LMFDB - Embedded newform 187.2.g.f.69.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (of order $5$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			69.2
Character	$\chi$	$=$	187.69
Dual form			187.2.g.f.103.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73247 + 1.25872i) q^{2} +(0.331943 + 1.02161i) q^{3} +(0.799065 - 2.45927i) q^{4} +(-2.02945 - 1.47448i) q^{5} +(-1.86100 - 1.35210i) q^{6} +(1.12029 - 3.44788i) q^{7} +(0.387671 + 1.19313i) q^{8} +(1.49354 - 1.08512i) q^{9} +O(q^{10})$	\(q+(-1.73247 + 1.25872i) q^{2} +(0.331943 + 1.02161i) q^{3} +(0.799065 - 2.45927i) q^{4} +(-2.02945 - 1.47448i) q^{5} +(-1.86100 - 1.35210i) q^{6} +(1.12029 - 3.44788i) q^{7} +(0.387671 + 1.19313i) q^{8} +(1.49354 - 1.08512i) q^{9} +5.37193 q^{10} +(-2.89354 - 1.62094i) q^{11} +2.77767 q^{12} +(-1.40903 + 1.02372i) q^{13} +(2.39904 + 7.38349i) q^{14} +(0.832691 - 2.56276i) q^{15} +(2.01052 + 1.46073i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-1.22166 + 3.75989i) q^{18} +(-0.663697 - 2.04265i) q^{19} +(-5.24782 + 3.81276i) q^{20} +3.89428 q^{21} +(7.05328 - 0.833914i) q^{22} +1.89296 q^{23} +(-1.09023 + 0.792100i) q^{24} +(0.399489 + 1.22950i) q^{25} +(1.15253 - 3.54713i) q^{26} +(4.21146 + 3.05980i) q^{27} +(-7.58410 - 5.51017i) q^{28} +(0.564916 - 1.73863i) q^{29} +(1.78317 + 5.48804i) q^{30} +(3.18443 - 2.31362i) q^{31} -7.83088 q^{32} +(0.695483 - 3.49414i) q^{33} +2.14146 q^{34} +(-7.35741 + 5.34547i) q^{35} +(-1.47517 - 4.54010i) q^{36} +(0.735451 - 2.26349i) q^{37} +(3.72095 + 2.70343i) q^{38} +(-1.51356 - 1.09967i) q^{39} +(0.972488 - 2.99301i) q^{40} +(-3.48197 - 10.7164i) q^{41} +(-6.74674 + 4.90179i) q^{42} -10.4456 q^{43} +(-6.29845 + 5.82076i) q^{44} -4.63106 q^{45} +(-3.27951 + 2.38270i) q^{46} +(4.03492 + 12.4182i) q^{47} +(-0.824925 + 2.53886i) q^{48} +(-4.96975 - 3.61073i) q^{49} +(-2.23970 - 1.62723i) q^{50} +(0.331943 - 1.02161i) q^{51} +(1.39169 + 4.28319i) q^{52} +(-4.38400 + 3.18517i) q^{53} -11.1477 q^{54} +(3.48225 + 7.55608i) q^{55} +4.54807 q^{56} +(1.86649 - 1.35608i) q^{57} +(1.20974 + 3.72320i) q^{58} +(4.42843 - 13.6293i) q^{59} +(-5.63715 - 4.09563i) q^{60} +(5.99682 + 4.35694i) q^{61} +(-2.60474 + 8.01658i) q^{62} +(-2.06818 - 6.36520i) q^{63} +(9.54575 - 6.93539i) q^{64} +4.36900 q^{65} +(3.19322 + 6.92892i) q^{66} -2.79859 q^{67} +(-2.09198 + 1.51991i) q^{68} +(0.628355 + 1.93388i) q^{69} +(6.01809 - 18.5218i) q^{70} +(6.61870 + 4.80877i) q^{71} +(1.87369 + 1.36132i) q^{72} +(1.32002 - 4.06260i) q^{73} +(1.57494 + 4.84715i) q^{74} +(-1.12347 + 0.816248i) q^{75} -5.55376 q^{76} +(-8.83039 + 8.16068i) q^{77} +4.00637 q^{78} +(2.91564 - 2.11834i) q^{79} +(-1.92644 - 5.92896i) q^{80} +(-0.0165308 + 0.0508765i) q^{81} +(19.5213 + 14.1831i) q^{82} +(10.8228 + 7.86320i) q^{83} +(3.11178 - 9.57708i) q^{84} +(0.775182 + 2.38576i) q^{85} +(18.0967 - 13.1480i) q^{86} +1.96373 q^{87} +(0.812243 - 4.08075i) q^{88} +2.84363 q^{89} +(8.02319 - 5.82919i) q^{90} +(1.95115 + 6.00501i) q^{91} +(1.51260 - 4.65530i) q^{92} +(3.42068 + 2.48527i) q^{93} +(-22.6214 - 16.4354i) q^{94} +(-1.66491 + 5.12407i) q^{95} +(-2.59940 - 8.00014i) q^{96} +(-4.19227 + 3.04586i) q^{97} +13.1548 q^{98} +(-6.08053 + 0.718905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.73247	+	1.25872i	−1.22504	+	0.890046i	−0.996509	−	0.0834892i	$-0.973394\pi$
$2$	−1.73247	+	1.25872i	−1.22504	+	0.890046i	−0.228535	+	0.973536i	$0.573394\pi$
$3$	0.331943	+	1.02161i	0.191647	+	0.589829i	0.999999	+	0.00113018i	$0.000359747\pi$
$3$	0.331943	+	1.02161i	0.191647	+	0.589829i	−0.808352	+	0.588699i	$0.799640\pi$
$4$	0.799065	−	2.45927i	0.399533	−	1.22964i
$5$	−2.02945	−	1.47448i	−0.907598	−	0.659409i	0.0328080	−	0.999462i	$-0.489555\pi$
$5$	−2.02945	−	1.47448i	−0.907598	−	0.659409i	−0.940406	+	0.340053i	$0.889555\pi$
$6$	−1.86100	−	1.35210i	−0.759752	−	0.551992i
$7$	1.12029	−	3.44788i	0.423428	−	1.30318i	−0.481063	−	0.876686i	$-0.659749\pi$
$7$	1.12029	−	3.44788i	0.423428	−	1.30318i	0.904491	−	0.426492i	$-0.140251\pi$
$8$	0.387671	+	1.19313i	0.137062	+	0.421834i
$9$	1.49354	−	1.08512i	0.497847	−	0.361707i
$10$	5.37193			1.69875
$11$	−2.89354	−	1.62094i	−0.872435	−	0.488731i
$11$	−2.89354	−	1.62094i	−0.872435	−	0.488731i
$12$	2.77767			0.801844
$13$	−1.40903	+	1.02372i	−0.390793	+	0.283928i	−0.765781	−	0.643102i	$-0.777647\pi$
$13$	−1.40903	+	1.02372i	−0.390793	+	0.283928i	0.374987	+	0.927030i	$0.377647\pi$
$14$	2.39904	+	7.38349i	0.641171	+	1.97332i
$15$	0.832691	−	2.56276i	0.215000	−	0.661702i
$16$	2.01052	+	1.46073i	0.502631	+	0.365183i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	−1.22166	+	3.75989i	−0.287948	+	0.886214i
$19$	−0.663697	−	2.04265i	−0.152262	−	0.468616i	0.845611	−	0.533800i	$-0.179236\pi$
$19$	−0.663697	−	2.04265i	−0.152262	−	0.468616i	−0.997873	+	0.0651843i	$0.979236\pi$
$20$	−5.24782	+	3.81276i	−1.17345	+	0.852560i
$21$	3.89428			0.849801
$22$	7.05328	−	0.833914i	1.50376	−	0.177791i
$23$	1.89296			0.394710			0.197355	−	0.980332i	$-0.436765\pi$
$23$	1.89296			0.394710			0.197355	+	0.980332i	$0.436765\pi$
$24$	−1.09023	+	0.792100i	−0.222543	+	0.161687i
$25$	0.399489	+	1.22950i	0.0798978	+	0.245900i
$26$	1.15253	−	3.54713i	0.226030	−	0.695649i
$27$	4.21146	+	3.05980i	0.810495	+	0.588859i
$28$	−7.58410	−	5.51017i	−1.43326	−	1.04132i
$29$	0.564916	−	1.73863i	0.104902	−	0.322856i	−0.884805	−	0.465961i	$-0.845709\pi$
$29$	0.564916	−	1.73863i	0.104902	−	0.322856i	0.989707	+	0.143105i	$0.0457087\pi$
$30$	1.78317	+	5.48804i	0.325561	+	1.00197i
$31$	3.18443	−	2.31362i	0.571940	−	0.415539i	−0.263869	−	0.964558i	$-0.584999\pi$
$31$	3.18443	−	2.31362i	0.571940	−	0.415539i	0.835809	+	0.549020i	$0.184999\pi$
$32$	−7.83088			−1.38432
$33$	0.695483	−	3.49414i	0.121068	−	0.608252i
$34$	2.14146			0.367257
$35$	−7.35741	+	5.34547i	−1.24363	+	0.903550i
$36$	−1.47517	−	4.54010i	−0.245862	−	0.756684i
$37$	0.735451	−	2.26349i	0.120907	−	0.372115i	−0.872226	−	0.489103i	$-0.837324\pi$
$37$	0.735451	−	2.26349i	0.120907	−	0.372115i	0.993133	+	0.116989i	$0.0373241\pi$
$38$	3.72095	+	2.70343i	0.603618	+	0.438554i
$39$	−1.51356	−	1.09967i	−0.242364	−	0.176087i
$40$	0.972488	−	2.99301i	0.153764	−	0.473236i
$41$	−3.48197	−	10.7164i	−0.543792	−	1.67362i	−0.723845	−	0.689962i	$-0.757627\pi$
$41$	−3.48197	−	10.7164i	−0.543792	−	1.67362i	0.180053	−	0.983657i	$-0.442373\pi$
$42$	−6.74674	+	4.90179i	−1.04104	+	0.756363i
$43$	−10.4456			−1.59294			−0.796469	−	0.604679i	$-0.793301\pi$
$43$	−10.4456			−1.59294			−0.796469	+	0.604679i	$0.793301\pi$
$44$	−6.29845	+	5.82076i	−0.949527	+	0.877513i
$45$	−4.63106			−0.690358
$46$	−3.27951	+	2.38270i	−0.483537	+	0.351310i
$47$	4.03492	+	12.4182i	0.588553	+	1.81138i	0.584508	+	0.811388i	$0.301288\pi$
$47$	4.03492	+	12.4182i	0.588553	+	1.81138i	0.00404545	+	0.999992i	$0.498712\pi$
$48$	−0.824925	+	2.53886i	−0.119068	+	0.366453i
$49$	−4.96975	−	3.61073i	−0.709964	−	0.515819i
$50$	−2.23970	−	1.62723i	−0.316741	−	0.230126i
$51$	0.331943	−	1.02161i	0.0464813	−	0.143055i
$52$	1.39169	+	4.28319i	0.192993	+	0.593972i
$53$	−4.38400	+	3.18517i	−0.602189	+	0.437516i	−0.846655	−	0.532142i	$-0.821387\pi$
$53$	−4.38400	+	3.18517i	−0.602189	+	0.437516i	0.244466	+	0.969658i	$0.421387\pi$
$54$	−11.1477			−1.51700
$55$	3.48225	+	7.55608i	0.469547	+	1.01886i
$56$	4.54807			0.607761
$57$	1.86649	−	1.35608i	0.247223	−	0.179618i
$58$	1.20974	+	3.72320i	0.158847	+	0.488880i
$59$	4.42843	−	13.6293i	0.576532	−	1.77438i	−0.0543710	−	0.998521i	$-0.517315\pi$
$59$	4.42843	−	13.6293i	0.576532	−	1.77438i	0.630903	−	0.775862i	$-0.282685\pi$
$60$	−5.63715	−	4.09563i	−0.727753	−	0.528743i
$61$	5.99682	+	4.35694i	0.767814	+	0.557850i	0.901297	−	0.433201i	$-0.142616\pi$
$61$	5.99682	+	4.35694i	0.767814	+	0.557850i	−0.133483	+	0.991051i	$0.542616\pi$
$62$	−2.60474	+	8.01658i	−0.330803	+	1.01811i
$63$	−2.06818	−	6.36520i	−0.260566	−	0.801940i
$64$	9.54575	−	6.93539i	1.19322	−	0.866924i
$65$	4.36900			0.541908
$66$	3.19322	+	6.92892i	0.393058	+	0.852891i
$67$	−2.79859			−0.341903			−0.170951	−	0.985279i	$-0.554684\pi$
$67$	−2.79859			−0.341903			−0.170951	+	0.985279i	$0.554684\pi$
$68$	−2.09198	+	1.51991i	−0.253690	+	0.184316i
$69$	0.628355	+	1.93388i	0.0756450	+	0.232811i
$70$	6.01809	−	18.5218i	0.719299	−	2.21378i
$71$	6.61870	+	4.80877i	0.785495	+	0.570696i	0.906623	−	0.421941i	$-0.138651\pi$
$71$	6.61870	+	4.80877i	0.785495	+	0.570696i	−0.121128	+	0.992637i	$0.538651\pi$
$72$	1.87369	+	1.36132i	0.220816	+	0.160433i
$73$	1.32002	−	4.06260i	0.154496	−	0.475491i	−0.843613	−	0.536951i	$-0.819576\pi$
$73$	1.32002	−	4.06260i	0.154496	−	0.475491i	0.998110	+	0.0614605i	$0.0195758\pi$
$74$	1.57494	+	4.84715i	0.183083	+	0.563470i
$75$	−1.12347	+	0.816248i	−0.129727	+	0.0942522i
