LMFDB - Embedded newform 35.5.i.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(19,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("35.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	35.19
Dual form			35.5.i.a.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.61273 - 3.81786i) q^{2} +(-0.705380 - 1.22175i) q^{3} +(21.1521 + 36.6365i) q^{4} +(-23.8771 + 7.40838i) q^{5} +10.7722i q^{6} +(43.2397 + 23.0505i) q^{7} -200.851i q^{8} +(39.5049 - 68.4245i) q^{9} +O(q^{10})$	\(q+(-6.61273 - 3.81786i) q^{2} +(-0.705380 - 1.22175i) q^{3} +(21.1521 + 36.6365i) q^{4} +(-23.8771 + 7.40838i) q^{5} +10.7722i q^{6} +(43.2397 + 23.0505i) q^{7} -200.851i q^{8} +(39.5049 - 68.4245i) q^{9} +(186.177 + 42.1698i) q^{10} +(39.0986 + 67.7207i) q^{11} +(29.8405 - 51.6853i) q^{12} +67.8948 q^{13} +(-197.929 - 317.510i) q^{14} +(25.8937 + 23.9462i) q^{15} +(-428.388 + 741.990i) q^{16} +(118.744 + 205.671i) q^{17} +(-522.470 + 301.648i) q^{18} +(409.691 + 236.535i) q^{19} +(-776.468 - 718.070i) q^{20} +(-2.33833 - 69.0877i) q^{21} -597.091i q^{22} +(413.986 + 239.015i) q^{23} +(-245.391 + 141.677i) q^{24} +(515.232 - 353.781i) q^{25} +(-448.970 - 259.213i) q^{26} -225.735 q^{27} +(70.1190 + 2071.72i) q^{28} +282.412 q^{29} +(-79.8044 - 257.208i) q^{30} +(-846.213 + 488.561i) q^{31} +(2882.55 - 1664.24i) q^{32} +(55.1587 - 95.5377i) q^{33} -1813.40i q^{34} +(-1203.21 - 230.044i) q^{35} +3342.44 q^{36} +(-430.777 - 248.709i) q^{37} +(-1806.11 - 3128.28i) q^{38} +(-47.8917 - 82.9508i) q^{39} +(1487.98 + 4795.75i) q^{40} +1183.05i q^{41} +(-248.304 + 465.786i) q^{42} -924.710i q^{43} +(-1654.03 + 2864.87i) q^{44} +(-436.347 + 1926.44i) q^{45} +(-1825.05 - 3161.08i) q^{46} +(624.360 - 1081.42i) q^{47} +1208.71 q^{48} +(1338.34 + 1993.40i) q^{49} +(-4757.77 + 372.377i) q^{50} +(167.520 - 290.153i) q^{51} +(1436.12 + 2487.43i) q^{52} +(-1059.25 + 611.561i) q^{53} +(1492.73 + 861.826i) q^{54} +(-1435.26 - 1327.32i) q^{55} +(4629.73 - 8684.75i) q^{56} -667.389i q^{57} +(-1867.52 - 1078.21i) q^{58} +(2778.16 - 1603.97i) q^{59} +(-329.601 + 1455.17i) q^{60} +(-3608.60 - 2083.43i) q^{61} +7461.03 q^{62} +(3285.40 - 2048.04i) q^{63} -11706.9 q^{64} +(-1621.13 + 502.991i) q^{65} +(-729.499 + 421.176i) q^{66} +(-3154.22 + 1821.09i) q^{67} +(-5023.38 + 8700.75i) q^{68} -674.386i q^{69} +(7078.20 + 6114.89i) q^{70} +4040.32 q^{71} +(-13743.1 - 7934.61i) q^{72} +(4211.59 + 7294.68i) q^{73} +(1899.07 + 3289.29i) q^{74} +(-795.668 - 379.936i) q^{75} +20012.8i q^{76} +(129.611 + 3829.47i) q^{77} +731.375i q^{78} +(5477.23 - 9486.83i) q^{79} +(4731.72 - 20890.2i) q^{80} +(-3040.67 - 5266.59i) q^{81} +(4516.70 - 7823.16i) q^{82} -4150.28 q^{83} +(2481.67 - 1547.02i) q^{84} +(-4358.96 - 4031.13i) q^{85} +(-3530.41 + 6114.85i) q^{86} +(-199.208 - 345.039i) q^{87} +(13601.8 - 7853.00i) q^{88} +(9874.04 + 5700.78i) q^{89} +(10240.3 - 11073.1i) q^{90} +(2935.75 + 1565.01i) q^{91} +20222.7i q^{92} +(1193.80 + 689.243i) q^{93} +(-8257.44 + 4767.44i) q^{94} +(-11534.6 - 2612.62i) q^{95} +(-4066.59 - 2347.85i) q^{96} +855.940 q^{97} +(-1239.59 - 18291.4i) q^{98} +6178.34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) $ 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9	$ 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) $ 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−6.61273	−	3.81786i	−1.65318	−	0.954465i	−0.975753	−	0.218876i	$-0.929761\pi$
$2$	−6.61273	−	3.81786i	−1.65318	−	0.954465i	−0.677429	−	0.735588i	$-0.736906\pi$
$3$	−0.705380	−	1.22175i	−0.0783756	−	0.135751i	0.824174	−	0.566337i	$-0.191640\pi$
$3$	−0.705380	−	1.22175i	−0.0783756	−	0.135751i	−0.902549	+	0.430587i	$0.858307\pi$
$4$	21.1521	+	36.6365i	1.32201	+	2.28978i
$5$	−23.8771	+	7.40838i	−0.955084	+	0.296335i
$5$	−23.8771	+	7.40838i	−0.955084	+	0.296335i
$6$			10.7722i			0.299227i
$7$	43.2397	+	23.0505i	0.882443	+	0.470419i
$7$	43.2397	+	23.0505i	0.882443	+	0.470419i
$8$		−	200.851i		−	3.13830i
$9$	39.5049	−	68.4245i	0.487715	−	0.844746i
$10$	186.177	+	42.1698i	1.86177	+	0.421698i
$11$	39.0986	+	67.7207i	0.323129	+	0.559675i	0.981132	−	0.193340i	$-0.0619320\pi$
$11$	39.0986	+	67.7207i	0.323129	+	0.559675i	−0.658003	+	0.753015i	$0.728599\pi$
$12$	29.8405	−	51.6853i	0.207226	−	0.358926i
$13$	67.8948			0.401745			0.200872	−	0.979617i	$-0.435622\pi$
$13$	67.8948			0.401745			0.200872	+	0.979617i	$0.435622\pi$
$14$	−197.929	−	317.510i	−1.00984	−	1.61995i
$15$	25.8937	+	23.9462i	0.115083	+	0.106428i
$16$	−428.388	+	741.990i	−1.67339	+	2.89840i
$17$	118.744	+	205.671i	0.410880	+	0.711665i	0.994986	−	0.100012i	$-0.0318882\pi$
$17$	118.744	+	205.671i	0.410880	+	0.711665i	−0.584106	+	0.811677i	$0.698555\pi$
$18$	−522.470	+	301.648i	−1.61256	+	0.931013i
$19$	409.691	+	236.535i	1.13488	+	0.655222i	0.945157	−	0.326617i	$-0.105909\pi$
$19$	409.691	+	236.535i	1.13488	+	0.655222i	0.189720	+	0.981838i	$0.439242\pi$
$20$	−776.468	−	718.070i	−1.94117	−	1.79518i
$21$	−2.33833	−	69.0877i	−0.00530233	−	0.156661i
$22$		−	597.091i		−	1.23366i
$23$	413.986	+	239.015i	0.782583	+	0.451824i	0.837345	−	0.546675i	$-0.184107\pi$
$23$	413.986	+	239.015i	0.782583	+	0.451824i	−0.0547620	+	0.998499i	$0.517440\pi$
$24$	−245.391	+	141.677i	−0.426026	+	0.245966i
$25$	515.232	−	353.781i	0.824371	−	0.566050i
$26$	−448.970	−	259.213i	−0.664157	−	0.383451i
$27$	−225.735			−0.309651
$28$	70.1190	+	2071.72i	0.0894375	+	2.64250i
$29$	282.412			0.335805			0.167903	−	0.985804i	$-0.446301\pi$
$29$	282.412			0.335805			0.167903	+	0.985804i	$0.446301\pi$
$30$	−79.8044	−	257.208i	−0.0886715	−	0.285787i
$31$	−846.213	+	488.561i	−0.880555	+	0.508388i	−0.870841	−	0.491564i	$-0.836425\pi$
$31$	−846.213	+	488.561i	−0.880555	+	0.508388i	−0.00971343	+	0.999953i	$0.503092\pi$
$32$	2882.55	−	1664.24i	2.81499	−	1.62524i
$33$	55.1587	−	95.5377i	0.0506508	−	0.0877298i
$34$		−	1813.40i		−	1.56868i
$35$	−1203.21	−	230.044i	−0.982209	−	0.187791i
$36$	3342.44			2.57905
$37$	−430.777	−	248.709i	−0.314666	−	0.181672i	0.334347	−	0.942450i	$-0.391484\pi$
$37$	−430.777	−	248.709i	−0.314666	−	0.181672i	−0.649012	+	0.760778i	$0.724818\pi$
$38$	−1806.11	−	3128.28i	−1.25077	−	2.16640i
$39$	−47.8917	−	82.9508i	−0.0314870	−	0.0545370i
$40$	1487.98	+	4795.75i	0.929990	+	2.99734i
$41$			1183.05i			0.703775i	0.936042	+	0.351888i	$0.114460\pi$
$41$			1183.05i			0.703775i	−0.936042	+	0.351888i	$0.885540\pi$
$42$	−248.304	+	465.786i	−0.140762	+	0.264051i
$43$		−	924.710i		−	0.500114i	−0.968231	−	0.250057i	$-0.919551\pi$
$43$		−	924.710i		−	0.500114i	0.968231	−	0.250057i	$-0.0804493\pi$
$44$	−1654.03	+	2864.87i	−0.854356	+	1.47979i
$45$	−436.347	+	1926.44i	−0.215480	+	0.951331i
$46$	−1825.05	−	3161.08i	−0.862501	−	1.49390i
$47$	624.360	−	1081.42i	0.282644	−	0.489553i	−0.689391	−	0.724389i	$-0.742122\pi$
$47$	624.360	−	1081.42i	0.282644	−	0.489553i	0.972035	+	0.234836i	$0.0754553\pi$
$48$	1208.71			0.524612
$49$	1338.34	+	1993.40i	0.557411	+	0.830236i
$50$	−4757.77	+	372.377i	−1.90311	+	0.148951i
$51$	167.520	−	290.153i	0.0644059	−	0.111554i
$52$	1436.12	+	2487.43i	0.531109	+	0.919907i
$53$	−1059.25	+	611.561i	−0.377093	+	0.217715i	−0.676553	−	0.736394i	$-0.736527\pi$
$53$	−1059.25	+	611.561i	−0.377093	+	0.217715i	0.299460	+	0.954109i	$0.403194\pi$
$54$	1492.73	+	861.826i	0.511909	+	0.295551i
$55$	−1435.26	−	1327.32i	−0.474466	−	0.438782i
$56$	4629.73	−	8684.75i	1.47632	−	2.76937i
$57$		−	667.389i		−	0.205414i
$58$	−1867.52	−	1078.21i	−0.555147	−	0.320514i
$59$	2778.16	−	1603.97i	0.798092	−	0.460779i	−0.0447114	−	0.999000i	$-0.514237\pi$
$59$	2778.16	−	1603.97i	0.798092	−	0.460779i	0.842804	+	0.538221i	$0.180903\pi$
$60$	−329.601	+	1455.17i	−0.0915558	+	0.404213i
$61$	−3608.60	−	2083.43i	−0.969794	−	0.559911i	−0.0706203	−	0.997503i	$-0.522498\pi$
$61$	−3608.60	−	2083.43i	−0.969794	−	0.559911i	−0.899173	+	0.437593i	$0.855831\pi$
$62$	7461.03			1.94096
$63$	3285.40	−	2048.04i	0.827765	−	0.516010i
$64$	−11706.9			−2.85814
$65$	−1621.13	+	502.991i	−0.383700	+	0.119051i
$66$	−729.499	+	421.176i	−0.167470	+	0.0966888i
$67$	−3154.22	+	1821.09i	−0.702656	+	0.405678i	−0.808336	−	0.588722i	$-0.799631\pi$
$67$	−3154.22	+	1821.09i	−0.702656	+	0.405678i	0.105680	+	0.994400i	$0.466298\pi$
$68$	−5023.38	+	8700.75i	−1.08637	+	1.88165i
$69$		−	674.386i		−	0.141648i
$70$	7078.20	+	6114.89i	1.44453	+	1.24794i
$71$	4040.32			0.801492			0.400746	−	0.916189i	$-0.368751\pi$
$71$	4040.32			0.801492			0.400746	+	0.916189i	$0.368751\pi$
$72$	−13743.1	−	7934.61i	−2.65107	−	1.53060i
$73$	4211.59	+	7294.68i	0.790315	+	1.36886i	0.925772	+	0.378082i	$0.123416\pi$
$73$	4211.59	+	7294.68i	0.790315	+	1.36886i	−0.135458	+	0.990783i	$0.543250\pi$
$74$	1899.07	+	3289.29i	0.346800	+	0.600675i
