LMFDB - Embedded newform 416.2.bi.a.395.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(99,416)]

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, 3, 2]))

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

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

chi := DirichletCharacter("416.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bi (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			395.11
Character	$\chi$	$=$	416.395
Dual form			416.2.bi.a.99.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21725 - 0.719929i) q^{2} +(-1.29743 - 3.13227i) q^{3} +(0.963404 + 1.75267i) q^{4} +(-0.636854 - 1.53750i) q^{5} +(-0.675714 + 4.74682i) q^{6} -1.05850 q^{7} +(0.0890924 - 2.82702i) q^{8} +(-6.00647 + 6.00647i) q^{9} +(-0.331680 + 2.33002i) q^{10} +(3.14023 - 1.30073i) q^{11} +(4.23989 - 5.29161i) q^{12} +(-3.48025 + 0.942251i) q^{13} +(1.28847 + 0.762048i) q^{14} +(-3.98960 + 3.98960i) q^{15} +(-2.14370 + 3.37706i) q^{16} -5.62421 q^{17} +(11.6356 - 2.98715i) q^{18} +(-1.25610 + 3.03250i) q^{19} +(2.08119 - 2.59743i) q^{20} +(1.37333 + 3.31552i) q^{21} +(-4.75888 - 0.677432i) q^{22} +(1.21545 - 1.21545i) q^{23} +(-8.97059 + 3.38880i) q^{24} +(1.57721 - 1.57721i) q^{25} +(4.91470 + 1.35858i) q^{26} +(17.2100 + 7.12863i) q^{27} +(-1.01977 - 1.85521i) q^{28} +(5.31142 - 2.20006i) q^{29} +(7.72857 - 1.98412i) q^{30} +(-3.16004 - 3.16004i) q^{31} +(5.04067 - 2.56742i) q^{32} +(-8.14844 - 8.14844i) q^{33} +(6.84608 + 4.04903i) q^{34} +(0.674112 + 1.62745i) q^{35} +(-16.3140 - 4.74070i) q^{36} +(0.815493 - 0.337788i) q^{37} +(3.71218 - 2.78701i) q^{38} +(7.46676 + 9.67859i) q^{39} +(-4.40329 + 1.66342i) q^{40} +8.14697i q^{41} +(0.715246 - 5.02452i) q^{42} +(1.82491 + 0.755903i) q^{43} +(5.30505 + 4.25066i) q^{44} +(13.0602 + 5.40971i) q^{45} +(-2.35455 + 0.604473i) q^{46} +(3.07748 + 3.07748i) q^{47} +(13.3592 + 2.33317i) q^{48} -5.87957 q^{49} +(-3.05533 + 0.784380i) q^{50} +(7.29701 + 17.6165i) q^{51} +(-5.00435 - 5.19197i) q^{52} +(-12.4975 - 5.17664i) q^{53} +(-15.8168 - 21.0673i) q^{54} +(-3.99973 - 3.99973i) q^{55} +(-0.0943046 + 2.99242i) q^{56} +11.1283 q^{57} +(-8.04923 - 1.14582i) q^{58} +(1.27800 + 3.08537i) q^{59} +(-10.8360 - 3.14885i) 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} +(1.51837 + 0.628931i) q^{67} +(-5.41839 - 9.85739i) q^{68} +(-5.38409 - 2.23016i) q^{69} +(0.351085 - 2.46633i) q^{70} -9.72841i q^{71} +(16.4453 + 17.5156i) q^{72} +0.936219 q^{73} +(-1.23584 - 0.175924i) q^{74} +(-6.98654 - 2.89392i) q^{75} +(-6.52511 + 0.719990i) q^{76} +(-3.32394 + 1.37682i) q^{77} +(-2.12104 - 17.1568i) q^{78} -15.7060 q^{79} +(6.55746 + 1.14525i) q^{80} -37.6721i q^{81} +(5.86524 - 9.91691i) q^{82} +(3.48783 - 8.42036i) q^{83} +(-4.48794 + 5.60118i) q^{84} +(3.58180 + 8.64724i) q^{85} +(-1.67718 - 2.23393i) q^{86} +(-13.7824 - 13.7824i) q^{87} +(-3.39741 - 8.99339i) q^{88} +15.6464i q^{89} +(-12.0029 - 15.9874i) q^{90} +(3.68386 - 0.997376i) q^{91} +(3.30126 + 0.959315i) q^{92} +(-5.79818 + 13.9980i) q^{93} +(-1.53050 - 5.96163i) q^{94} +5.46243 q^{95} +(-14.5818 - 12.4577i) q^{96} +(-7.61074 + 7.61074i) q^{97} +(7.15692 + 4.23287i) q^{98} +(-11.0489 + 26.6745i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{11} + 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{19} - 20 q^{20} - 16 q^{21} - 24 q^{22}+ \cdots - 116 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^11 + 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 - 4 * q^19 - 20 * q^20 - 16 * q^21 - 24 * q^22 + 28 * q^24 - 4 * q^26 - 8 * q^27 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 4 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 + 20 * q^39 - 8 * q^40 - 48 * q^42 + 32 * q^43 - 20 * q^44 + 4 * q^45 - 24 * q^46 - 8 * q^47 - 8 * q^48 + 168 * q^49 + 20 * q^50 - 4 * q^52 - 8 * q^53 + 20 * q^54 - 40 * q^55 - 56 * q^56 - 8 * q^57 + 32 * q^58 + 4 * 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 - 4 * q^70 + 56 * q^72 - 8 * q^73 - 8 * q^74 - 4 * q^76 - 56 * q^77 - 136 * q^78 - 16 * q^79 + 28 * q^80 + 88 * q^82 - 44 * q^83 + 44 * q^84 - 24 * q^85 + 64 * q^86 - 8 * q^87 - 64 * q^88 + 64 * q^90 + 16 * q^91 - 8 * q^92 + 56 * q^93 - 56 * q^94 - 28 * q^96 - 8 * q^97 - 76 * q^98 - 116 * q^99

Character values

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

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.21725	−	0.719929i	−0.860727	−	0.509067i
$2$	−1.21725	−	0.719929i	−0.860727	−	0.509067i
$3$	−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
$5$	−0.636854	−	1.53750i	−0.284810	−	0.687592i	0.715125	−	0.698996i	$-0.246370\pi$
$5$	−0.636854	−	1.53750i	−0.284810	−	0.687592i	−0.999935	+	0.0114048i	$0.996370\pi$
$6$	−0.675714	+	4.74682i	−0.275859	+	1.93788i
$7$	−1.05850			−0.400077			−0.200038	−	0.979788i	$-0.564107\pi$
$7$	−1.05850			−0.400077			−0.200038	+	0.979788i	$0.564107\pi$
$8$	0.0890924	−	2.82702i	0.0314989	−	0.999504i
$9$	−6.00647	+	6.00647i	−2.00216	+	2.00216i
$10$	−0.331680	+	2.33002i	−0.104887	+	0.736816i
$11$	3.14023	−	1.30073i	0.946815	−	0.392183i	0.144782	−	0.989464i	$-0.453752\pi$
$11$	3.14023	−	1.30073i	0.946815	−	0.392183i	0.802033	+	0.597280i	$0.203752\pi$
$12$	4.23989	−	5.29161i	1.22395	−	1.52755i
$13$	−3.48025	+	0.942251i	−0.965249	+	0.261333i
$13$	−3.48025	+	0.942251i	−0.965249	+	0.261333i
$14$	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	$-0.738905\pi$
$17$	−5.62421			−1.36407			−0.682036	+	0.731319i	$0.738905\pi$
$18$	11.6356	−	2.98715i	2.74254	−	0.704079i
$19$	−1.25610	+	3.03250i	−0.288170	+	0.695703i	−0.999978	−	0.00667081i	$-0.997877\pi$
$19$	−1.25610	+	3.03250i	−0.288170	+	0.695703i	0.711808	+	0.702374i	$0.247877\pi$
$20$	2.08119	−	2.59743i	0.465367	−	0.580803i
$21$	1.37333	+	3.31552i	0.299686	+	0.723506i
$22$	−4.75888	−	0.677432i	−1.01460	−	0.144429i
$23$	1.21545	−	1.21545i	0.253439	−	0.253439i	−0.568940	−	0.822379i	$-0.692646\pi$
$23$	1.21545	−	1.21545i	0.253439	−	0.253439i	0.822379	+	0.568940i	$0.192646\pi$
$24$	−8.97059	+	3.38880i	−1.83111	+	0.691736i
$25$	1.57721	−	1.57721i	0.315441	−	0.315441i
$26$	4.91470	+	1.35858i	0.963852	+	0.266439i
$27$	17.2100	+	7.12863i	3.31207	+	1.37191i
$28$	−1.01977	−	1.85521i	−0.192718	−	0.350601i
$29$	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	$-0.381450\pi$
$31$	−3.16004	−	3.16004i	−0.567560	−	0.567560i	−0.931444	+	0.363884i	$0.881450\pi$
$32$	5.04067	−	2.56742i	0.891073	−	0.453860i
$33$	−8.14844	−	8.14844i	−1.41846	−	1.41846i
$34$	6.84608	+	4.04903i	1.17409	+	0.694404i
$35$	0.674112	+	1.62745i	0.113946	+	0.275089i
$36$	−16.3140	−	4.74070i	−2.71900	−	0.790117i
$37$	0.815493	−	0.337788i	0.134066	−	0.0555320i	−0.314642	−	0.949211i	$-0.601884\pi$
$37$	0.815493	−	0.337788i	0.134066	−	0.0555320i	0.448708	+	0.893678i	$0.351884\pi$
$38$	3.71218	−	2.78701i	0.602195	−	0.452113i
$39$	7.46676	+	9.67859i	1.19564	+	1.54981i
$40$	−4.40329	+	1.66342i	−0.696222	+	0.263010i
$41$			8.14697i			1.27234i	0.771548	+	0.636171i	$0.219483\pi$
$41$			8.14697i			1.27234i	−0.771548	+	0.636171i	$0.780517\pi$
$42$	0.715246	−	5.02452i	0.110365	−	0.775301i
$43$	1.82491	+	0.755903i	0.278296	+	0.115274i	0.517466	−	0.855704i	$-0.326875\pi$
$43$	1.82491	+	0.755903i	0.278296	+	0.115274i	−0.239170	+	0.970978i	$0.576875\pi$
$44$	5.30505	+	4.25066i	0.799767	+	0.640811i
$45$	13.0602	+	5.40971i	1.94690	+	0.806432i
$46$	−2.35455	+	0.604473i	−0.347160	+	0.0891246i
$47$	3.07748	+	3.07748i	0.448897	+	0.448897i	0.894988	−	0.446091i	$-0.147184\pi$
$47$	3.07748	+	3.07748i	0.448897	+	0.448897i	−0.446091	+	0.894988i	$0.647184\pi$
$48$	13.3592	+	2.33317i	1.92823	+	0.336764i
$49$	−5.87957			−0.839939
$50$	−3.05533	+	0.784380i	−0.432089	+	0.110928i
$51$	7.29701	+	17.6165i	1.02179	+	2.46681i
$52$	−5.00435	−	5.19197i	−0.693978	−	0.719996i
$53$	−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	$-0.754376\pi$
$54$	−15.8168	−	21.0673i	−2.15240	−	2.86690i
$55$	−3.99973	−	3.99973i	−0.539324	−	0.539324i
$56$	−0.0943046	+	2.99242i	−0.0126020	+	0.399878i
$57$	11.1283			1.47398
$58$	−8.04923	−	1.14582i	−1.05692	−	0.150453i