$76$	−5.55376			−0.637060
$77$	−8.83039	+	8.16068i	−1.00632	+	0.929995i
$78$	4.00637			0.453632
$79$	2.91564	−	2.11834i	0.328035	−	0.238332i	−0.411561	−	0.911382i	$-0.635016\pi$
$79$	2.91564	−	2.11834i	0.328035	−	0.238332i	0.739596	+	0.673051i	$0.235016\pi$
$80$	−1.92644	−	5.92896i	−0.215382	−	0.662878i
$81$	−0.0165308	+	0.0508765i	−0.00183675	+	0.00565294i
$82$	19.5213	+	14.1831i	2.15577	+	1.56626i
$83$	10.8228	+	7.86320i	1.18795	+	0.863098i	0.993046	−	0.117724i	$-0.0375598\pi$
$83$	10.8228	+	7.86320i	1.18795	+	0.863098i	0.194906	+	0.980822i	$0.437560\pi$
$84$	3.11178	−	9.57708i	0.339523	−	1.04495i
$85$	0.775182	+	2.38576i	0.0840802	+	0.258772i
$86$	18.0967	−	13.1480i	1.95142	−	1.41779i
$87$	1.96373			0.210534
$88$	0.812243	−	4.08075i	0.0865854	−	0.435010i
$89$	2.84363			0.301424			0.150712	−	0.988578i	$-0.451843\pi$
$89$	2.84363			0.301424			0.150712	+	0.988578i	$0.451843\pi$
$90$	8.02319	−	5.82919i	0.845719	−	0.614451i
$91$	1.95115	+	6.00501i	0.204536	+	0.629496i
$92$	1.51260	−	4.65530i	0.157699	−	0.485349i
$93$	3.42068	+	2.48527i	0.354708	+	0.257710i
$94$	−22.6214	−	16.4354i	−2.33322	−	1.69518i
$95$	−1.66491	+	5.12407i	−0.170816	+	0.525718i
$96$	−2.59940	−	8.00014i	−0.265300	−	0.816511i
$97$	−4.19227	+	3.04586i	−0.425660	+	0.309260i	−0.779911	−	0.625890i	$-0.784736\pi$
$97$	−4.19227	+	3.04586i	−0.425660	+	0.309260i	0.354251	+	0.935150i	$0.384736\pi$
$98$	13.1548			1.32884
$99$	−6.08053	+	0.718905i	−0.611116	+	0.0722527i
$100$	3.34289			0.334289
$101$	−4.79884	+	3.48656i	−0.477502	+	0.346926i	−0.800358	−	0.599522i	$-0.795357\pi$
$101$	−4.79884	+	3.48656i	−0.477502	+	0.346926i	0.322855	+	0.946448i	$0.395357\pi$
$102$	0.710840	+	2.18774i	0.0703837	+	0.216619i
$103$	1.57669	−	4.85255i	0.155356	−	0.478136i	−0.842841	−	0.538163i	$-0.819119\pi$
$103$	1.57669	−	4.85255i	0.155356	−	0.478136i	0.998197	+	0.0600267i	$0.0191186\pi$
$104$	−1.76766	−	1.28428i	−0.173334	−	0.125934i
$105$	−7.90325	−	5.74205i	−0.771278	−	0.560366i
$106$	3.58595	−	11.0364i	0.348299	−	1.07195i
$107$	4.95500	+	15.2499i	0.479018	+	1.47427i	0.840461	+	0.541871i	$0.182284\pi$
$107$	4.95500	+	15.2499i	0.479018	+	1.47427i	−0.361444	+	0.932394i	$0.617716\pi$
$108$	10.8901	−	7.91213i	1.04790	−	0.761345i
$109$	−13.2308			−1.26728			−0.633640	−	0.773628i	$-0.718440\pi$
$109$	−13.2308			−1.26728			−0.633640	+	0.773628i	$0.718440\pi$
$110$	−15.5439	−	8.70755i	−1.48205	−	0.830232i
$111$	2.55654			0.242656
$112$	7.28879	−	5.29561i	0.688726	−	0.500389i
$113$	−2.65483	−	8.17073i	−0.249745	−	0.768637i	−0.994820	−	0.101656i	$-0.967586\pi$
$113$	−2.65483	−	8.17073i	−0.249745	−	0.768637i	0.745074	−	0.666982i	$-0.232414\pi$
$114$	−1.52672	+	4.69876i	−0.142990	+	0.440079i
$115$	−3.84167	−	2.79114i	−0.358238	−	0.260275i
$116$	−3.82436	−	2.77856i	−0.355083	−	0.257983i
$117$	−0.993581	+	3.05793i	−0.0918566	+	0.282705i
$118$	9.48327	+	29.1865i	0.873006	+	2.68684i
$119$	−2.93295	+	2.13091i	−0.268863	+	0.195340i
$120$	3.38051			0.308597
$121$	5.74513	+	9.38048i	0.522285	+	0.852771i
$122$	−15.8735			−1.43712
$123$	9.79221	−	7.11446i	0.882934	−	0.641489i
$124$	−3.14526	−	9.68011i	−0.282452	−	0.869299i
$125$	−2.87377	+	8.84457i	−0.257038	+	0.791082i
$126$	11.5950	+	8.42429i	1.03297	+	0.750496i
$127$	10.0678	+	7.31468i	0.893373	+	0.649073i	0.936755	−	0.349985i	$-0.113813\pi$
$127$	10.0678	+	7.31468i	0.893373	+	0.649073i	−0.0433825	+	0.999059i	$0.513813\pi$
$128$	−2.96832	+	9.13554i	−0.262365	+	0.807476i
$129$	−3.46734	−	10.6714i	−0.305282	−	0.939562i
$130$	−7.56918	+	5.49933i	−0.663861	+	0.482323i
$131$	15.0271			1.31293			0.656464	−	0.754358i	$-0.272051\pi$
$131$	15.0271			1.31293			0.656464	+	0.754358i	$0.272051\pi$
$132$	−8.03730	−	4.50243i	−0.699557	−	0.391886i
$133$	−7.78634			−0.675162
$134$	4.84849	−	3.52263i	0.418846	−	0.304309i
$135$	−4.03532	−	12.4194i	−0.347305	−	1.06890i
$136$	0.387671	−	1.19313i	0.0332425	−	0.102310i
$137$	−5.45624	−	3.96419i	−0.466158	−	0.338684i	0.329784	−	0.944056i	$-0.393024\pi$
$137$	−5.45624	−	3.96419i	−0.466158	−	0.338684i	−0.795942	+	0.605373i	$0.793024\pi$
$138$	−3.52281	−	2.55947i	−0.299881	−	0.217877i
$139$	1.47548	−	4.54106i	0.125148	−	0.385167i	−0.868780	−	0.495199i	$-0.835095\pi$
$139$	1.47548	−	4.54106i	0.125148	−	0.385167i	0.993928	+	0.110032i	$0.0350952\pi$
$140$	7.26691	+	22.3652i	0.614166	+	1.89021i
$141$	−11.3472	+	8.24426i	−0.955611	+	0.694292i
$142$	−17.5196			−1.47021
$143$	5.73645	−	0.678225i	0.479706	−	0.0567160i
$144$	4.58787			0.382322
$145$	−3.71005	+	2.69551i	−0.308103	+	0.223850i
$146$	2.82676	+	8.69987i	0.233944	+	0.720006i
$147$	2.03911	−	6.27572i	0.168183	−	0.517613i
$148$	−4.97885	−	3.61735i	−0.409259	−	0.297344i
$149$	1.08240	+	0.786410i	0.0886737	+	0.0644252i	0.631239	−	0.775589i	$-0.282547\pi$
$149$	1.08240	+	0.786410i	0.0886737	+	0.0644252i	−0.542565	+	0.840014i	$0.682547\pi$
$150$	0.918956	−	2.82825i	0.0750324	−	0.230926i
$151$	2.74706	+	8.45458i	0.223553	+	0.688024i	0.998435	+	0.0559190i	$0.0178089\pi$
$151$	2.74706	+	8.45458i	0.223553	+	0.688024i	−0.774883	+	0.632105i	$0.782191\pi$
$152$	2.17984	−	1.58375i	0.176809	−	0.128459i
$153$	−1.84612			−0.149250
$154$	5.02644	−	25.2531i	0.405042	−	2.03495i
$155$	−9.87404			−0.793102
$156$	−3.91381	+	2.84355i	−0.313355	+	0.227666i
$157$	2.31189	+	7.11527i	0.184509	+	0.567860i	0.999940	−	0.0109945i	$-0.00349974\pi$
$157$	2.31189	+	7.11527i	0.184509	+	0.567860i	−0.815431	+	0.578855i	$0.803500\pi$
$158$	−2.38489	+	7.33993i	−0.189731	+	0.583933i
$159$	−4.70925	−	3.42147i	−0.373468	−	0.271340i
$160$	15.8924	+	11.5465i	1.25640	+	0.912831i
$161$	2.12066	−	6.52671i	0.167131	−	0.514377i
$162$	−0.0353999	−	0.108950i	−0.00278128	−	0.00855990i
$163$	−6.07002	+	4.41012i	−0.475440	+	0.345428i	−0.799558	−	0.600589i	$-0.794933\pi$
$163$	−6.07002	+	4.41012i	−0.475440	+	0.345428i	0.324117	+	0.946017i	$0.394933\pi$
$164$	−29.1368			−2.27520
$165$	−6.56350	+	6.06571i	−0.510968	+	0.472215i
$166$	−28.6477			−2.22349
$167$	17.7204	−	12.8746i	1.37125	−	0.996269i	0.373608	−	0.927587i	$-0.378120\pi$
$167$	17.7204	−	12.8746i	1.37125	−	0.996269i	0.997639	−	0.0686824i	$-0.0218795\pi$
$168$	1.50970	+	4.64637i	0.116476	+	0.358475i
$169$	−3.07986	+	9.47885i	−0.236913	+	0.729142i
$170$	−4.34598	−	3.15754i	−0.333321	−	0.242172i
$171$	−3.20778	−	2.33059i	−0.245305	−	0.178224i
$172$	−8.34672	+	25.6886i	−0.636431	+	1.95873i
$173$	−4.90402	−	15.0930i	−0.372846	−	1.14750i	−0.944920	−	0.327300i	$-0.893861\pi$
$173$	−4.90402	−	15.0930i	−0.372846	−	1.14750i	0.572074	−	0.820202i	$-0.306139\pi$
$174$	−3.40211	+	2.47178i	−0.257913	+	0.187385i
$175$	4.68672			0.354283
$176$	−3.44978	−	7.48561i	−0.260037	−	0.564249i
$177$	15.3939			1.15707
$178$	−4.92652	+	3.57932i	−0.369258	+	0.268282i
$179$	−7.06432	−	21.7417i	−0.528012	−	1.62505i	−0.758281	−	0.651927i	$-0.773961\pi$
$179$	−7.06432	−	21.7417i	−0.528012	−	1.62505i	0.230269	−	0.973127i	$-0.426039\pi$
$180$	−3.70052	+	11.3890i	−0.275821	+	0.848888i
$181$	−1.34239	−	0.975303i	−0.0997791	−	0.0724937i	0.536777	−	0.843724i	$-0.319642\pi$
$181$	−1.34239	−	0.975303i	−0.0997791	−	0.0724937i	−0.636556	+	0.771230i	$0.719642\pi$
$182$	−10.9389	−	7.94759i	−0.810846	−	0.589114i
$183$	−2.46052	+	7.57269i	−0.181887	+	0.559790i
$184$	0.733846	+	2.25854i	0.0540998	+	0.166502i
$185$	−4.83003	+	3.50923i	−0.355111	+	0.258003i
$186$	−9.05448			−0.663907
$187$	1.38816	+	3.01214i	0.101512	+	0.220270i
$188$	33.7639			2.46248
$189$	15.2679	−	11.0928i	1.11057	−	0.806880i
$190$	−3.56533	−	10.9730i	−0.258656	−	0.796062i
$191$	−1.90605	+	5.86623i	−0.137917	+	0.424466i	−0.996032	−	0.0889917i	$-0.971636\pi$
$191$	−1.90605	+	5.86623i	−0.137917	+	0.424466i	0.858115	+	0.513457i	$0.171636\pi$
$192$	10.2539	+	7.44992i	0.740014	+	0.537652i
$193$	−17.1750	−	12.4784i	−1.23628	−	0.898213i	−0.238939	−	0.971035i	$-0.576800\pi$
$193$	−17.1750	−	12.4784i	−1.23628	−	0.898213i	−0.997345	+	0.0728216i	$0.976800\pi$
$194$	3.42912	−	10.5537i	0.246196	−	0.757714i
$195$	1.45026	+	4.46344i	0.103855	+	0.319633i
$196$	−12.8509	+	9.33674i	−0.917923	+	0.666910i
$197$	25.2566			1.79946			0.899729	−	0.436448i	$-0.143764\pi$
$197$	25.2566			1.79946			0.899729	+	0.436448i	$0.143764\pi$
$198$	9.62946	−	8.89914i	0.684336	−	0.632435i
$199$	23.8616			1.69150			0.845752	−	0.533576i	$-0.179152\pi$
$199$	23.8616			1.69150			0.845752	+	0.533576i	$0.179152\pi$
$200$	−1.31208	+	0.953283i	−0.0927782	+	0.0674073i
$201$	−0.928973	−	2.85908i	−0.0655247	−	0.201664i
$202$	3.92527	−	12.0808i	0.276181	−	0.849999i
$203$	−5.36173	−	3.89553i	−0.376320	−	0.273412i
$204$	−2.24718	−	1.63267i	−0.157334	−	0.114310i
$205$	−8.73465	+	26.8825i	−0.610055	+	1.87756i
$206$	3.37641	+	10.3915i	0.235246	+	0.724011i
$207$	2.82721	−	2.05409i	0.196505	−	0.142769i
$208$	−4.32825			−0.300110
