LMFDB - Embedded newform 416.2.bd.a.203.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(83,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 6]))

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

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

chi := DirichletCharacter("416.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			203.36
Character	$\chi$	$=$	416.203
Dual form			416.2.bd.a.291.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.719929 - 1.21725i) q^{2} +(-1.29743 - 3.13227i) q^{3} +(-0.963404 - 1.75267i) q^{4} +(1.53750 - 0.636854i) q^{5} +(-4.74682 - 0.675714i) q^{6} +1.05850i q^{7} +(-2.82702 - 0.0890924i) q^{8} +(-6.00647 + 6.00647i) q^{9} +(0.331680 - 2.33002i) q^{10} +(-1.30073 - 3.14023i) q^{11} +(-4.23989 + 5.29161i) q^{12} +(3.12718 - 1.79464i) q^{13} +(1.28847 + 0.762048i) q^{14} +(-3.98960 - 3.98960i) q^{15} +(-2.14370 + 3.37706i) q^{16} +5.62421 q^{17} +(2.98715 + 11.6356i) q^{18} +(-3.03250 - 1.25610i) q^{19} +(-2.59743 - 2.08119i) q^{20} +(3.31552 - 1.37333i) q^{21} +(-4.75888 - 0.677432i) q^{22} +(-1.21545 + 1.21545i) q^{23} +(3.38880 + 8.97059i) q^{24} +(-1.57721 + 1.57721i) q^{25} +(0.0668227 - 5.09858i) q^{26} +(17.2100 + 7.12863i) q^{27} +(1.85521 - 1.01977i) q^{28} +(5.31142 - 2.20006i) q^{29} +(-7.72857 + 1.98412i) q^{30} +(3.16004 - 3.16004i) q^{31} +(2.56742 + 5.04067i) q^{32} +(-8.14844 + 8.14844i) q^{33} +(4.04903 - 6.84608i) q^{34} +(0.674112 + 1.62745i) q^{35} +(16.3140 + 4.74070i) q^{36} +(-0.337788 - 0.815493i) q^{37} +(-3.71218 + 2.78701i) q^{38} +(-9.67859 - 7.46676i) q^{39} +(-4.40329 + 1.66342i) q^{40} -8.14697 q^{41} +(0.715246 - 5.02452i) q^{42} +(-1.82491 - 0.755903i) q^{43} +(-4.25066 + 5.30505i) q^{44} +(-5.40971 + 13.0602i) q^{45} +(0.604473 + 2.35455i) q^{46} +(3.07748 - 3.07748i) q^{47} +(13.3592 + 2.33317i) q^{48} +5.87957 q^{49} +(0.784380 + 3.05533i) q^{50} +(-7.29701 - 17.6165i) q^{51} +(-6.15815 - 3.75196i) q^{52} +(-12.4975 - 5.17664i) q^{53} +(21.0673 - 15.8168i) q^{54} +(-3.99973 - 3.99973i) q^{55} +(0.0943046 - 2.99242i) q^{56} +11.1283i q^{57} +(1.14582 - 8.04923i) q^{58} +(3.08537 - 1.27800i) q^{59} +(-3.14885 + 10.8360i) q^{60} +(-4.89167 + 2.02620i) q^{61} +(-1.57156 - 6.12157i) q^{62} +(-6.35787 - 6.35787i) q^{63} +(7.98413 + 0.503732i) q^{64} +(3.66513 - 4.75082i) q^{65} +(4.05241 + 15.7850i) q^{66} +(-0.628931 + 1.51837i) q^{67} +(-5.41839 - 9.85739i) q^{68} +(5.38409 + 2.23016i) q^{69} +(2.46633 + 0.351085i) q^{70} +9.72841 q^{71} +(17.5156 - 16.4453i) q^{72} -0.936219i q^{73} +(-1.23584 - 0.175924i) q^{74} +(6.98654 + 2.89392i) q^{75} +(0.719990 + 6.52511i) q^{76} +(3.32394 - 1.37682i) q^{77} +(-16.0568 + 6.40574i) q^{78} -15.7060 q^{79} +(-1.14525 + 6.55746i) q^{80} -37.6721i q^{81} +(-5.86524 + 9.91691i) q^{82} +(8.42036 + 3.48783i) q^{83} +(-5.60118 - 4.48794i) q^{84} +(8.64724 - 3.58180i) q^{85} +(-2.23393 + 1.67718i) q^{86} +(-13.7824 - 13.7824i) q^{87} +(3.39741 + 8.99339i) q^{88} +15.6464 q^{89} +(12.0029 + 15.9874i) q^{90} +(1.89963 + 3.31013i) q^{91} +(3.30126 + 0.959315i) q^{92} +(-13.9980 - 5.79818i) q^{93} +(-1.53050 - 5.96163i) q^{94} -5.46243 q^{95} +(12.4577 - 14.5818i) q^{96} +(-7.61074 - 7.61074i) q^{97} +(4.23287 - 7.15692i) q^{98} +(26.6745 + 11.0489i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24}+ \cdots - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.719929	−	1.21725i	0.509067	−	0.860727i
$2$	0.719929	−	1.21725i	0.509067	−	0.860727i
$3$	−1.29743	−	3.13227i	−0.749071	−	1.80842i	−0.564169	−	0.825660i	$-0.690803\pi$
$3$	−1.29743	−	3.13227i	−0.749071	−	1.80842i	−0.184902	−	0.982757i	$-0.559197\pi$
$4$	−0.963404	−	1.75267i	−0.481702	−	0.876335i
$5$	1.53750	−	0.636854i	0.687592	−	0.284810i	−0.0114048	−	0.999935i	$-0.503630\pi$
$5$	1.53750	−	0.636854i	0.687592	−	0.284810i	0.698996	+	0.715125i	$0.253630\pi$
$6$	−4.74682	−	0.675714i	−1.93788	−	0.275859i
$7$			1.05850i			0.400077i	0.979788	+	0.200038i	$0.0641067\pi$
$7$			1.05850i			0.400077i	−0.979788	+	0.200038i	$0.935893\pi$
$8$	−2.82702	−	0.0890924i	−0.999504	−	0.0314989i
$9$	−6.00647	+	6.00647i	−2.00216	+	2.00216i
$10$	0.331680	−	2.33002i	0.104887	−	0.736816i
$11$	−1.30073	−	3.14023i	−0.392183	−	0.946815i	−0.989464	−	0.144782i	$-0.953752\pi$
$11$	−1.30073	−	3.14023i	−0.392183	−	0.946815i	0.597280	−	0.802033i	$-0.296248\pi$
$12$	−4.23989	+	5.29161i	−1.22395	+	1.52755i
$13$	3.12718	−	1.79464i	0.867324	−	0.497743i
$13$	3.12718	−	1.79464i	0.867324	−	0.497743i
$14$	1.28847	+	0.762048i	0.344357	+	0.203666i
$15$	−3.98960	−	3.98960i	−1.03011	−	1.03011i
$16$	−2.14370	+	3.37706i	−0.535926	+	0.844265i
$17$	5.62421			1.36407			0.682036	−	0.731319i	$-0.261095\pi$
$17$	5.62421			1.36407			0.682036	+	0.731319i	$0.261095\pi$
$18$	2.98715	+	11.6356i	0.704079	+	2.74254i
$19$	−3.03250	−	1.25610i	−0.695703	−	0.288170i	0.00667081	−	0.999978i	$-0.497877\pi$
$19$	−3.03250	−	1.25610i	−0.695703	−	0.288170i	−0.702374	+	0.711808i	$0.747877\pi$
$20$	−2.59743	−	2.08119i	−0.580803	−	0.465367i
$21$	3.31552	−	1.37333i	0.723506	−	0.299686i
$22$	−4.75888	−	0.677432i	−1.01460	−	0.144429i
$23$	−1.21545	+	1.21545i	−0.253439	+	0.253439i	−0.822379	−	0.568940i	$-0.807354\pi$
$23$	−1.21545	+	1.21545i	−0.253439	+	0.253439i	0.568940	+	0.822379i	$0.307354\pi$
$24$	3.38880	+	8.97059i	0.691736	+	1.83111i
$25$	−1.57721	+	1.57721i	−0.315441	+	0.315441i
$26$	0.0668227	−	5.09858i	0.0131050	−	0.999914i
$27$	17.2100	+	7.12863i	3.31207	+	1.37191i
$28$	1.85521	−	1.01977i	0.350601	−	0.192718i
$29$	5.31142	−	2.20006i	0.986306	−	0.408541i	0.169548	−	0.985522i	$-0.445769\pi$
$29$	5.31142	−	2.20006i	0.986306	−	0.408541i	0.816758	+	0.576980i	$0.195769\pi$
$30$	−7.72857	+	1.98412i	−1.41104	+	0.362249i
$31$	3.16004	−	3.16004i	0.567560	−	0.567560i	−0.363884	−	0.931444i	$-0.618550\pi$
$31$	3.16004	−	3.16004i	0.567560	−	0.567560i	0.931444	+	0.363884i	$0.118550\pi$
$32$	2.56742	+	5.04067i	0.453860	+	0.891073i
$33$	−8.14844	+	8.14844i	−1.41846	+	1.41846i
$34$	4.04903	−	6.84608i	0.694404	−	1.17409i
$35$	0.674112	+	1.62745i	0.113946	+	0.275089i
$36$	16.3140	+	4.74070i	2.71900	+	0.790117i
$37$	−0.337788	−	0.815493i	−0.0555320	−	0.134066i	0.893678	−	0.448708i	$-0.148116\pi$
$37$	−0.337788	−	0.815493i	−0.0555320	−	0.134066i	−0.949211	+	0.314642i	$0.898116\pi$
$38$	−3.71218	+	2.78701i	−0.602195	+	0.452113i
$39$	−9.67859	−	7.46676i	−1.54981	−	1.19564i
$40$	−4.40329	+	1.66342i	−0.696222	+	0.263010i
$41$	−8.14697			−1.27234			−0.636171	−	0.771548i	$-0.719483\pi$
$41$	−8.14697			−1.27234			−0.636171	+	0.771548i	$0.719483\pi$
$42$	0.715246	−	5.02452i	0.110365	−	0.775301i
$43$	−1.82491	−	0.755903i	−0.278296	−	0.115274i	0.239170	−	0.970978i	$-0.423125\pi$
$43$	−1.82491	−	0.755903i	−0.278296	−	0.115274i	−0.517466	+	0.855704i	$0.673125\pi$
$44$	−4.25066	+	5.30505i	−0.640811	+	0.799767i
$45$	−5.40971	+	13.0602i	−0.806432	+	1.94690i
$46$	0.604473	+	2.35455i	0.0891246	+	0.347160i
$47$	3.07748	−	3.07748i	0.448897	−	0.448897i	−0.446091	−	0.894988i	$-0.647184\pi$
$47$	3.07748	−	3.07748i	0.448897	−	0.448897i	0.894988	+	0.446091i	$0.147184\pi$
$48$	13.3592	+	2.33317i	1.92823	+	0.336764i
$49$	5.87957			0.839939
$50$	0.784380	+	3.05533i	0.110928	+	0.432089i
$51$	−7.29701	−	17.6165i	−1.02179	−	2.46681i
$52$	−6.15815	−	3.75196i	−0.853982	−	0.520303i
$53$	−12.4975	−	5.17664i	−1.71667	−	0.711066i	−0.999906	−	0.0137457i	$-0.995624\pi$
$53$	−12.4975	−	5.17664i	−1.71667	−	0.711066i	−0.716760	−	0.697320i	$-0.754376\pi$
$54$	21.0673	−	15.8168i	2.86690	−	2.15240i
$55$	−3.99973	−	3.99973i	−0.539324	−	0.539324i
$56$	0.0943046	−	2.99242i	0.0126020	−	0.399878i
$57$			11.1283i			1.47398i
$58$	1.14582	−	8.04923i	0.150453	−	1.05692i
$59$	3.08537	−	1.27800i	0.401681	−	0.166382i	−0.172691	−	0.984976i	$-0.555246\pi$
$59$	3.08537	−	1.27800i	0.401681	−	0.166382i	0.574372	+	0.818594i	$0.305246\pi$
$60$	−3.14885	+	10.8360i	−0.406515	+	1.39893i
$61$	−4.89167	+	2.02620i	−0.626315	+	0.259428i	−0.673186	−	0.739473i	$-0.735075\pi$
$61$	−4.89167	+	2.02620i	−0.626315	+	0.259428i	0.0468717	+	0.998901i	$0.485075\pi$
$62$	−1.57156	−	6.12157i	−0.199588	−	0.777441i
$63$	−6.35787	−	6.35787i	−0.801016	−	0.801016i
$64$	7.98413	+	0.503732i	0.998016	+	0.0629666i
$65$	3.66513	−	4.75082i	0.454603	−	0.589267i
$66$	4.05241	+	15.7850i	0.498817	+	1.94300i
$67$	−0.628931	+	1.51837i	−0.0768361	+	0.185499i	−0.957630	−	0.288001i	$-0.907009\pi$
$67$	−0.628931	+	1.51837i	−0.0768361	+	0.185499i	0.880794	+	0.473500i	$0.157009\pi$
$68$	−5.41839	−	9.85739i	−0.657076	−	1.19538i
$69$	5.38409	+	2.23016i	0.648168	+	0.268480i
$70$	2.46633	+	0.351085i	0.294783	+	0.0419627i
$71$	9.72841			1.15455			0.577275	−	0.816550i	$-0.304116\pi$
$71$	9.72841			1.15455			0.577275	+	0.816550i	$0.304116\pi$
$72$	17.5156	−	16.4453i	2.06423	−	1.93810i
$73$		−	0.936219i		−	0.109576i	−0.998498	−	0.0547881i	$-0.982552\pi$
$73$		−	0.936219i		−	0.109576i	0.998498	−	0.0547881i	$-0.0174483\pi$
$74$	−1.23584	−	0.175924i	−0.143664	−	0.0204507i
