LMFDB - Embedded newform 69.2.e.b.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (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:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			13.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	69.13
Dual form			69.2.e.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.154861 - 0.178719i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(0.276671 - 1.92429i) q^{4} +(0.418382 - 0.916128i) q^{5} +(0.0336545 + 0.234072i) q^{6} +(1.97204 + 0.579043i) q^{7} +(-0.784630 + 0.504251i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.154861 - 0.178719i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(0.276671 - 1.92429i) q^{4} +(0.418382 - 0.916128i) q^{5} +(0.0336545 + 0.234072i) q^{6} +(1.97204 + 0.579043i) q^{7} +(-0.784630 + 0.504251i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-0.228520 + 0.0670996i) q^{10} +(-2.87491 + 3.31782i) q^{11} +(-1.27310 + 1.46924i) q^{12} +(2.00357 - 0.588302i) q^{13} +(-0.201906 - 0.442111i) q^{14} +(-0.847262 + 0.544502i) q^{15} +(-3.51903 - 1.03328i) q^{16} +(0.308705 + 2.14709i) q^{17} +(0.0982369 - 0.215109i) q^{18} +(-0.379638 + 2.64044i) q^{19} +(-1.64714 - 1.05855i) q^{20} +(-1.34593 - 1.55329i) q^{21} +1.03817 q^{22} +(4.79541 - 0.0634158i) q^{23} +0.932691 q^{24} +(2.61006 + 3.01216i) q^{25} +(-0.415415 - 0.266971i) q^{26} +(0.142315 - 0.989821i) q^{27} +(1.65985 - 3.63457i) q^{28} +(-1.13486 - 7.89311i) q^{29} +(0.228520 + 0.0670996i) q^{30} +(-6.58251 + 4.23032i) q^{31} +(1.13520 + 2.48574i) q^{32} +(4.21228 - 1.23684i) q^{33} +(0.335919 - 0.387671i) q^{34} +(1.35554 - 1.56438i) q^{35} +(1.86533 - 0.547710i) q^{36} +(-1.63123 - 3.57190i) q^{37} +(0.530688 - 0.341052i) q^{38} +(-2.00357 - 0.588302i) q^{39} +(0.133684 + 0.929791i) q^{40} +(2.62039 - 5.73785i) q^{41} +(-0.0691698 + 0.481086i) q^{42} +(-1.82238 - 1.17118i) q^{43} +(5.58904 + 6.45010i) q^{44} +1.00714 q^{45} +(-0.753955 - 0.847210i) q^{46} -7.22297 q^{47} +(2.40176 + 2.77178i) q^{48} +(-2.33513 - 1.50070i) q^{49} +(0.134135 - 0.932932i) q^{50} +(0.901106 - 1.97315i) q^{51} +(-0.577732 - 4.01822i) q^{52} +(10.8363 + 3.18183i) q^{53} +(-0.198939 + 0.127850i) q^{54} +(1.83674 + 4.02190i) q^{55} +(-1.83930 + 0.540068i) q^{56} +(1.74690 - 2.01603i) q^{57} +(-1.23490 + 1.42515i) q^{58} +(-11.6983 + 3.43493i) q^{59} +(0.813367 + 1.78102i) q^{60} +(-11.8725 + 7.63000i) q^{61} +(1.77541 + 0.521307i) q^{62} +(0.292499 + 2.03437i) q^{63} +(-2.77870 + 6.08450i) q^{64} +(0.299298 - 2.08166i) q^{65} +(-0.873362 - 0.561276i) q^{66} +(-0.466276 - 0.538111i) q^{67} +4.21704 q^{68} +(-4.06844 - 2.53925i) q^{69} -0.489504 q^{70} +(2.69650 + 3.11193i) q^{71} +(-0.784630 - 0.504251i) q^{72} +(0.00834536 - 0.0580433i) q^{73} +(-0.385752 + 0.844680i) q^{74} +(-0.567219 - 3.94510i) q^{75} +(4.97594 + 1.46107i) q^{76} +(-7.59059 + 4.87818i) q^{77} +(0.205134 + 0.449181i) q^{78} +(15.6376 - 4.59162i) q^{79} +(-2.41892 + 2.79158i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-1.43126 + 0.420255i) q^{82} +(-6.04169 - 13.2294i) q^{83} +(-3.36135 + 2.16021i) q^{84} +(2.09617 + 0.615490i) q^{85} +(0.0729047 + 0.507064i) q^{86} +(-3.31264 + 7.25366i) q^{87} +(0.582724 - 4.05294i) q^{88} +(2.31657 + 1.48877i) q^{89} +(-0.155967 - 0.179995i) q^{90} +4.29177 q^{91} +(1.20472 - 9.24531i) q^{92} +7.82464 q^{93} +(1.11855 + 1.29088i) q^{94} +(2.26015 + 1.45251i) q^{95} +(0.388902 - 2.70488i) q^{96} +(2.45330 - 5.37197i) q^{97} +(0.0934171 + 0.649730i) q^{98} +(-4.21228 - 1.23684i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9} + 12 q^{10} - 15 q^{11} - 8 q^{12} + 8 q^{13} + 9 q^{14} - 8 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 9 q^{19} - 9 q^{20} + 5 q^{21} - 28 q^{22} + 21 q^{23} + 18 q^{24} - 4 q^{25} + q^{26} + q^{27} + 29 q^{28} - 8 q^{29} - 12 q^{30} - 23 q^{31} - q^{32} + 4 q^{33} - 15 q^{34} + 18 q^{35} + 8 q^{36} + 3 q^{37} + 3 q^{38} - 8 q^{39} - 32 q^{40} - 15 q^{41} + 13 q^{42} + 22 q^{43} - q^{44} - 14 q^{45} + 26 q^{46} + 4 q^{47} + 21 q^{48} - 29 q^{49} + 49 q^{50} - 12 q^{51} + 2 q^{52} + 29 q^{53} + 7 q^{54} + 43 q^{55} - 2 q^{56} + 20 q^{57} + 21 q^{58} - 54 q^{59} - 2 q^{60} - 30 q^{61} - 7 q^{62} + 6 q^{63} - 31 q^{64} - 9 q^{65} - 27 q^{66} + q^{67} - 30 q^{68} + q^{69} - 94 q^{70} - 3 q^{71} - 7 q^{72} - 47 q^{73} - 12 q^{74} + 15 q^{75} + 50 q^{76} + 13 q^{77} - 12 q^{78} + 18 q^{79} + 3 q^{80} - q^{81} - 28 q^{82} + 18 q^{83} + 4 q^{84} + 58 q^{85} + 8 q^{87} + 16 q^{88} + 25 q^{89} + q^{90} + 18 q^{91} - 3 q^{92} - 10 q^{93} + 39 q^{94} - 16 q^{95} - 21 q^{96} + 21 q^{97} - 27 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9 + 12 * q^10 - 15 * q^11 - 8 * q^12 + 8 * q^13 + 9 * q^14 - 8 * q^15 + 12 * q^16 + q^17 + 4 * q^18 - 9 * q^19 - 9 * q^20 + 5 * q^21 - 28 * q^22 + 21 * q^23 + 18 * q^24 - 4 * q^25 + q^26 + q^27 + 29 * q^28 - 8 * q^29 - 12 * q^30 - 23 * q^31 - q^32 + 4 * q^33 - 15 * q^34 + 18 * q^35 + 8 * q^36 + 3 * q^37 + 3 * q^38 - 8 * q^39 - 32 * q^40 - 15 * q^41 + 13 * q^42 + 22 * q^43 - q^44 - 14 * q^45 + 26 * q^46 + 4 * q^47 + 21 * q^48 - 29 * q^49 + 49 * q^50 - 12 * q^51 + 2 * q^52 + 29 * q^53 + 7 * q^54 + 43 * q^55 - 2 * q^56 + 20 * q^57 + 21 * q^58 - 54 * q^59 - 2 * q^60 - 30 * q^61 - 7 * q^62 + 6 * q^63 - 31 * q^64 - 9 * q^65 - 27 * q^66 + q^67 - 30 * q^68 + q^69 - 94 * q^70 - 3 * q^71 - 7 * q^72 - 47 * q^73 - 12 * q^74 + 15 * q^75 + 50 * q^76 + 13 * q^77 - 12 * q^78 + 18 * q^79 + 3 * q^80 - q^81 - 28 * q^82 + 18 * q^83 + 4 * q^84 + 58 * q^85 + 8 * q^87 + 16 * q^88 + 25 * q^89 + q^90 + 18 * q^91 - 3 * q^92 - 10 * q^93 + 39 * q^94 - 16 * q^95 - 21 * q^96 + 21 * q^97 - 27 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.154861	−	0.178719i	−0.109503	−	0.126373i	0.698352	−	0.715755i	$-0.253917\pi$
$2$	−0.154861	−	0.178719i	−0.109503	−	0.126373i	−0.807855	+	0.589381i	$0.799372\pi$
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$4$	0.276671	−	1.92429i	0.138336	−	0.962145i
$5$	0.418382	−	0.916128i	0.187106	−	0.409705i	−0.792712	−	0.609596i	$-0.791332\pi$
$5$	0.418382	−	0.916128i	0.187106	−	0.409705i	0.979818	+	0.199891i	$0.0640589\pi$
$6$	0.0336545	+	0.234072i	0.0137394	+	0.0955594i
$7$	1.97204	+	0.579043i	0.745361	+	0.218858i	0.632293	−	0.774730i	$-0.282114\pi$
$7$	1.97204	+	0.579043i	0.745361	+	0.218858i	0.113068	+	0.993587i	$0.463932\pi$
$8$	−0.784630	+	0.504251i	−0.277408	+	0.178280i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	−0.228520	+	0.0670996i	−0.0722645	+	0.0212188i
$11$	−2.87491	+	3.31782i	−0.866817	+	1.00036i	0.133140	+	0.991097i	$0.457494\pi$
$11$	−2.87491	+	3.31782i	−0.866817	+	1.00036i	−0.999957	+	0.00926330i	$0.997051\pi$
$12$	−1.27310	+	1.46924i	−0.367512	+	0.424132i
$13$	2.00357	−	0.588302i	0.555691	−	0.163165i	0.00818349	−	0.999967i	$-0.497395\pi$
$13$	2.00357	−	0.588302i	0.555691	−	0.163165i	0.547507	+	0.836801i	$0.315577\pi$
$14$	−0.201906	−	0.442111i	−0.0539615	−	0.118159i
$15$	−0.847262	+	0.544502i	−0.218762	+	0.140590i
$16$	−3.51903	−	1.03328i	−0.879758	−	0.258320i
$17$	0.308705	+	2.14709i	0.0748720	+	0.520746i	0.992398	+	0.123070i	$0.0392740\pi$
$17$	0.308705	+	2.14709i	0.0748720	+	0.520746i	−0.917526	+	0.397676i	$0.869817\pi$
$18$	0.0982369	−	0.215109i	0.0231547	−	0.0507016i
$19$	−0.379638	+	2.64044i	−0.0870950	+	0.605759i	0.898796	+	0.438368i	$0.144443\pi$
$19$	−0.379638	+	2.64044i	−0.0870950	+	0.605759i	−0.985891	+	0.167391i	$0.946466\pi$
$20$	−1.64714	−	1.05855i	−0.368312	−	0.236700i
$21$	−1.34593	−	1.55329i	−0.293706	−	0.338955i
$22$	1.03817			0.221338
$23$	4.79541	−	0.0634158i	0.999913	−	0.0132231i
$23$	4.79541	−	0.0634158i	0.999913	−	0.0132231i
$24$	0.932691			0.190385
$25$	2.61006	+	3.01216i	0.522011	+	0.602433i
$26$	−0.415415	−	0.266971i	−0.0814696	−	0.0523573i
$27$	0.142315	−	0.989821i	0.0273885	−	0.190491i
$28$	1.65985	−	3.63457i	0.313683	−	0.686869i
$29$	−1.13486	−	7.89311i	−0.210738	−	1.46571i	−0.770701	−	0.637197i	$-0.780094\pi$
$29$	−1.13486	−	7.89311i	−0.210738	−	1.46571i	0.559963	−	0.828517i	$-0.310815\pi$
$30$	0.228520	+	0.0670996i	0.0417219	+	0.0122507i
$31$	−6.58251	+	4.23032i	−1.18225	+	0.759788i	−0.975799	−	0.218668i	$-0.929829\pi$
$31$	−6.58251	+	4.23032i	−1.18225	+	0.759788i	−0.206454	+	0.978456i	$0.566192\pi$
$32$	1.13520	+	2.48574i	0.200677	+	0.439421i
$33$	4.21228	−	1.23684i	0.733263	−	0.215305i
$34$	0.335919	−	0.387671i	0.0576097	−	0.0664851i
$35$	1.35554	−	1.56438i	0.229129	−	0.264428i
$36$	1.86533	−	0.547710i	0.310888	−	0.0912850i
$37$	−1.63123	−	3.57190i	−0.268173	−	0.587217i	0.726857	−	0.686789i	$-0.240980\pi$
$37$	−1.63123	−	3.57190i	−0.268173	−	0.587217i	−0.995030	+	0.0995712i	$0.968253\pi$
$38$	0.530688	−	0.341052i	0.0860889	−	0.0553260i
$39$	−2.00357	−	0.588302i	−0.320828	−	0.0942036i
$40$	0.133684	+	0.929791i	0.0211373	+	0.147013i
$41$	2.62039	−	5.73785i	0.409236	−	0.896102i	−0.587014	−	0.809577i	$-0.699696\pi$
$41$	2.62039	−	5.73785i	0.409236	−	0.896102i	0.996250	−	0.0865250i	$-0.0275762\pi$
$42$	−0.0691698	+	0.481086i	−0.0106731	+	0.0742332i
$43$	−1.82238	−	1.17118i	−0.277911	−	0.178603i	0.394259	−	0.918999i	$-0.371001\pi$
$43$	−1.82238	−	1.17118i	−0.277911	−	0.178603i	−0.672170	+	0.740397i	$0.734638\pi$
$44$	5.58904	+	6.45010i	0.842580	+	0.972389i
$45$	1.00714			0.150136
$46$	−0.753955	−	0.847210i	−0.111165	−	0.124914i
$47$	−7.22297			−1.05358			−0.526789	−	0.849996i	$-0.676604\pi$
$47$	−7.22297			−1.05358			−0.526789	+	0.849996i	$0.676604\pi$
$48$	2.40176	+	2.77178i	0.346665	+	0.400072i
$49$	−2.33513	−	1.50070i	−0.333590	−	0.214385i
$50$	0.134135	−	0.932932i	0.0189696	−	0.131937i
$51$	0.901106	−	1.97315i	0.126180	−	0.276296i
$52$	−0.577732	−	4.01822i	−0.0801171	−	0.557226i
$53$	10.8363	+	3.18183i	1.48848	+	0.437058i	0.922057	−	0.387054i	$-0.126507\pi$
$53$	10.8363	+	3.18183i	1.48848	+	0.437058i	0.566427	+	0.824112i	$0.308325\pi$