$209$	−1.39057	+	6.98629i	−0.0961877	+	0.483252i
$210$	20.9198			1.44360
$211$	−4.20202	+	3.05295i	−0.289279	+	0.210173i	−0.722954	−	0.690896i	$-0.757216\pi$
$211$	−4.20202	+	3.05295i	−0.289279	+	0.210173i	0.433676	+	0.901069i	$0.357216\pi$
$212$	4.33008	+	13.3266i	0.297391	+	0.915275i
$213$	−2.71568	+	8.35799i	−0.186075	+	0.572680i
$214$	−27.7797	−	20.1831i	−1.89898	−	1.37969i
$215$	21.1988	+	15.4019i	1.44575	+	1.05040i
$216$	−2.01808	+	6.21100i	−0.137313	+	0.422605i
$217$	−4.40963	−	13.5715i	−0.299345	−	0.921290i
$218$	22.9220	−	16.6538i	1.55247	−	1.12794i
$219$	4.58858			0.310067
$220$	21.3650	−	2.52600i	1.44043	−	0.170303i
$221$	1.74165			0.117156
$222$	−4.42913	+	3.21795i	−0.297264	+	0.215975i
$223$	4.60337	+	14.1677i	0.308265	+	0.948741i	0.978439	+	0.206537i	$0.0662195\pi$
$223$	4.60337	+	14.1677i	0.308265	+	0.948741i	−0.670174	+	0.742204i	$0.733781\pi$
$224$	−8.77282	+	27.0000i	−0.586159	+	1.80401i
$225$	1.93081	+	1.40282i	0.128721	+	0.0935211i
$226$	14.8840	+	10.8139i	0.990072	+	0.719329i
$227$	−1.98692	+	6.11513i	−0.131877	+	0.405875i	−0.995091	−	0.0989624i	$-0.968448\pi$
$227$	−1.98692	+	6.11513i	−0.131877	+	0.405875i	0.863214	+	0.504838i	$0.168448\pi$
$228$	−1.84353	−	5.67380i	−0.122091	−	0.375757i
$229$	−10.6103	+	7.70880i	−0.701145	+	0.509412i	−0.880305	−	0.474408i	$-0.842662\pi$
$229$	−10.6103	+	7.70880i	−0.701145	+	0.509412i	0.179160	+	0.983820i	$0.442662\pi$
$230$	10.1688			0.670514
$231$	−11.2682	−	6.31238i	−0.741396	−	0.415324i
$232$	2.29341			0.150570
$233$	−8.04765	+	5.84696i	−0.527219	+	0.383047i	−0.819317	−	0.573341i	$-0.805647\pi$
$233$	−8.04765	+	5.84696i	−0.527219	+	0.383047i	0.292097	+	0.956389i	$0.405647\pi$
$234$	−2.12771	−	6.54841i	−0.139093	−	0.428083i
$235$	10.1217	−	31.1515i	0.660270	−	2.03210i
$236$	−29.9795	−	21.7814i	−1.95150	−	1.41785i
$237$	3.13195	+	2.27549i	0.203442	+	0.147809i
$238$	2.39904	−	7.38349i	0.155507	−	0.478601i
$239$	0.00664491	+	0.0204509i	0.000429824	+	0.00132286i	0.951271	−	0.308355i	$-0.0997786\pi$
$239$	0.00664491	+	0.0204509i	0.000429824	+	0.00132286i	−0.950841	+	0.309678i	$0.899779\pi$
$240$	5.41765	−	3.93615i	0.349708	−	0.254078i
$241$	8.95301			0.576714			0.288357	−	0.957523i	$-0.406891\pi$
$241$	8.95301			0.576714			0.288357	+	0.957523i	$0.406891\pi$
$242$	−21.7607	−	9.01995i	−1.39883	−	0.579824i
$243$	15.5595			0.998141
$244$	15.5068	−	11.2663i	0.992718	−	0.721252i
$245$	4.76190	+	14.6556i	0.304226	+	0.936313i
$246$	−8.00966	+	24.6512i	−0.510678	+	1.57170i
$247$	3.02626	+	2.19871i	0.192556	+	0.139900i
$248$	3.99496	+	2.90251i	0.253680	+	0.184309i
$249$	−4.44062	+	13.6668i	−0.281413	+	0.866100i
$250$	−6.15406	−	18.9402i	−0.389217	−	1.19789i
$251$	8.86710	−	6.44232i	0.559686	−	0.406636i	−0.271658	−	0.962394i	$-0.587572\pi$
$251$	8.86710	−	6.44232i	0.559686	−	0.406636i	0.831344	+	0.555758i	$0.187572\pi$
$252$	−17.3064			−1.09020
$253$	−5.47736	−	3.06837i	−0.344358	−	0.192907i
$254$	−26.6493			−1.67213
$255$	−2.18001	+	1.58387i	−0.136518	+	0.0991860i
$256$	0.935781	+	2.88004i	0.0584863	+	0.180002i
$257$	5.92185	−	18.2256i	0.369395	−	1.13688i	−0.577788	−	0.816187i	$-0.696084\pi$
$257$	5.92185	−	18.2256i	0.369395	−	1.13688i	0.947183	−	0.320693i	$-0.103916\pi$
$258$	19.4393	+	14.1235i	1.21024	+	0.879289i
$259$	−6.98032	−	5.07150i	−0.433736	−	0.315128i
$260$	3.49112	−	10.7446i	0.216510	−	0.666349i
$261$	−1.04290	−	3.20972i	−0.0645540	−	0.198677i
$262$	−26.0341	+	18.9149i	−1.60839	+	1.16857i
$263$	−15.0292			−0.926742			−0.463371	−	0.886164i	$-0.653360\pi$
$263$	−15.0292			−0.926742			−0.463371	+	0.886164i	$0.653360\pi$
$264$	4.43857	−	0.524776i	0.273175	−	0.0322977i
$265$	13.5936			0.835048
$266$	13.4896	−	9.80079i	0.827103	−	0.600925i
$267$	0.943923	+	2.90510i	0.0577671	+	0.177789i
$268$	−2.23626	+	6.88250i	−0.136601	+	0.420416i
$269$	−2.54570	−	1.84956i	−0.155214	−	0.112770i	0.507468	−	0.861671i	$-0.330582\pi$
$269$	−2.54570	−	1.84956i	−0.155214	−	0.112770i	−0.662682	+	0.748901i	$0.730582\pi$
$270$	22.6236	+	16.4370i	1.37683	+	1.00033i
$271$	1.43035	−	4.40217i	0.0868876	−	0.267413i	−0.898167	−	0.439654i	$-0.855101\pi$
$271$	1.43035	−	4.40217i	0.0868876	−	0.267413i	0.985055	+	0.172242i	$0.0551010\pi$
$272$	−0.767951	−	2.36351i	−0.0465639	−	0.143309i
$273$	−5.48714	+	3.98664i	−0.332097	+	0.241282i
$274$	14.4426			0.872508
$275$	0.837005	−	4.20515i	0.0504733	−	0.253580i
$276$	5.25802			0.316496
$277$	19.0075	−	13.8098i	1.14205	−	0.829749i	0.154648	−	0.987970i	$-0.450576\pi$
$277$	19.0075	−	13.8098i	1.14205	−	0.829749i	0.987404	+	0.158220i	$0.0505757\pi$
$278$	3.15967	+	9.72447i	0.189504	+	0.583235i
$279$	2.24551	−	6.91098i	0.134435	−	0.413749i
$280$	−9.23008	−	6.70605i	−0.551603	−	0.400763i
$281$	16.2861	+	11.8326i	0.971549	+	0.705871i	0.955804	−	0.294005i	$-0.0949881\pi$
$281$	16.2861	+	11.8326i	0.971549	+	0.705871i	0.0157446	+	0.999876i	$0.494988\pi$
$282$	9.28163	−	28.5659i	0.552713	−	1.70108i
$283$	−2.37911	−	7.32214i	−0.141423	−	0.435256i	0.855110	−	0.518446i	$-0.173489\pi$
$283$	−2.37911	−	7.32214i	−0.141423	−	0.435256i	−0.996534	+	0.0831898i	$0.973489\pi$
$284$	17.1148	−	12.4347i	1.01558	−	0.737861i
$285$	−5.78747			−0.342820
$286$	−9.08456	+	8.39557i	−0.537181	+	0.496440i
$287$	−40.8497			−2.41128
$288$	−11.6957	+	8.49745i	−0.689178	+	0.500717i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	3.03469	−	9.33980i	0.178203	−	0.548452i
$291$	−4.50329	−	3.27183i	−0.263987	−	0.191798i
$292$	−8.93624	−	6.49256i	−0.522954	−	0.379948i
$293$	7.61768	−	23.4448i	0.445030	−	1.36966i	−0.437421	−	0.899257i	$-0.644108\pi$
$293$	7.61768	−	23.4448i	0.445030	−	1.36966i	0.882451	−	0.470404i	$-0.155892\pi$
$294$	4.36665	+	13.4392i	0.254668	+	0.783788i
$295$	−29.0834	+	21.1304i	−1.69330	+	1.23026i
$296$	2.98574			0.173543
$297$	−7.22627	−	15.6802i	−0.419311	−	0.909855i
$298$	−2.86510			−0.165971
$299$	−2.66723	+	1.93786i	−0.154250	+	0.112069i
$300$	1.10965	+	3.41515i	0.0640656	+	0.197174i
$301$	−11.7021	+	36.0152i	−0.674495	+	2.07588i
$302$	−15.4011	−	11.1896i	−0.886235	−	0.643887i
$303$	−5.15486	−	3.74523i	−0.296139	−	0.215158i
$304$	1.64938	−	5.07627i	0.0945985	−	0.291144i
$305$	−5.74602	−	17.6844i	−0.329016	−	1.01261i
$306$	3.19835	−	2.32374i	0.182838	−	0.132839i
$307$	−19.2822			−1.10050			−0.550248	−	0.835001i	$-0.685467\pi$
$307$	−19.2822			−1.10050			−0.550248	+	0.835001i	$0.685467\pi$
$308$	13.0132	+	28.2372i	0.741499	+	1.60897i
$309$	5.48081			0.311792
$310$	17.1065	−	12.4286i	0.971585	−	0.705898i
$311$	−4.68787	−	14.4278i	−0.265825	−	0.818125i	−0.991502	−	0.130090i	$-0.958473\pi$
$311$	−4.68787	−	14.4278i	−0.265825	−	0.818125i	0.725677	−	0.688035i	$-0.241527\pi$
$312$	0.725279	−	2.23218i	0.0410608	−	0.126372i
$313$	−2.95246	−	2.14508i	−0.166883	−	0.121247i	0.501209	−	0.865326i	$-0.332889\pi$
$313$	−2.95246	−	2.14508i	−0.166883	−	0.121247i	−0.668092	+	0.744079i	$0.732889\pi$
$314$	−12.9614	−	9.41700i	−0.731454	−	0.531432i
$315$	−5.18811	+	15.9674i	−0.292317	+	0.899659i
$316$	−2.87978	−	8.86304i	−0.162000	−	0.498585i
$317$	28.4718	−	20.6859i	1.59913	−	1.16184i	0.709988	−	0.704214i	$-0.248700\pi$
$317$	28.4718	−	20.6859i	1.59913	−	1.16184i	0.889145	−	0.457625i	$-0.151300\pi$
$318$	12.4653			0.699020
$319$	−4.45282	+	4.11511i	−0.249310	+	0.230402i
$320$	−29.5987			−1.65462
$321$	−13.9348	+	10.1242i	−0.777763	+	0.565078i
$322$	4.54129	+	13.9767i	0.253076	+	0.778889i
$323$	−0.663697	+	2.04265i	−0.0369291	+	0.113656i
$324$	0.111910	+	0.0813073i	0.00621722	+	0.00451707i
$325$	−1.82155	−	1.32343i	−0.101041	−	0.0734109i
$326$	4.96505	−	15.2808i	0.274989	−	0.846328i
$327$	−4.39187	−	13.5168i	−0.242871	−	0.747480i
$328$	11.4362	−	8.30886i	0.631457	−	0.458780i
$329$	47.3368			2.60976
$330$	3.73608	−	18.7703i	0.205665	−	1.03327i
$331$	28.9751			1.59261			0.796307	−	0.604892i	$-0.206784\pi$
$331$	28.9751			1.59261			0.796307	+	0.604892i	$0.206784\pi$
$332$	27.9858	−	20.3329i	1.53592	−	1.11591i
$333$	−1.35773	−	4.17866i	−0.0744031	−	0.228989i
$334$	−14.4946	+	44.6099i	−0.793112	+	2.44095i
$335$	5.67961	+	4.12648i	0.310310	+	0.225454i
$336$	7.82954	+	5.68849i	0.427136	+	0.310333i
$337$	−4.90072	+	15.0829i	−0.266959	+	0.821615i	0.724277	+	0.689510i	$0.242174\pi$
$337$	−4.90072	+	15.0829i	−0.266959	+	0.821615i	−0.991236	+	0.132106i	$0.957826\pi$
$338$	−6.59539	−	20.2985i	−0.358742	−	1.10409i
$339$	7.46608	−	5.42443i	0.405502	−	0.294614i
$340$	6.48666			0.351788
$341$	−12.9645	+	1.53280i	−0.702067	+	0.0830059i
$342$	8.49094			0.459137
$343$	2.51370	−	1.82631i	0.135727	−	0.0986114i
$344$	−4.04945	−	12.4629i	−0.218332	−	0.671956i
$345$	1.57625	−	4.85121i	0.0848626	−	0.261180i
$346$	27.4939	+	19.9755i	1.47808	+	1.07389i
$347$	28.0640	+	20.3897i	1.50656	+	1.09458i	0.967677	+	0.252194i	$0.0811520\pi$
$347$	28.0640	+	20.3897i	1.50656	+	1.09458i	0.538879	+	0.842383i	$0.318848\pi$
