LMFDB - Embedded newform 216.2.t.a.133.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,2,Mod(13,216)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("216.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			133.11
Character	$\chi$	$=$	216.133
Dual form			216.2.t.a.13.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.691259 - 1.23376i) q^{2} +(1.38208 - 1.04396i) q^{3} +(-1.04432 + 1.70569i) q^{4} +(1.90914 + 2.27523i) q^{5} +(-2.24337 - 0.983500i) q^{6} +(1.28267 - 0.466852i) q^{7} +(2.82631 + 0.109365i) q^{8} +(0.820275 - 2.88568i) q^{9} +(1.48737 - 3.92819i) q^{10} +(-2.78354 + 3.31729i) q^{11} +(0.337351 + 3.44764i) q^{12} +(4.65386 - 0.820601i) q^{13} +(-1.46264 - 1.25978i) q^{14} +(5.01384 + 1.15146i) q^{15} +(-1.81878 - 3.56259i) q^{16} +(0.356888 + 0.618149i) q^{17} +(-4.12726 + 0.982730i) q^{18} +(-6.43384 - 3.71458i) q^{19} +(-5.87460 + 0.880343i) q^{20} +(1.28537 - 1.98428i) q^{21} +(6.01689 + 1.14111i) q^{22} +(-4.17513 - 1.51962i) q^{23} +(4.02035 - 2.79942i) q^{24} +(-0.663593 + 3.76342i) q^{25} +(-4.22945 - 5.17449i) q^{26} +(-1.87886 - 4.84457i) q^{27} +(-0.543209 + 2.67538i) q^{28} +(-6.69820 - 1.18107i) q^{29} +(-2.04523 - 6.98183i) q^{30} +(5.02097 + 1.82748i) q^{31} +(-3.13812 + 4.70661i) q^{32} +(-0.383930 + 7.49067i) q^{33} +(0.515944 - 0.867615i) q^{34} +(3.51099 + 2.02707i) q^{35} +(4.06546 + 4.41272i) q^{36} +(0.547039 - 0.315833i) q^{37} +(-0.135445 + 10.5055i) q^{38} +(5.57532 - 5.99260i) q^{39} +(5.14700 + 6.63929i) q^{40} +(0.356345 + 2.02093i) q^{41} +(-3.33665 - 0.214178i) q^{42} +(2.43534 - 2.90233i) q^{43} +(-2.75138 - 8.21219i) q^{44} +(8.13160 - 3.64286i) q^{45} +(1.01125 + 6.20155i) q^{46} +(5.10473 - 1.85797i) q^{47} +(-6.23292 - 3.02502i) q^{48} +(-3.93503 + 3.30188i) q^{49} +(5.10187 - 1.78279i) q^{50} +(1.13857 + 0.481751i) q^{51} +(-3.46043 + 8.79504i) q^{52} +11.4745i q^{53} +(-4.67825 + 5.66692i) q^{54} -12.8618 q^{55} +(3.67627 - 1.17919i) q^{56} +(-12.7699 + 1.58287i) q^{57} +(3.17303 + 9.08039i) q^{58} +(-0.803086 - 0.957081i) q^{59} +(-7.20010 + 7.34958i) q^{60} +(0.216792 + 0.595632i) q^{61} +(-1.21612 - 7.45793i) q^{62} +(-0.295047 - 4.08431i) q^{63} +(7.97608 + 0.618197i) q^{64} +(10.7519 + 9.02195i) q^{65} +(9.50708 - 4.70432i) q^{66} +(-14.0227 + 2.47258i) q^{67} +(-1.42708 - 0.0368039i) q^{68} +(-7.35678 + 2.25845i) q^{69} +(0.0739130 - 5.73294i) q^{70} +(-0.414463 - 0.717870i) q^{71} +(2.63395 - 8.06612i) q^{72} +(7.29258 - 12.6311i) q^{73} +(-0.767808 - 0.456592i) q^{74} +(3.01174 + 5.89411i) q^{75} +(13.0549 - 7.09494i) q^{76} +(-2.02167 + 5.55448i) q^{77} +(-11.2474 - 2.73616i) q^{78} +(-1.22756 + 6.96183i) q^{79} +(4.63338 - 10.9396i) q^{80} +(-7.65430 - 4.73410i) q^{81} +(2.24702 - 1.83663i) q^{82} +(1.29008 + 0.227475i) q^{83} +(2.04225 + 4.26467i) q^{84} +(-0.725078 + 1.99214i) q^{85} +(-5.26422 - 0.998364i) q^{86} +(-10.4904 + 5.36035i) q^{87} +(-8.22995 + 9.07129i) q^{88} +(2.66374 - 4.61373i) q^{89} +(-10.1155 - 7.51427i) q^{90} +(5.58625 - 3.22522i) q^{91} +(6.95219 - 5.53452i) q^{92} +(8.84720 - 2.71599i) q^{93} +(-5.82098 - 5.01367i) q^{94} +(-3.83160 - 21.7301i) q^{95} +(0.576410 + 9.78099i) q^{96} +(-1.52072 - 1.27604i) q^{97} +(6.79385 + 2.57242i) q^{98} +(7.28938 + 10.7535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.691259	−	1.23376i	−0.488794	−	0.872399i
$2$	−0.691259	−	1.23376i	−0.488794	−	0.872399i
$3$	1.38208	−	1.04396i	0.797943	−	0.602733i
$3$	1.38208	−	1.04396i	0.797943	−	0.602733i
$4$	−1.04432	+	1.70569i	−0.522161	+	0.852847i
$5$	1.90914	+	2.27523i	0.853794	+	1.01751i	0.999602	+	0.0281995i	$0.00897737\pi$
$5$	1.90914	+	2.27523i	0.853794	+	1.01751i	−0.145808	+	0.989313i	$0.546578\pi$
$6$	−2.24337	−	0.983500i	−0.915854	−	0.401512i
$7$	1.28267	−	0.466852i	0.484802	−	0.176454i	−0.0880438	−	0.996117i	$-0.528062\pi$
$7$	1.28267	−	0.466852i	0.484802	−	0.176454i	0.572846	+	0.819663i	$0.305839\pi$
$8$	2.82631	+	0.109365i	0.999252	+	0.0386662i
$9$	0.820275	−	2.88568i	0.273425	−	0.961893i
$10$	1.48737	−	3.92819i	0.470348	−	1.24220i
$11$	−2.78354	+	3.31729i	−0.839269	+	1.00020i	0.160644	+	0.987012i	$0.448643\pi$
$11$	−2.78354	+	3.31729i	−0.839269	+	1.00020i	−0.999913	+	0.0131894i	$0.995802\pi$
$12$	0.337351	+	3.44764i	0.0973848	+	0.995247i
$13$	4.65386	−	0.820601i	1.29075	−	0.227594i	0.514211	−	0.857664i	$-0.328085\pi$
$13$	4.65386	−	0.820601i	1.29075	−	0.227594i	0.776538	+	0.630070i	$0.216974\pi$
$14$	−1.46264	−	1.25978i	−0.390906	−	0.336692i
$15$	5.01384	+	1.15146i	1.29457	+	0.297306i
$16$	−1.81878	−	3.56259i	−0.454696	−	0.890647i
$17$	0.356888	+	0.618149i	0.0865581	+	0.149923i	0.906054	−	0.423162i	$-0.139080\pi$
$17$	0.356888	+	0.618149i	0.0865581	+	0.149923i	−0.819496	+	0.573085i	$0.805746\pi$
$18$	−4.12726	+	0.982730i	−0.972804	+	0.231632i
$19$	−6.43384	−	3.71458i	−1.47602	−	0.852183i	−0.476389	−	0.879234i	$-0.658055\pi$
$19$	−6.43384	−	3.71458i	−1.47602	−	0.852183i	−0.999634	+	0.0270519i	$0.991388\pi$
$20$	−5.87460	+	0.880343i	−1.31360	+	0.196851i
$21$	1.28537	−	1.98428i	0.280490	−	0.433006i
$22$	6.01689	+	1.14111i	1.28280	+	0.243285i
$23$	−4.17513	−	1.51962i	−0.870574	−	0.316863i	−0.132175	−	0.991226i	$-0.542196\pi$
$23$	−4.17513	−	1.51962i	−0.870574	−	0.316863i	−0.738400	+	0.674363i	$0.764418\pi$
$24$	4.02035	−	2.79942i	0.820651	−	0.571429i
$25$	−0.663593	+	3.76342i	−0.132719	+	0.752685i
$26$	−4.22945	−	5.17449i	−0.829463	−	1.01480i
$27$	−1.87886	−	4.84457i	−0.361588	−	0.932338i
$28$	−0.543209	+	2.67538i	−0.102657	+	0.505599i
$29$	−6.69820	−	1.18107i	−1.24382	−	0.219320i	−0.487270	−	0.873251i	$-0.662007\pi$
$29$	−6.69820	−	1.18107i	−1.24382	−	0.219320i	−0.756554	+	0.653931i	$0.773118\pi$
$30$	−2.04523	−	6.98183i	−0.373407	−	1.27470i
$31$	5.02097	+	1.82748i	0.901793	+	0.328226i	0.750971	−	0.660335i	$-0.229586\pi$
$31$	5.02097	+	1.82748i	0.901793	+	0.328226i	0.150822	+	0.988561i	$0.451808\pi$
$32$	−3.13812	+	4.70661i	−0.554747	+	0.832019i
$33$	−0.383930	+	7.49067i	−0.0668336	+	1.30396i
$34$	0.515944	−	0.867615i	0.0884837	−	0.148795i
$35$	3.51099	+	2.02707i	0.593465	+	0.342637i
$36$	4.06546	+	4.41272i	0.677576	+	0.735453i
$37$	0.547039	−	0.315833i	0.0899327	−	0.0519226i	−0.454359	−	0.890819i	$-0.650132\pi$
$37$	0.547039	−	0.315833i	0.0899327	−	0.0519226i	0.544292	+	0.838896i	$0.316798\pi$
$38$	−0.135445	+	10.5055i	−0.0219720	+	1.70422i
$39$	5.57532	−	5.99260i	0.892765	−	0.959584i
$40$	5.14700	+	6.63929i	0.813812	+	1.04976i
$41$	0.356345	+	2.02093i	0.0556517	+	0.315617i	0.999908	−	0.0135959i	$-0.00432785\pi$
$41$	0.356345	+	2.02093i	0.0556517	+	0.315617i	−0.944256	+	0.329213i	$0.893217\pi$
$42$	−3.33665	−	0.214178i	−0.514856	−	0.0330483i
$43$	2.43534	−	2.90233i	0.371386	−	0.442601i	−0.547690	−	0.836682i	$-0.684493\pi$
$43$	2.43534	−	2.90233i	0.371386	−	0.442601i	0.919076	+	0.394081i	$0.128937\pi$
$44$	−2.75138	−	8.21219i	−0.414786	−	1.23803i
$45$	8.13160	−	3.64286i	1.21219	−	0.543046i
$46$	1.01125	+	6.20155i	0.149100	+	0.914369i
$47$	5.10473	−	1.85797i	0.744601	−	0.271013i	0.0582692	−	0.998301i	$-0.481442\pi$
$47$	5.10473	−	1.85797i	0.744601	−	0.271013i	0.686332	+	0.727288i	$0.259220\pi$
$48$	−6.23292	−	3.02502i	−0.899644	−	0.436625i
$49$	−3.93503	+	3.30188i	−0.562147	+	0.471697i
$50$	5.10187	−	1.78279i	0.721514	−	0.252124i
$51$	1.13857	+	0.481751i	0.159432	+	0.0674586i
$52$	−3.46043	+	8.79504i	−0.479876	+	1.21965i
$53$			11.4745i			1.57614i	0.615583	+	0.788072i	$0.288921\pi$
$53$			11.4745i			1.57614i	−0.615583	+	0.788072i	$0.711079\pi$
$54$	−4.67825	+	5.66692i	−0.636629	+	0.771170i
$55$	−12.8618			−1.73428
$56$	3.67627	−	1.17919i	0.491262	−	0.157576i
$57$	−12.7699	+	1.58287i	−1.69142	+	0.209656i
$58$	3.17303	+	9.08039i	0.416639	+	1.19231i
$59$	−0.803086	−	0.957081i	−0.104553	−	0.124601i	0.711230	−	0.702959i	$-0.248138\pi$
$59$	−0.803086	−	0.957081i	−0.104553	−	0.124601i	−0.815783	+	0.578358i	$0.803694\pi$
$60$	−7.20010	+	7.34958i	−0.929529	+	0.948826i
$61$	0.216792	+	0.595632i	0.0277574	+	0.0762629i	0.952797	−	0.303607i	$-0.0981910\pi$
$61$	0.216792	+	0.595632i	0.0277574	+	0.0762629i	−0.925040	+	0.379870i	$0.875969\pi$
$62$	−1.21612	−	7.45793i	−0.154447	−	0.947158i
$63$	−0.295047	−	4.08431i	−0.0371724	−	0.514575i
$64$	7.97608	+	0.618197i	0.997010	+	0.0772747i
$65$	10.7519	+	9.02195i	1.33361	+	1.11903i
$66$	9.50708	−	4.70432i	1.17024	−	0.579062i
$67$	−14.0227	+	2.47258i	−1.71314	+	0.302074i	−0.942255	−	0.334896i	$-0.891299\pi$
$67$	−14.0227	+	2.47258i	−1.71314	+	0.302074i	−0.770889	+	0.636969i	$0.780188\pi$
$68$	−1.42708	−	0.0368039i	−0.173059	−	0.00446312i
$69$	−7.35678	+	2.25845i	−0.885652	+	0.271885i
$70$	0.0739130	−	5.73294i	0.00883429	−	0.685217i
$71$	−0.414463	−	0.717870i	−0.0491877	−	0.0851955i	0.840383	−	0.541993i	$-0.182330\pi$
$71$	−0.414463	−	0.717870i	−0.0491877	−	0.0851955i	−0.889571	+	0.456797i	$0.848997\pi$
$72$	2.63395	−	8.06612i	0.310413	−	0.950602i
$73$	7.29258	−	12.6311i	0.853532	−	1.47836i	−0.0244686	−	0.999701i	$-0.507789\pi$
$73$	7.29258	−	12.6311i	0.853532	−	1.47836i	0.878000	−	0.478660i	$-0.158877\pi$
$74$	−0.767808	−	0.456592i	−0.0892558	−	0.0530777i
$75$	3.01174	+	5.89411i	0.347766	+	0.680593i
$76$	13.0549	−	7.09494i	1.49750	−	0.813846i
$77$	−2.02167	+	5.55448i	−0.230390	+	0.632992i
$78$	−11.2474	−	2.73616i	−1.27352	−	0.309809i
