LMFDB - Embedded newform 35.5.c.e.34.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(34,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("35.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.c (of order $2$, degree $1$, 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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 110x^{6} + 7113x^{4} + 190880x^{2} + 4177936 $ x^8 + 110x^6 + 7113x^4 + 190880*x^2 + 4177936
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.6
Root			$3.16228 + 4.78865i$ of defining polynomial
Character	$\chi$	$=$	35.34
Dual form			35.5.c.e.34.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.78865i q^{2} +9.48683 q^{3} -6.93120 q^{4} +(23.8259 + 7.57153i) q^{5} +45.4292i q^{6} +(-9.59562 - 48.0513i) q^{7} +43.4273i q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.78865i q^{2} +9.48683 q^{3} -6.93120 q^{4} +(23.8259 + 7.57153i) q^{5} +45.4292i q^{6} +(-9.59562 - 48.0513i) q^{7} +43.4273i q^{8} +9.00000 q^{9} +(-36.2574 + 114.094i) q^{10} -134.413 q^{11} -65.7551 q^{12} -54.4114 q^{13} +(230.101 - 45.9501i) q^{14} +(226.032 + 71.8298i) q^{15} -318.858 q^{16} +411.531 q^{17} +43.0979i q^{18} -561.335i q^{19} +(-165.142 - 52.4797i) q^{20} +(-91.0320 - 455.854i) q^{21} -643.656i q^{22} -30.3793i q^{23} +411.988i q^{24} +(510.344 + 360.796i) q^{25} -260.557i q^{26} -683.052 q^{27} +(66.5091 + 333.053i) q^{28} -66.2752 q^{29} +(-343.968 + 1082.39i) q^{30} +912.751i q^{31} -832.061i q^{32} -1275.15 q^{33} +1970.68i q^{34} +(135.197 - 1217.52i) q^{35} -62.3808 q^{36} -1602.70i q^{37} +2688.04 q^{38} -516.192 q^{39} +(-328.811 + 1034.69i) q^{40} -241.247i q^{41} +(2182.93 - 435.921i) q^{42} +2134.40i q^{43} +931.642 q^{44} +(214.433 + 68.1437i) q^{45} +145.476 q^{46} +517.961 q^{47} -3024.95 q^{48} +(-2216.85 + 922.163i) q^{49} +(-1727.73 + 2443.86i) q^{50} +3904.13 q^{51} +377.136 q^{52} +145.636i q^{53} -3270.90i q^{54} +(-3202.50 - 1017.71i) q^{55} +(2086.74 - 416.712i) q^{56} -5325.29i q^{57} -317.369i q^{58} -4874.46i q^{59} +(-1566.67 - 497.867i) q^{60} +4940.25i q^{61} -4370.85 q^{62} +(-86.3606 - 432.461i) q^{63} -1117.27 q^{64} +(-1296.40 - 411.978i) q^{65} -6106.26i q^{66} +3909.19i q^{67} -2852.40 q^{68} -288.203i q^{69} +(5830.26 + 647.414i) q^{70} +428.660 q^{71} +390.846i q^{72} +8360.13 q^{73} +7674.80 q^{74} +(4841.55 + 3422.81i) q^{75} +3890.72i q^{76} +(1289.77 + 6458.71i) q^{77} -2471.87i q^{78} -4050.04 q^{79} +(-7597.06 - 2414.24i) q^{80} -7209.00 q^{81} +1155.25 q^{82} -630.599 q^{83} +(630.961 + 3159.62i) q^{84} +(9805.09 + 3115.92i) q^{85} -10220.9 q^{86} -628.742 q^{87} -5837.19i q^{88} +13024.0i q^{89} +(-326.317 + 1026.84i) q^{90} +(522.111 + 2614.54i) q^{91} +210.565i q^{92} +8659.11i q^{93} +2480.33i q^{94} +(4250.16 - 13374.3i) q^{95} -7893.63i q^{96} +61.6477 q^{97} +(-4415.92 - 10615.7i) q^{98} -1209.72 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 172 q^{4} + 72 q^{9}+O(q^{10}) $ 8 * q - 172 * q^4 + 72 * q^9	$ 8 q - 172 q^{4} + 72 q^{9} - 376 q^{11} - 24 q^{14} + 60 q^{15} + 596 q^{16} + 1020 q^{21} + 3500 q^{25} - 64 q^{29} - 4500 q^{30} - 4160 q^{35} - 1548 q^{36} + 6360 q^{39} - 2104 q^{44} - 28440 q^{46} - 7828 q^{49} + 7740 q^{50} + 24240 q^{51} + 27300 q^{56} + 24180 q^{60} - 5092 q^{64} - 24940 q^{65} - 10620 q^{70} - 18016 q^{71} + 39720 q^{74} - 8624 q^{79} - 57672 q^{81} - 47400 q^{84} + 19000 q^{85} + 18000 q^{86} + 34480 q^{91} + 25260 q^{95} - 3384 q^{99}+O(q^{100}) $ 8 * q - 172 * q^4 + 72 * q^9 - 376 * q^11 - 24 * q^14 + 60 * q^15 + 596 * q^16 + 1020 * q^21 + 3500 * q^25 - 64 * q^29 - 4500 * q^30 - 4160 * q^35 - 1548 * q^36 + 6360 * q^39 - 2104 * q^44 - 28440 * q^46 - 7828 * q^49 + 7740 * q^50 + 24240 * q^51 + 27300 * q^56 + 24180 * q^60 - 5092 * q^64 - 24940 * q^65 - 10620 * q^70 - 18016 * q^71 + 39720 * q^74 - 8624 * q^79 - 57672 * q^81 - 47400 * q^84 + 19000 * q^85 + 18000 * q^86 + 34480 * q^91 + 25260 * q^95 - 3384 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$22$	$31$
$\chi(n)$	$-1$	$-1$

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 $

$2$			4.78865i			1.19716i	0.801062	+	0.598582i	$0.204269\pi$
$2$			4.78865i			1.19716i	−0.801062	+	0.598582i	$0.795731\pi$
$3$	9.48683			1.05409			0.527046	−	0.849837i	$-0.323299\pi$
$3$	9.48683			1.05409			0.527046	+	0.849837i	$0.323299\pi$
$4$	−6.93120			−0.433200
$5$	23.8259	+	7.57153i	0.953035	+	0.302861i
$5$	23.8259	+	7.57153i	0.953035	+	0.302861i
$6$			45.4292i			1.26192i
$7$	−9.59562	−	48.0513i	−0.195829	−	0.980638i
$7$	−9.59562	−	48.0513i	−0.195829	−	0.980638i
$8$			43.4273i			0.678552i
$9$	9.00000			0.111111
$10$	−36.2574	+	114.094i	−0.362574	+	1.14094i
$11$	−134.413			−1.11085			−0.555425	−	0.831567i	$-0.687444\pi$
$11$	−134.413			−1.11085			−0.555425	+	0.831567i	$0.687444\pi$
$12$	−65.7551			−0.456633
$13$	−54.4114			−0.321961			−0.160981	−	0.986958i	$-0.551466\pi$
$13$	−54.4114			−0.321961			−0.160981	+	0.986958i	$0.551466\pi$
$14$	230.101	−	45.9501i	1.17398	−	0.234439i
$15$	226.032	+	71.8298i	1.00459	+	0.319244i
$16$	−318.858			−1.24554
$17$	411.531			1.42398			0.711992	−	0.702188i	$-0.247793\pi$
$17$	411.531			1.42398			0.711992	+	0.702188i	$0.247793\pi$
$18$			43.0979i			0.133018i
$19$		−	561.335i		−	1.55494i	−0.628918	−	0.777472i	$-0.716502\pi$
$19$		−	561.335i		−	1.55494i	0.628918	−	0.777472i	$-0.283498\pi$
$20$	−165.142	−	52.4797i	−0.412855	−	0.131199i
$21$	−91.0320	−	455.854i	−0.206422	−	1.03368i
$22$		−	643.656i		−	1.32987i
$23$		−	30.3793i		−	0.0574277i	−0.999588	−	0.0287139i	$-0.990859\pi$
$23$		−	30.3793i		−	0.0574277i	0.999588	−	0.0287139i	$-0.00914116\pi$
$24$			411.988i			0.715257i
$25$	510.344	+	360.796i	0.816550	+	0.577274i
$26$		−	260.557i		−	0.385440i
$27$	−683.052			−0.936971
$28$	66.5091	+	333.053i	0.0848331	+	0.424812i
$29$	−66.2752			−0.0788052			−0.0394026	−	0.999223i	$-0.512545\pi$
$29$	−66.2752			−0.0788052			−0.0394026	+	0.999223i	$0.512545\pi$
$30$	−343.968	+	1082.39i	−0.382187	+	1.20265i
$31$			912.751i			0.949792i	0.880042	+	0.474896i	$0.157514\pi$
$31$			912.751i			0.949792i	−0.880042	+	0.474896i	$0.842486\pi$
$32$		−	832.061i		−	0.812560i
$33$	−1275.15			−1.17094
$34$			1970.68i			1.70474i
$35$	135.197	−	1217.52i	0.110365	−	0.993891i
$36$	−62.3808			−0.0481333
$37$		−	1602.70i		−	1.17071i	−0.810776	−	0.585356i	$-0.800955\pi$
$37$		−	1602.70i		−	1.17071i	0.810776	−	0.585356i	$-0.199045\pi$
$38$	2688.04			1.86152
$39$	−516.192			−0.339377
$40$	−328.811	+	1034.69i	−0.205507	+	0.646684i
$41$		−	241.247i		−	0.143514i	−0.997422	−	0.0717570i	$-0.977139\pi$
$41$		−	241.247i		−	0.143514i	0.997422	−	0.0717570i	$-0.0228606\pi$
$42$	2182.93	−	435.921i	1.23749	−	0.247121i
$43$			2134.40i			1.15435i	0.816619	+	0.577176i	$0.195846\pi$
$43$			2134.40i			1.15435i	−0.816619	+	0.577176i	$0.804154\pi$
$44$	931.642			0.481220
$45$	214.433	+	68.1437i	0.105893	+	0.0336512i
$46$	145.476			0.0687504
$47$	517.961			0.234478			0.117239	−	0.993104i	$-0.462596\pi$
$47$	517.961			0.234478			0.117239	+	0.993104i	$0.462596\pi$
$48$	−3024.95			−1.31291
$49$	−2216.85	+	922.163i	−0.923302	+	0.384075i
$50$	−1727.73	+	2443.86i	−0.691091	+	0.977544i
$51$	3904.13			1.50101
$52$	377.136			0.139474
$53$			145.636i			0.0518464i	0.999664	+	0.0259232i	$0.00825253\pi$
$53$			145.636i			0.0518464i	−0.999664	+	0.0259232i	$0.991747\pi$
$54$		−	3270.90i		−	1.12171i
$55$	−3202.50	−	1017.71i	−1.05868	−	0.336433i
$56$	2086.74	−	416.712i	0.665414	−	0.132880i
$57$		−	5325.29i		−	1.63905i
$58$		−	317.369i		−	0.0943427i
