LMFDB - Embedded newform 234.2.y.a.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(11,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 7]))

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

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

chi := DirichletCharacter("234.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.870336 + 1.49750i) q^{3} -1.00000i q^{4} +(1.35053 + 0.361873i) q^{5} +(0.443474 + 1.67432i) q^{6} +(0.977097 + 0.261812i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.48503 - 2.60666i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.870336 + 1.49750i) q^{3} -1.00000i q^{4} +(1.35053 + 0.361873i) q^{5} +(0.443474 + 1.67432i) q^{6} +(0.977097 + 0.261812i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.48503 - 2.60666i) q^{9} +(1.21085 - 0.699086i) q^{10} +(4.11206 + 4.11206i) q^{11} +(1.49750 + 0.870336i) q^{12} +(3.22602 + 1.61022i) q^{13} +(0.876041 - 0.505782i) q^{14} +(-1.71732 + 1.70747i) q^{15} -1.00000 q^{16} +(1.67305 - 2.89781i) q^{17} +(-2.89326 - 0.793114i) q^{18} +(-7.07605 + 1.89602i) q^{19} +(0.361873 - 1.35053i) q^{20} +(-1.24247 + 1.23534i) q^{21} +5.81533 q^{22} +(0.290218 - 0.502672i) q^{23} +(1.67432 - 0.443474i) q^{24} +(-2.63715 - 1.52256i) q^{25} +(3.41974 - 1.14254i) q^{26} +(5.19596 + 0.0448353i) q^{27} +(0.261812 - 0.977097i) q^{28} -1.03028i q^{29} +(-0.00696535 + 2.42169i) q^{30} +(2.28484 - 8.52714i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-9.73669 + 2.57895i) q^{33} +(-0.866036 - 3.23209i) q^{34} +(1.22486 + 0.707171i) q^{35} +(-2.60666 + 1.48503i) q^{36} +(-7.82443 - 2.09655i) q^{37} +(-3.66283 + 6.34422i) q^{38} +(-5.21903 + 3.42954i) q^{39} +(-0.699086 - 1.21085i) q^{40} +(-0.423606 - 1.58092i) q^{41} +(-0.00503937 + 1.75207i) q^{42} +(-7.25776 + 4.19027i) q^{43} +(4.11206 - 4.11206i) q^{44} +(-1.06230 - 4.05777i) q^{45} +(-0.150228 - 0.560658i) q^{46} +(-1.45080 + 0.388741i) q^{47} +(0.870336 - 1.49750i) q^{48} +(-5.17601 - 2.98837i) q^{49} +(-2.94136 + 0.788134i) q^{50} +(2.88336 + 5.02747i) q^{51} +(1.61022 - 3.22602i) q^{52} -2.77082i q^{53} +(3.70580 - 3.64239i) q^{54} +(4.06542 + 7.04151i) q^{55} +(-0.505782 - 0.876041i) q^{56} +(3.31924 - 12.2466i) q^{57} +(-0.728518 - 0.728518i) q^{58} +(8.47432 + 8.47432i) q^{59} +(1.70747 + 1.71732i) q^{60} +(-1.41408 - 2.44926i) q^{61} +(-4.41397 - 7.64523i) q^{62} +(-0.768562 - 2.93576i) q^{63} +1.00000i q^{64} +(3.77414 + 3.34206i) q^{65} +(-5.06129 + 8.70847i) q^{66} +(1.09561 - 0.293568i) q^{67} +(-2.89781 - 1.67305i) q^{68} +(0.500166 + 0.872096i) q^{69} +(1.36615 - 0.366058i) q^{70} +(2.71495 + 10.1323i) q^{71} +(-0.793114 + 2.89326i) q^{72} +(0.788181 - 0.788181i) q^{73} +(-7.01519 + 4.05022i) q^{74} +(4.57524 - 2.62400i) q^{75} +(1.89602 + 7.07605i) q^{76} +(2.94129 + 5.09447i) q^{77} +(-1.26536 + 6.11546i) q^{78} +(-0.827245 + 1.43283i) q^{79} +(-1.35053 - 0.361873i) q^{80} +(-4.58937 + 7.74194i) q^{81} +(-1.41741 - 0.818343i) q^{82} +(-4.21280 - 15.7224i) q^{83} +(1.23534 + 1.24247i) q^{84} +(3.30815 - 3.30815i) q^{85} +(-2.16904 + 8.09498i) q^{86} +(1.54285 + 0.896691i) q^{87} -5.81533i q^{88} +(-0.783797 + 2.92517i) q^{89} +(-3.62043 - 2.11812i) q^{90} +(2.73056 + 2.41795i) q^{91} +(-0.502672 - 0.290218i) q^{92} +(10.7808 + 10.8430i) q^{93} +(-0.750990 + 1.30075i) q^{94} -10.2425 q^{95} +(-0.443474 - 1.67432i) q^{96} +(3.18620 - 11.8911i) q^{97} +(-5.77308 + 1.54689i) q^{98} +(4.61222 - 16.8253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.870336	+	1.49750i	−0.502489	+	0.864584i
$3$	−0.870336	+	1.49750i	−0.502489	+	0.864584i
$4$		−	1.00000i		−	0.500000i
$5$	1.35053	+	0.361873i	0.603975	+	0.161835i	0.547833	−	0.836588i	$-0.315453\pi$
$5$	1.35053	+	0.361873i	0.603975	+	0.161835i	0.0561429	+	0.998423i	$0.482120\pi$
$6$	0.443474	+	1.67432i	0.181047	+	0.683536i
$7$	0.977097	+	0.261812i	0.369308	+	0.0989557i	0.438700	−	0.898634i	$-0.355439\pi$
$7$	0.977097	+	0.261812i	0.369308	+	0.0989557i	−0.0693918	+	0.997589i	$0.522106\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.48503	−	2.60666i	−0.495010	−	0.868887i
$10$	1.21085	−	0.699086i	0.382905	−	0.221070i
$11$	4.11206	+	4.11206i	1.23983	+	1.23983i	0.960069	+	0.279764i	$0.0902561\pi$
$11$	4.11206	+	4.11206i	1.23983	+	1.23983i	0.279764	+	0.960069i	$0.409744\pi$
$12$	1.49750	+	0.870336i	0.432292	+	0.251244i
$13$	3.22602	+	1.61022i	0.894736	+	0.446595i
$13$	3.22602	+	1.61022i	0.894736	+	0.446595i
$14$	0.876041	−	0.505782i	0.234132	−	0.135176i
$15$	−1.71732	+	1.70747i	−0.443411	+	0.440867i
$16$	−1.00000			−0.250000
$17$	1.67305	−	2.89781i	0.405775	−	0.702823i	−0.588636	−	0.808398i	$-0.700335\pi$
$17$	1.67305	−	2.89781i	0.405775	−	0.702823i	0.994411	+	0.105575i	$0.0336683\pi$
$18$	−2.89326	−	0.793114i	−0.681949	−	0.186939i
$19$	−7.07605	+	1.89602i	−1.62336	+	0.434977i	−0.951986	−	0.306143i	$-0.900961\pi$
$19$	−7.07605	+	1.89602i	−1.62336	+	0.434977i	−0.671372	+	0.741120i	$0.734295\pi$
$20$	0.361873	−	1.35053i	0.0809174	−	0.301988i
$21$	−1.24247	+	1.23534i	−0.271129	+	0.269573i
$22$	5.81533			1.23983
$23$	0.290218	−	0.502672i	0.0605146	−	0.104814i	−0.834181	−	0.551491i	$-0.814059\pi$
$23$	0.290218	−	0.502672i	0.0605146	−	0.104814i	0.894696	+	0.446676i	$0.147392\pi$
$24$	1.67432	−	0.443474i	0.341768	−	0.0905237i
$25$	−2.63715	−	1.52256i	−0.527430	−	0.304512i
$26$	3.41974	−	1.14254i	0.670666	−	0.224071i
$27$	5.19596	+	0.0448353i	0.999963	+	0.00862856i
$28$	0.261812	−	0.977097i	0.0494779	−	0.184654i
$29$		−	1.03028i		−	0.191318i	−0.995414	−	0.0956592i	$-0.969504\pi$
$29$		−	1.03028i		−	0.191318i	0.995414	−	0.0956592i	$-0.0304959\pi$
$30$	−0.00696535	+	2.42169i	−0.00127169	+	0.442139i
$31$	2.28484	−	8.52714i	0.410369	−	1.53152i	−0.383564	−	0.923514i	$-0.625303\pi$
$31$	2.28484	−	8.52714i	0.410369	−	1.53152i	0.793933	−	0.608005i	$-0.208030\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−9.73669	+	2.57895i	−1.69494	+	0.448937i
$34$	−0.866036	−	3.23209i	−0.148524	−	0.554299i
$35$	1.22486	+	0.707171i	0.207038	+	0.119534i
$36$	−2.60666	+	1.48503i	−0.434444	+	0.247505i
$37$	−7.82443	−	2.09655i	−1.28633	−	0.344671i	−0.450064	−	0.892996i	$-0.648599\pi$
$37$	−7.82443	−	2.09655i	−1.28633	−	0.344671i	−0.836265	+	0.548326i	$0.815265\pi$
$38$	−3.66283	+	6.34422i	−0.594190	+	1.02917i
$39$	−5.21903	+	3.42954i	−0.835714	+	0.549166i
$40$	−0.699086	−	1.21085i	−0.110535	−	0.191453i
$41$	−0.423606	−	1.58092i	−0.0661561	−	0.246898i	0.924927	−	0.380146i	$-0.124126\pi$
$41$	−0.423606	−	1.58092i	−0.0661561	−	0.246898i	−0.991083	+	0.133248i	$0.957459\pi$
$42$	−0.00503937	+	1.75207i	−0.000777592	+	0.270351i
$43$	−7.25776	+	4.19027i	−1.10680	+	0.639010i	−0.937998	−	0.346640i	$-0.887322\pi$
$43$	−7.25776	+	4.19027i	−1.10680	+	0.639010i	−0.168800	+	0.985650i	$0.553989\pi$
$44$	4.11206	−	4.11206i	0.619916	−	0.619916i
$45$	−1.06230	−	4.05777i	−0.158358	−	0.604896i
$46$	−0.150228	−	0.560658i	−0.0221499	−	0.0826645i
$47$	−1.45080	+	0.388741i	−0.211621	+	0.0567037i	−0.363072	−	0.931761i	$-0.618272\pi$
$47$	−1.45080	+	0.388741i	−0.211621	+	0.0567037i	0.151451	+	0.988465i	$0.451605\pi$
$48$	0.870336	−	1.49750i	0.125622	−	0.216146i
$49$	−5.17601	−	2.98837i	−0.739429	−	0.426910i
$50$	−2.94136	+	0.788134i	−0.415971	+	0.111459i
