LMFDB - Embedded newform 380.2.bj.a.187.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			187.26
Character	$\chi$	$=$	380.187
Dual form			380.2.bj.a.63.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.201238 + 1.39982i) q^{2} +(0.0221779 + 0.0103417i) q^{3} +(-1.91901 - 0.563395i) q^{4} +(1.45970 + 1.69389i) q^{5} +(-0.0189396 + 0.0289640i) q^{6} +(-4.53688 - 1.21565i) q^{7} +(1.17483 - 2.57289i) q^{8} +(-1.92798 - 2.29767i) q^{9} +O(q^{10})$	\(q+(-0.201238 + 1.39982i) q^{2} +(0.0221779 + 0.0103417i) q^{3} +(-1.91901 - 0.563395i) q^{4} +(1.45970 + 1.69389i) q^{5} +(-0.0189396 + 0.0289640i) q^{6} +(-4.53688 - 1.21565i) q^{7} +(1.17483 - 2.57289i) q^{8} +(-1.92798 - 2.29767i) q^{9} +(-2.66489 + 1.70245i) q^{10} +(-2.36413 - 1.36493i) q^{11} +(-0.0367331 - 0.0323408i) q^{12} +(-3.56425 + 1.66204i) q^{13} +(2.61469 - 6.10620i) q^{14} +(0.0148554 + 0.0526629i) q^{15} +(3.36517 + 2.16232i) q^{16} +(0.215131 + 2.45896i) q^{17} +(3.60432 - 2.23645i) q^{18} +(-2.57400 + 3.51775i) q^{19} +(-1.84685 - 4.07298i) q^{20} +(-0.0880467 - 0.0738800i) q^{21} +(2.38642 - 3.03469i) q^{22} +(0.862750 - 1.23214i) q^{23} +(0.0526635 - 0.0449116i) q^{24} +(-0.738534 + 4.94516i) q^{25} +(-1.60929 - 5.32378i) q^{26} +(-0.0379970 - 0.141807i) q^{27} +(8.02141 + 4.88891i) q^{28} +(-3.57396 - 4.25928i) q^{29} +(-0.0767082 + 0.0101972i) q^{30} +(7.84733 - 4.53066i) q^{31} +(-3.70406 + 4.27550i) q^{32} +(-0.0383158 - 0.0547207i) q^{33} +(-3.48539 - 0.193691i) q^{34} +(-4.56332 - 9.45948i) q^{35} +(2.40530 + 5.49547i) q^{36} +(-3.96378 - 3.96378i) q^{37} +(-4.40624 - 4.31104i) q^{38} -0.0962361 q^{39} +(6.07310 - 1.76562i) q^{40} +(0.890376 - 0.324070i) q^{41} +(0.121137 - 0.108382i) q^{42} +(-9.94350 + 6.96252i) q^{43} +(3.76779 + 3.95126i) q^{44} +(1.07774 - 6.61971i) q^{45} +(1.55115 + 1.45565i) q^{46} +(-0.301686 + 3.44829i) q^{47} +(0.0522704 + 0.0827575i) q^{48} +(13.0433 + 7.53056i) q^{49} +(-6.77372 - 2.02897i) q^{50} +(-0.0206587 + 0.0567594i) q^{51} +(7.77620 - 1.18138i) q^{52} +(8.67038 + 6.07106i) q^{53} +(0.206151 - 0.0246522i) q^{54} +(-1.13889 - 5.99698i) q^{55} +(-8.45782 + 10.2447i) q^{56} +(-0.0934655 + 0.0513968i) q^{57} +(6.68146 - 4.14579i) q^{58} +(0.113684 + 0.0953925i) q^{59} +(0.00116237 - 0.109430i) q^{60} +(-1.56220 - 8.85968i) q^{61} +(4.76294 + 11.8966i) q^{62} +(5.95383 + 12.7680i) q^{63} +(-5.23955 - 6.04542i) q^{64} +(-8.01806 - 3.61137i) q^{65} +(0.0843098 - 0.0426235i) q^{66} +(-1.06756 + 12.2022i) q^{67} +(0.972527 - 4.83996i) q^{68} +(0.0318764 - 0.0184039i) q^{69} +(14.1599 - 4.48423i) q^{70} +(-7.78761 - 1.37317i) q^{71} +(-8.17672 + 2.26110i) q^{72} +(3.36904 - 7.22494i) q^{73} +(6.34625 - 4.75092i) q^{74} +(-0.0675207 + 0.102036i) q^{75} +(6.92140 - 5.30040i) q^{76} +(9.06652 + 9.06652i) q^{77} +(0.0193664 - 0.134713i) q^{78} +(0.134546 - 0.0489707i) q^{79} +(1.24942 + 8.85658i) q^{80} +(-1.56190 + 8.85796i) q^{81} +(0.274464 + 1.31158i) q^{82} +(-1.85832 + 6.93534i) q^{83} +(0.127339 + 0.191381i) q^{84} +(-3.85118 + 3.95375i) q^{85} +(-7.74528 - 15.3203i) q^{86} +(-0.0352147 - 0.131423i) q^{87} +(-6.28928 + 4.47910i) q^{88} +(-1.35854 + 3.73255i) q^{89} +(9.04953 + 2.84077i) q^{90} +(18.1911 - 3.20757i) q^{91} +(-2.34980 + 1.87841i) q^{92} +(0.220892 - 0.0193256i) q^{93} +(-4.76628 - 1.11623i) q^{94} +(-9.71595 + 0.774799i) q^{95} +(-0.126365 + 0.0565154i) q^{96} +(-0.0974512 - 1.11387i) q^{97} +(-13.1663 + 16.7429i) q^{98} +(1.42183 + 8.06357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.201238	+	1.39982i	−0.142297	+	0.989824i
$2$	−0.201238	+	1.39982i	−0.142297	+	0.989824i
$3$	0.0221779	+	0.0103417i	0.0128044	+	0.00597081i	0.429010	−	0.903300i	$-0.358863\pi$
$3$	0.0221779	+	0.0103417i	0.0128044	+	0.00597081i	−0.416205	+	0.909271i	$0.636640\pi$
$4$	−1.91901	−	0.563395i	−0.959503	−	0.281698i
$5$	1.45970	+	1.69389i	0.652799	+	0.757531i
$5$	1.45970	+	1.69389i	0.652799	+	0.757531i
$6$	−0.0189396	+	0.0289640i	−0.00773208	+	0.0118245i
$7$	−4.53688	−	1.21565i	−1.71478	−	0.459474i	−0.738192	−	0.674590i	$-0.764320\pi$
$7$	−4.53688	−	1.21565i	−1.71478	−	0.459474i	−0.976588	+	0.215116i	$0.930987\pi$
$8$	1.17483	−	2.57289i	0.415365	−	0.909655i
$9$	−1.92798	−	2.29767i	−0.642659	−	0.765892i
$10$	−2.66489	+	1.70245i	−0.842714	+	0.538362i
$11$	−2.36413	−	1.36493i	−0.712813	−	0.411543i	0.0992885	−	0.995059i	$-0.468343\pi$
$11$	−2.36413	−	1.36493i	−0.712813	−	0.411543i	−0.812102	+	0.583516i	$0.801677\pi$
$12$	−0.0367331	−	0.0323408i	−0.0106039	−	0.00933599i
$13$	−3.56425	+	1.66204i	−0.988545	+	0.460966i	−0.848509	−	0.529180i	$-0.822500\pi$
$13$	−3.56425	+	1.66204i	−0.988545	+	0.460966i	−0.140036	+	0.990146i	$0.544722\pi$
$14$	2.61469	−	6.10620i	0.698806	−	1.63195i
$15$	0.0148554	+	0.0526629i	0.00383565	+	0.0135975i
$16$	3.36517	+	2.16232i	0.841293	+	0.540580i
$17$	0.215131	+	2.45896i	0.0521769	+	0.596384i	0.976607	+	0.215033i	$0.0689858\pi$
$17$	0.215131	+	2.45896i	0.0521769	+	0.596384i	−0.924430	+	0.381352i	$0.875459\pi$
$18$	3.60432	−	2.23645i	0.849546	−	0.527136i
$19$	−2.57400	+	3.51775i	−0.590515	+	0.807027i
$19$	−2.57400	+	3.51775i	−0.590515	+	0.807027i
$20$	−1.84685	−	4.07298i	−0.412968	−	0.910745i
$21$	−0.0880467	−	0.0738800i	−0.0192134	−	0.0161219i
$22$	2.38642	−	3.03469i	0.508786	−	0.646999i
$23$	0.862750	−	1.23214i	0.179896	−	0.256918i	−0.719069	−	0.694939i	$-0.755431\pi$
$23$	0.862750	−	1.23214i	0.179896	−	0.256918i	0.898965	+	0.438021i	$0.144320\pi$
$24$	0.0526635	−	0.0449116i	0.0107499	−	0.00916755i
$25$	−0.738534	+	4.94516i	−0.147707	+	0.989031i
$26$	−1.60929	−	5.32378i	−0.315609	−	1.04408i
$27$	−0.0379970	−	0.141807i	−0.00731253	−	0.0272907i
$28$	8.02141	+	4.88891i	1.51590	+	0.923917i
$29$	−3.57396	−	4.25928i	−0.663668	−	0.790929i	0.324239	−	0.945975i	$-0.394892\pi$
$29$	−3.57396	−	4.25928i	−0.663668	−	0.790929i	−0.987907	+	0.155046i	$0.950447\pi$
$30$	−0.0767082	+	0.0101972i	−0.0140049	+	0.00186174i
$31$	7.84733	−	4.53066i	1.40942	−	0.813730i	0.414089	−	0.910236i	$-0.364100\pi$
$31$	7.84733	−	4.53066i	1.40942	−	0.813730i	0.995332	+	0.0965061i	$0.0307667\pi$
$32$	−3.70406	+	4.27550i	−0.654792	+	0.755809i
$33$	−0.0383158	−	0.0547207i	−0.00666993	−	0.00952565i
$34$	−3.48539	−	0.193691i	−0.597740	−	0.0332177i
$35$	−4.56332	−	9.45948i	−0.771341	−	1.59894i
$36$	2.40530	+	5.49547i	0.400884	+	0.915911i
$37$	−3.96378	−	3.96378i	−0.651641	−	0.651641i	0.301747	−	0.953388i	$-0.402430\pi$
$37$	−3.96378	−	3.96378i	−0.651641	−	0.651641i	−0.953388	+	0.301747i	$0.902430\pi$
$38$	−4.40624	−	4.31104i	−0.714786	−	0.699343i
$39$	−0.0962361			−0.0154101
$40$	6.07310	−	1.76562i	0.960242	−	0.279170i
$41$	0.890376	−	0.324070i	0.139053	−	0.0506113i	−0.271556	−	0.962423i	$-0.587538\pi$
$41$	0.890376	−	0.324070i	0.139053	−	0.0506113i	0.410609	+	0.911811i	$0.365316\pi$
$42$	0.121137	−	0.108382i	0.0186919	−	0.0167238i
$43$	−9.94350	+	6.96252i	−1.51637	+	1.06177i	−0.541047	+	0.840993i	$0.681972\pi$
$43$	−9.94350	+	6.96252i	−1.51637	+	1.06177i	−0.975323	+	0.220781i	$0.929139\pi$
$44$	3.76779	+	3.95126i	0.568016	+	0.595675i
$45$	1.07774	−	6.61971i	0.160659	−	0.986808i
$46$	1.55115	+	1.45565i	0.228705	+	0.214624i
$47$	−0.301686	+	3.44829i	−0.0440055	+	0.502985i	0.941924	+	0.335825i	$0.109015\pi$
$47$	−0.301686	+	3.44829i	−0.0440055	+	0.502985i	−0.985930	+	0.167160i	$0.946540\pi$
$48$	0.0522704	+	0.0827575i	0.00754459	+	0.0119450i
$49$	13.0433	+	7.53056i	1.86333	+	1.07579i
$50$	−6.77372	−	2.02897i	−0.957949	−	0.286940i
$51$	−0.0206587	+	0.0567594i	−0.00289280	+	0.00794790i
$52$	7.77620	−	1.18138i	1.07837	−	0.163828i
$53$	8.67038	+	6.07106i	1.19097	+	0.833925i	0.989352	−	0.145540i	$-0.0464920\pi$
$53$	8.67038	+	6.07106i	1.19097	+	0.833925i	0.201615	+	0.979465i	$0.435381\pi$
$54$	0.206151	−	0.0246522i	0.0280536	−	0.00335473i
$55$	−1.13889	−	5.99698i	−0.153567	−	0.808633i
$56$	−8.45782	+	10.2447i	−1.13022	+	1.36901i
$57$	−0.0934655	+	0.0513968i	−0.0123798	+	0.00680767i
$58$	6.68146	−	4.14579i	0.877319	−	0.544368i
$59$	0.113684	+	0.0953925i	0.0148004	+	0.0124190i	0.650158	−	0.759799i	$-0.274703\pi$
$59$	0.113684	+	0.0953925i	0.0148004	+	0.0124190i	−0.635357	+	0.772218i	$0.719147\pi$
$60$	0.00116237	−	0.109430i	0.000150061	−	0.0141273i
$61$	−1.56220	−	8.85968i	−0.200019	−	1.13437i	−0.905087	−	0.425226i	$-0.860195\pi$
$61$	−1.56220	−	8.85968i	−0.200019	−	1.13437i	0.705068	−	0.709140i	$-0.250916\pi$
$62$	4.76294	+	11.8966i	0.604893	+	1.51087i
$63$	5.95383	+	12.7680i	0.750112	+	1.60862i
$64$	−5.23955	−	6.04542i	−0.654943	−	0.755678i
$65$	−8.01806	−	3.61137i	−0.994518	−	0.447935i
$66$	0.0843098	−	0.0426235i	0.0103778	−	0.00524659i
$67$	−1.06756	+	12.2022i	−0.130423	+	1.49074i	0.595718	+	0.803194i	$0.296868\pi$
$67$	−1.06756	+	12.2022i	−0.130423	+	1.49074i	−0.726141	+	0.687546i	$0.758688\pi$
$68$	0.972527	−	4.83996i	0.117936	−	0.586931i
$69$	0.0318764	−	0.0184039i	0.00383747	−	0.00221557i
$70$	14.1599	−	4.48423i	1.69243	−	0.535968i
$71$	−7.78761	−	1.37317i	−0.924219	−	0.162965i	−0.308766	−	0.951138i	$-0.599916\pi$
$71$	−7.78761	−	1.37317i	−0.924219	−	0.162965i	−0.615453	+	0.788173i	$0.711027\pi$
$72$	−8.17672	+	2.26110i	−0.963635	+	0.266473i
$73$	3.36904	−	7.22494i	0.394317	−	0.845615i	−0.604482	−	0.796619i	$-0.706620\pi$
$73$	3.36904	−	7.22494i	0.394317	−	0.845615i	0.998799	−	0.0489965i	$-0.0156023\pi$
$74$	6.34625	−	4.75092i	0.737736	−	0.552283i
$75$	−0.0675207	+	0.102036i	−0.00779662	+	0.0117821i
$76$	6.92140	−	5.30040i	0.793939	−	0.607998i
$77$	9.06652	+	9.06652i	1.03323	+	1.03323i
$78$	0.0193664	−	0.134713i	0.00219281	−	0.0152533i