$54$	−0.198939	+	0.127850i	−0.0270721	+	0.0173982i
$55$	1.83674	+	4.02190i	0.247666	+	0.542313i
$56$	−1.83930	+	0.540068i	−0.245787	+	0.0721696i
$57$	1.74690	−	2.01603i	0.231383	−	0.267030i
$58$	−1.23490	+	1.42515i	−0.162151	+	0.187132i
$59$	−11.6983	+	3.43493i	−1.52299	+	0.447190i	−0.932897	−	0.360145i	$-0.882727\pi$
$59$	−11.6983	+	3.43493i	−1.52299	+	0.447190i	−0.590094	+	0.807335i	$0.700909\pi$
$60$	0.813367	+	1.78102i	0.105005	+	0.229929i
$61$	−11.8725	+	7.63000i	−1.52012	+	0.976922i	−0.528331	+	0.849039i	$0.677182\pi$
$61$	−11.8725	+	7.63000i	−1.52012	+	0.976922i	−0.991789	+	0.127883i	$0.959182\pi$
$62$	1.77541	+	0.521307i	0.225477	+	0.0662061i
$63$	0.292499	+	2.03437i	0.0368514	+	0.256307i
$64$	−2.77870	+	6.08450i	−0.347337	+	0.760562i
$65$	0.299298	−	2.08166i	0.0371233	−	0.258199i
$66$	−0.873362	−	0.561276i	−0.107503	−	0.0690883i
$67$	−0.466276	−	0.538111i	−0.0569647	−	0.0657407i	0.726552	−	0.687111i	$-0.241122\pi$
$67$	−0.466276	−	0.538111i	−0.0569647	−	0.0657407i	−0.783517	+	0.621371i	$0.786576\pi$
$68$	4.21704			0.511391
$69$	−4.06844	−	2.53925i	−0.489783	−	0.305689i
$70$	−0.489504			−0.0585070
$71$	2.69650	+	3.11193i	0.320016	+	0.369318i	0.892851	−	0.450353i	$-0.148702\pi$
$71$	2.69650	+	3.11193i	0.320016	+	0.369318i	−0.572835	+	0.819671i	$0.694156\pi$
$72$	−0.784630	−	0.504251i	−0.0924695	−	0.0594265i
$73$	0.00834536	−	0.0580433i	0.000976751	−	0.00679345i	−0.989327	−	0.145711i	$-0.953453\pi$
$73$	0.00834536	−	0.0580433i	0.000976751	−	0.00679345i	0.990304	+	0.138917i	$0.0443622\pi$
$74$	−0.385752	+	0.844680i	−0.0448428	+	0.0981920i
$75$	−0.567219	−	3.94510i	−0.0654968	−	0.455541i
$76$	4.97594	+	1.46107i	0.570779	+	0.167596i
$77$	−7.59059	+	4.87818i	−0.865028	+	0.555920i
$78$	0.205134	+	0.449181i	0.0232268	+	0.0508597i
$79$	15.6376	−	4.59162i	1.75937	−	0.516598i	0.767190	−	0.641419i	$-0.221654\pi$
$79$	15.6376	−	4.59162i	1.75937	−	0.516598i	0.992179	+	0.124822i	$0.0398360\pi$
$80$	−2.41892	+	2.79158i	−0.270443	+	0.312108i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	−1.43126	+	0.420255i	−0.158056	+	0.0464094i
$83$	−6.04169	−	13.2294i	−0.663161	−	1.45212i	−0.879547	−	0.475812i	$-0.842154\pi$
$83$	−6.04169	−	13.2294i	−0.663161	−	1.45212i	0.216386	−	0.976308i	$-0.430573\pi$
$84$	−3.36135	+	2.16021i	−0.366754	+	0.235698i
$85$	2.09617	+	0.615490i	0.227361	+	0.0667593i
$86$	0.0729047	+	0.507064i	0.00786152	+	0.0546781i
$87$	−3.31264	+	7.25366i	−0.355152	+	0.777674i
$88$	0.582724	−	4.05294i	0.0621186	−	0.432044i
$89$	2.31657	+	1.48877i	0.245556	+	0.157809i	0.657630	−	0.753341i	$-0.271559\pi$
$89$	2.31657	+	1.48877i	0.245556	+	0.157809i	−0.412074	+	0.911151i	$0.635195\pi$
$90$	−0.155967	−	0.179995i	−0.0164403	−	0.0189732i
$91$	4.29177			0.449900
$92$	1.20472	−	9.24531i	0.125601	−	0.963890i
$93$	7.82464			0.811377
$94$	1.11855	+	1.29088i	0.115370	+	0.133144i
$95$	2.26015	+	1.45251i	0.231886	+	0.149024i
$96$	0.388902	−	2.70488i	0.0396922	−	0.276065i
$97$	2.45330	−	5.37197i	0.249095	−	0.545441i	−0.743239	−	0.669026i	$-0.766712\pi$
$97$	2.45330	−	5.37197i	0.249095	−	0.545441i	0.992334	+	0.123584i	$0.0394389\pi$
$98$	0.0934171	+	0.649730i	0.00943655	+	0.0656327i
$99$	−4.21228	−	1.23684i	−0.423350	−	0.124307i
$100$	6.51841	−	4.18912i	0.651841	−	0.418912i
$101$	−2.21732	−	4.85526i	−0.220632	−	0.483116i	0.766656	−	0.642058i	$-0.221919\pi$
$101$	−2.21732	−	4.85526i	−0.220632	−	0.483116i	−0.987288	+	0.158942i	$0.949192\pi$
$102$	−0.492184	+	0.144518i	−0.0487335	+	0.0143094i
$103$	3.24758	−	3.74790i	0.319993	−	0.369292i	−0.572849	−	0.819661i	$-0.694162\pi$
$103$	3.24758	−	3.74790i	0.319993	−	0.369292i	0.892843	+	0.450369i	$0.148707\pi$
$104$	−1.27541	+	1.47190i	−0.125064	+	0.144332i
$105$	−1.98612	+	0.583178i	−0.193826	+	0.0569124i
$106$	−1.10947	−	2.42940i	−0.107761	−	0.235964i
$107$	2.97773	−	1.91367i	0.287868	−	0.185002i	−0.388735	−	0.921350i	$-0.627088\pi$
$107$	2.97773	−	1.91367i	0.287868	−	0.185002i	0.676603	+	0.736348i	$0.263451\pi$
$108$	−1.86533	−	0.547710i	−0.179491	−	0.0527034i
$109$	−0.543576	−	3.78065i	−0.0520651	−	0.362121i	−0.999153	−	0.0411469i	$-0.986899\pi$
$109$	−0.543576	−	3.78065i	−0.0520651	−	0.362121i	0.947088	−	0.320974i	$-0.104010\pi$
$110$	0.434350	−	0.951095i	0.0414137	−	0.0906833i
$111$	−0.558836	+	3.88679i	−0.0530424	+	0.368918i
$112$	−6.34135	−	4.07534i	−0.599201	−	0.385083i
$113$	12.0127	+	13.8634i	1.13006	+	1.30416i	0.947064	+	0.321046i	$0.104034\pi$
$113$	12.0127	+	13.8634i	1.13006	+	1.30416i	0.182997	+	0.983114i	$0.441420\pi$
$114$	−0.630830			−0.0590826
$115$	1.94822	−	4.41975i	0.181672	−	0.412143i
$116$	−15.5026			−1.43938
$117$	1.36745	+	1.57812i	0.126421	+	0.145898i
$118$	2.42550	+	1.55877i	0.223285	+	0.143497i
$119$	−0.634479	+	4.41290i	−0.0581626	+	0.404530i
$120$	0.390221	−	0.854465i	0.0356221	−	0.0780016i
$121$	−1.17737	−	8.18882i	−0.107034	−	0.744438i
$122$	3.20221	+	0.940254i	0.289915	+	0.0851266i
$123$	−5.30653	+	3.41030i	−0.478474	+	0.307496i
$124$	6.31917	+	13.8371i	0.567478	+	1.24260i
$125$	8.68326	−	2.54963i	0.776654	−	0.228046i
$126$	0.318284	−	0.367319i	0.0283550	−	0.0327234i
$127$	−0.684944	+	0.790468i	−0.0607790	+	0.0701427i	−0.785325	−	0.619084i	$-0.787504\pi$
$127$	−0.684944	+	0.790468i	−0.0607790	+	0.0701427i	0.724546	+	0.689227i	$0.242050\pi$
$128$	6.76172	−	1.98542i	0.597657	−	0.175488i
$129$	0.899902	+	1.97051i	0.0792320	+	0.173494i
$130$	−0.418382	+	0.268878i	−0.0366945	+	0.0235821i
$131$	−8.80970	−	2.58676i	−0.769707	−	0.226006i	−0.126777	−	0.991931i	$-0.540463\pi$
$131$	−8.80970	−	2.58676i	−0.769707	−	0.226006i	−0.642930	+	0.765925i	$0.722281\pi$
$132$	−1.21462	−	8.44784i	−0.105719	−	0.735290i
$133$	−2.27759	+	4.98723i	−0.197492	+	0.432447i
$134$	−0.0239627	+	0.166665i	−0.00207007	+	0.0143976i
$135$	−0.847262	−	0.544502i	−0.0729207	−	0.0468633i
$136$	−1.32489	−	1.52901i	−0.113609	−	0.131111i
$137$	−14.8173			−1.26592			−0.632962	−	0.774183i	$-0.718161\pi$
$137$	−14.8173			−1.26592			−0.632962	+	0.774183i	$0.718161\pi$
$138$	0.176231	+	1.12034i	0.0150018	+	0.0953694i
$139$	16.3675			1.38827			0.694137	−	0.719843i	$-0.255786\pi$
$139$	16.3675			1.38827			0.694137	+	0.719843i	$0.255786\pi$
$140$	−2.63528	−	3.04128i	−0.222722	−	0.257035i
$141$	6.07635	+	3.90503i	0.511721	+	0.328863i
$142$	0.138578	−	0.963831i	0.0116292	−	0.0808829i
$143$	−3.80820	+	8.33880i	−0.318458	+	0.697326i
$144$	−0.521953	−	3.63026i	−0.0434961	−	0.302522i
$145$	−7.70591	−	2.26266i	−0.639941	−	0.187904i
$146$	−0.0116658	+	0.00749715i	−0.000965468	+	0.000620469i
$147$	1.15310	+	2.52493i	0.0951059	+	0.208253i
$148$	−7.32469	+	2.15072i	−0.602086	+	0.176788i
$149$	−0.467928	+	0.540018i	−0.0383342	+	0.0442400i	−0.774593	−	0.632460i	$-0.782045\pi$
$149$	−0.467928	+	0.540018i	−0.0383342	+	0.0442400i	0.736259	+	0.676700i	$0.236591\pi$
$150$	−0.617223	+	0.712313i	−0.0503961	+	0.0581601i
$151$	−6.92613	+	2.03369i	−0.563640	+	0.165500i	−0.551126	−	0.834422i	$-0.685802\pi$
$151$	−6.92613	+	2.03369i	−0.563640	+	0.165500i	−0.0125142	+	0.999922i	$0.503983\pi$
$152$	−1.03357	−	2.26320i	−0.0838336	−	0.183570i
$153$	−1.82482	+	1.17274i	−0.147528	+	0.0948106i
$154$	2.04731	+	0.601143i	0.164977	+	0.0484415i
$155$	1.12152	+	7.80031i	0.0900823	+	0.626536i
$156$	−1.68639	+	3.69269i	−0.135019	+	0.295651i
$157$	−2.55993	+	17.8047i	−0.204305	+	1.42097i	0.587018	+	0.809574i	$0.300302\pi$
$157$	−2.55993	+	17.8047i	−0.204305	+	1.42097i	−0.791323	+	0.611399i	$0.790607\pi$
$158$	−3.24226	−	2.08368i	−0.257940	−	0.165768i
$159$	−7.39587	−	8.53529i	−0.586531	−	0.676892i
$160$	2.75221			0.217581
$161$	9.49346	+	2.65169i	0.748189	+	0.208983i
$162$	0.236479			0.0185795
$163$	−3.00032	−	3.46255i	−0.235003	−	0.271208i	0.625983	−	0.779837i	$-0.284698\pi$
$163$	−3.00032	−	3.46255i	−0.235003	−	0.271208i	−0.860986	+	0.508629i	$0.830153\pi$
$164$	−10.3163	−	6.62989i	−0.805568	−	0.517707i
$165$	0.629239	−	4.37646i	0.0489862	−	0.340707i
$166$	−1.42873	+	3.12848i	−0.110891	+	0.242817i
$167$	2.39142	+	16.6327i	0.185054	+	1.28708i	0.844594	+	0.535407i	$0.179842\pi$
$167$	2.39142	+	16.6327i	0.185054	+	1.28708i	−0.659541	+	0.751669i	$0.729249\pi$
$168$	1.83930	+	0.540068i	0.141905	+	0.0416672i
$169$	−7.26810	+	4.67092i	−0.559084	+	0.359302i
$170$	−0.214614	−	0.469940i	−0.0164602	−	0.0360427i
$171$	−2.55954	+	0.751548i	−0.195733	+	0.0574723i
$172$	−2.75788	+	3.18277i	−0.210287	+	0.242684i
$173$	3.79367	−	4.37813i	0.288427	−	0.332863i	−0.592982	−	0.805215i	$-0.702050\pi$
$173$	3.79367	−	4.37813i	0.288427	−	0.332863i	0.881410	+	0.472353i	$0.156595\pi$
$174$	1.80936	−	0.531277i	0.137167	−	0.0402760i
$175$	3.40296	+	7.45144i	0.257239	+	0.563276i
$176$	13.5451	−	8.70493i	1.02100	−	0.656158i
$177$	11.6983	+	3.43493i	0.879299	+	0.258185i
$178$	−0.0926748	−	0.644568i	−0.00694627	−	0.0483124i
$179$	7.14495	−	15.6453i	0.534039	−	1.16938i	−0.429807	−	0.902921i	$-0.641418\pi$
$179$	7.14495	−	15.6453i	0.534039	−	1.16938i	0.963846	−	0.266461i	$-0.0858543\pi$
$180$	0.278647	−	1.93803i	0.0207691	−	0.144452i
$181$	−1.83512	−	1.17936i	−0.136403	−	0.0876611i	0.470659	−	0.882315i	$-0.344016\pi$
$181$	−1.83512	−	1.17936i	−0.136403	−	0.0876611i	−0.607063	+	0.794654i	$0.707652\pi$
$182$	−0.664627	−	0.767020i	−0.0492654	−	0.0568553i
$183$	14.1129			1.04325
$184$	−3.73065	+	2.46785i	−0.275027	+	0.181932i
$185$	−3.95480			−0.290763
$186$	−1.21173	−	1.39841i	−0.0888483	−	0.102536i
$187$	−8.01116	−	5.14846i	−0.585834	−	0.376493i
$188$	−1.99839	+	13.8991i	−0.145747	+	1.01369i
$189$	0.853799	−	1.86956i	0.0621048	−	0.135990i
$190$	−0.0904176	−	0.628868i	−0.00655958	−	0.0456229i
$191$	16.6139	+	4.87828i	1.20214	+	0.352980i	0.820671	−	0.571401i	$-0.193600\pi$
$191$	16.6139	+	4.87828i	1.20214	+	0.352980i	0.381469	+	0.924382i	$0.375418\pi$
$192$	5.62711	−	3.61633i	0.406102	−	0.260986i
$193$	−7.47369	−	16.3651i	−0.537968	−	1.17799i	−0.962178	−	0.272421i	$-0.912176\pi$
