LMFDB - Embedded newform 416.2.bd.a.411.4

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			411.4
Character	$\chi$	$=$	416.411
Dual form			416.2.bd.a.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37663 + 0.323857i) q^{2} +(-2.65712 + 1.10062i) q^{3} +(1.79023 - 0.891665i) q^{4} +(-1.41696 - 3.42085i) q^{5} +(3.30144 - 2.37567i) q^{6} -0.353777i q^{7} +(-2.17572 + 1.80728i) q^{8} +(3.72762 - 3.72762i) q^{9} +(3.05851 + 4.25036i) q^{10} +(2.46532 - 1.02117i) q^{11} +(-3.77548 + 4.33962i) q^{12} +(-3.60380 - 0.112275i) q^{13} +(0.114573 + 0.487021i) q^{14} +(7.53009 + 7.53009i) q^{15} +(2.40987 - 3.19258i) q^{16} +1.59116 q^{17} +(-3.92434 + 6.33878i) q^{18} +(-1.92428 + 4.64563i) q^{19} +(-5.58695 - 4.86066i) q^{20} +(0.389372 + 0.940028i) q^{21} +(-3.06313 + 2.20419i) q^{22} +(2.45672 - 2.45672i) q^{23} +(3.79204 - 7.19678i) q^{24} +(-6.15891 + 6.15891i) q^{25} +(4.99747 - 1.01256i) q^{26} +(-2.50021 + 6.03605i) q^{27} +(-0.315451 - 0.633343i) q^{28} +(-3.12000 - 7.53235i) q^{29} +(-12.8048 - 7.92748i) q^{30} +(-5.89587 + 5.89587i) q^{31} +(-2.28356 + 5.17546i) q^{32} +(-5.42675 + 5.42675i) q^{33} +(-2.19044 + 0.515309i) q^{34} +(-1.21022 + 0.501289i) q^{35} +(3.34952 - 9.99709i) q^{36} +(-9.34063 + 3.86902i) q^{37} +(1.14451 - 7.01852i) q^{38} +(9.69931 - 3.66807i) q^{39} +(9.26533 + 4.88197i) q^{40} +1.57288 q^{41} +(-0.840458 - 1.16797i) q^{42} +(0.399110 - 0.963538i) q^{43} +(3.50296 - 4.02637i) q^{44} +(-18.0335 - 7.46973i) q^{45} +(-2.58638 + 4.17763i) q^{46} +(-8.53183 + 8.53183i) q^{47} +(-2.88951 + 11.1354i) q^{48} +6.87484 q^{49} +(6.48394 - 10.4732i) q^{50} +(-4.22791 + 1.75126i) q^{51} +(-6.55176 + 3.01239i) q^{52} +(-1.84534 + 4.45505i) q^{53} +(1.48705 - 9.11913i) q^{54} +(-6.98654 - 6.98654i) q^{55} +(0.639372 + 0.769719i) q^{56} -14.4619i q^{57} +(6.73450 + 9.35884i) q^{58} +(0.791741 + 1.91143i) q^{59} +(20.1949 + 6.76629i) q^{60} +(2.66607 + 6.43647i) q^{61} +(6.20702 - 10.0259i) q^{62} +(-1.31875 - 1.31875i) q^{63} +(1.46751 - 7.86425i) q^{64} +(4.72238 + 12.4872i) q^{65} +(5.71314 - 9.22813i) q^{66} +(14.2881 + 5.91831i) q^{67} +(2.84855 - 1.41878i) q^{68} +(-3.82390 + 9.23172i) q^{69} +(1.50368 - 1.08203i) q^{70} -8.29142 q^{71} +(-1.37342 + 14.8471i) q^{72} +2.92849i q^{73} +(11.6056 - 8.35125i) q^{74} +(9.58637 - 23.1436i) q^{75} +(0.697433 + 10.0326i) q^{76} +(-0.361266 - 0.872174i) q^{77} +(-12.1645 + 8.19078i) q^{78} +0.975544 q^{79} +(-14.3360 - 3.72003i) q^{80} -2.97534i q^{81} +(-2.16528 + 0.509389i) q^{82} +(-1.97848 + 4.77649i) q^{83} +(1.53526 + 1.33568i) q^{84} +(-2.25462 - 5.44313i) q^{85} +(-0.237379 + 1.45569i) q^{86} +(16.5804 + 16.5804i) q^{87} +(-3.51832 + 6.67730i) q^{88} +5.86136 q^{89} +(27.2447 + 4.44278i) q^{90} +(-0.0397203 + 1.27494i) q^{91} +(2.20753 - 6.58868i) q^{92} +(9.17695 - 22.1551i) q^{93} +(8.98209 - 14.5083i) q^{94} +18.6187 q^{95} +(0.371507 - 16.2651i) q^{96} +(-0.254086 - 0.254086i) q^{97} +(-9.46413 + 2.22647i) q^{98} +(5.38325 - 12.9963i) 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 $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.37663	+	0.323857i	−0.973426	+	0.229002i
$2$	−1.37663	+	0.323857i	−0.973426	+	0.229002i
$3$	−2.65712	+	1.10062i	−1.53409	+	0.635441i	−0.980353	−	0.197251i	$-0.936799\pi$
$3$	−2.65712	+	1.10062i	−1.53409	+	0.635441i	−0.553737	+	0.832692i	$0.686799\pi$
$4$	1.79023	−	0.891665i	0.895116	−	0.445833i
$5$	−1.41696	−	3.42085i	−0.633685	−	1.52985i	−0.834957	−	0.550316i	$-0.814507\pi$
$5$	−1.41696	−	3.42085i	−0.633685	−	1.52985i	0.201271	−	0.979535i	$-0.435493\pi$
$6$	3.30144	−	2.37567i	1.34781	−	0.969864i
$7$		−	0.353777i		−	0.133715i	−0.997763	−	0.0668575i	$-0.978703\pi$
$7$		−	0.353777i		−	0.133715i	0.997763	−	0.0668575i	$-0.0212973\pi$
$8$	−2.17572	+	1.80728i	−0.769233	+	0.638968i
$9$	3.72762	−	3.72762i	1.24254	−	1.24254i
$10$	3.05851	+	4.25036i	0.967184	+	1.34408i
$11$	2.46532	−	1.02117i	0.743323	−	0.307894i	0.0213089	−	0.999773i	$-0.493217\pi$
$11$	2.46532	−	1.02117i	0.743323	−	0.307894i	0.722014	+	0.691879i	$0.243217\pi$
$12$	−3.77548	+	4.33962i	−1.08989	+	1.25274i
$13$	−3.60380	−	0.112275i	−0.999515	−	0.0311395i
$13$	−3.60380	−	0.112275i	−0.999515	−	0.0311395i
$14$	0.114573	+	0.487021i	0.0306210	+	0.130162i
$15$	7.53009	+	7.53009i	1.94426	+	1.94426i
$16$	2.40987	−	3.19258i	0.602467	−	0.798144i
$17$	1.59116			0.385913			0.192957	−	0.981207i	$-0.438192\pi$
$17$	1.59116			0.385913			0.192957	+	0.981207i	$0.438192\pi$
$18$	−3.92434	+	6.33878i	−0.924977	+	1.49406i
$19$	−1.92428	+	4.64563i	−0.441461	+	1.06578i	0.533976	+	0.845500i	$0.320697\pi$
$19$	−1.92428	+	4.64563i	−0.441461	+	1.06578i	−0.975436	+	0.220281i	$0.929303\pi$
$20$	−5.58695	−	4.86066i	−1.24928	−	1.08688i
$21$	0.389372	+	0.940028i	0.0849680	+	0.205131i
$22$	−3.06313	+	2.20419i	−0.653061	+	0.469935i
$23$	2.45672	−	2.45672i	0.512262	−	0.512262i	−0.402957	−	0.915219i	$-0.632018\pi$
$23$	2.45672	−	2.45672i	0.512262	−	0.512262i	0.915219	+	0.402957i	$0.132018\pi$
$24$	3.79204	−	7.19678i	0.774046	−	1.46904i
$25$	−6.15891	+	6.15891i	−1.23178	+	1.23178i
$26$	4.99747	−	1.01256i	0.980085	−	0.198579i
$27$	−2.50021	+	6.03605i	−0.481166	+	1.16164i
$28$	−0.315451	−	0.633343i	−0.0596146	−	0.119691i
$29$	−3.12000	−	7.53235i	−0.579369	−	1.39872i	−0.893380	−	0.449302i	$-0.851673\pi$
$29$	−3.12000	−	7.53235i	−0.579369	−	1.39872i	0.314010	−	0.949420i	$-0.398327\pi$
$30$	−12.8048	−	7.92748i	−2.33783	−	1.44735i
$31$	−5.89587	+	5.89587i	−1.05893	+	1.05893i	−0.0607782	+	0.998151i	$0.519358\pi$
$31$	−5.89587	+	5.89587i	−1.05893	+	1.05893i	−0.998151	+	0.0607782i	$0.980642\pi$
$32$	−2.28356	+	5.17546i	−0.403680	+	0.914900i
$33$	−5.42675	+	5.42675i	−0.944675	+	0.944675i
$34$	−2.19044	+	0.515309i	−0.375658	+	0.0883748i
$35$	−1.21022	+	0.501289i	−0.204564	+	0.0847333i
$36$	3.34952	−	9.99709i	0.558253	−	1.66618i
$37$	−9.34063	+	3.86902i	−1.53559	+	0.636062i	−0.980640	−	0.195821i	$-0.937263\pi$
$37$	−9.34063	+	3.86902i	−1.53559	+	0.636062i	−0.554951	+	0.831883i	$0.687263\pi$
$38$	1.14451	−	7.01852i	0.185664	−	1.13855i
$39$	9.69931	−	3.66807i	1.55313	−	0.587362i
$40$	9.26533	+	4.88197i	1.46498	+	0.771907i
$41$	1.57288			0.245643			0.122821	−	0.992429i	$-0.460806\pi$
$41$	1.57288			0.245643			0.122821	+	0.992429i	$0.460806\pi$
$42$	−0.840458	−	1.16797i	−0.129685	−	0.180222i
$43$	0.399110	−	0.963538i	0.0608638	−	0.146938i	−0.890522	−	0.454941i	$-0.849660\pi$
$43$	0.399110	−	0.963538i	0.0608638	−	0.146938i	0.951386	+	0.308002i	$0.0996605\pi$
$44$	3.50296	−	4.02637i	0.528091	−	0.606999i
$45$	−18.0335	−	7.46973i	−2.68828	−	1.11352i
$46$	−2.58638	+	4.17763i	−0.381340	+	0.615958i
$47$	−8.53183	+	8.53183i	−1.24449	+	1.24449i	−0.286378	+	0.958117i	$0.592451\pi$
$47$	−8.53183	+	8.53183i	−1.24449	+	1.24449i	−0.958117	+	0.286378i	$0.907549\pi$
$48$	−2.88951	+	11.1354i	−0.417064	+	1.60726i
$49$	6.87484			0.982120
$50$	6.48394	−	10.4732i	0.916968	−	1.48113i
$51$	−4.22791	+	1.75126i	−0.592026	+	0.245225i
$52$	−6.55176	+	3.01239i	−0.908565	+	0.417743i
$53$	−1.84534	+	4.45505i	−0.253477	+	0.611948i	−0.998480	−	0.0551131i	$-0.982448\pi$
$53$	−1.84534	+	4.45505i	−0.253477	+	0.611948i	0.745003	+	0.667061i	$0.232448\pi$
$54$	1.48705	−	9.11913i	0.202363	−	1.24096i
$55$	−6.98654	−	6.98654i	−0.942065	−	0.942065i
$56$	0.639372	+	0.769719i	0.0854397	+	0.102858i
$57$		−	14.4619i		−	1.91553i
$58$	6.73450	+	9.35884i	0.884283	+	1.22888i
$59$	0.791741	+	1.91143i	0.103076	+	0.248847i	0.967001	−	0.254774i	$-0.0820009\pi$
$59$	0.791741	+	1.91143i	0.103076	+	0.248847i	−0.863925	+	0.503621i	$0.832001\pi$
$60$	20.1949	+	6.76629i	2.60715	+	0.873524i
$61$	2.66607	+	6.43647i	0.341355	+	0.824105i	0.997579	+	0.0695386i	$0.0221527\pi$
$61$	2.66607	+	6.43647i	0.341355	+	0.824105i	−0.656224	+	0.754566i	$0.727847\pi$
$62$	6.20702	−	10.0259i	0.788293	−	1.27329i
$63$	−1.31875	−	1.31875i	−0.166146	−	0.166146i
$64$	1.46751	−	7.86425i	0.183439	−	0.983031i
$65$	4.72238	+	12.4872i	0.585739	+	1.54884i
$66$	5.71314	−	9.22813i	0.703239	−	1.13590i
$67$	14.2881	+	5.91831i	1.74557	+	0.723037i	0.998286	+	0.0585284i	$0.0186408\pi$
$67$	14.2881	+	5.91831i	1.74557	+	0.723037i	0.747280	+	0.664509i	$0.231359\pi$
$68$	2.84855	−	1.41878i	0.345437	−	0.172053i
$69$	−3.82390	+	9.23172i	−0.460344	+	1.11137i
$70$	1.50368	−	1.08203i	0.179724	−	0.129327i
$71$	−8.29142			−0.984011			−0.492005	−	0.870592i	$-0.663736\pi$
$71$	−8.29142			−0.984011			−0.492005	+	0.870592i	$0.663736\pi$
$72$	−1.37342	+	14.8471i	−0.161859	+	1.74975i
$73$			2.92849i			0.342754i	0.985206	+	0.171377i	$0.0548216\pi$
$73$			2.92849i			0.342754i	−0.985206	+	0.171377i	$0.945178\pi$
$74$	11.6056	−	8.35125i	1.34912	−	0.970813i
$75$	9.58637	−	23.1436i	1.10694	−	2.67239i
$76$	0.697433	+	10.0326i	0.0800010	+	1.15082i
$77$	−0.361266	−	0.872174i	−0.0411701	−	0.0993935i
$78$	−12.1645	+	8.19078i	−1.37735	+	0.927424i
$79$	0.975544			0.109757			0.0548787	−	0.998493i	$-0.482523\pi$