$59$	1.27800	+	3.08537i	0.166382	+	0.401681i	0.984976	−	0.172691i	$-0.0552463\pi$
$59$	1.27800	+	3.08537i	0.166382	+	0.401681i	−0.818594	+	0.574372i	$0.805246\pi$
$60$	−10.8360	−	3.14885i	−1.39893	−	0.406515i
$61$	−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
$67$	1.51837	+	0.628931i	0.185499	+	0.0768361i	0.473500	−	0.880794i	$-0.342991\pi$
$67$	1.51837	+	0.628931i	0.185499	+	0.0768361i	−0.288001	+	0.957630i	$0.592991\pi$
$68$	−5.41839	−	9.85739i	−0.657076	−	1.19538i
$69$	−5.38409	−	2.23016i	−0.648168	−	0.268480i
$70$	0.351085	−	2.46633i	0.0419627	−	0.294783i
$71$		−	9.72841i		−	1.15455i	−0.816550	−	0.577275i	$-0.804116\pi$
$71$		−	9.72841i		−	1.15455i	0.816550	−	0.577275i	$-0.195884\pi$
$72$	16.4453	+	17.5156i	1.93810	+	2.06423i
$73$	0.936219			0.109576			0.0547881	−	0.998498i	$-0.482552\pi$
$73$	0.936219			0.109576			0.0547881	+	0.998498i	$0.482552\pi$
$74$	−1.23584	−	0.175924i	−0.143664	−	0.0204507i
$75$	−6.98654	−	2.89392i	−0.806737	−	0.334161i
$76$	−6.52511	+	0.719990i	−0.748481	+	0.0825885i
$77$	−3.32394	+	1.37682i	−0.378799	+	0.156903i
$78$	−2.12104	−	17.1568i	−0.240160	−	1.94263i
$79$	−15.7060			−1.76706			−0.883529	−	0.468376i	$-0.844839\pi$
$79$	−15.7060			−1.76706			−0.883529	+	0.468376i	$0.844839\pi$
$80$	6.55746	+	1.14525i	0.733146	+	0.128043i
$81$		−	37.6721i		−	4.18579i
$82$	5.86524	−	9.91691i	0.647707	−	1.09514i
$83$	3.48783	−	8.42036i	0.382839	−	0.924254i	−0.608576	−	0.793496i	$-0.708259\pi$
$83$	3.48783	−	8.42036i	0.382839	−	0.924254i	0.991414	−	0.130758i	$-0.0417412\pi$
$84$	−4.48794	+	5.60118i	−0.489674	+	0.611139i
$85$	3.58180	+	8.64724i	0.388501	+	0.937924i
$86$	−1.67718	−	2.23393i	−0.180855	−	0.240891i
$87$	−13.7824	−	13.7824i	−1.47763	−	1.47763i
$88$	−3.39741	−	8.99339i	−0.362165	−	0.958698i
$89$			15.6464i			1.65851i	0.558871	+	0.829255i	$0.311235\pi$
$89$			15.6464i			1.65851i	−0.558871	+	0.829255i	$0.688765\pi$
$90$	−12.0029	−	15.9874i	−1.26522	−	1.68522i
$91$	3.68386	−	0.997376i	0.386174	−	0.104553i
$92$	3.30126	+	0.959315i	0.344180	+	0.100016i
$93$	−5.79818	+	13.9980i	−0.601243	+	1.45153i
$94$	−1.53050	−	5.96163i	−0.157859	−	0.614896i
$95$	5.46243			0.560433
$96$	−14.5818	−	12.4577i	−1.48824	−	1.27146i
$97$	−7.61074	+	7.61074i	−0.772753	+	0.772753i	−0.978587	−	0.205834i	$-0.934009\pi$
$97$	−7.61074	+	7.61074i	−0.772753	+	0.772753i	0.205834	+	0.978587i	$0.434009\pi$
$98$	7.15692	+	4.23287i	0.722958	+	0.427585i
$99$	−11.0489	+	26.6745i	−1.11046	+	2.68088i
$100$	4.28381	+	1.24483i	0.428381	+	0.124483i
$101$	−5.80190	−	2.40323i	−0.577311	−	0.239130i	0.0748702	−	0.997193i	$-0.476146\pi$
$101$	−5.80190	−	2.40323i	−0.577311	−	0.239130i	−0.652181	+	0.758063i	$0.726146\pi$
$102$	3.80036	−	26.6971i	0.376292	−	2.64341i
$103$	−4.80414	−	4.80414i	−0.473366	−	0.473366i	0.429636	−	0.903002i	$-0.358642\pi$
$103$	−4.80414	−	4.80414i	−0.473366	−	0.473366i	−0.903002	+	0.429636i	$0.858642\pi$
$104$	2.35370	+	9.92271i	0.230799	+	0.973001i
$105$	4.22300	−	4.22300i	0.412123	−	0.412123i
$106$	11.4858	+	15.2986i	1.11560	+	1.48593i
$107$	−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
$109$	−4.42535	−	1.83304i	−0.423872	−	0.175573i	0.160542	−	0.987029i	$-0.448676\pi$
$109$	−4.42535	−	1.83304i	−0.423872	−	0.175573i	−0.584414	+	0.811456i	$0.698676\pi$
$110$	1.98916	+	7.74821i	0.189659	+	0.738763i
$111$	−2.11609	−	2.11609i	−0.200850	−	0.200850i
$112$	2.26912	−	3.57463i	0.214412	−	0.337771i
$113$			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
$115$	−2.64283	−	1.09469i	−0.246445	−	0.102081i
$116$	8.97303	+	7.18962i	0.833125	+	0.667539i
$117$	15.2444	−	26.5636i	1.40935	−	2.45581i
$118$	0.665596	−	4.67574i	0.0612731	−	0.430437i
$119$	5.95325			0.545734
$120$	10.9232	+	11.6341i	0.997151	+	1.06205i
$121$	0.390975	−	0.390975i	0.0355432	−	0.0355432i
$122$	7.41312	+	1.05527i	0.671152	+	0.0955392i
$123$	25.5185	−	10.5701i	2.30093	−	0.953075i
$124$	2.49411	−	8.58291i	0.223978	−	0.770768i
$125$	−11.1169	−	4.60478i	−0.994327	−	0.411864i
$126$	−12.3163	+	3.16191i	−1.09723	+	0.281686i
$127$	−4.22739			−0.375120			−0.187560	−	0.982253i	$-0.560058\pi$
$127$	−4.22739			−0.375120			−0.187560	+	0.982253i	$0.560058\pi$
$128$	9.35604	+	6.36117i	0.826965	+	0.562254i
$129$		−	6.69685i		−	0.589624i
$130$	−1.04113	−	8.42157i	−0.0913131	−	0.738621i
$131$	−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	$-0.307821\pi$
$132$	6.43129	−	22.1318i	0.559772	−	1.92632i
$133$	1.32959	−	3.20991i	0.115290	−	0.278335i
$134$	−1.39546	−	1.85869i	−0.120549	−	0.160566i
$135$		−	31.0004i		−	2.66809i
$136$	−0.501074	+	15.8998i	−0.0429668	+	1.36340i
$137$	−2.95422			−0.252396			−0.126198	−	0.992005i	$-0.540277\pi$
$137$	−2.95422			−0.252396			−0.126198	+	0.992005i	$0.540277\pi$
$138$	4.94823	+	6.59083i	0.421222	+	0.561049i
$139$	−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
$141$	5.64668	−	13.6323i	0.475537	−	1.14805i
$142$	−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
$148$	1.37768	+	1.10386i	0.113245	+	0.0907370i
$149$	16.6411	−	6.89297i	1.36329	−	0.564694i	0.423331	−	0.905975i	$-0.360861\pi$
$149$	16.6411	−	6.89297i	1.36329	−	0.564694i	0.939961	+	0.341281i	$0.110861\pi$
$150$	6.42097	+	8.55245i	0.524270	+	0.698304i
$151$			15.1635i			1.23399i	0.786968	+	0.616994i	$0.211650\pi$
$151$			15.1635i			1.23399i	−0.786968	+	0.616994i	$0.788350\pi$
$152$	8.46104	+	3.82120i	0.686281	+	0.309941i
$153$	33.7817	−	33.7817i	2.73109	−	2.73109i
$154$	5.03729	+	0.717064i	0.405917	+	0.0577826i
$155$	−2.84608	+	6.87106i	−0.228603	+	0.551897i
$156$	−9.76986	+	22.4112i	−0.782215	+	1.79433i
$157$	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	$0.341004\pi$
$158$	19.1181	+	11.3072i	1.52095	+	0.899551i
$159$			45.8619i			3.63708i
$160$	−7.15758	−	6.11497i	−0.565856	−	0.483431i
$161$	−1.28656	+	1.28656i	−0.101395	+	0.101395i
$162$	−27.1212	+	45.8564i	−2.13084	+	3.60282i
$163$	0.936885	−	2.26184i	0.0733825	−	0.177161i	−0.882932	−	0.469501i	$-0.844434\pi$
$163$	0.936885	−	2.26184i	0.0733825	−	0.177161i	0.956314	+	0.292340i	$0.0944339\pi$
$164$	−14.2789	+	7.84883i	−1.11500	+	0.612890i
$165$	−7.33888	+	17.7176i	−0.571331	+	1.37931i
$166$	−10.3076	+	7.73871i	−0.800027	+	0.600640i
$167$	−11.7824			−0.911750			−0.455875	−	0.890044i	$-0.650674\pi$
$167$	−11.7824			−0.911750			−0.455875	+	0.890044i	$0.650674\pi$
$168$	9.49540	−	3.58706i	0.732586	−	0.276747i
$169$	11.2243	−	6.55855i	0.863410	−	0.504503i
$170$	1.86544	−	13.1045i	0.143073	−	1.00507i
$171$	−10.6699	−	25.7594i	−0.815946	−	1.96987i
$172$	0.433279	+	3.92671i	0.0330372	+	0.299409i
$173$	−17.4177	+	7.21464i	−1.32424	+	0.548519i	−0.929007	−	0.370062i	$-0.879337\pi$
$173$	−17.4177	+	7.21464i	−1.32424	+	0.548519i	−0.395234	+	0.918580i	$0.629337\pi$
$174$	6.85429	+	26.6990i	0.519622	+	2.02404i
$175$	−1.66948	+	1.66948i	−0.126201	+	0.126201i
$176$	−2.33909	+	13.3931i	−0.176316	+	1.00954i
$177$	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	$-0.916505\pi$
$179$	−6.23779	−	15.0593i	−0.466234	−	1.12559i	0.499560	−	0.866279i	$-0.333495\pi$
$180$	3.10081	+	28.1020i	0.231121	+	2.09460i
$181$	−3.92202	+	9.46859i	−0.291521	+	0.703795i	−0.999998	−	0.00193915i	$-0.999383\pi$
$181$	−3.92202	+	9.46859i	−0.291521	+	0.703795i	0.708477	+	0.705734i	$0.249383\pi$
$182$	−5.20223	−	1.43806i	−0.385615	−	0.106596i
$183$	12.6932	+	12.6932i	0.938308	+	0.938308i
$184$	−3.32783	−	3.54440i	−0.245331	−	0.261297i
$185$	−1.03870	−	1.03870i	−0.0763667	−	0.0763667i
$186$	17.1354	−	12.8649i	1.25643	−	0.943297i
$187$	−17.6613	+	7.31556i	−1.29152	+	0.534966i
$188$	−2.42895	+	8.35866i	−0.177149	+	0.609618i
$189$	−18.2169	−	7.54568i	−1.32508	−	0.548868i
$190$	−6.64915	−	3.93256i	−0.482380	−	0.285298i
$191$		−	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	0.949108	−	0.314950i	$-0.101988\pi$
$193$	8.81001	+	8.81001i	0.634158	+	0.634158i	−0.314950	+	0.949108i	$0.601988\pi$
$194$	14.7434	−	3.78499i	1.05851	−	0.271747i
$195$	10.1256	−	17.6440i	0.725110	−	1.26351i
$196$	−5.66440	−	10.3049i	−0.404600	−	0.736068i
$197$	2.47701	+	5.98004i	0.176480	+	0.426060i	0.987224	−	0.159341i	$-0.0509370\pi$