$193$	−7.47369	−	16.3651i	−0.537968	−	1.17799i	0.424210	−	0.905564i	$-0.360552\pi$
$194$	−1.33999	+	0.393457i	−0.0962058	+	0.0282486i
$195$	−1.37722	+	1.58939i	−0.0986246	+	0.113819i
$196$	−3.53384	+	4.07826i	−0.252417	+	0.291305i
$197$	4.70492	−	1.38149i	0.335212	−	0.0984271i	−0.109795	−	0.993954i	$-0.535019\pi$
$197$	4.70492	−	1.38149i	0.335212	−	0.0984271i	0.445007	+	0.895527i	$0.353201\pi$
$198$	0.431270	+	0.944350i	0.0306490	+	0.0671120i
$199$	10.5066	−	6.75221i	0.744796	−	0.478652i	−0.112386	−	0.993665i	$-0.535849\pi$
$199$	10.5066	−	6.75221i	0.744796	−	0.478652i	0.857182	+	0.515013i	$0.172213\pi$
$200$	−3.56681	−	1.04731i	−0.252212	−	0.0740561i
$201$	0.101331	+	0.704775i	0.00714737	+	0.0497110i
$202$	−0.524350	+	1.14817i	−0.0368931	+	0.0807846i
$203$	2.33247	−	16.2227i	0.163707	−	1.13861i
$204$	−3.54760	−	2.27990i	−0.248381	−	0.159625i
$205$	−4.16029	−	4.80123i	−0.290567	−	0.335332i
$206$	−1.17274			−0.0817089
$207$	2.04977	+	4.33572i	0.142469	+	0.301353i
$208$	−7.65851			−0.531022
$209$	−7.66909	−	8.85060i	−0.530482	−	0.612209i
$210$	0.411797	+	0.264646i	0.0284167	+	0.0182623i
$211$	2.56952	−	17.8714i	0.176893	−	1.23032i	−0.687005	−	0.726652i	$-0.741075\pi$
$211$	2.56952	−	17.8714i	0.176893	−	1.23032i	0.863898	−	0.503666i	$-0.168016\pi$
$212$	9.12087	−	19.9719i	0.626424	−	1.37168i
$213$	−0.586006	−	4.07576i	−0.0401525	−	0.279266i
$214$	−0.803143	−	0.235824i	−0.0549017	−	0.0161206i
$215$	−1.83540	+	1.17954i	−0.125173	+	0.0804440i
$216$	0.387454	+	0.848406i	0.0263629	+	0.0577267i
$217$	−15.4305	+	4.53080i	−1.04749	+	0.307571i
$218$	−0.591496	+	0.682622i	−0.0400611	+	0.0462330i
$219$	−0.0384011	+	0.0443173i	−0.00259491	+	0.00299468i
$220$	8.24748	−	2.42168i	0.556045	−	0.163269i
$221$	1.88165	+	4.12024i	0.126573	+	0.277157i
$222$	0.781184	−	0.502036i	0.0524296	−	0.0336945i
$223$	8.37729	+	2.45980i	0.560985	+	0.164720i	0.549918	−	0.835219i	$-0.314659\pi$
$223$	8.37729	+	2.45980i	0.560985	+	0.164720i	0.0110671	+	0.999939i	$0.496477\pi$
$224$	0.799308	+	5.55931i	0.0534060	+	0.371447i
$225$	−1.65571	+	3.62549i	−0.110380	+	0.241699i
$226$	0.617354	−	4.29379i	0.0410658	−	0.285619i
$227$	19.9524	+	12.8226i	1.32428	+	0.851066i	0.995630	−	0.0933842i	$-0.0297685\pi$
$227$	19.9524	+	12.8226i	1.32428	+	0.851066i	0.328654	+	0.944450i	$0.393405\pi$
$228$	−3.39611	−	3.91932i	−0.224913	−	0.259564i
$229$	−6.81277			−0.450201			−0.225100	−	0.974336i	$-0.572271\pi$
$229$	−6.81277			−0.450201			−0.225100	+	0.974336i	$0.572271\pi$
$230$	−1.09159	+	0.336262i	−0.0719776	+	0.0221725i
$231$	9.02295			0.593667
$232$	4.87055	+	5.62092i	0.319767	+	0.369031i
$233$	−1.15031	−	0.739259i	−0.0753593	−	0.0484305i	0.502419	−	0.864625i	$-0.332444\pi$
$233$	−1.15031	−	0.739259i	−0.0753593	−	0.0484305i	−0.577778	+	0.816194i	$0.696080\pi$
$234$	0.0702757	−	0.488779i	0.00459407	−	0.0319525i
$235$	−3.02196	+	6.61717i	−0.197131	+	0.431656i
$236$	3.37322	+	23.4613i	0.219578	+	1.52720i
$237$	−15.6376	−	4.59162i	−1.01577	−	0.298258i
$238$	0.886924	−	0.569992i	0.0574908	−	0.0369471i
$239$	−7.48160	−	16.3824i	−0.483945	−	1.05969i	−0.981360	−	0.192178i	$-0.938445\pi$
$239$	−7.48160	−	16.3824i	−0.483945	−	1.05969i	0.497415	−	0.867513i	$-0.334283\pi$
$240$	3.54416	−	1.04066i	0.228775	−	0.0671743i
$241$	0.193682	−	0.223521i	0.0124762	−	0.0143983i	−0.749477	−	0.662030i	$-0.769695\pi$
$241$	0.193682	−	0.223521i	0.0124762	−	0.0143983i	0.761953	+	0.647632i	$0.224241\pi$
$242$	−1.28117	+	1.47855i	−0.0823566	+	0.0950445i
$243$	0.959493	−	0.281733i	0.0615515	−	0.0180732i
$244$	11.3976	+	24.9572i	0.729654	+	1.59772i
$245$	−2.35181	+	1.51141i	−0.150251	+	0.0965607i
$246$	1.43126	+	0.420255i	0.0912537	+	0.0267945i
$247$	0.792744	+	5.51365i	0.0504411	+	0.350825i
$248$	3.03169	−	6.63847i	0.192512	−	0.421543i
$249$	−2.06979	+	14.3957i	−0.131168	+	0.912290i
$250$	−1.80036	−	1.15702i	−0.113865	−	0.0731766i
$251$	−9.84485	−	11.3616i	−0.621402	−	0.717136i	0.354571	−	0.935029i	$-0.384627\pi$
$251$	−9.84485	−	11.3616i	−0.621402	−	0.717136i	−0.975973	+	0.217893i	$0.930081\pi$
$252$	3.99565			0.251702
$253$	−13.5760	+	16.0926i	−0.853514	+	1.01174i
$254$	0.247342			0.0155196
$255$	−1.43065	−	1.65106i	−0.0895907	−	0.103393i
$256$	9.85227	+	6.33167i	0.615767	+	0.395729i
$257$	−2.06422	+	14.3570i	−0.128763	+	0.895564i	0.818363	+	0.574702i	$0.194882\pi$
$257$	−2.06422	+	14.3570i	−0.128763	+	0.895564i	−0.947126	+	0.320863i	$0.896027\pi$
$258$	0.212808	−	0.465984i	0.0132488	−	0.0290109i
$259$	−1.14857	−	7.98849i	−0.0713687	−	0.496381i
$260$	−3.92292	−	1.15187i	−0.243289	−	0.0714361i
$261$	6.70839	−	4.31122i	0.415239	−	0.266858i
$262$	0.901973	+	1.97505i	0.0557241	+	0.122019i
$263$	−14.6522	+	4.30227i	−0.903491	+	0.265289i	−0.700299	−	0.713850i	$-0.746950\pi$
$263$	−14.6522	+	4.30227i	−0.903491	+	0.265289i	−0.203193	+	0.979139i	$0.565132\pi$
$264$	−2.68140	+	3.09450i	−0.165029	+	0.190453i
$265$	7.44869	−	8.59625i	0.457569	−	0.528063i
$266$	1.24402	−	0.365277i	0.0762758	−	0.0223966i
$267$	−1.14394	−	2.50487i	−0.0700077	−	0.153295i
$268$	−1.16449	+	0.748370i	−0.0711323	+	0.0457140i
$269$	−13.0616	−	3.83523i	−0.796379	−	0.233838i	−0.141863	−	0.989886i	$-0.545309\pi$
$269$	−13.0616	−	3.83523i	−0.796379	−	0.233838i	−0.654516	+	0.756048i	$0.727127\pi$
$270$	0.0338948	+	0.235744i	0.00206277	+	0.0143469i
$271$	1.83450	−	4.01699i	0.111438	−	0.244015i	−0.845694	−	0.533669i	$-0.820813\pi$
$271$	1.83450	−	4.01699i	0.111438	−	0.244015i	0.957131	+	0.289654i	$0.0935402\pi$
$272$	1.13220	−	7.87466i	0.0686500	−	0.477471i
$273$	−3.61047	−	2.32031i	−0.218515	−	0.140431i
$274$	2.29461	+	2.64812i	0.138623	+	0.159979i
$275$	−17.4975			−1.05514
$276$	−6.01187	+	7.12633i	−0.361872	+	0.428954i
$277$	16.7884			1.00872			0.504358	−	0.863495i	$-0.331729\pi$
$277$	16.7884			1.00872			0.504358	+	0.863495i	$0.331729\pi$
$278$	−2.53468	−	2.92518i	−0.152020	−	0.175441i
$279$	−6.58251	−	4.23032i	−0.394084	−	0.253263i
$280$	−0.274759	+	1.91099i	−0.0164200	+	0.114204i
$281$	−11.6533	+	25.5171i	−0.695177	+	1.52223i	0.150546	+	0.988603i	$0.451897\pi$
$281$	−11.6533	+	25.5171i	−0.695177	+	1.52223i	−0.845723	+	0.533622i	$0.820830\pi$
$282$	−0.243085	−	1.69069i	−0.0144755	−	0.100679i
$283$	−27.2561	−	8.00311i	−1.62021	−	0.475736i	−0.659133	−	0.752026i	$-0.729077\pi$
$283$	−27.2561	−	8.00311i	−1.62021	−	0.475736i	−0.961074	+	0.276291i	$0.910895\pi$
$284$	6.73430	−	4.32787i	0.399607	−	0.256812i
$285$	−1.11607	−	2.44386i	−0.0661104	−	0.144762i
$286$	2.08004	−	0.610755i	0.122995	−	0.0361147i
$287$	8.48997	−	9.79795i	0.501147	−	0.578355i
$288$	−1.78953	+	2.06523i	−0.105449	+	0.121695i
$289$	11.7967	−	3.46382i	0.693922	−	0.203754i
$290$	0.788963	+	1.72759i	0.0463295	+	0.101447i
$291$	−4.96815	+	3.19284i	−0.291238	+	0.187167i
$292$	−0.109383	−	0.0321178i	−0.00640117	−	0.00187955i
$293$	2.19548	+	15.2699i	0.128261	+	0.892077i	0.947757	+	0.318992i	$0.103344\pi$
$293$	2.19548	+	15.2699i	0.128261	+	0.892077i	−0.819496	+	0.573085i	$0.805747\pi$
$294$	0.272683	−	0.597093i	0.0159032	−	0.0348232i
$295$	−1.74752	+	12.1543i	−0.101745	+	0.707649i
$296$	3.08105	+	1.98007i	0.179082	+	0.115089i
$297$	2.87491	+	3.31782i	0.166819	+	0.192519i
$298$	0.168975			0.00978846
$299$	9.57064	−	2.94821i	0.553484	−	0.170499i
$300$	−7.74844			−0.447357
$301$	−2.91565	−	3.36484i	−0.168055	−	0.193946i
$302$	1.43604	+	0.922890i	0.0826351	+	0.0531063i
$303$	−0.759620	+	5.28327i	−0.0436390	+	0.303516i
$304$	4.06428	−	8.89952i	0.233102	−	0.510423i
$305$	2.02282	+	14.0690i	0.115826	+	0.805589i
$306$	0.492184	+	0.144518i	0.0281363	+	0.00826156i
$307$	27.6327	−	17.7584i	1.57708	−	1.01353i	0.600170	−	0.799872i	$-0.295099\pi$
$307$	27.6327	−	17.7584i	1.57708	−	1.01353i	0.976909	−	0.213655i	$-0.0685369\pi$
$308$	7.28693	+	15.9561i	0.415211	+	0.909186i
$309$	−4.75830	+	1.39716i	−0.270690	+	0.0794819i
$310$	1.22038	−	1.40840i	0.0693131	−	0.0799916i
$311$	1.32337	−	1.52725i	0.0750416	−	0.0866026i	−0.716987	−	0.697086i	$-0.754479\pi$
$311$	1.32337	−	1.52725i	0.0750416	−	0.0866026i	0.792029	+	0.610484i	$0.209025\pi$
$312$	1.86871	−	0.548704i	0.105795	−	0.0310642i
$313$	−9.28462	−	20.3305i	−0.524798	−	1.14915i	−0.967591	−	0.252523i	$-0.918740\pi$
$313$	−9.28462	−	20.3305i	−0.524798	−	1.14915i	0.442793	−	0.896624i	$-0.353988\pi$
$314$	3.57847	−	2.29975i	0.201945	−	0.129782i
$315$	1.98612	+	0.583178i	0.111905	+	0.0328584i
$316$	−4.50913	−	31.3617i	−0.253658	−	1.76423i
$317$	5.85720	−	12.8255i	0.328973	−	0.720351i	−0.670800	−	0.741638i	$-0.734049\pi$
$317$	5.85720	−	12.8255i	0.328973	−	0.720351i	0.999773	+	0.0212873i	$0.00677647\pi$
$318$	−0.380087	+	2.64356i	−0.0213142	+	0.148244i
$319$	29.4505	+	18.9267i	1.64891	+	1.05969i
$320$	4.41162	+	5.09129i	0.246617	+	0.284611i
$321$	−3.53964			−0.197563
$322$	−0.996257	−	2.10730i	−0.0555192	−	0.117435i
$323$	−5.78646			−0.321967
$324$	1.27310	+	1.46924i	0.0707278	+	0.0816242i
$325$	7.00149	+	4.49959i	0.388373	+	0.249592i
$326$	−0.154192	+	1.07243i	−0.00853989	+	0.0593963i
$327$	−1.58669	+	3.47437i	−0.0877442	+	0.192133i
$328$	0.837282	+	5.82342i	0.0462312	+	0.321545i
$329$	−14.2440	−	4.18241i	−0.785296	−	0.230584i
$330$	−0.879599	+	0.565284i	−0.0484204	+	0.0311179i
$331$	0.326695	+	0.715363i	0.0179568	+	0.0393199i	0.918398	−	0.395658i	$-0.129483\pi$
$331$	0.326695	+	0.715363i	0.0179568	+	0.0393199i	−0.900441	+	0.434978i	$0.856756\pi$
$332$	−27.1288	+	7.96575i	−1.48889	+	0.437177i
$333$	2.57148	−	2.96765i	0.140916	−	0.162626i
$334$	2.60224	−	3.00314i	0.142388	−	0.164325i
$335$	−0.688060	+	0.202033i	−0.0375927	+	0.0110382i
$336$	3.13139	+	6.85679i	0.170831	+	0.374068i
$337$	4.37452	−	2.81133i	0.238295	−	0.153143i	−0.416043	−	0.909345i	$-0.636583\pi$
$337$	4.37452	−	2.81133i	0.238295	−	0.153143i	0.654339	+	0.756202i	$0.272947\pi$
$338$	1.96032	+	0.575603i	0.106628	+	0.0313087i
