LMFDB - Embedded newform 230.2.g.c.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} + 35 x^{18} - 66 x^{17} + 51 x^{16} - 52 x^{15} + 289 x^{14} - 451 x^{13} + 115 x^{12} + \cdots + 529 $ x^20 - 9x^19 + 35x^18 - 66x^17 + 51x^16 - 52x^15 + 289x^14 - 451x^13 + 115x^12 + 604x^11 - 265x^10 + 427x^9 + 3056x^8 + 7095x^7 + 12236x^6 + 14297x^5 + 13890x^4 + 9922x^3 + 5418x^2 + 2047*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			41.1
Root			$-0.577766 - 0.371308i$ of defining polynomial
Character	$\chi$	$=$	230.41
Dual form			230.2.g.c.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{2} +(-0.267311 + 0.308493i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.343396 + 0.220687i) q^{6} +(1.05127 + 2.30197i) q^{7} +(0.654861 + 0.755750i) q^{8} +(0.403232 + 2.80454i) q^{9} +O(q^{10})$	\(q+(0.959493 + 0.281733i) q^{2} +(-0.267311 + 0.308493i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.343396 + 0.220687i) q^{6} +(1.05127 + 2.30197i) q^{7} +(0.654861 + 0.755750i) q^{8} +(0.403232 + 2.80454i) q^{9} +(0.415415 - 0.909632i) q^{10} +(0.989357 - 0.290502i) q^{11} +(-0.391661 + 0.115002i) q^{12} +(1.97230 - 4.31874i) q^{13} +(0.360150 + 2.50490i) q^{14} +(0.267311 + 0.308493i) q^{15} +(0.415415 + 0.909632i) q^{16} +(2.04153 - 1.31201i) q^{17} +(-0.403232 + 2.80454i) q^{18} +(-5.54816 - 3.56559i) q^{19} +(0.654861 - 0.755750i) q^{20} +(-0.991159 - 0.291030i) q^{21} +1.03113 q^{22} +(0.0958668 + 4.79487i) q^{23} -0.408195 q^{24} +(-0.959493 - 0.281733i) q^{25} +(3.10914 - 3.58814i) q^{26} +(-2.00316 - 1.28735i) q^{27} +(-0.360150 + 2.50490i) q^{28} +(-8.51068 + 5.46948i) q^{29} +(0.169570 + 0.371308i) q^{30} +(-1.98997 - 2.29655i) q^{31} +(0.142315 + 0.989821i) q^{32} +(-0.174848 + 0.382865i) q^{33} +(2.32847 - 0.683702i) q^{34} +(2.42815 - 0.712969i) q^{35} +(-1.17703 + 2.57733i) q^{36} +(-1.65206 - 11.4903i) q^{37} +(-4.31888 - 4.98425i) q^{38} +(0.805085 + 1.76289i) q^{39} +(0.841254 - 0.540641i) q^{40} +(0.933580 - 6.49319i) q^{41} +(-0.869017 - 0.558483i) q^{42} +(-0.689322 + 0.795520i) q^{43} +(0.989357 + 0.290502i) q^{44} +2.83338 q^{45} +(-1.25889 + 4.62766i) q^{46} +2.53259 q^{47} +(-0.391661 - 0.115002i) q^{48} +(0.390148 - 0.450255i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(-0.140977 + 0.980515i) q^{51} +(3.99409 - 2.56685i) q^{52} +(-3.57090 - 7.81918i) q^{53} +(-1.55933 - 1.79956i) q^{54} +(-0.146744 - 1.02063i) q^{55} +(-1.05127 + 2.30197i) q^{56} +(2.58304 - 0.758450i) q^{57} +(-9.70687 + 2.85019i) q^{58} +(-4.89813 + 10.7254i) q^{59} +(0.0580923 + 0.404041i) q^{60} +(-1.43939 - 1.66115i) q^{61} +(-1.26235 - 2.76416i) q^{62} +(-6.03204 + 3.87656i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-3.99409 - 2.56685i) q^{65} +(-0.275631 + 0.318095i) q^{66} +(9.47782 + 2.78294i) q^{67} +2.42677 q^{68} +(-1.50481 - 1.25215i) q^{69} +2.53066 q^{70} +(3.24130 + 0.951732i) q^{71} +(-1.85547 + 2.14132i) q^{72} +(12.4083 + 7.97436i) q^{73} +(1.65206 - 11.4903i) q^{74} +(0.343396 - 0.220687i) q^{75} +(-2.73971 - 5.99912i) q^{76} +(1.70881 + 1.97207i) q^{77} +(0.275810 + 1.91830i) q^{78} +(-1.79491 + 3.93030i) q^{79} +(0.959493 - 0.281733i) q^{80} +(-7.22321 + 2.12093i) q^{81} +(2.72511 - 5.96715i) q^{82} +(0.515400 + 3.58468i) q^{83} +(-0.676473 - 0.780691i) q^{84} +(-1.00812 - 2.20747i) q^{85} +(-0.885523 + 0.569091i) q^{86} +(0.587700 - 4.08754i) q^{87} +(0.867438 + 0.557468i) q^{88} +(-3.82011 + 4.40864i) q^{89} +(2.71860 + 0.798254i) q^{90} +12.0150 q^{91} +(-2.51166 + 4.08553i) q^{92} +1.24041 q^{93} +(2.43000 + 0.713512i) q^{94} +(-4.31888 + 4.98425i) q^{95} +(-0.343396 - 0.220687i) q^{96} +(0.252252 - 1.75445i) q^{97} +(0.501196 - 0.322099i) q^{98} +(1.21366 + 2.65755i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{5} - q^{6} - 12 q^{7} + 2 q^{8} + 17 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + q^3 - 2 * q^4 + 2 * q^5 - q^6 - 12 * q^7 + 2 * q^8 + 17 * q^9	\( 20 q + 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{5} - q^{6} - 12 q^{7} + 2 q^{8} + 17 q^{9} - 2 q^{10} - 3 q^{11} + q^{12} - 18 q^{13} + q^{14} - q^{15} - 2 q^{16} + 14 q^{17} - 17 q^{18} - 7 q^{19} + 2 q^{20} - 43 q^{21} - 8 q^{22} + 9 q^{23} + 10 q^{24} - 2 q^{25} - 4 q^{26} + 10 q^{27} - q^{28} - 28 q^{29} + q^{30} - 7 q^{31} + 2 q^{32} + 35 q^{33} - 3 q^{34} - 10 q^{35} - 27 q^{36} + 30 q^{37} + 40 q^{38} + 69 q^{39} - 2 q^{40} - 2 q^{41} + 10 q^{42} - 26 q^{43} - 3 q^{44} - 6 q^{45} + 2 q^{46} - 26 q^{47} + q^{48} - 8 q^{49} + 2 q^{50} + 20 q^{51} + 15 q^{52} - q^{53} + 23 q^{54} + 3 q^{55} + 12 q^{56} + 3 q^{57} - 27 q^{58} - 48 q^{59} - q^{60} - 7 q^{61} - 26 q^{62} + 8 q^{63} - 2 q^{64} - 15 q^{65} + 20 q^{66} + 7 q^{67} - 8 q^{68} + 12 q^{69} + 10 q^{70} + 19 q^{71} - 17 q^{72} + 2 q^{73} - 30 q^{74} + q^{75} - 7 q^{76} - 34 q^{77} - 14 q^{78} - 49 q^{79} + 2 q^{80} - 56 q^{81} - 31 q^{82} + 23 q^{83} + 12 q^{84} + 8 q^{85} + 37 q^{86} - 31 q^{87} + 14 q^{88} + 43 q^{89} - 5 q^{90} + 128 q^{91} - 13 q^{92} - 50 q^{93} - 7 q^{94} + 40 q^{95} - q^{96} - 7 q^{97} - 36 q^{98} - 85 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + q^3 - 2 * q^4 + 2 * q^5 - q^6 - 12 * q^7 + 2 * q^8 + 17 * q^9 - 2 * q^10 - 3 * q^11 + q^12 - 18 * q^13 + q^14 - q^15 - 2 * q^16 + 14 * q^17 - 17 * q^18 - 7 * q^19 + 2 * q^20 - 43 * q^21 - 8 * q^22 + 9 * q^23 + 10 * q^24 - 2 * q^25 - 4 * q^26 + 10 * q^27 - q^28 - 28 * q^29 + q^30 - 7 * q^31 + 2 * q^32 + 35 * q^33 - 3 * q^34 - 10 * q^35 - 27 * q^36 + 30 * q^37 + 40 * q^38 + 69 * q^39 - 2 * q^40 - 2 * q^41 + 10 * q^42 - 26 * q^43 - 3 * q^44 - 6 * q^45 + 2 * q^46 - 26 * q^47 + q^48 - 8 * q^49 + 2 * q^50 + 20 * q^51 + 15 * q^52 - q^53 + 23 * q^54 + 3 * q^55 + 12 * q^56 + 3 * q^57 - 27 * q^58 - 48 * q^59 - q^60 - 7 * q^61 - 26 * q^62 + 8 * q^63 - 2 * q^64 - 15 * q^65 + 20 * q^66 + 7 * q^67 - 8 * q^68 + 12 * q^69 + 10 * q^70 + 19 * q^71 - 17 * q^72 + 2 * q^73 - 30 * q^74 + q^75 - 7 * q^76 - 34 * q^77 - 14 * q^78 - 49 * q^79 + 2 * q^80 - 56 * q^81 - 31 * q^82 + 23 * q^83 + 12 * q^84 + 8 * q^85 + 37 * q^86 - 31 * q^87 + 14 * q^88 + 43 * q^89 - 5 * q^90 + 128 * q^91 - 13 * q^92 - 50 * q^93 - 7 * q^94 + 40 * q^95 - q^96 - 7 * q^97 - 36 * q^98 - 85 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$3$	−0.267311	+	0.308493i	−0.154332	+	0.178109i	−0.827650	−	0.561244i	$-0.810323\pi$
$3$	−0.267311	+	0.308493i	−0.154332	+	0.178109i	0.673318	+	0.739353i	$0.264868\pi$
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$6$	−0.343396	+	0.220687i	−0.140191	+	0.0900951i
$7$	1.05127	+	2.30197i	0.397344	+	0.870062i	0.997533	+	0.0702034i	$0.0223648\pi$
$7$	1.05127	+	2.30197i	0.397344	+	0.870062i	−0.600189	+	0.799858i	$0.704908\pi$
$8$	0.654861	+	0.755750i	0.231528	+	0.267198i
$9$	0.403232	+	2.80454i	0.134411	+	0.934846i
$10$	0.415415	−	0.909632i	0.131366	−	0.287651i
$11$	0.989357	−	0.290502i	0.298302	−	0.0875895i	−0.129157	−	0.991624i	$-0.541227\pi$
$11$	0.989357	−	0.290502i	0.298302	−	0.0875895i	0.427459	+	0.904035i	$0.359409\pi$
$12$	−0.391661	+	0.115002i	−0.113063	+	0.0331982i
$13$	1.97230	−	4.31874i	0.547018	−	1.19780i	−0.411142	−	0.911571i	$-0.634870\pi$
$13$	1.97230	−	4.31874i	0.547018	−	1.19780i	0.958160	−	0.286231i	$-0.0924026\pi$
$14$	0.360150	+	2.50490i	0.0962542	+	0.669462i
$15$	0.267311	+	0.308493i	0.0690194	+	0.0796527i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	2.04153	−	1.31201i	0.495144	−	0.318210i	−0.269127	−	0.963105i	$-0.586735\pi$
$17$	2.04153	−	1.31201i	0.495144	−	0.318210i	0.764271	+	0.644895i	$0.223099\pi$
$18$	−0.403232	+	2.80454i	−0.0950426	+	0.661036i
$19$	−5.54816	−	3.56559i	−1.27283	−	0.818001i	−0.282849	−	0.959165i	$-0.591279\pi$
$19$	−5.54816	−	3.56559i	−1.27283	−	0.818001i	−0.989986	+	0.141163i	$0.954916\pi$
$20$	0.654861	−	0.755750i	0.146431	−	0.168991i
$21$	−0.991159	−	0.291030i	−0.216289	−	0.0635081i
$22$	1.03113			0.219837
$23$	0.0958668	+	4.79487i	0.0199896	+	0.999800i
$23$	0.0958668	+	4.79487i	0.0199896	+	0.999800i
$24$	−0.408195			−0.0833225
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	3.10914	−	3.58814i	0.609752	−	0.703692i
$27$	−2.00316	−	1.28735i	−0.385508	−	0.247751i
$28$	−0.360150	+	2.50490i	−0.0680620	+	0.473381i
$29$	−8.51068	+	5.46948i	−1.58039	+	1.01566i	−0.604718	+	0.796439i	$0.706714\pi$
$29$	−8.51068	+	5.46948i	−1.58039	+	1.01566i	−0.975676	+	0.219218i	$0.929649\pi$
$30$	0.169570	+	0.371308i	0.0309592	+	0.0677912i
$31$	−1.98997	−	2.29655i	−0.357409	−	0.412472i	0.548361	−	0.836242i	$-0.315252\pi$
$31$	−1.98997	−	2.29655i	−0.357409	−	0.412472i	−0.905770	+	0.423770i	$0.860707\pi$
$32$	0.142315	+	0.989821i	0.0251579	+	0.174977i
$33$	−0.174848	+	0.382865i	−0.0304372	+	0.0666482i
$34$	2.32847	−	0.683702i	0.399330	−	0.117254i
$35$	2.42815	−	0.712969i	0.410432	−	0.120514i
$36$	−1.17703	+	2.57733i	−0.196171	+	0.429555i
$37$	−1.65206	−	11.4903i	−0.271597	−	1.88900i	−0.431890	−	0.901926i	$-0.642153\pi$
$37$	−1.65206	−	11.4903i	−0.271597	−	1.88900i	0.160293	−	0.987069i	$-0.448756\pi$
$38$	−4.31888	−	4.98425i	−0.700615	−	0.808552i
$39$	0.805085	+	1.76289i	0.128917	+	0.282288i
$40$	0.841254	−	0.540641i	0.133014	−	0.0854828i
$41$	0.933580	−	6.49319i	0.145801	−	1.01407i	−0.777196	−	0.629259i	$-0.783359\pi$
$41$	0.933580	−	6.49319i	0.145801	−	1.01407i	0.922997	−	0.384808i	$-0.125732\pi$
$42$	−0.869017	−	0.558483i	−0.134092	−	0.0861759i
$43$	−0.689322	+	0.795520i	−0.105121	+	0.121316i	−0.805872	−	0.592090i	$-0.798303\pi$
$43$	−0.689322	+	0.795520i	−0.105121	+	0.121316i	0.700751	+	0.713406i	$0.252848\pi$
$44$	0.989357	+	0.290502i	0.149151	+	0.0437948i
$45$	2.83338			0.422375
$46$	−1.25889	+	4.62766i	−0.185613	+	0.682311i
$47$	2.53259			0.369416			0.184708	−	0.982793i	$-0.440866\pi$
$47$	2.53259			0.369416			0.184708	+	0.982793i	$0.440866\pi$
$48$	−0.391661	−	0.115002i	−0.0565313	−	0.0165991i
$49$	0.390148	−	0.450255i	0.0557354	−	0.0643221i
