} +(1.90663 + 5.20923i) q^{42} +(2.08364 - 3.60897i) q^{43} +(1.73368 + 1.25959i) q^{44} +(4.36213 + 5.09625i) q^{45} +(8.37572 - 6.08531i) q^{46} +(0.841878 + 8.00993i) q^{47} +(8.51139 - 2.13841i) q^{48} +(2.66917 + 4.62314i) q^{49} +(12.4216 - 0.154142i) q^{50} +(10.7773 - 5.28050i) q^{51} +(-20.3526 - 4.32609i) q^{52} +(2.21350 - 1.60820i) q^{53} +(-12.8463 - 1.28008i) q^{54} +(-1.14276 - 0.112945i) q^{55} +(-6.35720 + 2.83041i) q^{56} +(-8.11140 + 3.97429i) q^{57} +(-1.79960 + 17.1220i) q^{58} +(2.99263 - 0.636103i) q^{59} +(-11.5352 + 11.3193i) q^{60} +(-7.17717 - 1.52555i) q^{61} +(1.18008 - 3.63190i) q^{62} +(3.85674 - 0.283651i) q^{63} +(-1.75586 - 5.40400i) q^{64} +(10.5826 - 3.51124i) q^{65} +(1.73902 - 1.36372i) q^{66} +(0.0475303 - 0.452221i) q^{67} +(14.4568 + 25.0399i) q^{68} +(-2.48072 - 6.77772i) q^{69} +(4.17334 - 5.81969i) q^{70} +(1.33759 - 0.971819i) q^{71} +(0.506910 - 16.1873i) q^{72} +(-2.72548 - 8.38816i) q^{73} +(9.13854 - 15.8284i) q^{74} +(2.26856 - 8.35785i) q^{75} +(-10.8807 - 18.8459i) q^{76} +(-0.442959 + 0.491955i) q^{77} +(-10.0398 + 18.9644i) q^{78} +(0.359882 + 3.42405i) q^{79} +(-8.46644 - 7.52863i) q^{80} +(-3.31127 + 8.36872i) q^{81} -10.1232 q^{82} +(13.4120 - 5.97142i) q^{83} +(1.31324 + 9.22366i) q^{84} +(-13.4658 - 7.66350i) q^{85} +(6.92795 - 7.69427i) q^{86} +(11.1363 + 4.47604i) q^{87} +(1.85506 + 2.06025i) q^{88} +(-2.98202 - 9.17771i) q^{89} +(7.96843 + 14.6383i) q^{90} +(1.98628 - 6.11314i) q^{91} +(15.8848 - 7.07238i) q^{92} +(-2.20977 - 1.48473i) q^{93} +(-2.09166 + 19.9008i) q^{94} +(10.1349 + 5.76782i) q^{95} +(3.10118 - 0.113887i) q^{96} +(-0.842924 - 8.01989i) q^{97} +(4.09855 + 12.6140i) q^{98} +(-0.582277 - 1.42637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	2.43022	+	0.516560i	1.71843	+	0.365263i	0.958577	−	0.284835i	$-0.0919388\pi$
$2$	2.43022	+	0.516560i	1.71843	+	0.365263i	0.759851	+	0.650098i	$0.225272\pi$
$3$	0.810393	−	1.53077i	0.467881	−	0.883792i
$3$	0.810393	−	1.53077i	0.467881	−	0.883792i
$4$	3.81206	+	1.69724i	1.90603	+	0.848619i
$5$	−2.22233	+	0.247525i	−0.993854	+	0.110697i
$5$	−2.22233	+	0.247525i	−0.993854	+	0.110697i
$6$	2.76017	−	3.30150i	1.12684	−	1.34783i
$7$	−0.644527	+	1.11635i	−0.243608	+	0.421942i	−0.961739	−	0.273966i	$-0.911664\pi$
$7$	−0.644527	+	1.11635i	−0.243608	+	0.421942i	0.718131	+	0.695908i	$0.244998\pi$
$8$	4.36740	+	3.17310i	1.54411	+	1.12186i
$9$	−1.68652	−	2.48105i	−0.562175	−	0.827018i
$10$	−5.52861	−	0.546422i	−1.74830	−	0.172794i
$11$	0.502326	+	0.106773i	0.151457	+	0.0321932i	0.283016	−	0.959115i	$-0.408665\pi$
$11$	0.502326	+	0.106773i	0.151457	+	0.0321932i	−0.131559	+	0.991308i	$0.541998\pi$
$12$	5.68735	−	4.45996i	1.64180	−	1.28748i
$13$	−4.87743	+	1.03673i	−1.35276	+	0.287537i	−0.826571	−	0.562833i	$-0.809712\pi$
$13$	−4.87743	+	1.03673i	−1.35276	+	0.287537i	−0.526185	+	0.850370i	$0.676378\pi$
$14$	−2.14301	+	2.38005i	−0.572743	+	0.636095i
$15$	−1.42205	+	3.60247i	−0.367173	+	0.930153i
$16$	3.39033	+	3.76535i	0.847583	+	0.941337i
$17$	5.60571	+	4.07278i	1.35958	+	0.987795i	0.998471	+	0.0552732i	$0.0176030\pi$
$17$	5.60571	+	4.07278i	1.35958	+	0.987795i	0.361113	+	0.932522i	$0.382397\pi$
$18$	−2.81702	−	6.90071i	−0.663978	−	1.62651i
$19$	−4.21905	−	3.06532i	−0.967917	−	0.703233i	−0.0129412	−	0.999916i	$-0.504119\pi$
$19$	−4.21905	−	3.06532i	−0.967917	−	0.703233i	−0.954976	+	0.296683i	$0.904119\pi$
$20$	−8.89175	−	2.82823i	−1.98825	−	0.632412i
$21$	1.18656	+	1.89131i	0.258929	+	0.412717i
$22$	1.16561	+	0.518963i	0.248509	+	0.110643i
$23$	2.78826	−	3.09668i	0.581393	−	0.645702i	−0.378655	−	0.925538i	$-0.623613\pi$
$23$	2.78826	−	3.09668i	0.581393	−	0.645702i	0.960048	+	0.279836i	$0.0902800\pi$
$24$	8.39660	−	4.11403i	1.71395	−	0.839773i
$25$	4.87746	−	1.10016i	0.975492	−	0.220033i
$26$	−12.3888			−2.42964
$27$	−5.16468	+	0.571054i	−0.993943	+	0.109899i
$28$	−4.35169	+	3.16169i	−0.822392	+	0.597503i
$29$	0.724325	+	6.89149i	0.134504	+	1.27972i	0.828602	+	0.559838i	$0.189137\pi$
$29$	0.724325	+	6.89149i	0.134504	+	1.27972i	−0.694098	+	0.719880i	$0.744197\pi$
$30$	−5.31680	+	8.02022i	−0.970710	+	1.46429i
$31$	0.160665	−	1.52862i	0.0288562	−	0.274548i	−0.970574	−	0.240802i	$-0.922590\pi$
$31$	0.160665	−	1.52862i	0.0288562	−	0.274548i	0.999430	−	0.0337463i	$-0.0107438\pi$
$32$	0.895838	+	1.55164i	0.158363	+	0.274293i
$33$	0.570526	−	0.682419i	0.0993159	−	0.118794i
$34$	11.5193	+	12.7935i	1.97554	+	2.19406i
$35$	1.15602	−	2.64044i	0.195403	−	0.446315i
$36$	−2.21819	−	12.3204i	−0.369699	−	2.05339i
$37$	2.27325	−	6.99635i	0.373720	−	1.15019i	−0.570618	−	0.821216i	$-0.693296\pi$
$37$	2.27325	−	6.99635i	0.373720	−	1.15019i	0.944338	−	0.328977i	$-0.106704\pi$
$38$	−8.66982	−	9.62881i	−1.40643	−	1.56200i
$39$	−2.36564	+	8.30640i	−0.378806	+	1.33009i
$40$	−10.4912	−	5.97062i	−1.65880	−	0.944038i
$41$	−3.98547	+	0.847138i	−0.622426	+	0.132301i	−0.508321	−	0.861168i	$-0.669733\pi$
$41$	−3.98547	+	0.847138i	−0.622426	+	0.132301i	−0.114105	+	0.993469i	$0.536400\pi$
$42$	1.90663	+	5.20923i	0.294200	+	0.803802i
$43$	2.08364	−	3.60897i	0.317752	−	0.550362i	−0.662267	−	0.749268i	$-0.730405\pi$
$43$	2.08364	−	3.60897i	0.317752	−	0.550362i	0.980019	+	0.198906i	$0.0637387\pi$
$44$	1.73368	+	1.25959i	0.261362	+	0.189890i
$45$	4.36213	+	5.09625i	0.650268	+	0.759705i
$46$	8.37572	−	6.08531i	1.23493	−	0.897231i
$47$	0.841878	+	8.00993i	0.122801	+	1.16837i	0.866262	+	0.499590i	$0.166516\pi$
$47$	0.841878	+	8.00993i	0.122801	+	1.16837i	−0.743461	+	0.668779i	$0.766817\pi$
$48$	8.51139	−	2.13841i	1.22851	−	0.308654i
$49$	2.66917	+	4.62314i	0.381310	+	0.660448i
$50$	12.4216	−	0.154142i	1.75668	−	0.0217990i
$51$	10.7773	−	5.28050i	1.50913	−	0.739418i
$52$	−20.3526	−	4.32609i	−2.82240	−	0.599920i
$53$	2.21350	−	1.60820i	0.304047	−	0.220903i	−0.425291	−	0.905057i	$-0.639828\pi$
$53$	2.21350	−	1.60820i	0.304047	−	0.220903i	0.729338	+	0.684153i	$0.239828\pi$
$54$	−12.8463	−	1.28008i	−1.74816	−	0.174196i
$55$	−1.14276	−	0.112945i	−0.154090	−	0.0152295i
$56$	−6.35720	+	2.83041i	−0.849517	+	0.378229i
$57$	−8.11140	+	3.97429i	−1.07438	+	0.526408i
$58$	−1.79960	+	17.1220i	−0.236299	+	2.24823i
$59$	2.99263	−	0.636103i	0.389607	−	0.0828136i	−0.00894310	−	0.999960i	$-0.502847\pi$
$59$	2.99263	−	0.636103i	0.389607	−	0.0828136i	0.398550	+	0.917146i	$0.369513\pi$
$60$	−11.5352	+	11.3193i	−1.48919	+	1.46131i
$61$	−7.17717	−	1.52555i	−0.918942	−	0.195327i	−0.275925	−	0.961179i	$-0.588984\pi$
$61$	−7.17717	−	1.52555i	−0.918942	−	0.195327i	−0.643017	+	0.765852i	$0.722318\pi$
$62$	1.18008	−	3.63190i	0.149870	−	0.461251i
$63$	3.85674	−	0.283651i	0.485904	−	0.0357367i
$64$	−1.75586	−	5.40400i	−0.219483	−	0.675499i
$65$	10.5826	−	3.51124i	1.31261	−	0.435516i
$66$	1.73902	−	1.36372i	0.214058	−	0.167862i
$67$	0.0475303	−	0.452221i	0.00580675	−	0.0552476i	−0.991235	−	0.132112i	$-0.957824\pi$
$67$	0.0475303	−	0.452221i	0.00580675	−	0.0552476i	0.997042	+	0.0768644i	$0.0244908\pi$
$68$	14.4568	+	25.0399i	1.75314	+	3.03654i
$69$	−2.48072	−	6.77772i	−0.298643	−	0.815942i
$70$	4.17334	−	5.81969i	0.498809	−	0.695587i
$71$	1.33759	−	0.971819i	0.158743	−	0.115334i	−0.505578	−	0.862781i	$-0.668721\pi$
$71$	1.33759	−	0.971819i	0.158743	−	0.115334i	0.664321	+	0.747447i	$0.268721\pi$
$72$	0.506910	−	16.1873i	0.0597400	−	1.90769i
$73$	−2.72548	−	8.38816i	−0.318993	−	0.981760i	−0.974079	−	0.226206i	$-0.927368\pi$
$73$	−2.72548	−	8.38816i	−0.318993	−	0.981760i	0.655086	−	0.755554i	$-0.272632\pi$
$74$	9.13854	−	15.8284i	1.06233	−	1.84002i
$75$	2.26856	−	8.35785i	0.261951	−	0.965081i
$76$	−10.8807	−	18.8459i	−1.24810	−	2.16178i
$77$	−0.442959	+	0.491955i	−0.0504798	+	0.0560635i
$78$	−10.0398	+	18.9644i	−1.13678	+	2.14730i
$79$	0.359882	+	3.42405i	0.0404899	+	0.385236i	0.995936	+	0.0900686i	$0.0287086\pi$
$79$	0.359882	+	3.42405i	0.0404899	+	0.385236i	−0.955446	+	0.295167i	$0.904625\pi$
$80$	−8.46644	−	7.52863i	−0.946577	−	0.841727i
$81$	−3.31127	+	8.36872i	−0.367919	+	0.929858i
$82$	−10.1232			−1.11792
$83$	13.4120	−	5.97142i	1.47216	−	0.655448i	0.495183	−	0.868789i	$-0.335101\pi$
$83$	13.4120	−	5.97142i	1.47216	−	0.655448i	0.976978	+	0.213341i	$0.0684344\pi$
$84$	1.31324	+	9.22366i	0.143286	+	1.00638i
$85$	−13.4658	−	7.66350i	−1.46057	−	0.831223i
$86$	6.92795	−	7.69427i	0.747061	−	0.829695i
$87$	11.1363	+	4.47604i	1.19394	+	0.479882i
$88$	1.85506	+	2.06025i	0.197750	+	0.219623i
$89$	−2.98202	−	9.17771i	−0.316093	−	0.972835i	−0.975302	−	0.220875i	$-0.929109\pi$
$89$	−2.98202	−	9.17771i	−0.316093	−	0.972835i	0.659209	−	0.751960i	$-0.270891\pi$
$90$	7.96843	+	14.6383i	0.839947	+	1.54302i
$91$	1.98628	−	6.11314i	0.208219	−	0.640831i
$92$	15.8848	−	7.07238i	1.65611	−	0.737346i
$93$	−2.20977	−	1.48473i	−0.229142	−	0.153959i
$94$	−2.09166	+	19.9008i	−0.215738	+	2.05261i
$95$	10.1349	+	5.76782i	1.03981	+	0.591766i
$96$	3.10118	−	0.113887i	0.316513	−	0.0116236i
$97$	−0.842924	−	8.01989i	−0.0855860	−	0.814296i	−0.950154	−	0.311781i	$-0.899075\pi$
$97$	−0.842924	−	8.01989i	−0.0855860	−	0.814296i	0.864568	−	0.502516i	$-0.167592\pi$
