LMFDB - Embedded newform 690.2.m.c.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 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("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
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} - 4 x^{19} - 3 x^{18} + 66 x^{17} - 163 x^{16} - 52 x^{15} + 1567 x^{14} - 6182 x^{13} + \cdots + 529 $ x^20 - 4x^19 - 3x^18 + 66x^17 - 163x^16 - 52x^15 + 1567x^14 - 6182x^13 + 17043x^12 - 35832x^11 + 60906x^10 - 87666x^9 + 106197x^8 - 102542x^7 + 92618x^6 - 8374x^5 + 38352x^4 + 60038x^3 + 32919x^2 + 5681*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			211.2
Root			$0.706969 + 1.54805i$ of defining polynomial
Character	$\chi$	$=$	690.211
Dual form			690.2.m.c.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 + 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(0.654861 + 0.755750i) q^{6} +(0.0903198 + 0.628188i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 + 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(0.654861 + 0.755750i) q^{6} +(0.0903198 + 0.628188i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.142315 + 0.989821i) q^{10} +(-1.92870 + 4.22327i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(-0.580306 + 4.03612i) q^{13} +(-0.533899 + 0.343116i) q^{14} +(0.959493 + 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-0.821414 - 0.947963i) q^{17} +(0.841254 + 0.540641i) q^{18} +(0.992447 - 1.14534i) q^{19} +(-0.959493 + 0.281733i) q^{20} +(0.263642 + 0.577296i) q^{21} -4.64283 q^{22} +(4.65690 + 1.14600i) q^{23} -1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(-3.91245 + 1.14880i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-0.533899 - 0.343116i) q^{28} +(3.08455 + 3.55976i) q^{29} +(0.142315 + 0.989821i) q^{30} +(4.34190 + 1.27490i) q^{31} +(0.841254 - 0.540641i) q^{32} +(-0.660744 + 4.59558i) q^{33} +(0.521069 - 1.14098i) q^{34} +(-0.263642 + 0.577296i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(8.68671 - 5.58261i) q^{37} +(1.45412 + 0.426968i) q^{38} +(0.580306 + 4.03612i) q^{39} +(-0.654861 - 0.755750i) q^{40} +(-7.73059 - 4.96815i) q^{41} +(-0.415606 + 0.479635i) q^{42} +(-7.97050 + 2.34035i) q^{43} +(-1.92870 - 4.22327i) q^{44} +1.00000 q^{45} +(0.892108 + 4.71213i) q^{46} -5.16744 q^{47} +(-0.415415 - 0.909632i) q^{48} +(6.32999 - 1.85865i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(-1.05521 - 0.678144i) q^{51} +(-2.67027 - 3.08166i) q^{52} +(0.247376 + 1.72054i) q^{53} +(0.959493 + 0.281733i) q^{54} +(-3.90580 + 2.51011i) q^{55} +(0.0903198 - 0.628188i) q^{56} +(0.629565 - 1.37855i) q^{57} +(-1.95670 + 4.28458i) q^{58} +(0.112768 - 0.784317i) q^{59} +(-0.841254 + 0.540641i) q^{60} +(-9.73628 - 2.85883i) q^{61} +(0.644003 + 4.47914i) q^{62} +(0.415606 + 0.479635i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-2.67027 + 3.08166i) q^{65} +(-4.45477 + 1.30804i) q^{66} +(-0.0920044 - 0.201462i) q^{67} +1.25433 q^{68} +(4.79112 - 0.212422i) q^{69} -0.634648 q^{70} +(2.51178 + 5.50003i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(10.6779 - 12.3229i) q^{73} +(8.68671 + 5.58261i) q^{74} +(0.654861 + 0.755750i) q^{75} +(0.215679 + 1.50008i) q^{76} +(-2.82721 - 0.830143i) q^{77} +(-3.43031 + 2.20453i) q^{78} +(1.88753 - 13.1281i) q^{79} +(0.415415 - 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(1.30778 - 9.09584i) q^{82} +(0.774423 - 0.497691i) q^{83} +(-0.608940 - 0.178801i) q^{84} +(-0.178510 - 1.24157i) q^{85} +(-5.43992 - 6.27801i) q^{86} +(3.96250 + 2.54655i) q^{87} +(3.04041 - 3.50882i) q^{88} +(2.72265 - 0.799443i) q^{89} +(0.415415 + 0.909632i) q^{90} -2.58785 q^{91} +(-3.91571 + 2.76898i) q^{92} +4.52520 q^{93} +(-2.14663 - 4.70046i) q^{94} +(1.45412 - 0.426968i) q^{95} +(0.654861 - 0.755750i) q^{96} +(5.73275 + 3.68422i) q^{97} +(4.32026 + 4.98585i) q^{98} +(0.660744 + 4.59558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	0.415415	+	0.909632i	0.293743	+	0.643207i
$2$	0.415415	+	0.909632i	0.293743	+	0.643207i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	0.841254	+	0.540641i	0.376220	+	0.241782i
$5$	0.841254	+	0.540641i	0.376220	+	0.241782i
$6$	0.654861	+	0.755750i	0.267346	+	0.308533i
$7$	0.0903198	+	0.628188i	0.0341377	+	0.237433i	0.999745	−	0.0225712i	$-0.00718525\pi$
$7$	0.0903198	+	0.628188i	0.0341377	+	0.237433i	−0.965608	+	0.260004i	$0.916276\pi$
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	−0.142315	+	0.989821i	−0.0450039	+	0.313009i
$11$	−1.92870	+	4.22327i	−0.581526	+	1.27336i	0.358903	+	0.933375i	$0.383151\pi$
$11$	−1.92870	+	4.22327i	−0.581526	+	1.27336i	−0.940429	+	0.339989i	$0.889577\pi$
$12$	−0.415415	+	0.909632i	−0.119920	+	0.262588i
$13$	−0.580306	+	4.03612i	−0.160948	+	1.11942i	0.735904	+	0.677086i	$0.236757\pi$
$13$	−0.580306	+	4.03612i	−0.160948	+	1.11942i	−0.896852	+	0.442331i	$0.854152\pi$
$14$	−0.533899	+	0.343116i	−0.142691	+	0.0917017i
$15$	0.959493	+	0.281733i	0.247740	+	0.0727430i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	−0.821414	−	0.947963i	−0.199222	−	0.229915i	0.647344	−	0.762198i	$-0.275880\pi$
$17$	−0.821414	−	0.947963i	−0.199222	−	0.229915i	−0.846566	+	0.532283i	$0.821334\pi$
$18$	0.841254	+	0.540641i	0.198285	+	0.127430i
$19$	0.992447	−	1.14534i	0.227683	−	0.262760i	−0.630401	−	0.776270i	$-0.717109\pi$
$19$	0.992447	−	1.14534i	0.227683	−	0.262760i	0.858084	+	0.513510i	$0.171655\pi$
$20$	−0.959493	+	0.281733i	−0.214549	+	0.0629973i
$21$	0.263642	+	0.577296i	0.0575314	+	0.125976i
$22$	−4.64283			−0.989856
$23$	4.65690	+	1.14600i	0.971030	+	0.238957i
$23$	4.65690	+	1.14600i	0.971030	+	0.238957i
$24$	−1.00000			−0.204124
$25$	0.415415	+	0.909632i	0.0830830	+	0.181926i
$26$	−3.91245	+	1.14880i	−0.767294	+	0.225298i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	−0.533899	−	0.343116i	−0.100898	−	0.0648429i
$29$	3.08455	+	3.55976i	0.572786	+	0.661031i	0.966038	−	0.258400i	$-0.0831953\pi$
$29$	3.08455	+	3.55976i	0.572786	+	0.661031i	−0.393252	+	0.919431i	$0.628650\pi$
$30$	0.142315	+	0.989821i	0.0259830	+	0.180716i
$31$	4.34190	+	1.27490i	0.779828	+	0.228978i	0.647335	−	0.762206i	$-0.275884\pi$
$31$	4.34190	+	1.27490i	0.779828	+	0.228978i	0.132493	+	0.991184i	$0.457702\pi$
$32$	0.841254	−	0.540641i	0.148714	−	0.0955727i
$33$	−0.660744	+	4.59558i	−0.115021	+	0.799987i
$34$	0.521069	−	1.14098i	0.0893626	−	0.195677i
$35$	−0.263642	+	0.577296i	−0.0445637	+	0.0975808i
$36$	−0.142315	+	0.989821i	−0.0237191	+	0.164970i
$37$	8.68671	−	5.58261i	1.42809	−	0.917776i	0.428186	−	0.903691i	$-0.359153\pi$
$37$	8.68671	−	5.58261i	1.42809	−	0.917776i	0.999901	−	0.0140848i	$-0.00448348\pi$
$38$	1.45412	+	0.426968i	0.235889	+	0.0692634i
$39$	0.580306	+	4.03612i	0.0929233	+	0.646296i
$40$	−0.654861	−	0.755750i	−0.103543	−	0.119494i
$41$	−7.73059	−	4.96815i	−1.20732	−	0.775895i	−0.227108	−	0.973869i	$-0.572927\pi$
$41$	−7.73059	−	4.96815i	−1.20732	−	0.775895i	−0.980207	+	0.197975i	$0.936564\pi$
$42$	−0.415606	+	0.479635i	−0.0641294	+	0.0740092i
$43$	−7.97050	+	2.34035i	−1.21549	+	0.356900i	−0.825756	−	0.564027i	$-0.809251\pi$
$43$	−7.97050	+	2.34035i	−1.21549	+	0.356900i	−0.389734	+	0.920927i	$0.627433\pi$
$44$	−1.92870	−	4.22327i	−0.290763	−	0.636682i
$45$	1.00000			0.149071
$46$	0.892108	+	4.71213i	0.131534	+	0.694765i
$47$	−5.16744			−0.753748			−0.376874	−	0.926265i	$-0.623001\pi$
$47$	−5.16744			−0.753748			−0.376874	+	0.926265i	$0.623001\pi$
$48$	−0.415415	−	0.909632i	−0.0599600	−	0.131294i
$49$	6.32999	−	1.85865i	0.904284	−	0.265522i
$50$	−0.654861	+	0.755750i	−0.0926113	+	0.106879i
$51$	−1.05521	−	0.678144i	−0.147759	−	0.0949592i
$52$	−2.67027	−	3.08166i	−0.370300	−	0.427349i
$53$	0.247376	+	1.72054i	0.0339797	+	0.236334i	0.999732	−	0.0231300i	$-0.00736315\pi$
$53$	0.247376	+	1.72054i	0.0339797	+	0.236334i	−0.965753	+	0.259464i	$0.916454\pi$
$54$	0.959493	+	0.281733i	0.130570	+	0.0383389i
$55$	−3.90580	+	2.51011i	−0.526658	+	0.338463i
$56$	0.0903198	−	0.628188i	0.0120695	−	0.0839451i
$57$	0.629565	−	1.37855i	0.0833879	−	0.182594i
$58$	−1.95670	+	4.28458i	−0.256928	+	0.562593i
$59$	0.112768	−	0.784317i	0.0146811	−	0.102109i	−0.981163	−	0.193180i	$-0.938120\pi$
$59$	0.112768	−	0.784317i	0.0146811	−	0.102109i	0.995844	+	0.0910707i	$0.0290289\pi$
$60$	−0.841254	+	0.540641i	−0.108605	+	0.0697964i
$61$	−9.73628	−	2.85883i	−1.24660	−	0.366036i	−0.409110	−	0.912485i	$-0.634161\pi$
$61$	−9.73628	−	2.85883i	−1.24660	−	0.366036i	−0.837492	+	0.546449i	$0.815979\pi$
$62$	0.644003	+	4.47914i	0.0817885	+	0.568851i
$63$	0.415606	+	0.479635i	0.0523614	+	0.0604283i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−2.67027	+	3.08166i	−0.331207	+	0.382233i
$66$	−4.45477	+	1.30804i	−0.548344	+	0.161008i
$67$	−0.0920044	−	0.201462i	−0.0112401	−	0.0246125i	0.903929	−	0.427683i	$-0.140670\pi$
$67$	−0.0920044	−	0.201462i	−0.0112401	−	0.0246125i	−0.915169	+	0.403071i	$0.867943\pi$
$68$	1.25433			0.152110
$69$	4.79112	−	0.212422i	0.576784	−	0.0255726i
$70$	−0.634648			−0.0758549
$71$	2.51178	+	5.50003i	0.298093	+	0.652733i	0.998114	−	0.0613895i	$-0.0195532\pi$
$71$	2.51178	+	5.50003i	0.298093	+	0.652733i	−0.700021	+	0.714123i	$0.746826\pi$
$72$	−0.959493	+	0.281733i	−0.113077	+	0.0332025i
$73$	10.6779	−	12.3229i	1.24975	−	1.44229i	0.398804	−	0.917036i	$-0.369425\pi$