$339$	−2.61061	−	18.1572i	−0.141789	−	0.986164i
$340$	1.76433	−	3.86335i	0.0956843	−	0.209519i
$341$	4.88866	−	34.0014i	0.264736	−	1.84128i
$342$	0.530688	+	0.341052i	0.0286963	+	0.0184420i
$343$	−13.1575	−	15.1846i	−0.710439	−	0.819890i
$344$	2.02046			0.108936
$345$	−4.02844	+	2.66484i	−0.216884	+	0.143470i
$346$	−1.36994			−0.0736486
$347$	−6.84409	−	7.89850i	−0.367410	−	0.424014i	0.541699	−	0.840573i	$-0.317781\pi$
$347$	−6.84409	−	7.89850i	−0.367410	−	0.424014i	−0.909109	+	0.416559i	$0.863236\pi$
$348$	13.0416	+	8.38135i	0.699105	+	0.449287i
$349$	−2.24237	+	15.5960i	−0.120031	+	0.834836i	0.837486	+	0.546459i	$0.184025\pi$
$349$	−2.24237	+	15.5960i	−0.120031	+	0.834836i	−0.957517	+	0.288377i	$0.906884\pi$
$350$	0.804728	−	1.76211i	0.0430145	−	0.0941886i
$351$	−0.297176	−	2.06690i	−0.0158621	−	0.110323i
$352$	−11.5108	−	3.37989i	−0.613530	−	0.180149i
$353$	16.9217	−	10.8749i	0.900649	−	0.578812i	−0.00633380	−	0.999980i	$-0.502016\pi$
$353$	16.9217	−	10.8749i	0.900649	−	0.578812i	0.906983	+	0.421168i	$0.138380\pi$
$354$	−1.19772	−	2.62264i	−0.0636582	−	0.139392i
$355$	3.97909	−	1.16837i	0.211188	−	0.0620105i
$356$	3.50576	−	4.04586i	0.185805	−	0.214430i
$357$	2.91955	−	3.36934i	0.154519	−	0.178325i
$358$	−3.90257	+	1.14590i	−0.206257	+	0.0605627i
$359$	4.57381	+	10.0152i	0.241396	+	0.528584i	0.991089	−	0.133202i	$-0.0425259\pi$
$359$	4.57381	+	10.0152i	0.241396	+	0.528584i	−0.749693	+	0.661786i	$0.769799\pi$
$360$	−0.790233	+	0.507852i	−0.0416490	+	0.0267662i
$361$	11.4026	+	3.34809i	0.600135	+	0.176215i
$362$	0.0734142	+	0.510607i	0.00385857	+	0.0268369i
$363$	−3.43674	+	7.52541i	−0.180382	+	0.394982i
$364$	1.18741	−	8.25861i	0.0622372	−	0.432869i
$365$	−0.0496836	−	0.0319297i	−0.00260056	−	0.00167128i
$366$	−2.18553	−	2.52224i	−0.114240	−	0.131840i
$367$	20.5922			1.07490			0.537452	−	0.843294i	$-0.319387\pi$
$367$	20.5922			1.07490			0.537452	+	0.843294i	$0.319387\pi$
$368$	−16.9407	−	4.73184i	−0.883096	−	0.246664i
$369$	6.30788			0.328375
$370$	0.612444	+	0.706797i	0.0318394	+	0.0367447i
$371$	19.5272	+	12.5494i	1.01380	+	0.651532i
$372$	2.16485	−	15.0569i	0.112242	−	0.780663i
$373$	−9.58980	+	20.9987i	−0.496541	+	1.08727i	0.481037	+	0.876700i	$0.340260\pi$
$373$	−9.58980	+	20.9987i	−0.496541	+	1.08727i	−0.977578	+	0.210573i	$0.932467\pi$
$374$	0.320488	+	2.22904i	0.0165720	+	0.115261i
$375$	−8.68326	−	2.54963i	−0.448401	−	0.131663i
$376$	5.66736	−	3.64219i	0.292272	−	0.187832i
$377$	−6.91730	−	15.1468i	−0.356259	−	0.780098i
$378$	−0.466346	+	0.136931i	−0.0239862	+	0.00704299i
$379$	0.801510	−	0.924992i	0.0411708	−	0.0475136i	−0.734791	−	0.678294i	$-0.762720\pi$
$379$	0.801510	−	0.924992i	0.0411708	−	0.0475136i	0.775961	+	0.630780i	$0.217265\pi$
$380$	3.42037	−	3.94732i	0.175461	−	0.202493i
$381$	1.00357	−	0.294675i	0.0514145	−	0.0150967i
$382$	−1.70100	−	3.72467i	−0.0870307	−	0.190571i
$383$	−6.31856	+	4.06069i	−0.322863	+	0.207492i	−0.692025	−	0.721873i	$-0.743281\pi$
$383$	−6.31856	+	4.06069i	−0.322863	+	0.207492i	0.369162	+	0.929365i	$0.379645\pi$
$384$	−6.76172	−	1.98542i	−0.345058	−	0.101318i
$385$	1.29327	+	8.99490i	0.0659112	+	0.458422i
$386$	−1.76737	+	3.87000i	−0.0899567	+	0.196978i
$387$	0.308293	−	2.14422i	0.0156714	−	0.108997i
$388$	−9.65848	−	6.20713i	−0.490335	−	0.315119i
$389$	11.7596	+	13.5713i	0.596233	+	0.688090i	0.971014	−	0.239024i	$-0.0768274\pi$
$389$	11.7596	+	13.5713i	0.596233	+	0.688090i	−0.374780	+	0.927114i	$0.622282\pi$
$390$	0.497331			0.0251834
$391$	1.61653	+	10.2766i	0.0817513	+	0.519710i
$392$	2.58894			0.130761
$393$	6.01268	+	6.93900i	0.303300	+	0.350026i
$394$	−0.975506	−	0.626919i	−0.0491453	−	0.0315837i
$395$	2.33598	−	16.2471i	0.117536	−	0.817481i
$396$	−3.54545	+	7.76344i	−0.178165	+	0.390128i
$397$	4.74648	+	33.0125i	0.238219	+	1.65685i	0.660828	+	0.750538i	$0.270205\pi$
$397$	4.74648	+	33.0125i	0.238219	+	1.65685i	−0.422609	+	0.906312i	$0.638886\pi$
$398$	−2.83381	−	0.832083i	−0.142046	−	0.0417085i
$399$	4.61233	−	2.96416i	0.230905	−	0.148394i
$400$	−6.07245	−	13.2968i	−0.303623	−	0.664841i
$401$	7.79686	−	2.28936i	0.389357	−	0.114325i	−0.0811942	−	0.996698i	$-0.525873\pi$
$401$	7.79686	−	2.28936i	0.389357	−	0.114325i	0.470551	+	0.882373i	$0.344055\pi$
$402$	0.110264	−	0.127252i	0.00549949	−	0.00634675i
$403$	−10.6998	+	12.3482i	−0.532996	+	0.615110i
$404$	−9.95639	+	2.92346i	−0.495349	+	0.145448i
$405$	0.418382	+	0.916128i	0.0207896	+	0.0455228i
$406$	−3.26050	+	2.09540i	−0.161816	+	0.103993i
$407$	16.5406	+	4.85675i	0.819886	+	0.240740i
$408$	0.287926	+	2.00257i	0.0142545	+	0.0991421i
$409$	−6.41619	+	14.0495i	−0.317260	+	0.694702i	−0.999331	−	0.0365839i	$-0.988352\pi$
$409$	−6.41619	+	14.0495i	−0.317260	+	0.694702i	0.682071	+	0.731286i	$0.261080\pi$
$410$	−0.213805	+	1.48704i	−0.0105591	+	0.0734398i
$411$	12.4651	+	8.01081i	0.614856	+	0.395144i
$412$	−6.31354	−	7.28621i	−0.311046	−	0.358966i
$413$	−25.0585			−1.23305
$414$	0.457445	−	1.03776i	0.0224822	−	0.0510034i
$415$	−14.6476			−0.719023
$416$	3.73682	+	4.31252i	0.183213	+	0.211439i
$417$	−13.7692	−	8.84894i	−0.674282	−	0.433335i
$418$	−0.394128	+	2.74122i	−0.0192774	+	0.134077i
$419$	−8.97842	+	19.6600i	−0.438624	+	0.960454i	0.553224	+	0.833032i	$0.313397\pi$
$419$	−8.97842	+	19.6600i	−0.438624	+	0.960454i	−0.991849	+	0.127421i	$0.959330\pi$
$420$	0.572701	+	3.98322i	0.0279450	+	0.194361i
$421$	7.57450	+	2.22408i	0.369159	+	0.108395i	0.461050	−	0.887374i	$-0.347473\pi$
$421$	7.57450	+	2.22408i	0.369159	+	0.108395i	−0.0918910	+	0.995769i	$0.529291\pi$
$422$	−3.59188	+	2.30836i	−0.174850	+	0.112369i
$423$	−3.00053	−	6.57024i	−0.145891	−	0.319456i
$424$	−10.1069	+	2.96767i	−0.490837	+	0.144123i
$425$	−5.66165	+	6.53390i	−0.274631	+	0.316941i
$426$	−0.637666	+	0.735905i	−0.0308950	+	0.0356547i
$427$	−27.8312	+	8.17197i	−1.34684	+	0.395469i
$428$	−2.85861	−	6.25948i	−0.138176	−	0.302563i
$429$	7.71196	−	4.95618i	0.372337	−	0.239286i
$430$	0.495037	+	0.145356i	0.0238728	+	0.00700969i
$431$	−0.450585	−	3.13389i	−0.0217039	−	0.150954i	0.976088	−	0.217377i	$-0.0697503\pi$
$431$	−0.450585	−	3.13389i	−0.0217039	−	0.150954i	−0.997792	+	0.0664235i	$0.978841\pi$
$432$	−1.52357	+	3.33616i	−0.0733030	+	0.160511i
$433$	2.41253	−	16.7795i	0.115939	−	0.806370i	−0.846015	−	0.533159i	$-0.821005\pi$
$433$	2.41253	−	16.7795i	0.115939	−	0.806370i	0.961954	−	0.273212i	$-0.0880860\pi$
$434$	3.19932	+	2.05608i	0.153572	+	0.0986948i
$435$	5.25934	+	6.06960i	0.252166	+	0.291015i
$436$	−7.42547			−0.355615
$437$	−1.65308	+	12.6861i	−0.0790773	+	0.606858i
$438$	0.0138672			0.000662598
$439$	−9.03352	−	10.4252i	−0.431146	−	0.497569i	0.498054	−	0.867146i	$-0.334048\pi$
$439$	−9.03352	−	10.4252i	−0.431146	−	0.497569i	−0.929200	+	0.369577i	$0.879503\pi$
$440$	−3.46921	−	2.22952i	−0.165388	−	0.106288i
$441$	0.395034	−	2.74752i	0.0188111	−	0.130834i
$442$	0.444970	−	0.974349i	0.0211651	−	0.0463451i
$443$	1.13108	+	7.86686i	0.0537394	+	0.373766i	0.998889	+	0.0471276i	$0.0150067\pi$
$443$	1.13108	+	7.86686i	0.0537394	+	0.373766i	−0.945149	+	0.326638i	$0.894084\pi$
$444$	7.32469	+	2.15072i	0.347615	+	0.102069i
$445$	2.33312	−	1.49940i	0.110600	−	0.0710786i
$446$	−0.857702	−	1.87811i	−0.0406134	−	0.0889309i
$447$	0.685602	−	0.201311i	0.0324278	−	0.00952167i
$448$	−9.00288	+	10.3899i	−0.425346	+	0.490876i
$449$	20.6180	−	23.7945i	0.973025	−	1.12293i	−0.0193667	−	0.999812i	$-0.506165\pi$
$449$	20.6180	−	23.7945i	0.973025	−	1.12293i	0.992392	−	0.123119i	$-0.0392896\pi$
$450$	0.904347	−	0.265540i	0.0426313	−	0.0125177i
$451$	11.5038	+	25.1898i	0.541692	+	1.18614i
$452$	30.0008	−	19.2803i	1.41112	−	0.906870i
$453$	6.92613	+	2.03369i	0.325418	+	0.0955513i
$454$	−0.798197	−	5.55158i	−0.0374612	−	0.260549i
$455$	1.79560	−	3.93181i	0.0841790	−	0.184326i
$456$	−0.354085	+	2.46272i	−0.0165816	+	0.115327i
$457$	−17.9667	−	11.5465i	−0.840447	−	0.540123i	0.0481347	−	0.998841i	$-0.484672\pi$
$457$	−17.9667	−	11.5465i	−0.840447	−	0.540123i	−0.888582	+	0.458718i	$0.848309\pi$
$458$	1.05503	+	1.21757i	0.0492984	+	0.0568933i
$459$	2.16917			0.101248
$460$	−7.96586	−	4.97175i	−0.371410	−	0.231809i
$461$	1.51050			0.0703510			0.0351755	−	0.999381i	$-0.488801\pi$
$461$	1.51050			0.0703510			0.0351755	+	0.999381i	$0.488801\pi$
$462$	−1.39730	−	1.61257i	−0.0650083	−	0.0750236i
$463$	−2.56786	−	1.65026i	−0.119338	−	0.0766942i	0.479610	−	0.877482i	$-0.340778\pi$
$463$	−2.56786	−	1.65026i	−0.119338	−	0.0766942i	−0.598948	+	0.800788i	$0.704415\pi$
$464$	−4.16220	+	28.9487i	−0.193225	+	1.34391i
$465$	3.27369	−	7.16838i	0.151814	−	0.332425i
$466$	0.0460183	+	0.320064i	0.00213175	+	0.0148267i
$467$	5.11221	+	1.50108i	0.236565	+	0.0694618i	0.397866	−	0.917443i	$-0.369751\pi$
$467$	5.11221	+	1.50108i	0.236565	+	0.0694618i	−0.161301	+	0.986905i	$0.551569\pi$
$468$	3.41510	−	2.19475i	0.157863	−	0.101452i
$469$	−0.607925	−	1.33117i	−0.0280714	−	0.0614677i
$470$	1.65060	−	0.484658i	0.0761363	−	0.0223556i
$471$	11.7795	−	13.5943i	0.542772	−	0.626392i
$472$	7.44677	−	8.59403i	0.342765	−	0.395572i
$473$	9.12494	−	2.67932i	0.419565	−	0.123195i
$474$	1.60104	+	3.50580i	0.0735384	+	0.161027i
$475$	−8.94432	+	5.74817i	−0.410394	+	0.263744i
$476$	8.31616	+	2.44184i	0.381170	+	0.111922i
$477$	1.60728	+	11.1788i	0.0735921	+	0.511844i
$478$	−1.76924	+	3.87410i	−0.0809232	+	0.177197i
$479$	−1.34695	+	9.36824i	−0.0615437	+	0.428046i	0.935634	+	0.352971i	$0.114829\pi$
$479$	−1.34695	+	9.36824i	−0.0615437	+	0.428046i	−0.997178	+	0.0750746i	$0.976081\pi$
$480$	−2.31530	−	1.48796i	−0.105679	−	0.0679156i
$481$	−5.36965	−	6.19691i	−0.244835	−	0.282555i
$482$	−0.0699412			−0.00318573
$483$	−6.55279	−	7.36330i	−0.298162	−	0.335042i
$484$	−16.0834			−0.731064
$485$	−3.89500	−	4.49507i	−0.176863	−	0.204111i
$486$	−0.198939	−	0.127850i	−0.00902404	−	0.00579940i
$487$	−1.94113	+	13.5009i	−0.0879612	+	0.611784i	0.897389	+	0.441240i	$0.145461\pi$
