LMFDB - Embedded newform 62.2.g.a.45.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(7,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([28]))

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

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

chi := DirichletCharacter("62.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.495072492532$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			45.1
Root			$-0.978148 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	62.45
Dual form			62.2.g.a.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.413545 + 0.459289i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.78716 - 3.09546i) q^{5} +(0.309017 + 0.535233i) q^{6} +(-0.309017 + 2.94010i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.273659 + 2.60369i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.413545 + 0.459289i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.78716 - 3.09546i) q^{5} +(0.309017 + 0.535233i) q^{6} +(-0.309017 + 2.94010i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.273659 + 2.60369i) q^{9} +(-2.39169 - 2.65624i) q^{10} +(-2.16913 + 0.965759i) q^{11} +(0.604528 - 0.128496i) q^{12} +(-5.53062 - 1.17557i) q^{13} +(2.70071 + 1.20243i) q^{14} +(0.682636 + 2.10094i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.83399 + 1.26178i) q^{17} +(2.56082 + 0.544320i) q^{18} +(4.92610 - 1.04707i) q^{19} +(-3.26531 + 1.45381i) q^{20} +(-1.22256 - 1.35779i) q^{21} +(0.248193 + 2.36140i) q^{22} +(1.13377 - 0.823734i) q^{23} +(0.0646021 - 0.614648i) q^{24} +(-3.88791 - 6.73407i) q^{25} +(-2.82709 + 4.89667i) q^{26} +(-2.80902 - 2.04087i) q^{27} +(1.97815 - 2.19696i) q^{28} +(1.07120 - 3.29683i) q^{29} +2.20906 q^{30} +(-4.84421 - 2.74475i) q^{31} +1.00000 q^{32} +(0.453472 - 1.39564i) q^{33} +(2.07577 - 2.30538i) q^{34} +(8.54870 + 6.21099i) q^{35} +(1.30902 - 2.26728i) q^{36} +(-0.0938464 - 0.162547i) q^{37} +(0.526421 - 5.00856i) q^{38} +(2.82709 - 2.05400i) q^{39} +(0.373619 + 3.55475i) q^{40} +(1.60814 + 1.78602i) q^{41} +(-1.66913 + 0.743145i) q^{42} +(-11.0314 + 2.34480i) q^{43} +(2.32252 + 0.493667i) q^{44} +(8.54870 + 3.80613i) q^{45} +(-0.433063 - 1.33283i) q^{46} +(-0.00456840 - 0.0140601i) q^{47} +(-0.564602 - 0.251377i) q^{48} +(-1.70167 - 0.361700i) q^{49} +(-7.60591 + 1.61669i) q^{50} +(-1.75150 + 0.779820i) q^{51} +(3.78339 + 4.20188i) q^{52} +(-0.425506 - 4.04842i) q^{53} +(-2.80902 + 2.04087i) q^{54} +(-0.887125 + 8.44043i) q^{55} +(-1.47815 - 2.56023i) q^{56} +(-1.55626 + 2.69551i) q^{57} +(-2.80445 - 2.03755i) q^{58} +(5.00867 - 5.56269i) q^{59} +(0.682636 - 2.10094i) q^{60} +13.3669 q^{61} +(-4.10735 + 3.75894i) q^{62} -7.73968 q^{63} +(0.309017 - 0.951057i) q^{64} +(-13.5231 + 15.0189i) q^{65} +(-1.18720 - 0.862555i) q^{66} +(-1.40977 + 2.44179i) q^{67} +(-1.55110 - 2.68658i) q^{68} +(-0.0905347 + 0.861381i) q^{69} +(8.54870 - 6.21099i) q^{70} +(-0.911312 - 8.67056i) q^{71} +(-1.75181 - 1.94558i) q^{72} +(-7.19003 + 3.20121i) q^{73} +(-0.183591 + 0.0390235i) q^{74} +(4.70071 + 0.999167i) q^{75} +(-4.60075 - 2.04839i) q^{76} +(-2.16913 - 6.67590i) q^{77} +(-1.07985 - 3.32344i) q^{78} +(6.18024 + 2.75162i) q^{79} +(3.49622 + 0.743145i) q^{80} +(-5.58347 + 1.18680i) q^{81} +(2.19555 - 0.977522i) q^{82} +(10.3053 + 11.4452i) q^{83} +(0.190983 + 1.81708i) q^{84} +(8.97059 - 6.51752i) q^{85} +(-1.17886 + 11.2161i) q^{86} +(1.07120 + 1.85538i) q^{87} +(1.18720 - 2.05630i) q^{88} +(1.34437 + 0.976746i) q^{89} +(6.26153 - 6.95414i) q^{90} +(5.16535 - 15.8973i) q^{91} -1.40142 q^{92} +(3.26393 - 1.08981i) q^{93} -0.0147836 q^{94} +(5.56257 - 17.1198i) q^{95} +(-0.413545 + 0.459289i) q^{96} +(5.76515 + 4.18862i) q^{97} +(-0.869841 + 1.50661i) q^{98} +(-3.10814 - 5.38346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9} - 4 q^{10} - 13 q^{11} + 3 q^{12} + 2 q^{14} - 6 q^{15} - 2 q^{16} - 2 q^{17} + q^{18} - 3 q^{19} - 4 q^{20} + q^{21} + 17 q^{22} + 3 q^{23} - 2 q^{24} + q^{25} - 10 q^{26} - 18 q^{27} + 7 q^{28} + 11 q^{29} + 14 q^{30} + 11 q^{31} + 8 q^{32} - 2 q^{33} + 18 q^{34} + 16 q^{35} + 6 q^{36} + 6 q^{37} + 12 q^{38} + 10 q^{39} - 4 q^{40} - 19 q^{41} - 9 q^{42} - 26 q^{43} + 7 q^{44} + 16 q^{45} - 17 q^{46} + q^{47} - 2 q^{48} - 23 q^{49} - 19 q^{50} - 16 q^{51} + 17 q^{53} - 18 q^{54} + 7 q^{55} - 3 q^{56} + 6 q^{57} - 19 q^{58} + 8 q^{59} - 6 q^{60} + 48 q^{61} - 19 q^{62} - 14 q^{63} - 2 q^{64} - 30 q^{65} + 3 q^{66} + 12 q^{67} - 17 q^{68} - 7 q^{69} + 16 q^{70} + 9 q^{71} + q^{72} - 33 q^{73} - 19 q^{74} + 18 q^{75} - 18 q^{76} - 13 q^{77} - 10 q^{78} - 19 q^{79} + 11 q^{80} - 16 q^{81} + 21 q^{82} + 40 q^{83} + 6 q^{84} + 29 q^{85} + 19 q^{86} + 11 q^{87} - 3 q^{88} + 8 q^{89} + 11 q^{90} + 20 q^{91} + 28 q^{92} + 44 q^{93} + 26 q^{94} + 36 q^{95} + 3 q^{96} - 23 q^{97} + 17 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9 - 4 * q^10 - 13 * q^11 + 3 * q^12 + 2 * q^14 - 6 * q^15 - 2 * q^16 - 2 * q^17 + q^18 - 3 * q^19 - 4 * q^20 + q^21 + 17 * q^22 + 3 * q^23 - 2 * q^24 + q^25 - 10 * q^26 - 18 * q^27 + 7 * q^28 + 11 * q^29 + 14 * q^30 + 11 * q^31 + 8 * q^32 - 2 * q^33 + 18 * q^34 + 16 * q^35 + 6 * q^36 + 6 * q^37 + 12 * q^38 + 10 * q^39 - 4 * q^40 - 19 * q^41 - 9 * q^42 - 26 * q^43 + 7 * q^44 + 16 * q^45 - 17 * q^46 + q^47 - 2 * q^48 - 23 * q^49 - 19 * q^50 - 16 * q^51 + 17 * q^53 - 18 * q^54 + 7 * q^55 - 3 * q^56 + 6 * q^57 - 19 * q^58 + 8 * q^59 - 6 * q^60 + 48 * q^61 - 19 * q^62 - 14 * q^63 - 2 * q^64 - 30 * q^65 + 3 * q^66 + 12 * q^67 - 17 * q^68 - 7 * q^69 + 16 * q^70 + 9 * q^71 + q^72 - 33 * q^73 - 19 * q^74 + 18 * q^75 - 18 * q^76 - 13 * q^77 - 10 * q^78 - 19 * q^79 + 11 * q^80 - 16 * q^81 + 21 * q^82 + 40 * q^83 + 6 * q^84 + 29 * q^85 + 19 * q^86 + 11 * q^87 - 3 * q^88 + 8 * q^89 + 11 * q^90 + 20 * q^91 + 28 * q^92 + 44 * q^93 + 26 * q^94 + 36 * q^95 + 3 * q^96 - 23 * q^97 + 17 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.413545	+	0.459289i	−0.238761	+	0.265170i	−0.850602	−	0.525810i	$-0.823762\pi$
$3$	−0.413545	+	0.459289i	−0.238761	+	0.265170i	0.611842	+	0.790980i	$0.290429\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	1.78716	−	3.09546i	0.799244	−	1.38433i	−0.120865	−	0.992669i	$-0.538567\pi$
$5$	1.78716	−	3.09546i	0.799244	−	1.38433i	0.920109	−	0.391663i	$-0.128100\pi$
$6$	0.309017	+	0.535233i	0.126156	+	0.218508i
$7$	−0.309017	+	2.94010i	−0.116797	+	1.11125i	0.766436	+	0.642320i	$0.222028\pi$
$7$	−0.309017	+	2.94010i	−0.116797	+	1.11125i	−0.883234	+	0.468933i	$0.844639\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.273659	+	2.60369i	0.0912197	+	0.867897i
$10$	−2.39169	−	2.65624i	−0.756320	−	0.839978i
$11$	−2.16913	+	0.965759i	−0.654017	+	0.291187i	−0.706794	−	0.707419i	$-0.749859\pi$
$11$	−2.16913	+	0.965759i	−0.654017	+	0.291187i	0.0527770	+	0.998606i	$0.483193\pi$
$12$	0.604528	−	0.128496i	0.174512	−	0.0370937i
$13$	−5.53062	−	1.17557i	−1.53392	−	0.326045i	−0.637921	−	0.770102i	$-0.720205\pi$
$13$	−5.53062	−	1.17557i	−1.53392	−	0.326045i	−0.895998	+	0.444057i	$0.853539\pi$
$14$	2.70071	+	1.20243i	0.721795	+	0.321364i
$15$	0.682636	+	2.10094i	0.176256	+	0.542460i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.83399	+	1.26178i	0.687345	+	0.306026i	0.720530	−	0.693424i	$-0.243899\pi$
$17$	2.83399	+	1.26178i	0.687345	+	0.306026i	−0.0331855	+	0.999449i	$0.510565\pi$
$18$	2.56082	+	0.544320i	0.603592	+	0.128297i
$19$	4.92610	−	1.04707i	1.13012	−	0.240215i	0.395352	−	0.918530i	$-0.370623\pi$
$19$	4.92610	−	1.04707i	1.13012	−	0.240215i	0.734772	+	0.678314i	$0.237289\pi$
$20$	−3.26531	+	1.45381i	−0.730146	+	0.325082i
$21$	−1.22256	−	1.35779i	−0.266785	−	0.296295i
$22$	0.248193	+	2.36140i	0.0529150	+	0.503453i
$23$	1.13377	−	0.823734i	0.236408	−	0.171760i	−0.463274	−	0.886215i	$-0.653325\pi$
$23$	1.13377	−	0.823734i	0.236408	−	0.171760i	0.699681	+	0.714455i	$0.253325\pi$
$24$	0.0646021	−	0.614648i	0.0131869	−	0.125465i
$25$	−3.88791	−	6.73407i	−0.777583	−	1.34681i
$26$	−2.82709	+	4.89667i	−0.554438	+	0.960315i
$27$	−2.80902	−	2.04087i	−0.540596	−	0.392766i
$28$	1.97815	−	2.19696i	0.373835	−	0.415186i
$29$	1.07120	−	3.29683i	0.198918	−	0.612205i	−0.800991	−	0.598677i	$-0.795693\pi$
$29$	1.07120	−	3.29683i	0.198918	−	0.612205i	0.999908	−	0.0135289i	$-0.00430650\pi$
$30$	2.20906			0.403317
$31$	−4.84421	−	2.74475i	−0.870046	−	0.492971i
$31$	−4.84421	−	2.74475i	−0.870046	−	0.492971i
$32$	1.00000			0.176777
$33$	0.453472	−	1.39564i	0.0789393	−	0.242950i
$34$	2.07577	−	2.30538i	0.355992	−	0.395369i
$35$	8.54870	+	6.21099i	1.44499	+	1.04985i
$36$	1.30902	−	2.26728i	0.218169	−	0.377881i
$37$	−0.0938464	−	0.162547i	−0.0154282	−	0.0267225i	0.858208	−	0.513302i	$-0.171578\pi$
$37$	−0.0938464	−	0.162547i	−0.0154282	−	0.0267225i	−0.873636	+	0.486579i	$0.838244\pi$
$38$	0.526421	−	5.00856i	0.0853967	−	0.812496i
$39$	2.82709	−	2.05400i	0.452697	−	0.328904i
$40$	0.373619	+	3.55475i	0.0590744	+	0.562055i
$41$	1.60814	+	1.78602i	0.251150	+	0.278930i	0.855516	−	0.517777i	$-0.173240\pi$
$41$	1.60814	+	1.78602i	0.251150	+	0.278930i	−0.604366	+	0.796707i	$0.706574\pi$
$42$	−1.66913	+	0.743145i	−0.257552	+	0.114670i
$43$	−11.0314	+	2.34480i	−1.68227	+	0.357579i	−0.947258	−	0.320471i	$-0.896159\pi$
$43$	−11.0314	+	2.34480i	−1.68227	+	0.357579i	−0.735016	+	0.678049i	$0.762826\pi$
$44$	2.32252	+	0.493667i	0.350133	+	0.0744232i
$45$	8.54870	+	3.80613i	1.27436	+	0.567384i
$46$	−0.433063	−	1.33283i	−0.0638516	−	0.196515i
$47$	−0.00456840	−	0.0140601i	−0.000666369	−	0.00205087i	0.950723	−	0.310042i	$-0.100343\pi$
$47$	−0.00456840	−	0.0140601i	−0.000666369	−	0.00205087i	−0.951389	+	0.307991i	$0.900343\pi$
$48$	−0.564602	−	0.251377i	−0.0814933	−	0.0362832i
$49$	−1.70167	−	0.361700i	−0.243095	−	0.0516714i
$50$	−7.60591	+	1.61669i	−1.07564	+	0.228634i
$51$	−1.75150	+	0.779820i	−0.245260	+	0.109197i
$52$	3.78339	+	4.20188i	0.524661	+	0.582695i