$79$	−1.22756	+	6.96183i	−0.138111	+	0.783267i	0.834532	+	0.550960i	$0.185738\pi$
$79$	−1.22756	+	6.96183i	−0.138111	+	0.783267i	−0.972643	+	0.232306i	$0.925373\pi$
$80$	4.63338	−	10.9396i	0.518027	−	1.22309i
$81$	−7.65430	−	4.73410i	−0.850477	−	0.526012i
$82$	2.24702	−	1.83663i	0.248141	−	0.202822i
$83$	1.29008	+	0.227475i	0.141604	+	0.0249686i	0.244001	−	0.969775i	$-0.421540\pi$
$83$	1.29008	+	0.227475i	0.141604	+	0.0249686i	−0.102397	+	0.994744i	$0.532651\pi$
$84$	2.04225	+	4.26467i	0.222827	+	0.465314i
$85$	−0.725078	+	1.99214i	−0.0786458	+	0.216077i
$86$	−5.26422	−	0.998364i	−0.567656	−	0.107656i
$87$	−10.4904	+	5.36035i	−1.12469	+	0.574690i
$88$	−8.22995	+	9.07129i	−0.877315	+	0.967002i
$89$	2.66374	−	4.61373i	0.282356	−	0.489054i	−0.689609	−	0.724182i	$-0.742218\pi$
$89$	2.66374	−	4.61373i	0.282356	−	0.489054i	0.971964	+	0.235128i	$0.0755508\pi$
$90$	−10.1155	−	7.51427i	−1.06626	−	0.792074i
$91$	5.58625	−	3.22522i	0.585598	−	0.338095i
$92$	6.95219	−	5.53452i	0.724816	−	0.577013i
$93$	8.84720	−	2.71599i	0.917411	−	0.281635i
$94$	−5.82098	−	5.01367i	−0.600388	−	0.517120i
$95$	−3.83160	−	21.7301i	−0.393114	−	2.22946i
$96$	0.576410	+	9.78099i	0.0588296	+	0.998268i
$97$	−1.52072	−	1.27604i	−0.154406	−	0.129562i	0.562312	−	0.826925i	$-0.309912\pi$
$97$	−1.52072	−	1.27604i	−0.154406	−	0.129562i	−0.716718	+	0.697363i	$0.754356\pi$
$98$	6.79385	+	2.57242i	0.686283	+	0.259854i
$99$	7.28938	+	10.7535i	0.732610	+	1.08077i
$100$	−5.72624	−	5.06211i	−0.572624	−	0.506211i
$101$	1.46496	+	4.02494i	0.145769	+	0.400497i	0.990993	−	0.133916i	$-0.0427552\pi$
$101$	1.46496	+	4.02494i	0.145769	+	0.400497i	−0.845224	+	0.534412i	$0.820533\pi$
$102$	−0.192685	−	1.73774i	−0.0190786	−	0.172062i
$103$	−8.54275	+	7.16822i	−0.841743	+	0.706306i	−0.957955	−	0.286919i	$-0.907369\pi$
$103$	−8.54275	+	7.16822i	−0.841743	+	0.706306i	0.116212	+	0.993224i	$0.462925\pi$
$104$	13.2430	−	1.81031i	1.29858	−	0.177515i
$105$	6.96864	−	0.863780i	0.680070	−	0.0842963i
$106$	14.1568	−	7.93185i	1.37503	−	0.770410i
$107$		−	11.6290i		−	1.12422i	−0.827064	−	0.562108i	$-0.809991\pi$
$107$		−	11.6290i		−	1.12422i	0.827064	−	0.562108i	$-0.190009\pi$
$108$	10.2255	+	1.85452i	0.983949	+	0.178452i
$109$		−	2.12823i		−	0.203848i	−0.994792	−	0.101924i	$-0.967500\pi$
$109$		−	2.12823i		−	0.203848i	0.994792	−	0.101924i	$-0.0324998\pi$
$110$	8.89082	+	15.8683i	0.847706	+	1.51299i
$111$	0.426332	−	1.00760i	0.0404656	−	0.0956367i
$112$	−3.99609	−	3.72051i	−0.377595	−	0.351555i
$113$	−13.3788	+	11.2261i	−1.25857	+	1.05607i	−0.262739	+	0.964867i	$0.584626\pi$
$113$	−13.3788	+	11.2261i	−1.25857	+	1.05607i	−0.995833	+	0.0912002i	$0.970930\pi$
$114$	10.7802	+	14.6609i	1.00966	+	1.37312i
$115$	−4.51343	−	12.4005i	−0.420879	−	1.15636i
$116$	9.00962	−	10.1917i	0.836522	−	0.946271i
$117$	1.44946	−	14.1027i	0.134002	−	1.30379i
$118$	−0.625666	+	1.65241i	−0.0575973	+	0.152116i
$119$	0.746353	+	0.626264i	0.0684180	+	0.0574096i
$120$	14.0447	+	3.80273i	1.28210	+	0.347140i
$121$	−1.34621	−	7.63476i	−0.122383	−	0.694069i
$122$	0.585007	−	0.679206i	0.0529641	−	0.0614924i
$123$	2.60228	+	2.42107i	0.234640	+	0.218301i
$124$	−8.36063	+	6.65576i	−0.750807	+	0.597705i
$125$	3.03136	−	1.75016i	0.271133	−	0.156539i
$126$	−4.83510	+	3.18733i	−0.430745	+	0.283950i
$127$	2.78247	−	4.81937i	0.246904	−	0.427650i	−0.715761	−	0.698345i	$-0.753920\pi$
$127$	2.78247	−	4.81937i	0.246904	−	0.427650i	0.962665	+	0.270695i	$0.0872534\pi$
$128$	−4.75083	−	10.2679i	−0.419918	−	0.907562i
$129$	0.335903	−	6.55365i	0.0295746	−	0.577017i
$130$	3.69853	−	19.5018i	0.324383	−	1.71042i
$131$	3.27187	−	8.98940i	0.285865	−	0.785407i	−0.710769	−	0.703426i	$-0.751653\pi$
$131$	3.27187	−	8.98940i	0.285865	−	0.785407i	0.996634	−	0.0819818i	$-0.0261249\pi$
$132$	−12.3759	−	8.47754i	−1.07718	−	0.737875i
$133$	−9.98662	−	1.76091i	−0.865950	−	0.152690i
$134$	12.7439	+	15.5914i	1.10090	+	1.34689i
$135$	7.43548	−	13.5238i	0.639944	−	1.16394i
$136$	0.941074	+	1.78611i	0.0806964	+	0.153158i
$137$	0.661480	−	3.75144i	0.0565140	−	0.320507i	−0.943425	−	0.331587i	$-0.892416\pi$
$137$	0.661480	−	3.75144i	0.0565140	−	0.320507i	0.999939	+	0.0110802i	$0.00352701\pi$
$138$	7.87182	+	7.51532i	0.670094	+	0.639746i
$139$	−0.433062	+	1.18983i	−0.0367318	+	0.100920i	−0.956703	−	0.291067i	$-0.905990\pi$
$139$	−0.433062	+	1.18983i	−0.0367318	+	0.100920i	0.919971	+	0.391987i	$0.128212\pi$
$140$	−7.12416	+	3.87176i	−0.602101	+	0.327223i
$141$	5.11548	−	7.89702i	0.430801	−	0.665049i
$142$	−0.599178	+	1.00758i	−0.0502819	+	0.0845544i
$143$	−10.2320	+	17.7224i	−0.855646	+	1.48202i
$144$	−11.7724	+	2.32613i	−0.981032	+	0.193844i
$145$	−10.1006	−	17.4948i	−0.838809	−	1.45286i
$146$	−20.6248	−	0.265909i	−1.70692	−	0.0220068i
$147$	−1.99147	+	8.67149i	−0.164253	+	0.715212i
$148$	−0.0325701	+	1.26291i	−0.00267724	+	0.103811i
$149$	−9.84675	+	1.73625i	−0.806677	+	0.142239i	−0.561755	−	0.827304i	$-0.689874\pi$
$149$	−9.84675	+	1.73625i	−0.806677	+	0.142239i	−0.244922	+	0.969543i	$0.578762\pi$
$150$	5.19002	−	7.79012i	0.423763	−	0.636061i
$151$	16.1625	+	13.5620i	1.31529	+	1.10366i	0.987281	+	0.158983i	$0.0508216\pi$
$151$	16.1625	+	13.5620i	1.31529	+	1.10366i	0.328008	+	0.944675i	$0.393623\pi$
$152$	−17.7778	−	11.2022i	−1.44197	−	0.908618i
$153$	2.07653	−	0.522813i	0.167877	−	0.0422670i
$154$	8.25039	−	1.34534i	0.664835	−	0.108410i
$155$	5.42780	+	14.9128i	0.435972	+	1.19782i
$156$	4.39912	+	15.7680i	0.352211	+	1.26245i
$157$	5.71532	+	6.81126i	0.456133	+	0.543598i	0.944271	−	0.329168i	$-0.106768\pi$
$157$	5.71532	+	6.81126i	0.456133	+	0.543598i	−0.488139	+	0.872766i	$0.662324\pi$
$158$	9.43777	−	3.29792i	0.750829	−	0.262368i
$159$	11.9790	+	15.8587i	0.949995	+	1.25767i
$160$	−16.6997	+	1.84565i	−1.32023	+	0.145912i
$161$	−6.06473			−0.477968
$162$	−0.549641	+	12.7160i	−0.0431839	+	0.999067i
$163$			17.7771i			1.39241i	0.717845	+	0.696203i	$0.245129\pi$
$163$			17.7771i			1.39241i	−0.717845	+	0.696203i	$0.754871\pi$
$164$	−3.81923	−	1.50269i	−0.298232	−	0.117340i
$165$	−17.7760	+	13.4272i	−1.38386	+	1.04531i
$166$	−0.611127	−	1.74889i	−0.0474327	−	0.135740i
$167$	−5.29501	+	4.44304i	−0.409740	+	0.343813i	−0.824244	−	0.566235i	$-0.808400\pi$
$167$	−5.29501	+	4.44304i	−0.409740	+	0.343813i	0.414504	+	0.910048i	$0.363955\pi$
$168$	3.84986	−	5.46763i	0.297023	−	0.421837i
$169$	8.76904	−	3.19167i	0.674541	−	0.245513i
$170$	2.95903	−	0.482510i	0.226947	−	0.0370069i
$171$	−15.9966	+	15.5190i	−1.22329	+	1.18677i
$172$	2.40720	+	7.18491i	0.183547	+	0.547844i
$173$	14.6599	−	17.4709i	1.11457	−	1.32829i	0.175531	−	0.984474i	$-0.443836\pi$
$173$	14.6599	−	17.4709i	1.11457	−	1.32829i	0.939037	−	0.343817i	$-0.111720\pi$
$174$	13.8650	+	9.23727i	1.05110	+	0.700275i
$175$	0.905794	+	5.13702i	0.0684716	+	0.388322i
$176$	16.8808	+	3.88316i	1.27244	+	0.292704i
$177$	−2.10909	−	0.484366i	−0.158529	−	0.0364072i
$178$	−7.53356	−	0.0971278i	−0.564664	−	0.00728004i
$179$	10.8469	−	6.26245i	0.810734	−	0.468077i	−0.0364770	−	0.999334i	$-0.511614\pi$
$179$	10.8469	−	6.26245i	0.810734	−	0.468077i	0.847211	+	0.531257i	$0.178280\pi$
$180$	−2.27840	+	17.6743i	−0.169822	+	1.31737i
$181$	−10.6636	−	6.15662i	−0.792618	−	0.457618i	0.0482656	−	0.998835i	$-0.484631\pi$
$181$	−10.6636	−	6.15662i	−0.792618	−	0.457618i	−0.840883	+	0.541217i	$0.817964\pi$
$182$	−7.84069	−	4.66262i	−0.581191	−	0.345616i
$183$	0.921443	+	0.596886i	0.0681150	+	0.0441231i
$184$	−11.6340	−	4.75154i	−0.857671	−	0.350288i
$185$	1.76297	+	0.641668i	0.129616	+	0.0471763i
$186$	−9.46658	−	9.03785i	−0.694124	−	0.662687i
$187$	−3.04399	−	0.536738i	−0.222599	−	0.0392502i
$188$	−2.16185	+	10.6474i	−0.157669	+	0.776543i
$189$	−4.67165	−	5.33681i	−0.339813	−	0.388196i
$190$	−24.1611	+	19.7484i	−1.75283	+	1.43270i
$191$	0.0708406	−	0.401757i	0.00512584	−	0.0290701i	−0.982138	−	0.188164i	$-0.939746\pi$
$191$	0.0708406	−	0.401757i	0.00512584	−	0.0290701i	0.987263	+	0.159094i	$0.0508574\pi$
$192$	11.6689	−	7.47235i	0.842133	−	0.539270i
$193$	20.6767	+	7.52571i	1.48834	+	0.541712i	0.953013	−	0.302930i	$-0.0979650\pi$
$193$	20.6767	+	7.52571i	1.48834	+	0.541712i	0.535330	+	0.844643i	$0.320187\pi$
$194$	−0.523109	+	2.75828i	−0.0375571	+	0.198033i
$195$	24.2786	+	1.24438i	1.73863	+	0.0891122i
$196$	−1.52256	−	10.1602i	−0.108755	−	0.725727i
$197$	−18.0410	−	10.4160i	−1.28537	−	0.742108i	−0.307544	−	0.951534i	$-0.599507\pi$
$197$	−18.0410	−	10.4160i	−1.28537	−	0.742108i	−0.977824	+	0.209426i	$0.932840\pi$
$198$	8.22838	−	16.4268i	0.584765	−	1.16740i
$199$	−1.53489	−	2.65851i	−0.108805	−	0.188457i	0.806481	−	0.591260i	$-0.201369\pi$
$199$	−1.53489	−	2.65851i	−0.108805	−	0.188457i	−0.915287	+	0.402803i	$0.868036\pi$
$200$	−2.28711	+	10.5640i	−0.161723	+	0.746990i
$201$	−16.7992	+	18.0565i	−1.18492	+	1.27361i
$202$	3.95314	−	4.58968i	0.278142	−	0.322929i
$203$	−9.14294	+	1.61215i	−0.641708	+	0.113150i
$204$	−2.01076	+	1.43895i	−0.140781	+	0.100747i
$205$	−3.91777	+	4.66901i	−0.273629	+	0.326098i
$206$	14.7491	+	5.58460i	1.02762	+	0.389097i
$207$	−7.80990	+	10.8016i	−0.542825	+	0.750761i
$208$	−11.3878	−	15.0873i	−0.789604	−	1.04612i
$209$	30.2312	−	11.0033i	2.09114	−	0.761111i
$210$	−5.88283	−	8.00053i	−0.405954	−	0.552089i
$211$	1.48569	+	1.77058i	0.102279	+	0.121892i	0.814756	−	0.579804i	$-0.196871\pi$
