LMFDB - Embedded newform 414.2.p.a.113.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(5,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("414.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.p (of order $66$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			113.5
Character	$\chi$	$=$	414.113
Dual form			414.2.p.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.998867 - 0.0475819i) q^{2} +(-0.397495 + 1.68582i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-1.35562 + 1.29258i) q^{5} +(0.477260 - 1.66500i) q^{6} +(-0.763522 + 3.96153i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-2.68399 - 1.34021i) q^{9} +O(q^{10})$	\(q+(-0.998867 - 0.0475819i) q^{2} +(-0.397495 + 1.68582i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-1.35562 + 1.29258i) q^{5} +(0.477260 - 1.66500i) q^{6} +(-0.763522 + 3.96153i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-2.68399 - 1.34021i) q^{9} +(1.41559 - 1.22662i) q^{10} +(-2.80329 - 1.44520i) q^{11} +(-0.555943 + 1.64040i) q^{12} +(1.06637 - 0.205526i) q^{13} +(0.951154 - 3.92071i) q^{14} +(-1.64021 - 2.79914i) q^{15} +(0.981929 + 0.189251i) q^{16} +(2.58229 - 5.65443i) q^{17} +(2.61718 + 1.46640i) q^{18} +(-0.258219 + 0.117925i) q^{19} +(-1.47235 + 1.15787i) q^{20} +(-6.37493 - 2.86185i) q^{21} +(2.73135 + 1.57695i) q^{22} +(-0.840668 + 4.72158i) q^{23} +(0.633367 - 1.61209i) q^{24} +(-0.0709688 + 1.48982i) q^{25} +(-1.07494 + 0.154553i) q^{26} +(3.32624 - 3.99201i) q^{27} +(-1.13663 + 3.87101i) q^{28} +(-0.0980958 - 1.02731i) q^{29} +(1.50517 + 2.87401i) q^{30} +(-4.02666 - 3.16660i) q^{31} +(-0.971812 - 0.235759i) q^{32} +(3.55064 - 4.15139i) q^{33} +(-2.84841 + 5.52515i) q^{34} +(-4.08556 - 6.35726i) q^{35} +(-2.54445 - 1.58927i) q^{36} +(-0.0301730 - 0.102760i) q^{37} +(0.263538 - 0.105505i) q^{38} +(-0.0773969 + 1.87941i) q^{39} +(1.52578 - 1.08650i) q^{40} +(-6.42991 - 6.74349i) q^{41} +(6.23154 + 3.16194i) q^{42} +(-0.883792 - 1.12383i) q^{43} +(-2.65322 - 1.70512i) q^{44} +(5.37083 - 1.65247i) q^{45} +(1.06438 - 4.67623i) q^{46} +(-9.58561 + 5.53425i) q^{47} +(-0.709356 + 1.58013i) q^{48} +(-8.61215 - 3.44779i) q^{49} +(0.141777 - 1.48476i) q^{50} +(8.50591 + 6.60089i) q^{51} +(1.08108 - 0.103230i) q^{52} +(-2.33524 + 2.69502i) q^{53} +(-3.51242 + 3.82922i) q^{54} +(5.66824 - 1.66435i) q^{55} +(1.31953 - 3.81254i) q^{56} +(-0.0961592 - 0.482186i) q^{57} +(0.0491035 + 1.03081i) q^{58} +(1.11402 + 5.78010i) q^{59} +(-1.36671 - 2.94238i) q^{60} +(5.16453 + 12.9004i) q^{61} +(3.87143 + 3.35461i) q^{62} +(7.35858 - 9.60944i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-1.17994 + 1.65699i) q^{65} +(-3.74415 + 3.97774i) q^{66} +(0.764768 + 1.48344i) q^{67} +(3.10808 - 5.38336i) q^{68} +(-7.62558 - 3.29402i) q^{69} +(3.77844 + 6.54445i) q^{70} +(-3.34355 + 5.20267i) q^{71} +(2.46594 + 1.70854i) q^{72} +(-2.82590 - 6.18785i) q^{73} +(0.0252493 + 0.104079i) q^{74} +(-2.48336 - 0.711837i) q^{75} +(-0.268259 + 0.0928454i) q^{76} +(7.86555 - 10.0019i) q^{77} +(0.166735 - 1.87359i) q^{78} +(-3.84453 - 1.33061i) q^{79} +(-1.57575 + 1.01267i) q^{80} +(5.40766 + 7.19425i) q^{81} +(6.10176 + 7.04180i) q^{82} +(5.72306 + 5.45693i) q^{83} +(-6.07403 - 3.45487i) q^{84} +(3.80821 + 11.0031i) q^{85} +(0.829316 + 1.16461i) q^{86} +(1.77085 + 0.242977i) q^{87} +(2.56908 + 1.82944i) q^{88} +(0.618498 + 4.30175i) q^{89} +(-5.44337 + 1.39504i) q^{90} +4.38138i q^{91} +(-1.28568 + 4.62029i) q^{92} +(6.93891 - 5.52953i) q^{93} +(9.83808 - 5.07188i) q^{94} +(0.197620 - 0.493631i) q^{95} +(0.783738 - 1.54459i) q^{96} +(-4.55644 + 1.10538i) q^{97} +(8.43835 + 3.85366i) q^{98} +(5.58714 + 7.63590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.998867	−	0.0475819i	−0.706306	−	0.0336455i
$2$	−0.998867	−	0.0475819i	−0.706306	−	0.0336455i
$3$	−0.397495	+	1.68582i	−0.229494	+	0.973310i
$3$	−0.397495	+	1.68582i	−0.229494	+	0.973310i
$4$	0.995472	+	0.0950560i	0.497736	+	0.0475280i
$5$	−1.35562	+	1.29258i	−0.606253	+	0.578061i	−0.929761	−	0.368164i	$-0.879986\pi$
$5$	−1.35562	+	1.29258i	−0.606253	+	0.578061i	0.323507	+	0.946226i	$0.395138\pi$
$6$	0.477260	−	1.66500i	0.194841	−	0.679733i
$7$	−0.763522	+	3.96153i	−0.288584	+	1.49732i	0.491078	+	0.871116i	$0.336603\pi$
$7$	−0.763522	+	3.96153i	−0.288584	+	1.49732i	−0.779662	+	0.626201i	$0.784609\pi$
$8$	−0.989821	−	0.142315i	−0.349955	−	0.0503159i
$9$	−2.68399	−	1.34021i	−0.894665	−	0.446738i
$10$	1.41559	−	1.22662i	0.447650	−	0.387891i
$11$	−2.80329	−	1.44520i	−0.845224	−	0.435743i	−0.0194945	−	0.999810i	$-0.506206\pi$
$11$	−2.80329	−	1.44520i	−0.845224	−	0.435743i	−0.825729	+	0.564067i	$0.809236\pi$
$12$	−0.555943	+	1.64040i	−0.160487	+	0.473544i
$13$	1.06637	−	0.205526i	0.295758	−	0.0570027i	−0.0392138	−	0.999231i	$-0.512485\pi$
$13$	1.06637	−	0.205526i	0.295758	−	0.0570027i	0.334972	+	0.942228i	$0.391273\pi$
$14$	0.951154	−	3.92071i	0.254207	−	1.04785i
$15$	−1.64021	−	2.79914i	−0.423501	−	0.722734i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	2.58229	−	5.65443i	0.626297	−	1.37140i	−0.284552	−	0.958661i	$-0.591845\pi$
$17$	2.58229	−	5.65443i	0.626297	−	1.37140i	0.910849	−	0.412739i	$-0.135428\pi$
$18$	2.61718	+	1.46640i	0.616876	+	0.345635i
$19$	−0.258219	+	0.117925i	−0.0592395	+	0.0270538i	−0.444814	−	0.895623i	$-0.646730\pi$
$19$	−0.258219	+	0.117925i	−0.0592395	+	0.0270538i	0.385575	+	0.922677i	$0.374003\pi$
$20$	−1.47235	+	1.15787i	−0.329228	+	0.258908i
$21$	−6.37493	−	2.86185i	−1.39112	−	0.624507i
$22$	2.73135	+	1.57695i	0.582326	+	0.336206i
$23$	−0.840668	+	4.72158i	−0.175291	+	0.984517i
$23$	−0.840668	+	4.72158i	−0.175291	+	0.984517i
$24$	0.633367	−	1.61209i	0.129285	−	0.329067i
$25$	−0.0709688	+	1.48982i	−0.0141938	+	0.297964i
$26$	−1.07494	+	0.154553i	−0.210813	+	0.0303104i
$27$	3.32624	−	3.99201i	0.640135	−	0.768263i
$28$	−1.13663	+	3.87101i	−0.214803	+	0.731552i
$29$	−0.0980958	−	1.02731i	−0.0182159	−	0.190766i	−1.00000		0.000764250i	$-0.999757\pi$
$29$	−0.0980958	−	1.02731i	−0.0182159	−	0.190766i	0.981784	−	0.190002i	$-0.0608493\pi$
$30$	1.50517	+	2.87401i	0.274805	+	0.524720i
$31$	−4.02666	−	3.16660i	−0.723210	−	0.568739i	0.187262	−	0.982310i	$-0.440039\pi$
$31$	−4.02666	−	3.16660i	−0.723210	−	0.568739i	−0.910472	+	0.413571i	$0.864281\pi$
$32$	−0.971812	−	0.235759i	−0.171794	−	0.0416767i
$33$	3.55064	−	4.15139i	0.618087	−	0.722664i
$34$	−2.84841	+	5.52515i	−0.488499	+	0.947556i
$35$	−4.08556	−	6.35726i	−0.690586	−	1.07457i
$36$	−2.54445	−	1.58927i	−0.424074	−	0.264879i
$37$	−0.0301730	−	0.102760i	−0.00496040	−	0.0168936i	0.956976	−	0.290168i	$-0.0937113\pi$
$37$	−0.0301730	−	0.102760i	−0.00496040	−	0.0168936i	−0.961936	+	0.273275i	$0.911893\pi$
$38$	0.263538	−	0.105505i	0.0427514	−	0.0171151i
$39$	−0.0773969	+	1.87941i	−0.0123934	+	0.300946i
$40$	1.52578	−	1.08650i	0.241247	−	0.171791i
$41$	−6.42991	−	6.74349i	−1.00418	−	1.05316i	−0.998585	−	0.0531726i	$-0.983067\pi$
$41$	−6.42991	−	6.74349i	−1.00418	−	1.05316i	−0.00559780	−	0.999984i	$-0.501782\pi$
$42$	6.23154	+	3.16194i	0.961548	+	0.487898i
$43$	−0.883792	−	1.12383i	−0.134777	−	0.171383i	0.713980	−	0.700166i	$-0.246891\pi$
$43$	−0.883792	−	1.12383i	−0.134777	−	0.171383i	−0.848757	+	0.528783i	$0.822648\pi$
$44$	−2.65322	−	1.70512i	−0.399988	−	0.257057i
$45$	5.37083	−	1.65247i	0.800636	−	0.246335i
$46$	1.06438	−	4.67623i	0.156934	−	0.689472i
$47$	−9.58561	+	5.53425i	−1.39820	+	0.807254i	−0.994204	−	0.107505i	$-0.965714\pi$
$47$	−9.58561	+	5.53425i	−1.39820	+	0.807254i	−0.404000	+	0.914759i	$0.632380\pi$
$48$	−0.709356	+	1.58013i	−0.102387	+	0.228072i
$49$	−8.61215	−	3.44779i	−1.23031	−	0.492541i
$50$	0.141777	−	1.48476i	0.0200503	−	0.209976i
$51$	8.50591	+	6.60089i	1.19107	+	0.924310i
$52$	1.08108	−	0.103230i	0.149919	−	0.0143155i
$53$	−2.33524	+	2.69502i	−0.320770	+	0.370189i	−0.893118	−	0.449822i	$-0.851487\pi$
$53$	−2.33524	+	2.69502i	−0.320770	+	0.370189i	0.572348	+	0.820011i	$0.306033\pi$
$54$	−3.51242	+	3.82922i	−0.477979	+	0.521091i
$55$	5.66824	−	1.66435i	0.764306	−	0.224420i
$56$	1.31953	−	3.81254i	0.176330	−	0.509473i
$57$	−0.0961592	−	0.482186i	−0.0127366	−	0.0638671i
$58$	0.0491035	+	1.03081i	0.00644761	+	0.135352i
$59$	1.11402	+	5.78010i	0.145033	+	0.752505i	0.979500	+	0.201446i	$0.0645640\pi$
$59$	1.11402	+	5.78010i	0.145033	+	0.752505i	−0.834466	+	0.551059i	$0.814224\pi$
$60$	−1.36671	−	2.94238i	−0.176442	−	0.379859i
$61$	5.16453	+	12.9004i	0.661250	+	1.65172i	0.754676	+	0.656098i	$0.227794\pi$
$61$	5.16453	+	12.9004i	0.661250	+	1.65172i	−0.0934256	+	0.995626i	$0.529782\pi$
$62$	3.87143	+	3.35461i	0.491672	+	0.426036i
$63$	7.35858	−	9.60944i	0.927094	−	1.21068i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−1.17994	+	1.65699i	−0.146353	+	0.205524i
$66$	−3.74415	+	3.97774i	−0.460873	+	0.489626i
$67$	0.764768	+	1.48344i	0.0934313	+	0.181231i	0.930920	−	0.365223i	$-0.119007\pi$
$67$	0.764768	+	1.48344i	0.0934313	+	0.181231i	−0.837489	+	0.546455i	$0.815977\pi$
$68$	3.10808	−	5.38336i	0.376911	−	0.652828i
$69$	−7.62558	−	3.29402i	−0.918012	−	0.396554i
$70$	3.77844	+	6.54445i	0.451610	+	0.782212i
$71$	−3.34355	+	5.20267i	−0.396807	+	0.617443i	−0.980962	−	0.194199i	$-0.937789\pi$
$71$	−3.34355	+	5.20267i	−0.396807	+	0.617443i	0.584156	+	0.811642i	$0.301426\pi$
$72$	2.46594	+	1.70854i	0.290614	+	0.201354i
$73$	−2.82590	−	6.18785i	−0.330746	−	0.724234i	0.669074	−	0.743196i	$-0.266691\pi$
$73$	−2.82590	−	6.18785i	−0.330746	−	0.724234i	−0.999820	+	0.0189624i	$0.993964\pi$
