LMFDB - Embedded newform 731.2.e.b.307.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.e (of order $3$, degree $2$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			307.17
Character	$\chi$	$=$	731.307
Dual form			731.2.e.b.681.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.428243 q^{2} +(-1.51618 + 2.62610i) q^{3} -1.81661 q^{4} +(-1.16373 + 2.01564i) q^{5} +(-0.649294 + 1.12461i) q^{6} +(-0.814374 - 1.41054i) q^{7} -1.63444 q^{8} +(-3.09761 - 5.36521i) q^{9} +O(q^{10})$	\(q+0.428243 q^{2} +(-1.51618 + 2.62610i) q^{3} -1.81661 q^{4} +(-1.16373 + 2.01564i) q^{5} +(-0.649294 + 1.12461i) q^{6} +(-0.814374 - 1.41054i) q^{7} -1.63444 q^{8} +(-3.09761 - 5.36521i) q^{9} +(-0.498360 + 0.863184i) q^{10} -1.08921 q^{11} +(2.75431 - 4.77060i) q^{12} +(0.855654 + 1.48204i) q^{13} +(-0.348750 - 0.604052i) q^{14} +(-3.52885 - 6.11215i) q^{15} +2.93328 q^{16} +(-0.500000 - 0.866025i) q^{17} +(-1.32653 - 2.29761i) q^{18} +(-3.73184 + 6.46374i) q^{19} +(2.11404 - 3.66163i) q^{20} +4.93895 q^{21} -0.466447 q^{22} +(1.39528 - 2.41669i) q^{23} +(2.47810 - 4.29219i) q^{24} +(-0.208540 - 0.361201i) q^{25} +(0.366428 + 0.634672i) q^{26} +9.68904 q^{27} +(1.47940 + 2.56239i) q^{28} +(-1.14034 - 1.97512i) q^{29} +(-1.51121 - 2.61749i) q^{30} +(0.900539 - 1.55978i) q^{31} +4.52503 q^{32} +(1.65144 - 2.86038i) q^{33} +(-0.214121 - 0.370869i) q^{34} +3.79085 q^{35} +(5.62714 + 9.74649i) q^{36} +(0.926107 - 1.60406i) q^{37} +(-1.59813 + 2.76805i) q^{38} -5.18930 q^{39} +(1.90204 - 3.29443i) q^{40} +9.48138 q^{41} +2.11507 q^{42} +(-1.88349 - 6.28112i) q^{43} +1.97867 q^{44} +14.4191 q^{45} +(0.597517 - 1.03493i) q^{46} -1.90990 q^{47} +(-4.44738 + 7.70309i) q^{48} +(2.17359 - 3.76477i) q^{49} +(-0.0893056 - 0.154682i) q^{50} +3.03236 q^{51} +(-1.55439 - 2.69228i) q^{52} +(-5.90862 + 10.2340i) q^{53} +4.14926 q^{54} +(1.26755 - 2.19546i) q^{55} +(1.33104 + 2.30543i) q^{56} +(-11.3163 - 19.6004i) q^{57} +(-0.488341 - 0.845832i) q^{58} -1.56826 q^{59} +(6.41054 + 11.1034i) q^{60} +(-1.73774 - 3.00985i) q^{61} +(0.385649 - 0.667964i) q^{62} +(-5.04522 + 8.73857i) q^{63} -3.92875 q^{64} -3.98300 q^{65} +(0.707218 - 1.22494i) q^{66} +(-1.42720 + 2.47198i) q^{67} +(0.908304 + 1.57323i) q^{68} +(4.23098 + 7.32828i) q^{69} +1.62340 q^{70} +(-1.90509 - 3.29971i) q^{71} +(5.06284 + 8.76909i) q^{72} +(-6.16935 - 10.6856i) q^{73} +(0.396599 - 0.686929i) q^{74} +1.26474 q^{75} +(6.77929 - 11.7421i) q^{76} +(0.887026 + 1.53637i) q^{77} -2.22228 q^{78} +(-7.73638 - 13.3998i) q^{79} +(-3.41355 + 5.91244i) q^{80} +(-5.39752 + 9.34877i) q^{81} +4.06033 q^{82} +(1.20334 - 2.08424i) q^{83} -8.97214 q^{84} +2.32746 q^{85} +(-0.806593 - 2.68984i) q^{86} +6.91583 q^{87} +1.78025 q^{88} +(0.0185133 - 0.0320660i) q^{89} +6.17489 q^{90} +(1.39364 - 2.41386i) q^{91} +(-2.53467 + 4.39018i) q^{92} +(2.73076 + 4.72981i) q^{93} -0.817901 q^{94} +(-8.68572 - 15.0441i) q^{95} +(-6.86076 + 11.8832i) q^{96} -11.3889 q^{97} +(0.930825 - 1.61224i) q^{98} +(3.37395 + 5.84385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) $ 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9 + 4 * q^10 - 8 * q^12 + 2 * q^13 + 5 * q^14 - 5 * q^15 + 30 * q^16 - 29 * q^17 + 16 * q^18 - 4 * q^19 - 7 * q^20 - 26 * q^21 - 10 * q^22 + 5 * q^23 - 28 * q^24 - 24 * q^25 - 8 * q^26 + 28 * q^27 - 25 * q^28 + 10 * q^29 - 5 * q^30 + 3 * q^31 + 16 * q^32 - 23 * q^33 - q^34 - 26 * q^35 - 39 * q^36 - 16 * q^37 + q^38 + 130 * q^39 + 15 * q^40 - 22 * q^41 + 112 * q^42 + 7 * q^43 + 24 * q^44 + 2 * q^45 - 61 * q^46 + 12 * q^47 + 22 * q^48 - 36 * q^49 - 17 * q^50 + 10 * q^51 - 35 * q^52 - 10 * q^53 - 10 * q^54 - 20 * q^55 - 4 * q^56 + 9 * q^57 - 17 * q^58 - 36 * q^59 + 22 * q^60 - 35 * q^61 + 3 * q^62 - 22 * q^63 + 28 * q^64 - 28 * q^65 + 14 * q^66 - 17 * q^67 - 27 * q^68 - 23 * q^69 + 10 * q^70 - 6 * q^71 + 17 * q^72 - 14 * q^73 + 21 * q^74 + 70 * q^75 - 44 * q^76 - 11 * q^77 - 184 * q^78 - 10 * q^79 + 8 * q^80 - 13 * q^81 + 184 * q^82 + 9 * q^83 - 36 * q^84 + 6 * q^85 - 76 * q^86 + 8 * q^87 + 50 * q^88 - 54 * q^89 - 34 * q^90 - 23 * q^91 - 66 * q^92 + 96 * q^94 - 3 * q^95 - 60 * q^96 + 36 * q^97 - 16 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.428243			0.302813			0.151407	−	0.988472i	$-0.451620\pi$
$2$	0.428243			0.302813			0.151407	+	0.988472i	$0.451620\pi$
$3$	−1.51618	+	2.62610i	−0.875367	+	1.51618i	−0.0189962	+	0.999820i	$0.506047\pi$
$3$	−1.51618	+	2.62610i	−0.875367	+	1.51618i	−0.856371	+	0.516361i	$0.827286\pi$
$4$	−1.81661			−0.908304
$5$	−1.16373	+	2.01564i	−0.520436	+	0.901422i	0.479281	+	0.877661i	$0.340897\pi$
$5$	−1.16373	+	2.01564i	−0.520436	+	0.901422i	−0.999718	+	0.0237608i	$0.992436\pi$
$6$	−0.649294	+	1.12461i	−0.265073	+	0.459120i
$7$	−0.814374	−	1.41054i	−0.307804	−	0.533133i	0.670077	−	0.742291i	$-0.266261\pi$
$7$	−0.814374	−	1.41054i	−0.307804	−	0.533133i	−0.977882	+	0.209159i	$0.932928\pi$
$8$	−1.63444			−0.577860
$9$	−3.09761	−	5.36521i	−1.03254	−	1.78840i
$10$	−0.498360	+	0.863184i	−0.157595	+	0.272963i
$11$	−1.08921			−0.328410			−0.164205	−	0.986426i	$-0.552506\pi$
$11$	−1.08921			−0.328410			−0.164205	+	0.986426i	$0.552506\pi$
$12$	2.75431	−	4.77060i	0.795100	−	1.37715i
$13$	0.855654	+	1.48204i	0.237316	+	0.411043i	0.959943	−	0.280195i	$-0.0903991\pi$
$13$	0.855654	+	1.48204i	0.237316	+	0.411043i	−0.722627	+	0.691238i	$0.757066\pi$
$14$	−0.348750	−	0.604052i	−0.0932073	−	0.161440i
$15$	−3.52885	−	6.11215i	−0.911146	−	1.57815i
$16$	2.93328			0.733320
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$	−1.32653	−	2.29761i	−0.312666	−	0.541553i
$19$	−3.73184	+	6.46374i	−0.856143	+	1.48288i	0.0194369	+	0.999811i	$0.493813\pi$
$19$	−3.73184	+	6.46374i	−0.856143	+	1.48288i	−0.875580	+	0.483073i	$0.839521\pi$
$20$	2.11404	−	3.66163i	0.472714	−	0.818765i
$21$	4.93895			1.07777
$22$	−0.466447			−0.0994469
$23$	1.39528	−	2.41669i	0.290935	−	0.503915i	−0.683096	−	0.730329i	$-0.739367\pi$
$23$	1.39528	−	2.41669i	0.290935	−	0.503915i	0.974031	+	0.226414i	$0.0727002\pi$
$24$	2.47810	−	4.29219i	0.505840	−	0.876140i
$25$	−0.208540	−	0.361201i	−0.0417079	−	0.0722403i
$26$	0.366428	+	0.634672i	0.0718624	+	0.124469i
$27$	9.68904			1.86466
$28$	1.47940	+	2.56239i	0.279580	+	0.484247i
$29$	−1.14034	−	1.97512i	−0.211755	−	0.366771i	0.740509	−	0.672047i	$-0.234585\pi$
$29$	−1.14034	−	1.97512i	−0.211755	−	0.366771i	−0.952264	+	0.305276i	$0.901251\pi$
$30$	−1.51121	−	2.61749i	−0.275907	−	0.477885i
$31$	0.900539	−	1.55978i	0.161742	−	0.280145i	−0.773752	−	0.633489i	$-0.781622\pi$
$31$	0.900539	−	1.55978i	0.161742	−	0.280145i	0.935493	+	0.353344i	$0.114956\pi$
$32$	4.52503			0.799919
$33$	1.65144	−	2.86038i	0.287479	−	0.497929i
$34$	−0.214121	−	0.370869i	−0.0367215	−	0.0636035i
$35$	3.79085			0.640770
$36$	5.62714	+	9.74649i	0.937856	+	1.62441i
$37$	0.926107	−	1.60406i	0.152251	−	0.263706i	−0.779804	−	0.626024i	$-0.784681\pi$
$37$	0.926107	−	1.60406i	0.152251	−	0.263706i	0.932055	+	0.362318i	$0.118014\pi$
$38$	−1.59813	+	2.76805i	−0.259252	+	0.449037i
$39$	−5.18930			−0.830954
$40$	1.90204	−	3.29443i	0.300739	−	0.520896i
$41$	9.48138			1.48074			0.740371	−	0.672198i	$-0.234650\pi$
$41$	9.48138			1.48074			0.740371	+	0.672198i	$0.234650\pi$
$42$	2.11507			0.326362
$43$	−1.88349	−	6.28112i	−0.287230	−	0.957862i
$43$	−1.88349	−	6.28112i	−0.287230	−	0.957862i
$44$	1.97867			0.298296
$45$	14.4191			2.14948
$46$	0.597517	−	1.03493i	0.0880991	−	0.152592i
$47$	−1.90990			−0.278588			−0.139294	−	0.990251i	$-0.544483\pi$
$47$	−1.90990			−0.278588			−0.139294	+	0.990251i	$0.544483\pi$
$48$	−4.44738	+	7.70309i	−0.641924	+	1.11185i
$49$	2.17359	−	3.76477i	0.310513	−	0.537824i
$50$	−0.0893056	−	0.154682i	−0.0126297	−	0.0218753i
$51$	3.03236			0.424615
$52$	−1.55439	−	2.69228i	−0.215555	−	0.373352i
$53$	−5.90862	+	10.2340i	−0.811612	+	1.40575i	0.100123	+	0.994975i	$0.468076\pi$
$53$	−5.90862	+	10.2340i	−0.811612	+	1.40575i	−0.911735	+	0.410778i	$0.865257\pi$
$54$	4.14926			0.564643
$55$	1.26755	−	2.19546i	0.170916	−	0.296036i
$56$	1.33104	+	2.30543i	0.177868	+	0.308076i
$57$	−11.3163	−	19.6004i	−1.49888	−	2.59614i
$58$	−0.488341	−	0.845832i	−0.0641223	−	0.111063i
$59$	−1.56826			−0.204170			−0.102085	−	0.994776i	$-0.532551\pi$
$59$	−1.56826			−0.204170			−0.102085	+	0.994776i	$0.532551\pi$
$60$	6.41054	+	11.1034i	0.827597	+	1.43344i
$61$	−1.73774	−	3.00985i	−0.222494	−	0.385371i	0.733070	−	0.680153i	$-0.238087\pi$
$61$	−1.73774	−	3.00985i	−0.222494	−	0.385371i	−0.955565	+	0.294781i	$0.904753\pi$
$62$	0.385649	−	0.667964i	0.0489775	−	0.0848316i
