LMFDB - Embedded newform 416.2.bg.a.77.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(77,416)]

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([0, 7, 4]))

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

//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: 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			77.4
Character	$\chi$	$=$	416.77
Dual form			416.2.bg.a.389.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39490 + 0.232927i) q^{2} +(0.834650 - 2.01502i) q^{3} +(1.89149 - 0.649819i) q^{4} +(1.24361 + 3.00234i) q^{5} +(-0.694900 + 3.00517i) q^{6} +(-2.87336 - 2.87336i) q^{7} +(-2.48708 + 1.34701i) q^{8} +(-1.24236 - 1.24236i) q^{9} +(-2.43404 - 3.89829i) q^{10} +(3.47808 - 1.44067i) q^{11} +(0.269331 - 4.35377i) q^{12} +(0.827643 - 3.50927i) q^{13} +(4.67734 + 3.33877i) q^{14} +7.08777 q^{15} +(3.15547 - 2.45825i) q^{16} +2.25511i q^{17} +(2.02235 + 1.44359i) q^{18} +(1.81775 - 4.38843i) q^{19} +(4.30326 + 4.87078i) q^{20} +(-8.18815 + 3.39164i) q^{21} +(-4.51601 + 2.81973i) q^{22} +(-1.17023 - 1.17023i) q^{23} +(0.638421 + 6.13581i) q^{24} +(-3.93195 + 3.93195i) q^{25} +(-0.337075 + 5.08787i) q^{26} +(2.50475 - 1.03750i) q^{27} +(-7.30210 - 3.56777i) q^{28} +(1.76433 - 4.25947i) q^{29} +(-9.88673 + 1.65093i) q^{30} +2.08147i q^{31} +(-3.82897 + 4.16401i) q^{32} -8.21088i q^{33} +(-0.525277 - 3.14566i) q^{34} +(5.05347 - 12.2002i) q^{35} +(-3.15722 - 1.54260i) q^{36} +(2.27537 + 5.49323i) q^{37} +(-1.51339 + 6.54482i) q^{38} +(-6.38048 - 4.59674i) q^{39} +(-7.13715 - 5.79190i) q^{40} +(6.74017 - 6.74017i) q^{41} +(10.6316 - 6.63824i) q^{42} +(-0.248187 - 0.599175i) q^{43} +(5.64259 - 4.98514i) q^{44} +(2.18498 - 5.27500i) q^{45} +(1.90493 + 1.35978i) q^{46} -10.2817 q^{47} +(-2.31973 - 8.41013i) q^{48} +9.51242i q^{49} +(4.56882 - 6.40054i) q^{50} +(4.54411 + 1.88223i) q^{51} +(-0.714916 - 7.17558i) q^{52} +(-1.96533 - 4.74473i) q^{53} +(-3.25222 + 2.03064i) q^{54} +(8.65077 + 8.65077i) q^{55} +(11.0167 + 3.27582i) q^{56} +(-7.32561 - 7.32561i) q^{57} +(-1.46892 + 6.35250i) q^{58} +(1.98398 + 4.78976i) q^{59} +(13.4064 - 4.60577i) q^{60} +(-5.10645 + 12.3281i) q^{61} +(-0.484831 - 2.90345i) q^{62} +7.13950i q^{63} +(4.37112 - 6.70025i) q^{64} +(11.5653 - 1.87930i) q^{65} +(1.91254 + 11.4534i) q^{66} +(-10.1684 - 4.21189i) q^{67} +(1.46542 + 4.26552i) q^{68} +(-3.33477 + 1.38131i) q^{69} +(-4.20734 + 18.1951i) q^{70} +(8.84949 + 8.84949i) q^{71} +(4.76332 + 1.41637i) q^{72} +(8.94747 - 8.94747i) q^{73} +(-4.45343 - 7.13250i) q^{74} +(4.64117 + 11.2048i) q^{75} +(0.586564 - 9.48188i) q^{76} +(-14.1334 - 5.85423i) q^{77} +(9.97083 + 4.92580i) q^{78} -6.72086i q^{79} +(11.3047 + 6.41669i) q^{80} -11.1840i q^{81} +(-7.83189 + 10.9718i) q^{82} +(-4.41803 + 10.6661i) q^{83} +(-13.2838 + 11.7361i) q^{84} +(-6.77062 + 2.80448i) q^{85} +(0.485759 + 0.777980i) q^{86} +(-7.11034 - 7.11034i) q^{87} +(-6.70967 + 8.26808i) q^{88} +(-2.18425 - 2.18425i) q^{89} +(-1.81913 + 7.86703i) q^{90} +(-12.4615 + 7.70530i) q^{91} +(-2.97392 - 1.45304i) q^{92} +(4.19422 + 1.73730i) q^{93} +(14.3419 - 2.39488i) q^{94} +15.4361 q^{95} +(5.19473 + 11.1910i) q^{96} +6.54340i q^{97} +(-2.21570 - 13.2689i) q^{98} +(-6.11086 - 2.53120i) 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 $

$2$	−1.39490	+	0.232927i	−0.986343	+	0.164704i
$2$	−1.39490	+	0.232927i	−0.986343	+	0.164704i
$3$	0.834650	−	2.01502i	0.481885	−	1.16337i	−0.476827	−	0.878997i	$-0.658213\pi$
$3$	0.834650	−	2.01502i	0.481885	−	1.16337i	0.958712	−	0.284377i	$-0.0917868\pi$
$4$	1.89149	−	0.649819i	0.945745	−	0.324910i
$5$	1.24361	+	3.00234i	0.556159	+	1.34269i	0.912785	+	0.408440i	$0.133927\pi$
$5$	1.24361	+	3.00234i	0.556159	+	1.34269i	−0.356626	+	0.934247i	$0.616073\pi$
$6$	−0.694900	+	3.00517i	−0.283692	+	1.22685i
$7$	−2.87336	−	2.87336i	−1.08603	−	1.08603i	−0.995933	−	0.0900958i	$-0.971283\pi$
$7$	−2.87336	−	2.87336i	−1.08603	−	1.08603i	−0.0900958	−	0.995933i	$-0.528717\pi$
$8$	−2.48708	+	1.34701i	−0.879315	+	0.476241i
$9$	−1.24236	−	1.24236i	−0.414120	−	0.414120i
$10$	−2.43404	−	3.89829i	−0.769710	−	1.23275i
$11$	3.47808	−	1.44067i	1.04868	−	0.434378i	0.209261	−	0.977860i	$-0.432894\pi$
$11$	3.47808	−	1.44067i	1.04868	−	0.434378i	0.839421	+	0.543481i	$0.182894\pi$
$12$	0.269331	−	4.35377i	0.0777491	−	1.25682i
$13$	0.827643	−	3.50927i	0.229547	−	0.973298i
$13$	0.827643	−	3.50927i	0.229547	−	0.973298i
$14$	4.67734	+	3.33877i	1.25007	+	0.892323i
$15$	7.08777			1.83005
$16$	3.15547	−	2.45825i	0.788867	−	0.614564i
$17$			2.25511i			0.546945i	0.961880	+	0.273473i	$0.0881723\pi$
$17$			2.25511i			0.546945i	−0.961880	+	0.273473i	$0.911828\pi$
$18$	2.02235	+	1.44359i	0.476671	+	0.340257i
$19$	1.81775	−	4.38843i	0.417020	−	1.00678i	−0.566186	−	0.824277i	$-0.691582\pi$
$19$	1.81775	−	4.38843i	0.417020	−	1.00678i	0.983206	−	0.182498i	$-0.0584183\pi$
$20$	4.30326	+	4.87078i	0.962237	+	1.08914i
$21$	−8.18815	+	3.39164i	−1.78680	+	0.740117i
$22$	−4.51601	+	2.81973i	−0.962816	+	0.601168i
$23$	−1.17023	−	1.17023i	−0.244010	−	0.244010i	0.574497	−	0.818507i	$-0.305198\pi$
$23$	−1.17023	−	1.17023i	−0.244010	−	0.244010i	−0.818507	+	0.574497i	$0.805198\pi$
$24$	0.638421	+	6.13581i	0.130317	+	1.25247i
$25$	−3.93195	+	3.93195i	−0.786390	+	0.786390i
$26$	−0.337075	+	5.08787i	−0.0661058	+	0.997813i
$27$	2.50475	−	1.03750i	0.482040	−	0.199667i
$28$	−7.30210	−	3.56777i	−1.37997	−	0.674245i
$29$	1.76433	−	4.25947i	0.327628	−	0.790964i	−0.671139	−	0.741331i	$-0.734195\pi$
$29$	1.76433	−	4.25947i	0.327628	−	0.790964i	0.998768	−	0.0496331i	$-0.0158052\pi$
$30$	−9.88673	+	1.65093i	−1.80506	+	0.301418i
$31$			2.08147i			0.373844i	0.982375	+	0.186922i	$0.0598511\pi$
$31$			2.08147i			0.373844i	−0.982375	+	0.186922i	$0.940149\pi$
$32$	−3.82897	+	4.16401i	−0.676873	+	0.736100i
$33$		−	8.21088i		−	1.42933i
$34$	−0.525277	−	3.14566i	−0.0900842	−	0.539476i
$35$	5.05347	−	12.2002i	0.854192	−	2.06220i
$36$	−3.15722	−	1.54260i	−0.526203	−	0.257100i
$37$	2.27537	+	5.49323i	0.374068	+	0.903081i	0.993052	+	0.117677i	$0.0375447\pi$
$37$	2.27537	+	5.49323i	0.374068	+	0.903081i	−0.618984	+	0.785404i	$0.712455\pi$
$38$	−1.51339	+	6.54482i	−0.245505	+	1.06171i
$39$	−6.38048	−	4.59674i	−1.02169	−	0.736067i
$40$	−7.13715	−	5.79190i	−1.12848	−	0.915780i
$41$	6.74017	−	6.74017i	1.05264	−	1.05264i	0.0541020	−	0.998535i	$-0.482770\pi$
$41$	6.74017	−	6.74017i	1.05264	−	1.05264i	0.998535	−	0.0541020i	$-0.0172296\pi$
$42$	10.6316	−	6.63824i	1.64050	−	1.02430i
$43$	−0.248187	−	0.599175i	−0.0378481	−	0.0913734i	0.903825	−	0.427902i	$-0.140747\pi$
$43$	−0.248187	−	0.599175i	−0.0378481	−	0.0913734i	−0.941673	+	0.336529i	$0.890747\pi$
$44$	5.64259	−	4.98514i	0.850652	−	0.751538i
$45$	2.18498	−	5.27500i	0.325717	−	0.786350i
$46$	1.90493	+	1.35978i	0.280867	+	0.200488i
$47$	−10.2817			−1.49973			−0.749867	−	0.661589i	$-0.769883\pi$
$47$	−10.2817			−1.49973			−0.749867	+	0.661589i	$0.769883\pi$
$48$	−2.31973	−	8.41013i	−0.334824	−	1.21390i
$49$			9.51242i			1.35892i
$50$	4.56882	−	6.40054i	0.646129	−	0.905172i
$51$	4.54411	+	1.88223i	0.636302	+	0.263565i
$52$	−0.714916	−	7.17558i	−0.0991410	−	0.995073i
$53$	−1.96533	−	4.74473i	−0.269959	−	0.651739i	0.729522	−	0.683957i	$-0.239743\pi$
$53$	−1.96533	−	4.74473i	−0.269959	−	0.651739i	−0.999481	+	0.0322189i	$0.989743\pi$
$54$	−3.25222	+	2.03064i	−0.442571	+	0.276335i
$55$	8.65077	+	8.65077i	1.16647	+	1.16647i
$56$	11.0167	+	3.27582i	1.47217	+	0.437750i
$57$	−7.32561	−	7.32561i	−0.970301	−	0.970301i
$58$	−1.46892	+	6.35250i	−0.192879	+	0.834124i
$59$	1.98398	+	4.78976i	0.258293	+	0.623574i	0.998826	−	0.0484460i	$-0.0154269\pi$
$59$	1.98398	+	4.78976i	0.258293	+	0.623574i	−0.740533	+	0.672020i	$0.765427\pi$
$60$	13.4064	−	4.60577i	1.73076	−	0.594602i
$61$	−5.10645	+	12.3281i	−0.653814	+	1.57845i	0.153383	+	0.988167i	$0.450983\pi$
$61$	−5.10645	+	12.3281i	−0.653814	+	1.57845i	−0.807198	+	0.590281i	$0.799017\pi$
$62$	−0.484831	−	2.90345i	−0.0615736	−	0.368738i
$63$			7.13950i			0.899492i
$64$	4.37112	−	6.70025i	0.546390	−	0.837531i
$65$	11.5653	−	1.87930i	1.43450	−	0.233099i
$66$	1.91254	+	11.4534i	0.235417	+	1.40981i
$67$	−10.1684	−	4.21189i	−1.24227	−	0.514564i	−0.337845	−	0.941202i	$-0.609698\pi$
$67$	−10.1684	−	4.21189i	−1.24227	−	0.514564i	−0.904423	+	0.426637i	$0.859698\pi$
$68$	1.46542	+	4.26552i	0.177708	+	0.517271i
$69$	−3.33477	+	1.38131i	−0.401460	+	0.166290i
$70$	−4.20734	+	18.1951i	−0.502873	+	2.17473i
$71$	8.84949	+	8.84949i	1.05024	+	1.05024i	0.998669	+	0.0515716i	$0.0164231\pi$
$71$	8.84949	+	8.84949i	1.05024	+	1.05024i	0.0515716	+	0.998669i	$0.483577\pi$
$72$	4.76332	+	1.41637i	0.561362	+	0.166921i
$73$	8.94747	−	8.94747i	1.04722	−	1.04722i	0.0483937	−	0.998828i	$-0.484590\pi$
$73$	8.94747	−	8.94747i	1.04722	−	1.04722i	0.998828	−	0.0483937i	$-0.0154102\pi$
$74$	−4.45343	−	7.13250i	−0.517701	−	0.829137i
$75$	4.64117	+	11.2048i	0.535916	+	1.29382i
