LMFDB - Embedded newform 425.2.r.a.69.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.3
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.47862 + 0.805352i) q^{2} +(1.68980 + 2.32581i) q^{3} +(3.87693 - 2.81675i) q^{4} +(-1.39512 + 1.74746i) q^{5} +(-6.06145 - 4.40390i) q^{6} +3.88508i q^{7} +(-4.27721 + 5.88707i) q^{8} +(-1.62691 + 5.00711i) q^{9} +(2.05065 - 5.45486i) q^{10} +(-1.51229 - 4.65436i) q^{11} +(13.1024 + 4.25724i) q^{12} +(-2.40639 - 0.781885i) q^{13} +(-3.12886 - 9.62963i) q^{14} +(-6.42174 - 0.291924i) q^{15} +(2.89869 - 8.92126i) q^{16} +(-0.587785 + 0.809017i) q^{17} -13.7209i q^{18} +(3.92927 + 2.85478i) q^{19} +(-0.486613 + 10.7045i) q^{20} +(-9.03594 + 6.56499i) q^{21} +(7.49679 + 10.3185i) q^{22} +(-1.61047 + 0.523275i) q^{23} -20.9198 q^{24} +(-1.10727 - 4.87586i) q^{25} +6.59423 q^{26} +(-6.19226 + 2.01199i) q^{27} +(10.9433 + 15.0622i) q^{28} +(-0.834194 + 0.606078i) q^{29} +(16.1521 - 4.44819i) q^{30} +(7.37458 + 5.35794i) q^{31} +9.89323i q^{32} +(8.26966 - 11.3822i) q^{33} +(0.805352 - 2.47862i) q^{34} +(-6.78904 - 5.42016i) q^{35} +(7.79638 + 23.9948i) q^{36} +(-1.46451 - 0.475847i) q^{37} +(-12.0383 - 3.91147i) q^{38} +(-2.24780 - 6.91803i) q^{39} +(-4.32022 - 15.6874i) q^{40} +(-2.37460 + 7.30826i) q^{41} +(17.1095 - 23.5492i) q^{42} -8.69780i q^{43} +(-18.9732 - 13.7849i) q^{44} +(-6.48001 - 9.82849i) q^{45} +(3.57033 - 2.59400i) q^{46} +(3.91599 + 5.38990i) q^{47} +(25.6473 - 8.33332i) q^{48} -8.09384 q^{49} +(6.67127 + 11.1936i) q^{50} -2.87485 q^{51} +(-11.5318 + 3.74691i) q^{52} +(-0.695828 - 0.957725i) q^{53} +(13.7279 - 9.97389i) q^{54} +(10.2432 + 3.85072i) q^{55} +(-22.8717 - 16.6173i) q^{56} +13.9627i q^{57} +(1.57954 - 2.17406i) q^{58} +(2.12720 - 6.54686i) q^{59} +(-25.7189 + 16.9567i) q^{60} +(-2.73432 - 8.41538i) q^{61} +(-22.5938 - 7.34117i) q^{62} +(-19.4530 - 6.32067i) q^{63} +(-2.17015 - 6.67904i) q^{64} +(4.72353 - 3.11426i) q^{65} +(-11.3307 + 34.8722i) q^{66} +(-0.0931483 + 0.128208i) q^{67} +4.79215i q^{68} +(-3.93841 - 2.86142i) q^{69} +(21.1926 + 7.96695i) q^{70} +(-3.77323 + 2.74141i) q^{71} +(-22.5186 - 30.9941i) q^{72} +(-6.05516 + 1.96744i) q^{73} +4.01318 q^{74} +(9.46924 - 10.8145i) q^{75} +23.2747 q^{76} +(18.0825 - 5.87538i) q^{77} +(11.1429 + 15.3369i) q^{78} +(-4.70705 + 3.41987i) q^{79} +(11.5456 + 17.5116i) q^{80} +(-2.36524 - 1.71845i) q^{81} -20.0268i q^{82} +(-0.722444 + 0.994359i) q^{83} +(-16.5397 + 50.9040i) q^{84} +(-0.593696 - 2.15581i) q^{85} +(7.00480 + 21.5585i) q^{86} +(-2.81924 - 0.916026i) q^{87} +(33.8689 + 11.0047i) q^{88} +(1.70809 + 5.25696i) q^{89} +(23.9769 + 19.1424i) q^{90} +(3.03769 - 9.34903i) q^{91} +(-4.76976 + 6.56501i) q^{92} +26.2057i q^{93} +(-14.0470 - 10.2058i) q^{94} +(-10.4704 + 2.88349i) q^{95} +(-23.0097 + 16.7176i) q^{96} +(4.26881 + 5.87551i) q^{97} +(20.0616 - 6.51839i) q^{98} +25.7652 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.47862	+	0.805352i	−1.75265	+	0.569470i	−0.996397	−	0.0848112i	$-0.972971\pi$
$2$	−2.47862	+	0.805352i	−1.75265	+	0.569470i	−0.756251	+	0.654281i	$0.772971\pi$
$3$	1.68980	+	2.32581i	0.975605	+	1.34280i	0.939164	+	0.343469i	$0.111602\pi$
$3$	1.68980	+	2.32581i	0.975605	+	1.34280i	0.0364404	+	0.999336i	$0.488398\pi$
$4$	3.87693	−	2.81675i	1.93846	−	1.40838i
$5$	−1.39512	+	1.74746i	−0.623918	+	0.781490i
$5$	−1.39512	+	1.74746i	−0.623918	+	0.781490i
$6$	−6.06145	−	4.40390i	−2.47458	−	1.79789i
$7$			3.88508i			1.46842i	0.678921	+	0.734211i	$0.262448\pi$
$7$			3.88508i			1.46842i	−0.678921	+	0.734211i	$0.737552\pi$
$8$	−4.27721	+	5.88707i	−1.51222	+	2.08139i
$9$	−1.62691	+	5.00711i	−0.542303	+	1.66904i
$10$	2.05065	−	5.45486i	0.648473	−	1.72498i
$11$	−1.51229	−	4.65436i	−0.455973	−	1.40334i	−0.869989	−	0.493072i	$-0.835874\pi$
$11$	−1.51229	−	4.65436i	−0.455973	−	1.40334i	0.414015	−	0.910270i	$-0.364126\pi$
$12$	13.1024	+	4.25724i	3.78235	+	1.22896i
$13$	−2.40639	−	0.781885i	−0.667414	−	0.216856i	−0.0443371	−	0.999017i	$-0.514118\pi$
$13$	−2.40639	−	0.781885i	−0.667414	−	0.216856i	−0.623077	+	0.782161i	$0.714118\pi$
$14$	−3.12886	−	9.62963i	−0.836222	−	2.57363i
$15$	−6.42174	−	0.291924i	−1.65809	−	0.0753744i
$16$	2.89869	−	8.92126i	0.724673	−	2.23031i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$18$		−	13.7209i		−	3.23406i
$19$	3.92927	+	2.85478i	0.901436	+	0.654932i	0.938834	−	0.344369i	$-0.111907\pi$
$19$	3.92927	+	2.85478i	0.901436	+	0.654932i	−0.0373984	+	0.999300i	$0.511907\pi$
$20$	−0.486613	+	10.7045i	−0.108810	+	2.39360i
$21$	−9.03594	+	6.56499i	−1.97180	+	1.43260i
$22$	7.49679	+	10.3185i	1.59832	+	2.19990i
$23$	−1.61047	+	0.523275i	−0.335807	+	0.109110i	−0.472067	−	0.881563i	$-0.656492\pi$
$23$	−1.61047	+	0.523275i	−0.335807	+	0.109110i	0.136260	+	0.990673i	$0.456492\pi$
$24$	−20.9198			−4.27023
$25$	−1.10727	−	4.87586i	−0.221453	−	0.975171i
$26$	6.59423			1.29323
$27$	−6.19226	+	2.01199i	−1.19170	+	0.387207i
$28$	10.9433	+	15.0622i	2.06809	+	2.84648i
$29$	−0.834194	+	0.606078i	−0.154906	+	0.112546i	−0.662538	−	0.749028i	$-0.730521\pi$
$29$	−0.834194	+	0.606078i	−0.154906	+	0.112546i	0.507632	+	0.861574i	$0.330521\pi$
$30$	16.1521	−	4.44819i	2.94896	−	0.812125i
$31$	7.37458	+	5.35794i	1.32451	+	0.962315i	0.999864	+	0.0164804i	$0.00524610\pi$
$31$	7.37458	+	5.35794i	1.32451	+	0.962315i	0.324649	+	0.945835i	$0.394754\pi$
$32$			9.89323i			1.74889i
$33$	8.26966	−	11.3822i	1.43956	−	1.98139i
$34$	0.805352	−	2.47862i	0.138117	−	0.425080i
$35$	−6.78904	−	5.42016i	−1.14756	−	0.916175i
$36$	7.79638	+	23.9948i	1.29940	+	3.99913i
$37$	−1.46451	−	0.475847i	−0.240763	−	0.0782288i	0.186150	−	0.982521i	$-0.440399\pi$
$37$	−1.46451	−	0.475847i	−0.240763	−	0.0782288i	−0.426913	+	0.904293i	$0.640399\pi$
$38$	−12.0383	−	3.91147i	−1.95286	−	0.634524i
$39$	−2.24780	−	6.91803i	−0.359937	−	1.10777i
$40$	−4.32022	−	15.6874i	−0.683087	−	2.48040i
$41$	−2.37460	+	7.30826i	−0.370850	+	1.14136i	0.575386	+	0.817882i	$0.304852\pi$
$41$	−2.37460	+	7.30826i	−0.370850	+	1.14136i	−0.946236	+	0.323477i	$0.895148\pi$
$42$	17.1095	−	23.5492i	2.64006	−	3.63373i
$43$		−	8.69780i		−	1.32640i	−0.748441	−	0.663201i	$-0.769197\pi$
$43$		−	8.69780i		−	1.32640i	0.748441	−	0.663201i	$-0.230803\pi$
$44$	−18.9732	−	13.7849i	−2.86032	−	2.07814i
$45$	−6.48001	−	9.82849i	−0.965982	−	1.46515i
$46$	3.57033	−	2.59400i	0.526417	−	0.382464i
$47$	3.91599	+	5.38990i	0.571206	+	0.786198i	0.992697	−	0.120635i	$-0.0384930\pi$
$47$	3.91599	+	5.38990i	0.571206	+	0.786198i	−0.421491	+	0.906833i	$0.638493\pi$
$48$	25.6473	−	8.33332i	3.70187	−	1.20281i
$49$	−8.09384			−1.15626
$50$	6.67127	+	11.1936i	0.943460	+	1.58302i
$51$	−2.87485			−0.402560
$52$	−11.5318	+	3.74691i	−1.59917	+	0.519602i
$53$	−0.695828	−	0.957725i	−0.0955793	−	0.131554i	0.758549	−	0.651616i	$-0.225909\pi$
$53$	−0.695828	−	0.957725i	−0.0955793	−	0.131554i	−0.854128	+	0.520062i	$0.825909\pi$
$54$	13.7279	−	9.97389i	1.86813	−	1.35727i