$63$	−5.04522	+	8.73857i	−0.635638	+	1.10096i
$64$	−3.92875			−0.491094
$65$	−3.98300			−0.494031
$66$	0.707218	−	1.22494i	0.0870526	−	0.150779i
$67$	−1.42720	+	2.47198i	−0.174360	+	0.302000i	−0.939940	−	0.341341i	$-0.889119\pi$
$67$	−1.42720	+	2.47198i	−0.174360	+	0.302000i	0.765580	+	0.643341i	$0.222452\pi$
$68$	0.908304	+	1.57323i	0.110148	+	0.190782i
$69$	4.23098	+	7.32828i	0.509350	+	0.882221i
$70$	1.62340			0.194034
$71$	−1.90509	−	3.29971i	−0.226092	−	0.391603i	0.730554	−	0.682855i	$-0.239262\pi$
$71$	−1.90509	−	3.29971i	−0.226092	−	0.391603i	−0.956647	+	0.291251i	$0.905928\pi$
$72$	5.06284	+	8.76909i	0.596661	+	1.03345i
$73$	−6.16935	−	10.6856i	−0.722068	−	1.25066i	−0.960170	−	0.279418i	$-0.909859\pi$
$73$	−6.16935	−	10.6856i	−0.722068	−	1.25066i	0.238102	−	0.971240i	$-0.423475\pi$
$74$	0.396599	−	0.686929i	0.0461036	−	0.0798538i
$75$	1.26474			0.146039
$76$	6.77929	−	11.7421i	0.777638	−	1.34691i
$77$	0.887026	+	1.53637i	0.101086	+	0.175086i
$78$	−2.22228			−0.251624
$79$	−7.73638	−	13.3998i	−0.870410	−	1.50760i	−0.861573	−	0.507634i	$-0.830520\pi$
$79$	−7.73638	−	13.3998i	−0.870410	−	1.50760i	−0.00883779	−	0.999961i	$-0.502813\pi$
$80$	−3.41355	+	5.91244i	−0.381646	+	0.661031i
$81$	−5.39752	+	9.34877i	−0.599724	+	1.03875i
$82$	4.06033			0.448389
$83$	1.20334	−	2.08424i	0.132083	−	0.228775i	−0.792396	−	0.610007i	$-0.791167\pi$
$83$	1.20334	−	2.08424i	0.132083	−	0.228775i	0.924479	+	0.381232i	$0.124500\pi$
$84$	−8.97214			−0.978940
$85$	2.32746			0.252449
$86$	−0.806593	−	2.68984i	−0.0869771	−	0.290053i
$87$	6.91583			0.741454
$88$	1.78025			0.189775
$89$	0.0185133	−	0.0320660i	0.00196241	−	0.00339899i	−0.865043	−	0.501699i	$-0.832709\pi$
$89$	0.0185133	−	0.0320660i	0.00196241	−	0.00339899i	0.867005	+	0.498300i	$0.166042\pi$
$90$	6.17489			0.650890
$91$	1.39364	−	2.41386i	0.146094	−	0.253042i
$92$	−2.53467	+	4.39018i	−0.264258	+	0.457708i
$93$	2.73076	+	4.72981i	0.283167	+	0.490459i
$94$	−0.817901			−0.0843600
$95$	−8.68572	−	15.0441i	−0.891136	−	1.54349i
$96$	−6.86076	+	11.8832i	−0.700223	+	1.21282i
$97$	−11.3889			−1.15637			−0.578184	−	0.815906i	$-0.696238\pi$
$97$	−11.3889			−1.15637			−0.578184	+	0.815906i	$0.696238\pi$
$98$	0.930825	−	1.61224i	0.0940275	−	0.162860i
$99$	3.37395	+	5.84385i	0.339095	+	0.587330i
$100$	0.378835	+	0.656161i	0.0378835	+	0.0656161i
$101$	0.196473	+	0.340301i	0.0195498	+	0.0338612i	0.875635	−	0.482974i	$-0.160443\pi$
$101$	0.196473	+	0.340301i	0.0195498	+	0.0338612i	−0.856085	+	0.516835i	$0.827110\pi$
$102$	1.29859			0.128579
$103$	2.84642	+	4.93014i	0.280466	+	0.485781i	0.971500	−	0.237041i	$-0.0761777\pi$
$103$	2.84642	+	4.93014i	0.280466	+	0.485781i	−0.691034	+	0.722823i	$0.742844\pi$
$104$	−1.39851	−	2.42229i	−0.137135	−	0.237525i
$105$	−5.74761	+	9.95515i	−0.560909	+	0.971523i
$106$	−2.53033	+	4.38265i	−0.245767	+	0.425681i
$107$	−19.1662			−1.85287			−0.926435	−	0.376455i	$-0.877143\pi$
$107$	−19.1662			−1.85287			−0.926435	+	0.376455i	$0.877143\pi$
$108$	−17.6012			−1.69368
$109$	2.18018	−	3.77619i	0.208824	−	0.361693i	−0.742521	−	0.669823i	$-0.766370\pi$
$109$	2.18018	−	3.77619i	0.208824	−	0.361693i	0.951344	+	0.308130i	$0.0997032\pi$
$110$	0.542819	−	0.940191i	0.0517558	−	0.0896436i
$111$	2.80829	+	4.86410i	0.266551	+	0.461680i
$112$	−2.38879	−	4.13750i	−0.225719	−	0.390957i
$113$	13.9287			1.31030			0.655150	−	0.755499i	$-0.272606\pi$
$113$	13.9287			1.31030			0.655150	+	0.755499i	$0.272606\pi$
$114$	−4.84612	−	8.39373i	−0.453881	−	0.786145i
$115$	3.24745	+	5.62475i	0.302827	+	0.524511i
$116$	2.07154	+	3.58802i	0.192338	+	0.333139i
$117$	5.30096	−	9.18153i	0.490074	−	0.848833i
$118$	−0.671595			−0.0618253
$119$	−0.814374	+	1.41054i	−0.0746535	+	0.129304i
$120$	5.76768	+	9.98992i	0.526515	+	0.911950i
$121$	−9.81362			−0.892147
$122$	−0.744173	−	1.28895i	−0.0673743	−	0.116696i
$123$	−14.3755	+	24.8991i	−1.29619	+	2.24507i
$124$	−1.63593	+	2.83351i	−0.146911	+	0.254456i
$125$	−10.6666			−0.954047
$126$	−2.16058	+	3.74223i	−0.192480	+	0.333385i
$127$	−6.10276			−0.541532			−0.270766	−	0.962645i	$-0.587277\pi$
$127$	−6.10276			−0.541532			−0.270766	+	0.962645i	$0.587277\pi$
$128$	−10.7325			−0.948629
$129$	19.3506	+	4.57706i	1.70372	+	0.402988i
$130$	−1.70569			−0.149599
$131$	6.73115			0.588103			0.294052	−	0.955790i	$-0.404996\pi$
$131$	6.73115			0.588103			0.294052	+	0.955790i	$0.404996\pi$
$132$	−3.00002	+	5.19619i	−0.261119	+	0.452271i
$133$	12.1565			1.05410
$134$	−0.611187	+	1.05861i	−0.0527985	+	0.0914497i
$135$	−11.2754	+	19.5296i	−0.970435	+	1.68084i
$136$	0.817218	+	1.41546i	0.0700758	+	0.121375i
$137$	17.4489			1.49076			0.745381	−	0.666639i	$-0.232268\pi$
$137$	17.4489			1.49076			0.745381	+	0.666639i	$0.232268\pi$
$138$	1.81189	+	3.13828i	0.154238	+	0.267148i
$139$	2.11841	−	3.66919i	0.179681	−	0.311216i	−0.762090	−	0.647471i	$-0.775827\pi$
$139$	2.11841	−	3.66919i	0.179681	−	0.311216i	0.941771	+	0.336254i	$0.109160\pi$
$140$	−6.88648			−0.582014
$141$	2.89575	−	5.01559i	0.243866	−	0.422389i
$142$	−0.815840	−	1.41308i	−0.0684638	−	0.118583i
$143$	−0.931989	−	1.61425i	−0.0779368	−	0.134991i
$144$	−9.08615	−	15.7377i	−0.757179	−	1.31147i
$145$	5.30818			0.440820
$146$	−2.64198	−	4.57604i	−0.218652	−	0.378716i
$147$	6.59111	+	11.4161i	0.543626	+	0.941588i
$148$	−1.68237	+	2.91395i	−0.138290	+	0.239526i
$149$	−1.56872	+	2.71711i	−0.128515	+	0.222594i	−0.923101	−	0.384557i	$-0.874354\pi$
$149$	−1.56872	+	2.71711i	−0.128515	+	0.222594i	0.794586	+	0.607151i	$0.207688\pi$
$150$	0.541614			0.0442226
$151$	−17.7912			−1.44783			−0.723915	−	0.689889i	$-0.757659\pi$
$151$	−17.7912			−1.44783			−0.723915	+	0.689889i	$0.757659\pi$
$152$	6.09945	−	10.5646i	0.494731	−	0.856899i
$153$	−3.09761	+	5.36521i	−0.250427	+	0.433752i
$154$	0.379862	+	0.657941i	0.0306102	+	0.0530184i
$155$	2.09597	+	3.63033i	0.168352	+	0.291595i
$156$	9.42693			0.754759
$157$	6.39823	+	11.0821i	0.510634	+	0.884444i	0.999924	+	0.0123229i	$0.00392261\pi$
$157$	6.39823	+	11.0821i	0.510634	+	0.884444i	−0.489290	+	0.872121i	$0.662744\pi$
$158$	−3.31305	−	5.73837i	−0.263572	−	0.456520i
$159$	−17.9171	−	31.0333i	−1.42092	−	2.46110i
$160$	−5.26591	+	9.12083i	−0.416307	+	0.721065i
$161$	−4.54510			−0.358204
$162$	−2.31145	+	4.00355i	−0.181605	+	0.314548i
$163$	2.99186	+	5.18206i	0.234341	+	0.405890i	0.959081	−	0.283132i	$-0.0913735\pi$
$163$	2.99186	+	5.18206i	0.234341	+	0.405890i	−0.724740	+	0.689022i	$0.758040\pi$
$164$	−17.2239			−1.34496
$165$	3.84367	+	6.65743i	0.299229	+	0.518280i
$166$	0.515320	−	0.892560i	0.0399966	−	0.0692761i
$167$	8.78434	−	15.2149i	0.679753	−	1.17737i	−0.295303	−	0.955404i	$-0.595420\pi$
$167$	8.78434	−	15.2149i	0.679753	−	1.17737i	0.975055	−	0.221962i	$-0.0712462\pi$
$168$	−8.07239			−0.622799
$169$	5.03571	−	8.72211i	0.387362	−	0.670931i
$170$	0.996719			0.0764449
$171$	46.2391			3.53599
$172$	3.42157	+	11.4103i	0.260892	+	0.870030i
$173$	23.7552			1.80607			0.903036	−	0.429565i	$-0.141333\pi$
$173$	23.7552			1.80607			0.903036	+	0.429565i	$0.141333\pi$
$174$	2.96165			0.224522
$175$	−0.339658	+	0.588306i	−0.0256758	+	0.0444717i
$176$	−3.19497			−0.240830
$177$	2.37776	−	4.11840i	0.178723	−	0.309558i
$178$	0.00792820	−	0.0137320i	0.000594244	−	0.00102926i
$179$	−3.99747	−	6.92382i	−0.298785	−	0.517511i	0.677073	−	0.735916i	$-0.263248\pi$
$179$	−3.99747	−	6.92382i	−0.298785	−	0.517511i	−0.975858	+	0.218405i	$0.929915\pi$
$180$	−26.1939			−1.95238
$181$	−6.50792	−	11.2720i	−0.483730	−	0.837845i	0.516095	−	0.856531i	$-0.327385\pi$
$181$	−6.50792	−	11.2720i	−0.483730	−	0.837845i	−0.999825	+	0.0186862i	$0.994052\pi$
$182$	0.596818	−	1.03372i	0.0442391	−	0.0766244i
$183$	10.5389			0.779057
$184$	−2.28049	+	3.94992i	−0.168120	+	0.291192i
$185$	2.15548	+	3.73340i	0.158474	+	0.274485i
$186$	1.16943	+	2.02551i	0.0857466	+	0.148518i
$187$	0.544606	+	0.943285i	0.0398255	+	0.0689799i
$188$	3.46954			0.253042
$189$	−7.89050	−	13.6667i	−0.573949	−	0.994110i
$190$	−3.71960	−	6.44253i	−0.269848	−	0.467390i
$191$	−7.12731	+	12.3449i	−0.515714	+	0.893243i	0.484119	+	0.875002i	$0.339140\pi$
$191$	−7.12731	+	12.3449i	−0.515714	+	0.893243i	−0.999834	+	0.0182412i	$0.994193\pi$
$192$	5.95670	−	10.3173i	0.429887	−	0.744587i
$193$	−18.3538			−1.32114			−0.660569	−	0.750765i	$-0.729685\pi$
$193$	−18.3538			−1.32114			−0.660569	+	0.750765i	$0.729685\pi$
$194$	−4.87722			−0.350164
$195$	6.03895	−	10.4598i	0.432458	−	0.749040i
$196$	−3.94856	+	6.83911i	−0.282040	+	0.488508i
$197$	−6.20730	−	10.7514i	−0.442252	−	0.766003i	0.555604	−	0.831447i	$-0.312487\pi$