$76$	0.586564	−	9.48188i	0.0672835	−	1.08765i
$77$	−14.1334	−	5.85423i	−1.61065	−	0.667152i
$78$	9.97083	+	4.92580i	1.12897	+	0.557737i
$79$		−	6.72086i		−	0.756156i	−0.925774	−	0.378078i	$-0.876585\pi$
$79$		−	6.72086i		−	0.756156i	0.925774	−	0.378078i	$-0.123415\pi$
$80$	11.3047	+	6.41669i	1.26390	+	0.717407i
$81$		−	11.1840i		−	1.24266i
$82$	−7.83189	+	10.9718i	−0.864888	+	1.21164i
$83$	−4.41803	+	10.6661i	−0.484941	+	1.17075i	0.472294	+	0.881441i	$0.343426\pi$
$83$	−4.41803	+	10.6661i	−0.484941	+	1.17075i	−0.957235	+	0.289311i	$0.906574\pi$
$84$	−13.2838	+	11.7361i	−1.44939	+	1.28051i
$85$	−6.77062	+	2.80448i	−0.734377	+	0.304189i
$86$	0.485759	+	0.777980i	0.0523808	+	0.0838918i
$87$	−7.11034	−	7.11034i	−0.762308	−	0.762308i
$88$	−6.70967	+	8.26808i	−0.715253	+	0.881380i
$89$	−2.18425	−	2.18425i	−0.231530	−	0.231530i	0.581801	−	0.813331i	$-0.302348\pi$
$89$	−2.18425	−	2.18425i	−0.231530	−	0.231530i	−0.813331	+	0.581801i	$0.802348\pi$
$90$	−1.81913	+	7.86703i	−0.191753	+	0.829258i
$91$	−12.4615	+	7.70530i	−1.30632	+	0.807735i
$92$	−2.97392	−	1.45304i	−0.310052	−	0.151490i
$93$	4.19422	+	1.73730i	0.434920	+	0.180150i
$94$	14.3419	−	2.39488i	1.47925	−	0.247013i
$95$	15.4361			1.58371
$96$	5.19473	+	11.1910i	0.530185	+	1.14217i
$97$			6.54340i			0.664382i	0.943212	+	0.332191i	$0.107788\pi$
$97$			6.54340i			0.664382i	−0.943212	+	0.332191i	$0.892212\pi$
$98$	−2.21570	−	13.2689i	−0.223819	−	1.34036i
$99$	−6.11086	−	2.53120i	−0.614165	−	0.254395i
$100$	−4.88219	+	9.99231i	−0.488219	+	0.999231i
$101$	−2.72602	+	1.12915i	−0.271249	+	0.112355i	−0.514162	−	0.857693i	$-0.671897\pi$
$101$	−2.72602	+	1.12915i	−0.271249	+	0.112355i	0.242913	+	0.970048i	$0.421897\pi$
$102$	−6.77699	−	1.56708i	−0.671022	−	0.155164i
$103$	−5.98842	+	5.98842i	−0.590056	+	0.590056i	−0.937647	−	0.347590i	$-0.887000\pi$
$103$	−5.98842	+	5.98842i	−0.590056	+	0.590056i	0.347590	+	0.937647i	$0.387000\pi$
$104$	2.66862	+	9.84269i	0.261680	+	0.965155i
$105$	−20.3657	−	20.3657i	−1.98749	−	1.98749i
$106$	3.84661	+	6.16064i	0.373616	+	0.598374i
$107$	5.47830	+	13.2258i	0.529608	+	1.27859i	0.931780	+	0.363022i	$0.118255\pi$
$107$	5.47830	+	13.2258i	0.529608	+	1.27859i	−0.402173	+	0.915564i	$0.631745\pi$
$108$	4.06353	−	3.59006i	0.391013	−	0.345454i
$109$	−5.47648	+	13.2214i	−0.524551	+	1.26638i	0.410498	+	0.911862i	$0.365355\pi$
$109$	−5.47648	+	13.2214i	−0.524551	+	1.26638i	−0.935049	+	0.354518i	$0.884645\pi$
$110$	−14.0819	−	10.0520i	−1.34266	−	0.958416i
$111$	12.9681			1.23088
$112$	−16.1303	−	2.00335i	−1.52417	−	0.189299i
$113$			16.4622i			1.54864i	0.632796	+	0.774319i	$0.281907\pi$
$113$			16.4622i			1.54864i	−0.632796	+	0.774319i	$0.718093\pi$
$114$	11.9248	+	8.51216i	1.11686	+	0.797237i
$115$	2.05812	−	4.96874i	0.191921	−	0.463337i
$116$	0.569327	−	9.20325i	0.0528607	−	0.854500i
$117$	−5.38801	+	3.33155i	−0.498122	+	0.308002i
$118$	−3.88312	−	6.21911i	−0.357471	−	0.572516i
$119$	6.47976	−	6.47976i	0.593998	−	0.593998i
$120$	−17.6278	+	9.54731i	−1.60919	+	0.871546i
$121$	2.24337	−	2.24337i	0.203943	−	0.203943i
$122$	4.25145	−	18.3859i	0.384908	−	1.66458i
$123$	−7.95592	−	19.2073i	−0.717361	−	1.73186i
$124$	1.35258	+	3.93709i	0.121465	+	0.353561i
$125$	−1.68317	−	0.697192i	−0.150547	−	0.0623588i
$126$	−1.66298	−	9.95888i	−0.148150	−	0.887208i
$127$	13.6231			1.20886			0.604428	−	0.796660i	$-0.293402\pi$
$127$	13.6231			1.20886			0.604428	+	0.796660i	$0.293402\pi$
$128$	−4.53660	+	10.3643i	−0.400983	+	0.916086i
$129$	−1.41450			−0.124540
$130$	−15.6947	+	5.31531i	−1.37652	+	0.466184i
$131$	−2.67771	+	6.46457i	−0.233953	+	0.564812i	−0.996636	−	0.0819607i	$-0.973882\pi$
$131$	−2.67771	+	6.46457i	−0.233953	+	0.564812i	0.762683	+	0.646773i	$0.223882\pi$
$132$	−5.33559	−	15.5308i	−0.464403	−	1.35178i
$133$	−17.8326	+	7.38651i	−1.54628	+	0.640491i
$134$	15.1650	+	3.50667i	1.31005	+	0.302930i
$135$	6.22987	+	6.22987i	0.536182	+	0.536182i
$136$	−3.03766	−	5.60864i	−0.260478	−	0.480937i
$137$	−0.119983	+	0.119983i	−0.0102509	+	0.0102509i	−0.712214	−	0.701963i	$-0.752307\pi$
$137$	−0.119983	+	0.119983i	−0.0102509	+	0.0102509i	0.701963	+	0.712214i	$0.252307\pi$
$138$	4.32993	−	2.70355i	0.368588	−	0.230141i
$139$	−1.36639	−	3.29875i	−0.115895	−	0.279796i	0.855278	−	0.518169i	$-0.173386\pi$
$139$	−1.36639	−	3.29875i	−0.115895	−	0.279796i	−0.971174	+	0.238373i	$0.923386\pi$
$140$	1.63069	−	26.3603i	0.137818	−	2.22785i
$141$	−8.58159	+	20.7178i	−0.722700	+	1.74475i
$142$	−14.4054	−	10.2829i	−1.20888	−	0.862919i
$143$	−2.17709	−	13.3979i	−0.182058	−	1.12039i
$144$	−6.97426	−	0.866192i	−0.581188	−	0.0721827i
$145$	14.9825			1.24423
$146$	−10.3967	+	14.5649i	−0.860438	+	1.20540i
$147$	19.1678	+	7.93954i	1.58093	+	0.654843i
$148$	7.87344	+	8.91180i	0.647193	+	0.732546i
$149$	9.54946	−	3.95551i	0.782322	−	0.324048i	0.0444698	−	0.999011i	$-0.485840\pi$
$149$	9.54946	−	3.95551i	0.782322	−	0.324048i	0.737852	+	0.674962i	$0.235840\pi$
$150$	−9.08386	−	14.5485i	−0.741694	−	1.18788i
$151$	−6.06952	+	6.06952i	−0.493930	+	0.493930i	−0.909542	−	0.415612i	$-0.863567\pi$
$151$	−6.06952	+	6.06952i	−0.493930	+	0.493930i	0.415612	+	0.909542i	$0.363567\pi$
$152$	1.39039	+	13.3629i	0.112775	+	1.08387i
$153$	2.80166	−	2.80166i	0.226501	−	0.226501i
$154$	21.0782	+	4.87402i	1.69853	+	0.392760i
$155$	−6.24929	+	2.58854i	−0.501955	+	0.207917i
$156$	−15.0557	−	4.54852i	−1.20542	−	0.364173i
$157$	4.79664	−	11.5801i	0.382813	−	0.924193i	−0.608606	−	0.793473i	$-0.708271\pi$
$157$	4.79664	−	11.5801i	0.382813	−	0.924193i	0.991419	−	0.130721i	$-0.0417291\pi$
$158$	1.56547	+	9.37492i	0.124542	+	0.745829i
$159$	−11.2011			−0.888305
$160$	−17.2635	−	6.31746i	−1.36480	−	0.499439i
$161$			6.72499i			0.530004i
$162$	2.60505	+	15.6005i	0.204672	+	1.22569i
$163$	13.6962	+	5.67313i	1.07277	+	0.444354i	0.847966	−	0.530051i	$-0.177827\pi$
$163$	13.6962	+	5.67313i	1.07277	+	0.444354i	0.224800	+	0.974405i	$0.427827\pi$
$164$	8.36907	−	17.1289i	0.653514	−	1.33754i
$165$	24.6519	−	10.2111i	1.91914	−	0.794936i
$166$	3.67829	−	15.9072i	0.285491	−	1.23463i
$167$	7.47132	+	7.47132i	0.578148	+	0.578148i	0.934393	−	0.356245i	$-0.115943\pi$
$167$	7.47132	+	7.47132i	0.578148	+	0.578148i	−0.356245	+	0.934393i	$0.615943\pi$
$168$	15.7960	−	19.4648i	1.21869	−	1.50174i
$169$	−11.6300	−	5.80885i	−0.894616	−	0.446835i
$170$	8.79109	−	5.48903i	0.674246	−	0.420989i
$171$	−7.71030	+	3.19371i	−0.589622	+	0.244229i
$172$	−0.858798	−	0.972058i	−0.0654828	−	0.0741187i
$173$	−1.72425	−	0.714209i	−0.131093	−	0.0543003i	0.316173	−	0.948702i	$-0.397602\pi$
$173$	−1.72425	−	0.714209i	−0.131093	−	0.0543003i	−0.447265	+	0.894401i	$0.647602\pi$
$174$	11.5744	+	8.26202i	0.877453	+	0.626342i
$175$	22.5958			1.70809
$176$	7.43346	−	13.0960i	0.560318	−	0.987149i
$177$	11.3074			0.849918
$178$	3.55558	+	2.53804i	0.266502	+	0.190234i
$179$	3.94839	+	1.63548i	0.295116	+	0.122241i	0.525329	−	0.850899i	$-0.323942\pi$
$179$	3.94839	+	1.63548i	0.295116	+	0.122241i	−0.230213	+	0.973140i	$0.573942\pi$
$180$	0.705063	−	11.3974i	0.0525523	−	0.849515i
$181$	8.14284	+	19.6586i	0.605253	+	1.46121i	0.868109	+	0.496374i	$0.165336\pi$
$181$	8.14284	+	19.6586i	0.605253	+	1.46121i	−0.262856	+	0.964835i	$0.584664\pi$
$182$	15.5878	−	13.6507i	1.15545	−	1.01186i
$183$	20.5793	+	20.5793i	1.52126	+	1.52126i
$184$	4.48677	+	1.33414i	0.330769	+	0.0983541i
$185$	−13.6629	+	13.6629i	−1.00451	+	1.00451i
$186$	−6.25518	−	1.44642i	−0.458652	−	0.106056i
$187$	3.24887	+	7.84348i	0.237581	+	0.573572i
$188$	−19.4477	+	6.68122i	−1.41837	+	0.487278i
$189$	−10.1782	−	4.21594i	−0.740354	−	0.306665i
$190$	−21.5319	+	3.59549i	−1.56209	+	0.260844i
$191$	−6.30317			−0.456081			−0.228041	−	0.973652i	$-0.573232\pi$
$191$	−6.30317			−0.456081			−0.228041	+	0.973652i	$0.573232\pi$
$192$	−9.85281	−	14.4003i	−0.711065	−	1.03925i
$193$		−	8.56562i		−	0.616567i	−0.951295	−	0.308283i	$-0.900246\pi$
$193$		−	8.56562i		−	0.616567i	0.951295	−	0.308283i	$-0.0997545\pi$
$194$	−1.52414	−	9.12739i	−0.109427	−	0.655308i
$195$	5.86614	−	24.8729i	0.420083	−	1.78119i
$196$	6.18136	+	17.9927i	0.441526	+	1.28519i
$197$	0.635216	+	1.53355i	0.0452573	+	0.109261i	0.944892	−	0.327383i	$-0.106167\pi$
$197$	0.635216	+	1.53355i	0.0452573	+	0.109261i	−0.899634	+	0.436644i	$0.856167\pi$
$198$	9.11362	+	2.10739i	0.647677	+	0.149766i
$199$	8.74318	−	8.74318i	0.619788	−	0.619788i	−0.325689	−	0.945477i	$-0.605596\pi$
$199$	8.74318	−	8.74318i	0.619788	−	0.619788i	0.945477	+	0.325689i	$0.105596\pi$
$200$	4.48269	−	15.0755i	0.316974	−	1.06600i
$201$	−16.9741	+	16.9741i	−1.19726	+	1.19726i
$202$	3.53951	−	2.21002i	0.249039	−	0.155496i
$203$	−17.3086	+	7.16945i	−1.21482	+	0.503196i
$204$	9.81824	+	0.607372i	0.687414	+	0.0425245i
$205$	28.6184	+	11.8541i	1.99880	+	0.827929i
$206$	6.95838	−	9.74811i	0.484813	−	0.679183i
$207$			2.90769i			0.202099i
$208$	−6.01509	−	13.1080i	−0.417071	−	0.908874i
$209$		−	17.8821i		−	1.23693i
