LMFDB - Embedded newform 45.5.k.a.7.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(7,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.7"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([8, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.k (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.13
Character	$\chi$	$=$	45.7
Dual form			45.5.k.a.13.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.873962 - 0.234177i) q^{2} +(2.00485 - 8.77386i) q^{3} +(-13.1474 + 7.59068i) q^{4} +(-13.2061 - 21.2273i) q^{5} +(-0.302473 - 8.13751i) q^{6} +(-26.6745 + 7.14742i) q^{7} +(-19.9493 + 19.9493i) q^{8} +(-72.9611 - 35.1806i) q^{9} +(-16.5126 - 15.4593i) q^{10} +(42.6042 - 73.7926i) q^{11} +(40.2408 + 130.572i) q^{12} +(-25.7137 - 6.88997i) q^{13} +(-21.6388 + 12.4931i) q^{14} +(-212.722 + 73.3108i) q^{15} +(108.688 - 188.252i) q^{16} +(-45.4958 - 45.4958i) q^{17} +(-72.0037 - 13.6606i) q^{18} -534.305i q^{19} +(334.756 + 178.842i) q^{20} +(9.23191 + 248.368i) q^{21} +(19.9539 - 74.4688i) q^{22} +(522.453 + 139.991i) q^{23} +(135.037 + 215.028i) q^{24} +(-276.198 + 560.660i) q^{25} -24.0863 q^{26} +(-454.946 + 569.619i) q^{27} +(296.448 - 296.448i) q^{28} +(1228.42 + 709.227i) q^{29} +(-168.743 + 113.885i) q^{30} +(33.3546 + 57.7719i) q^{31} +(167.736 - 625.998i) q^{32} +(-562.030 - 521.746i) q^{33} +(-50.4157 - 29.1075i) q^{34} +(503.987 + 471.839i) q^{35} +(1226.30 - 91.2897i) q^{36} +(-1561.19 - 1561.19i) q^{37} +(-125.122 - 466.962i) q^{38} +(-112.004 + 211.795i) q^{39} +(686.924 + 160.018i) q^{40} +(-700.909 - 1214.01i) q^{41} +(66.2305 + 214.902i) q^{42} +(-280.245 - 1045.89i) q^{43} +1293.58i q^{44} +(216.742 + 2013.37i) q^{45} +489.387 q^{46} +(-2495.69 + 668.717i) q^{47} +(-1433.80 - 1331.03i) q^{48} +(-1418.88 + 819.191i) q^{49} +(-110.092 + 554.675i) q^{50} +(-490.387 + 307.962i) q^{51} +(390.369 - 104.599i) q^{52} +(1590.04 - 1590.04i) q^{53} +(-264.213 + 604.363i) q^{54} +(-2129.05 + 70.1402i) q^{55} +(389.553 - 674.726i) q^{56} +(-4687.92 - 1071.20i) q^{57} +(1239.68 + 332.170i) q^{58} +(-371.696 + 214.599i) q^{59} +(2240.27 - 2578.55i) q^{60} +(3022.82 - 5235.67i) q^{61} +(42.6796 + 42.6796i) q^{62} +(2197.66 + 416.942i) q^{63} +2891.62i q^{64} +(193.322 + 636.823i) q^{65} +(-613.374 - 324.371i) q^{66} +(-840.754 + 3137.74i) q^{67} +(943.498 + 252.810i) q^{68} +(2275.70 - 4303.27i) q^{69} +(550.960 + 294.347i) q^{70} -615.959 q^{71} +(2157.36 - 753.697i) q^{72} +(-3481.59 + 3481.59i) q^{73} +(-1730.02 - 998.826i) q^{74} +(4365.42 + 3547.36i) q^{75} +(4055.74 + 7024.74i) q^{76} +(-609.020 + 2272.89i) q^{77} +(-48.2894 + 211.329i) q^{78} +(9092.74 + 5249.69i) q^{79} +(-5431.43 + 178.935i) q^{80} +(4085.65 + 5133.63i) q^{81} +(-896.861 - 896.861i) q^{82} +(-320.620 - 1196.57i) q^{83} +(-2006.66 - 3195.33i) q^{84} +(-364.932 + 1566.58i) q^{85} +(-489.847 - 848.441i) q^{86} +(8685.46 - 9356.07i) q^{87} +(622.188 + 2322.04i) q^{88} -12146.5i q^{89} +(660.910 + 1708.85i) q^{90} +735.147 q^{91} +(-7931.55 + 2125.25i) q^{92} +(573.754 - 176.825i) q^{93} +(-2024.54 + 1168.87i) q^{94} +(-11341.9 + 7056.09i) q^{95} +(-5156.13 - 2726.72i) q^{96} +(6311.72 - 1691.22i) q^{97} +(-1048.21 + 1048.21i) q^{98} +(-5704.51 + 3885.15i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{2} + 6 q^{3} - 2 q^{5} + 120 q^{6} - 2 q^{7} - 72 q^{8} - 8 q^{10} - 160 q^{11} + 186 q^{12} - 2 q^{13} + 270 q^{15} + 2044 q^{16} - 908 q^{17} - 1656 q^{18} - 834 q^{20} - 1428 q^{21} + 62 q^{22}+ \cdots + 193724 q^{98}+O(q^{100}) $ 88 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 + 120 * q^6 - 2 * q^7 - 72 * q^8 - 8 * q^10 - 160 * q^11 + 186 * q^12 - 2 * q^13 + 270 * q^15 + 2044 * q^16 - 908 * q^17 - 1656 * q^18 - 834 * q^20 - 1428 * q^21 + 62 * q^22 + 778 * q^23 + 292 * q^25 + 4112 * q^26 + 126 * q^27 - 1096 * q^28 - 4158 * q^30 - 4 * q^31 + 3874 * q^32 + 828 * q^33 - 2528 * q^35 - 7320 * q^36 + 2092 * q^37 - 1590 * q^38 + 510 * q^40 - 4732 * q^41 - 14382 * q^42 - 2 * q^43 + 7308 * q^45 + 2984 * q^46 + 7348 * q^47 + 5850 * q^48 + 12982 * q^50 + 16716 * q^51 - 1058 * q^52 + 25792 * q^53 + 3944 * q^55 - 15312 * q^56 - 4830 * q^57 - 4866 * q^58 - 8238 * q^60 - 5572 * q^61 - 26404 * q^62 - 10476 * q^63 + 22354 * q^65 + 13260 * q^66 - 2732 * q^67 - 39694 * q^68 - 2502 * q^70 + 16712 * q^71 + 80910 * q^72 - 8 * q^73 - 6570 * q^75 - 1632 * q^76 + 14642 * q^77 + 9222 * q^78 - 125516 * q^80 - 67764 * q^81 - 15304 * q^82 - 37022 * q^83 + 14782 * q^85 - 31432 * q^86 - 78786 * q^87 - 4986 * q^88 + 44502 * q^90 - 22360 * q^91 + 47692 * q^92 + 33378 * q^93 + 51120 * q^95 + 163716 * q^96 - 15272 * q^97 + 193724 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.873962	−	0.234177i	0.218490	−	0.0585443i	−0.147913	−	0.989000i	$-0.547256\pi$
$2$	0.873962	−	0.234177i	0.218490	−	0.0585443i	0.366404	+	0.930456i	$0.380589\pi$
$3$	2.00485	−	8.77386i	0.222761	−	0.974873i
$3$	2.00485	−	8.77386i	0.222761	−	0.974873i
$4$	−13.1474	+	7.59068i	−0.821715	+	0.474417i
$5$	−13.2061	−	21.2273i	−0.528244	−	0.849093i
$5$	−13.2061	−	21.2273i	−0.528244	−	0.849093i
$6$	−0.302473	−	8.13751i	−0.00840204	−	0.226042i
$7$	−26.6745	+	7.14742i	−0.544379	+	0.145866i	−0.520520	−	0.853850i	$-0.674262\pi$
$7$	−26.6745	+	7.14742i	−0.544379	+	0.145866i	−0.0238586	+	0.999715i	$0.507595\pi$
$8$	−19.9493	+	19.9493i	−0.311708	+	0.311708i
$9$	−72.9611	−	35.1806i	−0.900755	−	0.434328i
$10$	−16.5126	−	15.4593i	−0.165126	−	0.154593i
$11$	42.6042	−	73.7926i	0.352100	−	0.609856i	−0.634517	−	0.772909i	$-0.718801\pi$
$11$	42.6042	−	73.7926i	0.352100	−	0.609856i	0.986617	+	0.163053i	$0.0521342\pi$
$12$	40.2408	+	130.572i	0.279450	+	0.906749i
$13$	−25.7137	−	6.88997i	−0.152152	−	0.0407690i	0.181939	−	0.983310i	$-0.441763\pi$
$13$	−25.7137	−	6.88997i	−0.152152	−	0.0407690i	−0.334091	+	0.942541i	$0.608429\pi$
$14$	−21.6388	+	12.4931i	−0.110402	+	0.0637405i
$15$	−212.722	+	73.3108i	−0.945430	+	0.325826i
$16$	108.688	−	188.252i	0.424561	−	0.735361i
$17$	−45.4958	−	45.4958i	−0.157425	−	0.157425i	0.624000	−	0.781425i	$-0.285507\pi$
$17$	−45.4958	−	45.4958i	−0.157425	−	0.157425i	−0.781425	+	0.624000i	$0.785507\pi$
$18$	−72.0037	−	13.6606i	−0.222234	−	0.0421625i
$19$		−	534.305i		−	1.48007i	−0.672569	−	0.740035i	$-0.734809\pi$
$19$		−	534.305i		−	1.48007i	0.672569	−	0.740035i	$-0.265191\pi$
$20$	334.756	+	178.842i	0.836890	+	0.447104i
$21$	9.23191	+	248.368i	0.0209340	+	0.563193i
$22$	19.9539	−	74.4688i	0.0412270	−	0.153861i
$23$	522.453	+	139.991i	0.987625	+	0.264633i	0.716252	−	0.697841i	$-0.245856\pi$
$23$	522.453	+	139.991i	0.987625	+	0.264633i	0.271372	+	0.962475i	$0.412523\pi$
$24$	135.037	+	215.028i	0.234440	+	0.373313i
$25$	−276.198	+	560.660i	−0.441916	+	0.897056i
$26$	−24.0863			−0.0356306
$27$	−454.946	+	569.619i	−0.624068	+	0.781370i
$28$	296.448	−	296.448i	0.378123	−	0.378123i
$29$	1228.42	+	709.227i	1.46066	+	0.843314i	0.999042	−	0.0437626i	$-0.0139345\pi$
$29$	1228.42	+	709.227i	1.46066	+	0.843314i	0.461621	+	0.887077i	$0.347268\pi$
$30$	−168.743	+	113.885i	−0.187492	+	0.126539i
$31$	33.3546	+	57.7719i	0.0347083	+	0.0601165i	0.882858	−	0.469641i	$-0.155616\pi$
$31$	33.3546	+	57.7719i	0.0347083	+	0.0601165i	−0.848149	+	0.529757i	$0.822283\pi$
$32$	167.736	−	625.998i	0.163804	−	0.611327i
$33$	−562.030	−	521.746i	−0.516098	−	0.479106i
$34$	−50.4157	−	29.1075i	−0.0436122	−	0.0251795i
$35$	503.987	+	471.839i	0.411418	+	0.385175i
$36$	1226.30	−	91.2897i	0.946216	−	0.0704396i
$37$	−1561.19	−	1561.19i	−1.14039	−	1.14039i	−0.988379	−	0.152009i	$-0.951426\pi$
$37$	−1561.19	−	1561.19i	−1.14039	−	1.14039i	−0.152009	−	0.988379i	$-0.548574\pi$
$38$	−125.122	−	466.962i	−0.0866497	−	0.323381i
$39$	−112.004	+	211.795i	−0.0736383	+	0.139247i
$40$	686.924	+	160.018i	0.429327	+	0.100011i
$41$	−700.909	−	1214.01i	−0.416959	−	0.722195i	0.578673	−	0.815560i	$-0.303571\pi$
$41$	−700.909	−	1214.01i	−0.416959	−	0.722195i	−0.995632	+	0.0933651i	$0.970238\pi$
$42$	66.2305	+	214.902i	0.0375457	+	0.121827i
$43$	−280.245	−	1045.89i	−0.151566	−	0.565652i	−0.999375	−	0.0353501i	$-0.988745\pi$
$43$	−280.245	−	1045.89i	−0.151566	−	0.565652i	0.847809	−	0.530302i	$-0.177921\pi$
$44$			1293.58i			0.668170i
$45$	216.742	+	2013.37i	0.107033	+	0.994255i
$46$	489.387			0.231279
$47$	−2495.69	+	668.717i	−1.12978	+	0.302724i	−0.774835	−	0.632163i	$-0.782167\pi$
$47$	−2495.69	+	668.717i	−1.12978	+	0.302724i	−0.354946	+	0.934887i	$0.615501\pi$
$48$	−1433.80	−	1331.03i	−0.622308	−	0.577703i
$49$	−1418.88	+	819.191i	−0.590954	+	0.341188i
$50$	−110.092	+	554.675i	−0.0440370	+	0.221870i
$51$	−490.387	+	307.962i	−0.188538	+	0.118401i
$52$	390.369	−	104.599i	0.144367	−	0.0386831i
$53$	1590.04	−	1590.04i	0.566051	−	0.566051i	−0.364969	−	0.931020i	$-0.618920\pi$
$53$	1590.04	−	1590.04i	0.566051	−	0.566051i	0.931020	+	0.364969i	$0.118920\pi$
$54$	−264.213	+	604.363i	−0.0906082	+	0.207257i
$55$	−2129.05	+	70.1402i	−0.703819	+	0.0231868i
$56$	389.553	−	674.726i	0.124220	−	0.215155i
$57$	−4687.92	−	1071.20i	−1.44288	−	0.329702i
$58$	1239.68	+	332.170i	0.368512	+	0.0987426i
$59$	−371.696	+	214.599i	−0.106779	+	0.0616487i	−0.552438	−	0.833554i	$-0.686302\pi$
$59$	−371.696	+	214.599i	−0.106779	+	0.0616487i	0.445660	+	0.895202i	$0.352969\pi$
$60$	2240.27	−	2578.55i	0.622296	−	0.716264i
$61$	3022.82	−	5235.67i	0.812367	−	1.40706i	−0.0988369	−	0.995104i	$-0.531512\pi$
$61$	3022.82	−	5235.67i	0.812367	−	1.40706i	0.911203	−	0.411957i	$-0.135154\pi$