$55$	10.2432	+	3.85072i	1.38119	+	0.519231i
$56$	−22.8717	−	16.6173i	−3.05636	−	2.22058i
$57$			13.9627i			1.84941i
$58$	1.57954	−	2.17406i	0.207404	−	0.285467i
$59$	2.12720	−	6.54686i	0.276938	−	0.852328i	−0.711762	−	0.702421i	$-0.752102\pi$
$59$	2.12720	−	6.54686i	0.276938	−	0.852328i	0.988700	−	0.149907i	$-0.0478975\pi$
$60$	−25.7189	+	16.9567i	−3.32029	+	2.18910i
$61$	−2.73432	−	8.41538i	−0.350094	−	1.07748i	−0.958800	−	0.284083i	$-0.908311\pi$
$61$	−2.73432	−	8.41538i	−0.350094	−	1.07748i	0.608705	−	0.793396i	$-0.291689\pi$
$62$	−22.5938	−	7.34117i	−2.86942	−	0.932329i
$63$	−19.4530	−	6.32067i	−2.45085	−	0.796329i
$64$	−2.17015	−	6.67904i	−0.271269	−	0.834880i
$65$	4.72353	−	3.11426i	0.585882	−	0.386277i
$66$	−11.3307	+	34.8722i	−1.39471	+	4.29247i
$67$	−0.0931483	+	0.128208i	−0.0113799	+	0.0156631i	−0.814669	−	0.579926i	$-0.803081\pi$
$67$	−0.0931483	+	0.128208i	−0.0113799	+	0.0156631i	0.803289	+	0.595589i	$0.203081\pi$
$68$			4.79215i			0.581133i
$69$	−3.93841	−	2.86142i	−0.474129	−	0.344475i
$70$	21.1926	+	7.96695i	2.53300	+	0.952233i
$71$	−3.77323	+	2.74141i	−0.447800	+	0.325346i	−0.788727	−	0.614744i	$-0.789259\pi$
$71$	−3.77323	+	2.74141i	−0.447800	+	0.325346i	0.340927	+	0.940090i	$0.389259\pi$
$72$	−22.5186	−	30.9941i	−2.65384	−	3.65270i
$73$	−6.05516	+	1.96744i	−0.708703	+	0.230272i	−0.641119	−	0.767442i	$-0.721529\pi$
$73$	−6.05516	+	1.96744i	−0.708703	+	0.230272i	−0.0675848	+	0.997714i	$0.521529\pi$
$74$	4.01318			0.466523
$75$	9.46924	−	10.8145i	1.09341	−	1.24875i
$76$	23.2747			2.66979
$77$	18.0825	−	5.87538i	2.06070	−	0.669561i
$78$	11.1429	+	15.3369i	1.26169	+	1.73656i
$79$	−4.70705	+	3.41987i	−0.529585	+	0.384766i	−0.820202	−	0.572073i	$-0.806139\pi$
$79$	−4.70705	+	3.41987i	−0.529585	+	0.384766i	0.290618	+	0.956839i	$0.406139\pi$
$80$	11.5456	+	17.5116i	1.29083	+	1.95786i
$81$	−2.36524	−	1.71845i	−0.262805	−	0.190939i
$82$		−	20.0268i		−	2.21159i
$83$	−0.722444	+	0.994359i	−0.0792985	+	0.109145i	−0.846824	−	0.531874i	$-0.821488\pi$
$83$	−0.722444	+	0.994359i	−0.0792985	+	0.109145i	0.767525	+	0.641019i	$0.221488\pi$
$84$	−16.5397	+	50.9040i	−1.80463	+	5.55408i
$85$	−0.593696	−	2.15581i	−0.0643954	−	0.233831i
$86$	7.00480	+	21.5585i	0.755347	+	2.32472i
$87$	−2.81924	−	0.916026i	−0.302254	−	0.0982083i
$88$	33.8689	+	11.0047i	3.61044	+	1.17310i
$89$	1.70809	+	5.25696i	0.181057	+	0.557237i	0.999858	−	0.0168408i	$-0.00536084\pi$
$89$	1.70809	+	5.25696i	0.181057	+	0.557237i	−0.818801	+	0.574077i	$0.805361\pi$
$90$	23.9769	+	19.1424i	2.52738	+	2.01779i
$91$	3.03769	−	9.34903i	0.318436	−	0.980045i
$92$	−4.76976	+	6.56501i	−0.497281	+	0.684449i
$93$			26.2057i			2.71740i
$94$	−14.0470	−	10.2058i	−1.44884	−	1.05264i
$95$	−10.4704	+	2.88349i	−1.07424	+	0.295840i
$96$	−23.0097	+	16.7176i	−2.34842	+	1.70623i
$97$	4.26881	+	5.87551i	0.433432	+	0.596567i	0.968737	−	0.248091i	$-0.0798033\pi$
$97$	4.26881	+	5.87551i	0.433432	+	0.596567i	−0.535305	+	0.844659i	$0.679803\pi$
$98$	20.0616	−	6.51839i	2.02652	−	0.658457i
$99$	25.7652			2.58950
$100$	−18.0269	−	15.7844i	−1.80269	−	1.57844i
$101$	9.30241			0.925625			0.462812	−	0.886456i	$-0.346840\pi$
$101$	9.30241			0.925625			0.462812	+	0.886456i	$0.346840\pi$
$102$	7.12567	−	2.31527i	0.705546	−	0.229246i
$103$	−2.93850	−	4.04450i	−0.289539	−	0.398516i	0.639325	−	0.768936i	$-0.279214\pi$
$103$	−2.93850	−	4.04450i	−0.289539	−	0.398516i	−0.928864	+	0.370420i	$0.879214\pi$
$104$	14.8957	−	10.8223i	1.46064	−	1.06122i
$105$	1.13415	−	24.9490i	0.110681	−	2.43477i
$106$	2.49600	+	1.81345i	0.242433	+	0.176138i
$107$			2.93523i			0.283759i	0.989884	+	0.141880i	$0.0453146\pi$
$107$			2.93523i			0.283759i	−0.989884	+	0.141880i	$0.954685\pi$
$108$	−18.3397	+	25.2424i	−1.76473	+	2.42895i
$109$	−6.14633	+	18.9165i	−0.588712	+	1.81187i	−0.00488993	+	0.999988i	$0.501557\pi$
$109$	−6.14633	+	18.9165i	−0.588712	+	1.81187i	−0.583822	+	0.811882i	$0.698443\pi$
$110$	−28.4901	−	1.29512i	−2.71642	−	0.123485i
$111$	−1.36799	−	4.21024i	−0.129844	−	0.399619i
$112$	34.6598	+	11.2616i	3.27504	+	1.06413i
$113$	4.29952	+	1.39700i	0.404465	+	0.131419i	0.504182	−	0.863597i	$-0.331794\pi$
$113$	4.29952	+	1.39700i	0.404465	+	0.131419i	−0.0997177	+	0.995016i	$0.531794\pi$
$114$	−11.2449	−	34.6083i	−1.05318	−	3.24136i
$115$	1.33240	−	3.54428i	0.124247	−	0.330506i
$116$	−1.52694	+	4.69944i	−0.141773	+	0.436332i
$117$	7.82996	−	10.7770i	0.723880	−	0.996336i
$118$			17.9403i			1.65154i
$119$	−3.14310	−	2.28359i	−0.288127	−	0.209337i
$120$	29.1857	−	36.5566i	2.66427	−	3.33714i
$121$	−10.4768	+	7.61186i	−0.952439	+	0.691987i
$122$	13.5547	+	18.6564i	1.22718	+	1.68907i
$123$	−21.0102	+	6.82662i	−1.89442	+	0.615536i
$124$	43.6827			3.92282
$125$	10.0652	+	4.86751i	0.900255	+	0.435363i
$126$	53.3070			4.74896
$127$	−14.5700	+	4.73409i	−1.29288	+	0.420083i	−0.873099	−	0.487542i	$-0.837893\pi$
$127$	−14.5700	+	4.73409i	−1.29288	+	0.420083i	−0.419782	+	0.907625i	$0.637893\pi$
$128$	−0.872231	−	1.20052i	−0.0770950	−	0.106112i
$129$	20.2294	−	14.6975i	1.78110	−	1.29404i
$130$	−9.19976	+	11.5232i	−0.806872	+	1.01065i
$131$	0.870333	+	0.632334i	0.0760413	+	0.0552473i	0.625156	−	0.780499i	$-0.285035\pi$
$131$	0.870333	+	0.632334i	0.0760413	+	0.0552473i	−0.549115	+	0.835747i	$0.685035\pi$
$132$		−	67.4216i		−	5.86830i
$133$	−11.0911	+	15.2655i	−0.961716	+	1.32369i
$134$	0.127627	−	0.392795i	0.0110253	−	0.0339323i
$135$	5.12308	−	13.6277i	0.440925	−	1.17289i
$136$	−2.24866	−	6.92066i	−0.192821	−	0.593442i
$137$	18.4260	+	5.98696i	1.57424	+	0.511501i	0.960564	−	0.278059i	$-0.0896911\pi$
$137$	18.4260	+	5.98696i	1.57424	+	0.511501i	0.613674	+	0.789560i	$0.289691\pi$
$138$	12.0663	+	3.92057i	1.02715	+	0.333741i
$139$	3.93597	+	12.1137i	0.333844	+	1.02747i	0.967289	+	0.253679i	$0.0816405\pi$
$139$	3.93597	+	12.1137i	0.333844	+	1.02747i	−0.633444	+	0.773788i	$0.718359\pi$
$140$	−41.5879	−	1.89053i	−3.51482	−	0.159779i
$141$	−5.91863	+	18.2157i	−0.498439	+	1.53404i
$142$	7.14460	−	9.83369i	0.599561	−	0.825225i
$143$			12.3827i			1.03549i
$144$	39.9538	+	29.0281i	3.32948	+	2.41901i
$145$	0.104704	−	2.30328i	0.00869519	−	0.191277i
$146$	13.4240	−	9.75308i	1.11098	−	0.807171i
$147$	−13.6769	−	18.8247i	−1.12806	−	1.55264i
$148$	−7.01813	+	2.28033i	−0.576887	+	0.187442i
$149$	−17.3063			−1.41779			−0.708896	−	0.705313i	$-0.750806\pi$
$149$	−17.3063			−1.41779			−0.708896	+	0.705313i	$0.750806\pi$
$150$	−14.7612	+	34.4311i	−1.20524	+	2.81129i
$151$	5.12056			0.416705			0.208353	−	0.978054i	$-0.433190\pi$
$151$	5.12056			0.416705			0.208353	+	0.978054i	$0.433190\pi$
$152$	−33.6126	+	10.9214i	−2.72634	+	0.885842i
$153$	−3.09456	−	4.25930i	−0.250181	−	0.344344i
$154$	−40.0880	+	29.1256i	−3.23038	+	2.34701i
$155$	−19.6513	+	5.41182i	−1.57843	+	0.434688i
$156$	−28.2010	−	20.4892i	−2.25788	−	1.64045i
$157$			7.04509i			0.562259i	0.959670	+	0.281130i	$0.0907091\pi$
$157$			7.04509i			0.562259i	−0.959670	+	0.281130i	$0.909291\pi$