$75$	6.98654	+	2.89392i	0.806737	+	0.334161i
$76$	0.719990	+	6.52511i	0.0825885	+	0.748481i
$77$	3.32394	−	1.37682i	0.378799	−	0.156903i
$78$	−16.0568	+	6.40574i	−1.81808	+	0.725307i
$79$	−15.7060			−1.76706			−0.883529	−	0.468376i	$-0.844839\pi$
$79$	−15.7060			−1.76706			−0.883529	+	0.468376i	$0.844839\pi$
$80$	−1.14525	+	6.55746i	−0.128043	+	0.733146i
$81$		−	37.6721i		−	4.18579i
$82$	−5.86524	+	9.91691i	−0.647707	+	1.09514i
$83$	8.42036	+	3.48783i	0.924254	+	0.382839i	0.793496	−	0.608576i	$-0.208259\pi$
$83$	8.42036	+	3.48783i	0.924254	+	0.382839i	0.130758	+	0.991414i	$0.458259\pi$
$84$	−5.60118	−	4.48794i	−0.611139	−	0.489674i
$85$	8.64724	−	3.58180i	0.937924	−	0.388501i
$86$	−2.23393	+	1.67718i	−0.240891	+	0.180855i
$87$	−13.7824	−	13.7824i	−1.47763	−	1.47763i
$88$	3.39741	+	8.99339i	0.362165	+	0.958698i
$89$	15.6464			1.65851			0.829255	−	0.558871i	$-0.188765\pi$
$89$	15.6464			1.65851			0.829255	+	0.558871i	$0.188765\pi$
$90$	12.0029	+	15.9874i	1.26522	+	1.68522i
$91$	1.89963	+	3.31013i	0.199136	+	0.346996i
$92$	3.30126	+	0.959315i	0.344180	+	0.100016i
$93$	−13.9980	−	5.79818i	−1.45153	−	0.601243i
$94$	−1.53050	−	5.96163i	−0.157859	−	0.614896i
$95$	−5.46243			−0.560433
$96$	12.4577	−	14.5818i	1.27146	−	1.48824i
$97$	−7.61074	−	7.61074i	−0.772753	−	0.772753i	0.205834	−	0.978587i	$-0.434009\pi$
$97$	−7.61074	−	7.61074i	−0.772753	−	0.772753i	−0.978587	+	0.205834i	$0.934009\pi$
$98$	4.23287	−	7.15692i	0.427585	−	0.722958i
$99$	26.6745	+	11.0489i	2.68088	+	1.11046i
$100$	4.28381	+	1.24483i	0.428381	+	0.124483i
$101$	5.80190	+	2.40323i	0.577311	+	0.239130i	0.652181	−	0.758063i	$-0.273854\pi$
$101$	5.80190	+	2.40323i	0.577311	+	0.239130i	−0.0748702	+	0.997193i	$0.523854\pi$
$102$	−26.6971	−	3.80036i	−2.64341	−	0.376292i
$103$	4.80414	+	4.80414i	0.473366	+	0.473366i	0.903002	−	0.429636i	$-0.141358\pi$
$103$	4.80414	+	4.80414i	0.473366	+	0.473366i	−0.429636	+	0.903002i	$0.641358\pi$
$104$	−9.00051	+	4.79488i	−0.882572	+	0.470176i
$105$	4.22300	−	4.22300i	0.412123	−	0.412123i
$106$	−15.2986	+	11.4858i	−1.48593	+	1.11560i
$107$	−1.55575	+	3.75590i	−0.150400	+	0.363097i	−0.981066	−	0.193674i	$-0.937960\pi$
$107$	−1.55575	+	3.75590i	−0.150400	+	0.363097i	0.830666	+	0.556770i	$0.187960\pi$
$108$	−4.08609	−	37.0313i	−0.393184	−	3.56334i
$109$	1.83304	−	4.42535i	0.175573	−	0.423872i	−0.811456	−	0.584414i	$-0.801324\pi$
$109$	1.83304	−	4.42535i	0.175573	−	0.423872i	0.987029	+	0.160542i	$0.0513244\pi$
$110$	−7.74821	+	1.98916i	−0.738763	+	0.189659i
$111$	−2.11609	+	2.11609i	−0.200850	+	0.200850i
$112$	−3.57463	−	2.26912i	−0.337771	−	0.214412i
$113$			0.602285i			0.0566582i	0.999599	+	0.0283291i	$0.00901864\pi$
$113$			0.602285i			0.0566582i	−0.999599	+	0.0283291i	$0.990981\pi$
$114$	13.5460	+	8.01159i	1.26870	+	0.750355i
$115$	−1.09469	+	2.64283i	−0.102081	+	0.246445i
$116$	−8.97303	−	7.18962i	−0.833125	−	0.667539i
$117$	−8.00389	+	29.5628i	−0.739960	+	2.73308i
$118$	0.665596	−	4.67574i	0.0612731	−	0.430437i
$119$			5.95325i			0.545734i
$120$	10.9232	+	11.6341i	0.997151	+	1.06205i
$121$	−0.390975	+	0.390975i	−0.0355432	+	0.0355432i
$122$	−1.05527	+	7.41312i	−0.0955392	+	0.671152i
$123$	10.5701	+	25.5185i	0.953075	+	2.30093i
$124$	−8.58291	−	2.49411i	−0.770768	−	0.223978i
$125$	−4.60478	+	11.1169i	−0.411864	+	0.994327i
$126$	−12.3163	+	3.16191i	−1.09723	+	0.281686i
$127$	4.22739			0.375120			0.187560	−	0.982253i	$-0.439942\pi$
$127$	4.22739			0.375120			0.187560	+	0.982253i	$0.439942\pi$
$128$	6.36117	−	9.35604i	0.562254	−	0.826965i
$129$			6.69685i			0.589624i
$130$	−3.14431	−	7.88163i	−0.275774	−	0.691265i
$131$	−4.75922	−	11.4898i	−0.415815	−	1.00387i	−0.983547	−	0.180653i	$-0.942179\pi$
$131$	−4.75922	−	11.4898i	−0.415815	−	1.00387i	0.567732	−	0.823214i	$-0.307821\pi$
$132$	22.1318	+	6.43129i	1.92632	+	0.559772i
$133$	1.32959	−	3.20991i	0.115290	−	0.278335i
$134$	1.39546	+	1.85869i	0.120549	+	0.160566i
$135$	31.0004			2.66809
$136$	−15.8998	−	0.501074i	−1.36340	−	0.0429668i
$137$			2.95422i			0.252396i	0.992005	+	0.126198i	$0.0402775\pi$
$137$			2.95422i			0.252396i	−0.992005	+	0.126198i	$0.959723\pi$
$138$	6.59083	−	4.94823i	0.561049	−	0.421222i
$139$	−2.21789	+	5.35445i	−0.188119	+	0.454159i	−0.989597	−	0.143865i	$-0.954047\pi$
$139$	−2.21789	+	5.35445i	−0.188119	+	0.454159i	0.801479	+	0.598023i	$0.204047\pi$
$140$	2.20294	−	2.74939i	0.186183	−	0.232366i
$141$	−13.6323	−	5.64668i	−1.14805	−	0.475537i
$142$	7.00376	−	11.8419i	0.587743	−	0.993752i
$143$	−9.70318	−	7.48574i	−0.811421	−	0.625989i
$144$	−7.40811	−	33.1603i	−0.617343	−	2.76336i
$145$	6.76520	−	6.76520i	0.561819	−	0.561819i
$146$	−1.13961	−	0.674011i	−0.0943151	−	0.0557815i
$147$	−7.62832	−	18.4164i	−0.629173	−	1.51896i
$148$	−1.10386	+	1.37768i	−0.0907370	+	0.113245i
$149$	6.89297	+	16.6411i	0.564694	+	1.36329i	0.905975	+	0.423331i	$0.139139\pi$
$149$	6.89297	+	16.6411i	0.564694	+	1.36329i	−0.341281	+	0.939961i	$0.610861\pi$
$150$	8.55245	−	6.42097i	0.698304	−	0.524270i
$151$	15.1635			1.23399			0.616994	−	0.786968i	$-0.288350\pi$
$151$	15.1635			1.23399			0.616994	+	0.786968i	$0.288350\pi$
$152$	8.46104	+	3.82120i	0.686281	+	0.309941i
$153$	−33.7817	+	33.7817i	−2.73109	+	2.73109i
$154$	0.717064	−	5.03729i	0.0577826	−	0.405917i
$155$	2.84608	−	6.87106i	0.228603	−	0.551897i
$156$	−3.76238	+	24.1569i	−0.301232	+	1.93410i
$157$	2.46803	−	1.02229i	0.196970	−	0.0815877i	−0.282018	−	0.959409i	$-0.591004\pi$
$157$	2.46803	−	1.02229i	0.196970	−	0.0815877i	0.478988	+	0.877821i	$0.341004\pi$
$158$	−11.3072	+	19.1181i	−0.899551	+	1.52095i
$159$			45.8619i			3.63708i
$160$	7.15758	+	6.11497i	0.565856	+	0.483431i
$161$	−1.28656	−	1.28656i	−0.101395	−	0.101395i
$162$	−45.8564	−	27.1212i	−3.60282	−	2.13084i
$163$	−2.26184	−	0.936885i	−0.177161	−	0.0733825i	0.292340	−	0.956314i	$-0.405566\pi$
$163$	−2.26184	−	0.936885i	−0.177161	−	0.0733825i	−0.469501	+	0.882932i	$0.655566\pi$
$164$	7.84883	+	14.2789i	0.612890	+	1.11500i
$165$	−7.33888	+	17.7176i	−0.571331	+	1.37931i
$166$	10.3076	−	7.73871i	0.800027	−	0.600640i
$167$			11.7824i			0.911750i	0.890044	+	0.455875i	$0.150674\pi$
$167$			11.7824i			0.911750i	−0.890044	+	0.455875i	$0.849326\pi$
$168$	−9.49540	+	3.58706i	−0.732586	+	0.276747i
$169$	6.55855	−	11.2243i	0.504503	−	0.863410i
$170$	1.86544	−	13.1045i	0.143073	−	1.00507i
$171$	25.7594	−	10.6699i	1.96987	−	0.815946i
$172$	0.433279	+	3.92671i	0.0330372	+	0.299409i
$173$	17.4177	−	7.21464i	1.32424	−	0.548519i	0.395234	−	0.918580i	$-0.370663\pi$
$173$	17.4177	−	7.21464i	1.32424	−	0.548519i	0.929007	+	0.370062i	$0.120663\pi$
$174$	−26.6990	+	6.85429i	−2.02404	+	0.519622i
$175$	−1.66948	−	1.66948i	−0.126201	−	0.126201i
$176$	13.3931	+	2.33909i	1.00954	+	0.176316i
$177$	−8.00608	−	8.00608i	−0.601774	−	0.601774i
$178$	11.2643	−	19.0455i	0.844292	−	1.42752i
$179$	6.23779	+	15.0593i	0.466234	+	1.12559i	0.965794	+	0.259309i	$0.0834949\pi$
$179$	6.23779	+	15.0593i	0.466234	+	1.12559i	−0.499560	+	0.866279i	$0.666505\pi$
$180$	28.1020	−	3.10081i	2.09460	−	0.231121i
$181$	3.92202	−	9.46859i	0.291521	−	0.703795i	−0.708477	−	0.705734i	$-0.750617\pi$
$181$	3.92202	−	9.46859i	0.291521	−	0.703795i	0.999998	+	0.00193915i	$0.000617251\pi$
$182$	5.39687	+	0.0707321i	0.400042	+	0.00524301i
$183$	12.6932	+	12.6932i	0.938308	+	0.938308i
$184$	3.54440	−	3.32783i	0.261297	−	0.245331i
$185$	−1.03870	−	1.03870i	−0.0763667	−	0.0763667i
$186$	−17.1354	+	12.8649i	−1.25643	+	0.943297i
$187$	−7.31556	−	17.6613i	−0.534966	−	1.29152i
$188$	−8.35866	−	2.42895i	−0.609618	−	0.177149i
$189$	−7.54568	+	18.2169i	−0.548868	+	1.32508i
$190$	−3.93256	+	6.64915i	−0.285298	+	0.482380i
$191$		−	12.2967i		−	0.889757i	−0.895591	−	0.444879i	$-0.853247\pi$
$191$		−	12.2967i		−	0.889757i	0.895591	−	0.444879i	$-0.146753\pi$
$192$	−8.78101	−	25.6620i	−0.633714	−	1.85199i
$193$	8.81001	−	8.81001i	0.634158	−	0.634158i	−0.314950	−	0.949108i	$-0.601988\pi$
$193$	8.81001	−	8.81001i	0.634158	−	0.634158i	0.949108	+	0.314950i	$0.101988\pi$
$194$	−14.7434	+	3.78499i	−1.05851	+	0.271747i
$195$	−19.6361	−	5.31631i	−1.40617	−	0.380709i
$196$	−5.66440	−	10.3049i	−0.404600	−	0.736068i
$197$	−5.98004	+	2.47701i	−0.426060	+	0.176480i	−0.585401	−	0.810744i	$-0.699063\pi$
$197$	−5.98004	+	2.47701i	−0.426060	+	0.176480i	0.159341	+	0.987224i	$0.449063\pi$
$198$	32.6530	−	24.5151i	2.32055	−	1.74221i
$199$	−6.94839	−	6.94839i	−0.492558	−	0.492558i	0.416553	−	0.909111i	$-0.363238\pi$
$199$	−6.94839	−	6.94839i	−0.492558	−	0.492558i	−0.909111	+	0.416553i	$0.863238\pi$
$200$	4.59931	−	4.31828i	0.325221	−	0.305349i
$201$	5.57195			0.393015
$202$	7.10229	−	5.33222i	0.499715	−	0.375174i
$203$	2.32877	+	5.62216i	0.163448	+	0.394598i
$204$	−23.8460	+	29.7611i	−1.66956	+	2.08369i
$205$	−12.5260	+	5.18843i	−0.874852	+	0.362376i
$206$	9.30648	−	2.38921i	0.648413	−	0.166464i
$207$		−	14.6012i		−	1.01485i
$208$	−0.643154	+	14.4079i	−0.0445947	+	0.999005i
$209$			11.1566i			0.771717i