$59$		−	4874.46i		−	1.40031i	−0.713993	−	0.700153i	$-0.753115\pi$
$59$		−	4874.46i		−	1.40031i	0.713993	−	0.700153i	$-0.246885\pi$
$60$	−1566.67	−	497.867i	−0.435187	−	0.138296i
$61$			4940.25i			1.32767i	0.747881	+	0.663833i	$0.231071\pi$
$61$			4940.25i			1.32767i	−0.747881	+	0.663833i	$0.768929\pi$
$62$	−4370.85			−1.13706
$63$	−86.3606	−	432.461i	−0.0217588	−	0.108960i
$64$	−1117.27			−0.272771
$65$	−1296.40	−	411.978i	−0.306840	−	0.0975095i
$66$		−	6106.26i		−	1.40180i
$67$			3909.19i			0.870837i	0.900228	+	0.435419i	$0.143400\pi$
$67$			3909.19i			0.870837i	−0.900228	+	0.435419i	$0.856600\pi$
$68$	−2852.40			−0.616869
$69$		−	288.203i		−	0.0605341i
$70$	5830.26	+	647.414i	1.18985	+	0.132125i
$71$	428.660			0.0850346			0.0425173	−	0.999096i	$-0.486462\pi$
$71$	428.660			0.0850346			0.0425173	+	0.999096i	$0.486462\pi$
$72$			390.846i			0.0753947i
$73$	8360.13			1.56880			0.784400	−	0.620256i	$-0.212971\pi$
$73$	8360.13			1.56880			0.784400	+	0.620256i	$0.212971\pi$
$74$	7674.80			1.40153
$75$	4841.55	+	3422.81i	0.860720	+	0.608500i
$76$			3890.72i			0.673601i
$77$	1289.77	+	6458.71i	0.217537	+	1.08934i
$78$		−	2471.87i		−	0.406290i
$79$	−4050.04			−0.648940			−0.324470	−	0.945896i	$-0.605186\pi$
$79$	−4050.04			−0.648940			−0.324470	+	0.945896i	$0.605186\pi$
$80$	−7597.06	−	2414.24i	−1.18704	−	0.377225i
$81$	−7209.00			−1.09877
$82$	1155.25			0.171810
$83$	−630.599			−0.0915370			−0.0457685	−	0.998952i	$-0.514574\pi$
$83$	−630.599			−0.0915370			−0.0457685	+	0.998952i	$0.514574\pi$
$84$	630.961	+	3159.62i	0.0894219	+	0.447791i
$85$	9805.09	+	3115.92i	1.35711	+	0.431269i
$86$	−10220.9			−1.38195
$87$	−628.742			−0.0830680
$88$		−	5837.19i		−	0.753770i
$89$			13024.0i			1.64424i	0.569317	+	0.822118i	$0.307208\pi$
$89$			13024.0i			1.64424i	−0.569317	+	0.822118i	$0.692792\pi$
$90$	−326.317	+	1026.84i	−0.0402860	+	0.126771i
$91$	522.111	+	2614.54i	0.0630493	+	0.315727i
$92$			210.565i			0.0248777i
$93$			8659.11i			1.00117i
$94$			2480.33i			0.280708i
$95$	4250.16	−	13374.3i	0.470932	−	1.48192i
$96$		−	7893.63i		−	0.856513i
$97$	61.6477			0.00655199			0.00327600	−	0.999995i	$-0.498957\pi$
$97$	61.6477			0.00655199			0.00327600	+	0.999995i	$0.498957\pi$
$98$	−4415.92	−	10615.7i	−0.459800	−	1.10534i
$99$	−1209.72			−0.123428
$100$	−3537.30	−	2500.75i	−0.353730	−	0.250075i
$101$			4375.30i			0.428909i	0.976734	+	0.214454i	$0.0687974\pi$
$101$			4375.30i			0.428909i	−0.976734	+	0.214454i	$0.931203\pi$
$102$			18695.5i			1.79695i
$103$	−10327.6			−0.973478			−0.486739	−	0.873547i	$-0.661814\pi$
$103$	−10327.6			−0.973478			−0.486739	+	0.873547i	$0.661814\pi$
$104$		−	2362.94i		−	0.218467i
$105$	1282.60	−	11550.4i	0.116335	−	1.04765i
$106$	−697.402			−0.0620686
$107$			772.444i			0.0674683i	0.999431	+	0.0337341i	$0.0107399\pi$
$107$			772.444i			0.0674683i	−0.999431	+	0.0337341i	$0.989260\pi$
$108$	4734.37			0.405896
$109$	−10145.5			−0.853926			−0.426963	−	0.904269i	$-0.640417\pi$
$109$	−10145.5			−0.853926			−0.426963	+	0.904269i	$0.640417\pi$
$110$	4873.46	−	15335.7i	0.402765	−	1.26741i
$111$		−	15204.6i		−	1.23404i
$112$	3059.64	+	15321.5i	0.243912	+	1.22142i
$113$			7157.54i			0.560541i	0.959921	+	0.280270i	$0.0904241\pi$
$113$			7157.54i			0.560541i	−0.959921	+	0.280270i	$0.909576\pi$
$114$	25501.0			1.96222
$115$	230.017	−	723.812i	0.0173926	−	0.0547306i
$116$	459.367			0.0341384
$117$	−489.703			−0.0357735
$118$	23342.1			1.67639
$119$	−3948.90	−	19774.6i	−0.278857	−	1.39641i
$120$	−3119.38	+	9815.97i	−0.216623	+	0.681665i
$121$	3425.80			0.233987
$122$	−23657.1			−1.58943
$123$		−	2288.67i		−	0.151277i
$124$		−	6326.45i		−	0.411450i
$125$	9427.61	+	12460.4i	0.603367	+	0.797464i
$126$	2070.91	−	413.551i	0.130443	−	0.0260488i
$127$		−	27311.1i		−	1.69329i	−0.532158	−	0.846645i	$-0.678619\pi$
$127$		−	27311.1i		−	1.69329i	0.532158	−	0.846645i	$-0.321381\pi$
$128$		−	18663.2i		−	1.13911i
$129$			20248.7i			1.21679i
$130$	1972.82	−	6208.01i	0.116735	−	0.367338i
$131$		−	8633.14i		−	0.503067i	−0.967849	−	0.251534i	$-0.919065\pi$
$131$		−	8633.14i		−	0.503067i	0.967849	−	0.251534i	$-0.0809349\pi$
$132$	8838.33			0.507250
$133$	−26972.8	+	5386.35i	−1.52484	+	0.304503i
$134$	−18719.7			−1.04253
$135$	−16274.3	−	5171.75i	−0.892966	−	0.283772i
$136$			17871.7i			0.966247i
$137$			21972.9i			1.17070i	0.810780	+	0.585350i	$0.199043\pi$
$137$			21972.9i			1.17070i	−0.810780	+	0.585350i	$0.800957\pi$
$138$	1380.10			0.0724693
$139$		−	20725.5i		−	1.07269i	−0.843998	−	0.536346i	$-0.819804\pi$
$139$		−	20725.5i		−	1.07269i	0.843998	−	0.536346i	$-0.180196\pi$
$140$	−937.080	+	8438.85i	−0.0478102	+	0.430553i
$141$	4913.81			0.247161
$142$			2052.70i			0.101800i
$143$	7313.59			0.357650
$144$	−2869.72			−0.138393
$145$	−1579.06	−	501.804i	−0.0751041	−	0.0238670i
$146$			40033.8i			1.87811i
$147$	−21030.9	+	8748.41i	−0.973246	+	0.404850i
$148$			11108.7i			0.507152i
$149$	25356.3			1.14213			0.571063	−	0.820906i	$-0.306531\pi$
$149$	25356.3			1.14213			0.571063	+	0.820906i	$0.306531\pi$
$150$	−16390.7	+	23184.5i	−0.728474	+	1.03042i
$151$	33662.7			1.47637			0.738186	−	0.674598i	$-0.235683\pi$
$151$	33662.7			1.47637			0.738186	+	0.674598i	$0.235683\pi$
$152$	24377.3			1.05511
$153$	3703.78			0.158220
$154$	−30928.5	+	6176.28i	−1.30412	+	0.260427i
$155$	−6910.91	+	21747.1i	−0.287655	+	0.905185i
$156$	3577.83			0.147018
$157$	14735.6			0.597819			0.298910	−	0.954281i	$-0.403377\pi$
$157$	14735.6			0.597819			0.298910	+	0.954281i	$0.403377\pi$
$158$		−	19394.2i		−	0.776887i
$159$			1381.63i			0.0546509i
$160$	6299.97	−	19824.6i	0.246093	−	0.774398i
$161$	−1459.76	+	291.508i	−0.0563158	+	0.0112460i
$162$		−	34521.4i		−	1.31540i
$163$			20294.3i			0.763835i	0.924196	+	0.381918i	$0.124736\pi$
$163$			20294.3i			0.763835i	−0.924196	+	0.381918i	$0.875264\pi$
$164$			1672.13i			0.0621702i
$165$	−30381.6	−	9654.84i	−1.11594	−	0.354632i
$166$		−	3019.72i		−	0.109585i
$167$	43049.6			1.54361			0.771803	−	0.635862i	$-0.219355\pi$
$167$	43049.6			1.54361			0.771803	+	0.635862i	$0.219355\pi$
$168$	19796.5	−	3953.28i	0.701408	−	0.140068i
$169$	−25600.4			−0.896341
$170$	−14921.1	+	46953.2i	−0.516300	+	1.62468i
$171$		−	5052.01i		−	0.172772i
$172$		−	14793.9i		−	0.500066i
$173$	22174.3			0.740898			0.370449	−	0.928853i	$-0.379204\pi$
$173$	22174.3			0.740898			0.370449	+	0.928853i	$0.379204\pi$
$174$		−	3010.83i		−	0.0994460i
$175$	12439.7	−	27984.7i	0.406193	−	0.913787i
$176$	42858.6			1.38361
$177$		−	46243.2i		−	1.47605i
$178$	−62367.4			−1.96842
$179$	45793.4			1.42921			0.714606	−	0.699528i	$-0.246606\pi$
$179$	45793.4			1.42921			0.714606	+	0.699528i	$0.246606\pi$
$180$	−1486.28	−	472.318i	−0.0458727	−	0.0145777i
$181$		−	52068.4i		−	1.58934i	−0.607041	−	0.794670i	$-0.707644\pi$
$181$		−	52068.4i		−	1.58934i	0.607041	−	0.794670i	$-0.292356\pi$
$182$	−12520.1	+	2500.21i	−0.377977	+	0.0754803i
$183$			46867.3i			1.39948i
$184$	1319.29			0.0389677
$185$	12134.9	−	38185.8i	0.354563	−	1.11573i
$186$	−41465.5			−1.19856
$187$	−55315.1			−1.58183
$188$	−3590.09			−0.101576
$189$	6554.31	+	32821.5i	0.183486	+	0.918830i
$190$	64044.8	+	20352.5i	1.77409	+	0.563782i
$191$	−64608.3			−1.77101			−0.885506	−	0.464629i	$-0.846188\pi$
$191$	−64608.3			−1.77101			−0.885506	+	0.464629i	$0.846188\pi$
$192$	−10599.4			−0.287526
$193$			15621.6i			0.419383i	0.977768	+	0.209691i	$0.0672459\pi$
$193$			15621.6i			0.419383i	−0.977768	+	0.209691i	$0.932754\pi$
$194$			295.209i			0.00784381i
$195$	−12298.7	−	3908.36i	−0.323438	−	0.102784i