$210$	33.1519	+	23.6644i	2.28770	+	1.63300i
$211$	−19.4007	−	8.03605i	−1.33560	−	0.553224i	−0.403354	−	0.915044i	$-0.632156\pi$
$211$	−19.4007	−	8.03605i	−1.33560	−	0.553224i	−0.932248	+	0.361820i	$0.882156\pi$
$212$	−6.80062	−	7.69750i	−0.467069	−	0.528666i
$213$	25.2182	−	10.4457i	1.72792	−	0.715728i
$214$	−10.7223	−	17.1726i	−0.732963	−	1.17390i
$215$	1.49028	−	1.49028i	0.101636	−	0.101636i
$216$	−4.83199	+	5.95428i	−0.328775	+	0.405138i
$217$	5.98083	−	5.98083i	0.406005	−	0.406005i
$218$	4.55952	−	19.7181i	0.308810	−	1.33548i
$219$	−10.5614	−	25.4974i	−0.713670	−	1.72295i
$220$	21.9843	+	10.7414i	1.48218	+	0.724185i
$221$	7.91381	+	1.86643i	0.532341	+	0.125550i
$222$	−18.0892	+	3.02062i	−1.21407	+	0.202731i
$223$			7.18407i			0.481081i	0.970639	+	0.240540i	$0.0773246\pi$
$223$			7.18407i			0.481081i	−0.970639	+	0.240540i	$0.922675\pi$
$224$	22.9667	−	0.962697i	1.53453	−	0.0643229i
$225$	9.76979			0.651320
$226$	−3.83450	−	22.9632i	−0.255067	−	1.52749i
$227$	−12.3393	−	5.11112i	−0.818991	−	0.339237i	−0.0664560	−	0.997789i	$-0.521169\pi$
$227$	−12.3393	−	5.11112i	−0.818991	−	0.339237i	−0.752535	+	0.658552i	$0.771169\pi$
$228$	−18.6166	−	9.09599i	−1.23292	−	0.602397i
$229$	−4.99410	−	12.0568i	−0.330019	−	0.796737i	−0.998590	−	0.0530886i	$-0.983093\pi$
$229$	−4.99410	−	12.0568i	−0.330019	−	0.796737i	0.668570	−	0.743649i	$-0.266907\pi$
$230$	−1.71352	+	7.41029i	−0.112986	+	0.488620i
$231$	−23.5928	+	23.5928i	−1.55229	+	1.55229i
$232$	1.34953	+	12.9702i	0.0886010	+	0.851537i
$233$	−4.25171	−	4.25171i	−0.278539	−	0.278539i	0.553987	−	0.832525i	$-0.313106\pi$
$233$	−4.25171	−	4.25171i	−0.278539	−	0.278539i	−0.832525	+	0.553987i	$0.813106\pi$
$234$	6.73973	−	5.90219i	0.440590	−	0.385838i
$235$	−12.7864	−	30.8690i	−0.834091	−	2.01367i
$236$	6.86517	+	7.77056i	0.446884	+	0.505820i
$237$	−13.5427	−	5.60957i	−0.879692	−	0.364380i
$238$	−7.52930	+	10.5479i	−0.488052	+	0.683720i
$239$	−17.4282			−1.12734			−0.563668	−	0.826001i	$-0.690610\pi$
$239$	−17.4282			−1.12734			−0.563668	+	0.826001i	$0.690610\pi$
$240$	22.3652	−	17.4235i	1.44367	−	1.12468i
$241$	−8.34776			−0.537727			−0.268863	−	0.963178i	$-0.586648\pi$
$241$	−8.34776			−0.537727			−0.268863	+	0.963178i	$0.586648\pi$
$242$	−2.60674	+	3.65182i	−0.167567	+	0.234748i
$243$	−15.0217	−	6.22220i	−0.963643	−	0.399154i
$244$	−1.64779	+	26.6367i	−0.105489	+	1.70524i
$245$	−28.5595	+	11.8297i	−1.82460	+	0.755775i
$246$	15.5716	+	24.9391i	0.992809	+	1.59006i
$247$	−13.8958	−	10.0110i	−0.884166	−	0.636987i
$248$	−2.80377	−	5.17679i	−0.178040	−	0.328726i
$249$	17.8049	+	17.8049i	1.12834	+	1.12834i
$250$	2.51025	+	0.580457i	0.158762	+	0.0367113i
$251$	4.90082	−	2.02999i	0.309337	−	0.128132i	−0.222614	−	0.974907i	$-0.571459\pi$
$251$	4.90082	−	2.02999i	0.309337	−	0.128132i	0.531951	+	0.846775i	$0.321459\pi$
$252$	4.63938	+	13.5043i	0.292254	+	0.850690i
$253$	−5.75608	−	2.38424i	−0.361881	−	0.149896i
$254$	−19.0029	+	3.17319i	−1.19235	+	0.199104i
$255$			15.9837i			1.00094i
$256$	3.91397	−	15.5139i	0.244623	−	0.969618i
$257$	6.64251			0.414348			0.207174	−	0.978304i	$-0.433573\pi$
$257$	6.64251			0.414348			0.207174	+	0.978304i	$0.433573\pi$
$258$	1.97309	−	0.329476i	0.122839	−	0.0205123i
$259$	9.24607	−	22.3220i	0.574523	−	1.38702i
$260$	20.6545	−	11.0700i	1.28093	−	0.686535i
$261$	−7.48373	+	3.09986i	−0.463231	+	0.191877i
$262$	2.22937	−	9.64114i	0.137731	−	0.595632i
$263$	9.72619	−	9.72619i	0.599742	−	0.599742i	−0.340502	−	0.940244i	$-0.610597\pi$
$263$	9.72619	−	9.72619i	0.599742	−	0.599742i	0.940244	+	0.340502i	$0.110597\pi$
$264$	11.0602	+	20.4211i	0.680705	+	1.25683i
$265$	11.8012	−	11.8012i	0.724941	−	0.724941i
$266$	23.1542	−	14.4571i	1.41967	−	0.886423i
$267$	−6.22440	+	2.57823i	−0.380927	+	0.157785i
$268$	−21.9704	−	1.35912i	−1.34206	−	0.0830216i
$269$	−11.5448	−	4.78201i	−0.703898	−	0.291564i	0.00187871	−	0.999998i	$-0.499402\pi$
$269$	−11.5448	−	4.78201i	−0.703898	−	0.291564i	−0.705777	+	0.708434i	$0.749402\pi$
$270$	−10.1412	−	7.23894i	−0.617171	−	0.440548i
$271$	12.6024			0.765539			0.382769	−	0.923844i	$-0.374970\pi$
$271$	12.6024			0.765539			0.382769	+	0.923844i	$0.374970\pi$
$272$	5.54364	+	7.11594i	0.336133	+	0.431467i
$273$	5.12534	+	31.5415i	0.310199	+	1.90898i
$274$	0.139417	−	0.195312i	0.00842251	−	0.0117992i
$275$	−8.01102	+	19.3403i	−0.483083	+	1.16626i
$276$	−5.41009	+	4.77973i	−0.325649	+	0.287706i
$277$	−6.03291	−	14.5647i	−0.362482	−	0.875110i	−0.994936	−	0.100512i	$-0.967952\pi$
$277$	−6.03291	−	14.5647i	−0.362482	−	0.875110i	0.632453	−	0.774598i	$-0.282048\pi$
$278$	2.67434	+	4.28316i	0.160396	+	0.256887i
$279$	2.58594	−	2.58594i	0.154816	−	0.154816i
$280$	3.86538	+	37.1498i	0.231001	+	2.22013i
$281$	2.98916	+	2.98916i	0.178318	+	0.178318i	0.790622	−	0.612304i	$-0.209757\pi$
$281$	2.98916	+	2.98916i	0.178318	+	0.178318i	−0.612304	+	0.790622i	$0.709757\pi$
$282$	7.14472	−	30.8981i	0.425462	−	1.83996i
$283$	−18.8591	+	7.81169i	−1.12106	+	0.464357i	−0.864732	−	0.502234i	$-0.832512\pi$
$283$	−18.8591	+	7.81169i	−1.12106	+	0.464357i	−0.256325	+	0.966591i	$0.582512\pi$
$284$	22.4893	+	10.9881i	1.33449	+	0.652027i
$285$	12.8838	−	31.1042i	0.763169	−	1.84245i
$286$	6.15756	+	18.1816i	0.364104	+	1.07510i
$287$	−38.7339			−2.28639
$288$	9.93015	−	0.416243i	0.585140	−	0.0245273i
$289$	11.9145			0.700851
$290$	−20.8991	+	3.48984i	−1.22724	+	0.204930i
$291$	13.1851	+	5.46145i	0.772925	+	0.320156i
$292$	11.1098	−	22.7383i	0.650152	−	1.33066i
$293$	−3.52542	−	8.51111i	−0.205957	−	0.497224i	0.786822	−	0.617180i	$-0.211725\pi$
$293$	−3.52542	−	8.51111i	−0.205957	−	0.497224i	−0.992779	+	0.119956i	$0.961725\pi$
$294$	−28.5864	−	6.61018i	−1.66719	−	0.385514i
$295$	−11.9132	+	11.9132i	−0.693613	+	0.693613i
$296$	−13.0585	−	10.5971i	−0.759008	−	0.615946i
$297$	7.21704	−	7.21704i	0.418775	−	0.418775i
$298$	−12.3992	+	7.74187i	−0.718266	+	0.448475i
$299$	−5.07519	+	3.13813i	−0.293506	+	0.181483i
$300$	16.0598	+	18.1778i	0.927214	+	1.04950i
$301$	−1.00852	+	2.43478i	−0.0581300	+	0.140338i
$302$	7.05261	−	9.88012i	0.405832	−	0.568537i
$303$			6.43544i			0.369706i
$304$	−5.05203	−	18.3160i	−0.289754	−	1.05050i
$305$	−43.3635			−2.48299
$306$	−3.25545	+	4.56062i	−0.186102	+	0.260713i
$307$	7.60426	−	18.3583i	0.433998	−	1.04776i	−0.543988	−	0.839093i	$-0.683086\pi$
$307$	7.60426	−	18.3583i	0.433998	−	1.04776i	0.977986	−	0.208671i	$-0.0669137\pi$
$308$	−30.5373	−	1.88909i	−1.74002	−	0.107641i
$309$	7.06857	+	17.0650i	0.402117	+	0.970796i
$310$	8.11420	−	5.06639i	0.460855	−	0.287751i
$311$	10.4332	+	10.4332i	0.591614	+	0.591614i	0.938067	−	0.346453i	$-0.112614\pi$
$311$	10.4332	+	10.4332i	0.591614	+	0.591614i	−0.346453	+	0.938067i	$0.612614\pi$
$312$	22.0606	+	2.83786i	1.24894	+	0.160662i
$313$	−10.5239	+	10.5239i	−0.594844	+	0.594844i	−0.938936	−	0.344092i	$-0.888187\pi$
$313$	−10.5239	+	10.5239i	−0.594844	+	0.594844i	0.344092	+	0.938936i	$0.388187\pi$
$314$	−3.99351	+	17.2704i	−0.225367	+	0.974623i
$315$	−21.4352	+	8.87875i	−1.20774	+	0.500261i
$316$	−4.36734	−	12.7124i	−0.245682	−	0.715131i
$317$	28.0044	+	11.5998i	1.57289	+	0.651511i	0.987266	−	0.159076i	$-0.0508514\pi$
$317$	28.0044	+	11.5998i	1.57289	+	0.651511i	0.585619	+	0.810586i	$0.300851\pi$
$318$	15.6244	−	2.60904i	0.876174	−	0.146308i
$319$		−	17.3566i		−	0.971785i
$320$	25.5524	+	4.79109i	1.42842	+	0.267830i
$321$	31.2228			1.74268
$322$	−1.56643	−	9.38069i	−0.0872938	−	0.522765i
$323$	9.89641	+	4.09923i	0.550651	+	0.228087i
$324$	−7.26756	−	21.1544i	−0.403753	−	1.17524i
$325$	10.5440	+	17.0526i	0.584878	+	0.945905i
$326$	−20.4262	−	4.72325i	−1.13130	−	0.261597i
$327$	22.0705	+	22.0705i	1.22050	+	1.22050i
$328$	−7.68424	+	25.8424i	−0.424291	+	1.42691i
$329$	29.5429	+	29.5429i	1.62875	+	1.62875i
$330$	−32.0084	+	19.9856i	−1.76201	+	1.10017i
$331$	−28.7817	+	11.9218i	−1.58199	+	0.655281i	−0.988727	−	0.149729i	$-0.952160\pi$
$331$	−28.7817	+	11.9218i	−1.58199	+	0.655281i	−0.593261	+	0.805010i	$0.702160\pi$
$332$	−1.42564	+	23.0457i	−0.0782422	+	1.26479i
$333$	3.99773	−	9.65139i	0.219075	−	0.528893i
$334$	−12.1620	−	8.68147i	−0.665475	−	0.475029i
$335$		−	35.7670i		−	1.95416i
$336$	−17.4999	+	30.8308i	−0.954699	+	1.68196i
$337$			6.39493i			0.348354i	0.984714	+	0.174177i	$0.0557265\pi$
$337$			6.39493i			0.348354i	−0.984714	+	0.174177i	$0.944274\pi$
$338$	17.5757	+	5.39382i	0.955994	+	0.293385i
$339$	33.1718	+	13.7402i	1.80165	+	0.746266i
$340$	−10.9842	+	9.70433i	−0.595699	+	0.526291i
$341$	2.99872	+	7.23954i	0.162390	+	0.392043i
$342$	10.0112	−	6.25085i	0.541344	−	0.338007i
$343$	7.21910	−	7.21910i	0.389795	−	0.389795i
$344$	1.42436	+	1.15589i	0.0767961	+	0.0623212i
$345$	−8.29432	−	8.29432i	−0.446551	−	0.446551i
$346$	2.57152	+	0.594625i	0.138246	+	0.0319672i
$347$	8.71857	−	3.61135i	0.468038	−	0.193867i	−0.136185	−	0.990683i	$-0.543484\pi$
$347$	8.71857	−	3.61135i	0.468038	−	0.193867i	0.604222	+	0.796816i	$0.293484\pi$