$487$	−1.94113	+	13.5009i	−0.0879612	+	0.611784i	−0.985350	+	0.170543i	$0.945448\pi$
$488$	5.46809	−	11.9735i	0.247529	−	0.542013i
$489$	0.652032	+	4.53498i	0.0294859	+	0.205079i
$490$	0.634320	+	0.186253i	0.0286557	+	0.00841406i
$491$	2.47271	−	1.58911i	0.111592	−	0.0717156i	−0.483655	−	0.875259i	$-0.660691\pi$
$491$	2.47271	−	1.58911i	0.111592	−	0.0717156i	0.595246	+	0.803543i	$0.297055\pi$
$492$	5.09424	+	11.1548i	0.229666	+	0.502899i
$493$	16.5969	−	4.87329i	0.747486	−	0.219482i
$494$	0.862629	−	0.995527i	0.0388115	−	0.0447909i
$495$	−2.89544	+	3.34152i	−0.130140	+	0.150190i
$496$	27.5351	−	8.08505i	1.23636	−	0.363029i
$497$	3.51567	+	7.69823i	0.157699	+	0.345313i
$498$	2.89331	−	1.85942i	0.129652	−	0.0833225i
$499$	−11.0072	−	3.23201i	−0.492750	−	0.144685i	0.0259111	−	0.999664i	$-0.491751\pi$
$499$	−11.0072	−	3.23201i	−0.492750	−	0.144685i	−0.518661	+	0.854980i	$0.673570\pi$
$500$	−2.50383	−	17.4145i	−0.111975	−	0.778801i
$501$	6.98052	−	15.2852i	0.311866	−	0.682892i
$502$	−0.505944	+	3.51892i	−0.0225814	+	0.157057i
$503$	−19.5471	−	12.5622i	−0.871563	−	0.560119i	0.0266675	−	0.999644i	$-0.491510\pi$
$503$	−19.5471	−	12.5622i	−0.871563	−	0.560119i	−0.898230	+	0.439525i	$0.855147\pi$
$504$	−1.25534	−	1.44874i	−0.0559172	−	0.0645319i
$505$	−5.37572			−0.239217
$506$	4.97844	−	0.0658362i	0.221319	−	0.00292678i
$507$	8.63960			0.383698
$508$	1.33158	+	1.53673i	0.0590795	+	0.0681814i
$509$	−3.33713	−	2.14465i	−0.147916	−	0.0950597i	0.464590	−	0.885526i	$-0.346202\pi$
$509$	−3.33713	−	2.14465i	−0.147916	−	0.0950597i	−0.612505	+	0.790466i	$0.709838\pi$
$510$	−0.0735236	+	0.511368i	−0.00325568	+	0.0226438i
$511$	0.0500669	−	0.109631i	0.00221483	−	0.00484980i
$512$	−2.39998	−	16.6922i	−0.106065	−	0.737699i
$513$	2.55954	+	0.751548i	0.113006	+	0.0331817i
$514$	2.88553	−	1.85442i	0.127275	−	0.0817949i
$515$	−2.07483	−	4.54325i	−0.0914281	−	0.200200i
$516$	4.04081	−	1.18649i	0.177887	−	0.0522323i
$517$	20.7654	−	23.9645i	0.913260	−	1.05396i
$518$	−1.24982	+	1.44237i	−0.0549141	+	0.0633743i
$519$	−5.55843	+	1.63210i	−0.243988	+	0.0716414i
$520$	0.814842	+	1.78426i	0.0357332	+	0.0782448i
$521$	−2.76085	+	1.77429i	−0.120955	+	0.0777331i	−0.599719	−	0.800210i	$-0.704721\pi$
$521$	−2.76085	+	1.77429i	−0.120955	+	0.0777331i	0.478764	+	0.877943i	$0.341085\pi$
$522$	−1.80936	−	0.531277i	−0.0791936	−	0.0232534i
$523$	−0.0245670	−	0.170867i	−0.00107424	−	0.00747149i	0.989277	−	0.146050i	$-0.0466559\pi$
$523$	−0.0245670	−	0.170867i	−0.00107424	−	0.00747149i	−0.990352	+	0.138578i	$0.955747\pi$
$524$	−7.41506	+	16.2367i	−0.323929	+	0.709305i
$525$	1.16580	−	8.10833i	0.0508798	−	0.353876i
$526$	3.03794	+	1.95237i	0.132461	+	0.0851272i
$527$	−11.1149	−	12.8273i	−0.484174	−	0.558767i
$528$	−16.1011			−0.700712
$529$	22.9920	−	0.608210i	0.999650	−	0.0264439i
$530$	−2.68982			−0.116838
$531$	−7.98418	−	9.21423i	−0.346484	−	0.399864i
$532$	8.96673	+	5.76256i	0.388757	+	0.249839i
$533$	1.87455	−	13.0378i	0.0811957	−	0.564729i
$534$	−0.270517	+	0.592349i	−0.0117064	+	0.0256334i
$535$	−0.507341	−	3.52863i	−0.0219342	−	0.152556i
$536$	0.637197	+	0.187098i	0.0275227	+	0.00808140i
$537$	−14.4692	+	9.29878i	−0.624391	+	0.401272i
$538$	1.33730	+	2.92828i	0.0576551	+	0.126247i
$539$	11.6923	−	3.43317i	0.503624	−	0.147877i
$540$	−1.28219	+	1.47973i	−0.0551768	+	0.0636774i
$541$	−10.7663	+	12.4250i	−0.462880	+	0.534192i	−0.938418	−	0.345503i	$-0.887708\pi$
$541$	−10.7663	+	12.4250i	−0.462880	+	0.534192i	0.475537	+	0.879696i	$0.342254\pi$
$542$	−1.00200	+	0.294215i	−0.0430397	+	0.0126376i
$543$	0.906191	+	1.98428i	0.0388884	+	0.0851537i
$544$	−4.98667	+	3.20474i	−0.213802	+	0.137402i
$545$	−3.69099	−	1.08377i	−0.158105	−	0.0464237i
$546$	0.144437	+	1.00458i	0.00618134	+	0.0429922i
$547$	0.131981	−	0.288998i	0.00564310	−	0.0123567i	−0.906789	−	0.421584i	$-0.861474\pi$
$547$	0.131981	−	0.288998i	0.00564310	−	0.0123567i	0.912433	+	0.409227i	$0.134202\pi$
$548$	−4.09951	+	28.5127i	−0.175122	+	1.21800i
$549$	−11.8725	−	7.63000i	−0.506707	−	0.325641i
$550$	2.70967	+	3.12713i	0.115541	+	0.133341i
$551$	21.2721			0.906223
$552$	4.47264	−	0.0591474i	0.190368	−	0.00251748i
$553$	33.4967			1.42443
$554$	−2.59986	−	3.00040i	−0.110457	−	0.127475i
$555$	3.32699	+	2.13813i	0.141223	+	0.0907584i
$556$	4.52842	−	31.4958i	0.192048	−	1.33572i
$557$	−0.756915	+	1.65741i	−0.0320715	+	0.0702268i	−0.924990	−	0.379992i	$-0.875927\pi$
$557$	−0.756915	+	1.65741i	−0.0320715	+	0.0702268i	0.892918	+	0.450219i	$0.148654\pi$
$558$	0.263334	+	1.83153i	0.0111478	+	0.0775348i
$559$	−4.34028	−	1.27442i	−0.183574	−	0.0539023i
$560$	−6.38664	+	4.10444i	−0.269885	+	0.173444i
$561$	3.95595	+	8.66232i	0.167020	+	0.365724i
$562$	6.36503	−	1.86894i	0.268493	−	0.0788366i
$563$	−1.67756	+	1.93600i	−0.0707006	+	0.0815929i	−0.789998	−	0.613109i	$-0.789918\pi$
$563$	−1.67756	+	1.93600i	−0.0707006	+	0.0815929i	0.719297	+	0.694702i	$0.244464\pi$
$564$	9.19556	−	10.6122i	0.387203	−	0.446856i
$565$	17.7266	−	5.20499i	0.745762	−	0.218975i
$566$	2.79059	+	6.11055i	0.117297	+	0.256845i
$567$	−1.72902	+	1.11118i	−0.0726121	+	0.0466650i
$568$	−3.68495	−	1.08200i	−0.154617	−	0.0453996i
$569$	−1.66783	−	11.6000i	−0.0699193	−	0.486299i	−0.994452	−	0.105195i	$-0.966453\pi$
$569$	−1.66783	−	11.6000i	−0.0699193	−	0.486299i	0.924532	−	0.381104i	$-0.124456\pi$
$570$	−0.263928	+	0.577921i	−0.0110547	+	0.0242064i
$571$	−0.0845608	+	0.588133i	−0.00353876	+	0.0246126i	−0.991514	−	0.129998i	$-0.958503\pi$
$571$	−0.0845608	+	0.588133i	−0.00353876	+	0.0246126i	0.987976	+	0.154610i	$0.0494121\pi$
$572$	14.9927	+	9.63519i	0.626874	+	0.402868i
$573$	−11.3391	−	13.0860i	−0.473698	−	0.546677i
$574$	−3.06584			−0.127966
$575$	12.7073	+	14.2791i	0.529932	+	0.595478i
$576$	−6.68896			−0.278707
$577$	−2.69616	−	3.11153i	−0.112243	−	0.129535i	0.696848	−	0.717219i	$-0.254585\pi$
$577$	−2.69616	−	3.11153i	−0.112243	−	0.129535i	−0.809090	+	0.587684i	$0.800040\pi$
$578$	−2.44589	−	1.57188i	−0.101736	−	0.0653816i
$579$	−2.56037	+	17.8078i	−0.106405	+	0.740066i
$580$	−6.48601	+	14.2024i	−0.269317	+	0.589722i
$581$	−4.25402	−	29.5874i	−0.176487	−	1.22749i
$582$	1.33999	+	0.393457i	0.0555445	+	0.0163093i
$583$	−41.7102	+	26.8055i	−1.72746	+	1.11017i
$584$	0.0227204	+	0.0497506i	0.000940175	+	0.00205870i
$585$	2.01788	−	0.592503i	0.0834291	−	0.0244970i
$586$	2.38903	−	2.75708i	0.0986897	−	0.113894i
$587$	−27.2790	+	31.4816i	−1.12592	+	1.29938i	−0.176882	+	0.984232i	$0.556601\pi$
$587$	−27.2790	+	31.4816i	−1.12592	+	1.29938i	−0.949041	+	0.315152i	$0.897944\pi$
$588$	5.17773	−	1.52032i	0.213526	−	0.0626969i
$589$	−8.67094	−	18.9867i	−0.357280	−	0.782334i
$590$	2.44282	−	1.56990i	0.100569	−	0.0646319i
$591$	−4.70492	−	1.38149i	−0.193535	−	0.0568269i
$592$	2.04958	+	14.2552i	0.0842373	+	0.585884i
$593$	0.569445	−	1.24691i	0.0233843	−	0.0512045i	−0.897579	−	0.440853i	$-0.854676\pi$
$593$	0.569445	−	1.24691i	0.0233843	−	0.0512045i	0.920964	+	0.389648i	$0.127403\pi$
$594$	0.147747	−	1.02760i	0.00606212	−	0.0421630i
$595$	3.77733	+	2.42754i	0.154855	+	0.0995195i
$596$	0.909688	+	1.04984i	0.0372623	+	0.0430030i
$597$	−12.4893			−0.511152
$598$	−2.00902	−	1.25389i	−0.0821548	−	0.0512755i
$599$	−26.0672			−1.06508			−0.532538	−	0.846406i	$-0.678762\pi$
$599$	−26.0672			−1.06508			−0.532538	+	0.846406i	$0.678762\pi$
$600$	2.43438	+	2.80942i	0.0993830	+	0.114694i
$601$	−0.0551746	−	0.0354586i	−0.00225062	−	0.00144639i	0.539515	−	0.841976i	$-0.318608\pi$
$601$	−0.0551746	−	0.0354586i	−0.00225062	−	0.00144639i	−0.541766	+	0.840530i	$0.682244\pi$
$602$	−0.149841	+	1.04216i	−0.00610705	+	0.0424754i
$603$	0.295785	−	0.647679i	0.0120453	−	0.0263755i
$604$	1.99716	+	13.8905i	0.0812632	+	0.565198i
$605$	−7.99461	−	2.34743i	−0.325027	−	0.0954365i
$606$	1.06186	−	0.682413i	0.0431349	−	0.0277211i
$607$	−6.25899	−	13.7053i	−0.254045	−	0.556280i	0.739043	−	0.673659i	$-0.235278\pi$
$607$	−6.25899	−	13.7053i	−0.254045	−	0.556280i	−0.993087	+	0.117379i	$0.962551\pi$
$608$	−6.99442	+	2.05375i	−0.283661	+	0.0832905i
$609$	−10.7328	+	12.3863i	−0.434916	+	0.501920i
$610$	2.20114	−	2.54025i	0.0891216	−	0.102852i
$611$	−14.4717	+	4.24928i	−0.585464	+	0.171908i
$612$	1.75182	+	3.83595i	0.0708131	+	0.155059i
$613$	38.1789	−	24.5361i	1.54203	−	0.991004i	0.554752	−	0.832016i	$-0.312813\pi$
$613$	38.1789	−	24.5361i	1.54203	−	0.991004i	0.987280	−	0.158989i	$-0.0508233\pi$
$614$	−7.45298	−	2.18839i	−0.300778	−	0.0883163i
$615$	0.904117	+	6.28827i	0.0364575	+	0.253568i
$616$	3.49598	−	7.65512i	0.140857	−	0.308434i
$617$	−6.26818	+	43.5962i	−0.252348	+	1.75512i	0.331689	+	0.943389i	$0.392381\pi$
$617$	−6.26818	+	43.5962i	−0.252348	+	1.75512i	−0.584037	+	0.811727i	$0.698528\pi$
$618$	0.986574	+	0.634033i	0.0396858	+	0.0255045i
$619$	13.0957	+	15.1133i	0.526361	+	0.607453i	0.955212	−	0.295922i	$-0.0956269\pi$
$619$	13.0957	+	15.1133i	0.526361	+	0.607453i	−0.428851	+	0.903375i	$0.641081\pi$
$620$	15.3204			0.615280
$621$	0.619688	−	4.75563i	0.0248672	−	0.190837i
$622$	−0.477888			−0.0191615
$623$	3.70631	+	4.27731i	0.148490	+	0.171367i
$624$	6.44275	+	4.14050i	0.257916	+	0.165753i
$625$	−1.53897	+	10.7038i	−0.0615589	+	0.428151i
$626$	−2.19562	+	4.80773i	−0.0877545	+	0.192156i
$627$	1.66665	+	11.5918i	0.0665597	+	0.462933i
$628$	33.5532	+	9.85211i	1.33892	+	0.393142i
$629$	7.16563	−	4.60507i	0.285712	−	0.183616i
$630$	−0.203348	−	0.445269i	−0.00810156	−	0.0177399i
$631$	−38.6248	+	11.3413i	−1.53763	+	0.451488i	−0.937375	−	0.348322i	$-0.886752\pi$
$631$	−38.6248	+	11.3413i	−1.53763	+	0.451488i	−0.600253	+	0.799810i	$0.704933\pi$
$632$	−9.95441	+	11.4880i	−0.395965	+	0.456968i
$633$	−11.8236	+	13.6452i	−0.469947	+	0.542348i
$634$	−3.19921	+	0.939371i	−0.127057	+	0.0373072i
$635$	0.437602	+	0.958214i	0.0173657	+	0.0380256i