$50$	−0.841254	−	0.540641i	−0.118971	−	0.0764582i
$51$	−0.140977	+	0.980515i	−0.0197407	+	0.137300i
$52$	3.99409	−	2.56685i	0.553881	−	0.355958i
$53$	−3.57090	−	7.81918i	−0.490501	−	1.07405i	−0.979441	−	0.201729i	$-0.935344\pi$
$53$	−3.57090	−	7.81918i	−0.490501	−	1.07405i	0.488941	−	0.872317i	$-0.337383\pi$
$54$	−1.55933	−	1.79956i	−0.212197	−	0.244889i
$55$	−0.146744	−	1.02063i	−0.0197870	−	0.137622i
$56$	−1.05127	+	2.30197i	−0.140482	+	0.307613i
$57$	2.58304	−	0.758450i	0.342133	−	0.100459i
$58$	−9.70687	+	2.85019i	−1.27457	+	0.374249i
$59$	−4.89813	+	10.7254i	−0.637682	+	1.39633i	0.264252	+	0.964454i	$0.414875\pi$
$59$	−4.89813	+	10.7254i	−0.637682	+	1.39633i	−0.901934	+	0.431875i	$0.857852\pi$
$60$	0.0580923	+	0.404041i	0.00749968	+	0.0521614i
$61$	−1.43939	−	1.66115i	−0.184295	−	0.212688i	0.656083	−	0.754689i	$-0.272212\pi$
$61$	−1.43939	−	1.66115i	−0.184295	−	0.212688i	−0.840378	+	0.542001i	$0.817667\pi$
$62$	−1.26235	−	2.76416i	−0.160319	−	0.351049i
$63$	−6.03204	+	3.87656i	−0.759966	+	0.488401i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−3.99409	−	2.56685i	−0.495406	−	0.318378i
$66$	−0.275631	+	0.318095i	−0.0339279	+	0.0391548i
$67$	9.47782	+	2.78294i	1.15790	+	0.339990i	0.803616	−	0.595148i	$-0.202907\pi$
$67$	9.47782	+	2.78294i	1.15790	+	0.339990i	0.354283	+	0.935138i	$0.384725\pi$
$68$	2.42677			0.294290
$69$	−1.50481	−	1.25215i	−0.181158	−	0.150741i
$70$	2.53066			0.302471
$71$	3.24130	+	0.951732i	0.384672	+	0.112950i	0.468350	−	0.883543i	$-0.344849\pi$
$71$	3.24130	+	0.951732i	0.384672	+	0.112950i	−0.0836783	+	0.996493i	$0.526667\pi$
$72$	−1.85547	+	2.14132i	−0.218669	+	0.252357i
$73$	12.4083	+	7.97436i	1.45229	+	0.933328i	0.999122	+	0.0419016i	$0.0133416\pi$
$73$	12.4083	+	7.97436i	1.45229	+	0.933328i	0.453165	+	0.891427i	$0.350295\pi$
$74$	1.65206	−	11.4903i	0.192048	−	1.33572i
$75$	0.343396	−	0.220687i	0.0396519	−	0.0254827i
$76$	−2.73971	−	5.99912i	−0.314266	−	0.688147i
$77$	1.70881	+	1.97207i	0.194737	+	0.224738i
$78$	0.275810	+	1.91830i	0.0312293	+	0.217205i
$79$	−1.79491	+	3.93030i	−0.201943	+	0.442193i	−0.983324	−	0.181861i	$-0.941788\pi$
$79$	−1.79491	+	3.93030i	−0.201943	+	0.442193i	0.781382	+	0.624053i	$0.214515\pi$
$80$	0.959493	−	0.281733i	0.107275	−	0.0314987i
$81$	−7.22321	+	2.12093i	−0.802579	+	0.235658i
$82$	2.72511	−	5.96715i	0.300938	−	0.658962i
$83$	0.515400	+	3.58468i	0.0565725	+	0.393470i	0.998359	+	0.0572596i	$0.0182363\pi$
$83$	0.515400	+	3.58468i	0.0565725	+	0.393470i	−0.941787	+	0.336210i	$0.890855\pi$
$84$	−0.676473	−	0.780691i	−0.0738092	−	0.0851804i
$85$	−1.00812	−	2.20747i	−0.109346	−	0.239434i
$86$	−0.885523	+	0.569091i	−0.0954884	+	0.0613667i
$87$	0.587700	−	4.08754i	0.0630081	−	0.438231i
$88$	0.867438	+	0.557468i	0.0924692	+	0.0594263i
$89$	−3.82011	+	4.40864i	−0.404931	+	0.467315i	−0.921188	−	0.389119i	$-0.872780\pi$
$89$	−3.82011	+	4.40864i	−0.404931	+	0.467315i	0.516257	+	0.856434i	$0.327325\pi$
$90$	2.71860	+	0.798254i	0.286566	+	0.0841434i
$91$	12.0150			1.25952
$92$	−2.51166	+	4.08553i	−0.261858	+	0.425946i
$93$	1.24041			0.128625
$94$	2.43000	+	0.713512i	0.250635	+	0.0735932i
$95$	−4.31888	+	4.98425i	−0.443108	+	0.511373i
$96$	−0.343396	−	0.220687i	−0.0350477	−	0.0225238i
$97$	0.252252	−	1.75445i	0.0256123	−	0.178137i	−0.973000	−	0.230806i	$-0.925864\pi$
$97$	0.252252	−	1.75445i	0.0256123	−	0.178137i	0.998612	+	0.0526689i	$0.0167728\pi$
$98$	0.501196	−	0.322099i	0.0506284	−	0.0325369i
$99$	1.21366	+	2.65755i	0.121978	+	0.267094i
$100$	−0.654861	−	0.755750i	−0.0654861	−	0.0755750i
$101$	0.747543	+	5.19928i	0.0743833	+	0.517347i	0.992615	+	0.121304i	$0.0387077\pi$
$101$	0.747543	+	5.19928i	0.0743833	+	0.517347i	−0.918232	+	0.396043i	$0.870383\pi$
$102$	−0.411509	+	0.901080i	−0.0407455	+	0.0892202i
$103$	9.33423	−	2.74078i	0.919729	−	0.270057i	0.212598	−	0.977140i	$-0.431807\pi$
$103$	9.33423	−	2.74078i	0.919729	−	0.270057i	0.707131	+	0.707083i	$0.249989\pi$
$104$	4.55547	−	1.33761i	0.446700	−	0.131163i
$105$	−0.429125	+	0.939652i	−0.0418783	+	0.0917007i
$106$	−1.22334	−	8.50848i	−0.118821	−	0.826417i
$107$	−6.72690	−	7.76326i	−0.650314	−	0.750503i	0.330849	−	0.943684i	$-0.392665\pi$
$107$	−6.72690	−	7.76326i	−0.650314	−	0.750503i	−0.981163	+	0.193181i	$0.938120\pi$
$108$	−0.989168	−	2.16598i	−0.0951828	−	0.208421i
$109$	3.83085	−	2.46194i	0.366929	−	0.235811i	−0.344163	−	0.938910i	$-0.611837\pi$
$109$	3.83085	−	2.46194i	0.366929	−	0.235811i	0.711092	+	0.703099i	$0.248201\pi$
$110$	0.146744	−	1.02063i	0.0139915	−	0.0973132i
$111$	3.98630	+	2.56184i	0.378363	+	0.243159i
$112$	−1.65723	+	1.91254i	−0.156593	+	0.180718i
$113$	−9.09687	−	2.67108i	−0.855761	−	0.251274i	−0.175713	−	0.984441i	$-0.556223\pi$
$113$	−9.09687	−	2.67108i	−0.855761	−	0.251274i	−0.680048	+	0.733167i	$0.738041\pi$
$114$	2.69209			0.252138
$115$	4.75971	+	0.587491i	0.443845	+	0.0547838i
$116$	−10.1167			−0.939309
$117$	12.9074	+	3.78994i	1.19329	+	0.350380i
$118$	−7.72141	+	8.91098i	−0.710814	+	0.820323i
$119$	5.16642	+	3.32026i	0.473605	+	0.304367i
$120$	−0.0580923	+	0.404041i	−0.00530307	+	0.0368837i
$121$	−8.35935	+	5.37223i	−0.759941	+	0.488384i
$122$	−0.913087	−	1.99938i	−0.0826670	−	0.181015i
$123$	1.75355	+	2.02371i	0.158112	+	0.182471i
$124$	−0.432462	−	3.00784i	−0.0388362	−	0.270112i
$125$	−0.415415	+	0.909632i	−0.0371558	+	0.0813600i
$126$	−6.87986	+	2.02011i	−0.612906	+	0.179966i
$127$	−0.670035	+	0.196740i	−0.0594560	+	0.0174579i	−0.311325	−	0.950303i	$-0.600773\pi$
$127$	−0.670035	+	0.196740i	−0.0594560	+	0.0174579i	0.251869	+	0.967761i	$0.418955\pi$
$128$	−0.415415	+	0.909632i	−0.0367178	+	0.0804009i
$129$	−0.0611493	−	0.425303i	−0.00538389	−	0.0374458i
$130$	−3.10914	−	3.58814i	−0.272690	−	0.314701i
$131$	7.21069	+	15.7892i	0.630001	+	1.37951i	0.908017	+	0.418933i	$0.137596\pi$
$131$	7.21069	+	15.7892i	0.630001	+	1.37951i	−0.278016	+	0.960576i	$0.589677\pi$
$132$	−0.354084	+	0.227556i	−0.0308191	+	0.0198062i
$133$	2.37523	−	16.5201i	0.205959	−	1.43247i
$134$	8.30985	+	5.34042i	0.717862	+	0.461342i
$135$	−1.55933	+	1.79956i	−0.134205	+	0.154881i
$136$	2.32847	+	0.683702i	0.199665	+	0.0586269i
$137$	4.41058			0.376822			0.188411	−	0.982090i	$-0.439666\pi$
$137$	4.41058			0.376822			0.188411	+	0.982090i	$0.439666\pi$
$138$	−1.09109	−	1.62538i	−0.0928795	−	0.138362i
$139$	−19.3073			−1.63762			−0.818810	−	0.574064i	$-0.805366\pi$
$139$	−19.3073			−1.63762			−0.818810	+	0.574064i	$0.805366\pi$
$140$	2.42815	+	0.712969i	0.205216	+	0.0602568i
$141$	−0.676989	+	0.781287i	−0.0570127	+	0.0657962i
$142$	2.84187	+	1.82636i	0.238485	+	0.153265i
$143$	0.696711	−	4.84573i	0.0582619	−	0.405221i
$144$	−2.38359	+	1.53184i	−0.198632	+	0.127653i
$145$	4.20262	+	9.20244i	0.349008	+	0.764221i
$146$	9.65908	+	11.1472i	0.799391	+	0.922547i
$147$	0.0346098	+	0.240716i	0.00285457	+	0.0198539i
$148$	4.82233	−	10.5594i	0.396393	−	0.867980i
$149$	20.0247	−	5.87979i	1.64049	−	0.481692i	0.674072	−	0.738665i	$-0.264544\pi$
$149$	20.0247	−	5.87979i	1.64049	−	0.481692i	0.966418	+	0.256974i	$0.0827254\pi$
$150$	0.391661	−	0.115002i	0.0319790	−	0.00938987i
$151$	−1.79087	+	3.92145i	−0.145739	+	0.319123i	−0.968397	−	0.249412i	$-0.919763\pi$
$151$	−1.79087	+	3.92145i	−0.145739	+	0.319123i	0.822659	+	0.568536i	$0.192490\pi$
$152$	−0.938582	−	6.52798i	−0.0761290	−	0.529489i
$153$	4.50280	+	5.19651i	0.364030	+	0.420113i
$154$	1.08399	+	2.37362i	0.0873507	+	0.191271i
$155$	−2.55638	+	1.64288i	−0.205333	+	0.131960i
$156$	−0.275810	+	1.91830i	−0.0220824	+	0.153587i
$157$	0.506429	+	0.325462i	0.0404174	+	0.0259747i	0.560694	−	0.828023i	$-0.310535\pi$
$157$	0.506429	+	0.325462i	0.0404174	+	0.0259747i	−0.520276	+	0.853998i	$0.674171\pi$
$158$	−2.82949	+	3.26541i	−0.225102	+	0.259782i
$159$	3.36671	+	0.988554i	0.266997	+	0.0783974i
$160$	1.00000			0.0790569
$161$	−10.9369	+	5.26140i	−0.861945	+	0.414657i
$162$	−7.52815			−0.591467
$163$	16.6314	+	4.88343i	1.30267	+	0.382500i	0.858211	−	0.513297i	$-0.171576\pi$
$163$	16.6314	+	4.88343i	1.30267	+	0.382500i	0.444463	+	0.895797i	$0.353394\pi$
$164$	4.29586	−	4.95769i	0.335451	−	0.387131i
$165$	0.354084	+	0.227556i	0.0275654	+	0.0177152i
$166$	−0.515400	+	3.58468i	−0.0400028	+	0.278225i
$167$	−10.9546	+	7.04011i	−0.847694	+	0.544780i	−0.890855	−	0.454288i	$-0.849894\pi$
$167$	−10.9546	+	7.04011i	−0.847694	+	0.544780i	0.0431609	+	0.999068i	$0.486257\pi$
$168$	−0.429125	−	0.939652i	−0.0331077	−	0.0724957i
$169$	−6.24834	−	7.21097i	−0.480642	−	0.554690i
$170$	−0.345366	−	2.40207i	−0.0264884	−	0.184231i
$171$	7.76262	−	16.9978i	0.593623	−	1.29985i
$172$	−1.00998	+	0.296558i	−0.0770106	+	0.0226124i
$173$	5.92954	−	1.74107i	0.450814	−	0.132371i	−0.0484407	−	0.998826i	$-0.515425\pi$
$173$	5.92954	−	1.74107i	0.450814	−	0.132371i	0.499255	+	0.866455i	$0.333607\pi$
$174$	1.71549	−	3.75640i	0.130051	−	0.284772i
$175$	−0.360150	−	2.50490i	−0.0272248	−	0.189353i
$176$	0.675243	+	0.779272i	0.0508984	+	0.0587399i
$177$	−1.99939	−	4.37806i	−0.150284	−	0.329075i
$178$	−4.90742	+	3.15381i	−0.367827	+	0.236388i
$179$	0.440239	−	3.06193i	0.0329050	−	0.228859i	−0.966732	−	0.255790i	$-0.917664\pi$
$179$	0.440239	−	3.06193i	0.0329050	−	0.228859i	0.999637	+	0.0269310i	$0.00857343\pi$
$180$	2.38359	+	1.53184i	0.177662	+	0.114177i
$181$	11.0450	−	12.7466i	0.820969	−	0.947449i	−0.178364	−	0.983965i	$-0.557080\pi$
$181$	11.0450	−	12.7466i	0.820969	−	0.947449i	0.999333	+	0.0365154i	$0.0116258\pi$
$182$	11.5283	+	3.38502i	0.854537	+	0.250915i
$183$	0.897218			0.0663242
$184$	−3.56094	+	3.21243i	−0.262516	+	0.236823i
$185$	−11.6085			−0.853472
$186$	1.19017	+	0.349464i	0.0872672	+	0.0256240i
$187$	1.63866	−	1.89112i	0.119831	−	0.138292i
$188$	2.13055	+	1.36922i	0.155386	+	0.0998606i
$189$	0.857574	−	5.96456i	0.0623793	−	0.433858i
$190$	−5.54816	+	3.56559i	−0.402506	+	0.258675i
