LMFDB - Embedded newform 416.2.bg.a.77.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,2,Mod(77,416)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("416.77"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			77.5
Character	$\chi$	$=$	416.77
Dual form			416.2.bg.a.389.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37997 - 0.309324i) q^{2} +(-0.935921 + 2.25951i) q^{3} +(1.80864 + 0.853715i) q^{4} +(-1.28599 - 3.10465i) q^{5} +(1.99046 - 2.82856i) q^{6} +(2.22807 + 2.22807i) q^{7} +(-2.23179 - 1.73756i) q^{8} +(-2.10813 - 2.10813i) q^{9} +(0.814283 + 4.68210i) q^{10} +(-4.66495 + 1.93228i) q^{11} +(-3.62172 + 3.28763i) q^{12} +(-1.78296 - 3.13385i) q^{13} +(-2.38548 - 3.76387i) q^{14} +8.21857 q^{15} +(2.54234 + 3.08812i) q^{16} -0.634552i q^{17} +(2.25707 + 3.56126i) q^{18} +(-1.76091 + 4.25122i) q^{19} +(0.324600 - 6.71304i) q^{20} +(-7.11965 + 2.94906i) q^{21} +(7.03519 - 1.22352i) q^{22} +(-3.31921 - 3.31921i) q^{23} +(6.01481 - 3.41655i) q^{24} +(-4.44953 + 4.44953i) q^{25} +(1.49106 + 4.87614i) q^{26} +(-0.0421381 + 0.0174542i) q^{27} +(2.12763 + 5.93191i) q^{28} +(1.65485 - 3.99517i) q^{29} +(-11.3414 - 2.54220i) q^{30} -7.09331i q^{31} +(-2.55313 - 5.04792i) q^{32} -12.3490i q^{33} +(-0.196282 + 0.875664i) q^{34} +(4.05210 - 9.78263i) q^{35} +(-2.01310 - 5.61259i) q^{36} +(-2.73286 - 6.59771i) q^{37} +(3.74501 - 5.32187i) q^{38} +(8.74970 - 1.09559i) q^{39} +(-2.52444 + 9.16340i) q^{40} +(-1.44734 + 1.44734i) q^{41} +(10.7371 - 1.86733i) q^{42} +(-3.79133 - 9.15307i) q^{43} +(-10.0868 - 0.487734i) q^{44} +(-3.83398 + 9.25604i) q^{45} +(3.55370 + 5.60712i) q^{46} -11.0654 q^{47} +(-9.35709 + 2.85421i) q^{48} +2.92859i q^{49} +(7.51656 - 4.76387i) q^{50} +(1.43378 + 0.593891i) q^{51} +(-0.549316 - 7.19015i) q^{52} +(4.94432 + 11.9366i) q^{53} +(0.0635484 - 0.0110519i) q^{54} +(11.9981 + 11.9981i) q^{55} +(-1.10119 - 8.84399i) q^{56} +(-7.95762 - 7.95762i) q^{57} +(-3.51945 + 5.00133i) q^{58} +(0.361544 + 0.872845i) q^{59} +(14.8644 + 7.01632i) q^{60} +(-0.529611 + 1.27860i) q^{61} +(-2.19413 + 9.78856i) q^{62} -9.39414i q^{63} +(1.96180 + 7.75573i) q^{64} +(-7.43664 + 9.56556i) q^{65} +(-3.81983 + 17.0412i) q^{66} +(-5.00766 - 2.07424i) q^{67} +(0.541727 - 1.14768i) q^{68} +(10.6063 - 4.39328i) q^{69} +(-8.61778 + 12.2463i) q^{70} +(8.90211 + 8.90211i) q^{71} +(1.04192 + 8.36792i) q^{72} +(-1.20136 + 1.20136i) q^{73} +(1.73044 + 9.94999i) q^{74} +(-5.88936 - 14.2182i) q^{75} +(-6.81419 + 6.18560i) q^{76} +(-14.6991 - 6.08857i) q^{77} +(-12.4132 - 1.19461i) q^{78} -5.84275i q^{79} +(6.31811 - 11.8643i) q^{80} -9.05560i q^{81} +(2.44499 - 1.54959i) q^{82} +(0.507311 - 1.22476i) q^{83} +(-15.3945 - 0.744380i) q^{84} +(-1.97006 + 0.816026i) q^{85} +(2.40066 + 13.8037i) q^{86} +(7.47832 + 7.47832i) q^{87} +(13.7686 + 3.79315i) q^{88} +(4.13029 + 4.13029i) q^{89} +(8.15388 - 11.5871i) q^{90} +(3.00988 - 10.9550i) q^{91} +(-3.16959 - 8.83691i) q^{92} +(16.0274 + 6.63878i) q^{93} +(15.2699 + 3.42279i) q^{94} +15.4630 q^{95} +(13.7954 - 1.04436i) q^{96} +4.83815i q^{97} +(0.905884 - 4.04137i) q^{98} +(13.9078 + 5.76082i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38}+ \cdots + 112 q^{95}+O(q^{100}) $ 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Character values

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

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.37997	−	0.309324i	−0.975787	−	0.218725i
$2$	−1.37997	−	0.309324i	−0.975787	−	0.218725i
$3$	−0.935921	+	2.25951i	−0.540354	+	1.30453i	0.384119	+	0.923284i	$0.374505\pi$
$3$	−0.935921	+	2.25951i	−0.540354	+	1.30453i	−0.924473	+	0.381247i	$0.875495\pi$
$4$	1.80864	+	0.853715i	0.904319	+	0.426858i
$5$	−1.28599	−	3.10465i	−0.575110	−	1.38844i	−0.897155	−	0.441715i	$-0.854370\pi$
$5$	−1.28599	−	3.10465i	−0.575110	−	1.38844i	0.322045	−	0.946724i	$-0.395630\pi$
$6$	1.99046	−	2.82856i	0.812604	−	1.15475i
$7$	2.22807	+	2.22807i	0.842131	+	0.842131i	0.989136	−	0.147004i	$-0.0469632\pi$
$7$	2.22807	+	2.22807i	0.842131	+	0.842131i	−0.147004	+	0.989136i	$0.546963\pi$
$8$	−2.23179	−	1.73756i	−0.789058	−	0.614319i
$9$	−2.10813	−	2.10813i	−0.702711	−	0.702711i
$10$	0.814283	+	4.68210i	0.257499	+	1.48061i
$11$	−4.66495	+	1.93228i	−1.40653	+	0.582606i	−0.951439	−	0.307837i	$-0.900395\pi$
$11$	−4.66495	+	1.93228i	−1.40653	+	0.582606i	−0.455096	+	0.890443i	$0.650395\pi$
$12$	−3.62172	+	3.28763i	−1.04550	+	0.949058i
$13$	−1.78296	−	3.13385i	−0.494505	−	0.869175i
$13$	−1.78296	−	3.13385i	−0.494505	−	0.869175i
$14$	−2.38548	−	3.76387i	−0.637545	−	1.00594i
$15$	8.21857			2.12203
$16$	2.54234	+	3.08812i	0.635585	+	0.772031i
$17$		−	0.634552i		−	0.153902i	−0.997035	−	0.0769508i	$-0.975482\pi$
$17$		−	0.634552i		−	0.153902i	0.997035	−	0.0769508i	$-0.0245184\pi$
$18$	2.25707	+	3.56126i	0.531996	+	0.839396i
$19$	−1.76091	+	4.25122i	−0.403981	+	0.975297i	0.582708	+	0.812681i	$0.301993\pi$
$19$	−1.76091	+	4.25122i	−0.403981	+	0.975297i	−0.986689	+	0.162616i	$0.948007\pi$
$20$	0.324600	−	6.71304i	0.0725827	−	1.50108i
$21$	−7.11965	+	2.94906i	−1.55364	+	0.643537i
$22$	7.03519	−	1.22352i	1.49991	−	0.260855i
$23$	−3.31921	−	3.31921i	−0.692103	−	0.692103i	0.270591	−	0.962694i	$-0.412781\pi$
$23$	−3.31921	−	3.31921i	−0.692103	−	0.692103i	−0.962694	+	0.270591i	$0.912781\pi$
$24$	6.01481	−	3.41655i	1.22777	−	0.697400i
$25$	−4.44953	+	4.44953i	−0.889905	+	0.889905i
$26$	1.49106	+	4.87614i	0.292421	+	0.956290i
$27$	−0.0421381	+	0.0174542i	−0.00810949	+	0.00335906i
$28$	2.12763	+	5.93191i	0.402085	+	1.12103i
$29$	1.65485	−	3.99517i	0.307298	−	0.741884i	−0.692492	−	0.721425i	$-0.743487\pi$
$29$	1.65485	−	3.99517i	0.307298	−	0.741884i	0.999791	−	0.0204587i	$-0.00651267\pi$
$30$	−11.3414	−	2.54220i	−2.07064	−	0.464140i
$31$		−	7.09331i		−	1.27400i	−0.770866	−	0.636998i	$-0.780176\pi$
$31$		−	7.09331i		−	1.27400i	0.770866	−	0.636998i	$-0.219824\pi$
$32$	−2.55313	−	5.04792i	−0.451333	−	0.892355i
$33$		−	12.3490i		−	2.14968i
$34$	−0.196282	+	0.875664i	−0.0336621	+	0.150175i
$35$	4.05210	−	9.78263i	0.684930	−	1.65357i
$36$	−2.01310	−	5.61259i	−0.335517	−	0.935432i
$37$	−2.73286	−	6.59771i	−0.449280	−	1.08466i	−0.972592	−	0.232517i	$-0.925304\pi$
$37$	−2.73286	−	6.59771i	−0.449280	−	1.08466i	0.523313	−	0.852141i	$-0.324696\pi$
$38$	3.74501	−	5.32187i	0.607521	−	0.863321i
$39$	8.74970	−	1.09559i	1.40107	−	0.175435i
$40$	−2.52444	+	9.16340i	−0.399149	+	1.44886i
$41$	−1.44734	+	1.44734i	−0.226037	+	0.226037i	−0.811035	−	0.584998i	$-0.801095\pi$
$41$	−1.44734	+	1.44734i	−0.226037	+	0.226037i	0.584998	+	0.811035i	$0.301095\pi$
$42$	10.7371	−	1.86733i	1.65677	−	0.288136i
$43$	−3.79133	−	9.15307i	−0.578172	−	1.39583i	−0.894452	−	0.447165i	$-0.852434\pi$
$43$	−3.79133	−	9.15307i	−0.578172	−	1.39583i	0.316280	−	0.948666i	$-0.397566\pi$
$44$	−10.0868	−	0.487734i	−1.52065	−	0.0735286i
$45$	−3.83398	+	9.25604i	−0.571535	+	1.37981i
$46$	3.55370	+	5.60712i	0.523965	+	0.826725i
$47$	−11.0654			−1.61405			−0.807027	−	0.590514i	$-0.798925\pi$
$47$	−11.0654			−1.61405			−0.807027	+	0.590514i	$0.798925\pi$
$48$	−9.35709	+	2.85421i	−1.35058	+	0.411970i
$49$			2.92859i			0.418371i
$50$	7.51656	−	4.76387i	1.06300	−	0.673713i
$51$	1.43378	+	0.593891i	0.200769	+	0.0831614i
$52$	−0.549316	−	7.19015i	−0.0761765	−	0.997094i
$53$	4.94432	+	11.9366i	0.679154	+	1.63962i	0.765561	+	0.643363i	$0.222461\pi$
$53$	4.94432	+	11.9366i	0.679154	+	1.63962i	−0.0864069	+	0.996260i	$0.527539\pi$
$54$	0.0635484	−	0.0110519i	0.00864784	−	0.00150398i
$55$	11.9981	+	11.9981i	1.61783	+	1.61783i
$56$	−1.10119	−	8.84399i	−0.147153	−	1.18183i
$57$	−7.95762	−	7.95762i	−1.05401	−	1.05401i
$58$	−3.51945	+	5.00133i	−0.462126	+	0.656707i
$59$	0.361544	+	0.872845i	0.0470691	+	0.113635i	0.945665	−	0.325142i	$-0.105412\pi$
$59$	0.361544	+	0.872845i	0.0470691	+	0.113635i	−0.898596	+	0.438776i	$0.855412\pi$
$60$	14.8644	+	7.01632i	1.91899	+	0.905803i
$61$	−0.529611	+	1.27860i	−0.0678098	+	0.163707i	−0.954151	−	0.299325i	$-0.903239\pi$
$61$	−0.529611	+	1.27860i	−0.0678098	+	0.163707i	0.886341	+	0.463032i	$0.153239\pi$
$62$	−2.19413	+	9.78856i	−0.278655	+	1.24315i
$63$		−	9.39414i		−	1.18355i
$64$	1.96180	+	7.75573i	0.245225	+	0.969466i
$65$	−7.43664	+	9.56556i	−0.922401	+	1.18646i
$66$	−3.81983	+	17.0412i	−0.470189	+	2.09763i
$67$	−5.00766	−	2.07424i	−0.611783	−	0.253409i	0.0552079	−	0.998475i	$-0.482418\pi$
$67$	−5.00766	−	2.07424i	−0.611783	−	0.253409i	−0.666991	+	0.745066i	$0.732418\pi$
$68$	0.541727	−	1.14768i	0.0656941	−	0.139176i
$69$	10.6063	−	4.39328i	1.27685	−	0.528889i
$70$	−8.61778	+	12.2463i	−1.03002	+	1.46372i
$71$	8.90211	+	8.90211i	1.05649	+	1.05649i	0.998306	+	0.0581803i	$0.0185298\pi$
$71$	8.90211	+	8.90211i	1.05649	+	1.05649i	0.0581803	+	0.998306i	$0.481470\pi$
$72$	1.04192	+	8.36792i	0.122791	+	0.986168i
$73$	−1.20136	+	1.20136i	−0.140608	+	0.140608i	−0.773907	−	0.633299i	$-0.781700\pi$
$73$	−1.20136	+	1.20136i	−0.140608	+	0.140608i	0.633299	+	0.773907i	$0.281700\pi$