$636$	−18.4706	+	11.8703i	−0.732407	+	0.470689i
$637$	−5.56146	−	1.63299i	−0.220353	−	0.0647015i
$638$	−1.17817	−	8.19437i	−0.0466443	−	0.324418i
$639$	−1.71054	+	3.74557i	−0.0676680	+	0.148172i
$640$	1.01008	−	7.02527i	0.0399270	−	0.277698i
$641$	−19.3506	−	12.4358i	−0.764301	−	0.491186i	0.0994890	−	0.995039i	$-0.468279\pi$
$641$	−19.3506	−	12.4358i	−0.764301	−	0.491186i	−0.863790	+	0.503852i	$0.831916\pi$
$642$	0.548151	+	0.632600i	0.0216338	+	0.0249667i
$643$	6.29862			0.248393			0.124197	−	0.992258i	$-0.460365\pi$
$643$	6.29862			0.248393			0.124197	+	0.992258i	$0.460365\pi$
$644$	7.72919	−	17.5345i	0.304573	−	0.690957i
$645$	2.18174			0.0859061
$646$	0.896096	+	1.03415i	0.0352564	+	0.0406881i
$647$	−0.198384	−	0.127493i	−0.00779927	−	0.00501229i	0.536735	−	0.843751i	$-0.319657\pi$
$647$	−0.198384	−	0.127493i	−0.00779927	−	0.00501229i	−0.544535	+	0.838738i	$0.683294\pi$
$648$	0.132736	−	0.923198i	0.00521435	−	0.0362666i
$649$	22.2351	−	48.6880i	0.872803	−	1.91117i
$650$	−0.280096	−	1.94811i	−0.0109863	−	0.0764111i
$651$	15.4305	+	4.53080i	0.604769	+	0.177576i
$652$	−7.49306	+	4.81550i	−0.293451	+	0.188589i
$653$	8.20843	+	17.9740i	0.321221	+	0.703375i	0.999506	−	0.0314233i	$-0.0100040\pi$
$653$	8.20843	+	17.9740i	0.321221	+	0.703375i	−0.678285	+	0.734798i	$0.737277\pi$
$654$	0.866651	−	0.254472i	0.0338887	−	0.00995063i
$655$	−6.05562	+	6.98856i	−0.236613	+	0.273066i
$656$	−15.1500	+	17.4841i	−0.591510	+	0.682639i
$657$	0.0562648	−	0.0165208i	0.00219510	−	0.000644539i
$658$	1.45836	+	3.19336i	0.0568527	+	0.124490i
$659$	−33.3690	+	21.4449i	−1.29987	+	0.835376i	−0.993198	−	0.116439i	$-0.962852\pi$
$659$	−33.3690	+	21.4449i	−1.29987	+	0.835376i	−0.306673	+	0.951815i	$0.599216\pi$
$660$	−8.24748	−	2.42168i	−0.321033	−	0.0942637i
$661$	5.24223	+	36.4605i	0.203899	+	1.41815i	0.792572	+	0.609778i	$0.208741\pi$
$661$	5.24223	+	36.4605i	0.203899	+	1.41815i	−0.588673	+	0.808371i	$0.700350\pi$
$662$	0.0772565	−	0.169168i	0.00300266	−	0.00657491i
$663$	0.644624	−	4.48346i	0.0250351	−	0.174123i
$664$	11.4114	+	7.33369i	0.442850	+	0.284602i
$665$	3.61604	+	4.17313i	0.140224	+	0.161827i
$666$	−0.928595			−0.0359823
$667$	−5.94266	−	37.7788i	−0.230101	−	1.46280i
$668$	32.6677			1.26395
$669$	−5.71756	−	6.59842i	−0.221054	−	0.255110i
$670$	0.142661	+	0.0916824i	0.00551146	+	0.00354200i
$671$	8.81741	−	61.3264i	0.340392	−	2.36748i
$672$	2.33317	−	5.10893i	0.0900040	−	0.197081i
$673$	−7.20136	−	50.0865i	−0.277592	−	1.93069i	−0.357545	−	0.933896i	$-0.616386\pi$
$673$	−7.20136	−	50.0865i	−0.277592	−	1.93069i	0.0799533	−	0.996799i	$-0.474523\pi$
$674$	−1.17988	−	0.346444i	−0.0454473	−	0.0133445i
$675$	3.35295	−	2.15481i	0.129055	−	0.0829388i
$676$	6.97734	+	15.2782i	0.268359	+	0.587624i
$677$	25.9195	−	7.61065i	0.996167	−	0.292501i	0.257285	−	0.966336i	$-0.417172\pi$
$677$	25.9195	−	7.61065i	0.996167	−	0.292501i	0.738882	+	0.673835i	$0.235354\pi$
$678$	−2.84075	+	3.27840i	−0.109098	+	0.125906i
$679$	7.94860	−	9.17317i	0.305039	−	0.352034i
$680$	−1.95508	+	0.574062i	−0.0749738	+	0.0220143i
$681$	−9.85257	−	21.5741i	−0.377551	−	0.826722i
$682$	−6.83374	+	4.39178i	−0.261678	+	0.168170i
$683$	26.3868	+	7.74786i	1.00966	+	0.296464i	0.744415	−	0.667717i	$-0.232728\pi$
$683$	26.3868	+	7.74786i	1.00966	+	0.296464i	0.265247	+	0.964181i	$0.414547\pi$
$684$	0.738046	+	5.13322i	0.0282199	+	0.196274i
$685$	−6.19927	+	13.5745i	−0.236862	+	0.518655i
$686$	−0.676188	+	4.70299i	−0.0258170	+	0.179561i
$687$	5.73127	+	3.68326i	0.218662	+	0.140525i
$688$	5.20287	+	6.00444i	0.198358	+	0.228917i
$689$	23.5832			0.898449
$690$	1.10010	+	0.307279i	0.0418803	+	0.0116979i
$691$	−3.58673			−0.136446			−0.0682229	−	0.997670i	$-0.521733\pi$
$691$	−3.58673			−0.136446			−0.0682229	+	0.997670i	$0.521733\pi$
$692$	−7.37519	−	8.51142i	−0.280363	−	0.323556i
$693$	−7.59059	−	4.87818i	−0.288343	−	0.185307i
$694$	−0.351730	+	2.44633i	−0.0133515	+	0.0928616i
$695$	6.84787	−	14.9947i	0.259754	−	0.568783i
$696$	−1.05847	−	7.36184i	−0.0401213	−	0.279050i
$697$	13.1286	+	3.85491i	0.497282	+	0.146015i
$698$	3.13456	−	2.01446i	0.118645	−	0.0762484i
$699$	0.568028	+	1.24381i	0.0214848	+	0.0470451i
$700$	15.2802	−	4.48668i	0.577538	−	0.169581i
$701$	−19.0432	+	21.9770i	−0.719250	+	0.830059i	−0.991217	−	0.132248i	$-0.957780\pi$
$701$	−19.0432	+	21.9770i	−0.719250	+	0.830059i	0.271967	+	0.962307i	$0.412326\pi$
$702$	−0.323373	+	0.373193i	−0.0122049	+	0.0140853i
$703$	10.0507	−	2.95115i	0.379069	−	0.111305i
$704$	−12.1988	−	26.7116i	−0.459758	−	1.00673i
$705$	6.11974	−	3.93292i	0.230483	−	0.148122i
$706$	−4.56405	−	1.34013i	−0.171770	−	0.0504363i
$707$	−1.56124	−	10.8587i	−0.0587165	−	0.408383i
$708$	9.84639	−	21.5606i	0.370050	−	0.810297i
$709$	−0.369984	+	2.57330i	−0.0138950	+	0.0966422i	−0.995589	−	0.0938241i	$-0.970091\pi$
$709$	−0.369984	+	2.57330i	−0.0138950	+	0.0966422i	0.981694	+	0.190466i	$0.0610000\pi$
$710$	−0.825015	−	0.530205i	−0.0309622	−	0.0198982i
$711$	10.6728	+	12.3171i	0.400261	+	0.461925i
$712$	−2.56837			−0.0962536
$713$	−31.2976	+	20.7036i	−1.17210	+	0.775355i
$714$	−1.05429			−0.0394558
$715$	6.04613	+	6.97761i	0.226112	+	0.260948i
$716$	−28.1292	−	18.0775i	−1.05124	−	0.675590i
$717$	−2.56308	+	17.8266i	−0.0957201	+	0.665748i
$718$	1.08161	−	2.36839i	0.0403653	−	0.0883877i
$719$	−2.69456	−	18.7410i	−0.100490	−	0.698923i	−0.976324	−	0.216311i	$-0.930597\pi$
$719$	−2.69456	−	18.7410i	−0.100490	−	0.698923i	0.875834	−	0.482612i	$-0.160312\pi$
$720$	−3.54416	−	1.04066i	−0.132083	−	0.0387831i
$721$	8.57454	−	5.51052i	0.319333	−	0.205223i
$722$	−1.16744	−	2.55634i	−0.0434477	−	0.0951371i
$723$	−0.283781	+	0.0833255i	−0.0105539	+	0.00309891i
$724$	−2.77716	+	3.20501i	−0.103212	+	0.119113i
$725$	20.8133	−	24.0198i	0.772987	−	0.892075i
$726$	1.87715	−	0.551181i	0.0696675	−	0.0204562i
$727$	−3.35777	−	7.35250i	−0.124533	−	0.272689i	0.837089	−	0.547066i	$-0.184256\pi$
$727$	−3.35777	−	7.35250i	−0.124533	−	0.272689i	−0.961622	+	0.274377i	$0.911528\pi$
$728$	−3.36745	+	2.16413i	−0.124806	+	0.0802080i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	0.00198760	+	0.0138240i	7.35643e−5	+	0.000511651i
$731$	1.95204	−	4.27437i	0.0721988	−	0.158093i
$732$	3.90463	−	27.1573i	0.144319	−	1.00376i
$733$	−5.31659	−	3.41676i	−0.196373	−	0.126201i	0.438759	−	0.898605i	$-0.355418\pi$
$733$	−5.31659	−	3.41676i	−0.196373	−	0.126201i	−0.635132	+	0.772403i	$0.719054\pi$
$734$	−3.18893	−	3.68022i	−0.117705	−	0.135839i
$735$	2.79560			0.103117
$736$	5.60139	+	11.8482i	0.206470	+	0.436729i
$737$	3.12586			0.115142
$738$	−0.976843	−	1.12734i	−0.0359581	−	0.0414979i
$739$	−19.4317	−	12.4880i	−0.714805	−	0.459378i	0.132021	−	0.991247i	$-0.457853\pi$
$739$	−19.4317	−	12.4880i	−0.714805	−	0.459378i	−0.846826	+	0.531869i	$0.821490\pi$
$740$	−1.09418	+	7.61018i	−0.0402228	+	0.279756i
$741$	2.31401	−	5.06697i	0.0850072	−	0.186140i
$742$	−0.781190	−	5.43329i	−0.0286784	−	0.199462i
$743$	25.5914	+	7.51430i	0.938856	+	0.275673i	0.715140	−	0.698981i	$-0.246363\pi$
$743$	25.5914	+	7.51430i	0.938856	+	0.275673i	0.223716	+	0.974654i	$0.428181\pi$
$744$	−6.13945	+	3.94558i	−0.225083	+	0.144652i
$745$	0.298953	+	0.654616i	0.0109528	+	0.0239833i
$746$	5.23795	−	1.53800i	0.191775	−	0.0563102i
$747$	9.52412	−	10.9914i	0.348469	−	0.402155i
$748$	−12.1236	+	13.9914i	−0.443282	+	0.511575i
$749$	6.98030	−	2.04960i	0.255055	−	0.0748908i
$750$	0.889028	+	1.94670i	0.0324627	+	0.0710834i
$751$	−26.5916	+	17.0894i	−0.970342	+	0.623601i	−0.926842	−	0.375453i	$-0.877487\pi$
$751$	−26.5916	+	17.0894i	−0.970342	+	0.623601i	−0.0435002	+	0.999053i	$0.513851\pi$
$752$	25.4178	+	7.46335i	0.926893	+	0.272160i
$753$	2.13949	+	14.8805i	0.0779674	+	0.542275i
$754$	−1.63580	+	3.58189i	−0.0595721	+	0.130445i
$755$	−1.03464	+	7.19608i	−0.0376544	+	0.261892i
$756$	−3.36135	−	2.16021i	−0.122251	−	0.0785661i
$757$	18.9716	+	21.8944i	0.689536	+	0.795767i	0.987299	−	0.158873i	$-0.0507860\pi$
$757$	18.9716	+	21.8944i	0.689536	+	0.795767i	−0.297763	+	0.954640i	$0.596241\pi$
$758$	−0.289436			−0.0105128
$759$	20.1212	−	6.19826i	0.730352	−	0.224983i
$760$	−2.50581			−0.0908953
$761$	29.5120	+	34.0586i	1.06981	+	1.23462i	0.970889	+	0.239529i	$0.0769931\pi$
$761$	29.5120	+	34.0586i	1.06981	+	1.23462i	0.0989193	+	0.995095i	$0.468461\pi$
$762$	−0.208078	−	0.133723i	−0.00753786	−	0.00484429i
$763$	1.11721	−	7.77035i	0.0404456	−	0.281306i
$764$	13.9838	−	30.6203i	0.505917	−	1.10780i
$765$	0.310910	+	2.16243i	0.0112410	+	0.0781826i
$766$	1.70422	+	0.500404i	0.0615760	+	0.0180803i
$767$	−21.4176	+	13.7643i	−0.773345	+	0.496999i
$768$	−4.86510	−	10.6531i	−0.175554	−	0.384410i
$769$	19.7184	−	5.78985i	0.711065	−	0.208787i	0.0938546	−	0.995586i	$-0.470081\pi$
$769$	19.7184	−	5.78985i	0.711065	−	0.208787i	0.617210	+	0.786799i	$0.288263\pi$
$770$	1.40728	−	1.62409i	0.0507149	−	0.0585281i
$771$	9.49851	−	10.9619i	0.342080	−	0.394782i
$772$	−33.5589	+	9.85379i	−1.20781	+	0.354646i
$773$	−7.65282	−	16.7573i	−0.275253	−	0.602720i	0.720635	−	0.693315i	$-0.243850\pi$
$773$	−7.65282	−	16.7573i	−0.275253	−	0.602720i	−0.995888	+	0.0905949i	$0.971123\pi$
$774$	−0.430955	+	0.276958i	−0.0154904	+	0.00995506i
$775$	−29.9231	−	8.78622i	−1.07487	−	0.315610i
$776$	0.783892	+	5.45209i	0.0281401	+	0.195719i
$777$	−3.35266	+	7.34131i	−0.120276	+	0.263368i
$778$	0.604345	−	4.20331i	0.0216668	−	0.150696i
$779$	14.1557	+	9.09729i	0.507179	+	0.325944i
$780$	2.67742	+	3.08990i	0.0958669	+	0.110636i
$781$	−18.0770			−0.646846
$782$	1.58629	−	1.88035i	0.0567255	−	0.0672411i
$783$	−7.97428			−0.284977
$784$	6.66675	+	7.69384i	0.238098	+	0.274780i
$785$	15.2404	+	9.79441i	0.543953	+	0.349577i
$786$	0.309002	−	2.14916i	0.0110217	−	0.0766579i
$787$	−8.24689	+	18.0582i	−0.293970	+	0.643705i	−0.997774	−	0.0666899i	$-0.978756\pi$
$787$	−8.24689	+	18.0582i	−0.293970	+	0.643705i	0.703804	+	0.710394i	$0.251483\pi$