$196$	15365.4	−	6391.70i	0.399974	−	0.166381i
$197$		−	50010.7i		−	1.28864i	−0.764757	−	0.644318i	$-0.777141\pi$
$197$		−	50010.7i		−	1.28864i	0.764757	−	0.644318i	$-0.222859\pi$
$198$		−	5792.91i		−	0.147763i
$199$		−	47729.6i		−	1.20526i	−0.798019	−	0.602632i	$-0.794119\pi$
$199$		−	47729.6i		−	1.20526i	0.798019	−	0.602632i	$-0.205881\pi$
$200$	−15668.4	+	22162.9i	−0.391711	+	0.554072i
$201$			37085.8i			0.917943i
$202$	−20951.8			−0.513474
$203$	635.952	+	3184.61i	0.0154323	+	0.0772794i
$204$	−27060.3			−0.650238
$205$	1826.61	−	5747.92i	0.0434648	−	0.136774i
$206$		−	49455.4i		−	1.16541i
$207$		−	273.413i		−	0.00638086i
$208$	17349.5			0.401015
$209$			75450.6i			1.72731i
$210$	55310.7	+	6141.90i	1.25421	+	0.139272i
$211$	−34019.8			−0.764129			−0.382064	−	0.924136i	$-0.624787\pi$
$211$	−34019.8			−0.764129			−0.382064	+	0.924136i	$0.624787\pi$
$212$		−	1009.43i		−	0.0224598i
$213$	4066.62			0.0896344
$214$	−3698.97			−0.0807706
$215$	−16160.7	+	50853.9i	−0.349609	+	1.10014i
$216$		−	29663.1i		−	0.635784i
$217$	43858.8	−	8758.41i	0.931403	−	0.185997i
$218$		−	48583.2i		−	1.02229i
$219$	79311.2			1.65366
$220$	22197.2	+	7053.95i	0.458619	+	0.145743i
$221$	−22392.0			−0.458467
$222$	72809.5			1.47735
$223$	−21688.7			−0.436137			−0.218068	−	0.975933i	$-0.569976\pi$
$223$	−21688.7			−0.436137			−0.218068	+	0.975933i	$0.569976\pi$
$224$	−39981.6	+	7984.14i	−0.796827	+	0.159123i
$225$	4593.10	+	3247.17i	0.0907278	+	0.0641416i
$226$	−34275.0			−0.671059
$227$	39551.8			0.767563			0.383782	−	0.923424i	$-0.374622\pi$
$227$	39551.8			0.767563			0.383782	+	0.923424i	$0.374622\pi$
$228$			36910.6i			0.710038i
$229$		−	24575.0i		−	0.468622i	−0.972162	−	0.234311i	$-0.924717\pi$
$229$		−	24575.0i		−	0.468622i	0.972162	−	0.234311i	$-0.0752834\pi$
$230$	3466.09	+	1101.47i	0.0655215	+	0.0208218i
$231$	12235.9	+	61272.7i	0.229304	+	1.14827i
$232$		−	2878.16i		−	0.0534735i
$233$			24450.9i			0.450385i	0.974314	+	0.225192i	$0.0723011\pi$
$233$			24450.9i			0.450385i	−0.974314	+	0.225192i	$0.927699\pi$
$234$		−	2345.02i		−	0.0428267i
$235$	12340.9	+	3921.75i	0.223465	+	0.0710141i
$236$			33785.9i			0.606612i
$237$	−38422.0			−0.684043
$238$	94693.7	−	18909.9i	1.67173	−	0.333838i
$239$	−16698.2			−0.292330			−0.146165	−	0.989260i	$-0.546693\pi$
$239$	−16698.2			−0.292330			−0.146165	+	0.989260i	$0.546693\pi$
$240$	−72072.0	−	22903.5i	−1.25125	−	0.397630i
$241$			29546.7i			0.508715i	0.967110	+	0.254357i	$0.0818639\pi$
$241$			29546.7i			0.508715i	−0.967110	+	0.254357i	$0.918136\pi$
$242$			16405.0i			0.280121i
$243$	−13063.4			−0.221229
$244$		−	34241.8i		−	0.575145i
$245$	−59800.5	+	5186.42i	−0.996260	+	0.0864043i
$246$	10959.6			0.181103
$247$			30543.0i			0.500632i
$248$	−39638.3			−0.644484
$249$	−5982.38			−0.0964885
$250$	−59668.4	+	45145.6i	−0.954694	+	0.722329i
$251$			77102.9i			1.22384i	0.790921	+	0.611918i	$0.209602\pi$
$251$			77102.9i			1.22384i	−0.790921	+	0.611918i	$0.790398\pi$
$252$	598.582	+	2997.48i	0.00942590	+	0.0472014i
$253$			4083.36i			0.0637936i
$254$	130783.			2.02714
$255$	93019.2	+	29560.2i	1.43052	+	0.454598i
$256$	71495.3			1.09093
$257$	−71422.5			−1.08136			−0.540678	−	0.841230i	$-0.681832\pi$
$257$	−71422.5			−1.08136			−0.540678	+	0.841230i	$0.681832\pi$
$258$	−96963.9			−1.45670
$259$	−77012.0	+	15378.9i	−1.14804	+	0.229259i
$260$	8985.60	+	2855.50i	0.132923	+	0.0422411i
$261$	−596.477			−0.00875614
$262$	41341.1			0.602254
$263$		−	103341.i		−	1.49404i	−0.664804	−	0.747018i	$-0.731485\pi$
$263$		−	103341.i		−	1.49404i	0.664804	−	0.747018i	$-0.268515\pi$
$264$		−	55376.5i		−	0.794543i
$265$	−1102.69	+	3469.91i	−0.0157022	+	0.0494114i
$266$	−25793.4	−	129164.i	−0.364540	−	1.82548i
$267$			123556.i			1.73318i
$268$		−	27095.4i		−	0.377247i
$269$		−	54702.4i		−	0.755965i	−0.925813	−	0.377983i	$-0.876618\pi$
$269$		−	54702.4i		−	0.755965i	0.925813	−	0.377983i	$-0.123382\pi$
$270$	24765.7	−	77932.0i	0.339721	−	1.06903i
$271$		−	64266.5i		−	0.875077i	−0.899200	−	0.437539i	$-0.855850\pi$
$271$		−	64266.5i		−	0.875077i	0.899200	−	0.437539i	$-0.144150\pi$
$272$	−131220.			−1.77363
$273$	4953.18	+	24803.7i	0.0664598	+	0.332806i
$274$	−105221.			−1.40152
$275$	−68596.8	−	48495.6i	−0.907065	−	0.641265i
$276$			1997.59i			0.0262234i
$277$		−	35442.4i		−	0.461916i	−0.972964	−	0.230958i	$-0.925814\pi$
$277$		−	35442.4i		−	0.461916i	0.972964	−	0.230958i	$-0.0741861\pi$
$278$	99247.1			1.28419
$279$			8214.75i			0.105532i
$280$	52873.5	+	5871.27i	0.674407	+	0.0748886i
$281$	71637.4			0.907250			0.453625	−	0.891193i	$-0.350130\pi$
$281$	71637.4			0.907250			0.453625	+	0.891193i	$0.350130\pi$
$282$			23530.5i			0.295892i
$283$	40369.4			0.504056			0.252028	−	0.967720i	$-0.418902\pi$
$283$	40369.4			0.504056			0.252028	+	0.967720i	$0.418902\pi$
$284$	−2971.12			−0.0368370
$285$	40320.6	−	126880.i	0.496406	−	1.56208i
$286$			35022.3i			0.428166i
$287$	−11592.2	+	2314.91i	−0.140735	+	0.0281042i
$288$		−	7488.55i		−	0.0902844i
$289$	85837.0			1.02773
$290$	2402.97	−	7561.59i	0.0285727	−	0.0899119i
$291$	584.841			0.00690641
$292$	−57945.7			−0.679604
$293$	−11461.9			−0.133512			−0.0667560	−	0.997769i	$-0.521265\pi$
$293$	−11461.9			−0.133512			−0.0667560	+	0.997769i	$0.521265\pi$
$294$	−41893.1	−	100710.i	−0.484672	−	1.16513i
$295$	36907.1	−	116138.i	0.424098	−	1.33454i
$296$	69601.2			0.794389
$297$	91810.9			1.04083
$298$			121423.i			1.36731i
$299$			1652.98i			0.0184895i
$300$	−33557.7	−	23724.2i	−0.372864	−	0.263602i
$301$	102561.	−	20480.9i	1.13200	−	0.226056i
$302$			161199.i			1.76746i
$303$			41507.7i			0.452110i
$304$			178986.i			1.93674i
$305$	−37405.2	+	117706.i	−0.402098	+	1.26531i
$306$			17736.1i			0.189416i
$307$	111649.			1.18462			0.592309	−	0.805711i	$-0.298216\pi$
$307$	111649.			1.18462			0.592309	+	0.805711i	$0.298216\pi$
$308$	−8939.68	−	44766.6i	−0.0942368	−	0.471903i
$309$	−97976.5			−1.02614
$310$	−104139.	−	33094.0i	−1.08365	−	0.344370i
$311$			26778.1i			0.276859i	0.990372	+	0.138429i	$0.0442054\pi$
$311$			26778.1i			0.276859i	−0.990372	+	0.138429i	$0.955795\pi$
$312$		−	22416.9i		−	0.230285i
$313$	−87491.2			−0.893050			−0.446525	−	0.894771i	$-0.647339\pi$
$313$	−87491.2			−0.893050			−0.446525	+	0.894771i	$0.647339\pi$
$314$			70563.9i			0.715687i
$315$	1216.78	−	10957.6i	0.0122628	−	0.110432i
$316$	28071.6			0.281121
$317$			46524.6i			0.462982i	0.972837	+	0.231491i	$0.0743603\pi$
$317$			46524.6i			0.462982i	−0.972837	+	0.231491i	$0.925640\pi$
$318$	−6616.14			−0.0654260
$319$	8908.24			0.0875408
$320$	−26619.9	−	8459.44i	−0.259960	−	0.0826117i
$321$			7328.05i			0.0711178i
$322$	−1395.93	−	6990.30i	−0.0134633	−	0.0674192i
$323$		−	231007.i		−	2.21421i
$324$	49967.0			0.475985
$325$	−27768.6	−	19631.4i	−0.262898	−	0.185860i
$326$	−97182.5			−0.914435
$327$	−96248.6			−0.900117
$328$	10476.7			0.0973817
$329$	−4970.15	−	24888.7i	−0.0459175	−	0.229938i
$330$	46233.7	−	145487.i	0.424552	−	1.33597i
$331$	−53803.7			−0.491085			−0.245542	−	0.969386i	$-0.578966\pi$
$331$	−53803.7			−0.491085			−0.245542	+	0.969386i	$0.578966\pi$
$332$	4370.80			0.0396538
$333$		−	14424.3i		−	0.130079i
$334$			206150.i			1.84795i
$335$	−29598.5	+	93139.8i	−0.263743	+	0.829938i
$336$	29026.3	+	145353.i	0.257106	+	1.28749i
$337$			90016.3i			0.792614i	0.918118	+	0.396307i	$0.129708\pi$
$337$			90016.3i			0.792614i	−0.918118	+	0.396307i	$0.870292\pi$
$338$		−	122591.i		−	1.07307i
$339$			67902.4i			0.590862i
$340$	−67961.0	−	21597.1i	−0.587898	−	0.186826i
$341$		−	122685.i		−	1.05508i