$73$	10.6779	−	12.3229i	1.24975	−	1.44229i	0.850946	−	0.525253i	$-0.176029\pi$
$74$	8.68671	+	5.58261i	1.00981	+	0.648965i
$75$	0.654861	+	0.755750i	0.0756168	+	0.0872664i
$76$	0.215679	+	1.50008i	0.0247401	+	0.172071i
$77$	−2.82721	−	0.830143i	−0.322190	−	0.0946036i
$78$	−3.43031	+	2.20453i	−0.388406	+	0.249614i
$79$	1.88753	−	13.1281i	0.212364	−	1.47702i	−0.552868	−	0.833269i	$-0.686466\pi$
$79$	1.88753	−	13.1281i	0.212364	−	1.47702i	0.765232	−	0.643755i	$-0.222624\pi$
$80$	0.415415	−	0.909632i	0.0464448	−	0.101700i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	1.30778	−	9.09584i	0.144421	−	1.00447i
$83$	0.774423	−	0.497691i	0.0850039	−	0.0546287i	−0.497448	−	0.867494i	$-0.665730\pi$
$83$	0.774423	−	0.497691i	0.0850039	−	0.0546287i	0.582452	+	0.812865i	$0.302093\pi$
$84$	−0.608940	−	0.178801i	−0.0664408	−	0.0195088i
$85$	−0.178510	−	1.24157i	−0.0193622	−	0.134667i
$86$	−5.43992	−	6.27801i	−0.586602	−	0.676975i
$87$	3.96250	+	2.54655i	0.424825	+	0.273018i
$88$	3.04041	−	3.50882i	0.324109	−	0.374041i
$89$	2.72265	−	0.799443i	0.288601	−	0.0847408i	−0.134228	−	0.990950i	$-0.542855\pi$
$89$	2.72265	−	0.799443i	0.288601	−	0.0847408i	0.422829	+	0.906210i	$0.361037\pi$
$90$	0.415415	+	0.909632i	0.0437886	+	0.0958836i
$91$	−2.58785			−0.271281
$92$	−3.91571	+	2.76898i	−0.408241	+	0.288686i
$93$	4.52520			0.469241
$94$	−2.14663	−	4.70046i	−0.221408	−	0.484816i
$95$	1.45412	−	0.426968i	0.149190	−	0.0438060i
$96$	0.654861	−	0.755750i	0.0668364	−	0.0771334i
$97$	5.73275	+	3.68422i	0.582073	+	0.374075i	0.798293	−	0.602269i	$-0.205737\pi$
$97$	5.73275	+	3.68422i	0.582073	+	0.374075i	−0.216220	+	0.976345i	$0.569373\pi$
$98$	4.32026	+	4.98585i	0.436412	+	0.503647i
$99$	0.660744	+	4.59558i	0.0664073	+	0.461873i
$100$	−0.959493	−	0.281733i	−0.0959493	−	0.0281733i
$101$	−11.7359	+	7.54218i	−1.16776	+	0.750474i	−0.973097	−	0.230396i	$-0.925998\pi$
$101$	−11.7359	+	7.54218i	−1.16776	+	0.750474i	−0.194664	+	0.980870i	$0.562362\pi$
$102$	0.178510	−	1.24157i	0.0176752	−	0.122933i
$103$	−0.422105	+	0.924280i	−0.0415912	+	0.0910720i	−0.929287	−	0.369358i	$-0.879578\pi$
$103$	−0.422105	+	0.924280i	−0.0415912	+	0.0910720i	0.887696	+	0.460430i	$0.152305\pi$
$104$	1.69390	−	3.70913i	0.166101	−	0.363710i
$105$	−0.0903198	+	0.628188i	−0.00881431	+	0.0613048i
$106$	−1.46229	+	0.939759i	−0.142030	+	0.0912775i
$107$	3.99701	+	1.17363i	0.386406	+	0.113459i	0.469165	−	0.883111i	$-0.344555\pi$
$107$	3.99701	+	1.17363i	0.386406	+	0.113459i	−0.0827590	+	0.996570i	$0.526373\pi$
$108$	0.142315	+	0.989821i	0.0136943	+	0.0952456i
$109$	−12.2888	−	14.1821i	−1.17706	−	1.35840i	−0.919960	−	0.392012i	$-0.871779\pi$
$109$	−12.2888	−	14.1821i	−1.17706	−	1.35840i	−0.257098	−	0.966385i	$-0.582766\pi$
$110$	−3.90580	−	2.51011i	−0.372403	−	0.239329i
$111$	6.76204	−	7.80381i	0.641824	−	0.740704i
$112$	0.608940	−	0.178801i	0.0575394	−	0.0168951i
$113$	−2.44726	−	5.35875i	−0.230219	−	0.504109i	0.758904	−	0.651203i	$-0.225735\pi$
$113$	−2.44726	−	5.35875i	−0.230219	−	0.504109i	−0.989122	+	0.147094i	$0.953008\pi$
$114$	1.51551			0.141940
$115$	3.29806	+	3.48178i	0.307545	+	0.324678i
$116$	−4.71024			−0.437334
$117$	1.69390	+	3.70913i	0.156602	+	0.342909i
$118$	0.760285	−	0.223240i	0.0699899	−	0.0205509i
$119$	0.521309	−	0.601622i	0.0477883	−	0.0551506i
$120$	−0.841254	−	0.540641i	−0.0767956	−	0.0493535i
$121$	−6.91265	−	7.97762i	−0.628423	−	0.725239i
$122$	−1.44411	−	10.0440i	−0.130744	−	0.909344i
$123$	−8.81714	−	2.58895i	−0.795014	−	0.233437i
$124$	−3.80684	+	2.44651i	−0.341864	+	0.219703i
$125$	−0.142315	+	0.989821i	−0.0127290	+	0.0885323i
$126$	−0.263642	+	0.577296i	−0.0234871	+	0.0514296i
$127$	6.38105	−	13.9726i	0.566227	−	1.23986i	−0.382555	−	0.923933i	$-0.624956\pi$
$127$	6.38105	−	13.9726i	0.566227	−	1.23986i	0.948782	−	0.315931i	$-0.102317\pi$
$128$	−0.142315	+	0.989821i	−0.0125790	+	0.0874887i
$129$	−6.98829	+	4.49110i	−0.615284	+	0.395419i
$130$	−3.91245	−	1.14880i	−0.343144	−	0.100756i
$131$	2.42640	+	16.8760i	0.211996	+	1.47446i	0.766481	+	0.642268i	$0.222006\pi$
$131$	2.42640	+	16.8760i	0.211996	+	1.47446i	−0.554485	+	0.832194i	$0.687085\pi$
$132$	−3.04041	−	3.50882i	−0.264634	−	0.305404i
$133$	0.809129	+	0.519996i	0.0701604	+	0.0450893i
$134$	0.145036	−	0.167380i	0.0125292	−	0.0144595i
$135$	0.959493	−	0.281733i	0.0825800	−	0.0242477i
$136$	0.521069	+	1.14098i	0.0446813	+	0.0978384i
$137$	5.52659			0.472169			0.236084	−	0.971733i	$-0.424136\pi$
$137$	5.52659			0.472169			0.236084	+	0.971733i	$0.424136\pi$
$138$	2.18353	+	4.26992i	0.185875	+	0.363479i
$139$	0.415639			0.0352540			0.0176270	−	0.999845i	$-0.494389\pi$
$139$	0.415639			0.0352540			0.0176270	+	0.999845i	$0.494389\pi$
$140$	−0.263642	−	0.577296i	−0.0222818	−	0.0487904i
$141$	−4.95812	+	1.45583i	−0.417549	+	0.122603i
$142$	−3.95957	+	4.56959i	−0.332280	+	0.383471i
$143$	−15.9264	−	10.2353i	−1.33183	−	0.855915i
$144$	−0.654861	−	0.755750i	−0.0545717	−	0.0629791i
$145$	0.670337	+	4.66229i	0.0556684	+	0.387182i
$146$	15.6451	+	4.59381i	1.29480	+	0.380186i
$147$	5.54994	−	3.56673i	0.457751	−	0.294179i
$148$	−1.46953	+	10.2208i	−0.120795	+	0.840146i
$149$	2.16320	−	4.73674i	0.177216	−	0.388049i	−0.800090	−	0.599879i	$-0.795215\pi$
$149$	2.16320	−	4.73674i	0.177216	−	0.388049i	0.977306	+	0.211831i	$0.0679425\pi$
$150$	−0.415415	+	0.909632i	−0.0339185	+	0.0742711i
$151$	2.91493	−	20.2738i	0.237213	−	1.64985i	−0.428423	−	0.903578i	$-0.640931\pi$
$151$	2.91493	−	20.2738i	0.237213	−	1.64985i	0.665636	−	0.746277i	$-0.268160\pi$
$152$	−1.27493	+	0.819346i	−0.103410	+	0.0664577i
$153$	−1.20352	−	0.353387i	−0.0972992	−	0.0285696i
$154$	−0.419340	−	2.91657i	−0.0337914	−	0.235024i
$155$	2.96338	+	3.41992i	0.238024	+	0.274694i
$156$	−3.43031	−	2.20453i	−0.274645	−	0.176503i
$157$	12.1505	−	14.0224i	0.969714	−	1.11911i	−0.0231352	−	0.999732i	$-0.507365\pi$
$157$	12.1505	−	14.0224i	0.969714	−	1.11911i	0.992849	−	0.119377i	$-0.0380897\pi$
$158$	12.7258	−	3.73664i	1.01241	−	0.297271i
$159$	0.722088	+	1.58115i	0.0572653	+	0.125393i
$160$	1.00000			0.0790569
$161$	−0.299292	+	3.02891i	−0.0235875	+	0.238712i
$162$	1.00000			0.0785674
$163$	7.35041	+	16.0952i	0.575729	+	1.26067i	0.943691	+	0.330829i	$0.107328\pi$
$163$	7.35041	+	16.0952i	0.575729	+	1.26067i	−0.367962	+	0.929841i	$0.619944\pi$
$164$	8.81714	−	2.58895i	0.688503	−	0.202163i
$165$	−3.04041	+	3.50882i	−0.236696	+	0.273161i
$166$	0.774423	+	0.497691i	0.0601069	+	0.0386283i
$167$	6.82003	+	7.87074i	0.527750	+	0.609056i	0.955554	−	0.294815i	$-0.0952582\pi$
$167$	6.82003	+	7.87074i	0.527750	+	0.609056i	−0.427804	+	0.903871i	$0.640713\pi$
$168$	−0.0903198	−	0.628188i	−0.00696832	−	0.0484657i
$169$	−3.48006	−	1.02184i	−0.267697	−	0.0786030i
$170$	1.05521	−	0.678144i	0.0809312	−	0.0520113i
$171$	0.215679	−	1.50008i	0.0164934	−	0.114714i
$172$	3.45085	−	7.55631i	0.263125	−	0.576163i
$173$	6.13672	−	13.4375i	0.466566	−	1.02164i	−0.519375	−	0.854546i	$-0.673835\pi$
$173$	6.13672	−	13.4375i	0.466566	−	1.02164i	0.985941	−	0.167091i	$-0.0534375\pi$
$174$	−0.670337	+	4.66229i	−0.0508181	+	0.353448i
$175$	−0.533899	+	0.343116i	−0.0403590	+	0.0259372i
$176$	4.45477	+	1.30804i	0.335791	+	0.0985970i
$177$	−0.112768	−	0.784317i	−0.00847614	−	0.0589529i
$178$	1.85823	+	2.14451i	0.139280	+	0.160738i
$179$	−7.79833	−	5.01168i	−0.582874	−	0.374591i	0.215725	−	0.976454i	$-0.430789\pi$
$179$	−7.79833	−	5.01168i	−0.582874	−	0.374591i	−0.798599	+	0.601864i	$0.794425\pi$
$180$	−0.654861	+	0.755750i	−0.0488104	+	0.0563302i
$181$	2.25536	−	0.662234i	0.167640	−	0.0492234i	−0.196836	−	0.980436i	$-0.563067\pi$
$181$	2.25536	−	0.662234i	0.167640	−	0.0492234i	0.364475	+	0.931213i	$0.381248\pi$
$182$	−1.07503	−	2.35399i	−0.0796867	−	0.174490i
$183$	−10.1473			−0.750111
$184$	−4.14539	−	2.41158i	−0.305603	−	0.177784i
$185$	10.3259			0.759176
$186$	1.87984	+	4.11627i	0.137836	+	0.301819i
$187$	5.58777	−	1.64072i	0.408618	−	0.119981i
$188$	3.38395	−	3.90529i	0.246800	−	0.284822i
$189$	0.533899	+	0.343116i	0.0388355	+	0.0249580i
$190$	0.992447	+	1.14534i	0.0719997	+	0.0830920i
$191$	2.20839	+	15.3597i	0.159793	+	1.11139i	0.899013	+	0.437922i	$0.144286\pi$
$191$	2.20839	+	15.3597i	0.159793	+	1.11139i	−0.739220	+	0.673465i	$0.764805\pi$
$192$	0.959493	+	0.281733i	0.0692454	+	0.0203323i
$193$	12.2985	−	7.90377i	0.885266	−	0.568926i	−0.0171204	−	0.999853i	$-0.505450\pi$
$193$	12.2985	−	7.90377i	0.885266	−	0.568926i	0.902387	+	0.430927i	$0.141814\pi$
$194$	−0.969809	+	6.74517i	−0.0696283	+	0.484275i
$195$	−1.69390	+	3.70913i	−0.121303	+	0.265617i
$196$	−2.74059	+	6.00104i	−0.195756	+	0.428646i
$197$	1.40666	−	9.78356i	0.100221	−	0.697049i	−0.876322	−	0.481726i	$-0.840010\pi$
$197$	1.40666	−	9.78356i	0.100221	−	0.697049i	0.976543	−	0.215324i	$-0.0690807\pi$
$198$	−3.90580	+	2.51011i	−0.277573	+	0.178385i
$199$	−0.653037	−	0.191749i	−0.0462926	−	0.0135927i	0.258504	−	0.966010i	$-0.416770\pi$
$199$	−0.653037	−	0.191749i	−0.0462926	−	0.0135927i	−0.304797	+	0.952417i	$0.598589\pi$
$200$	−0.142315	−	0.989821i	−0.0100632	−	0.0699909i
$201$	−0.145036	−	0.167380i	−0.0102300	−	0.0118061i
$202$	−11.7359	−	7.54218i	−0.825732	−	0.530666i
$203$	−1.95760	+	2.25919i	−0.137397	+	0.158564i
$204$	1.20352	−	0.353387i	0.0842636	−	0.0247420i
