LMFDB - Embedded newform 430.2.l.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(7,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("430.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.l (of order $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.3
Character	$\chi$	$=$	430.7
Dual form			430.2.l.a.123.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.424244 + 1.58330i) q^{3} -1.00000i q^{4} +(-1.40555 - 1.73909i) q^{5} +(-0.819577 - 1.41955i) q^{6} +(-0.632122 - 2.35911i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.271217 + 0.156587i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.424244 + 1.58330i) q^{3} -1.00000i q^{4} +(-1.40555 - 1.73909i) q^{5} +(-0.819577 - 1.41955i) q^{6} +(-0.632122 - 2.35911i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.271217 + 0.156587i) q^{9} +(2.22359 + 0.235851i) q^{10} +2.56071 q^{11} +(1.58330 + 0.424244i) q^{12} +(1.52730 + 5.69996i) q^{13} +(2.11512 + 1.22117i) q^{14} +(3.34980 - 1.48761i) q^{15} -1.00000 q^{16} +(0.305477 - 0.0818523i) q^{17} +(-0.302504 + 0.0810556i) q^{18} +(2.27687 + 3.94365i) q^{19} +(-1.73909 + 1.40555i) q^{20} +4.00336 q^{21} +(-1.81069 + 1.81069i) q^{22} +(5.71081 + 1.53021i) q^{23} +(-1.41955 + 0.819577i) q^{24} +(-1.04887 + 4.88875i) q^{25} +(-5.11045 - 2.95052i) q^{26} +(-3.84016 + 3.84016i) q^{27} +(-2.35911 + 0.632122i) q^{28} +(4.05854 - 7.02960i) q^{29} +(-1.31677 + 3.42056i) q^{30} +(-2.15995 - 3.74115i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.08637 + 4.05437i) q^{33} +(-0.158127 + 0.273883i) q^{34} +(-3.21423 + 4.41516i) q^{35} +(0.156587 - 0.271217i) q^{36} +(-4.28202 - 1.14736i) q^{37} +(-4.39857 - 1.17859i) q^{38} -9.67271 q^{39} +(0.235851 - 2.22359i) q^{40} +7.94375 q^{41} +(-2.83080 + 2.83080i) q^{42} +(-6.40203 + 1.41917i) q^{43} -2.56071i q^{44} +(-0.108889 - 0.691762i) q^{45} +(-5.12017 + 2.95613i) q^{46} +(6.44990 + 6.44990i) q^{47} +(0.424244 - 1.58330i) q^{48} +(0.896352 - 0.517509i) q^{49} +(-2.71520 - 4.19853i) q^{50} +0.518387i q^{51} +(5.69996 - 1.52730i) q^{52} +(8.28511 + 2.21999i) q^{53} -5.43080i q^{54} +(-3.59920 - 4.45330i) q^{55} +(1.22117 - 2.11512i) q^{56} +(-7.20993 + 1.93189i) q^{57} +(2.10086 + 7.84051i) q^{58} +1.85857i q^{59} +(-1.48761 - 3.34980i) q^{60} +(10.5244 + 6.07625i) q^{61} +(4.17271 + 1.11807i) q^{62} +(0.197965 - 0.738814i) q^{63} +1.00000i q^{64} +(7.76606 - 10.6677i) q^{65} +(-2.09870 - 3.63505i) q^{66} +(-2.17701 + 8.12473i) q^{67} +(-0.0818523 - 0.305477i) q^{68} +(-4.84556 + 8.39275i) q^{69} +(-0.849185 - 5.39479i) q^{70} +(-3.44277 - 1.98769i) q^{71} +(0.0810556 + 0.302504i) q^{72} +(10.4489 - 2.79978i) q^{73} +(3.83915 - 2.21654i) q^{74} +(-7.29538 - 3.73471i) q^{75} +(3.94365 - 2.27687i) q^{76} +(-1.61868 - 6.04099i) q^{77} +(6.83964 - 6.83964i) q^{78} +(-8.79950 - 5.08040i) q^{79} +(1.40555 + 1.73909i) q^{80} +(-3.98120 - 6.89564i) q^{81} +(-5.61708 + 5.61708i) q^{82} +(-7.81815 - 2.09487i) q^{83} -4.00336i q^{84} +(-0.571711 - 0.416205i) q^{85} +(3.52342 - 5.53042i) q^{86} +(9.40817 + 9.40817i) q^{87} +(1.81069 + 1.81069i) q^{88} +(-1.48260 - 2.56794i) q^{89} +(0.566146 + 0.412154i) q^{90} +(12.4814 - 7.20614i) q^{91} +(1.53021 - 5.71081i) q^{92} +(6.83971 - 1.83270i) q^{93} -9.12154 q^{94} +(3.65812 - 9.50266i) q^{95} +(0.819577 + 1.41955i) q^{96} +(1.07926 + 1.07926i) q^{97} +(-0.267882 + 0.999751i) q^{98} +(0.694508 + 0.400974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) $ 88 * q + 4 * q^6 + 12 * q^7	$ 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) $ 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.424244	+	1.58330i	−0.244938	+	0.914119i	0.728477	+	0.685070i	$0.240228\pi$
$3$	−0.424244	+	1.58330i	−0.244938	+	0.914119i	−0.973415	+	0.229049i	$0.926438\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−1.40555	−	1.73909i	−0.628580	−	0.777745i
$5$	−1.40555	−	1.73909i	−0.628580	−	0.777745i
$6$	−0.819577	−	1.41955i	−0.334591	−	0.579528i
$7$	−0.632122	−	2.35911i	−0.238920	−	0.891660i	−0.976343	−	0.216229i	$-0.930624\pi$
$7$	−0.632122	−	2.35911i	−0.238920	−	0.891660i	0.737423	−	0.675431i	$-0.236042\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.271217	+	0.156587i	0.0904057	+	0.0521958i
$10$	2.22359	+	0.235851i	0.703162	+	0.0745826i
$11$	2.56071			0.772082			0.386041	−	0.922482i	$-0.373842\pi$
$11$	2.56071			0.772082			0.386041	+	0.922482i	$0.373842\pi$
$12$	1.58330	+	0.424244i	0.457060	+	0.122469i
$13$	1.52730	+	5.69996i	0.423597	+	1.58089i	0.766968	+	0.641686i	$0.221765\pi$
$13$	1.52730	+	5.69996i	0.423597	+	1.58089i	−0.343371	+	0.939200i	$0.611569\pi$
$14$	2.11512	+	1.22117i	0.565290	+	0.326370i
$15$	3.34980	−	1.48761i	0.864915	−	0.384098i
$16$	−1.00000			−0.250000
$17$	0.305477	−	0.0818523i	0.0740891	−	0.0198521i	−0.221584	−	0.975141i	$-0.571123\pi$
$17$	0.305477	−	0.0818523i	0.0740891	−	0.0198521i	0.295673	+	0.955289i	$0.404456\pi$
$18$	−0.302504	+	0.0810556i	−0.0713008	+	0.0191050i
$19$	2.27687	+	3.94365i	0.522349	+	0.904735i	0.999662	+	0.0260015i	$0.00827747\pi$
$19$	2.27687	+	3.94365i	0.522349	+	0.904735i	−0.477313	+	0.878733i	$0.658389\pi$
$20$	−1.73909	+	1.40555i	−0.388873	+	0.314290i
$21$	4.00336			0.873604
$22$	−1.81069	+	1.81069i	−0.386041	+	0.386041i
$23$	5.71081	+	1.53021i	1.19079	+	0.319070i	0.799197	−	0.601070i	$-0.205259\pi$
$23$	5.71081	+	1.53021i	1.19079	+	0.319070i	0.391590	+	0.920140i	$0.371925\pi$
$24$	−1.41955	+	0.819577i	−0.289764	+	0.167295i
$25$	−1.04887	+	4.88875i	−0.209775	+	0.977750i
$26$	−5.11045	−	2.95052i	−1.00224	−	0.578644i
$27$	−3.84016	+	3.84016i	−0.739039	+	0.739039i
$28$	−2.35911	+	0.632122i	−0.445830	+	0.119460i
$29$	4.05854	−	7.02960i	0.753653	−	1.30536i	−0.192389	−	0.981319i	$-0.561623\pi$
$29$	4.05854	−	7.02960i	0.753653	−	1.30536i	0.946041	−	0.324046i	$-0.105043\pi$
$30$	−1.31677	+	3.42056i	−0.240408	+	0.624506i
$31$	−2.15995	−	3.74115i	−0.387939	−	0.671930i	0.604233	−	0.796808i	$-0.293480\pi$
$31$	−2.15995	−	3.74115i	−0.387939	−	0.671930i	−0.992172	+	0.124878i	$0.960146\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−1.08637	+	4.05437i	−0.189112	+	0.705775i
$34$	−0.158127	+	0.273883i	−0.0271185	+	0.0469706i
$35$	−3.21423	+	4.41516i	−0.543304	+	0.746298i
$36$	0.156587	−	0.271217i	0.0260979	−	0.0452029i
$37$	−4.28202	−	1.14736i	−0.703959	−	0.188625i	−0.110956	−	0.993825i	$-0.535391\pi$
$37$	−4.28202	−	1.14736i	−0.703959	−	0.188625i	−0.593003	+	0.805200i	$0.702058\pi$
$38$	−4.39857	−	1.17859i	−0.713542	−	0.191193i
$39$	−9.67271			−1.54887
$40$	0.235851	−	2.22359i	0.0372913	−	0.351581i
$41$	7.94375			1.24060			0.620302	−	0.784363i	$-0.287010\pi$
$41$	7.94375			1.24060			0.620302	+	0.784363i	$0.287010\pi$
$42$	−2.83080	+	2.83080i	−0.436802	+	0.436802i
$43$	−6.40203	+	1.41917i	−0.976300	+	0.216421i
$43$	−6.40203	+	1.41917i	−0.976300	+	0.216421i
$44$		−	2.56071i		−	0.386041i
$45$	−0.108889	−	0.691762i	−0.0162322	−	0.103122i
$46$	−5.12017	+	2.95613i	−0.754928	+	0.435858i
$47$	6.44990	+	6.44990i	0.940815	+	0.940815i	0.998344	−	0.0575287i	$-0.0183221\pi$
$47$	6.44990	+	6.44990i	0.940815	+	0.940815i	−0.0575287	+	0.998344i	$0.518322\pi$
$48$	0.424244	−	1.58330i	0.0612344	−	0.228530i
$49$	0.896352	−	0.517509i	0.128050	−	0.0739299i
$50$	−2.71520	−	4.19853i	−0.383988	−	0.593762i
$51$			0.518387i			0.0725888i
$52$	5.69996	−	1.52730i	0.790443	−	0.211799i
$53$	8.28511	+	2.21999i	1.13805	+	0.304939i	0.778166	−	0.628059i	$-0.216150\pi$
$53$	8.28511	+	2.21999i	1.13805	+	0.304939i	0.359882	+	0.932998i	$0.382817\pi$
$54$		−	5.43080i		−	0.739039i
$55$	−3.59920	−	4.45330i	−0.485315	−	0.600483i
$56$	1.22117	−	2.11512i	0.163185	−	0.282645i
$57$	−7.20993	+	1.93189i	−0.954978	+	0.255886i
$58$	2.10086	+	7.84051i	0.275856	+	1.02951i
$59$			1.85857i			0.241965i	0.992655	+	0.120982i	$0.0386045\pi$
$59$			1.85857i			0.241965i	−0.992655	+	0.120982i	$0.961396\pi$
$60$	−1.48761	−	3.34980i	−0.192049	−	0.432457i
$61$	10.5244	+	6.07625i	1.34751	+	0.777984i	0.987896	−	0.155118i	$-0.0495758\pi$
$61$	10.5244	+	6.07625i	1.34751	+	0.777984i	0.359612	+	0.933102i	$0.382909\pi$
$62$	4.17271	+	1.11807i	0.529935	+	0.141996i
$63$	0.197965	−	0.738814i	0.0249412	−	0.0930818i
$64$			1.00000i			0.125000i
$65$	7.76606	−	10.6677i	0.963261	−	1.32316i
$66$	−2.09870	−	3.63505i	−0.258332	−	0.447444i
$67$	−2.17701	+	8.12473i	−0.265965	+	0.992594i	0.695693	+	0.718340i	$0.255098\pi$
$67$	−2.17701	+	8.12473i	−0.265965	+	0.992594i	−0.961657	+	0.274254i	$0.911569\pi$
$68$	−0.0818523	−	0.305477i	−0.00992605	−	0.0370445i
$69$	−4.84556	+	8.39275i	−0.583337	+	1.01037i
$70$	−0.849185	−	5.39479i	−0.101497	−	0.644801i
$71$	−3.44277	−	1.98769i	−0.408582	−	0.235895i	0.281598	−	0.959532i	$-0.409135\pi$
$71$	−3.44277	−	1.98769i	−0.408582	−	0.235895i	−0.690180	+	0.723637i	$0.742469\pi$
$72$	0.0810556	+	0.302504i	0.00955249	+	0.0356504i
$73$	10.4489	−	2.79978i	1.22295	−	0.327689i	0.411121	−	0.911581i	$-0.365137\pi$
$73$	10.4489	−	2.79978i	1.22295	−	0.327689i	0.811832	+	0.583891i	$0.198471\pi$
$74$	3.83915	−	2.21654i	0.446292	−	0.257667i
$75$	−7.29538	−	3.73471i	−0.842398	−	0.431247i