$342$	24192.3			0.206836
$343$	65583.1	+	97673.6i	0.557448	+	0.830212i
$344$	−92691.3			−0.783289
$345$	2182.14	−	6866.69i	0.0183334	−	0.0576911i
$346$			106185.i			0.886976i
$347$			52980.3i			0.440003i	0.975500	+	0.220002i	$0.0706062\pi$
$347$			52980.3i			0.440003i	−0.975500	+	0.220002i	$0.929394\pi$
$348$	4357.93			0.0359851
$349$		−	122033.i		−	1.00191i	−0.865474	−	0.500954i	$-0.832982\pi$
$349$		−	122033.i		−	1.00191i	0.865474	−	0.500954i	$-0.167018\pi$
$350$	134009.	+	59569.2i	1.09395	+	0.486279i
$351$	37165.8			0.301668
$352$			111840.i			0.902632i
$353$	26076.8			0.209269			0.104635	−	0.994511i	$-0.466633\pi$
$353$	26076.8			0.209269			0.104635	+	0.994511i	$0.466633\pi$
$354$	221443.			1.76707
$355$	10213.2	+	3245.61i	0.0810410	+	0.0257537i
$356$		−	90271.9i		−	0.712283i
$357$	−37462.5	−	187598.i	−0.293941	−	1.47195i
$358$			219288.i			1.71100i
$359$	−105933.			−0.821946			−0.410973	−	0.911647i	$-0.634811\pi$
$359$	−105933.			−0.821946			−0.410973	+	0.911647i	$0.634811\pi$
$360$	−2959.30	+	9312.25i	−0.0228341	+	0.0718538i
$361$	−184776.			−1.41785
$362$	249338.			1.90270
$363$	32500.0			0.246644
$364$	−3618.86	−	18121.9i	−0.0273130	−	0.136773i
$365$	199187.	+	63299.0i	1.49512	+	0.475128i
$366$	−224431.			−1.67541
$367$	−222111.			−1.64906			−0.824532	−	0.565815i	$-0.808562\pi$
$367$	−222111.			−1.64906			−0.824532	+	0.565815i	$0.808562\pi$
$368$			9686.66i			0.0715284i
$369$		−	2171.22i		−	0.0159460i
$370$	182859.	+	58109.9i	1.33571	+	0.424470i
$371$	6998.01	−	1397.47i	0.0508425	−	0.0101530i
$372$		−	60018.0i		−	0.433706i
$373$		−	60638.8i		−	0.435846i	−0.975966	−	0.217923i	$-0.930072\pi$
$373$		−	60638.8i		−	0.435846i	0.975966	−	0.217923i	$-0.0699281\pi$
$374$		−	264885.i		−	1.89371i
$375$	89438.2	+	118209.i	0.636005	+	0.840600i
$376$			22493.7i			0.159105i
$377$	3606.13			0.0253722
$378$	−157171.	+	31386.3i	−1.09999	+	0.219663i
$379$	187024.			1.30202			0.651011	−	0.759068i	$-0.274345\pi$
$379$	187024.			1.30202			0.651011	+	0.759068i	$0.274345\pi$
$380$	−29458.7	+	92699.8i	−0.204008	+	0.641966i
$381$		−	259096.i		−	1.78488i
$382$		−	309387.i		−	2.12019i
$383$	66090.0			0.450545			0.225272	−	0.974296i	$-0.427673\pi$
$383$	66090.0			0.450545			0.225272	+	0.974296i	$0.427673\pi$
$384$		−	177055.i		−	1.20073i
$385$	−18172.3	+	163650.i	−0.122599	+	1.10406i
$386$	−74806.4			−0.502070
$387$			19209.6i			0.128261i
$388$	−427.292			−0.00283832
$389$	−8595.63			−0.0568039			−0.0284020	−	0.999597i	$-0.509042\pi$
$389$	−8595.63			−0.0568039			−0.0284020	+	0.999597i	$0.509042\pi$
$390$	18715.8	−	58894.3i	0.123049	−	0.387208i
$391$		−	12502.0i		−	0.0817761i
$392$	−40047.1	−	96271.8i	−0.260615	−	0.626509i
$393$		−	81901.1i		−	0.530279i
$394$	239484.			1.54271
$395$	−96495.6	−	30664.9i	−0.618463	−	0.196539i
$396$	8384.78			0.0534689
$397$	250.161			0.00158723			0.000793614	−	1.00000i	$-0.499747\pi$
$397$	250.161			0.00158723			0.000793614		1.00000i	$0.499747\pi$
$398$	228561.			1.44290
$399$	−255887.	+	51099.4i	−1.60732	+	0.320974i
$400$	−162727.	−	115043.i	−1.01704	−	0.719017i
$401$	92669.2			0.576297			0.288149	−	0.957586i	$-0.406960\pi$
$401$	92669.2			0.576297			0.288149	+	0.957586i	$0.406960\pi$
$402$	−177591.			−1.09893
$403$		−	49664.1i		−	0.305796i
$404$		−	30326.1i		−	0.185803i
$405$	−171761.	−	54583.1i	−1.04716	−	0.332773i
$406$	−15250.0	+	3045.35i	−0.0925161	+	0.0184750i
$407$			215424.i			1.30049i
$408$			169546.i			1.01851i
$409$		−	20412.9i		−	0.122027i	−0.998137	−	0.0610137i	$-0.980567\pi$
$409$		−	20412.9i		−	0.122027i	0.998137	−	0.0610137i	$-0.0194333\pi$
$410$	27524.8	+	8746.99i	0.163741	+	0.0520344i
$411$			208453.i			1.23403i
$412$	71582.9			0.421711
$413$	−234224.	+	46773.5i	−1.37319	+	0.274220i
$414$	1309.28			0.00763893
$415$	−15024.6	−	4774.59i	−0.0872380	−	0.0277230i
$416$			45273.6i			0.261613i
$417$		−	196619.i		−	1.13072i
$418$	−361307.			−2.06787
$419$		−	21558.5i		−	0.122798i	−0.998113	−	0.0613988i	$-0.980444\pi$
$419$		−	21558.5i		−	0.122798i	0.998113	−	0.0613988i	$-0.0195562\pi$
$420$	−8889.92	+	80057.9i	−0.0503964	+	0.453843i
$421$	−127669.			−0.720311			−0.360156	−	0.932892i	$-0.617276\pi$
$421$	−127669.			−0.720311			−0.360156	+	0.932892i	$0.617276\pi$
$422$		−	162909.i		−	0.914787i
$423$	4661.65			0.0260531
$424$	−6324.60			−0.0351805
$425$	210023.	+	148479.i	1.16275	+	0.822029i
$426$			19473.6i			0.107307i
$427$	237385.	−	47404.7i	1.30196	−	0.259995i
$428$		−	5353.96i		−	0.0292273i
$429$	69382.8			0.376997
$430$	−243522.	−	77387.8i	−1.31705	−	0.418538i
$431$	281440.			1.51507			0.757533	−	0.652797i	$-0.226405\pi$
$431$	281440.			1.51507			0.757533	+	0.652797i	$0.226405\pi$
$432$	217796.			1.16703
$433$	135595.			0.723214			0.361607	−	0.932331i	$-0.382228\pi$
$433$	135595.			0.723214			0.361607	+	0.932331i	$0.382228\pi$
$434$	41941.0	+	210025.i	0.222669	+	1.11504i
$435$	−14980.3	−	4760.53i	−0.0791667	−	0.0251581i
$436$	70320.4			0.369921
$437$	−17052.9			−0.0892969
$438$			379794.i			1.97970i
$439$			73384.2i			0.380779i	0.981709	+	0.190390i	$0.0609751\pi$
$439$			73384.2i			0.380779i	−0.981709	+	0.190390i	$0.939025\pi$
$440$	44196.4	−	139076.i	0.228287	−	0.718369i
$441$	−19951.6	+	8299.47i	−0.102589	+	0.0426750i
$442$		−	107228.i		−	0.548860i
$443$		−	72350.0i		−	0.368664i	−0.982864	−	0.184332i	$-0.940988\pi$
$443$		−	72350.0i		−	0.368664i	0.982864	−	0.184332i	$-0.0590122\pi$
$444$			105386.i			0.534585i
$445$	−98611.5	+	310308.i	−0.497975	+	1.56701i
$446$		−	103859.i		−	0.522127i
$447$	240551.			1.20391
$448$	10720.9	+	53686.3i	0.0534165	+	0.267490i
$449$	−323719.			−1.60574			−0.802870	−	0.596154i	$-0.796695\pi$
$449$	−323719.			−1.60574			−0.802870	+	0.596154i	$0.796695\pi$
$450$	−15549.6	+	21994.7i	−0.0767879	+	0.108616i
$451$			32426.7i			0.159422i
$452$		−	49610.3i		−	0.242826i
$453$	319353.			1.55623
$454$			189400.i			0.918899i
$455$	−7356.29	+	66246.8i	−0.0355333	+	0.319994i
$456$	231263.			1.11218
$457$		−	237414.i		−	1.13678i	−0.822761	−	0.568388i	$-0.807567\pi$
$457$		−	237414.i		−	1.13678i	0.822761	−	0.568388i	$-0.192433\pi$
$458$	117681.			0.561017
$459$	−281097.			−1.33423
$460$	−1594.30	+	5016.89i	−0.00753448	+	0.0237093i
$461$			85619.6i			0.402876i	0.979501	+	0.201438i	$0.0645614\pi$
$461$			85619.6i			0.402876i	−0.979501	+	0.201438i	$0.935439\pi$
$462$	−293414.	+	58593.3i	−1.37466	+	0.274514i
$463$		−	56174.0i		−	0.262044i	−0.991379	−	0.131022i	$-0.958174\pi$
$463$		−	56174.0i		−	0.262044i	0.991379	−	0.131022i	$-0.0418258\pi$
$464$	21132.4			0.0981549
$465$	−65562.7	+	206311.i	−0.303215	+	0.954149i
$466$	−117087.			−0.539184
$467$	−117912.			−0.540658			−0.270329	−	0.962768i	$-0.587132\pi$
$467$	−117912.			−0.540658			−0.270329	+	0.962768i	$0.587132\pi$
$468$	3394.23			0.0154971
$469$	187841.	−	37511.1i	0.853976	−	0.170535i
$470$	−18779.9	+	59096.1i	−0.0850155	+	0.267524i
$471$	139795.			0.630157
$472$	211685.			0.950181
$473$		−	286891.i		−	1.28231i
$474$		−	183990.i		−	0.818911i
$475$	202528.	−	286474.i	0.897629	−	1.26969i
$476$	27370.6	+	137062.i	0.120801	+	0.604926i
$477$			1310.73i			0.00576071i
$478$		−	79961.9i		−	0.349967i
$479$			252818.i			1.10189i	0.834543	+	0.550943i	$0.185732\pi$
$479$			252818.i			1.10189i	−0.834543	+	0.550943i	$0.814268\pi$
$480$	59766.8	−	188072.i	0.259404	−	0.816287i
$481$			87205.5i			0.376924i
$482$	−141489.			−0.609015
$483$	−13848.5	+	2765.49i	−0.0593621	+	0.0118543i
$484$	−23744.9			−0.101363
$485$	1468.81	+	466.767i	0.00624428	+	0.00198434i
$486$		−	62555.9i		−	0.264848i
$487$			212078.i			0.894207i	0.894482	+	0.447103i	$0.147544\pi$
