LMFDB - Embedded newform 82.6.f.b.25.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,6,Mod(23,82)] 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("82.23"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([9])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	82.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$13.1514732247$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	82.25
Dual form			82.6.f.b.23.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23607 + 3.80423i) q^{2} +7.71384i q^{3} +(-12.9443 - 9.40456i) q^{4} +(-79.0566 - 57.4380i) q^{5} +(-29.3452 - 9.53483i) q^{6} +(-36.5570 + 11.8781i) q^{7} +(51.7771 - 37.6183i) q^{8} +183.497 q^{9} +(316.226 - 229.752i) q^{10} +(147.060 + 202.411i) q^{11} +(72.5453 - 99.8500i) q^{12} +(655.014 + 212.827i) q^{13} -153.753i q^{14} +(443.067 - 609.830i) q^{15} +(79.1084 + 243.470i) q^{16} +(-176.110 - 242.394i) q^{17} +(-226.814 + 698.063i) q^{18} +(-142.507 + 46.3032i) q^{19} +(483.151 + 1486.99i) q^{20} +(-91.6257 - 281.995i) q^{21} +(-951.795 + 309.257i) q^{22} +(663.460 - 2041.92i) q^{23} +(290.181 + 399.400i) q^{24} +(1985.14 + 6109.64i) q^{25} +(-1619.28 + 2228.75i) q^{26} +3289.93i q^{27} +(584.912 + 190.049i) q^{28} +(2038.65 - 2805.97i) q^{29} +(1772.27 + 2439.32i) q^{30} +(8133.84 - 5909.58i) q^{31} -1024.00 q^{32} +(-1561.37 + 1134.40i) q^{33} +(1139.81 - 370.346i) q^{34} +(3572.33 + 1160.72i) q^{35} +(-2375.23 - 1725.71i) q^{36} +(5191.61 + 3771.93i) q^{37} -599.362i q^{38} +(-1641.71 + 5052.67i) q^{39} -6254.03 q^{40} +(1327.20 + 10681.5i) q^{41} +1186.03 q^{42} +(5007.77 - 15412.3i) q^{43} -4003.11i q^{44} +(-14506.6 - 10539.7i) q^{45} +(6947.84 + 5047.90i) q^{46} +(5373.08 + 1745.82i) q^{47} +(-1878.09 + 610.229i) q^{48} +(-12401.8 + 9010.45i) q^{49} -25696.2 q^{50} +(1869.79 - 1358.48i) q^{51} +(-6477.13 - 8915.01i) q^{52} +(9212.38 - 12679.8i) q^{53} +(-12515.6 - 4066.57i) q^{54} -24448.8i q^{55} +(-1445.98 + 1990.22i) q^{56} +(-357.176 - 1099.27i) q^{57} +(8154.62 + 11223.9i) q^{58} +(8557.52 - 26337.3i) q^{59} +(-11470.4 + 3726.95i) q^{60} +(4461.34 + 13730.6i) q^{61} +(12427.4 + 38247.6i) q^{62} +(-6708.09 + 2179.59i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-39558.8 - 54448.0i) q^{65} +(-2385.56 - 7342.00i) q^{66} +(8572.97 - 11799.7i) q^{67} +4793.85i q^{68} +(15751.0 + 5117.82i) q^{69} +(-8831.27 + 12155.2i) q^{70} +(-19646.1 - 27040.5i) q^{71} +(9500.92 - 6902.82i) q^{72} +31576.0 q^{73} +(-20766.4 + 15087.7i) q^{74} +(-47128.8 + 15313.1i) q^{75} +(2280.11 + 740.852i) q^{76} +(-7780.35 - 5652.76i) q^{77} +(-17192.2 - 12490.9i) q^{78} +56234.1i q^{79} +(7730.41 - 23791.8i) q^{80} +19211.7 q^{81} +(-42275.4 - 8154.12i) q^{82} -72334.2 q^{83} +(-1466.01 + 4511.92i) q^{84} +29278.3i q^{85} +(52442.1 + 38101.4i) q^{86} +(21644.8 + 15725.9i) q^{87} +(15228.7 + 4948.11i) q^{88} +(103183. - 33526.1i) q^{89} +(58026.5 - 42158.7i) q^{90} -26473.3 q^{91} +(-27791.4 + 20191.6i) q^{92} +(45585.5 + 62743.1i) q^{93} +(-13283.0 + 18282.5i) q^{94} +(13925.7 + 4524.72i) q^{95} -7898.97i q^{96} +(-86236.3 + 118694. i) q^{97} +(-18948.3 - 58316.9i) q^{98} +(26985.1 + 37141.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 160 q^{4} + 24 q^{5} - 100 q^{6} + 640 q^{8} - 4576 q^{9} - 96 q^{10} + 20 q^{11} + 400 q^{12} - 275 q^{13} + 1385 q^{15} - 2560 q^{16} - 105 q^{17} - 2476 q^{18} + 4720 q^{19} + 1424 q^{20}+ \cdots - 537690 q^{99}+O(q^{100}) $ 40 * q + 40 * q^2 - 160 * q^4 + 24 * q^5 - 100 * q^6 + 640 * q^8 - 4576 * q^9 - 96 * q^10 + 20 * q^11 + 400 * q^12 - 275 * q^13 + 1385 * q^15 - 2560 * q^16 - 105 * q^17 - 2476 * q^18 + 4720 * q^19 + 1424 * q^20 + 6961 * q^21 - 4140 * q^22 - 1019 * q^23 + 1600 * q^24 - 2006 * q^25 - 8620 * q^26 - 12525 * q^29 + 5540 * q^30 + 8900 * q^31 - 40960 * q^32 + 17684 * q^33 - 13100 * q^34 - 29955 * q^35 + 26704 * q^36 - 31651 * q^37 - 10104 * q^39 + 14464 * q^40 + 35044 * q^41 + 32776 * q^42 - 15615 * q^43 - 39955 * q^45 - 3224 * q^46 + 8330 * q^47 - 6400 * q^48 + 48406 * q^49 - 135016 * q^50 + 120325 * q^51 - 34480 * q^52 + 145425 * q^53 + 72200 * q^54 + 17600 * q^56 + 31992 * q^57 - 50100 * q^58 + 18978 * q^59 + 1680 * q^60 + 52673 * q^61 + 66140 * q^62 - 88455 * q^63 - 40960 * q^64 + 204480 * q^65 - 17556 * q^66 - 149205 * q^67 - 249735 * q^69 - 49100 * q^70 + 151175 * q^71 - 106816 * q^72 - 107670 * q^73 + 126604 * q^74 + 120180 * q^75 - 75520 * q^76 - 207367 * q^77 - 99284 * q^78 + 22784 * q^80 + 1167568 * q^81 + 84204 * q^82 - 281376 * q^83 + 111376 * q^84 - 131400 * q^86 - 141269 * q^87 + 66240 * q^88 - 277775 * q^89 + 159820 * q^90 - 518682 * q^91 + 12896 * q^92 - 172375 * q^93 + 16320 * q^94 + 149585 * q^95 + 330875 * q^97 - 171004 * q^98 - 537690 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$3$			7.71384i			0.494843i	0.968908	+	0.247422i	$0.0795832\pi$
$3$			7.71384i			0.494843i	−0.968908	+	0.247422i	$0.920417\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	−79.0566	−	57.4380i	−1.41421	−	1.02748i	−0.992694	−	0.120659i	$-0.961499\pi$
$5$	−79.0566	−	57.4380i	−1.41421	−	1.02748i	−0.421513	−	0.906822i	$-0.638501\pi$
$6$	−29.3452	−	9.53483i	−0.332781	−	0.108127i
$7$	−36.5570	+	11.8781i	−0.281985	+	0.0916224i	−0.446595	−	0.894736i	$-0.647363\pi$
$7$	−36.5570	+	11.8781i	−0.281985	+	0.0916224i	0.164610	+	0.986359i	$0.447363\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	183.497			0.755130
$10$	316.226	−	229.752i	0.999995	−	0.726539i
$11$	147.060	+	202.411i	0.366450	+	0.504374i	0.951932	−	0.306311i	$-0.0990947\pi$
$11$	147.060	+	202.411i	0.366450	+	0.504374i	−0.585482	+	0.810685i	$0.699095\pi$
$12$	72.5453	−	99.8500i	0.145431	−	0.200168i
$13$	655.014	+	212.827i	1.07496	+	0.349276i	0.792417	−	0.609979i	$-0.208822\pi$
$13$	655.014	+	212.827i	1.07496	+	0.349276i	0.282542	+	0.959255i	$0.408822\pi$
$14$		−	153.753i		−	0.209655i
$15$	443.067	−	609.830i	0.508442	−	0.699811i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	−176.110	−	242.394i	−0.147796	−	0.203423i	0.728700	−	0.684833i	$-0.240125\pi$
$17$	−176.110	−	242.394i	−0.147796	−	0.203423i	−0.876496	+	0.481410i	$0.840125\pi$
$18$	−226.814	+	698.063i	−0.165002	+	0.507824i
$19$	−142.507	+	46.3032i	−0.0905631	+	0.0294257i	−0.353948	−	0.935265i	$-0.615161\pi$
$19$	−142.507	+	46.3032i	−0.0905631	+	0.0294257i	0.263385	+	0.964691i	$0.415161\pi$
$20$	483.151	+	1486.99i	0.270089	+	0.831250i
$21$	−91.6257	−	281.995i	−0.0453387	−	0.139538i
$22$	−951.795	+	309.257i	−0.419263	+	0.136227i
$23$	663.460	−	2041.92i	0.261514	−	0.804858i	−0.730962	−	0.682418i	$-0.760928\pi$
$23$	663.460	−	2041.92i	0.261514	−	0.804858i	0.992476	−	0.122439i	$-0.0390717\pi$
$24$	290.181	+	399.400i	0.102835	+	0.141540i
$25$	1985.14	+	6109.64i	0.635246	+	1.95509i
$26$	−1619.28	+	2228.75i	−0.469775	+	0.646589i
$27$			3289.93i			0.868514i
$28$	584.912	+	190.049i	0.140992	+	0.0458112i
$29$	2038.65	−	2805.97i	0.450141	−	0.619566i	−0.522287	−	0.852770i	$-0.674921\pi$
$29$	2038.65	−	2805.97i	0.450141	−	0.619566i	0.972428	+	0.233204i	$0.0749210\pi$
$30$	1772.27	+	2439.32i	0.359523	+	0.494841i
$31$	8133.84	−	5909.58i	1.52017	−	1.10447i	0.558762	−	0.829328i	$-0.311277\pi$
$31$	8133.84	−	5909.58i	1.52017	−	1.10447i	0.961405	−	0.275138i	$-0.0887235\pi$
$32$	−1024.00			−0.176777
$33$	−1561.37	+	1134.40i	−0.249586	+	0.181335i
$34$	1139.81	−	370.346i	0.169096	−	0.0549427i
$35$	3572.33	+	1160.72i	0.492925	+	0.160161i
$36$	−2375.23	−	1725.71i	−0.305457	−	0.221927i
$37$	5191.61	+	3771.93i	0.623444	+	0.452959i	0.854123	−	0.520071i	$-0.174095\pi$
$37$	5191.61	+	3771.93i	0.623444	+	0.452959i	−0.230679	+	0.973030i	$0.574095\pi$
$38$		−	599.362i		−	0.0673333i
$39$	−1641.71	+	5052.67i	−0.172837	+	0.531936i
$40$	−6254.03			−0.618031
$41$	1327.20	+	10681.5i	0.123304	+	0.992369i
$41$	1327.20	+	10681.5i	0.123304	+	0.992369i
$42$	1186.03			0.103746
$43$	5007.77	−	15412.3i	0.413022	−	1.27115i	−0.500986	−	0.865456i	$-0.667029\pi$
$43$	5007.77	−	15412.3i	0.413022	−	1.27115i	0.914008	−	0.405696i	$-0.132971\pi$
$44$		−	4003.11i		−	0.311721i
$45$	−14506.6	−	10539.7i	−1.06791	−	0.775882i
$46$	6947.84	+	5047.90i	0.484123	+	0.351736i
$47$	5373.08	+	1745.82i	0.354796	+	0.115280i	0.480992	−	0.876725i	$-0.340277\pi$
$47$	5373.08	+	1745.82i	0.354796	+	0.115280i	−0.126196	+	0.992005i	$0.540277\pi$
$48$	−1878.09	+	610.229i	−0.117656	+	0.0382287i
$49$	−12401.8	+	9010.45i	−0.737896	+	0.536113i
$50$	−25696.2			−1.45360
$51$	1869.79	−	1358.48i	0.100662	−	0.0731356i
$52$	−6477.13	−	8915.01i	−0.332181	−	0.457208i
$53$	9212.38	−	12679.8i	0.450487	−	0.620042i	−0.522015	−	0.852936i	$-0.674820\pi$
$53$	9212.38	−	12679.8i	0.450487	−	0.620042i	0.972502	+	0.232894i	$0.0748196\pi$
$54$	−12515.6	−	4066.57i	−0.584074	−	0.189777i
$55$		−	24448.8i		−	1.08981i
$56$	−1445.98	+	1990.22i	−0.0616159	+	0.0848070i
$57$	−357.176	−	1099.27i	−0.0145611	−	0.0448145i
$58$	8154.62	+	11223.9i	0.318298	+	0.438099i
$59$	8557.52	−	26337.3i	0.320050	−	0.985012i	−0.653576	−	0.756861i	$-0.726732\pi$
$59$	8557.52	−	26337.3i	0.320050	−	0.985012i	0.973626	−	0.228151i	$-0.0732681\pi$
$60$	−11470.4	+	3726.95i	−0.411338	+	0.133652i
$61$	4461.34	+	13730.6i	0.153512	+	0.472460i	0.998007	−	0.0631028i	$-0.0200996\pi$
$61$	4461.34	+	13730.6i	0.153512	+	0.472460i	−0.844496	+	0.535563i	$0.820100\pi$
$62$	12427.4	+	38247.6i	0.410583	+	1.26364i
$63$	−6708.09	+	2179.59i	−0.212935	+	0.0691868i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	−39558.8	−	54448.0i	−1.16134	−	1.59845i