$76$	3.94365	−	2.27687i	0.452367	−	0.261174i
$77$	−1.61868	−	6.04099i	−0.184466	−	0.688435i
$78$	6.83964	−	6.83964i	0.774436	−	0.774436i
$79$	−8.79950	−	5.08040i	−0.990021	−	0.571589i	−0.0847407	−	0.996403i	$-0.527006\pi$
$79$	−8.79950	−	5.08040i	−0.990021	−	0.571589i	−0.905281	+	0.424814i	$0.860340\pi$
$80$	1.40555	+	1.73909i	0.157145	+	0.194436i
$81$	−3.98120	−	6.89564i	−0.442355	−	0.766182i
$82$	−5.61708	+	5.61708i	−0.620302	+	0.620302i
$83$	−7.81815	−	2.09487i	−0.858154	−	0.229942i	−0.197196	−	0.980364i	$-0.563183\pi$
$83$	−7.81815	−	2.09487i	−0.858154	−	0.229942i	−0.660958	+	0.750423i	$0.729850\pi$
$84$		−	4.00336i		−	0.436802i
$85$	−0.571711	−	0.416205i	−0.0620108	−	0.0451438i
$86$	3.52342	−	5.53042i	0.379940	−	0.596360i
$87$	9.40817	+	9.40817i	1.00866	+	1.00866i
$88$	1.81069	+	1.81069i	0.193021	+	0.193021i
$89$	−1.48260	−	2.56794i	−0.157156	−	0.272201i	0.776686	−	0.629888i	$-0.216899\pi$
$89$	−1.48260	−	2.56794i	−0.157156	−	0.272201i	−0.933842	+	0.357686i	$0.883566\pi$
$90$	0.566146	+	0.412154i	0.0596770	+	0.0434448i
$91$	12.4814	−	7.20614i	1.30841	−	0.755409i
$92$	1.53021	−	5.71081i	0.159535	−	0.595393i
$93$	6.83971	−	1.83270i	0.709245	−	0.190042i
$94$	−9.12154			−0.940815
$95$	3.65812	−	9.50266i	0.375315	−	0.974952i
$96$	0.819577	+	1.41955i	0.0836477	+	0.144882i
$97$	1.07926	+	1.07926i	0.109582	+	0.109582i	0.759772	−	0.650190i	$-0.225311\pi$
$97$	1.07926	+	1.07926i	0.109582	+	0.109582i	−0.650190	+	0.759772i	$0.725311\pi$
$98$	−0.267882	+	0.999751i	−0.0270602	+	0.100990i
$99$	0.694508	+	0.400974i	0.0698007	+	0.0402994i
$100$	4.88875	+	1.04887i	0.488875	+	0.104887i
$101$	−0.0604423	+	0.104689i	−0.00601424	+	0.0104170i	−0.869017	−	0.494782i	$-0.835248\pi$
$101$	−0.0604423	+	0.104689i	−0.00601424	+	0.0104170i	0.863003	+	0.505199i	$0.168581\pi$
$102$	−0.366555	−	0.366555i	−0.0362944	−	0.0362944i
$103$	1.84148	+	6.87248i	0.181446	+	0.677166i	0.995363	+	0.0961852i	$0.0306641\pi$
$103$	1.84148	+	6.87248i	0.181446	+	0.677166i	−0.813917	+	0.580981i	$0.802669\pi$
$104$	−2.95052	+	5.11045i	−0.289322	+	0.501121i
$105$	−5.62691	−	6.96220i	−0.549130	−	0.679441i
$106$	−7.42823	+	4.28869i	−0.721494	+	0.416554i
$107$	−7.38809	−	7.38809i	−0.714233	−	0.714233i	0.253185	−	0.967418i	$-0.418522\pi$
$107$	−7.38809	−	7.38809i	−0.714233	−	0.714233i	−0.967418	+	0.253185i	$0.918522\pi$
$108$	3.84016	+	3.84016i	0.369519	+	0.369519i
$109$	−0.0302156	+	0.0174450i	−0.00289413	+	0.00167093i	−0.501446	−	0.865189i	$-0.667199\pi$
$109$	−0.0302156	+	0.0174450i	−0.00289413	+	0.00167093i	0.498552	+	0.866860i	$0.333865\pi$
$110$	5.69398	+	0.603945i	0.542899	+	0.0575839i
$111$	3.63324	−	6.29296i	0.344852	−	0.597301i
$112$	0.632122	+	2.35911i	0.0597299	+	0.222915i
$113$	−12.0717	−	12.0717i	−1.13561	−	1.13561i	−0.989228	−	0.146380i	$-0.953238\pi$
$113$	−12.0717	−	12.0717i	−1.13561	−	1.13561i	−0.146380	−	0.989228i	$-0.546762\pi$
$114$	3.73213	−	6.46425i	0.349546	−	0.605432i
$115$	−5.36565	−	12.0824i	−0.500349	−	1.12669i
$116$	−7.02960	−	4.05854i	−0.652682	−	0.376826i
$117$	−0.478312	+	1.78508i	−0.0442200	+	0.165031i
$118$	−1.31421	−	1.31421i	−0.120982	−	0.120982i
$119$	−0.386197	−	0.668914i	−0.0354027	−	0.0613192i
$120$	3.42056	+	1.31677i	0.312253	+	0.120204i
$121$	−4.44278			−0.403889
$122$	−11.7384	+	3.14530i	−1.06275	+	0.284762i
$123$	−3.37009	+	12.5773i	−0.303871	+	1.13406i
$124$	−3.74115	+	2.15995i	−0.335965	+	0.193969i
$125$	9.97622	−	5.04728i	0.892300	−	0.451443i
$126$	0.382438	+	0.662402i	0.0340703	+	0.0590115i
$127$	−12.3430	−	12.3430i	−1.09527	−	1.09527i	−0.994956	−	0.100311i	$-0.968016\pi$
$127$	−12.3430	−	12.3430i	−1.09527	−	1.09527i	−0.100311	−	0.994956i	$-0.531984\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	0.469057	−	10.7384i	0.0412982	−	0.945464i
$130$	2.05176	+	13.0346i	0.179951	+	1.14321i
$131$			14.8684i			1.29906i	0.760336	+	0.649530i	$0.225034\pi$
$131$			14.8684i			1.29906i	−0.760336	+	0.649530i	$0.774966\pi$
$132$	4.05437	+	1.08637i	0.352888	+	0.0945560i
$133$	7.86425	−	7.86425i	0.681917	−	0.681917i
$134$	−4.20567	−	7.28443i	−0.363315	−	0.629279i
$135$	12.0759	+	1.28086i	1.03933	+	0.110239i
$136$	0.273883	+	0.158127i	0.0234853	+	0.0135592i
$137$	8.02710	−	8.02710i	0.685802	−	0.685802i	−0.275500	−	0.961301i	$-0.588843\pi$
$137$	8.02710	−	8.02710i	0.685802	−	0.685802i	0.961301	+	0.275500i	$0.0888433\pi$
$138$	−2.50825	−	9.36090i	−0.213516	−	0.796853i
$139$	−12.3069	+	7.10540i	−1.04386	+	0.602672i	−0.920924	−	0.389743i	$-0.872564\pi$
$139$	−12.3069	+	7.10540i	−1.04386	+	0.602672i	−0.122935	+	0.992415i	$0.539231\pi$
$140$	4.41516	+	3.21423i	0.373149	+	0.271652i
$141$	−12.9485	+	7.47580i	−1.09046	+	0.629576i
$142$	3.83991	−	1.02890i	0.322238	−	0.0863435i
$143$	3.91097	+	14.5959i	0.327052	+	1.22057i
$144$	−0.271217	−	0.156587i	−0.0226014	−	0.0130489i
$145$	−17.9296	+	2.82227i	−1.48897	+	0.234376i
$146$	−5.40876	+	9.36824i	−0.447632	+	0.775321i
$147$	0.439101	+	1.63875i	0.0362164	+	0.135161i
$148$	−1.14736	+	4.28202i	−0.0943127	+	0.351980i
$149$	−3.40135	−	5.89132i	−0.278650	−	0.482636i	0.692400	−	0.721514i	$-0.256554\pi$
$149$	−3.40135	−	5.89132i	−0.278650	−	0.482636i	−0.971049	+	0.238879i	$0.923220\pi$
$150$	7.79945	−	2.51778i	0.636822	−	0.205576i
$151$			6.02307i			0.490151i	0.969504	+	0.245075i	$0.0788127\pi$
$151$			6.02307i			0.490151i	−0.969504	+	0.245075i	$0.921187\pi$
$152$	−1.17859	+	4.39857i	−0.0955965	+	0.356771i
$153$	0.0956677	+	0.0256341i	0.00773427	+	0.00207239i
$154$	5.41621	+	3.12705i	0.436450	+	0.251985i
$155$	−3.47028	+	9.01471i	−0.278740	+	0.724079i
$156$			9.67271i			0.774436i
$157$	−0.978483	−	3.65175i	−0.0780914	−	0.291441i	0.915825	−	0.401577i	$-0.131538\pi$
$157$	−0.978483	−	3.65175i	−0.0780914	−	0.291441i	−0.993916	+	0.110136i	$0.964871\pi$
$158$	9.81457	−	2.62981i	0.780805	−	0.209216i
$159$	−7.02982	+	12.1760i	−0.557501	+	0.965621i
$160$	−2.22359	−	0.235851i	−0.175791	−	0.0186456i
$161$		−	14.4397i		−	1.13801i
$162$	7.69109	+	2.06082i	0.604269	+	0.161913i
$163$	20.6017	−	5.52022i	1.61365	−	0.432377i	0.664524	−	0.747267i	$-0.268634\pi$
$163$	20.6017	−	5.52022i	1.61365	−	0.432377i	0.949128	+	0.314890i	$0.101968\pi$
$164$		−	7.94375i		−	0.620302i
$165$	8.57786	−	3.80932i	0.667785	−	0.296555i
$166$	7.00957	−	4.04697i	0.544048	−	0.314106i
$167$	6.27317	−	23.4118i	0.485433	−	1.81166i	−0.0926718	−	0.995697i	$-0.529541\pi$
$167$	6.27317	−	23.4118i	0.485433	−	1.81166i	0.578104	−	0.815963i	$-0.303793\pi$
$168$	2.83080	+	2.83080i	0.218401	+	0.218401i
$169$	−18.8986	+	10.9111i	−1.45374	+	0.839317i
$170$	0.698562	−	0.109959i	0.0535773	−	0.00843350i
$171$			1.42611i			0.109058i
$172$	1.41917	+	6.40203i	0.108210	+	0.488150i
$173$	3.08833	−	3.08833i	0.234801	−	0.234801i	−0.579892	−	0.814693i	$-0.696905\pi$
$173$	3.08833	−	3.08833i	0.234801	−	0.234801i	0.814693	+	0.579892i	$0.196905\pi$
$174$	−13.3052			−1.00866
$175$	12.1961	−	0.615876i	0.921940	−	0.0465558i
$176$	−2.56071			−0.193021
$177$	−2.94267	−	0.788487i	−0.221185	−	0.0592663i
$178$	2.86417	+	0.767452i	0.214679	+	0.0575229i
$179$	0.520316	−	0.901214i	0.0388902	−	0.0673599i	−0.845925	−	0.533302i	$-0.820951\pi$
$179$	0.520316	−	0.901214i	0.0388902	−	0.0673599i	0.884815	+	0.465942i	$0.154284\pi$
$180$	−0.691762	+	0.108889i	−0.0515609	+	0.00811611i
$181$	5.20823	−	9.02092i	0.387125	−	0.670520i	−0.604937	−	0.796273i	$-0.706802\pi$
$181$	5.20823	−	9.02092i	0.387125	−	0.670520i	0.992061	+	0.125754i	$0.0401350\pi$
$182$	−3.73017	+	13.9212i	−0.276499	+	1.03191i
$183$	−14.0854	+	14.0854i	−1.04123	+	1.04123i
$184$	2.95613	+	5.12017i	0.217929	+	0.377464i
$185$	4.02321	+	9.05949i	0.295792	+	0.666067i
$186$	−3.54050	+	6.13232i	−0.259602	+	0.449643i
$187$	0.782237	−	0.209600i	0.0572029	−	0.0153275i
$188$	6.44990	−	6.44990i	0.470408	−	0.470408i
$189$	11.4868	+	6.63191i	0.835542	+	0.482400i
$190$	4.13272	+	9.30608i	0.299819	+	0.675134i
$191$	−12.2587	+	7.07758i	−0.887011	+	0.512116i	−0.872964	−	0.487785i	$-0.837805\pi$
$191$	−12.2587	+	7.07758i	−0.887011	+	0.512116i	−0.0140472	+	0.999901i	$0.504471\pi$
$192$	−1.58330	−	0.424244i	−0.114265	−	0.0306172i
$193$	−17.7179	+	17.7179i	−1.27536	+	1.27536i	−0.332129	+	0.943234i	$0.607767\pi$
$193$	−17.7179	+	17.7179i	−1.27536	+	1.27536i	−0.943234	+	0.332129i	$0.892233\pi$
$194$	−1.52630			−0.109582
$195$	13.5954	+	16.8217i	0.973590	+	1.20463i
$196$	−0.517509	−	0.896352i	−0.0369649	−	0.0640252i
$197$	8.33880	−	2.23438i	0.594115	−	0.159193i	0.0507818	−	0.998710i	$-0.483829\pi$
$197$	8.33880	−	2.23438i	0.594115	−	0.159193i	0.543333	+	0.839517i	$0.317162\pi$
$198$	−0.774623	+	0.207560i	−0.0550501	+	0.0147506i
$199$	12.2232			0.866476			0.433238	−	0.901279i	$-0.357371\pi$
$199$	12.2232			0.866476			0.433238	+	0.901279i	$0.357371\pi$
$200$	−4.19853	+	2.71520i	−0.296881	+	0.191994i
$201$	−11.9403	−	6.89374i	−0.842204	−	0.486247i
$202$	−0.0312873	−	0.116766i	−0.00220136	−	0.00821560i
$203$	−19.1491	−	5.13099i	−1.34400	−	0.360125i
$204$	0.518387			0.0362944
$205$	−11.1653	−	13.8149i	−0.779819	−	0.964874i
$206$	−6.16170	−	3.55746i	−0.429306	−	0.247860i
$207$	1.30926	+	1.30926i	0.0909998	+	0.0909998i
$208$	−1.52730	−	5.69996i	−0.105899	−	0.395221i