$210$	−2.10020	−	8.18072i	−0.144927	−	0.564523i
$211$	20.0757	−	8.31562i	1.38207	−	0.572471i	0.437033	−	0.899445i	$-0.356029\pi$
$211$	20.0757	−	8.31562i	1.38207	−	0.572471i	0.945033	+	0.326975i	$0.106029\pi$
$212$	2.96722	+	26.8912i	0.203789	+	1.84690i
$213$	−12.6219	−	30.4720i	−0.864839	−	2.08791i
$214$	3.45185	+	4.59772i	0.235964	+	0.314294i
$215$	−3.28720			−0.224186
$216$	−48.0181	−	21.6861i	−3.26722	−	1.47555i
$217$	3.34492	+	3.34492i	0.227068	+	0.227068i
$218$	−4.06711	−	5.41721i	−0.275459	−	0.366900i
$219$	−2.93249	+	1.21468i	−0.198159	+	0.0820802i
$220$	−3.15685	+	10.8636i	−0.212835	+	0.732422i
$221$	17.5879	−	10.0934i	1.18309	−	0.678958i
$222$	1.05238	+	4.09924i	0.0706310	+	0.275123i
$223$	1.25046	−	1.25046i	0.0837368	−	0.0837368i	−0.663998	−	0.747735i	$-0.731142\pi$
$223$	1.25046	−	1.25046i	0.0837368	−	0.0837368i	0.747735	+	0.663998i	$0.231142\pi$
$224$	−5.33557	+	2.71762i	−0.356498	+	0.181579i
$225$		−	18.9469i		−	1.26313i
$226$	0.733133	+	0.433603i	0.0487673	+	0.0288428i
$227$	0.0871923	−	0.210501i	0.00578716	−	0.0139714i	−0.920960	−	0.389658i	$-0.872593\pi$
$227$	0.0871923	−	0.210501i	0.00578716	−	0.0139714i	0.926747	+	0.375687i	$0.122593\pi$
$228$	19.5043	−	10.7211i	1.29170	−	0.710020i
$229$	−4.38426	−	10.5845i	−0.289720	−	0.699445i	0.710270	−	0.703929i	$-0.248573\pi$
$229$	−4.38426	−	10.5845i	−0.289720	−	0.699445i	−0.999990	+	0.00448378i	$0.998573\pi$
$230$	2.42888	+	3.23517i	0.160156	+	0.213321i
$231$	−8.62516	−	8.62516i	−0.567494	−	0.567494i
$232$	−15.2115	+	5.74642i	−0.998685	+	0.377271i
$233$	15.0215	+	15.0215i	0.984094	+	0.984094i	0.999875	−	0.0157814i	$-0.00502359\pi$
$233$	15.0215	+	15.0215i	0.984094	+	0.984094i	−0.0157814	+	0.999875i	$0.505024\pi$
$234$	30.2231	+	31.0258i	1.97575	+	2.02822i
$235$	2.77172	−	6.69153i	0.180807	−	0.436508i
$236$	−5.21237	−	4.17640i	−0.339296	−	0.271860i
$237$	20.3774	+	49.1953i	1.32365	+	3.19558i
$238$	7.24661	+	4.28592i	0.469728	+	0.277815i
$239$	15.1986	+	15.1986i	0.983117	+	0.983117i	0.999860	−	0.0167427i	$-0.00532962\pi$
$239$	15.1986	+	15.1986i	0.983117	+	0.983117i	−0.0167427	+	0.999860i	$0.505330\pi$
$240$	22.0256	−	4.92059i	1.42175	−	0.317623i
$241$	2.07099	+	2.07099i	0.133404	+	0.133404i	0.770656	−	0.637252i	$-0.219929\pi$
$241$	2.07099	+	2.07099i	0.133404	+	0.133404i	−0.637252	+	0.770656i	$0.719929\pi$
$242$	0.194441	+	0.757389i	0.0124991	+	0.0486868i
$243$	−66.3689	+	27.4909i	−4.25757	+	1.76354i
$244$	8.26392	+	6.62144i	0.529043	+	0.423894i
$245$	9.03985	−	3.74443i	0.577535	−	0.239223i
$246$	38.6722	+	5.50503i	2.46565	+	0.350988i
$247$	−11.7374	+	1.51418i	−0.746835	+	0.0963449i
$248$	−9.21505	+	8.65198i	−0.585156	+	0.549401i
$249$		−	30.9000i		−	1.95821i
$250$	10.2170	+	13.6086i	0.646178	+	0.860681i
$251$	−10.8472	+	26.1875i	−0.684670	+	1.65294i	0.0705829	+	0.997506i	$0.477514\pi$
$251$	−10.8472	+	26.1875i	−0.684670	+	1.65294i	−0.755253	+	0.655434i	$0.772486\pi$
$252$	−5.01805	+	17.2685i	−0.316107	+	1.08781i
$253$	5.39777	+	2.23583i	0.339355	+	0.140565i
$254$	3.04342	−	5.14579i	0.190961	−	0.322876i
$255$	−22.4383	−	22.4383i	−1.40514	−	1.40514i
$256$	−6.80906	−	14.4788i	−0.425566	−	0.904927i
$257$			21.7103i			1.35425i	0.735867	+	0.677126i	$0.236775\pi$
$257$			21.7103i			1.35425i	−0.735867	+	0.677126i	$0.763225\pi$
$258$	8.15175	+	4.82125i	0.507506	+	0.300158i
$259$	0.863202	−	0.357550i	0.0536368	−	0.0222171i
$260$	−11.8576	−	1.84680i	−0.735378	−	0.114534i
$261$	−18.6883	+	45.1175i	−1.15678	+	2.79270i
$262$	−17.4123	−	2.47865i	−1.07573	−	0.153132i
$263$	−15.3249	+	15.3249i	−0.944976	+	0.944976i	−0.998563	−	0.0535869i	$-0.982935\pi$
$263$	−15.3249	+	15.3249i	−0.944976	+	0.944976i	0.0535869	+	0.998563i	$0.482935\pi$
$264$	23.7618	−	22.3099i	1.46244	−	1.37308i
$265$	−22.5117			−1.38288
$266$	−2.95006	−	3.92935i	−0.180880	−	0.240924i
$267$	−20.3000	−	49.0086i	−1.24234	−	2.99928i
$268$	3.26712	−	0.360499i	0.199571	−	0.0220210i
$269$	−3.13713	−	7.57371i	−0.191274	−	0.461777i	0.798926	−	0.601429i	$-0.205402\pi$
$269$	−3.13713	−	7.57371i	−0.191274	−	0.461777i	−0.990201	+	0.139652i	$0.955402\pi$
$270$	22.3181	−	37.7352i	1.35823	−	2.29649i
$271$	−20.9153	+	20.9153i	−1.27051	+	1.27051i	−0.324696	+	0.945818i	$0.605262\pi$
$271$	−20.9153	+	20.9153i	−1.27051	+	1.27051i	−0.945818	+	0.324696i	$0.894738\pi$
$272$	−12.0566	+	18.9933i	−0.731042	+	1.15164i
$273$	7.90360	−	10.2448i	0.478347	−	0.620045i
$274$	3.59603	+	2.12683i	0.217244	+	0.128486i
$275$	7.00430	+	2.90128i	0.422375	+	0.174953i
$276$	−1.27832	−	11.5851i	−0.0769455	−	0.697340i
$277$	0.629068	−	1.51870i	0.0377970	−	0.0912501i	−0.903854	−	0.427842i	$-0.859274\pi$
$277$	0.629068	−	1.51870i	0.0377970	−	0.0912501i	0.941651	+	0.336591i	$0.109274\pi$
$278$	4.92100	+	6.55455i	0.295142	+	0.393116i
$279$			37.9614i			2.27269i
$280$	−1.76074	−	4.66090i	−0.105224	−	0.278542i
$281$	24.6758			1.47203			0.736016	−	0.676964i	$-0.236705\pi$
$281$	24.6758			1.47203			0.736016	+	0.676964i	$0.236705\pi$
$282$	−16.6877	+	12.5287i	−0.993740	+	0.746075i
$283$	3.43840	−	8.30103i	0.204392	−	0.493445i	−0.788131	−	0.615508i	$-0.788951\pi$
$283$	3.43840	−	8.30103i	0.204392	−	0.493445i	0.992522	+	0.122063i	$0.0389509\pi$
$284$	−9.37239	−	17.0507i	−0.556149	−	1.01177i
$285$	7.08711	+	17.1098i	0.419804	+	1.01350i
$286$	−16.0976	+	6.42202i	−0.951873	+	0.379742i
$287$		−	8.62360i		−	0.509035i
$288$	−45.6978	−	14.8555i	−2.69277	−	0.875370i
$289$	14.6318			0.860692
$290$	−3.36449	−	13.1054i	−0.197570	−	0.769577i
$291$	−13.9645	+	33.7133i	−0.818613	+	1.97631i
$292$	−1.64088	+	0.901957i	−0.0960254	+	0.0527830i
$293$	−4.84160	−	11.6887i	−0.282849	−	0.682859i	0.717050	−	0.697021i	$-0.245492\pi$
$293$	−4.84160	−	11.6887i	−0.282849	−	0.682859i	−0.999900	+	0.0141626i	$0.995492\pi$
$294$	−27.9092	−	3.97291i	−1.62770	−	0.231705i
$295$	3.92986	−	3.92986i	0.228805	−	0.228805i
$296$	0.882281	+	2.33551i	0.0512815	+	0.135749i
$297$		−	63.3158i		−	3.67396i
$298$	25.2189	+	3.58993i	1.46089	+	0.207959i
$299$	−1.61965	+	5.98224i	−0.0936665	+	0.345962i
$300$	−1.65878	−	15.0331i	−0.0957696	−	0.867938i
$301$	0.800126	−	1.93168i	0.0461185	−	0.111340i
$302$	10.9166	−	18.4578i	0.628182	−	1.06213i
$303$		−	21.2911i		−	1.22314i
$304$	10.7427	−	7.54822i	0.616137	−	0.432920i
$305$	−6.23056	+	6.23056i	−0.356761	+	0.356761i
$306$	16.8004	+	65.4412i	0.960415	+	3.74102i
$307$	−3.37624	+	8.15097i	−0.192692	+	0.465200i	−0.990466	−	0.137756i	$-0.956011\pi$
$307$	−3.37624	+	8.15097i	−0.192692	+	0.465200i	0.797774	+	0.602957i	$0.206011\pi$
$308$	−5.61542	−	4.49934i	−0.319968	−	0.256374i
$309$	8.81483	−	21.2809i	0.501458	−	1.21063i
$310$	−6.31483	−	8.41108i	−0.358658	−	0.477717i
$311$	−6.71893	+	6.71893i	−0.380996	+	0.380996i	−0.871461	−	0.490465i	$-0.836827\pi$
$311$	−6.71893	+	6.71893i	−0.380996	+	0.380996i	0.490465	+	0.871461i	$0.336827\pi$
$312$	26.6964	+	21.9710i	1.51138	+	1.24386i
$313$	−7.78012	−	7.78012i	−0.439758	−	0.439758i	0.452172	−	0.891931i	$-0.350649\pi$
$313$	−7.78012	−	7.78012i	−0.439758	−	0.439758i	−0.891931	+	0.452172i	$0.850649\pi$
$314$	0.532420	−	3.74019i	0.0300462	−	0.211071i
$315$	−13.8243	−	5.72620i	−0.778910	−	0.322635i
$316$	15.1312	+	27.5274i	0.851196	+	1.54854i
$317$	−5.99926	−	2.48498i	−0.336952	−	0.139570i	0.207791	−	0.978173i	$-0.433373\pi$
$317$	−5.99926	−	2.48498i	−0.336952	−	0.139570i	−0.544743	+	0.838603i	$0.683373\pi$
$318$	55.8255	+	33.0173i	3.13054	+	1.85152i
$319$	−13.8174	−	13.8174i	−0.773626	−	0.773626i
$320$	12.5964	−	4.31023i	0.704161	−	0.240949i
$321$	13.7830			0.769290
$322$	−2.49230	+	0.639836i	−0.138891	+	0.0356567i
$323$	−17.0554	−	7.06459i	−0.948989	−	0.393084i
$324$	−66.0267	+	36.2934i	−3.66815	+	2.01630i
$325$	−2.10170	+	7.76272i	−0.116581	+	0.430598i
$326$	−2.76879	+	2.07874i	−0.153349	+	0.115131i
$327$	−16.2396			−0.898053
$328$	23.0317	+	0.725833i	1.27171	+	0.0400774i
$329$	3.25752	+	3.25752i	0.179593	+	0.179593i
$330$	16.2833	+	21.6887i	0.896368	+	1.19392i
$331$	22.9688	−	9.51401i	1.26248	−	0.522937i	0.351812	−	0.936071i	$-0.385566\pi$
$331$	22.9688	−	9.51401i	1.26248	−	0.522937i	0.910670	+	0.413134i	$0.135566\pi$
$332$	−1.99920	−	18.1183i	−0.109720	−	0.994371i
$333$	6.92715	+	2.86932i	0.379605	+	0.157238i
$334$	14.3422	+	8.48250i	0.784768	+	0.464142i
$335$			2.73504i			0.149431i
$336$	−2.46967	+	14.1407i	−0.134731	+	0.771440i
$337$	−6.94575			−0.378359			−0.189180	−	0.981943i	$-0.560583\pi$
$337$	−6.94575			−0.378359			−0.189180	+	0.981943i	$0.560583\pi$
$338$	−8.94114	−	16.0641i	−0.486334	−	0.873773i
$339$	1.88652	−	0.781422i	0.102462	−	0.0424410i
$340$	−14.6085	−	11.7050i	−0.792257	−	0.634794i
$341$	−14.0336	−	5.81291i	−0.759962	−	0.314787i
$342$	5.55699	−	39.0372i	0.300487	−	2.11089i
$343$			13.6331i			0.736117i
$344$	5.09172	+	2.29954i	0.274527	+	0.123983i
$345$	9.69833			0.522141
$346$	3.75746	−	26.3957i	0.202002	−	1.41904i
$347$	9.32941	+	3.86437i	0.500829	+	0.207450i	0.618773	−	0.785570i	$-0.287630\pi$