$79$	0.134546	−	0.0489707i	0.0151376	−	0.00550963i	−0.334440	−	0.942417i	$-0.608547\pi$
$79$	0.134546	−	0.0489707i	0.0151376	−	0.00550963i	0.349578	+	0.936907i	$0.386325\pi$
$80$	1.24942	+	8.85658i	0.139689	+	0.990195i
$81$	−1.56190	+	8.85796i	−0.173544	+	0.984218i
$82$	0.274464	+	1.31158i	0.0303094	+	0.144840i
$83$	−1.85832	+	6.93534i	−0.203977	+	0.761252i	0.785782	+	0.618503i	$0.212261\pi$
$83$	−1.85832	+	6.93534i	−0.203977	+	0.761252i	−0.989759	+	0.142749i	$0.954406\pi$
$84$	0.127339	+	0.191381i	0.0138938	+	0.0208814i
$85$	−3.85118	+	3.95375i	−0.417719	+	0.428845i
$86$	−7.74528	−	15.3203i	−0.835194	−	1.65203i
$87$	−0.0352147	−	0.131423i	−0.00377541	−	0.0140900i
$88$	−6.28928	+	4.47910i	−0.670440	+	0.477473i
$89$	−1.35854	+	3.73255i	−0.144005	+	0.395650i	−0.990636	−	0.136530i	$-0.956405\pi$
$89$	−1.35854	+	3.73255i	−0.144005	+	0.395650i	0.846631	+	0.532180i	$0.178627\pi$
$90$	9.04953	+	2.84077i	0.953905	+	0.299444i
$91$	18.1911	−	3.20757i	1.90694	−	0.336245i
$92$	−2.34980	+	1.87841i	−0.244984	+	0.195837i
$93$	0.220892	−	0.0193256i	0.0229055	−	0.00200397i
$94$	−4.76628	−	1.11623i	−0.491605	−	0.115131i
$95$	−9.71595	+	0.774799i	−0.996835	+	0.0794927i
$96$	−0.126365	+	0.0565154i	−0.0128970	+	0.00576808i
$97$	−0.0974512	−	1.11387i	−0.00989467	−	0.113097i	0.989641	−	0.143564i	$-0.0458561\pi$
$97$	−0.0974512	−	1.11387i	−0.00989467	−	0.113097i	−0.999536	+	0.0304669i	$0.990301\pi$
$98$	−13.1663	+	16.7429i	−1.32999	+	1.69129i
$99$	1.42183	+	8.06357i	0.142899	+	0.810420i
$100$	4.20333	−	9.07370i	0.420333	−	0.907370i
$101$	−5.46378	−	1.98865i	−0.543666	−	0.197878i	0.0555640	−	0.998455i	$-0.482304\pi$
$101$	−5.46378	−	1.98865i	−0.543666	−	0.197878i	−0.599230	+	0.800577i	$0.704527\pi$
$102$	−0.0752958	−	0.0403407i	−0.00745539	−	0.00399433i
$103$	−2.85867	+	0.765979i	−0.281674	+	0.0754742i	−0.396890	−	0.917866i	$-0.629911\pi$
$103$	−2.85867	+	0.765979i	−0.281674	+	0.0754742i	0.115216	+	0.993340i	$0.463244\pi$
$104$	0.0888524	+	11.1230i	0.00871269	+	1.09070i
$105$	−0.00337745	−	0.256984i	−0.000329606	−	0.0250791i
$106$	−10.2432	+	10.9153i	−0.994910	+	1.06018i
$107$	−11.8644	−	3.17905i	−1.14697	−	0.307331i	−0.365222	−	0.930920i	$-0.619007\pi$
$107$	−11.8644	−	3.17905i	−1.14697	−	0.307331i	−0.781752	+	0.623590i	$0.785674\pi$
$108$	−0.00697675	+	0.293536i	−0.000671338	+	0.0282455i
$109$	−13.9514	−	2.46002i	−1.33631	−	0.235627i	−0.540584	−	0.841290i	$-0.681797\pi$
$109$	−13.9514	−	2.46002i	−1.33631	−	0.235627i	−0.795721	+	0.605663i	$0.792908\pi$
$110$	8.62390	−	0.387416i	0.822257	−	0.0369387i
$111$	−0.0469160	−	0.128901i	−0.00445307	−	0.0122347i
$112$	−12.6388	−	13.9011i	−1.19425	−	1.31353i
$113$	−3.15721	+	3.15721i	−0.297005	+	0.297005i	−0.839840	−	0.542835i	$-0.817351\pi$
$113$	−3.15721	+	3.15721i	−0.297005	+	0.297005i	0.542835	+	0.839840i	$0.317351\pi$
$114$	−0.0531375	−	0.141178i	−0.00497679	−	0.0132225i
$115$	3.34646	−	0.337146i	0.312059	−	0.0314391i
$116$	4.45880	+	10.1871i	0.413989	+	0.945853i
$117$	10.6906	+	4.98512i	0.988348	+	0.460874i
$118$	−0.156410	+	0.139941i	−0.0143987	+	0.0128826i
$119$	2.01322	−	11.4175i	0.184551	−	1.04664i
$120$	0.152948	+	0.0236486i	0.0139622	+	0.00215881i
$121$	−1.77391	−	3.07251i	−0.161265	−	0.279319i
$122$	12.7164	−	0.403899i	1.15128	−	0.0365673i
$123$	0.0230982	+	0.00202083i	0.00208269	+	0.000182212i
$124$	−17.6116	+	4.27321i	−1.58157	+	0.383746i
$125$	−9.45460	+	5.96746i	−0.845645	+	0.533746i
$126$	−19.0711	+	5.76490i	−1.69899	+	0.513578i
$127$	6.60364	−	3.07933i	0.585978	−	0.273246i	−0.106936	−	0.994266i	$-0.534104\pi$
$127$	6.60364	−	3.07933i	0.585978	−	0.273246i	0.692915	+	0.721020i	$0.256326\pi$
$128$	9.51692	−	6.11787i	0.841185	−	0.540748i
$129$	−0.292531	+	0.0515811i	−0.0257559	+	0.00454146i
$130$	6.66882	−	10.4971i	0.584894	−	0.920658i
$131$	9.68399	−	11.5409i	0.846094	−	1.00834i	−0.153701	−	0.988117i	$-0.549119\pi$
$131$	9.68399	−	11.5409i	0.846094	−	1.00834i	0.999796	−	0.0202185i	$-0.00643618\pi$
$132$	0.0426990	+	0.126596i	0.00371647	+	0.0110188i
$133$	15.9543	−	12.8305i	1.38341	−	1.11255i
$134$	−16.8661	−	3.94994i	−1.45701	−	0.341223i
$135$	0.184741	−	0.271359i	0.0159000	−	0.0233548i
$136$	6.57937	+	2.33535i	0.564176	+	0.200254i
$137$	5.64797	−	8.06614i	0.482539	−	0.689137i	−0.501888	−	0.864933i	$-0.667361\pi$
$137$	5.64797	−	8.06614i	0.482539	−	0.689137i	0.984427	+	0.175796i	$0.0562499\pi$
$138$	0.0193474	+	0.0483249i	0.00164696	+	0.00411369i
$139$	6.61701	+	2.40840i	0.561248	+	0.204278i	0.607037	−	0.794674i	$-0.292358\pi$
$139$	6.61701	+	2.40840i	0.561248	+	0.204278i	−0.0457891	+	0.998951i	$0.514580\pi$
$140$	3.42761	+	20.7238i	0.289686	+	1.75148i
$141$	−0.0423521	+	0.0733560i	−0.00356669	+	0.00617769i
$142$	3.48935	−	10.6249i	0.292820	−	0.891625i
$143$	10.6949	+	0.935686i	0.894356	+	0.0782460i
$144$	−1.51967	−	11.9010i	−0.126639	−	0.991748i
$145$	1.99784	−	12.2712i	0.165911	−	1.01907i
$146$	9.43565	+	6.17000i	0.780900	+	0.510633i
$147$	0.211395	+	0.301903i	0.0174355	+	0.0249005i
$148$	5.37334	+	9.83969i	0.441686	+	0.808817i
$149$	2.72950	+	7.49925i	0.223610	+	0.614363i	0.999871	−	0.0160483i	$-0.00510856\pi$
$149$	2.72950	+	7.49925i	0.223610	+	0.614363i	−0.776261	+	0.630411i	$0.782886\pi$
$150$	−0.129244	−	0.115050i	−0.0105527	−	0.00939383i
$151$			1.80767i			0.147106i	0.997291	+	0.0735532i	$0.0234339\pi$
$151$			1.80767i			0.147106i	−0.997291	+	0.0735532i	$0.976566\pi$
$152$	6.02678	+	10.7554i	0.488836	+	0.872376i
$153$	5.23511	−	5.23511i	0.423234	−	0.423234i
$154$	−14.5160	+	10.8670i	−1.16974	+	0.875687i
$155$	19.1292	+	6.67910i	1.53650	+	0.536479i
$156$	0.184678	+	0.0542189i	0.0147860	+	0.00434099i
$157$	−5.26905	+	3.68943i	−0.420516	+	0.294448i	−0.764618	−	0.644484i	$-0.777072\pi$
$157$	−5.26905	+	3.68943i	−0.420516	+	0.294448i	0.344102	+	0.938932i	$0.388183\pi$
$158$	0.0414745	+	0.198195i	0.00329954	+	0.0157676i
$159$	0.129506	+	0.224310i	0.0102705	+	0.0177890i
$160$	−12.6491	−	0.0333135i	−0.999997	−	0.00263366i
$161$	−5.41205	+	4.54125i	−0.426529	+	0.357900i
$162$	−12.0853	−	3.96894i	−0.949508	−	0.311829i
$163$	17.3124	−	4.63885i	1.35601	−	0.363342i	0.493662	−	0.869654i	$-0.335658\pi$
$163$	17.3124	−	4.63885i	1.35601	−	0.363342i	0.862351	+	0.506311i	$0.168991\pi$
$164$	−1.89122	+	0.120260i	−0.147679	+	0.00939070i
$165$	0.0367611	−	0.144779i	0.00286185	−	0.0112710i
$166$	−9.33428	−	3.99697i	−0.724480	−	0.310225i
$167$	−16.5942	−	11.6194i	−1.28409	−	0.899133i	−0.285845	−	0.958276i	$-0.592274\pi$
$167$	−16.5942	−	11.6194i	−1.28409	−	0.899133i	−0.998250	+	0.0591432i	$0.981163\pi$
$168$	−0.293525	+	0.139738i	−0.0226460	+	0.0107810i
$169$	1.58527	−	1.88926i	0.121944	−	0.145327i
$170$	−4.75955	−	6.18661i	−0.365041	−	0.474491i
$171$	13.0452	−	0.867935i	0.997595	−	0.0663727i
$172$	23.0043	−	7.75899i	1.75406	−	0.591617i
$173$	−6.09505	+	0.533248i	−0.463398	+	0.0405421i	−0.316465	−	0.948604i	$-0.602496\pi$
$173$	−6.09505	+	0.533248i	−0.463398	+	0.0405421i	−0.146934	+	0.989146i	$0.546940\pi$
$174$	0.191056	−	0.0228470i	0.0144839	−	0.00173203i
$175$	9.36224	−	21.5378i	0.707719	−	1.62810i
$176$	−5.00430	−	9.70525i	−0.377213	−	0.731561i
$177$	0.00153476	+	0.00329130i	0.000115360	+	0.000247390i
$178$	−4.95152	−	2.65284i	−0.371132	−	0.198839i
$179$	−7.23648	+	12.5340i	−0.540880	+	0.936832i	0.457974	+	0.888966i	$0.348575\pi$
$179$	−7.23648	+	12.5340i	−0.540880	+	0.936832i	−0.998854	+	0.0478662i	$0.984758\pi$
$180$	−5.79769	+	12.0961i	−0.432134	+	0.901588i
$181$	5.86006	−	4.91717i	0.435575	−	0.365490i	−0.398476	−	0.917179i	$-0.630461\pi$
$181$	5.86006	−	4.91717i	0.435575	−	0.365490i	0.834050	+	0.551688i	$0.186016\pi$
$182$	0.829301	+	26.1097i	0.0614719	+	1.93538i
$183$	0.0569781	−	0.212645i	0.00421194	−	0.0157192i
$184$	−2.15657	−	3.66731i	−0.158984	−	0.270358i
$185$	0.928269	−	12.5001i	0.0682477	−	0.919029i
$186$	−0.0173996	+	0.313099i	−0.00127580	+	0.0229575i
$187$	2.84771	−	6.10694i	0.208245	−	0.446584i
$188$	2.52169	−	6.44732i	0.183913	−	0.470219i
$189$			0.689552i			0.0501575i
$190$	0.870638	−	13.7565i	0.0631627	−	0.998003i
$191$		−	8.31668i		−	0.601774i	−0.953660	−	0.300887i	$-0.902717\pi$
$191$		−	8.31668i		−	0.601774i	0.953660	−	0.300887i	$-0.0972827\pi$
$192$	−0.0536821	−	0.188261i	−0.00387417	−	0.0135866i
$193$	−2.50773	+	5.37785i	−0.180510	+	0.387106i	−0.975654	−	0.219315i	$-0.929618\pi$
$193$	−2.50773	+	5.37785i	−0.180510	+	0.387106i	0.795144	+	0.606421i	$0.207395\pi$
$194$	1.57883	+	0.0877392i	0.113354	+	0.00629930i
$195$	−0.140476	−	0.163013i	−0.0100597	−	0.0116736i
$196$	−20.7875	−	21.7997i	−1.48482	−	1.55712i
$197$	0.550168	−	2.05325i	0.0391978	−	0.146288i	−0.943554	−	0.331220i	$-0.892540\pi$
$197$	0.550168	−	2.05325i	0.0391978	−	0.146288i	0.982751	+	0.184932i	$0.0592064\pi$
$198$	−11.5737	+	0.367606i	−0.822507	+	0.0261246i
$199$	6.45277	−	5.41451i	0.457425	−	0.383825i	−0.384758	−	0.923018i	$-0.625715\pi$
$199$	6.45277	−	5.41451i	0.457425	−	0.383825i	0.842182	+	0.539193i	$0.181271\pi$
$200$	11.8557	+	7.70989i	0.838325	+	0.545171i
$201$	−0.149869	+	0.259580i	−0.0105709	+	0.0183094i
$202$	3.88328	−	7.24813i	0.273227	−	0.509976i
$203$	11.0368	+	23.6686i	0.774634	+	1.66121i
$204$	0.0716222	−	0.0972826i	0.00501456	−	0.00681115i
$205$	1.84863	+	1.03515i	0.129114	+	0.0722983i
$206$	−0.496961	−	4.15578i	−0.0346249	−	0.289547i
$207$	−4.49441	+	0.393210i	−0.312383	+	0.0273300i
$208$	−15.5882	−	2.11400i	−1.08084	−	0.146580i
$209$	10.8868	−	4.80310i	0.753053	−	0.332237i
$210$	0.360412	+	0.0469872i	0.0248708	+	0.00324243i
$211$	2.64597	−	3.15335i	0.182156	−	0.217085i	−0.667237	−	0.744845i	$-0.732523\pi$