$211$	1.48569	+	1.77058i	0.102279	+	0.121892i	−0.712477	+	0.701696i	$0.752427\pi$
$212$	−19.5720	−	11.9831i	−1.34421	−	0.823001i
$213$	−1.32225	−	0.559468i	−0.0905991	−	0.0383341i
$214$	−14.3473	+	8.03863i	−0.980764	+	0.549510i
$215$	11.2529			0.767439
$216$	−4.78043	−	13.8978i	−0.325267	−	0.945622i
$217$	7.29339			0.495108
$218$	−2.62573	+	1.47116i	−0.177837	+	0.0996395i
$219$	−3.10753	−	25.0704i	−0.209988	−	1.69410i
$220$	13.4318	−	21.9382i	0.905574	−	1.47908i
$221$	2.16816	+	2.58392i	0.145846	+	0.173813i
$222$	−1.53784	+	0.170519i	−0.103213	+	0.0114445i
$223$	3.40012	−	1.23754i	0.227689	−	0.0828721i	−0.225656	−	0.974207i	$-0.572453\pi$
$223$	3.40012	−	1.23754i	0.227689	−	0.0828721i	0.453345	+	0.891335i	$0.350230\pi$
$224$	−1.82787	+	7.50205i	−0.122130	+	0.501252i
$225$	10.3157	+	5.00196i	0.687714	+	0.333464i
$226$	23.0986	+	8.74604i	1.53649	+	0.581778i
$227$	12.6692	−	15.0985i	0.840883	−	1.00212i	−0.159007	−	0.987277i	$-0.550829\pi$
$227$	12.6692	−	15.0985i	0.840883	−	1.00212i	0.999890	−	0.0148475i	$-0.00472629\pi$
$228$	10.6360	−	23.4346i	0.704390	−	1.55200i
$229$	17.3012	−	3.05066i	1.14329	−	0.201593i	0.430247	−	0.902711i	$-0.358426\pi$
$229$	17.3012	−	3.05066i	1.14329	−	0.201593i	0.713045	+	0.701118i	$0.247315\pi$
$230$	−12.1793	+	14.1405i	−0.803081	+	0.932394i
$231$	3.00458	+	9.78727i	0.197687	+	0.643955i
$232$	−18.8020	−	4.07063i	−1.23441	−	0.267250i
$233$	9.53675	+	16.5181i	0.624774	+	1.08214i	0.988585	+	0.150667i	$0.0481420\pi$
$233$	9.53675	+	16.5181i	0.624774	+	1.08214i	−0.363811	+	0.931473i	$0.618525\pi$
$234$	−18.4012	+	7.96032i	−1.20293	+	0.520383i
$235$	13.9730	+	8.06729i	0.911495	+	0.526252i
$236$	2.47117	−	0.370319i	0.160859	−	0.0241057i
$237$	5.57132	+	10.9033i	0.361896	+	0.708246i
$238$	0.256736	−	1.35373i	0.0166417	−	0.0877493i
$239$	−1.39969	−	0.509446i	−0.0905384	−	0.0329533i	0.296354	−	0.955078i	$-0.404229\pi$
$239$	−1.39969	−	0.509446i	−0.0905384	−	0.0329533i	−0.386892	+	0.922125i	$0.626451\pi$
$240$	−5.01691	−	19.9565i	−0.323840	−	1.28819i
$241$	0.766076	−	4.34463i	0.0493473	−	0.279862i	−0.950142	−	0.311817i	$-0.899062\pi$
$241$	0.766076	−	4.34463i	0.0493473	−	0.279862i	0.999489	+	0.0319552i	$0.0101734\pi$
$242$	−8.48887	+	6.93850i	−0.545685	+	0.446024i
$243$	−15.5211	+	1.44792i	−0.995677	+	0.0928839i
$244$	−1.24237	−	0.252250i	−0.0795345	−	0.0161487i
$245$	−15.0251	−	2.64932i	−0.959916	−	0.169259i
$246$	1.18817	−	4.88417i	0.0757551	−	0.311403i
$247$	−32.9904	−	12.0075i	−2.09913	−	0.764020i
$248$	13.9910	+	5.71415i	0.888427	+	0.362849i
$249$	2.02046	−	1.03241i	0.128041	−	0.0654260i
$250$	−4.25473	−	2.53016i	−0.269093	−	0.160021i
$251$	23.4897	+	13.5618i	1.48265	+	0.856011i	0.999806	−	0.0196931i	$-0.00626890\pi$
$251$	23.4897	+	13.5618i	1.48265	+	0.856011i	0.482848	+	0.875704i	$0.339602\pi$
$252$	7.27471	+	3.76207i	0.458264	+	0.236988i
$253$	16.6627	−	9.62020i	1.04757	−	0.604817i
$254$	−7.86935	−	0.101457i	−0.493767	−	0.00636598i
$255$	1.07761	+	3.51024i	0.0674823	+	0.219820i
$256$	−9.38405	+	12.9592i	−0.586503	+	0.809947i
$257$	−2.75518	−	15.6254i	−0.171864	−	0.974687i	−0.941702	−	0.336448i	$-0.890774\pi$
$257$	−2.75518	−	15.6254i	−0.171864	−	0.974687i	0.769839	−	0.638239i	$-0.220337\pi$
$258$	−8.31782	+	4.11585i	−0.517845	+	0.256241i
$259$	0.554221	−	0.660495i	0.0344376	−	0.0410412i
$260$	−26.6172	+	8.91770i	−1.65073	+	0.553052i
$261$	−8.90256	+	18.3600i	−0.551055	+	1.13646i
$262$	−13.3525	+	2.17730i	−0.824918	+	0.134514i
$263$	1.51313	−	0.550733i	0.0933034	−	0.0339597i	−0.294947	−	0.955514i	$-0.595302\pi$
$263$	1.51313	−	0.550733i	0.0933034	−	0.0339597i	0.388250	+	0.921554i	$0.373080\pi$
$264$	−1.90432	+	21.1290i	−0.117203	+	1.30040i
$265$	−26.1071	+	21.9065i	−1.60375	+	1.34570i
$266$	4.73080	+	13.5383i	0.290064	+	0.830088i
$267$	−1.13508	−	9.15738i	−0.0694657	−	0.560422i
$268$	10.4267	−	26.5006i	0.636914	−	1.61878i
$269$			2.95858i			0.180388i	0.995924	+	0.0901940i	$0.0287487\pi$
$269$			2.95858i			0.180388i	−0.995924	+	0.0901940i	$0.971251\pi$
$270$	−21.8250	+	0.174871i	−1.32823	+	0.0106423i
$271$	6.23755			0.378904			0.189452	−	0.981890i	$-0.439329\pi$
$271$	6.23755			0.378904			0.189452	+	0.981890i	$0.439329\pi$
$272$	1.55311	−	2.39572i	0.0941709	−	0.145262i
$273$	4.35361	−	10.2894i	0.263493	−	0.622740i
$274$	−5.08562	+	1.77711i	−0.307234	+	0.107359i
$275$	−10.6372	−	12.6770i	−0.641450	−	0.764450i
$276$	3.83062	−	14.9070i	0.230576	−	0.897294i
$277$	7.97956	+	21.9237i	0.479445	+	1.31727i	0.909965	+	0.414684i	$0.136108\pi$
$277$	7.97956	+	21.9237i	0.479445	+	1.31727i	−0.430520	+	0.902581i	$0.641670\pi$
$278$	1.76732	−	0.288185i	0.105997	−	0.0172842i
$279$	9.39211	−	12.9899i	0.562291	−	0.777683i
$280$	9.70145	+	6.11311i	0.579773	+	0.365328i
$281$	−5.53822	−	4.64712i	−0.330383	−	0.277224i	0.462473	−	0.886633i	$-0.346962\pi$
$281$	−5.53822	−	4.64712i	−0.330383	−	0.277224i	−0.792856	+	0.609409i	$0.791407\pi$
$282$	−13.2791	−	0.852381i	−0.790761	−	0.0507585i
$283$	1.34312	−	0.236829i	0.0798404	−	0.0140780i	−0.133585	−	0.991037i	$-0.542649\pi$
$283$	1.34312	−	0.236829i	0.0798404	−	0.0140780i	0.213426	+	0.976959i	$0.431538\pi$
$284$	1.65730	+	0.0427412i	0.0983426	+	0.00253622i
$285$	−27.9810	−	26.0326i	−1.65745	−	1.54204i
$286$	28.9382	+	0.373090i	1.71115	+	0.0220613i
$287$	1.40055	+	2.42582i	0.0826718	+	0.143192i
$288$	11.0077	+	12.9163i	0.648632	+	0.761102i
$289$	8.24526	−	14.2812i	0.485015	−	0.840071i
$290$	−14.6022	+	24.5551i	−0.857469	+	1.44193i
$291$	−3.43389	−	0.176002i	−0.201298	−	0.0103174i
$292$	13.9290	+	25.6299i	0.815134	+	1.49987i
$293$	5.01243	−	13.7715i	0.292829	−	0.804541i	−0.702821	−	0.711367i	$-0.748076\pi$
$293$	5.01243	−	13.7715i	0.292829	−	0.804541i	0.995650	−	0.0931743i	$-0.0297014\pi$
$294$	12.0751	−	3.53726i	0.704237	−	0.206297i
$295$	0.644371	−	3.65441i	0.0375167	−	0.212768i
$296$	1.58064	−	0.832816i	0.0918731	−	0.0484065i
$297$	21.3008	+	7.25231i	1.23600	+	0.420822i
$298$	8.94876	+	10.9483i	0.518388	+	0.634219i
$299$	−20.6775	−	3.64600i	−1.19581	−	0.210853i
$300$	−13.1988	−	1.01823i	−0.762032	−	0.0587877i
$301$	1.76877	−	4.85966i	0.101950	−	0.280106i
$302$	5.55971	−	29.3155i	0.319925	−	1.68692i
$303$	6.22658	+	4.03342i	0.357708	+	0.231714i
$304$	−1.53174	+	29.6771i	−0.0878515	+	1.70210i
$305$	−0.941311	+	1.63040i	−0.0538993	+	0.0933564i
$306$	−2.08044	−	2.20053i	−0.118931	−	0.125796i
$307$	9.62473	−	5.55684i	0.549313	−	0.317146i	−0.199532	−	0.979891i	$-0.563942\pi$
$307$	9.62473	−	5.55684i	0.549313	−	0.317146i	0.748845	+	0.662746i	$0.230609\pi$
$308$	−7.36298	−	9.24901i	−0.419545	−	0.527011i
$309$	−4.32338	+	18.8254i	−0.245948	+	1.07094i
$310$	14.6467	−	17.0052i	0.831879	−	0.965830i
$311$	1.91302	+	10.8493i	0.108477	+	0.615206i	0.989774	+	0.142643i	$0.0455601\pi$
$311$	1.91302	+	10.8493i	0.108477	+	0.615206i	−0.881297	+	0.472563i	$0.843329\pi$
$312$	16.4130	−	16.3272i	0.929201	−	0.924347i
$313$	−1.97229	−	1.65494i	−0.111480	−	0.0935430i	0.585344	−	0.810785i	$-0.300960\pi$
$313$	−1.97229	−	1.65494i	−0.111480	−	0.0935430i	−0.696824	+	0.717242i	$0.745404\pi$
$314$	4.45268	−	11.7597i	0.251279	−	0.663637i
$315$	8.72945	−	8.46883i	0.491849	−	0.477164i
$316$	−10.5928	−	9.36422i	−0.595890	−	0.526779i
$317$	−1.43808	−	3.95110i	−0.0807708	−	0.221916i	0.892733	−	0.450585i	$-0.148785\pi$
$317$	−1.43808	−	3.95110i	−0.0807708	−	0.221916i	−0.973504	+	0.228669i	$0.926563\pi$
$318$	11.2852	−	25.7416i	0.632841	−	1.44352i
$319$	22.5627	−	18.9323i	1.26327	−	1.06001i
$320$	13.8209	+	19.3276i	0.772613	+	1.08045i
$321$	−12.1402	−	16.0721i	−0.677602	−	0.897059i
$322$	4.19230	+	7.48242i	0.233628	+	0.416979i
$323$		−	5.30276i		−	0.295053i
$324$	16.0685	−	8.11196i	0.892693	−	0.450664i
$325$			18.0590i			1.00173i
$326$	21.9326	−	12.2886i	1.21473	−	0.680600i
$327$	−2.22180	−	2.94138i	−0.122866	−	0.162659i
$328$	0.786123	+	5.75076i	0.0434064	+	0.317532i
$329$	5.68027	−	4.76631i	0.313163	−	0.262775i
$330$	28.8538	+	12.6496i	1.58835	+	0.696335i
$331$	0.147225	+	0.404498i	0.00809223	+	0.0222332i	0.943673	−	0.330880i	$-0.107345\pi$
$331$	0.147225	+	0.404498i	0.00809223	+	0.0222332i	−0.935581	+	0.353113i	$0.885123\pi$
$332$	−1.73526	+	1.96292i	−0.0952346	+	0.107729i
$333$	−0.462671	−	1.83765i	−0.0253542	−	0.100703i
$334$	9.14187	+	3.46148i	0.500221	+	0.189403i
$335$	−32.3970	−	27.1843i	−1.77004	−	1.48524i
$336$	−9.40699	−	0.970245i	−0.513193	−	0.0529312i
$337$	2.69206	+	15.2674i	0.146646	+	0.831671i	0.966031	+	0.258427i	$0.0832041\pi$
$337$	2.69206	+	15.2674i	0.146646	+	0.831671i	−0.819385	+	0.573244i	$0.805685\pi$
$338$	−9.99943	−	8.61261i	−0.543897	−	0.468464i
$339$	−6.77084	+	29.4824i	−0.367741	+	1.60126i
$340$	−2.64076	−	3.31719i	−0.143215	−	0.179900i
$341$	−20.0384	+	11.5692i	−1.08514	+	0.626505i
$342$	30.2045	+	9.00828i	1.63327	+	0.487112i
$343$	−8.28328	+	14.3471i	−0.447255	+	0.774669i
$344$	7.20045	−	7.93654i	0.388222	−	0.427910i
$345$	−19.1836	−	12.4266i	−1.03281	−	0.669028i
$346$	−31.6887	−	6.00978i	−1.70359	−	0.323088i
$347$	−2.18648	+	6.00732i	−0.117377	+	0.322490i	−0.984443	−	0.175702i	$-0.943780\pi$
$347$	−2.18648	+	6.00732i	−0.117377	+	0.322490i	0.867067	+	0.498192i	$0.166003\pi$
$348$	1.81227	−	23.4914i	0.0971477	−	1.25927i
$349$	35.8064	+	6.31363i	1.91667	+	0.337961i	0.998327	−	0.0578197i	$-0.0184148\pi$
$349$	35.8064	+	6.31363i	1.91667	+	0.337961i	0.918345	+	0.395781i	$0.129526\pi$
