LMFDB - Embedded newform 92.5.c.a.47.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,5,Mod(47,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("92.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	92.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:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.17
Character	$\chi$	$=$	92.47
Dual form			92.5.c.a.47.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24134 - 3.80251i) q^{2} -3.60489i q^{3} +(-12.9181 + 9.44044i) q^{4} +30.7683 q^{5} +(-13.7076 + 4.47491i) q^{6} +33.9778i q^{7} +(51.9332 + 37.4025i) q^{8} +68.0048 q^{9} +(-38.1940 - 116.997i) q^{10} +104.464i q^{11} +(34.0318 + 46.5684i) q^{12} +108.728 q^{13} +(129.201 - 42.1781i) q^{14} -110.916i q^{15} +(77.7561 - 243.906i) q^{16} +64.7428 q^{17} +(-84.4173 - 258.589i) q^{18} -252.926i q^{19} +(-397.468 + 290.466i) q^{20} +122.486 q^{21} +(397.225 - 129.676i) q^{22} -110.304i q^{23} +(134.832 - 187.213i) q^{24} +321.686 q^{25} +(-134.968 - 413.438i) q^{26} -537.146i q^{27} +(-320.765 - 438.930i) q^{28} -154.191 q^{29} +(-421.760 + 137.685i) q^{30} -241.810i q^{31} +(-1023.98 + 7.10256i) q^{32} +376.581 q^{33} +(-80.3681 - 246.185i) q^{34} +1045.44i q^{35} +(-878.494 + 641.995i) q^{36} +2228.75 q^{37} +(-961.754 + 313.968i) q^{38} -391.951i q^{39} +(1597.89 + 1150.81i) q^{40} +1293.45 q^{41} +(-152.048 - 465.755i) q^{42} +1979.19i q^{43} +(-986.187 - 1349.48i) q^{44} +2092.39 q^{45} +(-419.432 + 136.925i) q^{46} +617.769i q^{47} +(-879.253 - 280.302i) q^{48} +1246.51 q^{49} +(-399.323 - 1223.21i) q^{50} -233.391i q^{51} +(-1404.56 + 1026.44i) q^{52} -3267.31 q^{53} +(-2042.50 + 666.783i) q^{54} +3214.18i q^{55} +(-1270.85 + 1764.58i) q^{56} -911.771 q^{57} +(191.405 + 586.314i) q^{58} +4106.92i q^{59} +(1047.10 + 1432.83i) q^{60} -5222.24 q^{61} +(-919.486 + 300.170i) q^{62} +2310.65i q^{63} +(1298.11 + 3884.86i) q^{64} +3345.36 q^{65} +(-467.467 - 1431.95i) q^{66} -2850.26i q^{67} +(-836.356 + 611.200i) q^{68} -397.634 q^{69} +(3975.29 - 1297.75i) q^{70} -7409.13i q^{71} +(3531.70 + 2543.54i) q^{72} -337.243 q^{73} +(-2766.65 - 8474.85i) q^{74} -1159.64i q^{75} +(2387.73 + 3267.33i) q^{76} -3549.46 q^{77} +(-1490.40 + 486.546i) q^{78} -2830.98i q^{79} +(2392.42 - 7504.56i) q^{80} +3572.03 q^{81} +(-1605.62 - 4918.36i) q^{82} +1617.19i q^{83} +(-1582.29 + 1156.32i) q^{84} +1992.02 q^{85} +(7525.89 - 2456.86i) q^{86} +555.843i q^{87} +(-3907.21 + 5425.15i) q^{88} +5269.08 q^{89} +(-2597.37 - 7956.32i) q^{90} +3694.33i q^{91} +(1041.32 + 1424.92i) q^{92} -871.700 q^{93} +(2349.07 - 766.864i) q^{94} -7782.10i q^{95} +(25.6039 + 3691.32i) q^{96} -17042.0 q^{97} +(-1547.35 - 4739.86i) q^{98} +7104.05i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 24 q^{5} + 33 q^{6} - 27 q^{8} - 1300 q^{9} - 46 q^{10} + 145 q^{12} + 472 q^{13} - 264 q^{14} + 272 q^{16} - 648 q^{17} + 1313 q^{18} + 324 q^{20} - 288 q^{21} + 796 q^{22} - 1028 q^{24} + 5604 q^{25}+ \cdots + 57204 q^{98}+O(q^{100}) $ 44 * q + 24 * q^5 + 33 * q^6 - 27 * q^8 - 1300 * q^9 - 46 * q^10 + 145 * q^12 + 472 * q^13 - 264 * q^14 + 272 * q^16 - 648 * q^17 + 1313 * q^18 + 324 * q^20 - 288 * q^21 + 796 * q^22 - 1028 * q^24 + 5604 * q^25 - 3015 * q^26 - 510 * q^28 - 840 * q^29 + 1390 * q^30 + 4200 * q^32 + 320 * q^33 - 4302 * q^34 - 3741 * q^36 - 680 * q^37 + 5940 * q^38 - 626 * q^40 + 7320 * q^41 + 1320 * q^42 - 378 * q^44 - 3240 * q^45 - 8813 * q^48 - 19444 * q^49 - 6960 * q^50 + 1519 * q^52 + 4152 * q^53 - 14405 * q^54 + 13026 * q^56 + 3840 * q^57 + 6771 * q^58 - 180 * q^60 + 6360 * q^61 + 9309 * q^62 - 12765 * q^64 - 15792 * q^65 - 5610 * q^66 - 5484 * q^68 + 4236 * q^70 + 39063 * q^72 - 2888 * q^73 + 43854 * q^74 - 13712 * q^76 + 4320 * q^77 + 18907 * q^78 + 12174 * q^80 + 31628 * q^81 - 31507 * q^82 - 16642 * q^84 - 1904 * q^85 - 25470 * q^86 + 540 * q^88 - 9768 * q^89 - 42044 * q^90 - 11136 * q^93 - 2219 * q^94 + 24435 * q^96 - 3752 * q^97 + 57204 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.24134	−	3.80251i	−0.310336	−	0.950627i
$2$	−1.24134	−	3.80251i	−0.310336	−	0.950627i
$3$		−	3.60489i		−	0.400543i	−0.979740	−	0.200272i	$-0.935818\pi$
$3$		−	3.60489i		−	0.400543i	0.979740	−	0.200272i	$-0.0641825\pi$
$4$	−12.9181	+	9.44044i	−0.807383	+	0.590028i
$5$	30.7683			1.23073			0.615365	−	0.788242i	$-0.289008\pi$
$5$	30.7683			1.23073			0.615365	+	0.788242i	$0.289008\pi$
$6$	−13.7076	+	4.47491i	−0.380767	+	0.124303i
$7$			33.9778i			0.693425i	0.937972	+	0.346712i	$0.112702\pi$
$7$			33.9778i			0.693425i	−0.937972	+	0.346712i	$0.887298\pi$
$8$	51.9332	+	37.4025i	0.811456	+	0.584413i
$9$	68.0048			0.839565
$10$	−38.1940	−	116.997i	−0.381940	−	1.16997i
$11$			104.464i			0.863339i	0.902032	+	0.431670i	$0.142075\pi$
$11$			104.464i			0.863339i	−0.902032	+	0.431670i	$0.857925\pi$
$12$	34.0318	+	46.5684i	0.236332	+	0.323392i
$13$	108.728			0.643359			0.321679	−	0.946849i	$-0.395753\pi$
$13$	108.728			0.643359			0.321679	+	0.946849i	$0.395753\pi$
$14$	129.201	−	42.1781i	0.659188	−	0.215195i
$15$		−	110.916i		−	0.492961i