$197$	2.47701	+	5.98004i	0.176480	+	0.426060i	−0.810744	+	0.585401i	$0.800937\pi$
$198$	32.6530	−	24.5151i	2.32055	−	1.74221i
$199$	6.94839	+	6.94839i	0.492558	+	0.492558i	0.909111	−	0.416553i	$-0.136762\pi$
$199$	6.94839	+	6.94839i	0.492558	+	0.492558i	−0.416553	+	0.909111i	$0.636762\pi$
$200$	−4.31828	−	4.59931i	−0.305349	−	0.325221i
$201$		−	5.57195i		−	0.393015i
$202$	5.33222	+	7.10229i	0.375174	+	0.499715i
$203$	−5.62216	+	2.32877i	−0.394598	+	0.163448i
$204$	−23.8460	+	29.7611i	−1.66956	+	2.08369i
$205$	12.5260	−	5.18843i	0.874852	−	0.362376i
$206$	2.38921	+	9.30648i	0.166464	+	0.648413i
$207$			14.6012i			1.01485i
$208$	4.27860	−	13.7729i	0.296667	−	0.954981i
$209$			11.1566i			0.771717i
$210$	−8.18072	+	2.10020i	−0.564523	+	0.144927i
$211$	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
$213$	−30.4720	+	12.6219i	−2.08791	+	0.864839i
$214$	4.59772	−	3.45185i	0.314294	−	0.235964i
$215$		−	3.28720i		−	0.224186i
$216$	21.6861	−	48.0181i	1.47555	−	3.26722i
$217$	3.34492	+	3.34492i	0.227068	+	0.227068i
$218$	4.06711	+	5.41721i	0.275459	+	0.366900i
$219$	−1.21468	−	2.93249i	−0.0820802	−	0.198159i
$220$	3.15685	−	10.8636i	0.212835	−	0.732422i
$221$	19.5737	−	5.29942i	1.31667	−	0.356478i
$222$	1.05238	+	4.09924i	0.0706310	+	0.275123i
$223$	−1.25046	−	1.25046i	−0.0837368	−	0.0837368i	0.663998	−	0.747735i	$-0.268858\pi$
$223$	−1.25046	−	1.25046i	−0.0837368	−	0.0837368i	−0.747735	+	0.663998i	$0.768858\pi$
$224$	−5.33557	+	2.71762i	−0.356498	+	0.181579i
$225$			18.9469i			1.26313i
$226$	0.433603	−	0.733133i	0.0288428	−	0.0487673i
$227$	−0.210501	−	0.0871923i	−0.0139714	−	0.00578716i	0.375687	−	0.926747i	$-0.377407\pi$
$227$	−0.210501	−	0.0871923i	−0.0139714	−	0.00578716i	−0.389658	+	0.920960i	$0.627407\pi$
$228$	10.7211	+	19.5043i	0.710020	+	1.29170i
$229$	10.5845	−	4.38426i	0.699445	−	0.289720i	−0.00448378	−	0.999990i	$-0.501427\pi$
$229$	10.5845	−	4.38426i	0.699445	−	0.289720i	0.703929	+	0.710270i	$0.251427\pi$
$230$	2.42888	+	3.23517i	0.160156	+	0.213321i
$231$	8.62516	+	8.62516i	0.567494	+	0.567494i
$232$	−5.74642	−	15.2115i	−0.377271	−	0.998685i
$233$	−15.0215	−	15.0215i	−0.984094	−	0.984094i	0.0157814	−	0.999875i	$-0.494976\pi$
$233$	−15.0215	−	15.0215i	−0.984094	−	0.984094i	−0.999875	+	0.0157814i	$0.994976\pi$
$234$	−37.6803	+	21.3597i	−2.46324	+	1.39633i
$235$	2.77172	−	6.69153i	0.180807	−	0.436508i
$236$	−4.17640	+	5.21237i	−0.271860	+	0.339296i
$237$	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	−0.0167427	−	0.999860i	$-0.505330\pi$
$239$	15.1986	−	15.1986i	0.983117	−	0.983117i	0.999860	+	0.0167427i	$0.00532962\pi$
$240$	−4.92059	−	22.0256i	−0.317623	−	1.42175i
$241$	−2.07099	+	2.07099i	−0.133404	+	0.133404i	−0.770656	−	0.637252i	$-0.780071\pi$
$241$	−2.07099	+	2.07099i	−0.133404	+	0.133404i	0.637252	+	0.770656i	$0.280071\pi$
$242$	−0.757389	+	0.194441i	−0.0486868	+	0.0124991i
$243$	−66.3689	+	27.4909i	−4.25757	+	1.76354i
$244$	−8.26392	−	6.62144i	−0.529043	−	0.423894i
$245$	3.74443	+	9.03985i	0.239223	+	0.577535i
$246$	−38.6722	−	5.50503i	−2.46565	−	0.350988i
$247$	1.51418	−	11.7374i	0.0963449	−	0.746835i
$248$	−9.21505	+	8.65198i	−0.585156	+	0.549401i
$249$	−30.9000			−1.95821
$250$	10.2170	+	13.6086i	0.646178	+	0.860681i
$251$	10.8472	−	26.1875i	0.684670	−	1.65294i	−0.0705829	−	0.997506i	$-0.522486\pi$
$251$	10.8472	−	26.1875i	0.684670	−	1.65294i	0.755253	−	0.655434i	$-0.227514\pi$
$252$	17.2685	+	5.01805i	1.08781	+	0.316107i
$253$	2.23583	−	5.39777i	0.140565	−	0.339355i
$254$	5.14579	+	3.04342i	0.322876	+	0.190961i
$255$	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	$-0.763225\pi$
$257$		−	21.7103i		−	1.35425i	0.735867	−	0.677126i	$-0.236775\pi$
$258$	−4.82125	+	8.15175i	−0.300158	+	0.507506i
$259$	−0.863202	+	0.357550i	−0.0536368	+	0.0222171i
$260$	−4.79562	+	11.0007i	−0.297412	+	0.682235i
$261$	−18.6883	+	45.1175i	−1.15678	+	2.79270i
$262$	−2.47865	+	17.4123i	−0.153132	+	1.07573i
$263$	−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
$265$			22.5117i			1.38288i
$266$	−3.92935	+	2.95006i	−0.240924	+	0.180880i
$267$	49.0086	−	20.3000i	2.99928	−	1.24234i
$268$	0.360499	+	3.26712i	0.0220210	+	0.199571i
$269$	−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	−0.945818	−	0.324696i	$-0.894738\pi$
$271$	−20.9153	−	20.9153i	−1.27051	−	1.27051i	−0.324696	−	0.945818i	$-0.605262\pi$
$272$	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
$275$	2.90128	−	7.00430i	0.174953	−	0.422375i
$276$	−1.27832	−	11.5851i	−0.0769455	−	0.697340i
$277$	−0.629068	+	1.51870i	−0.0377970	+	0.0912501i	−0.941651	−	0.336591i	$-0.890726\pi$
$277$	−0.629068	+	1.51870i	−0.0377970	+	0.0912501i	0.903854	+	0.427842i	$0.140726\pi$
$278$	6.55455	−	4.92100i	0.393116	−	0.295142i
$279$	37.9614			2.27269
$280$	4.66090	−	1.76074i	0.278542	−	0.105224i
$281$			24.6758i			1.47203i	0.676964	+	0.736016i	$0.263295\pi$
$281$			24.6758i			1.47203i	−0.676964	+	0.736016i	$0.736705\pi$
$282$	−16.6877	+	12.5287i	−0.993740	+	0.746075i
$283$	−3.43840	+	8.30103i	−0.204392	+	0.493445i	−0.992522	−	0.122063i	$-0.961049\pi$
$283$	−3.43840	+	8.30103i	−0.204392	+	0.493445i	0.788131	+	0.615508i	$0.211049\pi$
$284$	17.0507	−	9.37239i	1.01177	−	0.556149i
$285$	−7.08711	−	17.1098i	−0.419804	−	1.01350i
$286$	17.2004	−	2.12643i	1.01708	−	0.125738i
$287$		−	8.62360i		−	0.509035i
$288$	−14.8555	+	45.6978i	−0.875370	+	2.69277i
$289$	14.6318			0.860692
$290$	3.36449	+	13.1054i	0.197570	+	0.769577i
$291$	33.7133	+	13.9645i	1.97631	+	0.818613i
$292$	0.901957	+	1.64088i	0.0527830	+	0.0960254i
$293$	11.6887	−	4.84160i	0.682859	−	0.282849i	−0.0141626	−	0.999900i	$-0.504508\pi$
$293$	11.6887	−	4.84160i	0.682859	−	0.282849i	0.697021	+	0.717050i	$0.254508\pi$
$294$	3.97291	−	27.9092i	0.231705	−	1.62770i
$295$	3.92986	−	3.92986i	0.228805	−	0.228805i
$296$	−0.882281	−	2.33551i	−0.0512815	−	0.135749i
$297$	63.3158			3.67396
$298$	−25.2189	−	3.58993i	−1.46089	−	0.207959i
$299$	−3.08482	+	5.37535i	−0.178400	+	0.310864i
$300$	−1.65878	−	15.0331i	−0.0957696	−	0.867938i
$301$	−1.93168	−	0.800126i	−0.111340	−	0.0461185i
$302$	10.9166	−	18.4578i	0.628182	−	1.06213i
$303$			21.2911i			1.22314i
$304$	−7.54822	−	10.7427i	−0.432920	−	0.616137i
$305$	6.23056	+	6.23056i	0.356761	+	0.356761i
$306$	−65.4412	+	16.8004i	−3.74102	+	0.960415i
$307$	−8.15097	−	3.37624i	−0.465200	−	0.192692i	0.137756	−	0.990466i	$-0.456011\pi$
$307$	−8.15097	−	3.37624i	−0.465200	−	0.192692i	−0.602957	+	0.797774i	$0.706011\pi$
$308$	−5.61542	−	4.49934i	−0.319968	−	0.256374i
$309$	−8.81483	+	21.2809i	−0.501458	+	1.21063i
$310$	8.41108	−	6.31483i	0.477717	−	0.358658i
$311$	6.71893	−	6.71893i	0.380996	−	0.380996i	−0.490465	−	0.871461i	$-0.663173\pi$
$311$	6.71893	−	6.71893i	0.380996	−	0.380996i	0.871461	+	0.490465i	$0.163173\pi$
$312$	28.0268	−	20.2464i	1.58671	−	1.14623i
$313$	−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	$0.850649\pi$
$314$	−3.74019	−	0.532420i	−0.211071	−	0.0300462i
$315$	−13.8243	−	5.72620i	−0.778910	−	0.322635i
$316$	−15.1312	−	27.5274i	−0.851196	−	1.54854i
$317$	−2.48498	+	5.99926i	−0.139570	+	0.336952i	−0.978173	−	0.207791i	$-0.933373\pi$
$317$	−2.48498	+	5.99926i	−0.139570	+	0.336952i	0.838603	+	0.544743i	$0.183373\pi$
$318$	33.0173	−	55.8255i	1.85152	−	3.13054i
$319$	13.8174	−	13.8174i	0.773626	−	0.773626i
$320$	4.31023	+	12.5964i	0.240949	+	0.704161i
$321$	13.7830			0.769290
$322$	2.49230	−	0.639836i	0.138891	−	0.0356567i
$323$	7.06459	−	17.0554i	0.393084	−	0.948989i
$324$	66.0267	−	36.2934i	3.66815	−	2.01630i
$325$	−4.00295	+	6.97520i	−0.222044	+	0.386914i
$326$	−2.76879	+	2.07874i	−0.153349	+	0.115131i
$327$			16.2396i			0.898053i
$328$	23.0317	+	0.725833i	1.27171	+	0.0400774i
$329$	−3.25752	−	3.25752i	−0.179593	−	0.179593i
$330$	21.6887	−	16.2833i	1.19392	−	0.896368i
$331$	−9.51401	−	22.9688i	−0.522937	−	1.26248i	−0.936071	−	0.351812i	$-0.885566\pi$
$331$	−9.51401	−	22.9688i	−0.522937	−	1.26248i	0.413134	−	0.910670i	$-0.364434\pi$
$332$	18.1183	−	1.99920i	0.994371	−	0.109720i
$333$	−2.86932	+	6.92715i	−0.157238	+	0.379605i
$334$	14.3422	+	8.48250i	0.784768	+	0.464142i
$335$		−	2.73504i		−	0.149431i