$53$	−0.425506	−	4.04842i	−0.0584477	−	0.556093i	−0.984087	−	0.177686i	$-0.943139\pi$
$53$	−0.425506	−	4.04842i	−0.0584477	−	0.556093i	0.925640	−	0.378407i	$-0.123528\pi$
$54$	−2.80902	+	2.04087i	−0.382259	+	0.277727i
$55$	−0.887125	+	8.44043i	−0.119620	+	1.13811i
$56$	−1.47815	−	2.56023i	−0.197526	−	0.342125i
$57$	−1.55626	+	2.69551i	−0.206131	+	0.357029i
$58$	−2.80445	−	2.03755i	−0.368242	−	0.267544i
$59$	5.00867	−	5.56269i	0.652073	−	0.724201i	−0.322922	−	0.946426i	$-0.604665\pi$
$59$	5.00867	−	5.56269i	0.652073	−	0.724201i	0.974995	+	0.222225i	$0.0713319\pi$
$60$	0.682636	−	2.10094i	0.0881279	−	0.271230i
$61$	13.3669			1.71145			0.855725	−	0.517431i	$-0.173112\pi$
$61$	13.3669			1.71145			0.855725	+	0.517431i	$0.173112\pi$
$62$	−4.10735	+	3.75894i	−0.521634	+	0.477386i
$63$	−7.73968			−0.975108
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−13.5231	+	15.0189i	−1.67733	+	1.86286i
$66$	−1.18720	−	0.862555i	−0.146135	−	0.106173i
$67$	−1.40977	+	2.44179i	−0.172230	+	0.298312i	−0.939199	−	0.343372i	$-0.888431\pi$
$67$	−1.40977	+	2.44179i	−0.172230	+	0.298312i	0.766969	+	0.641684i	$0.221764\pi$
$68$	−1.55110	−	2.68658i	−0.188098	−	0.325795i
$69$	−0.0905347	+	0.861381i	−0.0108991	+	0.103698i
$70$	8.54870	−	6.21099i	1.02176	−	0.742356i
$71$	−0.911312	−	8.67056i	−0.108153	−	1.02901i	−0.905170	−	0.425049i	$-0.860257\pi$
$71$	−0.911312	−	8.67056i	−0.108153	−	1.02901i	0.797017	−	0.603956i	$-0.206410\pi$
$72$	−1.75181	−	1.94558i	−0.206452	−	0.229289i
$73$	−7.19003	+	3.20121i	−0.841529	+	0.374673i	−0.781791	−	0.623541i	$-0.785693\pi$
$73$	−7.19003	+	3.20121i	−0.841529	+	0.374673i	−0.0597386	+	0.998214i	$0.519027\pi$
$74$	−0.183591	+	0.0390235i	−0.0213420	+	0.00453639i
$75$	4.70071	+	0.999167i	0.542791	+	0.115374i
$76$	−4.60075	−	2.04839i	−0.527742	−	0.234966i
$77$	−2.16913	−	6.67590i	−0.247195	−	0.760789i
$78$	−1.07985	−	3.32344i	−0.122269	−	0.376306i
$79$	6.18024	+	2.75162i	0.695331	+	0.309581i	0.723797	−	0.690013i	$-0.242395\pi$
$79$	6.18024	+	2.75162i	0.695331	+	0.309581i	−0.0284655	+	0.999595i	$0.509062\pi$
$80$	3.49622	+	0.743145i	0.390889	+	0.0830861i
$81$	−5.58347	+	1.18680i	−0.620385	+	0.131867i
$82$	2.19555	−	0.977522i	0.242458	−	0.107949i
$83$	10.3053	+	11.4452i	1.13116	+	1.25628i	0.962700	+	0.270569i	$0.0872120\pi$
$83$	10.3053	+	11.4452i	1.13116	+	1.25628i	0.168458	+	0.985709i	$0.446121\pi$
$84$	0.190983	+	1.81708i	0.0208380	+	0.198260i
$85$	8.97059	−	6.51752i	0.972997	−	0.706924i
$86$	−1.17886	+	11.2161i	−0.127119	+	1.20946i
$87$	1.07120	+	1.85538i	0.114845	+	0.198918i
$88$	1.18720	−	2.05630i	0.126556	−	0.219202i
$89$	1.34437	+	0.976746i	0.142503	+	0.103535i	0.656753	−	0.754106i	$-0.271929\pi$
$89$	1.34437	+	0.976746i	0.142503	+	0.103535i	−0.514249	+	0.857641i	$0.671929\pi$
$90$	6.26153	−	6.95414i	0.660024	−	0.733030i
$91$	5.16535	−	15.8973i	0.541476	−	1.66649i
$92$	−1.40142			−0.146108
$93$	3.26393	−	1.08981i	0.338454	−	0.113008i
$94$	−0.0147836			−0.00152482
$95$	5.56257	−	17.1198i	0.570708	−	1.75646i
$96$	−0.413545	+	0.459289i	−0.0422073	+	0.0468760i
$97$	5.76515	+	4.18862i	0.585362	+	0.425290i	0.840653	−	0.541574i	$-0.182171\pi$
$97$	5.76515	+	4.18862i	0.585362	+	0.425290i	−0.255291	+	0.966864i	$0.582171\pi$
$98$	−0.869841	+	1.50661i	−0.0878672	+	0.152190i
$99$	−3.10814	−	5.38346i	−0.312380	−	0.541058i
$100$	−0.812795	+	7.73323i	−0.0812795	+	0.773323i
$101$	−1.00739	+	0.731913i	−0.100239	+	0.0728281i	−0.636776	−	0.771049i	$-0.719732\pi$
$101$	−1.00739	+	0.731913i	−0.100239	+	0.0728281i	0.536537	+	0.843877i	$0.319732\pi$
$102$	0.200408	+	1.90676i	0.0198434	+	0.188797i
$103$	−2.45695	−	2.72872i	−0.242090	−	0.268869i	0.609839	−	0.792525i	$-0.291234\pi$
$103$	−2.45695	−	2.72872i	−0.242090	−	0.268869i	−0.851929	+	0.523657i	$0.824567\pi$
$104$	5.16535	−	2.29976i	0.506504	−	0.225510i
$105$	−6.38791	+	1.35779i	−0.623397	+	0.132507i
$106$	−3.98176	−	0.846349i	−0.386743	−	0.0822047i
$107$	−16.6712	−	7.42251i	−1.61167	−	0.717561i	−0.614233	−	0.789124i	$-0.710535\pi$
$107$	−16.6712	−	7.42251i	−1.61167	−	0.717561i	−0.997436	+	0.0715631i	$0.977201\pi$
$108$	1.07295	+	3.30220i	0.103245	+	0.317754i
$109$	6.20780	+	19.1056i	0.594599	+	1.82999i	0.556710	+	0.830707i	$0.312063\pi$
$109$	6.20780	+	19.1056i	0.594599	+	1.82999i	0.0378894	+	0.999282i	$0.487937\pi$
$110$	7.75319	+	3.45194i	0.739237	+	0.329130i
$111$	0.113466	+	0.0241179i	0.0107697	+	0.00228917i
$112$	−2.89169	+	0.614648i	−0.273239	+	0.0580788i
$113$	−7.48038	+	3.33048i	−0.703695	+	0.313305i	−0.727207	−	0.686418i	$-0.759182\pi$
$113$	−7.48038	+	3.33048i	−0.703695	+	0.313305i	0.0235119	+	0.999724i	$0.492515\pi$
$114$	2.08268	+	2.31305i	0.195060	+	0.216637i
$115$	−0.523597	−	4.98170i	−0.0488257	−	0.464546i
$116$	−2.80445	+	2.03755i	−0.260387	+	0.189182i
$117$	1.54732	−	14.7217i	0.143050	−	1.36103i
$118$	−3.74267	−	6.48249i	−0.344541	−	0.596762i
$119$	−4.58550	+	7.94232i	−0.420352	+	0.728071i
$120$	−1.78716	−	1.29845i	−0.163145	−	0.118532i
$121$	−3.58800	+	3.98488i	−0.326182	+	0.362262i
$122$	4.13058	−	12.7126i	0.373966	−	1.15095i
$123$	−1.48534			−0.133929
$124$	2.30573	+	5.06790i	0.207060	+	0.455111i
$125$	−9.92173			−0.887426
$126$	−2.39169	+	7.36087i	−0.213069	+	0.655759i
$127$	−1.28170	+	1.42348i	−0.113733	+	0.126313i	−0.797323	−	0.603553i	$-0.793751\pi$
$127$	−1.28170	+	1.42348i	−0.113733	+	0.126313i	0.683590	+	0.729866i	$0.260418\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	3.48505	−	6.03629i	0.306842	−	0.531465i
$130$	10.1050	+	17.5023i	0.886263	+	1.53505i
$131$	0.920835	−	8.76116i	0.0804537	−	0.765466i	−0.877700	−	0.479211i	$-0.840923\pi$
$131$	0.920835	−	8.76116i	0.0804537	−	0.765466i	0.958153	−	0.286255i	$-0.0924105\pi$
$132$	−1.18720	+	0.862555i	−0.103333	+	0.0750757i
$133$	1.55626	+	14.8068i	0.134944	+	1.28391i
$134$	1.88664	+	2.09532i	0.162981	+	0.181008i
$135$	−11.3376	+	5.04783i	−0.975786	+	0.434448i
$136$	−3.03440	+	0.644982i	−0.260198	+	0.0553068i
$137$	11.4478	+	2.43330i	0.978050	+	0.207891i	0.669088	−	0.743183i	$-0.266685\pi$
$137$	11.4478	+	2.43330i	0.978050	+	0.207891i	0.308962	+	0.951074i	$0.400018\pi$
$138$	0.791245	+	0.352285i	0.0673552	+	0.0299885i
$139$	2.72461	+	8.38548i	0.231098	+	0.711248i	0.997615	+	0.0690232i	$0.0219882\pi$
$139$	2.72461	+	8.38548i	0.231098	+	0.711248i	−0.766517	+	0.642224i	$0.778012\pi$
$140$	−3.26531	−	10.0496i	−0.275969	−	0.849346i
$141$	0.00834687	+	0.00371627i	0.000702934	+	0.000312966i
$142$	−8.52780	−	1.81264i	−0.715637	−	0.152113i
$143$	13.1320	−	2.79129i	1.09815	−	0.233419i
$144$	−2.39169	+	1.06485i	−0.199308	+	0.0887375i
$145$	−8.29078	−	9.20784i	−0.688512	−	0.764670i
$146$	0.822688	+	7.82735i	0.0680861	+	0.647796i
$147$	0.869841	−	0.631976i	0.0717432	−	0.0521245i
$148$	−0.0196192	+	0.186665i	−0.00161269	+	0.0153437i
$149$	−3.73501	−	6.46923i	−0.305984	−	0.529980i	0.671496	−	0.741008i	$-0.265652\pi$
$149$	−3.73501	−	6.46923i	−0.305984	−	0.529980i	−0.977480	+	0.211028i	$0.932319\pi$
$150$	2.40286	−	4.16188i	0.196193	−	0.339816i
$151$	1.43822	+	1.04493i	0.117041	+	0.0850351i	0.644766	−	0.764380i	$-0.276955\pi$
$151$	1.43822	+	1.04493i	0.117041	+	0.0850351i	−0.527725	+	0.849415i	$0.676955\pi$
$152$	−3.36984	+	3.74259i	−0.273330	+	0.303564i
$153$	−2.50973	+	7.72415i	−0.202899	+	0.624460i
$154$	−7.01945			−0.565644
$155$	−17.1537	+	10.0897i	−1.37781	+	0.810428i
$156$	−3.49448			−0.279782
$157$	2.92658	−	9.00710i	0.233567	−	0.718845i	−0.763741	−	0.645522i	$-0.776640\pi$
$157$	2.92658	−	9.00710i	0.233567	−	0.718845i	0.997308	−	0.0733225i	$-0.0233603\pi$
$158$	4.52674	−	5.02746i	0.360128	−	0.399963i
$159$	2.03536	+	1.47877i	0.161414	+	0.117274i
$160$	1.78716	−	3.09546i	0.141288	−	0.244718i
$161$	2.07151	+	3.58795i	0.163258	+	0.282770i
$162$	−0.596670	+	5.67693i	−0.0468788	+	0.446022i
$163$	−6.22601	+	4.52346i	−0.487659	+	0.354305i	−0.804283	−	0.594246i	$-0.797451\pi$
$163$	−6.22601	+	4.52346i	−0.487659	+	0.354305i	0.316624	+	0.948551i	$0.397451\pi$
$164$	−0.251216	−	2.39016i	−0.0196167	−	0.186640i
$165$	−3.50973	−	3.89795i	−0.273232	−	0.303455i
$166$	14.0696	−	6.26419i	1.09201	−	0.486195i
$167$	20.8947	−	4.44130i	1.61688	−	0.343678i	0.691397	−	0.722475i	$-0.256996\pi$
$167$	20.8947	−	4.44130i	1.61688	−	0.343678i	0.925480	+	0.378797i	$0.123662\pi$
$168$	1.78716	+	0.379874i	0.137883	+	0.0293079i
$169$	17.3297	+	7.71570i	1.33306	+	0.593515i
$170$	−3.42646	−	10.5456i	−0.262798	−	0.808808i
$171$	4.07433	+	12.5395i	0.311572	+	0.958919i
$172$	10.3028	+	4.58712i	0.785584	+	0.349765i
$173$	−5.40997	−	1.14992i	−0.411312	−	0.0874271i	−0.00239172	−	0.999997i	$-0.500761\pi$
$173$	−5.40997	−	1.14992i	−0.411312	−	0.0874271i	−0.408920	+	0.912570i	$0.634095\pi$
$174$	2.09559	−	0.445432i	0.158866	−	0.0337681i
$175$	21.0003	−	9.34992i	1.58747	−	0.706787i
$176$	−1.58879	−	1.76453i	−0.119760	−	0.133006i
$177$	0.483569	+	4.60085i	0.0363473	+	0.345821i
$178$	1.34437	−	0.976746i	0.100765	−	0.0732102i
$179$	1.51807	−	14.4435i	0.113466	−	1.07956i	−0.778559	−	0.627572i	$-0.784049\pi$
$179$	1.51807	−	14.4435i	0.113466	−	1.07956i	0.892025	−	0.451987i	$-0.149285\pi$
$180$	−4.67886	−	8.10402i	−0.348741	−	0.604038i
$181$	−4.59161	+	7.95291i	−0.341292	+	0.591135i	−0.984673	−	0.174411i	$-0.944198\pi$
$181$	−4.59161	+	7.95291i	−0.341292	+	0.591135i	0.643381	+	0.765546i	$0.277531\pi$
$182$	−13.5231	−	9.82508i	−1.00240	−	0.728284i
$183$	−5.52780	+	6.13924i	−0.408627	+	0.453826i
$184$	−0.433063	+	1.33283i	−0.0319258	+	0.0982575i
$185$	−0.670876			−0.0493238
$186$	−0.0278640	−	3.44095i	−0.00204309	−	0.252303i
$187$	−7.36588			−0.538646
$188$	−0.00456840	+	0.0140601i	−0.000333184	+	0.00102544i
$189$	6.86840	−	7.62813i	0.499602	−	0.554865i
$190$	−14.5630	−	10.5806i	−1.05651	−	0.767600i
$191$	5.31700	−	9.20931i	0.384725	−	0.666362i	−0.607006	−	0.794697i	$-0.707630\pi$
$191$	5.31700	−	9.20931i	0.384725	−	0.666362i	0.991731	+	0.128334i	$0.0409631\pi$