$66$	−2385.56	−	7342.00i	−0.0674109	−	0.207470i
$67$	8572.97	−	11799.7i	0.233316	−	0.321132i	−0.676265	−	0.736658i	$-0.736403\pi$
$67$	8572.97	−	11799.7i	0.233316	−	0.321132i	0.909581	+	0.415526i	$0.136403\pi$
$68$			4793.85i			0.125722i
$69$	15751.0	+	5117.82i	0.398278	+	0.129408i
$70$	−8831.27	+	12155.2i	−0.215416	+	0.296495i
$71$	−19646.1	−	27040.5i	−0.462519	−	0.636603i	0.512510	−	0.858681i	$-0.328716\pi$
$71$	−19646.1	−	27040.5i	−0.462519	−	0.636603i	−0.975029	+	0.222079i	$0.928716\pi$
$72$	9500.92	−	6902.82i	0.215990	−	0.156926i
$73$	31576.0			0.693505			0.346752	−	0.937957i	$-0.387284\pi$
$73$	31576.0			0.693505			0.346752	+	0.937957i	$0.387284\pi$
$74$	−20766.4	+	15087.7i	−0.440842	+	0.320290i
$75$	−47128.8	+	15313.1i	−0.967461	+	0.314347i
$76$	2280.11	+	740.852i	0.0452816	+	0.0147129i
$77$	−7780.35	−	5652.76i	−0.149545	−	0.108651i
$78$	−17192.2	−	12490.9i	−0.319960	−	0.232465i
$79$			56234.1i			1.01375i	0.862019	+	0.506876i	$0.169200\pi$
$79$			56234.1i			1.01375i	−0.862019	+	0.506876i	$0.830800\pi$
$80$	7730.41	−	23791.8i	0.135045	−	0.415625i
$81$	19211.7			0.325352
$82$	−42275.4	−	8154.12i	−0.694309	−	0.133919i
$83$	−72334.2			−1.15252			−0.576260	−	0.817266i	$-0.695489\pi$
$83$	−72334.2			−1.15252			−0.576260	+	0.817266i	$0.695489\pi$
$84$	−1466.01	+	4511.92i	−0.0226694	+	0.0697691i
$85$			29278.3i			0.439539i
$86$	52442.1	+	38101.4i	0.764599	+	0.555514i
$87$	21644.8	+	15725.9i	0.306588	+	0.222749i
$88$	15228.7	+	4948.11i	0.209632	+	0.0681134i
$89$	103183.	−	33526.1i	1.38080	−	0.448650i	0.477869	−	0.878431i	$-0.341409\pi$
$89$	103183.	−	33526.1i	1.38080	−	0.448650i	0.902933	+	0.429781i	$0.141409\pi$
$90$	58026.5	−	42158.7i	0.755127	−	0.548632i
$91$	−26473.3			−0.335124
$92$	−27791.4	+	20191.6i	−0.342326	+	0.248715i
$93$	45585.5	+	62743.1i	0.546537	+	0.752244i
$94$	−13283.0	+	18282.5i	−0.155051	+	0.213410i
$95$	13925.7	+	4524.72i	0.158309	+	0.0514378i
$96$		−	7898.97i		−	0.0874767i
$97$	−86236.3	+	118694.i	−0.930595	+	1.28085i	0.0290321	+	0.999578i	$0.490757\pi$
$97$	−86236.3	+	118694.i	−0.930595	+	1.28085i	−0.959627	+	0.281276i	$0.909243\pi$
$98$	−18948.3	−	58316.9i	−0.199299	−	0.613379i
$99$	26985.1	+	37141.8i	0.276717	+	0.380868i
$100$	31762.3	−	97754.3i	0.317623	−	0.977543i
$101$	97450.7	−	31663.7i	0.950565	−	0.308857i	0.207620	−	0.978210i	$-0.433428\pi$
$101$	97450.7	−	31663.7i	0.950565	−	0.308857i	0.742945	+	0.669352i	$0.233428\pi$
$102$	2856.79	+	8792.29i	0.0271880	+	0.0836761i
$103$	25317.8	+	77920.1i	0.235143	+	0.723697i	0.997102	+	0.0760715i	$0.0242377\pi$
$103$	25317.8	+	77920.1i	0.235143	+	0.723697i	−0.761959	+	0.647625i	$0.775762\pi$
$104$	41920.9	−	13620.9i	0.380056	−	0.123488i
$105$	−8953.60	+	27556.3i	−0.0792546	+	0.243921i
$106$	36849.5	+	50719.0i	0.318542	+	0.438436i
$107$	−28700.0	−	88329.6i	−0.242339	−	0.745842i	−0.996063	−	0.0886508i	$-0.971744\pi$
$107$	−28700.0	−	88329.6i	−0.242339	−	0.745842i	0.753724	−	0.657191i	$-0.228256\pi$
$108$	30940.3	−	42585.7i	0.255250	−	0.351321i
$109$		−	1095.85i		−	0.00883458i	−0.999990	−	0.00441729i	$-0.998594\pi$
$109$		−	1095.85i		−	0.00883458i	0.999990	−	0.00441729i	$-0.00140607\pi$
$110$	93008.8	+	30220.4i	0.732896	+	0.238132i
$111$	−29096.0	+	40047.3i	−0.224144	+	0.308507i
$112$	−5783.93	−	7960.90i	−0.0435690	−	0.0599676i
$113$	67717.8	−	49199.8i	0.498892	−	0.362466i	−0.309702	−	0.950834i	$-0.600229\pi$
$113$	67717.8	−	49199.8i	0.498892	−	0.362466i	0.808594	+	0.588368i	$0.200229\pi$
$114$	4623.38			0.0333194
$115$	−169735.	+	123319.i	−1.19681	+	0.869534i
$116$	−52777.8	+	17148.5i	−0.364172	+	0.118327i
$117$	120193.	+	39053.0i	0.811735	+	0.263749i
$118$	89615.5	+	65109.5i	0.592486	+	0.430466i
$119$	9317.23	+	6769.36i	0.0603142	+	0.0438208i
$120$		−	48242.6i		−	0.305828i
$121$	30423.9	−	93635.2i	0.188909	−	0.581401i
$122$	−57748.8			−0.351272
$123$	−82395.5	+	10237.8i	−0.491067	+	0.0610159i
$124$	−160864.			−0.939515
$125$	99621.5	−	306603.i	0.570266	−	1.75510i
$126$		−	28213.2i		−	0.158316i
$127$	2673.57	+	1942.46i	0.0147090	+	0.0106867i	0.595115	−	0.803640i	$-0.297106\pi$
$127$	2673.57	+	1942.46i	0.0147090	+	0.0106867i	−0.580406	+	0.814327i	$0.697106\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	118888.	+	38629.2i	0.629021	+	0.204381i
$130$	256030.	−	83189.2i	1.32872	−	0.431726i
$131$	−277349.	+	201506.i	−1.41205	+	1.02591i	−0.419025	+	0.907975i	$0.637628\pi$
$131$	−277349.	+	201506.i	−1.41205	+	1.02591i	−0.993021	+	0.117937i	$0.962372\pi$
$132$	30879.3			0.154253
$133$	4659.63	−	3385.42i	0.0228414	−	0.0165952i
$134$	34291.9	+	47198.7i	0.164979	+	0.227075i
$135$	188967.	−	260090.i	0.892382	−	1.22826i
$136$	−18236.9	−	5925.53i	−0.0845481	−	0.0274713i
$137$			31456.3i			0.143188i	0.997434	+	0.0715938i	$0.0228085\pi$
$137$			31456.3i			0.143188i	−0.997434	+	0.0715938i	$0.977191\pi$
$138$	−38938.7	+	53594.5i	−0.174054	+	0.239565i
$139$	11896.7	+	36614.4i	0.0522265	+	0.160737i	0.973768	−	0.227543i	$-0.0730694\pi$
$139$	11896.7	+	36614.4i	0.0522265	+	0.160737i	−0.921541	+	0.388280i	$0.873069\pi$
$140$	−35325.1	−	48620.8i	−0.152322	−	0.209654i
$141$	−13467.0	+	41447.1i	−0.0570456	+	0.175568i
$142$	127152.	−	41314.2i	0.529179	−	0.171941i
$143$	53248.1	+	163881.i	0.217753	+	0.670174i
$144$	14516.1	+	44676.0i	0.0583370	+	0.179543i
$145$	−322338.	+	104734.i	−1.27318	+	0.413683i
$146$	−39030.0	+	120122.i	−0.151536	+	0.466381i
$147$	−69505.2	−	95665.7i	−0.265292	−	0.365143i
$148$	−31728.3	−	97649.7i	−0.119067	−	0.366451i
$149$	−94377.3	+	129899.i	−0.348259	+	0.479337i	−0.946831	−	0.321732i	$-0.895735\pi$
$149$	−94377.3	+	129899.i	−0.348259	+	0.479337i	0.598572	+	0.801069i	$0.295735\pi$
$150$		−	198217.i		−	0.719303i
$151$	481024.	+	156294.i	1.71682	+	0.557828i	0.991445	−	0.130529i	$-0.0416675\pi$
$151$	481024.	+	156294.i	1.71682	+	0.557828i	0.725373	+	0.688357i	$0.241668\pi$
$152$	−5636.74	+	7758.30i	−0.0197888	+	0.0272369i
$153$	−32315.6	−	44478.6i	−0.111605	−	0.153611i
$154$	31121.4	−	22611.0i	0.105744	−	0.0768278i
$155$	−982467.			−3.28465
$156$	68769.0	−	49963.6i	0.226246	−	0.164377i
$157$	−314261.	+	102110.i	−1.01752	+	0.330611i	−0.769843	−	0.638233i	$-0.779666\pi$
$157$	−314261.	+	102110.i	−1.01752	+	0.330611i	−0.247673	+	0.968844i	$0.579666\pi$
$158$	−213927.	−	69509.1i	−0.681747	−	0.221513i
$159$	97809.6	+	71062.8i	0.306823	+	0.222920i
$160$	80953.9	+	58816.5i	0.249999	+	0.181635i
$161$			82527.1i			0.250918i
$162$	−23747.0	+	73085.7i	−0.0710920	+	0.218799i
$163$	−377280.			−1.11223			−0.556116	−	0.831105i	$-0.687709\pi$
$163$	−377280.			−1.11223			−0.556116	+	0.831105i	$0.687709\pi$
$164$	83275.4	−	150746.i	0.241773	−	0.437660i
$165$	188594.			0.539285
$166$	89410.0	−	275176.i	0.251835	−	0.775068i
$167$		−	477936.i		−	1.32611i	−0.748572	−	0.663053i	$-0.769260\pi$
$167$		−	477936.i		−	1.32611i	0.748572	−	0.663053i	$-0.230740\pi$
$168$	−15352.3	−	11154.1i	−0.0419662	−	0.0304902i
$169$	83365.6	+	60568.6i	0.224528	+	0.163129i
$170$	−111381.	−	36189.9i	−0.295590	−	0.0960429i
$171$	−26149.5	+	8496.49i	−0.0683870	+	0.0222203i
$172$	−209768.	+	152406.i	−0.540653	+	0.392808i
$173$	−504346.			−1.28119			−0.640595	−	0.767879i	$-0.721312\pi$
$173$	−504346.			−1.28119			−0.640595	+	0.767879i	$0.721312\pi$
$174$	−86579.1	+	62903.4i	−0.216790	+	0.157507i
$175$	−145142.	−	199771.i	−0.358259	−	0.493102i
$176$	−37647.5	+	51817.3i	−0.0916124	+	0.126094i
$177$	203162.	+	66011.3i	0.487427	+	0.158374i
$178$			433970.i			1.02662i
$179$	359410.	−	494686.i	0.838413	−	1.15398i	−0.147885	−	0.989005i	$-0.547247\pi$
$179$	359410.	−	494686.i	0.838413	−	1.15398i	0.986298	−	0.164972i	$-0.0527534\pi$
$180$	88656.6	+	272857.i	0.203953	+	0.627702i
$181$	496990.	+	684049.i	1.12759	+	1.55200i	0.792566	+	0.609786i	$0.208745\pi$
$181$	496990.	+	684049.i	1.12759	+	1.55200i	0.335025	+	0.942209i	$0.391255\pi$
$182$	32722.8	−	100711.i	0.0732272	−	0.225370i
$183$	−105916.	+	34414.1i	−0.233793	+	0.0759641i
$184$	−42461.4	−	130683.i	−0.0924592	−	0.284560i
$185$	−193779.	−	596391.i	−0.416273	−	1.28116i
$186$	−295036.	+	95863.0i	−0.625306	+	0.203174i
$187$	23164.6	−	71293.2i	0.0484418	−	0.149089i
$188$	−53131.9	−	73129.8i	−0.109638	−	0.150904i
$189$	−39078.1	−	120270.i	−0.0795753	−	0.244908i
$190$	−34426.1	+	47383.5i	−0.0691837	+	0.0952232i
$191$			243222.i			0.482414i	0.970474	+	0.241207i	$0.0775432\pi$
$191$			243222.i			0.482414i	−0.970474	+	0.241207i	$0.922457\pi$
$192$	30049.5	+	9763.67i	0.0588280	+	0.0191144i
$193$	458372.	−	630895.i	0.885777	−	1.21917i	−0.0890095	−	0.996031i	$-0.528370\pi$
$193$	458372.	−	630895.i	0.885777	−	1.21917i	0.974787	−	0.223137i	$-0.0716298\pi$
$194$	−344945.	−	474776.i	−0.658030	−	0.905701i
$195$	420003.	−	305150.i	0.790981	−	0.574682i
$196$	245272.			0.456045
$197$	425285.	−	308987.i	0.780754	−	0.567251i	−0.124451	−	0.992226i	$-0.539717\pi$
$197$	425285.	−	308987.i	0.780754	−	0.567251i	0.905205	+	0.424975i	$0.139717\pi$
$198$	−174651.	+	56747.6i	−0.316598	+	0.102869i
$199$	590010.	+	191706.i	1.05615	+	0.343165i	0.785080	−	0.619394i	$-0.212622\pi$
$199$	590010.	+	191706.i	1.05615	+	0.343165i	0.271072	+	0.962559i	$0.412622\pi$
$200$	332619.	+	241662.i	0.587993	+	0.427202i
$201$	91020.9	+	66130.5i	0.158910	+	0.115455i
$202$			409863.i			0.706741i
$203$	−41197.6	+	126793.i	−0.0701668	+	0.215951i
$204$	−36979.0			−0.0622128
$205$	508601.	−	920675.i	0.845264	−	1.53011i