$350$	5.71170	−	4.66854i	0.305303	−	0.249544i
$351$	−12.7194	−	21.0042i	−0.678913	−	1.12112i
$352$	−6.87813	−	23.5111i	−0.366605	−	1.25315i
$353$	−2.81872	+	15.9857i	−0.150025	+	0.850835i	0.813169	+	0.582028i	$0.197741\pi$
$353$	−2.81872	+	15.9857i	−0.150025	+	0.850835i	−0.963194	+	0.268807i	$0.913370\pi$
$354$	0.860334	+	2.93693i	0.0457262	+	0.156096i
$355$	0.842050	−	2.31351i	0.0446914	−	0.122789i
$356$	5.08781	+	9.36174i	0.269653	+	0.496171i
$357$	1.68531	+	0.0863798i	0.0891963	+	0.00457170i
$358$	−15.2244	−	9.05346i	−0.804632	−	0.478490i
$359$	−2.92393	+	5.06440i	−0.154319	+	0.267289i	−0.932811	−	0.360366i	$-0.882652\pi$
$359$	−2.92393	+	5.06440i	−0.154319	+	0.267289i	0.778492	+	0.627655i	$0.215985\pi$
$360$	23.3808	−	9.40655i	1.23228	−	0.495769i
$361$	18.0962	+	31.3435i	0.952430	+	1.64966i
$362$	−0.224489	+	17.4121i	−0.0117989	+	0.915160i
$363$	−9.83099	−	9.14643i	−0.515993	−	0.480063i
$364$	−0.332599	+	12.8966i	−0.0174329	+	0.675966i
$365$	42.6612	−	7.52233i	2.23299	−	0.393737i
$366$	0.0994579	−	1.54944i	0.00519875	−	0.0809906i
$367$	14.7699	+	12.3934i	0.770981	+	0.646930i	0.940960	−	0.338518i	$-0.109925\pi$
$367$	14.7699	+	12.3934i	0.770981	+	0.646930i	−0.169979	+	0.985448i	$0.554370\pi$
$368$	2.17987	+	17.6381i	0.113634	+	0.919450i
$369$	6.12406	+	0.629424i	0.318806	+	0.0327665i
$370$	−0.427004	−	2.61864i	−0.0221989	−	0.136136i
$371$	5.35690	+	14.7180i	0.278116	+	0.764118i
$372$	−4.60667	+	17.9270i	−0.238845	+	0.929470i
$373$	−4.04624	−	4.82212i	−0.209506	−	0.249680i	0.651050	−	0.759034i	$-0.274329\pi$
$373$	−4.04624	−	4.82212i	−0.209506	−	0.249680i	−0.860557	+	0.509355i	$0.829884\pi$
$374$	1.44198	+	4.12658i	0.0745632	+	0.213380i
$375$	2.36248	−	5.58349i	0.121998	−	0.288330i
$376$	14.6308	−	4.69293i	0.754524	−	0.242019i
$377$	−32.1417			−1.65538
$378$	−3.35502	+	9.45282i	−0.172564	+	0.486200i
$379$			17.2449i			0.885812i	0.896568	+	0.442906i	$0.146052\pi$
$379$			17.2449i			0.885812i	−0.896568	+	0.442906i	$0.853948\pi$
$380$	41.0663	+	16.1577i	2.10666	+	0.828871i
$381$	−1.18567	−	9.56554i	−0.0607438	−	0.490058i
$382$	−0.544640	+	0.190318i	−0.0278662	+	0.00973751i
$383$	20.5611	−	17.2528i	1.05062	−	0.881578i	0.0574646	−	0.998348i	$-0.481698\pi$
$383$	20.5611	−	17.2528i	1.05062	−	0.881578i	0.993159	+	0.116770i	$0.0372539\pi$
$384$	−17.2853	−	9.23132i	−0.882088	−	0.471084i
$385$	−16.4974	+	6.00455i	−0.840783	+	0.306020i
$386$	−5.00806	−	30.7123i	−0.254903	−	1.56321i
$387$	−6.37754	−	9.40832i	−0.324188	−	0.478252i
$388$	3.76465	−	1.26129i	0.191121	−	0.0640324i
$389$	10.1688	−	12.1187i	0.515578	−	0.614442i	−0.443951	−	0.896051i	$-0.646424\pi$
$389$	10.1688	−	12.1187i	0.515578	−	0.614442i	0.959529	+	0.281609i	$0.0908681\pi$
$390$	−15.2475	−	30.8141i	−0.772089	−	1.56033i
$391$	−0.550702	−	3.12319i	−0.0278502	−	0.157946i
$392$	−11.4827	+	8.90180i	−0.579966	+	0.449609i
$393$	−4.86263	−	15.8398i	−0.245287	−	0.799010i
$394$	−0.379797	+	29.4584i	−0.0191339	+	1.48409i
$395$	−18.1833	+	10.4981i	−0.914902	+	0.528219i
$396$	−25.9546	+	1.20334i	−1.30427	+	0.0604699i
$397$	−31.3595	−	18.1054i	−1.57389	−	0.908686i	−0.995685	−	0.0927941i	$-0.970420\pi$
$397$	−31.3595	−	18.1054i	−1.57389	−	0.908686i	−0.578205	−	0.815892i	$-0.696246\pi$
$398$	−2.21895	+	3.73140i	−0.111226	+	0.187038i
$399$	−15.6406	+	7.99197i	−0.783010	+	0.400099i
$400$	14.6145	−	4.48075i	0.730723	−	0.224037i
$401$	−29.9275	−	10.8927i	−1.49451	−	0.543957i	−0.539876	−	0.841744i	$-0.681529\pi$
$401$	−29.9275	−	10.8927i	−1.49451	−	0.543957i	−0.954632	+	0.297788i	$0.903751\pi$
$402$	33.8899	+	8.24440i	1.69028	+	0.411193i
$403$	24.8665	+	4.38464i	1.23869	+	0.218414i
$404$	−8.39521	−	1.70456i	−0.417677	−	0.0848051i
$405$	−3.84198	−	26.4533i	−0.190909	−	1.31448i
$406$	8.30914	+	10.1658i	0.412376	+	0.504519i
$407$	−0.474994	+	2.69382i	−0.0235446	+	0.133528i
$408$	3.16528	+	1.48610i	0.156704	+	0.0735728i
$409$	−15.5146	−	5.64685i	−0.767147	−	0.279219i	−0.0713442	−	0.997452i	$-0.522729\pi$
$409$	−15.5146	−	5.64685i	−0.767147	−	0.279219i	−0.695802	+	0.718233i	$0.744951\pi$
$410$	8.46863	+	1.60608i	0.418236	+	0.0793187i
$411$	−3.00215	−	5.87534i	−0.148085	−	0.289809i
$412$	−3.30541	−	22.0573i	−0.162846	−	1.08668i
$413$	−1.47691	−	0.852693i	−0.0726738	−	0.0419583i
$414$	18.7252	+	2.16884i	0.920293	+	0.106593i
$415$	1.94538	+	3.36950i	0.0954950	+	0.165402i
$416$	−10.7421	+	24.4791i	−0.526676	+	1.20018i
$417$	0.643613	+	2.09654i	0.0315179	+	0.102668i
$418$	−34.4729	−	29.6919i	−1.68613	−	1.45228i
$419$	−18.1570	+	3.20156i	−0.887026	+	0.156407i	−0.598555	−	0.801082i	$-0.704258\pi$
$419$	−18.1570	+	3.20156i	−0.887026	+	0.156407i	−0.288471	+	0.957489i	$0.593147\pi$
$420$	−5.80416	+	12.7884i	−0.283214	+	0.624012i
$421$	−6.32940	+	7.54309i	−0.308476	+	0.367627i	−0.897902	−	0.440195i	$-0.854909\pi$
$421$	−6.32940	+	7.54309i	−0.308476	+	0.367627i	0.589426	+	0.807822i	$0.299354\pi$
$422$	1.15747	−	3.05692i	0.0563448	−	0.148808i
$423$	−1.17422	−	16.2547i	−0.0570926	−	0.790329i
$424$	−1.25491	+	32.4305i	−0.0609436	+	1.57497i
$425$	−2.56318	+	0.932923i	−0.124333	+	0.0452534i
$426$	0.223769	+	2.01808i	0.0108417	+	0.0977761i
$427$	0.556145	+	0.662787i	0.0269137	+	0.0320745i
$428$	19.8355	+	12.1444i	0.958783	+	0.587021i
$429$	4.36010	+	35.1756i	0.210508	+	1.69829i
$430$	−7.77865	−	13.8833i	−0.375120	−	0.669513i
$431$	5.60936			0.270193			0.135097	−	0.990832i	$-0.456866\pi$
$431$	5.60936			0.270193			0.135097	+	0.990832i	$0.456866\pi$
$432$	−13.8420	+	15.5048i	−0.665971	+	0.745977i
$433$	−21.7801			−1.04669			−0.523343	−	0.852122i	$-0.675315\pi$
$433$	−21.7801			−1.04669			−0.523343	+	0.852122i	$0.675315\pi$
$434$	−5.04162	−	8.99829i	−0.242006	−	0.431932i
$435$	−32.2237	−	13.6344i	−1.54501	−	0.653721i
$436$	3.63011	+	2.22256i	0.173851	+	0.106441i
$437$	21.2173	+	25.2858i	1.01496	+	1.20959i
$438$	−28.7827	+	21.1641i	−1.37529	+	1.01126i
$439$	14.2403	−	5.18304i	0.679652	−	0.247373i	0.0209536	−	0.999780i	$-0.493330\pi$
$439$	14.2403	−	5.18304i	0.679652	−	0.247373i	0.658698	+	0.752408i	$0.271108\pi$
$440$	−36.3514	−	1.40662i	−1.73298	−	0.0670581i
$441$	6.30037	+	14.0637i	0.300017	+	0.669700i
$442$	1.68917	−	4.46115i	0.0803455	−	0.212195i
$443$	6.71247	−	7.99962i	0.318919	−	0.380073i	−0.582639	−	0.812731i	$-0.697980\pi$
$443$	6.71247	−	7.99962i	0.318919	−	0.380073i	0.901558	+	0.432658i	$0.142424\pi$
$444$	1.27342	+	1.77944i	0.0604339	+	0.0844487i
$445$	15.5827	−	2.74766i	0.738692	−	0.130251i
$446$	−3.87720	−	3.33947i	−0.183591	−	0.158128i
$447$	−11.7964	+	12.6793i	−0.557950	+	0.599709i
$448$	10.5193	−	2.93071i	0.496988	−	0.138463i
$449$	−13.4948	−	23.3737i	−0.636860	−	1.10307i	−0.986118	−	0.166047i	$-0.946900\pi$
$449$	−13.4948	−	23.3737i	−0.636860	−	1.10307i	0.349258	−	0.937027i	$-0.386434\pi$
$450$	−0.959612	−	16.1847i	−0.0452366	−	0.762956i
$451$	−7.69593	−	4.44325i	−0.362387	−	0.209224i
$452$	−5.17660	−	34.5439i	−0.243487	−	1.62481i
$453$	36.4961	+	1.87059i	1.71474	+	0.0878878i
$454$	−27.3856	−	5.19371i	−1.28527	−	0.243753i
$455$	18.0031	+	6.55258i	0.843996	+	0.307190i
$456$	−36.2650	+	3.07709i	−1.69826	+	0.144098i
$457$	5.06627	−	28.7322i	0.236990	−	1.34404i	−0.601392	−	0.798954i	$-0.705387\pi$
$457$	5.06627	−	28.7322i	0.236990	−	1.34404i	0.838382	−	0.545083i	$-0.183502\pi$
$458$	−15.7234	−	19.2367i	−0.734704	−	0.898870i
$459$	2.32412	−	2.89039i	0.108481	−	0.134912i
$460$	25.8650	+	5.25163i	1.20596	+	0.244858i
$461$	−4.19983	−	0.740544i	−0.195606	−	0.0344906i	0.0749868	−	0.997185i	$-0.476109\pi$
$461$	−4.19983	−	0.740544i	−0.195606	−	0.0344906i	−0.270593	+	0.962694i	$0.587220\pi$
$462$	9.99819	−	10.4725i	0.465158	−	0.487224i
$463$	−26.4209	−	9.61641i	−1.22788	−	0.446912i	−0.355010	−	0.934862i	$-0.615523\pi$
$463$	−26.4209	−	9.61641i	−1.22788	−	0.446912i	−0.872872	+	0.487950i	$0.837745\pi$
$464$	7.97490	+	26.0110i	0.370225	+	1.20753i
$465$	23.0700	+	14.9442i	1.06985	+	0.693019i
$466$	13.7870	−	23.1844i	0.638672	−	1.07400i
$467$	−5.86716	−	3.38741i	−0.271500	−	0.156750i	0.358069	−	0.933695i	$-0.383435\pi$
$467$	−5.86716	−	3.38741i	−0.271500	−	0.156750i	−0.629569	+	0.776945i	$0.716769\pi$
$468$	22.5411	+	17.2001i	1.04197	+	0.795073i
$469$	−16.8321	+	9.71802i	−0.777234	+	0.448736i
$470$	0.294157	−	22.8158i	0.0135685	−	1.05242i
$471$	15.0097	+	3.44709i	0.691612	+	0.158833i
$472$	−2.16510	−	2.79284i	−0.0996569	−	0.128551i
$473$	2.84900	+	16.1575i	0.130997	+	0.742922i
$474$	9.60083	−	14.4107i	0.440981	−	0.661904i
$475$	18.2490	−	21.7483i	0.837321	−	0.997880i
$476$	−1.84765	+	0.619028i	−0.0846868	+	0.0283731i
$477$	33.1117	+	9.41225i	1.51608	+	0.430957i
$478$	0.339016	+	2.07904i	0.0155062	+	0.0950930i
$479$	−33.0606	+	12.0331i	−1.51058	+	0.549806i	−0.958775	−	0.284168i	$-0.908283\pi$
$479$	−33.0606	+	12.0331i	−1.51058	+	0.549806i	−0.551804	+	0.833974i	$0.686060\pi$
$480$	−21.1535	+	19.9848i	−0.965522	+	0.912175i
$481$	2.28667	−	1.91874i	0.104263	−	0.0874872i
$482$	−5.88978	+	2.05811i	−0.268272	+	0.0937445i
$483$	−8.38193	+	6.33137i	−0.381391	+	0.288087i
$484$	14.4284	+	5.67691i	0.655838	+	0.258042i
$485$		−	5.89612i		−	0.267729i
$486$	12.5155	+	18.1484i	0.567713	+	0.823227i
$487$	−6.71410			−0.304245			−0.152122	−	0.988362i	$-0.548611\pi$
$487$	−6.71410			−0.304245			−0.152122	+	0.988362i	$0.548611\pi$
$488$	0.547582	+	1.70715i	0.0247879	+	0.0772792i