$487$			212078.i			0.894207i	−0.894482	+	0.447103i	$0.852456\pi$
$488$	−214542.			−0.900891
$489$			192529.i			0.805153i
$490$	−24836.0	−	286364.i	−0.103440	−	1.19269i
$491$	−116891.			−0.484863			−0.242432	−	0.970168i	$-0.577945\pi$
$491$	−116891.			−0.484863			−0.242432	+	0.970168i	$0.577945\pi$
$492$			15863.2i			0.0655332i
$493$	−27274.3			−0.112217
$494$	−146260.			−0.599338
$495$	−28822.5	−	9159.39i	−0.117631	−	0.0373815i
$496$		−	291038.i		−	1.18300i
$497$	−4113.25	−	20597.6i	−0.0166522	−	0.0833882i
$498$		−	28647.6i		−	0.115513i
$499$	80616.5			0.323760			0.161880	−	0.986810i	$-0.448244\pi$
$499$	80616.5			0.323760			0.161880	+	0.986810i	$0.448244\pi$
$500$	−65344.6	−	86365.3i	−0.261379	−	0.345461i
$501$	408404.			1.62710
$502$	−369219.			−1.46513
$503$	−162668.			−0.642935			−0.321467	−	0.946921i	$-0.604176\pi$
$503$	−162668.			−0.642935			−0.321467	+	0.946921i	$0.604176\pi$
$504$	18780.7	−	3750.41i	0.0739349	−	0.0147645i
$505$	−33127.7	+	104245.i	−0.129900	+	0.408765i
$506$	−19553.8			−0.0763713
$507$	−242867.			−0.944826
$508$			189298.i			0.733533i
$509$		−	305987.i		−	1.18105i	−0.807020	−	0.590524i	$-0.798921\pi$
$509$		−	305987.i		−	1.18105i	0.807020	−	0.590524i	$-0.201079\pi$
$510$	−141554.	+	445437.i	−0.544227	+	1.71256i
$511$	−80220.6	−	401715.i	−0.307216	−	1.53842i
$512$			43754.8i			0.166911i
$513$			383421.i			1.45694i
$514$		−	342017.i		−	1.29456i
$515$	−246065.	−	78195.9i	−0.927759	−	0.294829i
$516$		−	140348.i		−	0.527115i
$517$	−69620.6			−0.260469
$518$	−73644.4	−	368784.i	−0.274461	−	1.37440i
$519$	210364.			0.780975
$520$	17891.1	−	56299.2i	0.0661653	−	0.208207i
$521$			497976.i			1.83456i	0.398239	+	0.917282i	$0.369622\pi$
$521$			497976.i			1.83456i	−0.398239	+	0.917282i	$0.630378\pi$
$522$		−	2856.32i		−	0.0104825i
$523$	−242152.			−0.885288			−0.442644	−	0.896697i	$-0.645959\pi$
$523$	−242152.			−0.885288			−0.442644	+	0.896697i	$0.645959\pi$
$524$			59838.0i			0.217929i
$525$	118013.	−	265487.i	0.428165	−	0.963217i
$526$	494864.			1.78860
$527$			375625.i			1.35249i
$528$	406592.			1.45845
$529$	278918.			0.996702
$530$	−16616.2	−	5280.40i	−0.0591535	−	0.0187981i
$531$		−	43870.2i		−	0.155590i
$532$	186954.	−	37333.9i	0.660559	−	0.131911i
$533$			13126.6i			0.0462059i
$534$	−591669.			−2.07490
$535$	−5848.58	+	18404.2i	−0.0204335	+	0.0642996i
$536$	−169766.			−0.590909
$537$	434434.			1.50652
$538$	261951.			0.905014
$539$	297973.	−	123951.i	1.02565	−	0.426649i
$540$	112800.	+	35846.4i	0.386833	+	0.122930i
$541$	−400699.			−1.36907			−0.684533	−	0.728982i	$-0.739994\pi$
$541$	−400699.			−1.36907			−0.684533	+	0.728982i	$0.739994\pi$
$542$	307750.			1.04761
$543$		−	493964.i		−	1.67531i
$544$		−	342419.i		−	1.15707i
$545$	−241725.	−	76816.9i	−0.813821	−	0.258621i
$546$	−118776.	+	23719.1i	−0.398423	+	0.0795633i
$547$		−	107818.i		−	0.360344i	−0.983635	−	0.180172i	$-0.942335\pi$
$547$		−	107818.i		−	0.360344i	0.983635	−	0.180172i	$-0.0576655\pi$
$548$		−	152298.i		−	0.507147i
$549$			44462.2i			0.147518i
$550$	232229.	−	328486.i	0.767699	−	1.08590i
$551$			37202.6i			0.122538i
$552$	12515.9			0.0410756
$553$	38862.6	+	194609.i	0.127081	+	0.636375i
$554$	169721.			0.552989
$555$	115122.	−	362263.i	0.373742	−	1.17608i
$556$			143652.i			0.464690i
$557$			143511.i			0.462567i	0.972886	+	0.231284i	$0.0742926\pi$
$557$			143511.i			0.462567i	−0.972886	+	0.231284i	$0.925707\pi$
$558$	−39337.6			−0.126340
$559$		−	116136.i		−	0.371657i
$560$	−43108.7	+	388214.i	−0.137464	+	1.23793i
$561$	−524765.			−1.66740
$562$			343047.i			1.08613i
$563$	84498.7			0.266584			0.133292	−	0.991077i	$-0.457445\pi$
$563$	84498.7			0.266584			0.133292	+	0.991077i	$0.457445\pi$
$564$	−34058.6			−0.107070
$565$	−54193.5	+	170535.i	−0.169766	+	0.534215i
$566$			193315.i			0.603438i
$567$	69174.8	+	346402.i	0.215170	+	1.07749i
$568$			18615.6i			0.0577005i
$569$	−160937.			−0.497086			−0.248543	−	0.968621i	$-0.579952\pi$
$569$	−160937.			−0.497086			−0.248543	+	0.968621i	$0.579952\pi$
$570$	607583.	+	193081.i	1.87006	+	0.594279i
$571$	−188608.			−0.578479			−0.289240	−	0.957257i	$-0.593402\pi$
$571$	−188608.			−0.578479			−0.289240	+	0.957257i	$0.593402\pi$
$572$	−50692.0			−0.154934
$573$	−612928.			−1.86681
$574$	−11085.3	−	55511.1i	−0.0336453	−	0.168483i
$575$	10960.7	−	15503.9i	0.0331515	−	0.0468926i
$576$	−10055.4			−0.0303079
$577$	−105363.			−0.316474			−0.158237	−	0.987401i	$-0.550581\pi$
$577$	−105363.			−0.316474			−0.158237	+	0.987401i	$0.550581\pi$
$578$			411043.i			1.23036i
$579$			148199.i			0.442068i
$580$	10944.8	+	3478.11i	0.0325351	+	0.0103392i
$581$	6050.98	+	30301.1i	0.0179256	+	0.0897647i
$582$			2800.60i			0.00826810i
$583$		−	19575.4i		−	0.0575935i
$584$			363058.i			1.06451i
$585$	−11667.6	−	3707.80i	−0.0340934	−	0.0108344i
$586$		−	54886.9i		−	0.159836i
$587$	−544367.			−1.57985			−0.789925	−	0.613204i	$-0.789880\pi$
$587$	−544367.			−1.57985			−0.789925	+	0.613204i	$0.789880\pi$
$588$	145769.	−	60637.0i	0.421610	−	0.175381i
$589$	512359.			1.47687
$590$	556146.	+	176735.i	1.59766	+	0.507714i
$591$		−	474443.i		−	1.35834i
$592$			511035.i			1.45817i
$593$	532984.			1.51567			0.757835	−	0.652447i	$-0.226257\pi$
$593$	532984.			1.51567			0.757835	+	0.652447i	$0.226257\pi$
$594$			439651.i			1.24605i
$595$	55638.0	−	501046.i	0.157158	−	1.41528i
$596$	−175750.			−0.494769
$597$		−	452803.i		−	1.27046i
$598$	−7915.55			−0.0221349
$599$	68054.5			0.189672			0.0948360	−	0.995493i	$-0.469767\pi$
$599$	68054.5			0.189672			0.0948360	+	0.995493i	$0.469767\pi$
$600$	−148644.	+	210256.i	−0.412899	+	0.584043i
$601$			537130.i			1.48707i	0.668699	+	0.743533i	$0.266851\pi$
$601$			537130.i			1.48707i	−0.668699	+	0.743533i	$0.733149\pi$
$602$	98075.8	+	491127.i	0.270626	+	1.35519i
$603$			35182.7i			0.0967597i
$604$	−233323.			−0.639564
$605$	81622.8	+	25938.6i	0.222998	+	0.0708656i
$606$	−198766.			−0.541249
$607$	−409948.			−1.11263			−0.556315	−	0.830971i	$-0.687785\pi$
$607$	−409948.			−1.11263			−0.556315	+	0.830971i	$0.687785\pi$
$608$	−467065.			−1.26348
$609$	6033.17	+	30211.8i	0.0162671	+	0.0814597i
$610$	−563651.	−	179120.i	−1.51478	−	0.481377i
$611$	−28183.0			−0.0754927
$612$	−25671.6			−0.0685411
$613$		−	336398.i		−	0.895224i	−0.894228	−	0.447612i	$-0.852275\pi$
$613$		−	336398.i		−	0.895224i	0.894228	−	0.447612i	$-0.147725\pi$
$614$			534649.i			1.41818i
$615$	17328.7	−	54529.5i	0.0458159	−	0.144172i
$616$	−280484.	+	56011.5i	−0.739175	+	0.147610i
$617$		−	494704.i		−	1.29950i	−0.760149	−	0.649749i	$-0.774874\pi$
$617$		−	494704.i		−	1.29950i	0.760149	−	0.649749i	$-0.225126\pi$
$618$		−	469176.i		−	1.22845i
$619$		−	259458.i		−	0.677151i	−0.940939	−	0.338575i	$-0.890055\pi$
$619$		−	259458.i		−	0.677151i	0.940939	−	0.338575i	$-0.109945\pi$
$620$	47900.9	−	150733.i	0.124612	−	0.392126i
$621$			20750.6i			0.0538081i
$622$	−128231.			−0.331445
$623$	625819.	−	124973.i	1.61240	−	0.321989i
$624$	164592.			0.422707
$625$	130277.	+	368260.i	0.333509	+	0.942747i
$626$		−	418965.i		−	1.06913i
$627$			715787.i			1.82074i
$628$	−102136.			−0.258975
$629$		−	659563.i		−	1.66707i
$630$	52472.4	+	5826.72i	0.132206	+	0.0146806i
$631$	−398747.			−1.00147			−0.500736	−	0.865600i	$-0.666937\pi$
$631$	−398747.			−1.00147			−0.500736	+	0.865600i	$0.666937\pi$
$632$		−	175882.i		−	0.440340i
$633$	−322740.			−0.805463
$634$	−222790.			−0.554265
$635$	206786.	−	650710.i	0.512831	−	1.61376i
$636$		−	9576.34i		−	0.0236747i
$637$	120622.	−	50176.2i	0.297267	−	0.123657i