$209$	5.83039	+	10.0985i	0.403296	+	0.698530i
$210$	8.90184	+	0.944195i	0.614286	+	0.0651557i
$211$			16.1919i			1.11470i	0.830279	+	0.557348i	$0.188181\pi$
$211$			16.1919i			1.11470i	−0.830279	+	0.557348i	$0.811819\pi$
$212$	2.21999	−	8.28511i	0.152470	−	0.569024i
$213$	4.60768	−	4.60768i	0.315713	−	0.315713i
$214$	10.4483			0.714233
$215$	11.4664	+	9.13900i	0.782003	+	0.623275i
$216$	−5.43080			−0.369519
$217$	−7.46043	+	7.46043i	−0.506447	+	0.506447i
$218$	0.00903020	−	0.0337012i	0.000611602	−	0.00228253i
$219$			17.7316i			1.19819i
$220$	−4.45330	+	3.59920i	−0.300242	+	0.242658i
$221$	0.933111	+	1.61620i	0.0627678	+	0.108717i
$222$	1.88070	+	7.01889i	0.126225	+	0.471077i
$223$	−18.3900	−	18.3900i	−1.23149	−	1.23149i	−0.963393	−	0.268092i	$-0.913607\pi$
$223$	−18.3900	−	18.3900i	−1.23149	−	1.23149i	−0.268092	−	0.963393i	$-0.586393\pi$
$224$	−2.11512	−	1.22117i	−0.141322	−	0.0815926i
$225$	−1.04999	+	1.16167i	−0.0699993	+	0.0774448i
$226$	17.0719			1.13561
$227$	3.12983	+	0.838636i	0.207734	+	0.0556622i	0.361185	−	0.932494i	$-0.382372\pi$
$227$	3.12983	+	0.838636i	0.207734	+	0.0556622i	−0.153451	+	0.988156i	$0.549039\pi$
$228$	1.93189	+	7.20993i	0.127943	+	0.477489i
$229$	17.4471	+	10.0731i	1.15293	+	0.665647i	0.949601	−	0.313462i	$-0.101489\pi$
$229$	17.4471	+	10.0731i	1.15293	+	0.665647i	0.203334	+	0.979109i	$0.434822\pi$
$230$	12.3376	+	4.74946i	0.813519	+	0.313170i
$231$	10.2514			0.674494
$232$	7.84051	−	2.10086i	0.514754	−	0.137928i
$233$	2.48965	−	0.667099i	0.163102	−	0.0437031i	−0.176344	−	0.984329i	$-0.556427\pi$
$233$	2.48965	−	0.667099i	0.163102	−	0.0437031i	0.339446	+	0.940626i	$0.389760\pi$
$234$	−0.924028	−	1.60046i	−0.0604056	−	0.104626i
$235$	2.15132	−	20.2826i	0.140337	−	1.32309i
$236$	1.85857			0.120982
$237$	11.7769	−	11.7769i	0.764994	−	0.764994i
$238$	0.746076	+	0.199910i	0.0483609	+	0.0129583i
$239$	4.65862	−	2.68965i	0.301341	−	0.173979i	−0.341704	−	0.939808i	$-0.611004\pi$
$239$	4.65862	−	2.68965i	0.301341	−	0.173979i	0.643045	+	0.765828i	$0.277671\pi$
$240$	−3.34980	+	1.48761i	−0.216229	+	0.0960245i
$241$	−2.27009	−	1.31064i	−0.146230	−	0.0844257i	0.425100	−	0.905146i	$-0.360239\pi$
$241$	−2.27009	−	1.31064i	−0.146230	−	0.0844257i	−0.571330	+	0.820721i	$0.693572\pi$
$242$	3.14152	−	3.14152i	0.201944	−	0.201944i
$243$	−3.13039	+	0.838785i	−0.200814	+	0.0538081i
$244$	6.07625	−	10.5244i	0.388992	−	0.673754i
$245$	−2.15986	−	0.831454i	−0.137988	−	0.0531197i
$246$	−6.51051	−	11.2765i	−0.415095	−	0.718966i
$247$	−19.0012	+	19.0012i	−1.20902	+	1.20902i
$248$	1.11807	−	4.17271i	0.0709978	−	0.264967i
$249$	6.63361	−	11.4898i	0.420388	−	0.728134i
$250$	−3.48529	+	10.6232i	−0.220429	+	0.671871i
$251$	2.79805	−	4.84636i	0.176611	−	0.305900i	−0.764106	−	0.645090i	$-0.776820\pi$
$251$	2.79805	−	4.84636i	0.176611	−	0.305900i	0.940718	+	0.339191i	$0.110153\pi$
$252$	−0.738814	−	0.197965i	−0.0465409	−	0.0124706i
$253$	14.6237	+	3.91841i	0.919385	+	0.246349i
$254$	17.4557			1.09527
$255$	0.901523	−	0.728618i	0.0564556	−	0.0456278i
$256$	1.00000			0.0625000
$257$	−21.4327	+	21.4327i	−1.33694	+	1.33694i	−0.437925	+	0.899011i	$0.644287\pi$
$257$	−21.4327	+	21.4327i	−1.33694	+	1.33694i	−0.899011	+	0.437925i	$0.855713\pi$
$258$	7.26153	+	7.92488i	0.452083	+	0.493381i
$259$			10.8270i			0.672759i
$260$	−10.6677	−	7.76606i	−0.661582	−	0.481631i
$261$	2.20149	−	1.27103i	0.136269	−	0.0786750i
$262$	−10.5136	−	10.5136i	−0.649530	−	0.649530i
$263$	−2.63733	+	9.84264i	−0.162625	+	0.606923i	0.835707	+	0.549176i	$0.185058\pi$
$263$	−2.63733	+	9.84264i	−0.162625	+	0.606923i	−0.998331	+	0.0577471i	$0.981608\pi$
$264$	−3.63505	+	2.09870i	−0.223722	+	0.129166i
$265$	−7.78436	−	17.5289i	−0.478189	−	1.07679i
$266$			11.1217i			0.681917i
$267$	4.69481	−	1.25797i	0.287318	−	0.0769866i
$268$	8.12473	+	2.17701i	0.496297	+	0.132982i
$269$		−	21.3269i		−	1.30033i	−0.759795	−	0.650163i	$-0.774700\pi$
$269$		−	21.3269i		−	1.30033i	0.759795	−	0.650163i	$-0.225300\pi$
$270$	−9.44466	+	7.63325i	−0.574784	+	0.464545i
$271$	−0.591209	+	1.02400i	−0.0359134	+	0.0622038i	−0.883423	−	0.468576i	$-0.844767\pi$
$271$	−0.591209	+	1.02400i	−0.0359134	+	0.0622038i	0.847510	+	0.530779i	$0.178101\pi$
$272$	−0.305477	+	0.0818523i	−0.0185223	+	0.00496303i
$273$	6.11433	+	22.8190i	0.370056	+	1.38107i
$274$			11.3520i			0.685802i
$275$	−2.68586	+	12.5187i	−0.161963	+	0.754903i
$276$	8.39275	+	4.84556i	0.505184	+	0.291668i
$277$	−13.4882	−	3.61414i	−0.810425	−	0.217153i	−0.170269	−	0.985398i	$-0.554464\pi$
$277$	−13.4882	−	3.61414i	−0.810425	−	0.217153i	−0.640156	+	0.768245i	$0.721130\pi$
$278$	3.67803	−	13.7266i	0.220593	−	0.823265i
$279$		−	1.35289i		−	0.0809951i
$280$	−5.39479	+	0.849185i	−0.322401	+	0.0507485i
$281$	−0.267075	−	0.462588i	−0.0159324	−	0.0275957i	0.857949	−	0.513734i	$-0.171738\pi$
$281$	−0.267075	−	0.462588i	−0.0159324	−	0.0275957i	−0.873882	+	0.486139i	$0.838405\pi$
$282$	3.86976	−	14.4421i	0.230441	−	0.860017i
$283$	−1.93030	−	7.20398i	−0.114745	−	0.428232i	0.884523	−	0.466496i	$-0.154484\pi$
$283$	−1.93030	−	7.20398i	−0.114745	−	0.428232i	−0.999268	+	0.0382639i	$0.987817\pi$
$284$	−1.98769	+	3.44277i	−0.117947	+	0.204291i
$285$	13.4936	+	9.82335i	0.799294	+	0.581885i
$286$	−13.0864	−	7.55542i	−0.773813	−	0.446761i
$287$	−5.02142	−	18.7402i	−0.296405	−	1.10620i
$288$	0.302504	−	0.0810556i	0.0178252	−	0.00477625i
$289$	−14.6358	+	8.44999i	−0.860930	+	0.497058i
$290$	10.6825	−	14.6738i	0.627298	−	0.861674i
$291$	−2.16666	+	1.25092i	−0.127012	+	0.0733304i
$292$	−2.79978	−	10.4489i	−0.163845	−	0.611477i
$293$	−11.1073	+	11.1073i	−0.648893	+	0.648893i	−0.952725	−	0.303833i	$-0.901734\pi$
$293$	−11.1073	+	11.1073i	−0.648893	+	0.648893i	0.303833	+	0.952725i	$0.401734\pi$
$294$	−1.46926	−	0.848277i	−0.0856889	−	0.0494725i
$295$	3.23222	−	2.61231i	0.188187	−	0.152094i
$296$	−2.21654	−	3.83915i	−0.128834	−	0.223146i
$297$	−9.83352	+	9.83352i	−0.570599	+	0.570599i
$298$	6.57091	+	1.76067i	0.380643	+	0.101993i
$299$			34.8885i			2.01765i
$300$	−3.73471	+	7.29538i	−0.215623	+	0.421199i
$301$	7.39483	+	14.2060i	0.426231	+	0.818821i
$302$	−4.25896	−	4.25896i	−0.245075	−	0.245075i
$303$	−0.140112	−	0.140112i	−0.00804924	−	0.00804924i
$304$	−2.27687	−	3.94365i	−0.130587	−	0.226184i
$305$	−4.22535	−	26.8433i	−0.241943	−	1.53704i
$306$	−0.0857733	+	0.0495212i	−0.00490333	+	0.00283094i
$307$	−1.55359	+	5.79808i	−0.0886682	+	0.330914i	−0.995984	−	0.0895366i	$-0.971461\pi$
$307$	−1.55359	+	5.79808i	−0.0886682	+	0.330914i	0.907315	+	0.420451i	$0.138128\pi$
$308$	−6.04099	+	1.61868i	−0.344218	+	0.0922328i
$309$	−11.6624			−0.663453
$310$	−3.92051	−	8.82822i	−0.222670	−	0.501409i
$311$	−5.25481	−	9.10160i	−0.297973	−	0.516104i	0.677699	−	0.735339i	$-0.262977\pi$
$311$	−5.25481	−	9.10160i	−0.297973	−	0.516104i	−0.975672	+	0.219235i	$0.929644\pi$
$312$	−6.83964	−	6.83964i	−0.387218	−	0.387218i
$313$	0.353288	−	1.31849i	0.0199690	−	0.0745253i	−0.955222	−	0.295889i	$-0.904384\pi$
$313$	0.353288	−	1.31849i	0.0199690	−	0.0745253i	0.975191	+	0.221364i	$0.0710508\pi$
$314$	3.27407	+	1.89028i	0.184766	+	0.106675i
$315$	−1.56311	+	0.694159i	−0.0880714	+	0.0391115i
$316$	−5.08040	+	8.79950i	−0.285795	+	0.495011i
$317$	17.4068	+	17.4068i	0.977663	+	0.977663i	0.999756	−	0.0220932i	$-0.00703304\pi$
$317$	17.4068	+	17.4068i	0.977663	+	0.977663i	−0.0220932	+	0.999756i	$0.507033\pi$
$318$	−3.63890	−	13.5806i	−0.204060	−	0.761561i
$319$	10.3927	−	18.0008i	0.581882	−	1.00785i
$320$	1.73909	−	1.40555i	0.0972181	−	0.0785725i
$321$	14.8319	−	8.56321i	0.827837	−	0.477952i
$322$	10.2104	+	10.2104i	0.569004	+	0.569004i
$323$	1.01833	+	1.01833i	0.0566612	+	0.0566612i
$324$	−6.89564	+	3.98120i	−0.383091	+	0.221178i
$325$	−29.4676	+	1.48805i	−1.63457	+	0.0825421i
$326$	−10.6642	+	18.4710i	−0.590638	+	1.02301i
$327$	−0.0148019	−	0.0552414i	−0.000818546	−	0.00305485i
$328$	5.61708	+	5.61708i	0.310151	+	0.310151i
$329$	11.1389	−	19.2932i	0.614108	−	1.06367i
$330$	−3.37186	+	8.75906i	−0.185615	+	0.482170i
$331$	10.1584	+	5.86496i	0.558357	+	0.322368i	0.752486	−	0.658608i	$-0.228855\pi$
$331$	10.1584	+	5.86496i	0.558357	+	0.322368i	−0.194129	+	0.980976i	$0.562188\pi$
$332$	−2.09487	+	7.81815i	−0.114971	+	0.429077i
$333$	−0.981694	−	0.981694i	−0.0537965	−	0.0537965i
$334$	12.1188	+	20.9904i	0.663113	+	1.14855i
$335$	17.1895	−	7.63367i	0.939165	−	0.417072i
$336$	−4.00336			−0.218401
$337$	−5.05225	+	1.35375i	−0.275214	+	0.0737433i	−0.393786	−	0.919202i	$-0.628835\pi$
$337$	−5.05225	+	1.35375i	−0.275214	+	0.0737433i	0.118572	+	0.992945i	$0.462168\pi$
$338$	5.64801	−	21.0787i	0.307211	−	1.14653i
$339$	24.2345	−	13.9918i	1.31624	−	0.759929i
$340$	−0.416205	+	0.571711i	−0.0225719	+	0.0310054i
$341$	−5.53101	−	9.57999i	−0.299521	−	0.518785i
$342$	−1.00841	−	1.00841i	−0.0545288	−	0.0545288i
$343$	−13.8764	−	13.8764i	−0.749255	−	0.749255i
$344$	−5.53042	−	3.52342i	−0.298180	−	0.189970i
$345$	21.4064	−	3.36955i	1.15248	−	0.181410i
$346$			4.36755i			0.234801i
$347$	−7.30940	−	1.95855i	−0.392389	−	0.105140i	0.0572293	−	0.998361i	$-0.481773\pi$
