LMFDB - Embedded newform 460.2.o.b.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	460.19
Dual form			460.2.o.b.339.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21441 - 0.724711i) q^{2} +(-0.381027 + 0.111880i) q^{3} +(0.949588 + 1.76019i) q^{4} +(-1.73128 - 1.41516i) q^{5} +(0.543804 + 0.140267i) q^{6} +(-2.86375 + 0.411745i) q^{7} +(0.122443 - 2.82578i) q^{8} +(-2.39110 + 1.53666i) q^{9} +O(q^{10})$	\(q+(-1.21441 - 0.724711i) q^{2} +(-0.381027 + 0.111880i) q^{3} +(0.949588 + 1.76019i) q^{4} +(-1.73128 - 1.41516i) q^{5} +(0.543804 + 0.140267i) q^{6} +(-2.86375 + 0.411745i) q^{7} +(0.122443 - 2.82578i) q^{8} +(-2.39110 + 1.53666i) q^{9} +(1.07690 + 2.97326i) q^{10} +(1.95921 - 4.29008i) q^{11} +(-0.558748 - 0.564442i) q^{12} +(4.51655 + 0.649381i) q^{13} +(3.77616 + 1.57536i) q^{14} +(0.817991 + 0.345518i) q^{15} +(-2.19657 + 3.34292i) q^{16} +(5.34194 + 6.16493i) q^{17} +(4.01741 - 0.133288i) q^{18} +(-2.02559 + 2.33766i) q^{19} +(0.846952 - 4.39120i) q^{20} +(1.04510 - 0.477281i) q^{21} +(-5.48836 + 3.79006i) q^{22} +(-4.44735 + 1.79473i) q^{23} +(0.269493 + 1.09040i) q^{24} +(0.994655 + 4.90007i) q^{25} +(-5.01433 - 4.06181i) q^{26} +(1.51931 - 1.75338i) q^{27} +(-3.44413 - 4.64976i) q^{28} +(3.60152 + 4.15637i) q^{29} +(-0.742976 - 1.01241i) q^{30} +(-0.942433 + 3.20963i) q^{31} +(5.09018 - 2.46780i) q^{32} +(-0.266541 + 1.85383i) q^{33} +(-2.01952 - 11.3581i) q^{34} +(5.54063 + 3.33981i) q^{35} +(-4.97538 - 2.74960i) q^{36} +(-2.89364 + 1.85963i) q^{37} +(4.15403 - 1.37091i) q^{38} +(-1.79358 + 0.257878i) q^{39} +(-4.21090 + 4.71893i) q^{40} +(-0.221064 - 0.142070i) q^{41} +(-1.61507 - 0.177780i) q^{42} +(2.77628 + 9.45516i) q^{43} +(9.41182 - 0.625210i) q^{44} +(6.31428 + 0.723384i) q^{45} +(6.70157 + 1.04351i) q^{46} +5.00682 q^{47} +(0.462947 - 1.51949i) q^{48} +(1.31507 - 0.386139i) q^{49} +(2.34321 - 6.67153i) q^{50} +(-2.72515 - 1.75135i) q^{51} +(3.14582 + 8.56664i) q^{52} +(-0.497986 - 3.46357i) q^{53} +(-3.11576 + 1.02826i) q^{54} +(-9.46309 + 4.65473i) q^{55} +(0.812853 + 8.14272i) q^{56} +(0.510269 - 1.11733i) q^{57} +(-1.36155 - 7.65760i) q^{58} +(4.18134 + 0.601186i) q^{59} +(0.168575 + 1.76792i) q^{60} +(1.46943 - 5.00443i) q^{61} +(3.47056 - 3.21482i) q^{62} +(6.21478 - 5.38514i) q^{63} +(-7.97002 - 0.691992i) q^{64} +(-6.90042 - 7.51589i) q^{65} +(1.66718 - 2.05815i) q^{66} +(1.84905 - 0.844431i) q^{67} +(-5.77883 + 15.2570i) q^{68} +(1.49377 - 1.18141i) q^{69} +(-4.30820 - 8.07126i) q^{70} +(-1.25739 + 0.574231i) q^{71} +(4.04950 + 6.94485i) q^{72} +(5.57478 + 4.83057i) q^{73} +(4.86177 - 0.161301i) q^{74} +(-0.927208 - 1.75578i) q^{75} +(-6.03821 - 1.34562i) q^{76} +(-3.84428 + 13.0924i) q^{77} +(2.36503 + 0.986656i) q^{78} +(1.21809 - 8.47201i) q^{79} +(8.53363 - 2.67903i) q^{80} +(3.15947 - 6.91828i) q^{81} +(0.165504 + 0.332739i) q^{82} +(-3.18533 - 4.95647i) q^{83} +(1.83252 + 1.38636i) q^{84} +(-0.524043 - 18.2329i) q^{85} +(3.48071 - 13.4945i) q^{86} +(-1.83729 - 1.18075i) q^{87} +(-11.8829 - 6.06159i) q^{88} +(3.17088 + 10.7990i) q^{89} +(-7.14388 - 5.45451i) q^{90} -13.2016 q^{91} +(-7.38222 - 6.12396i) q^{92} -1.32840i q^{93} +(-6.08034 - 3.62850i) q^{94} +(6.81502 - 1.18061i) q^{95} +(-1.66340 + 1.50979i) q^{96} +(2.88700 + 1.85536i) q^{97} +(-1.87687 - 0.484113i) q^{98} +(1.90774 + 13.2686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−1.21441	−	0.724711i	−0.858718	−	0.512448i
$2$	−1.21441	−	0.724711i	−0.858718	−	0.512448i
$3$	−0.381027	+	0.111880i	−0.219986	+	0.0645937i	−0.389868	−	0.920871i	$-0.627479\pi$
$3$	−0.381027	+	0.111880i	−0.219986	+	0.0645937i	0.169882	+	0.985464i	$0.445661\pi$
$4$	0.949588	+	1.76019i	0.474794	+	0.880097i
$5$	−1.73128	−	1.41516i	−0.774252	−	0.632878i
$5$	−1.73128	−	1.41516i	−0.774252	−	0.632878i
$6$	0.543804	+	0.140267i	0.222007	+	0.0572636i
$7$	−2.86375	+	0.411745i	−1.08239	+	0.155625i	−0.660356	−	0.750953i	$-0.729595\pi$
$7$	−2.86375	+	0.411745i	−1.08239	+	0.155625i	−0.422039	+	0.906578i	$0.638685\pi$
$8$	0.122443	−	2.82578i	0.0432901	−	0.999063i
$9$	−2.39110	+	1.53666i	−0.797032	+	0.512221i
$10$	1.07690	+	2.97326i	0.340547	+	0.940228i
$11$	1.95921	−	4.29008i	0.590725	−	1.29351i	−0.344278	−	0.938868i	$-0.611876\pi$
$11$	1.95921	−	4.29008i	0.590725	−	1.29351i	0.935003	−	0.354640i	$-0.115397\pi$
$12$	−0.558748	−	0.564442i	−0.161297	−	0.162940i
$13$	4.51655	+	0.649381i	1.25266	+	0.180106i	0.736532	−	0.676403i	$-0.236462\pi$
$13$	4.51655	+	0.649381i	1.25266	+	0.180106i	0.516132	+	0.856509i	$0.327371\pi$
$14$	3.77616	+	1.57536i	1.00922	+	0.421033i
$15$	0.817991	+	0.345518i	0.211204	+	0.0892125i
$16$	−2.19657	+	3.34292i	−0.549142	+	0.835729i
$17$	5.34194	+	6.16493i	1.29561	+	1.49522i	0.758442	+	0.651740i	$0.225961\pi$
$17$	5.34194	+	6.16493i	1.29561	+	1.49522i	0.537169	+	0.843475i	$0.319494\pi$
$18$	4.01741	−	0.133288i	0.946913	−	0.0314162i
$19$	−2.02559	+	2.33766i	−0.464703	+	0.536295i	−0.938931	−	0.344107i	$-0.888182\pi$
$19$	−2.02559	+	2.33766i	−0.464703	+	0.536295i	0.474228	+	0.880402i	$0.342727\pi$
$20$	0.846952	−	4.39120i	0.189384	−	0.981903i
$21$	1.04510	−	0.477281i	0.228059	−	0.104151i
$22$	−5.48836	+	3.79006i	−1.17012	+	0.808043i
$23$	−4.44735	+	1.79473i	−0.927337	+	0.374226i
$23$	−4.44735	+	1.79473i	−0.927337	+	0.374226i
$24$	0.269493	+	1.09040i	0.0550099	+	0.222576i
$25$	0.994655	+	4.90007i	0.198931	+	0.980013i
$26$	−5.01433	−	4.06181i	−0.983391	−	0.796586i
$27$	1.51931	−	1.75338i	0.292392	−	0.337438i
$28$	−3.44413	−	4.64976i	−0.650879	−	0.878723i
$29$	3.60152	+	4.15637i	0.668785	+	0.771819i	0.984186	−	0.177140i	$-0.0566845\pi$
$29$	3.60152	+	4.15637i	0.668785	+	0.771819i	−0.315401	+	0.948958i	$0.602139\pi$
$30$	−0.742976	−	1.01241i	−0.135648	−	0.184840i
$31$	−0.942433	+	3.20963i	−0.169266	+	0.576467i	0.830544	+	0.556954i	$0.188030\pi$
$31$	−0.942433	+	3.20963i	−0.169266	+	0.576467i	−0.999810	+	0.0195135i	$0.993788\pi$
$32$	5.09018	−	2.46780i	0.899826	−	0.436249i
$33$	−0.266541	+	1.85383i	−0.0463988	+	0.322711i
$34$	−2.01952	−	11.3581i	−0.346345	−	1.94790i
$35$	5.54063	+	3.33981i	0.936538	+	0.564531i
$36$	−4.97538	−	2.74960i	−0.829230	−	0.458266i
$37$	−2.89364	+	1.85963i	−0.475712	+	0.305722i	−0.756437	−	0.654067i	$-0.773062\pi$
$37$	−2.89364	+	1.85963i	−0.475712	+	0.305722i	0.280725	+	0.959788i	$0.409425\pi$
$38$	4.15403	−	1.37091i	0.673872	−	0.222391i
$39$	−1.79358	+	0.257878i	−0.287202	+	0.0412935i
$40$	−4.21090	+	4.71893i	−0.665802	+	0.746128i
$41$	−0.221064	−	0.142070i	−0.0345245	−	0.0221875i	0.523265	−	0.852170i	$-0.324714\pi$
$41$	−0.221064	−	0.142070i	−0.0345245	−	0.0221875i	−0.557789	+	0.829983i	$0.688350\pi$
$42$	−1.61507	−	0.177780i	−0.249211	−	0.0274320i
$43$	2.77628	+	9.45516i	0.423379	+	1.44190i	0.844824	+	0.535044i	$0.179705\pi$
$43$	2.77628	+	9.45516i	0.423379	+	1.44190i	−0.421445	+	0.906854i	$0.638477\pi$
$44$	9.41182	−	0.625210i	1.41888	−	0.0942539i
$45$	6.31428	+	0.723384i	0.941277	+	0.107836i
$46$	6.70157	+	1.04351i	0.988093	+	0.153858i
$47$	5.00682			0.730320			0.365160	−	0.930945i	$-0.381014\pi$
$47$	5.00682			0.730320			0.365160	+	0.930945i	$0.381014\pi$
$48$	0.462947	−	1.51949i	0.0668206	−	0.219320i
$49$	1.31507	−	0.386139i	0.187867	−	0.0551627i
$50$	2.34321	−	6.67153i	0.331380	−	0.943497i
$51$	−2.72515	−	1.75135i	−0.381598	−	0.245238i
$52$	3.14582	+	8.56664i	0.436247	+	1.18798i
$53$	−0.497986	−	3.46357i	−0.0684036	−	0.475758i	−0.995014	−	0.0997348i	$-0.968201\pi$
$53$	−0.497986	−	3.46357i	−0.0684036	−	0.475758i	0.926610	−	0.376023i	$-0.122709\pi$
$54$	−3.11576	+	1.02826i	−0.424001	+	0.139928i
$55$	−9.46309	+	4.65473i	−1.27600	+	0.627643i
$56$	0.812853	+	8.14272i	0.108622	+	1.08812i
$57$	0.510269	−	1.11733i	0.0675867	−	0.147994i
$58$	−1.36155	−	7.65760i	−0.178781	−	1.00549i
$59$	4.18134	+	0.601186i	0.544364	+	0.0782677i	0.409010	−	0.912530i	$-0.365874\pi$
$59$	4.18134	+	0.601186i	0.544364	+	0.0782677i	0.135353	+	0.990797i	$0.456783\pi$
$60$	0.168575	+	1.76792i	0.0217629	+	0.228238i
$61$	1.46943	−	5.00443i	0.188142	−	0.640751i	−0.810355	−	0.585939i	$-0.800726\pi$
$61$	1.46943	−	5.00443i	0.188142	−	0.640751i	0.998497	−	0.0548122i	$-0.0174560\pi$
$62$	3.47056	−	3.21482i	0.440761	−	0.408283i
$63$	6.21478	−	5.38514i	0.782989	−	0.678464i
$64$	−7.97002	−	0.691992i	−0.996252	−	0.0864990i
$65$	−6.90042	−	7.51589i	−0.855892	−	0.932231i
$66$	1.66718	−	2.05815i	0.205216	−	0.253341i
$67$	1.84905	−	0.844431i	0.225897	−	0.103164i	−0.299252	−	0.954174i	$-0.596737\pi$
$67$	1.84905	−	0.844431i	0.225897	−	0.103164i	0.525149	+	0.851011i	$0.324010\pi$
$68$	−5.77883	+	15.2570i	−0.700786	+	1.85018i
$69$	1.49377	−	1.18141i	0.179829	−	0.142225i
$70$	−4.30820	−	8.07126i	−0.514929	−	0.964700i
$71$	−1.25739	+	0.574231i	−0.149225	+	0.0681487i	−0.488628	−	0.872492i	$-0.662502\pi$
$71$	−1.25739	+	0.574231i	−0.149225	+	0.0681487i	0.339403	+	0.940641i	$0.389775\pi$
$72$	4.04950	+	6.94485i	0.477238	+	0.818459i
$73$	5.57478	+	4.83057i	0.652479	+	0.565376i	0.916942	−	0.399020i	$-0.130649\pi$
$73$	5.57478	+	4.83057i	0.652479	+	0.565376i	−0.264464	+	0.964396i	$0.585195\pi$
$74$	4.86177	−	0.161301i	0.565169	−	0.0187509i
$75$	−0.927208	−	1.75578i	−0.107065	−	0.202740i
$76$	−6.03821	−	1.34562i	−0.692630	−	0.154354i
$77$	−3.84428	+	13.0924i	−0.438096	+	1.49202i
$78$	2.36503	+	0.986656i	0.267787	+	0.111717i
$79$	1.21809	−	8.47201i	0.137046	−	0.953176i	−0.799008	−	0.601320i	$-0.794642\pi$