$347$	9.32941	+	3.86437i	0.500829	+	0.207450i	−0.117944	+	0.993020i	$0.537630\pi$
$348$	−10.8780	+	37.4340i	−0.583120	+	2.00667i
$349$	−6.30699	+	15.2264i	−0.337606	+	0.815052i	0.660339	+	0.750968i	$0.270413\pi$
$349$	−6.30699	+	15.2264i	−0.337606	+	0.815052i	−0.997944	+	0.0640841i	$0.979587\pi$
$350$	−3.23408	+	0.830270i	−0.172869	+	0.0443798i
$351$	66.6123	−	8.59326i	3.55550	−	0.458674i
$352$	12.4894	−	14.6188i	0.665685	−	0.779185i
$353$	19.4964	+	19.4964i	1.03769	+	1.03769i	0.999261	+	0.0384250i	$0.0122341\pi$
$353$	19.4964	+	19.4964i	1.03769	+	1.03769i	0.0384250	+	0.999261i	$0.487766\pi$
$354$	−15.5092	+	3.98161i	−0.824307	+	0.211620i
$355$	14.9574	−	6.19558i	0.793859	−	0.328827i
$356$	−15.0738	−	27.4229i	−0.798908	−	1.45341i
$357$	18.6472	−	7.72392i	0.986914	−	0.408793i
$358$	22.8218	+	3.24871i	1.20617	+	0.171699i
$359$		−	15.5873i		−	0.822664i	−0.911486	−	0.411332i	$-0.865064\pi$
$359$		−	15.5873i		−	0.822664i	0.911486	−	0.411332i	$-0.134936\pi$
$360$	16.4569	−	36.4395i	0.867357	−	1.92053i
$361$	−5.81677	−	5.81677i	−0.306146	−	0.306146i
$362$	−8.70209	−	11.5908i	−0.457372	−	0.609199i
$363$	1.73190	+	0.717376i	0.0909012	+	0.0376525i
$364$	3.97146	−	6.51843i	0.208161	−	0.341658i
$365$	−0.596235	−	1.43944i	−0.0312083	−	0.0753436i
$366$	24.5890	−	6.31261i	1.28529	−	0.329966i
$367$	−18.7960			−0.981143			−0.490571	−	0.871401i	$-0.663212\pi$
$367$	−18.7960			−0.981143			−0.490571	+	0.871401i	$0.663212\pi$
$368$	−1.49909	−	6.71023i	−0.0781452	−	0.349795i
$369$	48.9345	−	48.9345i	2.54743	−	2.54743i
$370$	−2.01215	+	0.516569i	−0.104607	+	0.0268551i
$371$	5.47949	−	13.2287i	0.284481	−	0.686798i
$372$	3.32348	+	30.1199i	0.172314	+	1.56165i
$373$	−12.6537	−	5.24133i	−0.655183	−	0.271386i	0.0302271	−	0.999543i	$-0.490377\pi$
$373$	−12.6537	−	5.24133i	−0.655183	−	0.271386i	−0.685410	+	0.728157i	$0.740377\pi$
$374$	−26.7649	−	3.81002i	−1.38398	−	0.197011i
$375$	40.7955			2.10667
$376$	−8.97429	+	8.42593i	−0.462814	+	0.434534i
$377$	12.6615	−	16.4121i	0.652099	−	0.845265i
$378$	16.7422	+	22.2999i	0.861125	+	1.14698i
$379$	2.45131	+	5.91799i	0.125915	+	0.303987i	0.974249	−	0.225476i	$-0.0723936\pi$
$379$	2.45131	+	5.91799i	0.125915	+	0.303987i	−0.848333	+	0.529462i	$0.822394\pi$
$380$	5.26253	+	9.57383i	0.269962	+	0.491127i
$381$	−5.48473	−	13.2413i	−0.280991	−	0.678373i
$382$	−14.9682	−	8.85274i	−0.765838	−	0.452946i
$383$	22.5175	−	22.5175i	1.15059	−	1.15059i	0.164154	−	0.986435i	$-0.447511\pi$
$383$	22.5175	−	22.5175i	1.15059	−	1.15059i	0.986435	−	0.164154i	$-0.0524893\pi$
$384$	−37.5588	−	7.78611i	−1.91666	−	0.397334i
$385$	4.23373	−	4.23373i	0.215771	−	0.215771i
$386$	−4.38142	−	17.0666i	−0.223008	−	0.868666i
$387$	15.5016	−	6.42097i	0.787990	−	0.326396i
$388$	−6.00689	+	20.6713i	−0.304954	+	1.04943i
$389$	8.36014	+	3.46288i	0.423876	+	0.175575i	0.584416	−	0.811454i	$-0.301324\pi$
$389$	8.36014	+	3.46288i	0.423876	+	0.175575i	−0.160540	+	0.987029i	$0.551324\pi$
$390$	−20.6079	+	20.0747i	−1.04352	+	1.01652i
$391$	−6.83597	+	6.83597i	−0.345710	+	0.345710i
$392$	−16.6217	−	0.523825i	−0.839522	−	0.0264571i
$393$	−29.8143	+	29.8143i	−1.50393	+	1.50393i
$394$	−1.29005	+	9.06248i	−0.0649920	+	0.456561i
$395$	−24.1479	+	10.0024i	−1.21501	+	0.503275i
$396$	−6.33317	−	57.3961i	−0.318254	−	2.88426i
$397$	−13.4091	−	5.55421i	−0.672981	−	0.278758i	0.0199082	−	0.999802i	$-0.493663\pi$
$397$	−13.4091	−	5.55421i	−0.672981	−	0.278758i	−0.692889	+	0.721044i	$0.743663\pi$
$398$	−13.4603	+	3.45559i	−0.674703	+	0.173213i
$399$	−11.7794			−0.589706
$400$	−1.94526	−	8.70738i	−0.0972628	−	0.435369i
$401$	17.6852	+	17.6852i	0.883155	+	0.883155i	0.993854	−	0.110699i	$-0.0353090\pi$
$401$	17.6852	+	17.6852i	0.883155	+	0.883155i	−0.110699	+	0.993854i	$0.535309\pi$
$402$	4.01141	−	6.78246i	0.200071	−	0.338278i
$403$	4.21090	−	15.5532i	0.209760	−	0.774758i
$404$	−1.37751	−	12.4841i	−0.0685339	−	0.621107i
$405$	−23.9916	−	57.9209i	−1.19215	−	2.87811i
$406$	8.52014	+	1.21285i	0.422847	+	0.0601928i
$407$	−2.12146	+	2.12146i	−0.105157	+	0.105157i
$408$	19.0593	+	50.4525i	0.943577	+	2.49777i
$409$		−	10.7729i		−	0.532684i	−0.963879	−	0.266342i	$-0.914185\pi$
$409$		−	10.7729i		−	0.532684i	0.963879	−	0.266342i	$-0.0858150\pi$
$410$	−2.70219	+	18.9826i	−0.133452	+	0.937482i
$411$	9.25342	−	3.83289i	0.456437	−	0.189063i
$412$	3.79174	−	13.0484i	0.186806	−	0.642848i
$413$	1.35277	+	3.26587i	0.0665654	+	0.160703i
$414$	−17.7733	−	10.5118i	−0.873510	−	0.516627i
$415$	15.1675			0.744546
$416$	17.0750	+	11.1555i	0.837169	+	0.546944i
$417$	19.6491			0.962222
$418$	13.5804	+	8.03195i	0.664238	+	0.392856i
$419$	2.02037	+	4.87760i	0.0987015	+	0.238287i	0.965516	−	0.260345i	$-0.0838362\pi$
$419$	2.02037	+	4.87760i	0.0987015	+	0.238287i	−0.866814	+	0.498631i	$0.833836\pi$
$420$	−11.4700	−	3.33307i	−0.559678	−	0.162637i
$421$	−2.23687	+	0.926542i	−0.109018	+	0.0451569i	−0.436526	−	0.899692i	$-0.643791\pi$
$421$	−2.23687	+	0.926542i	−0.109018	+	0.0451569i	0.327508	+	0.944849i	$0.393791\pi$
$422$	4.33086	−	30.4238i	0.210823	−	1.48101i
$423$			36.9696i			1.79752i
$424$	34.8696	+	15.7479i	1.69342	+	0.764786i
$425$	−8.87054	+	8.87054i	−0.430284	+	0.430284i
$426$	−46.1790	−	6.57363i	−2.23738	−	0.318493i
$427$	−2.14474	−	5.17785i	−0.103791	−	0.250574i
$428$	8.08167	−	0.891744i	0.390642	−	0.0431041i
$429$	−10.8582	+	40.1052i	−0.524237	+	1.93630i
$430$	−2.36655	+	4.00136i	−0.114125	+	0.192963i
$431$	2.20472	+	2.20472i	0.106198	+	0.106198i	0.758209	−	0.652011i	$-0.226075\pi$
$431$	2.20472	+	2.20472i	0.106198	+	0.106198i	−0.652011	+	0.758209i	$0.726075\pi$
$432$	−60.9670	+	42.8376i	−2.93328	+	2.06103i
$433$	−34.6879			−1.66699			−0.833497	−	0.552524i	$-0.813665\pi$
$433$	−34.6879			−1.66699			−0.833497	+	0.552524i	$0.813665\pi$
$434$	6.47971	−	1.66350i	0.311036	−	0.0798507i
$435$	−29.9678	−	12.4131i	−1.43685	−	0.595161i
$436$	−9.52214	+	1.05069i	−0.456028	+	0.0503188i
$437$	5.21260	−	2.15913i	0.249352	−	0.103285i
$438$	−0.632616	+	4.44406i	−0.0302276	+	0.212345i
$439$	−21.5727	+	21.5727i	−1.02961	+	1.02961i	−0.0300629	+	0.999548i	$0.509571\pi$
$439$	−21.5727	+	21.5727i	−1.02961	+	1.02961i	−0.999548	+	0.0300629i	$0.990429\pi$
$440$	10.9510	+	11.6637i	0.522068	+	0.556045i
$441$	−35.3155	+	35.3155i	−1.68169	+	1.68169i
$442$	0.375825	−	28.6755i	0.0178762	−	1.36395i
$443$	−11.1518	−	4.61923i	−0.529838	−	0.219466i	0.101694	−	0.994816i	$-0.467574\pi$
$443$	−11.1518	−	4.61923i	−0.529838	−	0.219466i	−0.631532	+	0.775350i	$0.717574\pi$
$444$	5.74745	+	1.67015i	0.272762	+	0.0792620i
$445$	24.0563	−	9.96444i	1.14038	−	0.472360i
$446$	−0.621881	−	2.42236i	−0.0294469	−	0.114702i
$447$	43.1813	−	43.1813i	2.04240	−	2.04240i
$448$	−0.533203	+	8.45123i	−0.0251915	+	0.399283i
$449$	−20.3698	+	20.3698i	−0.961308	+	0.961308i	−0.999279	−	0.0379705i	$-0.987911\pi$
$449$	−20.3698	+	20.3698i	−0.961308	+	0.961308i	0.0379705	+	0.999279i	$0.487911\pi$
$450$	−23.0631	−	13.6404i	−1.08721	−	0.643015i
$451$	10.5970	+	25.5833i	0.498992	+	1.20467i
$452$	1.05561	−	0.580244i	0.0496516	−	0.0272924i
$453$	−19.6736	−	47.4962i	−0.924344	−	2.23156i
$454$	−0.193460	−	0.257681i	−0.00907954	−	0.0120936i
$455$	5.02876	+	3.87955i	0.235752	+	0.181876i
$456$	0.991448	−	31.4600i	0.0464288	−	1.47325i
$457$	−3.60171			−0.168481			−0.0842403	−	0.996445i	$-0.526846\pi$
$457$	−3.60171			−0.168481			−0.0842403	+	0.996445i	$0.526846\pi$
$458$	−16.0404	−	2.28337i	−0.749518	−	0.106695i
$459$	96.7929	+	40.0929i	4.51791	+	1.87138i
$460$	5.68664	−	0.627472i	0.265141	−	0.0292560i
$461$	9.42616	−	22.7568i	0.439020	−	1.05989i	−0.537268	−	0.843412i	$-0.680544\pi$
$461$	9.42616	−	22.7568i	0.439020	−	1.05989i	0.976288	−	0.216476i	$-0.0694563\pi$
$462$	−16.7085	+	4.28949i	−0.777349	+	0.199565i
$463$	−12.5064	+	12.5064i	−0.581221	+	0.581221i	−0.935239	−	0.354018i	$-0.884815\pi$
$463$	−12.5064	+	12.5064i	−0.581221	+	0.581221i	0.354018	+	0.935239i	$0.384815\pi$
$464$	−3.95637	+	22.6533i	−0.183670	+	1.05165i
$465$	−25.2146			−1.16930
$466$	29.0994	−	7.47056i	1.34801	−	0.346067i
$467$	1.44805	+	3.49590i	0.0670077	+	0.161771i	0.953836	−	0.300329i	$-0.0970963\pi$
$467$	1.44805	+	3.49590i	0.0670077	+	0.161771i	−0.886828	+	0.462099i	$0.847096\pi$
$468$	59.5248	−	14.4527i	2.75153	−	0.668078i
$469$	−1.60720	−	0.665726i	−0.0742138	−	0.0307403i
$470$	−6.14984	−	8.19132i	−0.283671	−	0.377837i
$471$	−6.40418	−	6.40418i	−0.295089	−	0.295089i
$472$	−8.83626	+	3.33806i	−0.406722	+	0.153646i
$473$			6.71386i			0.308704i
$474$	74.5533	+	10.6127i	3.42435	+	0.487459i
$475$	6.76401	−	2.80174i	0.310354	−	0.128553i
$476$	10.4341	−	5.73539i	0.478245	−	0.262881i
$477$	106.159	−	43.9726i	4.86070	−	2.01337i
$478$	29.4425	−	7.55862i	1.34667	−	0.345723i
$479$	−7.44679	−	7.44679i	−0.340253	−	0.340253i	0.516210	−	0.856462i	$-0.327343\pi$
$479$	−7.44679	−	7.44679i	−0.340253	−	0.340253i	−0.856462	+	0.516210i	$0.827343\pi$
$480$	9.86729	−	30.3532i	0.450378	−	1.38543i
$481$	−2.51984	−	1.94399i	−0.114895	−	0.0886382i
