LMFDB - Embedded newform 507.2.p.b.25.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.12
Character	$\chi$	$=$	507.25
Dual form			507.2.p.b.142.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43480 + 0.544146i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(0.265521 + 0.235231i) q^{4} +(-3.88465 - 0.471682i) q^{5} +(-0.367233 - 1.48992i) q^{6} +(2.17406 + 4.14233i) q^{7} +(-1.17328 - 2.23550i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(1.43480 + 0.544146i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(0.265521 + 0.235231i) q^{4} +(-3.88465 - 0.471682i) q^{5} +(-0.367233 - 1.48992i) q^{6} +(2.17406 + 4.14233i) q^{7} +(-1.17328 - 2.23550i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-5.31702 - 2.79059i) q^{10} +(-2.83683 + 1.07587i) q^{11} +(0.0427583 - 0.352146i) q^{12} +(-1.33143 + 3.35071i) q^{13} +(0.865302 + 7.12641i) q^{14} +(1.81855 + 3.46495i) q^{15} +(-0.552495 - 4.55021i) q^{16} +(-2.82129 + 1.48073i) q^{17} +(-1.01757 + 1.14860i) q^{18} +0.995482i q^{19} +(-0.920502 - 1.03903i) q^{20} +(2.17406 - 4.14233i) q^{21} -4.65570 q^{22} -5.88647 q^{23} +(-1.17328 + 2.23550i) q^{24} +(10.0133 + 2.46806i) q^{25} +(-3.73361 + 4.08310i) q^{26} +(0.970942 - 0.239316i) q^{27} +(-0.397146 + 1.61128i) q^{28} +(-0.0567993 + 0.149767i) q^{29} +(0.723803 + 5.96105i) q^{30} +(0.233522 + 0.947434i) q^{31} +(0.474867 - 1.92661i) q^{32} +(2.49693 + 1.72350i) q^{33} +(-4.85371 + 0.589347i) q^{34} +(-6.49162 - 17.1170i) q^{35} +(-0.314100 + 0.164852i) q^{36} +(-1.51819 - 6.15955i) q^{37} +(-0.541688 + 1.42831i) q^{38} +(3.51392 - 0.807675i) q^{39} +(3.50334 + 9.23755i) q^{40} +(4.35219 - 3.00410i) q^{41} +(5.37337 - 4.76039i) q^{42} +(-10.0103 - 2.46731i) q^{43} +(-1.00632 - 0.381645i) q^{44} +(1.81855 - 3.46495i) q^{45} +(-8.44587 - 3.20310i) q^{46} +(5.08579 + 5.74067i) q^{47} +(-3.43090 + 3.03951i) q^{48} +(-8.45591 + 12.2505i) q^{49} +(13.0241 + 8.98988i) q^{50} +(2.82129 + 1.48073i) q^{51} +(-1.14172 + 0.576491i) q^{52} +(3.90997 - 2.05211i) q^{53} +(1.52333 + 0.184965i) q^{54} +(11.5276 - 2.84129i) q^{55} +(6.70939 - 9.72023i) q^{56} +(0.819266 - 0.565498i) q^{57} +(-0.162991 + 0.183978i) q^{58} +(-3.01050 - 0.365541i) q^{59} +(-0.332202 + 1.34780i) q^{60} +(5.71112 + 2.99743i) q^{61} +(-0.180487 + 1.48644i) q^{62} +(-4.64408 + 0.563893i) q^{63} +(-3.47790 + 5.03861i) q^{64} +(6.75262 - 12.3883i) q^{65} +(2.64474 + 3.83157i) q^{66} +(-7.14796 - 8.06838i) q^{67} +(-1.09743 - 0.270491i) q^{68} +(3.34389 + 4.84447i) q^{69} -28.0918i q^{70} +(7.89548 - 5.44986i) q^{71} +(2.50628 - 0.304317i) q^{72} +(12.2050 - 4.62875i) q^{73} +(1.17340 - 9.66380i) q^{74} +(-3.65704 - 9.64283i) q^{75} +(-0.234168 + 0.264321i) q^{76} +(-10.6241 - 9.41210i) q^{77} +(5.48125 + 0.753239i) q^{78} +(-5.36766 + 4.75533i) q^{79} +17.9366i q^{80} +(-0.748511 - 0.663123i) q^{81} +(7.87917 - 1.94204i) q^{82} +(4.69188 + 3.23857i) q^{83} +(1.55166 - 0.588469i) q^{84} +(11.6582 - 4.42136i) q^{85} +(-13.0201 - 8.98712i) q^{86} +(0.155522 - 0.0383327i) q^{87} +(5.73350 + 5.07944i) q^{88} +12.0958i q^{89} +(4.49468 - 3.98194i) q^{90} +(-16.7744 + 1.76943i) q^{91} +(-1.56298 - 1.38468i) q^{92} +(0.647068 - 0.730389i) q^{93} +(4.17331 + 11.0041i) q^{94} +(0.469551 - 3.86710i) q^{95} +(-1.85533 + 0.703632i) q^{96} +(-14.2969 + 1.73595i) q^{97} +(-18.7986 + 12.9757i) q^{98} -3.03399i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

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 $

$2$	1.43480	+	0.544146i	1.01455	+	0.384769i	0.805157	−	0.593061i	$-0.202081\pi$
$2$	1.43480	+	0.544146i	1.01455	+	0.384769i	0.209396	+	0.977831i	$0.432850\pi$
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$4$	0.265521	+	0.235231i	0.132760	+	0.117616i
$5$	−3.88465	−	0.471682i	−1.73727	−	0.210943i	−0.810283	−	0.586038i	$-0.800687\pi$
$5$	−3.88465	−	0.471682i	−1.73727	−	0.210943i	−0.926986	+	0.375096i	$0.877610\pi$
$6$	−0.367233	−	1.48992i	−0.149922	−	0.608259i
$7$	2.17406	+	4.14233i	0.821719	+	1.56565i	0.824640	+	0.565658i	$0.191378\pi$
$7$	2.17406	+	4.14233i	0.821719	+	1.56565i	−0.00292102	+	0.999996i	$0.500930\pi$
$8$	−1.17328	−	2.23550i	−0.414817	−	0.790368i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	−5.31702	−	2.79059i	−1.68139	−	0.882461i
$11$	−2.83683	+	1.07587i	−0.855337	+	0.324387i	−0.743007	−	0.669284i	$-0.766601\pi$
$11$	−2.83683	+	1.07587i	−0.855337	+	0.324387i	−0.112331	+	0.993671i	$0.535832\pi$
$12$	0.0427583	−	0.352146i	0.0123432	−	0.101656i
$13$	−1.33143	+	3.35071i	−0.369273	+	0.929321i
$13$	−1.33143	+	3.35071i	−0.369273	+	0.929321i
$14$	0.865302	+	7.12641i	0.231262	+	1.90461i
$15$	1.81855	+	3.46495i	0.469547	+	0.894647i
$16$	−0.552495	−	4.55021i	−0.138124	−	1.13755i
$17$	−2.82129	+	1.48073i	−0.684264	+	0.359129i	−0.770763	−	0.637123i	$-0.780125\pi$
$17$	−2.82129	+	1.48073i	−0.684264	+	0.359129i	0.0864985	+	0.996252i	$0.472432\pi$
$18$	−1.01757	+	1.14860i	−0.239844	+	0.270728i
$19$			0.995482i			0.228379i	0.993459	+	0.114190i	$0.0364271\pi$
$19$			0.995482i			0.228379i	−0.993459	+	0.114190i	$0.963573\pi$
$20$	−0.920502	−	1.03903i	−0.205831	−	0.232335i
$21$	2.17406	−	4.14233i	0.474419	−	0.903931i
$22$	−4.65570			−0.992600
$23$	−5.88647			−1.22741			−0.613706	−	0.789534i	$-0.710322\pi$
$23$	−5.88647			−1.22741			−0.613706	+	0.789534i	$0.710322\pi$
$24$	−1.17328	+	2.23550i	−0.239495	+	0.456319i
$25$	10.0133	+	2.46806i	2.00267	+	0.493613i
$26$	−3.73361	+	4.08310i	−0.732221	+	0.800761i
$27$	0.970942	−	0.239316i	0.186858	−	0.0460563i
$28$	−0.397146	+	1.61128i	−0.0750535	+	0.304504i
$29$	−0.0567993	+	0.149767i	−0.0105474	+	0.0278111i	−0.940187	−	0.340660i	$-0.889349\pi$
$29$	−0.0567993	+	0.149767i	−0.0105474	+	0.0278111i	0.929639	+	0.368471i	$0.120119\pi$
$30$	0.723803	+	5.96105i	0.132148	+	1.08833i
$31$	0.233522	+	0.947434i	0.0419417	+	0.170164i	0.988178	−	0.153313i	$-0.0489943\pi$
$31$	0.233522	+	0.947434i	0.0419417	+	0.170164i	−0.946236	+	0.323477i	$0.895148\pi$
$32$	0.474867	−	1.92661i	0.0839454	−	0.340580i
$33$	2.49693	+	1.72350i	0.434659	+	0.300024i
$34$	−4.85371	+	0.589347i	−0.832404	+	0.101072i
$35$	−6.49162	−	17.1170i	−1.09728	−	2.89330i
$36$	−0.314100	+	0.164852i	−0.0523500	+	0.0274754i
$37$	−1.51819	−	6.15955i	−0.249589	−	1.01262i	−0.953273	−	0.302110i	$-0.902309\pi$
$37$	−1.51819	−	6.15955i	−0.249589	−	1.01262i	0.703684	−	0.710513i	$-0.251537\pi$
$38$	−0.541688	+	1.42831i	−0.0878733	+	0.231703i
$39$	3.51392	−	0.807675i	0.562678	−	0.129332i
$40$	3.50334	+	9.23755i	0.553927	+	1.46058i
$41$	4.35219	−	3.00410i	0.679698	−	0.469162i	−0.177519	−	0.984117i	$-0.556807\pi$
$41$	4.35219	−	3.00410i	0.679698	−	0.469162i	0.857217	+	0.514956i	$0.172192\pi$
$42$	5.37337	−	4.76039i	0.829129	−	0.734544i
$43$	−10.0103	−	2.46731i	−1.52655	−	0.376261i	−0.615359	−	0.788247i	$-0.710989\pi$
$43$	−10.0103	−	2.46731i	−1.52655	−	0.376261i	−0.911190	+	0.411986i	$0.864835\pi$
$44$	−1.00632	−	0.381645i	−0.151708	−	0.0575352i
$45$	1.81855	−	3.46495i	0.271093	−	0.516525i
$46$	−8.44587	−	3.20310i	−1.24528	−	0.472271i
$47$	5.08579	+	5.74067i	0.741839	+	0.837363i	0.991382	−	0.131000i	$-0.0418189\pi$
$47$	5.08579	+	5.74067i	0.741839	+	0.837363i	−0.249543	+	0.968364i	$0.580280\pi$
$48$	−3.43090	+	3.03951i	−0.495207	+	0.438715i
$49$	−8.45591	+	12.2505i	−1.20799	+	1.75007i
$50$	13.0241	+	8.98988i	1.84188	+	1.27136i
$51$	2.82129	+	1.48073i	0.395060	+	0.207343i
$52$	−1.14172	+	0.576491i	−0.158327	+	0.0799449i
$53$	3.90997	−	2.05211i	0.537076	−	0.281879i	−0.174298	−	0.984693i	$-0.555766\pi$
$53$	3.90997	−	2.05211i	0.537076	−	0.281879i	0.711374	+	0.702814i	$0.248073\pi$
$54$	1.52333	+	0.184965i	0.207298	+	0.0251706i
$55$	11.5276	−	2.84129i	1.55438	−	0.383120i
$56$	6.70939	−	9.72023i	0.896580	−	1.29892i
$57$	0.819266	−	0.565498i	0.108514	−	0.0749021i
$58$	−0.162991	+	0.183978i	−0.0214017	+	0.0241575i
$59$	−3.01050	−	0.365541i	−0.391934	−	0.0475894i	−0.0778024	−	0.996969i	$-0.524790\pi$
$59$	−3.01050	−	0.365541i	−0.391934	−	0.0475894i	−0.314132	+	0.949379i	$0.601713\pi$
$60$	−0.332202	+	1.34780i	−0.0428871	+	0.174000i
$61$	5.71112	+	2.99743i	0.731234	+	0.383781i	0.788873	−	0.614556i	$-0.210665\pi$
$61$	5.71112	+	2.99743i	0.731234	+	0.383781i	−0.0576388	+	0.998338i	$0.518357\pi$
$62$	−0.180487	+	1.48644i	−0.0229219	+	0.188779i
$63$	−4.64408	+	0.563893i	−0.585099	+	0.0710439i
$64$	−3.47790	+	5.03861i	−0.434738	+	0.629826i
$65$	6.75262	−	12.3883i	0.837560	−	1.53659i
$66$	2.64474	+	3.83157i	0.325545	+	0.471634i
$67$	−7.14796	−	8.06838i	−0.873263	−	0.985710i	0.126718	−	0.991939i	$-0.459556\pi$
$67$	−7.14796	−	8.06838i	−0.873263	−	0.985710i	−0.999981	+	0.00622908i	$0.998017\pi$
$68$	−1.09743	−	0.270491i	−0.133082	−	0.0328019i
$69$	3.34389	+	4.84447i	0.402557	+	0.583205i
$70$		−	28.0918i		−	3.35761i
$71$	7.89548	−	5.44986i	0.937021	−	0.646779i	0.00148095	−	0.999999i	$-0.499529\pi$
$71$	7.89548	−	5.44986i	0.937021	−	0.646779i	0.935540	+	0.353220i	$0.114913\pi$
$72$	2.50628	−	0.304317i	0.295368	−	0.0358641i
$73$	12.2050	−	4.62875i	1.42849	−	0.541754i	0.485398	−	0.874293i	$-0.338675\pi$
$73$	12.2050	−	4.62875i	1.42849	−	0.541754i	0.943089	+	0.332539i	$0.107905\pi$
$74$	1.17340	−	9.66380i	0.136405	−	1.12339i
$75$	−3.65704	−	9.64283i	−0.422279	−	1.11346i