$211$	2.64597	−	3.15335i	0.182156	−	0.217085i	0.849394	+	0.527760i	$0.176968\pi$
$212$	−13.2181	−	16.5353i	−0.907823	−	1.13565i
$213$	−0.158512	−	0.110991i	−0.0108611	−	0.00760501i
$214$	6.83768	−	15.9683i	0.467414	−	1.09157i
$215$	−26.3083	−	6.68000i	−1.79421	−	0.455573i
$216$	−0.409494	−	0.0688367i	−0.0278625	−	0.00468375i
$217$	−41.1101	+	11.0154i	−2.79074	+	0.747776i
$218$	6.25115	−	19.0345i	0.423381	−	1.28918i
$219$	0.149437	−	0.125392i	0.0100980	−	0.00847324i
$220$	−1.19314	+	12.1499i	−0.0804417	+	0.819146i
$221$	−4.85366	−	8.40678i	−0.326492	−	0.565501i
$222$	0.189879	−	0.0397344i	0.0127439	−	0.00266680i
$223$	0.376199	−	0.263417i	0.0251921	−	0.0176397i	−0.560913	−	0.827875i	$-0.689550\pi$
$223$	0.376199	−	0.263417i	0.0251921	−	0.0176397i	0.586105	+	0.810235i	$0.300661\pi$
$224$	22.0024	−	14.8946i	1.47010	−	0.995187i
$225$	12.7862	−	7.83724i	0.852416	−	0.522483i
$226$	−3.78418	−	5.05488i	−0.251720	−	0.336245i
$227$	−0.502844	+	0.502844i	−0.0333749	+	0.0333749i	−0.723597	−	0.690222i	$-0.757513\pi$
$227$	−0.502844	+	0.502844i	−0.0333749	+	0.0333749i	0.690222	+	0.723597i	$0.257513\pi$
$228$	0.208318	−	0.0459727i	0.0137962	−	0.00304462i
$229$			3.29632i			0.217827i	0.994051	+	0.108914i	$0.0347372\pi$
$229$			3.29632i			0.217827i	−0.994051	+	0.108914i	$0.965263\pi$
$230$	−0.201490	+	4.75230i	−0.0132859	+	0.313357i
$231$	0.107313	+	0.294840i	0.00706068	+	0.0193991i
$232$	−15.1575	+	4.19149i	−0.995137	+	0.275185i
$233$	−14.1759	−	20.2454i	−0.928697	−	1.32632i	−0.945213	−	0.326454i	$-0.894146\pi$
$233$	−14.1759	−	20.2454i	−0.928697	−	1.32632i	0.0165159	−	0.999864i	$-0.494743\pi$
$234$	−9.12964	+	13.9618i	−0.596823	+	0.912710i
$235$	−6.28140	+	4.52246i	−0.409753	+	0.295012i
$236$	−0.164417	−	0.247108i	−0.0107027	−	0.0160854i
$237$	0.00349039		0.000305370i	0.000226725		1.98359e-5i
$238$	15.5774	+	5.11579i	1.00973	+	0.331607i
$239$	4.87528	−	8.44423i	0.315356	−	0.546212i	−0.664157	−	0.747593i	$-0.731210\pi$
$239$	4.87528	−	8.44423i	0.315356	−	0.546212i	0.979513	+	0.201381i	$0.0645428\pi$
$240$	−0.0638829	+	0.209342i	−0.00412362	+	0.0135130i
$241$	−13.3914	−	4.87408i	−0.862617	−	0.313967i	−0.127443	−	0.991846i	$-0.540677\pi$
$241$	−13.3914	−	4.87408i	−0.862617	−	0.313967i	−0.735173	+	0.677879i	$0.762899\pi$
$242$	4.65794	−	1.86486i	0.299424	−	0.119878i
$243$	−0.378865	+	0.541076i	−0.0243042	+	0.0347100i
$244$	−1.99363	+	17.8819i	−0.127629	+	1.14477i
$245$	6.28342	+	33.0863i	0.401433	+	2.11381i
$246$	−0.00747703	+	0.0319267i	−0.000476718	+	0.00203557i
$247$	3.32774	−	16.8162i	0.211739	−	1.06999i
$248$	−2.43761	−	25.5131i	−0.154788	−	1.62008i
$249$	−0.112937	+	0.134593i	−0.00715710	+	0.00852950i
$250$	−6.45077	−	14.4356i	−0.407982	−	0.912990i
$251$	−19.4871	+	3.43611i	−1.23002	+	0.216885i	−0.750633	−	0.660719i	$-0.770251\pi$
$251$	−19.4871	+	3.43611i	−1.23002	+	0.216885i	−0.479385	+	0.877605i	$0.659140\pi$
$252$	−4.23199	−	27.8563i	−0.266591	−	1.75478i
$253$	−3.72144	+	1.73534i	−0.233965	+	0.109100i
$254$	2.98161	+	9.86360i	0.187083	+	0.618898i
$255$	−0.126300	+	0.0478582i	−0.00790920	+	0.00299700i
$256$	6.64876	+	14.5531i	0.415548	+	0.909571i
$257$	−9.67283	−	0.846263i	−0.603374	−	0.0527884i	−0.218624	−	0.975809i	$-0.570157\pi$
$257$	−9.67283	−	0.846263i	−0.603374	−	0.0527884i	−0.384750	+	0.923021i	$0.625712\pi$
$258$	−0.0133360	−	0.419871i	−0.000830264	−	0.0261401i
$259$	13.1646	+	22.8018i	0.818009	+	1.41683i
$260$	13.3521	+	11.4476i	0.828061	+	0.709949i
$261$	−2.89593	+	16.4236i	−0.179253	+	1.01660i
$262$	14.2065	+	15.8783i	0.877679	+	0.980967i
$263$	−7.02792	−	3.27717i	−0.433360	−	0.202079i	0.193682	−	0.981064i	$-0.437957\pi$
$263$	−7.02792	−	3.27717i	−0.433360	−	0.202079i	−0.627042	+	0.778985i	$0.715735\pi$
$264$	−0.185805	+	0.0342950i	−0.0114355	+	0.00211071i
$265$	2.37246	+	23.5486i	0.145739	+	1.44658i
$266$	14.7498	+	24.9152i	0.904371	+	1.52765i
$267$	−0.0687307	+	0.0687307i	−0.00420625	+	0.00420625i
$268$	8.92333	−	22.8147i	0.545079	−	1.39363i
$269$	−0.938934	−	2.57970i	−0.0572478	−	0.157287i	0.907772	−	0.419464i	$-0.137782\pi$
$269$	−0.938934	−	2.57970i	−0.0572478	−	0.157287i	−0.965020	+	0.262177i	$0.915560\pi$
$270$	0.342677	+	0.313212i	0.0208547	+	0.0190615i
$271$	20.3854	+	3.59449i	1.23832	+	0.218350i	0.754197	−	0.656649i	$-0.228027\pi$
$271$	20.3854	+	3.59449i	1.23832	+	0.218350i	0.484126	+	0.874998i	$0.339138\pi$
$272$	−4.59309	+	8.73999i	−0.278497	+	0.529940i
$273$	0.436612	+	0.116990i	0.0264249	+	0.00708054i
$274$	10.1546	+	9.52937i	0.613460	+	0.575690i
$275$	8.49580	−	10.6830i	0.512316	−	0.644207i
$276$	−0.0715397	+	0.0173581i	−0.00430619	+	0.00104484i
$277$	15.1943	−	4.07131i	0.912940	−	0.244621i	0.228375	−	0.973573i	$-0.426659\pi$
$277$	15.1943	−	4.07131i	0.912940	−	0.244621i	0.684565	+	0.728952i	$0.259992\pi$
$278$	−4.70292	+	8.77799i	−0.282063	+	0.526469i
$279$	−25.5395	−	9.29560i	−1.52901	−	0.556513i
$280$	−29.6993	+	0.627636i	−1.77488	+	0.0375084i
$281$	2.14028	+	12.1381i	0.127678	+	0.724100i	0.979681	+	0.200562i	$0.0642769\pi$
$281$	2.14028	+	12.1381i	0.127678	+	0.724100i	−0.852003	+	0.523537i	$0.824612\pi$
$282$	−0.0941625	−	0.0740474i	−0.00560730	−	0.00440946i
$283$	0.498168	+	5.69408i	0.0296130	+	0.338478i	0.996520	+	0.0833502i	$0.0265620\pi$
$283$	0.498168	+	5.69408i	0.0296130	+	0.338478i	−0.966907	+	0.255128i	$0.917882\pi$
$284$	14.1708	+	7.02262i	0.840884	+	0.416716i
$285$	−0.223492	−	0.0832964i	−0.0132386	−	0.00493405i
$286$	−3.46202	+	14.7827i	−0.204714	+	0.874121i
$287$	−4.43349	+	0.387880i	−0.261701	+	0.0228958i
$288$	16.9651	+	0.267655i	0.999676	+	0.0157717i
$289$	10.7415	−	1.89402i	0.631856	−	0.111413i
$290$	16.7755	+	5.26605i	0.985089	+	0.309233i
$291$	0.00935811	−	0.0257112i	0.000548582	−	0.00150722i
$292$	−10.5357	+	11.9666i	−0.616556	+	0.700292i
$293$	4.26000	+	15.8985i	0.248872	+	0.928802i	0.971398	+	0.237458i	$0.0763143\pi$
$293$	4.26000	+	15.8985i	0.248872	+	0.928802i	−0.722526	+	0.691344i	$0.757019\pi$
$294$	−0.465151	+	0.235161i	−0.0271282	+	0.0137149i
$295$	0.00436091	+	0.331814i	0.000253902	+	0.0193189i
$296$	−14.8551	+	5.54160i	−0.863437	+	0.322099i
$297$	−0.103727	+	0.387114i	−0.00601884	+	0.0224626i
$298$	−11.0469	+	2.31169i	−0.639930	+	0.133912i
$299$	−1.02720	+	5.82556i	−0.0594047	+	0.336901i
$300$	0.187059	−	0.157766i	0.0107999	−	0.00910864i
$301$	53.5765	−	19.5003i	3.08810	−	1.12398i
$302$	−2.53042	−	0.363773i	−0.145609	−	0.0209328i
$303$	−0.100609	−	0.100609i	−0.00577985	−	0.00577985i
$304$	−16.2684	+	6.27203i	−0.933058	+	0.359725i
$305$	12.7270	−	15.5787i	0.728745	−	0.892034i
$306$	6.27473	+	8.38173i	0.358702	+	0.479152i
$307$	−3.39180	+	7.27374i	−0.193580	+	0.415134i	−0.979009	−	0.203818i	$-0.934665\pi$
$307$	−3.39180	+	7.27374i	−0.193580	+	0.415134i	0.785428	+	0.618952i	$0.212443\pi$
$308$	−12.2907	−	22.5067i	−0.700326	−	1.28244i
$309$	−0.0713210	−	0.0125758i	−0.00405731	−	0.000715414i
$310$	−13.1991	+	25.4334i	−0.749658	+	1.44452i
$311$	−3.24227	+	1.87192i	−0.183852	+	0.106147i	−0.589101	−	0.808059i	$-0.700518\pi$
$311$	−3.24227	+	1.87192i	−0.183852	+	0.106147i	0.405249	+	0.914206i	$0.367185\pi$
$312$	−0.113061	+	0.247605i	−0.00640082	+	0.0140179i
$313$	−2.32852	+	26.6151i	−0.131616	+	1.50437i	0.587352	+	0.809332i	$0.300170\pi$
$313$	−2.32852	+	26.6151i	−0.131616	+	1.50437i	−0.718968	+	0.695043i	$0.755385\pi$
$314$	−4.10421	−	8.11819i	−0.231614	−	0.458136i
$315$	−12.9368	+	28.7227i	−0.728908	+	1.61834i
$316$	−0.285784	+	0.0181726i	−0.0160766	+	0.00102229i
$317$	−12.8761	−	27.6129i	−0.723195	−	1.55090i	−0.830717	−	0.556694i	$-0.812069\pi$
$317$	−12.8761	−	27.6129i	−0.723195	−	1.55090i	0.107522	−	0.994203i	$-0.465708\pi$
$318$	−0.340056	+	0.136145i	−0.0190694	+	0.00763464i
$319$	2.63569	+	14.9477i	0.147570	+	0.836913i
$320$	2.59211	−	17.6997i	0.144903	−	0.989446i
$321$	−0.230251	−	0.193203i	−0.0128513	−	0.0107836i
$322$	−5.26783	−	8.48978i	−0.293565	−	0.473117i
$323$	−9.20373	−	5.57257i	−0.512109	−	0.310066i
$324$	7.98783	−	16.1185i	0.443768	−	0.895473i
$325$	−5.58671	−	18.8532i	−0.309895	−	1.04579i
$326$	3.00965	+	25.1678i	0.166689	+	1.39392i
$327$	−0.283973	−	0.198840i	−0.0157038	−	0.0109959i
$328$	0.212243	−	2.67157i	0.0117192	−	0.147513i
$329$	5.56064	−	15.2777i	0.306568	−	0.842289i
$330$	0.195267	+	0.0805941i	0.0107491	+	0.00443656i
$331$	16.7034	+	9.64372i	0.918103	+	0.530067i	0.883029	−	0.469318i	$-0.155500\pi$
$331$	16.7034	+	9.64372i	0.918103	+	0.530067i	0.0350737	+	0.999385i	$0.488833\pi$
$332$	7.47346	−	12.2620i	0.410159	−	0.672964i
$333$	−1.46540	+	16.7495i	−0.0803032	+	0.917869i
$334$	19.6044	−	20.8906i	1.07271	−	1.14308i
$335$	−22.2276	+	16.0033i	−1.21442	+	0.874354i
$336$	−0.136540	−	0.439004i	−0.00744889	−	0.0239496i
$337$	7.16047	−	5.01382i	0.390056	−	0.273120i	−0.362055	−	0.932157i	$-0.617925\pi$
$337$	7.16047	−	5.01382i	0.390056	−	0.273120i	0.752111	+	0.659037i	$0.229036\pi$
$338$	2.32560	+	2.59929i	0.126496	+	0.141383i
$339$	−0.102671	+	0.0373693i	−0.00557634	+	0.00202962i
$340$	9.61796	−	5.41755i	0.521607	−	0.293808i
$341$	−24.7362			−1.33954
$342$	−1.41024	+	18.4357i	−0.0762573	+	0.996888i
$343$	−26.7729	−	26.7729i	−1.44560	−	1.44560i
$344$	6.23187	+	33.7633i	0.336000	+	1.82040i
$345$	0.0777043	+	0.0271310i	0.00418346	+	0.00146069i
$346$	0.480104	−	8.63930i	0.0258106	−	0.464452i
$347$	3.61973	+	5.16951i	0.194317	+	0.277514i	0.904473	−	0.426531i	$-0.140264\pi$
$347$	3.61973	+	5.16951i	0.194317	+	0.277514i	−0.710156	+	0.704045i	$0.751375\pi$
$348$	−0.00646588	+	0.272042i	−0.000346608	+	0.0145830i
$349$	−3.35183	+	1.93518i	−0.179420	+	0.103588i	−0.587020	−	0.809572i	$-0.699699\pi$