$98$	4.09855	+	12.6140i	0.414016	+	1.27421i
$99$	−0.582277	−	1.42637i	−0.0585210	−	0.143356i
$100$	20.4604	+	4.08432i	2.04604	+	0.408432i
$101$	−7.80298	+	13.5152i	−0.776425	+	1.34481i	0.157565	+	0.987509i	$0.449636\pi$
$101$	−7.80298	+	13.5152i	−0.776425	+	1.34481i	−0.933990	+	0.357299i	$0.883698\pi$
$102$	28.9190	−	7.26566i	2.86341	−	0.719407i
$103$	13.8836	+	6.18136i	1.36799	+	0.609068i	0.953612	−	0.301038i	$-0.0973330\pi$
$103$	13.8836	+	6.18136i	1.36799	+	0.609068i	0.414376	+	0.910106i	$0.364000\pi$
$104$	−24.5913	−	10.9488i	−2.41138	−	1.07361i
$105$	−3.10507	−	3.90940i	−0.303024	−	0.381518i
$106$	6.21002	−	2.76488i	0.603171	−	0.268549i
$107$	−10.6981			−1.03422			−0.517111	−	0.855919i	$-0.672992\pi$
$107$	−10.6981			−1.03422			−0.517111	+	0.855919i	$0.672992\pi$
$108$	−20.6573	−	6.58879i	−1.98775	−	0.634007i
$109$	−4.10780	+	12.6425i	−0.393456	+	1.21093i	0.536702	+	0.843772i	$0.319670\pi$
$109$	−4.10780	+	12.6425i	−0.393456	+	1.21093i	−0.930158	+	0.367160i	$0.880330\pi$
$110$	−2.71882	−	0.864787i	−0.259229	−	0.0824542i
$111$	−8.86758	−	9.14962i	−0.841674	−	0.868444i
$112$	−6.38861	+	1.35794i	−0.603667	+	0.128313i
$113$	9.31537	−	1.98004i	0.876316	−	0.186267i	0.252272	−	0.967656i	$-0.418822\pi$
$113$	9.31537	−	1.98004i	0.876316	−	0.186267i	0.624044	+	0.781390i	$0.285489\pi$
$114$	−21.7655	+	5.46839i	−2.03852	+	0.512162i
$115$	−5.42992	+	7.57199i	−0.506343	+	0.706092i
$116$	−8.93533	+	27.5001i	−0.829625	+	2.55332i
$117$	10.7981	+	10.3527i	0.998284	+	0.957108i
$118$	7.60135			0.699761
$119$	−8.15969	+	3.63293i	−0.747998	+	0.333030i
$120$	−17.6417	+	11.2211i	−1.61046	+	1.02434i
$121$	−9.80807	−	4.36683i	−0.891643	−	0.396985i
$122$	−16.6541	−	7.41487i	−1.50779	−	0.671311i
$123$	−1.93302	+	6.78736i	−0.174295	+	0.611996i
$124$	3.20690	−	5.55451i	0.287988	−	0.498810i
$125$	−10.5670	+	3.65222i	−0.945140	+	0.326664i
$126$	9.51927	+	1.30290i	0.848044	+	0.116072i
$127$	4.08839	+	12.5828i	0.362786	+	1.11654i	0.951356	+	0.308094i	$0.0996913\pi$
$127$	4.08839	+	12.5828i	0.362786	+	1.11654i	−0.588570	+	0.808447i	$0.700309\pi$
$128$	−1.85022	−	17.6036i	−0.163538	−	1.55596i
$129$	−3.83594	−	6.11426i	−0.337736	−	0.538331i
$130$	27.5319	−	3.06654i	2.41471	−	0.268953i
$131$	−1.04806	+	9.97167i	−0.0915699	+	0.871229i	0.848259	+	0.529582i	$0.177651\pi$
$131$	−1.04806	+	9.97167i	−0.0915699	+	0.871229i	−0.939828	+	0.341647i	$0.889015\pi$
$132$	3.33311	−	1.63310i	0.290110	−	0.142143i
$133$	6.14127	−	2.73427i	0.532516	−	0.237091i
$134$	0.349108	−	1.07445i	0.0301584	−	0.0928179i
$135$	11.3362	−	2.54746i	0.975669	−	0.219250i
$136$	11.5590	+	35.5749i	0.991176	+	3.05053i
$137$	7.07228	+	7.85456i	0.604226	+	0.671060i	0.965199	−	0.261516i	$-0.0842223\pi$
$137$	7.07228	+	7.85456i	0.604226	+	0.671060i	−0.360974	+	0.932576i	$0.617556\pi$
$138$	−2.52760	−	17.7528i	−0.215164	−	1.51122i
$139$	0.398014	−	0.442039i	0.0337591	−	0.0374933i	−0.726029	−	0.687664i	$-0.758636\pi$
$139$	0.398014	−	0.442039i	0.0337591	−	0.0374933i	0.759788	+	0.650171i	$0.225303\pi$
$140$	8.88827	−	8.10345i	0.751196	−	0.684867i
$141$	12.9436	+	5.20247i	1.09005	+	0.438127i
$142$	3.75266	−	1.67079i	0.314916	−	0.140210i
$143$	−2.56076			−0.214141
$144$	3.62415	−	14.7620i	0.302012	−	1.23016i
$145$	−3.31550	−	15.1358i	−0.275338	−	1.25696i
$146$	−2.29053	−	21.7930i	−0.189566	−	1.80360i
$147$	9.24005	−	0.339330i	0.762107	−	0.0279874i
$148$	20.5402	−	22.8122i	1.68840	−	1.87515i
$149$	−1.01642	−	1.76049i	−0.0832683	−	0.144225i	0.821384	−	0.570376i	$-0.193203\pi$
$149$	−1.01642	−	1.76049i	−0.0832683	−	0.144225i	−0.904652	+	0.426151i	$0.859869\pi$
$150$	9.83044	−	19.1396i	0.802652	−	1.56274i
$151$	−2.10363	+	3.64359i	−0.171191	+	0.296511i	−0.938836	−	0.344363i	$-0.888095\pi$
$151$	−2.10363	+	3.64359i	−0.171191	+	0.296511i	0.767646	+	0.640874i	$0.221428\pi$
$152$	−8.69971	−	26.7750i	−0.705640	−	2.17174i
$153$	0.650637	−	20.7769i	0.0526009	−	1.67971i
$154$	−1.33061	+	0.966746i	−0.107224	+	0.0779027i
$155$	0.0213235	+	3.43686i	0.00171275	+	0.276055i
$156$	−23.1159	+	27.6494i	−1.85075	+	2.21372i
$157$	0.279109	+	0.483431i	0.0222753	+	0.0385820i	0.876948	−	0.480585i	$-0.159576\pi$
$157$	0.279109	+	0.483431i	0.0222753	+	0.0385820i	−0.854673	+	0.519167i	$0.826242\pi$
$158$	−0.894133	+	8.50710i	−0.0711334	+	0.676789i
$159$	−0.667984	−	4.69163i	−0.0529745	−	0.372071i
$160$	−2.37491	−	3.22650i	−0.187753	−	0.255077i
$161$	1.65988	+	5.10858i	0.130817	+	0.402612i
$162$	−12.3701	+	18.6274i	−0.971884	+	1.46351i
$163$	−5.35439	+	16.4791i	−0.419388	+	1.29074i	0.488879	+	0.872352i	$0.337406\pi$
$163$	−5.35439	+	16.4791i	−0.419388	+	1.29074i	−0.908267	+	0.418392i	$0.862594\pi$
$164$	−16.6306	−	3.53495i	−1.29864	−	0.276033i
$165$	−1.09898	+	1.65778i	−0.0855554	+	0.129058i
$166$	35.6788	−	7.58376i	2.76921	−	0.588614i
$167$	0.685292	−	6.52012i	0.0530295	−	0.504542i	−0.935480	−	0.353381i	$-0.885032\pi$
$167$	0.685292	−	6.52012i	0.0530295	−	0.504542i	0.988509	−	0.151161i	$-0.0483013\pi$
$168$	−0.819125	+	12.0252i	−0.0631969	+	0.927762i
$169$	10.8384	−	4.82559i	0.833727	−	0.371199i
$170$	−28.7663	−	25.5799i	−2.20627	−	1.96189i
$171$	−0.489693	+	15.6374i	−0.0374477	+	1.19583i
$172$	14.0682	−	10.2212i	1.07269	−	0.779357i
$173$	1.05159	+	0.223521i	0.0799506	+	0.0169940i	0.247713	−	0.968833i	$-0.420321\pi$
$173$	1.05159	+	0.223521i	0.0799506	+	0.0169940i	−0.167763	+	0.985827i	$0.553654\pi$
$174$	24.7515	+	16.6303i	1.87641	+	1.26074i
$175$	−1.91548	+	6.15405i	−0.144797	+	0.465203i
$176$	1.30102	+	2.25343i	0.0980678	+	0.169858i
$177$	1.45148	−	5.09653i	0.109100	−	0.383079i
$178$	−2.50613	−	23.8443i	−0.187843	−	1.78720i
$179$	15.2398	−	11.0724i	1.13908	−	0.827587i	0.152085	−	0.988367i	$-0.451401\pi$
$179$	15.2398	−	11.0724i	1.13908	−	0.827587i	0.986990	+	0.160781i	$0.0514012\pi$
$180$	7.97915	+	26.8308i	0.594730	+	1.99985i
$181$	−11.6647	−	8.47488i	−0.867029	−	0.629933i	0.0627594	−	0.998029i	$-0.480010\pi$
$181$	−11.6647	−	8.47488i	−0.867029	−	0.629933i	−0.929788	+	0.368096i	$0.880010\pi$
$182$	7.98490	−	13.8303i	0.591880	−	1.02517i
$183$	−8.15161	+	9.75031i	−0.602584	+	0.720764i
$184$	22.0035	−	4.67699i	1.62212	−	0.344792i
$185$	−3.32013	+	16.1109i	−0.244101	+	1.18449i
$186$	−4.60328	−	4.74969i	−0.337529	−	0.348264i
$187$	2.38103	+	2.64440i	0.174118	+	0.193378i
$188$	−10.3855	+	31.9632i	−0.757439	+	2.33116i
$189$	2.69127	−	6.13366i	0.195761	−	0.446158i
$190$	21.6505	+	19.2523i	1.57069	+	1.39671i
$191$	−12.3893	−	13.7597i	−0.896455	−	0.995614i	−1.00000		0.000989586i	$-0.999685\pi$
$191$	−12.3893	−	13.7597i	−0.896455	−	0.995614i	0.103544	−	0.994625i	$-0.466982\pi$
$192$	−9.69522	−	1.69153i	−0.699693	−	0.122076i
$193$	−2.70053	−	4.67746i	−0.194388	−	0.336691i	0.752311	−	0.658808i	$-0.228939\pi$
$193$	−2.70053	−	4.67746i	−0.194388	−	0.336691i	−0.946700	+	0.322117i	$0.895606\pi$
$194$	2.09426	−	19.9255i	0.150359	−	1.43057i
$195$	3.20118	−	19.0451i	0.229241	−	1.36385i
$196$	2.32847	+	22.1539i	0.166319	+	1.58242i
$197$	−12.6037	+	9.15716i	−0.897980	+	0.652421i	−0.937946	−	0.346780i	$-0.887275\pi$
$197$	−12.6037	+	9.15716i	−0.897980	+	0.652421i	0.0399665	+	0.999201i	$0.487275\pi$
$198$	−0.678255	−	3.76719i	−0.0482015	−	0.267722i
$199$	−17.1285			−1.21421			−0.607104	−	0.794623i	$-0.707669\pi$
$199$	−17.1285			−1.21421			−0.607104	+	0.794623i	$0.707669\pi$
$200$	24.7927	+	10.6718i	1.75311	+	0.754612i
$201$	−0.653729	−	0.439235i	−0.0461105	−	0.0309812i
$202$	−25.9444	+	28.8141i	−1.82544	+	2.02736i
$203$	−8.16018	−	3.63315i	−0.572733	−	0.254997i
$204$	50.0461	−	1.83788i	3.50393	−	0.128678i
$205$	8.64733	−	2.86912i	0.603955	−	0.200388i
$206$	30.5471	+	22.1938i	2.12832	+	1.54631i
$207$	−12.3855	−	1.69520i	−0.860852	−	0.117825i
$208$	−20.4398	−	14.8504i	−1.41724	−	1.02969i
$209$	−1.79205	−	1.99027i	−0.123959	−	0.137670i
$210$	−5.52658	−	11.1047i	−0.381370	−	0.766295i
$211$	−9.68372	+	10.7549i	−0.666655	+	0.740395i	−0.977702	−	0.209999i	$-0.932654\pi$
$211$	−9.68372	+	10.7549i	−0.666655	+	0.740395i	0.311047	+	0.950395i	$0.399320\pi$
$212$	11.1675	−	2.37372i	0.766986	−	0.163028i
$213$	−0.403656	−	2.83511i	−0.0276580	−	0.194258i
$214$	−25.9987	−	5.52619i	−1.77723	−	0.377763i
$215$	−3.73721	+	8.53606i	−0.254876	+	0.582154i
$216$	−24.3682	−	13.8940i	−1.65805	−	0.945368i
$217$	1.60293	+	1.16460i	0.108814	+	0.0790579i
$218$	−16.5135	+	28.6022i	−1.11843	+	1.93718i
$219$	−15.0491	−	2.62563i	−1.01692	−	0.177423i
$220$	−4.16458	−	2.37009i	−0.280776	−	0.159792i
$221$	−31.5638	−	14.0531i	−2.12321	−	0.945316i
$222$	−16.8239	−	26.8163i	−1.12914	−	1.79979i
$223$	18.2430	+	3.87767i	1.22164	+	0.259668i	0.773210	−	0.634150i	$-0.218650\pi$
$223$	18.2430	+	3.87767i	1.22164	+	0.259668i	0.448431	+	0.893818i	$0.351983\pi$
$224$	−2.30957			−0.154314
$225$	−10.9555	−	10.2458i	−0.730369	−	0.683053i
$226$	23.6612			1.57392
$227$	−16.6360	−	3.53610i	−1.10417	−	0.234699i	−0.380457	−	0.924799i	$-0.624233\pi$
$227$	−16.6360	−	3.53610i	−1.10417	−	0.234699i	−0.723714	+	0.690100i	$0.757567\pi$
$228$	−37.6665	+	1.38326i	−2.49452	+	0.0916083i