$75$	−795.668	−	379.936i	−0.141452	−	0.0675442i
$76$			20012.8i			3.46483i
$77$	129.611	+	3829.47i	0.0218606	+	0.645887i
$78$			731.375i			0.120213i
$79$	5477.23	−	9486.83i	0.877620	−	1.52008i	0.0236746	−	0.999720i	$-0.492463\pi$
$79$	5477.23	−	9486.83i	0.877620	−	1.52008i	0.853945	−	0.520363i	$-0.174203\pi$
$80$	4731.72	−	20890.2i	0.739332	−	3.26410i
$81$	−3040.67	−	5266.59i	−0.463445	−	0.802711i
$82$	4516.70	−	7823.16i	0.671728	−	1.16347i
$83$	−4150.28			−0.602450			−0.301225	−	0.953553i	$-0.597396\pi$
$83$	−4150.28			−0.602450			−0.301225	+	0.953553i	$0.597396\pi$
$84$	2481.67	−	1547.02i	0.351711	−	0.219249i
$85$	−4358.96	−	4031.13i	−0.603316	−	0.557942i
$86$	−3530.41	+	6114.85i	−0.477341	+	0.826778i
$87$	−199.208	−	345.039i	−0.0263189	−	0.0455858i
$88$	13601.8	−	7853.00i	1.75643	−	1.01407i
$89$	9874.04	+	5700.78i	1.24656	+	0.719704i	0.970423	−	0.241413i	$-0.0776107\pi$
$89$	9874.04	+	5700.78i	1.24656	+	0.719704i	0.276142	+	0.961117i	$0.410944\pi$
$90$	10240.3	−	11073.1i	1.26424	−	1.36705i
$91$	2935.75	+	1565.01i	0.354517	+	0.188988i
$92$			20222.7i			2.38926i
$93$	1193.80	+	689.243i	0.138028	+	0.0796905i
$94$	−8257.44	+	4767.44i	−0.934522	+	0.539547i
$95$	−11534.6	−	2612.62i	−1.27807	−	0.289487i
$96$	−4066.59	−	2347.85i	−0.441253	−	0.254758i
$97$	855.940			0.0909704			0.0454852	−	0.998965i	$-0.485517\pi$
$97$	855.940			0.0909704			0.0454852	+	0.998965i	$0.485517\pi$
$98$	−1239.59	−	18291.4i	−0.129071	−	1.90456i
$99$	6178.34			0.630378
$100$	23859.5	+	11393.1i	2.38595	+	1.13931i
$101$	−15805.5	+	9125.30i	−1.54941	+	0.894550i	−0.551219	+	0.834361i	$0.685837\pi$
$101$	−15805.5	+	9125.30i	−1.54941	+	0.894550i	−0.998187	+	0.0601890i	$0.980830\pi$
$102$	−2215.53	+	1279.13i	−0.212949	+	0.122946i
$103$	1949.18	−	3376.07i	0.183729	−	0.318227i	−0.759419	−	0.650602i	$-0.774517\pi$
$103$	1949.18	−	3376.07i	0.183729	−	0.318227i	0.943147	+	0.332375i	$0.107850\pi$
$104$		−	13636.8i		−	1.26080i
$105$	567.661	+	1632.29i	0.0514885	+	0.148054i
$106$	9339.41			0.831204
$107$	−5604.74	−	3235.90i	−0.489539	−	0.282636i	0.234844	−	0.972033i	$-0.424542\pi$
$107$	−5604.74	−	3235.90i	−0.489539	−	0.282636i	−0.724383	+	0.689397i	$0.757875\pi$
$108$	−4774.78	−	8270.16i	−0.409360	−	0.709033i
$109$	−4288.06	−	7427.14i	−0.360918	−	0.625128i	0.627194	−	0.778863i	$-0.284203\pi$
$109$	−4288.06	−	7427.14i	−0.360918	−	0.625128i	−0.988112	+	0.153735i	$0.950870\pi$
$110$	4423.48	+	14256.8i	0.365577	+	1.17825i
$111$			701.739i			0.0569547i
$112$	−35626.7	+	22208.9i	−2.84014	+	1.77048i
$113$		−	2544.14i		−	0.199244i	−0.995025	−	0.0996219i	$-0.968237\pi$
$113$		−	2544.14i		−	0.199244i	0.995025	−	0.0996219i	$-0.0317633\pi$
$114$	−2548.00	+	4413.26i	−0.196060	+	0.339586i
$115$	−11655.5	−	2640.02i	−0.881324	−	0.199623i
$116$	5973.61	+	10346.6i	0.443937	+	0.768921i
$117$	2682.18	−	4645.67i	0.195937	−	0.339372i
$118$	−24494.9			−1.75919
$119$	393.636	+	11630.3i	0.0277972	+	0.821290i
$120$	4809.63	−	5200.78i	0.334002	−	0.361165i
$121$	4263.11	−	7383.91i	0.291176	−	0.504331i
$122$	15908.5	+	27554.3i	1.06883	+	1.85127i
$123$	1445.39	−	834.497i	0.0955378	−	0.0551588i
$124$	−35798.3	−	20668.2i	−2.32820	−	1.34418i
$125$	−9681.29	+	12264.3i	−0.619603	+	0.784916i
$126$	−29544.6	+	999.961i	−1.86096	+	0.0629857i
$127$		−	24838.0i		−	1.53996i	−0.638068	−	0.769980i	$-0.720266\pi$
$127$		−	24838.0i		−	1.53996i	0.638068	−	0.769980i	$-0.279734\pi$
$128$	31293.9	+	18067.6i	1.91003	+	1.10276i
$129$	−1129.77	+	652.272i	−0.0678907	+	0.0391967i
$130$	12640.4	+	2863.11i	0.747955	+	0.169415i
$131$	1892.09	+	1092.40i	0.110255	+	0.0636558i	0.554114	−	0.832441i	$-0.313057\pi$
$131$	1892.09	+	1092.40i	0.110255	+	0.0636558i	−0.443858	+	0.896097i	$0.646391\pi$
$132$	4666.89			0.267843
$133$	12262.6	+	19671.3i	0.693235	+	1.11206i
$134$	27810.7			1.54882
$135$	5389.91	−	1672.34i	0.295743	−	0.0917605i
$136$	41309.3	−	23850.0i	2.23342	−	1.28947i
$137$	−3284.19	+	1896.13i	−0.174980	+	0.101024i	−0.584932	−	0.811083i	$-0.698879\pi$
$137$	−3284.19	+	1896.13i	−0.174980	+	0.101024i	0.409952	+	0.912107i	$0.365545\pi$
$138$	−2574.71	+	4459.53i	−0.135198	+	0.234170i
$139$		−	1679.16i		−	0.0869084i	−0.999055	−	0.0434542i	$-0.986164\pi$
$139$		−	1679.16i		−	0.0869084i	0.999055	−	0.0434542i	$-0.0138363\pi$
$140$	−17022.3	−	48947.2i	−0.868486	−	2.49730i
$141$	−1761.64			−0.0886095
$142$	−26717.5	−	15425.4i	−1.32501	−	0.764996i
$143$	2654.59	+	4597.89i	0.129815	+	0.224846i
$144$	33846.9	+	58624.5i	1.63228	+	2.82718i
$145$	−6743.19	+	2092.22i	−0.320722	+	0.0995110i
$146$		−	64317.0i		−	3.01731i
$147$	1491.40	−	3041.23i	0.0690176	−	0.140739i
$148$		−	21042.9i		−	0.960687i
$149$	−10143.1	+	17568.3i	−0.456875	+	0.791330i	−0.998794	−	0.0491002i	$-0.984365\pi$
$149$	−10143.1	+	17568.3i	−0.456875	+	0.791330i	0.541919	+	0.840431i	$0.317698\pi$
$150$	3810.99	+	5550.16i	0.169378	+	0.246674i
$151$	790.318	+	1368.87i	0.0346616	+	0.0600356i	0.882836	−	0.469682i	$-0.155631\pi$
$151$	790.318	+	1368.87i	0.0346616	+	0.0600356i	−0.848174	+	0.529717i	$0.822298\pi$
$152$	47508.4	−	82286.9i	2.05628	−	3.56159i
$153$	18763.9			0.801569
$154$	13763.3	−	25818.0i	0.580337	−	1.08863i
$155$	16585.7	−	17934.5i	0.690350	−	0.746493i
$156$	2026.02	−	3509.17i	0.0832519	−	0.144197i
$157$	20550.5	+	35594.5i	0.833726	+	1.44406i	0.895064	+	0.445938i	$0.147130\pi$
$157$	20550.5	+	35594.5i	0.833726	+	1.44406i	−0.0613383	+	0.998117i	$0.519537\pi$
$158$	−72438.8	+	41822.6i	−2.90173	+	1.67531i
$159$	1494.35	+	862.766i	0.0591098	+	0.0341271i
$160$	−56497.6	+	61092.3i	−2.20694	+	2.38642i
$161$	12391.2	+	19877.6i	0.478038	+	0.766851i
$162$			46435.3i			1.76937i
$163$	27787.0	+	16042.8i	1.04584	+	0.603817i	0.921482	−	0.388421i	$-0.126979\pi$
$163$	27787.0	+	16042.8i	1.04584	+	0.603817i	0.124359	+	0.992237i	$0.460313\pi$
$164$	−43342.7	+	25023.9i	−1.61149	+	0.930395i
$165$	−609.250	+	2689.80i	−0.0223783	+	0.0987989i
$166$	27444.6	+	15845.2i	0.995959	+	0.575017i
$167$	−28550.7			−1.02373			−0.511864	−	0.859067i	$-0.671045\pi$
$167$	−28550.7			−1.02373			−0.511864	+	0.859067i	$0.671045\pi$
$168$	−13876.4	+	469.657i	−0.491651	+	0.0166403i
$169$	−23951.3			−0.838601
$170$	13434.3	+	43298.6i	0.464856	+	1.49822i
$171$	32369.6	−	18688.6i	1.10699	−	0.639122i
$172$	33878.1	−	19559.6i	1.14515	−	0.661153i
$173$	11350.1	−	19659.0i	0.379234	−	0.656853i	−0.611717	−	0.791077i	$-0.709521\pi$
$173$	11350.1	−	19659.0i	0.379234	−	0.656853i	0.990951	+	0.134224i	$0.0428541\pi$
$174$			3042.19i			0.100482i
$175$	30433.3	−	3421.03i	0.993741	−	0.111707i
$176$	−66997.5			−2.16288
$177$	−3919.32	−	2262.82i	−0.125102	−	0.0722276i
$178$	−43529.5	−	75395.4i	−1.37386	−	2.37960i
$179$	−14383.6	−	24913.1i	−0.448911	−	0.777537i	0.549404	−	0.835557i	$-0.314855\pi$
$179$	−14383.6	−	24913.1i	−0.448911	−	0.777537i	−0.998315	+	0.0580196i	$0.981521\pi$
$180$	−79807.8	+	24762.1i	−2.46320	+	0.764262i
$181$			3100.45i			0.0946384i	0.998880	+	0.0473192i	$0.0150678\pi$
$181$			3100.45i			0.0946384i	−0.998880	+	0.0473192i	$0.984932\pi$
$182$	−13438.3	−	21557.3i	−0.405698	−	0.650806i
$183$			5878.44i			0.175533i
$184$	48006.5	−	83149.7i	1.41796	−	2.45598i
$185$	12128.2	+	2747.10i	0.354368	+	0.0802657i
$186$	−5262.87	−	9115.55i	−0.152124	−	0.263486i
$187$	−9285.46	+	16082.9i	−0.265534	+	0.459919i
$188$	52826.1			1.49463
$189$	−9760.74	−	5203.33i	−0.273249	−	0.145666i
$190$	66300.3	+	61313.9i	1.83657	+	1.69845i
$191$	8658.73	−	14997.4i	0.237349	−	0.411100i	−0.722604	−	0.691262i	$-0.757055\pi$
$191$	8658.73	−	14997.4i	0.237349	−	0.411100i	0.959953	+	0.280162i	$0.0903882\pi$
$192$	8257.85	+	14303.0i	0.224008	+	0.387994i
$193$	15856.7	−	9154.86i	0.425694	−	0.245775i	−0.271816	−	0.962349i	$-0.587624\pi$
$193$	15856.7	−	9154.86i	0.425694	−	0.245775i	0.697511	+	0.716574i	$0.254291\pi$
$194$	−5660.10	−	3267.86i	−0.150391	−	0.0868280i
$195$	1758.05	+	1625.83i	0.0462340	+	0.0427567i
$196$	−44722.3	+	91196.8i	−1.16416	+	2.37393i
$197$			11958.1i			0.308128i	0.988061	+	0.154064i	$0.0492361\pi$
$197$			11958.1i			0.308128i	−0.988061	+	0.154064i	$0.950764\pi$
$198$	−40855.6	−	23588.0i	−1.04213	−	0.601674i
$199$	−23716.5	+	13692.8i	−0.598887	+	0.345768i	−0.768604	−	0.639725i	$-0.779048\pi$
$199$	−23716.5	+	13692.8i	−0.598887	+	0.345768i	0.169716	+	0.985493i	$0.445715\pi$
$200$	−71057.5	−	103485.i	−1.77644	−	2.58712i
$201$	4449.85	+	2569.12i	0.110142	+	0.0635906i
$202$	139356.			3.41526
$203$	12211.4	+	6509.76i	0.296329	+	0.157969i
$204$	14173.6			0.340580
$205$	−8764.46	−	28247.7i	−0.208553	−	0.672164i
$206$	−25778.7	+	14883.4i	−0.607473	+	0.350725i
$207$	32709.0	−	18884.5i	0.763354	−	0.440723i
$208$	−29085.4	+	50377.3i	−0.672276	+	1.16442i
$209$			36992.7i			0.846883i
$210$	2478.07	−	12961.1i	0.0561921	−	0.293903i
