LMFDB - Embedded newform 207.2.o.a.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.564228 + 0.0268775i) q^{2} +(-1.39121 + 1.03176i) q^{3} +(-1.67331 + 0.159782i) q^{4} +(-0.444667 - 0.423989i) q^{5} +(0.757230 - 0.619541i) q^{6} +(-0.264997 - 1.37493i) q^{7} +(2.05807 - 0.295906i) q^{8} +(0.870940 - 2.87079i) q^{9} +O(q^{10})$	\(q+(-0.564228 + 0.0268775i) q^{2} +(-1.39121 + 1.03176i) q^{3} +(-1.67331 + 0.159782i) q^{4} +(-0.444667 - 0.423989i) q^{5} +(0.757230 - 0.619541i) q^{6} +(-0.264997 - 1.37493i) q^{7} +(2.05807 - 0.295906i) q^{8} +(0.870940 - 2.87079i) q^{9} +(0.262289 + 0.227275i) q^{10} +(4.60775 - 2.37546i) q^{11} +(2.16308 - 1.94875i) q^{12} +(0.228794 + 0.0440964i) q^{13} +(0.186474 + 0.768654i) q^{14} +(1.05608 + 0.131069i) q^{15} +(2.14782 - 0.413959i) q^{16} +(0.0507804 + 0.111194i) q^{17} +(-0.414249 + 1.64319i) q^{18} +(-6.74068 - 3.07837i) q^{19} +(0.811812 + 0.638416i) q^{20} +(1.78727 + 1.63941i) q^{21} +(-2.53598 + 1.46415i) q^{22} +(4.39598 - 1.91712i) q^{23} +(-2.55791 + 2.53511i) q^{24} +(-0.219948 - 4.61727i) q^{25} +(-0.130277 - 0.0187310i) q^{26} +(1.75031 + 4.89249i) q^{27} +(0.663112 + 2.25835i) q^{28} +(0.646580 - 6.77129i) q^{29} +(-0.599393 - 0.0455678i) q^{30} +(-6.92847 + 5.44861i) q^{31} +(-5.24199 + 1.27169i) q^{32} +(-3.95945 + 8.05887i) q^{33} +(-0.0316404 - 0.0613738i) q^{34} +(-0.465121 + 0.723743i) q^{35} +(-0.998654 + 4.94290i) q^{36} +(1.87583 - 6.38850i) q^{37} +(3.88602 + 1.55573i) q^{38} +(-0.363797 + 0.174713i) q^{39} +(-1.04062 - 0.741020i) q^{40} +(3.06862 - 3.21828i) q^{41} +(-1.05249 - 0.876965i) q^{42} +(-0.768994 + 0.977856i) q^{43} +(-7.33066 + 4.71113i) q^{44} +(-1.60446 + 0.907278i) q^{45} +(-2.42881 + 1.19985i) q^{46} +(-1.18303 - 0.683022i) q^{47} +(-2.56097 + 2.79195i) q^{48} +(4.67836 - 1.87293i) q^{49} +(0.248201 + 2.59928i) q^{50} +(-0.185372 - 0.102301i) q^{51} +(-0.389889 - 0.0372299i) q^{52} +(6.73594 + 7.77369i) q^{53} +(-1.11907 - 2.71344i) q^{54} +(-3.05608 - 0.897347i) q^{55} +(-0.952234 - 2.75130i) q^{56} +(12.5539 - 2.67211i) q^{57} +(-0.182823 + 3.83794i) q^{58} +(-0.273756 + 1.42038i) q^{59} +(-1.78809 - 0.0505762i) q^{60} +(-0.144795 + 0.361681i) q^{61} +(3.76279 - 3.26048i) q^{62} +(-4.17795 - 0.436734i) q^{63} +(-1.27400 + 0.374080i) q^{64} +(-0.0830405 - 0.116614i) q^{65} +(2.01743 - 4.65346i) q^{66} +(-4.80666 + 9.32362i) q^{67} +(-0.102738 - 0.177948i) q^{68} +(-4.13773 + 7.20272i) q^{69} +(0.242982 - 0.420858i) q^{70} +(-2.64612 - 4.11744i) q^{71} +(0.942972 - 6.16602i) q^{72} +(3.53798 - 7.74711i) q^{73} +(-0.886691 + 3.65499i) q^{74} +(5.06991 + 6.19667i) q^{75} +(11.7711 + 4.07403i) q^{76} +(-4.48714 - 5.70587i) q^{77} +(0.200569 - 0.108356i) q^{78} +(4.26049 - 1.47457i) q^{79} +(-1.13058 - 0.726579i) q^{80} +(-7.48293 - 5.00058i) q^{81} +(-1.64491 + 1.89832i) q^{82} +(-8.86147 + 8.44940i) q^{83} +(-3.25261 - 2.45767i) q^{84} +(0.0245645 - 0.0709744i) q^{85} +(0.407606 - 0.572403i) q^{86} +(6.08682 + 10.0874i) q^{87} +(8.78018 - 6.25234i) q^{88} +(1.59186 - 11.0716i) q^{89} +(0.880898 - 0.555036i) q^{90} -0.326261i q^{91} +(-7.04953 + 3.91034i) q^{92} +(4.01731 - 14.7287i) q^{93} +(0.685857 + 0.353584i) q^{94} +(1.69216 + 4.22682i) q^{95} +(5.98064 - 7.17767i) q^{96} +(7.79701 + 1.89153i) q^{97} +(-2.58932 + 1.18250i) q^{98} +(-2.80639 - 15.2968i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.564228	+	0.0268775i	−0.398970	+	0.0190053i	−0.246108	−	0.969242i	$-0.579152\pi$
$2$	−0.564228	+	0.0268775i	−0.398970	+	0.0190053i	−0.152862	+	0.988248i	$0.548849\pi$
$3$	−1.39121	+	1.03176i	−0.803216	+	0.595687i
$3$	−1.39121	+	1.03176i	−0.803216	+	0.595687i
$4$	−1.67331	+	0.159782i	−0.836656	+	0.0798910i
$5$	−0.444667	−	0.423989i	−0.198861	−	0.189613i	0.584105	−	0.811678i	$-0.301446\pi$
$5$	−0.444667	−	0.423989i	−0.198861	−	0.189613i	−0.782966	+	0.622065i	$0.786294\pi$
$6$	0.757230	−	0.619541i	0.309138	−	0.252927i
$7$	−0.264997	−	1.37493i	−0.100159	−	0.519676i	−0.997005	−	0.0773331i	$-0.975360\pi$
$7$	−0.264997	−	1.37493i	−0.100159	−	0.519676i	0.896846	−	0.442343i	$-0.145853\pi$
$8$	2.05807	−	0.295906i	0.727639	−	0.104619i
$9$	0.870940	−	2.87079i	0.290313	−	0.956932i
$10$	0.262289	+	0.227275i	0.0829432	+	0.0718707i
$11$	4.60775	−	2.37546i	1.38929	−	0.716229i	0.408768	−	0.912638i	$-0.365958\pi$
$11$	4.60775	−	2.37546i	1.38929	−	0.716229i	0.980522	+	0.196409i	$0.0629282\pi$
$12$	2.16308	−	1.94875i	0.624426	−	0.562555i
$13$	0.228794	+	0.0440964i	0.0634559	+	0.0122301i	0.220880	−	0.975301i	$-0.429107\pi$
$13$	0.228794	+	0.0440964i	0.0634559	+	0.0122301i	−0.157424	+	0.987531i	$0.550319\pi$
$14$	0.186474	+	0.768654i	0.0498371	+	0.205432i
$15$	1.05608	+	0.131069i	0.272679	+	0.0338418i
$16$	2.14782	−	0.413959i	0.536956	−	0.103490i
$17$	0.0507804	+	0.111194i	0.0123161	+	0.0269684i	0.915690	−	0.401885i	$-0.131645\pi$
$17$	0.0507804	+	0.111194i	0.0123161	+	0.0269684i	−0.903374	+	0.428854i	$0.858918\pi$
$18$	−0.414249	+	1.64319i	−0.0976395	+	0.387304i
$19$	−6.74068	−	3.07837i	−1.54642	−	0.706226i	−0.554392	−	0.832256i	$-0.687049\pi$
$19$	−6.74068	−	3.07837i	−1.54642	−	0.706226i	−0.992026	+	0.126030i	$0.959776\pi$
$20$	0.811812	+	0.638416i	0.181527	+	0.142754i
$21$	1.78727	+	1.63941i	0.390014	+	0.357749i
$22$	−2.53598	+	1.46415i	−0.540673	+	0.312158i
$23$	4.39598	−	1.91712i	0.916625	−	0.399748i
$23$	4.39598	−	1.91712i	0.916625	−	0.399748i
$24$	−2.55791	+	2.53511i	−0.522132	+	0.517477i
$25$	−0.219948	−	4.61727i	−0.0439895	−	0.923454i
$26$	−0.130277	−	0.0187310i	−0.0255494	−	0.00367345i
$27$	1.75031	+	4.89249i	0.336848	+	0.941559i
$28$	0.663112	+	2.25835i	0.125316	+	0.426788i
$29$	0.646580	−	6.77129i	0.120067	−	1.25740i	−0.711784	−	0.702398i	$-0.752112\pi$
$29$	0.646580	−	6.77129i	0.120067	−	1.25740i	0.831851	−	0.554999i	$-0.187281\pi$
$30$	−0.599393	−	0.0455678i	−0.109434	−	0.00831951i
$31$	−6.92847	+	5.44861i	−1.24439	+	0.978599i	−0.244429	+	0.969667i	$0.578601\pi$
$31$	−6.92847	+	5.44861i	−1.24439	+	0.978599i	−0.999960	+	0.00893158i	$0.997157\pi$
$32$	−5.24199	+	1.27169i	−0.926662	+	0.224806i
$33$	−3.95945	+	8.05887i	−0.689252	+	1.40287i
$34$	−0.0316404	−	0.0613738i	−0.00542628	−	0.0105255i
$35$	−0.465121	+	0.723743i	−0.0786198	+	0.122335i
$36$	−0.998654	+	4.94290i	−0.166442	+	0.823816i
$37$	1.87583	−	6.38850i	0.308385	−	1.05026i	−0.648842	−	0.760923i	$-0.724746\pi$
$37$	1.87583	−	6.38850i	0.308385	−	1.05026i	0.957227	−	0.289339i	$-0.0934356\pi$
$38$	3.88602	+	1.55573i	0.630396	+	0.252373i
$39$	−0.363797	+	0.174713i	−0.0582542	+	0.0279764i
$40$	−1.04062	−	0.741020i	−0.164536	−	0.117166i
$41$	3.06862	−	3.21828i	0.479239	−	0.502611i	−0.439083	−	0.898447i	$-0.644697\pi$
$41$	3.06862	−	3.21828i	0.479239	−	0.502611i	0.918321	+	0.395836i	$0.129545\pi$
$42$	−1.05249	−	0.876965i	−0.162403	−	0.135319i
$43$	−0.768994	+	0.977856i	−0.117271	+	0.149122i	−0.841144	−	0.540811i	$-0.818117\pi$
$43$	−0.768994	+	0.977856i	−0.117271	+	0.149122i	0.723874	+	0.689933i	$0.242360\pi$
$44$	−7.33066	+	4.71113i	−1.10514	+	0.710229i
$45$	−1.60446	+	0.907278i	−0.239179	+	0.135249i
$46$	−2.42881	+	1.19985i	−0.358108	+	0.176908i
$47$	−1.18303	−	0.683022i	−0.172563	−	0.0996290i	0.411231	−	0.911531i	$-0.365099\pi$
$47$	−1.18303	−	0.683022i	−0.172563	−	0.0996290i	−0.583794	+	0.811902i	$0.698432\pi$
$48$	−2.56097	+	2.79195i	−0.369644	+	0.402983i
$49$	4.67836	−	1.87293i	0.668337	−	0.267562i
$50$	0.248201	+	2.59928i	0.0351010	+	0.367594i
$51$	−0.185372	−	0.102301i	−0.0259572	−	0.0143250i
$52$	−0.389889	−	0.0372299i	−0.0540679	−	0.00516286i
$53$	6.73594	+	7.77369i	0.925252	+	1.06780i	0.997518	+	0.0704125i	$0.0224316\pi$
$53$	6.73594	+	7.77369i	0.925252	+	1.06780i	−0.0722658	+	0.997385i	$0.523023\pi$
$54$	−1.11907	−	2.71344i	−0.152287	−	0.369252i
$55$	−3.05608	−	0.897347i	−0.412082	−	0.120998i
$56$	−0.952234	−	2.75130i	−0.127248	−	0.367658i
$57$	12.5539	−	2.67211i	1.66280	−	0.353930i
$58$	−0.182823	+	3.83794i	−0.0240059	+	0.503946i
$59$	−0.273756	+	1.42038i	−0.0356400	+	0.184918i	−0.995386	−	0.0959514i	$-0.969411\pi$
$59$	−0.273756	+	1.42038i	−0.0356400	+	0.184918i	0.959746	+	0.280869i	$0.0906228\pi$
$60$	−1.78809	−	0.0505762i	−0.230842	−	0.00652936i
$61$	−0.144795	+	0.361681i	−0.0185391	+	0.0463085i	−0.937349	−	0.348393i	$-0.886728\pi$
$61$	−0.144795	+	0.361681i	−0.0185391	+	0.0463085i	0.918810	+	0.394701i	$0.129152\pi$
$62$	3.76279	−	3.26048i	0.477875	−	0.414081i
$63$	−4.17795	−	0.436734i	−0.526372	−	0.0550233i
$64$	−1.27400	+	0.374080i	−0.159250	+	0.0467599i
$65$	−0.0830405	−	0.116614i	−0.0102999	−	0.0144642i
$66$	2.01743	−	4.65346i	0.248329	−	0.572802i
$67$	−4.80666	+	9.32362i	−0.587227	+	1.13906i	0.388782	+	0.921330i	$0.372896\pi$
$67$	−4.80666	+	9.32362i	−0.587227	+	1.13906i	−0.976009	+	0.217731i	$0.930134\pi$
$68$	−0.102738	−	0.177948i	−0.0124588	−	0.0215794i
$69$	−4.13773	+	7.20272i	−0.498124	+	0.867106i
$70$	0.242982	−	0.420858i	0.0290419	−	0.0503021i
$71$	−2.64612	−	4.11744i	−0.314036	−	0.488650i	0.647974	−	0.761662i	$-0.275616\pi$
$71$	−2.64612	−	4.11744i	−0.314036	−	0.488650i	−0.962011	+	0.273012i	$0.911980\pi$
$72$	0.942972	−	6.16602i	0.111130	−	0.726673i
$73$	3.53798	−	7.74711i	0.414090	−	0.906730i	−0.581555	−	0.813507i	$-0.697556\pi$
$73$	3.53798	−	7.74711i	0.414090	−	0.906730i	0.995645	−	0.0932233i	$-0.0297171\pi$
$74$	−0.886691	+	3.65499i	−0.103076	+	0.424884i
$75$	5.06991	+	6.19667i	0.585423	+	0.715529i
$76$	11.7711	+	4.07403i	1.35024	+	0.467323i
$77$	−4.48714	−	5.70587i	−0.511357	−	0.650244i
$78$	0.200569	−	0.108356i	0.0227100	−	0.0122689i