$229$	−19.8898	−	8.85552i	−1.31436	−	0.585189i	−0.374649	−	0.927167i	$-0.622237\pi$
$229$	−19.8898	−	8.85552i	−1.31436	−	0.585189i	−0.939708	+	0.341977i	$0.888903\pi$
$230$	−17.1073	+	15.5968i	−1.12802	+	1.02842i
$231$	0.394101	+	1.07675i	0.0259299	+	0.0708447i
$232$	−18.7040	+	32.3962i	−1.22798	+	2.12692i
$233$	−7.60150	−	5.52281i	−0.497991	−	0.361811i	0.310258	−	0.950652i	$-0.399584\pi$
$233$	−7.60150	−	5.52281i	−0.497991	−	0.361811i	−0.808249	+	0.588841i	$0.799584\pi$
$234$	20.8940	+	30.7372i	1.36588	+	2.00936i
$235$	−3.85359	−	17.5923i	−0.251380	−	1.14759i
$236$	12.4877	+	2.65434i	0.812880	+	0.172783i
$237$	5.53308	+	2.22393i	0.359412	+	0.144460i
$238$	−21.7065	+	4.61386i	−1.40702	+	0.299072i
$239$	3.28802	−	3.65172i	0.212684	−	0.236210i	−0.627358	−	0.778731i	$-0.715864\pi$
$239$	3.28802	−	3.65172i	0.212684	−	0.236210i	0.840042	+	0.542521i	$0.182530\pi$
$240$	−18.3858	+	6.85904i	−1.18680	+	0.442749i
$241$	−5.34404	−	5.93515i	−0.344240	−	0.382317i	0.546019	−	0.837773i	$-0.316143\pi$
$241$	−5.34404	−	5.93515i	−0.344240	−	0.382317i	−0.890258	+	0.455456i	$0.849476\pi$
$242$	−21.5801	−	15.6788i	−1.38722	−	1.00787i
$243$	10.1272	+	11.8508i	0.649659	+	0.760226i
$244$	−24.7706	−	17.9969i	−1.58577	−	1.15213i
$245$	−7.07611	−	9.61343i	−0.452076	−	0.614180i
$246$	−8.20376	+	15.4963i	−0.523053	+	0.988007i
$247$	23.7561	+	10.5769i	1.51156	+	0.672991i
$248$	5.55215	−	6.16629i	0.352562	−	0.391560i
$249$	1.72814	−	25.3699i	0.109516	−	1.60775i
$250$	−27.5667	+	3.41722i	−1.74347	+	0.216124i
$251$	21.5099			1.35769			0.678847	−	0.734279i	$-0.262480\pi$
$251$	21.5099			1.35769			0.678847	+	0.734279i	$0.262480\pi$
$252$	15.1836	+	5.46452i	0.956474	+	0.344232i
$253$	1.73126	−	1.25783i	0.108843	−	0.0790792i
$254$	3.43595	+	32.6909i	0.215591	+	2.05121i
$255$	−22.6437	+	14.4027i	−1.41800	+	0.901929i
$256$	3.40901	−	32.4346i	0.213063	−	2.02716i
$257$	4.80713	+	8.32619i	0.299860	+	0.519373i	0.976104	−	0.217305i	$-0.0697266\pi$
$257$	4.80713	+	8.32619i	0.299860	+	0.519373i	−0.676243	+	0.736678i	$0.736393\pi$
$258$	−6.16381	−	16.8405i	−0.383742	−	1.04844i
$259$	6.34522	+	7.04708i	0.394273	+	0.437884i
$260$	46.3010	+	4.57618i	2.87147	+	0.283803i
$261$	15.8766	−	13.4198i	0.982735	−	0.830662i
$262$	−7.69800	+	23.6920i	−0.475584	+	1.46370i
$263$	6.46203	+	7.17681i	0.398466	+	0.442541i	0.908672	−	0.417511i	$-0.137098\pi$
$263$	6.46203	+	7.17681i	0.398466	+	0.442541i	−0.510206	+	0.860052i	$0.670431\pi$
$264$	4.65710	−	1.17006i	0.286625	−	0.0720120i
$265$	−4.52104	+	4.12184i	−0.277725	+	0.253203i
$266$	16.3371	−	3.47255i	1.00169	−	0.212916i
$267$	−16.4656	−	2.87276i	−1.00768	−	0.175810i
$268$	0.948715	−	1.64322i	0.0579520	−	0.100376i
$269$	14.7015	+	10.6812i	0.896364	+	0.651246i	0.937529	−	0.347906i	$-0.113107\pi$
$269$	14.7015	+	10.6812i	0.896364	+	0.651246i	−0.0411659	+	0.999152i	$0.513107\pi$
$270$	28.8655	−	0.335041i	1.75670	−	0.0203899i
$271$	−2.02436	+	1.47078i	−0.122971	+	0.0893437i	−0.647571	−	0.762005i	$-0.724215\pi$
$271$	−2.02436	+	1.47078i	−0.122971	+	0.0893437i	0.524600	+	0.851349i	$0.324215\pi$
$272$	3.66977	+	34.9155i	0.222512	+	2.11706i
$273$	−7.74815	−	7.99458i	−0.468939	−	0.483854i
$274$	13.1299	+	22.7416i	0.793204	+	1.37387i
$275$	2.56754	−	0.0318612i	0.154829	−	0.00192130i
$276$	2.04676	−	30.0474i	0.123200	−	1.80864i
$277$	−13.1783	−	2.80114i	−0.791809	−	0.168304i	−0.205784	−	0.978597i	$-0.565974\pi$
$277$	−13.1783	−	2.80114i	−0.791809	−	0.168304i	−0.586025	+	0.810293i	$0.699308\pi$
$278$	1.19560	−	0.868656i	0.0717075	−	0.0520985i
$279$	−4.06356	+	2.17944i	−0.243279	+	0.130480i
$280$	13.4272	−	7.86366i	0.802427	−	0.469944i
$281$	−0.690611	+	0.307480i	−0.0411984	+	0.0183427i	−0.427232	−	0.904142i	$-0.640511\pi$
$281$	−0.690611	+	0.307480i	−0.0411984	+	0.0183427i	0.386034	+	0.922485i	$0.373845\pi$
$282$	28.7685	+	19.3293i	1.71314	+	1.15105i
$283$	0.437736	−	4.16478i	0.0260207	−	0.247571i	−0.973778	−	0.227501i	$-0.926945\pi$
$283$	0.437736	−	4.16478i	0.0260207	−	0.247571i	0.999799	−	0.0200697i	$-0.00638881\pi$
$284$	6.74840	−	1.43442i	0.400444	−	0.0851169i
$285$	17.0424	−	10.8399i	1.00951	−	0.642103i
$286$	−6.22321	−	1.32278i	−0.367986	−	0.0782178i
$287$	1.62304	−	4.99519i	0.0958049	−	0.294857i
$288$	2.33884	−	4.83950i	0.137818	−	0.285170i
$289$	9.58309	+	29.4937i	0.563711	+	1.73492i
$290$	−0.238844	−	38.4961i	−0.0140254	−	2.26057i
$291$	−12.9597	−	5.20894i	−0.759712	−	0.305353i
$292$	3.84702	−	36.6020i	0.225130	−	2.14197i
$293$	−13.1006	−	22.6909i	−0.765344	−	1.32561i	−0.940065	−	0.340997i	$-0.889236\pi$
$293$	−13.1006	−	22.6909i	−0.765344	−	1.32561i	0.174721	−	0.984618i	$-0.444098\pi$
$294$	22.6307	+	3.94839i	1.31985	+	0.230275i
$295$	−6.49315	+	2.15438i	−0.378046	+	0.125433i
$296$	32.1283	−	23.3426i	1.86742	−	1.35676i
$297$	−2.65533	−	0.264591i	−0.154078	−	0.0153531i
$298$	−1.56073	−	4.80343i	−0.0904105	−	0.278255i
$299$	−10.3891	+	17.9945i	−0.600819	+	1.04065i
$300$	22.8332	−	28.0103i	1.31827	−	1.61718i
$301$	2.68592	+	4.65215i	0.154814	+	0.268146i
$302$	−6.99441	+	7.76808i	−0.402483	+	0.447003i
$303$	14.3651	+	22.8972i	0.825256	+	1.31541i
$304$	−2.76200	−	26.2787i	−0.158411	−	1.50718i
$305$	16.3276	+	1.61375i	0.934917	+	0.0924029i
$306$	12.3137	−	50.1565i	0.703928	−	2.86725i
$307$	13.6647			0.779887			0.389944	−	0.920839i	$-0.372495\pi$
$307$	13.6647			0.779887			0.389944	+	0.920839i	$0.372495\pi$
$308$	−2.52355	+	1.12356i	−0.143793	+	0.0640206i
$309$	20.7134	−	16.2432i	1.17834	−	0.924046i
$310$	−1.72352	+	8.36336i	−0.0978896	+	0.475007i
$311$	0.639250	−	0.709959i	0.0362486	−	0.0402581i	−0.724748	−	0.689014i	$-0.758044\pi$
$311$	0.639250	−	0.709959i	0.0362486	−	0.0402581i	0.760996	+	0.648756i	$0.224710\pi$
$312$	−36.6887	+	28.7709i	−2.07709	+	1.62883i
$313$	−8.02015	−	8.90728i	−0.453326	−	0.503469i	0.472547	−	0.881306i	$-0.343335\pi$
$313$	−8.02015	−	8.90728i	−0.453326	−	0.503469i	−0.925872	+	0.377836i	$0.876668\pi$
$314$	0.428576	+	1.31902i	0.0241859	+	0.0744367i
$315$	−8.50073	+	1.58501i	−0.478962	+	0.0893050i
$316$	−4.43953	+	13.6635i	−0.249743	+	0.768631i
$317$	2.06249	−	0.918281i	0.115841	−	0.0515758i	−0.347998	−	0.937495i	$-0.613138\pi$
$317$	2.06249	−	0.918281i	0.115841	−	0.0515758i	0.463839	+	0.885920i	$0.346472\pi$
$318$	0.800161	−	11.7468i	0.0448708	−	0.658726i
$319$	−0.371976	+	3.53911i	−0.0208266	+	0.198152i
$320$	5.23973	+	11.5748i	0.292910	+	0.647052i
$321$	−8.66964	+	16.3763i	−0.483892	+	0.914036i
$322$	1.39499	+	13.2724i	0.0777395	+	0.739642i
$323$	−11.1664	−	34.3666i	−0.621314	−	1.91221i
$324$	−26.8265	+	26.2821i	−1.49036	+	1.46011i
$325$	−22.6489	+	10.4226i	−1.25634	+	0.578141i
$326$	−21.5248	+	37.2821i	−1.19215	+	2.06486i
$327$	16.0239	+	16.5335i	0.886121	+	0.914305i
$328$	−20.0942	−	8.94651i	−1.10952	−	0.493988i
$329$	−9.48453	−	4.22278i	−0.522899	−	0.232810i
$330$	−3.52711	+	3.46108i	−0.194161	+	0.190526i
$331$	12.2444	−	5.45156i	0.673014	−	0.299645i	−0.0416306	−	0.999133i	$-0.513255\pi$
$331$	12.2444	−	5.45156i	0.673014	−	0.299645i	0.714644	+	0.699488i	$0.246589\pi$
$332$	61.2623			3.36221
$333$	−21.1922	+	6.15945i	−1.16133	+	0.337536i
$334$	5.03344	−	15.4913i	0.275418	−	0.847649i
$335$	0.00630826	+	1.01675i	0.000344657	+	0.0555508i
$336$	−3.09859	+	10.8800i	−0.169042	+	0.593552i
$337$	−11.7817	+	2.50428i	−0.641790	+	0.136417i	−0.517300	−	0.855804i	$-0.673063\pi$
$337$	−11.7817	+	2.50428i	−0.641790	+	0.136417i	−0.124490	+	0.992221i	$0.539730\pi$
$338$	28.8326	−	6.12855i	1.56828	−	0.333349i
$339$	4.51812	−	15.8643i	0.245390	−	0.861631i
$340$	−38.3257	−	52.0684i	−2.07850	−	2.82381i
$341$	0.243921	−	0.750712i	0.0132091	−	0.0406533i
$342$	−9.26774	+	37.7495i	−0.501142	+	2.04126i
$343$	−15.9048			−0.858777
$344$	20.5517	−	9.15020i	1.10807	−	0.493346i
$345$	7.19062	+	14.4483i	0.387130	+	0.777868i
$346$	2.44013	+	1.08641i	0.131182	+	0.0584060i
$347$	0.638552	+	0.284302i	0.0342793	+	0.0152621i	0.423805	−	0.905754i	$-0.360694\pi$
$347$	0.638552	+	0.284302i	0.0342793	+	0.0152621i	−0.389525	+	0.921016i	$0.627361\pi$
$348$	34.8553	+	35.9639i	1.86844	+	1.92787i
$349$	8.65614	−	14.9929i	0.463353	−	0.802551i	−0.535773	−	0.844362i	$-0.679980\pi$
$349$	8.65614	−	14.9929i	0.463353	−	0.802551i	0.999126	+	0.0418117i	$0.0133130\pi$
$350$	−7.83399	+	13.9663i	−0.418744	+	0.746528i
$351$	24.5983	−	8.13966i	1.31296	−	0.434463i
$352$	0.284330	+	0.875079i	0.0151549	+	0.0466419i
$353$	0.551935	+	5.25131i	0.0293765	+	0.279499i	0.999342	+	0.0362582i	$0.0115439\pi$
$353$	0.551935	+	5.25131i	0.0293765	+	0.279499i	−0.969966	+	0.243241i	$0.921789\pi$
$354$	6.16008	−	11.6359i	0.327405	−	0.618442i
$355$	−2.73202	+	2.49079i	−0.145001	+	0.132197i
$356$	4.20912	−	40.0471i	0.223083	−	2.12249i
$357$	−1.05138	+	15.4347i	−0.0556447	+	0.816893i
$358$	42.7556	−	19.0360i	2.25970	−	1.00609i
$359$	0.334961	−	1.03090i	0.0176786	−	0.0544091i	−0.941828	−	0.336095i	$-0.890894\pi$
$359$	0.334961	−	1.03090i	0.0176786	−	0.0544091i	0.959507	+	0.281686i	$0.0908937\pi$
$360$	2.88024	+	36.0988i	0.151802	+	1.90258i
$361$	2.53289	+	7.79543i	0.133310	+	0.410286i
$362$	−23.9700	−	26.6214i	−1.25983	−	1.39919i