$348$	1.56915	−	4.82935i	0.0841153	−	0.258880i
$349$	3.04400	+	9.36846i	0.162942	+	0.501482i	0.998879	−	0.0473427i	$-0.0150753\pi$
$349$	3.04400	+	9.36846i	0.162942	+	0.501482i	−0.835937	+	0.548825i	$0.815075\pi$
$350$	−8.11962	+	5.89925i	−0.434012	+	0.315328i
$351$	−9.06642			−0.483930
$352$	22.6590	+	12.6934i	1.20773	+	0.676558i
$353$	−33.0777			−1.76055			−0.880273	−	0.474467i	$-0.842641\pi$
$353$	−33.0777			−1.76055			−0.880273	+	0.474467i	$0.842641\pi$
$354$	−26.6695	+	19.3765i	−1.41747	+	1.02985i
$355$	−6.34189	−	19.5183i	−0.336592	−	1.03592i
$356$	2.27225	−	6.99326i	0.120429	−	0.370642i
$357$	−3.15054	−	2.28900i	−0.166744	−	0.121147i
$358$	39.6054	+	28.7750i	2.09321	+	1.52081i
$359$	−6.59556	+	20.2990i	−0.348100	+	1.07134i	0.611803	+	0.791010i	$0.290445\pi$
$359$	−6.59556	+	20.2990i	−0.348100	+	1.07134i	−0.959903	+	0.280332i	$0.909555\pi$
$360$	−1.79533	−	5.52545i	−0.0946220	−	0.291217i
$361$	11.6394	−	8.45652i	0.612600	−	0.445080i
$362$	3.55328			0.186756
$363$	−7.67618	+	8.98309i	−0.402895	+	0.471490i
$364$	16.3270			0.855770
$365$	−8.66914	+	6.29850i	−0.453764	+	0.329679i
$366$	−5.26909	−	16.2166i	−0.275420	−	0.847654i
$367$	1.39263	−	4.28608i	0.0726948	−	0.223732i	−0.908107	−	0.418738i	$-0.862473\pi$
$367$	1.39263	−	4.28608i	0.0726948	−	0.223732i	0.980802	+	0.195006i	$0.0624726\pi$
$368$	3.80584	+	2.76511i	0.198393	+	0.144141i
$369$	−16.8290	−	12.2270i	−0.876085	−	0.636513i
$370$	3.95079	−	12.1593i	0.205392	−	0.632131i
$371$	6.07075	+	18.6838i	0.315177	+	0.970016i
$372$	8.84529	−	6.42648i	0.458607	−	0.333197i
$373$	9.33318			0.483254			0.241627	−	0.970369i	$-0.422319\pi$
$373$	9.33318			0.483254			0.241627	+	0.970369i	$0.422319\pi$
$374$	−6.19638	−	3.47116i	−0.320407	−	0.179489i
$375$	−9.98966			−0.515864
$376$	−13.2523	+	9.62834i	−0.683434	+	0.496544i
$377$	0.983886	+	3.02809i	0.0506727	+	0.155955i
$378$	−12.4886	+	38.4358i	−0.642342	+	1.97693i
$379$	−0.917530	−	0.666625i	−0.0471304	−	0.0342422i	0.563971	−	0.825795i	$-0.309273\pi$
$379$	−0.917530	−	0.666625i	−0.0471304	−	0.0342422i	−0.611101	+	0.791553i	$0.709273\pi$
$380$	11.2711	+	8.18893i	0.578195	+	0.420083i
$381$	−4.13086	+	12.7135i	−0.211630	+	0.651331i
$382$	−4.08173	−	12.5623i	−0.208839	−	0.642742i
$383$	8.00759	−	5.81786i	0.409169	−	0.297279i	−0.364096	−	0.931361i	$-0.618622\pi$
$383$	8.00759	−	5.81786i	0.409169	−	0.297279i	0.773265	+	0.634083i	$0.218622\pi$
$384$	−10.3183			−0.526554
$385$	29.9536	−	3.54144i	1.52658	−	0.180488i
$386$	45.4620			2.31395
$387$	−15.6009	+	11.3347i	−0.793040	+	0.576177i
$388$	4.14070	+	12.7438i	0.210212	+	0.646966i
$389$	−0.488261	+	1.50271i	−0.0247558	+	0.0761906i	−0.962671	−	0.270674i	$-0.912754\pi$
$389$	−0.488261	+	1.50271i	−0.0247558	+	0.0761906i	0.937915	+	0.346864i	$0.112754\pi$
$390$	−8.13073	−	5.90732i	−0.411716	−	0.299129i
$391$	−1.53144	−	1.11265i	−0.0774481	−	0.0562694i
$392$	2.38144	−	7.32932i	0.120281	−	0.370186i
$393$	4.98815	+	15.3519i	0.251619	+	0.774403i
$394$	−43.7564	+	31.7909i	−2.20442	+	1.60160i
$395$	−9.04060			−0.454882
$396$	−3.09076	+	15.5281i	−0.155316	+	0.780317i
$397$	−6.05018			−0.303650			−0.151825	−	0.988407i	$-0.548515\pi$
$397$	−6.05018			−0.303650			−0.151825	+	0.988407i	$0.548515\pi$
$398$	−41.3396	+	30.0350i	−2.07217	+	1.50552i
$399$	−2.58462	−	7.95464i	−0.129393	−	0.398230i
$400$	−0.992787	+	3.05549i	−0.0496394	+	0.152774i
$401$	−2.11241	−	1.53475i	−0.105489	−	0.0766420i	0.533790	−	0.845617i	$-0.320767\pi$
$401$	−2.11241	−	1.53475i	−0.105489	−	0.0766420i	−0.639279	+	0.768975i	$0.720767\pi$
$402$	5.20820	+	3.78398i	0.259761	+	0.188728i
$403$	−2.11845	+	6.51991i	−0.105527	+	0.324780i
$404$	4.73981	+	14.5876i	0.235814	+	0.725762i
$405$	0.108565	−	0.0788770i	0.00539463	−	0.00391943i
$406$	14.1924			0.704358
$407$	−5.79702	+	5.35737i	−0.287348	+	0.265555i
$408$	1.34760			0.0667162
$409$	2.91872	−	2.12058i	0.144322	−	0.104856i	−0.513282	−	0.858220i	$-0.671570\pi$
$409$	2.91872	−	2.12058i	0.144322	−	0.104856i	0.657603	+	0.753364i	$0.271570\pi$
$410$	−18.7049	−	57.5677i	−0.923768	−	2.84306i
$411$	2.23872	−	6.89006i	0.110428	−	0.339861i
$412$	−10.6739	−	7.75501i	−0.525863	−	0.382062i
$413$	−42.0311	−	30.5374i	−2.06822	−	1.50265i
$414$	−2.31256	+	7.11732i	−0.113656	+	0.349797i
$415$	−10.3701	−	31.9160i	−0.509049	−	1.56669i
$416$	11.0339	−	8.01661i	0.540982	−	0.393046i
$417$	5.12898			0.251167
$418$	−6.38463	−	13.8539i	−0.312282	−	0.677616i
$419$	−9.63530			−0.470715			−0.235357	−	0.971909i	$-0.575626\pi$
$419$	−9.63530			−0.470715			−0.235357	+	0.971909i	$0.575626\pi$
$420$	−20.4365	+	14.8480i	−0.997197	+	0.724506i
$421$	−9.69929	−	29.8513i	−0.472714	−	1.45486i	−0.849016	−	0.528368i	$-0.822804\pi$
$421$	−9.69929	−	29.8513i	−0.472714	−	1.45486i	0.376302	−	0.926497i	$-0.377196\pi$
$422$	3.43710	−	10.5783i	0.167315	−	0.514943i
$423$	19.5016	+	14.1687i	0.948198	+	0.688906i
$424$	−5.49986	−	3.99588i	−0.267097	−	0.194057i
$425$	0.399489	−	1.22950i	0.0193781	−	0.0596396i
$426$	−5.81550	−	17.8983i	−0.281762	−	0.867174i
$427$	21.7404	−	15.7953i	1.05209	−	0.764389i
$428$	41.4630			2.00419
$429$	2.59706	+	5.63531i	0.125387	+	0.272075i
$430$	−56.1130			−2.70601
$431$	−19.6496	+	14.2763i	−0.946488	+	0.687664i	−0.949974	−	0.312330i	$-0.898890\pi$
$431$	−19.6496	+	14.2763i	−0.946488	+	0.687664i	0.00348579	+	0.999994i	$0.498890\pi$
$432$	3.99768	+	12.3036i	0.192339	+	0.591957i
$433$	7.50654	−	23.1028i	0.360741	−	1.11025i	−0.591864	−	0.806038i	$-0.701608\pi$
$433$	7.50654	−	23.1028i	0.360741	−	1.11025i	0.952605	−	0.304210i	$-0.0983924\pi$
$434$	24.7222	+	17.9617i	1.18670	+	0.862190i
$435$	−3.98530	−	2.89549i	−0.191080	−	0.138828i
$436$	−10.5723	+	32.5381i	−0.506320	+	1.55829i
$437$	−1.25635	−	3.86665i	−0.0600995	−	0.184967i
$438$	−7.94959	+	5.77571i	−0.379846	+	0.275974i
$439$	14.2401			0.679644			0.339822	−	0.940490i	$-0.389633\pi$
$439$	14.2401			0.679644			0.339822	+	0.940490i	$0.389633\pi$
$440$	−7.66541	+	7.08405i	−0.365434	+	0.337719i
$441$	−11.3406			−0.540028
$442$	−3.01737	+	2.19224i	−0.143521	+	0.104274i
$443$	11.3724	+	35.0008i	0.540321	+	1.66294i	0.731862	+	0.681453i	$0.238652\pi$
$443$	11.3724	+	35.0008i	0.540321	+	1.66294i	−0.191540	+	0.981485i	$0.561348\pi$
$444$	2.04284	−	6.28722i	0.0969490	−	0.298378i
$445$	−5.77101	−	4.19289i	−0.273572	−	0.198762i
$446$	−25.8084	−	18.7509i	−1.22206	−	0.887880i
$447$	−0.444113	+	1.36684i	−0.0210058	+	0.0646493i
$448$	−13.2185	−	40.6822i	−0.624514	−	1.92206i
$449$	−2.27259	+	1.65113i	−0.107250	+	0.0779217i	−0.640118	−	0.768277i	$-0.721114\pi$
$449$	−2.27259	+	1.65113i	−0.107250	+	0.0779217i	0.532868	+	0.846199i	$0.321114\pi$
$450$	−5.11082			−0.240927
$451$	−7.29538	+	36.6523i	−0.343526	+	1.72589i
$452$	−22.2154			−1.04493
$453$	−7.72546	+	5.61287i	−0.362974	+	0.263716i
$454$	−4.25491	−	13.0953i	−0.199693	−	0.614591i
$455$	4.89453	−	15.0638i	0.229459	−	0.706203i
$456$	2.34157	+	1.70125i	0.109654	+	0.0796682i
$457$	−10.5855	−	7.69083i	−0.495170	−	0.359762i	0.311999	−	0.950082i	$-0.399001\pi$
$457$	−10.5855	−	7.69083i	−0.495170	−	0.359762i	−0.807169	+	0.590320i	$0.799001\pi$
$458$	8.67880	−	26.7106i	0.405534	−	1.24810i
$459$	−1.60863	−	4.95086i	−0.0750846	−	0.231087i
$460$	−9.93391	+	7.21741i	−0.463171	+	0.336514i
$461$	−14.4433			−0.672691			−0.336345	−	0.941739i	$-0.609191\pi$
$461$	−14.4433			−0.672691			−0.336345	+	0.941739i	$0.609191\pi$
$462$	27.4674	−	3.24749i	1.27790	−	0.151087i
$463$	−3.47841			−0.161655			−0.0808277	−	0.996728i	$-0.525756\pi$
$463$	−3.47841			−0.161655			−0.0808277	+	0.996728i	$0.525756\pi$
$464$	3.67545	−	2.67037i	0.170628	−	0.123969i
$465$	−3.27761	−	10.0875i	−0.151996	−	0.467795i
$466$	6.58268	−	20.2594i	0.304937	−	0.938499i
$467$	−22.5070	−	16.3523i	−1.04150	−	0.756695i	−0.0709231	−	0.997482i	$-0.522594\pi$
$467$	−22.5070	−	16.3523i	−1.04150	−	0.756695i	−0.970578	+	0.240787i	$0.922594\pi$
$468$	6.72633	+	4.88697i	0.310925	+	0.225900i
$469$	−3.13522	+	9.64923i	−0.144771	+	0.445560i
$470$	21.6753	+	66.7096i	0.999806	+	3.07709i
$471$	−6.50165	+	4.72372i	−0.299580	+	0.217658i
$472$	17.9783			0.827516
$473$	30.2247	+	16.9316i	1.38974	+	0.778518i
$474$	−8.29022			−0.380782
$475$	2.24630	−	1.63203i	0.103067	−	0.0748827i
$476$	2.89687	+	8.91564i	0.132778	+	0.408648i
$477$	−3.09140	+	9.51435i	−0.141545	+	0.435632i
$478$	−0.0372541	−	0.0270667i	−0.00170396	−	0.00123800i
$479$	12.0785	+	8.77553i	0.551880	+	0.400964i	0.828478	−	0.560021i	$-0.189207\pi$
$479$	12.0785	+	8.77553i	0.551880	+	0.400964i	−0.276598	+	0.960986i	$0.589207\pi$
$480$	−6.52071	+	20.0687i	−0.297628	+	0.916005i
$481$	1.28090	+	3.94220i	0.0584040	+	0.179749i
$482$	−15.5108	+	11.2693i	−0.706500	+	0.513302i
$483$	7.37172			0.335425
$484$	27.6599	−	6.63322i	1.25727	−	0.301510i