$74$	0.0252493	+	0.104079i	0.00293517	+	0.0120989i
$75$	−2.48336	−	0.711837i	−0.286754	−	0.0821959i
$76$	−0.268259	+	0.0928454i	−0.0307714	+	0.0106501i
$77$	7.86555	−	10.0019i	0.896363	−	1.13982i
$78$	0.166735	−	1.87359i	0.0188790	−	0.212143i
$79$	−3.84453	−	1.33061i	−0.432544	−	0.149705i	0.102116	−	0.994773i	$-0.467439\pi$
$79$	−3.84453	−	1.33061i	−0.432544	−	0.149705i	−0.534659	+	0.845068i	$0.679560\pi$
$80$	−1.57575	+	1.01267i	−0.176174	+	0.113220i
$81$	5.40766	+	7.19425i	0.600851	+	0.799361i
$82$	6.10176	+	7.04180i	0.673826	+	0.777637i
$83$	5.72306	+	5.45693i	0.628188	+	0.598976i	0.935798	−	0.352536i	$-0.114681\pi$
$83$	5.72306	+	5.45693i	0.628188	+	0.598976i	−0.307610	+	0.951512i	$0.599529\pi$
$84$	−6.07403	−	3.45487i	−0.662731	−	0.376957i
$85$	3.80821	+	11.0031i	0.413059	+	1.19345i
$86$	0.829316	+	1.16461i	0.0894275	+	0.125583i
$87$	1.77085	+	0.242977i	0.189855	+	0.0260499i
$88$	2.56908	+	1.82944i	0.273865	+	0.195019i
$89$	0.618498	+	4.30175i	0.0655606	+	0.455984i	0.995986	+	0.0895039i	$0.0285282\pi$
$89$	0.618498	+	4.30175i	0.0655606	+	0.455984i	−0.930426	+	0.366480i	$0.880563\pi$
$90$	−5.44337	+	1.39504i	−0.573782	+	0.147050i
$91$			4.38138i			0.459293i
$92$	−1.28568	+	4.62029i	−0.134041	+	0.481698i
$93$	6.93891	−	5.52953i	0.719531	−	0.573385i
$94$	9.83808	−	5.07188i	1.01472	−	0.523125i
$95$	0.197620	−	0.493631i	0.0202754	−	0.0506455i
$96$	0.783738	−	1.54459i	0.0799900	−	0.157644i
$97$	−4.55644	+	1.10538i	−0.462636	+	0.112234i	−0.460301	−	0.887763i	$-0.652259\pi$
$97$	−4.55644	+	1.10538i	−0.462636	+	0.112234i	−0.00233542	+	0.999997i	$0.500743\pi$
$98$	8.43835	+	3.85366i	0.852402	+	0.389279i
$99$	5.58714	+	7.63590i	0.561529	+	0.767437i
$100$	−0.212264	+	1.47633i	−0.0212264	+	0.147633i
$101$	−9.30447	+	9.75825i	−0.925830	+	0.970982i	−0.999654	−	0.0262891i	$-0.991631\pi$
$101$	−9.30447	+	9.75825i	−0.925830	+	0.970982i	0.0738248	+	0.997271i	$0.476479\pi$
$102$	−8.18219	−	6.99814i	−0.810158	−	0.692919i
$103$	14.7309	−	0.701718i	1.45148	−	0.0691423i	0.693044	−	0.720895i	$-0.256269\pi$
$103$	14.7309	−	0.701718i	1.45148	−	0.0691423i	0.758432	+	0.651753i	$0.225966\pi$
$104$	−1.08477	+	0.0516737i	−0.106370	+	0.00506703i
$105$	12.3412	−	4.36055i	1.20438	−	0.425546i
$106$	2.46083	−	2.58085i	0.239017	−	0.250674i
$107$	−2.39822	+	16.6800i	−0.231844	+	1.61251i	0.458270	+	0.888813i	$0.348469\pi$
$107$	−2.39822	+	16.6800i	−0.231844	+	1.61251i	−0.690114	+	0.723701i	$0.742440\pi$
$108$	3.69064	−	3.65776i	0.355132	−	0.351968i
$109$	−12.4140	−	5.66926i	−1.18904	−	0.543017i	−0.280112	−	0.959967i	$-0.590372\pi$
$109$	−12.4140	−	5.66926i	−1.18904	−	0.543017i	−0.908929	+	0.416950i	$0.863099\pi$
$110$	−5.74102	+	1.39276i	−0.547384	+	0.132794i
$111$	0.185228	−	0.0100198i	0.0175811	−	0.000951034i
$112$	−1.49945	+	3.74544i	−0.141684	+	0.353911i
$113$	14.4505	−	7.44977i	1.35939	−	0.700816i	0.384424	−	0.923157i	$-0.374400\pi$
$113$	14.4505	−	7.44977i	1.35939	−	0.700816i	0.974969	+	0.222341i	$0.0713698\pi$
$114$	0.0731070	+	0.486215i	0.00684709	+	0.0455382i
$115$	−4.96341	−	7.48732i	−0.462840	−	0.698196i
$116$		−	1.03198i		−	0.0958168i
$117$	−3.13758	−	0.877533i	−0.290069	−	0.0811279i
$118$	−0.837733	−	5.82656i	−0.0771195	−	0.536378i
$119$	20.4285	+	14.5471i	1.87268	+	1.33353i
$120$	1.22516	+	3.00407i	0.111841	+	0.274233i
$121$	−0.610787	−	0.857730i	−0.0555261	−	0.0779755i
$122$	−4.54486	−	13.1315i	−0.411472	−	1.18887i
$123$	13.9242	−	8.15918i	1.25550	−	0.735688i
$124$	−3.70743	−	3.53502i	−0.332937	−	0.317454i
$125$	−7.96260	−	9.18933i	−0.712196	−	0.821918i
$126$	−7.80748	+	9.24842i	−0.695546	+	0.823914i
$127$	12.7333	−	8.18322i	1.12990	−	0.726144i	0.164362	−	0.986400i	$-0.447443\pi$
$127$	12.7333	−	8.18322i	1.12990	−	0.726144i	0.965540	+	0.260256i	$0.0838071\pi$
$128$	−0.945001	−	0.327068i	−0.0835271	−	0.0289090i
$129$	2.24588	−	1.04320i	0.197739	−	0.0918484i
$130$	1.25744	−	1.59897i	0.110285	−	0.140239i
$131$	11.0825	−	3.83569i	0.968283	−	0.335126i	0.203257	−	0.979125i	$-0.434847\pi$
$131$	11.0825	−	3.83569i	0.968283	−	0.335126i	0.765026	+	0.643999i	$0.222726\pi$
$132$	3.92918	−	3.79508i	0.341991	−	0.330319i
$133$	−0.270006	−	1.11298i	−0.0234125	−	0.0965076i
$134$	−0.693317	−	1.51815i	−0.0598934	−	0.131148i
$135$	0.650885	+	9.71111i	0.0560192	+	0.835799i
$136$	−3.36071	+	5.22937i	−0.288179	+	0.448415i
$137$	−2.52739	−	4.37757i	−0.215930	−	0.374001i	0.737630	−	0.675205i	$-0.235945\pi$
$137$	−2.52739	−	4.37757i	−0.215930	−	0.374001i	−0.953560	+	0.301204i	$0.902612\pi$
$138$	7.46020	+	3.65313i	0.635055	+	0.310975i
$139$	−9.89095	+	17.1316i	−0.838939	+	1.45309i	0.0518435	+	0.998655i	$0.483490\pi$
$139$	−9.89095	+	17.1316i	−0.838939	+	1.45309i	−0.890783	+	0.454430i	$0.849843\pi$
$140$	−3.46277	−	6.71683i	−0.292657	−	0.567676i
$141$	−5.51953	−	18.3595i	−0.464828	−	1.54615i
$142$	3.58732	−	5.03768i	0.301041	−	0.422753i
$143$	−3.28637	−	0.964965i	−0.274820	−	0.0806944i
$144$	−2.38185	−	1.82394i	−0.198488	−	0.151995i
$145$	1.46086	+	1.26584i	0.121318	+	0.105123i
$146$	2.52827	+	6.31531i	0.209241	+	0.522659i
$147$	9.23565	−	13.1481i	0.761743	−	1.08444i
$148$	−0.0202684	−	0.105162i	−0.00166605	−	0.00864430i
$149$	0.441829	+	9.27514i	0.0361961	+	0.759849i	0.941891	+	0.335919i	$0.109047\pi$
$149$	0.441829	+	9.27514i	0.0361961	+	0.759849i	−0.905695	+	0.423930i	$0.860650\pi$
$150$	2.44668	+	0.829194i	0.199770	+	0.0677034i
$151$	3.31497	−	9.57798i	0.269769	−	0.779445i	−0.726012	−	0.687682i	$-0.758628\pi$
$151$	3.31497	−	9.57798i	0.269769	−	0.779445i	0.995781	−	0.0917635i	$-0.0292504\pi$
$152$	0.272373	−	0.0799760i	0.0220924	−	0.00648691i
$153$	−14.5090	+	11.7156i	−1.17298	+	0.947153i
$154$	−8.33255	+	9.61628i	−0.671456	+	0.774902i
$155$	9.55174	−	0.912081i	0.767214	−	0.0732601i
$156$	−0.255695	+	1.86354i	−0.0204720	+	0.149203i
$157$	−2.02719	+	21.2297i	−0.161787	+	1.69431i	0.441878	+	0.897075i	$0.354312\pi$
$157$	−2.02719	+	21.2297i	−0.161787	+	1.69431i	−0.603665	+	0.797238i	$0.706294\pi$
$158$	3.77687	+	1.51203i	0.300471	+	0.120291i
$159$	−3.61507	−	5.00806i	−0.286694	−	0.397165i
$160$	1.62215	−	0.936548i	0.128242	−	0.0740406i
$161$	−18.0628	−	6.93535i	−1.42355	−	0.546582i
$162$	−5.05922	−	7.44341i	−0.397489	−	0.584809i
$163$	0.778196	+	0.500116i	0.0609530	+	0.0391721i	0.570762	−	0.821115i	$-0.306648\pi$
$163$	0.778196	+	0.500116i	0.0609530	+	0.0391721i	−0.509809	+	0.860287i	$0.670284\pi$
$164$	−5.75978	−	7.32416i	−0.449764	−	0.571921i
$165$	0.552692	+	10.2172i	0.0430270	+	0.795410i
$166$	−5.45693	−	5.72306i	−0.423540	−	0.444196i
$167$	−9.70265	+	6.90923i	−0.750814	+	0.534652i	−0.890191	−	0.455587i	$-0.849429\pi$
$167$	−9.70265	+	6.90923i	−0.750814	+	0.534652i	0.139377	+	0.990239i	$0.455490\pi$
$168$	5.90276	+	3.73997i	0.455408	+	0.288545i
$169$	−10.9739	+	4.39328i	−0.844145	+	0.337944i
$170$	−3.28035	−	11.1718i	−0.251591	−	0.856841i
$171$	0.851103	+	0.0295593i	0.0650855	+	0.00226046i
$172$	−0.772963	−	1.20275i	−0.0589378	−	0.0917091i
$173$	3.89275	−	7.55088i	0.295960	−	0.574082i	−0.693231	−	0.720716i	$-0.743813\pi$
$173$	3.89275	−	7.55088i	0.295960	−	0.574082i	0.989191	+	0.146633i	$0.0468437\pi$
$174$	−1.75728	−	0.326962i	−0.133219	−	0.0247869i
$175$	−5.84777	−	1.41865i	−0.442050	−	0.107240i
$176$	−2.47913	−	1.94961i	−0.186871	−	0.146957i
$177$	−10.1870	−	0.419518i	−0.765705	−	0.0315329i
$178$	−0.413112	−	4.32630i	−0.0309640	−	0.324270i
$179$	0.585242	−	1.99315i	0.0437431	−	0.148975i	−0.934726	−	0.355370i	$-0.884355\pi$
$179$	0.585242	−	1.99315i	0.0437431	−	0.148975i	0.978469	+	0.206395i	$0.0661731\pi$
$180$	5.50358	−	1.13445i	0.410213	−	0.0845572i
$181$	−19.6631	+	2.82713i	−1.46155	+	0.210139i	−0.826763	−	0.562550i	$-0.809820\pi$
$181$	−19.6631	+	2.82713i	−1.46155	+	0.210139i	−0.634785	+	0.772689i	$0.718911\pi$
$182$	0.208474	−	4.37641i	0.0154531	−	0.324401i
$183$	−23.8006	+	3.57864i	−1.75939	+	0.264541i
$184$	1.50406	−	4.55388i	0.110881	−	0.335716i
$185$	0.173729	+	0.100302i	0.0127728	+	0.00737437i
$186$	−7.19416	+	5.19310i	−0.527501	+	0.380776i
$187$	−15.4107	+	12.1191i	−1.12694	+	0.886235i
$188$	−10.0683	+	4.59802i	−0.734304	+	0.335345i
$189$	13.2748	+	16.2250i	0.965600	+	1.18019i
$190$	−0.220884	+	0.483669i	−0.0160246	+	0.0350891i
$191$	17.0256	+	3.28141i	1.23193	+	0.237434i	0.763348	−	0.645988i	$-0.223554\pi$
$191$	17.0256	+	3.28141i	1.23193	+	0.237434i	0.468578	+	0.883422i	$0.344766\pi$
$192$	−0.856345	+	1.50555i	−0.0618014	+	0.108654i
$193$	4.50386	−	18.5652i	0.324195	−	1.33635i	−0.543565	−	0.839367i	$-0.682926\pi$
$193$	4.50386	−	18.5652i	0.324195	−	1.33635i	0.867760	−	0.496983i	$-0.165559\pi$
$194$	4.60388	−	0.887324i	0.330539	−	0.0637062i
$195$	−2.32437	−	2.64781i	−0.166452	−	0.189614i
$196$	−8.24542	−	4.25081i	−0.588959	−	0.303629i
$197$	3.51908	−	3.04930i	0.250724	−	0.217254i	−0.520426	−	0.853907i	$-0.674227\pi$
$197$	3.51908	−	3.04930i	0.250724	−	0.217254i	0.771151	+	0.636653i	$0.219681\pi$
$198$	−5.21748	−	7.89310i	−0.370790	−	0.560938i
$199$	−2.51128	−	0.361067i	−0.178020	−	0.0255954i	0.0527284	−	0.998609i	$-0.483208\pi$
$199$	−2.51128	−	0.361067i	−0.178020	−	0.0255954i	−0.230748	+	0.973014i	$0.574117\pi$
$200$	0.282270	−	1.46456i	0.0199595	−	0.103560i
$201$	−2.80481	+	0.699601i	−0.197836	+	0.0493461i
$202$	9.75825	−	9.30447i	0.686588	−	0.654660i
$203$	4.14460	+	0.395761i	0.290894	+	0.0277770i
$204$	7.83994	+	7.37954i	0.548906	+	0.516671i
$205$	17.4331	+	0.830440i	1.21758	+	0.0580004i
$206$	−14.7476			−1.02751