$197$	−6.20730	−	10.7514i	−0.442252	−	0.766003i	−0.997856	+	0.0654440i	$0.979154\pi$
$198$	1.44487	+	2.50259i	0.102682	+	0.177851i
$199$	−5.36381			−0.380231			−0.190115	−	0.981762i	$-0.560886\pi$
$199$	−5.36381			−0.380231			−0.190115	+	0.981762i	$0.560886\pi$
$200$	0.340845	+	0.590360i	0.0241014	+	0.0417448i
$201$	−4.32778	−	7.49593i	−0.305258	−	0.528722i
$202$	0.0841380	+	0.145731i	0.00591993	+	0.0102536i
$203$	−1.85732	+	3.21697i	−0.130358	+	0.225787i
$204$	−5.50861			−0.385680
$205$	−11.0338	+	19.1111i	−0.770632	+	1.33477i
$206$	1.21896	+	2.11130i	0.0849288	+	0.147101i
$207$	−17.2881			−1.20160
$208$	2.50987	+	4.34723i	0.174028	+	0.301426i
$209$	4.06477	−	7.04038i	0.281166	−	0.486994i
$210$	−2.46137	+	4.26322i	−0.169851	+	0.294190i
$211$	8.48980			0.584462			0.292231	−	0.956348i	$-0.405602\pi$
$211$	8.48980			0.584462			0.292231	+	0.956348i	$0.405602\pi$
$212$	10.7337	−	18.5912i	0.737190	−	1.27685i
$213$	11.5538			0.791655
$214$	−8.20780			−0.561074
$215$	14.8524	+	3.51308i	1.01292	+	0.239590i
$216$	−15.8361			−1.07751
$217$	−2.93350			−0.199139
$218$	0.933647	−	1.61712i	0.0632346	−	0.109526i
$219$	37.4154			2.52830
$220$	−2.30264	+	3.98829i	−0.155244	+	0.268891i
$221$	0.855654	−	1.48204i	0.0575575	−	0.0996926i
$222$	1.20263	+	2.08302i	0.0807152	+	0.139803i
$223$	2.64844			0.177353			0.0886764	−	0.996060i	$-0.471736\pi$
$223$	2.64844			0.177353			0.0886764	+	0.996060i	$0.471736\pi$
$224$	−3.68506	−	6.38272i	−0.246219	−	0.426463i
$225$	−1.29195	+	2.23772i	−0.0861299	+	0.149181i
$226$	5.96486			0.396776
$227$	−7.05992	+	12.2281i	−0.468583	+	0.811610i	−0.999355	−	0.0359048i	$-0.988569\pi$
$227$	−7.05992	+	12.2281i	−0.468583	+	0.811610i	0.530772	+	0.847515i	$0.321902\pi$
$228$	20.5573	+	35.6062i	1.36144	+	2.35808i
$229$	−6.84512	−	11.8561i	−0.452338	−	0.783473i	0.546192	−	0.837660i	$-0.316077\pi$
$229$	−6.84512	−	11.8561i	−0.452338	−	0.783473i	−0.998531	+	0.0541866i	$0.982743\pi$
$230$	1.39070	+	2.40876i	0.0916999	+	0.158829i
$231$	−5.37956			−0.353949
$232$	1.86381	+	3.22821i	0.122365	+	0.211942i
$233$	3.69483	+	6.39963i	0.242056	+	0.419254i	0.961300	−	0.275504i	$-0.0888448\pi$
$233$	3.69483	+	6.39963i	0.242056	+	0.419254i	−0.719244	+	0.694758i	$0.755511\pi$
$234$	2.27010	−	3.93193i	0.148401	−	0.257038i
$235$	2.22261	−	3.84967i	0.144987	−	0.251125i
$236$	2.84891			0.185448
$237$	46.9190			3.04772
$238$	−0.348750	+	0.604052i	−0.0226061	+	0.0391549i
$239$	−6.82038	+	11.8132i	−0.441173	+	0.764135i	−0.997777	−	0.0666435i	$-0.978771\pi$
$239$	−6.82038	+	11.8132i	−0.441173	+	0.764135i	0.556603	+	0.830778i	$0.312104\pi$
$240$	−10.3511	−	17.9287i	−0.668162	−	1.15729i
$241$	11.0819	+	19.1944i	0.713848	+	1.23642i	0.963402	+	0.268060i	$0.0863824\pi$
$241$	11.0819	+	19.1944i	0.713848	+	1.23642i	−0.249555	+	0.968361i	$0.580284\pi$
$242$	−4.20261			−0.270154
$243$	−1.83366	−	3.17599i	−0.117629	−	0.203740i
$244$	3.15679	+	5.46771i	0.202093	+	0.350034i
$245$	5.05895	+	8.76236i	0.323205	+	0.559807i
$246$	−6.15620	+	10.6628i	−0.392505	+	0.679838i
$247$	−12.7727			−0.812705
$248$	−1.47187	+	2.54936i	−0.0934640	+	0.161884i
$249$	3.64895	+	6.32016i	0.231243	+	0.400524i
$250$	−4.56788			−0.288898
$251$	1.75240	+	3.03524i	0.110610	+	0.191583i	0.916016	−	0.401141i	$-0.131386\pi$
$251$	1.75240	+	3.03524i	0.110610	+	0.191583i	−0.805406	+	0.592723i	$0.798053\pi$
$252$	9.16518	−	15.8746i	0.577352	−	1.00000i
$253$	−1.51975	+	2.63229i	−0.0955460	+	0.165491i
$254$	−2.61346			−0.163983
$255$	−3.52885	+	6.11215i	−0.220985	+	0.382758i
$256$	3.26138			0.203836
$257$	17.4933			1.09120			0.545600	−	0.838046i	$-0.316302\pi$
$257$	17.4933			1.09120			0.545600	+	0.838046i	$0.316302\pi$
$258$	8.28675	+	1.96009i	0.515910	+	0.122030i
$259$	−3.01679			−0.187454
$260$	7.23556			0.448730
$261$	−7.06463	+	12.2363i	−0.437290	+	0.757408i
$262$	2.88257			0.178086
$263$	−15.5350	+	26.9075i	−0.957932	+	1.65919i	−0.230421	+	0.973091i	$0.574010\pi$
$263$	−15.5350	+	26.9075i	−0.957932	+	1.65919i	−0.727511	+	0.686096i	$0.759323\pi$
$264$	−2.69918	+	4.67511i	−0.166123	+	0.287733i
$265$	−13.7521	−	23.8193i	−0.844785	−	1.46321i
$266$	5.20592			0.319195
$267$	0.0561391	+	0.0972358i	0.00343566	+	0.00595073i
$268$	2.59266	−	4.49061i	0.158372	−	0.274308i
$269$	−11.7558			−0.716762			−0.358381	−	0.933575i	$-0.616671\pi$
$269$	−11.7558			−0.716762			−0.358381	+	0.933575i	$0.616671\pi$
$270$	−4.82863	+	8.36343i	−0.293861	+	0.508982i
$271$	−4.40540	−	7.63037i	−0.267609	−	0.463512i	0.700635	−	0.713520i	$-0.252900\pi$
$271$	−4.40540	−	7.63037i	−0.267609	−	0.463512i	−0.968244	+	0.250008i	$0.919567\pi$
$272$	−1.46664	−	2.54030i	−0.0889281	−	0.154028i
$273$	4.22603	+	7.31970i	0.255771	+	0.443009i
$274$	7.47238			0.451423
$275$	0.227144	+	0.393425i	0.0136973	+	0.0237244i
$276$	−7.68604	−	13.3126i	−0.462645	−	0.801325i
$277$	−4.14874	+	7.18584i	−0.249274	+	0.431755i	−0.963325	−	0.268339i	$-0.913525\pi$
$277$	−4.14874	+	7.18584i	−0.249274	+	0.431755i	0.714051	+	0.700094i	$0.246859\pi$
$278$	0.907193	−	1.57130i	0.0544098	−	0.0942405i
$279$	−11.1581			−0.668016
$280$	−6.19589			−0.370275
$281$	10.0800	−	17.4590i	0.601321	−	1.04152i	−0.391300	−	0.920263i	$-0.627975\pi$
$281$	10.0800	−	17.4590i	0.601321	−	1.04152i	0.992621	−	0.121256i	$-0.0386920\pi$
$282$	1.24009	−	2.14789i	0.0738460	−	0.127905i
$283$	−14.9096	−	25.8242i	−0.886285	−	1.53509i	−0.844233	−	0.535976i	$-0.819944\pi$
$283$	−14.9096	−	25.8242i	−0.886285	−	1.53509i	−0.0420518	−	0.999115i	$-0.513389\pi$
$284$	3.46080	+	5.99427i	0.205360	+	0.355695i
$285$	52.6765			3.12029
$286$	−0.399118	−	0.691292i	−0.0236003	−	0.0408769i
$287$	−7.72138	−	13.3738i	−0.455779	−	0.789432i
$288$	−14.0168	−	24.2777i	−0.825945	−	1.43058i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	2.27319			0.133486
$291$	17.2676	−	29.9084i	1.01225	−	1.75326i
$292$	11.2073	+	19.4116i	0.655857	+	1.13598i
$293$	5.11297			0.298703			0.149351	−	0.988784i	$-0.452281\pi$
$293$	5.11297			0.298703			0.149351	+	0.988784i	$0.452281\pi$
$294$	2.82260	+	4.88888i	0.164617	+	0.285125i
$295$	1.82503	−	3.16104i	0.106257	−	0.184043i
$296$	−1.51366	+	2.62174i	−0.0879798	+	0.152385i
$297$	−10.5534			−0.612372
$298$	−0.671795	+	1.16358i	−0.0389161	+	0.0674046i
$299$	4.77550			0.276174
$300$	−2.29753			−0.132648
$301$	−7.32588	+	7.77191i	−0.422257	+	0.447966i
$302$	−7.61897			−0.438423
$303$	−1.19155			−0.0684529
$304$	−10.9465	+	18.9600i	−0.627827	+	1.08743i
$305$	8.08903			0.463177
$306$	−1.32653	+	2.29761i	−0.0758326	+	0.131346i
$307$	−13.5523	+	23.4733i	−0.773472	+	1.33969i	0.162178	+	0.986762i	$0.448148\pi$
$307$	−13.5523	+	23.4733i	−0.773472	+	1.33969i	−0.935649	+	0.352931i	$0.885185\pi$
$308$	−1.61138	−	2.79099i	−0.0918168	−	0.159031i
$309$	−17.2627			−0.982043
$310$	0.897584	+	1.55466i	0.0509794	+	0.0882988i
$311$	5.01706	−	8.68980i	0.284491	−	0.492753i	−0.687994	−	0.725716i	$-0.741509\pi$
$311$	5.01706	−	8.68980i	0.284491	−	0.492753i	0.972486	+	0.232963i	$0.0748420\pi$
$312$	8.48158			0.480175
$313$	−5.07747	+	8.79444i	−0.286996	+	0.497091i	−0.973091	−	0.230420i	$-0.925990\pi$
$313$	−5.07747	+	8.79444i	−0.286996	+	0.497091i	0.686095	+	0.727511i	$0.259323\pi$
$314$	2.73999	+	4.74581i	0.154627	+	0.267822i
$315$	−11.7426	−	20.3387i	−0.661618	−	1.14596i
$316$	14.0540	+	24.3422i	0.790597	+	1.36935i
$317$	18.2461			1.02481			0.512403	−	0.858745i	$-0.328755\pi$
$317$	18.2461			1.02481			0.512403	+	0.858745i	$0.328755\pi$
$318$	−7.67286	−	13.2898i	−0.430273	−	0.745254i
$319$	1.24207	+	2.15133i	0.0695425	+	0.120451i
$320$	4.57201	−	7.91895i	0.255583	−	0.442683i
$321$	29.0595	−	50.3325i	1.62194	−	2.80928i
$322$	−1.94641			−0.108469
$323$	7.46368			0.415291
$324$	9.80517	−	16.9831i	0.544732	−	0.943503i
$325$	0.356876	−	0.618127i	0.0197959	−	0.0342875i
$326$	1.28124	+	2.21918i	0.0709615	+	0.122909i
$327$	6.61110	+	11.4508i	0.365595	+	0.633228i
$328$	−15.4967			−0.855662
$329$	1.55537	+	2.69398i	0.0857504	+	0.148524i
$330$	1.64602	+	2.85100i	0.0906106	+	0.156942i
$331$	−2.54067	−	4.40056i	−0.139648	−	0.241877i	0.787716	−	0.616039i	$-0.211264\pi$
$331$	−2.54067	−	4.40056i	−0.139648	−	0.241877i	−0.927363	+	0.374162i	$0.877930\pi$
$332$	−2.18599	+	3.78624i	−0.119972	+	0.207797i
$333$	−11.4749			−0.628818
$334$	3.76183	−	6.51568i	0.205838	−	0.356522i
$335$	−3.32175	−	5.75343i	−0.181486	−	0.314344i
$336$	14.4873			0.790348
$337$	−9.46913	−	16.4010i	−0.515816	−	0.893420i	−0.999831	−	0.0183605i	$-0.994155\pi$
$337$	−9.46913	−	16.4010i	−0.515816	−	0.893420i	0.484015	−	0.875060i	$-0.339178\pi$
$338$	2.15651	−	3.73518i	0.117299	−	0.203167i
$339$	−21.1184	+	36.5781i	−1.14699	+	1.98665i