$347$	−7.30940	−	1.95855i	−0.392389	−	0.105140i	−0.449618	+	0.893221i	$0.648440\pi$
$348$	9.40817	−	9.40817i	0.504331	−	0.504331i
$349$	−3.73723	−	6.47307i	−0.200049	−	0.346495i	0.748495	−	0.663141i	$-0.230777\pi$
$349$	−3.73723	−	6.47307i	−0.200049	−	0.346495i	−0.948544	+	0.316645i	$0.897444\pi$
$350$	−8.18847	+	9.05945i	−0.437692	+	0.484248i
$351$	−27.7538	−	16.0237i	−1.48139	−	0.855281i
$352$	1.81069	−	1.81069i	0.0965103	−	0.0965103i
$353$	−1.12779	−	4.20896i	−0.0600260	−	0.224020i	0.929396	−	0.369083i	$-0.120328\pi$
$353$	−1.12779	−	4.20896i	−0.0600260	−	0.224020i	−0.989422	+	0.145063i	$0.953662\pi$
$354$	2.63833	−	1.52324i	0.140226	−	0.0809593i
$355$	1.38221	+	8.78108i	0.0733603	+	0.466051i
$356$	−2.56794	+	1.48260i	−0.136101	+	0.0785778i
$357$	1.22293	−	0.327684i	0.0647245	−	0.0173429i
$358$	0.269335	+	1.00517i	0.0142348	+	0.0531251i
$359$	18.3223	+	10.5784i	0.967016	+	0.558307i	0.898325	−	0.439331i	$-0.144784\pi$
$359$	18.3223	+	10.5784i	0.967016	+	0.558307i	0.0686911	+	0.997638i	$0.478118\pi$
$360$	0.412154	−	0.566146i	0.0217224	−	0.0298385i
$361$	−0.868239	+	1.50383i	−0.0456968	+	0.0791492i
$362$	2.69598	+	10.0615i	0.141697	+	0.528822i
$363$	1.88482	−	7.03425i	0.0989275	−	0.369202i
$364$	−7.20614	−	12.4814i	−0.377705	−	0.654203i
$365$	−19.5555	−	14.2364i	−1.02358	−	0.745167i
$366$		−	19.9198i		−	1.04123i
$367$	1.79609	−	6.70309i	0.0937550	−	0.349898i	−0.903073	−	0.429488i	$-0.858694\pi$
$367$	1.79609	−	6.70309i	0.0937550	−	0.349898i	0.996828	+	0.0795892i	$0.0253608\pi$
$368$	−5.71081	−	1.53021i	−0.297697	−	0.0797676i
$369$	2.15448	+	1.24389i	0.112158	+	0.0647543i
$370$	−9.25087	−	3.56119i	−0.480930	−	0.185137i
$371$		−	20.9488i		−	1.08761i
$372$	−1.83270	−	6.83971i	−0.0950208	−	0.354623i
$373$	13.1108	−	3.51303i	0.678851	−	0.181898i	0.0971127	−	0.995273i	$-0.469039\pi$
$373$	13.1108	−	3.51303i	0.678851	−	0.181898i	0.581739	+	0.813376i	$0.302373\pi$
$374$	−0.404916	+	0.701335i	−0.0209377	+	0.0362652i
$375$	3.75901	+	17.9366i	0.194115	+	0.926244i
$376$			9.12154i			0.470408i
$377$	46.2671	+	12.3972i	2.38288	+	0.638490i
$378$	−12.8119	+	3.43293i	−0.658971	+	0.176571i
$379$		−	29.2895i		−	1.50450i	−0.658877	−	0.752250i	$-0.728968\pi$
$379$		−	29.2895i		−	1.50450i	0.658877	−	0.752250i	$-0.271032\pi$
$380$	−9.50266	−	3.65812i	−0.487476	−	0.187658i
$381$	24.7792	−	14.3063i	1.26948	−	0.732933i
$382$	3.66363	−	13.6728i	0.187447	−	0.699563i
$383$	−9.35826	−	9.35826i	−0.478185	−	0.478185i	0.426366	−	0.904551i	$-0.359794\pi$
$383$	−9.35826	−	9.35826i	−0.478185	−	0.478185i	−0.904551	+	0.426366i	$0.859794\pi$
$384$	1.41955	−	0.819577i	0.0724410	−	0.0418239i
$385$	−8.23071	+	11.3059i	−0.419476	+	0.576204i
$386$		−	25.0569i		−	1.27536i
$387$	−1.95856	−	0.617575i	−0.0995594	−	0.0313931i
$388$	1.07926	−	1.07926i	0.0547911	−	0.0547911i
$389$	−28.4339			−1.44165			−0.720827	−	0.693115i	$-0.756238\pi$
$389$	−28.4339			−1.44165			−0.720827	+	0.693115i	$0.756238\pi$
$390$	−21.5082	−	2.28132i	−1.08911	−	0.115519i
$391$	1.86977			0.0945585
$392$	0.999751	+	0.267882i	0.0504951	+	0.0135301i
$393$	−23.5412	−	6.30784i	−1.18750	−	0.318189i
$394$	−4.31648	+	7.47637i	−0.217461	+	0.376654i
$395$	3.53285	+	22.4439i	0.177757	+	1.12927i
$396$	0.400974	−	0.694508i	0.0201497	−	0.0349003i
$397$	−2.57878	+	9.62413i	−0.129425	+	0.483021i	−0.999959	−	0.00908773i	$-0.997107\pi$
$397$	−2.57878	+	9.62413i	−0.129425	+	0.483021i	0.870534	+	0.492109i	$0.163774\pi$
$398$	−8.64308	+	8.64308i	−0.433238	+	0.433238i
$399$	9.11511	+	15.7878i	0.456326	+	0.790380i
$400$	1.04887	−	4.88875i	0.0524437	−	0.244437i
$401$	−6.21585	+	10.7662i	−0.310404	+	0.537636i	−0.978450	−	0.206484i	$-0.933798\pi$
$401$	−6.21585	+	10.7662i	−0.310404	+	0.537636i	0.668045	+	0.744120i	$0.267131\pi$
$402$	13.3177	−	3.56846i	0.664226	−	0.177979i
$403$	18.0255	−	18.0255i	0.897915	−	0.897915i
$404$	0.104689	+	0.0604423i	0.00520848	+	0.00300712i
$405$	−6.39638	+	16.6158i	−0.317839	+	0.825646i
$406$	17.1686	−	9.91231i	0.852064	−	0.491940i
$407$	−10.9650	−	2.93806i	−0.543515	−	0.145634i
$408$	−0.366555	+	0.366555i	−0.0181472	+	0.0181472i
$409$	26.2100			1.29600			0.648000	−	0.761641i	$-0.275606\pi$
$409$	26.2100			1.29600			0.648000	+	0.761641i	$0.275606\pi$
$410$	17.6637	+	1.87354i	0.872347	+	0.0925275i
$411$	9.30387	+	16.1148i	0.458926	+	0.794883i
$412$	6.87248	−	1.84148i	0.338583	−	0.0907230i
$413$	4.38457	−	1.17484i	0.215750	−	0.0578102i
$414$	−1.85157			−0.0909998
$415$	7.34562	+	16.5409i	0.360582	+	0.811962i
$416$	5.11045	+	2.95052i	0.250560	+	0.144661i
$417$	−6.02885	−	22.5000i	−0.295234	−	1.10183i
$418$	−11.2634	−	3.01803i	−0.550913	−	0.147617i
$419$	−7.06051			−0.344929			−0.172464	−	0.985016i	$-0.555173\pi$
$419$	−7.06051			−0.344929			−0.172464	+	0.985016i	$0.555173\pi$
$420$	−6.96220	+	5.62691i	−0.339721	+	0.274565i
$421$	30.9819	+	17.8874i	1.50997	+	0.871780i	0.999932	+	0.0116256i	$0.00370063\pi$
$421$	30.9819	+	17.8874i	1.50997	+	0.871780i	0.510034	+	0.860154i	$0.329633\pi$
$422$	−11.4494	−	11.4494i	−0.557348	−	0.557348i
$423$	0.739352	+	2.75930i	0.0359485	+	0.134162i
$424$	4.28869	+	7.42823i	0.208277	+	0.360747i
$425$	0.0797487	+	1.57925i	0.00386838	+	0.0766050i
$426$			6.51625i			0.315713i
$427$	7.68186	−	28.6691i	0.371751	−	1.38739i
$428$	−7.38809	+	7.38809i	−0.357117	+	0.357117i
$429$	−24.7690			−1.19586
$430$	−14.5702	+	1.64573i	−0.702639	+	0.0793639i
$431$	−21.8508			−1.05251			−0.526257	−	0.850326i	$-0.676405\pi$
$431$	−21.8508			−1.05251			−0.526257	+	0.850326i	$0.676405\pi$
$432$	3.84016	−	3.84016i	0.184760	−	0.184760i
$433$	4.94826	−	18.4672i	0.237798	−	0.887476i	−0.739069	−	0.673630i	$-0.764734\pi$
$433$	4.94826	−	18.4672i	0.237798	−	0.887476i	0.976867	−	0.213846i	$-0.0685991\pi$
$434$		−	10.5506i		−	0.506447i
$435$	3.13803	−	29.5853i	0.150457	−	1.41851i
$436$	0.0174450	+	0.0302156i	0.000835464	+	0.00144707i
$437$	6.96815	+	26.0055i	0.333332	+	1.24401i
$438$	−12.5381	−	12.5381i	−0.599094	−	0.599094i
$439$	14.7835	+	8.53525i	0.705578	+	0.407365i	0.809421	−	0.587228i	$-0.199781\pi$
$439$	14.7835	+	8.53525i	0.705578	+	0.407365i	−0.103844	+	0.994594i	$0.533114\pi$
$440$	0.603945	−	5.69398i	0.0287920	−	0.271450i
$441$	0.324142			0.0154353
$442$	−1.80263	−	0.483014i	−0.0857424	−	0.0229746i
$443$	−5.54488	−	20.6938i	−0.263445	−	0.983192i	−0.963195	−	0.268803i	$-0.913372\pi$
$443$	−5.54488	−	20.6938i	−0.263445	−	0.983192i	0.699750	−	0.714388i	$-0.253295\pi$
$444$	−6.29296	−	3.63324i	−0.298651	−	0.172426i
$445$	−2.38202	+	6.18775i	−0.112919	+	0.293327i
$446$	26.0074			1.23149
$447$	10.7707	−	2.88601i	0.509438	−	0.136504i
$448$	2.35911	−	0.632122i	0.111458	−	0.0298649i
$449$	−14.7906	−	25.6181i	−0.698012	−	1.20899i	−0.969155	−	0.246454i	$-0.920735\pi$
$449$	−14.7906	−	25.6181i	−0.698012	−	1.20899i	0.271142	−	0.962539i	$-0.412599\pi$
$450$	−0.0789724	−	1.56388i	−0.00372279	−	0.0737220i
$451$	20.3416			0.957849
$452$	−12.0717	+	12.0717i	−0.567804	+	0.567804i
$453$	−9.53634	−	2.55525i	−0.448056	−	0.120056i
$454$	−2.80613	+	1.62012i	−0.131698	+	0.0760360i
$455$	−30.0753	−	11.5777i	−1.40995	−	0.542772i
$456$	−6.46425	−	3.73213i	−0.302716	−	0.174773i
$457$	21.9461	−	21.9461i	1.02659	−	1.02659i	0.0269573	−	0.999637i	$-0.491418\pi$
$457$	21.9461	−	21.9461i	1.02659	−	1.02659i	0.999637	−	0.0269573i	$-0.00858181\pi$
$458$	−19.4597	+	5.21420i	−0.909291	+	0.243644i
$459$	−0.858754	+	1.48741i	−0.0400832	+	0.0694262i
$460$	−12.0824	+	5.36565i	−0.563345	+	0.250175i
$461$	8.99583	+	15.5812i	0.418978	+	0.725691i	0.995837	−	0.0911530i	$-0.0290552\pi$
$461$	8.99583	+	15.5812i	0.418978	+	0.725691i	−0.576859	+	0.816844i	$0.695722\pi$
$462$	−7.24885	+	7.24885i	−0.337247	+	0.337247i
$463$	4.51407	−	16.8467i	0.209787	−	0.782934i	−0.778150	−	0.628078i	$-0.783842\pi$
$463$	4.51407	−	16.8467i	0.209787	−	0.782934i	0.987937	−	0.154856i	$-0.0494914\pi$
$464$	−4.05854	+	7.02960i	−0.188413	+	0.326341i
$465$	−12.8008	−	9.31894i	−0.593621	−	0.432155i
$466$	−1.28874	+	2.23216i	−0.0596996	+	0.103403i
$467$	6.45071	+	1.72846i	0.298503	+	0.0799838i	0.404962	−	0.914333i	$-0.367285\pi$
$467$	6.45071	+	1.72846i	0.298503	+	0.0799838i	−0.106459	+	0.994317i	$0.533951\pi$
$468$	1.78508	+	0.478312i	0.0825156	+	0.0221100i
$469$	20.5433			0.948600
$470$	12.8208	+	15.8632i	0.591377	+	0.731714i
$471$	6.19693			0.285540
$472$	−1.31421	+	1.31421i	−0.0604912	+	0.0604912i
$473$	−16.3937	+	3.63407i	−0.753784	+	0.167095i
$474$			16.6551i			0.764994i
$475$	−21.6676	+	6.99464i	−0.994180	+	0.320936i
$476$	−0.668914	+	0.386197i	−0.0306596	+	0.0177013i
$477$	1.89944	+	1.89944i	0.0869696	+	0.0869696i
$478$	−1.39227	+	5.19601i	−0.0636808	+	0.237660i
$479$	12.7750	−	7.37567i	0.583707	−	0.337003i	−0.178898	−	0.983868i	$-0.557253\pi$
$479$	12.7750	−	7.37567i	0.583707	−	0.337003i	0.762605	+	0.646864i	$0.223920\pi$
$480$	1.31677	−	3.42056i	0.0601021	−	0.156127i
$481$		−	26.1597i		−	1.19278i
$482$	2.53196	−	0.678437i	0.115328	−	0.0309020i
$483$	22.8624	+	6.12597i	1.04028	+	0.278741i
$484$			4.44278i			0.201944i
$485$	0.359980	−	3.39388i	0.0163458	−	0.154108i
$486$	1.62041	−	2.80663i	0.0735032	−	0.127311i