$74$	1.73044	+	9.94999i	0.201160	+	1.15666i
$75$	−5.88936	−	14.2182i	−0.680045	−	1.64177i
$76$	−6.81419	+	6.18560i	−0.781641	+	0.709537i
$77$	−14.6991	−	6.08857i	−1.67512	−	0.693856i
$78$	−12.4132	−	1.19461i	−1.40552	−	0.135263i
$79$		−	5.84275i		−	0.657361i	−0.944441	−	0.328680i	$-0.893396\pi$
$79$		−	5.84275i		−	0.657361i	0.944441	−	0.328680i	$-0.106604\pi$
$80$	6.31811	−	11.8643i	0.706386	−	1.32647i
$81$		−	9.05560i		−	1.00618i
$82$	2.44499	−	1.54959i	0.270003	−	0.171124i
$83$	0.507311	−	1.22476i	0.0556846	−	0.134435i	−0.893589	−	0.448887i	$-0.851821\pi$
$83$	0.507311	−	1.22476i	0.0556846	−	0.134435i	0.949273	+	0.314452i	$0.101821\pi$
$84$	−15.3945	−	0.744380i	−1.67968	−	0.0812185i
$85$	−1.97006	+	0.816026i	−0.213683	+	0.0885104i
$86$	2.40066	+	13.8037i	0.258870	+	1.48849i
$87$	7.47832	+	7.47832i	0.801761	+	0.801761i
$88$	13.7686	+	3.79315i	1.46774	+	0.404351i
$89$	4.13029	+	4.13029i	0.437810	+	0.437810i	0.891274	−	0.453464i	$-0.149812\pi$
$89$	4.13029	+	4.13029i	0.437810	+	0.437810i	−0.453464	+	0.891274i	$0.649812\pi$
$90$	8.15388	−	11.5871i	0.859495	−	1.22139i
$91$	3.00988	−	10.9550i	0.315521	−	1.14840i
$92$	−3.16959	−	8.83691i	−0.330452	−	0.921311i
$93$	16.0274	+	6.63878i	1.66197	+	0.688409i
$94$	15.2699	+	3.42279i	1.57497	+	0.353034i
$95$	15.4630			1.58647
$96$	13.7954	−	1.04436i	1.40799	−	0.106590i
$97$			4.83815i			0.491240i	0.969366	+	0.245620i	$0.0789916\pi$
$97$			4.83815i			0.491240i	−0.969366	+	0.245620i	$0.921008\pi$
$98$	0.905884	−	4.04137i	0.0915081	−	0.408240i
$99$	13.9078	+	5.76082i	1.39779	+	0.578984i
$100$	−11.8462	+	4.24895i	−1.18462	+	0.424895i
$101$	−4.45254	+	1.84430i	−0.443045	+	0.183515i	−0.593042	−	0.805171i	$-0.702073\pi$
$101$	−4.45254	+	1.84430i	−0.443045	+	0.183515i	0.149998	+	0.988686i	$0.452073\pi$
$102$	−1.79487	−	1.26305i	−0.177719	−	0.125061i
$103$	−8.82815	+	8.82815i	−0.869864	+	0.869864i	−0.992457	−	0.122593i	$-0.960879\pi$
$103$	−8.82815	+	8.82815i	−0.869864	+	0.869864i	0.122593	+	0.992457i	$0.460879\pi$
$104$	−1.46604	+	10.0921i	−0.143757	+	0.989613i
$105$	18.3116	+	18.3116i	1.78702	+	1.78702i
$106$	−3.13073	−	18.0016i	−0.304083	−	1.74847i
$107$	−4.53931	−	10.9589i	−0.438832	−	1.05943i	−0.976353	−	0.216183i	$-0.930639\pi$
$107$	−4.53931	−	10.9589i	−0.438832	−	1.05943i	0.537521	−	0.843250i	$-0.319361\pi$
$108$	−0.0911135	−	0.00440566i	−0.00876740	−	0.000423935i
$109$	−5.65351	+	13.6488i	−0.541508	+	1.30732i	0.382151	+	0.924100i	$0.375183\pi$
$109$	−5.65351	+	13.6488i	−0.541508	+	1.30732i	−0.923659	+	0.383216i	$0.874817\pi$
$110$	−12.8457	−	20.2683i	−1.22479	−	1.93251i
$111$	17.4654			1.65774
$112$	−1.21604	+	12.5451i	−0.114905	+	1.18540i
$113$			6.46983i			0.608630i	0.952571	+	0.304315i	$0.0984276\pi$
$113$			6.46983i			0.608630i	−0.952571	+	0.304315i	$0.901572\pi$
$114$	8.51980	+	13.4428i	0.797952	+	1.25903i
$115$	−6.03651	+	14.5734i	−0.562907	+	1.35898i
$116$	6.40376	−	5.81304i	0.594575	−	0.539727i
$117$	−2.84786	+	10.3653i	−0.263285	+	0.958273i
$118$	−0.228929	−	1.31634i	−0.0210746	−	0.121178i
$119$	1.41383	−	1.41383i	0.129605	−	0.129605i
$120$	−18.3421	−	14.2802i	−1.67440	−	1.30360i
$121$	10.2498	−	10.2498i	0.931804	−	0.931804i
$122$	1.12635	−	1.60060i	0.101975	−	0.144912i
$123$	−1.91569	−	4.62489i	−0.172732	−	0.417012i
$124$	6.05566	−	12.8292i	0.543815	−	1.15210i
$125$	4.01301	+	1.66224i	0.358934	+	0.148675i
$126$	−2.90583	+	12.9636i	−0.258872	+	1.15489i
$127$	−15.9128			−1.41203			−0.706016	−	0.708196i	$-0.749509\pi$
$127$	−15.9128			−1.41203			−0.706016	+	0.708196i	$0.749509\pi$
$128$	−0.308191	−	11.3095i	−0.0272405	−	0.999629i
$129$	24.2299			2.13332
$130$	13.2212	−	10.8999i	1.15958	−	0.955981i
$131$	−4.04676	+	9.76974i	−0.353567	+	0.853586i	0.642607	+	0.766196i	$0.277853\pi$
$131$	−4.04676	+	9.76974i	−0.353567	+	0.853586i	−0.996174	+	0.0873902i	$0.972147\pi$
$132$	10.5425	−	22.3348i	0.917608	−	1.94400i
$133$	−13.3955	+	5.54858i	−1.16153	+	0.481123i
$134$	6.26881	+	4.41138i	0.541543	+	0.381085i
$135$	0.108378	+	0.108378i	0.00932770	+	0.00932770i
$136$	−1.10257	+	1.41619i	−0.0945446	+	0.121437i
$137$	2.69678	−	2.69678i	0.230402	−	0.230402i	−0.582459	−	0.812860i	$-0.697909\pi$
$137$	2.69678	−	2.69678i	0.230402	−	0.230402i	0.812860	+	0.582459i	$0.197909\pi$
$138$	−15.9954	+	2.78181i	−1.36161	+	0.236804i
$139$	2.35390	+	5.68281i	0.199655	+	0.482009i	0.991719	−	0.128429i	$-0.0409934\pi$
$139$	2.35390	+	5.68281i	0.199655	+	0.482009i	−0.792064	+	0.610438i	$0.790993\pi$
$140$	15.6804	−	14.2339i	1.32523	−	1.20298i
$141$	10.3563	−	25.0024i	0.872161	−	2.10558i
$142$	−9.53102	−	15.0383i	−0.799825	−	1.26199i
$143$	14.3729	+	11.1741i	1.20192	+	0.934423i
$144$	1.15058	−	11.8698i	0.0958818	−	0.989147i
$145$	−14.5317			−1.20679
$146$	2.02945	−	1.28623i	0.167958	−	0.106449i
$147$	−6.61720	−	2.74093i	−0.545777	−	0.226068i
$148$	0.689810	−	14.2660i	0.0567020	−	1.17265i
$149$	3.75721	−	1.55629i	0.307803	−	0.127496i	−0.223435	−	0.974719i	$-0.571727\pi$
$149$	3.75721	−	1.55629i	0.307803	−	0.127496i	0.531238	+	0.847223i	$0.321727\pi$
$150$	3.72913	+	21.4424i	0.304482	+	1.75076i
$151$	−0.0811525	+	0.0811525i	−0.00660410	+	0.00660410i	−0.710401	−	0.703797i	$-0.751486\pi$
$151$	−0.0811525	+	0.0811525i	−0.00660410	+	0.00660410i	0.703797	+	0.710401i	$0.251486\pi$
$152$	11.3167	−	6.42816i	0.917908	−	0.521393i
$153$	−1.33772	+	1.33772i	−0.108148	+	0.108148i
$154$	18.4010	+	12.9488i	1.48279	+	1.04345i
$155$	−22.0222	+	9.12190i	−1.76887	+	0.732688i
$156$	16.7604	+	5.48823i	1.34190	+	0.439410i
$157$	6.07218	−	14.6595i	0.484612	−	1.16996i	−0.472783	−	0.881179i	$-0.656751\pi$
$157$	6.07218	−	14.6595i	0.484612	−	1.16996i	0.957396	−	0.288779i	$-0.0932493\pi$
$158$	−1.80730	+	8.06282i	−0.143781	+	0.641444i
$159$	−31.5985			−2.50592
$160$	−12.3887	+	14.4181i	−0.979415	+	1.13985i
$161$		−	14.7909i		−	1.16568i
$162$	−2.80111	+	12.4965i	−0.220076	+	0.981815i
$163$	8.72373	+	3.61349i	0.683295	+	0.283030i	0.697204	−	0.716873i	$-0.254427\pi$
$163$	8.72373	+	3.61349i	0.683295	+	0.283030i	−0.0139084	+	0.999903i	$0.504427\pi$
$164$	−3.85333	+	1.38210i	−0.300895	+	0.107924i
$165$	−38.3392	+	15.8806i	−2.98470	+	1.23630i
$166$	−1.07892	+	1.53321i	−0.0837405	+	0.119000i
$167$	−5.03583	−	5.03583i	−0.389684	−	0.389684i	0.484891	−	0.874575i	$-0.338859\pi$
$167$	−5.03583	−	5.03583i	−0.389684	−	0.389684i	−0.874575	+	0.484891i	$0.838859\pi$
$168$	21.0137	+	5.78911i	1.62125	+	0.446640i
$169$	−6.64208	+	11.1751i	−0.510929	+	0.859623i
$170$	2.97104	−	0.516705i	0.227868	−	0.0396295i
$171$	12.6744	−	5.24990i	0.969234	−	0.401470i
$172$	0.956980	−	19.7913i	0.0729690	−	1.50907i
$173$	5.43618	+	2.25174i	0.413305	+	0.171197i	0.579640	−	0.814873i	$-0.303193\pi$
$173$	5.43618	+	2.25174i	0.413305	+	0.171197i	−0.166335	+	0.986069i	$0.553193\pi$
$174$	−8.00665	−	12.6331i	−0.606982	−	0.957712i
$175$	−19.8277			−1.49883
$176$	−17.8270	−	9.49341i	−1.34376	−	0.715592i
$177$	−2.31058			−0.173674
$178$	−4.42208	−	6.97728i	−0.331449	−	0.522969i
$179$	10.3880	+	4.30286i	0.776438	+	0.321611i	0.735477	−	0.677550i	$-0.236958\pi$
$179$	10.3880	+	4.30286i	0.776438	+	0.321611i	0.0409609	+	0.999161i	$0.486958\pi$
$180$	−14.8363	+	13.4677i	−1.10583	+	1.00382i
$181$	−0.791590	−	1.91107i	−0.0588384	−	0.142049i	0.891726	−	0.452575i	$-0.149495\pi$
$181$	−0.791590	−	1.91107i	−0.0588384	−	0.142049i	−0.950565	+	0.310527i	$0.899495\pi$
$182$	−7.54219	+	14.1866i	−0.559064	+	1.05158i
$183$	−2.39333	−	2.39333i	−0.176920	−	0.176920i
$184$	1.64047	+	13.1751i	0.120937	+	0.971281i
$185$	−16.9691	+	16.9691i	−1.24760	+	1.24760i
$186$	−20.0638	−	14.1190i	−1.47115	−	1.03525i
$187$	1.22614	+	2.96015i	0.0896639	+	0.216468i
$188$	−20.0133	−	9.44670i	−1.45962	−	0.688971i
$189$	−0.132776	−	0.0549976i	−0.00965803	−	0.00400049i
$190$	−21.3385	−	4.78309i	−1.54806	−	0.347002i
$191$	14.3791			1.04044			0.520218	−	0.854034i	$-0.325851\pi$
$191$	14.3791			1.04044			0.520218	+	0.854034i	$0.325851\pi$
$192$	−19.3603	−	2.82605i	−1.39721	−	0.203952i
$193$			6.50987i			0.468591i	0.972165	+	0.234295i	$0.0752783\pi$
$193$			6.50987i			0.468591i	−0.972165	+	0.234295i	$0.924722\pi$
$194$	1.49656	−	6.67651i	0.107446	−	0.479346i
$195$	−14.6534	−	25.7558i	−1.04935	−	1.84441i
$196$	−2.50019	+	5.29677i	−0.178585	+	0.378340i
$197$	4.46714	+	10.7846i	0.318270	+	0.768372i	0.999346	+	0.0361594i	$0.0115124\pi$
$197$	4.46714	+	10.7846i	0.318270	+	0.768372i	−0.681076	+	0.732213i	$0.738488\pi$
$198$	−17.4105	−	12.2518i	−1.23731	−	0.870697i
$199$	−16.0116	+	16.0116i	−1.13503	+	1.13503i	−0.145700	+	0.989329i	$0.546544\pi$
$199$	−16.0116	+	16.0116i	−1.13503	+	1.13503i	−0.989329	+	0.145700i	$0.953456\pi$
$200$	17.6617	−	2.19912i	1.24887	−	0.155501i
$201$	9.37354	−	9.37354i	0.661159	−	0.661159i
$202$	6.71487	−	1.16781i	0.472456	−	0.0821667i
$203$	12.5886	−	5.21439i	0.883550	−	0.365978i
$204$	2.08617	+	2.29817i	0.146061	+	0.160904i
$205$	6.35474	+	2.63222i	0.443834	+	0.183842i
$206$	14.9134	−	9.45184i	1.03906	−	0.658541i