$336$	−14.1407	−	2.46967i	−0.771440	−	0.134731i
$337$	6.94575			0.378359			0.189180	−	0.981943i	$-0.439417\pi$
$337$	6.94575			0.378359			0.189180	+	0.981943i	$0.439417\pi$
$338$	−18.3845	−	0.0973164i	−0.999986	−	0.00529332i
$339$	1.88652	−	0.781422i	0.102462	−	0.0424410i
$340$	−11.7050	+	14.6085i	−0.634794	+	0.792257i
$341$	−14.0336	−	5.81291i	−0.759962	−	0.314787i
$342$	−5.55699	+	39.0372i	−0.300487	+	2.11089i
$343$	13.6331			0.736117
$344$	2.29954	−	5.09172i	0.123983	−	0.274527i
$345$			9.69833i			0.522141i
$346$	26.3957	+	3.75746i	1.41904	+	0.202002i
$347$	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
$349$	−15.2264	−	6.30699i	−0.815052	−	0.337606i	−0.0640841	−	0.997944i	$-0.520413\pi$
$349$	−15.2264	−	6.30699i	−0.815052	−	0.337606i	−0.750968	+	0.660339i	$0.770413\pi$
$350$	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	0.0384250	−	0.999261i	$-0.487766\pi$
$353$	19.4964	−	19.4964i	1.03769	−	1.03769i	0.999261	−	0.0384250i	$-0.0122341\pi$
$354$	−15.5092	+	3.98161i	−0.824307	+	0.211620i
$355$	−14.9574	+	6.19558i	−0.793859	+	0.328827i
$356$	−27.4229	+	15.0738i	−1.45341	+	0.798908i
$357$	−7.72392	−	18.6472i	−0.408793	−	0.986914i
$358$	−3.24871	+	22.8218i	−0.171699	+	1.20617i
$359$	15.5873			0.822664			0.411332	−	0.911486i	$-0.365064\pi$
$359$	15.5873			0.822664			0.411332	+	0.911486i	$0.365064\pi$
$360$	16.4569	−	36.4395i	0.867357	−	1.92053i
$361$	5.81677	+	5.81677i	0.306146	+	0.306146i
$362$	11.5908	−	8.70209i	0.609199	−	0.457372i
$363$	−1.73190	−	0.717376i	−0.0909012	−	0.0376525i
$364$	5.29712	+	5.49572i	0.277645	+	0.288054i
$365$	−0.596235	−	1.43944i	−0.0312083	−	0.0753436i
$366$	−6.31261	−	24.5890i	−0.329966	−	1.28529i
$367$	−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
$370$	0.516569	+	2.01215i	0.0268551	+	0.104607i
$371$	13.2287	+	5.47949i	0.686798	+	0.284481i
$372$	−30.1199	+	3.32348i	−1.56165	+	0.172314i
$373$	−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
$375$			40.7955i			2.10667i
$376$	8.97429	−	8.42593i	0.462814	−	0.434534i
$377$	−16.4121	+	12.6615i	−0.845265	+	0.652099i
$378$	16.7422	+	22.2999i	0.861125	+	1.14698i
$379$	5.91799	−	2.45131i	0.303987	−	0.125915i	−0.225476	−	0.974249i	$-0.572394\pi$
$379$	5.91799	−	2.45131i	0.303987	−	0.125915i	0.529462	+	0.848333i	$0.322394\pi$
$380$	5.26253	+	9.57383i	0.269962	+	0.491127i
$381$	5.48473	+	13.2413i	0.280991	+	0.678373i
$382$	−8.85274	+	14.9682i	−0.452946	+	0.765838i
$383$	−22.5175	−	22.5175i	−1.15059	−	1.15059i	−0.986435	−	0.164154i	$-0.947511\pi$
$383$	−22.5175	−	22.5175i	−1.15059	−	1.15059i	−0.164154	−	0.986435i	$-0.552489\pi$
$384$	7.78611	−	37.5588i	0.397334	−	1.91666i
$385$	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
$388$	−20.6713	−	6.00689i	−1.04943	−	0.304954i
$389$	−8.36014	−	3.46288i	−0.423876	−	0.175575i	0.160540	−	0.987029i	$-0.448676\pi$
$389$	−8.36014	−	3.46288i	−0.423876	−	0.175575i	−0.584416	+	0.811454i	$0.698676\pi$
$390$	−25.0278	+	14.1875i	−1.26733	+	0.718411i
$391$	−6.83597	+	6.83597i	−0.345710	+	0.345710i
$392$	−0.523825	+	16.6217i	−0.0264571	+	0.839522i
$393$	−29.8143	+	29.8143i	−1.50393	+	1.50393i
$394$	1.29005	−	9.06248i	0.0649920	−	0.456561i
$395$	10.0024	+	24.1479i	0.503275	+	1.21501i
$396$	−57.3961	+	6.33317i	−2.88426	+	0.318254i
$397$	5.55421	−	13.4091i	0.278758	−	0.672981i	−0.721044	−	0.692889i	$-0.756337\pi$
$397$	5.55421	−	13.4091i	0.278758	−	0.672981i	0.999802	+	0.0199082i	$0.00633740\pi$
$398$	−3.45559	−	13.4603i	−0.173213	−	0.674703i
$399$	−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	$-0.964691\pi$
$401$	−17.6852	+	17.6852i	−0.883155	+	0.883155i	0.110699	+	0.993854i	$0.464691\pi$
$402$	−4.01141	+	6.78246i	−0.200071	+	0.338278i
$403$	13.9753	+	8.02020i	0.696159	+	0.399514i
$404$	−1.37751	−	12.4841i	−0.0685339	−	0.621107i
$405$	−57.9209	+	23.9916i	−2.87811	+	1.19215i
$406$	8.52014	+	1.21285i	0.422847	+	0.0601928i
$407$	2.12146	−	2.12146i	0.105157	−	0.105157i
$408$	50.4525	−	19.0593i	2.49777	−	0.943577i
$409$	−10.7729			−0.532684			−0.266342	−	0.963879i	$-0.585815\pi$
$409$	−10.7729			−0.532684			−0.266342	+	0.963879i	$0.585815\pi$
$410$	−18.9826	−	2.70219i	−0.937482	−	0.133452i
$411$	3.83289	+	9.25342i	0.189063	+	0.456437i
$412$	3.79174	−	13.0484i	0.186806	−	0.642848i
$413$	−1.35277	−	3.26587i	−0.0665654	−	0.160703i
$414$	10.5118	−	17.7733i	0.516627	−	0.873510i
$415$	−15.1675			−0.744546
$416$	−15.1237	+	13.6848i	−0.741499	+	0.670955i
$417$	19.6491			0.962222
$418$	8.03195	−	13.5804i	0.392856	−	0.664238i
$419$	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
$421$	0.926542	+	2.23687i	0.0451569	+	0.109018i	0.944849	−	0.327508i	$-0.106209\pi$
$421$	0.926542	+	2.23687i	0.0451569	+	0.109018i	−0.899692	+	0.436526i	$0.856209\pi$
$422$	−30.4238	−	4.33086i	−1.48101	−	0.210823i
$423$	−36.9696			−1.79752
$424$	−15.7479	+	34.8696i	−0.764786	+	1.69342i
$425$	−8.87054	+	8.87054i	−0.430284	+	0.430284i
$426$	46.1790	+	6.57363i	2.23738	+	0.318493i
$427$	5.17785	−	2.14474i	0.250574	−	0.103791i
$428$	−8.08167	+	0.891744i	−0.390642	+	0.0431041i
$429$	36.0365	+	20.6808i	1.73986	+	0.998477i
$430$	−2.36655	+	4.00136i	−0.114125	+	0.192963i
$431$	2.20472	−	2.20472i	0.106198	−	0.106198i	−0.652011	−	0.758209i	$-0.726075\pi$
$431$	2.20472	−	2.20472i	0.106198	−	0.106198i	0.758209	+	0.652011i	$0.226075\pi$
$432$	−60.9670	+	42.8376i	−2.93328	+	2.06103i
$433$	34.6879			1.66699			0.833497	−	0.552524i	$-0.186335\pi$
$433$	34.6879			1.66699			0.833497	+	0.552524i	$0.186335\pi$
$434$	−1.66350	−	6.47971i	−0.0798507	−	0.311036i
$435$	−12.4131	+	29.9678i	−0.595161	+	1.43685i
$436$	−1.05069	−	9.52214i	−0.0503188	−	0.456028i
$437$	2.15913	+	5.21260i	0.103285	+	0.249352i
$438$	−0.632616	+	4.44406i	−0.0302276	+	0.212345i
$439$	21.5727	−	21.5727i	1.02961	−	1.02961i	0.0300629	−	0.999548i	$-0.490429\pi$
$439$	21.5727	−	21.5727i	1.02961	−	1.02961i	0.999548	−	0.0300629i	$-0.00957077\pi$
$440$	−11.6637	+	10.9510i	−0.556045	+	0.522068i
$441$	35.3155	−	35.3155i	1.68169	−	1.68169i
$442$	−27.6413	−	7.64093i	−1.31476	−	0.363442i
$443$	−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	$0.717574\pi$
$444$	1.67015	−	5.74745i	0.0792620	−	0.272762i
$445$	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
$448$	8.45123	+	0.533203i	0.399283	+	0.0251915i
$449$	−20.3698	−	20.3698i	−0.961308	−	0.961308i	0.0379705	−	0.999279i	$-0.487911\pi$
$449$	−20.3698	−	20.3698i	−0.961308	−	0.961308i	−0.999279	+	0.0379705i	$0.987911\pi$
$450$	13.6404	−	23.0631i	0.643015	−	1.08721i
$451$	10.5970	+	25.5833i	0.498992	+	1.20467i
$452$	−1.05561	+	0.580244i	−0.0496516	+	0.0272924i
$453$	47.4962	−	19.6736i	2.23156	−	0.924344i
$454$	0.193460	+	0.257681i	0.00907954	+	0.0120936i
$455$	−3.87955	−	5.02876i	−0.181876	−	0.235752i
$456$	0.991448	−	31.4600i	0.0464288	−	1.47325i
$457$			3.60171i			0.168481i	0.996445	+	0.0842403i	$0.0268463\pi$
$457$			3.60171i			0.168481i	−0.996445	+	0.0842403i	$0.973154\pi$
$458$	−16.0404	−	2.28337i	−0.749518	−	0.106695i
$459$	−96.7929	−	40.0929i	−4.51791	−	1.87138i
$460$	−0.627472	−	5.68664i	−0.0292560	−	0.265141i
$461$	−22.7568	−	9.42616i	−1.05989	−	0.439020i	−0.216476	−	0.976288i	$-0.569456\pi$
$461$	−22.7568	−	9.42616i	−1.05989	−	0.439020i	−0.843412	+	0.537268i	$0.819456\pi$
$462$	−4.28949	−	16.7085i	−0.199565	−	0.777349i
$463$	−12.5064	−	12.5064i	−0.581221	−	0.581221i	0.354018	−	0.935239i	$-0.384815\pi$
$463$	−12.5064	−	12.5064i	−0.581221	−	0.581221i	−0.935239	+	0.354018i	$0.884815\pi$
$464$	−3.95637	+	22.6533i	−0.183670	+	1.05165i
$465$	25.2146			1.16930
$466$	7.47056	+	29.0994i	0.346067	+	1.34801i
$467$	−1.44805	−	3.49590i	−0.0670077	−	0.161771i	0.886828	−	0.462099i	$-0.152904\pi$
$467$	−1.44805	−	3.49590i	−0.0670077	−	0.161771i	−0.953836	+	0.300329i	$0.902904\pi$
$468$	61.2438	+	1.12694i	2.83100	+	0.0520926i
$469$	−1.60720	−	0.665726i	−0.0742138	−	0.0307403i
$470$	−8.19132	+	6.14984i	−0.377837	+	0.283671i
$471$	−6.40418	−	6.40418i	−0.295089	−	0.295089i
$472$	8.83626	−	3.33806i	0.406722	−	0.153646i
$473$	6.71386			0.308704
$474$	10.6127	−	74.5533i	0.487459	−	3.42435i
$475$	2.80174	+	6.76401i	0.128553	+	0.310354i