$788$	−1.35667	−	9.43585i	−0.0483294	−	0.336138i
$789$	14.6522	+	4.30227i	0.521631	+	0.153165i
$790$	−3.26542	+	2.09856i	−0.116178	+	0.0746633i
$791$	15.6620	+	34.2950i	0.556877	+	1.21939i
$792$	3.92875	−	1.15359i	0.139602	−	0.0409909i
$793$	−19.2987	+	22.2719i	−0.685316	+	0.790897i
$794$	5.16491	−	5.96062i	0.183296	−	0.211535i
$795$	−10.9137	+	3.20456i	−0.387070	+	0.113654i
$796$	−10.0863	−	22.0860i	−0.357500	−	0.782817i
$797$	−21.6156	+	13.8915i	−0.765665	+	0.492063i	−0.864248	−	0.503066i	$-0.832205\pi$
$797$	−21.6156	+	13.8915i	−0.765665	+	0.492063i	0.0985829	+	0.995129i	$0.468569\pi$
$798$	−1.24402	−	0.365277i	−0.0440378	−	0.0129307i
$799$	−2.22977	−	15.5084i	−0.0788835	−	0.548647i
$800$	−4.52453	+	9.90734i	−0.159966	+	0.350277i
$801$	−0.391895	+	2.72569i	−0.0138469	+	0.0963074i
$802$	−1.61658	−	1.03891i	−0.0570834	−	0.0366853i
$803$	0.168585	+	0.194558i	0.00594924	+	0.00686579i
$804$	1.38423			0.0488179
$805$	6.40118	−	7.58781i	0.225612	−	0.267435i
$806$	3.86385			0.136098
$807$	8.91462	+	10.2880i	0.313810	+	0.362156i
$808$	4.18804	+	2.69149i	0.147335	+	0.0946863i
$809$	−2.20086	+	15.3073i	−0.0773781	+	0.538176i	0.913854	+	0.406043i	$0.133092\pi$
$809$	−2.20086	+	15.3073i	−0.0773781	+	0.538176i	−0.991232	+	0.132133i	$0.957817\pi$
$810$	0.0989385	−	0.216645i	0.00347634	−	0.00761213i
$811$	2.95308	+	20.5391i	0.103697	+	0.721225i	0.973643	+	0.228079i	$0.0732443\pi$
$811$	2.95308	+	20.5391i	0.103697	+	0.721225i	−0.869946	+	0.493147i	$0.835847\pi$
$812$	−30.5718	−	8.97668i	−1.07286	−	0.315020i
$813$	−3.71503	+	2.38750i	−0.130292	+	0.0837334i
$814$	−1.69349	−	3.70823i	−0.0593569	−	0.129974i
$815$	−4.42743	+	1.30001i	−0.155086	+	0.0455373i
$816$	−5.20983	+	6.01247i	−0.182381	+	0.210478i
$817$	3.78427	−	4.36728i	0.132395	−	0.152792i
$818$	3.50452	−	1.02902i	0.122533	−	0.0359789i
$819$	1.78287	+	3.90393i	0.0622984	+	0.136414i
$820$	−10.3900	+	6.67724i	−0.362834	+	0.233179i
$821$	−34.1963	−	10.0409i	−1.19346	−	0.350431i	−0.376110	−	0.926575i	$-0.622738\pi$
$821$	−34.1963	−	10.0409i	−1.19346	−	0.350431i	−0.817348	+	0.576144i	$0.804557\pi$
$822$	−0.498667	−	3.46830i	−0.0173930	−	0.120971i
$823$	19.3420	−	42.3532i	0.674221	−	1.47634i	−0.194431	−	0.980916i	$-0.562286\pi$
$823$	19.3420	−	42.3532i	0.674221	−	1.47634i	0.868652	−	0.495422i	$-0.164987\pi$
$824$	−0.658261	+	4.57831i	−0.0229316	+	0.159493i
$825$	14.7198	+	9.45986i	0.512479	+	0.329350i
$826$	3.88058	+	4.47842i	0.135023	+	0.155824i
$827$	46.6143			1.62094			0.810468	−	0.585782i	$-0.199213\pi$
$827$	46.6143			1.62094			0.810468	+	0.585782i	$0.199213\pi$
$828$	8.91029	−	2.74479i	0.309654	−	0.0953879i
$829$	−41.8838			−1.45468			−0.727342	−	0.686276i	$-0.759244\pi$
$829$	−41.8838			−1.45468			−0.727342	+	0.686276i	$0.759244\pi$
$830$	2.26834	+	2.61780i	0.0787352	+	0.0908652i
$831$	−14.1233	−	9.07648i	−0.489931	−	0.314859i
$832$	−1.98780	+	13.8254i	−0.0689144	+	0.479311i
$833$	2.50126	−	5.47700i	0.0866637	−	0.189767i
$834$	0.550840	+	3.83117i	0.0190740	+	0.132663i
$835$	16.2382	+	4.76797i	0.561946	+	0.165002i
$836$	−19.1529	+	12.3088i	−0.662418	+	0.425710i
$837$	3.25047	+	7.11754i	0.112353	+	0.246018i
$838$	4.90402	−	1.43995i	0.169406	−	0.0497422i
$839$	18.1745	−	20.9745i	0.627452	−	0.724119i	−0.349652	−	0.936880i	$-0.613700\pi$
$839$	18.1745	−	20.9745i	0.627452	−	0.724119i	0.977104	+	0.212761i	$0.0682456\pi$
$840$	1.26430	−	1.45908i	0.0436226	−	0.0503432i
$841$	−33.1880	+	9.74488i	−1.14441	+	0.336030i
$842$	−0.775509	−	1.69813i	−0.0267258	−	0.0585214i
$843$	23.5990	−	15.1661i	0.812792	−	0.522350i
$844$	−33.6789	−	9.88901i	−1.15927	−	0.340394i
$845$	1.23833	+	8.61274i	0.0425997	+	0.296287i
$846$	−0.709562	+	1.55372i	−0.0243952	+	0.0534181i
$847$	2.41985	−	16.8304i	0.0831470	−	0.578300i
$848$	−34.8456	−	22.3939i	−1.19660	−	0.769011i
$849$	18.6025	+	21.4684i	0.638436	+	0.736794i
$850$	2.04450			0.0701257
$851$	−8.04895	−	17.0253i	−0.275915	−	0.583620i
$852$	−8.00507			−0.274249
$853$	28.3739	+	32.7452i	0.971503	+	1.12117i	0.992604	+	0.121397i	$0.0387375\pi$
$853$	28.3739	+	32.7452i	0.971503	+	1.12117i	−0.0211006	+	0.999777i	$0.506717\pi$
$854$	5.77044	+	3.70844i	0.197460	+	0.126900i
$855$	−0.382349	+	2.65930i	−0.0130761	+	0.0909461i
$856$	−1.37145	+	3.00305i	−0.0468751	+	0.102642i
$857$	−7.14545	−	49.6977i	−0.244084	−	1.69764i	−0.631208	−	0.775613i	$-0.717441\pi$
$857$	−7.14545	−	49.6977i	−0.244084	−	1.69764i	0.387124	−	0.922027i	$-0.373468\pi$
$858$	−2.08004	−	0.610755i	−0.0710115	−	0.0208508i
$859$	−32.0372	+	20.5890i	−1.09309	+	0.702489i	−0.957546	−	0.288282i	$-0.906916\pi$
$859$	−32.0372	+	20.5890i	−1.09309	+	0.702489i	−0.135549	+	0.990771i	$0.543280\pi$
$860$	1.76197	+	3.85819i	0.0600828	+	0.131563i
$861$	−12.4394	+	3.65253i	−0.423933	+	0.124478i
$862$	−0.490307	+	0.565844i	−0.0166999	+	0.0192727i
$863$	−12.7109	+	14.6692i	−0.432685	+	0.499345i	−0.929659	−	0.368420i	$-0.879899\pi$
$863$	−12.7109	+	14.6692i	−0.432685	+	0.499345i	0.496975	+	0.867765i	$0.334444\pi$
$864$	2.62200	−	0.769888i	0.0892022	−	0.0261921i
$865$	−2.42372	−	5.30722i	−0.0824091	−	0.180451i
$866$	−3.37241	+	2.16732i	−0.114599	+	0.0736485i
$867$	−11.7967	−	3.46382i	−0.400636	−	0.117637i
$868$	4.44940	+	30.9463i	0.151023	+	1.05039i
$869$	−29.7225	+	65.0833i	−1.00827	+	2.20780i
$870$	0.270287	−	1.87988i	0.00916358	−	0.0637341i
$871$	−1.25079	−	0.803833i	−0.0423813	−	0.0272368i
$872$	2.33290	+	2.69232i	0.0790021	+	0.0911733i
$873$	5.90566			0.199876
$874$	2.52324	−	1.66914i	0.0853498	−	0.0564595i
$875$	18.6001			0.628797
$876$	0.0746548	+	0.0861562i	0.00252235	+	0.00291095i
$877$	−17.9387	−	11.5285i	−0.605748	−	0.389291i	0.201512	−	0.979486i	$-0.435414\pi$
$877$	−17.9387	−	11.5285i	−0.605748	−	0.389291i	−0.807261	+	0.590195i	$0.799051\pi$
$878$	−0.464248	+	3.22892i	−0.0156676	+	0.108971i
$879$	6.40858	−	14.0328i	0.216156	−	0.473315i
$880$	−2.30779	−	16.0511i	−0.0777957	−	0.541081i
$881$	−13.5081	−	3.96632i	−0.455098	−	0.133629i	0.0461463	−	0.998935i	$-0.485306\pi$
$881$	−13.5081	−	3.96632i	−0.455098	−	0.133629i	−0.501244	+	0.865306i	$0.667124\pi$
$882$	−0.552208	+	0.354883i	−0.0185938	+	0.0119495i
$883$	23.6063	+	51.6907i	0.794417	+	1.73953i	0.663553	+	0.748130i	$0.269048\pi$
$883$	23.6063	+	51.6907i	0.794417	+	1.73953i	0.130864	+	0.991400i	$0.458225\pi$
$884$	8.44913	−	2.48089i	0.284175	−	0.0834413i
$885$	8.04120	−	9.28004i	0.270302	−	0.311945i
$886$	1.23079	−	1.42041i	0.0413494	−	0.0477197i
$887$	19.7500	−	5.79913i	0.663141	−	0.194716i	0.0671945	−	0.997740i	$-0.478595\pi$
$887$	19.7500	−	5.79913i	0.663141	−	0.194716i	0.595947	+	0.803024i	$0.296777\pi$
$888$	−1.52144	−	3.33148i	−0.0510561	−	0.111797i
$889$	−1.80845	+	1.16222i	−0.0606535	+	0.0389796i
$890$	−0.629280	−	0.184773i	−0.0210935	−	0.00619362i
$891$	−0.624777	−	4.34542i	−0.0209308	−	0.145577i
$892$	7.05111	−	15.4398i	0.236089	−	0.516962i
$893$	2.74211	−	19.0718i	0.0917614	−	0.638214i
$894$	−0.142151	−	0.0913548i	−0.00475423	−	0.00305536i
$895$	−11.3437	−	13.0914i	−0.379180	−	0.437597i
$896$	14.4840			0.483877
$897$	−9.64526	−	2.69409i	−0.322046	−	0.0899531i
$898$	−7.44545			−0.248458
$899$	40.8606	+	47.1556i	1.36278	+	1.57273i
$900$	6.51841	+	4.18912i	0.217280	+	0.139637i
$901$	−3.48645	+	24.2488i	−0.116151	+	0.807845i
$902$	2.72040	−	5.95685i	0.0905795	−	0.198341i
$903$	0.633632	+	4.40701i	0.0210859	+	0.146656i
$904$	−16.4162	−	4.82022i	−0.545993	−	0.160318i
$905$	−1.84823	+	1.18778i	−0.0614371	+	0.0394832i
$906$	−0.709126	−	1.55277i	−0.0235591	−	0.0515873i
$907$	−0.365060	+	0.107191i	−0.0121216	+	0.00355923i	−0.287788	−	0.957694i	$-0.592920\pi$
$907$	−0.365060	+	0.107191i	−0.0121216	+	0.00355923i	0.275666	+	0.961253i	$0.411102\pi$
$908$	30.1946	−	34.8465i	1.00204	−	1.15642i
$909$	3.49539	−	4.03389i	0.115935	−	0.133796i
$910$	−0.980757	+	0.287976i	−0.0325118	+	0.00954632i
$911$	2.42027	+	5.29966i	0.0801872	+	0.175586i	0.945479	−	0.325683i	$-0.105594\pi$
$911$	2.42027	+	5.29966i	0.0801872	+	0.175586i	−0.865292	+	0.501268i	$0.832867\pi$
$912$	−8.23053	+	5.28944i	−0.272540	+	0.175151i
$913$	61.2622	+	17.9882i	2.02748	+	0.595323i
$914$	0.718760	+	4.99909i	0.0237745	+	0.165355i
$915$	5.90458	−	12.9292i	0.195199	−	0.427427i
$916$	−1.88490	+	13.1098i	−0.0622788	+	0.433158i
$917$	−15.8752	−	10.2024i	−0.524246	−	0.336912i
$918$	−0.335919	−	0.387671i	−0.0110870	−	0.0127951i
$919$	8.02685			0.264781			0.132391	−	0.991198i	$-0.457735\pi$
$919$	8.02685			0.264781			0.132391	+	0.991198i	$0.457735\pi$
$920$	0.700032	+	4.45025i	0.0230794	+	0.146721i
$921$	−32.8470			−1.08235
$922$	−0.233917	−	0.269955i	−0.00770365	−	0.00889048i
$923$	7.23338	+	4.64861i	0.238090	+	0.153011i
$924$	2.49639	−	17.3628i	0.0821252	−	0.571193i
$925$	6.50155	−	14.2364i	0.213770	−	0.468090i
$926$	0.102727	+	0.714485i	0.00337583	+	0.0234794i
$927$	4.75830	+	1.39716i	0.156283	+	0.0458889i
$928$	18.3320	−	11.7812i	0.601776	−	0.386738i
$929$	−1.68734	−	3.69476i	−0.0553598	−	0.121221i	0.879931	−	0.475102i	$-0.157589\pi$
$929$	−1.68734	−	3.69476i	−0.0553598	−	0.121221i	−0.935290	+	0.353881i	$0.884862\pi$
$930$	−1.78809	+	0.525030i	−0.0586338	+	0.0172164i
$931$	4.84900	−	5.59605i	0.158920	−	0.183403i
$932$	−1.74081	+	2.00900i	−0.0570220	+	0.0658069i
$933$	−1.93899	+	0.569338i	−0.0634796	+	0.0186393i
$934$	−0.523410	−	1.14611i	−0.0171265	−	0.0375018i
$935$	−8.06838	+	5.18523i	−0.263864	+	0.169575i
$936$	−1.86871	−	0.548704i	−0.0610808	−	0.0179349i
$937$	−4.29841	−	29.8961i	−0.140423	−	0.976662i	−0.931187	−	0.364542i	$-0.881226\pi$
$937$	−4.29841	−	29.8961i	−0.140423	−	0.976662i	0.790764	−	0.612121i	$-0.209683\pi$
$938$	−0.143761	+	0.314793i	−0.00469397	+	0.0102784i
$939$	−3.18077	+	22.1227i	−0.103800	+	0.721948i
$940$	11.8973	+	7.64590i	0.388046	+	0.249382i
$941$	−29.5625	−	34.1170i	−0.963710	−	1.11218i	−0.993637	−	0.112629i	$-0.964073\pi$