$62$	42.6796	+	42.6796i	0.0111029	+	0.0111029i
$63$	2197.66	+	416.942i	0.553705	+	0.105050i
$64$			2891.62i			0.705963i
$65$	193.322	+	636.823i	0.0457568	+	0.150727i
$66$	−613.374	−	324.371i	−0.140811	−	0.0744654i
$67$	−840.754	+	3137.74i	−0.187292	+	0.698983i	0.806836	+	0.590775i	$0.201178\pi$
$67$	−840.754	+	3137.74i	−0.187292	+	0.698983i	−0.994128	+	0.108208i	$0.965489\pi$
$68$	943.498	+	252.810i	0.204044	+	0.0546733i
$69$	2275.70	−	4303.27i	0.477988	−	0.903858i
$70$	550.960	+	294.347i	0.112441	+	0.0600708i
$71$	−615.959			−0.122190			−0.0610950	−	0.998132i	$-0.519459\pi$
$71$	−615.959			−0.122190			−0.0610950	+	0.998132i	$0.519459\pi$
$72$	2157.36	−	753.697i	0.416157	−	0.145389i
$73$	−3481.59	+	3481.59i	−0.653330	+	0.653330i	−0.953793	−	0.300464i	$-0.902859\pi$
$73$	−3481.59	+	3481.59i	−0.653330	+	0.653330i	0.300464	+	0.953793i	$0.402859\pi$
$74$	−1730.02	−	998.826i	−0.315927	−	0.182401i
$75$	4365.42	+	3547.36i	0.776074	+	0.630642i
$76$	4055.74	+	7024.74i	0.702171	+	1.21620i
$77$	−609.020	+	2272.89i	−0.102719	+	0.383352i
$78$	−48.2894	+	211.329i	−0.00793712	+	0.0347353i
$79$	9092.74	+	5249.69i	1.45694	+	0.841162i	0.998859	−	0.0477504i	$-0.0152052\pi$
$79$	9092.74	+	5249.69i	1.45694	+	0.841162i	0.458077	+	0.888913i	$0.348539\pi$
$80$	−5431.43	+	178.935i	−0.848661	+	0.0279586i
$81$	4085.65	+	5133.63i	0.622718	+	0.782446i
$82$	−896.861	−	896.861i	−0.133382	−	0.133382i
$83$	−320.620	−	1196.57i	−0.0465408	−	0.173693i	0.938743	−	0.344617i	$-0.111991\pi$
$83$	−320.620	−	1196.57i	−0.0465408	−	0.173693i	−0.985284	+	0.170924i	$0.945325\pi$
$84$	−2006.66	−	3195.33i	−0.284390	−	0.452853i
$85$	−364.932	+	1566.58i	−0.0505096	+	0.216827i
$86$	−489.847	−	848.441i	−0.0662314	−	0.114716i
$87$	8685.46	−	9356.07i	1.14750	−	1.23610i
$88$	622.188	+	2322.04i	0.0803445	+	0.299850i
$89$		−	12146.5i		−	1.53346i	−0.641972	−	0.766728i	$-0.721883\pi$
$89$		−	12146.5i		−	1.53346i	0.641972	−	0.766728i	$-0.278117\pi$
$90$	660.910	+	1708.85i	0.0815938	+	0.210969i
$91$	735.147			0.0887752
$92$	−7931.55	+	2125.25i	−0.937092	+	0.251093i
$93$	573.754	−	176.825i	0.0663376	−	0.0204445i
$94$	−2024.54	+	1168.87i	−0.229124	+	0.132285i
$95$	−11341.9	+	7056.09i	−1.25672	+	0.781838i
$96$	−5156.13	−	2726.72i	−0.559476	−	0.295869i
$97$	6311.72	−	1691.22i	0.670818	−	0.179745i	0.0926945	−	0.995695i	$-0.470452\pi$
$97$	6311.72	−	1691.22i	0.670818	−	0.179745i	0.578123	+	0.815950i	$0.303785\pi$
$98$	−1048.21	+	1048.21i	−0.109143	+	0.109143i
$99$	−5704.51	+	3885.15i	−0.582034	+	0.396403i
$100$	−624.496	−	9467.77i	−0.0624496	−	0.946777i
$101$	5932.48	−	10275.3i	0.581558	−	1.00729i	−0.413737	−	0.910397i	$-0.635777\pi$
$101$	5932.48	−	10275.3i	0.581558	−	1.00729i	0.995295	−	0.0968918i	$-0.0308901\pi$
$102$	−356.461	+	383.984i	−0.0342620	+	0.0369073i
$103$	−15962.2	−	4277.06i	−1.50459	−	0.403154i	−0.589957	−	0.807435i	$-0.700855\pi$
$103$	−15962.2	−	4277.06i	−1.50459	−	0.403154i	−0.914635	+	0.404280i	$0.867522\pi$
$104$	650.422	−	375.521i	0.0601352	−	0.0347191i
$105$	5150.27	−	3475.94i	0.467145	−	0.315278i
$106$	1017.28	−	1761.98i	0.0905376	−	0.156816i
$107$	13258.4	+	13258.4i	1.15804	+	1.15804i	0.984897	+	0.173140i	$0.0553912\pi$
$107$	13258.4	+	13258.4i	1.15804	+	1.15804i	0.173140	+	0.984897i	$0.444609\pi$
$108$	1657.58	−	10942.4i	0.142111	−	0.938132i
$109$			3375.11i			0.284076i	0.989861	+	0.142038i	$0.0453656\pi$
$109$			3375.11i			0.284076i	−0.989861	+	0.142038i	$0.954634\pi$
$110$	−1844.29	+	559.876i	−0.152420	+	0.0462707i
$111$	−16827.6	+	10567.7i	−1.36577	+	0.857699i
$112$	−1553.67	+	5798.38i	−0.123858	+	0.462243i
$113$	16189.5	+	4337.97i	1.26788	+	0.339727i	0.829218	−	0.558926i	$-0.188786\pi$
$113$	16189.5	+	4337.97i	1.26788	+	0.339727i	0.438661	+	0.898653i	$0.355453\pi$
$114$	−4347.91	+	161.613i	−0.334558	+	0.0124356i
$115$	−3927.94	−	12939.0i	−0.297009	−	0.978376i
$116$	−21534.1			−1.60033
$117$	1633.71	+	1407.32i	0.119345	+	0.102807i
$118$	−274.594	+	274.594i	−0.0197209	+	0.0197209i
$119$	1538.76	+	888.403i	0.108662	+	0.0627359i
$120$	2781.16	−	5706.16i	0.193136	−	0.396261i
$121$	3690.27	+	6391.74i	0.252051	+	0.436564i
$122$	1415.75	−	5283.65i	0.0951189	−	0.354989i
$123$	−12056.8	+	3715.76i	−0.796931	+	0.245605i
$124$	−877.056	−	506.369i	−0.0570406	−	0.0329324i
$125$	15548.8	−	1541.20i	0.995124	−	0.0986366i
$126$	2018.31	−	150.249i	0.127129	−	0.00946394i
$127$	−15633.6	−	15633.6i	−0.969288	−	0.969288i	0.0302544	−	0.999542i	$-0.490368\pi$
$127$	−15633.6	−	15633.6i	−0.969288	−	0.969288i	−0.999542	+	0.0302544i	$0.990368\pi$
$128$	3360.92	+	12543.1i	0.205135	+	0.765573i
$129$	−9738.34	+	361.977i	−0.585202	+	0.0217521i
$130$	318.086	+	511.287i	0.0188216	+	0.0302537i
$131$	−5108.96	−	8848.99i	−0.297708	−	0.515645i	0.677903	−	0.735151i	$-0.262889\pi$
$131$	−5108.96	−	8848.99i	−0.297708	−	0.515645i	−0.975611	+	0.219506i	$0.929555\pi$
$132$	11349.7	+	2593.43i	0.651381	+	0.148843i
$133$	3818.90	+	14252.3i	0.215891	+	0.805718i
$134$			2939.15i			0.163686i
$135$	18099.5	+	2134.84i	0.993116	+	0.117138i
$136$	1815.22			0.0981414
$137$	12550.7	−	3362.94i	0.668690	−	0.179175i	0.0915256	−	0.995803i	$-0.470826\pi$
$137$	12550.7	−	3362.94i	0.668690	−	0.179175i	0.577165	+	0.816628i	$0.304159\pi$
$138$	981.149	−	4293.81i	0.0515201	−	0.225468i
$139$	3734.49	−	2156.11i	0.193286	−	0.111594i	−0.400234	−	0.916413i	$-0.631071\pi$
$139$	3734.49	−	2156.11i	0.193286	−	0.111594i	0.593520	+	0.804819i	$0.297738\pi$
$140$	−10207.7	−	2377.87i	−0.520802	−	0.121320i
$141$	863.743	+	23237.5i	0.0434457	+	1.16883i
$142$	−538.325	+	144.244i	−0.0266973	+	0.00715353i
$143$	−1603.94	+	1603.94i	−0.0784361	+	0.0784361i
$144$	−14552.8	+	9911.41i	−0.701813	+	0.477981i
$145$	−1167.62	−	35442.1i	−0.0555347	−	1.68571i
$146$	−2227.47	+	3858.09i	−0.104498	+	0.180995i
$147$	4342.82	+	14091.4i	0.200973	+	0.652109i
$148$	32376.2	+	8675.17i	1.47809	+	0.396054i
$149$	28752.7	−	16600.4i	1.29511	−	0.747731i	0.315554	−	0.948908i	$-0.397810\pi$
$149$	28752.7	−	16600.4i	1.29511	−	0.747731i	0.979555	+	0.201176i	$0.0644764\pi$
$150$	4645.92	+	2077.98i	0.206485	+	0.0923545i
$151$	4853.99	−	8407.35i	0.212885	−	0.368727i	−0.739731	−	0.672902i	$-0.765047\pi$
$151$	4853.99	−	8407.35i	0.212885	−	0.368727i	0.952616	+	0.304175i	$0.0983807\pi$
$152$	10659.0	+	10659.0i	0.461350	+	0.461350i
$153$	1718.86	+	4920.00i	0.0734272	+	0.210176i
$154$			2129.04i			0.0897723i
$155$	785.858	−	1470.97i	0.0327100	−	0.0612267i
$156$	−135.105	−	3634.75i	−0.00555163	−	0.149357i
$157$	3542.87	−	13222.2i	0.143733	−	0.536419i	−0.856076	−	0.516851i	$-0.827104\pi$
$157$	3542.87	−	13222.2i	0.143733	−	0.536419i	0.999809	−	0.0195681i	$-0.00622911\pi$
$158$	9176.06	+	2458.72i	0.367572	+	0.0984906i
$159$	−10763.0	−	17138.6i	−0.425734	−	0.677922i
$160$	−15503.4	+	4706.42i	−0.605602	+	0.183844i
$161$	−14936.8			−0.576242
$162$	4772.88	+	3529.83i	0.181866	+	0.134500i
$163$	−24747.7	+	24747.7i	−0.931448	+	0.931448i	−0.997797	−	0.0663481i	$-0.978865\pi$
$163$	−24747.7	+	24747.7i	−0.931448	+	0.931448i	0.0663481	+	0.997797i	$0.478865\pi$
$164$	18430.3	+	10640.7i	0.685243	+	0.395625i
$165$	−3653.04	+	18820.6i	−0.134180	+	0.691299i
$166$	−560.418	−	970.673i	−0.0203374	−	0.0352255i
$167$	1154.98	−	4310.43i	0.0414134	−	0.154557i	−0.942123	−	0.335268i	$-0.891173\pi$
$167$	1154.98	−	4310.43i	0.0414134	−	0.154557i	0.983536	+	0.180711i	$0.0578399\pi$
$168$	−5138.95	−	4770.61i	−0.182077	−	0.169027i
$169$	−24120.8	−	13926.2i	−0.844537	−	0.487594i
$170$	47.9204	+	1454.59i	0.00165815	+	0.0503317i
$171$	−18797.2	+	38983.5i	−0.642836	+	1.33318i
$172$	11623.5	+	11623.5i	0.392899	+	0.392899i
$173$	2694.90	+	10057.5i	0.0900431	+	0.336045i	0.996221	−	0.0868505i	$-0.0276803\pi$
$173$	2694.90	+	10057.5i	0.0900431	+	0.336045i	−0.906178	+	0.422896i	$0.861014\pi$
$174$	5399.78	−	10210.8i	0.178352	−	0.337257i
$175$	3360.18	−	16929.5i	0.109720	−	0.552799i
$176$	−9261.08	−	16040.7i	−0.298976	−	0.517842i
$177$	1137.66	+	3691.45i	0.0363134	+	0.117829i
$178$	−2844.44	−	10615.6i	−0.0897752	−	0.335046i
$179$			8013.31i			0.250096i	0.992151	+	0.125048i	$0.0399084\pi$
$179$			8013.31i			0.250096i	−0.992151	+	0.125048i	$0.960092\pi$
$180$	−18132.4	−	24825.4i	−0.559643	−	0.766216i
$181$	51847.9			1.58261			0.791305	−	0.611422i	$-0.209402\pi$
$181$	51847.9			1.58261			0.791305	+	0.611422i	$0.209402\pi$
$182$	642.490	−	172.155i	0.0193965	−	0.00519728i
$183$	−39876.7	−	37018.5i	−1.19074	−	1.10539i
$184$	−13215.3	+	7629.87i	−0.390339	+	0.225363i
$185$	−12522.7	+	53757.2i	−0.365892	+	1.57070i
$186$	460.031	−	288.898i	0.0132972	−	0.00835062i
$187$	−5295.57	+	1418.94i	−0.151436	+	0.0405772i
$188$	27735.9	−	27735.9i	0.784740	−	0.784740i
$189$	8064.17	−	18446.0i	0.225754	−	0.516391i
$190$	−8259.98	+	8822.76i	−0.228808	+	0.244398i
$191$	12589.9	−	21806.4i	0.345109	−	0.597747i	−0.640264	−	0.768155i	$-0.721175\pi$
$191$	12589.9	−	21806.4i	0.345109	−	0.597747i	0.985374	+	0.170408i	$0.0545085\pi$
$192$	25370.7	+	5797.28i	0.688224	+	0.157261i
$193$	−39575.2	−	10604.1i	−1.06245	−	0.284682i	−0.315062	−	0.949071i	$-0.602025\pi$
$193$	−39575.2	−	10604.1i	−1.06245	−	0.284682i	−0.747387	+	0.664389i	$0.768692\pi$
$194$	5120.16	−	2956.12i	0.136044	−	0.0785451i
$195$	5974.97	−	419.446i	0.157133	−	0.0110308i
$196$	12436.4	−	21540.5i	0.323731	−	0.560718i
$197$	−24349.1	−	24349.1i	−0.627409	−	0.627409i	0.320006	−	0.947415i	$-0.396315\pi$
$197$	−24349.1	−	24349.1i	−0.627409	−	0.627409i	−0.947415	+	0.320006i	$0.896315\pi$
$198$	−4075.71	+	4731.34i	−0.103962	+	0.120685i