$340$	−4.22809			−0.229300
$341$	−0.980878	+	1.69893i	−0.0531175	+	0.0920022i
$342$	19.8016			1.07075
$343$	−18.4817			−0.997918
$344$	3.07845	+	10.2661i	0.165979	+	0.553510i
$345$	−19.6949			−1.06034
$346$	10.1730			0.546903
$347$	−14.4606	+	25.0464i	−0.776284	+	1.34456i	0.157786	+	0.987473i	$0.449564\pi$
$347$	−14.4606	+	25.0464i	−0.776284	+	1.34456i	−0.934070	+	0.357090i	$0.883769\pi$
$348$	−12.5633			−0.673466
$349$	6.92251	−	11.9901i	0.370553	−	0.641817i	−0.619097	−	0.785314i	$-0.712501\pi$
$349$	6.92251	−	11.9901i	0.370553	−	0.641817i	0.989651	+	0.143497i	$0.0458347\pi$
$350$	−0.145456	+	0.251938i	−0.00777497	+	0.0134666i
$351$	8.29047	+	14.3595i	0.442512	+	0.766454i
$352$	−4.92871			−0.262701
$353$	0.946655	+	1.63965i	0.0503854	+	0.0872700i	0.890118	−	0.455730i	$-0.150622\pi$
$353$	0.946655	+	1.63965i	0.0503854	+	0.0872700i	−0.839733	+	0.543000i	$0.817288\pi$
$354$	1.01826	−	1.76368i	0.0541198	−	0.0937383i
$355$	8.86803			0.470666
$356$	−0.0336315	+	0.0582514i	−0.00178246	+	0.00308732i
$357$	−2.46947	−	4.27726i	−0.130698	−	0.226376i
$358$	−1.71189	−	2.96508i	−0.0904761	−	0.156709i
$359$	−8.05498	−	13.9516i	−0.425126	−	0.736339i	0.571306	−	0.820737i	$-0.306437\pi$
$359$	−8.05498	−	13.9516i	−0.425126	−	0.736339i	−0.996432	+	0.0843975i	$0.973103\pi$
$360$	−23.5671			−1.24210
$361$	−18.3533	−	31.7888i	−0.965963	−	1.67310i
$362$	−2.78697	−	4.82717i	−0.146480	−	0.253711i
$363$	14.8792	−	25.7716i	0.780956	−	1.35266i
$364$	−2.53171	+	4.38504i	−0.132697	+	0.229839i
$365$	28.7178			1.50316
$366$	4.51320			0.235909
$367$	−16.0350	+	27.7735i	−0.837021	+	1.44976i	0.0553533	+	0.998467i	$0.482371\pi$
$367$	−16.0350	+	27.7735i	−0.837021	+	1.44976i	−0.892374	+	0.451296i	$0.850962\pi$
$368$	4.09274	−	7.08883i	0.213349	−	0.369531i
$369$	−29.3696	−	50.8696i	−1.52892	−	2.64817i
$370$	0.923068	+	1.59880i	0.0479880	+	0.0831177i
$371$	19.2473			0.999271
$372$	−4.96072	−	8.59222i	−0.257201	−	0.445486i
$373$	0.524059	+	0.907698i	0.0271348	+	0.0469988i	0.879274	−	0.476316i	$-0.158028\pi$
$373$	0.524059	+	0.907698i	0.0271348	+	0.0469988i	−0.852139	+	0.523315i	$0.824695\pi$
$374$	0.233224	+	0.403955i	0.0120597	+	0.0208880i
$375$	16.1725	−	28.0115i	0.835142	−	1.44651i
$376$	3.12161			0.160985
$377$	1.95147	−	3.38004i	0.100506	−	0.174081i
$378$	−3.37905	−	5.85269i	−0.173800	−	0.301030i
$379$	−10.0564			−0.516564			−0.258282	−	0.966070i	$-0.583156\pi$
$379$	−10.0564			−0.516564			−0.258282	+	0.966070i	$0.583156\pi$
$380$	15.7786	+	27.3293i	0.809423	+	1.40196i
$381$	9.25288	−	16.0265i	0.474040	−	0.821061i
$382$	−3.05222	+	5.28660i	−0.156165	+	0.270486i
$383$	−22.5167			−1.15055			−0.575275	−	0.817960i	$-0.695105\pi$
$383$	−22.5167			−1.15055			−0.575275	+	0.817960i	$0.695105\pi$
$384$	16.2724	−	28.1847i	0.830399	−	1.43829i
$385$	−4.12904			−0.210435
$386$	−7.85990			−0.400058
$387$	−27.8652	+	29.5618i	−1.41647	+	1.50271i
$388$	20.6892			1.05033
$389$	−5.03788			−0.255431			−0.127715	−	0.991811i	$-0.540764\pi$
$389$	−5.03788			−0.255431			−0.127715	+	0.991811i	$0.540764\pi$
$390$	2.58614	−	4.47932i	0.130954	−	0.226819i
$391$	−2.79055			−0.141124
$392$	−3.55259	+	6.15327i	−0.179433	+	0.310787i
$393$	−10.2056	+	17.6767i	−0.514806	+	0.891671i
$394$	−2.65823	−	4.60419i	−0.133920	−	0.231956i
$395$	36.0122			1.81197
$396$	−6.12915	−	10.6160i	−0.308001	−	0.533474i
$397$	10.3845	−	17.9864i	0.521181	−	0.902712i	−0.478515	−	0.878079i	$-0.658825\pi$
$397$	10.3845	−	17.9864i	0.521181	−	0.902712i	0.999697	−	0.0246332i	$-0.00784178\pi$
$398$	−2.29702			−0.115139
$399$	−18.4314	+	31.9241i	−0.922723	+	1.59820i
$400$	−0.611705	−	1.05950i	−0.0305853	−	0.0529752i
$401$	−6.77947	−	11.7424i	−0.338551	−	0.586387i	0.645610	−	0.763667i	$-0.276603\pi$
$401$	−6.77947	−	11.7424i	−0.338551	−	0.586387i	−0.984160	+	0.177281i	$0.943270\pi$
$402$	−1.85334	−	3.21008i	−0.0924361	−	0.160104i
$403$	3.08220			0.153535
$404$	−0.356914	−	0.618193i	−0.0177571	−	0.0307562i
$405$	−12.5625	−	21.7589i	−0.624236	−	1.08121i
$406$	−0.795384	+	1.37765i	−0.0394742	+	0.0683714i
$407$	−1.00873	+	1.74717i	−0.0500007	+	0.0866038i
$408$	−4.95620			−0.245368
$409$	−23.5830			−1.16611			−0.583053	−	0.812434i	$-0.698142\pi$
$409$	−23.5830			−1.16611			−0.583053	+	0.812434i	$0.698142\pi$
$410$	−4.72513	+	8.18417i	−0.233358	+	0.404188i
$411$	−26.4557	+	45.8226i	−1.30496	+	2.26026i
$412$	−5.17083	−	8.95613i	−0.254748	−	0.441237i
$413$	1.27715	+	2.21208i	0.0628443	+	0.108849i
$414$	−7.40349			−0.363862
$415$	2.80072	+	4.85098i	0.137482	+	0.238125i
$416$	3.87186	+	6.70625i	0.189833	+	0.328801i
$417$	6.42377	+	11.1263i	0.314574	+	0.544857i
$418$	1.74071	−	3.01499i	0.0851408	−	0.147468i
$419$	−8.37349			−0.409072			−0.204536	−	0.978859i	$-0.565568\pi$
$419$	−8.37349			−0.409072			−0.204536	+	0.978859i	$0.565568\pi$
$420$	10.4412	−	18.0846i	0.509476	−	0.882438i
$421$	−1.28984	−	2.23407i	−0.0628631	−	0.108882i	0.832881	−	0.553452i	$-0.186690\pi$
$421$	−1.28984	−	2.23407i	−0.0628631	−	0.108882i	−0.895744	+	0.444570i	$0.853356\pi$
$422$	3.63570			0.176983
$423$	5.91612	+	10.2470i	0.287652	+	0.498227i
$424$	9.65726	−	16.7269i	0.468998	−	0.812329i
$425$	−0.208540	+	0.361201i	−0.0101157	+	0.0175208i
$426$	4.94784			0.239724
$427$	−2.83033	+	4.90228i	−0.136969	+	0.237238i
$428$	34.8175			1.68297
$429$	5.65225			0.272893
$430$	6.36042	+	1.50445i	0.306727	+	0.0725512i
$431$	−13.2669			−0.639042			−0.319521	−	0.947579i	$-0.603522\pi$
$431$	−13.2669			−0.639042			−0.319521	+	0.947579i	$0.603522\pi$
$432$	28.4207			1.36739
$433$	12.9239	−	22.3849i	0.621085	−	1.07575i	−0.368199	−	0.929747i	$-0.620026\pi$
$433$	12.9239	−	22.3849i	0.621085	−	1.07575i	0.989284	−	0.146003i	$-0.0466411\pi$
$434$	−1.25625			−0.0603020
$435$	−8.04816	+	13.9398i	−0.385880	+	0.668363i
$436$	−3.96054	+	6.85985i	−0.189675	+	0.328527i
$437$	10.4139	+	18.0374i	0.498165	+	0.862846i
$438$	16.0229			0.765602
$439$	10.5212	+	18.2232i	0.502149	+	0.869748i	0.999997	+	0.00248356i	$0.000790542\pi$
$439$	10.5212	+	18.2232i	0.502149	+	0.869748i	−0.497848	+	0.867265i	$0.665876\pi$
$440$	−2.07173	+	3.58834i	−0.0987658	+	0.171067i
$441$	−26.9317			−1.28246
$442$	0.366428	−	0.634672i	0.0174292	−	0.0301882i
$443$	−15.2071	−	26.3395i	−0.722511	−	1.25143i	−0.959990	−	0.280033i	$-0.909654\pi$
$443$	−15.2071	−	26.3395i	−0.722511	−	1.25143i	0.237479	−	0.971393i	$-0.423679\pi$
$444$	−5.10156	−	8.83616i	−0.242109	−	0.419346i
$445$	0.0430891	+	0.0746325i	0.00204262	+	0.00353792i
$446$	1.13418			0.0537048
$447$	−4.75694	−	8.23926i	−0.224996	−	0.389704i
$448$	3.19947	+	5.54165i	0.151161	+	0.261818i
$449$	18.4474	−	31.9519i	0.870587	−	1.50790i	0.00919682	−	0.999958i	$-0.497073\pi$
$449$	18.4474	−	31.9519i	0.870587	−	1.50790i	0.861390	−	0.507944i	$-0.169594\pi$
$450$	−0.553267	+	0.958287i	−0.0260813	+	0.0451741i
$451$	−10.3272			−0.486290
$452$	−25.3029			−1.19015
$453$	26.9747	−	46.7216i	1.26738	−	2.19517i
$454$	−3.02336	+	5.23661i	−0.141893	+	0.245766i
$455$	3.24365	+	5.61817i	0.152065	+	0.263384i
$456$	18.4957	+	32.0356i	0.866143	+	1.50020i
$457$	4.03760			0.188871			0.0944355	−	0.995531i	$-0.469895\pi$
$457$	4.03760			0.188871			0.0944355	+	0.995531i	$0.469895\pi$
$458$	−2.93138	−	5.07729i	−0.136974	−	0.237246i
$459$	−4.84452	−	8.39096i	−0.226123	−	0.391656i
$460$	−5.89935	−	10.2180i	−0.275059	−	0.476415i
$461$	−12.0835	+	20.9293i	−0.562786	+	0.974773i	0.434466	+	0.900688i	$0.356937\pi$
$461$	−12.0835	+	20.9293i	−0.562786	+	0.974773i	−0.997252	+	0.0740853i	$0.976396\pi$
$462$	−2.30376			−0.107181
$463$	19.2353	−	33.3166i	0.893941	−	1.54835i	0.0588316	−	0.998268i	$-0.481263\pi$
$463$	19.2353	−	33.3166i	0.893941	−	1.54835i	0.835110	−	0.550084i	$-0.185404\pi$
$464$	−3.34493	−	5.79358i	−0.155284	−	0.268960i
$465$	−12.7115			−0.589481
$466$	1.58228	+	2.74060i	0.0732979	+	0.126956i
$467$	7.45144	−	12.9063i	0.344811	−	0.597231i	−0.640508	−	0.767951i	$-0.721276\pi$
$467$	7.45144	−	12.9063i	0.344811	−	0.597231i	0.985319	+	0.170721i	$0.0546095\pi$
$468$	−9.62977	+	16.6792i	−0.445136	+	0.770998i
$469$	4.64908			0.214675
$470$	0.951817	−	1.64860i	0.0439040	−	0.0760440i
$471$	−38.8035			−1.78797
$472$	2.56321			0.117981
$473$	2.05152	+	6.84147i	0.0943292	+	0.314571i
$474$	20.0927			0.922889
$475$	3.11295			0.142832
$476$	1.47940	−	2.56239i	0.0678081	−	0.117447i
$477$	73.2104			3.35207
$478$	−2.92078	+	5.05893i	−0.133593	+	0.231390i
$479$	14.4937	−	25.1038i	0.662232	−	1.14702i	−0.317796	−	0.948159i	$-0.602943\pi$
$479$	14.4937	−	25.1038i	0.662232	−	1.14702i	0.980028	−	0.198861i	$-0.0637241\pi$
$480$	−15.9682	−	27.6577i	−0.728843	−	1.26239i