$485$	12.9991			0.590257
$486$	−26.9564	+	19.5850i	−1.22277	+	0.888392i
$487$	−2.03077	−	6.25008i	−0.0920231	−	0.283218i	0.894443	−	0.447181i	$-0.147572\pi$
$487$	−2.03077	−	6.25008i	−0.0920231	−	0.283218i	−0.986466	+	0.163963i	$0.947572\pi$
$488$	−2.87360	+	8.84403i	−0.130082	+	0.400351i
$489$	−6.52034	−	4.73731i	−0.294860	−	0.214228i
$490$	−26.6971	−	19.3966i	−1.20605	−	0.876248i
$491$	0.0860231	−	0.264752i	0.00388217	−	0.0119481i	−0.949097	−	0.314985i	$-0.898001\pi$
$491$	0.0860231	−	0.264752i	0.00388217	−	0.0119481i	0.952979	+	0.303037i	$0.0980005\pi$
$492$	−9.67176	−	29.7666i	−0.436036	−	1.34198i
$493$	−1.47897	+	1.07453i	−0.0666094	+	0.0483946i
$494$	−8.01046			−0.360408
$495$	13.4002	+	7.50665i	0.602292	+	0.337399i
$496$	9.78194			0.439222
$497$	23.9949	−	17.4333i	1.07632	−	0.781991i
$498$	−9.50939	−	29.2669i	−0.426126	−	1.31148i
$499$	6.56305	−	20.1990i	0.293803	−	0.904231i	−0.689819	−	0.723982i	$-0.742310\pi$
$499$	6.56305	−	20.1990i	0.293803	−	0.904231i	0.983621	−	0.180249i	$-0.0576903\pi$
$500$	19.4548	+	14.1348i	0.870047	+	0.632126i
$501$	19.0351	+	13.8298i	0.850424	+	0.617869i
$502$	−7.25296	+	22.3223i	−0.323715	+	0.996294i
$503$	3.60564	+	11.0970i	0.160768	+	0.494792i	0.998700	−	0.0509830i	$-0.0162354\pi$
$503$	3.60564	+	11.0970i	0.160768	+	0.494792i	−0.837932	+	0.545775i	$0.816235\pi$
$504$	6.79273	−	4.93520i	0.302572	−	0.219831i
$505$	14.8799			0.662146
$506$	13.3516	−	1.57857i	0.593550	−	0.0701759i
$507$	−10.7061			−0.475473
$508$	26.0336	−	18.9145i	1.15505	−	0.839197i
$509$	6.24532	+	19.2211i	0.276819	+	0.851961i	0.988732	+	0.149694i	$0.0478287\pi$
$509$	6.24532	+	19.2211i	0.276819	+	0.851961i	−0.711914	+	0.702267i	$0.752171\pi$
$510$	1.78317	−	5.48804i	0.0789602	−	0.243014i
$511$	−12.5286	−	9.10253i	−0.554231	−	0.402672i
$512$	−20.7887	−	15.1039i	−0.918739	−	0.667503i
$513$	3.45497	−	10.6333i	0.152541	−	0.469472i
$514$	12.6814	+	39.0292i	0.559351	+	1.72151i
$515$	−10.3548	+	7.52321i	−0.456288	+	0.331512i
$516$	−29.0144			−1.27729
$517$	8.45391	−	42.4729i	0.371803	−	1.86795i
$518$	18.4768			0.811824
$519$	13.7914	−	10.0200i	0.605375	−	0.439831i
$520$	1.69373	+	5.21278i	0.0742752	+	0.228595i
$521$	9.44640	−	29.0730i	0.413854	−	1.27371i	−0.499418	−	0.866361i	$-0.666453\pi$
$521$	9.44640	−	29.0730i	0.413854	−	1.27371i	0.913272	−	0.407351i	$-0.133547\pi$
$522$	5.84692	+	4.24804i	0.255913	+	0.185932i
$523$	12.7371	+	9.25402i	0.556953	+	0.404650i	0.830342	−	0.557254i	$-0.188145\pi$
$523$	12.7371	+	9.25402i	0.556953	+	0.404650i	−0.273390	+	0.961903i	$0.588145\pi$
$524$	12.0077	−	36.9558i	0.524557	−	1.61442i
$525$	1.55572	+	4.78802i	0.0678973	+	0.208966i
$526$	26.0378	−	18.9175i	1.13530	−	0.824844i
$527$	−3.93617			−0.171462
$528$	6.50228	−	6.00913i	0.282975	−	0.261514i
$529$	−19.4167			−0.844204
$530$	−23.5505	+	17.1105i	−1.02297	+	0.743232i
$531$	−8.17540	−	25.1613i	−0.354782	−	1.09191i
$532$	−6.22180	+	19.1487i	−0.269749	+	0.830203i
$533$	15.8767	+	11.5351i	0.687698	+	0.499642i
$534$	−5.29201	−	3.84487i	−0.229008	−	0.166384i
$535$	12.4298	−	38.2550i	0.537388	−	1.65391i
$536$	−1.08493	−	3.33908i	−0.0468620	−	0.144226i
$537$	19.8667	−	14.4340i	0.857313	−	0.622874i
$538$	6.73843			0.290514
$539$	8.52739	+	18.5034i	0.367301	+	0.796999i
$540$	−33.7673			−1.45311
$541$	−27.4644	+	19.9541i	−1.18079	+	0.857892i	−0.992260	−	0.124176i	$-0.960371\pi$
$541$	−27.4644	+	19.9541i	−1.18079	+	0.857892i	−0.188527	+	0.982068i	$0.560371\pi$
$542$	3.06303	+	9.42705i	0.131569	+	0.404926i
$543$	0.550788	−	1.69515i	0.0236366	−	0.0727458i
$544$	6.33531	+	4.60288i	0.271624	+	0.197347i
$545$	26.8513	+	19.5086i	1.15018	+	0.835656i
$546$	4.48828	−	13.8135i	0.192081	−	0.591163i
$547$	−0.641807	−	1.97528i	−0.0274417	−	0.0844569i	0.936398	−	0.350941i	$-0.114138\pi$
$547$	−0.641807	−	1.97528i	−0.0274417	−	0.0844569i	−0.963839	+	0.266484i	$0.914138\pi$
$548$	−14.1089	+	10.2507i	−0.602703	+	0.437889i
$549$	13.6843			0.584032
$550$	3.84301	+	8.33887i	0.163866	+	0.355571i
$551$	−3.92635			−0.167268
$552$	−2.06377	+	1.49941i	−0.0878398	+	0.0638193i
$553$	−4.03743	−	12.4259i	−0.171689	−	0.528404i
$554$	−15.5475	+	47.8502i	−0.660548	+	2.03296i
$555$	−5.18837	−	3.76957i	−0.220234	−	0.160009i
$556$	−9.98868	−	7.25720i	−0.423614	−	0.307774i
$557$	−4.00324	+	12.3207i	−0.169623	+	0.522045i	−0.999347	−	0.0361282i	$-0.988498\pi$
$557$	−4.00324	+	12.3207i	−0.169623	+	0.522045i	0.829724	+	0.558173i	$0.188498\pi$
$558$	4.80867	+	14.7996i	0.203567	+	0.626515i
$559$	14.7181	−	10.6933i	0.622510	−	0.452280i
$560$	−22.6005			−0.955047
$561$	−2.61646	+	2.41802i	−0.110467	+	0.102089i
$562$	−43.1091			−1.81845
$563$	−20.9917	+	15.2514i	−0.884695	+	0.642768i	−0.934489	−	0.355991i	$-0.884143\pi$
$563$	−20.9917	+	15.2514i	−0.884695	+	0.642768i	0.0497947	+	0.998759i	$0.484143\pi$
$564$	11.2077	+	34.4937i	0.471928	+	1.45244i
$565$	−6.65975	+	20.4966i	−0.280178	+	0.862298i
$566$	13.3382	+	9.69079i	0.560648	+	0.407334i
$567$	0.156897	+	0.113992i	0.00658906	+	0.00478723i
$568$	−3.17160	+	9.76117i	−0.133077	+	0.409570i
$569$	9.18493	+	28.2683i	0.385052	+	1.18507i	0.936442	+	0.350821i	$0.114098\pi$
$569$	9.18493	+	28.2683i	0.385052	+	1.18507i	−0.551390	+	0.834248i	$0.685902\pi$
$570$	10.0266	−	7.28478i	0.419970	−	0.305126i
$571$	−2.80342			−0.117319			−0.0586597	−	0.998278i	$-0.518683\pi$
$571$	−2.80342			−0.117319			−0.0586597	+	0.998278i	$0.518683\pi$
$572$	2.91586	−	14.6494i	0.121918	−	0.612523i
$573$	−6.62573			−0.276794
$574$	70.7710	−	51.4181i	2.95392	−	2.14615i
$575$	0.756217	+	2.32740i	0.0315364	+	0.0970592i
$576$	6.73122	−	20.7166i	0.280468	−	0.863191i
$577$	29.7544	+	21.6178i	1.23869	+	0.899963i	0.997511	−	0.0705174i	$-0.0224650\pi$
$577$	29.7544	+	21.6178i	1.23869	+	0.899963i	0.241182	+	0.970480i	$0.422465\pi$
$578$	−1.73247	−	1.25872i	−0.0720614	−	0.0523557i
$579$	7.04697	−	21.6883i	0.292862	−	0.901337i
$580$	3.66442	+	11.2779i	0.152157	+	0.468290i
$581$	39.2360	−	28.5066i	1.62778	−	1.18265i
$582$	11.9201			0.494105
$583$	17.8482	−	2.11021i	0.739198	−	0.0873960i
$584$	5.35893			0.221754
$585$	6.52528	−	4.74090i	0.269787	−	0.196012i
$586$	16.3129	+	50.2060i	0.673881	+	2.07399i
$587$	1.00391	−	3.08971i	0.0414357	−	0.127526i	−0.928199	−	0.372085i	$-0.878643\pi$
$587$	1.00391	−	3.08971i	0.0414357	−	0.127526i	0.969634	+	0.244559i	$0.0786431\pi$
$588$	−13.8043	−	10.0294i	−0.569280	−	0.413606i
$589$	−6.83941	−	4.96912i	−0.281813	−	0.204749i
$590$	23.7892	−	73.2155i	0.979385	−	3.01424i
$591$	8.38375	+	25.8025i	0.344861	+	1.06137i
$592$	4.78498	−	3.47650i	0.196662	−	0.142883i
$593$	9.03571			0.371052			0.185526	−	0.982639i	$-0.440601\pi$
$593$	9.03571			0.371052			0.185526	+	0.982639i	$0.440601\pi$
$594$	32.2562	+	18.0696i	1.32349	+	0.741406i
$595$	9.09426			0.372828
$596$	2.79890	−	2.03352i	0.114648	−	0.0832964i
$597$	7.92068	+	24.3774i	0.324172	+	0.997699i
$598$	2.18170	−	6.71457i	0.0892162	−	0.274579i
$599$	−31.0473	−	22.5572i	−1.26856	−	0.921662i	−0.269414	−	0.963024i	$-0.586830\pi$
$599$	−31.0473	−	22.5572i	−1.26856	−	0.921662i	−0.999144	+	0.0413629i	$0.986830\pi$
$600$	−1.40942	−	1.02401i	−0.0575395	−	0.0418049i
$601$	11.4449	−	35.2237i	0.466846	−	1.43680i	−0.389800	−	0.920899i	$-0.627456\pi$
$601$	11.4449	−	35.2237i	0.466846	−	1.43680i	0.856646	−	0.515905i	$-0.172544\pi$
$602$	−25.0594	−	77.1250i	−1.02135	−	3.14338i
$603$	−4.17981	+	3.03681i	−0.170215	+	0.123669i
$604$	22.9872			0.935335
$605$	2.17189	−	27.5083i	0.0882999	−	1.11837i
$606$	13.6448			0.554284
$607$	−9.26781	+	6.73346i	−0.376169	+	0.273303i	−0.759764	−	0.650199i	$-0.774686\pi$
$607$	−9.26781	+	6.73346i	−0.376169	+	0.273303i	0.383595	+	0.923501i	$0.374686\pi$
$608$	5.19733	+	15.9957i	0.210780	+	0.648713i
$609$	2.19994	−	6.77072i	0.0891460	−	0.274363i
$610$	32.2145	+	23.4052i	1.30433	+	0.947648i
$611$	−18.3980	−	13.3669i	−0.744304	−	0.540769i
$612$	−1.47517	+	4.54010i	−0.0596302	+	0.183523i
$613$	−11.6146	−	35.7461i	−0.469110	−	1.44377i	−0.853739	−	0.520702i	$-0.825670\pi$
$613$	−11.6146	−	35.7461i	−0.469110	−	1.44377i	0.384628	−	0.923071i	$-0.374330\pi$
$614$	33.4060	−	24.2709i	1.34816	−	0.979492i
$615$	−30.3630			−1.22435
$616$	−13.1600	−	7.37213i	−0.530232	−	0.297031i
$617$	−46.2070			−1.86023			−0.930113	−	0.367274i	$-0.880291\pi$
$617$	−46.2070			−1.86023			−0.930113	+	0.367274i	$0.880291\pi$
$618$	−9.49535	+	6.89878i	−0.381959	+	0.277510i
$619$	10.9171	+	33.5994i	0.438796	+	1.35047i	0.889146	+	0.457623i	$0.151299\pi$
$619$	10.9171	+	33.5994i	0.438796	+	1.35047i	−0.450350	+	0.892852i	$0.648701\pi$
$620$	−7.89000	+	24.2829i	−0.316870	+	0.975226i
$621$	7.97212	+	5.79209i	0.319910	+	0.232428i
$622$	26.2821	+	19.0951i	1.05382	+	0.765642i
$623$	3.18568	−	9.80451i	0.127632	−	0.392810i
$624$	−1.43673	−	4.42181i	−0.0575153	−	0.177014i
