LMFDB - Embedded newform 207.4.m.a.4.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,4,Mod(4,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([22, 12])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.4"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.m (of order $33$, degree $20$, 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$1400$
Relative dimension:	$70$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.15
Character	$\chi$	$=$	207.4
Dual form			207.4.m.a.52.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.18200 + 3.06419i) q^{2} +(3.37679 + 3.94934i) q^{3} +(-2.01161 - 5.81215i) q^{4} +(-5.70696 + 2.94214i) q^{5} +(-19.4697 + 1.72968i) q^{6} +(19.1429 - 15.0541i) q^{7} +(-6.67574 - 1.96018i) q^{8} +(-4.19453 + 26.6722i) q^{9} +(3.43731 - 23.9070i) q^{10} +(-31.4455 + 3.00269i) q^{11} +(16.1614 - 27.5709i) q^{12} +(-50.2324 - 39.5032i) q^{13} +(4.35894 + 91.5055i) q^{14} +(-30.8907 - 12.6037i) q^{15} +(59.2493 - 46.5942i) q^{16} +(-70.5244 - 81.3895i) q^{17} +(-72.5763 - 71.0517i) q^{18} +(-22.8478 + 26.3678i) q^{19} +(28.5803 + 27.2513i) q^{20} +(124.095 + 24.7670i) q^{21} +(59.4134 - 102.907i) q^{22} +(-87.4531 - 67.2232i) q^{23} +(-14.8012 - 32.9839i) q^{24} +(-48.5939 + 68.2406i) q^{25} +(230.652 - 67.7257i) q^{26} +(-119.502 + 73.5009i) q^{27} +(-126.005 - 80.9782i) q^{28} +(-48.1171 + 139.025i) q^{29} +(106.024 - 67.1539i) q^{30} +(32.2921 - 30.7905i) q^{31} +(10.8430 + 227.622i) q^{32} +(-118.044 - 114.050i) q^{33} +(403.278 - 38.5083i) q^{34} +(-64.9562 + 142.234i) q^{35} +(163.461 - 29.2747i) q^{36} +(107.075 - 68.8130i) q^{37} +(-30.9420 - 127.545i) q^{38} +(-13.6130 - 331.779i) q^{39} +(43.8653 - 8.45435i) q^{40} +(47.1117 - 24.2878i) q^{41} +(-346.667 + 326.210i) q^{42} +(85.5815 + 81.6018i) q^{43} +(80.7081 + 176.726i) q^{44} +(-54.5354 - 164.558i) q^{45} +(396.808 - 121.292i) q^{46} +(234.939 + 406.927i) q^{47} +(384.089 + 76.6566i) q^{48} +(58.9574 - 243.026i) q^{49} +(-103.070 - 297.802i) q^{50} +(83.2883 - 553.360i) q^{51} +(-128.551 + 371.423i) q^{52} +(-74.3284 - 516.965i) q^{53} +(35.5318 - 526.555i) q^{54} +(170.624 - 109.653i) q^{55} +(-157.301 + 62.9740i) q^{56} +(-181.288 - 1.19517i) q^{57} +(-321.008 - 450.793i) q^{58} +(305.674 + 240.385i) q^{59} +(-11.1147 + 204.895i) q^{60} +(-89.8083 - 370.195i) q^{61} +(23.8865 + 166.134i) q^{62} +(321.231 + 573.727i) q^{63} +(-213.858 - 137.438i) q^{64} +(402.898 + 77.6522i) q^{65} +(607.042 - 112.852i) q^{66} +(-846.962 - 80.8751i) q^{67} +(-331.181 + 573.622i) q^{68} +(-29.8238 - 572.381i) q^{69} +(-294.099 - 509.394i) q^{70} +(476.503 + 1043.40i) q^{71} +(80.2838 - 169.835i) q^{72} +(-162.907 + 188.005i) q^{73} +(-22.7818 + 478.249i) q^{74} +(-433.597 + 38.5206i) q^{75} +(199.214 + 79.7534i) q^{76} +(-556.755 + 530.864i) q^{77} +(1046.34 + 682.229i) q^{78} +(-914.321 + 366.039i) q^{79} +(-201.047 + 440.231i) q^{80} +(-693.812 - 223.755i) q^{81} +(-28.3754 + 197.355i) q^{82} +(-1062.69 - 547.855i) q^{83} +(-105.681 - 771.082i) q^{84} +(641.940 + 256.994i) q^{85} +(-436.783 + 84.1830i) q^{86} +(-711.539 + 279.429i) q^{87} +(215.808 + 41.5936i) q^{88} +(-393.346 + 115.497i) q^{89} +(623.234 + 191.959i) q^{90} -1556.28 q^{91} +(-214.790 + 643.517i) q^{92} +(230.646 + 23.5594i) q^{93} +(-1759.54 - 168.016i) q^{94} +(52.8138 - 217.702i) q^{95} +(-862.343 + 811.456i) q^{96} +(-11.1322 + 233.694i) q^{97} +(616.033 + 710.939i) q^{98} +(51.8112 - 851.316i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) $ 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.18200	+	3.06419i	−0.771454	+	1.08336i	0.222647	+	0.974899i	$0.428530\pi$
$2$	−2.18200	+	3.06419i	−0.771454	+	1.08336i	−0.994101	+	0.108457i	$0.965409\pi$
$3$	3.37679	+	3.94934i	0.649864	+	0.760050i
$3$	3.37679	+	3.94934i	0.649864	+	0.760050i
$4$	−2.01161	−	5.81215i	−0.251451	−	0.726519i
$5$	−5.70696	+	2.94214i	−0.510446	+	0.263153i	−0.694153	−	0.719828i	$-0.744221\pi$
$5$	−5.70696	+	2.94214i	−0.510446	+	0.263153i	0.183706	+	0.982981i	$0.441190\pi$
$6$	−19.4697	+	1.72968i	−1.32475	+	0.117690i
$7$	19.1429	−	15.0541i	1.03362	−	0.812845i	0.0510390	−	0.998697i	$-0.483747\pi$
$7$	19.1429	−	15.0541i	1.03362	−	0.812845i	0.982578	+	0.185851i	$0.0595043\pi$
$8$	−6.67574	−	1.96018i	−0.295029	−	0.0866283i
$9$	−4.19453	+	26.6722i	−0.155353	+	0.987859i
$10$	3.43731	−	23.9070i	0.108697	−	0.756006i
$11$	−31.4455	+	3.00269i	−0.861926	+	0.0823040i	−0.516650	−	0.856197i	$-0.672821\pi$
$11$	−31.4455	+	3.00269i	−0.861926	+	0.0823040i	−0.345277	+	0.938501i	$0.612215\pi$
$12$	16.1614	−	27.5709i	0.388782	−	0.663254i
$13$	−50.2324	−	39.5032i	−1.07169	−	0.842785i	−0.0835734	−	0.996502i	$-0.526633\pi$
$13$	−50.2324	−	39.5032i	−1.07169	−	0.842785i	−0.988115	+	0.153717i	$0.950876\pi$
$14$	4.35894	+	91.5055i	0.0832126	+	1.74685i
$15$	−30.8907	−	12.6037i	−0.531730	−	0.216951i
$16$	59.2493	−	46.5942i	0.925770	−	0.728034i
$17$	−70.5244	−	81.3895i	−1.00616	−	1.16117i	−0.986897	−	0.161353i	$-0.948414\pi$
$17$	−70.5244	−	81.3895i	−1.00616	−	1.16117i	−0.0192610	−	0.999814i	$-0.506131\pi$
$18$	−72.5763	−	71.0517i	−0.950355	−	0.930391i
$19$	−22.8478	+	26.3678i	−0.275876	+	0.318378i	−0.876732	−	0.480979i	$-0.840281\pi$
$19$	−22.8478	+	26.3678i	−0.275876	+	0.318378i	0.600856	+	0.799358i	$0.294827\pi$
$20$	28.5803	+	27.2513i	0.319538	+	0.304679i
$21$	124.095	+	24.7670i	1.28951	+	0.257362i
$22$	59.4134	−	102.907i	0.575772	−	0.997267i
$23$	−87.4531	−	67.2232i	−0.792836	−	0.609435i
$23$	−87.4531	−	67.2232i	−0.792836	−	0.609435i
$24$	−14.8012	−	32.9839i	−0.125887	−	0.280534i
$25$	−48.5939	+	68.2406i	−0.388751	+	0.545925i
$26$	230.652	−	67.7257i	1.73980	−	0.510850i
$27$	−119.502	+	73.5009i	−0.851781	+	0.523898i
$28$	−126.005	−	80.9782i	−0.850451	−	0.546552i
$29$	−48.1171	+	139.025i	−0.308107	+	0.890218i	0.679556	+	0.733624i	$0.262173\pi$
$29$	−48.1171	+	139.025i	−0.308107	+	0.890218i	−0.987663	+	0.156594i	$0.949949\pi$
$30$	106.024	−	67.1539i	0.645241	−	0.408686i
$31$	32.2921	−	30.7905i	0.187091	−	0.178391i	−0.590745	−	0.806859i	$-0.701166\pi$
$31$	32.2921	−	30.7905i	0.187091	−	0.178391i	0.777836	+	0.628467i	$0.216317\pi$
$32$	10.8430	+	227.622i	0.0598996	+	1.25745i
$33$	−118.044	−	114.050i	−0.622690	−	0.601621i
$34$	403.278	−	38.5083i	2.03416	−	0.194239i
$35$	−64.9562	+	142.234i	−0.313703	+	0.686913i
$36$	163.461	−	29.2747i	0.756762	−	0.135531i
$37$	107.075	−	68.8130i	0.475758	−	0.305751i	−0.280698	−	0.959796i	$-0.590566\pi$
$37$	107.075	−	68.8130i	0.475758	−	0.305751i	0.756455	+	0.654045i	$0.226929\pi$
$38$	−30.9420	−	127.545i	−0.132091	−	0.544487i
$39$	−13.6130	−	331.779i	−0.0558928	−	1.36223i
$40$	43.8653	−	8.45435i	0.173393	−	0.0334187i
$41$	47.1117	−	24.2878i	0.179454	−	0.0925149i	−0.366159	−	0.930552i	$-0.619327\pi$
$41$	47.1117	−	24.2878i	0.179454	−	0.0925149i	0.545613	+	0.838037i	$0.316297\pi$
$42$	−346.667	+	326.210i	−1.27362	+	1.19846i
$43$	85.5815	+	81.6018i	0.303513	+	0.289399i	0.826494	−	0.562945i	$-0.190332\pi$
$43$	85.5815	+	81.6018i	0.303513	+	0.289399i	−0.522981	+	0.852344i	$0.675180\pi$
$44$	80.7081	+	176.726i	0.276527	+	0.605510i
$45$	−54.5354	−	164.558i	−0.180659	−	0.545131i
$46$	396.808	−	121.292i	1.27187	−	0.388772i
$47$	234.939	+	406.927i	0.729137	+	1.26290i	0.957248	+	0.289267i	$0.0934117\pi$
$47$	234.939	+	406.927i	0.729137	+	1.26290i	−0.228111	+	0.973635i	$0.573255\pi$
$48$	384.089	+	76.6566i	1.15497	+	0.230509i
$49$	58.9574	−	243.026i	0.171887	−	0.708530i
$50$	−103.070	−	297.802i	−0.291527	−	0.842312i
$51$	83.2883	−	553.360i	0.228680	−	1.51933i
$52$	−128.551	+	371.423i	−0.342823	+	0.990521i
$53$	−74.3284	−	516.965i	−0.192637	−	1.33982i	−0.824992	−	0.565144i	$-0.808821\pi$
$53$	−74.3284	−	516.965i	−0.192637	−	1.33982i	0.632355	−	0.774679i	$-0.282088\pi$
$54$	35.5318	−	526.555i	0.0895421	−	1.32695i
$55$	170.624	−	109.653i	0.418308	−	0.268830i
$56$	−157.301	+	62.9740i	−0.375362	+	0.150272i
$57$	−181.288	−	1.19517i	−0.421266	−	0.00277728i
$58$	−321.008	−	450.793i	−0.726732	−	1.02055i
$59$	305.674	+	240.385i	0.674498	+	0.530431i	0.895623	−	0.444815i	$-0.146730\pi$
$59$	305.674	+	240.385i	0.674498	+	0.530431i	−0.221125	+	0.975245i	$0.570973\pi$
$60$	−11.1147	+	204.895i	−0.0239150	+	0.440865i
$61$	−89.8083	−	370.195i	−0.188504	−	0.777026i	−0.985025	−	0.172414i	$-0.944843\pi$
$61$	−89.8083	−	370.195i	−0.188504	−	0.777026i	0.796520	−	0.604612i	$-0.206672\pi$
$62$	23.8865	+	166.134i	0.0489288	+	0.340307i
$63$	321.231	+	573.727i	0.642401	+	1.14735i
$64$	−213.858	−	137.438i	−0.417691	−	0.268434i
$65$	402.898	+	77.6522i	0.768821	+	0.148178i
$66$	607.042	−	112.852i	1.13215	−	0.210472i
$67$	−846.962	−	80.8751i	−1.54437	−	0.147470i	−0.712195	−	0.701981i	$-0.752299\pi$
$67$	−846.962	−	80.8751i	−1.54437	−	0.147470i	−0.832176	+	0.554512i	$0.812905\pi$
$68$	−331.181	+	573.622i	−0.590611	+	1.02297i
$69$	−29.8238	−	572.381i	−0.0520342	−	0.998645i
$70$	−294.099	−	509.394i	−0.502164	−	0.869774i
$71$	476.503	+	1043.40i	0.796486	+	1.74406i	0.657073	+	0.753827i	$0.271794\pi$
$71$	476.503	+	1043.40i	0.796486	+	1.74406i	0.139413	+	0.990234i	$0.455478\pi$
$72$	80.2838	−	169.835i	0.131410	−	0.277989i
$73$	−162.907	+	188.005i	−0.261190	+	0.301429i	−0.871164	−	0.490992i	$-0.836634\pi$
$73$	−162.907	+	188.005i	−0.261190	+	0.301429i	0.609974	+	0.792421i	$0.291180\pi$