$211$	−46061.6			−1.03460			−0.517302	−	0.855803i	$-0.673064\pi$
$211$	−46061.6			−1.03460			−0.517302	+	0.855803i	$0.673064\pi$
$212$	−44810.9	−	25871.6i	−0.997039	−	0.575640i
$213$	−2849.96	−	4936.28i	−0.0628174	−	0.108803i
$214$	24708.4	+	42796.2i	0.539532	+	0.934496i
$215$	6850.61	+	22079.4i	0.148201	+	0.477650i
$216$			45339.3i			0.971778i
$217$	−47851.6	+	1619.58i	−1.01620	+	0.0343939i
$218$			65484.9i			1.37793i
$219$	5941.54	−	10291.1i	0.123883	−	0.214571i
$220$	18269.5	−	80658.5i	0.377468	−	1.66650i
$221$	8062.13	+	13964.0i	0.165069	+	0.285908i
$222$	2679.14	−	4640.41i	0.0543613	−	0.0941565i
$223$	−75191.9			−1.51203			−0.756017	−	0.654552i	$-0.772857\pi$
$223$	−75191.9			−1.51203			−0.756017	+	0.654552i	$0.772857\pi$
$224$	163002.	−	5516.95i	3.24861	−	0.109952i
$225$	−3853.13	−	49230.5i	−0.0761113	−	0.972455i
$226$	−9713.18	+	16823.7i	−0.190171	+	0.329386i
$227$	−32647.8	−	56547.6i	−0.633581	−	1.09739i	−0.986814	−	0.161859i	$-0.948251\pi$
$227$	−32647.8	−	56547.6i	−0.633581	−	1.09739i	0.353233	−	0.935535i	$-0.385082\pi$
$228$	24450.8	−	14116.7i	0.470352	−	0.271558i
$229$	−55703.4	−	32160.4i	−1.06221	−	0.613267i	−0.136167	−	0.990686i	$-0.543478\pi$
$229$	−55703.4	−	32160.4i	−1.06221	−	0.613267i	−0.926043	+	0.377419i	$0.876812\pi$
$230$	66995.5	+	61956.8i	1.26645	+	1.17121i
$231$	4587.24	−	2859.58i	0.0859662	−	0.0535894i
$232$		−	56722.9i		−	1.05386i
$233$	10433.3	+	6023.66i	0.192181	+	0.110955i	0.593003	−	0.805200i	$-0.297942\pi$
$233$	10433.3	+	6023.66i	0.192181	+	0.110955i	−0.400822	+	0.916156i	$0.631276\pi$
$234$	−35473.0	+	20480.3i	−0.647838	+	0.374029i
$235$	−6896.31	+	30446.7i	−0.124877	+	0.551322i
$236$	117528.	+	67854.7i	2.11016	+	1.21830i
$237$	−15454.1			−0.275136
$238$	41799.8	−	78410.7i	0.737938	−	1.38427i
$239$	−58505.7			−1.02424			−0.512120	−	0.858914i	$-0.671140\pi$
$239$	−58505.7			−1.02424			−0.512120	+	0.858914i	$0.671140\pi$
$240$	−28860.4	+	8954.57i	−0.501049	+	0.155461i
$241$	9677.70	−	5587.42i	0.166624	−	0.0962005i	−0.414369	−	0.910109i	$-0.635998\pi$
$241$	9677.70	−	5587.42i	0.166624	−	0.0962005i	0.580993	+	0.813908i	$0.302664\pi$
$242$	−56381.5	+	32551.9i	−0.962733	+	0.555834i
$243$	−13431.9	+	23264.8i	−0.227471	+	0.393991i
$244$		−	176275.i		−	2.96082i
$245$	−46723.6	−	37681.6i	−0.778403	−	0.627765i
$246$	−12744.0			−0.210588
$247$	27815.9	+	16059.5i	0.455931	+	0.263232i
$248$	98128.2	+	169963.i	1.59548	+	2.76345i
$249$	2927.52	+	5070.62i	0.0472174	+	0.0817829i
$250$	110843.	−	44138.7i	1.77349	−	0.706219i
$251$			18160.0i			0.288249i	0.989560	+	0.144125i	$0.0460367\pi$
$251$			18160.0i			0.288249i	−0.989560	+	0.144125i	$0.953963\pi$
$252$	144526.	+	77045.1i	2.27586	+	1.21323i
$253$			37380.6i			0.583990i
$254$	−94828.1	+	164247.i	−1.46984	+	2.54583i
$255$	−1850.32	+	8169.06i	−0.0284556	+	0.125630i
$256$	−44303.3	−	76735.6i	−0.676015	−	1.17089i
$257$	13608.0	−	23569.8i	0.206029	−	0.356853i	−0.744431	−	0.667699i	$-0.767279\pi$
$257$	13608.0	−	23569.8i	0.206029	−	0.356853i	0.950460	+	0.310846i	$0.100613\pi$
$258$	9961.13			0.149647
$259$	−12893.8	−	20683.8i	−0.192212	−	0.308340i
$260$	−52718.2	−	48753.3i	−0.779854	−	0.721202i
$261$	11156.7	−	19323.9i	0.163777	−	0.283670i
$262$	−8341.24	−	14447.4i	−0.121514	−	0.210469i
$263$	81175.7	−	46866.8i	1.17359	−	0.677570i	0.219064	−	0.975711i	$-0.429700\pi$
$263$	81175.7	−	46866.8i	1.17359	−	0.677570i	0.954522	+	0.298141i	$0.0963665\pi$
$264$	−19188.9	−	11078.7i	−0.275322	−	0.158957i
$265$	20761.2	−	22449.7i	0.295639	−	0.319682i
$266$	−5987.25	−	176898.i	−0.0846183	−	2.50011i
$267$		−	16084.9i		−	0.225629i
$268$	−133437.	−	77039.8i	−1.85783	−	1.07262i
$269$	94452.3	−	54532.0i	1.30529	−	0.753611i	0.323986	−	0.946062i	$-0.394977\pi$
$269$	94452.3	−	54532.0i	1.30529	−	0.753611i	0.981307	+	0.192451i	$0.0616436\pi$
$270$	−42026.7	−	9519.22i	−0.576498	−	0.130579i
$271$	−37035.5	−	21382.5i	−0.504289	−	0.291152i	0.226194	−	0.974082i	$-0.427372\pi$
$271$	−37035.5	−	21382.5i	−0.504289	−	0.291152i	−0.730483	+	0.682931i	$0.760705\pi$
$272$	−203475.			−2.75025
$273$	−158.761	−	4690.70i	−0.00213018	−	0.0629379i
$274$	28956.6			0.385697
$275$	44103.1	+	21059.5i	0.583182	+	0.278473i
$276$	24707.1	−	14264.7i	0.324343	−	0.187260i
$277$	−37268.5	+	21517.0i	−0.485715	+	0.280428i	−0.722795	−	0.691062i	$-0.757143\pi$
$277$	−37268.5	+	21517.0i	−0.485715	+	0.280428i	0.237080	+	0.971490i	$0.423810\pi$
$278$	−6410.79	+	11103.8i	−0.0829510	+	0.143675i
$279$			77202.2i			0.991794i
$280$	−46204.6	+	241665.i	−0.589344	+	3.08247i
$281$	32578.6			0.412590			0.206295	−	0.978490i	$-0.433859\pi$
$281$	32578.6			0.412590			0.206295	+	0.978490i	$0.433859\pi$
$282$	11649.3	+	6725.71i	0.146488	+	0.0845746i
$283$	−4937.83	−	8552.57i	−0.0616543	−	0.106788i	0.833551	−	0.552443i	$-0.186304\pi$
$283$	−4937.83	−	8552.57i	−0.0616543	−	0.106788i	−0.895205	+	0.445655i	$0.852971\pi$
$284$	85461.2	+	148023.i	1.05958	+	1.83524i
$285$	4944.27	+	15935.3i	0.0608713	+	0.196187i
$286$		−	40539.4i		−	0.495616i
$287$	−27269.9	+	51154.6i	−0.331069	+	0.621041i
$288$		−	262983.i		−	3.17061i
$289$	13560.1	−	23486.7i	0.162355	−	0.281207i
$290$	52578.6	+	11909.3i	0.625192	+	0.141608i
$291$	−603.764	−	1045.75i	−0.00712986	−	0.0123493i
$292$	−178168.	+	308595.i	−2.08960	+	3.61929i
$293$	−106248.			−1.23762			−0.618808	−	0.785542i	$-0.712384\pi$
$293$	−106248.			−1.23762			−0.618808	+	0.785542i	$0.712384\pi$
$294$	−21473.2	+	14416.9i	−0.248429	+	0.166793i
$295$	−54451.5	+	58879.8i	−0.625700	+	0.676585i
$296$	−49953.6	+	86522.2i	−0.570142	+	0.987516i
$297$	−8825.93	−	15287.0i	−0.100057	−	0.173304i
$298$	134147.	−	77449.7i	1.51059	−	0.872142i
$299$	28107.5	+	16227.9i	0.314398	+	0.181518i
$300$	−2910.52	−	37186.9i	−0.0323391	−	0.413188i
$301$	21315.1	−	39984.2i	0.235263	−	0.441322i
$302$		−	12069.3i		−	0.132333i
$303$	22297.8	+	12873.6i	0.242871	+	0.140222i
$304$	−351013.	+	202658.i	−3.79819	+	2.19289i
$305$	101598.	+	23012.3i	1.09216	+	0.247378i
$306$	−124081.	−	71638.0i	−1.32514	−	0.765069i
$307$	115720.			1.22781			0.613907	−	0.789378i	$-0.289597\pi$
$307$	115720.			1.22781			0.613907	+	0.789378i	$0.289597\pi$
$308$	−137557.	+	85749.7i	−1.45004	+	0.903923i
$309$	−5499.64			−0.0575993
$310$	−178148.	+	55274.2i	−1.85378	+	0.575174i
$311$	55909.1	−	32279.2i	0.578046	−	0.333735i	−0.182311	−	0.983241i	$-0.558358\pi$
$311$	55909.1	−	32279.2i	0.578046	−	0.333735i	0.760356	+	0.649506i	$0.225024\pi$
$312$	−16660.8	+	9619.11i	−0.171154	+	0.0988156i
$313$	51328.3	−	88903.2i	0.523924	−	0.907463i	−0.475688	−	0.879614i	$-0.657801\pi$
$313$	51328.3	−	88903.2i	0.523924	−	0.907463i	0.999612	−	0.0278490i	$-0.00886577\pi$
$314$		−	313836.i		−	3.18305i
$315$	−63273.1	+	73240.9i	−0.637673	+	0.738129i
$316$	463419.			4.64087
$317$	126871.	+	73248.8i	1.26253	+	0.728923i	0.973564	−	0.228415i	$-0.0733544\pi$
$317$	126871.	+	73248.8i	1.26253	+	0.728923i	0.288968	+	0.957339i	$0.406688\pi$
$318$	−6587.84	−	11410.5i	−0.0651461	−	0.112836i
$319$	11041.9	+	19125.2i	0.108508	+	0.187942i
$320$	279528.	−	86729.5i	2.72976	−	0.846968i
$321$			9130.15i			0.0886070i
$322$	−6050.03	−	178753.i	−0.0583507	−	1.72401i
$323$			112349.i			1.07687i
$324$	128633.	−	222799.i	1.22536	−	2.12238i
$325$	34981.6	−	24019.9i	0.331187	−	0.227408i
$326$	−122498.	−	212173.i	−1.15264	−	1.99644i
$327$	−6049.43	+	10477.9i	−0.0565743	+	0.0979896i
$328$	237616.			2.20866
$329$	51924.5	−	32368.6i	0.479712	−	0.299042i
$330$	14298.1	−	15460.9i	0.131296	−	0.141973i
$331$	−77288.7	+	133868.i	−0.705440	+	1.22186i	0.261092	+	0.965314i	$0.415917\pi$
$331$	−77288.7	+	133868.i	−0.705440	+	1.22186i	−0.966532	+	0.256545i	$0.917416\pi$
$332$	−87787.0	−	152052.i	−0.796442	−	1.37948i
$333$	−34035.6	+	19650.5i	−0.306934	+	0.177208i
$334$	188798.	+	109003.i	1.69241	+	0.977112i
$335$	61822.3	−	66850.0i	0.550878	−	0.595679i
$336$	52264.1	+	27861.4i	0.462941	+	0.246788i
$337$		−	60058.7i		−	0.528830i	−0.964409	−	0.264415i	$-0.914821\pi$
$337$		−	60058.7i		−	0.528830i	0.964409	−	0.264415i	$-0.0851788\pi$
$338$	158383.	+	91442.6i	1.38636	+	0.800415i
$339$	−3108.32	+	1794.59i	−0.0270474	+	0.0156159i
$340$	55485.3	−	244964.i	0.479976	−	2.11906i
$341$	−66171.4	−	38204.1i	−0.569065	−	0.328550i
$342$	−285401.			−2.44008
$343$	11920.7	+	117044.i	0.101324	+	0.994853i
$344$	−185729.			−1.56951
$345$	4996.11	+	16102.4i	0.0419753	+	0.135286i
$346$	−150110.	+	86666.2i	−1.25389	+	0.723932i
$347$	65793.9	−	37986.1i	0.546420	−	0.315476i	−0.201257	−	0.979539i	$-0.564503\pi$
$347$	65793.9	−	37986.1i	0.546420	−	0.315476i	0.747677	+	0.664063i	$0.231169\pi$
$348$	8427.34	−	14596.6i	0.0695876	−	0.120529i
$349$			53756.7i			0.441348i	0.975348	+	0.220674i	$0.0708258\pi$
$349$			53756.7i			0.441348i	−0.975348	+	0.220674i	$0.929174\pi$