$199$			21437.6i			0.541339i	0.962672	+	0.270669i	$0.0872450\pi$
$199$			21437.6i			0.541339i	−0.962672	+	0.270669i	$0.912755\pi$
$200$	−5674.84	−	16694.8i	−0.141871	−	0.417369i
$201$	25844.5	+	13667.4i	0.639698	+	0.338292i
$202$	2778.50	−	10369.5i	0.0680939	−	0.254130i
$203$	−37836.6	−	10138.3i	−0.918164	−	0.246021i
$204$	4109.69	−	7771.27i	0.0987526	−	0.186738i
$205$	−16513.9	+	30910.7i	−0.392954	+	0.735532i
$206$	−14952.0			−0.352341
$207$	−33193.8	−	28594.1i	−0.774670	−	0.667323i
$208$	−4091.81	+	4091.81i	−0.0945778	+	0.0945778i
$209$	−39427.7	−	22763.6i	−0.902629	−	0.521133i
$210$	3687.15	−	4243.92i	0.0836089	−	0.0962340i
$211$	−3928.42	−	6804.23i	−0.0882375	−	0.152832i	0.818529	−	0.574466i	$-0.194790\pi$
$211$	−3928.42	−	6804.23i	−0.0882375	−	0.152832i	−0.906766	+	0.421634i	$0.861457\pi$
$212$	−8835.46	+	32974.4i	−0.196588	+	0.733677i
$213$	−1234.91	+	5404.34i	−0.0272192	+	0.119120i
$214$	14692.1	+	8482.49i	0.320816	+	0.185223i
$215$	−18500.5	+	19761.0i	−0.400227	+	0.427496i
$216$	−2287.64	−	20439.4i	−0.0490322	−	0.438087i
$217$	−1302.64	−	1302.64i	−0.0276634	−	0.0276634i
$218$	790.375	+	2949.72i	0.0166311	+	0.0620680i
$219$	23566.9	+	37527.1i	0.491377	+	0.782450i
$220$	27459.2	−	17083.1i	0.567338	−	0.352957i
$221$	856.402	+	1483.33i	0.0175345	+	0.0303706i
$222$	−12232.0	+	13176.4i	−0.248194	+	0.267357i
$223$	16245.9	+	60630.7i	0.326689	+	1.21922i	0.912603	+	0.408848i	$0.134069\pi$
$223$	16245.9	+	60630.7i	0.326689	+	1.21922i	−0.585913	+	0.810374i	$0.699264\pi$
$224$			17897.1i			0.356686i
$225$	39876.1	−	31189.6i	0.787675	−	0.616091i
$226$	15164.9			0.296908
$227$	−88879.4	+	23815.2i	−1.72484	+	0.462170i	−0.978985	−	0.203935i	$-0.934627\pi$
$227$	−88879.4	+	23815.2i	−1.72484	+	0.462170i	−0.745858	+	0.666105i	$0.767960\pi$
$228$	69765.2	−	21500.9i	1.34205	−	0.413606i
$229$	11683.8	−	6745.63i	0.222798	−	0.128633i	−0.384447	−	0.923147i	$-0.625608\pi$
$229$	11683.8	−	6745.63i	0.222798	−	0.128633i	0.607245	+	0.794514i	$0.292275\pi$
$230$	−6462.89	−	10388.4i	−0.122172	−	0.196378i
$231$	18721.0	+	9900.27i	0.350838	+	0.185534i
$232$	−38654.7	+	10357.5i	−0.718169	+	0.192433i
$233$	38693.3	−	38693.3i	0.712729	−	0.712729i	−0.254377	−	0.967105i	$-0.581870\pi$
$233$	38693.3	−	38693.3i	0.712729	−	0.712729i	0.967105	+	0.254377i	$0.0818703\pi$
$234$	1757.36	+	847.369i	0.0320944	+	0.0154754i
$235$	47153.4	+	44145.6i	0.853841	+	0.799377i
$236$	3257.90	−	5642.85i	0.0584944	−	0.101315i
$237$	64289.7	−	69253.5i	1.14458	−	1.23295i
$238$	1552.86	+	416.088i	0.0274144	+	0.00734566i
$239$	13019.6	−	7516.88i	0.227930	−	0.131596i	−0.381687	−	0.924292i	$-0.624657\pi$
$239$	13019.6	−	7516.88i	0.227930	−	0.131596i	0.609617	+	0.792696i	$0.291323\pi$
$240$	−9319.27	+	48013.3i	−0.161793	+	0.833565i
$241$	−13458.2	+	23310.3i	−0.231714	+	0.401341i	−0.958313	−	0.285721i	$-0.907767\pi$
$241$	−13458.2	+	23310.3i	−0.231714	+	0.401341i	0.726598	+	0.687062i	$0.241100\pi$
$242$	4721.96	+	4721.96i	0.0806290	+	0.0806290i
$243$	53232.9	−	25554.7i	0.901503	−	0.432772i
$244$			91780.9i			1.54160i
$245$	36127.1	+	19300.7i	0.601868	+	0.321545i
$246$	−9667.00	+	6070.85i	−0.159743	+	0.100318i
$247$	−3681.34	+	13739.0i	−0.0603410	+	0.225196i
$248$	−1817.91	−	487.109i	−0.0295577	−	0.00791995i
$249$	−11141.3	+	414.126i	−0.179696	+	0.00667934i
$250$	13228.1	−	4988.12i	0.211650	−	0.0798100i
$251$	21023.9			0.333707			0.166854	−	0.985982i	$-0.446639\pi$
$251$	21023.9			0.333707			0.166854	+	0.985982i	$0.446639\pi$
$252$	−32058.4	+	11200.0i	−0.504825	+	0.176366i
$253$	32589.0	−	32589.0i	0.509131	−	0.509131i
$254$	−17324.2	−	10002.2i	−0.268526	−	0.155034i
$255$	13013.3	+	6342.62i	0.200127	+	0.0975412i
$256$	−17258.3	−	29892.3i	−0.263341	−	0.456121i
$257$	11276.5	−	42084.5i	0.170729	−	0.637171i	−0.826510	−	0.562922i	$-0.809677\pi$
$257$	11276.5	−	42084.5i	0.170729	−	0.637171i	0.997240	−	0.0742494i	$-0.0236561\pi$
$258$	−8426.17	+	2596.85i	−0.126587	+	0.0390129i
$259$	52802.6	+	30485.6i	0.787147	+	0.454459i
$260$	−7375.61	−	6905.14i	−0.109107	−	0.102147i
$261$	−64675.7	−	94962.5i	−0.949424	−	1.39403i
$262$	−6537.27	−	6537.27i	−0.0952344	−	0.0952344i
$263$	13231.8	+	49381.7i	0.191297	+	0.713928i	0.993195	+	0.116467i	$0.0371570\pi$
$263$	13231.8	+	49381.7i	0.191297	+	0.713928i	−0.801898	+	0.597461i	$0.796176\pi$
$264$	21620.6	−	803.644i	0.310213	−	0.0115307i
$265$	−54750.4	−	12754.0i	−0.779643	−	0.181617i
$266$	6675.15	+	11561.7i	0.0943404	+	0.163402i
$267$	−106572.	−	24352.0i	−1.49493	−	0.341595i
$268$	−12763.8	−	47635.1i	−0.177709	−	0.663219i
$269$			6424.16i			0.0887793i	0.999014	+	0.0443897i	$0.0141343\pi$
$269$			6424.16i			0.0887793i	−0.999014	+	0.0443897i	$0.985866\pi$
$270$	16318.2	−	2372.73i	0.223844	−	0.0325478i
$271$	55829.3			0.760193			0.380096	−	0.924947i	$-0.375891\pi$
$271$	55829.3			0.760193			0.380096	+	0.924947i	$0.375891\pi$
$272$	−13509.5	+	3619.87i	−0.182601	+	0.0489277i
$273$	1473.86	−	6450.08i	0.0197757	−	0.0865445i
$274$	10181.3	−	5878.16i	0.135613	−	0.0782961i
$275$	29605.4	+	44267.8i	0.391476	+	0.585359i
$276$	2745.07	+	73851.1i	0.0360358	+	0.969480i
$277$	−55529.5	+	14879.1i	−0.723710	+	0.193917i	−0.601826	−	0.798627i	$-0.705560\pi$
$277$	−55529.5	+	14879.1i	−0.723710	+	0.193917i	−0.121884	+	0.992544i	$0.538893\pi$
$278$	2758.89	−	2758.89i	0.0356980	−	0.0356980i
$279$	−401.141	−	5388.54i	−0.00515334	−	0.0692250i
$280$	−19467.1	+	641.330i	−0.248305	+	0.00818024i
$281$	4905.93	−	8497.31i	0.0621310	−	0.107614i	−0.833287	−	0.552841i	$-0.813544\pi$
$281$	4905.93	−	8497.31i	0.0621310	−	0.107614i	0.895418	+	0.445227i	$0.146877\pi$
$282$	6196.57	+	20106.4i	0.0779207	+	0.252834i
$283$	−31217.8	−	8364.80i	−0.389789	−	0.104444i	0.0586012	−	0.998281i	$-0.481336\pi$
$283$	−31217.8	−	8364.80i	−0.389789	−	0.104444i	−0.448391	+	0.893838i	$0.648003\pi$
$284$	8098.29	−	4675.55i	0.100405	−	0.0579690i
$285$	39170.3	+	113658.i	0.482245	+	1.39930i
$286$	−1026.18	+	1777.39i	−0.0125455	+	0.0217295i
$287$	27373.5	+	27373.5i	0.332327	+	0.332327i
$288$	−34261.2	+	39772.5i	−0.413064	+	0.479510i
$289$		−	79381.3i		−	0.950435i
$290$	−9320.20	−	30701.6i	−0.110823	−	0.365061i
$291$	−2184.45	−	58768.8i	−0.0257962	−	0.694002i
$292$	19346.4	−	72201.7i	0.226900	−	0.846801i
$293$	−100479.	−	26923.2i	−1.17041	−	0.313612i	−0.379296	−	0.925275i	$-0.623834\pi$
$293$	−100479.	−	26923.2i	−1.17041	−	0.313612i	−0.791118	+	0.611664i	$0.790501\pi$
$294$	7095.35	+	11298.4i	0.0820879	+	0.130714i
$295$	9464.02	+	5056.10i	0.108751	+	0.0580994i
$296$	62289.5			0.710937
$297$	22651.0	+	57839.7i	0.256788	+	0.655712i
$298$	21241.3	−	21241.3i	0.239193	−	0.239193i
$299$	−12469.7	−	7199.37i	−0.139480	−	0.0805290i
$300$	−84320.9	−	13502.3i	−0.936899	−	0.150025i
$301$	14950.8	+	25895.6i	0.165018	+	0.285820i
$302$	2273.39	−	8484.40i	0.0249264	−	0.0930266i
$303$	−78260.7	−	72651.3i	−0.852429	−	0.791330i
$304$	−100584.	−	58072.3i	−1.08838	−	0.628379i
$305$	−151059.	+	4976.53i	−1.62385	+	0.0534967i
$306$	2654.37	+	3897.37i	0.0283477	+	0.0416226i
$307$	49500.0	+	49500.0i	0.525205	+	0.525205i	0.919139	−	0.393934i	$-0.128886\pi$
$307$	49500.0	+	49500.0i	0.525205	+	0.525205i	−0.393934	+	0.919139i	$0.628886\pi$
$308$	−9245.74	−	34505.6i	−0.0974632	−	0.363737i
$309$	−69528.2	+	131475.i	−0.728189	+	1.37698i
$310$	342.342	−	1469.60i	0.00356235	−	0.0152924i
$311$	−9057.78	−	15688.5i	−0.0936485	−	0.162204i	0.815395	−	0.578905i	$-0.196520\pi$
$311$	−9057.78	−	15688.5i	−0.0936485	−	0.162204i	−0.909044	+	0.416701i	$0.863186\pi$
$312$	−1990.77	−	6459.57i	−0.0204509	−	0.0663582i
$313$	−12132.5	−	45279.2i	−0.123840	−	0.462179i	0.875955	−	0.482392i	$-0.160232\pi$
$313$	−12132.5	−	45279.2i	−0.123840	−	0.462179i	−0.999796	+	0.0202135i	$0.993565\pi$
$314$		−	12385.3i		−	0.125617i
$315$	−20171.9	−	52156.5i	−0.203294	−	0.525639i
$316$	−159395.			−1.59625
$317$	163844.	−	43901.8i	1.63047	−	0.436882i	0.676413	−	0.736522i	$-0.263533\pi$
$317$	163844.	−	43901.8i	1.63047	−	0.436882i	0.954052	+	0.299640i	$0.0968666\pi$
$318$	−13419.9	−	12458.0i	−0.132707	−	0.123195i
$319$	104671.	−	60432.1i	1.02860	−	0.593863i
$320$	61381.4	−	38187.1i	0.599428	−	0.372921i
$321$	142908.	−	89745.9i	1.38691	−	0.870973i
$322$	−13054.2	+	3497.86i	−0.125903	+	0.0337357i
$323$	−24308.7	+	24308.7i	−0.233000	+	0.233000i
$324$	−92683.6	−	36481.2i	−0.882903	−	0.347520i
$325$	10965.0	−	12513.7i	0.103811	−	0.118473i
$326$	−15833.2	+	27423.8i	−0.148982	+	0.258044i
$327$	29612.7	+	6766.60i	0.276938	+	0.0632813i
$328$	38201.4	+	10236.0i	0.355084	+	0.0951445i
$329$	61791.7	−	35675.5i	0.570872	−	0.329593i
$330$	1214.75	+	17304.0i	0.0111547	+	0.158898i
$331$	−49343.4	+	85465.3i	−0.450374	+	0.780071i	−0.998409	−	0.0563846i	$-0.982043\pi$
$331$	−49343.4	+	85465.3i	−0.450374	+	0.780071i	0.548035	+	0.836455i	$0.315376\pi$
$332$	13298.1	+	13298.1i	0.120646	+	0.120646i
$333$	58982.7	+	168830.i	0.531907	+	1.52251i
$334$		−	4037.62i		−	0.0361937i
$335$	77708.8	−	23590.3i	0.692437	−	0.210205i
$336$	47759.3	+	25256.6i	0.423038	+	0.223716i
$337$	−21007.5	+	78401.2i	−0.184976	+	0.690340i	0.809660	+	0.586900i	$0.199652\pi$
$337$	−21007.5	+	78401.2i	−0.184976	+	0.690340i	−0.994636	+	0.103440i	$0.967015\pi$
$338$	−24341.9	−	6522.38i	−0.213069	−	0.0570917i
$339$	70518.4	−	133348.i	0.613625	−	1.16034i
$340$	−7093.46	−	23366.6i	−0.0613621	−	0.202133i
$341$	5684.18			0.0488832
$342$	−7298.95	+	38472.0i	−0.0624034	+	0.328921i
$343$	78877.5	−	78877.5i	0.670448	−	0.670448i
$344$	26455.5	+	15274.1i	0.223563	+	0.129074i