$205$	−3.81740	−	8.35895i	−0.266619	−	0.583814i
$206$	−1.01610			−0.0707953
$207$	4.53720	−	1.55363i	0.315357	−	0.107985i
$208$	4.07762			0.282732
$209$	2.92297	+	6.40040i	0.202186	+	0.442725i
$210$	−0.608940	+	0.178801i	−0.0420208	+	0.0123384i
$211$	−11.1605	+	12.8799i	−0.768321	+	0.886689i	−0.996208	−	0.0869981i	$-0.972273\pi$
$211$	−11.1605	+	12.8799i	−0.768321	+	0.886689i	0.227888	+	0.973687i	$0.426818\pi$
$212$	−1.46229	−	0.939759i	−0.100431	−	0.0645429i
$213$	3.95957	+	4.56959i	0.271305	+	0.313103i
$214$	0.592849	+	4.12335i	0.0405263	+	0.281867i
$215$	−7.97050	−	2.34035i	−0.543584	−	0.159611i
$216$	−0.841254	+	0.540641i	−0.0572401	+	0.0367859i
$217$	−0.408715	+	2.84268i	−0.0277454	+	0.192973i
$218$	7.79551	−	17.0698i	0.527978	−	1.15611i
$219$	6.77358	−	14.8321i	0.457716	−	1.00226i
$220$	0.660744	−	4.59558i	0.0445474	−	0.309834i
$221$	4.30276	−	2.76521i	0.289435	−	0.186008i
$222$	9.90764	+	2.90915i	0.664957	+	0.195249i
$223$	0.292102	+	2.03161i	0.0195606	+	0.136047i	0.997262	−	0.0739549i	$-0.0235621\pi$
$223$	0.292102	+	2.03161i	0.0195606	+	0.136047i	−0.977701	+	0.210002i	$0.932653\pi$
$224$	0.415606	+	0.479635i	0.0277688	+	0.0320469i
$225$	0.841254	+	0.540641i	0.0560836	+	0.0360427i
$226$	3.85786	−	4.45221i	0.256621	−	0.296156i
$227$	−10.1046	+	2.96697i	−0.670664	+	0.196925i	−0.599298	−	0.800526i	$-0.704554\pi$
$227$	−10.1046	+	2.96697i	−0.670664	+	0.196925i	−0.0713651	+	0.997450i	$0.522736\pi$
$228$	0.629565	+	1.37855i	0.0416939	+	0.0912970i
$229$	−13.4818			−0.890903			−0.445452	−	0.895306i	$-0.646957\pi$
$229$	−13.4818			−0.890903			−0.445452	+	0.895306i	$0.646957\pi$
$230$	−1.79708	+	4.44640i	−0.118496	+	0.293187i
$231$	−2.94656			−0.193870
$232$	−1.95670	−	4.28458i	−0.128464	−	0.281297i
$233$	19.8322	−	5.82327i	1.29925	−	0.381495i	0.442289	−	0.896872i	$-0.354166\pi$
$233$	19.8322	−	5.82327i	1.29925	−	0.381495i	0.856963	+	0.515377i	$0.172348\pi$
$234$	−2.67027	+	3.08166i	−0.174561	+	0.201454i
$235$	−4.34712	−	2.79373i	−0.283575	−	0.182243i
$236$	0.518900	+	0.598842i	0.0337775	+	0.0389813i
$237$	−1.88753	−	13.1281i	−0.122608	−	0.852760i
$238$	0.763814	+	0.224276i	0.0495107	+	0.0145377i
$239$	−19.9411	+	12.8153i	−1.28988	+	0.828955i	−0.992072	−	0.125671i	$-0.959892\pi$
$239$	−19.9411	+	12.8153i	−1.28988	+	0.828955i	−0.297807	+	0.954626i	$0.596255\pi$
$240$	0.142315	−	0.989821i	0.00918638	−	0.0638927i
$241$	−10.8214	+	23.6955i	−0.697066	+	1.52636i	0.146428	+	0.989221i	$0.453222\pi$
$241$	−10.8214	+	23.6955i	−0.697066	+	1.52636i	−0.843493	+	0.537140i	$0.819505\pi$
$242$	4.38508	−	9.60199i	0.281884	−	0.617239i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	8.53646	−	5.48605i	0.546491	−	0.351209i
$245$	6.32999	+	1.85865i	0.404408	+	0.118745i
$246$	−1.30778	−	9.09584i	−0.0833813	−	0.579929i
$247$	4.04682	+	4.67028i	0.257493	+	0.297163i
$248$	−3.80684	−	2.44651i	−0.241735	−	0.155353i
$249$	0.602837	−	0.695711i	0.0382033	−	0.0440889i
$250$	−0.959493	+	0.281733i	−0.0606837	+	0.0178183i
$251$	−1.14910	−	2.51618i	−0.0725307	−	0.158820i	0.869894	−	0.493239i	$-0.164187\pi$
$251$	−1.14910	−	2.51618i	−0.0725307	−	0.158820i	−0.942425	+	0.334419i	$0.891460\pi$
$252$	−0.634648			−0.0399790
$253$	−13.8216	+	17.4570i	−0.868958	+	1.09752i
$254$	15.3607			0.963814
$255$	−0.521069	−	1.14098i	−0.0326306	−	0.0714511i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	3.54282	−	4.08863i	0.220995	−	0.255042i	−0.634416	−	0.772992i	$-0.718759\pi$
$257$	3.54282	−	4.08863i	0.220995	−	0.255042i	0.855411	+	0.517950i	$0.173305\pi$
$258$	−6.98829	−	4.49110i	−0.435072	−	0.279604i
$259$	4.29151	+	4.95267i	0.266661	+	0.307744i
$260$	−0.580306	−	4.03612i	−0.0359890	−	0.250309i
$261$	4.51944	+	1.32703i	0.279746	+	0.0821409i
$262$	−14.3430	+	9.21767i	−0.886112	+	0.569469i
$263$	−0.702621	+	4.88684i	−0.0433255	+	0.301335i	0.956624	+	0.291324i	$0.0940958\pi$
$263$	−0.702621	+	4.88684i	−0.0433255	+	0.301335i	−0.999950	+	0.0100111i	$0.996813\pi$
$264$	1.92870	−	4.22327i	0.118703	−	0.259924i
$265$	−0.722088	+	1.58115i	−0.0443575	+	0.0971293i
$266$	−0.136880	+	0.952024i	−0.00839267	+	0.0583723i
$267$	2.38714	−	1.53412i	0.146091	−	0.0938867i
$268$	0.212505	+	0.0623970i	0.0129808	+	0.00381150i
$269$	−0.977048	−	6.79552i	−0.0595717	−	0.414330i	−0.997685	−	0.0680021i	$-0.978338\pi$
$269$	−0.977048	−	6.79552i	−0.0595717	−	0.414330i	0.938113	−	0.346328i	$-0.112572\pi$
$270$	0.654861	+	0.755750i	0.0398536	+	0.0459935i
$271$	3.50106	+	2.25000i	0.212674	+	0.136678i	0.642641	−	0.766167i	$-0.277838\pi$
$271$	3.50106	+	2.25000i	0.212674	+	0.136678i	−0.429967	+	0.902845i	$0.641475\pi$
$272$	−0.821414	+	0.947963i	−0.0498056	+	0.0574787i
$273$	−2.48303	+	0.729082i	−0.150280	+	0.0441260i
$274$	2.29583	+	5.02717i	0.138696	+	0.303702i
$275$	−4.64283			−0.279973
$276$	−2.97698	+	3.76000i	−0.179193	+	0.226325i
$277$	23.7731			1.42839			0.714193	−	0.699948i	$-0.246794\pi$
$277$	23.7731			1.42839			0.714193	+	0.699948i	$0.246794\pi$
$278$	0.172663	+	0.378078i	0.0103556	+	0.0226756i
$279$	4.34190	−	1.27490i	0.259943	−	0.0763260i
$280$	0.415606	−	0.479635i	0.0248372	−	0.0286637i
$281$	−11.0316	−	7.08959i	−0.658091	−	0.422929i	0.168524	−	0.985698i	$-0.446100\pi$
$281$	−11.0316	−	7.08959i	−0.658091	−	0.422929i	−0.826615	+	0.562768i	$0.809736\pi$
$282$	−3.38395	−	3.90529i	−0.201511	−	0.232556i
$283$	−0.578738	−	4.02521i	−0.0344024	−	0.239274i	0.965364	−	0.260908i	$-0.0840221\pi$
$283$	−0.578738	−	4.02521i	−0.0344024	−	0.239274i	−0.999766	+	0.0216346i	$0.993113\pi$
$284$	−5.80151	−	1.70348i	−0.344256	−	0.101083i
$285$	1.27493	−	0.819346i	0.0755201	−	0.0485338i
$286$	2.69426	−	18.7390i	0.159315	−	1.10806i
$287$	2.42271	−	5.30498i	0.143008	−	0.313143i
$288$	0.415415	−	0.909632i	0.0244786	−	0.0536006i
$289$	2.19544	−	15.2696i	0.129144	−	0.898213i
$290$	−3.96250	+	2.54655i	−0.232686	+	0.149538i
$291$	6.53850	+	1.91988i	0.383294	+	0.112545i
$292$	2.32052	+	16.1396i	0.135798	+	0.944498i
$293$	−19.3798	−	22.3655i	−1.13218	−	1.30660i	−0.946029	−	0.324083i	$-0.894944\pi$
$293$	−19.3798	−	22.3655i	−1.13218	−	1.30660i	−0.186150	−	0.982521i	$-0.559601\pi$
$294$	5.54994	+	3.56673i	0.323679	+	0.208016i
$295$	0.518900	−	0.598842i	0.0302115	−	0.0348660i
$296$	−9.90764	+	2.90915i	−0.575870	+	0.169091i
$297$	1.92870	+	4.22327i	0.111915	+	0.245059i
$298$	5.20731			0.301652
$299$	−7.32780	+	18.1307i	−0.423778	+	1.04853i
$300$	−1.00000			−0.0577350
$301$	−2.19007	−	4.79559i	−0.126234	−	0.276413i
$302$	19.6526	−	5.77051i	1.13088	−	0.332056i
$303$	−9.13559	+	10.5430i	−0.524826	+	0.605682i
$304$	−1.27493	−	0.819346i	−0.0731221	−	0.0469927i
$305$	−6.64508	−	7.66883i	−0.380496	−	0.439116i
$306$	−0.178510	−	1.24157i	−0.0102048	−	0.0709757i
$307$	16.0476	+	4.71199i	0.915883	+	0.268928i	0.705515	−	0.708695i	$-0.250716\pi$
$307$	16.0476	+	4.71199i	0.915883	+	0.268928i	0.210368	+	0.977622i	$0.432534\pi$
$308$	2.47881	−	1.59303i	0.141243	−	0.0907714i
$309$	−0.144607	+	1.00576i	−0.00822638	+	0.0572158i
$310$	−1.87984	+	4.11627i	−0.106768	+	0.233788i
$311$	−12.8962	+	28.2387i	−0.731274	+	1.60127i	0.0661225	+	0.997812i	$0.478937\pi$
$311$	−12.8962	+	28.2387i	−0.731274	+	1.60127i	−0.797397	+	0.603456i	$0.793790\pi$
$312$	0.580306	−	4.03612i	0.0328533	−	0.228500i
$313$	−16.2299	+	10.4303i	−0.917367	+	0.589556i	−0.911892	−	0.410429i	$-0.865379\pi$
$313$	−16.2299	+	10.4303i	−0.917367	+	0.589556i	−0.00547422	+	0.999985i	$0.501743\pi$
$314$	17.8027	+	5.22735i	1.00467	+	0.294996i
$315$	0.0903198	+	0.628188i	0.00508894	+	0.0353944i
$316$	8.68547	+	10.0236i	0.488596	+	0.563870i
$317$	21.6010	+	13.8821i	1.21323	+	0.779696i	0.981196	−	0.193012i	$-0.0618256\pi$
$317$	21.6010	+	13.8821i	1.21323	+	0.779696i	0.232034	+	0.972708i	$0.425462\pi$
$318$	−1.13830	+	1.31367i	−0.0638327	+	0.0736668i
$319$	−20.9830	+	6.16117i	−1.17482	+	0.344959i
$320$	0.415415	+	0.909632i	0.0232224	+	0.0508500i
$321$	4.16576			0.232510
$322$	−2.87953	+	0.986010i	−0.160470	+	0.0549482i
$323$	−1.90095			−0.105772
$324$	0.415415	+	0.909632i	0.0230786	+	0.0505351i
$325$	−3.91245	+	1.14880i	−0.217024	+	0.0637239i
$326$	−11.5872	+	13.3723i	−0.641755	+	0.740625i
$327$	−15.7866	−	10.1454i	−0.873002	−	0.561044i
$328$	6.01776	+	6.94486i	0.332275	+	0.383466i
$329$	−0.466722	−	3.24612i	−0.0257312	−	0.178964i
$330$	−4.45477	−	1.30804i	−0.245227	−	0.0720051i
$331$	−20.2940	+	13.0422i	−1.11546	+	0.716863i	−0.962476	−	0.271366i	$-0.912525\pi$
$331$	−20.2940	+	13.0422i	−1.11546	+	0.716863i	−0.152984	+	0.988229i	$0.548888\pi$
$332$	−0.131009	+	0.911188i	−0.00719006	+	0.0500079i
$333$	4.28954	−	9.39278i	0.235065	−	0.514721i
$334$	−4.32633	+	9.47334i	−0.236726	+	0.518358i
$335$	0.0315193	−	0.219222i	0.00172208	−	0.0119774i
$336$	0.533899	−	0.343116i	0.0291266	−	0.0187185i
$337$	−10.7411	−	3.15388i	−0.585106	−	0.171803i	−0.0242357	−	0.999706i	$-0.507715\pi$
$337$	−10.7411	−	3.15388i	−0.585106	−	0.171803i	−0.560870	+	0.827904i	$0.689533\pi$
$338$	−0.516173	−	3.59006i	−0.0280761	−	0.195274i
$339$	−3.85786	−	4.45221i	−0.209530	−	0.241811i
$340$	1.05521	+	0.678144i	0.0572270	+	0.0367775i
$341$	−13.7585	+	15.8781i	−0.745063	+	0.859848i
$342$	1.45412	−	0.426968i	0.0786298	−	0.0230878i
$343$	3.58480	+	7.84962i	0.193561	+	0.423840i
$344$	8.30699			0.447883