$158$	8.91279	−	12.2674i	0.709063	−	0.975942i
$159$	1.05167	−	3.23672i	0.0834032	−	0.256689i
$160$	−17.2881	−	13.8023i	−1.36674	−	1.09117i
$161$	−2.03296	−	6.25682i	−0.160220	−	0.493107i
$162$	7.24649	+	2.35453i	0.569338	+	0.184989i
$163$	−5.95265	−	1.93413i	−0.466248	−	0.151493i	0.0664658	−	0.997789i	$-0.478828\pi$
$163$	−5.95265	−	1.93413i	−0.466248	−	0.151493i	−0.532714	+	0.846296i	$0.678828\pi$
$164$	11.3794	+	35.0223i	0.888584	+	2.73478i
$165$	8.35283	+	30.3305i	0.650267	+	2.36123i
$166$	0.989854	−	3.04646i	0.0768276	−	0.236451i
$167$	−8.24217	+	11.3444i	−0.637798	+	0.877854i	−0.998496	−	0.0548288i	$-0.982539\pi$
$167$	−8.24217	+	11.3444i	−0.637798	+	0.877854i	0.360697	+	0.932683i	$0.382539\pi$
$168$		−	81.2750i		−	6.27050i
$169$	−5.33783	−	3.87816i	−0.410602	−	0.298320i
$170$	3.20773	+	4.86530i	0.246022	+	0.373152i
$171$	−20.6868	+	15.0298i	−1.58196	+	1.14936i
$172$	−24.4996	−	33.7208i	−1.86807	−	2.57118i
$173$	4.60523	−	1.49633i	0.350129	−	0.113764i	−0.128672	−	0.991687i	$-0.541071\pi$
$173$	4.60523	−	1.49633i	0.350129	−	0.113764i	0.478801	+	0.877923i	$0.341071\pi$
$174$	7.72554			0.585672
$175$	18.9431	−	4.30182i	1.43196	−	0.325187i
$176$	−45.9064			−3.46032
$177$	18.8213	−	6.11540i	1.41469	−	0.459661i
$178$	−8.46741	−	11.6544i	−0.634659	−	0.873533i
$179$	21.4288	−	15.5690i	1.60167	−	1.16368i	0.717439	−	0.696621i	$-0.245314\pi$
$179$	21.4288	−	15.5690i	1.60167	−	1.16368i	0.884227	−	0.467058i	$-0.154686\pi$
$180$	−52.8069	−	19.8518i	−3.93600	−	1.47966i
$181$	4.88074	+	3.54607i	0.362783	+	0.263577i	0.754212	−	0.656631i	$-0.228019\pi$
$181$	4.88074	+	3.54607i	0.362783	+	0.263577i	−0.391429	+	0.920208i	$0.628019\pi$
$182$			25.6191i			1.89901i
$183$	14.9521	−	20.5798i	1.10529	−	1.52130i
$184$	3.80778	−	11.7191i	0.280713	−	0.863946i
$185$	2.87469	−	1.89531i	0.211352	−	0.139346i
$186$	−21.1048	−	64.9539i	−1.54748	−	4.76265i
$187$	4.65436	+	1.51229i	0.340360	+	0.110590i
$188$	30.3640	+	9.86587i	2.21452	+	0.719543i
$189$	−7.81673	−	24.0574i	−0.568583	−	1.74992i
$190$	23.6300	−	15.5795i	1.71430	−	1.13025i
$191$	1.29085	−	3.97282i	0.0934024	−	0.287463i	−0.893432	−	0.449199i	$-0.851709\pi$
$191$	1.29085	−	3.97282i	0.0934024	−	0.287463i	0.986834	+	0.161736i	$0.0517094\pi$
$192$	11.8670	−	16.3336i	0.856430	−	1.17877i
$193$		−	10.3403i		−	0.744314i	−0.928170	−	0.372157i	$-0.878618\pi$
$193$		−	10.3403i		−	0.744314i	0.928170	−	0.372157i	$-0.121382\pi$
$194$	−15.3126	−	11.1253i	−1.09938	−	0.798747i
$195$	15.2250	+	5.72354i	1.09028	+	0.409871i
$196$	−31.3792	+	22.7984i	−2.24137	+	1.62845i
$197$	14.0896	+	19.3926i	1.00384	+	1.38167i	0.922939	+	0.384946i	$0.125780\pi$
$197$	14.0896	+	19.3926i	1.00384	+	1.38167i	0.0809016	+	0.996722i	$0.474220\pi$
$198$	−63.8622	+	20.7501i	−4.53849	+	1.47464i
$199$	5.38939			0.382044			0.191022	−	0.981586i	$-0.438820\pi$
$199$	5.38939			0.382044			0.191022	+	0.981586i	$0.438820\pi$
$200$	33.4405	+	14.3365i	2.36460	+	1.01374i
$201$	−0.455588			−0.0321347
$202$	−23.0571	+	7.49172i	−1.62229	+	0.527116i
$203$	−2.35466	−	3.24091i	−0.165265	−	0.227467i
$204$	−11.1456	+	8.09775i	−0.780348	+	0.566956i
$205$	−9.45808	−	14.3455i	−0.660581	−	1.00193i
$206$	10.5407	+	7.65825i	0.734404	+	0.533575i
$207$		−	8.91514i		−	0.619645i
$208$	−13.9508	+	19.2016i	−0.967314	+	1.33139i
$209$	7.34497	−	22.6055i	0.508062	−	1.56365i
$210$	17.2816	+	62.7524i	1.19254	+	4.33032i
$211$	−0.324597	−	0.999006i	−0.0223462	−	0.0687744i	0.939262	−	0.343202i	$-0.111512\pi$
$211$	−0.324597	−	0.999006i	−0.0223462	−	0.0687744i	−0.961608	+	0.274428i	$0.911512\pi$
$212$	−5.39535	−	1.75305i	−0.370554	−	0.120400i
$213$	−12.7520	−	4.14337i	−0.873751	−	0.283899i
$214$	−2.36389	−	7.27531i	−0.161592	−	0.497330i
$215$	15.1991	+	12.1345i	1.03657	+	0.827566i
$216$	14.6409	−	45.0599i	0.996184	−	3.06594i
$217$	−20.8160	+	28.6508i	−1.41308	+	1.94494i
$218$		−	51.8367i		−	3.51082i
$219$	−14.8079	−	10.7586i	−1.00062	−	0.726996i
$220$	50.5585	−	13.9235i	3.40865	−	0.938720i
$221$	2.04700	−	1.48723i	0.137696	−	0.100042i
$222$	6.78146	+	9.33388i	0.455142	+	0.626449i
$223$	14.5352	−	4.72278i	0.973350	−	0.316261i	0.221183	−	0.975232i	$-0.429008\pi$
$223$	14.5352	−	4.72278i	0.973350	−	0.316261i	0.752168	+	0.658972i	$0.229008\pi$
$224$	−38.4360			−2.56811
$225$	26.2153	+	2.38837i	1.74769	+	0.159224i
$226$	−11.7819			−0.783723
$227$	−9.79324	+	3.18202i	−0.650000	+	0.211198i	−0.615414	−	0.788204i	$-0.711011\pi$
$227$	−9.79324	+	3.18202i	−0.650000	+	0.211198i	−0.0345860	+	0.999402i	$0.511011\pi$
$228$	39.3295	+	54.1324i	2.60466	+	3.58501i
$229$	20.2255	−	14.6947i	1.33654	−	0.971054i	0.336978	−	0.941513i	$-0.390595\pi$
$229$	20.2255	−	14.6947i	1.33654	−	0.971054i	0.999564	−	0.0295415i	$-0.00940472\pi$
$230$	−0.448131	+	9.85798i	−0.0295489	+	0.650016i
$231$	44.2208	+	32.1283i	2.90952	+	2.11389i
$232$		−	7.50328i		−	0.492614i
$233$	0.706610	−	0.972565i	0.0462915	−	0.0637148i	−0.785244	−	0.619187i	$-0.787462\pi$
$233$	0.706610	−	0.972565i	0.0462915	−	0.0637148i	0.831535	+	0.555472i	$0.187462\pi$
$234$	−10.7282	+	33.0180i	−0.701324	+	2.15845i
$235$	−14.8820	−	0.676514i	−0.970792	−	0.0441309i
$236$	−10.1939	−	31.3735i	−0.663564	−	2.04224i
$237$	−15.9079	−	5.16880i	−1.03333	−	0.335750i
$238$	9.62963	+	3.12886i	0.624196	+	0.202814i
$239$	4.45012	+	13.6961i	0.287854	+	0.885924i	0.985529	+	0.169509i	$0.0542183\pi$
$239$	4.45012	+	13.6961i	0.287854	+	0.885924i	−0.697674	+	0.716415i	$0.745782\pi$
$240$	−21.2190	+	56.4438i	−1.36968	+	3.64343i
$241$	5.80512	−	17.8663i	0.373940	−	1.15087i	−0.570250	−	0.821471i	$-0.693154\pi$
$241$	5.80512	−	17.8663i	0.373940	−	1.15087i	0.944191	−	0.329399i	$-0.106846\pi$
$242$	19.8378	−	27.3044i	1.27522	−	1.75520i
$243$			11.1278i			0.713852i
$244$	−34.3048	−	24.9239i	−2.19614	−	1.59559i
$245$	11.2919	−	14.1437i	0.721413	−	0.903608i
$246$	46.5784	−	33.8412i	2.96973	−	2.15764i
$247$	−7.22326	−	9.94197i	−0.459605	−	0.632592i
$248$	−63.0852	+	20.4976i	−4.00591	+	1.30160i
$249$	−3.53347			−0.223924
$250$	−28.8677	−	3.95870i	−1.82576	−	0.250370i
$251$	−7.54394			−0.476169			−0.238085	−	0.971244i	$-0.576520\pi$
$251$	−7.54394			−0.476169			−0.238085	+	0.971244i	$0.576520\pi$
$252$	−93.2216	+	30.2895i	−5.87241	+	1.90806i
$253$	4.87102	+	6.70438i	0.306238	+	0.421501i
$254$	32.3009	−	23.4680i	2.02674	−	1.47251i
$255$	4.01077	−	5.02371i	0.251164	−	0.314597i
$256$	14.4918	+	10.5289i	0.905740	+	0.658058i
$257$			4.70430i			0.293446i	0.989178	+	0.146723i	$0.0468726\pi$
$257$			4.70430i			0.293446i	−0.989178	+	0.146723i	$0.953127\pi$
$258$	−38.3043	+	52.7214i	−2.38472	+	3.28229i
$259$	1.84870	−	5.68973i	0.114873	−	0.353542i
$260$	9.54068	−	25.3788i	0.591688	−	1.57393i
$261$	−1.67754	−	5.16293i	−0.103837	−	0.319577i
$262$	−2.66648	−	0.866390i	−0.164735	−	0.0535258i
$263$	15.7244	+	5.10916i	0.969606	+	0.315044i	0.750657	−	0.660692i	$-0.229737\pi$
$263$	15.7244	+	5.10916i	0.969606	+	0.315044i	0.218949	+	0.975736i	$0.429737\pi$
$264$	31.6368	+	97.3682i	1.94711	+	5.99260i