$206$	−327720.			−0.538066
$207$	121743.	−	374685.i	0.197477	−	0.607772i
$208$			176313.i			0.282570i
$209$	−30329.4	−	22035.6i	−0.0480284	−	0.0348947i
$210$	−93763.3	−	68123.0i	−0.146718	−	0.106597i
$211$	524306.	+	170357.i	0.810735	+	0.263424i	0.684909	−	0.728629i	$-0.259842\pi$
$211$	524306.	+	170357.i	0.810735	+	0.263424i	0.125826	+	0.992052i	$0.459842\pi$
$212$	−238495.	+	77491.7i	−0.364452	+	0.118417i
$213$	208586.	−	151547.i	0.315019	−	0.228874i
$214$	371501.			0.554530
$215$	−1.28115e6	+	930810.i	−1.89018	+	1.37330i
$216$	123761.	+	170343.i	0.180489	+	0.248422i
$217$	−227154.	+	312651.i	−0.327470	+	0.450724i
$218$	4168.87	+	1354.55i	0.00594124	+	0.00193043i
$219$			243572.i			0.343176i
$220$	−229930.	+	316472.i	−0.320287	+	0.440837i
$221$	−63766.3	−	196253.i	−0.0878235	−	0.270293i
$222$	−116384.	−	160189.i	−0.158493	−	0.218148i
$223$	4110.88	−	12652.0i	0.00553570	−	0.0170371i	−0.948251	−	0.317523i	$-0.897149\pi$
$223$	4110.88	−	12652.0i	0.00553570	−	0.0170371i	0.953786	+	0.300486i	$0.0971489\pi$
$224$	37434.4	−	12163.2i	0.0498483	−	0.0161967i
$225$	364267.	+	1.12110e6i	0.479694	+	1.47634i
$226$	103464.	+	318428.i	0.134746	+	0.414706i
$227$	−786291.	+	255481.i	−1.01279	+	0.329075i	−0.767964	−	0.640493i	$-0.778730\pi$
$227$	−786291.	+	255481.i	−1.01279	+	0.329075i	−0.244824	+	0.969568i	$0.578730\pi$
$228$	−5714.81	+	17588.4i	−0.00728056	+	0.0224073i
$229$	105102.	+	144660.i	0.132441	+	0.182289i	0.870087	−	0.492899i	$-0.164063\pi$
$229$	105102.	+	144660.i	0.132441	+	0.182289i	−0.737646	+	0.675188i	$0.764063\pi$
$230$	−259331.	−	798140.i	−0.323248	−	0.994854i
$231$	43604.5	−	60016.4i	0.0537652	−	0.0740014i
$232$		−	221975.i		−	0.270760i
$233$	1.54388e6	+	501636.i	1.86304	+	0.605340i	0.993832	+	0.110900i	$0.0353734\pi$
$233$	1.54388e6	+	501636.i	1.86304	+	0.605340i	0.869212	+	0.494439i	$0.164627\pi$
$234$	−297133.	+	408969.i	−0.354741	+	0.488259i
$235$	−324501.	−	446637.i	−0.383307	−	0.527576i
$236$	−358462.	+	260438.i	−0.418951	+	0.304386i
$237$	−433781.			−0.501648
$238$	−37268.9	+	27077.5i	−0.0426486	+	0.0309860i
$239$	−400163.	+	130021.i	−0.453150	+	0.147237i	−0.526695	−	0.850055i	$-0.676569\pi$
$239$	−400163.	+	130021.i	−0.453150	+	0.147237i	0.0735447	+	0.997292i	$0.476569\pi$
$240$	183526.	+	59631.2i	0.205669	+	0.0668260i
$241$	1.13619e6	+	825489.i	1.26011	+	0.915522i	0.998763	−	0.0497232i	$-0.0158339\pi$
$241$	1.13619e6	+	825489.i	1.26011	+	0.915522i	0.261345	+	0.965245i	$0.415834\pi$
$242$	318603.	+	231479.i	0.349713	+	0.254082i
$243$			947648.i			1.02951i
$244$	71381.5	−	219690.i	0.0767558	−	0.236230i
$245$	1.49799e6			1.59438
$246$	62899.6	−	326106.i	0.0662690	−	0.343574i
$247$	−103198.			−0.107629
$248$	198838.	−	611962.i	0.205292	−	0.631822i
$249$		−	557975.i		−	0.570317i
$250$	1.04325e6	+	757965.i	1.05569	+	0.767007i
$251$	−312339.	−	226928.i	−0.312926	−	0.227354i	0.420225	−	0.907420i	$-0.361951\pi$
$251$	−312339.	−	226928.i	−0.312926	−	0.227354i	−0.733151	+	0.680066i	$0.761951\pi$
$252$	107329.	+	34873.4i	0.106468	+	0.0345934i
$253$	510876.	−	165994.i	0.501781	−	0.163039i
$254$	−10694.3	+	7769.84i	−0.0104008	+	0.00755662i
$255$	−225848.			−0.217503
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	254894.	+	350831.i	0.240728	+	0.331334i	0.912237	−	0.409663i	$-0.134354\pi$
$257$	254894.	+	350831.i	0.240728	+	0.331334i	−0.671509	+	0.740996i	$0.734354\pi$
$258$	−293908.	+	404530.i	−0.274892	+	0.378357i
$259$	−234593.	−	76223.9i	−0.217303	−	0.0706060i
$260$			1.07682e6i			0.987896i
$261$	374086.	−	514885.i	0.339915	−	0.467853i
$262$	−423752.	−	1.30417e6i	−0.381381	−	1.17377i
$263$	−222651.	−	306453.i	−0.198489	−	0.273196i	0.698157	−	0.715944i	$-0.254004\pi$
$263$	−222651.	−	306453.i	−0.198489	−	0.273196i	−0.896646	+	0.442748i	$0.854004\pi$
$264$	−38168.9	+	117472.i	−0.0337055	+	0.103735i
$265$	−1.45660e6	+	473277.i	−1.27416	+	0.414001i
$266$	7119.28	+	21910.9i	0.00616924	+	0.0189870i
$267$	258615.	+	795934.i	0.222011	+	0.683280i
$268$	−221942.	+	72113.3i	−0.188757	+	0.0613307i
$269$	394453.	−	1.21400e6i	0.332365	−	1.02291i	−0.635641	−	0.771985i	$-0.719264\pi$
$269$	394453.	−	1.21400e6i	0.332365	−	1.02291i	0.968006	−	0.250929i	$-0.0807359\pi$
$270$	755867.	+	1.04036e6i	0.631009	+	0.868510i
$271$	−428231.	−	1.31796e6i	−0.354205	−	1.09013i	−0.956469	−	0.291835i	$-0.905734\pi$
$271$	−428231.	−	1.31796e6i	−0.354205	−	1.09013i	0.602263	−	0.798298i	$-0.294266\pi$
$272$	45084.1	−	62053.0i	0.0369489	−	0.0508558i
$273$		−	204211.i		−	0.165834i
$274$	−119667.	−	38882.1i	−0.0962935	−	0.0312877i
$275$	−944725.	+	1.30030e6i	−0.753310	+	1.03684i
$276$	−155755.	−	214378.i	−0.123075	−	0.169398i
$277$	555565.	−	403641.i	0.435046	−	0.316079i	−0.348617	−	0.937265i	$-0.613349\pi$
$277$	555565.	−	403641.i	0.435046	−	0.316079i	0.783663	+	0.621186i	$0.213349\pi$
$278$	−153995.			−0.119507
$279$	1.49253e6	−	1.08439e6i	1.14792	−	0.834016i
$280$	228629.	−	74286.0i	0.174275	−	0.0566255i
$281$	−985635.	−	320252.i	−0.744647	−	0.241950i	−0.0879706	−	0.996123i	$-0.528038\pi$
$281$	−985635.	−	320252.i	−0.744647	−	0.241950i	−0.656676	+	0.754173i	$0.728038\pi$
$282$	−141028.	−	102463.i	−0.105604	−	0.0767262i
$283$	−585149.	−	425136.i	−0.434310	−	0.315545i	0.349060	−	0.937100i	$-0.386501\pi$
$283$	−585149.	−	425136.i	−0.434310	−	0.315545i	−0.783370	+	0.621555i	$0.786501\pi$
$284$			534782.i			0.393442i
$285$	−34903.0	+	107420.i	−0.0254537	+	0.0783383i
$286$	−689257.			−0.498272
$287$	−175394.	−	374720.i	−0.125693	−	0.268536i
$288$	−187901.			−0.133489
$289$	411020.	−	1.26499e6i	0.289480	−	0.890926i
$290$		−	1.35570e6i		−	0.946608i
$291$	−915587.	−	665213.i	−0.633822	−	0.460498i
$292$	−408728.	−	296958.i	−0.280529	−	0.203816i
$293$	−2.28724e6	−	743170.i	−1.55648	−	0.505730i	−0.600613	−	0.799540i	$-0.705077\pi$
$293$	−2.28724e6	−	743170.i	−1.55648	−	0.505730i	−0.955864	+	0.293809i	$0.905077\pi$
$294$	449847.	−	146164.i	0.303526	−	0.0986217i
$295$	−2.18929e6	+	1.59061e6i	−1.46470	+	1.06417i
$296$	410700.			0.272455
$297$	−665919.	+	483818.i	−0.438056	+	0.318267i
$298$	−377509.	−	519597.i	−0.246256	−	0.338943i
$299$	869151.	−	1.19628e6i	0.562234	−	0.773849i
$300$	754061.	+	245009.i	0.483730	+	0.157174i
$301$			622912.i			0.396288i
$302$	−1.18916e6	+	1.63673e6i	−0.750277	+	1.03267i
$303$	244248.	+	751719.i	0.152836	+	0.470380i
$304$	−22546.9	−	31033.2i	−0.0139928	−	0.0192594i
$305$	435959.	−	1.34174e6i	0.268347	−	0.825886i
$306$	209151.	−	67957.2i	0.127690	−	0.0414889i
$307$	−592289.	−	1.82288e6i	−0.358664	−	1.10385i	−0.953854	−	0.300270i	$-0.902923\pi$
$307$	−592289.	−	1.82288e6i	−0.358664	−	1.10385i	0.595190	−	0.803585i	$-0.297077\pi$
$308$	47549.3	+	146342.i	0.0285606	+	0.0879004i
$309$	−601063.	+	195297.i	−0.358116	+	0.116359i
$310$	1.21440e6	−	3.73753e6i	0.717722	−	2.20892i
$311$	−47254.2	−	65039.9i	−0.0277038	−	0.0381310i	0.794940	−	0.606688i	$-0.207502\pi$
$311$	−47254.2	−	65039.9i	−0.0277038	−	0.0381310i	−0.822644	+	0.568556i	$0.807502\pi$
$312$	105070.	+	323371.i	0.0611070	+	0.188068i
$313$	−1.59612e6	+	2.19687e6i	−0.920882	+	1.26749i	0.0424296	+	0.999099i	$0.486490\pi$
$313$	−1.59612e6	+	2.19687e6i	−0.920882	+	1.26749i	−0.963312	+	0.268386i	$0.913510\pi$
$314$		−	1.32173e6i		−	0.756519i
$315$	655510.	+	212988.i	0.372223	+	0.120942i
$316$	528857.	−	727909.i	0.297934	−	0.410071i
$317$	187030.	+	257425.i	0.104535	+	0.143881i	0.858080	−	0.513516i	$-0.171657\pi$
$317$	187030.	+	257425.i	0.104535	+	0.143881i	−0.753544	+	0.657397i	$0.771657\pi$
$318$	−391238.	+	284251.i	−0.216957	+	0.157628i
$319$	867765.			0.477447
$320$	−323816.	+	235266.i	−0.176776	+	0.128435i
$321$	681360.	−	221387.i	0.369075	−	0.119920i
$322$	−313952.	−	102009.i	−0.168742	−	0.0548276i
$323$	36320.5	+	26388.4i	0.0193707	+	0.0140736i
$324$	−248682.	−	180678.i	−0.131608	−	0.0956186i
$325$			4.42439e6i			2.32351i
$326$	466344.	−	1.43526e6i	0.243032	−	0.747974i
$327$	8453.23			0.00437173
$328$	470538.	+	503131.i	0.241496	+	0.258224i
$329$	−217161.			−0.110609
$330$	−233115.	+	717455.i	−0.117838	+	0.362668i
$331$		−	1.28033e6i		−	0.642319i	−0.947025	−	0.321160i	$-0.895927\pi$
$331$		−	1.28033e6i		−	0.642319i	0.947025	−	0.321160i	$-0.104073\pi$
$332$	936314.	+	680272.i	0.466204	+	0.338717i
$333$	952643.	+	692136.i	0.470782	+	0.342043i
$334$	1.81818e6	+	590761.i	0.891804	+	0.289765i
$335$	−1.35550e6	+	440429.i	−0.659914	+	0.214419i
$336$	61409.1	−	44616.3i	0.0296746	−	0.0215598i
$337$	−1.69810e6			−0.814496			−0.407248	−	0.913318i	$-0.633511\pi$
$337$	−1.69810e6			−0.814496			−0.407248	+	0.913318i	$0.633511\pi$
$338$	−333462.	+	242275.i	−0.158765	+	0.115350i
$339$	379520.	+	522364.i	0.179364	+	0.246873i
$340$	275349.	−	378986.i	0.129177	−	0.177797i
$341$	2.39233e6	+	777316.i	1.11413	+	0.362002i
$342$		−	109981.i		−	0.0508454i
$343$	726075.	−	999357.i	0.333232	−	0.458654i
$344$	−320497.	−	986390.i	−0.146025	−	0.449420i
$345$	−951266.	−	1.30931e6i	−0.430283	−	0.592234i
$346$	623406.	−	1.91865e6i	0.279950	−	0.861598i
$347$	−1.36308e6	+	442890.i	−0.607710	+	0.197457i	−0.596676	−	0.802482i	$-0.703512\pi$
$347$	−1.36308e6	+	442890.i	−0.607710	+	0.197457i	−0.0110338	+	0.999939i	$0.503512\pi$
$348$	−132281.	−	407119.i	−0.0585531	−	0.180208i
$349$	−1.20925e6	−	3.72170e6i	−0.531439	−	1.63560i	−0.751220	−	0.660052i	$-0.770534\pi$
$349$	−1.20925e6	−	3.72170e6i	−0.531439	−	1.63560i	0.219781	−	0.975549i	$-0.429466\pi$