$345$	4.14539	+	2.41158i	0.223181	+	0.129835i
$346$	14.7725			0.794175
$347$	−3.80652	−	8.33512i	−0.204345	−	0.447453i	0.779517	−	0.626381i	$-0.215464\pi$
$347$	−3.80652	−	8.33512i	−0.204345	−	0.447453i	−0.983862	+	0.178928i	$0.942737\pi$
$348$	−4.51944	+	1.32703i	−0.242267	+	0.0711361i
$349$	1.69993	−	1.96182i	0.0909950	−	0.105014i	−0.708426	−	0.705785i	$-0.750594\pi$
$349$	1.69993	−	1.96182i	0.0909950	−	0.105014i	0.799421	+	0.600771i	$0.205140\pi$
$350$	−0.533899	−	0.343116i	−0.0285381	−	0.0183403i
$351$	2.67027	+	3.08166i	0.142529	+	0.164487i
$352$	0.660744	+	4.59558i	0.0352178	+	0.244945i
$353$	0.0427256	+	0.0125454i	0.00227406	+	0.000667723i	0.282869	−	0.959158i	$-0.408714\pi$
$353$	0.0427256	+	0.0125454i	0.00227406	+	0.000667723i	−0.280595	+	0.959826i	$0.590532\pi$
$354$	0.666594	−	0.428394i	0.0354291	−	0.0227689i
$355$	−0.860497	+	5.98489i	−0.0456704	+	0.317645i
$356$	−1.17878	+	2.58117i	−0.0624752	+	0.136802i
$357$	0.330695	−	0.724122i	0.0175023	−	0.0383246i
$358$	1.31924	−	9.17553i	0.0697241	−	0.484942i
$359$	−12.2268	+	7.85768i	−0.645305	+	0.414713i	−0.821948	−	0.569562i	$-0.807113\pi$
$359$	−12.2268	+	7.85768i	−0.645305	+	0.414713i	0.176643	+	0.984275i	$0.443476\pi$
$360$	−0.959493	−	0.281733i	−0.0505697	−	0.0148486i
$361$	2.37712	+	16.5332i	0.125111	+	0.870169i
$362$	1.53930	+	1.77645i	0.0809038	+	0.0933680i
$363$	−8.88020	−	5.70696i	−0.466089	−	0.299537i
$364$	1.69468	−	1.95577i	0.0888255	−	0.102510i
$365$	15.6451	−	4.59381i	0.818901	−	0.240451i
$366$	−4.21535	−	9.23032i	−0.220340	−	0.482477i
$367$	−12.1296			−0.633161			−0.316581	−	0.948566i	$-0.602535\pi$
$367$	−12.1296			−0.633161			−0.316581	+	0.948566i	$0.602535\pi$
$368$	0.471588	−	4.77259i	0.0245832	−	0.248788i
$369$	−9.18937			−0.478380
$370$	4.28954	+	9.39278i	0.223003	+	0.488307i
$371$	−1.05848	+	0.310797i	−0.0549535	+	0.0161358i
$372$	−2.96338	+	3.41992i	−0.153644	+	0.177314i
$373$	−9.69647	−	6.23154i	−0.502064	−	0.322657i	0.264977	−	0.964255i	$-0.414636\pi$
$373$	−9.69647	−	6.23154i	−0.502064	−	0.322657i	−0.767041	+	0.641598i	$0.778272\pi$
$374$	3.81369	+	4.40123i	0.197201	+	0.227582i
$375$	0.142315	+	0.989821i	0.00734911	+	0.0511142i
$376$	4.95812	+	1.45583i	0.255695	+	0.0750790i
$377$	−16.1576	+	10.3838i	−0.832158	+	0.534795i
$378$	−0.0903198	+	0.628188i	−0.00464555	+	0.0323105i
$379$	−8.76485	+	19.1923i	−0.450220	+	0.985844i	0.539389	+	0.842057i	$0.318655\pi$
$379$	−8.76485	+	19.1923i	−0.450220	+	0.985844i	−0.989609	+	0.143787i	$0.954072\pi$
$380$	−0.629565	+	1.37855i	−0.0322960	+	0.0707184i
$381$	2.18605	−	15.2043i	0.111995	−	0.778941i
$382$	−13.0543	+	8.38946i	−0.667914	+	0.429242i
$383$	−18.1179	−	5.31989i	−0.925780	−	0.271834i	−0.216111	−	0.976369i	$-0.569337\pi$
$383$	−18.1179	−	5.31989i	−0.925780	−	0.271834i	−0.709669	+	0.704535i	$0.751156\pi$
$384$	0.142315	+	0.989821i	0.00726247	+	0.0505116i
$385$	−1.92959	−	2.22686i	−0.0983409	−	0.113491i
$386$	12.2985	+	7.90377i	0.625978	+	0.402291i
$387$	−5.43992	+	6.27801i	−0.276527	+	0.319129i
$388$	−6.53850	+	1.91988i	−0.331942	+	0.0974669i
$389$	5.33480	+	11.6816i	0.270485	+	0.592280i	0.995319	−	0.0966437i	$-0.0308107\pi$
$389$	5.33480	+	11.6816i	0.270485	+	0.592280i	−0.724834	+	0.688924i	$0.758083\pi$
$390$	−4.07762			−0.206478
$391$	−2.73888	−	5.35590i	−0.138511	−	0.270860i
$392$	−6.59722			−0.333210
$393$	7.08263	+	15.5088i	0.357271	+	0.782315i
$394$	9.48378	−	2.78469i	0.477786	−	0.140291i
$395$	8.68547	−	10.0236i	0.437013	−	0.504340i
$396$	−3.90580	−	2.51011i	−0.196274	−	0.126138i
$397$	17.5657	+	20.2719i	0.881598	+	1.01742i	0.999702	+	0.0244169i	$0.00777292\pi$
$397$	17.5657	+	20.2719i	0.881598	+	1.01742i	−0.118104	+	0.993001i	$0.537682\pi$
$398$	−0.0968604	−	0.673679i	−0.00485517	−	0.0337685i
$399$	0.922853	+	0.270974i	0.0462005	+	0.0135657i
$400$	0.841254	−	0.540641i	0.0420627	−	0.0270320i
$401$	0.137366	−	0.955401i	0.00685973	−	0.0477105i	−0.986104	−	0.166129i	$-0.946873\pi$
$401$	0.137366	−	0.955401i	0.00685973	−	0.0477105i	0.992964	+	0.118418i	$0.0377824\pi$
$402$	0.0920044	−	0.201462i	0.00458876	−	0.0100480i
$403$	−7.66526	+	16.7846i	−0.381834	+	0.836099i
$404$	1.98535	−	13.8084i	0.0987751	−	0.686996i
$405$	0.841254	−	0.540641i	0.0418022	−	0.0268647i
$406$	−2.86825	−	0.842194i	−0.142349	−	0.0417974i
$407$	6.82279	+	47.4535i	0.338193	+	2.35218i
$408$	0.821414	+	0.947963i	0.0406661	+	0.0469311i
$409$	15.0330	+	9.66114i	0.743335	+	0.477712i	0.856683	−	0.515843i	$-0.172521\pi$
$409$	15.0330	+	9.66114i	0.743335	+	0.477712i	−0.113348	+	0.993555i	$0.536158\pi$
$410$	6.01776	−	6.94486i	0.297196	−	0.342982i
$411$	5.30273	−	1.55702i	0.261564	−	0.0768022i
$412$	−0.422105	−	0.924280i	−0.0207956	−	0.0455360i
$413$	0.502883			0.0247453
$414$	3.29806	+	3.48178i	0.162091	+	0.171120i
$415$	0.920558			0.0451884
$416$	1.69390	+	3.70913i	0.0830505	+	0.181855i
$417$	0.398803	−	0.117099i	0.0195294	−	0.00573436i
$418$	−4.60777	+	5.31765i	−0.225373	+	0.260095i
$419$	−2.45829	−	1.57985i	−0.120095	−	0.0771806i	0.479214	−	0.877698i	$-0.340922\pi$
$419$	−2.45829	−	1.57985i	−0.120095	−	0.0771806i	−0.599309	+	0.800517i	$0.704558\pi$
$420$	−0.415606	−	0.479635i	−0.0202795	−	0.0234038i
$421$	0.196990	+	1.37010i	0.00960071	+	0.0667744i	0.994059	−	0.108847i	$-0.0347158\pi$
$421$	0.196990	+	1.37010i	0.00960071	+	0.0667744i	−0.984458	+	0.175621i	$0.943807\pi$
$422$	−16.3522	−	4.80144i	−0.796013	−	0.233731i
$423$	−4.34712	+	2.79373i	−0.211364	+	0.135836i
$424$	0.247376	−	1.72054i	0.0120136	−	0.0835568i
$425$	0.521069	−	1.14098i	0.0252756	−	0.0553458i
$426$	−2.51178	+	5.50003i	−0.121696	+	0.266477i
$427$	0.916503	−	6.37442i	0.0443527	−	0.308480i
$428$	−3.50446	+	2.25218i	−0.169394	+	0.108863i
$429$	−18.1648	−	5.33368i	−0.877007	−	0.257512i
$430$	−1.18221	−	8.22244i	−0.0570111	−	0.396521i
$431$	−19.2651	−	22.2331i	−0.927966	−	1.07093i	−0.997307	−	0.0733368i	$-0.976635\pi$
$431$	−19.2651	−	22.2331i	−0.927966	−	1.07093i	0.0693413	−	0.997593i	$-0.477910\pi$
$432$	−0.841254	−	0.540641i	−0.0404748	−	0.0260116i
$433$	−9.05181	+	10.4463i	−0.435002	+	0.502019i	−0.930349	−	0.366676i	$-0.880496\pi$
$433$	−9.05181	+	10.4463i	−0.435002	+	0.502019i	0.495346	+	0.868696i	$0.335041\pi$
$434$	−2.75557	+	0.809110i	−0.132272	+	0.0388385i
$435$	1.95670	+	4.28458i	0.0938167	+	0.205430i
$436$	18.7656			0.898709
$437$	5.93429	−	4.19641i	0.283875	−	0.200742i
$438$	16.3056			0.779110
$439$	−2.97658	−	6.51780i	−0.142064	−	0.311078i	0.825203	−	0.564836i	$-0.191061\pi$
$439$	−2.97658	−	6.51780i	−0.142064	−	0.311078i	−0.967268	+	0.253758i	$0.918333\pi$
$440$	4.45477	−	1.30804i	0.212373	−	0.0623582i
$441$	4.32026	−	4.98585i	0.205727	−	0.237421i
$442$	4.30276	+	2.76521i	0.204661	+	0.131528i
$443$	−0.764927	−	0.882773i	−0.0363428	−	0.0419418i	0.737287	−	0.675579i	$-0.236106\pi$
$443$	−0.764927	−	0.882773i	−0.0363428	−	0.0419418i	−0.773630	+	0.633638i	$0.781561\pi$
$444$	1.46953	+	10.2208i	0.0697408	+	0.485058i
$445$	2.72265	+	0.799443i	0.129066	+	0.0378973i
$446$	−1.72668	+	1.10967i	−0.0817605	+	0.0525443i
$447$	0.741078	−	5.15431i	0.0350518	−	0.243790i
$448$	−0.263642	+	0.577296i	−0.0124559	+	0.0272747i
$449$	13.0187	−	28.5071i	0.614392	−	1.34533i	−0.305136	−	0.952309i	$-0.598702\pi$
$449$	13.0187	−	28.5071i	0.614392	−	1.34533i	0.919529	−	0.393023i	$-0.128571\pi$
$450$	−0.142315	+	0.989821i	−0.00670879	+	0.0466606i
$451$	35.8919	−	23.0663i	1.69008	−	1.08615i
$452$	5.65248	+	1.65972i	0.265870	+	0.0780666i
$453$	−2.91493	−	20.2738i	−0.136955	−	0.952544i
$454$	−6.89644	−	7.95891i	−0.323666	−	0.373530i
$455$	−2.17704	−	1.39910i	−0.102061	−	0.0655907i
$456$	−0.992447	+	1.14534i	−0.0464756	+	0.0536357i
$457$	−21.9219	+	6.43685i	−1.02546	+	0.301103i	−0.750865	−	0.660456i	$-0.770363\pi$
$457$	−21.9219	+	6.43685i	−1.02546	+	0.301103i	−0.274598	+	0.961559i	$0.588545\pi$
$458$	−5.60055	−	12.2635i	−0.261696	−	0.573035i
$459$	−1.25433			−0.0585473
$460$	−4.79112	+	0.212422i	−0.223387	+	0.00990424i
$461$	8.22119			0.382899			0.191450	−	0.981502i	$-0.438681\pi$
$461$	8.22119			0.382899			0.191450	+	0.981502i	$0.438681\pi$
$462$	−1.22405	−	2.68029i	−0.0569478	−	0.124698i
$463$	3.37475	−	0.990915i	0.156838	−	0.0460517i	−0.202371	−	0.979309i	$-0.564865\pi$
$463$	3.37475	−	0.990915i	0.156838	−	0.0460517i	0.359209	+	0.933257i	$0.383047\pi$
$464$	3.08455	−	3.55976i	0.143197	−	0.165258i
$465$	3.80684	+	2.44651i	0.176538	+	0.113454i
$466$	13.5356	+	15.6210i	0.627026	+	0.723627i
$467$	2.92102	+	20.3161i	0.135169	+	0.940118i	0.938670	+	0.344816i	$0.112059\pi$
$467$	2.92102	+	20.3161i	0.135169	+	0.940118i	−0.803502	+	0.595302i	$0.797032\pi$
$468$	−3.91245	−	1.14880i	−0.180853	−	0.0531032i
$469$	0.118246	−	0.0759920i	0.00546009	−	0.00350899i
$470$	0.735403	−	5.11484i	0.0339216	−	0.235930i
$471$	7.70773	−	16.8776i	0.355154	−	0.777678i
$472$	−0.329167	+	0.720776i	−0.0151512	+	0.0331764i
$473$	5.48880	−	38.1754i	0.252375	−	1.75531i
$474$	11.1576	−	7.17056i	0.512486	−	0.329355i
$475$	1.45412	+	0.426968i	0.0667196	+	0.0195906i
$476$	0.113291	+	0.787957i	0.00519269	+	0.0361160i
$477$	1.13830	+	1.31367i	0.0521192	+	0.0601487i
$478$	−19.9411	−	12.8153i	−0.912082	−	0.586160i
$479$	18.8025	−	21.6993i	0.859110	−	0.991465i	−0.140889	−	0.990025i	$-0.544996\pi$
$479$	18.8025	−	21.6993i	0.859110	−	0.991465i	0.999999	−	0.00143991i	$-0.000458337\pi$