$363$	−14.6330	+	11.4751i	−0.768034	+	0.602285i
$364$	17.9473	−	19.9324i	0.940692	−	1.04474i
$365$	8.13319	+	17.9666i	0.425710	+	0.940415i
$366$	−24.8468	+	19.4846i	−1.29877	+	1.01848i
$367$	28.5328	−	12.7036i	1.48940	−	0.663123i	0.509111	−	0.860701i	$-0.329974\pi$
$367$	28.5328	−	12.7036i	1.48940	−	0.663123i	0.980287	+	0.197578i	$0.0633075\pi$
$368$	21.1132			1.10060
$369$	8.82339	+	8.45945i	0.459327	+	0.440381i
$370$	−16.3909	+	37.4379i	−0.852121	+	1.94630i
$371$	0.368661	+	3.50757i	0.0191399	+	0.182104i
$372$	−5.90384	−	9.41036i	−0.306100	−	0.487905i
$373$	−0.165419	+	0.183716i	−0.00856507	+	0.00951248i	−0.747412	−	0.664361i	$-0.768704\pi$
$373$	−0.165419	+	0.183716i	−0.00856507	+	0.00951248i	0.738847	+	0.673873i	$0.235371\pi$
$374$	4.42044	+	7.65643i	0.228576	+	0.395905i
$375$	−2.97271	+	19.1354i	−0.153510	+	0.988147i
$376$	−21.7395	+	37.6539i	−1.12113	+	1.94185i
$377$	−10.6775	−	32.8619i	−0.549917	−	1.69247i
$378$	9.70880	−	13.5160i	0.499367	−	0.695186i
$379$	18.0726	−	13.1305i	0.928325	−	0.674467i	−0.0172574	−	0.999851i	$-0.505493\pi$
$379$	18.0726	−	13.1305i	0.928325	−	0.674467i	0.945582	+	0.325384i	$0.105493\pi$
$380$	28.8453	+	39.1885i	1.47973	+	2.01033i
$381$	22.5746	+	3.93860i	1.15653	+	0.201781i
$382$	−23.0010	−	39.8388i	−1.17683	−	2.03833i
$383$	−2.77196	+	26.3735i	−0.141641	+	1.34762i	0.660653	+	0.750692i	$0.270280\pi$
$383$	−2.77196	+	26.3735i	−0.141641	+	1.34762i	−0.802293	+	0.596930i	$0.796387\pi$
$384$	−28.4466	−	11.4336i	−1.45166	−	0.583469i
$385$	0.862627	−	1.20293i	0.0439635	−	0.0613069i
$386$	−4.14671	−	12.7622i	−0.211062	−	0.649581i
$387$	−12.4682	+	0.916993i	−0.633792	+	0.0466134i
$388$	10.3984	−	32.0029i	0.527898	−	1.62470i
$389$	12.7219	+	2.70413i	0.645028	+	0.137105i	0.518799	−	0.854896i	$-0.326379\pi$
$389$	12.7219	+	2.70413i	0.645028	+	0.137105i	0.126229	+	0.992001i	$0.459713\pi$
$390$	17.6175	−	44.6302i	0.892097	−	2.25994i
$391$	28.2423	−	6.00308i	1.42827	−	0.303589i
$392$	−3.01235	+	28.6606i	−0.152147	+	1.44758i
$393$	14.4150	+	9.68533i	0.727141	+	0.488560i
$394$	−35.3601	+	15.7433i	−1.78142	+	0.793138i
$395$	−1.64731	−	7.52027i	−0.0828854	−	0.378386i
$396$	0.201223	−	6.42568i	0.0101118	−	0.322903i
$397$	24.8748	−	18.0726i	1.24843	−	0.907040i	0.250303	−	0.968168i	$-0.419470\pi$
$397$	24.8748	−	18.0726i	1.24843	−	0.907040i	0.998130	+	0.0611280i	$0.0194698\pi$
$398$	−41.6261	−	8.84790i	−2.08653	−	0.443505i
$399$	0.791302	−	11.6167i	0.0396147	−	0.581564i
$400$	20.6787	+	14.6354i	1.03394	+	0.731771i
$401$	5.05931	+	8.76298i	0.252650	+	0.437602i	0.964255	−	0.264978i	$-0.0853646\pi$
$401$	5.05931	+	8.76298i	0.252650	+	0.437602i	−0.711605	+	0.702580i	$0.752031\pi$
$402$	−1.36182	−	1.40513i	−0.0679212	−	0.0700814i
$403$	0.801137	+	7.62231i	0.0399075	+	0.379694i
$404$	−52.6838	+	38.2771i	−2.62112	+	1.90435i
$405$	5.28724	−	19.4176i	0.262725	−	0.964871i
$406$	−17.9543	−	13.0446i	−0.891058	−	0.647392i
$407$	1.88893	−	3.27173i	0.0936309	−	0.162173i
$408$	63.8245	+	11.1355i	3.15978	+	0.551290i
$409$	17.3238	−	3.68229i	0.856607	−	0.182077i	0.241383	−	0.970430i	$-0.422399\pi$
$409$	17.3238	−	3.68229i	0.856607	−	0.182077i	0.615224	+	0.788353i	$0.289066\pi$
$410$	22.4970	−	2.50574i	1.11105	−	0.123750i
$411$	17.7549	−	4.46076i	0.875783	−	0.220033i
$412$	42.4337	+	47.1274i	2.09056	+	2.32180i
$413$	−1.21871	+	3.75082i	−0.0599690	+	0.184566i
$414$	−29.2239	−	10.5176i	−1.43627	−	0.516911i
$415$	−28.3278	+	16.5902i	−1.39056	+	0.814383i
$416$	−5.97802	−	6.63927i	−0.293097	−	0.325517i
$417$	−0.354113	−	0.967494i	−0.0173410	−	0.0473784i
$418$	−3.32698	−	5.76250i	−0.162728	−	0.281853i
$419$	1.40339	−	13.3523i	0.0685600	−	0.652305i	−0.905240	−	0.424900i	$-0.860309\pi$
$419$	1.40339	−	13.3523i	0.0685600	−	0.652305i	0.973800	−	0.227405i	$-0.0730241\pi$
$420$	−5.20154	−	20.1729i	−0.253809	−	0.984337i
$421$	3.40776	+	32.4227i	0.166084	+	1.58019i	0.687051	+	0.726609i	$0.258905\pi$
$421$	3.40776	+	32.4227i	0.166084	+	1.58019i	−0.520967	+	0.853577i	$0.674428\pi$
$422$	−29.0891	+	21.1345i	−1.41604	+	1.02881i
$423$	18.4532	−	15.5977i	0.897227	−	0.758386i
$424$	14.7702			0.717304
$425$	31.8224	+	13.6977i	1.54361	+	0.664434i
$426$	0.483529	−	7.09846i	0.0234271	−	0.343921i
$427$	6.32893	−	7.02899i	0.306279	−	0.340157i
$428$	−40.7817	−	18.1572i	−1.97126	−	0.877660i
$429$	−2.07522	+	3.91993i	−0.100193	+	0.189256i
$430$	−13.4916	+	18.8140i	−0.650625	+	0.907293i
$431$	7.24479	+	5.26365i	0.348969	+	0.253541i	0.748436	−	0.663206i	$-0.230805\pi$
$431$	7.24479	+	5.26365i	0.348969	+	0.253541i	−0.399467	+	0.916747i	$0.630805\pi$
$432$	−19.6602	−	17.5107i	−0.945902	−	0.842486i
$433$	22.5500	+	16.3836i	1.08369	+	0.787344i	0.978322	−	0.207090i	$-0.0663992\pi$
$433$	22.5500	+	16.3836i	1.08369	+	0.787344i	0.105364	+	0.994434i	$0.466399\pi$
$434$	3.29389	+	3.65823i	0.158112	+	0.175601i
$435$	−25.8564	−	7.19071i	−1.23972	−	0.344768i
$436$	−37.1165	+	41.2220i	−1.77756	+	1.97418i
$437$	−21.2561	+	4.51813i	−1.01682	+	0.216132i
$438$	−35.2163	−	14.1546i	−1.68270	−	0.676333i
$439$	3.07587	+	0.653797i	0.146803	+	0.0312040i	0.280727	−	0.959788i	$-0.409424\pi$
$439$	3.07587	+	0.653797i	0.146803	+	0.0312040i	−0.133924	+	0.990992i	$0.542758\pi$
$440$	−4.63250	−	4.11937i	−0.220846	−	0.196383i
$441$	6.96864	−	14.4194i	0.331840	−	0.686638i
$442$	−69.4479	−	50.4568i	−3.30330	−	2.39999i
$443$	9.86697	−	17.0901i	0.468794	−	0.811975i	−0.530570	−	0.847641i	$-0.678022\pi$
$443$	9.86697	−	17.0901i	0.468794	−	0.811975i	0.999364	+	0.0356665i	$0.0113554\pi$
$444$	−18.2747	−	49.9293i	−0.867277	−	2.36954i
$445$	8.89873	+	19.6577i	0.421840	+	0.931866i
$446$	42.3315	+	18.8472i	2.00445	+	0.892440i
$447$	−3.51861	+	0.129217i	−0.166425	+	0.00611174i
$448$	7.16447	+	1.52285i	0.338489	+	0.0719481i
$449$	−13.7726			−0.649970			−0.324985	−	0.945719i	$-0.605359\pi$
$449$	−13.7726			−0.649970			−0.324985	+	0.945719i	$0.605359\pi$
$450$	−21.3318	−	30.5588i	−1.00559	−	1.44055i
$451$	−2.09246			−0.0985300
$452$	38.8713	+	8.26235i	1.82835	+	0.388628i
$453$	3.87274	+	6.17291i	0.181957	+	0.290029i
$454$	−38.6026	−	17.1870i	−1.81171	−	0.806626i
$455$	−2.90100	+	14.0770i	−0.136001	+	0.659942i
$456$	−48.0365	−	8.38098i	−2.24952	−	0.392475i
$457$	8.03370	−	13.9148i	0.375801	−	0.650906i	−0.614646	−	0.788803i	$-0.710701\pi$
$457$	8.03370	−	13.9148i	0.375801	−	0.650906i	0.990447	+	0.137897i	$0.0440344\pi$
$458$	−43.7623	−	31.7952i	−2.04488	−	1.48569i
$459$	−31.2775	−	17.8335i	−1.45991	−	0.832395i
$460$	−33.5506	+	19.6490i	−1.56431	+	0.916140i
$461$	−10.0438	−	2.13487i	−0.467785	−	0.0994309i	−0.0320125	−	0.999487i	$-0.510192\pi$
$461$	−10.0438	−	2.13487i	−0.467785	−	0.0994309i	−0.435773	+	0.900057i	$0.643525\pi$
$462$	0.401549	+	2.82031i	0.0186817	+	0.131213i
$463$	−17.6285	+	3.74706i	−0.819268	+	0.174141i	−0.598435	−	0.801171i	$-0.704211\pi$
$463$	−17.6285	+	3.74706i	−0.819268	+	0.174141i	−0.220832	+	0.975312i	$0.570877\pi$
$464$	−23.4931	+	26.0918i	−1.09064	+	1.21128i
$465$	5.27833	+	2.75257i	0.244777	+	0.127647i
$466$	−15.6205	−	17.3483i	−0.723604	−	0.803644i
$467$	28.5731	+	20.7596i	1.32221	+	0.960639i	0.999902	+	0.0140027i	$0.00445734\pi$
$467$	28.5731	+	20.7596i	1.32221	+	0.960639i	0.322304	+	0.946636i	$0.395543\pi$
$468$	23.5920	+	57.7921i	1.09054	+	2.67144i
$469$	0.474203	+	0.344529i	0.0218967	+	0.0159089i
$470$	−0.277607	−	44.7438i	−0.0128050	−	2.06388i
$471$	0.966210	−	0.0354829i	0.0445206	−	0.00163497i
$472$	15.0884	+	6.71780i	0.694501	+	0.309212i
$473$	1.43201	−	1.59040i	0.0658437	−	0.0731268i
$474$	12.2978	+	8.26281i	0.564858	+	0.379524i
$475$	−23.9506	−	10.3093i	−1.09893	−	0.473025i
$476$	−37.2712			−1.70832
$477$	−7.72315	−	2.77954i	−0.353619	−	0.127266i
$478$	9.87695	−	7.17603i	0.451761	−	0.328224i
$479$	0.178641	+	1.69966i	0.00816233	+	0.0776594i	0.997845	−	0.0656191i	$-0.0209022\pi$
$479$	0.178641	+	1.69966i	0.00816233	+	0.0776594i	−0.989682	+	0.143278i	$0.954236\pi$
$480$	−6.86365	+	1.02072i	−0.313281	+	0.0465891i
$481$	−3.83430	+	36.4810i	−0.174829	+	1.66339i
$482$	−9.92134	−	17.1843i	−0.451905	−	0.782722i
$483$	9.16522	+	1.59906i	0.417032	+	0.0727599i
$484$	−29.9774	−	33.2933i	−1.36261	−	1.51333i
$485$	3.85838	+	17.6142i	0.175200	+	0.799818i
$486$	18.4897	+	34.0313i	0.838709	+	1.54369i
$487$	10.1084	−	31.1106i	0.458057	−	1.40975i	−0.409452	−	0.912332i	$-0.634280\pi$
$487$	10.1084	−	31.1106i	0.458057	−	1.40975i	0.867509	−	0.497422i	$-0.165720\pi$
$488$	−26.5048	−	29.4366i	−1.19982	−	1.33253i
$489$	20.8866	+	21.5509i	0.944525	+	0.974566i
$490$	−12.2306	−	27.0180i	−0.552523	−	1.22055i
$491$	−40.3627	+	8.57936i	−1.82154	+	0.387181i	−0.986600	−	0.163155i	$-0.947833\pi$
$491$	−40.3627	+	8.57936i	−1.82154	+	0.387181i	−0.834943	+	0.550336i	$0.814500\pi$
$492$	−18.8886	+	22.5930i	−0.851562	+	1.01857i
$493$	−24.0072	+	41.5817i	−1.08123	+	1.87275i
$494$	52.2689	+	37.9756i	2.35169	+	1.70860i
$495$	1.64707	+	3.02574i	0.0740304	+	0.135997i
$496$	6.30049	−	4.57758i	0.282901	−	0.205539i
$497$	0.222778	+	2.11959i	0.00999296	+	0.0950766i
$498$	17.3049	−	60.7619i	0.775449	−	2.72281i