$348$	−18.0696	−	8.82870i	−0.968631	−	0.473268i
$349$	−25.8315	−	10.6997i	−1.38273	−	0.572744i	−0.437518	−	0.899210i	$-0.644142\pi$
$349$	−25.8315	−	10.6997i	−1.38273	−	0.572744i	−0.945209	+	0.326466i	$0.894142\pi$
$350$	−31.5189	+	5.26318i	−1.68476	+	0.281329i
$351$	−1.56784	−	9.64855i	−0.0836851	−	0.515001i
$352$	−7.31851	+	19.9991i	−0.390078	+	1.06595i
$353$			30.2477i			1.60992i	0.593329	+	0.804960i	$0.297813\pi$
$353$			30.2477i			1.60992i	−0.593329	+	0.804960i	$0.702187\pi$
$354$	−15.7727	+	2.63380i	−0.838310	+	0.139985i
$355$	−15.5639	+	37.5745i	−0.826044	+	1.99425i
$356$	−5.55085	−	2.71212i	−0.294195	−	0.143742i
$357$	−7.64853	−	18.4652i	−0.404803	−	0.977282i
$358$	−5.88855	−	1.36164i	−0.311220	−	0.0719649i
$359$	−0.376316	−	0.376316i	−0.0198612	−	0.0198612i	0.697106	−	0.716968i	$-0.254470\pi$
$359$	−0.376316	−	0.376316i	−0.0198612	−	0.0198612i	−0.716968	+	0.697106i	$0.754470\pi$
$360$	1.67128	+	16.0625i	0.0880841	+	0.846569i
$361$	−2.51909	−	2.51909i	−0.132584	−	0.132584i
$362$	−15.9375	−	25.5250i	−0.837654	−	1.34157i
$363$	−2.64802	−	6.39287i	−0.138985	−	0.335539i
$364$	−18.5638	+	22.6722i	−0.973008	+	1.18835i
$365$	37.9905	+	15.7362i	1.98851	+	0.823670i
$366$	−33.4995	−	23.9125i	−1.75104	−	1.24993i
$367$		−	28.4922i		−	1.48728i	−0.668580	−	0.743640i	$-0.733097\pi$
$367$		−	28.4922i		−	1.48728i	0.668580	−	0.743640i	$-0.266903\pi$
$368$	−6.56935	−	0.815902i	−0.342451	−	0.0425319i
$369$	−16.7474			−0.871836
$370$	15.8759	−	22.2408i	0.825348	−	1.15624i
$371$	−7.98622	+	19.2804i	−0.414624	+	1.00099i
$372$	9.06225	+	0.560605i	0.469856	+	0.0290660i
$373$	6.56414	+	15.8472i	0.339879	+	0.820539i	0.997727	+	0.0673888i	$0.0214668\pi$
$373$	6.56414	+	15.8472i	0.339879	+	0.820539i	−0.657848	+	0.753150i	$0.728533\pi$
$374$	−6.35881	−	10.1841i	−0.328806	−	0.526608i
$375$	−2.80972	+	2.80972i	−0.145093	+	0.145093i
$376$	25.5713	−	13.8495i	1.31874	−	0.714234i
$377$	−13.4874	−	9.71685i	−0.694638	−	0.500443i
$378$	15.1795	+	3.51004i	0.780752	+	0.180537i
$379$	−11.6591	−	28.1475i	−0.598886	−	1.44584i	−0.874718	−	0.484632i	$-0.838953\pi$
$379$	−11.6591	−	28.1475i	−0.598886	−	1.44584i	0.275832	−	0.961206i	$-0.411047\pi$
$380$	29.1973	−	10.0307i	1.49779	−	0.514564i
$381$	11.3705	−	27.4509i	0.582530	−	1.40635i
$382$	8.79229	−	1.46818i	0.449853	−	0.0751185i
$383$		−	28.1530i		−	1.43855i	−0.694725	−	0.719276i	$-0.744474\pi$
$383$		−	28.1530i		−	1.43855i	0.694725	−	0.719276i	$-0.255526\pi$
$384$	17.0979	+	17.7919i	0.872523	+	0.907941i
$385$		−	49.7136i		−	2.53364i
$386$	1.99516	+	11.9482i	0.101551	+	0.608146i
$387$	−0.436054	+	1.05273i	−0.0221659	+	0.0535132i
$388$	4.25203	+	12.3768i	0.215864	+	0.628336i
$389$	−35.4664	+	14.6907i	−1.79822	+	0.744847i	−0.811090	+	0.584922i	$0.801125\pi$
$389$	−35.4664	+	14.6907i	−1.79822	+	0.744847i	−0.987129	+	0.159925i	$0.948875\pi$
$390$	−2.38911	+	36.0616i	−0.120977	+	1.82605i
$391$	2.63900	−	2.63900i	0.133460	−	0.133460i
$392$	−12.8133	−	23.6581i	−0.647172	−	1.19492i
$393$	10.7913	+	10.7913i	0.544350	+	0.544350i
$394$	−1.24327	−	1.99119i	−0.0626349	−	0.100314i
$395$	20.1783	−	8.35813i	1.01528	−	0.420543i
$396$	−13.2035	−	0.816786i	−0.663499	−	0.0410450i
$397$	5.33034	−	12.8686i	0.267522	−	0.645856i	−0.731843	−	0.681473i	$-0.761340\pi$
$397$	5.33034	−	12.8686i	0.267522	−	0.645856i	0.999366	+	0.0356170i	$0.0113396\pi$
$398$	−10.1593	+	14.2324i	−0.509242	+	0.713405i
$399$			42.0983i			2.10755i
$400$	−2.74142	+	22.0729i	−0.137071	+	1.10364i
$401$	29.6266			1.47948			0.739740	−	0.672893i	$-0.234949\pi$
$401$	29.6266			1.47948			0.739740	+	0.672893i	$0.234949\pi$
$402$	19.7235	−	27.6309i	0.983717	−	1.37810i
$403$	7.30446	+	1.72272i	0.363861	+	0.0858147i
$404$	−4.42249	+	3.90720i	−0.220027	+	0.194391i
$405$	33.5781	−	13.9085i	1.66851	−	0.691119i
$406$	22.4738	−	14.0323i	1.11535	−	0.696411i
$407$	15.8279	+	15.8279i	0.784558	+	0.784558i
$408$	−13.8369	+	1.43971i	−0.685030	+	0.0712763i
$409$	23.9240	+	23.9240i	1.18297	+	1.18297i	0.978972	+	0.203994i	$0.0653923\pi$
$409$	23.9240	+	23.9240i	1.18297	+	1.18297i	0.203994	+	0.978972i	$0.434608\pi$
$410$	−42.6810	−	9.86933i	−2.10786	−	0.487412i
$411$	0.141625	+	0.341913i	0.00698585	+	0.0168653i
$412$	−7.43564	+	15.2184i	−0.366328	+	0.749758i
$413$	8.06202	−	19.4634i	0.396706	−	0.957733i
$414$	−0.677280	−	4.05594i	−0.0332865	−	0.199339i
$415$	−37.5174			−1.84166
$416$	11.4436	+	16.8832i	0.561071	+	0.827768i
$417$	−7.78751			−0.381356
$418$	4.16523	+	24.9438i	0.203728	+	1.22004i
$419$	−8.00284	+	19.3206i	−0.390965	+	0.943872i	0.598766	+	0.800924i	$0.295658\pi$
$419$	−8.00284	+	19.3206i	−0.390965	+	0.943872i	−0.989730	+	0.142948i	$0.954342\pi$
$420$	−51.7556	−	25.2875i	−2.52542	−	1.23390i
$421$	−3.48988	−	8.42533i	−0.170087	−	0.410625i	0.815734	−	0.578427i	$-0.196333\pi$
$421$	−3.48988	−	8.42533i	−0.170087	−	0.410625i	−0.985821	+	0.167802i	$0.946333\pi$
$422$	28.9339	+	6.69053i	1.40848	+	0.325690i
$423$	12.7735	+	12.7735i	0.621069	+	0.621069i
$424$	11.2791	+	9.15319i	0.547763	+	0.444518i
$425$	−8.86700	−	8.86700i	−0.430112	−	0.430112i
$426$	−32.7437	+	20.4447i	−1.58644	+	0.990549i
$427$	50.0957	−	20.7503i	2.42430	−	1.00418i
$428$	18.9565	+	21.4566i	0.916299	+	1.03714i
$429$	−28.8142	−	6.79568i	−1.39116	−	0.328098i
$430$	−1.73167	+	2.42592i	−0.0835084	+	0.116988i
$431$	−33.9667			−1.63612			−0.818059	−	0.575134i	$-0.804950\pi$
$431$	−33.9667			−1.63612			−0.818059	+	0.575134i	$0.804950\pi$
$432$	5.35323	−	9.43112i	0.257557	−	0.453755i
$433$		−	18.4903i		−	0.888585i	−0.895882	−	0.444292i	$-0.853455\pi$
$433$		−	18.4903i		−	0.888585i	0.895882	−	0.444292i	$-0.146545\pi$
$434$	−6.94956	+	9.73575i	−0.333589	+	0.467331i
$435$	12.5052	−	30.1902i	0.599577	−	1.44751i
$436$	−1.76719	+	28.5668i	−0.0846330	+	1.36810i
$437$	−7.26266	+	3.00829i	−0.347420	+	0.143906i
$438$	20.6711	+	33.1062i	0.987701	+	1.58188i
$439$	20.8536	+	20.8536i	0.995288	+	0.995288i	0.999989	−	0.00470087i	$-0.00149634\pi$
$439$	20.8536	+	20.8536i	0.995288	+	0.995288i	−0.00470087	+	0.999989i	$0.501496\pi$
$440$	−33.1678	−	9.86245i	−1.58121	−	0.470174i
$441$	11.8178	−	11.8178i	0.562755	−	0.562755i
$442$	−11.4737	−	0.760141i	−0.545749	−	0.0361562i
$443$	−0.502852	+	0.208288i	−0.0238912	+	0.00989607i	−0.394597	−	0.918854i	$-0.629116\pi$
$443$	−0.502852	+	0.208288i	−0.0238912	+	0.00989607i	0.370706	+	0.928750i	$0.379116\pi$
$444$	24.5291	−	8.42694i	1.16410	−	0.399925i
$445$	3.84151	−	9.27422i	0.182105	−	0.439640i
$446$	−1.67336	−	10.0211i	−0.0792360	−	0.474510i
$447$		−	22.5439i		−	1.06629i
$448$	−31.8120	+	6.69244i	−1.50298	+	0.316188i
$449$			15.5164i			0.732266i	0.930562	+	0.366133i	$0.119319\pi$
$449$			15.5164i			0.732266i	−0.930562	+	0.366133i	$0.880681\pi$
$450$	−13.6279	+	2.27565i	−0.642424	+	0.107275i
$451$	13.7325	−	33.1532i	0.646639	−	1.56112i
$452$	10.6975	+	31.1382i	0.503167	+	1.46462i
$453$	7.16430	+	17.2961i	0.336608	+	0.812643i
$454$	18.4027	+	4.25534i	0.863680	+	0.199713i
$455$	−38.6312	−	27.8314i	−1.81106	−	1.30476i
$456$	28.0870	+	8.35168i	1.31530	+	0.391103i
$457$	−7.44650	+	7.44650i	−0.348332	+	0.348332i	−0.859488	−	0.511156i	$-0.829218\pi$
$457$	−7.44650	+	7.44650i	−0.348332	+	0.348332i	0.511156	+	0.859488i	$0.329218\pi$
$458$	9.77463	+	15.6548i	0.456738	+	0.731501i
$459$	2.33969	+	5.64850i	0.109207	+	0.263649i
$460$	0.664129	−	10.7357i	0.0309652	−	0.500556i
$461$	−11.1019	+	26.8023i	−0.517065	+	1.24831i	0.422633	+	0.906301i	$0.361106\pi$
$461$	−11.1019	+	26.8023i	−0.517065	+	1.24831i	−0.939698	+	0.342005i	$0.888894\pi$
$462$	27.4142	−	38.4050i	1.27543	−	1.78676i
$463$	33.8889			1.57495			0.787475	−	0.616347i	$-0.211388\pi$
$463$	33.8889			1.57495			0.787475	+	0.616347i	$0.211388\pi$
$464$	−4.90357	−	17.7778i	−0.227643	−	0.825314i
$465$			14.7530i			0.684154i
$466$	6.92104	+	4.94037i	0.320611	+	0.228858i
$467$	17.3307	+	7.17861i	0.801969	+	0.332186i	0.745745	−	0.666232i	$-0.232094\pi$
$467$	17.3307	+	7.17861i	0.801969	+	0.332186i	0.0562242	+	0.998418i	$0.482094\pi$
$468$	−8.02646	+	9.80283i	−0.371023	+	0.453136i
$469$	17.1152	+	41.3198i	0.790307	+	1.90797i
$470$	25.0259	+	40.0809i	1.15436	+	1.84880i
$471$	−19.3307	−	19.3307i	−0.890711	−	0.890711i
$472$	−11.3862	−	9.24006i	−0.524092	−	0.425308i
$473$	−1.72643	−	1.72643i	−0.0793812	−	0.0793812i
$474$	20.1973	+	4.67032i	0.927693	+	0.214515i
$475$	10.1078	+	24.4024i	0.463778	+	1.11966i
$476$	8.04572	−	16.4671i	0.368775	−	0.754767i
$477$	−3.45301	+	8.33630i	−0.158102	+	0.381693i
$478$	24.3106	−	4.05950i	1.11194	−	0.185677i
$479$		−	1.61603i		−	0.0738381i	−0.999318	−	0.0369190i	$-0.988246\pi$
$479$		−	1.61603i		−	0.0738381i	0.999318	−	0.0369190i	$-0.0117544\pi$
$480$	−27.1388	+	29.5135i	−1.23871	+	1.34710i
$481$	21.1604	−	3.43846i	0.964833	−	0.156780i
$482$	11.6443	−	1.94442i	0.530383	−	0.0885659i
$483$	13.5510	+	5.61301i	0.616593	+	0.255401i
$484$	2.78553	−	5.70110i	0.126615	−	0.259141i
$485$	−19.6455	+	8.13744i	−0.892058	+	0.369502i