$349$	−3.35183	+	1.93518i	−0.179420	+	0.103588i	0.407600	+	0.913160i	$0.366366\pi$
$350$	28.2651	+	17.4397i	1.51083	+	0.932191i
$351$	0.371119	+	0.442282i	0.0198089	+	0.0236073i
$352$	14.5927	−	5.05206i	0.777792	−	0.269276i
$353$	1.34049	+	5.00278i	0.0713471	+	0.266271i	0.992380	−	0.123213i	$-0.0393199\pi$
$353$	1.34049	+	5.00278i	0.0713471	+	0.266271i	−0.921033	+	0.389484i	$0.872653\pi$
$354$	−0.00491609	+	0.00148606i	−0.000261287	+	7.89830e-5i
$355$	−9.04160	−	15.1958i	−0.479879	−	0.806508i
$356$	4.70995	−	6.39740i	0.249627	−	0.339061i
$357$	0.162726	−	0.232397i	0.00861238	−	0.0122997i
$358$	−16.0891	−	12.6521i	−0.850333	−	0.668684i
$359$	15.5774	+	13.0710i	0.822146	+	0.689863i	0.953474	−	0.301476i	$-0.0974795\pi$
$359$	15.5774	+	13.0710i	0.822146	+	0.689863i	−0.131327	+	0.991339i	$0.541924\pi$
$360$	−15.7656	−	10.5499i	−0.830922	−	0.556030i
$361$	−5.74909	−	18.1093i	−0.302584	−	0.953123i
$362$	5.70390	+	9.19256i	0.299790	+	0.483150i
$363$	−0.00756665	−	0.0864872i	−0.000397146	−	0.00453940i
$364$	−36.7159	−	4.09340i	−1.92443	−	0.214552i
$365$	17.1561	−	4.83947i	0.897990	−	0.253310i
$366$	0.286199	+	0.122552i	0.0149599	+	0.00640587i
$367$	19.1444	−	8.92717i	0.999328	−	0.465994i	0.147076	−	0.989125i	$-0.453014\pi$
$367$	19.1444	−	8.92717i	0.999328	−	0.465994i	0.852252	+	0.523131i	$0.175236\pi$
$368$	5.56757	−	2.28081i	0.290230	−	0.118895i
$369$	−2.46123	−	1.42099i	−0.128127	−	0.0739740i
$370$	17.3112	+	3.81492i	0.899965	+	0.198328i
$371$	−31.9562	−	38.0839i	−1.65908	−	1.97722i
$372$	−0.434782	−	0.0873638i	−0.0225424	−	0.00452960i
$373$	−14.7393	−	3.94937i	−0.763169	−	0.204491i	−0.143818	−	0.989604i	$-0.545938\pi$
$373$	−14.7393	−	3.94937i	−0.763169	−	0.204491i	−0.619352	+	0.785114i	$0.712605\pi$
$374$	7.97557	+	5.21524i	0.412407	+	0.269674i
$375$	−0.271397	+	0.0345691i	−0.0140149	+	0.00178514i
$376$	8.51765	+	4.82736i	0.439264	+	0.248952i
$377$	19.8176	+	9.24109i	1.02066	+	0.475941i
$378$	−0.965251	−	0.138764i	−0.0496471	−	0.00713726i
$379$	−12.7902			−0.656988			−0.328494	−	0.944506i	$-0.606541\pi$
$379$	−12.7902			−0.656988			−0.328494	+	0.944506i	$0.606541\pi$
$380$	19.0815	+	3.98708i	0.978860	+	0.204533i
$381$	0.178301			0.00913462
$382$	11.6419	+	1.67363i	0.595651	+	0.0856305i
$383$	−31.7737	−	14.8163i	−1.62356	−	0.757078i	−0.623858	−	0.781538i	$-0.714436\pi$
$383$	−31.7737	−	14.8163i	−1.62356	−	0.757078i	−0.999701	+	0.0244596i	$0.992214\pi$
$384$	0.274335	−	0.0372601i	0.0139996	−	0.00190142i
$385$	−2.12327	+	28.5921i	−0.108212	+	1.45719i
$386$	−7.02338	−	4.59261i	−0.357481	−	0.233758i
$387$	35.1684	+	9.42336i	1.78771	+	0.479016i
$388$	−0.440541	+	2.19243i	−0.0223651	+	0.111304i
$389$	−12.4197	−	14.8012i	−0.629705	−	0.750453i	0.353002	−	0.935623i	$-0.385161\pi$
$389$	−12.4197	−	14.8012i	−0.629705	−	0.750453i	−0.982707	+	0.185170i	$0.940717\pi$
$390$	0.256459	−	0.163837i	0.0129863	−	0.00829621i
$391$	3.21537	+	1.85639i	0.162608	+	0.0938819i
$392$	34.6990	−	24.7119i	1.75256	−	1.24814i
$393$	0.334124	−	0.155805i	0.0168543	−	0.00785931i
$394$	2.76348	+	1.18333i	0.139222	+	0.0596153i
$395$	0.279348	+	0.156423i	0.0140555	+	0.00787051i
$396$	1.81449	−	16.2751i	0.0911814	−	0.817855i
$397$	0.744112	+	8.50524i	0.0373459	+	0.426866i	0.991735	+	0.128301i	$0.0409523\pi$
$397$	0.744112	+	8.50524i	0.0373459	+	0.426866i	−0.954389	+	0.298565i	$0.903492\pi$
$398$	6.28082	+	10.1223i	0.314829	+	0.507387i
$399$	0.486523	−	0.119559i	0.0243566	−	0.00598546i
$400$	−13.1783	+	15.0444i	−0.658915	+	0.752218i
$401$	27.7855	+	23.3148i	1.38754	+	1.16428i	0.966325	+	0.257323i	$0.0828404\pi$
$401$	27.7855	+	23.3148i	1.38754	+	1.16428i	0.421214	+	0.906961i	$0.361604\pi$
$402$	−0.333206	−	0.262027i	−0.0166188	−	0.0130687i
$403$	−20.4397	+	29.1909i	−1.01818	+	1.45410i
$404$	9.36463	+	6.89450i	0.465908	+	0.343014i
$405$	−17.2843	+	10.2843i	−0.858865	+	0.511032i
$406$	−35.3528	+	10.6866i	−1.75453	+	0.530367i
$407$	3.96061	+	14.7812i	0.196320	+	0.732677i
$408$	0.121765	+	0.119835i	0.00602828	+	0.00593273i
$409$	13.6678	+	16.2887i	0.675831	+	0.805424i	0.989565	−	0.144087i	$-0.0460245\pi$
$409$	13.6678	+	16.2887i	0.675831	+	0.805424i	−0.313734	+	0.949511i	$0.601580\pi$
$410$	−1.82105	+	2.37943i	−0.0899350	+	0.117512i
$411$	0.208678	−	0.120480i	0.0102933	−	0.00594286i
$412$	5.91736	+	0.140644i	0.291528	+	0.00692902i
$413$	−0.399808	−	0.570986i	−0.0196733	−	0.0280964i
$414$	0.354022	−	6.37050i	0.0173992	−	0.313093i
$415$	−14.4603	+	6.97574i	−0.709828	+	0.342426i
$416$	6.09616	−	21.3953i	0.298889	−	1.04899i
$417$	0.121845	+	0.121845i	0.00596676	+	0.00596676i
$418$	4.53265	+	16.2061i	0.221699	+	0.792666i
$419$	21.2371			1.03750			0.518750	−	0.854926i	$-0.326398\pi$
$419$	21.2371			1.03750			0.518750	+	0.854926i	$0.326398\pi$
$420$	−0.138302	+	0.495058i	−0.00674847	+	0.0241563i
$421$	−21.2770	+	7.74419i	−1.03698	+	0.377429i	−0.803734	−	0.594989i	$-0.797156\pi$
$421$	−21.2770	+	7.74419i	−1.03698	+	0.377429i	−0.233244	+	0.972418i	$0.574934\pi$
$422$	3.88166	+	4.33847i	0.188956	+	0.211193i
$423$	8.50469	−	5.95505i	0.413512	−	0.289544i
$424$	25.8064	−	15.1755i	1.25327	−	0.736986i
$425$	−12.3188	−	0.752166i	−0.597550	−	0.0364854i
$426$	0.187267	−	0.199553i	0.00907311	−	0.00966838i
$427$	−3.68278	+	42.0944i	−0.178222	+	2.03709i
$428$	20.9768	+	12.7850i	1.01395	+	0.617985i
$429$	0.227515	+	0.131356i	0.0109845	+	0.00634192i
$430$	14.6451	−	35.4827i	0.706247	−	1.71113i
$431$	−5.49245	+	15.0904i	−0.264562	+	0.726878i	0.734284	+	0.678843i	$0.237518\pi$
$431$	−5.49245	+	15.0904i	−0.264562	+	0.726878i	−0.998846	+	0.0480352i	$0.984704\pi$
$432$	0.178765	−	0.559366i	0.00860083	−	0.0269125i
$433$	−14.2979	−	10.0115i	−0.687111	−	0.481121i	0.177137	−	0.984186i	$-0.443317\pi$
$433$	−14.2979	−	10.0115i	−0.687111	−	0.481121i	−0.864248	+	0.503066i	$0.832205\pi$
$434$	−7.14672	−	59.7636i	−0.343053	−	2.86875i
$435$	0.171213	−	0.251489i	0.00820906	−	0.0120580i
$436$	25.3869	+	12.5810i	1.21581	+	0.602519i
$437$	2.11362	+	6.20645i	0.101108	+	0.296895i
$438$	0.145455	+	0.234419i	0.00695010	+	0.0112010i
$439$	17.3896	+	14.5916i	0.829960	+	0.696419i	0.955282	−	0.295697i	$-0.0955518\pi$
$439$	17.3896	+	14.5916i	0.829960	+	0.696419i	−0.125322	+	0.992116i	$0.539996\pi$
$440$	−16.7676	−	4.11521i	−0.799364	−	0.196185i
$441$	−7.84445	−	44.4881i	−0.373545	−	2.11848i
$442$	12.7447	−	5.10249i	0.606205	−	0.242701i
$443$	−2.56399	−	5.49849i	−0.121819	−	0.261241i	0.835936	−	0.548827i	$-0.184925\pi$
$443$	−2.56399	−	5.49849i	−0.121819	−	0.261241i	−0.957755	+	0.287585i	$0.907148\pi$
$444$	0.0174101	+	0.273794i	0.000826247	+	0.0129937i
$445$	−8.30560	+	3.14720i	−0.393723	+	0.149192i
$446$	0.293032	+	0.579621i	0.0138755	+	0.0274459i
$447$	−0.0170206	+	0.194546i	−0.000805044	+	0.00920170i
$448$	16.4221	+	33.7969i	0.775870	+	1.59675i
$449$	−33.9589	+	19.6062i	−1.60262	+	0.925274i	−0.611660	+	0.791121i	$0.709498\pi$
$449$	−33.9589	+	19.6062i	−1.60262	+	0.925274i	−0.990961	+	0.134153i	$0.957169\pi$
$450$	8.39767	+	19.4756i	0.395870	+	0.918089i
$451$	−2.54730	−	0.449158i	−0.119948	−	0.0211500i
$452$	7.83745	−	4.27994i	0.368643	−	0.201312i
$453$	−0.0186945	+	0.0400905i	−0.000878344	+	0.00188361i
$454$	−0.602701	−	0.805083i	−0.0282861	−	0.0377844i
$455$	31.9868	+	26.1316i	1.49956	+	1.22507i
$456$	0.0224322	+	0.300859i	0.00105048	+	0.0140890i
$457$	7.07771	+	7.07771i	0.331081	+	0.331081i	0.852997	−	0.521916i	$-0.174782\pi$
$457$	7.07771	+	7.07771i	0.331081	+	0.331081i	−0.521916	+	0.852997i	$0.674782\pi$
$458$	−4.61427	−	0.663346i	−0.215611	−	0.0309961i
$459$	0.340522	−	0.123940i	0.0158942	−	0.00578502i
$460$	−6.61183	−	1.23839i	−0.308278	−	0.0577404i
$461$	−4.63419	+	26.2818i	−0.215836	+	1.22407i	0.663614	+	0.748075i	$0.269022\pi$
$461$	−4.63419	+	26.2818i	−0.215836	+	1.22407i	−0.879450	+	0.475991i	$0.842090\pi$
$462$	−0.434319	+	0.0908861i	−0.0202064	+	0.00422841i
$463$	3.44784	−	12.8675i	0.160235	−	0.598004i	−0.838365	−	0.545109i	$-0.816488\pi$
$463$	3.44784	−	12.8675i	0.160235	−	0.598004i	0.998600	−	0.0528951i	$-0.0168449\pi$
$464$	−2.81707	−	22.0613i	−0.130779	−	1.02417i
$465$	0.355173	+	0.345958i	0.0164707	+	0.0160434i
$466$	31.1926	−	15.7697i	1.44497	−	0.730516i
$467$	−8.78475	−	32.7851i	−0.406510	−	1.51712i	−0.801254	−	0.598324i	$-0.795833\pi$
$467$	−8.78475	−	32.7851i	−0.406510	−	1.51712i	0.394744	−	0.918791i	$-0.370833\pi$
$468$	−17.7068	−	15.5895i	−0.818496	−	0.720625i
$469$	19.6771	−	54.0623i	0.908603	−	2.49637i
$470$	−5.06658	−	9.70293i	−0.233704	−	0.447563i
$471$	−0.155012	+	0.0273327i	−0.00714256	+	0.00125943i
$472$	0.378995	−	0.180428i	0.0174446	−	0.00830485i
$473$	33.0112	−	2.88810i	1.51785	−	0.132795i
$474$	−0.00112986	+	0.00482448i	−5.18963e−5	+	0.000221596i
$475$	−15.4948	−	15.3268i	−0.710951	−	0.703241i
$476$	−10.2960	+	20.7761i	−0.471914	+	0.952269i
$477$	−2.76697	−	31.6266i	−0.126691	−	1.44808i
$478$	10.8393	+	8.52383i	0.495780	+	0.389871i
$479$	−5.92171	−	33.5837i	−0.270570	−	1.53448i	−0.752691	−	0.658374i	$-0.771245\pi$
$479$	−5.92171	−	33.5837i	−0.270570	−	1.53448i	0.482121	−	0.876104i	$-0.339866\pi$
$480$	−0.280186	−	0.131552i	−0.0127887	−	0.00600451i
$481$	20.7158	+	7.53995i	0.944561	+	0.343792i
$482$	9.51770	−	17.7648i	0.433519	−	0.809162i
$483$	−0.166992	+	0.0447455i	−0.00759842	+	0.00203599i
$484$	1.67311	+	6.89557i	0.0760506	+	0.313435i
$485$	1.74453	−	1.79100i	0.0792150	−	0.0813249i
$486$	−0.681168	−	0.639229i	−0.0308984	−	0.0289960i
$487$	−31.5191	−	8.44552i	−1.42827	−	0.382703i	−0.539858	−	0.841756i	$-0.681522\pi$
$487$	−31.5191	−	8.44552i	−1.42827	−	0.382703i	−0.888409	+	0.459053i	$0.848189\pi$
$488$	−24.6303	−	6.38925i	−1.11496	−	0.289228i