$499$	1.73929	+	3.01255i	0.0778615	+	0.134860i	0.902327	−	0.431052i	$-0.141857\pi$
$499$	1.73929	+	3.01255i	0.0778615	+	0.134860i	−0.824466	+	0.565912i	$0.808524\pi$
$500$	−46.4807	−	4.01223i	−2.07868	−	0.179432i
$501$	−9.42546	−	6.33289i	−0.421098	−	0.282933i
$502$	52.2739	+	11.1112i	2.33310	+	0.495916i
$503$	13.8073	−	10.0316i	0.615638	−	0.447287i	−0.235757	−	0.971812i	$-0.575757\pi$
$503$	13.8073	−	10.0316i	0.615638	−	0.447287i	0.851395	+	0.524525i	$0.175757\pi$
$504$	17.7440	+	10.9990i	0.790380	+	0.489935i
$505$	13.9954	−	31.9665i	0.622788	−	1.42249i
$506$	4.85709	−	2.16251i	0.215924	−	0.0961355i
$507$	1.39653	−	20.5018i	0.0620222	−	0.910518i
$508$	−5.77078	+	54.9053i	−0.256037	+	2.43603i
$509$	−7.62861	+	1.62151i	−0.338132	+	0.0718723i	−0.373849	−	0.927490i	$-0.621962\pi$
$509$	−7.62861	+	1.62151i	−0.338132	+	0.0718723i	0.0357163	+	0.999362i	$0.488629\pi$
$510$	−62.4690	+	23.3048i	−2.76618	+	1.03196i
$511$	11.1208	+	2.36380i	0.491955	+	0.104568i
$512$	14.0995	−	43.3938i	0.623115	−	1.91775i
$513$	23.5405	+	13.4221i	1.03934	+	0.592600i
$514$	7.38142	+	22.7177i	0.325580	+	1.00203i
$515$	−32.3839	−	10.3005i	−1.42700	−	0.453893i
$516$	−4.24547	−	29.8184i	−0.186897	−	1.31268i
$517$	−0.432345	+	4.11349i	−0.0190145	+	0.180911i
$518$	11.7801	+	20.4037i	0.517586	+	0.896486i
$519$	1.19436	−	1.42860i	0.0524265	−	0.0627085i
$520$	57.3601	+	18.2447i	2.51540	+	0.800085i
$521$	−9.24944	+	6.72011i	−0.405225	+	0.294413i	−0.771666	−	0.636028i	$-0.780576\pi$
$521$	−9.24944	+	6.72011i	−0.405225	+	0.294413i	0.366441	+	0.930441i	$0.380576\pi$
$522$	45.5157	−	24.4118i	1.99217	−	1.06848i
$523$	6.03668	+	18.5790i	0.263966	+	0.812403i	0.991930	+	0.126788i	$0.0404667\pi$
$523$	6.03668	+	18.5790i	0.263966	+	0.812403i	−0.727964	+	0.685615i	$0.759533\pi$
$524$	−20.9196	+	36.2338i	−0.913876	+	1.58288i
$525$	7.86816	+	7.91937i	0.343395	+	0.345630i
$526$	11.9969	+	20.7793i	0.523090	+	0.906019i
$527$	7.12638	−	7.91465i	0.310430	−	0.344768i
$528$	4.50382	−	0.165397i	0.196003	−	0.00719799i
$529$	0.589142	+	5.60531i	0.0256149	+	0.243709i
$530$	−13.1163	+	7.68160i	−0.569736	+	0.333668i
$531$	−6.62535	−	6.35208i	−0.287516	−	0.275657i
$532$	28.0516			1.21619
$533$	18.5606	−	8.26372i	0.803949	−	0.357941i
$534$	−38.5311	−	15.4869i	−1.66740	−	0.670184i
$535$	23.7746	−	2.64804i	1.02786	−	0.114485i
$536$	1.64253	−	1.82421i	0.0709463	−	0.0787938i
$537$	−4.59902	−	32.3016i	−0.198463	−	1.39392i
$538$	30.2103	+	33.5520i	1.30246	+	1.44653i
$539$	0.847169	+	2.60732i	0.0364902	+	0.112305i
$540$	47.5381	+	9.52925i	2.04571	+	0.410074i
$541$	2.36879	−	7.29039i	0.101842	−	0.313439i	−0.887134	−	0.461512i	$-0.847307\pi$
$541$	2.36879	−	7.29039i	0.101842	−	0.313439i	0.988976	+	0.148073i	$0.0473072\pi$
$542$	−5.67939	+	2.52863i	−0.243951	+	0.108614i
$543$	−22.4261	+	10.9880i	−0.962396	+	0.471539i
$544$	−1.29768	+	12.3466i	−0.0556375	+	0.529355i
$545$	5.99952	−	29.1125i	0.256991	−	1.24704i
$546$	−14.7001	−	23.4310i	−0.629104	−	1.00275i
$547$	1.50602	+	14.3288i	0.0643929	+	0.612657i	0.978366	+	0.206882i	$0.0663317\pi$
$547$	1.50602	+	14.3288i	0.0643929	+	0.612657i	−0.913973	+	0.405775i	$0.867002\pi$
$548$	13.6289	+	41.9454i	0.582197	+	1.79182i
$549$	8.31949	+	20.3798i	0.355067	+	0.869790i
$550$	6.25616	+	1.24886i	0.266764	+	0.0532516i
$551$	18.0687	−	31.2959i	0.769751	−	1.33325i
$552$	10.6721	−	37.4726i	0.454235	−	1.59494i
$553$	−4.05440	−	1.80514i	−0.172411	−	0.0767622i
$554$	−30.5793	−	13.6148i	−1.29919	−	0.578437i
$555$	21.9714	+	18.1385i	0.932635	+	0.769936i
$556$	2.26750	−	1.00956i	0.0961633	−	0.0428147i
$557$	11.9602			0.506771			0.253386	−	0.967365i	$-0.418456\pi$
$557$	11.9602			0.506771			0.253386	+	0.967365i	$0.418456\pi$
$558$	−11.0012	+	3.19745i	−0.465716	+	0.135359i
$559$	−6.42128	+	19.7627i	−0.271591	+	0.835872i
$560$	13.8615	−	4.59913i	0.585753	−	0.194349i
$561$	5.97755	−	1.50181i	0.252372	−	0.0634064i
$562$	−1.83717	+	0.390502i	−0.0774963	+	0.0164724i
$563$	40.3973	−	8.58670i	1.70254	−	0.361886i	0.748865	−	0.662722i	$-0.230599\pi$
$563$	40.3973	−	8.58670i	1.70254	−	0.361886i	0.953676	+	0.300836i	$0.0972657\pi$
$564$	40.5121	+	41.8006i	1.70587	+	1.76012i
$565$	−20.2117	+	6.70609i	−0.850311	+	0.282127i
$566$	3.21516	−	9.89523i	0.135143	−	0.415928i
$567$	−7.20825	−	9.09041i	−0.302718	−	0.381761i
$568$	8.92549			0.374505
$569$	−13.3805	+	5.95739i	−0.560941	+	0.249747i	−0.667564	−	0.744553i	$-0.732663\pi$
$569$	−13.3805	+	5.95739i	−0.560941	+	0.249747i	0.106623	+	0.994300i	$0.465996\pi$
$570$	47.0164	−	17.5401i	1.96930	−	0.734672i
$571$	−21.3865	−	9.52187i	−0.894996	−	0.398478i	−0.0929016	−	0.995675i	$-0.529614\pi$
$571$	−21.3865	−	9.52187i	−0.894996	−	0.398478i	−0.802094	+	0.597197i	$0.796281\pi$
$572$	−9.76175	−	4.34621i	−0.408159	−	0.181724i
$573$	−31.1031	+	7.81439i	−1.29935	+	0.326451i
$574$	6.52466	−	11.3010i	0.272334	−	0.471696i
$575$	10.1928	−	18.1715i	0.425069	−	0.757803i
$576$	−10.4463	+	13.4704i	−0.435262	+	0.561265i
$577$	0.219132	+	0.674419i	0.00912259	+	0.0280764i	0.955514	−	0.294945i	$-0.0953014\pi$
$577$	0.219132	+	0.674419i	0.00912259	+	0.0280764i	−0.946392	+	0.323022i	$0.895301\pi$
$578$	8.05378	+	76.6266i	0.334993	+	3.18724i
$579$	−9.34861	+	0.343316i	−0.388515	+	0.0142677i
$580$	13.0502	−	63.3259i	0.541882	−	2.62947i
$581$	−1.97820	+	18.8213i	−0.0820694	+	0.780839i
$582$	−28.8043	−	19.3534i	−1.19398	−	0.802222i
$583$	1.28361	−	0.571500i	0.0531617	−	0.0236691i
$584$	14.7132	−	45.2827i	0.608838	−	1.87381i
$585$	−26.5594	−	20.3343i	−1.09810	−	0.840719i
$586$	−20.1161	−	61.9111i	−0.830990	−	2.55752i
$587$	−7.12521	−	7.91335i	−0.294089	−	0.326619i	0.577934	−	0.816083i	$-0.303859\pi$
$587$	−7.12521	−	7.91335i	−0.294089	−	0.326619i	−0.872023	+	0.489464i	$0.837192\pi$
$588$	35.7995	+	14.3890i	1.47635	+	0.593393i
$589$	−5.36357	+	5.95685i	−0.221002	+	0.245448i
$590$	−16.8927	+	1.88153i	−0.695460	+	0.0774612i
$591$	3.80353	+	26.7144i	0.156456	+	1.09888i
$592$	34.0507	−	15.1604i	1.39948	−	0.623087i
$593$	−47.7160			−1.95946			−0.979730	−	0.200323i	$-0.935801\pi$
$593$	−47.7160			−1.95946			−0.979730	+	0.200323i	$0.935801\pi$
$594$	−6.31636	−	2.01465i	−0.259163	−	0.0826621i
$595$	17.2343	−	10.0933i	0.706535	−	0.413784i
$596$	−0.886680	−	8.43620i	−0.0363198	−	0.345560i
$597$	−13.8808	+	26.2198i	−0.568104	+	1.07311i
$598$	−34.5432	+	38.3641i	−1.41257	+	1.56882i
$599$	1.95259	+	3.38199i	0.0797808	+	0.138184i	0.903155	−	0.429314i	$-0.141245\pi$
$599$	1.95259	+	3.38199i	0.0797808	+	0.138184i	−0.823374	+	0.567498i	$0.807911\pi$
$600$	36.4280	−	29.3037i	1.48717	−	1.19632i
$601$	−3.54162	+	6.13427i	−0.144466	+	0.250222i	−0.929174	−	0.369644i	$-0.879480\pi$
$601$	−3.54162	+	6.13427i	−0.144466	+	0.250222i	0.784708	+	0.619866i	$0.212813\pi$
$602$	4.12427	+	12.6932i	0.168093	+	0.517336i
$603$	−1.20215	+	0.644756i	−0.0489552	+	0.0262565i
$604$	−14.2032	+	10.3192i	−0.577920	+	0.419883i
$605$	22.8776	+	7.27678i	0.930108	+	0.295843i
$606$	23.0827	+	63.0657i	0.937672	+	2.56187i
$607$	2.38982	+	4.13929i	0.0969997	+	0.168008i	0.910441	−	0.413638i	$-0.135742\pi$
$607$	2.38982	+	4.13929i	0.0969997	+	0.168008i	−0.813442	+	0.581646i	$0.802409\pi$
$608$	0.976678	−	9.29247i	0.0396095	−	0.376860i
$609$	−12.1745	+	9.54710i	−0.493335	+	0.386868i
$610$	38.8462	+	12.3560i	1.57284	+	0.500278i
$611$	−12.4103	−	38.1951i	−0.502069	−	1.54521i
$612$	37.7436	−	78.0986i	1.52570	−	3.15695i
$613$	14.0778	−	43.3269i	0.568596	−	1.74996i	−0.0884219	−	0.996083i	$-0.528182\pi$
$613$	14.0778	−	43.3269i	0.568596	−	1.74996i	0.657018	−	0.753875i	$-0.271818\pi$
$614$	33.2083	+	7.05865i	1.34018	+	0.284864i
$615$	2.61577	−	15.5622i	0.105478	−	0.627528i
$616$	−3.49560	+	0.743013i	−0.140842	+	0.0299368i
$617$	2.02983	−	19.3126i	0.0817179	−	0.777494i	−0.874537	−	0.484959i	$-0.838834\pi$
$617$	2.02983	−	19.3126i	0.0817179	−	0.777494i	0.956255	−	0.292535i	$-0.0944989\pi$
$618$	58.7288	−	28.7750i	2.36242	−	1.15750i
$619$	24.9267	−	11.0981i	1.00189	−	0.446070i	0.160812	−	0.986985i	$-0.448589\pi$
$619$	24.9267	−	11.0981i	1.00189	−	0.446070i	0.841077	+	0.540915i	$0.181922\pi$
$620$	−5.75189	+	13.1377i	−0.231001	+	0.527623i
$621$	−12.6321	+	17.5856i	−0.506909	+	0.705686i
$622$	1.92026	−	1.39515i	0.0769953	−	0.0559404i
$623$	12.1675	+	2.58629i	0.487482	+	0.103618i
$624$	−39.2968	+	19.2540i	−1.57313	+	0.770776i
$625$	22.5793	−	10.7320i	0.903171	−	0.429281i
$626$	−14.8896	−	25.7896i	−0.595109	−	1.03076i
$627$	−4.49891	+	1.13031i	−0.179669	+	0.0451404i
$628$	0.243482	+	2.31658i	0.00971601	+	0.0924416i
$629$	41.2378	−	29.9610i	1.64426	−	1.19462i
$630$	−21.4774	−	0.539215i	−0.855681	−	0.0214828i
$631$	12.6772	+	9.21053i	0.504672	+	0.366665i	0.810799	−	0.585325i	$-0.199033\pi$
$631$	12.6772	+	9.21053i	0.504672	+	0.366665i	−0.306127	+	0.951991i	$0.599033\pi$
$632$	−9.29310	+	16.0961i	−0.369660	+	0.640269i
$633$	8.61562	+	23.5392i	0.342440	+	0.935601i
$634$	5.48667	−	1.16623i	0.217903	−	0.0463168i
$635$	−12.2003	−	26.9511i	−0.484154	−	1.06952i
$636$	5.41643	−	19.0185i	0.214775	−	0.754133i
$637$	−17.8116	−	19.7818i	−0.705723	−	0.783785i
$638$	−2.73215	+	8.40869i	−0.108167	+	0.332903i