$486$	22.4031	+	5.18038i	1.01622	+	0.234987i
$487$	−23.3489	−	23.3489i	−1.05804	−	1.05804i	−0.998209	−	0.0598301i	$-0.980944\pi$
$487$	−23.3489	−	23.3489i	−1.05804	−	1.05804i	−0.0598301	−	0.998209i	$-0.519056\pi$
$488$	−3.90591	−	37.5393i	−0.176812	−	1.69933i
$489$	22.8630	−	22.8630i	1.03390	−	1.03390i
$490$	37.0822	−	23.1536i	1.67520	−	1.04597i
$491$	−4.48885	−	10.8371i	−0.202579	−	0.489069i	0.789640	−	0.613570i	$-0.210267\pi$
$491$	−4.48885	−	10.8371i	−0.202579	−	0.489069i	−0.992220	+	0.124501i	$0.960267\pi$
$492$	−27.5298	−	31.1605i	−1.24114	−	1.40482i
$493$	9.60559	+	3.97877i	0.432614	+	0.179195i
$494$	21.7150	+	10.7277i	0.977006	+	0.482661i
$495$		−	21.4947i		−	0.966116i
$496$	5.11679	+	6.56803i	0.229751	+	0.294913i
$497$		−	50.8556i		−	2.28118i
$498$	−28.9832	−	20.6888i	−1.29877	−	0.927085i
$499$	3.66776	−	8.85477i	0.164192	−	0.396394i	−0.820274	−	0.571971i	$-0.806179\pi$
$499$	3.66776	−	8.85477i	0.164192	−	0.396394i	0.984466	+	0.175577i	$0.0561791\pi$
$500$	−3.63675	−	0.224975i	−0.162640	−	0.0100612i
$501$	21.2908	−	8.81894i	0.951203	−	0.394001i
$502$	−6.36332	+	3.97316i	−0.284009	+	0.177331i
$503$	1.91903	+	1.91903i	0.0855653	+	0.0855653i	0.748594	−	0.663029i	$-0.230729\pi$
$503$	1.91903	+	1.91903i	0.0855653	+	0.0855653i	−0.663029	+	0.748594i	$0.730729\pi$
$504$	−9.61699	−	17.7565i	−0.428375	−	0.790937i
$505$	−6.78021	−	6.78021i	−0.301715	−	0.301715i
$506$	8.58450	+	1.98504i	0.381628	+	0.0882457i
$507$	−21.4120	+	18.5864i	−0.950939	+	0.825451i
$508$	25.7680	−	8.85256i	1.14327	−	0.392769i
$509$	−23.7171	−	9.82394i	−1.05124	−	0.435438i	−0.210906	−	0.977506i	$-0.567642\pi$
$509$	−23.7171	−	9.82394i	−1.05124	−	0.435438i	−0.840335	+	0.542068i	$0.817642\pi$
$510$	−3.72304	−	22.2957i	−0.164859	−	0.987269i
$511$	−51.4186			−2.27463
$512$	−1.84600	+	22.5520i	−0.0815823	+	0.996667i
$513$		−	12.8779i		−	0.568571i
$514$	−9.26563	+	1.54722i	−0.408690	+	0.0682449i
$515$	−25.4265	−	10.5320i	−1.12043	−	0.464096i
$516$	−2.67552	+	0.919171i	−0.117783	+	0.0404642i
$517$	−35.7605	+	14.8125i	−1.57274	+	0.651452i
$518$	−7.69795	+	33.2906i	−0.338228	+	1.46270i
$519$	−2.87830	+	2.87830i	−0.126343	+	0.126343i
$520$	−26.2324	+	20.2526i	−1.15037	+	0.888134i
$521$	−9.75278	−	9.75278i	−0.427277	−	0.427277i	0.460423	−	0.887700i	$-0.347698\pi$
$521$	−9.75278	−	9.75278i	−0.427277	−	0.427277i	−0.887700	+	0.460423i	$0.847698\pi$
$522$	9.71701	−	6.06716i	0.425302	−	0.265552i
$523$	−5.52238	−	13.3322i	−0.241477	−	0.582977i	0.755953	−	0.654626i	$-0.227174\pi$
$523$	−5.52238	−	13.3322i	−0.241477	−	0.582977i	−0.997430	+	0.0716489i	$0.977174\pi$
$524$	−0.864063	+	13.9677i	−0.0377468	+	0.610182i
$525$	18.8596	−	45.5312i	0.823101	−	1.98714i
$526$	−11.3016	+	15.8325i	−0.492772	+	0.690332i
$527$	−4.69396			−0.204472
$528$	−20.1844	−	25.9092i	−0.878414	−	1.12755i
$529$		−	20.2611i		−	0.880918i
$530$	−13.7127	+	19.2103i	−0.595640	+	0.834441i
$531$	3.48578	−	8.41543i	0.151270	−	0.365198i
$532$	−28.9303	+	25.5595i	−1.25429	+	1.10814i
$533$	−18.0746	−	29.2316i	−0.782900	−	1.26616i
$534$	8.08187	−	5.04620i	0.349737	−	0.218371i
$535$	−32.8955	+	32.8955i	−1.42220	+	1.42220i
$536$	30.9631	−	3.22166i	1.33740	−	0.139154i
$537$	6.59105	−	6.59105i	0.284425	−	0.284425i
$538$	17.2177	+	3.98133i	0.742307	+	0.171647i
$539$	13.7043	+	33.0850i	0.590284	+	1.42507i
$540$	15.8320	+	7.73545i	0.681302	+	0.332881i
$541$	30.8513	+	12.7790i	1.32640	+	0.549413i	0.929627	−	0.368503i	$-0.120130\pi$
$541$	30.8513	+	12.7790i	1.32640	+	0.549413i	0.396774	+	0.917916i	$0.370130\pi$
$542$	−17.5790	+	2.93543i	−0.755084	+	0.126087i
$543$	46.4089			1.99160
$544$	−9.39032	−	8.63476i	−0.402607	−	0.370212i
$545$	−46.5057			−1.99209
$546$	−14.4962	−	42.8034i	−0.620380	−	1.83182i
$547$	−3.07696	+	7.42844i	−0.131561	+	0.317617i	−0.975909	−	0.218179i	$-0.929988\pi$
$547$	−3.07696	+	7.42844i	−0.131561	+	0.317617i	0.844347	+	0.535796i	$0.179988\pi$
$548$	−0.148980	+	0.304915i	−0.00636410	+	0.0130253i
$549$	21.6599	−	8.97184i	0.924424	−	0.382909i
$550$	6.66969	−	28.8438i	0.284396	−	1.22990i
$551$	−15.4853	−	15.4853i	−0.659696	−	0.659696i
$552$	6.43321	−	7.92740i	0.273815	−	0.337413i
$553$	−19.3115	+	19.3115i	−0.821207	+	0.821207i
$554$	11.8078	+	18.9111i	0.501666	+	0.803456i
$555$	16.1273	+	38.9347i	0.684565	+	1.65269i
$556$	−4.72810	−	5.35165i	−0.200516	−	0.226960i
$557$	3.62297	−	8.74662i	0.153510	−	0.370606i	−0.828351	−	0.560210i	$-0.810720\pi$
$557$	3.62297	−	8.74662i	0.153510	−	0.370606i	0.981861	+	0.189604i	$0.0607204\pi$
$558$	−3.00479	+	4.20946i	−0.127203	+	0.178201i
$559$	−2.30808	+	0.375051i	−0.0976214	+	0.0158630i
$560$	−14.0450	−	50.9199i	−0.593510	−	2.15176i
$561$	18.5165			0.781766
$562$	−4.86584	−	3.47332i	−0.205253	−	0.146513i
$563$	−8.67820	−	3.59463i	−0.365742	−	0.151495i	0.192241	−	0.981348i	$-0.438425\pi$
$563$	−8.67820	−	3.59463i	−0.365742	−	0.151495i	−0.557983	+	0.829852i	$0.688425\pi$
$564$	−2.76917	+	44.7640i	−0.116603	+	1.88490i
$565$	−49.4253	+	20.4726i	−2.07934	+	0.861289i
$566$	24.4870	−	15.2893i	1.02927	−	0.642658i
$567$	−32.1356	+	32.1356i	−1.34957	+	1.34957i
$568$	−33.9297	−	10.0890i	−1.42366	−	0.423325i
$569$	9.18281	−	9.18281i	0.384963	−	0.384963i	−0.487923	−	0.872887i	$-0.662245\pi$
$569$	9.18281	−	9.18281i	0.384963	−	0.384963i	0.872887	+	0.487923i	$0.162245\pi$
$570$	−10.7266	+	46.3882i	−0.449287	+	1.94299i
$571$	4.86098	−	2.01349i	0.203426	−	0.0842617i	−0.278644	−	0.960394i	$-0.589885\pi$
$571$	4.86098	−	2.01349i	0.203426	−	0.0842617i	0.482070	+	0.876133i	$0.339885\pi$
$572$	−12.8242	−	23.9273i	−0.536206	−	1.00045i
$573$	−5.26094	+	12.7010i	−0.219779	+	0.530593i
$574$	54.0299	−	9.02217i	2.25516	−	0.376578i
$575$	9.20258			0.383774
$576$	−13.7546	+	2.89362i	−0.573109	+	0.120567i
$577$			1.81881i			0.0757179i	0.999283	+	0.0378589i	$0.0120538\pi$
$577$			1.81881i			0.0757179i	−0.999283	+	0.0378589i	$0.987946\pi$
$578$	−16.6195	+	2.77520i	−0.691279	+	0.115433i
$579$	−17.2599	−	7.14929i	−0.717298	−	0.297115i
$580$	28.3393	−	9.73594i	1.17673	−	0.404263i
$581$	43.3420	−	17.9529i	1.79813	−	0.744810i
$582$	−19.6640	−	4.54701i	−0.815100	−	0.188480i
$583$	−13.6712	−	13.6712i	−0.566202	−	0.566202i
$584$	−10.2007	+	34.3054i	−0.422108	+	1.41957i
$585$	−16.7030	−	12.0335i	−0.690585	−	0.497524i
$586$	6.90007	+	11.0510i	0.285039	+	0.456512i
$587$	21.6786	−	8.97959i	0.894773	−	0.370627i	0.112565	−	0.993644i	$-0.464093\pi$
$587$	21.6786	−	8.97959i	0.894773	−	0.370627i	0.782208	+	0.623017i	$0.214093\pi$
$588$	41.4149	+	2.56199i	1.70792	+	0.105655i
$589$	9.13440	+	3.78359i	0.376377	+	0.155900i
$590$	13.8428	−	19.3926i	0.569899	−	0.798382i
$591$	3.62032			0.148920
$592$	20.6836	+	11.7403i	0.850091	+	0.482522i
$593$	−18.1583			−0.745673			−0.372837	−	0.927897i	$-0.621615\pi$
$593$	−18.1583			−0.745673			−0.372837	+	0.927897i	$0.621615\pi$
$594$	−8.38601	+	11.7481i	−0.344082	+	0.482030i
$595$	27.5127	+	11.3961i	1.12791	+	0.467197i
$596$	15.4923	−	13.6872i	0.634591	−	0.560651i
$597$	−10.3202	−	24.9152i	−0.422379	−	1.01971i
$598$	6.34843	−	5.55952i	0.259607	−	0.227346i
$599$	16.3184	+	16.3184i	0.666753	+	0.666753i	0.956963	−	0.290210i	$-0.0937253\pi$
$599$	16.3184	+	16.3184i	0.666753	+	0.666753i	−0.290210	+	0.956963i	$0.593725\pi$
$600$	−26.6359	−	21.6155i	−1.08741	−	0.882447i
$601$	5.89166	−	5.89166i	0.240326	−	0.240326i	−0.576659	−	0.816985i	$-0.695644\pi$
$601$	5.89166	−	5.89166i	0.240326	−	0.240326i	0.816985	+	0.576659i	$0.195644\pi$
$602$	0.839656	−	3.63118i	0.0342218	−	0.147996i
$603$	7.40013	+	17.8655i	0.301356	+	0.727539i
$604$	−7.53634	+	15.4245i	−0.306649	+	0.627615i
$605$	9.52524	+	3.94548i	0.387256	+	0.160407i
$606$	−1.49899	−	8.97679i	−0.0608922	−	0.364657i
$607$	10.4057			0.422353			0.211176	−	0.977448i	$-0.432271\pi$
$607$	10.4057			0.422353			0.211176	+	0.977448i	$0.432271\pi$
$608$	11.3134	+	24.3723i	0.458818	+	0.988427i
$609$			40.8612i			1.65578i
$610$	60.4878	−	10.1005i	2.44908	−	0.408959i
$611$	−8.50954	+	36.0812i	−0.344259	+	1.45969i
$612$	3.47874	−	7.11989i	0.140620	−	0.287804i
$613$	−0.669128	−	1.61542i	−0.0270258	−	0.0652461i	0.909790	−	0.415068i	$-0.136242\pi$
$613$	−0.669128	−	1.61542i	−0.0270258	−	0.0652461i	−0.936816	+	0.349822i	$0.886242\pi$
$614$	−6.33103	+	27.3792i	−0.255500	+	1.10494i
$615$	47.7727	−	47.7727i	1.92638	−	1.92638i
$616$	43.0365	−	4.47788i	1.73399	−	0.180419i
$617$	−2.87604	+	2.87604i	−0.115785	+	0.115785i	−0.762625	−	0.646840i	$-0.776090\pi$
$617$	−2.87604	+	2.87604i	−0.115785	+	0.115785i	0.646840	+	0.762625i	$0.276090\pi$
$618$	−13.8349	−	22.1576i	−0.556520	−	0.891308i
$619$	−20.3310	+	8.42139i	−0.817174	+	0.338484i	−0.751812	−	0.659377i	$-0.770820\pi$
$619$	−20.3310	+	8.42139i	−0.817174	+	0.338484i	−0.0653615	+	0.997862i	$0.520820\pi$
$620$	−10.1384	+	8.95711i	−0.407168	+	0.359726i
$621$	−4.14525	−	1.71702i	−0.166343	−	0.0689017i
$622$	−16.9835	−	12.1231i	−0.680976	−	0.486093i
$623$			12.5523i			0.502897i