$79$	0.975544			0.109757			0.0548787	+	0.998493i	$0.482523\pi$
$80$	−14.3360	−	3.72003i	−1.60282	−	0.415912i
$81$		−	2.97534i		−	0.330593i
$82$	−2.16528	+	0.509389i	−0.239115	+	0.0562526i
$83$	−1.97848	+	4.77649i	−0.217167	+	0.524287i	−0.994492	−	0.104812i	$-0.966576\pi$
$83$	−1.97848	+	4.77649i	−0.217167	+	0.524287i	0.777325	+	0.629099i	$0.216576\pi$
$84$	1.53526	+	1.33568i	0.167510	+	0.145735i
$85$	−2.25462	−	5.44313i	−0.244547	−	0.590390i
$86$	−0.237379	+	1.45569i	−0.0255973	+	0.156971i
$87$	16.5804	+	16.5804i	1.77761	+	1.77761i
$88$	−3.51832	+	6.67730i	−0.375054	+	0.711802i
$89$	5.86136			0.621303			0.310652	−	0.950524i	$-0.399453\pi$
$89$	5.86136			0.621303			0.310652	+	0.950524i	$0.399453\pi$
$90$	27.2447	+	4.44278i	2.87184	+	0.468310i
$91$	−0.0397203	+	1.27494i	−0.00416382	+	0.133650i
$92$	2.20753	−	6.58868i	0.230151	−	0.686917i
$93$	9.17695	−	22.1551i	0.951606	−	2.29738i
$94$	8.98209	−	14.5083i	0.926432	−	1.49642i
$95$	18.6187			1.91023
$96$	0.371507	−	16.2651i	0.0379168	−	1.66005i
$97$	−0.254086	−	0.254086i	−0.0257986	−	0.0257986i	0.694090	−	0.719888i	$-0.255807\pi$
$97$	−0.254086	−	0.254086i	−0.0257986	−	0.0257986i	−0.719888	+	0.694090i	$0.755807\pi$
$98$	−9.46413	+	2.22647i	−0.956021	+	0.224907i
$99$	5.38325	−	12.9963i	0.541037	−	1.30618i
$100$	−5.53419	+	16.5176i	−0.553419	+	1.65176i
$101$	−1.78843	+	4.31765i	−0.177955	+	0.429622i	−0.987537	−	0.157385i	$-0.949694\pi$
$101$	−1.78843	+	4.31765i	−0.177955	+	0.429622i	0.809582	+	0.587007i	$0.199694\pi$
$102$	5.25312	−	3.78008i	0.520136	−	0.374283i
$103$	−2.77664	−	2.77664i	−0.273591	−	0.273591i	0.556953	−	0.830544i	$-0.311970\pi$
$103$	−2.77664	−	2.77664i	−0.273591	−	0.273591i	−0.830544	+	0.556953i	$0.811970\pi$
$104$	8.04378	−	6.26878i	0.788757	−	0.614705i
$105$	2.66397	−	2.66397i	0.259977	−	0.259977i
$106$	1.09756	−	6.73059i	0.106604	−	0.653733i
$107$	−8.49296	−	3.51790i	−0.821046	−	0.340088i	−0.0676940	−	0.997706i	$-0.521564\pi$
$107$	−8.49296	−	3.51790i	−0.821046	−	0.340088i	−0.753352	+	0.657618i	$0.771564\pi$
$108$	0.906171	+	13.0353i	0.0871964	+	1.25432i
$109$	−6.49096	−	2.68864i	−0.621721	−	0.257525i	0.0495096	−	0.998774i	$-0.484234\pi$
$109$	−6.49096	−	2.68864i	−0.621721	−	0.257525i	−0.671231	+	0.741248i	$0.734234\pi$
$110$	11.8805	+	7.35526i	1.13277	+	0.701296i
$111$	20.5609	−	20.5609i	1.95155	−	1.95155i
$112$	−1.12946	−	0.852555i	−0.106724	−	0.0805589i
$113$		−	5.63040i		−	0.529664i	−0.964295	−	0.264832i	$-0.914684\pi$
$113$		−	5.63040i		−	0.529664i	0.964295	−	0.264832i	$-0.0853165\pi$
$114$	4.68360	+	19.9087i	0.438659	+	1.86462i
$115$	−11.8852	−	4.92300i	−1.10830	−	0.459072i
$116$	−12.3019	−	10.7027i	−1.14220	−	0.993717i
$117$	−13.8521	+	13.0151i	−1.28063	+	1.20325i
$118$	−1.70897	−	2.37493i	−0.157323	−	0.218630i
$119$		−	0.562916i		−	0.0516024i
$120$	−29.9923	−	2.77442i	−2.73791	−	0.253269i
$121$	−2.74315	+	2.74315i	−0.249377	+	0.249377i
$122$	−5.75470	−	7.99722i	−0.521006	−	0.724034i
$123$	−4.17933	+	1.73114i	−0.376838	+	0.156091i
$124$	−5.29784	+	15.8121i	−0.475760	+	1.41997i
$125$	12.6914	+	5.25695i	1.13515	+	0.470195i
$126$	2.24251	+	1.38834i	0.199779	+	0.123683i
$127$	1.50867			0.133873			0.0669363	−	0.997757i	$-0.478678\pi$
$127$	1.50867			0.133873			0.0669363	+	0.997757i	$0.478678\pi$
$128$	0.526671	+	11.3014i	0.0465516	+	0.998916i
$129$			2.99950i			0.264092i
$130$	−10.5450	−	15.6609i	−0.924861	−	1.37355i
$131$	−12.6190	+	5.22695i	−1.10253	+	0.456681i	−0.858358	−	0.513052i	$-0.828515\pi$
$131$	−12.6190	+	5.22695i	−1.10253	+	0.456681i	−0.244168	+	0.969733i	$0.578515\pi$
$132$	−4.87630	+	14.5540i	−0.424427	+	1.26676i
$133$	1.64352	+	0.680767i	0.142511	+	0.0590300i
$134$	−21.5861	−	3.52004i	−1.86476	−	0.304085i
$135$	24.1911			2.08204
$136$	−3.46192	+	2.87567i	−0.296857	+	0.246586i
$137$		−	4.14276i		−	0.353940i	−0.984216	−	0.176970i	$-0.943371\pi$
$137$		−	4.14276i		−	0.353940i	0.984216	−	0.176970i	$-0.0566295\pi$
$138$	2.27435	−	13.9471i	0.193605	−	1.18725i
$139$	−10.2116	−	4.22977i	−0.866133	−	0.358764i	−0.0950300	−	0.995474i	$-0.530295\pi$
$139$	−10.2116	−	4.22977i	−0.866133	−	0.358764i	−0.771103	+	0.636710i	$0.780295\pi$
$140$	−1.71959	+	1.97653i	−0.145332	+	0.167048i
$141$	13.2798	−	32.0604i	1.11836	−	2.69997i
$142$	11.4142	−	2.68524i	0.957861	−	0.225340i
$143$	−8.99919	+	3.40330i	−0.752550	+	0.284598i
$144$	−2.91765	−	20.8838i	−0.243137	−	1.74031i
$145$	−21.3461	+	21.3461i	−1.77270	+	1.77270i
$146$	−0.948414	−	4.03146i	−0.0784913	−	0.333646i
$147$	−18.2673	+	7.56656i	−1.50666	+	0.624079i
$148$	−13.2720	+	15.2552i	−1.09095	+	1.25397i
$149$	16.8714	−	6.98838i	1.38216	−	0.572510i	0.437103	−	0.899411i	$-0.356004\pi$
$149$	16.8714	−	6.98838i	1.38216	−	0.572510i	0.945059	+	0.326901i	$0.106004\pi$
$150$	−5.70170	+	34.9648i	−0.465542	+	2.85486i
$151$	−10.4562			−0.850914			−0.425457	−	0.904979i	$-0.639887\pi$
$151$	−10.4562			−0.850914			−0.425457	+	0.904979i	$0.639887\pi$
$152$	−4.20923	−	13.5853i	−0.341414	−	1.10191i
$153$	5.93124	−	5.93124i	0.479512	−	0.479512i
$154$	0.779791	+	1.08366i	0.0628374	+	0.0873242i
$155$	28.5231	+	11.8147i	2.29103	+	0.948977i
$156$	14.0933	−	15.2152i	1.12837	−	1.21819i
$157$	0.894726	+	2.16006i	0.0714069	+	0.172392i	0.955553	−	0.294818i	$-0.0952592\pi$
$157$	0.894726	+	2.16006i	0.0714069	+	0.172392i	−0.884146	+	0.467210i	$0.845259\pi$
$158$	−1.34297	+	0.315937i	−0.106841	+	0.0251346i
$159$		−	13.8686i		−	1.09985i
$160$	20.9402	+	0.478288i	1.65547	+	0.0378120i
$161$	−0.869132	−	0.869132i	−0.0684972	−	0.0684972i
$162$	0.963586	+	4.09595i	0.0757065	+	0.321808i
$163$	4.27941	−	10.3314i	0.335190	−	0.809219i	−0.662974	−	0.748643i	$-0.730706\pi$
$163$	4.27941	−	10.3314i	0.335190	−	0.809219i	0.998164	−	0.0605769i	$-0.0192940\pi$
$164$	2.81582	−	1.40248i	0.219879	−	0.109515i
$165$	26.2536	+	10.8746i	2.04384	+	0.846586i
$166$	1.17675	−	7.21621i	0.0913332	−	0.560087i
$167$			18.8148i			1.45593i	0.685615	+	0.727965i	$0.259534\pi$
$167$			18.8148i			1.45593i	−0.685615	+	0.727965i	$0.740466\pi$
$168$	−2.54605	−	1.34153i	−0.196432	−	0.103502i
$169$	12.9748	+	0.809233i	0.998061	+	0.0622487i
$170$	4.86657	+	6.76301i	0.373249	+	0.518699i
$171$	10.1441	+	24.4901i	0.775742	+	1.87281i
$172$	−0.144653	−	2.08083i	−0.0110297	−	0.158662i
$173$	−2.07624	−	5.01250i	−0.157854	−	0.381093i	0.825089	−	0.565002i	$-0.191125\pi$
$173$	−2.07624	−	5.01250i	−0.157854	−	0.381093i	−0.982943	+	0.183909i	$0.941125\pi$
$174$	−28.1949	−	17.4555i	−2.13745	−	1.32330i
$175$	2.17888	+	2.17888i	0.164708	+	0.164708i
$176$	2.68093	−	10.3316i	0.202083	−	0.778775i
$177$	−4.20750	−	4.20750i	−0.316255	−	0.316255i
$178$	−8.06894	+	1.89825i	−0.604793	+	0.142280i
$179$	−15.6779	+	6.49400i	−1.17182	+	0.485384i	−0.881794	−	0.471634i	$-0.843664\pi$
$179$	−15.6779	+	6.49400i	−1.17182	+	0.485384i	−0.290027	+	0.957019i	$0.593664\pi$
$180$	−38.9447	+	2.70731i	−2.90277	+	0.201791i
$181$	21.9954	+	9.11080i	1.63491	+	0.677200i	0.995769	−	0.0918931i	$-0.0292918\pi$
$181$	21.9954	+	9.11080i	1.63491	+	0.677200i	0.639137	+	0.769093i	$0.279292\pi$
$182$	−0.358219	−	1.76799i	−0.0265530	−	0.131052i
$183$	−14.1682	−	14.1682i	−1.04734	−	1.04734i
$184$	−0.905166	+	9.78511i	−0.0667297	+	0.721368i
$185$	26.4707	+	26.4707i	1.94616	+	1.94616i
$186$	−5.45819	+	33.4715i	−0.400214	+	2.45425i
$187$	3.92273	−	1.62485i	0.286858	−	0.118821i
$188$	−7.66642	+	22.8815i	−0.559131	+	1.66880i
$189$	2.13541	+	0.884518i	0.155329	+	0.0643392i
$190$	−25.6310	+	6.02979i	−1.85947	+	0.437447i
$191$			4.98552i			0.360739i	0.983599	+	0.180370i	$0.0577294\pi$
$191$			4.98552i			0.360739i	−0.983599	+	0.180370i	$0.942271\pi$
$192$	4.75616	+	22.5114i	0.343246	+	1.62462i
$193$	7.82300	−	7.82300i	0.563112	−	0.563112i	−0.367078	−	0.930190i	$-0.619642\pi$
$193$	7.82300	−	7.82300i	0.563112	−	0.563112i	0.930190	+	0.367078i	$0.119642\pi$
$194$	0.432071	+	0.267496i	0.0310209	+	0.0192051i
$195$	−26.2915	−	27.9824i	−1.88277	−	2.00386i
$196$	12.3076	−	6.13006i	0.879112	−	0.437861i
$197$	−6.87393	−	16.5951i	−0.489747	−	1.18235i	−0.954848	−	0.297096i	$-0.903982\pi$
$197$	−6.87393	−	16.5951i	−0.489747	−	1.18235i	0.465101	−	0.885258i	$-0.346018\pi$
$198$	−3.20180	+	19.6346i	−0.227542	+	1.39537i
$199$	−12.4837	−	12.4837i	−0.884943	−	0.884943i	0.109089	−	0.994032i	$-0.465207\pi$
$199$	−12.4837	−	12.4837i	−0.884943	−	0.884943i	−0.994032	+	0.109089i	$0.965207\pi$
$200$	2.26921	−	24.5309i	0.160458	−	1.73460i
$201$	−44.4789			−3.13730
$202$	1.06371	−	6.52301i	0.0748421	−	0.458957i
$203$	−2.66477	+	1.10378i	−0.187030	+	0.0774704i
$204$	−6.00740	+	6.90504i	−0.420602	+	0.483449i
$205$	−2.22871	−	5.38059i	−0.155660	−	0.375797i
$206$	4.72165	+	2.92318i	0.328973	+	0.203668i
$207$		−	18.3155i		−	1.27301i
$208$	−9.04313	+	11.2348i	−0.627028	+	0.778997i
$209$			13.4180i			0.928143i
$210$	−2.80456	+	4.53005i	−0.193533	+	0.312603i
$211$	7.42408	+	17.9233i	0.511095	+	1.23389i	0.943247	+	0.332092i	$0.107754\pi$
$211$	7.42408	+	17.9233i	0.511095	+	1.23389i	−0.432152	+	0.901801i	$0.642246\pi$