$638$			42658.5i			0.104801i
$639$	3857.94			0.00944829
$640$	141309.	−	444667.i	0.344992	−	1.08561i
$641$	289434.			0.704424			0.352212	−	0.935920i	$-0.385430\pi$
$641$	289434.			0.704424			0.352212	+	0.935920i	$0.385430\pi$
$642$	−35091.5			−0.0851396
$643$	446428.			1.07977			0.539883	−	0.841740i	$-0.318469\pi$
$643$	446428.			1.07977			0.539883	+	0.841740i	$0.318469\pi$
$644$	10117.9	−	2020.50i	0.0243960	−	0.00487177i
$645$	−153313.	+	482442.i	−0.368520	+	1.15965i
$646$	1.10621e6			2.65078
$647$	379786.			0.907257			0.453628	−	0.891191i	$-0.350129\pi$
$647$	379786.			0.907257			0.453628	+	0.891191i	$0.350129\pi$
$648$		−	313068.i		−	0.745570i
$649$			655190.i			1.55553i
$650$	94008.2	−	132974.i	0.222505	−	0.314731i
$651$	416081.	−	83089.5i	0.981785	−	0.196058i
$652$		−	140664.i		−	0.330893i
$653$			549238.i			1.28806i	0.765002	+	0.644028i	$0.222738\pi$
$653$			549238.i			1.28806i	−0.765002	+	0.644028i	$0.777262\pi$
$654$		−	460901.i		−	1.07759i
$655$	65366.0	−	205692.i	0.152359	−	0.479441i
$656$			76923.4i			0.178752i
$657$	75241.2			0.174311
$658$	119183.	−	23800.3i	0.275273	−	0.0549707i
$659$	101895.			0.234629			0.117314	−	0.993095i	$-0.462571\pi$
$659$	101895.			0.234629			0.117314	+	0.993095i	$0.462571\pi$
$660$	210581.	+	66919.6i	0.483427	+	0.153626i
$661$		−	339312.i		−	0.776597i	−0.921534	−	0.388299i	$-0.873063\pi$
$661$		−	339312.i		−	0.776597i	0.921534	−	0.388299i	$-0.126937\pi$
$662$		−	257647.i		−	0.587909i
$663$	−212429.			−0.483267
$664$		−	27385.2i		−	0.0621127i
$665$	−683434.	−	75891.0i	−1.54544	−	0.171612i
$666$	69073.2			0.155726
$667$			2013.39i			0.00452561i
$668$	−298385.			−0.668690
$669$	−205757.			−0.459729
$670$	−446014.	−	141737.i	−0.993571	−	0.315743i
$671$		−	664032.i		−	1.47484i
$672$	−379299.	+	75744.2i	−0.839929	+	0.167730i
$673$			685861.i			1.51428i	0.653253	+	0.757140i	$0.273404\pi$
$673$			685861.i			1.51428i	−0.653253	+	0.757140i	$0.726596\pi$
$674$	−431057.			−0.948888
$675$	−348591.	−	246443.i	−0.765084	−	0.540889i
$676$	177441.			0.388295
$677$	342300.			0.746844			0.373422	−	0.927662i	$-0.378184\pi$
$677$	342300.			0.746844			0.373422	+	0.927662i	$0.378184\pi$
$678$	−325161.			−0.707358
$679$	−591.548	−	2962.25i	−0.00128307	−	0.00642513i
$680$	−135316.	+	425809.i	−0.292639	+	0.920867i
$681$	375221.			0.809083
$682$	587498.			1.26310
$683$			171281.i			0.367170i	0.983004	+	0.183585i	$0.0587703\pi$
$683$			171281.i			0.367170i	−0.983004	+	0.183585i	$0.941230\pi$
$684$			35016.5i			0.0748446i
$685$	−166368.	+	523523.i	−0.354560	+	1.11572i
$686$	−467725.	+	314055.i	−0.993900	+	0.667356i
$687$		−	233139.i		−	0.493971i
$688$		−	680569.i		−	1.43779i
$689$		−	7924.29i		−	0.0166925i
$690$	32882.2	+	10449.5i	0.0690657	+	0.0219481i
$691$			226012.i			0.473343i	0.971590	+	0.236671i	$0.0760565\pi$
$691$			226012.i			0.473343i	−0.971590	+	0.236671i	$0.923944\pi$
$692$	−153695.			−0.320957
$693$	11608.0	+	58128.4i	0.0241707	+	0.121038i
$694$	−253704.			−0.526756
$695$	156924.	−	493803.i	0.324877	−	1.02231i
$696$		−	27304.6i		−	0.0563660i
$697$		−	99280.6i		−	0.204361i
$698$	584376.			1.19945
$699$			231962.i			0.474747i
$700$	−86221.7	+	193968.i	−0.175963	+	0.395853i
$701$	525569.			1.06953			0.534766	−	0.845000i	$-0.320400\pi$
$701$	525569.			1.06953			0.534766	+	0.845000i	$0.320400\pi$
$702$			177974.i			0.361146i
$703$	−899654.			−1.82039
$704$	150175.			0.303008
$705$	117076.	+	37205.0i	0.235553	+	0.0748554i
$706$			124873.i			0.250529i
$707$	210239.	−	41983.7i	0.420604	−	0.0839928i
$708$			320521.i			0.639425i
$709$	−819495.			−1.63025			−0.815124	−	0.579287i	$-0.803331\pi$
$709$	−819495.			−1.63025			−0.815124	+	0.579287i	$0.803331\pi$
$710$	−15542.1	+	48907.4i	−0.0308314	+	0.0970193i
$711$	−36450.3			−0.0721045
$712$	−565597.			−1.11570
$713$	27728.7			0.0545444
$714$	898343.	−	179395.i	1.76216	−	0.351896i
$715$	174253.	+	55375.1i	0.340853	+	0.108318i
$716$	−317403.			−0.619134
$717$	−158413.			−0.308143
$718$		−	507278.i		−	0.984004i
$719$			113789.i			0.220111i	0.993925	+	0.110056i	$0.0351029\pi$
$719$			113789.i			0.220111i	−0.993925	+	0.110056i	$0.964897\pi$
$720$	−68373.5	−	21728.1i	−0.131893	−	0.0419139i
$721$	99100.0	+	496256.i	0.190635	+	0.954630i
$722$		−	884827.i		−	1.69740i
$723$			280304.i			0.536232i
$724$			360896.i			0.688502i
$725$	−33823.2	−	23911.9i	−0.0643485	−	0.0454922i
$726$			155631.i			0.295273i
$727$	281594.			0.532788			0.266394	−	0.963864i	$-0.414168\pi$
$727$	281594.			0.532788			0.266394	+	0.963864i	$0.414168\pi$
$728$	−113542.	+	22673.9i	−0.214238	+	0.0427823i
$729$	459999.			0.865569
$730$	−303117.	+	953839.i	−0.568806	+	1.78990i
$731$			878372.i			1.64378i
$732$		−	324846.i		−	0.606256i
$733$	401713.			0.747666			0.373833	−	0.927496i	$-0.378043\pi$
$733$	401713.			0.747666			0.373833	+	0.927496i	$0.378043\pi$
$734$		−	1.06361e6i		−	1.97420i
$735$	−567318.	+	49202.7i	−1.05015	+	0.0910781i
$736$	−25277.4			−0.0466635
$737$		−	525445.i		−	0.967369i
$738$	10397.2			0.0190900
$739$	−331954.			−0.607839			−0.303919	−	0.952698i	$-0.598295\pi$
$739$	−331954.			−0.607839			−0.303919	+	0.952698i	$0.598295\pi$
$740$	−84109.5	+	264674.i	−0.153597	+	0.483334i
$741$			289757.i			0.527712i
$742$	6692.01	+	33511.1i	0.0121548	+	0.0608668i
$743$		−	132862.i		−	0.240671i	−0.992733	−	0.120335i	$-0.961603\pi$
$743$		−	132862.i		−	0.240671i	0.992733	−	0.120335i	$-0.0383970\pi$
$744$	−376042.			−0.679346
$745$	604137.	+	191986.i	1.08849	+	0.345905i
$746$	290378.			0.521778
$747$	−5675.39			−0.0101708
$748$	383400.			0.685249
$749$	37116.9	−	7412.08i	0.0661620	−	0.0132122i
$750$	−566064.	+	428288.i	−1.00634	+	0.761402i
$751$	6629.17			0.0117538			0.00587691	−	0.999983i	$-0.498129\pi$
$751$	6629.17			0.0117538			0.00587691	+	0.999983i	$0.498129\pi$
$752$	−165156.			−0.292051
$753$			731462.i			1.29004i
$754$			17268.5i			0.0303747i
$755$	802044.	+	254878.i	1.40703	+	0.447135i
$756$	−45429.2	−	227492.i	−0.0794861	−	0.398037i
$757$		−	1.09675e6i		−	1.91389i	−0.290273	−	0.956944i	$-0.593746\pi$
$757$		−	1.09675e6i		−	1.91389i	0.290273	−	0.956944i	$-0.406254\pi$
$758$			895592.i			1.55873i
$759$			38738.2i			0.0672443i
$760$	580810.	+	184573.i	1.00556	+	0.319552i
$761$		−	1.04930e6i		−	1.81188i	−0.423403	−	0.905941i	$-0.639165\pi$
$761$		−	1.04930e6i		−	1.81188i	0.423403	−	0.905941i	$-0.360835\pi$
$762$	1.24072e6			2.13680
$763$	97352.3	+	487504.i	0.167223	+	0.837392i
$764$	447813.			0.767202
$765$	88245.8	+	28043.3i	0.150790	+	0.0479188i
$766$			316482.i			0.539376i
$767$			265227.i			0.450844i
$768$	678264.			1.14994
$769$			775397.i			1.31121i	0.755105	+	0.655604i	$0.227586\pi$
$769$			775397.i			1.31121i	−0.755105	+	0.655604i	$0.772414\pi$
$770$	−783662.	−	87020.7i	−1.32174	−	0.146771i
$771$	−677573.			−1.13985
$772$		−	108276.i		−	0.181677i
$773$	−184420.			−0.308637			−0.154319	−	0.988021i	$-0.549318\pi$
$773$	−184420.			−0.308637			−0.154319	+	0.988021i	$0.549318\pi$
$774$	−91988.1			−0.153550
$775$	−329317.	+	465817.i	−0.548291	+	0.775553i
$776$			2677.20i			0.00444587i
$777$	−730600.	+	145897.i	−1.21015	+	0.241661i
$778$		−	41161.5i		−	0.0680036i
$779$	−135420.			−0.223156
$780$	85244.9	+	27089.6i	0.140113	+	0.0445260i
$781$	−57617.3			−0.0944607
$782$	59867.8			0.0978994
$783$	45269.4			0.0738382
$784$	706859.	−	294039.i	1.15001	−	0.478379i
$785$	351089.	+	111571.i	0.569742	+	0.181056i
$786$	392196.			0.634831
$787$	−367309.			−0.593038			−0.296519	−	0.955027i	$-0.595826\pi$
$787$	−367309.			−0.593038			−0.296519	+	0.955027i	$0.595826\pi$
