LMFDB - Embedded newform 37.2.f.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,2,Mod(7,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("37.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	37.f (of order $9$, degree $6$, 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:	$0.295446487479$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	37.7
Dual form			37.2.f.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26604 - 0.460802i) q^{2} +(-1.76604 - 0.642788i) q^{3} +(-0.141559 + 0.118782i) q^{4} +(0.233956 + 1.32683i) q^{5} -2.53209 q^{6} +(-0.120615 - 0.684040i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(0.407604 + 0.342020i) q^{9} +O(q^{10})$	\(q+(1.26604 - 0.460802i) q^{2} +(-1.76604 - 0.642788i) q^{3} +(-0.141559 + 0.118782i) q^{4} +(0.233956 + 1.32683i) q^{5} -2.53209 q^{6} +(-0.120615 - 0.684040i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(0.407604 + 0.342020i) q^{9} +(0.907604 + 1.57202i) q^{10} +(3.20574 - 5.55250i) q^{11} +(0.326352 - 0.118782i) q^{12} +(-1.75490 + 1.47254i) q^{13} +(-0.467911 - 0.810446i) q^{14} +(0.439693 - 2.49362i) q^{15} +(-0.624485 + 3.54163i) q^{16} +(2.97178 + 2.49362i) q^{17} +(0.673648 + 0.245188i) q^{18} +(-5.08512 - 1.85083i) q^{19} +(-0.190722 - 0.160035i) q^{20} +(-0.226682 + 1.28558i) q^{21} +(1.50000 - 8.50692i) q^{22} +(3.00000 + 5.19615i) q^{23} +(4.23783 - 3.55596i) q^{24} +(2.99273 - 1.08926i) q^{25} +(-1.54323 + 2.67296i) q^{26} +(2.31908 + 4.01676i) q^{27} +(0.0983261 + 0.0825054i) q^{28} +(0.979055 - 1.69577i) q^{29} +(-0.592396 - 3.35965i) q^{30} -7.10607 q^{31} +(-0.180922 - 1.02606i) q^{32} +(-9.23055 + 7.74535i) q^{33} +(4.91147 + 1.78763i) q^{34} +(0.879385 - 0.320070i) q^{35} -0.0983261 q^{36} +(-6.07532 + 0.300767i) q^{37} -7.29086 q^{38} +(4.04576 - 1.47254i) q^{39} +(-3.72668 - 1.35640i) q^{40} +(0.549163 - 0.460802i) q^{41} +(0.305407 + 1.73205i) q^{42} -2.65270 q^{43} +(0.205737 + 1.16679i) q^{44} +(-0.358441 + 0.620838i) q^{45} +(6.19253 + 5.19615i) q^{46} +(-0.134285 - 0.232589i) q^{47} +(3.37939 - 5.85327i) q^{48} +(6.12449 - 2.22913i) q^{49} +(3.28699 - 2.75811i) q^{50} +(-3.64543 - 6.31407i) q^{51} +(0.0735111 - 0.416902i) q^{52} +(0.926022 - 5.25173i) q^{53} +(4.78699 + 4.01676i) q^{54} +(8.11721 + 2.95442i) q^{55} +(1.92127 + 0.699287i) q^{56} +(7.79086 + 6.53731i) q^{57} +(0.458111 - 2.59808i) q^{58} +(0.358441 - 2.03282i) q^{59} +(0.233956 + 0.405223i) q^{60} +(-1.67365 + 1.40436i) q^{61} +(-8.99660 + 3.27449i) q^{62} +(0.184793 - 0.320070i) q^{63} +(-4.29813 - 7.44459i) q^{64} +(-2.36437 - 1.98394i) q^{65} +(-8.11721 + 14.0594i) q^{66} +(0.169778 + 0.962858i) q^{67} -0.716881 q^{68} +(-1.95811 - 11.1050i) q^{69} +(0.965852 - 0.810446i) q^{70} +(6.80453 + 2.47665i) q^{71} +(-1.47178 + 0.535685i) q^{72} +7.17024 q^{73} +(-7.55303 + 3.18031i) q^{74} -5.98545 q^{75} +(0.939693 - 0.342020i) q^{76} +(-4.18479 - 1.52314i) q^{77} +(4.44356 - 3.72859i) q^{78} +(2.04323 + 11.5878i) q^{79} -4.84524 q^{80} +(-1.79086 - 10.1565i) q^{81} +(0.482926 - 0.836452i) q^{82} +(-10.7456 - 9.01660i) q^{83} +(-0.120615 - 0.208911i) q^{84} +(-2.61334 + 4.52644i) q^{85} +(-3.35844 + 1.22237i) q^{86} +(-2.81908 + 2.36549i) q^{87} +(9.43629 + 16.3441i) q^{88} +(-0.486329 + 2.75811i) q^{89} +(-0.167718 + 0.951178i) q^{90} +(1.21894 + 1.02281i) q^{91} +(-1.04189 - 0.379217i) q^{92} +(12.5496 + 4.56769i) q^{93} +(-0.277189 - 0.232589i) q^{94} +(1.26604 - 7.18009i) q^{95} +(-0.340022 + 1.92836i) q^{96} +(-1.26217 - 2.18615i) q^{97} +(6.72668 - 5.64436i) q^{98} +(3.20574 - 1.16679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 6 q^{9} + 9 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} - 12 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} - 9 q^{19} - 21 q^{20} + 12 q^{21} + 9 q^{22} + 18 q^{23} + 6 q^{24} + 6 q^{26} - 3 q^{27} + 24 q^{28} + 9 q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{33} + 9 q^{34} - 6 q^{35} - 24 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} - 9 q^{40} + 15 q^{41} + 6 q^{42} - 18 q^{43} - 9 q^{44} + 6 q^{45} - 18 q^{46} + 9 q^{47} + 9 q^{48} + 24 q^{49} + 12 q^{50} - 6 q^{51} + 51 q^{52} + 21 q^{53} + 21 q^{54} + 18 q^{55} - 6 q^{56} + 15 q^{57} + 9 q^{58} - 6 q^{59} + 6 q^{60} - 9 q^{61} - 12 q^{62} - 6 q^{63} - 12 q^{64} - 33 q^{65} - 18 q^{66} + 24 q^{67} + 12 q^{68} - 18 q^{69} - 36 q^{70} - 12 q^{71} + 6 q^{72} - 33 q^{74} - 18 q^{77} - 3 q^{78} - 3 q^{79} + 24 q^{80} + 21 q^{81} - 18 q^{82} + 3 q^{83} - 12 q^{84} - 9 q^{85} - 12 q^{86} + 9 q^{88} - 24 q^{89} + 27 q^{90} + 42 q^{91} + 21 q^{93} + 9 q^{94} + 3 q^{95} + 18 q^{96} - 27 q^{97} + 27 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 6 * q^9 + 9 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 - 12 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 3 * q^18 - 9 * q^19 - 21 * q^20 + 12 * q^21 + 9 * q^22 + 18 * q^23 + 6 * q^24 + 6 * q^26 - 3 * q^27 + 24 * q^28 + 9 * q^29 - 18 * q^31 - 18 * q^32 - 18 * q^33 + 9 * q^34 - 6 * q^35 - 24 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 - 9 * q^40 + 15 * q^41 + 6 * q^42 - 18 * q^43 - 9 * q^44 + 6 * q^45 - 18 * q^46 + 9 * q^47 + 9 * q^48 + 24 * q^49 + 12 * q^50 - 6 * q^51 + 51 * q^52 + 21 * q^53 + 21 * q^54 + 18 * q^55 - 6 * q^56 + 15 * q^57 + 9 * q^58 - 6 * q^59 + 6 * q^60 - 9 * q^61 - 12 * q^62 - 6 * q^63 - 12 * q^64 - 33 * q^65 - 18 * q^66 + 24 * q^67 + 12 * q^68 - 18 * q^69 - 36 * q^70 - 12 * q^71 + 6 * q^72 - 33 * q^74 - 18 * q^77 - 3 * q^78 - 3 * q^79 + 24 * q^80 + 21 * q^81 - 18 * q^82 + 3 * q^83 - 12 * q^84 - 9 * q^85 - 12 * q^86 + 9 * q^88 - 24 * q^89 + 27 * q^90 + 42 * q^91 + 21 * q^93 + 9 * q^94 + 3 * q^95 + 18 * q^96 - 27 * q^97 + 27 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.26604	−	0.460802i	0.895229	−	0.325837i	0.146889	−	0.989153i	$-0.453074\pi$
$2$	1.26604	−	0.460802i	0.895229	−	0.325837i	0.748339	+	0.663316i	$0.230852\pi$
$3$	−1.76604	−	0.642788i	−1.01963	−	0.371114i	−0.222504	−	0.974932i	$-0.571423\pi$
$3$	−1.76604	−	0.642788i	−1.01963	−	0.371114i	−0.797122	+	0.603818i	$0.793645\pi$
$4$	−0.141559	+	0.118782i	−0.0707796	+	0.0593912i
$5$	0.233956	+	1.32683i	0.104628	+	0.593375i	0.991368	+	0.131107i	$0.0418532\pi$
$5$	0.233956	+	1.32683i	0.104628	+	0.593375i	−0.886740	+	0.462268i	$0.847036\pi$
$6$	−2.53209			−1.03372
$7$	−0.120615	−	0.684040i	−0.0455881	−	0.258543i	0.953492	−	0.301417i	$-0.0974597\pi$
$7$	−0.120615	−	0.684040i	−0.0455881	−	0.258543i	−0.999080	+	0.0428742i	$0.986349\pi$
$8$	−1.47178	+	2.54920i	−0.520353	+	0.901278i
$9$	0.407604	+	0.342020i	0.135868	+	0.114007i
$10$	0.907604	+	1.57202i	0.287010	+	0.497115i
$11$	3.20574	−	5.55250i	0.966566	−	1.67414i	0.261219	−	0.965280i	$-0.415876\pi$
$11$	3.20574	−	5.55250i	0.966566	−	1.67414i	0.705347	−	0.708862i	$-0.250791\pi$
$12$	0.326352	−	0.118782i	0.0942097	−	0.0342895i
$13$	−1.75490	+	1.47254i	−0.486722	+	0.408408i	−0.852850	−	0.522156i	$-0.825128\pi$
$13$	−1.75490	+	1.47254i	−0.486722	+	0.408408i	0.366128	+	0.930565i	$0.380683\pi$
$14$	−0.467911	−	0.810446i	−0.125055	−	0.216601i
$15$	0.439693	−	2.49362i	0.113528	−	0.643850i
$16$	−0.624485	+	3.54163i	−0.156121	+	0.885408i
$17$	2.97178	+	2.49362i	0.720763	+	0.604792i	0.927596	−	0.373584i	$-0.121871\pi$
$17$	2.97178	+	2.49362i	0.720763	+	0.604792i	−0.206833	+	0.978376i	$0.566316\pi$
$18$	0.673648	+	0.245188i	0.158780	+	0.0577913i
$19$	−5.08512	−	1.85083i	−1.16661	−	0.424610i	−0.315154	−	0.949041i	$-0.602056\pi$
$19$	−5.08512	−	1.85083i	−1.16661	−	0.424610i	−0.851453	+	0.524430i	$0.824278\pi$
$20$	−0.190722	−	0.160035i	−0.0426468	−	0.0357849i
$21$	−0.226682	+	1.28558i	−0.0494660	+	0.280536i
$22$	1.50000	−	8.50692i	0.319801	−	1.81368i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	4.23783	−	3.55596i	0.865043	−	0.725857i
$25$	2.99273	−	1.08926i	0.598545	−	0.217853i
$26$	−1.54323	+	2.67296i	−0.302653	+	0.524210i
$27$	2.31908	+	4.01676i	0.446307	+	0.773026i
$28$	0.0983261	+	0.0825054i	0.0185819	+	0.0155920i
$29$	0.979055	−	1.69577i	0.181806	−	0.314897i	−0.760690	−	0.649116i	$-0.775139\pi$
$29$	0.979055	−	1.69577i	0.181806	−	0.314897i	0.942496	+	0.334219i	$0.108472\pi$
$30$	−0.592396	−	3.35965i	−0.108156	−	0.613385i
$31$	−7.10607			−1.27629			−0.638144	−	0.769917i	$-0.720297\pi$
$31$	−7.10607			−1.27629			−0.638144	+	0.769917i	$0.720297\pi$
$32$	−0.180922	−	1.02606i	−0.0319828	−	0.181384i
$33$	−9.23055	+	7.74535i	−1.60683	+	1.34829i
$34$	4.91147	+	1.78763i	0.842311	+	0.306576i
$35$	0.879385	−	0.320070i	0.148643	−	0.0541017i
$36$	−0.0983261			−0.0163877
$37$	−6.07532	+	0.300767i	−0.998777	+	0.0494459i
$37$	−6.07532	+	0.300767i	−0.998777	+	0.0494459i
$38$	−7.29086			−1.18273
$39$	4.04576	−	1.47254i	0.647840	−	0.235794i
$40$	−3.72668	−	1.35640i	−0.589240	−	0.214466i
$41$	0.549163	−	0.460802i	0.0857649	−	0.0719653i	−0.598897	−	0.800826i	$-0.704394\pi$
$41$	0.549163	−	0.460802i	0.0857649	−	0.0719653i	0.684662	+	0.728861i	$0.259950\pi$
$42$	0.305407	+	1.73205i	0.0471254	+	0.267261i
$43$	−2.65270			−0.404534			−0.202267	−	0.979330i	$-0.564831\pi$
$43$	−2.65270			−0.404534			−0.202267	+	0.979330i	$0.564831\pi$
$44$	0.205737	+	1.16679i	0.0310160	+	0.175901i
$45$	−0.358441	+	0.620838i	−0.0534332	+	0.0925490i
$46$	6.19253	+	5.19615i	0.913039	+	0.766131i
$47$	−0.134285	−	0.232589i	−0.0195875	−	0.0339266i	0.856065	−	0.516867i	$-0.172902\pi$
$47$	−0.134285	−	0.232589i	−0.0195875	−	0.0339266i	−0.875653	+	0.482941i	$0.839569\pi$
$48$	3.37939	−	5.85327i	0.487772	−	0.844846i
$49$	6.12449	−	2.22913i	0.874926	−	0.318447i
$50$	3.28699	−	2.75811i	0.464850	−	0.390056i
$51$	−3.64543	−	6.31407i	−0.510462	−	0.884147i
$52$	0.0735111	−	0.416902i	0.0101942	−	0.0578139i
$53$	0.926022	−	5.25173i	0.127199	−	0.721381i	−0.852779	−	0.522273i	$-0.825084\pi$
$53$	0.926022	−	5.25173i	0.127199	−	0.721381i	0.979977	−	0.199108i	$-0.0638045\pi$