$489$	0.431927	+	0.0761604i	0.0195324	+	0.00344409i
$490$	−47.5795	+	2.13744i	−2.14942	+	0.0965596i
$491$	4.38913	+	12.0590i	0.198079	+	0.544217i	0.998472	−	0.0552582i	$-0.0175982\pi$
$491$	4.38913	+	12.0590i	0.198079	+	0.544217i	−0.800393	+	0.599475i	$0.795376\pi$
$492$	−0.0431870	−	0.0168914i	−0.00194702	−	0.000761522i
$493$	9.70452	−	9.70452i	0.437070	−	0.437070i
$494$	22.8700	+	8.04230i	1.02897	+	0.361840i
$495$	−11.5834	+	14.1788i	−0.520634	+	0.637292i
$496$	36.2043	+	1.72198i	1.62562	+	0.0773192i
$497$	33.6622	+	15.6969i	1.50996	+	0.704104i
$498$	−0.165679	−	0.185177i	−0.00742427	−	0.00829799i
$499$	−3.26611	+	18.5230i	−0.146211	+	0.829205i	0.820176	+	0.572112i	$0.193876\pi$
$499$	−3.26611	+	18.5230i	−0.146211	+	0.829205i	−0.966387	+	0.257093i	$0.917235\pi$
$500$	21.5055	−	6.12493i	0.961754	−	0.273915i
$501$	−0.247860	−	0.429306i	−0.0110736	−	0.0191800i
$502$	−0.888388	−	27.9700i	−0.0396507	−	1.24836i
$503$	−13.4598	−	1.17758i	−0.600142	−	0.0525056i	−0.216963	−	0.976180i	$-0.569615\pi$
$503$	−13.4598	−	1.17758i	−0.600142	−	0.0525056i	−0.383179	+	0.923674i	$0.625171\pi$
$504$	39.8455	−	0.318291i	1.77486	−	0.0141778i
$505$	−4.60693	−	12.1579i	−0.205006	−	0.541019i
$506$	−1.68027	−	5.55857i	−0.0746970	−	0.247109i
$507$	0.0546963	−	0.0255053i	0.00242915	−	0.00113273i
$508$	−14.4073	+	2.18879i	−0.639221	+	0.0971119i
$509$	0.214937	−	0.0378992i	0.00952692	−	0.00167985i	−0.168883	−	0.985636i	$-0.554016\pi$
$509$	0.214937	−	0.0378992i	0.00952692	−	0.00167985i	0.178410	+	0.983956i	$0.442905\pi$
$510$	−0.0415767	−	0.186428i	−0.00184105	−	0.00825518i
$511$	−24.0680	+	28.6831i	−1.06471	+	1.26887i
$512$	−21.7098	+	6.37844i	−0.959447	+	0.281890i
$513$	0.596645	+	0.231346i	0.0263425	+	0.0102142i
$514$	3.13116	−	13.3699i	0.138109	−	0.589723i
$515$	−5.47030	−	3.72418i	−0.241050	−	0.164107i
$516$	0.590429	+	0.0658261i	0.0259922	+	0.00289783i
$517$	5.41991	−	7.74044i	0.238368	−	0.340424i
$518$	−34.5677	+	13.8395i	−1.51882	+	0.608074i
$519$	−0.140690	−	0.0512071i	−0.00617562	−	0.00224774i
$520$	−18.7115	+	16.3868i	−0.820555	+	0.718611i
$521$	−19.5269	+	33.8215i	−0.855488	+	1.48175i	0.0207043	+	0.999786i	$0.493409\pi$
$521$	−19.5269	+	33.8215i	−0.855488	+	1.48175i	−0.876192	+	0.481962i	$0.839924\pi$
$522$	−22.4074	−	7.35884i	−0.980744	−	0.322088i
$523$	−10.2389	−	0.895788i	−0.447716	−	0.0391701i	−0.138931	−	0.990302i	$-0.544367\pi$
$523$	−10.2389	−	0.895788i	−0.447716	−	0.0391701i	−0.308785	+	0.951132i	$0.599922\pi$
$524$	−25.0857	+	16.6912i	−1.09588	+	0.729159i
$525$	0.430373	−	0.380842i	0.0187830	−	0.0166213i
$526$	6.00174	−	9.17834i	0.261688	−	0.400195i
$527$	12.8289	+	18.3216i	0.558835	+	0.798099i
$528$	−0.0106158	−	0.266995i	−0.000461995	−	0.0116195i
$529$	7.09264	+	19.4869i	0.308376	+	0.847256i
$530$	−33.4413	−	1.41786i	−1.45260	−	0.0615880i
$531$		−	0.445124i		−	0.0193168i
$532$	−37.8450	+	15.6333i	−1.64079	+	0.677789i
$533$	−2.63491	+	2.63491i	−0.114130	+	0.114130i
$534$	−0.0823795	−	0.110042i	−0.00356491	−	0.00476198i
$535$	−11.9335	−	24.7375i	−0.515931	−	1.06949i
$536$	30.1408	+	17.0823i	1.30189	+	0.737841i
$537$	−0.290113	+	0.203139i	−0.0125193	+	0.00876611i
$538$	3.80007	−	0.795207i	0.163833	−	0.0342838i
$539$	−20.5574	−	35.6065i	−0.885472	−	1.53368i
$540$	−0.507401	+	0.416657i	−0.0218351	+	0.0179301i
$541$	−13.9253	+	11.6847i	−0.598697	+	0.502366i	−0.891027	−	0.453951i	$-0.850014\pi$
$541$	−13.9253	+	11.6847i	−0.598697	+	0.502366i	0.292330	+	0.956318i	$0.405570\pi$
$542$	−9.13396	+	27.8125i	−0.392337	+	1.19465i
$543$	0.180816	−	0.0484495i	0.00775956	−	0.00207917i
$544$	−11.3101	−	8.18833i	−0.484918	−	0.351072i
$545$	−16.1980	−	27.2231i	−0.693844	−	1.16611i
$546$	−0.251628	+	0.587636i	−0.0107687	+	0.0251485i
$547$	−6.37279	−	4.46228i	−0.272481	−	0.190793i	0.429347	−	0.903139i	$-0.358744\pi$
$547$	−6.37279	−	4.46228i	−0.272481	−	0.190793i	−0.701828	+	0.712346i	$0.747633\pi$
$548$	−15.3829	+	12.2969i	−0.657126	+	0.525299i
$549$	−17.3448	+	20.6707i	−0.740257	+	0.882204i
$550$	13.2446	+	14.0424i	0.564751	+	0.598772i
$551$	24.1825	−	1.60892i	1.03021	−	0.0685424i
$552$	−0.00990176	−	0.103636i	−0.000421447	−	0.00441104i
$553$	−0.669950	+	0.0586131i	−0.0284892	+	0.00249248i
$554$	2.64143	+	22.0887i	0.112224	+	0.938459i
$555$	0.149860	−	0.267627i	0.00636122	−	0.0113602i
$556$	−11.3412	−	8.34972i	−0.480975	−	0.354107i
$557$	11.7426	+	25.1820i	0.497549	+	1.06700i	0.981422	+	0.191860i	$0.0614518\pi$
$557$	11.7426	+	25.1820i	0.497549	+	1.06700i	−0.483873	+	0.875138i	$0.660770\pi$
$558$	18.1517	−	33.8801i	0.768423	−	1.43426i
$559$	23.8692	−	41.3426i	1.00956	−	1.74861i
$560$	5.09806	−	41.7001i	0.215432	−	1.76215i
$561$	0.126313	−	0.105989i	0.00533293	−	0.00447486i
$562$	−17.4219	+	0.553358i	−0.734900	+	0.0233420i
$563$	7.05035	−	26.3123i	0.297137	−	1.10893i	−0.642369	−	0.766396i	$-0.722048\pi$
$563$	7.05035	−	26.3123i	0.297137	−	1.10893i	0.939505	−	0.342534i	$-0.111285\pi$
$564$	0.122602	−	0.116910i	0.00516249	−	0.00492278i
$565$	−9.95655	−	0.739379i	−0.418875	−	0.0311059i
$566$	−8.07095	−	0.448520i	−0.339247	−	0.0188527i
$567$	17.8544	−	38.2888i	0.749813	−	1.60798i
$568$	−12.6821	+	18.4234i	−0.532130	+	0.773030i
$569$		−	18.1792i		−	0.762113i	−0.924552	−	0.381057i	$-0.875560\pi$
$569$		−	18.1792i		−	0.762113i	0.924552	−	0.381057i	$-0.124440\pi$
$570$	0.161575	−	0.296087i	0.00676765	−	0.0124017i
$571$			29.5539i			1.23679i	0.785867	+	0.618396i	$0.212217\pi$
$571$			29.5539i			1.23679i	−0.785867	+	0.618396i	$0.787783\pi$
$572$	−19.9965	−	7.82106i	−0.836095	−	0.327015i
$573$	0.0860090	−	0.184447i	0.00359308	−	0.00770538i
$574$	0.349224	−	6.28416i	0.0145763	−	0.262296i
$575$	5.45593	+	5.17641i	0.227528	+	0.215871i
$576$	−3.78869	+	23.6942i	−0.157862	+	0.987259i
$577$	0.600206	−	2.24000i	0.0249869	−	0.0932524i	−0.952306	−	0.305144i	$-0.901296\pi$
$577$	0.600206	−	2.24000i	0.0249869	−	0.0932524i	0.977293	+	0.211891i	$0.0679622\pi$
$578$	0.489690	+	15.4174i	0.0203684	+	0.641280i
$579$	−0.111233	+	0.0933353i	−0.00462267	+	0.00387888i
$580$	−10.7474	+	22.4229i	−0.446261	+	0.931062i
$581$	16.8619	−	29.2057i	0.699551	−	1.21166i
$582$	0.0341079	+	0.0182738i	0.00141382	+	0.000757472i
$583$	−12.2113	−	26.1873i	−0.505742	−	1.08457i
$584$	−14.6309	−	17.1563i	−0.605432	−	0.709931i
$585$	7.16088	+	25.3855i	0.296066	+	1.04956i
$586$	−23.1124	+	2.76385i	−0.954764	+	0.114174i
$587$	5.06299	−	0.442955i	0.208972	−	0.0182827i	0.0178111	−	0.999841i	$-0.494330\pi$
$587$	5.06299	−	0.442955i	0.208972	−	0.0182827i	0.191161	+	0.981559i	$0.438775\pi$
$588$	−0.235577	−	0.698453i	−0.00971504	−	0.0288037i
$589$	−4.26128	+	39.2668i	−0.175583	+	1.61796i
$590$	−0.465358	−	0.0606691i	−0.0191585	−	0.00249771i
$591$	0.0334358	−	0.0398473i	0.00137537	−	0.00163910i
$592$	−4.76784	−	21.9097i	−0.195957	−	0.900485i
$593$	−14.7642	−	10.3380i	−0.606294	−	0.424532i	0.229707	−	0.973260i	$-0.426223\pi$
$593$	−14.7642	−	10.3380i	−0.606294	−	0.424532i	−0.836001	+	0.548728i	$0.815112\pi$
$594$	−0.521017	−	0.223101i	−0.0213776	−	0.00915395i
$595$	22.2787	−	13.2560i	0.913339	−	0.543444i
$596$	−1.01289	−	15.9289i	−0.0414898	−	0.652473i
$597$	0.199105	−	0.0533499i	0.00814881	−	0.00218347i
$598$	−7.94804	−	2.61023i	−0.325019	−	0.106740i
$599$	16.9304	−	14.2063i	0.691758	−	0.580453i	−0.227658	−	0.973741i	$-0.573107\pi$
$599$	16.9304	−	14.2063i	0.691758	−	0.580453i	0.919415	+	0.393288i	$0.128662\pi$
$600$	0.183201	+	0.293598i	0.00747916	+	0.0119861i
$601$	5.13119	+	8.88748i	0.209306	+	0.362528i	0.951496	−	0.307661i	$-0.0995463\pi$
$601$	5.13119	+	8.88748i	0.209306	+	0.362528i	−0.742190	+	0.670189i	$0.766213\pi$
$602$	16.5153	+	78.9218i	0.673112	+	3.21661i
$603$	30.0950	−	21.0727i	1.22556	−	0.858148i
$604$	1.01843	−	3.46894i	0.0414395	−	0.141149i
$605$	2.61510	−	7.48976i	0.106319	−	0.304502i
$606$	0.161081	−	0.120589i	0.00654348	−	0.00489858i
$607$	−7.59746	+	7.59746i	−0.308372	+	0.308372i	−0.844278	−	0.535906i	$-0.819970\pi$
$607$	−7.59746	+	7.59746i	−0.308372	+	0.308372i	0.535906	+	0.844278i	$0.319970\pi$
$608$	−5.50590	−	24.0351i	−0.223294	−	0.974751i
$609$			0.639060i			0.0258960i
$610$	19.2463	+	20.9505i	0.779258	+	0.848263i
$611$	−4.65590	−	12.7920i	−0.188358	−	0.517508i
$612$	−12.9957	+	7.09678i	−0.525318	+	0.286870i
$613$	−7.72449	−	11.0317i	−0.311989	−	0.445567i	0.632281	−	0.774740i	$-0.282119\pi$
$613$	−7.72449	−	11.0317i	−0.311989	−	0.445567i	−0.944270	+	0.329173i	$0.893230\pi$
$614$	−9.49939	−	6.21167i	−0.383364	−	0.250683i
$615$	0.0302934	+	0.0420756i	0.00122155	+	0.00169665i
$616$	33.9788	−	12.6755i	1.36904	−	0.510712i
$617$	−15.5871	−	1.36370i	−0.627514	−	0.0549004i	−0.231037	−	0.972945i	$-0.574212\pi$
$617$	−15.5871	−	1.36370i	−0.627514	−	0.0549004i	−0.396477	+	0.918045i	$0.629767\pi$
$618$	0.0319564	−	0.0973061i	0.00128548	−	0.00391422i
$619$	−6.51806	+	11.2896i	−0.261983	+	0.453768i	−0.966769	−	0.255652i	$-0.917710\pi$
$619$	−6.51806	+	11.2896i	−0.261983	+	0.453768i	0.704786	+	0.709420i	$0.251043\pi$
$620$	−32.9461	−	23.5946i	−1.32315	−	0.947580i
$621$	−0.207507	−	0.0755264i	−0.00832697	−	0.00303077i
$622$	−1.96789	−	4.91530i	−0.0789054	−	0.197086i
$623$	10.7010	−	15.2826i	0.428727	−	0.612286i
$624$	−0.323851	−	0.208093i	−0.0129644	−	0.00833039i
$625$	−23.9091	−	7.30433i	−0.956365	−	0.292173i
$626$	−36.7878	−	8.61549i	−1.47034	−	0.344344i
$627$	0.291118	+	0.00606536i	0.0116261	+	0.000242227i
$628$	12.1899	−	4.11148i	0.486432	−	0.164066i
$629$	8.89402	−	10.5995i	0.354628	−	0.422629i
$630$	−37.6033	−	23.8894i	−1.49815	−	0.951775i
$631$	−36.1213	+	6.36916i	−1.43797	+	0.253552i	−0.837649	−	0.546209i	$-0.816070\pi$