$788$			346634.i			0.558237i
$789$		−	980378.i		−	1.57485i
$790$	146844.	−	462084.i	0.235289	−	0.740401i
$791$	343929.	−	68681.0i	0.549687	−	0.109770i
$792$		−	52534.7i		−	0.0837522i
$793$		−	268806.i		−	0.427457i
$794$			1197.94i			0.00190017i
$795$	−10461.0	+	32918.5i	−0.0165516	+	0.0520842i
$796$			330824.i			0.522120i
$797$	−246896.			−0.388685			−0.194343	−	0.980934i	$-0.562257\pi$
$797$	−246896.			−0.388685			−0.194343	+	0.980934i	$0.562257\pi$
$798$	−244698.	−	1.22535e6i	−0.384259	−	1.92422i
$799$	213157.			0.333892
$800$	300205.	−	424637.i	0.469070	−	0.663496i
$801$			117216.i			0.182693i
$802$			443761.i			0.689922i
$803$	−1.12371e6			−1.74270
$804$		−	257049.i		−	0.397653i
$805$	−36987.3	−	4107.20i	−0.0570769	−	0.00633802i
$806$	237824.			0.366088
$807$		−	518952.i		−	0.796857i
$808$	−190008.			−0.291037
$809$	−400601.			−0.612089			−0.306044	−	0.952017i	$-0.599006\pi$
$809$	−400601.			−0.612089			−0.306044	+	0.952017i	$0.599006\pi$
$810$	261380.	−	822502.i	0.398384	−	1.25362i
$811$		−	198723.i		−	0.302138i	−0.988523	−	0.151069i	$-0.951728\pi$
$811$		−	198723.i		−	0.302138i	0.988523	−	0.151069i	$-0.0482716\pi$
$812$	−4407.91	−	22073.1i	−0.00668529	−	0.0334774i
$813$		−	609686.i		−	0.922412i
$814$	−1.03159e6			−1.55689
$815$	−153659.	+	483530.i	−0.231336	+	0.727961i
$816$	−1.24486e6			−1.86957
$817$	1.19811e6			1.79495
$818$	97750.2			0.146087
$819$	4699.00	+	23530.8i	0.00700548	+	0.0350808i
$820$	−12660.6	+	39840.0i	−0.0188289	+	0.0592504i
$821$	−509614.			−0.756058			−0.378029	−	0.925794i	$-0.623398\pi$
$821$	−509614.			−0.756058			−0.378029	+	0.925794i	$0.623398\pi$
$822$	−998210.			−1.47733
$823$		−	637647.i		−	0.941414i	−0.882290	−	0.470707i	$-0.843999\pi$
$823$		−	637647.i		−	0.941414i	0.882290	−	0.470707i	$-0.156001\pi$
$824$		−	448502.i		−	0.660556i
$825$	−650766.	−	460070.i	−0.956130	−	0.675952i
$826$	−223982.	−	1.12162e6i	−0.328287	−	1.64394i
$827$			1.02274e6i			1.49539i	0.664041	+	0.747696i	$0.268840\pi$
$827$			1.02274e6i			1.49539i	−0.664041	+	0.747696i	$0.731160\pi$
$828$			1895.08i			0.00276419i
$829$			627492.i			0.913059i	0.889708	+	0.456529i	$0.150908\pi$
$829$			627492.i			0.913059i	−0.889708	+	0.456529i	$0.849092\pi$
$830$	22863.9	−	71947.4i	0.0331890	−	0.104438i
$831$		−	336236.i		−	0.486903i
$832$	60792.3			0.0878217
$833$	−912302.	+	379499.i	−1.31477	+	0.546916i
$834$	941541.			1.35365
$835$	1.02569e6	+	325951.i	1.47111	+	0.467498i
$836$		−	522963.i		−	0.748270i
$837$		−	623456.i		−	0.889928i
$838$	103236.			0.147009
$839$			738068.i			1.04851i	0.851561	+	0.524255i	$0.175656\pi$
$839$			738068.i			1.04851i	−0.851561	+	0.524255i	$0.824344\pi$
$840$	501602.	+	55699.7i	0.710887	+	0.0789395i
$841$	−702889.			−0.993790
$842$		−	611361.i		−	0.862330i
$843$	679612.			0.956326
$844$	235798.			0.331021
$845$	−609952.	−	193834.i	−0.854244	−	0.271467i
$846$			22323.0i			0.0311898i
$847$	−32872.7	−	164614.i	−0.0458214	−	0.229457i
$848$		−	46437.3i		−	0.0645766i
$849$	382978.			0.531322
$850$	−711014.	+	1.00572e6i	−0.984103	+	1.39201i
$851$	−48689.0			−0.0672313
$852$	−28186.6			−0.0388296
$853$	789566.			1.08515			0.542576	−	0.840007i	$-0.317449\pi$
$853$	789566.			1.08515			0.542576	+	0.840007i	$0.317449\pi$
$854$	227005.	+	1.13675e6i	0.311257	+	1.55866i
$855$	38251.4	−	120369.i	0.0523258	−	0.164657i
$856$	−33545.2			−0.0457808
$857$	522419.			0.711307			0.355653	−	0.934618i	$-0.384258\pi$
$857$	522419.			0.711307			0.355653	+	0.934618i	$0.384258\pi$
$858$			332250.i			0.451327i
$859$		−	851038.i		−	1.15335i	−0.816972	−	0.576677i	$-0.804349\pi$
$859$		−	851038.i		−	1.15335i	0.816972	−	0.576677i	$-0.195651\pi$
$860$	112013.	−	352478.i	0.151450	−	0.476580i
$861$	−109973.	+	21961.2i	−0.148348	+	0.0296244i
$862$			1.34772e6i			1.81378i
$863$			911280.i			1.22357i	0.791022	+	0.611787i	$0.209549\pi$
$863$			911280.i			1.22357i	−0.791022	+	0.611787i	$0.790451\pi$
$864$			568341.i			0.761345i
$865$	528323.	+	167894.i	0.706102	+	0.224389i
$866$			649316.i			0.865805i
$867$	814321.			1.08332
$868$	−303994.	+	60706.2i	−0.403483	+	0.0805738i
$869$	544377.			0.720875
$870$	22796.5	−	71735.6i	0.0301183	−	0.0947755i
$871$		−	212705.i		−	0.280376i
$872$		−	440592.i		−	0.579433i
$873$	554.829			0.000727999
$874$		−	81660.6i		−	0.106903i
$875$	508273.	−	572574.i	0.663866	−	0.747851i
$876$	−549721.			−0.716365
$877$			809992.i			1.05313i	0.850135	+	0.526564i	$0.176520\pi$
$877$			809992.i			1.05313i	−0.850135	+	0.526564i	$0.823480\pi$
$878$	−351411.			−0.455855
$879$	−108737.			−0.140734
$880$	1.02114e6	+	324505.i	1.31862	+	0.419040i
$881$		−	798132.i		−	1.02831i	−0.857698	−	0.514153i	$-0.828106\pi$
$881$		−	798132.i		−	1.02831i	0.857698	−	0.514153i	$-0.171894\pi$
$882$	−39743.3	−	95541.5i	−0.0510889	−	0.122816i
$883$			893487.i			1.14595i	0.819572	+	0.572976i	$0.194211\pi$
$883$			893487.i			1.14595i	−0.819572	+	0.572976i	$0.805789\pi$
$884$	155203.			0.198608
$885$	350132.	−	1.10178e6i	0.447038	−	1.40673i
$886$	346459.			0.441352
$887$	−890142.			−1.13139			−0.565695	−	0.824615i	$-0.691392\pi$
$887$	−890142.			−1.13139			−0.565695	+	0.824615i	$0.691392\pi$
$888$	660295.			0.837360
$889$	−1.31233e6	+	262067.i	−1.66050	+	0.331595i
$890$	−1.48596e6	−	472216.i	−1.87597	−	0.596157i
$891$	968982.			1.22056
$892$	150328.			0.188934
$893$		−	290749.i		−	0.364599i
$894$			1.15192e6i			1.44127i
$895$	1.09107e6	+	346726.i	1.36209	+	0.432852i
$896$	−896790.	+	179085.i	−1.11706	+	0.223071i
$897$			15681.5i			0.0194896i
$898$		−	1.55018e6i		−	1.92233i
$899$		−	60492.7i		−	0.0748486i
$900$	−31835.7	−	22506.8i	−0.0393033	−	0.0277861i
$901$			59933.9i			0.0738284i
$902$	−155280.			−0.190855
$903$	972975.	−	194299.i	1.19324	−	0.238284i
$904$	−310833.			−0.380356
$905$	394237.	−	1.24057e6i	0.481349	−	1.51470i
$906$			1.52927e6i			1.86306i
$907$			91834.0i			0.111632i	0.998441	+	0.0558160i	$0.0177760\pi$
$907$			91834.0i			0.111632i	−0.998441	+	0.0558160i	$0.982224\pi$
$908$	−274141.			−0.332508
$909$			39377.7i			0.0476565i
$910$	−317233.	−	35226.7i	−0.383085	−	0.0425392i
$911$	−132543.			−0.159705			−0.0798526	−	0.996807i	$-0.525445\pi$
$911$	−132543.			−0.159705			−0.0798526	+	0.996807i	$0.525445\pi$
$912$			1.69801e6i			2.04150i
$913$	84760.5			0.101684
$914$	1.13690e6			1.36091
$915$	−354857.	+	1.11665e6i	−0.423849	+	1.33376i
$916$			170334.i			0.203007i
$917$	−414833.	+	82840.3i	−0.493327	+	0.0985151i
$918$		−	1.34608e6i		−	1.59729i
$919$	−903523.			−1.06981			−0.534907	−	0.844911i	$-0.679653\pi$
$919$	−903523.			−1.06981			−0.534907	+	0.844911i	$0.679653\pi$
$920$	31433.3	+	9989.05i	0.0371376	+	0.0118018i
$921$	1.05920e6			1.24870
$922$	−410002.			−0.482308
$923$	−23324.0			−0.0273779
$924$	−84809.2	−	424693.i	−0.0993343	−	0.497429i
$925$	578250.	−	817931.i	0.675822	−	0.955945i
$926$	268998.			0.313709
$927$	−92948.7			−0.108164
$928$			55145.0i			0.0640340i
$929$		−	727404.i		−	0.842838i	−0.906866	−	0.421419i	$-0.861532\pi$
$929$		−	727404.i		−	0.842838i	0.906866	−	0.421419i	$-0.138468\pi$
$930$	−987951.	−	313957.i	−1.14227	−	0.362998i
$931$	517642.	+	1.24439e6i	0.597215	+	1.43568i
$932$		−	169474.i		−	0.195107i
$933$			254039.i			0.291835i
$934$		−	564638.i		−	0.647256i
$935$	−1.31793e6	−	418819.i	−1.50754	−	0.479075i
$936$		−	21266.5i		−	0.0242742i
$937$	−1.35820e6			−1.54698			−0.773491	−	0.633807i	$-0.781491\pi$
$937$	−1.35820e6			−1.54698			−0.773491	+	0.633807i	$0.781491\pi$
$938$	179628.	+	899507.i	0.204158	+	1.02235i
$939$	−830015.			−0.941357