$79$	4.26049	−	1.47457i	0.479343	−	0.165902i	−0.0767029	−	0.997054i	$-0.524439\pi$
$79$	4.26049	−	1.47457i	0.479343	−	0.165902i	0.556045	+	0.831152i	$0.312318\pi$
$80$	−1.13058	−	0.726579i	−0.126403	−	0.0812340i
$81$	−7.48293	−	5.00058i	−0.831436	−	0.555620i
$82$	−1.64491	+	1.89832i	−0.181649	+	0.209635i
$83$	−8.86147	+	8.44940i	−0.972673	+	0.927442i	−0.997386	−	0.0722528i	$-0.976981\pi$
$83$	−8.86147	+	8.44940i	−0.972673	+	0.927442i	0.0247135	+	0.999695i	$0.492133\pi$
$84$	−3.25261	−	2.45767i	−0.354889	−	0.268154i
$85$	0.0245645	−	0.0709744i	0.00266439	−	0.00769826i
$86$	0.407606	−	0.572403i	0.0439533	−	0.0617238i
$87$	6.08682	+	10.0874i	0.652576	+	1.08148i
$88$	8.78018	−	6.25234i	0.935971	−	0.666502i
$89$	1.59186	−	11.0716i	0.168736	−	1.17359i	−0.712764	−	0.701404i	$-0.752557\pi$
$89$	1.59186	−	11.0716i	0.168736	−	1.17359i	0.881500	−	0.472184i	$-0.156534\pi$
$90$	0.880898	−	0.555036i	0.0928548	−	0.0585059i
$91$		−	0.326261i		−	0.0342015i
$92$	−7.04953	+	3.91034i	−0.734964	+	0.407681i
$93$	4.01731	−	14.7287i	0.416575	−	1.52729i
$94$	0.685857	+	0.353584i	0.0707407	+	0.0364694i
$95$	1.69216	+	4.22682i	0.173612	+	0.433663i
$96$	5.98064	−	7.17767i	0.610396	−	0.732568i
$97$	7.79701	+	1.89153i	0.791666	+	0.192056i	0.611149	−	0.791516i	$-0.290708\pi$
$97$	7.79701	+	1.89153i	0.791666	+	0.192056i	0.180517	+	0.983572i	$0.442223\pi$
$98$	−2.58932	+	1.18250i	−0.261561	+	0.119451i
$99$	−2.80639	−	15.2968i	−0.282053	−	1.53739i
$100$	1.10580	+	7.69099i	0.110580	+	0.769099i
$101$	−5.61663	−	5.89055i	−0.558875	−	0.586131i	0.382305	−	0.924036i	$-0.375130\pi$
$101$	−5.61663	−	5.89055i	−0.558875	−	0.586131i	−0.941180	+	0.337905i	$0.890282\pi$
$102$	0.107341	+	0.0527386i	0.0106284	+	0.00522190i
$103$	10.4641	+	0.498465i	1.03105	+	0.0491152i	0.556282	−	0.830994i	$-0.312227\pi$
$103$	10.4641	+	0.498465i	1.03105	+	0.0491152i	0.474772	+	0.880109i	$0.342530\pi$
$104$	0.483922	+	0.0230521i	0.0474525	+	0.00226044i
$105$	−0.0996471	−	1.48677i	−0.00972457	−	0.145094i
$106$	−4.00955	−	4.20509i	−0.389441	−	0.408434i
$107$	−1.18273	−	8.22610i	−0.114339	−	0.795247i	−0.963614	−	0.267296i	$-0.913870\pi$
$107$	−1.18273	−	8.22610i	−0.114339	−	0.795247i	0.849275	−	0.527950i	$-0.177039\pi$
$108$	−3.71055	−	7.90699i	−0.357048	−	0.760850i
$109$	−10.3444	+	4.72412i	−0.990812	+	0.452489i	−0.843807	−	0.536647i	$-0.819691\pi$
$109$	−10.3444	+	4.72412i	−0.990812	+	0.452489i	−0.147005	+	0.989136i	$0.546963\pi$
$110$	1.74845	+	0.424169i	0.166708	+	0.0404429i
$111$	3.98172	+	10.8232i	0.377928	+	1.02729i
$112$	−1.13833	−	2.84342i	−0.107562	−	0.268678i
$113$	5.80987	+	2.99520i	0.546547	+	0.281765i	0.709305	−	0.704901i	$-0.249009\pi$
$113$	5.80987	+	2.99520i	0.546547	+	0.281765i	−0.162758	+	0.986666i	$0.552039\pi$
$114$	−7.01142	+	1.84510i	−0.656680	+	0.172809i
$115$	−2.76758	−	1.01137i	−0.258078	−	0.0943103i
$116$			11.4338i			1.06160i
$117$	0.325857	−	0.618414i	0.0301255	−	0.0571724i
$118$	0.116285	−	0.808778i	0.0107049	−	0.0744541i
$119$	0.139427	−	0.0992857i	0.0127813	−	0.00910150i
$120$	2.21227	−	0.0427519i	0.201952	−	0.00390270i
$121$	9.20795	−	12.9308i	0.837086	−	1.17552i
$122$	0.0719765	−	0.207962i	0.00651645	−	0.0188280i
$123$	−0.948611	+	7.64339i	−0.0855334	+	0.689182i
$124$	10.7229	−	10.2243i	0.962945	−	0.918166i
$125$	−3.87162	+	4.46809i	−0.346288	+	0.399638i
$126$	2.36906	+	0.134125i	0.211052	+	0.0119488i
$127$	−4.39209	−	2.82262i	−0.389735	−	0.250467i	0.331069	−	0.943607i	$-0.392591\pi$
$127$	−4.39209	−	2.82262i	−0.389735	−	0.250467i	−0.720804	+	0.693139i	$0.756227\pi$
$128$	10.9035	−	3.77374i	0.963744	−	0.333555i
$129$	0.0609208	−	2.15382i	0.00536378	−	0.189633i
$130$	0.0499881	+	0.0635651i	0.00438425	+	0.00557502i
$131$	0.00363194	+	0.00125703i	0.000317324	+	0.000109827i	0.327227	−	0.944946i	$-0.393886\pi$
$131$	0.00363194	+	0.00125703i	0.000317324	+	0.000109827i	−0.326909	+	0.945056i	$0.606007\pi$
$132$	5.33774	−	14.1177i	0.464591	−	1.22878i
$133$	−2.44629	+	10.0837i	−0.212120	+	0.874372i
$134$	2.46146	−	5.38984i	0.212638	−	0.465611i
$135$	1.29605	−	2.91764i	0.111547	−	0.251110i
$136$	0.137413	+	0.213818i	0.0117830	+	0.0183348i
$137$	−3.39849	+	5.88637i	−0.290353	+	0.502906i	−0.973893	−	0.227007i	$-0.927106\pi$
$137$	−3.39849	+	5.88637i	−0.290353	+	0.502906i	0.683540	+	0.729913i	$0.260439\pi$
$138$	2.14103	−	4.17519i	0.182257	−	0.355416i
$139$	−5.14882	−	8.91801i	−0.436717	−	0.756416i	0.560717	−	0.828008i	$-0.310526\pi$
$139$	−5.14882	−	8.91801i	−0.436717	−	0.756416i	−0.997434	+	0.0715914i	$0.977192\pi$
$140$	0.662652	−	1.28537i	0.0560043	−	0.108633i
$141$	2.35056	−	0.270374i	0.197953	−	0.0227696i
$142$	1.60368	+	2.25206i	0.134578	+	0.188988i
$143$	1.15897	−	0.340305i	0.0969183	−	0.0284578i
$144$	0.682234	−	6.52650i	0.0568529	−	0.543875i
$145$	−3.15846	+	2.73682i	−0.262296	+	0.227281i
$146$	−1.78801	+	4.46623i	−0.147977	+	0.369628i
$147$	−4.57617	+	7.43259i	−0.377436	+	0.613029i
$148$	−2.11809	+	10.9897i	−0.174106	+	0.903346i
$149$	−0.784610	+	16.4710i	−0.0642778	+	1.34936i	0.704438	+	0.709766i	$0.251199\pi$
$149$	−0.784610	+	16.4710i	−0.0642778	+	1.34936i	−0.768716	+	0.639591i	$0.779104\pi$
$150$	−3.02714	−	3.36007i	−0.247165	−	0.274348i
$151$	7.17315	+	20.7255i	0.583743	+	1.68661i	0.718322	+	0.695711i	$0.244910\pi$
$151$	7.17315	+	20.7255i	0.583743	+	1.68661i	−0.134580	+	0.990903i	$0.542968\pi$
$152$	−14.7837	−	4.34089i	−1.19912	−	0.352093i
$153$	0.363441	−	0.0489372i	0.0293824	−	0.00395634i
$154$	2.68513	+	3.09881i	0.216374	+	0.249709i
$155$	5.39101	+	0.514779i	0.433016	+	0.0413480i
$156$	0.580830	−	0.350477i	0.0465037	−	0.0280607i
$157$	0.701863	+	7.35024i	0.0560148	+	0.586613i	0.979288	+	0.202470i	$0.0648969\pi$
$157$	0.701863	+	7.35024i	0.0560148	+	0.586613i	−0.923274	+	0.384143i	$0.874497\pi$
$158$	−2.36426	+	0.946506i	−0.188090	+	0.0752999i
$159$	−17.3917	−	3.86497i	−1.37925	−	0.306512i
$160$	2.87012	+	1.65707i	0.226903	+	0.131003i
$161$	−3.80084	−	5.53615i	−0.299548	−	0.436310i
$162$	4.35648	+	2.62035i	0.342278	+	0.205874i
$163$	8.42559	−	5.41480i	0.659943	−	0.424120i	−0.167344	−	0.985899i	$-0.553519\pi$
$163$	8.42559	−	5.41480i	0.659943	−	0.424120i	0.827287	+	0.561779i	$0.189883\pi$
$164$	−4.62054	+	5.87550i	−0.360804	+	0.458799i
$165$	5.17751	−	1.90475i	0.403068	−	0.148284i
$166$	4.77280	−	5.00556i	0.370441	−	0.388507i
$167$	1.01650	+	0.723845i	0.0786589	+	0.0560128i	0.618710	−	0.785620i	$-0.287656\pi$
$167$	1.01650	+	0.723845i	0.0786589	+	0.0560128i	−0.540051	+	0.841632i	$0.681595\pi$
$168$	4.16344	+	2.84516i	0.321217	+	0.219509i
$169$	−12.0184	−	4.81143i	−0.924491	−	0.370110i
$170$	−0.0119524	+	0.0407060i	−0.000916705	+	0.00312201i
$171$	−14.7081	+	16.6700i	−1.12476	+	1.27479i
$172$	1.13052	−	1.75913i	0.0862016	−	0.134132i
$173$	3.61350	+	7.00921i	0.274729	+	0.532900i	0.985323	−	0.170702i	$-0.0546037\pi$
$173$	3.61350	+	7.00921i	0.274729	+	0.532900i	−0.710593	+	0.703603i	$0.751573\pi$
$174$	−3.70548	−	5.52801i	−0.280912	−	0.419077i
$175$	−6.29015	+	1.52597i	−0.475491	+	0.115353i
$176$	8.91330	−	7.00950i	0.671865	−	0.528361i
$177$	−1.08464	−	2.25850i	−0.0815267	−	0.169760i
$178$	−0.600593	+	6.28970i	−0.0450164	+	0.471433i
$179$	0.0267319	+	0.0910405i	0.00199804	+	0.00680468i	0.960486	−	0.278328i	$-0.0897804\pi$
$179$	0.0267319	+	0.0910405i	0.00199804	+	0.00680468i	−0.958488	+	0.285133i	$0.907962\pi$
$180$	2.53980	−	1.77452i	0.189306	−	0.132265i
$181$	−10.1668	−	1.46177i	−0.755694	−	0.108652i	−0.246309	−	0.969191i	$-0.579218\pi$
$181$	−10.1668	−	1.46177i	−0.755694	−	0.108652i	−0.509385	+	0.860539i	$0.670127\pi$
$182$	0.00876910	+	0.184086i	0.000650009	+	0.0136454i
$183$	−0.171727	−	0.652569i	−0.0126945	−	0.0482393i
$184$	8.47996	−	5.24638i	0.625151	−	0.386768i
$185$	−3.54277	+	2.04542i	−0.260470	+	0.150382i
$186$	−1.87081	+	8.41832i	−0.137174	+	0.617261i
$187$	0.498120	+	0.391726i	0.0364261	+	0.0286458i
$188$	2.08871	+	0.953883i	0.152335	+	0.0695691i
$189$	6.26302	−	3.70305i	0.455567	−	0.269358i
$190$	−1.06837	−	2.33941i	−0.0775079	−	0.169719i
$191$	9.53716	−	1.83814i	0.690085	−	0.133003i	0.167860	−	0.985811i	$-0.446314\pi$
$191$	9.53716	−	1.83814i	0.690085	−	0.133003i	0.522225	+	0.852808i	$0.325102\pi$
$192$	1.38644	−	1.83488i	0.100058	−	0.132421i
$193$	3.65166	+	15.0524i	0.262853	+	1.08349i	0.938228	+	0.346019i	$0.112467\pi$
$193$	3.65166	+	15.0524i	0.262853	+	1.08349i	−0.675375	+	0.737474i	$0.736018\pi$
$194$	−4.45013	−	0.857693i	−0.319501	−	0.0615788i
$195$	0.235845	+	0.0765569i	0.0168892	+	0.00548236i
$196$	−7.52909	+	3.88152i	−0.537792	+	0.277251i
$197$	18.1586	+	15.7346i	1.29375	+	1.12104i	0.985489	+	0.169738i	$0.0542923\pi$
$197$	18.1586	+	15.7346i	1.29375	+	1.12104i	0.308260	+	0.951302i	$0.400253\pi$
$198$	1.99458	+	8.55546i	0.141749	+	0.608010i
$199$	−12.4910	+	1.79593i	−0.885463	+	0.127310i	−0.570017	−	0.821633i	$-0.693063\pi$
$199$	−12.4910	+	1.79593i	−0.885463	+	0.127310i	−0.315446	+	0.948943i	$0.602154\pi$
$200$	−1.81895	−	9.43760i	−0.128619	−	0.667339i
$201$	−2.93266	−	17.9304i	−0.206854	−	1.26472i
$202$	3.32738	+	3.17265i	0.234114	+	0.223227i
$203$	−9.48142	+	0.905366i	−0.665465	+	0.0635442i
$204$	0.326530	+	0.141562i	0.0228617	+	0.00991131i
$205$	−2.72903	+	0.130000i	−0.190604	+	0.00907957i
$206$	−5.91752			−0.412293
$207$	−1.67503	−	14.2897i	−0.116423	−	0.993200i
$208$	0.509663			0.0353387
$209$	−38.3719	+	1.82788i	−2.65424	+	0.126437i
$210$	0.0961845	+	0.836201i	0.00663736	+	0.0577034i
$211$	−23.4566	+	2.23984i	−1.61482	+	0.154197i	−0.863011	−	0.505184i	$-0.831424\pi$
$211$	−23.4566	+	2.23984i	−1.61482	+	0.154197i	−0.751809	+	0.659381i	$0.770818\pi$