$476$	5.73539	+	10.4341i	0.262881	+	0.478245i
$477$	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	$-0.672657\pi$
$479$	7.44679	−	7.44679i	0.340253	−	0.340253i	0.856462	+	0.516210i	$0.172657\pi$
$480$	−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
$483$	5.69908	+	2.36064i	0.259317	+	0.107413i
$484$	1.06192	+	0.308583i	0.0482689	+	0.0140265i
$485$	16.5484	+	6.85459i	0.751426	+	0.311251i
$486$	100.579	+	14.3176i	4.56237	+	0.649458i
$487$			35.5102i			1.60912i	0.593871	+	0.804560i	$0.297599\pi$
$487$			35.5102i			1.60912i	−0.593871	+	0.804560i	$0.702401\pi$
$488$	5.29230	+	14.0094i	0.239571	+	0.634176i
$489$	−8.30024			−0.375350
$490$	1.95014	−	13.6995i	0.0880982	−	0.618880i
$491$	18.5038	+	7.66454i	0.835067	+	0.345896i	0.758906	−	0.651200i	$-0.225734\pi$
$491$	18.5038	+	7.66454i	0.835067	+	0.345896i	0.0761602	+	0.997096i	$0.475734\pi$
$492$	43.1105	+	34.5422i	1.94357	+	1.55728i
$493$	−29.8726	+	12.3736i	−1.34539	+	0.557280i
$494$	−10.2933	+	13.1973i	−0.463115	+	0.593775i
$495$	48.0486			2.15962
$496$	17.4459	−	3.89746i	0.783342	−	0.175001i
$497$			10.2976i			0.461909i
$498$	37.6131	+	22.2458i	1.68548	+	0.996859i
$499$	10.3001	−	24.8667i	0.461096	−	1.11318i	−0.506852	−	0.862033i	$-0.669191\pi$
$499$	10.3001	−	24.8667i	0.461096	−	1.11318i	0.967948	−	0.251151i	$-0.0808092\pi$
$500$	−2.63943	−	23.9205i	−0.118039	−	1.06976i
$501$	15.2868	+	36.9057i	0.682965	+	1.64882i
$502$	−32.0569	+	24.0675i	−1.43077	+	1.07419i
$503$	−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
$505$			10.4509i			0.465061i
$506$	−6.60758	+	4.96081i	−0.293743	+	0.220535i
$507$	−35.1059	−	26.6484i	−1.55911	−	1.18350i
$508$	−4.07268	−	7.40921i	−0.180696	−	0.328731i
$509$	11.9975	−	28.9646i	0.531781	−	1.28383i	−0.398561	−	0.917142i	$-0.630490\pi$
$509$	11.9975	−	28.9646i	0.531781	−	1.28383i	0.930342	−	0.366692i	$-0.119510\pi$
$510$	−43.4671	+	11.1591i	−1.92476	+	0.494133i
$511$	−0.990991			−0.0438389
$512$	−2.13539	+	22.5264i	−0.0943717	+	0.995537i
$513$	−43.2352	+	43.2352i	−1.90888	+	1.90888i
$514$	−15.6299	+	26.4269i	−0.689405	+	1.16564i
$515$	−4.32683	+	10.4459i	−0.190663	+	0.460301i
$516$	11.7374	−	6.45177i	0.516708	−	0.284023i
$517$	13.6669	+	5.66103i	0.601072	+	0.248972i
$518$	1.30814	+	0.186216i	0.0574766	+	0.00818185i
$519$	45.1964	+	45.1964i	1.98390	+	1.98390i
$520$	13.7572	−	9.93814i	0.603294	−	0.435816i
$521$	−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	$0.368212\pi$
$522$	55.2297	−	41.4651i	2.41734	−	1.81488i
$523$	−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
$525$	7.39528	+	3.06323i	0.322757	+	0.133690i
$526$	29.6872	−	7.62144i	1.29442	−	0.332311i
$527$	17.7728	+	17.7728i	0.774193	+	0.774193i
$528$	44.9856	−	10.0499i	1.95775	−	0.437367i
$529$			20.0453i			0.871537i
$530$	16.2068	−	27.4024i	0.703980	−	1.19028i
$531$	−26.2084	−	10.8559i	−1.13735	−	0.471105i
$532$	6.90685	−	0.762112i	0.299450	−	0.0330418i
$533$	−7.67649	−	28.3535i	−0.332506	−	1.22813i
$534$	−74.2704	−	10.5725i	−3.21399	−	0.457515i
$535$	6.76549			0.292498
$536$	1.91328	−	4.23644i	0.0826410	−	0.182986i
$537$	−39.0769	+	39.0769i	−1.68629	+	1.68629i
$538$	−1.63385	+	11.4776i	−0.0704404	+	0.494836i
$539$	−18.4632	+	7.64770i	−0.795266	+	0.329410i
$540$	54.3334	−	29.8659i	2.33814	−	1.28522i
$541$	36.2317	+	15.0077i	1.55772	+	0.645230i	0.984692	−	0.174303i	$-0.0557671\pi$
$541$	36.2317	+	15.0077i	1.55772	+	0.645230i	0.573032	+	0.819533i	$0.305767\pi$
$542$	10.4017	+	40.5167i	0.446790	+	1.74034i
$543$	34.7467			1.49112
$544$	−28.3498	+	14.4397i	−1.21549	+	0.619097i
$545$			7.97136i			0.341456i
$546$	2.24512	+	18.1606i	0.0960825	+	0.777200i
$547$	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	$0.671340\pi$
$548$	−2.84611	−	5.17778i	−0.121580	−	0.221184i
$549$	17.2114	−	41.5520i	0.734564	−	1.77340i
$550$	−8.57418	+	6.43728i	−0.365604	+	0.274487i
$551$			18.8704i			0.803906i
$552$	−6.78440	+	15.0223i	−0.288763	+	0.639390i
$553$	16.6248			0.706959
$554$	1.85909	−	1.39576i	0.0789853	−	0.0593002i
$555$	−1.90585	+	4.60112i	−0.0808987	+	0.195307i
$556$	−11.5213	+	1.27128i	−0.488612	+	0.0539142i
$557$	17.4117	−	42.0355i	0.737756	−	1.78110i	0.122966	−	0.992411i	$-0.460759\pi$
$557$	17.4117	−	42.0355i	0.737756	−	1.78110i	0.614790	−	0.788690i	$-0.289241\pi$
$558$	−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	0.967580	−	0.252566i	$-0.0812745\pi$
$563$	2.48681	+	6.00368i	0.104806	+	0.253025i	−0.862773	+	0.505591i	$0.831274\pi$
$564$	29.3330	−	3.23664i	1.23514	−	0.136287i
$565$	0.926014	−	0.383568i	0.0389577	−	0.0161368i
$566$	10.1616	−	7.62904i	0.427122	−	0.320673i
$567$			39.8760i			1.67464i
$568$	−27.5024	−	0.866727i	−1.15398	−	0.0363671i
$569$	16.2205	−	16.2205i	0.679997	−	0.679997i	−0.280002	−	0.959999i	$-0.590335\pi$
$569$	16.2205	−	16.2205i	0.679997	−	0.679997i	0.959999	+	0.280002i	$0.0903353\pi$
$570$	−3.69104	+	25.9291i	−0.154601	+	1.08605i
$571$	−4.98239	+	12.0286i	−0.208507	+	0.503380i	−0.993188	−	0.116519i	$-0.962826\pi$
$571$	−4.98239	+	12.0286i	−0.208507	+	0.503380i	0.784682	+	0.619899i	$0.212826\pi$
$572$	−22.4681	−	9.79468i	−0.939439	−	0.409536i
$573$	−38.5165	+	15.9541i	−1.60905	+	0.666491i
$574$	−6.20838	+	10.4971i	−0.259133	+	0.438140i
$575$		−	3.83404i		−	0.159890i
$576$	50.9821	−	44.9308i	2.12425	−	1.87211i
$577$	−12.8984	+	12.8984i	−0.536969	+	0.536969i	−0.922638	−	0.385668i	$-0.873971\pi$
$577$	−12.8984	+	12.8984i	−0.536969	+	0.536969i	0.385668	+	0.922638i	$0.373971\pi$
$578$	−17.8106	−	10.5338i	−0.740821	−	0.438150i
$579$	16.1650	−	39.0257i	0.671793	−	1.62185i
$580$	5.33954	−	18.3748i	0.221712	−	0.762971i
$581$	−3.69188	+	8.91298i	−0.153165	+	0.369773i
$582$	−30.9841	−	41.2695i	−1.28433	−	1.71067i
$583$	−45.9784			−1.90423
$584$	0.0834099	−	2.64671i	0.00345153	−	0.109522i
$585$	−50.5501	−	6.52118i	−2.08999	−	0.269618i
$586$	−17.7137	−	2.52156i	−0.731744	−	0.104165i
$587$	7.27832	+	17.5714i	0.300409	+	0.725250i	0.999943	+	0.0106517i	$0.00339061\pi$
$587$	7.27832	+	17.5714i	0.300409	+	0.725250i	−0.699535	+	0.714599i	$0.746609\pi$
$588$	−24.9287	+	31.1124i	−1.02804	+	1.28305i
$589$	13.5522	−	5.61349i	0.558407	−	0.231300i
$590$	−7.61284	+	1.95441i	−0.313416	+	0.0804617i
$591$	15.5173	−	15.5173i	0.638298	−	0.638298i
$592$	−0.607444	+	3.47808i	−0.0249658	+	0.142948i
$593$	−30.0386	+	30.0386i	−1.23354	+	1.23354i	−0.270940	+	0.962596i	$0.587334\pi$
$593$	−30.0386	+	30.0386i	−1.23354	+	1.23354i	−0.962596	+	0.270940i	$0.912666\pi$
$594$	−77.0713	−	45.5829i	−3.16227	−	1.87029i
$595$	−3.79135	−	9.15313i	−0.155430	−	0.375242i
$596$	28.1132	+	22.5257i	1.15156	+	0.922687i
$597$	12.7492	−	30.7792i	0.521789	−	1.25971i
$598$	7.62487	−	4.32230i	0.311804	−	0.176752i
$599$	−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	$0.849171\pi$
$600$	−8.80363	+	19.4933i	−0.359407	+	0.795811i
$601$	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
$603$	−12.8977	+	5.34241i	−0.525236	+	0.217560i
$604$	−26.5766	+	14.6086i	−1.08139	+	0.594415i
$605$	−0.850118	−	0.352130i	−0.0345622	−	0.0143161i
$606$	15.3281	−	25.9167i	0.622662	−	1.05279i
$607$			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
$611$	−13.6102	−	7.81065i	−0.550608	−	0.315985i
$612$	91.7535	+	26.6627i	3.70892	+	1.07778i
$613$	10.2836	+	24.8268i	0.415351	+	1.00275i	0.983677	+	0.179942i	$0.0575912\pi$
$613$	10.2836	+	24.8268i	0.415351	+	1.00275i	−0.568326	+	0.822803i	$0.692409\pi$
$614$	7.49113	+	9.97786i	0.302317	+	0.402674i
$615$	−32.5031	−	32.5031i	−1.31065	−	1.31065i
$616$	3.59617	+	9.51953i	0.144894	+	0.383553i
$617$		−	5.33598i		−	0.214818i	−0.994215	−	0.107409i	$-0.965745\pi$
$617$		−	5.33598i		−	0.214818i	0.994215	−	0.107409i	$-0.0342555\pi$
$618$	26.0506	−	19.5581i	1.04791	−	0.786744i
$619$	8.60634	−	3.56486i	0.345918	−	0.143284i	−0.202959	−	0.979187i	$-0.565056\pi$
$619$	8.60634	−	3.56486i	0.345918	−	0.143284i	0.548877	+	0.835903i	$0.315056\pi$
$620$	−14.7846	+	1.63136i	−0.593765	+	0.0655169i
$621$	29.5825	−	12.2535i	1.18711	−	0.491715i
$622$	−13.0158	+	3.34148i	−0.521885	+	0.133981i
$623$		−	16.5617i		−	0.663531i
$624$	−48.6917	+	4.46768i	−1.94923	+	0.178850i