$74$	−22.7818	+	478.249i	−0.0357882	+	0.751288i
$75$	−433.597	+	38.5206i	−0.667566	+	0.0593064i
$76$	199.214	+	79.7534i	0.300677	+	0.120373i
$77$	−556.755	+	530.864i	−0.824001	+	0.785683i
$78$	1046.34	+	682.229i	1.51890	+	0.990349i
$79$	−914.321	+	366.039i	−1.30214	+	0.521299i	−0.916014	−	0.401146i	$-0.868612\pi$
$79$	−914.321	+	366.039i	−1.30214	+	0.521299i	−0.386128	+	0.922445i	$0.626188\pi$
$80$	−201.047	+	440.231i	−0.280971	+	0.615242i
$81$	−693.812	−	223.755i	−0.951731	−	0.306934i
$82$	−28.3754	+	197.355i	−0.0382139	+	0.265784i
$83$	−1062.69	−	547.855i	−1.40537	−	0.724516i	−0.422075	−	0.906561i	$-0.638698\pi$
$83$	−1062.69	−	547.855i	−1.40537	−	0.724516i	−0.983290	+	0.182044i	$0.941729\pi$
$84$	−105.681	−	771.082i	−0.137271	−	1.00157i
$85$	641.940	+	256.994i	0.819154	+	0.327940i
$86$	−436.783	+	84.1830i	−0.547669	+	0.105555i
$87$	−711.539	+	279.429i	−0.876838	+	0.344344i
$88$	215.808	+	41.5936i	0.261423	+	0.0503852i
$89$	−393.346	+	115.497i	−0.468479	+	0.137558i	−0.507448	−	0.861683i	$-0.669411\pi$
$89$	−393.346	+	115.497i	−0.468479	+	0.137558i	0.0389687	+	0.999240i	$0.487593\pi$
$90$	623.234	+	191.959i	0.729941	+	0.224825i
$91$	−1556.28			−1.79277
$92$	−214.790	+	643.517i	−0.243407	+	0.729253i
$93$	230.646	+	23.5594i	0.257170	+	0.0262688i
$94$	−1759.54	−	168.016i	−1.93067	−	0.184357i
$95$	52.8138	−	217.702i	0.0570377	−	0.235113i
$96$	−862.343	+	811.456i	−0.916797	+	0.862697i
$97$	−11.1322	+	233.694i	−0.0116526	+	0.244618i	0.985524	+	0.169533i	$0.0542260\pi$
$97$	−11.1322	+	233.694i	−0.0116526	+	0.244618i	−0.997177	+	0.0750854i	$0.976077\pi$
$98$	616.033	+	710.939i	0.634987	+	0.732814i
$99$	51.8112	−	851.316i	0.0525982	−	0.864248i
$100$	494.376	+	145.162i	0.494376	+	0.145162i
$101$	−577.029	−	297.479i	−0.568480	−	0.293072i	0.149924	−	0.988697i	$-0.452097\pi$
$101$	−577.029	−	297.479i	−0.568480	−	0.293072i	−0.718405	+	0.695625i	$0.755127\pi$
$102$	1513.87	+	1462.64i	1.46956	+	1.41984i
$103$	896.600	+	1259.10i	0.857715	+	1.20449i	0.977341	+	0.211673i	$0.0678911\pi$
$103$	896.600	+	1259.10i	0.857715	+	1.20449i	−0.119626	+	0.992819i	$0.538169\pi$
$104$	257.905	+	362.177i	0.243170	+	0.341485i
$105$	−781.075	+	223.762i	−0.725953	+	0.207970i
$106$	1746.27	+	900.263i	1.60012	+	0.824917i
$107$	996.605	+	292.630i	0.900424	+	0.264388i	0.699005	−	0.715117i	$-0.253626\pi$
$107$	996.605	+	292.630i	0.900424	+	0.264388i	0.201419	+	0.979505i	$0.435445\pi$
$108$	667.588	+	546.707i	0.594803	+	0.487101i
$109$	−830.275	−	958.189i	−0.729596	−	0.841998i	0.262830	−	0.964842i	$-0.415344\pi$
$109$	−830.275	−	958.189i	−0.729596	−	0.841998i	−0.992426	+	0.122844i	$0.960799\pi$
$110$	−36.3028	+	762.090i	−0.0314667	+	0.660567i
$111$	633.336	+	190.508i	0.541564	+	0.162903i
$112$	432.767	−	1783.89i	0.365113	−	1.50502i
$113$	676.928	+	64.6388i	0.563540	+	0.0538115i	0.372939	−	0.927856i	$-0.378350\pi$
$113$	676.928	+	64.6388i	0.563540	+	0.0538115i	0.190601	+	0.981668i	$0.438956\pi$
$114$	399.233	−	552.893i	0.327996	−	0.454238i
$115$	696.872	+	126.341i	0.565075	+	0.102446i
$116$	904.828			0.724234
$117$	1264.34	−	1174.11i	0.999043	−	0.927748i
$118$	−1403.57	+	412.124i	−1.09499	+	0.321518i
$119$	−2575.28	−	496.345i	−1.98383	−	0.382352i
$120$	181.513	+	144.690i	0.138082	+	0.110070i
$121$	−327.141	+	63.0513i	−0.245786	+	0.0473714i
$122$	1330.31	+	532.576i	0.987219	+	0.395223i
$123$	255.007	+	104.045i	0.186937	+	0.0762719i
$124$	−243.918	−	125.748i	−0.176649	−	0.0910689i
$125$	190.770	−	1326.84i	0.136504	−	0.949407i
$126$	−2458.94	−	267.560i	−1.73857	−	0.189176i
$127$	808.427	−	1770.21i	0.564853	−	1.23686i	−0.384640	−	0.923067i	$-0.625674\pi$
$127$	808.427	−	1770.21i	0.564853	−	1.23686i	0.949493	−	0.313789i	$-0.101598\pi$
$128$	−804.680	+	322.145i	−0.555659	+	0.222452i
$129$	−33.2820	+	613.543i	−0.0227156	+	0.418755i
$130$	−1117.07	+	1065.12i	−0.753640	+	0.718594i
$131$	−1199.53	−	480.218i	−0.800024	−	0.320281i	−0.0646195	−	0.997910i	$-0.520583\pi$
$131$	−1199.53	−	480.218i	−0.800024	−	0.320281i	−0.735404	+	0.677629i	$0.763008\pi$
$132$	−425.416	+	915.511i	−0.280513	+	0.603674i
$133$	−40.4290	+	848.709i	−0.0263582	+	0.553326i
$134$	2095.89	−	2418.79i	1.35117	−	1.55934i
$135$	465.741	−	771.057i	0.296923	−	0.491571i
$136$	311.265	+	681.576i	0.196256	+	0.429740i
$137$	−944.789	−	1636.42i	−0.589188	−	1.02050i	−0.994339	−	0.106254i	$-0.966114\pi$
$137$	−944.789	−	1636.42i	−0.589188	−	1.02050i	0.405151	−	0.914250i	$-0.367219\pi$
$138$	1818.96	+	1157.55i	1.12203	+	0.714038i
$139$	−795.891	+	1378.52i	−0.485659	+	0.841186i	−0.999864	−	0.0164810i	$-0.994754\pi$
$139$	−795.891	+	1378.52i	−0.485659	+	0.841186i	0.514205	+	0.857667i	$0.328087\pi$
$140$	957.353	+	91.4161i	0.577936	+	0.0551862i
$141$	−813.750	+	2301.96i	−0.486029	+	1.37490i
$142$	−4236.90	−	816.595i	−2.50389	−	0.482586i
$143$	1698.20	+	1091.37i	0.993081	+	0.638214i
$144$	994.245	+	1775.75i	0.575373	+	1.02763i
$145$	−134.430	−	934.978i	−0.0769915	−	0.535488i
$146$	−220.620	−	909.408i	−0.125059	−	0.515501i
$147$	1158.88	−	587.805i	0.650222	−	0.329805i
$148$	−615.344	−	483.912i	−0.341763	−	0.268766i
$149$	−6.96271	−	9.77775i	−0.00382824	−	0.00537601i	0.812657	−	0.582742i	$-0.198020\pi$
$149$	−6.96271	−	9.77775i	−0.00382824	−	0.00537601i	−0.816486	+	0.577366i	$0.804081\pi$
$150$	828.074	−	1412.68i	0.450747	−	0.768964i
$151$	1009.48	−	404.135i	0.544042	−	0.217802i	−0.0833289	−	0.996522i	$-0.526555\pi$
$151$	1009.48	−	404.135i	0.544042	−	0.217802i	0.627371	+	0.778720i	$0.284131\pi$
$152$	204.212	−	131.239i	0.108972	−	0.0700321i
$153$	2466.65	−	1539.65i	1.30338	−	0.813551i
$154$	−411.832	−	2864.35i	−0.215496	−	1.49881i
$155$	−93.6999	+	270.728i	−0.0485558	+	0.140293i
$156$	−1900.96	+	746.528i	−0.975634	+	0.383142i
$157$	866.815	+	2504.50i	0.440633	+	1.27313i	0.918754	+	0.394831i	$0.129197\pi$
$157$	866.815	+	2504.50i	0.440633	+	1.27313i	−0.478121	+	0.878294i	$0.658682\pi$
$158$	873.437	−	3600.36i	0.439791	−	1.81284i
$159$	1790.68	−	2039.23i	0.893145	−	1.01712i
$160$	−731.578	−	1267.13i	−0.361477	−	0.626097i
$161$	−2686.09	+	29.6837i	−1.31487	+	0.0145305i
$162$	2199.53	−	1637.74i	1.06674	−	0.794278i
$163$	−936.874	−	2051.47i	−0.450194	−	0.985788i	−0.989614	−	0.143751i	$-0.954084\pi$
$163$	−936.874	−	2051.47i	−0.450194	−	0.985788i	0.539420	−	0.842037i	$-0.318644\pi$
$164$	−235.934	−	224.963i	−0.112338	−	0.107114i
$165$	1009.22	+	303.575i	0.476168	+	0.143232i
$166$	3997.52	−	2060.87i	1.86908	−	0.963580i
$167$	−499.926	+	96.3528i	−0.231649	+	0.0446467i	−0.303755	−	0.952750i	$-0.598240\pi$
$167$	−499.926	+	96.3528i	−0.231649	+	0.0446467i	0.0721054	+	0.997397i	$0.477028\pi$
$168$	−779.880	−	408.586i	−0.358149	−	0.187638i
$169$	444.828	+	1833.60i	0.202470	+	0.834594i
$170$	−2188.19	+	1406.27i	−0.987216	+	0.634445i
$171$	−607.451	−	720.002i	−0.271655	−	0.321988i
$172$	302.126	−	661.564i	0.133935	−	0.293278i
$173$	−2522.76	+	240.894i	−1.10868	+	0.105866i	−0.633294	−	0.773911i	$-0.718298\pi$
$173$	−2522.76	+	240.894i	−1.10868	+	0.105866i	−0.475386	+	0.879777i	$0.657692\pi$
$174$	696.356	−	2790.01i	0.303394	−	1.21557i
$175$	97.0751	+	2037.86i	0.0419325	+	0.880272i
$176$	−1723.22	+	1643.09i	−0.738026	+	0.703706i
$177$	82.8377	+	2018.94i	0.0351777	+	0.857360i
$178$	504.378	−	1457.30i	0.212386	−	0.613649i
$179$	3401.95	+	2186.30i	1.42052	+	0.912914i	0.999984	+	0.00563888i	$0.00179492\pi$
$179$	3401.95	+	2186.30i	1.42052	+	0.912914i	0.420538	+	0.907275i	$0.361841\pi$
$180$	−846.733	+	647.994i	−0.350621	+	0.268326i
$181$	−1086.35	+	318.980i	−0.446118	+	0.130992i	−0.497073	−	0.867709i	$-0.665592\pi$
$181$	−1086.35	+	318.980i	−0.446118	+	0.130992i	0.0509544	+	0.998701i	$0.483774\pi$
$182$	3395.80	−	4768.73i	1.38304	−	1.94221i
$183$	1158.76	−	1604.75i	0.468077	−	0.648234i
$184$	452.045	+	620.188i	0.181115	+	0.248483i
$185$	−408.616	+	707.743i	−0.162389	+	0.281267i
$186$	−575.460	+	655.337i	−0.226854	+	0.258342i
$187$	2462.07	+	2347.57i	0.962802	+	0.918030i
$188$	1892.52	−	2184.08i	0.734181	−	0.847290i
$189$	−1181.11	+	3206.01i	−0.454567	+	1.23388i
$190$	551.840	+	636.857i	0.210709	+	0.243171i
$191$	2011.75	−	1582.06i	0.762120	−	0.599338i	−0.159606	−	0.987181i	$-0.551022\pi$
$191$	2011.75	−	1582.06i	0.762120	−	0.599338i	0.921725	+	0.387843i	$0.126780\pi$
$192$	−179.364	−	1308.70i	−0.0674193	−	0.491912i
$193$	74.1403	+	1556.40i	0.0276515	+	0.580476i	0.969597	+	0.244709i	$0.0786925\pi$
$193$	74.1403	+	1556.40i	0.0276515	+	0.580476i	−0.941945	+	0.335767i	$0.891005\pi$
$194$	−691.792	−	544.031i	−0.256019	−	0.201336i
$195$	1053.83	+	1853.40i	0.387006	+	0.680638i
$196$	−1531.10	+	146.202i	−0.557981	+	0.0532808i
$197$	537.650	−	3739.44i	0.194447	−	1.35241i	−0.625616	−	0.780131i	$-0.715152\pi$
$197$	537.650	−	3739.44i	0.194447	−	1.35241i	0.820062	−	0.572274i	$-0.193939\pi$
$198$	2495.55	+	2016.33i	0.895711	+	0.723710i
$199$	2570.21	+	754.683i	0.915566	+	0.268834i	0.705382	−	0.708827i	$-0.250775\pi$
$199$	2570.21	+	754.683i	0.915566	+	0.268834i	0.210184	+	0.977662i	$0.432594\pi$
$200$	458.164	−	360.304i	0.161985	−	0.127387i
$201$	−2540.61	−	3618.04i	−0.891547	−	1.26963i
$202$	2170.61	−	1119.03i	0.756058	−	0.389775i
$203$	1171.80	+	3385.70i	0.405144	+	1.17059i
$204$	−3383.76	+	629.058i	−1.16133	+	0.215897i
$205$	−197.407	+	277.219i	−0.0672560	+	0.0944478i
$206$	−5814.51			−1.96658
$207$	2159.82	−	2050.60i	0.725206	−	0.688532i