$212$	−12.5134	−	11.9315i	−0.859425	−	0.819460i
$213$	7.92952	+	2.99807i	0.543322	+	0.205424i
$214$	0.888429	+	4.60961i	0.0607318	+	0.315106i
$215$	0.756546	−	0.108775i	0.0515960	−	0.00741838i
$216$	5.04999	+	9.55117i	0.343608	+	0.649875i
$217$	9.32749	+	8.08232i	0.633192	+	0.548664i
$218$	5.70962	−	2.94352i	0.386704	−	0.199360i
$219$	3.07107	+	14.4282i	0.207524	+	0.974969i
$220$	5.25716	+	1.01323i	0.354438	+	0.0683123i
$221$	0.00671500	+	0.0276796i	0.000451700	+	0.00186193i
$222$	−2.53750	−	5.99972i	−0.170306	−	0.402675i
$223$	12.6669	−	2.44135i	0.848241	−	0.163485i	0.253433	−	0.967353i	$-0.418440\pi$
$223$	12.6669	−	2.44135i	0.848241	−	0.163485i	0.594808	+	0.803868i	$0.297228\pi$
$224$	3.13760	+	6.87040i	0.209640	+	0.459048i
$225$	−13.4468	−	3.38994i	−0.896453	−	0.225996i
$226$	−3.35860	−	1.53382i	−0.223411	−	0.102028i
$227$	17.7313	+	13.9440i	1.17687	+	0.925498i	0.998292	−	0.0584280i	$-0.0186088\pi$
$227$	17.7313	+	13.9440i	1.17687	+	0.925498i	0.178575	+	0.983926i	$0.442851\pi$
$228$	−20.5796	+	6.47716i	−1.36291	+	0.428960i
$229$	3.30476	−	1.90800i	0.218385	−	0.126084i	−0.386818	−	0.922156i	$-0.626426\pi$
$229$	3.30476	−	1.90800i	0.218385	−	0.126084i	0.605202	+	0.796072i	$0.293092\pi$
$230$	1.58873	+	0.496256i	0.104758	+	0.0327221i
$231$	12.1297	+	3.30841i	0.798073	+	0.217677i
$232$	−0.672959	−	14.1271i	−0.0441819	−	0.927493i
$233$	1.86081	+	0.267544i	0.121906	+	0.0175274i	0.202998	−	0.979179i	$-0.434932\pi$
$233$	1.86081	+	0.267544i	0.121906	+	0.0175274i	−0.0810919	+	0.996707i	$0.525841\pi$
$234$	−0.167236	+	0.357685i	−0.0109326	+	0.0233826i
$235$	0.236460	+	0.805308i	0.0154249	+	0.0525325i
$236$	0.231128	−	2.42048i	0.0150452	−	0.157560i
$237$	−4.40584	+	6.44724i	−0.286190	+	0.418793i
$238$	−0.0760003	+	0.0597673i	−0.00492636	+	0.00387414i
$239$	9.42674	−	2.28690i	0.609765	−	0.147927i	0.0810263	−	0.996712i	$-0.474180\pi$
$239$	9.42674	−	2.28690i	0.609765	−	0.147927i	0.528739	+	0.848785i	$0.322665\pi$
$240$	2.32253	−	0.155662i	0.149919	−	0.0100479i
$241$	3.97845	+	7.71711i	0.256274	+	0.497103i	0.981513	−	0.191395i	$-0.0613010\pi$
$241$	3.97845	+	7.71711i	0.256274	+	0.497103i	−0.725239	+	0.688497i	$0.758271\pi$
$242$	−4.84784	+	7.54339i	−0.311631	+	0.484907i
$243$	15.5697	−	0.763723i	0.998799	−	0.0489928i
$244$	0.184498	−	0.628341i	0.0118112	−	0.0402254i
$245$	−2.87441	−	1.15074i	−0.183639	−	0.0735181i
$246$	0.329798	−	4.33812i	0.0210271	−	0.276588i
$247$	−1.40648	−	1.00155i	−0.0894922	−	0.0637271i
$248$	−12.6470	+	13.2638i	−0.803086	+	0.842253i
$249$	3.61043	−	20.8978i	0.228802	−	1.32435i
$250$	2.06439	−	2.62508i	0.130563	−	0.166025i
$251$	3.93521	−	2.52901i	0.248388	−	0.159630i	−0.410523	−	0.911850i	$-0.634654\pi$
$251$	3.93521	−	2.52901i	0.248388	−	0.159630i	0.658911	+	0.752221i	$0.271017\pi$
$252$	7.06080	+	0.0632308i	0.444788	+	0.00398316i
$253$	15.7015	−	19.2761i	0.987148	−	1.21188i
$254$	2.55401	+	1.47456i	0.160253	+	0.0925219i
$255$	0.0390542	+	0.124085i	0.00244567	+	0.00777051i
$256$	−3.58530	+	1.43534i	−0.224082	+	0.0897087i
$257$	−0.286687	−	3.00232i	−0.0178830	−	0.187280i	0.982116	−	0.188274i	$-0.0602894\pi$
$257$	−0.286687	−	3.00232i	−0.0178830	−	0.187280i	−1.00000		0.000994778i	$0.999683\pi$
$258$	0.0235162	+	1.21689i	0.00146405	+	0.0757600i
$259$	−9.28085	−	0.886214i	−0.576684	−	0.0550667i
$260$	0.157586	+	0.181863i	0.00977304	+	0.0112787i
$261$	−18.8759	−	7.75359i	−1.16839	−	0.479935i
$262$	−0.00208303		0.000611632i	−0.000128690		3.77868e-5i
$263$	−1.00174	−	2.89434i	−0.0617699	−	0.178473i	0.909893	−	0.414843i	$-0.136163\pi$
$263$	−1.00174	−	2.89434i	−0.0617699	−	0.178473i	−0.971663	+	0.236370i	$0.924042\pi$
$264$	−5.76417	+	17.7574i	−0.354760	+	1.09289i
$265$	0.300709	−	6.31266i	0.0184724	−	0.387784i
$266$	1.10924	−	5.75529i	0.0680119	−	0.352879i
$267$	9.20864	+	17.0454i	0.563559	+	1.04316i
$268$	6.55329	−	16.3693i	0.400306	−	0.999917i
$269$	23.7164	−	20.5503i	1.44601	−	1.25298i	0.532336	−	0.846533i	$-0.321314\pi$
$269$	23.7164	−	20.5503i	1.44601	−	1.25298i	0.913676	−	0.406443i	$-0.133231\pi$
$270$	−0.652852	+	1.68105i	−0.0397313	+	0.102305i
$271$	22.5945	−	6.63434i	1.37252	−	0.403007i	0.489359	−	0.872082i	$-0.337231\pi$
$271$	22.5945	−	6.63434i	1.37252	−	0.403007i	0.883158	+	0.469075i	$0.155413\pi$
$272$	0.155097	+	0.217803i	0.00940414	+	0.0132063i
$273$	0.336624	+	0.453899i	0.0203734	+	0.0274712i
$274$	1.75932	−	3.41260i	0.106284	−	0.206163i
$275$	−11.9816	−	20.7528i	−0.722519	−	1.25144i
$276$	5.77285	−	12.7135i	0.347484	−	0.765265i
$277$	−6.60156	+	11.4342i	−0.396649	+	0.687017i	−0.993310	−	0.115477i	$-0.963160\pi$
$277$	−6.60156	+	11.4342i	−0.396649	+	0.687017i	0.596661	+	0.802494i	$0.296494\pi$
$278$	3.14480	+	4.89341i	0.188613	+	0.293487i
$279$	9.60755	+	24.6356i	0.575189	+	1.47490i
$280$	−0.743093	+	1.62715i	−0.0444083	+	0.0972407i
$281$	4.57705	−	18.8669i	0.273044	−	1.12550i	−0.655771	−	0.754960i	$-0.727656\pi$
$281$	4.57705	−	18.8669i	0.273044	−	1.12550i	0.928815	−	0.370543i	$-0.120829\pi$
$282$	−1.31899	+	0.215730i	−0.0785445	+	0.0128465i
$283$	−23.8133	−	8.24187i	−1.41555	−	0.489928i	−0.491061	−	0.871125i	$-0.663391\pi$
$283$	−23.8133	−	8.24187i	−1.41555	−	0.489928i	−0.924494	+	0.381197i	$0.875512\pi$
$284$	5.08568	+	6.46696i	0.301779	+	0.383744i
$285$	−6.71522	−	4.13449i	−0.397775	−	0.244906i
$286$	−0.644780	+	0.223160i	−0.0381266	+	0.0131957i
$287$	−5.23810	−	3.36632i	−0.309195	−	0.198708i
$288$	−0.914689	+	16.1562i	−0.0538986	+	0.952016i
$289$	11.1228	−	12.8364i	0.654285	−	0.755085i
$290$	1.70854	−	1.62909i	0.100329	−	0.0956632i
$291$	−12.7989	+	5.41312i	−0.750285	+	0.317323i
$292$	−4.68231	+	13.5286i	−0.274011	+	0.791703i
$293$	0.567576	−	0.797049i	0.0331581	−	0.0465641i	−0.797664	−	0.603102i	$-0.793931\pi$
$293$	0.567576	−	0.797049i	0.0331581	−	0.0465641i	0.830822	+	0.556538i	$0.187871\pi$
$294$	2.38223	−	4.31667i	0.138935	−	0.251754i
$295$	0.723956	−	0.515527i	0.0421504	−	0.0300151i
$296$	1.97020	−	13.7031i	0.114516	−	0.796475i
$297$	19.6869	+	18.3856i	1.14235	+	1.06684i
$298$		−	9.31449i		−	0.539574i
$299$	1.09031	−	0.244779i	0.0630543	−	0.0141559i
$300$	−9.47366	−	9.55888i	−0.546962	−	0.551882i
$301$	1.54827	+	0.798188i	0.0892407	+	0.0460068i
$302$	−4.60434	−	11.5011i	−0.264950	−	0.661814i
$303$	13.8915	+	2.39999i	0.798049	+	0.137876i
$304$	−15.7521	−	3.82142i	−0.903446	−	0.219174i
$305$	0.217734	−	0.0994359i	0.0124674	−	0.00569368i
$306$	−0.203748	+	0.0373802i	−0.0116475	+	0.00213688i
$307$	4.79627	+	33.3588i	0.273737	+	1.90389i	0.408073	+	0.912949i	$0.366201\pi$
$307$	4.79627	+	33.3588i	0.273737	+	1.90389i	−0.134335	+	0.990936i	$0.542890\pi$
$308$	8.42009	+	8.83073i	0.479779	+	0.503178i
$309$	−15.0720	+	10.1029i	−0.857417	+	0.574736i
$310$	−3.05559	−	0.145556i	−0.173546	−	0.00826702i
$311$	32.7165	+	1.55848i	1.85518	+	0.0883733i	0.945243	−	0.326367i	$-0.105824\pi$
$311$	32.7165	+	1.55848i	1.85518	+	0.0883733i	0.909940	+	0.414740i	$0.136127\pi$
$312$	−0.697023	+	0.467222i	−0.0394611	+	0.0264512i
$313$	−14.8865	−	15.6125i	−0.841436	−	0.882473i	0.152955	−	0.988233i	$-0.451121\pi$
$313$	−14.8865	−	15.6125i	−0.841436	−	0.882473i	−0.994392	+	0.105760i	$0.966272\pi$
$314$	−0.593567	−	4.12835i	−0.0334969	−	0.232976i
$315$	1.67262	+	1.96560i	0.0942417	+	0.110749i
$316$	−6.89352	+	3.14817i	−0.387791	+	0.177098i
$317$	8.06252	+	1.95595i	0.452836	+	0.109857i	0.455689	−	0.890139i	$-0.349393\pi$
$317$	8.06252	+	1.95595i	0.452836	+	0.109857i	−0.00285271	+	0.999996i	$0.500908\pi$
$318$	9.91677	+	1.71328i	0.556105	+	0.0960760i
$319$	−13.1057	−	32.7364i	−0.733777	−	1.83289i
$320$	0.725110	+	0.373820i	0.0405349	+	0.0208972i
$321$	10.1328	+	10.2239i	0.565558	+	0.570645i
$322$	2.29334	+	3.02150i	0.127803	+	0.168381i
$323$		−	0.905842i		−	0.0504024i
$324$	13.3203	+	7.17190i	0.740015	+	0.398439i
$325$	0.153282	−	1.06610i	0.00850256	−	0.0591366i
$326$	−4.60842	+	3.28164i	−0.255237	+	0.181753i
$327$	9.51707	−	17.2452i	0.526295	−	0.953661i
$328$	5.36314	−	7.53148i	0.296130	−	0.415857i
$329$	−0.625611	+	1.80759i	−0.0344911	+	0.0996554i
$330$	−2.87010	+	1.21387i	−0.157994	+	0.0668214i
$331$	−3.28670	+	3.13386i	−0.180653	+	0.172253i	−0.775010	−	0.631949i	$-0.782255\pi$
$331$	−3.28670	+	3.13386i	−0.180653	+	0.172253i	0.594357	+	0.804202i	$0.297407\pi$
$332$	13.4779	−	15.5544i	0.739699	−	0.853658i
$333$	−16.7063	−	10.9491i	−0.915501	−	0.600009i
$334$	−0.592992	−	0.381093i	−0.0324471	−	0.0208525i
$335$	6.09047	−	2.10793i	0.332758	−	0.115169i
$336$	4.51739	+	2.78131i	0.246444	+	0.151733i
$337$	−6.32833	−	8.04712i	−0.344726	−	0.438355i	0.582515	−	0.812820i	$-0.302069\pi$
$337$	−6.32833	−	8.04712i	−0.344726	−	0.438355i	−0.927241	+	0.374465i	$0.877826\pi$
$338$	6.91043	+	2.39172i	0.375878	+	0.130093i
$339$	−11.1731	+	1.82744i	−0.606839	+	0.0992531i
$340$	−0.0297636	+	0.122687i	−0.00161416	+	0.00665365i
$341$	−18.9817	+	41.5642i	−1.02792	+	2.25083i
$342$	7.85067	−	9.80103i	0.424516	−	0.529979i
$343$	−9.11409	−	14.1818i	−0.492114	−	0.765745i
$344$	−1.29329	+	2.24005i	−0.0697297	+	0.120775i
$345$	4.89378	−	1.44846i	0.263472	−	0.0779825i
$346$	−2.22723	−	3.85767i	−0.119737	−	0.207390i
$347$	11.1425	−	21.6134i	0.598159	−	1.16027i	−0.374325	−	0.927298i	$-0.622126\pi$
$347$	11.1425	−	21.6134i	0.598159	−	1.16027i	0.972484	−	0.232969i	$-0.0748441\pi$
$348$	−11.7969	−	15.9068i	−0.632383	−	0.852696i
$349$	−4.26125	−	5.98408i	−0.228099	−	0.320321i	0.684626	−	0.728895i	$-0.259966\pi$
$349$	−4.26125	−	5.98408i	−0.228099	−	0.320321i	−0.912725	+	0.408574i	$0.866026\pi$