$345$	−121400.	+	8522.35i	−1.01995	+	0.0716013i
$346$	4710.48	+	8158.79i	0.0393471	+	0.0681512i
$347$	4907.89	−	18316.5i	0.0407601	−	0.152119i	−0.942547	−	0.334075i	$-0.891576\pi$
$347$	4907.89	−	18316.5i	0.0407601	−	0.152119i	0.983307	+	0.181956i	$0.0582428\pi$
$348$	−43172.6	+	188937.i	−0.356492	+	1.56012i
$349$	−49516.8	−	28588.5i	−0.406539	−	0.234715i	0.282763	−	0.959190i	$-0.408749\pi$
$349$	−49516.8	−	28588.5i	−0.406539	−	0.234715i	−0.689301	+	0.724475i	$0.742082\pi$
$350$	−1027.83	−	15582.6i	−0.00839045	−	0.127205i
$351$	15623.0	−	11512.4i	0.126809	−	0.0934444i
$352$	−39047.8	−	39047.8i	−0.315145	−	0.315145i
$353$	60582.0	+	226095.i	0.486177	+	1.81444i	0.574701	+	0.818363i	$0.305118\pi$
$353$	60582.0	+	226095.i	0.486177	+	1.81444i	−0.0885245	+	0.996074i	$0.528215\pi$
$354$	1858.73	+	2959.77i	0.0148323	+	0.0236185i
$355$	8134.42	+	13075.2i	0.0645461	+	0.103751i
$356$	92200.2	+	159695.i	0.727498	+	1.26006i
$357$	10879.7	−	11719.7i	0.0853652	−	0.0919563i
$358$	1876.54	+	7003.33i	0.0146417	+	0.0546435i
$359$			172399.i			1.33766i	0.743414	+	0.668831i	$0.233205\pi$
$359$			172399.i			1.33766i	−0.743414	+	0.668831i	$0.766795\pi$
$360$	−44489.2	−	35841.5i	−0.343281	−	0.276555i
$361$	−155161.			−1.19061
$362$	45313.1	−	12141.6i	0.345785	−	0.0926528i
$363$	63478.7	−	19563.4i	0.481742	−	0.148468i
$364$	−9665.30	+	5580.26i	−0.0729479	+	0.0421165i
$365$	119883.	+	27926.6i	0.899855	+	0.209620i
$366$	−43519.6	−	23014.5i	−0.324880	−	0.171807i
$367$	161374.	−	43240.0i	1.19812	−	0.321036i	0.396031	−	0.918237i	$-0.370387\pi$
$367$	161374.	−	43240.0i	1.19812	−	0.321036i	0.802092	+	0.597201i	$0.203720\pi$
$368$	83137.8	−	83137.8i	0.613907	−	0.613907i
$369$	8429.52	+	113234.i	0.0619084	+	0.831618i
$370$	1644.39	+	49914.2i	0.0120116	+	0.364603i
$371$	−31048.9	+	53778.2i	−0.225579	+	0.390714i
$372$	−6201.17	+	6679.97i	−0.0448113	+	0.0482713i
$373$	67470.2	+	18078.6i	0.484947	+	0.129941i	0.493005	−	0.870026i	$-0.335898\pi$
$373$	67470.2	+	18078.6i	0.484947	+	0.129941i	−0.00805807	+	0.999968i	$0.502565\pi$
$374$	−4295.84	+	2480.20i	−0.0307118	+	0.0177314i
$375$	17650.8	−	139513.i	0.125517	−	0.992091i
$376$	36446.8	−	63127.8i	0.257801	−	0.446524i
$377$	−26700.6	−	26700.6i	−0.187862	−	0.187862i
$378$	2728.14	−	18009.5i	0.0190934	−	0.126043i
$379$		−	228057.i		−	1.58769i	−0.608121	−	0.793844i	$-0.708077\pi$
$379$		−	228057.i		−	1.58769i	0.608121	−	0.793844i	$-0.291923\pi$
$380$	95555.9	−	178862.i	0.661745	−	1.23866i
$381$	−168511.	+	105824.i	−1.16085	+	0.729013i
$382$	5896.55	−	22006.2i	0.0404084	−	0.150806i
$383$	−86335.7	−	23133.6i	−0.588563	−	0.157705i	−0.0477664	−	0.998859i	$-0.515210\pi$
$383$	−86335.7	−	23133.6i	−0.588563	−	0.157705i	−0.540796	+	0.841154i	$0.681877\pi$
$384$	116790.	−	4341.11i	0.792032	−	0.0294400i
$385$	56290.2	−	17088.2i	0.379762	−	0.115286i
$386$	−37070.4			−0.248801
$387$	−16348.0	+	86168.5i	−0.109155	+	0.575343i
$388$	−70145.5	+	70145.5i	−0.465947	+	0.465947i
$389$	−208777.	−	120538.i	−1.37970	−	0.796569i	−0.387575	−	0.921838i	$-0.626687\pi$
$389$	−208777.	−	120538.i	−1.37970	−	0.796569i	−0.992123	+	0.125270i	$0.960020\pi$
$390$	5123.67	−	1765.78i	0.0336862	−	0.0116094i
$391$	−17400.5	−	30138.5i	−0.113817	−	0.197137i
$392$	11963.4	−	44648.1i	0.0778544	−	0.290556i
$393$	−87882.5	+	27084.4i	−0.569006	+	0.175361i
$394$	−26982.2	−	15578.2i	−0.173814	−	0.100352i
$395$	−8642.69	−	262342.i	−0.0553930	−	1.68141i
$396$	45508.8	−	94380.9i	0.290205	−	0.601857i
$397$	68920.5	+	68920.5i	0.437288	+	0.437288i	0.891098	−	0.453810i	$-0.149936\pi$
$397$	68920.5	+	68920.5i	0.437288	+	0.437288i	−0.453810	+	0.891098i	$0.649936\pi$
$398$	5020.19	+	18735.6i	0.0316923	+	0.118277i
$399$	132704.	−	4932.66i	0.833565	−	0.0309838i
$400$	75526.3	+	112932.i	0.472040	+	0.705823i
$401$	32454.4	+	56212.7i	0.201830	+	0.349580i	0.949118	−	0.314921i	$-0.101978\pi$
$401$	32454.4	+	56212.7i	0.201830	+	0.349580i	−0.747288	+	0.664500i	$0.768645\pi$
$402$	25787.6	+	5892.56i	0.159573	+	0.0364629i
$403$	−459.625	−	1715.34i	−0.00283004	−	0.0105619i
$404$			180126.i			1.10361i
$405$	55017.7	−	154523.i	0.335423	−	0.942068i
$406$	−35441.9			−0.215013
$407$	−181718.	+	48691.1i	−1.09700	+	0.293941i
$408$	3639.26	−	15926.5i	0.0218621	−	0.0956754i
$409$	−170811.	+	98617.6i	−1.02110	+	0.589532i	−0.914422	−	0.404761i	$-0.867355\pi$
$409$	−170811.	+	98617.6i	−1.02110	+	0.589532i	−0.106678	+	0.994294i	$0.534021\pi$
$410$	−7193.91	+	30882.0i	−0.0427954	+	0.183712i
$411$	−4343.71	−	116860.i	−0.0257145	−	0.691802i
$412$	242328.	−	64931.6i	1.42761	−	0.382527i
$413$	8381.00	−	8381.00i	0.0491355	−	0.0491355i
$414$	−35706.2	−	17216.9i	−0.208326	−	0.100451i
$415$	−21165.8	+	22607.9i	−0.122896	+	0.131270i
$416$	−8626.22	+	14941.0i	−0.0498464	+	0.0863365i
$417$	−11430.3	−	37088.5i	−0.0657332	−	0.213289i
$418$	−39789.1	−	10661.4i	−0.227725	−	0.0610188i
$419$	−275405.	+	159005.i	−1.56872	+	0.905699i	−0.572397	+	0.819977i	$0.693986\pi$
$419$	−275405.	+	159005.i	−1.56872	+	0.905699i	−0.996319	+	0.0857217i	$0.972680\pi$
$420$	−41328.1	+	84793.8i	−0.234286	+	0.480690i
$421$	−79958.5	+	138492.i	−0.451129	+	0.781378i	−0.998456	−	0.0555407i	$-0.982312\pi$
$421$	−79958.5	+	138492.i	−0.451129	+	0.781378i	0.547328	+	0.836918i	$0.315645\pi$
$422$	−5026.69	−	5026.69i	−0.0282265	−	0.0282265i
$423$	205614.	+	39009.4i	1.14914	+	0.218016i
$424$			63440.4i			0.352886i
$425$	38073.6	−	12941.9i	0.210788	−	0.0716504i
$426$	186.311	+	5012.37i	0.00102664	+	0.0276200i
$427$	−43210.7	+	161264.i	−0.236993	+	0.884470i
$428$	−274953.	−	73673.6i	−1.50097	−	0.402183i
$429$	10857.1	+	17288.4i	0.0589927	+	0.0939377i
$430$	−11541.1	+	21602.7i	−0.0624183	+	0.116835i
$431$	−81678.4			−0.439696			−0.219848	−	0.975534i	$-0.570556\pi$
$431$	−81678.4			−0.439696			−0.219848	+	0.975534i	$0.570556\pi$
$432$	57785.1	+	147555.i	0.309634	+	0.790654i
$433$	5656.17	−	5656.17i	0.0301680	−	0.0301680i	−0.691862	−	0.722030i	$-0.743209\pi$
$433$	5656.17	−	5656.17i	0.0301680	−	0.0301680i	0.722030	+	0.691862i	$0.243209\pi$
$434$	−1443.51	−	833.409i	−0.00766371	−	0.00442465i
$435$	−313305.	−	60811.8i	−1.65573	−	0.321373i
$436$	−25619.4	−	44374.1i	−0.134771	−	0.233430i
$437$	74797.9	−	279150.i	0.391676	−	1.46175i
$438$	29384.6	+	27278.4i	0.153169	+	0.142191i
$439$	195123.	+	112654.i	1.01246	+	0.584547i	0.911912	−	0.410385i	$-0.134606\pi$
$439$	195123.	+	112654.i	1.01246	+	0.584547i	0.100552	+	0.994932i	$0.467939\pi$
$440$	41073.9	−	43872.4i	0.212159	−	0.226614i
$441$	132343.	−	9852.05i	0.680492	−	0.0506582i
$442$	1095.83	+	1095.83i	0.00560915	+	0.00560915i
$443$	−36595.5	−	136576.i	−0.186475	−	0.695933i	−0.994310	−	0.106525i	$-0.966028\pi$
$443$	−36595.5	−	136576.i	−0.186475	−	0.695933i	0.807835	−	0.589408i	$-0.200639\pi$
$444$	141024.	−	266671.i	0.715365	−	1.35273i
$445$	−257838.	+	160408.i	−1.30205	+	0.810039i
$446$	28396.7	+	49184.4i	0.142757	+	0.247262i
$447$	−88004.4	−	285553.i	−0.440443	−	1.42913i
$448$	−20667.7	−	77132.7i	−0.102976	−	0.384311i
$449$		−	43851.5i		−	0.217516i	−0.994068	−	0.108758i	$-0.965313\pi$
$449$		−	43851.5i		−	0.217516i	0.994068	−	0.108758i	$-0.0346874\pi$
$450$	27546.3	−	36596.6i	0.136031	−	0.180724i
$451$	−119446.			−0.587246
$452$	−245779.	+	65856.3i	−1.20301	+	0.322345i
$453$	−64033.4	−	59443.7i	−0.312040	−	0.289674i
$454$	−72100.2	+	41627.1i	−0.349804	+	0.201960i
$455$	−9708.43	−	15605.2i	−0.0468949	−	0.0753783i
$456$	114891.	−	72151.0i	0.552529	−	0.346987i
$457$	99435.5	−	26643.7i	0.476112	−	0.127574i	−0.0127796	−	0.999918i	$-0.504068\pi$
$457$	99435.5	−	26643.7i	0.476112	−	0.127574i	0.488892	+	0.872344i	$0.337401\pi$
$458$	8631.49	−	8631.49i	0.0411486	−	0.0411486i
$459$	46613.4	−	5217.13i	0.221251	−	0.0247632i
$460$	149858.	+	140299.i	0.708215	+	0.663040i
$461$	7439.11	−	12884.9i	0.0350041	−	0.0606289i	−0.847993	−	0.530008i	$-0.822189\pi$
$461$	7439.11	−	12884.9i	0.0350041	−	0.0606289i	0.882997	+	0.469379i	$0.155522\pi$
$462$	18679.9	+	4268.41i	0.0875166	+	0.0199978i
$463$	18001.0	+	4823.37i	0.0839723	+	0.0225003i	0.300561	−	0.953763i	$-0.402826\pi$
$463$	18001.0	+	4823.37i	0.0839723	+	0.0225003i	−0.216588	+	0.976263i	$0.569493\pi$
$464$	267027.	−	154168.i	1.24028	−	0.716076i
$465$	−11330.6	−	9844.09i	−0.0524017	−	0.0455271i
$466$	24755.4	−	42877.6i	0.113998	−	0.197451i
$467$	245596.	+	245596.i	1.12613	+	1.12613i	0.990801	+	0.135326i	$0.0432081\pi$
$467$	245596.	+	245596.i	1.12613	+	1.12613i	0.135326	+	0.990801i	$0.456792\pi$
$468$	−32161.6	−	6101.75i	−0.146841	−	0.0278588i
$469$		−	89706.9i		−	0.407831i
$470$	51548.1	+	27539.3i	0.233355	+	0.124669i
$471$	−108907.	−	57593.2i	−0.490922	−	0.259615i
$472$	3133.99	−	11696.2i	0.0140674	−	0.0525002i
$473$	−89118.5	−	23879.2i	−0.398332	−	0.106733i
$474$	39969.1	−	75580.1i	0.177897	−	0.336396i
$475$	299564.	+	147574.i	1.32771	+	0.654067i
$476$	−26974.3			−0.119052
$477$	−171949.	+	60072.5i	−0.755725	+	0.264021i
$478$	9618.36	−	9618.36i	0.0420964	−	0.0420964i
$479$	−264040.	−	152443.i	−1.15080	−	0.664413i	−0.201715	−	0.979444i	$-0.564652\pi$
$479$	−264040.	−	152443.i	−1.15080	−	0.664413i	−0.949081	+	0.315032i	$0.897985\pi$
$480$	10211.4	+	145460.i	0.0443203	+	0.631338i
$481$	29387.5	+	50900.6i	0.127020	+	0.220005i
$482$	−6303.21	+	23523.9i	−0.0271311	+	0.101255i
$483$	−29946.1	+	131053.i	−0.128365	+	0.561763i
$484$	−97035.2	−	56023.3i	−0.414227	−	0.239154i
$485$	−119253.	−	111646.i	−0.506976	−	0.474637i
$486$	40539.2	−	34799.8i	0.171634	−	0.147334i