$79$	1.21809	−	8.47201i	0.137046	−	0.953176i	0.936054	−	0.351856i	$-0.114449\pi$
$80$	8.53363	−	2.67903i	0.954088	−	0.299525i
$81$	3.15947	−	6.91828i	0.351053	−	0.768698i
$82$	0.165504	+	0.332739i	0.0182768	+	0.0367448i
$83$	−3.18533	−	4.95647i	−0.349636	−	0.544044i	0.621242	−	0.783619i	$-0.286628\pi$
$83$	−3.18533	−	4.95647i	−0.349636	−	0.544044i	−0.970878	+	0.239575i	$0.922992\pi$
$84$	1.83252	+	1.38636i	0.199944	+	0.151264i
$85$	−0.524043	−	18.2329i	−0.0568405	−	1.97764i
$86$	3.48071	−	13.4945i	0.375334	−	1.45514i
$87$	−1.83729	−	1.18075i	−0.196978	−	0.126590i
$88$	−11.8829	−	6.06159i	−1.26672	−	0.646167i
$89$	3.17088	+	10.7990i	0.336112	+	1.14469i	0.938151	+	0.346226i	$0.112537\pi$
$89$	3.17088	+	10.7990i	0.336112	+	1.14469i	−0.602039	+	0.798467i	$0.705645\pi$
$90$	−7.14388	−	5.45451i	−0.753031	−	0.574956i
$91$	−13.2016			−1.38391
$92$	−7.38222	−	6.12396i	−0.769649	−	0.638467i
$93$		−	1.32840i		−	0.137748i
$94$	−6.08034	−	3.62850i	−0.627139	−	0.374251i
$95$	6.81502	−	1.18061i	0.699206	−	0.121128i
$96$	−1.66340	+	1.50979i	−0.169770	+	0.154092i
$97$	2.88700	+	1.85536i	0.293131	+	0.188384i	0.678938	−	0.734196i	$-0.262441\pi$
$97$	2.88700	+	1.85536i	0.293131	+	0.188384i	−0.385807	+	0.922579i	$0.626077\pi$
$98$	−1.87687	−	0.484113i	−0.189593	−	0.0489028i
$99$	1.90774	+	13.2686i	0.191735	+	1.33355i
$100$	−7.68056	+	6.40383i	−0.768056	+	0.640383i
$101$	−10.8313	+	6.96088i	−1.07776	+	0.692634i	−0.954039	−	0.299684i	$-0.903119\pi$
$101$	−10.8313	+	6.96088i	−1.07776	+	0.692634i	−0.123720	+	0.992317i	$0.539483\pi$
$102$	2.04023	+	4.10181i	0.202013	+	0.406139i
$103$	−14.8732	−	6.79234i	−1.46550	−	0.669269i	−0.486599	−	0.873625i	$-0.661763\pi$
$103$	−14.8732	−	6.79234i	−1.46550	−	0.669269i	−0.978897	+	0.204356i	$0.934490\pi$
$104$	2.38802	−	12.6832i	0.234165	−	1.24369i
$105$	−2.48479	−	0.652674i	−0.242490	−	0.0636945i
$106$	−1.90533	+	4.56709i	−0.185062	+	0.443595i
$107$	−2.87032	+	9.77541i	−0.277484	+	0.945025i	0.696338	+	0.717714i	$0.254811\pi$
$107$	−2.87032	+	9.77541i	−0.277484	+	0.945025i	−0.973822	+	0.227311i	$0.927007\pi$
$108$	4.52901	+	1.00930i	0.435804	+	0.0971196i
$109$	−8.23912	+	7.13924i	−0.789164	+	0.683815i	−0.953100	−	0.302656i	$-0.902127\pi$
$109$	−8.23912	+	7.13924i	−0.789164	+	0.683815i	0.163935	+	0.986471i	$0.447581\pi$
$110$	14.8654	+	1.20525i	1.41736	+	0.114916i
$111$	0.894501	−	1.03231i	0.0849023	−	0.0979825i
$112$	4.91399	−	10.4777i	0.464328	−	0.990049i
$113$	−3.42267	−	7.49461i	−0.321978	−	0.705034i	0.677559	−	0.735469i	$-0.263038\pi$
$113$	−3.42267	−	7.49461i	−0.321978	−	0.705034i	−0.999537	+	0.0304350i	$0.990311\pi$
$114$	−1.42942	+	0.987103i	−0.133877	+	0.0924507i
$115$	10.2394	+	3.18654i	0.954832	+	0.297146i
$116$	−3.89607	+	10.2862i	−0.361741	+	0.955050i
$117$	−11.7974	+	5.38768i	−1.09067	+	0.498091i
$118$	−4.64218	−	3.76035i	−0.427347	−	0.346168i
$119$	−17.8364	−	15.4553i	−1.63506	−	1.41678i
$120$	1.07651	−	2.26915i	0.0982719	−	0.207144i
$121$	−7.36280	−	8.49712i	−0.669345	−	0.772465i
$122$	−5.41126	+	5.01252i	−0.489912	+	0.453812i
$123$	0.100126	+	0.0293997i	0.00902807	+	0.00265088i
$124$	−6.54450	+	1.38896i	−0.587714	+	0.124732i
$125$	5.21234	−	9.89098i	0.466206	−	0.884676i
$126$	−11.4500	+	2.03585i	−1.02004	+	0.181368i
$127$	−6.62652	+	14.5101i	−0.588009	+	1.28756i	0.348629	+	0.937261i	$0.386647\pi$
$127$	−6.62652	+	14.5101i	−0.588009	+	1.28756i	−0.936638	+	0.350299i	$0.886080\pi$
$128$	9.17738	+	6.61632i	0.811173	+	0.584806i
$129$	−2.11568	−	3.29206i	−0.186275	−	0.289850i
$130$	2.93310	+	14.1282i	0.257250	+	1.23912i
$131$	7.17748	−	1.03197i	0.627099	−	0.0901633i	0.178564	−	0.983928i	$-0.442855\pi$
$131$	7.17748	−	1.03197i	0.627099	−	0.0901633i	0.448535	+	0.893765i	$0.351946\pi$
$132$	−3.51621	+	1.29121i	−0.306047	+	0.112386i
$133$	4.83826	−	7.52849i	0.419531	−	0.652803i
$134$	−2.85747	−	0.314538i	−0.246848	−	0.0271719i
$135$	−5.11166	+	0.885522i	−0.439942	+	0.0762136i
$136$	18.0748	−	14.3403i	1.54990	−	1.22967i
$137$	0.514344			0.0439434			0.0219717	−	0.999759i	$-0.493006\pi$
$137$	0.514344			0.0439434			0.0219717	+	0.999759i	$0.493006\pi$
$138$	−2.67023	+	0.352163i	−0.227305	+	0.0299781i
$139$			12.2052i			1.03523i	0.855613	+	0.517616i	$0.173180\pi$
$139$			12.2052i			1.03523i	−0.855613	+	0.517616i	$0.826820\pi$
$140$	−0.617401	+	12.9240i	−0.0521799	+	1.09228i
$141$	−1.90773	+	0.560161i	−0.160660	+	0.0471741i
$142$	1.94314	+	0.213892i	0.163065	+	0.0179495i
$143$	11.6348	−	18.1041i	0.972949	−	1.51394i
$144$	0.115262	−	11.3686i	0.00960514	−	0.947385i
$145$	−0.353308	−	12.2926i	−0.0293406	−	1.02084i
$146$	−3.26930	−	9.90641i	−0.270569	−	0.819860i
$147$	−0.457875	+	0.294258i	−0.0377649	+	0.0242700i
$148$	−6.02108	−	3.32749i	−0.494930	−	0.273518i
$149$	4.20550	+	1.92059i	0.344528	+	0.157341i	0.580162	−	0.814501i	$-0.302989\pi$
$149$	4.20550	+	1.92059i	0.344528	+	0.157341i	−0.235634	+	0.971842i	$0.575717\pi$
$150$	−0.146419	+	2.80419i	−0.0119550	+	0.228961i
$151$	13.9637	+	2.00768i	1.13635	+	0.163382i	0.684708	−	0.728817i	$-0.259930\pi$
$151$	13.9637	+	2.00768i	1.13635	+	0.163382i	0.451641	+	0.892200i	$0.350839\pi$
$152$	6.35767	+	6.01010i	0.515676	+	0.487483i
$153$	−22.2465	−	6.53217i	−1.79852	−	0.528095i
$154$	14.1567	−	13.1136i	1.14078	−	1.05672i
$155$	6.17375	−	4.22308i	0.495888	−	0.339206i
$156$	−2.15707	−	2.91217i	−0.172704	−	0.233160i
$157$	3.18309	−	3.67348i	0.254038	−	0.293176i	−0.614378	−	0.789012i	$-0.710593\pi$
$157$	3.18309	−	3.67348i	0.254038	−	0.293176i	0.868416	+	0.495836i	$0.165138\pi$
$158$	−7.61902	+	9.40574i	−0.606137	+	0.748280i
$159$	0.577248	+	1.26400i	0.0457788	+	0.100242i
$160$	−12.3049	−	2.93097i	−0.972784	−	0.231713i
$161$	11.9971	−	6.97082i	0.945507	−	0.549377i
$162$	−8.85065	+	6.11193i	−0.695373	+	0.480199i
$163$	3.35601	+	7.34863i	0.262863	+	0.575589i	0.994336	−	0.106281i	$-0.0338943\pi$
$163$	3.35601	+	7.34863i	0.262863	+	0.575589i	−0.731474	+	0.681870i	$0.761167\pi$
$164$	0.0401498	−	0.524024i	0.00313518	−	0.0409194i
$165$	3.08492	−	2.83230i	0.240161	−	0.220494i
$166$	0.276290	+	8.32764i	0.0214443	+	0.646350i
$167$	3.81211	+	4.39941i	0.294990	+	0.340437i	0.883826	−	0.467816i	$-0.154959\pi$
$167$	3.81211	+	4.39941i	0.294990	+	0.340437i	−0.588836	+	0.808253i	$0.700414\pi$
$168$	−1.22072	−	3.01165i	−0.0941809	−	0.232354i
$169$	7.50408	+	2.20340i	0.577237	+	0.169492i
$170$	−12.5772	+	22.5220i	−0.964626	+	1.72736i
$171$	1.25119	−	8.70222i	0.0956809	−	0.665475i
$172$	−14.0066	+	13.8653i	−1.06799	+	1.05722i
$173$	2.76946	+	1.26477i	0.210558	+	0.0961588i	0.517902	−	0.855440i	$-0.326713\pi$
$173$	2.76946	+	1.26477i	0.210558	+	0.0961588i	−0.307344	+	0.951598i	$0.599440\pi$
$174$	1.37552	+	2.76542i	0.104278	+	0.209646i
$175$	−4.86602	−	13.6230i	−0.367837	−	1.02980i
$176$	10.0378	+	15.9729i	0.756630	+	1.20401i
$177$	−1.66046	+	0.238738i	−0.124808	+	0.0179447i
$178$	3.97542	−	15.4124i	0.297970	−	1.15521i
$179$	−9.24531	+	14.3860i	−0.691027	+	1.07526i	0.301528	+	0.953457i	$0.402503\pi$
$179$	−9.24531	+	14.3860i	−0.691027	+	1.07526i	−0.992555	+	0.121801i	$0.961133\pi$
$180$	4.72266	+	11.8013i	0.352007	+	0.879615i
$181$	0.369973	+	1.26001i	0.0274999	+	0.0936559i	0.972100	−	0.234569i	$-0.0753678\pi$
$181$	0.369973	+	1.26001i	0.0274999	+	0.0936559i	−0.944600	+	0.328225i	$0.893550\pi$
$182$	16.0322	+	9.56737i	1.18839	+	0.709180i
$183$			2.07122i			0.153109i
$184$	4.52695	+	12.7870i	0.333731	+	0.942668i
$185$	7.64138	+	0.875421i	0.561805	+	0.0643622i
$186$	−0.962703	+	1.61322i	−0.0705888	+	0.118287i
$187$	36.9140	−	10.8389i	2.69942	−	0.792622i
$188$	4.75442	+	8.81298i	0.346752	+	0.642753i
$189$	−3.62898	+	5.64680i	−0.263969	+	0.410744i
$190$	−9.13183	−	3.50518i	−0.662493	−	0.254292i
$191$	−1.93086	−	13.4295i	−0.139712	−	0.971722i	−0.932228	−	0.361870i	$-0.882138\pi$
$191$	−1.93086	−	13.4295i	−0.139712	−	0.971722i	0.792516	−	0.609851i	$-0.208771\pi$
$192$	3.11421	−	0.628015i	0.224749	−	0.0453230i
$193$	5.85623	+	9.11248i	0.421541	+	0.655930i	0.985462	−	0.169899i	$-0.0543440\pi$
$193$	5.85623	+	9.11248i	0.421541	+	0.655930i	−0.563921	+	0.825829i	$0.690708\pi$
$194$	−2.16140	−	4.34541i	−0.155180	−	0.311983i
$195$	3.47012	+	2.09174i	0.248501	+	0.149792i
$196$	1.92845	+	1.94810i	0.137746	+	0.139150i
$197$	−10.1133	−	1.45407i	−0.720540	−	0.103598i	−0.227716	−	0.973727i	$-0.573126\pi$
$197$	−10.1133	−	1.45407i	−0.720540	−	0.103598i	−0.492823	+	0.870130i	$0.664035\pi$
$198$	7.29915	−	17.4962i	0.518728	−	1.24340i
$199$	−22.9653	−	6.74323i	−1.62797	−	0.478015i	−0.664825	−	0.746999i	$-0.731494\pi$
$199$	−22.9653	−	6.74323i	−1.62797	−	0.478015i	−0.963145	+	0.268984i	$0.913312\pi$
$200$	13.9683	−	2.21070i	0.987707	−	0.156320i
$201$	−0.610061	+	0.528621i	−0.0430304	+	0.0372861i
$202$	18.1983	−	0.603775i	1.28043	−	0.0424815i
$203$	−12.0252	−	10.4199i	−0.844003	−	0.731333i
$204$	0.494944	−	6.45986i	0.0346530	−	0.452281i
$205$	0.181674	+	0.558803i	0.0126886	+	0.0390285i
$206$	13.1396	+	19.0274i	0.915482	+	1.32570i
$207$	7.87616	−	11.1255i	0.547431	−	0.773272i
$208$	−12.0917	+	13.6720i	−0.838410	+	0.947985i
$209$	6.06017	+	13.2699i	0.419191	+	0.917899i
$210$	2.54455	+	2.59337i	0.175591	+	0.178959i
$211$	19.9953	+	17.3260i	1.37653	+	1.19277i	0.958759	+	0.284220i	$0.0917345\pi$
$211$	19.9953	+	17.3260i	1.37653	+	1.19277i	0.417772	+	0.908552i	$0.362811\pi$
$212$	5.62367	−	4.16551i	0.386235	−	0.286089i