$51$	2.88336	+	5.02747i	0.403752	+	0.703987i
$52$	1.61022	−	3.22602i	0.223297	−	0.447368i
$53$		−	2.77082i		−	0.380601i	−0.981726	−	0.190300i	$-0.939054\pi$
$53$		−	2.77082i		−	0.380601i	0.981726	−	0.190300i	$-0.0609462\pi$
$54$	3.70580	−	3.64239i	0.504296	−	0.495667i
$55$	4.06542	+	7.04151i	0.548180	+	0.949476i
$56$	−0.505782	−	0.876041i	−0.0675880	−	0.117066i
$57$	3.31924	−	12.2466i	0.439645	−	1.62210i
$58$	−0.728518	−	0.728518i	−0.0956592	−	0.0956592i
$59$	8.47432	+	8.47432i	1.10326	+	1.10326i	0.994014	+	0.109248i	$0.0348444\pi$
$59$	8.47432	+	8.47432i	1.10326	+	1.10326i	0.109248	+	0.994014i	$0.465156\pi$
$60$	1.70747	+	1.71732i	0.220434	+	0.221705i
$61$	−1.41408	−	2.44926i	−0.181054	−	0.313595i	0.761186	−	0.648534i	$-0.224618\pi$
$61$	−1.41408	−	2.44926i	−0.181054	−	0.313595i	−0.942240	+	0.334939i	$0.891284\pi$
$62$	−4.41397	−	7.64523i	−0.560575	−	0.970945i
$63$	−0.768562	−	2.93576i	−0.0968297	−	0.369871i
$64$			1.00000i			0.125000i
$65$	3.77414	+	3.34206i	0.468124	+	0.414532i
$66$	−5.06129	+	8.70847i	−0.623002	+	1.07194i
$67$	1.09561	−	0.293568i	0.133850	−	0.0358650i	−0.191272	−	0.981537i	$-0.561261\pi$
$67$	1.09561	−	0.293568i	0.133850	−	0.0358650i	0.325122	+	0.945672i	$0.394595\pi$
$68$	−2.89781	−	1.67305i	−0.351411	−	0.202887i
$69$	0.500166	+	0.872096i	0.0602129	+	0.104988i
$70$	1.36615	−	0.366058i	0.163286	−	0.0437524i
$71$	2.71495	+	10.1323i	0.322205	+	1.20249i	0.917091	+	0.398677i	$0.130530\pi$
$71$	2.71495	+	10.1323i	0.322205	+	1.20249i	−0.594886	+	0.803810i	$0.702803\pi$
$72$	−0.793114	+	2.89326i	−0.0934693	+	0.340974i
$73$	0.788181	−	0.788181i	0.0922496	−	0.0922496i	−0.659476	−	0.751726i	$-0.729222\pi$
$73$	0.788181	−	0.788181i	0.0922496	−	0.0922496i	0.751726	+	0.659476i	$0.229222\pi$
$74$	−7.01519	+	4.05022i	−0.815500	+	0.470829i
$75$	4.57524	−	2.62400i	0.528303	−	0.302993i
$76$	1.89602	+	7.07605i	0.217489	+	0.811679i
$77$	2.94129	+	5.09447i	0.335191	+	0.580568i
$78$	−1.26536	+	6.11546i	−0.143274	+	0.692440i
$79$	−0.827245	+	1.43283i	−0.0930723	+	0.161206i	−0.908802	−	0.417227i	$-0.863002\pi$
$79$	−0.827245	+	1.43283i	−0.0930723	+	0.161206i	0.815730	+	0.578433i	$0.196335\pi$
$80$	−1.35053	−	0.361873i	−0.150994	−	0.0404587i
$81$	−4.58937	+	7.74194i	−0.509930	+	0.860216i
$82$	−1.41741	−	0.818343i	−0.156527	−	0.0903709i
$83$	−4.21280	−	15.7224i	−0.462415	−	1.72576i	−0.665321	−	0.746557i	$-0.731705\pi$
$83$	−4.21280	−	15.7224i	−0.462415	−	1.72576i	0.202906	−	0.979198i	$-0.434961\pi$
$84$	1.23534	+	1.24247i	0.134787	+	0.135564i
$85$	3.30815	−	3.30815i	0.358819	−	0.358819i
$86$	−2.16904	+	8.09498i	−0.233894	+	0.872904i
$87$	1.54285	+	0.896691i	0.165411	+	0.0961353i
$88$		−	5.81533i		−	0.619916i
$89$	−0.783797	+	2.92517i	−0.0830824	+	0.310068i	−0.994944	−	0.100430i	$-0.967978\pi$
$89$	−0.783797	+	2.92517i	−0.0830824	+	0.310068i	0.911862	+	0.410497i	$0.134645\pi$
$90$	−3.62043	−	2.11812i	−0.381627	−	0.223269i
$91$	2.73056	+	2.41795i	0.286240	+	0.253470i
$92$	−0.502672	−	0.290218i	−0.0524072	−	0.0302573i
$93$	10.7808	+	10.8430i	1.11792	+	1.12437i
$94$	−0.750990	+	1.30075i	−0.0774587	+	0.134162i
$95$	−10.2425			−1.05086
$96$	−0.443474	−	1.67432i	−0.0452619	−	0.170884i
$97$	3.18620	−	11.8911i	0.323510	−	1.20736i	−0.592291	−	0.805724i	$-0.701777\pi$
$97$	3.18620	−	11.8911i	0.323510	−	1.20736i	0.915801	−	0.401632i	$-0.131557\pi$
$98$	−5.77308	+	1.54689i	−0.583170	+	0.156260i
$99$	4.61222	−	16.8253i	0.463545	−	1.69100i
$100$	−1.52256	+	2.63715i	−0.152256	+	0.263715i
$101$	10.1915			1.01409			0.507044	−	0.861920i	$-0.330738\pi$
$101$	10.1915			1.01409			0.507044	+	0.861920i	$0.330738\pi$
$102$	5.59381	+	1.51611i	0.553869	+	0.150118i
$103$	8.54265	−	4.93210i	0.841732	−	0.485974i	−0.0161205	−	0.999870i	$-0.505132\pi$
$103$	8.54265	−	4.93210i	0.841732	−	0.485974i	0.857853	+	0.513896i	$0.171798\pi$
$104$	−1.14254	−	3.41974i	−0.112035	−	0.335333i
$105$	−2.12503	+	1.21875i	−0.207381	+	0.118938i
$106$	−1.95926	−	1.95926i	−0.190300	−	0.190300i
$107$	−8.58323	+	4.95553i	−0.829773	+	0.479069i	−0.853775	−	0.520642i	$-0.825692\pi$
$107$	−8.58323	+	4.95553i	−0.829773	+	0.479069i	0.0240022	+	0.999712i	$0.492359\pi$
$108$	0.0448353	−	5.19596i	0.00431428	−	0.499981i
$109$	6.99609	+	6.99609i	0.670103	+	0.670103i	0.957740	−	0.287636i	$-0.0928694\pi$
$109$	6.99609	+	6.99609i	0.670103	+	0.670103i	−0.287636	+	0.957740i	$0.592869\pi$
$110$	7.85378	+	2.10441i	0.748828	+	0.200648i
$111$	9.94948	−	9.89241i	0.944362	−	0.938946i
$112$	−0.977097	−	0.261812i	−0.0923269	−	0.0247389i
$113$		−	10.1473i		−	0.954580i	−0.878746	−	0.477290i	$-0.841619\pi$
$113$		−	10.1473i		−	0.954580i	0.878746	−	0.477290i	$-0.158381\pi$
$114$	−6.31258	−	11.0067i	−0.591228	−	1.03087i
$115$	0.573852	−	0.573852i	0.0535120	−	0.0535120i
$116$	−1.03028			−0.0956592
$117$	−0.593434	−	10.8004i	−0.0548630	−	0.998494i
$118$	11.9845			1.10326
$119$	2.39342	−	2.39342i	0.219404	−	0.219404i
$120$	2.42169	+	0.00696535i	0.221069	+	0.000635847i
$121$			22.8181i			2.07437i
$122$	−2.73179	−	0.731981i	−0.247325	−	0.0662704i
$123$	2.73611	+	0.741579i	0.246707	+	0.0668659i
$124$	−8.52714	−	2.28484i	−0.765760	−	0.205185i
$125$	−7.95386	−	7.95386i	−0.711415	−	0.711415i
$126$	−2.61935	−	1.53244i	−0.233350	−	0.136521i
$127$	−13.1106	+	7.56941i	−1.16338	+	0.671677i	−0.952111	−	0.305752i	$-0.901092\pi$
$127$	−13.1106	+	7.56941i	−1.16338	+	0.671677i	−0.211267	+	0.977428i	$0.567759\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	0.0417498	−	14.5155i	0.00367587	−	1.27801i
$130$	5.03191	−	0.305525i	0.441328	−	0.0267963i
$131$	3.29059	−	1.89982i	0.287500	−	0.165988i	−0.349314	−	0.937006i	$-0.613585\pi$
$131$	3.29059	−	1.89982i	0.287500	−	0.165988i	0.636814	+	0.771018i	$0.280252\pi$
$132$	2.57895	+	9.73669i	0.224469	+	0.847471i
$133$	−7.41039			−0.642562
$134$	0.567130	−	0.982297i	0.0489925	−	0.0848576i
$135$	7.00107	+	1.94083i	0.602557	+	0.167040i
$136$	−3.23209	+	0.866036i	−0.277149	+	0.0742620i
$137$	−1.50633	+	5.62169i	−0.128694	+	0.480293i	−0.999944	−	0.0105460i	$-0.996643\pi$
$137$	−1.50633	+	5.62169i	−0.128694	+	0.480293i	0.871250	+	0.490839i	$0.163310\pi$
$138$	0.970336	+	0.262994i	0.0826004	+	0.0223876i
$139$	2.27675			0.193112			0.0965559	−	0.995328i	$-0.469217\pi$
$139$	2.27675			0.193112			0.0965559	+	0.995328i	$0.469217\pi$
$140$	0.707171	−	1.22486i	0.0597668	−	0.103519i
$141$	0.680544	−	2.51091i	0.0573121	−	0.211457i
$142$	9.08440	+	5.24488i	0.762346	+	0.440141i
$143$	6.64426	+	19.8869i	0.555621	+	1.66303i
$144$	1.48503	+	2.60666i	0.123752	+	0.217222i
$145$	0.372831	−	1.39143i	0.0309620	−	0.115552i
$146$		−	1.11466i		−	0.0922496i
$147$	8.97996	−	5.15020i	0.740654	−	0.424781i
$148$	−2.09655	+	7.82443i	−0.172335	+	0.643164i
$149$	10.1646	−	10.1646i	0.832715	−	0.832715i	−0.155172	−	0.987887i	$-0.549593\pi$
$149$	10.1646	−	10.1646i	0.832715	−	0.832715i	0.987887	+	0.155172i	$0.0495933\pi$
$150$	1.37974	−	5.09063i	0.112655	−	0.415648i
$151$	0.728858	+	2.72013i	0.0593136	+	0.221361i	0.989220	−	0.146434i	$-0.0467795\pi$
$151$	0.728858	+	2.72013i	0.0593136	+	0.221361i	−0.929907	+	0.367795i	$0.880113\pi$
$152$	6.34422	+	3.66283i	0.514584	+	0.297095i
$153$	−10.0382	−	0.0577446i	−0.811537	−	0.00466837i
$154$	5.68214	+	1.52252i	0.457880	+	0.122689i
$155$	6.17149	−	10.6893i	0.495706	−	0.858588i