$350$	−214308.	−	93567.8i	−1.74945	−	0.763819i
$351$	−15326.3			−0.124401
$352$	225407.	+	130139.i	1.81921	+	1.05032i
$353$	−80904.6	−	140131.i	−0.649268	−	1.12457i	−0.983298	−	0.182003i	$-0.941742\pi$
$353$	−80904.6	−	140131.i	−0.649268	−	1.12457i	0.334030	−	0.942562i	$-0.391591\pi$
$354$	17278.2	+	29926.8i	0.137877	+	0.238811i
$355$	−96471.1	+	29932.2i	−0.765492	+	0.237510i
$356$			482333.i			3.80581i
$357$	13931.7	−	8684.70i	0.109312	−	0.0681426i
$358$			219658.i			1.71388i
$359$	−11534.9	+	19979.0i	−0.0895002	+	0.155019i	−0.907300	−	0.420484i	$-0.861860\pi$
$359$	−11534.9	+	19979.0i	−0.0895002	+	0.155019i	0.817800	+	0.575503i	$0.195194\pi$
$360$	386929.	+	87640.9i	2.98556	+	0.676242i
$361$	46737.1	+	80951.0i	0.358631	+	0.621167i
$362$	11837.1	−	20502.4i	0.0903290	−	0.156454i
$363$	−12028.4			−0.0912843
$364$	4760.72	+	140659.i	0.0359310	+	1.06161i
$365$	−154602.	−	142975.i	−1.16046	−	1.07318i
$366$	22443.0	−	38872.5i	0.167540	−	0.290188i
$367$	−31425.7	−	54431.0i	−0.233321	−	0.404123i	0.725463	−	0.688262i	$-0.241626\pi$
$367$	−31425.7	−	54431.0i	−0.233321	−	0.404123i	−0.958783	+	0.284138i	$0.908293\pi$
$368$	−354694.	+	204783.i	−2.61914	+	1.51216i
$369$	80949.3	+	46736.1i	0.594511	+	0.343241i
$370$	−69712.7	−	64469.7i	−0.509224	−	0.470926i
$371$	−59898.7	+	2027.32i	−0.435180	+	0.0147290i
$372$			58315.7i			0.421405i
$373$	−183272.	−	105812.i	−1.31728	−	0.760532i	−0.333990	−	0.942577i	$-0.608395\pi$
$373$	−183272.	−	105812.i	−1.31728	−	0.760532i	−0.983290	+	0.182044i	$0.941729\pi$
$374$	122804.	−	70901.2i	0.877952	−	0.506886i
$375$	21813.0	+	3177.16i	0.155114	+	0.0225931i
$376$	−217205.	−	125403.i	−1.53637	−	0.887021i
$377$	19174.3			0.134908
$378$	44679.5	+	71673.3i	0.312698	+	0.501619i
$379$	104107.			0.724770			0.362385	−	0.932028i	$-0.381963\pi$
$379$	104107.			0.724770			0.362385	+	0.932028i	$0.381963\pi$
$380$	−148263.	−	477849.i	−1.02675	−	3.30920i
$381$	−30346.0	+	17520.3i	−0.209050	+	0.120695i
$382$	−114516.	+	66115.6i	−0.784762	+	0.453082i
$383$	99243.6	−	171895.i	0.676558	−	1.17183i	−0.299453	−	0.954111i	$-0.596804\pi$
$383$	99243.6	−	171895.i	0.676558	−	1.17183i	0.976011	−	0.217722i	$-0.0698625\pi$
$384$		−	50978.0i		−	0.345717i
$385$	−31464.9	−	90476.3i	−0.212278	−	0.610399i
$386$	−139808.			−0.938333
$387$	−63272.8	−	36530.6i	−0.422469	−	0.243913i
$388$	18104.9	+	31358.7i	0.120263	+	0.208302i
$389$	9373.83	+	16235.9i	0.0619467	+	0.107295i	0.895335	−	0.445392i	$-0.146936\pi$
$389$	9373.83	+	16235.9i	0.0619467	+	0.107295i	−0.833389	+	0.552687i	$0.813602\pi$
$390$	−5418.31	−	17463.1i	−0.0356233	−	0.114813i
$391$			113527.i			0.742582i
$392$	400376.	−	268808.i	2.60553	−	1.74932i
$393$		−	3082.22i		−	0.0199563i
$394$	45654.4	−	79075.8i	0.294097	−	0.509391i
$395$	−60498.2	+	267095.i	−0.387747	+	1.71188i
$396$	130685.	+	226353.i	0.833363	+	1.44343i
$397$	−144975.	+	251104.i	−0.919841	+	1.59321i	−0.120186	+	0.992751i	$0.538349\pi$
$397$	−144975.	+	251104.i	−0.919841	+	1.59321i	−0.799655	+	0.600460i	$0.794984\pi$
$398$	209108.			1.32009
$399$	15383.7	−	28857.7i	0.0966305	−	0.181266i
$400$	41783.1	+	533853.i	0.261145	+	3.33658i
$401$	18271.2	−	31646.6i	0.113626	−	0.196806i	−0.803604	−	0.595165i	$-0.797087\pi$
$401$	18271.2	−	31646.6i	0.113626	−	0.196806i	0.917230	+	0.398359i	$0.130420\pi$
$402$	−19617.1	−	33977.8i	−0.121390	−	0.210254i
$403$	−57453.5	+	33170.8i	−0.353758	+	0.204242i
$404$	−668638.	−	386038.i	−4.09665	−	2.36520i
$405$	111619.	+	103224.i	0.680501	+	0.629321i
$406$	−55897.5	−	89668.7i	−0.339110	−	0.543988i
$407$		−	38896.7i		−	0.234814i
$408$	−58277.6	−	33646.6i	−0.350091	−	0.202125i
$409$	149443.	−	86280.8i	0.893364	−	0.515784i	0.0183226	−	0.999832i	$-0.494167\pi$
$409$	149443.	−	86280.8i	0.893364	−	0.515784i	0.875041	+	0.484048i	$0.160834\pi$
$410$	−49888.8	+	220256.i	−0.296780	+	1.31027i
$411$	4633.21	+	2674.98i	0.0274283	+	0.0158357i
$412$	164917.			0.971561
$413$	157099.	−	5317.15i	0.921030	−	0.0311730i
$414$	−288394.			−1.68262
$415$	99096.6	−	30746.8i	0.575390	−	0.178527i
$416$	195710.	−	112993.i	1.13091	−	0.652930i
$417$	−2051.52	+	1184.45i	−0.0117979	+	0.00681150i
$418$	141233.	−	244623.i	0.808320	−	1.40005i
$419$		−	134509.i		−	0.766168i	−0.923714	−	0.383084i	$-0.874862\pi$
$419$		−	134509.i		−	0.766168i	0.923714	−	0.383084i	$-0.125138\pi$
$420$	−47794.2	+	55323.5i	−0.270942	+	0.313625i
$421$	−193414.			−1.09125			−0.545625	−	0.838029i	$-0.683708\pi$
$421$	−193414.			−1.09125			−0.545625	+	0.838029i	$0.683708\pi$
$422$	304593.	+	175857.i	1.71039	+	0.987493i
$423$	−49330.5	−	85443.0i	−0.275699	−	0.477524i
$424$	122833.	+	212753.i	0.683255	+	1.18343i
$425$	133943.	+	63958.8i	0.741556	+	0.354097i
$426$			43523.0i			0.239828i
$427$	−108011.	−	173267.i	−0.592395	−	0.950299i
$428$		−	273784.i		−	1.49458i
$429$	3744.99	−	6486.52i	0.0203487	−	0.0352450i
$430$	38994.8	−	172160.i	0.210897	−	0.931096i
$431$	−98074.3	−	169870.i	−0.527960	−	0.914453i	−0.999469	−	0.0325919i	$-0.989624\pi$
$431$	−98074.3	−	169870.i	−0.527960	−	0.914453i	0.471509	−	0.881861i	$-0.343709\pi$
$432$	96702.5	−	167494.i	0.518167	−	0.897492i
$433$	−241173.			−1.28633			−0.643167	−	0.765726i	$-0.722380\pi$
$433$	−241173.			−1.28633			−0.643167	+	0.765726i	$0.722380\pi$
$434$	322613.	+	171981.i	1.71278	+	0.913063i
$435$	7312.69	+	6762.71i	0.0386455	+	0.0357390i
$436$	181403.	−	314199.i	0.954271	−	1.65285i
$437$	113071.	+	195844.i	0.592090	+	1.02553i
$438$	−78579.6	+	45367.9i	−0.409601	+	0.236483i
$439$	147422.	+	85114.1i	0.764950	+	0.441644i	0.831070	−	0.556168i	$-0.187729\pi$
$439$	147422.	+	85114.1i	0.764950	+	0.441644i	−0.0661202	+	0.997812i	$0.521062\pi$
$440$	−266593.	+	288274.i	−1.37703	+	1.48902i
$441$	189268.	−	12826.6i	0.973197	−	0.0659528i
$442$		−	123120.i		−	0.630209i
$443$	−96915.8	−	55954.3i	−0.493841	−	0.285119i	0.232326	−	0.972638i	$-0.425366\pi$
$443$	−96915.8	−	55954.3i	−0.493841	−	0.285119i	−0.726166	+	0.687519i	$0.758700\pi$
$444$	−25709.3	+	14843.2i	−0.130414	+	0.0752944i
$445$	−277997.	−	62967.4i	−1.40385	−	0.317977i
$446$	497223.	+	287072.i	2.49967	+	1.44318i
$447$	28618.9			0.143231
$448$	−506205.	−	269851.i	−2.52215	−	1.34452i
$449$	253393.			1.25691			0.628453	−	0.777848i	$-0.283689\pi$
$449$	253393.			1.25691			0.628453	+	0.777848i	$0.283689\pi$
$450$	−162476.	+	340259.i	−0.802348	+	1.68029i
$451$	−80116.7	+	46255.4i	−0.393885	+	0.227410i
$452$	93208.5	−	53814.0i	0.456225	−	0.263401i
$453$	1114.95	−	1931.15i	0.00543324	−	0.00941065i
$454$			498578.i			2.41892i
$455$	−81691.5	−	15618.8i	−0.394597	−	0.0754440i
$456$	−134046.			−0.644650
$457$	11982.5	+	6918.10i	0.0573740	+	0.0331249i	0.528413	−	0.848988i	$-0.322787\pi$
$457$	11982.5	+	6918.10i	0.0573740	+	0.0331249i	−0.471039	+	0.882113i	$0.656121\pi$
$458$	245567.	+	425335.i	1.17068	+	2.02768i
$459$	−26804.8	−	46427.3i	−0.127229	−	0.220368i
$460$	−149817.	−	482859.i	−0.708021	−	2.28194i
$461$		−	387906.i		−	1.82526i	−0.408788	−	0.912630i	$-0.634048\pi$
$461$		−	387906.i		−	1.82526i	0.408788	−	0.912630i	$-0.365952\pi$
$462$	−41251.7	+	1396.20i	−0.193267	+	0.00654127i
$463$			360475.i			1.68156i	0.541373	+	0.840782i	$0.317905\pi$
$463$			360475.i			1.68156i	−0.541373	+	0.840782i	$0.682095\pi$
$464$	−120982.	+	209547.i	−0.561934	+	0.973298i
$465$	−33610.8	−	7612.97i	−0.155443	−	0.0352085i
$466$	−45995.0	−	79665.7i	−0.211806	−	0.366859i
$467$	23257.8	−	40283.7i	0.106644	−	0.184712i	−0.807765	−	0.589505i	$-0.799323\pi$
$467$	23257.8	−	40283.7i	0.106644	−	0.184712i	0.914409	+	0.404792i	$0.132656\pi$
$468$	226935.			1.03612
$469$	−178365.	+	6036.90i	−0.810893	+	0.0274453i
$470$	161845.	−	175007.i	0.732661	−	0.792245i
$471$	28991.8	−	50215.3i	0.130687	−	0.226357i
$472$	−322160.	−	557997.i	−1.44606	−	2.50465i
$473$	62622.0	−	36154.8i	0.279901	−	0.161601i
$474$	102194.	+	59001.6i	0.454850	+	0.262608i
$475$	294767.	−	23070.6i	1.30645	−	0.102252i
$476$	−417767.	+	260426.i	−1.84383	+	1.14940i
$477$			96638.6i			0.424731i
$478$	386882.	+	223366.i	1.69326	+	0.977602i
$479$	−249037.	+	143781.i	−1.08541	+	0.626660i	−0.932350	−	0.361558i	$-0.882245\pi$
$479$	−249037.	+	143781.i	−1.08541	+	0.626660i	−0.153057	+	0.988217i	$0.548912\pi$
$480$	114492.	+	25932.9i	0.496928	+	0.112556i
$481$	−29247.6	−	16886.1i	−0.126415	−	0.0729859i
$482$	−85328.0			−0.367280
$483$	15545.0	−	29160.3i	0.0666340	−	0.124996i
$484$	360694.			1.53974
$485$	−20437.4	+	6341.13i	−0.0868843	+	0.0269577i
$486$	177643.	−	102562.i	0.752102	−	0.434226i
$487$	70263.8	−	40566.8i	0.296260	−	0.171046i	−0.344501	−	0.938786i	$-0.611952\pi$
$487$	70263.8	−	40566.8i	0.296260	−	0.171046i	0.640762	+	0.767740i	$0.278619\pi$
$488$	−418459.	+	724792.i	−1.75717	+	3.04350i
$489$		−	45265.1i		−	0.189298i
$490$	165108.	+	427562.i	0.687662	+	1.78077i