$265$	2.64436	+	0.120209i	0.162441	+	0.00738438i
$266$	15.1964	−	46.7696i	0.931749	−	2.86763i
$267$	−9.34034	+	12.8559i	−0.571620	+	0.786767i
$268$			0.759428i			0.0463894i
$269$	18.2182	+	13.2363i	1.11078	+	0.807029i	0.982786	−	0.184746i	$-0.0591461\pi$
$269$	18.2182	+	13.2363i	1.11078	+	0.807029i	0.127994	+	0.991775i	$0.459146\pi$
$270$	−1.72306	+	37.9038i	−0.104862	+	2.30675i
$271$	−20.2931	+	14.7438i	−1.23272	+	0.895621i	−0.997091	−	0.0762231i	$-0.975714\pi$
$271$	−20.2931	+	14.7438i	−1.23272	+	0.895621i	−0.235625	+	0.971844i	$0.575714\pi$
$272$	5.51364	+	7.58887i	0.334314	+	0.460143i
$273$	26.8771	−	8.73290i	1.62668	−	0.528539i
$274$	−50.4926			−3.05037
$275$	−21.0195	+	12.5273i	−1.26752	+	0.755426i
$276$	−23.3288			−1.40423
$277$	17.3905	−	5.65052i	1.04489	−	0.339507i	0.264232	−	0.964459i	$-0.414882\pi$
$277$	17.3905	−	5.65052i	1.04489	−	0.339507i	0.780663	+	0.624953i	$0.214882\pi$
$278$	−19.5115	−	26.8553i	−1.17022	−	1.61067i
$279$	−38.8256	+	28.2084i	−2.32442	+	1.68879i
$280$	60.9470	−	16.7844i	3.64228	−	1.00306i
$281$	−22.3650	−	16.2491i	−1.33418	−	0.969340i	−0.999637	−	0.0269597i	$-0.991417\pi$
$281$	−22.3650	−	16.2491i	−1.33418	−	0.969340i	−0.334545	−	0.942380i	$-0.608583\pi$
$282$		−	49.9163i		−	2.97247i
$283$	8.30361	−	11.4289i	0.493599	−	0.679380i	−0.487448	−	0.873152i	$-0.662072\pi$
$283$	8.30361	−	11.4289i	0.493599	−	0.679380i	0.981047	+	0.193772i	$0.0620722\pi$
$284$	−6.90666	+	21.2565i	−0.409835	+	1.26134i
$285$	−24.3994	−	19.4797i	−1.44529	−	1.15388i
$286$	−9.97240	−	30.6919i	−0.589680	−	1.81485i
$287$	−28.3932	−	9.22551i	−1.67600	−	0.544564i
$288$	−49.5365	−	16.0954i	−2.91896	−	0.948429i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	1.59543	+	5.79327i	0.0936868	+	0.340193i
$291$	−6.45187	+	19.8568i	−0.378216	+	1.16403i
$292$	−17.9336	+	24.6835i	−1.04949	+	1.44449i
$293$			6.30729i			0.368476i	0.982882	+	0.184238i	$0.0589817\pi$
$293$			6.30729i			0.368476i	−0.982882	+	0.184238i	$0.941018\pi$
$294$	49.0605	+	35.6445i	2.86126	+	2.07883i
$295$	8.47269	+	12.8509i	0.493299	+	0.748207i
$296$	9.06534	−	6.58636i	0.526912	−	0.382824i
$297$	18.7290	+	25.7783i	1.08677	+	1.49581i
$298$	42.8958	−	13.9377i	2.48489	−	0.807390i
$299$	4.28458			0.247784
$300$	6.24980	−	68.5995i	0.360832	−	3.96059i
$301$	33.7917			1.94772
$302$	−12.6919	+	4.12385i	−0.730337	+	0.237301i
$303$	15.7192	+	21.6356i	0.903044	+	1.24293i
$304$	36.8580	−	26.7789i	2.11395	−	1.53587i
$305$	18.5203	+	6.96236i	1.06047	+	0.398663i
$306$	11.1005	+	8.06497i	0.634572	+	0.461044i
$307$			22.9323i			1.30882i	0.756141	+	0.654408i	$0.227082\pi$
$307$			22.9323i			1.30882i	−0.756141	+	0.654408i	$0.772918\pi$
$308$	53.5552	−	73.7125i	3.05159	−	4.20016i
$309$	4.44125	−	13.6688i	0.252654	−	0.777589i
$310$	44.3496	−	29.2400i	2.51889	−	1.66072i
$311$	1.37002	+	4.21649i	0.0776868	+	0.239095i	0.982356	−	0.187018i	$-0.0598824\pi$
$311$	1.37002	+	4.21649i	0.0776868	+	0.239095i	−0.904670	+	0.426114i	$0.859882\pi$
$312$	50.3413	+	16.3569i	2.85001	+	0.926025i
$313$	−8.44244	−	2.74311i	−0.477195	−	0.155050i	0.0605370	−	0.998166i	$-0.480719\pi$
$313$	−8.44244	−	2.74311i	−0.477195	−	0.155050i	−0.537732	+	0.843116i	$0.680719\pi$
$314$	−5.67378	−	17.4621i	−0.320190	−	0.985443i
$315$	38.1845	−	25.1753i	2.15145	−	1.41847i
$316$	−8.61596	+	26.5172i	−0.484686	+	1.49171i
$317$	9.82764	−	13.5266i	0.551975	−	0.759729i	−0.438303	−	0.898827i	$-0.644420\pi$
$317$	9.82764	−	13.5266i	0.551975	−	0.759729i	0.990279	+	0.139098i	$0.0444204\pi$
$318$			8.86956i			0.497380i
$319$	4.08245	+	2.96607i	0.228573	+	0.166068i
$320$	14.6990	+	5.52582i	0.821700	+	0.308903i
$321$	−6.82677	+	4.95994i	−0.381033	+	0.276837i
$322$	10.0779	+	13.8710i	0.561619	+	0.773002i
$323$	−4.61913	+	1.50085i	−0.257015	+	0.0835094i
$324$	−14.0103			−0.778351
$325$	−1.14784	+	12.5990i	−0.0636707	+	0.698866i
$326$	16.3120			0.903439
$327$	−54.3821	+	17.6698i	−3.00734	+	0.977143i
$328$	−32.8676	−	45.2384i	−1.81481	−	2.49787i
$329$	−20.9402	+	15.2139i	−1.15447	+	0.838772i
$330$	−45.1302	−	68.4509i	−2.48434	−	3.76810i
$331$	−7.62231	−	5.53793i	−0.418960	−	0.304392i	0.358259	−	0.933622i	$-0.383370\pi$
$331$	−7.62231	−	5.53793i	−0.418960	−	0.304392i	−0.777219	+	0.629230i	$0.783370\pi$
$332$			5.89000i			0.323256i
$333$	4.76524	−	6.55878i	0.261133	−	0.359419i
$334$	11.2930	−	34.7562i	0.617925	−	1.90178i
$335$	−0.0940851	−	0.341639i	−0.00514042	−	0.0186657i
$336$	32.3756	+	99.6418i	1.76623	+	5.43591i
$337$	6.74155	+	2.19046i	0.367235	+	0.119322i	0.486821	−	0.873502i	$-0.338157\pi$
$337$	6.74155	+	2.19046i	0.367235	+	0.119322i	−0.119585	+	0.992824i	$0.538157\pi$
$338$	16.3537	+	5.31365i	0.889526	+	0.289024i
$339$	4.01616	+	12.3605i	0.218128	+	0.671329i
$340$	−8.37410	−	6.68563i	−0.454150	−	0.362579i
$341$	13.7853	−	42.4267i	0.746514	−	2.29753i
$342$	39.1703	−	53.9133i	2.11809	−	2.91530i
$343$		−	4.24967i		−	0.229461i
$344$	51.2046	+	37.2023i	2.76077	+	2.00581i
$345$	10.4948	−	2.89020i	0.565021	−	0.155603i
$346$	−10.2095	+	7.41766i	−0.548868	+	0.398776i
$347$	−11.4516	−	15.7618i	−0.614755	−	0.846138i	0.382203	−	0.924078i	$-0.375165\pi$
$347$	−11.4516	−	15.7618i	−0.614755	−	0.846138i	−0.996958	+	0.0779408i	$0.975165\pi$
$348$	−13.5102	+	4.38973i	−0.724222	+	0.235314i
$349$	−6.57622			−0.352017			−0.176008	−	0.984389i	$-0.556319\pi$
$349$	−6.57622			−0.352017			−0.176008	+	0.984389i	$0.556319\pi$
$350$	−43.4882	+	25.9184i	−2.32454	+	1.38540i
$351$	16.4742			0.879325
$352$	46.0466	−	14.9615i	2.45429	−	0.797449i
$353$	−20.2486	−	27.8698i	−1.07772	−	1.48336i	−0.862002	−	0.506904i	$-0.830790\pi$
$353$	−20.2486	−	27.8698i	−1.07772	−	1.48336i	−0.215721	−	0.976455i	$-0.569210\pi$
$354$	−41.7257	+	30.3155i	−2.21769	+	1.61125i
$355$	0.473597	−	10.4182i	0.0251359	−	0.552940i
$356$	21.4297	+	15.5696i	1.13577	+	0.825186i
$357$		−	11.1690i		−	0.591128i
$358$	−40.5754	+	55.8473i	−2.14448	+	2.95162i
$359$	0.798907	−	2.45878i	0.0421647	−	0.129770i	−0.927758	−	0.373182i	$-0.878267\pi$
$359$	0.798907	−	2.45878i	0.0421647	−	0.129770i	0.969923	+	0.243412i	$0.0782668\pi$
$360$	85.5773	+	3.89023i	4.51032	+	0.205033i
$361$	1.41806	+	4.36433i	0.0746345	+	0.229701i
$362$	−14.9533	−	4.85863i	−0.785929	−	0.255364i
$363$	−35.4074	−	11.5046i	−1.85841	−	0.603833i
$364$	−14.5570	−	44.8019i	−0.762996	−	2.34826i
$365$	5.00966	−	13.3260i	0.262218	−	0.697515i
$366$	−20.4866	+	63.0512i	−1.07085	+	3.29574i
$367$	13.2679	−	18.2616i	0.692577	−	0.953250i	−0.307422	−	0.951573i	$-0.599466\pi$
$367$	13.2679	−	18.2616i	0.692577	−	0.953250i	0.999999	−	0.00167676i	$-0.000533730\pi$
$368$			15.8843i			0.828025i
$369$	−32.7300	−	23.7797i	−1.70386	−	1.23792i
$370$	−5.59888	+	7.01289i	−0.291072	+	0.364583i
$371$	3.72084	−	2.70335i	0.193176	−	0.140351i
$372$	73.8149	+	101.597i	3.82712	+	5.26758i
$373$	2.00767	−	0.652331i	0.103953	−	0.0337764i	−0.256579	−	0.966523i	$-0.582595\pi$
$373$	2.00767	−	0.652331i	0.103953	−	0.0337764i	0.360532	+	0.932747i	$0.382595\pi$