$156$	3.42954	+	5.21903i	0.274583	+	0.417857i
$157$	3.93908	+	6.82268i	0.314372	+	0.544509i	0.979304	−	0.202395i	$-0.0648726\pi$
$157$	3.93908	+	6.82268i	0.314372	+	0.544509i	−0.664931	+	0.746904i	$0.731539\pi$
$158$	0.428214	+	1.59811i	0.0340668	+	0.127139i
$159$	4.14931	+	2.41154i	0.329061	+	0.191248i
$160$	−1.21085	+	0.699086i	−0.0957263	+	0.0552676i
$161$	0.415177	−	0.415177i	0.0327205	−	0.0327205i
$162$	2.22920	+	8.71956i	0.175143	+	0.685073i
$163$	−1.79021	−	6.68116i	−0.140220	−	0.523309i	−0.999922	−	0.0125123i	$-0.996017\pi$
$163$	−1.79021	−	6.68116i	−0.140220	−	0.523309i	0.859701	−	0.510797i	$-0.170650\pi$
$164$	−1.58092	+	0.423606i	−0.123449	+	0.0330780i
$165$	−14.0830	−	0.0405058i	−1.09636	−	0.00315337i
$166$	−14.0963	−	8.13850i	−1.09409	−	0.631670i
$167$	−15.3104	+	4.10240i	−1.18475	+	0.317453i	−0.796809	−	0.604231i	$-0.793481\pi$
$167$	−15.3104	+	4.10240i	−1.18475	+	0.317453i	−0.387942	+	0.921684i	$0.626814\pi$
$168$	1.75207	+	0.00503937i	0.135175	+	0.000388796i
$169$	7.81438	+	10.3892i	0.601106	+	0.799169i
$170$		−	4.67843i		−	0.358819i
$171$	15.4504	+	15.6292i	1.18152	+	1.19520i
$172$	4.19027	+	7.25776i	0.319505	+	0.553399i
$173$	−1.30226	−	2.25559i	−0.0990092	−	0.171489i	0.812266	−	0.583288i	$-0.198234\pi$
$173$	−1.30226	−	2.25559i	−0.0990092	−	0.171489i	−0.911275	+	0.411799i	$0.864901\pi$
$174$	1.72501	−	0.456903i	0.130773	−	0.0346377i
$175$	−2.17812	−	2.17812i	−0.164651	−	0.164651i
$176$	−4.11206	−	4.11206i	−0.309958	−	0.309958i
$177$	−20.0658	+	5.31481i	−1.50824	+	0.399486i
$178$	1.51418	+	2.62264i	0.113493	+	0.196575i
$179$	−1.79612	−	3.11097i	−0.134248	−	0.232525i	0.791062	−	0.611736i	$-0.209529\pi$
$179$	−1.79612	−	3.11097i	−0.134248	−	0.232525i	−0.925310	+	0.379211i	$0.876195\pi$
$180$	−4.05777	+	1.06230i	−0.302448	+	0.0791789i
$181$			16.3443i			1.21486i	0.794373	+	0.607430i	$0.207799\pi$
$181$			16.3443i			1.21486i	−0.794373	+	0.607430i	$0.792201\pi$
$182$	3.64054	−	0.221045i	0.269855	−	0.0163849i
$183$	4.89849	+	0.0140892i	0.362107	+	0.00104150i
$184$	−0.560658	+	0.150228i	−0.0413322	+	0.0110749i
$185$	−9.80845	−	5.66291i	−0.721131	−	0.416345i
$186$	15.2904	+	0.0439787i	1.12115	+	0.00322467i
$187$	18.7957	−	5.03629i	1.37448	−	0.368290i
$188$	0.388741	+	1.45080i	0.0283519	+	0.105811i
$189$	5.06522	+	1.40417i	0.368440	+	0.102139i
$190$	−7.24257	+	7.24257i	−0.525431	+	0.525431i
$191$	−22.0297	+	12.7189i	−1.59401	+	0.920305i	−0.601406	+	0.798944i	$0.705393\pi$
$191$	−22.0297	+	12.7189i	−1.59401	+	0.920305i	−0.992608	+	0.121361i	$0.961274\pi$
$192$	−1.49750	−	0.870336i	−0.108073	−	0.0628111i
$193$	3.26525	+	12.1861i	0.235038	+	0.877172i	0.978132	+	0.207985i	$0.0666906\pi$
$193$	3.26525	+	12.1861i	0.235038	+	0.877172i	−0.743094	+	0.669187i	$0.766643\pi$
$194$	−6.15527	−	10.6612i	−0.441923	−	0.765433i
$195$	−8.28952	+	2.74307i	−0.593625	+	0.196435i
$196$	−2.98837	+	5.17601i	−0.213455	+	0.369715i
$197$	−0.680083	−	0.182228i	−0.0484539	−	0.0129832i	0.234511	−	0.972114i	$-0.424651\pi$
$197$	−0.680083	−	0.182228i	−0.0484539	−	0.0129832i	−0.282965	+	0.959130i	$0.591318\pi$
$198$	−8.63594	−	15.1586i	−0.613730	−	1.07727i
$199$	8.58639	+	4.95735i	0.608673	+	0.351418i	0.772446	−	0.635081i	$-0.219033\pi$
$199$	8.58639	+	4.95735i	0.608673	+	0.351418i	−0.163773	+	0.986498i	$0.552366\pi$
$200$	0.788134	+	2.94136i	0.0557295	+	0.207985i
$201$	−0.513930	+	1.89618i	−0.0362499	+	0.133746i
$202$	7.20645	−	7.20645i	0.507044	−	0.507044i
$203$	0.269740	−	1.00668i	0.0189320	−	0.0706553i
$204$	5.02747	−	2.88336i	0.351994	−	0.201876i
$205$		−	2.28837i		−	0.159827i
$206$	2.55304	−	9.52809i	0.177879	−	0.663853i
$207$	−1.74128	−	0.0100167i	−0.121027	−	0.000696210i
$208$	−3.22602	−	1.61022i	−0.223684	−	0.111649i
$209$	−36.8937	−	21.3006i	−2.55199	−	1.47339i
$210$	−0.640835	+	2.36441i	−0.0442218	+	0.163160i
$211$	3.01444	−	5.22116i	0.207522	−	0.359439i	−0.743411	−	0.668835i	$-0.766793\pi$
$211$	3.01444	−	5.22116i	0.207522	−	0.359439i	0.950933	+	0.309396i	$0.100127\pi$
$212$	−2.77082			−0.190300
$213$	−17.5361	−	4.75289i	−1.20156	−	0.325663i
$214$	−2.56517	+	9.57335i	−0.175352	+	0.654421i
$215$	−11.3182	+	3.03269i	−0.771893	+	0.206828i
$216$	−3.64239	−	3.70580i	−0.247834	−	0.252148i
$217$	4.46502	−	7.73364i	0.303105	−	0.524994i
$218$	9.89396			0.670103
$219$	0.494321	+	1.86628i	0.0334031	+	0.126112i
$220$	7.04151	−	4.06542i	0.474738	−	0.274090i
$221$	10.0634	−	6.65441i	0.676939	−	0.447624i
$222$	0.0403545	−	14.0303i	0.00270842	−	0.941654i
$223$	−20.6159	−	20.6159i	−1.38054	−	1.38054i	−0.843653	−	0.536889i	$-0.819599\pi$
$223$	−20.6159	−	20.6159i	−1.38054	−	1.38054i	−0.536889	−	0.843653i	$-0.680401\pi$
$224$	−0.876041	+	0.505782i	−0.0585329	+	0.0337940i
$225$	−0.0525503	+	9.13520i	−0.00350335	+	0.609013i
$226$	−7.17524	−	7.17524i	−0.477290	−	0.477290i
$227$	14.0103	+	3.75404i	0.929894	+	0.249164i	0.691809	−	0.722080i	$-0.256814\pi$
$227$	14.0103	+	3.75404i	0.929894	+	0.249164i	0.238084	+	0.971244i	$0.423481\pi$
$228$	−12.2466	−	3.31924i	−0.811050	−	0.219822i
$229$	9.53135	+	2.55392i	0.629849	+	0.168768i	0.559601	−	0.828762i	$-0.310954\pi$
$229$	9.53135	+	2.55392i	0.629849	+	0.168768i	0.0702479	+	0.997530i	$0.477621\pi$
$230$		−	0.811549i		−	0.0535120i
$231$	−10.1889	−	0.0293056i	−0.670380	−	0.00192817i
$232$	−0.728518	+	0.728518i	−0.0478296	+	0.0478296i
$233$	2.06808			0.135484			0.0677421	−	0.997703i	$-0.478420\pi$
$233$	2.06808			0.135484			0.0677421	+	0.997703i	$0.478420\pi$
$234$	−8.05663	−	7.21739i	−0.526678	−	0.471815i
$235$	−2.10003			−0.136991
$236$	8.47432	−	8.47432i	0.551631	−	0.551631i
$237$	−1.42569	−	2.48585i	−0.0926083	−	0.161473i
$238$		−	3.38480i		−	0.219404i
$239$	19.0682	+	5.10931i	1.23342	+	0.330494i	0.815910	−	0.578179i	$-0.196236\pi$
$239$	19.0682	+	5.10931i	1.23342	+	0.330494i	0.417510	+	0.908672i	$0.362903\pi$
$240$	1.71732	−	1.70747i	0.110853	−	0.110217i
$241$	9.79587	+	2.62479i	0.631007	+	0.169078i	0.560127	−	0.828407i	$-0.310752\pi$
$241$	9.79587	+	2.62479i	0.631007	+	0.169078i	0.0708805	+	0.997485i	$0.477419\pi$
$242$	16.1348	+	16.1348i	1.03718	+	1.03718i
$243$	−7.59928	−	13.6107i	−0.487494	−	0.873126i
$244$	−2.44926	+	1.41408i	−0.156797	+	0.0905271i
$245$	−5.90894	−	5.90894i	−0.377508	−	0.377508i
$246$	2.45910	−	1.41034i	0.156786	−	0.0899203i
$247$	−25.8805	−	5.27740i	−1.64674	−	0.335793i
$248$	−7.64523	+	4.41397i	−0.485472	+	0.280288i
$249$	27.2109	+	7.37508i	1.72442	+	0.467377i
$250$	−11.2485			−0.711415
$251$	−4.78920	+	8.29514i	−0.302292	+	0.523585i	−0.976655	−	0.214815i	$-0.931085\pi$
$251$	−4.78920	+	8.29514i	−0.302292	+	0.523585i	0.674363	+	0.738400i	$0.264418\pi$
$252$	−2.93576	+	0.768562i	−0.184935	+	0.0484148i
$253$	3.26041	−	0.873624i	0.204980	−	0.0549243i
$254$	−3.91822	+	14.6230i	−0.245851	+	0.917527i
$255$	2.07476	+	7.83317i	0.129927	+	0.490532i
$256$	1.00000			0.0625000
$257$	−2.88755	+	5.00138i	−0.180120	+	0.311977i	−0.941921	−	0.335834i	$-0.890982\pi$
$257$	−2.88755	+	5.00138i	−0.180120	+	0.311977i	0.761801	+	0.647811i	$0.224315\pi$
$258$	−10.2345	−	10.2935i	−0.637170	−	0.640845i
$259$	−7.09632	−	4.09706i	−0.440944	−	0.254579i
$260$	3.34206	−	3.77414i	0.207266	−	0.234062i
$261$	−2.68559	+	1.53000i	−0.166234	+	0.0947045i
$262$	0.983420	−	3.67017i	0.0607559	−	0.226744i