$350$	3.50807	−	1.03006i	0.187514	−	0.0550591i
$351$	0.184719	+	1.19655i	0.00985958	+	0.0638672i
$352$	−21.1329	+	18.3118i	−1.12639	+	0.976022i
$353$	10.7970	−	26.9696i	0.574666	−	1.43545i	−0.301513	−	0.953462i	$-0.597492\pi$
$353$	10.7970	−	26.9696i	0.574666	−	1.43545i	0.876180	−	0.481985i	$-0.160084\pi$
$354$	0.672689	+	1.24516i	0.0357530	+	0.0661795i
$355$	−0.569108	+	2.95281i	−0.0302051	+	0.156719i
$356$	−0.894630	+	18.7806i	−0.0474153	+	0.995370i
$357$	−0.0915337	+	0.281983i	−0.00484448	+	0.0149241i
$358$	−0.0175298	−	0.0506491i	−0.000926481	−	0.00267689i
$359$	−29.7399	−	8.73242i	−1.56961	−	0.460880i	−0.622724	−	0.782442i	$-0.713974\pi$
$359$	−29.7399	−	8.73242i	−1.56961	−	0.460880i	−0.946888	+	0.321562i	$0.895792\pi$
$360$	−3.03363	+	2.34201i	−0.159886	+	0.123435i
$361$	23.5181	+	27.1413i	1.23779	+	1.42849i
$362$	5.77570	+	0.551513i	0.303564	+	0.0289869i
$363$	0.531237	+	27.4898i	0.0278827	+	1.44284i
$364$	0.0521307	+	0.545937i	0.00273239	+	0.0286149i
$365$	−4.85791	+	1.94481i	−0.254275	+	0.101796i
$366$	0.114433	+	0.363582i	0.00598150	+	0.0190047i
$367$	−15.8019	−	9.12322i	−0.824851	−	0.476228i	0.0272353	−	0.999629i	$-0.491330\pi$
$367$	−15.8019	−	9.12322i	−0.824851	−	0.476228i	−0.852087	+	0.523401i	$0.824663\pi$
$368$	8.64818	−	5.93740i	0.450818	−	0.309508i
$369$	−6.56644	−	11.6123i	−0.341835	−	0.604513i
$370$	1.94396	−	1.24930i	0.101061	−	0.0649483i
$371$	8.90330	−	11.3215i	0.462236	−	0.587781i
$372$	−4.36883	+	25.2876i	−0.226513	+	1.31110i
$373$	2.32466	−	2.43804i	0.120367	−	0.126237i	−0.660793	−	0.750568i	$-0.729780\pi$
$373$	2.32466	−	2.43804i	0.120367	−	0.126237i	0.781160	+	0.624331i	$0.214628\pi$
$374$	−0.291582	−	0.207635i	−0.0150774	−	0.0107365i
$375$	0.776246	−	10.2106i	0.0400852	−	0.527275i
$376$	−2.63687	−	1.05564i	−0.135986	−	0.0544407i
$377$	0.446523	−	1.52072i	0.0229971	−	0.0783209i
$378$	−3.43424	+	2.25770i	−0.176638	+	0.116124i
$379$	9.34372	−	14.5391i	0.479955	−	0.746824i	−0.513860	−	0.857874i	$-0.671785\pi$
$379$	9.34372	−	14.5391i	0.479955	−	0.746824i	0.993815	+	0.111050i	$0.0354214\pi$
$380$	−3.50689	−	6.80241i	−0.179900	−	0.348956i
$381$	9.02260	−	0.604716i	0.462242	−	0.0309806i
$382$	−5.33173	+	1.29346i	−0.272795	+	0.0661794i
$383$	−5.63768	+	4.43352i	−0.288072	+	0.226542i	−0.751729	−	0.659473i	$-0.770780\pi$
$383$	−5.63768	+	4.43352i	−0.288072	+	0.226542i	0.463656	+	0.886015i	$0.346537\pi$
$384$	−11.2755	+	16.4999i	−0.575400	+	0.842007i
$385$	−0.423940	+	4.43971i	−0.0216060	+	0.226268i
$386$	−2.46494	−	8.39483i	−0.125462	−	0.427285i
$387$	2.13748	+	3.05928i	0.108654	+	0.155512i
$388$	−13.3491	−	1.91931i	−0.677696	−	0.0974380i
$389$	0.780066	+	16.3756i	0.0395509	+	0.830276i	0.928289	+	0.371860i	$0.121280\pi$
$389$	0.780066	+	16.3756i	0.0395509	+	0.830276i	−0.888738	+	0.458416i	$0.848417\pi$
$390$	−0.135128	−	0.0368567i	−0.00684247	−	0.00186631i
$391$	0.436402	+	0.391453i	0.0220698	+	0.0197966i
$392$	9.07419	−	5.23899i	0.458316	−	0.264609i
$393$	−0.00634974	+	0.00199850i	−0.000320302	+	0.000100811i
$394$	−10.6685	−	8.38982i	−0.537473	−	0.422673i
$395$	−2.51970	−	1.15071i	−0.126780	−	0.0578984i
$396$	7.14012	+	25.1479i	0.358804	+	1.26373i
$397$	11.1788	+	24.4782i	0.561049	+	1.22853i	0.951428	+	0.307872i	$0.0996168\pi$
$397$	11.1788	+	24.4782i	0.561049	+	1.22853i	−0.390379	+	0.920654i	$0.627656\pi$
$398$	6.99951	−	1.34904i	0.350854	−	0.0676215i
$399$	−7.00071	−	16.5526i	−0.350474	−	0.828667i
$400$	−2.38377	−	9.82603i	−0.119188	−	0.491302i
$401$	−15.1070	−	2.91164i	−0.754410	−	0.145401i	−0.202475	−	0.979288i	$-0.564898\pi$
$401$	−15.1070	−	2.91164i	−0.754410	−	0.145401i	−0.551935	+	0.833887i	$0.686110\pi$
$402$	2.13662	+	10.0380i	0.106565	+	0.500652i
$403$	−1.82545	+	0.941086i	−0.0909323	+	0.0468788i
$404$	10.3396	+	8.95929i	0.514413	+	0.445741i
$405$	1.20722	+	5.39627i	0.0599871	+	0.268143i
$406$	5.32535	−	0.765670i	0.264293	−	0.0379996i
$407$	−6.53226	−	33.8926i	−0.323792	−	1.67999i
$408$	−0.411780	−	0.155690i	−0.0203861	−	0.00770778i
$409$	8.71007	+	8.30503i	0.430685	+	0.410657i	0.874167	−	0.485626i	$-0.161408\pi$
$409$	8.71007	+	8.30503i	0.430685	+	0.410657i	−0.443482	+	0.896284i	$0.646257\pi$
$410$	1.53630	−	0.146699i	0.0758725	−	0.00724495i
$411$	−1.34529	−	11.6956i	−0.0663585	−	0.576902i
$412$	−17.5893	+	0.837881i	−0.866562	+	0.0412794i
$413$	2.02548			0.0996672
$414$	1.32917	+	8.01761i	0.0653252	+	0.394044i
$415$	7.52285			0.369282
$416$	−1.25541	+	0.0598026i	−0.0615516	+	0.00293206i
$417$	16.3644	+	7.09450i	0.801366	+	0.347419i
$418$	21.6014	−	2.06269i	1.05656	−	0.100889i
$419$	20.5671	+	19.6107i	1.00477	+	0.958045i	0.999120	−	0.0419387i	$-0.0133534\pi$
$419$	20.5671	+	19.6107i	1.00477	+	0.958045i	0.00564885	+	0.999984i	$0.498202\pi$
$420$	0.404300	+	2.47191i	0.0197278	+	0.120617i
$421$	3.18465	+	16.5235i	0.155210	+	0.805307i	0.973180	+	0.230045i	$0.0738875\pi$
$421$	3.18465	+	16.5235i	0.155210	+	0.805307i	−0.817970	+	0.575261i	$0.804900\pi$
$422$	13.1747	−	1.89423i	0.641334	−	0.0922099i
$423$	−2.99116	+	2.80136i	−0.145435	+	0.136207i
$424$	16.1633	+	14.0056i	0.784961	+	0.680173i
$425$	0.502242	−	0.258924i	0.0243623	−	0.0125596i
$426$	−4.55464	−	1.47847i	−0.220673	−	0.0716322i
$427$	0.535658	+	0.103240i	0.0259223	+	0.00499611i
$428$	3.29347	+	13.5759i	0.159196	+	0.656214i
$429$	−1.26126	+	1.66922i	−0.0608944	+	0.0805907i
$430$	−0.423941	+	0.0817079i	−0.0204443	+	0.00394031i
$431$	11.2956	+	24.7339i	0.544089	+	1.19139i	0.959488	+	0.281749i	$0.0909147\pi$
$431$	11.2956	+	24.7339i	0.544089	+	1.19139i	−0.415399	+	0.909639i	$0.636358\pi$
$432$	5.78465	+	9.78364i	0.278314	+	0.470716i
$433$	−13.4786	−	6.15546i	−0.647739	−	0.295813i	0.0643228	−	0.997929i	$-0.479511\pi$
$433$	−13.4786	−	6.15546i	−0.647739	−	0.295813i	−0.712062	+	0.702117i	$0.752239\pi$
$434$	−5.48007	−	4.30958i	−0.263052	−	0.206866i
$435$	1.57034	−	7.06628i	0.0752923	−	0.338802i
$436$	16.5546	−	9.55778i	0.792819	−	0.457735i
$437$	−35.5335	−	0.609724i	−1.69980	−	0.0291671i
$438$	−2.12058	−	8.05827i	−0.101325	−	0.385039i
$439$	0.292186	+	6.13373i	0.0139453	+	0.292747i	0.995057	+	0.0993052i	$0.0316620\pi$
$439$	0.292186	+	6.13373i	0.0139453	+	0.292747i	−0.981112	+	0.193442i	$0.938035\pi$
$440$	−6.55517	−	0.942492i	−0.312506	−	0.0449315i
$441$	−1.30223	−	15.0618i	−0.0620111	−	0.717229i
$442$	−0.00453276	−	0.0154371i	−0.000215601	−	0.000734270i
$443$	−3.04151	+	31.8521i	−0.144506	+	1.51334i	0.574597	+	0.818436i	$0.305159\pi$
$443$	−3.04151	+	31.8521i	−0.144506	+	1.51334i	−0.719104	+	0.694903i	$0.755447\pi$
$444$	−8.39201	−	17.4743i	−0.398267	−	0.829295i
$445$	−5.40208	+	4.24824i	−0.256083	+	0.201386i
$446$	−7.08143	+	1.71794i	−0.335315	+	0.0813466i
$447$	−15.9026	−	23.7242i	−0.752165	−	1.12211i
$448$	0.851940	+	1.65253i	0.0402504	+	0.0780748i
$449$	−13.8805	+	21.5984i	−0.655059	+	1.01929i	0.341775	+	0.939782i	$0.388972\pi$
$449$	−13.8805	+	21.5984i	−0.655059	+	1.01929i	−0.996834	+	0.0795099i	$0.974664\pi$
$450$	7.67818	+	1.55128i	0.361953	+	0.0731283i
$451$	6.49456	−	22.1184i	0.305817	−	1.04152i
$452$	−10.2003	−	4.08359i	−0.479782	−	0.192076i
$453$	−31.3631	−	21.4325i	−1.47357	−	1.00699i
$454$	−10.3793	−	7.39105i	−0.487124	−	0.346879i
$455$	−0.138331	+	0.145078i	−0.00648506	+	0.00680134i
$456$	25.0461	−	9.21417i	1.17289	−	0.431493i
$457$	2.31950	−	2.94949i	0.108502	−	0.137971i	−0.728769	−	0.684759i	$-0.759907\pi$
$457$	2.31950	−	2.94949i	0.108502	−	0.137971i	0.837271	+	0.546788i	$0.184150\pi$
$458$	−1.81336	+	1.16537i	−0.0847326	+	0.0544543i
$459$	−0.455132	+	0.443066i	−0.0212437	+	0.0206805i
$460$	4.79263	+	1.25012i	0.223458	+	0.0582872i
$461$	−2.08258	−	1.20238i	−0.0969953	−	0.0560002i	0.450718	−	0.892667i	$-0.351168\pi$
$461$	−2.08258	−	1.20238i	−0.0969953	−	0.0560002i	−0.547713	+	0.836666i	$0.684501\pi$
$462$	−6.93282	−	1.54068i	−0.322544	−	0.0716791i
$463$	16.2085	−	6.48890i	0.753272	−	0.301565i	0.0369336	−	0.999318i	$-0.488241\pi$
$463$	16.2085	−	6.48890i	0.753272	−	0.301565i	0.716338	+	0.697753i	$0.245817\pi$
$464$	−1.41430	−	14.8112i	−0.0656572	−	0.687593i
$465$	−8.03116	+	4.84606i	−0.372436	+	0.224731i
$466$	−1.05711	−	0.100942i	−0.0489698	−	0.00467605i
$467$	10.6973	+	12.3453i	0.495011	+	0.571273i	0.947198	−	0.320650i	$-0.103901\pi$
$467$	10.6973	+	12.3453i	0.495011	+	0.571273i	−0.452187	+	0.891923i	$0.649356\pi$
$468$	−0.446449	+	1.08687i	−0.0206371	+	0.0502404i
$469$	14.0931	+	4.13811i	0.650759	+	0.191080i
$470$	−0.155062	−	0.448022i	−0.00715248	−	0.0206657i
$471$	−8.56013	−	9.50159i	−0.394430	−	0.437810i
$472$	−0.143110	+	3.00426i	−0.00658719	+	0.138282i
$473$	−1.22048	+	6.33244i	−0.0561176	+	0.291166i
$474$	2.31261	−	3.75614i	0.106222	−	0.172525i
$475$	−12.7311	+	31.8006i	−0.584141	+	1.45911i
$476$	−0.217441	+	0.188414i	−0.00996640	+	0.00863594i
$477$	28.1833	−	12.5671i	1.29042	−	0.575407i
$478$	−5.25737	+	1.54370i	−0.240466	+	0.0706073i
$479$	12.8909	+	18.1027i	0.589001	+	0.827136i	0.996281	−	0.0861677i	$-0.0274621\pi$
$479$	12.8909	+	18.1027i	0.589001	+	0.827136i	−0.407280	+	0.913303i	$0.633523\pi$
$480$	−5.70264	+	0.655949i	−0.260289	+	0.0299399i
$481$	0.710888	−	1.37893i	0.0324137	−	0.0628738i
$482$	−2.45217	−	4.24728i	−0.111693	−	0.193458i
$483$	10.9998	+	3.78040i	0.500506	+	0.172014i
$484$	−13.3417	+	23.1085i	−0.606440	+	1.05038i
$485$	−2.66508	−	4.14694i	−0.121015	−	0.188303i
$486$	−8.76436	+	0.849390i	−0.397560	+	0.0385291i
$487$	−6.08758	+	13.3299i	−0.275855	+	0.604037i	−0.995957	−	0.0898305i	$-0.971367\pi$
$487$	−6.08758	+	13.3299i	−0.275855	+	0.604037i	0.720103	+	0.693868i	$0.244095\pi$