$76$	−0.234168	+	0.264321i	−0.0268609	+	0.0303197i
$77$	−10.6241	−	9.41210i	−1.21072	−	1.07261i
$78$	5.48125	+	0.753239i	0.620630	+	0.0852875i
$79$	−5.36766	+	4.75533i	−0.603909	+	0.535017i	−0.908725	−	0.417394i	$-0.862943\pi$
$79$	−5.36766	+	4.75533i	−0.603909	+	0.535017i	0.304816	+	0.952411i	$0.401405\pi$
$80$			17.9366i			2.00537i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	7.87917	−	1.94204i	0.870109	−	0.214463i
$83$	4.69188	+	3.23857i	0.515001	+	0.355479i	0.797043	−	0.603923i	$-0.206396\pi$
$83$	4.69188	+	3.23857i	0.515001	+	0.355479i	−0.282042	+	0.959402i	$0.591012\pi$
$84$	1.55166	−	0.588469i	0.169300	−	0.0642072i
$85$	11.6582	−	4.42136i	1.26451	−	0.479564i
$86$	−13.0201	−	8.98712i	−1.40399	−	0.969106i
$87$	0.155522	−	0.0383327i	0.0166737	−	0.00410969i
$88$	5.73350	+	5.07944i	0.611193	+	0.541470i
$89$			12.0958i			1.28216i	0.767476	+	0.641078i	$0.221513\pi$
$89$			12.0958i			1.28216i	−0.767476	+	0.641078i	$0.778487\pi$
$90$	4.49468	−	3.98194i	0.473781	−	0.419734i
$91$	−16.7744	+	1.76943i	−1.75843	+	0.185487i
$92$	−1.56298	−	1.38468i	−0.162952	−	0.144363i
$93$	0.647068	−	0.730389i	0.0670978	−	0.0757378i
$94$	4.17331	+	11.0041i	0.430444	+	1.13499i
$95$	0.469551	−	3.86710i	0.0481749	−	0.396756i
$96$	−1.85533	+	0.703632i	−0.189358	+	0.0718142i
$97$	−14.2969	+	1.73595i	−1.45163	+	0.176259i	−0.808047	−	0.589119i	$-0.799475\pi$
$97$	−14.2969	+	1.73595i	−1.45163	+	0.176259i	−0.643581	+	0.765378i	$0.722552\pi$
$98$	−18.7986	+	12.9757i	−1.89894	+	1.31074i
$99$		−	3.03399i		−	0.304928i
$100$	2.07818	+	3.01077i	0.207818	+	0.301077i
$101$	−8.33210	−	2.05368i	−0.829075	−	0.204349i	−0.198130	−	0.980176i	$-0.563487\pi$
$101$	−8.33210	−	2.05368i	−0.829075	−	0.204349i	−0.630946	+	0.775827i	$0.717333\pi$
$102$	3.24224	+	3.65974i	0.321030	+	0.362368i
$103$	1.61643	+	2.34181i	0.159272	+	0.230745i	0.894493	−	0.447083i	$-0.147537\pi$
$103$	1.61643	+	2.34181i	0.159272	+	0.230745i	−0.735221	+	0.677828i	$0.762922\pi$
$104$	9.05266	−	0.954911i	0.887686	−	0.0936368i
$105$	−10.3993	+	15.0661i	−1.01487	+	1.47030i
$106$	6.72666	−	0.816764i	0.653351	−	0.0793311i
$107$	−0.205063	+	1.68885i	−0.0198242	+	0.163267i	−0.999259	−	0.0384950i	$-0.987744\pi$
$107$	−0.205063	+	1.68885i	−0.0198242	+	0.163267i	0.979435	+	0.201762i	$0.0646667\pi$
$108$	0.314100	+	0.164852i	0.0302243	+	0.0158629i
$109$	−0.748035	+	3.03490i	−0.0716487	+	0.290690i	−0.995826	−	0.0912739i	$-0.970906\pi$
$109$	−0.748035	+	3.03490i	−0.0716487	+	0.290690i	0.924177	+	0.381964i	$0.124752\pi$
$110$	18.0858	+	2.19601i	1.72441	+	0.209382i
$111$	−4.20678	+	4.74847i	−0.399289	+	0.450705i
$112$	17.6473	−	12.1811i	1.66751	−	1.15100i
$113$	−11.7003	+	16.9508i	−1.10067	+	1.59460i	−0.346338	+	0.938110i	$0.612575\pi$
$113$	−11.7003	+	16.9508i	−1.10067	+	1.59460i	−0.754335	+	0.656490i	$0.772040\pi$
$114$	1.48319	−	0.365574i	0.138914	−	0.0342391i
$115$	22.8669	+	2.77654i	2.13235	+	0.258914i
$116$	−0.0503113	+	0.0264054i	−0.00467129	+	0.00245168i
$117$	−2.66084	−	2.43309i	−0.245995	−	0.224939i
$118$	−4.12055	−	2.16263i	−0.379327	−	0.199086i
$119$	−12.2673	−	8.46753i	−1.12455	−	0.776217i
$120$	5.61223	−	8.13072i	0.512324	−	0.742230i
$121$	−1.34349	+	1.19023i	−0.122135	+	0.108203i
$122$	6.56325	+	7.40838i	0.594209	+	0.670723i
$123$	−4.94465	−	1.87526i	−0.445844	−	0.169086i
$124$	−0.160861	+	0.306495i	−0.0144458	+	0.0275241i
$125$	−19.4397	−	7.37251i	−1.73874	−	0.659418i
$126$	−6.97015	−	1.71799i	−0.620950	−	0.153050i
$127$	4.44058	−	3.93401i	0.394038	−	0.349087i	−0.442720	−	0.896660i	$-0.645987\pi$
$127$	4.44058	−	3.93401i	0.394038	−	0.349087i	0.836758	+	0.547573i	$0.184448\pi$
$128$	−10.9979	+	7.59128i	−0.972083	+	0.670980i
$129$	3.65592	+	9.63987i	0.321886	+	0.848743i
$130$	16.4297	−	14.1003i	1.44098	−	1.23668i
$131$	−5.69181	+	15.0081i	−0.497296	+	1.31126i	0.417988	+	0.908453i	$0.362735\pi$
$131$	−5.69181	+	15.0081i	−0.497296	+	1.31126i	−0.915284	+	0.402809i	$0.868034\pi$
$132$	0.257565	+	1.04498i	0.0224181	+	0.0909540i
$133$	−4.12362	+	2.16424i	−0.357563	+	0.187664i
$134$	−5.86548	−	15.4660i	−0.506701	−	1.33606i
$135$	−3.88465	+	0.471682i	−0.334338	+	0.0405959i
$136$	6.62033	+	4.56969i	0.567689	+	0.391847i
$137$	3.24047	−	13.1471i	0.276852	−	1.12323i	−0.653607	−	0.756834i	$-0.726745\pi$
$137$	3.24047	−	13.1471i	0.276852	−	1.12323i	0.930458	−	0.366397i	$-0.119409\pi$
$138$	2.16171	+	8.77038i	0.184017	+	0.746585i
$139$	2.57651	+	21.2195i	0.218537	+	1.79982i	0.528359	+	0.849021i	$0.322807\pi$
$139$	2.57651	+	21.2195i	0.218537	+	1.79982i	−0.309822	+	0.950794i	$0.600270\pi$
$140$	2.30279	−	6.07195i	0.194621	−	0.513173i
$141$	1.83542	−	7.44660i	0.154570	−	0.627117i
$142$	14.2939	−	3.52313i	1.19952	−	0.295655i
$143$	0.172122	−	10.9379i	0.0143936	−	0.914670i
$144$	4.45044	+	1.09693i	0.370870	+	0.0914112i
$145$	0.291288	−	0.555003i	0.0241902	−	0.0460905i
$146$	20.0304			1.65773
$147$	14.8855			1.22773
$148$	1.04580	−	1.99261i	0.0859646	−	0.163792i
$149$	2.06494	+	2.33084i	0.169167	+	0.190950i	0.826980	−	0.562231i	$-0.190057\pi$
$149$	2.06494	+	2.33084i	0.169167	+	0.190950i	−0.657813	+	0.753181i	$0.728518\pi$
$150$		−	15.8255i		−	1.29214i
$151$	−2.67405	+	3.01838i	−0.217611	+	0.245632i	−0.847172	−	0.531319i	$-0.821696\pi$
$151$	−2.67405	+	3.01838i	−0.217611	+	0.245632i	0.629561	+	0.776951i	$0.283235\pi$
$152$	2.22540	−	1.16798i	0.180504	−	0.0947356i
$153$	−0.384061	−	3.16303i	−0.0310495	−	0.255716i
$154$	−10.1218	−	19.2855i	−0.815638	−	1.55407i
$155$	−0.460262	−	3.79060i	−0.0369692	−	0.304468i
$156$	1.12301	+	0.612129i	0.0899128	+	0.0490096i
$157$	2.76498	−	22.7716i	0.220669	−	1.81738i	−0.289362	−	0.957220i	$-0.593443\pi$
$157$	2.76498	−	22.7716i	0.220669	−	1.81738i	0.510031	−	0.860156i	$-0.329634\pi$
$158$	−10.2891	+	3.90214i	−0.818556	+	0.310437i
$159$	−3.90997	−	2.05211i	−0.310081	−	0.162743i
$160$	−2.75344	+	7.26023i	−0.217679	+	0.573972i
$161$	−12.7975	−	24.3837i	−1.00859	−	1.92170i
$162$	−0.713124	−	1.35874i	−0.0560283	−	0.106753i
$163$	5.18796	+	21.0484i	0.406353	+	1.64864i	0.716233	+	0.697861i	$0.245865\pi$
$163$	5.18796	+	21.0484i	0.406353	+	1.64864i	−0.309880	+	0.950776i	$0.600289\pi$
$164$	1.86226	+	0.226119i	0.145418	+	0.0176569i
$165$	−8.88675	−	7.87297i	−0.691833	−	0.612910i
$166$	4.96963	+	7.19975i	0.385718	+	0.558809i
$167$	12.8993	+	4.89207i	0.998181	+	0.378560i	0.798953	−	0.601393i	$-0.205387\pi$
$167$	12.8993	+	4.89207i	0.998181	+	0.378560i	0.199228	+	0.979953i	$0.436157\pi$
$168$	−11.8110			−0.911235
$169$	−9.45458	−	8.92250i	−0.727275	−	0.686346i
$170$	19.1330			1.46743
$171$	−0.930792	−	0.353003i	−0.0711794	−	0.0269948i
$172$	−2.07755	−	3.00984i	−0.158411	−	0.229498i
$173$	−0.0319208	−	0.0282793i	−0.00242689	−	0.00215004i	0.661908	−	0.749585i	$-0.269747\pi$
$173$	−0.0319208	−	0.0282793i	−0.00242689	−	0.00215004i	−0.664335	+	0.747435i	$0.731285\pi$
$174$	0.244000	+	0.0296270i	0.0184976	+	0.00224602i
$175$	11.5461	+	46.8443i	0.872801	+	3.54109i
$176$	6.46277	+	12.3138i	0.487149	+	0.928186i
$177$	1.40933	+	2.68525i	0.105931	+	0.201836i
$178$	−6.58190	+	17.3550i	−0.493334	+	1.30082i
$179$	−4.60322	−	2.41596i	−0.344061	−	0.180577i	0.283838	−	0.958872i	$-0.408392\pi$
$179$	−4.60322	−	2.41596i	−0.344061	−	0.180577i	−0.627898	+	0.778295i	$0.716085\pi$
$180$	1.29793	−	0.492239i	0.0967417	−	0.0366893i
$181$	−1.04591	+	8.61386i	−0.0777420	+	0.640263i	0.900803	+	0.434229i	$0.142979\pi$
$181$	−1.04591	+	8.61386i	−0.0777420	+	0.640263i	−0.978545	+	0.206034i	$0.933944\pi$
$182$	−25.0306	−	6.58895i	−1.85539	−	0.488405i
$183$	−0.777452	−	6.40289i	−0.0574709	−	0.473316i
$184$	6.90647	+	13.1592i	0.509152	+	0.970108i
$185$	2.99230	+	24.6438i	0.219998	+	1.81185i
$186$	1.32585	−	0.695859i	0.0972159	−	0.0510228i
$187$	6.41047	−	7.23592i	0.468780	−	0.529143i
$188$			2.72061i			0.198421i
$189$	3.10221	+	3.50168i	0.225653	+	0.254709i
$190$	2.77798	−	5.29300i	0.201536	−	0.383994i
$191$	1.48973			0.107793			0.0538964	−	0.998547i	$-0.482836\pi$
$191$	1.48973			0.107793			0.0538964	+	0.998547i	$0.482836\pi$
$192$	6.12237			0.441844
$193$	9.84216	−	18.7527i	0.708455	−	1.34985i	−0.218931	−	0.975740i	$-0.570257\pi$
$193$	9.84216	−	18.7527i	0.708455	−	1.34985i	0.927386	−	0.374107i	$-0.122051\pi$
$194$	−21.4577	−	5.28885i	−1.54057	−	0.379717i
$195$	−14.0313	+	1.48008i	−1.00481	+	0.105991i
$196$	−5.12692	+	1.26367i	−0.366208	+	0.0902622i
$197$	−6.24008	+	25.3170i	−0.444588	+	1.80376i	0.137342	+	0.990524i	$0.456144\pi$
$197$	−6.24008	+	25.3170i	−0.444588	+	1.80376i	−0.581930	+	0.813239i	$0.697702\pi$
$198$	1.65094	−	4.35316i	0.117327	−	0.309366i
$199$	−0.428083	−	3.52558i	−0.0303460	−	0.249922i	−0.999986	−	0.00538311i	$-0.998286\pi$
$199$	−0.428083	−	3.52558i	−0.0303460	−	0.249922i	0.969639	−	0.244539i	$-0.0786366\pi$
$200$	−6.23109	−	25.2805i	−0.440604	−	1.78760i
$201$	−2.57964	+	10.4660i	−0.181954	+	0.738216i
$202$	−10.8374	−	7.48049i	−0.762514	−	0.526325i
$203$	−0.743871	+	0.0903223i	−0.0522095	+	0.00633938i
$204$	0.400799	+	1.05682i	0.0280615	+	0.0739922i
$205$	−18.3237	+	9.61703i	−1.27978	+	0.671683i
$206$	1.04496	+	4.23959i	0.0728061	+	0.295386i
$207$	2.08737	−	5.50394i	0.145082	−	0.382550i
$208$	15.9821	+	4.20704i	1.10816	+	0.291706i
$209$	−1.07101	−	2.82402i	−0.0740832	−	0.195341i