$192$	0.309017	+	0.535233i	0.0223014	+	0.0386271i
$193$	0.241757	−	2.30016i	0.0174020	−	0.165569i	−0.982369	−	0.186950i	$-0.940140\pi$
$193$	0.241757	−	2.30016i	0.0174020	−	0.165569i	0.999771	+	0.0213811i	$0.00680634\pi$
$194$	5.76515	−	4.18862i	0.413913	−	0.300726i
$195$	−1.30560	−	12.4220i	−0.0934962	−	0.889557i
$196$	1.16407	+	1.29284i	0.0831481	+	0.0923454i
$197$	−2.77737	+	1.23657i	−0.197880	+	0.0881017i	−0.503284	−	0.864121i	$-0.667875\pi$
$197$	−2.77737	+	1.23657i	−0.197880	+	0.0881017i	0.305404	+	0.952223i	$0.401208\pi$
$198$	−6.08044	+	1.29244i	−0.432118	+	0.0918496i
$199$	−18.9024	−	4.01784i	−1.33996	−	0.284817i	−0.518496	−	0.855080i	$-0.673508\pi$
$199$	−18.9024	−	4.01784i	−1.33996	−	0.284817i	−0.821462	+	0.570263i	$0.806841\pi$
$200$	7.10357	+	3.16271i	0.502298	+	0.223638i
$201$	−0.538483	−	1.65728i	−0.0379817	−	0.116896i
$202$	0.384789	+	1.18426i	0.0270737	+	0.0833243i
$203$	9.36198	+	4.16822i	0.657082	+	0.292552i
$204$	1.87536	+	0.398621i	0.131302	+	0.0279090i
$205$	8.40257	−	1.78602i	0.586861	−	0.124741i
$206$	−3.35440	+	1.49348i	−0.233712	+	0.104055i
$207$	2.45502	+	2.72657i	0.170635	+	0.189510i
$208$	−0.591023	−	5.62321i	−0.0409801	−	0.389899i
$209$	−9.67412	+	7.02866i	−0.669173	+	0.486183i
$210$	−0.682636	+	6.49485i	−0.0471064	+	0.448187i
$211$	4.05764	+	7.02803i	0.279339	+	0.483830i	0.971221	−	0.238181i	$-0.0765513\pi$
$211$	4.05764	+	7.02803i	0.279339	+	0.483830i	−0.691882	+	0.722011i	$0.743218\pi$
$212$	−2.03536	+	3.52534i	−0.139789	+	0.242122i
$213$	4.35916	+	3.16711i	0.298685	+	0.217007i
$214$	−12.2109	+	13.5616i	−0.834722	+	0.927052i
$215$	−12.4567	+	38.3378i	−0.849541	+	2.61462i
$216$	3.47214			0.236249
$217$	9.56677	−	13.3943i	0.649435	−	0.909264i
$218$	20.0889			1.36059
$219$	1.50313	−	4.62614i	0.101572	−	0.312606i
$220$	5.67886	−	6.30701i	0.382869	−	0.425219i
$221$	−14.1905	−	10.3100i	−0.954553	−	0.693523i
$222$	0.0580002	−	0.100459i	0.00389272	−	0.00674239i
$223$	−4.07102	−	7.05121i	−0.272616	−	0.472184i	0.696915	−	0.717153i	$-0.254555\pi$
$223$	−4.07102	−	7.05121i	−0.272616	−	0.472184i	−0.969531	+	0.244970i	$0.921222\pi$
$224$	−0.309017	+	2.94010i	−0.0206471	+	0.196444i
$225$	16.4695	−	11.9658i	1.09796	−	0.797718i
$226$	0.855910	+	8.14344i	0.0569343	+	0.541694i
$227$	12.8352	+	14.2549i	0.851903	+	0.946134i	0.999076	−	0.0429768i	$-0.0136842\pi$
$227$	12.8352	+	14.2549i	0.851903	+	0.946134i	−0.147173	+	0.989111i	$0.547017\pi$
$228$	2.84342	−	1.26597i	0.188310	−	0.0838410i
$229$	−7.95458	+	1.69080i	−0.525654	+	0.111731i	−0.463092	−	0.886310i	$-0.653260\pi$
$229$	−7.95458	+	1.69080i	−0.525654	+	0.111731i	−0.0625613	+	0.998041i	$0.519927\pi$
$230$	−4.89968	−	1.04146i	−0.323075	−	0.0686717i
$231$	3.96320	+	1.76453i	0.260759	+	0.116098i
$232$	1.07120	+	3.29683i	0.0703280	+	0.216447i
$233$	1.28921	+	3.96778i	0.0844590	+	0.259938i	0.984364	−	0.176149i	$-0.0563640\pi$
$233$	1.28921	+	3.96778i	0.0844590	+	0.259938i	−0.899905	+	0.436087i	$0.856364\pi$
$234$	−13.5231	−	6.02086i	−0.884031	−	0.393596i
$235$	−0.0516869	−	0.0109864i	−0.00337168	−	0.000716673i
$236$	−7.32177	+	1.55629i	−0.476606	+	0.101306i
$237$	−3.81960	+	1.70059i	−0.248109	+	0.110465i
$238$	6.13660	+	6.81538i	0.397776	+	0.441775i
$239$	1.94575	+	18.5126i	0.125860	+	1.19748i	0.857024	+	0.515277i	$0.172311\pi$
$239$	1.94575	+	18.5126i	0.125860	+	1.19748i	−0.731164	+	0.682202i	$0.761022\pi$
$240$	−1.78716	+	1.29845i	−0.115361	+	0.0838147i
$241$	1.71665	−	16.3329i	0.110579	−	1.05209i	−0.788718	−	0.614755i	$-0.789255\pi$
$241$	1.71665	−	16.3329i	0.110579	−	1.05209i	0.899298	−	0.437337i	$-0.144078\pi$
$242$	2.68109	+	4.64379i	0.172347	+	0.298514i
$243$	6.97214	−	12.0761i	0.447263	−	0.774682i
$244$	−10.8140	−	7.85684i	−0.692296	−	0.502983i
$245$	−4.16078	+	4.62102i	−0.265823	+	0.295226i
$246$	−0.458995	+	1.41264i	−0.0292645	+	0.0900668i
$247$	−28.4753			−1.81184
$248$	5.53237	−	0.626809i	0.351306	−	0.0398024i
$249$	−9.51840			−0.603204
$250$	−3.06598	+	9.43612i	−0.193910	+	0.596793i
$251$	−14.1329	+	15.6962i	−0.892062	+	0.990735i	−0.999994	−	0.00342306i	$-0.998910\pi$
$251$	−14.1329	+	15.6962i	−0.892062	+	0.990735i	0.107932	+	0.994158i	$0.465577\pi$
$252$	6.26153	+	4.54927i	0.394440	+	0.286577i
$253$	−1.66377	+	2.88174i	−0.104600	+	0.181173i
$254$	0.957738	+	1.65885i	0.0600939	+	0.104086i
$255$	−0.716325	+	6.81538i	−0.0448580	+	0.426796i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−0.433618	−	4.12560i	−0.0270484	−	0.257348i	−0.999687	−	0.0250242i	$-0.992034\pi$
$257$	−0.433618	−	4.12560i	−0.0270484	−	0.257348i	0.972638	−	0.232324i	$-0.0746329\pi$
$258$	−4.66391	−	5.17980i	−0.290362	−	0.322480i
$259$	0.506904	−	0.225688i	0.0314975	−	0.0140236i
$260$	19.7683	−	4.20188i	1.22598	−	0.260589i
$261$	8.87707	+	1.88688i	0.549477	+	0.116795i
$262$	−8.04781	−	3.58311i	−0.497195	−	0.221366i
$263$	−6.15790	−	18.9521i	−0.379712	−	1.16863i	−0.940244	−	0.340501i	$-0.889403\pi$
$263$	−6.15790	−	18.9521i	−0.379712	−	1.16863i	0.560532	−	0.828133i	$-0.310597\pi$
$264$	0.453472	+	1.39564i	0.0279093	+	0.0858959i
$265$	−13.2922	−	5.91805i	−0.816531	−	0.363543i
$266$	14.5630	+	3.09546i	0.892914	+	0.189795i
$267$	−1.00457	+	0.213528i	−0.0614786	+	0.0130677i
$268$	2.57577	−	1.14681i	0.157340	−	0.0700524i
$269$	−10.4242	−	11.5772i	−0.635573	−	0.705875i	0.336201	−	0.941790i	$-0.390858\pi$
$269$	−10.4242	−	11.5772i	−0.635573	−	0.705875i	−0.971774	+	0.235915i	$0.924191\pi$
$270$	1.29726	+	12.3426i	0.0789485	+	0.751145i
$271$	0.697852	−	0.507019i	0.0423915	−	0.0307992i	−0.566388	−	0.824139i	$-0.691660\pi$
$271$	0.697852	−	0.507019i	0.0423915	−	0.0307992i	0.608779	+	0.793340i	$0.291660\pi$
$272$	−0.324267	+	3.08520i	−0.0196616	+	0.187068i
$273$	5.16535	+	8.94665i	0.312621	+	0.541476i
$274$	5.85177	−	10.1356i	0.353518	−	0.612311i
$275$	14.9369	+	10.8523i	0.900728	+	0.654417i
$276$	0.579551	−	0.643657i	0.0348849	−	0.0387436i
$277$	2.47845	−	7.62788i	0.148916	−	0.458315i	−0.848578	−	0.529070i	$-0.822541\pi$
$277$	2.47845	−	7.62788i	0.148916	−	0.458315i	0.997494	+	0.0707550i	$0.0225409\pi$
$278$	8.81702			0.528810
$279$	5.82081	−	13.3640i	0.348483	−	0.800079i
$280$	−10.5668			−0.631485
$281$	−3.38217	+	10.4092i	−0.201763	+	0.620963i	0.798068	+	0.602568i	$0.205856\pi$
$281$	−3.38217	+	10.4092i	−0.201763	+	0.620963i	−0.999831	+	0.0183952i	$0.994144\pi$
$282$	0.00611371	−	0.00678996i	0.000364066	−	0.000404336i
$283$	8.37756	+	6.08665i	0.497994	+	0.361814i	0.808250	−	0.588839i	$-0.200415\pi$
$283$	8.37756	+	6.08665i	0.497994	+	0.361814i	−0.310256	+	0.950653i	$0.600415\pi$
$284$	−4.35916	+	7.55028i	−0.258668	+	0.448027i
$285$	5.56257	+	9.63465i	0.329498	+	0.570708i
$286$	1.40333	−	13.3518i	0.0829807	−	0.789508i
$287$	−5.74803	+	4.17619i	−0.339295	+	0.246513i
$288$	0.273659	+	2.60369i	0.0161255	+	0.153424i
$289$	−4.93577	−	5.48173i	−0.290340	−	0.322455i
$290$	−11.3192	+	5.03962i	−0.664684	+	0.295937i
$291$	−4.30794	+	0.915681i	−0.252536	+	0.0536781i
$292$	7.69848	+	1.63636i	0.450519	+	0.0957608i
$293$	−9.98781	−	4.44686i	−0.583494	−	0.259788i	0.0936906	−	0.995601i	$-0.470134\pi$
$293$	−9.98781	−	4.44686i	−0.583494	−	0.259788i	−0.677185	+	0.735813i	$0.736800\pi$
$294$	−0.332250	−	1.02256i	−0.0193772	−	0.0596369i
$295$	−8.26777	−	25.4456i	−0.481368	−	1.48150i
$296$	0.171466	+	0.0763415i	0.00996625	+	0.00443726i
$297$	8.06411	+	1.71408i	0.467927	+	0.0994610i
$298$	−7.30678	+	1.55310i	−0.423271	+	0.0899689i
$299$	−7.23883	+	3.22293i	−0.418632	+	0.186387i
$300$	−3.21566	−	3.57135i	−0.185656	−	0.206192i
$301$	−3.48505	−	33.1580i	−0.200875	−	1.91120i
$302$	1.43822	−	1.04493i	0.0827603	−	0.0601289i
$303$	0.0804429	−	0.765363i	0.00462132	−	0.0439690i
$304$	2.51807	+	4.36143i	0.144421	+	0.250145i
$305$	23.8888	−	41.3766i	1.36787	−	2.36921i
$306$	6.57055	+	4.77378i	0.375613	+	0.272899i
$307$	8.86320	−	9.84359i	0.505850	−	0.561803i	−0.435086	−	0.900389i	$-0.643282\pi$
$307$	8.86320	−	9.84359i	0.505850	−	0.561803i	0.940935	+	0.338586i	$0.109949\pi$
$308$	−2.16913	+	6.67590i	−0.123598	+	0.380395i
$309$	2.26933			0.129098
$310$	4.29515	+	19.4320i	0.243948	+	1.10366i
$311$	16.7168			0.947923			0.473962	−	0.880546i	$-0.342824\pi$
$311$	16.7168			0.947923			0.473962	+	0.880546i	$0.342824\pi$
$312$	−1.07985	+	3.32344i	−0.0611346	+	0.188153i
$313$	13.3538	−	14.8309i	0.754801	−	0.838292i	−0.236261	−	0.971690i	$-0.575922\pi$
$313$	13.3538	−	14.8309i	0.754801	−	0.838292i	0.991063	+	0.133398i	$0.0425888\pi$
$314$	−7.66190	−	5.56669i	−0.432386	−	0.314147i
$315$	−13.8321	+	23.9579i	−0.779350	+	1.34987i
$316$	−3.38256	−	5.85876i	−0.190284	−	0.329581i
$317$	0.213404	−	2.03041i	0.0119860	−	0.114039i	−0.986893	−	0.161376i	$-0.948407\pi$
$317$	0.213404	−	2.03041i	0.0119860	−	0.114039i	0.998879	+	0.0473370i	$0.0150735\pi$
$318$	2.03536	−	1.47877i	0.114137	−	0.0829255i
$319$	0.860359	+	8.18577i	0.0481709	+	0.458315i
$320$	−2.39169	−	2.65624i	−0.133700	−	0.148489i
$321$	10.3034	−	4.58737i	0.575079	−	0.256042i
$322$	4.05248	−	0.861381i	0.225836	−	0.0480029i
$323$	15.2817	+	3.24823i	0.850297	+	0.180736i
$324$	5.21470	+	2.32174i	0.289706	+	0.128985i
$325$	13.5862	+	41.8141i	0.753628	+	2.31943i
$326$	2.37812	+	7.31911i	0.131712	+	0.405368i
$327$	−11.3422	−	5.04988i	−0.627226	−	0.279259i
$328$	−2.35081	−	0.499680i	−0.129802	−	0.0275902i
$329$	0.0427497	−	0.00908674i	0.00235687	−	0.000500968i
$330$	−4.79173	+	2.13342i	−0.263776	+	0.117441i
$331$	0.461267	+	0.512289i	0.0253535	+	0.0281580i	0.755688	−	0.654932i	$-0.227303\pi$
$331$	0.461267	+	0.512289i	0.0253535	+	0.0281580i	−0.730335	+	0.683089i	$0.760636\pi$
$332$	−1.60985	−	15.3167i	−0.0883521	−	0.840614i
$333$	0.397540	−	0.288829i	0.0217850	−	0.0158278i
$334$	2.23288	−	21.2444i	0.122178	−	1.16244i
$335$	5.03897	+	8.72775i	0.275308	+	0.476848i
$336$	0.913545	−	1.58231i	0.0498380	−	0.0863219i
$337$	15.0704	+	10.9493i	0.820936	+	0.596445i	0.916981	−	0.398932i	$-0.130619\pi$