$374$	−12.7543			−0.659510
$375$	5.68719	+	31.6347i	0.293685	+	1.63361i
$376$	−48.4802			−2.50018
$377$	2.48128	−	0.806218i	0.127793	−	0.0415223i
$378$	38.7494	+	53.3339i	1.99305	+	2.74320i
$379$	−22.7087	+	16.4988i	−1.16647	+	0.847488i	−0.990582	−	0.136923i	$-0.956279\pi$
$379$	−22.7087	+	16.4988i	−1.16647	+	0.847488i	−0.175885	+	0.984411i	$0.556279\pi$
$380$	−32.4711	+	40.6717i	−1.66573	+	2.08641i
$381$	−35.6310	−	25.8874i	−1.82543	−	1.32625i
$382$			10.8867i			0.557012i
$383$	5.21515	−	7.17804i	0.266482	−	0.366781i	−0.654716	−	0.755875i	$-0.727212\pi$
$383$	5.21515	−	7.17804i	0.266482	−	0.366781i	0.921198	+	0.389094i	$0.127212\pi$
$384$	1.31829	−	4.05728i	0.0672737	−	0.207047i
$385$	−14.9604	+	39.7955i	−0.762451	+	2.02817i
$386$	8.32761	+	25.6298i	0.423864	+	1.30452i
$387$	43.5508	+	14.1505i	2.21381	+	0.719312i
$388$	33.0997	+	10.7547i	1.68038	+	0.545989i
$389$	7.33005	+	22.5596i	0.371648	+	1.14382i	0.945712	+	0.325005i	$0.105366\pi$
$389$	7.33005	+	22.5596i	0.371648	+	1.14382i	−0.574064	+	0.818811i	$0.694634\pi$
$390$	−42.3464	−	1.92501i	−2.14429	−	0.0974768i
$391$	0.523275	−	1.61047i	0.0264631	−	0.0814452i
$392$	34.6190	−	47.6490i	1.74853	−	2.40664i
$393$			3.09274i			0.156008i
$394$	−50.5406	−	36.7199i	−2.54620	−	1.84992i
$395$	0.590806	−	12.9966i	0.0297267	−	0.653928i
$396$	99.8899	−	72.5743i	5.01966	−	3.64699i
$397$	13.6625	+	18.8049i	0.685703	+	0.943789i	0.999985	−	0.00554089i	$-0.00176373\pi$
$397$	13.6625	+	18.8049i	0.685703	+	0.943789i	−0.314282	+	0.949330i	$0.601764\pi$
$398$	−13.3582	+	4.34036i	−0.669588	+	0.217562i
$399$	−54.2463			−2.71571
$400$	−46.7084	−	4.25540i	−2.33542	−	0.212770i
$401$	−0.294042			−0.0146838			−0.00734188	−	0.999973i	$-0.502337\pi$
$401$	−0.294042			−0.0146838			−0.00734188	+	0.999973i	$0.502337\pi$
$402$	1.12923	−	0.366909i	0.0563208	−	0.0182997i
$403$	−13.5568	−	18.6594i	−0.675315	−	0.929491i
$404$	36.0648	−	26.2026i	1.79429	−	1.30363i
$405$	6.30273	−	1.73573i	0.313185	−	0.0862491i
$406$	8.44638	+	6.13665i	0.419187	+	0.304557i
$407$			7.53596i			0.373544i
$408$	12.2963	−	16.9245i	0.608760	−	0.837886i
$409$	−0.209720	+	0.645452i	−0.0103700	+	0.0319155i	−0.956108	−	0.293016i	$-0.905341\pi$
$409$	−0.209720	+	0.645452i	−0.0103700	+	0.0319155i	0.945738	+	0.324931i	$0.105341\pi$
$410$	34.9961	+	27.9398i	1.72833	+	1.37985i
$411$	17.2116	+	52.9720i	0.848988	+	2.61292i
$412$	−22.7847	−	7.40320i	−1.12252	−	0.364730i
$413$	25.4351	+	8.26435i	1.25158	+	0.406662i
$414$	7.17983	+	22.0972i	0.352869	+	1.08602i
$415$	−0.729709	−	2.64970i	−0.0358200	−	0.130069i
$416$	7.73537	−	23.8070i	0.379258	−	1.16724i
$417$	−21.5230	+	29.6239i	−1.05399	+	1.45069i
$418$			61.9457i			3.02986i
$419$	16.3993	+	11.9148i	0.801156	+	0.582074i	0.911253	−	0.411847i	$-0.135116\pi$
$419$	16.3993	+	11.9148i	0.801156	+	0.582074i	−0.110097	+	0.993921i	$0.535116\pi$
$420$	−65.8780	−	99.9199i	−3.21452	−	4.87559i
$421$	4.72151	−	3.43038i	0.230112	−	0.167186i	−0.466754	−	0.884387i	$-0.654577\pi$
$421$	4.72151	−	3.43038i	0.230112	−	0.167186i	0.696867	+	0.717200i	$0.254577\pi$
$422$	1.60910	+	2.21474i	0.0783300	+	0.107812i
$423$	−33.3588	+	10.8389i	−1.62196	+	0.527006i
$424$	8.61439			0.418352
$425$	4.59548	+	1.97016i	0.222914	+	0.0955667i
$426$	34.9442			1.69305
$427$	32.6944	−	10.6231i	1.58219	−	0.514086i
$428$	8.26781	+	11.3797i	0.399640	+	0.550057i
$429$	−28.7997	+	20.9242i	−1.39046	+	1.01023i
$430$	−47.4453	−	17.8362i	−2.28802	−	0.860137i
$431$	−19.6552	−	14.2803i	−0.946755	−	0.687858i	0.00328187	−	0.999995i	$-0.498955\pi$
$431$	−19.6552	−	14.2803i	−0.946755	−	0.687858i	−0.950037	+	0.312137i	$0.898955\pi$
$432$			61.0748i			2.93846i
$433$	14.1155	−	19.4283i	0.678345	−	0.933662i	−0.321567	−	0.946887i	$-0.604210\pi$
$433$	14.1155	−	19.4283i	0.678345	−	0.933662i	0.999913	+	0.0132244i	$0.00420959\pi$
$434$	28.5210	−	87.7787i	1.36905	−	4.21351i
$435$	5.53390	−	3.64855i	0.265330	−	0.174935i
$436$	29.4541	+	90.6505i	1.41060	+	4.34137i
$437$	−7.82182	−	2.54146i	−0.374168	−	0.121575i
$438$	45.3675	+	14.7408i	2.16774	+	0.704343i
$439$	−2.39480	−	7.37045i	−0.114298	−	0.351772i	0.877502	−	0.479573i	$-0.159208\pi$
$439$	−2.39480	−	7.37045i	−0.114298	−	0.351772i	−0.991800	+	0.127800i	$0.959208\pi$
$440$	−66.4816	+	43.8319i	−3.16938	+	2.08960i
$441$	13.1679	−	40.5267i	0.627045	−	1.92984i
$442$	−3.87599	+	5.33484i	−0.184362	+	0.253753i
$443$			0.875253i			0.0415845i	0.999784	+	0.0207923i	$0.00661886\pi$
$443$			0.875253i			0.0415845i	−0.999784	+	0.0207923i	$0.993381\pi$
$444$	−17.1628	−	12.4695i	−0.814511	−	0.591777i
$445$	−11.5693	−	4.34928i	−0.548440	−	0.206175i
$446$	−32.2238	+	23.4119i	−1.52584	+	1.10859i
$447$	−29.2442	−	40.2512i	−1.38320	−	1.90382i
$448$	25.9486	−	8.43121i	1.22596	−	0.398337i
$449$	15.6454			0.738353			0.369176	−	0.929359i	$-0.379640\pi$
$449$	15.6454			0.738353			0.369176	+	0.929359i	$0.379640\pi$
$450$	−66.9013	+	15.1927i	−3.15376	+	0.716192i
$451$	37.6064			1.77081
$452$	20.6039	−	6.69462i	0.969127	−	0.314888i
$453$	8.65270	+	11.9094i	0.406539	+	0.559553i
$454$	21.7111	−	15.7740i	1.01895	−	0.740311i
$455$	12.0992	+	18.3513i	0.567218	+	0.860322i
$456$	−82.1995	−	59.7214i	−3.84934	−	2.79671i
$457$		−	23.8888i		−	1.11747i	−0.829346	−	0.558736i	$-0.811287\pi$
$457$		−	23.8888i		−	1.11747i	0.829346	−	0.558736i	$-0.188713\pi$
$458$	−38.2970	+	52.7113i	−1.78950	+	2.46304i
$459$	2.01199	−	6.19226i	0.0939115	−	0.289030i
$460$	−4.81772	−	17.4940i	−0.224627	−	0.815660i
$461$	9.83796	+	30.2781i	0.458199	+	1.41019i	0.867338	+	0.497720i	$0.165829\pi$
$461$	9.83796	+	30.2781i	0.458199	+	1.41019i	−0.409138	+	0.912472i	$0.634171\pi$
$462$	−135.481	−	44.0205i	−6.30315	−	2.04802i
$463$	1.84550	+	0.599640i	0.0857678	+	0.0278677i	0.351587	−	0.936155i	$-0.385642\pi$
$463$	1.84550	+	0.599640i	0.0857678	+	0.0278677i	−0.265819	+	0.964023i	$0.585642\pi$
$464$	2.98890	+	9.19889i	0.138756	+	0.427048i
$465$	−45.7935	−	36.5601i	−2.12362	−	1.69543i
$466$	−0.968159	+	2.97969i	−0.0448491	+	0.138031i
$467$	−18.3398	+	25.2426i	−0.848665	+	1.16809i	0.135490	+	0.990779i	$0.456739\pi$
$467$	−18.3398	+	25.2426i	−0.848665	+	1.16809i	−0.984155	+	0.177309i	$0.943261\pi$
$468$		−	63.8368i		−	2.95086i
$469$	−0.498097	−	0.361889i	−0.0230000	−	0.0167105i
$470$	37.4315	−	10.3084i	1.72659	−	0.475491i
$471$	−16.3855	+	11.9048i	−0.755005	+	0.548543i
$472$	29.4433	+	40.5252i	1.35524	+	1.86533i
$473$	−40.4827	+	13.1536i	−1.86140	+	0.604804i
$474$	43.5924			2.00226
$475$	9.56875	−	22.3195i	0.439044	−	1.02409i
$476$	−18.6179			−0.853348
$477$	5.92748	−	1.92595i	0.271401	−	0.0881834i
$478$	−22.0603	−	30.3634i	−1.00901	−	1.38879i
$479$	24.2906	−	17.6482i	1.10987	−	0.806365i	0.127223	−	0.991874i	$-0.459393\pi$
$479$	24.2906	−	17.6482i	1.10987	−	0.806365i	0.982643	+	0.185509i	$0.0593935\pi$
$480$	2.88807	−	63.5317i	0.131822	−	2.89981i
$481$	3.15212	+	2.29015i	0.143724	+	0.104422i
$482$			48.9589i			2.23002i
$483$	11.1169	−	15.3010i	0.505834	−	0.696221i