$208$	−4816.85			−1.60571
$209$	639.288	−	897.755i	0.211581	−	0.297124i
$210$	1018.66	−	2881.61i	0.334734	−	0.946905i
$211$	−599.822	−	1733.07i	−0.195704	−	0.565449i	0.803865	−	0.594812i	$-0.202773\pi$
$211$	−599.822	−	1733.07i	−0.195704	−	0.565449i	−0.999569	+	0.0293629i	$0.990652\pi$
$212$	−2855.16	+	1471.94i	−0.924968	+	0.476854i
$213$	−2511.67	+	5405.20i	−0.807967	+	1.73877i
$214$	−3071.27	+	2415.27i	−0.981063	+	0.771517i
$215$	−728.495	−	213.905i	−0.231083	−	0.0678522i
$216$	941.836	−	256.429i	0.296684	−	0.0807767i
$217$	154.640	−	1075.55i	0.0483763	−	0.336465i
$218$	4747.74	−	453.354i	1.47503	−	0.140849i
$219$	−1292.60	−	8.52172i	−0.398840	−	0.00262943i
$220$	−980.551	−	771.114i	−0.300494	−	0.236311i
$221$	327.464	+	6874.32i	0.0996726	+	2.09238i
$222$	−1965.70	+	1524.97i	−0.594274	+	0.461034i
$223$	−2859.86	+	2249.02i	−0.858792	+	0.675362i	−0.947172	−	0.320725i	$-0.896073\pi$
$223$	−2859.86	+	2249.02i	−0.858792	+	0.675362i	0.0883802	+	0.996087i	$0.471831\pi$
$224$	3634.22	+	4194.11i	1.08402	+	1.25103i
$225$	−1616.30	−	1582.34i	−0.478903	−	0.468843i
$226$	−1675.12	+	1933.20i	−0.493042	+	0.569001i
$227$	−1684.69	−	1606.35i	−0.492584	−	0.469678i	0.402599	−	0.915376i	$-0.368107\pi$
$227$	−1684.69	−	1606.35i	−0.492584	−	0.469678i	−0.895183	+	0.445698i	$0.852955\pi$
$228$	357.733	+	1056.08i	0.103910	+	0.306756i
$229$	−411.741	+	713.156i	−0.118815	+	0.205793i	−0.919298	−	0.393562i	$-0.871243\pi$
$229$	−411.741	+	713.156i	−0.118815	+	0.205793i	0.800483	+	0.599355i	$0.204576\pi$
$230$	−1907.71	+	1859.67i	−0.546916	+	0.533145i
$231$	−3976.61	−	406.192i	−1.13265	−	0.115695i
$232$	593.731	−	833.778i	0.168019	−	0.235949i
$233$	2099.37	−	616.431i	0.590276	−	0.173321i	0.0270651	−	0.999634i	$-0.491384\pi$
$233$	2099.37	−	616.431i	0.590276	−	0.173321i	0.563211	+	0.826313i	$0.309566\pi$
$234$	838.913	+	6436.09i	0.234365	+	1.79803i
$235$	−2538.03	−	1631.09i	−0.704522	−	0.452769i
$236$	782.257	−	2260.18i	0.215765	−	0.623413i
$237$	−4533.09	−	2374.93i	−1.24243	−	0.650920i
$238$	7140.18	−	6808.14i	1.94466	−	1.85423i
$239$	−144.962	−	3043.12i	−0.0392334	−	0.823611i	−0.929645	−	0.368456i	$-0.879887\pi$
$239$	−144.962	−	3043.12i	−0.0392334	−	0.823611i	0.890412	−	0.455156i	$-0.150416\pi$
$240$	−2417.51	+	692.568i	−0.650208	+	0.186271i
$241$	122.183	−	11.6671i	0.0326577	−	0.00311843i	−0.0787144	−	0.996897i	$-0.525082\pi$
$241$	122.183	−	11.6671i	0.0326577	−	0.00311843i	0.111372	+	0.993779i	$0.464475\pi$
$242$	520.621	−	1140.00i	0.138293	−	0.302819i
$243$	−1459.18	−	3495.67i	−0.385211	−	0.922829i
$244$	−1970.97	+	1266.67i	−0.517125	+	0.332336i
$245$	378.549	+	1560.40i	0.0987126	+	0.406899i
$246$	−875.241	+	554.364i	−0.226843	+	0.143679i
$247$	2189.31	−	421.955i	0.563978	−	0.108698i
$248$	−275.929	+	142.251i	−0.0706511	+	0.0364232i
$249$	−1424.82	−	6046.91i	−0.362628	−	1.53899i
$250$	3649.43	+	3479.72i	0.923240	+	0.880307i
$251$	−2104.31	−	4607.80i	−0.529175	−	1.15873i	−0.965848	−	0.259111i	$-0.916571\pi$
$251$	−2104.31	−	4607.80i	−0.529175	−	1.15873i	0.436673	−	0.899620i	$-0.356157\pi$
$252$	2688.40	−	3021.15i	0.672036	−	0.755217i
$253$	2951.86	+	1851.28i	0.733525	+	0.460035i
$254$	3660.27	+	6339.78i	0.904197	+	1.56611i
$255$	1152.74	+	3403.05i	0.283088	+	0.835715i
$256$	1248.16	−	5145.00i	0.304727	−	1.25610i
$257$	432.421	+	1249.40i	0.104956	+	0.303251i	0.985235	−	0.171205i	$-0.0547661\pi$
$257$	432.421	+	1249.40i	0.104956	+	0.303251i	−0.880279	+	0.474456i	$0.842645\pi$
$258$	−1807.39	−	1440.73i	−0.436137	−	0.347660i
$259$	1013.80	−	2929.20i	0.243223	−	0.702747i
$260$	−359.145	−	2497.91i	−0.0856663	−	0.595822i
$261$	−3506.28	−	1866.53i	−0.831544	−	0.442665i
$262$	4088.85	−	2627.74i	0.964160	−	0.619628i
$263$	−4289.31	+	1717.18i	−1.00567	+	0.402608i	−0.815259	−	0.579097i	$-0.803405\pi$
$263$	−4289.31	+	1717.18i	−1.00567	+	0.402608i	−0.190408	+	0.981705i	$0.560981\pi$
$264$	564.472	+	992.752i	0.131594	+	0.231438i
$265$	1945.17	+	2731.62i	0.450910	+	0.633214i
$266$	−2512.39	−	1975.77i	−0.579115	−	0.455421i
$267$	−1784.39	−	1163.45i	−0.408999	−	0.266674i
$268$	1233.69	+	5085.36i	0.281194	+	1.15910i
$269$	727.794	+	5061.92i	0.164961	+	1.14733i	0.889114	+	0.457687i	$0.151322\pi$
$269$	727.794	+	5061.92i	0.164961	+	1.14733i	−0.724153	+	0.689639i	$0.757769\pi$
$270$	1346.42	+	3109.57i	0.303484	+	0.700898i
$271$	6095.97	+	3917.65i	1.36644	+	0.878155i	0.998660	−	0.0517594i	$-0.0164829\pi$
$271$	6095.97	+	3917.65i	1.36644	+	0.878155i	0.367776	+	0.929914i	$0.380119\pi$
$272$	−7970.80	−	1536.25i	−1.77684	−	0.342458i
$273$	−5255.22	−	6146.26i	−1.16506	−	1.36259i
$274$	7075.84	+	675.661i	1.56010	+	0.148971i
$275$	1323.16	−	2291.77i	0.290143	−	0.502543i
$276$	−3266.77	+	1324.74i	−0.712451	+	0.288914i
$277$	2111.34	+	3656.96i	0.457973	+	0.793232i	0.998854	−	0.0478672i	$-0.0152424\pi$
$277$	2111.34	+	3656.96i	0.457973	+	0.793232i	−0.540881	+	0.841099i	$0.681909\pi$
$278$	−2487.43	−	5446.71i	−0.536640	−	1.17508i
$279$	685.799	+	990.453i	0.147160	+	0.212534i
$280$	712.435	−	822.194i	0.152058	−	0.175484i
$281$	−36.0808	+	757.429i	−0.00765978	+	0.160799i	0.991797	+	0.127827i	$0.0408002\pi$
$281$	−36.0808	+	757.429i	−0.00765978	+	0.160799i	−0.999456	+	0.0329718i	$0.989503\pi$
$282$	−5278.06	−	7516.38i	−1.11455	−	1.58721i
$283$	943.273	+	377.629i	0.198133	+	0.0793206i	0.468607	−	0.883407i	$-0.344756\pi$
$283$	943.273	+	377.629i	0.198133	+	0.0793206i	−0.270474	+	0.962727i	$0.587180\pi$
$284$	5105.84	−	4868.41i	1.06682	−	1.01721i
$285$	1038.12	−	526.554i	0.215764	−	0.109440i
$286$	−7049.63	+	2822.25i	−1.45753	+	0.583507i
$287$	536.222	−	1174.16i	0.110286	−	0.241493i
$288$	−6116.67	−	665.563i	−1.25149	−	0.136176i
$289$	−951.367	+	6616.90i	−0.193643	+	1.34681i
$290$	3158.28	+	1628.21i	0.639520	+	0.329695i
$291$	−960.526	+	745.170i	−0.193495	+	0.150112i
$292$	1420.42	+	568.651i	0.284671	+	0.113965i
$293$	5621.82	−	1083.52i	1.12092	−	0.216040i	0.405066	−	0.914288i	$-0.367249\pi$
$293$	5621.82	−	1083.52i	1.12092	−	0.216040i	0.715856	+	0.698248i	$0.246037\pi$
$294$	−727.525	+	4833.62i	−0.144320	+	0.958851i
$295$	−2451.72	−	472.530i	−0.483879	−	0.0932601i
$296$	−849.691	+	249.492i	−0.166849	+	0.0489913i
$297$	3537.09	−	2670.10i	0.691053	−	0.521666i
$298$	45.1536			0.00877744
$299$	1737.44	+	6831.45i	0.336050	+	1.32131i
$300$	1096.11	+	2442.64i	0.210947	+	0.470087i
$301$	2866.72	+	273.738i	0.548953	+	0.0524186i
$302$	−964.341	+	3975.07i	−0.183747	+	0.757415i
$303$	−773.662	−	3283.41i	−0.146686	−	0.622531i
$304$	−125.132	+	2626.85i	−0.0236080	+	0.495593i
$305$	1601.70	+	1848.46i	0.300698	+	0.347024i
$306$	−664.459	+	10917.8i	−0.124133	+	2.03964i
$307$	−6499.72	−	1908.49i	−1.20833	−	0.354799i	−0.385301	−	0.922791i	$-0.625902\pi$
$307$	−6499.72	−	1908.49i	−1.20833	−	0.354799i	−0.823034	+	0.567992i	$0.807720\pi$
$308$	4205.44	+	2168.05i	0.778009	+	0.401092i
$309$	−1944.97	+	7792.69i	−0.358076	+	1.43466i
$310$	−625.110	−	877.844i	−0.114529	−	0.160833i
$311$	−4307.24	−	6048.67i	−0.785341	−	1.10286i	−0.992221	−	0.124491i	$-0.960270\pi$
$311$	−4307.24	−	6048.67i	−0.785341	−	1.10286i	0.206879	−	0.978366i	$-0.433669\pi$
$312$	−559.467	+	2241.55i	−0.101518	+	0.406740i
$313$	8296.29	+	4277.04i	1.49819	+	0.772372i	0.995738	−	0.0922319i	$-0.0294001\pi$
$313$	8296.29	+	4277.04i	1.49819	+	0.772372i	0.502455	+	0.864604i	$0.332430\pi$
$314$	−9565.66	−	2808.73i	−1.71918	−	0.504796i
$315$	−3521.24	−	2329.13i	−0.629839	−	0.416608i
$316$	3966.73	+	4577.85i	0.706158	+	0.814950i
$317$	−33.4769	+	702.766i	−0.00593138	+	0.124515i	0.993960	+	0.109747i	$0.0350040\pi$
$317$	−33.4769	+	702.766i	−0.00593138	+	0.124515i	−0.999891	+	0.0147681i	$0.995299\pi$
$318$	2341.34	+	9936.59i	0.412880	+	1.75225i
$319$	1095.62	−	4516.20i	0.192297	−	0.792661i
$320$	1624.84	+	155.154i	0.283848	+	0.0271042i
$321$	2209.64	+	4924.08i	0.384205	+	0.856184i
$322$	5770.09	−	8295.46i	0.998617	−	1.43568i
$323$	3757.39			0.647266
$324$	95.1786	+	4482.65i	0.0163201	+	0.768629i
$325$	5136.71	−	1508.27i	0.876717	−	0.257427i
$326$	8330.36	+	1605.54i	1.41526	+	0.272770i
$327$	980.543	−	6514.64i	0.165823	−	1.10171i
$328$	−362.114	+	69.7917i	−0.0609585	+	0.0117488i
$329$	10623.3	+	4252.94i	1.78019	+	0.712682i
$330$	−3132.34	+	2430.05i	−0.522514	+	0.405363i
$331$	−5101.00	−	2629.75i	−0.847058	−	0.436689i	−0.0206678	−	0.999786i	$-0.506579\pi$
$331$	−5101.00	−	2629.75i	−0.847058	−	0.436689i	−0.826390	+	0.563098i	$0.809610\pi$
$332$	−1046.50	+	7278.58i	−0.172995	+	1.20320i
$333$	1386.26	+	3144.56i	0.228128	+	0.517481i
$334$	795.596	−	1742.11i	0.130339	−	0.285402i
$335$	5071.52	−	2030.33i	0.827125	−	0.331131i
$336$	8506.55	−	4314.69i	1.38116	−	0.700552i
$337$	2244.99	−	2140.60i	0.362886	−	0.346011i	−0.486597	−	0.873626i	$-0.661762\pi$
$337$	2244.99	−	2140.60i	0.362886	−	0.346011i	0.849484	+	0.527615i	$0.176914\pi$
$338$	−6589.13	−	2637.89i	−1.06036	−	0.424504i
$339$	2030.57	+	2891.69i	0.325325	+	0.463289i
$340$	202.358	−	4248.02i	0.0322777	−	0.677592i
$341$	−922.989	+	1065.19i	−0.146577	+	0.169159i
$342$	3531.69	−	290.301i	0.558397	−	0.0458996i
$343$	940.092	+	2058.51i	0.147989	+	0.324050i
$344$	−411.366	−	712.508i	−0.0644750	−	0.111674i
$345$	1854.23	+	3178.81i	0.289357	+	0.496062i
$346$	4766.52	−	8255.85i	0.740605	−	1.28277i
$347$	−2972.61	−	283.850i	−0.459880	−	0.0439132i	−0.137454	−	0.990508i	$-0.543892\pi$