$625$	24.1027	−	17.5117i	0.964109	−	0.700466i
$626$	7.81510			0.312354
$627$	−7.59889	+	0.898422i	−0.303470	+	0.0358795i
$628$	19.3457			0.771979
$629$	−1.92544	+	1.39891i	−0.0767722	+	0.0557783i
$630$	−11.1101	−	34.1934i	−0.442637	−	1.36230i
$631$	−2.63590	+	8.11246i	−0.104933	+	0.322952i	−0.989715	−	0.143054i	$-0.954308\pi$
$631$	−2.63590	+	8.11246i	−0.104933	+	0.322952i	0.884781	+	0.466006i	$0.154308\pi$
$632$	3.65776	+	2.65751i	0.145498	+	0.105710i
$633$	−4.51376	−	3.27944i	−0.179406	−	0.130346i
$634$	−23.2888	+	71.6757i	−0.924918	+	2.84661i
$635$	−9.64673	−	29.6896i	−0.382819	−	1.17820i
$636$	−12.1773	+	8.84734i	−0.482862	+	0.350820i
$637$	10.6989			0.423905
$638$	2.53464	−	12.7341i	0.100347	−	0.504150i
$639$	15.1034			0.597481
$640$	19.4943	−	14.1634i	0.770578	−	0.559858i
$641$	4.35619	+	13.4070i	0.172059	+	0.529543i	0.999487	−	0.0320287i	$-0.0101968\pi$
$641$	4.35619	+	13.4070i	0.172059	+	0.529543i	−0.827428	+	0.561572i	$0.810197\pi$
$642$	11.3981	−	35.0798i	0.449848	−	1.38449i
$643$	−28.2721	−	20.5409i	−1.11494	−	0.810054i	−0.131509	−	0.991315i	$-0.541982\pi$
$643$	−28.2721	−	20.5409i	−1.11494	−	0.810054i	−0.983435	+	0.181261i	$0.941982\pi$
$644$	−14.3564	−	10.4305i	−0.565722	−	0.411021i
$645$	−8.69796	+	26.7696i	−0.342482	+	1.05405i
$646$	−1.42128	−	4.37424i	−0.0559194	−	0.172102i
$647$	−33.6527	+	24.4501i	−1.32302	+	0.961234i	−0.323135	+	0.946353i	$0.604737\pi$
$647$	−33.6527	+	24.4501i	−1.32302	+	0.961234i	−0.999889	+	0.0148809i	$0.995263\pi$
$648$	−0.0671107			−0.00263636
$649$	−34.9060	+	32.2587i	−1.37018	+	1.26626i
$650$	4.82162			0.189119
$651$	12.4011	−	9.00989i	0.486035	−	0.353125i
$652$	5.99535	+	18.4518i	0.234796	+	0.722628i
$653$	−13.7569	+	42.3395i	−0.538350	+	1.65687i	0.197947	+	0.980213i	$0.436573\pi$
$653$	−13.7569	+	42.3395i	−0.538350	+	1.65687i	−0.736297	+	0.676659i	$0.763427\pi$
$654$	24.6226	+	17.8893i	0.962819	+	0.699529i
$655$	−30.4969	−	22.1573i	−1.19161	−	0.865756i
$656$	8.65319	−	26.6318i	0.337850	−	1.03980i
$657$	−2.43691	−	7.50003i	−0.0950728	−	0.292604i
$658$	−82.0097	+	59.5835i	−3.19707	+	2.32281i
$659$	14.7560			0.574813			0.287407	−	0.957809i	$-0.407207\pi$
$659$	14.7560			0.574813			0.287407	+	0.957809i	$0.407207\pi$
$660$	9.67256	+	20.9883i	0.376504	+	0.816969i
$661$	15.7217			0.611503			0.305751	−	0.952111i	$-0.401092\pi$
$661$	15.7217			0.611503			0.305751	+	0.952111i	$0.401092\pi$
$662$	−50.1986	+	36.4714i	−1.95102	+	1.41750i
$663$	0.578128	+	1.77930i	0.0224526	+	0.0691021i
$664$	−5.18613	+	15.9613i	−0.201261	+	0.619417i
$665$	15.8020	+	11.4808i	0.612776	+	0.445208i
$666$	7.61198	+	5.53043i	0.294958	+	0.214300i
$667$	1.06936	−	3.29116i	0.0414059	−	0.127434i
$668$	−17.5024	−	53.8670i	−0.677190	−	2.08418i
$669$	−12.9459	+	9.40575i	−0.500517	+	0.363647i
$670$	−15.0338			−0.580808
$671$	−10.2897	−	22.3274i	−0.397230	−	0.861942i
$672$	−30.4956			−1.17639
$673$	−15.4633	+	11.2347i	−0.596065	+	0.433067i	−0.844480	−	0.535587i	$-0.820090\pi$
$673$	−15.4633	+	11.2347i	−0.596065	+	0.433067i	0.248415	+	0.968654i	$0.420090\pi$
$674$	−10.4947	−	32.2993i	−0.404239	−	1.24412i
$675$	−2.07960	+	6.40035i	−0.0800438	+	0.246349i
$676$	20.8500	+	15.1484i	0.801925	+	0.582632i
$677$	20.7074	+	15.0448i	0.795848	+	0.578218i	0.909693	−	0.415281i	$-0.136317\pi$
$677$	20.7074	+	15.0448i	0.795848	+	0.578218i	−0.113845	+	0.993499i	$0.536317\pi$
$678$	−6.10698	+	18.7953i	−0.234537	+	0.721831i
$679$	5.80524	+	17.8667i	0.222784	+	0.685660i
$680$	−2.54601	+	1.84978i	−0.0976349	+	0.0709359i
$681$	−6.90685			−0.264671
$682$	20.5313	−	18.9742i	0.786184	−	0.726558i
$683$	29.3088			1.12147			0.560735	−	0.827995i	$-0.310519\pi$
$683$	29.3088			1.12147			0.560735	+	0.827995i	$0.310519\pi$
$684$	−8.29477	+	6.02650i	−0.317158	+	0.230429i
$685$	5.22804	+	16.0903i	0.199753	+	0.614777i
$686$	−2.05611	+	6.32807i	−0.0785028	+	0.241607i
$687$	−11.3974	−	8.28071i	−0.434839	−	0.315929i
$688$	−21.0011	−	15.2582i	−0.800660	−	0.581714i
$689$	2.91647	−	8.97596i	0.111109	−	0.341957i
$690$	3.37547	+	10.3886i	0.128502	+	0.395489i
$691$	11.7655	−	8.54814i	0.447581	−	0.325186i	−0.341059	−	0.940042i	$-0.610786\pi$
$691$	11.7655	−	8.54814i	0.447581	−	0.325186i	0.788640	+	0.614855i	$0.210786\pi$
$692$	−41.0365			−1.55997
$693$	−4.33323	+	21.7703i	−0.164606	+	0.826987i
$694$	−74.2850			−2.81982
$695$	−9.69012	+	7.04029i	−0.367567	+	0.267053i
$696$	0.761281	+	2.34298i	0.0288563	+	0.0888105i
$697$	−3.48197	+	10.7164i	−0.131889	+	0.405912i
$698$	−17.0659	−	12.3991i	−0.645953	−	0.469312i
$699$	−8.64470	−	6.28074i	−0.326973	−	0.237560i
$700$	3.74499	−	11.5259i	0.141547	−	0.435638i
$701$	3.07272	+	9.45685i	0.116055	+	0.357180i	0.992166	−	0.124930i	$-0.0398705\pi$
$701$	3.07272	+	9.45685i	0.116055	+	0.357180i	−0.876111	+	0.482110i	$0.839871\pi$
$702$	15.7073	−	11.4120i	0.592835	−	0.430720i
$703$	−5.11162			−0.192789
$704$	−38.8628	+	4.59478i	−1.46470	+	0.173172i
$705$	35.1847			1.32513
$706$	57.3062	−	41.6354i	2.15675	−	1.56697i
$707$	6.64519	+	20.4518i	0.249918	+	0.769169i
$708$	12.3007	−	37.8577i	0.462289	−	1.42278i
$709$	−42.3055	−	30.7368i	−1.58882	−	1.15434i	−0.905604	−	0.424124i	$-0.860582\pi$
$709$	−42.3055	−	30.7368i	−1.58882	−	1.15434i	−0.683213	−	0.730220i	$-0.739418\pi$
$710$	35.5552	+	25.8323i	1.33436	+	0.969470i
$711$	2.05598	−	6.32765i	0.0771051	−	0.237305i
$712$	1.10239	+	3.39282i	0.0413139	+	0.127151i
$713$	6.02800	−	4.37960i	0.225750	−	0.164017i
$714$	8.33942			0.312095
$715$	−12.6419	−	7.08187i	−0.472779	−	0.264847i
$716$	−59.1137			−2.20918
$717$	−0.0186872	+	0.0135771i	−0.000697888	+	0.000507045i
$718$	−14.1241	−	43.4695i	−0.527106	−	1.62227i
$719$	−6.63051	+	20.4066i	−0.247276	+	0.761038i	0.747978	+	0.663724i	$0.231025\pi$
$719$	−6.63051	+	20.4066i	−0.247276	+	0.761038i	−0.995254	+	0.0973138i	$0.968975\pi$
$720$	−9.31085	−	6.76473i	−0.346995	−	0.252107i
$721$	−14.9647	−	10.8725i	−0.557314	−	0.404912i
$722$	−9.52060	+	29.3014i	−0.354320	+	1.09049i
$723$	2.97188	+	9.14652i	0.110526	+	0.340163i
$724$	−3.47119	+	2.52197i	−0.129006	+	0.0937282i
$725$	2.36333			0.0877718
$726$	1.99162	−	25.2251i	0.0739160	−	0.936191i
$727$	21.5067			0.797641			0.398820	−	0.917029i	$-0.369420\pi$
$727$	21.5067			0.797641			0.398820	+	0.917029i	$0.369420\pi$
$728$	−6.40834	+	4.65594i	−0.237509	+	0.172560i
$729$	5.21445	+	16.0484i	0.193128	+	0.594386i
$730$	7.09104	−	21.8240i	0.262451	−	0.807741i
$731$	8.45067	+	6.13977i	0.312559	+	0.227088i
$732$	16.6572	+	12.1022i	0.615667	+	0.447309i
$733$	−11.3828	+	35.0326i	−0.420433	+	1.29396i	0.486867	+	0.873476i	$0.338140\pi$
$733$	−11.3828	+	35.0326i	−0.420433	+	1.29396i	−0.907300	+	0.420483i	$0.861860\pi$
$734$	2.98226	+	9.17845i	0.110077	+	0.338783i
$735$	−13.3917	+	9.72964i	−0.493961	+	0.358883i
$736$	−14.8236			−0.546403
$737$	8.09784	+	4.53634i	0.298288	+	0.167098i
$738$	44.5462			1.63977
$739$	−35.6489	+	25.9005i	−1.31137	+	0.952764i	−0.311371	+	0.950289i	$0.600788\pi$
$739$	−35.6489	+	25.9005i	−1.31137	+	0.952764i	−0.999997	+	0.00247583i	$0.999212\pi$
$740$	4.77062	+	14.6825i	0.175372	+	0.539738i
$741$	−1.24169	+	3.82151i	−0.0456145	+	0.140387i
$742$	−34.0350	−	24.7279i	−1.24947	−	0.907790i
$743$	−20.6771	−	15.0228i	−0.758570	−	0.551133i	0.139902	−	0.990165i	$-0.455321\pi$
$743$	−20.6771	−	15.0228i	−0.758570	−	0.551133i	−0.898471	+	0.439032i	$0.855321\pi$
$744$	−1.63915	+	5.04477i	−0.0600940	+	0.184950i
$745$	−1.03713	−	3.19196i	−0.0379976	−	0.116944i
$746$	−16.1695	+	11.7478i	−0.592007	+	0.430118i
$747$	24.6968			0.903607
$748$	8.51691	−	1.00696i	0.311409	−	0.0368181i
$749$	58.1310			2.12406
$750$	17.3068	−	12.5741i	0.631956	−	0.459143i
$751$	1.70231	+	5.23918i	0.0621183	+	0.191180i	0.977300	−	0.211862i	$-0.0679527\pi$
$751$	1.70231	+	5.23918i	0.0621183	+	0.191180i	−0.915181	+	0.403042i	$0.867953\pi$
$752$	−10.0273	+	30.8610i	−0.365660	+	1.12538i
$753$	9.52494	+	6.92027i	0.347108	+	0.252189i
$754$	−5.51606	−	4.00765i	−0.200883	−	0.145950i
$755$	6.89111	−	21.2087i	0.250793	−	0.771862i
$756$	−15.0801	−	46.4117i	−0.548457	−	1.68798i
$757$	−29.2621	+	21.2602i	−1.06355	+	0.772715i	−0.974742	−	0.223334i	$-0.928306\pi$
$757$	−29.2621	+	21.2602i	−1.06355	+	0.772715i	−0.0888088	+	0.996049i	$0.528306\pi$
$758$	2.42869			0.0882139
$759$	1.31652	−	6.61427i	0.0477867	−	0.240083i
$760$	−6.75910			−0.245178
$761$	6.08133	−	4.41835i	0.220448	−	0.160165i	−0.472080	−	0.881556i	$-0.656497\pi$
$761$	6.08133	−	4.41835i	0.220448	−	0.160165i	0.692528	+	0.721391i	$0.256497\pi$
$762$	−8.84604	−	27.2253i	−0.320458	−	0.986269i
$763$	−14.8223	+	45.6183i	−0.536602	+	1.65149i
$764$	12.9036	+	9.37501i	0.466835	+	0.339176i
$765$	3.74661	+	2.72207i	0.135459	+	0.0984166i
$766$	−6.54992	+	20.1586i	−0.236658	+	0.728359i
$767$	7.71277	+	23.7375i	0.278492	+	0.857111i