$212$	0.668821	+	9.62100i	0.0459348	+	0.660773i
$213$	22.0313	−	9.12567i	1.50956	−	0.625280i
$214$	12.8310	+	2.09235i	0.877108	+	0.143030i
$215$	−3.86164			−0.263362
$216$	−5.46904	−	17.6513i	−0.372121	−	1.20102i
$217$	2.08582	+	2.08582i	0.141595	+	0.141595i
$218$	9.80640	+	1.59913i	0.664174	+	0.108307i
$219$	−3.22315	−	7.78136i	−0.217800	−	0.525816i
$220$	−18.7372	−	6.27788i	−1.26326	−	0.423255i
$221$	−5.73423	−	0.178647i	−0.385726	−	0.0120171i
$222$	−21.6460	+	34.9636i	−1.45278	+	2.34660i
$223$	13.7154	−	13.7154i	0.918450	−	0.918450i	−0.0784671	−	0.996917i	$-0.525003\pi$
$223$	13.7154	−	13.7154i	0.918450	−	0.918450i	0.996917	+	0.0784671i	$0.0250025\pi$
$224$	1.83096	+	0.807871i	0.122336	+	0.0539781i
$225$			45.9161i			3.06107i
$226$	1.82345	+	7.75099i	0.121294	+	0.515588i
$227$	−12.1243	−	5.02203i	−0.804715	−	0.333324i	−0.0578720	−	0.998324i	$-0.518432\pi$
$227$	−12.1243	−	5.02203i	−0.804715	−	0.333324i	−0.746843	+	0.665000i	$0.768432\pi$
$228$	−12.8952	−	25.8902i	−0.854004	−	1.71462i
$229$	−18.7008	+	7.74614i	−1.23579	+	0.511879i	−0.902395	−	0.430910i	$-0.858193\pi$
$229$	−18.7008	+	7.74614i	−1.23579	+	0.511879i	−0.333391	+	0.942789i	$0.608193\pi$
$230$	17.9559	+	2.92806i	1.18397	+	0.193070i
$231$	1.91986	+	1.91986i	0.126317	+	0.126317i
$232$	20.4013	+	10.7496i	1.33941	+	0.705744i
$233$	−9.84366	−	9.84366i	−0.644880	−	0.644880i	0.306871	−	0.951751i	$-0.400718\pi$
$233$	−9.84366	−	9.84366i	−0.644880	−	0.644880i	−0.951751	+	0.306871i	$0.900718\pi$
$234$	14.8542	−	22.4031i	0.971052	−	1.46454i
$235$	41.2754	+	17.0968i	2.69251	+	1.11527i
$236$	3.12176	+	2.71594i	0.203209	+	0.176793i
$237$	−2.59214	+	1.07370i	−0.168378	+	0.0697443i
$238$	0.182305	+	0.774928i	0.0118170	+	0.0502311i
$239$	−1.97560	−	1.97560i	−0.127791	−	0.127791i	0.640319	−	0.768109i	$-0.278802\pi$
$239$	−1.97560	−	1.97560i	−0.127791	−	0.127791i	−0.768109	+	0.640319i	$0.778802\pi$
$240$	42.1869	−	5.89387i	2.72315	−	0.380448i
$241$	−16.0083	−	16.0083i	−1.03119	−	1.03119i	−0.999498	−	0.0316884i	$-0.989912\pi$
$241$	−16.0083	−	16.0083i	−1.03119	−	1.03119i	−0.0316884	−	0.999498i	$-0.510088\pi$
$242$	2.88792	−	4.66469i	0.185642	−	0.299858i
$243$	−4.22593	−	10.2023i	−0.271094	−	0.654478i
$244$	10.5121	+	9.14553i	0.672966	+	0.585482i
$245$	−9.74140	−	23.5178i	−0.622355	−	1.50250i
$246$	5.19276	−	3.73665i	0.331079	−	0.238240i
$247$	7.45633	−	16.5259i	0.474435	−	1.05152i
$248$	2.17230	−	23.4832i	0.137941	−	1.49119i
$249$		−	14.8693i		−	0.942301i
$250$	−19.1739	−	3.12668i	−1.21266	−	0.197749i
$251$	2.90534	+	1.20343i	0.183384	+	0.0759600i	0.472486	−	0.881338i	$-0.343357\pi$
$251$	2.90534	+	1.20343i	0.183384	+	0.0759600i	−0.289102	+	0.957298i	$0.593357\pi$
$252$	−3.53674	−	1.18498i	−0.222794	−	0.0746468i
$253$	3.54788	−	8.56534i	0.223053	−	0.538499i
$254$	−2.07688	+	0.488593i	−0.130315	+	0.0306571i
$255$	11.9816	+	11.9816i	0.750316	+	0.750316i
$256$	−4.38509	−	15.3874i	−0.274068	−	0.961710i
$257$		−	20.2150i		−	1.26098i	−0.776198	−	0.630490i	$-0.782854\pi$
$257$		−	20.2150i		−	1.26098i	0.776198	−	0.630490i	$-0.217146\pi$
$258$	−0.971412	−	4.12921i	−0.0604775	−	0.257074i
$259$	1.36877	+	3.30450i	0.0850511	+	0.205332i
$260$	19.5885	+	18.1441i	1.21483	+	1.12525i
$261$	−39.7079	−	16.4475i	−2.45786	−	1.01808i
$262$	15.6789	−	11.2823i	0.968646	−	0.697025i
$263$	−6.40220	+	6.40220i	−0.394776	+	0.394776i	−0.876386	−	0.481610i	$-0.840052\pi$
$263$	−6.40220	+	6.40220i	−0.394776	+	0.394776i	0.481610	+	0.876386i	$0.340052\pi$
$264$	1.99945	−	21.6147i	0.123058	−	1.33029i
$265$	17.8548			1.09681
$266$	−2.48299	−	0.404901i	−0.152242	−	0.0248261i
$267$	−15.5744	+	6.45111i	−0.953135	+	0.394801i
$268$	30.8561	−	2.14502i	1.88484	−	0.131028i
$269$	20.1893	−	8.36268i	1.23096	−	0.509881i	0.330084	−	0.943952i	$-0.392923\pi$
$269$	20.1893	−	8.36268i	1.23096	−	0.509881i	0.900879	+	0.434070i	$0.142923\pi$
$270$	−33.3023	+	7.83448i	−2.02671	+	0.476791i
$271$	−21.7642	+	21.7642i	−1.32208	+	1.32208i	−0.409988	+	0.912091i	$0.634467\pi$
$271$	−21.7642	+	21.7642i	−1.32208	+	1.32208i	−0.912091	+	0.409988i	$0.865533\pi$
$272$	3.83449	−	5.07990i	0.232500	−	0.308014i
$273$	−1.29768	−	3.43139i	−0.0785392	−	0.207677i
$274$	1.34166	+	5.70305i	0.0810528	+	0.344534i
$275$	−8.89440	+	21.4730i	−0.536353	+	1.29487i
$276$	1.38593	+	19.9366i	0.0834229	+	1.20004i
$277$	19.2556	+	7.97591i	1.15695	+	0.479226i	0.876860	−	0.480746i	$-0.159634\pi$
$277$	19.2556	+	7.97591i	1.15695	+	0.479226i	0.280095	+	0.959972i	$0.409634\pi$
$278$	15.4274	+	2.51574i	0.925274	+	0.150884i
$279$			43.9551i			2.63152i
$280$	1.72713	−	3.27786i	0.103216	−	0.195890i
$281$	−30.1434			−1.79821			−0.899103	−	0.437737i	$-0.855780\pi$
$281$	−30.1434			−1.79821			−0.899103	+	0.437737i	$0.855780\pi$
$282$	−7.89847	+	48.4361i	−0.470347	+	2.88433i
$283$	3.68558	+	1.52662i	0.219085	+	0.0907480i	0.489527	−	0.871988i	$-0.337170\pi$
$283$	3.68558	+	1.52662i	0.219085	+	0.0907480i	−0.270441	+	0.962736i	$0.587170\pi$
$284$	−14.8436	+	7.39317i	−0.880804	+	0.438704i
$285$	−49.4720	+	20.4920i	−2.93047	+	1.21384i
$286$	11.2864	−	7.59955i	0.667378	−	0.449371i
$287$		−	0.556449i		−	0.0328461i
$288$	10.7799	+	27.8044i	0.635211	+	1.63839i
$289$	−14.4682			−0.851071
$290$	22.4726	−	36.2988i	1.31964	−	2.13154i
$291$	0.954790	+	0.395487i	0.0559708	+	0.0231838i
$292$	2.61124	+	5.24268i	0.152811	+	0.306805i
$293$	7.49438	−	3.10427i	0.437826	−	0.181354i	−0.152872	−	0.988246i	$-0.548852\pi$
$293$	7.49438	−	3.10427i	0.437826	−	0.181354i	0.590698	+	0.806892i	$0.298852\pi$
$294$	22.6969	−	16.3324i	1.32371	−	0.952523i
$295$	5.41685	−	5.41685i	0.315381	−	0.315381i
$296$	13.3302	−	25.2990i	0.774803	−	1.47047i
$297$			17.4339i			1.01162i
$298$	−20.9625	+	15.0844i	−1.21433	+	0.873814i
$299$	−9.12937	+	8.57771i	−0.527965	+	0.496062i
$300$	−3.47446	−	49.9802i	−0.200598	−	2.88561i
$301$	−0.340877	−	0.141196i	−0.0196478	−	0.00813840i
$302$	14.3944	−	3.38632i	0.828302	−	0.194861i
$303$		−	13.4409i		−	0.772159i
$304$	10.1943	+	17.3388i	0.584681	+	0.994447i
$305$	18.2405	−	18.2405i	1.04445	−	1.04445i
$306$	−6.24426	+	10.0860i	−0.356961	+	0.576579i
$307$	−0.366292	−	0.151723i	−0.0209054	−	0.00865930i	0.372206	−	0.928150i	$-0.378601\pi$
$307$	−0.366292	−	0.151723i	−0.0209054	−	0.00865930i	−0.393112	+	0.919491i	$0.628601\pi$
$308$	−1.42444	−	1.23927i	−0.0811649	−	0.0706137i
$309$	10.4339	+	4.32186i	0.593563	+	0.245862i
$310$	−43.0921	−	7.02702i	−2.44747	−	0.399108i
$311$	8.51083	−	8.51083i	0.482605	−	0.482605i	−0.423358	−	0.905963i	$-0.639149\pi$
$311$	8.51083	−	8.51083i	0.482605	−	0.482605i	0.905963	+	0.423358i	$0.139149\pi$
$312$	−14.4738	+	25.5100i	−0.819416	+	1.44422i
$313$	−14.1585	−	14.1585i	−0.800285	−	0.800285i	0.182855	−	0.983140i	$-0.441466\pi$
$313$	−14.1585	−	14.1585i	−0.800285	−	0.800285i	−0.983140	+	0.182855i	$0.941466\pi$
$314$	−1.93126	−	2.68384i	−0.108987	−	0.151458i
$315$	−2.64262	+	6.37985i	−0.148895	+	0.359464i
$316$	1.74645	−	0.869859i	0.0982456	−	0.0489334i
$317$	−6.31088	+	15.2358i	−0.354454	+	0.855728i	0.641605	+	0.767035i	$0.278269\pi$
$317$	−6.31088	+	15.2358i	−0.354454	+	0.855728i	−0.996059	+	0.0886929i	$0.971731\pi$
$318$	4.49146	+	19.0920i	0.251868	+	1.07063i
$319$	−15.3836	−	15.3836i	−0.861317	−	0.861317i
$320$	−28.9818	+	6.12321i	−1.62013	+	0.342298i
$321$	26.4387			1.47566
$322$	1.47795	+	0.915000i	0.0823629	+	0.0509910i
$323$	−3.06184	+	7.39195i	−0.170366	+	0.411299i
$324$	−2.65301	−	5.32655i	−0.147389	−	0.295919i
$325$	22.8870	−	21.5040i	1.26954	−	1.19283i
$326$	−2.54527	+	15.6085i	−0.140970	+	0.864474i
$327$	20.2064			1.11742
$328$	−3.42215	+	2.84263i	−0.188956	+	0.156958i
$329$	3.01836	+	3.01836i	0.166408	+	0.166408i
$330$	−39.6634	−	6.46789i	−2.18340	−	0.356046i
$331$	−4.25527	−	10.2731i	−0.233891	−	0.564662i	0.762738	−	0.646708i	$-0.223855\pi$
$331$	−4.25527	−	10.2731i	−0.233891	−	0.564662i	−0.996629	+	0.0820456i	$0.973855\pi$
$332$	0.717077	+	10.3152i	0.0393547	+	0.566118i
$333$	−20.3961	+	49.2405i	−1.11770	+	2.69836i
$334$	−6.09330	−	25.9010i	−0.333410	−	1.41724i
$335$		−	57.2634i		−	3.12863i
$336$	3.93945	+	1.02224i	0.214914	+	0.0557678i
$337$	−2.85453			−0.155496			−0.0777480	−	0.996973i	$-0.524773\pi$
$337$	−2.85453			−0.155496			−0.0777480	+	0.996973i	$0.524773\pi$
$338$	−18.1236	+	3.08797i	−0.985793	+	0.167963i
$339$	6.19691	+	14.9607i	0.336570	+	0.812552i
$340$	−8.88973	−	7.73410i	−0.482113	−	0.419440i
$341$	−8.51454	+	20.5559i	−0.461088	+	1.11316i
$342$	−21.8961	−	30.4287i	−1.18400	−	1.64539i
$343$		−	4.90860i		−	0.265039i
$344$	0.873026	+	2.81769i	0.0470704	+	0.151920i
$345$	36.9987			1.99194
$346$	4.48156	+	6.22796i	0.240930	+	0.334817i
$347$	−3.27675	+	7.91078i	−0.175905	+	0.424673i	−0.987100	−	0.160103i	$-0.948817\pi$
$347$	−3.27675	+	7.91078i	−0.175905	+	0.424673i	0.811195	+	0.584776i	$0.198817\pi$
$348$	44.4670	+	14.8986i	2.38368	+	0.798651i
$349$	10.4538	+	4.33012i	0.559581	+	0.231786i	0.644503	−	0.764601i	$-0.277064\pi$