$213$	0.414855	−	0.359474i	0.0284254	−	0.0246307i
$214$	10.5701	−	9.79121i	0.722557	−	0.669313i
$215$	8.57402	−	20.2984i	0.584743	−	1.38434i
$216$	−4.76863	−	4.50792i	−0.324464	−	0.306725i
$217$	1.37734	−	9.57962i	0.0935001	−	0.650307i
$218$	15.1796	−	2.69899i	1.02809	−	0.182798i
$219$	−2.66458	−	1.21687i	−0.180056	−	0.0822288i
$220$	−17.1793	−	12.2368i	−1.15823	−	0.825005i
$221$	20.1237	+	31.3131i	1.35367	+	2.10635i
$222$	−1.83442	+	0.605393i	−0.123118	+	0.0406313i
$223$	2.49550	+	17.3566i	0.167111	+	1.16228i	0.884818	+	0.465937i	$0.154283\pi$
$223$	2.49550	+	17.3566i	0.167111	+	1.16228i	−0.717707	+	0.696345i	$0.754808\pi$
$224$	−13.5609	+	9.16301i	−0.906076	+	0.612229i
$225$	−9.90807	−	10.1881i	−0.660538	−	0.679205i
$226$	−1.27490	+	11.5820i	−0.0848048	+	0.770423i
$227$	−5.27128	−	17.9523i	−0.349867	−	1.19154i	−0.927055	−	0.374926i	$-0.877668\pi$
$227$	−5.27128	−	17.9523i	−0.349867	−	1.19154i	0.577188	−	0.816612i	$-0.304150\pi$
$228$	2.45127	−	0.162833i	0.162339	−	0.0107839i
$229$			10.7533i			0.710597i	0.934753	+	0.355298i	$0.115621\pi$
$229$			10.7533i			0.710597i	−0.934753	+	0.355298i	$0.884379\pi$
$230$	−10.1256	−	11.2904i	−0.667660	−	0.744467i
$231$		−	5.41865i		−	0.356521i
$232$	12.1860	−	9.66816i	0.800047	−	0.634746i
$233$	−4.09657	−	13.9516i	−0.268375	−	0.914002i	−0.977856	−	0.209277i	$-0.932889\pi$
$233$	−4.09657	−	13.9516i	−0.268375	−	0.914002i	0.709481	−	0.704724i	$-0.248929\pi$
$234$	18.2314	+	2.00683i	1.19182	+	0.131191i
$235$	−8.66821	−	7.08545i	−0.565452	−	0.462204i
$236$	2.91234	+	7.93084i	0.189577	+	0.516254i
$237$	0.483720	+	3.36434i	0.0314210	+	0.218538i
$238$	10.4600	+	31.6953i	0.678024	+	2.05450i
$239$	−1.56553	−	2.43602i	−0.101266	−	0.157573i	0.786923	−	0.617051i	$-0.211673\pi$
$239$	−1.56553	−	2.43602i	−0.101266	−	0.157573i	−0.888189	+	0.459478i	$0.848036\pi$
$240$	−2.95181	+	1.97552i	−0.190539	+	0.127519i
$241$	−17.1494	−	7.83185i	−1.10469	−	0.504494i	−0.222281	−	0.974983i	$-0.571350\pi$
$241$	−17.1494	−	7.83185i	−1.10469	−	0.504494i	−0.882406	+	0.470489i	$0.844078\pi$
$242$	2.78350	+	15.6549i	0.178930	+	1.00633i
$243$	−1.42036	+	9.87884i	−0.0911163	+	0.633728i
$244$	10.2041	−	2.16566i	0.653252	−	0.138642i
$245$	−2.82320	−	1.19251i	−0.180367	−	0.0761870i
$246$	−0.100288	−	0.108266i	−0.00639413	−	0.00690278i
$247$	−10.6667	+	9.24275i	−0.678706	+	0.588102i
$248$	8.95431	+	3.05610i	0.568599	+	0.194063i
$249$	1.76822	+	1.53218i	0.112057	+	0.0970977i
$250$	−13.4980	+	8.23427i	−0.853690	+	0.520781i
$251$	11.7417	+	25.7108i	0.741132	+	1.62285i	0.781684	+	0.623675i	$0.214361\pi$
$251$	11.7417	+	25.7108i	0.741132	+	1.62285i	−0.0405523	+	0.999177i	$0.512912\pi$
$252$	15.3804	+	5.82556i	0.968872	+	0.366976i
$253$	−1.01380	+	22.5958i	−0.0637372	+	1.42058i
$254$	18.5629	−	12.8189i	1.16474	−	0.804327i
$255$	2.23956	+	6.88860i	0.140247	+	0.431381i
$256$	−6.35019	−	14.6859i	−0.396887	−	0.917868i
$257$	−16.2599	−	14.0893i	−1.01427	−	0.878867i	−0.0216017	−	0.999767i	$-0.506877\pi$
$257$	−16.2599	−	14.0893i	−1.01427	−	0.878867i	−0.992665	+	0.120900i	$0.961422\pi$
$258$	0.183510	+	5.53117i	0.0114249	+	0.344355i
$259$	7.52097	−	6.51696i	0.467331	−	0.404944i
$260$	6.67686	−	19.2831i	0.414081	−	1.19589i
$261$	−14.9985	−	4.40396i	−0.928385	−	0.272598i
$262$	−9.46429	−	3.94837i	−0.584705	−	0.243931i
$263$	19.1002	+	2.74619i	1.17777	+	0.169337i	0.703272	−	0.710921i	$-0.251722\pi$
$263$	19.1002	+	2.74619i	1.17777	+	0.169337i	0.474495	+	0.880258i	$0.342631\pi$
$264$	5.20588	+	0.980173i	0.320400	+	0.0603255i
$265$	−4.03934	+	6.70113i	−0.248135	+	0.411647i
$266$	−11.3316	+	5.63633i	−0.694786	+	0.345586i
$267$	−2.41638	−	3.75996i	−0.147880	−	0.230106i
$268$	3.24219	+	2.45282i	0.198048	+	0.149830i
$269$	−1.24756	−	8.67695i	−0.0760649	−	0.529043i	−0.991854	−	0.127383i	$-0.959342\pi$
$269$	−1.24756	−	8.67695i	−0.0760649	−	0.529043i	0.915789	−	0.401660i	$-0.131567\pi$
$270$	6.84940	+	2.62909i	0.416841	+	0.160001i
$271$	−0.00308903	+	0.00480663i	−0.000187645	+	0.000291982i	−0.841347	−	0.540495i	$-0.818237\pi$
$271$	−0.00308903	+	0.00480663i	−0.000187645	+	0.000291982i	0.841160	+	0.540787i	$0.181873\pi$
$272$	−32.3428	+	4.31599i	−1.96107	+	0.261695i
$273$	5.03017	−	1.47699i	0.304440	−	0.0893916i
$274$	−0.624625	−	0.372751i	−0.0377350	−	0.0225187i
$275$	22.9704	+	5.33313i	1.38517	+	0.321600i
$276$	3.49797	+	1.50747i	0.210553	+	0.0907392i
$277$			0.317913i			0.0191016i	0.999954	+	0.00955078i	$0.00304015\pi$
$277$			0.317913i			0.0191016i	−0.999954	+	0.00955078i	$0.996960\pi$
$278$	8.84525	−	14.8221i	0.530503	−	0.888972i
$279$	−2.67868	−	9.12275i	−0.160368	−	0.546165i
$280$	10.1160	−	15.2476i	0.604545	−	0.911221i
$281$	5.99252	−	9.32454i	0.357484	−	0.556256i	−0.615206	−	0.788367i	$-0.710927\pi$
$281$	5.99252	−	9.32454i	0.357484	−	0.556256i	0.972689	+	0.232111i	$0.0745633\pi$
$282$	2.72273	+	0.702290i	0.162136	+	0.0418208i
$283$	14.0548	−	2.02078i	0.835472	−	0.120123i	0.288716	−	0.957415i	$-0.406772\pi$
$283$	14.0548	−	2.02078i	0.835472	−	0.120123i	0.546756	+	0.837292i	$0.315863\pi$
$284$	−2.20476	−	1.66797i	−0.130828	−	0.0989757i
$285$	−2.46462	+	1.21230i	−0.145991	+	0.0718107i
$286$	−27.2496	+	13.5539i	−1.61130	+	0.801460i
$287$	0.691569	+	0.315829i	0.0408220	+	0.0186428i
$288$	−8.37894	+	13.7226i	−0.493734	+	0.808615i
$289$	−7.05066	+	49.0384i	−0.414745	+	2.88461i
$290$	−8.47949	+	15.1843i	−0.497933	+	0.891650i
$291$	−1.30760	−	0.383947i	−0.0766530	−	0.0225074i
$292$	−3.20901	+	14.3997i	−0.187793	+	0.842682i
$293$	−11.9647	−	13.8080i	−0.698983	−	0.806669i	0.289632	−	0.957138i	$-0.406467\pi$
$293$	−11.9647	−	13.8080i	−0.698983	−	0.806669i	−0.988615	+	0.150469i	$0.951922\pi$
$294$	0.769301	−	0.0255235i	0.0448665	−	0.00148856i
$295$	−6.38829	−	6.95807i	−0.371941	−	0.405115i
$296$	4.90060	+	8.40449i	0.284841	+	0.488501i
$297$	−4.54548	−	9.95321i	−0.263755	−	0.577544i
$298$	−3.71534	−	5.38016i	−0.215224	−	0.311664i
$299$	−21.2521	+	5.21793i	−1.22904	+	0.301761i
$300$	2.21004	−	3.29933i	0.127597	−	0.190487i
$301$	−11.8437	−	25.9341i	−0.682659	−	1.49481i
$302$	−15.5027	−	12.5578i	−0.892079	−	0.722620i
$303$	3.34825	−	3.86409i	0.192352	−	0.221986i
$304$	−3.36525	−	11.9062i	−0.193010	−	0.682868i
$305$	−9.62605	+	6.58458i	−0.551186	+	0.377032i
$306$	22.2825	+	24.0550i	1.27380	+	1.37514i
$307$	−23.5997	−	6.92949i	−1.34690	−	0.395487i	−0.472776	−	0.881183i	$-0.656748\pi$
$307$	−23.5997	−	6.92949i	−1.34690	−	0.395487i	−0.874128	+	0.485696i	$0.838566\pi$
$308$	−26.6956	+	5.66571i	−1.52113	+	0.322834i
$309$	6.42700	+	0.924063i	0.365619	+	0.0525681i
$310$	−10.5580	+	0.654365i	−0.599653	+	0.0371655i
$311$	5.17173	+	2.36185i	0.293262	+	0.133928i	0.556613	−	0.830772i	$-0.312101\pi$
$311$	5.17173	+	2.36185i	0.293262	+	0.133928i	−0.263351	+	0.964700i	$0.584828\pi$
$312$	0.509093	+	5.09982i	0.0288217	+	0.288721i
$313$	11.5961	−	7.45234i	0.655448	−	0.421231i	−0.170205	−	0.985409i	$-0.554443\pi$
$313$	11.5961	−	7.45234i	0.655448	−	0.421231i	0.825653	+	0.564178i	$0.190807\pi$
$314$	−6.52780	+	2.15430i	−0.368385	+	0.121574i
$315$	−18.3803	+	0.528281i	−1.03562	+	0.0297653i
$316$	16.0691	−	5.90084i	0.903956	−	0.331948i
$317$	0.667472	−	1.03861i	0.0374889	−	0.0583339i	−0.822003	−	0.569483i	$-0.807144\pi$
$317$	0.667472	−	1.03861i	0.0374889	−	0.0583339i	0.859492	+	0.511149i	$0.170780\pi$
$318$	0.215016	−	1.95335i	0.0120575	−	0.109538i
$319$	24.8873	−	7.30757i	1.39342	−	0.409145i
$320$	12.8190	+	12.4769i	0.716606	+	0.697478i
$321$		−	4.04582i		−	0.225816i
$322$	−19.6213	−	0.229020i	−1.09345	−	0.0127628i
$323$	−25.2321			−1.40395
$324$	15.1777	−	1.00823i	0.843206	−	0.0560127i
$325$	1.31039	+	22.7773i	0.0726876	+	1.26346i
$326$	1.25006	−	11.3564i	0.0692345	−	0.628972i
$327$	2.34059	−	3.64203i	0.129435	−	0.201405i
$328$	−0.428524	+	0.607283i	−0.0236613	+	0.0335316i
$329$	−14.3383	+	2.06153i	−0.790495	+	0.113656i
$330$	−5.79896	+	1.20390i	−0.319222	+	0.0662727i
$331$	10.2793	+	15.9950i	0.565004	+	0.879163i	0.999771	−	0.0213798i	$-0.00680593\pi$
$331$	10.2793	+	15.9950i	0.565004	+	0.879163i	−0.434768	+	0.900543i	$0.643170\pi$
$332$	5.69960	−	10.3134i	0.312806	−	0.566022i
$333$	4.06135	−	8.89312i	0.222561	−	0.487340i
$334$	−1.44117	−	8.10538i	−0.0788572	−	0.443506i
$335$	−4.39622	−	1.15475i	−0.240191	−	0.0630905i
$336$	−0.700120	+	4.54206i	−0.0381947	+	0.247790i
$337$	27.2451	+	7.99988i	1.48413	+	0.435781i	0.920664	−	0.390355i	$-0.127648\pi$
$337$	27.2451	+	7.99988i	1.48413	+	0.435781i	0.563470	+	0.826136i	$0.309466\pi$
$338$	−7.51621	−	8.11412i	−0.408828	−	0.441350i
$339$	2.14263	+	2.47272i	0.116371	+	0.134300i
$340$	31.5958	−	18.2362i	1.71352	−	0.988995i
$341$	11.9232	+	10.3315i	0.645675	+	0.559481i
$342$	−7.82605	+	9.66131i	−0.423184	+	0.522424i
$343$	14.8152	−	6.76586i	0.799944	−	0.365322i
$344$	27.0581	−	6.68744i	1.45887	−	0.360563i
$345$	−4.25801	−	0.0685732i	−0.229243	−	0.00369186i
$346$	−2.44667	−	3.54301i	−0.131534	−	0.190473i
$347$	−8.33539	−	18.2519i	−0.447467	−	0.979816i	−0.990167	−	0.139889i	$-0.955325\pi$
$347$	−8.33539	−	18.2519i	−0.447467	−	0.979816i	0.542700	−	0.839927i	$-0.317402\pi$
$348$	0.333689	−	4.35521i	0.0178876	−	0.233464i
$349$	22.9240	−	26.4558i	1.22710	−	1.41614i	0.349367	−	0.936986i	$-0.386397\pi$
$349$	22.9240	−	26.4558i	1.22710	−	1.41614i	0.877729	−	0.479158i	$-0.159058\pi$
$350$	−3.96340	+	20.0704i	−0.211853	+	1.07281i