$191$	4.22197	+	9.24482i	0.305491	+	0.668932i	0.998655	−	0.0518482i	$-0.0165112\pi$
$191$	4.22197	+	9.24482i	0.305491	+	0.668932i	−0.693164	+	0.720780i	$0.743784\pi$
$192$	−0.267311	−	0.308493i	−0.0192915	−	0.0222636i
$193$	0.178942	+	1.24457i	0.0128805	+	0.0895858i	0.995248	−	0.0973761i	$-0.0310450\pi$
$193$	0.178942	+	1.24457i	0.0128805	+	0.0895858i	−0.982367	+	0.186962i	$0.940136\pi$
$194$	0.736319	−	1.61231i	0.0528646	−	0.115757i
$195$	1.85952	−	0.546005i	0.133163	−	0.0391002i
$196$	0.571640	−	0.167849i	0.0408314	−	0.0119892i
$197$	−8.86137	+	19.4037i	−0.631346	+	1.38246i	0.275626	+	0.961265i	$0.411115\pi$
$197$	−8.86137	+	19.4037i	−0.631346	+	1.38246i	−0.906972	+	0.421190i	$0.861612\pi$
$198$	0.415782	+	2.89183i	0.0295484	+	0.205513i
$199$	−11.7526	−	13.5632i	−0.833119	−	0.961470i	0.166580	−	0.986028i	$-0.446728\pi$
$199$	−11.7526	−	13.5632i	−0.833119	−	0.961470i	−0.999698	+	0.0245576i	$0.992182\pi$
$200$	−0.415415	−	0.909632i	−0.0293743	−	0.0643207i
$201$	−3.39204	+	2.17993i	−0.239256	+	0.153761i
$202$	−0.747543	+	5.19928i	−0.0525969	+	0.365820i
$203$	−21.5376	−	13.8414i	−1.51164	−	0.971475i
$204$	−0.648704	+	0.748644i	−0.0454184	+	0.0524156i
$205$	−6.29424	−	1.84816i	−0.439609	−	0.129081i
$206$	9.72829			0.677802
$207$	−13.4087	+	2.20231i	−0.931972	+	0.153071i
$208$	4.74779			0.329200
$209$	−6.52492	−	1.91589i	−0.451338	−	0.132525i
$210$	−0.676473	+	0.780691i	−0.0466811	+	0.0538728i
$211$	−9.38372	−	6.03055i	−0.646002	−	0.415160i	0.176201	−	0.984354i	$-0.443619\pi$
$211$	−9.38372	−	6.03055i	−0.646002	−	0.415160i	−0.822203	+	0.569194i	$0.807255\pi$
$212$	1.22334	−	8.50848i	0.0840190	−	0.584365i
$213$	−1.16004	+	0.745512i	−0.0794846	+	0.0510816i
$214$	−4.26725	−	9.34398i	−0.291704	−	0.638742i
$215$	0.689322	+	0.795520i	0.0470114	+	0.0542540i
$216$	−0.338874	−	2.35692i	−0.0230575	−	0.160368i
$217$	3.19458	−	6.99515i	0.216862	−	0.474862i
$218$	4.36928	−	1.28294i	0.295925	−	0.0868914i
$219$	−5.77693	+	1.69626i	−0.390369	+	0.114623i
$220$	0.428345	−	0.937945i	0.0288790	−	0.0632362i
$221$	−1.63972	−	11.4045i	−0.110300	−	0.767152i
$222$	3.10307	+	3.58114i	0.208265	+	0.240350i
$223$	−8.41536	−	18.4271i	−0.563534	−	1.23397i	−0.950169	−	0.311735i	$-0.899090\pi$
$223$	−8.41536	−	18.4271i	−0.563534	−	1.23397i	0.386635	−	0.922233i	$-0.373637\pi$
$224$	−2.12892	+	1.36818i	−0.142245	+	0.0914152i
$225$	0.403232	−	2.80454i	0.0268821	−	0.186969i
$226$	−7.97585	−	5.12577i	−0.530546	−	0.340961i
$227$	−13.1297	+	15.1524i	−0.871446	+	1.00570i	0.128456	+	0.991715i	$0.458998\pi$
$227$	−13.1297	+	15.1524i	−0.871446	+	1.00570i	−0.999902	+	0.0139869i	$0.995548\pi$
$228$	2.58304	+	0.758450i	0.171066	+	0.0502296i
$229$	10.9126			0.721123			0.360561	−	0.932735i	$-0.382585\pi$
$229$	10.9126			0.721123			0.360561	+	0.932735i	$0.382585\pi$
$230$	4.40139	+	1.90466i	0.290219	+	0.125589i
$231$	−1.06516			−0.0700821
$232$	−9.70687	−	2.85019i	−0.637287	−	0.187124i
$233$	−6.05991	+	6.99351i	−0.396998	+	0.458160i	−0.918693	−	0.394972i	$-0.870754\pi$
$233$	−6.05991	+	6.99351i	−0.396998	+	0.458160i	0.521695	+	0.853132i	$0.325300\pi$
$234$	11.3168	+	7.27285i	0.739800	+	0.475441i
$235$	0.360425	−	2.50681i	0.0235115	−	0.163526i
$236$	−9.91916	+	6.37465i	−0.645682	+	0.414955i
$237$	−0.732672	−	1.60433i	−0.0475922	−	0.104212i
$238$	4.02172	+	4.64131i	0.260689	+	0.300852i
$239$	0.736356	+	5.12147i	0.0476309	+	0.331280i	0.999679	+	0.0253322i	$0.00806434\pi$
$239$	0.736356	+	5.12147i	0.0476309	+	0.331280i	−0.952048	+	0.305948i	$0.901027\pi$
$240$	−0.169570	+	0.371308i	−0.0109457	+	0.0239678i
$241$	4.84965	−	1.42399i	0.312393	−	0.0917270i	−0.121778	−	0.992557i	$-0.538859\pi$
$241$	4.84965	−	1.42399i	0.312393	−	0.0917270i	0.434171	+	0.900830i	$0.357041\pi$
$242$	−9.53427	+	2.79951i	−0.612886	+	0.179960i
$243$	4.24406	−	9.29319i	0.272256	−	0.596158i
$244$	−0.312810	−	2.17564i	−0.0200256	−	0.139281i
$245$	−0.390148	−	0.450255i	−0.0249256	−	0.0287657i
$246$	1.11238	+	2.43576i	0.0709225	+	0.155299i
$247$	−26.3415	+	16.9286i	−1.67607	+	1.07714i
$248$	0.432462	−	3.00784i	0.0274614	−	0.190998i
$249$	−1.24362	−	0.799228i	−0.0788114	−	0.0506490i
$250$	−0.654861	+	0.755750i	−0.0414170	+	0.0477978i
$251$	−1.77009	−	0.519746i	−0.111727	−	0.0328061i	0.225391	−	0.974268i	$-0.427634\pi$
$251$	−1.77009	−	0.519746i	−0.111727	−	0.0328061i	−0.337118	+	0.941462i	$0.609452\pi$
$252$	−7.17031			−0.451687
$253$	1.48776	+	4.71599i	0.0935350	+	0.296492i
$254$	−0.698322			−0.0438166
$255$	0.950472	+	0.279084i	0.0595209	+	0.0174769i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	8.01581	+	5.15145i	0.500012	+	0.321339i	0.766221	−	0.642577i	$-0.222135\pi$
$257$	8.01581	+	5.15145i	0.500012	+	0.321339i	−0.266209	+	0.963915i	$0.585771\pi$
$258$	0.0611493	−	0.425303i	0.00380699	−	0.0264782i
$259$	24.7136	−	15.8824i	1.53563	−	0.986887i
$260$	−1.97230	−	4.31874i	−0.122317	−	0.267837i
$261$	−18.7711	−	21.6631i	−1.16190	−	1.34091i
$262$	2.47027	+	17.1811i	0.152614	+	1.06145i
$263$	6.11013	−	13.3793i	0.376767	−	0.825005i	−0.622340	−	0.782747i	$-0.713818\pi$
$263$	6.11013	−	13.3793i	0.376767	−	0.825005i	0.999107	−	0.0422575i	$-0.0134550\pi$
$264$	−0.403851	+	0.118581i	−0.0248553	+	0.00729818i
$265$	−8.24778	+	2.42177i	−0.506657	+	0.148768i
$266$	6.93326	−	15.1817i	0.425106	−	0.930851i
$267$	−0.338879	−	2.35696i	−0.0207391	−	0.144243i
$268$	6.46868	+	7.46525i	0.395137	+	0.456013i
$269$	−4.00237	−	8.76396i	−0.244029	−	0.534348i	0.747496	−	0.664266i	$-0.231256\pi$
$269$	−4.00237	−	8.76396i	−0.244029	−	0.534348i	−0.991525	+	0.129918i	$0.958529\pi$
$270$	−2.00316	+	1.28735i	−0.121908	+	0.0783457i
$271$	3.79840	−	26.4184i	0.230736	−	1.60481i	−0.464197	−	0.885732i	$-0.653657\pi$
$271$	3.79840	−	26.4184i	0.230736	−	1.60481i	0.694933	−	0.719074i	$-0.255434\pi$
$272$	2.04153	+	1.31201i	0.123786	+	0.0795525i
$273$	−3.21175	+	3.70656i	−0.194384	+	0.224331i
$274$	4.23192	+	1.24261i	0.255660	+	0.0750685i
$275$	−1.03113			−0.0621792
$276$	−0.588967	−	1.86694i	−0.0354516	−	0.112376i
$277$	−1.68097			−0.101000			−0.0505000	−	0.998724i	$-0.516081\pi$
$277$	−1.68097			−0.101000			−0.0505000	+	0.998724i	$0.516081\pi$
$278$	−18.5252	−	5.43949i	−1.11107	−	0.326239i
$279$	5.63834	−	6.50699i	0.337558	−	0.389563i
$280$	2.12892	+	1.36818i	0.127228	+	0.0817642i
$281$	−0.998755	+	6.94649i	−0.0595807	+	0.414393i	0.938102	+	0.346358i	$0.112582\pi$
$281$	−0.998755	+	6.94649i	−0.0595807	+	0.414393i	−0.997683	+	0.0680346i	$0.978327\pi$
$282$	−0.869680	+	0.558909i	−0.0517887	+	0.0332826i
$283$	9.62071	+	21.0664i	0.571892	+	1.25227i	0.945784	+	0.324796i	$0.105296\pi$
$283$	9.62071	+	21.0664i	0.571892	+	1.25227i	−0.373892	+	0.927472i	$0.621977\pi$
$284$	2.21221	+	2.55303i	0.131271	+	0.151494i
$285$	−0.383125	−	2.66469i	−0.0226944	−	0.157843i
$286$	2.03369	−	4.45316i	0.120255	−	0.263321i
$287$	15.9286	−	4.67705i	0.940234	−	0.276078i
$288$	−2.71860	+	0.798254i	−0.160195	+	0.0470376i
$289$	−4.61558	+	10.1067i	−0.271505	+	0.594512i
$290$	1.43975	+	10.0137i	0.0845451	+	0.588024i
$291$	0.473806	+	0.546801i	0.0277750	+	0.0320541i
$292$	6.12730	+	13.4169i	0.358573	+	0.785166i
$293$	−14.8423	+	9.53857i	−0.867096	+	0.557249i	−0.896863	−	0.442308i	$-0.854160\pi$
$293$	−14.8423	+	9.53857i	−0.867096	+	0.557249i	0.0297668	+	0.999557i	$0.490524\pi$
$294$	−0.0346098	+	0.240716i	−0.00201848	+	0.0140389i
$295$	9.91916	+	6.37465i	0.577516	+	0.371147i
$296$	7.60193	−	8.77310i	0.441853	−	0.509926i
$297$	−2.35582	−	0.691730i	−0.136698	−	0.0401382i
$298$	20.8701			1.20897
$299$	20.8969	+	9.04291i	1.20850	+	0.522965i
$300$	0.408195			0.0235672
$301$	−2.55593	−	0.750488i	−0.147321	−	0.0432574i
$302$	−2.82313	+	3.25806i	−0.162453	+	0.187480i
$303$	−1.80377	−	1.15921i	−0.103624	−	0.0665950i
$304$	0.938582	−	6.52798i	0.0538314	−	0.374405i
$305$	−1.84908	+	1.18833i	−0.105878	+	0.0680438i
$306$	2.85638	+	6.25460i	0.163288	+	0.357552i
$307$	−9.19148	−	10.6075i	−0.524585	−	0.605404i	0.430188	−	0.902740i	$-0.358447\pi$
$307$	−9.19148	−	10.6075i	−0.524585	−	0.605404i	−0.954773	+	0.297336i	$0.903902\pi$
$308$	0.371360	+	2.58286i	0.0211602	+	0.147172i
$309$	−1.64963	+	3.61219i	−0.0938442	+	0.205490i
$310$	−2.91568	+	0.856120i	−0.165599	+	0.0486244i
$311$	26.1540	−	7.67951i	1.48306	−	0.435465i	0.562739	−	0.826635i	$-0.309748\pi$
$311$	26.1540	−	7.67951i	1.48306	−	0.435465i	0.920319	+	0.391169i	$0.127929\pi$
$312$	−0.805085	+	1.76289i	−0.0455789	+	0.0998039i
$313$	2.79580	+	19.4452i	0.158028	+	1.09911i	0.902262	+	0.431189i	$0.141906\pi$
$313$	2.79580	+	19.4452i	0.158028	+	1.09911i	−0.744234	+	0.667919i	$0.767185\pi$
$314$	0.394221	+	0.454956i	0.0222472	+	0.0256746i
$315$	2.97865	+	6.52234i	0.167828	+	0.367492i
$316$	−3.63485	+	2.33598i	−0.204476	+	0.131409i
$317$	−1.77153	+	12.3213i	−0.0994991	+	0.692031i	0.877623	+	0.479352i	$0.159128\pi$
$317$	−1.77153	+	12.3213i	−0.0994991	+	0.692031i	−0.977122	+	0.212680i	$0.931781\pi$
$318$	2.95182	+	1.89702i	0.165530	+	0.106380i
$319$	−6.83121	+	7.88364i	−0.382475	+	0.441399i
$320$	0.959493	+	0.281733i	0.0536373	+	0.0157493i
$321$	4.19309			0.234036
$322$	−11.9761	+	1.96701i	−0.667405	+	0.109617i
$323$	−16.0048			−0.890533
$324$	−7.22321	−	2.12093i	−0.401289	−	0.117829i
$325$	−3.10914	+	3.58814i	−0.172464	+	0.199034i
$326$	14.5819	+	9.37123i	0.807618	+	0.519024i
$327$	−0.264537	+	1.83989i	−0.0146289	+	0.101746i
$328$	5.51859	−	3.54659i	0.304713	−	0.195827i
$329$	2.66244	+	5.82993i	0.146785	+	0.321415i
$330$	0.275631	+	0.318095i	0.0151730	+	0.0175106i
$331$	3.49835	+	24.3316i	0.192287	+	1.33738i	0.825937	+	0.563763i	$0.190647\pi$
$331$	3.49835	+	24.3316i	0.192287	+	1.33738i	−0.633650	+	0.773620i	$0.718444\pi$
$332$	−1.50444	+	3.29427i	−0.0825671	+	0.180797i
$333$	31.5588	−	9.26651i	1.72941	−	0.507802i
$334$	−12.4943	+	3.66866i	−0.683658	+	0.200740i
$335$	4.10345	−	8.98529i	0.224195	−	0.490919i
$336$	−0.147012	−	1.02249i	−0.00802014	−	0.0557813i