$54$	4.78699	+	4.01676i	0.651427	+	0.546612i
$55$	8.11721	+	2.95442i	1.09452	+	0.398374i
$56$	1.92127	+	0.699287i	0.256741	+	0.0934461i
$57$	7.79086	+	6.53731i	1.03192	+	0.865887i
$58$	0.458111	−	2.59808i	0.0601529	−	0.341144i
$59$	0.358441	−	2.03282i	0.0466650	−	0.264650i	−0.952545	−	0.304399i	$-0.901544\pi$
$59$	0.358441	−	2.03282i	0.0466650	−	0.264650i	0.999210	+	0.0397483i	$0.0126556\pi$
$60$	0.233956	+	0.405223i	0.0302035	+	0.0523141i
$61$	−1.67365	+	1.40436i	−0.214289	+	0.179810i	−0.743614	−	0.668610i	$-0.766890\pi$
$61$	−1.67365	+	1.40436i	−0.214289	+	0.179810i	0.529325	+	0.848419i	$0.322445\pi$
$62$	−8.99660	+	3.27449i	−1.14257	+	0.415861i
$63$	0.184793	−	0.320070i	0.0232817	−	0.0403250i
$64$	−4.29813	−	7.44459i	−0.537267	−	0.930573i
$65$	−2.36437	−	1.98394i	−0.293264	−	0.246078i
$66$	−8.11721	+	14.0594i	−0.999160	+	1.73060i
$67$	0.169778	+	0.962858i	0.0207417	+	0.117632i	0.993421	−	0.114522i	$-0.0365337\pi$
$67$	0.169778	+	0.962858i	0.0207417	+	0.117632i	−0.972679	+	0.232154i	$0.925423\pi$
$68$	−0.716881			−0.0869346
$69$	−1.95811	−	11.1050i	−0.235729	−	1.33688i
$70$	0.965852	−	0.810446i	0.115441	−	0.0968668i
$71$	6.80453	+	2.47665i	0.807549	+	0.293924i	0.712611	−	0.701559i	$-0.247512\pi$
$71$	6.80453	+	2.47665i	0.807549	+	0.293924i	0.0949381	+	0.995483i	$0.469735\pi$
$72$	−1.47178	+	0.535685i	−0.173451	+	0.0631310i
$73$	7.17024			0.839214			0.419607	−	0.907706i	$-0.362168\pi$
$73$	7.17024			0.839214			0.419607	+	0.907706i	$0.362168\pi$
$74$	−7.55303	+	3.18031i	−0.878022	+	0.369703i
$75$	−5.98545			−0.691140
$76$	0.939693	−	0.342020i	0.107790	−	0.0392324i
$77$	−4.18479	−	1.52314i	−0.476901	−	0.173578i
$78$	4.44356	−	3.72859i	0.503134	−	0.422180i
$79$	2.04323	+	11.5878i	0.229882	+	1.30372i	0.853129	+	0.521699i	$0.174702\pi$
$79$	2.04323	+	11.5878i	0.229882	+	1.30372i	−0.623248	+	0.782025i	$0.714187\pi$
$80$	−4.84524			−0.541714
$81$	−1.79086	−	10.1565i	−0.198984	−	1.12850i
$82$	0.482926	−	0.836452i	0.0533302	−	0.0923707i
$83$	−10.7456	−	9.01660i	−1.17948	−	0.989701i	−0.999982	−	0.00594199i	$-0.998109\pi$
$83$	−10.7456	−	9.01660i	−1.17948	−	0.989701i	−0.179497	−	0.983759i	$-0.557447\pi$
$84$	−0.120615	−	0.208911i	−0.0131601	−	0.0227940i
$85$	−2.61334	+	4.52644i	−0.283457	+	0.490961i
$86$	−3.35844	+	1.22237i	−0.362150	+	0.131812i
$87$	−2.81908	+	2.36549i	−0.302237	+	0.253607i
$88$	9.43629	+	16.3441i	1.00591	+	1.74229i
$89$	−0.486329	+	2.75811i	−0.0515508	+	0.292359i	−0.999674	−	0.0255449i	$-0.991868\pi$
$89$	−0.486329	+	2.75811i	−0.0515508	+	0.292359i	0.948123	+	0.317904i	$0.102979\pi$
$90$	−0.167718	+	0.951178i	−0.0176791	+	0.100263i
$91$	1.21894	+	1.02281i	0.127780	+	0.107220i
$92$	−1.04189	−	0.379217i	−0.108624	−	0.0395361i
$93$	12.5496	+	4.56769i	1.30134	+	0.473648i
$94$	−0.277189	−	0.232589i	−0.0285898	−	0.0239897i
$95$	1.26604	−	7.18009i	0.129893	−	0.736662i
$96$	−0.340022	+	1.92836i	−0.0347034	+	0.196813i
$97$	−1.26217	−	2.18615i	−0.128154	−	0.221970i	0.794807	−	0.606862i	$-0.207572\pi$
$97$	−1.26217	−	2.18615i	−0.128154	−	0.221970i	−0.922962	+	0.384892i	$0.874239\pi$
$98$	6.72668	−	5.64436i	0.679497	−	0.570166i
$99$	3.20574	−	1.16679i	0.322189	−	0.117267i
$100$	−0.294263	+	0.509678i	−0.0294263	+	0.0509678i
$101$	3.38666	+	5.86587i	0.336985	+	0.583675i	0.983864	−	0.178917i	$-0.0572594\pi$
$101$	3.38666	+	5.86587i	0.336985	+	0.583675i	−0.646879	+	0.762593i	$0.723926\pi$
$102$	−7.52481	−	6.31407i	−0.745068	−	0.625186i
$103$	4.91534	−	8.51363i	0.484323	−	0.838873i	−0.515515	−	0.856881i	$-0.672399\pi$
$103$	4.91534	−	8.51363i	0.484323	−	0.838873i	0.999838	+	0.0180083i	$0.00573252\pi$
$104$	−1.17096	−	6.64084i	−0.114822	−	0.651188i
$105$	−1.75877			−0.171638
$106$	−1.24763	−	7.07564i	−0.121180	−	0.687247i
$107$	−3.56418	+	2.99070i	−0.344562	+	0.289122i	−0.798602	−	0.601859i	$-0.794427\pi$
$107$	−3.56418	+	2.99070i	−0.344562	+	0.289122i	0.454040	+	0.890981i	$0.349982\pi$
$108$	−0.805407	−	0.293144i	−0.0775004	−	0.0282078i
$109$	2.87939	−	1.04801i	0.275795	−	0.100381i	−0.200420	−	0.979710i	$-0.564231\pi$
$109$	2.87939	−	1.04801i	0.275795	−	0.100381i	0.476215	+	0.879329i	$0.342008\pi$
$110$	11.6382			1.10965
$111$	10.9226	+	3.37397i	1.03673	+	0.320243i
$112$	2.49794			0.236033
$113$	−14.7626	+	5.37316i	−1.38875	+	0.505465i	−0.924820	−	0.380406i	$-0.875784\pi$
$113$	−14.7626	+	5.37316i	−1.38875	+	0.505465i	−0.463933	+	0.885870i	$0.653562\pi$
$114$	12.8760	+	4.68647i	1.20595	+	0.438929i
$115$	−6.19253	+	5.19615i	−0.577457	+	0.484544i
$116$	0.0628336	+	0.356347i	0.00583395	+	0.0330860i
$117$	−1.21894			−0.112691
$118$	−0.482926	−	2.73881i	−0.0444569	−	0.252128i
$119$	1.34730	−	2.33359i	0.123506	−	0.213919i
$120$	5.70961	+	4.79093i	0.521213	+	0.437350i
$121$	−15.0535	−	26.0734i	−1.36850	−	2.37031i
$122$	−1.47178	+	2.54920i	−0.133249	+	0.230794i
$123$	−1.26604	+	0.460802i	−0.114155	+	0.0415492i
$124$	1.00593	−	0.844075i	0.0903352	−	0.0758002i
$125$	5.51367	+	9.54996i	0.493158	+	0.854174i
$126$	0.0864665	−	0.490376i	0.00770305	−	0.0436861i
$127$	−2.38532	+	13.5278i	−0.211662	+	1.20040i	0.674943	+	0.737870i	$0.264168\pi$
$127$	−2.38532	+	13.5278i	−0.211662	+	1.20040i	−0.886605	+	0.462527i	$0.846943\pi$
$128$	−7.27584	−	6.10516i	−0.643100	−	0.539625i
$129$	4.68479	+	1.70513i	0.412473	+	0.150128i
$130$	−3.90760	−	1.42225i	−0.342720	−	0.124740i
$131$	7.40033	+	6.20961i	0.646570	+	0.542536i	0.906028	−	0.423218i	$-0.139100\pi$
$131$	7.40033	+	6.20961i	0.646570	+	0.542536i	−0.259458	+	0.965754i	$0.583544\pi$
$132$	0.386659	−	2.19285i	0.0336544	−	0.190863i
$133$	−0.652704	+	3.70167i	−0.0565966	+	0.320975i
$134$	0.658633	+	1.14079i	0.0568973	+	0.0985489i
$135$	−4.78699	+	4.01676i	−0.411998	+	0.345708i
$136$	−10.7306	+	3.90560i	−0.920137	+	0.334903i
$137$	2.68479	−	4.65020i	0.229377	−	0.397293i	−0.728246	−	0.685315i	$-0.759664\pi$
$137$	2.68479	−	4.65020i	0.229377	−	0.397293i	0.957624	+	0.288022i	$0.0929977\pi$
$138$	−7.59627	−	13.1571i	−0.646637	−	1.12001i
$139$	−0.699807	−	0.587208i	−0.0593569	−	0.0498063i	0.612627	−	0.790372i	$-0.290113\pi$
$139$	−0.699807	−	0.587208i	−0.0593569	−	0.0498063i	−0.671983	+	0.740566i	$0.734557\pi$
$140$	−0.0864665	+	0.149764i	−0.00730775	+	0.0126574i
$141$	0.0876485	+	0.497079i	0.00738134	+	0.0418616i
$142$	9.75608			0.818712
$143$	2.55051	+	14.4646i	0.213284	+	1.20959i
$144$	−1.46585	+	1.23000i	−0.122154	+	0.102500i
$145$	2.47906	+	0.902302i	0.205874	+	0.0749321i
$146$	9.07785	−	3.30407i	0.751288	−	0.273446i
$147$	−12.2490			−1.01028
$148$	0.824292	−	0.764217i	0.0677564	−	0.0628183i
$149$	−3.89899			−0.319417			−0.159709	−	0.987164i	$-0.551055\pi$
$149$	−3.89899			−0.319417			−0.159709	+	0.987164i	$0.551055\pi$
$150$	−7.57785	+	2.75811i	−0.618729	+	0.225199i
$151$	1.56031	+	0.567905i	0.126976	+	0.0462155i	0.404727	−	0.914438i	$-0.367367\pi$
$151$	1.56031	+	0.567905i	0.126976	+	0.0462155i	−0.277751	+	0.960653i	$0.589589\pi$
$152$	12.2023	−	10.2390i	0.989740	−	0.830490i
$153$	0.358441	+	2.03282i	0.0289782	+	0.164344i
$154$	−6.00000			−0.483494
$155$	−1.66250	−	9.42853i	−0.133536	−	0.757318i
$156$	−0.397804	+	0.689016i	−0.0318498	+	0.0551654i
$157$	−5.23783	−	4.39506i	−0.418024	−	0.350764i	0.409387	−	0.912361i	$-0.365743\pi$
$157$	−5.23783	−	4.39506i	−0.418024	−	0.350764i	−0.827411	+	0.561597i	$0.810187\pi$
$158$	7.92649	+	13.7291i	0.630598	+	1.09223i
$159$	−5.01114	+	8.67956i	−0.397410	+	0.688334i
$160$	1.31908	−	0.480105i	0.104282	−	0.0379556i
$161$	3.19253	−	2.67885i	0.251607	−	0.211123i
$162$	−6.94743	−	12.0333i	−0.545842	−	0.945426i
$163$	−1.94222	+	11.0149i	−0.152126	+	0.862751i	0.809240	+	0.587478i	$0.199879\pi$
$163$	−1.94222	+	11.0149i	−0.152126	+	0.862751i	−0.961366	+	0.275273i	$0.911232\pi$
$164$	−0.0230039	+	0.130462i	−0.00179630	+	0.0101874i
$165$	−12.4363	−	10.4353i	−0.968164	−	0.812386i
$166$	−17.7592	−	6.46383i	−1.37838	−	0.501691i
$167$	7.30928	+	2.66036i	0.565609	+	0.205865i	0.608968	−	0.793195i	$-0.291584\pi$
$167$	7.30928	+	2.66036i	0.565609	+	0.205865i	−0.0433592	+	0.999060i	$0.513806\pi$
$168$	−2.94356	−	2.46994i	−0.227101	−	0.190560i
$169$	−1.34611	+	7.63419i	−0.103547	+	0.587246i
$170$	−1.22281	+	6.93491i	−0.0937853	+	0.531883i
$171$	−1.43969	−	2.49362i	−0.110096	−	0.190692i
$172$	0.375515	−	0.315094i	0.0286327	−	0.0240257i
$173$	15.6766	−	5.70583i	1.19187	−	0.433806i	0.331492	−	0.943458i	$-0.392448\pi$
$173$	15.6766	−	5.70583i	1.19187	−	0.433806i	0.860381	+	0.509652i	$0.170226\pi$
$174$	−2.47906	+	4.29385i	−0.187937	+	0.325516i
$175$	−1.10607	−	1.91576i	−0.0836108	−	0.144818i
$176$	17.6630	+	14.8210i	1.33140	+	1.11717i
$177$	−1.93969	+	3.35965i	−0.145796	+	0.252526i
$178$	0.655230	+	3.71599i	0.0491116	+	0.278525i
$179$	−4.94087			−0.369298			−0.184649	−	0.982805i	$-0.559115\pi$
$179$	−4.94087			−0.369298			−0.184649	+	0.982805i	$0.559115\pi$
$180$	−0.0230039	−	0.130462i	−0.00171461	−	0.00972404i
$181$	18.4834	−	15.5094i	1.37386	−	1.15281i	0.402437	−	0.915447i	$-0.368163\pi$
$181$	18.4834	−	15.5094i	1.37386	−	1.15281i	0.971422	−	0.237358i	$-0.0762814\pi$
$182$	2.01455	+	0.733235i	0.149328	+	0.0543510i
$183$	3.85844	−	1.40436i	0.285224	−	0.103813i
$184$	−17.6614			−1.30201
$185$	−1.82042	−	7.99054i	−0.133840	−	0.587476i
$186$	17.9932			1.31932
$187$	23.3726	−	8.50692i	1.70917	−	0.622088i
$188$	0.0466368	+	0.0169744i	0.00340134	+	0.00123799i
$189$	2.46791	−	2.07082i	0.179514	−	0.150630i
$190$	−1.70574	−	9.67372i	−0.123747	−	0.701805i
$191$	17.2267			1.24648			0.623239	−	0.782031i	$-0.285816\pi$
$191$	17.2267			1.24648			0.623239	+	0.782031i	$0.285816\pi$
$192$	2.80541	+	15.9103i	0.202463	+	1.14822i
$193$	5.43969	−	9.42182i	0.391558	−	0.678198i	−0.601098	−	0.799176i	$-0.705270\pi$
$193$	5.43969	−	9.42182i	0.391558	−	0.678198i	0.992655	+	0.120978i	$0.0386030\pi$
$194$	−2.60535	−	2.18615i	−0.187053	−	0.156956i