$350$	939378.	−	305222.i	0.409893	−	0.133182i
$351$	−700185.	+	2.15495e6i	−0.303351	+	0.933618i
$352$	−150590.	−	207269.i	−0.0647797	−	0.0891617i
$353$	848858.	+	2.61252e6i	0.362575	+	1.11589i	0.951485	+	0.307694i	$0.0995573\pi$
$353$	848858.	+	2.61252e6i	0.362575	+	1.11589i	−0.588910	+	0.808199i	$0.700443\pi$
$354$	−502244.	+	691279.i	−0.213013	+	0.293188i
$355$			3.26616e6i			1.37552i
$356$	−1.65092e6	−	536417.i	−0.690401	−	0.224325i
$357$	−52217.8	+	71871.6i	−0.0216844	+	0.0298461i
$358$	1.43764e6	+	1.97874e6i	0.592848	+	0.815985i
$359$	315663.	−	229342.i	0.129267	−	0.0939179i	−0.521273	−	0.853390i	$-0.674543\pi$
$359$	315663.	−	229342.i	0.129267	−	0.0939179i	0.650540	+	0.759472i	$0.274543\pi$
$360$	−1.14759e6			−0.466694
$361$	−1.98504e6	+	1.44222e6i	−0.801681	+	0.582455i
$362$	−3.21659e6	+	1.04513e6i	−1.29010	+	0.419180i
$363$	722287.	+	234685.i	0.287702	+	0.0934801i
$364$	342678.	+	248970.i	0.135560	+	0.0984904i
$365$	−2.49629e6	−	1.81366e6i	−0.980759	−	0.712563i
$366$		−	445465.i		−	0.173825i
$367$	−1.42077e6	+	4.37268e6i	−0.550628	+	1.69466i	0.156589	+	0.987664i	$0.449950\pi$
$367$	−1.42077e6	+	4.37268e6i	−0.550628	+	1.69466i	−0.707218	+	0.706996i	$0.750050\pi$
$368$	549632.			0.211569
$369$	243536.	+	1.96002e6i	0.0931102	+	0.749368i
$370$	2.50833e6			0.952534
$371$	−186166.	+	572959.i	−0.0702207	+	0.216117i
$372$		−	1.24088e6i		−	0.464912i
$373$	−697155.	−	506513.i	−0.259452	−	0.188503i	0.450453	−	0.892800i	$-0.351262\pi$
$373$	−697155.	−	506513.i	−0.259452	−	0.188503i	−0.709905	+	0.704297i	$0.751262\pi$
$374$	242583.	+	176247.i	0.0896769	+	0.0651541i
$375$	2.36509e6	+	768464.i	0.868499	+	0.282192i
$376$	343877.	−	111732.i	0.125439	−	0.0407577i
$377$	1.93253e6	−	1.40407e6i	0.700283	−	0.508785i
$378$	505837.			0.182088
$379$	2.07021e6	−	1.50409e6i	0.740314	−	0.537869i	−0.152496	−	0.988304i	$-0.548731\pi$
$379$	2.07021e6	−	1.50409e6i	0.740314	−	0.537869i	0.892809	+	0.450435i	$0.148731\pi$
$380$	−137704.	−	189534.i	−0.0489203	−	0.0673330i
$381$	−14983.8	+	20623.5i	−0.00528823	+	0.00727862i
$382$	−925272.	−	300639.i	−0.324422	−	0.105411i
$383$		−	5.05285e6i		−	1.76011i	−0.474874	−	0.880054i	$-0.657506\pi$
$383$		−	5.05285e6i		−	1.76011i	0.474874	−	0.880054i	$-0.342494\pi$
$384$	−74286.4	+	102246.i	−0.0257088	+	0.0353851i
$385$	290405.	+	893775.i	0.0998510	+	0.307310i
$386$	1.83349e6	+	2.52358e6i	0.626339	+	0.862082i
$387$	918910.	−	2.82811e6i	0.311886	−	0.959885i
$388$	2.23253e6	−	725394.i	0.752867	−	0.244621i
$389$	586452.	+	1.80491e6i	0.196498	+	0.604759i	0.999956	+	0.00939721i	$0.00299127\pi$
$389$	586452.	+	1.80491e6i	0.196498	+	0.604759i	−0.803458	+	0.595362i	$0.797009\pi$
$390$	641708.	+	1.97497e6i	0.213637	+	0.657506i
$391$	−611792.	+	198783.i	−0.202377	+	0.0657563i
$392$	−303173.	+	933070.i	−0.0996495	+	0.306690i
$393$	−1.55439e6	−	2.13943e6i	−0.507665	−	0.698741i
$394$	649777.	+	1.99981e6i	0.210874	+	0.649005i
$395$	3.22997e6	−	4.44567e6i	1.04161	−	1.43366i
$396$		−	734557.i		−	0.235390i
$397$	3.97981e6	+	1.29312e6i	1.26732	+	0.411777i	0.864097	−	0.503325i	$-0.167890\pi$
$397$	3.97981e6	+	1.29312e6i	1.26732	+	0.411777i	0.403223	+	0.915102i	$0.367890\pi$
$398$	−1.45858e6	+	2.00757e6i	−0.461555	+	0.635276i
$399$	26114.6	+	35943.6i	0.00821203	+	0.0113029i
$400$	−1.33048e6	+	966648.i	−0.415774	+	0.302077i
$401$	−1.42750e6			−0.443317			−0.221658	−	0.975124i	$-0.571147\pi$
$401$	−1.42750e6			−0.443317			−0.221658	+	0.975124i	$0.571147\pi$
$402$	−364084.	+	264522.i	−0.112366	+	0.0816389i
$403$	6.58549e6	−	2.13976e6i	2.01988	−	0.656299i
$404$	−1.55921e6	−	506619.i	−0.475282	−	0.154429i
$405$	−1.51881e6	−	1.10348e6i	−0.460115	−	0.334293i
$406$	−431426.	−	313450.i	−0.129895	−	0.0943741i
$407$			1.60554e6i			0.480436i
$408$	45708.6	−	140677.i	0.0135940	−	0.0418380i
$409$	3.82688e6			1.13119			0.565596	−	0.824683i	$-0.308646\pi$
$409$	3.82688e6			1.13119			0.565596	+	0.824683i	$0.308646\pi$
$410$	2.87379e6	+	3.07285e6i	0.844298	+	0.902779i
$411$	−242649.			−0.0708554
$412$	405085.	−	1.24672e6i	0.117572	−	0.361848i
$413$			1.06446e6i			0.307082i
$414$	1.27491e6	+	926273.i	0.365576	+	0.265606i
$415$	5.71850e6	+	4.15473e6i	1.62990	+	1.18419i
$416$	−670734.	−	217935.i	−0.190028	−	0.0617438i
$417$	−282437.	+	91769.5i	−0.0795394	+	0.0258439i
$418$	121318.	−	88142.4i	0.0339612	−	0.0246743i
$419$	−1.38342e6			−0.384964			−0.192482	−	0.981301i	$-0.561654\pi$
$419$	−1.38342e6			−0.384964			−0.192482	+	0.981301i	$0.561654\pi$
$420$	375053.	−	272492.i	0.103746	−	0.0753756i
$421$	−1.21048e6	−	1.66609e6i	−0.332854	−	0.458134i	0.609483	−	0.792799i	$-0.291377\pi$
$421$	−1.21048e6	−	1.66609e6i	−0.332854	−	0.458134i	−0.942337	+	0.334665i	$0.891377\pi$
$422$	−1.29616e6	+	1.78401e6i	−0.354304	+	0.487658i
$423$	985942.	+	320352.i	0.267917	+	0.0870515i
$424$		−	1.00307e6i		−	0.270968i
$425$	1.13134e6	−	1.55716e6i	0.303823	−	0.418177i
$426$	318691.	+	980830.i	0.0850836	+	0.261860i
$427$	−326187.	−	448957.i	−0.0865758	−	0.119161i
$428$	−459200.	+	1.41327e6i	−0.121169	+	0.372921i
$429$	−1.26415e6	+	410747.i	−0.331631	+	0.107753i
$430$	−1.95742e6	−	6.02433e6i	−0.510521	−	1.57122i
$431$	370605.	+	1.14060e6i	0.0960988	+	0.295762i	0.987538	−	0.157378i	$-0.0503040\pi$
$431$	370605.	+	1.14060e6i	0.0960988	+	0.295762i	−0.891440	+	0.453139i	$0.850304\pi$
$432$	−801000.	+	260261.i	−0.206502	+	0.0670964i
$433$	−1.24542e6	+	3.83300e6i	−0.319223	+	0.982469i	0.654757	+	0.755839i	$0.272771\pi$
$433$	−1.24542e6	+	3.83300e6i	−0.319223	+	0.982469i	−0.973981	+	0.226630i	$0.927229\pi$
$434$	−908617.	−	1.25060e6i	−0.231556	−	0.318710i
$435$	−807901.	−	2.48646e6i	−0.204708	−	0.630027i
$436$	−10306.0	+	14185.0i	−0.00259642	+	0.00357366i
$437$			321708.i			0.0805857i
$438$	−926603.	−	301072.i	−0.230785	−	0.0749867i
$439$	2.62064e6	−	3.60700e6i	0.649002	−	0.893275i	−0.350053	−	0.936730i	$-0.613837\pi$
$439$	2.62064e6	−	3.60700e6i	0.649002	−	0.893275i	0.999055	+	0.0434551i	$0.0138365\pi$
$440$	−919721.	−	1.26589e6i	−0.226477	−	0.311719i
$441$	−2.27569e6	+	1.65339e6i	−0.557208	+	0.404835i
$442$	825409.			0.200962
$443$	−3.21065e6	+	2.33267e6i	−0.777291	+	0.564735i	−0.904165	−	0.427184i	$-0.859506\pi$
$443$	−3.21065e6	+	2.33267e6i	−0.777291	+	0.564735i	0.126874	+	0.991919i	$0.459506\pi$
$444$	753254.	−	244747.i	0.181336	−	0.0589196i
$445$	−1.00829e7	−	3.27614e6i	−2.41372	−	0.784265i
$446$	43049.7	+	31277.4i	0.0102478	+	0.00744549i
$447$	−1.00202e6	−	728012.i	−0.237197	−	0.172333i
$448$			157443.i			0.0370620i
$449$	1.41429e6	−	4.35273e6i	0.331072	−	1.01893i	−0.637553	−	0.770407i	$-0.720053\pi$
$449$	1.41429e6	−	4.35273e6i	0.331072	−	1.01893i	0.968625	−	0.248528i	$-0.0799468\pi$
$450$	−4.71517e6			−1.09766
$451$	−1.96688e6	+	1.83947e6i	−0.455341	+	0.425844i
$452$	−1.33926e6			−0.308332
$453$	−1.20563e6	+	3.71054e6i	−0.276037	+	0.849555i
$454$		−	3.30702e6i		−	0.753004i
$455$	2.09289e6	+	1.52057e6i	0.473934	+	0.344333i
$456$	−59846.3	−	43480.9i	−0.0134780	−	0.00979233i
$457$	−4.48208e6	−	1.45632e6i	−1.00390	−	0.326186i	−0.239475	−	0.970902i	$-0.576975\pi$
$457$	−4.48208e6	−	1.45632e6i	−1.00390	−	0.326186i	−0.764422	+	0.644717i	$0.776975\pi$
$458$	−680233.	+	221021.i	−0.151528	+	0.0492346i
$459$	797460.	−	579388.i	0.176676	−	0.128362i
$460$	3.35686e6			0.739670
$461$	−1.25801e6	+	913997.i	−0.275697	+	0.200305i	−0.717038	−	0.697034i	$-0.754503\pi$
$461$	−1.25801e6	+	913997.i	−0.275697	+	0.200305i	0.441342	+	0.897339i	$0.354503\pi$
$462$	174418.	+	240066.i	0.0380177	+	0.0523269i
$463$	−3.32077e6	+	4.57065e6i	−0.719924	+	0.990891i	0.279602	+	0.960116i	$0.409797\pi$
$463$	−3.32077e6	+	4.57065e6i	−0.719924	+	0.990891i	−0.999526	+	0.0307747i	$0.990203\pi$
$464$	844444.	+	274377.i	0.182086	+	0.0591633i
$465$		−	7.57860e6i		−	1.62539i
$466$	−3.81668e6	+	5.25320e6i	−0.814180	+	1.12062i
$467$	1.79441e6	+	5.52261e6i	0.380740	+	1.17180i	0.939524	+	0.342484i	$0.111268\pi$
$467$	1.79441e6	+	5.52261e6i	0.380740	+	1.17180i	−0.558784	+	0.829313i	$0.688732\pi$
$468$	−1.18853e6	−	1.63587e6i	−0.250840	−	0.345251i
$469$	−173245.	+	533192.i	−0.0363687	+	0.111931i
$470$	2.10021e6	−	682401.i	0.438550	−	0.142493i
$471$	−787657.	−	2.42416e6i	−0.163601	−	0.503511i
$472$	−547681.	−	1.68559e6i	−0.113155	−	0.348254i
$473$	3.85608e6	−	1.25292e6i	0.792488	−	0.257495i
$474$	536182.	−	1.65020e6i	0.109614	−	0.337358i
$475$	−565793.	−	778747.i	−0.115060	−	0.158366i
$476$	−56941.8	−	175249.i	−0.0115190	−	0.0354518i
$477$	1.69044e6	−	2.32669e6i	0.340176	−	0.468212i
$478$		−	1.68302e6i		−	0.336915i
$479$	6.68193e6	+	2.17109e6i	1.33065	+	0.432353i	0.886138	−	0.463421i	$-0.153378\pi$
$479$	6.68193e6	+	2.17109e6i	1.33065	+	0.432353i	0.444509	+	0.895774i	$0.353378\pi$
$480$	−453701.	+	624466.i	−0.0898807	+	0.123710i
$481$	2.59781e6	+	3.57558e6i	0.511970	+	0.704666i
$482$	−4.54475e6	+	3.30196e6i	−0.891031	+	0.647372i
$483$	−636601.			−0.124165
$484$	−1.27441e6	+	925916.i	−0.247285	+	0.179663i
$485$	1.36351e7	−	4.43031e6i	2.63211	−	0.855224i
$486$	−3.60507e6	−	1.17136e6i	−0.692346	−	0.224957i
$487$	−2.42070e6	−	1.75874e6i	−0.462507	−	0.336031i	0.332007	−	0.943277i	$-0.392274\pi$
$487$	−2.42070e6	−	1.75874e6i	−0.462507	−	0.336031i	−0.794514	+	0.607246i	$0.792274\pi$
$488$	747516.	+	543102.i	0.142093	+	0.103236i
$489$		−	2.91028e6i		−	0.550380i
$490$	−1.85161e6	+	5.69868e6i	−0.348386	+	1.07222i
$491$	3.91634e6			0.733123			0.366562	−	0.930394i	$-0.380535\pi$
$491$	3.91634e6			0.733123			0.366562	+	0.930394i	$0.380535\pi$