$768$	−2.63166	+	1.91201i	−0.0949619	+	0.0689939i
$769$	25.7102			0.927135			0.463567	−	0.886062i	$-0.346569\pi$
$769$	25.7102			0.927135			0.463567	+	0.886062i	$0.346569\pi$
$770$	−47.4362	+	43.8385i	−1.70948	+	1.57983i
$771$	20.5852			0.741359
$772$	−44.4117	+	32.2670i	−1.59841	+	1.16131i
$773$	8.12814	+	25.0158i	0.292349	+	0.899757i	0.984099	+	0.177620i	$0.0568399\pi$
$773$	8.12814	+	25.0158i	0.292349	+	0.899757i	−0.691750	+	0.722137i	$0.743160\pi$
$774$	12.7610	−	39.2743i	0.458684	−	1.41168i
$775$	4.11674	+	2.99099i	0.147878	+	0.107440i
$776$	−5.25932	−	3.82112i	−0.188799	−	0.137170i
$777$	2.86405	−	8.81465i	0.102747	−	0.316224i
$778$	−1.04559	−	3.21799i	−0.0374862	−	0.115371i
$779$	−19.5788	+	14.2249i	−0.701485	+	0.509659i
$780$	12.1356			0.434526
$781$	−11.3568	−	24.6428i	−0.406377	−	0.881790i
$782$	4.05369			0.144960
$783$	7.69899	−	5.59364i	0.275139	−	0.199900i
$784$	−4.71748	−	14.5189i	−0.168482	−	0.518533i
$785$	5.79947	−	17.8489i	0.206992	−	0.637056i
$786$	−27.9656	−	20.3182i	−0.997499	−	0.724725i
$787$	−12.2990	−	8.93573i	−0.438411	−	0.318524i	0.346592	−	0.938016i	$-0.387339\pi$
$787$	−12.2990	−	8.93573i	−0.438411	−	0.318524i	−0.785003	+	0.619491i	$0.787339\pi$
$788$	20.1817	−	62.1128i	0.718943	−	2.21268i
$789$	−4.98884	−	15.3541i	−0.177608	−	0.546620i
$790$	15.6626	−	11.3796i	0.557251	−	0.404866i
$791$	−31.1459			−1.10742
$792$	−3.21499	−	6.97615i	−0.114240	−	0.247887i
$793$	−12.9100			−0.458446
$794$	10.4818	−	7.61545i	0.371984	−	0.270262i
$795$	4.51229	+	13.8874i	0.160035	+	0.492536i
$796$	19.0670	−	58.6821i	0.675811	−	2.07993i
$797$	20.7958	+	15.1090i	0.736623	+	0.535188i	0.891652	−	0.452722i	$-0.149547\pi$
$797$	20.7958	+	15.1090i	0.736623	+	0.535188i	−0.155029	+	0.987910i	$0.549547\pi$
$798$	14.4904	+	10.5279i	0.512955	+	0.372684i
$799$	4.03492	−	12.4182i	0.142745	−	0.439324i
$800$	−3.12835	−	9.62807i	−0.110604	−	0.340404i
$801$	4.24708	−	3.08568i	0.150063	−	0.109027i
$802$	5.59151			0.197443
$803$	−10.4047	+	9.61562i	−0.367175	+	0.339328i
$804$	−7.77357			−0.274153
$805$	−13.9273	+	10.1188i	−0.490873	+	0.356640i
$806$	−4.53656	−	13.9621i	−0.159793	−	0.491794i
$807$	1.04451	−	3.21467i	0.0367685	−	0.113162i
$808$	−6.02028	−	4.37399i	−0.211793	−	0.153877i
$809$	−0.795547	−	0.577999i	−0.0279700	−	0.0203214i	0.573712	−	0.819057i	$-0.305503\pi$
$809$	−0.795547	−	0.577999i	−0.0279700	−	0.0203214i	−0.601682	+	0.798735i	$0.705503\pi$
$810$	−0.0888021	+	0.273305i	−0.00312019	+	0.00960295i
$811$	5.11303	+	15.7363i	0.179543	+	0.552576i	0.999812	−	0.0194022i	$-0.00617628\pi$
$811$	5.11303	+	15.7363i	0.179543	+	0.552576i	−0.820269	+	0.571978i	$0.806176\pi$
$812$	−13.8645	+	10.0732i	−0.486550	+	0.353499i
$813$	4.97211			0.174380
$814$	3.29979	−	16.5783i	0.115658	−	0.581069i
$815$	18.8215			0.659287
$816$	2.15968	−	1.56910i	0.0756040	−	0.0549295i
$817$	6.93271	+	21.3367i	0.242545	+	0.746476i
$818$	−2.38741	+	7.34769i	−0.0834738	+	0.256906i
$819$	9.43028	+	6.85150i	0.329521	+	0.239411i
$820$	59.1318	+	42.9618i	2.06497	+	1.50029i
$821$	−3.02040	+	9.29584i	−0.105413	+	0.324427i	−0.989827	−	0.142276i	$-0.954558\pi$
$821$	−3.02040	+	9.29584i	−0.105413	+	0.324427i	0.884414	+	0.466702i	$0.154558\pi$
$822$	4.79411	+	14.7547i	0.167214	+	0.514631i
$823$	9.92778	−	7.21295i	0.346061	−	0.251428i	−0.401154	−	0.916011i	$-0.631391\pi$
$823$	9.92778	−	7.21295i	0.346061	−	0.251428i	0.747215	+	0.664583i	$0.231391\pi$
$824$	6.40095			0.222988
$825$	4.57388	−	0.540774i	0.159242	−	0.0188273i
$826$	111.256			3.87108
$827$	−6.66606	+	4.84317i	−0.231801	+	0.168414i	−0.697623	−	0.716465i	$-0.745759\pi$
$827$	−6.66606	+	4.84317i	−0.231801	+	0.168414i	0.465821	+	0.884879i	$0.345759\pi$
$828$	−2.79244	−	8.59424i	−0.0970439	−	0.298670i
$829$	−8.69726	+	26.7674i	−0.302068	+	0.929671i	0.678687	+	0.734428i	$0.262549\pi$
$829$	−8.69726	+	26.7674i	−0.302068	+	0.929671i	−0.980755	+	0.195243i	$0.937451\pi$
$830$	58.1391	+	42.2405i	2.01804	+	1.46619i
$831$	20.4177	+	14.8343i	0.708281	+	0.514597i
$832$	−6.35032	+	19.5443i	−0.220158	+	0.677576i
$833$	1.89827	+	5.84229i	0.0657713	+	0.202423i
$834$	−8.88583	+	6.45593i	−0.307691	+	0.223551i
$835$	−54.9461			−1.90149
$836$	16.0700	+	9.00229i	0.555793	+	0.311351i
$837$	20.4903			0.708249
$838$	16.6929	−	12.1281i	0.576646	−	0.418958i
$839$	−8.96514	−	27.5919i	−0.309511	−	0.952577i	−0.977955	−	0.208815i	$-0.933039\pi$
$839$	−8.96514	−	27.5919i	−0.309511	−	0.952577i	0.668444	−	0.743762i	$-0.266961\pi$
$840$	3.78714	−	11.6556i	0.130669	−	0.402157i
$841$	20.7578	+	15.0814i	0.715786	+	0.520049i
$842$	54.3781	+	39.5080i	1.87399	+	1.36154i
$843$	−6.68226	+	20.5659i	−0.230149	+	0.708326i
$844$	4.15033	+	12.7734i	0.142860	+	0.439679i
$845$	20.2268	−	14.6957i	0.695824	−	0.505546i
$846$	−51.6203			−1.77474
$847$	38.7790	−	9.29974i	1.33246	−	0.319543i
$848$	−13.4668			−0.462452
$849$	6.69068	−	4.86106i	0.229623	−	0.166831i
$850$	0.855488	+	2.63292i	0.0293430	+	0.0903084i
$851$	1.39218	−	4.28469i	0.0477233	−	0.146877i
$852$	18.3846	+	13.3572i	0.629845	+	0.457609i
$853$	−11.3191	−	8.22380i	−0.387558	−	0.281578i	0.376896	−	0.926256i	$-0.376991\pi$
$853$	−11.3191	−	8.22380i	−0.387558	−	0.281578i	−0.764454	+	0.644678i	$0.776991\pi$
$854$	−17.7828	+	54.7299i	−0.608516	+	1.87282i
$855$	3.07362	+	9.45963i	0.105116	+	0.323512i
$856$	−16.2742	+	11.8239i	−0.556241	+	0.404132i
$857$	−17.8699			−0.610425			−0.305212	−	0.952284i	$-0.598727\pi$
$857$	−17.8699			−0.610425			−0.305212	+	0.952284i	$0.598727\pi$
$858$	−11.5926	−	6.49407i	−0.395764	−	0.221704i
$859$	10.2947			0.351252			0.175626	−	0.984457i	$-0.443805\pi$
$859$	10.2947			0.351252			0.175626	+	0.984457i	$0.443805\pi$
$860$	54.8166	−	39.8266i	1.86923	−	1.35808i
$861$	−13.5597	−	41.7326i	−0.462115	−	1.42224i
$862$	16.0726	−	49.4665i	0.547436	−	1.68484i
$863$	5.18431	+	3.76662i	0.176476	+	0.128217i	0.672517	−	0.740082i	$-0.265213\pi$
$863$	5.18431	+	3.76662i	0.176476	+	0.128217i	−0.496041	+	0.868299i	$0.665213\pi$
$864$	−32.9794	−	23.9609i	−1.12198	−	0.815168i
$865$	−12.3019	+	37.8615i	−0.418278	+	1.28733i
$866$	16.0749	+	49.4735i	0.546248	+	1.68118i
$867$	−0.869037	+	0.631392i	−0.0295140	+	0.0214432i
$868$	−36.8995			−1.25245
$869$	−11.8702	+	1.40342i	−0.402669	+	0.0476079i
$870$	10.5490			0.357645
$871$	3.94329	−	2.86497i	0.133613	−	0.0970758i
$872$	−5.12919	−	15.7860i	−0.173696	−	0.534583i
$873$	−2.95619	+	9.09823i	−0.100052	+	0.307928i
$874$	7.04362	+	5.11749i	0.238254	+	0.173102i
$875$	27.2756	+	19.8169i	0.922083	+	0.669933i
$876$	3.66657	−	11.2846i	0.123882	−	0.381270i
$877$	−5.04773	−	15.5353i	−0.170450	−	0.524590i	0.828947	−	0.559327i	$-0.188940\pi$
$877$	−5.04773	−	15.5353i	−0.170450	−	0.524590i	−0.999396	+	0.0347375i	$0.988940\pi$
$878$	−24.6706	+	17.9243i	−0.832593	+	0.604914i
$879$	26.4802			0.893155
$880$	−4.03625	+	20.2783i	−0.136062	+	0.683582i
$881$	−18.2921			−0.616275			−0.308138	−	0.951342i	$-0.599706\pi$
$881$	−18.2921			−0.616275			−0.308138	+	0.951342i	$0.599706\pi$
$882$	19.6473	−	14.2746i	0.661559	−	0.480650i
$883$	−10.3438	−	31.8349i	−0.348096	−	1.07133i	−0.959905	−	0.280325i	$-0.909558\pi$
$883$	−10.3438	−	31.8349i	−0.348096	−	1.07133i	0.611809	−	0.791006i	$-0.290442\pi$
$884$	1.39169	−	4.28319i	0.0468077	−	0.144059i
$885$	−31.2411	−	22.6980i	−1.05016	−	0.762985i
$886$	−63.7585	−	46.3233i	−2.14201	−	1.55626i
$887$	7.16620	−	22.0553i	0.240617	−	0.740544i	−0.755709	−	0.654908i	$-0.772708\pi$
$887$	7.16620	−	22.0553i	0.240617	−	0.740544i	0.996326	−	0.0856368i	$-0.0272925\pi$
$888$	0.991095	+	3.05028i	0.0332590	+	0.102361i
$889$	36.4990	−	26.5181i	1.22414	−	0.889387i
$890$	15.2758			0.512045
$891$	0.130300	−	0.120418i	0.00436521	−	0.00403415i
$892$	38.5207			1.28977
$893$	22.6880	−	16.4838i	0.759227	−	0.551610i
$894$	−0.951048	−	2.92703i	−0.0318078	−	0.0978944i
$895$	−17.7211	+	54.5400i	−0.592352	+	1.82307i
$896$	28.1729	+	20.4688i	0.941192	+	0.683816i
$897$	−2.86511	−	2.08162i	−0.0956632	−	0.0695034i
$898$	1.85889	−	5.72108i	0.0620321	−	0.190915i
$899$	−2.22360	−	6.84355i	−0.0741614	−	0.228245i
$900$	4.99275	−	3.62744i	0.166425	−	0.120915i
$901$	5.41893			0.180531
$902$	−33.4958	−	72.6820i	−1.11529	−	2.42005i
$903$	−40.6781			−1.35368
$904$	8.71952	−	6.33510i	0.290007	−	0.210702i
$905$	1.28625	+	3.95866i	0.0427563	+	0.131590i
$906$	6.31914	−	19.4483i	0.209939	−	0.646127i
$907$	−28.9961	−	21.0669i	−0.962799	−	0.699514i	−0.00899963	−	0.999960i	$-0.502865\pi$
$907$	−28.9961	−	21.0669i	−0.962799	−	0.699514i	−0.953799	+	0.300445i	$0.902865\pi$
$908$	13.4511	+	9.77277i	0.446389	+	0.324321i
$909$	−3.38392	+	10.4146i	−0.112238	+	0.345432i
$910$	10.4814	+	32.2585i	0.347456	+	1.06936i
$911$	−40.1750	+	29.1889i	−1.33106	+	0.967071i	−0.331336	+	0.943513i	$0.607499\pi$
$911$	−40.1750	+	29.1889i	−1.33106	+	0.967071i	−0.999722	+	0.0235580i	$0.992501\pi$