$16$	77.7561	−	243.906i	0.303735	−	0.952757i
$17$	64.7428			0.224023			0.112012	−	0.993707i	$-0.464271\pi$
$17$	64.7428			0.224023			0.112012	+	0.993707i	$0.464271\pi$
$18$	−84.4173	−	258.589i	−0.260547	−	0.798113i
$19$		−	252.926i		−	0.700627i	−0.936633	−	0.350313i	$-0.886075\pi$
$19$		−	252.926i		−	0.700627i	0.936633	−	0.350313i	$-0.113925\pi$
$20$	−397.468	+	290.466i	−0.993671	+	0.726165i
$21$	122.486			0.277747
$22$	397.225	−	129.676i	0.820713	−	0.267925i
$23$		−	110.304i		−	0.208514i
$23$		−	110.304i		−	0.208514i
$24$	134.832	−	187.213i	0.234083	−	0.325023i
$25$	321.686			0.514698
$26$	−134.968	−	413.438i	−0.199657	−	0.611594i
$27$		−	537.146i		−	0.736826i
$28$	−320.765	−	438.930i	−0.409140	−	0.559859i
$29$	−154.191			−0.183343			−0.0916715	−	0.995789i	$-0.529221\pi$
$29$	−154.191			−0.183343			−0.0916715	+	0.995789i	$0.529221\pi$
$30$	−421.760	+	137.685i	−0.468622	+	0.152984i
$31$		−	241.810i		−	0.251624i	−0.992054	−	0.125812i	$-0.959846\pi$
$31$		−	241.810i		−	0.251624i	0.992054	−	0.125812i	$-0.0401536\pi$
$32$	−1023.98	+	7.10256i	−0.999976	+	0.00693609i
$33$	376.581			0.345805
$34$	−80.3681	−	246.185i	−0.0695226	−	0.212963i
$35$			1045.44i			0.853419i
$36$	−878.494	+	641.995i	−0.677851	+	0.495366i
$37$	2228.75			1.62802			0.814008	−	0.580854i	$-0.197281\pi$
$37$	2228.75			1.62802			0.814008	+	0.580854i	$0.197281\pi$
$38$	−961.754	+	313.968i	−0.666034	+	0.217430i
$39$		−	391.951i		−	0.257693i
$40$	1597.89	+	1150.81i	0.998684	+	0.719255i
$41$	1293.45			0.769453			0.384727	−	0.923031i	$-0.374296\pi$
$41$	1293.45			0.769453			0.384727	+	0.923031i	$0.374296\pi$
$42$	−152.048	−	465.755i	−0.0861948	−	0.264033i
$43$			1979.19i			1.07041i	0.844722	+	0.535206i	$0.179766\pi$
$43$			1979.19i			1.07041i	−0.844722	+	0.535206i	$0.820234\pi$
$44$	−986.187	−	1349.48i	−0.509394	−	0.697045i
$45$	2092.39			1.03328
$46$	−419.432	+	136.925i	−0.198219	+	0.0647095i
$47$			617.769i			0.279660i	0.990176	+	0.139830i	$0.0446556\pi$
$47$			617.769i			0.279660i	−0.990176	+	0.139830i	$0.955344\pi$
$48$	−879.253	−	280.302i	−0.381620	−	0.121659i
$49$	1246.51			0.519162
$50$	−399.323	−	1223.21i	−0.159729	−	0.489286i
$51$		−	233.391i		−	0.0897311i
$52$	−1404.56	+	1026.44i	−0.519437	+	0.379599i
$53$	−3267.31			−1.16316			−0.581580	−	0.813489i	$-0.697565\pi$
$53$	−3267.31			−1.16316			−0.581580	+	0.813489i	$0.697565\pi$
$54$	−2042.50	+	666.783i	−0.700446	+	0.228664i
$55$			3214.18i			1.06254i
$56$	−1270.85	+	1764.58i	−0.405247	+	0.562684i
$57$	−911.771			−0.280631
$58$	191.405	+	586.314i	0.0568979	+	0.174291i