$207$	8.58427	−	11.5460i	0.596648	−	0.802503i
$208$	1.08600			0.0753002
$209$	0.894287	+	0.0426001i	0.0618591	+	0.00294671i
$210$	−12.5347	+	3.76839i	−0.864977	+	0.260044i
$211$	−22.5804	−	2.15617i	−1.55450	−	0.148437i	−0.717860	−	0.696187i	$-0.754878\pi$
$211$	−22.5804	−	2.15617i	−1.55450	−	0.148437i	−0.836642	+	0.547750i	$0.815484\pi$
$212$	−2.58085	+	2.46083i	−0.177253	+	0.169011i
$213$	−7.44173	−	7.70467i	−0.509899	−	0.527915i
$214$	3.18917	−	16.5470i	0.218007	−	1.13113i
$215$	2.65074	+	0.381119i	0.180779	+	0.0259921i
$216$	−3.86050	+	3.47800i	−0.262674	+	0.236648i
$217$	15.6190	−	13.5340i	1.06029	−	0.918745i
$218$	12.1301	+	6.25352i	0.821557	+	0.423542i
$219$	11.5549	−	2.30432i	0.780808	−	0.155711i
$220$	5.80078	−	1.11801i	0.391089	−	0.0753762i
$221$	1.59155	−	6.56044i	0.107059	−	0.441303i
$222$	−0.185495	+	0.00119490i	−0.0124496	+	8.01965e-5i
$223$	−25.2717	−	4.87072i	−1.69232	−	0.326168i	−0.750140	−	0.661279i	$-0.770014\pi$
$223$	−25.2717	−	4.87072i	−1.69232	−	0.326168i	−0.942179	+	0.335111i	$0.891226\pi$
$224$	1.67596	−	3.66985i	0.111980	−	0.245202i
$225$	2.18716	−	3.90355i	0.145810	−	0.260237i
$226$	−14.7886	+	6.75375i	−0.983726	+	0.449253i
$227$	−17.9218	+	14.0939i	−1.18951	+	0.935443i	−0.998931	−	0.0462282i	$-0.985280\pi$
$227$	−17.9218	+	14.0939i	−1.18951	+	0.935443i	−0.190582	+	0.981671i	$0.561037\pi$
$228$	−0.0498891	−	0.489143i	−0.00330399	−	0.0323943i
$229$	9.82640	+	5.67327i	0.649346	+	0.374900i	0.788206	−	0.615412i	$-0.211010\pi$
$229$	9.82640	+	5.67327i	0.649346	+	0.374900i	−0.138859	+	0.990312i	$0.544344\pi$
$230$	4.60152	+	7.71500i	0.303416	+	0.508712i
$231$	13.7348	+	17.2356i	0.903687	+	1.13402i
$232$	−0.0491035	+	1.03081i	−0.00322380	+	0.0676760i
$233$	−23.5025	+	3.37915i	−1.53970	+	0.221376i	−0.859303	−	0.511467i	$-0.829102\pi$
$233$	−23.5025	+	3.37915i	−1.53970	+	0.221376i	−0.680398	+	0.732842i	$0.738193\pi$
$234$	3.09227	+	1.02583i	0.202148	+	0.0670607i
$235$	5.84099	−	19.8926i	0.381024	−	1.29765i
$236$	0.559545	+	5.85982i	0.0364233	+	0.381442i
$237$	3.77135	−	5.95229i	0.244975	−	0.386643i
$238$	−19.7132	−	15.5026i	−1.27782	−	1.00489i
$239$	14.5592	+	3.53201i	0.941754	+	0.228467i	0.677112	−	0.735880i	$-0.263231\pi$
$239$	14.5592	+	3.53201i	0.941754	+	0.228467i	0.264642	+	0.964347i	$0.414746\pi$
$240$	−1.08083	−	3.05897i	−0.0697675	−	0.197455i
$241$	9.73280	−	18.8790i	0.626945	−	1.21610i	−0.334834	−	0.942277i	$-0.608680\pi$
$241$	9.73280	−	18.8790i	0.626945	−	1.21610i	0.961779	−	0.273826i	$-0.0882893\pi$
$242$	0.569282	+	0.885821i	0.0365949	+	0.0569427i
$243$	−14.2777	+	6.25667i	−0.915918	+	0.401365i
$244$	3.91489	+	13.3329i	0.250625	+	0.853550i
$245$	16.1314	−	6.45804i	1.03060	−	0.412589i
$246$	−14.2967	+	7.48740i	−0.911521	+	0.477379i
$247$	−0.251120	+	0.178822i	−0.0159784	+	0.0113782i
$248$	3.53502	+	3.70743i	0.224474	+	0.235422i
$249$	−11.4743	+	7.47897i	−0.727155	+	0.473960i
$250$	7.51633	+	9.55780i	0.475375	+	0.604488i
$251$	2.19838	+	1.41281i	0.138761	+	0.0891760i	0.608179	−	0.793800i	$-0.291900\pi$
$251$	2.19838	+	1.41281i	0.138761	+	0.0891760i	−0.469419	+	0.882976i	$0.655537\pi$
$252$	8.23869	−	8.86645i	0.518989	−	0.558534i
$253$	9.18024	−	12.0210i	0.577157	−	0.755755i
$254$	−13.1083	+	7.56808i	−0.822488	+	0.474863i
$255$	−20.0630	+	2.04629i	−1.25640	+	0.128143i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	−2.53551	+	26.5531i	−0.158161	+	1.65633i	0.473281	+	0.880911i	$0.343069\pi$
$257$	−2.53551	+	26.5531i	−0.158161	+	1.65633i	−0.631442	+	0.775423i	$0.717537\pi$
$258$	−2.29298	+	0.935152i	−0.142755	+	0.0582200i
$259$	0.430123	−	0.0410717i	0.0267265	−	0.00255207i
$260$	−1.33210	+	1.53733i	−0.0826134	+	0.0953409i
$261$	−1.11352	+	2.88875i	−0.0689252	+	0.178809i
$262$	−11.2525	+	3.30402i	−0.695179	+	0.204123i
$263$	3.57467	−	10.3283i	0.220424	−	0.636872i	−0.779521	−	0.626376i	$-0.784538\pi$
$263$	3.57467	−	10.3283i	0.220424	−	0.636872i	0.999945	−	0.0104966i	$-0.00334124\pi$
$264$	−4.10530	+	3.60383i	−0.252664	+	0.221800i
$265$	−0.317823	−	6.67193i	−0.0195237	−	0.409853i
$266$	0.216742	+	1.12457i	0.0132893	+	0.0689516i
$267$	−7.49783	−	0.667247i	−0.458860	−	0.0408348i
$268$	0.620295	+	1.54942i	0.0378905	+	0.0946460i
$269$	17.7170	+	15.3518i	1.08022	+	0.936018i	0.998162	−	0.0606093i	$-0.0193044\pi$
$269$	17.7170	+	15.3518i	1.08022	+	0.936018i	0.0820609	+	0.996627i	$0.473850\pi$
$270$	−0.188074	−	9.73108i	−0.0114458	−	0.592215i
$271$	17.1977	+	5.04969i	1.04468	+	0.306747i	0.758668	−	0.651478i	$-0.225851\pi$
$271$	17.1977	+	5.04969i	1.04468	+	0.306747i	0.286017	+	0.958225i	$0.407669\pi$
$272$	3.60573	−	5.06354i	0.218630	−	0.307022i
$273$	−7.38622	−	1.74158i	−0.447035	−	0.105405i
$274$	2.31624	+	4.49287i	0.139929	+	0.271424i
$275$	2.35203	−	4.07383i	0.141833	−	0.245661i
$276$	−7.27793	−	4.00396i	−0.438080	−	0.241010i
$277$	1.77074	+	3.06701i	0.106394	+	0.184279i	0.914307	−	0.405023i	$-0.132736\pi$
$277$	1.77074	+	3.06701i	0.106394	+	0.184279i	−0.807913	+	0.589302i	$0.799403\pi$
$278$	10.6949	−	16.6416i	0.641437	−	0.998096i
$279$	6.56362	+	13.8957i	0.392954	+	0.831916i
$280$	3.13924	+	6.87398i	0.187606	+	0.410799i
$281$	3.62177	+	14.9292i	0.216057	+	0.890599i	0.971814	+	0.235747i	$0.0757537\pi$
$281$	3.62177	+	14.9292i	0.216057	+	0.890599i	−0.755757	+	0.654852i	$0.772731\pi$
$282$	4.63970	+	18.6013i	0.276290	+	1.10769i
$283$	24.0110	−	8.31028i	1.42731	−	0.493995i	0.499256	−	0.866454i	$-0.333607\pi$
$283$	24.0110	−	8.31028i	1.42731	−	0.493995i	0.928049	+	0.372459i	$0.121485\pi$
$284$	−3.82296	+	4.86129i	−0.226851	+	0.288464i
$285$	0.753622	+	0.529369i	0.0446407	+	0.0313571i
$286$	3.23673	+	1.12024i	0.191392	+	0.0662414i
$287$	31.6239	−	20.3235i	1.86670	−	1.19966i
$288$	2.29237	+	1.93521i	0.135079	+	0.114033i
$289$	−14.1717	−	16.3550i	−0.833628	−	0.962058i
$290$	−1.39897	−	1.33392i	−0.0821506	−	0.0783305i
$291$	−0.0523112	−	8.12073i	−0.00306654	−	0.476046i
$292$	−2.22491	−	6.42845i	−0.130203	−	0.376197i
$293$	2.96978	+	4.17047i	0.173496	+	0.243641i	0.892163	−	0.451713i	$-0.149187\pi$
$293$	2.96978	+	4.17047i	0.173496	+	0.243641i	−0.718667	+	0.695354i	$0.755247\pi$
$294$	−9.85080	+	12.6937i	−0.574510	+	0.740314i
$295$	−8.98146	−	6.39567i	−0.522921	−	0.372370i
$296$	0.0152416	+	0.106008i	0.000885901	+	0.00616158i
$297$	−15.0936	+	6.38369i	−0.875822	+	0.370420i
$298$		−	9.28566i		−	0.537904i
$299$	0.0739434	+	5.20773i	0.00427626	+	0.301171i
$300$	−2.40445	−	0.944672i	−0.138821	−	0.0545407i
$301$	5.12689	−	2.64309i	0.295509	−	0.152345i
$302$	−3.76696	+	9.40940i	−0.216764	+	0.541450i
$303$	−12.7522	−	19.5645i	−0.732594	−	1.12395i
$304$	−0.275870	+	0.0669254i	−0.0158222	+	0.00383843i
$305$	−23.6760	−	10.8125i	−1.35568	−	0.619120i
$306$	15.0500	−	11.0120i	0.860352	−	0.629514i
$307$	−2.73208	+	19.0020i	−0.155928	+	1.08450i	0.750113	+	0.661310i	$0.229999\pi$
$307$	−2.73208	+	19.0020i	−0.155928	+	1.08450i	−0.906040	+	0.423191i	$0.860910\pi$
$308$	8.78068	−	9.20891i	0.500326	−	0.524726i
$309$	−4.67248	+	25.1126i	−0.265808	+	1.42860i
$310$	−9.58432	+	0.456558i	−0.544353	+	0.0259307i
$311$	−1.88248	+	0.0896734i	−0.106745	+	0.00508491i	−0.100887	−	0.994898i	$-0.532168\pi$
$311$	−1.88248	+	0.0896734i	−0.106745	+	0.00508491i	−0.00585878	+	0.999983i	$0.501865\pi$
$312$	0.344076	−	1.84926i	0.0194795	−	0.104694i
$313$	16.1889	−	16.9784i	0.915049	−	0.959675i	−0.0842753	−	0.996443i	$-0.526858\pi$
$313$	16.1889	−	16.9784i	0.915049	−	0.959675i	0.999324	+	0.0367672i	$0.0117060\pi$
$314$	3.03504	−	21.1092i	0.171277	−	1.19126i
$315$	2.44554	+	22.5384i	0.137791	+	1.26989i
$316$	−3.70064	−	1.69003i	−0.208177	−	0.0950714i
$317$	13.5771	−	3.29378i	0.762568	−	0.184997i	0.164428	−	0.986389i	$-0.447422\pi$
$317$	13.5771	−	3.29378i	0.762568	−	0.184997i	0.598139	+	0.801392i	$0.295907\pi$
$318$	3.37268	+	5.17440i	0.189131	+	0.290166i
$319$	−1.20967	+	3.02160i	−0.0677284	+	0.169177i
$320$	−1.66487	+	0.858303i	−0.0930693	+	0.0479806i
$321$	−27.1662	−	10.6732i	−1.51627	−	0.595719i
$322$	17.7123	+	7.78696i	0.987069	+	0.433950i
$323$			1.76460i			0.0981848i
$324$	4.69931	+	7.67571i	0.261073	+	0.426428i
$325$	0.230518	+	1.60328i	0.0127868	+	0.0889342i
$326$	−0.753518	−	0.536578i	−0.0417335	−	0.0297183i
$327$	14.4919	−	18.6742i	0.801402	−	1.03269i
$328$	5.40476	+	7.58993i	0.298428	+	0.419084i
$329$	−14.6053	−	42.1992i	−0.805215	−	2.32651i
$330$	−0.0659110	−	10.2319i	−0.00362828	−	0.563250i
$331$	−20.9550	−	19.9805i	−1.15179	−	1.09823i	−0.993845	−	0.110782i	$-0.964665\pi$
$331$	−20.9550	−	19.9805i	−1.15179	−	1.09823i	−0.157945	−	0.987448i	$-0.550487\pi$
$332$	5.17844	+	5.97623i	0.284204	+	0.327988i
$333$	−0.0567358	+	0.316245i	−0.00310910	+	0.0173301i
$334$	10.0204	−	6.43973i	0.548293	−	0.352366i
$335$	−2.95421	−	1.02246i	−0.161406	−	0.0558631i
$336$	−5.71812	−	4.01660i	−0.311949	−	0.219123i
$337$	0.700748	−	0.891074i	0.0381722	−	0.0485399i	−0.766592	−	0.642134i	$-0.778049\pi$
$337$	0.700748	−	0.891074i	0.0381722	−	0.0485399i	0.804764	+	0.593594i	$0.202292\pi$
$338$	11.1705	−	3.86614i	0.607595	−	0.210291i
$339$	6.81497	+	27.3223i	0.370138	+	1.48394i
$340$	2.74506	+	11.3153i	0.148872	+	0.613657i
$341$	6.71154	+	14.6962i	0.363450	+	0.795845i
$342$	−0.848732	−	0.0700230i	−0.0458942	−	0.00378641i
$343$	4.96580	−	7.72694i	0.268128	−	0.417215i
$344$	0.714858	+	1.23817i	0.0385426	+	0.0667577i
$345$	14.5952	−	5.39125i	0.785780	−	0.290255i
$346$	−4.24762	+	7.35710i	−0.228354	+	0.395520i
$347$	1.48317	+	2.87694i	0.0796206	+	0.154442i	0.925285	−	0.379273i	$-0.123826\pi$