$488$	−0.190976	+	0.787212i	−0.00864505	+	0.0356354i
$489$	−6.13500	+	16.2263i	−0.277434	+	0.733780i
$490$	1.65275	+	0.572023i	0.0746638	+	0.0258414i
$491$	−19.7766	−	25.1480i	−0.892505	−	1.13491i	−0.990194	−	0.139696i	$-0.955388\pi$
$491$	−19.7766	−	25.1480i	−0.892505	−	1.13491i	0.0976894	−	0.995217i	$-0.468855\pi$
$492$	0.366046	−	12.9414i	0.0165026	−	0.583442i
$493$	0.785758	−	0.271954i	0.0353888	−	0.0122482i
$494$	0.820495	+	0.527300i	0.0369158	+	0.0237244i
$495$	−5.23776	+	7.99185i	−0.235420	+	0.359207i
$496$	−12.6256	+	14.5708i	−0.566907	+	0.654246i
$497$	−4.95999	+	4.72935i	−0.222486	+	0.212140i
$498$	−1.47543	+	11.8882i	−0.0661154	+	0.532722i
$499$	1.51202	−	4.36868i	0.0676871	−	0.195569i	−0.906084	−	0.423097i	$-0.860943\pi$
$499$	1.51202	−	4.36868i	0.0676871	−	0.195569i	0.973772	+	0.227528i	$0.0730642\pi$
$500$	5.76451	−	8.09512i	0.257797	−	0.362025i
$501$	−2.16100	+	0.0417610i	−0.0965463	+	0.00186574i
$502$	−2.15239	+	1.53271i	−0.0960657	+	0.0684081i
$503$	−3.21306	+	22.3473i	−0.143263	+	0.996417i	0.783666	+	0.621182i	$0.213347\pi$
$503$	−3.21306	+	22.3473i	−0.143263	+	0.996417i	−0.926930	+	0.375235i	$0.877562\pi$
$504$	−8.72776	+	0.337452i	−0.388765	+	0.0150313i
$505$			5.00071i			0.222529i
$506$	−8.34116	+	11.2982i	−0.370810	+	0.502264i
$507$	21.6844	−	5.70637i	0.963036	−	0.253429i
$508$	7.80034	+	4.02135i	0.346084	+	0.178419i
$509$	12.7151	+	31.7607i	0.563586	+	1.40777i	0.887114	+	0.461550i	$0.152707\pi$
$509$	12.7151	+	31.7607i	0.563586	+	1.40777i	−0.323528	+	0.946218i	$0.604869\pi$
$510$	−0.0253706	−	0.0689627i	−0.00112343	−	0.00305372i
$511$	−11.5893	−	2.81154i	−0.512681	−	0.124375i
$512$	−19.0065	+	8.67998i	−0.839977	+	0.383604i
$513$	3.26257	−	38.3668i	0.144046	−	1.69394i
$514$	0.242452	+	1.68629i	0.0106941	+	0.0743790i
$515$	−4.44167	−	4.65829i	−0.195724	−	0.205269i
$516$	0.242202	+	3.61375i	0.0106624	+	0.159087i
$517$	−7.07360	−	0.336957i	−0.311097	−	0.0148194i
$518$	5.26034	+	0.250581i	0.231126	+	0.0110099i
$519$	−12.2590	−	6.02303i	−0.538109	−	0.264382i
$520$	−0.205410	−	0.215428i	−0.00900784	−	0.00944715i
$521$	−3.81055	−	26.5030i	−0.166943	−	1.16112i	−0.885157	−	0.465293i	$-0.845949\pi$
$521$	−3.81055	−	26.5030i	−0.166943	−	1.16112i	0.718213	−	0.695823i	$-0.244960\pi$
$522$	10.8587	+	3.86746i	0.475272	+	0.169274i
$523$	−27.1301	+	12.3899i	−1.18632	+	0.541772i	−0.908103	−	0.418747i	$-0.862469\pi$
$523$	−27.1301	+	12.3899i	−1.18632	+	0.541772i	−0.278213	+	0.960519i	$0.589742\pi$
$524$	−0.00627821	−	0.00152308i	−0.000274265	−	6.65360e-5i
$525$	7.17650	−	8.61289i	0.313208	−	0.375897i
$526$	0.643003	+	1.60614i	0.0280363	+	0.0700312i
$527$	−0.957681	−	0.493719i	−0.0417172	−	0.0215067i
$528$	−5.16817	+	18.9481i	−0.224916	+	0.824610i
$529$	15.6493	−	16.8553i	0.680404	−	0.732838i
$530$			3.56986i			0.155065i
$531$	3.83920	+	2.02297i	0.166607	+	0.0877892i
$532$	2.48221	−	17.2641i	0.107617	−	0.748495i
$533$	0.843996	−	0.601007i	0.0365575	−	0.0260325i
$534$	−5.65391	−	9.36997i	−0.244669	−	0.405478i
$535$	−2.96185	+	4.15934i	−0.128052	+	0.179824i
$536$	−7.13354	+	20.6110i	−0.308122	+	0.890260i
$537$	−0.131122	−	0.0990756i	−0.00565832	−	0.00427543i
$538$	−12.8291	+	12.2325i	−0.553102	+	0.527382i
$539$	17.1076	−	19.7433i	0.736878	−	0.850403i
$540$	−1.70252	+	5.08920i	−0.0732647	+	0.219004i
$541$	21.5087	+	13.8228i	0.924732	+	0.594289i	0.914027	−	0.405654i	$-0.132956\pi$
$541$	21.5087	+	13.8228i	0.924732	+	0.594289i	0.0107049	+	0.999943i	$0.496592\pi$
$542$	−12.5701	+	4.35057i	−0.539934	+	0.186873i
$543$	15.6524	−	8.45610i	0.671709	−	0.362886i
$544$	−0.407595	−	0.518299i	−0.0174755	−	0.0222219i
$545$	6.60278	+	2.28524i	0.282832	+	0.0978890i
$546$	−0.202132	−	0.247055i	−0.00865047	−	0.0105730i
$547$	4.11304	−	16.9542i	0.175861	−	0.724908i	−0.813760	−	0.581201i	$-0.802583\pi$
$547$	4.11304	−	16.9542i	0.175861	−	0.724908i	0.989620	−	0.143706i	$-0.0459020\pi$
$548$	4.74621	−	10.3927i	0.202748	−	0.443956i
$549$	0.912204	+	0.730680i	0.0389319	+	0.0311847i
$550$	7.31815	+	11.3873i	0.312047	+	0.485555i
$551$	−25.2029	+	43.6527i	−1.07368	+	1.85967i
$552$	−6.38442	+	16.0481i	−0.271739	+	0.683053i
$553$	−3.15645	−	5.46713i	−0.134226	−	0.232486i
$554$	3.41747	−	6.62896i	0.145194	−	0.281637i
$555$	2.81836	−	6.50090i	0.119633	−	0.275948i
$556$	10.0405	+	14.0999i	0.425813	+	0.597970i
$557$	−38.9028	+	11.4229i	−1.64837	+	0.484004i	−0.968434	−	0.249272i	$-0.919809\pi$
$557$	−38.9028	+	11.4229i	−1.64837	+	0.484004i	−0.679932	+	0.733276i	$0.737991\pi$
$558$	−6.08300	−	13.6419i	−0.257514	−	0.577507i
$559$	−0.219061	+	0.189817i	−0.00926529	+	0.00802842i
$560$	−0.699398	+	1.74701i	−0.0295550	+	0.0738248i
$561$	−1.09716	−	0.0310331i	−0.0463220	−	0.00131022i
$562$	−2.07541	+	10.7682i	−0.0875459	+	0.454231i
$563$	1.00059	−	21.0049i	0.0421698	−	0.885252i	−0.874358	−	0.485281i	$-0.838717\pi$
$563$	1.00059	−	21.0049i	0.0421698	−	0.885252i	0.916528	−	0.399971i	$-0.130980\pi$
$564$	−3.89002	+	0.827998i	−0.163799	+	0.0348650i
$565$	−1.31353	−	3.79518i	−0.0552605	−	0.159665i
$566$	13.6577	+	4.01025i	0.574075	+	0.168564i
$567$	−4.89252	+	11.6137i	−0.205466	+	0.487728i
$568$	−6.66428	−	7.69099i	−0.279627	−	0.322707i
$569$	17.5766	+	1.67836i	0.736848	+	0.0703605i	0.456730	−	0.889605i	$-0.349020\pi$
$569$	17.5766	+	1.67836i	0.736848	+	0.0703605i	0.280118	+	0.959966i	$0.409627\pi$
$570$	3.90005	+	2.15231i	0.163355	+	0.0901504i
$571$	−2.87233	−	30.0804i	−0.120203	−	1.25883i	−0.831337	−	0.555769i	$-0.812424\pi$
$571$	−2.87233	−	30.0804i	−0.120203	−	1.25883i	0.711133	−	0.703057i	$-0.248182\pi$
$572$	−1.88495	+	0.754620i	−0.0788137	+	0.0315523i
$573$	−11.3717	+	12.3973i	−0.475059	+	0.517905i
$574$	3.04596	+	1.75859i	0.127136	+	0.0734020i
$575$	−9.81876	−	19.8758i	−0.409470	−	0.828876i
$576$	−0.0356702	+	3.98319i	−0.00148626	+	0.165966i
$577$	10.1408	−	6.51710i	0.422167	−	0.271310i	−0.312261	−	0.949996i	$-0.601087\pi$
$577$	10.1408	−	6.51710i	0.422167	−	0.271310i	0.734429	+	0.678686i	$0.237450\pi$
$578$	−5.93082	+	7.54165i	−0.246689	+	0.313691i
$579$	−20.6107	−	17.1734i	−0.856550	−	0.713701i
$580$	4.84780	−	5.08423i	0.201294	−	0.211111i
$581$	13.9656	+	9.94487i	0.579392	+	0.412583i
$582$	7.07601	−	3.39824i	0.293310	−	0.140862i
$583$	49.5036	+	19.8183i	2.05023	+	0.820789i
$584$	4.98901	−	16.9910i	0.206447	−	0.703094i
$585$	−0.407098	+	0.136828i	−0.0168314	+	0.00565716i
$586$	−0.298820	+	0.464973i	−0.0123441	+	0.0192078i
$587$	−18.8381	−	36.5408i	−0.777532	−	1.50820i	−0.859256	−	0.511547i	$-0.829073\pi$
$587$	−18.8381	−	36.5408i	−0.777532	−	1.50820i	0.0817235	−	0.996655i	$-0.473958\pi$
$588$	6.46976	−	13.1682i	0.266809	−	0.543049i
$589$	63.4754	−	15.3990i	2.61546	−	0.634503i
$590$	−0.394621	+	0.310333i	−0.0162463	+	0.0127762i
$591$	−41.4968	−	3.15472i	−1.70695	−	0.129768i
$592$	1.38438	−	14.4979i	0.0568977	−	0.595860i
$593$	−10.0681	−	34.2890i	−0.413449	−	1.40808i	−0.858611	−	0.512628i	$-0.828672\pi$
$593$	−10.0681	−	34.2890i	−0.413449	−	1.40808i	0.445161	−	0.895450i	$-0.353146\pi$
$594$	−11.6021	−	9.84453i	−0.476039	−	0.403926i
$595$	−0.104095	−	0.0149665i	−0.00426746	−	0.000613569i
$596$	−1.31887	−	27.6865i	−0.0540230	−	1.13408i
$597$	15.5246	−	15.3862i	0.635382	−	0.629717i
$598$	−0.608605	+	0.167416i	−0.0248877	+	0.00684615i
$599$	3.14496	−	1.81574i	0.128500	−	0.0741892i	−0.434372	−	0.900733i	$-0.643030\pi$
$599$	3.14496	−	1.81574i	0.128500	−	0.0741892i	0.562872	+	0.826544i	$0.309696\pi$
$600$	12.2679	+	11.2530i	0.500834	+	0.459401i
$601$	23.8620	+	18.7653i	0.973352	+	0.765453i	0.972105	−	0.234546i	$-0.0753605\pi$
$601$	23.8620	+	18.7653i	0.973352	+	0.765453i	0.00124745	+	0.999999i	$0.499603\pi$
$602$	−0.895030	−	0.408747i	−0.0364787	−	0.0166593i
$603$	22.5799	+	21.9192i	0.919524	+	0.892620i
$604$	−15.3145	−	33.5340i	−0.623137	−	1.36448i
$605$	−9.57696	+	1.84581i	−0.389359	+	0.0750428i
$606$	−7.90251	−	0.980770i	−0.321018	−	0.0398411i
$607$	3.67475	+	15.1475i	0.149153	+	0.614818i	0.996486	+	0.0837563i	$0.0266917\pi$
$607$	3.67475	+	15.1475i	0.149153	+	0.614818i	−0.847333	+	0.531062i	$0.821793\pi$
$608$	39.2493	+	7.56469i	1.59177	+	0.306789i
$609$	12.2565	−	11.0421i	0.496660	−	0.447449i
$610$	−0.120179	+	0.0619567i	−0.00486592	+	0.00250855i
$611$	−0.240551	−	0.208438i	−0.00973164	−	0.00843251i
$612$	−0.600331	+	0.139959i	−0.0242669	+	0.00565749i
$613$	46.7918	−	6.72764i	1.88990	−	0.271727i	0.902588	−	0.430505i	$-0.141664\pi$
$613$	46.7918	−	6.72764i	1.88990	−	0.271727i	0.987314	+	0.158778i	$0.0507553\pi$
$614$	−3.60279	−	18.6931i	−0.145397	−	0.754390i
$615$	3.66253	−	2.99656i	0.147687	−	0.120833i
$616$	−10.9233	−	10.4153i	−0.440111	−	0.419645i
$617$	7.04931	−	0.673127i	0.283794	−	0.0270991i	0.0478118	−	0.998856i	$-0.484775\pi$
$617$	7.04931	−	0.673127i	0.283794	−	0.0270991i	0.235983	+	0.971757i	$0.424169\pi$
$618$	8.23252	−	6.10546i	0.331161	−	0.245598i
$619$	41.7826	−	1.99035i	1.67938	−	0.0799989i	0.813922	−	0.580974i	$-0.197328\pi$
$619$	41.7826	−	1.99035i	1.67938	−	0.0799989i	0.865462	+	0.500975i	$0.167025\pi$
$620$	−9.10309			−0.365589
$621$	17.0738	+	18.1517i	0.685149	+	0.728403i
$622$	−18.5015			−0.741842
$623$	−15.6446	+	0.745242i	−0.626786	+	0.0298575i
$624$	−0.709048	+	0.525850i	−0.0283847	+	0.0210508i
$625$	−19.3919	+	1.85170i	−0.775675	+	0.0740680i
$626$	8.81903	+	8.40893i	0.352479	+	0.336088i
$627$	51.4976	−	42.1336i	2.05661	−	1.68266i
$628$	−2.34887	−	12.1871i	−0.0937302	−	0.486318i
$629$	0.805616	−	0.115830i	0.0321220	−	0.00461845i
$630$	−0.996573	−	1.06409i	−0.0397044	−	0.0423945i