$492$	1.16283e6	+	642373.i	0.216573	+	0.119640i
$493$	−1.03918e6			−0.192563
$494$	127560.	−	392590.i	0.0235179	−	0.0723806i
$495$		−	4.48627e6i		−	0.822949i
$496$	2.08226e6	+	1.51285e6i	0.380042	+	0.276116i
$497$	1.03939e6	+	755162.i	0.188750	+	0.137135i
$498$	2.12266e6	+	689695.i	0.383537	+	0.124619i
$499$	−6.25720e6	+	2.03309e6i	−1.12494	+	0.365514i	−0.811650	−	0.584144i	$-0.801430\pi$
$499$	−6.25720e6	+	2.03309e6i	−1.12494	+	0.365514i	−0.313287	+	0.949658i	$0.601430\pi$
$500$	−4.17300e6	+	3.03186e6i	−0.746489	+	0.542356i
$501$	3.68672e6			0.656214
$502$	1.24936e6	−	907711.i	0.221272	−	0.160764i
$503$	1.89127e6	+	2.60312e6i	0.333299	+	0.458747i	0.942469	−	0.334292i	$-0.108497\pi$
$503$	1.89127e6	+	2.60312e6i	0.333299	+	0.458747i	−0.609170	+	0.793040i	$0.708497\pi$
$504$	−265333.	+	365199.i	−0.0465281	+	0.0640404i
$505$	−9.52282e6	−	3.09415e6i	−1.66164	−	0.539900i
$506$			2.14867e6i			0.373072i
$507$	−467217.	+	643069.i	−0.0807232	+	0.111106i
$508$	−16339.4	−	50287.5i	−0.00280916	−	0.00864571i
$509$	−6.86402e6	−	9.44751e6i	−1.17431	−	1.61630i	−0.624564	−	0.780973i	$-0.714723\pi$
$509$	−6.86402e6	−	9.44751e6i	−1.17431	−	1.61630i	−0.549749	−	0.835330i	$-0.685277\pi$
$510$	279163.	−	859176.i	0.0475262	−	0.146270i
$511$	−1.15432e6	+	375062.i	−0.195558	+	0.0635406i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	−152334.	−	468837.i	−0.0255567	−	0.0786553i
$514$	−1.64971e6	+	536023.i	−0.275422	+	0.0894901i
$515$	2.47404e6	−	7.61430e6i	0.411044	−	1.26506i
$516$	−1.17563e6	−	1.61812e6i	−0.194378	−	0.267538i
$517$	436794.	+	1.34431e6i	0.0718704	+	0.221194i
$518$	579946.	−	798227.i	0.0949649	−	0.130708i
$519$		−	3.89045e6i		−	0.633988i
$520$	−4.09648e6	−	1.33103e6i	−0.664358	−	0.215863i
$521$	−3.31826e6	+	4.56719e6i	−0.535569	+	0.737148i	−0.987966	−	0.154669i	$-0.950569\pi$
$521$	−3.31826e6	+	4.56719e6i	−0.535569	+	0.737148i	0.452397	+	0.891817i	$0.350569\pi$
$522$	1.49634e6	+	2.05954e6i	0.240356	+	0.330822i
$523$	−6.59630e6	+	4.79249e6i	−1.05450	+	0.766138i	−0.973063	−	0.230540i	$-0.925951\pi$
$523$	−6.59630e6	+	4.79249e6i	−1.05450	+	0.766138i	−0.0814359	+	0.996679i	$0.525951\pi$
$524$	5.48516e6			0.872693
$525$	1.54100e6	−	1.11960e6i	0.244008	−	0.177282i
$526$	1.44103e6	−	468219.i	0.227095	−	0.0737878i
$527$	−2.86490e6	−	930861.i	−0.449348	−	0.146002i
$528$	−399710.	−	290407.i	−0.0623966	−	0.0453338i
$529$	1.47785e6	+	1.07372e6i	0.229611	+	0.166822i
$530$		−	6.12623e6i		−	0.947335i
$531$	1.57028e6	−	4.83281e6i	0.241679	−	0.743813i
$532$	−92153.8			−0.0141167
$533$	−1.40398e6	+	7.27900e6i	−0.214064	+	1.10982i
$534$	−3.34758e6			−0.508016
$535$	−2.80455e6	+	8.63150e6i	−0.423622	+	1.30377i
$536$		−	933454.i		−	0.140340i
$537$	3.81593e6	+	2.77243e6i	0.571037	+	0.414883i
$538$	4.13077e6	+	3.00118e6i	0.615283	+	0.447030i
$539$	−3.64764e6	−	1.18519e6i	−0.540803	−	0.175718i
$540$	−4.89207e6	+	1.58953e6i	−0.721952	+	0.234577i
$541$	−5.10102e6	+	3.70611e6i	−0.749314	+	0.544409i	−0.895614	−	0.444832i	$-0.853264\pi$
$541$	−5.10102e6	+	3.70611e6i	−0.749314	+	0.544409i	0.146300	+	0.989240i	$0.453264\pi$
$542$	5.54314e6			0.810509
$543$	−5.27664e6	+	3.83370e6i	−0.767994	+	0.557981i
$544$	180336.	+	248212.i	0.0261268	+	0.0359605i
$545$	−62943.5	+	86634.3i	−0.00907737	+	0.0124939i
$546$	776865.	+	252419.i	0.111523	+	0.0362360i
$547$		−	9.24524e6i		−	1.32114i	−0.750763	−	0.660571i	$-0.770314\pi$
$547$		−	9.24524e6i		−	1.32114i	0.750763	−	0.660571i	$-0.229686\pi$
$548$	295832.	−	407178.i	0.0420818	−	0.0579206i
$549$	818641.	+	2.51952e6i	0.115921	+	0.356769i
$550$	−3.77890e6	−	5.20121e6i	−0.532671	−	0.733158i
$551$	−160597.	+	494265.i	−0.0225350	+	0.0693555i
$552$	1.00807e6	−	327541.i	0.140813	−	0.0457528i
$553$	−667953.	−	2.05575e6i	−0.0928824	−	0.285863i
$554$	848827.	+	2.61242e6i	0.117502	+	0.361634i
$555$	4.60046e6	−	1.49478e6i	0.633971	−	0.205990i
$556$	190348.	−	585830.i	0.0261132	−	0.0803683i
$557$	531200.	+	731134.i	0.0725471	+	0.0998526i	0.843749	−	0.536739i	$-0.180344\pi$
$557$	531200.	+	731134.i	0.0725471	+	0.0998526i	−0.771201	+	0.636591i	$0.780344\pi$
$558$	2.28039e6	+	7.01831e6i	0.310044	+	0.954216i
$559$	6.56032e6	−	9.02951e6i	0.887965	−	1.22218i
$560$			961578.i			0.129573i
$561$	549945.	+	178688.i	0.0737754	+	0.0239711i
$562$	2.43662e6	−	3.35372e6i	0.325423	−	0.447906i
$563$	6.35735e6	+	8.75014e6i	0.845289	+	1.16344i	0.984881	+	0.173231i	$0.0554208\pi$
$563$	6.35735e6	+	8.75014e6i	0.845289	+	1.16344i	−0.139592	+	0.990209i	$0.544579\pi$
$564$	564112.	−	409851.i	0.0746737	−	0.0542536i
$565$	−8.17947e6			−1.07796
$566$	2.34060e6	−	1.70054e6i	0.307104	−	0.223124i
$567$	−702323.	+	228199.i	−0.0917443	+	0.0298095i
$568$	−2.03443e6	−	661027.i	−0.264589	−	0.0859703i
$569$	150126.	+	109073.i	0.0194390	+	0.0141233i	0.597462	−	0.801897i	$-0.296176\pi$
$569$	150126.	+	109073.i	0.0194390	+	0.0141233i	−0.578023	+	0.816020i	$0.696176\pi$
$570$	−365509.	−	265558.i	−0.0471206	−	0.0342351i
$571$			3.60458e6i			0.462662i	0.972875	+	0.231331i	$0.0743081\pi$
$571$			3.60458e6i			0.462662i	−0.972875	+	0.231331i	$0.925692\pi$
$572$	851969.	−	2.62209e6i	0.108876	−	0.335087i
$573$	−1.87618e6			−0.238719
$574$	1.64232e6	−	204061.i	0.208055	−	0.0258511i
$575$	1.37925e7			1.73969
$576$	232258.	−	714816.i	0.0291685	−	0.0897715i
$577$			4.54336e6i			0.568117i	0.958807	+	0.284058i	$0.0916809\pi$
$577$			4.54336e6i			0.568117i	−0.958807	+	0.284058i	$0.908319\pi$
$578$	4.30425e6	+	3.12722e6i	0.535893	+	0.389349i
$579$	4.86662e6	+	3.53581e6i	0.603297	+	0.438321i
$580$	5.15741e6	+	1.67574e6i	0.636592	+	0.206841i
$581$	2.64432e6	−	859193.i	0.324993	−	0.105597i
$582$	3.66235e6	−	2.66085e6i	0.448180	−	0.325622i
$583$	3.92130e6			0.477814
$584$	1.63491e6	−	1.18783e6i	0.198364	−	0.144120i
$585$	−7.25891e6	−	9.99103e6i	−0.876964	−	1.20704i
$586$	5.65437e6	−	7.78257e6i	0.680206	−	0.936223i
$587$	−300804.	−	97737.3i	−0.0360321	−	0.0117075i	0.290946	−	0.956740i	$-0.406030\pi$
$587$	−300804.	−	97737.3i	−0.0360321	−	0.0117075i	−0.326978	+	0.945032i	$0.606030\pi$
$588$			1.89199e6i			0.225671i
$589$	−885494.	+	1.21878e6i	−0.105171	+	0.144756i
$590$	−3.34494e6	−	1.02947e7i	−0.395602	−	1.21754i
$591$	2.38348e6	+	3.28058e6i	0.280700	+	0.386351i
$592$	−507653.	+	1.56239e6i	−0.0595336	+	0.183226i
$593$	7.86014e6	−	2.55392e6i	0.917897	−	0.298243i	0.188293	−	0.982113i	$-0.439705\pi$
$593$	7.86014e6	−	2.55392e6i	0.917897	−	0.298243i	0.729604	+	0.683870i	$0.239705\pi$
$594$	−1.01743e6	−	3.13134e6i	−0.118315	−	0.364136i
$595$	−347770.	−	1.07033e6i	−0.0402717	−	0.123943i
$596$	2.44329e6	−	793874.i	0.281747	−	0.0915452i
$597$	−1.47879e6	+	4.55124e6i	−0.169813	+	0.522630i
$598$	3.47660e6	+	4.78513e6i	0.397560	+	0.547194i
$599$	3.30769e6	+	1.01800e7i	0.376667	+	1.15926i	0.942347	+	0.334637i	$0.108614\pi$
$599$	3.30769e6	+	1.01800e7i	0.376667	+	1.15926i	−0.565680	+	0.824625i	$0.691386\pi$
$600$	−1.86414e6	+	2.56577e6i	−0.211398	+	0.290964i
$601$			4.73395e6i			0.534610i	0.963612	+	0.267305i	$0.0861332\pi$
$601$			4.73395e6i			0.534610i	−0.963612	+	0.267305i	$0.913867\pi$
$602$	−2.36970e6	−	769961.i	−0.266503	−	0.0865920i
$603$	1.57311e6	−	2.16520e6i	0.176184	−	0.242496i
$604$	−4.75662e6	−	6.54693e6i	−0.530526	−	0.730206i
$605$	−7.78343e6	+	5.65499e6i	−0.864535	+	0.628121i
$606$	−3.16162e6			−0.349726
$607$	1.26594e7	−	9.19759e6i	1.39457	−	1.01322i	0.399227	−	0.916852i	$-0.369279\pi$
$607$	1.26594e7	−	9.19759e6i	1.39457	−	1.01322i	0.995346	−	0.0963641i	$-0.0307213\pi$
$608$	145927.	−	47414.5i	0.0160094	−	0.00520179i
$609$	−978061.	−	317791.i	−0.106862	−	0.0347215i
$610$	4.56542e6	+	3.31697e6i	0.496771	+	0.360925i
$611$	3.14788e6	+	2.28707e6i	0.341127	+	0.247843i
$612$			879656.i			0.0949368i
$613$	−2.49343e6	+	7.67400e6i	−0.268007	+	0.824842i	0.722978	+	0.690871i	$0.242773\pi$
$613$	−2.49343e6	+	7.67400e6i	−0.268007	+	0.824842i	−0.990985	+	0.133971i	$0.957227\pi$
$614$	7.66675e6			0.820711
$615$	7.10194e6	+	3.92327e6i	0.757163	+	0.418273i
$616$	−615491.			−0.0653536
$617$	−2.18487e6	+	6.72433e6i	−0.231053	+	0.711109i	0.766567	+	0.642164i	$0.221963\pi$
$617$	−2.18487e6	+	6.72433e6i	−0.231053	+	0.711109i	−0.997620	+	0.0689446i	$0.978037\pi$
$618$		−	2.52798e6i		−	0.266258i
$619$	−1.32272e7	−	9.61012e6i	−1.38753	−	1.00810i	−0.996132	−	0.0878733i	$-0.971993\pi$
$619$	−1.32272e7	−	9.61012e6i	−1.38753	−	1.00810i	−0.391394	−	0.920223i	$-0.628007\pi$
$620$	1.27173e7	+	9.23968e6i	1.32867	+	0.965334i
$621$	6.71777e6	+	2.18273e6i	0.699030	+	0.227129i
$622$	305836.	−	99372.1i	0.0316966	−	0.0102988i
$623$	−3.37382e6	+	2.45123e6i	−0.348259	+	0.253025i
$624$	−1.36005e6			−0.139828
$625$	−9.24523e6	+	6.71705e6i	−0.946712	+	0.687826i
$626$	−6.38447e6	−	8.78747e6i	−0.651162	−	0.896247i
$627$	169979.	−	233956.i	0.0172674	−	0.0237665i
$628$	5.02818e6	+	1.63375e6i	0.508758	+	0.165306i
$629$		−	1.92269e6i		−	0.193768i
$630$	−1.62051e6	+	2.23044e6i	−0.162667	+	0.223892i
$631$	1.21709e6	+	3.74582e6i	0.121688	+	0.374518i	0.993283	−	0.115709i	$-0.0369139\pi$
$631$	1.21709e6	+	3.74582e6i	0.121688	+	0.374518i	−0.871595	+	0.490227i	$0.836914\pi$
$632$	2.11543e6	+	2.91164e6i	0.210671	+	0.289964i
$633$	−1.31411e6	+	4.04442e6i	−0.130353	+	0.401187i
$634$	−1.21048e6	+	393310.i	−0.119601	+	0.0388608i
$635$	−99792.1	−	307128.i	−0.00982114	−	0.0302264i
$636$	−597759.	−	1.83971e6i	−0.0585981	−	0.180346i
$637$	−1.00410e7	+	3.26253e6i	−0.980460	+	0.318571i