$263$		−	4.45725i		−	0.274846i	−0.990512	−	0.137423i	$-0.956118\pi$
$263$		−	4.45725i		−	0.274846i	0.990512	−	0.137423i	$-0.0438819\pi$
$264$	8.70847	+	5.06129i	0.535970	+	0.311501i
$265$	1.00269	−	3.74207i	0.0615945	−	0.229874i
$266$	−5.23994	+	5.23994i	−0.321281	+	0.321281i
$267$	−3.69829	−	3.71962i	−0.226331	−	0.227637i
$268$	−0.293568	−	1.09561i	−0.0179325	−	0.0669250i
$269$	−11.4786	−	6.62715i	−0.699860	−	0.404064i	0.107435	−	0.994212i	$-0.465736\pi$
$269$	−11.4786	−	6.62715i	−0.699860	−	0.404064i	−0.807295	+	0.590148i	$0.799069\pi$
$270$	6.32288	−	3.57813i	0.384798	−	0.217758i
$271$	−5.62562	−	1.50738i	−0.341732	−	0.0915668i	0.0838714	−	0.996477i	$-0.473272\pi$
$271$	−5.62562	−	1.50738i	−0.341732	−	0.0915668i	−0.425604	+	0.904910i	$0.639938\pi$
$272$	−1.67305	+	2.89781i	−0.101444	+	0.175706i
$273$	−5.99739	+	1.98458i	−0.362979	+	0.120113i
$274$	2.91000	+	5.04027i	0.175799	+	0.304494i
$275$	−4.58326	−	17.1050i	−0.276381	−	1.03147i
$276$	0.872096	−	0.500166i	0.0524940	−	0.0301064i
$277$	−16.8351	+	9.71973i	−1.01152	+	0.584002i	−0.911637	−	0.410997i	$-0.865181\pi$
$277$	−16.8351	+	9.71973i	−1.01152	+	0.584002i	−0.0998845	+	0.994999i	$0.531847\pi$
$278$	1.60991	−	1.60991i	0.0965559	−	0.0965559i
$279$	−25.6204	+	6.70725i	−1.53386	+	0.401553i
$280$	−0.366058	−	1.36615i	−0.0218762	−	0.0816430i
$281$	−1.40349	+	0.376063i	−0.0837250	+	0.0224340i	−0.300438	−	0.953801i	$-0.597133\pi$
$281$	−1.40349	+	0.376063i	−0.0837250	+	0.0224340i	0.216713	+	0.976235i	$0.430466\pi$
$282$	−1.29427	−	2.25670i	−0.0770725	−	0.134385i
$283$	−17.9556	−	10.3666i	−1.06735	−	0.616233i	−0.139892	−	0.990167i	$-0.544675\pi$
$283$	−17.9556	−	10.3666i	−1.06735	−	0.616233i	−0.927455	+	0.373934i	$0.878009\pi$
$284$	10.1323	−	2.71495i	0.601243	−	0.161103i
$285$	8.91446	−	15.3382i	0.528047	−	0.908559i
$286$	18.7604	+	9.36396i	1.10932	+	0.553703i
$287$		−	1.65561i		−	0.0977278i
$288$	2.89326	+	0.793114i	0.170487	+	0.0467347i
$289$	2.90179	+	5.02604i	0.170693	+	0.295649i
$290$	−0.720255	−	1.24752i	−0.0422948	−	0.0732568i
$291$	15.0338	+	15.1206i	0.881300	+	0.886384i
$292$	−0.788181	−	0.788181i	−0.0461248	−	0.0461248i
$293$	16.7878	+	16.7878i	0.980753	+	0.980753i	0.999818	−	0.0190656i	$-0.00606914\pi$
$293$	16.7878	+	16.7878i	0.980753	+	0.980753i	−0.0190656	+	0.999818i	$0.506069\pi$
$294$	2.70805	−	9.99153i	0.157936	−	0.582718i
$295$	8.37820	+	14.5115i	0.487797	+	0.844890i
$296$	4.05022	+	7.01519i	0.235414	+	0.407750i
$297$	21.1817	+	21.5505i	1.22909	+	1.25048i
$298$		−	14.3749i		−	0.832715i
$299$	1.74566	−	1.15431i	0.100954	−	0.0667557i
$300$	−2.62400	−	4.57524i	−0.151497	−	0.264152i
$301$	−8.18860	+	2.19413i	−0.471983	+	0.126467i
$302$	2.43881	+	1.40805i	0.140337	+	0.0810239i
$303$	−8.87000	+	15.2617i	−0.509568	+	0.876765i
$304$	7.07605	−	1.89602i	0.405839	−	0.108744i
$305$	−1.02343	−	3.81951i	−0.0586017	−	0.218705i
$306$	−7.13888	+	7.05721i	−0.408102	+	0.403434i
$307$	14.7696	−	14.7696i	0.842947	−	0.842947i	−0.146294	−	0.989241i	$-0.546735\pi$
$307$	14.7696	−	14.7696i	0.842947	−	0.842947i	0.989241	+	0.146294i	$0.0467346\pi$
$308$	5.09447	−	2.94129i	0.290284	−	0.167596i
$309$	−0.0491411	+	17.0852i	−0.00279554	+	0.971945i
$310$	−3.19460	−	11.9224i	−0.181441	−	0.677147i
$311$	14.0548	+	24.3437i	0.796976	+	1.38040i	0.921577	+	0.388195i	$0.126901\pi$
$311$	14.0548	+	24.3437i	0.796976	+	1.38040i	−0.124602	+	0.992207i	$0.539765\pi$
$312$	6.11546	+	1.26536i	0.346220	+	0.0716370i
$313$	8.76521	−	15.1818i	0.495439	−	0.858125i	−0.504547	−	0.863384i	$-0.668341\pi$
$313$	8.76521	−	15.1818i	0.495439	−	0.858125i	0.999986	+	0.00525876i	$0.00167392\pi$
$314$	7.60971	+	2.03902i	0.429441	+	0.115068i
$315$	0.0244076	−	4.24295i	0.00137521	−	0.239063i
$316$	1.43283	+	0.827245i	0.0806030	+	0.0465362i
$317$	5.72585	+	21.3692i	0.321596	+	1.20021i	0.917690	+	0.397298i	$0.130052\pi$
$317$	5.72585	+	21.3692i	0.321596	+	1.20021i	−0.596094	+	0.802915i	$0.703281\pi$
$318$	4.63922	−	1.22878i	0.260155	−	0.0689068i
$319$	4.23658	−	4.23658i	0.237203	−	0.237203i
$320$	−0.361873	+	1.35053i	−0.0202293	+	0.0754969i
$321$	0.0493745	−	17.1664i	0.00275582	−	0.958135i
$322$		−	0.587148i		−	0.0327205i
$323$	−6.34429	+	23.6772i	−0.353006	+	1.31744i
$324$	7.74194	+	4.58937i	0.430108	+	0.254965i
$325$	−6.05583	−	9.15819i	−0.335917	−	0.508005i
$326$	−5.99017	−	3.45843i	−0.331765	−	0.191544i
$327$	−16.5656	+	4.38771i	−0.916080	+	0.242641i
$328$	−0.818343	+	1.41741i	−0.0451854	+	0.0782635i
$329$	−1.51935			−0.0837645
$330$	−9.98679	+	9.92951i	−0.549755	+	0.546602i
$331$	5.85855	−	21.8644i	0.322015	−	1.20178i	−0.595263	−	0.803531i	$-0.702952\pi$
$331$	5.85855	−	21.8644i	0.322015	−	1.20178i	0.917279	−	0.398246i	$-0.130381\pi$
$332$	−15.7224	+	4.21280i	−0.862878	+	0.231207i
$333$	6.15452	+	23.5091i	0.337266	+	1.28829i
$334$	−7.92523	+	13.7269i	−0.433649	+	0.751102i
$335$	1.58589			0.0866464
$336$	1.24247	−	1.23534i	0.0677821	−	0.0673933i
$337$	26.9968	−	15.5866i	1.47061	−	0.849058i	0.471156	−	0.882050i	$-0.343837\pi$
$337$	26.9968	−	15.5866i	1.47061	−	0.849058i	0.999456	+	0.0329922i	$0.0105036\pi$
$338$	12.8719	+	1.82067i	0.700138	+	0.0990314i
$339$	15.1956	+	8.83158i	0.825314	+	0.479666i
$340$	−3.30815	−	3.30815i	−0.179410	−	0.179410i
$341$	44.4595	−	25.6687i	2.40762	−	1.39004i
$342$	21.9766	+	0.126421i	1.18836	+	0.00683606i
$343$	−9.28206	−	9.28206i	−0.501184	−	0.501184i
$344$	8.09498	+	2.16904i	0.436452	+	0.116947i
$345$	0.359901	+	1.35879i	0.0193764	+	0.0731547i
$346$	−2.51578	−	0.674101i	−0.135249	−	0.0362399i
$347$			20.3582i			1.09289i	0.837496	+	0.546444i	$0.184019\pi$
$347$			20.3582i			1.09289i	−0.837496	+	0.546444i	$0.815981\pi$
$348$	0.896691	−	1.54285i	0.0480677	−	0.0827054i
$349$	−20.7926	+	20.7926i	−1.11300	+	1.11300i	−0.120259	+	0.992743i	$0.538373\pi$
$349$	−20.7926	+	20.7926i	−1.11300	+	1.11300i	−0.992743	+	0.120259i	$0.961627\pi$
$350$	−3.08033			−0.164651
$351$	16.6901	+	8.51128i	0.890850	+	0.454298i
$352$	−5.81533			−0.309958
$353$	8.11406	−	8.11406i	0.431868	−	0.431868i	−0.457395	−	0.889263i	$-0.651218\pi$
$353$	8.11406	−	8.11406i	0.431868	−	0.431868i	0.889263	+	0.457395i	$0.151218\pi$
$354$	−10.4305	+	17.9468i	−0.554377	+	0.953863i
$355$			14.6665i			0.778417i
$356$	2.92517	+	0.783797i	0.155034	+	0.0415412i
$357$	1.50107	+	5.66723i	0.0794451	+	0.299941i
$358$	−3.46984	−	0.929741i	−0.183387	−	0.0491383i
$359$	−25.9734	−	25.9734i	−1.37083	−	1.37083i	−0.859221	−	0.511605i	$-0.829051\pi$
$359$	−25.9734	−	25.9734i	−1.37083	−	1.37083i	−0.511605	−	0.859221i	$-0.670949\pi$
$360$	−2.11812	+	3.62043i	−0.111635	+	0.190814i
$361$	30.0211	−	17.3327i	1.58006	−	0.912248i
$362$	11.5571	+	11.5571i	0.607430	+	0.607430i
$363$	−34.1701	−	19.8594i	−1.79347	−	1.04235i
$364$	2.41795	−	2.73056i	0.126735	−	0.143120i
$365$	1.34968	−	0.779240i	0.0706457	−	0.0407873i
$366$	3.47372	−	3.45379i	0.181574	−	0.180533i
$367$	−5.57250			−0.290882			−0.145441	−	0.989367i	$-0.546460\pi$
$367$	−5.57250			−0.290882			−0.145441	+	0.989367i	$0.546460\pi$
$368$	−0.290218	+	0.502672i	−0.0151287	+	0.0262036i
$369$	−3.49185	+	3.45191i	−0.181778	+	0.179699i
$370$	−10.9399	+	2.93134i	−0.568738	+	0.152393i
$371$	0.725434	−	2.70736i	0.0376626	−	0.140559i
$372$	10.8430	−	10.7808i	0.562185	−	0.558960i
$373$	2.87844			0.149040			0.0745200	−	0.997220i	$-0.476258\pi$