$631$	−13.1549	−	11.3988i	−0.523689	−	0.453779i	0.352455	−	0.935829i	$-0.385347\pi$
$631$	−13.1549	−	11.3988i	−0.523689	−	0.453779i	−0.876144	+	0.482050i	$0.839892\pi$
$632$	8.33207	−	4.29548i	0.331432	−	0.170865i
$633$	30.3222	−	27.3177i	1.20520	−	1.08578i
$634$	−4.60168	−	0.886900i	−0.182756	−	0.0352233i
$635$	0.756254	+	3.11732i	0.0300110	+	0.123707i
$636$	29.7193	+	3.68842i	1.17845	+	0.146255i
$637$	1.15297	−	0.222216i	0.0456822	−	0.00880453i
$638$	8.27447	+	18.1186i	0.327589	+	0.717320i
$639$	−14.1249	+	4.01042i	−0.558774	+	0.158650i
$640$	−6.44845	−	2.94491i	−0.254898	−	0.116408i
$641$	24.7102	+	19.4323i	0.975994	+	0.767530i	0.972605	−	0.232464i	$-0.0746788\pi$
$641$	24.7102	+	19.4323i	0.975994	+	0.767530i	0.00338920	+	0.999994i	$0.498921\pi$
$642$	−5.99201	−	5.49630i	−0.236486	−	0.216922i
$643$	−10.7225	+	6.19062i	−0.422853	+	0.244134i	−0.696297	−	0.717754i	$-0.745170\pi$
$643$	−10.7225	+	6.19062i	−0.422853	+	0.244134i	0.273444	+	0.961888i	$0.411837\pi$
$644$	7.24456	+	8.65640i	0.285476	+	0.341110i
$645$	−0.940286	+	0.931903i	−0.0370237	+	0.0366936i
$646$	0.0243468	+	0.511102i	0.000957911	+	0.0201090i
$647$	−16.8919	−	2.42868i	−0.664087	−	0.0954813i	−0.197975	−	0.980207i	$-0.563437\pi$
$647$	−16.8919	−	2.42868i	−0.664087	−	0.0954813i	−0.466112	+	0.884726i	$0.654346\pi$
$648$	−16.8801	−	8.07732i	−0.663114	−	0.317307i
$649$	2.11266	+	7.19507i	0.0829293	+	0.282431i
$650$	−0.0578320	+	0.605644i	−0.00226836	+	0.0237553i
$651$	−21.3155	−	1.62048i	−0.835422	−	0.0635115i
$652$	−13.2335	+	10.4069i	−0.518262	+	0.407566i
$653$	−21.4941	+	5.21441i	−0.841129	+	0.204056i	−0.633103	−	0.774068i	$-0.718219\pi$
$653$	−21.4941	+	5.21441i	−0.841129	+	0.204056i	−0.208026	+	0.978123i	$0.566704\pi$
$654$	−4.90629	+	9.98602i	−0.191851	+	0.390484i
$655$	−0.00108204	−	0.00209886i	−4.22786e−5	−	8.20091e-5i
$656$	5.25863	−	8.18259i	0.205315	−	0.319476i
$657$	−19.1590	−	16.9041i	−0.747463	−	0.659491i
$658$	0.304404	−	1.03671i	0.0118669	−	0.0404150i
$659$	25.6157	+	10.2550i	0.997846	+	0.399477i	0.812352	−	0.583168i	$-0.198187\pi$
$659$	25.6157	+	10.2550i	0.997846	+	0.399477i	0.185495	+	0.982645i	$0.440611\pi$
$660$	−8.35924	+	4.01451i	−0.325383	+	0.156265i
$661$	11.1053	+	7.90802i	0.431944	+	0.307586i	0.775270	−	0.631630i	$-0.217614\pi$
$661$	11.1053	+	7.90802i	0.431944	+	0.307586i	−0.343325	+	0.939217i	$0.611553\pi$
$662$	1.77022	−	1.85655i	0.0688015	−	0.0721570i
$663$	−0.0379007	−	0.0315799i	−0.00147194	−	0.00122646i
$664$	−15.7373	+	20.0116i	−0.610727	+	0.776602i
$665$	5.36318	−	3.44671i	0.207975	−	0.133658i
$666$	9.72047	+	5.72879i	0.376661	+	0.221986i
$667$	−10.1390	−	31.0060i	−0.392585	−	1.20056i
$668$	−1.81658	−	1.04880i	−0.0702854	−	0.0405793i
$669$	−15.1035	+	16.4657i	−0.583935	+	0.636600i
$670$	−3.37976	+	1.35305i	−0.130571	+	0.0522729i
$671$	0.191979	+	2.01049i	0.00741126	+	0.0776142i
$672$	−11.4537	−	6.32092i	−0.441835	−	0.243835i
$673$	−16.3312	−	1.55944i	−0.629520	−	0.0601119i	−0.224581	−	0.974455i	$-0.572101\pi$
$673$	−16.3312	−	1.55944i	−0.629520	−	0.0601119i	−0.404939	+	0.914344i	$0.632707\pi$
$674$	3.78691	+	4.37033i	0.145866	+	0.168339i
$675$	22.2049	−	9.15775i	0.854669	−	0.352482i
$676$	20.8793	+	6.13071i	0.803050	+	0.235797i
$677$	−2.08293	−	6.01822i	−0.0800534	−	0.231299i	0.897871	−	0.440259i	$-0.145113\pi$
$677$	−2.08293	−	6.01822i	−0.0800534	−	0.231299i	−0.977924	+	0.208960i	$0.932992\pi$
$678$	6.25506	−	1.33140i	0.240224	−	0.0511321i
$679$	0.534552	−	11.2216i	0.0205142	−	0.430646i
$680$	0.0295537	−	0.153339i	0.00113333	−	0.00588030i
$681$	−39.0549	−	1.10467i	−1.49659	−	0.0423309i
$682$	9.59288	−	23.9619i	0.367330	−	0.917547i
$683$	2.67966	−	2.32194i	0.102534	−	0.0888465i	−0.602085	−	0.798432i	$-0.705663\pi$
$683$	2.67966	−	2.32194i	0.102534	−	0.0888465i	0.704619	+	0.709585i	$0.251118\pi$
$684$	21.9477	−	30.2443i	0.839190	−	1.15642i
$685$	4.00695	−	1.17655i	0.153098	−	0.0449535i
$686$	5.52360	+	7.75681i	0.210892	+	0.296156i
$687$	−2.62902	+	6.06415i	−0.100303	+	0.231362i
$688$	−1.24687	+	2.41859i	−0.0475366	+	0.0922080i
$689$	1.19835	+	2.07560i	0.0456534	+	0.0790741i
$690$	−2.72228	+	0.948795i	−0.103635	+	0.0361200i
$691$	12.2075	−	21.1440i	0.464395	−	0.804356i	−0.534779	−	0.844992i	$-0.679605\pi$
$691$	12.2075	−	21.1440i	0.464395	−	0.804356i	0.999174	+	0.0406362i	$0.0129385\pi$
$692$	−7.16646	−	11.1512i	−0.272428	−	0.423906i
$693$	−20.2884	+	7.91220i	−0.770693	+	0.300560i
$694$	−5.70598	+	12.4944i	−0.216596	+	0.474280i
$695$	−1.49163	+	6.14858i	−0.0565808	+	0.233229i
$696$	15.5121	+	18.9595i	0.587983	+	0.718659i
$697$	0.513678	+	0.177786i	0.0194570	+	0.00673412i
$698$	2.56515	+	3.26186i	0.0970925	+	0.123463i
$699$	−2.86482	+	1.54770i	−0.108358	+	0.0585394i
$700$	10.2816	−	3.55849i	0.388607	−	0.134498i
$701$	−21.7944	−	14.0064i	−0.823165	−	0.529016i	0.0599343	−	0.998202i	$-0.480911\pi$
$701$	−21.7944	−	14.0064i	−0.823165	−	0.529016i	−0.883099	+	0.469186i	$0.844547\pi$
$702$	−0.136384	−	0.670164i	−0.00514749	−	0.0252937i
$703$	−32.3105	+	37.2883i	−1.21861	+	1.40636i
$704$	−4.98166	+	4.75000i	−0.187753	+	0.179022i
$705$	−1.15985	−	0.876384i	−0.0436825	−	0.0330065i
$706$	−5.36710	+	15.5072i	−0.201993	+	0.583622i
$707$	−6.61072	+	9.28346i	−0.248622	+	0.349141i
$708$	2.17581	+	3.60588i	0.0817720	+	0.135517i
$709$	−38.9830	+	27.7596i	−1.46404	+	1.04253i	−0.477565	+	0.878596i	$0.658480\pi$
$709$	−38.9830	+	27.7596i	−1.46404	+	1.04253i	−0.986471	+	0.163939i	$0.947580\pi$
$710$	0.241743	−	1.68136i	0.00907244	−	0.0631002i
$711$	−0.522556	−	13.5153i	−0.0195974	−	0.506862i
$712$		−	23.2572i		−	0.871601i
$713$	−20.0118	+	37.2347i	−0.749446	+	1.39445i
$714$	0.0440669	−	0.161563i	0.00164916	−	0.00604634i
$715$	−0.659643	−	0.340069i	−0.0246692	−	0.0127179i
$716$	−0.0592774	−	0.148068i	−0.00221530	−	0.00553356i
$717$	−10.7551	+	12.9077i	−0.401655	+	0.482047i
$718$	17.0148	+	4.12775i	0.634987	+	0.154046i
$719$	−2.12937	+	0.972451i	−0.0794121	+	0.0362663i	−0.454725	−	0.890632i	$-0.650262\pi$
$719$	−2.12937	+	0.972451i	−0.0794121	+	0.0362663i	0.375313	+	0.926898i	$0.377535\pi$
$720$	−3.07053	+	2.61285i	−0.114432	+	0.0973753i
$721$	−2.08759	−	14.5195i	−0.0777458	−	0.540734i
$722$	−13.9991	−	14.6818i	−0.520992	−	0.546400i
$723$	−13.4971	−	6.63133i	−0.501961	−	0.246622i
$724$	17.2458	+	0.821521i	0.640937	+	0.0305316i
$725$	−31.4071	−	1.49610i	−1.16643	−	0.0555639i
$726$	−1.03860	−	15.4963i	−0.0385460	−	0.575120i
$727$	9.62597	+	10.0954i	0.357007	+	0.374419i	0.877606	−	0.479383i	$-0.159140\pi$
$727$	9.62597	+	10.0954i	0.357007	+	0.374419i	−0.520598	+	0.853802i	$0.674291\pi$
$728$	−0.0965428	−	0.671470i	−0.00357811	−	0.0248863i
$729$	−20.8728	+	17.1267i	−0.773067	+	0.634324i
$730$	2.68870	−	1.22789i	0.0995132	−	0.0454462i
$731$	−0.147781	−	0.0358513i	−0.00546588	−	0.00132601i
$732$	0.391622	+	1.06451i	0.0144748	+	0.0393455i
$733$	3.87251	+	9.67306i	0.143034	+	0.357282i	0.982535	−	0.186075i	$-0.0595769\pi$
$733$	3.87251	+	9.67306i	0.143034	+	0.357282i	−0.839501	+	0.543358i	$0.817153\pi$
$734$	9.16108	+	4.72286i	0.338142	+	0.174324i
$735$	5.18620	−	1.36478i	0.191296	−	0.0503407i
$736$	−20.6057	+	15.6399i	−0.759536	+	0.576493i
$737$			54.3790i			2.00307i
$738$	4.01708	+	6.37551i	0.147871	+	0.234686i
$739$	2.92779	−	20.3632i	0.107700	−	0.749073i	−0.862375	−	0.506270i	$-0.831024\pi$
$739$	2.92779	−	20.3632i	0.107700	−	0.749073i	0.970076	−	0.242803i	$-0.0780670\pi$
$740$	5.60134	−	3.98870i	0.205909	−	0.146627i
$741$	2.99007	−	0.0577828i	0.109843	−	0.00212270i
$742$	−4.71920	+	6.62719i	−0.173247	+	0.243292i
$743$	3.49280	−	10.0918i	0.128139	−	0.370232i	−0.862623	−	0.505847i	$-0.831180\pi$
$743$	3.49280	−	10.0918i	0.128139	−	0.370232i	0.990762	+	0.135615i	$0.0433011\pi$
$744$	3.90960	−	31.5015i	0.143333	−	1.15490i
$745$	7.33240	−	6.99143i	0.268638	−	0.256146i
$746$	−1.24611	+	1.43809i	−0.0456235	+	0.0526523i
$747$	16.5387	+	32.7984i	0.605118	+	1.20003i
$748$	−0.896101	−	0.575889i	−0.0327647	−	0.0210566i
$749$	−10.9969	+	3.80607i	−0.401819	+	0.139071i
$750$	−0.163544	+	5.78200i	−0.00597176	+	0.211129i
$751$	5.89375	+	7.49451i	0.215066	+	0.273479i	0.881601	−	0.471995i	$-0.156466\pi$
$751$	5.89375	+	7.49451i	0.215066	+	0.273479i	−0.666535	+	0.745473i	$0.732223\pi$
$752$	−2.82368	−	0.977286i	−0.102969	−	0.0356379i
$753$	−2.86538	+	7.57858i	−0.104420	+	0.276179i
$754$	−0.211068	+	0.870033i	−0.00768663	+	0.0316847i
$755$	5.59770	−	12.2572i	0.203721	−	0.446087i
$756$	−9.88830	+	7.19708i	−0.359634	+	0.261755i
$757$	15.9605	+	24.8351i	0.580096	+	0.902646i	0.999988	−	0.00492756i	$-0.00156850\pi$
$757$	15.9605	+	24.8351i	0.580096	+	0.902646i	−0.419892	+	0.907574i	$0.637932\pi$
$758$	−4.88122	+	8.45451i	−0.177294	+	0.307082i
$759$	−1.95584	+	43.0174i	−0.0709923	+	1.56143i
$760$	4.73334	+	8.19838i	0.171696	+	0.297387i
$761$	7.62033	−	14.7814i	0.276237	−	0.535824i	−0.709379	−	0.704827i	$-0.751024\pi$
$761$	7.62033	−	14.7814i	0.276237	−	0.535824i	0.985616	+	0.169003i	$0.0540548\pi$
$762$	−5.07455	+	0.583703i	−0.183832	+	0.0211453i
$763$	9.23658	+	12.9710i	0.334387	+	0.469580i
$764$	−15.6650	+	4.59964i	−0.566738	+	0.166409i
$765$	−0.182359	−	0.132334i	−0.00659320	−	0.00478455i
$766$	3.06178	−	2.65305i	0.110627	−	0.0958585i
$767$	−0.125267	+	0.312903i	−0.00452314	+	0.0112983i
$768$	3.50699	−	5.69604i	0.126548	−	0.205538i
$769$	−0.0105558	+	0.0547688i	−0.000380653	+	0.00197501i	−0.982119	−	0.188264i	$-0.939714\pi$
$769$	−0.0105558	+	0.0547688i	−0.000380653	+	0.00197501i	0.981738	+	0.190239i	$0.0609262\pi$
$770$	0.119871	−	2.51640i	0.00431985	−	0.0906849i
$771$	3.49652	+	3.88107i	0.125924	+	0.139773i