$480$	0.959493	−	0.281733i	0.0437947	−	0.0128593i
$481$	17.4911	+	38.3002i	0.797526	+	1.74634i
$482$	−26.0495			−1.18652
$483$	0.566174	+	2.99054i	0.0257618	+	0.136074i
$484$	10.5559			0.479814
$485$	2.83086	+	6.19872i	0.128543	+	0.281469i
$486$	0.959493	−	0.281733i	0.0435235	−	0.0127796i
$487$	−12.0282	+	13.8813i	−0.545051	+	0.629022i	−0.959723	−	0.280949i	$-0.909351\pi$
$487$	−12.0282	+	13.8813i	−0.545051	+	0.629022i	0.414672	+	0.909971i	$0.363896\pi$
$488$	8.53646	+	5.48605i	0.386428	+	0.248342i
$489$	11.5872	+	13.3723i	0.523991	+	0.604718i
$490$	0.938883	+	6.53007i	0.0424144	+	0.294999i
$491$	24.6127	+	7.22694i	1.11075	+	0.326147i	0.785117	−	0.619347i	$-0.212603\pi$
$491$	24.6127	+	7.22694i	1.11075	+	0.326147i	0.325638	+	0.945495i	$0.394421\pi$
$492$	7.73059	−	4.96815i	0.348522	−	0.223981i
$493$	0.840826	−	5.84807i	0.0378689	−	0.263384i
$494$	−2.56713	+	5.62122i	−0.115500	+	0.252911i
$495$	−1.92870	+	4.22327i	−0.0866888	+	0.189822i
$496$	0.644003	−	4.47914i	0.0289166	−	0.201119i
$497$	−3.22819	+	2.07463i	−0.144804	+	0.0930598i
$498$	0.883269	+	0.259351i	0.0395802	+	0.0116218i
$499$	2.12257	+	14.7628i	0.0950193	+	0.660874i	0.980547	+	0.196286i	$0.0628883\pi$
$499$	2.12257	+	14.7628i	0.0950193	+	0.660874i	−0.885527	+	0.464587i	$0.846203\pi$
$500$	−0.654861	−	0.755750i	−0.0292863	−	0.0337981i
$501$	8.76122	+	5.63049i	0.391422	+	0.251552i
$502$	1.81145	−	2.09052i	0.0808488	−	0.0933045i
$503$	30.1016	−	8.83863i	1.34216	−	0.394095i	0.469723	−	0.882814i	$-0.344354\pi$
$503$	30.1016	−	8.83863i	1.34216	−	0.394095i	0.872441	+	0.488719i	$0.162536\pi$
$504$	−0.263642	−	0.577296i	−0.0117436	−	0.0257148i
$505$	−13.9504			−0.620786
$506$	−21.6212	−	5.32068i	−0.961180	−	0.236533i
$507$	−3.62698			−0.161080
$508$	6.38105	+	13.9726i	0.283113	+	0.619932i
$509$	−20.2277	+	5.93938i	−0.896575	+	0.263258i	−0.697380	−	0.716701i	$-0.745651\pi$
$509$	−20.2277	+	5.93938i	−0.896575	+	0.263258i	−0.199195	+	0.979960i	$0.563833\pi$
$510$	0.821414	−	0.947963i	0.0363728	−	0.0419765i
$511$	8.70553	+	5.59471i	0.385110	+	0.247495i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	−0.215679	−	1.50008i	−0.00952247	−	0.0662303i
$514$	5.19089	+	1.52418i	0.228960	+	0.0672288i
$515$	−0.854801	+	0.549347i	−0.0376670	+	0.0242071i
$516$	1.18221	−	8.22244i	0.0520438	−	0.361973i
$517$	9.96645	−	21.8235i	0.438324	−	0.959796i
$518$	−2.72235	+	5.96111i	−0.119613	+	0.261916i
$519$	2.10235	−	14.6221i	0.0922828	−	0.641841i
$520$	3.43031	−	2.20453i	0.150429	−	0.0966749i
$521$	−20.3503	−	5.97539i	−0.891563	−	0.261787i	−0.196302	−	0.980544i	$-0.562893\pi$
$521$	−20.3503	−	5.97539i	−0.891563	−	0.261787i	−0.695261	+	0.718757i	$0.744711\pi$
$522$	0.670337	+	4.66229i	0.0293398	+	0.204063i
$523$	8.68322	+	10.0210i	0.379691	+	0.438187i	0.913140	−	0.407645i	$-0.133650\pi$
$523$	8.68322	+	10.0210i	0.379691	+	0.438187i	−0.533449	+	0.845832i	$0.679105\pi$
$524$	−14.3430	−	9.21767i	−0.626575	−	0.402676i
$525$	−0.415606	+	0.479635i	−0.0181385	+	0.0209330i
$526$	−4.73710	+	1.39094i	−0.206547	+	0.0606478i
$527$	−2.35794	−	5.16317i	−0.102714	−	0.224911i
$528$	4.64283			0.202053
$529$	20.3734	+	10.6736i	0.885799	+	0.464069i
$530$	−1.73823			−0.0755040
$531$	−0.329167	−	0.720776i	−0.0142846	−	0.0312790i
$532$	−0.922853	+	0.270974i	−0.0400108	+	0.0117482i
$533$	24.5381	−	28.3185i	1.06286	−	1.22661i
$534$	2.38714	+	1.53412i	0.103302	+	0.0663879i
$535$	2.72799	+	3.14827i	0.117941	+	0.136111i
$536$	0.0315193	+	0.219222i	0.00136143	+	0.00946893i
$537$	−8.89439	−	2.61163i	−0.383821	−	0.112700i
$538$	5.77554	−	3.71171i	0.249001	−	0.160023i
$539$	−4.35908	+	30.3180i	−0.187759	+	1.30589i
$540$	−0.415415	+	0.909632i	−0.0178766	+	0.0391443i
$541$	5.73338	−	12.5544i	0.246497	−	0.539754i	−0.745427	−	0.666588i	$-0.767754\pi$
$541$	5.73338	−	12.5544i	0.246497	−	0.539754i	0.991924	+	0.126834i	$0.0404815\pi$
$542$	−0.592275	+	4.11936i	−0.0254404	+	0.176942i
$543$	1.97743	−	1.27082i	0.0848596	−	0.0545360i
$544$	−1.20352	−	0.353387i	−0.0516007	−	0.0151513i
$545$	−2.67062	−	18.5746i	−0.114397	−	0.795648i
$546$	−1.69468	−	1.95577i	−0.0725257	−	0.0836991i
$547$	13.2660	+	8.52553i	0.567213	+	0.364525i	0.792598	−	0.609744i	$-0.208728\pi$
$547$	13.2660	+	8.52553i	0.567213	+	0.364525i	−0.225386	+	0.974270i	$0.572364\pi$
$548$	−3.61915	+	4.17672i	−0.154602	+	0.178421i
$549$	−9.73628	+	2.85883i	−0.415534	+	0.122012i
$550$	−1.92870	−	4.22327i	−0.0822402	−	0.180081i
$551$	7.13840			0.304106
$552$	−4.65690	−	1.14600i	−0.198211	−	0.0487769i
$553$	8.41738			0.357943
$554$	9.87570	+	21.6248i	0.419578	+	0.918748i
$555$	9.90764	−	2.90915i	0.420556	−	0.123486i
$556$	−0.272186	+	0.314119i	−0.0115432	+	0.0133216i
$557$	−36.0032	−	23.1378i	−1.52550	−	0.980381i	−0.990799	−	0.135341i	$-0.956787\pi$
$557$	−36.0032	−	23.1378i	−1.52550	−	0.980381i	−0.534704	−	0.845040i	$-0.679577\pi$
$558$	2.96338	+	3.41992i	0.125450	+	0.144777i
$559$	−4.82060	−	33.5280i	−0.203889	−	1.41808i
$560$	0.608940	+	0.178801i	0.0257324	+	0.00755572i
$561$	4.89918	−	3.14851i	0.206844	−	0.132930i
$562$	1.86622	−	12.9798i	0.0787216	−	0.547521i
$563$	−9.62893	+	21.0844i	−0.405811	+	0.888602i	0.590837	+	0.806791i	$0.298798\pi$
$563$	−9.62893	+	21.0844i	−0.405811	+	0.888602i	−0.996648	+	0.0818113i	$0.973930\pi$
$564$	2.14663	−	4.70046i	0.0903894	−	0.197925i
$565$	0.838393	−	5.83115i	0.0352715	−	0.245318i
$566$	3.42104	−	2.19857i	0.143797	−	0.0924128i
$567$	0.608940	+	0.178801i	0.0255731	+	0.00750893i
$568$	−0.860497	−	5.98489i	−0.0361056	−	0.251120i
$569$	−13.8040	−	15.9307i	−0.578695	−	0.667850i	0.388628	−	0.921395i	$-0.372949\pi$
$569$	−13.8040	−	15.9307i	−0.578695	−	0.667850i	−0.967324	+	0.253545i	$0.918404\pi$
$570$	1.27493	+	0.819346i	0.0534008	+	0.0343186i
$571$	14.3126	−	16.5176i	0.598962	−	0.691239i	−0.372608	−	0.927989i	$-0.621537\pi$
$571$	14.3126	−	16.5176i	0.598962	−	0.691239i	0.971571	+	0.236749i	$0.0760820\pi$
$572$	18.1648	−	5.33368i	0.759510	−	0.223012i
$573$	6.44625	+	14.1153i	0.269296	+	0.589676i
$574$	5.83201			0.243423
$575$	0.892108	+	4.71213i	0.0372035	+	0.196509i
$576$	1.00000			0.0416667
$577$	6.95792	+	15.2357i	0.289662	+	0.634271i	0.997389	−	0.0722148i	$-0.0230067\pi$
$577$	6.95792	+	15.2357i	0.289662	+	0.634271i	−0.707727	+	0.706486i	$0.750279\pi$
$578$	14.8018	−	4.34619i	0.615672	−	0.180778i
$579$	9.57358	−	11.0485i	0.397865	−	0.459160i
$580$	−3.96250	−	2.54655i	−0.164534	−	0.105740i
$581$	0.382589	+	0.441531i	0.0158725	+	0.0183178i
$582$	0.969809	+	6.74517i	0.0401999	+	0.279596i
$583$	−7.74342	−	2.27367i	−0.320700	−	0.0941659i
$584$	−13.7171	+	8.81545i	−0.567618	+	0.364786i
$585$	−0.580306	+	4.03612i	−0.0239927	+	0.166873i
$586$	12.2937	−	26.9194i	0.507847	−	1.11203i
$587$	−11.5142	+	25.2125i	−0.475240	+	1.04063i	0.508504	+	0.861059i	$0.330199\pi$
$587$	−11.5142	+	25.2125i	−0.475240	+	1.04063i	−0.983745	+	0.179572i	$0.942529\pi$
$588$	−0.938883	+	6.53007i	−0.0387189	+	0.269296i
$589$	5.76930	−	3.70770i	0.237720	−	0.152773i
$590$	0.760285	+	0.223240i	0.0313004	+	0.00919064i
$591$	−1.40666	−	9.78356i	−0.0578624	−	0.402442i
$592$	−6.76204	−	7.80381i	−0.277918	−	0.320734i
$593$	−36.3331	−	23.3499i	−1.49202	−	0.958865i	−0.995885	−	0.0906211i	$-0.971115\pi$
$593$	−36.3331	−	23.3499i	−1.49202	−	0.958865i	−0.496138	−	0.868244i	$-0.665249\pi$
$594$	−3.04041	+	3.50882i	−0.124750	+	0.143969i
$595$	0.763814	−	0.224276i	0.0313133	−	0.00919442i
$596$	2.16320	+	4.73674i	0.0886080	+	0.194024i
$597$	−0.680607			−0.0278554
$598$	−19.5364	+	0.866177i	−0.798902	+	0.0354206i
$599$	−28.5126			−1.16499			−0.582496	−	0.812834i	$-0.697924\pi$
$599$	−28.5126			−1.16499			−0.582496	+	0.812834i	$0.697924\pi$
$600$	−0.415415	−	0.909632i	−0.0169592	−	0.0371356i
$601$	4.55155	−	1.33646i	0.185662	−	0.0545152i	−0.187580	−	0.982249i	$-0.560064\pi$
$601$	4.55155	−	1.33646i	0.185662	−	0.0545152i	0.373242	+	0.927734i	$0.378246\pi$
$602$	3.45243	−	3.98432i	0.140711	−	0.162389i
$603$	−0.186317	−	0.119739i	−0.00758743	−	0.00487615i
$604$	13.4130	+	15.4794i	0.545768	+	0.629850i
$605$	−1.50226	−	10.4485i	−0.0610757	−	0.424791i
$606$	−13.3853	−	3.93029i	−0.543742	−	0.159657i
$607$	14.7705	−	9.49245i	0.599518	−	0.385287i	−0.205396	−	0.978679i	$-0.565848\pi$
$607$	14.7705	−	9.49245i	0.599518	−	0.385287i	0.804913	+	0.593392i	$0.202212\pi$
$608$	0.215679	−	1.50008i	0.00874695	−	0.0608364i
$609$	−1.24182	+	2.71920i	−0.0503210	+	0.110188i
$610$	4.21535	−	9.23032i	0.170674	−	0.373725i
$611$	2.99869	−	20.8564i	0.121314	−	0.843758i
$612$	1.05521	−	0.678144i	0.0426545	−	0.0274124i
$613$	35.1406	+	10.3182i	1.41932	+	0.416749i	0.899272	−	0.437391i	$-0.144097\pi$
$613$	35.1406	+	10.3182i	1.41932	+	0.416749i	0.520044	+	0.854139i	$0.325915\pi$
$614$	2.38022	+	16.5548i	0.0960580	+	0.668098i
$615$	−6.01776	−	6.94486i	−0.242659	−	0.280044i
$616$	2.47881	+	1.59303i	0.0998740	+	0.0641851i
$617$	4.38651	−	5.06230i	0.176594	−	0.203800i	−0.660551	−	0.750781i	$-0.729677\pi$
$617$	4.38651	−	5.06230i	0.176594	−	0.203800i	0.837145	+	0.546980i	$0.184223\pi$
$618$	−0.974944	+	0.286269i	−0.0392180	+	0.0115154i
$619$	5.43286	+	11.8963i	0.218365	+	0.478153i	0.986834	−	0.161734i	$-0.0517085\pi$
$619$	5.43286	+	11.8963i	0.218365	+	0.478153i	−0.768469	+	0.639887i	$0.778981\pi$
$620$	−4.52520			−0.181736