$487$	16906.1	+	16906.1i	0.0712829	+	0.0712829i	0.741849	−	0.670566i	$-0.233949\pi$
$487$	16906.1	+	16906.1i	0.0712829	+	0.0712829i	−0.670566	+	0.741849i	$0.733949\pi$
$488$	44145.0	+	164751.i	0.185371	+	0.691814i
$489$	167517.	+	266748.i	0.700553	+	1.11553i
$490$	36093.5	+	8407.93i	0.150327	+	0.0350185i
$491$	183397.	+	317653.i	0.760728	+	1.31762i	0.942476	+	0.334275i	$0.108491\pi$
$491$	183397.	+	317653.i	0.760728	+	1.31762i	−0.181747	+	0.983345i	$0.558175\pi$
$492$	130310.	−	140372.i	0.538330	−	0.579895i
$493$	−23621.0	−	88154.8i	−0.0971862	−	0.362704i
$494$			12869.4i			0.0527357i
$495$	157806.	+	69783.8i	0.644039	+	0.284803i
$496$	14500.9			0.0589431
$497$	16430.4	−	4402.52i	0.0665176	−	0.0178233i
$498$	−9640.11	+	2970.97i	−0.0388708	+	0.0119795i
$499$	175902.	−	101557.i	0.706430	−	0.407857i	−0.103308	−	0.994649i	$-0.532943\pi$
$499$	175902.	−	101557.i	0.706430	−	0.407857i	0.809738	+	0.586792i	$0.199609\pi$
$500$	−192728.	+	138289.i	−0.770913	+	0.553155i
$501$	−35503.6	−	18775.4i	−0.141448	−	0.0748021i
$502$	18374.1	−	4923.32i	0.0729118	−	0.0195367i
$503$	162838.	−	162838.i	0.643606	−	0.643606i	−0.307834	−	0.951440i	$-0.599604\pi$
$503$	162838.	−	162838.i	0.643606	−	0.643606i	0.951440	+	0.307834i	$0.0996041\pi$
$504$	−52159.5	+	35524.1i	−0.205339	+	0.139850i
$505$	−296463.	+	9766.77i	−1.16249	+	0.0382973i
$506$	20849.9	−	36113.1i	0.0814335	−	0.141047i
$507$	−170545.	+	183713.i	−0.663472	+	0.714699i
$508$	324212.	+	86872.4i	1.25632	+	0.336631i
$509$	70625.7	−	40775.8i	0.272601	−	0.157386i	−0.357468	−	0.933925i	$-0.616360\pi$
$509$	70625.7	−	40775.8i	0.272601	−	0.157386i	0.630069	+	0.776539i	$0.283027\pi$
$510$	12858.4	+	2495.79i	0.0494364	+	0.00959549i
$511$	67985.5	−	117754.i	0.260360	−	0.450957i
$512$	−168999.	−	168999.i	−0.644679	−	0.644679i
$513$	304350.	+	243080.i	1.15648	+	0.923665i
$514$		−	39421.0i		−	0.149211i
$515$	120008.	+	395318.i	0.452477	+	1.49050i
$516$	125287.	−	78679.6i	0.470549	−	0.295504i
$517$	−56980.3	+	212653.i	−0.213178	+	0.795593i
$518$	53286.5	+	14278.1i	0.198590	+	0.0532120i
$519$	93646.0	−	3480.85i	0.347660	−	0.0129226i
$520$	−16560.8	−	8847.54i	−0.0612457	−	0.0327202i
$521$	81846.6			0.301526			0.150763	−	0.988570i	$-0.451827\pi$
$521$	81846.6			0.301526			0.150763	+	0.988570i	$0.451827\pi$
$522$	−78762.2	−	67848.0i	−0.289052	−	0.248998i
$523$	63438.9	−	63438.9i	0.231927	−	0.231927i	−0.581569	−	0.813497i	$-0.697561\pi$
$523$	63438.9	−	63438.9i	0.231927	−	0.231927i	0.813497	+	0.581569i	$0.197561\pi$
$524$	134340.	+	77561.0i	0.489262	+	0.282476i
$525$	−141800.	−	63422.8i	−0.514467	−	0.230105i
$526$	23128.2	+	40059.1i	0.0835929	+	0.144787i
$527$	1110.89	−	4145.88i	0.00399989	−	0.0149278i
$528$	−159306.	+	49096.2i	−0.571430	+	0.176108i
$529$	11010.6	+	6357.00i	0.0393461	+	0.0227165i
$530$	−50836.5	+	1674.77i	−0.180977	+	0.00596217i
$531$	34669.1	−	2580.89i	0.122957	−	0.00915334i
$532$	−158394.	−	158394.i	−0.559648	−	0.559648i
$533$	9658.48	+	36045.9i	0.0339981	+	0.126883i
$534$	−98842.3	+	3673.99i	−0.346625	+	0.0128842i
$535$	106348.	−	456531.i	0.371554	−	1.59501i
$536$	−45823.3	−	79368.2i	−0.159498	−	0.276259i
$537$	70307.7	+	16065.5i	0.243811	+	0.0557117i
$538$	1504.39	+	5614.47i	0.00519753	+	0.0193974i
$539$			139604.i			0.480529i
$540$	−254167.	+	109320.i	−0.871630	+	0.374897i
$541$	21035.6			0.0718722			0.0359361	−	0.999354i	$-0.488559\pi$
$541$	21035.6			0.0718722			0.0359361	+	0.999354i	$0.488559\pi$
$542$	48792.7	−	13074.0i	0.166095	−	0.0445050i
$543$	103947.	−	454906.i	0.352545	−	1.54284i
$544$	−36111.6	+	20849.0i	−0.122025	+	0.0704512i
$545$	71644.6	−	44572.1i	0.241207	−	0.150062i
$546$	−222.362	−	5982.26i	−0.000745892	−	0.0200669i
$547$	−480393.	+	128721.i	−1.60554	+	0.430204i	−0.946711	−	0.322085i	$-0.895616\pi$
$547$	−480393.	+	128721.i	−1.60554	+	0.430204i	−0.658833	+	0.752289i	$0.728950\pi$
$548$	−139482.	+	139482.i	−0.464469	+	0.464469i
$549$	−404742.	+	275656.i	−1.34287	+	0.914582i
$550$	36240.5	+	31755.4i	0.119803	+	0.104977i
$551$	378944.	−	656350.i	1.24816	−	2.16188i
$552$	40448.6	+	131246.i	0.132747	+	0.430733i
$553$	−280066.	−	75043.6i	−0.915821	−	0.245394i
$554$	−45046.3	+	26007.5i	−0.146771	+	0.0847382i
$555$	446552.	+	217647.i	1.44973	+	0.706589i
$556$	−32732.6	+	56694.6i	−0.105884	+	0.183397i
$557$	66417.7	+	66417.7i	0.214079	+	0.214079i	0.805998	−	0.591919i	$-0.201629\pi$
$557$	66417.7	+	66417.7i	0.214079	+	0.214079i	−0.591919	+	0.805998i	$0.701629\pi$
$558$	−1612.46	−	4615.44i	−0.00517869	−	0.0148233i
$559$			28824.6i			0.0922443i
$560$	143602.	−	43593.7i	0.457915	−	0.139011i
$561$	1832.77	+	49307.3i	0.00582346	+	0.156670i
$562$	2297.71	−	8575.18i	0.00727484	−	0.0271501i
$563$	−95930.1	−	25704.4i	−0.302648	−	0.0810944i	0.104299	−	0.994546i	$-0.466740\pi$
$563$	−95930.1	−	25704.4i	−0.302648	−	0.0810944i	−0.406947	+	0.913452i	$0.633407\pi$
$564$	−187744.	−	298957.i	−0.590212	−	0.939832i
$565$	−121717.	−	400948.i	−0.381289	−	1.25600i
$566$	−29242.0			−0.0912798
$567$	−145675.	−	107735.i	−0.453126	−	0.335114i
$568$	12288.0	−	12288.0i	0.0380876	−	0.0380876i
$569$	247974.	+	143168.i	0.765918	+	0.442203i	0.831416	−	0.555650i	$-0.187531\pi$
$569$	247974.	+	143168.i	0.765918	+	0.442203i	−0.0654988	+	0.997853i	$0.520864\pi$
$570$	60849.6	+	90160.2i	0.187287	+	0.277501i
$571$	−15953.5	−	27632.2i	−0.0489309	−	0.0847508i	0.840523	−	0.541776i	$-0.182248\pi$
$571$	−15953.5	−	27632.2i	−0.0489309	−	0.0847508i	−0.889454	+	0.457026i	$0.848915\pi$
$572$	8912.71	−	33262.7i	0.0272407	−	0.101664i
$573$	−166085.	−	154181.i	−0.505850	−	0.469593i
$574$	30333.6	+	17513.1i	0.0920662	+	0.0531544i
$575$	−222788.	+	254254.i	−0.673838	+	0.769009i
$576$	101729.	−	210976.i	0.306620	−	0.635899i
$577$	−189414.	−	189414.i	−0.568932	−	0.568932i	0.362897	−	0.931829i	$-0.381788\pi$
$577$	−189414.	−	189414.i	−0.568932	−	0.568932i	−0.931829	+	0.362897i	$0.881788\pi$
$578$	−18589.3	−	69376.2i	−0.0556426	−	0.207661i
$579$	−172382.	+	325967.i	−0.514202	+	0.972336i
$580$	284381.	+	457110.i	0.845366	+	1.35883i
$581$	17104.8	+	29626.3i	0.0506716	+	0.0877658i
$582$	−15671.4	−	50850.1i	−0.0462661	−	0.150123i
$583$	−49590.7	−	185075.i	−0.145903	−	0.544516i
$584$		−	138911.i		−	0.407297i
$585$	8298.78	−	53264.5i	0.0242495	−	0.155642i
$586$	−94119.5			−0.274085
$587$	−52908.0	+	14176.6i	−0.153548	+	0.0411431i	−0.334774	−	0.942298i	$-0.608660\pi$
$587$	−52908.0	+	14176.6i	−0.153548	+	0.0411431i	0.181226	+	0.983441i	$0.441993\pi$
$588$	−164060.	−	152301.i	−0.474514	−	0.440503i
$589$	30867.8	−	17821.6i	0.0889766	−	0.0513706i
$590$	9455.21	+	2202.58i	0.0271623	+	0.00632743i
$591$	−262452.	+	164819.i	−0.751407	+	0.471882i
$592$	−463580.	+	124216.i	−1.32276	+	0.354433i
$593$	181906.	−	181906.i	0.517295	−	0.517295i	−0.399457	−	0.916752i	$-0.630801\pi$
$593$	181906.	−	181906.i	0.517295	−	0.517295i	0.916752	+	0.399457i	$0.130801\pi$
$594$	33340.9	+	45245.4i	0.0944940	+	0.128233i
$595$	−1462.60	−	44396.1i	−0.00413134	−	0.125404i
$596$	−252016.	+	436505.i	−0.709473	+	1.22884i
$597$	188090.	+	42979.2i	0.527736	+	0.120589i
$598$	−12584.0	−	3371.86i	−0.0351896	−	0.00942903i
$599$	278802.	−	160966.i	0.777037	−	0.448623i	−0.0583419	−	0.998297i	$-0.518581\pi$
$599$	278802.	−	160966.i	0.777037	−	0.448623i	0.835379	+	0.549674i	$0.185248\pi$
$600$	−157855.	+	16319.6i	−0.438485	+	0.0453323i
$601$	84912.6	−	147073.i	0.235084	−	0.407178i	−0.724213	−	0.689576i	$-0.757797\pi$
$601$	84912.6	−	147073.i	0.235084	−	0.407178i	0.959297	+	0.282399i	$0.0911301\pi$
$602$	19130.6	+	19130.6i	0.0527881	+	0.0527881i
$603$	171730.	−	199355.i	0.472292	−	0.548266i
$604$			147380.i			0.403985i
$605$	86945.3	−	162745.i	0.237539	−	0.444627i
$606$	−85410.1	−	45167.5i	−0.232576	−	0.122993i
$607$	109337.	−	408050.i	0.296748	−	1.10748i	−0.643071	−	0.765807i	$-0.722340\pi$
$607$	109337.	−	408050.i	0.296748	−	1.10748i	0.939819	−	0.341672i	$-0.110993\pi$
$608$	−334474.	−	89622.1i	−0.904806	−	0.242442i
$609$	−164809.	+	311647.i	−0.444371	+	0.840290i
$610$	−130854.	+	39723.9i	−0.351664	+	0.106756i
$611$	68780.8			0.184240
$612$	−59944.7	−	51638.1i	−0.160047	−	0.137869i
$613$	124468.	−	124468.i	0.331236	−	0.331236i	−0.521820	−	0.853056i	$-0.674747\pi$
$613$	124468.	−	124468.i	0.331236	−	0.331236i	0.853056	+	0.521820i	$0.174747\pi$
$614$	54852.9	+	31669.3i	0.145500	+	0.0840044i
$615$	238099.	+	206862.i	0.629516	+	0.546928i
$616$	−33193.2	−	57492.3i	−0.0874757	−	0.151512i
$617$	122037.	−	455450.i	0.320570	−	1.19638i	−0.598121	−	0.801406i	$-0.704086\pi$
$617$	122037.	−	455450.i	0.320570	−	1.19638i	0.918691	−	0.394977i	$-0.129248\pi$
$618$	−29976.5	+	131186.i	−0.0784881	+	0.343488i
$619$	143136.	+	82639.6i	0.373566	+	0.215678i	0.675015	−	0.737804i	$-0.264137\pi$
$619$	143136.	+	82639.6i	0.373566	+	0.215678i	−0.301449	+	0.953482i	$0.597470\pi$
$620$	833.646	+	25304.7i	0.00216869	+	0.0658291i
$621$	−317429.	+	233911.i	−0.823122	+	0.606551i
$622$	−11590.1	−	11590.1i	−0.0299574	−	0.0299574i
$623$	86816.2	+	324003.i	0.223679	+	0.834781i
$624$	27697.5	+	44104.5i	0.0711330	+	0.113270i
$625$	−238055.	−	309706.i	−0.609420	−	0.792848i
$626$	−21206.7	−	36731.1i	−0.0541159	−	0.0937315i
$627$	−278772.	+	300296.i	−0.709110	+	0.763860i
$628$	53785.6	+	200731.i	0.136379	+	0.508973i
$629$			142055.i			0.359051i
$630$	−29843.3	−	40859.0i	−0.0751911	−	0.102945i
$631$	541522.			1.36006			0.680029	−	0.733185i	$-0.261967\pi$
$631$	541522.			1.36006			0.680029	+	0.733185i	$0.261967\pi$
$632$	−286122.	+	76666.2i	−0.716337	+	0.191942i