$638$	−1.07262e6	+	3.30117e6i	−0.104326	+	0.321082i
$639$	−3.60499e6	−	4.96184e6i	−0.349262	−	0.480718i
$640$	−494746.	−	1.52267e6i	−0.0477455	−	0.146946i
$641$	−8.47814e6	+	1.16692e7i	−0.814996	+	1.12175i	0.175537	+	0.984473i	$0.443834\pi$
$641$	−8.47814e6	+	1.16692e7i	−0.814996	+	1.12175i	−0.990533	+	0.137273i	$0.956166\pi$
$642$			2.86570e6i			0.274406i
$643$	−1.21162e7	−	3.93680e6i	−1.15569	−	0.375505i	−0.332404	−	0.943137i	$-0.607860\pi$
$643$	−1.21162e7	−	3.93680e6i	−1.15569	−	0.375505i	−0.823283	+	0.567632i	$0.807860\pi$
$644$	776132.	−	1.06825e6i	0.0737430	−	0.101499i
$645$	−7.18012e6	−	9.88259e6i	−0.679568	−	0.935344i
$646$	−145282.	+	105553.i	−0.0136972	+	0.00995156i
$647$	−5.92854e6			−0.556784			−0.278392	−	0.960468i	$-0.589801\pi$
$647$	−5.92854e6			−0.556784			−0.278392	+	0.960468i	$0.589801\pi$
$648$	994727.	−	722711.i	0.0930607	−	0.0676125i
$649$	6.58945e6	−	2.14104e6i	0.614097	−	0.199532i
$650$	−1.68314e7	−	5.46885e6i	−1.56256	−	0.507707i
$651$	−2.41174e6	−	1.75223e6i	−0.223038	−	0.162046i
$652$	4.88362e6	+	3.54816e6i	0.449907	+	0.326877i
$653$			1.41160e7i			1.29548i	0.761862	+	0.647739i	$0.224285\pi$
$653$			1.41160e7i			1.29548i	−0.761862	+	0.647739i	$0.775715\pi$
$654$	−10448.8	+	32158.0i	−0.000955258	+	0.00293998i
$655$	3.35004e7			3.05103
$656$	−2.49564e6	+	1.16813e6i	−0.226424	+	0.105982i
$657$	5.79408e6			0.523687
$658$	268425.	−	826128.i	0.0241690	−	0.0743846i
$659$		−	1.87473e7i		−	1.68161i	−0.541337	−	0.840806i	$-0.682082\pi$
$659$		−	1.87473e7i		−	1.68161i	0.541337	−	0.840806i	$-0.317918\pi$
$660$	−2.44121e6	−	1.77365e6i	−0.218145	−	0.158492i
$661$	4.82047e6	+	3.50228e6i	0.429127	+	0.311779i	0.781300	−	0.624156i	$-0.214557\pi$
$661$	4.82047e6	+	3.50228e6i	0.429127	+	0.311779i	−0.352173	+	0.935935i	$0.614557\pi$
$662$	4.87065e6	+	1.58257e6i	0.431959	+	0.140352i
$663$	1.51386e6	−	491883.i	0.133753	−	0.0434589i
$664$	−3.74526e6	+	2.72109e6i	−0.329656	+	0.239509i
$665$	−562825.			−0.0493537
$666$	−3.81057e6	+	2.76854e6i	−0.332893	+	0.241861i
$667$	−4.37699e6	−	6.02441e6i	−0.380944	−	0.524325i
$668$	−4.49478e6	+	6.18653e6i	−0.389733	+	0.536421i
$669$	97595.3	+	31710.6i	0.00843070	+	0.00273930i
$670$		−	5.70103e6i		−	0.490643i
$671$	−2.12314e6	+	2.92225e6i	−0.182042	+	0.250560i
$672$	93824.7	+	288763.i	0.00801483	+	0.0246671i
$673$	−4.90950e6	−	6.75734e6i	−0.417830	−	0.575093i	0.547276	−	0.836952i	$-0.315665\pi$
$673$	−4.90950e6	−	6.75734e6i	−0.417830	−	0.575093i	−0.965106	+	0.261858i	$0.915665\pi$
$674$	2.09897e6	−	6.45996e6i	0.177974	−	0.547747i
$675$	−2.01003e7	+	6.53098e6i	−1.69802	+	0.551720i
$676$	−509485.	−	1.56803e6i	−0.0428810	−	0.131974i
$677$	1.65467e6	+	5.09255e6i	0.138752	+	0.427036i	0.996155	−	0.0876108i	$-0.0279232\pi$
$677$	1.65467e6	+	5.09255e6i	0.138752	+	0.427036i	−0.857403	+	0.514646i	$0.827923\pi$
$678$	−2.45630e6	+	798101.i	−0.205214	+	0.0666782i
$679$	1.74268e6	−	5.36342e6i	0.145059	−	0.446445i
$680$	1.10140e6	+	1.51594e6i	0.0913422	+	0.125722i
$681$	−1.97074e6	−	6.06532e6i	−0.162840	−	0.501171i
$682$	−5.91417e6	+	8.14015e6i	−0.486892	+	0.670150i
$683$			1.30564e7i			1.07096i	0.844549	+	0.535478i	$0.179869\pi$
$683$			1.30564e7i			1.07096i	−0.844549	+	0.535478i	$0.820131\pi$
$684$	418392.	+	135944.i	0.0341935	+	0.0111101i
$685$	1.80678e6	−	2.48682e6i	0.147123	−	0.202497i
$686$	2.90430e6	+	3.99743e6i	0.235630	+	0.324317i
$687$	−1.11589e6	+	810739.i	−0.0902045	+	0.0655374i
$688$	4.14861e6			0.334142
$689$	8.73283e6	−	6.34477e6i	0.700821	−	0.509176i
$690$	6.15672e6	−	2.00044e6i	0.492297	−	0.159957i
$691$	−9.57835e6	−	3.11219e6i	−0.763125	−	0.247954i	−0.0985055	−	0.995137i	$-0.531406\pi$
$691$	−9.57835e6	−	3.11219e6i	−0.763125	−	0.247954i	−0.664619	+	0.747182i	$0.731406\pi$
$692$	6.52840e6	+	4.74316e6i	0.518252	+	0.376532i
$693$	−1.42767e6	−	1.03726e6i	−0.112926	−	0.0820456i
$694$		−	5.73289e6i		−	0.451830i
$695$	1.16254e6	−	3.57793e6i	0.0912948	−	0.280976i
$696$	1.71228e6			0.133984
$697$	2.35541e6	−	2.20282e6i	0.183647	−	0.171750i
$698$	1.56529e7			1.21606
$699$	−3.86954e6	+	1.19092e7i	−0.299548	+	0.921914i
$700$			3.95088e6i			0.304754i
$701$	1.84667e6	+	1.34168e6i	0.141936	+	0.103123i	0.656488	−	0.754337i	$-0.272041\pi$
$701$	1.84667e6	+	1.34168e6i	0.141936	+	0.103123i	−0.514551	+	0.857460i	$0.672041\pi$
$702$	−7.33243e6	−	5.32732e6i	−0.561572	−	0.408006i
$703$	−914492.	−	297136.i	−0.0697897	−	0.0226761i
$704$	974638.	−	316679.i	0.0741160	−	0.0240817i
$705$	3.44529e6	−	2.50315e6i	0.261067	−	0.189677i
$706$	−1.09879e7			−0.829662
$707$	−3.18640e6	+	2.31506e6i	−0.239746	+	0.174186i
$708$	−2.00898e6	−	2.76512e6i	−0.150623	−	0.207315i
$709$	1.18698e7	−	1.63374e7i	0.886806	−	1.22058i	−0.0876824	−	0.996148i	$-0.527946\pi$
$709$	1.18698e7	−	1.63374e7i	0.886806	−	1.22058i	0.974489	−	0.224436i	$-0.0720539\pi$
$710$	−1.24252e7	−	4.03719e6i	−0.925034	−	0.300562i
$711$			1.03188e7i			0.765515i
$712$	4.08130e6	−	5.61743e6i	0.301716	−	0.415277i
$713$	−6.67041e6	−	2.05294e7i	−0.491393	−	1.51235i
$714$	−208871.	−	287487.i	−0.0153332	−	0.0211043i
$715$	5.20336e6	−	1.60143e7i	0.380644	−	1.17150i
$716$	−9.30461e6	+	3.02325e6i	−0.678290	+	0.220390i
$717$	−1.00296e6	−	3.08679e6i	−0.0728594	−	0.224238i
$718$	482290.	+	1.48434e6i	0.0349138	+	0.107454i
$719$	−7.79678e6	+	2.53333e6i	−0.562462	+	0.182755i	−0.576429	−	0.817147i	$-0.695554\pi$
$719$	−7.79678e6	+	2.53333e6i	−0.562462	+	0.182755i	0.0139667	+	0.999902i	$0.495554\pi$
$720$	1.41850e6	−	4.36571e6i	0.101976	−	0.313851i
$721$	−1.85108e6	−	2.54780e6i	−0.132614	−	0.182527i
$722$	−3.03287e6	−	9.33423e6i	−0.216527	−	0.666401i
$723$	−6.36769e6	+	8.76438e6i	−0.453040	+	0.623556i
$724$		−	1.35285e7i		−	0.959186i
$725$	2.11905e7	+	6.88520e6i	1.49725	+	0.486488i
$726$	−1.78559e6	+	2.45766e6i	−0.125730	+	0.173053i
$727$	−3.41063e6	−	4.69433e6i	−0.239331	−	0.329411i	0.672408	−	0.740181i	$-0.265260\pi$
$727$	−3.41063e6	−	4.69433e6i	−0.239331	−	0.329411i	−0.911739	+	0.410770i	$0.865260\pi$
$728$	−1.37071e6	+	995880.i	−0.0958557	+	0.0696432i
$729$	−2.64156e6			−0.184095
$730$	9.98515e6	−	7.25464e6i	0.693502	−	0.503858i
$731$	−4.61778e6	+	1.50041e6i	−0.319624	+	0.103852i
$732$	1.69465e6	+	550625.i	0.116897	+	0.0379821i
$733$	−1.24121e7	−	9.01795e6i	−0.853271	−	0.619938i	0.0727749	−	0.997348i	$-0.476815\pi$
$733$	−1.24121e7	−	9.01795e6i	−0.853271	−	0.619938i	−0.926046	+	0.377411i	$0.876815\pi$
$734$	−1.48785e7	−	1.08099e7i	−1.01934	−	0.740593i
$735$			1.15552e7i			0.788970i
$736$	−679383.	+	2.09093e6i	−0.0462296	+	0.142280i
$737$	3.64913e6			0.247469
$738$	−7.75740e6	−	1.49625e6i	−0.524294	−	0.101126i
$739$	−2.07114e7			−1.39508			−0.697538	−	0.716548i	$-0.745721\pi$
$739$	−2.07114e7			−1.39508			−0.697538	+	0.716548i	$0.745721\pi$
$740$	−3.10047e6	+	9.54226e6i	−0.208136	+	0.640578i
$741$		−	796057.i		−	0.0532597i
$742$	−1.94955e6	−	1.41643e6i	−0.129995	−	0.0944466i
$743$	−1.92630e7	−	1.39954e7i	−1.28013	−	0.930066i	−0.280569	−	0.959834i	$-0.590523\pi$
$743$	−1.92630e7	−	1.39954e7i	−1.28013	−	0.930066i	−0.999557	+	0.0297677i	$0.990523\pi$
$744$	4.72057e6	+	1.53381e6i	0.312653	+	0.101587i
$745$	1.49223e7	−	4.84855e6i	0.985020	−	0.320052i
$746$	2.78862e6	−	2.02605e6i	0.183460	−	0.133292i
$747$	−1.32731e7			−0.870303
$748$	−970330.	+	704986.i	−0.0634112	+	0.0460709i
$749$	2.09837e6	+	2.88816e6i	0.136672	+	0.188112i
$750$	−5.84682e6	+	8.04746e6i	−0.379548	+	0.522403i
$751$	1.96279e7	+	6.37748e6i	1.26991	+	0.412619i	0.865016	−	0.501744i	$-0.167308\pi$
$751$	1.96279e7	+	6.37748e6i	1.26991	+	0.412619i	0.404895	+	0.914363i	$0.367308\pi$
$752$			1.44629e6i			0.0932636i
$753$	1.75048e6	−	2.40934e6i	0.112505	−	0.154849i
$754$	2.95265e6	+	9.08731e6i	0.189140	+	0.582113i
$755$	−2.90509e7	−	3.99851e7i	−1.85478	−	2.55288i
$756$	−625249.	+	1.92432e6i	−0.0397877	+	0.122454i
$757$	1.84096e7	−	5.98165e6i	1.16763	−	0.379386i	0.339872	−	0.940472i	$-0.389616\pi$
$757$	1.84096e7	−	5.98165e6i	1.16763	−	0.379386i	0.827758	+	0.561085i	$0.189616\pi$
$758$	3.16300e6	+	9.73470e6i	0.199952	+	0.615389i
$759$	1.28045e6	+	3.94082e6i	0.0806786	+	0.248303i
$760$	891242.	−	289582.i	0.0559708	−	0.0181860i
$761$	−1.69944e6	+	5.23035e6i	−0.106376	+	0.327393i	−0.990051	−	0.140709i	$-0.955062\pi$
$761$	−1.69944e6	+	5.23035e6i	−0.106376	+	0.327393i	0.883675	+	0.468102i	$0.155062\pi$
$762$	−59935.3	−	82493.9i	−0.00373934	−	0.00514676i
$763$	13016.6	+	40061.1i	0.000809445	+	0.00249122i
$764$	2.28740e6	−	3.14833e6i	0.141778	−	0.195140i
$765$			5.37246e6i			0.331910i
$766$	1.92222e7	+	6.24566e6i	1.18367	+	0.384598i
$767$	1.12106e7	−	1.54300e7i	0.688081	−	0.947063i
$768$	−297146.	−	408986.i	−0.0181788	−	0.0250210i
$769$	1.73588e6	−	1.26119e6i	0.105853	−	0.0769069i	−0.533599	−	0.845737i	$-0.679161\pi$
$769$	1.73588e6	−	1.26119e6i	0.105853	−	0.0769069i	0.639453	+	0.768830i	$0.279161\pi$
$770$	−3.75908e6			−0.228484
$771$	−2.70626e6	+	1.96621e6i	−0.163958	+	0.119123i
$772$	−1.18666e7	+	3.85569e6i	−0.716609	+	0.232840i
$773$	−2.17387e7	−	7.06334e6i	−1.30853	−	0.425169i	−0.429992	−	0.902833i	$-0.641484\pi$
$773$	−2.17387e7	−	7.06334e6i	−1.30853	−	0.425169i	−0.878543	+	0.477664i	$0.841484\pi$
$774$	9.62295e6	+	6.99148e6i	0.577372	+	0.419485i
$775$	5.22523e7	+	3.79635e7i	3.12501	+	2.27045i
$776$			9.38969e6i			0.559754i
$777$	587979.	−	1.80961e6i	0.0349389	−	0.107531i
$778$	−7.59119e6			−0.449636
$779$	−683723.	−	1.46073e6i	−0.0403679	−	0.0862437i
$780$	−8.30644e6			−0.488853