$337$	−6.18993	−	7.14356i	−0.337187	−	0.389135i	0.561681	−	0.827354i	$-0.310155\pi$
$337$	−6.18993	−	7.14356i	−0.337187	−	0.389135i	−0.898868	+	0.438219i	$0.855609\pi$
$338$	−3.96367	−	8.67924i	−0.215595	−	0.472088i
$339$	3.25570	−	2.09231i	0.176826	−	0.113639i
$340$	0.345366	−	2.40207i	0.0187301	−	0.130271i
$341$	−2.63594	−	1.69402i	−0.142744	−	0.0917362i
$342$	12.2370	−	14.1223i	0.661702	−	0.763644i
$343$	18.4437	+	5.41555i	0.995864	+	0.292412i
$344$	−1.05262			−0.0567537
$345$	−1.45356	+	1.31130i	−0.0782571	+	0.0705979i
$346$	6.17987			0.332232
$347$	18.1903	+	5.34116i	0.976507	+	0.286728i	0.730782	−	0.682611i	$-0.239156\pi$
$347$	18.1903	+	5.34116i	0.976507	+	0.286728i	0.245725	+	0.969340i	$0.420974\pi$
$348$	2.70430	−	3.12093i	0.144966	−	0.167299i
$349$	11.4867	+	7.38205i	0.614869	+	0.395152i	0.810680	−	0.585489i	$-0.199098\pi$
$349$	11.4867	+	7.38205i	0.614869	+	0.395152i	−0.195811	+	0.980642i	$0.562734\pi$
$350$	0.360150	−	2.50490i	0.0192508	−	0.133892i
$351$	−9.51056	+	6.11207i	−0.507636	+	0.326238i
$352$	0.428345	+	0.937945i	0.0228309	+	0.0499926i
$353$	6.67824	+	7.70710i	0.355447	+	0.410208i	0.905109	−	0.425179i	$-0.139789\pi$
$353$	6.67824	+	7.70710i	0.355447	+	0.410208i	−0.549662	+	0.835387i	$0.685244\pi$
$354$	−0.684961	−	4.76401i	−0.0364053	−	0.253204i
$355$	1.40333	−	3.07286i	0.0744810	−	0.163091i
$356$	−5.59717	+	1.64348i	−0.296649	+	0.0871041i
$357$	−2.40532	+	0.706265i	−0.127303	+	0.0373795i
$358$	1.28505	−	2.81387i	0.0679171	−	0.148718i
$359$	−4.75234	−	33.0533i	−0.250819	−	1.74449i	−0.593319	−	0.804968i	$-0.702183\pi$
$359$	−4.75234	−	33.0533i	−0.250819	−	1.74449i	0.342500	−	0.939518i	$-0.388726\pi$
$360$	1.85547	+	2.14132i	0.0977917	+	0.112858i
$361$	10.1758	+	22.2819i	0.535568	+	1.17273i
$362$	14.1888	−	9.11856i	0.745744	−	0.479261i
$363$	0.577250	−	4.01486i	0.0302978	−	0.210726i
$364$	10.1077	+	6.49581i	0.529786	+	0.340473i
$365$	9.65908	−	11.1472i	0.505580	−	0.583470i
$366$	0.860874	+	0.252775i	0.0449986	+	0.0132128i
$367$	−30.7937			−1.60742			−0.803710	−	0.595021i	$-0.797144\pi$
$367$	−30.7937			−1.60742			−0.803710	+	0.595021i	$0.797144\pi$
$368$	−4.32175	+	2.07907i	−0.225287	+	0.108379i
$369$	18.5869			0.967593
$370$	−11.1382	−	3.27048i	−0.579050	−	0.170024i
$371$	14.2455	−	16.4402i	0.739589	−	0.853532i
$372$	1.04350	+	0.670617i	0.0541030	+	0.0347699i
$373$	0.954017	−	6.63534i	0.0493972	−	0.343565i	−0.950103	−	0.311938i	$-0.899022\pi$
$373$	0.954017	−	6.63534i	0.0493972	−	0.343565i	0.999500	−	0.0316271i	$-0.0100689\pi$
$374$	2.10508	−	1.35285i	0.108851	−	0.0699542i
$375$	−0.169570	−	0.371308i	−0.00875658	−	0.0191742i
$376$	1.65849	+	1.91400i	0.0855302	+	0.0987071i
$377$	6.83564	+	47.5429i	0.352053	+	2.44858i
$378$	2.50325	−	5.48135i	0.128753	−	0.281930i
$379$	−34.9309	+	10.2566i	−1.79428	+	0.526848i	−0.997045	−	0.0768204i	$-0.975523\pi$
$379$	−34.9309	+	10.2566i	−1.79428	+	0.526848i	−0.797235	+	0.603669i	$0.793705\pi$
$380$	−6.32796	+	1.85806i	−0.324618	+	0.0953163i
$381$	0.118415	−	0.259292i	0.00606657	−	0.0132839i
$382$	1.44638	+	10.0598i	0.0740033	+	0.514704i
$383$	−10.9586	−	12.6469i	−0.559959	−	0.646227i	0.403215	−	0.915105i	$-0.367893\pi$
$383$	−10.9586	−	12.6469i	−0.559959	−	0.646227i	−0.963174	+	0.268878i	$0.913347\pi$
$384$	−0.169570	−	0.371308i	−0.00865336	−	0.0189482i
$385$	2.19519	−	1.41076i	0.111877	−	0.0718991i
$386$	−0.178942	+	1.24457i	−0.00910789	+	0.0633467i
$387$	−2.50902	−	1.61245i	−0.127541	−	0.0819654i
$388$	1.16073	−	1.33956i	0.0589273	−	0.0680058i
$389$	36.1575	+	10.6168i	1.83326	+	0.538293i	0.999896	−	0.0144348i	$-0.00459489\pi$
$389$	36.1575	+	10.6168i	1.83326	+	0.538293i	0.833362	+	0.552728i	$0.186413\pi$
$390$	1.93802			0.0981357
$391$	6.48665	+	9.66311i	0.328044	+	0.488685i
$392$	0.595773			0.0300911
$393$	−6.79836	−	1.99618i	−0.342932	−	0.100694i
$394$	−13.9691	+	16.1212i	−0.703752	+	0.812173i
$395$	3.63485	+	2.33598i	0.182889	+	0.117536i
$396$	−0.415782	+	2.89183i	−0.0208938	+	0.145320i
$397$	13.2434	−	8.51103i	0.664668	−	0.427156i	−0.164332	−	0.986405i	$-0.552547\pi$
$397$	13.2434	−	8.51103i	0.664668	−	0.427156i	0.829000	+	0.559249i	$0.188910\pi$
$398$	−7.45533	−	16.3249i	−0.373702	−	0.818293i
$399$	4.46141	+	5.14874i	0.223350	+	0.257760i
$400$	−0.142315	−	0.989821i	−0.00711574	−	0.0494911i
$401$	−12.2142	+	26.7453i	−0.609947	+	1.33560i	0.312663	+	0.949864i	$0.398779\pi$
$401$	−12.2142	+	26.7453i	−0.609947	+	1.33560i	−0.922610	+	0.385733i	$0.873948\pi$
$402$	−3.86880	+	1.13598i	−0.192958	+	0.0566576i
$403$	−13.8430	+	4.06468i	−0.689570	+	0.202476i
$404$	−2.18207	+	4.77806i	−0.108562	+	0.237717i
$405$	1.07137	+	7.45153i	0.0532367	+	0.370269i
$406$	−16.7656	−	19.3486i	−0.832064	−	0.960253i
$407$	−4.97243	−	10.8881i	−0.246474	−	0.539703i
$408$	−0.833344	+	0.535558i	−0.0412567	+	0.0265141i
$409$	3.42196	−	23.8003i	0.169205	−	1.17685i	−0.711327	−	0.702861i	$-0.751905\pi$
$409$	3.42196	−	23.8003i	0.169205	−	1.17685i	0.880532	−	0.473987i	$-0.157185\pi$
$410$	−5.51859	−	3.54659i	−0.272544	−	0.175153i
$411$	−1.17900	+	1.36064i	−0.0581557	+	0.0671152i
$412$	9.33423	+	2.74078i	0.459864	+	0.135028i
$413$	−29.8388			−1.46827
$414$	−13.4861	−	1.66458i	−0.662803	−	0.0818097i
$415$	3.62154			0.177775
$416$	4.55547	+	1.33761i	0.223350	+	0.0655815i
$417$	5.16105	−	5.95617i	0.252738	−	0.291675i
$418$	−5.72085	−	3.67656i	−0.279816	−	0.179827i
$419$	0.582282	−	4.04986i	0.0284463	−	0.197849i	−0.970643	−	0.240527i	$-0.922680\pi$
$419$	0.582282	−	4.04986i	0.0284463	−	0.197849i	0.999089	+	0.0426781i	$0.0135890\pi$
$420$	−0.869017	+	0.558483i	−0.0424037	+	0.0272512i
$421$	5.13166	+	11.2368i	0.250102	+	0.547646i	0.992490	−	0.122323i	$-0.0390344\pi$
$421$	5.13166	+	11.2368i	0.250102	+	0.547646i	−0.742389	+	0.669969i	$0.766307\pi$
$422$	−7.30461	−	8.42997i	−0.355583	−	0.410365i
$423$	1.02122	+	7.10273i	0.0496534	+	0.345347i
$424$	3.57090	−	7.81918i	0.173418	−	0.379733i
$425$	−2.32847	+	0.683702i	−0.112948	+	0.0331644i
$426$	−1.32308	+	0.388493i	−0.0641036	+	0.0188225i
$427$	2.31071	−	5.05975i	0.111823	−	0.244858i
$428$	−1.46190	−	10.1677i	−0.0706634	−	0.491475i
$429$	1.30864	+	1.51025i	0.0631817	+	0.0729155i
$430$	0.437276	+	0.957500i	0.0210873	+	0.0461748i
$431$	1.61269	−	1.03641i	0.0776806	−	0.0499223i	−0.501224	−	0.865318i	$-0.667117\pi$
$431$	1.61269	−	1.03641i	0.0776806	−	0.0499223i	0.578905	+	0.815395i	$0.303480\pi$
$432$	0.338874	−	2.35692i	0.0163041	−	0.113397i
$433$	9.19095	+	5.90666i	0.441689	+	0.283856i	0.742523	−	0.669820i	$-0.233629\pi$
$433$	9.19095	+	5.90666i	0.441689	+	0.283856i	−0.300835	+	0.953676i	$0.597265\pi$
$434$	5.03594	−	5.81178i	0.241733	−	0.278974i
$435$	−3.96230	−	1.16344i	−0.189978	−	0.0557825i
$436$	4.55374			0.218084
$437$	16.5646	−	26.9445i	0.792394	−	1.28893i
$438$	−6.02081			−0.287686
$439$	13.0839	+	3.84179i	0.624462	+	0.183358i	0.578629	−	0.815591i	$-0.303588\pi$
$439$	13.0839	+	3.84179i	0.624462	+	0.183358i	0.0458323	+	0.998949i	$0.485406\pi$
$440$	0.675243	−	0.779272i	0.0321910	−	0.0371504i
$441$	1.42008	+	0.912628i	0.0676227	+	0.0434585i
$442$	1.63972	−	11.4045i	0.0779937	−	0.542458i
$443$	−1.63213	+	1.04890i	−0.0775446	+	0.0498349i	−0.578839	−	0.815442i	$-0.696494\pi$
$443$	−1.63213	+	1.04890i	−0.0775446	+	0.0498349i	0.501294	+	0.865277i	$0.332858\pi$
$444$	1.96845	+	4.31031i	0.0934187	+	0.204558i
$445$	3.82011	+	4.40864i	0.181090	+	0.208990i
$446$	−2.88297	−	20.0515i	−0.136513	−	0.949467i
$447$	−3.53896	+	7.74924i	−0.167387	+	0.366526i
$448$	−2.42815	+	0.712969i	−0.114719	+	0.0336846i
$449$	5.00104	−	1.46844i	0.236014	−	0.0692999i	−0.161587	−	0.986858i	$-0.551661\pi$
$449$	5.00104	−	1.46844i	0.236014	−	0.0692999i	0.397600	+	0.917559i	$0.369843\pi$
$450$	1.17703	−	2.57733i	0.0554856	−	0.121496i
$451$	−0.962638	−	6.69530i	−0.0453289	−	0.315269i
$452$	−6.20868	−	7.16519i	−0.292032	−	0.337022i
$453$	−0.731024	−	1.60072i	−0.0343465	−	0.0752084i
$454$	−16.8667	+	10.8396i	−0.791595	+	0.508728i
$455$	1.70992	−	11.8927i	0.0801621	−	0.557540i
$456$	2.26473	+	1.45546i	0.106056	+	0.0681579i
$457$	−5.50734	+	6.35581i	−0.257622	+	0.297312i	−0.869796	−	0.493411i	$-0.835750\pi$
$457$	−5.50734	+	6.35581i	−0.257622	+	0.297312i	0.612174	+	0.790723i	$0.290295\pi$
$458$	10.4705	+	3.07443i	0.489256	+	0.143658i
$459$	−5.77853			−0.269719
$460$	3.68650	+	3.06752i	0.171884	+	0.143024i
$461$	−35.9115			−1.67257			−0.836283	−	0.548297i	$-0.815276\pi$
$461$	−35.9115			−1.67257			−0.836283	+	0.548297i	$0.815276\pi$
$462$	−1.02201	−	0.300089i	−0.0475482	−	0.0139614i
$463$	−2.26820	+	2.61764i	−0.105412	+	0.121652i	−0.806004	−	0.591910i	$-0.798374\pi$
$463$	−2.26820	+	2.61764i	−0.105412	+	0.121652i	0.700592	+	0.713562i	$0.252919\pi$
$464$	−8.51068	−	5.46948i	−0.395099	−	0.253914i
$465$	0.176529	−	1.22779i	0.00818634	−	0.0569372i
$466$	−7.78474	+	5.00295i	−0.360621	+	0.231757i
$467$	−9.84617	−	21.5601i	−0.455626	−	0.997683i	−0.988463	−	0.151464i	$-0.951601\pi$
$467$	−9.84617	−	21.5601i	−0.455626	−	0.997683i	0.532836	−	0.846218i	$-0.321126\pi$
$468$	8.80936	+	10.1665i	0.407213	+	0.469949i
$469$	3.55754	+	24.7432i	0.164272	+	1.14254i
$470$	1.05207	−	2.30372i	0.0485286	−	0.106263i
$471$	−0.235777	+	0.0692303i	−0.0108640	+	0.00318997i
$472$	−11.3133	+	3.32189i	−0.520737	+	0.152902i
$473$	−0.450886	+	0.987302i	−0.0207318	+	0.0453962i
$474$	−0.251002	−	1.74576i	−0.0115289	−	0.0801854i
$475$	4.31888	+	4.98425i	0.198164	+	0.228693i
$476$	2.55120	+	5.58636i	0.116934	+	0.256050i
$477$	20.4893	−	13.1677i	0.938139	−	0.602905i
$478$	−0.736356	+	5.12147i	−0.0336801	+	0.234251i
$479$	−9.95638	−	6.39857i	−0.454918	−	0.292358i	0.293045	−	0.956099i	$-0.405332\pi$
$479$	−9.95638	−	6.39857i	−0.454918	−	0.292358i	−0.747963	+	0.663740i	$0.768968\pi$
$480$	−0.267311	+	0.308493i	−0.0122010	+	0.0140807i
$481$	−52.8820	−	15.5276i	−2.41121	−	0.707996i
$482$	5.05439			0.230221