$351$	8.00065	−	6.93260i	0.427043	−	0.370035i
$352$	−0.614293	−	26.6722i	−0.0327419	−	1.42164i
$353$	−0.244144	+	0.831479i	−0.0129945	+	0.0442552i	−0.965735	−	0.259530i	$-0.916432\pi$
$353$	−0.244144	+	0.831479i	−0.0129945	+	0.0442552i	0.952741	+	0.303785i	$0.0982505\pi$
$354$	2.18950	+	0.913429i	0.116371	+	0.0485482i
$355$	2.98952	+	0.785252i	0.158667	+	0.0416768i
$356$	−15.9973	+	15.8360i	−0.847857	+	0.839304i
$357$	8.52526	+	3.89336i	0.451205	+	0.206058i
$358$	21.6533	−	10.7703i	1.14441	−	0.569229i
$359$	−16.6891	+	10.7254i	−0.880818	+	0.566068i	−0.901044	−	0.433728i	$-0.857198\pi$
$359$	−16.6891	+	10.7254i	−0.880818	+	0.566068i	0.0202256	+	0.999795i	$0.493562\pi$
$360$	2.81726	−	17.7542i	0.148483	−	0.935726i
$361$	1.34236	+	9.33633i	0.0706506	+	0.491386i
$362$	0.463845	−	1.79830i	0.0243792	−	0.0945163i
$363$	3.75608	+	2.41388i	0.197143	+	0.126696i
$364$	−12.5361	−	23.2374i	−0.657070	−	1.21797i
$365$	−2.81547	−	16.2523i	−0.147369	−	0.850683i
$366$	1.50104	−	2.51531i	0.0784604	−	0.131477i
$367$			23.3234i			1.21747i	0.793372	+	0.608737i	$0.208323\pi$
$367$			23.3234i			1.21747i	−0.793372	+	0.608737i	$0.791677\pi$
$368$	3.76929	−	18.8094i	0.196488	−	0.980506i
$369$	0.746900			0.0388820
$370$	−8.64535	−	6.60091i	−0.449450	−	0.343165i
$371$	2.85221	+	9.71374i	0.148079	+	0.504312i
$372$	2.33823	−	1.26143i	0.121232	−	0.0654020i
$373$	4.54685	+	2.92208i	0.235427	+	0.151300i	0.653035	−	0.757327i	$-0.273495\pi$
$373$	4.54685	+	2.92208i	0.235427	+	0.151300i	−0.417609	+	0.908627i	$0.637132\pi$
$374$	−52.6839	−	13.5891i	−2.72422	−	0.702675i
$375$	−0.879444	+	4.35188i	−0.0454143	+	0.224730i
$376$	0.613049	−	14.1482i	0.0316156	−	0.729636i
$377$	13.5673	+	21.1112i	0.698754	+	1.08728i
$378$	8.49937	−	4.22758i	0.437161	−	0.217443i
$379$	3.33124	−	7.29439i	0.171114	−	0.374688i	−0.804574	−	0.593853i	$-0.797606\pi$
$379$	3.33124	−	7.29439i	0.171114	−	0.374688i	0.975688	+	0.219165i	$0.0703334\pi$
$380$	8.54955	+	10.8747i	0.438583	+	0.557859i
$381$	0.901504	−	6.27010i	0.0461854	−	0.321227i
$382$	−7.38762	+	17.7082i	−0.377983	+	0.906030i
$383$	−5.44549	+	18.5456i	−0.278252	+	0.947638i	0.695214	+	0.718803i	$0.255310\pi$
$383$	−5.44549	+	18.5456i	−0.278252	+	0.947638i	−0.973465	+	0.228835i	$0.926508\pi$
$384$	−4.23706	−	1.49423i	−0.216222	−	0.0762523i
$385$	25.1833	−	17.2263i	1.28346	−	0.877936i
$386$	−0.507960	−	15.3104i	−0.0258545	−	0.779277i
$387$	−21.1678	−	18.3420i	−1.07602	−	0.932375i
$388$	−0.524339	+	6.84351i	−0.0266193	+	0.347427i
$389$	17.8219	−	8.13898i	0.903605	−	0.412663i	0.0912515	−	0.995828i	$-0.470913\pi$
$389$	17.8219	−	8.13898i	0.903605	−	0.412663i	0.812354	+	0.583165i	$0.198186\pi$
$390$	−2.69825	−	5.05506i	−0.136631	−	0.255973i
$391$	−34.8219	−	17.8303i	−1.76102	−	0.901717i
$392$	−0.930121	−	3.76337i	−0.0469782	−	0.190079i
$393$	−2.61936	+	1.19622i	−0.132129	+	0.0603413i
$394$	11.2279	+	9.09502i	0.565652	+	0.458201i
$395$	−14.0981	+	12.9436i	−0.709352	+	0.651264i
$396$	−21.5438	+	15.9577i	−1.08262	+	0.801907i
$397$	23.5793	−	20.4316i	1.18341	−	1.02543i	0.184319	−	0.982866i	$-0.440992\pi$
$397$	23.5793	−	20.4316i	1.18341	−	1.02543i	0.999094	−	0.0425669i	$-0.0135536\pi$
$398$	23.0025	+	24.8323i	1.15301	+	1.24473i
$399$	−1.00122	+	3.40986i	−0.0501239	+	0.170706i
$400$	−18.5653	−	7.43828i	−0.928267	−	0.371914i
$401$	16.2447	+	2.33564i	0.811224	+	0.116636i	0.535429	−	0.844580i	$-0.320150\pi$
$401$	16.2447	+	2.33564i	0.811224	+	0.116636i	0.275795	+	0.961217i	$0.411059\pi$
$402$	1.12396	−	0.199845i	0.0560582	−	0.00996737i
$403$	−6.34082	+	13.8845i	−0.315859	+	0.691634i
$404$	−22.5378	−	12.4553i	−1.12130	−	0.619674i
$405$	−15.2604	+	7.50632i	−0.758295	+	0.372992i
$406$	7.05212	+	21.3688i	0.349991	+	1.06052i
$407$	2.30870	+	16.0574i	0.114438	+	0.795935i
$408$	−5.28260	+	7.48623i	−0.261527	+	0.370624i
$409$	−23.8345	−	15.3175i	−1.17854	−	0.757403i	−0.203424	−	0.979091i	$-0.565207\pi$
$409$	−23.8345	−	15.3175i	−1.17854	−	0.757403i	−0.975118	+	0.221688i	$0.928843\pi$
$410$	0.184345	−	0.810277i	0.00910413	−	0.0400168i
$411$	−0.195979	+	0.0575446i	−0.00966693	+	0.00283847i
$412$	−2.16752	−	32.6296i	−0.106786	−	1.60754i
$413$	−12.2218			−0.601397
$414$	−17.6276	+	7.80293i	−0.866351	+	0.383493i
$415$	−1.49949	+	13.0888i	−0.0736073	+	0.642503i
$416$	24.5926	−	7.84045i	1.20575	−	0.384410i
$417$	−1.36551	−	4.65051i	−0.0668695	−	0.227736i
$418$	2.25732	−	20.5070i	0.110409	−	1.00303i
$419$	0.0315012	+	0.0202446i	0.00153893	+	0.000989012i	0.541410	−	0.840759i	$-0.317891\pi$
$419$	0.0315012	+	0.0202446i	0.00153893	+	0.000989012i	−0.539871	+	0.841748i	$0.681527\pi$
$420$	−1.21069	−	4.99348i	−0.0590756	−	0.243657i
$421$	16.1157	−	2.31709i	0.785431	−	0.112928i	0.262081	−	0.965046i	$-0.415591\pi$
$421$	16.1157	−	2.31709i	0.785431	−	0.112928i	0.523350	+	0.852118i	$0.324682\pi$
$422$	−11.7261	−	35.5317i	−0.570819	−	1.72966i
$423$	−11.9718	+	7.69381i	−0.582089	+	0.374086i
$424$	−9.84824	+	0.983107i	−0.478273	+	0.0477439i
$425$	−24.8952	+	32.3079i	−1.20759	+	1.56716i
$426$	−0.764319	+	0.135899i	−0.0370314	+	0.00658432i
$427$	−2.14754	+	14.9364i	−0.103927	+	0.722825i
$428$	−19.9322	+	4.23029i	−0.963461	+	0.204479i
$429$	−2.40769	+	8.19983i	−0.116244	+	0.395891i
$430$	−25.1229	+	18.4369i	−1.21153	+	0.889107i
$431$	−12.0814	−	13.9427i	−0.581942	−	0.671597i	0.386079	−	0.922466i	$-0.373829\pi$
$431$	−12.0814	−	13.9427i	−0.581942	−	0.671597i	−0.968021	+	0.250869i	$0.919284\pi$
$432$	2.52413	+	8.93034i	0.121442	+	0.429661i
$433$	−18.6616	+	21.5366i	−0.896820	+	1.03499i	0.102370	+	0.994746i	$0.467357\pi$
$433$	−18.6616	+	21.5366i	−0.896820	+	1.03499i	−0.999190	+	0.0402389i	$0.987188\pi$
$434$	−8.61512	+	10.6354i	−0.413539	+	0.510517i
$435$	1.50991	+	4.64426i	0.0723944	+	0.222675i
$436$	−20.3902	−	7.72312i	−0.976514	−	0.369870i
$437$	4.81307	−	14.0318i	0.230240	−	0.671231i
$438$	2.35402	+	3.40884i	0.112479	+	0.162881i
$439$	−14.1653	+	6.46910i	−0.676075	+	0.308753i	−0.723703	−	0.690112i	$-0.757561\pi$
$439$	−14.1653	+	6.46910i	−0.676075	+	0.308753i	0.0476275	+	0.998865i	$0.484834\pi$
$440$	11.9945	+	27.3105i	0.571817	+	1.30198i
$441$	−2.55109	+	2.94411i	−0.121480	+	0.140196i
$442$	−1.74550	−	52.6109i	−0.0830250	−	2.50245i
$443$	−3.69095	−	4.25958i	−0.175362	−	0.202379i	0.661264	−	0.750154i	$-0.270020\pi$
$443$	−3.69095	−	4.25958i	−0.175362	−	0.202379i	−0.836626	+	0.547775i	$0.815475\pi$
$444$	2.66647	+	0.594228i	0.126545	+	0.0282008i
$445$	9.79263	−	23.1834i	0.464215	−	1.09900i
$446$	9.54794	−	22.8865i	0.452108	−	1.08371i
$447$	−1.81729	−	0.261286i	−0.0859546	−	0.0123584i
$448$	23.1090	−	1.29992i	1.09180	−	0.0614156i
$449$	0.921412	−	2.01761i	0.0434841	−	0.0952169i	−0.886643	−	0.462454i	$-0.846969\pi$
$449$	0.921412	−	2.01761i	0.0434841	−	0.0952169i	0.930127	+	0.367237i	$0.119696\pi$
$450$	4.64906	+	19.5530i	0.219159	+	0.921738i
$451$	−1.04260	+	0.670040i	−0.0490942	+	0.0315509i
$452$	9.94184	−	13.1414i	0.467625	−	0.618118i
$453$	−5.54516	+	0.797274i	−0.260534	+	0.0374592i
$454$	−6.60875	+	25.6217i	−0.310164	+	1.20248i
$455$	22.8557	+	18.6824i	1.07149	+	0.875844i
$456$	−3.09485	−	1.57871i	−0.144930	−	0.0739300i
$457$	−13.2196	+	3.88164i	−0.618389	+	0.181575i	−0.575898	−	0.817521i	$-0.695348\pi$
$457$	−13.2196	+	3.88164i	−0.618389	+	0.181575i	−0.0424908	+	0.999097i	$0.513529\pi$
$458$	7.79302	−	13.0589i	0.364144	−	0.610202i
$459$	18.9255			0.883368
$460$	4.11431	+	21.0493i	0.191831	+	0.981428i
$461$	−36.8265			−1.71518			−0.857591	−	0.514333i	$-0.828040\pi$
$461$	−36.8265			−1.71518			−0.857591	+	0.514333i	$0.828040\pi$
$462$	−3.92696	+	6.58047i	−0.182699	+	0.306151i
$463$	−3.47399	+	1.02006i	−0.161450	+	0.0474060i	−0.361459	−	0.932388i	$-0.617721\pi$
$463$	−3.47399	+	1.02006i	−0.161450	+	0.0474060i	0.200009	+	0.979794i	$0.435903\pi$
$464$	−21.8054	+	2.90982i	−1.01229	+	0.135085i
$465$	−1.87989	+	2.29982i	−0.0871778	+	0.106652i
$466$	−5.13599	+	19.9118i	−0.237920	+	0.922398i
$467$	14.0350	−	2.01792i	0.649460	−	0.0933783i	0.190292	−	0.981728i	$-0.439057\pi$
$467$	14.0350	−	2.01792i	0.649460	−	0.0933783i	0.459168	+	0.888349i	$0.348147\pi$
$468$	−20.6860	−	15.6496i	−0.956211	−	0.723403i
$469$	−4.94751	+	3.17957i	−0.228455	+	0.146819i
$470$	5.39187	+	14.8866i	0.248708	+	0.686667i
$471$	−0.801856	+	1.75582i	−0.0369476	+	0.0809039i
$472$	2.21079	−	11.7419i	0.101760	−	0.540465i
$473$	46.0027	+	6.61419i	2.11521	+	0.304121i
$474$	1.85074	−	4.43625i	0.0850074	−	0.203764i
$475$	−13.4694	−	7.60037i	−0.618020	−	0.348729i
$476$	10.2671	−	46.0716i	0.470593	−	2.11169i
$477$	6.51307	+	7.51649i	0.298213	+	0.344156i
$478$	0.135792	+	4.09289i	0.00621097	+	0.187204i
$479$	19.7824	−	22.8301i	0.903880	−	1.04313i	−0.0949837	−	0.995479i	$-0.530280\pi$
$479$	19.7824	−	22.8301i	0.903880	−	1.04313i	0.998864	−	0.0476546i	$-0.0151747\pi$
$480$	5.01640	−	0.259885i	0.228966	−	0.0118621i
$481$	−14.2769	+	6.52003i	−0.650970	+	0.297288i
$482$	15.1505	+	21.9394i	0.690088	+	0.999313i
$483$	−3.79134	+	3.99830i	−0.172512	+	0.181929i
$484$	7.96496	−	21.0287i	0.362044	−	0.955850i
$485$	−2.37257	−	7.29771i	−0.107733	−	0.331372i
$486$	8.88421	−	10.9676i	0.402996	−	0.497501i
$487$	15.8445	−	18.2856i	0.717985	−	0.828599i	−0.273078	−	0.961992i	$-0.588042\pi$
$487$	15.8445	−	18.2856i	0.717985	−	0.828599i	0.991063	+	0.133393i	$0.0425873\pi$
$488$	−13.9615	−	4.76504i	−0.632006	−	0.215703i
$489$	−2.10089	−	2.42456i	−0.0950055	−	0.109642i