$621$	3.91571	−	2.76898i	0.157132	−	0.111115i
$622$	−31.0440			−1.24475
$623$	0.748110	+	1.63813i	0.0299724	+	0.0656304i
$624$	3.91245	−	1.14880i	0.156623	−	0.0459887i
$625$	−0.654861	+	0.755750i	−0.0261944	+	0.0302300i
$626$	−16.2299	−	10.4303i	−0.648676	−	0.416879i
$627$	4.60777	+	5.31765i	0.184016	+	0.212366i
$628$	2.64055	+	18.3654i	0.105369	+	0.732861i
$629$	−12.4275	−	3.64904i	−0.495517	−	0.145497i
$630$	−0.533899	+	0.343116i	−0.0212711	+	0.0136701i
$631$	5.54580	−	38.5719i	0.220775	−	1.53552i	−0.514343	−	0.857584i	$-0.671964\pi$
$631$	5.54580	−	38.5719i	0.220775	−	1.53552i	0.735118	−	0.677939i	$-0.237127\pi$
$632$	−5.50968	+	12.0645i	−0.219163	+	0.479901i
$633$	−7.07973	+	15.5025i	−0.281394	+	0.616167i
$634$	−3.65423	+	25.4157i	−0.145128	+	1.00939i
$635$	12.9222	−	8.30460i	0.512803	−	0.329558i
$636$	−1.66782	−	0.489716i	−0.0661334	−	0.0194185i
$637$	3.82841	+	26.6272i	0.151687	+	1.05501i
$638$	−14.3210	−	16.5274i	−0.566976	−	0.654325i
$639$	5.08658	+	3.26895i	0.201222	+	0.129318i
$640$	−0.654861	+	0.755750i	−0.0258856	+	0.0298736i
$641$	12.5748	−	3.69231i	0.496676	−	0.145837i	−0.0237944	−	0.999717i	$-0.507575\pi$
$641$	12.5748	−	3.69231i	0.496676	−	0.145837i	0.520471	+	0.853880i	$0.325757\pi$
$642$	1.73052	+	3.78930i	0.0682981	+	0.149552i
$643$	−47.2323			−1.86266			−0.931330	−	0.364177i	$-0.881350\pi$
$643$	−47.2323			−1.86266			−0.931330	+	0.364177i	$0.881350\pi$
$644$	−2.09310	−	2.20971i	−0.0824799	−	0.0870746i
$645$	−8.30699			−0.327088
$646$	−0.789685	−	1.72917i	−0.0310697	−	0.0680332i
$647$	8.13751	−	2.38939i	0.319919	−	0.0939366i	−0.117831	−	0.993034i	$-0.537594\pi$
$647$	8.13751	−	2.38939i	0.319919	−	0.0939366i	0.437749	+	0.899097i	$0.355776\pi$
$648$	−0.654861	+	0.755750i	−0.0257254	+	0.0296886i
$649$	3.09489	+	1.98896i	0.121485	+	0.0780736i
$650$	−2.67027	−	3.08166i	−0.104737	−	0.120873i
$651$	0.408715	+	2.84268i	0.0160188	+	0.111413i
$652$	−16.9774	−	4.98501i	−0.664886	−	0.195228i
$653$	29.2716	−	18.8117i	1.14549	−	0.736159i	0.176751	−	0.984256i	$-0.443441\pi$
$653$	29.2716	−	18.8117i	1.14549	−	0.736159i	0.968735	+	0.248096i	$0.0798050\pi$
$654$	2.67062	−	18.5746i	0.104430	−	0.726324i
$655$	−7.08263	+	15.5088i	−0.276741	+	0.605979i
$656$	−3.81740	+	8.35895i	−0.149045	+	0.326362i
$657$	2.32052	−	16.1396i	0.0905322	−	0.629666i
$658$	2.75889	−	1.77303i	0.107553	−	0.0691200i
$659$	44.2875	+	13.0040i	1.72520	+	0.506564i	0.985974	−	0.166898i	$-0.0533749\pi$
$659$	44.2875	+	13.0040i	1.72520	+	0.506564i	0.739223	+	0.673461i	$0.235193\pi$
$660$	−0.660744	−	4.59558i	−0.0257194	−	0.178883i
$661$	−30.3754	−	35.0551i	−1.18147	−	1.36348i	−0.916900	−	0.399117i	$-0.869317\pi$
$661$	−30.3754	−	35.0551i	−1.18147	−	1.36348i	−0.264566	−	0.964368i	$-0.585229\pi$
$662$	−20.2940	−	13.0422i	−0.788750	−	0.506899i
$663$	3.34941	−	3.86543i	0.130080	−	0.150121i
$664$	−0.883269	+	0.259351i	−0.0342775	+	0.0100648i
$665$	0.399552	+	0.874896i	0.0154940	+	0.0339270i
$666$	10.3259			0.400121
$667$	10.2849	+	20.1123i	0.398235	+	0.778752i
$668$	−10.4145			−0.402948
$669$	0.852642	+	1.86702i	0.0329650	+	0.0721833i
$670$	0.212505	−	0.0623970i	0.00820977	−	0.00241061i
$671$	30.8520	−	35.6051i	1.19103	−	1.37452i
$672$	0.533899	+	0.343116i	0.0205956	+	0.0132360i
$673$	25.0481	+	28.9070i	0.965533	+	1.11428i	0.993403	+	0.114673i	$0.0365819\pi$
$673$	25.0481	+	28.9070i	0.965533	+	1.11428i	−0.0278705	+	0.999612i	$0.508873\pi$
$674$	−1.59315	−	11.0806i	−0.0613660	−	0.426810i
$675$	0.959493	+	0.281733i	0.0369309	+	0.0108439i
$676$	3.05121	−	1.96089i	0.117354	−	0.0754190i
$677$	0.243339	−	1.69246i	0.00935229	−	0.0650466i	−0.984611	−	0.174761i	$-0.944085\pi$
$677$	0.243339	−	1.69246i	0.00935229	−	0.0650466i	0.993963	+	0.109715i	$0.0349937\pi$
$678$	2.44726	−	5.35875i	0.0939864	−	0.205801i
$679$	−1.79660	+	3.93400i	−0.0689471	+	0.150973i
$680$	−0.178510	+	1.24157i	−0.00684556	+	0.0476119i
$681$	−8.85937	+	5.69357i	−0.339492	+	0.218178i
$682$	−20.1587	−	5.91913i	−0.771917	−	0.226655i
$683$	−2.52837	−	17.5852i	−0.0967454	−	0.672879i	−0.979262	−	0.202598i	$-0.935062\pi$
$683$	−2.52837	−	17.5852i	−0.0967454	−	0.672879i	0.882517	−	0.470281i	$-0.155848\pi$
$684$	0.992447	+	1.14534i	0.0379472	+	0.0437933i
$685$	4.64927	+	2.98790i	0.177639	+	0.114162i
$686$	−5.65108	+	6.52170i	−0.215759	+	0.249000i
$687$	−12.9357	+	3.79827i	−0.493528	+	0.144913i
$688$	3.45085	+	7.55631i	0.131562	+	0.288081i
$689$	−7.08785			−0.270025
$690$	−0.471588	+	4.77259i	−0.0179530	+	0.181689i
$691$	−5.60823			−0.213347			−0.106674	−	0.994294i	$-0.534020\pi$
$691$	−5.60823			−0.213347			−0.106674	+	0.994294i	$0.534020\pi$
$692$	6.13672	+	13.4375i	0.233283	+	0.510819i
$693$	−2.82721	+	0.830143i	−0.107397	+	0.0315345i
$694$	6.00061	−	6.92507i	0.227780	−	0.262872i
$695$	0.349658	+	0.224711i	0.0132633	+	0.00852379i
$696$	−3.08455	−	3.55976i	−0.116920	−	0.134932i
$697$	1.64040	+	11.4092i	0.0621345	+	0.432155i
$698$	2.49071	+	0.731338i	0.0942747	+	0.0276816i
$699$	17.3883	−	11.1748i	0.657685	−	0.422669i
$700$	0.0903198	−	0.628188i	0.00341377	−	0.0237433i
$701$	3.23513	−	7.08395i	0.122189	−	0.267557i	−0.838646	−	0.544676i	$-0.816652\pi$
$701$	3.23513	−	7.08395i	0.122189	−	0.267557i	0.960836	+	0.277119i	$0.0893797\pi$
$702$	−1.69390	+	3.70913i	−0.0639323	+	0.139992i
$703$	2.22709	−	15.4897i	0.0839961	−	0.584206i
$704$	−3.90580	+	2.51011i	−0.147205	+	0.0946032i
$705$	−4.95812	−	1.45583i	−0.186734	−	0.0548299i
$706$	0.00633719	+	0.0440761i	0.000238503	+	0.00165883i
$707$	−5.79788	−	6.69111i	−0.218052	−	0.251645i
$708$	0.666594	+	0.428394i	0.0250521	+	0.0161000i
$709$	−0.982644	+	1.13403i	−0.0369040	+	0.0425895i	−0.773901	−	0.633306i	$-0.781697\pi$
$709$	−0.982644	+	1.13403i	−0.0369040	+	0.0425895i	0.736998	+	0.675895i	$0.236243\pi$
$710$	−5.80151	+	1.70348i	−0.217727	+	0.0639303i
$711$	−5.50968	−	12.0645i	−0.206629	−	0.452455i
$712$	−2.83760			−0.106343
$713$	18.7587	+	10.9129i	0.702520	+	0.408690i
$714$	0.796060			0.0297918
$715$	−7.86452	−	17.2209i	−0.294116	−	0.644025i
$716$	8.89439	−	2.61163i	0.332399	−	0.0976012i
$717$	−15.5228	+	17.9143i	−0.579710	+	0.669021i
$718$	−12.2268	−	7.85768i	−0.456300	−	0.293246i
$719$	−34.7050	−	40.0517i	−1.29428	−	1.49368i	−0.762852	−	0.646574i	$-0.776201\pi$
$719$	−34.7050	−	40.0517i	−1.29428	−	1.49368i	−0.531427	−	0.847104i	$-0.678344\pi$
$720$	−0.142315	−	0.989821i	−0.00530376	−	0.0368885i
$721$	−0.618746	−	0.181680i	−0.0230433	−	0.00676612i
$722$	−14.0517	+	9.03045i	−0.522948	+	0.336079i
$723$	−3.70724	+	25.7844i	−0.137874	+	0.958932i
$724$	−0.976464	+	2.13816i	−0.0362900	+	0.0794640i
$725$	−1.95670	+	4.28458i	−0.0726701	+	0.159125i
$726$	1.50226	−	10.4485i	0.0557542	−	0.387779i
$727$	17.1945	−	11.0502i	0.637708	−	0.409830i	−0.181448	−	0.983400i	$-0.558078\pi$
$727$	17.1945	−	11.0502i	0.637708	−	0.409830i	0.819156	+	0.573570i	$0.194442\pi$
$728$	2.48303	+	0.729082i	0.0920270	+	0.0270216i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	10.6779	+	12.3229i	0.395206	+	0.456092i
$731$	8.76565	+	5.63334i	0.324209	+	0.208357i
$732$	6.64508	−	7.66883i	0.245609	−	0.283448i
$733$	−22.9686	+	6.74420i	−0.848366	+	0.249103i	−0.676889	−	0.736085i	$-0.736672\pi$
$733$	−22.9686	+	6.74420i	−0.848366	+	0.249103i	−0.171477	+	0.985188i	$0.554854\pi$
$734$	−5.03883	−	11.0335i	−0.185987	−	0.407254i
$735$	6.59722			0.243342
$736$	4.53720	−	1.55363i	0.167244	−	0.0572677i
$737$	1.02828			0.0378770
$738$	−3.81740	−	8.35895i	−0.140521	−	0.307697i
$739$	−3.24418	+	0.952577i	−0.119339	+	0.0350411i	−0.340857	−	0.940115i	$-0.610717\pi$
$739$	−3.24418	+	0.952577i	−0.119339	+	0.0350411i	0.221518	+	0.975156i	$0.428899\pi$
$740$	−6.76204	+	7.80381i	−0.248577	+	0.286874i
$741$	5.19867	+	3.34098i	0.190978	+	0.122734i
$742$	−0.722419	−	0.833716i	−0.0265208	−	0.0306067i
$743$	0.431420	+	3.00059i	0.0158272	+	0.110081i	0.996204	−	0.0870542i	$-0.0277453\pi$
$743$	0.431420	+	3.00059i	0.0158272	+	0.110081i	−0.980376	+	0.197135i	$0.936836\pi$
$744$	−4.34190	−	1.27490i	−0.159182	−	0.0467400i
$745$	4.38067	−	2.81529i	0.160495	−	0.103144i
$746$	1.64035	−	11.4089i	0.0600575	−	0.417709i
$747$	0.382414	−	0.837369i	0.0139918	−	0.0306377i
$748$	−2.41924	+	5.29739i	−0.0884561	+	0.193692i
$749$	−0.376250	+	2.61688i	−0.0137479	+	0.0956186i
$750$	−0.841254	+	0.540641i	−0.0307182	+	0.0197414i
$751$	−14.4623	−	4.24650i	−0.527735	−	0.154957i	0.00700200	−	0.999975i	$-0.497771\pi$
$751$	−14.4623	−	4.24650i	−0.527735	−	0.154957i	−0.534737	+	0.845018i	$0.679589\pi$
$752$	0.735403	+	5.11484i	0.0268174	+	0.186519i
$753$	−1.81145	−	2.09052i	−0.0660128	−	0.0761828i
$754$	−16.1576	−	10.3838i	−0.588424	−	0.378157i
$755$	13.4130	−	15.4794i	0.488150	−	0.563355i
$756$	−0.608940	+	0.178801i	−0.0221469	+	0.00650292i
$757$	8.64045	+	18.9199i	0.314042	+	0.687657i	0.999169	−	0.0407675i	$-0.0129803\pi$
$757$	8.64045	+	18.9199i	0.314042	+	0.687657i	−0.685126	+	0.728424i	$0.740253\pi$
$758$	−21.0990			−0.766351
$759$	−8.34354	+	20.6439i	−0.302851	+	0.749327i
$760$	−1.51551			−0.0549733
$761$	16.1754	+	35.4192i	0.586358	+	1.28394i	0.937618	+	0.347667i	$0.113026\pi$
$761$	16.1754	+	35.4192i	0.586358	+	1.28394i	−0.351260	+	0.936278i	$0.614247\pi$
$762$	14.7385	−	4.32760i	0.533918	−	0.156772i
$763$	7.79909	−	9.00063i	0.282346	−	0.325845i