$940$	−85537.0	−	27182.4i	−0.0968051	−	0.0307633i
$941$		−	635488.i		−	0.717675i	−0.933400	−	0.358837i	$-0.883173\pi$
$941$		−	635488.i		−	0.717675i	0.933400	−	0.358837i	$-0.116827\pi$
$942$			669428.i			0.754400i
$943$	−7328.91			−0.00824168
$944$			1.55426e6i			1.74413i
$945$	−92346.9	+	831627.i	−0.103409	+	0.931247i
$946$	1.37382e6			1.53514
$947$			461458.i			0.514555i	0.966338	+	0.257278i	$0.0828255\pi$
$947$			461458.i			0.514555i	−0.966338	+	0.257278i	$0.917175\pi$
$948$	266311.			0.296327
$949$	−454887.			−0.505092
$950$	1.37182e6	+	969834.i	1.52003	+	1.07461i
$951$			441371.i			0.488026i
$952$	858758.	−	171490.i	0.947539	−	0.189219i
$953$			33374.1i			0.0367471i	0.999831	+	0.0183736i	$0.00584882\pi$
$953$			33374.1i			0.0367471i	−0.999831	+	0.0183736i	$0.994151\pi$
$954$	−6276.62			−0.00689651
$955$	−1.53935e6	−	489183.i	−1.68784	−	0.536370i
$956$	115739.			0.126637
$957$	84511.0			0.0922761
$958$	−1.21066e6			−1.31914
$959$	1.05582e6	−	210843.i	1.14803	−	0.229257i
$960$	−252539.	−	80253.3i	−0.274022	−	0.0870804i
$961$	90407.5			0.0978943
$962$	−417597.			−0.451239
$963$			6952.00i			0.00749648i
$964$		−	204794.i		−	0.220375i
$965$	−118279.	+	372198.i	−0.127015	+	0.399686i
$966$	−13243.0	−	66315.8i	−0.0141916	−	0.0710661i
$967$			792088.i			0.847073i	0.905879	+	0.423536i	$0.139211\pi$
$967$			792088.i			0.847073i	−0.905879	+	0.423536i	$0.860789\pi$
$968$			148774.i			0.158772i
$969$		−	2.19152e6i		−	2.33399i
$970$	−2235.19	+	7033.62i	−0.00237558	+	0.00747542i
$971$			1.02728e6i			1.08956i	0.838580	+	0.544779i	$0.183386\pi$
$971$			1.02728e6i			1.08956i	−0.838580	+	0.544779i	$0.816614\pi$
$972$	90544.8			0.0958365
$973$	−995886.	+	198874.i	−1.05192	+	0.210064i
$974$	−1.01557e6			−1.07051
$975$	−263436.	−	186240.i	−0.277118	−	0.195913i
$976$		−	1.57524e6i		−	1.65366i
$977$		−	249431.i		−	0.261313i	−0.991428	−	0.130657i	$-0.958291\pi$
$977$		−	249431.i		−	0.261313i	0.991428	−	0.130657i	$-0.0417086\pi$
$978$	−921954.			−0.963899
$979$		−	1.75059e6i		−	1.82650i
$980$	414489.	−	35948.1i	0.431580	−	0.0374303i
$981$	−91309.4			−0.0948806
$982$		−	559752.i		−	0.580461i
$983$	1.55175e6			1.60589			0.802944	−	0.596055i	$-0.203266\pi$
$983$	1.55175e6			1.60589			0.802944	+	0.596055i	$0.203266\pi$
$984$	99390.8			0.102649
$985$	378657.	−	1.19155e6i	0.390278	−	1.22812i
$986$		−	130607.i		−	0.134343i
$987$	−47151.0	−	236115.i	−0.0484013	−	0.242375i
$988$		−	211700.i		−	0.216874i
$989$	64841.5			0.0662919
$990$	43861.1	−	138021.i	0.0447517	−	0.140823i
$991$	993147.			1.01127			0.505634	−	0.862748i	$-0.331259\pi$
$991$	993147.			1.01127			0.505634	+	0.862748i	$0.331259\pi$
$992$	759464.			0.771763
$993$	−510427.			−0.517649
$994$	98634.9	−	19696.9i	0.0998293	−	0.0199355i
$995$	361386.	−	1.13720e6i	0.365027	−	1.14866i
$996$	41465.1			0.0417988
$997$	784005.			0.788731			0.394365	−	0.918954i	$-0.370964\pi$
$997$	784005.			0.788731			0.394365	+	0.918954i	$0.370964\pi$
$998$			386044.i			0.387593i
$999$			1.09473e6i			1.09692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.c.e.34.6	yes	8
3.2	odd	2		315.5.e.e.244.3		8
4.3	odd	2		560.5.p.g.209.4		8
5.2	odd	4		175.5.d.g.76.3		8
5.3	odd	4		175.5.d.g.76.6		8
5.4	even	2	inner	35.5.c.e.34.3	✓	8
7.6	odd	2	inner	35.5.c.e.34.5	yes	8
15.14	odd	2		315.5.e.e.244.6		8
20.19	odd	2		560.5.p.g.209.6		8
21.20	even	2		315.5.e.e.244.4		8
28.27	even	2		560.5.p.g.209.5		8
35.13	even	4		175.5.d.g.76.5		8
35.27	even	4		175.5.d.g.76.4		8
35.34	odd	2	inner	35.5.c.e.34.4	yes	8
105.104	even	2		315.5.e.e.244.5		8
140.139	even	2		560.5.p.g.209.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.c.e.34.3	✓	8	5.4	even	2	inner
35.5.c.e.34.4	yes	8	35.34	odd	2	inner
35.5.c.e.34.5	yes	8	7.6	odd	2	inner
35.5.c.e.34.6	yes	8	1.1	even	1	trivial
175.5.d.g.76.3		8	5.2	odd	4
175.5.d.g.76.4		8	35.27	even	4
175.5.d.g.76.5		8	35.13	even	4
175.5.d.g.76.6		8	5.3	odd	4
315.5.e.e.244.3		8	3.2	odd	2
315.5.e.e.244.4		8	21.20	even	2
315.5.e.e.244.5		8	105.104	even	2
315.5.e.e.244.6		8	15.14	odd	2
560.5.p.g.209.3		8	140.139	even	2
560.5.p.g.209.4		8	4.3	odd	2
560.5.p.g.209.5		8	28.27	even	2
560.5.p.g.209.6		8	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.78865i q^{2} +9.48683 q^{3} -6.93120 q^{4} +(23.8259 + 7.57153i) q^{5} +45.4292i q^{6} +(-9.59562 - 48.0513i) q^{7} +43.4273i q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.78865i q^{2} +9.48683 q^{3} -6.93120 q^{4} +(23.8259 + 7.57153i) q^{5} +45.4292i q^{6} +(-9.59562 - 48.0513i) q^{7} +43.4273i q^{8} +9.00000 q^{9} +(-36.2574 + 114.094i) q^{10} -134.413 q^{11} -65.7551 q^{12} -54.4114 q^{13} +(230.101 - 45.9501i) q^{14} +(226.032 + 71.8298i) q^{15} -318.858 q^{16} +411.531 q^{17} +43.0979i q^{18} -561.335i q^{19} +(-165.142 - 52.4797i) q^{20} +(-91.0320 - 455.854i) q^{21} -643.656i q^{22} -30.3793i q^{23} +411.988i q^{24} +(510.344 + 360.796i) q^{25} -260.557i q^{26} -683.052 q^{27} +(66.5091 + 333.053i) q^{28} -66.2752 q^{29} +(-343.968 + 1082.39i) q^{30} +912.751i q^{31} -832.061i q^{32} -1275.15 q^{33} +1970.68i q^{34} +(135.197 - 1217.52i) q^{35} -62.3808 q^{36} -1602.70i q^{37} +2688.04 q^{38} -516.192 q^{39} +(-328.811 + 1034.69i) q^{40} -241.247i q^{41} +(2182.93 - 435.921i) q^{42} +2134.40i q^{43} +931.642 q^{44} +(214.433 + 68.1437i) q^{45} +145.476 q^{46} +517.961 q^{47} -3024.95 q^{48} +(-2216.85 + 922.163i) q^{49} +(-1727.73 + 2443.86i) q^{50} +3904.13 q^{51} +377.136 q^{52} +145.636i q^{53} -3270.90i q^{54} +(-3202.50 - 1017.71i) q^{55} +(2086.74 - 416.712i) q^{56} -5325.29i q^{57} -317.369i q^{58} -4874.46i q^{59} +(-1566.67 - 497.867i) q^{60} +4940.25i q^{61} -4370.85 q^{62} +(-86.3606 - 432.461i) q^{63} -1117.27 q^{64} +(-1296.40 - 411.978i) q^{65} -6106.26i q^{66} +3909.19i q^{67} -2852.40 q^{68} -288.203i q^{69} +(5830.26 + 647.414i) q^{70} +428.660 q^{71} +390.846i q^{72} +8360.13 q^{73} +7674.80 q^{74} +(4841.55 + 3422.81i) q^{75} +3890.72i q^{76} +(1289.77 + 6458.71i) q^{77} -2471.87i q^{78} -4050.04 q^{79} +(-7597.06 - 2414.24i) q^{80} -7209.00 q^{81} +1155.25 q^{82} -630.599 q^{83} +(630.961 + 3159.62i) q^{84} +(9805.09 + 3115.92i) q^{85} -10220.9 q^{86} -628.742 q^{87} -5837.19i q^{88} +13024.0i q^{89} +(-326.317 + 1026.84i) q^{90} +(522.111 + 2614.54i) q^{91} +210.565i q^{92} +8659.11i q^{93} +2480.33i q^{94} +(4250.16 - 13374.3i) q^{95} -7893.63i q^{96} +61.6477 q^{97} +(-4415.92 - 10615.7i) q^{98} -1209.72 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 172 q^{4} + 72 q^{9}+O(q^{10}) \) 8 * q - 172 * q^4 + 72 * q^9	\( 8 q - 172 q^{4} + 72 q^{9} - 376 q^{11} - 24 q^{14} + 60 q^{15} + 596 q^{16} + 1020 q^{21} + 3500 q^{25} - 64 q^{29} - 4500 q^{30} - 4160 q^{35} - 1548 q^{36} + 6360 q^{39} - 2104 q^{44} - 28440 q^{46} - 7828 q^{49} + 7740 q^{50} + 24240 q^{51} + 27300 q^{56} + 24180 q^{60} - 5092 q^{64} - 24940 q^{65} - 10620 q^{70} - 18016 q^{71} + 39720 q^{74} - 8624 q^{79} - 57672 q^{81} - 47400 q^{84} + 19000 q^{85} + 18000 q^{86} + 34480 q^{91} + 25260 q^{95} - 3384 q^{99}+O(q^{100}) \) 8 * q - 172 * q^4 + 72 * q^9 - 376 * q^11 - 24 * q^14 + 60 * q^15 + 596 * q^16 + 1020 * q^21 + 3500 * q^25 - 64 * q^29 - 4500 * q^30 - 4160 * q^35 - 1548 * q^36 + 6360 * q^39 - 2104 * q^44 - 28440 * q^46 - 7828 * q^49 + 7740 * q^50 + 24240 * q^51 + 27300 * q^56 + 24180 * q^60 - 5092 * q^64 - 24940 * q^65 - 10620 * q^70 - 18016 * q^71 + 39720 * q^74 - 8624 * q^79 - 57672 * q^81 - 47400 * q^84 + 19000 * q^85 + 18000 * q^86 + 34480 * q^91 + 25260 * q^95 - 3384 * q^99

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