$349$	10.4538	+	4.33012i	0.559581	+	0.231786i	−0.0849220	+	0.996388i	$0.527064\pi$
$350$	−3.70516	−	2.29387i	−0.198049	−	0.122612i
$351$	9.68797	−	21.4720i	0.517106	−	1.14609i
$352$	−0.344690	+	15.0911i	−0.0183721	+	0.804357i
$353$	0.176228	+	0.176228i	0.00937969	+	0.00937969i	0.711781	−	0.702401i	$-0.247889\pi$
$353$	0.176228	+	0.176228i	0.00937969	+	0.00937969i	−0.702401	+	0.711781i	$0.747889\pi$
$354$	7.15481	+	4.42955i	0.380274	+	0.235428i
$355$	11.7486	+	28.3637i	0.623553	+	1.50539i
$356$	10.4932	−	5.22637i	0.556139	−	0.276997i
$357$	0.619554	+	1.49574i	0.0327903	+	0.0791628i
$358$	19.4796	−	14.0173i	1.02953	−	0.740835i
$359$			0.365637i			0.0192976i	0.999953	+	0.00964878i	$0.00307135\pi$
$359$			0.365637i			0.0192976i	−0.999953	+	0.00964878i	$0.996929\pi$
$360$	52.7358	−	16.3395i	2.77942	−	0.861168i
$361$	−4.44400	−	4.44400i	−0.233895	−	0.233895i
$362$	−33.2302	−	5.41884i	−1.74654	−	0.284808i
$363$	4.26972	−	10.3080i	0.224102	−	0.541031i
$364$	1.06571	+	2.31786i	0.0558585	+	0.121489i
$365$	10.0179	−	4.14957i	0.524363	−	0.217198i
$366$	24.0928	+	14.9159i	1.25935	+	0.779665i
$367$	7.56357			0.394815			0.197408	−	0.980322i	$-0.436748\pi$
$367$	7.56357			0.394815			0.197408	+	0.980322i	$0.436748\pi$
$368$	−1.92290	−	13.7636i	−0.100238	−	0.717480i
$369$	5.86310	−	5.86310i	0.305221	−	0.305221i
$370$	−45.0131	−	27.8676i	−2.34012	−	1.44877i
$371$	1.57609	+	0.652839i	0.0818267	+	0.0338937i
$372$	−3.32607	−	47.8456i	−0.172449	−	2.48068i
$373$	−11.2013	+	27.0424i	−0.579982	+	1.40020i	0.312847	+	0.949804i	$0.398717\pi$
$373$	−11.2013	+	27.0424i	−0.579982	+	1.40020i	−0.892829	+	0.450396i	$0.851283\pi$
$374$	−4.87393	+	3.50722i	−0.252025	+	0.181354i
$375$	−39.5084			−2.04021
$376$	3.14350	−	33.9822i	0.162114	−	1.75250i
$377$	10.3982	+	27.4954i	0.535533	+	1.41608i
$378$	−3.22614	−	0.526086i	−0.165935	−	0.0270589i
$379$	−6.36739	+	2.63746i	−0.327071	+	0.135477i	−0.540176	−	0.841552i	$-0.681642\pi$
$379$	−6.36739	+	2.63746i	−0.327071	+	0.135477i	0.213105	+	0.977029i	$0.431642\pi$
$380$	33.3317	−	16.6016i	1.70988	−	0.851644i
$381$	−4.00871	+	1.66046i	−0.205372	+	0.0850681i
$382$	−1.61460	−	6.86323i	−0.0826100	−	0.351153i
$383$	16.6127	−	16.6127i	0.848868	−	0.848868i	−0.141124	−	0.989992i	$-0.545071\pi$
$383$	16.6127	−	16.6127i	0.848868	−	0.848868i	0.989992	+	0.141124i	$0.0450715\pi$
$384$	−13.8380	−	29.4496i	−0.706166	−	1.50285i
$385$	−2.47168	+	2.47168i	−0.125968	+	0.125968i
$386$	−8.23585	+	13.3029i	−0.419194	+	0.677101i
$387$	−2.10397	−	5.07943i	−0.106951	−	0.258202i
$388$	−0.681434	−	0.228314i	−0.0345946	−	0.0115909i
$389$	6.34049	−	15.3073i	0.321475	−	0.776110i	−0.677693	−	0.735345i	$-0.737020\pi$
$389$	6.34049	−	15.3073i	0.321475	−	0.776110i	0.999169	−	0.0407656i	$-0.0129797\pi$
$390$	45.2560	+	30.0068i	2.29163	+	1.51945i
$391$	3.90904	−	3.90904i	0.197689	−	0.197689i
$392$	−14.9577	+	12.4247i	−0.755479	+	0.627544i
$393$	27.7773	−	27.7773i	1.40118	−	1.40118i
$394$	14.8373	+	20.6192i	0.747494	+	1.03878i
$395$	−1.38231	−	3.33719i	−0.0695516	−	0.167912i
$396$	−1.95109	−	28.0665i	−0.0980461	−	1.41039i
$397$	−5.23840	+	12.6466i	−0.262908	+	0.634716i	−0.999116	−	0.0420396i	$-0.986614\pi$
$397$	−5.23840	+	12.6466i	−0.262908	+	0.634716i	0.736208	+	0.676755i	$0.236614\pi$
$398$	21.2283	+	13.1425i	1.06408	+	0.658773i
$399$	−5.11629			−0.256135
$400$	4.82064	+	34.5049i	0.241032	+	1.72525i
$401$	23.9777	+	23.9777i	1.19739	+	1.19739i	0.974945	+	0.222445i	$0.0714039\pi$
$401$	23.9777	+	23.9777i	1.19739	+	1.19739i	0.222445	+	0.974945i	$0.428596\pi$
$402$	61.2311	−	14.4048i	3.05393	−	0.718448i
$403$	21.9095	−	20.5856i	1.09139	−	1.02544i
$404$	0.648193	+	9.32427i	0.0322488	+	0.463900i
$405$	−10.1782	+	4.21595i	−0.505759	+	0.209492i
$406$	3.31094	−	2.38251i	0.164319	−	0.118242i
$407$	−19.0767	+	19.0767i	−0.945599	+	0.945599i
$408$	6.03374	−	11.4512i	0.298715	−	0.566921i
$409$			1.21937i			0.0602939i	0.999545	+	0.0301470i	$0.00959753\pi$
$409$			1.21937i			0.0602939i	−0.999545	+	0.0301470i	$0.990402\pi$
$410$	4.81066	+	6.68531i	0.237582	+	0.330164i
$411$	4.55958	+	11.0078i	0.224908	+	0.542975i
$412$	−7.44667	−	2.49500i	−0.366871	−	0.122920i
$413$	0.676220	−	0.280100i	0.0332746	−	0.0137828i
$414$	5.93160	+	25.2136i	0.291522	+	1.23918i
$415$	19.1431			0.939697
$416$	8.81057	−	18.3949i	0.431974	−	0.901886i
$417$	31.7887			1.55670
$418$	−4.34552	−	18.4717i	−0.212546	−	0.903478i
$419$	−11.5662	+	4.79088i	−0.565046	+	0.234050i	−0.646874	−	0.762597i	$-0.723924\pi$
$419$	−11.5662	+	4.79088i	−0.565046	+	0.234050i	0.0818282	+	0.996646i	$0.473924\pi$
$420$	2.39376	−	7.14450i	0.116803	−	0.348616i
$421$	2.81125	+	6.78695i	0.137012	+	0.330776i	0.977461	−	0.211114i	$-0.0677091\pi$
$421$	2.81125	+	6.78695i	0.137012	+	0.330776i	−0.840450	+	0.541890i	$0.817709\pi$
$422$	−16.0248	−	22.2695i	−0.780077	−	1.08406i
$423$			63.6068i			3.09267i
$424$	−4.03655	−	13.0280i	−0.196032	−	0.632695i
$425$	−9.79981	+	9.79981i	−0.475361	+	0.475361i
$426$	−27.3736	+	19.6977i	−1.32626	+	0.954356i
$427$	2.27707	−	0.943194i	0.110195	−	0.0456444i
$428$	−18.3412	+	1.27502i	−0.886554	+	0.0616304i
$429$	20.1662	−	18.9476i	0.973634	−	0.914800i
$430$	5.31606	−	1.25062i	0.256363	−	0.0603104i
$431$	−11.4808	−	11.4808i	−0.553009	−	0.553009i	0.374299	−	0.927308i	$-0.377883\pi$
$431$	−11.4808	−	11.4808i	−0.553009	−	0.553009i	−0.927308	+	0.374299i	$0.877883\pi$
$432$	13.2454	+	22.5282i	0.637268	+	1.08389i
$433$	10.0079			0.480949			0.240475	−	0.970655i	$-0.422697\pi$
$433$	10.0079			0.480949			0.240475	+	0.970655i	$0.422697\pi$
$434$	−3.54692	−	2.19590i	−0.170258	−	0.105407i
$435$	33.2253	−	80.2131i	1.59303	−	3.84592i
$436$	−14.0177	+	0.974466i	−0.671326	+	0.0466684i
$437$	6.68560	+	16.1405i	0.319815	+	0.772103i
$438$	6.95714	+	9.66823i	0.332425	+	0.461966i
$439$	11.3029	−	11.3029i	0.539457	−	0.539457i	−0.383912	−	0.923370i	$-0.625424\pi$
$439$	11.3029	−	11.3029i	0.539457	−	0.539457i	0.923370	+	0.383912i	$0.125424\pi$
$440$	27.8274	+	2.57415i	1.32662	+	0.122718i
$441$	25.6268	−	25.6268i	1.22032	−	1.22032i
$442$	7.95178	−	1.61114i	0.378228	−	0.0766342i
$443$	0.195059	−	0.470913i	0.00926752	−	0.0223738i	−0.919178	−	0.393842i	$-0.871146\pi$
$443$	0.195059	−	0.470913i	0.00926752	−	0.0223738i	0.928446	+	0.371468i	$0.121146\pi$
$444$	18.4754	−	55.1422i	0.876801	−	2.61693i
$445$	−8.30533	−	20.0509i	−0.393711	−	0.950502i
$446$	−14.4392	+	23.3229i	−0.683716	+	1.10437i
$447$	−37.1379	+	37.1379i	−1.75656	+	1.75656i
$448$	−2.78219	−	0.519172i	−0.131446	−	0.0245286i
$449$	−27.7903	+	27.7903i	−1.31151	+	1.31151i	−0.391202	+	0.920305i	$0.627941\pi$
$449$	−27.7903	+	27.7903i	−1.31151	+	1.31151i	−0.920305	+	0.391202i	$0.872059\pi$
$450$	−14.8703	−	63.2096i	−0.700991	−	2.97973i
$451$	3.87766	−	1.60618i	0.182592	−	0.0756320i
$452$	−5.02043	−	10.0797i	−0.236141	−	0.474111i
$453$	27.7834	−	11.5083i	1.30538	−	0.540706i
$454$	18.3171	+	2.98696i	0.859663	+	0.140185i
$455$	4.41767	−	1.67067i	0.207104	−	0.0783222i
$456$	26.1366	+	31.4650i	1.22396	+	1.47349i
$457$	−10.4561			−0.489114			−0.244557	−	0.969635i	$-0.578643\pi$
$457$	−10.4561			−0.489114			−0.244557	+	0.969635i	$0.578643\pi$
$458$	23.2355	−	16.7200i	1.08572	−	0.781274i
$459$	−3.97824	+	9.60432i	−0.185688	+	0.448291i
$460$	−25.6669	+	1.78428i	−1.19672	+	0.0831924i
$461$	23.5526	+	9.75582i	1.09696	+	0.454374i	0.856427	−	0.516268i	$-0.172679\pi$
$461$	23.5526	+	9.75582i	1.09696	+	0.454374i	0.240528	+	0.970642i	$0.422679\pi$
$462$	−3.26470	−	2.02118i	−0.151887	−	0.0940337i
$463$	22.0162	−	22.0162i	1.02318	−	1.02318i	0.0234560	−	0.999725i	$-0.492533\pi$
$463$	22.0162	−	22.0162i	1.02318	−	1.02318i	0.999725	−	0.0234560i	$-0.00746696\pi$
$464$	−31.5664	−	8.19111i	−1.46543	−	0.380263i
$465$	−88.7928			−4.11767
$466$	16.7390	+	10.3632i	0.775421	+	0.480064i
$467$	−26.1364	+	10.8261i	−1.20945	+	0.500970i	−0.894040	−	0.447986i	$-0.852141\pi$
$467$	−26.1364	+	10.8261i	−1.20945	+	0.500970i	−0.315408	+	0.948956i	$0.602141\pi$
$468$	−13.1934	+	35.6515i	−0.609866	+	1.64799i
$469$	2.09376	−	5.05479i	0.0966810	−	0.233409i
$470$	−62.3580	−	10.1687i	−2.87636	−	0.469047i
$471$	−4.75479	−	4.75479i	−0.219089	−	0.219089i
$472$	−5.17709	−	2.72784i	−0.238295	−	0.125559i
$473$		−	2.78299i		−	0.127962i
$474$	3.22070	−	2.31757i	0.147932	−	0.106450i
$475$	−16.7605	−	40.4635i	−0.769026	−	1.85659i
$476$	−0.501933	−	1.00775i	−0.0230060	−	0.0461902i
$477$	9.72800	+	23.4855i	0.445414	+	1.07533i
$478$	3.35949	+	2.07986i	0.153659	+	0.0951307i
$479$	−20.9333	−	20.9333i	−0.956469	−	0.956469i	0.0426225	−	0.999091i	$-0.486429\pi$
$479$	−20.9333	−	20.9333i	−0.956469	−	0.956469i	−0.999091	+	0.0426225i	$0.986429\pi$
$480$	−56.1670	+	21.7762i	−2.56366	+	0.993944i
$481$	34.0962	−	12.8945i	1.55465	−	0.587936i
$482$	27.2220	+	16.8531i	1.23993	+	0.767640i
$483$	3.26597	+	1.35281i	0.148607	+	0.0615549i
$484$	−2.46490	+	7.35684i	−0.112041	+	0.334402i
$485$	−0.509161	+	1.22922i	−0.0231198	+	0.0558161i