$207$			13.9947i			0.972697i
$208$	5.14483	−	13.4733i	0.356729	−	0.934208i
$209$		−	23.2343i		−	1.60715i
$210$	−19.6052	−	30.9336i	−1.35289	−	2.13462i
$211$	−3.98050	−	1.64878i	−0.274029	−	0.113507i	0.241437	−	0.970416i	$-0.422381\pi$
$211$	−3.98050	−	1.64878i	−0.274029	−	0.113507i	−0.515466	+	0.856910i	$0.672381\pi$
$212$	−1.24801	+	25.8101i	−0.0857136	+	1.77264i
$213$	−28.4461	+	11.7828i	−1.94910	+	0.807342i
$214$	2.87428	+	16.5270i	0.196482	+	1.12976i
$215$	−23.5414	+	23.5414i	−1.60551	+	1.60551i
$216$	0.124371	+	0.0342633i	0.00846239	+	0.00233132i
$217$	15.8044	−	15.8044i	1.07287	−	1.07287i
$218$	12.0236	−	17.0861i	0.814339	−	1.15722i
$219$	−1.59011	−	3.83886i	−0.107450	−	0.259406i
$220$	11.4573	+	31.9432i	0.772449	+	2.15361i
$221$	−1.98859	+	1.13138i	−0.133767	+	0.0761051i
$222$	−24.1017	−	5.40245i	−1.61760	−	0.362589i
$223$		−	12.3619i		−	0.827814i	−0.910319	−	0.413907i	$-0.864164\pi$
$223$		−	12.3619i		−	0.827814i	0.910319	−	0.413907i	$-0.135836\pi$
$224$	5.55859	−	16.9357i	0.371399	−	1.13156i
$225$	18.7604			1.25069
$226$	2.00127	−	8.92817i	0.133123	−	0.593893i
$227$	10.3564	+	4.28974i	0.687375	+	0.284720i	0.698906	−	0.715213i	$-0.253670\pi$
$227$	10.3564	+	4.28974i	0.687375	+	0.284720i	−0.0115309	+	0.999934i	$0.503670\pi$
$228$	−7.59891	−	21.1860i	−0.503250	−	1.40308i
$229$	1.27104	+	3.06855i	0.0839924	+	0.202776i	0.960296	−	0.278984i	$-0.0899977\pi$
$229$	1.27104	+	3.06855i	0.0839924	+	0.202776i	−0.876303	+	0.481760i	$0.839998\pi$
$230$	12.8381	−	18.2437i	0.846520	−	1.20295i
$231$	27.5144	−	27.5144i	1.81031	−	1.81031i
$232$	−10.6351	+	6.04099i	−0.698230	+	0.396610i
$233$	−14.4454	−	14.4454i	−0.946352	−	0.946352i	0.0522801	−	0.998632i	$-0.483351\pi$
$233$	−14.4454	−	14.4454i	−0.946352	−	0.946352i	−0.998632	+	0.0522801i	$0.983351\pi$
$234$	7.13619	−	13.4229i	0.466508	−	0.877483i
$235$	14.2299	+	34.3541i	0.928259	+	2.24102i
$236$	−0.0912585	+	1.88732i	−0.00594042	+	0.122854i
$237$	13.2018	+	5.46835i	0.857547	+	0.355208i
$238$	−2.38837	+	1.51371i	−0.154815	+	0.0981192i
$239$	22.7262			1.47004			0.735018	−	0.678048i	$-0.237174\pi$
$239$	22.7262			1.47004			0.735018	+	0.678048i	$0.237174\pi$
$240$	20.8944	+	25.3800i	1.34873	+	1.63827i
$241$	4.61900			0.297536			0.148768	−	0.988872i	$-0.452469\pi$
$241$	4.61900			0.297536			0.148768	+	0.988872i	$0.452469\pi$
$242$	−17.3150	+	10.9740i	−1.11305	+	0.705433i
$243$	20.3348	+	8.42297i	1.30448	+	0.540333i
$244$	−2.04943	+	1.86038i	−0.131201	+	0.119098i
$245$	9.09225	−	3.76613i	0.580882	−	0.240609i
$246$	1.21301	+	6.97477i	0.0773387	+	0.444695i
$247$	16.4624	−	2.06133i	1.04747	−	0.131159i
$248$	−12.3250	+	15.8308i	−0.782640	+	1.00526i
$249$	2.29255	+	2.29255i	0.145285	+	0.145285i
$250$	−5.02366	−	3.53516i	−0.317724	−	0.223583i
$251$	8.41569	−	3.48589i	0.531194	−	0.220028i	−0.100932	−	0.994893i	$-0.532183\pi$
$251$	8.41569	−	3.48589i	0.531194	−	0.220028i	0.632126	+	0.774866i	$0.282183\pi$
$252$	8.01992	−	16.9906i	0.505207	−	1.07031i
$253$	21.8976	+	9.07028i	1.37669	+	0.570244i
$254$	21.9592	+	4.92221i	1.37784	+	0.308847i
$255$		−	5.21511i		−	0.326583i
$256$	−3.07301	+	15.7021i	−0.192063	+	0.981383i
$257$	−24.6272			−1.53620			−0.768102	−	0.640327i	$-0.778799\pi$
$257$	−24.6272			−1.53620			−0.768102	+	0.640327i	$0.778799\pi$
$258$	−33.4365	−	7.49487i	−2.08167	−	0.466611i
$259$	8.61116	−	20.7892i	0.535071	−	1.29178i
$260$	−21.6164	+	10.9519i	−1.34060	+	0.679206i
$261$	−11.9110	+	4.93370i	−0.737272	+	0.305388i
$262$	8.60642	−	12.2302i	0.531706	−	0.755584i
$263$	1.88068	−	1.88068i	0.115967	−	0.115967i	−0.646742	−	0.762709i	$-0.723869\pi$
$263$	1.88068	−	1.88068i	0.115967	−	0.115967i	0.762709	+	0.646742i	$0.223869\pi$
$264$	−21.4570	+	27.5604i	−1.32059	+	1.69622i
$265$	30.7007	−	30.7007i	1.88593	−	1.88593i
$266$	20.2016	−	3.51335i	1.23864	−	0.215417i
$267$	−13.1981	+	5.46682i	−0.807709	+	0.334564i
$268$	−7.28623	−	8.02666i	−0.445077	−	0.490306i
$269$	−19.9510	−	8.26396i	−1.21643	−	0.503863i	−0.320158	−	0.947364i	$-0.603736\pi$
$269$	−19.9510	−	8.26396i	−1.21643	−	0.503863i	−0.896274	+	0.443502i	$0.853736\pi$
$270$	−0.116035	−	0.183083i	−0.00706165	−	0.0111420i
$271$	3.00235			0.182380			0.0911900	−	0.995834i	$-0.470933\pi$
$271$	3.00235			0.182380			0.0911900	+	0.995834i	$0.470933\pi$
$272$	1.95958	−	1.61325i	0.118817	−	0.0978176i
$273$	21.9360	+	17.0539i	1.32763	+	1.03215i
$274$	−4.55566	+	2.88730i	−0.275217	+	0.174428i
$275$	12.1591	−	29.3546i	0.733219	−	1.77015i
$276$	22.9336	+	1.10892i	1.38044	+	0.0667492i
$277$	−5.21127	−	12.5811i	−0.313115	−	0.755926i	−0.999586	−	0.0287690i	$-0.990841\pi$
$277$	−5.21127	−	12.5811i	−0.313115	−	0.755926i	0.686471	−	0.727157i	$-0.259159\pi$
$278$	−1.49048	−	8.57022i	−0.0893931	−	0.514008i
$279$	−14.9536	+	14.9536i	−0.895251	+	0.895251i
$280$	−26.0413	+	14.7921i	−1.55627	+	0.883995i
$281$	−19.2863	−	19.2863i	−1.15052	−	1.15052i	−0.986448	−	0.164077i	$-0.947536\pi$
$281$	−19.2863	−	19.2863i	−1.15052	−	1.15052i	−0.164077	−	0.986448i	$-0.552464\pi$
$282$	−22.0253	+	31.2991i	−1.31159	+	1.86384i
$283$	9.12641	−	3.78028i	0.542509	−	0.224714i	−0.0945632	−	0.995519i	$-0.530145\pi$
$283$	9.12641	−	3.78028i	0.542509	−	0.224714i	0.637072	+	0.770804i	$0.280145\pi$
$284$	8.50083	+	23.7006i	0.504431	+	1.40637i
$285$	−14.4722	+	34.9390i	−0.857259	+	2.06961i
$286$	−16.3778	−	19.8658i	−0.968441	−	1.17469i
$287$	−6.44956			−0.380705
$288$	−5.25937	+	16.0240i	−0.309911	+	0.944225i
$289$	16.5973			0.976314
$290$	20.0533	+	4.49500i	1.17757	+	0.263955i
$291$	−10.9319	−	4.52813i	−0.640838	−	0.265444i
$292$	−3.19844	+	1.14720i	−0.187175	+	0.0671351i
$293$	−0.587392	−	1.41809i	−0.0343158	−	0.0828457i	0.905793	−	0.423721i	$-0.139276\pi$
$293$	−0.587392	−	1.41809i	−0.0343158	−	0.0828457i	−0.940108	+	0.340876i	$0.889276\pi$
$294$	8.28371	+	5.82926i	0.483115	+	0.339970i
$295$	2.24493	−	2.24493i	0.130705	−	0.130705i
$296$	−5.36472	+	19.4732i	−0.311818	+	1.13186i
$297$	0.162846	−	0.162846i	0.00944927	−	0.00944927i
$298$	−5.66623	+	0.985437i	−0.328236	+	0.0570848i
$299$	−4.48389	+	16.3199i	−0.259310	+	0.943807i
$300$	1.48655	−	30.7434i	0.0858260	−	1.77497i
$301$	11.9463	−	28.8410i	0.688576	−	1.66237i
$302$	0.137091	−	0.0868857i	0.00788867	−	0.00499971i
$303$		−	11.7867i		−	0.677129i
$304$	−17.6051	+	5.37014i	−1.00972	+	0.307998i
$305$	4.65066			0.266296
$306$	2.25980	−	1.43223i	0.129184	−	0.0818750i
$307$	−9.12347	+	22.0260i	−0.520704	+	1.25709i	0.416763	+	0.909015i	$0.363165\pi$
$307$	−9.12347	+	22.0260i	−0.520704	+	1.25709i	−0.937467	+	0.348075i	$0.886835\pi$
$308$	−21.3874	−	23.5609i	−1.21866	−	1.34250i
$309$	−11.6849	−	28.2098i	−0.664730	−	1.60480i
$310$	33.2116	−	5.77596i	1.88629	−	0.328052i
$311$	−14.2949	−	14.2949i	−0.810588	−	0.810588i	0.174134	−	0.984722i	$-0.444287\pi$
$311$	−14.2949	−	14.2949i	−0.810588	−	0.810588i	−0.984722	+	0.174134i	$0.944287\pi$
$312$	−21.4312	−	12.7580i	−1.21330	−	0.722278i
$313$	13.8121	−	13.8121i	0.780704	−	0.780704i	−0.199245	−	0.979950i	$-0.563849\pi$
$313$	13.8121	−	13.8121i	0.780704	−	0.780704i	0.979950	+	0.199245i	$0.0638491\pi$
$314$	−12.9140	+	18.3515i	−0.728777	+	1.03563i
$315$	−29.1655	+	12.0807i	−1.64329	+	0.680672i
$316$	4.98804	−	10.5674i	0.280599	−	0.594464i
$317$	11.4708	+	4.75137i	0.644265	+	0.266863i	0.680800	−	0.732469i	$-0.261632\pi$
$317$	11.4708	+	4.75137i	0.644265	+	0.266863i	−0.0365352	+	0.999332i	$0.511632\pi$
$318$	43.6050	+	9.77416i	2.44525	+	0.548108i
$319$			21.8349i			1.22252i
$320$	21.5559	−	16.0644i	1.20501	−	0.898030i
$321$	29.0101			1.61919
$322$	−4.57516	+	20.4110i	−0.254964	+	1.13746i
$323$	2.69762	+	1.11739i	0.150100	+	0.0621734i
$324$	7.73090	−	16.3783i	0.429495	−	0.909906i
$325$	21.8775	+	6.01082i	1.21355	+	0.333421i
$326$	−10.9208	−	7.68496i	−0.604845	−	0.425631i
$327$	−25.5484	−	25.5484i	−1.41283	−	1.41283i
$328$	5.74500	−	0.715329i	0.317215	−	0.0394974i
$329$	−24.6545	−	24.6545i	−1.35925	−	1.35925i
$330$	57.8192	−	10.0556i	3.18284	−	0.553540i
$331$	−22.1053	+	9.15631i	−1.21502	+	0.503276i	−0.895822	−	0.444413i	$-0.853412\pi$
$331$	−22.1053	+	9.15631i	−1.21502	+	0.503276i	−0.319195	+	0.947689i	$0.603412\pi$
$332$	1.96314	−	1.78204i	0.107741	−	0.0978023i
$333$	−8.14762	+	19.6701i	−0.446487	+	1.07791i
$334$	5.39159	+	8.50699i	0.295015	+	0.465482i
$335$			18.2144i			0.995161i
$336$	−27.2076	−	14.4889i	−1.48430	−	0.790432i
$337$			15.3189i			0.834476i	0.908797	+	0.417238i	$0.137002\pi$
$337$			15.3189i			0.834476i	−0.908797	+	0.417238i	$0.862998\pi$
$338$	12.6226	−	13.3667i	0.686579	−	0.727055i
$339$	−14.6187	−	6.05525i	−0.793977	−	0.328876i
$340$	−4.25978	−	0.205975i	−0.231019	−	0.0111706i
$341$	13.7063	+	33.0899i	0.742237	+	1.79192i
$342$	−19.1142	+	3.32422i	−1.03358	+	0.179753i
$343$	9.07138	−	9.07138i	0.489808	−	0.489808i
$344$	−7.44252	+	27.0154i	−0.401274	+	1.45657i
$345$	−27.2792	−	27.2792i	−1.46866	−	1.46866i
$346$	−6.80525	−	4.78887i	−0.365852	−	0.257451i
$347$	−15.8075	+	6.54768i	−0.848591	+	0.351498i	−0.764235	−	0.644938i	$-0.776883\pi$