$764$	−13.0543	−	8.38946i	−0.472286	−	0.303520i
$765$	−0.821414	−	0.947963i	−0.0296983	−	0.0342737i
$766$	−2.68730	−	18.6906i	−0.0970960	−	0.675318i
$767$	3.10015	+	0.910287i	0.111940	+	0.0328686i
$768$	−0.841254	+	0.540641i	−0.0303561	+	0.0195087i
$769$	7.10462	−	49.4137i	0.256199	−	1.78190i	−0.303122	−	0.952952i	$-0.598029\pi$
$769$	7.10462	−	49.4137i	0.256199	−	1.78190i	0.559321	−	0.828951i	$-0.311062\pi$
$770$	1.22405	−	2.68029i	0.0441116	−	0.0965909i
$771$	2.24741	−	4.92114i	0.0809385	−	0.177231i
$772$	−2.08054	+	14.4705i	−0.0748802	+	0.520803i
$773$	26.5063	−	17.0346i	0.953365	−	0.612690i	0.0312107	−	0.999513i	$-0.490064\pi$
$773$	26.5063	−	17.0346i	0.953365	−	0.612690i	0.922154	+	0.386822i	$0.126427\pi$
$774$	−7.97050	−	2.34035i	−0.286494	−	0.0841222i
$775$	0.644003	+	4.47914i	0.0231333	+	0.160895i
$776$	−4.46257	−	5.15008i	−0.160197	−	0.184877i
$777$	5.51300	+	3.54299i	0.197778	+	0.127104i
$778$	−8.40979	+	9.70541i	−0.301506	+	0.347956i
$779$	−13.3624	+	3.92357i	−0.478759	+	0.140576i
$780$	−1.69390	−	3.70913i	−0.0606515	−	0.132808i
$781$	−28.0726			−1.00452
$782$	3.73413	−	4.71629i	0.133532	−	0.168654i
$783$	4.71024			0.168330
$784$	−2.74059	−	6.00104i	−0.0978780	−	0.214323i
$785$	17.8027	−	5.22735i	0.635406	−	0.186572i
$786$	−11.1651	+	12.8852i	−0.398245	+	0.459599i
$787$	−41.0166	−	26.3598i	−1.46209	−	0.939625i	−0.998566	−	0.0535385i	$-0.982950\pi$
$787$	−41.0166	−	26.3598i	−1.46209	−	0.939625i	−0.463520	−	0.886087i	$-0.653414\pi$
$788$	6.47275	+	7.46995i	0.230582	+	0.266106i
$789$	0.702621	+	4.88684i	0.0250140	+	0.173976i
$790$	12.7258	+	3.73664i	0.452765	+	0.132944i
$791$	3.14526	−	2.02134i	0.111833	−	0.0718705i
$792$	0.660744	−	4.59558i	0.0234785	−	0.163297i
$793$	17.1886	−	37.6377i	0.610384	−	1.33656i
$794$	−11.1429	+	24.3996i	−0.395447	+	0.865909i
$795$	−0.247376	+	1.72054i	−0.00877353	+	0.0610212i
$796$	0.572563	−	0.367964i	0.0202939	−	0.0130421i
$797$	12.7486	+	3.74332i	0.451578	+	0.132595i	0.499610	−	0.866251i	$-0.333477\pi$
$797$	12.7486	+	3.74332i	0.451578	+	0.132595i	−0.0480321	+	0.998846i	$0.515295\pi$
$798$	0.136880	+	0.952024i	0.00484551	+	0.0337013i
$799$	4.24461	+	4.89854i	0.150163	+	0.173298i
$800$	0.841254	+	0.540641i	0.0297428	+	0.0191145i
$801$	1.85823	−	2.14451i	0.0656574	−	0.0757726i
$802$	0.926128	−	0.271936i	0.0327027	−	0.00960238i
$803$	31.4486	+	68.8628i	1.10980	+	2.43012i
$804$	0.221476			0.00781085
$805$	−1.88933	+	2.38627i	−0.0665903	+	0.0841051i
$806$	−18.4520			−0.649946
$807$	−2.85199	−	6.24499i	−0.100395	−	0.219834i
$808$	13.3853	−	3.93029i	0.470895	−	0.138267i
$809$	8.94747	−	10.3259i	0.314576	−	0.363040i	−0.576338	−	0.817211i	$-0.695519\pi$
$809$	8.94747	−	10.3259i	0.314576	−	0.363040i	0.890915	+	0.454171i	$0.150064\pi$
$810$	0.841254	+	0.540641i	0.0295586	+	0.0189962i
$811$	−23.6610	−	27.3063i	−0.830852	−	0.958854i	0.168789	−	0.985652i	$-0.446014\pi$
$811$	−23.6610	−	27.3063i	−0.830852	−	0.958854i	−0.999641	+	0.0267982i	$0.991469\pi$
$812$	−0.425427	−	2.95891i	−0.0149296	−	0.103837i
$813$	3.99314	+	1.17249i	0.140046	+	0.0411211i
$814$	−40.3310	+	25.9191i	−1.41360	+	0.908465i
$815$	−2.51814	+	17.5140i	−0.0882065	+	0.613490i
$816$	−0.521069	+	1.14098i	−0.0182411	+	0.0399424i
$817$	−5.22979	+	11.4516i	−0.182967	+	0.400642i
$818$	−2.54314	+	17.6879i	−0.0889187	+	0.618443i
$819$	−2.17704	+	1.39910i	−0.0760719	+	0.0488884i
$820$	8.81714	+	2.58895i	0.307908	+	0.0904099i
$821$	4.33056	+	30.1197i	0.151138	+	1.05119i	0.914317	+	0.404999i	$0.132728\pi$
$821$	4.33056	+	30.1197i	0.151138	+	1.05119i	−0.763179	+	0.646187i	$0.776363\pi$
$822$	3.61915	+	4.17672i	0.126232	+	0.145680i
$823$	23.2186	+	14.9217i	0.809348	+	0.520137i	0.878654	−	0.477459i	$-0.158442\pi$
$823$	23.2186	+	14.9217i	0.809348	+	0.520137i	−0.0693057	+	0.997595i	$0.522078\pi$
$824$	0.665406	−	0.767920i	0.0231805	−	0.0267518i
$825$	−4.45477	+	1.30804i	−0.155095	+	0.0455400i
$826$	0.208905	+	0.457439i	0.00726874	+	0.0159163i
$827$	−20.1298			−0.699981			−0.349991	−	0.936753i	$-0.613815\pi$
$827$	−20.1298			−0.699981			−0.349991	+	0.936753i	$0.613815\pi$
$828$	−1.79708	+	4.44640i	−0.0624528	+	0.154523i
$829$	−46.8228			−1.62622			−0.813112	−	0.582107i	$-0.802229\pi$
$829$	−46.8228			−1.62622			−0.813112	+	0.582107i	$0.802229\pi$
$830$	0.382414	+	0.837369i	0.0132738	+	0.0290655i
$831$	22.8101	−	6.69765i	0.791274	−	0.232339i
$832$	−2.67027	+	3.08166i	−0.0925751	+	0.106837i
$833$	−6.96148	−	4.47387i	−0.241201	−	0.155010i
$834$	0.272186	+	0.314119i	0.00942502	+	0.0108770i
$835$	1.48213	+	10.3085i	0.0512914	+	0.356739i
$836$	−6.75124	−	1.98234i	−0.233496	−	0.0685607i
$837$	3.80684	−	2.44651i	0.131584	−	0.0845637i
$838$	0.415869	−	2.89243i	0.0143659	−	0.0999173i
$839$	16.0164	−	35.0709i	0.552946	−	1.21078i	−0.402447	−	0.915443i	$-0.631840\pi$
$839$	16.0164	−	35.0709i	0.552946	−	1.21078i	0.955392	−	0.295339i	$-0.0954327\pi$
$840$	0.263642	−	0.577296i	0.00909652	−	0.0199186i
$841$	0.969687	−	6.74432i	0.0334375	−	0.232563i
$842$	−1.16445	+	0.748347i	−0.0401296	+	0.0257897i
$843$	−12.5821	−	3.69444i	−0.433351	−	0.127243i
$844$	−2.42541	−	16.8691i	−0.0834860	−	0.580658i
$845$	−2.37517	−	2.74109i	−0.0817082	−	0.0942963i
$846$	−4.34712	−	2.79373i	−0.149457	−	0.0960503i
$847$	4.38710	−	5.06298i	0.150742	−	0.173966i
$848$	1.66782	−	0.489716i	0.0572732	−	0.0168169i
$849$	−1.68933	−	3.69911i	−0.0579776	−	0.126953i
$850$	1.25433			0.0430233
$851$	46.8508	−	16.0427i	1.60602	−	0.549936i
$852$	−6.04643			−0.207147
$853$	−8.95331	−	19.6050i	−0.306556	−	0.671263i	0.692170	−	0.721735i	$-0.256655\pi$
$853$	−8.95331	−	19.6050i	−0.306556	−	0.671263i	−0.998726	+	0.0504714i	$0.983928\pi$
$854$	6.17910	−	1.81435i	0.211445	−	0.0620857i
$855$	0.992447	−	1.14534i	0.0339410	−	0.0391700i
$856$	−3.50446	−	2.25218i	−0.119780	−	0.0769778i
$857$	−15.9708	−	18.4312i	−0.545550	−	0.629599i	0.414290	−	0.910145i	$-0.364030\pi$
$857$	−15.9708	−	18.4312i	−0.545550	−	0.629599i	−0.959841	+	0.280546i	$0.909484\pi$
$858$	−2.69426	−	18.7390i	−0.0919806	−	0.639739i
$859$	7.47010	+	2.19342i	0.254877	+	0.0748385i	0.406675	−	0.913573i	$-0.366688\pi$
$859$	7.47010	+	2.19342i	0.254877	+	0.0748385i	−0.151798	+	0.988412i	$0.548506\pi$
$860$	6.98829	−	4.49110i	0.238299	−	0.153145i
$861$	0.829982	−	5.77265i	0.0282857	−	0.196731i
$862$	12.2209	−	26.7601i	0.416246	−	0.911452i
$863$	−4.49301	+	9.83831i	−0.152944	+	0.334900i	−0.970558	−	0.240866i	$-0.922569\pi$
$863$	−4.49301	+	9.83831i	−0.152944	+	0.334900i	0.817615	+	0.575766i	$0.195296\pi$
$864$	0.142315	−	0.989821i	0.00484165	−	0.0336744i
$865$	12.4274	−	7.98662i	0.422545	−	0.271553i
$866$	−13.2626	−	3.89425i	−0.450681	−	0.132332i
$867$	−2.19544	−	15.2696i	−0.0745611	−	0.518584i
$868$	−1.88070	−	2.17044i	−0.0638351	−	0.0736696i
$869$	51.8029	+	33.2917i	1.75729	+	1.12934i
$870$	−3.08455	+	3.55976i	−0.104576	+	0.120687i
$871$	0.866513	−	0.254431i	0.0293607	−	0.00862107i
$872$	7.79551	+	17.0698i	0.263989	+	0.578056i
$873$	6.81453			0.230637
$874$	6.28238	+	3.65476i	0.212505	+	0.123624i
$875$	−0.634648			−0.0214550
$876$	6.77358	+	14.8321i	0.228858	+	0.501129i
$877$	−27.4129	+	8.04915i	−0.925668	+	0.271801i	−0.709622	−	0.704583i	$-0.751134\pi$
$877$	−27.4129	+	8.04915i	−0.925668	+	0.271801i	−0.216046	+	0.976383i	$0.569316\pi$
$878$	4.69228	−	5.41519i	0.158357	−	0.182754i
$879$	−24.8958	−	15.9996i	−0.839716	−	0.539653i
$880$	3.04041	+	3.50882i	0.102492	+	0.118282i
$881$	−1.84317	−	12.8195i	−0.0620980	−	0.431901i	−0.997026	−	0.0770641i	$-0.975445\pi$
$881$	−1.84317	−	12.8195i	−0.0620980	−	0.431901i	0.934928	−	0.354837i	$-0.115464\pi$
$882$	6.32999	+	1.85865i	0.213142	+	0.0625841i
$883$	−6.40418	+	4.11572i	−0.215518	+	0.138505i	−0.643946	−	0.765071i	$-0.722704\pi$
$883$	−6.40418	+	4.11572i	−0.215518	+	0.138505i	0.428428	+	0.903576i	$0.359067\pi$
$884$	−0.727897	+	5.06264i	−0.0244818	+	0.170275i
$885$	0.329167	−	0.720776i	0.0110648	−	0.0242286i
$886$	0.485236	−	1.06252i	0.0163018	−	0.0356960i
$887$	1.83673	−	12.7747i	0.0616714	−	0.428934i	−0.935472	−	0.353401i	$-0.885025\pi$
$887$	1.83673	−	12.7747i	0.0616714	−	0.428934i	0.997143	−	0.0755328i	$-0.0240658\pi$
$888$	−8.68671	+	5.58261i	−0.291507	+	0.187340i
$889$	9.35372	+	2.74650i	0.313714	+	0.0921147i
$890$	0.403832	+	2.80871i	0.0135365	+	0.0941483i
$891$	3.04041	+	3.50882i	0.101858	+	0.117550i
$892$	−1.72668	−	1.10967i	−0.0578134	−	0.0371544i
$893$	−5.12840	+	5.91849i	−0.171616	+	0.198055i
$894$	4.99638	−	1.46707i	0.167104	−	0.0490661i
$895$	−3.85085	−	8.43219i	−0.128720	−	0.281857i
$896$	−0.634648			−0.0212021
$897$	−1.92296	+	19.4608i	−0.0642056	+	0.649777i
$898$	31.3391			1.04580
$899$	8.85447	+	19.3886i	0.295313	+	0.646646i
$900$	−0.959493	+	0.281733i	−0.0319831	+	0.00939109i
$901$	1.42781	−	1.64778i	0.0475672	−	0.0548955i
$902$	35.8919	+	23.0663i	1.19507	+	0.768024i
$903$	−3.45243	−	3.98432i	−0.114890	−	0.132590i
$904$	0.838393	+	5.83115i	0.0278845	+	0.193941i
$905$	2.25536	+	0.662234i	0.0749707	+	0.0220134i
$906$	17.2308	−	11.0735i	0.572453	−	0.367894i
$907$	6.39350	−	44.4677i	0.212293	−	1.47653i	−0.553182	−	0.833061i	$-0.686586\pi$
$907$	6.39350	−	44.4677i	0.212293	−	1.47653i	0.765474	−	0.643467i	$-0.222504\pi$
$908$	4.37480	−	9.57947i	0.145183	−	0.317906i
$909$	−5.79522	+	12.6898i	−0.192215	+	0.420893i