$631$	−36.1213	+	6.36916i	−1.43797	+	0.253552i	−0.600318	+	0.799761i	$0.704959\pi$
$632$	0.0320723	−	0.403704i	0.00127577	−	0.0160585i
$633$	0.0912933	−	0.0425708i	0.00362858	−	0.00169204i
$634$	41.2444	−	12.4675i	1.63802	−	0.495148i
$635$	14.8554	+	6.69094i	0.589519	+	0.265522i
$636$	−0.122147	−	0.503416i	−0.00484344	−	0.0199617i
$637$	−59.0057	−	5.16233i	−2.33789	−	0.204539i
$638$	−21.4546	+	0.681444i	−0.849396	+	0.0269786i
$639$	11.8593	+	20.5408i	0.469145	+	0.812582i
$640$	24.2549	+	7.19035i	0.958758	+	0.284224i
$641$	4.40737	−	24.9954i	0.174081	−	0.987260i	−0.765119	−	0.643889i	$-0.777320\pi$
$641$	4.40737	−	24.9954i	0.174081	−	0.987260i	0.939200	−	0.343371i	$-0.111569\pi$
$642$	0.316785	−	0.283430i	0.0125025	−	0.0111861i
$643$	35.2575	+	16.4408i	1.39042	+	0.648363i	0.966341	−	0.257263i	$-0.0828207\pi$
$643$	35.2575	+	16.4408i	1.39042	+	0.648363i	0.424077	+	0.905626i	$0.360598\pi$
$644$	12.9443	−	5.66556i	0.510076	−	0.223254i
$645$	−0.514381	−	0.420222i	−0.0202537	−	0.0165462i
$646$	9.65275	−	11.7622i	0.379782	−	0.462777i
$647$	9.26218	−	9.26218i	0.364134	−	0.364134i	−0.501199	−	0.865332i	$-0.667107\pi$
$647$	9.26218	−	9.26218i	0.364134	−	0.364134i	0.865332	+	0.501199i	$0.167107\pi$
$648$	20.9556	+	14.4252i	0.823214	+	0.566675i
$649$	−0.138561	−	0.380692i	−0.00543898	−	0.0149435i
$650$	27.5155	−	4.02642i	1.07924	−	0.157929i
$651$	−1.02566	−	0.180851i	−0.0401986	−	0.00708811i
$652$	−35.8361	−	0.851753i	−1.40345	−	0.0333572i
$653$	−17.9099	−	4.79894i	−0.700868	−	0.187797i	−0.109248	−	0.994014i	$-0.534844\pi$
$653$	−17.9099	−	4.79894i	−0.700868	−	0.187797i	−0.591619	+	0.806218i	$0.701511\pi$
$654$	0.335487	−	0.357498i	0.0131186	−	0.0139793i
$655$	33.6848	−	0.442708i	1.31618	−	0.0172980i
$656$	3.69701	+	0.834724i	0.144344	+	0.0325905i
$657$	−23.0960	+	6.18856i	−0.901061	+	0.241439i
$658$	20.2671	+	10.8584i	0.790094	+	0.423304i
$659$	5.78808	+	2.10669i	0.225472	+	0.0820650i	0.452286	−	0.891873i	$-0.350609\pi$
$659$	5.78808	+	2.10669i	0.225472	+	0.0820650i	−0.226814	+	0.973938i	$0.572831\pi$
$660$	−0.152113	+	0.257120i	−0.00592097	+	0.0100084i
$661$	−1.14318	−	6.48329i	−0.0444645	−	0.252171i	0.954471	−	0.298305i	$-0.0964211\pi$
$661$	−1.14318	−	6.48329i	−0.0444645	−	0.252171i	−0.998935	+	0.0461337i	$0.985310\pi$
$662$	−16.8609	+	21.4411i	−0.655316	+	0.833334i
$663$	−0.0207033	−	0.236640i	−0.000804051	−	0.00919035i
$664$	15.6607	+	12.9291i	0.607752	+	0.501746i
$665$	45.0220	+	8.29606i	1.74588	+	0.321708i
$666$	−23.1515	−	5.42194i	−0.897102	−	0.210096i
$667$	−8.33145	+	0.728908i	−0.322595	+	0.0282234i
$668$	25.2980	+	31.6467i	0.978809	+	1.22445i
$669$	0.0110675	−	0.00195150i	0.000427895	−	7.54494e-5i
$670$	−17.9288	−	34.3351i	−0.692648	−	1.32648i
$671$	−8.39962	+	23.0778i	−0.324264	+	0.890908i
$672$	0.642005	−	0.102788i	0.0247659	−	0.00396513i
$673$	1.12416	+	4.19542i	0.0433331	+	0.161722i	0.984202	−	0.177050i	$-0.0566554\pi$
$673$	1.12416	+	4.19542i	0.0433331	+	0.161722i	−0.940869	+	0.338771i	$0.889989\pi$
$674$	5.57749	+	11.0324i	0.214837	+	0.424951i
$675$	0.729319	−	0.0831721i	0.0280715	−	0.00320130i
$676$	−4.10655	+	2.73236i	−0.157944	+	0.105091i
$677$	−3.77539	+	14.0899i	−0.145100	+	0.541520i	0.854651	+	0.519203i	$0.173771\pi$
$677$	−3.77539	+	14.0899i	−0.145100	+	0.541520i	−0.999751	+	0.0223172i	$0.992896\pi$
$678$	−0.0316490	−	0.151242i	−0.00121547	−	0.00580840i
$679$	−0.911959	+	5.17198i	−0.0349978	+	0.198482i
$680$	5.64810	+	14.5537i	0.216595	+	0.558107i
$681$	−0.0163523	+	0.00595175i	−0.000626622	+	0.000228072i
$682$	4.97786	−	34.6263i	0.190612	−	1.32591i
$683$	7.15802	+	7.15802i	0.273894	+	0.273894i	0.830666	−	0.556772i	$-0.187960\pi$
$683$	7.15802	+	7.15802i	0.273894	+	0.273894i	−0.556772	+	0.830666i	$0.687960\pi$
$684$	−25.5229	−	5.68406i	−0.975893	−	0.217335i
$685$	21.9075	−	2.20712i	0.837043	−	0.0843297i
$686$	42.8650	−	32.0895i	1.63659	−	1.22518i
$687$	−0.0340897	+	0.0731057i	−0.00130060	+	0.00278916i
$688$	−48.5168	+	1.92904i	−1.84968	+	0.0735441i
$689$	−40.9937	−	7.22830i	−1.56174	−	0.275376i
$690$	−0.0536157	+	0.103312i	−0.00204111	+	0.00393304i
$691$	−14.5975	+	8.42786i	−0.555314	+	0.320611i	−0.751263	−	0.660003i	$-0.770555\pi$
$691$	−14.5975	+	8.42786i	−0.555314	+	0.320611i	0.195948	+	0.980614i	$0.437221\pi$
$692$	11.9969	+	2.41062i	0.456053	+	0.0916379i
$693$	3.35186	−	38.3119i	0.127327	−	1.45535i
$694$	−7.96483	+	4.02668i	−0.302341	+	0.152851i
$695$	5.57932	+	14.7240i	0.211636	+	0.558515i
$696$	−0.379509	−	0.0637962i	−0.0143852	−	0.00241819i
$697$	0.988422	+	2.11968i	0.0374392	+	0.0802886i
$698$	−2.03439	−	5.08140i	−0.0770030	−	0.192334i
$699$	−0.105021	−	0.595604i	−0.00397226	−	0.0225278i
$700$	−30.1005	+	36.0565i	−1.13769	+	1.36281i
$701$	20.9395	+	17.5704i	0.790876	+	0.663624i	0.945962	−	0.324277i	$-0.105121\pi$
$701$	20.9395	+	17.5704i	0.790876	+	0.663624i	−0.155086	+	0.987901i	$0.549566\pi$
$702$	−0.693800	+	0.430497i	−0.0261858	+	0.0162481i
$703$	24.1463	−	3.74082i	0.910695	−	0.141088i
$704$	4.13539	+	21.4438i	0.155858	+	0.808195i
$705$	−0.186079	+	0.0353381i	−0.00700812	+	0.00133091i
$706$	−7.27276	+	0.869699i	−0.273714	+	0.0327316i
$707$	22.3710	+	15.6643i	0.841348	+	0.589118i
$708$	−0.00109091	−	0.00718071i	−4.09989e−5	−	0.000269868i
$709$	1.14151	−	3.13627i	0.0428703	−	0.117785i	−0.916410	−	0.400240i	$-0.868927\pi$
$709$	1.14151	−	3.13627i	0.0428703	−	0.117785i	0.959280	+	0.282455i	$0.0911489\pi$
$710$	23.0909	−	9.59867i	0.866586	−	0.360232i
$711$	−0.371920	−	0.214728i	−0.0139481	−	0.00805294i
$712$	8.00740	+	7.88049i	0.300090	+	0.295334i
$713$	1.18790	−	13.5778i	0.0444873	−	0.508492i
$714$	0.292568	+	0.274555i	0.0109491	+	0.0102750i
$715$	14.0265	+	19.4819i	0.524561	+	0.728581i
$716$	20.9484	−	19.9757i	0.782880	−	0.746529i
$717$	0.195452	−	0.136857i	0.00729928	−	0.00511101i
$718$	−21.4319	+	19.1753i	−0.799831	+	0.715615i
$719$	−10.0055	+	3.64169i	−0.373141	+	0.135812i	−0.521782	−	0.853079i	$-0.674732\pi$
$719$	−10.0055	+	3.64169i	−0.373141	+	0.135812i	0.148641	+	0.988891i	$0.452510\pi$
$720$	17.9407	−	19.9460i	0.668610	−	0.743345i
$721$	13.9006			0.517687
$722$	26.5068	−	4.40342i	0.986481	−	0.163878i
$723$	−0.246587	−	0.246587i	−0.00917069	−	0.00917069i
$724$	−14.0158	+	6.13456i	−0.520893	+	0.227989i
$725$	23.7023	−	14.5282i	0.880282	−	0.539563i
$726$	0.122589	+	0.00681255i	0.00454972	+	0.000252837i
$727$	−9.59630	−	13.7049i	−0.355907	−	0.508288i	0.600777	−	0.799417i	$-0.294858\pi$
$727$	−9.59630	−	13.7049i	−0.355907	−	0.508288i	−0.956684	+	0.291129i	$0.905969\pi$
$728$	13.1187	−	50.5720i	0.486210	−	1.87432i
$729$	23.3547	−	13.4838i	0.864988	−	0.499401i
$730$	3.32195	+	24.9893i	0.122951	+	0.924897i
$731$	−19.2597	−	22.9528i	−0.712345	−	0.848939i
$732$	−0.229145	+	0.375966i	−0.00846943	+	0.0138961i
$733$	9.21174	+	34.3787i	0.340243	+	1.26981i	0.898072	+	0.439849i	$0.144968\pi$
$733$	9.21174	+	34.3787i	0.340243	+	1.26981i	−0.557828	+	0.829956i	$0.688365\pi$
$734$	8.64388	+	28.5952i	0.319051	+	1.05547i
$735$	−0.202817	+	0.798768i	−0.00748102	+	0.0294630i
$736$	2.07232	+	8.25260i	0.0763866	+	0.304195i
$737$	19.1791	−	27.3906i	0.706471	−	1.00894i
$738$	2.48443	−	3.15933i	0.0914533	−	0.116297i
$739$	−33.3423	−	27.9775i	−1.22652	−	1.02917i	−0.998457	−	0.0555238i	$-0.982317\pi$
$739$	−33.3423	−	27.9775i	−1.22652	−	1.02917i	−0.228061	−	0.973647i	$-0.573238\pi$
$740$	−8.82387	+	23.4649i	−0.324372	+	0.862586i
$741$	0.247711	−	0.338534i	0.00909990	−	0.0124364i
$742$	59.7415	−	37.0690i	2.19318	−	1.36085i
$743$	0.0583186	+	0.666584i	0.00213950	+	0.0244546i	0.997189	−	0.0749219i	$-0.0238707\pi$
$743$	0.0583186	+	0.666584i	0.00213950	+	0.0244546i	−0.995050	+	0.0993765i	$0.968315\pi$
$744$	0.209789	−	0.591037i	0.00769122	−	0.0216685i
$745$	−8.71865	+	15.5702i	−0.319427	+	0.570447i
$746$	8.49452	−	19.8376i	0.311006	−	0.726305i
$747$	19.5179	−	9.10137i	0.714124	−	0.333002i
$748$	−8.90540	+	10.1149i	−0.325614	+	0.369836i
$749$	49.9627	+	28.8460i	1.82560	+	1.05401i
$750$	0.00622493	−	0.386865i	0.000227302	−	0.0141263i
$751$	31.7524	+	37.8411i	1.15866	+	1.38084i	0.911211	+	0.411941i	$0.135149\pi$
$751$	31.7524	+	37.8411i	1.15866	+	1.38084i	0.247452	+	0.968900i	$0.420407\pi$
$752$	−8.47152	+	10.9517i	−0.308925	+	0.399369i
$753$	−0.467720	−	0.125325i	−0.0170447	−	0.00456710i
$754$	−16.9239	+	25.8815i	−0.616334	+	0.942547i
$755$	−3.06200	+	2.63867i	−0.111438	+	0.0960309i
$756$	0.388490	−	1.32326i	0.0141293	−	0.0481263i
$757$	31.8052	+	14.8310i	1.15598	+	0.539042i	0.903511	−	0.428564i	$-0.140980\pi$
$757$	31.8052	+	14.8310i	1.15598	+	0.539042i	0.252467	+	0.967606i	$0.418758\pi$
$758$	2.57388	−	17.9040i	0.0934874	−	0.650303i
$759$	−0.100480			−0.00364720
$760$	−9.42112	+	25.9083i	−0.341740	+	0.939795i
$761$	−25.1702			−0.912421			−0.456210	−	0.889872i	$-0.650794\pi$
$761$	−25.1702			−0.912421			−0.456210	+	0.889872i	$0.650794\pi$
$762$	−0.0358809	+	0.249589i	−0.00129983	+	0.00904167i
$763$	60.3055	+	28.1209i	2.18321	+	1.01805i
$764$	−4.68558	+	15.9598i	−0.169518	+	0.577404i
$765$	16.5094	+	1.22600i	0.596899	+	0.0443261i
$766$	27.1343	−	41.4959i	0.980401	−	1.49931i
$767$	−0.563745	−	0.151055i	−0.0203557	−	0.00545429i
$768$	−0.00304904	+	0.391518i	−0.000110023	+	0.0141277i
$769$	−32.2664	−	38.4536i	−1.16356	−	1.38667i	−0.907523	−	0.420003i	$-0.862029\pi$
$769$	−32.2664	−	38.4536i	−1.16356	−	1.38667i	−0.256032	−	0.966668i	$-0.582415\pi$
$770$	−39.5966	−	8.72602i	−1.42696	−	0.314464i
$771$	−0.205771	−	0.118802i	−0.00741068	−	0.00427856i
$772$	7.84221	−	8.90728i	0.282247	−	0.320580i
$773$	−29.7678	+	13.8810i	−1.07067	+	0.499263i	−0.876350	−	0.481674i	$-0.840029\pi$