$373$	2.87844			0.149040			0.0745200	+	0.997220i	$0.476258\pi$
$374$	9.72936	−	16.8517i	0.503093	−	0.871383i
$375$	18.8335	−	4.98840i	0.972555	−	0.257600i
$376$	1.30075	+	0.750990i	0.0670812	+	0.0387294i
$377$	1.65898	−	3.32370i	0.0854418	−	0.171179i
$378$	4.57455	−	2.58875i	0.235289	−	0.133151i
$379$	5.51954	−	20.5992i	0.283520	−	1.05811i	−0.666394	−	0.745600i	$-0.732163\pi$
$379$	5.51954	−	20.5992i	0.283520	−	1.05811i	0.949914	−	0.312511i	$-0.101170\pi$
$380$			10.2425i			0.525431i
$381$	0.0754180	−	26.2211i	0.00386378	−	1.34335i
$382$	−6.58377	+	24.5710i	−0.336855	+	1.25716i
$383$	9.17790	−	9.17790i	0.468969	−	0.468969i	−0.432612	−	0.901580i	$-0.642408\pi$
$383$	9.17790	−	9.17790i	0.468969	−	0.468969i	0.901580	+	0.432612i	$0.142408\pi$
$384$	−1.67432	+	0.443474i	−0.0854420	+	0.0226309i
$385$	2.12875	+	7.94461i	0.108491	+	0.404895i
$386$	10.9257	+	6.30797i	0.556105	+	0.321067i
$387$	21.7006	+	12.6958i	1.10310	+	0.645366i
$388$	−11.8911	−	3.18620i	−0.603678	−	0.161755i
$389$	−15.6511	+	27.1085i	−0.793543	+	1.37446i	0.130216	+	0.991486i	$0.458433\pi$
$389$	−15.6511	+	27.1085i	−0.793543	+	1.37446i	−0.923760	+	0.382972i	$0.874901\pi$
$390$	−3.92193	+	7.80121i	−0.198595	+	0.395030i
$391$	−0.971100	−	1.68199i	−0.0491106	−	0.0850621i
$392$	1.54689	+	5.77308i	0.0781299	+	0.291585i
$393$	−0.0189289	+	6.58115i	−0.000954837	+	0.331975i
$394$	−0.609746	+	0.352037i	−0.0307186	+	0.0177354i
$395$	−1.63572	+	1.63572i	−0.0823021	+	0.0823021i
$396$	−16.8253	−	4.61222i	−0.845502	−	0.231773i
$397$	0.644906	+	2.40682i	0.0323669	+	0.120795i	0.980219	−	0.197915i	$-0.0634170\pi$
$397$	0.644906	+	2.40682i	0.0323669	+	0.120795i	−0.947852	+	0.318710i	$0.896750\pi$
$398$	9.57687	−	2.56612i	0.480045	−	0.128628i
$399$	6.44953	−	11.0971i	0.322880	−	0.555549i
$400$	2.63715	+	1.52256i	0.131857	+	0.0761279i
$401$	19.8142	−	5.30920i	0.989473	−	0.265129i	0.272444	−	0.962172i	$-0.412168\pi$
$401$	19.8142	−	5.30920i	0.989473	−	0.265129i	0.717029	+	0.697043i	$0.245501\pi$
$402$	0.977400	+	1.70421i	0.0487483	+	0.0849981i
$403$	21.1015	−	23.8296i	1.05114	−	1.18704i
$404$		−	10.1915i		−	0.507044i
$405$	−8.99969	+	8.79495i	−0.447198	+	0.437025i
$406$	−0.521098	−	0.902568i	−0.0258617	−	0.0447937i
$407$	−23.5534	−	40.7957i	−1.16750	−	2.02217i
$408$	1.51611	−	5.59381i	0.0750588	−	0.276935i
$409$	−6.92695	−	6.92695i	−0.342516	−	0.342516i	0.514797	−	0.857312i	$-0.327867\pi$
$409$	−6.92695	−	6.92695i	−0.342516	−	0.342516i	−0.857312	+	0.514797i	$0.827867\pi$
$410$	−1.61812	−	1.61812i	−0.0799133	−	0.0799133i
$411$	−7.10748	−	7.14848i	−0.350586	−	0.352609i
$412$	−4.93210	−	8.54265i	−0.242987	−	0.420866i
$413$	6.06155	+	10.4989i	0.298269	+	0.516618i
$414$	−1.23835	+	1.22419i	−0.0608617	+	0.0601655i
$415$		−	22.7581i		−	1.11715i
$416$	−3.41974	+	1.14254i	−0.167666	+	0.0560177i
$417$	−1.98154	+	3.40945i	−0.0970365	+	0.166961i
$418$	−41.1496	+	11.0260i	−2.01269	+	0.539299i
$419$	1.49988	+	0.865956i	0.0732739	+	0.0423047i	0.536189	−	0.844098i	$-0.319863\pi$
$419$	1.49988	+	0.865956i	0.0732739	+	0.0423047i	−0.462915	+	0.886402i	$0.653197\pi$
$420$	1.21875	+	2.12503i	0.0594688	+	0.103691i
$421$	−3.43418	+	0.920185i	−0.167372	+	0.0448471i	−0.341532	−	0.939870i	$-0.610946\pi$
$421$	−3.43418	+	0.920185i	−0.167372	+	0.0448471i	0.174160	+	0.984717i	$0.444279\pi$
$422$	−1.56039	−	5.82344i	−0.0759584	−	0.283481i
$423$	3.16780	+	3.20446i	0.154024	+	0.155806i
$424$	−1.95926	+	1.95926i	−0.0951502	+	0.0951502i
$425$	−8.82418	+	5.09464i	−0.428035	+	0.247126i
$426$	−15.7607	+	9.03911i	−0.763609	+	0.437946i
$427$	−0.740446	−	2.76338i	−0.0358327	−	0.133729i
$428$	4.95553	+	8.58323i	0.239535	+	0.414886i
$429$	−35.5634	−	7.35849i	−1.71702	−	0.355271i
$430$	−5.85872	+	10.1476i	−0.282532	+	0.489360i
$431$	14.3219	+	3.83753i	0.689860	+	0.184847i	0.586684	−	0.809816i	$-0.300433\pi$
$431$	14.3219	+	3.83753i	0.689860	+	0.184847i	0.103176	+	0.994663i	$0.467100\pi$
$432$	−5.19596	−	0.0448353i	−0.249991	−	0.00215714i
$433$	−9.94854	−	5.74379i	−0.478096	−	0.276029i	0.241527	−	0.970394i	$-0.422352\pi$
$433$	−9.94854	−	5.74379i	−0.478096	−	0.276029i	−0.719623	+	0.694365i	$0.755685\pi$
$434$	−2.31126	−	8.62576i	−0.110944	−	0.414050i
$435$	1.75917	+	1.76932i	0.0843460	+	0.0848326i
$436$	6.99609	−	6.99609i	0.335052	−	0.335052i
$437$	−1.10052	+	4.10719i	−0.0526450	+	0.196474i
$438$	1.66920	+	0.970125i	0.0797575	+	0.0463544i
$439$			40.7022i			1.94261i	0.237834	+	0.971306i	$0.423563\pi$
$439$			40.7022i			1.94261i	−0.237834	+	0.971306i	$0.576437\pi$
$440$	2.10441	−	7.85378i	0.100324	−	0.374414i
$441$	−0.103142	+	17.9299i	−0.00491152	+	0.853805i
$442$	2.41053	−	11.8213i	0.114657	−	0.562281i
$443$	10.6734	+	6.16232i	0.507111	+	0.292780i	0.731645	−	0.681686i	$-0.238753\pi$
$443$	10.6734	+	6.16232i	0.507111	+	0.292780i	−0.224535	+	0.974466i	$0.572086\pi$
$444$	−9.89241	−	9.94948i	−0.469473	−	0.472181i
$445$	−2.11708	+	3.66690i	−0.100359	+	0.173828i
$446$	−29.1553			−1.38054
$447$	6.37489	+	24.0681i	0.301522	+	1.13838i
$448$	−0.261812	+	0.977097i	−0.0123695	+	0.0461635i
$449$	27.3580	−	7.33055i	1.29110	−	0.345950i	0.453024	−	0.891498i	$-0.350345\pi$
$449$	27.3580	−	7.33055i	1.29110	−	0.345950i	0.838080	+	0.545548i	$0.183678\pi$
$450$	6.42240	+	6.49672i	0.302755	+	0.306258i
$451$	4.75894	−	8.24272i	0.224090	−	0.388134i
$452$	−10.1473			−0.477290
$453$	−4.70776	−	1.27596i	−0.221190	−	0.0599500i
$454$	12.5613	−	7.25224i	0.589529	−	0.340365i
$455$	2.81271	+	4.25363i	0.131862	+	0.199413i
$456$	−11.0067	+	6.31258i	−0.515436	+	0.295614i
$457$	21.3025	+	21.3025i	0.996490	+	0.996490i	0.999994	−	0.00350346i	$-0.00111519\pi$
$457$	21.3025	+	21.3025i	0.996490	+	0.996490i	−0.00350346	+	0.999994i	$0.501115\pi$
$458$	8.54557	−	4.93379i	0.399308	−	0.230541i
$459$	8.82304	−	14.9819i	0.411824	−	0.699295i
$460$	−0.573852	−	0.573852i	−0.0267560	−	0.0267560i
$461$	27.5031	+	7.36943i	1.28095	+	0.343228i	0.834215	−	0.551440i	$-0.185921\pi$
$461$	27.5031	+	7.36943i	1.28095	+	0.343228i	0.446731	+	0.894668i	$0.352588\pi$
$462$	−7.22536	+	7.18391i	−0.336154	+	0.334226i
$463$	−3.49672	−	0.936943i	−0.162506	−	0.0435434i	0.176649	−	0.984274i	$-0.443474\pi$
$463$	−3.49672	−	0.936943i	−0.162506	−	0.0435434i	−0.339155	+	0.940731i	$0.610141\pi$
$464$			1.03028i			0.0478296i
$465$	10.6360	+	18.5451i	0.493235	+	0.860011i
$466$	1.46235	−	1.46235i	0.0677421	−	0.0677421i
$467$	−36.6235			−1.69473			−0.847366	−	0.531010i	$-0.821813\pi$
$467$	−36.6235			−1.69473			−0.847366	+	0.531010i	$0.821813\pi$
$468$	−10.8004	+	0.593434i	−0.499247	+	0.0274315i
$469$	1.14738			0.0529809
$470$	−1.48494	+	1.48494i	−0.0684953	+	0.0684953i
$471$	−13.6453	−	0.0392470i	−0.628742	−	0.00180841i
$472$		−	11.9845i		−	0.551631i
$473$	−47.0750	−	12.6137i	−2.16451	−	0.579979i
$474$	−2.76587	−	0.749646i	−0.127041	−	0.0344324i
$475$	21.5474	+	5.77361i	0.988662	+	0.264911i
$476$	−2.39342	−	2.39342i	−0.109702	−	0.109702i
$477$	−7.22258	+	4.11475i	−0.330699	+	0.188401i
$478$	17.0961	−	9.87043i	0.781957	−	0.451463i
$479$	−3.57024	−	3.57024i	−0.163128	−	0.163128i	0.620823	−	0.783951i	$-0.286799\pi$
$479$	−3.57024	−	3.57024i	−0.163128	−	0.163128i	−0.783951	+	0.620823i	$0.786799\pi$
$480$	0.00696535	−	2.42169i	0.000317923	−	0.110535i
$481$	−21.8658	−	19.3626i	−0.996997	−	0.882857i