$347$	1.48317	+	2.87694i	0.0796206	+	0.154442i	−0.845664	+	0.533715i	$0.820795\pi$
$348$	1.73973	+	0.410207i	0.0932595	+	0.0219894i
$349$	16.3279	−	22.9293i	0.874011	−	1.22738i	−0.0986439	−	0.995123i	$-0.531450\pi$
$349$	16.3279	−	22.9293i	0.874011	−	1.22738i	0.972655	−	0.232254i	$-0.0746101\pi$
$350$	5.77365	+	1.69530i	0.308614	+	0.0906174i
$351$	2.72654	−	4.94059i	0.145532	−	0.263709i
$352$	2.38355	+	2.06536i	0.127044	+	0.110084i
$353$	−2.36337	−	5.90342i	−0.125790	−	0.314207i	0.852084	−	0.523406i	$-0.175339\pi$
$353$	−2.36337	−	5.90342i	−0.125790	−	0.314207i	−0.977873	+	0.209199i	$0.932915\pi$
$354$	10.1555	+	0.903762i	0.539761	+	0.0480344i
$355$	−2.19229	−	11.3747i	−0.116355	−	0.603706i
$356$	0.206790	+	4.34106i	0.0109599	+	0.230076i
$357$	−32.6441	+	28.6565i	−1.72771	+	1.51666i
$358$	−0.679418	+	1.96305i	−0.0359083	+	0.103750i
$359$	11.2402	−	3.30042i	0.593235	−	0.174189i	0.0286849	−	0.999589i	$-0.490868\pi$
$359$	11.2402	−	3.30042i	0.593235	−	0.174189i	0.564550	+	0.825399i	$0.309050\pi$
$360$	−5.55133	+	0.871298i	−0.292581	+	0.0459214i
$361$	−12.3896	+	14.2983i	−0.652083	+	0.752544i
$362$	19.7754	−	1.88832i	1.03937	−	0.0992478i
$363$	1.68877	−	0.688734i	0.0886372	−	0.0361492i
$364$	−0.416476	+	4.36154i	−0.0218293	+	0.228607i
$365$	11.8292	+	4.73569i	0.619168	+	0.247877i
$366$	23.9439	−	2.44211i	1.25157	−	0.127651i
$367$	3.13419	−	1.80953i	0.163604	−	0.0944565i	−0.415963	−	0.909382i	$-0.636555\pi$
$367$	3.13419	−	1.80953i	0.163604	−	0.0944565i	0.579566	+	0.814925i	$0.303222\pi$
$368$	−1.71904	+	4.47715i	−0.0896112	+	0.233388i
$369$	8.22012	+	26.7170i	0.427922	+	1.39083i
$370$	−0.168759	−	0.108455i	−0.00877338	−	0.00563831i
$371$	−8.89337	−	11.3088i	−0.461721	−	0.587125i
$372$	7.43310	−	4.84491i	0.385389	−	0.251197i
$373$	18.7793	+	19.6952i	0.972357	+	1.01978i	0.999797	+	0.0201553i	$0.00641607\pi$
$373$	18.7793	+	19.6952i	0.972357	+	1.01978i	−0.0274398	+	0.999623i	$0.508735\pi$
$374$	15.9699	−	11.3721i	0.825782	−	0.588036i
$375$	18.6567	−	9.77081i	0.963426	−	0.504563i
$376$	10.2756	−	4.11375i	0.529926	−	0.212150i
$377$	−0.315744	−	1.07533i	−0.0162617	−	0.0553822i
$378$	−12.4877	−	16.8382i	−0.642301	−	0.866065i
$379$	10.8494	+	16.8819i	0.557295	+	0.867167i	0.999558	−	0.0297178i	$-0.00946086\pi$
$379$	10.8494	+	16.8819i	0.557295	+	0.867167i	−0.442264	+	0.896885i	$0.645825\pi$
$380$	0.243648	−	0.472611i	0.0124989	−	0.0242444i
$381$	8.73402	+	24.7190i	0.447457	+	1.26639i
$382$	−16.8501	−	4.08780i	−0.862128	−	0.209150i
$383$	−11.5948	−	9.11825i	−0.592466	−	0.465921i	0.276349	−	0.961057i	$-0.410876\pi$
$383$	−11.5948	−	9.11825i	−0.592466	−	0.465921i	−0.868815	+	0.495137i	$0.835118\pi$
$384$	0.927012	−	1.46310i	0.0473064	−	0.0746633i
$385$	2.26553	+	23.7257i	0.115462	+	1.20917i
$386$	−5.38212	+	18.3298i	−0.273943	+	0.932964i
$387$	0.865917	+	4.20083i	0.0440170	+	0.213540i
$388$	−4.64088	+	0.667258i	−0.235605	+	0.0338749i
$389$	0.663769	−	13.9342i	0.0336544	−	0.706493i	−0.917492	−	0.397754i	$-0.869790\pi$
$389$	0.663769	−	13.9342i	0.0336544	−	0.706493i	0.951147	−	0.308740i	$-0.0999071\pi$
$390$	2.19575	+	2.75541i	0.111186	+	0.139526i
$391$	24.5270	+	16.9460i	1.24038	+	0.856995i
$392$	8.03382	+	4.63833i	0.405769	+	0.234271i
$393$	2.06105	+	20.2078i	0.103966	+	1.01935i
$394$	−3.66019	+	2.87841i	−0.184398	+	0.145012i
$395$	6.93166	−	3.16558i	0.348770	−	0.159278i
$396$	4.83601	+	8.13242i	0.243018	+	0.408669i
$397$	−11.5002	+	25.1820i	−0.577181	+	1.26385i	0.365704	+	0.930731i	$0.380828\pi$
$397$	−11.5002	+	25.1820i	−0.577181	+	1.26385i	−0.942885	+	0.333118i	$0.891899\pi$
$398$	2.49125	+	0.480149i	0.124875	+	0.0240677i
$399$	1.98361	−	0.0127778i	0.0993048	−	0.000639690i
$400$	−0.351637	+	1.44947i	−0.0175818	+	0.0724733i
$401$	−0.727852	+	0.140282i	−0.0363472	+	0.00700535i	−0.207392	−	0.978258i	$-0.566498\pi$
$401$	−0.727852	+	0.140282i	−0.0363472	+	0.00700535i	0.171045	+	0.985263i	$0.445286\pi$
$402$	2.83492	−	0.565350i	0.141393	−	0.0281971i
$403$	−4.94473	−	2.54919i	−0.246315	−	0.126984i
$404$	−10.1899	+	8.82962i	−0.506968	+	0.439290i
$405$	−16.6299	−	2.76284i	−0.826348	−	0.137287i
$406$	−4.12107	−	0.592521i	−0.204525	−	0.0294063i
$407$	−0.0639243	+	0.331671i	−0.00316861	+	0.0164403i
$408$	−7.47993	−	7.74422i	−0.370312	−	0.383396i
$409$	2.47181	−	2.35686i	0.122223	−	0.116539i	−0.626503	−	0.779419i	$-0.715514\pi$
$409$	2.47181	−	2.35686i	0.122223	−	0.116539i	0.748726	+	0.662880i	$0.230666\pi$
$410$	−17.3738	−	1.65900i	−0.858032	−	0.0819321i
$411$	8.38444	−	2.52067i	0.413574	−	0.124336i
$412$	14.7309	+	0.701718i	0.725738	+	0.0345712i
$413$	−23.7486			−1.16859
$414$	−9.12393	+	11.1245i	−0.448416	+	0.546738i
$415$	−14.8119			−0.727086
$416$	−1.08477	−	0.0516737i	−0.0531850	−	0.00253351i
$417$	−24.9493	−	23.4841i	−1.22177	−	1.15002i
$418$	−0.891247	−	0.0851038i	−0.0435923	−	0.00416256i
$419$	−12.7921	+	12.1972i	−0.624935	+	0.595874i	−0.934916	−	0.354869i	$-0.884526\pi$
$419$	−12.7921	+	12.1972i	−0.624935	+	0.595874i	0.309982	+	0.950743i	$0.399677\pi$
$420$	12.6998	−	3.16770i	0.619687	−	0.154568i
$421$	−0.119558	+	0.620327i	−0.00582691	+	0.0302329i	−0.984726	−	0.174112i	$-0.944294\pi$
$421$	−0.119558	+	0.620327i	−0.00582691	+	0.0302329i	0.978899	+	0.204345i	$0.0655065\pi$
$422$	22.4523	+	3.22815i	1.09296	+	0.157144i
$423$	33.1448	−	2.00715i	1.61156	−	0.0975908i
$424$	2.69502	−	2.33524i	0.130882	−	0.113409i
$425$	8.24081	+	4.24843i	0.399738	+	0.206079i
$426$	7.06670	+	8.05004i	0.342383	+	0.390026i
$427$	−55.0484	+	10.6097i	−2.66398	+	0.513440i
$428$	−3.97289	+	16.3765i	−0.192037	+	0.791587i
$429$	2.93308	−	5.15667i	0.141610	−	0.248966i
$430$	−2.62960	−	0.506814i	−0.126811	−	0.0244407i
$431$	11.0881	−	24.2796i	0.534096	−	1.16951i	−0.429726	−	0.902959i	$-0.641390\pi$
$431$	11.0881	−	24.2796i	0.534096	−	1.16951i	0.963822	−	0.266547i	$-0.0858828\pi$
$432$	4.02162	−	3.29037i	0.193490	−	0.158308i
$433$	14.1487	−	6.46151i	0.679945	−	0.310520i	−0.0453377	−	0.998972i	$-0.514436\pi$
$433$	14.1487	−	6.46151i	0.679945	−	0.310520i	0.725283	+	0.688451i	$0.241709\pi$
$434$	−16.2453	+	12.7754i	−0.779800	+	0.613241i
$435$	−2.71467	+	1.95958i	−0.130159	+	0.0939549i
$436$	−11.8188	−	6.82362i	−0.566020	−	0.326792i
$437$	−0.339714	−	1.31834i	−0.0162507	−	0.0630646i
$438$	−11.6515	+	1.75191i	−0.556728	+	0.0837093i
$439$	−0.439674	+	9.22989i	−0.0209845	+	0.440519i	0.963788	+	0.266670i	$0.0859234\pi$
$439$	−0.439674	+	9.22989i	−0.0209845	+	0.440519i	−0.984772	+	0.173849i	$0.944380\pi$
$440$	−5.84741	+	0.840731i	−0.278764	+	0.0400803i
$441$	18.4942	+	20.7960i	0.880676	+	0.990284i
$442$	−1.90190	+	6.47728i	−0.0904642	+	0.308093i
$443$	−0.764031	−	8.00130i	−0.0363002	−	0.380153i	−0.995307	−	0.0967694i	$-0.969149\pi$
$443$	−0.764031	−	8.00130i	−0.0363002	−	0.380153i	0.959007	−	0.283384i	$-0.0914570\pi$
$444$	0.185342	+	0.00763266i	0.00879594	+	0.000362230i
$445$	−6.39882	−	5.03209i	−0.303333	−	0.238544i
$446$	25.0113	+	6.06768i	1.18432	+	0.287313i
$447$	−15.8119	−	2.94198i	−0.747875	−	0.139151i
$448$	−1.84868	+	3.58595i	−0.0873421	+	0.169420i
$449$	−6.65450	−	10.3546i	−0.314045	−	0.488664i	0.647968	−	0.761668i	$-0.275619\pi$
$449$	−6.65450	−	10.3546i	−0.314045	−	0.488664i	−0.962013	+	0.273004i	$0.911983\pi$
$450$	−2.37042	+	3.79506i	−0.111743	+	0.178901i
$451$	8.27922	+	28.1964i	0.389853	+	1.32772i
$452$	15.0933	−	6.04243i	0.709927	−	0.284212i
$453$	14.8291	+	9.39566i	0.696732	+	0.441447i
$454$	18.5721	−	13.2252i	0.871633	−	0.620687i
$455$	−5.66330	−	5.93950i	−0.265500	−	0.278448i
$456$	0.0265582	+	0.490963i	0.00124370	+	0.0229914i
$457$	20.0376	+	25.4799i	0.937319	+	1.19190i	0.981226	+	0.192863i	$0.0617772\pi$
$457$	20.0376	+	25.4799i	0.937319	+	1.19190i	−0.0439067	+	0.999036i	$0.513980\pi$
$458$	−9.54532	−	6.13440i	−0.446024	−	0.286642i
$459$	−13.9832	−	29.1165i	−0.652681	−	1.35904i
$460$	−4.22922	−	7.92521i	−0.197188	−	0.369515i
$461$	3.08918	−	1.78354i	0.143878	−	0.0830678i	−0.426333	−	0.904566i	$-0.640195\pi$
$461$	3.08918	−	1.78354i	0.143878	−	0.0830678i	0.570211	+	0.821498i	$0.306862\pi$
$462$	−12.8992	−	17.8696i	−0.600125	−	0.831371i
$463$	7.45645	+	2.98511i	0.346531	+	0.138730i	0.538398	−	0.842691i	$-0.319030\pi$
$463$	7.45645	+	2.98511i	0.346531	+	0.138730i	−0.191867	+	0.981421i	$0.561454\pi$
$464$	0.0980958	−	1.02731i	0.00455398	−	0.0476915i
$465$	−2.25917	+	16.4651i	−0.104766	+	0.763550i
$466$	23.6367	−	2.25703i	1.09495	−	0.104555i
$467$	−22.8922	+	26.4190i	−1.05933	+	1.22253i	−0.0852367	+	0.996361i	$0.527165\pi$
$467$	−22.8922	+	26.4190i	−1.05933	+	1.22253i	−0.974089	+	0.226166i	$0.927381\pi$
$468$	−3.03996	−	1.17181i	−0.140522	−	0.0541667i
$469$	−6.46062	+	1.89701i	−0.298323	+	0.0875957i
$470$	−6.78090	+	19.5921i	−0.312779	+	0.903717i
$471$	−34.9837	−	11.8562i	−1.61196	−	0.546304i
$472$	−0.280090	−	5.87981i	−0.0128922	−	0.270640i
$473$	0.853365	+	4.42768i	0.0392378	+	0.203585i
$474$	−4.05030	+	5.76610i	−0.186036	+	0.264846i
$475$	−0.157361	−	0.393069i	−0.00722022	−	0.0180352i
$476$	18.9532	+	16.4231i	0.868720	+	0.752750i
$477$	9.87968	−	4.10368i	0.452359	−	0.187895i
$478$	−14.3746	−	4.22077i	−0.657479	−	0.193053i
$479$	−20.9173	+	29.3743i	−0.955738	+	1.34215i	−0.0161380	+	0.999870i	$0.505137\pi$
$479$	−20.9173	+	29.3743i	−0.955738	+	1.34215i	−0.939600	+	0.342276i	$0.888802\pi$
$480$	0.934057	+	3.10693i	0.0426337	+	0.141811i
$481$	−0.0532953	−	0.103379i	−0.00243006	−	0.00471365i
$482$	−10.6201	+	18.3945i	−0.483731	+	0.837847i
$483$	18.8716	−	27.6939i	0.858690	−	1.26011i
