LMFDB - Embedded newform 637.2.bl.a.235.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			235.17
Character	$\chi$	$=$	637.235
Dual form			637.2.bl.a.534.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.893058 + 0.134607i) q^{2} +(1.14821 - 0.782835i) q^{3} +(-1.13171 - 0.349087i) q^{4} +(0.316529 + 4.22378i) q^{5} +(1.13079 - 0.544561i) q^{6} +(-2.63452 - 0.243568i) q^{7} +(-2.59111 - 1.24781i) q^{8} +(-0.390471 + 0.994905i) q^{9} +O(q^{10})$	\(q+(0.893058 + 0.134607i) q^{2} +(1.14821 - 0.782835i) q^{3} +(-1.13171 - 0.349087i) q^{4} +(0.316529 + 4.22378i) q^{5} +(1.13079 - 0.544561i) q^{6} +(-2.63452 - 0.243568i) q^{7} +(-2.59111 - 1.24781i) q^{8} +(-0.390471 + 0.994905i) q^{9} +(-0.285872 + 3.81469i) q^{10} +(0.753267 + 1.91929i) q^{11} +(-1.57272 + 0.485119i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(-2.31999 - 0.572145i) q^{14} +(3.66997 + 4.60199i) q^{15} +(-0.188970 - 0.128837i) q^{16} +(-3.82770 - 3.55159i) q^{17} +(-0.482635 + 0.835948i) q^{18} +(3.24603 + 5.62229i) q^{19} +(1.11625 - 4.89060i) q^{20} +(-3.21565 + 1.78272i) q^{21} +(0.414361 + 1.81543i) q^{22} +(0.00756129 - 0.00701585i) q^{23} +(-3.95196 + 0.595662i) q^{24} +(-12.7960 + 1.92869i) q^{25} +(-0.662053 + 0.614295i) q^{26} +(1.25820 + 5.51255i) q^{27} +(2.89649 + 1.19532i) q^{28} +(-1.28924 + 5.64854i) q^{29} +(2.65804 + 4.60385i) q^{30} +(4.56139 - 7.90056i) q^{31} +(4.06497 + 3.77174i) q^{32} +(2.36740 + 1.61406i) q^{33} +(-2.94029 - 3.68701i) q^{34} +(0.194880 - 11.2047i) q^{35} +(0.789209 - 0.989637i) q^{36} +(2.37047 - 0.731193i) q^{37} +(2.14210 + 5.45797i) q^{38} +(-0.103851 + 1.38580i) q^{39} +(4.45033 - 11.3392i) q^{40} +(2.45238 + 1.18101i) q^{41} +(-3.11173 + 1.15923i) q^{42} +(2.44739 - 1.17860i) q^{43} +(-0.182481 - 2.43504i) q^{44} +(-4.32586 - 1.33435i) q^{45} +(0.00769705 - 0.00524776i) q^{46} +(-1.39673 - 0.210523i) q^{47} -0.317835 q^{48} +(6.88135 + 1.28337i) q^{49} -11.6872 q^{50} +(-7.17530 - 1.08150i) q^{51} +(0.978538 - 0.667156i) q^{52} +(-6.50779 - 2.00739i) q^{53} +(0.381622 + 5.09239i) q^{54} +(-7.86825 + 3.78915i) q^{55} +(6.52239 + 3.91849i) q^{56} +(8.12845 + 3.91445i) q^{57} +(-1.91170 + 4.87094i) q^{58} +(-0.315554 + 4.21078i) q^{59} +(-2.54685 - 6.48927i) q^{60} +(11.5990 - 3.57782i) q^{61} +(5.13706 - 6.44167i) q^{62} +(1.27103 - 2.52599i) q^{63} +(3.40775 + 4.27318i) q^{64} +(-3.49964 - 2.38601i) q^{65} +(1.89696 + 1.76012i) q^{66} +(5.71508 - 9.89880i) q^{67} +(3.09204 + 5.35557i) q^{68} +(0.00318968 - 0.0139749i) q^{69} +(1.68227 - 9.98024i) q^{70} +(2.48837 + 10.9023i) q^{71} +(2.25321 - 2.09067i) q^{72} +(2.16716 - 0.326646i) q^{73} +(2.21539 - 0.333916i) q^{74} +(-13.1826 + 12.2317i) q^{75} +(-1.71090 - 7.49596i) q^{76} +(-1.51701 - 5.23988i) q^{77} +(-0.279283 + 1.22362i) q^{78} +(6.68721 + 11.5826i) q^{79} +(0.484366 - 0.838947i) q^{80} +(3.40967 + 3.16371i) q^{81} +(2.03115 + 1.38481i) q^{82} +(-8.35688 - 10.4792i) q^{83} +(4.26151 - 0.894990i) q^{84} +(13.7896 - 17.2916i) q^{85} +(2.34431 - 0.723124i) q^{86} +(2.94156 + 7.49497i) q^{87} +(0.443120 - 5.91303i) q^{88} +(-0.898896 + 2.29035i) q^{89} +(-3.68363 - 1.77394i) q^{90} +(1.83302 - 1.90789i) q^{91} +(-0.0110063 + 0.00530037i) q^{92} +(-0.947410 - 12.6423i) q^{93} +(-1.21902 - 0.376019i) q^{94} +(-22.7199 + 15.4902i) q^{95} +(7.62008 + 1.14854i) q^{96} -13.2600 q^{97} +(5.97269 + 2.07240i) q^{98} -2.20364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	0.893058	+	0.134607i	0.631487	+	0.0951814i	0.456984	−	0.889475i	$-0.348930\pi$
$2$	0.893058	+	0.134607i	0.631487	+	0.0951814i	0.174504	+	0.984657i	$0.444168\pi$
$3$	1.14821	−	0.782835i	0.662919	−	0.451970i	−0.184545	−	0.982824i	$-0.559081\pi$
$3$	1.14821	−	0.782835i	0.662919	−	0.451970i	0.847463	+	0.530854i	$0.178129\pi$
$4$	−1.13171	−	0.349087i	−0.565856	−	0.174543i
$5$	0.316529	+	4.22378i	0.141556	+	1.88893i	0.390775	+	0.920486i	$0.372207\pi$
$5$	0.316529	+	4.22378i	0.141556	+	1.88893i	−0.249219	+	0.968447i	$0.580174\pi$
$6$	1.13079	−	0.544561i	0.461644	−	0.222316i
$7$	−2.63452	−	0.243568i	−0.995753	−	0.0920602i
$7$	−2.63452	−	0.243568i	−0.995753	−	0.0920602i
$8$	−2.59111	−	1.24781i	−0.916095	−	0.441168i
$9$	−0.390471	+	0.994905i	−0.130157	+	0.331635i
$10$	−0.285872	+	3.81469i	−0.0904005	+	1.20631i
$11$	0.753267	+	1.91929i	0.227118	+	0.578688i	0.998322	−	0.0578997i	$-0.0184404\pi$
$11$	0.753267	+	1.91929i	0.227118	+	0.578688i	−0.771204	+	0.636588i	$0.780345\pi$
$12$	−1.57272	+	0.485119i	−0.454005	+	0.140042i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$14$	−2.31999	−	0.572145i	−0.620043	−	0.152912i
$15$	3.66997	+	4.60199i	0.947582	+	1.18823i
$16$	−0.188970	−	0.128837i	−0.0472424	−	0.0322093i
$17$	−3.82770	−	3.55159i	−0.928353	−	0.861386i	0.0622628	−	0.998060i	$-0.480168\pi$
$17$	−3.82770	−	3.55159i	−0.928353	−	0.861386i	−0.990616	+	0.136674i	$0.956359\pi$
$18$	−0.482635	+	0.835948i	−0.113758	+	0.197035i
$19$	3.24603	+	5.62229i	0.744691	+	1.28984i	0.950339	+	0.311216i	$0.100736\pi$
$19$	3.24603	+	5.62229i	0.744691	+	1.28984i	−0.205649	+	0.978626i	$0.565930\pi$
$20$	1.11625	−	4.89060i	0.249601	−	1.09357i
$21$	−3.21565	+	1.78272i	−0.701712	+	0.389022i
$22$	0.414361	+	1.81543i	0.0883421	+	0.387052i
$23$	0.00756129	−	0.00701585i	0.00157664	−	0.00146291i	−0.679384	−	0.733783i	$-0.737753\pi$
$23$	0.00756129	−	0.00701585i	0.00157664	−	0.00146291i	0.680961	+	0.732320i	$0.261562\pi$
$24$	−3.95196	+	0.595662i	−0.806691	+	0.121589i
$25$	−12.7960	+	1.92869i	−2.55920	+	0.385737i
$26$	−0.662053	+	0.614295i	−0.129839	+	0.120473i
$27$	1.25820	+	5.51255i	0.242141	+	1.06089i
$28$	2.89649	+	1.19532i	0.547384	+	0.225895i
$29$	−1.28924	+	5.64854i	−0.239406	+	1.04891i	0.702144	+	0.712035i	$0.252226\pi$
$29$	−1.28924	+	5.64854i	−0.239406	+	1.04891i	−0.941550	+	0.336873i	$0.890631\pi$
$30$	2.65804	+	4.60385i	0.485289	+	0.840544i
$31$	4.56139	−	7.90056i	0.819250	−	1.41898i	−0.0869854	−	0.996210i	$-0.527723\pi$
$31$	4.56139	−	7.90056i	0.819250	−	1.41898i	0.906235	−	0.422773i	$-0.138943\pi$
$32$	4.06497	+	3.77174i	0.718591	+	0.666755i
$33$	2.36740	+	1.61406i	0.412111	+	0.280973i
$34$	−2.94029	−	3.68701i	−0.504256	−	0.632316i
$35$	0.194880	−	11.2047i	0.0329407	−	1.89394i
$36$	0.789209	−	0.989637i	0.131535	−	0.164940i
$37$	2.37047	−	0.731193i	0.389703	−	0.120207i	−0.0937109	−	0.995599i	$-0.529873\pi$
$37$	2.37047	−	0.731193i	0.389703	−	0.120207i	0.483414	+	0.875392i	$0.339397\pi$
$38$	2.14210	+	5.45797i	0.347494	+	0.885400i
$39$	−0.103851	+	1.38580i	−0.0166295	+	0.221905i
$40$	4.45033	−	11.3392i	0.703658	−	1.79289i
$41$	2.45238	+	1.18101i	0.382998	+	0.184442i	0.615469	−	0.788161i	$-0.288967\pi$
$41$	2.45238	+	1.18101i	0.382998	+	0.184442i	−0.232471	+	0.972603i	$0.574681\pi$
$42$	−3.11173	+	1.15923i	−0.480150	+	0.178873i
$43$	2.44739	−	1.17860i	0.373224	−	0.179735i	−0.237863	−	0.971299i	$-0.576447\pi$
$43$	2.44739	−	1.17860i	0.373224	−	0.179735i	0.611087	+	0.791564i	$0.290733\pi$
$44$	−0.182481	−	2.43504i	−0.0275101	−	0.367096i
$45$	−4.32586	−	1.33435i	−0.644861	−	0.198913i
$46$	0.00769705	−	0.00524776i	0.00113487	−	0.000773740i
$47$	−1.39673	−	0.210523i	−0.203734	−	0.0307079i	0.0463823	−	0.998924i	$-0.485231\pi$
$47$	−1.39673	−	0.210523i	−0.203734	−	0.0307079i	−0.250116	+	0.968216i	$0.580469\pi$
$48$	−0.317835			−0.0458755
$49$	6.88135	+	1.28337i	0.983050	+	0.183339i
$50$	−11.6872			−1.65282
$51$	−7.17530	−	1.08150i	−1.00474	−	0.151441i
$52$	0.978538	−	0.667156i	0.135699	−	0.0925179i
$53$	−6.50779	−	2.00739i	−0.893913	−	0.275736i	−0.186432	−	0.982468i	$-0.559692\pi$
$53$	−6.50779	−	2.00739i	−0.893913	−	0.275736i	−0.707481	+	0.706732i	$0.750169\pi$
$54$	0.381622	+	5.09239i	0.0519322	+	0.692987i
$55$	−7.86825	+	3.78915i	−1.06095	+	0.510929i
$56$	6.52239	+	3.91849i	0.871590	+	0.523630i
$57$	8.12845	+	3.91445i	1.07664	+	0.518482i
$58$	−1.91170	+	4.87094i	−0.251019	+	0.639585i
$59$	−0.315554	+	4.21078i	−0.0410816	+	0.548196i	0.938253	+	0.345950i	$0.112443\pi$
$59$	−0.315554	+	4.21078i	−0.0410816	+	0.548196i	−0.979335	+	0.202247i	$0.935176\pi$
$60$	−2.54685	−	6.48927i	−0.328797	−	0.837761i
$61$	11.5990	−	3.57782i	1.48510	−	0.458093i	0.557028	−	0.830493i	$-0.311941\pi$
$61$	11.5990	−	3.57782i	1.48510	−	0.458093i	0.928072	+	0.372401i	$0.121465\pi$
$62$	5.13706	−	6.44167i	0.652407	−	0.818092i
$63$	1.27103	−	2.52599i	0.160135	−	0.318244i
$64$	3.40775	+	4.27318i	0.425968	+	0.534147i
$65$	−3.49964	−	2.38601i	−0.434077	−	0.295949i
$66$	1.89696	+	1.76012i	0.233500	+	0.216656i
$67$	5.71508	−	9.89880i	0.698208	−	1.20933i	−0.270879	−	0.962613i	$-0.587314\pi$
$67$	5.71508	−	9.89880i	0.698208	−	1.20933i	0.969087	−	0.246718i	$-0.0793522\pi$
$68$	3.09204	+	5.35557i	0.374965	+	0.649458i
$69$	0.00318968	−	0.0139749i	0.000383992	−	0.00168238i
$70$	1.68227	−	9.98024i	0.201070	−	1.19287i
$71$	2.48837	+	10.9023i	0.295315	+	1.29386i	0.877018	+	0.480458i	$0.159530\pi$
$71$	2.48837	+	10.9023i	0.295315	+	1.29386i	−0.581703	+	0.813401i	$0.697613\pi$
$72$	2.25321	−	2.09067i	0.265543	−	0.246388i
$73$	2.16716	−	0.326646i	0.253646	−	0.0382310i	−0.0209881	−	0.999780i	$-0.506681\pi$
$73$	2.16716	−	0.326646i	0.253646	−	0.0382310i	0.274635	+	0.961549i	$0.411443\pi$
$74$	2.21539	−	0.333916i	0.257534	−	0.0388170i
$75$	−13.1826	+	12.2317i	−1.52220	+	1.41240i
$76$	−1.71090	−	7.49596i	−0.196254	−	0.859845i