$59$			4106.92i			1.17981i	0.807473	+	0.589905i	$0.200835\pi$
$59$			4106.92i			1.17981i	−0.807473	+	0.589905i	$0.799165\pi$
$60$	1047.10	+	1432.83i	0.290861	+	0.398008i
$61$	−5222.24			−1.40345			−0.701725	−	0.712448i	$-0.747586\pi$
$61$	−5222.24			−1.40345			−0.701725	+	0.712448i	$0.747586\pi$
$62$	−919.486	+	300.170i	−0.239200	+	0.0780879i
$63$			2310.65i			0.582175i
$64$	1298.11	+	3884.86i	0.316922	+	0.948452i
$65$	3345.36			0.791801
$66$	−467.467	−	1431.95i	−0.107316	−	0.328731i
$67$		−	2850.26i		−	0.634942i	−0.948268	−	0.317471i	$-0.897166\pi$
$67$		−	2850.26i		−	0.634942i	0.948268	−	0.317471i	$-0.102834\pi$
$68$	−836.356	+	611.200i	−0.180873	+	0.132180i
$69$	−397.634			−0.0835191
$70$	3975.29	−	1297.75i	0.811283	−	0.264847i
$71$		−	7409.13i		−	1.46977i	−0.678189	−	0.734887i	$-0.737235\pi$
$71$		−	7409.13i		−	1.46977i	0.678189	−	0.734887i	$-0.262765\pi$
$72$	3531.70	+	2543.54i	0.681270	+	0.490653i
$73$	−337.243			−0.0632845			−0.0316422	−	0.999499i	$-0.510074\pi$
$73$	−337.243			−0.0632845			−0.0316422	+	0.999499i	$0.510074\pi$
$74$	−2766.65	−	8474.85i	−0.505232	−	1.54764i
$75$		−	1159.64i		−	0.206159i
$76$	2387.73	+	3267.33i	0.413389	+	0.565674i
$77$	−3549.46			−0.598661
$78$	−1490.40	+	486.546i	−0.244970	+	0.0799715i
$79$		−	2830.98i		−	0.453610i	−0.973940	−	0.226805i	$-0.927172\pi$
$79$		−	2830.98i		−	0.453610i	0.973940	−	0.226805i	$-0.0728279\pi$
$80$	2392.42	−	7504.56i	0.373816	−	1.17259i
$81$	3572.03			0.544434
$82$	−1605.62	−	4918.36i	−0.238789	−	0.731463i
$83$			1617.19i			0.234749i	0.993088	+	0.117374i	$0.0374478\pi$
$83$			1617.19i			0.234749i	−0.993088	+	0.117374i	$0.962552\pi$
$84$	−1582.29	+	1156.32i	−0.224248	+	0.163878i
$85$	1992.02			0.275713
$86$	7525.89	−	2456.86i	1.01756	−	0.332187i
$87$			555.843i			0.0734368i
$88$	−3907.21	+	5425.15i	−0.504547	+	0.700562i
$89$	5269.08			0.665203			0.332602	−	0.943067i	$-0.392074\pi$
$89$	5269.08			0.665203			0.332602	+	0.943067i	$0.392074\pi$
$90$	−2597.37	−	7956.32i	−0.320663	−	0.982262i
$91$			3694.33i			0.446121i
$92$	1041.32	+	1424.92i	0.123029	+	0.168351i
$93$	−871.700			−0.100786
$94$	2349.07	−	766.864i	0.265852	−	0.0867885i
$95$		−	7782.10i		−	0.862283i
$96$	25.6039	+	3691.32i	0.00277820	+	0.400534i
$97$	−17042.0			−1.81125			−0.905625	−	0.424080i	$-0.860598\pi$
$97$	−17042.0			−1.81125			−0.905625	+	0.424080i	$0.860598\pi$
$98$	−1547.35	−	4739.86i	−0.161115	−	0.493530i
$99$			7104.05i			0.724829i
$100$	−4155.58	+	3036.86i	−0.415558	+	0.303686i