$772$	−8.51547	−	24.6038i	−0.306479	−	0.885512i
$773$	−14.4224	−	4.23479i	−0.518737	−	0.152315i	0.0118756	−	0.999929i	$-0.496220\pi$
$773$	−14.4224	−	4.23479i	−0.518737	−	0.152315i	−0.530612	+	0.847615i	$0.678038\pi$
$774$	−1.28825	−	1.66868i	−0.0463052	−	0.0599795i
$775$	26.6816	+	30.7922i	0.958431	+	1.10609i
$776$	16.6065	+	1.58573i	0.596140	+	0.0569244i
$777$	13.8260	−	8.34271i	0.496005	−	0.299293i
$778$	−0.880271	−	9.21862i	−0.0315593	−	0.330503i
$779$	−30.5917	+	12.2471i	−1.09606	+	0.438796i
$780$	−0.406874	−	0.0904199i	−0.0145684	−	0.00323755i
$781$	−21.9735	−	12.6864i	−0.786273	−	0.453955i
$782$	−0.256751	−	0.209139i	−0.00918141	−	0.00747881i
$783$	34.2602	−	8.68849i	1.22436	−	0.310501i
$784$	9.27297	−	5.95938i	0.331177	−	0.212835i
$785$	2.80432	−	3.56599i	0.100091	−	0.127276i
$786$	0.00352899	−	0.00129828i	0.000125875	−	4.63080e-5i
$787$	−30.2064	+	31.6796i	−1.07674	+	1.12926i	−0.0856172	+	0.996328i	$0.527286\pi$
$787$	−30.2064	+	31.6796i	−1.07674	+	1.12926i	−0.991126	+	0.132927i	$0.957562\pi$
$788$	−32.8992	−	23.4274i	−1.17198	−	0.834567i
$789$	4.37990	+	2.99308i	0.155928	+	0.106557i
$790$	1.45261	+	0.581539i	0.0516817	+	0.0206902i
$791$	2.57860	−	8.78191i	0.0916845	−	0.312249i
$792$	−10.3022	−	30.6515i	−0.366072	−	1.08915i
$793$	−0.0490770	+	0.0763653i	−0.00174278	+	0.00271181i
$794$	−6.96532	−	13.5108i	−0.247190	−	0.479482i
$795$	6.09480	+	9.09251i	0.216160	+	0.322478i
$796$	20.6144	−	5.00100i	0.730658	−	0.177256i
$797$	−33.1900	+	26.1009i	−1.17565	+	0.924540i	−0.998223	−	0.0595940i	$-0.981019\pi$
$797$	−33.1900	+	26.1009i	−1.17565	+	0.924540i	−0.177426	+	0.984134i	$0.556777\pi$
$798$	4.39489	+	9.15130i	0.155577	+	0.323952i
$799$	0.0158730	−	0.166229i	0.000561546	−	0.00588078i
$800$	7.02471	+	23.9240i	0.248361	+	0.845840i
$801$	−30.3979	−	14.2126i	−1.07406	−	0.502177i
$802$	8.60208	+	1.23679i	0.303750	+	0.0436727i
$803$	−2.10079	−	44.1011i	−0.0741354	−	1.55629i
$804$	7.77222	+	29.5346i	0.274105	+	1.04161i
$805$	−0.657160	+	4.07325i	−0.0231618	+	0.143563i
$806$	1.00468	−	0.580051i	0.0353883	−	0.0204314i
$807$	−11.7914	+	53.0595i	−0.415078	+	1.86778i
$808$	−13.3025	−	10.4612i	−0.467980	−	0.368023i
$809$	24.7636	+	11.3091i	0.870640	+	0.397608i	0.800076	−	0.599899i	$-0.204793\pi$
$809$	24.7636	+	11.3091i	0.870640	+	0.397608i	0.0705647	+	0.997507i	$0.477520\pi$
$810$	−0.826185	−	3.01228i	−0.0290292	−	0.105841i
$811$	−12.9882	−	28.4401i	−0.456076	−	0.998668i	−0.988364	−	0.152104i	$-0.951395\pi$
$811$	−12.9882	−	28.4401i	−0.456076	−	0.998668i	0.532288	−	0.846563i	$-0.321332\pi$
$812$	15.7207	−	3.02992i	0.551689	−	0.106329i
$813$	−24.5887	+	32.5419i	−0.862362	+	1.14129i
$814$	4.59664	+	18.9476i	0.161112	+	0.664113i
$815$	−6.04239	−	1.16458i	−0.211656	−	0.0407933i
$816$	−0.440494	−	0.142988i	−0.0154204	−	0.00500556i
$817$	8.19374	−	4.22417i	0.286663	−	0.147785i
$818$	−5.13769	−	4.45183i	−0.179635	−	0.155655i
$819$	−0.936630	−	0.284154i	−0.0327285	−	0.00992915i
$820$	4.54575	−	0.653580i	0.158744	−	0.0228240i
$821$	−1.26104	−	6.54290i	−0.0440106	−	0.228349i	0.953263	−	0.302142i	$-0.0977017\pi$
$821$	−1.26104	−	6.54290i	−0.0440106	−	0.228349i	−0.997274	+	0.0737932i	$0.976490\pi$
$822$	1.07340	+	6.56284i	0.0374392	+	0.228905i
$823$	8.14028	+	7.76174i	0.283752	+	0.270557i	0.818566	−	0.574413i	$-0.194770\pi$
$823$	8.14028	+	7.76174i	0.283752	+	0.270557i	−0.534813	+	0.844970i	$0.679618\pi$
$824$	21.6833	−	2.07050i	0.755374	−	0.0721294i
$825$	38.0808	+	16.5093i	1.32580	+	0.574781i
$826$	−1.14283	+	0.0544398i	−0.0397642	+	0.00189420i
$827$	26.0422			0.905575			0.452787	−	0.891619i	$-0.350430\pi$
$827$	26.0422			0.905575			0.452787	+	0.891619i	$0.350430\pi$
$828$	5.08608	+	23.6434i	0.176753	+	0.821666i
$829$	−53.7674			−1.86742			−0.933709	−	0.358033i	$-0.883448\pi$
$829$	−53.7674			−1.86742			−0.933709	+	0.358033i	$0.883448\pi$
$830$	−4.24461	+	0.202195i	−0.147332	+	0.00701831i
$831$	−2.61323	−	22.7187i	−0.0906519	−	0.788102i
$832$	−0.307978	+	0.0294083i	−0.0106772	+	0.00101955i
$833$	0.445827	+	0.425095i	0.0154470	+	0.0147287i
$834$	−9.42392	−	3.56309i	−0.326324	−	0.123380i
$835$	−0.145101	−	0.752853i	−0.00502141	−	0.0260535i
$836$	63.9162	−	9.18976i	2.21059	−	0.317835i
$837$	−38.7842	−	24.3607i	−1.34058	−	0.842028i
$838$	−12.1316	−	10.5121i	−0.419080	−	0.363135i
$839$	7.19150	−	3.70748i	0.248278	−	0.127996i	−0.329596	−	0.944122i	$-0.606913\pi$
$839$	7.19150	−	3.70748i	0.248278	−	0.127996i	0.577874	+	0.816126i	$0.303882\pi$
$840$	−0.645027	−	3.03040i	−0.0222555	−	0.104559i
$841$	−16.9564	−	3.26808i	−0.584704	−	0.112692i
$842$	−2.24098	−	9.23744i	−0.0772292	−	0.318343i
$843$	13.0984	+	30.9702i	0.451134	+	1.06667i
$844$	38.8924	−	7.49589i	1.33873	−	0.258019i
$845$	3.30418	+	7.23514i	0.113667	+	0.248896i
$846$	1.61241	−	1.66100i	0.0554357	−	0.0571065i
$847$	−20.2190	−	9.23371i	−0.694733	−	0.317274i
$848$	17.6856	+	13.9081i	0.607326	+	0.477606i
$849$	41.6330	−	13.1035i	1.42884	−	0.449710i
$850$	−0.276420	+	0.159591i	−0.00948113	+	0.00547393i
$851$	−4.00141	−	31.6799i	−0.137167	−	1.08597i
$852$	−13.7476	−	3.74971i	−0.470985	−	0.128463i
$853$	0.497904	+	10.4523i	0.0170479	+	0.357880i	0.991233	+	0.132128i	$0.0421809\pi$
$853$	0.497904	+	10.4523i	0.0170479	+	0.357880i	−0.974185	+	0.225752i	$0.927516\pi$
$854$	−0.305008	−	0.0438535i	−0.0104372	−	0.00150064i
$855$	13.6081	−	1.17655i	0.465387	−	0.0402371i
$856$	−4.86831	−	16.5799i	−0.166395	−	0.566690i
$857$	−0.938520	+	9.82863i	−0.0320592	+	0.335740i	0.965186	+	0.261564i	$0.0842384\pi$
$857$	−0.938520	+	9.82863i	−0.0320592	+	0.335740i	−0.997245	+	0.0741750i	$0.976368\pi$
$858$	0.666777	−	0.975721i	0.0227634	−	0.0333106i
$859$	−13.6124	+	10.7049i	−0.464450	+	0.365248i	−0.822792	−	0.568343i	$-0.807585\pi$
$859$	−13.6124	+	10.7049i	−0.464450	+	0.365248i	0.358341	+	0.933591i	$0.383342\pi$
$860$	−1.24856	+	0.302897i	−0.0425754	+	0.0103287i
$861$	10.7605	−	0.721198i	0.366718	−	0.0245784i
$862$	−7.03807	−	13.6520i	−0.239718	−	0.464988i
$863$	8.39880	−	13.0688i	0.285898	−	0.444867i	−0.668365	−	0.743833i	$-0.733006\pi$
$863$	8.39880	−	13.0688i	0.285898	−	0.444867i	0.954264	+	0.298967i	$0.0966419\pi$
$864$	−15.3969	−	23.4205i	−0.523812	−	0.796782i
$865$	1.36502	−	4.64884i	0.0464122	−	0.158065i
$866$	7.77044	+	3.11082i	0.264050	+	0.105710i
$867$	−2.23009	+	29.3343i	−0.0757379	+	0.996246i
$868$	−16.8992	−	12.0339i	−0.573597	−	0.408457i
$869$	16.1285	−	16.9151i	0.547122	−	0.573805i
$870$	−0.696109	+	4.02920i	−0.0236003	+	0.136603i
$871$	−1.51087	+	1.92123i	−0.0511939	+	0.0650983i
$872$	−19.8916	+	12.7836i	−0.673615	+	0.432906i
$873$	12.2209	−	20.7362i	0.413616	−	0.701814i
$874$	20.0654	−	0.611029i	0.678723	−	0.0206684i
$875$	7.16929	+	4.13919i	0.242366	+	0.139930i
$876$	−7.44423	−	23.6522i	−0.251517	−	0.799134i
$877$	−12.1031	+	4.84535i	−0.408692	+	0.163616i	−0.566893	−	0.823791i	$-0.691855\pi$
$877$	−12.1031	+	4.84535i	−0.408692	+	0.163616i	0.158201	+	0.987407i	$0.449431\pi$
$878$	−0.329719	−	3.45297i	−0.0111275	−	0.116532i
$879$	0.0327453	+	1.69447i	0.00110447	+	0.0571529i
$880$	−6.93539	−	0.662250i	−0.233792	−	0.0223244i
$881$	30.4389	+	35.1284i	1.02551	+	1.18351i	0.982848	+	0.184416i	$0.0590394\pi$
$881$	30.4389	+	35.1284i	1.02551	+	1.18351i	0.0426650	+	0.999089i	$0.486415\pi$
$882$	1.13958	+	8.46330i	0.0383717	+	0.284974i
$883$	−28.9134	−	8.48974i	−0.973013	−	0.285702i	−0.243676	−	0.969857i	$-0.578353\pi$
$883$	−28.9134	−	8.48974i	−0.973013	−	0.285702i	−0.729337	+	0.684154i	$0.760171\pi$
$884$	−0.0156590	−	0.0452437i	−0.000526669	−	0.00152171i
$885$	−0.475276	+	1.46416i	−0.0159762	+	0.0492171i
$886$	0.859999	−	18.0536i	0.0288922	−	0.606523i
$887$	5.00590	−	25.9731i	0.168082	−	0.872091i	−0.795759	−	0.605613i	$-0.792928\pi$
$887$	5.00590	−	25.9731i	0.168082	−	0.872091i	0.963841	−	0.266478i	$-0.0858599\pi$
$888$	11.3973	+	21.0967i	0.382469	+	0.707957i
$889$	−2.71703	+	6.78682i	−0.0911263	+	0.227622i
$890$	2.93383	−	2.54217i	0.0983420	−	0.0852139i
$891$	−46.3582	−	5.26604i	−1.55306	−	0.176419i
$892$	−20.8057	+	6.10909i	−0.696625	+	0.204548i
$893$	5.87183	+	8.24583i	0.196493	+	0.275936i
$894$	9.61033	+	12.9584i	0.321417	+	0.433395i
$895$	0.0267133	−	0.0518167i	0.000892929	−	0.00173204i
$896$	−8.07804	−	13.9916i	−0.269869	−	0.467426i
$897$	−1.26430	+	1.46548i	−0.0422137	+	0.0489309i
$898$	7.25123	−	12.5595i	0.241977	−	0.419116i
$899$	32.4143	+	50.4376i	1.08108	+	1.68219i
$900$	23.0423	+	3.52387i	0.768078	+	0.117462i
$901$	−0.522331	+	1.14374i	−0.0174014	+	0.0381037i
$902$	−3.06993	+	12.6544i	−0.102217	+	0.421346i
$903$	−2.97751	+	0.486994i	−0.0990852	+	0.0162061i
$904$	12.8434	+	4.44516i	0.427167	+	0.147844i
$905$	3.90107	+	4.96062i	0.129676	+	0.164897i
$906$	18.2720	+	11.2499i	0.607046	+	0.373752i
$907$	16.7511	−	5.79763i	0.556213	−	0.192507i	−0.0344776	−	0.999405i	$-0.510977\pi$
$907$	16.7511	−	5.79763i	0.556213	−	0.192507i	0.590690	+	0.806898i	$0.298856\pi$
$908$	−31.8980	−	20.4996i	−1.05857	−	0.680303i
$909$	−21.8023	+	10.9939i	−0.723137	+	0.364644i
$910$	0.0741511	−	0.0855749i	0.00245808	−	0.00283678i
$911$	0.0865671	−	0.0825415i	0.00286810	−	0.00273472i	−0.688644	−	0.725100i	$-0.741794\pi$
$911$	0.0865671	−	0.0825415i	0.00286810	−	0.00273472i	0.691512	+	0.722365i	$0.256945\pi$
$912$	25.8573	−	10.9360i	0.856222	−	0.362127i
$913$	−20.7603	+	59.9828i	−0.687064	+	1.98514i
$914$	−1.22945	+	1.72653i	−0.0406667	+	0.0571085i
$915$	−0.200320	+	0.362986i	−0.00662239	+	0.0119999i
$916$	−5.22503	+	3.72073i	−0.172640	+	0.122936i
$917$	0.000765875	−	0.00532678i	2.52914e−5	−	0.000175906i