$489$	18.5586	+	24.5693i	0.839250	+	1.11106i
$490$	7.11758	+	20.3687i	0.321540	+	0.920163i
$491$	−2.85750	−	3.40543i	−0.128957	−	0.153685i	0.697702	−	0.716388i	$-0.254206\pi$
$491$	−2.85750	−	3.40543i	−0.128957	−	0.153685i	−0.826659	+	0.562703i	$0.809761\pi$
$492$	−6.84723	+	1.91031i	−0.308697	+	0.0861235i
$493$	−1.66043	−	4.56199i	−0.0747820	−	0.205462i
$494$	7.99052	+	49.0025i	0.359510	+	2.20473i
$495$	−10.5502	+	37.1150i	−0.474196	+	1.66819i
$496$	−2.62149	−	21.2114i	−0.117708	−	0.952422i
$497$	−0.866757	−	0.727295i	−0.0388793	−	0.0326236i
$498$	−2.67040	−	1.77910i	−0.119664	−	0.0797235i
$499$	−19.6511	+	3.46501i	−0.879702	+	0.155115i	−0.595217	−	0.803565i	$-0.702934\pi$
$499$	−19.6511	+	3.46501i	−0.879702	+	0.155115i	−0.284485	+	0.958680i	$0.591823\pi$
$500$	−0.180484	+	6.99831i	−0.00807148	+	0.312974i
$501$	−2.67974	+	11.6684i	−0.119722	+	0.521307i
$502$	0.494502	−	38.3553i	0.0220707	−	1.71188i
$503$	17.6903	+	30.6405i	0.788771	+	1.36619i	0.926720	+	0.375753i	$0.122616\pi$
$503$	17.6903	+	30.6405i	0.788771	+	1.36619i	−0.137949	+	0.990439i	$0.544051\pi$
$504$	−0.387215	−	11.5758i	−0.0172479	−	0.515627i
$505$	−6.36084	+	11.0173i	−0.283054	+	0.490263i
$506$	−23.3872	−	13.9077i	−1.03969	−	0.618271i
$507$	8.78750	−	13.5657i	0.390267	−	0.602474i
$508$	5.31459	+	9.77901i	0.235797	+	0.433874i
$509$	−10.5192	+	28.9013i	−0.466256	+	1.28103i	0.454451	+	0.890772i	$0.349836\pi$
$509$	−10.5192	+	28.9013i	−0.466256	+	1.28103i	−0.920707	+	0.390255i	$0.872387\pi$
$510$	3.58589	−	3.75599i	0.158786	−	0.166318i
$511$	3.45708	−	19.6061i	0.152932	−	0.867321i
$512$	22.4753	+	2.61952i	0.993276	+	0.115768i
$513$	−5.90723	+	38.1484i	−0.260811	+	1.68429i
$514$	−17.3734	+	14.2004i	−0.766310	+	0.626355i
$515$	−32.6187	−	5.75155i	−1.43735	−	0.253444i
$516$	10.8277	+	7.41707i	0.476664	+	0.326518i
$517$	−8.04579	+	22.1056i	−0.353853	+	0.972204i
$518$	−1.19800	−	0.227202i	−0.0526372	−	0.00998268i
$519$	2.02201	−	39.4506i	0.0887565	−	1.73169i
$520$	29.4016	+	26.6747i	1.28935	+	1.16976i
$521$	−7.26319	+	12.5802i	−0.318206	+	0.551149i	−0.980114	−	0.198436i	$-0.936414\pi$
$521$	−7.26319	+	12.5802i	−0.318206	+	0.551149i	0.661908	+	0.749585i	$0.269747\pi$
$522$	28.8059	−	1.70793i	1.26080	−	0.0747542i
$523$	−27.5376	+	15.8989i	−1.20414	+	0.695209i	−0.961472	−	0.274901i	$-0.911355\pi$
$523$	−27.5376	+	15.8989i	−1.20414	+	0.695209i	−0.242665	+	0.970110i	$0.578021\pi$
$524$	11.9163	+	14.9686i	0.520565	+	0.653908i
$525$	6.61474	+	6.15414i	0.288691	+	0.268588i
$526$	−1.72544	−	1.48614i	−0.0752326	−	0.0647986i
$527$	0.662269	+	3.75591i	0.0288489	+	0.163610i
$528$	27.3845	−	12.2561i	1.19176	−	0.533380i
$529$	−2.49659	−	2.09488i	−0.108547	−	0.0910819i
$530$	45.0741	+	17.0668i	1.95789	+	0.741336i
$531$	−3.42058	+	1.53238i	−0.148441	+	0.0664996i
$532$	13.4328	−	15.1952i	0.582387	−	0.658794i
$533$	3.31676	+	9.11272i	0.143665	+	0.394716i
$534$	−10.5134	+	7.73054i	−0.454958	+	0.334533i
$535$	26.4585	−	22.2014i	1.14390	−	0.959848i
$536$	−39.9029	+	5.45469i	−1.72354	+	0.235607i
$537$	8.45345	−	19.9789i	0.364793	−	0.862155i
$538$	3.65018	−	2.04515i	0.157370	−	0.0881726i
$539$		−	22.2446i		−	0.958142i
$540$	15.3025	+	26.8059i	0.658513	+	1.15354i
$541$		−	35.1941i		−	1.51311i	−0.653929	−	0.756556i	$-0.726880\pi$
$541$		−	35.1941i		−	1.51311i	0.653929	−	0.756556i	$-0.273120\pi$
$542$	−4.31176	−	7.69563i	−0.185206	−	0.330556i
$543$	−21.1652	+	2.62348i	−0.908285	+	0.112584i
$544$	−4.02935	−	0.260091i	−0.172757	−	0.0111513i
$545$	4.84221	−	4.06310i	0.207418	−	0.174044i
$546$	−15.7041	+	1.74131i	−0.672072	+	0.0745210i
$547$	1.10913	+	3.04730i	0.0474228	+	0.130293i	0.961143	−	0.276051i	$-0.0890258\pi$
$547$	1.10913	+	3.04730i	0.0474228	+	0.130293i	−0.913720	+	0.406344i	$0.866804\pi$
$548$	5.70801	+	5.04599i	0.243834	+	0.215554i
$549$	1.89663	−	0.137011i	0.0809464	−	0.00584749i
$550$	−8.28724	+	21.8869i	−0.353369	+	0.933259i
$551$	38.7079	+	32.4798i	1.64901	+	1.38369i
$552$	−21.0396	+	5.57851i	−0.895503	+	0.237437i
$553$	1.67560	+	9.50278i	0.0712536	+	0.404100i
$554$	21.5326	−	24.9998i	0.914831	−	1.06214i
$555$	3.10644	−	0.953641i	0.131861	−	0.0404798i
$556$	−1.57723	−	1.98123i	−0.0668893	−	0.0840231i
$557$	20.4301	−	11.7954i	0.865653	−	0.499785i	−0.000248175	−	1.00000i	$-0.500079\pi$
$557$	20.4301	−	11.7954i	0.865653	−	0.499785i	0.865901	+	0.500215i	$0.166746\pi$
$558$	−22.5187	−	2.60823i	−0.953295	−	0.110415i
$559$	8.95209	−	15.5055i	0.378633	−	0.655812i
$560$	0.835882	−	16.1950i	0.0353225	−	0.684363i
$561$	−4.76737	+	2.43601i	−0.201279	+	0.102848i
$562$	−1.90508	+	10.0452i	−0.0803609	+	0.423731i
$563$	−7.83509	+	21.5267i	−0.330210	+	0.907244i	0.657847	+	0.753152i	$0.271467\pi$
$563$	−7.83509	+	21.5267i	−0.330210	+	0.907244i	−0.988057	+	0.154092i	$0.950755\pi$
$564$	8.12769	+	16.9725i	0.342237	+	0.714670i
$565$	−51.0841	−	9.00750i	−2.14912	−	0.378948i
$566$	−1.22064	−	1.49338i	−0.0513072	−	0.0627715i
$567$	−12.0280	−	2.49885i	−0.505130	−	0.104942i
$568$	−1.09289	−	2.07425i	−0.0458567	−	0.0870337i
$569$	5.27628	−	29.9233i	0.221193	−	1.25445i	−0.648637	−	0.761098i	$-0.724661\pi$
$569$	5.27628	−	29.9233i	0.221193	−	1.25445i	0.869830	−	0.493351i	$-0.164228\pi$
$570$	−12.7758	+	52.5171i	−0.535121	+	2.19970i
$571$	11.6641	−	32.0469i	0.488129	−	1.34112i	−0.414244	−	0.910166i	$-0.635954\pi$
$571$	11.6641	−	32.0469i	0.488129	−	1.34112i	0.902373	−	0.430957i	$-0.141824\pi$
$572$	−19.5435	−	35.9606i	−0.817153	−	1.50359i
$573$	−0.321513	−	0.629214i	−0.0134314	−	0.0262858i
$574$	2.02474	−	3.40481i	0.0845109	−	0.142114i
$575$	8.48957	−	14.7044i	0.354039	−	0.613214i
$576$	8.32650	−	22.5093i	0.346938	−	0.937888i
$577$	5.70949	+	9.88913i	0.237689	+	0.411690i	0.960051	−	0.279826i	$-0.0902767\pi$
$577$	5.70949	+	9.88913i	0.237689	+	0.411690i	−0.722362	+	0.691516i	$0.756943\pi$
$578$	−23.3192	−	0.300647i	−0.969950	−	0.0125053i
$579$	36.4334	−	11.1847i	1.51412	−	0.464818i
$580$	40.3890	+	1.04162i	1.67706	+	0.0432508i
$581$	1.76093	−	0.310500i	0.0730558	−	0.0128817i
$582$	2.15657	+	4.35826i	0.0893925	+	0.180656i
$583$	−38.0643	−	31.9397i	−1.57646	−	1.32281i
$584$	21.9925	−	34.9019i	0.910056	−	1.44425i
$585$	34.8540	−	23.6262i	1.44104	−	0.976822i
$586$	−20.4556	+	3.33557i	−0.845014	+	0.137791i
$587$	10.9697	+	30.1389i	0.452766	+	1.24396i	0.930770	+	0.365606i	$0.119138\pi$
$587$	10.9697	+	30.1389i	0.452766	+	1.24396i	−0.478004	+	0.878358i	$0.658639\pi$
$588$	−12.7112	−	12.4527i	−0.524200	−	0.513539i
$589$	−25.5158	−	30.4085i	−1.05136	−	1.25296i
$590$	−4.95408	+	1.73114i	−0.203956	+	0.0712701i
$591$	−35.8080	+	4.43848i	−1.47294	+	0.182575i
$592$	−2.12013	−	1.37444i	−0.0871368	−	0.0564892i
$593$	19.2802			0.791741			0.395871	−	0.918306i	$-0.370443\pi$
$593$	19.2802			0.791741			0.395871	+	0.918306i	$0.370443\pi$
$594$	−5.77674	−	31.2932i	−0.237022	−	1.28398i
$595$			2.89375i			0.118632i
$596$	7.32166	−	18.6087i	0.299907	−	0.762244i
$597$	−4.89672	−	2.07189i	−0.200410	−	0.0847969i
$598$	9.79521	+	28.0313i	0.400556	+	1.14629i
$599$	31.8430	−	26.7195i	1.30107	−	1.09173i	0.311111	−	0.950374i	$-0.399299\pi$
$599$	31.8430	−	26.7195i	1.30107	−	1.09173i	0.989959	−	0.141354i	$-0.0451454\pi$
$600$	7.86752	+	16.9880i	0.321190	+	0.693531i
$601$	−5.75768	+	2.09562i	−0.234861	+	0.0854822i	−0.456769	−	0.889585i	$-0.650994\pi$
$601$	−5.75768	+	2.09562i	−0.234861	+	0.0854822i	0.221909	+	0.975067i	$0.428771\pi$
$602$	−7.21833	+	1.17705i	−0.294197	+	0.0479728i
$603$	−4.36740	+	42.4932i	−0.177854	+	1.73046i
$604$	−40.0115	+	13.4053i	−1.62804	+	0.545453i
$605$	14.8007	−	17.6388i	0.601734	−	0.717118i
$606$	0.672079	−	10.4702i	0.0273013	−	0.425324i
$607$	3.21106	+	18.2108i	0.130333	+	0.739155i	0.977997	+	0.208621i	$0.0668975\pi$
$607$	3.21106	+	18.2108i	0.130333	+	0.739155i	−0.847664	+	0.530534i	$0.821991\pi$
$608$	37.6732	−	18.6248i	1.52785	−	0.755334i
$609$	−10.9532	+	11.7730i	−0.443847	+	0.477067i
$610$	2.66221	+	0.0343230i	0.107790	+	0.00138970i
$611$	22.2321	−	12.8357i	0.899413	−	0.519276i
$612$	−1.27680	+	4.08790i	−0.0516117	+	0.165244i
$613$	−16.0146	−	9.24602i	−0.646823	−	0.373443i	0.140415	−	0.990093i	$-0.455156\pi$
$613$	−16.0146	−	9.24602i	−0.646823	−	0.373443i	−0.787238	+	0.616650i	$0.788490\pi$
$614$	−13.5090	−	8.03338i	−0.545178	−	0.324201i
$615$	−0.540372	+	10.5429i	−0.0217899	+	0.425133i
$616$	−6.32132	+	15.4776i	−0.254693	+	0.623610i
$617$	29.7070	+	10.8125i	1.19596	+	0.435294i	0.861813	−	0.507227i	$-0.169329\pi$
$617$	29.7070	+	10.8125i	1.19596	+	0.435294i	0.334148	+	0.942521i	$0.391552\pi$
$618$	26.2145	−	7.67920i	1.05450	−	0.308903i
$619$	−15.2623	−	2.69116i	−0.613445	−	0.108167i	−0.141712	−	0.989908i	$-0.545261\pi$
$619$	−15.2623	−	2.69116i	−0.613445	−	0.108167i	−0.471734	+	0.881741i	$0.656372\pi$
$620$	−31.1050	−	6.31556i	−1.24921	−	0.253639i
$621$	0.482579	+	23.0819i	0.0193652	+	0.926243i
$622$	12.0630	−	9.85987i	0.483682	−	0.395345i
$623$	1.26276	−	7.16145i	0.0505913	−	0.286917i
$624$	−31.4895	−	8.96330i	−1.26059	−	0.358819i
$625$	27.7244	+	10.0909i	1.10898	+	0.403634i
$626$	−0.678441	+	3.57732i	−0.0271160	+	0.142978i
$627$	30.2948	−	46.7676i	1.20986	−	1.86772i
$628$	−17.5866	+	2.63545i	−0.701780	+	0.105166i
$629$	0.390464	+	0.225434i	0.0155688	+	0.00898866i
$630$	−16.4828	−	4.91588i	−0.656691	−	0.195853i
$631$	11.8337	+	20.4966i	0.471093	+	0.815957i	0.999453	−	0.0330630i	$-0.0105262\pi$