$781$	2.58414e6	−	7.95317e6i	0.151596	−	0.466566i
$782$		−	2.57310e6i		−	0.150467i
$783$	9.23142e6	+	6.70702e6i	0.538102	+	0.390954i
$784$	−3.17487e6	−	2.30668e6i	−0.184474	−	0.134028i
$785$	3.07094e7	+	9.97807e6i	1.77867	+	0.577927i
$786$	1.00602e7	−	3.26876e6i	0.580831	−	0.188724i
$787$	−2.01131e7	+	1.46130e7i	−1.15755	+	0.841012i	−0.989467	−	0.144760i	$-0.953759\pi$
$787$	−2.01131e7	+	1.46130e7i	−1.15755	+	0.841012i	−0.168088	+	0.985772i	$0.553759\pi$
$788$	−8.41089e6			−0.482533
$789$	2.36393e6	−	1.71750e6i	0.135189	−	0.0982207i
$790$	1.29199e7	+	1.77827e7i	0.736530	+	1.01375i
$791$	−1.89116e6	+	2.60296e6i	−0.107470	+	0.147920i
$792$	2.79442e6	+	907962.i	0.158299	+	0.0514345i
$793$			9.94323e6i			0.561493i
$794$	−9.83864e6	+	1.35417e7i	−0.553839	+	0.762294i
$795$	−3.65079e6	−	1.12360e7i	−0.204865	−	0.630511i
$796$	−5.83434e6	−	8.03028e6i	−0.326369	−	0.449208i
$797$	1.33496e6	−	4.10859e6i	0.0744428	−	0.229111i	−0.906911	−	0.421323i	$-0.861566\pi$
$797$	1.33496e6	−	4.10859e6i	0.0744428	−	0.229111i	0.981354	+	0.192211i	$0.0615660\pi$
$798$	−169017.	+	54917.0i	−0.00939557	+	0.00305281i
$799$	−523075.	−	1.60986e6i	−0.0289866	−	0.0892116i
$800$	−2.03279e6	−	6.25628e6i	−0.112297	−	0.345614i
$801$	1.89337e7	−	6.15192e6i	1.04269	−	0.338789i
$802$	1.76448e6	−	5.43052e6i	0.0968682	−	0.298130i
$803$	4.64358e6	+	6.39133e6i	0.254135	+	0.349786i
$804$	−556270.	−	1.71202e6i	−0.0303491	−	0.0934049i
$805$	4.74019e6	−	6.52431e6i	0.257814	−	0.354850i
$806$			2.76976e7i			1.50177i
$807$	9.36462e6	+	3.04275e6i	0.506182	+	0.164468i
$808$	3.85458e6	−	5.30538e6i	0.207706	−	0.285883i
$809$	−1.64121e7	−	2.25894e7i	−0.881645	−	1.21348i	−0.975963	−	0.217938i	$-0.930067\pi$
$809$	−1.64121e7	−	2.25894e7i	−0.881645	−	1.21348i	0.0943177	−	0.995542i	$-0.469933\pi$
$810$	6.07525e6	−	4.41393e6i	0.325351	−	0.236381i
$811$	−3.56633e7			−1.90401			−0.952004	−	0.306084i	$-0.900981\pi$
$811$	−3.56633e7			−1.90401			−0.952004	+	0.306084i	$0.900981\pi$
$812$	1.72571e6	−	1.25380e6i	0.0918495	−	0.0667326i
$813$	1.01665e7	−	3.30331e6i	0.539444	−	0.175276i
$814$	−6.10784e6	−	1.98456e6i	−0.323093	−	0.104979i
$815$	2.98265e7	+	2.16702e7i	1.57293	+	1.14280i
$816$	478667.	+	347772.i	0.0251656	+	0.0182839i
$817$			2.42824e6i			0.127273i
$818$	−4.73028e6	+	1.45583e7i	−0.247174	+	0.760725i
$819$	−4.85777e6			−0.253062
$820$	−1.52420e7	+	7.13430e6i	−0.791604	+	0.370524i
$821$	210782.			0.0109138			0.00545690	−	0.999985i	$-0.498263\pi$
$821$	210782.			0.0109138			0.00545690	+	0.999985i	$0.498263\pi$
$822$	299930.	−	923090.i	0.0154825	−	0.0476502i
$823$		−	1.04021e7i		−	0.535330i	−0.963512	−	0.267665i	$-0.913748\pi$
$823$		−	1.04021e7i		−	0.535330i	0.963512	−	0.267665i	$-0.0862520\pi$
$824$	4.24210e6	+	3.08207e6i	0.217652	+	0.158134i
$825$	−1.00303e7	−	7.28746e6i	−0.513074	−	0.372770i
$826$	−4.04945e6	−	1.31575e6i	−0.206512	−	0.0670999i
$827$	2.54852e7	−	8.28064e6i	1.29576	−	0.421017i	0.421654	−	0.906757i	$-0.361450\pi$
$827$	2.54852e7	−	8.28064e6i	1.29576	−	0.421017i	0.874104	+	0.485739i	$0.161450\pi$
$828$	−5.09962e6	+	3.70509e6i	−0.258501	+	0.187812i
$829$	1.07097e7			0.541243			0.270621	−	0.962686i	$-0.412771\pi$
$829$	1.07097e7			0.541243			0.270621	+	0.962686i	$0.412771\pi$
$830$	−2.28740e7	+	1.66189e7i	−1.15252	+	0.837351i
$831$	3.11362e6	+	4.28554e6i	0.156410	+	0.215279i
$832$	1.65815e6	−	2.28224e6i	0.0830452	−	0.114302i
$833$	4.36817e6	+	1.41930e6i	0.218116	+	0.0708700i
$834$		−	1.18789e6i		−	0.0591372i
$835$	−2.74516e7	+	3.77840e7i	−1.36255	+	1.87539i
$836$	185357.	+	570470.i	0.00917261	+	0.0282304i
$837$	1.94421e7	+	2.67597e7i	0.959244	+	1.32029i
$838$	1.71000e6	−	5.26285e6i	0.0841176	−	0.258887i
$839$	−1.85167e7	+	6.01644e6i	−0.908152	+	0.295077i	−0.725598	−	0.688119i	$-0.758437\pi$
$839$	−1.85167e7	+	6.01644e6i	−0.908152	+	0.295077i	−0.182555	+	0.983196i	$0.558437\pi$
$840$	573030.	+	1.76361e6i	0.0280207	+	0.0862389i
$841$	2.62096e6	+	8.06647e6i	0.127782	+	0.393273i
$842$	7.83442e6	−	2.54556e6i	0.380826	−	0.123738i
$843$	2.47037e6	−	7.60303e6i	0.119727	−	0.368483i
$844$	−5.18463e6	−	7.13603e6i	−0.250531	−	0.344826i
$845$	−3.11166e6	−	9.57670e6i	−0.149917	−	0.461396i
$846$	−2.43738e6	+	3.35477e6i	−0.117084	+	0.161152i
$847$			3.78440e6i			0.181254i
$848$	3.81592e6	+	1.23987e6i	0.182226	+	0.0592087i
$849$	3.27943e6	−	4.51375e6i	0.156145	−	0.214916i
$850$	4.52536e6	+	6.22862e6i	0.214835	+	0.295696i
$851$	1.11464e7	−	8.09833e6i	0.527607	−	0.383329i
$852$	−4.12522e6			−0.194692
$853$	1.44754e6	−	1.05170e6i	0.0681174	−	0.0494902i	−0.553205	−	0.833045i	$-0.686596\pi$
$853$	1.44754e6	−	1.05170e6i	0.0681174	−	0.0494902i	0.621323	+	0.783555i	$0.286596\pi$
$854$	2.11112e6	−	685946.i	0.0990533	−	0.0321844i
$855$	2.55531e6	+	830271.i	0.119544	+	0.0388423i
$856$	−4.80881e6	−	3.49380e6i	−0.224312	−	0.162972i
$857$	1.63217e7	+	1.18584e7i	0.759124	+	0.551536i	0.898642	−	0.438684i	$-0.144555\pi$
$857$	1.63217e7	+	1.18584e7i	0.759124	+	0.551536i	−0.139518	+	0.990220i	$0.544555\pi$
$858$		−	5.31682e6i		−	0.246566i
$859$	1.01159e7	−	3.11335e7i	0.467757	−	1.43961i	−0.387724	−	0.921776i	$-0.626739\pi$
$859$	1.01159e7	−	3.11335e7i	0.467757	−	1.43961i	0.855481	−	0.517834i	$-0.173261\pi$
$860$	2.53374e7			1.16820
$861$	2.89053e6	−	1.35296e6i	0.132883	−	0.0621983i
$862$	−4.79721e6			−0.219898
$863$	−3.09373e6	+	9.52152e6i	−0.141402	+	0.435191i	−0.996531	−	0.0832250i	$-0.973478\pi$
$863$	−3.09373e6	+	9.52152e6i	−0.141402	+	0.435191i	0.855129	+	0.518416i	$0.173478\pi$
$864$		−	3.36889e6i		−	0.153533i
$865$	3.98719e7	+	2.89686e7i	1.81187	+	1.31640i
$866$	−1.30422e7	−	9.47569e6i	−0.590956	−	0.429355i
$867$	9.75792e6	+	3.17054e6i	0.440869	+	0.143247i
$868$	5.88069e6	−	1.91075e6i	0.264929	−	0.0860806i
$869$	−1.13824e7	+	8.26981e6i	−0.511311	+	0.371489i
$870$	1.04577e7			0.468422
$871$	8.12671e6	−	5.90440e6i	0.362969	−	0.263712i
$872$	−41224.1	−	56740.0i	−0.00183594	−	0.00252696i
$873$	−1.58241e7	+	2.17800e7i	−0.702720	+	0.967212i
$874$	−1.22385e6	−	397653.i	−0.0541937	−	0.0176086i
$875$			1.23918e7i			0.547161i
$876$	2.29069e6	−	3.15286e6i	0.100857	−	0.138818i
$877$	−6.61988e6	−	2.03739e7i	−0.290637	−	0.894489i	−0.984652	−	0.174528i	$-0.944160\pi$
$877$	−6.61988e6	−	2.03739e7i	−0.290637	−	0.894489i	0.694015	−	0.719961i	$-0.255840\pi$
$878$	1.04826e7	+	1.44280e7i	0.458914	+	0.631641i
$879$	5.73269e6	−	1.76434e7i	0.250257	−	0.770212i
$880$	5.95256e6	−	1.93410e6i	0.259118	−	0.0841924i
$881$	1.19067e7	+	3.66451e7i	0.516835	+	1.59065i	0.779919	+	0.625881i	$0.215260\pi$
$881$	1.19067e7	+	3.66451e7i	0.516835	+	1.59065i	−0.263084	+	0.964773i	$0.584740\pi$
$882$	−3.47695e6	−	1.07010e7i	−0.150497	−	0.463181i
$883$	−3.29249e7	+	1.06980e7i	−1.42110	+	0.461742i	−0.915950	−	0.401292i	$-0.868561\pi$
$883$	−3.29249e7	+	1.06980e7i	−1.42110	+	0.461742i	−0.505145	+	0.863034i	$0.668561\pi$
$884$	−1.02026e6	+	3.14004e6i	−0.0439117	+	0.135146i
$885$	−1.22697e7	−	1.68878e7i	−0.526595	−	0.724796i
$886$	−4.90543e6	−	1.50974e7i	−0.209939	−	0.646126i
$887$	−203017.	+	279428.i	−0.00866408	+	0.0119251i	−0.813327	−	0.581807i	$-0.802346\pi$
$887$	−203017.	+	279428.i	−0.00866408	+	0.0119251i	0.804663	+	0.593732i	$0.202346\pi$
$888$			3.16807e6i			0.134823i
$889$	−120810.	−	39253.7i	−0.00512684	−	0.00166581i
$890$	2.49264e7	−	3.43082e7i	1.05483	−	1.45185i
$891$	2.82528e6	+	3.88867e6i	0.119225	+	0.164099i
$892$	−172199.	+	125110.i	−0.00724632	+	0.00526476i
$893$	−846537.			−0.0355236
$894$	4.00809e6	−	2.91205e6i	0.167723	−	0.121858i
$895$	−5.68275e7	+	1.84644e7i	−2.37138	+	0.770508i
$896$	−598950.	−	194611.i	−0.0249242	−	0.00809835i
$897$	9.22794e6	+	6.70449e6i	0.382934	+	0.278218i
$898$	1.48106e7	+	1.07606e7i	0.612890	+	0.445291i
$899$		−	3.48709e7i		−	1.43901i
$900$	5.82828e6	−	1.79376e7i	0.239847	−	0.738172i
$901$	−4.69589e6			−0.192711
$902$	−4.56655e6	−	9.75617e6i	−0.186884	−	0.399267i
$903$	−4.80504e6			−0.196100
$904$	1.65542e6	−	5.09485e6i	0.0673731	−	0.207353i
$905$		−	8.26246e7i		−	3.35342i
$906$	−1.26255e7	−	9.17296e6i	−0.511008	−	0.371269i
$907$	2.49935e7	+	1.81588e7i	1.00881	+	0.732942i	0.963959	−	0.266052i	$-0.0857191\pi$
$907$	2.49935e7	+	1.81588e7i	1.00881	+	0.732942i	0.0448496	+	0.998994i	$0.485719\pi$
$908$	1.25807e7	+	4.08770e6i	0.506394	+	0.164537i
$909$	1.78819e7	−	5.81018e6i	0.717800	−	0.233227i
$910$	−8.37156e6	+	6.08230e6i	−0.335122	+	0.243480i
$911$	−1.74567e7			−0.696894			−0.348447	−	0.937328i	$-0.613291\pi$
$911$	−1.74567e7			−0.696894			−0.348447	+	0.937328i	$0.613291\pi$
$912$	239385.	−	173924.i	0.00953038	−	0.00692423i
$913$	−1.06375e7	−	1.46413e7i	−0.422341	−	0.581302i
$914$	1.10803e7	−	1.52507e7i	0.438719	−	0.603845i
$915$	1.03500e7	+	3.36292e6i	0.408684	+	0.132789i
$916$		−	2.86096e6i		−	0.112661i
$917$	7.74555e6	−	1.06608e7i	0.304179	−	0.418666i
$918$	1.21841e6	+	3.74988e6i	0.0477185	+	0.146862i
$919$	−6.04562e6	−	8.32108e6i	−0.236130	−	0.325006i	0.674463	−	0.738308i	$-0.264375\pi$
$919$	−6.04562e6	−	8.32108e6i	−0.236130	−	0.325006i	−0.910594	+	0.413303i	$0.864375\pi$
$920$	−4.14930e6	+	1.27702e7i	−0.161624	+	0.497427i
$921$	1.40614e7	−	4.56882e6i	0.546235	−	0.177482i
$922$	−1.92207e6	−	5.91551e6i	−0.0744631	−	0.229174i
$923$	−7.11350e6	−	2.18931e7i	−0.274839	−	0.845869i
$924$	−1.12886e6	+	366788.i	−0.0434969	+	0.0141330i
$925$	−1.27390e7	+	3.92067e7i	−0.489533	+	1.50663i
$926$	−1.32831e7	−	1.82826e7i	−0.509063	−	0.700666i