$624$	−31.4334	+	1.17997i	−1.25834	+	0.0472368i
$625$			21.8826i			0.875304i
$626$	12.2284	−	17.1310i	0.488747	−	0.684693i
$627$	−36.0329	−	14.9253i	−1.43901	−	0.596059i
$628$	1.54781	−	25.0206i	0.0617645	−	0.998431i
$629$	−12.3878	+	5.13121i	−0.493936	+	0.204595i
$630$	27.8319	−	17.3778i	1.10885	−	0.692348i
$631$	7.07947	−	7.07947i	0.281829	−	0.281829i	−0.552009	−	0.833838i	$-0.686139\pi$
$631$	7.07947	−	7.07947i	0.281829	−	0.281829i	0.833838	+	0.552009i	$0.186139\pi$
$632$	9.05308	+	16.7153i	0.360112	+	0.664899i
$633$	−32.3857	+	32.3857i	−1.28721	+	1.28721i
$634$	−41.7653	−	9.65759i	−1.65871	−	0.383552i
$635$	16.9418	+	40.9012i	0.672316	+	1.62312i
$636$	−21.1868	+	7.27869i	−0.840110	+	0.288619i
$637$	33.3817	+	7.87289i	1.32263	+	0.311935i
$638$	4.04283	+	24.2108i	0.160057	+	0.958513i
$639$		−	21.9885i		−	0.869851i
$640$	−36.7590	−	0.731244i	−1.45303	−	0.0289050i
$641$	15.6584			0.618470			0.309235	−	0.950986i	$-0.399927\pi$
$641$	15.6584			0.618470			0.309235	+	0.950986i	$0.399927\pi$
$642$	−43.5526	+	7.27262i	−1.71888	+	0.287027i
$643$	34.2761	+	14.1976i	1.35172	+	0.559900i	0.936770	−	0.349945i	$-0.113800\pi$
$643$	34.2761	+	14.1976i	1.35172	+	0.559900i	0.414948	+	0.909845i	$0.363800\pi$
$644$	4.37003	+	12.7203i	0.172203	+	0.501248i
$645$	−1.75909	−	4.24682i	−0.0692641	−	0.167218i
$646$	−14.7593	−	3.41287i	−0.580698	−	0.134278i
$647$	14.6709	−	14.6709i	0.576772	−	0.576772i	−0.357240	−	0.934012i	$-0.616282\pi$
$647$	14.6709	−	14.6709i	0.576772	−	0.576772i	0.934012	+	0.357240i	$0.116282\pi$
$648$	15.0649	+	27.8154i	0.591807	+	1.09269i
$649$	13.8009	+	13.8009i	0.541734	+	0.541734i
$650$	−18.6799	−	21.3306i	−0.732685	−	0.836655i
$651$	−7.05961	−	17.0434i	−0.276688	−	0.667984i
$652$	29.5927	+	1.83065i	1.15894	+	0.0716937i
$653$	−0.0690258	−	0.0285914i	−0.00270119	−	0.00111887i	0.381332	−	0.924438i	$-0.375465\pi$
$653$	−0.0690258	−	0.0285914i	−0.00270119	−	0.00111887i	−0.384034	+	0.923319i	$0.625465\pi$
$654$	−35.9269	−	25.6453i	−1.40485	−	1.00281i
$655$	−22.7389			−0.888481
$656$	4.69935	−	37.8374i	0.183479	−	1.47730i
$657$	−22.2319			−0.867351
$658$	−48.0908	−	34.3281i	−1.87477	−	1.33825i
$659$	7.04181	+	2.91681i	0.274310	+	0.113623i	0.515598	−	0.856831i	$-0.327570\pi$
$659$	7.04181	+	2.91681i	0.274310	+	0.113623i	−0.241288	+	0.970454i	$0.577570\pi$
$660$	39.9934	−	35.3335i	1.55674	−	1.37536i
$661$	−13.6308	+	5.64607i	−0.530177	+	0.219607i	−0.631681	−	0.775229i	$-0.717635\pi$
$661$	−13.6308	+	5.64607i	−0.530177	+	0.219607i	0.101504	+	0.994835i	$0.467635\pi$
$662$	37.3707	−	23.3337i	1.45246	−	0.906892i
$663$	10.3662	−	14.3887i	0.402588	−	0.558811i
$664$	−3.37933	−	32.4785i	−0.131143	−	1.26041i
$665$	−44.3536	−	44.3536i	−1.71996	−	1.71996i
$666$	−3.32837	+	14.3939i	−0.128972	+	0.557752i
$667$	−7.04924	+	2.91989i	−0.272948	+	0.113059i
$668$	18.9869	+	9.27691i	0.734626	+	0.358935i
$669$	14.4761	+	5.99618i	0.559677	+	0.231826i
$670$	8.33109	+	49.8913i	0.321858	+	1.92747i
$671$			50.2348i			1.93929i
$672$	17.2293	−	47.0820i	0.664636	−	1.81623i
$673$	40.2500			1.55152			0.775761	−	0.631026i	$-0.217366\pi$
$673$	40.2500			1.55152			0.775761	+	0.631026i	$0.217366\pi$
$674$	−1.48955	−	8.92028i	−0.0573754	−	0.343596i
$675$	−5.76916	+	13.9280i	−0.222055	+	0.536088i
$676$	−25.7728	−	3.42998i	−0.991260	−	0.131922i
$677$	−0.679043	+	0.281269i	−0.0260977	+	0.0108100i	−0.395694	−	0.918382i	$-0.629496\pi$
$677$	−0.679043	+	0.281269i	−0.0260977	+	0.0108100i	0.369596	+	0.929192i	$0.379496\pi$
$678$	−49.4718	−	11.4396i	−1.89995	−	0.439336i
$679$	18.8016	−	18.8016i	0.721538	−	0.721538i
$680$	13.0614	−	16.0951i	0.500881	−	0.617218i
$681$	−20.5981	+	20.5981i	−0.789320	+	0.789320i
$682$	−5.86919	−	9.39995i	−0.224743	−	0.359943i
$683$	18.1054	−	7.49951i	0.692784	−	0.286961i	−0.00837541	−	0.999965i	$-0.502666\pi$
$683$	18.1054	−	7.49951i	0.692784	−	0.286961i	0.701160	+	0.713004i	$0.252666\pi$
$684$	−12.5086	+	11.0512i	−0.478279	+	0.422552i
$685$	−0.509444	−	0.211018i	−0.0194648	−	0.00806260i
$686$	−8.38840	+	11.7514i	−0.320270	+	0.448672i
$687$	−28.4631			−1.08594
$688$	−2.25607	−	1.28057i	−0.0860119	−	0.0488214i
$689$	−18.2771	+	2.96994i	−0.696304	+	0.113146i
$690$	13.5017	+	9.63777i	0.514002	+	0.366904i
$691$	−6.16942	+	14.8943i	−0.234696	+	0.566606i	−0.996719	−	0.0809445i	$-0.974206\pi$
$691$	−6.16942	+	14.8943i	−0.234696	+	0.566606i	0.762023	+	0.647550i	$0.224206\pi$
$692$	−3.72552	−	0.230466i	−0.141623	−	0.00876101i
$693$	10.2857	+	24.8318i	0.390720	+	0.943281i
$694$	−11.3204	+	7.06826i	−0.429715	+	0.268308i
$695$	8.20472	−	8.20472i	0.311223	−	0.311223i
$696$	27.2617	+	8.10626i	1.03335	+	0.307267i
$697$	15.1998	+	15.1998i	0.575735	+	0.575735i
$698$	38.5246	+	8.90823i	1.45818	+	0.337181i
$699$	−12.1160	+	5.01860i	−0.458269	+	0.189821i
$700$	42.7398	−	14.6832i	1.61541	−	0.554974i
$701$	14.7362	−	35.5762i	0.556577	−	1.34370i	−0.355883	−	0.934531i	$-0.615820\pi$
$701$	14.7362	−	35.5762i	0.556577	−	1.34370i	0.912460	−	0.409166i	$-0.134180\pi$
$702$	4.43438	+	13.0936i	0.167365	+	0.494185i
$703$	28.2427			1.06519
$704$	5.55027	−	29.6014i	0.209184	−	1.11564i
$705$	−72.8740			−2.74459
$706$	−7.04550	−	42.1924i	−0.265161	−	1.58793i
$707$	11.0773	+	4.58837i	0.416605	+	0.172563i
$708$	21.3879	−	7.34778i	0.803805	−	0.276146i
$709$	−6.94545	−	16.7678i	−0.260842	−	0.629728i	0.738149	−	0.674637i	$-0.235700\pi$
$709$	−6.94545	−	16.7678i	−0.260842	−	0.629728i	−0.998991	+	0.0449098i	$0.985700\pi$
$710$	12.9579	−	56.0379i	0.486302	−	2.10306i
$711$	−8.34972	+	8.34972i	−0.313139	+	0.313139i
$712$	8.37461	+	2.49019i	0.313852	+	0.0933238i
$713$	2.43580	−	2.43580i	0.0912215	−	0.0912215i
$714$	14.9700	+	23.9755i	0.560237	+	0.897262i
$715$	37.5177	−	23.1982i	1.40308	−	0.867562i
$716$	8.53110	+	0.527747i	0.318822	+	0.0197228i
$717$	−14.5465	+	35.1182i	−0.543247	+	1.31151i
$718$	0.612577	+	0.437269i	0.0228612	+	0.0163187i
$719$		−	8.73876i		−	0.325901i	−0.986634	−	0.162950i	$-0.947899\pi$
$719$		−	8.73876i		−	0.325901i	0.986634	−	0.162950i	$-0.0521010\pi$
$720$	−6.07266	−	22.0163i	−0.226315	−	0.820500i
$721$	34.4138			1.28164
$722$	4.10065	+	2.92712i	0.152610	+	0.108936i
$723$	−6.96746	+	16.8209i	−0.259123	+	0.625577i
$724$	28.1766	+	31.8926i	1.04718	+	1.18528i
$725$	9.81078	+	23.6853i	0.364363	+	0.879650i
$726$	5.18279	+	8.30062i	0.192351	+	0.308065i
$727$	−2.20849	−	2.20849i	−0.0819084	−	0.0819084i	0.664966	−	0.746874i	$-0.268446\pi$
$727$	−2.20849	−	2.20849i	−0.0819084	−	0.0819084i	−0.746874	+	0.664966i	$0.768446\pi$
$728$	20.6137	−	35.9495i	0.763994	−	1.33238i
$729$	−1.35096	+	1.35096i	−0.0500355	+	0.0500355i
$730$	−56.6583	−	13.1014i	−2.09702	−	0.484904i
$731$	1.35121	−	0.559689i	0.0499762	−	0.0207008i
$732$	52.2983	+	25.5527i	1.93300	+	0.944453i
$733$	−24.5165	−	10.1551i	−0.905538	−	0.375086i	−0.119191	−	0.992871i	$-0.538030\pi$
$733$	−24.5165	−	10.1551i	−0.905538	−	0.375086i	−0.786347	+	0.617785i	$0.788030\pi$
$734$	6.63660	+	39.7438i	0.244961	+	1.46697i
$735$			67.4218i			2.48689i
$736$	9.35363	−	0.392076i	0.344779	−	0.0144521i
$737$	−41.4345			−1.52626
$738$	23.3610	−	3.90093i	0.859929	−	0.143595i
$739$	−13.0459	−	5.40379i	−0.479902	−	0.198782i	0.129600	−	0.991566i	$-0.458631\pi$
$739$	−13.0459	−	5.40379i	−0.479902	−	0.198782i	−0.609502	+	0.792785i	$0.708631\pi$
$740$	−16.9648	+	34.7216i	−0.623638	+	1.27639i
$741$	−31.7706	+	19.6446i	−1.16712	+	0.721662i
$742$	6.64904	−	28.7545i	0.244094	−	1.05561i
$743$	−0.824311	−	0.824311i	−0.0302410	−	0.0302410i	0.691825	−	0.722066i	$-0.256807\pi$
$743$	−0.824311	−	0.824311i	−0.0302410	−	0.0302410i	−0.722066	+	0.691825i	$0.756807\pi$
$744$	−12.7715	+	1.32886i	−0.468226	+	0.0487182i
$745$	23.7516	+	23.7516i	0.870192	+	0.870192i
$746$	−12.8476	−	20.5764i	−0.470383	−	0.753354i
$747$	18.7398	−	7.76230i	0.685655	−	0.284008i
$748$	11.2421	+	12.7247i	0.411050	+	0.465260i
$749$	22.2614	−	53.7437i	0.813412	−	1.96375i
$750$	3.26482	−	4.57373i	0.119214	−	0.167009i
$751$		−	42.0982i		−	1.53619i	−0.640338	−	0.768093i	$-0.721206\pi$
$751$		−	42.0982i		−	1.53619i	0.640338	−	0.768093i	$-0.278794\pi$
$752$	−32.4435	+	25.2749i	−1.18309	+	0.921682i
$753$		−	11.5696i		−	0.421620i
$754$	21.0769	+	10.4124i	0.767576	+	0.379199i
$755$	−25.7709	−	10.6746i	−0.937898	−	0.388490i
$756$	−21.9915	−	1.36043i	−0.799824	−	0.0494784i
$757$	−4.58106	−	11.0597i	−0.166502	−	0.401970i	0.818502	−	0.574503i	$-0.194805\pi$
$757$	−4.58106	−	11.0597i	−0.166502	−	0.401970i	−0.985004	+	0.172533i	$0.944805\pi$
$758$	22.8195	+	36.5472i	0.828842	+	1.32745i
$759$	−9.60862	+	9.60862i	−0.348771	+	0.348771i
$760$	−38.3909	+	20.7927i	−1.39258	+	0.754229i
$761$	−17.5193	−	17.5193i	−0.635075	−	0.635075i	0.314262	−	0.949336i	$-0.398243\pi$
$761$	−17.5193	−	17.5193i	−0.635075	−	0.635075i	−0.949336	+	0.314262i	$0.898243\pi$
$762$	−9.46670	+	40.9397i	−0.342942	+	1.48309i
$763$	53.7257	−	22.2539i	1.94500	−	0.805646i
$764$	−11.9224	+	4.09592i	−0.431337	+	0.148185i