$918$	0.244890	−	0.262223i	0.00808256	−	0.00865466i
$919$		−	0.381165i		−	0.0125735i	−0.999980	−	0.00628674i	$-0.997999\pi$
$919$		−	0.381165i		−	0.0125735i	0.999980	−	0.00628674i	$-0.00200115\pi$
$920$	−5.99516	−	1.26252i	−0.197655	−	0.0416240i
$921$	−41.0909	−	41.4605i	−1.35399	−	1.36617i
$922$	1.20737	+	0.622440i	0.0397625	+	0.0204990i
$923$	−0.423851	−	1.05873i	−0.0139512	−	0.0348485i
$924$	−20.8253	−	3.59791i	−0.685103	−	0.118362i
$925$	−29.9100	−	7.25609i	−0.983435	−	0.238579i
$926$	−8.97088	+	4.09686i	−0.294801	+	0.134631i
$927$	10.5446	−	29.6060i	0.346329	−	0.972390i
$928$	5.22164	+	36.3173i	0.171409	+	1.19217i
$929$	27.1601	+	28.4847i	0.891094	+	0.934553i	0.998217	−	0.0596929i	$-0.0190122\pi$
$929$	27.1601	+	28.4847i	0.891094	+	0.934553i	−0.107122	+	0.994246i	$0.534164\pi$
$930$	4.40116	−	2.95014i	0.144320	−	0.0967390i
$931$	−37.3009	−	1.77686i	−1.22249	−	0.0582342i
$932$	−3.15647	−	0.150361i	−0.103393	−	0.00492524i
$933$	−47.1236	+	31.5874i	−1.54276	+	1.03413i
$934$	−6.36752	−	6.67806i	−0.208351	−	0.218513i
$935$	−0.0554099	−	0.385385i	−0.00181210	−	0.0126034i
$936$	0.487645	−	1.36917i	0.0159392	−	0.0447526i
$937$	−41.3210	+	18.8707i	−1.34990	+	0.616479i	−0.953443	−	0.301575i	$-0.902488\pi$
$937$	−41.3210	+	18.8707i	−1.34990	+	0.616479i	−0.396457	+	0.918053i	$0.629760\pi$
$938$	−8.06295	−	1.95605i	−0.263265	−	0.0638673i
$939$	36.8187	+	6.36102i	1.20153	+	0.207584i
$940$	−0.524345	−	1.30975i	−0.0171022	−	0.0427193i
$941$	33.8246	+	17.4378i	1.10265	+	0.568456i	0.910750	−	0.412958i	$-0.135504\pi$
$941$	33.8246	+	17.4378i	1.10265	+	0.568456i	0.191901	+	0.981414i	$0.438535\pi$
$942$	5.08525	+	5.13099i	0.165686	+	0.167177i
$943$	7.31977	−	20.0304i	0.238365	−	0.652280i
$944$			3.16406i			0.102981i
$945$	−4.35501	−	1.00882i	−0.141668	−	0.0328170i
$946$	0.518428	−	3.60574i	0.0168555	−	0.117233i
$947$	34.3331	−	24.4485i	1.11568	−	0.794469i	0.135143	−	0.990826i	$-0.456851\pi$
$947$	34.3331	−	24.4485i	1.11568	−	0.794469i	0.980532	+	0.196357i	$0.0629113\pi$
$948$	6.34219	−	11.4922i	0.205985	−	0.373250i
$949$	1.15109	−	1.61648i	0.0373659	−	0.0524730i
$950$	6.32850	−	18.2850i	0.205324	−	0.593244i
$951$	−13.2347	+	5.59746i	−0.429166	+	0.181510i
$952$	0.257572	−	0.245595i	0.00834796	−	0.00795977i
$953$	28.8251	−	33.2659i	0.933735	−	1.07759i	−0.0630931	−	0.998008i	$-0.520097\pi$
$953$	28.8251	−	33.2659i	0.933735	−	1.07759i	0.996828	−	0.0795803i	$-0.0253580\pi$
$954$	−15.5640	+	7.84820i	−0.503904	+	0.254095i
$955$	−5.02021	−	3.22629i	−0.162450	−	0.104400i
$956$	−15.4085	+	5.33293i	−0.498346	+	0.172479i
$957$	52.0089	+	32.0213i	1.68121	+	1.03510i
$958$	−7.75997	−	9.86761i	−0.250713	−	0.318808i
$959$	8.99395	+	3.11284i	0.290430	+	0.100519i
$960$	−1.39447	+	0.228077i	−0.0450065	+	0.00736115i
$961$	11.0078	−	45.3748i	0.355091	−	1.46370i
$962$	−0.364041	+	0.797139i	−0.0117372	+	0.0257008i
$963$	−24.6455	−	3.76905i	−0.794191	−	0.121456i
$964$	−7.89024	−	12.2774i	−0.254127	−	0.395430i
$965$	4.75826	−	8.24155i	0.153174	−	0.265305i
$966$	−6.30798	−	1.83737i	−0.202956	−	0.0591163i
$967$	−4.17771	−	7.23601i	−0.134346	−	0.232694i	0.791001	−	0.611814i	$-0.209560\pi$
$967$	−4.17771	−	7.23601i	−0.134346	−	0.232694i	−0.925347	+	0.379120i	$0.876227\pi$
$968$	15.1243	−	29.3371i	0.486115	−	0.942931i
$969$	0.934612	+	1.26022i	0.0300241	+	0.0404840i
$970$	1.61517	+	2.26819i	0.0518601	+	0.0728273i
$971$	19.5369	−	5.73655i	0.626969	−	0.184095i	0.0472129	−	0.998885i	$-0.484966\pi$
$971$	19.5369	−	5.73655i	0.626969	−	0.184095i	0.579756	+	0.814790i	$0.303148\pi$
$972$	−25.9310	+	3.76571i	−0.831737	+	0.120785i
$973$	−10.8973	+	9.44253i	−0.349350	+	0.302714i
$974$	3.07651	−	7.68475i	0.0985777	−	0.246235i
$975$	0.886713	+	1.64132i	0.0283975	+	0.0525644i
$976$	−0.161273	+	0.836766i	−0.00516224	+	0.0267842i
$977$	−1.39674	+	29.3211i	−0.0446855	+	0.938065i	0.859556	+	0.511042i	$0.170740\pi$
$977$	−1.39674	+	29.3211i	−0.0446855	+	0.938065i	−0.904241	+	0.427022i	$0.859563\pi$
$978$	3.02542	−	9.32025i	0.0967423	−	0.298029i
$979$	−18.9653	−	54.7966i	−0.606133	−	1.75131i
$980$	4.99365	+	1.46627i	0.159516	+	0.0468382i
$981$	4.55265	+	33.8110i	0.145355	+	1.07950i
$982$	11.8344	+	13.6577i	0.377652	+	0.435834i
$983$	−17.0185	−	1.62507i	−0.542807	−	0.0518318i	−0.179949	−	0.983676i	$-0.557593\pi$
$983$	−17.0185	−	1.62507i	−0.542807	−	0.0518318i	−0.362859	+	0.931844i	$0.618199\pi$
$984$	0.309418	+	16.0114i	0.00986388	+	0.510424i
$985$	−1.40327	−	14.6957i	−0.0447118	−	0.468244i
$986$	−0.436038	+	0.174563i	−0.0138863	+	0.00555922i
$987$	−0.994638	−	3.16022i	−0.0316597	−	0.100591i
$988$	2.51351	+	1.45118i	0.0799654	+	0.0461681i
$989$	−1.50581	+	5.77289i	−0.0478821	+	0.183567i
$990$	2.74049	−	4.65001i	0.0870986	−	0.147787i
$991$	30.0832	−	19.3333i	0.955625	−	0.614143i	0.0328413	−	0.999461i	$-0.489544\pi$
$991$	30.0832	−	19.3333i	0.955625	−	0.614143i	0.922784	+	0.385317i	$0.125908\pi$
$992$	29.3900	−	37.3724i	0.933134	−	1.18658i
$993$	1.33910	−	7.75095i	0.0424951	−	0.245969i
$994$	2.67146	−	2.80174i	0.0847335	−	0.0888659i
$995$	6.31578	+	4.49745i	0.200224	+	0.142579i
$996$	−2.70228	+	35.5455i	−0.0856251	+	1.12630i
$997$	−4.00568	−	1.60363i	−0.126861	−	0.0507876i	0.307363	−	0.951592i	$-0.400553\pi$
$997$	−4.00568	−	1.60363i	−0.126861	−	0.0507876i	−0.434225	+	0.900805i	$0.642978\pi$
$998$	−0.735703	+	2.50557i	−0.0232883	+	0.0793126i
$999$	34.5389	−	2.00438i	1.09276	−	0.0634157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.11.10	✓	440
3.2	odd	2		621.2.s.a.494.13		440
9.4	even	3		621.2.s.a.287.13		440
9.5	odd	6	inner	207.2.o.a.149.10	yes	440
23.21	odd	22	inner	207.2.o.a.182.10	yes	440
69.44	even	22		621.2.s.a.251.13		440
207.67	odd	66		621.2.s.a.44.13		440
207.113	even	66	inner	207.2.o.a.113.10	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.10	✓	440	1.1	even	1	trivial
207.2.o.a.113.10	yes	440	207.113	even	66	inner
207.2.o.a.149.10	yes	440	9.5	odd	6	inner
207.2.o.a.182.10	yes	440	23.21	odd	22	inner
621.2.s.a.44.13		440	207.67	odd	66
621.2.s.a.251.13		440	69.44	even	22
621.2.s.a.287.13		440	9.4	even	3
621.2.s.a.494.13		440	3.2	odd	2

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.564228 + 0.0268775i) q^{2} +(-1.39121 + 1.03176i) q^{3} +(-1.67331 + 0.159782i) q^{4} +(-0.444667 - 0.423989i) q^{5} +(0.757230 - 0.619541i) q^{6} +(-0.264997 - 1.37493i) q^{7} +(2.05807 - 0.295906i) q^{8} +(0.870940 - 2.87079i) q^{9} +O(q^{10})\)	\(q+(-0.564228 + 0.0268775i) q^{2} +(-1.39121 + 1.03176i) q^{3} +(-1.67331 + 0.159782i) q^{4} +(-0.444667 - 0.423989i) q^{5} +(0.757230 - 0.619541i) q^{6} +(-0.264997 - 1.37493i) q^{7} +(2.05807 - 0.295906i) q^{8} +(0.870940 - 2.87079i) q^{9} +(0.262289 + 0.227275i) q^{10} +(4.60775 - 2.37546i) q^{11} +(2.16308 - 1.94875i) q^{12} +(0.228794 + 0.0440964i) q^{13} +(0.186474 + 0.768654i) q^{14} +(1.05608 + 0.131069i) q^{15} +(2.14782 - 0.413959i) q^{16} +(0.0507804 + 0.111194i) q^{17} +(-0.414249 + 1.64319i) q^{18} +(-6.74068 - 3.07837i) q^{19} +(0.811812 + 0.638416i) q^{20} +(1.78727 + 1.63941i) q^{21} +(-2.53598 + 1.46415i) q^{22} +(4.39598 - 1.91712i) q^{23} +(-2.55791 + 2.53511i) q^{24} +(-0.219948 - 4.61727i) q^{25} +(-0.130277 - 0.0187310i) q^{26} +(1.75031 + 4.89249i) q^{27} +(0.663112 + 2.25835i) q^{28} +(0.646580 - 6.77129i) q^{29} +(-0.599393 - 0.0455678i) q^{30} +(-6.92847 + 5.44861i) q^{31} +(-5.24199 + 1.27169i) q^{32} +(-3.95945 + 8.05887i) q^{33} +(-0.0316404 - 0.0613738i) q^{34} +(-0.465121 + 0.723743i) q^{35} +(-0.998654 + 4.94290i) q^{36} +(1.87583 - 6.38850i) q^{37} +(3.88602 + 1.55573i) q^{38} +(-0.363797 + 0.174713i) q^{39} +(-1.04062 - 0.741020i) q^{40} +(3.06862 - 3.21828i) q^{41} +(-1.05249 - 0.876965i) q^{42} +(-0.768994 + 0.977856i) q^{43} +(-7.33066 + 4.71113i) q^{44} +(-1.60446 + 0.907278i) q^{45} +(-2.42881 + 1.19985i) q^{46} +(-1.18303 - 0.683022i) q^{47} +(-2.56097 + 2.79195i) q^{48} +(4.67836 - 1.87293i) q^{49} +(0.248201 + 2.59928i) q^{50} +(-0.185372 - 0.102301i) q^{51} +(-0.389889 - 0.0372299i) q^{52} +(6.73594 + 7.77369i) q^{53} +(-1.11907 - 2.71344i) q^{54} +(-3.05608 - 0.897347i) q^{55} +(-0.952234 - 2.75130i) q^{56} +(12.5539 - 2.67211i) q^{57} +(-0.182823 + 3.83794i) q^{58} +(-0.273756 + 1.42038i) q^{59} +(-1.78809 - 0.0505762i) q^{60} +(-0.144795 + 0.361681i) q^{61} +(3.76279 - 3.26048i) q^{62} +(-4.17795 - 0.436734i) q^{63} +(-1.27400 + 0.374080i) q^{64} +(-0.0830405 - 0.116614i) q^{65} +(2.01743 - 4.65346i) q^{66} +(-4.80666 + 9.32362i) q^{67} +(-0.102738 - 0.177948i) q^{68} +(-4.13773 + 7.20272i) q^{69} +(0.242982 - 0.420858i) q^{70} +(-2.64612 - 4.11744i) q^{71} +(0.942972 - 6.16602i) q^{72} +(3.53798 - 7.74711i) q^{73} +(-0.886691 + 3.65499i) q^{74} +(5.06991 + 6.19667i) q^{75} +(11.7711 + 4.07403i) q^{76} +(-4.48714 - 5.70587i) q^{77} +(0.200569 - 0.108356i) q^{78} +(4.26049 - 1.47457i) q^{79} +(-1.13058 - 0.726579i) q^{80} +(-7.48293 - 5.00058i) q^{81} +(-1.64491 + 1.89832i) q^{82} +(-8.86147 + 8.44940i) q^{83} +(-3.25261 - 2.45767i) q^{84} +(0.0245645 - 0.0709744i) q^{85} +(0.407606 - 0.572403i) q^{86} +(6.08682 + 10.0874i) q^{87} +(8.78018 - 6.25234i) q^{88} +(1.59186 - 11.0716i) q^{89} +(0.880898 - 0.555036i) q^{90} -0.326261i q^{91} +(-7.04953 + 3.91034i) q^{92} +(4.01731 - 14.7287i) q^{93} +(0.685857 + 0.353584i) q^{94} +(1.69216 + 4.22682i) q^{95} +(5.98064 - 7.17767i) q^{96} +(7.79701 + 1.89153i) q^{97} +(-2.58932 + 1.18250i) q^{98} +(-2.80639 - 15.2968i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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