$195$	2.90033	+	5.02352i	0.207697	+	0.359742i
$196$	−0.602196	+	1.04303i	−0.0430140	+	0.0745025i
$197$	−3.18732	+	1.16009i	−0.227087	+	0.0826529i	−0.453058	−	0.891481i	$-0.649667\pi$
$197$	−3.18732	+	1.16009i	−0.227087	+	0.0826529i	0.225971	+	0.974134i	$0.427445\pi$
$198$	3.52094	−	2.95442i	0.250223	−	0.209962i
$199$	−6.90033	−	11.9517i	−0.489151	−	0.847235i	0.510771	−	0.859717i	$-0.329360\pi$
$199$	−6.90033	−	11.9517i	−0.489151	−	0.847235i	−0.999922	+	0.0124819i	$0.996027\pi$
$200$	−1.62789	+	9.23222i	−0.115109	+	0.652816i
$201$	0.319078	−	1.80958i	0.0225060	−	0.127638i
$202$	6.99067	+	5.86587i	0.491862	+	0.412721i
$203$	−1.27807	−	0.465178i	−0.0897027	−	0.0326491i
$204$	1.26604	+	0.460802i	0.0886408	+	0.0322626i
$205$	0.739885	+	0.620838i	0.0516758	+	0.0433612i
$206$	2.29994	−	13.0436i	0.160245	−	0.908793i
$207$	−0.554378	+	3.14403i	−0.0385319	+	0.218525i
$208$	−4.11927	−	7.13479i	−0.285620	−	0.494708i
$209$	−26.5783	+	22.3019i	−1.83846	+	1.54265i
$210$	−2.22668	+	0.810446i	−0.153656	+	0.0559261i
$211$	−4.10607	+	7.11192i	−0.282673	+	0.489605i	−0.972042	−	0.234806i	$-0.924555\pi$
$211$	−4.10607	+	7.11192i	−0.282673	+	0.489605i	0.689369	+	0.724410i	$0.257888\pi$
$212$	0.492726	+	0.853427i	0.0338406	+	0.0586136i
$213$	−10.4251	−	8.74774i	−0.714319	−	0.599385i
$214$	−3.13429	+	5.42874i	−0.214255	+	0.371101i
$215$	−0.620615	−	3.51968i	−0.0423256	−	0.240040i
$216$	−13.6527			−0.928949
$217$	0.857097	+	4.86084i	0.0581835	+	0.329975i
$218$	3.16250	−	2.65366i	0.214192	−	0.179728i
$219$	−12.6630	−	4.60894i	−0.855684	−	0.311444i
$220$	−1.50000	+	0.545955i	−0.101130	+	0.0368083i
$221$	−8.88713			−0.597813
$222$	15.3833	−	0.761570i	1.03246	−	0.0511132i
$223$	−10.7537			−0.720122			−0.360061	−	0.932929i	$-0.617244\pi$
$223$	−10.7537			−0.720122			−0.360061	+	0.932929i	$0.617244\pi$
$224$	−0.680045	+	0.247516i	−0.0454374	+	0.0165379i
$225$	1.59240	+	0.579585i	0.106160	+	0.0386390i
$226$	−16.2142	+	13.6053i	−1.07855	+	0.905013i
$227$	−0.161322	−	0.914901i	−0.0107073	−	0.0607241i	0.978986	−	0.203928i	$-0.0653707\pi$
$227$	−0.161322	−	0.914901i	−0.0107073	−	0.0607241i	−0.989693	+	0.143204i	$0.954260\pi$
$228$	−1.87939			−0.124465
$229$	4.60994	+	26.1443i	0.304633	+	1.72766i	0.625226	+	0.780444i	$0.285007\pi$
$229$	4.60994	+	26.1443i	0.304633	+	1.72766i	−0.320593	+	0.947217i	$0.603882\pi$
$230$	−5.44562	+	9.43209i	−0.359074	+	0.621934i
$231$	6.41147	+	5.37987i	0.421844	+	0.353969i
$232$	2.88191	+	4.99162i	0.189207	+	0.327716i
$233$	2.02094	−	3.50038i	0.132396	−	0.229317i	−0.792203	−	0.610257i	$-0.791066\pi$
$233$	2.02094	−	3.50038i	0.132396	−	0.229317i	0.924600	+	0.380940i	$0.124399\pi$
$234$	−1.54323	+	0.561691i	−0.100884	+	0.0367189i
$235$	0.277189	−	0.232589i	0.0180818	−	0.0151724i
$236$	0.190722	+	0.330341i	0.0124150	+	0.0215034i
$237$	3.84002	−	21.7778i	0.249436	−	1.41462i
$238$	0.630415	−	3.57526i	0.0408637	−	0.231750i
$239$	−11.7246	−	9.83813i	−0.758403	−	0.636375i	0.179308	−	0.983793i	$-0.442614\pi$
$239$	−11.7246	−	9.83813i	−0.758403	−	0.636375i	−0.937711	+	0.347418i	$0.887059\pi$
$240$	8.55690	+	3.11446i	0.552346	+	0.201037i
$241$	−25.2866	−	9.20356i	−1.62885	−	0.592854i	−0.643812	−	0.765183i	$-0.722648\pi$
$241$	−25.2866	−	9.20356i	−1.62885	−	0.592854i	−0.985039	+	0.172330i	$0.944871\pi$
$242$	−31.0731	−	26.0734i	−1.99745	−	1.67606i
$243$	−0.949493	+	5.38484i	−0.0609100	+	0.345438i
$244$	0.0701076	−	0.397600i	0.00448818	−	0.0254537i
$245$	4.39053	+	7.60462i	0.280501	+	0.485841i
$246$	−1.39053	+	1.16679i	−0.0886569	+	0.0743920i
$247$	11.6493	−	4.24000i	0.741227	−	0.269785i
$248$	10.4586	−	18.1148i	0.664120	−	1.15029i
$249$	13.1814	+	22.8308i	0.835337	+	1.44685i
$250$	11.3812	+	9.54996i	0.719810	+	0.603992i
$251$	11.6630	−	20.2009i	0.736160	−	1.27507i	−0.218052	−	0.975937i	$-0.569970\pi$
$251$	11.6630	−	20.2009i	0.736160	−	1.27507i	0.954212	−	0.299130i	$-0.0966963\pi$
$252$	0.0118596	+	0.0672590i	0.000747083	+	0.00423692i
$253$	38.4688			2.41852
$254$	3.21373	+	18.2259i	0.201647	+	1.14360i
$255$	7.52481	−	6.31407i	0.471222	−	0.395402i
$256$	4.13088	+	1.50352i	0.258180	+	0.0939699i
$257$	−2.80066	+	1.01936i	−0.174700	+	0.0635857i	−0.427889	−	0.903831i	$-0.640743\pi$
$257$	−2.80066	+	1.01936i	−0.174700	+	0.0635857i	0.253189	+	0.967417i	$0.418521\pi$
$258$	6.71688			0.418175
$259$	0.938511	+	4.11949i	0.0583162	+	0.255973i
$260$	0.570356			0.0353720
$261$	0.979055	−	0.356347i	0.0606020	−	0.0220573i
$262$	12.2306	+	4.45156i	0.755606	+	0.275018i
$263$	−10.1434	+	8.51130i	−0.625467	+	0.524829i	−0.899517	−	0.436886i	$-0.856081\pi$
$263$	−10.1434	+	8.51130i	−0.625467	+	0.524829i	0.274050	+	0.961716i	$0.411637\pi$
$264$	−6.15910	−	34.9300i	−0.379066	−	2.14979i
$265$	7.18479			0.441358
$266$	0.879385	+	4.98724i	0.0539186	+	0.305787i
$267$	2.63176	−	4.55834i	0.161061	−	0.278966i
$268$	−0.138404	−	0.116135i	−0.00845438	−	0.00709406i
$269$	11.4572	+	19.8445i	0.698560	+	1.20994i	0.968966	+	0.247195i	$0.0795088\pi$
$269$	11.4572	+	19.8445i	0.698560	+	1.20994i	−0.270406	+	0.962746i	$0.587158\pi$
$270$	−4.20961	+	7.29125i	−0.256189	+	0.443732i
$271$	−20.5865	+	7.49286i	−1.25054	+	0.455159i	−0.880584	−	0.473891i	$-0.842849\pi$
$271$	−20.5865	+	7.49286i	−1.25054	+	0.455159i	−0.369955	+	0.929050i	$0.620627\pi$
$272$	−10.6873	+	8.96773i	−0.648014	+	0.543748i
$273$	−1.49525	−	2.58985i	−0.0904968	−	0.156745i
$274$	1.25624	−	7.12452i	0.0758925	−	0.430408i
$275$	3.54576	−	20.1090i	0.213817	−	1.21262i
$276$	1.59627	+	1.33943i	0.0960840	+	0.0806240i
$277$	−10.5642	−	3.84505i	−0.634740	−	0.231026i	0.00455313	−	0.999990i	$-0.498551\pi$
$277$	−10.5642	−	3.84505i	−0.634740	−	0.231026i	−0.639293	+	0.768963i	$0.720773\pi$
$278$	−1.15657	−	0.420959i	−0.0693667	−	0.0252474i
$279$	−2.89646	−	2.43042i	−0.173406	−	0.145505i
$280$	−0.478340	+	2.71280i	−0.0285863	+	0.162121i
$281$	0.698463	−	3.96118i	0.0416668	−	0.236304i	−0.956861	−	0.290546i	$-0.906163\pi$
$281$	0.698463	−	3.96118i	0.0416668	−	0.236304i	0.998528	+	0.0542418i	$0.0172742\pi$
$282$	0.340022	+	0.588936i	0.0202480	+	0.0350706i
$283$	16.6348	−	13.9582i	0.988833	−	0.829730i	0.00343496	−	0.999994i	$-0.498907\pi$
$283$	16.6348	−	13.9582i	0.988833	−	0.829730i	0.985398	+	0.170264i	$0.0544622\pi$
$284$	−1.25743	+	0.457666i	−0.0746145	+	0.0271575i
$285$	−6.85117	+	11.8666i	−0.405828	+	0.702915i
$286$	9.89440	+	17.1376i	0.585068	+	1.01337i
$287$	−0.381445	−	0.320070i	−0.0225160	−	0.0188931i
$288$	0.277189	−	0.480105i	0.0163335	−	0.0282905i
$289$	−0.338678	−	1.92074i	−0.0199222	−	0.112985i
$290$	3.55438			0.208720
$291$	0.823826	+	4.67215i	0.0482935	+	0.273886i
$292$	−1.01501	+	0.851698i	−0.0593992	+	0.0498419i
$293$	−21.6300	−	7.87268i	−1.26364	−	0.459927i	−0.378650	−	0.925540i	$-0.623612\pi$
$293$	−21.6300	−	7.87268i	−1.26364	−	0.459927i	−0.884988	+	0.465613i	$0.845834\pi$
$294$	−15.5077	+	5.64436i	−0.904430	+	0.329186i
$295$	2.78106			0.161920
$296$	8.17483	−	15.9299i	0.475152	−	0.925905i
$297$	29.7374			1.72554
$298$	−4.93629	+	1.79666i	−0.285952	+	0.104078i
$299$	−12.9162	−	4.70112i	−0.746964	−	0.271873i
$300$	0.847296	−	0.710966i	0.0489187	−	0.0410476i
$301$	0.319955	+	1.81456i	0.0184419	+	0.104589i
$302$	2.23711			0.128731
$303$	−2.21048	−	12.5363i	−0.126989	−	0.720191i
$304$	9.73055	−	16.8538i	0.558085	−	0.966632i
$305$	−2.25490	−	1.89209i	−0.129115	−	0.108341i
$306$	1.39053	+	2.40847i	0.0794913	+	0.137683i
$307$	−3.41740	+	5.91912i	−0.195042	+	0.337822i	−0.946914	−	0.321487i	$-0.895818\pi$
$307$	−3.41740	+	5.91912i	−0.195042	+	0.337822i	0.751873	+	0.659308i	$0.229151\pi$
$308$	0.773318	−	0.281465i	0.0440639	−	0.0160380i
$309$	−14.1532	+	11.8759i	−0.805146	+	0.675597i
$310$	−6.44949	−	11.1708i	−0.366307	−	0.634462i
$311$	−0.267389	+	1.51644i	−0.0151622	+	0.0859892i	−0.991450	−	0.130488i	$-0.958346\pi$
$311$	−0.267389	+	1.51644i	−0.0151622	+	0.0859892i	0.976288	+	0.216477i	$0.0694567\pi$
$312$	−2.20068	+	12.4807i	−0.124589	+	0.706581i
$313$	16.7442	+	14.0501i	0.946439	+	0.794157i	0.978694	−	0.205323i	$-0.0658244\pi$
$313$	16.7442	+	14.0501i	0.946439	+	0.794157i	−0.0322549	+	0.999480i	$0.510269\pi$
$314$	−8.65657	−	3.15074i	−0.488519	−	0.177806i
$315$	0.467911	+	0.170306i	0.0263638	+	0.00959564i
$316$	−1.66566	−	1.39765i	−0.0937006	−	0.0786242i
$317$	−4.72937	+	26.8216i	−0.265628	+	1.50645i	0.501613	+	0.865092i	$0.332740\pi$
$317$	−4.72937	+	26.8216i	−0.265628	+	1.50645i	−0.767241	+	0.641359i	$0.778371\pi$
$318$	−2.34477	+	13.2979i	−0.131488	+	0.745707i
$319$	−6.27719	−	10.8724i	−0.351455	−	0.608738i
$320$	8.87211	−	7.44459i	0.495966	−	0.416165i
$321$	8.21688	−	2.99070i	0.458622	−	0.166925i
$322$	2.80747	−	4.86267i	0.156454	−	0.270986i
$323$	−10.4966	−	18.1806i	−0.584046	−	1.01160i
$324$	1.45992	+	1.22502i	0.0811068	+	0.0680567i
$325$	−3.64796	+	6.31844i	−0.202352	+	0.350484i
$326$	2.61674	+	14.8403i	0.144928	+	0.821928i
$327$	−5.75877			−0.318461
$328$	0.366430	+	2.07813i	0.0202327	+	0.114745i
$329$	−0.142903	+	0.119910i	−0.00787852	+	0.00661087i
$330$	−20.5535	−	7.48086i	−1.13143	−	0.411808i
$331$	−14.1912	+	5.16517i	−0.780018	+	0.283903i	−0.701180	−	0.712984i	$-0.747343\pi$
$331$	−14.1912	+	5.16517i	−0.780018	+	0.283903i	−0.0788380	+	0.996887i	$0.525121\pi$
$332$	2.59215			0.142263
$333$	−2.57919	−	1.95529i	−0.141339	−	0.107149i
$334$	10.4798			0.573428
$335$	−1.23783	+	0.450532i	−0.0676297	+	0.0246152i
$336$	−4.41147	−	1.60565i	−0.240666	−	0.0875951i
$337$	−10.7083	+	8.98530i	−0.583316	+	0.489460i	−0.886034	−	0.463620i	$-0.846550\pi$
$337$	−10.7083	+	8.98530i	−0.583316	+	0.489460i	0.302718	+	0.953080i	$0.402106\pi$
$338$	1.81361	+	10.2855i	0.0986476	+	0.559459i
$339$	29.5253			1.60359
$340$	−0.167718	−	0.951178i	−0.00909581	−	0.0515849i
$341$	−22.7802	+	39.4564i	−1.23362	+	2.13669i
$342$	−2.97178	−	2.49362i	−0.160696	−	0.134840i