$625$			8.87232i			0.354893i
$626$	3.86923	+	15.0715i	0.154646	+	0.602378i
$627$	34.9454	−	14.4749i	1.39559	−	0.578071i
$628$	4.16945	+	3.34076i	0.166379	+	0.133311i
$629$	−4.58650	+	1.89979i	−0.182876	+	0.0757497i
$630$	12.7052	+	16.9227i	0.506186	+	0.674218i
$631$			32.8797i			1.30892i	0.756096	+	0.654461i	$0.227104\pi$
$631$			32.8797i			1.30892i	−0.756096	+	0.654461i	$0.772896\pi$
$632$	−1.39928	+	44.4011i	−0.0556604	+	1.76618i
$633$	−52.0935	−	52.0935i	−2.07053	−	2.07053i
$634$	7.34389	−	5.51361i	0.291663	−	0.218973i
$635$	2.69223	+	6.49961i	0.106838	+	0.257929i
$636$	−80.3808	+	44.1835i	−3.18730	+	1.75199i
$637$	20.4624	−	5.54003i	0.810749	−	0.219504i
$638$	−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	$-0.934445\pi$
$641$		−	10.3548i		−	0.408990i	0.978868	−	0.204495i	$-0.0655552\pi$
$642$	−16.7773	−	9.92276i	−0.662149	−	0.391620i
$643$	26.7298	+	11.0719i	1.05412	+	0.436632i	0.841362	−	0.540473i	$-0.181755\pi$
$643$	26.7298	+	11.0719i	1.05412	+	0.436632i	0.212761	+	0.977104i	$0.431755\pi$
$644$	−3.49440	−	1.01544i	−0.137699	−	0.0400139i
$645$	−10.2964	+	4.26491i	−0.405421	+	0.167931i
$646$	−20.8781	+	15.6747i	−0.821437	+	0.616715i
$647$	11.4350	+	11.4350i	0.449556	+	0.449556i	0.895207	−	0.445651i	$-0.147028\pi$
$647$	11.4350	+	11.4350i	0.449556	+	0.449556i	−0.445651	+	0.895207i	$0.647028\pi$
$648$	−106.500	−	3.35629i	−4.18371	−	0.131848i
$649$	8.02643	+	8.02643i	0.315065	+	0.315065i
$650$	9.89425	−	5.60873i	0.388084	−	0.219993i
$651$	6.13739	−	14.8170i	0.240543	−	0.580723i
$652$	4.86686	−	0.537017i	0.190601	−	0.0210312i
$653$	−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
$656$	−27.5128	−	17.4647i	−1.07419	−	0.681882i
$657$	−5.62337	+	5.62337i	−0.219389	+	0.219389i
$658$	1.62004	+	6.31041i	0.0631558	+	0.246005i
$659$	−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
$661$	−7.34980	−	17.7440i	−0.285874	−	0.690161i	0.714077	−	0.700067i	$-0.246847\pi$
$661$	−7.34980	−	17.7440i	−0.285874	−	0.690161i	−0.999951	+	0.00990622i	$0.996847\pi$
$662$	−4.95500	+	34.8083i	−0.192581	+	1.35286i
$663$	−41.9947	−	54.4344i	−1.63094	−	2.11406i
$664$	−23.4938	−	10.6104i	−0.911737	−	0.411762i
$665$	−5.78200			−0.224216
$666$	8.47974	−	6.36638i	0.328583	−	0.246692i
$667$	3.78171	−	9.12986i	0.146428	−	0.353509i
$668$	−11.3512	−	20.6507i	−0.439192	−	0.798999i
$669$	−2.29439	+	5.53915i	−0.0887062	+	0.214156i
$670$	−1.96903	+	3.32923i	−0.0760704	+	0.128619i
$671$	−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	$-0.929431\pi$
$673$		−	11.4087i		−	0.439774i	0.975525	−	0.219887i	$-0.0705689\pi$
$674$	−8.45473	−	5.00045i	−0.325664	−	0.192610i
$675$	38.3871	−	15.9005i	1.47752	−	0.612009i
$676$	22.3085	+	13.3540i	0.858020	+	0.513616i
$677$	−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	$0.167907\pi$
$678$	−2.85894	−	0.406973i	−0.109797	−	0.0156297i
$679$	8.05599	−	8.05599i	0.309161	−	0.309161i
$680$	24.7651	−	9.35544i	0.949696	−	0.358765i
$681$			0.772471i			0.0296012i
$682$	12.8975	+	17.1790i	0.493873	+	0.657817i
$683$	−26.9470	+	11.1618i	−1.03110	+	0.427095i	−0.833109	−	0.553109i	$-0.813441\pi$
$683$	−26.9470	+	11.1618i	−1.03110	+	0.427095i	−0.197989	+	0.980204i	$0.563441\pi$
$684$	34.8683	−	43.5175i	1.33322	−	1.66393i
$685$	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
$691$	5.90265	−	14.2502i	0.224547	−	0.542105i	−0.770950	−	0.636896i	$-0.780218\pi$
$691$	5.90265	−	14.2502i	0.224547	−	0.542105i	0.995497	+	0.0947907i	$0.0302182\pi$
$692$	−29.4251	−	23.5768i	−1.11858	−	0.896256i
$693$	11.6953	−	28.2350i	0.444269	−	1.07256i
$694$	−8.57417	−	11.4204i	−0.325471	−	0.433513i
$695$	9.64495			0.365854
$696$	−40.1910	+	37.7352i	−1.52344	+	1.43035i
$697$		−	45.8203i		−	1.73557i
$698$	13.9938	+	18.6391i	0.529673	+	0.705502i
$699$	−27.5621	+	66.5409i	−1.04250	+	2.51681i
$700$	−4.53443	−	1.31766i	−0.171385	−	0.0498029i
$701$	9.19668	+	22.2027i	0.347354	+	0.838586i	0.996931	+	0.0782900i	$0.0249460\pi$
$701$	9.19668	+	22.2027i	0.347354	+	0.838586i	−0.649577	+	0.760296i	$0.725054\pi$
$702$	74.8973	+	58.4163i	2.82682	+	2.20478i
$703$			2.89728i			0.109273i
$704$	−25.7272	+	8.80332i	−0.969630	+	0.331788i
$705$	−24.5558			−0.924825
$706$	−37.7680	+	9.69598i	−1.42142	+	0.364913i
$707$	6.14133	+	2.54382i	0.230969	+	0.0956703i
$708$	21.7451	+	6.31893i	0.817232	+	0.237480i
$709$	−1.97605	+	0.818505i	−0.0742119	+	0.0307396i	−0.419481	−	0.907764i	$-0.637788\pi$
$709$	−1.97605	+	0.818505i	−0.0742119	+	0.0307396i	0.345269	+	0.938504i	$0.387788\pi$
$710$	22.6674	+	3.22672i	0.850691	+	0.121097i
$711$	94.3374	−	94.3374i	3.53793	−	3.53793i
$712$	44.2326	+	1.39397i	1.65769	+	0.0522412i
$713$	−7.68177			−0.287684
$714$	−4.02270	+	28.2590i	−0.150546	+	1.05757i
$715$	17.6888	+	10.1513i	0.661525	+	0.379638i
$716$	20.3846	−	25.4410i	0.761807	−	0.950776i
$717$	−67.3253	−	27.8871i	−2.51431	−	1.04146i
$718$	−18.9736	−	11.2217i	−0.708089	−	0.418791i
$719$			25.3324i			0.944737i	0.881401	+	0.472369i	$0.156601\pi$
$719$			25.3324i			0.944737i	−0.881401	+	0.472369i	$0.843399\pi$
$720$	−46.2661	+	32.5083i	−1.72424	+	1.21151i
$721$	5.08520	+	5.08520i	0.189383	+	0.189383i
$722$	−2.89281	−	11.2681i	−0.107659	−	0.419356i
$723$	9.17384	+	3.79993i	0.341179	+	0.141321i
$724$	−20.3738	+	2.24808i	−0.757187	+	0.0835491i
$725$	4.90725	−	11.8472i	0.182251	−	0.439992i
$726$	1.59170	+	2.12007i	0.0590735	+	0.0786833i
$727$	20.6104	−	20.6104i	0.764399	−	0.764399i	−0.212716	−	0.977114i	$-0.568231\pi$
$727$	20.6104	−	20.6104i	0.764399	−	0.764399i	0.977114	+	0.212716i	$0.0682308\pi$
$728$	−2.49140	−	10.5032i	−0.0923375	−	0.389275i
$729$	92.3034	+	92.3034i	3.41864	+	3.41864i
$730$	−0.310525	+	2.18140i	−0.0114931	+	0.0807374i
$731$	−10.2637	−	4.25136i	−0.379616	−	0.157242i
$732$	−10.0183	+	34.4757i	−0.370287	+	1.27426i
$733$	8.09900	−	19.5527i	0.299143	−	0.722196i	−0.700817	−	0.713341i	$-0.747181\pi$
$733$	8.09900	−	19.5527i	0.299143	−	0.722196i	0.999961	−	0.00885534i	$-0.00281878\pi$
$734$	22.8795	+	13.5318i	0.844496	+	0.499467i
$735$	23.4571	−	23.4571i	0.865229	−	0.865229i
$736$	3.00612	−	9.24727i	0.110807	−	0.340859i
$737$	5.58610			0.205767
$738$	24.3363	+	94.7950i	0.895830	+	3.48945i
$739$	1.77972	−	4.29663i	0.0654681	−	0.158054i	−0.887759	−	0.460308i	$-0.847739\pi$
$739$	1.77972	−	4.29663i	0.0654681	−	0.158054i	0.953227	+	0.302254i	$0.0977390\pi$
$740$	0.819810	−	2.82118i	0.0301368	−	0.103709i
$741$	−38.7293	+	10.4857i	−1.42276	+	0.385200i
$742$	−12.1578	−	16.1936i	−0.446326	−	0.594486i
$743$		−	27.6232i		−	1.01340i	−0.862124	−	0.506698i	$-0.830866\pi$
$743$		−	27.6232i		−	1.01340i	0.862124	−	0.506698i	$-0.169134\pi$
$744$	39.0562	+	17.6387i	1.43187	+	0.646666i
$745$	−21.1959	−	21.1959i	−0.776558	−	0.776558i
$746$	11.6293	+	15.4898i	0.425780	+	0.567121i
$747$	29.6271	+	71.5261i	1.08400	+	2.61700i
$748$	−29.8367	−	23.9066i	−1.09094	−	0.874113i
$749$	1.64676	−	3.97564i	0.0601714	−	0.145267i
$750$	29.3699	−	49.6584i	1.07244	−	1.81327i
$751$			46.5203i			1.69755i	0.528754	+	0.848775i	$0.322659\pi$
$751$			46.5203i			1.69755i	−0.528754	+	0.848775i	$0.677341\pi$
$752$	−16.9900	+	3.79563i	−0.619563	+	0.138412i
$753$	−96.0997			−3.50207
$754$	29.0930	−	3.59666i	1.05950	−	0.130983i
$755$	23.3139	−	9.65694i	0.848480	−	0.351452i
$756$	−4.32514	−	39.1977i	−0.157304	−	1.42561i
$757$	−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
$759$	−19.8081			−0.718988
$760$	0.486661	−	15.4424i	0.0176530	−	0.560155i
$761$			8.31466i			0.301406i	0.988579	+	0.150703i	$0.0481537\pi$
$761$			8.31466i			0.301406i	−0.988579	+	0.150703i	$0.951846\pi$
$762$	2.85651	−	20.0666i	0.103480	−	0.726937i
$763$	4.68425	+	1.94028i	0.169581	+	0.0702428i
$764$	21.5520	−	11.8467i	0.779725	−	0.428598i
$765$	−73.4534	−	30.4254i	−2.65571	−	1.10003i
$766$	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	−0.336420	−	0.941712i	$-0.609216\pi$
$769$	16.7853	−	16.7853i	0.605292	−	0.605292i	0.941712	+	0.336420i	$0.109216\pi$
$770$	−2.10553	−	8.20151i	−0.0758781	−	0.295562i
$771$	−68.0025	+	28.1676i	−2.44905	+	1.01443i
$772$	−6.95344	+	23.9286i	−0.250260	+	0.861211i