$337$	15.0704	+	10.9493i	0.820936	+	0.596445i	−0.0960443	+	0.995377i	$0.530619\pi$
$338$	12.6933	−	14.0973i	0.690422	−	0.766791i
$339$	1.56383	−	4.81296i	0.0849353	−	0.261404i
$340$	−11.0883			−0.601345
$341$	13.1585	+	1.27537i	0.712572	+	0.0690653i
$342$	13.1848			0.712953
$343$	−4.80554	+	14.7899i	−0.259475	+	0.798581i
$344$	7.54636	−	8.38109i	0.406873	−	0.451878i
$345$	2.50457	+	1.81968i	0.134841	+	0.0979680i
$346$	−2.76541	+	4.78984i	−0.148670	+	0.257503i
$347$	−3.25240	−	5.63332i	−0.174598	−	0.302412i	0.765424	−	0.643526i	$-0.222529\pi$
$347$	−3.25240	−	5.63332i	−0.174598	−	0.302412i	−0.940022	+	0.341114i	$0.889196\pi$
$348$	0.223943	−	2.13067i	0.0120046	−	0.114216i
$349$	−25.5751	+	18.5814i	−1.36900	+	0.994638i	−0.371187	+	0.928558i	$0.621049\pi$
$349$	−25.5751	+	18.5814i	−1.36900	+	0.994638i	−0.997814	+	0.0660796i	$0.978951\pi$
$350$	−2.40286	−	22.8617i	−0.128438	−	1.22201i
$351$	13.1364	+	14.5895i	0.701171	+	0.778729i
$352$	−2.16913	+	0.965759i	−0.115615	+	0.0514751i
$353$	−30.7341	+	6.53274i	−1.63581	+	0.347703i	−0.931937	−	0.362620i	$-0.881882\pi$
$353$	−30.7341	+	6.53274i	−1.63581	+	0.347703i	−0.703876	+	0.710323i	$0.748549\pi$
$354$	4.52510	+	0.961840i	0.240506	+	0.0511212i
$355$	−28.4680	−	12.6748i	−1.51093	−	0.672708i
$356$	−0.513506	−	1.58041i	−0.0272157	−	0.0837614i
$357$	−1.75150	−	5.39058i	−0.0926995	−	0.285300i
$358$	−13.2675	−	5.90706i	−0.701208	−	0.312198i
$359$	−15.5898	−	3.31372i	−0.822798	−	0.174891i	−0.222771	−	0.974871i	$-0.571510\pi$
$359$	−15.5898	−	3.31372i	−0.822798	−	0.174891i	−0.600027	+	0.799980i	$0.704844\pi$
$360$	−9.15323	+	1.94558i	−0.482417	+	0.102541i
$361$	5.81269	−	2.58798i	0.305931	−	0.136209i
$362$	6.14478	+	6.82447i	0.322962	+	0.358686i
$363$	−0.346408	−	3.29586i	−0.0181817	−	0.172988i
$364$	−13.5231	+	9.82508i	−0.708801	+	0.514974i
$365$	−2.94056	+	27.9775i	−0.153916	+	1.46441i
$366$	4.13058	+	7.15438i	0.215909	+	0.373966i
$367$	−9.92623	+	17.1927i	−0.518145	+	0.897454i	0.481633	+	0.876373i	$0.340044\pi$
$367$	−9.92623	+	17.1927i	−0.518145	+	0.897454i	−0.999778	+	0.0210805i	$0.993289\pi$
$368$	1.13377	+	0.823734i	0.0591020	+	0.0429401i
$369$	−4.21017	+	4.67587i	−0.219173	+	0.243416i
$370$	−0.207312	+	0.638041i	−0.0107776	+	0.0331702i
$371$	12.0342			0.624786
$372$	−3.28115	−	1.03681i	−0.170120	−	0.0537563i
$373$	3.09370			0.160186			0.0800929	−	0.996787i	$-0.474478\pi$
$373$	3.09370			0.160186			0.0800929	+	0.996787i	$0.474478\pi$
$374$	−2.27618	+	7.00536i	−0.117699	+	0.362239i
$375$	4.10309	−	4.55694i	0.211882	−	0.235319i
$376$	0.0119602	+	0.00868960i	0.000616801	+	0.000448132i
$377$	−9.80008	+	16.9742i	−0.504730	+	0.874218i
$378$	−5.13233	−	8.88946i	−0.263979	−	0.457224i
$379$	0.385049	−	3.66350i	0.0197787	−	0.188181i	−0.980172	−	0.198150i	$-0.936507\pi$
$379$	0.385049	−	3.66350i	0.0197787	−	0.188181i	0.999950	+	0.00996891i	$0.00317326\pi$
$380$	−14.5630	+	10.5806i	−0.747066	+	0.542775i
$381$	−0.123744	−	1.17734i	−0.00633959	−	0.0603172i
$382$	−7.11553	−	7.90260i	−0.364062	−	0.404332i
$383$	23.9308	−	10.6547i	1.22281	−	0.544430i	0.309190	−	0.951000i	$-0.399942\pi$
$383$	23.9308	−	10.6547i	1.22281	−	0.544430i	0.913619	+	0.406571i	$0.133276\pi$
$384$	0.604528	−	0.128496i	0.0308497	−	0.00655731i
$385$	−24.5416	−	5.21647i	−1.25075	−	0.265856i
$386$	−2.11288	−	0.940713i	−0.107543	−	0.0478810i
$387$	−9.12398	−	28.0807i	−0.463798	−	1.42742i
$388$	−2.20209	−	6.77734i	−0.111794	−	0.344067i
$389$	−12.4460	−	5.54133i	−0.631039	−	0.280957i	0.0661878	−	0.997807i	$-0.478916\pi$
$389$	−12.4460	−	5.54133i	−0.631039	−	0.280957i	−0.697227	+	0.716850i	$0.745583\pi$
$390$	−12.2175	−	2.59690i	−0.618655	−	0.131499i
$391$	4.25247	−	0.903891i	0.215057	−	0.0457117i
$392$	1.58928	−	0.707592i	0.0802707	−	0.0357388i
$393$	3.64310	+	4.04607i	0.183770	+	0.204097i
$394$	0.317789	+	3.02356i	0.0160100	+	0.152325i
$395$	19.5626	−	14.2131i	0.984303	−	0.715138i
$396$	−0.649779	+	6.18223i	−0.0326526	+	0.310669i
$397$	14.4954	+	25.1068i	0.727503	+	1.26007i	0.957935	+	0.286984i	$0.0926528\pi$
$397$	14.4954	+	25.1068i	0.727503	+	1.26007i	−0.230432	+	0.973088i	$0.574014\pi$
$398$	−9.66236	+	16.7357i	−0.484331	+	0.838885i
$399$	−7.44417	−	5.40851i	−0.372675	−	0.270764i
$400$	5.20305	−	5.77857i	0.260152	−	0.288928i
$401$	−4.86965	+	14.9873i	−0.243179	+	0.748428i	0.752752	+	0.658305i	$0.228726\pi$
$401$	−4.86965	+	14.9873i	−0.243179	+	0.748428i	−0.995931	+	0.0901232i	$0.971274\pi$
$402$	−1.74257			−0.0869114
$403$	23.5649	+	20.8749i	1.17385	+	1.03985i
$404$	1.24520			0.0619513
$405$	−6.30487	+	19.4044i	−0.313292	+	0.964213i
$406$	6.85723	−	7.61572i	0.340318	−	0.377962i
$407$	0.360546	+	0.261952i	0.0178716	+	0.0129845i
$408$	0.958630	−	1.66040i	0.0474593	−	0.0822019i
$409$	−14.2696	−	24.7157i	−0.705587	−	1.22211i	−0.966479	−	0.256745i	$-0.917350\pi$
$409$	−14.2696	−	24.7157i	−0.705587	−	1.22211i	0.260892	−	0.965368i	$-0.415983\pi$
$410$	0.897930	−	8.54323i	0.0443456	−	0.421920i
$411$	−5.85177	+	4.25156i	−0.288646	+	0.209714i
$412$	0.383813	+	3.65174i	0.0189091	+	0.179908i
$413$	14.8071	+	16.4450i	0.728610	+	0.809203i
$414$	3.35177	−	1.49230i	0.164730	−	0.0733427i
$415$	53.8456	−	11.4452i	2.64318	−	0.561825i
$416$	−5.53062	−	1.17557i	−0.271161	−	0.0576371i
$417$	−4.97811	−	2.21640i	−0.243779	−	0.108537i
$418$	3.69519	+	11.3726i	0.180737	+	0.556253i
$419$	−9.46027	−	29.1157i	−0.462165	−	1.42240i	−0.862514	−	0.506034i	$-0.831111\pi$
$419$	−9.46027	−	29.1157i	−0.462165	−	1.42240i	0.400349	−	0.916363i	$-0.368889\pi$
$420$	5.96602	+	2.65624i	0.291112	+	0.129611i
$421$	−18.3182	−	3.89366i	−0.892775	−	0.189765i	−0.261389	−	0.965234i	$-0.584180\pi$
$421$	−18.3182	−	3.89366i	−0.892775	−	0.189765i	−0.631386	+	0.775468i	$0.717514\pi$
$422$	7.93793	−	1.68726i	0.386413	−	0.0821345i
$423$	0.0353579	−	0.0157424i	0.00171916	−	0.000765420i
$424$	2.72384	+	3.02513i	0.132281	+	0.146913i
$425$	−2.52145	−	23.9900i	−0.122308	−	1.16369i
$426$	4.35916	−	3.16711i	0.211202	−	0.153447i
$427$	−4.13058	+	39.2999i	−0.199893	+	1.90185i
$428$	9.12447	+	15.8040i	0.441048	+	0.763917i
$429$	−4.14866	+	7.18569i	−0.200299	+	0.346928i
$430$	32.6121	+	23.6941i	1.57270	+	1.14263i
$431$	−21.3140	+	23.6716i	−1.02666	+	1.14022i	−0.0366333	+	0.999329i	$0.511663\pi$
$431$	−21.3140	+	23.6716i	−1.02666	+	1.14022i	−0.990025	+	0.140891i	$0.955003\pi$
$432$	1.07295	−	3.30220i	0.0516223	−	0.158877i
$433$	21.0681			1.01247			0.506234	−	0.862396i	$-0.331037\pi$
$433$	21.0681			1.01247			0.506234	+	0.862396i	$0.331037\pi$
$434$	−9.78243	−	13.2376i	−0.469572	−	0.635425i
$435$	7.65767			0.367157
$436$	6.20780	−	19.1056i	0.297300	−	0.914994i
$437$	4.72256	−	5.24494i	0.225911	−	0.250899i
$438$	−3.93523	−	2.85911i	−0.188033	−	0.136614i
$439$	8.91610	−	15.4431i	0.425542	−	0.737061i	−0.570929	−	0.821000i	$-0.693417\pi$
$439$	8.91610	−	15.4431i	0.425542	−	0.737061i	0.996471	+	0.0839388i	$0.0267500\pi$
$440$	−4.24346	−	7.34989i	−0.202299	−	0.350392i
$441$	0.476080	−	4.52959i	0.0226705	−	0.215695i
$442$	−14.1905	+	10.3100i	−0.674971	+	0.490395i
$443$	−1.70725	−	16.2434i	−0.0811138	−	0.771747i	−0.957168	−	0.289534i	$-0.906500\pi$
$443$	−1.70725	−	16.2434i	−0.0811138	−	0.771747i	0.876054	−	0.482213i	$-0.160167\pi$
$444$	−0.0776195	−	0.0862052i	−0.00368366	−	0.00409112i
$445$	5.42610	−	2.41585i	0.257222	−	0.114522i
$446$	−7.96411	+	1.69282i	−0.377112	+	0.0801576i
$447$	4.51584	+	0.959872i	0.213592	+	0.0454004i
$448$	2.70071	+	1.20243i	0.127597	+	0.0568096i
$449$	6.61570	+	20.3610i	0.312214	+	0.960896i	0.976886	+	0.213761i	$0.0685713\pi$
$449$	6.61570	+	20.3610i	0.312214	+	0.960896i	−0.664672	+	0.747135i	$0.731429\pi$
$450$	−6.29078	−	19.3610i	−0.296550	−	0.912687i
$451$	−5.21314	−	2.32104i	−0.245477	−	0.109293i
$452$	8.00936	+	1.70244i	0.376729	+	0.0800762i
$453$	−1.07469	+	0.228433i	−0.0504935	+	0.0107327i
$454$	17.5236	−	7.80199i	0.822421	−	0.366166i
$455$	−39.9782	−	44.4003i	−1.87421	−	2.08152i
$456$	−0.325346	−	3.09546i	−0.0152357	−	0.144958i
$457$	−4.33054	+	3.14632i	−0.202574	+	0.147179i	−0.684447	−	0.729062i	$-0.739957\pi$
$457$	−4.33054	+	3.14632i	−0.202574	+	0.147179i	0.481873	+	0.876241i	$0.339957\pi$
$458$	−0.850056	+	8.08775i	−0.0397205	+	0.377916i
$459$	−5.38562	−	9.32816i	−0.251379	−	0.435401i
$460$	−2.50457	+	4.33804i	−0.116776	+	0.202262i
$461$	1.54419	+	1.12192i	0.0719202	+	0.0522531i	0.623164	−	0.782091i	$-0.285847\pi$
$461$	1.54419	+	1.12192i	0.0719202	+	0.0522531i	−0.551244	+	0.834344i	$0.685847\pi$
$462$	2.90286	−	3.22396i	0.135053	−	0.149992i
$463$	5.87363	−	18.0772i	0.272971	−	0.840118i	−0.716778	−	0.697301i	$-0.754384\pi$
$463$	5.87363	−	18.0772i	0.272971	−	0.840118i	0.989749	−	0.142817i	$-0.0456160\pi$
$464$	3.46649			0.160928
$465$	2.45971	−	12.0510i	0.114066	−	0.558854i
$466$	4.17198			0.193263
$467$	−2.94982	+	9.07860i	−0.136501	+	0.420108i	−0.995821	−	0.0913319i	$-0.970888\pi$
$467$	−2.94982	+	9.07860i	−0.136501	+	0.420108i	0.859319	+	0.511440i	$0.170888\pi$
$468$	−9.90503	+	11.0007i	−0.457860	+	0.508505i
$469$	−6.74346	−	4.89941i	−0.311384	−	0.226234i
$470$	−0.0264208	+	0.0457622i	−0.00121870	+	0.00211085i
$471$	2.92658	+	5.06899i	0.134850	+	0.233567i
$472$	−0.782431	+	7.44433i	−0.0360143	+	0.342653i
$473$	21.6641	−	15.7399i	0.996115	−	0.723720i
$474$	0.437041	+	4.15817i	0.0200739	+	0.190991i
$475$	−26.2033	−	29.1017i	−1.20229	−	1.33528i
$476$	8.37812	−	3.73018i	0.384011	−	0.170973i
$477$	10.4244	−	2.21577i	0.477300	−	0.101453i
$478$	18.2078	+	3.87018i	0.832804	+	0.177018i
$479$	19.2093	+	8.55254i	0.877696	+	0.390775i	0.795581	−	0.605847i	$-0.207166\pi$
$479$	19.2093	+	8.55254i	0.877696	+	0.390775i	0.0821152	+	0.996623i	$0.473832\pi$
$480$	0.682636	+	2.10094i	0.0311579	+	0.0958943i
$481$	0.327944	+	1.00931i	0.0149530	+	0.0460205i
$482$	−15.0030	−	6.67977i	−0.683368	−	0.304255i
$483$	−2.50457	−	0.532362i	−0.113962	−	0.0242233i
$484$	5.24501	−	1.11486i	0.238409	−	0.0506755i