$343$	−4.69459	−	8.13127i	−0.253484	−	0.439047i
$344$	3.90420	−	6.76227i	0.210500	−	0.364597i
$345$	14.2763	−	5.19615i	0.768611	−	0.279751i
$346$	17.2181	−	14.4477i	0.925649	−	0.776712i
$347$	−1.91147	−	3.31077i	−0.102613	−	0.177731i	0.810147	−	0.586226i	$-0.199387\pi$
$347$	−1.91147	−	3.31077i	−0.102613	−	0.177731i	−0.912761	+	0.408495i	$0.866054\pi$
$348$	0.118089	−	0.669713i	0.00633021	−	0.0359004i
$349$	3.08630	−	17.5033i	0.165206	−	0.936930i	−0.783646	−	0.621208i	$-0.786642\pi$
$349$	3.08630	−	17.5033i	0.165206	−	0.936930i	0.948852	−	0.315722i	$-0.102247\pi$
$350$	−2.28312	−	1.91576i	−0.122038	−	0.102402i
$351$	−9.98457	−	3.63409i	−0.532937	−	0.193973i
$352$	−6.27719	−	2.28471i	−0.334575	−	0.121775i
$353$	−3.58718	−	3.01000i	−0.190926	−	0.160206i	0.542314	−	0.840176i	$-0.317548\pi$
$353$	−3.58718	−	3.01000i	−0.190926	−	0.160206i	−0.733240	+	0.679970i	$0.761993\pi$
$354$	−0.907604	+	5.14728i	−0.0482386	+	0.273575i
$355$	−1.69413	+	9.60787i	−0.0899149	+	0.509933i
$356$	−0.258770	−	0.448204i	−0.0137148	−	0.0237547i
$357$	−3.87939	+	3.25519i	−0.205319	+	0.172283i
$358$	−6.25537	+	2.27677i	−0.330606	+	0.120331i
$359$	8.81908	−	15.2751i	0.465453	−	0.806188i	−0.533769	−	0.845630i	$-0.679225\pi$
$359$	8.81908	−	15.2751i	0.465453	−	0.806188i	0.999222	+	0.0394420i	$0.0125580\pi$
$360$	−1.05509	−	1.82747i	−0.0556083	−	0.0963164i
$361$	7.87804	+	6.61046i	0.414634	+	0.347919i
$362$	16.2540	−	28.1528i	0.854292	−	1.47968i
$363$	9.82547	+	55.7230i	0.515704	+	2.92470i
$364$	−0.294045			−0.0154121
$365$	1.67752	+	9.51368i	0.0878053	+	0.497969i
$366$	4.23783	−	3.55596i	0.221515	−	0.185873i
$367$	−13.3084	−	4.84386i	−0.694693	−	0.252848i	−0.0295496	−	0.999563i	$-0.509407\pi$
$367$	−13.3084	−	4.84386i	−0.694693	−	0.252848i	−0.665143	+	0.746716i	$0.731630\pi$
$368$	−20.2763	+	7.37997i	−1.05698	+	0.384708i
$369$	0.381445			0.0198572
$370$	−5.98680	−	9.27752i	−0.311239	−	0.482316i
$371$	−3.70409			−0.192307
$372$	−2.31908	+	0.844075i	−0.120239	+	0.0437633i
$373$	−17.8960	−	6.51363i	−0.926622	−	0.337263i	−0.165752	−	0.986167i	$-0.553005\pi$
$373$	−17.8960	−	6.51363i	−0.926622	−	0.337263i	−0.760870	+	0.648904i	$0.775227\pi$
$374$	25.6707	−	21.5403i	1.32740	−	1.11382i
$375$	−3.59879	−	20.4098i	−0.185841	−	1.05396i
$376$	0.790555			0.0407697
$377$	0.778943	+	4.41761i	0.0401176	+	0.227518i
$378$	2.17024	−	3.75897i	0.111625	−	0.193341i
$379$	11.5608	+	9.70064i	0.593837	+	0.498288i	0.889458	−	0.457017i	$-0.151082\pi$
$379$	11.5608	+	9.70064i	0.593837	+	0.498288i	−0.295621	+	0.955305i	$0.595527\pi$
$380$	0.673648	+	1.16679i	0.0345574	+	0.0598552i
$381$	12.9081	−	22.3574i	0.661300	−	1.14541i
$382$	21.8097	−	7.93810i	1.11588	−	0.406148i
$383$	7.86824	−	6.60224i	0.402048	−	0.337359i	−0.419236	−	0.907877i	$-0.637702\pi$
$383$	7.86824	−	6.60224i	0.402048	−	0.337359i	0.821285	+	0.570518i	$0.193258\pi$
$384$	8.92514	+	15.4588i	0.455459	+	0.788879i
$385$	1.04189	−	5.90885i	0.0530996	−	0.301143i
$386$	2.54529	−	14.4351i	0.129552	−	0.734726i
$387$	−1.08125	−	0.907278i	−0.0549631	−	0.0461195i
$388$	0.438348	+	0.159546i	0.0222538	+	0.00809971i
$389$	21.6789	+	7.89046i	1.09916	+	0.400062i	0.827007	−	0.562191i	$-0.190042\pi$
$389$	21.6789	+	7.89046i	1.09916	+	0.400062i	0.272155	+	0.962254i	$0.412264\pi$
$390$	5.98680	+	5.02352i	0.303153	+	0.254376i
$391$	−4.04189	+	22.9227i	−0.204407	+	1.15925i
$392$	−3.33140	+	18.8933i	−0.168261	+	0.954257i
$393$	−9.07785	−	15.7233i	−0.457917	−	0.793135i
$394$	−3.50072	+	2.93745i	−0.176363	+	0.147987i
$395$	−14.8969	+	5.42204i	−0.749546	+	0.272812i
$396$	−0.315207	+	0.545955i	−0.0158398	+	0.0274353i
$397$	−10.0098	−	17.3375i	−0.502377	−	0.870143i	−0.999996	−	0.00274745i	$-0.999125\pi$
$397$	−10.0098	−	17.3375i	−0.502377	−	0.870143i	0.497619	−	0.867396i	$-0.334208\pi$
$398$	−14.2435	−	11.9517i	−0.713963	−	0.599086i
$399$	3.53209	−	6.11776i	0.176826	−	0.306271i
$400$	1.98886	+	11.2794i	0.0994428	+	0.563968i
$401$	15.1753			0.757818			0.378909	−	0.925434i	$-0.376299\pi$
$401$	15.1753			0.757818			0.378909	+	0.925434i	$0.376299\pi$
$402$	−0.429892	−	2.43804i	−0.0214411	−	0.121598i
$403$	12.4704	−	10.4639i	0.621197	−	0.521246i
$404$	−1.17617	−	0.428092i	−0.0585169	−	0.0212984i
$405$	13.0569	−	4.75232i	0.648803	−	0.236145i
$406$	−1.83244			−0.0909427
$407$	−17.8059	+	34.6974i	−0.882604	+	1.71989i
$408$	21.4611			1.06248
$409$	−3.31016	+	1.20480i	−0.163677	+	0.0595734i	−0.422559	−	0.906335i	$-0.638868\pi$
$409$	−3.31016	+	1.20480i	−0.163677	+	0.0595734i	0.258882	+	0.965909i	$0.416646\pi$
$410$	1.22281	+	0.445067i	0.0603903	+	0.0219803i
$411$	−7.73055	+	6.48670i	−0.381320	+	0.319965i
$412$	0.315456	+	1.78904i	0.0155414	+	0.0881396i
$413$	−1.43376			−0.0705509
$414$	0.746911	+	4.23594i	0.0367087	+	0.208185i
$415$	9.44949	−	16.3670i	0.463857	−	0.803425i
$416$	1.82841	+	1.53422i	0.0896452	+	0.0752213i
$417$	0.858441	+	1.48686i	0.0420380	+	0.0728120i
$418$	−23.3726	+	40.4825i	−1.14319	+	1.98006i
$419$	5.24510	−	1.90906i	0.256240	−	0.0932637i	−0.210706	−	0.977549i	$-0.567576\pi$
$419$	5.24510	−	1.90906i	0.256240	−	0.0932637i	0.466946	+	0.884286i	$0.345354\pi$
$420$	0.248970	−	0.208911i	0.0121485	−	0.0101938i
$421$	−5.20099	−	9.00838i	−0.253481	−	0.439041i	0.711001	−	0.703191i	$-0.248242\pi$
$421$	−5.20099	−	9.00838i	−0.253481	−	0.439041i	−0.964482	+	0.264149i	$0.914909\pi$
$422$	−1.92127	+	10.8961i	−0.0935262	+	0.530413i
$423$	0.0248149	−	0.140732i	0.00120654	−	0.00684265i
$424$	12.0248	+	10.0900i	0.583977	+	0.490015i
$425$	11.6099	+	4.22567i	0.563165	+	0.204975i
$426$	−17.2297	−	6.27109i	−0.834780	−	0.303835i
$427$	1.16250	+	0.975457i	0.0562575	+	0.0472057i
$428$	0.149300	−	0.846723i	0.00721669	−	0.0409279i
$429$	4.79339	−	27.1846i	0.231427	−	1.31249i
$430$	−2.40760	−	4.17009i	−0.116105	−	0.201100i
$431$	23.6648	−	19.8571i	1.13989	−	0.956483i	0.140457	−	0.990087i	$-0.455143\pi$
$431$	23.6648	−	19.8571i	1.13989	−	0.956483i	0.999435	+	0.0336034i	$0.0106983\pi$
$432$	−15.6741	+	5.70491i	−0.754121	+	0.274478i
$433$	−6.65998	+	11.5354i	−0.320058	+	0.554357i	−0.980500	−	0.196521i	$-0.937036\pi$
$433$	−6.65998	+	11.5354i	−0.320058	+	0.554357i	0.660442	+	0.750877i	$0.270369\pi$
$434$	3.32501	+	5.75908i	0.159605	+	0.276445i
$435$	−3.79813	−	3.18701i	−0.182107	−	0.152806i
$436$	−0.283119	+	0.490376i	−0.0135589	+	0.0234847i
$437$	−5.63816	−	31.9756i	−0.269710	−	1.52960i
$438$	−18.1557			−0.867513
$439$	−4.35962	−	24.7246i	−0.208073	−	1.18004i	−0.892530	−	0.450989i	$-0.851071\pi$
$439$	−4.35962	−	24.7246i	−0.208073	−	1.18004i	0.684456	−	0.729054i	$-0.260040\pi$
$440$	−19.4782	+	16.3441i	−0.928586	+	0.779176i
$441$	3.25877	+	1.18610i	0.155180	+	0.0564807i
$442$	−11.2515	+	4.09521i	−0.535179	+	0.194789i
$443$	28.8384			1.37016			0.685078	−	0.728470i	$-0.259768\pi$
$443$	28.8384			1.37016			0.685078	+	0.728470i	$0.259768\pi$
$444$	−1.94697	+	0.819797i	−0.0923989	+	0.0389058i
$445$	−3.77332			−0.178872
$446$	−13.6147	+	4.95534i	−0.644674	+	0.234642i
$447$	6.88578	+	2.50622i	0.325686	+	0.118540i
$448$	−4.57398	+	3.83802i	−0.216100	+	0.181330i
$449$	−2.62877	−	14.9085i	−0.124059	−	0.703574i	−0.981862	−	0.189596i	$-0.939282\pi$
$449$	−2.62877	−	14.9085i	−0.124059	−	0.703574i	0.857803	−	0.513978i	$-0.171829\pi$
$450$	2.28312			0.107627
$451$	−0.798133	−	4.52644i	−0.0375826	−	0.213142i
$452$	1.45155	−	2.51416i	0.0682753	−	0.118256i
$453$	−2.39053	−	2.00589i	−0.112317	−	0.0942451i
$454$	−0.625829	−	1.08397i	−0.0293716	−	0.0508731i
$455$	−1.07192	+	1.85662i	−0.0502523	+	0.0870396i
$456$	−28.1313	+	10.2390i	−1.31737	+	0.479484i
$457$	−22.9290	+	19.2397i	−1.07257	+	0.899997i	−0.995283	−	0.0970121i	$-0.969071\pi$
$457$	−22.9290	+	19.2397i	−1.07257	+	0.899997i	−0.0772909	+	0.997009i	$0.524627\pi$
$458$	17.8837	+	30.9755i	0.835651	+	1.44739i
$459$	−3.12449	+	17.7198i	−0.145838	+	0.827091i
$460$	0.259399	−	1.47113i	0.0120946	−	0.0685917i
$461$	−29.6826	−	24.9066i	−1.38246	−	1.16002i	−0.968294	−	0.249814i	$-0.919630\pi$
$461$	−29.6826	−	24.9066i	−1.38246	−	1.16002i	−0.414161	−	0.910203i	$-0.635925\pi$
$462$	10.5963	+	3.85673i	0.492983	+	0.179431i
$463$	6.81180	+	2.47929i	0.316571	+	0.115223i	0.495419	−	0.868654i	$-0.335015\pi$
$463$	6.81180	+	2.47929i	0.316571	+	0.115223i	−0.178847	+	0.983877i	$0.557237\pi$
$464$	5.39440	+	4.52644i	0.250429	+	0.210135i
$465$	−3.12449	+	17.7198i	−0.144895	+	0.821738i
$466$	0.945622	−	5.36289i	0.0438051	−	0.248431i
$467$	−2.51707	−	4.35970i	−0.116476	−	0.201743i	0.801893	−	0.597468i	$-0.203827\pi$
$467$	−2.51707	−	4.35970i	−0.116476	−	0.201743i	−0.918369	+	0.395725i	$0.870493\pi$
$468$	0.172552	−	0.144789i	0.00797624	−	0.00669286i
$469$	0.638156	−	0.232270i	0.0294673	−	0.0107252i
$470$	0.243756	−	0.422197i	0.0112436	−	0.0194745i
$471$	6.42514	+	11.1287i	0.296055	+	0.512782i
$472$	4.65451	+	3.90560i	0.214241	+	0.179770i
$473$	−8.50387	+	14.7291i	−0.391008	+	0.677246i
$474$	−5.17365	−	29.3412i	−0.237634	−	1.34769i
$475$	−17.2344			−0.790770
$476$	0.0864665	+	0.490376i	0.00396318	+	0.0224763i
$477$	2.17365	−	1.82391i	0.0995245	−	0.0835110i
$478$	−19.3773	−	7.05277i	−0.886298	−	0.322586i
$479$	−2.69119	+	0.979513i	−0.122964	+	0.0447551i	−0.402769	−	0.915302i	$-0.631952\pi$
$479$	−2.69119	+	0.979513i	−0.122964	+	0.0447551i	0.279806	+	0.960057i	$0.409730\pi$
$480$	−2.63816			−0.120415
$481$	10.2187	−	9.47395i	0.465932	−	0.431975i
$482$	−36.2550			−1.65137
$483$	−7.36009	+	2.67885i	−0.334896	+	0.121892i
$484$	5.22803	+	1.90285i	0.237638	+	0.0864930i
$485$	2.60535	−	2.18615i	0.118303	−	0.0992679i
$486$	1.27925	+	7.25498i	0.0580279	+	0.329092i
$487$	14.4439			0.654514			0.327257	−	0.944935i	$-0.393876\pi$
$487$	14.4439			0.654514			0.327257	+	0.944935i	$0.393876\pi$
$488$	−1.11674	−	6.33337i	−0.0505526	−	0.286698i
$489$	10.5103	−	18.2043i	0.475291	−	0.823228i