$491$	384808.			1.59618			0.798089	−	0.602540i	$-0.205844\pi$
$491$	384808.			1.59618			0.798089	+	0.602540i	$0.205844\pi$
$492$	61146.1	+	35302.7i	0.252603	+	0.145840i
$493$	33534.9	+	58084.1i	0.137976	+	0.238981i
$494$	−122626.	−	212394.i	−0.502491	−	0.870340i
$495$	−147521.	+	45771.5i	−0.602064	+	0.186803i
$496$		−	837176.i		−	3.40293i
$497$	174702.	+	93131.6i	0.707271	+	0.377037i
$498$		−	44707.5i		−	0.180269i
$499$	136746.	−	236851.i	0.549178	−	0.951204i	−0.449153	−	0.893455i	$-0.648274\pi$
$499$	136746.	−	236851.i	0.549178	−	0.951204i	0.998331	−	0.0577491i	$-0.0183924\pi$
$500$	−654101.	−	95272.8i	−2.61640	−	0.381091i
$501$	20139.1	+	34882.0i	0.0802353	+	0.138972i
$502$	69332.3	−	120087.i	0.275124	−	0.476529i
$503$	−423388.			−1.67341			−0.836706	−	0.547653i	$-0.815522\pi$
$503$	−423388.			−1.67341			−0.836706	+	0.547653i	$0.815522\pi$
$504$	−411352.	−	659877.i	−1.61940	−	2.59778i
$505$	309785.	−	334979.i	1.21473	−	1.31351i
$506$	142714.	−	247188.i	0.557397	−	0.965441i
$507$	16894.8	+	29262.6i	0.0657259	+	0.113841i
$508$	909978.	−	525376.i	3.52617	−	2.03584i
$509$	−213041.	−	122999.i	−0.822295	−	0.474752i	0.0289125	−	0.999582i	$-0.490796\pi$
$509$	−213041.	−	122999.i	−0.822295	−	0.474752i	−0.851207	+	0.524830i	$0.824129\pi$
$510$	43424.0	−	46955.5i	0.166951	−	0.180529i
$511$	13961.4	+	412499.i	0.0534670	+	1.57972i
$512$			98412.9i			0.375416i
$513$	−92481.7	−	53394.3i	−0.351416	−	0.202890i
$514$	−179972.	+	103907.i	−0.681207	+	0.393295i
$515$	−21529.4	+	95051.1i	−0.0811742	+	0.358379i
$516$	−47793.9	−	27593.8i	−0.179504	−	0.103637i
$517$	97646.3			0.365321
$518$	6295.42	+	186003.i	0.0234620	+	0.693202i
$519$	−32024.6			−0.118891
$520$	101026.	+	325606.i	0.373618	+	1.20417i
$521$	36129.5	−	20859.4i	0.133102	−	0.0768468i	−0.431970	−	0.901888i	$-0.642181\pi$
$521$	36129.5	−	20859.4i	0.133102	−	0.0768468i	0.565073	+	0.825041i	$0.308848\pi$
$522$	−147552.	+	85189.1i	−0.541507	+	0.312639i
$523$	38764.0	−	67141.3i	0.141718	−	0.245463i	−0.786426	−	0.617685i	$-0.788071\pi$
$523$	38764.0	−	67141.3i	0.141718	−	0.245463i	0.928144	+	0.372222i	$0.121404\pi$
$524$			92426.0i			0.336613i
$525$	−25646.7	−	34768.9i	−0.0930494	−	0.126146i
$526$	−715724.			−2.58687
$527$	−200966.	−	116028.i	−0.723605	−	0.417773i
$528$	47258.7	+	81854.5i	0.169517	+	0.293613i
$529$	−25664.1	−	44451.4i	−0.0917094	−	0.158845i
$530$	−222998.	+	69190.0i	−0.793870	+	0.246315i
$531$		−	253459.i		−	0.898914i
$532$	−461307.	+	865349.i	−1.62992	+	3.05751i
$533$			80322.7i			0.282738i
$534$	−61409.8	+	106365.i	−0.215355	+	0.373006i
$535$	157798.	+	35741.8i	0.551306	+	0.124873i
$536$	365768.	+	633529.i	1.27314	+	2.20515i
$537$	−20291.8	+	35146.4i	−0.0703674	+	0.121880i
$538$	−832783.			−2.87718
$539$	−82666.9	+	168573.i	−0.284547	+	0.580242i
$540$	175276.	+	162094.i	0.601085	+	0.555878i
$541$	−229097.	+	396808.i	−0.782755	+	1.35577i	0.147577	+	0.989051i	$0.452853\pi$
$541$	−229097.	+	396808.i	−0.782755	+	1.35577i	−0.930331	+	0.366720i	$0.880481\pi$
$542$	163270.	+	282793.i	0.555788	+	0.962653i
$543$	3787.99	−	2186.99i	0.0128472	−	0.00741734i
$544$	684573.	+	395239.i	2.31325	+	1.33555i
$545$	157410.	+	145571.i	0.529954	+	0.490097i
$546$	−16858.6	+	31624.4i	−0.0565504	+	0.106081i
$547$		−	301896.i		−	1.00898i	−0.863417	−	0.504491i	$-0.831680\pi$
$547$		−	301896.i		−	1.00898i	0.863417	−	0.504491i	$-0.168320\pi$
$548$	−138935.	−	80214.2i	−0.462648	−	0.267110i
$549$	−285115.	+	164611.i	−0.945965	+	0.546153i
$550$	−211240.	−	307640.i	−0.698313	−	1.01699i
$551$	115702.	+	66800.4i	0.381098	+	0.220027i
$552$	−135451.			−0.444534
$553$	455510.	−	283955.i	1.48953	−	0.928537i
$554$	328595.			1.07063
$555$	−5198.75	−	16755.5i	−0.0168777	−	0.0543965i
$556$	61518.5	−	35517.7i	0.199001	−	0.114893i
$557$	−458893.	+	264942.i	−1.47911	+	0.853966i	−0.999721	−	0.0236353i	$-0.992476\pi$
$557$	−458893.	+	264942.i	−1.47911	+	0.853966i	−0.479392	+	0.877601i	$0.659143\pi$
$558$	294747.	−	510517.i	0.946632	−	1.63961i
$559$		−	62783.0i		−	0.200918i
$560$	686130.	−	794219.i	2.18791	−	2.53259i
$561$	26199.1			0.0832456
$562$	−215433.	−	124380.i	−0.682087	−	0.393803i
$563$	−121918.	−	211168.i	−0.384637	−	0.666210i	0.607082	−	0.794639i	$-0.292340\pi$
$563$	−121918.	−	211168.i	−0.384637	−	0.666210i	−0.991719	+	0.128429i	$0.959007\pi$
$564$	−37262.5	−	64540.5i	−0.117142	−	0.202896i
$565$	18848.0	+	60746.8i	0.0590430	+	0.190295i
$566$			75407.7i			0.235387i
$567$	−10079.8	−	297815.i	−0.0313534	−	0.926360i
$568$		−	811503.i		−	2.51532i
$569$	−292824.	+	507186.i	−0.904446	+	1.56655i	−0.0827859	+	0.996567i	$0.526382\pi$
$569$	−292824.	+	507186.i	−0.904446	+	1.56655i	−0.821660	+	0.569978i	$0.806952\pi$
$570$	28143.6	−	124252.i	0.0866224	−	0.382432i
$571$	−127634.	−	221068.i	−0.391466	−	0.678039i	0.601177	−	0.799116i	$-0.294699\pi$
$571$	−127634.	−	221068.i	−0.391466	−	0.678039i	−0.992643	+	0.121077i	$0.961365\pi$
$572$	−112300.	+	194510.i	−0.343233	+	0.594497i
$573$	−24430.8			−0.0744095
$574$	375629.	−	234159.i	1.14008	−	0.710700i
$575$	297858.	−	23312.5i	0.900894	−	0.0705104i
$576$	−462481.	+	801041.i	−1.39396	+	2.41440i
$577$	237680.	+	411674.i	0.713905	+	1.23652i	0.963380	+	0.268139i	$0.0864087\pi$
$577$	237680.	+	411674.i	0.713905	+	1.23652i	−0.249475	+	0.968381i	$0.580258\pi$
$578$	−179338.	+	103541.i	−0.536805	+	0.309925i
$579$	−22370.0	−	12915.3i	−0.0667281	−	0.0385255i
$580$	−219284.	−	202792.i	−0.651855	−	0.602830i
$581$	−179457.	−	95666.2i	−0.531628	−	0.283404i
$582$			9220.33i			0.0272208i
$583$	−82830.7	−	47822.3i	−0.243699	−	0.140700i
$584$	1.46515e6	−	845902.i	4.29591	−	2.48025i
$585$	−29625.7	+	130796.i	−0.0865680	+	0.382192i
$586$	702590.	+	405640.i	2.04600	+	1.18126i
$587$	155412.			0.451033			0.225517	−	0.974239i	$-0.427593\pi$
$587$	155412.			0.451033			0.225517	+	0.974239i	$0.427593\pi$
$588$	142966.	−	9688.72i	0.413503	−	0.0280228i
$589$	−462247.			−1.33243
$590$	584868.	−	181468.i	1.68017	−	0.521310i
$591$	14609.9	−	8435.02i	0.0418285	−	0.0241497i
$592$	369080.	−	213088.i	1.05312	−	0.608018i
$593$	172179.	−	298222.i	0.489632	−	0.848068i	−0.510297	−	0.859998i	$-0.670464\pi$
$593$	172179.	−	298222.i	0.489632	−	0.848068i	0.999929	+	0.0119306i	$0.00379773\pi$
$594$			134785.i			0.382004i
$595$	−95560.5	−	274781.i	−0.269926	−	0.776163i
$596$	−858189.			−2.41596
$597$	33458.4	+	19317.2i	0.0938763	+	0.0541995i
$598$	−123912.	−	214621.i	−0.346505	−	0.600164i
$599$	−22836.5	−	39553.9i	−0.0636466	−	0.110239i	0.832446	−	0.554106i	$-0.186940\pi$
$599$	−22836.5	−	39553.9i	−0.0636466	−	0.110239i	−0.896093	+	0.443867i	$0.853606\pi$
$600$	−76310.7	+	159811.i	−0.211974	+	0.443920i
$601$			295730.i			0.818740i	0.912368	+	0.409370i	$0.134251\pi$
$601$			295730.i			0.818740i	−0.912368	+	0.409370i	$0.865749\pi$
$602$	−293605.	+	183027.i	−0.810159	+	0.505035i
$603$			287768.i			0.791421i
$604$	−33433.8	+	57909.0i	−0.0916455	+	0.158735i
$605$	−47087.7	+	207889.i	−0.128646	+	0.567964i
$606$	−98299.3	−	170259.i	−0.267673	−	0.463624i
$607$	281847.	−	488174.i	0.764956	−	1.32494i	−0.175315	−	0.984512i	$-0.556094\pi$
$607$	281847.	−	488174.i	0.764956	−	1.32494i	0.940270	−	0.340429i	$-0.110572\pi$
$608$	1.57461e6			4.25956
$609$	−660.373	−	19511.2i	−0.00178055	−	0.0526078i
$610$	−583981.	−	540060.i	−1.56942	−	1.45138i
$611$	42390.8	−	73423.0i	0.113551	−	0.196675i
$612$	396896.	+	687444.i	1.05968	+	1.83542i
$613$	−241515.	+	139439.i	−0.642723	+	0.371076i	−0.785663	−	0.618655i	$-0.787678\pi$
$613$	−241515.	+	139439.i	−0.642723	+	0.371076i	0.142940	+	0.989731i	$0.454344\pi$
$614$	−765227.	−	441804.i	−2.02980	−	1.17191i
$615$	−28329.5	+	30633.4i	−0.0749011	+	0.0809925i
$616$	769153.	−	26032.6i	2.02699	−	0.0686051i
$617$			2927.93i			0.00769112i	0.999993	+	0.00384556i	$0.00122408\pi$
$617$			2927.93i			0.00769112i	−0.999993	+	0.00384556i	$0.998776\pi$
$618$	36367.6	+	20996.9i	0.0952222	+	0.0549765i
$619$	−192229.	+	110983.i	−0.501691	+	0.289652i	−0.729412	−	0.684075i	$-0.760206\pi$
$619$	−192229.	+	110983.i	−0.501691	+	0.289652i	0.227720	+	0.973727i	$0.426873\pi$
$620$	1.00788e6	+	228288.i	2.62195	+	0.593883i
$621$	−93451.4	−	53954.2i	−0.242327	−	0.139908i
$622$	−492949.			−1.27415
$623$	295544.	+	474102.i	0.761459	+	1.22151i
$624$	82065.0			0.210760
$625$	140302.	−	364559.i	0.359174	−	0.933271i
$626$	−678840.	+	391928.i	−1.73228	+	1.00013i
$627$	45196.0	−	26093.9i	0.114965	−	0.0663750i
$628$	−869372.	+	1.50580e6i	−2.20438	+	3.81810i
$629$		−	118131.i		−	0.298582i
$630$	698031.	−	242754.i	1.75871	−	0.611625i
$631$	470302.			1.18119			0.590593	−	0.806970i	$-0.298894\pi$
$631$	470302.			1.18119			0.590593	+	0.806970i	$0.298894\pi$
$632$	−1.90544e6	−	1.10011e6i	−4.77048	−	2.75424i
$633$	32490.9	+	56276.0i	0.0810877	+	0.140448i