$77$	−1.51701	−	5.23988i	−0.172880	−	0.597140i
$78$	−0.279283	+	1.22362i	−0.0316225	+	0.138547i
$79$	6.68721	+	11.5826i	0.752370	+	1.30314i	0.946671	+	0.322201i	$0.104423\pi$
$79$	6.68721	+	11.5826i	0.752370	+	1.30314i	−0.194301	+	0.980942i	$0.562244\pi$
$80$	0.484366	−	0.838947i	0.0541538	−	0.0937971i
$81$	3.40967	+	3.16371i	0.378853	+	0.351524i
$82$	2.03115	+	1.38481i	0.224303	+	0.152927i
$83$	−8.35688	−	10.4792i	−0.917287	−	1.15024i	−0.988263	−	0.152764i	$-0.951183\pi$
$83$	−8.35688	−	10.4792i	−0.917287	−	1.15024i	0.0709755	−	0.997478i	$-0.477389\pi$
$84$	4.26151	−	0.894990i	0.464969	−	0.0976515i
$85$	13.7896	−	17.2916i	1.49569	−	1.87553i
$86$	2.34431	−	0.723124i	0.252794	−	0.0779765i
$87$	2.94156	+	7.49497i	0.315368	+	0.803545i
$88$	0.443120	−	5.91303i	0.0472368	−	0.630331i
$89$	−0.898896	+	2.29035i	−0.0952828	+	0.242776i	−0.970567	−	0.240833i	$-0.922579\pi$
$89$	−0.898896	+	2.29035i	−0.0952828	+	0.242776i	0.875284	+	0.483610i	$0.160675\pi$
$90$	−3.68363	−	1.77394i	−0.388289	−	0.186990i
$91$	1.83302	−	1.90789i	0.192153	−	0.200001i
$92$	−0.0110063	+	0.00530037i	−0.00114749	+	0.000552602i
$93$	−0.947410	−	12.6423i	−0.0982419	−	1.31095i
$94$	−1.21902	−	0.376019i	−0.125733	−	0.0387834i
$95$	−22.7199	+	15.4902i	−2.33101	+	1.58926i
$96$	7.62008	+	1.14854i	0.777721	+	0.117223i
$97$	−13.2600			−1.34635			−0.673175	−	0.739484i	$-0.735070\pi$
$97$	−13.2600			−1.34635			−0.673175	+	0.739484i	$0.735070\pi$
$98$	5.97269	+	2.07240i	0.603333	+	0.209344i
$99$	−2.20364			−0.221474
$100$	15.1547	+	2.28420i	1.51547	+	0.228420i
$101$	−6.09072	+	4.15258i	−0.606049	+	0.413197i	−0.827092	−	0.562067i	$-0.810006\pi$
$101$	−6.09072	+	4.15258i	−0.606049	+	0.413197i	0.221043	+	0.975264i	$0.429054\pi$
$102$	−6.26239	−	1.93169i	−0.620069	−	0.191266i
$103$	0.522686	+	6.97476i	0.0515018	+	0.687244i	0.961881	+	0.273469i	$0.0881710\pi$
$103$	0.522686	+	6.97476i	0.0515018	+	0.687244i	−0.910379	+	0.413775i	$0.864210\pi$
$104$	2.59111	−	1.24781i	0.254079	−	0.122358i
$105$	−8.54769	−	13.0179i	−0.834169	−	1.27042i
$106$	−5.54162	−	2.66870i	−0.538250	−	0.259208i
$107$	−2.56333	+	6.53127i	−0.247807	+	0.631402i	−0.999608	−	0.0279879i	$-0.991090\pi$
$107$	−2.56333	+	6.53127i	−0.247807	+	0.631402i	0.751801	+	0.659390i	$0.229185\pi$
$108$	0.500435	−	6.67784i	0.0481544	−	0.642575i
$109$	0.0587610	+	0.149721i	0.00562829	+	0.0143406i	0.933660	−	0.358160i	$-0.116596\pi$
$109$	0.0587610	+	0.149721i	0.00562829	+	0.0143406i	−0.928032	+	0.372501i	$0.878500\pi$
$110$	−7.53685	+	2.32481i	−0.718610	+	0.221662i
$111$	2.14939	−	2.69525i	0.204011	−	0.255822i
$112$	0.466463	+	0.385451i	0.0440766	+	0.0364217i
$113$	−1.13165	−	1.41904i	−0.106456	−	0.133492i	0.725749	−	0.687960i	$-0.241493\pi$
$113$	−1.13165	−	1.41904i	−0.106456	−	0.133492i	−0.832205	+	0.554467i	$0.812922\pi$
$114$	6.73226	+	4.58998i	0.630534	+	0.429891i
$115$	0.0320268	+	0.0297165i	0.00298651	+	0.00277108i
$116$	3.43088	−	5.94247i	0.318550	−	0.551744i
$117$	−0.534393	−	0.925596i	−0.0494046	−	0.0855714i
$118$	−0.848607	+	3.71799i	−0.0781206	+	0.342269i
$119$	9.21908	+	10.2890i	0.845112	+	0.943192i
$120$	−3.76686	−	16.5037i	−0.343866	−	1.50657i
$121$	4.94730	−	4.59042i	0.449754	−	0.417311i
$122$	10.8402	−	1.63390i	0.981424	−	0.147926i
$123$	3.74038	−	0.563771i	0.337259	−	0.0508336i
$124$	−7.92016	+	7.34884i	−0.711252	+	0.659945i
$125$	−7.48408	−	32.7899i	−0.669397	−	2.93282i
$126$	1.47512	−	2.08476i	0.131414	−	0.185725i
$127$	0.310105	−	1.35866i	0.0275174	−	0.120561i	−0.959304	−	0.282376i	$-0.908877\pi$
$127$	0.310105	−	1.35866i	0.0275174	−	0.120561i	0.986821	+	0.161814i	$0.0517346\pi$
$128$	−3.07715	−	5.32978i	−0.271984	−	0.471090i
$129$	1.88746	−	3.26919i	0.166182	−	0.287836i
$130$	−2.80421	−	2.60192i	−0.245945	−	0.228204i
$131$	−12.8247	−	8.74376i	−1.12050	−	0.763946i	−0.146215	−	0.989253i	$-0.546709\pi$
$131$	−12.8247	−	8.74376i	−1.12050	−	0.763946i	−0.974288	+	0.225307i	$0.927661\pi$
$132$	−2.11576	−	2.65308i	−0.184154	−	0.230921i
$133$	−7.18231	−	15.6026i	−0.622785	−	1.35292i
$134$	6.43634	−	8.07092i	0.556015	−	0.697221i
$135$	−22.8856	+	7.05926i	−1.96968	+	0.607564i
$136$	5.48627	+	13.9788i	0.470444	+	1.19867i
$137$	0.409096	−	5.45901i	0.0349514	−	0.466394i	−0.952078	−	0.305855i	$-0.901058\pi$
$137$	0.409096	−	5.45901i	0.0349514	−	0.466394i	0.987029	−	0.160539i	$-0.0513233\pi$
$138$	0.00472969	−	0.0120510i	0.000402618	−	0.00102585i
$139$	−4.78736	−	2.30547i	−0.406059	−	0.195548i	0.219694	−	0.975569i	$-0.429494\pi$
$139$	−4.78736	−	2.30547i	−0.406059	−	0.195548i	−0.625753	+	0.780021i	$0.715208\pi$
$140$	−4.13197	+	12.6125i	−0.349215	+	1.06595i
$141$	−1.76854	+	0.851685i	−0.148938	+	0.0717248i
$142$	0.754739	+	10.0713i	0.0633363	+	0.845164i
$143$	−1.97022	−	0.607732i	−0.164758	−	0.0508211i
$144$	0.201968	−	0.137699i	0.0168307	−	0.0114750i
$145$	−24.2663	−	3.65756i	−2.01521	−	0.303744i
$146$	1.97937			0.163813
$147$	8.90589	−	3.91339i	0.734545	−	0.322771i
$148$	−2.93794			−0.241497
$149$	20.0692	+	3.02495i	1.64414	+	0.247814i	0.904898	−	0.425629i	$-0.139947\pi$
$149$	20.0692	+	3.02495i	1.64414	+	0.247814i	0.739239	+	0.673443i	$0.235185\pi$
$150$	−13.4193	+	9.14915i	−1.09568	+	0.747025i
$151$	15.9511	+	4.92025i	1.29808	+	0.400404i	0.865372	−	0.501131i	$-0.167082\pi$
$151$	15.9511	+	4.92025i	1.29808	+	0.400404i	0.432707	+	0.901535i	$0.357559\pi$
$152$	−1.39526	−	18.6184i	−0.113170	−	1.51015i
$153$	5.02810	−	2.42140i	0.406497	−	0.195759i
$154$	−0.649458	−	4.88372i	−0.0523349	−	0.393541i
$155$	34.8141	+	16.7656i	2.79633	+	1.34664i
$156$	0.601292	−	1.53207i	0.0481419	−	0.122664i
$157$	−0.817139	+	10.9040i	−0.0652148	+	0.870231i	0.864661	+	0.502356i	$0.167533\pi$
$157$	−0.817139	+	10.9040i	−0.0652148	+	0.870231i	−0.929876	+	0.367874i	$0.880086\pi$
$158$	4.41297	+	11.2441i	0.351077	+	0.894530i
$159$	−9.04375	+	2.78963i	−0.717216	+	0.221232i
$160$	−14.6443	+	18.3634i	−1.15774	+	1.45175i
$161$	−0.0216292	+	0.0166417i	−0.00170462	+	0.00131155i
$162$	2.61918	+	3.28435i	0.205782	+	0.258043i
$163$	−3.23492	−	2.20553i	−0.253379	−	0.172751i	0.429969	−	0.902844i	$-0.358524\pi$
$163$	−3.23492	−	2.20553i	−0.253379	−	0.172751i	−0.683348	+	0.730093i	$0.739477\pi$
$164$	−2.36312	−	2.19265i	−0.184528	−	0.171217i
$165$	−6.06811	+	10.5103i	−0.472402	+	0.818224i
$166$	−6.05261	−	10.4834i	−0.469774	−	0.813672i
$167$	−4.69358	+	20.5639i	−0.363200	+	1.59128i	0.381817	+	0.924238i	$0.375298\pi$
$167$	−4.69358	+	20.5639i	−0.363200	+	1.59128i	−0.745017	+	0.667045i	$0.767559\pi$
$168$	10.5566	−	0.606709i	0.814459	−	0.0468086i
$169$	−0.222521	−	0.974928i	−0.0171170	−	0.0749945i
$170$	14.6424	−	13.5862i	1.12302	−	1.04201i
$171$	−6.86113	+	1.03415i	−0.524683	+	0.0790833i
$172$	−3.18118	+	0.479485i	−0.242562	+	0.0365604i
$173$	4.46789	−	4.14559i	0.339687	−	0.315184i	−0.491821	−	0.870696i	$-0.663668\pi$
$173$	4.46789	−	4.14559i	0.339687	−	0.315184i	0.831508	+	0.555513i	$0.187478\pi$
$174$	1.61811	+	7.08940i	0.122669	+	0.537446i
$175$	34.1810	−	1.96446i	2.58384	−	0.148499i
$176$	0.104932	−	0.459737i	0.00790954	−	0.0346540i
$177$	2.93402	+	5.08188i	0.220535	+	0.381977i
$178$	−1.11106	+	1.92442i	−0.0832777	+	0.144241i
$179$	11.5323	+	10.7004i	0.861961	+	0.799783i	0.981182	−	0.193085i	$-0.0618492\pi$
$179$	11.5323	+	10.7004i	0.861961	+	0.799783i	−0.119221	+	0.992868i	$0.538040\pi$
$180$	4.42982	+	3.02020i	0.330179	+	0.225112i
$181$	−2.10404	−	2.63839i	−0.156392	−	0.196110i	0.697462	−	0.716622i	$-0.254313\pi$
$181$	−2.10404	−	2.63839i	−0.156392	−	0.196110i	−0.853854	+	0.520512i	$0.825741\pi$
$182$	1.89381	−	1.45711i	0.140379	−	0.108009i
$183$	10.5172	−	13.1882i	0.777456	−	0.974899i
$184$	−0.0283466	+	0.00874376i	−0.00208974	+	0.000644598i
$185$	3.83872	+	9.78090i	0.282228	+	0.719106i
$186$	0.855649	−	11.4178i	0.0627393	−	0.837197i
$187$	3.93325	−	10.0218i	0.287628	−	0.732864i
$188$	1.50720	+	0.725831i	0.109924	+	0.0529367i
$189$	−1.97207	−	14.8294i	−0.143447	−	1.07868i
$190$	−22.3753	+	10.7754i	−1.62327	+	0.781726i
$191$	0.375864	+	5.01556i	0.0271966	+	0.362913i	0.994154	+	0.107974i	$0.0344364\pi$
$191$	0.375864	+	5.01556i	0.0271966	+	0.362913i	−0.966957	+	0.254939i	$0.917945\pi$
$192$	7.25800	+	2.23880i	0.523801	+	0.161571i
$193$	4.13403	−	2.81854i	0.297574	−	0.202883i	−0.405324	−	0.914173i	$-0.632841\pi$
$193$	4.13403	−	2.81854i	0.297574	−	0.202883i	0.702898	+	0.711290i	$0.251889\pi$
$194$	−11.8420	−	1.78489i	−0.850203	−	0.128147i
$195$	−5.88617			−0.421518
$196$	−7.33970	−	3.85459i	−0.524264	−	0.275328i
$197$	21.1910			1.50980			0.754898	−	0.655842i	$-0.227686\pi$
$197$	21.1910			1.50980			0.754898	+	0.655842i	$0.227686\pi$
$198$	−1.96798	−	0.296625i	−0.139858	−	0.0210802i
$199$	−5.10551	+	3.48088i	−0.361920	+	0.246753i	−0.730603	−	0.682802i	$-0.760761\pi$
$199$	−5.10551	+	3.48088i	−0.361920	+	0.246753i	0.368683	+	0.929555i	$0.379809\pi$
$200$	35.5625	+	10.9696i	2.51465	+	0.775665i
$201$	−1.18703	−	15.8399i	−0.0837269	−	1.11726i
$202$	−5.99833	+	2.88864i	−0.422041	+	0.203244i
$203$	4.77234	−	14.5672i	0.334953	−	1.02241i
$204$	7.74284	+	3.72875i	0.542107	+	0.261065i
$205$	−4.21206	+	10.7322i	−0.294183	+	0.749566i
$206$	−0.472062	+	6.29922i	−0.0328901	+	0.438888i
$207$	0.00402764	+	0.0102622i	0.000279940	+	0.000713276i
$208$	0.218550	−	0.0674136i	0.0151537	−	0.00467429i
$209$	−8.34569	+	10.4652i	−0.577284	+	0.723891i
$210$	−5.88128	−	12.7763i	−0.405847	−	0.881651i