$912$	5.73349			0.189855
$913$	−18.5703	−	40.2955i	−0.614589	−	1.33359i
$914$	28.0197			0.926810
$915$	16.1593	−	11.7404i	0.534210	−	0.388126i
$916$	10.4797	+	32.2533i	0.346260	+	1.06568i
$917$	16.8347	−	51.8118i	0.555930	−	1.71098i
$918$	9.01865	+	6.55243i	0.297660	+	0.216262i
$919$	−32.9193	−	23.9173i	−1.08591	−	0.788958i	−0.107204	−	0.994237i	$-0.534190\pi$
$919$	−32.9193	−	23.9173i	−1.08591	−	0.788958i	−0.978704	+	0.205279i	$0.934190\pi$
$920$	1.84088	−	5.66565i	0.0606921	−	0.186791i
$921$	−6.40060	−	19.6990i	−0.210907	−	0.649105i
$922$	25.0226	−	18.1800i	0.824076	−	0.598726i
$923$	−14.2487			−0.469003
$924$	−24.5279	+	22.6677i	−0.806909	+	0.745711i
$925$	3.07676			0.101163
$926$	6.02626	−	4.37833i	0.198035	−	0.143881i
$927$	−2.91075	−	8.95838i	−0.0956017	−	0.294232i
$928$	−4.42379	+	13.6150i	−0.145218	+	0.446935i
$929$	−15.9376	−	11.5794i	−0.522896	−	0.379906i	0.294798	−	0.955560i	$-0.404748\pi$
$929$	−15.9376	−	11.5794i	−0.522896	−	0.379906i	−0.817694	+	0.575653i	$0.804748\pi$
$930$	18.3756	+	13.3507i	0.602561	+	0.437786i
$931$	−4.07705	+	12.5479i	−0.133620	+	0.411240i
$932$	7.94866	+	24.4635i	0.260367	+	0.801327i
$933$	13.1835	−	9.57840i	0.431610	−	0.313583i
$934$	59.5757			1.94938
$935$	1.62415	−	8.15982i	0.0531154	−	0.266855i
$936$	−4.03368			−0.131845
$937$	27.8845	−	20.2593i	0.910948	−	0.661843i	−0.0303063	−	0.999541i	$-0.509648\pi$
$937$	27.8845	−	20.2593i	0.910948	−	0.661843i	0.941254	+	0.337698i	$0.109648\pi$
$938$	−6.71394	−	20.6634i	−0.219218	−	0.674684i
$939$	1.21140	−	3.72832i	0.0395327	−	0.121669i
$940$	−68.5221	−	49.7842i	−2.23495	−	1.62378i
$941$	28.1791	+	20.4733i	0.918613	+	0.667411i	0.943178	−	0.332287i	$-0.107820\pi$
$941$	28.1791	+	20.4733i	0.918613	+	0.667411i	−0.0245657	+	0.999698i	$0.507820\pi$
$942$	5.31811	−	16.3675i	0.173273	−	0.533280i
$943$	−6.59123	−	20.2857i	−0.214640	−	0.660594i
$944$	28.8122	−	20.9333i	0.937756	−	0.681320i
$945$	−47.3415			−1.54002
$946$	−73.6757	+	8.71073i	−2.39540	+	0.283210i
$947$	14.8176			0.481507			0.240753	−	0.970586i	$-0.422605\pi$
$947$	14.8176			0.481507			0.240753	+	0.970586i	$0.422605\pi$
$948$	8.09869	−	5.88404i	0.263033	−	0.191105i
$949$	2.29901	+	7.07563i	0.0746290	+	0.229685i
$950$	−1.83739	+	5.65490i	−0.0596128	+	0.183469i
$951$	30.5841	+	22.2206i	0.991756	+	0.720553i
$952$	−3.67946	−	2.67329i	−0.119252	−	0.0866417i
$953$	6.70828	−	20.6460i	0.217302	−	0.668788i	−0.781680	−	0.623680i	$-0.785637\pi$
$953$	6.70828	−	20.6460i	0.217302	−	0.668788i	0.998982	−	0.0451080i	$-0.0143632\pi$
$954$	−6.62009	−	20.3746i	−0.214333	−	0.659650i
$955$	12.5179	−	9.09479i	0.405070	−	0.294300i
$956$	0.0556041			0.00179837
$957$	−5.68213	−	3.18308i	−0.183677	−	0.102894i
$958$	−31.9715			−1.03295
$959$	−19.7806	+	14.3715i	−0.638749	+	0.464078i
$960$	−9.82509	−	30.2385i	−0.317103	−	0.975944i
$961$	−4.79179	+	14.7476i	−0.154574	+	0.475730i
$962$	−7.18124	−	5.21748i	−0.231532	−	0.168218i
$963$	23.9485	+	17.3996i	0.771730	+	0.560694i
$964$	7.15404	−	22.0179i	0.230416	−	0.709148i
$965$	16.4567	+	50.6485i	0.529760	+	1.63043i
$966$	−12.7713	+	9.27890i	−0.410910	+	0.298544i
$967$	18.6125			0.598536			0.299268	−	0.954169i	$-0.403257\pi$
$967$	18.6125			0.598536			0.299268	+	0.954169i	$0.403257\pi$
$968$	−8.96489	+	10.4912i	−0.288143	+	0.337200i
$969$	−2.30711			−0.0741150
$970$	−22.5205	+	16.3621i	−0.723091	+	0.525356i
$971$	−11.2621	−	34.6611i	−0.361417	−	1.11233i	−0.952194	−	0.305493i	$-0.901179\pi$
$971$	−11.2621	−	34.6611i	−0.361417	−	1.11233i	0.590778	−	0.806835i	$-0.298821\pi$
$972$	12.4330	−	38.2650i	0.398790	−	1.22735i
$973$	−14.0041	−	10.1746i	−0.448950	−	0.326181i
$974$	11.3853	+	8.27193i	0.364810	+	0.265050i
$975$	0.747389	−	2.30023i	0.0239356	−	0.0736662i
$976$	5.69242	+	17.5195i	0.182210	+	0.560785i
$977$	13.1113	−	9.52590i	0.419467	−	0.304761i	−0.357956	−	0.933738i	$-0.616526\pi$
$977$	13.1113	−	9.52590i	0.419467	−	0.304761i	0.777423	+	0.628978i	$0.216526\pi$
$978$	17.2592			0.551890
$979$	−8.22816	−	4.60935i	−0.262973	−	0.147315i
$980$	39.8472			1.27287
$981$	−19.7607	+	14.3570i	−0.630912	+	0.458384i
$982$	0.184215	+	0.566954i	0.00587852	+	0.0180922i
$983$	4.17909	−	12.8619i	0.133292	−	0.410232i	−0.862028	−	0.506860i	$-0.830806\pi$
$983$	4.17909	−	12.8619i	0.133292	−	0.410232i	0.995321	+	0.0966286i	$0.0308059\pi$
$984$	12.2846	+	8.92529i	0.391619	+	0.284528i
$985$	−51.2571	−	37.2404i	−1.63319	−	1.18658i
$986$	1.20974	−	3.72320i	0.0385260	−	0.118571i
$987$	15.7131	+	48.3599i	0.500153	+	1.53931i
$988$	7.82539	−	5.68548i	0.248959	−	0.180879i
$989$	−19.7731			−0.628748
$990$	−32.6642	+	3.86191i	−1.03814	+	0.122739i
$991$	33.7435			1.07190			0.535949	−	0.844250i	$-0.319954\pi$
$991$	33.7435			1.07190			0.535949	+	0.844250i	$0.319954\pi$
$992$	−24.9369	+	18.1177i	−0.791747	+	0.575238i
$993$	9.61807	+	29.6014i	0.305220	+	0.939371i
$994$	−19.6269	+	60.4055i	−0.622529	+	1.91595i
$995$	−48.4260	−	35.1835i	−1.53521	−	1.11539i
$996$	30.0621	+	21.8414i	0.952553	+	0.692070i
$997$	−10.8973	+	33.5383i	−0.345120	+	1.06217i	0.616400	+	0.787433i	$0.288590\pi$
$997$	−10.8973	+	33.5383i	−0.345120	+	1.06217i	−0.961520	+	0.274736i	$0.911410\pi$
$998$	14.0545	+	43.2552i	0.444887	+	1.36922i
$999$	10.0231	−	7.28224i	0.317118	−	0.230400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.f.69.2	✓	36
11.2	odd	10		2057.2.a.be.1.3		18
11.4	even	5	inner	187.2.g.f.103.2	yes	36
11.9	even	5		2057.2.a.bd.1.16		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.f.69.2	✓	36	1.1	even	1	trivial
187.2.g.f.103.2	yes	36	11.4	even	5	inner
2057.2.a.bd.1.16		18	11.9	even	5
2057.2.a.be.1.3		18	11.2	odd	10

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73247 + 1.25872i) q^{2} +(0.331943 + 1.02161i) q^{3} +(0.799065 - 2.45927i) q^{4} +(-2.02945 - 1.47448i) q^{5} +(-1.86100 - 1.35210i) q^{6} +(1.12029 - 3.44788i) q^{7} +(0.387671 + 1.19313i) q^{8} +(1.49354 - 1.08512i) q^{9} +O(q^{10})\)	\(q+(-1.73247 + 1.25872i) q^{2} +(0.331943 + 1.02161i) q^{3} +(0.799065 - 2.45927i) q^{4} +(-2.02945 - 1.47448i) q^{5} +(-1.86100 - 1.35210i) q^{6} +(1.12029 - 3.44788i) q^{7} +(0.387671 + 1.19313i) q^{8} +(1.49354 - 1.08512i) q^{9} +5.37193 q^{10} +(-2.89354 - 1.62094i) q^{11} +2.77767 q^{12} +(-1.40903 + 1.02372i) q^{13} +(2.39904 + 7.38349i) q^{14} +(0.832691 - 2.56276i) q^{15} +(2.01052 + 1.46073i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-1.22166 + 3.75989i) q^{18} +(-0.663697 - 2.04265i) q^{19} +(-5.24782 + 3.81276i) q^{20} +3.89428 q^{21} +(7.05328 - 0.833914i) q^{22} +1.89296 q^{23} +(-1.09023 + 0.792100i) q^{24} +(0.399489 + 1.22950i) q^{25} +(1.15253 - 3.54713i) q^{26} +(4.21146 + 3.05980i) q^{27} +(-7.58410 - 5.51017i) q^{28} +(0.564916 - 1.73863i) q^{29} +(1.78317 + 5.48804i) q^{30} +(3.18443 - 2.31362i) q^{31} -7.83088 q^{32} +(0.695483 - 3.49414i) q^{33} +2.14146 q^{34} +(-7.35741 + 5.34547i) q^{35} +(-1.47517 - 4.54010i) q^{36} +(0.735451 - 2.26349i) q^{37} +(3.72095 + 2.70343i) q^{38} +(-1.51356 - 1.09967i) q^{39} +(0.972488 - 2.99301i) q^{40} +(-3.48197 - 10.7164i) q^{41} +(-6.74674 + 4.90179i) q^{42} -10.4456 q^{43} +(-6.29845 + 5.82076i) q^{44} -4.63106 q^{45} +(-3.27951 + 2.38270i) q^{46} +(4.03492 + 12.4182i) q^{47} +(-0.824925 + 2.53886i) q^{48} +(-4.96975 - 3.61073i) q^{49} +(-2.23970 - 1.62723i) q^{50} +(0.331943 - 1.02161i) q^{51} +(1.39169 + 4.28319i) q^{52} +(-4.38400 + 3.18517i) q^{53} -11.1477 q^{54} +(3.48225 + 7.55608i) q^{55} +4.54807 q^{56} +(1.86649 - 1.35608i) q^{57} +(1.20974 + 3.72320i) q^{58} +(4.42843 - 13.6293i) q^{59} +(-5.63715 - 4.09563i) q^{60} +(5.99682 + 4.35694i) q^{61} +(-2.60474 + 8.01658i) q^{62} +(-2.06818 - 6.36520i) q^{63} +(9.54575 - 6.93539i) q^{64} +4.36900 q^{65} +(3.19322 + 6.92892i) q^{66} -2.79859 q^{67} +(-2.09198 + 1.51991i) q^{68} +(0.628355 + 1.93388i) q^{69} +(6.01809 - 18.5218i) q^{70} +(6.61870 + 4.80877i) q^{71} +(1.87369 + 1.36132i) q^{72} +(1.32002 - 4.06260i) q^{73} +(1.57494 + 4.84715i) q^{74} +(-1.12347 + 0.816248i) q^{75} -5.55376 q^{76} +(-8.83039 + 8.16068i) q^{77} +4.00637 q^{78} +(2.91564 - 2.11834i) q^{79} +(-1.92644 - 5.92896i) q^{80} +(-0.0165308 + 0.0508765i) q^{81} +(19.5213 + 14.1831i) q^{82} +(10.8228 + 7.86320i) q^{83} +(3.11178 - 9.57708i) q^{84} +(0.775182 + 2.38576i) q^{85} +(18.0967 - 13.1480i) q^{86} +1.96373 q^{87} +(0.812243 - 4.08075i) q^{88} +2.84363 q^{89} +(8.02319 - 5.82919i) q^{90} +(1.95115 + 6.00501i) q^{91} +(1.51260 - 4.65530i) q^{92} +(3.42068 + 2.48527i) q^{93} +(-22.6214 - 16.4354i) q^{94} +(-1.66491 + 5.12407i) q^{95} +(-2.59940 - 8.00014i) q^{96} +(-4.19227 + 3.04586i) q^{97} +13.1548 q^{98} +(-6.08053 + 0.718905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

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