$484$	−19.1772	+	59.0213i	−0.871689	+	2.68278i
$485$	−16.2228	−	0.737465i	−0.736637	−	0.0334866i
$486$	−8.96184	−	27.5817i	−0.406517	−	1.25113i
$487$	−0.288888	−	0.0938655i	−0.0130908	−	0.00425345i	0.302464	−	0.953161i	$-0.402191\pi$
$487$	−0.288888	−	0.0938655i	−0.0130908	−	0.00425345i	−0.315555	+	0.948907i	$0.602191\pi$
$488$	61.2372	+	19.8972i	2.77208	+	0.900703i
$489$	−5.56035	−	17.1130i	−0.251448	−	0.773877i
$490$	−16.5977	+	44.1508i	−0.749806	+	1.99453i
$491$	9.89022	−	30.4390i	0.446339	−	1.37369i	−0.434669	−	0.900590i	$-0.643135\pi$
$491$	9.89022	−	30.4390i	0.446339	−	1.37369i	0.881008	−	0.473101i	$-0.156865\pi$
$492$	−62.2261	+	85.6468i	−2.80537	+	3.86126i
$493$		−	1.03112i		−	0.0464393i
$494$	25.9105	+	18.8251i	1.16577	+	0.846980i
$495$	−35.9456	+	45.0238i	−1.61564	+	2.02367i
$496$	69.1762	−	50.2595i	3.10610	−	2.25672i
$497$	−10.6506	−	14.6593i	−0.477745	−	0.657559i
$498$	8.75812	−	2.84569i	0.392461	−	0.127518i
$499$	23.1280			1.03535			0.517676	−	0.855577i	$-0.326797\pi$
$499$	23.1280			1.03535			0.517676	+	0.855577i	$0.326797\pi$
$500$	52.7324	−	9.48008i	2.35827	−	0.423962i
$501$	−40.3124			−1.80103
$502$	18.6986	−	6.07553i	0.834557	−	0.271164i
$503$	−7.26419	−	9.99830i	−0.323894	−	0.445802i	0.615757	−	0.787936i	$-0.288850\pi$
$503$	−7.26419	−	9.99830i	−0.323894	−	0.445802i	−0.939651	+	0.342134i	$0.888850\pi$
$504$	120.415	−	87.4864i	5.36370	−	3.89695i
$505$	−12.9780	+	16.2556i	−0.577514	+	0.723367i
$506$	−17.4728	−	12.6947i	−0.776760	−	0.564349i
$507$		−	18.9681i		−	0.842401i
$508$	−43.1522	+	59.3939i	−1.91457	+	2.63518i
$509$	9.10893	−	28.0344i	0.403746	−	1.24260i	−0.518191	−	0.855265i	$-0.673395\pi$
$509$	9.10893	−	28.0344i	0.403746	−	1.24260i	0.921938	−	0.387338i	$-0.126605\pi$
$510$	−5.89533	+	15.6819i	−0.261049	+	0.694408i
$511$	−7.64367	−	23.5248i	−0.338136	−	1.04068i
$512$	−41.5766	−	13.5091i	−1.83745	−	0.597022i
$513$	−30.0748	−	9.77190i	−1.32784	−	0.431440i
$514$	−3.78862	−	11.6602i	−0.167109	−	0.514308i
$515$	11.1672	+	0.507646i	0.492085	+	0.0223696i
$516$	37.0286	−	113.962i	1.63009	−	5.01692i
$517$	19.1644	−	26.3775i	0.842849	−	1.16008i
$518$			15.5915i			0.685052i
$519$	11.2621	+	8.18238i	0.494350	+	0.359166i
$520$	−1.86963	+	41.1281i	−0.0819887	+	1.80359i
$521$	20.2581	−	14.7184i	0.887525	−	0.644825i	−0.0477064	−	0.998861i	$-0.515191\pi$
$521$	20.2581	−	14.7184i	0.887525	−	0.644825i	0.935232	+	0.354037i	$0.115191\pi$
$522$	8.31596	+	11.4459i	0.363980	+	0.500975i
$523$	−5.42379	+	1.76230i	−0.237166	+	0.0770598i	−0.425188	−	0.905105i	$-0.639792\pi$
$523$	−5.42379	+	1.76230i	−0.237166	+	0.0770598i	0.188023	+	0.982165i	$0.439792\pi$
$524$	5.15534			0.225212
$525$	42.0151	+	36.7887i	1.83369	+	1.60559i
$526$	−43.0894			−1.87879
$527$	−8.66933	+	2.81684i	−0.377642	+	0.122703i
$528$	−77.5725	−	106.769i	−3.37591	−	4.64654i
$529$	−16.2876	+	11.8336i	−0.708156	+	0.514505i
$530$	−6.65116	+	1.83169i	−0.288908	+	0.0795633i
$531$	29.3201	+	21.3023i	1.27238	+	0.924439i
$532$			90.4241i			3.92038i
$533$	11.4284	−	15.7299i	0.495021	−	0.681338i
$534$	12.7976	−	39.3871i	0.553808	−	1.70445i
$535$	−5.12921	−	4.09500i	−0.221755	−	0.177042i
$536$	−0.356353	−	1.09674i	−0.0153921	−	0.0473720i
$537$	72.4207	+	23.5309i	3.12519	+	1.01543i
$538$	−55.8157	−	18.1356i	−2.40639	−	0.781883i
$539$	12.2403	+	37.6716i	0.527225	+	1.62263i
$540$	−18.5241	−	67.2641i	−0.797150	−	2.89459i
$541$	8.78504	−	27.0376i	0.377698	−	1.16244i	−0.563942	−	0.825815i	$-0.690716\pi$
$541$	8.78504	−	27.0376i	0.377698	−	1.16244i	0.941640	−	0.336622i	$-0.109284\pi$
$542$	38.4249	−	52.8873i	1.65049	−	2.27170i
$543$			17.3438i			0.744293i
$544$	−8.00379	−	5.81510i	−0.343160	−	0.249320i
$545$	−24.4810	−	37.1313i	−1.04865	−	1.59053i
$546$	−59.5850	+	43.2911i	−2.55000	+	1.85269i
$547$	−0.470018	−	0.646924i	−0.0200965	−	0.0276605i	0.798851	−	0.601530i	$-0.205442\pi$
$547$	−0.470018	−	0.646924i	−0.0200965	−	0.0276605i	−0.818947	+	0.573869i	$0.805442\pi$
$548$	88.3000	−	28.6904i	3.77199	−	1.22559i
$549$	46.5852			1.98821
$550$	42.0103	−	47.9785i	1.79133	−	2.04581i
$551$	−5.00799			−0.213348
$552$	33.6908	−	10.9468i	1.43397	−	0.465927i
$553$	−13.2865	−	18.2873i	−0.564999	−	0.777654i
$554$	−38.5538	+	28.0110i	−1.63799	+	1.19007i
$555$	9.26577	+	3.48329i	0.393310	+	0.147857i
$556$	49.3806	+	35.8771i	2.09420	+	1.52153i
$557$		−	45.0494i		−	1.90880i	−0.298526	−	0.954401i	$-0.596495\pi$
$557$		−	45.0494i		−	1.90880i	0.298526	−	0.954401i	$-0.403505\pi$
$558$	73.5160	−	101.186i	3.11218	−	4.28355i
$559$	−6.80068	+	20.9303i	−0.287638	+	0.885259i
$560$	−68.0340	+	44.8554i	−2.87496	+	1.89549i
$561$	4.34762	+	13.3806i	0.183557	+	0.564929i
$562$	68.5204	+	22.2636i	2.89036	+	0.939135i
$563$	21.3329	+	6.93149i	0.899075	+	0.292127i	0.721855	−	0.692044i	$-0.243290\pi$
$563$	21.3329	+	6.93149i	0.899075	+	0.292127i	0.177220	+	0.984171i	$0.443290\pi$
$564$	28.3629	+	87.2922i	1.19430	+	3.67566i
$565$	−8.43956	+	5.56427i	−0.355055	+	0.234091i
$566$	−11.3772	+	35.0153i	−0.478218	+	1.47180i
$567$	6.67631	−	9.18915i	0.280379	−	0.385908i
$568$		−	33.9388i		−	1.42404i
$569$	10.9260	+	7.93819i	0.458041	+	0.332786i	0.792762	−	0.609531i	$-0.208642\pi$
$569$	10.9260	+	7.93819i	0.458041	+	0.332786i	−0.334721	+	0.942317i	$0.608642\pi$
$570$	76.1647	+	28.6327i	3.19019	+	1.19929i
$571$	−15.8153	+	11.4905i	−0.661849	+	0.480862i	−0.867287	−	0.497809i	$-0.834138\pi$
$571$	−15.8153	+	11.4905i	−0.661849	+	0.480862i	0.205438	+	0.978670i	$0.434138\pi$
$572$	34.8789	+	48.0067i	1.45836	+	2.00726i
$573$	11.4213	−	3.71100i	0.477130	−	0.155029i
$574$	77.8057			3.24755
$575$	4.33464	+	7.27304i	0.180767	+	0.303307i
$576$	36.9733			1.54055
$577$	−7.13499	+	2.31830i	−0.297034	+	0.0965121i	−0.453743	−	0.891133i	$-0.649911\pi$
$577$	−7.13499	+	2.31830i	−0.297034	+	0.0965121i	0.156709	+	0.987645i	$0.449911\pi$
$578$	1.53187	+	2.10844i	0.0637174	+	0.0876995i
$579$	24.0496	−	17.4731i	0.999468	−	0.726156i
$580$	−6.08183	−	9.22456i	−0.252534	−	0.383029i
$581$	−3.86316	−	2.80675i	−0.160271	−	0.116444i
$582$		−	54.4135i		−	2.25551i
$583$	−3.40530	+	4.68699i	−0.141033	+	0.194115i
$584$	14.3167	−	44.0623i	0.592430	−	1.82331i
$585$	7.90870	+	28.7179i	0.326985	+	1.18734i
$586$	−5.07959	−	15.6334i	−0.209836	−	0.645809i
$587$	−32.0506	−	10.4139i	−1.32287	−	0.429826i	−0.439390	−	0.898296i	$-0.644806\pi$
$587$	−32.0506	−	10.4139i	−1.32287	−	0.429826i	−0.883480	+	0.468470i	$0.844806\pi$
$588$	−106.049	−	34.4574i	−4.37339	−	1.42100i
$589$	13.6809	+	42.1056i	0.563713	+	1.73493i
$590$	−31.3501	−	25.0289i	−1.29066	−	1.03042i
$591$	−21.2950	+	65.5392i	−0.875959	+	2.69592i
$592$	−8.49031	+	11.6859i	−0.348950	+	0.480288i
$593$		−	5.59917i		−	0.229930i	−0.993370	−	0.114965i	$-0.963324\pi$
$593$		−	5.59917i		−	0.229930i	0.993370	−	0.114965i	$-0.0366756\pi$
$594$	−67.1826	−	48.8110i	−2.75654	−	2.00274i
$595$	8.37550	−	2.30656i	0.343362	−	0.0945596i
$596$	−67.0955	+	48.7477i	−2.74834	+	1.99678i
$597$	9.10697	+	12.5347i	0.372724	+	0.513010i