$211$	−0.886177	−	1.11123i	−0.0610070	−	0.0765003i	0.750392	−	0.660993i	$-0.229865\pi$
$211$	−0.886177	−	1.11123i	−0.0610070	−	0.0765003i	−0.811399	+	0.584493i	$0.801293\pi$
$212$	6.66419	+	4.54356i	0.457698	+	0.312053i
$213$	11.3918	+	10.5701i	0.780556	+	0.724250i
$214$	−3.16836	+	5.48776i	−0.216585	+	0.375136i
$215$	5.75283	+	9.96419i	0.392340	+	0.679552i
$216$	3.61848	−	15.8536i	0.246207	−	1.07870i
$217$	−13.9414	+	19.7031i	−0.946403	+	1.33754i
$218$	0.0323236	+	0.141619i	0.00218923	+	0.00959164i
$219$	2.23264	−	2.07158i	0.150868	−	0.139985i
$220$	10.2273	−	1.54152i	0.689526	−	0.103929i
$221$	5.16327	−	0.778238i	0.347319	−	0.0523500i
$222$	2.28233	−	2.11769i	0.153180	−	0.142130i
$223$	1.76958	+	7.75303i	0.118500	+	0.519181i	0.998982	+	0.0451028i	$0.0143615\pi$
$223$	1.76958	+	7.75303i	0.118500	+	0.519181i	−0.880483	+	0.474078i	$0.842781\pi$
$224$	−9.79054	−	10.9268i	−0.654158	−	0.730078i
$225$	3.07761	−	13.4839i	0.205174	−	0.898927i
$226$	−0.819615	−	1.41961i	−0.0545199	−	0.0944313i
$227$	0.294727	−	0.510482i	0.0195617	−	0.0338819i	−0.856079	−	0.516845i	$-0.827106\pi$
$227$	0.294727	−	0.510482i	0.0195617	−	0.0338819i	0.875641	+	0.482963i	$0.160440\pi$
$228$	−7.83258	−	7.26757i	−0.518725	−	0.481306i
$229$	−11.9259	−	8.13096i	−0.788088	−	0.537309i	0.101087	−	0.994878i	$-0.467768\pi$
$229$	−11.9259	−	8.13096i	−0.788088	−	0.537309i	−0.889174	+	0.457569i	$0.848720\pi$
$230$	0.0246017	+	0.0308496i	0.00162219	+	0.00203416i
$231$	−5.84381	−	4.82890i	−0.384495	−	0.317718i
$232$	10.3889	−	13.0272i	0.682064	−	0.855281i
$233$	−23.1296	+	7.13453i	−1.51527	+	0.467399i	−0.937260	−	0.348632i	$-0.886646\pi$
$233$	−23.1296	+	7.13453i	−1.51527	+	0.467399i	−0.578009	+	0.816030i	$0.696170\pi$
$234$	−0.352652	−	0.898544i	−0.0230536	−	0.0587396i
$235$	0.447099	−	5.96612i	0.0291655	−	0.389187i
$236$	1.82704	−	4.65523i	0.118930	−	0.303030i
$237$	16.7456	+	8.06424i	1.08774	+	0.523829i
$238$	6.84820	+	10.4296i	0.443903	+	0.676053i
$239$	−2.73962	+	1.31933i	−0.177211	+	0.0853403i	−0.520386	−	0.853931i	$-0.674212\pi$
$239$	−2.73962	+	1.31933i	−0.177211	+	0.0853403i	0.343175	+	0.939271i	$0.388498\pi$
$240$	−0.100604	−	1.34247i	−0.00649395	−	0.0866558i
$241$	20.3998	+	6.29251i	1.31407	+	0.405336i	0.871057	−	0.491181i	$-0.163435\pi$
$241$	20.3998	+	6.29251i	1.31407	+	0.405336i	0.443009	+	0.896517i	$0.353911\pi$
$242$	5.03613	−	3.43357i	0.323734	−	0.220718i
$243$	−10.3818	−	1.56480i	−0.665993	−	0.100382i
$244$	−14.3757			−0.920310
$245$	−3.24253	+	29.4716i	−0.207158	+	1.88287i
$246$	3.41626			0.217813
$247$	−6.41955	−	0.967592i	−0.408466	−	0.0615664i
$248$	−21.6775	+	14.7794i	−1.37652	+	0.938496i
$249$	−17.7989	−	5.49024i	−1.12796	−	0.347930i
$250$	−2.26997	−	30.2907i	−0.143566	−	1.91575i
$251$	8.33788	−	4.01531i	0.526283	−	0.253444i	−0.151825	−	0.988407i	$-0.548515\pi$
$251$	8.33788	−	4.01531i	0.526283	−	0.253444i	0.678107	+	0.734963i	$0.262801\pi$
$252$	−2.32023	+	2.41499i	−0.146161	+	0.152130i
$253$	0.0191611	+	0.00922752i	0.00120465	+	0.000580129i
$254$	0.459827	−	1.17162i	0.0288521	−	0.0735139i
$255$	2.29684	−	30.6493i	0.143834	−	1.91933i
$256$	−6.02426	−	15.3496i	−0.376517	−	0.959348i
$257$	19.6190	−	6.05167i	1.22380	−	0.377493i	0.385504	−	0.922706i	$-0.374028\pi$
$257$	19.6190	−	6.05167i	1.22380	−	0.377493i	0.838297	+	0.545214i	$0.183551\pi$
$258$	2.12567	−	2.66551i	0.132338	−	0.165947i
$259$	−6.42313	+	1.34897i	−0.399114	+	0.0838208i
$260$	3.12766	+	3.92196i	0.193969	+	0.243230i
$261$	−5.11635	−	3.48827i	−0.316694	−	0.215918i
$262$	−10.2763	−	9.53498i	−0.634870	−	0.589073i
$263$	2.36624	−	4.09845i	0.145909	−	0.252722i	−0.783803	−	0.621010i	$-0.786723\pi$
$263$	2.36624	−	4.09845i	0.145909	−	0.252722i	0.929712	+	0.368288i	$0.120056\pi$
$264$	−4.12013	−	7.13628i	−0.253577	−	0.439208i
$265$	6.41886	−	28.1229i	0.394308	−	1.72757i
$266$	−4.31400	−	14.9009i	−0.264508	−	0.913630i
$267$	0.760846	+	3.33349i	0.0465630	+	0.204006i
$268$	−9.92336	+	9.20754i	−0.606166	+	0.562440i
$269$	−10.8877	+	1.64106i	−0.663837	+	0.100057i	−0.472313	−	0.881431i	$-0.656581\pi$
$269$	−10.8877	+	1.64106i	−0.663837	+	0.100057i	−0.191524	+	0.981488i	$0.561343\pi$
$270$	−21.3884	+	3.22378i	−1.30165	+	0.196193i
$271$	11.1488	−	10.3446i	0.677243	−	0.628390i	−0.264633	−	0.964349i	$-0.585251\pi$
$271$	11.1488	−	10.3446i	0.677243	−	0.628390i	0.941877	+	0.335959i	$0.109060\pi$
$272$	0.265742	+	1.16429i	0.0161130	+	0.0705955i
$273$	0.611133	−	3.62561i	0.0369875	−	0.219432i
$274$	1.10017	−	4.82014i	0.0664635	−	0.291195i
$275$	−13.3405	−	23.1065i	−0.804464	−	1.39337i
$276$	−0.00848825	+	0.0147021i	−0.000510933	+	0.000884961i
$277$	13.8942	+	12.8920i	0.834823	+	0.774602i	0.976547	−	0.215304i	$-0.0690742\pi$
$277$	13.8942	+	12.8920i	0.834823	+	0.774602i	−0.141724	+	0.989906i	$0.545265\pi$
$278$	−3.96506	−	2.70333i	−0.237809	−	0.162135i
$279$	6.07921	+	7.62309i	0.363953	+	0.456383i
$280$	−14.4863	+	28.7895i	−0.865724	+	1.72050i
$281$	−0.615133	+	0.771352i	−0.0366957	+	0.0460150i	−0.799841	−	0.600212i	$-0.795083\pi$
$281$	−0.615133	+	0.771352i	−0.0366957	+	0.0460150i	0.763145	+	0.646227i	$0.223654\pi$
$282$	−1.69405	+	0.522546i	−0.100879	+	0.0311172i
$283$	2.08910	+	5.32295i	0.124184	+	0.316416i	0.979423	−	0.201818i	$-0.0646848\pi$
$283$	2.08910	+	5.32295i	0.124184	+	0.316416i	−0.855239	+	0.518234i	$0.826590\pi$
$284$	0.989718	−	13.2069i	0.0587289	−	0.783683i
$285$	−13.9609	+	35.5718i	−0.826974	+	2.10709i
$286$	−1.67771	−	0.807944i	−0.0992053	−	0.0477748i
$287$	−6.17319	−	3.70870i	−0.364392	−	0.218918i
$288$	−5.33977	+	2.57150i	−0.314649	+	0.151527i
$289$	0.767107	+	10.2363i	0.0451240	+	0.602137i
$290$	−21.1789	−	6.53282i	−1.24367	−	0.383621i
$291$	−15.2252	+	10.3804i	−0.892520	+	0.608510i
$292$	−2.56662	−	0.386856i	−0.150200	−	0.0226391i
$293$	15.8451			0.925681			0.462840	−	0.886442i	$-0.346830\pi$
$293$	15.8451			0.925681			0.462840	+	0.886442i	$0.346830\pi$
$294$	8.48025	−	2.29609i	0.494578	−	0.133911i
$295$	−17.8853			−1.04132
$296$	−7.05453	−	1.06330i	−0.410036	−	0.0618030i
$297$	−9.63243	+	6.56728i	−0.558930	+	0.381072i
$298$	17.5158	+	5.40292i	1.01466	+	0.312983i
$299$	0.000770826		0.0102860i	4.45780e−5		0.000594853i
$300$	19.1889	−	9.24087i	1.10787	−	0.533522i
$301$	−6.73476	+	2.50894i	−0.388185	+	0.144613i
$302$	13.5829	+	6.54119i	0.781609	+	0.376403i
$303$	−3.74263	+	9.53606i	−0.215008	+	0.547832i
$304$	0.110959	−	1.48065i	0.00636396	−	0.0849212i
$305$	18.7834	+	47.8592i	1.07553	+	2.74041i
$306$	4.81632	−	1.48564i	0.275331	−	0.0849283i
$307$	−18.8772	+	23.6712i	−1.07738	+	1.35099i	−0.145029	+	0.989427i	$0.546328\pi$
$307$	−18.8772	+	23.6712i	−1.07738	+	1.35099i	−0.932348	+	0.361561i	$0.882244\pi$
$308$	−0.112350	+	6.45960i	−0.00640172	+	0.368070i
$309$	6.06024	+	7.59930i	0.344755	+	0.432309i
$310$	28.8342	+	19.6588i	1.63767	+	1.11655i
$311$	−1.09918	−	1.01989i	−0.0623290	−	0.0578329i	0.648393	−	0.761306i	$-0.275441\pi$
$311$	−1.09918	−	1.01989i	−0.0623290	−	0.0578329i	−0.710722	+	0.703473i	$0.751632\pi$
$312$	1.99830	−	3.46116i	0.113131	−	0.195949i
$313$	−2.73792	−	4.74222i	−0.154756	−	0.268046i	0.778214	−	0.627999i	$-0.216126\pi$
$313$	−2.73792	−	4.74222i	−0.154756	−	0.268046i	−0.932970	+	0.359953i	$0.882793\pi$
$314$	−2.19750	+	9.62788i	−0.124012	+	0.543333i
$315$	11.0715	+	4.56901i	0.623810	+	0.257435i
$316$	−3.52467	−	15.4426i	−0.198278	−	0.868712i
$317$	−18.1959	+	16.8833i	−1.02198	+	0.948263i	−0.998675	−	0.0514649i	$-0.983611\pi$
$317$	−18.1959	+	16.8833i	−1.02198	+	0.948263i	−0.0233101	+	0.999728i	$0.507421\pi$
$318$	−8.45210	+	1.27395i	−0.473970	+	0.0714395i
$319$	−11.8124	+	1.78043i	−0.661365	+	0.0996847i
$320$	−16.9703	+	15.7462i	−0.948671	+	0.880238i
$321$	2.16967	+	9.50593i	0.121099	+	0.530569i
$322$	−0.0215562	+	0.0119505i	−0.00120128	+	0.000665978i
$323$	7.54322	−	33.0490i	0.419716	−	1.83890i
$324$	−2.75436	−	4.77068i	−0.153020	−	0.265038i
$325$	6.47027	−	11.2068i	0.358906	−	0.621643i
$326$	−2.59209	−	2.40511i	−0.143563	−	0.133207i
$327$	0.184677	+	0.125910i	0.0102126	+	0.00696286i
$328$	−4.88071	−	6.12022i	−0.269492	−	0.337933i
$329$	3.62843	+	0.894826i	0.200042	+	0.0493333i
$330$	−6.83393	+	8.56948i	−0.376195	+	0.471734i
$331$	1.81092	−	0.558596i	0.0995374	−	0.0307032i	−0.244586	−	0.969627i	$-0.578652\pi$
$331$	1.81092	−	0.558596i	0.0995374	−	0.0307032i	0.344124	+	0.938924i	$0.388176\pi$
$332$	5.79943	+	14.7767i	0.318285	+	0.810978i
$333$	−0.198133	+	2.64390i	−0.0108576	+	0.144885i
$334$	−6.95968	+	17.7330i	−0.380817	+	0.970306i
$335$	43.6194	+	21.0060i	2.38318	+	1.14768i
$336$	0.837341	+	0.0774145i	0.0456807	+	0.00422331i
$337$	−16.0312	+	7.72023i	−0.873276	+	0.420548i	−0.816164	−	0.577820i	$-0.803903\pi$
$337$	−16.0312	+	7.72023i	−0.873276	+	0.420548i	−0.0571120	+	0.998368i	$0.518189\pi$
$338$	−0.0674922	−	0.900620i	−0.00367109	−	0.0489873i
$339$	−2.41024	−	0.743462i	−0.130906	−	0.0403793i
$340$	−21.6421	+	14.7553i	−1.17371	+	0.800219i
$341$	18.5994	+	2.80341i	1.00722	+	0.151813i
$342$	−6.26659			−0.338858
$343$	−17.8164	−	5.05714i	−0.961997	−	0.273060i
$344$	−7.81213			−0.421202
$345$	0.0600366	+	0.00904906i	0.00323226	+	0.000487185i
$346$	4.54811	−	3.10085i	0.244508	−	0.166703i
$347$	−26.5676	−	8.19501i	−1.42622	−	0.439931i	−0.516908	−	0.856041i	$-0.672917\pi$
$347$	−26.5676	−	8.19501i	−1.42622	−	0.439931i	−0.909315	+	0.416110i	$0.863393\pi$