$490$	2.56429	+	3.49420i	0.115843	+	0.157852i
$491$	1.44278	−	4.91366i	0.0651117	−	0.221750i	−0.920509	−	0.390720i	$-0.872226\pi$
$491$	1.44278	−	4.91366i	0.0651117	−	0.221750i	0.985621	+	0.168970i	$0.0540441\pi$
$492$	0.0433294	+	0.204159i	0.00195344	+	0.00920420i
$493$	−6.38465	+	44.4062i	−0.287550	+	1.99995i
$494$	19.6521	−	3.49422i	0.884189	−	0.157212i
$495$	15.4744	−	25.6715i	0.695522	−	1.15385i
$496$	−8.65942	−	10.2007i	−0.388819	−	0.458023i
$497$	3.36441	−	2.16218i	0.150915	−	0.0969869i
$498$	−1.03697	−	3.14214i	−0.0464676	−	0.140803i
$499$	5.06538	−	0.728292i	0.226758	−	0.0326028i	−0.0279993	−	0.999608i	$-0.508914\pi$
$499$	5.06538	−	0.728292i	0.226758	−	0.0326028i	0.254757	+	0.967005i	$0.418005\pi$
$500$	22.3596	−	0.217615i	0.999953	−	0.00973202i
$501$	−1.94472	−	1.24980i	−0.0868838	−	0.0558368i
$502$	4.37362	−	39.7329i	0.195204	−	1.77336i
$503$	−5.20281	−	17.7192i	−0.231982	−	0.790058i	−0.990393	−	0.138281i	$-0.955842\pi$
$503$	−5.20281	−	17.7192i	−0.231982	−	0.790058i	0.758411	−	0.651777i	$-0.225976\pi$
$504$	−14.4562	−	18.2210i	−0.643932	−	0.811626i
$505$	28.6028	+	3.27683i	1.27281	+	0.145817i
$506$	17.6066	−	26.7058i	0.782707	−	1.18722i
$507$	−3.10577			−0.137932
$508$	−31.8330	+	2.11461i	−1.41236	+	0.0938205i
$509$	−20.5602	+	6.03702i	−0.911314	+	0.267586i	−0.703594	−	0.710602i	$-0.748423\pi$
$509$	−20.5602	+	6.03702i	−0.911314	+	0.267586i	−0.207720	+	0.978188i	$0.566604\pi$
$510$	2.27249	−	9.98862i	0.100628	−	0.442304i
$511$	−17.9537	−	11.5382i	−0.794226	−	0.510418i
$512$	−2.93128	+	22.4367i	−0.129546	+	0.991573i
$513$	1.02129	+	7.10326i	0.0450912	+	0.313616i
$514$	9.53555	+	28.8940i	0.420595	+	1.27446i
$515$	16.1373	+	32.8073i	0.711097	+	1.44566i
$516$	3.78564	−	6.85010i	0.166654	−	0.301559i
$517$	9.80944	−	21.4797i	0.431419	−	0.944675i
$518$	−13.8565	+	2.46373i	−0.608818	+	0.108250i
$519$	−1.19674	−	0.172065i	−0.0525311	−	0.00755283i
$520$	−22.0831	+	18.5788i	−0.968409	+	0.814734i
$521$	11.6739	−	39.7577i	0.511443	−	1.74182i	−0.146953	−	0.989143i	$-0.546947\pi$
$521$	11.6739	−	39.7577i	0.511443	−	1.74182i	0.658396	−	0.752672i	$-0.271235\pi$
$522$	15.0228	+	16.2178i	0.657528	+	0.709834i
$523$	6.22478	−	5.39380i	0.272191	−	0.235854i	−0.508060	−	0.861322i	$-0.669637\pi$
$523$	6.22478	−	5.39380i	0.272191	−	0.235854i	0.780250	+	0.625467i	$0.215092\pi$
$524$	8.63210	+	11.6538i	0.377095	+	0.509099i
$525$	3.37822	+	4.64633i	0.147438	+	0.202782i
$526$	−21.2053	−	17.1771i	−0.924593	−	0.748958i
$527$	−24.8216	+	11.3356i	−1.08125	+	0.493788i
$528$	−5.61173	−	4.96309i	−0.244219	−	0.215991i
$529$	16.5579	−	15.9636i	0.719910	−	0.694068i
$530$	9.76181	−	5.21057i	0.424026	−	0.226333i
$531$	−10.9218	+	4.98782i	−0.473966	+	0.216453i
$532$	17.8460	+	1.36733i	0.773720	+	0.0592812i
$533$	−0.906190	−	0.785219i	−0.0392515	−	0.0340116i
$534$	0.209593	+	6.31731i	0.00906996	+	0.273377i
$535$	18.8031	−	12.8620i	0.812928	−	0.556073i
$536$	−2.15977	−	5.32838i	−0.0932878	−	0.230151i
$537$	1.91321	−	6.51581i	0.0825612	−	0.281178i
$538$	−4.77324	+	11.4415i	−0.205789	+	0.493278i
$539$	0.919933	−	6.39827i	0.0396243	−	0.275593i
$540$	−6.41266	−	8.15663i	−0.275957	−	0.351006i
$541$	4.07339	−	8.91947i	0.175129	−	0.383478i	−0.801630	−	0.597820i	$-0.796034\pi$
$541$	4.07339	−	8.91947i	0.175129	−	0.383478i	0.976759	+	0.214342i	$0.0687609\pi$
$542$	0.00723477	−	0.00359857i	0.000310760	−	0.000154572i
$543$	−0.281939	−	0.438706i	−0.0120992	−	0.0188267i
$544$	42.4053	+	18.1978i	1.81811	+	0.780224i
$545$	24.3674	−	0.700357i	1.04378	−	0.0300000i
$546$	−7.17909	−	1.85175i	−0.307237	−	0.0792475i
$547$	27.0701	+	17.3969i	1.15743	+	0.743837i	0.971106	−	0.238650i	$-0.0767050\pi$
$547$	27.0701	+	17.3969i	1.15743	+	0.743837i	0.186328	+	0.982488i	$0.440341\pi$
$548$	0.488415	+	0.905346i	0.0208641	+	0.0386745i
$549$	4.17657	+	14.2241i	0.178252	+	0.607069i
$550$	−24.0306	−	23.1235i	−1.02467	−	0.985991i
$551$	−17.0114			−0.724709
$552$	−3.15549	−	4.36571i	−0.134307	−	0.185817i
$553$			24.7632i			1.05304i
$554$	0.230395	−	0.386077i	0.00978856	−	0.0164029i
$555$	−3.00951	+	0.521355i	−0.127747	+	0.0221303i
$556$	−21.4835	+	11.5899i	−0.911104	+	0.491522i
$557$	−28.5593	−	18.3539i	−1.21010	−	0.777681i	−0.229421	−	0.973327i	$-0.573683\pi$
$557$	−28.5593	−	18.3539i	−1.21010	−	0.777681i	−0.980674	+	0.195647i	$0.937319\pi$
$558$	−3.35834	+	13.0200i	−0.142170	+	0.551182i
$559$	6.39921	+	44.5075i	0.270658	+	1.88247i
$560$	−23.3351	+	11.1858i	−0.986087	+	0.472684i
$561$	−12.8526	+	8.25986i	−0.542637	+	0.348731i
$562$	−14.0350	+	6.98098i	−0.592030	+	0.294475i
$563$	26.9791	+	12.3209i	1.13703	+	0.519266i	0.892801	−	0.450451i	$-0.148737\pi$
$563$	26.9791	+	12.3209i	1.13703	+	0.519266i	0.244232	+	0.969717i	$0.421464\pi$
$564$	−2.79755	−	2.82606i	−0.117798	−	0.118999i
$565$	−4.68046	+	17.8189i	−0.196908	+	0.749646i
$566$	−18.5328	−	7.73163i	−0.778992	−	0.324985i
$567$	−6.19937	+	21.1131i	−0.260349	+	0.886667i
$568$	1.46869	+	3.62341i	0.0616248	+	0.152035i
$569$	13.3679	−	11.5834i	0.560412	−	0.485600i	−0.327980	−	0.944685i	$-0.606368\pi$
$569$	13.3679	−	11.5834i	0.560412	−	0.485600i	0.888393	+	0.459084i	$0.151822\pi$
$570$	3.87163	+	0.313902i	0.162165	+	0.0131479i
$571$	6.15567	−	7.10403i	0.257607	−	0.297294i	−0.612183	−	0.790716i	$-0.709709\pi$
$571$	6.15567	−	7.10403i	0.257607	−	0.297294i	0.869790	+	0.493422i	$0.164254\pi$
$572$	42.9149	+	3.28807i	1.79436	+	0.137481i
$573$	2.23819	+	4.90096i	0.0935019	+	0.204741i
$574$	−0.610964	−	0.884734i	−0.0255012	−	0.0369281i
$575$	−13.2179	−	20.0072i	−0.551223	−	0.834358i
$576$	20.1204	−	10.5926i	0.838351	−	0.441359i
$577$	2.29570	−	1.04841i	0.0955714	−	0.0436460i	−0.367056	−	0.930199i	$-0.619634\pi$
$577$	2.29570	−	1.04841i	0.0955714	−	0.0436460i	0.462627	+	0.886553i	$0.346907\pi$
$578$	44.1011	−	54.4431i	1.83436	−	2.26453i
$579$	−3.25088	−	2.81691i	−0.135102	−	0.117067i
$580$	21.3018	−	12.2947i	0.884508	−	0.510512i
$581$	11.1628	+	12.8825i	0.463110	+	0.534458i
$582$	1.30972	+	1.41390i	0.0542895	+	0.0586082i
$583$	−15.8346	−	4.64947i	−0.655804	−	0.192561i
$584$	14.3327	−	15.1616i	0.593092	−	0.627392i
$585$	28.0490	+	7.36757i	1.15968	+	0.304612i
$586$	4.52324	+	25.4394i	0.186853	+	1.05089i
$587$	2.39796	−	5.25079i	0.0989742	−	0.216723i	−0.853667	−	0.520819i	$-0.825627\pi$
$587$	2.39796	−	5.25079i	0.0989742	−	0.216723i	0.952642	+	0.304095i	$0.0983541\pi$
$588$	−0.952744	−	0.526525i	−0.0392905	−	0.0217135i
$589$	−5.59404	−	8.70449i	−0.230498	−	0.358662i
$590$	2.71542	+	13.0796i	0.111792	+	0.538480i
$591$	4.01610	−	0.577428i	0.165200	−	0.0237522i
$592$	0.139487	−	13.7580i	0.00573287	−	0.565451i
$593$	−10.5921	+	16.4816i	−0.434966	+	0.676820i	−0.987669	−	0.156558i	$-0.949960\pi$
$593$	−10.5921	+	16.4816i	−0.434966	+	0.676820i	0.552703	+	0.833378i	$0.313596\pi$
$594$	−1.69312	+	15.3814i	−0.0694697	+	0.631108i
$595$	9.00803	+	51.9987i	0.369293	+	2.13174i
$596$	0.612884	+	9.22627i	0.0251047	+	0.377923i
$597$	9.50484			0.389007
$598$	29.5903	+	9.06495i	1.21004	+	0.370693i
$599$			18.1517i			0.741659i	0.928701	+	0.370830i	$0.120927\pi$
$599$			18.1517i			0.741659i	−0.928701	+	0.370830i	$0.879073\pi$
$600$	−5.07496	+	2.40510i	−0.207184	+	0.0981878i
$601$	4.02189	−	1.18093i	0.164056	−	0.0481713i	−0.198673	−	0.980066i	$-0.563663\pi$
$601$	4.02189	−	1.18093i	0.164056	−	0.0481713i	0.362729	+	0.931895i	$0.381845\pi$
$602$	−4.41160	+	40.0779i	−0.179803	+	1.63345i
$603$	−3.12364	+	4.86048i	−0.127204	+	0.197934i
$604$	9.72585	+	26.4853i	0.395739	+	1.07767i
$605$	0.722289	+	25.1304i	0.0293652	+	1.02170i
$606$	−6.86650	+	2.26608i	−0.278933	+	0.0920530i
$607$	−31.6252	+	20.3243i	−1.28363	+	0.824938i	−0.991331	−	0.131389i	$-0.958056\pi$
$607$	−31.6252	+	20.3243i	−1.28363	+	0.824938i	−0.292298	+	0.956327i	$0.594420\pi$
$608$	−4.54177	+	16.8979i	−0.184193	+	0.685298i
$609$	5.74770	+	2.62489i	0.232908	+	0.106366i
$610$	16.4619	−	1.02028i	0.666523	−	0.0413099i
$611$	22.6135	+	3.25134i	0.914846	+	0.131535i
$612$	−9.62714	−	45.3611i	−0.389154	−	1.83361i
$613$	25.0636	+	7.35935i	1.01231	+	0.297241i	0.745499	−	0.666507i	$-0.232211\pi$
$613$	25.0636	+	7.35935i	1.01231	+	0.297241i	0.266812	+	0.963749i	$0.414030\pi$
$614$	23.6378	+	25.5182i	0.953944	+	1.02983i
$615$	−0.131741	−	0.192593i	−0.00531232	−	0.00776612i
$616$	36.5255	+	12.4661i	1.47165	+	0.502275i
$617$	−11.6604	+	13.4569i	−0.469431	+	0.541753i	−0.940253	−	0.340476i	$-0.889412\pi$
$617$	−11.6604	+	13.4569i	−0.469431	+	0.541753i	0.470822	+	0.882228i	$0.343957\pi$
$618$	−7.13534	−	5.77991i	−0.287025	−	0.232502i
$619$	−1.18076	−	2.58550i	−0.0474586	−	0.103920i	0.884417	−	0.466697i	$-0.154556\pi$
$619$	−1.18076	−	2.58550i	−0.0474586	−	0.103920i	−0.931876	+	0.362777i	$0.881829\pi$
$620$	13.2960	+	6.85682i	0.533979	+	0.275377i
$621$	−3.61008	+	10.5246i	−0.144868	+	0.422339i
$622$	−4.56895	−	6.61627i	−0.183198	−	0.265288i
$623$	−13.5270	−	29.6200i	−0.541949	−	1.18670i
$624$	3.07765	−	6.56223i	0.123205	−	0.262699i
$625$	−23.0213	+	9.74776i	−0.920853	+	0.389910i
$626$	−19.4832	+	0.646403i	−0.778704	+	0.0258355i
$627$	−3.79372	−	4.37819i	−0.151507	−	0.174848i
$628$	9.48867	+	2.11456i	0.378639	+	0.0843803i
$629$	−26.9222	−	7.90506i	−1.07346	−	0.315196i
$630$	22.7041	+	12.6789i	0.904555	+	0.505139i
$631$	6.04132	−	42.0183i	0.240501	−	1.67272i	−0.409133	−	0.912475i	$-0.634169\pi$