$347$	−15.8075	+	6.54768i	−0.848591	+	0.351498i	−0.0843557	+	0.996436i	$0.526883\pi$
$348$	7.14122	+	19.9099i	0.382810	+	1.06728i
$349$	9.46456	+	3.92035i	0.506627	+	0.209852i	0.621331	−	0.783548i	$-0.286592\pi$
$349$	9.46456	+	3.92035i	0.506627	+	0.209852i	−0.114705	+	0.993400i	$0.536592\pi$
$350$	27.3617	+	6.13318i	1.46254	+	0.327832i
$351$	0.129830	+	0.100935i	0.00692979	+	0.00538749i
$352$	21.6642	+	18.6149i	1.15471	+	0.992180i
$353$			4.93876i			0.262864i	0.991325	+	0.131432i	$0.0419574\pi$
$353$			4.93876i			0.262864i	−0.991325	+	0.131432i	$0.958043\pi$
$354$	3.18854	+	0.714718i	0.169469	+	0.0379868i
$355$	16.1899	−	39.0859i	0.859271	−	2.07446i
$356$	3.94411	+	10.9963i	0.209037	+	0.582802i
$357$	1.87133	+	4.51779i	0.0990414	+	0.239107i
$358$	−13.0042	−	9.15109i	−0.687293	−	0.483650i
$359$	7.13644	+	7.13644i	0.376647	+	0.376647i	0.869891	−	0.493244i	$-0.164189\pi$
$359$	7.13644	+	7.13644i	0.376647	+	0.376647i	−0.493244	+	0.869891i	$0.664189\pi$
$360$	24.6395	−	13.9958i	1.29862	−	0.737644i
$361$	−1.53704	−	1.53704i	−0.0808969	−	0.0808969i
$362$	0.501233	+	2.88207i	0.0263442	+	0.151478i
$363$	13.5666	+	32.7527i	0.712062	+	1.71907i
$364$	14.7962	−	17.2441i	0.775534	−	0.903835i
$365$	5.27472	+	2.18486i	0.276092	+	0.114361i
$366$	2.56241	+	4.04304i	0.133939	+	0.211333i
$367$		−	10.3150i		−	0.538440i	−0.963079	−	0.269220i	$-0.913234\pi$
$367$		−	10.3150i		−	0.538440i	0.963079	−	0.269220i	$-0.0867658\pi$
$368$	1.81156	−	18.6887i	0.0944343	−	0.974215i
$369$	6.10238			0.317677
$370$	28.6659	−	18.1680i	1.49027	−	0.944507i
$371$	−15.5794	+	37.6120i	−0.808841	+	1.95272i
$372$	23.3202	+	25.6900i	1.20910	+	1.33196i
$373$	8.73521	+	21.0887i	0.452292	+	1.09193i	0.971448	+	0.237251i	$0.0762463\pi$
$373$	8.73521	+	21.0887i	0.452292	+	1.09193i	−0.519156	+	0.854679i	$0.673754\pi$
$374$	−0.776386	−	4.46420i	−0.0401460	−	0.230838i
$375$	−7.51171	+	7.51171i	−0.387903	+	0.387903i
$376$	24.6957	+	19.2268i	1.27358	+	0.991544i
$377$	−15.4708	+	1.93717i	−0.796788	+	0.0997694i
$378$	0.166215	+	0.116966i	0.00854917	+	0.00601607i
$379$	−12.8614	−	31.0503i	−0.660648	−	1.59494i	−0.796790	−	0.604256i	$-0.793471\pi$
$379$	−12.8614	−	31.0503i	−0.660648	−	1.59494i	0.136143	−	0.990689i	$-0.456529\pi$
$380$	27.9670	+	13.2010i	1.43468	+	0.677199i
$381$	14.8931	−	35.9552i	0.762998	−	1.84204i
$382$	−19.8427	−	4.44780i	−1.01524	−	0.227569i
$383$		−	20.5964i		−	1.05243i	−0.850352	−	0.526215i	$-0.823611\pi$
$383$		−	20.5964i		−	1.05243i	0.850352	−	0.526215i	$-0.176389\pi$
$384$	25.8424	+	9.88845i	1.31877	+	0.504618i
$385$			53.4653i			2.72484i
$386$	2.01366	−	8.98343i	0.102492	−	0.457244i
$387$	−11.3033	+	27.2885i	−0.574578	+	1.38715i
$388$	−4.13041	+	8.75047i	−0.209690	+	0.444238i
$389$	23.7492	−	9.83726i	1.20413	−	0.498769i	0.311802	−	0.950147i	$-0.399068\pi$
$389$	23.7492	−	9.83726i	1.20413	−	0.498769i	0.892333	+	0.451378i	$0.149068\pi$
$390$	12.2544	+	40.0749i	0.620525	+	2.02927i
$391$	−2.10621	+	2.10621i	−0.106516	+	0.106516i
$392$	5.08860	−	6.53602i	0.257013	−	0.330119i
$393$	−18.2874	−	18.2874i	−0.922478	−	0.922478i
$394$	−2.82858	−	16.2642i	−0.142502	−	0.819381i
$395$	−18.1397	+	7.51369i	−0.912705	+	0.378055i
$396$	20.2362	+	22.2926i	1.01691	+	1.12024i
$397$	5.21850	−	12.5986i	0.261909	−	0.632305i	−0.737147	−	0.675732i	$-0.763828\pi$
$397$	5.21850	−	12.5986i	0.261909	−	0.632305i	0.999057	+	0.0434273i	$0.0138277\pi$
$398$	27.0482	−	17.1427i	1.35581	−	0.859287i
$399$		−	35.4603i		−	1.77523i
$400$	−25.0529	−	2.42847i	−1.25264	−	0.121424i
$401$	2.47879			0.123785			0.0618924	−	0.998083i	$-0.480286\pi$
$401$	2.47879			0.123785			0.0618924	+	0.998083i	$0.480286\pi$
$402$	−15.8347	+	10.0358i	−0.789762	+	0.500538i
$403$	−22.2294	+	12.6471i	−1.10732	+	0.629997i
$404$	−9.62755	−	0.465526i	−0.478988	−	0.0231608i
$405$	−28.1144	+	11.6454i	−1.39702	+	0.578663i
$406$	−18.9849	+	3.30174i	−0.942204	+	0.163862i
$407$	25.4973	+	25.4973i	1.26386	+	1.26386i
$408$	−2.16798	−	3.81672i	−0.107331	−	0.188956i
$409$	−13.8069	−	13.8069i	−0.682710	−	0.682710i	0.277900	−	0.960610i	$-0.410362\pi$
$409$	−13.8069	−	13.8069i	−0.682710	−	0.682710i	−0.960610	+	0.277900i	$0.910362\pi$
$410$	−7.95515	−	5.59806i	−0.392877	−	0.276468i
$411$	3.56944	+	8.61739i	0.176068	+	0.425065i
$412$	−23.5037	+	8.43020i	−1.15794	+	0.415326i
$413$	−1.13921	+	2.75031i	−0.0560571	+	0.135334i
$414$	4.32888	−	19.3122i	0.212753	−	0.949144i
$415$	−4.45483			−0.218679
$416$	−11.2673	+	17.0014i	−0.552426	+	0.833562i
$417$	−15.0434			−0.736680
$418$	−7.18692	+	32.0627i	−0.351524	+	1.56824i
$419$	−4.90512	+	11.8420i	−0.239631	+	0.578520i	−0.997245	−	0.0741833i	$-0.976365\pi$
$419$	−4.90512	+	11.8420i	−0.239631	+	0.578520i	0.757614	+	0.652703i	$0.226365\pi$
$420$	17.4861	+	48.7518i	0.853235	+	2.37884i
$421$	0.996806	+	2.40650i	0.0485813	+	0.117286i	0.946307	−	0.323269i	$-0.104782\pi$
$421$	0.996806	+	2.40650i	0.0485813	+	0.117286i	−0.897726	+	0.440555i	$0.854782\pi$
$422$	4.98297	+	3.50653i	0.242567	+	0.170695i
$423$	23.3273	+	23.3273i	1.13421	+	1.13421i
$424$	9.70589	−	35.2311i	0.471360	−	1.71097i
$425$	2.82346	+	2.82346i	0.136958	+	0.136958i
$426$	42.8995	−	7.46082i	2.07849	−	0.361478i
$427$	−4.02881	+	1.66879i	−0.194968	+	0.0807583i
$428$	1.14578	−	23.6959i	0.0553834	−	1.14538i
$429$	−38.6999	+	22.0178i	−1.86845	+	1.06303i
$430$	39.7684	−	25.2046i	1.91780	−	1.21547i
$431$	1.37030			0.0660051			0.0330025	−	0.999455i	$-0.489493\pi$
$431$	1.37030			0.0660051			0.0330025	+	0.999455i	$0.489493\pi$
$432$	−0.161030	−	0.0857533i	−0.00774757	−	0.00412581i
$433$			12.4496i			0.598292i	0.954207	+	0.299146i	$0.0967018\pi$
$433$			12.4496i			0.598292i	−0.954207	+	0.299146i	$0.903298\pi$
$434$	−26.6983	+	16.9209i	−1.28156	+	0.812230i
$435$	13.6005	−	32.8346i	0.652095	−	1.57430i
$436$	−21.8773	+	19.8592i	−1.04773	+	0.951083i
$437$	19.9555	−	8.26585i	0.954603	−	0.395409i
$438$	1.00685	+	5.78938i	0.0481093	+	0.276627i
$439$	3.52920	+	3.52920i	0.168440	+	0.168440i	0.786293	−	0.617854i	$-0.211998\pi$
$439$	3.52920	+	3.52920i	0.168440	+	0.168440i	−0.617854	+	0.786293i	$0.711998\pi$
$440$	−5.92991	−	47.6247i	−0.282697	−	2.27042i
$441$	6.17387	−	6.17387i	0.293994	−	0.293994i
$442$	3.09417	−	0.946157i	0.147174	−	0.0450041i
$443$	20.2445	−	8.38554i	0.961845	−	0.398409i	0.154174	−	0.988044i	$-0.450728\pi$
$443$	20.2445	−	8.38554i	0.961845	−	0.398409i	0.807670	+	0.589635i	$0.200728\pi$
$444$	31.5885	+	14.9104i	1.49912	+	0.707619i
$445$	7.51159	−	18.1346i	0.356083	−	0.859662i
$446$	−3.82383	+	17.0590i	−0.181063	+	0.807769i
$447$			9.94603i			0.470431i
$448$	−12.9093	+	21.6513i	−0.609907	+	1.02293i
$449$		−	2.29865i		−	0.108480i	−0.998528	−	0.0542400i	$-0.982726\pi$
$449$		−	2.29865i		−	0.108480i	0.998528	−	0.0542400i	$-0.0172736\pi$
$450$	−25.8888	−	5.80303i	−1.22041	−	0.273558i
$451$	3.95510	−	9.54845i	0.186238	−	0.449619i
$452$	−5.52339	+	11.7016i	−0.259798	+	0.550396i
$453$	−0.107413	−	0.259318i	−0.00504670	−	0.0121838i
$454$	−12.9645	−	9.12318i	−0.608456	−	0.428172i
$455$	−37.8821	+	4.74339i	−1.77594	+	0.222374i
$456$	3.93294	+	31.5866i	0.184177	+	1.47918i
$457$	−7.18767	+	7.18767i	−0.336225	+	0.336225i	−0.854945	−	0.518719i	$-0.826409\pi$
$457$	−7.18767	+	7.18767i	−0.336225	+	0.336225i	0.518719	+	0.854945i	$0.326409\pi$
$458$	−0.804816	−	4.62767i	−0.0376066	−	0.216237i
$459$	0.0110756	+	0.0267389i	0.000516965	+	0.00124806i
$460$	−23.3594	+	21.2046i	−1.08914	+	0.988669i
$461$	−10.4480	+	25.2237i	−0.486612	+	1.17479i	0.469802	+	0.882772i	$0.344325\pi$
$461$	−10.4480	+	25.2237i	−0.486612	+	1.17479i	−0.956414	+	0.292014i	$0.905675\pi$
$462$	−46.4799	+	29.4582i	−2.16244	+	1.37052i
$463$	4.77027			0.221693			0.110847	−	0.993838i	$-0.464644\pi$
$463$	4.77027			0.221693			0.110847	+	0.993838i	$0.464644\pi$
$464$	16.5448	−	5.04669i	0.768072	−	0.234287i
$465$		−	58.2968i		−	2.70345i
$466$	15.4660	+	24.4026i	0.716447	+	1.13043i
$467$	−25.9975	−	10.7685i	−1.20302	−	0.498307i	−0.311046	−	0.950395i	$-0.600679\pi$
$467$	−25.9975	−	10.7685i	−1.20302	−	0.498307i	−0.891974	+	0.452087i	$0.850679\pi$
$468$	−13.9998	+	16.3158i	−0.647139	+	0.754199i
$469$	−6.53586	−	15.7790i	−0.301798	−	0.728605i
$470$	−9.01036	−	51.8094i	−0.415617	−	2.38979i
$471$	27.4403	+	27.4403i	1.26438	+	1.26438i
$472$	0.709726	−	2.57621i	0.0326678	−	0.118580i
$473$	35.3727	+	35.3727i	1.62644	+	1.62644i
$474$	−16.5266	−	11.6298i	−0.759090	−	0.534174i
$475$	−11.0807	−	26.7512i	−0.508417	−	1.22743i
$476$	3.76411	−	1.35010i	0.172528	−	0.0618815i
$477$	14.7407	−	35.5873i	0.674932	−	1.62943i
$478$	−31.3615	−	7.02975i	−1.43444	−	0.321533i
$479$			25.6703i			1.17291i	0.809983	+	0.586454i	$0.199476\pi$
$479$			25.6703i			1.17291i	−0.809983	+	0.586454i	$0.800524\pi$
$480$	−20.9830	−	41.4867i	−0.957741	−	1.89360i
$481$	−15.8037	+	20.3279i	−0.720586	+	0.926871i
$482$	−6.37408	−	1.42877i	−0.290331	−	0.0650785i
$483$	33.4202	+	13.8431i	1.52067	+	0.629882i
$484$	27.2887	−	9.78780i	1.24040	−	0.444900i