$348$	−0.712602	−	9.50901i	−0.0381995	−	0.509736i
$349$	27.6482	−	13.3147i	1.47997	−	0.712718i	0.492473	−	0.870328i	$-0.336093\pi$
$349$	27.6482	−	13.3147i	1.47997	−	0.712718i	0.987502	+	0.157609i	$0.0503787\pi$
$350$	30.7901	+	2.84663i	1.64580	+	0.152159i
$351$	−5.09436	−	2.45332i	−0.271917	−	0.130948i
$352$	−4.17706	+	10.6430i	−0.222638	+	0.567273i
$353$	1.42092	−	18.9609i	0.0756281	−	1.00919i	−0.822303	−	0.569050i	$-0.807311\pi$
$353$	1.42092	−	18.9609i	0.0756281	−	1.00919i	0.897931	−	0.440137i	$-0.145070\pi$
$354$	1.93620	+	4.93335i	0.102908	+	0.262205i
$355$	−45.2611	+	13.9612i	−2.40221	+	0.740984i
$356$	1.81682	−	2.27822i	0.0962913	−	0.120746i
$357$	18.6400	+	4.59691i	0.986535	+	0.243294i
$358$	8.85863	+	11.1084i	0.468193	+	0.587096i
$359$	2.01098	+	1.37106i	0.106135	+	0.0723618i	0.615225	−	0.788352i	$-0.289065\pi$
$359$	2.01098	+	1.37106i	0.106135	+	0.0723618i	−0.509089	+	0.860714i	$0.670018\pi$
$360$	9.54374	+	8.85530i	0.502999	+	0.466715i
$361$	−11.5734	+	20.0458i	−0.609128	+	1.05504i
$362$	−1.52389	−	2.63945i	−0.0800938	−	0.138727i
$363$	2.08699	−	9.14368i	0.109538	−	0.479919i
$364$	−2.74047	+	1.51929i	−0.143640	+	0.0796325i
$365$	2.06565	+	9.05021i	0.108121	+	0.473709i
$366$	11.1677	−	10.3621i	0.583746	−	0.541637i
$367$	8.11827	−	1.22363i	0.423770	−	0.0638731i	0.0663047	−	0.997799i	$-0.478879\pi$
$367$	8.11827	−	1.22363i	0.423770	−	0.0638731i	0.357465	+	0.933926i	$0.383641\pi$
$368$	−0.00233276		0.000351606i	−0.000121603		1.83287e-5i
$369$	−2.13257	+	1.97874i	−0.111017	+	0.103009i
$370$	2.11163	+	9.25163i	0.109778	+	0.480970i
$371$	16.6559	+	6.87358i	0.864733	+	0.356859i
$372$	−3.34107	+	14.6382i	−0.173226	+	0.758954i
$373$	13.4715	+	23.3333i	0.697528	+	1.20815i	0.969321	+	0.245798i	$0.0790499\pi$
$373$	13.4715	+	23.3333i	0.697528	+	1.20815i	−0.271793	+	0.962356i	$0.587617\pi$
$374$	4.86162	−	8.42058i	0.251388	−	0.435418i
$375$	−34.2624	−	31.7909i	−1.76930	−	1.64167i
$376$	3.35638	+	2.28834i	0.173092	+	0.118012i
$377$	−3.61238	−	4.52978i	−0.186047	−	0.233296i
$378$	0.234957	−	13.5089i	0.0120849	−	0.694825i
$379$	4.55085	−	5.70658i	0.233761	−	0.293127i	−0.651090	−	0.759000i	$-0.725688\pi$
$379$	4.55085	−	5.70658i	0.233761	−	0.293127i	0.884852	+	0.465873i	$0.154260\pi$
$380$	31.1198	−	9.59917i	1.59641	−	0.492427i
$381$	−0.707541	−	1.80278i	−0.0362484	−	0.0923595i
$382$	−0.339460	+	4.52978i	−0.0173683	+	0.231764i
$383$	−6.87410	+	17.5149i	−0.351250	+	0.894970i	0.640637	+	0.767844i	$0.278670\pi$
$383$	−6.87410	+	17.5149i	−0.351250	+	0.894970i	−0.991887	+	0.127126i	$0.959425\pi$
$384$	−7.70554	−	3.71079i	−0.393222	−	0.189366i
$385$	21.6519	−	8.06611i	1.10348	−	0.411087i
$386$	4.07133	−	1.96065i	0.207225	−	0.0997943i
$387$	0.216960	+	2.89513i	0.0110287	+	0.147168i
$388$	15.0065	+	4.62889i	0.761840	+	0.234996i
$389$	17.5013	−	11.9322i	0.887353	−	0.604987i	−0.0315361	−	0.999503i	$-0.510040\pi$
$389$	17.5013	−	11.9322i	0.887353	−	0.604987i	0.918889	+	0.394515i	$0.129088\pi$
$390$	−5.25669	−	0.792319i	−0.266183	−	0.0401206i
$391$	−0.0538597			−0.00272380
$392$	−16.2289	−	11.9120i	−0.819684	−	0.601646i
$393$	−21.5704			−1.08808
$394$	18.9248	+	2.85245i	0.953418	+	0.143705i
$395$	−46.8057	+	31.9116i	−2.35505	+	1.60564i
$396$	2.49389	+	0.769263i	0.125323	+	0.0386569i
$397$	−1.06602	−	14.2250i	−0.0535018	−	0.713933i	−0.957874	−	0.287188i	$-0.907279\pi$
$397$	−1.06602	−	14.2250i	−0.0535018	−	0.713933i	0.904372	−	0.426744i	$-0.140340\pi$
$398$	−5.02806	+	2.42139i	−0.252034	+	0.121373i
$399$	−20.4611	−	12.2925i	−1.02434	−	0.615396i
$400$	2.66654	+	1.28414i	0.133327	+	0.0642069i
$401$	2.96456	−	7.55357i	0.148043	−	0.377207i	−0.837546	−	0.546367i	$-0.816010\pi$
$401$	2.96456	−	7.55357i	0.148043	−	0.377207i	0.985589	+	0.169160i	$0.0541055\pi$
$402$	1.07206	−	14.3057i	0.0534697	−	0.713503i
$403$	3.33293	+	8.49216i	0.166025	+	0.423025i
$404$	8.34255	−	2.57334i	0.415057	−	0.128028i
$405$	−12.2836	+	15.4031i	−0.610376	+	0.765387i
$406$	6.22282	−	12.3669i	0.308833	−	0.613760i
$407$	3.18897	+	3.99884i	0.158071	+	0.198215i
$408$	17.2425	+	11.7557i	0.853629	+	0.581995i
$409$	−24.2519	−	22.5025i	−1.19918	−	1.11268i	−0.990899	−	0.134608i	$-0.957023\pi$
$409$	−24.2519	−	22.5025i	−1.19918	−	1.11268i	−0.208281	−	0.978069i	$-0.566787\pi$
$410$	−5.20624	+	9.01747i	−0.257118	+	0.445341i
$411$	−3.80378	−	6.58833i	−0.187626	−	0.324978i
$412$	1.84327	−	8.07588i	0.0908113	−	0.397870i
$413$	1.85694	−	11.0165i	0.0913743	−	0.542086i
$414$	0.00221554	+	0.00970693i	0.000108888	+	0.000477070i
$415$	41.6167	−	38.6146i	2.04288	−	1.89552i
$416$	−5.48333	+	0.826479i	−0.268842	+	0.0405215i
$417$	−7.30170	+	1.10055i	−0.357566	+	0.0538944i
$418$	−8.86187	+	8.22262i	−0.433448	+	0.402181i
$419$	−6.05621	−	26.5340i	−0.295865	−	1.29627i	−0.876222	−	0.481907i	$-0.839944\pi$
$419$	−6.05621	−	26.5340i	−0.295865	−	1.29627i	0.580357	−	0.814362i	$-0.302913\pi$
$420$	5.12914	+	17.7164i	0.250276	+	0.864473i
$421$	−1.26720	+	5.55196i	−0.0617595	+	0.270586i	−0.996375	−	0.0850749i	$-0.972887\pi$
$421$	−1.26720	+	5.55196i	−0.0617595	+	0.270586i	0.934615	+	0.355661i	$0.115744\pi$
$422$	−0.641829	−	1.11168i	−0.0312437	−	0.0541157i
$423$	0.754833	−	1.30741i	0.0367012	−	0.0635684i
$424$	14.3575	+	13.3218i	0.697263	+	0.646966i
$425$	55.8292	+	38.0637i	2.70811	+	1.84636i
$426$	8.75077	+	10.9731i	0.423976	+	0.531649i
$427$	−31.4292	+	6.60067i	−1.52097	+	0.319429i
$428$	5.18094	−	6.49669i	0.250430	−	0.314029i
$429$	−2.73797	+	0.844553i	−0.132191	+	0.0407754i
$430$	3.79636	+	9.67297i	0.183077	+	0.466472i
$431$	−0.151865	+	2.02649i	−0.00731506	+	0.0976127i	−0.999666	−	0.0258342i	$-0.991776\pi$
$431$	−0.151865	+	2.02649i	−0.00731506	+	0.0976127i	0.992351	+	0.123447i	$0.0393948\pi$
$432$	0.472460	−	1.20381i	0.0227312	−	0.0579182i
$433$	−36.7382	−	17.6922i	−1.76552	−	0.850231i	−0.969547	−	0.244904i	$-0.921244\pi$
$433$	−36.7382	−	17.6922i	−1.76552	−	0.850231i	−0.795977	−	0.605327i	$-0.793042\pi$
$434$	−15.1026	+	15.7194i	−0.724950	+	0.754558i
$435$	−30.7261	+	14.7969i	−1.47320	+	0.709456i
$436$	−0.0142350	−	0.189953i	−0.000681735	−	0.00909711i
$437$	0.0639893	+	0.0197381i	0.00306102	+	0.000944201i
$438$	2.27272	−	1.54952i	0.108595	−	0.0740388i
$439$	37.4616	+	5.64643i	1.78795	+	0.269489i	0.957671	−	0.287865i	$-0.0929456\pi$
$439$	37.4616	+	5.64643i	1.78795	+	0.269489i	0.830274	+	0.557355i	$0.188184\pi$
$440$	25.1156			1.19734
$441$	−3.96380	+	6.34517i	−0.188752	+	0.302151i
$442$	4.71586			0.224311
$443$	26.9004	+	4.05459i	1.27808	+	0.192639i	0.752776	−	0.658277i	$-0.228714\pi$
$443$	26.9004	+	4.05459i	1.27808	+	0.192639i	0.525302	+	0.850916i	$0.323952\pi$
$444$	−3.37336	+	2.29992i	−0.160093	+	0.109149i
$445$	−9.95846	−	3.07178i	−0.472077	−	0.145616i
$446$	0.536725	+	7.16210i	0.0254147	+	0.339135i
$447$	25.4117	−	12.2376i	1.20193	−	0.578821i
$448$	−7.93695	−	12.0878i	−0.374986	−	0.571094i
$449$	−16.1729	−	7.78847i	−0.763247	−	0.367561i	0.0114156	−	0.999935i	$-0.496366\pi$
$449$	−16.1729	−	7.78847i	−0.763247	−	0.367561i	−0.774663	+	0.632374i	$0.782081\pi$
$450$	4.56351	−	11.6276i	0.215126	−	0.548132i
$451$	−0.419396	+	5.59645i	−0.0197486	+	0.263527i
$452$	0.785330	+	2.00099i	0.0369388	+	0.0941186i
$453$	22.1669	−	6.83758i	1.04149	−	0.321257i
$454$	0.331923	−	0.416218i	0.0155779	−	0.0195341i
$455$	8.63870	+	7.13839i	0.404988	+	0.334653i
$456$	−16.1772	−	20.2855i	−0.757566	−	0.949957i
$457$	−5.15405	−	3.51397i	−0.241096	−	0.164377i	0.436744	−	0.899586i	$-0.356132\pi$
$457$	−5.15405	−	3.51397i	−0.241096	−	0.164377i	−0.677840	+	0.735209i	$0.737084\pi$
$458$	−9.55606	−	8.86673i	−0.446526	−	0.414315i
$459$	14.7623	−	25.5690i	0.689044	−	1.19346i
$460$	−0.0258715	−	0.0448107i	−0.00120626	−	0.00208931i
$461$	2.74412	−	12.0228i	0.127806	−	0.559955i	−0.869958	−	0.493125i	$-0.835854\pi$
$461$	2.74412	−	12.0228i	0.127806	−	0.559955i	0.997764	−	0.0668300i	$-0.0212885\pi$
$462$	−4.56886	−	5.09911i	−0.212563	−	0.237232i
$463$	5.37646	+	23.5558i	0.249865	+	1.09473i	0.931701	+	0.363226i	$0.118325\pi$
$463$	5.37646	+	23.5558i	0.249865	+	1.09473i	−0.681836	+	0.731506i	$0.738818\pi$
$464$	0.971371	−	0.901300i	0.0450947	−	0.0418418i
$465$	53.0985	−	8.00331i	2.46238	−	0.371145i
$466$	−21.6164	+	3.25815i	−1.00136	+	0.150931i
$467$	−30.2779	+	28.0938i	−1.40110	+	1.30003i	−0.500254	+	0.865879i	$0.666760\pi$
$467$	−30.2779	+	28.0938i	−1.40110	+	1.30003i	−0.900842	+	0.434148i	$0.857049\pi$
$468$	0.281666	+	1.23406i	0.0130200	+	0.0570443i
$469$	−17.4675	+	24.6865i	−0.806574	+	1.13992i
$470$	1.20237	−	5.26791i	0.0554610	−	0.242991i
$471$	7.59776	+	13.1597i	0.350086	+	0.606367i
$472$	6.07189	−	10.5168i	0.279481	−	0.484076i
$473$	4.10562	+	3.80946i	0.188777	+	0.175159i
$474$	13.8693	+	9.45591i	0.637037	+	0.434324i
$475$	−52.3799	−	65.6823i	−2.40335	−	3.01371i
$476$	−6.84158	−	14.8625i	−0.313583	−	0.681220i
$477$	4.53826	−	5.69080i	0.207793	−	0.260564i
$478$	−2.62423	+	0.809467i	−0.120029	+	0.0370241i
$479$	15.2870	+	38.9505i	0.698479	+	1.77970i	0.622547	+	0.782583i	$0.286098\pi$
$479$	15.2870	+	38.9505i	0.698479	+	1.77970i	0.0759324	+	0.997113i	$0.475807\pi$
$480$	−2.43922	+	32.5491i	−0.111335	+	1.48566i
$481$	−0.906294	+	2.30920i	−0.0413234	+	0.105290i
$482$	17.3712	+	8.36553i	0.791236	+	0.381039i
$483$	−0.0118071	+	0.0360402i	−0.000537242	+	0.00163989i
$484$	−7.20137	+	3.46800i	−0.327335	+	0.157636i