$631$	6.04132	−	42.0183i	0.240501	−	1.67272i	0.649634	−	0.760247i	$-0.274922\pi$
$632$	−23.7909	−	4.47939i	−0.946349	−	0.178181i
$633$	−9.55716	−	4.36461i	−0.379863	−	0.173478i
$634$	−1.56327	+	0.777571i	−0.0620856	+	0.0308813i
$635$	32.0064	−	15.7434i	1.27014	−	0.624757i
$636$	−1.67673	+	2.21635i	−0.0664868	+	0.0878838i
$637$	6.19031	−	0.890033i	0.245269	−	0.0352644i
$638$	−35.5193	−	9.16171i	−1.40622	−	0.362716i
$639$	2.12414	−	3.30523i	0.0840297	−	0.130753i
$640$	−6.52547	−	24.4421i	−0.257942	−	0.966160i
$641$	5.89599	+	20.0799i	0.232878	+	0.793108i	0.990150	+	0.140009i	$0.0447132\pi$
$641$	5.89599	+	20.0799i	0.232878	+	0.793108i	−0.757273	+	0.653099i	$0.773469\pi$
$642$	−2.93205	+	4.91329i	−0.115719	+	0.193912i
$643$		−	22.5817i		−	0.890537i	−0.895397	−	0.445269i	$-0.853108\pi$
$643$		−	22.5817i		−	0.890537i	0.895397	−	0.445269i	$-0.146892\pi$
$644$	23.6623	+	14.4979i	0.932426	+	0.571297i
$645$	−0.995955	+	8.69349i	−0.0392157	+	0.342306i
$646$	30.6421	+	18.2860i	1.20560	+	0.719452i
$647$	−17.8038	+	5.22768i	−0.699941	+	0.205521i	−0.612294	−	0.790630i	$-0.709753\pi$
$647$	−17.8038	+	5.22768i	−0.699941	+	0.205521i	−0.0876472	+	0.996152i	$0.527935\pi$
$648$	−19.1627	−	9.77506i	−0.752780	−	0.384000i
$649$	10.7713	−	16.7604i	0.422809	−	0.657904i
$650$	14.9156	−	28.6106i	0.585038	−	1.12220i
$651$	0.546960	+	3.80419i	0.0214371	+	0.149098i
$652$	−9.74819	+	12.8854i	−0.381769	+	0.504631i
$653$	−16.7103	−	26.0017i	−0.653925	−	1.01753i	−0.996938	−	0.0781959i	$-0.975084\pi$
$653$	−16.7103	−	26.0017i	−0.653925	−	1.01753i	0.343013	−	0.939330i	$-0.388552\pi$
$654$	−5.48186	+	2.72667i	−0.214358	+	0.106621i
$655$	−13.8866	−	8.37065i	−0.542595	−	0.327068i
$656$	0.960510	−	0.426935i	0.0375016	−	0.0166690i
$657$	−20.7528	−	2.98380i	−0.809644	−	0.116409i
$658$	18.9066	+	7.88756i	0.737055	+	0.307489i
$659$	−7.94962	−	2.33422i	−0.309673	−	0.0909283i	0.123203	−	0.992381i	$-0.460683\pi$
$659$	−7.94962	−	2.33422i	−0.309673	−	0.0909283i	−0.432877	+	0.901453i	$0.642501\pi$
$660$	7.91481	+	2.74054i	0.308083	+	0.106675i
$661$	−24.5807	+	21.2993i	−0.956077	+	0.828445i	−0.985249	−	0.171129i	$-0.945259\pi$
$661$	−24.5807	+	21.2993i	−0.956077	+	0.828445i	0.0291716	+	0.999574i	$0.490713\pi$
$662$	−0.891613	−	26.8740i	−0.0346535	−	1.04449i
$663$	−11.1710	−	9.67971i	−0.433845	−	0.375929i
$664$	−14.3959	+	8.39415i	−0.558669	+	0.325756i
$665$	−19.0304	+	6.18700i	−0.737967	+	0.239922i
$666$	−11.3771	+	7.85659i	−0.440853	+	0.304437i
$667$	−23.4768	−	12.0211i	−0.909024	−	0.465460i
$668$	−4.12389	+	10.8877i	−0.159558	+	0.421257i
$669$	−2.89270	−	6.33412i	−0.111838	−	0.244891i
$670$	4.50196	+	4.58832i	0.173926	+	0.177262i
$671$	−18.5905	−	16.1087i	−0.717677	−	0.621870i
$672$	4.14191	−	5.00854i	0.159778	−	0.193209i
$673$	15.7675	−	13.6626i	0.607793	−	0.526655i	−0.295688	−	0.955285i	$-0.595549\pi$
$673$	15.7675	−	13.6626i	0.607793	−	0.526655i	0.903480	+	0.428629i	$0.141003\pi$
$674$	−27.2891	−	29.4600i	−1.05114	−	1.13476i
$675$	10.1029	+	5.70072i	0.388859	+	0.219421i
$676$	3.24737	+	15.3010i	0.124899	+	0.588498i
$677$	3.35268	−	23.3184i	0.128854	−	0.896200i	−0.818156	−	0.574996i	$-0.805003\pi$
$677$	3.35268	−	23.3184i	0.128854	−	0.896200i	0.947010	−	0.321204i	$-0.104087\pi$
$678$	−0.810019	−	4.55568i	−0.0311086	−	0.174960i
$679$	−9.03158	−	4.12458i	−0.346600	−	0.158287i
$680$	−51.5863	−	0.751659i	−1.97824	−	0.0288248i
$681$	4.01700	+	6.25057i	0.153932	+	0.239522i
$682$	−6.99228	−	21.1875i	−0.267748	−	0.811311i
$683$	6.25312	+	43.4914i	0.239269	+	1.66415i	0.655727	+	0.754998i	$0.272362\pi$
$683$	6.25312	+	43.4914i	0.239269	+	1.66415i	−0.416458	+	0.909155i	$0.636729\pi$
$684$	16.5057	−	6.06118i	0.631111	−	0.231755i
$685$	−0.890474	−	0.727879i	−0.0340232	−	0.0278108i
$686$	−22.8950	−	2.52018i	−0.874136	−	0.0962211i
$687$	−1.20307	−	4.09729i	−0.0459001	−	0.156321i
$688$	−37.7061	−	11.4880i	−1.43753	−	0.437976i
$689$		−	15.9667i		−	0.608284i
$690$	5.12127	+	3.16910i	0.194964	+	0.120646i
$691$		−	18.7665i		−	0.713910i	−0.934122	−	0.356955i	$-0.883815\pi$
$691$		−	18.7665i		−	0.713910i	0.934122	−	0.356955i	$-0.116185\pi$
$692$	0.403604	+	6.07580i	0.0153427	+	0.230967i
$693$	−10.9266	−	37.2126i	−0.415067	−	1.41359i
$694$	−3.10481	+	28.2061i	−0.117857	+	1.07069i
$695$	17.2723	−	21.1306i	0.655175	−	0.801530i
$696$	−3.56151	+	5.04719i	−0.134999	+	0.191313i
$697$	−0.305065	−	2.12177i	−0.0115552	−	0.0803679i
$698$	−47.0120	+	15.5148i	−1.77943	+	0.587246i
$699$	3.12181	+	4.85762i	0.118078	+	0.183732i
$700$	19.3584	−	21.5014i	0.731680	−	0.812676i
$701$	42.5006	+	19.4094i	1.60522	+	0.733082i	0.998105	−	0.0615288i	$-0.0195976\pi$
$701$	42.5006	+	19.4094i	1.60522	+	0.733082i	0.607120	+	0.794610i	$0.292325\pi$
$702$	−14.7402	+	2.62087i	−0.556333	+	0.0989183i
$703$	1.51416	−	10.5312i	0.0571076	−	0.397192i
$704$	−18.5837	+	32.8362i	−0.700398	+	1.23756i
$705$	4.09554	+	1.72995i	0.154247	+	0.0651537i
$706$	0.899074	−	0.832823i	0.0338371	−	0.0313437i
$707$	28.1521	−	24.3940i	1.05877	−	0.917429i
$708$	−1.99698	−	2.69603i	−0.0750511	−	0.101323i
$709$	27.0686	+	23.4551i	1.01658	+	0.880874i	0.992913	−	0.118846i	$-0.0379195\pi$
$709$	27.0686	+	23.4551i	1.01658	+	0.880874i	0.0236698	+	0.999720i	$0.492465\pi$
$710$	−3.06143	−	3.12016i	−0.114893	−	0.117097i
$711$	10.1061	+	22.1292i	0.379007	+	0.829910i
$712$	30.9038	−	7.63792i	1.15817	−	0.286243i
$713$	−1.56908	−	15.9658i	−0.0587624	−	0.597923i
$714$	−7.53161	−	10.9065i	−0.281863	−	0.408165i
$715$	−45.7632	+	14.8781i	−1.71144	+	0.556411i
$716$	−34.1013	−	2.61279i	−1.27443	−	0.0976445i
$717$	0.869051	+	0.753037i	0.0324553	+	0.0281227i
$718$	28.0403	−	0.930308i	1.04645	−	0.0347188i
$719$	18.7275	−	16.2274i	0.698417	−	0.605182i	−0.231551	−	0.972823i	$-0.574380\pi$
$719$	18.7275	−	16.2274i	0.698417	−	0.605182i	0.929968	+	0.367641i	$0.119834\pi$
$720$	−16.2879	+	19.5191i	−0.607016	+	0.727436i
$721$	45.3897	+	13.3276i	1.69040	+	0.496346i
$722$	5.13597	−	12.3110i	0.191141	−	0.458167i
$723$	7.41059	+	1.06548i	0.275603	+	0.0396257i
$724$	−1.86654	+	1.84772i	−0.0693695	+	0.0686698i
$725$	−16.7842	+	21.7818i	−0.623351	+	0.808957i
$726$	−2.81205	−	5.65352i	−0.104365	−	0.209822i
$727$	−0.679892	−	1.05793i	−0.0252158	−	0.0392366i	0.828417	−	0.560112i	$-0.189242\pi$
$727$	−0.679892	−	1.05793i	−0.0252158	−	0.0392366i	−0.853633	+	0.520876i	$0.825606\pi$
$728$	−1.61644	+	37.3048i	−0.0599094	+	1.38261i
$729$	2.68312	+	18.6615i	0.0993747	+	0.691166i
$730$	−8.35906	+	21.7773i	−0.309383	+	0.806015i
$731$	−43.4596	+	67.6245i	−1.60741	+	2.50118i
$732$	−3.64575	+	1.96681i	−0.134751	+	0.0726952i
$733$	5.85844	−	1.72019i	0.216387	−	0.0635368i	−0.171742	−	0.985142i	$-0.554940\pi$
$733$	5.85844	−	1.72019i	0.216387	−	0.0635368i	0.388129	+	0.921605i	$0.373122\pi$
$734$	16.9028	−	28.3242i	0.623892	−	1.04547i
$735$	1.20913	+	0.138522i	0.0445995	+	0.00510946i
$736$	−18.2088	+	20.1107i	−0.671186	+	0.741289i
$737$		−	9.58697i		−	0.353141i
$738$	−0.907043	−	0.541286i	−0.0333887	−	0.0199250i
$739$	3.21384	+	10.9453i	0.118223	+	0.402630i	0.997247	−	0.0741463i	$-0.0236232\pi$
$739$	3.21384	+	10.9453i	0.118223	+	0.402630i	−0.879024	+	0.476777i	$0.841805\pi$
$740$	5.71525	+	14.2816i	0.210097	+	0.525002i
$741$	3.03023	−	4.71512i	0.111318	−	0.173214i
$742$	3.57590	−	13.8635i	0.131275	−	0.508945i
$743$	−23.3866	+	3.36248i	−0.857971	+	0.123358i	−0.557240	−	0.830351i	$-0.688140\pi$
$743$	−23.3866	+	3.36248i	−0.857971	+	0.123358i	−0.300731	+	0.953709i	$0.597231\pi$
$744$	−3.75375	−	0.162652i	−0.137619	−	0.00596313i
$745$	−4.56297	−	9.27653i	−0.167174	−	0.339866i
$746$	−3.40408	−	6.84376i	−0.124632	−	0.250568i
$747$	15.2329	+	6.95662i	0.557341	+	0.254529i
$748$	54.1318	+	54.6834i	1.97925	+	1.99942i
$749$	4.19490	−	29.1761i	0.153278	−	1.06607i
$750$	4.22187	−	4.64763i	0.154161	−	0.169708i
$751$	2.04403	+	0.600182i	0.0745878	+	0.0219009i	0.318814	−	0.947817i	$-0.396716\pi$
$751$	2.04403	+	0.600182i	0.0745878	+	0.0219009i	−0.244226	+	0.969718i	$0.578534\pi$
$752$	−10.9978	+	16.7374i	−0.401049	+	0.610350i
$753$	−7.35043	−	8.48285i	−0.267865	−	0.309132i
$754$	−1.17681	−	35.4701i	−0.0428569	−	1.29174i
$755$	−21.3339	−	23.2367i	−0.776419	−	0.845669i
$756$	−13.3855	−	1.02558i	−0.486826	−	0.0372998i
$757$	11.4564	+	25.0861i	0.416392	+	0.911771i	0.995342	+	0.0964078i	$0.0307353\pi$
$757$	11.4564	+	25.0861i	0.416392	+	0.911771i	−0.578950	+	0.815363i	$0.696537\pi$
$758$	−9.33182	+	6.44421i	−0.338947	+	0.234064i
$759$	−2.14172	−	8.72301i	−0.0777394	−	0.316625i
$760$	−2.50168	−	19.4023i	−0.0907453	−	0.703794i
$761$	1.11010	+	2.43079i	0.0402412	+	0.0881159i	0.928685	−	0.370869i	$-0.120940\pi$
$761$	1.11010	+	2.43079i	0.0402412	+	0.0881159i	−0.888444	+	0.458985i	$0.848213\pi$
$762$	−5.63880	+	6.96114i	−0.204272	+	0.252176i
$763$	20.6552	−	23.8374i	0.747769	−	0.862971i
$764$	21.8049	−	16.1511i	0.788875	−	0.584328i
$765$	29.2709	+	42.7914i	1.05829	+	1.54712i
$766$	20.0533	−	18.5756i	0.724555	−	0.671164i
$767$	18.4948	+	5.43056i	0.667809	+	0.196086i
$768$	4.06264	+	4.88526i	0.146598	+	0.176282i
$769$	−12.1791	−	1.75108i	−0.439188	−	0.0631457i	−0.0808255	−	0.996728i	$-0.525756\pi$
$769$	−12.1791	−	1.75108i	−0.439188	−	0.0631457i	−0.358362	+	0.933583i	$0.616665\pi$
$770$	−43.0670	+	2.66922i	−1.55203	+	0.0961920i
$771$	7.77177	+	3.54925i	0.279894	+	0.127823i
$772$	−10.4787	+	18.9612i	−0.377137	+	0.682429i