$210$	−23.1191	+	15.9579i	−1.59537	+	1.10120i
$211$	9.90075	−	8.77130i	0.681596	−	0.603841i	−0.249605	−	0.968348i	$-0.580301\pi$
$211$	9.90075	−	8.77130i	0.681596	−	0.603841i	0.931201	+	0.364507i	$0.118762\pi$
$212$	1.52090	+	0.374868i	0.104456	+	0.0257460i
$213$	−8.97029	−	3.40198i	−0.614634	−	0.233100i
$214$	−1.21320	+	2.31156i	−0.0829328	+	0.158015i
$215$	37.7226	+	14.3063i	2.57266	+	0.975681i
$216$	−1.67418	−	1.88975i	−0.113913	−	0.128582i
$217$	−3.41690	+	3.02711i	−0.231954	+	0.205493i
$218$	−2.72470	+	3.94741i	−0.184540	+	0.267353i
$219$	−10.7426	−	7.41509i	−0.725919	−	0.501065i
$220$	3.72917	+	1.95722i	0.251421	+	0.131956i
$221$	−1.20514	−	11.4248i	−0.0810664	−	0.768518i
$222$	−8.61972	+	4.52398i	−0.578518	+	0.303630i
$223$	−5.89260	−	0.715492i	−0.394598	−	0.0479129i	−0.0791669	−	0.996861i	$-0.525226\pi$
$223$	−5.89260	−	0.715492i	−0.394598	−	0.0479129i	−0.315431	+	0.948949i	$0.602149\pi$
$224$	9.01305	−	2.22152i	0.602210	−	0.148431i
$225$	−5.85846	+	8.48744i	−0.390564	+	0.565829i
$226$	−26.0113	+	17.9543i	−1.73024	+	1.19430i
$227$	2.94332	−	3.32232i	0.195355	−	0.220510i	−0.642669	−	0.766144i	$-0.722173\pi$
$227$	2.94332	−	3.32232i	0.195355	−	0.220510i	0.838023	+	0.545634i	$0.183711\pi$
$228$	0.350555	+	0.0425651i	0.0232161	+	0.00281894i
$229$	4.78836	−	19.4271i	0.316424	−	1.28378i	−0.570283	−	0.821449i	$-0.693166\pi$
$229$	4.78836	−	19.4271i	0.316424	−	1.28378i	0.886706	−	0.462333i	$-0.152988\pi$
$230$	31.2984	+	16.4267i	2.06376	+	1.08314i
$231$	−1.71085	+	14.0901i	−0.112566	+	0.927061i
$232$	0.401446	−	0.0487444i	0.0263562	−	0.00320023i
$233$	−8.57205	+	12.4188i	−0.561573	+	0.813580i	−0.996206	−	0.0870284i	$-0.972263\pi$
$233$	−8.57205	+	12.4188i	−0.561573	+	0.813580i	0.434632	+	0.900608i	$0.356878\pi$
$234$	−2.49380	−	4.93887i	−0.163025	−	0.322864i
$235$	−17.0488	−	24.6994i	−1.11214	−	1.61121i
$236$	−0.713365	−	0.805223i	−0.0464361	−	0.0524155i
$237$	6.96274	+	1.71616i	0.452279	+	0.111477i
$238$	−12.9935	−	18.8244i	−0.842246	−	1.22020i
$239$			22.9006i			1.48131i	0.671883	+	0.740657i	$0.265486\pi$
$239$			22.9006i			1.48131i	−0.671883	+	0.740657i	$0.734514\pi$
$240$	14.7615	−	10.1891i	0.952852	−	0.657706i
$241$	−3.51394	+	0.426670i	−0.226353	+	0.0274842i	−0.232927	−	0.972494i	$-0.574830\pi$
$241$	−3.51394	+	0.426670i	−0.226353	+	0.0274842i	0.00657434	+	0.999978i	$0.497907\pi$
$242$	−2.57529	+	0.976679i	−0.165546	+	0.0627833i
$243$	−0.120537	+	0.992709i	−0.00773243	+	0.0636823i
$244$	0.811334	+	2.13931i	0.0519404	+	0.136955i
$245$	38.6266	−	43.6004i	2.46776	−	2.78553i
$246$	−6.07415	−	5.38123i	−0.387274	−	0.343094i
$247$	−3.33558	−	1.32542i	−0.212238	−	0.0843343i
$248$	1.84400	−	1.63364i	0.117094	−	0.103736i
$249$		−	5.70106i		−	0.361290i
$250$	−23.8803	−	21.1561i	−1.51032	−	1.33803i
$251$	0.820412	−	0.202213i	0.0517839	−	0.0127636i	−0.213339	−	0.976978i	$-0.568434\pi$
$251$	0.820412	−	0.202213i	0.0517839	−	0.0127636i	0.265123	+	0.964215i	$0.414588\pi$
$252$	−1.36575	−	0.942706i	−0.0860339	−	0.0593849i
$253$	16.6989	−	6.33307i	1.04985	−	0.398156i
$254$	8.51200	−	3.22817i	0.534090	−	0.202554i
$255$	−10.2613	−	7.08287i	−0.642588	−	0.443547i
$256$	−8.02152	+	1.97713i	−0.501345	+	0.123570i
$257$	−20.2823	−	17.9686i	−1.26518	−	1.12085i	−0.987069	−	0.160298i	$-0.948755\pi$
$257$	−20.2823	−	17.9686i	−1.26518	−	1.12085i	−0.278107	−	0.960550i	$-0.589707\pi$
$258$			15.8206i			0.984947i
$259$	22.2142	−	19.6801i	1.38033	−	1.22286i
$260$	4.70709	−	1.70094i	0.291921	−	0.105488i
$261$	−0.119894	−	0.106216i	−0.00742123	−	0.00657463i
$262$	−16.3332	+	18.4363i	−1.00907	+	1.13900i
$263$	−8.70334	−	22.9488i	−0.536671	−	1.41508i	−0.879596	−	0.475722i	$-0.842187\pi$
$263$	−8.70334	−	22.9488i	−0.536671	−	1.41508i	0.342925	−	0.939363i	$-0.388582\pi$
$264$	0.923297	−	7.60403i	0.0568250	−	0.467996i
$265$	−16.1568	+	6.12747i	−0.992506	+	0.376408i
$266$	−7.09421	+	0.861393i	−0.434974	+	0.0528154i
$267$	9.95468	−	6.87122i	0.609216	−	0.420512i
$268$		−	3.82375i		−	0.233573i
$269$	6.83424	+	9.90110i	0.416691	+	0.603681i	0.973979	−	0.226638i	$-0.0727735\pi$
$269$	6.83424	+	9.90110i	0.416691	+	0.603681i	−0.557288	+	0.830319i	$0.688158\pi$
$270$	−5.83035	−	1.43705i	−0.354823	−	0.0874561i
$271$	15.7929	+	17.8265i	0.959349	+	1.08288i	0.996502	+	0.0835715i	$0.0266327\pi$
$271$	15.7929	+	17.8265i	0.959349	+	1.08288i	−0.0371529	+	0.999310i	$0.511829\pi$
$272$	8.29638	+	12.0194i	0.503042	+	0.728782i
$273$	10.9852	+	12.7999i	0.664852	+	0.774685i
$274$	11.8033	−	17.1001i	0.713066	−	1.03305i
$275$	−31.0615	+	3.77154i	−1.87308	+	0.227433i
$276$	−0.251695	+	2.07289i	−0.0151503	+	0.124774i
$277$	3.28113	+	1.72207i	0.197144	+	0.103469i	0.560407	−	0.828218i	$-0.310645\pi$
$277$	3.28113	+	1.72207i	0.197144	+	0.103469i	−0.363262	+	0.931687i	$0.618337\pi$
$278$	−7.84974	+	31.8477i	−0.470796	+	1.91010i
$279$	−0.968674	−	0.117618i	−0.0579930	−	0.00704163i
$280$	−30.6485	+	34.5950i	−1.83160	+	2.06745i
$281$	11.4477	−	7.90177i	0.682912	−	0.471380i	−0.175407	−	0.984496i	$-0.556124\pi$
$281$	11.4477	−	7.90177i	0.682912	−	0.471380i	0.858319	+	0.513116i	$0.171509\pi$
$282$	6.68549	−	9.68561i	0.398115	−	0.576770i
$283$	−4.95208	+	1.22058i	−0.294371	+	0.0725558i	−0.383735	−	0.923443i	$-0.625362\pi$
$283$	−4.95208	+	1.22058i	−0.294371	+	0.0725558i	0.0893647	+	0.995999i	$0.471516\pi$
$284$	3.37839	+	0.410211i	0.200471	+	0.0243415i
$285$	−3.44930	+	1.81033i	−0.204319	+	0.107235i
$286$	6.19876	−	15.5999i	0.366540	−	0.922444i
$287$	21.9059	+	11.4971i	1.29307	+	0.678653i
$288$	1.63302	+	1.12719i	0.0962268	+	0.0664206i
$289$	−3.88996	+	5.63559i	−0.228821	+	0.331505i
$290$	0.719941	−	0.637812i	0.0422764	−	0.0374536i
$291$	9.55021	+	10.7800i	0.559843	+	0.631932i
$292$	4.32951	+	1.64197i	0.253365	+	0.0960888i
$293$	−0.966818	+	1.84212i	−0.0564821	+	0.107618i	−0.912061	−	0.410055i	$-0.865509\pi$
$293$	−0.966818	+	1.84212i	−0.0564821	+	0.107618i	0.855578	+	0.517673i	$0.173202\pi$
$294$	21.3576	+	8.09986i	1.24560	+	0.472394i
$295$	11.5223	+	2.84000i	0.670857	+	0.165351i
$296$	−11.9884	+	10.6208i	−0.696811	+	0.617321i
$297$	−2.49693	+	1.72350i	−0.144886	+	0.100008i
$298$	1.69445	+	4.46791i	0.0981571	+	0.258819i
$299$	7.83743	−	19.7239i	0.453250	−	1.14066i
$300$	1.29727	−	3.42062i	0.0748980	−	0.197490i
$301$	−11.5425	−	46.8299i	−0.665300	−	2.69923i
$302$	−5.47915	+	2.87568i	−0.315290	+	0.165477i
$303$	3.04303	+	8.02381i	0.174817	+	0.460956i
$304$	4.52965	−	0.549999i	0.259793	−	0.0315446i
$305$	−20.7719	−	14.3378i	−1.18940	−	0.820980i
$306$	1.17010	−	4.74728i	0.0668902	−	0.271384i
$307$	1.38474	+	5.61813i	0.0790315	+	0.320643i	0.997130	−	0.0757090i	$-0.0241220\pi$
$307$	1.38474	+	5.61813i	0.0790315	+	0.320643i	−0.918098	+	0.396352i	$0.870276\pi$
$308$	−0.606893	−	4.99822i	−0.0345810	−	0.284800i
$309$	1.00903	−	2.66059i	0.0574017	−	0.151356i
$310$	1.40226	−	5.68919i	0.0796429	−	0.323124i
$311$	0.402311	−	0.0991608i	0.0228130	−	0.00562289i	−0.227893	−	0.973686i	$-0.573184\pi$
$311$	0.402311	−	0.0991608i	0.0228130	−	0.00562289i	0.250706	+	0.968063i	$0.419337\pi$
$312$	−5.92837	−	6.90774i	−0.335628	−	0.391074i
$313$	−24.1080	−	5.94208i	−1.36266	−	0.335866i	−0.510830	−	0.859682i	$-0.670662\pi$
$313$	−24.1080	−	5.94208i	−1.36266	−	0.335866i	−0.851832	+	0.523816i	$0.824508\pi$
$314$	16.3583	−	31.1681i	0.923151	−	1.75892i
$315$	18.3066			1.03146
$316$	−2.54383			−0.143102
$317$	1.14253	−	2.17691i	0.0641710	−	0.122268i	−0.851258	−	0.524748i	$-0.824160\pi$
$317$	1.14253	−	2.17691i	0.0641710	−	0.122268i	0.915429	+	0.402480i	$0.131852\pi$
$318$	−4.49336	−	5.07195i	−0.251975	−	0.284421i
$319$		−	0.485974i		−	0.0272093i
$320$	15.8871	−	17.9328i	0.888114	−	1.00247i
$321$	1.50638	−	0.790610i	0.0840781	−	0.0441276i
$322$	−5.09357	−	41.9493i	−0.283854	−	2.33775i
$323$	−1.47404	−	2.80855i	−0.0820177	−	0.156272i
$324$	−0.0427583	−	0.352146i	−0.00237546	−	0.0195637i
$325$	−21.6019	+	30.2658i	−1.19826	+	1.67884i
$326$	−4.00973	+	33.0231i	−0.222079	+	1.82898i
$327$	2.92260	−	1.10840i	0.161620	−	0.0612945i
$328$	−11.8220	−	6.20466i	−0.652761	−	0.342595i
$329$	−12.7229	+	33.5476i	−0.701438	+	1.84954i
$330$	−8.46662	−	16.1318i	−0.466072	−	0.888026i
$331$	4.82902	+	9.20093i	0.265427	+	0.505729i	0.981296	−	0.192506i	$-0.0616615\pi$
$331$	4.82902	+	9.20093i	0.265427	+	0.505729i	−0.715869	+	0.698235i	$0.753969\pi$
$332$	0.483980	+	1.96358i	0.0265618	+	0.107766i
$333$	6.29763	+	0.764671i	0.345108	+	0.0419037i
$334$	15.8459	+	14.0382i	0.867049	+	0.768139i
$335$	23.9616	+	34.7144i	1.30916	+	1.89665i
$336$	−20.0496	−	7.60382i	−1.09380	−	0.414823i
$337$	−2.90834			−0.158428			−0.0792138	−	0.996858i	$-0.525241\pi$
$337$	−2.90834			−0.158428			−0.0792138	+	0.996858i	$0.525241\pi$
$338$	−8.71024	−	17.9466i	−0.473774	−	0.976168i
$339$	20.5968			1.11866
$340$	4.13553	+	1.56840i	0.224281	+	0.0850584i
$341$	−1.68178	−	2.43647i	−0.0910733	−	0.131942i
$342$	−1.14341	−	1.01297i	−0.0618286	−	0.0547753i
$343$	−36.6207	−	4.44656i	−1.97733	−	0.240092i
$344$	6.22917	+	25.2727i	0.335854	+	1.36262i
$345$	−10.7048	−	20.3963i	−0.576328	−	1.09810i
$346$	−0.0304117	−	0.0579446i	−0.00163494	−	0.00311512i
$347$	0.871994	−	2.29926i	0.0468111	−	0.123431i	−0.909572	−	0.415547i	$-0.863590\pi$
$347$	0.871994	−	2.29926i	0.0468111	−	0.123431i	0.956383	+	0.292116i	$0.0943594\pi$