$485$	−4.19717	−	56.0074i	−0.190584	−	2.54316i
$486$	−9.06092	−	2.79492i	−0.411012	−	0.126780i
$487$	30.5870	−	20.8538i	1.38603	−	0.944978i	0.386283	−	0.922380i	$-0.373759\pi$
$487$	30.5870	−	20.8538i	1.38603	−	0.944978i	0.999745	−	0.0225976i	$-0.00719366\pi$
$488$	−34.5187	−	5.20286i	−1.56259	−	0.235522i
$489$	−5.44093			−0.246048
$490$	−6.86284	+	25.8833i	−0.310032	+	1.16929i
$491$	30.1027			1.35852			0.679258	−	0.733900i	$-0.262302\pi$
$491$	30.1027			1.35852			0.679258	+	0.733900i	$0.262302\pi$
$492$	−4.42984	−	0.667690i	−0.199712	−	0.0301018i
$493$	24.9961	−	17.0421i	1.12577	−	0.767536i
$494$	−5.60279	−	1.72823i	−0.252081	−	0.0777568i
$495$	−0.697516	−	9.30771i	−0.0313510	−	0.418350i
$496$	−1.87985	+	0.905288i	−0.0844078	+	0.0406486i
$497$	−3.90020	−	29.3282i	−0.174948	−	1.31555i
$498$	−15.1565	−	7.29897i	−0.679177	−	0.327075i
$499$	−0.480687	+	1.22477i	−0.0215185	+	0.0548282i	−0.941229	−	0.337768i	$-0.890328\pi$
$499$	−0.480687	+	1.22477i	−0.0215185	+	0.0548282i	0.919711	+	0.392597i	$0.128423\pi$
$500$	−2.97670	+	39.7213i	−0.133122	+	1.77639i
$501$	10.7089	+	27.2860i	0.478441	+	1.21905i
$502$	7.98670	−	2.46357i	0.356464	−	0.109955i
$503$	6.00394	−	7.52870i	0.267702	−	0.335688i	−0.629751	−	0.776797i	$-0.716843\pi$
$503$	6.00394	−	7.52870i	0.267702	−	0.335688i	0.897454	+	0.441109i	$0.145415\pi$
$504$	−6.44533	+	4.95909i	−0.287098	+	0.220896i
$505$	−19.4675	−	24.4115i	−0.866292	−	1.08630i
$506$	0.0158699	+	0.0108199i	0.000705504	+	0.000481004i
$507$	−1.01871	−	0.945223i	−0.0452424	−	0.0419788i
$508$	−0.825239	+	1.42936i	−0.0366141	+	0.0634174i
$509$	−16.7527	−	29.0166i	−0.742552	−	1.28614i	−0.951330	−	0.308175i	$-0.900282\pi$
$509$	−16.7527	−	29.0166i	−0.742552	−	1.28614i	0.208777	−	0.977963i	$-0.433052\pi$
$510$	6.17682	−	27.0624i	0.273514	−	1.19834i
$511$	−5.78897	+	0.332704i	−0.256089	+	0.0147180i
$512$	−0.574941	−	2.51898i	−0.0254091	−	0.111324i
$513$	−26.9090	+	24.9679i	−1.18806	+	1.10236i
$514$	18.3355	−	2.76364i	0.808745	−	0.121899i
$515$	−29.2944	+	4.41543i	−1.29087	+	0.194567i
$516$	−3.27730	+	3.04089i	−0.144275	+	0.133868i
$517$	−0.648055	−	2.83931i	−0.0285014	−	0.124873i
$518$	−5.91781	+	0.340109i	−0.260014	+	0.0149435i
$519$	1.88475	−	8.25763i	0.0827313	−	0.362470i
$520$	6.09065	+	10.5493i	0.267092	+	0.462618i
$521$	5.19426	−	8.99672i	0.227565	−	0.394154i	−0.729521	−	0.683958i	$-0.760257\pi$
$521$	5.19426	−	8.99672i	0.227565	−	0.394154i	0.957086	+	0.289805i	$0.0935904\pi$
$522$	−4.09965	−	3.80392i	−0.179437	−	0.166493i
$523$	−0.668160	−	0.455544i	−0.0292166	−	0.0199195i	0.548624	−	0.836069i	$-0.315152\pi$
$523$	−0.668160	−	0.455544i	−0.0292166	−	0.0199195i	−0.577840	+	0.816150i	$0.696104\pi$
$524$	11.4616	+	14.3724i	0.500701	+	0.627859i
$525$	37.7091	−	29.0137i	1.64576	−	1.26626i
$526$	2.66487	−	3.34165i	0.116194	−	0.145703i
$527$	−45.5192	+	14.0408i	−1.98285	+	0.611627i
$528$	−0.239414	−	0.610018i	−0.0104192	−	0.0265476i
$529$	−1.71878	+	22.9356i	−0.0747297	+	0.997199i
$530$	9.51795	−	24.2513i	0.413433	−	1.05341i
$531$	−4.06611	−	1.95813i	−0.176454	−	0.0849758i
$532$	2.68162	+	20.1649i	0.116263	+	0.874261i
$533$	−2.45238	+	1.18101i	−0.106224	+	0.0511550i
$534$	0.230770	+	3.07941i	0.00998639	+	0.133259i
$535$	−28.3980	−	8.75964i	−1.22775	−	0.378712i
$536$	−27.1602	+	18.5175i	−1.17314	+	0.799835i
$537$	21.6181	+	3.25840i	0.932888	+	0.140610i
$538$	−9.94428			−0.428728
$539$	2.72033	+	14.1740i	0.117173	+	0.610519i
$540$	28.3642			1.22060
$541$	−21.6639	−	3.26531i	−0.931406	−	0.140387i	−0.334225	−	0.942493i	$-0.608474\pi$
$541$	−21.6639	−	3.26531i	−0.931406	−	0.140387i	−0.597181	+	0.802107i	$0.703713\pi$
$542$	11.3490	−	7.73762i	0.487482	−	0.332359i
$543$	−4.48130	−	1.38230i	−0.192311	−	0.0593201i
$544$	−2.16382	−	28.8742i	−0.0927730	−	1.23797i
$545$	−0.613788	+	0.295585i	−0.0262918	+	0.0126615i
$546$	1.03381	−	3.15561i	0.0442429	−	0.135048i
$547$	11.7997	+	5.68244i	0.504519	+	0.242964i	0.668790	−	0.743452i	$-0.266813\pi$
$547$	11.7997	+	5.68244i	0.504519	+	0.242964i	−0.164271	+	0.986415i	$0.552527\pi$
$548$	−2.36865	+	6.03521i	−0.101184	+	0.257811i
$549$	−0.969490	+	12.9369i	−0.0413768	+	0.552135i
$550$	−8.80357	−	22.4311i	−0.375386	−	0.956467i
$551$	−35.9427	+	11.0868i	−1.53121	+	0.472316i
$552$	−0.0257028	+	0.0322303i	−0.00109399	+	0.00137181i
$553$	−14.7964	−	32.1433i	−0.629207	−	1.36687i
$554$	10.6730	+	13.3835i	0.453452	+	0.568611i
$555$	12.0645	+	8.22543i	0.512109	+	0.349150i
$556$	4.61311	+	4.28034i	0.195639	+	0.181527i
$557$	14.8906	−	25.7913i	0.630935	−	1.09281i	−0.356425	−	0.934324i	$-0.616005\pi$
$557$	14.8906	−	25.7913i	0.630935	−	1.09281i	0.987361	−	0.158489i	$-0.0506621\pi$
$558$	4.40297	+	7.62617i	0.186393	+	0.322842i
$559$	−0.604456	+	2.64829i	−0.0255658	+	0.112011i
$560$	−1.48041	+	2.09224i	−0.0625588	+	0.0884134i
$561$	−3.32920	−	14.5862i	−0.140559	−	0.615828i
$562$	−0.653178	+	0.606061i	−0.0275527	+	0.0255651i
$563$	23.5713	−	3.55280i	0.993412	−	0.149733i	0.367832	−	0.929892i	$-0.380100\pi$
$563$	23.5713	−	3.55280i	0.993412	−	0.149733i	0.625581	+	0.780160i	$0.284862\pi$
$564$	2.29879	−	0.346487i	0.0967966	−	0.0145897i
$565$	5.63552	−	5.22900i	0.237088	−	0.219986i
$566$	1.14919	+	5.03491i	0.0483039	+	0.211633i
$567$	−8.21226	−	9.16534i	−0.344882	−	0.384908i
$568$	7.15633	−	31.3539i	0.300273	−	1.31558i
$569$	6.63197	+	11.4869i	0.278026	+	0.481556i	0.970894	−	0.239509i	$-0.0769864\pi$
$569$	6.63197	+	11.4869i	0.278026	+	0.481556i	−0.692868	+	0.721065i	$0.743653\pi$
$570$	−17.2561	+	29.8885i	−0.722780	+	1.25189i
$571$	−25.3905	−	23.5590i	−1.06256	−	0.985913i	−0.0626348	−	0.998037i	$-0.519950\pi$
$571$	−25.3905	−	23.5590i	−1.06256	−	0.985913i	−0.999927	+	0.0121237i	$0.996141\pi$
$572$	2.01757	+	1.37555i	0.0843587	+	0.0575148i
$573$	4.35793	+	5.46467i	0.182055	+	0.228290i
$574$	−5.01380	−	4.14304i	−0.209272	−	0.172927i
$575$	−0.0832229	+	0.104358i	−0.00347063	+	0.00435204i
$576$	−5.58203	+	1.72183i	−0.232585	+	0.0717429i
$577$	−11.0149	−	28.0654i	−0.458555	−	1.16838i	−0.954018	−	0.299750i	$-0.903097\pi$
$577$	−11.0149	−	28.0654i	−0.458555	−	1.16838i	0.495463	−	0.868629i	$-0.334998\pi$
$578$	−0.692810	+	9.24490i	−0.0288171	+	0.384537i
$579$	2.54028	−	6.47253i	0.105571	−	0.268989i
$580$	26.1857	+	12.6104i	1.08730	+	0.523616i
$581$	19.4639	+	29.6431i	0.807500	+	1.22980i
$582$	−14.9943	+	7.22088i	−0.621534	+	0.299315i
$583$	−1.04934	−	14.0024i	−0.0434591	−	0.579922i
$584$	−6.02293	−	1.85783i	−0.249230	−	0.0768774i
$585$	3.74037	−	2.55014i	0.154645	−	0.105435i
$586$	14.1506	+	2.13286i	0.584556	+	0.0881076i
$587$	10.7715			0.444589			0.222295	−	0.974980i	$-0.428645\pi$
$587$	10.7715			0.444589			0.222295	+	0.974980i	$0.428645\pi$
$588$	−11.4450	+	1.31990i	−0.471984	+	0.0544316i
$589$	59.2257			2.44035
$590$	−15.9726	−	2.40748i	−0.657582	−	0.0991145i
$591$	24.3317	−	16.5891i	1.00087	−	0.682383i
$592$	−0.542151	−	0.167232i	−0.0222823	−	0.00687317i
$593$	0.0334093	+	0.445816i	0.00137195	+	0.0183075i	0.997848	−	0.0655732i	$-0.0208876\pi$
$593$	0.0334093	+	0.445816i	0.00137195	+	0.0183075i	−0.996476	+	0.0838807i	$0.973269\pi$
$594$	−9.48632	+	4.56837i	−0.389229	+	0.187443i
$595$	−40.5405	+	42.1962i	−1.66200	+	1.72987i
$596$	−21.6566	−	10.4293i	−0.887090	−	0.427200i
$597$	−3.13723	+	7.99354i	−0.128398	+	0.327154i
$598$	−0.000696168		0.00928972i	−2.84684e−5		0.000379885i
$599$	5.89460	+	15.0192i	0.240847	+	0.613668i	0.999274	−	0.0380898i	$-0.0121273\pi$
$599$	5.89460	+	15.0192i	0.240847	+	0.613668i	−0.758428	+	0.651757i	$0.774032\pi$
$600$	49.4205	−	15.2442i	2.01758	−	0.622342i
$601$	18.7816	−	23.5514i	0.766118	−	0.960681i	−0.233815	−	0.972281i	$-0.575121\pi$
$601$	18.7816	−	23.5514i	0.766118	−	0.960681i	0.999933	+	0.0115997i	$0.00369237\pi$
$602$	−6.35225	+	1.33408i	−0.258899	+	0.0543731i
$603$	7.61679	+	9.55116i	0.310180	+	0.388953i
$604$	−16.3344	−	11.1366i	−0.664637	−	0.453142i
$605$	20.9549	+	19.4433i	0.851938	+	0.790483i
$606$	−4.62600	+	8.01247i	−0.187919	+	0.325484i
$607$	−6.80181	−	11.7811i	−0.276077	−	0.478179i	0.694329	−	0.719657i	$-0.255701\pi$
$607$	−6.80181	−	11.7811i	−0.276077	−	0.478179i	−0.970406	+	0.241478i	$0.922368\pi$
$608$	−8.01080	+	35.0976i	−0.324881	+	1.42340i
$609$	−5.92405	−	20.4621i	−0.240055	−	0.829166i
$610$	10.3325	+	45.2694i	0.418349	+	1.83291i
$611$	1.03544	−	0.960748i	0.0418894	−	0.0388677i
$612$	−6.53564	+	0.985089i	−0.264187	+	0.0398198i
$613$	26.1050	−	3.93470i	1.05437	−	0.158921i	0.401092	−	0.916038i	$-0.368631\pi$
$613$	26.1050	−	3.93470i	1.05437	−	0.158921i	0.653280	+	0.757117i	$0.273393\pi$
$614$	−20.0447	+	18.5988i	−0.808939	+	0.750586i
$615$	3.56519	+	15.6201i	0.143762	+	0.629863i
$616$	−2.60763	+	15.4700i	−0.105065	+	0.623305i
$617$	−9.63610	+	42.2185i	−0.387935	+	1.69965i	0.283818	+	0.958878i	$0.408399\pi$
$617$	−9.63610	+	42.2185i	−0.387935	+	1.69965i	−0.671752	+	0.740776i	$0.734458\pi$
$618$	4.38923	+	7.60237i	0.176561	+	0.305812i
$619$	23.5692	−	40.8231i	0.947326	−	1.64082i	0.196301	−	0.980544i	$-0.437107\pi$
$619$	23.5692	−	40.8231i	0.947326	−	1.64082i	0.751025	−	0.660273i	$-0.229560\pi$
$620$	−33.5469	−	31.1269i	−1.34727	−	1.25009i
$621$	0.0481889	+	0.0328546i	0.00193375	+	0.00131841i
$622$	−0.844351	−	1.05878i	−0.0338554	−	0.0424533i
$623$	2.92601	−	5.81502i	0.117228	−	0.232974i
$624$	0.198167	−	0.248493i	0.00793302	−	0.00994769i