$484$	−0.526489	−	0.911905i	−0.0239313	−	0.0414502i
$485$	4.74802	−	7.38807i	0.215597	−	0.335475i
$486$	14.5593	−	5.57022i	0.660422	−	0.252670i
$487$	−2.88724	−	6.32218i	−0.130833	−	0.286485i	0.832866	−	0.553475i	$-0.186698\pi$
$487$	−2.88724	−	6.32218i	−0.130833	−	0.286485i	−0.963699	+	0.266989i	$0.913971\pi$
$488$	−3.27605	−	13.5041i	−0.148300	−	0.611300i
$489$	−1.15244	+	1.11311i	−0.0521150	+	0.0503364i
$490$	−16.4204	+	5.68316i	−0.741798	+	0.256739i
$491$	7.33260	−	9.32416i	0.330916	−	0.420794i	−0.591914	−	0.806001i	$-0.701628\pi$
$491$	7.33260	−	9.32416i	0.330916	−	0.420794i	0.922830	+	0.385207i	$0.125870\pi$
$492$	14.6367	−	6.79865i	0.659874	−	0.306507i
$493$	−6.06214	−	2.09813i	−0.273025	−	0.0944948i
$494$	0.259345	−	0.166671i	0.0116685	−	0.00749887i
$495$	−17.4441	−	3.12956i	−0.784055	−	0.140663i
$496$	−3.35461	−	3.87143i	−0.150627	−	0.173832i
$497$	−18.0576	−	17.2179i	−0.809996	−	0.772329i
$498$	11.8172	−	6.92453i	0.529540	−	0.310295i
$499$	−5.43467	−	15.7025i	−0.243289	−	0.702939i	−0.998854	−	0.0478642i	$-0.984759\pi$
$499$	−5.43467	−	15.7025i	−0.243289	−	0.702939i	0.755564	−	0.655074i	$-0.227363\pi$
$500$	−7.05304	−	9.90461i	−0.315422	−	0.442948i
$501$	−7.79097	−	19.1033i	−0.348075	−	0.853474i
$502$	−2.12867	−	1.51582i	−0.0950071	−	0.0676542i
$503$	−1.24949	−	8.69041i	−0.0557121	−	0.387486i	−0.998531	−	0.0541811i	$-0.982745\pi$
$503$	−1.24949	−	8.69041i	−0.0557121	−	0.387486i	0.942819	−	0.333305i	$-0.108164\pi$
$504$	−8.65124	+	8.46439i	−0.385357	+	0.377034i
$505$		−	25.2553i		−	1.12385i
$506$	−9.74182	+	11.5706i	−0.433077	+	0.514375i
$507$	−3.04422	−	20.2463i	−0.135199	−	0.899171i
$508$	13.4536	−	6.93579i	0.596905	−	0.307726i
$509$	10.9313	−	27.3050i	0.484521	−	1.21027i	−0.461782	−	0.886994i	$-0.652790\pi$
$509$	10.9313	−	27.3050i	0.484521	−	1.21027i	0.946303	−	0.323281i	$-0.104786\pi$
$510$	20.1377	−	1.08933i	0.891711	−	0.0482363i
$511$	26.6710	−	6.47031i	1.17985	−	0.286230i
$512$	−0.909632	−	0.415415i	−0.0402004	−	0.0183589i
$513$	−0.388141	+	1.42306i	−0.0171369	+	0.0628296i
$514$	3.79608	−	26.4023i	0.167438	−	1.16456i
$515$	−19.0625	+	19.9922i	−0.839994	+	0.880960i
$516$	2.33488	−	0.824989i	0.102787	−	0.0363181i
$517$	34.8693	−	1.66103i	1.53355	−	0.0730520i
$518$	−0.431590	+	0.0205592i	−0.0189630	+	0.000903318i
$519$	11.1821	+	9.56392i	0.490839	+	0.419809i
$520$	1.40374	−	1.47220i	0.0615581	−	0.0645603i
$521$	2.93756	−	20.4312i	0.128697	−	0.895107i	−0.818512	−	0.574490i	$-0.805201\pi$
$521$	2.93756	−	20.4312i	0.128697	−	0.895107i	0.947209	−	0.320618i	$-0.103890\pi$
$522$	1.24971	−	2.83250i	0.0546984	−	0.123975i
$523$	28.1924	+	12.8751i	1.23277	+	0.562987i	0.921886	−	0.387461i	$-0.126648\pi$
$523$	28.1924	+	12.8751i	1.23277	+	0.562987i	0.310883	+	0.950448i	$0.399375\pi$
$524$	11.3969	−	2.76486i	0.497877	−	0.120784i
$525$	4.71606	−	9.29440i	0.205826	−	0.405641i
$526$	−4.06206	+	10.1465i	−0.177114	+	0.442410i
$527$	−28.3033	+	14.5914i	−1.23291	+	0.635611i
$528$	4.27213	−	3.40441i	0.185921	−	0.148158i
$529$	−21.5866	−	7.93855i	−0.938546	−	0.345155i
$530$			6.67949i			0.290139i
$531$	4.75653	−	17.0068i	0.206416	−	0.738031i
$532$	−0.162988	−	1.13361i	−0.00706642	−	0.0491480i
$533$	−8.24263	−	5.86955i	−0.357028	−	0.254238i
$534$	7.45759	+	1.02325i	0.322721	+	0.0442804i
$535$	−18.3092	−	25.7117i	−0.791576	−	1.11161i
$536$	−0.545868	−	1.57718i	−0.0235779	−	0.0681239i
$537$	3.12747	+	1.77888i	0.134960	+	0.0767645i
$538$	−16.9664	−	16.1775i	−0.731475	−	0.697460i
$539$	19.1596	+	22.1114i	0.825264	+	0.952405i
$540$	−0.275162	+	9.72901i	−0.0118411	+	0.418670i
$541$	−1.11062	+	0.713750i	−0.0477492	+	0.0306865i	−0.564298	−	0.825571i	$-0.690853\pi$
$541$	−1.11062	+	0.713750i	−0.0477492	+	0.0306865i	0.516548	+	0.856258i	$0.327217\pi$
$542$	−16.9379	−	5.86227i	−0.727546	−	0.251806i
$543$	3.04996	−	34.2723i	0.130886	−	1.47077i
$544$	−3.84258	+	4.88624i	−0.164749	+	0.209496i
$545$	24.1567	−	8.36070i	1.03476	−	0.358133i
$546$	7.29499	+	2.09106i	0.312197	+	0.0894889i
$547$	−4.64753	−	19.1574i	−0.198714	−	0.819111i	−0.980653	−	0.195756i	$-0.937284\pi$
$547$	−4.64753	−	19.1574i	−0.198714	−	0.819111i	0.781939	−	0.623356i	$-0.214231\pi$
$548$	−2.09983	−	4.59800i	−0.0897005	−	0.196417i
$549$	3.42768	−	41.5461i	0.146290	−	1.77315i
$550$	−2.54320	+	3.95730i	−0.108443	+	0.168740i
$551$	0.146475	+	0.253702i	0.00624004	+	0.0108081i
$552$	7.07917	+	4.34573i	0.301310	+	0.184966i
$553$	8.20662	−	14.2143i	0.348981	−	0.604452i
$554$	−1.62280	−	3.14779i	−0.0689462	−	0.133737i
$555$	−0.238148	+	0.253006i	−0.0101088	+	0.0107395i
$556$	−11.4746	+	16.1139i	−0.486632	+	0.683380i
$557$	13.4398	+	3.94627i	0.569461	+	0.167209i	0.553772	−	0.832668i	$-0.313188\pi$
$557$	13.4398	+	3.94627i	0.569461	+	0.167209i	0.0156884	+	0.999877i	$0.495006\pi$
$558$	−5.89500	−	14.1923i	−0.249555	−	0.600808i
$559$	−1.17343	−	1.01678i	−0.0496306	−	0.0430052i
$560$	−2.80861	−	7.01557i	−0.118685	−	0.296462i
$561$	−14.3049	−	30.7969i	−0.603955	−	1.30025i
$562$	−2.90731	−	15.0846i	−0.122638	−	0.636305i
$563$	−0.500265	−	10.5018i	−0.0210836	−	0.442600i	−0.984586	−	0.174901i	$-0.944040\pi$
$563$	−0.500265	−	10.5018i	−0.0210836	−	0.442600i	0.963502	−	0.267700i	$-0.0862635\pi$
$564$	−3.74936	−	18.8010i	−0.157877	−	0.791665i
$565$	−9.96004	+	28.7776i	−0.419022	+	1.21068i
$566$	−24.3792	+	7.15838i	−1.02473	+	0.300889i
$567$	−32.6291	+	15.9296i	−1.37029	+	0.668981i
$568$	4.04994	−	4.67388i	0.169932	−	0.196111i
$569$	−11.2541	+	1.07464i	−0.471798	+	0.0450513i	−0.328248	−	0.944592i	$-0.606458\pi$
$569$	−11.2541	+	1.07464i	−0.471798	+	0.0450513i	−0.143551	+	0.989643i	$0.545852\pi$
$570$	−0.727580	−	0.564628i	−0.0304750	−	0.0236497i
$571$	−2.91589	+	30.5366i	−0.122026	+	1.27792i	0.702332	+	0.711849i	$0.252142\pi$
$571$	−2.91589	+	30.5366i	−0.122026	+	1.27792i	−0.824358	+	0.566068i	$0.808464\pi$
$572$	−3.17976	−	1.27298i	−0.132953	−	0.0532262i
$573$	−12.2995	+	27.3977i	−0.513817	+	1.14456i
$574$	−32.5551	+	18.7957i	−1.35882	+	0.784518i
$575$	−6.97463	−	1.58753i	−0.290862	−	0.0662045i
$576$	−2.19769	−	2.04209i	−0.0915705	−	0.0850872i
$577$	26.8567	+	17.2598i	1.11806	+	0.718534i	0.963035	−	0.269377i	$-0.0868177\pi$
$577$	26.8567	+	17.2598i	1.11806	+	0.718534i	0.155025	+	0.987910i	$0.450454\pi$
$578$	13.3774	+	17.0108i	0.556428	+	0.707555i
$579$	29.5073	+	14.9723i	1.22628	+	0.622227i
$580$	1.33392	+	1.39897i	0.0553880	+	0.0580893i
$581$	−25.9875	+	18.5056i	−1.07814	+	0.767741i
$582$	−0.334148	+	8.11403i	−0.0138509	+	0.336337i
$583$	10.4412	−	4.18002i	0.432430	−	0.173119i
$584$	1.91651	+	6.52704i	0.0793058	+	0.270091i
$585$	5.38766	−	2.86598i	0.222753	−	0.118494i
$586$	−2.76798	−	4.30705i	−0.114344	−	0.177923i
$587$	6.80067	−	13.1915i	0.280694	−	0.544470i	−0.705772	−	0.708439i	$-0.749400\pi$
$587$	6.80067	−	13.1915i	0.280694	−	0.544470i	0.986465	+	0.163969i	$0.0524298\pi$
$588$	10.4436	−	12.2106i	0.430688	−	0.503558i
$589$	1.41318	+	0.342834i	0.0582291	+	0.0141262i
$590$	8.66697	+	6.81578i	0.356814	+	0.280601i
$591$	3.74177	+	7.14464i	0.153916	+	0.293891i
$592$	−0.0101803	−	0.106613i	−0.000418408	−	0.00438176i
$593$	−7.28998	+	24.8274i	−0.299364	+	1.01954i	0.663191	+	0.748450i	$0.269202\pi$
$593$	−7.28998	+	24.8274i	−0.299364	+	1.01954i	−0.962554	+	0.271088i	$0.912616\pi$
$594$	15.3803	−	5.65828i	0.631061	−	0.232162i
$595$	−46.4967	+	6.68522i	−1.90618	+	0.274067i
$596$	−0.441829	+	9.27514i	−0.0180980	+	0.379924i
$597$	1.60692	−	4.09004i	0.0657667	−	0.167394i
$598$	0.173934	−	5.20535i	0.00711269	−	0.212862i
$599$	−29.2529	−	16.8892i	−1.19524	−	0.690073i	−0.235751	−	0.971813i	$-0.575755\pi$
$599$	−29.2529	−	16.8892i	−1.19524	−	0.690073i	−0.959491	+	0.281740i	$0.909088\pi$
$600$	2.35678	+	1.05801i	0.0962151	+	0.0431931i
$601$	−21.2251	+	16.6916i	−0.865791	+	0.680865i	−0.948866	−	0.315678i	$-0.897768\pi$
$601$	−21.2251	+	16.6916i	−0.865791	+	0.680865i	0.0830757	+	0.996543i	$0.473526\pi$
$602$	−5.24684	+	2.39615i	−0.213845	+	0.0976599i
$603$	−0.0645033	−	5.00651i	−0.00262678	−	0.203881i
$604$	4.21041	−	9.21951i	0.171319	−	0.375136i
$605$	1.93669	+	0.373266i	0.0787375	+	0.0151754i
$606$	11.8068	+	20.1492i	0.479620	+	0.818504i
$607$	−6.94002	+	28.6072i	−0.281687	+	1.16113i	0.638491	+	0.769629i	$0.279559\pi$
$607$	−6.94002	+	28.6072i	−0.281687	+	1.16113i	−0.920178	+	0.391500i	$0.871956\pi$
$608$	0.278742	−	0.0537231i	0.0113045	−	0.00217876i
$609$	−2.31464	+	6.82974i	−0.0937940	+	0.276755i
$610$	23.1347	+	11.9268i	0.936696	+	0.482901i
$611$	−9.08437	+	7.87165i	−0.367514	+	0.318453i
$612$	−15.5569	+	10.2834i	−0.628852	+	0.415682i
$613$	37.1138	+	5.33616i	1.49901	+	0.215526i	0.842462	−	0.538756i	$-0.181105\pi$
$613$	37.1138	+	5.33616i	1.49901	+	0.215526i	0.656551	+	0.754281i	$0.272014\pi$
$614$	3.63313	−	18.8505i	0.146621	−	0.760743i
$615$	−8.32954	+	29.0590i	−0.335880	+	1.17177i
$616$	−9.20891	+	8.78068i	−0.371038	+	0.353784i
$617$	11.9708	+	1.14307i	0.481925	+	0.0460183i	0.333192	−	0.942859i	$-0.391874\pi$
$617$	11.9708	+	1.14307i	0.481925	+	0.0460183i	0.148733	+	0.988877i	$0.452480\pi$
$618$	5.86209	−	24.8618i	0.235808	−	1.00009i
$619$	−11.5446	−	0.549938i	−0.464017	−	0.0221039i	−0.185728	−	0.982601i	$-0.559464\pi$
$619$	−11.5446	−	0.549938i	−0.464017	−	0.0221039i	−0.278289	+	0.960497i	$0.589767\pi$
$620$	9.59519			0.385352
$621$	16.0523	+	19.0610i	0.644157	+	0.764893i
$622$	1.88461			0.0755660
$623$	−17.5137	−	0.834281i	−0.701672	−	0.0334248i
$624$	−0.431678	+	1.83080i	−0.0172810	+	0.0732905i