$773$	−1.93807	+	1.24552i	−0.0697077	+	0.0447984i	−0.575030	−	0.818132i	$-0.695010\pi$
$773$	−1.93807	+	1.24552i	−0.0697077	+	0.0447984i	0.505323	+	0.862930i	$0.331373\pi$
$774$	12.4137	+	37.6152i	0.446202	+	1.35205i
$775$	−16.6648	−	1.42551i	−0.598618	−	0.0512058i
$776$	5.59633	−	7.93084i	0.200897	−	0.284701i
$777$	−2.13658	+	3.32458i	−0.0766493	+	0.119269i
$778$	−27.5415	−	3.03165i	−0.987410	−	0.108690i
$779$	0.779896	−	0.228998i	0.0279427	−	0.00820471i
$780$	−0.386681	+	8.09437i	−0.0138454	+	0.289825i
$781$			6.51935i			0.233281i
$782$	29.3662	+	46.8891i	1.05013	+	1.67675i
$783$	12.7595			0.455988
$784$	−1.59780	+	5.24434i	−0.0570644	+	0.187298i
$785$	−10.7094	+	1.85525i	−0.382234	+	0.0662166i
$786$	4.04789	+	0.445574i	0.144383	+	0.0158931i
$787$	4.60959	−	7.17266i	0.164314	−	0.255678i	−0.749326	−	0.662201i	$-0.769623\pi$
$787$	4.60959	−	7.17266i	0.164314	−	0.255678i	0.913641	+	0.406523i	$0.133259\pi$
$788$	−7.04398	−	19.1821i	−0.250931	−	0.683332i
$789$	−7.58492	+	1.09055i	−0.270030	+	0.0388245i
$790$	26.5013	−	5.50184i	0.942873	−	0.195747i
$791$	12.8875	+	20.0534i	0.458228	+	0.713017i
$792$	37.7278	−	3.76620i	1.34060	−	0.133826i
$793$	9.88654	−	21.6485i	0.351081	−	0.768761i
$794$	−43.4420	+	7.72416i	−1.54170	+	0.274120i
$795$	0.789378	−	3.00523i	0.0279964	−	0.106585i
$796$	−9.93820	−	46.8267i	−0.352250	−	1.65973i
$797$	2.52383	+	0.741065i	0.0893988	+	0.0262499i	0.326126	−	0.945326i	$-0.394257\pi$
$797$	2.52383	+	0.741065i	0.0893988	+	0.0262499i	−0.236727	+	0.971576i	$0.576075\pi$
$798$	3.68706	−	3.41537i	0.130521	−	0.120903i
$799$	26.7462	+	30.8667i	0.946211	+	1.09199i
$800$	17.1554	+	22.4876i	0.606533	+	0.795058i
$801$	−24.1763	−	20.9489i	−0.854228	−	0.740193i
$802$	−18.0351	−	14.6092i	−0.636842	−	0.515868i
$803$	31.6457	−	14.4521i	1.11675	−	0.510004i
$804$	−1.50978	−	0.571854i	−0.0532459	−	0.0201677i
$805$	−30.6352	−	4.90941i	−1.07975	−	0.173034i
$806$	17.7626	−	12.2662i	0.625660	−	0.432058i
$807$	1.44613	+	3.16658i	0.0509061	+	0.111469i
$808$	18.3437	+	31.4593i	0.645328	+	1.10673i
$809$	−24.9317	+	28.7728i	−0.876553	+	1.01160i	0.123262	+	0.992374i	$0.460664\pi$
$809$	−24.9317	+	28.7728i	−0.876553	+	1.01160i	−0.999815	+	0.0192220i	$0.993881\pi$
$810$	23.9723	+	1.94362i	0.842301	+	0.0682917i
$811$	20.6637	−	17.9052i	0.725601	−	0.628737i	−0.211669	−	0.977341i	$-0.567890\pi$
$811$	20.6637	−	17.9052i	0.725601	−	0.628737i	0.937270	+	0.348605i	$0.113344\pi$
$812$	6.92206	−	31.0613i	0.242917	−	1.09004i
$813$	0.000639241	−	0.00217705i	2.24192e−5	−	7.63526e-5i
$814$	8.83325	−	21.1734i	0.309605	−	0.742127i
$815$	4.58929	−	17.4718i	0.160756	−	0.612011i
$816$	11.8406	−	5.26300i	0.414504	−	0.184242i
$817$	−27.7265	−	12.6623i	−0.970029	−	0.442997i
$818$	17.8441	+	35.8749i	0.623906	+	1.25434i
$819$	31.5664	−	20.2865i	1.10302	−	0.708867i
$820$	−0.811087	+	0.850413i	−0.0283244	+	0.0296977i
$821$	−5.90242	−	41.0523i	−0.205996	−	1.43273i	−0.786054	−	0.618158i	$-0.787879\pi$
$821$	−5.90242	−	41.0523i	−0.205996	−	1.43273i	0.580058	−	0.814575i	$-0.303030\pi$
$822$	0.279702	+	0.0721453i	0.00975574	+	0.00251636i
$823$	28.6997	+	18.4442i	1.00041	+	0.642923i	0.934893	−	0.354929i	$-0.115495\pi$
$823$	28.6997	+	18.4442i	1.00041	+	0.642923i	0.0655142	+	0.997852i	$0.479131\pi$
$824$	−21.0147	+	41.1965i	−0.732083	+	1.43515i
$825$	−9.34902	+	0.537856i	−0.325491	+	0.0187257i
$826$	14.8423	+	8.85730i	0.516431	+	0.308185i
$827$			3.88776i			0.135191i	0.997713	+	0.0675953i	$0.0215327\pi$
$827$			3.88776i			0.135191i	−0.997713	+	0.0675953i	$0.978467\pi$
$828$	27.0621	+	3.29898i	0.940472	+	0.114648i
$829$	−11.3531			−0.394310			−0.197155	−	0.980372i	$-0.563170\pi$
$829$	−11.3531			−0.394310			−0.197155	+	0.980372i	$0.563170\pi$
$830$	11.3066	−	14.8085i	0.392457	−	0.514009i
$831$	−0.0355680	−	0.121134i	−0.00123384	−	0.00420208i
$832$	−35.5476	−	8.30099i	−1.23239	−	0.287785i
$833$	9.40553	+	6.04457i	0.325882	+	0.209432i
$834$	−1.71198	+	6.63723i	−0.0592811	+	0.229829i
$835$	−0.373967	−	13.0114i	−0.0129417	−	0.450276i
$836$	−17.6030	+	23.2680i	−0.608811	+	0.804741i
$837$	4.19585	+	6.52887i	0.145030	+	0.225671i
$838$	−0.0235839	−	0.0474145i	−0.000814692	−	0.00163791i
$839$	12.7773	−	27.9783i	0.441120	−	0.965919i	−0.550271	−	0.834986i	$-0.685476\pi$
$839$	12.7773	−	27.9783i	0.441120	−	0.965919i	0.991391	−	0.130932i	$-0.0417971\pi$
$840$	−2.14855	+	6.94153i	−0.0741322	+	0.239506i
$841$	−0.177372	+	1.23365i	−0.00611628	+	0.0425397i
$842$	−21.2503	−	8.86533i	−0.732333	−	0.305519i
$843$	−1.24008	+	4.22334i	−0.0427108	+	0.145460i
$844$	−11.5099	+	51.6481i	−0.396186	+	1.77780i
$845$	−9.87350	−	14.4341i	−0.339659	−	0.496550i
$846$	20.1145	−	0.667348i	0.691550	−	0.0229439i
$847$	24.5838	+	21.3020i	0.844711	+	0.731946i
$848$	12.6723	+	5.94323i	0.435168	+	0.204091i
$849$	−5.12918	+	2.34242i	−0.176033	+	0.0803915i
$850$	53.6468	−	21.1932i	1.84007	−	0.726921i
$851$	9.53153	−	13.4637i	0.326737	−	0.461531i
$852$	1.02668	+	0.388873i	0.0351736	+	0.0133226i
$853$	3.15894	−	1.44264i	0.108160	−	0.0493951i	−0.360600	−	0.932721i	$-0.617428\pi$
$853$	3.15894	−	1.44264i	0.108160	−	0.0493951i	0.468760	+	0.883325i	$0.344701\pi$
$854$	13.4326	−	16.5826i	0.459654	−	0.567446i
$855$	−14.4812	+	13.2953i	−0.495246	+	0.454691i
$856$	27.2717	+	9.30781i	0.932126	+	0.318134i
$857$	3.94702	−	3.42012i	0.134828	−	0.116829i	−0.584836	−	0.811151i	$-0.698841\pi$
$857$	3.94702	−	3.42012i	0.134828	−	0.116829i	0.719664	+	0.694322i	$0.244296\pi$
$858$	8.86643	−	8.21308i	0.302695	−	0.280390i
$859$	7.24891	−	24.6875i	0.247330	−	0.842328i	−0.738453	−	0.674305i	$-0.764444\pi$
$859$	7.24891	−	24.6875i	0.247330	−	0.842328i	0.985783	−	0.168023i	$-0.0537383\pi$
$860$	43.8709	−	4.18317i	1.49599	−	0.142645i
$861$	−0.298841	−	0.0429669i	−0.0101845	−	0.00146431i
$862$	4.56738	+	25.6877i	0.155566	+	0.874928i
$863$	1.90899	−	4.18010i	0.0649826	−	0.142292i	−0.874354	−	0.485288i	$-0.838715\pi$
$863$	1.90899	−	4.18010i	0.0649826	−	0.142292i	0.939337	+	0.342996i	$0.111442\pi$
$864$	3.40659	−	12.6744i	0.115894	−	0.431191i
$865$	−3.00486	−	6.10890i	−0.102168	−	0.207709i
$866$	38.2707	−	12.6301i	1.30049	−	0.429187i
$867$	−2.79991	−	19.4738i	−0.0950898	−	0.661364i
$868$	18.1699	−	6.67230i	0.616727	−	0.226473i
$869$	−33.9591	−	21.8242i	−1.15198	−	0.740335i
$870$	1.53210	−	6.73429i	0.0519432	−	0.228314i
$871$	8.89965	−	2.61317i	0.301553	−	0.0885440i
$872$	19.1651	+	24.1560i	0.649011	+	0.818027i
$873$	−9.75417			−0.330129
$874$	−16.0140	+	13.5522i	−0.541682	+	0.458412i
$875$	−10.8543	+	30.4714i	−0.366942	+	1.03012i
$876$	−0.388320	−	5.84571i	−0.0131201	−	0.197508i
$877$	1.73918	+	5.92311i	0.0587280	+	0.200009i	0.983631	−	0.180193i	$-0.0576724\pi$
$877$	1.73918	+	5.92311i	0.0587280	+	0.200009i	−0.924903	+	0.380203i	$0.875854\pi$
$878$	21.8908	+	2.40964i	0.738778	+	0.0813215i
$879$	6.10368	+	3.92260i	0.205872	+	0.132306i
$880$	5.22593	−	41.8587i	0.176166	−	1.41106i
$881$	−51.1432	+	7.35328i	−1.72306	+	0.247738i	−0.931600	−	0.363485i	$-0.881587\pi$
$881$	−51.1432	+	7.35328i	−1.72306	+	0.247738i	−0.791458	+	0.611223i	$0.790678\pi$
$882$	5.23170	−	1.72656i	0.176160	−	0.0581363i
$883$	−5.05057	+	3.24581i	−0.169965	+	0.109230i	−0.622858	−	0.782335i	$-0.714029\pi$
$883$	−5.05057	+	3.24581i	−0.169965	+	0.109230i	0.452892	+	0.891565i	$0.350392\pi$
$884$	−36.0080	+	65.1562i	−1.21108	+	2.19144i
$885$	3.21258	+	1.93649i	0.107990	+	0.0650945i
$886$	1.39536	+	7.84775i	0.0468781	+	0.263650i
$887$	2.05374	−	14.2841i	0.0689579	−	0.479613i	−0.925854	−	0.377881i	$-0.876653\pi$
$887$	2.05374	−	14.2841i	0.0689579	−	0.479613i	0.994812	−	0.101731i	$-0.0324382\pi$
$888$	−2.80755	−	2.65406i	−0.0942152	−	0.0890644i
$889$	13.0023	−	44.2816i	0.436081	−	1.48516i
$890$	−28.6935	+	21.0573i	−0.961810	+	0.705843i
$891$	−23.4899	−	27.1088i	−0.786941	−	0.908178i
$892$	−28.1812	+	20.8741i	−0.943577	+	0.698918i
$893$	−10.1418	+	11.7042i	−0.339382	+	0.391667i
$894$	2.01757	+	1.63432i	0.0674778	+	0.0546597i
$895$	36.3646	−	11.8226i	1.21554	−	0.395185i
$896$	−29.0059	−	15.1687i	−0.969020	−	0.506752i
$897$	7.51386	−	4.36585i	0.250880	−	0.145772i
$898$	−2.58116	+	1.78245i	−0.0861343	+	0.0594811i
$899$	−16.7346	+	7.64244i	−0.558131	+	0.254890i
$900$	8.52442	−	27.1146i	0.284147	−	0.903820i
$901$	18.6924	−	21.5722i	0.622735	−	0.718675i
$902$	1.75173	−	0.0581181i	0.0583263	−	0.00193512i
$903$	7.41426	+	8.55651i	0.246731	+	0.284743i
$904$	−21.5972	+	8.75405i	−0.718311	+	0.291155i
$905$	1.14259	−	2.70500i	0.0379810	−	0.0899173i
$906$	7.31190	+	3.05042i	0.242921	+	0.101343i
$907$	−57.9834	−	8.33675i	−1.92531	−	0.276817i	−0.929539	−	0.368724i	$-0.879795\pi$
$907$	−57.9834	−	8.33675i	−1.92531	−	0.276817i	−0.995768	+	0.0919065i	$0.970704\pi$
$908$	26.5940	−	26.3258i	0.882554	−	0.873652i
$909$	15.2022	−	33.2883i	0.504227	−	1.10410i
$910$	−14.2169	−	39.2519i	−0.471285	−	1.30119i
$911$	−37.0470	+	23.8087i	−1.22742	+	0.788817i	−0.983488	−	0.180974i	$-0.942075\pi$
$911$	−37.0470	+	23.8087i	−1.22742	+	0.788817i	−0.243936	+	0.969791i	$0.578439\pi$
$912$	2.61431	+	4.16008i	0.0865685	+	0.137754i
$913$	−27.5044	+	3.95454i	−0.910263	+	0.130876i
$914$	18.8671	+	4.86652i	0.624070	+	0.160970i
$915$	2.93110	−	3.58586i	0.0968993	−	0.118545i
$916$	−18.9279	+	10.2112i	−0.625394	+	0.337387i
$917$	−20.1296	+	5.91058i	−0.664737	+	0.195185i
$918$	−22.9834	−	13.7155i	−0.758564	−	0.452680i
$919$	−7.30266			−0.240893			−0.120446	−	0.992720i	$-0.538433\pi$