$486$	9.12165	+	12.6762i	0.413766	+	0.575005i
$487$	−26.1553			−1.18521			−0.592605	−	0.805493i	$-0.701901\pi$
$487$	−26.1553			−1.18521			−0.592605	+	0.805493i	$0.701901\pi$
$488$	−17.4331	−	9.18562i	−0.789159	−	0.415813i
$489$			32.1618i			1.45441i
$490$	21.0267	+	29.2206i	0.949891	+	1.32005i
$491$	2.91967	−	7.04871i	0.131763	−	0.318104i	−0.844204	−	0.536022i	$-0.819926\pi$
$491$	2.91967	−	7.04871i	0.131763	−	0.318104i	0.975967	+	0.217918i	$0.0699265\pi$
$492$	−5.93839	+	6.82570i	−0.267723	+	0.307726i
$493$	−4.96442	−	11.9852i	−0.223586	−	0.539785i
$494$	−4.91259	+	25.1649i	−0.221028	+	1.13222i
$495$	−52.0863			−2.34111
$496$	4.61476	+	33.0313i	0.207209	+	1.48315i
$497$			2.93331i			0.131577i
$498$	4.81552	+	20.4695i	0.215789	+	0.917260i
$499$	−5.20677	+	12.5702i	−0.233087	+	0.562722i	−0.996537	−	0.0831447i	$-0.973504\pi$
$499$	−5.20677	+	12.5702i	−0.233087	+	0.562722i	0.763451	+	0.645866i	$0.223504\pi$
$500$	27.4080	−	1.90531i	1.22572	−	0.0852082i
$501$	−20.7078	−	49.9931i	−0.925157	−	2.23353i
$502$	−4.38933	−	0.715767i	−0.195905	−	0.0319463i
$503$	−8.12326	−	8.12326i	−0.362198	−	0.362198i	0.502423	−	0.864622i	$-0.332442\pi$
$503$	−8.12326	−	8.12326i	−0.362198	−	0.362198i	−0.864622	+	0.502423i	$0.832442\pi$
$504$	5.25256	+	0.485884i	0.233967	+	0.0216430i
$505$	17.3042			0.770025
$506$	−2.11018	+	12.9403i	−0.0938089	+	0.575268i
$507$	−35.3662	+	12.1300i	−1.57067	+	0.538713i
$508$	2.70086	−	1.34523i	0.119832	−	0.0596847i
$509$	−3.12959	+	7.55550i	−0.138717	+	0.334892i	−0.977937	−	0.208900i	$-0.933012\pi$
$509$	−3.12959	+	7.55550i	−0.138717	+	0.334892i	0.839220	+	0.543791i	$0.183012\pi$
$510$	−20.3746	−	12.6139i	−0.902200	−	0.558553i
$511$	1.03603			0.0458314
$512$	11.0200	+	19.7626i	0.487018	+	0.873392i
$513$	−23.2301	−	23.2301i	−1.02564	−	1.02564i
$514$	6.54679	+	27.8287i	0.288767	+	1.22747i
$515$	−5.56408	+	13.4329i	−0.245183	+	0.591923i
$516$	2.67455	+	5.36981i	0.117741	+	0.236393i
$517$	−12.3213	+	29.7462i	−0.541888	+	1.30823i
$518$	−2.95448	−	4.10580i	−0.129812	−	0.180398i
$519$	11.0337	+	11.0337i	0.484324	+	0.484324i
$520$	−32.8423	−	18.6339i	−1.44023	−	0.817152i
$521$	−14.0233	+	14.0233i	−0.614373	+	0.614373i	−0.944082	−	0.329709i	$-0.893049\pi$
$521$	−14.0233	+	14.0233i	−0.614373	+	0.614373i	0.329709	+	0.944082i	$0.393049\pi$
$522$	59.9898	+	9.78253i	2.62568	+	0.428170i
$523$	−6.69070	−	2.77138i	−0.292564	−	0.121184i	0.231574	−	0.972817i	$-0.425612\pi$
$523$	−6.69070	−	2.77138i	−0.292564	−	0.121184i	−0.524138	+	0.851633i	$0.675612\pi$
$524$	−17.9302	+	20.6094i	−0.783285	+	0.900324i
$525$	−8.18765	−	3.39144i	−0.357339	−	0.148014i
$526$	6.74007	−	10.8869i	0.293881	−	0.474690i
$527$	−9.38128	+	9.38128i	−0.408655	+	0.408655i
$528$	4.24757	+	30.4030i	0.184852	+	1.32312i
$529$			10.9290i			0.475175i
$530$	−24.5796	+	5.78242i	−1.06767	+	0.251172i
$531$	10.0764	+	4.17378i	0.437278	+	0.181127i
$532$	3.54929	−	0.246736i	0.153881	−	0.0106973i
$533$	−5.66835	−	0.176595i	−0.245523	−	0.00764918i
$534$	19.3509	−	13.9247i	0.837396	−	0.602580i
$535$			34.0379i			1.47159i
$536$	−41.7829	+	12.9459i	−1.80475	+	0.559177i
$537$	34.5107	−	34.5107i	1.48925	−	1.48925i
$538$	−25.0849	+	18.0508i	−1.08149	+	0.778224i
$539$	16.9487	−	7.02038i	0.730032	−	0.302389i
$540$	43.3078	−	21.5704i	1.86367	−	0.928242i
$541$	3.28934	+	1.36249i	0.141420	+	0.0585780i	0.452271	−	0.891881i	$-0.350614\pi$
$541$	3.28934	+	1.36249i	0.141420	+	0.0585780i	−0.310851	+	0.950459i	$0.600614\pi$
$542$	22.9128	−	37.0097i	0.984187	−	1.58970i
$543$	−68.4719			−2.93841
$544$	−3.63351	+	8.23498i	−0.155786	+	0.353072i
$545$			26.0143i			1.11433i
$546$	2.89771	+	4.30350i	0.124011	+	0.184173i
$547$	11.5180	−	4.77093i	0.492476	−	0.203990i	−0.122603	−	0.992456i	$-0.539124\pi$
$547$	11.5180	−	4.77093i	0.492476	−	0.203990i	0.615079	+	0.788466i	$0.289124\pi$
$548$	−3.69395	−	7.41650i	−0.157798	−	0.316817i
$549$	33.9308	+	14.0546i	1.44813	+	0.599835i
$550$	5.29013	−	32.4409i	0.225572	−	1.38329i
$551$	40.9963			1.74650
$552$	−8.36451	−	26.9965i	−0.356017	−	1.14905i
$553$		−	0.345125i		−	0.0146762i
$554$	−29.0909	−	4.74384i	−1.23595	−	0.201547i
$555$	−99.4698	−	41.2017i	−4.22226	−	1.74892i
$556$	−22.0526	+	1.53303i	−0.935239	+	0.0650148i
$557$	−7.00735	+	16.9172i	−0.296911	+	0.716807i	0.703073	+	0.711118i	$0.251811\pi$
$557$	−7.00735	+	16.9172i	−0.296911	+	0.716807i	−0.999984	+	0.00568880i	$0.998189\pi$
$558$	−14.2352	−	60.5100i	−0.602624	−	2.56159i
$559$	−1.54650	+	3.42759i	−0.0654098	+	0.144972i
$560$	−1.31606	+	5.07175i	−0.0556137	+	0.214321i
$561$	−8.63483	+	8.63483i	−0.364563	+	0.364563i
$562$	41.4964	−	9.76217i	1.75042	−	0.411792i
$563$	−1.44990	+	0.600569i	−0.0611061	+	0.0253110i	−0.413027	−	0.910719i	$-0.635529\pi$
$563$	−1.44990	+	0.600569i	−0.0611061	+	0.0253110i	0.351921	+	0.936030i	$0.385529\pi$
$564$	−4.81311	−	69.2367i	−0.202669	−	2.91539i
$565$	−19.2608	+	7.97807i	−0.810307	+	0.335640i
$566$	−5.56810	−	0.907988i	−0.234045	−	0.0381656i
$567$	−1.05261			−0.0442053
$568$	18.0398	−	14.9849i	0.756933	−	0.628752i
$569$	−25.2684	+	25.2684i	−1.05931	+	1.05931i	−0.0611796	+	0.998127i	$0.519486\pi$
$569$	−25.2684	+	25.2684i	−1.05931	+	1.05931i	−0.998127	+	0.0611796i	$0.980514\pi$
$570$	61.4683	−	44.2318i	2.57462	−	1.85267i
$571$	20.4365	+	8.46509i	0.855242	+	0.354253i	0.766845	−	0.641832i	$-0.221826\pi$
$571$	20.4365	+	8.46509i	0.855242	+	0.354253i	0.0883972	+	0.996085i	$0.471826\pi$
$572$	−13.0760	+	14.1170i	−0.546737	+	0.590260i
$573$	−5.48714	−	13.2471i	−0.229229	−	0.553407i
$574$	0.180210	+	0.766025i	0.00752182	+	0.0319733i
$575$			30.2614i			1.26199i
$576$	−23.8446	−	34.7852i	−0.993525	−	1.44939i
$577$	−14.7312	−	14.7312i	−0.613267	−	0.613267i	0.330529	−	0.943796i	$-0.392773\pi$
$577$	−14.7312	−	14.7312i	−0.613267	−	0.613267i	−0.943796	+	0.330529i	$0.892773\pi$
$578$	19.9174	−	4.68564i	0.828455	−	0.194897i
$579$	−12.1765	+	29.3968i	−0.506040	+	1.22169i
$580$	−19.1809	+	57.2481i	−0.796444	+	2.37710i
$581$	1.68981	+	0.699942i	0.0701051	+	0.0290385i
$582$	−1.44248	−	0.235224i	−0.0597925	−	0.00975036i
$583$			12.8675i			0.532919i
$584$	−5.29259	−	6.37158i	−0.219009	−	0.263658i
$585$	64.1506	+	28.9442i	2.65230	+	1.19669i
$586$	−9.31166	+	6.70055i	−0.384661	+	0.276797i
$587$	1.90840	+	4.60730i	0.0787683	+	0.190163i	0.958358	−	0.285570i	$-0.0921828\pi$
$587$	1.90840	+	4.60730i	0.0787683	+	0.190163i	−0.879590	+	0.475733i	$0.842183\pi$
$588$	−25.9559	+	29.8342i	−1.07040	+	1.23034i
$589$	−16.0447	−	38.7354i	−0.661111	−	1.59606i
$590$	−5.70273	+	9.21130i	−0.234778	+	0.379223i
$591$	36.5297	+	36.5297i	1.50263	+	1.50263i
$592$	−10.1575	+	39.1445i	−0.417472	+	1.60883i
$593$	−29.4587	−	29.4587i	−1.20973	−	1.20973i	−0.971116	−	0.238610i	$-0.923308\pi$
$593$	−29.4587	−	29.4587i	−1.20973	−	1.20973i	−0.238610	−	0.971116i	$-0.576692\pi$
$594$	−5.64611	−	24.0001i	−0.231663	−	0.984738i
$595$	−1.92565	+	0.797631i	−0.0789440	+	0.0326997i
$596$	23.9725	−	27.5545i	0.981952	−	1.12868i
$597$	46.9103	+	19.4309i	1.91991	+	0.795253i
$598$	9.78983	−	14.7650i	0.400336	−	0.603785i
$599$	7.80699	+	7.80699i	0.318985	+	0.318985i	0.848377	−	0.529392i	$-0.177580\pi$
$599$	7.80699	+	7.80699i	0.318985	+	0.318985i	−0.529392	+	0.848377i	$0.677580\pi$
$600$	20.9695	+	67.6791i	0.856077	+	2.76299i
$601$	−15.2437	−	15.2437i	−0.621805	−	0.621805i	0.324188	−	0.945993i	$-0.394909\pi$
$601$	−15.2437	−	15.2437i	−0.621805	−	0.621805i	−0.945993	+	0.324188i	$0.894909\pi$
$602$	0.514990	+	0.0839793i	0.0209894	+	0.00342274i
$603$	75.3217	−	31.1993i	3.06734	−	1.27053i
$604$	−18.7191	+	9.32344i	−0.761667	+	0.379365i
$605$	13.2708	+	5.49696i	0.539536	+	0.223483i
$606$	4.35293	+	18.5032i	0.176826	+	0.751639i
$607$			41.2527i			1.67439i	0.546902	+	0.837197i	$0.315807\pi$
$607$			41.2527i			1.67439i	−0.546902	+	0.837197i	$0.684193\pi$
$608$	−19.6490	−	20.5676i	−0.796874	−	0.834127i
$609$	5.86578	−	5.86578i	0.237693	−	0.237693i
$610$	−19.2031	+	31.0177i	−0.777511	+	1.25587i
$611$	31.7049	−	29.7891i	1.28264	−	1.20514i
$612$	5.32962	−	15.9070i	0.215437	−	0.643002i
$613$	8.64630	+	20.8740i	0.349221	+	0.843093i	0.996712	+	0.0810209i	$0.0258180\pi$
$613$	8.64630	+	20.8740i	0.349221	+	0.843093i	−0.647492	+	0.762073i	$0.724182\pi$
$614$	0.553386	+	0.0902406i	0.0223329	+	0.00364181i
$615$	11.8439	+	11.8439i	0.477593	+	0.477593i
$616$	2.36227	+	1.24470i	0.0951787	+	0.0501503i
$617$	38.0732			1.53277			0.766385	−	0.642382i	$-0.222054\pi$
$617$	38.0732			1.53277			0.766385	+	0.642382i	$0.222054\pi$
$618$	−15.7633	−	2.57052i	−0.634093	−	0.103401i
$619$	−2.84679	+	1.17918i	−0.114422	+	0.0473952i	−0.439160	−	0.898409i	$-0.644724\pi$
$619$	−2.84679	+	1.17918i	−0.114422	+	0.0473952i	0.324738	+	0.945804i	$0.394724\pi$
$620$	61.5978	−	4.28208i	2.47383	−	0.171972i
$621$	8.68657	+	20.9712i	0.348580	+	0.841546i
$622$	−8.95999	+	14.4726i	−0.359263	+	0.580298i
$623$		−	2.07361i		−	0.0830776i
$624$	11.6634	−	39.8054i	0.466911	−	1.59349i
$625$		−	7.31421i		−	0.292568i