$347$	−2972.61	−	283.850i	−0.459880	−	0.0439132i	−0.322425	+	0.946595i	$0.604498\pi$
$348$	3055.42	+	3573.47i	0.470654	+	0.550454i
$349$	−7762.27	−	1496.05i	−1.19056	−	0.229461i	−0.444770	−	0.895645i	$-0.646715\pi$
$349$	−7762.27	−	1496.05i	−1.19056	−	0.229461i	−0.745788	+	0.666184i	$0.767927\pi$
$350$	−6456.21	−	4149.15i	−0.985997	−	0.633662i
$351$	8906.36	+	1028.57i	1.35438	+	0.156413i
$352$	−1024.44	−	7125.15i	−0.155122	−	1.07890i
$353$	−15.3271	−	63.1790i	−0.00231098	−	0.00952600i	0.970644	−	0.240519i	$-0.0773177\pi$
$353$	−15.3271	−	63.1790i	−0.00231098	−	0.00952600i	−0.972955	+	0.230993i	$0.925803\pi$
$354$	−6367.17	−	4151.50i	−0.955965	−	0.623304i
$355$	−5789.21	−	4552.68i	−0.865519	−	0.680651i
$356$	1462.54	+	2053.85i	0.217738	+	0.305770i
$357$	−6735.97	−	11846.7i	−0.998614	−	1.75629i
$358$	−14122.3	+	5653.71i	−2.08488	+	0.834660i
$359$	−10199.1	+	6554.56i	−1.49941	+	0.963611i	−0.504437	+	0.863449i	$0.668300\pi$
$359$	−10199.1	+	6554.56i	−1.49941	+	0.963611i	−0.994971	+	0.100162i	$0.968064\pi$
$360$	41.5015	+	1205.45i	0.00607588	+	0.176479i
$361$	802.900	+	5584.29i	0.117058	+	0.814155i
$362$	1392.99	−	4024.79i	0.202249	−	0.584360i
$363$	−1353.70	−	1079.08i	−0.195732	−	0.156025i
$364$	3130.61	+	9045.31i	0.450793	+	1.30248i
$365$	376.568	−	1552.24i	0.0540013	−	0.222597i
$366$	2388.86	+	7052.25i	0.341169	+	1.00718i
$367$	4688.78	+	8121.21i	0.666901	+	1.15511i	0.978766	+	0.204980i	$0.0657128\pi$
$367$	4688.78	+	8121.21i	0.666901	+	1.15511i	−0.311866	+	0.950126i	$0.600954\pi$
$368$	−8313.74	+	91.8744i	−1.17767	+	0.0130144i
$369$	450.197	+	1358.45i	0.0635130	+	0.191648i
$370$	−1277.06	−	2796.37i	−0.179436	−	0.392910i
$371$	−9205.30	−	8777.24i	−1.28818	−	1.22828i
$372$	−327.037	−	1387.94i	−0.0455809	−	0.193444i
$373$	−1368.02	+	705.264i	−0.189902	+	0.0979012i	−0.550555	−	0.834799i	$-0.685584\pi$
$373$	−1368.02	+	705.264i	−0.189902	+	0.0979012i	0.360653	+	0.932700i	$0.382554\pi$
$374$	−12565.7	+	2421.83i	−1.73731	+	0.334839i
$375$	5884.32	−	3727.04i	0.810307	−	0.513236i
$376$	−770.747	−	3177.06i	−0.105713	−	0.435757i
$377$	7908.97	−	5082.78i	1.08046	−	0.694368i
$378$	−7246.63	−	10614.7i	−0.986049	−	1.44434i
$379$	−333.008	+	729.187i	−0.0451332	+	0.0988280i	−0.930855	−	0.365388i	$-0.880936\pi$
$379$	−333.008	+	729.187i	−0.0451332	+	0.0988280i	0.885722	+	0.464216i	$0.153664\pi$
$380$	−1371.56	+	130.968i	−0.185156	+	0.0176803i
$381$	9721.04	−	2784.88i	1.30715	−	0.374471i
$382$	458.087	+	9616.43i	0.0613554	+	1.28801i
$383$	8348.13	−	7959.92i	1.11376	−	1.06197i	0.116123	−	0.993235i	$-0.462953\pi$
$383$	8348.13	−	7959.92i	1.11376	−	1.06197i	0.997635	−	0.0687313i	$-0.0218951\pi$
$384$	−3989.50	−	2090.13i	−0.530177	−	0.277765i
$385$	1615.50	−	4667.67i	0.213853	−	0.617888i
$386$	−4930.88	−	3168.88i	−0.650194	−	0.417854i
$387$	−2535.47	+	1940.37i	−0.333037	+	0.254869i
$388$	1380.66	−	405.397i	0.180650	−	0.0530436i
$389$	599.117	−	841.342i	0.0780885	−	0.109660i	−0.773684	−	0.633571i	$-0.781588\pi$
$389$	599.117	−	841.342i	0.0780885	−	0.109660i	0.851773	+	0.523911i	$0.175528\pi$
$390$	−7978.62	−	814.980i	−1.03593	−	0.105816i
$391$	696.312	+	11858.6i	0.0900614	+	1.53380i
$392$	−869.957	+	1506.81i	−0.112090	+	0.194146i
$393$	−2154.01	−	6358.93i	−0.276477	−	0.816197i
$394$	10285.2	+	9806.92i	1.31513	+	1.25397i
$395$	4141.06	−	4779.04i	0.527492	−	0.608758i
$396$	−5052.20	+	1411.38i	−0.641118	+	0.179102i
$397$	−7786.26	−	8985.82i	−0.984336	−	1.13598i	−0.990708	−	0.136004i	$-0.956574\pi$
$397$	−7786.26	−	8985.82i	−0.984336	−	1.13598i	0.00637273	−	0.999980i	$-0.497971\pi$
$398$	−7920.71	+	6228.91i	−0.997561	+	0.784491i
$399$	−3488.36	+	2706.25i	−0.437685	+	0.339553i
$400$	300.458	+	6307.40i	0.0375573	+	0.788425i
$401$	−5172.03	−	4067.33i	−0.644087	−	0.506515i	0.241855	−	0.970312i	$-0.422244\pi$
$401$	−5172.03	−	4067.33i	−0.644087	−	0.506515i	−0.885941	+	0.463797i	$0.846487\pi$
$402$	16630.0	+	109.636i	2.06325	+	0.0136024i
$403$	−2838.43	+	271.037i	−0.350849	+	0.0335020i
$404$	−568.239	+	3952.19i	−0.0699776	+	0.486705i
$405$	4617.88	−	764.334i	0.566578	−	0.0937779i
$406$	−12931.3	−	3796.97i	−1.58071	−	0.464140i
$407$	−3160.41	+	2485.37i	−0.384903	+	0.302691i
$408$	−1640.69	+	3530.83i	−0.199084	+	0.428437i
$409$	−11938.1	+	6154.50i	−1.44327	+	0.744060i	−0.989154	−	0.146881i	$-0.953077\pi$
$409$	−11938.1	+	6154.50i	−1.44327	+	0.744060i	−0.454120	+	0.890940i	$0.650046\pi$
$410$	−418.710	−	1209.78i	−0.0504357	−	0.145724i
$411$	3272.43	−	9257.15i	0.392742	−	1.11100i
$412$	5514.47	−	7743.98i	0.659413	−	0.926016i
$413$	9470.25			1.12833
$414$	1570.70	+	11092.5i	0.186463	+	1.31683i
$415$	7676.60			0.908022
$416$	8447.13	−	11862.3i	0.995565	−	1.39807i
$417$	−8131.82	+	1511.75i	−0.954956	+	0.177531i
$418$	1355.97	+	3917.81i	0.158666	+	0.458436i
$419$	6488.96	−	3345.29i	0.756578	−	0.390043i	−0.0363651	−	0.999339i	$-0.511578\pi$
$419$	6488.96	−	3345.29i	0.756578	−	0.390043i	0.792943	+	0.609295i	$0.208548\pi$
$420$	2871.75	+	4089.60i	0.333636	+	0.475124i
$421$	−8575.49	+	6743.84i	−0.992741	+	0.780700i	−0.975690	−	0.219155i	$-0.929670\pi$
$421$	−8575.49	+	6743.84i	−0.992741	+	0.780700i	−0.0170507	+	0.999855i	$0.505428\pi$
$422$	6619.29	+	1943.60i	0.763559	+	0.224201i
$423$	−11839.1	+	4559.48i	−1.36084	+	0.524089i
$424$	−517.145	+	3596.82i	−0.0592330	+	0.411974i
$425$	8981.12	−	857.593i	1.02506	−	0.0978809i
$426$	−11082.1	−	19490.4i	−1.26040	−	2.21670i
$427$	−7292.14	−	5734.60i	−0.826443	−	0.649922i
$428$	−303.968	−	6381.07i	−0.0343291	−	0.720656i
$429$	1424.29	+	10392.1i	0.160293	+	1.16954i
$430$	2245.03	−	1765.51i	0.251778	−	0.198001i
$431$	−6701.01	−	7733.38i	−0.748901	−	0.864278i	0.245560	−	0.969381i	$-0.421028\pi$
$431$	−6701.01	−	7733.38i	−0.748901	−	0.864278i	−0.994461	+	0.105103i	$0.966483\pi$
$432$	−3655.67	+	9922.95i	−0.407138	+	1.10513i
$433$	10019.7	−	11563.3i	1.11204	−	1.28337i	0.156774	−	0.987635i	$-0.449891\pi$
$433$	10019.7	−	11563.3i	1.11204	−	1.28337i	0.955271	−	0.295733i	$-0.0955639\pi$
$434$	2958.26	+	2820.69i	0.327191	+	0.311976i
$435$	3238.60	−	3688.14i	0.356964	−	0.406512i
$436$	−3898.95	+	6753.18i	−0.428271	+	0.741786i
$437$	3770.64	−	770.041i	0.412756	−	0.0842930i
$438$	2846.57	−	3942.19i	0.310535	−	0.430057i
$439$	6269.36	−	8804.08i	0.681595	−	0.957166i	−0.318363	−	0.947969i	$-0.603133\pi$
$439$	6269.36	−	8804.08i	0.681595	−	0.957166i	0.999958	−	0.00919709i	$-0.00292757\pi$
$440$	−1353.98	+	397.565i	−0.146701	+	0.0430754i
$441$	6234.73	+	2591.90i	0.673224	+	0.279873i
$442$	−21778.8	−	13996.4i	−2.34369	−	1.50620i
$443$	−2358.22	+	6813.63i	−0.252918	+	0.730757i	0.745049	+	0.667010i	$0.232426\pi$
$443$	−2358.22	+	6813.63i	−0.252918	+	0.730757i	−0.997966	+	0.0637470i	$0.979695\pi$
$444$	−166.758	−	4064.27i	−0.0178243	−	0.434419i
$445$	1905.00	−	1816.42i	0.202934	−	0.193498i
$446$	−651.208	−	13670.5i	−0.0691381	−	1.45139i
$447$	15.1040	−	60.5155i	0.00159820	−	0.00640333i
$448$	−6162.86	+	588.482i	−0.649928	+	0.0620606i
$449$	247.594	−	542.155i	0.0260238	−	0.0569841i	−0.896174	−	0.443703i	$-0.853664\pi$
$449$	247.594	−	542.155i	0.0260238	−	0.0569841i	0.922198	+	0.386719i	$0.126392\pi$
$450$	8375.37	−	1499.97i	0.877375	−	0.157132i
$451$	−1408.52	+	905.204i	−0.147062	+	0.0945108i
$452$	−986.021	−	4064.43i	−0.102607	−	0.422953i
$453$	5004.87	+	2622.10i	0.519094	+	0.271958i
$454$	8598.15	−	1657.16i	0.888835	−	0.171309i
$455$	8881.60	−	4578.78i	0.915112	−	0.471773i
$456$	1207.89	+	363.334i	0.124045	+	0.0373129i
$457$	−7970.63	−	7599.98i	−0.815865	−	0.777926i	0.162082	−	0.986777i	$-0.448179\pi$
$457$	−7970.63	−	7599.98i	−0.815865	−	0.777926i	−0.977947	+	0.208851i	$0.933028\pi$
$458$	−1286.83	−	2817.76i	−0.131287	−	0.287479i
$459$	14410.0	+	4542.57i	1.46536	+	0.461937i
$460$	−667.519	−	4304.47i	−0.0676592	−	0.436298i
$461$	1014.61	+	1757.36i	0.102506	+	0.177545i	0.912716	−	0.408594i	$-0.133981\pi$
$461$	1014.61	+	1757.36i	0.102506	+	0.177545i	−0.810211	+	0.586139i	$0.800647\pi$
$462$	9921.62	−	11298.8i	0.999125	−	1.13781i
$463$	2136.97	−	8808.69i	0.214499	−	0.884179i	−0.758184	−	0.652041i	$-0.773913\pi$
$463$	2136.97	−	8808.69i	0.214499	−	0.884179i	0.972683	−	0.232138i	$-0.0745719\pi$
$464$	3626.86	+	10479.1i	0.362872	+	1.04845i
$465$	−1385.60	+	544.140i	−0.138184	+	0.0542664i
$466$	−2691.97	+	7777.94i	−0.267603	+	0.773189i
$467$	382.371	+	2659.45i	0.0378887	+	0.263522i	0.999957	−	0.00928744i	$-0.00295633\pi$
$467$	382.371	+	2659.45i	0.0378887	+	0.263522i	−0.962068	+	0.272809i	$0.912047\pi$
$468$	−9367.45	−	4986.67i	−0.925236	−	0.492541i
$469$	−17430.8	+	11202.1i	−1.71616	+	1.10291i
$470$	10536.0	−	4217.96i	1.03402	−	0.413958i
$471$	−6964.05	+	11880.5i	−0.681288	+	1.16226i
$472$	−1569.41	−	2203.92i	−0.153046	−	0.214923i
$473$	−2936.18	−	2309.04i	−0.285425	−	0.224460i
$474$	17168.4	−	8708.16i	1.66366	−	0.843838i
$475$	−689.089	−	2840.46i	−0.0665633	−	0.274378i
$476$	2295.62	+	15966.4i	0.221050	+	1.53743i
$477$	14100.4	+	185.927i	1.35348	+	0.0178470i
$478$	9641.02	+	6195.91i	0.922531	+	0.592875i
$479$	−3173.78	−	611.696i	−0.302742	−	0.0583488i	0.0356178	−	0.999365i	$-0.488660\pi$
$479$	−3173.78	−	611.696i	−0.302742	−	0.0583488i	−0.338360	+	0.941017i	$0.609872\pi$
$480$	2533.94	−	7168.09i	0.240954	−	0.681619i
$481$	−8096.96	−	773.166i	−0.767546	−	0.0732918i