$631$	11.8337	+	20.4966i	0.471093	+	0.815957i	−0.528360	+	0.849020i	$0.677193\pi$
$632$	−4.23084	+	19.5420i	−0.168294	+	0.777341i
$633$	3.90177	+	0.896068i	0.155081	+	0.0356155i
$634$	−3.88062	+	4.50548i	−0.154119	+	0.178936i
$635$	16.2773	−	2.87013i	0.645945	−	0.113897i
$636$	−39.5599	+	3.87094i	−1.56865	+	0.153493i
$637$	−15.6036	+	18.5956i	−0.618235	+	0.736784i
$638$	−38.9546	−	14.7497i	−1.54223	−	0.583948i
$639$	−2.41152	+	0.607155i	−0.0953982	+	0.0240187i
$640$	14.2918	−	30.4121i	0.564932	−	1.20214i
$641$	−11.7394	+	4.27278i	−0.463677	+	0.168765i	−0.563286	−	0.826262i	$-0.690463\pi$
$641$	−11.7394	+	4.27278i	−0.463677	+	0.168765i	0.0996090	+	0.995027i	$0.468241\pi$
$642$	−11.4371	+	26.0881i	−0.451386	+	1.02962i
$643$	9.44368	+	11.2545i	0.372422	+	0.443836i	0.919407	−	0.393307i	$-0.128669\pi$
$643$	9.44368	+	11.2545i	0.372422	+	0.443836i	−0.546985	+	0.837142i	$0.684225\pi$
$644$	6.33353	−	10.3446i	0.249576	−	0.407633i
$645$	15.5523	−	11.7476i	0.612372	−	0.462561i
$646$	−6.54232	+	3.66558i	−0.257404	+	0.144220i
$647$	9.10943			0.358129			0.179064	−	0.983837i	$-0.442693\pi$
$647$	9.10943			0.358129			0.179064	+	0.983837i	$0.442693\pi$
$648$	−21.1157	−	14.2172i	−0.829502	−	0.558503i
$649$	5.41034			0.212375
$650$	22.2805	−	12.4834i	0.873911	−	0.489641i
$651$	10.0800	−	7.61404i	0.395068	−	0.298418i
$652$	−30.3222	−	18.5650i	−1.18751	−	0.727060i
$653$	−11.0736	−	13.1970i	−0.433345	−	0.516440i	0.504540	−	0.863389i	$-0.331662\pi$
$653$	−11.0736	−	13.1970i	−0.433345	−	0.516440i	−0.937884	+	0.346949i	$0.887218\pi$
$654$	−2.09312	+	4.77442i	−0.0818473	+	0.186695i
$655$	26.6994	−	9.71778i	1.04323	−	0.379705i
$656$	6.55163	−	4.94515i	0.255798	−	0.193076i
$657$	−30.4674	−	31.4050i	−1.18865	−	1.22523i
$658$	−9.80701	−	3.71332i	−0.382317	−	0.144760i
$659$	−13.0287	+	15.5270i	−0.507525	+	0.604844i	−0.957584	−	0.288154i	$-0.906958\pi$
$659$	−13.0287	+	15.5270i	−0.507525	+	0.604844i	0.450059	+	0.892999i	$0.351403\pi$
$660$	−4.33893	−	44.3427i	−0.168893	−	1.72604i
$661$	28.8852	−	5.09323i	1.12350	−	0.198104i	0.419125	−	0.907929i	$-0.362337\pi$
$661$	28.8852	−	5.09323i	1.12350	−	0.198104i	0.704378	+	0.709825i	$0.251226\pi$
$662$	0.397282	−	0.461253i	0.0154408	−	0.0179271i
$663$	5.69409	+	1.30769i	0.221140	+	0.0507863i
$664$	3.62128	+	0.784005i	0.140533	+	0.0304253i
$665$	−15.0594	−	26.0837i	−0.583979	−	1.01148i
$666$	−1.94739	+	1.84112i	−0.0754599	+	0.0713418i
$667$	26.1710	+	15.1099i	1.01335	+	0.585056i
$668$	−2.04878	−	13.6716i	−0.0792695	−	0.528972i
$669$	3.40728	−	5.25999i	0.131733	−	0.203363i
$670$	−11.1442	+	58.7615i	−0.430536	+	2.27015i
$671$	−2.57934	−	0.938803i	−0.0995743	−	0.0362421i
$672$	5.30562	+	12.2766i	0.204669	+	0.473582i
$673$	−8.11942	+	46.0475i	−0.312980	+	1.77500i	0.270346	+	0.962763i	$0.412862\pi$
$673$	−8.11942	+	46.0475i	−0.312980	+	1.77500i	−0.583327	+	0.812237i	$0.698249\pi$
$674$	16.9754	−	13.8751i	0.653869	−	0.534450i
$675$	19.4790	−	3.85614i	0.749746	−	0.148423i
$676$	−3.71369	+	18.2904i	−0.142834	+	0.703478i
$677$	10.5443	+	1.85925i	0.405251	+	0.0714567i	0.372558	−	0.928009i	$-0.378481\pi$
$677$	10.5443	+	1.85925i	0.405251	+	0.0714567i	0.0326928	+	0.999465i	$0.489592\pi$
$678$	41.0546	−	12.0264i	1.57669	−	0.461871i
$679$	−2.54630	−	0.926777i	−0.0977180	−	0.0355664i
$680$	−2.26717	+	5.55110i	−0.0869419	+	0.212875i
$681$	1.74744	−	34.0935i	0.0669621	−	1.30647i
$682$	28.1253	+	16.7252i	1.07697	+	0.640442i
$683$	−17.0645	−	9.85219i	−0.652955	−	0.376984i	0.136632	−	0.990622i	$-0.456372\pi$
$683$	−17.0645	−	9.85219i	−0.652955	−	0.376984i	−0.789587	+	0.613638i	$0.789705\pi$
$684$	−9.76510	−	43.4922i	−0.373378	−	1.66296i
$685$	9.79823	−	5.65701i	0.374371	−	0.216143i
$686$	23.4267	+	0.302033i	0.894436	+	0.0115317i
$687$	20.7267	−	22.2780i	0.790775	−	0.849960i
$688$	−14.7692	−	3.39741i	−0.563069	−	0.129525i
$689$	9.41599	+	53.4008i	0.358721	+	2.03441i
$690$	−2.07062	+	32.2580i	−0.0788273	+	1.22804i
$691$	4.57312	−	5.45003i	0.173970	−	0.207329i	−0.672013	−	0.740539i	$-0.734570\pi$
$691$	4.57312	−	5.45003i	0.173970	−	0.207329i	0.845983	+	0.533210i	$0.179015\pi$
$692$	14.4905	+	43.2505i	0.550845	+	1.64414i
$693$	14.3701	+	10.3901i	0.545876	+	0.394687i
$694$	8.92301	−	1.45502i	0.338713	−	0.0552317i
$695$	−3.53391	+	1.28624i	−0.134049	+	0.0487897i
$696$	−30.2354	+	14.0027i	−1.14607	+	0.530772i
$697$	−1.12206	+	0.941521i	−0.0425011	+	0.0356627i
$698$	−16.9620	−	48.5408i	−0.642021	−	1.83730i
$699$	30.4249	+	12.8733i	1.15077	+	0.486913i
$700$	−9.70812	−	3.81969i	−0.366932	−	0.144371i
$701$			10.6994i			0.404109i	0.979374	+	0.202055i	$0.0647618\pi$
$701$			10.6994i			0.404109i	−0.979374	+	0.202055i	$0.935238\pi$
$702$	−17.1217	+	30.2120i	−0.646215	+	1.14028i
$703$	−4.69275			−0.176990
$704$	−24.2525	+	24.7382i	−0.914050	+	0.932357i
$705$	27.7337	−	3.43765i	1.04451	−	0.129470i
$706$	21.6710	−	7.57267i	0.815600	−	0.285001i
$707$	3.75811	+	4.47874i	0.141338	+	0.168440i
$708$	3.02875	−	3.09162i	0.113827	−	0.116190i
$709$	−9.95367	−	27.3475i	−0.373818	−	1.02706i	−0.973872	−	0.227097i	$-0.927077\pi$
$709$	−9.95367	−	27.3475i	−0.373818	−	1.02706i	0.600054	−	0.799959i	$-0.295146\pi$
$710$	−3.43639	+	0.560350i	−0.128965	+	0.0210296i
$711$	19.0827	+	9.25295i	0.715656	+	0.347013i
$712$	8.03313	−	12.7485i	0.301054	−	0.477771i
$713$	−18.1861	−	15.2600i	−0.681075	−	0.571490i
$714$	−1.05842	−	2.13898i	−0.0396103	−	0.0800494i
$715$	−59.8569	+	10.5544i	−2.23852	+	0.394712i
$716$	−0.645810	+	25.0415i	−0.0241351	+	0.935843i
$717$	−2.46632	+	0.757134i	−0.0921065	+	0.0282757i
$718$	8.26944	+	0.106615i	0.308613	+	0.00397885i
$719$	−4.95129	−	8.57588i	−0.184652	−	0.319826i	0.758807	−	0.651315i	$-0.225782\pi$
$719$	−4.95129	−	8.57588i	−0.184652	−	0.319826i	−0.943459	+	0.331489i	$0.892449\pi$
$720$	−27.7676	−	22.3439i	−1.03484	−	0.832710i
$721$	−7.61100	+	13.1826i	−0.283448	+	0.490947i
$722$	26.1612	−	43.9928i	0.973618	−	1.63724i
$723$	−3.47687	−	6.80437i	−0.129306	−	0.253057i
$724$	21.6375	−	11.7593i	0.804152	−	0.437031i
$725$	8.88976	−	24.4244i	0.330157	−	0.907100i
$726$	−4.48872	+	18.4516i	−0.166592	+	0.684804i
$727$	−4.91637	+	27.8821i	−0.182338	+	1.03409i	0.746990	+	0.664835i	$0.231498\pi$
$727$	−4.91637	+	27.8821i	−0.182338	+	1.03409i	−0.929328	+	0.369255i	$0.879613\pi$
$728$	16.1412	−	8.50455i	0.598233	−	0.315200i
$729$	−19.9397	+	18.2046i	−0.738509	+	0.674244i
$730$	−38.7707	−	47.4338i	−1.43497	−	1.75560i
$731$	2.66321	+	0.469597i	0.0985026	+	0.0173687i
$732$	−1.98039	+	0.948359i	−0.0731973	+	0.0350524i
$733$	−13.4575	+	36.9742i	−0.497065	+	1.36567i	0.397033	+	0.917804i	$0.370040\pi$
$733$	−13.4575	+	36.9742i	−0.497065	+	1.36567i	−0.894098	+	0.447871i	$0.852182\pi$
$734$	5.08065	−	26.7895i	0.187530	−	0.988819i
$735$	−23.5316	+	12.0241i	−0.867976	+	0.443514i
$736$	20.2543	−	14.8819i	0.746584	−	0.548556i
$737$	30.8304	−	53.3999i	1.13565	−	1.96701i
$738$	−3.45676	−	7.99071i	−0.127245	−	0.294142i
$739$	40.7334	−	23.5175i	1.49840	−	0.865104i	0.498405	−	0.866944i	$-0.333919\pi$
$739$	40.7334	−	23.5175i	1.49840	−	0.865104i	0.999998	+	0.00184073i	$0.000585924\pi$
$740$	−2.93559	+	2.33698i	−0.107915	+	0.0859089i
$741$	−58.1307	+	17.8455i	−2.13548	+	0.655570i
$742$	14.4554	−	16.7830i	0.530675	−	0.616125i
$743$	4.48040	+	25.4096i	0.164370	+	0.932189i	0.949712	+	0.313126i	$0.101376\pi$
$743$	4.48040	+	25.4096i	0.164370	+	0.932189i	−0.785342	+	0.619063i	$0.787513\pi$
$744$	25.3020	−	6.70867i	0.927615	−	0.245952i
$745$	−22.7492	−	19.0888i	−0.833466	−	0.699361i
$746$	−3.15233	+	8.32542i	−0.115415	+	0.304815i
$747$	1.71464	−	3.53615i	0.0627353	−	0.129381i
$748$	4.09442	−	4.63160i	0.149707	−	0.169348i
$749$	−5.42901	−	14.9161i	−0.198372	−	0.545022i
$750$	−8.52176	+	0.944915i	−0.311171	+	0.0345034i
$751$	27.2407	−	22.8576i	0.994026	−	0.834087i	0.00788021	−	0.999969i	$-0.497492\pi$
$751$	27.2407	−	22.8576i	0.994026	−	0.834087i	0.986146	+	0.165882i	$0.0530472\pi$
$752$	−15.9036	−	14.8068i	−0.579944	−	0.539948i
$753$	46.6225	−	5.77897i	1.69902	−	0.210598i
$754$	22.2182	+	39.6551i	0.809140	+	1.44415i
$755$			62.6652i			2.28062i
$756$	13.9817	−	2.39506i	0.508509	−	0.0871075i
$757$			4.81926i			0.175159i	0.996158	+	0.0875795i	$0.0279132\pi$
$757$			4.81926i			0.175159i	−0.996158	+	0.0875795i	$0.972087\pi$
$758$	21.2761	−	11.9207i	0.772782	−	0.432979i
$759$	12.9860	−	30.6911i	0.471360	−	1.11402i
$760$	−8.45280	−	61.8351i	−0.306615	−	2.24299i
$761$	5.92907	−	4.97508i	0.214929	−	0.180347i	−0.528967	−	0.848642i	$-0.677420\pi$
$761$	5.92907	−	4.97508i	0.214929	−	0.180347i	0.743896	+	0.668296i	$0.232976\pi$
$762$	−10.9820	+	8.07510i	−0.397835	+	0.292530i
$763$	−0.993570	−	2.72981i	−0.0359697	−	0.0988258i
$764$	0.611294	+	0.540396i	0.0221158	+	0.0195508i
$765$	5.15390	+	3.72644i	0.186340	+	0.134730i
$766$	−35.4989	−	13.4413i	−1.28263	−	0.485653i
$767$	−4.52284	−	3.79511i	−0.163310	−	0.137033i
$768$	0.559419	+	27.7072i	0.0201863	+	0.999796i
$769$	−5.50477	−	31.2191i	−0.198507	−	1.12579i	−0.907335	−	0.420409i	$-0.861887\pi$
$769$	−5.50477	−	31.2191i	−0.198507	−	1.12579i	0.708828	−	0.705382i	$-0.249224\pi$
$770$	18.8121	+	16.2031i	0.677941	+	0.583918i
$771$	−20.1203	−	18.7192i	−0.724613	−	0.674156i
$772$	−34.4297	+	27.4089i	−1.23915	+	0.986468i
$773$	−27.4650	+	15.8569i	−0.987847	+	0.570334i	−0.904630	−	0.426197i	$-0.859853\pi$