$487$	−5.25166	+	1.40718i	−0.237975	+	0.0637653i	−0.375835	−	0.926686i	$-0.622644\pi$
$487$	−5.25166	+	1.40718i	−0.237975	+	0.0637653i	0.137860	+	0.990452i	$0.455978\pi$
$488$	3.14530	+	11.7384i	0.142381	+	0.531373i
$489$			34.9607i			1.58098i
$490$	2.11518	−	0.939325i	0.0955541	−	0.0424344i
$491$	−3.08470	−	1.78095i	−0.139210	−	0.0803731i	0.428777	−	0.903410i	$-0.358945\pi$
$491$	−3.08470	−	1.78095i	−0.139210	−	0.0803731i	−0.567988	+	0.823037i	$0.692278\pi$
$492$	12.5773	+	3.37009i	0.567030	+	0.151935i
$493$	0.664403	−	2.47958i	0.0299232	−	0.111675i
$494$		−	26.8717i		−	1.20902i
$495$	−0.278833	−	1.77140i	−0.0125326	−	0.0796186i
$496$	2.15995	+	3.74115i	0.0969847	+	0.167983i
$497$	−2.51292	+	9.37834i	−0.112720	+	0.420676i
$498$	3.43381	+	12.8152i	0.153873	+	0.574261i
$499$	−22.2723	+	38.5768i	−0.997047	+	1.72694i	−0.432021	+	0.901863i	$0.642200\pi$
$499$	−22.2723	+	38.5768i	−0.997047	+	1.72694i	−0.565026	+	0.825073i	$0.691134\pi$
$500$	−5.04728	−	9.97622i	−0.225721	−	0.446150i
$501$	34.4066	+	19.8646i	1.53717	+	0.887487i
$502$	1.44838	+	5.40541i	0.0646442	+	0.241255i
$503$	−20.7832	+	5.56884i	−0.926676	+	0.248302i	−0.690437	−	0.723393i	$-0.742582\pi$
$503$	−20.7832	+	5.56884i	−0.926676	+	0.248302i	−0.236239	+	0.971695i	$0.575915\pi$
$504$	0.662402	−	0.382438i	0.0295057	−	0.0170351i
$505$	0.267019	−	0.0420309i	0.0118822	−	0.00187035i
$506$	−13.1113	+	7.56979i	−0.582867	+	0.336518i
$507$	−9.25796	−	34.5512i	−0.411160	−	1.53447i
$508$	−12.3430	+	12.3430i	−0.547634	+	0.547634i
$509$	−13.2246	−	7.63521i	−0.586169	−	0.338425i	0.177412	−	0.984137i	$-0.443227\pi$
$509$	−13.2246	−	7.63521i	−0.586169	−	0.338425i	−0.763581	+	0.645712i	$0.776561\pi$
$510$	−0.122262	+	1.15268i	−0.00541386	+	0.0510417i
$511$	−13.2100	−	22.8803i	−0.584375	−	1.01217i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−23.8878	−	6.40070i	−1.05467	−	0.282598i
$514$		−	30.3104i		−	1.33694i
$515$	9.36359	−	12.8621i	0.412609	−	0.566771i
$516$	−10.7384	−	0.469057i	−0.472732	−	0.0206491i
$517$	16.5163	+	16.5163i	0.726387	+	0.726387i
$518$	−7.65586	−	7.65586i	−0.336379	−	0.336379i
$519$	3.57955	+	6.19996i	0.157125	+	0.272148i
$520$	13.0346	−	2.05176i	0.571606	−	0.0899755i
$521$	−27.0599	+	15.6230i	−1.18552	+	0.684458i	−0.957284	−	0.289149i	$-0.906628\pi$
$521$	−27.0599	+	15.6230i	−1.18552	+	0.684458i	−0.228232	+	0.973607i	$0.573294\pi$
$522$	−0.657935	+	2.45545i	−0.0287970	+	0.107472i
$523$	−13.1848	+	3.53286i	−0.576532	+	0.154481i	−0.535291	−	0.844668i	$-0.679798\pi$
$523$	−13.1848	+	3.53286i	−0.576532	+	0.154481i	−0.0412413	+	0.999149i	$0.513131\pi$
$524$	14.8684			0.649530
$525$	−4.19901	+	19.5714i	−0.183260	+	0.854166i
$526$	−5.09493	−	8.82467i	−0.222149	−	0.384774i
$527$	−0.966038	−	0.966038i	−0.0420813	−	0.0420813i
$528$	1.08637	−	4.05437i	0.0472780	−	0.176444i
$529$	10.3533	+	5.97745i	0.450141	+	0.259889i
$530$	17.8992	+	6.89041i	0.777490	+	0.299300i
$531$	−0.291028	+	0.504076i	−0.0126296	+	0.0218750i
$532$	−7.86425	−	7.86425i	−0.340958	−	0.340958i
$533$	12.1325	+	45.2791i	0.525517	+	1.96125i
$534$	−2.43021	+	4.20925i	−0.105166	+	0.182152i
$535$	−2.46425	+	23.2329i	−0.106539	+	1.00444i
$536$	−7.28443	+	4.20567i	−0.314640	+	0.181657i
$537$	1.20615	+	1.20615i	0.0520493	+	0.0520493i
$538$	15.0804	+	15.0804i	0.650163	+	0.650163i
$539$	2.29530	−	1.32519i	0.0988654	−	0.0570800i
$540$	1.28086	−	12.0759i	0.0551194	−	0.519664i
$541$	−3.01635	+	5.22448i	−0.129683	+	0.224618i	−0.923554	−	0.383469i	$-0.874729\pi$
$541$	−3.01635	+	5.22448i	−0.129683	+	0.224618i	0.793871	+	0.608087i	$0.208063\pi$
$542$	−0.306032	−	1.14213i	−0.0131452	−	0.0490586i
$543$	12.0733	+	12.0733i	0.518114	+	0.518114i
$544$	0.158127	−	0.273883i	0.00677962	−	0.0117426i
$545$	0.0728079	+	0.0280279i	0.00311875	+	0.00120059i
$546$	−20.4589	−	11.8120i	−0.875562	−	0.505506i
$547$	0.804053	−	3.00077i	0.0343788	−	0.128304i	−0.946604	−	0.322399i	$-0.895511\pi$
$547$	0.804053	−	3.00077i	0.0343788	−	0.128304i	0.980983	+	0.194096i	$0.0621773\pi$
$548$	−8.02710	−	8.02710i	−0.342901	−	0.342901i
$549$	1.90293	+	3.29597i	0.0812150	+	0.140668i
$550$	−6.95284	−	10.7512i	−0.296470	−	0.458433i
$551$	36.9630			1.57468
$552$	−9.36090	+	2.50825i	−0.398426	+	0.106758i
$553$	−6.42286	+	23.9704i	−0.273128	+	1.01933i
$554$	12.0931	−	6.98198i	0.513789	−	0.296636i
$555$	−16.0507	+	2.52652i	−0.681315	+	0.107245i
$556$	7.10540	+	12.3069i	0.301336	+	0.521929i
$557$	28.0642	+	28.0642i	1.18912	+	1.18912i	0.977311	+	0.211809i	$0.0679354\pi$
$557$	28.0642	+	28.0642i	1.18912	+	1.18912i	0.211809	+	0.977311i	$0.432065\pi$
$558$	0.956634	+	0.956634i	0.0404976	+	0.0404976i
$559$	−17.8670	−	34.3238i	−0.755694	−	1.45174i
$560$	3.21423	−	4.41516i	0.135826	−	0.186575i
$561$			1.32744i			0.0560445i
$562$	0.515950	+	0.138248i	0.0217640	+	0.00583165i
$563$	1.85514	−	1.85514i	0.0781847	−	0.0781847i	−0.666933	−	0.745118i	$-0.732393\pi$
$563$	1.85514	−	1.85514i	0.0781847	−	0.0781847i	0.745118	+	0.666933i	$0.232393\pi$
$564$	7.47580	+	12.9485i	0.314788	+	0.545229i
$565$	−4.02643	+	37.9611i	−0.169393	+	1.59703i
$566$	6.45892	+	3.72906i	0.271488	+	0.156744i
$567$	−13.7510	+	13.7510i	−0.577487	+	0.577487i
$568$	−1.02890	−	3.83991i	−0.0431718	−	0.161119i
$569$	36.3705	−	20.9985i	1.52473	−	0.880302i	0.525158	−	0.851005i	$-0.324006\pi$
$569$	36.3705	−	20.9985i	1.52473	−	0.880302i	0.999571	−	0.0292976i	$-0.00932706\pi$
$570$	−16.4876	+	2.59528i	−0.690590	+	0.108704i
$571$	−25.2499	+	14.5780i	−1.05668	+	0.610072i	−0.924511	−	0.381156i	$-0.875526\pi$
$571$	−25.2499	+	14.5780i	−1.05668	+	0.610072i	−0.132165	+	0.991228i	$0.542193\pi$
$572$	14.5959	−	3.91097i	0.610287	−	0.163526i
$573$	−6.00525	−	22.4119i	−0.250873	−	0.936270i
$574$	16.8020	+	9.70063i	0.701301	+	0.404896i
$575$	−13.4707	+	26.3137i	−0.561768	+	1.09736i
$576$	−0.156587	+	0.271217i	−0.00652447	+	0.0113007i
$577$	−10.1257	−	37.7895i	−0.421537	−	1.57320i	−0.771370	−	0.636387i	$-0.780428\pi$
$577$	−10.1257	−	37.7895i	−0.421537	−	1.57320i	0.349832	−	0.936812i	$-0.386239\pi$
$578$	4.37404	−	16.3241i	0.181936	−	0.678994i
$579$	−20.5361	−	35.5695i	−0.853450	−	1.47822i
$580$	2.82227	+	17.9296i	0.117188	+	0.744486i
$581$			19.7681i			0.820119i
$582$	0.647525	−	2.41660i	0.0268408	−	0.100171i
$583$	21.2158	+	5.68475i	0.878667	+	0.235438i
$584$	9.36824	+	5.40876i	0.387661	+	0.223816i
$585$	3.77671	−	1.67719i	0.156148	−	0.0693434i
$586$		−	15.7080i		−	0.648893i
$587$	−3.44784	−	12.8675i	−0.142308	−	0.531099i	−0.999860	−	0.0167032i	$-0.994683\pi$
$587$	−3.44784	−	12.8675i	−0.142308	−	0.531099i	0.857553	−	0.514396i	$-0.171984\pi$
$588$	1.63875	−	0.439101i	0.0675807	−	0.0181082i
$589$	9.83585	−	17.0362i	0.405279	−	0.701964i
$590$	−0.438345	+	4.13270i	−0.0180464	+	0.170141i
$591$			14.1508i			0.582084i
$592$	4.28202	+	1.14736i	0.175990	+	0.0471563i
$593$	11.1836	−	2.99663i	0.459254	−	0.123057i	−0.0217722	−	0.999763i	$-0.506931\pi$
$593$	11.1836	−	2.99663i	0.459254	−	0.123057i	0.481026	+	0.876706i	$0.340264\pi$
$594$		−	13.9067i		−	0.570599i
$595$	−0.620483	+	1.61182i	−0.0254373	+	0.0660783i
$596$	−5.89132	+	3.40135i	−0.241318	+	0.139325i
$597$	−5.18560	+	19.3529i	−0.212233	+	0.792063i
$598$	−24.6699	−	24.6699i	−1.00883	−	1.00883i
$599$	−24.6716	+	14.2442i	−1.00805	+	0.582000i	−0.910621	−	0.413242i	$-0.864396\pi$
$599$	−24.6716	+	14.2442i	−1.00805	+	0.582000i	−0.0974329	+	0.995242i	$0.531063\pi$
$600$	−2.51778	−	7.79945i	−0.102788	−	0.318411i
$601$			31.2127i			1.27319i	0.771197	+	0.636597i	$0.219658\pi$
$601$			31.2127i			1.27319i	−0.771197	+	0.636597i	$0.780342\pi$
$602$	−15.2741	−	4.81623i	−0.622526	−	0.196295i
$603$	−1.86267	+	1.86267i	−0.0758539	+	0.0758539i
$604$	6.02307			0.245075
$605$	6.24453	+	7.72639i	0.253876	+	0.314122i
$606$	0.198149			0.00804924
$607$	12.0795	+	3.23669i	0.490291	+	0.131373i	0.495491	−	0.868613i	$-0.334988\pi$
$607$	12.0795	+	3.23669i	0.490291	+	0.131373i	−0.00519916	+	0.999986i	$0.501655\pi$
$608$	4.39857	+	1.17859i	0.178385	+	0.0477982i
$609$	16.2478	−	28.1420i	0.658394	−	1.14037i
$610$	21.9689	+	15.9933i	0.889493	+	0.647550i
$611$	−26.9133	+	46.6152i	−1.08879	+	1.88585i
$612$	0.0256341	−	0.0956677i	0.00103620	−	0.00386714i
$613$	25.8810	−	25.8810i	1.04533	−	1.04533i	0.0464028	−	0.998923i	$-0.485224\pi$
$613$	25.8810	−	25.8810i	1.04533	−	1.04533i	0.998923	−	0.0464028i	$-0.0147758\pi$
$614$	−3.00131	−	5.19842i	−0.121123	−	0.209791i
$615$	26.6100	−	11.8172i	1.07302	−	0.476514i
$616$	3.12705	−	5.41621i	0.125992	−	0.218225i
$617$	42.6174	−	11.4193i	1.71571	−	0.459724i	0.738900	−	0.673815i	$-0.235346\pi$
$617$	42.6174	−	11.4193i	1.71571	−	0.459724i	0.976814	+	0.214091i	$0.0686790\pi$
$618$	8.24659	−	8.24659i	0.331727	−	0.331727i
$619$	26.7676	+	15.4543i	1.07588	+	0.621159i	0.929782	−	0.368111i	$-0.119995\pi$
$619$	26.7676	+	15.4543i	1.07588	+	0.621159i	0.146098	+	0.989270i	$0.453329\pi$
$620$	9.01471	+	3.47028i	0.362040	+	0.139370i
$621$	−27.8067	+	16.0542i	−1.11584	+	0.644232i
$622$	10.1515	+	2.72009i	0.407039	+	0.109066i
$623$	−5.12088	+	5.12088i	−0.205164	+	0.205164i
$624$	9.67271			0.387218
$625$	−22.7997	−	10.2554i	−0.911989	−	0.410214i