$481$	3.16971			0.144526
$482$	4.74574	+	8.21987i	0.216163	+	0.374405i
$483$	6.89120	−	11.9359i	0.313560	−	0.543103i
$484$	17.8275			0.810341
$485$	13.2536	−	22.9559i	0.601816	−	1.04238i
$486$	−0.785251	−	1.36009i	−0.0356197	−	0.0616951i
$487$	21.2228	+	36.7589i	0.961695	+	1.66570i	0.718243	+	0.695792i	$0.244946\pi$
$487$	21.2228	+	36.7589i	0.961695	+	1.66570i	0.243452	+	0.969913i	$0.421720\pi$
$488$	2.84022	+	4.91940i	0.128571	+	0.222691i
$489$	−18.1448			−0.820537
$490$	2.16646	+	3.75242i	0.0978707	+	0.169517i
$491$	5.48706	+	9.50387i	0.247628	+	0.428904i	0.962867	−	0.269976i	$-0.0870157\pi$
$491$	5.48706	+	9.50387i	0.247628	+	0.428904i	−0.715239	+	0.698880i	$0.753682\pi$
$492$	26.1146	−	45.2318i	1.17734	−	2.03921i
$493$	−1.14034	+	1.97512i	−0.0513582	+	0.0889550i
$494$	−5.46980			−0.246098
$495$	−15.7055			−0.705909
$496$	2.64153	−	4.57527i	0.118608	−	0.205436i
$497$	−3.10290	+	5.37439i	−0.139184	+	0.241074i
$498$	1.56264	+	2.70656i	0.0700234	+	0.121284i
$499$	−12.1758	−	21.0891i	−0.545065	−	0.944080i	−0.998603	−	0.0528429i	$-0.983172\pi$
$499$	−12.1758	−	21.0891i	−0.545065	−	0.944080i	0.453538	−	0.891237i	$-0.350162\pi$
$500$	19.3770			0.866565
$501$	26.6373	+	46.1371i	1.19007	+	2.06126i
$502$	0.750451	+	1.29982i	0.0334943	+	0.0580138i
$503$	9.82004	+	17.0088i	0.437854	+	0.758386i	0.997524	−	0.0703303i	$-0.0224053\pi$
$503$	9.82004	+	17.0088i	0.437854	+	0.758386i	−0.559670	+	0.828716i	$0.689072\pi$
$504$	8.24608	−	14.2826i	0.367310	−	0.636199i
$505$	−0.914565			−0.0406976
$506$	−0.650823	+	1.12726i	−0.0289326	+	0.0501128i
$507$	15.2701	+	26.4486i	0.678169	+	1.17462i
$508$	11.0863			0.491876
$509$	−13.5798	−	23.5209i	−0.601913	−	1.04254i	−0.992531	−	0.121992i	$-0.961072\pi$
$509$	−13.5798	−	23.5209i	−0.601913	−	1.04254i	0.390618	−	0.920553i	$-0.372261\pi$
$510$	−1.51121	+	2.61749i	−0.0669173	+	0.115904i
$511$	−10.0483	+	17.4042i	−0.444511	+	0.769916i
$512$	22.8617			1.01035
$513$	−36.1580	+	62.6275i	−1.59641	+	2.76507i
$514$	7.49137			0.330430
$515$	−13.2499			−0.583858
$516$	−35.1524	−	8.31473i	−1.54750	−	0.366036i
$517$	2.08029			0.0914909
$518$	−1.29192			−0.0567636
$519$	−36.0171	+	62.3835i	−1.58098	+	2.73833i
$520$	6.50996			0.285481
$521$	1.10289	−	1.91027i	0.0483187	−	0.0836904i	−0.840855	−	0.541261i	$-0.817947\pi$
$521$	1.10289	−	1.91027i	0.0483187	−	0.0836904i	0.889173	+	0.457571i	$0.151280\pi$
$522$	−3.02538	+	5.24011i	−0.132417	+	0.229353i
$523$	−12.1743	−	21.0864i	−0.532343	−	0.922046i	−0.999287	−	0.0377587i	$-0.987978\pi$
$523$	−12.1743	−	21.0864i	−0.532343	−	0.922046i	0.466943	−	0.884287i	$-0.345355\pi$
$524$	−12.2279			−0.534177
$525$	−1.02997	−	1.78395i	−0.0449514	−	0.0778582i
$526$	−6.65277	+	11.5229i	−0.290075	+	0.502424i
$527$	−1.80108			−0.0784562
$528$	4.84414	−	8.39030i	0.210814	−	0.365141i
$529$	7.60641	+	13.1747i	0.330713	+	0.572812i
$530$	−5.88924	−	10.2005i	−0.255812	−	0.443080i
$531$	4.85784	+	8.41403i	0.210812	+	0.365138i
$532$	−22.0835			−0.957442
$533$	8.11278	+	14.0517i	0.351403	+	0.608649i
$534$	0.0240412	+	0.0416405i	0.00104036	+	0.00180196i
$535$	22.3043	−	38.6322i	0.964301	−	1.67022i
$536$	2.33266	−	4.04029i	0.100756	−	0.174514i
$537$	24.2436			1.04619
$538$	−5.03432			−0.217045
$539$	−2.36750	+	4.10063i	−0.101976	+	0.176627i
$540$	20.4831	−	35.4777i	0.881450	−	1.52672i
$541$	−8.22864	−	14.2524i	−0.353777	−	0.612759i	0.633131	−	0.774045i	$-0.281769\pi$
$541$	−8.22864	−	14.2524i	−0.353777	−	0.612759i	−0.986908	+	0.161285i	$0.948436\pi$
$542$	−1.88658	−	3.26765i	−0.0810356	−	0.140358i
$543$	39.4687			1.69377
$544$	−2.26251	−	3.91879i	−0.0970045	−	0.168017i
$545$	5.07429	+	8.78893i	0.217359	+	0.376476i
$546$	1.80977	+	3.13461i	0.0774509	+	0.134149i
$547$	−2.92334	+	5.06338i	−0.124993	+	0.216494i	−0.921730	−	0.387832i	$-0.873224\pi$
$547$	−2.92334	+	5.06338i	−0.124993	+	0.216494i	0.796737	+	0.604326i	$0.206558\pi$
$548$	−31.6978			−1.35407
$549$	−10.7656	+	18.6467i	−0.459467	+	0.795820i
$550$	0.0972728	+	0.168481i	0.00414773	+	0.00718407i
$551$	17.0222			0.725171
$552$	−6.91527	−	11.9776i	−0.294333	−	0.509800i
$553$	−12.6006	+	21.8249i	−0.535832	+	0.928088i
$554$	−1.77667	+	3.07728i	−0.0754835	+	0.130741i
$555$	−13.0724			−0.554891
$556$	−3.84831	+	6.66548i	−0.163205	+	0.282679i
$557$	−11.6140			−0.492103			−0.246051	−	0.969257i	$-0.579133\pi$
$557$	−11.6140			−0.492103			−0.246051	+	0.969257i	$0.579133\pi$
$558$	−4.77836			−0.202284
$559$	7.69723	−	8.16587i	0.325558	−	0.345380i
$560$	11.1196			0.469890
$561$	−3.30288			−0.139448
$562$	4.31668	−	7.47671i	0.182088	−	0.315386i
$563$	27.0160			1.13859			0.569294	−	0.822134i	$-0.307217\pi$
$563$	27.0160			1.13859			0.569294	+	0.822134i	$0.307217\pi$
$564$	−5.26045	+	9.11136i	−0.221505	+	0.383658i
$565$	−16.2092	+	28.0752i	−0.681928	+	1.18113i
$566$	−6.38494	−	11.0590i	−0.268379	−	0.464846i
$567$	17.5824			0.738391
$568$	3.11374	+	5.39316i	0.130650	+	0.226292i
$569$	−22.8377	+	39.5560i	−0.957405	+	1.65827i	−0.228638	+	0.973512i	$0.573427\pi$
$569$	−22.8377	+	39.5560i	−0.957405	+	1.65827i	−0.728767	+	0.684762i	$0.759906\pi$
$570$	22.5583			0.944865
$571$	−19.0771	+	33.0425i	−0.798352	+	1.38279i	0.122337	+	0.992489i	$0.460961\pi$
$571$	−19.0771	+	33.0425i	−0.798352	+	1.38279i	−0.920689	+	0.390297i	$0.872372\pi$
$572$	1.69306	+	2.93246i	0.0707903	+	0.122612i
$573$	−21.6126	−	37.4341i	−0.902879	−	1.56383i
$574$	−3.30663	−	5.72725i	−0.138016	−	0.239051i
$575$	−1.16388			−0.0485372
$576$	12.1697	+	21.0786i	0.507072	+	0.878274i
$577$	23.9470	+	41.4774i	0.996926	+	1.72673i	0.566320	+	0.824185i	$0.308367\pi$
$577$	23.9470	+	41.4774i	0.996926	+	1.72673i	0.430605	+	0.902540i	$0.358300\pi$
$578$	−0.214121	+	0.370869i	−0.00890628	+	0.0154261i
$579$	27.8277	−	48.1990i	1.15648	−	2.00308i
$580$	−9.64288			−0.400399
$581$	−3.91986			−0.162623
$582$	7.39474	−	12.8081i	0.306522	−	0.530912i
$583$	6.43575	−	11.1470i	0.266541	−	0.461663i
$584$	10.0834	+	17.4650i	0.417254	+	0.722705i
$585$	12.3378	+	21.3697i	0.510105	+	0.883527i
$586$	2.18959			0.0904513
$587$	−2.49985	−	4.32986i	−0.103180	−	0.178712i	0.809813	−	0.586688i	$-0.199568\pi$
$587$	−2.49985	−	4.32986i	−0.103180	−	0.178712i	−0.912993	+	0.407975i	$0.866235\pi$
$588$	−11.9735	−	20.7387i	−0.493778	−	0.855248i
$589$	6.72134	+	11.6417i	0.276948	+	0.479688i
$590$	0.781556	−	1.35369i	0.0321761	−	0.0557307i
$591$	37.6456			1.54853
$592$	2.71653	−	4.70517i	0.111649	−	0.193381i
$593$	10.6999	+	18.5327i	0.439391	+	0.761048i	0.997643	−	0.0686237i	$-0.0218608\pi$
$593$	10.6999	+	18.5327i	0.439391	+	0.761048i	−0.558251	+	0.829672i	$0.688527\pi$
$594$	−4.51943			−0.185434
$595$	−1.89542	−	3.28297i	−0.0777048	−	0.134589i
$596$	2.84976	−	4.93593i	0.116731	−	0.202183i
$597$	8.13251	−	14.0859i	0.332841	−	0.576498i
$598$	2.04507			0.0836292
$599$	−11.0281	+	19.1013i	−0.450597	+	0.780457i	−0.998423	−	0.0561349i	$-0.982122\pi$
$599$	−11.0281	+	19.1013i	−0.450597	+	0.780457i	0.547826	+	0.836592i	$0.315456\pi$
$600$	−2.06713			−0.0843901
$601$	−38.8016			−1.58275			−0.791376	−	0.611330i	$-0.790635\pi$
$601$	−38.8016			−1.58275			−0.791376	+	0.611330i	$0.790635\pi$
$602$	−3.13726	+	3.32827i	−0.127865	+	0.135650i
$603$	17.6836			0.720131
$604$	32.3197			1.31507
$605$	11.4204	−	19.7807i	0.464306	−	0.804201i
$606$	−0.510274			−0.0207285
$607$	−14.5542	+	25.2086i	−0.590737	+	1.02319i	0.403396	+	0.915025i	$0.367830\pi$
$607$	−14.5542	+	25.2086i	−0.590737	+	1.02319i	−0.994133	+	0.108161i	$0.965504\pi$
$608$	−16.8867	+	29.2486i	−0.684846	+	1.18619i
$609$	−5.63207	−	9.75502i	−0.228223	−	0.395293i
$610$	3.46407			0.140256
$611$	−1.63421	−	2.83054i	−0.0661132	−	0.114511i
$612$	5.62714	−	9.74649i	0.227464	−	0.393978i
$613$	−9.28321			−0.374945			−0.187473	−	0.982270i	$-0.560030\pi$
$613$	−9.28321			−0.374945			−0.187473	+	0.982270i	$0.560030\pi$
$614$	−5.80368	+	10.0523i	−0.234218	+	0.405677i
$615$	−33.4584	−	57.9516i	−1.34917	−	2.33683i
$616$	−1.44979	−	2.51110i	−0.0584135	−	0.101175i
$617$	19.8747	+	34.4241i	0.800127	+	1.38586i	0.919532	+	0.393015i	$0.128568\pi$
$617$	19.8747	+	34.4241i	0.800127	+	1.38586i	−0.119405	+	0.992846i	$0.538099\pi$
$618$	−7.39264			−0.297376
$619$	−21.6417	−	37.4845i	−0.869854	−	1.50663i	−0.862146	−	0.506660i	$-0.830880\pi$
$619$	−21.6417	−	37.4845i	−0.869854	−	1.50663i	−0.00770767	−	0.999970i	$-0.502453\pi$
$620$	−3.80756	−	6.59488i	−0.152915	−	0.264857i
$621$	13.5189	−	23.4154i	0.542494	−	0.939628i
$622$	2.14852	−	3.72134i	0.0861478	−	0.149212i
$623$	−0.0603071			−0.00241615
$624$	−15.2217			−0.609355
$625$	13.4557	−	23.3060i	0.538229	−	0.932240i