$626$	24.0763	+	14.9057i	0.962284	+	0.595751i
$627$	−14.7681	−	35.6533i	−0.589780	−	1.42385i
$628$	3.52782	+	3.06921i	0.140775	+	0.122475i
$629$	−14.8624	+	6.15623i	−0.592605	+	0.245465i
$630$	1.57175	−	9.63853i	0.0626202	−	0.384008i
$631$	−22.2524			−0.885853			−0.442927	−	0.896558i	$-0.646060\pi$
$631$	−22.2524			−0.885853			−0.442927	+	0.896558i	$0.646060\pi$
$632$	−2.12251	+	1.76308i	−0.0844290	+	0.0701314i
$633$	−39.4534	−	39.4534i	−1.56813	−	1.56813i
$634$	3.75353	−	23.0179i	0.149072	−	0.914159i
$635$	−2.13773	−	5.16093i	−0.0848330	−	0.204805i
$636$	−12.3662	−	24.8281i	−0.490350	−	0.984496i
$637$	−24.7756	−	0.771872i	−0.981644	−	0.0305827i
$638$	26.1597	+	16.1955i	1.03567	+	0.641185i
$639$	−30.9073	+	30.9073i	−1.22267	+	1.22267i
$640$	37.9143	−	17.8154i	1.49869	−	0.704215i
$641$		−	22.7437i		−	0.898322i	−0.893451	−	0.449161i	$-0.851723\pi$
$641$		−	22.7437i		−	0.898322i	0.893451	−	0.449161i	$-0.148277\pi$
$642$	−36.3964	+	8.56237i	−1.43645	+	0.337930i
$643$	−14.2276	−	5.89327i	−0.561082	−	0.232408i	0.0840729	−	0.996460i	$-0.473207\pi$
$643$	−14.2276	−	5.89327i	−0.561082	−	0.232408i	−0.645155	+	0.764052i	$0.723207\pi$
$644$	−2.33092	−	0.780973i	−0.0918512	−	0.0307747i
$645$	10.2609	−	4.25019i	0.404021	−	0.167351i
$646$	1.82110	−	11.1676i	0.0716501	−	0.439383i
$647$	−16.0729	−	16.0729i	−0.631892	−	0.631892i	0.316650	−	0.948542i	$-0.397442\pi$
$647$	−16.0729	−	16.0729i	−0.631892	−	0.631892i	−0.948542	+	0.316650i	$0.897442\pi$
$648$	5.37726	+	6.47351i	0.211239	+	0.254303i
$649$	3.90379	+	3.90379i	0.153237	+	0.153237i
$650$	−24.5427	+	37.0152i	−0.962645	+	1.45186i
$651$	−7.83797	−	3.24659i	−0.307194	−	0.127244i
$652$	−1.55102	−	22.3115i	−0.0607427	−	0.873784i
$653$	−21.2018	+	8.78207i	−0.829690	+	0.343669i	−0.756780	−	0.653670i	$-0.773229\pi$
$653$	−21.2018	+	8.78207i	−0.829690	+	0.343669i	−0.0729100	+	0.997339i	$0.523229\pi$
$654$	−27.8168	+	6.54401i	−1.08772	+	0.255891i
$655$	35.7613	+	35.7613i	1.39731	+	1.39731i
$656$	3.79043	−	5.02154i	0.147991	−	0.196058i
$657$	10.9163	+	10.9163i	0.425886	+	0.425886i
$658$	−5.13270	−	3.17766i	−0.200093	−	0.123878i
$659$	−7.90917	−	19.0944i	−0.308098	−	0.743814i	−0.999767	−	0.0215990i	$-0.993124\pi$
$659$	−7.90917	−	19.0944i	−0.308098	−	0.743814i	0.691669	−	0.722215i	$-0.256876\pi$
$660$	56.6965	−	3.94136i	2.20691	−	0.153417i
$661$	−13.2440	−	31.9740i	−0.515134	−	1.24364i	−0.940862	−	0.338791i	$-0.889982\pi$
$661$	−13.2440	−	31.9740i	−0.515134	−	1.24364i	0.425728	−	0.904851i	$-0.360018\pi$
$662$	9.18497	+	12.7642i	0.356984	+	0.496095i
$663$	15.4332	−	5.83650i	0.599375	−	0.226671i
$664$	−4.32780	−	13.9680i	−0.167951	−	0.542062i
$665$		−	6.58685i		−	0.255427i
$666$	12.1310	−	74.3915i	0.470067	−	2.88261i
$667$	−26.1699	−	10.8399i	−1.01330	−	0.419723i
$668$	16.7765	+	33.6828i	0.649101	+	1.30323i
$669$	−21.3481	+	51.5388i	−0.825364	+	1.99260i
$670$	18.5452	+	78.8307i	0.716463	+	3.04549i
$671$	13.1455	+	13.1455i	0.507475	+	0.507475i
$672$	−5.75423	−	0.131431i	−0.221974	−	0.00507004i
$673$		−	3.14540i		−	0.121246i	−0.998161	−	0.0606231i	$-0.980691\pi$
$673$		−	3.14540i		−	0.121246i	0.998161	−	0.0606231i	$-0.0193088\pi$
$674$	3.92963	−	0.924460i	0.151364	−	0.0356089i
$675$	−21.7769	−	52.5740i	−0.838192	−	2.02358i
$676$	23.9495	−	10.1205i	0.921133	−	0.389248i
$677$	−20.8407	−	8.63252i	−0.800975	−	0.331775i	−0.0556280	−	0.998452i	$-0.517716\pi$
$677$	−20.8407	−	8.63252i	−0.800975	−	0.331775i	−0.745347	+	0.666677i	$0.767716\pi$
$678$	−13.3760	−	18.5884i	−0.513702	−	0.713884i
$679$	−0.0898899	+	0.0898899i	−0.00344966	+	0.00344966i
$680$	14.7426	+	7.76800i	0.565354	+	0.297889i
$681$	37.7430			1.44631
$682$	5.06420	−	31.0554i	0.193918	−	1.18917i
$683$	42.8294	−	17.7405i	1.63882	−	0.678822i	0.642643	−	0.766166i	$-0.277838\pi$
$683$	42.8294	−	17.7405i	1.63882	−	0.678822i	0.996178	+	0.0873440i	$0.0278379\pi$
$684$	39.9974	+	34.7979i	1.52934	+	1.33053i
$685$	−14.1718	+	5.87013i	−0.541475	+	0.224286i
$686$	1.58969	+	6.75734i	0.0606945	+	0.257996i
$687$	41.1649	−	41.1649i	1.57054	−	1.57054i
$688$	−2.11437	−	3.59619i	−0.0806094	−	0.137103i
$689$	7.15044	−	15.8479i	0.272410	−	0.603758i
$690$	−50.9336	+	11.9823i	−1.93901	+	0.456158i
$691$	17.8719	−	43.1467i	0.679881	−	1.64138i	−0.0843517	−	0.996436i	$-0.526882\pi$
$691$	17.8719	−	43.1467i	0.679881	−	1.64138i	0.764232	−	0.644941i	$-0.223118\pi$
$692$	−8.18643	−	7.12222i	−0.311201	−	0.270746i
$693$	−4.59780	−	1.90447i	−0.174656	−	0.0723448i
$694$	1.94892	−	11.9514i	0.0739799	−	0.453670i
$695$			40.9256i			1.55240i
$696$	−66.0398	−	6.10897i	−2.50323	−	0.231560i
$697$	2.50271			0.0947967
$698$	−15.7934	−	2.57543i	−0.597791	−	0.0974816i
$699$	36.9899	+	15.3217i	1.39909	+	0.579520i
$700$	5.84353	+	1.95787i	0.220865	+	0.0740005i
$701$	−21.1619	+	8.76555i	−0.799274	+	0.331070i	−0.744666	−	0.667438i	$-0.767391\pi$
$701$	−21.1619	+	8.76555i	−0.799274	+	0.331070i	−0.0546083	+	0.998508i	$0.517391\pi$
$702$	−6.38290	+	32.6966i	−0.240907	+	1.23405i
$703$		−	50.8382i		−	1.91740i
$704$	−4.41284	−	20.8865i	−0.166315	−	0.787189i
$705$	−128.491			−4.83924
$706$	−0.299675	−	0.185529i	−0.0112784	−	0.00698247i
$707$	1.52748	+	0.632705i	0.0574469	+	0.0237953i
$708$	−11.2841	−	3.78072i	−0.424082	−	0.142088i
$709$	−5.42719	+	2.24801i	−0.203822	+	0.0844260i	−0.482259	−	0.876029i	$-0.660184\pi$
$709$	−5.42719	+	2.24801i	−0.203822	+	0.0844260i	0.278437	+	0.960455i	$0.410184\pi$
$710$	−25.3594	−	35.2415i	−0.951720	−	1.32259i
$711$	3.63646	−	3.63646i	0.136378	−	0.136378i
$712$	−12.7527	+	10.5931i	−0.477927	+	0.396993i
$713$			28.9690i			1.08490i
$714$	−1.33730	−	1.85843i	−0.0500473	−	0.0695500i
$715$	24.3937	+	25.9625i	0.912273	+	0.970944i
$716$	−22.2766	+	25.6052i	−0.832516	+	0.956911i
$717$	7.42379	+	3.07503i	0.277246	+	0.114839i
$718$	−0.118414	−	0.503347i	−0.00441918	−	0.0187848i
$719$		−	29.1752i		−	1.08805i	−0.839069	−	0.544025i	$-0.816900\pi$
$719$		−	29.1752i		−	1.08805i	0.839069	−	0.544025i	$-0.183100\pi$
$720$	−67.3061	+	39.5724i	−2.50835	+	1.47477i
$721$	−0.982312	+	0.982312i	−0.0365832	+	0.0365832i
$722$	7.55697	+	4.67853i	0.281241	+	0.174117i
$723$	60.1550	+	24.9170i	2.23719	+	0.926674i
$724$	47.5007	−	3.30209i	1.76535	−	0.122721i
$725$	65.6068	+	27.1752i	2.43658	+	1.00926i
$726$	−2.53951	+	15.5731i	−0.0942500	+	0.577974i
$727$	−0.875628	+	0.875628i	−0.0324752	+	0.0324752i	−0.723158	−	0.690683i	$-0.757310\pi$
$727$	−0.875628	+	0.875628i	−0.0324752	+	0.0324752i	0.690683	+	0.723158i	$0.257310\pi$
$728$	−2.21775	−	2.84570i	−0.0821953	−	0.105469i
$729$	28.7693	+	28.7693i	1.06553	+	1.06553i
$730$	−12.4472	+	8.95681i	−0.460690	+	0.331506i
$731$	0.635049	−	1.53314i	0.0234881	−	0.0567054i
$732$	−37.9975	−	12.7310i	−1.40443	−	0.470553i
$733$	−0.221050	+	0.533662i	−0.00816467	+	0.0197113i	−0.927909	−	0.372806i	$-0.878396\pi$
$733$	−0.221050	+	0.533662i	−0.00816467	+	0.0197113i	0.919745	+	0.392517i	$0.128396\pi$
$734$	−10.4123	+	2.44952i	−0.384323	+	0.0904134i
$735$	51.7681	+	51.7681i	1.90950	+	1.90950i
$736$	7.10459	+	18.3247i	0.261879	+	0.675459i
$737$	41.2683			1.52014
$738$	−6.17252	+	9.97014i	−0.227214	+	0.367006i
$739$	14.3778	−	34.7112i	0.528897	−	1.27687i	−0.403349	−	0.915046i	$-0.632154\pi$
$739$	14.3778	−	34.7112i	0.528897	−	1.27687i	0.932246	−	0.361825i	$-0.117846\pi$
$740$	70.9916	+	23.7857i	2.60970	+	0.874379i
$741$	−1.62371	+	52.1178i	−0.0596484	+	1.91460i
$742$	−2.38113	−	0.388290i	−0.0874140	−	0.0142546i
$743$	−27.0184			−0.991210			−0.495605	−	0.868548i	$-0.665054\pi$
$743$	−27.0184			−0.991210			−0.495605	+	0.868548i	$0.665054\pi$
$744$	20.0739	+	64.7886i	0.735946	+	2.37527i
$745$	−47.8124	−	47.8124i	−1.75171	−	1.75171i
$746$	6.66222	−	40.8550i	0.243921	−	1.49581i
$747$	10.4299	+	25.1800i	0.381609	+	0.921286i
$748$	5.57377	−	6.40661i	0.203797	−	0.234249i
$749$	−1.24455	+	3.00461i	−0.0454749	+	0.109786i
$750$	54.3886	−	12.7951i	1.98599	−	0.467211i
$751$		−	27.8107i		−	1.01483i	−0.861703	−	0.507414i	$-0.830602\pi$
$751$		−	27.8107i		−	1.01483i	0.861703	−	0.507414i	$-0.169398\pi$
$752$	6.67795	+	47.7991i	0.243520	+	1.74305i
$753$	−9.04437			−0.329595
$754$	−23.2190	−	34.4835i	−0.845588	−	1.25582i
$755$	14.8161	+	35.7691i	0.539212	+	1.30177i
$756$	4.61158	−	0.320582i	0.167722	−	0.0116595i
$757$	−3.97154	+	9.58814i	−0.144348	+	0.348487i	−0.979474	−	0.201572i	$-0.935395\pi$
$757$	−3.97154	+	9.58814i	−0.144348	+	0.348487i	0.835126	+	0.550059i	$0.185395\pi$
$758$	7.91139	−	5.69293i	0.287355	−	0.206777i
$759$			26.6640i			0.967842i
$760$	−40.5090	+	33.6490i	−1.46941	+	1.22058i
$761$	4.70902			0.170702			0.0853509	−	0.996351i	$-0.472799\pi$
$761$	4.70902			0.170702			0.0853509	+	0.996351i	$0.472799\pi$
$762$	4.98077	−	3.58410i	0.180434	−	0.129838i
$763$	−0.951180	+	2.29635i	−0.0344350	+	0.0831335i
$764$	4.44541	+	8.92524i	0.160829	+	0.322904i
$765$	−28.6942	−	11.8855i	−1.03744	−	0.429723i
$766$	−17.4894	+	28.2497i	−0.631918	+	1.02070i
$767$	−2.63867	−	6.97731i	−0.0952769	−	0.251936i