$626$	0.682499	+	1.18212i	0.0272782	+	0.0472472i
$627$	−18.4625	+	4.94702i	−0.737322	+	0.197565i
$628$	−3.65175	+	0.978483i	−0.145721	+	0.0390457i
$629$	−1.40197			−0.0559003
$630$	0.614443	−	1.59613i	0.0244800	−	0.0635914i
$631$	−3.05633	−	1.76457i	−0.121670	−	0.0702465i	0.437930	−	0.899009i	$-0.355712\pi$
$631$	−3.05633	−	1.76457i	−0.121670	−	0.0702465i	−0.559600	+	0.828763i	$0.689045\pi$
$632$	−2.62981	−	9.81457i	−0.104608	−	0.390403i
$633$	−25.6366	−	6.86931i	−1.01896	−	0.273031i
$634$	−24.6169			−0.977663
$635$	−4.11694	+	38.8144i	−0.163376	+	1.54030i
$636$	12.1760	+	7.02982i	0.482810	+	0.278751i
$637$	4.31878	+	4.31878i	0.171116	+	0.171116i
$638$	5.37968	+	20.0772i	0.212984	+	0.794866i
$639$	−0.622493	−	1.07819i	−0.0246254	−	0.0426525i
$640$	−0.235851	+	2.22359i	−0.00932282	+	0.0878953i
$641$		−	8.07600i		−	0.318983i	−0.987199	−	0.159491i	$-0.949015\pi$
$641$		−	8.07600i		−	0.318983i	0.987199	−	0.159491i	$-0.0509854\pi$
$642$	−4.43264	+	16.5429i	−0.174943	+	0.652894i
$643$	13.5488	−	13.5488i	0.534312	−	0.534312i	−0.387541	−	0.921853i	$-0.626675\pi$
$643$	13.5488	−	13.5488i	0.534312	−	0.534312i	0.921853	+	0.387541i	$0.126675\pi$
$644$	−14.4397			−0.569004
$645$	−19.3344	+	14.2776i	−0.761289	+	0.562180i
$646$	−1.44013			−0.0566612
$647$	1.43661	−	1.43661i	0.0564789	−	0.0564789i	−0.678303	−	0.734782i	$-0.737284\pi$
$647$	1.43661	−	1.43661i	0.0564789	−	0.0564789i	0.734782	+	0.678303i	$0.237284\pi$
$648$	2.06082	−	7.69109i	0.0809567	−	0.302134i
$649$			4.75925i			0.186817i
$650$	19.7846	−	21.8890i	0.776014	−	0.858556i
$651$	−8.64706	−	14.9771i	−0.338905	−	0.587001i
$652$	−5.52022	−	20.6017i	−0.216188	−	0.806826i
$653$	−15.4439	−	15.4439i	−0.604365	−	0.604365i	0.337103	−	0.941468i	$-0.390553\pi$
$653$	−15.4439	−	15.4439i	−0.604365	−	0.604365i	−0.941468	+	0.337103i	$0.890553\pi$
$654$	0.0495281	+	0.0285950i	0.00193670	+	0.00111815i
$655$	25.8575	−	20.8983i	1.01034	−	0.816563i
$656$	−7.94375			−0.310151
$657$	3.27234	+	0.876820i	0.127666	+	0.0342080i
$658$	5.76593	+	21.5187i	0.224779	+	0.838887i
$659$	8.14335	+	4.70156i	0.317220	+	0.183147i	0.650153	−	0.759804i	$-0.274705\pi$
$659$	8.14335	+	4.70156i	0.317220	+	0.183147i	−0.332933	+	0.942951i	$0.608038\pi$
$660$	−3.80932	−	8.57786i	−0.148278	−	0.333893i
$661$	−31.5180			−1.22591			−0.612953	−	0.790119i	$-0.710019\pi$
$661$	−31.5180			−1.22591			−0.612953	+	0.790119i	$0.710019\pi$
$662$	−11.3302	+	3.03593i	−0.440362	+	0.117995i
$663$	−2.95479	+	0.791734i	−0.114755	+	0.0307484i
$664$	−4.04697	−	7.00957i	−0.157053	−	0.272024i
$665$	−24.7302	−	2.62307i	−0.958996	−	0.101718i
$666$	1.38833			0.0537965
$667$	33.9343	−	33.9343i	1.31394	−	1.31394i
$668$	−23.4118	−	6.27317i	−0.905830	−	0.242716i
$669$	36.9188	−	21.3151i	1.42736	−	0.824088i
$670$	−6.75702	+	17.5527i	−0.261047	+	0.678118i
$671$	26.9498	+	15.5595i	1.04039	+	0.600668i
$672$	2.83080	−	2.83080i	0.109201	−	0.109201i
$673$	−24.1009	+	6.45781i	−0.929021	+	0.248930i	−0.691437	−	0.722437i	$-0.743022\pi$
$673$	−24.1009	+	6.45781i	−0.929021	+	0.248930i	−0.237584	+	0.971367i	$0.576355\pi$
$674$	2.61524	−	4.52973i	0.100735	−	0.174479i
$675$	−14.7457	−	22.8014i	−0.567563	−	0.877627i
$676$	10.9111	+	18.8986i	0.419658	+	0.726870i
$677$	−3.82513	+	3.82513i	−0.147012	+	0.147012i	−0.776782	−	0.629770i	$-0.783149\pi$
$677$	−3.82513	+	3.82513i	−0.147012	+	0.147012i	0.629770	+	0.776782i	$0.283149\pi$
$678$	−7.24267	+	27.0300i	−0.278153	+	1.03808i
$679$	1.86387	−	3.22832i	0.0715287	−	0.123891i
$680$	−0.109959	−	0.698562i	−0.00421675	−	0.0267886i
$681$	−2.65563	+	4.59968i	−0.101764	+	0.176260i
$682$	10.6851	+	2.86306i	0.409153	+	0.109632i
$683$	33.9373	+	9.09348i	1.29858	+	0.347952i	0.840912	−	0.541173i	$-0.182019\pi$
$683$	33.9373	+	9.09348i	1.29858	+	0.347952i	0.457665	+	0.889125i	$0.348686\pi$
$684$	1.42611			0.0545288
$685$	−25.2423	−	2.67739i	−0.964460	−	0.102298i
$686$	19.6242			0.749255
$687$	−23.3505	+	23.3505i	−0.890878	+	0.890878i
$688$	6.40203	−	1.41917i	0.244075	−	0.0541052i
$689$			50.6155i			1.92830i
$690$	−12.7540	+	17.5193i	−0.485536	+	0.666947i
$691$	12.2168	−	7.05334i	0.464747	−	0.268322i	−0.249291	−	0.968429i	$-0.580198\pi$
$691$	12.2168	−	7.05334i	0.464747	−	0.268322i	0.714038	+	0.700107i	$0.246864\pi$
$692$	−3.08833	−	3.08833i	−0.117401	−	0.117401i
$693$	0.506929	−	1.89189i	0.0192567	−	0.0718668i
$694$	6.55343	−	3.78362i	0.248765	−	0.143624i
$695$	29.6549	+	11.4159i	1.12487	+	0.433028i
$696$			13.3052i			0.504331i
$697$	2.42663	−	0.650214i	0.0919152	−	0.0246286i
$698$	7.21977	+	1.93453i	0.273272	+	0.0732231i
$699$			4.22488i			0.159800i
$700$	−0.615876	−	12.1961i	−0.0232779	−	0.460970i
$701$	4.08946	−	7.08316i	0.154457	−	0.267527i	−0.778404	−	0.627763i	$-0.783971\pi$
$701$	4.08946	−	7.08316i	0.154457	−	0.267527i	0.932861	+	0.360236i	$0.117304\pi$
$702$	30.9554	−	8.29447i	1.16834	−	0.313055i
$703$	−5.22478	−	19.4992i	−0.197056	−	0.735425i
$704$			2.56071i			0.0965103i
$705$	31.2008	+	12.0110i	1.17509	+	0.452359i
$706$	3.77365	+	2.17872i	0.142023	+	0.0819971i
$707$	0.285180	+	0.0764138i	0.0107253	+	0.00287384i
$708$	−0.788487	+	2.94267i	−0.0296331	+	0.110592i
$709$		−	33.5235i		−	1.25900i	−0.776999	−	0.629501i	$-0.783259\pi$
$709$		−	33.5235i		−	1.25900i	0.776999	−	0.629501i	$-0.216741\pi$
$710$	−7.18653	−	5.23179i	−0.269706	−	0.196346i
$711$	−1.59105	−	2.75578i	−0.0596691	−	0.103350i
$712$	0.767452	−	2.86417i	0.0287615	−	0.107339i
$713$	−6.61035	−	24.6702i	−0.247560	−	0.923905i
$714$	−0.633037	+	1.09645i	−0.0236908	+	0.0410337i
$715$	19.8866	−	27.3168i	0.743717	−	1.02159i
$716$	−0.901214	−	0.520316i	−0.0336799	−	0.0194451i
$717$	2.28214	+	8.51707i	0.0852281	+	0.318076i
$718$	−20.4359	+	5.47579i	−0.762662	+	0.204355i
$719$	27.0060	−	15.5919i	1.00715	−	0.581480i	0.0967965	−	0.995304i	$-0.469140\pi$
$719$	27.0060	−	15.5919i	1.00715	−	0.581480i	0.910357	+	0.413824i	$0.135807\pi$
$720$	0.108889	+	0.691762i	0.00405806	+	0.0257805i
$721$	15.0489	−	8.68849i	0.560451	−	0.323576i
$722$	−0.449434	−	1.67731i	−0.0167262	−	0.0624230i
$723$	3.03821	−	3.03821i	0.112992	−	0.112992i
$724$	−9.02092	−	5.20823i	−0.335260	−	0.193562i
$725$	30.1091	+	27.2144i	1.11822	+	1.01072i
$726$	3.64120	+	6.30674i	0.135137	+	0.234065i
$727$	−18.4402	+	18.4402i	−0.683909	+	0.683909i	−0.960879	−	0.276970i	$-0.910670\pi$
$727$	−18.4402	+	18.4402i	−0.683909	+	0.683909i	0.276970	+	0.960879i	$0.410670\pi$
$728$	13.9212	+	3.73017i	0.515954	+	0.138249i
$729$		−	29.1994i		−	1.08146i
$730$	23.8945	−	3.76119i	0.884375	−	0.139208i
$731$	−1.83951	+	0.957543i	−0.0680368	+	0.0354160i
$732$	14.0854	+	14.0854i	0.520613	+	0.520613i
$733$	10.1197	+	10.1197i	0.373778	+	0.373778i	0.868851	−	0.495073i	$-0.164859\pi$
$733$	10.1197	+	10.1197i	0.373778	+	0.373778i	−0.495073	+	0.868851i	$0.664859\pi$
$734$	3.46977	+	6.00983i	0.128072	+	0.221827i
$735$	2.23275	−	3.06697i	0.0823563	−	0.113127i
$736$	5.12017	−	2.95613i	0.188732	−	0.108965i
$737$	−5.57470	+	20.8051i	−0.205347	+	0.766364i
$738$	−2.40301	+	0.643885i	−0.0884561	+	0.0237017i
$739$	−13.0294			−0.479295			−0.239648	−	0.970860i	$-0.577032\pi$
$739$	−13.0294			−0.479295			−0.239648	+	0.970860i	$0.577032\pi$
$740$	9.05949	−	4.02321i	0.333034	−	0.147896i
$741$	−22.0235	−	38.1458i	−0.809052	−	1.40132i
$742$	14.8130	+	14.8130i	0.543804	+	0.543804i
$743$	12.9578	−	48.3591i	0.475374	−	1.77412i	−0.144590	−	0.989492i	$-0.546186\pi$
$743$	12.9578	−	48.3591i	0.475374	−	1.77412i	0.619964	−	0.784630i	$-0.287147\pi$
$744$	6.13232	+	3.54050i	0.224822	+	0.129801i
$745$	−5.46477	+	14.1958i	−0.200214	+	0.520094i
$746$	−6.78665	+	11.7548i	−0.248477	+	0.430375i
$747$	−1.79239	−	1.79239i	−0.0655801	−	0.0655801i
$748$	−0.209600	−	0.782237i	−0.00766373	−	0.0286014i
$749$	−12.7591	+	22.0995i	−0.466209	+	0.807498i
$750$	−15.3411	−	10.0251i	−0.560179	−	0.366065i
$751$	9.33106	−	5.38729i	0.340495	−	0.196585i	−0.319996	−	0.947419i	$-0.603681\pi$
$751$	9.33106	−	5.38729i	0.340495	−	0.196585i	0.660491	+	0.750834i	$0.270348\pi$
$752$	−6.44990	−	6.44990i	−0.235204	−	0.235204i
$753$	6.48619	+	6.48619i	0.236370	+	0.236370i
$754$	−41.4820	+	23.9496i	−1.51068	+	0.872194i
$755$	10.4747	−	8.46571i	0.381212	−	0.308099i
$756$	6.63191	−	11.4868i	0.241200	−	0.417771i
$757$	−7.15685	−	26.7097i	−0.260120	−	0.970781i	−0.965170	−	0.261624i	$-0.915742\pi$
$757$	−7.15685	−	26.7097i	−0.260120	−	0.970781i	0.705050	−	0.709158i	$-0.250925\pi$
$758$	20.7108	+	20.7108i	0.752250	+	0.752250i
$759$	−12.4081	+	21.4914i	−0.450384	+	0.780088i
$760$	9.30608	−	4.13272i	0.337567	−	0.149909i
$761$	25.6088	+	14.7852i	0.928318	+	0.535965i	0.886279	−	0.463151i	$-0.153281\pi$
$761$	25.6088	+	14.7852i	0.928318	+	0.535965i	0.0420389	+	0.999116i	$0.486615\pi$
$762$	−7.40547	+	27.6376i	−0.268272	+	1.00120i
$763$	0.0602546	+	0.0602546i	0.00218136	+	0.00218136i
$764$	7.07758	+	12.2587i	0.256058	+	0.443505i
$765$	−0.0898855	−	0.202405i	−0.00324982	−	0.00731796i
$766$	13.2346			0.478185
$767$	−10.5938	+	2.83859i	−0.382519	+	0.102496i
$768$	−0.424244	+	1.58330i	−0.0153086	+	0.0571325i
$769$	−28.6962	+	16.5677i	−1.03481	+	0.597448i	−0.918359	−	0.395748i	$-0.870485\pi$