$625$	15.2485	+	1.45605i	0.609940	+	0.0582422i
$626$	−16.9784	+	16.1889i	−0.678593	+	0.647037i
$627$	−0.427291	+	1.49068i	−0.0170644	+	0.0595318i
$628$	−4.03602	+	20.9409i	−0.161055	+	0.835631i
$629$	−0.658962	−	0.0947445i	−0.0262745	−	0.00377771i
$630$	−1.37036	−	22.6292i	−0.0545963	−	0.901569i
$631$	−4.27264	+	3.70226i	−0.170091	+	0.147385i	−0.735747	−	0.677257i	$-0.763169\pi$
$631$	−4.27264	+	3.70226i	−0.170091	+	0.147385i	0.565656	+	0.824642i	$0.308623\pi$
$632$	3.61604	+	1.86420i	0.143838	+	0.0741538i
$633$	12.6105	−	37.2096i	0.501224	−	1.47895i
$634$	−13.7185	+	2.64402i	−0.544830	+	0.105007i
$635$	−6.68412	+	27.5523i	−0.265251	+	1.09338i
$636$	−3.12265	−	5.32902i	−0.123821	−	0.211309i
$637$	−9.89235	−	1.90659i	−0.391949	−	0.0755420i
$638$	1.35207	−	2.96062i	0.0535290	−	0.117212i
$639$	15.9468	−	9.48286i	0.630844	−	0.375136i
$640$	1.70383	−	0.778112i	0.0673497	−	0.0307576i
$641$	11.5043	−	9.04706i	0.454391	−	0.357337i	−0.364580	−	0.931172i	$-0.618787\pi$
$641$	11.5043	−	9.04706i	0.454391	−	0.357337i	0.818971	+	0.573835i	$0.194545\pi$
$642$	26.6276	+	11.9537i	1.05091	+	0.471775i
$643$	−12.3300	−	7.11875i	−0.486249	−	0.280736i	0.236768	−	0.971566i	$-0.423912\pi$
$643$	−12.3300	−	7.11875i	−0.486249	−	0.280736i	−0.723017	+	0.690830i	$0.757245\pi$
$644$	−17.3217	−	8.62093i	−0.682572	−	0.339712i
$645$	−1.69615	+	4.31718i	−0.0667860	+	0.169989i
$646$	0.0839629	−	1.76260i	0.00330347	−	0.0693485i
$647$	10.3014	−	1.48112i	0.404990	−	0.0582287i	0.0631899	−	0.998002i	$-0.479873\pi$
$647$	10.3014	−	1.48112i	0.404990	−	0.0582287i	0.341800	+	0.939773i	$0.388964\pi$
$648$	−4.32877	−	7.89061i	−0.170050	−	0.309973i
$649$	5.23045	−	17.8133i	0.205313	−	0.699232i
$650$	−0.153969	−	1.61244i	−0.00603916	−	0.0632450i
$651$	16.6074	+	31.7106i	0.650894	+	1.24284i
$652$	0.727133	+	0.571824i	0.0284767	+	0.0223943i
$653$	16.6334	+	4.03522i	0.650915	+	0.157910i	0.547602	−	0.836739i	$-0.315541\pi$
$653$	16.6334	+	4.03522i	0.650915	+	0.157910i	0.103312	+	0.994649i	$0.467056\pi$
$654$	−15.3640	+	17.9635i	−0.600780	+	0.702429i
$655$	−10.0657	+	19.5248i	−0.393301	+	0.762898i
$656$	−5.03750	−	7.83850i	−0.196681	−	0.306042i
$657$	−0.708348	+	20.3955i	−0.0276353	+	0.795703i
$658$	12.5808	+	42.8463i	0.490451	+	1.67032i
$659$	−20.8109	+	8.33144i	−0.810679	+	0.324547i	−0.739705	−	0.672931i	$-0.765035\pi$
$659$	−20.8109	+	8.33144i	−0.810679	+	0.324547i	−0.0709738	+	0.997478i	$0.522611\pi$
$660$	−0.421019	+	10.2235i	−0.0163882	+	0.397949i
$661$	11.1668	−	7.95185i	0.434339	−	0.309291i	−0.341893	−	0.939739i	$-0.611068\pi$
$661$	11.1668	−	7.95185i	0.434339	−	0.309291i	0.776232	+	0.630448i	$0.217129\pi$
$662$	19.9805	+	20.9550i	0.776566	+	0.814439i
$663$	10.4271	+	5.29081i	0.404955	+	0.205478i
$664$	−4.88821	−	6.21586i	−0.189699	−	0.241222i
$665$	1.80465	+	1.15978i	0.0699812	+	0.0449742i
$666$	0.0717191	−	0.313187i	0.00277906	−	0.0121357i
$667$	4.93297	+	0.400456i	0.191005	+	0.0155057i
$668$	−10.3155	+	5.95565i	−0.399118	+	0.230431i
$669$	18.2566	−	40.6675i	0.705840	−	1.57230i
$670$	2.90222	+	1.16187i	0.112122	+	0.0448870i
$671$	4.16590	−	43.6272i	0.160823	−	1.68421i
$672$	5.52053	+	4.28413i	0.212959	+	0.165264i
$673$	34.6113	−	3.30498i	1.33417	−	0.127398i	0.596528	−	0.802592i	$-0.296546\pi$
$673$	34.6113	−	3.30498i	1.33417	−	0.127398i	0.737640	+	0.675194i	$0.235940\pi$
$674$	−0.742353	+	0.856721i	−0.0285944	+	0.0329997i
$675$	5.71131	+	5.23880i	0.219829	+	0.201642i
$676$	−11.3418	+	3.33025i	−0.436223	+	0.128087i
$677$	8.46404	−	24.4552i	0.325299	−	0.939891i	−0.657215	−	0.753703i	$-0.728266\pi$
$677$	8.46404	−	24.4552i	0.325299	−	0.939891i	0.982514	−	0.186188i	$-0.0596133\pi$
$678$	−5.50720	−	27.6156i	−0.211503	−	1.06057i
$679$	−0.900053	−	18.8944i	−0.0345409	−	0.725102i
$680$	−2.20354	−	11.4331i	−0.0845021	−	0.438438i
$681$	−16.6359	−	35.8152i	−0.637490	−	1.37244i
$682$	−6.00466	−	14.9989i	−0.229930	−	0.574338i
$683$	33.4566	+	28.9903i	1.28018	+	1.10928i	0.988250	+	0.152845i	$0.0488436\pi$
$683$	33.4566	+	28.9903i	1.28018	+	1.10928i	0.291932	+	0.956439i	$0.405702\pi$
$684$	0.844439	+	0.110328i	0.0322879	+	0.00421849i
$685$	9.08458	+	2.66747i	0.347104	+	0.101919i
$686$	−5.32784	+	7.48190i	−0.203418	+	0.285660i
$687$	−13.4701	+	14.3105i	−0.513915	+	0.545978i
$688$	−0.655134	−	1.27078i	−0.0249767	−	0.0484481i
$689$	−1.93634	+	3.35384i	−0.0737686	+	0.127771i
$690$	−14.8352	+	4.69068i	−0.564767	+	0.178571i
$691$	−14.6109	−	25.3068i	−0.555824	−	0.962715i	−0.997839	−	0.0657077i	$-0.979070\pi$
$691$	−14.6109	−	25.3068i	−0.555824	−	0.962715i	0.442015	−	0.897008i	$-0.354264\pi$
$692$	4.59288	−	7.14666i	0.174595	−	0.271675i
$693$	−34.5157	+	16.3034i	−1.31114	+	0.619316i
$694$	−1.34460	−	2.94426i	−0.0510402	−	0.111762i
$695$	−8.73567	−	36.0089i	−0.331363	−	1.36590i
$696$	−1.71824	−	0.492522i	−0.0651299	−	0.0186690i
$697$	−54.7345	+	18.9438i	−2.07322	+	0.717547i
$698$	−17.4004	+	22.1264i	−0.658615	+	0.837497i
$699$	3.64549	−	40.9643i	0.137885	−	1.54941i
$700$	−5.68644	−	1.96810i	−0.214927	−	0.0743871i
$701$	30.7621	−	19.7696i	1.16187	−	0.746687i	0.189900	−	0.981803i	$-0.439184\pi$
$701$	30.7621	−	19.7696i	1.16187	−	0.746687i	0.971967	+	0.235116i	$0.0755472\pi$
$702$	−2.95853	+	4.80526i	−0.111663	+	0.181363i
$703$	0.0199091	+	0.0229764i	0.000750887	+	0.000866570i
$704$	−2.28258	−	2.17643i	−0.0860279	−	0.0820274i
$705$	31.2136	+	17.7541i	1.17557	+	0.668657i
$706$	2.07980	+	6.00918i	0.0782742	+	0.226159i
$707$	−31.5534	−	44.3105i	−1.18669	−	1.66647i
$708$	−10.1010	−	1.38596i	−0.379620	−	0.0520875i
$709$	−2.44991	−	1.74457i	−0.0920082	−	0.0655187i	0.533127	−	0.846035i	$-0.321017\pi$
$709$	−2.44991	−	1.74457i	−0.0920082	−	0.0655187i	−0.625135	+	0.780516i	$0.714956\pi$
$710$	1.64858	+	11.4661i	0.0618701	+	0.430316i
$711$	8.53541	+	8.72383i	0.320103	+	0.327169i
$712$		−	4.34598i		−	0.162873i
$713$	18.3364	−	16.3501i	0.686705	−	0.612317i
$714$	33.9706	−	27.0707i	1.27132	−	1.01310i
$715$	5.70238	−	2.93978i	0.213257	−	0.109942i
$716$	0.772054	−	1.92850i	0.0288530	−	0.0720713i
$717$	−11.7415	+	23.1402i	−0.438496	+	0.864187i
$718$	−11.3845	+	2.76185i	−0.424866	+	0.103071i
$719$	−21.1732	−	9.66949i	−0.789628	−	0.360611i	−0.0205686	−	0.999788i	$-0.506548\pi$
$719$	−21.1732	−	9.66949i	−0.789628	−	0.360611i	−0.769059	+	0.639177i	$0.779275\pi$
$720$	5.58650	−	0.606168i	0.208197	−	0.0225905i
$721$	−8.46747	+	58.8925i	−0.315345	+	2.19327i
$722$	13.0559	−	13.6926i	0.485890	−	0.509587i
$723$	27.9579	+	23.9121i	1.03977	+	0.889300i
$724$	−19.8428	+	0.945230i	−0.737453	+	0.0351292i
$725$	1.53746	−	0.0732383i	0.0570999	−	0.00272000i
$726$	−1.71962	+	0.607600i	−0.0638212	+	0.0225501i
$727$	−20.4172	+	21.4129i	−0.757232	+	0.794162i	−0.983693	−	0.179858i	$-0.942436\pi$
$727$	−20.4172	+	21.4129i	−0.757232	+	0.794162i	0.226461	+	0.974020i	$0.427285\pi$
$728$	0.623535	−	4.33678i	0.0231097	−	0.160732i
$729$	−4.87229	−	26.5567i	−0.180455	−	0.983583i
$730$	−11.5905	−	5.29318i	−0.428982	−	0.195909i
$731$	−8.63683	+	2.09527i	−0.319445	+	0.0774965i
$732$	−24.0330	+	1.30005i	−0.888286	+	0.0480511i
$733$	−6.67530	+	16.6741i	−0.246558	+	0.615872i	−0.999089	−	0.0426852i	$-0.986409\pi$
$733$	−6.67530	+	16.6741i	−0.246558	+	0.615872i	0.752531	+	0.658557i	$0.228833\pi$
$734$	−3.21674	+	1.65835i	−0.118732	+	0.0612107i
$735$	4.47495	+	29.7617i	0.165061	+	1.09778i
$736$	1.93012	−	4.39029i	0.0711453	−	0.161828i
$737$		−	5.26376i		−	0.193893i
$738$	−6.93957	−	27.0778i	−0.255449	−	0.996748i
$739$	−1.83437	−	12.7583i	−0.0674784	−	0.469323i	−0.995342	−	0.0964036i	$-0.969266\pi$
$739$	−1.83437	−	12.7583i	−0.0674784	−	0.469323i	0.927864	−	0.372919i	$-0.121643\pi$
$740$	0.163408	+	0.116362i	0.00600699	+	0.00427756i
$741$	−0.201643	−	0.494425i	−0.00740754	−	0.0181632i
$742$	8.34520	+	11.7192i	0.306362	+	0.430225i
$743$	11.1282	+	32.1529i	0.408256	+	1.17958i	0.942488	+	0.334240i	$0.108479\pi$
$743$	11.1282	+	32.1529i	0.408256	+	1.17958i	−0.534232	+	0.845338i	$0.679399\pi$
$744$	−7.65522	+	4.48574i	−0.280654	+	0.164455i
$745$	−12.5879	−	12.0025i	−0.461183	−	0.439737i
$746$	−17.8209	−	20.5664i	−0.652471	−	0.752991i
$747$	−8.04722	−	22.3165i	−0.294433	−	0.816518i
$748$	−16.4929	+	10.5993i	−0.603039	+	0.387550i
$749$	−64.2471	−	22.2361i	−2.34754	−	0.812490i
$750$	−19.1005	+	8.87202i	−0.697450	+	0.323961i
$751$	12.2828	−	15.6189i	0.448207	−	0.569941i	−0.508475	−	0.861077i	$-0.669791\pi$
$751$	12.2828	−	15.6189i	0.448207	−	0.569941i	0.956682	+	0.291135i	$0.0940330\pi$
$752$	−10.4597	+	3.62015i	−0.381428	+	0.132013i
$753$	−3.25560	+	3.14449i	−0.118641	+	0.114592i
$754$	0.264221	+	1.08913i	0.00962235	+	0.0396639i
$755$	7.88650	+	17.2690i	0.287019	+	0.628484i
$756$	11.6724	+	17.4133i	0.424521	+	0.633317i
$757$	20.2936	−	31.5775i	0.737585	−	1.14770i	−0.246351	−	0.969181i	$-0.579232\pi$
$757$	20.2936	−	31.5775i	0.737585	−	1.14770i	0.983936	−	0.178523i	$-0.0571320\pi$
$758$	−10.0338	−	17.3791i	−0.364444	−	0.631236i
$759$	16.6162	+	20.2545i	0.603130	+	0.735194i
$760$	−0.265860	+	0.460483i	−0.00964375	+	0.0167035i
$761$	15.7961	+	30.6401i	0.572607	+	1.11070i	0.980287	+	0.197577i	$0.0633073\pi$
$761$	15.7961	+	30.6401i	0.572607	+	1.11070i	−0.407681	+	0.913125i	$0.633662\pi$
$762$	−7.54795	−	25.1065i	−0.273433	−	0.909514i
$763$	31.9373	−	44.8496i	1.15621	−	1.62367i
$764$	16.6366	+	4.88493i	0.601889	+	0.176731i
$765$	4.52529	−	34.6361i	0.163612	−	1.25227i
$766$	11.1478	+	9.65962i	0.402786	+	0.349016i
$767$	2.37592	+	5.93476i	0.0857895	+	0.214292i