$773$	−29.7678	+	13.8810i	−1.07067	+	0.499263i	−0.194323	+	0.980938i	$0.562251\pi$
$774$	−20.2683	+	47.3333i	−0.728528	+	1.70136i
$775$	16.6093	+	42.1523i	0.596623	+	1.51416i
$776$	−2.98036	−	1.05788i	−0.106989	−	0.0379757i
$777$	0.0561538	+	0.641841i	0.00201451	+	0.0230259i
$778$	23.2184	−	14.4068i	0.832421	−	0.516510i
$779$	−1.15183	+	3.96628i	−0.0412685	+	0.142107i
$780$	0.177734	+	0.391967i	0.00636388	+	0.0140347i
$781$	16.5367	+	13.8759i	0.591729	+	0.496519i
$782$	−3.24568	+	4.12737i	−0.116065	+	0.147594i
$783$	−0.468196	+	0.668653i	−0.0167319	+	0.0238957i
$784$	27.6095	+	53.5454i	0.986055	+	1.91234i
$785$	−13.9407	−	3.53972i	−0.497566	−	0.126338i
$786$	0.150860	+	0.499068i	0.00538101	+	0.0178012i
$787$	−1.74250	−	6.50308i	−0.0621133	−	0.231810i	0.927890	−	0.372854i	$-0.121621\pi$
$787$	−1.74250	−	6.50308i	−0.0621133	−	0.231810i	−0.990003	+	0.141044i	$0.954954\pi$
$788$	−2.21257	+	3.63025i	−0.0788195	+	0.129322i
$789$	−0.121973	−	0.145362i	−0.00434235	−	0.00517502i
$790$	−0.275180	+	0.359559i	−0.00979048	+	0.0127925i
$791$	18.1619	−	10.4858i	0.645764	−	0.372832i
$792$	22.4171	+	5.81513i	0.796557	+	0.206632i
$793$	20.2932	+	28.9817i	0.720632	+	1.02917i
$794$	−12.0556	−	0.669953i	−0.427836	−	0.0237757i
$795$	−0.190918	+	0.546795i	−0.00677115	+	0.0193928i
$796$	−15.4334	+	6.75503i	−0.547023	+	0.239426i
$797$	−15.0851	−	15.0851i	−0.534341	−	0.534341i	0.387521	−	0.921861i	$-0.373332\pi$
$797$	−15.0851	−	15.0851i	−0.534341	−	0.534341i	−0.921861	+	0.387521i	$0.873332\pi$
$798$	0.0694550	+	0.705106i	0.00245868	+	0.0249605i
$799$	−8.54409			−0.302268
$800$	−18.4075	−	21.4748i	−0.650802	−	0.759248i
$801$	11.1954	−	4.07480i	0.395571	−	0.143976i
$802$	−38.2280	+	34.2029i	−1.34988	+	1.20775i
$803$	−17.8264	+	12.4822i	−0.629081	+	0.440488i
$804$	0.433845	−	0.413700i	0.0153005	−	0.0145901i
$805$	−15.5924	−	2.53855i	−0.549559	−	0.0894720i
$806$	−36.7489	−	34.4863i	−1.29442	−	1.21473i
$807$	0.00585497	−	0.0669226i	0.000206105	−	0.00235579i
$808$	−11.5356	+	11.7214i	−0.405821	+	0.412357i
$809$	−1.02287	−	0.590557i	−0.0359624	−	0.0207629i	0.481911	−	0.876220i	$-0.339943\pi$
$809$	−1.02287	−	0.590557i	−0.0359624	−	0.0207629i	−0.517873	+	0.855457i	$0.673276\pi$
$810$	−10.9179	−	26.2646i	−0.383617	−	0.922844i
$811$	−7.71596	+	21.1994i	−0.270944	+	0.744412i	0.727363	+	0.686253i	$0.240745\pi$
$811$	−7.71596	+	21.1994i	−0.270944	+	0.744412i	−0.998307	+	0.0581597i	$0.981477\pi$
$812$	−7.84500	−	51.6383i	−0.275306	−	1.81215i
$813$	0.414932	+	0.290538i	0.0145523	+	0.0101896i
$814$	−21.4881	+	2.56961i	−0.753157	+	0.0900648i
$815$	33.1287	+	22.5540i	1.16045	+	0.790032i
$816$	−0.192252	+	0.146334i	−0.00673017	+	0.00512273i
$817$	1.10216	−	52.9002i	0.0385597	−	1.85074i
$818$	−25.5518	+	15.8546i	−0.893397	+	0.554344i
$819$	−42.4419	−	35.6130i	−1.48304	−	1.24442i
$820$	−2.96432	−	3.02797i	−0.103519	−	0.105741i
$821$	−6.32452	−	35.8681i	−0.220727	−	1.25181i	−0.870687	−	0.491838i	$-0.836325\pi$
$821$	−6.32452	−	35.8681i	−0.220727	−	1.25181i	0.649959	−	0.759969i	$-0.274786\pi$
$822$	0.126657	+	0.316358i	0.00441768	+	0.0110342i
$823$	−6.98873	−	14.9874i	−0.243612	−	0.522427i	0.746043	−	0.665898i	$-0.231951\pi$
$823$	−6.98873	−	14.9874i	−0.243612	−	0.522427i	−0.989655	+	0.143471i	$0.954174\pi$
$824$	−1.38768	+	8.25496i	−0.0483420	+	0.287575i
$825$	0.298900	−	0.149065i	0.0104064	−	0.00518977i
$826$	0.879735	−	0.444757i	0.0306099	−	0.0154751i
$827$	−4.74172	+	54.1981i	−0.164886	+	1.88465i	0.240704	+	0.970599i	$0.422622\pi$
$827$	−4.74172	+	54.1981i	−0.164886	+	1.88465i	−0.405590	+	0.914055i	$0.632934\pi$
$828$	8.84633	+	1.77756i	0.307431	+	0.0617743i
$829$	28.3381	−	16.3610i	0.984224	−	0.568242i	0.0806812	−	0.996740i	$-0.474290\pi$
$829$	28.3381	−	16.3610i	0.984224	−	0.568242i	0.903543	+	0.428498i	$0.140957\pi$
$830$	−6.85484	−	21.6456i	−0.237935	−	0.751331i
$831$	0.379084	+	0.0668427i	0.0131503	+	0.00231875i
$832$	28.7228	+	12.8391i	0.995783	+	0.445115i
$833$	−15.7113	+	33.6930i	−0.544364	+	1.16739i
$834$	−0.195081	+	0.146041i	−0.00675509	+	0.00505699i
$835$	−4.54062	−	45.0695i	−0.157135	−	1.55969i
$836$	−23.5978	+	3.08362i	−0.816147	+	0.106649i
$837$	−0.940653	−	0.940653i	−0.0325137	−	0.0325137i
$838$	−4.27371	+	29.7282i	−0.147633	+	1.02694i
$839$	5.82574	−	2.12040i	0.201127	−	0.0732042i	−0.239493	−	0.970898i	$-0.576981\pi$
$839$	5.82574	−	2.12040i	0.201127	−	0.0732042i	0.440619	+	0.897694i	$0.354759\pi$
$840$	−0.665161	−	0.293223i	−0.0229502	−	0.0101172i
$841$	−0.332489	+	1.88564i	−0.0114651	+	0.0650219i
$842$	−6.55875	−	31.3424i	−0.226030	−	1.08013i
$843$	−0.0780624	+	0.291333i	−0.00268861	+	0.0100340i
$844$	−6.85422	+	4.56057i	−0.235932	+	0.156981i
$845$	5.51422	−	0.0724714i	0.189695	−	0.00249309i
$846$	6.62454	+	13.1034i	0.227757	+	0.450506i
$847$	4.31293	+	16.0961i	0.148194	+	0.553067i
$848$	16.0497	+	39.1783i	0.551150	+	1.34539i
$849$	−0.0478384	+	0.131435i	−0.00164181	+	0.00451083i
$850$	3.53191	−	17.0928i	0.121144	−	0.586277i
$851$	−8.30366	+	1.46416i	−0.284646	+	0.0501907i
$852$	0.241654	+	0.302298i	0.00827892	+	0.0103566i
$853$	16.8064	−	1.47037i	0.575440	−	0.0503445i	0.204279	−	0.978913i	$-0.434515\pi$
$853$	16.8064	−	1.47037i	0.575440	−	0.0503445i	0.371162	+	0.928568i	$0.378960\pi$
$854$	−58.1836	−	13.6262i	−1.99100	−	0.466281i
$855$	20.5124	+	20.8303i	0.701508	+	0.712381i
$856$	−22.1180	+	26.7909i	−0.755978	+	0.915696i
$857$	−3.06578	−	35.0420i	−0.104725	−	1.19701i	−0.848726	−	0.528833i	$-0.822630\pi$
$857$	−3.06578	−	35.0420i	−0.104725	−	1.19701i	0.744001	−	0.668179i	$-0.232926\pi$
$858$	−0.229660	+	0.292047i	−0.00784045	+	0.00997031i
$859$	1.74612	+	9.90271i	0.0595767	+	0.337876i	0.999998	−	0.00213600i	$-0.000679912\pi$
$859$	1.74612	+	9.90271i	0.0595767	+	0.337876i	−0.940421	+	0.340012i	$0.889569\pi$
$860$	46.7223	+	27.6409i	1.59322	+	0.942548i
$861$	−0.102337	−	0.0372476i	−0.00348764	−	0.00126940i
$862$	−20.0186	−	10.7252i	−0.681835	−	0.365302i
$863$	11.9023	−	3.18920i	0.405158	−	0.108562i	−0.0504842	−	0.998725i	$-0.516076\pi$
$863$	11.9023	−	3.18920i	0.405158	−	0.108562i	0.455642	+	0.890163i	$0.349410\pi$
$864$	0.747039	+	0.362805i	0.0254148	+	0.0123429i
$865$	−9.80023	−	9.54597i	−0.333218	−	0.324573i
$866$	16.8916	−	17.9998i	0.573999	−	0.611658i
$867$	0.257813	+	0.0690807i	0.00875578	+	0.00234611i
$868$	85.0966	+	2.02258i	2.88837	+	0.0686507i
$869$	−0.384926	−	0.0678729i	−0.0130577	−	0.00230243i
$870$	0.317585	+	0.290278i	0.0107671	+	0.00984133i
$871$	−16.4755	−	45.2661i	−0.558252	−	1.53378i
$872$	−22.7199	+	33.0054i	−0.769394	+	1.11771i
$873$	−2.37143	+	2.37143i	−0.0802608	+	0.0802608i
$874$	−9.11327	+	1.70973i	−0.308261	+	0.0578323i
$875$	50.1488	−	15.5802i	1.69534	−	0.526706i
$876$	−0.357416	+	0.156437i	−0.0120760	+	0.00528551i
$877$	35.9363	+	16.7574i	1.21348	+	0.565857i	0.920681	−	0.390316i	$-0.127634\pi$
$877$	35.9363	+	16.7574i	1.21348	+	0.565857i	0.292803	+	0.956173i	$0.405412\pi$
$878$	−23.9251	+	21.4060i	−0.807433	+	0.722416i
$879$	−0.0699405	+	0.396652i	−0.00235903	+	0.0133787i
$880$	9.13484	−	22.6435i	0.307935	−	0.763313i
$881$	3.24958	+	5.62843i	0.109481	+	0.189627i	0.915560	−	0.402181i	$-0.131748\pi$
$881$	3.24958	+	5.62843i	0.109481	+	0.189627i	−0.806079	+	0.591808i	$0.798414\pi$
$882$	63.8540	−	2.02814i	2.15008	−	0.0682910i
$883$	−21.9166	−	1.91745i	−0.737551	−	0.0645274i	−0.287812	−	0.957687i	$-0.592928\pi$
$883$	−21.9166	−	1.91745i	−0.737551	−	0.0645274i	−0.449740	+	0.893160i	$0.648483\pi$
$884$	4.57786	+	18.8672i	0.153970	+	0.634572i
$885$	−0.00333482	+	0.00740404i	−0.000112099	+	0.000248884i
$886$	8.21289	−	2.48262i	0.275917	−	0.0834054i
$887$	27.3370	−	12.7475i	0.917888	−	0.428018i	0.0945181	−	0.995523i	$-0.469869\pi$
$887$	27.3370	−	12.7475i	0.917888	−	0.428018i	0.823370	+	0.567505i	$0.192091\pi$
$888$	−0.386766	−	0.0307266i	−0.0129790	−	0.00103112i
$889$	−33.7033	+	5.94281i	−1.13037	+	0.199315i
$890$	−2.73412	−	12.2597i	−0.0916480	−	0.410946i
$891$	15.7831	−	18.8095i	0.528753	−	0.630143i
$892$	−0.870336	+	0.293551i	−0.0291410	+	0.00982881i
$893$	−11.3537	−	9.93714i	−0.379936	−	0.332534i
$894$	−0.268904	−	0.0629758i	−0.00899351	−	0.00210622i
$895$	−31.7943	+	6.03804i	−1.06277	+	0.201829i
$896$	−50.6144	+	16.1868i	−1.69091	+	0.540762i
$897$	−0.0830277	+	0.118576i	−0.00277221	+	0.00395913i
$898$	−20.6114	−	51.4820i	−0.687810	−	1.71798i
$899$	−47.3434	−	17.2316i	−1.57899	−	0.574706i
$900$	−28.9523	+	7.83601i	−0.965078	+	0.261200i
$901$	−13.0632	+	22.6261i	−0.435199	+	0.753786i
$902$	1.14136	−	3.47539i	0.0380030	−	0.115718i
$903$	1.38988	+	0.121599i	0.0462524	+	0.00404656i
$904$	4.41397	+	11.8323i	0.146806	+	0.393537i
$905$	16.8831	+	2.74869i	0.561213	+	0.0913694i
$906$	−0.0523575	−	0.0342367i	−0.00173946	−	0.00113744i
$907$	−29.3086	−	41.8570i	−0.973175	−	1.38984i	−0.920290	−	0.391238i	$-0.872047\pi$
$907$	−29.3086	−	41.8570i	−0.973175	−	1.38984i	−0.0528858	−	0.998601i	$-0.516842\pi$
$908$	1.24826	−	0.681661i	0.0414250	−	0.0226217i
$909$	5.96477	+	16.3881i	0.197839	+	0.543558i
$910$	−43.0165	+	39.5172i	−1.42598	+	1.30998i
$911$		−	4.86869i		−	0.161307i	−0.996742	−	0.0806534i	$-0.974299\pi$
$911$		−	4.86869i		−	0.161307i	0.996742	−	0.0806534i	$-0.0257007\pi$
$912$	−0.425664	−	0.0291432i	−0.0140951	−	0.000965029i
$913$	13.8596	−	13.8596i	0.458685	−	0.458685i
$914$	−11.3318	+	8.48323i	−0.374824	+	0.280600i
$915$	0.443369	−	0.213884i	0.0146573	−	0.00707079i
$916$	1.85713	−	6.32567i	0.0613614	−	0.209006i
$917$	−57.9649	+	40.5875i	−1.91417	+	1.34032i
$918$	0.104968	+	0.501612i	0.00346446	+	0.0165557i