$633$	−67575.2	+	20825.9i	−0.168648	+	0.0519753i
$634$	132912.	−	76737.0i	0.330664	−	0.190909i
$635$	−125401.	+	538320.i	−0.310995	+	1.33504i
$636$	271599.	+	143630.i	0.671450	+	0.355083i
$637$	42128.9	−	11288.4i	0.103825	−	0.0278198i
$638$	77327.0	−	77327.0i	0.189972	−	0.189972i
$639$	44941.1	+	21669.8i	0.110063	+	0.0530705i
$640$	221873.	−	236989.i	0.541681	−	0.578587i
$641$	120283.	−	208336.i	0.292744	−	0.507048i	−0.681713	−	0.731619i	$-0.738765\pi$
$641$	120283.	−	208336.i	0.292744	−	0.507048i	0.974458	+	0.224571i	$0.0720982\pi$
$642$	103880.	−	111900.i	0.252035	−	0.271495i
$643$	−215954.	−	57864.8i	−0.522324	−	0.139956i	−0.0119825	−	0.999928i	$-0.503814\pi$
$643$	−215954.	−	57864.8i	−0.522324	−	0.139956i	−0.510341	+	0.859972i	$0.670481\pi$
$644$	196380.	−	113380.i	0.473507	−	0.273379i
$645$	136289.	+	201938.i	0.327599	+	0.485400i
$646$	−15552.3	+	26937.4i	−0.0372674	+	0.0645491i
$647$	404160.	+	404160.i	0.965483	+	0.965483i	0.999424	−	0.0339413i	$-0.0108059\pi$
$647$	404160.	+	404160.i	0.965483	+	0.965483i	−0.0339413	+	0.999424i	$0.510806\pi$
$648$	−183919.	−	20906.5i	−0.438002	−	0.0497888i
$649$			36571.2i			0.0868261i
$650$	6652.57	−	13504.2i	0.0157457	−	0.0319626i
$651$	−14040.8	+	8817.58i	−0.0331306	+	0.0208059i
$652$	137517.	−	513220.i	0.323490	−	1.20728i
$653$	814185.	+	218160.i	1.90940	+	0.511622i	0.994044	+	0.108976i	$0.0347570\pi$
$653$	814185.	+	218160.i	1.90940	+	0.511622i	0.915356	+	0.402647i	$0.131910\pi$
$654$	27465.0	−	1020.88i	0.0642131	−	0.00238682i
$655$	−120371.	+	225310.i	−0.280568	+	0.525168i
$656$	−304720.			−0.708098
$657$	376505.	−	131536.i	0.872249	−	0.304730i
$658$	45649.2	−	45649.2i	0.105434	−	0.105434i
$659$	−372043.	−	214799.i	−0.856687	−	0.494609i	0.00621442	−	0.999981i	$-0.498022\pi$
$659$	−372043.	−	214799.i	−0.856687	−	0.494609i	−0.862901	+	0.505372i	$0.831355\pi$
$660$	−94833.2	−	275172.i	−0.217707	−	0.631708i
$661$	23175.6	+	40141.3i	0.0530430	+	0.0918732i	0.891328	−	0.453360i	$-0.149775\pi$
$661$	23175.6	+	40141.3i	0.0530430	+	0.0918732i	−0.838285	+	0.545233i	$0.816441\pi$
$662$	−23110.2	+	86248.5i	−0.0527337	+	0.196805i
$663$	14731.5	−	4540.09i	0.0335135	−	0.0103285i
$664$	30266.9	+	17474.6i	0.0686486	+	0.0396343i
$665$	252106.	−	269283.i	0.570086	−	0.608928i
$666$	91084.7	+	133739.i	0.205351	+	0.301514i
$667$	542506.	+	542506.i	1.21942	+	1.21942i
$668$	17534.1	+	65438.2i	0.0392944	+	0.146649i
$669$	564536.	−	20983.9i	1.26136	−	0.0468851i
$670$	62390.2	−	38814.7i	0.138985	−	0.0864662i
$671$	−257569.	−	446123.i	−0.572069	−	0.990853i
$672$	157027.	+	35881.1i	0.347724	+	0.0794560i
$673$	162968.	+	608203.i	0.359808	+	1.34282i	0.874325	+	0.485342i	$0.161305\pi$
$673$	162968.	+	608203.i	0.359808	+	1.34282i	−0.514517	+	0.857480i	$0.672029\pi$
$674$			73439.1i			0.161662i
$675$	−193707.	−	412397.i	−0.425146	−	0.905125i
$676$	422836.			0.925292
$677$	−125015.	+	33497.8i	−0.272763	+	0.0730867i	−0.392608	−	0.919706i	$-0.628427\pi$
$677$	−125015.	+	33497.8i	−0.272763	+	0.0730867i	0.119845	+	0.992793i	$0.461760\pi$
$678$	30403.4	−	133055.i	0.0661397	−	0.289448i
$679$	−156274.	+	90225.1i	−0.338960	+	0.195699i
$680$	−23972.0	−	38532.3i	−0.0518426	−	0.0833312i
$681$	30760.7	+	827561.i	0.0663287	+	1.78446i
$682$	4967.76	−	1331.11i	0.0106805	−	0.00286183i
$683$	−52768.8	+	52768.8i	−0.113119	+	0.113119i	−0.761401	−	0.648282i	$-0.775488\pi$
$683$	−52768.8	+	52768.8i	−0.113119	+	0.113119i	0.648282	+	0.761401i	$0.275488\pi$
$684$	−48776.5	−	655216.i	−0.104255	−	1.40047i
$685$	−237131.	−	222005.i	−0.505368	−	0.473132i
$686$	50464.6	−	87407.3i	0.107236	−	0.185737i
$687$	−35760.9	−	116036.i	−0.0757696	−	0.245854i
$688$	−227350.	−	60918.4i	−0.480307	−	0.128698i
$689$	−51841.1	+	29930.5i	−0.109203	+	0.0630485i
$690$	−104103.	+	35877.3i	−0.218658	+	0.0753567i
$691$	−182987.	+	316943.i	−0.383235	+	0.663782i	−0.991523	−	0.129934i	$-0.958523\pi$
$691$	−182987.	+	316943.i	−0.383235	+	0.663782i	0.608288	+	0.793717i	$0.291857\pi$
$692$	−111774.	−	111774.i	−0.233415	−	0.233415i
$693$	124396.	−	144407.i	0.259025	−	0.300692i
$694$		−	17157.2i		−	0.0356228i
$695$	−95086.4	−	50799.4i	−0.196856	−	0.105169i
$696$	13378.2	+	359917.i	0.0276172	+	0.742991i
$697$	−23344.0	+	87120.8i	−0.0480517	+	0.179331i
$698$	−49970.6	−	13389.6i	−0.102566	−	0.0274825i
$699$	−261915.	−	417064.i	−0.536051	−	0.853588i
$700$	84328.3	+	248085.i	0.172099	+	0.506296i
$701$	−745246.			−1.51657			−0.758287	−	0.651920i	$-0.773964\pi$
$701$	−745246.			−1.51657			−0.758287	+	0.651920i	$0.773964\pi$
$702$	10957.9	−	13720.0i	0.0222359	−	0.0278407i
$703$	−834153.	+	834153.i	−1.68785	+	1.68785i
$704$	213380.	+	123195.i	0.430535	+	0.248570i
$705$	481863.	−	325211.i	0.969494	−	0.654316i
$706$	105893.	+	183412.i	0.212450	+	0.367974i
$707$	−84803.8	+	316492.i	−0.169659	+	0.633176i
$708$	−42978.0	−	39897.5i	−0.0857392	−	0.0795937i
$709$	−288901.	−	166797.i	−0.574720	−	0.331815i	0.184312	−	0.982868i	$-0.440994\pi$
$709$	−288901.	−	166797.i	−0.574720	−	0.331815i	−0.759032	+	0.651053i	$0.774328\pi$
$710$	10171.1	+	9522.30i	0.0201767	+	0.0188897i
$711$	−478729.	−	702911.i	−0.947001	−	1.39047i
$712$	242315.	+	242315.i	0.477991	+	0.477991i
$713$	9338.70	+	34852.5i	0.0183699	+	0.0685575i
$714$	6763.95	−	12790.4i	0.0132680	−	0.0250892i
$715$	55229.1	+	12865.5i	0.108033	+	0.0251661i
$716$	−60826.5	−	105355.i	−0.118650	−	0.205507i
$717$	−39849.6	−	129302.i	−0.0775150	−	0.251518i
$718$	40372.0	+	150670.i	0.0783126	+	0.292267i
$719$		−	725995.i		−	1.40435i	−0.712003	−	0.702176i	$-0.752212\pi$
$719$		−	725995.i		−	1.40435i	0.712003	−	0.702176i	$-0.247788\pi$
$720$	402578.	+	178026.i	0.776579	+	0.343414i
$721$	456355.			0.877874
$722$	−135605.	+	36335.2i	−0.260136	+	0.0697032i
$723$	177539.	+	164814.i	0.339639	+	0.315295i
$724$	−681667.	+	393560.i	−1.30045	+	0.750817i
$725$	−736922.	+	492838.i	−1.40199	+	0.937623i
$726$	50896.6	−	31962.9i	0.0965641	−	0.0606420i
$727$	256377.	−	68696.0i	0.485077	−	0.129976i	−0.00798880	−	0.999968i	$-0.502543\pi$
$727$	256377.	−	68696.0i	0.485077	−	0.129976i	0.493066	+	0.869992i	$0.335876\pi$
$728$	−14665.7	+	14665.7i	−0.0276720	+	0.0276720i
$729$	−117490.	−	518291.i	−0.221077	−	0.975256i
$730$	111313.	−	3667.13i	0.208882	−	0.00688147i
$731$	−34833.6	+	60333.6i	−0.0651875	+	0.112908i
$732$	805272.	+	184007.i	1.50287	+	0.343410i
$733$	446942.	+	119758.i	0.831846	+	0.222892i	0.649519	−	0.760346i	$-0.274970\pi$
$733$	446942.	+	119758.i	0.831846	+	0.222892i	0.182327	+	0.983238i	$0.441637\pi$
$734$	130909.	−	75580.3i	0.242984	−	0.140287i
$735$	241771.	−	278279.i	0.447538	−	0.515117i
$736$	175268.	−	303573.i	0.323555	−	0.560413i
$737$	195722.	+	195722.i	0.360333	+	0.360333i
$738$	33883.9	+	96988.1i	0.0622129	+	0.178076i
$739$			629981.i			1.15356i	0.816901	+	0.576778i	$0.195690\pi$
$739$			629981.i			1.15356i	−0.816901	+	0.576778i	$0.804310\pi$
$740$	−243412.	−	801824.i	−0.444508	−	1.46425i
$741$	113163.	+	59844.2i	0.206096	+	0.108990i
$742$	−14541.9	+	54271.0i	−0.0264127	+	0.0985735i
$743$	−295798.	−	79258.8i	−0.535818	−	0.143572i	−0.0192445	−	0.999815i	$-0.506126\pi$
$743$	−295798.	−	79258.8i	−0.535818	−	0.143572i	−0.516574	+	0.856243i	$0.672793\pi$
$744$	−7918.48	+	14973.5i	−0.0143053	+	0.0270507i
$745$	−732093.	−	391116.i	−1.31903	−	0.704683i
$746$	63200.0			0.113564
$747$	−18703.2	+	98582.6i	−0.0335178	+	0.176668i
$748$	58852.4	−	58852.4i	0.105187	−	0.105187i
$749$	−448424.	−	258898.i	−0.799328	−	0.461492i
$750$	−17244.6	−	126062.i	−0.0306571	−	0.224111i
$751$	−358430.	−	620819.i	−0.635513	−	1.10074i	−0.986406	−	0.164325i	$-0.947455\pi$
$751$	−358430.	−	620819.i	−0.635513	−	1.10074i	0.350893	−	0.936415i	$-0.385878\pi$
$752$	−145362.	+	542500.i	−0.257049	+	0.959321i
$753$	42149.8	−	184461.i	0.0743371	−	0.325322i
$754$	−29588.0	−	17082.6i	−0.0520443	−	0.0300478i
$755$	−242568.	+	7991.23i	−0.425539	+	0.0140191i
$756$	33994.5	+	303730.i	0.0594792	+	0.531428i
$757$	−149824.	−	149824.i	−0.261451	−	0.261451i	0.564192	−	0.825643i	$-0.309188\pi$
$757$	−149824.	−	149824.i	−0.261451	−	0.261451i	−0.825643	+	0.564192i	$0.809188\pi$
$758$	−53405.8	−	199313.i	−0.0929501	−	0.346895i
$759$	−220595.	−	351267.i	−0.382923	−	0.609753i
$760$	85498.4	−	367027.i	0.148024	−	0.635434i
$761$	−66718.7	−	115560.i	−0.115207	−	0.199544i	0.802656	−	0.596443i	$-0.203420\pi$
$761$	−66718.7	−	115560.i	−0.115207	−	0.199544i	−0.917862	+	0.396899i	$0.870086\pi$
$762$	−122490.	+	131948.i	−0.210956	+	0.227244i
$763$	−24123.4	−	90029.6i	−0.0414370	−	0.154645i
$764$			382264.i			0.654903i
$765$	81739.0	−	101461.i	0.139671	−	0.173370i
$766$	−80871.4			−0.137828
$767$	11036.3	−	2957.16i	0.0187599	−	0.00502671i
$768$	−296871.	+	91492.5i	−0.503322	+	0.155118i
$769$	629568.	−	363481.i	1.06461	−	0.614652i	0.137905	−	0.990446i	$-0.455963\pi$
$769$	629568.	−	363481.i	1.06461	−	0.614652i	0.926703	+	0.375794i	$0.122630\pi$
$770$	45193.8	−	28116.3i	0.0762250	−	0.0474217i
$771$	−346636.	−	183312.i	−0.583129	−	0.308377i
$772$	600804.	−	160985.i	1.00809	−	0.270116i
$773$	664525.	−	664525.i	1.11212	−	1.11212i	0.119259	−	0.992863i	$-0.461948\pi$
$773$	664525.	−	664525.i	1.11212	−	1.11212i	0.992863	−	0.119259i	$-0.0380518\pi$
$774$	5891.17	+	79136.3i	0.00983377	+	0.132097i
$775$	−41602.9	+	2744.14i	−0.0692660	+	0.00456880i
$776$	−92176.0	+	159653.i	−0.153071	+	0.265128i
$777$	373338.	−	402163.i	0.618386	−	0.666132i
$778$	−210690.	−	56454.3i	−0.348085	−	0.0932691i
$779$	−648651.	+	374499.i	−1.06890	+	0.617129i