$625$	74.3004	−	22.9187i	2.97202	−	0.916746i
$626$	−1.80679	−	4.60362i	−0.0722137	−	0.183998i
$627$	−1.39009	+	18.5495i	−0.0555150	+	0.740796i
$628$	4.73119	−	12.0549i	0.188795	−	0.481042i
$629$	−11.6703	−	5.62014i	−0.465327	−	0.224090i
$630$	9.27251	+	5.57070i	0.369425	+	0.221942i
$631$	6.44455	−	3.10353i	0.256553	−	0.123550i	−0.301187	−	0.953565i	$-0.597383\pi$
$631$	6.44455	−	3.10353i	0.256553	−	0.123550i	0.557740	+	0.830016i	$0.311669\pi$
$632$	−2.87439	−	38.3561i	−0.114337	−	1.52572i
$633$	−1.88743	−	0.582194i	−0.0750185	−	0.0231401i
$634$	−18.5226	+	12.6285i	−0.735628	+	0.501542i
$635$	5.83684	+	0.879762i	0.231628	+	0.0349123i
$636$	11.2087			0.444455
$637$	−5.29383	+	4.57989i	−0.209749	+	0.181462i
$638$	−10.7888			−0.427132
$639$	−11.8183	−	1.78133i	−0.467526	−	0.0704683i
$640$	21.5378	−	14.6842i	0.851357	−	0.580445i
$641$	4.06822	+	1.25488i	0.160685	+	0.0495647i	0.374054	−	0.927407i	$-0.377967\pi$
$641$	4.06822	+	1.25488i	0.160685	+	0.0495647i	−0.213369	+	0.976972i	$0.568444\pi$
$642$	0.658075	+	8.78140i	0.0259721	+	0.346574i
$643$	1.76714	−	0.851009i	0.0696892	−	0.0335605i	−0.398715	−	0.917075i	$-0.630544\pi$
$643$	1.76714	−	0.851009i	0.0696892	−	0.0335605i	0.468404	+	0.883515i	$0.344829\pi$
$644$	0.0302874	−	0.0112831i	0.00119349	−	0.000444617i
$645$	14.4058	+	6.93745i	0.567227	+	0.273162i
$646$	11.1852	−	28.4993i	0.440074	−	1.12129i
$647$	−0.624887	+	8.33854i	−0.0245669	+	0.327822i	0.971357	+	0.237625i	$0.0763688\pi$
$647$	−0.624887	+	8.33854i	−0.0245669	+	0.327822i	−0.995924	+	0.0901973i	$0.971250\pi$
$648$	−4.88711	−	12.4521i	−0.191984	−	0.489167i
$649$	−8.31941	+	2.56620i	−0.326565	+	0.100732i
$650$	7.28684	−	9.13741i	0.285814	−	0.358399i
$651$	−0.583300	+	33.5371i	−0.0228613	+	1.31442i
$652$	2.89108	+	3.62530i	0.113223	+	0.141978i
$653$	−30.1708	−	20.5701i	−1.18068	−	0.804971i	−0.196213	−	0.980561i	$-0.562864\pi$
$653$	−30.1708	−	20.5701i	−1.18068	−	0.804971i	−0.984463	+	0.175590i	$0.943817\pi$
$654$	0.147978	+	0.137304i	0.00578642	+	0.00536901i
$655$	32.8723	−	56.9366i	1.28443	−	2.22470i
$656$	−0.311268	−	0.539132i	−0.0121530	−	0.0210496i
$657$	−0.521230	+	2.28366i	−0.0203351	+	0.0890941i
$658$	3.11995	+	1.28754i	0.121628	+	0.0501936i
$659$	0.126670	+	0.554979i	0.00493438	+	0.0216189i	0.977335	−	0.211698i	$-0.0678993\pi$
$659$	0.126670	+	0.554979i	0.00493438	+	0.0216189i	−0.972401	+	0.233317i	$0.925042\pi$
$660$	10.5363	−	9.77630i	0.410127	−	0.380542i
$661$	−46.3166	+	6.98110i	−1.80151	+	0.271533i	−0.962243	−	0.272192i	$-0.912251\pi$
$661$	−46.3166	+	6.98110i	−1.80151	+	0.271533i	−0.839263	+	0.543726i	$0.817013\pi$
$662$	1.69245	−	0.255096i	0.0657790	−	0.00991459i
$663$	5.31928	−	4.93557i	0.206584	−	0.191682i
$664$	8.57751	+	37.5805i	0.332872	+	1.45841i
$665$	63.6288	−	35.2752i	2.46742	−	1.36791i
$666$	−0.532831	+	2.33449i	−0.0206468	+	0.0904595i
$667$	0.0298810	+	0.0517554i	0.00115700	+	0.00200398i
$668$	12.4904	−	21.6340i	0.483267	−	0.837043i
$669$	8.10119	+	7.51680i	0.313210	+	0.290616i
$670$	36.1271	+	24.6310i	1.39571	+	0.951580i
$671$	15.6040	+	19.5668i	0.602387	+	0.755369i
$672$	−19.7955	−	4.88186i	−0.763627	−	0.188322i
$673$	1.64966	−	2.06861i	0.0635898	−	0.0797391i	−0.749019	−	0.662548i	$-0.769475\pi$
$673$	1.64966	−	2.06861i	0.0635898	−	0.0797391i	0.812609	+	0.582809i	$0.198046\pi$
$674$	−15.3560	+	4.73670i	−0.591491	+	0.182451i
$675$	−26.7320	−	68.1119i	−1.02891	−	2.62163i
$676$	−0.0885050	+	1.18102i	−0.00340404	+	0.0454237i
$677$	−7.19267	+	18.3266i	−0.276437	+	0.704350i	0.723465	+	0.690361i	$0.242548\pi$
$677$	−7.19267	+	18.3266i	−0.276437	+	0.704350i	−0.999902	+	0.0139888i	$0.995547\pi$
$678$	−2.05241	−	0.988390i	−0.0788224	−	0.0379589i
$679$	34.9337	+	3.22972i	1.34063	+	0.123945i
$680$	−57.3068	+	27.5975i	−2.19762	+	1.05832i
$681$	−0.0612154	−	0.816862i	−0.00234578	−	0.0313022i
$682$	16.2330	+	5.00722i	0.621594	+	0.191736i
$683$	19.9357	−	13.5919i	0.762819	−	0.520081i	−0.118299	−	0.992978i	$-0.537744\pi$
$683$	19.9357	−	13.5919i	0.762819	−	0.520081i	0.881118	+	0.472897i	$0.156792\pi$
$684$	8.12582	+	1.22477i	0.310699	+	0.0468303i
$685$	23.1872			0.885935
$686$	−15.2304	−	6.91453i	−0.581499	−	0.263998i
$687$	−20.0587			−0.765285
$688$	−0.614330	−	0.0925954i	−0.0234211	−	0.00353017i
$689$	5.62698	−	3.83641i	0.214371	−	0.146155i
$690$	0.0523981	+	0.0161627i	0.00199476	+	0.000615302i
$691$	−2.77697	−	37.0561i	−0.105641	−	1.40968i	−0.758239	−	0.651977i	$-0.773940\pi$
$691$	−2.77697	−	37.0561i	−0.105641	−	1.40968i	0.652598	−	0.757704i	$-0.273679\pi$
$692$	−6.50354	+	3.13194i	−0.247227	+	0.119058i
$693$	5.80553	+	0.536738i	0.220534	+	0.0203890i
$694$	−22.6233	−	10.8948i	−0.858768	−	0.413561i
$695$	8.22248	−	20.9505i	0.311896	−	0.794699i
$696$	1.73042	−	23.0908i	0.0655912	−	0.875254i
$697$	−5.19254	−	13.2304i	−0.196682	−	0.501136i
$698$	26.4837	−	8.16914i	1.00242	−	0.309207i
$699$	−20.9724	+	26.2986i	−0.793250	+	0.994704i
$700$	−39.3689	−	9.70896i	−1.48800	−	0.366964i
$701$	−16.0747	−	20.1571i	−0.607134	−	0.761322i	0.379337	−	0.925259i	$-0.376152\pi$
$701$	−16.0747	−	20.1571i	−0.607134	−	0.761322i	−0.986471	+	0.163936i	$0.947581\pi$
$702$	−4.21933	−	2.87669i	−0.159248	−	0.108574i
$703$	11.8056	+	10.9540i	0.445256	+	0.413138i
$704$	−5.63454	+	9.75931i	−0.212360	+	0.367818i
$705$	−4.15713	−	7.20035i	−0.156566	−	0.271181i
$706$	3.82124	−	16.7419i	0.143814	−	0.630091i
$707$	17.0575	−	9.45654i	0.641515	−	0.355650i
$708$	−1.54645	−	6.77545i	−0.0581192	−	0.254637i
$709$	−12.4290	+	11.5324i	−0.466782	+	0.433110i	−0.878169	−	0.478351i	$-0.841235\pi$
$709$	−12.4290	+	11.5324i	−0.466782	+	0.433110i	0.411387	+	0.911461i	$0.365044\pi$
$710$	−42.3001	+	6.37571i	−1.58749	+	0.239276i
$711$	−14.1347	+	2.13047i	−0.530094	+	0.0798988i
$712$	5.18706	−	4.81289i	0.194393	−	0.180371i
$713$	−0.0209392	−	0.0917405i	−0.000784178	−	0.00343571i
$714$	16.0279	+	6.61439i	0.599827	+	0.247537i
$715$	1.94330	−	8.51414i	0.0726752	−	0.318411i
$716$	−9.31583	−	16.1355i	−0.348149	−	0.603012i
$717$	−2.11283	+	3.65953i	−0.0789052	+	0.136668i
$718$	1.61137	+	1.49513i	0.0601356	+	0.0557977i
$719$	−35.9811	−	24.5315i	−1.34187	−	0.914869i	−0.342174	−	0.939637i	$-0.611163\pi$
$719$	−35.9811	−	24.5315i	−1.34187	−	0.914869i	−0.999693	+	0.0247673i	$0.992116\pi$
$720$	0.645541	+	0.809483i	0.0240579	+	0.0301677i
$721$	0.321807	−	18.5024i	0.0119847	−	0.689067i
$722$	−13.0340	+	16.3442i	−0.485077	+	0.608267i
$723$	28.3492	−	8.74458i	1.05432	−	0.325214i
$724$	1.46014	+	3.72039i	0.0542659	+	0.138267i
$725$	5.60289	−	74.7653i	0.208086	−	2.77672i
$726$	3.09460	−	7.88492i	0.114851	−	0.292637i
$727$	−4.20107	−	2.02313i	−0.155809	−	0.0750338i	0.354354	−	0.935111i	$-0.384701\pi$
$727$	−4.20107	−	2.02313i	−0.155809	−	0.0750338i	−0.510163	+	0.860078i	$0.670415\pi$
$728$	−7.13024	+	2.65627i	−0.264264	+	0.0984478i
$729$	−25.7176	+	12.3849i	−0.952503	+	0.458701i
$730$	0.626526	+	8.36041i	0.0231888	+	0.309433i
$731$	−13.5538	−	4.18079i	−0.501305	−	0.154632i
$732$	−16.5063	+	11.2538i	−0.610091	+	0.415953i
$733$	39.9217	+	6.01723i	1.47454	+	0.222252i	0.836592	−	0.547826i	$-0.184544\pi$
$733$	39.9217	+	6.01723i	1.47454	+	0.222252i	0.637950	+	0.770077i	$0.279782\pi$
$734$	7.41479			0.273685
$735$	19.3483	+	36.3779i	0.713672	+	1.34182i
$736$	0.0571983			0.00210836
$737$	23.3037	+	3.51246i	0.858402	+	0.129383i
$738$	−2.17086	+	1.48007i	−0.0799106	+	0.0544821i
$739$	4.22926	+	1.30456i	0.155576	+	0.0479888i	0.371565	−	0.928407i	$-0.378821\pi$
$739$	4.22926	+	1.30456i	0.155576	+	0.0479888i	−0.215989	+	0.976396i	$0.569298\pi$
$740$	−0.929942	−	12.4092i	−0.0341853	−	0.456172i
$741$	−8.12845	+	3.91445i	−0.298606	+	0.143801i
$742$	13.9495	+	8.38051i	0.512102	+	0.307658i
$743$	23.3828	+	11.2606i	0.857831	+	0.413110i	0.810478	−	0.585769i	$-0.199207\pi$
$743$	23.3828	+	11.2606i	0.857831	+	0.413110i	0.0473527	+	0.998878i	$0.484922\pi$
$744$	−13.3204	+	33.9398i	−0.488349	+	1.24429i
$745$	−6.42425	+	85.7257i	−0.235366	+	3.14074i
$746$	8.89001	+	22.6514i	0.325486	+	0.829325i
$747$	13.6889	−	4.22248i	0.500852	−	0.154492i
$748$	−7.94978	+	9.96870i	−0.290673	+	0.364492i
$749$	8.34396	−	16.5824i	0.304882	−	0.605907i
$750$	−26.3190	−	33.0030i	−0.961036	−	1.20510i
$751$	−25.4345	−	17.3410i	−0.928118	−	0.632780i	0.00201681	−	0.999998i	$-0.499358\pi$
$751$	−25.4345	−	17.3410i	−0.928118	−	0.632780i	−0.930135	+	0.367218i	$0.880310\pi$
$752$	0.236816	+	0.219733i	0.00863579	+	0.00801285i
$753$	6.43030	−	11.1376i	0.234333	−	0.405877i
$754$	−2.61633	−	4.53161i	−0.0952809	−	0.165031i
$755$	−15.7331	+	68.9312i	−0.572586	+	2.50866i
$756$	−2.94491	+	17.4710i	−0.107106	+	0.635414i
$757$	−3.46668	−	15.1885i	−0.125998	−	0.552035i	−0.998039	−	0.0626011i	$-0.980060\pi$
$757$	−3.46668	−	15.1885i	−0.125998	−	0.552035i	0.872040	−	0.489434i	$-0.162797\pi$
$758$	4.83232	−	4.48373i	0.175518	−	0.162857i
$759$	0.0292246	−	0.00440490i	0.00106079	−	0.000159888i
$760$	78.1984	−	11.7865i	2.83655	−	0.427542i
$761$	18.3736	−	17.0482i	0.666041	−	0.617996i	−0.272913	−	0.962039i	$-0.587987\pi$
$761$	18.3736	−	17.0482i	0.666041	−	0.617996i	0.938954	+	0.344043i	$0.111797\pi$
$762$	−0.389208	−	1.70523i	−0.0140995	−	0.0617740i
$763$	−0.118340	−	0.408754i	−0.00428418	−	0.0147979i
$764$	1.32550	−	5.80738i	0.0479548	−	0.210104i
$765$	11.8190	+	20.4711i	0.427318	+	0.740136i
$766$	−8.49659	+	14.7165i	−0.306994	+	0.531730i