$490$	9.06283	+	7.60462i	0.409417	+	0.343542i
$491$	17.1887	+	29.7716i	0.775713	+	1.34358i	0.934393	+	0.356245i	$0.115943\pi$
$491$	17.1887	+	29.7716i	0.775713	+	1.34358i	−0.158679	+	0.987330i	$0.550724\pi$
$492$	0.124485	−	0.215615i	0.00561222	−	0.00972066i
$493$	7.13816	−	2.59808i	0.321486	−	0.117011i
$494$	12.7947	−	10.7361i	0.575662	−	0.483038i
$495$	2.29813	+	3.98048i	0.103293	+	0.178909i
$496$	4.43763	−	25.1671i	0.199256	−	1.13003i
$497$	0.873399	−	4.95329i	0.0391773	−	0.222186i
$498$	27.2087	+	22.8308i	1.21925	+	1.02307i
$499$	37.9800	+	13.8236i	1.70022	+	0.618829i	0.995850	−	0.0910068i	$-0.0290085\pi$
$499$	37.9800	+	13.8236i	1.70022	+	0.618829i	0.704368	+	0.709835i	$0.251231\pi$
$500$	−1.91488	−	0.696958i	−0.0856359	−	0.0311689i
$501$	−11.1985	−	9.39663i	−0.500310	−	0.419810i
$502$	5.45723	−	30.9495i	0.243568	−	1.38134i
$503$	−2.52188	+	14.3023i	−0.112445	+	0.637707i	0.875539	+	0.483148i	$0.160507\pi$
$503$	−2.52188	+	14.3023i	−0.112445	+	0.637707i	−0.987984	+	0.154559i	$0.950604\pi$
$504$	0.543948	+	0.942146i	0.0242294	+	0.0419665i
$505$	−6.99067	+	5.86587i	−0.311081	+	0.261028i
$506$	48.7033	−	17.7265i	2.16512	−	0.788041i
$507$	7.28446	−	12.6171i	0.323514	−	0.560343i
$508$	−1.26920	−	2.19832i	−0.0563116	−	0.0975346i
$509$	16.5726	+	13.9061i	0.734569	+	0.616377i	0.931373	−	0.364066i	$-0.118612\pi$
$509$	16.5726	+	13.9061i	0.734569	+	0.616377i	−0.196804	+	0.980443i	$0.563056\pi$
$510$	6.61721	−	11.4613i	0.293015	−	0.507517i
$511$	−0.864837	−	4.90474i	−0.0382582	−	0.216973i
$512$	24.9186			1.10126
$513$	−4.35844	−	24.7179i	−0.192430	−	1.09132i
$514$	−3.07604	+	2.58110i	−0.135678	+	0.113848i
$515$	12.4461	+	4.53001i	0.548440	+	0.199616i
$516$	−0.865715	+	0.315094i	−0.0381110	+	0.0138713i
$517$	−1.72193			−0.0757306
$518$	3.08647	+	4.78299i	0.135612	+	0.210152i
$519$	−31.3533			−1.37626
$520$	8.53730	−	3.10732i	0.374386	−	0.136265i
$521$	21.6018	+	7.86241i	0.946391	+	0.344458i	0.768687	−	0.639626i	$-0.220911\pi$
$521$	21.6018	+	7.86241i	0.946391	+	0.344458i	0.177705	+	0.984084i	$0.443133\pi$
$522$	1.07532	−	0.902302i	0.0470656	−	0.0394927i
$523$	2.28400	+	12.9532i	0.0998722	+	0.566403i	0.993145	+	0.116888i	$0.0372920\pi$
$523$	2.28400	+	12.9532i	0.0998722	+	0.566403i	−0.893273	+	0.449515i	$0.851597\pi$
$524$	−1.78518			−0.0779859
$525$	0.721934	+	4.09429i	0.0315078	+	0.178689i
$526$	−8.91993	+	15.4498i	−0.388927	+	0.673642i
$527$	−21.1177	−	17.7198i	−0.919901	−	0.771888i
$528$	−21.6668	−	37.5281i	−0.942928	−	1.63320i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	9.09627	−	3.31077i	0.395117	−	0.143811i
$531$	0.841367	−	0.705990i	0.0365122	−	0.0306374i
$532$	−0.347296	−	0.601535i	−0.0150572	−	0.0260798i
$533$	−0.285178	+	1.61732i	−0.0123524	+	0.0700541i
$534$	1.23143	−	6.98378i	0.0532892	−	0.302218i
$535$	−4.80200	−	4.02936i	−0.207609	−	0.174204i
$536$	−2.70439	−	0.984319i	−0.116812	−	0.0425161i
$537$	8.72580	+	3.17593i	0.376546	+	0.137052i
$538$	23.6498	+	19.8445i	1.01961	+	0.855558i
$539$	7.25624	−	41.1522i	0.312549	−	1.77255i
$540$	0.200522	−	1.13722i	0.00862911	−	0.0489381i
$541$	17.5988	+	30.4820i	0.756631	+	1.31052i	0.944559	+	0.328341i	$0.106489\pi$
$541$	17.5988	+	30.4820i	0.756631	+	1.31052i	−0.187928	+	0.982183i	$0.560177\pi$
$542$	−22.6107	+	18.9726i	−0.971211	+	0.814943i
$543$	−42.6117	+	15.5094i	−1.82865	+	0.665572i
$544$	2.02094	−	3.50038i	0.0866473	−	0.150077i
$545$	2.06418	+	3.57526i	0.0884197	+	0.153147i
$546$	−3.08647	−	2.58985i	−0.132089	−	0.110835i
$547$	−12.3033	+	21.3100i	−0.526053	+	0.911151i	0.473486	+	0.880801i	$0.342995\pi$
$547$	−12.3033	+	21.3100i	−0.526053	+	0.911151i	−0.999539	+	0.0303496i	$0.990338\pi$
$548$	0.172304	+	0.977185i	0.00736046	+	0.0417433i
$549$	−1.16250			−0.0496145
$550$	−4.77719	−	27.0928i	−0.203700	−	1.15524i
$551$	−8.11721	+	6.81115i	−0.345805	+	0.290165i
$552$	31.1908	+	11.3525i	1.32757	+	0.483195i
$553$	7.68004	−	2.79531i	0.326589	−	0.118869i
$554$	−15.1465			−0.643514
$555$	−1.92127	+	15.2818i	−0.0815536	+	0.648676i
$556$	0.168814			0.00715932
$557$	−7.10354	+	2.58548i	−0.300987	+	0.109550i	−0.488099	−	0.872788i	$-0.662309\pi$
$557$	−7.10354	+	2.58548i	−0.300987	+	0.109550i	0.187112	+	0.982339i	$0.440087\pi$
$558$	−4.78699	−	1.74232i	−0.202649	−	0.0737584i
$559$	4.65523	−	3.90620i	0.196895	−	0.165215i
$560$	0.584407	+	3.31434i	0.0246957	+	0.140056i
$561$	−46.7452			−1.97358
$562$	−0.941037	−	5.33688i	−0.0396952	−	0.225123i
$563$	−1.31046	+	2.26978i	−0.0552293	+	0.0956599i	−0.892318	−	0.451407i	$-0.850922\pi$
$563$	−1.31046	+	2.26978i	−0.0552293	+	0.0956599i	0.837089	+	0.547067i	$0.184256\pi$
$564$	−0.0714517	−	0.0599551i	−0.00300866	−	0.00252457i
$565$	−10.5831	−	18.3304i	−0.445233	−	0.771166i
$566$	14.6284	−	25.3371i	0.614876	−	1.06500i
$567$	−6.73143	+	2.45004i	−0.282693	+	0.102892i
$568$	−16.3282	+	13.7010i	−0.685118	+	0.574882i
$569$	−8.19728	−	14.1981i	−0.343648	−	0.595216i	0.641459	−	0.767157i	$-0.278329\pi$
$569$	−8.19728	−	14.1981i	−0.343648	−	0.595216i	−0.985107	+	0.171941i	$0.944996\pi$
$570$	−3.20574	+	18.1806i	−0.134274	+	0.761503i
$571$	−4.94444	+	28.0413i	−0.206918	+	1.17349i	0.687474	+	0.726209i	$0.258720\pi$
$571$	−4.94444	+	28.0413i	−0.206918	+	1.17349i	−0.894392	+	0.447283i	$0.852392\pi$
$572$	−2.07919	−	1.74465i	−0.0869354	−	0.0729475i
$573$	−30.4231	−	11.0731i	−1.27094	−	0.462585i
$574$	−0.630415	−	0.229452i	−0.0263130	−	0.00957715i
$575$	14.6382	+	12.2829i	0.610453	+	0.512231i
$576$	0.794263	−	4.50449i	0.0330943	−	0.187687i
$577$	4.23870	−	24.0389i	0.176460	−	1.00075i	−0.759986	−	0.649939i	$-0.774794\pi$
$577$	4.23870	−	24.0389i	0.176460	−	1.00075i	0.936446	−	0.350812i	$-0.114095\pi$
$578$	−1.31386	−	2.27568i	−0.0546495	−	0.0946557i
$579$	−15.6630	+	13.1428i	−0.650931	+	0.546196i
$580$	−0.458111	+	0.166739i	−0.0190220	+	0.00692345i
$581$	−4.87164	+	8.43794i	−0.202110	+	0.350065i
$582$	3.19594	+	5.53553i	0.132476	+	0.229455i
$583$	−26.1917	−	21.9774i	−1.08475	−	0.910211i
$584$	−10.5530	+	18.2784i	−0.436688	+	0.756365i
$585$	−0.285178	−	1.61732i	−0.0117907	−	0.0668681i
$586$	−31.0123			−1.28111
$587$	6.35045	+	36.0152i	0.262111	+	1.48651i	0.777137	+	0.629332i	$0.216671\pi$
$587$	6.35045	+	36.0152i	0.262111	+	1.48651i	−0.515026	+	0.857175i	$0.672218\pi$
$588$	1.73396	−	1.45496i	0.0715071	−	0.0600016i
$589$	36.1352	+	13.1521i	1.48893	+	0.541925i
$590$	3.52094	−	1.28152i	0.144955	−	0.0527593i
$591$	6.37464			0.262218
$592$	2.72874	−	21.7044i	0.112151	−	0.892044i
$593$	22.2344			0.913058			0.456529	−	0.889708i	$-0.349092\pi$
$593$	22.2344			0.913058			0.456529	+	0.889708i	$0.349092\pi$
$594$	37.6489	−	13.7031i	1.54475	−	0.562244i
$595$	3.41147	+	1.24168i	0.139857	+	0.0509037i
$596$	0.551938	−	0.463131i	0.0226082	−	0.0189706i
$597$	4.50387	+	25.5427i	0.184331	+	1.04539i
$598$	−18.5188			−0.757290
$599$	−0.0346151	−	0.196312i	−0.00141433	−	0.00802109i	0.984092	−	0.177657i	$-0.0568518\pi$
$599$	−0.0346151	−	0.196312i	−0.00141433	−	0.00802109i	−0.985507	+	0.169636i	$0.945741\pi$
$600$	8.80928	−	15.2581i	0.359637	−	0.622910i
$601$	6.14337	+	5.15490i	0.250593	+	0.210273i	0.759428	−	0.650592i	$-0.225479\pi$
$601$	6.14337	+	5.15490i	0.250593	+	0.210273i	−0.508834	+	0.860864i	$0.669923\pi$
$602$	1.24123	+	2.14987i	0.0505887	+	0.0876223i
$603$	−0.260115	+	0.450532i	−0.0105927	+	0.0183471i
$604$	−0.288333	+	0.104945i	−0.0117321	+	0.00427014i
$605$	31.0731	−	26.0734i	1.26330	−	1.06004i
$606$	−8.57532	−	14.8529i	−0.348349	−	0.603358i
$607$	−0.0727959	+	0.412846i	−0.00295469	+	0.0167569i	−0.986249	−	0.165263i	$-0.947153\pi$
$607$	−0.0727959	+	0.412846i	−0.00295469	+	0.0167569i	0.983295	+	0.182020i	$0.0582637\pi$
$608$	−0.979055	+	5.55250i	−0.0397059	+	0.225184i
$609$	1.95811	+	1.64305i	0.0793467	+	0.0665798i
$610$	−3.72668	−	1.35640i	−0.150889	−	0.0549191i
$611$	0.578153	+	0.210430i	0.0233896	+	0.00851311i
$612$	−0.292204	−	0.245188i	−0.0118116	−	0.00991113i
$613$	0.326514	−	1.85175i	0.0131878	−	0.0747916i	−0.977504	−	0.210919i	$-0.932354\pi$
$613$	0.326514	−	1.85175i	0.0131878	−	0.0747916i	0.990691	+	0.136127i	$0.0434656\pi$
$614$	−1.59904	+	9.06861i	−0.0645321	+	0.365979i
$615$	−0.907604	−	1.57202i	−0.0365981	−	0.0633898i
$616$	10.0419	−	8.42615i	0.404599	−	0.339499i
$617$	16.2442	−	5.91241i	0.653968	−	0.238025i	0.00633794	−	0.999980i	$-0.497983\pi$
$617$	16.2442	−	5.91241i	0.653968	−	0.238025i	0.647630	+	0.761955i	$0.275760\pi$
$618$	−12.4461	+	21.5573i	−0.500655	+	0.867160i
$619$	−19.9204	−	34.5031i	−0.800668	−	1.38680i	−0.919177	−	0.393845i	$-0.871145\pi$
$619$	−19.9204	−	34.5031i	−0.800668	−	1.38680i	0.118508	−	0.992953i	$-0.462189\pi$
$620$	1.35529	+	1.13722i	0.0544296	+	0.0456718i
$621$	−13.9145	+	24.1006i	−0.558368	+	0.967122i
$622$	0.360252	+	2.04309i	0.0144448	+	0.0819204i
$623$	1.94532			0.0779375
$624$	2.68866	+	15.2482i	0.107633	+	0.610415i
$625$	0.817267	−	0.685768i	0.0326907	−	0.0274307i
$626$	27.6732	+	10.0722i	1.10605	+	0.402567i
$627$	61.2738	−	22.3019i	2.44704	−	0.890650i
$628$	1.26352			0.0504199
$629$	−18.8045	−	14.2557i	−0.749786	−	0.568413i
$630$	0.670874			0.0267282
$631$	1.14883	−	0.418141i	0.0457343	−	0.0166459i	−0.319052	−	0.947737i	$-0.603364\pi$
$631$	1.14883	−	0.418141i	0.0457343	−	0.0166459i	0.364786	+	0.931091i	$0.381142\pi$
$632$	−32.5467	−	11.8460i	−1.29464	−	0.471210i
$633$	11.8229	−	9.92063i	0.469920	−	0.394310i
$634$	6.37186	+	36.1366i	0.253059	+	1.43517i
$635$	−18.5071			−0.734432
$636$	−0.321604	−	1.82391i	−0.0127524	−	0.0723226i
$637$	−7.46538	+	12.9304i	−0.295789	+	0.512322i
$638$	−12.9572	−	10.8724i	−0.512982	−	0.430443i
$639$	1.92649	+	3.33678i	0.0762107	+	0.132001i
$640$	6.39827	−	11.0821i	0.252914	−	0.438060i
$641$	−32.0171	+	11.6533i	−1.26460	+	0.460277i	−0.885310	−	0.465001i	$-0.846054\pi$
$641$	−32.0171	+	11.6533i	−1.26460	+	0.460277i	−0.379290	+	0.925278i	$0.623832\pi$