$768$	−0.995579	+	1.41733i	−0.0359249	+	0.0511435i
$769$	6.86599	+	35.6241i	0.247594	+	1.28464i	0.866501	+	0.499175i	$0.166364\pi$
$769$	6.86599	+	35.6241i	0.247594	+	1.28464i	−0.618907	+	0.785464i	$0.712424\pi$
$770$	−1.13405	−	23.8066i	−0.0408682	−	0.857930i
$771$	−43.7559	−	14.8291i	−1.57583	−	0.534058i
$772$	6.24820	−	18.0530i	0.224878	−	0.649741i
$773$	32.8699	−	9.65149i	1.18225	−	0.347140i	0.369209	−	0.929346i	$-0.379629\pi$
$773$	32.8699	−	9.65149i	1.18225	−	0.347140i	0.813041	+	0.582207i	$0.197811\pi$
$774$	−0.665053	−	4.23727i	−0.0239048	−	0.152306i
$775$	5.00343	−	5.77427i	0.179729	−	0.207418i
$776$	4.66738	−	0.445680i	0.167549	−	0.0159990i
$777$	−0.101732	+	0.741437i	−0.00364962	+	0.0265989i
$778$	−1.32603	+	13.8869i	−0.0475406	+	0.497868i
$779$	2.45555	+	0.983054i	0.0879792	+	0.0352216i
$780$	−2.06216	−	2.85677i	−0.0738370	−	0.102289i
$781$	16.8918	−	9.75250i	0.604437	−	0.348972i
$782$	−23.6929	−	18.0938i	−0.847255	−	0.647034i
$783$	−4.42730	−	3.02546i	−0.158219	−	0.108121i
$784$	−7.80402	−	5.01534i	−0.278715	−	0.179119i
$785$	−24.6931	−	31.3998i	−0.881333	−	1.12071i
$786$	−1.09719	−	20.2830i	−0.0391355	−	0.723470i
$787$	19.9341	+	20.9063i	0.710573	+	0.745228i	0.975730	−	0.218977i	$-0.0702721\pi$
$787$	19.9341	+	20.9063i	0.710573	+	0.745228i	−0.265157	+	0.964205i	$0.585424\pi$
$788$	3.79300	−	2.70099i	0.135120	−	0.0962186i
$789$	15.9908	+	10.1317i	0.569288	+	0.360699i
$790$	−7.07444	+	2.83218i	−0.251697	+	0.100764i
$791$	18.4792	+	62.9343i	0.657044	+	2.23769i
$792$	−4.44357	−	8.35332i	−0.157895	−	0.296822i
$793$	8.15866	+	12.6951i	0.289723	+	0.450817i
$794$	12.6854	−	24.6063i	0.450189	−	0.873245i
$795$	11.3740	+	2.11627i	0.403395	+	0.0750563i
$796$	−2.46558	−	0.598144i	−0.0873903	−	0.0212007i
$797$	−14.0287	−	11.0323i	−0.496922	−	0.390784i	0.338005	−	0.941144i	$-0.390248\pi$
$797$	−14.0287	−	11.0323i	−0.496922	−	0.390784i	−0.834927	+	0.550360i	$0.814490\pi$
$798$	−1.98197	−	0.0816207i	−0.0701611	−	0.00288934i
$799$	6.54021	+	68.4921i	0.231376	+	2.42308i
$800$	0.420207	−	1.43109i	0.0148565	−	0.0505967i
$801$	4.10521	−	12.3748i	0.145051	−	0.437241i
$802$	0.733703	−	0.105491i	0.0259079	−	0.00372500i
$803$	−1.02085	+	21.4303i	−0.0360251	+	0.756260i
$804$	−2.85861	+	0.429819i	−0.100816	+	0.0151585i
$805$	33.4509	−	13.9459i	1.17899	−	0.491530i
$806$	4.81784	+	2.78158i	0.169701	+	0.0979769i
$807$	−32.9229	+	23.7654i	−1.15894	+	0.836581i
$808$	10.5985	−	8.33476i	0.372854	−	0.293216i
$809$	−7.95450	+	3.63270i	−0.279665	+	0.127719i	−0.550310	−	0.834960i	$-0.685490\pi$
$809$	−7.95450	+	3.63270i	−0.279665	+	0.127719i	0.270645	+	0.962679i	$0.412763\pi$
$810$	16.4796	+	3.55100i	0.579035	+	0.124769i
$811$	19.4984	−	42.6955i	0.684681	−	1.49924i	−0.172926	−	0.984935i	$-0.555322\pi$
$811$	19.4984	−	42.6955i	0.684681	−	1.49924i	0.857606	−	0.514306i	$-0.171951\pi$
$812$	4.08821	+	0.787938i	0.143468	+	0.0276512i
$813$	−15.3489	+	26.9850i	−0.538309	+	0.946405i
$814$	0.0796335	−	0.328254i	0.00279115	−	0.0115053i
$815$	−1.70138	+	0.327915i	−0.0595968	+	0.0114864i
$816$	7.10297	+	8.09136i	0.248654	+	0.283254i
$817$	0.360739	+	0.185974i	0.0126207	+	0.00650641i
$818$	−2.58115	+	2.23658i	−0.0902478	+	0.0782002i
$819$	5.87198	−	11.7596i	0.205184	−	0.410913i
$820$	17.2752	+	2.48380i	0.603276	+	0.0867380i
$821$	−7.70440	+	39.9742i	−0.268886	+	1.39511i	0.556644	+	0.830751i	$0.312089\pi$
$821$	−7.70440	+	39.9742i	−0.268886	+	1.39511i	−0.825529	+	0.564359i	$0.809123\pi$
$822$	−8.49488	+	2.11887i	−0.296293	+	0.0739040i
$823$	−19.3815	+	18.4802i	−0.675596	+	0.644179i	−0.948099	−	0.317976i	$-0.896997\pi$
$823$	−19.3815	+	18.4802i	−0.675596	+	0.644179i	0.272503	+	0.962155i	$0.412149\pi$
$824$	−14.6808	−	1.40185i	−0.511430	−	0.0488356i
$825$	5.93284	+	5.58443i	0.206555	+	0.194425i
$826$	23.7217	+	1.13000i	0.825383	+	0.0393179i
$827$	14.5182			0.504846			0.252423	−	0.967617i	$-0.418773\pi$
$827$	14.5182			0.504846			0.252423	+	0.967617i	$0.418773\pi$
$828$	9.64291	−	10.6777i	0.335114	−	0.371077i
$829$	22.8532			0.793725			0.396862	−	0.917878i	$-0.370099\pi$
$829$	22.8532			0.793725			0.396862	+	0.917878i	$0.370099\pi$
$830$	14.7951	+	0.704777i	0.513545	+	0.0244632i
$831$	−5.87430	+	1.76603i	−0.203777	+	0.0612629i
$832$	1.08108	+	0.103230i	0.0374796	+	0.00357887i
$833$	−41.7343	+	39.7936i	−1.44601	+	1.37877i
$834$	23.8036	+	24.6447i	0.824251	+	0.853375i
$835$	4.22238	−	21.9078i	0.146122	−	0.758151i
$836$	0.886188	+	0.127415i	0.0306495	+	0.00440673i
$837$	−26.0347	+	5.54161i	−0.899892	+	0.191546i
$838$	13.3580	−	11.5747i	0.461444	−	0.399843i
$839$	−43.1068	−	22.2231i	−1.48821	−	0.767227i	−0.493483	−	0.869756i	$-0.664276\pi$
$839$	−43.1068	−	22.2231i	−1.48821	−	0.767227i	−0.994730	+	0.102528i	$0.967307\pi$
$840$	−12.8362	+	2.55983i	−0.442889	+	0.0883225i
$841$	27.4302	−	5.28674i	0.945869	−	0.182301i
$842$	0.148939	−	0.613936i	0.00513278	−	0.0211576i
$843$	−26.6075	+	0.171397i	−0.916413	+	0.00590324i
$844$	−22.2732	−	4.29282i	−0.766677	−	0.147765i
$845$	9.19777	−	20.1403i	0.316413	−	0.692847i
$846$	−33.2028	+	0.427781i	−1.14153	+	0.0147074i
$847$	3.86427	−	1.76475i	0.132778	−	0.0606376i
$848$	−2.80308	+	2.20437i	−0.0962581	+	0.0756982i
$849$	4.46541	+	43.7816i	0.153252	+	1.50258i
$850$	−8.02933	−	4.63574i	−0.275404	−	0.159004i
$851$	0.510553	−	0.0560772i	0.0175015	−	0.00192230i
$852$	−6.67566	−	8.37717i	−0.228704	−	0.286997i
$853$	−1.61534	+	33.9102i	−0.0553083	+	1.16106i	0.785192	+	0.619252i	$0.212564\pi$
$853$	−1.61534	+	33.9102i	−0.0553083	+	1.16106i	−0.840500	+	0.541811i	$0.817739\pi$
$854$	55.4909	−	7.97839i	1.89886	−	0.273015i
$855$	−1.19198	+	1.06005i	−0.0407650	+	0.0362530i
$856$	4.74762	−	16.1689i	0.162270	−	0.552641i
$857$	1.39406	+	14.5992i	0.0476200	+	0.498700i	0.987547	+	0.157324i	$0.0502867\pi$
$857$	1.39406	+	14.5992i	0.0476200	+	0.498700i	−0.939927	+	0.341376i	$0.889107\pi$
$858$	−3.17512	+	5.01126i	−0.108397	+	0.171082i
$859$	−35.3217	−	27.7773i	−1.20516	−	0.947749i	−0.205638	−	0.978628i	$-0.565927\pi$
$859$	−35.3217	−	27.7773i	−1.20516	−	0.947749i	−0.999523	+	0.0308790i	$0.990169\pi$
$860$	2.60251	+	0.631361i	0.0887448	+	0.0215292i
$861$	21.6914	+	61.3908i	0.739240	+	2.09219i
$862$	−12.2308	+	23.7245i	−0.416583	+	0.808059i
$863$	−19.4724	−	30.2997i	−0.662849	−	1.03141i	−0.996070	−	0.0885644i	$-0.971772\pi$
$863$	−19.4724	−	30.2997i	−0.662849	−	1.03141i	0.333222	−	0.942849i	$-0.391864\pi$
$864$	−4.17363	+	3.09529i	−0.141990	+	0.105304i
$865$	4.48305	+	15.2679i	0.152428	+	0.519123i
$866$	−14.4402	+	5.78097i	−0.490697	+	0.196445i
$867$	33.2048	−	17.3899i	1.12769	−	0.590592i
$868$	16.8348	−	11.9880i	0.571410	−	0.406899i
$869$	8.85435	+	9.28618i	0.300363	+	0.315012i
$870$	2.80484	−	1.82820i	0.0950929	−	0.0619817i
$871$	1.12041	+	1.42472i	0.0379637	+	0.0482748i
$872$	11.4808	+	7.37825i	0.388788	+	0.249859i
$873$	13.7109	+	3.13977i	0.464044	+	0.106265i
$874$	0.276600	+	1.33301i	0.00935614	+	0.0450896i
$875$	42.4834	−	24.5278i	1.43620	−	0.829191i
$876$	11.7216	−	1.19552i	0.396037	−	0.0403929i
$877$	18.1058	+	7.24849i	0.611391	+	0.244764i	0.656631	−	0.754212i	$-0.271981\pi$
$877$	18.1058	+	7.24849i	0.611391	+	0.244764i	−0.0452400	+	0.998976i	$0.514405\pi$
$878$	0.878352	−	9.19852i	0.0296429	−	0.310435i
$879$	−8.21115	+	3.34878i	−0.276955	+	0.112951i
$880$	5.88079	−	0.561547i	0.198241	−	0.0189298i
$881$	21.0682	−	24.3140i	0.709807	−	0.819161i	−0.280235	−	0.959931i	$-0.590413\pi$
$881$	21.0682	−	24.3140i	0.709807	−	0.819161i	0.990042	+	0.140771i	$0.0449580\pi$
$882$	−17.4837	−	21.6524i	−0.588708	−	0.729074i
$883$	32.9397	−	9.67197i	1.10851	−	0.325488i	0.324281	−	0.945961i	$-0.394878\pi$
$883$	32.9397	−	9.67197i	1.10851	−	0.325488i	0.784228	+	0.620473i	$0.213059\pi$
$884$	2.20795	−	6.37945i	0.0742613	−	0.214564i
$885$	14.3521	−	12.5989i	0.482439	−	0.423507i
$886$	0.382449	+	8.02859i	0.0128486	+	0.269726i
$887$	8.76997	+	45.5029i	0.294467	+	1.52784i	0.764170	+	0.645015i	$0.223149\pi$
$887$	8.76997	+	45.5029i	0.294467	+	1.52784i	−0.469703	+	0.882824i	$0.655639\pi$
$888$	−0.184769	−	0.0164429i	−0.00620043	−	0.000551789i
$889$	22.6959	+	56.6915i	0.761195	+	1.90137i
$890$	6.15214	+	5.33086i	0.206220	+	0.178691i
$891$	−4.76212	−	27.9827i	−0.159537	−	0.937455i
$892$	−24.6943	−	7.25090i	−0.826826	−	0.242778i
$893$	1.82256	−	2.55943i	0.0609897	−	0.0856480i
$894$	15.6540	+	3.69101i	0.523547	+	0.123446i
$895$	1.78295	+	3.45844i	0.0595975	+	0.115603i
$896$	2.01722	−	3.49392i	0.0673905	−	0.116724i
$897$	−8.80869	−	1.94539i	−0.294114	−	0.0649547i
$898$	6.15427	+	10.6595i	0.205371	+	0.355712i
$899$	−2.85807	+	4.44724i	−0.0953220	+	0.148324i
$900$	2.54831	−	3.67798i	0.0849436	−	0.122599i
$901$	9.20849	+	20.1638i	0.306779	+	0.671753i
$902$	−6.92821	−	28.5585i	−0.230684	−	0.950892i
$903$	2.41787	+	9.69364i	0.0804618	+	0.322584i
$904$	−15.3637	+	5.31742i	−0.510988	+	0.176855i
$905$	23.0015	−	29.2488i	0.764595	−	0.972262i
$906$	−14.3652	−	10.0906i	−0.477253	−	0.335238i
$907$	−3.53879	−	1.22479i	−0.117503	−	0.0406684i	0.267684	−	0.963507i	$-0.413742\pi$
$907$	−3.53879	−	1.22479i	−0.117503	−	0.0406684i	−0.385187	+	0.922839i	$0.625863\pi$
$908$	−19.1804	+	12.3265i	−0.636523	+	0.409068i
$909$	38.0513	−	13.7211i	1.26208	−	0.455101i
$910$	5.37427	+	6.20224i	0.178155	+	0.205602i
$911$	24.9102	+	23.7518i	0.825310	+	0.786932i	0.979571	−	0.201098i	$-0.0644511\pi$
$911$	24.9102	+	23.7518i	0.825310	+	0.786932i	−0.154261	+	0.988030i	$0.549300\pi$
$912$	−0.00316719	−	0.491670i	−0.000104876	−	0.0162808i