$910$	0.368290	−	2.56151i	0.0122087	−	0.0849133i
$911$	35.3873	−	22.7420i	1.17243	−	0.753478i	0.198454	−	0.980110i	$-0.436408\pi$
$911$	35.3873	−	22.7420i	1.17243	−	0.753478i	0.973980	+	0.226633i	$0.0727717\pi$
$912$	−1.45412	−	0.426968i	−0.0481507	−	0.0141383i
$913$	0.608253	+	4.23049i	0.0201302	+	0.140009i
$914$	−14.9618	−	17.2669i	−0.494894	−	0.571138i
$915$	−8.53646	−	5.48605i	−0.282207	−	0.181363i
$916$	8.82871	−	10.1889i	0.291709	−	0.336650i
$917$	−10.3821	+	3.04847i	−0.342848	+	0.100669i
$918$	−0.521069	−	1.14098i	−0.0171978	−	0.0376580i
$919$	24.2486			0.799889			0.399944	−	0.916539i	$-0.369029\pi$
$919$	24.2486			0.799889			0.399944	+	0.916539i	$0.369029\pi$
$920$	−2.18353	−	4.26992i	−0.0719889	−	0.140775i
$921$	16.7251			0.551109
$922$	3.41521	+	7.47826i	0.112474	+	0.246283i
$923$	−23.6563	+	6.94613i	−0.778658	+	0.228635i
$924$	1.92959	−	2.22686i	0.0634788	−	0.0732584i
$925$	8.68671	+	5.58261i	0.285617	+	0.183555i
$926$	2.30329	+	2.65814i	0.0756907	+	0.0873518i
$927$	0.144607	+	1.00576i	0.00474950	+	0.0330335i
$928$	4.51944	+	1.32703i	0.148358	+	0.0435618i
$929$	−44.9260	+	28.8722i	−1.47397	+	0.947266i	−0.476287	+	0.879290i	$0.658018\pi$
$929$	−44.9260	+	28.8722i	−1.47397	+	0.947266i	−0.997687	+	0.0679760i	$0.978346\pi$
$930$	−0.644003	+	4.47914i	−0.0211177	+	0.146877i
$931$	4.15338	−	9.09463i	0.136122	−	0.298065i
$932$	−8.58642	+	18.8016i	−0.281257	+	0.615868i
$933$	−4.41803	+	30.7281i	−0.144640	+	1.00599i
$934$	−17.2668	+	11.0967i	−0.564986	+	0.363094i
$935$	5.58777	+	1.64072i	0.182740	+	0.0536572i
$936$	−0.580306	−	4.03612i	−0.0189679	−	0.131925i
$937$	−16.7448	−	19.3245i	−0.547028	−	0.631304i	0.413160	−	0.910658i	$-0.364425\pi$
$937$	−16.7448	−	19.3245i	−0.547028	−	0.631304i	−0.960188	+	0.279355i	$0.909879\pi$
$938$	0.118246	+	0.0759920i	0.00386087	+	0.00248123i
$939$	−12.6339	+	14.5803i	−0.412291	+	0.475810i
$940$	4.95812	−	1.45583i	0.161716	−	0.0474841i
$941$	3.15179	+	6.90145i	0.102745	+	0.224981i	0.954022	−	0.299736i	$-0.0968985\pi$
$941$	3.15179	+	6.90145i	0.102745	+	0.224981i	−0.851277	+	0.524717i	$0.824171\pi$
$942$	18.5543			0.604532
$943$	−30.3071	−	31.9954i	−0.986934	−	1.04191i
$944$	−0.792382			−0.0257898
$945$	0.263642	+	0.577296i	0.00857628	+	0.0187794i
$946$	37.0057	−	10.8659i	1.20316	−	0.353280i
$947$	24.0807	−	27.7907i	0.782519	−	0.903075i	−0.214769	−	0.976665i	$-0.568900\pi$
$947$	24.0807	−	27.7907i	0.782519	−	0.903075i	0.997289	+	0.0735895i	$0.0234455\pi$
$948$	11.1576	+	7.17056i	0.362382	+	0.232889i
$949$	43.5403	+	50.2482i	1.41338	+	1.63113i
$950$	0.215679	+	1.50008i	0.00699756	+	0.0486691i
$951$	24.6370	+	7.23408i	0.798909	+	0.234581i
$952$	−0.669688	+	0.430383i	−0.0217047	+	0.0139488i
$953$	−6.20970	+	43.1894i	−0.201152	+	1.39904i	0.599721	+	0.800209i	$0.295278\pi$
$953$	−6.20970	+	43.1894i	−0.201152	+	1.39904i	−0.800873	+	0.598834i	$0.795631\pi$
$954$	−0.722088	+	1.58115i	−0.0233784	+	0.0511917i
$955$	−6.44625	+	14.1153i	−0.208596	+	0.456761i
$956$	3.37343	−	23.4627i	0.109104	−	0.758838i
$957$	−18.3972	+	11.8232i	−0.594698	+	0.382189i
$958$	27.5492	+	8.08918i	0.890075	+	0.261349i
$959$	0.499161	+	3.47174i	0.0161187	+	0.112108i
$960$	0.654861	+	0.755750i	0.0211355	+	0.0243917i
$961$	−8.85214	−	5.68893i	−0.285553	−	0.183514i
$962$	−27.5730	+	31.8209i	−0.888989	+	1.02595i
$963$	3.99701	−	1.17363i	0.128802	−	0.0378197i
$964$	−10.8214	−	23.6955i	−0.348533	−	0.763180i
$965$	14.6193			0.470611
$966$	−2.48509	+	1.75733i	−0.0799566	+	0.0565410i
$967$	−32.1585			−1.03415			−0.517074	−	0.855941i	$-0.672979\pi$
$967$	−32.1585			−1.03415			−0.517074	+	0.855941i	$0.672979\pi$
$968$	4.38508	+	9.60199i	0.140942	+	0.308620i
$969$	−1.82395	+	0.535561i	−0.0585938	+	0.0172047i
$970$	−4.46257	+	5.15008i	−0.143285	+	0.165359i
$971$	41.7837	+	26.8527i	1.34090	+	0.861745i	0.997011	−	0.0772647i	$-0.0246187\pi$
$971$	41.7837	+	26.8527i	1.34090	+	0.861745i	0.343891	+	0.939010i	$0.388255\pi$
$972$	0.654861	+	0.755750i	0.0210047	+	0.0242407i
$973$	0.0375404	+	0.261099i	0.00120349	+	0.00837046i
$974$	−17.6236	−	5.17475i	−0.564696	−	0.165810i
$975$	−3.43031	+	2.20453i	−0.109858	+	0.0706014i
$976$	−1.44411	+	10.0440i	−0.0462249	+	0.321502i
$977$	−18.2997	+	40.0708i	−0.585459	+	1.28198i	0.352688	+	0.935741i	$0.385268\pi$
$977$	−18.2997	+	40.0708i	−0.585459	+	1.28198i	−0.938147	+	0.346236i	$0.887460\pi$
$978$	−7.35041	+	16.0952i	−0.235040	+	0.514666i
$979$	−1.87493	+	13.0404i	−0.0599229	+	0.416773i
$980$	−5.54994	+	3.56673i	−0.177286	+	0.113935i
$981$	−18.0055	−	5.28688i	−0.574870	−	0.168797i
$982$	3.65063	+	25.3907i	0.116496	+	0.810249i
$983$	−4.33330	−	5.00089i	−0.138211	−	0.159504i	0.682424	−	0.730956i	$-0.260926\pi$
$983$	−4.33330	−	5.00089i	−0.138211	−	0.159504i	−0.820635	+	0.571452i	$0.806380\pi$
$984$	7.73059	+	4.96815i	0.246442	+	0.158379i
$985$	6.47275	−	7.46995i	0.206239	−	0.238012i
$986$	5.66889	−	1.66454i	0.180534	−	0.0530096i
$987$	−1.36235	−	2.98314i	−0.0433642	−	0.0949543i
$988$	−6.17967			−0.196601
$989$	−39.7998	+	1.76459i	−1.26556	+	0.0561107i
$990$	−4.64283			−0.147559
$991$	2.94513	+	6.44893i	0.0935550	+	0.204857i	0.950624	−	0.310344i	$-0.100444\pi$
$991$	2.94513	+	6.44893i	0.0935550	+	0.204857i	−0.857069	+	0.515201i	$0.827717\pi$
$992$	4.34190	−	1.27490i	0.137855	−	0.0404780i
$993$	−15.7976	+	18.2314i	−0.501321	+	0.578555i
$994$	−3.22819	−	2.07463i	−0.102392	−	0.0658032i
$995$	−0.445702	−	0.514368i	−0.0141297	−	0.0163066i
$996$	0.131009	+	0.911188i	0.00415118	+	0.0288721i
$997$	−45.8307	−	13.4571i	−1.45147	−	0.426191i	−0.541445	−	0.840736i	$-0.682123\pi$
$997$	−45.8307	−	13.4571i	−1.45147	−	0.426191i	−0.910029	+	0.414545i	$0.863941\pi$
$998$	−12.5470	+	8.06345i	−0.397167	+	0.255244i
$999$	1.46953	−	10.2208i	0.0464939	−	0.323372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.c.211.2	yes	20
23.6	even	11	inner	690.2.m.c.121.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.c.121.2	✓	20	23.6	even	11	inner
690.2.m.c.211.2	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 + 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(0.654861 + 0.755750i) q^{6} +(0.0903198 + 0.628188i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 + 0.909632i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.841254 + 0.540641i) q^{5} +(0.654861 + 0.755750i) q^{6} +(0.0903198 + 0.628188i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.142315 + 0.989821i) q^{10} +(-1.92870 + 4.22327i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(-0.580306 + 4.03612i) q^{13} +(-0.533899 + 0.343116i) q^{14} +(0.959493 + 0.281733i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-0.821414 - 0.947963i) q^{17} +(0.841254 + 0.540641i) q^{18} +(0.992447 - 1.14534i) q^{19} +(-0.959493 + 0.281733i) q^{20} +(0.263642 + 0.577296i) q^{21} -4.64283 q^{22} +(4.65690 + 1.14600i) q^{23} -1.00000 q^{24} +(0.415415 + 0.909632i) q^{25} +(-3.91245 + 1.14880i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-0.533899 - 0.343116i) q^{28} +(3.08455 + 3.55976i) q^{29} +(0.142315 + 0.989821i) q^{30} +(4.34190 + 1.27490i) q^{31} +(0.841254 - 0.540641i) q^{32} +(-0.660744 + 4.59558i) q^{33} +(0.521069 - 1.14098i) q^{34} +(-0.263642 + 0.577296i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(8.68671 - 5.58261i) q^{37} +(1.45412 + 0.426968i) q^{38} +(0.580306 + 4.03612i) q^{39} +(-0.654861 - 0.755750i) q^{40} +(-7.73059 - 4.96815i) q^{41} +(-0.415606 + 0.479635i) q^{42} +(-7.97050 + 2.34035i) q^{43} +(-1.92870 - 4.22327i) q^{44} +1.00000 q^{45} +(0.892108 + 4.71213i) q^{46} -5.16744 q^{47} +(-0.415415 - 0.909632i) q^{48} +(6.32999 - 1.85865i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(-1.05521 - 0.678144i) q^{51} +(-2.67027 - 3.08166i) q^{52} +(0.247376 + 1.72054i) q^{53} +(0.959493 + 0.281733i) q^{54} +(-3.90580 + 2.51011i) q^{55} +(0.0903198 - 0.628188i) q^{56} +(0.629565 - 1.37855i) q^{57} +(-1.95670 + 4.28458i) q^{58} +(0.112768 - 0.784317i) q^{59} +(-0.841254 + 0.540641i) q^{60} +(-9.73628 - 2.85883i) q^{61} +(0.644003 + 4.47914i) q^{62} +(0.415606 + 0.479635i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-2.67027 + 3.08166i) q^{65} +(-4.45477 + 1.30804i) q^{66} +(-0.0920044 - 0.201462i) q^{67} +1.25433 q^{68} +(4.79112 - 0.212422i) q^{69} -0.634648 q^{70} +(2.51178 + 5.50003i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(10.6779 - 12.3229i) q^{73} +(8.68671 + 5.58261i) q^{74} +(0.654861 + 0.755750i) q^{75} +(0.215679 + 1.50008i) q^{76} +(-2.82721 - 0.830143i) q^{77} +(-3.43031 + 2.20453i) q^{78} +(1.88753 - 13.1281i) q^{79} +(0.415415 - 0.909632i) q^{80} +(0.415415 - 0.909632i) q^{81} +(1.30778 - 9.09584i) q^{82} +(0.774423 - 0.497691i) q^{83} +(-0.608940 - 0.178801i) q^{84} +(-0.178510 - 1.24157i) q^{85} +(-5.43992 - 6.27801i) q^{86} +(3.96250 + 2.54655i) q^{87} +(3.04041 - 3.50882i) q^{88} +(2.72265 - 0.799443i) q^{89} +(0.415415 + 0.909632i) q^{90} -2.58785 q^{91} +(-3.91571 + 2.76898i) q^{92} +4.52520 q^{93} +(-2.14663 - 4.70046i) q^{94} +(1.45412 - 0.426968i) q^{95} +(0.654861 - 0.755750i) q^{96} +(5.73275 + 3.68422i) q^{97} +(4.32026 + 4.98585i) q^{98} +(0.660744 + 4.59558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Introduction

L-functions

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