$773$	−27.4650	+	15.8569i	−0.987847	+	0.570334i	−0.0832173	+	0.996531i	$0.526520\pi$
$774$	−7.19907	+	14.3719i	−0.258765	+	0.516588i
$775$	−10.2095	+	17.6833i	−0.366735	+	0.635204i
$776$	−4.15848	−	3.77279i	−0.149281	−	0.135435i
$777$	0.0764429	−	1.49144i	0.00274238	−	0.0535052i
$778$	−21.9808	−	4.16868i	−0.788050	−	0.149454i
$779$	5.21424	−	14.3260i	0.186820	−	0.513283i
$780$	−27.4772	+	40.1123i	−0.983842	+	1.43625i
$781$	3.53506	+	0.623327i	0.126494	+	0.0223044i
$782$	−3.47258	+	2.83836i	−0.124179	+	0.101500i
$783$	6.86321	+	34.6690i	0.245271	+	1.23897i
$784$	18.9202	+	8.01347i	0.675722	+	0.286196i
$785$	−4.58579	+	26.0073i	−0.163674	+	0.928241i
$786$	−16.1811	+	16.9487i	−0.577161	+	0.604540i
$787$	−2.68876	+	7.38730i	−0.0958438	+	0.263329i	−0.978345	−	0.206982i	$-0.933636\pi$
$787$	−2.68876	+	7.38730i	−0.0958438	+	0.263329i	0.882501	+	0.470311i	$0.155858\pi$
$788$	36.6071	−	19.8948i	1.30407	−	0.708723i
$789$	1.51631	−	2.34081i	0.0539822	−	0.0833350i
$790$	25.5216	+	15.1769i	0.908016	+	0.539969i
$791$	−11.9196	+	20.6453i	−0.423812	+	0.734063i
$792$	19.4260	+	31.1899i	0.690273	+	1.10829i
$793$	1.49770	+	2.59409i	0.0531849	+	0.0921189i
$794$	−0.660178	+	51.2057i	−0.0234288	+	1.81722i
$795$	−13.2125	+	57.5313i	−0.468598	+	2.04043i
$796$	6.13752	+	0.158284i	0.217539	+	0.00561024i
$797$	−34.5495	+	6.09202i	−1.22381	+	0.215790i	−0.747964	−	0.663740i	$-0.768968\pi$
$797$	−34.5495	+	6.09202i	−1.22381	+	0.215790i	−0.475844	+	0.879530i	$0.657857\pi$
$798$	20.6719	+	13.7722i	0.731776	+	0.487531i
$799$	2.97032	+	2.49239i	0.105082	+	0.0881746i
$800$	−15.6305	−	14.9334i	−0.552623	−	0.527974i
$801$	−11.1287	−	11.4712i	−0.393215	−	0.405316i
$802$	7.24867	+	44.4530i	0.255959	+	1.56969i
$803$	21.6019	+	59.3509i	0.762316	+	2.09445i
$804$	−13.2551	−	47.5110i	−0.467472	−	1.67558i
$805$	−11.5784	−	13.7986i	−0.408086	−	0.486338i
$806$	−11.7796	−	33.7102i	−0.414920	−	1.18739i
$807$	3.08866	+	4.08899i	0.108726	+	0.143939i
$808$	3.70024	+	11.5360i	0.130174	+	0.405834i
$809$	42.6190			1.49840			0.749202	−	0.662341i	$-0.230437\pi$
$809$	42.6190			1.49840			0.749202	+	0.662341i	$0.230437\pi$
$810$	−29.9812	+	23.0262i	−1.05343	+	0.809058i
$811$		−	40.0596i		−	1.40668i	−0.710852	−	0.703341i	$-0.751691\pi$
$811$		−	40.0596i		−	1.40668i	0.710852	−	0.703341i	$-0.248309\pi$
$812$	6.79834	−	17.2787i	0.238575	−	0.606362i
$813$	8.62077	−	6.51178i	0.302344	−	0.228378i
$814$	3.65187	−	1.27610i	0.127998	−	0.0447274i
$815$	−40.4468	+	33.9389i	−1.41679	+	1.18883i
$816$	−0.354540	−	4.93246i	−0.0124114	−	0.172671i
$817$	−26.4495	+	9.62683i	−0.925351	+	0.336800i
$818$	3.75775	+	23.0447i	0.131387	+	0.805739i
$819$	−4.72470	−	18.7657i	−0.165094	−	0.655727i
$820$	−3.87250	−	11.5585i	−0.135233	−	0.403639i
$821$	1.07655	−	1.28299i	0.0375720	−	0.0447766i	−0.746931	−	0.664901i	$-0.768474\pi$
$821$	1.07655	−	1.28299i	0.0375720	−	0.0447766i	0.784503	+	0.620125i	$0.212918\pi$
$822$	−5.17349	+	7.76531i	−0.180446	+	0.270846i
$823$	0.234450	+	1.32963i	0.00817242	+	0.0463481i	0.988621	−	0.150426i	$-0.0480645\pi$
$823$	0.234450	+	1.32963i	0.00817242	+	0.0463481i	−0.980449	+	0.196774i	$0.936953\pi$
$824$	−24.9284	+	19.3254i	−0.868423	+	0.673231i
$825$	−27.9358	−	6.41565i	−0.972600	−	0.223364i
$826$	−0.0310917	+	2.41158i	−0.00108182	+	0.0839096i
$827$	10.0199	−	5.78501i	0.348427	−	0.201165i	−0.315565	−	0.948904i	$-0.602194\pi$
$827$	10.0199	−	5.78501i	0.348427	−	0.201165i	0.663992	+	0.747739i	$0.268861\pi$
$828$	−10.2681	−	24.6016i	−0.356842	−	0.854965i
$829$	34.1730	+	19.7298i	1.18688	+	0.685243i	0.957595	−	0.288117i	$-0.0930292\pi$
$829$	34.1730	+	19.7298i	1.18688	+	0.685243i	0.229281	+	0.973360i	$0.426363\pi$
$830$	2.81239	−	4.72933i	0.0976193	−	0.164157i
$831$	33.9159	+	21.9698i	1.17653	+	0.762124i
$832$	37.6269	−	3.66818i	1.30448	−	0.127171i
$833$	−3.44542	−	1.25403i	−0.119377	−	0.0434496i
$834$	2.14172	−	2.24331i	0.0741616	−	0.0776796i
$835$	−20.2179	−	3.56496i	−0.699668	−	0.123370i
$836$	−12.8029	+	63.0561i	−0.442798	+	2.18084i
$837$	−0.580345	−	27.7580i	−0.0200596	−	0.959458i
$838$	16.5011	+	20.1882i	0.570022	+	0.697390i
$839$	−6.51330	+	36.9388i	−0.224864	+	1.27527i	0.638080	+	0.769970i	$0.279729\pi$
$839$	−6.51330	+	36.9388i	−0.224864	+	1.27527i	−0.862945	+	0.505299i	$0.831382\pi$
$840$	19.7900	−	1.67919i	0.682821	−	0.0579375i
$841$	16.2198	+	5.90354i	0.559305	+	0.203570i
$842$	13.6816	+	2.59473i	0.471499	+	0.0894202i
$843$	−12.5057	−	0.640971i	−0.430718	−	0.0220762i
$844$	−4.57161	+	0.685083i	−0.157361	+	0.0235815i
$845$	24.0031	+	13.8582i	0.825732	+	0.476737i
$846$	−19.2426	+	12.6849i	−0.661576	+	0.436116i
$847$	−5.29105	−	9.16436i	−0.181803	−	0.314891i
$848$	40.8789	−	20.8696i	1.40379	−	0.716667i
$849$	1.60906	−	1.72949i	0.0552228	−	0.0593559i
$850$	2.92283	+	2.51746i	0.100252	+	0.0863482i
$851$	−2.76390	+	0.487351i	−0.0947454	+	0.0167062i
$852$	2.33514	−	1.67109i	0.0800005	−	0.0572506i
$853$	16.8181	−	20.0430i	0.575840	−	0.686260i	−0.396978	−	0.917828i	$-0.629941\pi$
$853$	16.8181	−	20.0430i	0.575840	−	0.686260i	0.972819	+	0.231568i	$0.0743856\pi$
$854$	0.433280	−	1.14431i	0.0148265	−	0.0391574i
$855$	−65.8491	−	6.76789i	−2.25199	−	0.231457i
$856$	1.27180	−	32.8671i	0.0434692	−	1.12337i
$857$	−19.6602	+	7.15571i	−0.671578	+	0.244434i	−0.655227	−	0.755432i	$-0.727427\pi$
$857$	−19.6602	+	7.15571i	−0.671578	+	0.244434i	−0.0163509	+	0.999866i	$0.505205\pi$
$858$	40.3843	−	29.6948i	1.37870	−	1.01376i
$859$	18.2371	+	21.7341i	0.622241	+	0.741558i	0.981454	−	0.191698i	$-0.0613993\pi$
$859$	18.2371	+	21.7341i	0.622241	+	0.741558i	−0.359213	+	0.933256i	$0.616955\pi$
$860$	−11.7516	+	19.1939i	−0.400727	+	0.654508i
$861$	4.46814	+	1.89055i	0.152274	+	0.0644297i
$862$	−3.87752	−	6.92060i	−0.132069	−	0.235716i
$863$	−37.5798			−1.27923			−0.639616	−	0.768694i	$-0.720907\pi$
$863$	−37.5798			−1.27923			−0.639616	+	0.768694i	$0.720907\pi$
$864$	28.6976	+	6.35977i	0.976313	+	0.216364i
$865$	67.7381			2.30316
$866$	15.0557	+	26.8714i	0.511614	+	0.913129i
$867$	−3.51349	−	28.3455i	−0.119324	−	0.962664i
$868$	−7.61665	+	12.4403i	−0.258526	+	0.422251i
$869$	−19.6775	−	23.4507i	−0.667512	−	0.795510i
$870$	5.45334	+	49.1812i	0.184885	+	1.66740i
$871$	−63.2307	+	23.0141i	−2.14249	+	0.779802i
$872$	0.232753	−	6.01505i	0.00788203	−	0.203695i
$873$	−4.92964	+	3.34161i	−0.166843	+	0.113096i
$874$	16.5299	−	43.6561i	0.559134	−	1.47669i
$875$	3.07116	−	3.66007i	0.103824	−	0.123733i
$876$	46.0077	+	20.8810i	1.55445	+	0.705505i
$877$	−23.8777	+	4.21027i	−0.806291	+	0.142171i	−0.561577	−	0.827424i	$-0.689805\pi$
$877$	−23.8777	+	4.21027i	−0.806291	+	0.142171i	−0.244714	+	0.969595i	$0.578694\pi$
$878$	−16.2383	−	13.9862i	−0.548018	−	0.472013i
$879$	−7.44943	−	24.2661i	−0.251263	−	0.818476i
$880$	23.3928	+	45.8212i	0.788571	+	1.54463i
$881$	−15.8494	−	27.4519i	−0.533980	−	0.924880i	−0.999212	−	0.0396911i	$-0.987363\pi$
$881$	−15.8494	−	27.4519i	−0.533980	−	0.924880i	0.465232	−	0.885189i	$-0.345971\pi$
$882$	12.9960	−	17.4948i	0.437599	−	0.589080i
$883$	−19.1513	−	11.0570i	−0.644492	−	0.372098i	0.141851	−	0.989888i	$-0.454695\pi$
$883$	−19.1513	−	11.0570i	−0.644492	−	0.372098i	−0.786343	+	0.617790i	$0.788028\pi$
$884$	−6.67163	+	0.999783i	−0.224391	+	0.0336263i
$885$	−2.92450	−	5.72337i	−0.0983061	−	0.192389i
$886$	−14.5097	−	2.75177i	−0.487461	−	0.0924474i
$887$	0.923934	+	0.336285i	0.0310227	+	0.0112913i	0.357485	−	0.933919i	$-0.383634\pi$
$887$	0.923934	+	0.336285i	0.0310227	+	0.0112913i	−0.326462	+	0.945210i	$0.605857\pi$
$888$	1.31514	−	2.80115i	0.0441333	−	0.0940005i
$889$	1.31904	−	7.48065i	0.0442392	−	0.250893i
$890$	−14.1617	−	17.3260i	−0.474700	−	0.580769i
$891$	37.0105	−	12.2140i	1.23990	−	0.409184i
$892$	−1.43995	+	7.09197i	−0.0482132	+	0.237457i
$893$	−39.7446	−	7.00804i	−1.33000	−	0.234515i
$894$	23.7975	+	5.78922i	0.795909	+	0.193621i
$895$	34.9567	+	12.7232i	1.16847	+	0.425290i
$896$	−10.8873	−	10.9523i	−0.363720	−	0.365892i
$897$	−32.3842	+	16.5475i	−1.08128	+	0.552505i
$898$	−19.5091	+	32.8067i	−0.651028	+	1.09477i
$899$	−31.4731	−	18.1710i	−1.04969	−	0.606036i
$900$	−19.3047	+	12.3718i	−0.643491	+	0.412393i
$901$	−7.09295	+	4.09512i	−0.236300	+	0.136428i
$902$	−0.162014	+	12.5664i	−0.00539447	+	0.418414i
$903$	−2.62873	−	8.56296i	−0.0874788	−	0.284958i
$904$	−39.0404	+	30.2654i	−1.29846	+	1.00661i
$905$	−6.35058	−	36.0159i	−0.211100	−	1.19721i
$906$	−22.9204	−	46.3205i	−0.761480	−	1.53889i
$907$	−26.0101	+	30.9976i	−0.863651	+	1.02926i	0.135607	+	0.990763i	$0.456701\pi$
$907$	−26.0101	+	30.9976i	−0.863651	+	1.02926i	−0.999259	+	0.0384971i	$0.987743\pi$
$908$	12.5228	+	37.3775i	0.415583	+	1.24041i
$909$	12.8164	−	0.925842i	0.425092	−	0.0307082i
$910$	−4.36048	−	26.7410i	−0.144548	−	0.886454i
$911$	28.6333	−	10.4217i	0.948664	−	0.345286i	0.179083	−	0.983834i	$-0.442687\pi$
$911$	28.6333	−	10.4217i	0.948664	−	0.345286i	0.769582	+	0.638548i	$0.220465\pi$
$912$	28.8649	+	42.6152i	0.955812	+	1.41113i
$913$	−4.34558	+	3.64637i	−0.143818	+	0.120677i
$914$	−38.9507	+	13.6109i	−1.28838	+	0.450207i
$915$	0.401114	+	3.23603i	0.0132604	+	0.106980i
$916$	−12.8645	+	32.6963i	−0.425054	+	1.08032i
$917$		−	13.0579i		−	0.431209i
$918$	−5.17261	−	0.869398i	−0.170722	−	0.0286944i
$919$	−28.9703			−0.955641			−0.477820	−	0.878458i	$-0.658573\pi$