$639$	−4.66702	−	1.67965i	−0.184625	−	0.0664458i
$640$	8.46913	+	38.6631i	0.334772	+	1.52829i
$641$	23.6349	+	26.2493i	0.933524	+	1.03678i	0.999241	+	0.0389455i	$0.0123999\pi$
$641$	23.6349	+	26.2493i	0.933524	+	1.03678i	−0.0657170	+	0.997838i	$0.520933\pi$
$642$	−29.5285	+	35.3197i	−1.16540	+	1.39396i
$643$	5.45444	+	9.44736i	0.215102	+	0.372567i	0.953304	−	0.302012i	$-0.0976583\pi$
$643$	5.45444	+	9.44736i	0.215102	+	0.372567i	−0.738202	+	0.674580i	$0.764325\pi$
$644$	−2.34292	+	22.2914i	−0.0923240	+	0.878404i
$645$	10.0381	+	12.6384i	0.395251	+	0.497636i
$646$	−9.38440	−	89.2866i	−0.369224	−	3.51293i
$647$	−28.4306	+	20.6560i	−1.11772	+	0.812072i	−0.983862	−	0.178928i	$-0.942737\pi$
$647$	−28.4306	+	20.6560i	−1.11772	+	0.812072i	−0.133860	+	0.991000i	$0.542737\pi$
$648$	−41.0164	+	26.0426i	−1.61128	+	1.02305i
$649$	1.57119			0.0616748
$650$	−60.4258	+	13.6297i	−2.37010	+	0.534600i
$651$	3.08173	−	1.50994i	0.120783	−	0.0591791i
$652$	−48.3802	+	53.7317i	−1.89472	+	2.10429i
$653$	−11.5270	−	5.13214i	−0.451086	−	0.200836i	0.168603	−	0.985684i	$-0.446074\pi$
$653$	−11.5270	−	5.13214i	−0.451086	−	0.200836i	−0.619689	+	0.784848i	$0.712741\pi$
$654$	30.4010	+	48.4574i	1.18877	+	1.89483i
$655$	−0.139100	−	22.4197i	−0.00543509	−	0.876011i
$656$	−16.7018	−	12.1346i	−0.652097	−	0.473776i
$657$	−16.2149	+	20.9089i	−0.632604	+	0.815734i
$658$	−20.8682	−	15.1616i	−0.813527	−	0.591062i
$659$	−11.9432	−	13.2643i	−0.465242	−	0.516703i	0.464171	−	0.885746i	$-0.346352\pi$
$659$	−11.9432	−	13.2643i	−0.465242	−	0.516703i	−0.929413	+	0.369043i	$0.879686\pi$
$660$	−7.00302	+	4.45431i	−0.272592	+	0.173384i
$661$	24.5369	−	27.2510i	0.954375	−	1.05994i	−0.0437689	−	0.999042i	$-0.513937\pi$
$661$	24.5369	−	27.2510i	0.954375	−	1.05994i	0.998144	−	0.0608991i	$-0.0193968\pi$
$662$	32.5727	−	6.92354i	1.26597	−	0.269091i
$663$	−47.0913	+	36.9285i	−1.82887	+	1.43418i
$664$	77.5235	+	16.4781i	3.00850	+	0.639476i
$665$	−12.9711	+	7.59656i	−0.502998	+	0.294582i
$666$	−54.6835	+	4.02180i	−2.11894	+	0.155842i
$667$	23.3603	+	16.9723i	0.904516	+	0.657169i
$668$	13.6786	−	23.6920i	0.529240	−	0.916670i
$669$	20.7198	−	24.7834i	0.801075	−	0.958182i
$670$	−0.509880	+	2.47418i	−0.0196984	+	0.0955859i
$671$	−3.44239	−	1.53265i	−0.132892	−	0.0591674i
$672$	−1.87166	+	3.53542i	−0.0722008	+	0.136382i
$673$	−20.3716	−	4.33013i	−0.785269	−	0.166914i	−0.202208	−	0.979343i	$-0.564812\pi$
$673$	−20.3716	−	4.33013i	−0.785269	−	0.166914i	−0.583061	+	0.812428i	$0.698145\pi$
$674$	−29.9258			−1.15270
$675$	−24.5623	+	8.46729i	−0.945402	+	0.325906i
$676$	49.5070			1.90411
$677$	−6.76634	−	1.43823i	−0.260052	−	0.0552757i	0.0760407	−	0.997105i	$-0.475772\pi$
$677$	−6.76634	−	1.43823i	−0.260052	−	0.0552757i	−0.336092	+	0.941829i	$0.609105\pi$
$678$	19.1749	−	36.2199i	0.736408	−	1.39102i
$679$	9.49631	+	4.22803i	0.364435	+	0.162257i
$680$	−34.4936	−	76.1980i	−1.32277	−	2.92206i
$681$	−18.8947	+	22.6003i	−0.724046	+	0.866046i
$682$	0.980570	−	1.69840i	0.0375480	−	0.0650350i
$683$	25.6445	+	18.6318i	0.981258	+	0.712926i	0.957989	−	0.286803i	$-0.0925926\pi$
$683$	25.6445	+	18.6318i	0.981258	+	0.712926i	0.0232689	+	0.999729i	$0.492593\pi$
$684$	−28.4072	+	58.7797i	−1.08618	+	2.24750i
$685$	−17.6611	−	15.7048i	−0.674796	−	0.600050i
$686$	−38.6522	−	8.21577i	−1.47575	−	0.313680i
$687$	−29.6744	+	23.2703i	−1.13215	+	0.887819i
$688$	20.6532	−	4.38998i	0.787398	−	0.167367i
$689$	−9.12892	+	10.1387i	−0.347784	+	0.386253i
$690$	10.0114	+	38.8269i	0.381128	+	1.47811i
$691$	−2.74243	−	3.04578i	−0.104327	−	0.115867i	0.688720	−	0.725028i	$-0.258173\pi$
$691$	−2.74243	−	3.04578i	−0.104327	−	0.115867i	−0.793047	+	0.609161i	$0.791506\pi$
$692$	3.62934	+	2.63687i	0.137967	+	0.100239i
$693$	1.96763	+	0.269310i	0.0747440	+	0.0102302i
$694$	1.40496	+	1.02077i	0.0533317	+	0.0387478i
$695$	−0.775101	+	1.08087i	−0.0294012	+	0.0409999i
$696$	34.4337	+	54.8852i	1.30520	+	2.08042i
$697$	−25.7916	−	11.4832i	−0.976926	−	0.434956i
$698$	28.7811	−	31.9646i	1.08938	−	1.20988i
$699$	−14.6144	+	7.16051i	−0.552766	+	0.270835i
$700$	−17.7468	+	20.2086i	−0.670767	+	0.763813i
$701$	1.75231			0.0661838			0.0330919	−	0.999452i	$-0.489465\pi$
$701$	1.75231			0.0661838			0.0330919	+	0.999452i	$0.489465\pi$
$702$	63.9841	−	7.07467i	2.41492	−	0.267016i
$703$	−31.0370	+	22.5497i	−1.17058	+	0.850479i
$704$	−0.305017	−	2.90205i	−0.0114958	−	0.109375i
$705$	−30.0527	−	8.35771i	−1.13185	−	0.314770i
$706$	−1.37129	+	13.0470i	−0.0516092	+	0.491029i
$707$	−10.0585	−	17.4218i	−0.378287	−	0.655213i
$708$	14.1831	−	16.9648i	0.533035	−	0.637575i
$709$	−17.0356	−	18.9200i	−0.639787	−	0.710556i	0.332825	−	0.942989i	$-0.391998\pi$
$709$	−17.0356	−	18.9200i	−0.639787	−	0.710556i	−0.972612	+	0.232433i	$0.925331\pi$
$710$	−7.92606	+	4.64192i	−0.297460	+	0.174208i
$711$	7.88830	−	6.66763i	0.295835	−	0.250056i
$712$	16.0981	−	49.5449i	0.603303	−	1.85677i
$713$	−4.28567	−	4.75972i	−0.160500	−	0.178253i
$714$	−10.5280	+	36.9667i	−0.394002	+	1.38345i
$715$	5.69083	−	0.633852i	0.212825	−	0.0237047i
$716$	76.8874	−	16.3429i	2.87342	−	0.610763i
$717$	−2.92535	−	7.99254i	−0.109249	−	0.298487i
$718$	1.34655	−	2.33230i	0.0502530	−	0.0870407i
$719$	9.49736	+	6.90024i	0.354192	+	0.257335i	0.750625	−	0.660728i	$-0.229752\pi$
$719$	9.49736	+	6.90024i	0.354192	+	0.257335i	−0.396434	+	0.918063i	$0.629752\pi$
$720$	−4.40008	+	33.7029i	−0.163981	+	1.25603i
$721$	−15.8489	+	11.5149i	−0.590244	+	0.428838i
$722$	2.12868	+	20.2530i	0.0792213	+	0.753740i
$723$	−13.4161	+	3.37069i	−0.498952	+	0.125357i
$724$	−30.0825	−	52.1045i	−1.11801	−	1.93645i
$725$	11.1146	+	32.8161i	0.412787	+	1.21876i
$726$	−41.4891	+	20.3281i	−1.53980	+	0.754448i
$727$	−19.9336	−	4.23701i	−0.739295	−	0.157142i	−0.177154	−	0.984183i	$-0.556689\pi$
$727$	−19.9336	−	4.23701i	−0.739295	−	0.157142i	−0.562141	+	0.827041i	$0.690022\pi$
$728$	28.0725	−	20.3958i	1.04043	−	0.755920i
$729$	26.3478	−	5.89862i	0.975844	−	0.218468i
$730$	10.4846	+	47.8641i	0.388054	+	1.77153i
$731$	26.3788	−	11.7446i	0.975656	−	0.434390i
$732$	−47.6230	+	23.3335i	−1.76020	+	0.862432i
$733$	4.53737	−	43.1702i	0.167592	−	1.59453i	−0.510716	−	0.859749i	$-0.670620\pi$
$733$	4.53737	−	43.1702i	0.167592	−	1.59453i	0.678308	−	0.734778i	$-0.262714\pi$
$734$	75.9032	−	16.1337i	2.80164	−	0.595506i
$735$	−20.4504	+	3.04125i	−0.754325	+	0.112178i
$736$	7.30275	+	1.55225i	0.269183	+	0.0572166i
$737$	0.0721606	−	0.222087i	0.00265807	−	0.00818069i
$738$	17.0730	+	25.1162i	0.628466	+	0.924539i
$739$	−2.42742	−	7.47084i	−0.0892942	−	0.274819i	0.896431	−	0.443184i	$-0.146151\pi$
$739$	−2.42742	−	7.47084i	−0.0892942	−	0.274819i	−0.985725	+	0.168365i	$0.946151\pi$
$740$	−40.0005	+	55.7805i	−1.47045	+	2.05053i
$741$	35.4425	−	27.7937i	1.30201	−	1.02103i
$742$	−0.915943	+	8.71462i	−0.0336253	+	0.319924i
$743$	−16.6131	−	28.7747i	−0.609475	−	1.05564i	−0.991327	−	0.131418i	$-0.958047\pi$
$743$	−16.6131	−	28.7747i	−0.609475	−	1.05564i	0.381852	−	0.924223i	$-0.375286\pi$
$744$	−4.93976	−	13.4962i	−0.181100	−	0.494795i
$745$	2.69458	+	3.66079i	0.0987218	+	0.134121i
$746$	−0.496906	+	0.361023i	−0.0181930	+	0.0132180i
$747$	−37.4351	−	23.2050i	−1.36968	−	0.849027i
$748$	4.58845	+	14.1218i	0.167770	+	0.516344i
$749$	6.89519	−	11.9428i	0.251945	−	0.436381i
$750$	−17.1089	+	44.9677i	−0.624729	+	1.64199i
$751$	−16.9328	−	29.3284i	−0.617886	−	1.07021i	−0.989871	−	0.141971i	$-0.954656\pi$
$751$	−16.9328	−	29.3284i	−0.617886	−	1.07021i	0.371985	−	0.928239i	$-0.378677\pi$
$752$	−27.3059	+	30.3263i	−0.995745	+	1.10589i
$753$	17.4315	−	32.9268i	0.635239	−	1.19992i
$754$	−8.97350	−	85.3772i	−0.326796	−	3.10925i
$755$	3.77306	−	8.61794i	0.137316	−	0.313639i
$756$	20.6696	−	18.8142i	0.751745	−	0.684264i
$757$	−9.25569			−0.336404			−0.168202	−	0.985753i	$-0.553796\pi$
$757$	−9.25569			−0.336404			−0.168202	+	0.985753i	$0.553796\pi$
$758$	50.7030	−	22.5744i	1.84162	−	0.819940i
$759$	−0.522454	−	3.66950i	−0.0189639	−	0.133194i
$760$	25.9611	+	57.3493i	0.941707	+	2.08028i
$761$	10.3134	−	11.4542i	0.373861	−	0.415214i	−0.526627	−	0.850097i	$-0.676543\pi$
$761$	10.3134	−	11.4542i	0.373861	−	0.415214i	0.900487	+	0.434882i	$0.143210\pi$
$762$	52.8267	+	21.2328i	1.91371	+	0.769183i
$763$	−11.4659	−	12.7342i	−0.415094	−	0.461008i
$764$	−23.8752	−	73.4802i	−0.863773	−	2.65842i
$765$	3.69689	+	46.3341i	0.133661	+	1.67521i
$766$	−20.3600	+	62.6615i	−0.735636	+	2.26405i
$767$	−13.9369	+	6.20510i	−0.503232	+	0.224053i
$768$	−46.8873	−	31.5032i	−1.69190	−	1.13677i
$769$	−1.77895	+	16.9256i	−0.0641505	+	0.610351i	0.914467	+	0.404661i	$0.132611\pi$
$769$	−1.77895	+	16.9256i	−0.0641505	+	0.610351i	−0.978617	+	0.205690i	$0.934056\pi$
$770$	2.71776	−	2.47779i	0.0979413	−	0.0892932i
$771$	16.6412	−	0.611127i	0.599317	−	0.0220092i
$772$	−2.35583	−	22.4142i	−0.0847880	−	0.806704i
$773$	8.95270	+	27.5536i	0.322006	+	0.991033i	0.972774	+	0.231756i	$0.0744471\pi$
$773$	8.95270	+	27.5536i	0.322006	+	0.991033i	−0.650768	+	0.759277i	$0.725553\pi$
$774$	−30.7741	−	4.21205i	−1.10615	−	0.151399i