$348$	0.0503113	+	0.0264054i	0.00269697	+	0.00141548i
$349$	17.8747	−	6.77899i	0.956813	−	0.362871i	0.173733	−	0.984793i	$-0.444417\pi$
$349$	17.8747	−	6.77899i	0.956813	−	0.362871i	0.783080	+	0.621922i	$0.213648\pi$
$350$	−8.92387	+	73.4947i	−0.477001	+	3.92846i
$351$	−0.490865	+	3.57198i	−0.0262004	+	0.190658i
$352$	0.725663	+	5.97637i	0.0386780	+	0.318542i
$353$	1.86850	+	3.56013i	0.0994502	+	0.189487i	0.930098	−	0.367312i	$-0.119722\pi$
$353$	1.86850	+	3.56013i	0.0994502	+	0.189487i	−0.830648	+	0.556799i	$0.812030\pi$
$354$	0.560928	+	4.61966i	0.0298130	+	0.245532i
$355$	−33.2418	+	17.4466i	−1.76429	+	0.925972i
$356$	−2.84532	+	3.21170i	−0.150801	+	0.170220i
$357$			14.9059i			0.788905i
$358$	−5.29004	−	5.97122i	−0.279587	−	0.315589i
$359$	5.75809	−	10.9711i	0.303900	−	0.579034i	−0.684837	−	0.728697i	$-0.740126\pi$
$359$	5.75809	−	10.9711i	0.303900	−	0.579034i	0.988737	+	0.149663i	$0.0478188\pi$
$360$	−9.87956			−0.520699
$361$	18.0090			0.947843
$362$	−6.18787	+	11.7900i	−0.325227	+	0.619668i
$363$	1.74273	+	0.429544i	0.0914695	+	0.0225452i
$364$	−4.87018	−	3.47604i	−0.255267	−	0.182194i
$365$	−49.5955	+	12.2242i	−2.59595	+	0.639843i
$366$	2.36863	−	9.60989i	0.123810	−	0.502317i
$367$	−8.08750	+	21.3250i	−0.422164	+	1.11316i	0.540235	+	0.841514i	$0.318335\pi$
$367$	−8.08750	+	21.3250i	−0.422164	+	1.11316i	−0.962399	+	0.271641i	$0.912434\pi$
$368$	3.25225	+	26.7847i	0.169535	+	1.39625i
$369$	1.26557	+	5.13464i	0.0658832	+	0.267299i
$370$	−9.11649	+	36.9871i	−0.473944	+	1.92287i
$371$	17.0010	+	11.7350i	0.882650	+	0.609250i
$372$	0.343620	−	0.0417230i	0.0178159	−	0.00216324i
$373$	−6.92274	−	18.2538i	−0.358446	−	0.945144i	−0.986026	−	0.166592i	$-0.946724\pi$
$373$	−6.92274	−	18.2538i	−0.358446	−	0.945144i	0.627580	−	0.778552i	$-0.284045\pi$
$374$	13.1351	−	6.89384i	0.679200	−	0.356472i
$375$	4.97556	+	20.1866i	0.256937	+	1.04243i
$376$	6.86621	−	18.1047i	0.354098	−	0.933679i
$377$	−0.426203	−	0.389723i	−0.0219506	−	0.0200718i
$378$	2.54562	+	6.71224i	0.130932	+	0.345241i
$379$	−10.8717	+	7.50423i	−0.558444	+	0.385466i	−0.813592	−	0.581436i	$-0.802491\pi$
$379$	−10.8717	+	7.50423i	−0.558444	+	0.385466i	0.255148	+	0.966902i	$0.417876\pi$
$380$	1.03434	−	0.916344i	0.0530604	−	0.0470074i
$381$	−5.76016	−	1.41975i	−0.295102	−	0.0727361i
$382$	2.13745	+	0.810628i	0.109362	+	0.0414753i
$383$	1.03665	−	1.97517i	0.0529702	−	0.100926i	−0.857532	−	0.514431i	$-0.828003\pi$
$383$	1.03665	−	1.97517i	0.0529702	−	0.100926i	0.910502	+	0.413505i	$0.135695\pi$
$384$	12.4950	+	4.73873i	0.637633	+	0.241822i
$385$	36.8313	+	41.5739i	1.87710	+	2.11880i
$386$	24.3257	−	21.5507i	1.23814	−	1.09690i
$387$	5.85666	−	8.48483i	0.297711	−	0.431308i
$388$	−4.20447	−	2.90214i	−0.213450	−	0.147334i
$389$	−11.6289	−	6.10331i	−0.589608	−	0.309450i	0.143406	−	0.989664i	$-0.454195\pi$
$389$	−11.6289	−	6.10331i	−0.589608	−	0.309450i	−0.733014	+	0.680214i	$0.761887\pi$
$390$	−20.9375	−	5.51148i	−1.06021	−	0.279085i
$391$	16.6074	−	8.71626i	0.839874	−	0.440800i
$392$	37.3071	+	4.52990i	1.88429	+	0.228795i
$393$	15.5847	−	3.84129i	0.786145	−	0.193767i
$394$	−22.7294	+	32.9292i	−1.14509	+	1.65895i
$395$	23.0945	−	15.9410i	1.16201	−	0.802078i
$396$	0.713689	−	0.805589i	0.0358642	−	0.0404824i
$397$	−23.3136	−	2.83078i	−1.17008	−	0.142073i	−0.487658	−	0.873035i	$-0.662149\pi$
$397$	−23.3136	−	2.83078i	−1.17008	−	0.142073i	−0.682419	+	0.730962i	$0.739072\pi$
$398$	1.30422	−	5.29143i	0.0653747	−	0.265235i
$399$	4.12362	+	2.16424i	0.206439	+	0.108348i
$400$	5.69789	−	46.9264i	0.284895	−	2.34632i
$401$	−5.76740	+	0.700289i	−0.288010	+	0.0349708i	−0.263267	−	0.964723i	$-0.584800\pi$
$401$	−5.76740	+	0.700289i	−0.288010	+	0.0349708i	−0.0247433	+	0.999694i	$0.507877\pi$
$402$	−9.39630	+	13.6129i	−0.468645	+	0.678949i
$403$	−3.48550	−	0.478981i	−0.173625	−	0.0238597i
$404$	−1.72926	−	2.50526i	−0.0860339	−	0.124642i
$405$	2.59492	+	2.92906i	0.128943	+	0.145546i
$406$	−1.11645	−	0.275181i	−0.0554086	−	0.0136570i
$407$	10.9337	+	15.8402i	0.541964	+	0.785171i
$408$		−	8.04430i		−	0.398252i
$409$	−6.40330	+	4.41988i	−0.316623	+	0.218549i	−0.715767	−	0.698339i	$-0.753923\pi$
$409$	−6.40330	+	4.41988i	−0.316623	+	0.218549i	0.399144	+	0.916888i	$0.369307\pi$
$410$	−31.5239	+	3.82769i	−1.55685	+	0.189036i
$411$	−12.6606	+	4.80155i	−0.624503	+	0.236843i
$412$	−0.121669	+	1.00203i	−0.00599420	+	0.0493666i
$413$	−5.03083	−	13.2652i	−0.247551	−	0.652739i
$414$	5.98990	−	6.76119i	0.294387	−	0.332295i
$415$	−16.6987	−	14.7938i	−0.819709	−	0.726199i
$416$	5.82327	+	4.15630i	0.285509	+	0.203779i
$417$	15.9997	−	14.1745i	0.783508	−	0.694128i
$418$		−	4.63467i		−	0.226689i
$419$	0.649200	+	0.575141i	0.0317155	+	0.0280975i	0.678832	−	0.734294i	$-0.262487\pi$
$419$	0.649200	+	0.575141i	0.0317155	+	0.0280975i	−0.647116	+	0.762391i	$0.724025\pi$
$420$	−6.30525	+	1.55410i	−0.307665	+	0.0758325i
$421$	−8.62065	−	5.95040i	−0.420145	−	0.290005i	0.339174	−	0.940724i	$-0.389852\pi$
$421$	−8.62065	−	5.95040i	−0.420145	−	0.290005i	−0.759319	+	0.650719i	$0.774468\pi$
$422$	18.9784	−	7.19756i	0.923855	−	0.350372i
$423$	−7.17107	+	2.71963i	−0.348669	+	0.132233i
$424$	−9.17498	−	6.33303i	−0.445576	−	0.307559i
$425$	−31.9051	+	7.86390i	−1.54762	+	0.381455i
$426$	−11.0194	−	9.76230i	−0.533889	−	0.472985i
$427$			30.1740i			1.46022i
$428$	−0.451718	+	0.400187i	−0.0218346	+	0.0193438i
$429$	−9.09946	+	6.07176i	−0.439326	+	0.293147i
$430$	46.3395	+	41.0532i	2.23469	+	1.97976i
$431$	19.5624	−	22.0814i	0.942289	−	1.06362i	−0.0555853	−	0.998454i	$-0.517702\pi$
$431$	19.5624	−	22.0814i	0.942289	−	1.06362i	0.997874	−	0.0651704i	$-0.0207591\pi$
$432$	−1.62538	−	4.28577i	−0.0782010	−	0.206199i
$433$	0.663307	−	5.46283i	0.0318765	−	0.262527i	−0.968054	−	0.250742i	$-0.919326\pi$
$433$	0.663307	−	5.46283i	0.0318765	−	0.262527i	0.999931	−	0.0117851i	$-0.00375139\pi$
$434$	−6.54973	+	2.48399i	−0.314397	+	0.119235i
$435$	−0.622229	+	0.0755523i	−0.0298336	+	0.00362245i
$436$	−0.912521	+	0.629868i	−0.0437018	+	0.0301652i
$437$		−	5.85987i		−	0.280316i
$438$	−11.3786	−	16.4847i	−0.543689	−	0.787669i
$439$	11.7060	+	2.88527i	0.558697	+	0.137706i	0.508545	−	0.861035i	$-0.330183\pi$
$439$	11.7060	+	2.88527i	0.558697	+	0.137706i	0.0501514	+	0.998742i	$0.484030\pi$
$440$	−19.8768	−	22.4363i	−0.947589	−	1.06961i
$441$	−8.45591	−	12.2505i	−0.402662	−	0.583357i
$442$	4.48765	−	17.0481i	0.213456	−	0.810894i
$443$	16.0763	−	23.2906i	0.763809	−	1.10657i	−0.227340	−	0.973815i	$-0.573003\pi$
$443$	16.0763	−	23.2906i	0.763809	−	1.10657i	0.991149	−	0.132753i	$-0.0423816\pi$
$444$	−2.23397	+	0.271254i	−0.106020	+	0.0128731i
$445$	5.70539	−	46.9881i	0.270461	−	2.22745i
$446$	−8.06535	−	4.23302i	−0.381905	−	0.200439i
$447$	0.745222	−	3.02348i	0.0352478	−	0.143006i
$448$	−28.4328	−	3.45236i	−1.34332	−	0.163109i
$449$	1.28348	−	1.44875i	0.0605713	−	0.0683709i	−0.717444	−	0.696616i	$-0.754688\pi$
$449$	1.28348	−	1.44875i	0.0605713	−	0.0683709i	0.778015	+	0.628245i	$0.216227\pi$
$450$	−13.0241	+	8.98988i	−0.613962	+	0.423787i
$451$	−9.11442	+	13.2045i	−0.429181	+	0.621776i
$452$	−7.09404	+	1.74852i	−0.333676	+	0.0822436i
$453$	4.00311	+	0.486065i	0.188082	+	0.0228373i
$454$	6.03088	−	3.16525i	0.283043	−	0.148553i
$455$	65.9973	+	1.03856i	3.09400	+	0.0486883i
$456$	−2.22540	−	1.16798i	−0.104214	−	0.0546956i
$457$	0.267429	+	0.184593i	0.0125098	+	0.00863490i	0.574303	−	0.818643i	$-0.305273\pi$
$457$	0.267429	+	0.184593i	0.0125098	+	0.00863490i	−0.561793	+	0.827278i	$0.689888\pi$
$458$	17.4415	−	25.2684i	0.814989	−	1.18071i
$459$	−2.38495	+	2.11288i	−0.111320	+	0.0986208i
$460$	5.41851	+	6.11623i	0.252639	+	0.285171i
$461$	−21.2371	−	8.05416i	−0.989109	−	0.375120i	−0.193613	−	0.981078i	$-0.562021\pi$
$461$	−21.2371	−	8.05416i	−0.989109	−	0.375120i	−0.795496	+	0.605958i	$0.792790\pi$
$462$	−10.1218	+	19.2855i	−0.470909	+	0.897241i
$463$	7.19912	+	2.73026i	0.334571	+	0.126886i	0.516169	−	0.856487i	$-0.327358\pi$
$463$	7.19912	+	2.73026i	0.334571	+	0.126886i	−0.181598	+	0.983373i	$0.558127\pi$
$464$	0.712854	+	0.175703i	0.0330934	+	0.00815680i
$465$	−2.85814	+	2.53210i	−0.132543	+	0.117423i
$466$	−19.0567	+	13.1539i	−0.882787	+	0.609344i
$467$	−3.43303	−	9.05215i	−0.158862	−	0.418884i	0.831826	−	0.555036i	$-0.187296\pi$
$467$	−3.43303	−	9.05215i	−0.158862	−	0.418884i	−0.990688	+	0.136152i	$0.956526\pi$
$468$	−0.134170	−	1.27195i	−0.00620203	−	0.0587959i
$469$	17.8818	−	47.1504i	0.825704	−	2.17720i
$470$	−11.0214	−	44.7156i	−0.508380	−	2.06258i
$471$	−20.3114	+	10.6602i	−0.935899	+	0.491198i
$472$	2.71500	+	7.15886i	0.124968	+	0.329513i
$473$	31.0519	−	3.77039i	1.42777	−	0.173363i
$474$	9.05627	+	6.25109i	0.415968	+	0.287122i
$475$	−2.45691	+	9.96809i	−0.112731	+	0.457367i
$476$	−1.26541	−	5.13397i	−0.0579999	−	0.235315i
$477$	0.532262	+	4.38358i	0.0243706	+	0.200710i
$478$	−12.4613	+	32.8576i	−0.569965	+	1.50287i
$479$	−2.03078	+	8.23922i	−0.0927889	+	0.376459i	−0.998916	−	0.0465458i	$-0.985179\pi$
$479$	−2.03078	+	8.23922i	−0.0927889	+	0.376459i	0.906127	+	0.423005i	$0.139025\pi$
$480$	7.53919	−	1.85824i	0.344115	−	0.0848168i
$481$	22.6602	+	3.11399i	1.03322	+	0.141986i
$482$	−5.27396	−	1.29991i	−0.240222	−	0.0592094i