$941$	−29.5625	−	34.1170i	−0.963710	−	1.11218i	0.0299269	−	0.999552i	$-0.490473\pi$
$942$	−4.25374			−0.138594
$943$	12.2020	−	27.6815i	0.397351	−	0.901435i
$944$	44.7160			1.45538
$945$	−1.35554	−	1.56438i	−0.0440958	−	0.0508893i
$946$	−1.89194	−	1.21588i	−0.0615123	−	0.0395315i
$947$	7.50877	−	52.2246i	0.244002	−	1.69707i	−0.387639	−	0.921811i	$-0.626709\pi$
$947$	7.50877	−	52.2246i	0.244002	−	1.69707i	0.631641	−	0.775261i	$-0.282382\pi$
$948$	−13.1621	+	28.8209i	−0.427485	+	0.936061i
$949$	−0.0174264	−	0.121203i	−0.000565686	−	0.00393443i
$950$	2.41243	+	0.708353i	0.0782696	+	0.0229820i
$951$	−11.8614	+	7.62284i	−0.384631	+	0.247188i
$952$	−1.72738	−	3.78243i	−0.0559846	−	0.122589i
$953$	23.2377	−	6.82320i	0.752743	−	0.221025i	0.117218	−	0.993106i	$-0.462602\pi$
$953$	23.2377	−	6.82320i	0.752743	−	0.221025i	0.635524	+	0.772081i	$0.280784\pi$
$954$	1.74897	−	2.01842i	0.0566249	−	0.0653486i
$955$	11.4201	−	13.1795i	0.369545	−	0.426478i
$956$	−33.5945	+	9.86423i	−1.08652	+	0.319032i
$957$	−14.5428	−	31.8443i	−0.470103	−	1.02938i
$958$	1.88287	−	1.21005i	0.0608328	−	0.0390948i
$959$	−29.2202	−	8.57982i	−0.943569	−	0.277057i
$960$	−0.958737	−	6.66817i	−0.0309431	−	0.215214i
$961$	12.5559	−	27.4936i	0.405030	−	0.886891i
$962$	−0.275956	+	1.91931i	−0.00889717	+	0.0618812i
$963$	2.97773	+	1.91367i	0.0959561	+	0.0616672i
$964$	−0.376533	−	0.434543i	−0.0121273	−	0.0139957i
$965$	−18.1194			−0.583284
$966$	−0.301189	+	2.31139i	−0.00969060	+	0.0743679i
$967$	5.47721			0.176135			0.0880675	−	0.996115i	$-0.471931\pi$
$967$	5.47721			0.176135			0.0880675	+	0.996115i	$0.471931\pi$
$968$	5.05302	+	5.83150i	0.162410	+	0.187432i
$969$	4.86788	+	3.12840i	0.156379	+	0.100499i
$970$	−0.200171	+	1.39222i	−0.00642711	+	0.0447015i
$971$	−4.36602	+	9.56026i	−0.140112	+	0.306803i	−0.966660	−	0.256064i	$-0.917574\pi$
$971$	−4.36602	+	9.56026i	−0.140112	+	0.306803i	0.826548	+	0.562867i	$0.190302\pi$
$972$	−0.276671	−	1.92429i	−0.00887423	−	0.0617216i
$973$	32.2774	+	9.47749i	1.03476	+	0.303834i
$974$	2.71347	−	1.74384i	0.0869451	−	0.0558762i
$975$	−3.45737	−	7.57059i	−0.110724	−	0.242453i
$976$	49.6637	−	14.5826i	1.58970	−	0.466777i
$977$	−15.4808	+	17.8658i	−0.495275	+	0.571578i	−0.947268	−	0.320444i	$-0.896168\pi$
$977$	−15.4808	+	17.8658i	−0.495275	+	0.571578i	0.451992	+	0.892022i	$0.350713\pi$
$978$	0.709513	−	0.818821i	0.0226877	−	0.0261830i
$979$	−11.5994	+	3.40590i	−0.370719	+	0.108853i
$980$	2.25772	+	4.94372i	0.0721203	+	0.157921i
$981$	3.21319	−	2.06499i	0.102589	−	0.0659302i
$982$	−0.666930	−	0.195828i	−0.0212826	−	0.00624913i
$983$	−2.63486	−	18.3258i	−0.0840389	−	0.584503i	−0.987713	−	0.156281i	$-0.950049\pi$
$983$	−2.63486	−	18.3258i	−0.0840389	−	0.584503i	0.903674	−	0.428222i	$-0.140860\pi$
$984$	2.44401	−	5.35164i	0.0779123	−	0.170604i
$985$	0.702832	−	4.88830i	0.0223941	−	0.155754i
$986$	−3.44116	−	2.21150i	−0.109589	−	0.0704284i
$987$	9.72161	+	11.2193i	0.309442	+	0.357116i
$988$	10.8292			0.344523
$989$	−8.81336	−	5.50070i	−0.280248	−	0.174912i
$990$	1.04558			0.0332308
$991$	−11.7871	−	13.6031i	−0.374431	−	0.432116i	0.536992	−	0.843587i	$-0.319561\pi$
$991$	−11.7871	−	13.6031i	−0.374431	−	0.432116i	−0.911423	+	0.411471i	$0.865015\pi$
$992$	−17.9880	−	11.5602i	−0.571118	−	0.367035i
$993$	0.111921	−	0.778426i	0.00355170	−	0.0247026i
$994$	0.831381	−	1.82047i	0.0263698	−	0.0577418i
$995$	−1.79010	−	12.4504i	−0.0567501	−	0.394705i
$996$	27.1288	+	7.96575i	0.859610	+	0.252404i
$997$	−1.62042	+	1.04138i	−0.0513193	+	0.0329809i	−0.566049	−	0.824372i	$-0.691529\pi$
$997$	−1.62042	+	1.04138i	−0.0513193	+	0.0329809i	0.514730	+	0.857353i	$0.327892\pi$
$998$	1.12696	+	2.46771i	0.0356734	+	0.0781139i
$999$	−3.76770	+	1.10630i	−0.119205	+	0.0350016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.b.13.1	✓	10
3.2	odd	2		207.2.i.a.82.1		10
23.4	even	11		1587.2.a.q.1.2		5
23.16	even	11	inner	69.2.e.b.16.1	yes	10
23.19	odd	22		1587.2.a.r.1.2		5
69.50	odd	22		4761.2.a.bp.1.4		5
69.62	odd	22		207.2.i.a.154.1		10
69.65	even	22		4761.2.a.bm.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.b.13.1	✓	10	1.1	even	1	trivial
69.2.e.b.16.1	yes	10	23.16	even	11	inner
207.2.i.a.82.1		10	3.2	odd	2
207.2.i.a.154.1		10	69.62	odd	22
1587.2.a.q.1.2		5	23.4	even	11
1587.2.a.r.1.2		5	23.19	odd	22
4761.2.a.bm.1.4		5	69.65	even	22
4761.2.a.bp.1.4		5	69.50	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.154861 - 0.178719i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(0.276671 - 1.92429i) q^{4} +(0.418382 - 0.916128i) q^{5} +(0.0336545 + 0.234072i) q^{6} +(1.97204 + 0.579043i) q^{7} +(-0.784630 + 0.504251i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.154861 - 0.178719i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(0.276671 - 1.92429i) q^{4} +(0.418382 - 0.916128i) q^{5} +(0.0336545 + 0.234072i) q^{6} +(1.97204 + 0.579043i) q^{7} +(-0.784630 + 0.504251i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-0.228520 + 0.0670996i) q^{10} +(-2.87491 + 3.31782i) q^{11} +(-1.27310 + 1.46924i) q^{12} +(2.00357 - 0.588302i) q^{13} +(-0.201906 - 0.442111i) q^{14} +(-0.847262 + 0.544502i) q^{15} +(-3.51903 - 1.03328i) q^{16} +(0.308705 + 2.14709i) q^{17} +(0.0982369 - 0.215109i) q^{18} +(-0.379638 + 2.64044i) q^{19} +(-1.64714 - 1.05855i) q^{20} +(-1.34593 - 1.55329i) q^{21} +1.03817 q^{22} +(4.79541 - 0.0634158i) q^{23} +0.932691 q^{24} +(2.61006 + 3.01216i) q^{25} +(-0.415415 - 0.266971i) q^{26} +(0.142315 - 0.989821i) q^{27} +(1.65985 - 3.63457i) q^{28} +(-1.13486 - 7.89311i) q^{29} +(0.228520 + 0.0670996i) q^{30} +(-6.58251 + 4.23032i) q^{31} +(1.13520 + 2.48574i) q^{32} +(4.21228 - 1.23684i) q^{33} +(0.335919 - 0.387671i) q^{34} +(1.35554 - 1.56438i) q^{35} +(1.86533 - 0.547710i) q^{36} +(-1.63123 - 3.57190i) q^{37} +(0.530688 - 0.341052i) q^{38} +(-2.00357 - 0.588302i) q^{39} +(0.133684 + 0.929791i) q^{40} +(2.62039 - 5.73785i) q^{41} +(-0.0691698 + 0.481086i) q^{42} +(-1.82238 - 1.17118i) q^{43} +(5.58904 + 6.45010i) q^{44} +1.00714 q^{45} +(-0.753955 - 0.847210i) q^{46} -7.22297 q^{47} +(2.40176 + 2.77178i) q^{48} +(-2.33513 - 1.50070i) q^{49} +(0.134135 - 0.932932i) q^{50} +(0.901106 - 1.97315i) q^{51} +(-0.577732 - 4.01822i) q^{52} +(10.8363 + 3.18183i) q^{53} +(-0.198939 + 0.127850i) q^{54} +(1.83674 + 4.02190i) q^{55} +(-1.83930 + 0.540068i) q^{56} +(1.74690 - 2.01603i) q^{57} +(-1.23490 + 1.42515i) q^{58} +(-11.6983 + 3.43493i) q^{59} +(0.813367 + 1.78102i) q^{60} +(-11.8725 + 7.63000i) q^{61} +(1.77541 + 0.521307i) q^{62} +(0.292499 + 2.03437i) q^{63} +(-2.77870 + 6.08450i) q^{64} +(0.299298 - 2.08166i) q^{65} +(-0.873362 - 0.561276i) q^{66} +(-0.466276 - 0.538111i) q^{67} +4.21704 q^{68} +(-4.06844 - 2.53925i) q^{69} -0.489504 q^{70} +(2.69650 + 3.11193i) q^{71} +(-0.784630 - 0.504251i) q^{72} +(0.00834536 - 0.0580433i) q^{73} +(-0.385752 + 0.844680i) q^{74} +(-0.567219 - 3.94510i) q^{75} +(4.97594 + 1.46107i) q^{76} +(-7.59059 + 4.87818i) q^{77} +(0.205134 + 0.449181i) q^{78} +(15.6376 - 4.59162i) q^{79} +(-2.41892 + 2.79158i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-1.43126 + 0.420255i) q^{82} +(-6.04169 - 13.2294i) q^{83} +(-3.36135 + 2.16021i) q^{84} +(2.09617 + 0.615490i) q^{85} +(0.0729047 + 0.507064i) q^{86} +(-3.31264 + 7.25366i) q^{87} +(0.582724 - 4.05294i) q^{88} +(2.31657 + 1.48877i) q^{89} +(-0.155967 - 0.179995i) q^{90} +4.29177 q^{91} +(1.20472 - 9.24531i) q^{92} +7.82464 q^{93} +(1.11855 + 1.29088i) q^{94} +(2.26015 + 1.45251i) q^{95} +(0.388902 - 2.70488i) q^{96} +(2.45330 - 5.37197i) q^{97} +(0.0934171 + 0.649730i) q^{98} +(-4.21228 - 1.23684i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9} + 12 q^{10} - 15 q^{11} - 8 q^{12} + 8 q^{13} + 9 q^{14} - 8 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 9 q^{19} - 9 q^{20} + 5 q^{21} - 28 q^{22} + 21 q^{23} + 18 q^{24} - 4 q^{25} + q^{26} + q^{27} + 29 q^{28} - 8 q^{29} - 12 q^{30} - 23 q^{31} - q^{32} + 4 q^{33} - 15 q^{34} + 18 q^{35} + 8 q^{36} + 3 q^{37} + 3 q^{38} - 8 q^{39} - 32 q^{40} - 15 q^{41} + 13 q^{42} + 22 q^{43} - q^{44} - 14 q^{45} + 26 q^{46} + 4 q^{47} + 21 q^{48} - 29 q^{49} + 49 q^{50} - 12 q^{51} + 2 q^{52} + 29 q^{53} + 7 q^{54} + 43 q^{55} - 2 q^{56} + 20 q^{57} + 21 q^{58} - 54 q^{59} - 2 q^{60} - 30 q^{61} - 7 q^{62} + 6 q^{63} - 31 q^{64} - 9 q^{65} - 27 q^{66} + q^{67} - 30 q^{68} + q^{69} - 94 q^{70} - 3 q^{71} - 7 q^{72} - 47 q^{73} - 12 q^{74} + 15 q^{75} + 50 q^{76} + 13 q^{77} - 12 q^{78} + 18 q^{79} + 3 q^{80} - q^{81} - 28 q^{82} + 18 q^{83} + 4 q^{84} + 58 q^{85} + 8 q^{87} + 16 q^{88} + 25 q^{89} + q^{90} + 18 q^{91} - 3 q^{92} - 10 q^{93} + 39 q^{94} - 16 q^{95} - 21 q^{96} + 21 q^{97} - 27 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9 + 12 * q^10 - 15 * q^11 - 8 * q^12 + 8 * q^13 + 9 * q^14 - 8 * q^15 + 12 * q^16 + q^17 + 4 * q^18 - 9 * q^19 - 9 * q^20 + 5 * q^21 - 28 * q^22 + 21 * q^23 + 18 * q^24 - 4 * q^25 + q^26 + q^27 + 29 * q^28 - 8 * q^29 - 12 * q^30 - 23 * q^31 - q^32 + 4 * q^33 - 15 * q^34 + 18 * q^35 + 8 * q^36 + 3 * q^37 + 3 * q^38 - 8 * q^39 - 32 * q^40 - 15 * q^41 + 13 * q^42 + 22 * q^43 - q^44 - 14 * q^45 + 26 * q^46 + 4 * q^47 + 21 * q^48 - 29 * q^49 + 49 * q^50 - 12 * q^51 + 2 * q^52 + 29 * q^53 + 7 * q^54 + 43 * q^55 - 2 * q^56 + 20 * q^57 + 21 * q^58 - 54 * q^59 - 2 * q^60 - 30 * q^61 - 7 * q^62 + 6 * q^63 - 31 * q^64 - 9 * q^65 - 27 * q^66 + q^67 - 30 * q^68 + q^69 - 94 * q^70 - 3 * q^71 - 7 * q^72 - 47 * q^73 - 12 * q^74 + 15 * q^75 + 50 * q^76 + 13 * q^77 - 12 * q^78 + 18 * q^79 + 3 * q^80 - q^81 - 28 * q^82 + 18 * q^83 + 4 * q^84 + 58 * q^85 + 8 * q^87 + 16 * q^88 + 25 * q^89 + q^90 + 18 * q^91 - 3 * q^92 - 10 * q^93 + 39 * q^94 - 16 * q^95 - 21 * q^96 + 21 * q^97 - 27 * q^98 - 4 * q^99

Introduction

L-functions

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