$482$	−230.854	+	399.851i	−0.0218156	+	0.0377857i
$483$	−9187.59	−	10508.0i	−0.865528	−	0.989921i
$484$	1024.54	+	1774.56i	0.0962192	+	0.166657i
$485$	−624.029	−	1366.43i	−0.0584241	−	0.127931i
$486$	13895.3	+	3156.36i	1.29692	+	0.294600i
$487$	−11447.4	+	13211.0i	−1.06516	+	1.22926i	−0.0928185	+	0.995683i	$0.529588\pi$
$487$	−11447.4	+	13211.0i	−1.06516	+	1.22926i	−0.972339	+	0.233574i	$0.924958\pi$
$488$	−126.110	+	2647.37i	−0.0116982	+	0.245575i
$489$	4938.31	−	10627.4i	0.456683	−	0.982798i
$490$	−5607.36	−	2244.85i	−0.516969	−	0.206963i
$491$	11805.6	−	11256.6i	1.08509	−	1.03463i	0.0858215	−	0.996311i	$-0.472649\pi$
$491$	11805.6	−	11256.6i	1.08509	−	1.03463i	0.999266	−	0.0383179i	$-0.0122000\pi$
$492$	91.7531	−	1691.44i	0.00840762	−	0.154992i
$493$	14708.6	−	5888.44i	1.34370	−	0.537935i
$494$	−3484.13	+	7629.18i	−0.317325	+	0.694845i
$495$	2209.01	+	5010.87i	0.200581	+	0.454993i
$496$	478.629	−	3328.94i	0.0433288	−	0.301358i
$497$	24829.0	+	12800.3i	2.24091	+	1.15527i
$498$	21637.9	+	8828.45i	1.94702	+	0.794402i
$499$	11133.6	+	4457.22i	0.998813	+	0.399864i	0.812712	−	0.582666i	$-0.197990\pi$
$499$	11133.6	+	4457.22i	0.998813	+	0.399864i	0.186101	+	0.982531i	$0.440415\pi$
$500$	−8095.53	+	1560.29i	−0.724087	+	0.139556i
$501$	−2068.68	−	1649.01i	−0.184474	−	0.147051i
$502$	18710.8	+	3606.21i	1.66355	+	0.320623i
$503$	2207.03	−	648.043i	0.195639	−	0.0574449i	−0.182445	−	0.983216i	$-0.558401\pi$
$503$	2207.03	−	648.043i	0.195639	−	0.0574449i	0.378084	+	0.925771i	$0.376583\pi$
$504$	−1019.85	−	4459.72i	−0.0901343	−	0.394150i
$505$	4168.31			0.367302
$506$	−12113.6	+	5005.58i	−1.06426	+	0.439773i
$507$	−5739.43	+	7948.48i	−0.502756	+	0.696261i
$508$	−11915.0	−	1137.74i	−1.04063	−	0.0993683i
$509$	196.589	−	810.351i	0.0171192	−	0.0705662i	−0.962611	−	0.270887i	$-0.912683\pi$
$509$	196.589	−	810.351i	0.0171192	−	0.0705662i	0.979730	+	0.200320i	$0.0641983\pi$
$510$	−12942.9	−	3893.24i	−1.12377	−	0.338031i
$511$	−288.263	+	6051.38i	−0.0249550	+	0.523870i
$512$	8500.87	+	9810.53i	0.733768	+	0.846813i
$513$	792.295	−	4830.33i	0.0681885	−	0.415720i
$514$	−4771.95	−	1401.17i	−0.409497	−	0.120239i
$515$	−8821.31	−	4547.70i	−0.754783	−	0.389118i
$516$	3632.95	−	1040.77i	0.309946	−	0.0887930i
$517$	−8609.67	−	12090.6i	−0.732404	−	1.02852i
$518$	6763.50	+	9498.01i	0.573689	+	0.805634i
$519$	−9470.20	−	9149.77i	−0.800955	−	0.773854i
$520$	−2537.43	−	1308.14i	−0.213988	−	0.110318i
$521$	3908.36	+	1147.60i	0.328653	+	0.0965013i	0.441897	−	0.897066i	$-0.354306\pi$
$521$	3908.36	+	1147.60i	0.328653	+	0.0965013i	−0.113243	+	0.993567i	$0.536124\pi$
$522$	13370.1	−	6671.13i	1.12106	−	0.559363i
$523$	3306.95	+	3816.43i	0.276488	+	0.319084i	0.876961	−	0.480561i	$-0.159567\pi$
$523$	3306.95	+	3816.43i	0.276488	+	0.319084i	−0.600474	+	0.799644i	$0.705021\pi$
$524$	−378.126	+	7937.84i	−0.0315239	+	0.661767i
$525$	−7720.38	+	7264.81i	−0.641800	+	0.603928i
$526$	4097.51	−	16890.2i	0.339658	−	1.40009i
$527$	−4783.40	−	456.760i	−0.395386	−	0.0377548i
$528$	−12308.1	−	1257.21i	−1.01447	−	0.103623i
$529$	3129.08	+	11757.8i	0.257178	+	0.966364i
$530$	−12614.6			−1.03385
$531$	−7693.75	+	7144.69i	−0.628776	+	0.583905i
$532$	5014.15	−	1472.29i	0.408630	−	0.119984i
$533$	−3325.98	−	641.029i	−0.270289	−	0.0520939i
$534$	7458.56	−	2929.06i	0.604426	−	0.237364i
$535$	−6548.54	+	1262.13i	−0.529193	+	0.101994i
$536$	5495.57	+	2200.09i	0.442859	+	0.177294i
$537$	2853.24	+	20818.1i	0.229286	+	1.67294i
$538$	−17098.8	−	8815.02i	−1.37022	−	0.706399i
$539$	−1124.22	+	7819.10i	−0.0898395	+	0.624847i
$540$	−5418.39	−	1155.89i	−0.431797	−	0.0921143i
$541$	2977.68	−	6520.22i	0.236637	−	0.518163i	−0.753637	−	0.657290i	$-0.771702\pi$
$541$	2977.68	−	6520.22i	0.236637	−	0.518163i	0.990274	+	0.139127i	$0.0444298\pi$
$542$	−25305.9	+	10130.9i	−2.00550	+	0.802880i
$543$	−4928.12	−	3213.22i	−0.389477	−	0.253945i
$544$	17761.4	−	16935.4i	1.39984	−	1.33474i
$545$	7557.48	+	3025.56i	0.593994	+	0.237799i
$546$	30300.2	−	2691.87i	2.37496	−	0.210991i
$547$	986.062	−	20700.0i	0.0770767	−	1.61804i	−0.547314	−	0.836927i	$-0.684350\pi$
$547$	986.062	−	20700.0i	0.0770767	−	1.61804i	0.624391	−	0.781112i	$-0.285347\pi$
$548$	−7610.59	+	8783.09i	−0.593263	+	0.684662i
$549$	10250.6	−	842.590i	0.796877	−	0.0655025i
$550$	4135.31	+	9055.07i	0.320600	+	0.702017i
$551$	−2566.42	−	4445.16i	−0.198427	−	0.343685i
$552$	−922.870	+	3879.53i	−0.0711594	+	0.299137i
$553$	−11992.3	+	20771.3i	−0.922180	+	1.59726i
$554$	−15812.6	−	1509.92i	−1.21266	−	0.115795i
$555$	−4174.93	+	776.141i	−0.319308	+	0.0593610i
$556$	9613.21	+	1852.79i	0.733257	+	0.141324i
$557$	−1256.24	−	807.334i	−0.0955627	−	0.0614144i	0.491987	−	0.870603i	$-0.336271\pi$
$557$	−1256.24	−	807.334i	−0.0955627	−	0.0614144i	−0.587549	+	0.809188i	$0.699907\pi$
$558$	−4531.36	−	59.7503i	−0.343777	−	0.00453303i
$559$	−1075.43	−	7479.79i	−0.0813702	−	0.565942i
$560$	2778.68	+	11453.9i	0.209679	+	0.864310i
$561$	−957.478	+	17650.8i	−0.0720584	+	1.32837i
$562$	−2242.18	−	1763.27i	−0.168293	−	0.132347i
$563$	361.832	+	508.122i	0.0270860	+	0.0380369i	0.827897	−	0.560880i	$-0.189537\pi$
$563$	361.832	+	508.122i	0.0270860	+	0.0380369i	−0.800811	+	0.598917i	$0.795598\pi$
$564$	15016.3	+	98.9979i	1.12110	+	0.00739107i
$565$	−4053.38	+	1622.73i	−0.301817	+	0.120829i
$566$	−3215.35	+	2066.38i	−0.238783	+	0.153457i
$567$	−16650.0	+	6161.41i	−1.23321	+	0.456358i
$568$	−1135.77	−	7899.47i	−0.0839014	−	0.583547i
$569$	−4798.81	+	13865.3i	−0.353562	+	1.02155i	0.618288	+	0.785951i	$0.287826\pi$
$569$	−4798.81	+	13865.3i	−0.353562	+	1.02155i	−0.971850	+	0.235599i	$0.924295\pi$
$570$	−651.715	+	4329.94i	−0.0478901	+	0.318177i
$571$	−1168.16	−	3375.18i	−0.0856148	−	0.247368i	0.894064	−	0.447938i	$-0.147842\pi$
$571$	−1168.16	−	3375.18i	−0.0856148	−	0.247368i	−0.979679	+	0.200571i	$0.935720\pi$
$572$	2927.08	−	12065.6i	0.213964	−	0.881971i
$573$	13041.3	+	2602.79i	0.950801	+	0.189761i
$574$	2427.82	+	4205.11i	0.176542	+	0.305780i
$575$	8837.04	−	2701.21i	0.640922	−	0.195910i
$576$	4562.81	−	5127.57i	0.330065	−	0.370918i
$577$	−5998.57	−	13135.0i	−0.432797	−	0.947693i	−0.992865	−	0.119246i	$-0.961952\pi$
$577$	−5998.57	−	13135.0i	−0.432797	−	0.947693i	0.560068	−	0.828447i	$-0.310775\pi$
$578$	−18199.6	−	17353.3i	−1.30969	−	1.24879i
$579$	−5896.38	+	5548.44i	−0.423221	+	0.398247i
$580$	−5163.82	+	2662.13i	−0.369683	+	0.190585i
$581$	−28590.4	+	5510.34i	−2.04153	+	0.393473i
$582$	−187.476	−	4569.20i	−0.0133524	−	0.325429i
$583$	3889.58	+	16033.1i	0.276312	+	1.13897i
$584$	1456.05	−	935.747i	0.103171	−	0.0663039i
$585$	−3761.13	+	10420.5i	−0.265818	+	0.736467i
$586$	−8946.72	+	19590.6i	−0.630692	+	1.38102i
$587$	−4287.19	+	409.377i	−0.301450	+	0.0287850i	−0.244685	−	0.969603i	$-0.578685\pi$
$587$	−4287.19	+	409.377i	−0.301450	+	0.0287850i	−0.0567649	+	0.998388i	$0.518079\pi$
$588$	−5747.61	−	5553.14i	−0.403108	−	0.389469i
$589$	74.0722	+	1554.97i	0.00518182	+	0.108780i
$590$	6797.57	−	6481.47i	0.474325	−	0.452268i
$591$	16583.8	−	10503.9i	1.15426	−	0.731091i
$592$	3137.84	−	9066.19i	0.217845	−	0.629423i
$593$	22266.1	+	14309.5i	1.54192	+	0.990931i	0.987307	+	0.158821i	$0.0507692\pi$
$593$	22266.1	+	14309.5i	1.54192	+	0.990931i	0.554611	+	0.832110i	$0.312867\pi$
$594$	463.761	+	16664.5i	0.0320342	+	1.15110i
$595$	16157.4	−	4744.23i	1.11326	−	0.326882i
$596$	−42.8236	+	60.1373i	−0.00294316	+	0.00413309i
$597$	5698.58	+	12699.1i	0.390666	+	0.870582i
$598$	−24724.0	−	9582.38i	−1.69070	−	0.655272i
$599$	388.176	−	672.340i	0.0264782	−	0.0458615i	−0.852483	−	0.522755i	$-0.824904\pi$
$599$	388.176	−	672.340i	0.0264782	−	0.0458615i	0.878961	+	0.476894i	$0.158237\pi$
$600$	2970.09	+	592.772i	0.202089	+	0.0403330i
$601$	2544.51	+	2426.18i	0.172700	+	0.164669i	0.771500	−	0.636230i	$-0.219507\pi$
$601$	2544.51	+	2426.18i	0.172700	+	0.164669i	−0.598800	+	0.800899i	$0.704355\pi$
$602$	−7093.97	+	8186.88i	−0.480280	+	0.554273i
$603$	5709.72	−	22251.1i	0.385602	−	1.50271i
$604$	−4379.57	−	5054.29i	−0.295037	−	0.340491i
$605$	1681.48	−	1322.33i	0.112995	−	0.0888599i
$606$	11749.1	+	4793.75i	0.787584	+	0.321341i
$607$	424.230	+	8905.68i	0.0283673	+	0.595503i	0.967641	+	0.252333i	$0.0811978\pi$
$607$	424.230	+	8905.68i	0.0283673	+	0.595503i	−0.939273	+	0.343170i	$0.888499\pi$
$608$	−6249.64	−	4914.77i	−0.416869	−	0.327829i
$609$	−9414.33	+	16060.6i	−0.626417	+	1.06865i
$610$	−9158.95	+	874.573i	−0.607926	+	0.0580499i
$611$	4273.34	−	29721.8i	0.282948	−	1.96794i
$612$	−13910.6	−	11239.4i	−0.918796	−	0.742362i
$613$	−859.073	−	252.247i	−0.0566030	−	0.0166201i	0.253308	−	0.967386i	$-0.418481\pi$
$613$	−859.073	−	252.247i	−0.0566030	−	0.0166201i	−0.309911	+	0.950765i	$0.600299\pi$
$614$	20030.4	−	15752.1i	1.31655	−	1.03535i
$615$	−1761.43	+	156.485i	−0.115492	+	0.0102603i
$616$	4757.34	−	2452.58i	0.311167	−	0.160418i
$617$	933.683	+	2697.70i	0.0609216	+	0.176022i	0.971354	−	0.237636i	$-0.0763724\pi$
$617$	933.683	+	2697.70i	0.0609216	+	0.176022i	−0.910433	+	0.413657i	$0.864251\pi$
$618$	−19634.4	−	22963.4i	−1.27801	−	1.49470i
$619$	−6714.94	+	9429.82i	−0.436020	+	0.612304i	−0.972864	−	0.231377i	$-0.925677\pi$
$619$	−6714.94	+	9429.82i	−0.436020	+	0.612304i	0.536844	+	0.843681i	$0.319616\pi$
$620$	1762.00			0.114135
$621$	15391.7	+	1605.40i	0.994604	+	0.103740i