$482$	4.01188	−	1.02995i	0.182736	−	0.0469129i
$483$	−2.36064	+	5.69908i	−0.107413	+	0.259317i
$484$	1.06192	+	0.308583i	0.0482689	+	0.0140265i
$485$	−16.5484	−	6.85459i	−0.751426	−	0.311251i
$486$	−14.3176	+	100.579i	−0.649458	+	4.56237i
$487$	−35.5102			−1.60912			−0.804560	−	0.593871i	$-0.797599\pi$
$487$	−35.5102			−1.60912			−0.804560	+	0.593871i	$0.797599\pi$
$488$	14.0094	−	5.29230i	0.634176	−	0.239571i
$489$			8.30024i			0.375350i
$490$	1.95014	−	13.6995i	0.0880982	−	0.618880i
$491$	−18.5038	−	7.66454i	−0.835067	−	0.345896i	−0.0761602	−	0.997096i	$-0.524266\pi$
$491$	−18.5038	−	7.66454i	−0.835067	−	0.345896i	−0.758906	+	0.651200i	$0.774266\pi$
$492$	34.5422	−	43.1105i	1.55728	−	1.94357i
$493$	29.8726	−	12.3736i	1.34539	−	0.557280i
$494$	−6.60698	+	15.3775i	−0.297262	+	0.691867i
$495$	48.0486			2.15962
$496$	3.89746	+	17.4459i	0.175001	+	0.783342i
$497$			10.2976i			0.461909i
$498$	−37.6131	−	22.2458i	−1.68548	−	0.996859i
$499$	24.8667	+	10.3001i	1.11318	+	0.461096i	0.862033	−	0.506852i	$-0.169191\pi$
$499$	24.8667	+	10.3001i	1.11318	+	0.461096i	0.251151	+	0.967948i	$0.419191\pi$
$500$	23.9205	−	2.63943i	1.06976	−	0.118039i
$501$	36.9057	−	15.2868i	1.64882	−	0.682965i
$502$	24.0675	+	32.0569i	1.07419	+	1.43077i
$503$	−5.37603	−	5.37603i	−0.239705	−	0.239705i	0.577023	−	0.816728i	$-0.304214\pi$
$503$	−5.37603	−	5.37603i	−0.239705	−	0.239705i	−0.816728	+	0.577023i	$0.804214\pi$
$504$	17.4074	+	18.5403i	0.775388	+	0.825850i
$505$	10.4509			0.465061
$506$	6.60758	−	4.96081i	0.293743	−	0.220535i
$507$	−43.6669	−	5.98037i	−1.93931	−	0.265598i
$508$	−4.07268	−	7.40921i	−0.180696	−	0.328731i
$509$	28.9646	+	11.9975i	1.28383	+	0.531781i	0.917142	−	0.398561i	$-0.130490\pi$
$509$	28.9646	+	11.9975i	1.28383	+	0.531781i	0.366692	+	0.930342i	$0.380490\pi$
$510$	−43.4671	+	11.1591i	−1.92476	+	0.494133i
$511$	0.990991			0.0438389
$512$	−22.5264	−	2.13539i	−0.995537	−	0.0943717i
$513$	−43.2352	−	43.2352i	−1.90888	−	1.90888i
$514$	26.4269	+	15.6299i	1.16564	+	0.689405i
$515$	10.4459	+	4.32683i	0.460301	+	0.190663i
$516$	11.7374	−	6.45177i	0.516708	−	0.284023i
$517$	−13.6669	−	5.66103i	−0.601072	−	0.248972i
$518$	0.186216	−	1.30814i	0.00818185	−	0.0574766i
$519$	−45.1964	−	45.1964i	−1.98390	−	1.98390i
$520$	−10.7847	+	13.1041i	−0.472939	+	0.574655i
$521$	−11.7143	+	11.7143i	−0.513212	+	0.513212i	−0.915509	−	0.402297i	$-0.868212\pi$
$521$	−11.7143	+	11.7143i	−0.513212	+	0.513212i	0.402297	+	0.915509i	$0.368212\pi$
$522$	41.4651	+	55.2297i	1.81488	+	2.41734i
$523$	−4.02270	+	9.71165i	−0.175900	+	0.424661i	−0.987099	−	0.160109i	$-0.948815\pi$
$523$	−4.02270	+	9.71165i	−0.175900	+	0.424661i	0.811199	+	0.584770i	$0.198815\pi$
$524$	−15.5527	+	19.4106i	−0.679424	+	0.847958i
$525$	−3.06323	+	7.39528i	−0.133690	+	0.322757i
$526$	7.62144	+	29.6872i	0.332311	+	1.29442i
$527$	17.7728	−	17.7728i	0.774193	−	0.774193i
$528$	−10.0499	−	44.9856i	−0.437367	−	1.95775i
$529$			20.0453i			0.871537i
$530$	−16.2068	+	27.4024i	−0.703980	+	1.19028i
$531$	−10.8559	+	26.2084i	−0.471105	+	1.13735i
$532$	−6.90685	+	0.762112i	−0.299450	+	0.0330418i
$533$	−25.4771	+	14.6209i	−1.10353	+	0.633300i
$534$	−74.2704	−	10.5725i	−3.21399	−	0.457515i
$535$			6.76549i			0.292498i
$536$	1.91328	−	4.23644i	0.0826410	−	0.182986i
$537$	39.0769	−	39.0769i	1.68629	−	1.68629i
$538$	−11.4776	−	1.63385i	−0.494836	−	0.0704404i
$539$	−7.64770	−	18.4632i	−0.329410	−	0.795266i
$540$	−29.8659	−	54.3334i	−1.28522	−	2.33814i
$541$	15.0077	−	36.2317i	0.645230	−	1.55772i	−0.174303	−	0.984692i	$-0.555767\pi$
$541$	15.0077	−	36.2317i	0.645230	−	1.55772i	0.819533	−	0.573032i	$-0.194233\pi$
$542$	10.4017	+	40.5167i	0.446790	+	1.74034i
$543$	−34.7467			−1.49112
$544$	14.4397	+	28.3498i	0.619097	+	1.21549i
$545$		−	7.97136i		−	0.341456i
$546$	−6.78050	−	16.9962i	−0.290179	−	0.727371i
$547$	10.6874	+	25.8017i	0.456960	+	1.10320i	0.969622	+	0.244609i	$0.0786595\pi$
$547$	10.6874	+	25.8017i	0.456960	+	1.10320i	−0.512662	+	0.858591i	$0.671340\pi$
$548$	5.17778	−	2.84611i	0.221184	−	0.121580i
$549$	17.2114	−	41.5520i	0.734564	−	1.77340i
$550$	8.57418	−	6.43728i	0.365604	−	0.274487i
$551$	−18.8704			−0.803906
$552$	−15.0223	−	6.78440i	−0.639390	−	0.288763i
$553$		−	16.6248i		−	0.706959i
$554$	−1.39576	−	1.85909i	−0.0593002	−	0.0789853i
$555$	−1.90585	+	4.60112i	−0.0808987	+	0.195307i
$556$	11.5213	−	1.27128i	0.488612	−	0.0539142i
$557$	−42.0355	−	17.4117i	−1.78110	−	0.737756i	−0.992411	−	0.122966i	$-0.960759\pi$
$557$	−42.0355	−	17.4117i	−1.78110	−	0.737756i	−0.788690	−	0.614790i	$-0.789241\pi$
$558$	46.2086	+	27.3295i	1.95617	+	1.15695i
$559$	−7.06341	+	0.911209i	−0.298750	+	0.0385400i
$560$	−6.94110	−	1.21226i	−0.293315	−	0.0512272i
$561$	−45.8286	+	45.8286i	−1.93488	+	1.93488i
$562$	17.7648	−	30.0366i	0.749362	−	1.26702i
$563$	−2.48681	−	6.00368i	−0.104806	−	0.253025i	0.862773	−	0.505591i	$-0.168726\pi$
$563$	−2.48681	−	6.00368i	−0.104806	−	0.253025i	−0.967580	+	0.252566i	$0.918726\pi$
$564$	3.23664	+	29.3330i	0.136287	+	1.23514i
$565$	0.383568	+	0.926014i	0.0161368	+	0.0389577i
$566$	−7.62904	−	10.1616i	−0.320673	−	0.427122i
$567$	39.8760			1.67464
$568$	−27.5024	−	0.866727i	−1.15398	−	0.0363671i
$569$	−16.2205	+	16.2205i	−0.679997	+	0.679997i	−0.959999	−	0.280002i	$-0.909665\pi$
$569$	−16.2205	+	16.2205i	−0.679997	+	0.679997i	0.280002	+	0.959999i	$0.409665\pi$
$570$	25.9291	+	3.69104i	1.08605	+	0.154601i
$571$	4.98239	−	12.0286i	0.208507	−	0.503380i	−0.784682	−	0.619899i	$-0.787174\pi$
$571$	4.98239	−	12.0286i	0.208507	−	0.503380i	0.993188	+	0.116519i	$0.0371737\pi$
$572$	−3.77194	+	24.2183i	−0.157713	+	1.01262i
$573$	−38.5165	+	15.9541i	−1.60905	+	0.666491i
$574$	−10.4971	−	6.20838i	−0.438140	−	0.259133i
$575$		−	3.83404i		−	0.159890i
$576$	−50.9821	+	44.9308i	−2.12425	+	1.87211i
$577$	−12.8984	−	12.8984i	−0.536969	−	0.536969i	0.385668	−	0.922638i	$-0.373971\pi$
$577$	−12.8984	−	12.8984i	−0.536969	−	0.536969i	−0.922638	+	0.385668i	$0.873971\pi$
$578$	10.5338	−	17.8106i	0.438150	−	0.740821i
$579$	−39.0257	−	16.1650i	−1.62185	−	0.671793i
$580$	−18.3748	−	5.33954i	−0.762971	−	0.221712i
$581$	−3.69188	+	8.91298i	−0.153165	+	0.369773i
$582$	30.9841	+	41.2695i	1.28433	+	1.71067i
$583$			45.9784i			1.90423i
$584$	−0.0834099	+	2.64671i	−0.00345153	+	0.109522i
$585$	6.52118	+	50.5501i	0.269618	+	2.08999i
$586$	−17.7137	−	2.52156i	−0.731744	−	0.104165i
$587$	−17.5714	+	7.27832i	−0.725250	+	0.300409i	−0.714599	−	0.699535i	$-0.753391\pi$
$587$	−17.5714	+	7.27832i	−0.725250	+	0.300409i	−0.0106517	+	0.999943i	$0.503391\pi$
$588$	−24.9287	+	31.1124i	−1.02804	+	1.28305i
$589$	−13.5522	+	5.61349i	−0.558407	+	0.231300i
$590$	−1.95441	−	7.61284i	−0.0804617	−	0.313416i
$591$	15.5173	+	15.5173i	0.638298	+	0.638298i
$592$	3.47808	+	0.607444i	0.142948	+	0.0249658i
$593$	30.0386	+	30.0386i	1.23354	+	1.23354i	0.962596	+	0.270940i	$0.0873344\pi$
$593$	30.0386	+	30.0386i	1.23354	+	1.23354i	0.270940	+	0.962596i	$0.412666\pi$
$594$	−77.0713	−	45.5829i	−3.16227	−	1.87029i
$595$	3.79135	+	9.15313i	0.155430	+	0.375242i
$596$	22.5257	−	28.1132i	0.922687	−	1.15156i
$597$	−12.7492	+	30.7792i	−0.521789	+	1.25971i
$598$	6.11587	+	6.27831i	0.250096	+	0.256739i
$599$	−10.6099	−	10.6099i	−0.433510	−	0.433510i	0.456310	−	0.889821i	$-0.349171\pi$
$599$	−10.6099	−	10.6099i	−0.433510	−	0.433510i	−0.889821	+	0.456310i	$0.849171\pi$
$600$	−19.4933	−	8.80363i	−0.795811	−	0.359407i
$601$	11.6612	+	11.6612i	0.475671	+	0.475671i	0.903744	−	0.428073i	$-0.140807\pi$
$601$	11.6612	+	11.6612i	0.475671	+	0.475671i	−0.428073	+	0.903744i	$0.640807\pi$
$602$	−1.77530	−	2.36463i	−0.0723559	−	0.0963749i
$603$	−5.34241	−	12.8977i	−0.217560	−	0.525236i
$604$	−14.6086	−	26.5766i	−0.594415	−	1.08139i
$605$	−0.352130	+	0.850118i	−0.0143161	+	0.0345622i
$606$	−25.9167	−	15.3281i	−1.05279	−	0.622662i
$607$			26.3898i			1.07113i	0.844494	+	0.535564i	$0.179901\pi$
$607$			26.3898i			1.07113i	−0.844494	+	0.535564i	$0.820099\pi$
$608$	−1.45409	−	18.5108i	−0.0589712	−	0.750711i
$609$	14.5887	−	14.5887i	0.591164	−	0.591164i
$610$	3.09860	+	12.0697i	0.125459	+	0.488689i
$611$	4.10088	−	15.1468i	0.165904	−	0.612774i
$612$	91.7535	+	26.6627i	3.70892	+	1.07778i
$613$	−24.8268	+	10.2836i	−1.00275	+	0.415351i	−0.822803	−	0.568326i	$-0.807591\pi$
$613$	−24.8268	+	10.2836i	−1.00275	+	0.415351i	−0.179942	+	0.983677i	$0.557591\pi$
$614$	7.49113	+	9.97786i	0.302317	+	0.402674i
$615$	32.5031	+	32.5031i	1.31065	+	1.31065i
$616$	−9.51953	+	3.59617i	−0.383553	+	0.144894i
$617$	5.33598			0.214818			0.107409	−	0.994215i	$-0.465745\pi$
$617$	5.33598			0.214818			0.107409	+	0.994215i	$0.465745\pi$
$618$	−19.5581	−	26.0506i	−0.786744	−	1.04791i
$619$	−3.56486	−	8.60634i	−0.143284	−	0.345918i	0.835903	−	0.548877i	$-0.184944\pi$
$619$	−3.56486	−	8.60634i	−0.143284	−	0.345918i	−0.979187	+	0.202959i	$0.934944\pi$
$620$	−14.7846	+	1.63136i	−0.593765	+	0.0655169i
$621$	−29.5825	+	12.2535i	−1.18711	+	0.491715i