$483$	−12.7975	+	24.3837i	−0.582309	+	1.10950i
$484$	−0.636703			−0.0289411
$485$	56.3572			2.55905
$486$	−0.713124	+	1.35874i	−0.0323480	+	0.0616339i
$487$	−2.53237	−	2.85845i	−0.114752	−	0.129529i	0.688327	−	0.725400i	$-0.258345\pi$
$487$	−2.53237	−	2.85845i	−0.114752	−	0.129529i	−0.803080	+	0.595871i	$0.796807\pi$
$488$		−	16.2840i		−	0.737143i
$489$	14.3754	−	16.2265i	0.650077	−	0.733786i
$490$	79.1462	−	41.5392i	3.57546	−	1.87655i
$491$	−3.14401	−	25.8933i	−0.141887	−	1.16855i	−0.873499	−	0.486825i	$-0.838155\pi$
$491$	−3.14401	−	25.8933i	−0.141887	−	1.16855i	0.731612	−	0.681721i	$-0.238768\pi$
$492$	−0.871790	−	1.66106i	−0.0393033	−	0.0748862i
$493$	−0.0615175	−	0.506642i	−0.00277061	−	0.0228180i
$494$	−4.06465	−	3.71674i	−0.182877	−	0.167224i
$495$	−1.43108	+	11.7860i	−0.0643223	+	0.529742i
$496$	4.18201	−	1.58603i	0.187778	−	0.0712146i
$497$	39.7404	+	20.8574i	1.78260	+	0.935581i
$498$	3.10221	−	8.17985i	0.139013	−	0.366548i
$499$	−7.34322	−	13.9913i	−0.328728	−	0.626338i	0.663862	−	0.747855i	$-0.268916\pi$
$499$	−7.34322	−	13.9913i	−0.328728	−	0.626338i	−0.992589	+	0.121517i	$0.961224\pi$
$500$	−3.42741	−	6.53038i	−0.153278	−	0.292048i
$501$	−3.30156	−	13.3950i	−0.147503	−	0.598443i
$502$	1.28716	+	0.156289i	0.0574486	+	0.00697553i
$503$	0.732770	+	0.649178i	0.0326726	+	0.0289454i	0.679301	−	0.733860i	$-0.262283\pi$
$503$	0.732770	+	0.649178i	0.0326726	+	0.0289454i	−0.646628	+	0.762805i	$0.723822\pi$
$504$	6.70939	+	9.72023i	0.298860	+	0.432973i
$505$	31.3986	+	11.9079i	1.39722	+	0.529896i
$506$	27.4056			1.21833
$507$	−1.97226	+	12.8495i	−0.0875913	+	0.570667i
$508$	2.10447			0.0933707
$509$	8.21930	+	3.11717i	0.364314	+	0.138166i	0.529967	−	0.848018i	$-0.322204\pi$
$509$	8.21930	+	3.11717i	0.364314	+	0.138166i	−0.165654	+	0.986184i	$0.552973\pi$
$510$	−10.8688	−	15.7461i	−0.481277	−	0.697250i
$511$	45.7082	+	40.4940i	2.02201	+	1.79135i
$512$	13.9469	+	1.69345i	0.616370	+	0.0748408i
$513$	0.238234	+	0.966555i	0.0105183	+	0.0426745i
$514$	−19.3234	−	36.8177i	−0.852320	−	1.62396i
$515$	−5.17469	−	9.85954i	−0.228024	−	0.434463i
$516$	−1.29687	+	3.41957i	−0.0570916	+	0.150538i
$517$	−20.6038	−	10.8137i	−0.906152	−	0.475585i
$518$	42.5817	−	16.1491i	1.87093	−	0.709552i
$519$	−0.00514037	+	0.0423348i	−0.000225637	+	0.00185829i
$520$	−35.6169	−	0.560479i	−1.56190	−	0.0245787i
$521$	3.23792	+	26.6666i	0.141856	+	1.16829i	0.873578	+	0.486684i	$0.161794\pi$
$521$	3.23792	+	26.6666i	0.141856	+	1.16829i	−0.731722	+	0.681603i	$0.761283\pi$
$522$	−0.114226	−	0.217639i	−0.00499951	−	0.00952578i
$523$	3.19775	+	26.3359i	0.139828	+	1.15159i	0.878575	+	0.477605i	$0.158495\pi$
$523$	3.19775	+	26.3359i	0.139828	+	1.15159i	−0.738747	+	0.673983i	$0.764582\pi$
$524$	−5.04166	+	2.64607i	−0.220246	+	0.115594i
$525$	31.9932	−	36.1128i	1.39630	−	1.57609i
$526$		−	37.6627i		−	1.64217i
$527$	−2.06173	−	2.32721i	−0.0898102	−	0.101375i
$528$	6.46277	−	12.3138i	0.281256	−	0.535888i
$529$	11.6505			0.506542
$530$	−26.5160			−1.15178
$531$	1.40933	−	2.68525i	0.0611596	−	0.116530i
$532$	−1.60400	−	0.395351i	−0.0695424	−	0.0171407i
$533$	4.27123	+	18.5827i	0.185008	+	0.804906i
$534$	18.0219	−	4.44199i	0.779883	−	0.192224i
$535$	1.59320	−	6.46386i	0.0688799	−	0.279457i
$536$	−9.65029	+	25.4457i	−0.416829	+	1.09909i
$537$	0.626634	+	5.16079i	0.0270412	+	0.222705i
$538$	4.41809	+	17.9249i	0.190477	+	0.772796i
$539$	10.8081	−	43.8501i	0.465536	−	1.88876i
$540$	−1.14241	−	0.788549i	−0.0491615	−	0.0339338i
$541$	−12.4333	+	1.50968i	−0.534550	+	0.0649061i	−0.383361	−	0.923599i	$-0.625233\pi$
$541$	−12.4333	+	1.50968i	−0.534550	+	0.0649061i	−0.151189	+	0.988505i	$0.548310\pi$
$542$	12.9593	+	34.1710i	0.556651	+	1.46777i
$543$	7.68321	−	4.03246i	0.329718	−	0.173049i
$544$	1.51305	+	6.13868i	0.0648715	+	0.263194i
$545$	4.33736	−	11.4367i	0.185792	−	0.489894i
$546$	8.79643	+	24.3428i	0.376452	+	1.04177i
$547$	6.26663	+	16.5237i	0.267942	+	0.706504i	0.999689	+	0.0249283i	$0.00793574\pi$
$547$	6.26663	+	16.5237i	0.267942	+	0.706504i	−0.731748	+	0.681576i	$0.761295\pi$
$548$	3.95302	−	2.72857i	0.168864	−	0.116559i
$549$	−4.82784	+	4.27709i	−0.206047	+	0.182542i
$550$	−46.6191	−	11.4906i	−1.98785	−	0.489960i
$551$	−0.149091	−	0.0565427i	−0.00635148	−	0.00240880i
$552$	6.90647	−	13.1592i	0.293959	−	0.560092i
$553$	−31.3678	−	11.8962i	−1.33389	−	0.505880i
$554$	3.77070	+	4.25624i	0.160202	+	0.180830i
$555$	18.5816	−	16.4619i	0.788746	−	0.698768i
$556$	−4.30737	+	6.24030i	−0.182673	+	0.264648i
$557$	9.01113	+	6.21993i	0.381814	+	0.263547i	0.743477	−	0.668762i	$-0.233175\pi$
$557$	9.01113	+	6.21993i	0.381814	+	0.263547i	−0.361663	+	0.932309i	$0.617791\pi$
$558$	−1.32585	−	0.695859i	−0.0561276	−	0.0294580i
$559$	21.5952	−	30.2565i	0.913380	−	1.27971i
$560$	−74.2993	+	38.9953i	−3.13972	+	1.64785i
$561$	−9.59661	−	1.16524i	−0.405169	−	0.0491964i
$562$	20.7248	−	5.10821i	0.874223	−	0.215477i
$563$	−15.2577	+	22.1046i	−0.643035	+	0.931597i	−0.999997	−	0.00252231i	$-0.999197\pi$
$563$	−15.2577	+	22.1046i	−0.643035	+	0.931597i	0.356962	+	0.934119i	$0.383813\pi$
$564$	2.23901	−	1.54548i	0.0942795	−	0.0650765i
$565$	53.4471	−	60.3293i	2.24853	−	2.53807i
$566$	−7.76939	−	0.943375i	−0.326572	−	0.0396530i
$567$	1.11956	−	4.54225i	0.0470173	−	0.190757i
$568$	−21.4468	−	11.2561i	−0.899886	−	0.472297i
$569$	2.61213	−	21.5128i	0.109506	−	0.901864i	−0.829629	−	0.558315i	$-0.811448\pi$
$569$	2.61213	−	21.5128i	0.109506	−	0.901864i	0.939135	−	0.343549i	$-0.111629\pi$
$570$	−5.93412	+	0.720533i	−0.248553	+	0.0301798i
$571$	0.507470	−	0.735197i	0.0212370	−	0.0307670i	−0.812222	−	0.583349i	$-0.801742\pi$
$571$	0.507470	−	0.735197i	0.0212370	−	0.0307670i	0.833459	+	0.552582i	$0.186357\pi$
$572$	2.61863	−	2.86374i	0.109490	−	0.119739i
$573$	−0.846261	−	1.22602i	−0.0353530	−	0.0512177i
$574$	25.1744	+	28.4160i	1.05076	+	1.18606i
$575$	−58.9431	−	14.5282i	−2.45810	−	0.605867i
$576$	−3.47790	−	5.03861i	−0.144913	−	0.209942i
$577$			4.65212i			0.193670i	0.995300	+	0.0968351i	$0.0308720\pi$
$577$			4.65212i			0.193670i	−0.995300	+	0.0968351i	$0.969128\pi$
$578$	−8.64789	+	5.96920i	−0.359705	+	0.248286i
$579$	−21.0241	+	2.55279i	−0.873733	+	0.106090i
$580$	0.207897	−	0.0788449i	0.00863245	−	0.00327386i
$581$	−3.21479	+	26.4762i	−0.133372	+	1.09842i
$582$	7.83672	+	20.6637i	0.324843	+	0.856540i
$583$	−8.88413	+	10.0281i	−0.367943	+	0.415322i
$584$	−24.6674	−	21.8534i	−1.02075	−	0.904302i
$585$	9.18879	+	10.7068i	0.379910	+	0.442671i
$586$	−2.38957	+	2.11697i	−0.0987121	+	0.0874513i
$587$			27.4945i			1.13482i	0.823436	+	0.567409i	$0.192054\pi$
$587$			27.4945i			1.13482i	−0.823436	+	0.567409i	$0.807946\pi$
$588$	3.95240	+	3.50152i	0.162994	+	0.144400i
$589$	−0.943154	+	0.232467i	−0.0388620	+	0.00957862i
$590$	14.9868	+	10.3447i	0.616998	+	0.425883i
$591$	24.3803	−	9.24622i	1.00287	−	0.380339i
$592$	−27.1884	+	10.3112i	−1.11744	+	0.423788i
$593$	−29.8147	−	20.5796i	−1.22434	−	0.845104i	−0.232505	−	0.972595i	$-0.574692\pi$
$593$	−29.8147	−	20.5796i	−1.22434	−	0.845104i	−0.991840	+	0.127491i	$0.959308\pi$
$594$	−4.52042	+	1.11418i	−0.185475	+	0.0457155i
$595$	43.6604	+	38.6797i	1.78990	+	1.58571i
$596$			1.10463i			0.0452472i
$597$	−2.65832	+	2.35507i	−0.108798	+	0.0963864i
$598$	21.9778	−	24.0350i	0.898738	−	0.982864i
$599$	15.9104	+	14.0954i	0.650083	+	0.575923i	0.922377	−	0.386291i	$-0.126244\pi$
$599$	15.9104	+	14.0954i	0.650083	+	0.575923i	−0.272294	+	0.962214i	$0.587782\pi$
$600$	−17.2658	+	19.4891i	−0.704873	+	0.795637i
$601$	13.0941	+	34.5264i	0.534121	+	1.40836i	0.882190	+	0.470893i	$0.156068\pi$
$601$	13.0941	+	34.5264i	0.534121	+	1.40836i	−0.348069	+	0.937469i	$0.613162\pi$
$602$	8.92113	−	73.4721i	0.363598	−	2.99450i
$603$	10.0788	−	3.82237i	0.410439	−	0.155659i
$604$	−1.42003	+	0.172423i	−0.0577803	+	0.00701580i
$605$	5.78040	−	3.98992i	0.235007	−	0.162213i
$606$			13.1684i			0.534929i
$607$	−7.81341	−	11.3197i	−0.317136	−	0.459451i	0.631703	−	0.775211i	$-0.282356\pi$
$607$	−7.81341	−	11.3197i	−0.317136	−	0.459451i	−0.948839	+	0.315759i	$0.897741\pi$
$608$	1.91791	+	0.472722i	0.0777814	+	0.0191714i
$609$	0.496901	+	0.560885i	0.0201354	+	0.0227282i
$610$	−22.0016	−	31.8748i	−0.890817	−	1.29057i
$611$	−26.0068	+	9.39772i	−1.05212	+	0.380191i
$612$	0.642066	−	0.930193i	0.0259540	−	0.0376008i
$613$	12.0174	−	1.45917i	0.485378	−	0.0589355i	0.125810	−	0.992054i	$-0.459847\pi$
$613$	12.0174	−	1.45917i	0.485378	−	0.0589355i	0.359568	+	0.933119i	$0.382924\pi$
$614$	−1.07026	+	8.81436i	−0.0431921	+	0.355719i
$615$	18.3237	+	9.61703i	0.738884	+	0.387796i
$616$	−8.57573	+	34.7931i	−0.345526	+	1.40185i
$617$	−27.4232	−	3.32979i	−1.10402	−	0.134052i	−0.451826	−	0.892106i	$-0.649227\pi$
$617$	−27.4232	−	3.32979i	−1.10402	−	0.134052i	−0.652192	+	0.758054i	$0.726150\pi$
$618$	2.89550	−	3.26835i	0.116474	−	0.131472i
$619$	−26.4336	+	18.2458i	−1.06246	+	0.733362i	−0.965098	−	0.261888i	$-0.915655\pi$
$619$	−26.4336	+	18.2458i	−1.06246	+	0.733362i	−0.0973593	+	0.995249i	$0.531040\pi$
$620$	0.769458	−	1.11475i	0.0309022	−	0.0447695i
$621$	−5.71542	+	1.40872i	−0.229352	+	0.0565301i
$622$	0.631192	+	0.0766406i	0.0253085	+	0.00307301i
$623$	−50.1050	+	26.2971i	−2.00741	+	1.05357i