$622$	27932.7			1.80064
$623$	−5791.07	+	8132.42i	−0.372414	+	0.522983i
$624$	−16265.5	−	19023.4i	−1.04350	−	1.22042i
$625$	−609.964	−	1762.37i	−0.0390377	−	0.112792i
$626$	−31208.2	+	16088.9i	−1.99254	+	1.02723i
$627$	5704.28	−	506.767i	0.363329	−	0.0322780i
$628$	12812.8	−	10076.1i	0.814152	−	0.640256i
$629$	−13152.1	−	3861.79i	−0.833715	−	0.244801i
$630$	14820.3	−	5707.59i	0.937227	−	0.360946i
$631$	429.760	−	2989.04i	0.0271132	−	0.188577i	−0.971764	−	0.235956i	$-0.924178\pi$
$631$	429.760	−	2989.04i	0.0271132	−	0.188577i	0.998877	+	0.0473793i	$0.0150870\pi$
$632$	6821.28	−	651.353i	0.429329	−	0.0409959i
$633$	4819.01	−	8221.13i	0.302589	−	0.516210i
$634$	−2080.36	−	1636.02i	−0.130318	−	0.102483i
$635$	594.544	+	12481.0i	0.0371556	+	0.779991i
$636$	−15454.5	−	6305.56i	−0.963537	−	0.393132i
$637$	−12561.8	+	9878.75i	−0.781348	+	0.614459i
$638$	11447.9	+	13211.6i	0.710385	+	0.819828i
$639$	−29828.4	+	8332.82i	−1.84662	+	0.515871i
$640$	3644.48	−	4205.95i	0.225095	−	0.259773i
$641$	9331.33	+	8897.41i	0.574985	+	0.548247i	0.920790	−	0.390059i	$-0.127545\pi$
$641$	9331.33	+	8897.41i	0.574985	+	0.548247i	−0.345805	+	0.938307i	$0.612394\pi$
$642$	−19909.8	−	3973.60i	−1.22395	−	0.244276i
$643$	3493.34	−	6050.65i	0.214252	−	0.371095i	−0.738789	−	0.673937i	$-0.764602\pi$
$643$	3493.34	−	6050.65i	0.214252	−	0.371095i	0.953041	+	0.302842i	$0.0979353\pi$
$644$	5575.87	+	15552.2i	0.341180	+	0.951621i
$645$	−1615.19	−	3599.39i	−0.0986017	−	0.219730i
$646$	−8198.64	+	11513.4i	−0.499336	+	0.701219i
$647$	−5832.54	+	1712.59i	−0.354406	+	0.104063i	−0.454089	−	0.890956i	$-0.650035\pi$
$647$	−5832.54	+	1712.59i	−0.354406	+	0.104063i	0.0996832	+	0.995019i	$0.468217\pi$
$648$	4193.11	+	2853.72i	0.254199	+	0.173001i
$649$	−10333.9	−	6641.18i	−0.625024	−	0.401678i
$650$	−6586.67	+	19030.9i	−0.397462	+	1.14839i
$651$	4769.88	−	3021.17i	0.287168	−	0.181888i
$652$	−10038.8	+	9572.00i	−0.602992	+	0.574951i
$653$	1229.67	+	25813.9i	0.0736915	+	1.54698i	0.668868	+	0.743381i	$0.266779\pi$
$653$	1229.67	+	25813.9i	0.0736915	+	1.54698i	−0.595177	+	0.803595i	$0.702918\pi$
$654$	17822.6	+	17219.5i	1.06562	+	1.02957i
$655$	8258.52	−	788.593i	0.492652	−	0.0470426i
$656$	1659.67	−	3634.16i	0.0987791	−	0.216296i
$657$	−4331.19	−	5133.69i	−0.257193	−	0.304847i
$658$	−36212.0	+	23272.0i	−2.14543	+	1.37878i
$659$	4853.39	+	20005.9i	0.286891	+	1.18258i	0.914674	+	0.404193i	$0.132447\pi$
$659$	4853.39	+	20005.9i	0.286891	+	1.18258i	−0.627783	+	0.778389i	$0.716037\pi$
$660$	−265.729	−	6476.42i	−0.0156720	−	0.381961i
$661$	15577.6	−	3002.34i	0.916640	−	0.176668i	0.290949	−	0.956739i	$-0.406029\pi$
$661$	15577.6	−	3002.34i	0.916640	−	0.176668i	0.625691	+	0.780071i	$0.284817\pi$
$662$	19188.5	−	9892.33i	1.12656	−	0.580780i
$663$	−26043.2	+	24506.4i	−1.52554	+	1.43552i
$664$	6020.35	+	5740.39i	0.351860	+	0.335498i
$665$	−2266.30	−	4962.49i	−0.132155	−	0.289379i
$666$	−12660.4	−	2613.67i	−0.736607	−	0.152069i
$667$	13553.7	−	8923.59i	0.786809	−	0.518025i
$668$	1565.67	+	2711.82i	0.0906851	+	0.157071i
$669$	−18539.3	−	3700.09i	−1.07141	−	0.213832i
$670$	−4844.75	+	19970.3i	−0.279357	+	1.15152i
$671$	3935.65	+	11371.3i	0.226429	+	0.654224i
$672$	−4291.96	+	28515.4i	−0.246378	+	1.63691i
$673$	−3231.02	+	9335.42i	−0.185062	+	0.534701i	−0.998925	−	0.0463554i	$-0.985239\pi$
$673$	−3231.02	+	9335.42i	−0.185062	+	0.534701i	0.813863	+	0.581057i	$0.197361\pi$
$674$	1660.62	+	11549.9i	0.0949033	+	0.660067i
$675$	791.306	−	11726.6i	0.0451220	−	0.668674i
$676$	9762.37	−	6273.89i	0.555437	−	0.356958i
$677$	−7167.19	+	2869.31i	−0.406879	+	0.162890i	−0.566069	−	0.824358i	$-0.691536\pi$
$677$	−7167.19	+	2869.31i	−0.406879	+	0.162890i	0.159189	+	0.987248i	$0.449112\pi$
$678$	−13291.4	−	87.6261i	−0.752880	−	0.00496351i
$679$	3304.95	+	4641.15i	0.186793	+	0.262314i
$680$	−3781.67	−	2973.94i	−0.213265	−	0.167714i
$681$	655.162	−	12077.7i	0.0368662	−	0.679616i
$682$	−1249.97	−	5152.46i	−0.0701817	−	0.289293i
$683$	−3727.60	−	25926.0i	−0.208832	−	1.45246i	−0.776975	−	0.629532i	$-0.783247\pi$
$683$	−3727.60	−	25926.0i	−0.208832	−	1.45246i	0.568142	−	0.822930i	$-0.307662\pi$
$684$	−2962.81	+	4978.96i	−0.165623	+	0.278326i
$685$	10206.5	+	6559.29i	0.569297	+	0.365865i
$686$	−8358.97	−	1611.06i	−0.465229	−	0.0896655i
$687$	−4206.86	+	782.077i	−0.233627	+	0.0434324i
$688$	8872.81	+	847.251i	0.491676	+	0.0469493i
$689$	−16688.1	+	28904.6i	−0.922735	+	1.59822i
$690$	−13786.4	−	1254.45i	−0.760638	−	0.0692118i
$691$	−4490.67	−	7778.07i	−0.247226	−	0.428208i	0.715529	−	0.698583i	$-0.246186\pi$
$691$	−4490.67	−	7778.07i	−0.247226	−	0.428208i	−0.962755	+	0.270375i	$0.912852\pi$
$692$	6474.90	+	14178.1i	0.355692	+	0.778857i
$693$	−11824.0	−	17076.6i	−0.648133	−	0.936055i
$694$	7356.02	−	8489.30i	0.402350	−	0.464337i
$695$	486.306	−	10208.8i	0.0265419	−	0.557183i
$696$	5297.78	−	470.654i	0.288523	−	0.0256323i
$697$	−5299.29	−	2121.52i	−0.287984	−	0.115292i
$698$	21521.5	−	20520.7i	1.16705	−	1.11278i
$699$	9523.64	+	6209.57i	0.515332	+	0.336005i
$700$	11649.1	−	4663.58i	0.628990	−	0.251810i
$701$	−5942.55	+	13012.4i	−0.320181	+	0.701099i	−0.999463	−	0.0327792i	$-0.989564\pi$
$701$	−5942.55	+	13012.4i	−0.320181	+	0.701099i	0.679282	+	0.733878i	$0.262291\pi$
$702$	−22585.4	+	25046.5i	−1.21429	+	1.34661i
$703$	−631.986	+	4395.56i	−0.0339058	+	0.235820i
$704$	7137.56	+	3679.67i	0.382112	+	0.196993i
$705$	−2128.67	−	15531.4i	−0.113717	−	0.829711i
$706$	227.036	+	90.8916i	0.0121029	+	0.00484526i
$707$	−15524.3	+	2992.06i	−0.825813	+	0.159162i
$708$	11567.7	−	4542.77i	0.614043	−	0.241141i
$709$	−3250.70	−	626.520i	−0.172190	−	0.0331868i	0.102428	−	0.994740i	$-0.467339\pi$
$709$	−3250.70	−	626.520i	−0.172190	−	0.0331868i	−0.274617	+	0.961554i	$0.588551\pi$
$710$	26582.4	−	7805.29i	1.40510	−	0.412573i
$711$	−5927.91	−	25922.3i	−0.312678	−	1.36732i
$712$	2852.27			0.150131
$713$	−4893.88	+	521.941i	−0.257051	+	0.0274149i
$714$	50998.6	+	5209.27i	2.67307	+	0.273042i
$715$	−12902.5	−	1232.04i	−0.674862	−	0.0644416i
$716$	5863.72	−	24170.6i	0.306058	−	1.26159i
$717$	11528.8	−	10848.5i	0.600490	−	0.565055i
$718$	2170.01	−	45554.1i	0.112791	−	2.36777i
$719$	1923.92	+	2220.32i	0.0997913	+	0.115165i	0.803448	−	0.595374i	$-0.202996\pi$
$719$	1923.92	+	2220.32i	0.0997913	+	0.115165i	−0.703657	+	0.710540i	$0.748451\pi$
$720$	−10898.6	−	7208.92i	−0.564122	−	0.373140i
$721$	36118.1	+	10605.2i	1.86561	+	0.547794i
$722$	−18863.3	−	9724.70i	−0.972325	−	0.501268i
$723$	458.665	+	443.145i	0.0235933	+	0.0227950i
$724$	4039.26	+	5672.34i	0.207345	+	0.291175i
$725$	−7148.96	−	10039.3i	−0.366215	−	0.514277i
$726$	6260.28	−	1793.44i	0.320029	−	0.0916816i
$727$	−34360.4	−	17714.0i	−1.75290	−	0.903681i	−0.952682	−	0.303967i	$-0.901689\pi$
$727$	−34360.4	−	17714.0i	−1.75290	−	0.903681i	−0.800215	−	0.599714i	$-0.795281\pi$
$728$	10389.3	+	3050.57i	0.528919	+	0.155305i
$729$	8878.25	−	17566.9i	0.451062	−	0.892493i
$730$	3934.68	+	4540.86i	0.199492	+	0.230226i
$731$	605.945	−	12720.4i	0.0306590	−	0.643611i
$732$	−11658.0	−	3506.76i	−0.588653	−	0.177068i
$733$	−403.954	+	1665.12i	−0.0203552	+	0.0839055i	−0.981083	−	0.193586i	$-0.937988\pi$
$733$	−403.954	+	1665.12i	−0.0203552	+	0.0839055i	0.960728	+	0.277492i	$0.0895032\pi$
$734$	−35115.9	−	3353.16i	−1.76587	−	0.168621i
$735$	−4884.26	+	6764.16i	−0.245114	+	0.339456i
$736$	14353.3	−	20635.2i	0.718842	−	1.03345i
$737$	26876.0			1.34327
$738$	−5144.88	−	1584.65i	−0.256620	−	0.0790403i
$739$	35508.7	−	10426.3i	1.76753	−	0.518995i	0.774066	−	0.633105i	$-0.218220\pi$
$739$	35508.7	−	10426.3i	1.76753	−	0.518995i	0.993468	+	0.114110i	$0.0364017\pi$
$740$	4935.48	+	951.237i	0.245178	+	0.0472543i
$741$	9059.30	+	7221.48i	0.449125	+	0.358013i
$742$	46981.2	−	9054.88i	2.32444	−	0.447999i
$743$	32989.4	+	13207.0i	1.62889	+	0.652109i	0.992830	−	0.119533i	$-0.0381396\pi$
$743$	32989.4	+	13207.0i	1.62889	+	0.652109i	0.636058	+	0.771641i	$0.280564\pi$
$744$	−1493.55	−	609.383i	−0.0735971	−	0.0300283i
$745$	68.5035	+	35.3160i	0.00336882	+	0.00173675i
$746$	823.960	−	5730.77i	0.0404388	−	0.281258i
$747$	19070.0	−	26046.3i	0.934048	−	1.27575i
$748$	8691.76	−	19032.3i	0.424869	−	0.930333i
$749$	23483.1	−	9401.23i	1.14560	−	0.458629i
$750$	−1419.23	+	26163.1i	−0.0690974	+	1.27379i
$751$	802.007	−	764.712i	0.0389689	−	0.0371568i	−0.670344	−	0.742050i	$-0.733854\pi$
$751$	802.007	−	764.712i	0.0389689	−	0.0371568i	0.709313	+	0.704893i	$0.249005\pi$
$752$	32880.4	+	13163.3i	1.59445	+	0.638321i
$753$	11091.9	−	23870.2i	0.536802	−	1.15522i
$754$	−1682.75	+	35325.3i	−0.0812760	+	1.70619i
$755$	−4572.04	+	5276.42i	−0.220389	+	0.254343i
$756$	21009.7	+	415.580i	1.01074	+	0.0199927i
$757$	−3099.37	−	6786.68i	−0.148809	−	0.325847i	0.820518	−	0.571621i	$-0.193685\pi$
$757$	−3099.37	−	6786.68i	−0.148809	−	0.325847i	−0.969327	+	0.245774i	$0.920958\pi$
$758$	−1507.74	−	2611.49i	−0.0722477	−	0.125137i
$759$	2656.50	+	17909.3i	0.127042	+	0.856476i
$760$	−779.305	+	1349.80i	−0.0371952	+	0.0644240i
$761$	13244.0	+	1264.65i	0.630876	+	0.0602413i	0.405595	−	0.914053i	$-0.367064\pi$
$761$	13244.0	+	1264.65i	0.630876	+	0.0602413i	0.225280	+	0.974294i	$0.427670\pi$
$762$	−12677.9	+	35863.8i	−0.602721	+	1.70500i
$763$	−30318.5	−	5843.41i	−1.43854	−	0.277255i
$764$	−13242.0	−	8510.11i	−0.627066	−	0.402991i