$622$	3.34148	+	13.0158i	0.133981	+	0.521885i
$623$			16.5617i			0.663531i
$624$	45.9637	−	16.6786i	1.84002	−	0.667680i
$625$			8.87232i			0.354893i
$626$	−15.0715	+	3.86923i	−0.602378	+	0.154646i
$627$	34.9454	−	14.4749i	1.39559	−	0.578071i
$628$	−4.16945	−	3.34076i	−0.166379	−	0.133311i
$629$	−1.89979	−	4.58650i	−0.0757497	−	0.182876i
$630$	−16.9227	+	12.7052i	−0.674218	+	0.506186i
$631$	32.8797			1.30892			0.654461	−	0.756096i	$-0.272896\pi$
$631$	32.8797			1.30892			0.654461	+	0.756096i	$0.272896\pi$
$632$	44.4011	+	1.39928i	1.76618	+	0.0556604i
$633$	−52.0935	−	52.0935i	−2.07053	−	2.07053i
$634$	−7.34389	+	5.51361i	−0.291663	+	0.218973i
$635$	6.49961	−	2.69223i	0.257929	−	0.106838i
$636$	80.3808	−	44.1835i	3.18730	−	1.75199i
$637$	18.3865	−	10.5517i	0.728499	−	0.418074i
$638$	−26.7668	+	6.87171i	−1.05971	+	0.272054i
$639$	−58.4334	+	58.4334i	−2.31159	+	2.31159i
$640$	3.82188	−	18.4361i	0.151073	−	0.728749i
$641$			10.3548i			0.408990i	0.978868	+	0.204495i	$0.0655552\pi$
$641$			10.3548i			0.408990i	−0.978868	+	0.204495i	$0.934445\pi$
$642$	9.92276	−	16.7773i	0.391620	−	0.662149i
$643$	−11.0719	+	26.7298i	−0.436632	+	1.05412i	0.540473	+	0.841362i	$0.318245\pi$
$643$	−11.0719	+	26.7298i	−0.436632	+	1.05412i	−0.977104	+	0.212761i	$0.931755\pi$
$644$	−1.01544	+	3.49440i	−0.0400139	+	0.137699i
$645$	4.26491	+	10.2964i	0.167931	+	0.405421i
$646$	−20.8781	+	15.6747i	−0.821437	+	0.616715i
$647$	−11.4350	−	11.4350i	−0.449556	−	0.449556i	0.445651	−	0.895207i	$-0.352972\pi$
$647$	−11.4350	−	11.4350i	−0.449556	−	0.449556i	−0.895207	+	0.445651i	$0.852972\pi$
$648$	−3.35629	+	106.500i	−0.131848	+	4.18371i
$649$	−8.02643	−	8.02643i	−0.315065	−	0.315065i
$650$	7.93612	+	8.14691i	0.311280	+	0.319548i
$651$	6.13739	−	14.8170i	0.240543	−	0.580723i
$652$	0.537017	+	4.86686i	0.0210312	+	0.190601i
$653$	−15.4257	−	37.2410i	−0.603656	−	1.45735i	−0.869792	−	0.493418i	$-0.835747\pi$
$653$	−15.4257	−	37.2410i	−0.603656	−	1.45735i	0.266136	−	0.963935i	$-0.414253\pi$
$654$	−11.6914	+	19.7677i	−0.457169	+	0.772979i
$655$	−14.6346	−	14.6346i	−0.571822	−	0.571822i
$656$	17.4647	−	27.5128i	0.681882	−	1.07419i
$657$	5.62337	+	5.62337i	0.219389	+	0.219389i
$658$	6.31041	−	1.62004i	0.246005	−	0.0631558i
$659$	−10.8420	+	4.49090i	−0.422344	+	0.174941i	−0.583725	−	0.811951i	$-0.698405\pi$
$659$	−10.8420	+	4.49090i	−0.422344	+	0.174941i	0.161381	+	0.986892i	$0.448405\pi$
$660$	38.1234	−	4.20660i	1.48395	−	0.163742i
$661$	−17.7440	+	7.34980i	−0.690161	+	0.285874i	−0.700067	−	0.714077i	$-0.746847\pi$
$661$	−17.7440	+	7.34980i	−0.690161	+	0.285874i	0.00990622	+	0.999951i	$0.496847\pi$
$662$	4.95500	−	34.8083i	0.192581	−	1.35286i
$663$	−54.4344	−	41.9947i	−2.11406	−	1.63094i
$664$	−23.4938	−	10.6104i	−0.911737	−	0.411762i
$665$		−	5.78200i		−	0.224216i
$666$	8.47974	−	6.36638i	0.328583	−	0.246692i
$667$	−3.78171	+	9.12986i	−0.146428	+	0.353509i
$668$	20.6507	−	11.3512i	0.798999	−	0.439192i
$669$	−5.53915	−	2.29439i	−0.214156	−	0.0887062i
$670$	3.32923	+	1.96903i	0.128619	+	0.0760704i
$671$	12.7254	+	12.7254i	0.491260	+	0.491260i
$672$	15.4348	+	13.1865i	0.595412	+	0.508681i
$673$			11.4087i			0.439774i	0.975525	+	0.219887i	$0.0705689\pi$
$673$			11.4087i			0.439774i	−0.975525	+	0.219887i	$0.929431\pi$
$674$	−5.00045	+	8.45473i	−0.192610	+	0.325664i
$675$	−38.3871	+	15.9005i	−1.47752	+	0.612009i
$676$	−25.9911	−	0.681402i	−0.999657	−	0.0262078i
$677$	−2.67627	+	6.46108i	−0.102857	+	0.248319i	−0.966927	−	0.255052i	$-0.917907\pi$
$677$	−2.67627	+	6.46108i	−0.102857	+	0.248319i	0.864070	+	0.503372i	$0.167907\pi$
$678$	0.406973	−	2.85894i	0.0156297	−	0.109797i
$679$	8.05599	−	8.05599i	0.309161	−	0.309161i
$680$	−24.7651	+	9.35544i	−0.949696	+	0.358765i
$681$	−0.772471			−0.0296012
$682$	−17.1790	+	12.8975i	−0.657817	+	0.493873i
$683$	11.1618	+	26.9470i	0.427095	+	1.03110i	0.980204	+	0.197989i	$0.0634411\pi$
$683$	11.1618	+	26.9470i	0.427095	+	1.03110i	−0.553109	+	0.833109i	$0.686559\pi$
$684$	−43.5175	−	34.8683i	−1.66393	−	1.33322i
$685$	1.88141	+	4.54212i	0.0718849	+	0.173545i
$686$	16.5949	+	9.81485i	0.633596	+	0.374733i
$687$	−27.4653	+	27.4653i	−1.04787	+	1.04787i
$688$	6.46480	−	4.54240i	0.246468	−	0.173177i
$689$	−48.3722	+	6.24022i	−1.84283	+	0.237733i
$690$	6.98211	−	11.8053i	0.265804	−	0.449421i
$691$	14.2502	+	5.90265i	0.542105	+	0.224547i	0.636896	−	0.770950i	$-0.280218\pi$
$691$	14.2502	+	5.90265i	0.542105	+	0.224547i	−0.0947907	+	0.995497i	$0.530218\pi$
$692$	−29.4251	−	23.5768i	−1.11858	−	0.896256i
$693$	−11.6953	+	28.2350i	−0.444269	+	1.07256i
$694$	11.4204	−	8.57417i	0.433513	−	0.325471i
$695$			9.64495i			0.365854i
$696$	37.7352	+	40.1910i	1.43035	+	1.52344i
$697$	−45.8203			−1.73557
$698$	13.9938	+	18.6391i	0.529673	+	0.705502i
$699$	27.5621	−	66.5409i	1.04250	−	2.51681i
$700$	−1.31766	+	4.53443i	−0.0498029	+	0.171385i
$701$	−9.19668	−	22.2027i	−0.347354	−	0.838586i	−0.996931	−	0.0782900i	$-0.975054\pi$
$701$	−9.19668	−	22.2027i	−0.347354	−	0.838586i	0.649577	−	0.760296i	$-0.274946\pi$
$702$	37.4959	−	87.2704i	1.41519	−	3.29381i
$703$			2.89728i			0.109273i
$704$	−8.80332	−	25.7272i	−0.331788	−	0.969630i
$705$	−24.5558			−0.924825
$706$	37.7680	−	9.69598i	1.42142	−	0.364913i
$707$	−2.54382	+	6.14133i	−0.0956703	+	0.230969i
$708$	−6.31893	+	21.7451i	−0.237480	+	0.817232i
$709$	0.818505	+	1.97605i	0.0307396	+	0.0742119i	0.938504	−	0.345269i	$-0.112212\pi$
$709$	0.818505	+	1.97605i	0.0307396	+	0.0742119i	−0.907764	+	0.419481i	$0.862212\pi$
$710$	3.22672	−	22.6674i	0.121097	−	0.850691i
$711$	94.3374	−	94.3374i	3.53793	−	3.53793i
$712$	−44.2326	−	1.39397i	−1.65769	−	0.0522412i
$713$			7.68177i			0.287684i
$714$	4.02270	−	28.2590i	0.150546	−	1.05757i
$715$	−19.6860	−	5.32982i	−0.736214	−	0.199324i
$716$	20.3846	−	25.4410i	0.761807	−	0.950776i
$717$	27.8871	−	67.3253i	1.04146	−	2.51431i
$718$	−18.9736	−	11.2217i	−0.708089	−	0.418791i
$719$		−	25.3324i		−	0.944737i	−0.881401	−	0.472369i	$-0.843399\pi$
$719$		−	25.3324i		−	0.944737i	0.881401	−	0.472369i	$-0.156601\pi$
$720$	−32.5083	−	46.2661i	−1.21151	−	1.72424i
$721$	−5.08520	+	5.08520i	−0.189383	+	0.189383i
$722$	−11.2681	+	2.89281i	−0.419356	+	0.107659i
$723$	3.79993	−	9.17384i	0.141321	−	0.341179i
$724$	−20.3738	+	2.24808i	−0.757187	+	0.0835491i
$725$	−4.90725	+	11.8472i	−0.182251	+	0.439992i
$726$	2.12007	−	1.59170i	0.0786833	−	0.0590735i
$727$	−20.6104	+	20.6104i	−0.764399	+	0.764399i	−0.977114	−	0.212716i	$-0.931769\pi$
$727$	−20.6104	+	20.6104i	−0.764399	+	0.764399i	0.212716	+	0.977114i	$0.431769\pi$
$728$	−5.07540	−	9.52707i	−0.188107	−	0.353097i
$729$	92.3034	+	92.3034i	3.41864	+	3.41864i
$730$	−2.18140	−	0.310525i	−0.0807374	−	0.0114931i
$731$	−10.2637	−	4.25136i	−0.379616	−	0.157242i
$732$	10.0183	−	34.4757i	0.370287	−	1.27426i
$733$	19.5527	+	8.09900i	0.722196	+	0.299143i	0.713341	−	0.700817i	$-0.247181\pi$
$733$	19.5527	+	8.09900i	0.722196	+	0.299143i	0.00885534	+	0.999961i	$0.497181\pi$
$734$	−13.5318	+	22.8795i	−0.499467	+	0.844496i
$735$	−23.4571	−	23.4571i	−0.865229	−	0.865229i
$736$	−9.24727	−	3.00612i	−0.340859	−	0.110807i
$737$	5.58610			0.205767
$738$	−24.3363	−	94.7950i	−0.895830	−	3.48945i
$739$	−4.29663	−	1.77972i	−0.158054	−	0.0654681i	0.302254	−	0.953227i	$-0.402261\pi$
$739$	−4.29663	−	1.77972i	−0.158054	−	0.0654681i	−0.460308	+	0.887759i	$0.652261\pi$
$740$	−0.819810	+	2.82118i	−0.0301368	+	0.103709i
$741$	19.9713	+	34.8003i	0.733664	+	1.27842i
$742$	−12.1578	−	16.1936i	−0.446326	−	0.594486i
$743$	27.6232			1.01340			0.506698	−	0.862124i	$-0.330866\pi$
$743$	27.6232			1.01340			0.506698	+	0.862124i	$0.330866\pi$
$744$	39.0562	+	17.6387i	1.43187	+	0.646666i
$745$	21.1959	+	21.1959i	0.776558	+	0.776558i
$746$	−15.4898	+	11.6293i	−0.567121	+	0.425780i
$747$	−71.5261	+	29.6271i	−2.61700	+	1.08400i
$748$	−23.9066	+	29.8367i	−0.874113	+	1.09094i
$749$	−3.97564	−	1.64676i	−0.145267	−	0.0601714i
$750$	29.3699	−	49.6584i	1.07244	−	1.81327i
$751$		−	46.5203i		−	1.69755i	−0.528754	−	0.848775i	$-0.677341\pi$
$751$		−	46.5203i		−	1.69755i	0.528754	−	0.848775i	$-0.322659\pi$
$752$	3.79563	+	16.9900i	0.138412	+	0.619563i
$753$	96.0997			3.50207
$754$	−10.8623	−	27.2277i	−0.395581	−	0.991575i
$755$	23.3139	−	9.65694i	0.848480	−	0.351452i
$756$	39.1977	−	4.32514i	1.42561	−	0.157304i
$757$	−6.85497	−	2.83942i	−0.249148	−	0.103201i	0.254615	−	0.967043i	$-0.418051\pi$
$757$	−6.85497	−	2.83942i	−0.249148	−	0.103201i	−0.503763	+	0.863842i	$0.668051\pi$
$758$	8.96846	+	1.27667i	0.325749	+	0.0463707i
$759$		−	19.8081i		−	0.718988i
$760$	15.4424	+	0.486661i	0.560155	+	0.0176530i
$761$	8.31466			0.301406			0.150703	−	0.988579i	$-0.451846\pi$
$761$	8.31466			0.301406			0.150703	+	0.988579i	$0.451846\pi$
$762$	−20.0666	−	2.85651i	−0.726937	−	0.103480i
$763$	4.68425	+	1.94028i	0.169581	+	0.0702428i
$764$	−21.5520	+	11.8467i	−0.779725	+	0.428598i
$765$	−30.4254	+	73.4534i	−1.10003	+	2.65571i
$766$	−11.1984	−	43.6204i	−0.404616	−	1.57607i