$767$	−3.09537	−	2.87209i	−0.111767	−	0.103705i
$768$	−18.9333	−	12.9085i	−0.683197	−	0.465796i
$769$	0.655857	+	0.822418i	0.0236508	+	0.0296572i	0.793516	−	0.608549i	$-0.208248\pi$
$769$	0.655857	+	0.822418i	0.0236508	+	0.0296572i	−0.769865	+	0.638206i	$0.779677\pi$
$770$	20.4222	−	4.28901i	0.735965	−	0.154565i
$771$	17.7893	−	22.3070i	0.640665	−	0.803368i
$772$	−5.66245	+	1.74663i	−0.203796	+	0.0628627i
$773$	−0.707193	−	1.80190i	−0.0254360	−	0.0648098i	0.917592	−	0.397524i	$-0.130131\pi$
$773$	−0.707193	−	1.80190i	−0.0254360	−	0.0648098i	−0.943028	+	0.332715i	$0.892035\pi$
$774$	−0.195947	+	2.61473i	−0.00704315	+	0.0939844i
$775$	−43.1299	+	109.893i	−1.54927	+	3.94748i
$776$	34.3581	+	16.5460i	1.23338	+	0.593966i
$777$	−6.31908	+	6.57715i	−0.226696	+	0.235954i
$778$	17.2359	−	8.30036i	0.617936	−	0.297582i
$779$	1.32056	+	17.6216i	0.0473138	+	0.631359i
$780$	6.66145	+	2.05479i	0.238518	+	0.0735731i
$781$	−19.0502	+	12.9882i	−0.681670	+	0.464755i
$782$	−0.0480999	−	0.00724989i	−0.00172005	−	0.000259255i
$783$	−32.7600			−1.17075
$784$	−1.13502	−	1.12909i	−0.0405364	−	0.0403247i
$785$	−46.3146			−1.65304
$786$	−19.2636	−	2.90352i	−0.687110	−	0.103565i
$787$	1.07525	−	0.733093i	0.0383285	−	0.0261319i	−0.544004	−	0.839082i	$-0.683092\pi$
$787$	1.07525	−	0.733093i	0.0383285	−	0.0261319i	0.582333	+	0.812951i	$0.302140\pi$
$788$	−23.9821	−	7.39750i	−0.854327	−	0.263525i
$789$	−0.491474	−	6.55826i	−0.0174969	−	0.233480i
$790$	−46.0957	+	22.1985i	−1.64001	+	0.789788i
$791$	2.63571	+	4.01412i	0.0937151	+	0.142726i
$792$	5.70987	+	2.74973i	0.202892	+	0.0977074i
$793$	−4.43461	+	11.2992i	−0.157478	+	0.401246i
$794$	0.962768	−	12.8472i	0.0341674	−	0.455932i
$795$	−14.6454	−	37.3158i	−0.519418	−	1.32346i
$796$	6.99309	−	2.15708i	0.247863	−	0.0764558i
$797$	24.3248	−	30.5023i	0.861627	−	1.08045i	−0.134359	−	0.990933i	$-0.542897\pi$
$797$	24.3248	−	30.5023i	0.861627	−	1.08045i	0.995986	−	0.0895132i	$-0.0285311\pi$
$798$	−16.6183	−	13.7321i	−0.588281	−	0.486113i
$799$	4.59857	+	5.76642i	0.162686	+	0.204001i
$800$	−59.2898	−	40.4231i	−2.09621	−	1.42917i
$801$	−1.92769	−	1.78863i	−0.0681114	−	0.0631982i
$802$	3.66429	−	6.34673i	0.129390	−	0.224111i
$803$	2.25938	+	3.91335i	0.0797317	+	0.138099i
$804$	−4.18611	+	18.3405i	−0.147633	+	0.646821i
$805$	−0.0771371	−	0.0860894i	−0.00271873	−	0.00303425i
$806$	1.83339	+	8.03263i	0.0645786	+	0.282937i
$807$	−11.2167	+	10.4076i	−0.394847	+	0.366364i
$808$	20.9633	−	3.15972i	0.737488	−	0.111158i
$809$	29.8523	−	4.49951i	1.04955	−	0.158194i	0.398454	−	0.917188i	$-0.369547\pi$
$809$	29.8523	−	4.49951i	1.04955	−	0.158194i	0.651098	+	0.758994i	$0.274309\pi$
$810$	−13.0433	+	12.1024i	−0.458296	+	0.425236i
$811$	−7.28978	−	31.9386i	−0.255979	−	1.12152i	−0.925507	−	0.378730i	$-0.876361\pi$
$811$	−7.28978	−	31.9386i	−0.255979	−	1.12152i	0.669528	−	0.742786i	$-0.266496\pi$
$812$	−10.4861	+	14.8199i	−0.367991	+	0.520075i
$813$	4.70306	−	20.6055i	0.164944	−	0.722665i
$814$	2.30966	+	4.00045i	0.0809536	+	0.140216i
$815$	8.29175	−	14.3617i	0.290447	−	0.503069i
$816$	1.21658	+	1.12882i	0.0425887	+	0.0395165i
$817$	14.5708	+	9.93417i	0.509766	+	0.347553i
$818$	−18.6294	−	23.3605i	−0.651361	−	0.816781i
$819$	1.18242	+	2.56866i	0.0413171	+	0.0897562i
$820$	8.51329	−	10.6753i	0.297297	−	0.372799i
$821$	6.25766	−	1.93023i	0.218394	−	0.0673656i	−0.183627	−	0.982996i	$-0.558784\pi$
$821$	6.25766	−	1.93023i	0.218394	−	0.0673656i	0.402021	+	0.915630i	$0.368308\pi$
$822$	−2.51016	−	6.39578i	−0.0875518	−	0.223078i
$823$	3.02474	−	40.3623i	0.105436	−	1.40694i	−0.654066	−	0.756437i	$-0.726938\pi$
$823$	3.02474	−	40.3623i	0.105436	−	1.40694i	0.759502	−	0.650505i	$-0.225443\pi$
$824$	7.34885	−	18.7246i	0.256009	−	0.652301i
$825$	−33.4063	−	16.0876i	−1.16306	−	0.560098i
$826$	3.14126	−	9.58842i	0.109298	−	0.333624i
$827$	13.2928	−	6.40150i	0.462238	−	0.222602i	−0.188246	−	0.982122i	$-0.560280\pi$
$827$	13.2928	−	6.40150i	0.462238	−	0.222602i	0.650484	+	0.759520i	$0.274566\pi$
$828$	−0.000975707	−	0.0130199i	−3.39082e−5	−	0.000452473i
$829$	−31.2689	−	9.64518i	−1.08601	−	0.334991i	−0.300466	−	0.953792i	$-0.597142\pi$
$829$	−31.2689	−	9.64518i	−1.08601	−	0.334991i	−0.785547	+	0.618802i	$0.787618\pi$
$830$	42.3639	−	28.8832i	1.47047	−	1.00255i
$831$	26.0457	+	3.92576i	0.903517	+	0.136183i
$832$	−5.46560			−0.189486
$833$	−21.7817	−	29.3521i	−0.754692	−	1.01699i
$834$	−6.66898			−0.230928
$835$	−88.3432	−	13.3156i	−3.05724	−	0.460805i
$836$	13.0982	−	8.93018i	0.453010	−	0.308857i
$837$	49.2914	+	15.2044i	1.70376	+	0.525540i
$838$	−1.83689	−	24.5116i	−0.0634543	−	0.846739i
$839$	−22.3956	+	10.7852i	−0.773182	+	0.372345i	−0.778503	−	0.627641i	$-0.784021\pi$
$839$	−22.3956	+	10.7852i	−0.773182	+	0.372345i	0.00532093	+	0.999986i	$0.498306\pi$
$840$	5.90407	+	44.3967i	0.203710	+	1.53183i
$841$	−4.11580	−	1.98207i	−0.141924	−	0.0683471i
$842$	−1.87901	+	4.78765i	−0.0647551	+	0.164993i
$843$	−0.102459	+	1.36722i	−0.00352888	+	0.0470896i
$844$	0.614981	+	1.56695i	0.0211685	+	0.0539365i
$845$	4.04745	−	1.24847i	0.139237	−	0.0429488i
$846$	0.850096	−	1.06599i	0.0292269	−	0.0366494i
$847$	−14.1518	+	10.8885i	−0.486262	+	0.374134i
$848$	0.971147	+	1.21778i	0.0333493	+	0.0418187i
$849$	6.56572	+	4.47643i	0.225335	+	0.153631i
$850$	44.7350	+	41.5081i	1.53440	+	1.42371i
$851$	0.0127939	−	0.0221596i	0.000438568	−	0.000759622i
$852$	−9.20240	−	15.9390i	−0.315269	−	0.546062i
$853$	6.16561	−	27.0133i	0.211106	−	0.924918i	−0.752710	−	0.658352i	$-0.771254\pi$
$853$	6.16561	−	27.0133i	0.211106	−	0.924918i	0.963817	−	0.266566i	$-0.0858890\pi$
$854$	−28.9566	+	1.66420i	−0.990875	+	0.0569476i
$855$	−6.53976	−	28.6526i	−0.223655	−	0.979897i
$856$	14.7917	−	13.7247i	0.505569	−	0.469099i
$857$	35.7202	−	5.38395i	1.22018	−	0.183912i	0.492796	−	0.870145i	$-0.335975\pi$
$857$	35.7202	−	5.38395i	1.22018	−	0.183912i	0.727382	+	0.686233i	$0.240737\pi$
$858$	−2.55885	+	0.385685i	−0.0873578	+	0.0131671i
$859$	23.4845	−	21.7904i	0.801281	−	0.743480i	−0.168959	−	0.985623i	$-0.554041\pi$
$859$	23.4845	−	21.7904i	0.801281	−	0.743480i	0.970241	+	0.242143i	$0.0778502\pi$
$860$	−3.03218	−	13.2848i	−0.103396	−	0.453009i
$861$	−9.99141	+	0.574227i	−0.340506	+	0.0195696i
$862$	−0.408403	+	1.78933i	−0.0139103	+	0.0609449i
$863$	−1.81396	−	3.14188i	−0.0617481	−	0.106951i	0.833499	−	0.552521i	$-0.186334\pi$
$863$	−1.81396	−	3.14188i	−0.0617481	−	0.106951i	−0.895247	+	0.445570i	$0.853001\pi$
$864$	−15.6773	+	27.1539i	−0.533354	+	0.923796i
$865$	18.9243	+	17.5592i	0.643446	+	0.597031i
$866$	−30.4278	−	20.7453i	−1.03398	−	0.704956i
$867$	8.89416	+	11.1529i	0.302062	+	0.378773i
$868$	22.6557	−	17.4315i	0.768986	−	0.591665i
$869$	−17.1931	+	21.5595i	−0.583237	+	0.731356i
$870$	−29.4319	+	9.07854i	−0.997835	+	0.307791i
$871$	4.17590	+	10.6400i	0.141495	+	0.360524i
$872$	0.0345670	−	0.461265i	0.00117059	−	0.0156204i
$873$	5.17765	−	13.1924i	0.175237	−	0.446496i
$874$	0.0544893	+	0.0262407i	0.00184313	+	0.000887604i
$875$	11.7304	+	88.2084i	0.396558	+	2.98199i
$876$	−3.24986	+	1.56505i	−0.109803	+	0.0528782i
$877$	1.35427	+	18.0715i	0.0457304	+	0.610230i	0.972244	+	0.233969i	$0.0751715\pi$
$877$	1.35427	+	18.0715i	0.0457304	+	0.610230i	−0.926514	+	0.376261i	$0.877209\pi$
$878$	32.6954	+	10.0852i	1.10341	+	0.340358i
$879$	18.1935	−	12.4041i	0.613651	−	0.418380i
$880$	1.97504	+	0.297690i	0.0665787	+	0.0100351i
$881$	37.3614			1.25874			0.629368	−	0.777107i	$-0.283314\pi$
$881$	37.3614			1.25874			0.629368	+	0.777107i	$0.283314\pi$
$882$	−4.39401	+	5.13305i	−0.147954	+	0.172839i
$883$	−19.5472			−0.657815			−0.328908	−	0.944362i	$-0.606680\pi$
$883$	−19.5472			−0.657815			−0.328908	+	0.944362i	$0.606680\pi$
$884$	−6.11501	−	0.921689i	−0.205670	−	0.0309998i
$885$	−20.5360	+	14.0012i	−0.690312	+	0.470646i
$886$	23.4779	+	7.24197i	0.788755	+	0.243299i
$887$	1.91983	+	25.6183i	0.0644614	+	0.860178i	0.931919	+	0.362667i	$0.118134\pi$
$887$	1.91983	+	25.6183i	0.0644614	+	0.860178i	−0.867457	+	0.497511i	$0.834247\pi$
$888$	−8.93246	+	4.30165i	−0.299754	+	0.144354i
$889$	−1.14790	+	3.50388i	−0.0384994	+	0.117516i
$890$	−8.48001	−	4.08376i	−0.284250	−	0.136888i
$891$	−3.50370	+	8.92728i	−0.117378	+	0.299075i
$892$	0.703828	−	9.39193i	0.0235659	−	0.314465i
$893$	−3.35021	−	8.53618i	−0.112110	−	0.285652i
$894$	24.3414	−	7.50833i	0.814099	−	0.251116i
$895$	−41.5457	+	52.0967i	−1.38872	+	1.74140i
$896$	6.80863	+	14.7909i	0.227460	+	0.494128i
$897$	0.00893728	+	0.0112070i	0.000298407	+	0.000374191i
$898$	−13.3950	−	9.13254i	−0.446996	−	0.304757i
$899$	38.7459	+	35.9510i	1.29225	+	1.19903i
$900$	−8.19002	+	14.1855i	−0.273001	+	0.472851i
$901$	17.7804	+	30.7966i	0.592352	+	1.02598i
$902$	−1.12787	+	4.94150i	−0.0375538	+	0.164534i
$903$	−5.76883	+	8.15299i	−0.191975	+	0.271315i
$904$	1.16152	+	5.08897i	0.0386317	+	0.169257i
$905$	10.4780	−	9.72215i	0.348300	−	0.323175i
$906$	20.7167	−	3.12254i	0.688266	−	0.103739i
$907$	−23.3053	+	3.51270i	−0.773838	+	0.116637i	−0.524078	−	0.851670i	$-0.675590\pi$
$907$	−23.3053	+	3.51270i	−0.773838	+	0.116637i	−0.249760	+	0.968308i	$0.580352\pi$
$908$	−0.511748	+	0.474833i	−0.0169830	+	0.0157579i
$909$	−1.75317	−	7.68115i	−0.0581491	−	0.254768i
$910$	6.75398	+	7.53783i	0.223892	+	0.249877i
$911$	−5.94513	+	26.0473i	−0.196971	+	0.862987i	0.775756	+	0.631033i	$0.217369\pi$