$927$	4.64573e6	+	1.42981e7i	0.177564	+	0.546485i
$928$	−2.08758e6	+	2.87331e6i	−0.0795744	+	0.109525i
$929$			3.50004e7i			1.33056i	0.746594	+	0.665280i	$0.231688\pi$
$929$			3.50004e7i			1.33056i	−0.746594	+	0.665280i	$0.768312\pi$
$930$	2.88307e7	+	9.36766e6i	1.09307	+	0.355160i
$931$	1.35013e6	−	1.85829e6i	0.0510507	−	0.0702652i
$932$	−1.52667e7	−	2.10128e7i	−0.575712	−	0.792400i
$933$	501707.	−	364512.i	0.0188689	−	0.0137090i
$934$	−2.32273e7			−0.871226
$935$	−5.92625e6	+	4.30567e6i	−0.221692	+	0.161069i
$936$	7.69234e6	−	2.49939e6i	0.286992	−	0.0932492i
$937$	−2.35373e7	−	7.64774e6i	−0.875807	−	0.284567i	−0.163592	−	0.986528i	$-0.552308\pi$
$937$	−2.35373e7	−	7.64774e6i	−0.875807	−	0.284567i	−0.712215	+	0.701961i	$0.752308\pi$
$938$	−1.81424e6	−	1.31812e6i	−0.0673267	−	0.0489157i
$939$	−1.69463e7	−	1.23122e7i	−0.627206	−	0.455692i
$940$			8.83318e6i			0.326060i
$941$	−1.76094e6	+	5.41962e6i	−0.0648292	+	0.199524i	−0.978224	−	0.207550i	$-0.933451\pi$
$941$	−1.76094e6	+	5.41962e6i	−0.0648292	+	0.199524i	0.913395	+	0.407074i	$0.133451\pi$
$942$	1.01956e7			0.374358
$943$	2.26913e7	+	4.37673e6i	0.830961	+	0.160277i
$944$	7.08933e6			0.258926
$945$	−3.81868e6	+	1.17527e7i	−0.139102	+	0.428112i
$946$			1.62181e7i			0.589212i
$947$	2.03783e7	+	1.48057e7i	0.738403	+	0.536481i	0.892211	−	0.451619i	$-0.149154\pi$
$947$	2.03783e7	+	1.48057e7i	0.738403	+	0.536481i	−0.153807	+	0.988101i	$0.549154\pi$
$948$	5.61497e6	+	4.07952e6i	0.202921	+	0.147431i
$949$	2.06827e7	+	6.72022e6i	0.745490	+	0.242224i
$950$	3.66189e6	−	1.18982e6i	0.131642	−	0.0427732i
$951$	−1.98573e6	+	1.44272e6i	−0.0711983	+	0.0517286i
$952$	737071.			0.0263583
$953$	−4.28595e7	+	3.11393e7i	−1.52867	+	1.11065i	−0.571704	+	0.820460i	$0.693717\pi$
$953$	−4.28595e7	+	3.11393e7i	−1.52867	+	1.11065i	−0.956970	+	0.290187i	$0.906283\pi$
$954$	6.76176e6	+	9.30677e6i	0.240541	+	0.331076i
$955$	1.39702e7	−	1.92283e7i	0.495671	−	0.682233i
$956$	6.40260e6	+	2.08033e6i	0.226575	+	0.0736186i
$957$			6.69380e6i			0.236261i
$958$	−1.65186e7	+	2.27359e7i	−0.581514	+	0.800386i
$959$	−373640.	−	1.14995e6i	−0.0131192	−	0.0403767i
$960$	−1.81480e6	−	2.49786e6i	−0.0635553	−	0.0874763i
$961$	2.23893e7	−	6.89072e7i	0.782045	−	2.40689i
$962$	−1.68134e7	+	5.46300e6i	−0.585757	+	0.190324i
$963$	−5.26636e6	−	1.62082e7i	−0.182997	−	0.563208i
$964$	−6.94377e6	−	2.13707e7i	−0.240659	−	0.740673i
$965$	−7.24746e7	+	2.35484e7i	−2.50535	+	0.814036i
$966$	786882.	−	2.42177e6i	0.0271311	−	0.0835008i
$967$	−2.29049e7	−	3.15259e7i	−0.787703	−	1.08418i	−0.994390	−	0.105774i	$-0.966268\pi$
$967$	−2.29049e7	−	3.15259e7i	−0.787703	−	1.08418i	0.206687	−	0.978407i	$-0.433732\pi$
$968$	−1.94713e6	−	5.99265e6i	−0.0667893	−	0.205556i
$969$	−203556.	+	280170.i	−0.00696424	+	0.00958546i
$970$			5.73471e7i			1.95696i
$971$	−1.15605e7	−	3.75623e6i	−0.393485	−	0.127851i	0.105590	−	0.994410i	$-0.466327\pi$
$971$	−1.15605e7	−	3.75623e6i	−0.393485	−	0.127851i	−0.499075	+	0.866559i	$0.666327\pi$
$972$	8.91222e6	−	1.22666e7i	0.302566	−	0.416446i
$973$	−869818.	−	1.19720e6i	−0.0294541	−	0.0405401i
$974$	9.68279e6	−	7.03496e6i	0.327042	−	0.237610i
$975$	−3.41291e7			−1.14978
$976$	−2.99007e6	+	2.17241e6i	−0.100475	+	0.0729991i
$977$	−6.38382e6	+	2.07423e6i	−0.213966	+	0.0695217i	−0.414039	−	0.910259i	$-0.635882\pi$
$977$	−6.38382e6	+	2.07423e6i	−0.213966	+	0.0695217i	0.200073	+	0.979781i	$0.435882\pi$
$978$	1.10714e7	+	3.59731e6i	0.370130	+	0.120262i
$979$	2.19601e7	+	1.59550e7i	0.732282	+	0.532034i
$980$	−1.93904e7	−	1.40879e7i	−0.644942	−	0.468578i
$981$		−	201085.i		−	0.00667126i
$982$	−4.84086e6	+	1.48986e7i	−0.160193	+	0.493024i
$983$	−3.92966e7			−1.29709			−0.648546	−	0.761175i	$-0.724623\pi$
$983$	−3.92966e7			−1.29709			−0.648546	+	0.761175i	$0.724623\pi$
$984$	−3.88107e6	+	3.62966e6i	−0.127780	+	0.119503i
$985$	−5.13692e7			−1.68699
$986$	1.28449e6	−	3.95327e6i	0.0420765	−	0.129498i
$987$		−	1.67514e6i		−	0.0547342i
$988$	1.33583e6	+	970537.i	0.0435370	+	0.0316315i
$989$	−2.81483e7	−	2.04509e7i	−0.915085	−	0.664848i
$990$	1.70668e7	+	5.54534e6i	0.553432	+	0.179821i
$991$	5.60827e6	−	1.82224e6i	0.181403	−	0.0589415i	−0.216907	−	0.976192i	$-0.569597\pi$
$991$	5.60827e6	−	1.82224e6i	0.181403	−	0.0589415i	0.398310	+	0.917251i	$0.369597\pi$
$992$	−8.32905e6	+	6.05141e6i	−0.268730	+	0.195244i
$993$	9.87624e6			0.317847
$994$	−4.15756e6	+	3.02065e6i	−0.133467	+	0.0969692i
$995$	−3.56330e7	−	4.90446e7i	−1.14102	−	1.57048i
$996$	−5.24751e6	+	7.22258e6i	−0.167612	+	0.230698i
$997$	3.48174e7	+	1.13128e7i	1.10932	+	0.360441i	0.805684	−	0.592346i	$-0.201798\pi$
$997$	3.48174e7	+	1.13128e7i	1.10932	+	0.360441i	0.303639	+	0.952787i	$0.401798\pi$
$998$		−	2.63168e7i		−	0.836387i
$999$	−1.24094e7	+	1.70800e7i	−0.393401	+	0.541470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.f.b.25.6	yes	40
41.23	even	10	inner	82.6.f.b.23.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.f.b.23.5	✓	40	41.23	even	10	inner
82.6.f.b.25.6	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	82.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +7.71384i q^{3} +(-12.9443 - 9.40456i) q^{4} +(-79.0566 - 57.4380i) q^{5} +(-29.3452 - 9.53483i) q^{6} +(-36.5570 + 11.8781i) q^{7} +(51.7771 - 37.6183i) q^{8} +183.497 q^{9} +(316.226 - 229.752i) q^{10} +(147.060 + 202.411i) q^{11} +(72.5453 - 99.8500i) q^{12} +(655.014 + 212.827i) q^{13} -153.753i q^{14} +(443.067 - 609.830i) q^{15} +(79.1084 + 243.470i) q^{16} +(-176.110 - 242.394i) q^{17} +(-226.814 + 698.063i) q^{18} +(-142.507 + 46.3032i) q^{19} +(483.151 + 1486.99i) q^{20} +(-91.6257 - 281.995i) q^{21} +(-951.795 + 309.257i) q^{22} +(663.460 - 2041.92i) q^{23} +(290.181 + 399.400i) q^{24} +(1985.14 + 6109.64i) q^{25} +(-1619.28 + 2228.75i) q^{26} +3289.93i q^{27} +(584.912 + 190.049i) q^{28} +(2038.65 - 2805.97i) q^{29} +(1772.27 + 2439.32i) q^{30} +(8133.84 - 5909.58i) q^{31} -1024.00 q^{32} +(-1561.37 + 1134.40i) q^{33} +(1139.81 - 370.346i) q^{34} +(3572.33 + 1160.72i) q^{35} +(-2375.23 - 1725.71i) q^{36} +(5191.61 + 3771.93i) q^{37} -599.362i q^{38} +(-1641.71 + 5052.67i) q^{39} -6254.03 q^{40} +(1327.20 + 10681.5i) q^{41} +1186.03 q^{42} +(5007.77 - 15412.3i) q^{43} -4003.11i q^{44} +(-14506.6 - 10539.7i) q^{45} +(6947.84 + 5047.90i) q^{46} +(5373.08 + 1745.82i) q^{47} +(-1878.09 + 610.229i) q^{48} +(-12401.8 + 9010.45i) q^{49} -25696.2 q^{50} +(1869.79 - 1358.48i) q^{51} +(-6477.13 - 8915.01i) q^{52} +(9212.38 - 12679.8i) q^{53} +(-12515.6 - 4066.57i) q^{54} -24448.8i q^{55} +(-1445.98 + 1990.22i) q^{56} +(-357.176 - 1099.27i) q^{57} +(8154.62 + 11223.9i) q^{58} +(8557.52 - 26337.3i) q^{59} +(-11470.4 + 3726.95i) q^{60} +(4461.34 + 13730.6i) q^{61} +(12427.4 + 38247.6i) q^{62} +(-6708.09 + 2179.59i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-39558.8 - 54448.0i) q^{65} +(-2385.56 - 7342.00i) q^{66} +(8572.97 - 11799.7i) q^{67} +4793.85i q^{68} +(15751.0 + 5117.82i) q^{69} +(-8831.27 + 12155.2i) q^{70} +(-19646.1 - 27040.5i) q^{71} +(9500.92 - 6902.82i) q^{72} +31576.0 q^{73} +(-20766.4 + 15087.7i) q^{74} +(-47128.8 + 15313.1i) q^{75} +(2280.11 + 740.852i) q^{76} +(-7780.35 - 5652.76i) q^{77} +(-17192.2 - 12490.9i) q^{78} +56234.1i q^{79} +(7730.41 - 23791.8i) q^{80} +19211.7 q^{81} +(-42275.4 - 8154.12i) q^{82} -72334.2 q^{83} +(-1466.01 + 4511.92i) q^{84} +29278.3i q^{85} +(52442.1 + 38101.4i) q^{86} +(21644.8 + 15725.9i) q^{87} +(15228.7 + 4948.11i) q^{88} +(103183. - 33526.1i) q^{89} +(58026.5 - 42158.7i) q^{90} -26473.3 q^{91} +(-27791.4 + 20191.6i) q^{92} +(45585.5 + 62743.1i) q^{93} +(-13283.0 + 18282.5i) q^{94} +(13925.7 + 4524.72i) q^{95} -7898.97i q^{96} +(-86236.3 + 118694. i) q^{97} +(-18948.3 - 58316.9i) q^{98} +(26985.1 + 37141.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 24 q^{5} - 100 q^{6} + 640 q^{8} - 4576 q^{9} - 96 q^{10} + 20 q^{11} + 400 q^{12} - 275 q^{13} + 1385 q^{15} - 2560 q^{16} - 105 q^{17} - 2476 q^{18} + 4720 q^{19} + 1424 q^{20}+ \cdots - 537690 q^{99}+O(q^{100}) \) 40 * q + 40 * q^2 - 160 * q^4 + 24 * q^5 - 100 * q^6 + 640 * q^8 - 4576 * q^9 - 96 * q^10 + 20 * q^11 + 400 * q^12 - 275 * q^13 + 1385 * q^15 - 2560 * q^16 - 105 * q^17 - 2476 * q^18 + 4720 * q^19 + 1424 * q^20 + 6961 * q^21 - 4140 * q^22 - 1019 * q^23 + 1600 * q^24 - 2006 * q^25 - 8620 * q^26 - 12525 * q^29 + 5540 * q^30 + 8900 * q^31 - 40960 * q^32 + 17684 * q^33 - 13100 * q^34 - 29955 * q^35 + 26704 * q^36 - 31651 * q^37 - 10104 * q^39 + 14464 * q^40 + 35044 * q^41 + 32776 * q^42 - 15615 * q^43 - 39955 * q^45 - 3224 * q^46 + 8330 * q^47 - 6400 * q^48 + 48406 * q^49 - 135016 * q^50 + 120325 * q^51 - 34480 * q^52 + 145425 * q^53 + 72200 * q^54 + 17600 * q^56 + 31992 * q^57 - 50100 * q^58 + 18978 * q^59 + 1680 * q^60 + 52673 * q^61 + 66140 * q^62 - 88455 * q^63 - 40960 * q^64 + 204480 * q^65 - 17556 * q^66 - 149205 * q^67 - 249735 * q^69 - 49100 * q^70 + 151175 * q^71 - 106816 * q^72 - 107670 * q^73 + 126604 * q^74 + 120180 * q^75 - 75520 * q^76 - 207367 * q^77 - 99284 * q^78 + 22784 * q^80 + 1167568 * q^81 + 84204 * q^82 - 281376 * q^83 + 111376 * q^84 - 131400 * q^86 - 141269 * q^87 + 66240 * q^88 - 277775 * q^89 + 159820 * q^90 - 518682 * q^91 + 12896 * q^92 - 172375 * q^93 + 16320 * q^94 + 149585 * q^95 + 330875 * q^97 - 171004 * q^98 - 537690 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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