$634$	−559307.	−	968748.i	−1.39146	−	2.41008i
$635$	184010.	+	593060.i	0.456345	+	1.47079i
$636$			72997.2i			0.180465i
$637$	90866.7	+	135341.i	0.223937	+	0.333543i
$638$		−	168626.i		−	0.414269i
$639$	159612.	−	276457.i	0.390899	−	0.677057i
$640$	−881060.	−	199564.i	−2.15103	−	0.487216i
$641$	326406.	+	565352.i	0.794405	+	1.37595i	0.923216	+	0.384281i	$0.125551\pi$
$641$	326406.	+	565352.i	0.794405	+	1.37595i	−0.128811	+	0.991669i	$0.541116\pi$
$642$	34857.6	−	60375.2i	0.0845722	−	0.146483i
$643$	368975.			0.892432			0.446216	−	0.894925i	$-0.352771\pi$
$643$	368975.			0.892432			0.446216	+	0.894925i	$0.352771\pi$
$644$	−466144.	+	874423.i	−1.12395	+	2.10838i
$645$	22143.3	−	23944.1i	0.0532259	−	0.0575546i
$646$	428932.	−	742931.i	1.02783	−	1.78026i
$647$	−331031.	−	573362.i	−0.790787	−	1.36968i	−0.925480	−	0.378796i	$-0.876338\pi$
$647$	−331031.	−	573362.i	−0.790787	−	1.36968i	0.134693	−	0.990887i	$-0.456995\pi$
$648$	−1.05780e6	+	610722.i	−2.51915	+	1.45443i
$649$	217244.	+	125426.i	0.515773	+	0.297782i
$650$	−323028.	+	25282.5i	−0.764564	+	0.0598402i
$651$	35732.3	+	57320.5i	0.0843139	+	0.135253i
$652$			1.35736e6i			3.19300i
$653$	190546.	+	110012.i	0.446863	+	0.257996i	0.706504	−	0.707709i	$-0.250271\pi$
$653$	190546.	+	110012.i	0.446863	+	0.257996i	−0.259642	+	0.965705i	$0.583604\pi$
$654$	80006.5	−	46191.8i	0.187055	−	0.107996i
$655$	−53270.5	−	12066.0i	−0.124166	−	0.0281242i
$656$	−877809.	−	506803.i	−2.03982	−	1.17769i
$657$	665513.			1.54179
$658$	−466941.	+	15804.0i	−1.07848	+	0.0365019i
$659$	147645.			0.339976			0.169988	−	0.985446i	$-0.445627\pi$
$659$	147645.			0.339976			0.169988	+	0.985446i	$0.445627\pi$
$660$	−111432.	+	34574.1i	−0.255812	+	0.0793712i
$661$	236648.	−	136629.i	0.541627	−	0.312708i	−0.204111	−	0.978948i	$-0.565430\pi$
$661$	236648.	−	136629.i	0.541627	−	0.312708i	0.745738	+	0.666239i	$0.232097\pi$
$662$	1.02218e6	−	590155.i	2.33244	−	1.34664i
$663$	11373.7	−	19699.9i	0.0258747	−	0.0448164i
$664$			833589.i			1.89067i
$665$	−438529.	−	378847.i	−0.991642	−	0.856684i
$666$	300091.			0.676557
$667$	116915.	+	67500.8i	0.262796	+	0.151725i
$668$	−603908.	−	1.04600e6i	−1.35337	−	2.34411i
$669$	53038.9	+	91866.1i	0.118507	+	0.205259i
$670$	−664038.	+	206032.i	−1.47926	+	0.458971i
$671$		−	325836.i		−	0.723693i
$672$	−121719.	−	195257.i	−0.269538	−	0.432383i
$673$			422662.i			0.933175i	0.884475	+	0.466588i	$0.154517\pi$
$673$			422662.i			0.933175i	−0.884475	+	0.466588i	$0.845483\pi$
$674$	−229296.	+	397151.i	−0.504749	+	0.874251i
$675$	−116306.	+	79861.0i	−0.255267	+	0.175278i
$676$	−506620.	−	877491.i	−1.10864	−	1.92021i
$677$	−318177.	+	551098.i	−0.694210	+	1.20241i	0.276236	+	0.961090i	$0.410913\pi$
$677$	−318177.	+	551098.i	−0.694210	+	1.20241i	−0.970446	+	0.241317i	$0.922421\pi$
$678$	27406.0			0.0596191
$679$	37010.6	+	19729.9i	0.0802762	+	0.0427942i
$680$	−809657.	+	875503.i	−1.75099	+	1.89339i
$681$	−46058.2	+	79775.1i	−0.0993145	+	0.172018i
$682$	291716.	+	505266.i	0.627178	+	1.08630i
$683$	289886.	−	167366.i	0.621422	−	0.358778i	−0.156000	−	0.987757i	$-0.549860\pi$
$683$	289886.	−	167366.i	0.621422	−	0.358778i	0.777422	+	0.628979i	$0.216527\pi$
$684$	1.36937e6	+	790605.i	2.92690	+	1.68985i
$685$	64369.7	−	69604.6i	0.137183	−	0.148339i
$686$	368027.	−	819488.i	0.782045	−	1.74138i
$687$			90741.1i			0.192261i
$688$	686126.	+	396135.i	1.44953	+	0.836886i
$689$	−71917.9	+	41521.8i	−0.151495	+	0.0874658i
$690$	28438.7	−	125555.i	0.0597327	−	0.263716i
$691$	−245980.	−	142017.i	−0.515162	−	0.297429i	0.219791	−	0.975547i	$-0.429462\pi$
$691$	−245980.	−	142017.i	−0.515162	−	0.297429i	−0.734953	+	0.678118i	$0.762796\pi$
$692$	960314.			2.00540
$693$	267149.	+	142414.i	0.556273	+	0.296542i
$694$	−580103.			−1.20444
$695$	12439.8	+	40093.4i	0.0257540	+	0.0830049i
$696$	−69301.4	+	40011.2i	−0.143062	+	0.0825968i
$697$	−243318.	+	140480.i	−0.500852	+	0.289167i
$698$	205235.	−	355478.i	0.421252	−	0.729629i
$699$		−	16995.9i		−	0.0347848i
$700$	769063.	+	1.04261e6i	1.56952	+	2.12777i
$701$	158519.			0.322586			0.161293	−	0.986907i	$-0.448434\pi$
$701$	158519.			0.322586			0.161293	+	0.986907i	$0.448434\pi$
$702$	101348.	+	58513.6i	0.205657	+	0.118736i
$703$	−117657.	−	203788.i	−0.238071	−	0.412351i
$704$	−457725.	−	792802.i	−0.923547	−	1.59963i
$705$	42063.0	−	13050.9i	0.0846295	−	0.0262581i
$706$			1.23553e6i			2.47881i
$707$	−893768.	+	30250.3i	−1.78808	+	0.0605189i
$708$		−	191453.i		−	0.381941i
$709$	314009.	−	543880.i	0.624669	−	1.08196i	−0.363936	−	0.931424i	$-0.618567\pi$
$709$	314009.	−	543880.i	0.624669	−	1.08196i	0.988605	−	0.150534i	$-0.0480994\pi$
$710$	752214.	+	170379.i	1.49219	+	0.337987i
$711$	−432754.	−	749552.i	−0.856056	−	1.48273i
$712$	1.14501e6	−	1.98321e6i	2.25865	−	3.91209i
$713$	−467094.			−0.918809
$714$	−125283.	+	4240.32i	−0.245752	+	0.00831768i
$715$	−97446.8	−	90117.9i	−0.190614	−	0.176278i
$716$	608485.	−	1.05393e6i	1.18693	−	2.05582i
$717$	41268.8	+	71479.6i	0.0802755	+	0.139041i
$718$	152554.	−	88077.1i	0.295920	−	0.170850i
$719$	73349.0	+	42348.0i	0.141885	+	0.0819173i	0.569262	−	0.822156i	$-0.307229\pi$
$719$	73349.0	+	42348.0i	0.141885	+	0.0819173i	−0.427377	+	0.904073i	$0.640562\pi$
$720$	−1.24248e6	−	1.14903e6i	−2.39675	−	2.21650i
$721$	162102.	−	101051.i	0.311830	−	0.194388i
$722$		−	713743.i		−	1.36920i
$723$	−13652.9	−	7882.52i	−0.0261185	−	0.0150795i
$724$	−113590.	+	65580.9i	−0.216701	+	0.125112i
$725$	145508.	−	99912.2i	0.276828	−	0.190083i
$726$	79540.8	+	45922.9i	0.150910	+	0.0871277i
$727$	29108.2			0.0550740			0.0275370	−	0.999621i	$-0.491234\pi$
$727$	29108.2			0.0550740			0.0275370	+	0.999621i	$0.491234\pi$
$728$	314335.	−	589650.i	0.593103	−	1.11258i
$729$	−454689.			−0.855578
$730$	476485.	+	1.53570e6i	0.894135	+	2.88178i
$731$	190186.	−	109804.i	0.355913	−	0.205487i
$732$	−215365.	+	124341.i	−0.401933	+	0.232056i
$733$	389831.	−	675208.i	0.725552	−	1.25669i	−0.233194	−	0.972430i	$-0.574918\pi$
$733$	389831.	−	675208.i	0.725552	−	1.25669i	0.958746	−	0.284263i	$-0.0917490\pi$
$734$			479916.i			0.890785i
$735$	−13079.7	+	83664.7i	−0.0242116	+	0.154870i
$736$	1.59112e6			2.93729
$737$	−246651.	−	142404.i	−0.454096	−	0.262173i
$738$	−356864.	−	618106.i	−0.655223	−	1.13488i
$739$	175832.	+	304550.i	0.321966	+	0.557661i	0.980894	−	0.194545i	$-0.0623231\pi$
$739$	175832.	+	304550.i	0.321966	+	0.557661i	−0.658928	+	0.752206i	$0.728990\pi$
$740$	155894.	+	502443.i	0.284686	+	0.917537i
$741$		−	45312.2i		−	0.0825238i
$742$	403833.	+	215279.i	0.733491	+	0.391015i
$743$			523794.i			0.948818i	0.880305	+	0.474409i	$0.157338\pi$
$743$			523794.i			0.948818i	−0.880305	+	0.474409i	$0.842662\pi$
$744$	138435.	−	239777.i	0.250093	−	0.433173i
$745$	112034.	−	494625.i	0.201855	−	0.891175i
$746$	807951.	+	1.39941e6i	1.45180	+	2.51460i
$747$	−163956.	+	283980.i	−0.293824	+	0.508917i
$748$	−785628.			−1.40415
$749$	−167758.	−	269111.i	−0.299033	−	0.479699i
$750$	−132113.	−	104289.i	−0.234868	−	0.185402i
$751$	−422676.	+	732096.i	−0.749424	+	1.29804i	0.198675	+	0.980065i	$0.436336\pi$
$751$	−422676.	+	732096.i	−0.749424	+	1.29804i	−0.948099	+	0.317975i	$0.896997\pi$
$752$	534937.	+	926538.i	0.945947	+	1.63843i
$753$	22187.1	−	12809.7i	0.0391300	−	0.0225917i
$754$	−126795.	−	73204.9i	−0.223027	−	0.128765i
$755$	−29011.6	−	26829.7i	−0.0508954	−	0.0470676i
$756$	−15828.3	−	467660.i	−0.0276944	−	0.818252i
$757$			279306.i			0.487403i	0.969850	+	0.243701i	$0.0783617\pi$
$757$			279306.i			0.487403i	−0.969850	+	0.243701i	$0.921638\pi$
$758$	−688429.	−	397465.i	−1.19818	−	0.691768i
$759$	45669.9	−	26367.5i	0.0792769	−	0.0457705i
$760$	−524749.	+	2.31673e6i	−0.908499	+	4.01096i
$761$	−762641.	−	440311.i	−1.31689	−	0.760309i	−0.333666	−	0.942691i	$-0.608286\pi$
$761$	−762641.	−	440311.i	−1.31689	−	0.760309i	−0.983228	+	0.182382i	$0.941619\pi$
$762$	267559.			0.460798
$763$	−14214.9	−	419990.i	−0.0244171	−	0.721422i
$764$	732601.			1.25511
$765$	−448028.	+	139010.i	−0.765565	+	0.237533i
$766$	−1.31254e6	+	757796.i	−2.23695	+	1.29150i
$767$	188623.	−	108901.i	0.320629	−	0.185115i
$768$	−62501.4	+	108256.i	−0.105966	+	0.183539i
$769$		−	247022.i		−	0.417718i	−0.977946	−	0.208859i	$-0.933025\pi$
$769$		−	247022.i		−	0.417718i	0.977946	−	0.208859i	$-0.0669750\pi$
$770$	−137357.	+	718424.i	−0.231670	+	1.21171i
$771$	−38395.3			−0.0645906
$772$	670804.	+	387289.i	1.12554	+	0.649831i
$773$	193144.	+	334535.i	0.323238	+	0.559864i	0.981154	−	0.193227i	$-0.0618954\pi$
$773$	193144.	+	334535.i	0.323238	+	0.559864i	−0.657917	+	0.753091i	$0.728562\pi$
$774$	278937.	+	483133.i	0.465612	+	0.806464i
$775$	−263152.	+	551097.i	−0.438130	+	0.917539i
$776$		−	171917.i		−	0.285492i
$777$	−16175.5	+	30343.0i	−0.0267926	+	0.0502593i