$485$	15.0208	−	6.22180i	0.682057	−	0.282517i
$486$	−25.4561	−	17.9135i	−1.15471	−	0.812572i
$487$	−18.5898	−	18.5898i	−0.842383	−	0.842383i	0.146786	−	0.989168i	$-0.453107\pi$
$487$	−18.5898	−	18.5898i	−0.842383	−	0.842383i	−0.989168	+	0.146786i	$0.953107\pi$
$488$	3.40361	−	1.93333i	0.154074	−	0.0875177i
$489$	−16.3294	+	16.3294i	−0.738443	+	0.738443i
$490$	−13.7120	+	2.38470i	−0.619444	+	0.107730i
$491$	−0.952373	−	2.29923i	−0.0429800	−	0.103763i	0.900932	−	0.433961i	$-0.142884\pi$
$491$	−0.952373	−	2.29923i	−0.0429800	−	0.103763i	−0.943912	+	0.330198i	$0.892884\pi$
$492$	0.483545	−	10.0002i	0.0217999	−	0.450844i
$493$	−2.53514	−	1.05009i	−0.114177	−	0.0472937i
$494$	−23.3552	−	2.24763i	−1.05080	−	0.101125i
$495$		−	50.5873i		−	2.27373i
$496$	21.9050	−	18.0336i	0.983564	−	0.809733i
$497$			39.6691i			1.77940i
$498$	−2.45451	−	3.87280i	−0.109989	−	0.173544i
$499$	16.4331	−	39.6731i	0.735649	−	1.77601i	0.112878	−	0.993609i	$-0.463993\pi$
$499$	16.4331	−	39.6731i	0.735649	−	1.77601i	0.622771	−	0.782404i	$-0.286007\pi$
$500$	5.83899	+	6.43236i	0.261128	+	0.287664i
$501$	16.0917	−	6.66538i	0.718922	−	0.297787i
$502$	−12.6917	+	2.20726i	−0.566457	+	0.0985147i
$503$	−11.7252	−	11.7252i	−0.522802	−	0.522802i	0.395615	−	0.918416i	$-0.370531\pi$
$503$	−11.7252	−	11.7252i	−0.522802	−	0.522802i	−0.918416	+	0.395615i	$0.870531\pi$
$504$	−16.3228	+	20.9658i	−0.727077	+	0.933890i
$505$	11.4518	+	11.4518i	0.509599	+	0.509599i
$506$	−27.4124	−	19.2902i	−1.21863	−	0.857552i
$507$	−19.0338	−	25.4669i	−0.845321	−	1.13102i
$508$	−28.7805	−	13.5850i	−1.27693	−	0.602737i
$509$	−25.9308	−	10.7409i	−1.14936	−	0.476081i	−0.275043	−	0.961432i	$-0.588692\pi$
$509$	−25.9308	−	10.7409i	−1.14936	−	0.476081i	−0.874320	+	0.485351i	$0.838692\pi$
$510$	−1.61316	+	7.19670i	−0.0714318	+	0.318675i
$511$	−5.35342			−0.236821
$512$	9.09769	−	20.7179i	0.402065	−	0.915611i
$513$		−	0.209874i		−	0.00926616i
$514$	33.9849	+	7.61779i	1.49901	+	0.336006i
$515$	38.7612	+	16.0554i	1.70802	+	0.707486i
$516$	43.8231	+	20.6854i	1.92920	+	0.910625i
$517$	51.6195	−	21.3815i	2.27022	−	0.940357i
$518$	−18.3137	+	26.0248i	−0.804659	+	1.14346i
$519$	−10.1757	+	10.1757i	−0.446662	+	0.446662i
$520$	33.2177	−	8.42677i	1.45669	−	0.369538i
$521$	−4.46506	−	4.46506i	−0.195618	−	0.195618i	0.602501	−	0.798118i	$-0.294171\pi$
$521$	−4.46506	−	4.46506i	−0.195618	−	0.195618i	−0.798118	+	0.602501i	$0.794171\pi$
$522$	17.9629	−	3.12400i	0.786216	−	0.136734i
$523$	−2.41027	−	5.81891i	−0.105394	−	0.254443i	0.862381	−	0.506259i	$-0.168972\pi$
$523$	−2.41027	−	5.81891i	−0.105394	−	0.254443i	−0.967775	+	0.251816i	$0.918972\pi$
$524$	−15.6597	+	14.2151i	−0.684097	+	0.620991i
$525$	18.5572	−	44.8010i	0.809902	−	1.95528i
$526$	−3.17702	+	2.01354i	−0.138524	+	0.0877945i
$527$	−4.50108			−0.196070
$528$	38.1352	−	31.3953i	1.65962	−	1.36631i
$529$		−	0.965704i		−	0.0419871i
$530$	−51.8625	+	32.8696i	−2.25276	+	1.42776i
$531$	1.07789	−	2.60226i	0.0467765	−	0.112928i
$532$	−28.9644	−	1.40053i	−1.25577	−	0.0607208i
$533$	7.11631	+	1.95520i	0.308242	+	0.0846891i
$534$	19.9040	−	3.46158i	0.861329	−	0.149797i
$535$	−28.1859	+	28.1859i	−1.21858	+	1.21858i
$536$	7.57194	+	13.3304i	0.327058	+	0.575784i
$537$	−19.4448	+	19.4448i	−0.839103	+	0.839103i
$538$	24.9755	+	17.5753i	1.07677	+	0.757726i
$539$	−5.65888	−	13.6617i	−0.243745	−	0.588453i
$540$	0.103493	+	0.288541i	0.00445362	+	0.0124168i
$541$	−26.2325	−	10.8659i	−1.12782	−	0.467160i	−0.260783	−	0.965397i	$-0.583981\pi$
$541$	−26.2325	−	10.8659i	−1.12782	−	0.467160i	−0.867041	+	0.498238i	$0.833981\pi$
$542$	−4.14316	−	0.928699i	−0.177964	−	0.0398910i
$543$	5.05895			0.217100
$544$	−3.20317	+	1.62009i	−0.137335	+	0.0694609i
$545$	49.6449			2.12656
$546$	−24.9959	−	30.3192i	−1.06972	−	1.29754i
$547$	−8.43890	+	20.3733i	−0.360821	+	0.871100i	0.634359	+	0.773038i	$0.281264\pi$
$547$	−8.43890	+	20.3733i	−0.360821	+	0.871100i	−0.995180	+	0.0980611i	$0.968736\pi$
$548$	7.17979	−	2.57522i	0.306705	−	0.110008i
$549$	3.81194	−	1.57896i	0.162690	−	0.0673883i
$550$	−25.8592	+	36.7474i	−1.10264	+	1.56691i
$551$	14.0703	+	14.0703i	0.599415	+	0.599415i
$552$	−31.3047	−	8.62418i	−1.33242	−	0.367070i
$553$	13.0181	−	13.0181i	0.553584	−	0.553584i
$554$	3.29976	+	18.9735i	0.140193	+	0.806108i
$555$	−22.4602	−	54.2238i	−0.953383	−	2.30167i
$556$	−0.594154	+	12.2877i	−0.0251977	+	0.521114i
$557$	14.4125	−	34.7948i	0.610677	−	1.47431i	−0.251581	−	0.967836i	$-0.580951\pi$
$557$	14.4125	−	34.7948i	0.610677	−	1.47431i	0.862258	−	0.506469i	$-0.169049\pi$
$558$	25.2611	−	16.0101i	1.06939	−	0.677760i
$559$	−21.9246	+	28.2011i	−0.927312	+	1.19278i
$560$	40.5118	−	12.3574i	1.71194	−	0.522196i
$561$	−7.83608			−0.330839
$562$	20.6488	+	32.5802i	0.871018	+	1.37431i
$563$	−14.2655	−	5.90897i	−0.601220	−	0.249033i	0.0612493	−	0.998122i	$-0.480492\pi$
$563$	−14.2655	−	5.90897i	−0.601220	−	0.249033i	−0.662469	+	0.749089i	$0.730492\pi$
$564$	40.0758	−	36.3790i	1.68750	−	1.53183i
$565$	20.0865	−	8.32011i	0.845046	−	0.350030i
$566$	−13.7635	+	2.39366i	−0.578523	+	0.100613i
$567$	20.1765	−	20.1765i	0.847334	−	0.847334i
$568$	−4.39975	−	35.3356i	−0.184609	−	1.48265i
$569$	−21.9655	+	21.9655i	−0.920843	+	0.920843i	−0.997089	−	0.0762456i	$-0.975707\pi$
$569$	−21.9655	+	21.9655i	−0.920843	+	0.920843i	0.0762456	+	0.997089i	$0.475707\pi$
$570$	30.7786	−	43.7381i	1.28918	−	1.83199i
$571$	6.67638	−	2.76545i	0.279398	−	0.115730i	−0.238584	−	0.971122i	$-0.576683\pi$
$571$	6.67638	−	2.76545i	0.279398	−	0.115730i	0.517982	+	0.855391i	$0.326683\pi$
$572$	16.4559	+	32.4802i	0.688058	+	1.35807i
$573$	−13.4577	+	32.4898i	−0.562204	+	1.35728i
$574$	8.90020	+	1.99500i	0.371487	+	0.0832697i
$575$	29.5378			1.23181
$576$	12.2144	−	20.4858i	0.508933	−	0.853577i
$577$			22.0981i			0.919954i	0.887931	+	0.459977i	$0.152142\pi$
$577$			22.0981i			0.919954i	−0.887931	+	0.459977i	$0.847858\pi$
$578$	−22.9038	−	5.13395i	−0.952674	−	0.213544i
$579$	−14.7091	−	6.09272i	−0.611291	−	0.253205i
$580$	−26.2826	−	12.4059i	−1.09132	−	0.515128i
$581$	3.85917	−	1.59852i	0.160105	−	0.0663178i
$582$	13.6850	+	9.63018i	0.567262	+	0.399184i
$583$	−46.1300	−	46.1300i	−1.91051	−	1.91051i
$584$	4.76861	−	0.593755i	0.197327	−	0.0245698i
$585$	35.8429	−	4.48805i	1.48192	−	0.185558i
$586$	0.371935	+	2.13862i	0.0153645	+	0.0883455i
$587$	−28.5635	+	11.8314i	−1.17894	+	0.488334i	−0.884139	−	0.467225i	$-0.845254\pi$
$587$	−28.5635	+	11.8314i	−1.17894	+	0.488334i	−0.294803	+	0.955558i	$0.595254\pi$
$588$	−9.62814	−	10.6066i	−0.397058	−	0.437407i
$589$	30.1552	+	12.4907i	1.24252	+	0.514670i
$590$	−3.79235	+	2.40353i	−0.156129	+	0.0989518i
$591$	−28.5489			−1.17434
$592$	13.4267	−	25.2131i	0.551833	−	1.03625i
$593$	−25.6781			−1.05447			−0.527237	−	0.849719i	$-0.676772\pi$
$593$	−25.6781			−1.05447			−0.527237	+	0.849719i	$0.676772\pi$
$594$	−0.275094	+	0.174350i	−0.0112873	+	0.00715368i
$595$	−6.20759	−	2.57127i	−0.254487	−	0.105412i
$596$	8.12406	+	0.392827i	0.332774	+	0.0160908i
$597$	−21.1928	−	51.1639i	−0.867362	−	2.09400i
$598$	11.2358	−	21.1341i	0.459465	−	0.864236i
$599$	−32.1143	−	32.1143i	−1.31216	−	1.31216i	−0.919823	−	0.392333i	$-0.871668\pi$
$599$	−32.1143	−	32.1143i	−1.31216	−	1.31216i	−0.392333	−	0.919823i	$-0.628332\pi$
$600$	−11.5610	+	41.9651i	−0.471978	+	1.71322i
$601$	−29.8119	+	29.8119i	−1.21605	+	1.21605i	−0.247048	+	0.969003i	$0.579461\pi$
$601$	−29.8119	+	29.8119i	−1.21605	+	1.21605i	−0.969003	+	0.247048i	$0.920539\pi$
$602$	−25.4068	+	36.1045i	−1.03550	+	1.47151i
$603$	6.18404	+	14.9296i	0.251833	+	0.607980i
$604$	−0.216057	+	0.0774944i	−0.00879122	+	0.00315320i
$605$	−45.0033	−	18.6410i	−1.82964	−	0.757863i
$606$	−3.64591	+	16.2653i	−0.148105	+	0.660733i
$607$	−31.9997			−1.29883			−0.649414	−	0.760435i	$-0.724986\pi$
$607$	−31.9997			−1.29883			−0.649414	+	0.760435i	$0.724986\pi$
$608$	25.9557	−	1.96495i	1.05264	−	0.0796891i
$609$			33.3245i			1.35038i
$610$	−6.41777	−	1.43856i	−0.259848	−	0.0582455i
$611$	19.7292	+	34.6773i	0.798158	+	1.40290i
$612$	−3.56149	+	1.27742i	−0.143965	+	0.0516367i
$613$	−0.835584	−	2.01728i	−0.0337489	−	0.0814771i	0.906106	−	0.423050i	$-0.139040\pi$
$613$	−0.835584	−	2.01728i	−0.0337489	−	0.0814771i	−0.939855	+	0.341573i	$0.889040\pi$
$614$	19.4033	−	27.5731i	0.783053	−	1.11276i
$615$	−11.8951	+	11.8951i	−0.479656	+	0.479656i
$616$	22.2261	+	39.1289i	0.895516	+	1.57655i
$617$	27.0859	−	27.0859i	1.09044	−	1.09044i	0.0949553	−	0.995482i	$-0.469729\pi$
$617$	27.0859	−	27.0859i	1.09044	−	1.09044i	0.995482	−	0.0949553i	$-0.0302708\pi$
$618$	7.39883	+	42.5431i	0.297625	+	1.71133i
$619$	−2.22210	+	0.920422i	−0.0893136	+	0.0369949i	−0.426893	−	0.904302i	$-0.640392\pi$
$619$	−2.22210	+	0.920422i	−0.0893136	+	0.0369949i	0.337579	+	0.941297i	$0.390392\pi$
$620$	−47.6177	−	2.30248i	−1.91237	−	0.0924700i
$621$	0.197799	+	0.0819312i	0.00793742	+	0.00328779i
$622$	15.3048	+	24.1482i	0.613665	+	0.968256i
$623$			18.4052i			0.737387i