$769$	−28.6962	+	16.5677i	−1.03481	+	0.597448i	−0.116452	+	0.993196i	$0.537152\pi$
$770$	−2.17451	−	13.8145i	−0.0783640	−	0.497840i
$771$	−24.8417	−	43.0272i	−0.894654	−	1.54959i
$772$	17.7179	+	17.7179i	0.637681	+	0.637681i
$773$	−25.5444	−	25.5444i	−0.918770	−	0.918770i	0.0781702	−	0.996940i	$-0.475092\pi$
$773$	−25.5444	−	25.5444i	−0.918770	−	0.918770i	−0.996940	+	0.0781702i	$0.975092\pi$
$774$	1.82160	−	0.948223i	0.0654762	−	0.0340832i
$775$	20.5551	−	6.63548i	0.738359	−	0.238353i
$776$			1.52630i			0.0547911i
$777$	−17.1424	−	4.59330i	−0.614982	−	0.164784i
$778$	20.1058	−	20.1058i	0.720827	−	0.720827i
$779$	18.0868	+	31.3273i	0.648029	+	1.12242i
$780$	16.8217	−	13.5954i	0.602314	−	0.486795i
$781$	−8.81593	−	5.08988i	−0.315459	−	0.182130i
$782$	−1.32213	+	1.32213i	−0.0472792	+	0.0472792i
$783$	11.4093	+	42.5802i	0.407737	+	1.52169i
$784$	−0.896352	+	0.517509i	−0.0320126	+	0.0184825i
$785$	−4.97542	+	6.83438i	−0.177580	+	0.243929i
$786$	21.1065	−	12.1858i	0.752842	−	0.434654i
$787$	14.4722	−	3.87782i	0.515878	−	0.138229i	0.00851891	−	0.999964i	$-0.497288\pi$
$787$	14.4722	−	3.87782i	0.515878	−	0.138229i	0.507359	+	0.861735i	$0.330622\pi$
$788$	−2.23438	−	8.33880i	−0.0795963	−	0.297058i
$789$	−14.4650	−	8.35137i	−0.514967	−	0.297317i
$790$	−18.3683	−	13.3721i	−0.653515	−	0.475758i
$791$	−20.8477	+	36.1092i	−0.741258	+	1.28390i
$792$	0.207560	+	0.774623i	0.00737531	+	0.0275250i
$793$	−18.5605	+	69.2688i	−0.659103	+	2.45981i
$794$	−4.98182	−	8.62876i	−0.176798	−	0.306223i
$795$	31.0559	−	4.88846i	1.10144	−	0.173376i
$796$		−	12.2232i		−	0.433238i
$797$	−5.27377	+	19.6820i	−0.186806	+	0.697171i	0.807430	+	0.589963i	$0.200858\pi$
$797$	−5.27377	+	19.6820i	−0.186806	+	0.697171i	−0.994237	+	0.107208i	$0.965809\pi$
$798$	−17.6090	−	4.71833i	−0.623353	−	0.167027i
$799$	2.49824	+	1.44236i	0.0883813	+	0.0510270i
$800$	2.71520	+	4.19853i	0.0959969	+	0.148441i
$801$		−	0.928628i		−	0.0328114i
$802$	−3.21756	−	12.0081i	−0.113616	−	0.424020i
$803$	26.7566	−	7.16941i	0.944221	−	0.253003i
$804$	−6.89374	+	11.9403i	−0.243123	+	0.421102i
$805$	−25.1120	+	20.2957i	−0.885081	+	0.715330i
$806$			25.4919i			0.897915i
$807$	33.7670	+	9.04783i	1.18865	+	0.318499i
$808$	−0.116766	+	0.0312873i	−0.00410780	+	0.00110068i
$809$		−	5.69718i		−	0.200302i	−0.994972	−	0.100151i	$-0.968067\pi$
$809$		−	5.69718i		−	0.200302i	0.994972	−	0.100151i	$-0.0319326\pi$
$810$	−7.22623	−	16.2721i	−0.253904	−	0.571742i
$811$	−15.4664	+	8.92951i	−0.543098	+	0.313558i	−0.746333	−	0.665572i	$-0.768188\pi$
$811$	−15.4664	+	8.92951i	−0.543098	+	0.313558i	0.203236	+	0.979130i	$0.434854\pi$
$812$	−5.13099	+	19.1491i	−0.180062	+	0.672002i
$813$	−1.37049	−	1.37049i	−0.0480651	−	0.0480651i
$814$	9.83095	−	5.67590i	0.344574	−	0.198940i
$815$	−38.5569	−	28.0694i	−1.35059	−	0.983227i
$816$		−	0.518387i		−	0.0181472i
$817$	−20.1733	−	22.0161i	−0.705773	−	0.770246i
$818$	−18.5332	+	18.5332i	−0.648000	+	0.648000i
$819$	4.51356			0.157717
$820$	−13.8149	+	11.1653i	−0.482437	+	0.389910i
$821$	−38.5694			−1.34608			−0.673040	−	0.739606i	$-0.735012\pi$
$821$	−38.5694			−1.34608			−0.673040	+	0.739606i	$0.735012\pi$
$822$	−17.9737	−	4.81604i	−0.626904	−	0.167979i
$823$	−25.2306	−	6.76052i	−0.879483	−	0.235657i	−0.209299	−	0.977852i	$-0.567118\pi$
$823$	−25.2306	−	6.76052i	−0.879483	−	0.235657i	−0.670184	+	0.742195i	$0.733785\pi$
$824$	−3.55746	+	6.16170i	−0.123930	+	0.214653i
$825$	−18.6813	−	9.56349i	−0.650401	−	0.332958i
$826$	−2.26962	+	3.93110i	−0.0789702	+	0.136780i
$827$	−6.38105	+	23.8144i	−0.221891	+	0.828108i	0.761735	+	0.647888i	$0.224348\pi$
$827$	−6.38105	+	23.8144i	−0.221891	+	0.828108i	−0.983626	+	0.180220i	$0.942319\pi$
$828$	1.30926	−	1.30926i	0.0454999	−	0.0454999i
$829$	−24.0064	−	41.5803i	−0.833776	−	1.44414i	−0.895023	−	0.446020i	$-0.852841\pi$
$829$	−24.0064	−	41.5803i	−0.833776	−	1.44414i	0.0612473	−	0.998123i	$-0.480492\pi$
$830$	−16.8903	−	6.50206i	−0.586272	−	0.225690i
$831$	11.4445	−	19.8225i	0.397007	−	0.687636i
$832$	−5.69996	+	1.52730i	−0.197611	+	0.0529496i
$833$	0.231456	−	0.231456i	0.00801946	−	0.00801946i
$834$	20.1729	+	11.6468i	0.698531	+	0.403297i
$835$	−49.5325	+	21.9968i	−1.71414	+	0.761230i
$836$	10.0985	−	5.83039i	0.349265	−	0.201648i
$837$	22.6612	+	6.07204i	0.783284	+	0.209880i
$838$	4.99254	−	4.99254i	0.172464	−	0.172464i
$839$	−16.3828			−0.565596			−0.282798	−	0.959180i	$-0.591263\pi$
$839$	−16.3828			−0.565596			−0.282798	+	0.959180i	$0.591263\pi$
$840$	0.944195	−	8.90184i	0.0325778	−	0.307143i
$841$	−18.4436	−	31.9452i	−0.635985	−	1.10156i
$842$	−34.5558	+	9.25921i	−1.19087	+	0.319094i
$843$	0.845721	−	0.226610i	0.0291282	−	0.00780487i
$844$	16.1919			0.557348
$845$	45.5383	+	17.5303i	1.56657	+	0.603061i
$846$	−2.47392	−	1.42832i	−0.0850551	−	0.0491066i
$847$	2.80838	+	10.4810i	0.0964969	+	0.360131i
$848$	−8.28511	−	2.21999i	−0.284512	−	0.0762348i
$849$	12.2250			0.419561
$850$	−1.17309	−	1.06031i	−0.0402367	−	0.0363683i
$851$	−22.6981	−	13.1048i	−0.778081	−	0.449225i
$852$	−4.60768	−	4.60768i	−0.157857	−	0.157857i
$853$	−11.1191	−	41.4972i	−0.380712	−	1.42084i	−0.844816	−	0.535057i	$-0.820290\pi$
$853$	−11.1191	−	41.4972i	−0.380712	−	1.42084i	0.464104	−	0.885781i	$-0.346376\pi$
$854$	14.8402	+	25.7040i	0.507822	+	0.879573i
$855$	2.48014	−	2.00447i	0.0848190	−	0.0685514i
$856$		−	10.4483i		−	0.357117i
$857$	3.56991	−	13.3231i	0.121946	−	0.455108i	−0.877766	−	0.479089i	$-0.840967\pi$
$857$	3.56991	−	13.3231i	0.121946	−	0.455108i	0.999712	+	0.0239803i	$0.00763388\pi$
$858$	17.5143	−	17.5143i	0.597929	−	0.597929i
$859$	0.477729			0.0162999			0.00814994	−	0.999967i	$-0.497406\pi$
$859$	0.477729			0.0162999			0.00814994	+	0.999967i	$0.497406\pi$
$860$	9.13900	−	11.4664i	0.311637	−	0.391001i
$861$	31.8017			1.08380
$862$	15.4508	−	15.4508i	0.526257	−	0.526257i
$863$	0.203603	−	0.759855i	0.00693071	−	0.0258658i	−0.962374	−	0.271729i	$-0.912405\pi$
$863$	0.203603	−	0.759855i	0.00693071	−	0.0258658i	0.969305	+	0.245863i	$0.0790713\pi$
$864$			5.43080i			0.184760i
$865$	−9.71167	−	1.03009i	−0.330207	−	0.0350242i
$866$	9.55931	+	16.5572i	0.324839	+	0.562637i
$867$	−7.16972	−	26.7578i	−0.243496	−	0.908741i
$868$	7.46043	+	7.46043i	0.253223	+	0.253223i
$869$	−22.5330	−	13.0094i	−0.764378	−	0.441314i
$870$	18.7010	+	23.1389i	0.634024	+	0.784481i
$871$	−49.6356			−1.68184
$872$	−0.0337012	−	0.00903020i	−0.00114127	−	0.000305801i
$873$	0.123715	+	0.461712i	0.00418713	+	0.0156266i
$874$	−23.3159	−	13.4614i	−0.788672	−	0.455340i
$875$	−18.2133	−	20.3445i	−0.615721	−	0.687770i
$876$	17.7316			0.599094
$877$	11.7255	−	3.14183i	0.395941	−	0.106092i	−0.0553544	−	0.998467i	$-0.517629\pi$
$877$	11.7255	−	3.14183i	0.395941	−	0.106092i	0.451295	+	0.892375i	$0.350962\pi$
$878$	−16.4888	+	4.41817i	−0.556471	+	0.149106i
$879$	−12.8739	−	22.2983i	−0.434227	−	0.752103i
$880$	3.59920	+	4.45330i	0.121329	+	0.150121i
$881$	34.5045			1.16248			0.581242	−	0.813730i	$-0.302567\pi$
$881$	34.5045			1.16248			0.581242	+	0.813730i	$0.302567\pi$
$882$	−0.229203	+	0.229203i	−0.00771766	+	0.00771766i
$883$	48.0149	+	12.8655i	1.61583	+	0.432960i	0.949772	−	0.312941i	$-0.101314\pi$
$883$	48.0149	+	12.8655i	1.61583	+	0.432960i	0.666056	+	0.745901i	$0.267981\pi$
$884$	1.61620	−	0.933111i	0.0543585	−	0.0313839i
$885$	2.76482	+	6.22583i	0.0929383	+	0.209279i
$886$	18.5535	+	10.7119i	0.623319	+	0.359873i
$887$	−10.4291	+	10.4291i	−0.350175	+	0.350175i	−0.860175	−	0.509999i	$-0.829646\pi$
$887$	−10.4291	+	10.4291i	−0.350175	+	0.350175i	0.509999	+	0.860175i	$0.329646\pi$
$888$	7.01889	−	1.88070i	0.235538	−	0.0631123i
$889$	−21.3163	+	36.9209i	−0.714925	+	1.23829i
$890$	−2.69106	−	6.05974i	−0.0902044	−	0.203123i
$891$	−10.1947	−	17.6577i	−0.341535	−	0.591556i
$892$	−18.3900	+	18.3900i	−0.615743	+	0.615743i
$893$	−10.7506	+	40.1217i	−0.359754	+	1.34262i
$894$	−5.57534	+	9.65678i	−0.186467	+	0.322971i
$895$	−2.29862	+	0.361822i	−0.0768344	+	0.0120944i
$896$	−1.22117	+	2.11512i	−0.0407963	+	0.0706612i
$897$	−55.2390	−	14.8012i	−1.84438	−	0.494199i
$898$	28.5733	+	7.65619i	0.953503	+	0.255490i
$899$	−35.0651			−1.16949
$900$	1.16167	+	1.04999i	0.0387224	+	0.0349996i
$901$	2.71262			0.0903706
$902$	−14.3837	+	14.3837i	−0.478925	+	0.478925i
$903$	−25.6296	+	5.68143i	−0.852900	+	0.189066i
$904$		−	17.0719i		−	0.567804i
$905$	−23.0086	+	3.62174i	−0.764832	+	0.120391i
$906$	8.55005	−	4.93637i	0.284056	−	0.164000i
$907$	−37.4213	−	37.4213i	−1.24255	−	1.24255i	−0.958938	−	0.283616i	$-0.908466\pi$
$907$	−37.4213	−	37.4213i	−1.24255	−	1.24255i	−0.283616	−	0.958938i	$-0.591534\pi$
$908$	0.838636	−	3.12983i	0.0278311	−	0.103867i
$909$	−0.0327860	+	0.0189290i	−0.00108744	+	0.000627836i
$910$	29.4532	−	13.0798i	0.976363	−	0.433591i
$911$		−	15.6975i		−	0.520082i	−0.965598	−	0.260041i	$-0.916264\pi$
$911$		−	15.6975i		−	0.520082i	0.965598	−	0.260041i	$-0.0837361\pi$
$912$	7.20993	−	1.93189i	0.238745	−	0.0639714i
$913$	−20.0200	−	5.36435i	−0.662566	−	0.177534i
$914$			31.0364i			1.02659i
$915$	44.2936	+	4.69810i	1.46430	+	0.155315i