$778$		−	143152.i		−	0.236504i
$779$	−279832.	+	484683.i	−0.461129	+	0.798698i
$780$	−22378.2	+	98798.3i	−0.0367820	+	0.162390i
$781$	157971.	+	273613.i	0.258985	+	0.448575i
$782$	433429.	−	750721.i	0.708769	−	1.22762i
$783$	−63750.5			−0.103982
$784$	−2.05241e6	+	139091.i	−3.33913	+	0.226290i
$785$	−754384.	−	697648.i	−1.22420	−	1.13213i
$786$	−11767.5	+	20381.9i	−0.0190475	+	0.0329913i
$787$	−367664.	−	636812.i	−0.593610	−	1.02816i	−0.993741	−	0.111705i	$-0.964369\pi$
$787$	−367664.	−	636812.i	−0.593610	−	1.02816i	0.400132	−	0.916458i	$-0.368964\pi$
$788$	−438104.	+	252939.i	−0.705544	+	0.407346i
$789$	−114520.	−	66117.9i	−0.183961	−	0.106210i
$790$	1.41979e6	−	1.53526e6i	2.27494	−	2.45995i
$791$	58643.9	−	110008.i	0.0937281	−	0.175821i
$792$		−	1.24093e6i		−	1.97832i
$793$	−245005.	−	141454.i	−0.389609	−	0.224941i
$794$	1.91736e6	−	1.10699e6i	3.04133	−	1.75591i
$795$	−42072.6	−	9529.60i	−0.0665679	−	0.0150779i
$796$	−1.00331e6	−	579261.i	−1.58347	−	0.914214i
$797$	−609394.			−0.959360			−0.479680	−	0.877443i	$-0.659247\pi$
$797$	−609394.			−0.959360			−0.479680	+	0.877443i	$0.659247\pi$
$798$	−211903.	+	132095.i	−0.332759	+	0.207435i
$799$	296557.			0.464531
$800$	896404.	−	1.87726e6i	1.40063	−	2.93322i
$801$	780145.	−	450417.i	1.21594	−	0.702021i
$802$	−241644.	+	139513.i	−0.375689	+	0.216904i
$803$	−329334.	+	570423.i	−0.510746	+	0.884639i
$804$			217369.i			0.336268i
$805$	−443127.	−	382819.i	−0.683811	−	0.590748i
$806$	506566.			0.779768
$807$	−133250.	−	76931.7i	−0.204606	−	0.118129i
$808$	1.83283e6	+	3.17455e6i	2.80737	+	4.86250i
$809$	370315.	+	641404.i	0.565814	+	0.980019i	0.996973	+	0.0777430i	$0.0247713\pi$
$809$	370315.	+	641404.i	0.565814	+	0.980019i	−0.431159	+	0.902276i	$0.641895\pi$
$810$	−344011.	−	1.10874e6i	−0.524327	−	1.68990i
$811$			706920.i			1.07480i	0.843327	+	0.537401i	$0.180594\pi$
$811$			706920.i			1.07480i	−0.843327	+	0.537401i	$0.819406\pi$
$812$	19802.5	+	585079.i	0.0300336	+	0.887365i
$813$			60331.1i			0.0912767i
$814$	−148502.	+	257213.i	−0.224122	+	0.388190i
$815$	−782323.	−	177199.i	−1.17780	−	0.266776i
$816$	143527.	+	248596.i	0.215553	+	0.373348i
$817$	218726.	−	378845.i	0.327685	−	0.567567i
$818$	−1.31763e6			−1.96919
$819$	223062.	−	139052.i	0.332550	−	0.207304i
$820$	849510.	−	918597.i	1.26340	−	1.36615i
$821$	−311949.	+	540312.i	−0.462804	+	0.801600i	−0.999099	−	0.0424301i	$-0.986490\pi$
$821$	−311949.	+	540312.i	−0.462804	+	0.801600i	0.536295	+	0.844030i	$0.319823\pi$
$822$	−20425.4	−	35377.9i	−0.0302293	−	0.0523586i
$823$	1.05623e6	−	609812.i	1.55940	−	0.900319i	0.562084	−	0.827080i	$-0.310000\pi$
$823$	1.05623e6	−	609812.i	1.55940	−	0.900319i	0.997314	−	0.0732388i	$-0.0233335\pi$
$824$	−678089.	−	391495.i	−0.998693	−	0.576596i
$825$	−5379.94	−	68738.2i	−0.00790442	−	0.100993i
$826$	−1.05915e6	−	564622.i	−1.55238	−	0.827556i
$827$		−	602917.i		−	0.881549i	−0.897618	−	0.440774i	$-0.854704\pi$
$827$		−	602917.i		−	0.881549i	0.897618	−	0.440774i	$-0.145296\pi$
$828$	1.38373e6	+	798894.i	2.01832	+	1.16528i
$829$	687377.	−	396857.i	1.00020	−	0.577465i	0.0918911	−	0.995769i	$-0.470709\pi$
$829$	687377.	−	396857.i	1.00020	−	0.577465i	0.908307	+	0.418305i	$0.137376\pi$
$830$	−772686.	−	175016.i	−1.12162	−	0.254052i
$831$	52576.9	+	30355.3i	0.0761365	+	0.0439574i
$832$	−794841.			−1.14824
$833$	−251064.	+	511964.i	−0.361821	+	0.737818i
$834$	18088.2			0.0260053
$835$	681709.	−	211515.i	0.977746	−	0.303367i
$836$	−1.35528e6	+	782473.i	−1.93918	+	1.11958i
$837$	191020.	−	110286.i	0.272665	−	0.157423i
$838$	−513537.	+	889472.i	−0.731280	+	1.26661i
$839$		−	670502.i		−	0.952524i	−0.879303	−	0.476262i	$-0.841991\pi$
$839$		−	670502.i		−	0.952524i	0.879303	−	0.476262i	$-0.158009\pi$
$840$	327848.	−	114015.i	0.464637	−	0.161586i
$841$	−627524.			−0.887235
$842$	1.27900e6	+	738429.i	1.80404	+	1.04156i
$843$	−22980.3	−	39803.0i	−0.0323370	−	0.0560094i
$844$	−974299.	−	1.68754e6i	−1.36775	−	2.36902i
$845$	571887.	−	177440.i	0.800935	−	0.248507i
$846$			753348.i			1.05258i
$847$	354539.	−	221011.i	0.494193	−	0.308069i
$848$		−	1.04794e6i		−	1.45729i
$849$	−6966.10	+	12065.6i	−0.00966438	+	0.0167392i
$850$	−641546.	−	934319.i	−0.887953	−	1.29318i
$851$	−118891.	−	205925.i	−0.164168	−	0.284347i
$852$	120565.	−	208825.i	0.166090	−	0.287676i
$853$	−31947.9			−0.0439080			−0.0219540	−	0.999759i	$-0.506989\pi$
$853$	−31947.9			−0.0439080			−0.0219540	+	0.999759i	$0.506989\pi$
$854$	52736.4	+	1.55814e6i	0.0723094	+	2.13644i
$855$	−634439.	+	686035.i	−0.867876	+	0.938456i
$856$	−649934.	+	1.12572e6i	−0.886996	+	1.53632i
$857$	649767.	+	1.12543e6i	0.884700	+	1.53235i	0.846057	+	0.533093i	$0.178970\pi$
$857$	649767.	+	1.12543e6i	0.884700	+	1.53235i	0.0386436	+	0.999253i	$0.487696\pi$
$858$	−49529.2	+	28595.7i	−0.0672801	+	0.0388442i
$859$	142067.	+	82022.4i	0.192534	+	0.111159i	0.593168	−	0.805079i	$-0.297877\pi$
$859$	142067.	+	82022.4i	0.192534	+	0.111159i	−0.400634	+	0.916238i	$0.631210\pi$
$860$	−664007.	+	718008.i	−0.897792	+	0.970805i
$861$	81733.9	−	2766.35i	0.110254	−	0.00373165i
$862$			1.49774e6i			2.01568i
$863$	870716.	+	502708.i	1.16911	+	0.674985i	0.953470	−	0.301488i	$-0.0974834\pi$
$863$	870716.	+	502708.i	1.16911	+	0.674985i	0.215639	+	0.976473i	$0.430817\pi$
$864$	−650694.	+	375679.i	−0.871665	+	0.503256i
$865$	−125366.	+	553485.i	−0.167552	+	0.739731i
$866$	1.59481e6	+	920766.i	2.12654	+	1.22776i
$867$	−38260.0			−0.0508987
$868$	−1.07150e6	−	1.71886e6i	−1.42217	−	2.28140i
$869$	856607.			1.13434
$870$	−22537.7	−	72638.8i	−0.0297764	−	0.0959688i
$871$	−214155.	+	123643.i	−0.282288	+	0.162979i
$872$	−1.49175e6	+	861263.i	−1.96184	+	1.13267i
$873$	33813.8	−	58567.2i	0.0443676	−	0.0768469i
$874$		−	1.72675e6i		−	2.26052i
$875$	−701315.	+	307146.i	−0.916003	+	0.401170i
$876$	502704.			0.655095
$877$	−298544.	−	172365.i	−0.388159	−	0.224104i	0.293203	−	0.956050i	$-0.405279\pi$
$877$	−298544.	−	172365.i	−0.388159	−	0.224104i	−0.681362	+	0.731947i	$0.738612\pi$
$878$	−649907.	−	1.12567e6i	−0.843067	−	1.46024i
$879$	74945.3	+	129809.i	0.0969989	+	0.168007i
$880$	1.59971e6	−	496343.i	2.06574	−	0.640939i
$881$		−	197921.i		−	0.255000i	−0.991839	−	0.127500i	$-0.959305\pi$
$881$		−	197921.i		−	0.255000i	0.991839	−	0.127500i	$-0.0406953\pi$
$882$	−1.30055e6	−	637781.i	−1.67182	−	0.819850i
$883$			864339.i			1.10857i	0.832327	+	0.554285i	$0.187008\pi$
$883$			864339.i			1.10857i	−0.832327	+	0.554285i	$0.812992\pi$
$884$	−341062.	+	590736.i	−0.436444	+	0.755943i
$885$	110346.	+	24993.7i	0.140886	+	0.0319113i
$886$	427252.	+	740021.i	0.544272	+	0.942707i
$887$	−275256.	+	476758.i	−0.349857	+	0.605969i	−0.986224	−	0.165417i	$-0.947103\pi$
$887$	−275256.	+	476758.i	−0.349857	+	0.605969i	0.636367	+	0.771386i	$0.280436\pi$
$888$	140945.			0.178741
$889$	572530.	−	1.07399e6i	0.724427	−	1.35893i
$890$	1.59792e6	+	1.47774e6i	2.01732	+	1.86560i
$891$	237771.	−	411832.i	0.299505	−	0.518758i
$892$	−1.59047e6	−	2.75477e6i	−1.99892	−	3.46222i
$893$	511589.	−	295366.i	0.641532	−	0.370388i
$894$	−189249.	−	109263.i	−0.236787	−	0.136709i
$895$	528003.	+	488293.i	0.659160	+	0.609585i
$896$	936674.	+	1.50258e6i	1.16674	+	1.87164i
$897$		−	45787.3i		−	0.0569063i
$898$	−1.67562e6	−	967420.i	−2.07789	−	1.19967i
$899$	−238981.	+	137976.i	−0.295695	+	0.170720i
$900$	1.72213e6	−	1.18249e6i	2.12609	−	1.45987i
$901$	−251561.	−	145239.i	−0.309880	−	0.178909i
$902$	706386.			0.868219
$903$	−63886.1	+	2162.28i	−0.0783485	+	0.00265177i
$904$	−510995.			−0.625287
$905$	−22969.3	−	74029.7i	−0.0280447	−	0.0903876i
$906$	−14745.7	+	8513.44i	−0.0179643	+	0.0103717i
$907$	711728.	−	410916.i	0.865166	−	0.499504i	−0.000573013	−	1.00000i	$-0.500182\pi$
$907$	711728.	−	410916.i	0.865166	−	0.499504i	0.865739	+	0.500496i	$0.166849\pi$
$908$	1.38114e6	−	2.39220e6i	1.67519	−	2.90152i
$909$			1.44198e6i			1.74514i
$910$	480573.	+	415169.i	0.580332	+	0.501352i
$911$	−131027.			−0.157879			−0.0789393	−	0.996879i	$-0.525153\pi$
$911$	−131027.			−0.157879			−0.0789393	+	0.996879i	$0.525153\pi$
$912$	495196.	+	285902.i	0.595371	+	0.343737i
$913$	−162270.	−	281060.i	−0.194669	−	0.337176i
$914$	−52824.6	−	91494.9i	−0.0632330	−	0.109523i
$915$	−43549.7	−	140360.i	−0.0520167	−	0.167649i
$916$		−	2.72103e6i		−	3.24297i
$917$	56633.0	+	90848.6i	0.0673489	+	0.108039i
$918$			409348.i			0.485744i
$919$	349660.	−	605628.i	0.414014	−	0.717093i	−0.581311	−	0.813682i	$-0.697460\pi$
$919$	349660.	−	605628.i	0.414014	−	0.717093i	0.995324	+	0.0965891i	$0.0307933\pi$
$920$	−530251.	+	2.34102e6i	−0.626478	+	2.76586i
$921$	−81626.9	−	141382.i	−0.0962307	−	0.166677i
$922$	−1.48097e6	+	2.56511e6i	−1.74215	+	3.01748i
$923$	274317.			0.321995