$773$	−0.546860	−	1.32024i	−0.0196692	−	0.0474856i	0.913740	−	0.406300i	$-0.133181\pi$
$773$	−0.546860	−	1.32024i	−0.0196692	−	0.0474856i	−0.933409	+	0.358814i	$0.883181\pi$
$774$	23.4920	+	3.34411i	0.844402	+	0.120201i
$775$	−9.96807			−0.358064
$776$	20.8377	+	22.1938i	0.748029	+	0.796711i
$777$	2.23989	+	2.23989i	0.0803554	+	0.0803554i
$778$	7.68336	+	10.2339i	0.275462	+	0.366903i
$779$	−24.7057	−	10.2334i	−0.885173	−	0.366651i
$780$	40.6792	+	0.748530i	1.45655	+	0.0268017i
$781$	−12.6540	−	30.5494i	−0.452795	−	1.09314i
$782$	13.2425	−	3.39968i	0.473551	−	0.121572i
$783$	107.093			3.82720
$784$	12.6041	−	19.8557i	0.450145	−	0.709131i
$785$	−3.14355	−	3.14355i	−0.112198	−	0.112198i
$786$	57.7557	−	14.8273i	2.06008	−	0.528874i
$787$	−7.79398	−	3.22837i	−0.277826	−	0.115079i	0.239420	−	0.970916i	$-0.423043\pi$
$787$	−7.79398	−	3.22837i	−0.277826	−	0.115079i	−0.517246	+	0.855837i	$0.673043\pi$
$788$	−8.09467	+	10.1026i	−0.288361	+	0.359889i
$789$	67.8849	+	28.1188i	2.41676	+	1.00106i
$790$	5.20936	−	36.5951i	0.185341	−	1.30200i
$791$		−	0.637521i		−	0.0226676i
$792$	74.4249	+	33.6121i	2.64458	+	1.19435i
$793$	15.1151	−	11.6609i	0.536752	−	0.414089i
$794$	−16.4144	+	12.3236i	−0.582527	+	0.437347i
$795$	70.5127	−	29.2073i	2.50083	−	1.03588i
$796$	−5.48412	+	18.8723i	−0.194380	+	0.668912i
$797$	−13.2139	−	31.9013i	−0.468062	−	1.13000i	−0.965008	−	0.262220i	$-0.915545\pi$
$797$	−13.2139	−	31.9013i	−0.468062	−	1.13000i	0.496947	−	0.867781i	$-0.334455\pi$
$798$	14.3384	+	8.48030i	0.507576	+	0.300199i
$799$	−17.3084	−	17.3084i	−0.612327	−	0.612327i
$800$	3.90083	−	11.9995i	0.137915	−	0.424247i
$801$	−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
$804$	9.76578	−	5.36804i	0.344413	−	0.189316i
$805$	2.79744	+	1.15874i	0.0985969	+	0.0408402i
$806$	−11.2375	−	19.8238i	−0.395824	−	0.698264i
$807$	−19.6527	+	19.6527i	−0.691808	+	0.691808i
$808$	−7.31088	+	16.1880i	−0.257196	+	0.569492i
$809$	−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
$811$	−3.94896	−	9.53362i	−0.138667	−	0.334771i	0.839257	−	0.543736i	$-0.182991\pi$
$811$	−3.94896	−	9.53362i	−0.138667	−	0.334771i	−0.977923	+	0.208965i	$0.932991\pi$
$812$	−9.49799	−	7.61024i	−0.333314	−	0.267067i
$813$	−38.3763	+	92.6485i	−1.34591	+	3.24932i
$814$	−4.10966	+	1.05505i	−0.144043	+	0.0369796i
$815$	−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
$819$	−16.1363	+	28.1177i	−0.563848	+	0.982512i
$820$	21.1612	+	16.9554i	0.738981	+	0.592107i
$821$	−35.7630	+	14.8135i	−1.24814	+	0.516996i	−0.906249	−	0.422745i	$-0.861067\pi$
$821$	−35.7630	+	14.8135i	−1.24814	+	0.516996i	−0.341889	+	0.939740i	$0.611067\pi$
$822$	1.99621	−	14.0231i	0.0696258	−	0.489113i
$823$	19.6371	−	19.6371i	0.684507	−	0.684507i	−0.276505	−	0.961012i	$-0.589176\pi$
$823$	19.6371	−	19.6371i	0.684507	−	0.684507i	0.961012	+	0.276505i	$0.0891763\pi$
$824$	−14.0094	+	13.1534i	−0.488041	+	0.458220i
$825$	−25.7035			−0.894883
$826$	−0.704536	+	4.94929i	−0.0245140	+	0.172208i
$827$	−0.865904	−	2.09048i	−0.0301104	−	0.0726931i	0.908109	−	0.418734i	$-0.137526\pi$
$827$	−0.865904	−	2.09048i	−0.0301104	−	0.0726931i	−0.938220	+	0.346041i	$0.887526\pi$
$828$	−25.5910	+	14.0668i	−0.889349	+	0.488856i
$829$	8.31769	+	20.0807i	0.288885	+	0.697431i	0.999984	−	0.00566138i	$-0.00180208\pi$
$829$	8.31769	+	20.0807i	0.288885	+	0.697431i	−0.711099	+	0.703092i	$0.751802\pi$
$830$	18.4627	+	10.9196i	0.640851	+	0.379023i
$831$	5.57316			0.193331
$832$	28.2614	−	5.76993i	0.979788	−	0.200036i
$833$	33.0680			1.14574
$834$	−23.9180	−	14.1460i	−0.828211	−	0.489835i
$835$	7.50368	+	18.1155i	0.259675	+	0.626912i
$836$	−19.5538	+	10.7483i	−0.676283	+	0.371738i
$837$	−31.8577	−	76.9112i	−1.10116	−	2.65844i
$838$	1.05223	−	7.39180i	0.0363487	−	0.255345i
$839$	18.0082			0.621711			0.310856	−	0.950457i	$-0.399384\pi$
$839$	18.0082			0.621711			0.310856	+	0.950457i	$0.399384\pi$
$840$	−11.5623	−	12.3148i	−0.398937	−	0.424900i
$841$	2.86482	−	2.86482i	0.0987870	−	0.0987870i
$842$	0.482553	−	3.38988i	0.0166299	−	0.116823i
$843$	77.2911	−	32.0150i	2.66205	−	1.10266i
$844$	33.9155	+	27.1747i	1.16742	+	0.935393i
$845$	−17.2320	−	13.0806i	−0.592800	−	0.449986i
$846$	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
$850$	17.1838	−	4.41152i	0.589401	−	0.151314i
$851$	0.580627	−	1.40176i	0.0199036	−	0.0480517i
$852$	−51.4789	−	41.2473i	−1.76364	−	1.41311i
$853$	2.87811	+	6.94838i	0.0985447	+	0.237908i	0.965462	−	0.260544i	$-0.0839020\pi$
$853$	2.87811	+	6.94838i	0.0985447	+	0.237908i	−0.866917	+	0.498452i	$0.833902\pi$
$854$	−7.84681	−	1.11700i	−0.268512	−	0.0382230i
$855$	−32.8099	+	32.8099i	−1.12208	+	1.12208i
$856$	10.4794	+	4.73275i	0.358179	+	0.161762i
$857$	−7.97152	+	7.97152i	−0.272302	+	0.272302i	−0.830026	−	0.557724i	$-0.811675\pi$
$857$	−7.97152	+	7.97152i	−0.272302	+	0.272302i	0.557724	+	0.830026i	$0.311675\pi$
$858$	−28.9768	−	51.1174i	−0.989253	−	1.74512i
$859$	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	$0.590167\pi$
$860$	5.76139	−	3.16691i	0.196462	−	0.107991i
$861$	−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	$-0.239164\pi$
$863$	1.41408	+	1.41408i	0.0481357	+	0.0481357i	−0.682629	+	0.730765i	$0.739164\pi$
$864$	105.052	−	8.25226i	3.57395	−	0.280748i
$865$	22.1850	+	22.1850i	0.754314	+	0.754314i
$866$	−42.2239	−	24.9728i	−1.43483	−	0.848611i
$867$	−18.9837	−	45.8306i	−0.644719	−	1.55649i
$868$	−2.64003	+	9.08504i	−0.0896084	+	0.308366i
$869$	−49.3203	+	20.4291i	−1.67308	+	0.693011i
$870$	36.6845	−	27.5418i	1.24372	−	0.933755i
$871$	−5.87693	−	0.758149i	−0.199132	−	0.0256889i
$872$	−5.57631	+	12.3473i	−0.188838	+	0.418131i
$873$		−	91.4273i		−	3.09435i
$874$	1.12450	−	7.89946i	0.0380367	−	0.267203i
$875$	11.7673	+	4.87417i	0.397807	+	0.164777i
$876$	3.96946	−	4.95410i	0.134116	−	0.167384i
$877$	1.87456	+	0.776470i	0.0632995	+	0.0262195i	0.414109	−	0.910227i	$-0.364093\pi$
$877$	1.87456	+	0.776470i	0.0632995	+	0.0262195i	−0.350809	+	0.936447i	$0.614093\pi$
$878$	−41.7903	+	10.7286i	−1.41035	+	0.362073i
$879$	−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	$-0.590699\pi$
$881$	−16.6870			−0.562200			−0.281100	+	0.959679i	$0.590699\pi$
$882$	−68.4124	+	17.5632i	−2.30357	+	0.591383i
$883$	−17.5231	−	42.3045i	−0.589699	−	1.42366i	−0.883791	−	0.467883i	$-0.845017\pi$
$883$	−17.5231	−	42.3045i	−0.589699	−	1.42366i	0.294091	−	0.955777i	$-0.404983\pi$
$884$	28.1455	+	29.2007i	0.946636	+	0.982127i
$885$	−17.4081	−	7.21066i	−0.585166	−	0.242384i
$886$	10.2490	+	13.6513i	0.344323	+	0.458624i
$887$	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
$889$	4.47470			0.150077
$890$	−36.4563	−	5.18959i	−1.22202	−	0.173955i
$891$	−49.0010	−	118.299i	−1.64160	−	3.96316i
$892$	0.986943	−	3.39633i	0.0330453	−	0.113718i
$893$	−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
$899$	−23.7366	−	9.83203i	−0.791660	−	0.327916i
$900$	−33.2076	+	18.2535i	−1.10692	+	0.608450i
$901$	70.2887	+	29.1145i	2.34165	+	0.969945i
$902$	5.51901	−	38.7704i	0.183763	−	1.29091i
$903$			7.08864i			0.235895i
$904$	1.70267	+	0.0536590i	0.0566301	+	0.00178467i
$905$	17.0557			0.566952
$906$	−71.9784	−	10.2462i	−2.39132	−	0.340407i
$907$	−36.7076	−	15.2048i	−1.21886	−	0.504867i	−0.321811	−	0.946804i	$-0.604292\pi$
$907$	−36.7076	−	15.2048i	−1.21886	−	0.504867i	−0.897046	+	0.441937i	$0.854292\pi$
$908$	−0.0499781	−	0.452940i	−0.00165858	−	0.0150313i
$909$	49.2838	−	20.4140i	1.63464	−	0.677091i
$910$	1.10204	+	8.91427i	0.0365322	+	0.295505i
$911$	4.50171			0.149148			0.0745742	−	0.997215i	$-0.476240\pi$
$911$	4.50171			0.149148			0.0745742	+	0.997215i	$0.476240\pi$
$912$	−23.8558	+	37.5810i	−0.789945	+	1.24443i
$913$		−	30.9785i		−	1.02524i
$914$	2.59297	−	4.38418i	0.0857679	−	0.145016i
$915$	11.4321	−	27.5995i	0.377933	−	0.912412i
$916$	17.8813	+	14.3274i	0.590816	+	0.473390i
$917$	5.03765	+	12.1620i	0.166358	+	0.401624i
$918$	88.9573	+	118.487i	2.93603	+	3.91066i
$919$	−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
$921$			29.9115i			0.985616i
$922$	20.9145	+	27.8573i	0.688784	+	0.917430i
$923$	9.16660	+	33.8573i	0.301722	+	1.11443i