$626$	−2.17439	+	3.76616i	−0.0869062	+	0.150526i
$627$	12.3258	+	21.3490i	0.492247	+	0.852597i
$628$	−11.6231	−	20.1317i	−0.463811	−	0.803344i
$629$	−1.85221			−0.0738526
$630$	−5.02867	−	8.70990i	−0.200347	−	0.347011i
$631$	−21.2767	−	36.8523i	−0.847013	−	1.46707i	−0.883862	−	0.467748i	$-0.845065\pi$
$631$	−21.2767	−	36.8523i	−0.847013	−	1.46707i	0.0368493	−	0.999321i	$-0.488268\pi$
$632$	12.6446	+	21.9011i	0.502975	+	0.871179i
$633$	−12.8721	+	22.2951i	−0.511619	+	0.886150i
$634$	7.81378			0.310325
$635$	7.10197	−	12.3010i	0.281833	−	0.488149i
$636$	32.5483	+	56.3753i	1.29062	+	2.23543i
$637$	7.43937			0.294759
$638$	0.531907	+	0.921290i	0.0210584	+	0.0364742i
$639$	−11.8024	+	20.4424i	−0.466896	+	0.808688i
$640$	12.4898	−	21.6329i	0.493701	−	0.855115i
$641$	41.4954			1.63897			0.819485	−	0.573101i	$-0.194260\pi$
$641$	41.4954			1.63897			0.819485	+	0.573101i	$0.194260\pi$
$642$	12.4445	−	21.5545i	0.491146	−	0.850689i
$643$	−0.800116			−0.0315535			−0.0157767	−	0.999876i	$-0.505022\pi$
$643$	−0.800116			−0.0315535			−0.0157767	+	0.999876i	$0.505022\pi$
$644$	8.25667			0.325359
$645$	−31.7446	+	33.6773i	−1.24994	+	1.32604i
$646$	3.19627			0.125756
$647$	−34.2950			−1.34827			−0.674137	−	0.738606i	$-0.735484\pi$
$647$	−34.2950			−1.34827			−0.674137	+	0.738606i	$0.735484\pi$
$648$	8.82189	−	15.2800i	0.346557	−	0.600254i
$649$	1.70816			0.0670513
$650$	0.152829	−	0.264708i	0.00599446	−	0.0103827i
$651$	4.44772	−	7.70367i	0.174320	−	0.301931i
$652$	−5.43504	−	9.41377i	−0.212853	−	0.368672i
$653$	1.27527			0.0499051			0.0249525	−	0.999689i	$-0.492057\pi$
$653$	1.27527			0.0499051			0.0249525	+	0.999689i	$0.492057\pi$
$654$	2.83116	+	4.90371i	0.110707	+	0.191750i
$655$	−7.83325	+	13.5676i	−0.306070	+	0.530129i
$656$	27.8115			1.08586
$657$	−38.2204	+	66.1997i	−1.49112	+	2.58270i
$658$	0.666077	+	1.15368i	0.0259664	+	0.0449751i
$659$	14.2810	+	24.7354i	0.556307	+	0.963553i	0.997801	+	0.0662880i	$0.0211156\pi$
$659$	14.2810	+	24.7354i	0.556307	+	0.963553i	−0.441493	+	0.897265i	$0.645551\pi$
$660$	−6.98244	−	12.0939i	−0.271791	−	0.470756i
$661$	−16.7010			−0.649594			−0.324797	−	0.945784i	$-0.605296\pi$
$661$	−16.7010			−0.649594			−0.324797	+	0.945784i	$0.605296\pi$
$662$	−1.08802	−	1.88451i	−0.0422872	−	0.0732436i
$663$	2.59465	+	4.49407i	0.100768	+	0.174535i
$664$	−1.96677	+	3.40655i	−0.0763256	+	0.132200i
$665$	−14.1468	+	24.5031i	−0.548591	+	0.950188i
$666$	−4.91403			−0.190415
$667$	−6.36434			−0.246428
$668$	−15.9577	+	27.6396i	−0.617422	+	1.06941i
$669$	−4.01551	+	6.95507i	−0.155249	+	0.268899i
$670$	−1.42251	−	2.46387i	−0.0549565	−	0.0951875i
$671$	1.89276	+	3.27836i	0.0730693	+	0.126560i
$672$	22.3489			0.862127
$673$	3.01749	+	5.22645i	0.116316	+	0.201465i	0.918305	−	0.395874i	$-0.129558\pi$
$673$	3.01749	+	5.22645i	0.116316	+	0.201465i	−0.801989	+	0.597339i	$0.796225\pi$
$674$	−4.05509	−	7.02362i	−0.156196	−	0.270540i
$675$	−2.02055	−	3.49969i	−0.0777710	−	0.134703i
$676$	−9.14792	+	15.8447i	−0.351843	+	0.609410i
$677$	−3.82615			−0.147051			−0.0735255	−	0.997293i	$-0.523425\pi$
$677$	−3.82615			−0.147051			−0.0735255	+	0.997293i	$0.523425\pi$
$678$	−9.04380	+	15.6643i	−0.347325	+	0.601585i
$679$	9.27482	+	16.0645i	0.355935	+	0.616498i
$680$	−3.80409			−0.145880
$681$	−21.4082	−	37.0801i	−0.820365	−	1.42091i
$682$	−0.420054	+	0.727555i	−0.0160847	+	0.0278595i
$683$	24.4752	−	42.3923i	0.936517	−	1.62209i	0.164611	−	0.986359i	$-0.447363\pi$
$683$	24.4752	−	42.3923i	0.936517	−	1.62209i	0.771906	−	0.635736i	$-0.219303\pi$
$684$	−83.9984			−3.21176
$685$	−20.3059	+	35.1708i	−0.775847	+	1.34381i
$686$	−7.91465			−0.302183
$687$	41.5138			1.58385
$688$	−5.52482	−	18.4243i	−0.210632	−	0.702419i
$689$	−20.2230			−0.770433
$690$	−8.43420			−0.321085
$691$	4.71248	−	8.16225i	0.179271	−	0.310507i	−0.762360	−	0.647153i	$-0.775959\pi$
$691$	4.71248	−	8.16225i	0.179271	−	0.310507i	0.941631	+	0.336646i	$0.109293\pi$
$692$	−43.1538			−1.64046
$693$	5.49531	−	9.51816i	0.208750	−	0.361565i
$694$	−6.19263	+	10.7260i	−0.235069	+	0.407152i
$695$	4.93051	+	8.53990i	0.187025	+	0.323937i
$696$	−11.3035			−0.428457
$697$	−4.74069	−	8.21111i	−0.179566	−	0.311018i
$698$	2.96452	−	5.13469i	0.112209	−	0.194351i
$699$	−22.4081			−0.847553
$700$	0.617026	−	1.06872i	0.0233214	−	0.0403938i
$701$	−24.9980	−	43.2978i	−0.944161	−	1.63533i	−0.757423	−	0.652925i	$-0.773542\pi$
$701$	−24.9980	−	43.2978i	−0.944161	−	1.63533i	−0.186738	−	0.982410i	$-0.559792\pi$
$702$	3.55033	+	6.14936i	0.133999	+	0.232093i
$703$	6.91217	+	11.9722i	0.260697	+	0.451541i
$704$	4.27924			0.161280
$705$	6.73976	+	11.6736i	0.253834	+	0.439653i
$706$	0.405398	+	0.702170i	0.0152574	+	0.0264265i
$707$	0.320004	−	0.554264i	0.0120350	−	0.0208452i
$708$	−4.31946	+	7.48152i	−0.162335	+	0.281173i
$709$	−25.2659			−0.948882			−0.474441	−	0.880287i	$-0.657350\pi$
$709$	−25.2659			−0.948882			−0.474441	+	0.880287i	$0.657350\pi$
$710$	3.79767			0.142524
$711$	−47.9285	+	83.0146i	−1.79746	+	3.11329i
$712$	−0.0302588	+	0.0524098i	−0.00113400	+	0.00196414i
$713$	−2.51300	−	4.35265i	−0.0941126	−	0.163008i
$714$	−1.05753	−	1.83170i	−0.0395773	−	0.0685498i
$715$	4.33834			0.162245
$716$	7.26184	+	12.5779i	0.271388	+	0.470057i
$717$	−20.6818	−	35.8220i	−0.772378	−	1.33780i
$718$	−3.44949	−	5.97469i	−0.128734	−	0.222973i
$719$	12.6644	−	21.9354i	0.472303	−	0.818052i	−0.527195	−	0.849744i	$-0.676756\pi$
$719$	12.6644	−	21.9354i	0.472303	−	0.818052i	0.999498	+	0.0316921i	$0.0100896\pi$
$720$	42.2953			1.57625
$721$	4.63609	−	8.02995i	0.172657	−	0.299051i
$722$	−7.85967	−	13.6133i	−0.292507	−	0.506636i
$723$	−67.2086			−2.49952
$724$	11.8223	+	20.4769i	0.439374	+	0.761018i
$725$	−0.475611	+	0.823782i	−0.0176637	+	0.0305945i
$726$	6.37192	−	11.0365i	0.236484	−	0.409602i
$727$	−30.8120			−1.14276			−0.571378	−	0.820687i	$-0.693591\pi$
$727$	−30.8120			−1.14276			−0.571378	+	0.820687i	$0.693591\pi$
$728$	−2.27782	+	3.94530i	−0.0844217	+	0.146223i
$729$	−21.2645			−0.787573
$730$	12.2982			0.455177
$731$	−4.49786	+	4.77171i	−0.166359	+	0.176488i
$732$	−19.1450			−0.707621
$733$	−38.2562			−1.41302			−0.706512	−	0.707701i	$-0.749732\pi$
$733$	−38.2562			−1.41302			−0.706512	+	0.707701i	$0.749732\pi$
$734$	−6.86688	+	11.8938i	−0.253461	+	0.439008i
$735$	−30.6811			−1.13169
$736$	6.31366	−	10.9356i	0.232725	−	0.403091i
$737$	1.55452	−	2.69251i	0.0572615	−	0.0991798i
$738$	−12.5773	−	21.7845i	−0.462977	−	0.801900i
$739$	5.92867			0.218090			0.109045	−	0.994037i	$-0.465221\pi$
$739$	5.92867			0.218090			0.109045	+	0.994037i	$0.465221\pi$
$740$	−3.91566	−	6.78212i	−0.143942	−	0.249316i
$741$	19.3657	−	33.5423i	0.711416	−	1.23221i
$742$	8.24252			0.302593
$743$	6.10204	−	10.5690i	0.223862	−	0.387741i	−0.732115	−	0.681181i	$-0.761467\pi$
$743$	6.10204	−	10.5690i	0.223862	−	0.387741i	0.955977	+	0.293440i	$0.0948001\pi$
$744$	−4.46325	−	7.73057i	−0.163631	−	0.283417i
$745$	−3.65115	−	6.32397i	−0.133768	−	0.231692i
$746$	0.224425	+	0.388715i	0.00821677	+	0.0142319i
$747$	−14.9098			−0.545522
$748$	−0.989336	−	1.71358i	−0.0361737	−	0.0626547i
$749$	15.6085	+	27.0347i	0.570321	+	0.987825i
$750$	6.92574	−	11.9957i	0.252892	−	0.438022i
$751$	18.9067	−	32.7474i	0.689915	−	1.19497i	−0.281949	−	0.959429i	$-0.590981\pi$
$751$	18.9067	−	32.7474i	0.689915	−	1.19497i	0.971865	−	0.235539i	$-0.0756856\pi$
$752$	−5.60227			−0.204294
$753$	−10.6278			−0.387298
$754$	0.835702	−	1.44748i	0.0304345	−	0.0527141i
$755$	20.7042	−	35.8608i	0.753504	−	1.30511i
$756$	14.3339	+	24.8271i	0.521321	+	0.902954i
$757$	4.55771	+	7.89418i	0.165653	+	0.286919i	0.936887	−	0.349633i	$-0.113694\pi$
$757$	4.55771	+	7.89418i	0.165653	+	0.286919i	−0.771234	+	0.636552i	$0.780360\pi$
$758$	−4.30659			−0.156422
$759$	−4.60844	−	7.98205i	−0.167276	−	0.289730i
$760$	14.1962	+	24.5886i	0.514952	+	0.891923i
$761$	5.28830	+	9.15961i	0.191701	+	0.332036i	0.945814	−	0.324709i	$-0.105266\pi$
$761$	5.28830	+	9.15961i	0.191701	+	0.332036i	−0.754113	+	0.656744i	$0.771933\pi$
$762$	3.96248	−	6.86322i	0.143546	−	0.248628i
$763$	−7.10193			−0.257107
$764$	12.9475	−	22.4258i	0.468425	−	0.811336i
$765$	−7.20956	−	12.4873i	−0.260662	−	0.451480i
$766$	−9.64261			−0.348402
$767$	−1.34189	−	2.32421i	−0.0484527	−	0.0839225i
$768$	−4.94484	+	8.56471i	−0.178432	+	0.309053i
$769$	−10.1134	+	17.5169i	−0.364698	+	0.631675i	−0.988728	−	0.149725i	$-0.952161\pi$
$769$	−10.1134	+	17.5169i	−0.364698	+	0.631675i	0.624030	+	0.781400i	$0.285494\pi$
$770$	−1.76823			−0.0637226
$771$	−26.5230	+	45.9391i	−0.955201	+	1.65446i
$772$	33.3417			1.19999