$642$	9.02481	−	7.57272i	0.356181	−	0.298871i
$643$	−0.711829	−	1.23292i	−0.0280718	−	0.0486218i	0.851648	−	0.524114i	$-0.175603\pi$
$643$	−0.711829	−	1.23292i	−0.0280718	−	0.0486218i	−0.879720	+	0.475492i	$0.842270\pi$
$644$	−0.133732	+	0.758433i	−0.00526979	+	0.0298865i
$645$	−1.16637	+	6.61484i	−0.0459259	+	0.260459i
$646$	−21.6668	−	18.1806i	−0.852470	−	0.715308i
$647$	−15.0052	−	5.46145i	−0.589916	−	0.214712i	0.0297766	−	0.999557i	$-0.490520\pi$
$647$	−15.0052	−	5.46145i	−0.589916	−	0.214712i	−0.619692	+	0.784845i	$0.712743\pi$
$648$	28.5266	+	10.3828i	1.12063	+	0.407877i
$649$	−10.1382	−	8.50692i	−0.397957	−	0.333926i
$650$	−1.70692	+	9.68042i	−0.0669509	+	0.379697i
$651$	1.61081	−	9.13538i	0.0631328	−	0.358044i
$652$	−1.03343	−	1.78996i	−0.0404724	−	0.0701002i
$653$	0.0996702	−	0.0836332i	0.00390040	−	0.00327282i	−0.640835	−	0.767678i	$-0.721412\pi$
$653$	0.0996702	−	0.0836332i	0.00390040	−	0.00327282i	0.644736	+	0.764406i	$0.276967\pi$
$654$	−7.29086	+	2.65366i	−0.285095	+	0.103766i
$655$	−6.50774	+	11.2717i	−0.254278	+	0.440423i
$656$	1.28905	+	2.23270i	0.0503289	+	0.0871722i
$657$	2.92262	+	2.45237i	0.114022	+	0.0956760i
$658$	−0.125667	+	0.217662i	−0.00489902	+	0.00848535i
$659$	−4.27925	−	24.2688i	−0.166696	−	0.945379i	−0.947299	−	0.320352i	$-0.896199\pi$
$659$	−4.27925	−	24.2688i	−0.166696	−	0.945379i	0.780603	−	0.625027i	$-0.214912\pi$
$660$	3.00000			0.116775
$661$	5.06402	+	28.7195i	0.196967	+	1.11706i	0.909589	+	0.415509i	$0.136397\pi$
$661$	5.06402	+	28.7195i	0.196967	+	1.11706i	−0.712622	+	0.701549i	$0.752492\pi$
$662$	−15.5866	+	13.0787i	−0.605789	+	0.508317i
$663$	15.6951	+	5.71253i	0.609546	+	0.221856i
$664$	38.8002	−	14.1221i	1.50574	−	0.548045i
$665$	−5.06418			−0.196380
$666$	−4.16637	−	1.28698i	−0.161444	−	0.0498696i
$667$	11.7487			0.454910
$668$	−1.35070	+	0.491615i	−0.0522601	+	0.0190211i
$669$	18.9915	+	6.91236i	0.734256	+	0.267247i
$670$	−1.35954	+	1.14079i	−0.0525235	+	0.0440724i
$671$	2.43242	+	13.7949i	0.0939025	+	0.532547i
$672$	1.36009			0.0524666
$673$	−8.14496	−	46.1924i	−0.313965	−	1.78059i	−0.577964	−	0.816062i	$-0.696153\pi$
$673$	−8.14496	−	46.1924i	−0.313965	−	1.78059i	0.263999	−	0.964523i	$-0.414959\pi$
$674$	−9.41669	+	16.3102i	−0.362717	+	0.628245i
$675$	11.3157	+	9.49498i	0.435541	+	0.365462i
$676$	−0.716252	−	1.24059i	−0.0275482	−	0.0477148i
$677$	19.3089	−	33.4439i	0.742100	−	1.28535i	−0.209437	−	0.977822i	$-0.567163\pi$
$677$	19.3089	−	33.4439i	0.742100	−	1.28535i	0.951537	−	0.307533i	$-0.0995034\pi$
$678$	37.3803	−	13.6053i	1.43558	−	0.522509i
$679$	−1.34318	+	1.12706i	−0.0515464	+	0.0432526i
$680$	−7.69253	−	13.3239i	−0.294995	−	0.510947i
$681$	−0.303186	+	1.71945i	−0.0116181	+	0.0658895i
$682$	−10.6591	+	60.4508i	−0.408158	+	2.31478i
$683$	10.8701	+	9.12106i	0.415931	+	0.349008i	0.826613	−	0.562771i	$-0.190265\pi$
$683$	10.8701	+	9.12106i	0.415931	+	0.349008i	−0.410682	+	0.911779i	$0.634709\pi$
$684$	0.500000	+	0.181985i	0.0191180	+	0.00695837i
$685$	6.79813	+	2.47432i	0.259743	+	0.0945388i
$686$	−9.69047	−	8.13127i	−0.369984	−	0.310453i
$687$	8.66385	−	49.1351i	0.330546	−	1.87462i
$688$	1.65657	−	9.39490i	0.0631563	−	0.358177i
$689$	6.10829	+	10.5799i	0.232707	+	0.403061i
$690$	15.6800	−	13.1571i	0.596929	−	0.500883i
$691$	2.53936	−	0.924252i	0.0966019	−	0.0351602i	−0.293267	−	0.956031i	$-0.594743\pi$
$691$	2.53936	−	0.924252i	0.0966019	−	0.0351602i	0.389869	+	0.920870i	$0.372520\pi$
$692$	−1.54142	+	2.66982i	−0.0585961	+	0.101491i
$693$	−1.18479	−	2.05212i	−0.0450065	−	0.0779536i
$694$	−3.94562	−	3.31077i	−0.149774	−	0.125675i
$695$	0.615400	−	1.06590i	0.0233435	−	0.0404321i
$696$	−1.88103	−	10.6679i	−0.0713004	−	0.404365i
$697$	2.78106			0.105340
$698$	−4.15817	−	23.5821i	−0.157389	−	0.892597i
$699$	−5.81908	+	4.88279i	−0.220098	+	0.184684i
$700$	0.384133	+	0.139813i	0.0145189	+	0.00528443i
$701$	7.82800	−	2.84916i	0.295660	−	0.107611i	−0.189932	−	0.981797i	$-0.560827\pi$
$701$	7.82800	−	2.84916i	0.295660	−	0.107611i	0.485591	+	0.874186i	$0.338604\pi$
$702$	−14.3155			−0.540304
$703$	31.4504	+	9.71497i	1.18618	+	0.366407i
$704$	−55.1147			−2.07721
$705$	−0.639033	+	0.232589i	−0.0240674	+	0.00875981i
$706$	−5.92855	−	2.15782i	−0.223124	−	0.0812104i
$707$	3.60401	−	3.02412i	0.135543	−	0.113734i
$708$	−0.124485	−	0.705990i	−0.00467844	−	0.0265327i
$709$	−6.95399			−0.261163			−0.130581	−	0.991438i	$-0.541684\pi$
$709$	−6.95399			−0.261163			−0.130581	+	0.991438i	$0.541684\pi$
$710$	2.28249	+	12.9446i	0.0856603	+	0.485804i
$711$	−3.13041	+	5.42204i	−0.117400	+	0.203342i
$712$	−6.31521	−	5.29909i	−0.236672	−	0.198592i
$713$	−21.3182	−	36.9242i	−0.798373	−	1.38282i
$714$	−3.41147	+	5.90885i	−0.127671	+	0.221133i
$715$	−18.5954	+	6.76817i	−0.695428	+	0.253115i
$716$	0.699427	−	0.586889i	0.0261388	−	0.0219331i
$717$	14.3824	+	24.9110i	0.537120	+	0.930319i
$718$	4.12654	−	23.4028i	0.154001	−	0.873385i
$719$	−7.11112	+	40.3292i	−0.265200	+	1.50402i	0.503265	+	0.864132i	$0.332132\pi$
$719$	−7.11112	+	40.3292i	−0.265200	+	1.50402i	−0.768465	+	0.639892i	$0.778979\pi$
$720$	−1.97494	−	1.65717i	−0.0736015	−	0.0617590i
$721$	−6.41653	−	2.33542i	−0.238964	−	0.0869758i
$722$	13.0201	+	4.73892i	0.484557	+	0.176364i
$723$	38.7413	+	32.5078i	1.44080	+	1.20898i
$724$	−0.774252	+	4.39100i	−0.0287749	+	0.163190i
$725$	1.08290	−	6.14144i	0.0402179	−	0.228087i
$726$	38.1168	+	66.0202i	1.41465	+	2.45024i
$727$	7.88010	−	6.61219i	0.292257	−	0.245233i	−0.484856	−	0.874594i	$-0.661128\pi$
$727$	7.88010	−	6.61219i	0.292257	−	0.245233i	0.777113	+	0.629362i	$0.216684\pi$
$728$	−4.40137	+	1.60197i	−0.163126	+	0.0593729i
$729$	−10.3316	+	17.8948i	−0.382651	+	0.662770i
$730$	6.50774	+	11.2717i	0.240862	+	0.417186i
$731$	−7.88326	−	6.61484i	−0.291573	−	0.244659i
$732$	−0.379385	+	0.657115i	−0.0140225	+	0.0242877i
$733$	−3.08822	−	17.5142i	−0.114066	−	0.646901i	−0.987208	−	0.159435i	$-0.949033\pi$
$733$	−3.08822	−	17.5142i	−0.114066	−	0.646901i	0.873142	−	0.487465i	$-0.162078\pi$
$734$	−19.0811			−0.704296
$735$	−2.86571	−	16.2523i	−0.105703	−	0.599474i
$736$	4.78880	−	4.01828i	0.176518	−	0.148116i
$737$	5.89053	+	2.14398i	0.216980	+	0.0789744i
$738$	0.482926	−	0.175771i	0.0177767	−	0.00647021i
$739$	−38.0651			−1.40025			−0.700124	−	0.714021i	$-0.746872\pi$
$739$	−38.0651			−1.40025			−0.700124	+	0.714021i	$0.746872\pi$
$740$	1.20683	+	0.914901i	0.0443641	+	0.0336324i
$741$	−23.2986			−0.855895
$742$	−4.68954	+	1.70685i	−0.172158	+	0.0626605i
$743$	16.1284	+	5.87024i	0.591692	+	0.215358i	0.620473	−	0.784227i	$-0.286940\pi$
$743$	16.1284	+	5.87024i	0.591692	+	0.215358i	−0.0287815	+	0.999586i	$0.509163\pi$
$744$	−30.1143	+	25.2689i	−1.10404	+	0.926402i
$745$	−0.912189	−	5.17328i	−0.0334200	−	0.189534i
$746$	−25.6587			−0.939431
$747$	−1.29607	−	7.35040i	−0.0474209	−	0.268937i
$748$	−2.29813	+	3.98048i	−0.0840281	+	0.145541i
$749$	2.47565	+	2.07732i	0.0904584	+	0.0759036i
$750$	−13.9611	−	24.1813i	−0.509787	−	0.882978i
$751$	16.1702	−	28.0077i	0.590061	−	1.02201i	−0.404163	−	0.914687i	$-0.632437\pi$
$751$	16.1702	−	28.0077i	0.590061	−	1.02201i	0.994224	−	0.107328i	$-0.0342295\pi$
$752$	0.907604	−	0.330341i	0.0330969	−	0.0120463i
$753$	−33.5822	+	28.1788i	−1.22380	+	1.02689i
$754$	3.02182	+	5.23395i	0.110048	+	0.190609i
$755$	−0.388470	+	2.20312i	−0.0141379	+	0.0801799i
$756$	−0.103378	+	0.586289i	−0.00375984	+	0.0213231i
$757$	7.11540	+	5.97053i	0.258614	+	0.217003i	0.762871	−	0.646551i	$-0.223789\pi$
$757$	7.11540	+	5.97053i	0.258614	+	0.217003i	−0.504257	+	0.863554i	$0.668234\pi$
$758$	19.1065	+	6.95421i	0.693981	+	0.252588i
$759$	−67.9377	−	24.7273i	−2.46598	−	0.897544i
$760$	16.4402	+	13.7949i	0.596347	+	0.500395i
$761$	2.18685	−	12.4023i	0.0792733	−	0.449581i	−0.919173	−	0.393855i	$-0.871141\pi$
$761$	2.18685	−	12.4023i	0.0792733	−	0.449581i	0.998446	−	0.0557267i	$-0.0177476\pi$
$762$	6.03983	−	34.2536i	0.218800	−	1.24088i
$763$	−1.06418	−	1.84321i	−0.0385258	−	0.0667287i
$764$	−2.43860	+	2.04623i	−0.0882253	+	0.0740298i
$765$	−2.61334	+	0.951178i	−0.0944855	+	0.0343899i
$766$	6.91921	−	11.9844i	0.250001	−	0.433015i
$767$	2.36437	+	4.09521i	0.0853725	+	0.147869i
$768$	−6.32888	−	5.31056i	−0.228374	−	0.191628i
$769$	−1.92602	+	3.33597i	−0.0694541	+	0.120298i	−0.898661	−	0.438644i	$-0.855459\pi$
$769$	−1.92602	+	3.33597i	−0.0694541	+	0.120298i	0.829207	+	0.558942i	$0.188792\pi$
$770$	−1.40373	−	7.96097i	−0.0505870	−	0.286893i
$771$	5.60132			0.201727
$772$	0.349107	+	1.97989i	0.0125646	+	0.0712577i
$773$	−30.1673	+	25.3134i	−1.08504	+	0.910459i	−0.996330	−	0.0855984i	$-0.972720\pi$
$773$	−30.1673	+	25.3134i	−1.08504	+	0.910459i	−0.0887129	+	0.996057i	$0.528275\pi$
$774$	−1.78699	−	0.650411i	−0.0642320	−	0.0233785i
$775$	−21.2665	+	7.74038i	−0.763916	+	0.278043i
$776$	7.43058			0.266742
$777$	0.990505	−	7.87846i	0.0355342	−	0.282638i
$778$	31.0823			1.11436
$779$	−3.64543	+	1.32683i	−0.130611	+	0.0475385i
$780$	−1.00727	−	0.366618i	−0.0360662	−	0.0131270i
$781$	35.5651	−	29.8427i	1.27262	−	1.06785i
$782$	5.44562	+	30.8837i	0.194735	+	1.10440i
$783$	9.08202			0.324565
$784$	4.07011	+	23.0827i	0.145361	+	0.824383i
$785$	4.60607	−	7.97794i	0.164398	−	0.284745i
$786$	−18.7383	−	15.7233i	−0.668373	−	0.560831i
$787$	19.4342	+	33.6611i	0.692755	+	1.19989i	0.970931	+	0.239358i	$0.0769368\pi$
$787$	19.4342	+	33.6611i	0.692755	+	1.19989i	−0.278176	+	0.960530i	$0.589730\pi$
$788$	0.313396	−	0.542819i	0.0111643	−	0.0193371i
$789$	23.3846	−	8.51130i	0.832514	−	0.303010i
$790$	−16.3617	+	13.7291i	−0.582123	+	0.488459i
$791$	5.45605	+	9.45016i	0.193995	+	0.336009i
$792$	−1.74376	+	9.88933i	−0.0619617	+	0.351402i
$793$	0.869118	−	4.92901i	0.0308633	−	0.175034i
$794$	−20.6620	−	17.3375i	−0.733267	−	0.615284i
$795$	−12.6887	−	4.61830i	−0.450020	−	0.163794i