$767$	7.35496	−	9.53366i	0.265572	−	0.344241i
$768$	−36.5173	+	40.1131i	−1.31771	+	1.44746i
$769$	16.7853	+	16.7853i	0.605292	+	0.605292i	0.941712	−	0.336420i	$-0.109216\pi$
$769$	16.7853	+	16.7853i	0.605292	+	0.605292i	−0.336420	+	0.941712i	$0.609216\pi$
$770$	−2.10553	−	8.20151i	−0.0758781	−	0.295562i
$771$	68.0025	−	28.1676i	2.44905	−	1.01443i
$772$	−23.9286	−	6.95344i	−0.861211	−	0.250260i
$773$	1.32024	−	0.546860i	0.0474856	−	0.0196692i	−0.358814	−	0.933409i	$-0.616819\pi$
$773$	1.32024	−	0.546860i	0.0474856	−	0.0196692i	0.406300	+	0.913740i	$0.366819\pi$
$774$	3.34411	−	23.4920i	0.120201	−	0.844402i
$775$			9.96807i			0.358064i
$776$	20.8377	+	22.1938i	0.748029	+	0.796711i
$777$	−2.23989	−	2.23989i	−0.0803554	−	0.0803554i
$778$	10.2339	−	7.68336i	0.366903	−	0.275462i
$779$	24.7057	+	10.2334i	0.885173	+	0.366651i
$780$	9.59974	+	39.5373i	0.343726	+	1.41566i
$781$	−12.6540	−	30.5494i	−0.452795	−	1.09314i
$782$	3.39968	+	13.2425i	0.121572	+	0.473551i
$783$	107.093			3.82720
$784$	−12.6041	+	19.8557i	−0.450145	+	0.709131i
$785$	3.14355	−	3.14355i	0.112198	−	0.112198i
$786$	14.8273	+	57.7557i	0.528874	+	2.06008i
$787$	−3.22837	+	7.79398i	−0.115079	+	0.277826i	−0.970916	−	0.239420i	$-0.923043\pi$
$787$	−3.22837	+	7.79398i	−0.115079	+	0.277826i	0.855837	+	0.517246i	$0.173043\pi$
$788$	10.1026	+	8.09467i	0.359889	+	0.288361i
$789$	67.8849	+	28.1188i	2.41676	+	1.00106i
$790$	−5.20936	+	36.5951i	−0.185341	+	1.30200i
$791$	−0.637521			−0.0226676
$792$	−74.4249	−	33.6121i	−2.64458	−	1.19435i
$793$	−11.6609	+	15.1151i	−0.414089	+	0.536752i
$794$	−16.4144	+	12.3236i	−0.582527	+	0.437347i
$795$	29.2073	+	70.5127i	1.03588	+	2.50083i
$796$	−5.48412	+	18.8723i	−0.194380	+	0.668912i
$797$	13.2139	+	31.9013i	0.468062	+	1.13000i	0.965008	+	0.262220i	$0.0844545\pi$
$797$	13.2139	+	31.9013i	0.468062	+	1.13000i	−0.496947	+	0.867781i	$0.665545\pi$
$798$	−8.48030	+	14.3384i	−0.300199	+	0.507576i
$799$	17.3084	−	17.3084i	0.612327	−	0.612327i
$800$	−11.9995	−	3.90083i	−0.424247	−	0.137915i
$801$	−93.9793	+	93.9793i	−3.32060	+	3.32060i
$802$	34.2594	−	8.79523i	1.20974	−	0.310571i
$803$	−2.93994	+	1.21776i	−0.103748	+	0.0429739i
$804$	−5.36804	−	9.76578i	−0.189316	−	0.344413i
$805$	−2.79744	−	1.15874i	−0.0985969	−	0.0408402i
$806$	−15.9006	−	16.3229i	−0.560074	−	0.574950i
$807$	−19.6527	+	19.6527i	−0.691808	+	0.691808i
$808$	−16.1880	−	7.31088i	−0.569492	−	0.257196i
$809$	−6.82100	+	6.82100i	−0.239813	+	0.239813i	−0.816773	−	0.576959i	$-0.804239\pi$
$809$	−6.82100	+	6.82100i	−0.239813	+	0.239813i	0.576959	+	0.816773i	$0.304239\pi$
$810$	−87.7765	−	12.4951i	−3.08415	−	0.439033i
$811$	9.53362	−	3.94896i	0.334771	−	0.138667i	−0.208965	−	0.977923i	$-0.567009\pi$
$811$	9.53362	−	3.94896i	0.334771	−	0.138667i	0.543736	+	0.839257i	$0.317009\pi$
$812$	7.61024	−	9.49799i	0.267067	−	0.333314i
$813$	92.6485	+	38.3763i	3.24932	+	1.34591i
$814$	1.05505	+	4.10966i	0.0369796	+	0.144043i
$815$	−4.07424			−0.142715
$816$	75.1348	+	13.1222i	2.63024	+	0.459370i
$817$	4.58455	+	4.58455i	0.160393	+	0.160393i
$818$	−13.1133	−	7.75570i	−0.458495	−	0.271172i
$819$	−31.2923	−	8.47215i	−1.09344	−	0.296041i
$820$	21.1612	+	16.9554i	0.738981	+	0.592107i
$821$	−14.8135	−	35.7630i	−0.516996	−	1.24814i	−0.939740	−	0.341889i	$-0.888933\pi$
$821$	−14.8135	−	35.7630i	−0.516996	−	1.24814i	0.422745	−	0.906249i	$-0.361067\pi$
$822$	1.99621	−	14.0231i	0.0696258	−	0.489113i
$823$	−19.6371	+	19.6371i	−0.684507	+	0.684507i	−0.961012	−	0.276505i	$-0.910824\pi$
$823$	−19.6371	+	19.6371i	−0.684507	+	0.684507i	0.276505	+	0.961012i	$0.410824\pi$
$824$	−13.1534	−	14.0094i	−0.458220	−	0.488041i
$825$		−	25.7035i		−	0.894883i
$826$	4.94929	+	0.704536i	0.172208	+	0.0245140i
$827$	−2.09048	+	0.865904i	−0.0726931	+	0.0301104i	−0.418734	−	0.908109i	$-0.637526\pi$
$827$	−2.09048	+	0.865904i	−0.0726931	+	0.0301104i	0.346041	+	0.938220i	$0.387526\pi$
$828$	−25.5910	+	14.0668i	−0.889349	+	0.488856i
$829$	−8.31769	−	20.0807i	−0.288885	−	0.697431i	0.711099	−	0.703092i	$-0.248198\pi$
$829$	−8.31769	−	20.0807i	−0.288885	−	0.697431i	−0.999984	+	0.00566138i	$0.998198\pi$
$830$	10.9196	−	18.4627i	0.379023	−	0.640851i
$831$	−5.57316			−0.193331
$832$	25.8718	−	12.7534i	0.896945	−	0.442143i
$833$	33.0680			1.14574
$834$	14.1460	−	23.9180i	0.489835	−	0.828211i
$835$	7.50368	+	18.1155i	0.259675	+	0.626912i
$836$	19.5538	−	10.7483i	0.676283	−	0.371738i
$837$	76.9112	−	31.8577i	2.65844	−	1.10116i
$838$	7.39180	+	1.05223i	0.255345	+	0.0363487i
$839$		−	18.0082i		−	0.621711i	−0.950457	−	0.310856i	$-0.899384\pi$
$839$		−	18.0082i		−	0.621711i	0.950457	−	0.310856i	$-0.100616\pi$
$840$	−12.3148	+	11.5623i	−0.424900	+	0.398937i
$841$	2.86482	−	2.86482i	0.0987870	−	0.0987870i
$842$	−0.482553	+	3.38988i	−0.0166299	+	0.116823i
$843$	−32.0150	−	77.2911i	−1.10266	−	2.66205i
$844$	−33.9155	−	27.1747i	−1.16742	−	0.935393i
$845$	2.93552	−	21.4343i	0.100985	−	0.737361i
$846$	45.0013	+	26.6155i	1.54718	+	0.915059i
$847$	−0.413848	−	0.413848i	−0.0142200	−	0.0142200i
$848$	44.2728	−	31.1077i	1.52033	−	1.06824i
$849$	−30.4621			−1.04546
$850$	4.41152	+	17.1838i	0.151314	+	0.589401i
$851$	1.40176	+	0.580627i	0.0480517	+	0.0199036i
$852$	−41.2473	+	51.4789i	−1.41311	+	1.76364i
$853$	6.94838	−	2.87811i	0.237908	−	0.0985447i	−0.260544	−	0.965462i	$-0.583902\pi$
$853$	6.94838	−	2.87811i	0.237908	−	0.0985447i	0.498452	+	0.866917i	$0.333902\pi$
$854$	−7.84681	−	1.11700i	−0.268512	−	0.0382230i
$855$	32.8099	−	32.8099i	1.12208	−	1.12208i
$856$	4.73275	−	10.4794i	0.161762	−	0.358179i
$857$	7.97152	−	7.97152i	0.272302	−	0.272302i	−0.557724	−	0.830026i	$-0.688325\pi$
$857$	7.97152	−	7.97152i	0.272302	−	0.272302i	0.830026	+	0.557724i	$0.188325\pi$
$858$	41.0010	+	42.0900i	1.39975	+	1.43693i
$859$	5.91444	+	2.44984i	0.201798	+	0.0835875i	0.481293	−	0.876560i	$-0.340167\pi$
$859$	5.91444	+	2.44984i	0.201798	+	0.0835875i	−0.279495	+	0.960147i	$0.590167\pi$
$860$	3.16691	+	5.76139i	0.107991	+	0.196462i
$861$	−27.0114	+	11.1885i	−0.920547	+	0.381303i
$862$	4.27095	−	1.09646i	0.145469	−	0.0373456i
$863$	−1.41408	+	1.41408i	−0.0481357	+	0.0481357i	−0.730765	−	0.682629i	$-0.760836\pi$
$863$	−1.41408	+	1.41408i	−0.0481357	+	0.0481357i	0.682629	+	0.730765i	$0.260836\pi$
$864$	8.25226	+	105.052i	0.280748	+	3.57395i
$865$	22.1850	−	22.1850i	0.754314	−	0.754314i
$866$	−24.9728	+	42.2239i	−0.848611	+	1.43483i
$867$	−18.9837	−	45.8306i	−0.644719	−	1.55649i
$868$	2.64003	−	9.08504i	0.0896084	−	0.308366i
$869$	20.4291	+	49.3203i	0.693011	+	1.67308i
$870$	−36.6845	+	27.5418i	−1.24372	+	0.933755i
$871$	0.758149	+	5.87693i	0.0256889	+	0.199132i
$872$	−5.57631	+	12.3473i	−0.188838	+	0.418131i
$873$	91.4273			3.09435
$874$	1.12450	−	7.89946i	0.0380367	−	0.267203i
$875$	−11.7673	−	4.87417i	−0.397807	−	0.164777i
$876$	4.95410	+	3.96946i	0.167384	+	0.134116i
$877$	−0.776470	+	1.87456i	−0.0262195	+	0.0632995i	−0.936447	−	0.350809i	$-0.885907\pi$
$877$	−0.776470	+	1.87456i	−0.0262195	+	0.0632995i	0.910227	+	0.414109i	$0.135907\pi$
$878$	10.7286	+	41.7903i	0.362073	+	1.41035i
$879$	−30.3304	+	30.3304i	−1.02302	+	1.02302i
$880$	22.0816	−	4.93309i	0.744370	−	0.166295i
$881$	16.6870			0.562200			0.281100	−	0.959679i	$-0.409301\pi$
$881$	16.6870			0.562200			0.281100	+	0.959679i	$0.409301\pi$
$882$	17.5632	+	68.4124i	0.591383	+	2.30357i
$883$	17.5231	+	42.3045i	0.589699	+	1.42366i	0.883791	+	0.467883i	$0.154983\pi$
$883$	17.5231	+	42.3045i	0.589699	+	1.42366i	−0.294091	+	0.955777i	$0.595017\pi$
$884$	−34.6347	−	21.1018i	−1.16489	−	0.709731i
$885$	−17.4081	−	7.21066i	−0.585166	−	0.242384i
$886$	−13.6513	+	10.2490i	−0.458624	+	0.344323i
$887$	5.58480	+	5.58480i	0.187519	+	0.187519i	0.794623	−	0.607104i	$-0.207669\pi$
$887$	5.58480	+	5.58480i	0.187519	+	0.187519i	−0.607104	+	0.794623i	$0.707669\pi$
$888$	6.17075	−	5.79370i	0.207077	−	0.194424i
$889$			4.47470i			0.150077i
$890$	5.18959	−	36.4563i	0.173955	−	1.22202i
$891$	−118.299	+	49.0010i	−3.96316	+	1.64160i
$892$	−3.39633	−	0.986943i	−0.113718	−	0.0330453i
$893$	−13.1981	+	5.46683i	−0.441657	+	0.182940i
$894$	−21.4750	−	83.6500i	−0.718233	−	2.79767i
$895$	19.1812	+	19.1812i	0.641157	+	0.641157i
$896$	9.90340	+	6.73333i	0.330849	+	0.224945i
$897$	20.8394	−	2.68837i	0.695806	−	0.0897620i
$898$	10.1303	+	39.4599i	0.338054	+	1.31679i
$899$	9.83203	−	23.7366i	0.327916	−	0.791660i
$900$	−33.2076	+	18.2535i	−1.10692	+	0.608450i
$901$	−70.2887	−	29.1145i	−2.34165	−	0.969945i
$902$	38.7704	+	5.51901i	1.29091	+	0.183763i
$903$	−7.08864			−0.235895
$904$	0.0536590	−	1.70267i	0.00178467	−	0.0566301i
$905$		−	17.0557i		−	0.566952i
$906$	−71.9784	−	10.2462i	−2.39132	−	0.340407i
$907$	36.7076	+	15.2048i	1.21886	+	0.504867i	0.897046	−	0.441937i	$-0.145708\pi$
$907$	36.7076	+	15.2048i	1.21886	+	0.504867i	0.321811	+	0.946804i	$0.395708\pi$
$908$	−0.452940	+	0.0499781i	−0.0150313	+	0.00165858i
$909$	−49.2838	+	20.4140i	−1.63464	+	0.677091i