$485$	23.2690	−	10.3600i	1.05659	−	0.470424i
$486$	−9.33054	−	10.3626i	−0.423242	−	0.470058i
$487$	3.03282	+	28.8553i	0.137430	+	1.30756i	0.818146	+	0.575011i	$0.195002\pi$
$487$	3.03282	+	28.8553i	0.137430	+	1.30756i	−0.680716	+	0.732548i	$0.738331\pi$
$488$	−10.8140	+	7.85684i	−0.489527	+	0.355662i
$489$	0.497163	−	4.73019i	0.0224825	−	0.213907i
$490$	3.10910	+	5.38511i	0.140455	+	0.243275i
$491$	3.67758	−	6.36975i	0.165967	−	0.287463i	−0.771031	−	0.636797i	$-0.780259\pi$
$491$	3.67758	−	6.36975i	0.165967	−	0.287463i	0.936998	+	0.349334i	$0.113592\pi$
$492$	1.20167	+	0.873061i	0.0541752	+	0.0393606i
$493$	7.19564	−	7.99157i	0.324075	−	0.359922i
$494$	−8.79935	+	27.0816i	−0.395901	+	1.21846i
$495$	−22.2190			−0.998672
$496$	1.11347	−	5.45529i	0.0499961	−	0.244950i
$497$	25.7739			1.15612
$498$	−2.94135	+	9.05253i	−0.131805	+	0.405654i
$499$	6.37051	−	7.07517i	0.285183	−	0.316728i	−0.583483	−	0.812125i	$-0.698311\pi$
$499$	6.37051	−	7.07517i	0.285183	−	0.316728i	0.868667	+	0.495397i	$0.164977\pi$
$500$	8.02685	+	5.83184i	0.358971	+	0.260808i
$501$	−6.60105	+	11.4334i	−0.294913	+	0.510805i
$502$	10.5607	+	18.2916i	0.471345	+	0.816394i
$503$	−0.494705	+	4.70680i	−0.0220578	+	0.209866i	0.977942	+	0.208878i	$0.0669811\pi$
$503$	−0.494705	+	4.70680i	−0.0220578	+	0.209866i	−1.00000		0.000987951i	$0.999686\pi$
$504$	6.26153	−	4.54927i	0.278911	−	0.202641i
$505$	0.465232	+	4.42639i	0.0207026	+	0.196972i
$506$	2.22656	+	2.47285i	0.0989828	+	0.109931i
$507$	−10.7104	+	4.76857i	−0.475664	+	0.211779i
$508$	1.87362	−	0.398250i	0.0831284	−	0.0176695i
$509$	−37.9520	−	8.06695i	−1.68219	−	0.357561i	−0.734961	−	0.678110i	$-0.762799\pi$
$509$	−37.9520	−	8.06695i	−1.68219	−	0.357561i	−0.947232	+	0.320549i	$0.896133\pi$
$510$	6.26046	+	2.78733i	0.277218	+	0.123425i
$511$	−7.19003	−	22.1286i	−0.318068	−	0.978913i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−15.9744	−	7.11227i	−0.705288	−	0.314015i
$514$	−4.05768	−	0.862486i	−0.178976	−	0.0380426i
$515$	−12.8376	+	2.72872i	−0.565693	+	0.120242i
$516$	−6.36751	+	2.83500i	−0.280314	+	0.124804i
$517$	0.0234881	+	0.0260862i	0.00103301	+	0.00114727i
$518$	−0.0580002	−	0.551835i	−0.00254838	−	0.0242463i
$519$	2.76541	−	2.00919i	0.121388	−	0.0881937i
$520$	2.11251	−	20.0992i	0.0926397	−	0.881408i
$521$	0.711392	+	1.23217i	0.0311667	+	0.0539822i	0.881188	−	0.472766i	$-0.156744\pi$
$521$	0.711392	+	1.23217i	0.0311667	+	0.0539822i	−0.850021	+	0.526748i	$0.823411\pi$
$522$	4.53769	−	7.85952i	0.198609	−	0.344002i
$523$	1.08570	+	0.788807i	0.0474743	+	0.0344921i	0.611269	−	0.791423i	$-0.290659\pi$
$523$	1.08570	+	0.788807i	0.0474743	+	0.0344921i	−0.563795	+	0.825915i	$0.690659\pi$
$524$	−5.89465	+	6.54668i	−0.257509	+	0.285993i
$525$	−4.39025	+	13.5118i	−0.191606	+	0.589703i
$526$	−19.9274			−0.868875
$527$	−10.2652	−	13.8909i	−0.447160	−	0.605097i
$528$	1.46747			0.0638632
$529$	−6.50049	+	20.0064i	−0.282630	+	0.869845i
$530$	−9.73590	+	10.8128i	−0.422901	+	0.469679i
$531$	15.8542	+	11.5188i	0.688014	+	0.499871i
$532$	7.44417	−	12.8937i	0.322746	−	0.559012i
$533$	−6.79443	−	11.7683i	−0.294300	−	0.509742i
$534$	−0.107352	+	1.02138i	−0.00464557	+	0.0441997i
$535$	−52.7703	+	38.3399i	−2.28146	+	1.65758i
$536$	−0.294722	−	2.80409i	−0.0127300	−	0.121118i
$537$	6.00595	+	6.67028i	0.259176	+	0.287844i
$538$	−14.2318	+	6.33642i	−0.613577	+	0.273182i
$539$	4.04045	−	0.858824i	0.174034	−	0.0369922i
$540$	12.1394	+	2.58030i	0.522395	+	0.111038i
$541$	−1.83418	−	0.816630i	−0.0788576	−	0.0351097i	0.366929	−	0.930249i	$-0.380409\pi$
$541$	−1.83418	−	0.816630i	−0.0788576	−	0.0351097i	−0.445786	+	0.895139i	$0.647076\pi$
$542$	−0.266556	−	0.820374i	−0.0114496	−	0.0352381i
$543$	−1.75384	−	5.39777i	−0.0752645	−	0.231640i
$544$	2.83399	+	1.26178i	0.121507	+	0.0540982i
$545$	70.2351	+	14.9289i	3.00854	+	0.639485i
$546$	10.1050	−	2.14787i	0.432452	−	0.0919205i
$547$	−22.3311	+	9.94246i	−0.954810	+	0.425109i	−0.824184	−	0.566323i	$-0.808366\pi$
$547$	−22.3311	+	9.94246i	−0.954810	+	0.425109i	−0.130627	+	0.991432i	$0.541699\pi$
$548$	−7.83119	−	8.69742i	−0.334532	−	0.371535i
$549$	3.65796	+	34.8032i	0.156118	+	1.48536i
$550$	14.9369	−	10.8523i	0.636911	−	0.462743i
$551$	1.82483	−	17.3621i	0.0777405	−	0.739651i
$552$	−0.433063	−	0.750086i	−0.0184324	−	0.0319258i
$553$	−9.99983	+	17.3202i	−0.425236	+	0.736531i
$554$	−6.48866	−	4.71429i	−0.275677	−	0.200291i
$555$	0.277438	−	0.308126i	0.0117766	−	0.0130792i
$556$	2.72461	−	8.38548i	0.115549	−	0.355624i
$557$	−27.0163			−1.14472			−0.572358	−	0.820004i	$-0.693971\pi$
$557$	−27.0163			−1.14472			−0.572358	+	0.820004i	$0.693971\pi$
$558$	−10.9111	−	9.66561i	−0.461906	−	0.409178i
$559$	63.7671			2.69706
$560$	−3.26531	+	10.0496i	−0.137985	+	0.424673i
$561$	3.04612	−	3.38306i	0.128607	−	0.142833i
$562$	8.85462	+	6.43326i	0.373510	+	0.271371i
$563$	1.42051	−	2.46040i	0.0598674	−	0.103693i	−0.834538	−	0.550950i	$-0.814266\pi$
$563$	1.42051	−	2.46040i	0.0598674	−	0.103693i	0.894406	+	0.447256i	$0.147599\pi$
$564$	−0.00456840	−	0.00791269i	−0.000192364	−	0.000333184i
$565$	−3.05930	+	29.1073i	−0.128706	+	1.22455i
$566$	8.37756	−	6.08665i	0.352135	−	0.255841i
$567$	−1.76393	−	16.7827i	−0.0740782	−	0.704807i
$568$	5.83369	+	6.47897i	0.244776	+	0.271852i
$569$	10.2494	−	4.56333i	0.429678	−	0.191305i	−0.180491	−	0.983577i	$-0.557769\pi$
$569$	10.2494	−	4.56333i	0.429678	−	0.191305i	0.610168	+	0.792272i	$0.291102\pi$
$570$	10.8820	−	2.31305i	0.455798	−	0.0968828i
$571$	30.4402	+	6.47027i	1.27388	+	0.270772i	0.794732	−	0.606960i	$-0.207611\pi$
$571$	30.4402	+	6.47027i	1.27388	+	0.270772i	0.479151	+	0.877733i	$0.340945\pi$
$572$	−12.2647	−	5.46058i	−0.512811	−	0.228318i
$573$	2.03091	+	6.25051i	0.0848426	+	0.261119i
$574$	2.19555	+	6.75721i	0.0916405	+	0.282041i
$575$	−9.95509	−	4.43229i	−0.415156	−	0.184839i
$576$	2.56082	+	0.544320i	0.106701	+	0.0226800i
$577$	11.1198	−	2.36359i	0.462924	−	0.0983975i	0.0294551	−	0.999566i	$-0.490623\pi$
$577$	11.1198	−	2.36359i	0.462924	−	0.0983975i	0.433469	+	0.901169i	$0.357289\pi$
$578$	−6.73867	+	3.00025i	−0.280292	+	0.124794i
$579$	0.956460	+	1.06226i	0.0397491	+	0.0441459i
$580$	1.29515	+	12.3225i	0.0537780	+	0.511664i
$581$	−36.8347	+	26.7620i	−1.52816	+	1.11027i
$582$	−0.460362	+	4.38005i	−0.0190826	+	0.181559i
$583$	4.83277	+	8.37061i	0.200153	+	0.346675i
$584$	3.93523	−	6.81602i	0.162841	−	0.282049i
$585$	−42.8053	−	31.0998i	−1.76978	−	1.28582i
$586$	−7.31562	+	8.12482i	−0.302205	+	0.335633i
$587$	2.73530	−	8.41839i	0.112898	−	0.347464i	−0.878605	−	0.477549i	$-0.841525\pi$
$587$	2.73530	−	8.41839i	0.112898	−	0.347464i	0.991503	+	0.130085i	$0.0415252\pi$
$588$	−1.07518			−0.0443398
$589$	−26.7370	−	8.44864i	−1.10168	−	0.348120i
$590$	−26.7551			−1.10149
$591$	0.580629	−	1.78699i	0.0238839	−	0.0735071i
$592$	0.125591	−	0.139483i	0.00516176	−	0.00573271i
$593$	−30.9714	−	22.5021i	−1.27184	−	0.924049i	−0.272570	−	0.962136i	$-0.587874\pi$
$593$	−30.9714	−	22.5021i	−1.27184	−	0.924049i	−0.999274	+	0.0380867i	$0.987874\pi$
$594$	4.12214	−	7.13975i	0.169133	−	0.292947i
$595$	16.3901	+	28.3885i	0.671928	+	1.16381i
$596$	−0.780830	+	7.42910i	−0.0319840	+	0.304308i
$597$	9.66236	−	7.02012i	0.395454	−	0.287314i
$598$	0.828271	+	7.88048i	0.0338705	+	0.322257i
$599$	12.6855	+	14.0886i	0.518314	+	0.575646i	0.944301	−	0.329083i	$-0.106740\pi$
$599$	12.6855	+	14.0886i	0.518314	+	0.575646i	−0.425987	+	0.904729i	$0.640073\pi$
$600$	−4.39025	+	1.95467i	−0.179231	+	0.0797989i
$601$	15.4061	−	3.27467i	0.628428	−	0.133576i	0.117321	−	0.993094i	$-0.462569\pi$
$601$	15.4061	−	3.27467i	0.628428	−	0.133576i	0.511106	+	0.859518i	$0.329236\pi$
$602$	−32.6121	−	6.93192i	−1.32917	−	0.282524i
$603$	−6.74346	−	3.00238i	−0.274615	−	0.122266i
$604$	−0.549352	−	1.69073i	−0.0223528	−	0.0687948i
$605$	5.92268	+	18.2281i	0.240791	+	0.741079i
$606$	−0.703045	−	0.313016i	−0.0285593	−	0.0127154i
$607$	9.07360	+	1.92865i	0.368286	+	0.0782816i	0.388337	−	0.921517i	$-0.373050\pi$
$607$	9.07360	+	1.92865i	0.368286	+	0.0782816i	−0.0200512	+	0.999799i	$0.506383\pi$
$608$	4.92610	−	1.04707i	0.199780	−	0.0424645i
$609$	−5.78602	+	2.57610i	−0.234461	+	0.104389i
$610$	−31.9694	−	35.5056i	−1.29440	−	1.43758i
$611$	0.00873747	+	0.0831315i	0.000353480	+	0.00336314i
$612$	6.57055	−	4.77378i	0.265599	−	0.192969i
$613$	3.56390	−	33.9083i	0.143945	−	1.36954i	−0.649251	−	0.760574i	$-0.724917\pi$
$613$	3.56390	−	33.9083i	0.143945	−	1.36954i	0.793195	−	0.608967i	$-0.208416\pi$
$614$	−6.62293	−	11.4712i	−0.267280	−	0.462942i
$615$	−2.65455	+	4.59781i	−0.107042	+	0.185402i
$616$	5.67886	+	4.12593i	0.228808	+	0.166239i
$617$	29.2187	−	32.4507i	1.17630	−	1.30642i	0.233773	−	0.972291i	$-0.424893\pi$
$617$	29.2187	−	32.4507i	1.17630	−	1.30642i	0.942529	−	0.334125i	$-0.108441\pi$
$618$	0.701261	−	2.15826i	0.0282089	−	0.0868180i
$619$	25.4295			1.02210			0.511048	−	0.859552i	$-0.329257\pi$
$619$	25.4295			1.02210			0.511048	+	0.859552i	$0.329257\pi$
$620$	19.8082	+	1.91989i	0.795516	+	0.0771046i
$621$	−4.86592			−0.195263
$622$	5.16578	−	15.8986i	0.207129	−	0.637477i
$623$	−3.28716	+	3.65077i	−0.131697	+	0.146265i
$624$	2.82709	+	2.05400i	0.113174	+	0.0822259i
$625$	1.70781	−	2.95802i	0.0683125	−	0.118321i
$626$	−9.97847	−	17.2832i	−0.398820	−	0.690776i
$627$	0.772504	−	7.34989i	0.0308509	−	0.293526i
$628$	−7.66190	+	5.56669i	−0.305743	+	0.222135i
$629$	−0.0608626	−	0.579069i	−0.00242675	−	0.0230890i
$630$	18.5109	+	20.5585i	0.737494	+	0.819070i
$631$	1.31736	−	0.586528i	0.0524434	−	0.0233493i	−0.380347	−	0.924844i	$-0.624196\pi$
$631$	1.31736	−	0.586528i	0.0524434	−	0.0233493i	0.432791	+	0.901494i	$0.357529\pi$
$632$	−6.61728	+	1.40655i	−0.263221	+	0.0559494i
$633$	−4.90591	−	1.04278i	−0.194993	−	0.0414469i
$634$	−1.86509	−	0.830390i	−0.0740720	−	0.0329790i
$635$	2.11570	+	6.51145i	0.0839589	+	0.258399i