$624$	−5.61652	−	15.5429i	−0.224841	−	0.622212i
$625$	26.3805	+	13.8456i	1.05522	+	0.553822i
$626$	−31.3566	−	21.6439i	−1.25326	−	0.865065i
$627$	−1.71572	+	2.48565i	−0.0685192	+	0.0992672i
$628$	6.09076	−	5.39594i	0.243048	−	0.215321i
$629$	13.4039	+	15.1299i	0.534448	+	0.603267i
$630$	26.2662	+	9.96147i	1.04647	+	0.396875i
$631$	11.1750	−	21.2922i	0.444869	−	0.847628i	−0.555006	−	0.831846i	$-0.687284\pi$
$631$	11.1750	−	21.2922i	0.444869	−	0.847628i	0.999875	−	0.0157813i	$-0.00502356\pi$
$632$	16.9283	+	6.42006i	0.673372	+	0.255376i
$633$	−12.8429	−	3.16549i	−0.510460	−	0.125817i
$634$	2.82386	−	2.50172i	0.112150	−	0.0993560i
$635$	−19.1057	+	13.1877i	−0.758187	+	0.523339i
$636$	−0.555459	−	1.46463i	−0.0220254	−	0.0580762i
$637$	−29.7894	−	44.6440i	−1.18030	−	1.76886i
$638$	0.264441	−	0.697273i	0.0104693	−	0.0276053i
$639$	2.29593	+	9.31495i	0.0908255	+	0.368494i
$640$	46.3035	−	24.3020i	1.83031	−	0.960620i
$641$	8.33806	+	21.9857i	0.329334	+	0.868381i	0.992757	+	0.120137i	$0.0383335\pi$
$641$	8.33806	+	21.9857i	0.329334	+	0.868381i	−0.663424	+	0.748244i	$0.730897\pi$
$642$	2.59156	−	0.314672i	0.102281	−	0.0124191i
$643$	14.2923	+	9.86526i	0.563633	+	0.389048i	0.815538	−	0.578704i	$-0.196441\pi$
$643$	14.2923	+	9.86526i	0.563633	+	0.389048i	−0.251904	+	0.967752i	$0.581057\pi$
$644$	2.33778	−	9.48476i	0.0921216	−	0.373752i
$645$	−9.65502	−	39.1720i	−0.380166	−	1.54239i
$646$	−0.586685	−	4.83178i	−0.0230828	−	0.190104i
$647$	−17.8056	+	46.9496i	−0.700012	+	1.84578i	−0.199909	+	0.979814i	$0.564065\pi$
$647$	−17.8056	+	46.9496i	−0.700012	+	1.84578i	−0.500103	+	0.865966i	$0.666704\pi$
$648$	−0.604197	+	2.45132i	−0.0237351	+	0.0962971i
$649$	8.93357	−	2.20193i	0.350673	−	0.0864332i
$650$	−47.4632	+	31.6706i	−1.86166	+	1.24222i
$651$	4.43228	+	1.09246i	0.173715	+	0.0428168i
$652$	−3.57372	+	6.80916i	−0.139958	+	0.266667i
$653$	4.20136			0.164412			0.0822059	−	0.996615i	$-0.473803\pi$
$653$	4.20136			0.164412			0.0822059	+	0.996615i	$0.473803\pi$
$654$	4.79647			0.187557
$655$	29.1898	−	55.6164i	1.14054	−	2.17311i
$656$	−16.0739	−	18.1436i	−0.627578	−	0.708390i
$657$			13.0533i			0.509256i
$658$	−36.5096	+	41.2108i	−1.42329	+	1.60657i
$659$	−32.7770	+	17.2027i	−1.27681	+	0.670123i	−0.960433	−	0.278510i	$-0.910159\pi$
$659$	−32.7770	+	17.2027i	−1.27681	+	0.670123i	−0.316379	+	0.948633i	$0.602467\pi$
$660$	−0.507651	−	4.18088i	−0.0197603	−	0.162740i
$661$	−11.7974	−	22.4781i	−0.458866	−	0.874297i	−0.999455	−	0.0330097i	$-0.989491\pi$
$661$	−11.7974	−	22.4781i	−0.458866	−	0.874297i	0.540589	−	0.841287i	$-0.318202\pi$
$662$	1.92201	+	15.8291i	0.0747008	+	0.615217i
$663$	−8.71786	+	7.48186i	−0.338574	+	0.290571i
$664$	1.73493	−	14.2884i	0.0673283	−	0.554499i
$665$	17.0397	−	6.46229i	0.660769	−	0.250597i
$666$	8.61972	+	4.52398i	0.334007	+	0.175301i
$667$	0.334347	−	0.881600i	0.0129460	−	0.0341357i
$668$	2.27428	+	4.33327i	0.0879944	+	0.167659i
$669$	2.75854	+	5.25596i	0.106651	+	0.203207i
$670$	15.4903	+	62.8467i	0.598444	+	2.42798i
$671$	−19.4263	−	2.35878i	−0.749946	−	0.0910599i
$672$	−6.94827	−	6.15563i	−0.268035	−	0.237459i
$673$	18.6760	+	27.0569i	0.719908	+	1.04297i	0.996631	+	0.0820172i	$0.0261362\pi$
$673$	18.6760	+	27.0569i	0.719908	+	1.04297i	−0.276723	+	0.960950i	$0.589248\pi$
$674$	−4.17288	−	1.58256i	−0.160733	−	0.0609581i
$675$	10.3130			0.396948
$676$	−0.411539	−	4.59312i	−0.0158284	−	0.176658i
$677$	23.6915			0.910538			0.455269	−	0.890354i	$-0.349543\pi$
$677$	23.6915			0.910538			0.455269	+	0.890354i	$0.349543\pi$
$678$	29.5522	+	11.2077i	1.13494	+	0.430428i
$679$	−38.2732	−	55.4483i	−1.46879	−	2.12791i
$680$	−23.5623	−	20.8743i	−0.903571	−	0.800494i
$681$	−4.40621	−	0.535010i	−0.168846	−	0.0205016i
$682$	−1.08721	−	4.41097i	−0.0416313	−	0.168905i
$683$	−7.41646	−	14.1309i	−0.283783	−	0.540703i	0.701283	−	0.712883i	$-0.252611\pi$
$683$	−7.41646	−	14.1309i	−0.283783	−	0.540703i	−0.985065	+	0.172180i	$0.944919\pi$
$684$	−0.164108	−	0.312681i	−0.00627481	−	0.0119556i
$685$	−18.7893	+	49.5434i	−0.717904	+	1.89296i
$686$	−50.1236	−	26.3069i	−1.91373	−	1.00440i
$687$	−18.7083	+	7.09513i	−0.713767	+	0.270696i
$688$	−5.69614	+	46.9119i	−0.217163	+	1.78850i
$689$	1.67018	+	15.8334i	0.0636286	+	0.603206i
$690$	−4.26064	−	35.0895i	−0.162200	−	1.33584i
$691$	−8.64240	−	16.4667i	−0.328772	−	0.626423i	0.663823	−	0.747889i	$-0.268933\pi$
$691$	−8.64240	−	16.4667i	−0.328772	−	0.626423i	−0.992596	+	0.121466i	$0.961240\pi$
$692$	−0.00182346	−	0.0150175i	−6.93174e−5	−	0.000570880i
$693$	12.5678	−	6.59609i	0.477411	−	0.250565i
$694$	2.50227	−	2.82447i	0.0949847	−	0.107216i
$695$		−	83.6457i		−	3.17286i
$696$	−0.268163	−	0.302694i	−0.0101647	−	0.0114736i
$697$	−7.83055	+	14.9199i	−0.296603	+	0.565130i
$698$	29.3353			1.11036
$699$	15.0899			0.570753
$700$	−7.95350	+	15.1541i	−0.300614	+	0.572772i
$701$	41.5030	+	10.2296i	1.56755	+	0.386365i	0.925026	−	0.379904i	$-0.124043\pi$
$701$	41.5030	+	10.2296i	1.56755	+	0.386365i	0.642520	+	0.766269i	$0.277889\pi$
$702$	−2.64797	+	4.85796i	−0.0999412	+	0.183352i
$703$	6.13172	−	1.51133i	0.231262	−	0.0570010i
$704$	4.44534	−	18.0355i	0.167540	−	0.679737i
$705$	−10.6424	+	28.0617i	−0.400816	+	1.05687i
$706$	0.743685	+	6.12479i	0.0279889	+	0.230510i
$707$	−9.60750	−	38.9792i	−0.361327	−	1.46596i
$708$	−0.257448	+	1.04451i	−0.00967548	+	0.0392550i
$709$	20.0808	+	13.8608i	0.754149	+	0.520551i	0.882004	−	0.471241i	$-0.156194\pi$
$709$	20.0808	+	13.8608i	0.754149	+	0.520551i	−0.127855	+	0.991793i	$0.540809\pi$
$710$	−57.1887	+	6.94397i	−2.14625	+	0.260602i
$711$	−2.54292	−	6.70512i	−0.0953668	−	0.251462i
$712$	27.0402	−	14.1918i	1.01338	−	0.531860i
$713$	−1.37462	−	5.57704i	−0.0514798	−	0.208862i
$714$	−8.11100	+	21.3870i	−0.303547	+	0.800387i
$715$	−5.82783	+	42.4086i	−0.217949	+	1.58599i
$716$	−0.653943	−	1.72431i	−0.0244390	−	0.0644404i
$717$	18.8468	−	13.0090i	0.703847	−	0.485830i
$718$	14.2316	−	12.6081i	0.531118	−	0.470529i
$719$	45.1928	+	11.1390i	1.68541	+	0.415416i	0.961571	−	0.274555i	$-0.0885305\pi$
$719$	45.1928	+	11.1390i	1.68541	+	0.415416i	0.723837	+	0.689971i	$0.242377\pi$
$720$	−16.7710	−	6.36040i	−0.625018	−	0.237038i
$721$	−6.18631	+	11.7870i	−0.230390	+	0.438972i
$722$	25.8392	+	9.79953i	0.961637	+	0.364701i
$723$	2.34729	+	2.64954i	0.0872966	+	0.0985375i
$724$	−2.30396	+	2.04113i	−0.0856259	+	0.0758580i
$725$	−0.938385	+	1.35949i	−0.0348508	+	0.0504900i
$726$	2.26672	+	1.56461i	0.0841260	+	0.0580680i
$727$	−30.3362	−	15.9217i	−1.12511	−	0.590502i	−0.203674	−	0.979039i	$-0.565288\pi$
$727$	−30.3362	−	15.9217i	−1.12511	−	0.590502i	−0.921433	+	0.388537i	$0.872981\pi$
$728$	23.6366	+	35.4231i	0.876031	+	1.31287i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	−77.8111	−	9.44798i	−2.87992	−	0.349685i
$731$	31.8953	−	7.86148i	1.17969	−	0.290767i
$732$	1.29973	−	1.88298i	0.0480394	−	0.0695971i
$733$	32.1519	−	22.1928i	1.18756	−	0.819711i	0.200439	−	0.979706i	$-0.435763\pi$
$733$	32.1519	−	22.1928i	1.18756	−	0.819711i	0.987118	+	0.159995i	$0.0511477\pi$
$734$	−23.2078	+	26.1962i	−0.856616	+	0.966920i
$735$	−57.8248	−	7.02121i	−2.13290	−	0.258981i
$736$	−2.79529	+	11.3409i	−0.103036	+	0.418032i
$737$	28.9581	+	15.1984i	1.06669	+	0.559840i
$738$	−0.978152	+	8.05581i	−0.0360063	+	0.296538i
$739$	−17.8195	+	2.16368i	−0.655502	+	0.0795923i	−0.441528	−	0.897247i	$-0.645564\pi$
$739$	−17.8195	+	2.16368i	−0.655502	+	0.0795923i	−0.213973	+	0.976840i	$0.568640\pi$
$740$	−5.00247	+	7.24733i	−0.183894	+	0.266417i
$741$	0.804026	+	3.49805i	0.0295366	+	0.128504i
$742$	18.0075	+	26.0883i	0.661075	+	0.957733i
$743$	−22.5002	−	25.3975i	−0.825454	−	0.931745i	0.173133	−	0.984899i	$-0.444611\pi$
$743$	−22.5002	−	25.3975i	−0.825454	−	0.931745i	−0.998586	+	0.0531538i	$0.983073\pi$
$744$	−2.39197	−	0.589569i	−0.0876940	−	0.0216146i
$745$	−6.92217	−	10.0285i	−0.253609	−	0.367416i
$746$		−	29.9574i		−	1.09682i
$747$	−4.69188	+	3.23857i	−0.171667	+	0.118493i
$748$	3.40423	−	0.413348i	0.124471	−	0.0151135i
$749$	−7.44158	+	2.82222i	−0.271909	+	0.103122i
$750$	−3.84557	+	31.6711i	−0.140420	+	1.15647i
$751$	17.7710	+	46.8582i	0.648472	+	1.70988i	0.702829	+	0.711359i	$0.251920\pi$
$751$	17.7710	+	46.8582i	0.648472	+	1.70988i	−0.0543562	+	0.998522i	$0.517311\pi$
$752$	23.3114	−	26.3131i	0.850079	−	0.959541i
$753$	−0.632466	−	0.560316i	−0.0230483	−	0.0204190i
$754$	−0.399448	−	0.791090i	−0.0145470	−	0.0288098i
$755$	11.8115	−	10.4640i	0.429863	−	0.380826i
$756$			1.65951i			0.0603556i
$757$	−24.9211	−	22.0782i	−0.905773	−	0.802445i	0.0750831	−	0.997177i	$-0.476078\pi$
$757$	−24.9211	−	22.0782i	−0.905773	−	0.802445i	−0.980856	+	0.194732i	$0.937616\pi$
$758$	−19.6821	+	4.85121i	−0.714887	+	0.176204i
$759$	−14.6981	−	10.1454i	−0.533506	−	0.368253i
$760$	−9.19582	+	3.48751i	−0.333567	+	0.126505i
$761$	13.4798	−	5.11221i	0.488642	−	0.185317i	−0.0979642	−	0.995190i	$-0.531233\pi$
$761$	13.4798	−	5.11221i	0.488642	−	0.185317i	0.586606	+	0.809873i	$0.300464\pi$
$762$	−7.49210	−	5.17142i	−0.271410	−	0.187341i
$763$	−14.1978	+	3.49945i	−0.513996	+	0.126689i
$764$	0.395553	+	0.350430i	0.0143106	+	0.0126781i
$765$			12.4684i			0.450797i
$766$	2.56215	−	2.26987i	0.0925744	−	0.0820137i
$767$	5.23311	−	9.60065i	0.188957	−	0.346659i