$482$	8.78273	−	5.07071i	0.400043	−	0.230965i
$483$	0.260385	+	0.983071i	0.0118479	+	0.0447313i
$484$	22.8181			1.03718
$485$	8.60613	−	14.9063i	0.390784	−	0.676858i
$486$	−14.9977	−	4.25071i	−0.680310	−	0.192816i
$487$	−28.6137	+	7.66702i	−1.29661	+	0.347426i	−0.840167	−	0.542327i	$-0.817543\pi$
$487$	−28.6137	+	7.66702i	−1.29661	+	0.347426i	−0.456443	+	0.889753i	$0.650877\pi$
$488$	−0.731981	+	2.73179i	−0.0331352	+	0.123662i
$489$	11.5632	+	3.13401i	0.522904	+	0.141725i
$490$	−8.35650			−0.377508
$491$	−0.987608	+	1.71059i	−0.0445701	+	0.0771978i	−0.887450	−	0.460904i	$-0.847525\pi$
$491$	−0.987608	+	1.71059i	−0.0445701	+	0.0771978i	0.842880	+	0.538102i	$0.180858\pi$
$492$	0.741579	−	2.73611i	0.0334330	−	0.123353i
$493$	−2.98556	−	1.72371i	−0.134463	−	0.0776322i
$494$	−22.0320	+	14.5686i	−0.991264	+	0.655471i
$495$	12.3176	−	21.0540i	0.553633	−	0.946307i
$496$	−2.28484	+	8.52714i	−0.102592	+	0.382880i
$497$			10.6111i			0.475972i
$498$	24.4560	−	14.0260i	1.09590	−	0.628521i
$499$	1.03754	−	3.87214i	0.0464465	−	0.173341i	−0.938806	−	0.344445i	$-0.888067\pi$
$499$	1.03754	−	3.87214i	0.0464465	−	0.173341i	0.985253	+	0.171105i	$0.0547336\pi$
$500$	−7.95386	+	7.95386i	−0.355707	+	0.355707i
$501$	7.18181	−	26.4978i	0.320859	−	1.18383i
$502$	2.47907	+	9.25203i	0.110646	+	0.412938i
$503$	6.37037	+	3.67794i	0.284041	+	0.163991i	0.635251	−	0.772305i	$-0.280897\pi$
$503$	6.37037	+	3.67794i	0.284041	+	0.163991i	−0.351211	+	0.936297i	$0.614230\pi$
$504$	−1.53244	+	2.61935i	−0.0682603	+	0.116675i
$505$	13.7639	+	3.68802i	0.612485	+	0.164115i
$506$	1.68771	−	2.92320i	0.0750280	−	0.129952i
$507$	−22.3590	+	2.65997i	−0.992998	+	0.118133i
$508$	7.56941	+	13.1106i	0.335838	+	0.581689i
$509$	−3.68759	−	13.7623i	−0.163449	−	0.610002i	−0.998233	−	0.0594233i	$-0.981074\pi$
$509$	−3.68759	−	13.7623i	−0.163449	−	0.610002i	0.834783	−	0.550579i	$-0.185593\pi$
$510$	7.00596	+	4.07181i	0.310229	+	0.180303i
$511$	0.976484	−	0.563773i	0.0431971	−	0.0249399i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−36.8519	+	9.53440i	−1.62705	+	0.420954i
$514$	1.49470	+	5.57831i	0.0659286	+	0.246049i
$515$	13.3219	−	3.56959i	0.587033	−	0.157295i
$516$	−14.5155	−	0.0417498i	−0.639007	−	0.00183793i
$517$	−7.56431	−	4.36726i	−0.332678	−	0.192072i
$518$	−7.91492	+	2.12080i	−0.347762	+	0.0931824i
$519$	4.51115	+	0.0129751i	0.198018	+	0.000569544i
$520$	−0.305525	−	5.03191i	−0.0133982	−	0.220664i
$521$			28.5428i			1.25048i	0.780431	+	0.625242i	$0.215000\pi$
$521$			28.5428i			1.25048i	−0.780431	+	0.625242i	$0.785000\pi$
$522$	−0.817130	+	2.98087i	−0.0357648	+	0.130469i
$523$	7.95336	+	13.7756i	0.347776	+	0.602366i	0.985854	−	0.167606i	$-0.0536037\pi$
$523$	7.95336	+	13.7756i	0.347776	+	0.602366i	−0.638078	+	0.769972i	$0.720270\pi$
$524$	−1.89982	−	3.29059i	−0.0829941	−	0.143750i
$525$	5.15745	−	1.36605i	0.225089	−	0.0596192i
$526$	−3.15175	−	3.15175i	−0.137423	−	0.137423i
$527$	−20.8874	−	20.8874i	−0.909869	−	0.909869i
$528$	9.73669	−	2.57895i	0.423735	−	0.112234i
$529$	11.3315	+	19.6268i	0.492676	+	0.853340i
$530$	−1.93704	−	3.35505i	−0.0841396	−	0.145734i
$531$	9.50507	−	34.6743i	0.412485	−	1.50474i
$532$			7.41039i			0.321281i
$533$	1.17907	−	5.78217i	0.0510710	−	0.250453i
$534$	−5.24525	−	0.0150866i	−0.226984	−	0.000652859i
$535$	−13.3852	+	3.58655i	−0.578692	+	0.155060i
$536$	−0.982297	−	0.567130i	−0.0424288	−	0.0244963i
$537$	6.22192	+	0.0178957i	0.268496	+	0.000772256i
$538$	−12.8027	+	3.43046i	−0.551962	+	0.147898i
$539$	−8.99570	−	33.5724i	−0.387472	−	1.44607i
$540$	1.94083	−	7.00107i	0.0835201	−	0.301278i
$541$	20.5826	−	20.5826i	0.884913	−	0.884913i	−0.109116	−	0.994029i	$-0.534802\pi$
$541$	20.5826	−	20.5826i	0.884913	−	0.884913i	0.994029	+	0.109116i	$0.0348019\pi$
$542$	−5.04379	+	2.91204i	−0.216649	+	0.125083i
$543$	−24.4756	−	14.2250i	−1.05035	−	0.610453i
$544$	0.866036	+	3.23209i	0.0371310	+	0.138575i
$545$	6.91673	+	11.9801i	0.296280	+	0.513172i
$546$	−2.83748	+	5.64411i	−0.121433	+	0.241546i
$547$	−11.8581	+	20.5389i	−0.507017	+	0.878180i	0.492950	+	0.870058i	$0.335919\pi$
$547$	−11.8581	+	20.5389i	−0.507017	+	0.878180i	−0.999967	+	0.00812189i	$0.997415\pi$
$548$	5.62169	+	1.50633i	0.240147	+	0.0643471i
$549$	−4.28443	+	7.32324i	−0.182855	+	0.312548i
$550$	−15.3359	−	8.85418i	−0.653924	−	0.377543i
$551$	1.95344	+	7.29032i	0.0832191	+	0.310578i
$552$	0.262994	−	0.970336i	0.0111938	−	0.0413002i
$553$	−1.18343	+	1.18343i	−0.0503246	+	0.0503246i
$554$	−5.03130	+	18.7771i	−0.213760	+	0.797762i
$555$	17.0169	−	9.75954i	0.722326	−	0.414269i
$556$		−	2.27675i		−	0.0965559i
$557$	1.55296	−	5.79572i	0.0658010	−	0.245573i	−0.925189	−	0.379506i	$-0.876094\pi$
$557$	1.55296	−	5.79572i	0.0658010	−	0.245573i	0.990990	+	0.133933i	$0.0427607\pi$
$558$	−13.3736	+	22.8591i	−0.566151	+	0.967704i
$559$	−30.1609	+	1.83129i	−1.27567	+	0.0774555i
$560$	−1.22486	−	0.707171i	−0.0517596	−	0.0298834i
$561$	−8.81670	+	32.5298i	−0.372241	+	1.37341i
$562$	−0.726498	+	1.25833i	−0.0306455	+	0.0530795i
$563$	34.2938			1.44531			0.722656	−	0.691208i	$-0.242921\pi$
$563$	34.2938			1.44531			0.722656	+	0.691208i	$0.242921\pi$
$564$	−2.51091	−	0.680544i	−0.105729	−	0.0286561i
$565$	3.67205	−	13.7043i	0.154484	−	0.576543i
$566$	−20.0268	+	5.36617i	−0.841790	+	0.225557i
$567$	−6.51119	+	6.36307i	−0.273444	+	0.267224i
$568$	5.24488	−	9.08440i	0.220070	−	0.381173i
$569$	35.6813			1.49584			0.747919	−	0.663790i	$-0.231053\pi$
$569$	35.6813			1.49584			0.747919	+	0.663790i	$0.231053\pi$
$570$	−4.54230	−	17.1492i	−0.190256	−	0.718303i
$571$	−25.3581	+	14.6405i	−1.06121	+	0.612687i	−0.925765	−	0.378099i	$-0.876578\pi$
$571$	−25.3581	+	14.6405i	−1.06121	+	0.612687i	−0.135440	+	0.990786i	$0.543245\pi$
$572$	19.8869	−	6.64426i	0.831513	−	0.277810i
$573$	0.126725	−	44.0593i	0.00529400	−	1.84060i
$574$	−1.17070	−	1.17070i	−0.0488639	−	0.0488639i
$575$	−1.53069	+	0.883747i	−0.0638344	+	0.0368548i
$576$	2.60666	−	1.48503i	0.108611	−	0.0618762i
$577$	−19.2968	−	19.2968i	−0.803337	−	0.803337i	0.180278	−	0.983616i	$-0.442300\pi$
$577$	−19.2968	−	19.2968i	−0.803337	−	0.803337i	−0.983616	+	0.180278i	$0.942300\pi$
$578$	5.60582	+	1.50208i	0.233171	+	0.0624781i
$579$	−21.0905	−	5.71626i	−0.876492	−	0.237559i
$580$	−1.39143	−	0.372831i	−0.0577758	−	0.0154810i
$581$		−	16.4652i		−	0.683094i
$582$	21.3224	+	0.0613282i	0.883842	+	0.00254213i
$583$	11.3938	−	11.3938i	0.471881	−	0.471881i
$584$	−1.11466			−0.0461248
$585$	3.10691	−	14.8010i	0.128455	−	0.611945i
$586$	23.7415			0.980753
$587$	14.0938	−	14.0938i	0.581712	−	0.581712i	−0.353662	−	0.935373i	$-0.615064\pi$
$587$	14.0938	−	14.0938i	0.581712	−	0.581712i	0.935373	+	0.353662i	$0.115064\pi$
$588$	−5.15020	−	8.97996i	−0.212391	−	0.370327i
$589$			64.6706i			2.66471i
$590$	16.1854	+	4.33687i	0.666344	+	0.178546i
$591$	0.864788	−	0.859827i	0.0355726	−	0.0353686i
$592$	7.82443	+	2.09655i	0.321582	+	0.0861677i
$593$	−3.24522	−	3.24522i	−0.133265	−	0.133265i	0.637328	−	0.770593i	$-0.280040\pi$
$593$	−3.24522	−	3.24522i	−0.133265	−	0.133265i	−0.770593	+	0.637328i	$0.780040\pi$
$594$	30.2162	+	0.260732i	1.23979	+	0.0106980i
$595$	4.09850	−	2.36627i	0.168022	−	0.0970075i
$596$	−10.1646	−	10.1646i	−0.416358	−	0.416358i