$636$	−0.777438	−	2.39271i	−0.0308274	−	0.0948770i
$637$	8.98607	+	4.00085i	0.356041	+	0.158520i
$638$	8.05100	+	1.71129i	0.318742	+	0.0677507i
$639$	22.3261	−	4.74555i	0.883206	−	0.187731i
$640$	−3.26531	+	1.45381i	−0.129073	+	0.0574669i
$641$	30.2086	+	33.5500i	1.19317	+	1.32515i	0.933126	+	0.359549i	$0.117069\pi$
$641$	30.2086	+	33.5500i	1.19317	+	1.32515i	0.260041	+	0.965598i	$0.416264\pi$
$642$	−1.17892	−	11.2167i	−0.0465283	−	0.442687i
$643$	13.2740	−	9.64414i	0.523476	−	0.380328i	−0.294436	−	0.955671i	$-0.595132\pi$
$643$	13.2740	−	9.64414i	0.523476	−	0.380328i	0.817912	+	0.575344i	$0.195132\pi$
$644$	0.433063	−	4.12032i	0.0170651	−	0.162363i
$645$	−12.4567	−	21.5757i	−0.490483	−	0.849541i
$646$	7.81155	−	13.5300i	0.307341	−	0.532331i
$647$	1.88302	+	1.36810i	0.0740293	+	0.0537854i	0.624184	−	0.781277i	$-0.285431\pi$
$647$	1.88302	+	1.36810i	0.0740293	+	0.0537854i	−0.550155	+	0.835063i	$0.685431\pi$
$648$	3.81953	−	4.24202i	0.150045	−	0.166642i
$649$	−5.49224	+	16.9034i	−0.215589	+	0.663515i
$650$	43.9660			1.72449
$651$	2.19555	+	9.93306i	0.0860504	+	0.389307i
$652$	7.69577			0.301390
$653$	−9.16191	+	28.1975i	−0.358533	+	1.10345i	0.595399	+	0.803430i	$0.296994\pi$
$653$	−9.16191	+	28.1975i	−0.358533	+	1.10345i	−0.953932	+	0.300022i	$0.903006\pi$
$654$	−8.30766	+	9.22659i	−0.324855	+	0.360788i
$655$	−25.4741	−	18.5080i	−0.995357	−	0.723169i
$656$	−1.20167	+	2.08135i	−0.0469171	+	0.0812629i
$657$	−10.3026	−	17.8446i	−0.401942	−	0.696183i
$658$	0.00456840	−	0.0434654i	0.000178095	−	0.00169446i
$659$	20.1171	−	14.6159i	0.783652	−	0.569356i	−0.122421	−	0.992478i	$-0.539066\pi$
$659$	20.1171	−	14.6159i	0.783652	−	0.569356i	0.906073	+	0.423122i	$0.139066\pi$
$660$	0.548273	+	5.21647i	0.0213415	+	0.203051i
$661$	−33.0620	−	36.7191i	−1.28596	−	1.42821i	−0.848700	−	0.528874i	$-0.822614\pi$
$661$	−33.0620	−	36.7191i	−1.28596	−	1.42821i	−0.437264	−	0.899333i	$-0.644052\pi$
$662$	0.629756	−	0.280385i	0.0244761	−	0.0108975i
$663$	10.6036	−	2.25388i	0.411812	−	0.0875333i
$664$	−15.0645	−	3.20207i	−0.584617	−	0.124264i
$665$	48.6151	+	21.6448i	1.88521	+	0.839350i
$666$	−0.151847	−	0.467336i	−0.00588394	−	0.0181089i
$667$	−1.50121	−	4.62024i	−0.0581270	−	0.178896i
$668$	−19.5147	−	8.68849i	−0.755045	−	0.336168i
$669$	4.92209	+	1.04622i	0.190299	+	0.0404493i
$670$	9.85772	−	2.09532i	0.380837	−	0.0809494i
$671$	−28.9944	+	12.9092i	−1.11932	+	0.498353i
$672$	−1.22256	−	1.35779i	−0.0471614	−	0.0523780i
$673$	0.301365	+	2.86730i	0.0116168	+	0.110526i	0.998794	−	0.0491038i	$-0.0156365\pi$
$673$	0.301365	+	2.86730i	0.0116168	+	0.110526i	−0.987177	+	0.159630i	$0.948970\pi$
$674$	15.0704	−	10.9493i	0.580490	−	0.421750i
$675$	−2.82214	+	26.8508i	−0.108624	+	1.03349i
$676$	−9.48489	−	16.4283i	−0.364803	−	0.631858i
$677$	18.3782	−	31.8319i	0.706330	−	1.22340i	−0.259879	−	0.965641i	$-0.583683\pi$
$677$	18.3782	−	31.8319i	0.706330	−	1.22340i	0.966209	−	0.257758i	$-0.0829839\pi$
$678$	−4.09415	−	2.97457i	−0.157235	−	0.114238i
$679$	−14.0965	+	15.6558i	−0.540974	+	0.600813i
$680$	−3.42646	+	10.5456i	−0.131399	+	0.404404i
$681$	−11.8551			−0.454288
$682$	5.27915	−	12.1204i	0.202149	−	0.464112i
$683$	−50.0128			−1.91369			−0.956843	−	0.290605i	$-0.906143\pi$
$683$	−50.0128			−1.91369			−0.956843	+	0.290605i	$0.906143\pi$
$684$	4.07433	−	12.5395i	0.155786	−	0.479460i
$685$	27.9913	−	31.0874i	1.06949	−	1.18779i
$686$	12.5811	+	9.14068i	0.480347	+	0.348993i
$687$	2.51302	−	4.35267i	0.0958776	−	0.166065i
$688$	−5.63893	−	9.76692i	−0.214982	−	0.372360i
$689$	−2.40589	+	22.8905i	−0.0916570	+	0.872058i
$690$	2.50457	−	1.81968i	0.0953473	−	0.0692739i
$691$	2.01114	+	19.1347i	0.0765072	+	0.727917i	0.963785	+	0.266682i	$0.0859272\pi$
$691$	2.01114	+	19.1347i	0.0765072	+	0.727917i	−0.887278	+	0.461236i	$0.847406\pi$
$692$	3.70085	+	4.11021i	0.140685	+	0.156247i
$693$	16.7884	−	7.47467i	0.637738	−	0.283939i
$694$	−6.36265	+	1.35242i	−0.241523	+	0.0513373i
$695$	30.8263	+	6.55232i	1.16931	+	0.248544i
$696$	−1.95719	−	0.871396i	−0.0741870	−	0.0330302i
$697$	2.30391	+	7.09069i	0.0872666	+	0.268579i
$698$	9.76880	+	30.0653i	0.369755	+	1.13799i
$699$	−2.35551	−	1.04874i	−0.0890934	−	0.0396669i
$700$	−22.4853	−	4.77940i	−0.849865	−	0.180644i
$701$	−46.4620	+	9.87579i	−1.75484	+	0.373004i	−0.969315	−	0.245822i	$-0.920942\pi$
$701$	−46.4620	+	9.87579i	−1.75484	+	0.373004i	−0.785529	+	0.618825i	$0.787609\pi$
$702$	17.9348	−	7.98509i	0.676906	−	0.301378i
$703$	−0.632495	−	0.702456i	−0.0238550	−	0.0264936i
$704$	0.248193	+	2.36140i	0.00935414	+	0.0889987i
$705$	0.0264208	−	0.0191958i	0.000995065	−	0.000722957i
$706$	−3.28436	+	31.2486i	−0.123609	+	1.17606i
$707$	−1.84060	−	3.18801i	−0.0692228	−	0.119897i
$708$	2.31310	−	4.00640i	0.0869315	−	0.150570i
$709$	26.3642	+	19.1547i	0.990128	+	0.719370i	0.959949	−	0.280175i	$-0.0903923\pi$
$709$	26.3642	+	19.1547i	0.990128	+	0.719370i	0.0301787	+	0.999545i	$0.490392\pi$
$710$	−20.8515	+	23.1580i	−0.782544	+	0.869103i
$711$	−5.47309	+	16.8444i	−0.205257	+	0.631716i
$712$	−1.66174			−0.0622763
$713$	−7.75317	+	0.878422i	−0.290359	+	0.0328972i
$714$	−5.66799			−0.212119
$715$	14.8287	−	45.6380i	0.554561	−	1.70676i
$716$	−9.71783	+	10.7927i	−0.363172	+	0.403344i
$717$	−9.30727	−	6.76213i	−0.347586	−	0.252536i
$718$	−7.96905	+	13.8028i	−0.297402	+	0.515116i
$719$	13.5424	+	23.4562i	0.505047	+	0.874767i	0.999983	+	0.00583764i	$0.00185819\pi$
$719$	13.5424	+	23.4562i	0.505047	+	0.874767i	−0.494936	+	0.868929i	$0.664808\pi$
$720$	−0.978148	+	9.30645i	−0.0364534	+	0.346831i
$721$	8.78194	−	6.38045i	0.327057	−	0.237621i
$722$	−0.665092	−	6.32793i	−0.0247522	−	0.235501i
$723$	6.79159	+	7.54282i	0.252582	+	0.280520i
$724$	8.38929	−	3.73515i	0.311786	−	0.138816i
$725$	−26.3658	+	5.60422i	−0.979201	+	0.208136i
$726$	−3.24159	−	0.689022i	−0.120307	−	0.0255720i
$727$	−18.9170	−	8.42239i	−0.701592	−	0.312369i	0.0247581	−	0.999693i	$-0.492118\pi$
$727$	−18.9170	−	8.42239i	−0.701592	−	0.312369i	−0.726351	+	0.687324i	$0.758785\pi$
$728$	5.16535	+	15.8973i	0.191441	+	0.589194i
$729$	−2.62868	−	8.09024i	−0.0973584	−	0.299638i
$730$	25.6995	+	11.4422i	0.951182	+	0.423494i
$731$	−34.2216	−	7.27402i	−1.26573	−	0.269039i
$732$	8.08064	−	1.71759i	0.298669	−	0.0634841i
$733$	38.1037	−	16.9648i	1.40739	−	0.626611i	0.444322	−	0.895867i	$-0.353444\pi$
$733$	38.1037	−	16.9648i	1.40739	−	0.626611i	0.963069	+	0.269256i	$0.0867778\pi$
$734$	13.2839	+	14.7533i	0.490317	+	0.544553i
$735$	−0.401709	−	3.82200i	−0.0148172	−	0.140977i
$736$	1.13377	−	0.823734i	0.0417914	−	0.0303632i
$737$	0.699790	−	6.65805i	0.0257771	−	0.245253i
$738$	3.14600	+	5.44903i	0.115806	+	0.200582i
$739$	−24.9736	+	43.2555i	−0.918667	+	1.59118i	−0.117225	+	0.993105i	$0.537400\pi$
$739$	−24.9736	+	43.2555i	−0.918667	+	1.59118i	−0.801442	+	0.598073i	$0.795933\pi$
$740$	0.542750	+	0.394331i	0.0199519	+	0.0144959i
$741$	11.7758	−	13.0784i	0.432596	−	0.480446i
$742$	3.71878	−	11.4452i	0.136521	−	0.420168i
$743$	18.3665			0.673800			0.336900	−	0.941540i	$-0.390622\pi$
$743$	18.3665			0.673800			0.336900	+	0.941540i	$0.390622\pi$
$744$	−2.00000	+	2.80017i	−0.0733236	+	0.102659i
$745$	−26.7003			−0.978224
$746$	0.956007	−	2.94229i	0.0350019	−	0.107725i
$747$	−26.9797	+	29.9640i	−0.987137	+	1.09633i
$748$	5.95912	+	4.32955i	0.217887	+	0.158304i
$749$	26.9746	−	46.7214i	0.985631	−	1.70716i
$750$	−3.06598	−	5.31044i	−0.111954	−	0.193910i
$751$	4.93229	−	46.9276i	0.179982	−	1.71241i	−0.415960	−	0.909383i	$-0.636554\pi$
$751$	4.93229	−	46.9276i	0.179982	−	1.71241i	0.595941	−	0.803028i	$-0.296779\pi$
$752$	0.0119602	−	0.00868960i	0.000436144	−	0.000316877i
$753$	−1.36448	−	12.9822i	−0.0497245	−	0.473097i
$754$	13.1151	+	14.5658i	0.477623	+	0.530454i
$755$	5.80487	−	2.58450i	0.211261	−	0.0940595i
$756$	−10.0404	+	2.13414i	−0.365164	+	0.0776180i
$757$	−15.8403	−	3.36695i	−0.575724	−	0.122374i	−0.0891578	−	0.996018i	$-0.528418\pi$
$757$	−15.8403	−	3.36695i	−0.575724	−	0.122374i	−0.486566	+	0.873644i	$0.661751\pi$
$758$	−3.36521	−	1.49829i	−0.122230	−	0.0544203i
$759$	−0.635504	−	1.95588i	−0.0230674	−	0.0709940i
$760$	5.56257	+	17.1198i	0.201776	+	0.621001i
$761$	9.52778	+	4.24204i	0.345382	+	0.153774i	0.572094	−	0.820188i	$-0.306131\pi$
$761$	9.52778	+	4.24204i	0.345382	+	0.153774i	−0.226713	+	0.973962i	$0.572798\pi$
$762$	−1.15796	−	0.246132i	−0.0419485	−	0.00891642i
$763$	−58.0908	+	12.3476i	−2.10303	+	0.447013i
$764$	−9.71464	+	4.32524i	−0.351463	+	0.156482i
$765$	19.4245	+	21.5731i	0.702294	+	0.779976i
$766$	−2.73818	−	26.0521i	−0.0989345	−	0.941299i
$767$	−34.2404	+	24.8771i	−1.23635	+	0.898260i
$768$	0.0646021	−	0.614648i	0.00233113	−	0.0221792i
$769$	−1.63414	−	2.83041i	−0.0589285	−	0.102067i	0.835056	−	0.550165i	$-0.185435\pi$
$769$	−1.63414	−	2.83041i	−0.0589285	−	0.102067i	−0.893985	+	0.448098i	$0.852102\pi$
$770$	−12.5449	+	21.7284i	−0.452088	+	0.783039i
$771$	2.07416	+	1.50697i	0.0746992	+	0.0542721i
$772$	−1.54759	+	1.71877i	−0.0556988	+	0.0618598i
$773$	11.0442	−	33.9905i	0.397231	−	1.22255i	−0.529979	−	0.848011i	$-0.677800\pi$
$773$	11.0442	−	33.9905i	0.397231	−	1.22255i	0.927210	−	0.374541i	$-0.122200\pi$
$774$	−29.5258			−1.06128
$775$	0.350573	+	43.2926i	0.0125930	+	1.55511i
$776$	−7.12611			−0.255813
$777$	−0.105972	+	0.326147i	−0.00380171	+	0.0117005i
$778$	−9.11616	+	10.1245i	−0.326830	+	0.362982i
$779$	9.79196	+	7.11427i	0.350833	+	0.254895i
$780$	−6.24520	+	10.8170i	−0.223614	+	0.387311i
$781$	10.3504	+	17.9275i	0.370367	+	0.641495i
$782$	0.454435	−	4.32366i	0.0162506	−	0.154614i
$783$	−9.73743	+	7.07465i	−0.347987	+	0.252828i
$784$	−0.181846	−	1.73015i	−0.00649451	−	0.0617911i
$785$	−22.6508	−	25.1563i	−0.808443	−	0.897867i
$786$	4.97382	−	2.21449i	0.177410	−	0.0789881i
$787$	−21.6659	+	4.60524i	−0.772307	+	0.164159i	−0.577178	−	0.816619i	$-0.695846\pi$