$765$	11.8957	+	4.92737i	0.430090	+	0.178149i
$766$	6.55759	+	39.2706i	0.236935	+	1.41890i
$767$	18.4506	−	2.99813i	0.666213	−	0.108256i
$768$	−27.9941	−	20.8354i	−1.01015	−	0.751834i
$769$			8.03675i			0.289813i	0.989445	+	0.144906i	$0.0462881\pi$
$769$			8.03675i			0.289813i	−0.989445	+	0.144906i	$0.953712\pi$
$770$	11.5796	+	69.3454i	0.417301	+	2.49904i
$771$	5.54417	−	13.3848i	0.199668	−	0.482042i
$772$	−5.56611	−	16.2018i	−0.200329	−	0.583115i
$773$	14.9753	+	36.1536i	0.538625	+	1.30036i	0.925683	+	0.378300i	$0.123491\pi$
$773$	14.9753	+	36.1536i	0.538625	+	1.30036i	−0.387058	+	0.922055i	$0.626509\pi$
$774$	0.363043	−	1.57002i	0.0130493	−	0.0564332i
$775$	−8.18425	−	8.18425i	−0.293987	−	0.293987i
$776$	−8.81404	−	16.2740i	−0.316406	−	0.584201i
$777$	−37.2621	−	37.2621i	−1.33677	−	1.33677i
$778$	46.0502	−	28.7531i	1.65098	−	1.03085i
$779$	−17.3268	−	41.8307i	−0.620798	−	1.49874i
$780$	−5.06716	−	50.8588i	−0.181433	−	1.82104i
$781$	43.5285	+	18.0301i	1.55757	+	0.645167i
$782$	−3.06645	+	4.29584i	−0.109656	+	0.153619i
$783$		−	12.4994i		−	0.446693i
$784$	23.3840	+	30.0162i	0.835141	+	1.07201i
$785$	40.7326			1.45381
$786$	−17.5664	−	12.5392i	−0.626572	−	0.447259i
$787$	−9.87207	+	23.8333i	−0.351901	+	0.849564i	0.644484	+	0.764617i	$0.277072\pi$
$787$	−9.87207	+	23.8333i	−0.351901	+	0.849564i	−0.996385	+	0.0849470i	$0.972928\pi$
$788$	2.19803	+	2.48791i	0.0783017	+	0.0886283i
$789$	−11.4805	−	27.7165i	−0.408718	−	0.986732i
$790$	−26.1999	+	16.3588i	−0.932150	+	0.582021i
$791$	47.3020	−	47.3020i	1.68187	−	1.68187i
$792$	18.6077	−	1.93611i	0.661198	−	0.0687965i
$793$	39.0363	+	28.1232i	1.38622	+	0.998684i
$794$	−4.43785	+	19.1920i	−0.157494	+	0.681098i
$795$	−13.9298	−	33.6295i	−0.494039	−	1.19272i
$796$	10.8562	−	22.2191i	0.384786	−	0.787536i
$797$	−18.0864	+	43.6644i	−0.640652	+	1.54667i	0.185149	+	0.982711i	$0.440723\pi$
$797$	−18.0864	+	43.6644i	−0.640652	+	1.54667i	−0.825801	+	0.563961i	$0.809277\pi$
$798$	−9.80582	−	58.7228i	−0.347122	−	2.07877i
$799$		−	23.1863i		−	0.820272i
$800$	−1.31737	−	31.4280i	−0.0465760	−	1.11115i
$801$			5.42725i			0.191762i
$802$	−41.3261	+	6.90082i	−1.45927	+	0.243677i
$803$	18.2297	−	44.0104i	0.643312	−	1.55309i
$804$	−21.0763	+	43.1365i	−0.743302	+	1.52131i
$805$	−20.1907	+	8.36327i	−0.711629	+	0.294766i
$806$	−10.5903	−	0.701612i	−0.373026	−	0.0247132i
$807$	−19.2717	+	19.2717i	−0.678397	+	0.678397i
$808$	5.25884	−	6.48027i	0.185005	−	0.227975i
$809$	−12.2083	−	12.2083i	−0.429223	−	0.429223i	0.459141	−	0.888363i	$-0.348157\pi$
$809$	−12.2083	−	12.2083i	−0.429223	−	0.429223i	−0.888363	+	0.459141i	$0.848157\pi$
$810$	−43.5984	+	27.2222i	−1.53189	+	0.956491i
$811$	−33.9417	+	14.0591i	−1.19185	+	0.493682i	−0.888358	−	0.459151i	$-0.848154\pi$
$811$	−33.9417	+	14.0591i	−1.19185	+	0.493682i	−0.303496	+	0.952833i	$0.598154\pi$
$812$	−28.0801	+	24.8084i	−0.985420	+	0.870603i
$813$	10.5186	−	25.3941i	0.368902	−	0.890608i
$814$	−25.7650	−	18.3915i	−0.903063	−	0.644623i
$815$			48.1757i			1.68752i
$816$	18.9658	−	5.23125i	0.663935	−	0.183130i
$817$	−3.08058			−0.107776
$818$	−38.9441	−	27.7990i	−1.36165	−	0.971971i
$819$	25.0545	+	5.90896i	0.875473	+	0.206476i
$820$	61.8345	+	3.82518i	2.15936	+	0.133581i
$821$	34.3468	−	14.2269i	1.19871	−	0.496523i	0.308130	−	0.951344i	$-0.400297\pi$
$821$	34.3468	−	14.2269i	1.19871	−	0.496523i	0.890583	+	0.454821i	$0.150297\pi$
$822$	−0.277194	−	0.443947i	−0.00966824	−	0.0154844i
$823$	26.1011	+	26.1011i	0.909828	+	0.909828i	0.996258	−	0.0864298i	$-0.0275458\pi$
$823$	26.1011	+	26.1011i	0.909828	+	0.909828i	−0.0864298	+	0.996258i	$0.527546\pi$
$824$	6.82720	−	22.9601i	0.237837	−	0.799854i
$825$	32.2848	+	32.2848i	1.12401	+	1.12401i
$826$	−6.71215	+	29.0274i	−0.233545	+	1.00999i
$827$	15.7584	+	38.0442i	0.547974	+	1.32293i	0.918983	+	0.394297i	$0.129012\pi$
$827$	15.7584	+	38.0442i	0.547974	+	1.32293i	−0.371009	+	0.928629i	$0.620988\pi$
$828$	1.88948	+	5.49987i	0.0656638	+	0.191134i
$829$	13.1135	−	31.6589i	0.455452	−	1.09956i	−0.514767	−	0.857330i	$-0.672121\pi$
$829$	13.1135	−	31.6589i	0.455452	−	1.09956i	0.970219	−	0.242229i	$-0.0778785\pi$
$830$	52.3331	−	8.73882i	1.81651	−	0.303329i
$831$	−34.3837			−1.19276
$832$	−19.8953	−	20.8849i	−0.689745	−	0.724052i
$833$	−21.4516			−0.743253
$834$	10.8628	−	1.81392i	0.376148	−	0.0628110i
$835$	−13.1400	+	31.7228i	−0.454730	+	1.09781i
$836$	−11.6201	−	33.8238i	−0.401891	−	1.16982i
$837$	2.15953	+	5.21358i	0.0746444	+	0.180208i
$838$	6.66288	−	28.8143i	0.230165	−	0.995375i
$839$	−12.1499	−	12.1499i	−0.419461	−	0.419461i	0.465557	−	0.885018i	$-0.345854\pi$
$839$	−12.1499	−	12.1499i	−0.419461	−	0.419461i	−0.885018	+	0.465557i	$0.845854\pi$
$840$	78.0840	+	23.2183i	2.69416	+	0.801107i
$841$	5.47585	+	5.47585i	0.188823	+	0.188823i
$842$	6.83052	+	10.9396i	0.235395	+	0.377003i
$843$	8.51814	−	3.52833i	0.293380	−	0.121522i
$844$	−41.9183	−	2.59313i	−1.44289	−	0.0892592i
$845$	2.97696	−	42.1412i	0.102410	−	1.44970i
$846$	−20.7931	−	14.8425i	−0.714880	−	0.510295i
$847$	−12.8920			−0.442976
$848$	−17.8653	−	10.1406i	−0.613497	−	0.348228i
$849$			44.5216i			1.52798i
$850$	14.4339	+	10.3032i	0.495080	+	0.353397i
$851$	3.76563	−	9.09104i	0.129084	−	0.311637i
$852$	40.9121	−	36.1452i	1.40162	−	1.23831i
$853$	7.57954	−	3.13955i	0.259518	−	0.107496i	−0.249131	−	0.968470i	$-0.580145\pi$
$853$	7.57954	−	3.13955i	0.259518	−	0.107496i	0.508649	+	0.860974i	$0.330145\pi$
$854$	−65.0452	+	40.6133i	−2.22580	+	1.38976i
$855$	−19.1772	−	19.1772i	−0.655847	−	0.655847i
$856$	−31.4403	−	25.5142i	−1.07461	−	0.872059i
$857$	4.13716	−	4.13716i	0.141323	−	0.141323i	−0.632906	−	0.774229i	$-0.718138\pi$
$857$	4.13716	−	4.13716i	0.141323	−	0.141323i	0.774229	+	0.632906i	$0.218138\pi$
$858$	41.7759	+	2.76768i	1.42620	+	0.0944870i
$859$	−30.4827	+	12.6263i	−1.04005	+	0.430805i	−0.836332	−	0.548224i	$-0.815304\pi$
$859$	−30.4827	+	12.6263i	−1.04005	+	0.430805i	−0.203723	+	0.979029i	$0.565304\pi$
$860$	1.85044	−	3.78727i	0.0630994	−	0.129145i
$861$	−32.3292	+	78.0497i	−1.10178	+	2.65993i
$862$	47.3801	−	7.91176i	1.61377	−	0.269476i
$863$			12.6563i			0.430826i	0.976523	+	0.215413i	$0.0691098\pi$
$863$			12.6563i			0.430826i	−0.976523	+	0.215413i	$0.930890\pi$
$864$	−5.27045	+	14.4024i	−0.179304	+	0.489979i
$865$		−	6.06500i		−	0.206216i
$866$	4.30688	+	25.7920i	0.146354	+	0.876449i
$867$	9.94441	−	24.0079i	0.337730	−	0.815352i
$868$	7.42622	−	15.1991i	0.252062	−	0.515892i
$869$	−9.68254	−	23.3757i	−0.328458	−	0.792967i
$870$	−10.4114	+	45.0250i	−0.352978	+	1.52649i
$871$	−23.1965	+	32.1978i	−0.785983	+	1.09098i
$872$	−4.18894	−	40.2595i	−0.141855	−	1.36336i
$873$	8.12926	−	8.12926i	0.275134	−	0.275134i
$874$	9.42997	−	5.88793i	0.318973	−	0.199162i
$875$	2.83307	+	6.83965i	0.0957754	+	0.231222i
$876$	−36.5454	−	41.3650i	−1.23475	−	1.39760i
$877$	−4.18616	+	10.1063i	−0.141357	+	0.341265i	−0.978664	−	0.205467i	$-0.934129\pi$
$877$	−4.18616	+	10.1063i	−0.141357	+	0.341265i	0.837307	+	0.546732i	$0.184129\pi$
$878$	−33.9460	−	24.2313i	−1.14562	−	0.817767i
$879$	−20.0926			−0.677705
$880$	48.5630	+	6.03145i	1.63706	+	0.203320i
$881$			17.2321i			0.580564i	0.956941	+	0.290282i	$0.0937491\pi$
$881$			17.2321i			0.580564i	−0.956941	+	0.290282i	$0.906251\pi$
$882$	−13.7320	+	19.2374i	−0.462381	+	0.647757i
$883$	1.93851	+	0.802957i	0.0652360	+	0.0270216i	0.415063	−	0.909793i	$-0.363760\pi$
$883$	1.93851	+	0.802957i	0.0652360	+	0.0270216i	−0.349827	+	0.936814i	$0.613760\pi$
$884$	16.1817	−	1.61222i	0.544251	−	0.0542247i
$885$	14.0620	+	33.9487i	0.472690	+	1.14117i
$886$	0.652913	−	0.407669i	0.0219350	−	0.0136959i
$887$	−25.5261	−	25.5261i	−0.857082	−	0.857082i	0.133912	−	0.990993i	$-0.457246\pi$
$887$	−25.5261	−	25.5261i	−0.857082	−	0.857082i	−0.990993	+	0.133912i	$0.957246\pi$
$888$	−32.2527	+	17.4682i	−1.08233	+	0.586195i
$889$	−39.1441	−	39.1441i	−1.31285	−	1.31285i
$890$	−3.19830	+	13.8314i	−0.107207	+	0.463629i
$891$	−16.1124	−	38.8988i	−0.539786	−	1.30316i
$892$	4.66835	+	13.5886i	0.156308	+	0.454980i
$893$	−18.6895	+	45.1204i	−0.625419	+	1.50989i
$894$	5.25107	+	31.4464i	0.175622	+	1.05173i
$895$			13.8883i			0.464235i
$896$	42.8158	−	16.7452i	1.43037	−	0.559417i
$897$	2.08739	+	12.8459i	0.0696959	+	0.428911i
$898$	−3.61420	−	21.6439i	−0.120607	−	0.722266i
$899$	8.86598	+	3.67241i	0.295697	+	0.122482i
$900$	18.4795	−	6.34860i	0.615982	−	0.211620i
$901$	10.6999	−	4.43204i	0.356465	−	0.147653i
$902$	−11.4332	+	49.4441i	−0.380684	+	1.64631i
$903$	4.06438	+	4.06438i	0.135254	+	0.135254i
$904$	−22.1748	−	40.9429i	−0.737524	−	1.36174i
$905$	−48.8952	+	48.8952i	−1.62533	+	1.62533i
$906$	−14.0222	−	22.4576i	−0.465857	−	0.746104i
$907$	6.38390	+	15.4121i	0.211974	+	0.511750i	0.993726	−	0.111838i	$-0.0356739\pi$
$907$	6.38390	+	15.4121i	0.211974	+	0.511750i	−0.781752	+	0.623589i	$0.785674\pi$
$908$	−26.6611	−	1.64929i	−0.884778	−	0.0547337i
$909$	4.78951	+	1.98388i	0.158858	+	0.0658011i