$919$	−28.9703			−0.955641			−0.477820	+	0.878458i	$0.658573\pi$
$920$	−11.4002	−	35.5414i	−0.375852	−	1.17177i
$921$	7.50098	−	17.7279i	0.247166	−	0.584153i
$922$	1.98952	+	5.69349i	0.0655214	+	0.187505i
$923$	−2.51794	−	3.00076i	−0.0828789	−	0.0987713i
$924$	−19.8318	−	5.09616i	−0.652420	−	0.167651i
$925$	0.825603	+	2.26832i	0.0271456	+	0.0745821i
$926$	6.39933	+	39.2444i	0.210295	+	1.28965i
$927$	13.6778	+	30.5316i	0.449237	+	1.00279i
$928$	26.5786	−	27.8195i	0.872486	−	0.913219i
$929$	−21.4798	−	18.0237i	−0.704730	−	0.591338i	0.218385	−	0.975863i	$-0.429921\pi$
$929$	−21.4798	−	18.0237i	−0.704730	−	0.591338i	−0.923115	+	0.384524i	$0.874366\pi$
$930$	2.49011	−	38.7932i	0.0816540	−	1.27208i
$931$	37.5824	−	6.62680i	1.23171	−	0.217185i
$932$	−38.1343	−	0.983471i	−1.24913	−	0.0322147i
$933$	13.9702	+	12.9974i	0.457364	+	0.425516i
$934$	−0.123515	+	9.58023i	−0.00404153	+	0.313475i
$935$	−4.59022	−	7.95049i	−0.150116	−	0.260009i
$936$	5.63895	−	39.7000i	0.184315	−	1.29764i
$937$	−10.0264	+	17.3662i	−0.327548	+	0.567329i	−0.982025	−	0.188753i	$-0.939556\pi$
$937$	−10.0264	+	17.3662i	−0.327548	+	0.567329i	0.654477	+	0.756082i	$0.272889\pi$
$938$	23.6250	+	14.0491i	0.771385	+	0.458719i
$939$	−4.45355	−	0.228264i	−0.145336	−	0.00744912i
$940$	−28.3526	+	15.4087i	−0.924760	+	0.502578i
$941$	−7.11484	+	19.5479i	−0.231937	+	0.637242i	−0.999995	−	0.00313816i	$-0.999001\pi$
$941$	−7.11484	+	19.5479i	−0.231937	+	0.637242i	0.768058	+	0.640380i	$0.221223\pi$
$942$	−6.12274	−	20.9012i	−0.199490	−	0.680999i
$943$	1.58327	−	8.97916i	0.0515583	−	0.292402i
$944$	−1.94904	+	4.60179i	−0.0634360	+	0.149775i
$945$	3.22361	−	20.8178i	0.104864	−	0.677203i
$946$	17.9650	−	14.6840i	0.584094	−	0.477418i
$947$	31.3017	+	5.51933i	1.01717	+	0.179354i	0.657284	−	0.753643i	$-0.271705\pi$
$947$	31.3017	+	5.51933i	1.01717	+	0.179354i	0.359884	+	0.932997i	$0.382816\pi$
$948$	−24.4160	−	1.88359i	−0.792993	−	0.0611763i
$949$	23.5735	−	64.7678i	0.765230	−	2.10245i
$950$	−39.4469	−	7.48114i	−1.27983	−	0.242720i
$951$	−6.11235	−	3.95942i	−0.198207	−	0.128393i
$952$	2.04093	+	1.85164i	0.0661471	+	0.0600121i
$953$	−6.86849	+	11.8966i	−0.222492	+	0.385368i	−0.955564	−	0.294783i	$-0.904753\pi$
$953$	−6.86849	+	11.8966i	−0.222492	+	0.385368i	0.733072	+	0.680151i	$0.238086\pi$
$954$	−11.2763	−	47.3582i	−0.365085	−	1.53328i
$955$	1.04933	−	0.605833i	0.0339556	−	0.0196043i
$956$	2.33069	−	1.85542i	0.0753798	−	0.0600085i
$957$	11.4187	−	49.7206i	0.369113	−	1.60724i
$958$	37.6994	+	32.4709i	1.21801	+	1.04909i
$959$	−0.902910	−	5.12065i	−0.0291565	−	0.165355i
$960$	39.2789	+	12.2837i	1.26772	+	0.396455i
$961$	−1.87694	−	1.57494i	−0.0605465	−	0.0508046i
$962$	−3.94795	−	1.49485i	−0.127287	−	0.0481959i
$963$	−33.5575	−	9.53896i	−1.08137	−	0.307389i
$964$	6.61058	+	5.84388i	0.212913	+	0.188219i
$965$	22.3521	+	61.4119i	0.719539	+	1.97692i
$966$	13.6055	+	5.96466i	0.437749	+	0.191910i
$967$	10.5560	−	8.85755i	0.339458	−	0.284839i	−0.457082	−	0.889424i	$-0.651105\pi$
$967$	10.5560	−	8.85755i	0.339458	−	0.284839i	0.796541	+	0.604585i	$0.206661\pi$
$968$	−2.96985	−	21.7254i	−0.0954545	−	0.698282i
$969$	−5.53589	−	7.32882i	−0.177838	−	0.235436i
$970$	−7.27439	+	4.07575i	−0.233567	+	0.130864i
$971$		−	1.88573i		−	0.0605161i	−0.999542	−	0.0302580i	$-0.990367\pi$
$971$		−	1.88573i		−	0.0605161i	0.999542	−	0.0302580i	$-0.00963290\pi$
$972$	13.7393	−	27.9863i	0.440688	−	0.897660i
$973$			1.72833i			0.0554077i
$974$	4.64118	+	8.28358i	0.148713	+	0.265423i
$975$	18.8530	+	24.9589i	0.603778	+	0.799326i
$976$	1.72769	−	1.85567i	0.0553021	−	0.0593985i
$977$	−19.2464	+	16.1496i	−0.615746	+	0.516672i	−0.896463	−	0.443119i	$-0.853872\pi$
$977$	−19.2464	+	16.1496i	−0.615746	+	0.516672i	0.280717	+	0.959790i	$0.409428\pi$
$978$	17.4837	−	39.8806i	0.559068	−	1.27524i
$979$	7.89048	+	21.6789i	0.252181	+	0.692861i
$980$	20.2099	−	22.8614i	0.645583	−	0.730281i
$981$	−6.14140	−	1.74574i	−0.196080	−	0.0557371i
$982$	−2.22621	+	5.87949i	−0.0710412	+	0.187622i
$983$	−38.8553	−	32.6035i	−1.23929	−	1.03989i	−0.997579	−	0.0695429i	$-0.977846\pi$
$983$	−38.8553	−	32.6035i	−1.23929	−	1.03989i	−0.241714	−	0.970348i	$-0.577710\pi$
$984$	7.09007	+	7.12731i	0.226023	+	0.227210i
$985$	−10.7441	−	60.9330i	−0.342336	−	1.94149i
$986$	−4.48061	+	5.20209i	−0.142692	+	0.165668i
$987$	2.87471	−	12.5174i	0.0915030	−	0.398433i
$988$	54.9337	−	43.7318i	1.74767	−	1.39129i
$989$	−14.5783	+	8.41679i	−0.463563	+	0.267638i
$990$	53.0838	−	12.6397i	1.68711	−	0.401715i
$991$	−16.9675	+	29.3886i	−0.538991	+	0.933559i	0.459968	+	0.887936i	$0.347861\pi$
$991$	−16.9675	+	29.3886i	−0.538991	+	0.933559i	−0.998959	+	0.0456239i	$0.985472\pi$
$992$	−24.3577	+	17.8969i	−0.773357	+	0.568227i
$993$	0.625758	+	0.405350i	0.0198578	+	0.0128634i
$994$	−0.298153	+	1.57212i	−0.00945685	+	0.0498646i
$995$	3.11838	−	8.56769i	0.0988594	−	0.271614i
$996$	−0.349043	+	4.52445i	−0.0110599	+	0.143363i
$997$	−14.9293	−	2.63244i	−0.472817	−	0.0833703i	−0.0678377	−	0.997696i	$-0.521610\pi$
$997$	−14.9293	−	2.63244i	−0.472817	−	0.0833703i	−0.404979	+	0.914326i	$0.632721\pi$
$998$	17.8590	+	21.8494i	0.565316	+	0.691632i
$999$	−2.55789	−	2.05676i	−0.0809280	−	0.0650731i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.133.11	yes	204
3.2	odd	2		648.2.t.a.397.24		204
4.3	odd	2		864.2.bf.a.241.7		204
8.3	odd	2		864.2.bf.a.241.28		204
8.5	even	2	inner	216.2.t.a.133.27	yes	204
24.5	odd	2		648.2.t.a.397.8		204
27.13	even	9	inner	216.2.t.a.13.27	yes	204
27.14	odd	18		648.2.t.a.253.8		204
108.67	odd	18		864.2.bf.a.337.28		204
216.13	even	18	inner	216.2.t.a.13.11	✓	204
216.67	odd	18		864.2.bf.a.337.7		204
216.149	odd	18		648.2.t.a.253.24		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.11	✓	204	216.13	even	18	inner
216.2.t.a.13.27	yes	204	27.13	even	9	inner
216.2.t.a.133.11	yes	204	1.1	even	1	trivial
216.2.t.a.133.27	yes	204	8.5	even	2	inner
648.2.t.a.253.8		204	27.14	odd	18
648.2.t.a.253.24		204	216.149	odd	18
648.2.t.a.397.8		204	24.5	odd	2
648.2.t.a.397.24		204	3.2	odd	2
864.2.bf.a.241.7		204	4.3	odd	2
864.2.bf.a.241.28		204	8.3	odd	2
864.2.bf.a.337.7		204	216.67	odd	18
864.2.bf.a.337.28		204	108.67	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.691259 - 1.23376i) q^{2} +(1.38208 - 1.04396i) q^{3} +(-1.04432 + 1.70569i) q^{4} +(1.90914 + 2.27523i) q^{5} +(-2.24337 - 0.983500i) q^{6} +(1.28267 - 0.466852i) q^{7} +(2.82631 + 0.109365i) q^{8} +(0.820275 - 2.88568i) q^{9} +(1.48737 - 3.92819i) q^{10} +(-2.78354 + 3.31729i) q^{11} +(0.337351 + 3.44764i) q^{12} +(4.65386 - 0.820601i) q^{13} +(-1.46264 - 1.25978i) q^{14} +(5.01384 + 1.15146i) q^{15} +(-1.81878 - 3.56259i) q^{16} +(0.356888 + 0.618149i) q^{17} +(-4.12726 + 0.982730i) q^{18} +(-6.43384 - 3.71458i) q^{19} +(-5.87460 + 0.880343i) q^{20} +(1.28537 - 1.98428i) q^{21} +(6.01689 + 1.14111i) q^{22} +(-4.17513 - 1.51962i) q^{23} +(4.02035 - 2.79942i) q^{24} +(-0.663593 + 3.76342i) q^{25} +(-4.22945 - 5.17449i) q^{26} +(-1.87886 - 4.84457i) q^{27} +(-0.543209 + 2.67538i) q^{28} +(-6.69820 - 1.18107i) q^{29} +(-2.04523 - 6.98183i) q^{30} +(5.02097 + 1.82748i) q^{31} +(-3.13812 + 4.70661i) q^{32} +(-0.383930 + 7.49067i) q^{33} +(0.515944 - 0.867615i) q^{34} +(3.51099 + 2.02707i) q^{35} +(4.06546 + 4.41272i) q^{36} +(0.547039 - 0.315833i) q^{37} +(-0.135445 + 10.5055i) q^{38} +(5.57532 - 5.99260i) q^{39} +(5.14700 + 6.63929i) q^{40} +(0.356345 + 2.02093i) q^{41} +(-3.33665 - 0.214178i) q^{42} +(2.43534 - 2.90233i) q^{43} +(-2.75138 - 8.21219i) q^{44} +(8.13160 - 3.64286i) q^{45} +(1.01125 + 6.20155i) q^{46} +(5.10473 - 1.85797i) q^{47} +(-6.23292 - 3.02502i) q^{48} +(-3.93503 + 3.30188i) q^{49} +(5.10187 - 1.78279i) q^{50} +(1.13857 + 0.481751i) q^{51} +(-3.46043 + 8.79504i) q^{52} +11.4745i q^{53} +(-4.67825 + 5.66692i) q^{54} -12.8618 q^{55} +(3.67627 - 1.17919i) q^{56} +(-12.7699 + 1.58287i) q^{57} +(3.17303 + 9.08039i) q^{58} +(-0.803086 - 0.957081i) q^{59} +(-7.20010 + 7.34958i) q^{60} +(0.216792 + 0.595632i) q^{61} +(-1.21612 - 7.45793i) q^{62} +(-0.295047 - 4.08431i) q^{63} +(7.97608 + 0.618197i) q^{64} +(10.7519 + 9.02195i) q^{65} +(9.50708 - 4.70432i) q^{66} +(-14.0227 + 2.47258i) q^{67} +(-1.42708 - 0.0368039i) q^{68} +(-7.35678 + 2.25845i) q^{69} +(0.0739130 - 5.73294i) q^{70} +(-0.414463 - 0.717870i) q^{71} +(2.63395 - 8.06612i) q^{72} +(7.29258 - 12.6311i) q^{73} +(-0.767808 - 0.456592i) q^{74} +(3.01174 + 5.89411i) q^{75} +(13.0549 - 7.09494i) q^{76} +(-2.02167 + 5.55448i) q^{77} +(-11.2474 - 2.73616i) q^{78} +(-1.22756 + 6.96183i) q^{79} +(4.63338 - 10.9396i) q^{80} +(-7.65430 - 4.73410i) q^{81} +(2.24702 - 1.83663i) q^{82} +(1.29008 + 0.227475i) q^{83} +(2.04225 + 4.26467i) q^{84} +(-0.725078 + 1.99214i) q^{85} +(-5.26422 - 0.998364i) q^{86} +(-10.4904 + 5.36035i) q^{87} +(-8.22995 + 9.07129i) q^{88} +(2.66374 - 4.61373i) q^{89} +(-10.1155 - 7.51427i) q^{90} +(5.58625 - 3.22522i) q^{91} +(6.95219 - 5.53452i) q^{92} +(8.84720 - 2.71599i) q^{93} +(-5.82098 - 5.01367i) q^{94} +(-3.83160 - 21.7301i) q^{95} +(0.576410 + 9.78099i) q^{96} +(-1.52072 - 1.27604i) q^{97} +(6.79385 + 2.57242i) q^{98} +(7.28938 + 10.7535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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