$483$	1.30044	−	4.78038i	0.0591718	−	0.217515i
$484$	−9.93678			−0.451672
$485$	−1.70069	−	0.499368i	−0.0772244	−	0.0226751i
$486$	6.69034	−	7.72106i	0.303480	−	0.350234i
$487$	22.1370	+	14.2266i	1.00312	+	0.644667i	0.935604	−	0.353051i	$-0.114856\pi$
$487$	22.1370	+	14.2266i	1.00312	+	0.644667i	0.0675178	+	0.997718i	$0.478492\pi$
$488$	0.312810	−	2.17564i	0.0141602	−	0.0984865i
$489$	−5.95227	+	3.82529i	−0.269171	+	0.172986i
$490$	−0.247493	−	0.541934i	−0.0111806	−	0.0244821i
$491$	−15.0887	−	17.4133i	−0.680943	−	0.785850i	0.305104	−	0.952319i	$-0.401309\pi$
$491$	−15.0887	−	17.4133i	−0.680943	−	0.785850i	−0.986047	+	0.166469i	$0.946763\pi$
$492$	0.381083	+	2.65049i	0.0171806	+	0.119493i
$493$	−10.1988	+	22.3323i	−0.459331	+	1.00579i
$494$	−30.0438	+	8.82166i	−1.35173	+	0.396905i
$495$	2.80322	−	0.823100i	0.125995	−	0.0369956i
$496$	1.26235	−	2.76416i	0.0566812	−	0.124115i
$497$	1.21664	+	8.46190i	0.0545736	+	0.379568i
$498$	−0.968079	−	1.11722i	−0.0433807	−	0.0500640i
$499$	−15.1736	−	33.2256i	−0.679265	−	1.48738i	−0.863420	−	0.504485i	$-0.831682\pi$
$499$	−15.1736	−	33.2256i	−0.679265	−	1.48738i	0.184155	−	0.982897i	$-0.441045\pi$
$500$	−0.841254	+	0.540641i	−0.0376220	+	0.0241782i
$501$	0.756465	−	5.26133i	0.0337963	−	0.235059i
$502$	−1.55196	−	0.997385i	−0.0692674	−	0.0445155i
$503$	−1.18260	+	1.36480i	−0.0527296	+	0.0608532i	−0.781502	−	0.623903i	$-0.785546\pi$
$503$	−1.18260	+	1.36480i	−0.0527296	+	0.0608532i	0.728772	+	0.684756i	$0.240091\pi$
$504$	−6.87986	−	2.02011i	−0.306453	−	0.0899828i
$505$	5.25274			0.233744
$506$	0.0988507	+	4.94411i	0.00439445	+	0.219793i
$507$	3.89479			0.172974
$508$	−0.670035	−	0.196740i	−0.0297280	−	0.00872893i
$509$	−2.56500	+	2.96017i	−0.113692	+	0.131207i	−0.809743	−	0.586785i	$-0.800393\pi$
$509$	−2.56500	+	2.96017i	−0.113692	+	0.131207i	0.696051	+	0.717992i	$0.254939\pi$
$510$	0.833344	+	0.535558i	0.0369011	+	0.0237149i
$511$	−5.31215	+	36.9468i	−0.234996	+	1.63443i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$	6.52367	+	14.2849i	0.288027	+	0.630692i
$514$	6.23978	+	7.20109i	0.275225	+	0.317627i
$515$	−1.38448	−	9.62927i	−0.0610075	−	0.424316i
$516$	0.178494	−	0.390847i	0.00785776	−	0.0172061i
$517$	2.50563	−	0.735720i	0.110198	−	0.0323569i
$518$	28.1871	−	8.27648i	1.23847	−	0.363647i
$519$	−1.04792	+	2.29463i	−0.0459987	+	0.100723i
$520$	−0.675681	−	4.69946i	−0.0296306	−	0.206085i
$521$	4.99849	+	5.76857i	0.218988	+	0.252726i	0.854605	−	0.519279i	$-0.173800\pi$
$521$	4.99849	+	5.76857i	0.218988	+	0.252726i	−0.635617	+	0.772005i	$0.719254\pi$
$522$	−11.9076	−	26.0740i	−0.521181	−	1.14123i
$523$	−5.03652	+	3.23678i	−0.220232	+	0.141534i	−0.646105	−	0.763248i	$-0.723603\pi$
$523$	−5.03652	+	3.23678i	−0.220232	+	0.141534i	0.425873	+	0.904783i	$0.359967\pi$
$524$	−2.47027	+	17.1811i	−0.107914	+	0.750561i
$525$	0.869017	+	0.558483i	0.0379270	+	0.0243742i
$526$	9.63202	−	11.1159i	0.419976	−	0.484678i
$527$	−7.07570	−	2.07761i	−0.308222	−	0.0905022i
$528$	−0.420901			−0.0183173
$529$	−22.9816	+	0.919338i	−0.999201	+	0.0399712i
$530$	−8.59598			−0.373385
$531$	−32.0549	−	9.41216i	−1.39106	−	0.408453i
$532$	10.9296	−	12.6134i	0.473858	−	0.546862i
$533$	−26.2011	−	16.8384i	−1.13490	−	0.729353i
$534$	0.338879	−	2.35696i	0.0146647	−	0.101995i
$535$	−8.64158	+	5.55361i	−0.373608	+	0.240103i
$536$	4.10345	+	8.98529i	0.177242	+	0.388105i
$537$	0.826904	+	0.954299i	0.0356836	+	0.0411810i
$538$	−1.37115	−	9.53656i	−0.0591145	−	0.411150i
$539$	0.255196	−	0.558802i	0.0109921	−	0.0240693i
$540$	−2.28470	+	0.670850i	−0.0983180	+	0.0288688i
$541$	19.7447	−	5.79755i	0.848889	−	0.249256i	0.171777	−	0.985136i	$-0.445049\pi$
$541$	19.7447	−	5.79755i	0.848889	−	0.249256i	0.677112	+	0.735880i	$0.263231\pi$
$542$	11.0875	−	24.2782i	0.476248	−	1.04284i
$543$	0.979796	+	6.81463i	0.0420471	+	0.292444i
$544$	1.58920	+	1.83403i	0.0681364	+	0.0786336i
$545$	−1.89169	−	4.14222i	−0.0810311	−	0.177433i
$546$	−4.12591	+	2.65156i	−0.176573	+	0.113476i
$547$	−1.44612	+	10.0580i	−0.0618315	+	0.430048i	0.935268	+	0.353940i	$0.115158\pi$
$547$	−1.44612	+	10.0580i	−0.0618315	+	0.430048i	−0.997100	+	0.0761075i	$0.975751\pi$
$548$	3.71042	+	2.38454i	0.158501	+	0.101863i
$549$	4.07834	−	4.70665i	0.174059	−	0.200875i
$550$	−0.989357	−	0.290502i	−0.0421863	−	0.0123870i
$551$	66.7205			2.84239
$552$	−0.0391324	−	1.95725i	−0.00166558	−	0.0833059i
$553$	−10.9343			−0.464976
$554$	−1.61288	−	0.473585i	−0.0685248	−	0.0201207i
$555$	3.10307	−	3.58114i	0.131718	−	0.152011i
$556$	−16.2423	−	10.4383i	−0.688827	−	0.442682i
$557$	5.40342	−	37.5816i	0.228950	−	1.59238i	−0.473594	−	0.880743i	$-0.657044\pi$
$557$	5.40342	−	37.5816i	0.228950	−	1.59238i	0.702544	−	0.711640i	$-0.252047\pi$
$558$	7.24318	−	4.65491i	0.306628	−	0.197058i
$559$	2.07609	+	4.54601i	0.0878093	+	0.192276i
$560$	1.65723	+	1.91254i	0.0700307	+	0.0808197i
$561$	0.145365	+	1.01103i	0.00613731	+	0.0426859i
$562$	−2.91535	+	6.38373i	−0.122977	+	0.269281i
$563$	19.8149	−	5.81819i	0.835100	−	0.245208i	0.163894	−	0.986478i	$-0.447595\pi$
$563$	19.8149	−	5.81819i	0.835100	−	0.245208i	0.671206	+	0.741270i	$0.265776\pi$
$564$	−0.991915	+	0.291252i	−0.0417671	+	0.0122639i
$565$	−3.93851	+	8.62414i	−0.165694	+	0.362820i
$566$	3.29591	+	22.9235i	0.138537	+	0.963549i
$567$	−12.4759	−	14.3979i	−0.523937	−	0.604656i
$568$	1.40333	+	3.07286i	0.0588824	+	0.128934i
$569$	−5.75989	+	3.70165i	−0.241467	+	0.155181i	−0.655778	−	0.754954i	$-0.727659\pi$
$569$	−5.75989	+	3.70165i	−0.241467	+	0.155181i	0.414311	+	0.910136i	$0.364023\pi$
$570$	0.383125	−	2.66469i	0.0160473	−	0.111612i
$571$	12.9553	+	8.32584i	0.542161	+	0.348426i	0.782883	−	0.622168i	$-0.213748\pi$
$571$	12.9553	+	8.32584i	0.542161	+	0.348426i	−0.240723	+	0.970594i	$0.577384\pi$
$572$	3.20591	−	3.69982i	0.134046	−	0.154697i
$573$	−3.98054	−	1.16879i	−0.166290	−	0.0488270i
$574$	16.6010			0.692913
$575$	1.25889	−	4.62766i	0.0524993	−	0.192987i
$576$	−2.83338			−0.118057
$577$	20.1770	+	5.92449i	0.839978	+	0.246640i	0.673298	−	0.739371i	$-0.264877\pi$
$577$	20.1770	+	5.92449i	0.839978	+	0.246640i	0.166680	+	0.986011i	$0.446695\pi$
$578$	−7.27600	+	8.39695i	−0.302642	+	0.349267i
$579$	−0.431774	−	0.277484i	−0.0179439	−	0.0115318i
$580$	−1.43975	+	10.0137i	−0.0597824	+	0.415796i
$581$	−7.71000	+	4.95491i	−0.319865	+	0.205564i
$582$	0.300562	+	0.658139i	0.0124587	+	0.0272807i
$583$	−5.80438	−	6.69861i	−0.240393	−	0.277428i
$584$	2.09912	+	14.5997i	0.0868622	+	0.604140i
$585$	5.58827	−	12.2366i	0.231047	−	0.505922i
$586$	−16.9284	+	4.97063i	−0.699306	+	0.205335i
$587$	33.2978	−	9.77712i	1.37435	−	0.403545i	0.490550	−	0.871413i	$-0.336796\pi$
$587$	33.2978	−	9.77712i	1.37435	−	0.403545i	0.883798	+	0.467868i	$0.154978\pi$
$588$	−0.101025	+	0.221215i	−0.00416622	+	0.00912275i
$589$	2.85213	+	19.8370i	0.117520	+	0.817371i
$590$	7.72141	+	8.91098i	0.317886	+	0.366859i
$591$	−3.61717	−	7.92049i	−0.148790	−	0.325806i
$592$	9.76567	−	6.27601i	0.401366	−	0.257943i
$593$	2.72637	−	18.9623i	0.111959	−	0.778690i	−0.854052	−	0.520188i	$-0.825862\pi$
$593$	2.72637	−	18.9623i	0.111959	−	0.778690i	0.966011	−	0.258502i	$-0.0832290\pi$
$594$	−2.06551	−	1.32742i	−0.0847487	−	0.0544647i
$595$	4.02172	−	4.64131i	0.164874	−	0.190275i
$596$	20.0247	+	5.87979i	0.820245	+	0.240846i
$597$	7.32576			0.299823
$598$	17.5027	+	14.5639i	0.715740	+	0.595564i
$599$	20.8106			0.850296			0.425148	−	0.905124i	$-0.360222\pi$
$599$	20.8106			0.850296			0.425148	+	0.905124i	$0.360222\pi$
$600$	0.391661	+	0.115002i	0.0159895	+	0.00469493i
$601$	−17.9111	+	20.6705i	−0.730608	+	0.843166i	−0.992540	−	0.121920i	$-0.961095\pi$
$601$	−17.9111	+	20.6705i	−0.730608	+	0.843166i	0.261932	+	0.965086i	$0.415640\pi$
$602$	−2.24096	−	1.44018i	−0.0913346	−	0.0586972i
$603$	−3.98310	+	27.7031i	−0.162204	+	1.12816i
$604$	−3.62667	+	2.33072i	−0.147567	+	0.0948357i
$605$	4.12789	+	9.03881i	0.167823	+	0.367480i
$606$	−1.40412	−	1.62044i	−0.0570383	−	0.0658257i
$607$	−3.62123	−	25.1862i	−0.146981	−	1.02228i	−0.921125	−	0.389267i	$-0.872728\pi$
$607$	−3.62123	−	25.1862i	−0.146981	−	1.02228i	0.774144	−	0.633010i	$-0.218181\pi$
$608$	2.73971	−	5.99912i	0.111110	−	0.243297i
$609$	10.0272	−	2.94426i	0.406324	−	0.119307i
$610$	−2.10898	+	0.619251i	−0.0853899	+	0.0250727i
$611$	4.99503	−	10.9376i	0.202077	−	0.442487i
$612$	0.978552	+	6.80598i	0.0395556	+	0.275115i
$613$	6.91879	+	7.98471i	0.279447	+	0.322499i	0.878070	−	0.478531i	$-0.158831\pi$
$613$	6.91879	+	7.98471i	0.279447	+	0.322499i	−0.598623	+	0.801031i	$0.704285\pi$
$614$	−5.83067	−	12.7674i	−0.235307	−	0.515250i
$615$	2.25266	−	1.44770i	0.0908362	−	0.0583769i
$616$	−0.371360	+	2.58286i	−0.0149625	+	0.104067i
$617$	13.8438	+	8.89685i	0.557329	+	0.358174i	0.788783	−	0.614672i	$-0.210712\pi$
$617$	13.8438	+	8.89685i	0.557329	+	0.358174i	−0.231454	+	0.972846i	$0.574348\pi$
$618$	−2.60048	+	3.00111i	−0.104607	+	0.120723i
$619$	−5.67153	−	1.66531i	−0.227958	−	0.0669345i	0.165759	−	0.986166i	$-0.446993\pi$
$619$	−5.67153	−	1.66531i	−0.227958	−	0.0669345i	−0.393717	+	0.919232i	$0.628811\pi$
$620$	−3.03877			−0.122040
$621$	5.98065	−	9.72830i	0.239995	−	0.390383i
$622$	27.2582			1.09295
$623$	−14.1645	−	4.15908i	−0.567489	−	0.166630i
$624$	−1.26914	+	1.46466i	−0.0508061	+	0.0586334i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	−2.79580	+	19.4452i	−0.111743	+	0.777187i
$627$	2.33522	−	1.50076i	0.0932598	−	0.0599345i
$628$	0.250077	+	0.547592i	0.00997915	+	0.0218513i
$629$	−18.4482	−	21.2903i	−0.735577	−	0.848901i
$630$	1.02044	+	7.09732i	0.0406553	+	0.282764i
$631$	−14.9100	+	32.6484i	−0.593558	+	1.29971i	0.339710	+	0.940530i	$0.389671\pi$
$631$	−14.9100	+	32.6484i	−0.593558	+	1.29971i	−0.933268	+	0.359181i	$0.883056\pi$
$632$	−4.14573	+	1.21730i	−0.164908	+	0.0484215i
$633$	4.36876	−	1.28278i	0.173643	−	0.0509861i