$773$	−1.26426			−0.0454724			−0.0227362	−	0.999741i	$-0.507238\pi$
$773$	−1.26426			−0.0454724			−0.0227362	+	0.999741i	$0.507238\pi$
$774$	−11.9331	+	12.6596i	−0.428926	+	0.455041i
$775$	−0.751192			−0.0269836
$776$	18.6144			0.668219
$777$	4.57399	−	7.92239i	0.164091	−	0.284214i
$778$	−2.15744			−0.0773478
$779$	−35.3830	+	61.2852i	−1.26773	+	2.19577i
$780$	−10.9704	+	19.0013i	−0.392804	+	0.680356i
$781$	2.07504	+	3.59408i	0.0742509	+	0.128606i
$782$	−1.19503			−0.0427343
$783$	−11.0488	−	19.1370i	−0.394851	−	0.683902i
$784$	6.37575	−	11.0431i	0.227705	−	0.394397i
$785$	−29.7833			−1.06301
$786$	−4.37049	+	7.56991i	−0.155890	+	0.270010i
$787$	−1.21274	−	2.10052i	−0.0432294	−	0.0748755i	0.843601	−	0.536970i	$-0.180431\pi$
$787$	−1.21274	−	2.10052i	−0.0432294	−	0.0748755i	−0.886831	+	0.462095i	$0.847098\pi$
$788$	11.2762	+	19.5310i	0.401699	+	0.695764i
$789$	−47.1079	−	81.5932i	−1.67708	−	2.90480i
$790$	15.4220			0.548690
$791$	−11.3431	−	19.6469i	−0.403316	−	0.698563i
$792$	−5.51450	−	9.55140i	−0.195949	−	0.339394i
$793$	2.97380	−	5.15078i	0.105603	−	0.182909i
$794$	4.44707	−	7.70255i	0.157821	−	0.273353i
$795$	83.4027			2.95799
$796$	9.74395			0.345365
$797$	−14.8520	+	25.7244i	−0.526084	+	0.911205i	0.473454	+	0.880819i	$0.343007\pi$
$797$	−14.8520	+	25.7244i	−0.526084	+	0.911205i	−0.999538	+	0.0303863i	$0.990326\pi$
$798$	−7.89311	+	13.6713i	−0.279413	+	0.483957i
$799$	0.954950	+	1.65402i	0.0337837	+	0.0585151i
$800$	−0.943648	−	1.63445i	−0.0333630	−	0.0577864i
$801$	−0.229388			−0.00810503
$802$	−2.90326	−	5.02859i	−0.102518	−	0.177566i
$803$	6.71973	+	11.6389i	0.237134	+	0.410728i
$804$	7.86187	+	13.6172i	0.277267	+	0.480240i
$805$	5.28928	−	9.16130i	0.186423	−	0.322893i
$806$	1.31993			0.0464925
$807$	17.8239	−	30.8718i	0.627430	−	1.08674i
$808$	−0.321122	−	0.556199i	−0.0112970	−	0.0195670i
$809$	−7.03160			−0.247218			−0.123609	−	0.992331i	$-0.539447\pi$
$809$	−7.03160			−0.247218			−0.123609	+	0.992331i	$0.539447\pi$
$810$	−5.37981	−	9.31810i	−0.189027	−	0.327405i
$811$	−4.55719	+	7.89328i	−0.160025	+	0.277171i	−0.934877	−	0.354971i	$-0.884491\pi$
$811$	−4.55719	+	7.89328i	−0.160025	+	0.277171i	0.774853	+	0.632142i	$0.217824\pi$
$812$	3.37402	−	5.84398i	0.118405	−	0.205083i
$813$	26.7175			0.937024
$814$	−0.431980	+	0.748211i	−0.0151409	+	0.0262248i
$815$	−13.9269			−0.487838
$816$	8.89477			0.311379
$817$	47.6284	+	11.2657i	1.66631	+	0.394138i
$818$	−10.0993			−0.353113
$819$	−17.2678			−0.603387
$820$	20.0440	−	34.7173i	0.699968	−	1.21238i
$821$	22.1901			0.774439			0.387219	−	0.921988i	$-0.373436\pi$
$821$	22.1901			0.774439			0.387219	+	0.921988i	$0.373436\pi$
$822$	−11.3295	+	19.6232i	−0.395161	+	0.684438i
$823$	−27.5718	+	47.7558i	−0.961094	+	1.66466i	−0.241332	+	0.970443i	$0.577584\pi$
$823$	−27.5718	+	47.7558i	−0.961094	+	1.66466i	−0.719762	+	0.694221i	$0.755749\pi$
$824$	−4.65229	−	8.05799i	−0.162070	−	0.280714i
$825$	−1.37756			−0.0479607
$826$	0.546929	+	0.947309i	0.0190301	+	0.0329611i
$827$	−10.1348	+	17.5540i	−0.352421	+	0.610411i	−0.986673	−	0.162715i	$-0.947975\pi$
$827$	−10.1348	+	17.5540i	−0.352421	+	0.610411i	0.634252	+	0.773126i	$0.281308\pi$
$828$	31.4056			1.09142
$829$	1.89730	−	3.28622i	0.0658959	−	0.114135i	−0.831195	−	0.555981i	$-0.812343\pi$
$829$	1.89730	−	3.28622i	0.0658959	−	0.114135i	0.897091	+	0.441846i	$0.145676\pi$
$830$	1.19939	+	2.07740i	0.0416313	+	0.0721076i
$831$	−12.5805	−	21.7901i	−0.436412	−	0.755888i
$832$	−3.36165	−	5.82255i	−0.116544	−	0.201861i
$833$	−4.34718			−0.150621
$834$	2.75094	+	4.76476i	0.0952571	+	0.164990i
$835$	20.4452	+	35.4122i	0.707536	+	1.22549i
$836$	−7.38409	+	12.7896i	−0.255384	+	0.442338i
$837$	8.72536	−	15.1128i	0.301593	−	0.522374i
$838$	−3.58589			−0.123872
$839$	18.3916			0.634949			0.317475	−	0.948267i	$-0.397165\pi$
$839$	18.3916			0.634949			0.317475	+	0.948267i	$0.397165\pi$
$840$	9.39409	−	16.2710i	0.324127	−	0.561404i
$841$	11.8993	−	20.6101i	0.410319	−	0.710694i
$842$	−0.552366	−	0.956726i	−0.0190358	−	0.0329710i
$843$	30.5661	+	52.9421i	1.05275	+	1.82342i
$844$	−15.4226			−0.530869
$845$	11.7204	+	20.3004i	0.403195	+	0.698354i
$846$	2.53354	+	4.38821i	0.0871048	+	0.150870i
$847$	7.99195	+	13.8425i	0.274607	+	0.475633i
$848$	−17.3317	+	30.0193i	−0.595172	+	1.03087i
$849$	90.4227			3.10330
$850$	−0.0893056	+	0.154682i	−0.00306316	+	0.00530554i
$851$	−2.58435	−	4.47622i	−0.0885903	−	0.153443i
$852$	−20.9888			−0.719063
$853$	−24.2419	−	41.9883i	−0.830028	−	1.43765i	−0.898015	−	0.439965i	$-0.854991\pi$
$853$	−24.2419	−	41.9883i	−0.830028	−	1.43765i	0.0679868	−	0.997686i	$-0.478342\pi$
$854$	−1.21207	+	2.09937i	−0.0414762	+	0.0718389i
$855$	−53.8099	+	93.2015i	−1.84026	+	3.18742i
$856$	31.3260			1.07070
$857$	10.8770	−	18.8396i	0.371552	−	0.643547i	−0.618252	−	0.785980i	$-0.712159\pi$
$857$	10.8770	−	18.8396i	0.371552	−	0.643547i	0.989805	+	0.142432i	$0.0454923\pi$
$858$	2.42054			0.0826358
$859$	36.3386			1.23986			0.619928	−	0.784659i	$-0.287162\pi$
$859$	36.3386			1.23986			0.619928	+	0.784659i	$0.287162\pi$
$860$	−26.9809	−	6.38190i	−0.920042	−	0.217621i
$861$	46.8280			1.59590
$862$	−5.68144			−0.193511
$863$	3.20359	−	5.54878i	0.109051	−	0.188883i	−0.806335	−	0.591459i	$-0.798552\pi$
$863$	3.20359	−	5.54878i	0.109051	−	0.188883i	0.915386	+	0.402577i	$0.131885\pi$
$864$	43.8432			1.49158
$865$	−27.6446	+	47.8819i	−0.939946	+	1.62803i
$866$	5.53458	−	9.58618i	0.188073	−	0.325752i
$867$	−1.51618	−	2.62610i	−0.0514922	−	0.0891871i
$868$	5.32902			0.180879
$869$	8.42656	+	14.5952i	0.285851	+	0.495109i
$870$	−3.44657	+	5.96963i	−0.116850	+	0.202389i
$871$	−4.88475			−0.165513
$872$	−3.56337	+	6.17193i	−0.120671	+	0.209008i
$873$	35.2784	+	61.1039i	1.19399	+	2.06805i
$874$	4.45968	+	7.72439i	0.150851	+	0.261281i
$875$	8.68658	+	15.0456i	0.293660	+	0.508634i
$876$	−67.9691			−2.29646
$877$	−0.815420	−	1.41235i	−0.0275348	−	0.0476917i	0.851930	−	0.523656i	$-0.175432\pi$
$877$	−0.815420	−	1.41235i	−0.0275348	−	0.0476917i	−0.879464	+	0.475965i	$0.842099\pi$
$878$	4.50563	+	7.80398i	0.152058	+	0.263371i
$879$	−7.75219	+	13.4272i	−0.261475	+	0.452888i
$880$	3.71808	−	6.43990i	0.125336	−	0.217089i
$881$	−27.6782			−0.932501			−0.466250	−	0.884653i	$-0.654395\pi$
$881$	−27.6782			−0.932501			−0.466250	+	0.884653i	$0.654395\pi$
$882$	−11.5333			−0.388347
$883$	−2.71761	+	4.70703i	−0.0914547	+	0.158404i	−0.908123	−	0.418703i	$-0.862485\pi$
$883$	−2.71761	+	4.70703i	−0.0914547	+	0.158404i	0.816669	+	0.577107i	$0.195818\pi$
$884$	−1.55439	+	2.69228i	−0.0522797	+	0.0905511i
$885$	5.53415	+	9.58542i	0.186028	+	0.322210i
$886$	−6.51233	−	11.2797i	−0.218786	−	0.378949i
$887$	51.0625			1.71451			0.857255	−	0.514892i	$-0.172168\pi$
$887$	51.0625			1.71451			0.857255	+	0.514892i	$0.172168\pi$
$888$	−4.58997	−	7.95006i	−0.154029	−	0.266786i
$889$	4.96992	+	8.60816i	0.166686	+	0.288709i
$890$	0.0184526	+	0.0319608i	0.000618532	+	0.00107133i
$891$	5.87904	−	10.1828i	0.196955	−	0.341137i
$892$	−4.81118			−0.161090
$893$	7.12745	−	12.3451i	0.238511	−	0.413113i
$894$	−2.03713	−	3.52841i	−0.0681317	−	0.118008i
$895$	18.6079			0.621994
$896$	8.74028	+	15.1386i	0.291992	+	0.505745i
$897$	−7.24051	+	12.5409i	−0.241754	+	0.418730i
$898$	7.89997	−	13.6832i	0.263626	−	0.456613i
$899$	−4.10767			−0.136998
$900$	2.34696	−	4.06506i	0.0782321	−	0.135502i
$901$	11.8172			0.393690
$902$	−4.42256			−0.147255
$903$	−9.30248	−	31.0221i	−0.309567	−	1.03235i
$904$	−22.7655			−0.757170
$905$	30.2939			1.00700
$906$	11.5517	−	20.0082i	0.383781	−	0.664728i
$907$	30.6902			1.01905			0.509526	−	0.860455i	$-0.329821\pi$
$907$	30.6902			1.01905			0.509526	+	0.860455i	$0.329821\pi$
$908$	12.8251	−	22.2137i	0.425616	−	0.737188i
$909$	1.21719	−	2.10824i	0.0403716	−	0.0699257i
$910$	1.38907	+	2.40594i	0.0460473	+	0.0797562i
$911$	−28.0872			−0.930570			−0.465285	−	0.885161i	$-0.654048\pi$
$911$	−28.0872			−0.930570			−0.465285	+	0.885161i	$0.654048\pi$
$912$	−33.1939	−	57.4935i	−1.09916	−	1.90380i
$913$	−1.31069	+	2.27018i	−0.0433774	+	0.0751319i
$914$	1.72907			0.0571927
$915$	−12.2644	+	21.2426i	−0.405450	+	0.702259i
$916$	12.4349	+	21.5379i	0.410861	+	0.711632i
$917$	−5.48167	−	9.49453i	−0.181021	−	0.313537i
$918$	−2.07463	−	3.59337i	−0.0684731	−	0.118599i
$919$	41.3170			1.36292			0.681461	−	0.731855i	$-0.261345\pi$
$919$	41.3170			1.36292			0.681461	+	0.731855i	$0.261345\pi$
$920$	−5.30775	−	9.19329i	−0.174991	−	0.303094i
$921$	−41.0955	−	71.1795i	−1.35414	−	2.34545i
$922$	−5.17468	+	8.96281i	−0.170419	+	0.295174i
$923$	3.26019	−	5.64681i	0.107310	−	0.185867i