$910$	60.3694	+	29.8237i	2.00123	+	0.988648i
$911$			50.7138i			1.68022i	0.542414	+	0.840111i	$0.317510\pi$
$911$			50.7138i			1.68022i	−0.542414	+	0.840111i	$0.682490\pi$
$912$	−41.1239	−	5.10753i	−1.36175	−	0.169127i
$913$			43.4624i			1.43839i
$914$	8.65263	−	12.1216i	0.286203	−	0.400947i
$915$	−36.1934	+	87.3785i	−1.19652	+	2.88864i
$916$	−17.2811	−	19.5601i	−0.570982	−	0.646284i
$917$	26.2691	−	10.8810i	0.867482	−	0.359323i
$918$	−4.57931	−	7.33411i	−0.151140	−	0.242062i
$919$	−5.41705	−	5.41705i	−0.178692	−	0.178692i	0.612093	−	0.790785i	$-0.290328\pi$
$919$	−5.41705	−	5.41705i	−0.178692	−	0.178692i	−0.790785	+	0.612093i	$0.790328\pi$
$920$	1.57425	+	15.1300i	0.0519014	+	0.498820i
$921$	−30.6455	−	30.6455i	−1.00980	−	1.00980i
$922$	9.24302	−	39.9724i	0.304403	−	1.31642i
$923$	38.3795	−	23.7311i	1.26328	−	0.781117i
$924$	−29.2945	+	59.9567i	−0.963719	+	1.97243i
$925$	−30.5457	−	12.6525i	−1.00434	−	0.416010i
$926$	−47.2716	+	7.89363i	−1.55344	+	0.259401i
$927$	14.8795			0.488708
$928$	10.9809	+	23.6561i	0.360466	+	0.776549i
$929$			6.95206i			0.228090i	0.993476	+	0.114045i	$0.0363807\pi$
$929$			6.95206i			0.228090i	−0.993476	+	0.114045i	$0.963619\pi$
$930$	−3.43637	−	20.5790i	−0.112683	−	0.674811i
$931$	41.7446	+	17.2912i	1.36812	+	0.566696i
$932$	−10.8049	−	5.27922i	−0.353927	−	0.172927i
$933$	29.7313	−	12.3151i	0.973359	−	0.403179i
$934$	−25.8467	−	5.97665i	−0.845729	−	0.195562i
$935$	−19.5085	+	19.5085i	−0.637995	+	0.637995i
$936$	8.91277	−	15.5435i	0.291323	−	0.508056i
$937$	−8.83114	−	8.83114i	−0.288501	−	0.288501i	0.547987	−	0.836487i	$-0.315395\pi$
$937$	−8.83114	−	8.83114i	−0.288501	−	0.288501i	−0.836487	+	0.547987i	$0.815395\pi$
$938$	−33.4985	−	53.6504i	−1.09376	−	1.75175i
$939$	12.4221	+	29.9896i	0.405380	+	0.978673i
$940$	−44.2446	−	50.0797i	−1.44310	−	1.63342i
$941$	−17.5267	+	42.3133i	−0.571355	+	1.37937i	0.329046	+	0.944314i	$0.393273\pi$
$941$	−17.5267	+	42.3133i	−0.571355	+	1.37937i	−0.900401	+	0.435060i	$0.856727\pi$
$942$	31.4670	+	22.4617i	1.02525	+	0.731842i
$943$	−15.7751			−0.513708
$944$	18.0349	+	10.2368i	0.586985	+	0.333180i
$945$		−	35.8014i		−	1.16462i
$946$	2.81033	+	2.00606i	0.0913716	+	0.0652227i
$947$	1.89555	−	4.57626i	0.0615970	−	0.148708i	−0.890084	−	0.455796i	$-0.849355\pi$
$947$	1.89555	−	4.57626i	0.0615970	−	0.148708i	0.951681	+	0.307088i	$0.0993546\pi$
$948$	−29.2611	−	1.81013i	−0.950355	−	0.0587904i
$949$	−23.9938	−	38.8044i	−0.778872	−	1.25965i
$950$	−19.7833	−	31.6845i	−0.641857	−	1.02798i
$951$	46.7478	−	46.7478i	1.51590	−	1.51590i
$952$	−7.38735	+	24.8440i	−0.239426	+	0.805198i
$953$	−25.3136	+	25.3136i	−0.819989	+	0.819989i	−0.986106	−	0.166117i	$-0.946877\pi$
$953$	−25.3136	+	25.3136i	−0.819989	+	0.819989i	0.166117	+	0.986106i	$0.446877\pi$
$954$	2.87485	−	12.4326i	0.0930768	−	0.402520i
$955$	−7.83869	−	18.9243i	−0.253654	−	0.612375i
$956$	−32.9653	+	11.3252i	−1.06617	+	0.366283i
$957$	−34.9740	−	14.4867i	−1.13055	−	0.468289i
$958$	0.376416	+	2.25419i	0.0121614	+	0.0728297i
$959$	0.689511			0.0222655
$960$	30.9815	−	47.4898i	0.999923	−	1.53273i
$961$	26.6675			0.860241
$962$	−28.7158	+	9.72514i	−0.925834	+	0.313551i
$963$	9.62517	−	23.2372i	0.310167	−	0.748809i
$964$	−15.7897	+	5.42454i	−0.508552	+	0.174713i
$965$	25.7169	−	10.6523i	0.827857	−	0.342909i
$966$	−20.2097	−	4.67320i	−0.650237	−	0.150358i
$967$	18.3618	+	18.3618i	0.590475	+	0.590475i	0.937760	−	0.347285i	$-0.112896\pi$
$967$	18.3618	+	18.3618i	0.590475	+	0.590475i	−0.347285	+	0.937760i	$0.612896\pi$
$968$	−2.55759	+	8.60129i	−0.0822041	+	0.276456i
$969$	16.5201	−	16.5201i	0.530701	−	0.530701i
$970$	25.5081	−	15.9269i	0.819016	−	0.511382i
$971$	22.5048	+	54.3313i	0.722213	+	1.74358i	0.666949	+	0.745104i	$0.267600\pi$
$971$	22.5048	+	54.3313i	0.722213	+	1.74358i	0.0552640	+	0.998472i	$0.482400\pi$
$972$	−32.4567	−	2.00782i	−1.04105	−	0.0644009i
$973$	−5.55238	+	13.4046i	−0.178001	+	0.429733i
$974$	38.0079	+	27.1308i	1.21785	+	0.869326i
$975$	43.1619	−	7.01359i	1.38229	−	0.224615i
$976$	14.1923	+	51.4538i	0.454284	+	1.64700i
$977$	−30.4208			−0.973248			−0.486624	−	0.873612i	$-0.661772\pi$
$977$	−30.4208			−0.973248			−0.486624	+	0.873612i	$0.661772\pi$
$978$	−26.5662	+	37.2170i	−0.849493	+	1.19007i
$979$	−10.7438	−	4.45022i	−0.343373	−	0.142230i
$980$	−46.3329	+	40.9344i	−1.48005	+	1.30760i
$981$	23.2295	−	9.62196i	0.741660	−	0.307206i
$982$	8.78574	+	14.0710i	0.280364	+	0.449024i
$983$	−9.40494	+	9.40494i	−0.299971	+	0.299971i	−0.841002	−	0.541031i	$-0.818034\pi$
$983$	−9.40494	+	9.40494i	−0.299971	+	0.299971i	0.541031	+	0.841002i	$0.318034\pi$
$984$	45.6594	+	37.0533i	1.45557	+	1.18122i
$985$	−3.81427	+	3.81427i	−0.121533	+	0.121533i
$986$	−14.3256	−	3.31258i	−0.456220	−	0.105494i
$987$	84.1877	−	34.8717i	2.67972	−	1.10998i
$988$	−32.7891	−	9.90603i	−1.04316	−	0.315153i
$989$	−0.410738	+	0.991609i	−0.0130607	+	0.0315313i
$990$	5.00670	+	29.9830i	0.159123	+	0.952921i
$991$	28.4865			0.904902			0.452451	−	0.891789i	$-0.350550\pi$
$991$	28.4865			0.904902			0.452451	+	0.891789i	$0.350550\pi$
$992$	−8.66728	−	7.96990i	−0.275186	−	0.253045i
$993$			67.9464i			2.15621i
$994$	11.8456	+	70.9384i	0.375721	+	2.25003i
$995$	37.1231	+	15.3769i	1.17688	+	0.487481i
$996$	45.2476	+	22.1078i	1.43373	+	0.700511i
$997$	10.2470	−	4.24443i	0.324524	−	0.134422i	−0.214473	−	0.976730i	$-0.568803\pi$
$997$	10.2470	−	4.24443i	0.324524	−	0.134422i	0.538997	+	0.842308i	$0.318803\pi$
$998$	−3.05365	+	13.2058i	−0.0966616	+	0.418023i
$999$	11.3985	+	11.3985i	0.360632	+	0.360632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bg.a.77.4	✓	216
13.12	even	2	inner	416.2.bg.a.77.51	yes	216
32.5	even	8	inner	416.2.bg.a.389.51	yes	216
416.389	even	8	inner	416.2.bg.a.389.4	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bg.a.77.4	✓	216	1.1	even	1	trivial
416.2.bg.a.77.51	yes	216	13.12	even	2	inner
416.2.bg.a.389.4	yes	216	416.389	even	8	inner
416.2.bg.a.389.51	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.39490 + 0.232927i) q^{2} +(0.834650 - 2.01502i) q^{3} +(1.89149 - 0.649819i) q^{4} +(1.24361 + 3.00234i) q^{5} +(-0.694900 + 3.00517i) q^{6} +(-2.87336 - 2.87336i) q^{7} +(-2.48708 + 1.34701i) q^{8} +(-1.24236 - 1.24236i) q^{9} +(-2.43404 - 3.89829i) q^{10} +(3.47808 - 1.44067i) q^{11} +(0.269331 - 4.35377i) q^{12} +(0.827643 - 3.50927i) q^{13} +(4.67734 + 3.33877i) q^{14} +7.08777 q^{15} +(3.15547 - 2.45825i) q^{16} +2.25511i q^{17} +(2.02235 + 1.44359i) q^{18} +(1.81775 - 4.38843i) q^{19} +(4.30326 + 4.87078i) q^{20} +(-8.18815 + 3.39164i) q^{21} +(-4.51601 + 2.81973i) q^{22} +(-1.17023 - 1.17023i) q^{23} +(0.638421 + 6.13581i) q^{24} +(-3.93195 + 3.93195i) q^{25} +(-0.337075 + 5.08787i) q^{26} +(2.50475 - 1.03750i) q^{27} +(-7.30210 - 3.56777i) q^{28} +(1.76433 - 4.25947i) q^{29} +(-9.88673 + 1.65093i) q^{30} +2.08147i q^{31} +(-3.82897 + 4.16401i) q^{32} -8.21088i q^{33} +(-0.525277 - 3.14566i) q^{34} +(5.05347 - 12.2002i) q^{35} +(-3.15722 - 1.54260i) q^{36} +(2.27537 + 5.49323i) q^{37} +(-1.51339 + 6.54482i) q^{38} +(-6.38048 - 4.59674i) q^{39} +(-7.13715 - 5.79190i) q^{40} +(6.74017 - 6.74017i) q^{41} +(10.6316 - 6.63824i) q^{42} +(-0.248187 - 0.599175i) q^{43} +(5.64259 - 4.98514i) q^{44} +(2.18498 - 5.27500i) q^{45} +(1.90493 + 1.35978i) q^{46} -10.2817 q^{47} +(-2.31973 - 8.41013i) q^{48} +9.51242i q^{49} +(4.56882 - 6.40054i) q^{50} +(4.54411 + 1.88223i) q^{51} +(-0.714916 - 7.17558i) q^{52} +(-1.96533 - 4.74473i) q^{53} +(-3.25222 + 2.03064i) q^{54} +(8.65077 + 8.65077i) q^{55} +(11.0167 + 3.27582i) q^{56} +(-7.32561 - 7.32561i) q^{57} +(-1.46892 + 6.35250i) q^{58} +(1.98398 + 4.78976i) q^{59} +(13.4064 - 4.60577i) q^{60} +(-5.10645 + 12.3281i) q^{61} +(-0.484831 - 2.90345i) q^{62} +7.13950i q^{63} +(4.37112 - 6.70025i) q^{64} +(11.5653 - 1.87930i) q^{65} +(1.91254 + 11.4534i) q^{66} +(-10.1684 - 4.21189i) q^{67} +(1.46542 + 4.26552i) q^{68} +(-3.33477 + 1.38131i) q^{69} +(-4.20734 + 18.1951i) q^{70} +(8.84949 + 8.84949i) q^{71} +(4.76332 + 1.41637i) q^{72} +(8.94747 - 8.94747i) q^{73} +(-4.45343 - 7.13250i) q^{74} +(4.64117 + 11.2048i) q^{75} +(0.586564 - 9.48188i) q^{76} +(-14.1334 - 5.85423i) q^{77} +(9.97083 + 4.92580i) q^{78} -6.72086i q^{79} +(11.3047 + 6.41669i) q^{80} -11.1840i q^{81} +(-7.83189 + 10.9718i) q^{82} +(-4.41803 + 10.6661i) q^{83} +(-13.2838 + 11.7361i) q^{84} +(-6.77062 + 2.80448i) q^{85} +(0.485759 + 0.777980i) q^{86} +(-7.11034 - 7.11034i) q^{87} +(-6.70967 + 8.26808i) q^{88} +(-2.18425 - 2.18425i) q^{89} +(-1.81913 + 7.86703i) q^{90} +(-12.4615 + 7.70530i) q^{91} +(-2.97392 - 1.45304i) q^{92} +(4.19422 + 1.73730i) q^{93} +(14.3419 - 2.39488i) q^{94} +15.4361 q^{95} +(5.19473 + 11.1910i) q^{96} +6.54340i q^{97} +(-2.21570 - 13.2689i) q^{98} +(-6.11086 - 2.53120i) 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

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