$796$	2.39646	+	0.872240i	0.0849403	+	0.0309157i
$797$	−18.9971	−	15.9404i	−0.672911	−	0.564639i	0.241015	−	0.970521i	$-0.422520\pi$
$797$	−18.9971	−	15.9404i	−0.672911	−	0.564639i	−0.913925	+	0.405882i	$0.866964\pi$
$798$	1.65270	−	9.37295i	0.0585051	−	0.331799i
$799$	0.180922	−	1.02606i	0.00640057	−	0.0362994i
$800$	−1.65910	−	2.87365i	−0.0586581	−	0.101599i
$801$	−1.14156	+	0.957882i	−0.0403350	+	0.0338451i
$802$	19.2126	−	6.99281i	0.678421	−	0.246925i
$803$	22.9859	−	39.8128i	0.811155	−	1.40496i
$804$	0.169778	+	0.294064i	0.00598760	+	0.0103708i
$805$	4.30129	+	3.60921i	0.151600	+	0.127208i
$806$	10.9663	−	18.9942i	0.386272	−	0.669043i
$807$	−7.47818	−	42.4109i	−0.263244	−	1.49293i
$808$	−19.9377			−0.701405
$809$	−2.95858	−	16.7789i	−0.104018	−	0.589916i	−0.991608	−	0.129281i	$-0.958733\pi$
$809$	−2.95858	−	16.7789i	−0.104018	−	0.589916i	0.887590	−	0.460634i	$-0.152378\pi$
$810$	14.3407	−	12.0333i	0.503882	−	0.422807i
$811$	15.5722	+	5.66783i	0.546815	+	0.199024i	0.600631	−	0.799527i	$-0.294916\pi$
$811$	15.5722	+	5.66783i	0.546815	+	0.199024i	−0.0538160	+	0.998551i	$0.517138\pi$
$812$	0.236177	−	0.0859614i	0.00828819	−	0.00301665i
$813$	41.1729			1.44400
$814$	−6.55438	+	52.1334i	−0.229731	+	1.82728i
$815$	−15.0692			−0.527852
$816$	24.6386	−	8.96773i	0.862524	−	0.313933i
$817$	13.4893	+	4.90971i	0.471932	+	0.171769i
$818$	−3.63563	+	3.05066i	−0.127117	+	0.106664i
$819$	0.147022	+	0.833805i	0.00513737	+	0.0291355i
$820$	−0.178482			−0.00623287
$821$	−0.429892	−	2.43804i	−0.0150033	−	0.0850882i	0.976387	−	0.216030i	$-0.0693110\pi$
$821$	−0.429892	−	2.43804i	−0.0150033	−	0.0850882i	−0.991390	+	0.130942i	$0.958200\pi$
$822$	−6.79813	+	11.7747i	−0.237112	+	0.410690i
$823$	24.0835	+	20.2085i	0.839499	+	0.704423i	0.957451	−	0.288596i	$-0.0931884\pi$
$823$	24.0835	+	20.2085i	0.839499	+	0.704423i	−0.117952	+	0.993019i	$0.537633\pi$
$824$	14.4686	+	25.0604i	0.504038	+	0.873020i
$825$	−19.1878	+	33.2342i	−0.668033	+	1.15707i
$826$	−1.81521	+	0.660681i	−0.0631591	+	0.0229880i
$827$	19.1197	−	16.0434i	0.664858	−	0.557882i	−0.246680	−	0.969097i	$-0.579340\pi$
$827$	19.1197	−	16.0434i	0.664858	−	0.557882i	0.911539	+	0.411214i	$0.134895\pi$
$828$	−0.294978	−	0.510917i	−0.0102512	−	0.0177556i
$829$	−3.05674	+	17.3356i	−0.106165	+	0.602092i	0.884584	+	0.466382i	$0.154443\pi$
$829$	−3.05674	+	17.3356i	−0.106165	+	0.602092i	−0.990749	+	0.135710i	$0.956668\pi$
$830$	4.42152	−	25.0757i	0.153473	−	0.870390i
$831$	16.1853	+	13.5810i	0.561460	+	0.471121i
$832$	18.5052	+	6.73535i	0.641553	+	0.233506i
$833$	23.7592	+	8.64766i	0.823209	+	0.299623i
$834$	1.77197	+	1.48686i	0.0613584	+	0.0514859i
$835$	−1.81979	+	10.3206i	−0.0629765	+	0.357158i
$836$	1.11334	−	6.31407i	0.0385057	−	0.218377i
$837$	−16.4795	−	28.5434i	−0.569616	−	0.986603i
$838$	5.76083	−	4.83391i	0.199005	−	0.166985i
$839$	33.9244	−	12.3475i	1.17120	−	0.426282i	0.318115	−	0.948052i	$-0.396950\pi$
$839$	33.9244	−	12.3475i	1.17120	−	0.426282i	0.853086	+	0.521770i	$0.174728\pi$
$840$	2.58853	−	4.48346i	0.0893126	−	0.154694i
$841$	12.5829	+	21.7942i	0.433893	+	0.751525i
$842$	−10.7358	−	9.00838i	−0.369979	−	0.310449i
$843$	−3.77972	+	6.54666i	−0.130180	+	0.225479i
$844$	−0.263518	−	1.49449i	−0.00907067	−	0.0514423i
$845$	−10.4442			−0.359291
$846$	−0.0334331	−	0.189608i	−0.00114945	−	0.00651887i
$847$	−16.0196	+	13.4420i	−0.550440	+	0.461874i
$848$	18.0214	+	6.55926i	0.618858	+	0.225246i
$849$	−38.3499	+	13.9582i	−1.31616	+	0.479045i
$850$	16.6459			0.570950
$851$	−19.7888	−	30.6660i	−0.678351	−	1.05122i
$852$	2.51485			0.0861574
$853$	−15.6043	+	5.67951i	−0.534281	+	0.194463i	−0.595049	−	0.803689i	$-0.702867\pi$
$853$	−15.6043	+	5.67951i	−0.534281	+	0.194463i	0.0607676	+	0.998152i	$0.480645\pi$
$854$	1.92127	+	0.699287i	0.0657447	+	0.0239291i
$855$	2.97178	−	2.49362i	0.101633	−	0.0852800i
$856$	−2.37820	−	13.4875i	−0.0812853	−	0.460992i
$857$	−37.6255			−1.28526			−0.642631	−	0.766176i	$-0.722157\pi$
$857$	−37.6255			−1.28526			−0.642631	+	0.766176i	$0.722157\pi$
$858$	−6.45811	−	36.6258i	−0.220476	−	1.25038i
$859$	16.6866	−	28.9020i	0.569340	−	0.986125i	−0.427292	−	0.904114i	$-0.640532\pi$
$859$	16.6866	−	28.9020i	0.569340	−	0.986125i	0.996631	−	0.0820113i	$-0.0261344\pi$
$860$	0.505930	+	0.424525i	0.0172521	+	0.0144762i
$861$	0.467911	+	0.810446i	0.0159464	+	0.0276199i
$862$	20.8105	−	36.0448i	0.708807	−	1.22769i
$863$	−30.4761	+	11.0924i	−1.03742	+	0.377590i	−0.803901	−	0.594763i	$-0.797246\pi$
$863$	−30.4761	+	11.0924i	−1.03742	+	0.377590i	−0.233518	+	0.972353i	$0.575024\pi$
$864$	3.70187	−	3.10623i	0.125940	−	0.105676i
$865$	11.2383	+	19.4653i	0.382113	+	0.661840i
$866$	−3.11628	+	17.6733i	−0.105895	+	0.600563i
$867$	−0.636507	+	3.60981i	−0.0216169	+	0.122596i
$868$	−0.698711	−	0.586289i	−0.0237158	−	0.0198999i
$869$	70.8911	+	25.8022i	2.40481	+	0.875281i
$870$	−6.27719	−	2.28471i	−0.212817	−	0.0774589i
$871$	−1.71579	−	1.43972i	−0.0581372	−	0.0487829i
$872$	−1.56624	+	8.88257i	−0.0530395	+	0.300802i
$873$	0.233240	−	1.32277i	0.00789399	−	0.0447690i
$874$	−21.8726	−	37.8844i	−0.739851	−	1.28146i
$875$	5.86753	−	4.92344i	0.198359	−	0.166443i
$876$	2.34002	−	0.851698i	0.0790620	−	0.0287762i
$877$	−18.2187	+	31.5557i	−0.615202	+	1.06556i	0.375148	+	0.926965i	$0.377592\pi$
$877$	−18.2187	+	31.5557i	−0.615202	+	1.06556i	−0.990349	+	0.138595i	$0.955741\pi$
$878$	−16.9127	−	29.2936i	−0.570774	−	0.988610i
$879$	33.1391	+	27.8070i	1.11775	+	0.937907i
$880$	−15.5326	+	26.9032i	−0.523602	+	0.906906i
$881$	6.79396	+	38.5305i	0.228894	+	1.29812i	0.855099	+	0.518465i	$0.173496\pi$
$881$	6.79396	+	38.5305i	0.228894	+	1.29812i	−0.626205	+	0.779659i	$0.715393\pi$
$882$	4.67230			0.157325
$883$	−7.40208	−	41.9793i	−0.249100	−	1.41272i	−0.810775	−	0.585358i	$-0.800954\pi$
$883$	−7.40208	−	41.9793i	−0.249100	−	1.41272i	0.561675	−	0.827358i	$-0.310157\pi$
$884$	1.25806	−	1.05563i	0.0423130	−	0.0355048i
$885$	−4.91147	−	1.78763i	−0.165097	−	0.0600905i
$886$	36.5107	−	13.2888i	1.22660	−	0.446447i
$887$	−24.6973			−0.829254			−0.414627	−	0.909992i	$-0.636088\pi$
$887$	−24.6973			−0.829254			−0.414627	+	0.909992i	$0.636088\pi$
$888$	−24.6766	+	22.8782i	−0.828094	+	0.767742i
$889$	9.54126			0.320004
$890$	−4.77719	+	1.73875i	−0.160132	+	0.0582832i
$891$	−62.1348	−	22.6152i	−2.08159	−	0.757638i
$892$	1.52229	−	1.27735i	0.0509700	−	0.0427689i
$893$	0.252374	+	1.43128i	0.00844537	+	0.0478961i
$894$	9.87258			0.330188
$895$	−1.15595	−	6.55569i	−0.0386390	−	0.219133i
$896$	−3.29860	+	5.71334i	−0.110198	+	0.190869i
$897$	19.7888	+	16.6048i	0.660729	+	0.554417i
$898$	−10.1980	−	17.6634i	−0.340312	−	0.589437i
$899$	−6.95723	+	12.0503i	−0.232037	+	0.401899i
$900$	−0.294263	+	0.107103i	−0.00980876	+	0.00357010i
$901$	15.8478	−	13.2979i	0.527966	−	0.443016i
$902$	−3.09627	−	5.36289i	−0.103094	−	0.178565i
$903$	0.601319	−	3.41025i	0.0200106	−	0.113486i
$904$	8.03012	−	45.5410i	0.267078	−	1.51467i
$905$	24.9026	+	20.8958i	0.827791	+	0.694599i
$906$	−3.95084	−	1.43799i	−0.131258	−	0.0477739i
$907$	−9.36736	−	3.40944i	−0.311038	−	0.113209i	0.181785	−	0.983338i	$-0.441813\pi$
$907$	−9.36736	−	3.40944i	−0.311038	−	0.113209i	−0.492823	+	0.870130i	$0.664035\pi$
$908$	0.131511	+	0.110351i	0.00436434	+	0.00366211i
$909$	−0.625829	+	3.54925i	−0.0207574	+	0.117721i
$910$	−0.501563	+	2.84450i	−0.0166266	+	0.0942944i
$911$	8.91834	+	15.4470i	0.295478	+	0.511782i	0.975096	−	0.221784i	$-0.0711879\pi$
$911$	8.91834	+	15.4470i	0.295478	+	0.511782i	−0.679618	+	0.733566i	$0.737855\pi$
$912$	−28.0180	+	23.5099i	−0.927769	+	0.778491i
$913$	−84.5121	+	30.7599i	−2.79694	+	1.01800i
$914$	−20.1634	+	34.9241i	−0.666947	+	1.15519i
$915$	2.76604	+	4.79093i	0.0914426	+	0.158383i
$916$	−3.75806	−	3.15338i	−0.124170	−	0.104191i
$917$	3.35504	−	5.81109i	0.110793	−	0.191899i
$918$	4.20961	+	23.8739i	0.138938	+	0.787955i
$919$	−33.5689			−1.10734			−0.553668	−	0.832737i	$-0.686772\pi$
$919$	−33.5689			−1.10734			−0.553668	+	0.832737i	$0.686772\pi$
$920$	−4.13198	−	23.4336i	−0.136227	−	0.772583i
$921$	9.84002	−	8.25676i	0.324240	−	0.272069i
$922$	−49.0565	−	17.8551i	−1.61559	−	0.588027i
$923$	−15.5882	+	5.67365i	−0.513093	+	0.186750i
$924$	−1.54664			−0.0508806
$925$	−17.8542	+	7.51774i	−0.587041	+	0.247182i
$926$	9.76651			0.320947
$927$	4.91534	−	1.78904i	0.161441	−	0.0587598i
$928$	−1.91710	−	0.697767i	−0.0629319	−	0.0229053i
$929$	7.69434	−	6.45632i	0.252443	−	0.211825i	−0.507780	−	0.861487i	$-0.669534\pi$
$929$	7.69434	−	6.45632i	0.252443	−	0.211825i	0.760224	+	0.649662i	$0.225089\pi$
$930$	4.20961	+	23.8739i	0.138038	+	0.782855i
$931$	−35.2695			−1.15591
$932$	0.129700	+	0.735564i	0.00424846	+	0.0240942i
$933$	1.44697	−	2.50622i	0.0473716	−	0.0820499i
$934$	−5.19569	−	4.35970i	−0.170008	−	0.142654i
$935$	16.7554	+	29.0211i	0.547959	+	0.949093i
$936$	1.79401	−	3.10732i	0.0586392	−	0.101566i
$937$	52.7893	−	19.2137i	1.72455	−	0.627685i	0.726331	−	0.687345i	$-0.241224\pi$
$937$	52.7893	−	19.2137i	1.72455	−	0.627685i	0.998219	+	0.0596597i	$0.0190016\pi$
$938$	0.700903	−	0.588127i	0.0228853	−	0.0192030i
$939$	−20.5398	−	35.5760i	−0.670292	−	1.16098i
$940$	−0.0116112	+	0.0658503i	−0.000378715	+	0.00214780i
$941$	4.44238	−	25.1940i	0.144817	−	0.821301i	−0.822696	−	0.568481i	$-0.807531\pi$
$941$	4.44238	−	25.1940i	0.144817	−	0.821301i	0.967514	−	0.252819i	$-0.0813578\pi$
$942$	13.2626	+	11.1287i	0.432120	+	0.362592i
$943$	4.04189	+	1.47113i	0.131622	+	0.0479065i
$944$	6.97565	+	2.53893i	0.227038	+	0.0826351i
$945$	3.32501	+	2.79001i	0.108163	+	0.0907591i
$946$	−3.97906	+	22.5663i	−0.129370	+	0.733695i
$947$	−4.46275	+	25.3095i	−0.145020	+	0.822449i	0.822331	+	0.569009i	$0.192673\pi$
$947$	−4.46275	+	25.3095i	−0.145020	+	0.822449i	−0.967351	+	0.253440i	$0.918438\pi$