$919$	−7.30266			−0.240893			−0.120446	+	0.992720i	$0.538433\pi$
$920$	10.2582	−	28.5442i	0.338202	−	0.941073i
$921$	9.76737			0.321846
$922$	44.7225	+	26.6886i	1.47286	+	0.878942i
$923$	−6.05196	+	1.77701i	−0.199203	+	0.0584911i
$924$	9.53788	−	5.14549i	0.313773	−	0.169274i
$925$	−11.9905	−	12.3294i	−0.394245	−	0.405387i
$926$	4.95810	+	1.27887i	0.162933	+	0.0420264i
$927$	46.0007	−	6.61390i	1.51086	−	0.217229i
$928$	28.5895	+	12.2689i	0.938495	+	0.402746i
$929$	10.4621	−	6.72356i	0.343249	−	0.220593i	−0.357646	−	0.933857i	$-0.616421\pi$
$929$	10.4621	−	6.72356i	0.343249	−	0.220593i	0.700895	+	0.713265i	$0.252784\pi$
$930$	3.94967	−	1.43055i	0.129515	−	0.0469097i
$931$	−1.76113	+	3.85634i	−0.0577187	+	0.126386i
$932$	20.6675	−	20.4591i	0.676987	−	0.670159i
$933$	−2.23481	−	0.321318i	−0.0731645	−	0.0105195i
$934$	−18.5066	−	7.72070i	−0.605555	−	0.252629i
$935$	−79.2473	−	33.4740i	−2.59166	−	1.09472i
$936$	13.7799	+	33.9964i	0.450409	+	1.11121i
$937$	−17.1095	−	19.7454i	−0.558943	−	0.645054i	0.404000	−	0.914759i	$-0.367619\pi$
$937$	−17.1095	−	19.7454i	−0.558943	−	0.645054i	−0.962943	+	0.269705i	$0.913074\pi$
$938$	8.31258	−	0.275791i	0.271415	−	0.00900489i
$939$	−3.58465	+	4.13690i	−0.116981	+	0.135003i
$940$	4.24054	−	21.9860i	0.138311	−	0.717104i
$941$	−29.6488	+	13.5402i	−0.966523	+	0.441396i	−0.835202	−	0.549943i	$-0.814649\pi$
$941$	−29.6488	+	13.5402i	−0.966523	+	0.441396i	−0.131321	+	0.991340i	$0.541922\pi$
$942$	2.24624	−	1.55117i	0.0731866	−	0.0505399i
$943$	1.23813	+	0.235083i	0.0403190	+	0.00765537i
$944$	−11.1943	+	12.6573i	−0.364343	+	0.411961i
$945$	14.2739	−	4.64061i	0.464330	−	0.150959i
$946$	−51.0728	−	41.3710i	−1.66052	−	1.34509i
$947$	17.2179	−	19.8705i	0.559507	−	0.645705i	−0.403565	−	0.914951i	$-0.632229\pi$
$947$	17.2179	−	19.8705i	0.559507	−	0.645705i	0.963071	+	0.269246i	$0.0867744\pi$
$948$	−5.46256	+	4.04618i	−0.177416	+	0.131414i
$949$	22.0419	+	25.4377i	0.715509	+	0.825742i
$950$	10.8494	+	18.9914i	0.352000	+	0.616163i
$951$	−0.138126	+	0.470413i	−0.00447904	+	0.0152542i
$952$	−45.8571	+	48.5091i	−1.48624	+	1.57219i
$953$	5.63091	−	39.1638i	0.182403	−	1.26864i	−0.668656	−	0.743572i	$-0.733130\pi$
$953$	5.63091	−	39.1638i	0.182403	−	1.26864i	0.851059	−	0.525070i	$-0.175961\pi$
$954$	−2.46226	−	13.8482i	−0.0797188	−	0.448352i
$955$	−15.6619	+	25.9826i	−0.506809	+	0.840778i
$956$	2.80125	−	5.06886i	0.0905990	−	0.163939i
$957$	−8.66516	+	5.56876i	−0.280105	+	0.180012i
$958$	−40.5692	+	13.3886i	−1.31073	+	0.432566i
$959$	−1.47295	+	0.211779i	−0.0475641	+	0.00683869i
$960$	−6.28031	−	3.31983i	−0.202696	−	0.107147i
$961$	16.6653	+	10.7101i	0.537590	+	0.345488i
$962$	22.0631	+	2.42862i	0.711344	+	0.0783017i
$963$	−8.15831	−	27.7847i	−0.262898	−	0.895348i
$964$	−2.49924	−	37.6232i	−0.0804952	−	1.21176i
$965$	2.75682	−	24.0637i	0.0887452	−	0.774639i
$966$	7.50186	−	2.10796i	0.241368	−	0.0678224i
$967$	0.981296			0.0315563			0.0157782	−	0.999876i	$-0.494977\pi$
$967$	0.981296			0.0315563			0.0157782	+	0.999876i	$0.494977\pi$
$968$	−24.9125	+	19.7652i	−0.800717	+	0.635278i
$969$	9.61410	−	2.82295i	0.308849	−	0.0906864i
$970$	−2.40746	+	10.5819i	−0.0772987	+	0.339763i
$971$	−15.1508	−	9.73682i	−0.486212	−	0.312469i	0.274468	−	0.961596i	$-0.411498\pi$
$971$	−15.1508	−	9.73682i	−0.486212	−	0.312469i	−0.760680	+	0.649127i	$0.775134\pi$
$972$	−18.7374	+	6.88071i	−0.601004	+	0.220699i
$973$	−5.02543	−	34.9526i	−0.161108	−	1.12053i
$974$	−32.4935	+	10.7235i	−1.04116	+	0.343603i
$975$	−3.04761	−	8.53215i	−0.0976016	−	0.273248i
$976$	13.5017	+	15.9047i	0.432178	+	0.509099i
$977$	−14.4323	+	31.6023i	−0.461730	+	1.01105i	0.525360	+	0.850880i	$0.323930\pi$
$977$	−14.4323	+	31.6023i	−0.461730	+	1.01105i	−0.987090	+	0.160167i	$0.948797\pi$
$978$	0.794241	+	4.46694i	0.0253970	+	0.142837i
$979$	52.5410	+	7.55426i	1.67922	+	0.241435i
$980$	−0.581815	−	6.10177i	−0.0185854	−	0.194914i
$981$	8.72991	−	29.7314i	0.278725	−	0.949249i
$982$	−5.31311	+	4.92160i	−0.169548	+	0.157055i
$983$	−10.9021	+	9.44677i	−0.347725	+	0.301305i	−0.811158	−	0.584826i	$-0.801163\pi$
$983$	−10.9021	+	9.44677i	−0.347725	+	0.301305i	0.463434	+	0.886131i	$0.346617\pi$
$984$	0.0953367	−	0.279334i	0.00303922	−	0.00890485i
$985$	15.4511	+	16.8292i	0.492314	+	0.536224i
$986$	39.9352	−	49.3003i	1.27180	−	1.57004i
$987$	5.23263	−	2.38966i	0.166556	−	0.0760637i
$988$	−26.3980	−	9.99867i	−0.839833	−	0.318100i
$989$	−29.3165	−	37.0678i	−0.932212	−	1.17869i
$990$	−37.3967	+	19.9613i	−1.18854	+	0.634411i
$991$	49.8386	−	22.7605i	1.58318	−	0.723013i	0.586935	−	0.809634i	$-0.300334\pi$
$991$	49.8386	−	22.7605i	1.58318	−	0.723013i	0.996241	+	0.0866212i	$0.0276070\pi$
$992$	3.12357	+	18.6634i	0.0991734	+	0.592562i
$993$	−5.70621	−	4.94446i	−0.181081	−	0.156908i
$994$	−5.65273	+	0.187544i	−0.179294	+	0.00594852i
$995$	30.2167	+	44.1740i	0.957933	+	1.40041i
$996$	−1.01784	+	4.56735i	−0.0322516	+	0.144722i
$997$	−2.41840	+	8.23631i	−0.0765915	+	0.260847i	−0.988883	−	0.148694i	$-0.952493\pi$
$997$	−2.41840	+	8.23631i	−0.0765915	+	0.260847i	0.912292	+	0.409541i	$0.134311\pi$
$998$	−6.67925	−	2.78649i	−0.211428	−	0.0882049i
$999$	−1.13571	+	7.89901i	−0.0359322	+	0.249914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.b.19.12	✓	640
4.3	odd	2	inner	460.2.o.b.19.28	yes	640
5.4	even	2	inner	460.2.o.b.19.53	yes	640
20.19	odd	2	inner	460.2.o.b.19.37	yes	640
23.17	odd	22	inner	460.2.o.b.339.37	yes	640
92.63	even	22	inner	460.2.o.b.339.53	yes	640
115.109	odd	22	inner	460.2.o.b.339.28	yes	640
460.339	even	22	inner	460.2.o.b.339.12	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.b.19.12	✓	640	1.1	even	1	trivial
460.2.o.b.19.28	yes	640	4.3	odd	2	inner
460.2.o.b.19.37	yes	640	20.19	odd	2	inner
460.2.o.b.19.53	yes	640	5.4	even	2	inner
460.2.o.b.339.12	yes	640	460.339	even	22	inner
460.2.o.b.339.28	yes	640	115.109	odd	22	inner
460.2.o.b.339.37	yes	640	23.17	odd	22	inner
460.2.o.b.339.53	yes	640	92.63	even	22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21441 - 0.724711i) q^{2} +(-0.381027 + 0.111880i) q^{3} +(0.949588 + 1.76019i) q^{4} +(-1.73128 - 1.41516i) q^{5} +(0.543804 + 0.140267i) q^{6} +(-2.86375 + 0.411745i) q^{7} +(0.122443 - 2.82578i) q^{8} +(-2.39110 + 1.53666i) q^{9} +O(q^{10})\)	\(q+(-1.21441 - 0.724711i) q^{2} +(-0.381027 + 0.111880i) q^{3} +(0.949588 + 1.76019i) q^{4} +(-1.73128 - 1.41516i) q^{5} +(0.543804 + 0.140267i) q^{6} +(-2.86375 + 0.411745i) q^{7} +(0.122443 - 2.82578i) q^{8} +(-2.39110 + 1.53666i) q^{9} +(1.07690 + 2.97326i) q^{10} +(1.95921 - 4.29008i) q^{11} +(-0.558748 - 0.564442i) q^{12} +(4.51655 + 0.649381i) q^{13} +(3.77616 + 1.57536i) q^{14} +(0.817991 + 0.345518i) q^{15} +(-2.19657 + 3.34292i) q^{16} +(5.34194 + 6.16493i) q^{17} +(4.01741 - 0.133288i) q^{18} +(-2.02559 + 2.33766i) q^{19} +(0.846952 - 4.39120i) q^{20} +(1.04510 - 0.477281i) q^{21} +(-5.48836 + 3.79006i) q^{22} +(-4.44735 + 1.79473i) q^{23} +(0.269493 + 1.09040i) q^{24} +(0.994655 + 4.90007i) q^{25} +(-5.01433 - 4.06181i) q^{26} +(1.51931 - 1.75338i) q^{27} +(-3.44413 - 4.64976i) q^{28} +(3.60152 + 4.15637i) q^{29} +(-0.742976 - 1.01241i) q^{30} +(-0.942433 + 3.20963i) q^{31} +(5.09018 - 2.46780i) q^{32} +(-0.266541 + 1.85383i) q^{33} +(-2.01952 - 11.3581i) q^{34} +(5.54063 + 3.33981i) q^{35} +(-4.97538 - 2.74960i) q^{36} +(-2.89364 + 1.85963i) q^{37} +(4.15403 - 1.37091i) q^{38} +(-1.79358 + 0.257878i) q^{39} +(-4.21090 + 4.71893i) q^{40} +(-0.221064 - 0.142070i) q^{41} +(-1.61507 - 0.177780i) q^{42} +(2.77628 + 9.45516i) q^{43} +(9.41182 - 0.625210i) q^{44} +(6.31428 + 0.723384i) q^{45} +(6.70157 + 1.04351i) q^{46} +5.00682 q^{47} +(0.462947 - 1.51949i) q^{48} +(1.31507 - 0.386139i) q^{49} +(2.34321 - 6.67153i) q^{50} +(-2.72515 - 1.75135i) q^{51} +(3.14582 + 8.56664i) q^{52} +(-0.497986 - 3.46357i) q^{53} +(-3.11576 + 1.02826i) q^{54} +(-9.46309 + 4.65473i) q^{55} +(0.812853 + 8.14272i) q^{56} +(0.510269 - 1.11733i) q^{57} +(-1.36155 - 7.65760i) q^{58} +(4.18134 + 0.601186i) q^{59} +(0.168575 + 1.76792i) q^{60} +(1.46943 - 5.00443i) q^{61} +(3.47056 - 3.21482i) q^{62} +(6.21478 - 5.38514i) q^{63} +(-7.97002 - 0.691992i) q^{64} +(-6.90042 - 7.51589i) q^{65} +(1.66718 - 2.05815i) q^{66} +(1.84905 - 0.844431i) q^{67} +(-5.77883 + 15.2570i) q^{68} +(1.49377 - 1.18141i) q^{69} +(-4.30820 - 8.07126i) q^{70} +(-1.25739 + 0.574231i) q^{71} +(4.04950 + 6.94485i) q^{72} +(5.57478 + 4.83057i) q^{73} +(4.86177 - 0.161301i) q^{74} +(-0.927208 - 1.75578i) q^{75} +(-6.03821 - 1.34562i) q^{76} +(-3.84428 + 13.0924i) q^{77} +(2.36503 + 0.986656i) q^{78} +(1.21809 - 8.47201i) q^{79} +(8.53363 - 2.67903i) q^{80} +(3.15947 - 6.91828i) q^{81} +(0.165504 + 0.332739i) q^{82} +(-3.18533 - 4.95647i) q^{83} +(1.83252 + 1.38636i) q^{84} +(-0.524043 - 18.2329i) q^{85} +(3.48071 - 13.4945i) q^{86} +(-1.83729 - 1.18075i) q^{87} +(-11.8829 - 6.06159i) q^{88} +(3.17088 + 10.7990i) q^{89} +(-7.14388 - 5.45451i) q^{90} -13.2016 q^{91} +(-7.38222 - 6.12396i) q^{92} -1.32840i q^{93} +(-6.08034 - 3.62850i) q^{94} +(6.81502 - 1.18061i) q^{95} +(-1.66340 + 1.50979i) q^{96} +(2.88700 + 1.85536i) q^{97} +(-1.87687 - 0.484113i) q^{98} +(1.90774 + 13.2686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Introduction

L-functions

Modular forms

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