$597$	−14.8967	+	8.54358i	−0.609681	+	0.349665i
$598$	0.418145	−	2.05059i	0.0170992	−	0.0838550i
$599$	−36.4947	+	21.0702i	−1.49113	+	0.860906i	−0.999949	−	0.0101486i	$-0.996770\pi$
$599$	−36.4947	+	21.0702i	−1.49113	+	0.860906i	−0.491185	+	0.871055i	$0.663436\pi$
$600$	−5.09063	−	1.37974i	−0.207824	−	0.0563275i
$601$	4.63910			0.189233			0.0946164	−	0.995514i	$-0.469838\pi$
$601$	4.63910			0.189233			0.0946164	+	0.995514i	$0.469838\pi$
$602$	−4.23873	+	7.34169i	−0.172758	+	0.299225i
$603$	−2.39225	−	2.41993i	−0.0974198	−	0.0985471i
$604$	2.72013	−	0.728858i	0.110681	−	0.0296568i
$605$	−8.25725	+	30.8165i	−0.335705	+	1.25287i
$606$	4.51965	+	17.0637i	0.183598	+	0.693166i
$607$	11.5014			0.466829			0.233414	−	0.972377i	$-0.425010\pi$
$607$	11.5014			0.466829			0.233414	+	0.972377i	$0.425010\pi$
$608$	3.66283	−	6.34422i	0.148548	−	0.257292i
$609$	1.27275	+	1.28009i	0.0515743	+	0.0518719i
$610$	−3.42448	−	1.97712i	−0.138653	−	0.0800514i
$611$	−5.30627	−	1.08202i	−0.214669	−	0.0437740i
$612$	−0.0577446	+	10.0382i	−0.00233419	+	0.405768i
$613$	−3.05394	+	11.3975i	−0.123347	+	0.460339i	−0.999775	−	0.0211942i	$-0.993253\pi$
$613$	−3.05394	+	11.3975i	−0.123347	+	0.460339i	0.876428	+	0.481533i	$0.159920\pi$
$614$		−	20.8874i		−	0.842947i
$615$	3.42684	+	1.99165i	0.138183	+	0.0803111i
$616$	1.52252	−	5.68214i	0.0613443	−	0.228940i
$617$	−22.5562	+	22.5562i	−0.908079	+	0.908079i	−0.996117	−	0.0880383i	$-0.971940\pi$
$617$	−22.5562	+	22.5562i	−0.908079	+	0.908079i	0.0880383	+	0.996117i	$0.471940\pi$
$618$	12.0463	+	12.1158i	0.484575	+	0.487370i
$619$	5.99924	+	22.3895i	0.241130	+	0.899909i	0.975289	+	0.220932i	$0.0709097\pi$
$619$	5.99924	+	22.3895i	0.241130	+	0.899909i	−0.734160	+	0.678977i	$0.762424\pi$
$620$	−10.6893	−	6.17149i	−0.429294	−	0.247853i
$621$	1.53050	−	2.59885i	0.0614168	−	0.104288i
$622$	27.1518	+	7.27531i	1.08869	+	0.291713i
$623$	−1.53169	+	2.65297i	−0.0613659	+	0.106289i
$624$	5.21903	−	3.42954i	0.208928	−	0.137291i
$625$	−0.250846	−	0.434477i	−0.0100338	−	0.0173791i
$626$	−4.53721	−	16.9331i	−0.181343	−	0.676782i
$627$	64.0076	−	36.7098i	2.55622	−	1.46605i
$628$	6.82268	−	3.93908i	0.272255	−	0.157186i
$629$	−19.1661	+	19.1661i	−0.764202	+	0.764202i
$630$	−2.98296	−	3.01748i	−0.118844	−	0.120219i
$631$	6.12810	+	22.8704i	0.243956	+	0.910456i	0.973905	+	0.226955i	$0.0728770\pi$
$631$	6.12810	+	22.8704i	0.243956	+	0.910456i	−0.729949	+	0.683501i	$0.760456\pi$
$632$	1.59811	−	0.428214i	0.0635696	−	0.0170334i
$633$	5.19512	+	9.05829i	0.206488	+	0.360035i
$634$	19.1591	+	11.0615i	0.760904	+	0.439308i
$635$	−20.4454	+	5.47834i	−0.811353	+	0.217401i
$636$	2.41154	−	4.14931i	0.0956239	−	0.164531i
$637$	−11.8860	−	17.9750i	−0.470939	−	0.712197i
$638$		−	5.99142i		−	0.237203i
$639$	22.3798	−	22.1238i	0.885331	−	0.875203i
$640$	0.699086	+	1.21085i	0.0276338	+	0.0478631i
$641$	−14.3524	−	24.8590i	−0.566884	−	0.981872i	−0.996872	−	0.0790369i	$-0.974815\pi$
$641$	−14.3524	−	24.8590i	−0.566884	−	0.981872i	0.429988	−	0.902835i	$-0.358518\pi$
$642$	−12.1036	−	12.1734i	−0.477690	−	0.480445i
$643$	16.1427	+	16.1427i	0.636607	+	0.636607i	0.949717	−	0.313110i	$-0.101371\pi$
$643$	16.1427	+	16.1427i	0.636607	+	0.636607i	−0.313110	+	0.949717i	$0.601371\pi$
$644$	−0.415177	−	0.415177i	−0.0163603	−	0.0163603i
$645$	5.30914	−	19.5885i	0.209047	−	0.771295i
$646$	12.2562	+	21.2284i	0.482215	+	0.835221i
$647$	18.5692	+	32.1627i	0.730029	+	1.26445i	0.956870	+	0.290516i	$0.0938270\pi$
$647$	18.5692	+	32.1627i	0.730029	+	1.26445i	−0.226841	+	0.973932i	$0.572840\pi$
$648$	8.71956	−	2.22920i	0.342536	−	0.0875714i
$649$			69.6938i			2.73572i
$650$	−10.7579	−	2.19370i	−0.421961	−	0.0860439i
$651$	7.69508	+	13.4172i	0.301594	+	0.525863i
$652$	−6.68116	+	1.79021i	−0.261655	+	0.0701101i
$653$	−38.5101	−	22.2338i	−1.50702	−	0.870076i	−0.999967	−	0.00815952i	$-0.997403\pi$
$653$	−38.5101	−	22.2338i	−1.50702	−	0.870076i	−0.507050	−	0.861917i	$-0.669264\pi$
$654$	−8.61107	+	14.8162i	−0.336720	+	0.579361i
$655$	5.13153	−	1.37499i	0.200506	−	0.0537253i
$656$	0.423606	+	1.58092i	0.0165390	+	0.0617245i
$657$	−3.22499	−	0.884048i	−0.125819	−	0.0344900i
$658$	−1.07434	+	1.07434i	−0.0418822	+	0.0418822i
$659$	0.358832	−	0.207172i	0.0139781	−	0.00807026i	−0.492995	−	0.870032i	$-0.664098\pi$
$659$	0.358832	−	0.207172i	0.0139781	−	0.00807026i	0.506973	+	0.861962i	$0.330764\pi$
$660$	−0.0405058	+	14.0830i	−0.00157669	+	0.548178i
$661$	−7.37782	−	27.5344i	−0.286964	−	1.07096i	−0.947392	−	0.320075i	$-0.896292\pi$
$661$	−7.37782	−	27.5344i	−0.286964	−	1.07096i	0.660428	−	0.750889i	$-0.270375\pi$
$662$	−11.3179	−	19.6031i	−0.439881	−	0.761896i
$663$	1.20645	+	20.8616i	0.0468545	+	0.810196i
$664$	−8.13850	+	14.0963i	−0.315835	+	0.547043i
$665$	−10.0080	−	2.68162i	−0.388092	−	0.103989i
$666$	20.9753	+	12.2715i	0.812778	+	0.475512i
$667$	−0.517893	−	0.299006i	−0.0200529	−	0.0115776i
$668$	4.10240	+	15.3104i	0.158727	+	0.592376i
$669$	48.8151	−	12.9296i	1.88730	−	0.499887i
$670$	1.12139	−	1.12139i	0.0433232	−	0.0433232i
$671$	4.25671	−	15.8863i	0.164328	−	0.613282i
$672$	0.00503937	−	1.75207i	0.000194398	−	0.0675877i
$673$		−	4.15724i		−	0.160250i	−0.996785	−	0.0801248i	$-0.974468\pi$
$673$		−	4.15724i		−	0.160250i	0.996785	−	0.0801248i	$-0.0255319\pi$
$674$	8.06823	−	30.1111i	0.310777	−	1.15983i
$675$	−13.6342	−	8.02939i	−0.524782	−	0.309051i
$676$	10.3892	−	7.81438i	0.399585	−	0.300553i
$677$	17.6062	+	10.1649i	0.676659	+	0.390669i	0.798595	−	0.601869i	$-0.205577\pi$
$677$	17.6062	+	10.1649i	0.676659	+	0.390669i	−0.121936	+	0.992538i	$0.538910\pi$
$678$	16.9898	−	4.50007i	0.652490	−	0.172824i
$679$	6.22646	−	10.7845i	0.238949	−	0.413873i
$680$	−4.67843			−0.179410
$681$	−17.8153	+	17.7131i	−0.682684	+	0.678769i
$682$	13.2871	−	49.5881i	0.508789	−	1.89883i
$683$	9.85750	−	2.64131i	0.377187	−	0.101067i	−0.0652445	−	0.997869i	$-0.520783\pi$
$683$	9.85750	−	2.64131i	0.377187	−	0.101067i	0.442431	+	0.896802i	$0.354116\pi$
$684$	15.6292	−	15.4504i	0.597598	−	0.590762i
$685$	−4.06868	+	7.04716i	−0.155456	+	0.269258i
$686$	−13.1268			−0.501184
$687$	−12.1200	+	12.0505i	−0.462406	+	0.459753i
$688$	7.25776	−	4.19027i	0.276699	−	0.159753i
$689$	4.46162	−	8.93870i	0.169974	−	0.340537i
$690$	1.21530	+	0.706320i	0.0462656	+	0.0268892i
$691$	−29.9191	−	29.9191i	−1.13818	−	1.13818i	−0.988777	−	0.149400i	$-0.952266\pi$
$691$	−29.9191	−	29.9191i	−1.13818	−	1.13818i	−0.149400	−	0.988777i	$-0.547734\pi$
$692$	−2.25559	+	1.30226i	−0.0857445	+	0.0495046i
$693$	8.91165	−	15.2324i	0.338525	−	0.578631i
$694$	14.3954	+	14.3954i	0.546444	+	0.546444i
$695$	3.07483	+	0.823897i	0.116635	+	0.0312522i
$696$	−0.456903	−	1.72501i	−0.0173188	−	0.0653865i
$697$	−5.28992	−	1.41743i	−0.200370	−	0.0536890i
$698$			29.4052i			1.11300i
$699$	−1.79992	+	3.09695i	−0.0680793	+	0.117137i
$700$	−2.17812	+	2.17812i	−0.0823253	+	0.0823253i
$701$	16.7670			0.633280			0.316640	−	0.948546i	$-0.397445\pi$
$701$	16.7670			0.633280			0.316640	+	0.948546i	$0.397445\pi$
$702$	17.8200	−	5.78327i	0.672574	−	0.218276i
$703$	59.3412			2.23810
$704$	−4.11206	+	4.11206i	−0.154979	+	0.154979i
$705$	1.82773	−	3.14480i	0.0688362	−	0.118440i
$706$		−	11.4750i		−	0.431868i
$707$	9.95805	+	2.66825i	0.374511	+	0.100350i