$916$	10.0731	−	17.4471i	0.332824	−	0.576467i
$917$	35.0763	−	9.39866i	1.15832	−	0.310371i
$918$	−0.444524	−	1.65899i	−0.0146715	−	0.0547547i
$919$			6.80213i			0.224382i	0.993687	+	0.112191i	$0.0357868\pi$
$919$			6.80213i			0.224382i	−0.993687	+	0.112191i	$0.964213\pi$
$920$	4.74946	−	12.3376i	0.156585	−	0.406760i
$921$	−8.52101	−	4.91961i	−0.280777	−	0.162107i
$922$	−17.3786	−	4.65658i	−0.572334	−	0.153356i
$923$	6.07159	−	22.6595i	0.199849	−	0.745846i
$924$		−	10.2514i		−	0.337247i
$925$	10.1005	−	19.7303i	0.332101	−	0.648727i
$926$	8.72051	+	15.1044i	0.286574	+	0.496360i
$927$	−0.576704	+	2.15229i	−0.0189414	+	0.0706904i
$928$	−2.10086	−	7.84051i	−0.0689640	−	0.257377i
$929$	−19.5131	+	33.7978i	−0.640205	+	1.10887i	0.345181	+	0.938536i	$0.387817\pi$
$929$	−19.5131	+	33.7978i	−0.640205	+	1.10887i	−0.985387	+	0.170332i	$0.945516\pi$
$930$	15.6410	−	2.46202i	0.512888	−	0.0807328i
$931$	4.08175	+	2.35660i	0.133774	+	0.0772344i
$932$	−0.667099	−	2.48965i	−0.0218516	−	0.0815512i
$933$	16.6399	−	4.45865i	0.544766	−	0.145970i
$934$	−5.78355	+	3.33914i	−0.189244	+	0.109260i
$935$	−1.46398	−	1.06578i	−0.0478774	−	0.0348547i
$936$	−1.60046	+	0.924028i	−0.0523128	+	0.0302028i
$937$	−10.4248	−	38.9058i	−0.340563	−	1.27100i	−0.897711	−	0.440585i	$-0.854771\pi$
$937$	−10.4248	−	38.9058i	−0.340563	−	1.27100i	0.557148	−	0.830413i	$-0.311896\pi$
$938$	−14.5263	+	14.5263i	−0.474300	+	0.474300i
$939$	1.93768	+	1.11872i	0.0632339	+	0.0365081i
$940$	−20.2826	−	2.15132i	−0.661546	−	0.0701684i
$941$	−14.4004	−	24.9423i	−0.469441	−	0.813096i	0.529948	−	0.848030i	$-0.322211\pi$
$941$	−14.4004	−	24.9423i	−0.469441	−	0.813096i	−0.999390	+	0.0349338i	$0.988878\pi$
$942$	−4.38189	+	4.38189i	−0.142770	+	0.142770i
$943$	45.3652	+	12.1556i	1.47730	+	0.395840i
$944$		−	1.85857i		−	0.0604912i
$945$	−4.61175	−	29.2981i	−0.150020	−	0.953066i
$946$	9.02244	−	14.1618i	0.293345	−	0.460439i
$947$	−33.3912	−	33.3912i	−1.08507	−	1.08507i	−0.996028	−	0.0890396i	$-0.971620\pi$
$947$	−33.3912	−	33.3912i	−1.08507	−	1.08507i	−0.0890396	−	0.996028i	$-0.528380\pi$
$948$	−11.7769	−	11.7769i	−0.382497	−	0.382497i
$949$	31.9173	+	55.2823i	1.03608	+	1.79454i
$950$	10.3754	−	20.2673i	0.336622	−	0.657558i
$951$	−34.9449	+	20.1755i	−1.13317	+	0.654234i
$952$	0.199910	−	0.746076i	0.00647914	−	0.0241805i
$953$	52.2666	−	14.0048i	1.69308	−	0.453660i	0.721899	−	0.691999i	$-0.243270\pi$
$953$	52.2666	−	14.0048i	1.69308	−	0.453660i	0.971182	+	0.238339i	$0.0766030\pi$
$954$	−2.68622			−0.0869696
$955$	29.5388	+	11.3712i	0.955853	+	0.367962i
$956$	−2.68965	−	4.65862i	−0.0869896	−	0.150670i
$957$	24.0916	+	24.0916i	0.778770	+	0.778770i
$958$	−3.81793	+	14.2487i	−0.123352	+	0.460355i
$959$	−24.0109	−	13.8627i	−0.775353	−	0.447650i
$960$	1.48761	+	3.34980i	0.0480123	+	0.108114i
$961$	6.16921	−	10.6854i	0.199007	−	0.344690i
$962$	18.4977	+	18.4977i	0.596390	+	0.596390i
$963$	−0.846896	−	3.16066i	−0.0272908	−	0.101851i
$964$	−1.31064	+	2.27009i	−0.0422129	+	0.0731148i
$965$	55.7164	+	5.90969i	1.79357	+	0.190240i
$966$	−20.4979	+	11.8345i	−0.659508	+	0.380767i
$967$	−38.0800	−	38.0800i	−1.22457	−	1.22457i	−0.965990	−	0.258581i	$-0.916745\pi$
$967$	−38.0800	−	38.0800i	−1.22457	−	1.22457i	−0.258581	−	0.965990i	$-0.583255\pi$
$968$	−3.14152	−	3.14152i	−0.100972	−	0.100972i
$969$	−2.04434	+	1.18030i	−0.0656736	+	0.0379167i
$970$	2.14529	+	2.65438i	0.0688811	+	0.0852270i
$971$	19.3224	−	33.4673i	0.620085	−	1.07402i	−0.369385	−	0.929276i	$-0.620432\pi$
$971$	19.3224	−	33.4673i	0.620085	−	1.07402i	0.989470	−	0.144741i	$-0.0462350\pi$
$972$	0.838785	+	3.13039i	0.0269040	+	0.100407i
$973$	24.5419	+	24.5419i	0.786777	+	0.786777i
$974$	2.71846	−	4.70851i	0.0871050	−	0.150870i
$975$	10.1454	−	47.2874i	0.324914	−	1.51441i
$976$	−10.5244	−	6.07625i	−0.336877	−	0.194496i
$977$	−10.4662	+	39.0605i	−0.334844	+	1.24965i	0.569194	+	0.822203i	$0.307255\pi$
$977$	−10.4662	+	39.0605i	−0.334844	+	1.24965i	−0.904038	+	0.427452i	$0.859411\pi$
$978$	−24.7209	−	24.7209i	−0.790488	−	0.790488i
$979$	−3.79651	−	6.57575i	−0.121337	−	0.210162i
$980$	−0.831454	+	2.15986i	−0.0265598	+	0.0689942i
$981$	−0.0109267			−0.000348862
$982$	3.44053	−	0.921888i	0.109792	−	0.0294186i
$983$	6.68880	−	24.9630i	0.213340	−	0.796195i	−0.773405	−	0.633913i	$-0.781448\pi$
$983$	6.68880	−	24.9630i	0.213340	−	0.796195i	0.986744	−	0.162282i	$-0.0518855\pi$
$984$	−11.2765	+	6.51051i	−0.359483	+	0.207548i
$985$	−15.6064	−	11.3614i	−0.497260	−	0.362005i
$986$	1.28353	+	2.22313i	0.0408758	+	0.0707990i
$987$	25.8213	+	25.8213i	0.821900	+	0.821900i
$988$	19.0012	+	19.0012i	0.604508	+	0.604508i
$989$	−38.7324	−	1.69184i	−1.23162	−	0.0537975i
$990$	1.44973	+	1.05541i	0.0460756	+	0.0335430i
$991$			2.77410i			0.0881222i	0.999029	+	0.0440611i	$0.0140296\pi$
$991$			2.77410i			0.0881222i	−0.999029	+	0.0440611i	$0.985970\pi$
$992$	−4.17271	−	1.11807i	−0.132484	−	0.0354989i
$993$	−13.5957	+	13.5957i	−0.431445	+	0.431445i
$994$	−4.85459	−	8.40839i	−0.153978	−	0.266698i
$995$	−17.1802	−	21.2572i	−0.544650	−	0.673898i
$996$	−11.4898	−	6.63361i	−0.364067	−	0.210194i
$997$	−25.3279	+	25.3279i	−0.802143	+	0.802143i	−0.983430	−	0.181287i	$-0.941974\pi$
$997$	−25.3279	+	25.3279i	−0.802143	+	0.802143i	0.181287	+	0.983430i	$0.441974\pi$
$998$	−11.5290	−	43.0269i	−0.364945	−	1.36199i
$999$	20.8497	−	12.0376i	0.659655	−	0.380852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.l.a.7.3	✓	88
5.3	odd	4	inner	430.2.l.a.93.14	yes	88
43.37	odd	6	inner	430.2.l.a.37.14	yes	88
215.123	even	12	inner	430.2.l.a.123.3	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.l.a.7.3	✓	88	1.1	even	1	trivial
430.2.l.a.37.14	yes	88	43.37	odd	6	inner
430.2.l.a.93.14	yes	88	5.3	odd	4	inner
430.2.l.a.123.3	yes	88	215.123	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.424244 + 1.58330i) q^{3} -1.00000i q^{4} +(-1.40555 - 1.73909i) q^{5} +(-0.819577 - 1.41955i) q^{6} +(-0.632122 - 2.35911i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.271217 + 0.156587i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.424244 + 1.58330i) q^{3} -1.00000i q^{4} +(-1.40555 - 1.73909i) q^{5} +(-0.819577 - 1.41955i) q^{6} +(-0.632122 - 2.35911i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.271217 + 0.156587i) q^{9} +(2.22359 + 0.235851i) q^{10} +2.56071 q^{11} +(1.58330 + 0.424244i) q^{12} +(1.52730 + 5.69996i) q^{13} +(2.11512 + 1.22117i) q^{14} +(3.34980 - 1.48761i) q^{15} -1.00000 q^{16} +(0.305477 - 0.0818523i) q^{17} +(-0.302504 + 0.0810556i) q^{18} +(2.27687 + 3.94365i) q^{19} +(-1.73909 + 1.40555i) q^{20} +4.00336 q^{21} +(-1.81069 + 1.81069i) q^{22} +(5.71081 + 1.53021i) q^{23} +(-1.41955 + 0.819577i) q^{24} +(-1.04887 + 4.88875i) q^{25} +(-5.11045 - 2.95052i) q^{26} +(-3.84016 + 3.84016i) q^{27} +(-2.35911 + 0.632122i) q^{28} +(4.05854 - 7.02960i) q^{29} +(-1.31677 + 3.42056i) q^{30} +(-2.15995 - 3.74115i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.08637 + 4.05437i) q^{33} +(-0.158127 + 0.273883i) q^{34} +(-3.21423 + 4.41516i) q^{35} +(0.156587 - 0.271217i) q^{36} +(-4.28202 - 1.14736i) q^{37} +(-4.39857 - 1.17859i) q^{38} -9.67271 q^{39} +(0.235851 - 2.22359i) q^{40} +7.94375 q^{41} +(-2.83080 + 2.83080i) q^{42} +(-6.40203 + 1.41917i) q^{43} -2.56071i q^{44} +(-0.108889 - 0.691762i) q^{45} +(-5.12017 + 2.95613i) q^{46} +(6.44990 + 6.44990i) q^{47} +(0.424244 - 1.58330i) q^{48} +(0.896352 - 0.517509i) q^{49} +(-2.71520 - 4.19853i) q^{50} +0.518387i q^{51} +(5.69996 - 1.52730i) q^{52} +(8.28511 + 2.21999i) q^{53} -5.43080i q^{54} +(-3.59920 - 4.45330i) q^{55} +(1.22117 - 2.11512i) q^{56} +(-7.20993 + 1.93189i) q^{57} +(2.10086 + 7.84051i) q^{58} +1.85857i q^{59} +(-1.48761 - 3.34980i) q^{60} +(10.5244 + 6.07625i) q^{61} +(4.17271 + 1.11807i) q^{62} +(0.197965 - 0.738814i) q^{63} +1.00000i q^{64} +(7.76606 - 10.6677i) q^{65} +(-2.09870 - 3.63505i) q^{66} +(-2.17701 + 8.12473i) q^{67} +(-0.0818523 - 0.305477i) q^{68} +(-4.84556 + 8.39275i) q^{69} +(-0.849185 - 5.39479i) q^{70} +(-3.44277 - 1.98769i) q^{71} +(0.0810556 + 0.302504i) q^{72} +(10.4489 - 2.79978i) q^{73} +(3.83915 - 2.21654i) q^{74} +(-7.29538 - 3.73471i) q^{75} +(3.94365 - 2.27687i) q^{76} +(-1.61868 - 6.04099i) q^{77} +(6.83964 - 6.83964i) q^{78} +(-8.79950 - 5.08040i) q^{79} +(1.40555 + 1.73909i) q^{80} +(-3.98120 - 6.89564i) q^{81} +(-5.61708 + 5.61708i) q^{82} +(-7.81815 - 2.09487i) q^{83} -4.00336i q^{84} +(-0.571711 - 0.416205i) q^{85} +(3.52342 - 5.53042i) q^{86} +(9.40817 + 9.40817i) q^{87} +(1.81069 + 1.81069i) q^{88} +(-1.48260 - 2.56794i) q^{89} +(0.566146 + 0.412154i) q^{90} +(12.4814 - 7.20614i) q^{91} +(1.53021 - 5.71081i) q^{92} +(6.83971 - 1.83270i) q^{93} -9.12154 q^{94} +(3.65812 - 9.50266i) q^{95} +(0.819577 + 1.41955i) q^{96} +(1.07926 + 1.07926i) q^{97} +(-0.267882 + 0.999751i) q^{98} +(0.694508 + 0.400974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) \) 88 * q + 4 * q^6 + 12 * q^7	\( 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) \) 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

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