$598$	−10.6198	+	3.45059i	−0.434277	+	0.141105i
$599$	−4.01377			−0.163998			−0.0819992	−	0.996632i	$-0.526130\pi$
$599$	−4.01377			−0.163998			−0.0819992	+	0.996632i	$0.526130\pi$
$600$	23.1638	+	102.002i	0.945657	+	4.16421i
$601$	28.5064			1.16280			0.581400	−	0.813618i	$-0.302505\pi$
$601$	28.5064			1.16280			0.581400	+	0.813618i	$0.302505\pi$
$602$	−83.7567	+	27.2142i	−3.41367	+	1.10917i
$603$	−0.490406	−	0.674986i	−0.0199709	−	0.0274875i
$604$	19.8520	−	14.4233i	0.807768	−	0.586877i
$605$	1.31500	−	28.9274i	0.0534624	−	1.17606i
$606$	−56.3862	−	40.9669i	−2.29053	−	1.66417i
$607$			4.00324i			0.162486i	0.996694	+	0.0812432i	$0.0258890\pi$
$607$			4.00324i			0.162486i	−0.996694	+	0.0812432i	$0.974111\pi$
$608$	−28.2430	+	38.8732i	−1.14541	+	1.57652i
$609$	3.55883	−	10.9530i	0.144211	−	0.443836i
$610$	−51.5119	−	2.34167i	−2.08566	−	0.0948113i
$611$	−5.20914	−	16.0321i	−0.210739	−	0.648589i
$612$	−23.9948	−	7.79638i	−0.969932	−	0.315150i
$613$	0.139605	+	0.0453603i	0.00563858	+	0.00183208i	0.311835	−	0.950136i	$-0.399056\pi$
$613$	0.139605	+	0.0453603i	0.00563858	+	0.00183208i	−0.306196	+	0.951968i	$0.599056\pi$
$614$	−18.4686	−	56.8405i	−0.745332	−	2.29390i
$615$	17.3825	−	46.2385i	0.700930	−	1.86452i
$616$	−42.7540	+	131.583i	−1.72261	+	5.30165i
$617$	13.7192	−	18.8829i	0.552314	−	0.760196i	−0.438010	−	0.898970i	$-0.644316\pi$
$617$	13.7192	−	18.8829i	0.552314	−	0.760196i	0.990324	+	0.138775i	$0.0443164\pi$
$618$			37.4564i			1.50672i
$619$	−25.5224	−	18.5431i	−1.02583	−	0.745310i	−0.0583611	−	0.998296i	$-0.518587\pi$
$619$	−25.5224	−	18.5431i	−1.02583	−	0.745310i	−0.967470	+	0.252986i	$0.918587\pi$
$620$	−60.9427	+	76.3340i	−2.44752	+	3.06565i
$621$	8.91965	−	6.48050i	0.357933	−	0.260054i
$622$	−6.79152	−	9.34773i	−0.272315	−	0.374810i
$623$	−20.4237	+	6.63606i	−0.818259	+	0.265868i
$624$	−68.2332			−2.73152
$625$	−22.5479	+	10.7977i	−0.901917	+	0.431909i
$626$	23.1348			0.924651
$627$	64.9875	−	21.1157i	2.59535	−	0.843280i
$628$	19.8443	+	27.3133i	0.791873	+	1.08992i
$629$	1.24578	−	0.905115i	0.0496727	−	0.0360893i
$630$	−74.3698	+	93.1520i	−2.96296	+	3.71127i
$631$	18.3909	+	13.3617i	0.732129	+	0.531923i	0.890236	−	0.455499i	$-0.150539\pi$
$631$	18.3909	+	13.3617i	0.732129	+	0.531923i	−0.158107	+	0.987422i	$0.550539\pi$
$632$		−	42.3383i		−	1.68413i
$633$	1.77499	−	2.44307i	0.0705496	−	0.0971032i
$634$	−13.4653	+	41.4420i	−0.534776	+	1.64587i
$635$	12.0543	−	32.0653i	0.478361	−	1.27247i
$636$	−5.03978	−	15.5108i	−0.199840	−	0.615045i
$637$	19.4770	+	6.32845i	0.771706	+	0.250743i
$638$	−12.5076	−	4.06395i	−0.495179	−	0.160893i
$639$	−7.58785	−	23.3530i	−0.300171	−	0.923830i
$640$	3.31474	+	0.150684i	0.131027	+	0.00595630i
$641$	−11.9956	+	36.9187i	−0.473799	+	1.45820i	0.373773	+	0.927520i	$0.378064\pi$
$641$	−11.9956	+	36.9187i	−0.473799	+	1.45820i	−0.847571	+	0.530682i	$0.821936\pi$
$642$	12.9265	−	17.7918i	0.510167	−	0.702184i
$643$		−	32.4371i		−	1.27919i	−0.768711	−	0.639597i	$-0.779101\pi$
$643$		−	32.4371i		−	1.27919i	0.768711	−	0.639597i	$-0.220899\pi$
$644$	−25.5056	−	18.5309i	−1.00506	−	0.730219i
$645$	−2.53910	+	55.8550i	−0.0999768	+	2.19929i
$646$	10.2404	−	7.44006i	0.402902	−	0.292725i
$647$	−3.73593	−	5.14207i	−0.146875	−	0.202156i	0.729241	−	0.684257i	$-0.239874\pi$
$647$	−3.73593	−	5.14207i	−0.146875	−	0.202156i	−0.876115	+	0.482102i	$0.839874\pi$
$648$	20.2332	−	6.57418i	0.794837	−	0.258258i
$649$	−33.6884			−1.32238
$650$	−7.30156	−	32.1525i	−0.286391	−	1.26112i
$651$	−101.811			−3.99029
$652$	−28.5260	+	9.26865i	−1.11716	+	0.362988i
$653$	20.9160	+	28.7883i	0.818505	+	1.12658i	0.989955	+	0.141382i	$0.0451547\pi$
$653$	20.9160	+	28.7883i	0.818505	+	1.12658i	−0.171450	+	0.985193i	$0.554845\pi$
$654$	120.562	−	87.5935i	4.71435	−	3.42518i
$655$	−2.31920	+	0.638693i	−0.0906187	+	0.0249558i
$656$	58.3157	+	42.3688i	2.27684	+	1.65422i
$657$		−	33.5197i		−	1.30773i
$658$	39.6502	−	54.5738i	1.54573	−	2.12751i
$659$	7.85108	−	24.1632i	0.305835	−	0.941263i	−0.673530	−	0.739160i	$-0.735223\pi$
$659$	7.85108	−	24.1632i	0.305835	−	0.941263i	0.979364	−	0.202103i	$-0.0647774\pi$
$660$	117.817	+	94.0614i	4.58602	+	3.66134i
$661$	10.1074	+	31.1073i	0.393131	+	1.20993i	0.930408	+	0.366526i	$0.119453\pi$
$661$	10.1074	+	31.1073i	0.393131	+	1.20993i	−0.537277	+	0.843406i	$0.680547\pi$
$662$	23.3528	+	7.58778i	0.907632	+	0.294908i
$663$	6.91803	+	2.24780i	0.268674	+	0.0872975i
$664$	−2.76382	−	8.50615i	−0.107257	−	0.330103i
$665$	−11.2026	−	40.6785i	−0.434418	−	1.57744i
$666$	−6.52907	+	20.0944i	−0.252996	+	0.778643i
$667$	1.02630	−	1.41259i	0.0397386	−	0.0546955i
$668$			67.1975i			2.59995i
$669$	35.5458	+	25.8256i	1.37428	+	0.998474i
$670$	0.508341	+	0.771021i	0.0196389	+	0.0297871i
$671$	−35.0331	+	25.4530i	−1.35244	+	0.982604i
$672$	−64.9490	−	89.3947i	−2.50546	−	3.44847i
$673$	43.8040	−	14.2328i	1.68852	−	0.548633i	0.701985	−	0.712192i	$-0.252297\pi$
$673$	43.8040	−	14.2328i	1.68852	−	0.548633i	0.986534	+	0.163559i	$0.0522973\pi$
$674$	−18.4738			−0.711585
$675$	16.6666	+	27.9647i	0.641499	+	1.07636i
$676$	−31.6182			−1.21608
$677$	32.0286	−	10.4067i	1.23096	−	0.399963i	0.379899	−	0.925028i	$-0.375959\pi$
$677$	32.0286	−	10.4067i	1.23096	−	0.399963i	0.851062	+	0.525065i	$0.175959\pi$
$678$	−19.9091	−	27.4025i	−0.764604	−	1.05239i
$679$	−22.8268	+	16.5847i	−0.876013	+	0.636461i
$680$	15.2308	+	5.72572i	0.584074	+	0.219571i
$681$	−23.9493	−	17.4002i	−0.917741	−	0.666778i
$682$			116.262i			4.45189i
$683$	−9.81023	+	13.5026i	−0.375378	+	0.516664i	−0.954353	−	0.298682i	$-0.903453\pi$
$683$	−9.81023	+	13.5026i	−0.375378	+	0.516664i	0.578975	+	0.815346i	$0.303453\pi$
$684$	−37.8658	+	116.539i	−1.44783	+	4.45598i
$685$	−36.1685	+	23.8462i	−1.38193	+	0.911116i
$686$	3.42248	+	10.5333i	0.130671	+	0.402164i
$687$	68.3541	+	22.2096i	2.60787	+	0.847349i
$688$	−77.5954	−	25.2123i	−2.95830	−	0.961208i
$689$	0.925606	+	2.84872i	0.0352628	+	0.108528i
$690$	−23.6850	+	15.6157i	−0.901672	+	0.594480i
$691$	7.91349	−	24.3552i	0.301043	−	0.926517i	−0.680081	−	0.733137i	$-0.738055\pi$
$691$	7.91349	−	24.3552i	0.301043	−	0.926517i	0.981124	−	0.193379i	$-0.0619448\pi$
$692$	13.6393	−	18.7730i	0.518490	−	0.713641i
$693$			100.100i			3.80248i
$694$	41.0780	+	29.8449i	1.55930	+	1.13290i
$695$	−26.6593	−	10.0221i	−1.01125	−	0.380159i
$696$	17.4512	−	12.6790i	0.661485	−	0.480597i
$697$	−4.51676	−	6.21678i	−0.171084	−	0.235477i
$698$	16.2999	−	5.29617i	0.616962	−	0.200463i
$699$	3.45602			0.130719
$700$	61.3238	−	70.0358i	2.31782	−	2.64710i
$701$	34.0273			1.28519			0.642597	−	0.766205i	$-0.277857\pi$
$701$	34.0273			1.28519			0.642597	+	0.766205i	$0.277857\pi$
$702$	−40.8331	+	13.2675i	−1.54115	+	0.500749i
$703$	−4.39600	−	6.05058i	−0.165798	−	0.228202i
$704$	−27.8047	+	20.2013i	−1.04793	+	0.761366i
$705$	−23.5740	−	35.7557i	−0.887849	−	1.34664i
$706$	72.6335	+	52.7713i	2.73360	+	1.98608i
$707$			36.1406i			1.35921i
$708$	55.7431	−	76.7238i	2.09495	−	2.88346i