$624$	25.6280	+	24.2348i	1.02594	+	0.970168i
$625$			16.8663i			0.674653i
$626$	−23.3326	+	14.7878i	−0.932560	+	0.591041i
$627$	52.4983	+	21.7455i	2.09658	+	0.868431i
$628$	23.4974	−	21.3299i	0.937650	−	0.851155i
$629$	−4.18660	+	1.73414i	−0.166930	+	0.0691449i
$630$	43.9843	−	7.64949i	1.75238	−	0.304763i
$631$	32.4929	−	32.4929i	1.29352	−	1.29352i	0.360927	−	0.932594i	$-0.382460\pi$
$631$	32.4929	−	32.4929i	1.29352	−	1.29352i	0.932594	−	0.360927i	$-0.117540\pi$
$632$	−10.1521	+	13.0398i	−0.403829	+	0.518696i
$633$	7.45087	−	7.45087i	0.296146	−	0.296146i
$634$	−14.3597	−	10.1049i	−0.570296	−	0.401318i
$635$	20.4636	+	49.4036i	0.812075	+	1.96052i
$636$	−57.1502	−	26.9761i	−2.26615	−	1.06967i
$637$	9.17779	−	5.22158i	0.363637	−	0.206886i
$638$	6.75405	−	30.1315i	0.267395	−	1.19292i
$639$		−	37.5337i		−	1.48481i
$640$	−34.7157	+	15.5007i	−1.37226	+	0.612719i
$641$	−32.4529			−1.28181			−0.640906	−	0.767619i	$-0.721441\pi$
$641$	−32.4529			−1.28181			−0.640906	+	0.767619i	$0.721441\pi$
$642$	−40.0331	−	8.97352i	−1.57998	−	0.354157i
$643$	−5.17971	−	2.14551i	−0.204268	−	0.0846105i	0.278204	−	0.960522i	$-0.410261\pi$
$643$	−5.17971	−	2.14551i	−0.204268	−	0.0846105i	−0.482472	+	0.875912i	$0.660261\pi$
$644$	12.6272	−	26.7513i	0.497581	−	1.05415i
$645$	−31.1593	−	75.2252i	−1.22690	−	2.96199i
$646$	−3.37700	−	2.37641i	−0.132866	−	0.0934985i
$647$	21.0672	−	21.0672i	0.828238	−	0.828238i	−0.159035	−	0.987273i	$-0.550838\pi$
$647$	21.0672	−	21.0672i	0.828238	−	0.828238i	0.987273	+	0.159035i	$0.0508382\pi$
$648$	−15.7346	+	20.2102i	−0.618114	+	0.793932i
$649$	−3.37317	−	3.37317i	−0.132409	−	0.132409i
$650$	−28.3310	−	15.0620i	−1.11123	−	0.590780i
$651$	20.9186	+	50.5019i	0.819863	+	1.97933i
$652$	12.6932	+	13.9831i	0.497103	+	0.547619i
$653$	38.6901	+	16.0260i	1.51406	+	0.627144i	0.976391	−	0.216011i	$-0.0693048\pi$
$653$	38.6901	+	16.0260i	1.51406	+	0.627144i	0.537670	+	0.843156i	$0.319305\pi$
$654$	27.3533	+	43.1587i	1.06960	+	1.68764i
$655$	35.5356			1.38849
$656$	−8.14920	−	0.789933i	−0.318173	−	0.0308417i
$657$	5.06525			0.197614
$658$	26.3962	+	41.6487i	1.02903	+	1.62363i
$659$	35.4205	+	14.6717i	1.37979	+	0.571527i	0.944425	−	0.328728i	$-0.106620\pi$
$659$	35.4205	+	14.6717i	1.37979	+	0.571527i	0.435363	+	0.900255i	$0.356620\pi$
$660$	−82.8992	−	4.00847i	−3.22685	−	0.156030i
$661$	−18.4684	+	7.64988i	−0.718339	+	0.297546i	−0.711750	−	0.702432i	$-0.752097\pi$
$661$	−18.4684	+	7.64988i	−0.718339	+	0.297546i	−0.00658875	+	0.999978i	$0.502097\pi$
$662$	33.3369	−	5.79775i	1.29568	−	0.225336i
$663$	−0.695209	−	5.55214i	−0.0269997	−	0.215627i
$664$	−3.26030	+	1.85192i	−0.126524	+	0.0718685i
$665$	34.4528	+	34.4528i	1.33602	+	1.33602i
$666$	17.3279	−	24.6239i	0.671443	−	0.954157i
$667$	−18.7536	+	7.76799i	−0.726142	+	0.300778i
$668$	−4.80882	−	13.4071i	−0.186059	−	0.518738i
$669$	27.9319	+	11.5698i	1.07991	+	0.447313i
$670$	5.63416	−	25.1354i	0.217666	−	0.971065i
$671$		−	6.98794i		−	0.269766i
$672$	33.0640	+	28.4102i	1.27547	+	1.09595i
$673$	36.2655			1.39793			0.698967	−	0.715154i	$-0.253644\pi$
$673$	36.2655			1.39793			0.698967	+	0.715154i	$0.253644\pi$
$674$	4.73851	−	21.1397i	0.182521	−	0.814271i
$675$	0.109832	−	0.265158i	0.00422743	−	0.0102059i
$676$	−21.5535	+	14.5413i	−0.828980	+	0.559279i
$677$	−2.79938	+	1.15954i	−0.107589	+	0.0445649i	−0.435829	−	0.900030i	$-0.643545\pi$
$677$	−2.79938	+	1.15954i	−0.107589	+	0.0445649i	0.328240	+	0.944594i	$0.393545\pi$
$678$	18.3003	+	12.8780i	0.702819	+	0.494575i
$679$	−10.7797	+	10.7797i	−0.413689	+	0.413689i
$680$	5.81466	+	1.60189i	0.222982	+	0.0614297i
$681$	−19.3855	+	19.3855i	−0.742853	+	0.742853i
$682$	−8.67878	−	49.9028i	−0.332328	−	1.91088i
$683$	13.1568	−	5.44973i	0.503431	−	0.208528i	−0.116490	−	0.993192i	$-0.537164\pi$
$683$	13.1568	−	5.44973i	0.503431	−	0.208528i	0.619921	+	0.784664i	$0.287164\pi$
$684$	27.4053	+	1.32514i	1.04787	+	0.0506681i
$685$	−11.8406	−	4.90453i	−0.452405	−	0.187392i
$686$	−15.3242	+	9.71224i	−0.585082	+	0.370815i
$687$	−8.12303			−0.309913
$688$	18.6270	−	34.9783i	0.710146	−	1.33354i
$689$	28.5921	−	36.7774i	1.08927	−	1.40111i
$690$	29.2063	+	46.0825i	1.11187	+	1.75433i
$691$	11.0640	−	26.7109i	0.420895	−	1.01613i	−0.561189	−	0.827688i	$-0.689656\pi$
$691$	11.0640	−	26.7109i	0.420895	−	1.01613i	0.982084	−	0.188443i	$-0.0603441\pi$
$692$	7.90973	+	8.71353i	0.300683	+	0.331239i
$693$	18.1522	+	43.8232i	0.689543	+	1.66470i
$694$	23.8392	−	4.14597i	0.904925	−	0.157379i
$695$	14.6160	−	14.6160i	0.554417	−	0.554417i
$696$	−3.69606	−	29.6841i	−0.140099	−	1.12517i
$697$	0.918414	+	0.918414i	0.0347874	+	0.0347874i
$698$	−11.8482	−	8.33758i	−0.448460	−	0.315582i
$699$	46.1595	−	19.1199i	1.74591	−	0.723180i
$700$	−35.8612	−	16.9272i	−1.35542	−	0.639789i
$701$	−16.7285	+	40.3861i	−0.631825	+	1.52536i	0.205501	+	0.978657i	$0.434117\pi$
$701$	−16.7285	+	40.3861i	−0.631825	+	1.52536i	−0.837326	+	0.546703i	$0.815883\pi$
$702$	−0.147940	−	0.179446i	−0.00558362	−	0.00677276i
$703$	32.8607			1.23936
$704$	−24.1380	−	32.3893i	−0.909734	−	1.22072i
$705$	−90.9417			−3.42506
$706$	1.52768	−	6.81534i	0.0574948	−	0.256499i
$707$	−14.0298	−	5.81134i	−0.527646	−	0.218558i
$708$	−4.17901	−	1.97258i	−0.157057	−	0.0741341i
$709$	−8.72454	−	21.0629i	−0.327657	−	0.791034i	−0.998765	−	0.0496750i	$-0.984181\pi$
$709$	−8.72454	−	21.0629i	−0.327657	−	0.791034i	0.671108	−	0.741359i	$-0.265819\pi$
$710$	−34.4318	+	48.9295i	−1.29220	+	1.83629i
$711$	−12.3173	+	12.3173i	−0.461935	+	0.461935i
$712$	−2.04134	−	16.3946i	−0.0765024	−	0.614412i
$713$	−23.5442	+	23.5442i	−0.881736	+	0.881736i
$714$	−1.18492	−	6.81327i	−0.0443446	−	0.254980i
$715$	16.2081	−	58.9925i	0.606150	−	2.20620i
$716$	15.1148	+	16.6507i	0.564865	+	0.622267i
$717$	−21.2699	+	51.3502i	−0.794340	+	1.91771i
$718$	−7.64061	−	12.0556i	−0.285145	−	0.449909i
$719$			3.46431i			0.129197i	0.997911	+	0.0645984i	$0.0205766\pi$
$719$			3.46431i			0.129197i	−0.997911	+	0.0645984i	$0.979423\pi$
$720$	−38.3310	+	11.6922i	−1.42851	+	0.435743i
$721$	−39.3395			−1.46508
$722$	1.64563	+	2.59651i	0.0612439	+	0.0966322i
$723$	−4.32302	+	10.4367i	−0.160775	+	0.388145i
$724$	0.199808	−	4.13222i	0.00742579	−	0.153573i
$725$	10.4133	+	25.1399i	0.386740	+	0.933673i
$726$	−8.59034	−	49.3942i	−0.318817	−	1.83319i
$727$	9.49585	+	9.49585i	0.352182	+	0.352182i	0.860921	−	0.508739i	$-0.169888\pi$
$727$	9.49585	+	9.49585i	0.352182	+	0.352182i	−0.508739	+	0.860921i	$0.669888\pi$
$728$	−25.7524	+	19.2195i	−0.954447	+	0.712322i
$729$	−18.8538	+	18.8538i	−0.698288	+	0.698288i
$730$	−6.60313	−	4.64664i	−0.244393	−	0.171980i
$731$	−5.80810	+	2.40580i	−0.214821	+	0.0889816i
$732$	−2.28544	−	6.37188i	−0.0844724	−	0.235512i
$733$	−18.4524	−	7.64324i	−0.681555	−	0.282310i	0.0149215	−	0.999889i	$-0.495250\pi$
$733$	−18.4524	−	7.64324i	−0.681555	−	0.282310i	−0.696477	+	0.717579i	$0.745250\pi$
$734$	−3.19068	+	14.2344i	−0.117770	+	0.525402i
$735$			24.0689i			0.887793i
$736$	−8.28076	+	25.2295i	−0.305233	+	0.929971i
$737$	27.3685			1.00813
$738$	−8.42110	−	1.88761i	−0.309985	−	0.0694839i
$739$	16.7593	+	6.94194i	0.616502	+	0.255364i	0.669006	−	0.743257i	$-0.266720\pi$
$739$	16.7593	+	6.94194i	0.616502	+	0.255364i	−0.0525036	+	0.998621i	$0.516720\pi$
$740$	−45.1778	+	16.2042i	−1.66077	+	0.595679i
$741$	−10.7499	+	39.1262i	−0.394906	+	1.43734i
$742$	33.1334	−	47.0843i	1.21636	−	1.72852i
$743$	6.80777	+	6.80777i	0.249753	+	0.249753i	0.820869	−	0.571116i	$-0.193489\pi$
$743$	6.80777	+	6.80777i	0.249753	+	0.249753i	−0.571116	+	0.820869i	$0.693489\pi$
$744$	−24.2346	−	42.6649i	−0.888485	−	1.56417i
$745$	−9.66344	−	9.66344i	−0.354041	−	0.354041i
$746$	−5.53111	−	31.8038i	−0.202508	−	1.16442i
$747$	−3.65143	+	1.51247i	−0.133599	+	0.0553385i
$748$	−0.309493	+	6.40062i	−0.0113162	+	0.234030i
$749$	14.3032	−	34.5310i	0.522628	−	1.26174i
$750$	12.6895	−	8.04239i	0.463355	−	0.293667i
$751$		−	7.63930i		−	0.278762i	−0.990239	−	0.139381i	$-0.955489\pi$
$751$		−	7.63930i		−	0.278762i	0.990239	−	0.139381i	$-0.0445113\pi$
$752$	−28.1320	−	34.1713i	−1.02587	−	1.24610i
$753$			22.2779i			0.811851i
$754$	21.9485	+	2.11225i	0.799317	+	0.0769236i
$755$	0.356311	+	0.147589i	0.0129675	+	0.00537131i
$756$	−0.193191	−	0.212823i	−0.00702630	−	0.00774032i
$757$	−0.573498	−	1.38455i	−0.0208441	−	0.0503222i	0.913115	−	0.407703i	$-0.133670\pi$
$757$	−0.573498	−	1.38455i	−0.0208441	−	0.0503222i	−0.933959	+	0.357380i	$0.883670\pi$
$758$	8.14383	+	46.8268i	0.295797	+	1.70083i
$759$	−40.9888	+	40.9888i	−1.48780	+	1.48780i
$760$	−34.5103	−	26.8679i	−1.25182	−	0.974602i
$761$	−5.44366	−	5.44366i	−0.197332	−	0.197332i	0.601523	−	0.798855i	$-0.294561\pi$
$761$	−5.44366	−	5.44366i	−0.197332	−	0.197332i	−0.798855	+	0.601523i	$0.794561\pi$
$762$	−31.6739	+	45.0103i	−1.14742	+	1.63055i
$763$	−43.0068	+	17.8140i	−1.55695	+	0.644911i
$764$	26.0066	+	12.2757i	0.940885	+	0.444118i
$765$	5.87344	+	2.43286i	0.212355	+	0.0879602i