$910$	8.34274	−	3.32827i	0.276559	−	0.110331i
$911$	4.50171			0.149148			0.0745742	−	0.997215i	$-0.476240\pi$
$911$	4.50171			0.149148			0.0745742	+	0.997215i	$0.476240\pi$
$912$	−37.5810	−	23.8558i	−1.24443	−	0.789945i
$913$		−	30.9785i		−	1.02524i
$914$	−2.59297	+	4.38418i	−0.0857679	+	0.145016i
$915$	27.5995	+	11.4321i	0.912412	+	0.377933i
$916$	−14.3274	+	17.8813i	−0.473390	+	0.590816i
$917$	12.1620	−	5.03765i	0.401624	−	0.166358i
$918$	118.487	−	88.9573i	3.91066	−	2.93603i
$919$	−3.30749	−	3.30749i	−0.109104	−	0.109104i	0.650447	−	0.759551i	$-0.274581\pi$
$919$	−3.30749	−	3.30749i	−0.109104	−	0.109104i	−0.759551	+	0.650447i	$0.774581\pi$
$920$	3.33018	−	7.37381i	0.109793	−	0.243107i
$921$	29.9115			0.985616
$922$	−20.9145	−	27.8573i	−0.688784	−	0.917430i
$923$	30.4225	−	17.4590i	1.00137	−	0.574669i
$924$	−6.80754	+	23.4266i	−0.223952	+	0.770678i
$925$	1.81896	+	0.753438i	0.0598071	+	0.0247729i
$926$	6.21971	+	24.2271i	0.204392	+	0.796153i
$927$	−57.7118			−1.89550
$928$	24.7264	+	21.1247i	0.811685	+	0.693451i
$929$	12.4771	+	12.4771i	0.409360	+	0.409360i	0.881515	−	0.472155i	$-0.156524\pi$
$929$	12.4771	+	12.4771i	0.409360	+	0.409360i	−0.472155	+	0.881515i	$0.656524\pi$
$930$	−18.1527	+	30.6925i	−0.595251	+	1.00645i
$931$	−17.8298	−	7.38534i	−0.584348	−	0.242045i
$932$	11.8560	−	40.7996i	0.388356	−	1.33644i
$933$	29.7628	+	12.3282i	0.974391	+	0.403606i
$934$	5.29788	+	0.754159i	0.173352	+	0.0246768i
$935$	−22.4954	−	22.4954i	−0.735677	−	0.735677i
$936$	25.2610	−	82.8616i	0.825682	−	2.70842i
$937$	4.12802	−	4.12802i	0.134857	−	0.134857i	−0.636456	−	0.771313i	$-0.719600\pi$
$937$	4.12802	−	4.12802i	0.134857	−	0.134857i	0.771313	+	0.636456i	$0.219600\pi$
$938$	−1.96743	+	1.47710i	−0.0642388	+	0.0482289i
$939$	−14.2753	+	34.4636i	−0.465856	+	1.12468i
$940$	−14.3983	+	1.58874i	−0.469622	+	0.0518188i
$941$	−10.8267	+	26.1380i	−0.352940	+	0.852073i	0.643314	+	0.765602i	$0.277559\pi$
$941$	−10.8267	+	26.1380i	−0.352940	+	0.852073i	−0.996254	+	0.0864710i	$0.972441\pi$
$942$	−12.4061	+	3.18495i	−0.404211	+	0.103771i
$943$	9.90226	−	9.90226i	0.322462	−	0.322462i
$944$	−2.29823	+	13.1591i	−0.0748010	+	0.428293i
$945$			32.8140i			1.06744i
$946$	8.17246	+	4.83350i	0.265710	+	0.157151i
$947$	5.85737	−	14.1409i	0.190339	−	0.459519i	−0.799685	−	0.600420i	$-0.795000\pi$
$947$	5.85737	−	14.1409i	0.190339	−	0.459519i	0.990024	+	0.140901i	$0.0450000\pi$
$948$	66.5915	−	83.1097i	2.16279	−	2.69928i
$949$	−1.68017	−	2.92773i	−0.0545408	−	0.0950380i
$950$	1.45918	−	10.2506i	0.0473420	−	0.332572i
$951$			22.0154i			0.713898i
$952$	0.530389	−	16.8300i	0.0171900	−	0.545463i
$953$	4.13664	−	4.13664i	0.133999	−	0.133999i	−0.636926	−	0.770925i	$-0.719794\pi$
$953$	4.13664	−	4.13664i	0.133999	−	0.133999i	0.770925	+	0.636926i	$0.219794\pi$
$954$	22.9014	−	160.880i	0.741460	−	5.20867i
$955$	−7.83120	−	18.9062i	−0.253412	−	0.611790i
$956$	11.9958	−	41.2806i	0.387970	−	1.33511i
$957$	−25.3527	+	61.2069i	−0.819537	+	1.97854i
$958$	−14.4258	+	3.70346i	−0.466076	+	0.119653i
$959$	−3.12705			−0.100978
$960$	−29.8437	−	33.8631i	−0.963203	−	1.09293i
$961$			11.0283i			0.355750i
$962$	−4.18043	+	1.66775i	−0.134782	+	0.0537703i
$963$	−13.2152	−	31.9043i	−0.425853	−	1.02810i
$964$	1.63456	−	5.62495i	0.0526456	−	0.181168i
$965$	7.93471	−	19.1561i	0.255427	−	0.616656i
$966$	5.23772	+	6.97642i	0.168521	+	0.224463i
$967$	10.9842			0.353229			0.176614	−	0.984280i	$-0.443485\pi$
$967$	10.9842			0.353229			0.176614	+	0.984280i	$0.443485\pi$
$968$	1.14013	−	1.07046i	0.0366451	−	0.0344059i
$969$			62.5880i			2.01062i
$970$	−20.2575	+	15.2088i	−0.650428	+	0.488325i
$971$	17.7948	−	42.9603i	0.571061	−	1.37866i	−0.329592	−	0.944124i	$-0.606911\pi$
$971$	17.7948	−	42.9603i	0.571061	−	1.37866i	0.900653	−	0.434540i	$-0.143089\pi$
$972$	112.123	+	89.8380i	3.59634	+	2.88155i
$973$	−5.66771	−	2.34764i	−0.181698	−	0.0752619i
$974$	−25.5648	+	43.2248i	−0.819149	+	1.38501i
$975$	27.0417	−	3.48850i	0.866029	−	0.111721i
$976$	3.64371	−	20.8630i	0.116632	−	0.667810i
$977$	−11.7036	+	11.7036i	−0.374432	+	0.374432i	−0.869089	−	0.494657i	$-0.835294\pi$
$977$	−11.7036	+	11.7036i	−0.374432	+	0.374432i	0.494657	+	0.869089i	$0.335294\pi$
$978$	10.1035	+	5.97558i	0.323074	+	0.191078i
$979$	−20.3516	−	49.1331i	−0.650440	−	1.57030i
$980$	−15.2718	−	12.2365i	−0.487839	−	0.390880i
$981$	15.5706	+	37.5908i	0.497132	+	1.20018i
$982$	−22.6511	+	17.0059i	−0.722827	+	0.542680i
$983$	35.5119			1.13265			0.566327	−	0.824181i	$-0.308364\pi$
$983$	35.5119			1.13265			0.566327	+	0.824181i	$0.308364\pi$
$984$	−27.6084	−	73.0831i	−0.880125	−	2.32980i
$985$	−7.61682	+	7.61682i	−0.242692	+	0.242692i
$986$	6.44431	−	45.2706i	0.205229	−	1.44171i
$987$	5.97704	−	14.4298i	0.190251	−	0.459307i
$988$	13.9617	+	19.1131i	0.444182	+	0.608068i
$989$	3.13686	−	1.29933i	0.0997463	−	0.0413163i
$990$	34.5916	−	58.4872i	1.09939	−	1.85885i
$991$		−	10.6683i		−	0.338890i	−0.985540	−	0.169445i	$-0.945803\pi$
$991$		−	10.6683i		−	0.338890i	0.985540	−	0.169445i	$-0.0541974\pi$
$992$	24.0419	+	7.81559i	0.763331	+	0.248145i
$993$	−59.6009	−	59.6009i	−1.89138	−	1.89138i
$994$	12.5347	+	7.41351i	0.397577	+	0.235142i
$995$	−15.1083	−	6.25805i	−0.478964	−	0.198393i
$996$	−54.1576	+	29.7692i	−1.71605	+	0.943274i
$997$	−20.5673	+	49.6538i	−0.651373	+	1.57255i	0.159415	+	0.987212i	$0.449039\pi$
$997$	−20.5673	+	49.6538i	−0.651373	+	1.57255i	−0.810787	+	0.585341i	$0.800961\pi$
$998$	30.4401	−	22.8536i	0.963563	−	0.723419i
$999$		−	16.4426i		−	0.520222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bd.a.203.36	✓	216
13.5	odd	4		416.2.bi.a.395.11	yes	216
32.3	odd	8		416.2.bi.a.99.11	yes	216
416.291	even	8	inner	416.2.bd.a.291.36	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bd.a.203.36	✓	216	1.1	even	1	trivial
416.2.bd.a.291.36	yes	216	416.291	even	8	inner
416.2.bi.a.99.11	yes	216	32.3	odd	8
416.2.bi.a.395.11	yes	216	13.5	odd	4

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.719929 - 1.21725i) q^{2} +(-1.29743 - 3.13227i) q^{3} +(-0.963404 - 1.75267i) q^{4} +(1.53750 - 0.636854i) q^{5} +(-4.74682 - 0.675714i) q^{6} +1.05850i q^{7} +(-2.82702 - 0.0890924i) q^{8} +(-6.00647 + 6.00647i) q^{9} +(0.331680 - 2.33002i) q^{10} +(-1.30073 - 3.14023i) q^{11} +(-4.23989 + 5.29161i) q^{12} +(3.12718 - 1.79464i) q^{13} +(1.28847 + 0.762048i) q^{14} +(-3.98960 - 3.98960i) q^{15} +(-2.14370 + 3.37706i) q^{16} +5.62421 q^{17} +(2.98715 + 11.6356i) q^{18} +(-3.03250 - 1.25610i) q^{19} +(-2.59743 - 2.08119i) q^{20} +(3.31552 - 1.37333i) q^{21} +(-4.75888 - 0.677432i) q^{22} +(-1.21545 + 1.21545i) q^{23} +(3.38880 + 8.97059i) q^{24} +(-1.57721 + 1.57721i) q^{25} +(0.0668227 - 5.09858i) q^{26} +(17.2100 + 7.12863i) q^{27} +(1.85521 - 1.01977i) q^{28} +(5.31142 - 2.20006i) q^{29} +(-7.72857 + 1.98412i) q^{30} +(3.16004 - 3.16004i) q^{31} +(2.56742 + 5.04067i) q^{32} +(-8.14844 + 8.14844i) q^{33} +(4.04903 - 6.84608i) q^{34} +(0.674112 + 1.62745i) q^{35} +(16.3140 + 4.74070i) q^{36} +(-0.337788 - 0.815493i) q^{37} +(-3.71218 + 2.78701i) q^{38} +(-9.67859 - 7.46676i) q^{39} +(-4.40329 + 1.66342i) q^{40} -8.14697 q^{41} +(0.715246 - 5.02452i) q^{42} +(-1.82491 - 0.755903i) q^{43} +(-4.25066 + 5.30505i) q^{44} +(-5.40971 + 13.0602i) q^{45} +(0.604473 + 2.35455i) q^{46} +(3.07748 - 3.07748i) q^{47} +(13.3592 + 2.33317i) q^{48} +5.87957 q^{49} +(0.784380 + 3.05533i) q^{50} +(-7.29701 - 17.6165i) q^{51} +(-6.15815 - 3.75196i) q^{52} +(-12.4975 - 5.17664i) q^{53} +(21.0673 - 15.8168i) q^{54} +(-3.99973 - 3.99973i) q^{55} +(0.0943046 - 2.99242i) q^{56} +11.1283i q^{57} +(1.14582 - 8.04923i) q^{58} +(3.08537 - 1.27800i) q^{59} +(-3.14885 + 10.8360i) q^{60} +(-4.89167 + 2.02620i) q^{61} +(-1.57156 - 6.12157i) q^{62} +(-6.35787 - 6.35787i) q^{63} +(7.98413 + 0.503732i) q^{64} +(3.66513 - 4.75082i) q^{65} +(4.05241 + 15.7850i) q^{66} +(-0.628931 + 1.51837i) q^{67} +(-5.41839 - 9.85739i) q^{68} +(5.38409 + 2.23016i) q^{69} +(2.46633 + 0.351085i) q^{70} +9.72841 q^{71} +(17.5156 - 16.4453i) q^{72} -0.936219i q^{73} +(-1.23584 - 0.175924i) q^{74} +(6.98654 + 2.89392i) q^{75} +(0.719990 + 6.52511i) q^{76} +(3.32394 - 1.37682i) q^{77} +(-16.0568 + 6.40574i) q^{78} -15.7060 q^{79} +(-1.14525 + 6.55746i) q^{80} -37.6721i q^{81} +(-5.86524 + 9.91691i) q^{82} +(8.42036 + 3.48783i) q^{83} +(-5.60118 - 4.48794i) q^{84} +(8.64724 - 3.58180i) q^{85} +(-2.23393 + 1.67718i) q^{86} +(-13.7824 - 13.7824i) q^{87} +(3.39741 + 8.99339i) q^{88} +15.6464 q^{89} +(12.0029 + 15.9874i) q^{90} +(1.89963 + 3.31013i) q^{91} +(3.30126 + 0.959315i) q^{92} +(-13.9980 - 5.79818i) q^{93} +(-1.53050 - 5.96163i) q^{94} -5.46243 q^{95} +(12.4577 - 14.5818i) q^{96} +(-7.61074 - 7.61074i) q^{97} +(4.23287 - 7.15692i) q^{98} +(26.6745 + 11.0489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24}+ \cdots - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

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