$924$	9.77256			0.321494
$925$	−0.772520			−0.0254003
$926$	8.23739	−	14.2676i	0.270697	−	0.468862i
$927$	17.6342	−	30.5433i	0.579182	−	1.00317i
$928$	−5.16005	−	8.93748i	−0.169387	−	0.293387i
$929$	4.87657	+	8.44647i	0.159995	+	0.277120i	0.934867	−	0.354999i	$-0.115519\pi$
$929$	4.87657	+	8.44647i	0.159995	+	0.277120i	−0.774872	+	0.632119i	$0.782185\pi$
$930$	−5.44360			−0.178503
$931$	16.2230	+	28.0991i	0.531687	+	0.920910i
$932$	−6.71206	−	11.6256i	−0.219861	−	0.380810i
$933$	15.2135	+	26.3506i	0.498069	+	0.862680i
$934$	3.19103	−	5.52702i	0.104414	−	0.180850i
$935$	−2.53510			−0.0829066
$936$	−8.66408	+	15.0066i	−0.283194	+	0.490507i
$937$	−2.20403	−	3.81749i	−0.0720024	−	0.124712i	0.827776	−	0.561058i	$-0.189606\pi$
$937$	−2.20403	−	3.81749i	−0.0720024	−	0.124712i	−0.899779	+	0.436346i	$0.856272\pi$
$938$	1.99094			0.0650064
$939$	−15.3967	−	26.6679i	−0.502453	−	0.870275i
$940$	−4.03761	+	6.99335i	−0.131692	+	0.228098i
$941$	−15.7041	+	27.2004i	−0.511940	+	0.886706i	0.487964	+	0.872864i	$0.337740\pi$
$941$	−15.7041	+	27.2004i	−0.511940	+	0.886706i	−0.999904	+	0.0138427i	$0.995594\pi$
$942$	−16.6173			−0.541421
$943$	13.2291	−	22.9135i	0.430800	−	0.746168i
$944$	−4.60014			−0.149722
$945$	36.7297			1.19482
$946$	0.878551	+	2.92981i	0.0285641	+	0.0952564i
$947$	−39.8953			−1.29642			−0.648212	−	0.761460i	$-0.724483\pi$
$947$	−39.8953			−1.29642			−0.648212	+	0.761460i	$0.724483\pi$
$948$	−85.2334			−2.76825
$949$	10.5577	−	18.2864i	0.342716	−	0.593601i
$950$	1.33310			0.0432514
$951$	−27.6645	+	47.9162i	−0.897081	+	1.55379i
$952$	1.33104	−	2.30543i	0.0431393	−	0.0747194i
$953$	6.79590	+	11.7708i	0.220141	+	0.381295i	0.954851	−	0.297086i	$-0.0960150\pi$
$953$	6.79590	+	11.7708i	0.220141	+	0.381295i	−0.734710	+	0.678382i	$0.762682\pi$
$954$	31.3518			1.01505
$955$	−16.5885	−	28.7322i	−0.536793	−	0.929752i
$956$	12.3899	−	21.4600i	0.400720	−	0.694067i
$957$	−7.53280			−0.243501
$958$	6.20681	−	10.7505i	0.200533	−	0.347333i
$959$	−14.2099	−	24.6123i	−0.458863	−	0.794774i
$960$	13.8640	+	24.0131i	0.447458	+	0.775020i
$961$	13.8781	+	24.0375i	0.447679	+	0.775403i
$962$	1.35740			0.0437645
$963$	59.3695	+	102.831i	1.91315	+	3.31368i
$964$	−20.1315	−	34.8687i	−0.648391	−	1.12305i
$965$	21.3589	−	36.9947i	0.687568	−	1.19090i
$966$	2.95111	−	5.11147i	0.0949503	−	0.164459i
$967$	34.1431			1.09797			0.548984	−	0.835833i	$-0.315015\pi$
$967$	34.1431			1.09797			0.548984	+	0.835833i	$0.315015\pi$
$968$	16.0397			0.515536
$969$	−11.3163	+	19.6004i	−0.363532	+	0.629655i
$970$	5.67577	−	9.83072i	0.182238	−	0.315645i
$971$	−14.8341	−	25.6934i	−0.476049	−	0.824542i	0.523574	−	0.851980i	$-0.324598\pi$
$971$	−14.8341	−	25.6934i	−0.476049	−	0.824542i	−0.999623	+	0.0274383i	$0.991265\pi$
$972$	3.33104	+	5.76953i	0.106843	+	0.185058i
$973$	−6.90070			−0.221226
$974$	9.08850	+	15.7417i	0.291214	+	0.504398i
$975$	1.08218	+	1.87438i	0.0346574	+	0.0600283i
$976$	−5.09727	−	8.82873i	−0.163160	−	0.282601i
$977$	1.98694	−	3.44148i	0.0635679	−	0.110103i	−0.832490	−	0.554040i	$-0.813085\pi$
$977$	1.98694	−	3.44148i	0.0635679	−	0.110103i	0.896058	+	0.443937i	$0.146419\pi$
$978$	−7.77039			−0.248470
$979$	−0.0201649	+	0.0349267i	−0.000644474	+	0.00111626i
$980$	−9.19013	−	15.9178i	−0.293568	−	0.508475i
$981$	−27.0134			−0.862471
$982$	2.34980	+	4.06997i	0.0749850	+	0.129878i
$983$	25.6941	−	44.5035i	0.819515	−	1.41944i	−0.0865258	−	0.996250i	$-0.527577\pi$
$983$	25.6941	−	44.5035i	0.819515	−	1.41944i	0.906040	−	0.423191i	$-0.139090\pi$
$984$	23.4958	−	40.6959i	0.749018	−	1.29734i
$985$	28.8945			0.920656
$986$	−0.488341	+	0.845832i	−0.0155519	+	0.0269368i
$987$	−9.43290			−0.300252
$988$	23.2029			0.738183
$989$	−17.8075	−	4.21208i	−0.566246	−	0.133936i
$990$	−6.72576			−0.213759
$991$	56.2288			1.78617			0.893084	−	0.449891i	$-0.148537\pi$
$991$	56.2288			1.78617			0.893084	+	0.449891i	$0.148537\pi$
$992$	4.07496	−	7.05804i	0.129380	−	0.224093i
$993$	15.4084			0.488972
$994$	−1.32880	+	2.30154i	−0.0421469	+	0.0730005i
$995$	6.24204	−	10.8115i	0.197886	−	0.342748i
$996$	−6.62871	−	11.4813i	−0.210039	−	0.363797i
$997$	−26.2689			−0.831946			−0.415973	−	0.909377i	$-0.636559\pi$
$997$	−26.2689			−0.831946			−0.415973	+	0.909377i	$0.636559\pi$
$998$	−5.21421	−	9.03128i	−0.165053	−	0.285880i
$999$	8.97309	−	15.5418i	0.283896	−	0.491722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.b.307.17	✓	58
43.36	even	3	inner	731.2.e.b.681.17	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.b.307.17	✓	58	1.1	even	1	trivial
731.2.e.b.681.17	yes	58	43.36	even	3	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.428243 q^{2} +(-1.51618 + 2.62610i) q^{3} -1.81661 q^{4} +(-1.16373 + 2.01564i) q^{5} +(-0.649294 + 1.12461i) q^{6} +(-0.814374 - 1.41054i) q^{7} -1.63444 q^{8} +(-3.09761 - 5.36521i) q^{9} +O(q^{10})\)	\(q+0.428243 q^{2} +(-1.51618 + 2.62610i) q^{3} -1.81661 q^{4} +(-1.16373 + 2.01564i) q^{5} +(-0.649294 + 1.12461i) q^{6} +(-0.814374 - 1.41054i) q^{7} -1.63444 q^{8} +(-3.09761 - 5.36521i) q^{9} +(-0.498360 + 0.863184i) q^{10} -1.08921 q^{11} +(2.75431 - 4.77060i) q^{12} +(0.855654 + 1.48204i) q^{13} +(-0.348750 - 0.604052i) q^{14} +(-3.52885 - 6.11215i) q^{15} +2.93328 q^{16} +(-0.500000 - 0.866025i) q^{17} +(-1.32653 - 2.29761i) q^{18} +(-3.73184 + 6.46374i) q^{19} +(2.11404 - 3.66163i) q^{20} +4.93895 q^{21} -0.466447 q^{22} +(1.39528 - 2.41669i) q^{23} +(2.47810 - 4.29219i) q^{24} +(-0.208540 - 0.361201i) q^{25} +(0.366428 + 0.634672i) q^{26} +9.68904 q^{27} +(1.47940 + 2.56239i) q^{28} +(-1.14034 - 1.97512i) q^{29} +(-1.51121 - 2.61749i) q^{30} +(0.900539 - 1.55978i) q^{31} +4.52503 q^{32} +(1.65144 - 2.86038i) q^{33} +(-0.214121 - 0.370869i) q^{34} +3.79085 q^{35} +(5.62714 + 9.74649i) q^{36} +(0.926107 - 1.60406i) q^{37} +(-1.59813 + 2.76805i) q^{38} -5.18930 q^{39} +(1.90204 - 3.29443i) q^{40} +9.48138 q^{41} +2.11507 q^{42} +(-1.88349 - 6.28112i) q^{43} +1.97867 q^{44} +14.4191 q^{45} +(0.597517 - 1.03493i) q^{46} -1.90990 q^{47} +(-4.44738 + 7.70309i) q^{48} +(2.17359 - 3.76477i) q^{49} +(-0.0893056 - 0.154682i) q^{50} +3.03236 q^{51} +(-1.55439 - 2.69228i) q^{52} +(-5.90862 + 10.2340i) q^{53} +4.14926 q^{54} +(1.26755 - 2.19546i) q^{55} +(1.33104 + 2.30543i) q^{56} +(-11.3163 - 19.6004i) q^{57} +(-0.488341 - 0.845832i) q^{58} -1.56826 q^{59} +(6.41054 + 11.1034i) q^{60} +(-1.73774 - 3.00985i) q^{61} +(0.385649 - 0.667964i) q^{62} +(-5.04522 + 8.73857i) q^{63} -3.92875 q^{64} -3.98300 q^{65} +(0.707218 - 1.22494i) q^{66} +(-1.42720 + 2.47198i) q^{67} +(0.908304 + 1.57323i) q^{68} +(4.23098 + 7.32828i) q^{69} +1.62340 q^{70} +(-1.90509 - 3.29971i) q^{71} +(5.06284 + 8.76909i) q^{72} +(-6.16935 - 10.6856i) q^{73} +(0.396599 - 0.686929i) q^{74} +1.26474 q^{75} +(6.77929 - 11.7421i) q^{76} +(0.887026 + 1.53637i) q^{77} -2.22228 q^{78} +(-7.73638 - 13.3998i) q^{79} +(-3.41355 + 5.91244i) q^{80} +(-5.39752 + 9.34877i) q^{81} +4.06033 q^{82} +(1.20334 - 2.08424i) q^{83} -8.97214 q^{84} +2.32746 q^{85} +(-0.806593 - 2.68984i) q^{86} +6.91583 q^{87} +1.78025 q^{88} +(0.0185133 - 0.0320660i) q^{89} +6.17489 q^{90} +(1.39364 - 2.41386i) q^{91} +(-2.53467 + 4.39018i) q^{92} +(2.73076 + 4.72981i) q^{93} -0.817901 q^{94} +(-8.68572 - 15.0441i) q^{95} +(-6.86076 + 11.8832i) q^{96} -11.3889 q^{97} +(0.930825 - 1.61224i) q^{98} +(3.37395 + 5.84385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9 + 4 * q^10 - 8 * q^12 + 2 * q^13 + 5 * q^14 - 5 * q^15 + 30 * q^16 - 29 * q^17 + 16 * q^18 - 4 * q^19 - 7 * q^20 - 26 * q^21 - 10 * q^22 + 5 * q^23 - 28 * q^24 - 24 * q^25 - 8 * q^26 + 28 * q^27 - 25 * q^28 + 10 * q^29 - 5 * q^30 + 3 * q^31 + 16 * q^32 - 23 * q^33 - q^34 - 26 * q^35 - 39 * q^36 - 16 * q^37 + q^38 + 130 * q^39 + 15 * q^40 - 22 * q^41 + 112 * q^42 + 7 * q^43 + 24 * q^44 + 2 * q^45 - 61 * q^46 + 12 * q^47 + 22 * q^48 - 36 * q^49 - 17 * q^50 + 10 * q^51 - 35 * q^52 - 10 * q^53 - 10 * q^54 - 20 * q^55 - 4 * q^56 + 9 * q^57 - 17 * q^58 - 36 * q^59 + 22 * q^60 - 35 * q^61 + 3 * q^62 - 22 * q^63 + 28 * q^64 - 28 * q^65 + 14 * q^66 - 17 * q^67 - 27 * q^68 - 23 * q^69 + 10 * q^70 - 6 * q^71 + 17 * q^72 - 14 * q^73 + 21 * q^74 + 70 * q^75 - 44 * q^76 - 11 * q^77 - 184 * q^78 - 10 * q^79 + 8 * q^80 - 13 * q^81 + 184 * q^82 + 9 * q^83 - 36 * q^84 + 6 * q^85 - 76 * q^86 + 8 * q^87 + 50 * q^88 - 54 * q^89 - 34 * q^90 - 23 * q^91 - 66 * q^92 + 96 * q^94 - 3 * q^95 - 60 * q^96 + 36 * q^97 - 16 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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