$766$	−6.37097	+	28.4225i	−0.230192	+	1.02695i
$767$	2.09075	−	2.68928i	0.0754926	−	0.0971042i
$768$	−32.6031	−	21.6394i	−1.17646	−	0.780846i
$769$		−	36.2837i		−	1.30842i	−0.756311	−	0.654212i	$-0.773000\pi$
$769$		−	36.2837i		−	1.30842i	0.756311	−	0.654212i	$-0.227000\pi$
$770$	16.5381	−	73.7805i	0.595991	−	2.65887i
$771$	23.0491	−	55.6456i	0.830095	−	2.00403i
$772$	−5.55757	+	11.7740i	−0.200021	+	0.423755i
$773$	−11.9261	−	28.7921i	−0.428952	−	1.03558i	−0.979621	−	0.200857i	$-0.935627\pi$
$773$	−11.9261	−	28.7921i	−0.428952	−	1.03558i	0.550669	−	0.834724i	$-0.314373\pi$
$774$	24.0392	−	34.1610i	0.864070	−	1.22789i
$775$	31.5619	+	31.5619i	1.13374	+	1.13374i
$776$	8.40657	−	10.7978i	0.301778	−	0.387617i
$777$	38.9141	+	38.9141i	1.39603	+	1.39603i
$778$	−35.8162	+	6.22893i	−1.28407	+	0.223318i
$779$	−3.60433	−	8.70161i	−0.129138	−	0.311768i
$780$	−4.51459	−	59.0927i	−0.161648	−	2.11586i
$781$	−58.7293	−	24.3265i	−2.10150	−	0.870470i
$782$	3.55801	−	2.25501i	0.127234	−	0.0806390i
$783$			0.197233i			0.00704853i
$784$	−9.04386	+	7.44549i	−0.322995	+	0.265910i
$785$	−53.3214			−1.90312
$786$	19.5794	+	30.8928i	0.698373	+	1.10191i
$787$	10.5362	−	25.4365i	0.375574	−	0.906715i	−0.617210	−	0.786798i	$-0.711737\pi$
$787$	10.5362	−	25.4365i	0.375574	−	0.906715i	0.992784	−	0.119917i	$-0.0382627\pi$
$788$	−1.12756	+	23.3191i	−0.0401678	+	0.830710i
$789$	2.48925	+	6.00958i	0.0886196	+	0.213947i
$790$	27.3564	−	4.75765i	0.973296	−	0.169270i
$791$	−14.4152	+	14.4152i	−0.512547	+	0.512547i
$792$	−21.0297	−	37.0226i	−0.747257	−	1.31554i
$793$	4.95121	−	0.619963i	0.175823	−	0.0220155i
$794$	−11.0984	+	15.7715i	−0.393868	+	0.559708i
$795$	40.6352	+	98.1021i	1.44118	+	3.47932i
$796$	−42.6284	+	15.2898i	−1.51092	+	0.541932i
$797$	−2.52511	+	6.09616i	−0.0894440	+	0.215937i	−0.962271	−	0.272093i	$-0.912284\pi$
$797$	−2.52511	+	6.09616i	−0.0894440	+	0.215937i	0.872827	+	0.488030i	$0.162284\pi$
$798$	−10.9687	+	48.9341i	−0.388288	+	1.73225i
$799$			7.02158i			0.248405i
$800$	33.8211	+	11.1007i	1.19576	+	0.392468i
$801$		−	17.4144i		−	0.615308i
$802$	−3.42066	−	0.766748i	−0.120788	−	0.0270748i
$803$	3.28291	−	7.92564i	0.115851	−	0.279690i
$804$	24.9557	−	8.95101i	0.880119	−	0.315678i
$805$	−45.9204	+	19.0208i	−1.61848	+	0.670397i
$806$	34.5880	−	10.5766i	1.21831	−	0.372543i
$807$	37.3451	−	37.3451i	1.31461	−	1.31461i
$808$	13.1417	+	3.62044i	0.462325	+	0.127367i
$809$	−33.3778	−	33.3778i	−1.17350	−	1.17350i	−0.981369	−	0.192133i	$-0.938459\pi$
$809$	−33.3778	−	33.3778i	−1.17350	−	1.17350i	−0.192133	−	0.981369i	$-0.561541\pi$
$810$	42.3993	−	7.37382i	1.48976	−	0.259090i
$811$	−18.7640	+	7.77232i	−0.658895	+	0.272923i	−0.686973	−	0.726683i	$-0.741061\pi$
$811$	−18.7640	+	7.77232i	−0.658895	+	0.272923i	0.0280786	+	0.999606i	$0.491061\pi$
$812$	27.2199	+	1.31618i	0.955231	+	0.0461888i
$813$	−2.80997	+	6.78386i	−0.0985498	+	0.237920i
$814$	−27.2986	−	43.0725i	−0.956816	−	1.50969i
$815$		−	31.7310i		−	1.11149i
$816$	1.81115	+	5.93756i	0.0634029	+	0.207856i
$817$	45.5879			1.59492
$818$	14.7824	+	23.3240i	0.516853	+	0.815505i
$819$	−29.4399	+	16.7494i	−1.02871	+	0.585272i
$820$	9.24626	+	10.1859i	0.322893	+	0.355706i
$821$	19.4812	−	8.06939i	0.679900	−	0.281624i	−0.0158853	−	0.999874i	$-0.505057\pi$
$821$	19.4812	−	8.06939i	0.679900	−	0.281624i	0.695785	+	0.718250i	$0.255057\pi$
$822$	−2.26016	−	12.9959i	−0.0788322	−	0.453283i
$823$	−14.7116	−	14.7116i	−0.512815	−	0.512815i	0.402573	−	0.915388i	$-0.368116\pi$
$823$	−14.7116	−	14.7116i	−0.512815	−	0.512815i	−0.915388	+	0.402573i	$0.868116\pi$
$824$	35.0420	−	4.36319i	1.22075	−	0.151999i
$825$	54.9471	+	54.9471i	1.91301	+	1.91301i
$826$	2.42282	−	3.44296i	0.0843006	−	0.119796i
$827$	−8.56610	−	20.6804i	−0.297872	−	0.719127i	−0.999975	−	0.00705187i	$-0.997755\pi$
$827$	−8.56610	−	20.6804i	−0.297872	−	0.719127i	0.702103	−	0.712076i	$-0.252245\pi$
$828$	−11.9475	+	25.3113i	−0.415203	+	0.879628i
$829$	−5.77079	+	13.9319i	−0.200428	+	0.483876i	−0.991853	−	0.127391i	$-0.959340\pi$
$829$	−5.77079	+	13.9319i	−0.200428	+	0.483876i	0.791425	+	0.611267i	$0.209340\pi$
$830$	6.14754	+	1.37798i	0.213384	+	0.0478305i
$831$	33.3045			1.15532
$832$	20.8075	−	19.9762i	0.721371	−	0.692549i
$833$	1.85835			0.0643879
$834$	20.7595	+	4.65329i	0.718843	+	0.161130i
$835$	−9.15845	+	22.1105i	−0.316941	+	0.765164i
$836$	19.8355	−	42.0225i	0.686025	−	1.45338i
$837$	0.123808	+	0.298899i	0.00427943	+	0.0103315i
$838$	10.4319	−	14.8243i	0.360365	−	0.512098i
$839$	−2.45089	−	2.45089i	−0.0846140	−	0.0846140i	0.663533	−	0.748147i	$-0.269056\pi$
$839$	−2.45089	−	2.45089i	−0.0846140	−	0.0846140i	−0.748147	+	0.663533i	$0.769056\pi$
$840$	−9.05023	−	72.6849i	−0.312263	−	2.50787i
$841$	7.28327	+	7.28327i	0.251147	+	0.251147i
$842$	−0.631174	−	3.62924i	−0.0217517	−	0.125072i
$843$	61.6281	−	25.5272i	2.12259	−	0.879204i
$844$	−5.79170	−	6.38026i	−0.199359	−	0.219618i
$845$	43.2363	+	6.25029i	1.48737	+	0.215017i
$846$	−24.9753	−	39.4067i	−0.858670	−	1.35483i
$847$	45.6747			1.56940
$848$	−24.2917	+	45.6157i	−0.834179	+	1.56645i
$849$			24.1593i			0.829145i
$850$	−3.02293	−	4.76965i	−0.103686	−	0.163598i
$851$	−12.8282	+	30.9701i	−0.439747	+	1.06164i
$852$	−61.5079	−	2.97412i	−2.10722	−	0.101892i
$853$	29.8126	−	12.3488i	1.02076	−	0.422814i	0.191394	−	0.981513i	$-0.438699\pi$
$853$	29.8126	−	12.3488i	1.02076	−	0.422814i	0.829371	+	0.558699i	$0.188699\pi$
$854$	6.07584	−	1.05667i	0.207911	−	0.0361586i
$855$	−32.5982	−	32.5982i	−1.11483	−	1.11483i
$856$	−8.91085	+	32.3452i	−0.304566	+	1.10554i
$857$	−4.55635	+	4.55635i	−0.155642	+	0.155642i	−0.780632	−	0.624990i	$-0.785103\pi$
$857$	−4.55635	+	4.55635i	−0.155642	+	0.155642i	0.624990	+	0.780632i	$0.285103\pi$
$858$	60.2153	−	18.4131i	2.05572	−	0.628613i
$859$	−20.7631	+	8.60036i	−0.708428	+	0.293440i	−0.707654	−	0.706559i	$-0.750246\pi$
$859$	−20.7631	+	8.60036i	−0.708428	+	0.293440i	−0.000774052		1.00000i	$0.500246\pi$
$860$	−62.6756	+	22.4803i	−2.13722	+	0.766571i
$861$	6.03628	−	14.5729i	0.205716	−	0.496642i
$862$	−1.89097	−	0.423866i	−0.0644068	−	0.0144369i
$863$			30.7336i			1.04618i	0.852277	+	0.523091i	$0.175221\pi$
$863$			30.7336i			1.04618i	−0.852277	+	0.523091i	$0.824779\pi$
$864$	0.195691	+	0.168147i	0.00665756	+	0.00572049i
$865$		−	19.7731i		−	0.672306i
$866$	3.85097	−	17.1801i	0.130861	−	0.583805i
$867$	−15.5338	+	37.5019i	−0.527556	+	1.27363i
$868$	42.0769	−	15.0920i	1.42818	−	0.512255i
$869$	11.2899	+	27.2561i	0.382982	+	0.924601i
$870$	−28.9248	+	41.1038i	−0.980644	+	1.39355i
$871$	2.42811	+	19.3916i	0.0822732	+	0.657058i
$872$	36.3330	−	20.6379i	1.23039	−	0.698889i
$873$	10.1995	−	10.1995i	0.345200	−	0.345200i
$874$	−30.0949	+	5.23391i	−1.01797	+	0.177040i
$875$	5.23767	+	12.6448i	0.177066	+	0.427474i
$876$	0.401364	−	8.30061i	0.0135608	−	0.280452i
$877$	−15.5426	+	37.5233i	−0.524838	+	1.26707i	0.410029	+	0.912072i	$0.365519\pi$
$877$	−15.5426	+	37.5233i	−0.524838	+	1.26707i	−0.934867	+	0.354998i	$0.884481\pi$
$878$	−3.77853	−	5.96186i	−0.127519	−	0.201203i
$879$	3.75395			0.126617
$880$	−6.54835	+	67.5550i	−0.220745	+	2.27728i
$881$			7.29370i			0.245731i	0.992423	+	0.122865i	$0.0392084\pi$
$881$			7.29370i			0.245731i	−0.992423	+	0.122865i	$0.960792\pi$
$882$	−10.4295	+	6.61003i	−0.351179	+	0.222571i
$883$	43.4180	+	17.9843i	1.46113	+	0.605221i	0.964817	−	0.262921i	$-0.0846858\pi$
$883$	43.4180	+	17.9843i	1.46113	+	0.605221i	0.496316	+	0.868142i	$0.334686\pi$
$884$	−4.56253	+	0.348570i	−0.153454	+	0.0117237i
$885$	2.97138	+	7.17354i	0.0998818	+	0.241136i
$886$	−30.5306	+	5.30970i	−1.02570	+	0.178383i
$887$	−36.1831	−	36.1831i	−1.21491	−	1.21491i	−0.969392	−	0.245519i	$-0.921042\pi$
$887$	−36.1831	−	36.1831i	−1.21491	−	1.21491i	−0.245519	−	0.969392i	$-0.578958\pi$
$888$	−38.9791	−	30.3471i	−1.30805	−	1.01838i
$889$	−35.4548	−	35.4548i	−1.18912	−	1.18912i
$890$	−15.9752	+	22.7017i	−0.535491	+	0.760962i
$891$	17.4980	+	42.2439i	0.586205	+	1.41522i
$892$	10.5535	−	22.3582i	0.353358	−	0.748607i
$893$	19.4852	−	47.0415i	0.652048	−	1.57418i
$894$	3.07654	−	13.7252i	0.102895	−	0.459040i
$895$		−	37.7846i		−	1.26300i
$896$	24.5117	−	25.8851i	0.818879	−	0.864759i
$897$	−32.6786	−	25.4056i	−1.09111	−	0.848268i
$898$	−0.711027	+	3.17207i	−0.0237273	+	0.105853i
$899$	−28.3390	−	11.7384i	−0.945157	−	0.391497i
$900$	33.9308	+	16.0160i	1.13103	+	0.533868i
$901$	7.57442	−	3.13743i	0.252341	−	0.104523i
$902$	−8.41148	+	11.9532i	−0.280072	+	0.397997i
$903$	53.9859	+	53.9859i	1.79654	+	1.79654i
$904$	11.2417	−	14.4393i	0.373893	−	0.480244i
$905$	−4.91521	+	4.91521i	−0.163387	+	0.163387i
$906$	0.0680135	+	0.391076i	0.00225960	+	0.0129926i
$907$	9.91147	+	23.9284i	0.329105	+	0.794530i	0.998659	+	0.0517665i	$0.0164852\pi$
$907$	9.91147	+	23.9284i	0.329105	+	0.794530i	−0.669554	+	0.742763i	$0.733515\pi$
$908$	15.0687	+	16.6000i	0.500072	+	0.550889i
$909$	13.2746	+	5.49852i	0.440290	+	0.182374i
$910$	53.7434	+	5.17209i	1.78158	+	0.171453i