$913$	−8.15707	−	23.5683i	−0.269960	−	0.779997i
$914$	−18.8025	−	26.4044i	−0.621932	−	0.873381i
$915$	27.6390	−	35.6156i	0.913717	−	1.17742i
$916$	9.24262	+	6.58164i	0.305385	+	0.217464i
$917$	6.73346	+	46.8323i	0.222359	+	1.54654i
$918$	12.5820	+	29.7489i	0.415267	+	0.981859i
$919$		−	17.5387i		−	0.578548i	−0.957246	−	0.289274i	$-0.906586\pi$
$919$		−	17.5387i		−	0.578548i	0.957246	−	0.289274i	$-0.0934139\pi$
$920$	3.84733	+	8.11747i	0.126843	+	0.267625i
$921$	−30.9480	−	12.1590i	−1.01977	−	0.400653i
$922$	−3.17055	+	1.63453i	−0.104416	+	0.0538304i
$923$	−2.49618	+	6.23516i	−0.0821628	+	0.205233i
$924$	12.0343	+	18.4632i	0.395900	+	0.607393i
$925$	0.155235	−	0.0376595i	0.00510408	−	0.00123824i
$926$	−7.30597	−	3.33653i	−0.240089	−	0.109645i
$927$	−40.4780	−	17.8591i	−1.32947	−	0.586570i
$928$	−0.146866	+	1.02147i	−0.00482111	+	0.0335315i
$929$	−3.18893	+	3.34446i	−0.104625	+	0.109728i	−0.773964	−	0.633229i	$-0.781729\pi$
$929$	−3.18893	+	3.34446i	−0.104625	+	0.109728i	0.669339	+	0.742957i	$0.266577\pi$
$930$	3.04005	−	16.3389i	0.0996871	−	0.535775i
$931$	2.63040	−	0.125301i	0.0862079	−	0.00410659i
$932$	−23.7173	+	1.12979i	−0.776886	+	0.0370077i
$933$	0.597102	−	3.20917i	0.0195483	−	0.105063i
$934$	24.1234	−	25.2998i	0.789340	−	0.827836i
$935$	5.22612	−	36.3485i	0.170913	−	1.18872i
$936$	2.98076	+	1.31513i	0.0974291	+	0.0429862i
$937$	−26.4021	−	12.0574i	−0.862519	−	0.393899i	−0.0654992	−	0.997853i	$-0.520864\pi$
$937$	−26.4021	−	12.0574i	−0.862519	−	0.393899i	−0.797020	+	0.603953i	$0.793591\pi$
$938$	6.54356	−	1.58745i	0.213655	−	0.0518321i
$939$	22.1876	+	34.0404i	0.724063	+	1.11087i
$940$	7.70545	−	19.2473i	0.251324	−	0.627777i
$941$	−47.9860	+	24.7385i	−1.56430	+	0.806451i	−0.999820	−	0.0189966i	$-0.993953\pi$
$941$	−47.9860	+	24.7385i	−1.56430	+	0.806451i	−0.564478	+	0.825448i	$0.690923\pi$
$942$	34.3799	+	13.5073i	1.12016	+	0.440093i
$943$	37.2453	−	24.6903i	1.21288	−	0.804026i
$944$			5.88647i			0.191588i
$945$	−38.9678	−	4.83614i	−1.26762	−	0.157320i
$946$	−0.641721	−	4.46327i	−0.0208642	−	0.145113i
$947$	−6.97687	−	4.96820i	−0.226718	−	0.161445i	0.461054	−	0.887372i	$-0.347472\pi$
$947$	−6.97687	−	4.96820i	−0.226718	−	0.161445i	−0.687772	+	0.725927i	$0.741411\pi$
$948$	4.32007	−	5.56685i	0.140309	−	0.180803i
$949$	−4.28522	−	6.01775i	−0.139104	−	0.195344i
$950$	0.138480	+	0.400111i	0.00449288	+	0.0129813i
$951$	0.155875	+	24.1979i	0.00505460	+	0.784671i
$952$	−18.1503	−	17.3063i	−0.588255	−	0.560900i
$953$	21.2941	+	24.5748i	0.689785	+	0.796055i	0.987335	−	0.158652i	$-0.0507148\pi$
$953$	21.2941	+	24.5748i	0.689785	+	0.796055i	−0.297549	+	0.954706i	$0.596169\pi$
$954$	−10.0637	+	3.62894i	−0.325826	+	0.117491i
$955$	−27.3218	+	17.5586i	−0.884111	+	0.568184i
$956$	14.1575	+	4.89996i	0.457886	+	0.158476i
$957$	−4.61305	−	3.24036i	−0.149119	−	0.104746i
$958$	22.2913	−	28.3457i	0.720200	−	0.915809i
$959$	19.2716	−	6.66997i	0.622312	−	0.215384i
$960$	−0.785166	−	3.14785i	−0.0253411	−	0.101597i
$961$	−1.12189	−	4.62448i	−0.0361899	−	0.149177i
$962$	0.0483160	+	0.105797i	0.00155777	+	0.00341104i
$963$	28.7915	−	41.5548i	0.927794	−	1.33909i
$964$	11.4833	−	17.8683i	0.369852	−	0.575501i
$965$	17.8915	+	30.9890i	0.575948	+	0.997571i
$966$	−20.1680	+	26.7646i	−0.648895	+	0.861135i
$967$	11.4975	−	19.9143i	0.369736	−	0.640402i	−0.619788	−	0.784769i	$-0.712781\pi$
$967$	11.4975	−	19.9143i	0.369736	−	0.640402i	0.989524	+	0.144367i	$0.0461147\pi$
$968$	0.482502	+	0.935924i	0.0155082	+	0.0300817i
$969$	−2.97480	−	0.701419i	−0.0955642	−	0.0225328i
$970$	−5.09418	+	7.15378i	−0.163564	+	0.229694i
$971$	−20.6304	−	6.05763i	−0.662061	−	0.194399i	−0.0665963	−	0.997780i	$-0.521214\pi$
$971$	−20.6304	−	6.05763i	−0.662061	−	0.194399i	−0.595465	+	0.803381i	$0.703032\pi$
$972$	−14.8078	+	4.87115i	−0.474961	+	0.156242i
$973$	−60.3154	−	52.2636i	−1.93362	−	1.67549i
$974$	2.58315	+	6.45239i	0.0827694	+	0.206748i
$975$	−2.79448	−	0.248687i	−0.0894951	−	0.00796435i
$976$	2.62979	+	13.6446i	0.0841775	+	0.436754i
$977$	0.339070	+	7.11796i	0.0108478	+	0.227724i	0.997780	+	0.0665901i	$0.0212120\pi$
$977$	0.339070	+	7.11796i	0.0108478	+	0.227724i	−0.986933	+	0.161134i	$0.948485\pi$
$978$	1.20409	−	1.05701i	0.0385027	−	0.0337995i
$979$	4.48304	−	12.9529i	0.143279	−	0.413976i
$980$	16.6722	−	4.89541i	0.532575	−	0.156378i
$981$	25.7210	+	31.8536i	0.821208	+	1.01701i
$982$	−7.76796	+	8.96470i	−0.247886	+	0.286075i
$983$	−11.4710	+	1.09535i	−0.365868	+	0.0349362i	−0.276371	−	0.961051i	$-0.589132\pi$
$983$	−11.4710	+	1.09535i	−0.365868	+	0.0349362i	−0.0894968	+	0.995987i	$0.528526\pi$
$984$	−14.9436	+	6.09451i	−0.476386	+	0.194286i
$985$	−0.829071	+	8.68242i	−0.0264164	+	0.276645i
$986$	5.95544	+	2.38420i	0.189660	+	0.0759283i
$987$	76.9458	−	7.84792i	2.44921	−	0.249802i
$988$	−0.266981	+	0.154142i	−0.00849381	+	0.00490391i
$989$	6.04923	−	3.22812i	0.192354	−	0.102648i
$990$	17.2754	+	3.95604i	0.549050	+	0.125731i
$991$	14.0268	+	9.01447i	0.445575	+	0.286354i	0.744125	−	0.668040i	$-0.232867\pi$
$991$	14.0268	+	9.01447i	0.445575	+	0.286354i	−0.298550	+	0.954394i	$0.596503\pi$
$992$	3.16660	+	4.02666i	0.100540	+	0.127847i
$993$	42.0131	−	27.3842i	1.33325	−	0.869012i
$994$	17.2179	+	18.0576i	0.546119	+	0.572753i
$995$	3.87105	−	2.75657i	0.122721	−	0.0873890i
$996$	−12.1333	+	6.35440i	−0.384457	+	0.201347i
$997$	−2.56383	+	1.02640i	−0.0811974	+	0.0325065i	−0.411906	−	0.911227i	$-0.635137\pi$
$997$	−2.56383	+	1.02640i	−0.0811974	+	0.0325065i	0.330708	+	0.943733i	$0.392712\pi$
$998$	4.68136	+	15.9433i	0.148186	+	0.504675i
$999$	−0.510580	−	0.221352i	−0.0161540	−	0.00700328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.p.a.113.5	yes	480
9.2	odd	6	inner	414.2.p.a.389.9	yes	480
23.11	odd	22	inner	414.2.p.a.149.9	yes	480
207.11	even	66	inner	414.2.p.a.11.5	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.p.a.11.5	✓	480	207.11	even	66	inner
414.2.p.a.113.5	yes	480	1.1	even	1	trivial
414.2.p.a.149.9	yes	480	23.11	odd	22	inner
414.2.p.a.389.9	yes	480	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.998867 - 0.0475819i) q^{2} +(-0.397495 + 1.68582i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-1.35562 + 1.29258i) q^{5} +(0.477260 - 1.66500i) q^{6} +(-0.763522 + 3.96153i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-2.68399 - 1.34021i) q^{9} +O(q^{10})\)	\(q+(-0.998867 - 0.0475819i) q^{2} +(-0.397495 + 1.68582i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-1.35562 + 1.29258i) q^{5} +(0.477260 - 1.66500i) q^{6} +(-0.763522 + 3.96153i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-2.68399 - 1.34021i) q^{9} +(1.41559 - 1.22662i) q^{10} +(-2.80329 - 1.44520i) q^{11} +(-0.555943 + 1.64040i) q^{12} +(1.06637 - 0.205526i) q^{13} +(0.951154 - 3.92071i) q^{14} +(-1.64021 - 2.79914i) q^{15} +(0.981929 + 0.189251i) q^{16} +(2.58229 - 5.65443i) q^{17} +(2.61718 + 1.46640i) q^{18} +(-0.258219 + 0.117925i) q^{19} +(-1.47235 + 1.15787i) q^{20} +(-6.37493 - 2.86185i) q^{21} +(2.73135 + 1.57695i) q^{22} +(-0.840668 + 4.72158i) q^{23} +(0.633367 - 1.61209i) q^{24} +(-0.0709688 + 1.48982i) q^{25} +(-1.07494 + 0.154553i) q^{26} +(3.32624 - 3.99201i) q^{27} +(-1.13663 + 3.87101i) q^{28} +(-0.0980958 - 1.02731i) q^{29} +(1.50517 + 2.87401i) q^{30} +(-4.02666 - 3.16660i) q^{31} +(-0.971812 - 0.235759i) q^{32} +(3.55064 - 4.15139i) q^{33} +(-2.84841 + 5.52515i) q^{34} +(-4.08556 - 6.35726i) q^{35} +(-2.54445 - 1.58927i) q^{36} +(-0.0301730 - 0.102760i) q^{37} +(0.263538 - 0.105505i) q^{38} +(-0.0773969 + 1.87941i) q^{39} +(1.52578 - 1.08650i) q^{40} +(-6.42991 - 6.74349i) q^{41} +(6.23154 + 3.16194i) q^{42} +(-0.883792 - 1.12383i) q^{43} +(-2.65322 - 1.70512i) q^{44} +(5.37083 - 1.65247i) q^{45} +(1.06438 - 4.67623i) q^{46} +(-9.58561 + 5.53425i) q^{47} +(-0.709356 + 1.58013i) q^{48} +(-8.61215 - 3.44779i) q^{49} +(0.141777 - 1.48476i) q^{50} +(8.50591 + 6.60089i) q^{51} +(1.08108 - 0.103230i) q^{52} +(-2.33524 + 2.69502i) q^{53} +(-3.51242 + 3.82922i) q^{54} +(5.66824 - 1.66435i) q^{55} +(1.31953 - 3.81254i) q^{56} +(-0.0961592 - 0.482186i) q^{57} +(0.0491035 + 1.03081i) q^{58} +(1.11402 + 5.78010i) q^{59} +(-1.36671 - 2.94238i) q^{60} +(5.16453 + 12.9004i) q^{61} +(3.87143 + 3.35461i) q^{62} +(7.35858 - 9.60944i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-1.17994 + 1.65699i) q^{65} +(-3.74415 + 3.97774i) q^{66} +(0.764768 + 1.48344i) q^{67} +(3.10808 - 5.38336i) q^{68} +(-7.62558 - 3.29402i) q^{69} +(3.77844 + 6.54445i) q^{70} +(-3.34355 + 5.20267i) q^{71} +(2.46594 + 1.70854i) q^{72} +(-2.82590 - 6.18785i) q^{73} +(0.0252493 + 0.104079i) q^{74} +(-2.48336 - 0.711837i) q^{75} +(-0.268259 + 0.0928454i) q^{76} +(7.86555 - 10.0019i) q^{77} +(0.166735 - 1.87359i) q^{78} +(-3.84453 - 1.33061i) q^{79} +(-1.57575 + 1.01267i) q^{80} +(5.40766 + 7.19425i) q^{81} +(6.10176 + 7.04180i) q^{82} +(5.72306 + 5.45693i) q^{83} +(-6.07403 - 3.45487i) q^{84} +(3.80821 + 11.0031i) q^{85} +(0.829316 + 1.16461i) q^{86} +(1.77085 + 0.242977i) q^{87} +(2.56908 + 1.82944i) q^{88} +(0.618498 + 4.30175i) q^{89} +(-5.44337 + 1.39504i) q^{90} +4.38138i q^{91} +(-1.28568 + 4.62029i) q^{92} +(6.93891 - 5.52953i) q^{93} +(9.83808 - 5.07188i) q^{94} +(0.197620 - 0.493631i) q^{95} +(0.783738 - 1.54459i) q^{96} +(-4.55644 + 1.10538i) q^{97} +(8.43835 + 3.85366i) q^{98} +(5.58714 + 7.63590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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