$775$	−0.898098	−	7.63255i	−0.0322606	−	0.274169i
$776$	21.7665	−	37.7007i	0.781372	−	1.35338i
$777$	15.9296	−	4.00218i	0.571471	−	0.143577i
$778$	29.5203	+	13.1433i	1.05835	+	0.471210i
$779$	19.4117	+	8.64263i	0.695495	+	0.309654i
$780$	44.5271	−	67.1678i	1.59433	−	2.40499i
$781$	0.775672	−	0.345352i	0.0277557	−	0.0123576i
$782$	71.7360			2.56527
$783$	−7.67632	−	35.1787i	−0.274329	−	1.25718i
$784$	−8.35834	+	25.7243i	−0.298512	+	0.918726i
$785$	−0.739932	−	1.00525i	−0.0264093	−	0.0358791i
$786$	30.0286	+	30.9837i	1.07109	+	1.10515i
$787$	−7.31133	+	1.55407i	−0.260621	+	0.0553967i	−0.336369	−	0.941730i	$-0.609199\pi$
$787$	−7.31133	+	1.55407i	−0.260621	+	0.0553967i	0.0757480	+	0.997127i	$0.475866\pi$
$788$	−63.5881	+	13.5161i	−2.26523	+	0.481490i
$789$	16.2228	−	4.07585i	0.577548	−	0.145104i
$790$	−0.118670	−	19.1269i	−0.00422209	−	0.680504i
$791$	−3.79358	+	11.6754i	−0.134884	+	0.415130i
$792$	1.98299	−	8.07716i	0.0704626	−	0.287009i
$793$	36.5877			1.29927
$794$	69.7870	−	31.0712i	2.47665	−	1.10268i
$795$	2.64578	+	10.2610i	0.0938360	+	0.363920i
$796$	−65.2949	−	29.0711i	−2.31431	−	1.03040i
$797$	14.5045	+	6.45782i	0.513776	+	0.228748i	0.647212	−	0.762310i	$-0.275935\pi$
$797$	14.5045	+	6.45782i	0.513776	+	0.228748i	−0.133437	+	0.991057i	$0.542601\pi$
$798$	7.92377	−	27.8225i	0.280499	−	0.984905i
$799$	−27.9034	+	48.3301i	−0.987152	+	1.70980i
$800$	6.07647	+	6.58249i	0.214836	+	0.232726i
$801$	−17.7411	+	22.8770i	−0.626853	+	0.808318i
$802$	7.76865	+	23.9094i	0.274320	+	0.844271i
$803$	−0.473453	−	4.50460i	−0.0167078	−	0.158964i
$804$	−1.74657	−	2.78392i	−0.0615966	−	0.0981814i
$805$	−4.95329	−	10.9421i	−0.174580	−	0.385657i
$806$	−1.99044	+	18.9378i	−0.0701102	+	0.667054i
$807$	28.2645	−	13.8486i	0.994957	−	0.487493i
$808$	−76.9636	+	34.2664i	−2.70757	+	1.20549i
$809$	−0.927281	+	2.85388i	−0.0326015	+	0.100337i	−0.966033	−	0.258418i	$-0.916799\pi$
$809$	−0.927281	+	2.85388i	−0.0326015	+	0.100337i	0.933432	+	0.358755i	$0.116799\pi$
$810$	22.8796	−	44.4580i	0.803906	−	1.56210i
$811$	−11.0539	−	34.0205i	−0.388156	−	1.19462i	−0.934165	−	0.356841i	$-0.883854\pi$
$811$	−11.0539	−	34.0205i	−0.388156	−	1.19462i	0.546009	−	0.837779i	$-0.316146\pi$
$812$	−24.9408	−	27.6995i	−0.875250	−	0.972063i
$813$	0.610906	+	4.29074i	0.0214254	+	0.150483i
$814$	6.28057	−	6.97528i	0.220134	−	0.244483i
$815$	7.82020	−	37.9473i	0.273930	−	1.32924i
$816$	56.4217	+	22.6777i	1.97515	+	0.793879i
$817$	−19.8536	+	8.83941i	−0.694591	+	0.309252i
$818$	44.0028			1.53852
$819$	−18.5169	+	5.38189i	−0.647034	+	0.188059i
$820$	37.8337	+	3.73931i	1.32121	+	0.130582i
$821$	4.85653	+	46.2068i	0.169494	+	1.61263i	0.666924	+	0.745126i	$0.267611\pi$
$821$	4.85653	+	46.2068i	0.169494	+	1.61263i	−0.497430	+	0.867504i	$0.665723\pi$
$822$	45.4525	−	1.66919i	1.58534	−	0.0582197i
$823$	27.4590	−	30.4963i	0.957159	−	1.06303i	−0.0407992	−	0.999167i	$-0.512990\pi$
$823$	27.4590	−	30.4963i	0.957159	−	1.06303i	0.997959	−	0.0638657i	$-0.0203429\pi$
$824$	41.0210	+	71.0504i	1.42903	+	2.47516i
$825$	2.03195	−	3.95614i	0.0707434	−	0.137735i
$826$	−4.89927	+	8.48578i	−0.170467	+	0.295258i
$827$	12.0368	+	37.0454i	0.418560	+	1.28820i	0.909028	+	0.416736i	$0.136826\pi$
$827$	12.0368	+	37.0454i	0.418560	+	1.28820i	−0.490468	+	0.871459i	$0.663174\pi$
$828$	−44.3371	−	27.4834i	−1.54082	−	0.955113i
$829$	−4.44553	+	3.22987i	−0.154400	+	0.112178i	−0.662303	−	0.749236i	$-0.730421\pi$
$829$	−4.44553	+	3.22987i	−0.154400	+	0.112178i	0.507903	+	0.861414i	$0.330421\pi$
$830$	−77.4127	+	25.6850i	−2.68704	+	0.891539i
$831$	−14.9675	+	17.9030i	−0.519218	+	0.621048i
$832$	14.1666	+	24.5373i	0.491138	+	0.850677i
$833$	−3.86646	+	36.7869i	−0.133965	+	1.27459i
$834$	−0.360806	−	2.53415i	−0.0124937	−	0.0877503i
$835$	0.0909525	+	14.6595i	0.00314754	+	0.507311i
$836$	−3.45343	−	10.6286i	−0.119439	−	0.367596i
$837$	0.0431451	+	7.98658i	0.00149131	+	0.276057i
$838$	10.3078	−	31.7242i	0.356078	−	1.09590i
$839$	−15.3782	−	3.26874i	−0.530916	−	0.112850i	−0.0653491	−	0.997862i	$-0.520816\pi$
$839$	−15.3782	−	3.26874i	−0.530916	−	0.112850i	−0.465567	+	0.885013i	$0.654149\pi$
$840$	−1.15617	−	26.9266i	−0.0398918	−	0.929056i
$841$	−18.6017	+	3.95392i	−0.641439	+	0.136342i
$842$	−8.46664	+	80.5547i	−0.291780	+	2.77610i
$843$	−0.0889851	+	1.30635i	−0.00306481	+	0.0449930i
$844$	−55.1685	+	24.5626i	−1.89898	+	0.845479i
$845$	−22.8921	+	13.4068i	−0.787512	+	0.461209i
$846$	52.9026	−	28.3737i	1.81883	−	0.975507i
$847$	11.1965	−	8.13473i	0.384716	−	0.279512i
$848$	13.5599	+	2.88225i	0.465650	+	0.0989769i
$849$	−6.02059	−	4.04519i	−0.206626	−	0.138830i
$850$	70.2598	+	49.7265i	2.40989	+	1.70561i
$851$	−15.3270	−	26.5472i	−0.525403	−	0.910025i
$852$	3.27309	−	11.4927i	0.112134	−	0.393733i
$853$	−0.145516	−	1.38449i	−0.00498237	−	0.0474041i	0.991748	−	0.128201i	$-0.0409202\pi$
$853$	−0.145516	−	1.38449i	−0.00498237	−	0.0474041i	−0.996731	+	0.0807967i	$0.974254\pi$
$854$	19.0116	−	13.8127i	0.650564	−	0.472662i
$855$	−2.78241	−	34.8727i	−0.0951563	−	1.19262i
$856$	−46.7227	−	33.9460i	−1.59695	−	1.16025i
$857$	−12.7340	+	22.0559i	−0.434985	+	0.753415i	−0.997294	−	0.0735113i	$-0.976580\pi$
$857$	−12.7340	+	22.0559i	−0.434985	+	0.753415i	0.562310	+	0.826927i	$0.309913\pi$
$858$	−7.06813	+	8.45434i	−0.241302	+	0.288626i
$859$	6.26793	−	1.33229i	0.213859	−	0.0454572i	−0.0997361	−	0.995014i	$-0.531800\pi$
$859$	6.26793	−	1.33229i	0.213859	−	0.0454572i	0.313595	+	0.949557i	$0.398467\pi$
$860$	−28.7342	+	26.1970i	−0.979828	+	0.893311i
$861$	−6.33120	−	6.53257i	−0.215767	−	0.222629i
$862$	14.8875	+	16.5342i	0.507069	+	0.563157i
$863$	−3.68829	+	11.3514i	−0.125551	+	0.386406i	−0.994001	−	0.109370i	$-0.965117\pi$
$863$	−3.68829	+	11.3514i	−0.125551	+	0.386406i	0.868450	+	0.495777i	$0.165117\pi$
$864$	−5.51279	−	7.50214i	−0.187549	−	0.255228i
$865$	−2.39229	−	0.236443i	−0.0813404	−	0.00803931i
$866$	46.3386	+	51.4642i	1.57465	+	1.74882i
$867$	52.9142	+	9.23199i	1.79706	+	0.313535i
$868$	4.13386	+	7.16006i	0.140312	+	0.243028i
$869$	−0.184817	+	1.75841i	−0.00626948	+	0.0596501i
$870$	−59.1224	−	30.8314i	−2.00444	−	1.04528i
$871$	0.237005	+	2.25495i	0.00803061	+	0.0764062i
$872$	−58.0563	+	42.1804i	−1.96603	+	1.42841i
$873$	−18.4762	+	15.6171i	−0.625323	+	0.528558i
$874$	−53.9910			−1.82627
$875$	2.73354	−	14.1504i	0.0924106	−	0.478372i
$876$	−52.9116	−	35.5509i	−1.78772	−	1.20115i
$877$	−0.560532	+	0.622534i	−0.0189278	+	0.0210215i	−0.752534	−	0.658553i	$-0.771169\pi$
$877$	−0.560532	+	0.622534i	−0.0189278	+	0.0210215i	0.733607	+	0.679574i	$0.237836\pi$
$878$	7.13733	+	3.17775i	0.240873	+	0.107244i
$879$	−45.3512	+	1.66547i	−1.52966	+	0.0561748i
$880$	−3.44906	−	4.68581i	−0.116268	−	0.157959i
$881$	−8.77572	−	6.37593i	−0.295661	−	0.214811i	0.430058	−	0.902801i	$-0.358493\pi$
$881$	−8.77572	−	6.37593i	−0.295661	−	0.214811i	−0.725720	+	0.687991i	$0.758493\pi$
$882$	24.3838	−	31.4426i	0.821046	−	1.05873i
$883$	−29.2715	−	21.2670i	−0.985064	−	0.715691i	−0.0262292	−	0.999656i	$-0.508350\pi$
$883$	−29.2715	−	21.2670i	−0.985064	−	0.715691i	−0.958835	+	0.283965i	$0.908350\pi$
$884$	−96.4717	−	107.143i	−3.24469	−	3.60360i
$885$	−1.96414	+	11.6854i	−0.0660238	+	0.392801i
$886$	32.8070	−	36.4358i	1.10217	−	1.22409i
$887$	44.3753	−	9.43226i	1.48998	−	0.316704i	0.610259	−	0.792202i	$-0.291065\pi$
$887$	44.3753	−	9.43226i	1.48998	−	0.316704i	0.879717	+	0.475497i	$0.157732\pi$
$888$	−9.69560	−	68.0978i	−0.325363	−	2.28521i
$889$	−16.6819	−	3.54585i	−0.559493	−	0.118924i
$890$	11.4715	+	52.3694i	0.384526	+	1.75543i
$891$	−2.55689	+	3.85027i	−0.0856589	+	0.128989i
$892$	62.9620	+	45.7446i	2.10812	+	1.53164i
$893$	21.0011	−	36.3750i	0.702775	−	1.21724i
$894$	−8.61775	−	1.50355i	−0.288221	−	0.0502861i
$895$	−31.1271	+	28.3786i	−1.04046	+	0.948592i
$896$	20.8444	+	9.28052i	0.696362	+	0.310041i
$897$	19.1262	+	30.4860i	0.638605	+	1.01790i
$898$	−33.4705	−	7.11438i	−1.11693	−	0.237410i
$899$	10.6509			0.355226
$900$	−24.3736	−	57.6517i	−0.812452	−	1.92172i
$901$	18.9581			0.631585
$902$	−5.08514	−	1.08088i	−0.169317	−	0.0359893i
$903$	9.29804	−	0.341459i	0.309419	−	0.0113631i
$904$	46.9668	+	20.9110i	1.56209	+	0.695488i
$905$	28.0205	+	15.9466i	0.931432	+	0.530084i
$906$	6.22294	+	17.0021i	0.206743	+	0.564856i
$907$	−8.10153	+	14.0323i	−0.269007	+	0.465933i	−0.968606	−	0.248602i	$-0.920029\pi$
$907$	−8.10153	+	14.0323i	−0.269007	+	0.465933i	0.699599	+	0.714536i	$0.253362\pi$
$908$	−57.4159	−	41.7151i	−1.90541	−	1.38436i
$909$	46.6918	−	3.43403i	1.54867	−	0.113900i
$910$	−14.3217	+	32.7118i	−0.474760	+	1.08439i
$911$	13.5590	+	2.88206i	0.449231	+	0.0954869i	0.426971	−	0.904265i	$-0.359581\pi$
$911$	13.5590	+	2.88206i	0.449231	+	0.0954869i	0.0222596	+	0.999752i	$0.492914\pi$
$912$	−42.4649	−	17.0681i	−1.40615	−	0.565180i
$913$	7.37479	−	1.56756i	0.244070	−	0.0518787i
$914$	26.7115	−	29.6661i	0.883538	−	0.981268i
$915$	15.7021	−	23.6861i	0.519095	−	0.783038i
$916$	−60.7913	−	67.5156i	−2.00860	−	2.23078i
$917$	−10.4564	−	7.59702i	−0.345301	−	0.250876i