$634$	−5.17107	+	11.3231i	−0.205370	+	0.449697i
$635$	0.0993816	+	0.691214i	0.00394384	+	0.0274300i
$636$	2.29780	+	2.65180i	0.0911137	+	0.105151i
$637$	−1.17504	−	2.57299i	−0.0465569	−	0.101945i
$638$	−8.77558	+	5.63972i	−0.347429	+	0.223279i
$639$	−1.36217	+	9.47412i	−0.0538867	+	0.374790i
$640$	0.841254	+	0.540641i	0.0332535	+	0.0213707i
$641$	10.0417	−	11.5888i	0.396625	−	0.457730i	−0.521950	−	0.852976i	$-0.674795\pi$
$641$	10.0417	−	11.5888i	0.396625	−	0.457730i	0.918575	+	0.395246i	$0.129341\pi$
$642$	4.02324	+	1.18133i	0.158785	+	0.0466234i
$643$	−44.1108			−1.73956			−0.869779	−	0.493441i	$-0.835739\pi$
$643$	−44.1108			−1.73956			−0.869779	+	0.493441i	$0.835739\pi$
$644$	−12.0452	−	1.48674i	−0.474647	−	0.0585857i
$645$	−0.429676			−0.0169185
$646$	−15.3565	−	4.50909i	−0.604195	−	0.177408i
$647$	18.4318	−	21.2714i	0.724628	−	0.836265i	−0.267228	−	0.963633i	$-0.586108\pi$
$647$	18.4318	−	21.2714i	0.724628	−	0.836265i	0.991855	+	0.127368i	$0.0406531\pi$
$648$	−6.33308	−	4.07003i	−0.248787	−	0.159886i
$649$	−1.73025	+	12.0342i	−0.0679183	+	0.472382i
$650$	−3.99409	+	2.56685i	−0.156661	+	0.100680i
$651$	1.30401	+	2.85539i	0.0511082	+	0.111911i
$652$	11.3511	+	13.0998i	0.444542	+	0.513029i
$653$	0.964492	+	6.70819i	0.0377435	+	0.262512i	0.999952	−	0.00980218i	$-0.00312018\pi$
$653$	0.964492	+	6.70819i	0.0377435	+	0.262512i	−0.962208	+	0.272314i	$0.912211\pi$
$654$	−0.772179	+	1.69084i	−0.0301946	+	0.0661170i
$655$	16.6547	−	4.89026i	0.650752	−	0.191078i
$656$	6.29424	−	1.84816i	0.245749	−	0.0721584i
$657$	−17.3609	+	38.0152i	−0.677315	+	1.48311i
$658$	0.912112	+	6.34387i	0.0355578	+	0.247310i
$659$	28.3768	+	32.7486i	1.10540	+	1.27570i	0.958044	+	0.286622i	$0.0925324\pi$
$659$	28.3768	+	32.7486i	1.10540	+	1.27570i	0.147361	+	0.989083i	$0.452922\pi$
$660$	0.174848	+	0.382865i	0.00680597	+	0.0149030i
$661$	−4.86213	+	3.12470i	−0.189115	+	0.121537i	−0.631772	−	0.775154i	$-0.717672\pi$
$661$	−4.86213	+	3.12470i	−0.189115	+	0.121537i	0.442657	+	0.896691i	$0.354036\pi$
$662$	−3.49835	+	24.3316i	−0.135967	+	0.945673i
$663$	3.95654	+	2.54271i	0.153659	+	0.0987509i
$664$	−2.37161	+	2.73698i	−0.0920362	+	0.106215i
$665$	−16.0139	−	4.70211i	−0.620992	−	0.182340i
$666$	32.8912			1.27451
$667$	−27.0414	−	40.2833i	−1.04705	−	1.55978i
$668$	−13.0218			−0.503828
$669$	7.93415	+	2.32968i	0.306752	+	0.0900705i
$670$	6.46868	−	7.46525i	0.249907	−	0.288408i
$671$	−1.90664	−	1.22532i	−0.0736049	−	0.0473030i
$672$	0.147012	−	1.02249i	0.00567110	−	0.0394433i
$673$	25.5224	−	16.4023i	0.983817	−	0.632261i	0.0533264	−	0.998577i	$-0.483018\pi$
$673$	25.5224	−	16.4023i	0.983817	−	0.632261i	0.930490	+	0.366317i	$0.119381\pi$
$674$	−3.92662	−	8.59810i	−0.151248	−	0.331187i
$675$	1.55933	+	1.79956i	0.0600185	+	0.0692650i
$676$	−1.35789	−	9.44436i	−0.0522267	−	0.363245i
$677$	11.5180	−	25.2210i	0.442675	−	0.969322i	−0.548425	−	0.836200i	$-0.684772\pi$
$677$	11.5180	−	25.2210i	0.442675	−	0.969322i	0.991100	−	0.133122i	$-0.0425003\pi$
$678$	3.71330	−	1.09032i	0.142608	−	0.0418736i
$679$	4.30387	−	1.26373i	0.165167	−	0.0484975i
$680$	1.00812	−	2.20747i	0.0386596	−	0.0846527i
$681$	−1.16472	−	8.10083i	−0.0446323	−	0.310424i
$682$	−2.05191	−	2.36803i	−0.0785717	−	0.0906765i
$683$	5.26022	+	11.5183i	0.201277	+	0.440734i	0.983174	−	0.182673i	$-0.0584750\pi$
$683$	5.26022	+	11.5183i	0.201277	+	0.440734i	−0.781897	+	0.623408i	$0.785748\pi$
$684$	15.7200	−	10.1026i	0.601070	−	0.386284i
$685$	0.627691	−	4.36569i	0.0239829	−	0.166804i
$686$	16.1708	+	10.3924i	0.617405	+	0.396782i
$687$	−2.91705	+	3.36646i	−0.111292	+	0.128438i
$688$	−1.00998	−	0.296558i	−0.0385053	−	0.0113062i
$689$	−40.8119			−1.55481
$690$	−1.76412	+	0.848665i	−0.0671588	+	0.0323081i
$691$	43.7840			1.66562			0.832811	−	0.553557i	$-0.186730\pi$
$691$	43.7840			1.66562			0.832811	+	0.553557i	$0.186730\pi$
$692$	5.92954	+	1.74107i	0.225407	+	0.0661855i
$693$	−4.84170	+	5.58762i	−0.183921	+	0.212256i
$694$	15.9487	+	10.2496i	0.605404	+	0.389070i
$695$	−2.74771	+	19.1107i	−0.104227	+	0.724912i
$696$	3.47402	−	2.23262i	0.131682	−	0.0846272i
$697$	−6.61322	−	14.4809i	−0.250494	−	0.548505i
$698$	8.94164	+	10.3192i	0.338446	+	0.390588i
$699$	−0.537571	−	3.73889i	−0.0203328	−	0.141418i
$700$	1.05127	−	2.30197i	0.0397344	−	0.0870062i
$701$	−45.9463	+	13.4910i	−1.73537	+	0.509550i	−0.987946	−	0.154800i	$-0.950527\pi$
$701$	−45.9463	+	13.4910i	−1.73537	+	0.509550i	−0.747422	+	0.664350i	$0.768709\pi$
$702$	−10.8473	+	3.18505i	−0.409404	+	0.120212i
$703$	−31.8038	+	69.6406i	−1.19950	+	2.62655i
$704$	0.146744	+	1.02063i	0.00553064	+	0.0384664i
$705$	0.676989	+	0.781287i	0.0254969	+	0.0294250i
$706$	4.23638	+	9.27639i	0.159438	+	0.349121i
$707$	−11.1827	+	7.18668i	−0.420568	+	0.270283i
$708$	0.684961	−	4.76401i	0.0257424	−	0.179042i
$709$	5.42468	+	3.48623i	0.203728	+	0.130928i	0.638527	−	0.769600i	$-0.279544\pi$
$709$	5.42468	+	3.48623i	0.203728	+	0.130928i	−0.434799	+	0.900528i	$0.643180\pi$
$710$	2.21221	−	2.55303i	0.0830228	−	0.0958134i
$711$	−11.7464	−	3.44906i	−0.440525	−	0.129350i
$712$	−5.83347			−0.218618
$713$	10.8209	−	9.76182i	0.405245	−	0.365583i
$714$	−2.50687			−0.0938171
$715$	−4.69726	−	1.37924i	−0.175667	−	0.0515806i
$716$	2.02576	−	2.33785i	0.0757061	−	0.0873695i
$717$	−1.77678	−	1.14186i	−0.0663549	−	0.0426437i
$718$	4.75234	−	33.0533i	0.177356	−	1.23354i
$719$	−22.4326	+	14.4166i	−0.836595	+	0.537647i	−0.887367	−	0.461063i	$-0.847468\pi$
$719$	−22.4326	+	14.4166i	−0.836595	+	0.537647i	0.0507722	+	0.998710i	$0.483832\pi$
$720$	1.17703	+	2.57733i	0.0438652	+	0.0960514i
$721$	16.1220	+	18.6058i	0.600415	+	0.692916i
$722$	3.48607	+	24.2461i	0.129738	+	0.902348i
$723$	−0.857075	+	1.87673i	−0.0318750	+	0.0697964i
$724$	16.1830	−	4.75176i	0.601437	−	0.176598i
$725$	9.70687	−	2.85019i	0.360504	−	0.105854i
$726$	1.68498	−	3.68960i	0.0625356	−	0.136934i
$727$	−5.88570	−	40.9359i	−0.218288	−	1.51823i	−0.744354	−	0.667785i	$-0.767242\pi$
$727$	−5.88570	−	40.9359i	−0.218288	−	1.51823i	0.526065	−	0.850444i	$-0.323667\pi$
$728$	7.86817	+	9.08035i	0.291614	+	0.336540i
$729$	−7.64952	−	16.7501i	−0.283315	−	0.620374i
$730$	12.4083	−	7.97436i	0.459253	−	0.295144i
$731$	−0.363540	+	2.52848i	−0.0134460	+	0.0935192i
$732$	0.754788	+	0.485073i	0.0278978	+	0.0179288i
$733$	17.3205	−	19.9889i	0.639746	−	0.738306i	−0.339584	−	0.940576i	$-0.610286\pi$
$733$	17.3205	−	19.9889i	0.639746	−	0.738306i	0.979330	+	0.202269i	$0.0648317\pi$
$734$	−29.5464	−	8.67560i	−1.09058	−	0.320222i
$735$	0.243192			0.00897026
$736$	−4.73243	+	0.777273i	−0.174440	+	0.0286506i
$737$	10.1854			0.375184
$738$	17.8340	+	5.23652i	0.656477	+	0.192759i
$739$	23.9019	−	27.5842i	0.879244	−	1.01470i	−0.120514	−	0.992712i	$-0.538454\pi$
$739$	23.9019	−	27.5842i	0.879244	−	1.01470i	0.999758	−	0.0219902i	$-0.00700026\pi$
$740$	−9.76567	−	6.27601i	−0.358993	−	0.230711i
$741$	1.81899	−	12.6514i	0.0668224	−	0.464760i
$742$	18.3002	−	11.7608i	0.671821	−	0.431753i
$743$	−4.61887	−	10.1139i	−0.169450	−	0.371043i	0.805787	−	0.592205i	$-0.201742\pi$
$743$	−4.61887	−	10.1139i	−0.169450	−	0.371043i	−0.975237	+	0.221162i	$0.929015\pi$
$744$	0.812297	+	0.937441i	0.0297803	+	0.0343682i
$745$	−2.97013	−	20.6577i	−0.108817	−	0.756840i
$746$	2.78476	−	6.09778i	0.101957	−	0.223256i
$747$	−9.84555	+	2.89091i	−0.360230	+	0.105773i
$748$	2.40095	−	0.704982i	0.0877873	−	0.0257767i
$749$	10.7990	−	23.6464i	0.394585	−	0.864021i
$750$	−0.0580923	−	0.404041i	−0.00212123	−	0.0147535i
$751$	−24.6564	−	28.4550i	−0.899724	−	1.03834i	−0.999063	−	0.0432828i	$-0.986218\pi$
$751$	−24.6564	−	28.4550i	−0.899724	−	1.03834i	0.0993392	−	0.995054i	$-0.468327\pi$
$752$	1.05207	+	2.30372i	0.0383652	+	0.0840081i
$753$	0.633504	−	0.407128i	0.0230862	−	0.0148366i
$754$	−6.83564	+	47.5429i	−0.248939	+	1.73141i
$755$	3.62667	+	2.33072i	0.131988	+	0.0848236i
$756$	3.94612	−	4.55407i	0.143519	−	0.165630i
$757$	17.7351	+	5.20751i	0.644595	+	0.189270i	0.587660	−	0.809108i	$-0.300049\pi$
$757$	17.7351	+	5.20751i	0.644595	+	0.189270i	0.0569346	+	0.998378i	$0.481867\pi$
$758$	−36.4056			−1.32231
$759$	−1.85255	−	0.801672i	−0.0672433	−	0.0290988i
$760$	−6.59511			−0.239230
$761$	10.3736	+	3.04598i	0.376044	+	0.110417i	0.464292	−	0.885682i	$-0.346309\pi$
$761$	10.3736	+	3.04598i	0.376044	+	0.110417i	−0.0882481	+	0.996099i	$0.528127\pi$
$762$	0.186669	−	0.215428i	0.00676231	−	0.00780412i
$763$	9.69456	+	6.23032i	0.350967	+	0.225553i
$764$	−1.44638	+	10.0598i	−0.0523282	+	0.363951i
$765$	5.78443	−	3.71743i	0.209137	−	0.134404i
$766$	−6.95166	−	15.2220i	−0.251174	−	0.549994i
$767$	36.6596	+	42.3075i	1.32370	+	1.52763i
$768$	−0.0580923	−	0.404041i	−0.00209622	−	0.0145796i
$769$	−3.26452	+	7.14831i	−0.117722	+	0.257775i	−0.959315	−	0.282336i	$-0.908891\pi$
$769$	−3.26452	+	7.14831i	−0.117722	+	0.257775i	0.841594	+	0.540111i	$0.181618\pi$
$770$	2.50372	−	0.735160i	0.0902280	−	0.0264933i
$771$	−3.73190	+	1.09579i	−0.134401	+	0.0394638i
$772$	−0.522328	+	1.14374i	−0.0187990	+	0.0411641i
$773$	−3.01621	−	20.9782i	−0.108486	−	0.754534i	−0.969347	−	0.245695i	$-0.920984\pi$
$773$	−3.01621	−	20.9782i	−0.108486	−	0.754534i	0.860862	−	0.508839i	$-0.169925\pi$
$774$	−1.95311	−	2.25401i	−0.0702030	−	0.0810186i
$775$	1.26235	+	2.76416i	0.0453450	+	0.0992916i
$776$	1.49111	−	0.958280i	0.0535278	−	0.0344002i
$777$	−1.70658	+	11.8695i	−0.0612232	+	0.425817i
$778$	31.7018	+	20.3735i	1.13656	+	0.730425i
$779$	−28.3317	+	32.6965i	−1.01509	+	1.17147i
$780$	1.85952	+	0.546005i	0.0665815	+	0.0195501i
$781$	3.48328			0.124642
$782$	3.50149	+	11.0992i	0.125213	+	0.396906i
$783$	24.0894			0.860884
$784$	0.571640	+	0.167849i	0.0204157	+	0.00599459i
$785$	0.394221	−	0.454956i	0.0140704	−	0.0162381i
$786$	−5.96059	−	3.83064i	−0.212607	−	0.136634i
$787$	−2.52655	+	17.5726i	−0.0900619	+	0.626394i	0.893933	+	0.448200i	$0.147935\pi$