$768$	28.5873	+	36.0598i	1.03155	+	1.30120i
$769$	−36.1755	−	36.1755i	−1.30452	−	1.30452i	−0.925310	−	0.379211i	$-0.876196\pi$
$769$	−36.1755	−	36.1755i	−1.30452	−	1.30452i	−0.379211	−	0.925310i	$-0.623804\pi$
$770$	2.60212	−	4.20306i	0.0937739	−	0.151468i
$771$	22.2490	+	53.7138i	0.801278	+	1.93446i
$772$	7.02949	−	20.9805i	0.252997	−	0.755104i
$773$	9.80928	+	23.6817i	0.352815	+	0.851771i	0.996270	+	0.0862874i	$0.0275003\pi$
$773$	9.80928	+	23.6817i	0.352815	+	0.851771i	−0.643455	+	0.765484i	$0.722500\pi$
$774$	4.54141	+	6.31113i	0.163237	+	0.226849i
$775$		−	72.6242i		−	2.60874i
$776$	1.01202	+	0.0936167i	0.0363296	+	0.00336064i
$777$	−7.27397	−	7.27397i	−0.260952	−	0.260952i
$778$	−3.77114	+	23.1259i	−0.135202	+	0.829104i
$779$	−3.02667	+	7.30702i	−0.108442	+	0.261801i
$780$	−72.0188	−	26.6518i	−2.57869	−	0.954286i
$781$	−20.4410	+	8.46695i	−0.731437	+	0.302971i
$782$	−4.11534	+	6.64728i	−0.147164	+	0.237706i
$783$	53.2663			1.90358
$784$	16.5674	−	21.9485i	0.591695	−	0.783874i
$785$	6.12145	−	6.12145i	0.218484	−	0.218484i
$786$	−29.2432	+	47.2350i	−1.04307	+	1.68482i
$787$	−22.6223	−	9.37045i	−0.806397	−	0.334020i	−0.0588813	−	0.998265i	$-0.518753\pi$
$787$	−22.6223	−	9.37045i	−0.806397	−	0.334020i	−0.747515	+	0.664245i	$0.768753\pi$
$788$	−27.1032	−	23.5799i	−0.965513	−	0.839999i
$789$	9.96505	−	24.0578i	0.354765	−	0.856479i
$790$	2.98371	+	4.14642i	0.106156	+	0.147523i
$791$	−1.99191			−0.0708240
$792$	11.7755	+	38.0054i	0.418423	+	1.35046i
$793$	−8.88534	−	23.4951i	−0.315528	−	0.834335i
$794$	3.11565	−	19.1062i	0.110570	−	0.678055i
$795$	−47.4425	+	19.6513i	−1.68261	+	0.696961i
$796$	−33.4799	−	11.2174i	−1.18666	−	0.397591i
$797$	32.9639	−	13.6541i	1.16764	−	0.483653i	0.287230	−	0.957862i	$-0.407266\pi$
$797$	32.9639	−	13.6541i	1.16764	−	0.483653i	0.880413	+	0.474208i	$0.157266\pi$
$798$	7.04325	−	1.65695i	0.249328	−	0.0586553i
$799$	−13.5755	+	13.5755i	−0.480267	+	0.480267i
$800$	−17.8109	−	45.9394i	−0.629711	−	1.62420i
$801$	21.8489	−	21.8489i	0.771994	−	0.771994i
$802$	−40.7739	−	25.2431i	−1.43978	−	0.891367i
$803$	2.99049	+	7.21968i	0.105532	+	0.254777i
$804$	−79.6277	+	39.6603i	−2.80825	+	1.39871i
$805$	−1.74164	+	4.20470i	−0.0613848	+	0.148196i
$806$	−23.4945	+	35.4343i	−0.827560	+	1.24812i
$807$	−44.4413	+	44.4413i	−1.56441	+	1.56441i
$808$	−3.91206	−	12.6262i	−0.137626	−	0.444187i
$809$	−0.504496	+	0.504496i	−0.0177371	+	0.0177371i	−0.715920	−	0.698183i	$-0.753992\pi$
$809$	−0.504496	+	0.504496i	−0.0177371	+	0.0177371i	0.698183	+	0.715920i	$0.253992\pi$
$810$	12.6463	−	9.10009i	0.444345	−	0.319745i
$811$	−0.230008	−	0.555288i	−0.00807666	−	0.0194988i	0.919790	−	0.392412i	$-0.128359\pi$
$811$	−0.230008	−	0.555288i	−0.00807666	−	0.0194988i	−0.927866	+	0.372913i	$0.878359\pi$
$812$	−3.78635	+	4.35211i	−0.132875	+	0.152729i
$813$	33.8760	−	81.7840i	1.18808	−	2.86829i
$814$	20.0835	−	32.4398i	0.703927	−	1.13701i
$815$	−41.4060			−1.45039
$816$	−4.59767	+	17.7182i	−0.160951	+	0.620262i
$817$	3.70824	+	3.70824i	0.129735	+	0.129735i
$818$	−0.394902	−	1.67862i	−0.0138074	−	0.0586917i
$819$	4.60444	+	4.90056i	0.160892	+	0.171239i
$820$	−8.78760	−	7.64524i	−0.306876	−	0.266983i
$821$	−17.4331	+	7.22101i	−0.608418	+	0.252015i	−0.665552	−	0.746352i	$-0.731804\pi$
$821$	−17.4331	+	7.22101i	−0.608418	+	0.252015i	0.0571339	+	0.998367i	$0.481804\pi$
$822$	−9.84183	−	13.6770i	−0.343273	−	0.477042i
$823$	2.24800	−	2.24800i	0.0783604	−	0.0783604i	−0.666840	−	0.745201i	$-0.732354\pi$
$823$	2.24800	−	2.24800i	0.0783604	−	0.0783604i	0.745201	+	0.666840i	$0.232354\pi$
$824$	11.0594	+	1.02304i	0.385271	+	0.0356392i
$825$		−	66.8456i		−	2.32727i
$826$	−0.840194	+	0.604593i	−0.0292341	+	0.0210365i
$827$	−6.48486	−	15.6558i	−0.225501	−	0.544407i	0.770119	−	0.637900i	$-0.220197\pi$
$827$	−6.48486	−	15.6558i	−0.225501	−	0.544407i	−0.995620	+	0.0934930i	$0.970197\pi$
$828$	−16.3313	−	32.7889i	−0.567550	−	1.13949i
$829$	35.0138	−	14.5032i	1.21608	−	0.503717i	0.319919	−	0.947445i	$-0.396344\pi$
$829$	35.0138	−	14.5032i	1.21608	−	0.503717i	0.896162	+	0.443728i	$0.146344\pi$
$830$	−26.3530	+	6.19963i	−0.914726	+	0.215192i
$831$	−59.9428			−2.07939
$832$	−6.17158	+	28.1764i	−0.213961	+	0.976842i
$833$	10.9390			0.379013
$834$	−43.7613	+	10.2950i	−1.51533	+	0.356487i
$835$	64.3625	−	26.6598i	2.22736	−	0.922601i
$836$	11.9644	+	24.0213i	0.413796	+	0.830796i
$837$	−20.8468	−	50.3287i	−0.720572	−	1.73961i
$838$	14.3708	−	10.3411i	0.496433	−	0.357227i
$839$		−	12.8567i		−	0.443862i	−0.975062	−	0.221931i	$-0.928764\pi$
$839$		−	12.8567i		−	0.443862i	0.975062	−	0.221931i	$-0.0712360\pi$
$840$	−0.981525	+	10.6106i	−0.0338658	+	0.366100i
$841$	−26.4957	+	26.4957i	−0.913646	+	0.913646i
$842$	−6.06806	−	8.43269i	−0.209119	−	0.290610i
$843$	80.0947	−	33.1763i	2.75861	−	1.14265i
$844$	29.2724	+	25.4671i	1.00760	+	0.876614i
$845$	−15.6165	−	45.5315i	−0.537225	−	1.56633i
$846$	−20.5995	−	87.5632i	−0.708227	−	3.01048i
$847$	0.970462	+	0.970462i	0.0333455	+	0.0333455i
$848$	9.77606	+	16.6275i	0.335711	+	0.570990i
$849$	−11.4733			−0.393761
$850$	10.3170	−	16.6645i	0.353870	−	0.571587i
$851$	−13.4422	+	32.4524i	−0.460794	+	1.11246i
$852$	31.3041	−	35.9816i	1.07246	−	1.23271i
$853$	−17.3435	−	41.8708i	−0.593829	−	1.43363i	−0.879778	−	0.475385i	$-0.842309\pi$
$853$	−17.3435	−	41.8708i	−0.593829	−	1.43363i	0.285949	−	0.958245i	$-0.407691\pi$
$854$	−2.82923	+	2.03588i	−0.0968143	+	0.0696663i
$855$	69.4032	−	69.4032i	2.37354	−	2.37354i
$856$	24.8361	−	7.69516i	0.848881	−	0.263015i
$857$	1.55766	−	1.55766i	0.0532086	−	0.0532086i	−0.680002	−	0.733210i	$-0.738021\pi$
$857$	1.55766	−	1.55766i	0.0532086	−	0.0532086i	0.733210	+	0.680002i	$0.238021\pi$
$858$	−21.6251	+	32.6149i	−0.738269	+	1.11345i
$859$	−13.2914	+	32.0883i	−0.453498	+	1.09484i	0.517485	+	0.855692i	$0.326868\pi$
$859$	−13.2914	+	32.0883i	−0.453498	+	1.09484i	−0.970983	+	0.239148i	$0.923132\pi$
$860$	−6.91324	+	3.44329i	−0.235740	+	0.117415i
$861$	0.612436	+	1.47855i	0.0208718	+	0.0503889i
$862$	19.5229	+	12.0867i	0.664953	+	0.411673i
$863$	21.2676	−	21.2676i	0.723958	−	0.723958i	−0.245451	−	0.969409i	$-0.578936\pi$
$863$	21.2676	−	21.2676i	0.723958	−	0.723958i	0.969409	+	0.245451i	$0.0789361\pi$
$864$	−25.5299	−	26.7234i	−0.868546	−	0.909149i
$865$	−14.2050	+	14.2050i	−0.482986	+	0.482986i
$866$	−13.7772	+	3.24113i	−0.468168	+	0.110138i
$867$	38.4438	−	15.9239i	1.30562	−	0.540805i
$868$	5.59396	+	1.87425i	0.189871	+	0.0636163i
$869$	2.40503	−	0.996197i	0.0815851	−	0.0337937i
$870$	−19.7615	+	121.184i	−0.669977	+	4.10853i
$871$	−50.8269	−	22.9326i	−1.72220	−	0.777043i
$872$	18.9816	−	5.88122i	0.642799	−	0.199163i
$873$	−1.89427			−0.0641115
$874$	−14.4308	−	20.0543i	−0.488130	−	0.678347i
$875$	1.85979	−	4.48992i	0.0628722	−	0.151787i
$876$	−12.7086	−	11.0565i	−0.429382	−	0.373564i
$877$	37.4417	+	15.5088i	1.26431	+	0.523696i	0.911231	−	0.411895i	$-0.135133\pi$
$877$	37.4417	+	15.5088i	1.26431	+	0.523696i	0.353084	+	0.935592i	$0.385133\pi$
$878$	−11.8994	+	19.2204i	−0.401585	+	0.648658i
$879$	−16.4969	+	16.4969i	−0.556425	+	0.556425i
$880$	−39.1417	+	5.46844i	−1.31947	+	0.184341i
$881$	30.8194			1.03833			0.519166	−	0.854673i	$-0.326243\pi$
$881$	30.8194			1.03833			0.519166	+	0.854673i	$0.326243\pi$
$882$	−26.9792	+	43.5781i	−0.908438	+	1.46735i
$883$	18.6304	−	7.71698i	0.626964	−	0.259697i	−0.0464982	−	0.998918i	$-0.514806\pi$
$883$	18.6304	−	7.71698i	0.626964	−	0.259697i	0.673463	+	0.739221i	$0.264806\pi$
$884$	−10.4249	+	4.79319i	−0.350627	+	0.161213i
$885$	−8.43136	+	20.3551i	−0.283417	+	0.684230i
$886$	−0.116015	+	0.711446i	−0.00389761	+	0.0239015i
$887$	7.51281	+	7.51281i	0.252255	+	0.252255i	0.821895	−	0.569639i	$-0.192917\pi$
$887$	7.51281	+	7.51281i	0.252255	+	0.252255i	−0.569639	+	0.821895i	$0.692917\pi$
$888$	−7.57555	+	81.8939i	−0.254219	+	2.74818i
$889$		−	0.533732i		−	0.0179008i
$890$	17.9270	+	24.9129i	0.600915	+	0.835082i
$891$	−3.03833	−	7.33517i	−0.101788	−	0.245738i
$892$	12.3242	−	36.7832i	0.412645	−	1.23159i
$893$	−23.2181	−	56.0534i	−0.776963	−	1.87575i
$894$	39.0979	−	63.1527i	1.30763	−	2.11214i
$895$	44.4300	+	44.4300i	1.48513	+	1.48513i
$896$	3.99819	−	0.186324i	0.133570	−	0.00622465i
$897$	14.8171	−	32.8400i	0.494728	−	1.09649i
$898$	29.2570	−	47.2572i	0.976318	−	1.57699i
$899$	62.8048	+	26.0146i	2.09466	+	0.867636i
$900$	40.9418	+	82.2005i	1.36473	+	2.74002i
$901$	−2.93624	+	7.08870i	−0.0978202	+	0.236159i
$902$	−4.81793	+	3.46692i	−0.160420	+	0.115436i
$903$	1.06116			0.0353130
$904$	10.1757	+	12.2502i	0.338438	+	0.407435i
$905$		−	88.1527i		−	2.93029i
$906$	−34.5205	+	24.8405i	−1.14687	+	0.825271i
$907$	−3.34022	+	8.06401i	−0.110910	+	0.267761i	−0.969583	−	0.244763i	$-0.921290\pi$
$907$	−3.34022	+	8.06401i	−0.110910	+	0.267761i	0.858672	+	0.512525i	$0.171290\pi$
$908$	−26.1832	+	1.82017i	−0.868921	+	0.0604046i
$909$	9.42797	+	22.7611i	0.312706	+	0.754939i