$919$	17.1341	+	29.6771i	0.565201	+	0.978957i	0.997031	+	0.0770018i	$0.0245347\pi$
$919$	17.1341	+	29.6771i	0.565201	+	0.978957i	−0.431830	+	0.901955i	$0.642132\pi$
$920$	3.06408	−	9.00617i	0.101020	−	0.296925i
$921$	−0.150446	+	0.126239i	−0.00495737	+	0.00415973i
$922$	−35.8573	−	11.7759i	−1.18090	−	0.387820i
$923$	30.0392	−	8.04899i	0.988754	−	0.264936i
$924$	−0.0398229	−	0.626260i	−0.00131008	−	0.0206024i
$925$	22.5289	−	16.6741i	0.740745	−	0.548241i
$926$	17.3184	+	7.41579i	0.569118	+	0.243698i
$927$	7.27143	+	5.09151i	0.238825	+	0.167227i
$928$	31.4488	+	0.496163i	1.03236	+	0.0162873i
$929$	−23.5793	+	28.1007i	−0.773611	+	0.921953i	−0.998626	−	0.0524020i	$-0.983312\pi$
$929$	−23.5793	+	28.1007i	−0.773611	+	0.921953i	0.225016	+	0.974355i	$0.427757\pi$
$930$	−0.555754	+	0.427559i	−0.0182239	+	0.0140202i
$931$	−60.0641	+	26.4995i	−1.96852	+	0.868485i
$932$	15.7976	+	46.8376i	0.517468	+	1.53422i
$933$	−0.0912658	+	0.00798472i	−0.00298791	+	0.000261408i
$934$	47.6612	−	5.69948i	1.55952	−	0.186493i
$935$	14.5013	−	4.09061i	0.474244	−	0.133777i
$936$	25.3858	−	21.6491i	0.829762	−	0.707624i
$937$	16.8456	+	36.1255i	0.550322	+	1.18017i	0.963052	+	0.269315i	$0.0867973\pi$
$937$	16.8456	+	36.1255i	0.550322	+	1.18017i	−0.412731	+	0.910853i	$0.635425\pi$
$938$	71.7179	+	38.4238i	2.34167	+	1.25458i
$939$	−0.326888	+	0.566187i	−0.0106676	+	0.0184768i
$940$	14.6020	−	5.13971i	0.476264	−	0.167639i
$941$	−3.52101	+	2.95448i	−0.114782	+	0.0963132i	−0.698372	−	0.715735i	$-0.746092\pi$
$941$	−3.52101	+	2.95448i	−0.114782	+	0.0963132i	0.583590	+	0.812048i	$0.301647\pi$
$942$	−0.00706674	−	0.222489i	−0.000230247	−	0.00724909i
$943$	0.368874	−	1.37666i	0.0120122	−	0.0448301i
$944$	0.176298	+	0.566834i	0.00573803	+	0.0184489i
$945$	−1.16803	+	1.00654i	−0.0379959	+	0.0327428i
$946$	−2.60027	+	46.7910i	−0.0845421	+	1.52131i
$947$	−13.6469	+	29.2660i	−0.443466	+	0.951016i	0.549815	+	0.835287i	$0.314698\pi$
$947$	−13.6469	+	29.2660i	−0.443466	+	0.951016i	−0.993281	+	0.115730i	$0.963079\pi$
$948$	−0.00652604	−	0.00255248i	−0.000211956	−	8.29006e-5i
$949$			31.3510i			1.01770i
$950$	24.5729	−	18.6057i	0.797251	−	0.603648i
$951$		−	0.745559i		−	0.0241764i
$952$	−27.0109	−	18.5934i	−0.875427	−	0.602617i
$953$	6.58222	−	14.1156i	0.213219	−	0.457250i	−0.770388	−	0.637576i	$-0.779937\pi$
$953$	6.58222	−	14.1156i	0.213219	−	0.457250i	0.983607	+	0.180326i	$0.0577152\pi$
$954$	44.8284	+	2.49121i	1.45137	+	0.0806559i
$955$	14.0876	−	12.1399i	0.455863	−	0.392838i
$956$	−14.1131	+	13.4578i	−0.456451	+	0.435257i
$957$	−0.0961315	+	0.358768i	−0.00310749	+	0.0115973i
$958$	48.2029	−	1.53103i	1.55736	−	0.0494652i
$959$	−35.4298	+	29.7291i	−1.14409	+	0.960004i
$960$	0.240534	−	0.365737i	0.00776319	−	0.0118041i
$961$	25.5537	−	44.2603i	0.824313	−	1.42775i
$962$	−14.7234	+	27.4812i	−0.474702	+	0.886029i
$963$	15.5698	+	33.3896i	0.501731	+	1.07597i
$964$	22.9522	+	16.8980i	0.739240	+	0.544249i
$965$	−12.7700	+	3.60224i	−0.411082	+	0.115960i
$966$	−0.0290305	−	0.242764i	−0.000934041	−	0.00781081i
$967$	20.2396	−	1.77073i	0.650861	−	0.0569430i	0.243056	−	0.970012i	$-0.421850\pi$
$967$	20.2396	−	1.77073i	0.650861	−	0.0569430i	0.407805	+	0.913069i	$0.366294\pi$
$968$	−9.98927	+	0.954410i	−0.321067	+	0.0306759i
$969$	−0.146490	−	0.218771i	−0.00470593	−	0.00702792i
$970$	2.15601	+	2.80245i	0.0692253	+	0.0899812i
$971$	30.1359	−	35.9145i	0.967106	−	1.15255i	−0.0211547	−	0.999776i	$-0.506734\pi$
$971$	30.1359	−	35.9145i	0.967106	−	1.15255i	0.988261	−	0.152776i	$-0.0488213\pi$
$972$	1.03188	−	0.824877i	0.0330977	−	0.0264579i
$973$	−27.0928	−	18.9706i	−0.868557	−	0.608170i
$974$	18.1651	−	42.4216i	0.582046	−	1.35928i
$975$	0.0710736	−	0.475902i	0.00227618	−	0.0152411i
$976$	13.9004	−	33.1923i	0.444940	−	1.06246i
$977$	−50.5761	+	13.5518i	−1.61807	+	0.433561i	−0.950434	−	0.310926i	$-0.899361\pi$
$977$	−50.5761	+	13.5518i	−1.61807	+	0.433561i	−0.667637	+	0.744487i	$0.732694\pi$
$978$	−0.193531	+	0.589295i	−0.00618845	+	0.0188436i
$979$	8.30645	−	6.96994i	0.265475	−	0.222760i
$980$	6.58277	−	67.0330i	0.210279	−	2.14129i
$981$	21.2458	+	36.7987i	0.678325	+	1.17489i
$982$	−17.7638	+	3.71727i	−0.566865	+	0.118623i
$983$	−48.1655	+	33.7259i	−1.53624	+	1.07569i	−0.568837	+	0.822450i	$0.692607\pi$
$983$	−48.1655	+	33.7259i	−1.53624	+	1.07569i	−0.967404	+	0.253238i	$0.918504\pi$
$984$	0.0323358	−	0.0570549i	0.00103083	−	0.00181885i
$985$	4.28107	−	2.06522i	0.136406	−	0.0658033i
$986$	11.6317	+	15.5375i	0.370429	+	0.494816i
$987$	0.281322	−	0.281322i	0.00895458	−	0.00895458i
$988$	−15.8601	+	30.3956i	−0.504578	+	0.967012i
$989$			18.2587i			0.580591i
$990$	−17.5168	−	19.0680i	−0.556722	−	0.606020i
$991$	−1.83200	−	5.03338i	−0.0581954	−	0.159891i	0.907188	−	0.420725i	$-0.138224\pi$
$991$	−1.83200	−	5.03338i	−0.0581954	−	0.159891i	−0.965383	+	0.260835i	$0.916002\pi$
$992$	−9.69616	+	50.3331i	−0.307853	+	1.59808i
$993$	0.270714	+	0.386620i	0.00859086	+	0.0122690i
$994$	−28.7470	+	43.9623i	−0.911800	+	1.39440i
$995$	18.5907	+	3.02670i	0.589365	+	0.0959529i
$996$	0.292556	−	0.194657i	0.00927000	−	0.00616794i
$997$	24.5073	+	2.14411i	0.776155	+	0.0679048i	0.468348	−	0.883544i	$-0.344849\pi$
$997$	24.5073	+	2.14411i	0.776155	+	0.0679048i	0.307807	+	0.951449i	$0.400405\pi$
$998$	−25.2717	−	8.29952i	−0.799962	−	0.262717i
$999$	−0.411479	+	0.712702i	−0.0130186	+	0.0225489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.187.26	yes	672
4.3	odd	2	inner	380.2.bj.a.187.33	yes	672
5.3	odd	4	inner	380.2.bj.a.263.55	yes	672
19.6	even	9	inner	380.2.bj.a.367.52	yes	672
20.3	even	4	inner	380.2.bj.a.263.52	yes	672
76.63	odd	18	inner	380.2.bj.a.367.55	yes	672
95.63	odd	36	inner	380.2.bj.a.63.33	yes	672
380.63	even	36	inner	380.2.bj.a.63.26	✓	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.63.26	✓	672	380.63	even	36	inner
380.2.bj.a.63.33	yes	672	95.63	odd	36	inner
380.2.bj.a.187.26	yes	672	1.1	even	1	trivial
380.2.bj.a.187.33	yes	672	4.3	odd	2	inner
380.2.bj.a.263.52	yes	672	20.3	even	4	inner
380.2.bj.a.263.55	yes	672	5.3	odd	4	inner
380.2.bj.a.367.52	yes	672	19.6	even	9	inner
380.2.bj.a.367.55	yes	672	76.63	odd	18	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.201238 + 1.39982i) q^{2} +(0.0221779 + 0.0103417i) q^{3} +(-1.91901 - 0.563395i) q^{4} +(1.45970 + 1.69389i) q^{5} +(-0.0189396 + 0.0289640i) q^{6} +(-4.53688 - 1.21565i) q^{7} +(1.17483 - 2.57289i) q^{8} +(-1.92798 - 2.29767i) q^{9} +O(q^{10})\)	\(q+(-0.201238 + 1.39982i) q^{2} +(0.0221779 + 0.0103417i) q^{3} +(-1.91901 - 0.563395i) q^{4} +(1.45970 + 1.69389i) q^{5} +(-0.0189396 + 0.0289640i) q^{6} +(-4.53688 - 1.21565i) q^{7} +(1.17483 - 2.57289i) q^{8} +(-1.92798 - 2.29767i) q^{9} +(-2.66489 + 1.70245i) q^{10} +(-2.36413 - 1.36493i) q^{11} +(-0.0367331 - 0.0323408i) q^{12} +(-3.56425 + 1.66204i) q^{13} +(2.61469 - 6.10620i) q^{14} +(0.0148554 + 0.0526629i) q^{15} +(3.36517 + 2.16232i) q^{16} +(0.215131 + 2.45896i) q^{17} +(3.60432 - 2.23645i) q^{18} +(-2.57400 + 3.51775i) q^{19} +(-1.84685 - 4.07298i) q^{20} +(-0.0880467 - 0.0738800i) q^{21} +(2.38642 - 3.03469i) q^{22} +(0.862750 - 1.23214i) q^{23} +(0.0526635 - 0.0449116i) q^{24} +(-0.738534 + 4.94516i) q^{25} +(-1.60929 - 5.32378i) q^{26} +(-0.0379970 - 0.141807i) q^{27} +(8.02141 + 4.88891i) q^{28} +(-3.57396 - 4.25928i) q^{29} +(-0.0767082 + 0.0101972i) q^{30} +(7.84733 - 4.53066i) q^{31} +(-3.70406 + 4.27550i) q^{32} +(-0.0383158 - 0.0547207i) q^{33} +(-3.48539 - 0.193691i) q^{34} +(-4.56332 - 9.45948i) q^{35} +(2.40530 + 5.49547i) q^{36} +(-3.96378 - 3.96378i) q^{37} +(-4.40624 - 4.31104i) q^{38} -0.0962361 q^{39} +(6.07310 - 1.76562i) q^{40} +(0.890376 - 0.324070i) q^{41} +(0.121137 - 0.108382i) q^{42} +(-9.94350 + 6.96252i) q^{43} +(3.76779 + 3.95126i) q^{44} +(1.07774 - 6.61971i) q^{45} +(1.55115 + 1.45565i) q^{46} +(-0.301686 + 3.44829i) q^{47} +(0.0522704 + 0.0827575i) q^{48} +(13.0433 + 7.53056i) q^{49} +(-6.77372 - 2.02897i) q^{50} +(-0.0206587 + 0.0567594i) q^{51} +(7.77620 - 1.18138i) q^{52} +(8.67038 + 6.07106i) q^{53} +(0.206151 - 0.0246522i) q^{54} +(-1.13889 - 5.99698i) q^{55} +(-8.45782 + 10.2447i) q^{56} +(-0.0934655 + 0.0513968i) q^{57} +(6.68146 - 4.14579i) q^{58} +(0.113684 + 0.0953925i) q^{59} +(0.00116237 - 0.109430i) q^{60} +(-1.56220 - 8.85968i) q^{61} +(4.76294 + 11.8966i) q^{62} +(5.95383 + 12.7680i) q^{63} +(-5.23955 - 6.04542i) q^{64} +(-8.01806 - 3.61137i) q^{65} +(0.0843098 - 0.0426235i) q^{66} +(-1.06756 + 12.2022i) q^{67} +(0.972527 - 4.83996i) q^{68} +(0.0318764 - 0.0184039i) q^{69} +(14.1599 - 4.48423i) q^{70} +(-7.78761 - 1.37317i) q^{71} +(-8.17672 + 2.26110i) q^{72} +(3.36904 - 7.22494i) q^{73} +(6.34625 - 4.75092i) q^{74} +(-0.0675207 + 0.102036i) q^{75} +(6.92140 - 5.30040i) q^{76} +(9.06652 + 9.06652i) q^{77} +(0.0193664 - 0.134713i) q^{78} +(0.134546 - 0.0489707i) q^{79} +(1.24942 + 8.85658i) q^{80} +(-1.56190 + 8.85796i) q^{81} +(0.274464 + 1.31158i) q^{82} +(-1.85832 + 6.93534i) q^{83} +(0.127339 + 0.191381i) q^{84} +(-3.85118 + 3.95375i) q^{85} +(-7.74528 - 15.3203i) q^{86} +(-0.0352147 - 0.131423i) q^{87} +(-6.28928 + 4.47910i) q^{88} +(-1.35854 + 3.73255i) q^{89} +(9.04953 + 2.84077i) q^{90} +(18.1911 - 3.20757i) q^{91} +(-2.34980 + 1.87841i) q^{92} +(0.220892 - 0.0193256i) q^{93} +(-4.76628 - 1.11623i) q^{94} +(-9.71595 + 0.774799i) q^{95} +(-0.126365 + 0.0565154i) q^{96} +(-0.0974512 - 1.11387i) q^{97} +(-13.1663 + 16.7429i) q^{98} +(1.42183 + 8.06357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

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