$924$	−6.80754	+	23.4266i	−0.223952	+	0.770678i
$925$	0.753438	−	1.81896i	0.0247729	−	0.0598071i
$926$	6.21971	+	24.2271i	0.204392	+	0.796153i
$927$	57.7118			1.89550
$928$	21.1247	−	24.7264i	0.693451	−	0.811685i
$929$	12.4771	−	12.4771i	0.409360	−	0.409360i	−0.472155	−	0.881515i	$-0.656524\pi$
$929$	12.4771	−	12.4771i	0.409360	−	0.409360i	0.881515	+	0.472155i	$0.156524\pi$
$930$	−30.6925	−	18.1527i	−1.00645	−	0.595251i
$931$	7.38534	−	17.8298i	0.242045	−	0.584348i
$932$	11.8560	−	40.7996i	0.388356	−	1.33644i
$933$	−29.7628	−	12.3282i	−0.974391	−	0.403606i
$934$	−0.754159	+	5.29788i	−0.0246768	+	0.173352i
$935$	22.4954	+	22.4954i	0.735677	+	0.735677i
$936$	−73.7379	−	45.4630i	−2.41020	−	1.48600i
$937$	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	$0.219600\pi$
$938$	1.47710	+	1.96743i	0.0482289	+	0.0642388i
$939$	−14.2753	+	34.4636i	−0.465856	+	1.12468i
$940$	14.3983	−	1.58874i	0.469622	−	0.0518188i
$941$	26.1380	+	10.8267i	0.852073	+	0.352940i	0.765602	−	0.643314i	$-0.222441\pi$
$941$	26.1380	+	10.8267i	0.852073	+	0.352940i	0.0864710	+	0.996254i	$0.472441\pi$
$942$	3.18495	+	12.4061i	0.103771	+	0.404211i
$943$	9.90226	+	9.90226i	0.322462	+	0.322462i
$944$	−13.1591	−	2.29823i	−0.428293	−	0.0748010i
$945$			32.8140i			1.06744i
$946$	−8.17246	−	4.83350i	−0.265710	−	0.157151i
$947$	14.1409	+	5.85737i	0.459519	+	0.190339i	0.600420	−	0.799685i	$-0.295000\pi$
$947$	14.1409	+	5.85737i	0.459519	+	0.190339i	−0.140901	+	0.990024i	$0.545000\pi$
$948$	−66.5915	+	83.1097i	−2.16279	+	2.69928i
$949$	−3.25828	+	0.882153i	−0.105768	+	0.0286359i
$950$	1.45918	−	10.2506i	0.0473420	−	0.332572i
$951$	22.0154			0.713898
$952$	0.530389	−	16.8300i	0.0171900	−	0.545463i
$953$	−4.13664	+	4.13664i	−0.133999	+	0.133999i	−0.770925	−	0.636926i	$-0.780206\pi$
$953$	−4.13664	+	4.13664i	−0.133999	+	0.133999i	0.636926	+	0.770925i	$0.280206\pi$
$954$	−160.880	−	22.9014i	−5.20867	−	0.741460i
$955$	−18.9062	+	7.83120i	−0.611790	+	0.253412i
$956$	41.2806	+	11.9958i	1.33511	+	0.387970i
$957$	−61.2069	−	25.3527i	−1.97854	−	0.819537i
$958$	−14.4258	+	3.70346i	−0.466076	+	0.119653i
$959$	3.12705			0.100978
$960$	33.8631	−	29.8437i	1.09293	−	0.963203i
$961$		−	11.0283i		−	0.355750i
$962$	4.46681	−	0.552216i	0.144016	−	0.0178042i
$963$	−13.2152	−	31.9043i	−0.425853	−	1.02810i
$964$	−5.62495	−	1.63456i	−0.181168	−	0.0526456i
$965$	7.93471	−	19.1561i	0.255427	−	0.616656i
$966$	−5.23772	−	6.97642i	−0.168521	−	0.224463i
$967$		−	10.9842i		−	0.353229i	−0.984280	−	0.176614i	$-0.943485\pi$
$967$		−	10.9842i		−	0.353229i	0.984280	−	0.176614i	$-0.0565145\pi$
$968$	−1.07046	−	1.14013i	−0.0344059	−	0.0366451i
$969$	−62.5880			−2.01062
$970$	−15.2088	−	20.2575i	−0.488325	−	0.650428i
$971$	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
$973$	2.34764	−	5.66771i	0.0752619	−	0.181698i
$974$	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	$-0.164706\pi$
$977$	11.7036	+	11.7036i	0.374432	+	0.374432i	−0.494657	+	0.869089i	$0.664706\pi$
$978$	10.1035	+	5.97558i	0.323074	+	0.191078i
$979$	20.3516	+	49.1331i	0.650440	+	1.57030i
$980$	−12.2365	+	15.2718i	−0.390880	+	0.487839i
$981$	37.5908	−	15.5706i	1.20018	−	0.497132i
$982$	−17.0059	−	22.6511i	−0.542680	−	0.722827i
$983$			35.5119i			1.13265i	0.824181	+	0.566327i	$0.191636\pi$
$983$			35.5119i			1.13265i	−0.824181	+	0.566327i	$0.808364\pi$
$984$	−27.6084	−	73.0831i	−0.880125	−	2.32980i
$985$	7.61682	−	7.61682i	0.242692	−	0.242692i
$986$	45.2706	+	6.44431i	1.44171	+	0.205229i
$987$	−5.97704	+	14.4298i	−0.190251	+	0.459307i
$988$	22.0306	−	8.65404i	0.700887	−	0.275322i
$989$	3.13686	−	1.29933i	0.0997463	−	0.0413163i
$990$	−58.4872	−	34.5916i	−1.85885	−	1.09939i
$991$		−	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
$994$	7.41351	−	12.5347i	0.235142	−	0.397577i
$995$	6.25805	−	15.1083i	0.198393	−	0.478964i
$996$	−29.7692	−	54.1576i	−0.943274	−	1.71605i
$997$	−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
$999$	16.4426			0.520222

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bd.a.203.36	✓	216	13.8	odd	4
416.2.bd.a.291.36	yes	216	32.3	odd	8
416.2.bi.a.99.11	yes	216	416.99	even	8	inner
416.2.bi.a.395.11	yes	216	1.1	even	1	trivial

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.bi (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21725 - 0.719929i) q^{2} +(-1.29743 - 3.13227i) q^{3} +(0.963404 + 1.75267i) q^{4} +(-0.636854 - 1.53750i) q^{5} +(-0.675714 + 4.74682i) q^{6} -1.05850 q^{7} +(0.0890924 - 2.82702i) q^{8} +(-6.00647 + 6.00647i) q^{9} +(-0.331680 + 2.33002i) q^{10} +(3.14023 - 1.30073i) q^{11} +(4.23989 - 5.29161i) q^{12} +(-3.48025 + 0.942251i) q^{13} +(1.28847 + 0.762048i) q^{14} +(-3.98960 + 3.98960i) q^{15} +(-2.14370 + 3.37706i) q^{16} -5.62421 q^{17} +(11.6356 - 2.98715i) q^{18} +(-1.25610 + 3.03250i) q^{19} +(2.08119 - 2.59743i) q^{20} +(1.37333 + 3.31552i) q^{21} +(-4.75888 - 0.677432i) q^{22} +(1.21545 - 1.21545i) q^{23} +(-8.97059 + 3.38880i) q^{24} +(1.57721 - 1.57721i) q^{25} +(4.91470 + 1.35858i) q^{26} +(17.2100 + 7.12863i) q^{27} +(-1.01977 - 1.85521i) q^{28} +(5.31142 - 2.20006i) q^{29} +(7.72857 - 1.98412i) q^{30} +(-3.16004 - 3.16004i) q^{31} +(5.04067 - 2.56742i) q^{32} +(-8.14844 - 8.14844i) q^{33} +(6.84608 + 4.04903i) q^{34} +(0.674112 + 1.62745i) q^{35} +(-16.3140 - 4.74070i) q^{36} +(0.815493 - 0.337788i) q^{37} +(3.71218 - 2.78701i) q^{38} +(7.46676 + 9.67859i) q^{39} +(-4.40329 + 1.66342i) q^{40} +8.14697i q^{41} +(0.715246 - 5.02452i) q^{42} +(1.82491 + 0.755903i) q^{43} +(5.30505 + 4.25066i) q^{44} +(13.0602 + 5.40971i) q^{45} +(-2.35455 + 0.604473i) q^{46} +(3.07748 + 3.07748i) q^{47} +(13.3592 + 2.33317i) q^{48} -5.87957 q^{49} +(-3.05533 + 0.784380i) q^{50} +(7.29701 + 17.6165i) q^{51} +(-5.00435 - 5.19197i) q^{52} +(-12.4975 - 5.17664i) q^{53} +(-15.8168 - 21.0673i) q^{54} +(-3.99973 - 3.99973i) q^{55} +(-0.0943046 + 2.99242i) q^{56} +11.1283 q^{57} +(-8.04923 - 1.14582i) q^{58} +(1.27800 + 3.08537i) q^{59} +(-10.8360 - 3.14885i) 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} +(1.51837 + 0.628931i) q^{67} +(-5.41839 - 9.85739i) q^{68} +(-5.38409 - 2.23016i) q^{69} +(0.351085 - 2.46633i) q^{70} -9.72841i q^{71} +(16.4453 + 17.5156i) q^{72} +0.936219 q^{73} +(-1.23584 - 0.175924i) q^{74} +(-6.98654 - 2.89392i) q^{75} +(-6.52511 + 0.719990i) q^{76} +(-3.32394 + 1.37682i) q^{77} +(-2.12104 - 17.1568i) q^{78} -15.7060 q^{79} +(6.55746 + 1.14525i) q^{80} -37.6721i q^{81} +(5.86524 - 9.91691i) q^{82} +(3.48783 - 8.42036i) q^{83} +(-4.48794 + 5.60118i) q^{84} +(3.58180 + 8.64724i) q^{85} +(-1.67718 - 2.23393i) q^{86} +(-13.7824 - 13.7824i) q^{87} +(-3.39741 - 8.99339i) q^{88} +15.6464i q^{89} +(-12.0029 - 15.9874i) q^{90} +(3.68386 - 0.997376i) q^{91} +(3.30126 + 0.959315i) q^{92} +(-5.79818 + 13.9980i) q^{93} +(-1.53050 - 5.96163i) q^{94} +5.46243 q^{95} +(-14.5818 - 12.4577i) q^{96} +(-7.61074 + 7.61074i) q^{97} +(7.15692 + 4.23287i) q^{98} +(-11.0489 + 26.6745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{11} + 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{19} - 20 q^{20} - 16 q^{21} - 24 q^{22}+ \cdots - 116 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^11 + 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 - 4 * q^19 - 20 * q^20 - 16 * q^21 - 24 * q^22 + 28 * q^24 - 4 * q^26 - 8 * q^27 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 4 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 + 20 * q^39 - 8 * q^40 - 48 * q^42 + 32 * q^43 - 20 * q^44 + 4 * q^45 - 24 * q^46 - 8 * q^47 - 8 * q^48 + 168 * q^49 + 20 * q^50 - 4 * q^52 - 8 * q^53 + 20 * q^54 - 40 * q^55 - 56 * q^56 - 8 * q^57 + 32 * q^58 + 4 * 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 - 4 * q^70 + 56 * q^72 - 8 * q^73 - 8 * q^74 - 4 * q^76 - 56 * q^77 - 136 * q^78 - 16 * q^79 + 28 * q^80 + 88 * q^82 - 44 * q^83 + 44 * q^84 - 24 * q^85 + 64 * q^86 - 8 * q^87 - 64 * q^88 + 64 * q^90 + 16 * q^91 - 8 * q^92 + 56 * q^93 - 56 * q^94 - 28 * q^96 - 8 * q^97 - 76 * q^98 - 116 * q^99

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