$924$	201795.	+	107574.i	0.236356	+	0.125998i
$925$	−309939.	+	24258.0i	−0.362237	+	0.0283512i
$926$	1.37624e6	−	2.38372e6i	1.60499	−	2.77993i
$927$	−154004.	−	266743.i	−0.179214	−	0.310408i
$928$	814068.	−	470003.i	0.945290	−	0.545763i
$929$	783644.	+	452437.i	0.908003	+	0.524236i	0.879788	−	0.475366i	$-0.157684\pi$
$929$	783644.	+	452437.i	0.908003	+	0.524236i	0.0282149	+	0.999602i	$0.491018\pi$
$930$	193193.	+	178664.i	0.223371	+	0.206571i
$931$	76798.9	+	1.13324e6i	0.0886045	+	1.30744i
$932$			509652.i			0.586735i
$933$	−78874.4	−	45538.2i	−0.0906093	−	0.0523133i
$934$	−307595.	+	177590.i	−0.352603	+	0.203575i
$935$	102562.	−	452803.i	0.117317	−	0.517948i
$936$	−933088.	−	538719.i	−1.06505	−	0.614908i
$937$	−196278.			−0.223559			−0.111780	−	0.993733i	$-0.535655\pi$
$937$	−196278.			−0.223559			−0.111780	+	0.993733i	$0.535655\pi$
$938$	1.20253e6	+	641051.i	1.36675	+	0.728596i
$939$	−144824.			−0.164251
$940$	−1.26133e6	+	391356.i	−1.42749	+	0.442911i
$941$	842347.	−	486329.i	0.951288	−	0.549226i	0.0578069	−	0.998328i	$-0.481589\pi$
$941$	842347.	−	486329.i	0.951288	−	0.549226i	0.893481	+	0.449102i	$0.148256\pi$
$942$	−383430.	+	221374.i	−0.432100	+	0.249473i
$943$	−282766.	+	489765.i	−0.317983	+	0.550762i
$944$			2.74849e6i			3.08425i
$945$	271606.	+	51929.1i	0.304142	+	0.0581496i
$946$	−552136.			−0.616970
$947$	1.08729e6	+	627745.i	1.21239	+	0.699976i	0.963280	−	0.268498i	$-0.0865273\pi$
$947$	1.08729e6	+	627745.i	1.21239	+	0.699976i	0.249114	+	0.968474i	$0.419861\pi$
$948$	−326887.	−	566184.i	−0.363731	−	0.630001i
$949$	285945.	+	495271.i	0.317505	+	0.549934i
$950$	−2.03730e6	−	972820.i	−2.25739	−	1.07792i
$951$		−	206673.i		−	0.228519i
$952$	2.33596e6	−	79062.4i	2.57745	−	0.0872360i
$953$		−	1.28332e6i		−	1.41302i	−0.707703	−	0.706510i	$-0.750268\pi$
$953$		−	1.28332e6i		−	1.41302i	0.707703	−	0.706510i	$-0.249732\pi$
$954$	368952.	−	639044.i	0.405390	−	0.702157i
$955$	−95639.1	+	422241.i	−0.104865	+	0.462970i
$956$	−1.23752e6	−	2.14344e6i	−1.35405	−	2.34529i
$957$	15577.5	−	26981.0i	0.0170088	−	0.0294601i
$958$	2.19575e6			2.39250
$959$	−185714.	+	6285.65i	−0.201933	+	0.00683460i
$960$	−303136.	−	280337.i	−0.328923	−	0.304185i
$961$	15623.9	−	27061.3i	0.0169177	−	0.0293023i
$962$	128937.	+	223326.i	0.139325	+	0.241318i
$963$	−442829.	+	255667.i	−0.477511	+	0.275691i
$964$	409407.	+	236371.i	0.440556	+	0.254355i
$965$	−310789.	+	336064.i	−0.333742	+	0.360884i
$966$	−214124.	+	133480.i	−0.229463	+	0.143042i
$967$			753710.i			0.806030i	0.915193	+	0.403015i	$0.132038\pi$
$967$			753710.i			0.806030i	−0.915193	+	0.403015i	$0.867962\pi$
$968$	−1.48307e6	−	856250.i	−1.58274	−	0.913797i
$969$	137263.	−	79248.6i	0.146186	−	0.0844003i
$970$	159356.	+	36094.8i	0.169366	+	0.0383620i
$971$	−579735.	−	334710.i	−0.614880	−	0.355001i	0.159993	−	0.987118i	$-0.448853\pi$
$971$	−579735.	−	334710.i	−0.614880	−	0.355001i	−0.774873	+	0.632117i	$0.782186\pi$
$972$	−1.13645e6			−1.20287
$973$	38705.5	−	72606.3i	0.0408834	−	0.0766917i
$974$	−619513.			−0.653030
$975$	−54021.8	−	25795.7i	−0.0568276	−	0.0271355i
$976$	3.09177e6	−	1.78503e6i	3.24569	−	1.87390i
$977$	202562.	−	116949.i	0.212211	−	0.122520i	−0.390127	−	0.920761i	$-0.627569\pi$
$977$	202562.	−	116949.i	0.212211	−	0.122520i	0.602339	+	0.798241i	$0.294236\pi$
$978$	−172816.	+	299326.i	−0.180678	+	0.312944i
$979$			891569.i			0.930228i
$980$	392218.	−	2.50883e6i	0.408391	−	2.61228i
$981$	−677598.			−0.704099
$982$	−2.54463e6	−	1.46914e6i	−2.63877	−	1.52350i
$983$	−331858.	−	574795.i	−0.343435	−	0.594848i	0.641633	−	0.767012i	$-0.278257\pi$
$983$	−331858.	−	574795.i	−0.343435	−	0.594848i	−0.985068	+	0.172164i	$0.944924\pi$
$984$	−167610.	−	290309.i	−0.173105	−	0.299826i
$985$	−88590.3	−	285525.i	−0.0913091	−	0.294288i
$986$		−	512125.i		−	0.526772i
$987$	−76173.0	−	40606.9i	−0.0781928	−	0.0416836i
$988$			1.35877e6i			1.39198i
$989$	221020.	−	382817.i	0.225964	−	0.391380i
$990$	1.15026e6	+	260539.i	1.17362	+	0.265829i
$991$	809825.	+	1.40266e6i	0.824601	+	1.42825i	0.902224	+	0.431268i	$0.141934\pi$
$991$	809825.	+	1.40266e6i	0.824601	+	1.42825i	−0.0776233	+	0.996983i	$0.524733\pi$
$992$	−1.62617e6	+	2.81661e6i	−1.65250	+	2.86222i
$993$	218072.			0.221157
$994$	−799695.	−	1.28284e6i	−0.809378	−	1.29838i
$995$	464841.	−	502644.i	0.469525	−	0.507709i
$996$	−123847.	+	214508.i	−0.124843	+	0.216235i
$997$	−195161.	−	338029.i	−0.196337	−	0.340066i	0.751001	−	0.660301i	$-0.229571\pi$
$997$	−195161.	−	338029.i	−0.196337	−	0.340066i	−0.947338	+	0.320235i	$0.896238\pi$
$998$	−1.80853e6	+	1.04415e6i	−1.81578	+	1.04834i
$999$	97241.7	+	56142.5i	0.0974365	+	0.0562550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.i.a.19.1	✓	28
5.2	odd	4		175.5.i.e.26.14		28
5.3	odd	4		175.5.i.e.26.1		28
5.4	even	2	inner	35.5.i.a.19.14	yes	28
7.2	even	3		245.5.c.a.244.22		28
7.3	odd	6	inner	35.5.i.a.24.14	yes	28
7.5	odd	6		245.5.c.a.244.8		28
35.3	even	12		175.5.i.e.101.1		28
35.9	even	6		245.5.c.a.244.7		28
35.17	even	12		175.5.i.e.101.14		28
35.19	odd	6		245.5.c.a.244.21		28
35.24	odd	6	inner	35.5.i.a.24.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.i.a.19.1	✓	28	1.1	even	1	trivial
35.5.i.a.19.14	yes	28	5.4	even	2	inner
35.5.i.a.24.1	yes	28	35.24	odd	6	inner
35.5.i.a.24.14	yes	28	7.3	odd	6	inner
175.5.i.e.26.1		28	5.3	odd	4
175.5.i.e.26.14		28	5.2	odd	4
175.5.i.e.101.1		28	35.3	even	12
175.5.i.e.101.14		28	35.17	even	12
245.5.c.a.244.7		28	35.9	even	6
245.5.c.a.244.8		28	7.5	odd	6
245.5.c.a.244.21		28	35.19	odd	6
245.5.c.a.244.22		28	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.61273 - 3.81786i) q^{2} +(-0.705380 - 1.22175i) q^{3} +(21.1521 + 36.6365i) q^{4} +(-23.8771 + 7.40838i) q^{5} +10.7722i q^{6} +(43.2397 + 23.0505i) q^{7} -200.851i q^{8} +(39.5049 - 68.4245i) q^{9} +O(q^{10})\)	\(q+(-6.61273 - 3.81786i) q^{2} +(-0.705380 - 1.22175i) q^{3} +(21.1521 + 36.6365i) q^{4} +(-23.8771 + 7.40838i) q^{5} +10.7722i q^{6} +(43.2397 + 23.0505i) q^{7} -200.851i q^{8} +(39.5049 - 68.4245i) q^{9} +(186.177 + 42.1698i) q^{10} +(39.0986 + 67.7207i) q^{11} +(29.8405 - 51.6853i) q^{12} +67.8948 q^{13} +(-197.929 - 317.510i) q^{14} +(25.8937 + 23.9462i) q^{15} +(-428.388 + 741.990i) q^{16} +(118.744 + 205.671i) q^{17} +(-522.470 + 301.648i) q^{18} +(409.691 + 236.535i) q^{19} +(-776.468 - 718.070i) q^{20} +(-2.33833 - 69.0877i) q^{21} -597.091i q^{22} +(413.986 + 239.015i) q^{23} +(-245.391 + 141.677i) q^{24} +(515.232 - 353.781i) q^{25} +(-448.970 - 259.213i) q^{26} -225.735 q^{27} +(70.1190 + 2071.72i) q^{28} +282.412 q^{29} +(-79.8044 - 257.208i) q^{30} +(-846.213 + 488.561i) q^{31} +(2882.55 - 1664.24i) q^{32} +(55.1587 - 95.5377i) q^{33} -1813.40i q^{34} +(-1203.21 - 230.044i) q^{35} +3342.44 q^{36} +(-430.777 - 248.709i) q^{37} +(-1806.11 - 3128.28i) q^{38} +(-47.8917 - 82.9508i) q^{39} +(1487.98 + 4795.75i) q^{40} +1183.05i q^{41} +(-248.304 + 465.786i) q^{42} -924.710i q^{43} +(-1654.03 + 2864.87i) q^{44} +(-436.347 + 1926.44i) q^{45} +(-1825.05 - 3161.08i) q^{46} +(624.360 - 1081.42i) q^{47} +1208.71 q^{48} +(1338.34 + 1993.40i) q^{49} +(-4757.77 + 372.377i) q^{50} +(167.520 - 290.153i) q^{51} +(1436.12 + 2487.43i) q^{52} +(-1059.25 + 611.561i) q^{53} +(1492.73 + 861.826i) q^{54} +(-1435.26 - 1327.32i) q^{55} +(4629.73 - 8684.75i) q^{56} -667.389i q^{57} +(-1867.52 - 1078.21i) q^{58} +(2778.16 - 1603.97i) q^{59} +(-329.601 + 1455.17i) q^{60} +(-3608.60 - 2083.43i) q^{61} +7461.03 q^{62} +(3285.40 - 2048.04i) q^{63} -11706.9 q^{64} +(-1621.13 + 502.991i) q^{65} +(-729.499 + 421.176i) q^{66} +(-3154.22 + 1821.09i) q^{67} +(-5023.38 + 8700.75i) q^{68} -674.386i q^{69} +(7078.20 + 6114.89i) q^{70} +4040.32 q^{71} +(-13743.1 - 7934.61i) q^{72} +(4211.59 + 7294.68i) q^{73} +(1899.07 + 3289.29i) q^{74} +(-795.668 - 379.936i) q^{75} +20012.8i q^{76} +(129.611 + 3829.47i) q^{77} +731.375i q^{78} +(5477.23 - 9486.83i) q^{79} +(4731.72 - 20890.2i) q^{80} +(-3040.67 - 5266.59i) q^{81} +(4516.70 - 7823.16i) q^{82} -4150.28 q^{83} +(2481.67 - 1547.02i) q^{84} +(-4358.96 - 4031.13i) q^{85} +(-3530.41 + 6114.85i) q^{86} +(-199.208 - 345.039i) q^{87} +(13601.8 - 7853.00i) q^{88} +(9874.04 + 5700.78i) q^{89} +(10240.3 - 11073.1i) q^{90} +(2935.75 + 1565.01i) q^{91} +20222.7i q^{92} +(1193.80 + 689.243i) q^{93} +(-8257.44 + 4767.44i) q^{94} +(-11534.6 - 2612.62i) q^{95} +(-4066.59 - 2347.85i) q^{96} +855.940 q^{97} +(-1239.59 - 18291.4i) q^{98} +6178.34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) \) 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9	\( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) \) 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * q^99

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