$768$	6.18388	+	5.47844i	0.223142	+	0.197686i
$769$	−27.6101	+	31.1653i	−0.995644	+	1.12385i	−0.00334379	+	0.999994i	$0.501064\pi$
$769$	−27.6101	+	31.1653i	−0.995644	+	1.12385i	−0.992300	+	0.123855i	$0.960474\pi$
$770$	30.2230	+	79.6916i	1.08916	+	2.87189i
$771$	−3.26617	+	26.8993i	−0.117628	+	0.968755i
$772$	7.02451	−	2.66405i	0.252818	−	0.0958811i
$773$	−7.73197	+	0.938831i	−0.278100	+	0.0337674i	−0.258398	−	0.966039i	$-0.583195\pi$
$773$	−7.73197	+	0.938831i	−0.278100	+	0.0337674i	−0.0197014	+	0.999806i	$0.506272\pi$
$774$	13.0201	−	8.98712i	0.467998	−	0.323035i
$775$			10.0633i			0.361485i
$776$	20.6550	+	29.9239i	0.741470	+	1.07420i
$777$	−28.8155	−	7.10239i	−1.03375	−	0.254797i
$778$	−13.3640	−	15.0848i	−0.479122	−	0.540817i
$779$	2.99053	+	4.33253i	0.107147	+	0.155229i
$780$	−4.07378	−	2.90761i	−0.145865	−	0.104109i
$781$	−16.5348	+	23.9548i	−0.591663	+	0.857172i
$782$	28.5712	−	3.46917i	1.02170	−	0.124057i
$783$	−0.0193071	+	0.159008i	−0.000689980	+	0.00568249i
$784$	60.4142	+	31.7078i	2.15765	+	1.13242i
$785$	−21.4820	+	87.1558i	−0.766724	+	3.11072i
$786$	24.4511	+	2.96890i	0.872142	+	0.105897i
$787$	22.5314	−	25.4327i	0.803158	−	0.906578i	−0.194070	−	0.980988i	$-0.562169\pi$
$787$	22.5314	−	25.4327i	0.803158	−	0.906578i	0.997228	+	0.0744099i	$0.0237073\pi$
$788$	−7.61222	+	5.25434i	−0.271174	+	0.187178i
$789$	−13.9424	+	20.1991i	−0.496364	+	0.719108i
$790$	41.8101	−	10.3053i	1.48754	−	0.366645i
$791$	−95.6532	−	11.6144i	−3.40104	−	0.412960i
$792$	−6.78249	+	3.55972i	−0.241005	+	0.126489i
$793$	−17.6475	+	15.1455i	−0.626681	+	0.537831i
$794$	−31.9099	−	16.7476i	−1.13244	−	0.594350i
$795$	14.2209	+	9.81600i	0.504365	+	0.348138i
$796$	0.715662	−	1.03681i	0.0253660	−	0.0367489i
$797$	−13.7482	+	12.1799i	−0.486987	+	0.431433i	−0.870548	−	0.492083i	$-0.836236\pi$
$797$	−13.7482	+	12.1799i	−0.486987	+	0.431433i	0.383562	+	0.923515i	$0.374697\pi$
$798$	4.73888	+	5.34909i	0.167755	+	0.189356i
$799$	−22.8489	−	8.66544i	−0.808336	−	0.306561i
$800$	9.51000	−	18.1198i	0.336229	−	0.640632i
$801$	−11.3098	−	4.28924i	−0.399612	−	0.151553i
$802$	−8.65609	−	2.13354i	−0.305657	−	0.0753377i
$803$	−29.6436	+	26.2620i	−1.04610	+	0.926765i
$804$	−3.14688	+	2.17214i	−0.110982	+	0.0766053i
$805$	38.2127	+	100.759i	1.34682	+	3.55127i
$806$	−4.74034	−	2.58386i	−0.166971	−	0.0910126i
$807$	4.26616	−	11.2489i	0.150176	−	0.395981i
$808$	5.18489	+	21.0359i	0.182404	+	0.740042i
$809$	5.36377	−	2.81512i	0.188580	−	0.0989744i	−0.367791	−	0.929909i	$-0.619886\pi$
$809$	5.36377	−	2.81512i	0.188580	−	0.0989744i	0.556371	+	0.830934i	$0.312193\pi$
$810$	2.12934	+	5.61462i	0.0748175	+	0.197278i
$811$	−1.65197	+	0.200586i	−0.0580087	+	0.00704353i	−0.149490	−	0.988763i	$-0.547763\pi$
$811$	−1.65197	+	0.200586i	−0.0580087	+	0.00704353i	0.0914809	+	0.995807i	$0.470840\pi$
$812$	−0.218760	−	0.150999i	−0.00767697	−	0.00529903i
$813$	5.69952	−	23.1239i	0.199891	−	0.810990i
$814$	7.06825	+	28.6770i	0.247742	+	1.00513i
$815$	−10.2253	−	84.2127i	−0.358176	−	2.94984i
$816$	5.17887	−	13.6556i	0.181297	−	0.478041i
$817$	2.45616	−	9.96503i	0.0859301	−	0.348632i
$818$	−11.5925	+	2.85729i	−0.405321	+	0.0999028i
$819$	4.29383	−	16.3118i	0.150039	−	0.569980i
$820$	−7.12756	−	1.75679i	−0.248905	−	0.0613496i
$821$	−4.82967	+	9.20216i	−0.168556	+	0.321158i	−0.955052	−	0.296439i	$-0.904201\pi$
$821$	−4.82967	+	9.20216i	−0.168556	+	0.321158i	0.786495	+	0.617596i	$0.211893\pi$
$822$	−20.7782			−0.724722
$823$	−5.88721			−0.205215			−0.102608	−	0.994722i	$-0.532719\pi$
$823$	−5.88721			−0.205215			−0.102608	+	0.994722i	$0.532719\pi$
$824$	3.33858	−	6.36112i	0.116305	−	0.221600i
$825$	20.7488	+	23.4206i	0.722382	+	0.815401i
$826$		−	21.7704i		−	0.757488i
$827$	14.1156	−	15.9332i	0.490848	−	0.554053i	−0.449935	−	0.893061i	$-0.648553\pi$
$827$	14.1156	−	15.9332i	0.490848	−	0.554053i	0.940783	+	0.339008i	$0.110091\pi$
$828$	1.84894	−	0.970398i	0.0642550	−	0.0337236i
$829$	−6.65358	−	54.7972i	−0.231088	−	1.90318i	−0.398286	−	0.917261i	$-0.630395\pi$
$829$	−6.65358	−	54.7972i	−0.231088	−	1.90318i	0.167198	−	0.985923i	$-0.446528\pi$
$830$	−15.9093	−	30.3126i	−0.552220	−	1.05217i
$831$	−0.446659	−	3.67857i	−0.0154944	−	0.127608i
$832$	−12.2524	−	18.3620i	−0.424774	−	0.636589i
$833$	5.71693	−	47.0831i	0.198080	−	1.63133i
$834$	30.6693	−	11.6313i	1.06199	−	0.402760i
$835$	−47.8019	−	25.0884i	−1.65425	−	0.868220i
$836$	0.379921	−	1.00177i	0.0131399	−	0.0346469i
$837$	0.453472	+	0.864018i	0.0156743	+	0.0298648i
$838$	0.618508	+	1.17847i	0.0213660	+	0.0407095i
$839$	−2.91759	−	11.8371i	−0.100727	−	0.408664i	0.898835	−	0.438288i	$-0.144415\pi$
$839$	−2.91759	−	11.8371i	−0.100727	−	0.408664i	−0.999561	+	0.0296244i	$0.990569\pi$
$840$	45.8815	+	5.57102i	1.58306	+	0.192218i
$841$	21.6876	+	19.2135i	0.747849	+	0.662536i
$842$	−9.13097	−	13.2285i	−0.314674	−	0.455884i
$843$	−13.0061	−	4.93255i	−0.447952	−	0.169886i
$844$	4.69214			0.161510
$845$	32.5192	+	39.1204i	1.11869	+	1.34578i
$846$	−11.7689			−0.404623
$847$	−7.85115	−	2.97755i	−0.269769	−	0.102310i
$848$	−11.4978	−	16.6574i	−0.394835	−	0.572018i
$849$	3.81762	+	3.38211i	0.131020	+	0.116074i
$850$	−50.0564	−	6.07794i	−1.71692	−	0.208472i
$851$	8.93678	+	36.2580i	0.306349	+	1.24291i
$852$	−1.58155	−	3.01339i	−0.0541829	−	0.103237i
$853$	−8.61898	−	16.4221i	−0.295108	−	0.562282i	0.692084	−	0.721817i	$-0.256693\pi$
$853$	−8.61898	−	16.4221i	−0.295108	−	0.562282i	−0.987192	+	0.159535i	$0.949001\pi$
$854$	−16.4190	+	43.2935i	−0.561848	+	1.48147i
$855$	3.44930	+	1.81033i	0.117964	+	0.0619120i
$856$	4.01601	−	1.52307i	0.137264	−	0.0520575i
$857$	2.74137	−	22.5772i	0.0936433	−	0.771222i	−0.867933	−	0.496682i	$-0.834551\pi$
$857$	2.74137	−	22.5772i	0.0936433	−	0.771222i	0.961576	−	0.274540i	$-0.0885254\pi$
$858$	−16.3598	+	3.76030i	−0.558514	+	0.128374i
$859$	0.500362	+	4.12085i	0.0170721	+	0.140602i	0.998753	−	0.0499332i	$-0.0159008\pi$
$859$	0.500362	+	4.12085i	0.0170721	+	0.140602i	−0.981680	+	0.190535i	$0.938978\pi$
$860$	6.65085	+	12.6721i	0.226792	+	0.432116i
$861$	−2.98204	−	24.5593i	−0.101628	−	0.836979i
$862$	40.0836	−	21.0375i	1.36525	−	0.716540i
$863$	−22.5901	+	25.4990i	−0.768976	+	0.867994i	−0.994336	−	0.106281i	$-0.966106\pi$
$863$	−22.5901	+	25.4990i	−0.768976	+	0.867994i	0.225360	+	0.974276i	$0.427644\pi$
$864$		−	1.98427i		−	0.0675063i
$865$	0.110662	+	0.124912i	0.00376263	+	0.00424713i
$866$	3.92429	−	7.47710i	0.133353	−	0.254082i
$867$	6.84775			0.232562
$868$	−1.61933			−0.0549635
$869$	10.1110	−	19.2650i	0.342994	−	0.653520i
$870$	−0.933883	−	0.230181i	−0.0316616	−	0.00780388i
$871$	36.5519	−	13.2083i	1.23851	−	0.447545i
$872$	7.66216	−	1.88855i	0.259473	−	0.0639545i
$873$	3.44659	−	13.9834i	0.116650	−	0.473266i
$874$	3.18863	−	8.40772i	0.107857	−	0.284395i
$875$	−11.7238	−	96.5541i	−0.396336	−	3.26412i
$876$	−1.10813	−	4.49586i	−0.0374402	−	0.151901i
$877$	−2.53248	+	10.2747i	−0.0855157	+	0.346951i	−0.998077	−	0.0619896i	$-0.980255\pi$
$877$	−2.53248	+	10.2747i	−0.0855157	+	0.346951i	0.912561	+	0.408940i	$0.134102\pi$
$878$	15.2257	+	10.5095i	0.513842	+	0.354680i
$879$	2.06525	−	0.250767i	0.0696591	−	0.00845814i
$880$	−19.2974	−	50.8831i	−0.650516	−	1.71527i
$881$	−44.9578	+	23.5957i	−1.51467	+	0.794959i	−0.998119	−	0.0612990i	$-0.980476\pi$
$881$	−44.9578	+	23.5957i	−1.51467	+	0.794959i	−0.516548	+	0.856258i	$0.672783\pi$
$882$	−5.46643	−	22.1782i	−0.184064	−	0.746779i
$883$	−14.9184	+	39.3365i	−0.502043	+	1.32378i	0.409402	+	0.912354i	$0.365737\pi$
$883$	−14.9184	+	39.3365i	−0.502043	+	1.32378i	−0.911444	+	0.411423i	$0.865032\pi$
$884$	2.36749	−	3.31702i	0.0796272	−	0.111563i
$885$	−4.20816	−	11.0960i	−0.141456	−	0.372988i
$886$	35.7397	−	24.6693i	1.20070	−	0.828782i
$887$	−17.1076	+	15.1560i	−0.574417	+	0.508889i	−0.899572	−	0.436772i	$-0.856122\pi$
$887$	−17.1076	+	15.1560i	−0.574417	+	0.508889i	0.325156	+	0.945660i	$0.394583\pi$
$888$	15.5509	+	3.83296i	0.521855	+	0.128626i
$889$	25.9501	+	9.84156i	0.870337	+	0.330075i
$890$	33.7545	−	64.3138i	1.13145	−	2.15580i
$891$	2.83683	+	1.07587i	0.0950375	+	0.0360430i
$892$	−1.39630	−	1.57610i	−0.0467517	−	0.0527718i
$893$	−5.71474	+	5.06282i	−0.191236	+	0.169421i
$894$	2.71446	−	3.93257i	0.0907850	−	0.131525i
$895$	16.7423	+	11.5564i	0.559635	+	0.386288i
$896$	−55.3556	−	29.0529i	−1.84930	−	0.970588i
$897$	−20.6846	+	4.75435i	−0.690638	+	0.158743i
$898$	2.62987	−	1.38026i	0.0877599	−	0.0460599i
$899$	−0.155159	−	0.0188397i	−0.00517483	−	0.000628338i
$900$	−3.55205	+	0.875502i	−0.118402	+	0.0291834i
$901$	−7.99255	+	11.5792i	−0.266271	+	0.385760i
$902$	−20.2625	+	13.9862i	−0.674668	+	0.465690i
$903$	−31.9833	+	36.1017i	−1.06434	+	1.20139i
$904$	51.6213	+	6.26796i	1.71690	+	0.208469i
$905$	8.12601	−	32.9685i	0.270118	−	1.09591i
$906$	5.47915	+	2.87568i	0.182033	+	0.0955381i
$907$	−1.69693	+	13.9755i	−0.0563457	+	0.464049i	0.937040	+	0.349222i	$0.113554\pi$
$907$	−1.69693	+	13.9755i	−0.0563457	+	0.464049i	−0.993386	+	0.114826i	$0.963369\pi$
$908$	1.56302	−	0.189785i	0.0518708	−	0.00629825i
$909$	4.87483	−	7.06241i	0.161688	−	0.234245i
$910$	94.1275	+	37.4023i	3.12029	+	1.23987i
$911$	−7.74629	−	11.2224i	−0.256646	−	0.371816i	0.673388	−	0.739289i	$-0.264838\pi$