$911$		−	11.7740i		−	0.390091i	−0.980794	−	0.195045i	$-0.937515\pi$
$911$		−	11.7740i		−	0.390091i	0.980794	−	0.195045i	$-0.0624854\pi$
$912$	4.34312	−	44.8051i	0.143815	−	1.48364i
$913$			6.69370i			0.221529i
$914$	12.1421	−	7.69546i	0.401625	−	0.254543i
$915$	−4.35265	+	10.5082i	−0.143894	+	0.347391i
$916$	−0.320826	+	6.63500i	−0.0106004	+	0.219227i
$917$	−30.7841	+	12.7512i	−1.01658	+	0.421082i
$918$	−0.00701304	−	0.0403248i	−0.000231465	−	0.00133092i
$919$	23.0049	+	23.0049i	0.758863	+	0.758863i	0.976115	−	0.217253i	$-0.0697096\pi$
$919$	23.0049	+	23.0049i	0.758863	+	0.758863i	−0.217253	+	0.976115i	$0.569710\pi$
$920$	38.7944	−	22.0361i	1.27901	−	0.726508i
$921$	−41.2292	−	41.2292i	−1.35855	−	1.35855i
$922$	22.2202	−	31.5762i	0.731784	−	1.03991i
$923$	12.0258	−	43.7701i	0.395833	−	1.44071i
$924$	73.2530	−	26.2741i	2.40985	−	0.864355i
$925$	41.5166	+	17.1968i	1.36506	+	0.565426i
$926$	−6.58283	−	1.47556i	−0.216325	−	0.0484898i
$927$	37.2219			1.22253
$928$	−24.3924	+	1.84660i	−0.800718	+	0.0606175i
$929$			30.6659i			1.00611i	0.864253	+	0.503057i	$0.167791\pi$
$929$			30.6659i			1.00611i	−0.864253	+	0.503057i	$0.832209\pi$
$930$	−18.0326	+	80.4479i	−0.591312	+	2.63799i
$931$	−12.4501	−	5.15700i	−0.408036	−	0.169014i
$932$	−13.7943	−	38.4589i	−0.451847	−	1.25976i
$933$	45.6783	−	18.9206i	1.49544	−	0.619432i
$934$	32.5448	+	22.9019i	1.06490	+	0.749372i
$935$	7.61343	−	7.61343i	0.248986	−	0.248986i
$936$	24.3661	−	18.1849i	0.796432	−	0.594392i
$937$	−32.9639	−	32.9639i	−1.07688	−	1.07688i	−0.996787	−	0.0800959i	$-0.974477\pi$
$937$	−32.9639	−	32.9639i	−1.07688	−	1.07688i	−0.0800959	−	0.996787i	$-0.525523\pi$
$938$	4.13849	+	23.7962i	0.135126	+	0.776973i
$939$	18.2815	+	44.1356i	0.596596	+	1.44031i
$940$	−3.59182	+	74.2825i	−0.117152	+	2.42283i
$941$	11.3055	−	27.2939i	0.368549	−	0.889756i	−0.625439	−	0.780273i	$-0.715080\pi$
$941$	11.3055	−	27.2939i	0.368549	−	0.889756i	0.993989	−	0.109484i	$-0.0349198\pi$
$942$	−29.3789	−	46.3548i	−0.957216	−	1.51032i
$943$	9.60806			0.312881
$944$	−1.77628	+	3.33556i	−0.0578131	+	0.108563i
$945$			0.482948i			0.0157103i
$946$	−37.8717	−	59.7549i	−1.23131	−	1.94280i
$947$	14.1486	−	34.1577i	0.459768	−	1.10998i	−0.508724	−	0.860930i	$-0.669882\pi$
$947$	14.1486	−	34.1577i	0.459768	−	1.10998i	0.968491	−	0.249048i	$-0.0801176\pi$
$948$	19.2088	+	21.1608i	0.623873	+	0.687272i
$949$	5.90686	+	1.62290i	0.191745	+	0.0526817i
$950$	7.01626	+	40.3433i	0.227638	+	1.30891i
$951$	−21.4716	+	21.4716i	−0.696263	+	0.696263i
$952$	−5.61197	+	0.698765i	−0.181885	+	0.0226471i
$953$	−23.3545	+	23.3545i	−0.756527	+	0.756527i	−0.975689	−	0.219161i	$-0.929668\pi$
$953$	−23.3545	+	23.3545i	−0.756527	+	0.756527i	0.219161	+	0.975689i	$0.429668\pi$
$954$	−31.3498	+	44.5498i	−1.01499	+	1.44235i
$955$	−18.4913	−	44.6420i	−0.598365	−	1.44458i
$956$	41.1035	+	19.4017i	1.32938	+	0.627496i
$957$	−49.3362	−	20.4357i	−1.59481	−	0.660594i
$958$	7.94044	−	35.4243i	0.256544	−	1.14451i
$959$	12.0172			0.388057
$960$	16.1232	+	63.7410i	0.520373	+	2.05723i
$961$	−19.3150			−0.623065
$962$	28.0965	−	23.1634i	0.905868	−	0.746819i
$963$	−13.5333	+	32.6722i	−0.436104	+	1.05285i
$964$	8.35409	+	3.94331i	0.269067	+	0.127005i
$965$	20.2108	−	8.37160i	0.650610	−	0.269491i
$966$	−41.8368	−	29.4407i	−1.34608	−	0.947239i
$967$	−4.88330	−	4.88330i	−0.157036	−	0.157036i	0.624216	−	0.781252i	$-0.285419\pi$
$967$	−4.88330	−	4.88330i	−0.157036	−	0.157036i	−0.781252	+	0.624216i	$0.785419\pi$
$968$	−40.6852	+	5.06584i	−1.30767	+	0.162822i
$969$	−5.04953	+	5.04953i	−0.162214	+	0.162214i
$970$	−22.6527	+	3.93963i	−0.727336	+	0.126494i
$971$	18.0792	+	43.6470i	0.580189	+	1.40070i	0.892642	+	0.450767i	$0.148849\pi$
$971$	18.0792	+	43.6470i	0.580189	+	1.40070i	−0.312453	+	0.949933i	$0.601151\pi$
$972$	29.5875	+	32.5943i	0.949021	+	1.04546i
$973$	−7.41705	+	17.9063i	−0.237780	+	0.574051i
$974$	19.9031	+	31.4036i	0.637736	+	1.00624i
$975$	−34.0572	+	43.8069i	−1.09070	+	1.40294i
$976$	−5.29491	+	1.61512i	−0.169486	+	0.0516987i
$977$	−25.7766			−0.824667			−0.412333	−	0.911033i	$-0.635286\pi$
$977$	−25.7766			−0.824667			−0.412333	+	0.911033i	$0.635286\pi$
$978$	27.5852	−	17.4831i	0.882079	−	0.559047i
$979$	−27.2485	−	11.2867i	−0.870865	−	0.360724i
$980$	19.6598	+	0.950620i	0.628009	+	0.0303665i
$981$	40.6918	−	16.8551i	1.29919	−	0.538142i
$982$	0.603040	+	3.46747i	0.0192438	+	0.110651i
$983$	16.0467	−	16.0467i	0.511810	−	0.511810i	−0.403271	−	0.915081i	$-0.632127\pi$
$983$	16.0467	−	16.0467i	0.511810	−	0.511810i	0.915081	+	0.403271i	$0.132127\pi$
$984$	−3.76057	+	13.6504i	−0.119883	+	0.435159i
$985$	27.7377	−	27.7377i	0.883798	−	0.883798i
$986$	3.17361	+	2.23327i	0.101068	+	0.0711219i
$987$	78.7818	−	32.6325i	2.50765	−	1.03870i
$988$	31.5342	+	10.3260i	1.00324	+	0.328513i
$989$	−17.7968	+	42.9652i	−0.565904	+	1.36621i
$990$	−15.6478	+	69.8089i	−0.497321	+	2.21867i
$991$	25.9658			0.824832			0.412416	−	0.910996i	$-0.364685\pi$
$991$	25.9658			0.824832			0.412416	+	0.910996i	$0.364685\pi$
$992$	−35.8065	+	18.1101i	−1.13686	+	0.574997i
$993$		−	58.5168i		−	1.85697i
$994$	12.2706	−	54.7421i	0.389199	−	1.73632i
$995$	70.3008	+	29.1196i	2.22869	+	0.923152i
$996$	2.18921	+	6.10358i	0.0693678	+	0.193399i
$997$	−51.8584	+	21.4804i	−1.64237	+	0.680292i	−0.996534	−	0.0831830i	$-0.973491\pi$
$997$	−51.8584	+	21.4804i	−1.64237	+	0.680292i	−0.645837	+	0.763475i	$0.723491\pi$
$998$	−34.9491	+	49.6646i	−1.10629	+	1.57211i
$999$	0.230315	+	0.230315i	0.00728686	+	0.00728686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bg.a.77.5	✓	216
13.12	even	2	inner	416.2.bg.a.77.50	yes	216
32.5	even	8	inner	416.2.bg.a.389.50	yes	216
416.389	even	8	inner	416.2.bg.a.389.5	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bg.a.77.5	✓	216	1.1	even	1	trivial
416.2.bg.a.77.50	yes	216	13.12	even	2	inner
416.2.bg.a.389.5	yes	216	416.389	even	8	inner
416.2.bg.a.389.50	yes	216	32.5	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.37997 - 0.309324i) q^{2} +(-0.935921 + 2.25951i) q^{3} +(1.80864 + 0.853715i) q^{4} +(-1.28599 - 3.10465i) q^{5} +(1.99046 - 2.82856i) q^{6} +(2.22807 + 2.22807i) q^{7} +(-2.23179 - 1.73756i) q^{8} +(-2.10813 - 2.10813i) q^{9} +(0.814283 + 4.68210i) q^{10} +(-4.66495 + 1.93228i) q^{11} +(-3.62172 + 3.28763i) q^{12} +(-1.78296 - 3.13385i) q^{13} +(-2.38548 - 3.76387i) q^{14} +8.21857 q^{15} +(2.54234 + 3.08812i) q^{16} -0.634552i q^{17} +(2.25707 + 3.56126i) q^{18} +(-1.76091 + 4.25122i) q^{19} +(0.324600 - 6.71304i) q^{20} +(-7.11965 + 2.94906i) q^{21} +(7.03519 - 1.22352i) q^{22} +(-3.31921 - 3.31921i) q^{23} +(6.01481 - 3.41655i) q^{24} +(-4.44953 + 4.44953i) q^{25} +(1.49106 + 4.87614i) q^{26} +(-0.0421381 + 0.0174542i) q^{27} +(2.12763 + 5.93191i) q^{28} +(1.65485 - 3.99517i) q^{29} +(-11.3414 - 2.54220i) q^{30} -7.09331i q^{31} +(-2.55313 - 5.04792i) q^{32} -12.3490i q^{33} +(-0.196282 + 0.875664i) q^{34} +(4.05210 - 9.78263i) q^{35} +(-2.01310 - 5.61259i) q^{36} +(-2.73286 - 6.59771i) q^{37} +(3.74501 - 5.32187i) q^{38} +(8.74970 - 1.09559i) q^{39} +(-2.52444 + 9.16340i) q^{40} +(-1.44734 + 1.44734i) q^{41} +(10.7371 - 1.86733i) q^{42} +(-3.79133 - 9.15307i) q^{43} +(-10.0868 - 0.487734i) q^{44} +(-3.83398 + 9.25604i) q^{45} +(3.55370 + 5.60712i) q^{46} -11.0654 q^{47} +(-9.35709 + 2.85421i) q^{48} +2.92859i q^{49} +(7.51656 - 4.76387i) q^{50} +(1.43378 + 0.593891i) q^{51} +(-0.549316 - 7.19015i) q^{52} +(4.94432 + 11.9366i) q^{53} +(0.0635484 - 0.0110519i) q^{54} +(11.9981 + 11.9981i) q^{55} +(-1.10119 - 8.84399i) q^{56} +(-7.95762 - 7.95762i) q^{57} +(-3.51945 + 5.00133i) q^{58} +(0.361544 + 0.872845i) q^{59} +(14.8644 + 7.01632i) q^{60} +(-0.529611 + 1.27860i) q^{61} +(-2.19413 + 9.78856i) q^{62} -9.39414i q^{63} +(1.96180 + 7.75573i) q^{64} +(-7.43664 + 9.56556i) q^{65} +(-3.81983 + 17.0412i) q^{66} +(-5.00766 - 2.07424i) q^{67} +(0.541727 - 1.14768i) q^{68} +(10.6063 - 4.39328i) q^{69} +(-8.61778 + 12.2463i) q^{70} +(8.90211 + 8.90211i) q^{71} +(1.04192 + 8.36792i) q^{72} +(-1.20136 + 1.20136i) q^{73} +(1.73044 + 9.94999i) q^{74} +(-5.88936 - 14.2182i) q^{75} +(-6.81419 + 6.18560i) q^{76} +(-14.6991 - 6.08857i) q^{77} +(-12.4132 - 1.19461i) q^{78} -5.84275i q^{79} +(6.31811 - 11.8643i) q^{80} -9.05560i q^{81} +(2.44499 - 1.54959i) q^{82} +(0.507311 - 1.22476i) q^{83} +(-15.3945 - 0.744380i) q^{84} +(-1.97006 + 0.816026i) q^{85} +(2.40066 + 13.8037i) q^{86} +(7.47832 + 7.47832i) q^{87} +(13.7686 + 3.79315i) q^{88} +(4.13029 + 4.13029i) q^{89} +(8.15388 - 11.5871i) q^{90} +(3.00988 - 10.9550i) q^{91} +(-3.16959 - 8.83691i) q^{92} +(16.0274 + 6.63878i) q^{93} +(15.2699 + 3.42279i) q^{94} +15.4630 q^{95} +(13.7954 - 1.04436i) q^{96} +4.83815i q^{97} +(0.905884 - 4.04137i) q^{98} +(13.9078 + 5.76082i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38}+ \cdots + 112 q^{95}+O(q^{100}) \) 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more