$910$	−5.54045	+	3.73059i	−0.183664	+	0.123668i
$911$	−10.4135			−0.345016			−0.172508	−	0.985008i	$-0.555187\pi$
$911$	−10.4135			−0.345016			−0.172508	+	0.985008i	$0.555187\pi$
$912$	−46.1707	−	34.8513i	−1.52887	−	1.15404i
$913$			13.7959i			0.456579i
$914$	14.3942	−	3.38628i	0.476117	−	0.112008i
$915$	−28.3914	+	68.5429i	−0.938590	+	2.26596i
$916$	−26.5719	+	30.5423i	−0.877959	+	1.00914i
$917$	1.84918	+	4.46430i	0.0610651	+	0.147424i
$918$	2.36614	−	14.5100i	0.0780944	−	0.478902i
$919$	26.9299	+	26.9299i	0.888336	+	0.888336i	0.994363	−	0.106027i	$-0.0338131\pi$
$919$	26.9299	+	26.9299i	0.888336	+	0.888336i	−0.106027	+	0.994363i	$0.533813\pi$
$920$	34.7560	−	10.7687i	1.14587	−	0.355034i
$921$	1.14027			0.0375732
$922$	−35.5828	−	5.80248i	−1.17186	−	0.191095i
$923$	29.8806	+	0.930919i	0.983533	+	0.0306416i
$924$	5.14886	+	1.72512i	0.169385	+	0.0567523i
$925$	33.6992	−	81.3570i	1.10802	−	2.67500i
$926$	−23.1781	+	37.4384i	−0.761681	+	1.23030i
$927$	−20.7005			−0.679895
$928$	46.1080	+	1.05314i	1.51357	+	0.0345710i
$929$	30.2570	+	30.2570i	0.992700	+	0.992700i	0.999974	−	0.00727337i	$-0.00231521\pi$
$929$	30.2570	+	30.2570i	0.992700	+	0.992700i	−0.00727337	+	0.999974i	$0.502315\pi$
$930$	122.235	−	28.7562i	4.00825	−	0.942953i
$931$	−13.2291	+	31.9380i	−0.433568	+	1.04673i
$932$	−26.3997	−	8.84519i	−0.864751	−	0.289734i
$933$	−13.2472	+	31.9815i	−0.433693	+	1.04703i
$934$	32.4741	−	23.3680i	1.06259	−	0.764623i
$935$	−11.1167	−	11.1167i	−0.363555	−	0.363555i
$936$	6.61649	−	53.3518i	0.216267	−	1.74386i
$937$	−33.5308	+	33.5308i	−1.09540	+	1.09540i	−0.100463	+	0.994941i	$0.532033\pi$
$937$	−33.5308	+	33.5308i	−1.09540	+	1.09540i	−0.994941	+	0.100463i	$0.967967\pi$
$938$	−1.24531	+	7.63667i	−0.0406608	+	0.249346i
$939$	53.2038	+	22.0378i	1.73624	+	0.719175i
$940$	89.1372	−	6.19653i	2.90734	−	0.202109i
$941$	−37.7314	−	15.6289i	−1.23001	−	0.509486i	−0.329430	−	0.944180i	$-0.606857\pi$
$941$	−37.7314	−	15.6289i	−1.23001	−	0.509486i	−0.900578	+	0.434694i	$0.856857\pi$
$942$	8.08547	+	5.00573i	0.263439	+	0.163095i
$943$	3.86413	−	3.86413i	0.125833	−	0.125833i
$944$	8.01038	+	2.07860i	0.260716	+	0.0676527i
$945$		−	8.55826i		−	0.278400i
$946$	0.901292	+	3.83116i	0.0293035	+	0.124562i
$947$	−9.68070	−	4.00988i	−0.314581	−	0.130304i	0.219806	−	0.975544i	$-0.429457\pi$
$947$	−9.68070	−	4.00988i	−0.314581	−	0.130304i	−0.534387	+	0.845240i	$0.679457\pi$
$948$	−3.68315	+	4.23349i	−0.119623	+	0.137497i
$949$	0.328796	−	10.5537i	0.0106732	−	0.342588i
$950$	36.1775	+	50.2753i	1.17375	+	1.63115i
$951$		−	47.4292i		−	1.53800i
$952$	1.01734	+	1.22475i	0.0329723	+	0.0396943i
$953$	−12.6320	+	12.6320i	−0.409191	+	0.409191i	−0.881456	−	0.472265i	$-0.843436\pi$
$953$	−12.6320	+	12.6320i	−0.409191	+	0.409191i	0.472265	+	0.881456i	$0.343436\pi$
$954$	−20.9978	−	29.1804i	−0.679829	−	0.944749i
$955$	17.0547	−	7.06430i	0.551878	−	0.228595i
$956$	−5.29836	−	1.77521i	−0.171361	−	0.0574144i
$957$	57.8076	+	23.9447i	1.86865	+	0.774022i
$958$	35.5969	+	22.0381i	1.15008	+	0.712019i
$959$	−1.46561			−0.0473271
$960$	70.2690	−	48.1680i	2.26792	−	1.55461i
$961$		−	38.5226i		−	1.24266i
$962$	−42.7619	+	28.7932i	−1.37870	+	0.928331i
$963$	−44.7719	+	18.5451i	−1.44275	+	0.597609i
$964$	−42.9327	−	14.3846i	−1.38277	−	0.463295i
$965$	−37.8462	−	15.6764i	−1.21831	−	0.504641i
$966$	−4.93415	−	0.804611i	−0.158754	−	0.0258879i
$967$	46.2503			1.48731			0.743655	−	0.668563i	$-0.233090\pi$
$967$	46.2503			1.48731			0.743655	+	0.668563i	$0.233090\pi$
$968$	1.01070	−	10.9259i	0.0324850	−	0.351173i
$969$		−	23.0112i		−	0.739227i
$970$	0.302834	−	1.85708i	0.00972342	−	0.0596273i
$971$	−4.79346	−	1.98552i	−0.153830	−	0.0637183i	0.304440	−	0.952531i	$-0.401531\pi$
$971$	−4.79346	−	1.98552i	−0.153830	−	0.0637183i	−0.458270	+	0.888813i	$0.651531\pi$
$972$	−16.6624	−	14.4964i	−0.534448	−	0.464972i
$973$	−1.49639	+	3.61261i	−0.0479722	+	0.115815i
$974$	36.0062	−	8.47059i	1.15371	−	0.271415i
$975$	−37.1458	+	82.3285i	−1.18962	+	2.63662i
$976$	26.9738	+	6.99938i	0.863410	+	0.224045i
$977$	34.5161	−	34.5161i	1.10427	−	1.10427i	0.110378	−	0.993890i	$-0.464794\pi$
$977$	34.5161	−	34.5161i	1.10427	−	1.10427i	0.993890	−	0.110378i	$-0.0352061\pi$
$978$	−10.4158	−	44.2750i	−0.333062	−	1.41576i
$979$	14.4502	−	5.98545i	0.461829	−	0.191296i
$980$	−38.4094	−	33.4163i	−1.22694	−	1.06744i
$981$	−34.2181	+	14.1736i	−1.09250	+	0.452528i
$982$	−1.73654	+	10.6490i	−0.0554151	+	0.339825i
$983$	−2.43091			−0.0775339			−0.0387670	−	0.999248i	$-0.512343\pi$
$983$	−2.43091			−0.0775339			−0.0387670	+	0.999248i	$0.512343\pi$
$984$	5.96442	−	11.3197i	0.190139	−	0.360858i
$985$	−47.0294	+	47.0294i	−1.49848	+	1.49848i
$986$	10.7157	+	14.8914i	0.341257	+	0.474239i
$987$	−11.3422	−	4.69810i	−0.361027	−	0.149542i
$988$	−1.38700	−	36.2337i	−0.0441264	−	1.15275i
$989$	−1.38664	−	3.34765i	−0.0440926	−	0.106449i
$990$	71.7037	−	16.8685i	2.27889	−	0.536118i
$991$			18.5002i			0.587680i	0.955855	+	0.293840i	$0.0949332\pi$
$991$			18.5002i			0.587680i	−0.955855	+	0.293840i	$0.905067\pi$
$992$	−17.0502	−	43.9774i	−0.541346	−	1.39628i
$993$	22.6135	+	22.6135i	0.717619	+	0.717619i
$994$	−0.949975	−	4.03809i	−0.0301314	−	0.128081i
$995$	−25.0159	+	60.3936i	−0.793056	+	1.91461i
$996$	−13.2584	−	26.6194i	−0.420108	−	0.843469i
$997$	−9.97366	−	4.13123i	−0.315869	−	0.130837i	0.219116	−	0.975699i	$-0.429683\pi$
$997$	−9.97366	−	4.13123i	−0.315869	−	0.130837i	−0.534985	+	0.844862i	$0.679683\pi$
$998$	3.09683	−	18.9909i	0.0980286	−	0.601145i
$999$		−	66.0539i		−	2.08985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bd.a.411.4	yes	216
13.5	odd	4		416.2.bi.a.187.32	yes	216
32.19	odd	8		416.2.bi.a.307.32	yes	216
416.83	even	8	inner	416.2.bd.a.83.4	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bd.a.83.4	✓	216	416.83	even	8	inner
416.2.bd.a.411.4	yes	216	1.1	even	1	trivial
416.2.bi.a.187.32	yes	216	13.5	odd	4
416.2.bi.a.307.32	yes	216	32.19	odd	8

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+(-1.37663 + 0.323857i) q^{2} +(-2.65712 + 1.10062i) q^{3} +(1.79023 - 0.891665i) q^{4} +(-1.41696 - 3.42085i) q^{5} +(3.30144 - 2.37567i) q^{6} -0.353777i q^{7} +(-2.17572 + 1.80728i) q^{8} +(3.72762 - 3.72762i) q^{9} +(3.05851 + 4.25036i) q^{10} +(2.46532 - 1.02117i) q^{11} +(-3.77548 + 4.33962i) q^{12} +(-3.60380 - 0.112275i) q^{13} +(0.114573 + 0.487021i) q^{14} +(7.53009 + 7.53009i) q^{15} +(2.40987 - 3.19258i) q^{16} +1.59116 q^{17} +(-3.92434 + 6.33878i) q^{18} +(-1.92428 + 4.64563i) q^{19} +(-5.58695 - 4.86066i) q^{20} +(0.389372 + 0.940028i) q^{21} +(-3.06313 + 2.20419i) q^{22} +(2.45672 - 2.45672i) q^{23} +(3.79204 - 7.19678i) q^{24} +(-6.15891 + 6.15891i) q^{25} +(4.99747 - 1.01256i) q^{26} +(-2.50021 + 6.03605i) q^{27} +(-0.315451 - 0.633343i) q^{28} +(-3.12000 - 7.53235i) q^{29} +(-12.8048 - 7.92748i) q^{30} +(-5.89587 + 5.89587i) q^{31} +(-2.28356 + 5.17546i) q^{32} +(-5.42675 + 5.42675i) q^{33} +(-2.19044 + 0.515309i) q^{34} +(-1.21022 + 0.501289i) q^{35} +(3.34952 - 9.99709i) q^{36} +(-9.34063 + 3.86902i) q^{37} +(1.14451 - 7.01852i) q^{38} +(9.69931 - 3.66807i) q^{39} +(9.26533 + 4.88197i) q^{40} +1.57288 q^{41} +(-0.840458 - 1.16797i) q^{42} +(0.399110 - 0.963538i) q^{43} +(3.50296 - 4.02637i) q^{44} +(-18.0335 - 7.46973i) q^{45} +(-2.58638 + 4.17763i) q^{46} +(-8.53183 + 8.53183i) q^{47} +(-2.88951 + 11.1354i) q^{48} +6.87484 q^{49} +(6.48394 - 10.4732i) q^{50} +(-4.22791 + 1.75126i) q^{51} +(-6.55176 + 3.01239i) q^{52} +(-1.84534 + 4.45505i) q^{53} +(1.48705 - 9.11913i) q^{54} +(-6.98654 - 6.98654i) q^{55} +(0.639372 + 0.769719i) q^{56} -14.4619i q^{57} +(6.73450 + 9.35884i) q^{58} +(0.791741 + 1.91143i) q^{59} +(20.1949 + 6.76629i) q^{60} +(2.66607 + 6.43647i) q^{61} +(6.20702 - 10.0259i) q^{62} +(-1.31875 - 1.31875i) q^{63} +(1.46751 - 7.86425i) q^{64} +(4.72238 + 12.4872i) q^{65} +(5.71314 - 9.22813i) q^{66} +(14.2881 + 5.91831i) q^{67} +(2.84855 - 1.41878i) q^{68} +(-3.82390 + 9.23172i) q^{69} +(1.50368 - 1.08203i) q^{70} -8.29142 q^{71} +(-1.37342 + 14.8471i) q^{72} +2.92849i q^{73} +(11.6056 - 8.35125i) q^{74} +(9.58637 - 23.1436i) q^{75} +(0.697433 + 10.0326i) q^{76} +(-0.361266 - 0.872174i) q^{77} +(-12.1645 + 8.19078i) q^{78} +0.975544 q^{79} +(-14.3360 - 3.72003i) q^{80} -2.97534i q^{81} +(-2.16528 + 0.509389i) q^{82} +(-1.97848 + 4.77649i) q^{83} +(1.53526 + 1.33568i) q^{84} +(-2.25462 - 5.44313i) q^{85} +(-0.237379 + 1.45569i) q^{86} +(16.5804 + 16.5804i) q^{87} +(-3.51832 + 6.67730i) q^{88} +5.86136 q^{89} +(27.2447 + 4.44278i) q^{90} +(-0.0397203 + 1.27494i) q^{91} +(2.20753 - 6.58868i) q^{92} +(9.17695 - 22.1551i) q^{93} +(8.98209 - 14.5083i) q^{94} +18.6187 q^{95} +(0.371507 - 16.2651i) q^{96} +(-0.254086 - 0.254086i) q^{97} +(-9.46413 + 2.22647i) q^{98} +(5.38325 - 12.9963i) 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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