$787$	−2.52655	+	17.5726i	−0.0900619	+	0.626394i	−0.983995	+	0.178194i	$0.942974\pi$
$788$	−17.9451	+	11.5326i	−0.639267	+	0.410832i
$789$	2.49413	+	5.46138i	0.0887933	+	0.194430i
$790$	2.82949	+	3.26541i	0.100669	+	0.116178i
$791$	−3.41455	−	23.7487i	−0.121407	−	0.844407i
$792$	−1.21366	+	2.65755i	−0.0431256	+	0.0944319i
$793$	−10.0130	+	2.94007i	−0.355571	+	0.104405i
$794$	15.1048	−	4.43517i	0.536049	−	0.157398i
$795$	1.45762	−	3.19175i	0.0516966	−	0.113200i
$796$	−2.55408	−	17.7640i	−0.0905270	−	0.629629i
$797$	0.165981	+	0.191553i	0.00587936	+	0.00678515i	0.758682	−	0.651462i	$-0.225844\pi$
$797$	0.165981	+	0.191553i	0.00587936	+	0.00678515i	−0.752802	+	0.658247i	$0.771298\pi$
$798$	2.83013	+	6.19711i	0.100185	+	0.219375i
$799$	5.17036	−	3.32279i	0.182914	−	0.117552i
$800$	0.142315	−	0.989821i	0.00503159	−	0.0349955i
$801$	−13.9046	−	8.93593i	−0.491294	−	0.315736i
$802$	−19.2544	+	22.2208i	−0.679898	+	0.784644i
$803$	14.5929	+	4.28485i	0.514971	+	0.151209i
$804$	−4.03213			−0.142202
$805$	3.65137	+	11.5743i	0.128694	+	0.407941i
$806$	−14.4274			−0.508185
$807$	3.77350	+	1.10800i	0.132834	+	0.0390035i
$808$	−3.43981	+	3.96976i	−0.121012	+	0.139656i
$809$	−20.4859	−	13.1655i	−0.720246	−	0.462874i	0.128477	−	0.991713i	$-0.458991\pi$
$809$	−20.4859	−	13.1655i	−0.720246	−	0.462874i	−0.848722	+	0.528839i	$0.822628\pi$
$810$	−1.07137	+	7.45153i	−0.0376440	+	0.261820i
$811$	−31.5933	+	20.3038i	−1.10939	+	0.712961i	−0.961160	−	0.275992i	$-0.910994\pi$
$811$	−31.5933	+	20.3038i	−1.10939	+	0.712961i	−0.148230	+	0.988953i	$0.547357\pi$
$812$	−10.6354	−	23.2882i	−0.373229	−	0.817257i
$813$	7.13456	+	8.23372i	0.250220	+	0.288769i
$814$	−1.70348	−	11.8480i	−0.0597069	−	0.415270i
$815$	7.20062	−	15.7672i	0.252227	−	0.552300i
$816$	−0.950472	+	0.279084i	−0.0332732	+	0.00976989i
$817$	6.66096	−	1.95583i	0.233038	−	0.0684260i
$818$	9.98866	−	21.8721i	0.349245	−	0.764741i
$819$	4.84484	+	33.6966i	0.169292	+	1.17745i
$820$	−4.29586	−	4.95769i	−0.150018	−	0.173130i
$821$	13.6063	+	29.7936i	0.474863	+	1.03980i	0.983844	+	0.179027i	$0.0572950\pi$
$821$	13.6063	+	29.7936i	0.474863	+	1.03980i	−0.508981	+	0.860778i	$0.669978\pi$
$822$	−1.51458	+	0.973359i	−0.0528269	+	0.0339498i
$823$	0.889300	−	6.18522i	0.0309990	−	0.215603i	−0.968434	−	0.249270i	$-0.919809\pi$
$823$	0.889300	−	6.18522i	0.0309990	−	0.215603i	0.999433	+	0.0336667i	$0.0107185\pi$
$824$	8.18396	+	5.25951i	0.285102	+	0.183224i
$825$	0.275631	−	0.318095i	0.00959625	−	0.0110747i
$826$	−28.6301	−	8.40656i	−0.996169	−	0.292502i
$827$	−47.6477			−1.65687			−0.828436	−	0.560084i	$-0.810769\pi$
$827$	−47.6477			−1.65687			−0.828436	+	0.560084i	$0.810769\pi$
$828$	−12.4708	−	5.39662i	−0.433391	−	0.187545i
$829$	33.8572			1.17591			0.587955	−	0.808893i	$-0.299933\pi$
$829$	33.8572			1.17591			0.587955	+	0.808893i	$0.299933\pi$
$830$	3.47485	+	1.02031i	0.120614	+	0.0354154i
$831$	0.449343	−	0.518569i	0.0155875	−	0.0179890i
$832$	3.99409	+	2.56685i	0.138470	+	0.0889894i
$833$	0.205760	−	1.43109i	0.00712915	−	0.0495843i
$834$	6.63003	−	4.26086i	0.229579	−	0.147542i
$835$	5.40944	+	11.8450i	0.187201	+	0.409914i
$836$	−4.45330	−	5.13939i	−0.154021	−	0.177749i
$837$	1.02976	+	7.16214i	0.0355937	+	0.247560i
$838$	1.69967	−	3.72176i	0.0587142	−	0.128566i
$839$	−0.882710	+	0.259187i	−0.0304745	+	0.00894813i	−0.296934	−	0.954898i	$-0.595964\pi$
$839$	−0.882710	+	0.259187i	−0.0304745	+	0.00894813i	0.266460	+	0.963846i	$0.414146\pi$
$840$	−0.991159	+	0.291030i	−0.0341982	+	0.0100415i
$841$	30.4694	−	66.7188i	1.05067	−	2.30065i
$842$	1.75803	+	12.2273i	0.0605856	+	0.421382i
$843$	−1.87597	−	2.16498i	−0.0646118	−	0.0745660i
$844$	−4.63373	−	10.1464i	−0.159499	−	0.349255i
$845$	−8.02680	+	5.15851i	−0.276130	+	0.177458i
$846$	−1.02122	+	7.10273i	−0.0351102	+	0.244197i
$847$	−21.1547	−	13.5953i	−0.726883	−	0.467139i
$848$	5.62917	−	6.49641i	0.193306	−	0.223088i
$849$	−9.07058	−	2.66336i	−0.311301	−	0.0914063i
$850$	−2.42677			−0.0832377
$851$	54.9362	−	9.02295i	1.88319	−	0.309303i
$852$	−1.37894			−0.0472417
$853$	−37.1706	−	10.9143i	−1.27270	−	0.373698i	−0.425492	−	0.904962i	$-0.639899\pi$
$853$	−37.1706	−	10.9143i	−1.27270	−	0.373698i	−0.847206	+	0.531264i	$0.821717\pi$
$854$	3.64261	−	4.20379i	0.124647	−	0.143851i
$855$	−15.7200	−	10.1026i	−0.537613	−	0.345503i
$856$	1.46190	−	10.1677i	0.0499666	−	0.347525i
$857$	38.3321	−	24.6345i	1.30940	−	0.841499i	0.315196	−	0.949026i	$-0.397930\pi$
$857$	38.3321	−	24.6345i	1.30940	−	0.841499i	0.994202	+	0.107527i	$0.0342932\pi$
$858$	0.830143	+	1.81776i	0.0283406	+	0.0620573i
$859$	−2.21874	−	2.56056i	−0.0757023	−	0.0873651i	0.716635	−	0.697448i	$-0.245681\pi$
$859$	−2.21874	−	2.56056i	−0.0757023	−	0.0873651i	−0.792337	+	0.610083i	$0.791136\pi$
$860$	0.149804	+	1.04191i	0.00510827	+	0.0355288i
$861$	−2.81504	+	6.16409i	−0.0959364	+	0.210072i
$862$	1.83936	−	0.540084i	0.0626488	−	0.0183953i
$863$	−38.3603	+	11.2636i	−1.30580	+	0.383417i	−0.859348	−	0.511391i	$-0.829130\pi$
$863$	−38.3603	+	11.2636i	−1.30580	+	0.383417i	−0.446450	+	0.894808i	$0.647312\pi$
$864$	0.989168	−	2.16598i	0.0336522	−	0.0736880i
$865$	−0.879487	−	6.11696i	−0.0299034	−	0.207983i
$866$	7.15455	+	8.25679i	0.243122	+	0.280577i
$867$	−1.88406	−	4.12551i	−0.0639859	−	0.140110i
$868$	6.46931	−	4.15757i	0.219583	−	0.141117i
$869$	−0.634046	+	4.40989i	−0.0215086	+	0.149595i
$870$	−3.47402	−	2.23262i	−0.117780	−	0.0756928i
$871$	30.7119	−	35.4434i	1.04063	−	1.20095i
$872$	4.36928	+	1.28294i	0.147962	+	0.0434457i
$873$	5.02213			0.169973
$874$	23.4848	−	21.1863i	0.794386	−	0.716637i
$875$	−2.53066			−0.0855518
$876$	−5.77693	−	1.69626i	−0.195184	−	0.0573113i
$877$	−34.8874	+	40.2622i	−1.17806	+	1.35956i	−0.258794	+	0.965932i	$0.583325\pi$
$877$	−34.8874	+	40.2622i	−1.17806	+	1.35956i	−0.919270	+	0.393627i	$0.871220\pi$
$878$	11.4716	+	7.37233i	0.387147	+	0.248804i
$879$	1.02493	−	7.12852i	0.0345699	−	0.240439i
$880$	0.867438	−	0.557468i	0.0292413	−	0.0187923i
$881$	12.2455	+	26.8139i	0.412561	+	0.903383i	0.995841	+	0.0911117i	$0.0290420\pi$
$881$	12.2455	+	26.8139i	0.412561	+	0.903383i	−0.583279	+	0.812272i	$0.698231\pi$
$882$	1.10544	+	1.27574i	0.0372220	+	0.0429565i
$883$	−7.66845	−	53.3352i	−0.258064	−	1.79487i	−0.546590	−	0.837401i	$-0.684074\pi$
$883$	−7.66845	−	53.3352i	−0.258064	−	1.79487i	0.288526	−	0.957472i	$-0.406835\pi$
$884$	4.78633	−	10.4806i	0.160982	−	0.352501i
$885$	−4.61804	+	1.35598i	−0.155234	+	0.0455807i
$886$	−1.86152	+	0.546593i	−0.0625391	+	0.0183631i
$887$	−6.26814	+	13.7253i	−0.210464	+	0.460851i	−0.985195	−	0.171440i	$-0.945158\pi$
$887$	−6.26814	+	13.7253i	−0.210464	+	0.460851i	0.774731	+	0.632291i	$0.217885\pi$
$888$	0.674362	+	4.69029i	0.0226301	+	0.157396i
$889$	−1.15728	−	1.33557i	−0.0388139	−	0.0447936i
$890$	2.42331	+	5.30631i	0.0812295	+	0.177868i
$891$	−6.53020	+	4.19671i	−0.218770	+	0.140595i
$892$	2.88297	−	20.0515i	0.0965291	−	0.671374i
$893$	−14.0512	−	9.03015i	−0.470205	−	0.302183i
$894$	−5.57882	+	6.43830i	−0.186584	+	0.215329i
$895$	−2.96811	−	0.871516i	−0.0992130	−	0.0291316i
$896$	−2.53066			−0.0845433
$897$	−8.37565	+	4.02928i	−0.279655	+	0.134534i
$898$	5.21217			0.173932
$899$	29.4969	+	8.66109i	0.983778	+	0.288863i
$900$	1.85547	−	2.14132i	0.0618489	−	0.0713774i
$901$	−17.5490	−	11.2780i	−0.584641	−	0.375726i
$902$	0.962638	−	6.69530i	0.0320524	−	0.222929i
$903$	0.914748	−	0.587873i	0.0304409	−	0.0195632i
$904$	−3.93851	−	8.62414i	−0.130993	−	0.286835i
$905$	−11.0450	−	12.7466i	−0.367149	−	0.423712i
$906$	−0.250438	−	1.74183i	−0.00832024	−	0.0578685i
$907$	−22.8646	+	50.0666i	−0.759208	+	1.66243i	−0.0101322	+	0.999949i	$0.503225\pi$
$907$	−22.8646	+	50.0666i	−0.759208	+	1.66243i	−0.749076	+	0.662484i	$0.769502\pi$
$908$	−19.2374	+	5.64861i	−0.638415	+	0.187456i
$909$	−14.2801	+	4.19302i	−0.473642	+	0.139074i
$910$	4.99122	−	10.9292i	0.165457	−	0.362301i
$911$	3.53294	+	24.5722i	0.117052	+	0.814112i	0.960774	+	0.277332i	$0.0894502\pi$
$911$	3.53294	+	24.5722i	0.117052	+	0.814112i	−0.843723	+	0.536780i	$0.819641\pi$
$912$	1.76295	+	2.03455i	0.0583770	+	0.0673706i
$913$	1.55127	+	3.39681i	0.0513396	+	0.112418i
$914$	−7.07489	+	4.54676i	−0.234017	+	0.150393i
$915$	0.127687	−	0.888085i	0.00422122	−	0.0293592i
$916$	9.18024	+	5.89978i	0.303324	+	0.194934i
$917$	−28.7658	+	33.1975i	−0.949931	+	1.09628i
$918$	−5.54446	−	1.62800i	−0.182995	−	0.0537320i
$919$	−38.6080			−1.27356			−0.636780	−	0.771046i	$-0.719734\pi$
$919$	−38.6080			−1.27356			−0.636780	+	0.771046i	$0.719734\pi$
$920$	2.67295	+	3.98187i	0.0881246	+	0.131279i
$921$	5.72934			0.188788
$922$	−34.4569	−	10.1174i	−1.13478	−	0.333200i
$923$	10.5031	−	12.1212i	0.345714	−	0.398975i
$924$	−0.896066	−	0.575866i	−0.0294784	−	0.0189446i
$925$	−1.65206	+	11.4903i	−0.0543193	+	0.377799i
$926$	−2.91380	+	1.87259i	−0.0957534	+	0.0615370i
$927$	11.4505	+	25.0730i	0.376083	+	0.823506i
$928$	−6.62501	−	7.64567i	−0.217477	−	0.250981i
$929$	0.748150	+	5.20350i	0.0245460	+	0.170721i	0.998407	−	0.0564241i	$-0.0179699\pi$
$929$	0.748150	+	5.20350i	0.0245460	+	0.170721i	−0.973861	+	0.227145i	$0.927061\pi$
$930$	0.515286	−	1.12832i	0.0168969	−	0.0369990i
$931$	−3.77003	+	1.10698i	−0.123558	+	0.0362798i
$932$	−8.87890	+	2.60708i	−0.290838	+	0.0853977i
$933$	−4.62218	+	10.1212i	−0.151323	+	0.331352i
$934$	−3.37315	−	23.4608i	−0.110373	−	0.767659i
$935$	−1.63866	−	1.89112i	−0.0535900	−	0.0618462i
$936$	5.58827	+	12.2366i	0.182658	+	0.399966i
$937$	6.67144	−	4.28748i	0.217947	−	0.140066i	−0.427112	−	0.904199i	$-0.640469\pi$
$937$	6.67144	−	4.28748i	0.217947	−	0.140066i	0.645059	+	0.764133i	$0.276833\pi$
$938$	−3.55754	+	24.7432i	−0.116158	+	0.807896i
$939$	−6.74607	−	4.33543i	−0.220150	−	0.141482i
$940$	1.65849	−	1.91400i	0.0540940	−	0.0624278i
$941$	−53.3135	−	15.6543i	−1.73797	−	0.510314i	−0.749536	−	0.661964i	$-0.769723\pi$