$787$	−21.6659	+	4.60524i	−0.772307	+	0.164159i	−0.195129	+	0.980778i	$0.562513\pi$
$788$	2.97378	+	0.632096i	0.105936	+	0.0225175i
$789$	11.2510	+	5.00928i	0.400548	+	0.178335i
$790$	−7.47226	−	22.9972i	−0.265851	−	0.818205i
$791$	−7.48038	−	23.0222i	−0.265972	−	0.818577i
$792$	5.67886	+	2.52839i	0.201789	+	0.0898424i
$793$	−73.9270	−	15.7137i	−2.62523	−	0.558009i
$794$	28.3573	−	6.02753i	1.00636	−	0.213909i
$795$	8.21501	−	3.65756i	0.291356	−	0.129720i
$796$	12.9308	+	14.3611i	0.458319	+	0.509015i
$797$	−3.08072	−	29.3111i	−0.109125	−	1.03825i	−0.902844	−	0.429969i	$-0.858525\pi$
$797$	−3.08072	−	29.3111i	−0.109125	−	1.03825i	0.793719	−	0.608285i	$-0.208142\pi$
$798$	−7.44417	+	5.40851i	−0.263521	+	0.191459i
$799$	0.00479385	−	0.0456105i	0.000169594	−	0.00161358i
$800$	−3.88791	−	6.73407i	−0.137459	−	0.238085i
$801$	−2.17524	+	3.76763i	−0.0768585	+	0.133123i
$802$	12.7489	+	9.26263i	0.450180	+	0.327075i
$803$	12.5045	−	13.8877i	0.441275	−	0.490085i
$804$	−0.538483	+	1.65728i	−0.0189908	+	0.0584478i
$805$	14.8085			0.521931
$806$	27.1351	−	15.9608i	0.955794	−	0.562196i
$807$	9.62815			0.338927
$808$	0.384789	−	1.18426i	0.0135368	−	0.0416621i
$809$	27.9566	−	31.0490i	0.982902	−	1.09162i	−0.0128840	−	0.999917i	$-0.504101\pi$
$809$	27.9566	−	31.0490i	0.982902	−	1.09162i	0.995786	−	0.0917064i	$-0.0292321\pi$
$810$	16.5064	+	11.9926i	0.579975	+	0.421376i
$811$	−10.6396	+	18.4283i	−0.373606	+	0.647105i	−0.990117	−	0.140241i	$-0.955212\pi$
$811$	−10.6396	+	18.4283i	−0.373606	+	0.647105i	0.616511	+	0.787346i	$0.288545\pi$
$812$	−5.12398	−	8.87500i	−0.179817	−	0.311451i
$813$	−0.0557253	+	0.530191i	−0.00195437	+	0.0185946i
$814$	0.360546	−	0.261952i	0.0126371	−	0.00918141i
$815$	2.87529	+	27.3565i	0.100717	+	0.958258i
$816$	−1.28290	−	1.42480i	−0.0449104	−	0.0498781i
$817$	−51.8866	+	23.1014i	−1.81528	+	0.808216i
$818$	−27.9156	+	5.93364i	−0.976046	+	0.207465i
$819$	42.8053	+	9.09854i	1.49574	+	0.317929i
$820$	−7.84762	−	3.49399i	−0.274051	−	0.122015i
$821$	9.23613	+	28.4259i	0.322343	+	0.992070i	0.972626	+	0.232378i	$0.0746506\pi$
$821$	9.23613	+	28.4259i	0.322343	+	0.992070i	−0.650282	+	0.759693i	$0.725349\pi$
$822$	2.23518	+	6.87916i	0.0779607	+	0.239938i
$823$	24.6231	+	10.9629i	0.858308	+	0.382143i	0.788217	−	0.615397i	$-0.211004\pi$
$823$	24.6231	+	10.9629i	0.858308	+	0.382143i	0.0700910	+	0.997541i	$0.477671\pi$
$824$	3.59161	+	0.763421i	0.125120	+	0.0265950i
$825$	−11.1614	+	2.37243i	−0.388590	+	0.0825974i
$826$	20.2157	−	9.00062i	0.703395	−	0.313172i
$827$	25.9000	+	28.7649i	0.900633	+	1.00025i	0.999986	+	0.00520186i	$0.00165581\pi$
$827$	25.9000	+	28.7649i	0.900633	+	1.00025i	−0.0993537	+	0.995052i	$0.531678\pi$
$828$	−0.383511	−	3.64887i	−0.0133279	−	0.126807i
$829$	3.17237	−	2.30486i	0.110181	−	0.0800510i	−0.531330	−	0.847165i	$-0.678308\pi$
$829$	3.17237	−	2.30486i	0.110181	−	0.0800510i	0.641511	+	0.767114i	$0.278308\pi$
$830$	5.75414	−	54.7470i	0.199729	−	1.90030i
$831$	2.47845	+	4.29280i	0.0859765	+	0.148916i
$832$	−2.82709	+	4.89667i	−0.0980117	+	0.169761i
$833$	−4.36613	−	3.17218i	−0.151277	−	0.109909i
$834$	−3.64624	+	4.04956i	−0.126259	+	0.140225i
$835$	23.5943	−	72.6159i	0.816516	−	2.51298i
$836$	11.9579			0.413572
$837$	8.00580	+	17.5964i	0.276721	+	0.608222i
$838$	−30.6141			−1.05755
$839$	−1.76168	+	5.42190i	−0.0608200	+	0.187185i	−0.976850	−	0.213925i	$-0.931375\pi$
$839$	−1.76168	+	5.42190i	−0.0608200	+	0.187185i	0.916030	+	0.401109i	$0.131375\pi$
$840$	4.36984	−	4.85320i	0.150774	−	0.167451i
$841$	13.7399	+	9.98262i	0.473790	+	0.344228i
$842$	−9.36373	+	16.2185i	−0.322695	+	0.558925i
$843$	−3.38217	−	5.85808i	−0.116488	−	0.201763i
$844$	0.848277	−	8.07081i	0.0291989	−	0.277809i
$845$	54.8548	−	39.8543i	1.88706	−	1.37103i
$846$	−0.00404568	−	0.0384920i	−0.000139093	−	0.00132338i
$847$	−10.6072	−	11.7805i	−0.364467	−	0.404782i
$848$	3.71878	−	1.65571i	0.127704	−	0.0568573i
$849$	−6.26003	+	1.33061i	−0.214844	+	0.0456664i
$850$	−23.5950	−	5.01527i	−0.809302	−	0.172022i
$851$	−0.240296	−	0.106987i	−0.00823723	−	0.00366745i
$852$	−1.66505	−	5.12450i	−0.0570437	−	0.175562i
$853$	7.44515	+	22.9138i	0.254917	+	0.784554i	0.993846	+	0.110770i	$0.0353318\pi$
$853$	7.44515	+	22.9138i	0.254917	+	0.784554i	−0.738929	+	0.673783i	$0.764668\pi$
$854$	36.1000	+	16.0728i	1.23532	+	0.549998i
$855$	46.0970	+	9.79822i	1.57648	+	0.335092i
$856$	17.8502	−	3.79417i	0.610106	−	0.129682i
$857$	−5.68509	+	2.53117i	−0.194199	+	0.0864630i	−0.501532	−	0.865139i	$-0.667230\pi$
$857$	−5.68509	+	2.53117i	−0.194199	+	0.0864630i	0.307333	+	0.951602i	$0.400563\pi$
$858$	5.55199	+	6.16611i	0.189542	+	0.210507i
$859$	0.0541741	+	0.515432i	0.00184839	+	0.0175863i	0.995407	−	0.0957312i	$-0.0305189\pi$
$859$	0.0541741	+	0.515432i	0.00184839	+	0.0175863i	−0.993559	+	0.113318i	$0.963852\pi$
$860$	32.6121	−	23.6941i	1.11206	−	0.807962i
$861$	0.458995	−	4.36705i	0.0156425	−	0.148829i
$862$	15.9266	+	27.5857i	0.542463	+	0.939573i
$863$	20.6251	−	35.7237i	0.702087	−	1.21605i	−0.265646	−	0.964071i	$-0.585585\pi$
$863$	20.6251	−	35.7237i	0.702087	−	1.21605i	0.967733	−	0.251979i	$-0.0810814\pi$
$864$	−2.80902	−	2.04087i	−0.0955647	−	0.0694318i
$865$	−13.2280	+	14.6912i	−0.449767	+	0.499517i
$866$	6.51039	−	20.0369i	0.221232	−	0.680883i
$867$	4.55886			0.154827
$868$	−15.6126	+	5.21300i	−0.529928	+	0.176941i
$869$	−16.0631			−0.544905
$870$	2.36635	−	7.28288i	0.0802268	−	0.246913i
$871$	10.6674	−	11.8473i	0.361451	−	0.401432i
$872$	−16.2522	−	11.8079i	−0.550370	−	0.399867i
$873$	−9.32820	+	16.1569i	−0.315712	+	0.546829i
$874$	−3.52888	−	6.11220i	−0.119366	−	0.206748i
$875$	3.06598	−	29.1709i	0.103649	−	0.986156i
$876$	−3.93523	+	2.85911i	−0.132959	+	0.0966005i
$877$	2.12888	+	20.2550i	0.0718872	+	0.683961i	0.969819	+	0.243826i	$0.0784027\pi$
$877$	2.12888	+	20.2550i	0.0718872	+	0.683961i	−0.897932	+	0.440135i	$0.854931\pi$
$878$	−11.9321	−	13.2519i	−0.402688	−	0.447230i
$879$	6.17281	−	2.74831i	0.208204	−	0.0926982i
$880$	−8.30146	+	1.76453i	−0.279842	+	0.0594823i
$881$	5.88720	+	1.25136i	0.198345	+	0.0421595i	0.306013	−	0.952027i	$-0.401005\pi$
$881$	5.88720	+	1.25136i	0.198345	+	0.0421595i	−0.107668	+	0.994187i	$0.534338\pi$
$882$	−4.16078	−	1.85250i	−0.140101	−	0.0623769i
$883$	−10.3542	−	31.8671i	−0.348448	−	1.07241i	−0.959712	−	0.280986i	$-0.909339\pi$
$883$	−10.3542	−	31.8671i	−0.348448	−	1.07241i	0.611264	−	0.791427i	$-0.290661\pi$
$884$	5.42027	+	16.6819i	0.182303	+	0.561072i
$885$	15.1060	+	6.72561i	0.507782	+	0.226079i
$886$	−15.9759	−	3.39579i	−0.536723	−	0.114084i
$887$	−24.5369	+	5.21547i	−0.823868	+	0.175118i	−0.600509	−	0.799618i	$-0.705035\pi$
$887$	−24.5369	+	5.21547i	−0.823868	+	0.175118i	−0.223358	+	0.974736i	$0.571702\pi$
$888$	−0.105972	+	0.0471816i	−0.00355618	+	0.00158331i
$889$	−3.78910	−	4.20822i	−0.127082	−	0.141139i
$890$	−0.620857	−	5.90706i	−0.0208112	−	0.198005i
$891$	10.9651	−	7.96661i	0.367345	−	0.266892i
$892$	−0.851074	+	8.09743i	−0.0284961	+	0.271122i
$893$	−0.0372263	−	0.0644778i	−0.00124573	−	0.00215767i
$894$	2.30836	−	3.99820i	0.0772032	−	0.133720i
$895$	−41.9963	−	30.5121i	−1.40378	−	1.01991i
$896$	1.97815	−	2.19696i	0.0660853	−	0.0733951i
$897$	1.51333	−	4.65754i	0.0505285	−	0.155511i
$898$	21.4089			0.714423
$899$	−14.2381	+	13.0303i	−0.474867	+	0.434586i
$900$	−20.3574			−0.678580
$901$	3.90231	−	12.0101i	0.130005	−	0.400114i
$902$	−3.81839	+	4.24075i	−0.127138	+	0.141201i
$903$	16.6703	+	12.1117i	0.554754	+	0.403053i
$904$	4.09415	−	7.09127i	0.136169	−	0.235852i
$905$	16.4119	+	28.4263i	0.545551	+	0.944922i
$906$	−0.114846	+	1.09268i	−0.00381550	+	0.0363020i
$907$	33.4422	−	24.2972i	1.11043	−	0.806775i	0.127699	−	0.991813i	$-0.459241\pi$
$907$	33.4422	−	24.2972i	1.11043	−	0.806775i	0.982731	+	0.185038i	$0.0592410\pi$
$908$	−2.00506	−	19.0768i	−0.0665401	−	0.633087i
$909$	−2.18136	−	2.42264i	−0.0723511	−	0.0803540i
$910$	−54.5811	+	24.3011i	−1.80935	+	0.805573i
$911$	−21.8927	+	4.65343i	−0.725337	+	0.154175i	−0.555761	−	0.831342i	$-0.687573\pi$
$911$	−21.8927	+	4.65343i	−0.725337	+	0.154175i	−0.169576	+	0.985517i	$0.554240\pi$
$912$	−3.04449	−	0.647127i	−0.100813	−	0.0214285i
$913$	−33.4070	−	14.8737i	−1.10561	−	0.492249i
$914$	1.65412	+	5.09085i	0.0547134	+	0.168390i
$915$	9.12470	+	28.0829i	0.301653	+	0.928393i
$916$	7.42922	+	3.30770i	0.245468	+	0.109290i
$917$	25.4741	+	5.41470i	0.841230	+	0.178809i
$918$	−10.5359	+	2.23947i	−0.347735	+	0.0739134i
$919$	2.41544	−	1.07542i	0.0796779	−	0.0354749i	−0.366511	−	0.930414i	$-0.619448\pi$
$919$	2.41544	−	1.07542i	0.0796779	−	0.0354749i	0.446189	+	0.894939i	$0.352781\pi$
$920$	3.35177	+	3.72251i	0.110504	+	0.122728i
$921$	0.855710	+	8.14154i	0.0281966	+	0.268273i
$922$	1.54419	−	1.12192i	0.0508553	−	0.0369485i
$923$	−5.15273	+	49.0249i	−0.169604	+	1.61367i
$924$	−2.16913	−	3.75704i	−0.0713592	−	0.123598i
$925$	−0.729733	+	1.26394i	−0.0239935	+	0.0415579i
$926$	−15.3774	−	11.1723i	−0.505332	−	0.367145i
$927$	6.43237	−	7.14388i	0.211267	−	0.234636i
$928$	1.07120	−	3.29683i	0.0351640	−	0.108224i
$929$	−19.9744			−0.655338			−0.327669	−	0.944793i	$-0.606263\pi$
$929$	−19.9744			−0.655338			−0.327669	+	0.944793i	$0.606263\pi$
$930$	−10.7011	−	6.06330i	−0.350904	−	0.198823i
$931$	−8.76129			−0.287140
$932$	1.28921	−	3.96778i	0.0422295	−	0.129969i
$933$	−6.91316	+	7.67784i	−0.226327	+	0.251361i
$934$	7.72272	+	5.61088i	0.252695	+	0.183594i
$935$	−13.1640	+	22.8008i	−0.430510	+	0.745665i
$936$	7.40142	+	12.8196i	0.241923	+	0.419023i
$937$	−0.247243	+	2.35236i	−0.00807707	+	0.0768482i	−0.997818	−	0.0660263i	$-0.978968\pi$
$937$	−0.247243	+	2.35236i	−0.00807707	+	0.0768482i	0.989741	+	0.142875i	$0.0456345\pi$
$938$	−6.74346	+	4.89941i	−0.220182	+	0.159971i
$939$	1.28926	+	12.2665i	0.0420734	+	0.400302i
$940$	0.0353579	+	0.0392690i	0.00115325	+	0.00128081i
$941$	−8.46295	+	3.76795i	−0.275884	+	0.122832i	−0.540015	−	0.841655i	$-0.681582\pi$