$918$	−66.7991	−	59.4960i	−2.20470	−	1.96366i
$919$	33.8071	+	24.5623i	1.11519	+	0.810236i	0.983474	−	0.181051i	$-0.0579500\pi$
$919$	33.8071	+	24.5623i	1.11519	+	0.810236i	0.131720	+	0.991287i	$0.457950\pi$
$920$	−47.7413	+	15.8402i	−1.57398	+	0.522237i
$921$	11.0738	−	20.9176i	0.364894	−	0.689258i
$922$	−23.3058	−	10.3764i	−0.767537	−	0.341729i
$923$	−5.51651	+	6.12671i	−0.181578	+	0.201663i
$924$	−0.325159	+	4.77350i	−0.0106969	+	0.157037i
$925$	3.39057	−	36.6254i	0.111481	−	1.20423i
$926$	−44.7769			−1.47146
$927$	−8.07868	−	44.8709i	−0.265339	−	1.47375i
$928$	−10.0442	+	7.29755i	−0.329718	+	0.239554i
$929$	3.25692	+	30.9875i	0.106856	+	1.01667i	0.908221	+	0.418491i	$0.137441\pi$
$929$	3.25692	+	30.9875i	0.106856	+	1.01667i	−0.801365	+	0.598176i	$0.795892\pi$
$930$	11.4057	+	9.41593i	0.374006	+	0.308761i
$931$	2.91004	−	27.6871i	0.0953726	−	0.907409i
$932$	−19.6038	−	33.9548i	−0.642145	−	1.11223i
$933$	−0.568742	−	1.55389i	−0.0186198	−	0.0508722i
$934$	58.7155	+	65.2101i	1.92123	+	2.13374i
$935$	−5.94598	−	5.28736i	−0.194454	−	0.172915i
$936$	14.3094	+	79.4778i	0.467718	+	2.59781i
$937$	−11.2706	+	34.6872i	−0.368193	+	1.13318i	0.579764	+	0.814784i	$0.303145\pi$
$937$	−11.2706	+	34.6872i	−0.368193	+	1.13318i	−0.947957	+	0.318398i	$0.896855\pi$
$938$	0.974450	+	1.08224i	0.0318169	+	0.0353363i
$939$	−20.1345	+	5.05862i	−0.657064	+	0.165082i
$940$	15.1682	−	73.6033i	0.494732	−	2.40068i
$941$	−15.2034	+	3.23158i	−0.495617	+	0.105347i	−0.448937	−	0.893563i	$-0.648197\pi$
$941$	−15.2034	+	3.23158i	−0.495617	+	0.105347i	−0.0466795	+	0.998910i	$0.514864\pi$
$942$	2.36644	+	0.412874i	0.0771026	+	0.0134522i
$943$	−8.48922	+	14.7038i	−0.276447	+	0.478820i
$944$	12.5412	+	9.11169i	0.408180	+	0.296560i
$945$	−4.46265	+	14.2972i	−0.145170	+	0.465086i
$946$	4.30163	−	3.12532i	0.139858	−	0.101613i
$947$	1.69965	+	16.1711i	0.0552313	+	0.525490i	0.986802	+	0.161931i	$0.0517721\pi$
$947$	1.69965	+	16.1711i	0.0552313	+	0.525490i	−0.931571	+	0.363560i	$0.881561\pi$
$948$	17.3179	+	17.8687i	0.562459	+	0.580349i
$949$	21.9896	+	38.0871i	0.713813	+	1.23636i
$950$	−52.8800	−	37.4259i	−1.71565	−	1.21426i
$951$	0.265752	−	3.90138i	0.00861760	−	0.126511i
$952$	−47.1643	−	10.0251i	−1.52860	−	0.324915i
$953$	29.6469	−	21.5397i	0.960357	−	0.697741i	0.00712369	−	0.999975i	$-0.497732\pi$
$953$	29.6469	−	21.5397i	0.960357	−	0.697741i	0.953234	+	0.302234i	$0.0977324\pi$
$954$	−17.3332	−	10.7444i	−0.561183	−	0.347862i
$955$	30.9388	+	27.5118i	1.00116	+	0.890261i
$956$	18.7320	−	8.34000i	0.605835	−	0.269735i
$957$	5.11613	+	3.43748i	0.165381	+	0.111118i
$958$	−0.443837	+	4.22283i	−0.0143397	+	0.136433i
$959$	−13.3267	+	2.83268i	−0.430343	+	0.0914722i
$960$	21.9646	+	1.35933i	0.708906	+	0.0438721i
$961$	28.0117	+	5.95407i	0.903603	+	0.192067i
$962$	−28.1628	+	86.6762i	−0.908006	+	2.79455i
$963$	18.0426	+	26.5425i	0.581413	+	0.855320i
$964$	−10.2984	−	31.6953i	−0.331690	−	1.02084i
$965$	7.15925	+	9.72638i	0.230464	+	0.313103i
$966$	21.4475	+	8.62046i	0.690062	+	0.277359i
$967$	4.26366	−	40.5660i	0.137110	−	1.30452i	−0.682200	−	0.731165i	$-0.738977\pi$
$967$	4.26366	−	40.5660i	0.137110	−	1.30452i	0.819310	−	0.573350i	$-0.194357\pi$
$968$	−28.9793	−	50.1937i	−0.931431	−	1.61329i
$969$	−61.6566	−	10.7573i	−1.98069	−	0.345573i
$970$	0.277952	+	44.7994i	0.00892449	+	1.43842i
$971$	36.3301	−	26.3954i	1.16589	−	0.847068i	0.175378	−	0.984501i	$-0.443885\pi$
$971$	36.3301	−	26.3954i	1.16589	−	0.847068i	0.990511	+	0.137433i	$0.0438852\pi$
$972$	18.4918	+	62.3640i	0.593126	+	2.00033i
$973$	0.236941	+	0.729230i	0.00759599	+	0.0233780i
$974$	40.6362	−	70.3840i	1.30207	−	2.25525i
$975$	−2.39993	+	43.1167i	−0.0768593	+	1.38084i
$976$	−18.5888	−	32.1967i	−0.595011	−	1.03059i
$977$	−4.45973	+	4.95303i	−0.142679	+	0.158462i	−0.810249	−	0.586086i	$-0.800668\pi$
$977$	−4.45973	+	4.95303i	−0.142679	+	0.158462i	0.667569	+	0.744548i	$0.267335\pi$
$978$	39.6268	+	63.1627i	1.26712	+	2.01972i
$979$	−0.518017	−	4.92860i	−0.0165559	−	0.157519i
$980$	−10.6583	−	48.6568i	−0.340466	−	1.55429i
$981$	38.2946	−	11.1302i	1.22265	−	0.355361i
$982$	−102.522			−3.27161
$983$	−28.5768	+	12.7232i	−0.911458	+	0.405807i	−0.808241	−	0.588851i	$-0.799580\pi$
$983$	−28.5768	+	12.7232i	−0.911458	+	0.405807i	−0.103217	+	0.994659i	$0.532914\pi$
$984$	−29.9793	+	23.5094i	−0.955704	+	0.749453i
$985$	25.7430	−	23.4699i	0.820240	−	0.747814i
$986$	−79.8223	+	88.6517i	−2.54206	+	2.82324i
$987$	−14.1503	+	11.0965i	−0.450409	+	0.353206i
$988$	72.6080	+	80.6394i	2.30997	+	2.56548i
$989$	−5.36608	−	16.5151i	−0.170632	−	0.525150i
$990$	2.43978	+	8.20403i	0.0775412	+	0.260741i
$991$	−1.60963	+	4.95394i	−0.0511317	+	0.157367i	−0.973362	−	0.229274i	$-0.926365\pi$
$991$	−1.60963	+	4.95394i	−0.0511317	+	0.157367i	0.922230	+	0.386641i	$0.126365\pi$
$992$	2.51580	−	1.12010i	0.0798766	−	0.0355634i
$993$	1.57769	−	23.1613i	0.0500665	−	0.735002i
$994$	−0.553495	+	5.26616i	−0.0175558	+	0.167032i
$995$	38.0651	−	4.23974i	1.20675	−	0.134409i
$996$	49.6466	−	93.7787i	1.57311	−	2.97149i
$997$	2.39822	+	22.8176i	0.0759524	+	0.722639i	0.964541	+	0.263934i	$0.0850200\pi$
$997$	2.39822	+	22.8176i	0.0759524	+	0.722639i	−0.888588	+	0.458705i	$0.848313\pi$
$998$	2.67071	+	8.21961i	0.0845399	+	0.260187i
$999$	−7.74532	+	37.4320i	−0.245051	+	1.18430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.27	yes	224
3.2	odd	2		675.2.r.a.181.2		224
9.4	even	3	inner	225.2.q.a.31.2	✓	224
9.5	odd	6		675.2.r.a.631.27		224
25.21	even	5	inner	225.2.q.a.196.2	yes	224
75.71	odd	10		675.2.r.a.46.27		224
225.121	even	15	inner	225.2.q.a.121.27	yes	224
225.221	odd	30		675.2.r.a.496.2		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.2	✓	224	9.4	even	3	inner
225.2.q.a.106.27	yes	224	1.1	even	1	trivial
225.2.q.a.121.27	yes	224	225.121	even	15	inner
225.2.q.a.196.2	yes	224	25.21	even	5	inner
675.2.r.a.46.27		224	75.71	odd	10
675.2.r.a.181.2		224	3.2	odd	2
675.2.r.a.496.2		224	225.221	odd	30
675.2.r.a.631.27		224	9.5	odd	6

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.43022 + 0.516560i) q^{2} +(0.810393 - 1.53077i) q^{3} +(3.81206 + 1.69724i) q^{4} +(-2.22233 + 0.247525i) q^{5} +(2.76017 - 3.30150i) q^{6} +(-0.644527 + 1.11635i) q^{7} +(4.36740 + 3.17310i) q^{8} +(-1.68652 - 2.48105i) q^{9} +(-5.52861 - 0.546422i) q^{10} +(0.502326 + 0.106773i) q^{11} +(5.68735 - 4.45996i) q^{12} +(-4.87743 + 1.03673i) q^{13} +(-2.14301 + 2.38005i) q^{14} +(-1.42205 + 3.60247i) q^{15} +(3.39033 + 3.76535i) q^{16} +(5.60571 + 4.07278i) q^{17} +(-2.81702 - 6.90071i) q^{18} +(-4.21905 - 3.06532i) q^{19} +(-8.89175 - 2.82823i) q^{20} +(1.18656 + 1.89131i) q^{21} +(1.16561 + 0.518963i) q^{22} +(2.78826 - 3.09668i) q^{23} +(8.39660 - 4.11403i) q^{24} +(4.87746 - 1.10016i) q^{25} -12.3888 q^{26} +(-5.16468 + 0.571054i) q^{27} +(-4.35169 + 3.16169i) q^{28} +(0.724325 + 6.89149i) q^{29} +(-5.31680 + 8.02022i) q^{30} +(0.160665 - 1.52862i) q^{31} +(0.895838 + 1.55164i) q^{32} +(0.570526 - 0.682419i) q^{33} +(11.5193 + 12.7935i) q^{34} +(1.15602 - 2.64044i) q^{35} +(-2.21819 - 12.3204i) q^{36} +(2.27325 - 6.99635i) q^{37} +(-8.66982 - 9.62881i) q^{38} +(-2.36564 + 8.30640i) q^{39} +(-10.4912 - 5.97062i) q^{40} +(-3.98547 + 0.847138i) q^{41} +(1.90663 + 5.20923i) q^{42} +(2.08364 - 3.60897i) q^{43} +(1.73368 + 1.25959i) q^{44} +(4.36213 + 5.09625i) q^{45} +(8.37572 - 6.08531i) q^{46} +(0.841878 + 8.00993i) q^{47} +(8.51139 - 2.13841i) q^{48} +(2.66917 + 4.62314i) q^{49} +(12.4216 - 0.154142i) q^{50} +(10.7773 - 5.28050i) q^{51} +(-20.3526 - 4.32609i) q^{52} +(2.21350 - 1.60820i) q^{53} +(-12.8463 - 1.28008i) q^{54} +(-1.14276 - 0.112945i) q^{55} +(-6.35720 + 2.83041i) q^{56} +(-8.11140 + 3.97429i) q^{57} +(-1.79960 + 17.1220i) q^{58} +(2.99263 - 0.636103i) q^{59} +(-11.5352 + 11.3193i) q^{60} +(-7.17717 - 1.52555i) q^{61} +(1.18008 - 3.63190i) q^{62} +(3.85674 - 0.283651i) q^{63} +(-1.75586 - 5.40400i) q^{64} +(10.5826 - 3.51124i) q^{65} +(1.73902 - 1.36372i) q^{66} +(0.0475303 - 0.452221i) q^{67} +(14.4568 + 25.0399i) q^{68} +(-2.48072 - 6.77772i) q^{69} +(4.17334 - 5.81969i) q^{70} +(1.33759 - 0.971819i) q^{71} +(0.506910 - 16.1873i) q^{72} +(-2.72548 - 8.38816i) q^{73} +(9.13854 - 15.8284i) q^{74} +(2.26856 - 8.35785i) q^{75} +(-10.8807 - 18.8459i) q^{76} +(-0.442959 + 0.491955i) q^{77} +(-10.0398 + 18.9644i) q^{78} +(0.359882 + 3.42405i) q^{79} +(-8.46644 - 7.52863i) q^{80} +(-3.31127 + 8.36872i) q^{81} -10.1232 q^{82} +(13.4120 - 5.97142i) q^{83} +(1.31324 + 9.22366i) q^{84} +(-13.4658 - 7.66350i) q^{85} +(6.92795 - 7.69427i) q^{86} +(11.1363 + 4.47604i) q^{87} +(1.85506 + 2.06025i) q^{88} +(-2.98202 - 9.17771i) q^{89} +(7.96843 + 14.6383i) q^{90} +(1.98628 - 6.11314i) q^{91} +(15.8848 - 7.07238i) q^{92} +(-2.20977 - 1.48473i) q^{93} +(-2.09166 + 19.9008i) q^{94} +(10.1349 + 5.76782i) q^{95} +(3.10118 - 0.113887i) q^{96} +(-0.842924 - 8.01989i) q^{97} +(4.09855 + 12.6140i) q^{98} +(-0.582277 - 1.42637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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