$709$	−0.0384822	+	0.118436i	−0.00144523	+	0.00444796i	−0.951777	−	0.306792i	$-0.900744\pi$
$709$	−0.0384822	+	0.118436i	−0.00144523	+	0.00444796i	0.950331	+	0.311240i	$0.100744\pi$
$710$	7.21644	+	26.2041i	0.270828	+	0.983424i
$711$	−9.46574	−	29.1325i	−0.354993	−	1.09256i
$712$	−38.2539	−	12.4295i	−1.43363	−	0.465814i
$713$	−14.6802	−	4.76990i	−0.549779	−	0.178634i
$714$	8.99501	+	27.6838i	0.336630	+	1.03604i
$715$	−21.6383	−	17.2753i	−0.809225	−	0.646061i
$716$	39.2241	−	120.719i	1.46587	−	4.51150i
$717$	−24.3346	+	33.4937i	−0.908791	+	1.25084i
$718$			6.73779i			0.251452i
$719$	−11.0440	−	8.02390i	−0.411870	−	0.299241i	0.362488	−	0.931988i	$-0.381927\pi$
$719$	−11.0440	−	8.02390i	−0.411870	−	0.299241i	−0.774358	+	0.632747i	$0.781927\pi$
$720$	−106.466	+	29.3200i	−3.96776	+	1.09269i
$721$	15.7132	−	11.4163i	0.585190	−	0.425166i
$722$	−7.02964	−	9.67547i	−0.261616	−	0.360084i
$723$	51.3630	−	16.6889i	1.91021	−	0.620665i
$724$	28.9107			1.07446
$725$	3.87882	+	3.39632i	0.144056	+	0.126136i
$726$	97.0267			3.60100
$727$	−32.4333	+	10.5382i	−1.20288	+	0.390841i	−0.840821	−	0.541313i	$-0.817928\pi$
$727$	−32.4333	+	10.5382i	−1.20288	+	0.390841i	−0.362063	+	0.932154i	$0.617928\pi$
$728$	42.0456	+	57.8708i	1.55831	+	2.14483i
$729$	−32.9769	+	23.9591i	−1.22137	+	0.887376i
$730$	−1.68491	+	37.0646i	−0.0623613	+	1.37182i
$731$	7.03667	+	5.11244i	0.260261	+	0.189090i
$732$		−	121.903i		−	4.50565i
$733$	23.5530	−	32.4180i	0.869951	−	1.19738i	−0.109153	−	0.994025i	$-0.534814\pi$
$733$	23.5530	−	32.4180i	0.869951	−	1.19738i	0.979104	−	0.203360i	$-0.0651860\pi$
$734$	−18.1789	+	55.9490i	−0.670996	+	2.06511i
$735$	51.9765	+	2.36279i	1.91718	+	0.0871527i
$736$	−5.17688	−	15.9328i	−0.190822	−	0.587291i
$737$	0.737592	+	0.239658i	0.0271695	+	0.00882792i
$738$	100.276	+	32.5817i	3.69122	+	1.19935i
$739$	−0.956358	−	2.94337i	−0.0351802	−	0.108273i	0.931924	−	0.362653i	$-0.118129\pi$
$739$	−0.956358	−	2.94337i	−0.0351802	−	0.108273i	−0.967105	+	0.254379i	$0.918129\pi$
$740$	5.80636	−	15.4453i	0.213446	−	0.567780i
$741$	10.9172	−	33.5998i	0.401055	−	1.23432i
$742$	−7.04539	+	9.69715i	−0.258644	+	0.355994i
$743$		−	14.8862i		−	0.546122i	−0.961997	−	0.273061i	$-0.911964\pi$
$743$		−	14.8862i		−	0.546122i	0.961997	−	0.273061i	$-0.0880360\pi$
$744$	−154.275	−	112.087i	−5.65598	−	4.10931i
$745$	24.1445	−	30.2422i	0.884585	−	1.10799i
$746$	−4.45089	+	3.23376i	−0.162959	+	0.118396i
$747$	−3.80351	−	5.23508i	−0.139163	−	0.191542i
$748$	22.3044	−	7.24712i	0.815528	−	0.264981i
$749$	−11.4036			−0.416678
$750$	−39.5735	−	73.8302i	−1.44502	−	2.69590i
$751$	−45.4277			−1.65768			−0.828841	−	0.559485i	$-0.810999\pi$
$751$	−45.4277			−1.65768			−0.828841	+	0.559485i	$0.810999\pi$
$752$	59.4360	−	19.3119i	2.16741	−	0.704233i
$753$	−12.7477	−	17.5457i	−0.464553	−	0.639402i
$754$	−5.50087	+	3.99661i	−0.200330	+	0.145548i
$755$	−7.14381	+	8.94799i	−0.259990	+	0.325651i
$756$	−98.0686	−	71.2510i	−3.56672	−	2.59137i
$757$		−	48.6400i		−	1.76785i	−0.467626	−	0.883926i	$-0.654891\pi$
$757$		−	48.6400i		−	1.76785i	0.467626	−	0.883926i	$-0.345109\pi$
$758$	42.9988	−	59.1828i	1.56179	−	2.14962i
$759$	−7.36205	+	22.6581i	−0.267226	+	0.822436i
$760$	27.8089	−	73.9735i	1.00874	−	2.68330i
$761$	−2.30645	−	7.09852i	−0.0836087	−	0.257321i	0.900509	−	0.434837i	$-0.143194\pi$
$761$	−2.30645	−	7.09852i	−0.0836087	−	0.257321i	−0.984118	+	0.177516i	$0.943194\pi$
$762$	109.164	+	35.4696i	3.95460	+	1.28493i
$763$	−73.4920	−	23.8790i	−2.66059	−	0.864478i
$764$	−6.18593	−	19.0383i	−0.223799	−	0.688782i
$765$	11.7603	+	0.534607i	0.425193	+	0.0193287i
$766$	−7.14552	+	21.9917i	−0.258178	+	0.794591i
$767$	−10.2378	+	14.0911i	−0.369665	+	0.508800i
$768$			51.4970i			1.85824i
$769$	−1.65094	−	1.19948i	−0.0595344	−	0.0432543i	0.557620	−	0.830096i	$-0.311715\pi$
$769$	−1.65094	−	1.19948i	−0.0595344	−	0.0432543i	−0.617154	+	0.786842i	$0.711715\pi$
$770$	5.03165	−	110.686i	0.181328	−	3.98885i
$771$	−10.9413	+	7.94931i	−0.394041	+	0.286288i
$772$	−29.1262

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.47862 + 0.805352i) q^{2} +(1.68980 + 2.32581i) q^{3} +(3.87693 - 2.81675i) q^{4} +(-1.39512 + 1.74746i) q^{5} +(-6.06145 - 4.40390i) q^{6} +3.88508i q^{7} +(-4.27721 + 5.88707i) q^{8} +(-1.62691 + 5.00711i) q^{9} +(2.05065 - 5.45486i) q^{10} +(-1.51229 - 4.65436i) q^{11} +(13.1024 + 4.25724i) q^{12} +(-2.40639 - 0.781885i) q^{13} +(-3.12886 - 9.62963i) q^{14} +(-6.42174 - 0.291924i) q^{15} +(2.89869 - 8.92126i) q^{16} +(-0.587785 + 0.809017i) q^{17} -13.7209i q^{18} +(3.92927 + 2.85478i) q^{19} +(-0.486613 + 10.7045i) q^{20} +(-9.03594 + 6.56499i) q^{21} +(7.49679 + 10.3185i) q^{22} +(-1.61047 + 0.523275i) q^{23} -20.9198 q^{24} +(-1.10727 - 4.87586i) q^{25} +6.59423 q^{26} +(-6.19226 + 2.01199i) q^{27} +(10.9433 + 15.0622i) q^{28} +(-0.834194 + 0.606078i) q^{29} +(16.1521 - 4.44819i) q^{30} +(7.37458 + 5.35794i) q^{31} +9.89323i q^{32} +(8.26966 - 11.3822i) q^{33} +(0.805352 - 2.47862i) q^{34} +(-6.78904 - 5.42016i) q^{35} +(7.79638 + 23.9948i) q^{36} +(-1.46451 - 0.475847i) q^{37} +(-12.0383 - 3.91147i) q^{38} +(-2.24780 - 6.91803i) q^{39} +(-4.32022 - 15.6874i) q^{40} +(-2.37460 + 7.30826i) q^{41} +(17.1095 - 23.5492i) q^{42} -8.69780i q^{43} +(-18.9732 - 13.7849i) q^{44} +(-6.48001 - 9.82849i) q^{45} +(3.57033 - 2.59400i) q^{46} +(3.91599 + 5.38990i) q^{47} +(25.6473 - 8.33332i) q^{48} -8.09384 q^{49} +(6.67127 + 11.1936i) q^{50} -2.87485 q^{51} +(-11.5318 + 3.74691i) q^{52} +(-0.695828 - 0.957725i) q^{53} +(13.7279 - 9.97389i) q^{54} +(10.2432 + 3.85072i) q^{55} +(-22.8717 - 16.6173i) q^{56} +13.9627i q^{57} +(1.57954 - 2.17406i) q^{58} +(2.12720 - 6.54686i) q^{59} +(-25.7189 + 16.9567i) q^{60} +(-2.73432 - 8.41538i) q^{61} +(-22.5938 - 7.34117i) q^{62} +(-19.4530 - 6.32067i) q^{63} +(-2.17015 - 6.67904i) q^{64} +(4.72353 - 3.11426i) q^{65} +(-11.3307 + 34.8722i) q^{66} +(-0.0931483 + 0.128208i) q^{67} +4.79215i q^{68} +(-3.93841 - 2.86142i) q^{69} +(21.1926 + 7.96695i) q^{70} +(-3.77323 + 2.74141i) q^{71} +(-22.5186 - 30.9941i) q^{72} +(-6.05516 + 1.96744i) q^{73} +4.01318 q^{74} +(9.46924 - 10.8145i) q^{75} +23.2747 q^{76} +(18.0825 - 5.87538i) q^{77} +(11.1429 + 15.3369i) q^{78} +(-4.70705 + 3.41987i) q^{79} +(11.5456 + 17.5116i) q^{80} +(-2.36524 - 1.71845i) q^{81} -20.0268i q^{82} +(-0.722444 + 0.994359i) q^{83} +(-16.5397 + 50.9040i) q^{84} +(-0.593696 - 2.15581i) q^{85} +(7.00480 + 21.5585i) q^{86} +(-2.81924 - 0.916026i) q^{87} +(33.8689 + 11.0047i) q^{88} +(1.70809 + 5.25696i) q^{89} +(23.9769 + 19.1424i) q^{90} +(3.03769 - 9.34903i) q^{91} +(-4.76976 + 6.56501i) q^{92} +26.2057i q^{93} +(-14.0470 - 10.2058i) q^{94} +(-10.4704 + 2.88349i) q^{95} +(-23.0097 + 16.7176i) q^{96} +(4.26881 + 5.87551i) q^{97} +(20.0616 - 6.51839i) q^{98} +25.7652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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