$941$	−8.46295	+	3.76795i	−0.275884	+	0.122832i	0.264131	+	0.964487i	$0.414915\pi$
$942$	5.72526	−	1.21694i	0.186539	−	0.0396501i
$943$	3.29447	+	0.700262i	0.107283	+	0.0228037i
$944$	6.83820	+	3.04456i	0.222564	+	0.0990921i
$945$	−11.3376	−	34.8936i	−0.368812	−	1.13509i
$946$	−8.27494	−	25.4676i	−0.269041	−	0.828024i
$947$	33.0387	+	14.7098i	1.07361	+	0.478004i	0.865916	−	0.500189i	$-0.166736\pi$
$947$	33.0387	+	14.7098i	1.07361	+	0.478004i	0.207698	+	0.978193i	$0.433403\pi$
$948$	4.08970	+	0.869293i	0.132827	+	0.0282333i
$949$	43.5286	−	9.25229i	1.41300	−	0.300342i
$950$	−35.7746	+	15.9279i	−1.16068	+	0.516769i
$951$	0.844291	+	0.937680i	0.0273780	+	0.0304063i
$952$	−0.958630	−	9.12076i	−0.0310694	−	0.295606i
$953$	−25.1215	+	18.2519i	−0.813766	+	0.591236i	−0.914920	−	0.403635i	$-0.867747\pi$
$953$	−25.1215	+	18.2519i	−0.813766	+	0.591236i	0.101154	+	0.994871i	$0.467747\pi$
$954$	1.11399	−	10.5989i	0.0360667	−	0.343152i
$955$	−19.0047	−	32.9171i	−0.614978	−	1.06517i
$956$	9.30727	−	16.1207i	0.301019	−	0.521380i
$957$	−4.11543	−	2.99004i	−0.133033	−	0.0966541i
$958$	14.0700	−	15.6263i	0.454580	−	0.504862i
$959$	−10.6917	+	32.9057i	−0.345253	+	1.06258i
$960$	2.20906			0.0712970
$961$	15.9327	+	26.5923i	0.513959	+	0.857815i
$962$	1.06125			0.0342160
$963$	14.7637	−	45.4380i	0.475754	−	1.46422i
$964$	−10.9890	+	12.2045i	−0.353932	+	0.393082i
$965$	−6.68799	−	4.85911i	−0.215294	−	0.156420i
$966$	−1.28026	+	2.21748i	−0.0411917	+	0.0713462i
$967$	29.3954	+	50.9143i	0.945292	+	1.63729i	0.755166	+	0.655533i	$0.227556\pi$
$967$	29.3954	+	50.9143i	0.945292	+	1.63729i	0.190126	+	0.981760i	$0.439110\pi$
$968$	0.560501	−	5.33281i	0.0180152	−	0.171403i
$969$	−7.81155	+	5.67542i	−0.250943	+	0.182321i
$970$	−2.66245	−	25.3315i	−0.0854862	−	0.813347i
$971$	6.22320	+	6.91157i	0.199712	+	0.221803i	0.834679	−	0.550736i	$-0.185653\pi$
$971$	6.22320	+	6.91157i	0.199712	+	0.221803i	−0.634967	+	0.772539i	$0.718986\pi$
$972$	−12.7387	+	5.67165i	−0.408595	+	0.181918i
$973$	−25.4961	+	5.41937i	−0.817368	+	0.173737i
$974$	28.3802	+	6.03240i	0.909361	+	0.193291i
$975$	−24.8233	−	11.0520i	−0.794981	−	0.353948i
$976$	4.13058	+	12.7126i	0.132217	+	0.406921i
$977$	9.41352	+	28.9718i	0.301165	+	0.926891i	0.981080	+	0.193601i	$0.0620166\pi$
$977$	9.41352	+	28.9718i	0.301165	+	0.926891i	−0.679915	+	0.733291i	$0.737983\pi$
$978$	−4.34505	−	1.93454i	−0.138939	−	0.0618598i
$979$	−3.85943	−	0.820346i	−0.123348	−	0.0262184i
$980$	6.08231	−	1.29284i	0.194292	−	0.0412981i
$981$	−48.0464	+	21.3916i	−1.53400	+	0.682982i
$982$	−4.92156	−	5.46595i	−0.157053	−	0.174425i
$983$	0.0589163	+	0.560551i	0.00187914	+	0.0178788i	0.995421	−	0.0955848i	$-0.0304721\pi$
$983$	0.0589163	+	0.560551i	0.00187914	+	0.0178788i	−0.993542	+	0.113464i	$0.963805\pi$
$984$	1.20167	−	0.873061i	0.0383077	−	0.0278322i
$985$	−1.13588	+	10.8072i	−0.0361922	+	0.344346i
$986$	−5.37686	−	9.31299i	−0.171234	−	0.296586i
$987$	−0.0135055	+	0.0233923i	−0.000429886	+	0.000744584i
$988$	23.0370	+	16.7374i	0.732905	+	0.532486i
$989$	−10.5756	+	11.7454i	−0.336285	+	0.373483i
$990$	−6.86606	+	21.1316i	−0.218218	+	0.671605i
$991$	−42.9591			−1.36464			−0.682321	−	0.731053i	$-0.739029\pi$
$991$	−42.9591			−1.36464			−0.682321	+	0.731053i	$0.739029\pi$
$992$	−4.84421	−	2.74475i	−0.153804	−	0.0871458i
$993$	−0.426044			−0.0135201
$994$	7.96458	−	24.5125i	0.252621	−	0.777488i
$995$	−46.2188	+	51.3312i	−1.46523	+	1.62731i
$996$	7.70054	+	5.59477i	0.244001	+	0.177277i
$997$	24.1253	−	41.7862i	0.764056	−	1.32338i	−0.176688	−	0.984267i	$-0.556538\pi$
$997$	24.1253	−	41.7862i	0.764056	−	1.32338i	0.940744	−	0.339117i	$-0.110128\pi$
$998$	−4.76029	−	8.24506i	−0.150684	−	0.260993i
$999$	−0.0681206	+	0.648125i	−0.00215524	+	0.0205058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.g.a.45.1	✓	8
3.2	odd	2		558.2.ba.f.541.1		8
4.3	odd	2		496.2.bg.a.417.1		8
31.12	odd	30		1922.2.a.o.1.3		4
31.19	even	15		1922.2.a.q.1.1		4
31.20	even	15	inner	62.2.g.a.51.1	yes	8
93.20	odd	30		558.2.ba.f.361.1		8
124.51	odd	30		496.2.bg.a.113.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.g.a.45.1	✓	8	1.1	even	1	trivial
62.2.g.a.51.1	yes	8	31.20	even	15	inner
496.2.bg.a.113.1		8	124.51	odd	30
496.2.bg.a.417.1		8	4.3	odd	2
558.2.ba.f.361.1		8	93.20	odd	30
558.2.ba.f.541.1		8	3.2	odd	2
1922.2.a.o.1.3		4	31.12	odd	30
1922.2.a.q.1.1		4	31.19	even	15

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.413545 + 0.459289i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.78716 - 3.09546i) q^{5} +(0.309017 + 0.535233i) q^{6} +(-0.309017 + 2.94010i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.273659 + 2.60369i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.413545 + 0.459289i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.78716 - 3.09546i) q^{5} +(0.309017 + 0.535233i) q^{6} +(-0.309017 + 2.94010i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.273659 + 2.60369i) q^{9} +(-2.39169 - 2.65624i) q^{10} +(-2.16913 + 0.965759i) q^{11} +(0.604528 - 0.128496i) q^{12} +(-5.53062 - 1.17557i) q^{13} +(2.70071 + 1.20243i) q^{14} +(0.682636 + 2.10094i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.83399 + 1.26178i) q^{17} +(2.56082 + 0.544320i) q^{18} +(4.92610 - 1.04707i) q^{19} +(-3.26531 + 1.45381i) q^{20} +(-1.22256 - 1.35779i) q^{21} +(0.248193 + 2.36140i) q^{22} +(1.13377 - 0.823734i) q^{23} +(0.0646021 - 0.614648i) q^{24} +(-3.88791 - 6.73407i) q^{25} +(-2.82709 + 4.89667i) q^{26} +(-2.80902 - 2.04087i) q^{27} +(1.97815 - 2.19696i) q^{28} +(1.07120 - 3.29683i) q^{29} +2.20906 q^{30} +(-4.84421 - 2.74475i) q^{31} +1.00000 q^{32} +(0.453472 - 1.39564i) q^{33} +(2.07577 - 2.30538i) q^{34} +(8.54870 + 6.21099i) q^{35} +(1.30902 - 2.26728i) q^{36} +(-0.0938464 - 0.162547i) q^{37} +(0.526421 - 5.00856i) q^{38} +(2.82709 - 2.05400i) q^{39} +(0.373619 + 3.55475i) q^{40} +(1.60814 + 1.78602i) q^{41} +(-1.66913 + 0.743145i) q^{42} +(-11.0314 + 2.34480i) q^{43} +(2.32252 + 0.493667i) q^{44} +(8.54870 + 3.80613i) q^{45} +(-0.433063 - 1.33283i) q^{46} +(-0.00456840 - 0.0140601i) q^{47} +(-0.564602 - 0.251377i) q^{48} +(-1.70167 - 0.361700i) q^{49} +(-7.60591 + 1.61669i) q^{50} +(-1.75150 + 0.779820i) q^{51} +(3.78339 + 4.20188i) q^{52} +(-0.425506 - 4.04842i) q^{53} +(-2.80902 + 2.04087i) q^{54} +(-0.887125 + 8.44043i) q^{55} +(-1.47815 - 2.56023i) q^{56} +(-1.55626 + 2.69551i) q^{57} +(-2.80445 - 2.03755i) q^{58} +(5.00867 - 5.56269i) q^{59} +(0.682636 - 2.10094i) q^{60} +13.3669 q^{61} +(-4.10735 + 3.75894i) q^{62} -7.73968 q^{63} +(0.309017 - 0.951057i) q^{64} +(-13.5231 + 15.0189i) q^{65} +(-1.18720 - 0.862555i) q^{66} +(-1.40977 + 2.44179i) q^{67} +(-1.55110 - 2.68658i) q^{68} +(-0.0905347 + 0.861381i) q^{69} +(8.54870 - 6.21099i) q^{70} +(-0.911312 - 8.67056i) q^{71} +(-1.75181 - 1.94558i) q^{72} +(-7.19003 + 3.20121i) q^{73} +(-0.183591 + 0.0390235i) q^{74} +(4.70071 + 0.999167i) q^{75} +(-4.60075 - 2.04839i) q^{76} +(-2.16913 - 6.67590i) q^{77} +(-1.07985 - 3.32344i) q^{78} +(6.18024 + 2.75162i) q^{79} +(3.49622 + 0.743145i) q^{80} +(-5.58347 + 1.18680i) q^{81} +(2.19555 - 0.977522i) q^{82} +(10.3053 + 11.4452i) q^{83} +(0.190983 + 1.81708i) q^{84} +(8.97059 - 6.51752i) q^{85} +(-1.17886 + 11.2161i) q^{86} +(1.07120 + 1.85538i) q^{87} +(1.18720 - 2.05630i) q^{88} +(1.34437 + 0.976746i) q^{89} +(6.26153 - 6.95414i) q^{90} +(5.16535 - 15.8973i) q^{91} -1.40142 q^{92} +(3.26393 - 1.08981i) q^{93} -0.0147836 q^{94} +(5.56257 - 17.1198i) q^{95} +(-0.413545 + 0.459289i) q^{96} +(5.76515 + 4.18862i) q^{97} +(-0.869841 + 1.50661i) q^{98} +(-3.10814 - 5.38346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9} - 4 q^{10} - 13 q^{11} + 3 q^{12} + 2 q^{14} - 6 q^{15} - 2 q^{16} - 2 q^{17} + q^{18} - 3 q^{19} - 4 q^{20} + q^{21} + 17 q^{22} + 3 q^{23} - 2 q^{24} + q^{25} - 10 q^{26} - 18 q^{27} + 7 q^{28} + 11 q^{29} + 14 q^{30} + 11 q^{31} + 8 q^{32} - 2 q^{33} + 18 q^{34} + 16 q^{35} + 6 q^{36} + 6 q^{37} + 12 q^{38} + 10 q^{39} - 4 q^{40} - 19 q^{41} - 9 q^{42} - 26 q^{43} + 7 q^{44} + 16 q^{45} - 17 q^{46} + q^{47} - 2 q^{48} - 23 q^{49} - 19 q^{50} - 16 q^{51} + 17 q^{53} - 18 q^{54} + 7 q^{55} - 3 q^{56} + 6 q^{57} - 19 q^{58} + 8 q^{59} - 6 q^{60} + 48 q^{61} - 19 q^{62} - 14 q^{63} - 2 q^{64} - 30 q^{65} + 3 q^{66} + 12 q^{67} - 17 q^{68} - 7 q^{69} + 16 q^{70} + 9 q^{71} + q^{72} - 33 q^{73} - 19 q^{74} + 18 q^{75} - 18 q^{76} - 13 q^{77} - 10 q^{78} - 19 q^{79} + 11 q^{80} - 16 q^{81} + 21 q^{82} + 40 q^{83} + 6 q^{84} + 29 q^{85} + 19 q^{86} + 11 q^{87} - 3 q^{88} + 8 q^{89} + 11 q^{90} + 20 q^{91} + 28 q^{92} + 44 q^{93} + 26 q^{94} + 36 q^{95} + 3 q^{96} - 23 q^{97} + 17 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9 - 4 * q^10 - 13 * q^11 + 3 * q^12 + 2 * q^14 - 6 * q^15 - 2 * q^16 - 2 * q^17 + q^18 - 3 * q^19 - 4 * q^20 + q^21 + 17 * q^22 + 3 * q^23 - 2 * q^24 + q^25 - 10 * q^26 - 18 * q^27 + 7 * q^28 + 11 * q^29 + 14 * q^30 + 11 * q^31 + 8 * q^32 - 2 * q^33 + 18 * q^34 + 16 * q^35 + 6 * q^36 + 6 * q^37 + 12 * q^38 + 10 * q^39 - 4 * q^40 - 19 * q^41 - 9 * q^42 - 26 * q^43 + 7 * q^44 + 16 * q^45 - 17 * q^46 + q^47 - 2 * q^48 - 23 * q^49 - 19 * q^50 - 16 * q^51 + 17 * q^53 - 18 * q^54 + 7 * q^55 - 3 * q^56 + 6 * q^57 - 19 * q^58 + 8 * q^59 - 6 * q^60 + 48 * q^61 - 19 * q^62 - 14 * q^63 - 2 * q^64 - 30 * q^65 + 3 * q^66 + 12 * q^67 - 17 * q^68 - 7 * q^69 + 16 * q^70 + 9 * q^71 + q^72 - 33 * q^73 - 19 * q^74 + 18 * q^75 - 18 * q^76 - 13 * q^77 - 10 * q^78 - 19 * q^79 + 11 * q^80 - 16 * q^81 + 21 * q^82 + 40 * q^83 + 6 * q^84 + 29 * q^85 + 19 * q^86 + 11 * q^87 - 3 * q^88 + 8 * q^89 + 11 * q^90 + 20 * q^91 + 28 * q^92 + 44 * q^93 + 26 * q^94 + 36 * q^95 + 3 * q^96 - 23 * q^97 + 17 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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