$780$	−75371.7	+	50868.7i	−0.123885	+	0.0836107i
$781$	−26242.4	+	45453.2i	−0.0430231	+	0.0745182i
$782$	−22265.1	−	22265.1i	−0.0364092	−	0.0364092i
$783$	−962853.	+	377070.i	−1.57049	+	0.615032i
$784$			356144.i			0.579419i
$785$	−327459.	+	99407.8i	−0.531395	+	0.161317i
$786$	−70463.4	+	44250.8i	−0.114056	+	0.0716269i
$787$	−32752.1	+	122232.i	−0.0528797	+	0.197350i	−0.987312	−	0.158790i	$-0.949241\pi$
$787$	−32752.1	+	122232.i	−0.0528797	+	0.197350i	0.934433	+	0.356140i	$0.115907\pi$
$788$	504955.	+	135302.i	0.813205	+	0.217898i
$789$	459796.	−	17090.7i	0.738603	−	0.0274541i
$790$	−68988.0	−	227253.i	−0.110540	−	0.364130i
$791$	−462854.			−0.739760
$792$	36295.1	−	191307.i	0.0578626	−	0.304987i
$793$	−113801.	+	113801.i	−0.180968	+	0.180968i
$794$	76373.5	+	44094.3i	0.121144	+	0.0699425i
$795$	−221669.	+	454802.i	−0.350728	+	0.719596i
$796$	−162726.	−	281849.i	−0.256820	−	0.444826i
$797$	31550.9	−	117750.i	0.0496701	−	0.185371i	−0.936634	−	0.350310i	$-0.886076\pi$
$797$	31550.9	−	117750.i	0.0496701	−	0.185371i	0.986304	+	0.164939i	$0.0527427\pi$
$798$	114823.	−	35387.3i	0.180312	−	0.0555702i
$799$	143967.	+	83119.5i	0.225512	+	0.130200i
$800$	304644.	+	266942.i	0.476006	+	0.417097i
$801$	−427321.	+	886223.i	−0.666024	+	1.38127i
$802$	41527.7	+	41527.7i	0.0645638	+	0.0645638i
$803$	108585.	+	405246.i	0.168399	+	0.628474i
$804$	−443533.	+	16486.2i	−0.686141	+	0.0255041i
$805$	197257.	+	317068.i	0.304397	+	0.489283i
$806$	−803.389	−	1391.51i	−0.00123668	−	0.00214198i
$807$	56364.7	+	12879.5i	0.0865486	+	0.0197766i
$808$	86637.5	+	323335.i	0.132704	+	0.495257i
$809$		−	246922.i		−	0.377280i	−0.982046	−	0.188640i	$-0.939592\pi$
$809$		−	246922.i		−	0.377280i	0.982046	−	0.188640i	$-0.0604079\pi$
$810$	11897.6	−	147931.i	0.0181339	−	0.225470i
$811$	464777.			0.706647			0.353324	−	0.935501i	$-0.385051\pi$
$811$	464777.			0.706647			0.353324	+	0.935501i	$0.385051\pi$
$812$	574411.	−	153913.i	0.871186	−	0.233434i
$813$	111930.	−	489838.i	0.169342	−	0.741091i
$814$	−147412.	+	85108.3i	−0.222476	+	0.128447i
$815$	852146.	+	198506.i	1.28292	+	0.298854i
$816$	4675.57	+	125788.i	0.00702190	+	0.188912i
$817$	−558824.	+	149737.i	−0.837204	+	0.224328i
$818$	−126188.	+	126188.i	−0.188587	+	0.188587i
$819$	−53637.2	−	25862.9i	−0.0799646	−	0.0385576i
$820$	−17518.1	−	531749.i	−0.0260531	−	0.790822i
$821$	−235581.	+	408038.i	−0.349505	+	0.605361i	−0.986162	−	0.165787i	$-0.946984\pi$
$821$	−235581.	+	408038.i	−0.349505	+	0.605361i	0.636656	+	0.771148i	$0.280317\pi$
$822$	−31162.2	−	101114.i	−0.0461194	−	0.149647i
$823$	51986.4	+	13929.7i	0.0767520	+	0.0205656i	0.296991	−	0.954880i	$-0.404017\pi$
$823$	51986.4	+	13929.7i	0.0767520	+	0.0205656i	−0.220239	+	0.975446i	$0.570684\pi$
$824$	403760.	−	233111.i	0.594661	−	0.343327i
$825$	447754.	−	171003.i	0.657857	−	0.251244i
$826$	5362.03	−	9287.31i	0.00785904	−	0.0136123i
$827$	−510882.	−	510882.i	−0.746981	−	0.746981i	0.226930	−	0.973911i	$-0.427131\pi$
$827$	−510882.	−	510882.i	−0.746981	−	0.746981i	−0.973911	+	0.226930i	$0.927131\pi$
$828$	653462.	+	123976.i	0.953147	+	0.180832i
$829$		−	68175.2i		−	0.0992013i	−0.998769	−	0.0496006i	$-0.984205\pi$
$829$		−	68175.2i		−	0.0992013i	0.998769	−	0.0496006i	$-0.0157949\pi$
$830$	−13203.8	+	24715.0i	−0.0191666	+	0.0358760i
$831$	19218.5	+	517039.i	0.0278302	+	0.748723i
$832$	19923.2	−	74354.4i	0.0287814	−	0.107414i
$833$	101823.	+	27283.4i	0.146742	+	0.0393195i
$834$	−18674.9	−	29737.3i	−0.0268489	−	0.0427532i
$835$	−106752.	+	32407.0i	−0.153109	+	0.0464799i
$836$	691165.			0.988938
$837$	−48082.5	−	7283.68i	−0.0686335	−	0.0103968i
$838$	−203458.	+	203458.i	−0.289726	+	0.289726i
$839$	971425.	+	560852.i	1.38002	+	0.796755i	0.992161	−	0.124964i	$-0.0398816\pi$
$839$	971425.	+	560852.i	1.38002	+	0.796755i	0.387859	+	0.921719i	$0.373215\pi$
$840$	−33401.7	+	172087.i	−0.0473381	+	0.243888i
$841$	652367.	+	1.12993e6i	0.922358	+	1.59757i
$842$	−37448.9	+	139761.i	−0.0528220	+	0.197135i
$843$	−64718.6	−	60079.8i	−0.0910697	−	0.0845421i
$844$	103297.	+	59638.8i	0.145012	+	0.0837228i
$845$	22927.0	+	695931.i	0.0321095	+	0.974659i
$846$	188834.	−	14057.4i	0.263839	−	0.0196411i
$847$	−144121.	−	144121.i	−0.200891	−	0.200891i
$848$	−126511.	−	472146.i	−0.175929	−	0.656575i
$849$	−135979.	+	257131.i	−0.188649	+	0.356729i
$850$	30244.1	−	20226.6i	0.0418604	−	0.0279954i
$851$	−597097.	−	1.03420e6i	−0.824491	−	1.42806i
$852$	−24786.7	−	80427.0i	−0.0341460	−	0.110796i
$853$	−215658.	−	804846.i	−0.296393	−	1.10615i	−0.940105	−	0.340885i	$-0.889273\pi$
$853$	−215658.	−	804846.i	−0.296393	−	1.10615i	0.643712	−	0.765267i	$-0.277393\pi$
$854$			151058.i			0.207123i
$855$	1.07575e6	−	115807.i	1.47157	−	0.158417i
$856$	−528991.			−0.721940
$857$	708145.	−	189747.i	0.964186	−	0.258353i	0.257815	−	0.966194i	$-0.416998\pi$
$857$	708145.	−	189747.i	0.964186	−	0.258353i	0.706371	+	0.707842i	$0.250331\pi$
$858$	13537.2	+	12566.9i	0.0183889	+	0.0170708i
$859$	424820.	−	245270.i	0.575730	−	0.332398i	−0.183705	−	0.982981i	$-0.558809\pi$
$859$	424820.	−	245270.i	0.575730	−	0.332398i	0.759434	+	0.650584i	$0.225476\pi$
$860$	93234.7	−	400237.i	0.126061	−	0.541154i
$861$	295051.	−	185291.i	0.398007	−	0.249947i
$862$	−71383.8	+	19127.2i	−0.0960694	+	0.0257417i
$863$	−683502.	+	683502.i	−0.917736	+	0.917736i	−0.996864	−	0.0791280i	$-0.974786\pi$
$863$	−683502.	+	683502.i	−0.917736	+	0.917736i	0.0791280	+	0.996864i	$0.474786\pi$
$864$	280270.	+	380341.i	0.375447	+	0.509501i
$865$	177905.	−	190026.i	0.237769	−	0.253969i
$866$	3618.73	−	6267.82i	0.00482525	−	0.00835758i
$867$	−696480.	−	159148.i	−0.926553	−	0.211720i
$868$	27014.3	+	7238.46i	0.0358554	+	0.00960742i
$869$	774777.	−	447318.i	1.02598	−	0.592347i
$870$	−288057.	+	20221.8i	−0.380575	+	0.0267166i
$871$	43237.8	−	74890.1i	0.0569937	−	0.0987161i
$872$	−67331.3	−	67331.3i	−0.0885490	−	0.0885490i
$873$	−520008.	−	98656.7i	−0.682310	−	0.129449i
$874$		−	261482.i		−	0.342309i
$875$	−403742.	+	152245.i	−0.527336	+	0.198850i
$876$	−594700.	−	314496.i	−0.774979	−	0.409833i
$877$	66779.6	−	249225.i	0.0868250	−	0.324035i	−0.908829	−	0.417170i	$-0.863022\pi$
$877$	66779.6	−	249225.i	0.0868250	−	0.324035i	0.995654	+	0.0931346i	$0.0296887\pi$
$878$	196911.	+	52762.2i	0.255436	+	0.0684438i
$879$	−437666.	+	827610.i	−0.566455	+	1.07114i
$880$	−218197.	+	408423.i	−0.281763	+	0.527405i
$881$	615251.			0.792685			0.396342	−	0.918103i	$-0.370279\pi$
$881$	615251.			0.792685			0.396342	+	0.918103i	$0.370279\pi$
$882$	113355.	−	39602.0i	0.145715	−	0.0509073i
$883$	215199.	−	215199.i	0.276007	−	0.276007i	−0.555506	−	0.831513i	$-0.687475\pi$
$883$	215199.	−	215199.i	0.276007	−	0.276007i	0.831513	+	0.555506i	$0.187475\pi$
$884$	−22519.0	−	13001.3i	−0.0288167	−	0.0166373i
$885$	63335.5	−	72899.2i	0.0808650	−	0.0930757i
$886$	−63966.1	−	110793.i	−0.0814859	−	0.141138i
$887$	−62842.4	+	234531.i	−0.0798740	+	0.298094i	−0.994294	−	0.106672i	$-0.965980\pi$
$887$	−62842.4	+	234531.i	−0.0798740	+	0.298094i	0.914420	+	0.404766i	$0.132647\pi$
$888$	124881.	−	546519.i	0.158369	−	0.693074i
$889$	528761.	+	305280.i	0.669045	+	0.386274i
$890$	−187776.	+	200570.i	−0.237061	+	0.253213i
$891$	552890.	−	82776.7i	0.696439	−	0.104268i
$892$	−673820.	−	673820.i	−0.846865	−	0.846865i
$893$	357299.	+	1.33346e6i	0.448053	+	1.67215i
$894$	−143783.	−	228954.i	−0.179900	−	0.286466i
$895$	170101.	−	105825.i	0.212354	−	0.132112i
$896$	−179302.	−	310561.i	−0.223342	−	0.386839i
$897$	−88166.2	+	94973.5i	−0.109576	+	0.118037i
$898$	−10269.0	−	38324.5i	−0.0127343	−	0.0475252i
$899$			94624.1i			0.117080i
$900$	−287518.	+	712749.i	−0.354960	+	0.879938i
$901$	−144680.			−0.178221
$902$	−104392.	+	27971.7i	−0.128308	+	0.0343799i
$903$	257179.	−	79259.6i	0.315398	−	0.0972023i
$904$	−409510.	+	236431.i	−0.501104	+	0.289313i
$905$	−684708.	−	1.10059e6i	−0.836004	−	1.34378i
$906$	−69883.1	−	36956.4i	−0.0851365	−	0.0450228i
$907$	−615009.	+	164791.i	−0.747596	+	0.200318i	−0.612451	−	0.790508i	$-0.709816\pi$
$907$	−615009.	+	164791.i	−0.747596	+	0.200318i	−0.135144	+	0.990826i	$0.543150\pi$
$908$	987763.	−	987763.i	1.19807	−	1.19807i
$909$	−794333.	+	540993.i	−0.961335	+	0.654733i
$910$	−12139.2	−	11364.9i	−0.0146591	−	0.0137240i
$911$	357233.	−	618745.i	0.430442	−	0.745547i	−0.566470	−	0.824083i	$-0.691691\pi$
$911$	357233.	−	618745.i	0.430442	−	0.745547i	0.996911	+	0.0785356i	$0.0250244\pi$
$912$	−711175.	+	766085.i	−0.855040	+	0.921058i
$913$	−101958.	−	27319.5i	−0.122315	−	0.0327741i
$914$	80663.5	−	46571.1i	0.0965572	−	0.0557473i
$915$	−259187.	+	1.33535e6i	−0.309579	+	1.59497i
$916$	−102408.	+	177375.i	−0.122051	+	0.211399i
$917$	199527.	+	199527.i	0.237281	+	0.237281i
$918$	39516.6	−	15475.4i	0.0468915	−	0.0183635i
$919$		−	601979.i		−	0.712772i	−0.934339	−	0.356386i	$-0.884009\pi$
$919$		−	601979.i		−	0.712772i	0.934339	−	0.356386i	$-0.115991\pi$
$920$	336485.	+	179765.i	0.397548	+	0.212388i
$921$	533546.	−	335066.i	0.629003	−	0.395013i
$922$	3484.14	−	13003.0i	0.00409858	−	0.0152961i
$923$	15838.6	+	4243.94i	0.0185915	+	0.00498157i
$924$	−321283.	+	11942.2i	−0.376309	+	0.0139875i
$925$	1.30650e6	−	444100.i	1.52695	−	0.519036i
$926$	16861.7			0.0196644
$927$	1.01415e6	+	873620.i	1.18017	+	1.01663i
$928$	650025.	−	650025.i	0.754804	−	0.754804i
$929$	−997722.	−	576035.i	−1.15605	−	0.667448i	−0.205699	−	0.978615i	$-0.565947\pi$
$929$	−997722.	−	576035.i	−1.15605	−	0.667448i	−0.950355	+	0.311167i	$0.899280\pi$