$911$	−5.94513	+	26.0473i	−0.196971	+	0.862987i	−0.972727	+	0.231953i	$0.925488\pi$
$912$	−1.03170	−	1.78696i	−0.0341631	−	0.0591721i
$913$	13.8177	−	23.9329i	0.457299	−	0.792065i
$914$	−4.12986	−	3.83195i	−0.136604	−	0.126750i
$915$	59.0331	+	40.2481i	1.95157	+	1.33056i
$916$	10.6583	+	13.3651i	0.352160	+	0.441595i
$917$	31.6573	+	26.1593i	1.04542	+	0.863855i
$918$	16.6253	−	20.8475i	0.548718	−	0.688070i
$919$	−12.9990	+	4.00967i	−0.428798	+	0.132267i	−0.501639	−	0.865077i	$-0.667270\pi$
$919$	−12.9990	+	4.00967i	−0.428798	+	0.132267i	0.0728413	+	0.997344i	$0.476793\pi$
$920$	−0.0459042	−	0.116962i	−0.00151342	−	0.00385613i
$921$	−3.14426	+	41.9572i	−0.103607	+	1.38254i
$922$	4.06900	−	10.3676i	0.134005	−	0.341440i
$923$	−10.0752	−	4.85196i	−0.331629	−	0.159704i
$924$	4.92780	+	7.50492i	0.162113	+	0.246894i
$925$	−28.9223	+	13.9282i	−0.950959	+	0.457958i
$926$	1.63072	+	21.7604i	0.0535887	+	0.715092i
$927$	−7.14332	−	2.20342i	−0.234617	−	0.0723699i
$928$	−26.5456	+	18.0985i	−0.871401	+	0.594111i
$929$	−7.19435	−	1.08437i	−0.236039	−	0.0355772i	0.0299574	−	0.999551i	$-0.490463\pi$
$929$	−7.19435	−	1.08437i	−0.236039	−	0.0355772i	−0.265996	+	0.963974i	$0.585701\pi$
$930$	48.4974			1.59029
$931$	15.1216	+	42.8548i	0.495590	+	1.40451i
$932$	28.6666			0.939005
$933$	−2.06050	−	0.310571i	−0.0674578	−	0.0101676i
$934$	−30.8216	+	21.0138i	−1.00851	+	0.687592i
$935$	43.5748	+	13.4410i	1.42505	+	0.439569i
$936$	0.229700	+	3.06514i	0.00750799	+	0.100187i
$937$	−42.8507	+	20.6358i	−1.39987	+	0.674143i	−0.973135	−	0.230233i	$-0.926051\pi$
$937$	−42.8507	+	20.6358i	−1.39987	+	0.674143i	−0.426736	+	0.904376i	$0.640337\pi$
$938$	−18.9225	+	19.6953i	−0.617841	+	0.643074i
$939$	−6.85608	−	3.30171i	−0.223740	−	0.107747i
$940$	−2.58868	+	6.59585i	−0.0844335	+	0.215133i
$941$	−0.512373	+	6.83715i	−0.0167029	+	0.222885i	0.982606	+	0.185704i	$0.0594566\pi$
$941$	−0.512373	+	6.83715i	−0.0167029	+	0.222885i	−0.999309	+	0.0371803i	$0.988162\pi$
$942$	5.01385	+	12.7751i	0.163360	+	0.416235i
$943$	0.0268289	−	0.00827563i	0.000873670	−	0.000269491i
$944$	0.602135	−	0.755053i	0.0195978	−	0.0245749i
$945$	62.0118	−	13.0235i	2.01724	−	0.423656i
$946$	3.15378	+	3.95471i	0.102538	+	0.128579i
$947$	23.0865	+	15.7401i	0.750212	+	0.511486i	0.877027	−	0.480441i	$-0.159523\pi$
$947$	23.0865	+	15.7401i	0.750212	+	0.511486i	−0.126815	+	0.991926i	$0.540476\pi$
$948$	−16.1360	−	14.9721i	−0.524074	−	0.486270i
$949$	−1.09582	+	1.89801i	−0.0355717	+	0.0616121i
$950$	−37.9370	−	65.7088i	−1.23084	−	2.13187i
$951$	−7.67583	+	33.6300i	−0.248906	+	1.09053i
$952$	−11.0489	−	38.1636i	−0.358096	−	1.23689i
$953$	5.51434	+	24.1599i	0.178627	+	0.782615i	0.982265	+	0.187497i	$0.0600376\pi$
$953$	5.51434	+	24.1599i	0.178627	+	0.782615i	−0.803638	+	0.595118i	$0.797105\pi$
$954$	4.81895	−	4.47133i	0.156019	−	0.144765i
$955$	−21.0657	+	3.17514i	−0.681669	+	0.102745i
$956$	3.56102	−	0.536737i	0.115171	−	0.0173593i
$957$	−12.1693	+	11.2914i	−0.393376	+	0.365000i
$958$	8.40913	+	36.8428i	0.271687	+	1.19034i
$959$	−2.40741	+	14.2822i	−0.0777394	+	0.461196i
$960$	−7.15883	+	31.3649i	−0.231050	+	1.01230i
$961$	−26.1126	−	45.2283i	−0.842342	−	1.45898i
$962$	−1.12021	+	1.94026i	−0.0361169	+	0.0625563i
$963$	−5.49708	−	5.10055i	−0.177141	−	0.164363i
$964$	−20.8901	−	14.2426i	−0.672824	−	0.458723i
$965$	13.2134	+	16.5691i	0.425355	+	0.533379i
$966$	−0.0153957	+	0.0305967i	−0.000495348	+	0.000984432i
$967$	5.92635	−	7.43141i	0.190578	−	0.238978i	−0.677357	−	0.735654i	$-0.736875\pi$
$967$	5.92635	−	7.43141i	0.190578	−	0.238978i	0.867936	+	0.496676i	$0.165446\pi$
$968$	−18.5470	+	5.72098i	−0.596122	+	0.183879i
$969$	−17.2107	−	43.8522i	−0.552888	−	1.40874i
$970$	3.79066	−	50.5828i	0.121711	−	1.62412i
$971$	−14.9726	+	38.1495i	−0.480493	+	1.22428i	0.461048	+	0.887375i	$0.347474\pi$
$971$	−14.9726	+	38.1495i	−0.480493	+	1.22428i	−0.941540	+	0.336900i	$0.890621\pi$
$972$	11.2030	+	5.39506i	0.359335	+	0.173047i
$973$	12.0508	+	7.23986i	0.386332	+	0.232099i
$974$	30.1230	−	14.5065i	0.965204	−	0.464818i
$975$	−1.34389	−	17.9329i	−0.0430389	−	0.574314i
$976$	−2.65282	−	0.818285i	−0.0849145	−	0.0261927i
$977$	14.3782	−	9.80290i	0.460000	−	0.313623i	−0.311054	−	0.950392i	$-0.600682\pi$
$977$	14.3782	−	9.80290i	0.460000	−	0.313623i	0.771054	+	0.636769i	$0.219730\pi$
$978$	−4.85907	−	0.732387i	−0.155376	−	0.0234192i
$979$	−5.07296			−0.162132
$980$	13.9577	−	32.2214i	0.445864	−	1.02927i
$981$	−0.171902			−0.00548842
$982$	26.8835	+	4.05203i	0.857886	+	0.129305i
$983$	−5.66035	+	3.85916i	−0.180537	+	0.123088i	−0.650217	−	0.759749i	$-0.725322\pi$
$983$	−5.66035	+	3.85916i	−0.180537	+	0.123088i	0.469679	+	0.882837i	$0.344369\pi$
$984$	−10.3952	−	3.20650i	−0.331387	−	0.102219i
$985$	6.70757	+	89.5062i	0.213721	+	2.85191i
$986$	24.6170	−	11.8549i	0.783964	−	0.377537i
$987$	4.86669	−	1.81302i	0.154909	−	0.0577089i
$988$	6.92731	+	3.33602i	0.220387	+	0.106133i
$989$	0.0102365	−	0.0260823i	0.000325503	−	0.000829368i
$990$	0.629959	−	8.40622i	0.0200214	−	0.267167i
$991$	0.0675557	+	0.172129i	0.00214598	+	0.00546787i	0.931943	−	0.362606i	$-0.118113\pi$
$991$	0.0675557	+	0.172129i	0.00214598	+	0.00546787i	−0.929797	+	0.368073i	$0.880018\pi$
$992$	48.3408	−	14.9111i	1.53482	−	0.473429i
$993$	1.64203	−	2.05904i	0.0521082	−	0.0653417i
$994$	0.464677	−	26.7168i	0.0147387	−	0.847406i
$995$	−16.3185	−	20.4628i	−0.517331	−	0.648713i
$996$	18.2267	+	12.4267i	0.577535	+	0.393757i
$997$	−29.5135	−	27.3845i	−0.934701	−	0.867276i	0.0566656	−	0.998393i	$-0.481953\pi$
$997$	−29.5135	−	27.3845i	−0.934701	−	0.867276i	−0.991367	+	0.131117i	$0.958144\pi$
$998$	−0.594144	+	1.02909i	−0.0188073	+	0.0325752i
$999$	7.01327	+	12.1473i	0.221890	+	0.384325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.235.17	✓	324
49.44	even	21	inner	637.2.bl.a.534.17	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.235.17	✓	324	1.1	even	1	trivial
637.2.bl.a.534.17	yes	324	49.44	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.893058 + 0.134607i) q^{2} +(1.14821 - 0.782835i) q^{3} +(-1.13171 - 0.349087i) q^{4} +(0.316529 + 4.22378i) q^{5} +(1.13079 - 0.544561i) q^{6} +(-2.63452 - 0.243568i) q^{7} +(-2.59111 - 1.24781i) q^{8} +(-0.390471 + 0.994905i) q^{9} +O(q^{10})\)	\(q+(0.893058 + 0.134607i) q^{2} +(1.14821 - 0.782835i) q^{3} +(-1.13171 - 0.349087i) q^{4} +(0.316529 + 4.22378i) q^{5} +(1.13079 - 0.544561i) q^{6} +(-2.63452 - 0.243568i) q^{7} +(-2.59111 - 1.24781i) q^{8} +(-0.390471 + 0.994905i) q^{9} +(-0.285872 + 3.81469i) q^{10} +(0.753267 + 1.91929i) q^{11} +(-1.57272 + 0.485119i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(-2.31999 - 0.572145i) q^{14} +(3.66997 + 4.60199i) q^{15} +(-0.188970 - 0.128837i) q^{16} +(-3.82770 - 3.55159i) q^{17} +(-0.482635 + 0.835948i) q^{18} +(3.24603 + 5.62229i) q^{19} +(1.11625 - 4.89060i) q^{20} +(-3.21565 + 1.78272i) q^{21} +(0.414361 + 1.81543i) q^{22} +(0.00756129 - 0.00701585i) q^{23} +(-3.95196 + 0.595662i) q^{24} +(-12.7960 + 1.92869i) q^{25} +(-0.662053 + 0.614295i) q^{26} +(1.25820 + 5.51255i) q^{27} +(2.89649 + 1.19532i) q^{28} +(-1.28924 + 5.64854i) q^{29} +(2.65804 + 4.60385i) q^{30} +(4.56139 - 7.90056i) q^{31} +(4.06497 + 3.77174i) q^{32} +(2.36740 + 1.61406i) q^{33} +(-2.94029 - 3.68701i) q^{34} +(0.194880 - 11.2047i) q^{35} +(0.789209 - 0.989637i) q^{36} +(2.37047 - 0.731193i) q^{37} +(2.14210 + 5.45797i) q^{38} +(-0.103851 + 1.38580i) q^{39} +(4.45033 - 11.3392i) q^{40} +(2.45238 + 1.18101i) q^{41} +(-3.11173 + 1.15923i) q^{42} +(2.44739 - 1.17860i) q^{43} +(-0.182481 - 2.43504i) q^{44} +(-4.32586 - 1.33435i) q^{45} +(0.00769705 - 0.00524776i) q^{46} +(-1.39673 - 0.210523i) q^{47} -0.317835 q^{48} +(6.88135 + 1.28337i) q^{49} -11.6872 q^{50} +(-7.17530 - 1.08150i) q^{51} +(0.978538 - 0.667156i) q^{52} +(-6.50779 - 2.00739i) q^{53} +(0.381622 + 5.09239i) q^{54} +(-7.86825 + 3.78915i) q^{55} +(6.52239 + 3.91849i) q^{56} +(8.12845 + 3.91445i) q^{57} +(-1.91170 + 4.87094i) q^{58} +(-0.315554 + 4.21078i) q^{59} +(-2.54685 - 6.48927i) q^{60} +(11.5990 - 3.57782i) q^{61} +(5.13706 - 6.44167i) q^{62} +(1.27103 - 2.52599i) q^{63} +(3.40775 + 4.27318i) q^{64} +(-3.49964 - 2.38601i) q^{65} +(1.89696 + 1.76012i) q^{66} +(5.71508 - 9.89880i) q^{67} +(3.09204 + 5.35557i) q^{68} +(0.00318968 - 0.0139749i) q^{69} +(1.68227 - 9.98024i) q^{70} +(2.48837 + 10.9023i) q^{71} +(2.25321 - 2.09067i) q^{72} +(2.16716 - 0.326646i) q^{73} +(2.21539 - 0.333916i) q^{74} +(-13.1826 + 12.2317i) q^{75} +(-1.71090 - 7.49596i) q^{76} +(-1.51701 - 5.23988i) q^{77} +(-0.279283 + 1.22362i) q^{78} +(6.68721 + 11.5826i) q^{79} +(0.484366 - 0.838947i) q^{80} +(3.40967 + 3.16371i) q^{81} +(2.03115 + 1.38481i) q^{82} +(-8.35688 - 10.4792i) q^{83} +(4.26151 - 0.894990i) q^{84} +(13.7896 - 17.2916i) q^{85} +(2.34431 - 0.723124i) q^{86} +(2.94156 + 7.49497i) q^{87} +(0.443120 - 5.91303i) q^{88} +(-0.898896 + 2.29035i) q^{89} +(-3.68363 - 1.77394i) q^{90} +(1.83302 - 1.90789i) q^{91} +(-0.0110063 + 0.00530037i) q^{92} +(-0.947410 - 12.6423i) q^{93} +(-1.21902 - 0.376019i) q^{94} +(-22.7199 + 15.4902i) q^{95} +(7.62008 + 1.14854i) q^{96} -13.2600 q^{97} +(5.97269 + 2.07240i) q^{98} -2.20364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

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