$948$	2.04323	+	3.53898i	0.0663611	+	0.114941i
$949$	−12.5831	+	10.5584i	−0.408464	+	0.342742i
$950$	−21.8195	+	7.94166i	−0.707920	+	0.257662i
$951$	25.5929	−	44.3281i	0.829905	−	1.43744i
$952$	3.96585	+	6.86906i	0.128534	+	0.222627i
$953$	−3.14471	−	2.63873i	−0.101867	−	0.0854768i	0.590432	−	0.807088i	$-0.298958\pi$
$953$	−3.14471	−	2.63873i	−0.101867	−	0.0854768i	−0.692299	+	0.721611i	$0.743402\pi$
$954$	1.91147	−	3.31077i	0.0618863	−	0.107190i
$955$	4.03028	+	22.8568i	0.130417	+	0.739630i
$956$	2.82832			0.0914746
$957$	4.09714	+	23.2361i	0.132442	+	0.751115i
$958$	−2.95580	+	2.48021i	−0.0954977	+	0.0801321i
$959$	−3.50475	−	1.27562i	−0.113174	−	0.0411920i
$960$	−20.4538	+	7.44459i	−0.660145	+	0.240273i
$961$	19.4962			0.628909
$962$	8.57170	−	16.7032i	0.276363	−	0.538534i
$963$	−2.47565			−0.0797768
$964$	4.67277	−	1.70075i	0.150500	−	0.0547775i
$965$	13.7738	+	5.01325i	0.443394	+	0.161382i
$966$	−8.08378	+	6.78310i	−0.260091	+	0.218243i
$967$	−9.98457	−	56.6253i	−0.321082	−	1.82095i	−0.535885	−	0.844291i	$-0.680022\pi$
$967$	−9.98457	−	56.6253i	−0.321082	−	1.82095i	0.214803	−	0.976657i	$-0.431089\pi$
$968$	88.6219			2.84841
$969$	6.85117	+	38.8549i	0.220091	+	1.24820i
$970$	2.29111	−	3.96832i	0.0735630	−	0.127415i
$971$	−4.91329	−	4.12274i	−0.157675	−	0.132305i	0.560537	−	0.828129i	$-0.310595\pi$
$971$	−4.91329	−	4.12274i	−0.157675	−	0.132305i	−0.718212	+	0.695824i	$0.755039\pi$
$972$	−0.505215	−	0.875057i	−0.0162048	−	0.0280675i
$973$	−0.317267	+	0.549522i	−0.0101711	+	0.0176169i
$974$	18.2866	−	6.65577i	0.585940	−	0.213265i
$975$	10.5039	−	8.81379i	0.336393	−	0.282267i
$976$	−3.92855	−	6.80445i	−0.125750	−	0.217805i
$977$	8.11381	−	46.0157i	0.259584	−	1.47217i	−0.524443	−	0.851445i	$-0.675726\pi$
$977$	8.11381	−	46.0157i	0.259584	−	1.47217i	0.784027	−	0.620727i	$-0.213162\pi$
$978$	4.91787	−	27.8906i	0.157256	−	0.891844i
$979$	13.7554	+	11.5421i	0.439623	+	0.368888i
$980$	−1.52481	−	0.554987i	−0.0487084	−	0.0177284i
$981$	1.53209	+	0.557635i	0.0489158	+	0.0178039i
$982$	35.4805	+	29.7716i	1.13223	+	0.950051i
$983$	−7.68273	+	43.5709i	−0.245041	+	1.38970i	0.575356	+	0.817903i	$0.304864\pi$
$983$	−7.68273	+	43.5709i	−0.245041	+	1.38970i	−0.820397	+	0.571794i	$0.806248\pi$
$984$	0.688663	−	3.90560i	0.0219538	−	0.124506i
$985$	−2.28493	−	3.95761i	−0.0728039	−	0.126100i
$986$	7.84002	−	6.57856i	0.249677	−	0.209504i
$987$	0.329451	−	0.119910i	0.0104865	−	0.00381679i
$988$	−1.14543	+	1.98394i	−0.0364410	+	0.0631176i
$989$	−7.95811	−	13.7839i	−0.253053	−	0.438301i
$990$	4.74376	+	3.98048i	0.150766	+	0.126508i
$991$	16.7010	−	28.9270i	0.530524	−	0.918895i	−0.468841	−	0.883282i	$-0.655328\pi$
$991$	16.7010	−	28.9270i	0.530524	−	0.918895i	0.999366	−	0.0356128i	$-0.0113383\pi$
$992$	1.28564	+	7.29125i	0.0408193	+	0.231498i
$993$	28.3824			0.900688
$994$	−1.17673	−	6.67355i	−0.0373235	−	0.211672i
$995$	14.2435	−	11.9517i	0.451550	−	0.378895i
$996$	−4.57785	−	1.66620i	−0.145055	−	0.0527956i
$997$	−57.8085	+	21.0406i	−1.83081	+	0.666361i	−0.838150	+	0.545440i	$0.816363\pi$
$997$	−57.8085	+	21.0406i	−1.83081	+	0.666361i	−0.992662	+	0.120922i	$0.961415\pi$
$998$	54.4543			1.72372
$999$	−15.2973	−	23.7056i	−0.483984	−	0.750012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.f.b.7.1	✓	6
3.2	odd	2		333.2.x.a.118.1		6
4.3	odd	2		592.2.bc.c.81.1		6
5.2	odd	4		925.2.bc.b.599.2		12
5.3	odd	4		925.2.bc.b.599.1		12
5.4	even	2		925.2.p.a.451.1		6
37.4	even	18		1369.2.a.l.1.2		3
37.13	odd	36		1369.2.b.e.1368.5		6
37.16	even	9	inner	37.2.f.b.16.1	yes	6
37.24	odd	36		1369.2.b.e.1368.2		6
37.33	even	9		1369.2.a.i.1.2		3
111.53	odd	18		333.2.x.a.127.1		6
148.127	odd	18		592.2.bc.c.497.1		6
185.53	odd	36		925.2.bc.b.349.2		12
185.127	odd	36		925.2.bc.b.349.1		12
185.164	even	18		925.2.p.a.201.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.f.b.7.1	✓	6	1.1	even	1	trivial
37.2.f.b.16.1	yes	6	37.16	even	9	inner
333.2.x.a.118.1		6	3.2	odd	2
333.2.x.a.127.1		6	111.53	odd	18
592.2.bc.c.81.1		6	4.3	odd	2
592.2.bc.c.497.1		6	148.127	odd	18
925.2.p.a.201.1		6	185.164	even	18
925.2.p.a.451.1		6	5.4	even	2
925.2.bc.b.349.1		12	185.127	odd	36
925.2.bc.b.349.2		12	185.53	odd	36
925.2.bc.b.599.1		12	5.3	odd	4
925.2.bc.b.599.2		12	5.2	odd	4
1369.2.a.i.1.2		3	37.33	even	9
1369.2.a.l.1.2		3	37.4	even	18
1369.2.b.e.1368.2		6	37.24	odd	36
1369.2.b.e.1368.5		6	37.13	odd	36

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26604 - 0.460802i) q^{2} +(-1.76604 - 0.642788i) q^{3} +(-0.141559 + 0.118782i) q^{4} +(0.233956 + 1.32683i) q^{5} -2.53209 q^{6} +(-0.120615 - 0.684040i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(0.407604 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(1.26604 - 0.460802i) q^{2} +(-1.76604 - 0.642788i) q^{3} +(-0.141559 + 0.118782i) q^{4} +(0.233956 + 1.32683i) q^{5} -2.53209 q^{6} +(-0.120615 - 0.684040i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(0.407604 + 0.342020i) q^{9} +(0.907604 + 1.57202i) q^{10} +(3.20574 - 5.55250i) q^{11} +(0.326352 - 0.118782i) q^{12} +(-1.75490 + 1.47254i) q^{13} +(-0.467911 - 0.810446i) q^{14} +(0.439693 - 2.49362i) q^{15} +(-0.624485 + 3.54163i) q^{16} +(2.97178 + 2.49362i) q^{17} +(0.673648 + 0.245188i) q^{18} +(-5.08512 - 1.85083i) q^{19} +(-0.190722 - 0.160035i) q^{20} +(-0.226682 + 1.28558i) q^{21} +(1.50000 - 8.50692i) q^{22} +(3.00000 + 5.19615i) q^{23} +(4.23783 - 3.55596i) q^{24} +(2.99273 - 1.08926i) q^{25} +(-1.54323 + 2.67296i) q^{26} +(2.31908 + 4.01676i) q^{27} +(0.0983261 + 0.0825054i) q^{28} +(0.979055 - 1.69577i) q^{29} +(-0.592396 - 3.35965i) q^{30} -7.10607 q^{31} +(-0.180922 - 1.02606i) q^{32} +(-9.23055 + 7.74535i) q^{33} +(4.91147 + 1.78763i) q^{34} +(0.879385 - 0.320070i) q^{35} -0.0983261 q^{36} +(-6.07532 + 0.300767i) q^{37} -7.29086 q^{38} +(4.04576 - 1.47254i) q^{39} +(-3.72668 - 1.35640i) q^{40} +(0.549163 - 0.460802i) q^{41} +(0.305407 + 1.73205i) q^{42} -2.65270 q^{43} +(0.205737 + 1.16679i) q^{44} +(-0.358441 + 0.620838i) q^{45} +(6.19253 + 5.19615i) q^{46} +(-0.134285 - 0.232589i) q^{47} +(3.37939 - 5.85327i) q^{48} +(6.12449 - 2.22913i) q^{49} +(3.28699 - 2.75811i) q^{50} +(-3.64543 - 6.31407i) q^{51} +(0.0735111 - 0.416902i) q^{52} +(0.926022 - 5.25173i) q^{53} +(4.78699 + 4.01676i) q^{54} +(8.11721 + 2.95442i) q^{55} +(1.92127 + 0.699287i) q^{56} +(7.79086 + 6.53731i) q^{57} +(0.458111 - 2.59808i) q^{58} +(0.358441 - 2.03282i) q^{59} +(0.233956 + 0.405223i) q^{60} +(-1.67365 + 1.40436i) q^{61} +(-8.99660 + 3.27449i) q^{62} +(0.184793 - 0.320070i) q^{63} +(-4.29813 - 7.44459i) q^{64} +(-2.36437 - 1.98394i) q^{65} +(-8.11721 + 14.0594i) q^{66} +(0.169778 + 0.962858i) q^{67} -0.716881 q^{68} +(-1.95811 - 11.1050i) q^{69} +(0.965852 - 0.810446i) q^{70} +(6.80453 + 2.47665i) q^{71} +(-1.47178 + 0.535685i) q^{72} +7.17024 q^{73} +(-7.55303 + 3.18031i) q^{74} -5.98545 q^{75} +(0.939693 - 0.342020i) q^{76} +(-4.18479 - 1.52314i) q^{77} +(4.44356 - 3.72859i) q^{78} +(2.04323 + 11.5878i) q^{79} -4.84524 q^{80} +(-1.79086 - 10.1565i) q^{81} +(0.482926 - 0.836452i) q^{82} +(-10.7456 - 9.01660i) q^{83} +(-0.120615 - 0.208911i) q^{84} +(-2.61334 + 4.52644i) q^{85} +(-3.35844 + 1.22237i) q^{86} +(-2.81908 + 2.36549i) q^{87} +(9.43629 + 16.3441i) q^{88} +(-0.486329 + 2.75811i) q^{89} +(-0.167718 + 0.951178i) q^{90} +(1.21894 + 1.02281i) q^{91} +(-1.04189 - 0.379217i) q^{92} +(12.5496 + 4.56769i) q^{93} +(-0.277189 - 0.232589i) q^{94} +(1.26604 - 7.18009i) q^{95} +(-0.340022 + 1.92836i) q^{96} +(-1.26217 - 2.18615i) q^{97} +(6.72668 - 5.64436i) q^{98} +(3.20574 - 1.16679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 6 q^{9} + 9 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} - 12 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} - 9 q^{19} - 21 q^{20} + 12 q^{21} + 9 q^{22} + 18 q^{23} + 6 q^{24} + 6 q^{26} - 3 q^{27} + 24 q^{28} + 9 q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{33} + 9 q^{34} - 6 q^{35} - 24 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} - 9 q^{40} + 15 q^{41} + 6 q^{42} - 18 q^{43} - 9 q^{44} + 6 q^{45} - 18 q^{46} + 9 q^{47} + 9 q^{48} + 24 q^{49} + 12 q^{50} - 6 q^{51} + 51 q^{52} + 21 q^{53} + 21 q^{54} + 18 q^{55} - 6 q^{56} + 15 q^{57} + 9 q^{58} - 6 q^{59} + 6 q^{60} - 9 q^{61} - 12 q^{62} - 6 q^{63} - 12 q^{64} - 33 q^{65} - 18 q^{66} + 24 q^{67} + 12 q^{68} - 18 q^{69} - 36 q^{70} - 12 q^{71} + 6 q^{72} - 33 q^{74} - 18 q^{77} - 3 q^{78} - 3 q^{79} + 24 q^{80} + 21 q^{81} - 18 q^{82} + 3 q^{83} - 12 q^{84} - 9 q^{85} - 12 q^{86} + 9 q^{88} - 24 q^{89} + 27 q^{90} + 42 q^{91} + 21 q^{93} + 9 q^{94} + 3 q^{95} + 18 q^{96} - 27 q^{97} + 27 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 6 * q^9 + 9 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 - 12 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 3 * q^18 - 9 * q^19 - 21 * q^20 + 12 * q^21 + 9 * q^22 + 18 * q^23 + 6 * q^24 + 6 * q^26 - 3 * q^27 + 24 * q^28 + 9 * q^29 - 18 * q^31 - 18 * q^32 - 18 * q^33 + 9 * q^34 - 6 * q^35 - 24 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 - 9 * q^40 + 15 * q^41 + 6 * q^42 - 18 * q^43 - 9 * q^44 + 6 * q^45 - 18 * q^46 + 9 * q^47 + 9 * q^48 + 24 * q^49 + 12 * q^50 - 6 * q^51 + 51 * q^52 + 21 * q^53 + 21 * q^54 + 18 * q^55 - 6 * q^56 + 15 * q^57 + 9 * q^58 - 6 * q^59 + 6 * q^60 - 9 * q^61 - 12 * q^62 - 6 * q^63 - 12 * q^64 - 33 * q^65 - 18 * q^66 + 24 * q^67 + 12 * q^68 - 18 * q^69 - 36 * q^70 - 12 * q^71 + 6 * q^72 - 33 * q^74 - 18 * q^77 - 3 * q^78 - 3 * q^79 + 24 * q^80 + 21 * q^81 - 18 * q^82 + 3 * q^83 - 12 * q^84 - 9 * q^85 - 12 * q^86 + 9 * q^88 - 24 * q^89 + 27 * q^90 + 42 * q^91 + 21 * q^93 + 9 * q^94 + 3 * q^95 + 18 * q^96 - 27 * q^97 + 27 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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