$941$	−53.3135	−	15.6543i	−1.73797	−	0.510314i	−0.988434	+	0.151650i	$0.951541\pi$
$942$	−0.245731			−0.00800634
$943$	31.2235	+	3.85392i	1.01678	+	0.125501i
$944$	−11.7909			−0.383762
$945$	−5.78180	−	1.69769i	−0.188082	−	0.0552259i
$946$	−0.710777	+	0.820281i	−0.0231094	+	0.0266696i
$947$	20.1187	+	12.9295i	0.653769	+	0.420152i	0.825042	−	0.565072i	$-0.191152\pi$
$947$	20.1187	+	12.9295i	0.653769	+	0.420152i	−0.171273	+	0.985224i	$0.554788\pi$
$948$	0.251002	−	1.74576i	0.00815218	−	0.0566996i
$949$	58.9122	−	37.8606i	1.91237	−	1.22901i
$950$	2.73971	+	5.99912i	0.0888878	+	0.194637i
$951$	−3.32748	−	3.84012i	−0.107901	−	0.124524i
$952$	0.874003	+	6.07883i	0.0283266	+	0.197016i
$953$	13.0866	−	28.6557i	0.423917	−	0.928249i	−0.570358	−	0.821396i	$-0.693195\pi$
$953$	13.0866	−	28.6557i	0.423917	−	0.928249i	0.994275	−	0.106853i	$-0.0340773\pi$
$954$	23.3691	−	6.86178i	0.756602	−	0.222158i
$955$	9.75157	−	2.86332i	0.315553	−	0.0926548i
$956$	−2.14941	+	4.70656i	−0.0695170	+	0.152221i
$957$	−0.605992	−	4.21477i	−0.0195890	−	0.136244i
$958$	−7.75039	−	8.94442i	−0.250404	−	0.288981i
$959$	4.63673	+	10.1530i	0.149728	+	0.327858i
$960$	−0.343396	+	0.220687i	−0.0110831	+	0.00712264i
$961$	3.09761	−	21.5443i	0.0999228	−	0.694978i
$962$	−46.3653	−	29.7972i	−1.49488	−	0.960699i
$963$	19.0599	−	21.9962i	0.614195	−	0.708819i
$964$	4.84965	+	1.42399i	0.156197	+	0.0458635i
$965$	1.25736			0.0404760
$966$	2.59455	−	4.22037i	0.0834782	−	0.135788i
$967$	18.3112			0.588850			0.294425	−	0.955675i	$-0.404872\pi$
$967$	18.3112			0.588850			0.294425	+	0.955675i	$0.404872\pi$
$968$	−9.53427	−	2.79951i	−0.306443	−	0.0899798i
$969$	4.27827	−	4.93739i	0.137438	−	0.158612i
$970$	−1.49111	−	0.958280i	−0.0478767	−	0.0307685i
$971$	−4.16281	+	28.9530i	−0.133591	+	0.929146i	0.807229	+	0.590239i	$0.200966\pi$
$971$	−4.16281	+	28.9530i	−0.133591	+	0.929146i	−0.940820	+	0.338907i	$0.889943\pi$
$972$	8.59461	−	5.52342i	0.275672	−	0.177164i
$973$	−20.2972	−	44.4447i	−0.650699	−	1.42483i
$974$	17.2322	+	19.8870i	0.552155	+	0.637221i
$975$	−0.275810	−	1.91830i	−0.00883298	−	0.0614347i
$976$	0.913087	−	1.99938i	0.0292272	−	0.0639986i
$977$	−33.2983	+	9.77726i	−1.06531	+	0.312802i	−0.766986	−	0.641663i	$-0.778245\pi$
$977$	−33.2983	+	9.77726i	−1.06531	+	0.312802i	−0.298321	+	0.954466i	$0.596426\pi$
$978$	−6.78887	+	1.99339i	−0.217084	+	0.0637417i
$979$	−2.49874	+	5.47147i	−0.0798599	+	0.174869i
$980$	−0.0847873	−	0.589708i	−0.00270843	−	0.0188375i
$981$	8.44931	+	9.75102i	0.269766	+	0.311326i
$982$	−9.57160	−	20.9589i	−0.305442	−	0.668825i
$983$	35.9192	−	23.0839i	1.14565	−	0.736262i	0.176878	−	0.984233i	$-0.443400\pi$
$983$	35.9192	−	23.0839i	1.14565	−	0.736262i	0.968767	+	0.247971i	$0.0797638\pi$
$984$	−0.381083	+	2.65049i	−0.0121485	+	0.0844946i
$985$	17.9451	+	11.5326i	0.571778	+	0.367459i
$986$	−16.0774	+	18.5543i	−0.512009	+	0.590890i
$987$	−2.51020	−	0.737060i	−0.0799004	−	0.0234609i
$988$	−31.3122			−0.996173
$989$	−3.88050	−	3.22895i	−0.123393	−	0.102675i
$990$	2.92157			0.0928535
$991$	20.0149	+	5.87691i	0.635794	+	0.186686i	0.583717	−	0.811957i	$-0.301598\pi$
$991$	20.0149	+	5.87691i	0.635794	+	0.186686i	0.0520772	+	0.998643i	$0.483416\pi$
$992$	1.98997	−	2.29655i	0.0631816	−	0.0729155i
$993$	−8.44127	−	5.42488i	−0.267876	−	0.172153i
$994$	−1.21664	+	8.46190i	−0.0385894	+	0.268395i
$995$	−15.0977	+	9.70272i	−0.478630	+	0.307597i
$996$	−0.614107	−	1.34471i	−0.0194587	−	0.0426087i
$997$	−32.4585	−	37.4591i	−1.02797	−	1.18634i	−0.982287	−	0.187385i	$-0.939999\pi$
$997$	−32.4585	−	37.4591i	−1.02797	−	1.18634i	−0.0456836	−	0.998956i	$-0.514547\pi$
$998$	−5.19825	−	36.1546i	−0.164548	−	1.14446i
$999$	−11.4827	+	25.1437i	−0.363298	+	0.795511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.c.41.1	✓	20
23.3	even	11		5290.2.a.bg.1.6		10
23.9	even	11	inner	230.2.g.c.101.1	yes	20
23.20	odd	22		5290.2.a.bh.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.c.41.1	✓	20	1.1	even	1	trivial
230.2.g.c.101.1	yes	20	23.9	even	11	inner
5290.2.a.bg.1.6		10	23.3	even	11
5290.2.a.bh.1.6		10	23.20	odd	22

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(-0.267311 + 0.308493i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.343396 + 0.220687i) q^{6} +(1.05127 + 2.30197i) q^{7} +(0.654861 + 0.755750i) q^{8} +(0.403232 + 2.80454i) q^{9} +O(q^{10})\)	\(q+(0.959493 + 0.281733i) q^{2} +(-0.267311 + 0.308493i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.343396 + 0.220687i) q^{6} +(1.05127 + 2.30197i) q^{7} +(0.654861 + 0.755750i) q^{8} +(0.403232 + 2.80454i) q^{9} +(0.415415 - 0.909632i) q^{10} +(0.989357 - 0.290502i) q^{11} +(-0.391661 + 0.115002i) q^{12} +(1.97230 - 4.31874i) q^{13} +(0.360150 + 2.50490i) q^{14} +(0.267311 + 0.308493i) q^{15} +(0.415415 + 0.909632i) q^{16} +(2.04153 - 1.31201i) q^{17} +(-0.403232 + 2.80454i) q^{18} +(-5.54816 - 3.56559i) q^{19} +(0.654861 - 0.755750i) q^{20} +(-0.991159 - 0.291030i) q^{21} +1.03113 q^{22} +(0.0958668 + 4.79487i) q^{23} -0.408195 q^{24} +(-0.959493 - 0.281733i) q^{25} +(3.10914 - 3.58814i) q^{26} +(-2.00316 - 1.28735i) q^{27} +(-0.360150 + 2.50490i) q^{28} +(-8.51068 + 5.46948i) q^{29} +(0.169570 + 0.371308i) q^{30} +(-1.98997 - 2.29655i) q^{31} +(0.142315 + 0.989821i) q^{32} +(-0.174848 + 0.382865i) q^{33} +(2.32847 - 0.683702i) q^{34} +(2.42815 - 0.712969i) q^{35} +(-1.17703 + 2.57733i) q^{36} +(-1.65206 - 11.4903i) q^{37} +(-4.31888 - 4.98425i) q^{38} +(0.805085 + 1.76289i) q^{39} +(0.841254 - 0.540641i) q^{40} +(0.933580 - 6.49319i) q^{41} +(-0.869017 - 0.558483i) q^{42} +(-0.689322 + 0.795520i) q^{43} +(0.989357 + 0.290502i) q^{44} +2.83338 q^{45} +(-1.25889 + 4.62766i) q^{46} +2.53259 q^{47} +(-0.391661 - 0.115002i) q^{48} +(0.390148 - 0.450255i) q^{49} +(-0.841254 - 0.540641i) q^{50} +(-0.140977 + 0.980515i) q^{51} +(3.99409 - 2.56685i) q^{52} +(-3.57090 - 7.81918i) q^{53} +(-1.55933 - 1.79956i) q^{54} +(-0.146744 - 1.02063i) q^{55} +(-1.05127 + 2.30197i) q^{56} +(2.58304 - 0.758450i) q^{57} +(-9.70687 + 2.85019i) q^{58} +(-4.89813 + 10.7254i) q^{59} +(0.0580923 + 0.404041i) q^{60} +(-1.43939 - 1.66115i) q^{61} +(-1.26235 - 2.76416i) q^{62} +(-6.03204 + 3.87656i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-3.99409 - 2.56685i) q^{65} +(-0.275631 + 0.318095i) q^{66} +(9.47782 + 2.78294i) q^{67} +2.42677 q^{68} +(-1.50481 - 1.25215i) q^{69} +2.53066 q^{70} +(3.24130 + 0.951732i) q^{71} +(-1.85547 + 2.14132i) q^{72} +(12.4083 + 7.97436i) q^{73} +(1.65206 - 11.4903i) q^{74} +(0.343396 - 0.220687i) q^{75} +(-2.73971 - 5.99912i) q^{76} +(1.70881 + 1.97207i) q^{77} +(0.275810 + 1.91830i) q^{78} +(-1.79491 + 3.93030i) q^{79} +(0.959493 - 0.281733i) q^{80} +(-7.22321 + 2.12093i) q^{81} +(2.72511 - 5.96715i) q^{82} +(0.515400 + 3.58468i) q^{83} +(-0.676473 - 0.780691i) q^{84} +(-1.00812 - 2.20747i) q^{85} +(-0.885523 + 0.569091i) q^{86} +(0.587700 - 4.08754i) q^{87} +(0.867438 + 0.557468i) q^{88} +(-3.82011 + 4.40864i) q^{89} +(2.71860 + 0.798254i) q^{90} +12.0150 q^{91} +(-2.51166 + 4.08553i) q^{92} +1.24041 q^{93} +(2.43000 + 0.713512i) q^{94} +(-4.31888 + 4.98425i) q^{95} +(-0.343396 - 0.220687i) q^{96} +(0.252252 - 1.75445i) q^{97} +(0.501196 - 0.322099i) q^{98} +(1.21366 + 2.65755i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{5} - q^{6} - 12 q^{7} + 2 q^{8} + 17 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + q^3 - 2 * q^4 + 2 * q^5 - q^6 - 12 * q^7 + 2 * q^8 + 17 * q^9	\( 20 q + 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{5} - q^{6} - 12 q^{7} + 2 q^{8} + 17 q^{9} - 2 q^{10} - 3 q^{11} + q^{12} - 18 q^{13} + q^{14} - q^{15} - 2 q^{16} + 14 q^{17} - 17 q^{18} - 7 q^{19} + 2 q^{20} - 43 q^{21} - 8 q^{22} + 9 q^{23} + 10 q^{24} - 2 q^{25} - 4 q^{26} + 10 q^{27} - q^{28} - 28 q^{29} + q^{30} - 7 q^{31} + 2 q^{32} + 35 q^{33} - 3 q^{34} - 10 q^{35} - 27 q^{36} + 30 q^{37} + 40 q^{38} + 69 q^{39} - 2 q^{40} - 2 q^{41} + 10 q^{42} - 26 q^{43} - 3 q^{44} - 6 q^{45} + 2 q^{46} - 26 q^{47} + q^{48} - 8 q^{49} + 2 q^{50} + 20 q^{51} + 15 q^{52} - q^{53} + 23 q^{54} + 3 q^{55} + 12 q^{56} + 3 q^{57} - 27 q^{58} - 48 q^{59} - q^{60} - 7 q^{61} - 26 q^{62} + 8 q^{63} - 2 q^{64} - 15 q^{65} + 20 q^{66} + 7 q^{67} - 8 q^{68} + 12 q^{69} + 10 q^{70} + 19 q^{71} - 17 q^{72} + 2 q^{73} - 30 q^{74} + q^{75} - 7 q^{76} - 34 q^{77} - 14 q^{78} - 49 q^{79} + 2 q^{80} - 56 q^{81} - 31 q^{82} + 23 q^{83} + 12 q^{84} + 8 q^{85} + 37 q^{86} - 31 q^{87} + 14 q^{88} + 43 q^{89} - 5 q^{90} + 128 q^{91} - 13 q^{92} - 50 q^{93} - 7 q^{94} + 40 q^{95} - q^{96} - 7 q^{97} - 36 q^{98} - 85 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + q^3 - 2 * q^4 + 2 * q^5 - q^6 - 12 * q^7 + 2 * q^8 + 17 * q^9 - 2 * q^10 - 3 * q^11 + q^12 - 18 * q^13 + q^14 - q^15 - 2 * q^16 + 14 * q^17 - 17 * q^18 - 7 * q^19 + 2 * q^20 - 43 * q^21 - 8 * q^22 + 9 * q^23 + 10 * q^24 - 2 * q^25 - 4 * q^26 + 10 * q^27 - q^28 - 28 * q^29 + q^30 - 7 * q^31 + 2 * q^32 + 35 * q^33 - 3 * q^34 - 10 * q^35 - 27 * q^36 + 30 * q^37 + 40 * q^38 + 69 * q^39 - 2 * q^40 - 2 * q^41 + 10 * q^42 - 26 * q^43 - 3 * q^44 - 6 * q^45 + 2 * q^46 - 26 * q^47 + q^48 - 8 * q^49 + 2 * q^50 + 20 * q^51 + 15 * q^52 - q^53 + 23 * q^54 + 3 * q^55 + 12 * q^56 + 3 * q^57 - 27 * q^58 - 48 * q^59 - q^60 - 7 * q^61 - 26 * q^62 + 8 * q^63 - 2 * q^64 - 15 * q^65 + 20 * q^66 + 7 * q^67 - 8 * q^68 + 12 * q^69 + 10 * q^70 + 19 * q^71 - 17 * q^72 + 2 * q^73 - 30 * q^74 + q^75 - 7 * q^76 - 34 * q^77 - 14 * q^78 - 49 * q^79 + 2 * q^80 - 56 * q^81 - 31 * q^82 + 23 * q^83 + 12 * q^84 + 8 * q^85 + 37 * q^86 - 31 * q^87 + 14 * q^88 + 43 * q^89 - 5 * q^90 + 128 * q^91 - 13 * q^92 - 50 * q^93 - 7 * q^94 + 40 * q^95 - q^96 - 7 * q^97 - 36 * q^98 - 85 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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