$708$	5.31481	+	20.0658i	0.199743	+	0.754120i
$709$	−12.3741	−	3.31563i	−0.464719	−	0.124521i	0.0188591	−	0.999822i	$-0.493997\pi$
$709$	−12.3741	−	3.31563i	−0.464719	−	0.124521i	−0.483579	+	0.875301i	$0.660663\pi$
$710$	10.3708	+	10.3708i	0.389208	+	0.389208i
$711$	4.96339	+	0.0285519i	0.186142	+	0.00107078i
$712$	2.62264	−	1.51418i	0.0982875	−	0.0567463i
$713$	−3.62325	−	3.62325i	−0.135692	−	0.135692i
$714$	5.06875	+	2.94592i	0.189693	+	0.110248i
$715$	1.77673	+	29.2622i	0.0664459	+	1.09435i
$716$	−3.11097	+	1.79612i	−0.116262	+	0.0671242i
$717$	−24.2470	+	24.1079i	−0.905519	+	0.900325i
$718$	−36.7320			−1.37083
$719$	8.63433	−	14.9551i	0.322006	−	0.557731i	−0.658896	−	0.752234i	$-0.728976\pi$
$719$	8.63433	−	14.9551i	0.322006	−	0.557731i	0.980902	+	0.194503i	$0.0623095\pi$
$720$	1.06230	+	4.05777i	0.0395894	+	0.151224i
$721$	9.63828	−	2.58257i	0.358948	−	0.0961799i
$722$	8.97207	−	33.4842i	0.333906	−	1.24615i
$723$	−12.4563	+	12.3849i	−0.463256	+	0.460599i
$724$	16.3443			0.607430
$725$	−1.56866	+	2.71700i	−0.0582586	+	0.100907i
$726$	−38.2046	+	10.1192i	−1.41791	+	0.375559i
$727$	−12.1283	−	7.00226i	−0.449813	−	0.259700i	0.257938	−	0.966161i	$-0.416957\pi$
$727$	−12.1283	−	7.00226i	−0.449813	−	0.259700i	−0.707751	+	0.706462i	$0.750290\pi$
$728$	−0.221045	−	3.64054i	−0.00819245	−	0.134928i
$729$	26.9960	+	0.465925i	0.999851	+	0.0172565i
$730$	0.403364	−	1.50538i	0.0149292	−	0.0557165i
$731$			28.0422i			1.03718i
$732$	0.0140892	−	4.89849i	0.000520752	−	0.181053i
$733$	−1.76174	+	6.57489i	−0.0650712	+	0.242849i	−0.990799	−	0.135341i	$-0.956787\pi$
$733$	−1.76174	+	6.57489i	−0.0650712	+	0.242849i	0.925728	+	0.378190i	$0.123454\pi$
$734$	−3.94035	+	3.94035i	−0.145441	+	0.145441i
$735$	13.9914	−	3.70589i	0.516081	−	0.136694i
$736$	0.150228	+	0.560658i	0.00553747	+	0.0206661i
$737$	5.71238	+	3.29805i	0.210418	+	0.121485i
$738$	−0.0282447	+	4.90998i	−0.00103970	+	0.180739i
$739$	−17.1161	−	4.58625i	−0.629626	−	0.168708i	−0.0701262	−	0.997538i	$-0.522340\pi$
$739$	−17.1161	−	4.58625i	−0.629626	−	0.168708i	−0.559500	+	0.828830i	$0.689007\pi$
$740$	−5.66291	+	9.80845i	−0.208173	+	0.360566i
$741$	30.4276	−	34.1630i	1.11779	−	1.25501i
$742$	−1.40143	−	2.42735i	−0.0514481	−	0.0891108i
$743$	−8.04786	−	30.0350i	−0.295247	−	1.10188i	−0.941021	−	0.338349i	$-0.890132\pi$
$743$	−8.04786	−	30.0350i	−0.295247	−	1.10188i	0.645773	−	0.763529i	$-0.276535\pi$
$744$	0.0439787	−	15.2904i	0.00161234	−	0.560573i
$745$	17.4059	−	10.0493i	0.637702	−	0.368177i
$746$	2.03537	−	2.03537i	0.0745200	−	0.0745200i
$747$	−34.7268	+	34.3296i	−1.27059	+	1.25605i
$748$	−5.03629	−	18.7957i	−0.184145	−	0.687238i
$749$	−9.68407	+	2.59484i	−0.353848	+	0.0948133i
$750$	9.78994	−	16.8446i	0.357478	−	0.615078i
$751$	−4.97436	−	2.87195i	−0.181517	−	0.104799i	0.406488	−	0.913656i	$-0.366753\pi$
$751$	−4.97436	−	2.87195i	−0.181517	−	0.104799i	−0.588005	+	0.808857i	$0.700087\pi$
$752$	1.45080	−	0.388741i	0.0529053	−	0.0141759i
$753$	−8.25378	−	14.3914i	−0.300785	−	0.524452i
$754$	−1.17714	−	3.52329i	−0.0428689	−	0.128311i
$755$			3.93738i			0.143296i
$756$	1.40417	−	5.06522i	0.0510693	−	0.184220i
$757$	−13.1210	−	22.7262i	−0.476891	−	0.825999i	0.522759	−	0.852481i	$-0.324903\pi$
$757$	−13.1210	−	22.7262i	−0.476891	−	0.825999i	−0.999649	+	0.0264817i	$0.991570\pi$
$758$	−10.6629	−	18.4687i	−0.387295	−	0.670815i
$759$	−1.52940	+	5.64282i	−0.0555136	+	0.204821i
$760$	7.24257	+	7.24257i	0.262716	+	0.262716i
$761$	2.64360	+	2.64360i	0.0958306	+	0.0958306i	0.753397	−	0.657566i	$-0.228414\pi$
$761$	2.64360	+	2.64360i	0.0958306	+	0.0958306i	−0.657566	+	0.753397i	$0.728414\pi$
$762$	−18.4878	−	18.5945i	−0.669742	−	0.673606i
$763$	5.00419	+	8.66751i	0.181164	+	0.313785i
$764$	12.7189	+	22.0297i	0.460152	+	0.797007i
$765$	−13.5359	−	3.71053i	−0.489393	−	0.134154i
$766$		−	12.9795i		−	0.468969i
$767$	13.6928	+	40.9838i	0.494418	+	1.47984i
$768$	−0.870336	+	1.49750i	−0.0314056	+	0.0540365i
$769$	−47.3247	+	12.6806i	−1.70657

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.870336 + 1.49750i) q^{3} -1.00000i q^{4} +(1.35053 + 0.361873i) q^{5} +(0.443474 + 1.67432i) q^{6} +(0.977097 + 0.261812i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.48503 - 2.60666i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.870336 + 1.49750i) q^{3} -1.00000i q^{4} +(1.35053 + 0.361873i) q^{5} +(0.443474 + 1.67432i) q^{6} +(0.977097 + 0.261812i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.48503 - 2.60666i) q^{9} +(1.21085 - 0.699086i) q^{10} +(4.11206 + 4.11206i) q^{11} +(1.49750 + 0.870336i) q^{12} +(3.22602 + 1.61022i) q^{13} +(0.876041 - 0.505782i) q^{14} +(-1.71732 + 1.70747i) q^{15} -1.00000 q^{16} +(1.67305 - 2.89781i) q^{17} +(-2.89326 - 0.793114i) q^{18} +(-7.07605 + 1.89602i) q^{19} +(0.361873 - 1.35053i) q^{20} +(-1.24247 + 1.23534i) q^{21} +5.81533 q^{22} +(0.290218 - 0.502672i) q^{23} +(1.67432 - 0.443474i) q^{24} +(-2.63715 - 1.52256i) q^{25} +(3.41974 - 1.14254i) q^{26} +(5.19596 + 0.0448353i) q^{27} +(0.261812 - 0.977097i) q^{28} -1.03028i q^{29} +(-0.00696535 + 2.42169i) q^{30} +(2.28484 - 8.52714i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-9.73669 + 2.57895i) q^{33} +(-0.866036 - 3.23209i) q^{34} +(1.22486 + 0.707171i) q^{35} +(-2.60666 + 1.48503i) q^{36} +(-7.82443 - 2.09655i) q^{37} +(-3.66283 + 6.34422i) q^{38} +(-5.21903 + 3.42954i) q^{39} +(-0.699086 - 1.21085i) q^{40} +(-0.423606 - 1.58092i) q^{41} +(-0.00503937 + 1.75207i) q^{42} +(-7.25776 + 4.19027i) q^{43} +(4.11206 - 4.11206i) q^{44} +(-1.06230 - 4.05777i) q^{45} +(-0.150228 - 0.560658i) q^{46} +(-1.45080 + 0.388741i) q^{47} +(0.870336 - 1.49750i) q^{48} +(-5.17601 - 2.98837i) q^{49} +(-2.94136 + 0.788134i) q^{50} +(2.88336 + 5.02747i) q^{51} +(1.61022 - 3.22602i) q^{52} -2.77082i q^{53} +(3.70580 - 3.64239i) q^{54} +(4.06542 + 7.04151i) q^{55} +(-0.505782 - 0.876041i) q^{56} +(3.31924 - 12.2466i) q^{57} +(-0.728518 - 0.728518i) q^{58} +(8.47432 + 8.47432i) q^{59} +(1.70747 + 1.71732i) q^{60} +(-1.41408 - 2.44926i) q^{61} +(-4.41397 - 7.64523i) q^{62} +(-0.768562 - 2.93576i) q^{63} +1.00000i q^{64} +(3.77414 + 3.34206i) q^{65} +(-5.06129 + 8.70847i) q^{66} +(1.09561 - 0.293568i) q^{67} +(-2.89781 - 1.67305i) q^{68} +(0.500166 + 0.872096i) q^{69} +(1.36615 - 0.366058i) q^{70} +(2.71495 + 10.1323i) q^{71} +(-0.793114 + 2.89326i) q^{72} +(0.788181 - 0.788181i) q^{73} +(-7.01519 + 4.05022i) q^{74} +(4.57524 - 2.62400i) q^{75} +(1.89602 + 7.07605i) q^{76} +(2.94129 + 5.09447i) q^{77} +(-1.26536 + 6.11546i) q^{78} +(-0.827245 + 1.43283i) q^{79} +(-1.35053 - 0.361873i) q^{80} +(-4.58937 + 7.74194i) q^{81} +(-1.41741 - 0.818343i) q^{82} +(-4.21280 - 15.7224i) q^{83} +(1.23534 + 1.24247i) q^{84} +(3.30815 - 3.30815i) q^{85} +(-2.16904 + 8.09498i) q^{86} +(1.54285 + 0.896691i) q^{87} -5.81533i q^{88} +(-0.783797 + 2.92517i) q^{89} +(-3.62043 - 2.11812i) q^{90} +(2.73056 + 2.41795i) q^{91} +(-0.502672 - 0.290218i) q^{92} +(10.7808 + 10.8430i) q^{93} +(-0.750990 + 1.30075i) q^{94} -10.2425 q^{95} +(-0.443474 - 1.67432i) q^{96} +(3.18620 - 11.8911i) q^{97} +(-5.77308 + 1.54689i) q^{98} +(4.61222 - 16.8253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

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