$765$	−9547.23	+	16044.0i	−0.451217	+	0.758263i
$766$	6175.11	+	42948.8i	0.291274	+	2.02586i
$767$	−5858.77	−	24150.2i	−0.275812	−	1.13691i
$768$	24534.1	−	12444.2i	1.15273	−	0.584688i
$769$	−2181.17	−	1715.29i	−0.102282	−	0.0804355i	0.565708	−	0.824605i	$-0.308603\pi$
$769$	−2181.17	−	1715.29i	−0.102282	−	0.0804355i	−0.667990	+	0.744170i	$0.732845\pi$
$770$	10777.6	+	15135.1i	0.504415	+	0.708351i
$771$	−3474.10	+	5926.74i	−0.162279	+	0.276844i
$772$	8896.87	−	3561.77i	0.414774	−	0.166050i
$773$	−14584.3	+	9372.75i	−0.678603	+	0.436112i	−0.834018	−	0.551737i	$-0.813965\pi$
$773$	−14584.3	+	9372.75i	−0.678603	+	0.436112i	0.155414	+	0.987849i	$0.450329\pi$
$774$	−413.245	−	12003.1i	−0.0191909	−	0.557418i
$775$	531.960	+	3699.86i	0.0246562	+	0.171488i
$776$	532.396	−	1538.26i	0.0246287	−	0.0711601i
$777$	14991.8	−	5887.43i	0.692185	−	0.271828i
$778$	1270.76	+	3671.62i	0.0585591	+	0.169195i
$779$	−435.985	+	1797.15i	−0.0200524	+	0.0826569i
$780$	8652.33	−	9853.31i	0.397184	−	0.452314i
$781$	−18116.9	−	31379.4i	−0.830055	−	1.43770i
$782$	−37856.5	−	23741.9i	−1.73113	−	1.08569i
$783$	−4468.40	−	20150.4i	−0.203943	−	0.919688i
$784$	−7830.39	−	17146.2i	−0.356705	−	0.781075i
$785$	−12315.5	−	11742.8i	−0.559947	−	0.533908i
$786$	24185.0	+	7274.90i	1.09752	+	0.330136i
$787$	−14181.9	+	7311.29i	−0.642352	+	0.331155i	−0.748441	−	0.663201i	$-0.769197\pi$
$787$	−14181.9	+	7311.29i	−0.642352	+	0.331155i	0.106089	+	0.994357i	$0.466167\pi$
$788$	−22815.7	+	4397.37i	−1.03144	+	0.198794i
$789$	−21265.8	−	11141.4i	−0.959549	−	0.502716i
$790$	5608.09	+	23116.9i	0.252566	+	1.04109i
$791$	13931.4	−	8953.17i	0.626225	−	0.402450i
$792$	−2014.61	+	5581.61i	−0.0903863	+	0.250422i
$793$	−10112.6	+	22143.5i	−0.452848	+	0.991599i
$794$	44523.9	−	4251.52i	1.99005	−	0.190026i
$795$	−4219.62	+	16906.2i	−0.188245	+	0.754217i
$796$	−783.924	−	16456.6i	−0.0349064	−	0.732775i
$797$	−6805.66	+	6489.19i	−0.302470	+	0.288405i	−0.826079	−	0.563554i	$-0.809434\pi$
$797$	−6805.66	+	6489.19i	−0.302470	+	0.288405i	0.523609	+	0.851959i	$0.324585\pi$
$798$	−680.858	−	16594.0i	−0.0302032	−	0.736118i
$799$	16550.6	−	47819.9i	0.732815	−	2.11733i
$800$	−16060.0	−	10321.1i	−0.709758	−	0.456134i
$801$	−1430.65	−	10975.9i	−0.0631081	−	0.484161i
$802$	23748.5	−	6973.18i	1.04562	−	0.307022i
$803$	4558.19	−	6401.09i	0.200318	−	0.281307i
$804$	−15917.9	+	22044.5i	−0.698234	+	0.966976i
$805$	15242.1	−	8072.25i	0.667344	−	0.353428i
$806$	5362.95	−	9288.90i	0.234370	−	0.405940i
$807$	−17533.6	+	19967.4i	−0.764824	+	0.870984i
$808$	3268.99	+	3116.97i	0.142330	+	0.135711i
$809$	−2039.53	+	2353.74i	−0.0886354	+	0.102291i	−0.798335	−	0.602214i	$-0.794285\pi$
$809$	−2039.53	+	2353.74i	−0.0886354	+	0.102291i	0.709699	+	0.704505i	$0.248831\pi$
$810$	−7734.15	+	15817.8i	−0.335494	+	0.686151i
$811$	2578.99	+	2976.32i	0.111666	+	0.128869i	0.808831	−	0.588042i	$-0.200101\pi$
$811$	2578.99	+	2976.32i	0.111666	+	0.128869i	−0.697165	+	0.716911i	$0.745556\pi$
$812$	17321.0	−	13621.4i	0.748581	−	0.588690i
$813$	5112.74	+	37304.1i	0.220556	+	1.60924i
$814$	−719.645	−	15107.2i	−0.0309871	−	0.650500i
$815$	11382.4	+	8951.23i	0.489213	+	0.384721i
$816$	−20848.6	−	36667.0i	−0.894420	−	1.57304i
$817$	−4107.01	+	392.172i	−0.175871	+	0.0167936i
$818$	7190.31	−	50009.7i	0.307339	−	2.13759i
$819$	6527.85	−	41509.3i	0.278512	−	1.77100i
$820$	2008.34	+	589.702i	0.0855297	+	0.0251138i
$821$	−10158.3	+	7988.61i	−0.431825	+	0.339591i	−0.810295	−	0.586023i	$-0.800693\pi$
$821$	−10158.3	+	7988.61i	−0.431825	+	0.339591i	0.378469	+	0.925614i	$0.376451\pi$
$822$	21225.3	+	30226.5i	0.900627	+	1.28257i
$823$	−24533.1	+	12647.7i	−1.03909	+	0.535688i	−0.891339	−	0.453336i	$-0.850234\pi$
$823$	−24533.1	+	12647.7i	−1.03909	+	0.535688i	−0.147751	+	0.989025i	$0.547203\pi$
$824$	−3517.42	−	10162.9i	−0.148708	−	0.429662i
$825$	13519.0	−	2513.26i	0.570511	−	0.106061i
$826$	−20664.1	+	29018.7i	−0.870456	+	1.22238i
$827$	5485.25			0.230642			0.115321	−	0.993328i	$-0.463210\pi$
$827$	5485.25			0.230642			0.115321	+	0.993328i	$0.463210\pi$
$828$	−16263.1	−	8428.19i	−0.682585	−	0.353744i
$829$	−45712.7			−1.91516			−0.957579	−	0.288170i	$-0.906953\pi$
$829$	−45712.7			−1.91516			−0.957579	+	0.288170i	$0.906953\pi$
$830$	−16750.4	+	23522.6i	−0.700498	+	0.983712i
$831$	−7312.98	+	20687.2i	−0.305276	+	0.863575i
$832$	5313.35	+	15351.9i	0.221403	+	0.639702i
$833$	−23937.7	+	12340.7i	−0.995668	+	0.513302i
$834$	13111.4	−	28216.1i	0.544376	−	1.17152i
$835$	2569.57	−	2020.74i	0.106496	−	0.0837490i
$836$	−6503.88	−	1909.71i	−0.269069	−	0.0790057i
$837$	−1595.83	+	6053.01i	−0.0659021	+	0.249967i
$838$	−3908.30	+	27182.9i	−0.161110	+	1.12054i
$839$	−2430.20	+	232.056i	−0.0999997	+	0.00954881i	−0.144936	−	0.989441i	$-0.546298\pi$
$839$	−2430.20	+	232.056i	−0.0999997	+	0.00954881i	0.0449362	+	0.998990i	$0.485692\pi$
$840$	5652.86	+	37.2676i	0.232193	+	0.00153078i
$841$	2158.31	+	1697.31i	0.0884952	+	0.0695934i
$842$	−1952.69	−	40992.1i	−0.0799219	−	1.67777i
$843$	−3113.18	+	2415.18i	−0.127193	+	0.0986754i
$844$	−8866.28	+	6972.52i	−0.361599	+	0.284365i
$845$	−7933.34	−	9155.56i	−0.322977	−	0.372735i
$846$	11861.8	−	46226.1i	0.482054	−	1.87859i
$847$	−5313.23	+	6131.80i	−0.215543	+	0.248750i
$848$	−28491.5	−	27166.5i	−1.15377	−	1.10012i
$849$	1693.85	+	5000.48i	0.0684721	+	0.202139i
$850$	−16969.0	+	29391.2i	−0.684744	+	1.18601i
$851$	−13989.9	−	1180.02i	−0.563533	−	0.0475332i
$852$	36468.4	+	3725.08i	1.46641	+	0.149788i
$853$	13058.8	−	18338.5i	0.524178	−	0.736106i	−0.464596	−	0.885523i	$-0.653800\pi$
$853$	13058.8	−	18338.5i	0.524178	−	0.736106i	0.988774	+	0.149417i	$0.0477398\pi$
$854$	33483.4	−	9831.61i	1.34166	−	0.393947i
$855$	5585.05	+	2321.82i	0.223397	+	0.0928707i
$856$	−6079.47	−	3907.04i	−0.242748	−	0.156005i
$857$	10008.4	−	28917.4i	0.398927	−	1.15263i	−0.549462	−	0.835518i	$-0.685167\pi$
$857$	10008.4	−	28917.4i	0.398927	−	1.15263i	0.948390	−	0.317107i	$-0.102711\pi$
$858$	−34951.2	−	18311.2i	−1.39069	−	0.728596i
$859$	−20638.0	+	19678.3i	−0.819745	+	0.781625i	−0.978621	−	0.205673i	$-0.934062\pi$
$859$	−20638.0	+	19678.3i	−0.819745	+	0.781625i	0.158876	+	0.987299i	$0.449213\pi$
$860$	222.194	+	4664.42i	0.00881016	+	0.184948i
$861$	6447.87	−	1847.18i	0.255218	−	0.0731147i
$862$	38318.2	−	3658.94i	1.51406	−	0.144576i
$863$	9683.28	−	21203.4i	0.381950	−	0.836354i	−0.616836	−	0.787092i	$-0.711586\pi$
$863$	9683.28	−	21203.4i	0.381950	−	0.836354i	0.998786	−	0.0492620i	$-0.0156869\pi$
$864$	−18026.2	−	26404.3i	−0.709796	−	1.03969i
$865$	13688.5	−	8797.09i	0.538062	−	0.345792i
$866$	13569.3	+	55933.5i	0.532453	+	2.19480i
$867$	−29344.9	+	18586.6i	−1.14949	+	0.728068i
$868$	−6562.31	+	1264.78i	−0.256612	+	0.0494579i
$869$	27652.2	−	14255.7i	1.07945	−	0.556493i
$870$	4234.52	+	17971.2i	0.165016	+	0.700324i
$871$	39350.1	+	37520.2i	1.53080	+	1.45961i
$872$	3664.49	+	8024.11i	0.142311	+	0.311618i
$873$	−6186.43	−	1277.16i	−0.239838	−	0.0495134i
$874$	−5867.99	+	13234.2i	−0.227103	+	0.512190i
$875$	−16322.5	−	28271.3i	−0.630628	−	1.09228i
$876$	2550.67	+	7529.94i	0.0983782	+	0.290426i
$877$	−7732.94	+	31875.6i	−0.297746	+	1.22732i	0.604677	+	0.796471i	$0.293302\pi$
$877$	−7732.94	+	31875.6i	−0.297746	+	1.22732i	−0.902422	+	0.430853i	$0.858213\pi$
$878$	13297.7	+	38421.1i	0.511132	+	1.47682i
$879$	23262.9	+	18543.6i	0.892648	+	0.711561i
$880$	5000.15	−	14447.0i	0.191540	−	0.553418i
$881$	−4314.15	−	30005.5i	−0.164980	−	1.14746i	−0.889075	−	0.457761i	$-0.848652\pi$
$881$	−4314.15	−	30005.5i	−0.164980	−	1.14746i	0.724096	−	0.689700i	$-0.242257\pi$
$882$	−21546.3	+	13448.9i	−0.822564	+	0.513432i
$883$	9071.74	−	5830.05i	0.345740	−	0.222194i	−0.356233	−	0.934397i	$-0.615939\pi$
$883$	9071.74	−	5830.05i	0.345740	−	0.222194i	0.701973	+	0.712204i	$0.252303\pi$
$884$	39295.9	−	15731.7i	1.49509	−	0.598546i
$885$	−6412.76	−	11278.3i	−0.243574	−	0.428379i
$886$	−15732.6	−	22093.4i	−0.596556	−	0.837746i
$887$	7775.88	+	6115.02i	0.294350	+	0.231480i	0.754402	−	0.656412i	$-0.227927\pi$
$887$	7775.88	+	6115.02i	0.294350	+	0.231480i	−0.460052	+	0.887892i	$0.652169\pi$
$888$	−3854.56	−	2513.23i	−0.145665	−	0.0949759i
$889$	−11173.3	−	46057.0i	−0.421531	−	1.73757i
$890$	1409.13	+	9800.73i	0.0530721	+	0.369125i
$891$	22489.2	+	4952.79i	0.845584	+	0.186223i
$892$	18824.6	+	12097.8i	0.706607	+	0.454109i
$893$	−16097.6	−	3102.56i	−0.603232	−	0.116264i
$894$	152.474	+	178.327i	0.00570414	+	0.00667129i
$895$	−25847.2	−	2468.11i	−0.965336	−	0.0921784i
$896$	−10554.3	+	18280.5i	−0.393519	+	0.681595i
$897$	−21112.7	+	29930.2i	−0.785879	+	1.11409i
$898$	1121.02	+	1941.66i	0.0416579	+	0.0721536i
$899$	2726.85	+	5970.96i	0.101163	+	0.221516i
$900$	−5945.47	+	12577.2i	−0.220203	+	0.465823i
$901$	−36833.6	+	42508.2i	−1.36194	+	1.57176i
$902$	299.684	−	6291.15i	0.0110625	−	0.232231i
$903$	8599.23	+	12246.0i	0.316904	+	0.451297i
$904$	−4392.29	−	1758.41i	−0.161599	−	0.0646945i
$905$	5261.25	−	5016.59i	0.193248	−	0.184262i
$906$	−18955.3	+	9614.48i	−0.695085	+	0.352560i
$907$	36251.9	−	14513.1i	1.32715	−	0.531310i	0.403650	−	0.914913i	$-0.367741\pi$
$907$	36251.9	−	14513.1i	1.32715	−	0.531310i	0.923498	+	0.383603i	$0.125317\pi$
$908$	−5947.40	+	13023.0i	−0.217369	+	0.475973i
$909$	10354.8	−	14142.8i	0.377829	−	0.516049i