$911$	−7.74629	−	11.2224i	−0.256646	−	0.371816i	−0.930034	+	0.367473i	$0.880223\pi$
$912$	−3.02578	−	3.41540i	−0.100193	−	0.113095i
$913$	−16.7944	−	4.13944i	−0.555812	−	0.136995i
$914$	0.283261	+	0.410374i	0.00936943	+	0.0135740i
$915$			25.2397i			0.834400i
$916$	5.84128	−	4.03194i	0.193001	−	0.133219i
$917$	−74.5428	+	9.05113i	−2.46162	+	0.298895i
$918$	−4.57163	+	1.73379i	−0.150886	+	0.0572236i
$919$	2.45310	−	20.2031i	0.0809202	−	0.666438i	−0.894653	−	0.446762i	$-0.852577\pi$
$919$	2.45310	−	20.2031i	0.0809202	−	0.666438i	0.975573	−	0.219676i	$-0.0704999\pi$
$920$	−20.6223	−	54.3765i	−0.679897	−	1.79274i
$921$	3.83700	−	4.33108i	0.126434	−	0.142714i
$922$	−26.0882	−	23.1121i	−0.859169	−	0.761158i
$923$	7.74862	+	33.7116i	0.255049	+	1.10963i
$924$	−3.76870	+	3.33877i	−0.123981	+	0.109838i
$925$		−	65.4246i		−	2.15115i
$926$	8.84359	+	7.83474i	0.290619	+	0.257466i
$927$	−2.76282	+	0.680974i	−0.0907429	+	0.0223661i
$928$	0.261571	+	0.180550i	0.00858650	+	0.00592683i
$929$	−15.6503	+	5.93536i	−0.513468	+	0.194733i	−0.597710	−	0.801713i	$-0.703923\pi$
$929$	−15.6503	+	5.93536i	−0.513468	+	0.194733i	0.0842415	+	0.996445i	$0.473153\pi$
$930$	−5.47868	+	2.07779i	−0.179653	+	0.0681334i
$931$	−12.1951	−	8.41770i	−0.399680	−	0.275879i
$932$	−5.19733	+	1.28103i	−0.170244	+	0.0419615i
$933$	−0.310146	−	0.274766i	−0.0101537	−	0.00899543i
$934$		−	14.8561i		−	0.486105i
$935$	−28.3155	+	25.0853i	−0.926016	+	0.820378i
$936$	−2.31726	+	8.80300i	−0.0757420	+	0.287735i
$937$	−30.0467	−	26.6191i	−0.981583	−	0.869606i	0.00988594	−	0.999951i	$-0.496853\pi$
$937$	−30.0467	−	26.6191i	−0.981583	−	0.869606i	−0.991469	+	0.130345i	$0.958392\pi$
$938$	51.3134	−	57.9209i	1.67544	−	1.89118i
$939$	8.80464	+	23.2159i	0.287329	+	0.757624i
$940$	1.28326	−	10.5686i	0.0418554	−	0.344710i
$941$	−27.4357	+	10.4050i	−0.894377	+	0.339193i	−0.758608	−	0.651548i	$-0.774120\pi$
$941$	−27.4357	+	10.4050i	−0.894377	+	0.339193i	−0.135770	+	0.990740i	$0.543351\pi$
$942$	−34.9434	+	4.24290i	−1.13852	+	0.138241i
$943$	−25.6190	+	17.6835i	−0.834270	+	0.575855i
$944$			13.9004i			0.452419i
$945$	−10.3993	−	15.0661i	−0.338291	−	0.490099i
$946$	46.6048	+	11.4870i	1.51525	+	0.373476i
$947$	34.5702	+	39.0217i	1.12338	+	1.26803i	0.959548	+	0.281546i	$0.0908471\pi$
$947$	34.5702	+	39.0217i	1.12338	+	1.26803i	0.163832	+	0.986488i	$0.447614\pi$
$948$	1.44506	+	2.09353i	0.0469334	+	0.0679947i
$949$	−0.740527	+	47.0583i	−0.0240385	+	1.52758i
$950$	−8.94927	+	12.9653i	−0.290353	+	0.420648i
$951$	−2.44060	+	0.296342i	−0.0791418	+	0.00960955i
$952$	−4.53613	+	37.3584i	−0.147017	+	1.21079i
$953$	−21.5943	−	11.3336i	−0.699507	−	0.367130i	0.0771790	−	0.997017i	$-0.475409\pi$
$953$	−21.5943	−	11.3336i	−0.699507	−	0.367130i	−0.776686	+	0.629887i	$0.783101\pi$
$954$	−1.62162	+	6.57916i	−0.0525018	+	0.213008i
$955$	−5.78707	−	0.702677i	−0.187265	−	0.0227381i
$956$	−5.38692	+	6.08058i	−0.174226	+	0.196660i
$957$	−0.399948	+	0.276064i	−0.0129285	+	0.00892390i
$958$	−7.39710	+	10.7165i	−0.238989	+	0.346236i
$959$	61.5046	−	15.1595i	1.98609	−	0.489526i
$960$	−23.7833	−	2.88781i	−0.767602	−	0.0932037i
$961$	26.6060	−	13.9639i	0.858259	−	0.450449i
$962$	30.8184	+	16.7984i	0.993623	+	0.541603i
$963$	−1.50638	−	0.790610i	−0.0485425	−	0.0254771i
$964$	−1.03339	−	0.713298i	−0.0332833	−	0.0229738i
$965$	−47.0787	+	68.2053i	−1.51552	+	2.19561i
$966$	−31.6302	+	28.0219i	−1.01768	+	0.901589i
$967$	5.40164	+	6.09719i	0.173705	+	0.196072i	0.828915	−	0.559374i	$-0.188958\pi$
$967$	5.40164	+	6.09719i	0.173705	+	0.196072i	−0.655210	+	0.755447i	$0.727420\pi$
$968$	4.23704	+	1.60690i	0.136184	+	0.0516477i
$969$	−1.47404	+	2.80855i	−0.0473530	+	0.0902235i
$970$	80.8610	+	30.6665i	2.59629	+	0.984643i
$971$	15.9943	+	3.94224i	0.513282	+	0.126513i	0.487445	−	0.873154i	$-0.337929\pi$
$971$	15.9943	+	3.94224i	0.513282	+	0.126513i	0.0258365	+	0.999666i	$0.491775\pi$
$972$	−0.265521	+	0.235231i	−0.00851659	+	0.00754504i
$973$	−82.2967	+	56.8053i	−2.63831	+	1.82110i
$974$	−2.07801	−	5.47927i	−0.0665838	−	0.175567i
$975$	37.1795	+	0.585070i	1.19070	+	0.0187372i
$976$	10.4836	−	27.6429i	0.335570	−	0.884827i
$977$	−6.39772	−	25.9566i	−0.204681	−	0.830424i	−0.980023	−	0.198882i	$-0.936269\pi$
$977$	−6.39772	−	25.9566i	−0.204681	−	0.830424i	0.775342	−	0.631541i	$-0.217577\pi$
$978$	29.4553	−	15.4593i	0.941877	−	0.494335i
$979$	−13.0135	−	34.3139i	−0.415914	−	1.09668i
$980$	20.5123	−	2.49065i	0.655243	−	0.0795609i
$981$	−2.57242	−	1.77561i	−0.0821311	−	0.0566910i
$982$	9.57870	−	38.8623i	0.305669	−	1.24015i
$983$	−1.81056	−	7.34575i	−0.0577480	−	0.234293i	0.934975	−	0.354714i	$-0.115422\pi$
$983$	−1.81056	−	7.34575i	−0.0577480	−	0.234293i	−0.992723	+	0.120421i	$0.961576\pi$
$984$	1.60932	+	13.2540i	0.0513033	+	0.422521i
$985$	36.1821	−	95.4045i	1.15286	−	3.03984i
$986$	0.187422	−	0.760402i	0.00596874	−	0.0242161i
$987$	34.8366	−	8.58645i	1.10886	−	0.273310i
$988$	−0.573886	−	1.13656i	−0.0182578	−	0.0361587i
$989$	58.9250	+	14.5237i	1.87371	+	0.461827i
$990$	−8.46662	+	16.1318i	−0.269087	+	0.512702i
$991$	47.7167			1.51577			0.757885	−	0.652388i	$-0.226233\pi$
$991$	47.7167			1.51577			0.757885	+	0.652388i	$0.226233\pi$
$992$	1.93623			0.0614754
$993$	4.82902	−	9.20093i	0.153244	−	0.291983i
$994$	45.6699	+	51.5506i	1.44856	+	1.63509i
$995$			13.8976i			0.440583i
$996$	1.34107	−	1.51375i	0.0424933	−	0.0479650i
$997$	−28.0712	+	14.7329i	−0.889023	+	0.466595i	−0.846432	−	0.532498i	$-0.821254\pi$
$997$	−28.0712	+	14.7329i	−0.889023	+	0.466595i	−0.0425911	+	0.999093i	$0.513561\pi$
$998$	−2.92269	−	24.0705i	−0.0925160	−	0.761938i
$999$	−2.94815	−	5.61723i	−0.0932754	−	0.177721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.25.12	✓	192
169.142	even	26	inner	507.2.p.b.142.12	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.25.12	✓	192	1.1	even	1	trivial
507.2.p.b.142.12	yes	192	169.142	even	26	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43480 + 0.544146i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(0.265521 + 0.235231i) q^{4} +(-3.88465 - 0.471682i) q^{5} +(-0.367233 - 1.48992i) q^{6} +(2.17406 + 4.14233i) q^{7} +(-1.17328 - 2.23550i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(1.43480 + 0.544146i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(0.265521 + 0.235231i) q^{4} +(-3.88465 - 0.471682i) q^{5} +(-0.367233 - 1.48992i) q^{6} +(2.17406 + 4.14233i) q^{7} +(-1.17328 - 2.23550i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-5.31702 - 2.79059i) q^{10} +(-2.83683 + 1.07587i) q^{11} +(0.0427583 - 0.352146i) q^{12} +(-1.33143 + 3.35071i) q^{13} +(0.865302 + 7.12641i) q^{14} +(1.81855 + 3.46495i) q^{15} +(-0.552495 - 4.55021i) q^{16} +(-2.82129 + 1.48073i) q^{17} +(-1.01757 + 1.14860i) q^{18} +0.995482i q^{19} +(-0.920502 - 1.03903i) q^{20} +(2.17406 - 4.14233i) q^{21} -4.65570 q^{22} -5.88647 q^{23} +(-1.17328 + 2.23550i) q^{24} +(10.0133 + 2.46806i) q^{25} +(-3.73361 + 4.08310i) q^{26} +(0.970942 - 0.239316i) q^{27} +(-0.397146 + 1.61128i) q^{28} +(-0.0567993 + 0.149767i) q^{29} +(0.723803 + 5.96105i) q^{30} +(0.233522 + 0.947434i) q^{31} +(0.474867 - 1.92661i) q^{32} +(2.49693 + 1.72350i) q^{33} +(-4.85371 + 0.589347i) q^{34} +(-6.49162 - 17.1170i) q^{35} +(-0.314100 + 0.164852i) q^{36} +(-1.51819 - 6.15955i) q^{37} +(-0.541688 + 1.42831i) q^{38} +(3.51392 - 0.807675i) q^{39} +(3.50334 + 9.23755i) q^{40} +(4.35219 - 3.00410i) q^{41} +(5.37337 - 4.76039i) q^{42} +(-10.0103 - 2.46731i) q^{43} +(-1.00632 - 0.381645i) q^{44} +(1.81855 - 3.46495i) q^{45} +(-8.44587 - 3.20310i) q^{46} +(5.08579 + 5.74067i) q^{47} +(-3.43090 + 3.03951i) q^{48} +(-8.45591 + 12.2505i) q^{49} +(13.0241 + 8.98988i) q^{50} +(2.82129 + 1.48073i) q^{51} +(-1.14172 + 0.576491i) q^{52} +(3.90997 - 2.05211i) q^{53} +(1.52333 + 0.184965i) q^{54} +(11.5276 - 2.84129i) q^{55} +(6.70939 - 9.72023i) q^{56} +(0.819266 - 0.565498i) q^{57} +(-0.162991 + 0.183978i) q^{58} +(-3.01050 - 0.365541i) q^{59} +(-0.332202 + 1.34780i) q^{60} +(5.71112 + 2.99743i) q^{61} +(-0.180487 + 1.48644i) q^{62} +(-4.64408 + 0.563893i) q^{63} +(-3.47790 + 5.03861i) q^{64} +(6.75262 - 12.3883i) q^{65} +(2.64474 + 3.83157i) q^{66} +(-7.14796 - 8.06838i) q^{67} +(-1.09743 - 0.270491i) q^{68} +(3.34389 + 4.84447i) q^{69} -28.0918i q^{70} +(7.89548 - 5.44986i) q^{71} +(2.50628 - 0.304317i) q^{72} +(12.2050 - 4.62875i) q^{73} +(1.17340 - 9.66380i) q^{74} +(-3.65704 - 9.64283i) q^{75} +(-0.234168 + 0.264321i) q^{76} +(-10.6241 - 9.41210i) q^{77} +(5.48125 + 0.753239i) q^{78} +(-5.36766 + 4.75533i) q^{79} +17.9366i q^{80} +(-0.748511 - 0.663123i) q^{81} +(7.87917 - 1.94204i) q^{82} +(4.69188 + 3.23857i) q^{83} +(1.55166 - 0.588469i) q^{84} +(11.6582 - 4.42136i) q^{85} +(-13.0201 - 8.98712i) q^{86} +(0.155522 - 0.0383327i) q^{87} +(5.73350 + 5.07944i) q^{88} +12.0958i q^{89} +(4.49468 - 3.98194i) q^{90} +(-16.7744 + 1.76943i) q^{91} +(-1.56298 - 1.38468i) q^{92} +(0.647068 - 0.730389i) q^{93} +(4.17331 + 11.0041i) q^{94} +(0.469551 - 3.86710i) q^{95} +(-1.85533 + 0.703632i) q^{96} +(-14.2969 + 1.73595i) q^{97} +(-18.7986 + 12.9757i) q^{98} -3.03399i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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