$930$	−12207.7	−	5950.00i	−0.0141146	−	0.00687940i
$931$	437698.	+	758115.i	0.504981	+	0.874653i
$932$	−215010.	+	802426.i	−0.247529	+	0.923790i
$933$	−155808.	+	48018.5i	−0.178990	+	0.0551626i
$934$	272154.	+	157128.i	0.311976	+	0.180120i
$935$	100054.	+	93672.0i	0.114449	+	0.107149i
$936$	−60666.6	+	4516.23i	−0.0692465	+	0.00515494i
$937$	−803144.	−	803144.i	−0.914775	−	0.914775i	0.0818686	−	0.996643i	$-0.473911\pi$
$937$	−803144.	−	803144.i	−0.914775	−	0.914775i	−0.996643	+	0.0818686i	$0.973911\pi$
$938$	−21007.3	−	78400.4i	−0.0238762	−	0.0891071i
$939$	−421597.	+	15670.9i	−0.478153	+	0.0177731i
$940$	−955041.	−	222475.i	−1.08085	−	0.251783i
$941$	335325.	+	580799.i	0.378692	+	0.655914i	0.990872	−	0.134804i	$-0.0430406\pi$
$941$	335325.	+	580799.i	0.378692	+	0.655914i	−0.612180	+	0.790718i	$0.709707\pi$
$942$	−108667.	−	24830.8i	−0.122461	−	0.0279827i
$943$	−196242.	−	732384.i	−0.220683	−	0.823599i
$944$			93296.9i			0.104694i
$945$	−498055.	+	72419.2i	−0.557717	+	0.0810942i
$946$	−83478.1			−0.0932804
$947$	160738.	−	43069.7i	0.179233	−	0.0480255i	−0.168086	−	0.985772i	$-0.553759\pi$
$947$	160738.	−	43069.7i	0.179233	−	0.0480255i	0.347319	+	0.937747i	$0.387092\pi$
$948$	−319563.	+	1.39851e6i	−0.355583	+	1.55614i
$949$	113513.	−	65536.6i	0.126041	−	0.0727699i
$950$	296366.	+	58822.9i	0.328383	+	0.0651778i
$951$	−56705.5	−	1.52556e6i	−0.0626995	−	1.68682i
$952$	−48420.3	+	12974.2i	−0.0534261	+	0.0143155i
$953$	−967336.	+	967336.i	−1.06510	+	1.06510i	−0.0673748	+	0.997728i	$0.521462\pi$
$953$	−967336.	+	967336.i	−1.06510	+	1.06510i	−0.997728	+	0.0673748i	$0.978538\pi$
$954$	−136210.	+	92767.7i	−0.149662	+	0.101930i
$955$	−629155.	+	20727.1i	−0.689844	+	0.0227265i
$956$	−114116.	+	197655.i	−0.124863	+	0.216268i
$957$	−320371.	−	1.03953e6i	−0.349808	−	1.13504i
$958$	−266460.	−	71397.6i	−0.290336	−	0.0777952i
$959$	−310747.	+	179410.i	−0.337885	+	0.195078i
$960$	−211987.	−	615111.i	−0.230021	−	0.667438i
$961$	459535.	−	795939.i	0.497591	−	0.861852i
$962$	37603.3	+	37603.3i	0.0406327	+	0.0406327i
$963$	−500908.	−	1.43378e6i	−0.540139	−	1.54608i
$964$		−	408627.i		−	0.439717i
$965$	297536.	+	980113.i	0.319511	+	1.05250i
$966$	4517.98	+	121548.i	0.00484161	+	0.130255i
$967$	−317121.	+	1.18351e6i	−0.339135	+	1.26567i	0.560182	+	0.828370i	$0.310731\pi$
$967$	−317121.	+	1.18351e6i	−0.339135	+	1.26567i	−0.899316	+	0.437298i	$0.855935\pi$
$968$	−201129.	−	53892.5i	−0.214647	−	0.0575145i
$969$	164545.	+	262016.i	0.175242	+	0.279049i
$970$	−130368.	−	69648.3i	−0.138557	−	0.0740231i
$971$	916740.			0.972316			0.486158	−	0.873871i	$-0.338398\pi$
$971$	916740.			0.972316			0.486158	+	0.873871i	$0.338398\pi$
$972$	−505898.	+	740053.i	−0.535464	+	0.783304i
$973$	−84205.2	+	84205.2i	−0.0889433	+	0.0889433i
$974$	18734.3	+	10816.3i	0.0197479	+	0.0114014i
$975$	−87809.8	−	121293.i	−0.0923706	−	0.127593i
$976$	−657085.	−	1.13810e6i	−0.689798	−	1.19476i
$977$	62789.5	−	234334.i	0.0657806	−	0.245497i	−0.925204	−	0.379469i	$-0.876107\pi$
$977$	62789.5	−	234334.i	0.0657806	−	0.245497i	0.990985	+	0.133972i	$0.0427733\pi$
$978$	208870.	+	193899.i	0.218372	+	0.202720i
$979$	−896322.	−	517492.i	−0.935187	−	0.539931i
$980$	−621485.	+	20474.4i	−0.647110	+	0.0213186i
$981$	118738.	−	246252.i	0.123382	−	0.255883i
$982$	234669.	+	234669.i	0.243351	+	0.243351i
$983$	−473176.	−	1.76592e6i	−0.489684	−	1.82753i	−0.557971	−	0.829860i	$-0.688420\pi$
$983$	−473176.	−	1.76592e6i	−0.489684	−	1.82753i	0.0682870	−	0.997666i	$-0.478247\pi$
$984$	166398.	−	314652.i	0.171853	−	0.324967i
$985$	−195310.	+	838424.i	−0.201303	+	0.864154i
$986$	−41287.7	−	71512.4i	−0.0424685	−	0.0735576i
$987$	−189128.	−	613676.i	−0.194143	−	0.629948i
$988$	−55887.8	−	208576.i	−0.0572536	−	0.213673i
$989$		−	585661.i		−	0.598761i
$990$	154258.	+	24033.9i	0.157390	+	0.0245219i
$991$	53321.8			0.0542947			0.0271473	−	0.999631i	$-0.491358\pi$
$991$	53321.8			0.0542947			0.0271473	+	0.999631i	$0.491358\pi$
$992$	41759.9	−	11189.5i	0.0424362	−	0.0113707i
$993$	650934.	+	604278.i	0.660144	+	0.612827i
$994$	13328.6	−	7695.27i	0.0134900	−	0.00778845i
$995$	455062.	−	283107.i	0.459647	−	0.285959i
$996$	143336.	−	90014.8i	0.144490	−	0.0907393i
$997$	1.36781e6	−	366504.i	1.37605	−	0.368713i	0.506368	−	0.862317i	$-0.330988\pi$
$997$	1.36781e6	−	366504.i	1.37605	−	0.368713i	0.869686	+	0.493605i	$0.164321\pi$
$998$	129949.	−	129949.i	0.130470	−	0.130470i
$999$	1.59954e6	−	179026.i	1.60275	−	0.179385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.k.a.7.13	✓	88
3.2	odd	2		135.5.l.a.127.10		88
5.3	odd	4	inner	45.5.k.a.43.10	yes	88
9.4	even	3	inner	45.5.k.a.22.10	yes	88
9.5	odd	6		135.5.l.a.37.13		88
15.8	even	4		135.5.l.a.73.13		88
45.13	odd	12	inner	45.5.k.a.13.13	yes	88
45.23	even	12		135.5.l.a.118.10		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.k.a.7.13	✓	88	1.1	even	1	trivial
45.5.k.a.13.13	yes	88	45.13	odd	12	inner
45.5.k.a.22.10	yes	88	9.4	even	3	inner
45.5.k.a.43.10	yes	88	5.3	odd	4	inner
135.5.l.a.37.13		88	9.5	odd	6
135.5.l.a.73.13		88	15.8	even	4
135.5.l.a.118.10		88	45.23	even	12
135.5.l.a.127.10		88	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.873962 - 0.234177i) q^{2} +(2.00485 - 8.77386i) q^{3} +(-13.1474 + 7.59068i) q^{4} +(-13.2061 - 21.2273i) q^{5} +(-0.302473 - 8.13751i) q^{6} +(-26.6745 + 7.14742i) q^{7} +(-19.9493 + 19.9493i) q^{8} +(-72.9611 - 35.1806i) q^{9} +(-16.5126 - 15.4593i) q^{10} +(42.6042 - 73.7926i) q^{11} +(40.2408 + 130.572i) q^{12} +(-25.7137 - 6.88997i) q^{13} +(-21.6388 + 12.4931i) q^{14} +(-212.722 + 73.3108i) q^{15} +(108.688 - 188.252i) q^{16} +(-45.4958 - 45.4958i) q^{17} +(-72.0037 - 13.6606i) q^{18} -534.305i q^{19} +(334.756 + 178.842i) q^{20} +(9.23191 + 248.368i) q^{21} +(19.9539 - 74.4688i) q^{22} +(522.453 + 139.991i) q^{23} +(135.037 + 215.028i) q^{24} +(-276.198 + 560.660i) q^{25} -24.0863 q^{26} +(-454.946 + 569.619i) q^{27} +(296.448 - 296.448i) q^{28} +(1228.42 + 709.227i) q^{29} +(-168.743 + 113.885i) q^{30} +(33.3546 + 57.7719i) q^{31} +(167.736 - 625.998i) q^{32} +(-562.030 - 521.746i) q^{33} +(-50.4157 - 29.1075i) q^{34} +(503.987 + 471.839i) q^{35} +(1226.30 - 91.2897i) q^{36} +(-1561.19 - 1561.19i) q^{37} +(-125.122 - 466.962i) q^{38} +(-112.004 + 211.795i) q^{39} +(686.924 + 160.018i) q^{40} +(-700.909 - 1214.01i) q^{41} +(66.2305 + 214.902i) q^{42} +(-280.245 - 1045.89i) q^{43} +1293.58i q^{44} +(216.742 + 2013.37i) q^{45} +489.387 q^{46} +(-2495.69 + 668.717i) q^{47} +(-1433.80 - 1331.03i) q^{48} +(-1418.88 + 819.191i) q^{49} +(-110.092 + 554.675i) q^{50} +(-490.387 + 307.962i) q^{51} +(390.369 - 104.599i) q^{52} +(1590.04 - 1590.04i) q^{53} +(-264.213 + 604.363i) q^{54} +(-2129.05 + 70.1402i) q^{55} +(389.553 - 674.726i) q^{56} +(-4687.92 - 1071.20i) q^{57} +(1239.68 + 332.170i) q^{58} +(-371.696 + 214.599i) q^{59} +(2240.27 - 2578.55i) q^{60} +(3022.82 - 5235.67i) q^{61} +(42.6796 + 42.6796i) q^{62} +(2197.66 + 416.942i) q^{63} +2891.62i q^{64} +(193.322 + 636.823i) q^{65} +(-613.374 - 324.371i) q^{66} +(-840.754 + 3137.74i) q^{67} +(943.498 + 252.810i) q^{68} +(2275.70 - 4303.27i) q^{69} +(550.960 + 294.347i) q^{70} -615.959 q^{71} +(2157.36 - 753.697i) q^{72} +(-3481.59 + 3481.59i) q^{73} +(-1730.02 - 998.826i) q^{74} +(4365.42 + 3547.36i) q^{75} +(4055.74 + 7024.74i) q^{76} +(-609.020 + 2272.89i) q^{77} +(-48.2894 + 211.329i) q^{78} +(9092.74 + 5249.69i) q^{79} +(-5431.43 + 178.935i) q^{80} +(4085.65 + 5133.63i) q^{81} +(-896.861 - 896.861i) q^{82} +(-320.620 - 1196.57i) q^{83} +(-2006.66 - 3195.33i) q^{84} +(-364.932 + 1566.58i) q^{85} +(-489.847 - 848.441i) q^{86} +(8685.46 - 9356.07i) q^{87} +(622.188 + 2322.04i) q^{88} -12146.5i q^{89} +(660.910 + 1708.85i) q^{90} +735.147 q^{91} +(-7931.55 + 2125.25i) q^{92} +(573.754 - 176.825i) q^{93} +(-2024.54 + 1168.87i) q^{94} +(-11341.9 + 7056.09i) q^{95} +(-5156.13 - 2726.72i) q^{96} +(6311.72 - 1691.22i) q^{97} +(-1048.21 + 1048.21i) q^{98} +(-5704.51 + 3885.15i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{2} + 6 q^{3} - 2 q^{5} + 120 q^{6} - 2 q^{7} - 72 q^{8} - 8 q^{10} - 160 q^{11} + 186 q^{12} - 2 q^{13} + 270 q^{15} + 2044 q^{16} - 908 q^{17} - 1656 q^{18} - 834 q^{20} - 1428 q^{21} + 62 q^{22}+ \cdots + 193724 q^{98}+O(q^{100}) \) 88 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 + 120 * q^6 - 2 * q^7 - 72 * q^8 - 8 * q^10 - 160 * q^11 + 186 * q^12 - 2 * q^13 + 270 * q^15 + 2044 * q^16 - 908 * q^17 - 1656 * q^18 - 834 * q^20 - 1428 * q^21 + 62 * q^22 + 778 * q^23 + 292 * q^25 + 4112 * q^26 + 126 * q^27 - 1096 * q^28 - 4158 * q^30 - 4 * q^31 + 3874 * q^32 + 828 * q^33 - 2528 * q^35 - 7320 * q^36 + 2092 * q^37 - 1590 * q^38 + 510 * q^40 - 4732 * q^41 - 14382 * q^42 - 2 * q^43 + 7308 * q^45 + 2984 * q^46 + 7348 * q^47 + 5850 * q^48 + 12982 * q^50 + 16716 * q^51 - 1058 * q^52 + 25792 * q^53 + 3944 * q^55 - 15312 * q^56 - 4830 * q^57 - 4866 * q^58 - 8238 * q^60 - 5572 * q^61 - 26404 * q^62 - 10476 * q^63 + 22354 * q^65 + 13260 * q^66 - 2732 * q^67 - 39694 * q^68 - 2502 * q^70 + 16712 * q^71 + 80910 * q^72 - 8 * q^73 - 6570 * q^75 - 1632 * q^76 + 14642 * q^77 + 9222 * q^78 - 125516 * q^80 - 67764 * q^81 - 15304 * q^82 - 37022 * q^83 + 14782 * q^85 - 31432 * q^86 - 78786 * q^87 - 4986 * q^88 + 44502 * q^90 - 22360 * q^91 + 47692 * q^92 + 33378 * q^93 + 51120 * q^95 + 163716 * q^96 - 15272 * q^97 + 193724 * q^98

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