$910$	−5349.40	+	37205.9i	−0.194869	+	1.35534i
$911$	−32831.9	−	16926.0i	−1.19404	−	0.615569i	−0.257548	−	0.966265i	$-0.582915\pi$
$911$	−32831.9	−	16926.0i	−1.19404	−	0.615569i	−0.936489	+	0.350696i	$0.885945\pi$
$912$	−10796.9	+	8376.14i	−0.392017	+	0.304125i
$913$	35061.9	+	14036.7i	1.27095	+	0.508812i
$914$	40679.8	−	7840.38i	1.47217	−	0.283738i
$915$	−1891.58	+	12567.5i	−0.0683429	+	0.454065i
$916$	4973.23	+	958.511i	0.179389	+	0.0345744i
$917$	−30191.6	+	8865.05i	−1.08726	+	0.319247i
$918$	−45361.9	+	34243.1i	−1.63090	+	1.23114i
$919$	16989.3			0.609820			0.304910	−	0.952381i	$-0.401374\pi$
$919$	16989.3			0.609820			0.304910	+	0.952381i	$0.401374\pi$
$920$	−4404.49	−	2209.41i	−0.157839	−	0.0791762i
$921$	−14410.9	−	32114.2i	−0.515588	−	1.14897i
$922$	−7598.77	−	725.595i	−0.271423	−	0.0259178i
$923$	17281.6	−	71235.6i	0.616284	−	2.54036i
$924$	5638.51	+	23929.7i	0.200751	+	0.851982i
$925$	−507.358	+	10650.8i	−0.0180344	+	0.378589i
$926$	22328.7	+	25768.7i	0.792404	+	0.914483i
$927$	−37343.7	+	18633.0i	−1.32312	+	0.660180i
$928$	−32167.0	−	9445.07i	−1.13786	−	0.334105i
$929$	−27703.6	−	14282.2i	−0.978392	−	0.504396i	−0.106616	−	0.994300i	$-0.534001\pi$
$929$	−27703.6	−	14282.2i	−0.978392	−	0.504396i	−0.871776	+	0.489904i	$0.837032\pi$
$930$	1356.04	−	5433.07i	0.0478131	−	0.191567i
$931$	5061.00	+	7107.18i	0.178161	+	0.250192i
$932$	−7805.90	−	10961.9i	−0.274346	−	0.385265i
$933$	9343.59	−	37435.9i	0.327862	−	1.31361i
$934$	−8983.40	−	4631.27i	−0.314717	−	0.162248i
$935$	−20957.8	−	6153.77i	−0.733041	−	0.215240i
$936$	−10741.9	+	5359.73i	−0.375116	+	0.187167i
$937$	−23576.7	−	27209.0i	−0.822004	−	0.948643i	0.177366	−	0.984145i	$-0.443242\pi$
$937$	−23576.7	−	27209.0i	−0.822004	−	0.948643i	−0.999370	+	0.0355020i	$0.988697\pi$
$938$	3708.65	−	77854.2i	0.129096	−	2.71005i
$939$	11123.4	+	47207.5i	0.386580	+	1.64064i
$940$	−4374.64	+	18032.5i	−0.151793	+	0.625698i
$941$	−42547.9	−	4062.83i	−1.47399	−	0.140749i	−0.673094	−	0.739557i	$-0.735035\pi$
$941$	−42547.9	−	4062.83i	−1.47399	−	0.140749i	−0.800893	+	0.598808i	$0.795641\pi$
$942$	−21208.6	−	47262.5i	−0.733561	−	1.63471i
$943$	−5752.77	−	1042.96i	−0.198659	−	0.0360164i
$944$	29311.5			1.01060
$945$	−2691.97	−	21771.5i	−0.0926665	−	0.749448i
$946$	13482.1	−	3958.70i	0.463363	−	0.136056i
$947$	−1845.91	−	355.769i	−0.0633410	−	0.0122080i	0.157482	−	0.987522i	$-0.449662\pi$
$947$	−1845.91	−	355.769i	−0.0633410	−	0.0122080i	−0.220823	+	0.975314i	$0.570874\pi$
$948$	−4684.65	+	31124.4i	−0.160496	+	1.06632i
$949$	15610.0	−	3008.59i	0.533955	−	0.102911i
$950$	10207.3	+	4086.40i	0.348599	+	0.139558i
$951$	−2888.50	+	2240.88i	−0.0984923	+	0.0764097i
$952$	16219.0	+	8361.48i	0.552165	+	0.284661i
$953$	−1092.91	+	7601.37i	−0.0371489	+	0.258376i	−0.999929	−	0.0119093i	$-0.996209\pi$
$953$	−1092.91	+	7601.37i	−0.0371489	+	0.258376i	0.962780	+	0.270286i	$0.0871182\pi$
$954$	−31336.7	+	42800.6i	−1.06349	+	1.45254i
$955$	−6826.33	+	14947.6i	−0.231303	+	0.506484i
$956$	−17395.5	+	6964.10i	−0.588504	+	0.235601i
$957$	21535.7	−	10923.3i	0.727429	−	0.368966i
$958$	8799.55	−	8390.35i	0.296765	−	0.282964i
$959$	−42720.8	−	17102.8i	−1.43851	−	0.575891i
$960$	4874.00	+	6940.97i	0.163862	+	0.233353i
$961$	−1322.79	+	27768.7i	−0.0444022	+	0.932116i
$962$	20036.7	−	23123.6i	0.671528	−	0.774985i
$963$	−11985.4	+	25354.2i	−0.401062	+	0.848419i
$964$	−313.595	−	686.678i	−0.0104774	−	0.0229423i
$965$	−5002.26	−	8664.16i	−0.166869	−	0.289025i
$966$	52246.0	−	5224.02i	1.74015	−	0.173996i
$967$	26227.1	−	45426.7i	0.872189	−	1.51068i	0.0124621	−	0.999922i	$-0.496033\pi$
$967$	26227.1	−	45426.7i	0.872189	−	1.51068i	0.859727	−	0.510754i	$-0.170634\pi$
$968$	2307.50	+	220.340i	0.0766177	+	0.00731610i
$969$	12687.9	+	14839.2i	0.420635	+	0.491955i
$970$	5548.65	+	1069.41i	0.183666	+	0.0353988i
$971$	1166.58	+	749.712i	0.0385553	+	0.0247780i	0.559776	−	0.828644i	$-0.310887\pi$
$971$	1166.58	+	749.712i	0.0385553	+	0.0247780i	−0.521221	+	0.853422i	$0.674523\pi$
$972$	−17382.1	+	15512.9i	−0.573591	+	0.511909i
$973$	5516.82	+	38370.3i	0.181769	+	1.26423i
$974$	−15502.8	−	63903.6i	−0.510003	−	2.10226i
$975$	23302.3	+	15193.5i	0.765405	+	0.499057i
$976$	−22570.0	−	17749.2i	−0.740213	−	0.582110i
$977$	11404.4	+	16015.3i	0.373450	+	0.524437i	0.957942	−	0.286963i	$-0.0926456\pi$
$977$	11404.4	+	16015.3i	0.373450	+	0.524437i	−0.584492	+	0.811399i	$0.698706\pi$
$978$	21789.1	+	38321.0i	0.712410	+	1.25293i
$979$	12022.2	−	4812.96i	0.392473	−	0.157122i
$980$	8307.79	−	5339.09i	0.270798	−	0.174032i
$981$	29039.6	−	18126.1i	0.945121	−	0.589931i
$982$	8732.58	+	60736.4i	0.283776	+	1.97370i
$983$	−17405.6	+	50290.2i	−0.564753	+	1.63175i	0.194464	+	0.980910i	$0.437703\pi$
$983$	−17405.6	+	50290.2i	−0.564753	+	1.63175i	−0.759217	+	0.650837i	$0.774418\pi$
$984$	−1498.42	−	1194.44i	−0.0485444	−	0.0386964i
$985$	7933.61	+	22922.7i	0.256635	+	0.741499i
$986$	−14050.9	+	57918.6i	−0.453826	+	1.87070i
$987$	19076.5	+	56316.4i	0.615209	+	1.81618i
$988$	−6856.50	−	11875.8i	−0.220784	−	0.382409i
$989$	−1998.83	−	12889.4i	−0.0642661	−	0.414418i
$990$	−20174.3	−	4164.89i	−0.647659	−	0.133706i
$991$	−13902.3	−	30441.8i	−0.445632	−	0.975799i	−0.990530	−	0.137296i	$-0.956159\pi$
$991$	−13902.3	−	30441.8i	−0.445632	−	0.975799i	0.544898	−	0.838503i	$-0.316569\pi$
$992$	7358.74	+	7016.55i	0.235524	+	0.224572i
$993$	−6839.26	−	29025.7i	−0.218567	−	0.927595i
$994$	−93399.4	+	48150.8i	−2.98033	+	1.53647i
$995$	−16888.5	+	3254.99i	−0.538092	+	0.103709i
$996$	−32279.4	+	20445.3i	−1.02692	+	0.650435i
$997$	7825.44	+	32256.9i	0.248580	+	1.02466i	0.950084	+	0.311995i	$0.100997\pi$
$997$	7825.44	+	32256.9i	0.248580	+	1.02466i	−0.701504	+	0.712666i	$0.747488\pi$
$998$	−37951.3	+	24389.8i	−1.20373	+	0.773593i
$999$	−7737.83	+	16093.4i	−0.245059	+	0.509681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.m.a.4.15	✓	1400
9.7	even	3	inner	207.4.m.a.142.56	yes	1400
23.6	even	11	inner	207.4.m.a.121.56	yes	1400
207.52	even	33	inner	207.4.m.a.52.15	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.m.a.4.15	✓	1400	1.1	even	1	trivial
207.4.m.a.52.15	yes	1400	207.52	even	33	inner
207.4.m.a.121.56	yes	1400	23.6	even	11	inner
207.4.m.a.142.56	yes	1400	9.7	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18200 + 3.06419i) q^{2} +(3.37679 + 3.94934i) q^{3} +(-2.01161 - 5.81215i) q^{4} +(-5.70696 + 2.94214i) q^{5} +(-19.4697 + 1.72968i) q^{6} +(19.1429 - 15.0541i) q^{7} +(-6.67574 - 1.96018i) q^{8} +(-4.19453 + 26.6722i) q^{9} +(3.43731 - 23.9070i) q^{10} +(-31.4455 + 3.00269i) q^{11} +(16.1614 - 27.5709i) q^{12} +(-50.2324 - 39.5032i) q^{13} +(4.35894 + 91.5055i) q^{14} +(-30.8907 - 12.6037i) q^{15} +(59.2493 - 46.5942i) q^{16} +(-70.5244 - 81.3895i) q^{17} +(-72.5763 - 71.0517i) q^{18} +(-22.8478 + 26.3678i) q^{19} +(28.5803 + 27.2513i) q^{20} +(124.095 + 24.7670i) q^{21} +(59.4134 - 102.907i) q^{22} +(-87.4531 - 67.2232i) q^{23} +(-14.8012 - 32.9839i) q^{24} +(-48.5939 + 68.2406i) q^{25} +(230.652 - 67.7257i) q^{26} +(-119.502 + 73.5009i) q^{27} +(-126.005 - 80.9782i) q^{28} +(-48.1171 + 139.025i) q^{29} +(106.024 - 67.1539i) q^{30} +(32.2921 - 30.7905i) q^{31} +(10.8430 + 227.622i) q^{32} +(-118.044 - 114.050i) q^{33} +(403.278 - 38.5083i) q^{34} +(-64.9562 + 142.234i) q^{35} +(163.461 - 29.2747i) q^{36} +(107.075 - 68.8130i) q^{37} +(-30.9420 - 127.545i) q^{38} +(-13.6130 - 331.779i) q^{39} +(43.8653 - 8.45435i) q^{40} +(47.1117 - 24.2878i) q^{41} +(-346.667 + 326.210i) q^{42} +(85.5815 + 81.6018i) q^{43} +(80.7081 + 176.726i) q^{44} +(-54.5354 - 164.558i) q^{45} +(396.808 - 121.292i) q^{46} +(234.939 + 406.927i) q^{47} +(384.089 + 76.6566i) q^{48} +(58.9574 - 243.026i) q^{49} +(-103.070 - 297.802i) q^{50} +(83.2883 - 553.360i) q^{51} +(-128.551 + 371.423i) q^{52} +(-74.3284 - 516.965i) q^{53} +(35.5318 - 526.555i) q^{54} +(170.624 - 109.653i) q^{55} +(-157.301 + 62.9740i) q^{56} +(-181.288 - 1.19517i) q^{57} +(-321.008 - 450.793i) q^{58} +(305.674 + 240.385i) q^{59} +(-11.1147 + 204.895i) q^{60} +(-89.8083 - 370.195i) q^{61} +(23.8865 + 166.134i) q^{62} +(321.231 + 573.727i) q^{63} +(-213.858 - 137.438i) q^{64} +(402.898 + 77.6522i) q^{65} +(607.042 - 112.852i) q^{66} +(-846.962 - 80.8751i) q^{67} +(-331.181 + 573.622i) q^{68} +(-29.8238 - 572.381i) q^{69} +(-294.099 - 509.394i) q^{70} +(476.503 + 1043.40i) q^{71} +(80.2838 - 169.835i) q^{72} +(-162.907 + 188.005i) q^{73} +(-22.7818 + 478.249i) q^{74} +(-433.597 + 38.5206i) q^{75} +(199.214 + 79.7534i) q^{76} +(-556.755 + 530.864i) q^{77} +(1046.34 + 682.229i) q^{78} +(-914.321 + 366.039i) q^{79} +(-201.047 + 440.231i) q^{80} +(-693.812 - 223.755i) q^{81} +(-28.3754 + 197.355i) q^{82} +(-1062.69 - 547.855i) q^{83} +(-105.681 - 771.082i) q^{84} +(641.940 + 256.994i) q^{85} +(-436.783 + 84.1830i) q^{86} +(-711.539 + 279.429i) q^{87} +(215.808 + 41.5936i) q^{88} +(-393.346 + 115.497i) q^{89} +(623.234 + 191.959i) q^{90} -1556.28 q^{91} +(-214.790 + 643.517i) q^{92} +(230.646 + 23.5594i) q^{93} +(-1759.54 - 168.016i) q^{94} +(52.8138 - 217.702i) q^{95} +(-862.343 + 811.456i) q^{96} +(-11.1322 + 233.694i) q^{97} +(616.033 + 710.939i) q^{98} +(51.8112 - 851.316i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) \) 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more