$101$	7019.72			0.688140			0.344070	−	0.938944i	$-0.388194\pi$
$101$	7019.72			0.688140			0.344070	+	0.938944i	$0.388194\pi$
$102$	−887.470	+	289.718i	−0.0853008	+	0.0278468i
$103$		−	5024.23i		−	0.473582i	−0.971561	−	0.236791i	$-0.923904\pi$
$103$		−	5024.23i		−	0.473582i	0.971561	−	0.236791i	$-0.0760957\pi$
$104$	5646.57	+	4066.68i	0.522057	+	0.375987i
$105$	3768.69			0.341831
$106$	4055.86	+	12424.0i	0.360970	+	1.10573i
$107$		−	17690.6i		−	1.54517i	−0.634912	−	0.772584i	$-0.718964\pi$
$107$		−	17690.6i		−	1.54517i	0.634912	−	0.772584i	$-0.281036\pi$
$108$	5070.89	+	6938.92i	0.434747	+	0.594901i
$109$	−17000.1			−1.43087			−0.715434	−	0.698680i	$-0.753771\pi$
$109$	−17000.1			−1.43087			−0.715434	+	0.698680i	$0.753771\pi$
$110$	12221.9	−	3989.90i	1.01008	−	0.329744i
$111$		−	8034.41i		−	0.652091i
$112$	8287.38	+	2641.98i	0.660665	+	0.210617i
$113$	−8038.92			−0.629566			−0.314783	−	0.949164i	$-0.601932\pi$
$113$	−8038.92			−0.629566			−0.314783	+	0.949164i	$0.601932\pi$
$114$	1131.82	+	3467.02i	0.0870900	+	0.266776i
$115$		−	3393.87i		−	0.256625i
$116$	1991.87	−	1455.64i	0.148028	−	0.108177i
$117$	7394.00			0.540141
$118$	15616.6	−	5098.10i	1.12156	−	0.366137i
$119$			2199.82i			0.155343i
$120$	4148.54	−	5760.23i	0.288093	−	0.400016i
$121$	3728.26			0.254646
$122$	6482.59	+	19857.6i	0.435541	+	1.33416i
$123$		−	4662.75i		−	0.308199i
$124$	2282.80	+	3123.74i	0.148465	+	0.203157i
$125$	−9332.44			−0.597276
$126$	8786.27	−	2868.31i	0.553431	−	0.180670i
$127$			28494.1i			1.76663i	0.468775	+	0.883317i	$0.344695\pi$
$127$			28494.1i			1.76663i	−0.468775	+	0.883317i	$0.655305\pi$
$128$	13160.8	−	9758.53i	0.803271	−	0.595613i
$129$	7134.77			0.428746
$130$	−4152.74	−	12720.8i	−0.245724	−	0.752708i
$131$		−	18553.7i		−	1.08115i	−0.841294	−	0.540577i	$-0.818206\pi$
$131$		−	18553.7i		−	1.08115i	0.841294	−	0.540577i	$-0.181794\pi$
$132$	−4864.73	+	3555.10i	−0.279197	+	0.204034i
$133$	8593.88			0.485832
$134$	−10838.1	+	3538.15i	−0.603593	+	0.197045i
$135$		−	16527.0i		−	0.906834i
$136$	3362.30	+	2421.54i	0.181785	+	0.130922i
$137$	−33934.8			−1.80802			−0.904012	−	0.427508i	$-0.859392\pi$
$137$	−33934.8			−1.80802			−0.904012	+	0.427508i	$0.859392\pi$
$138$	493.601	+	1512.01i	0.0259190	+	0.0793955i
$139$			29726.7i			1.53857i	0.638907	+	0.769284i	$0.279387\pi$
$139$			29726.7i			1.53857i	−0.638907	+	0.769284i	$0.720613\pi$
$140$	−9869.40	−	13505.1i	−0.503541	−	0.689036i
$141$	2226.99			0.112016
$142$	−28173.3	+	9197.28i	−1.39721	+	0.456124i
$143$			11358.1i			0.555437i
$144$	5287.79	−	16586.7i	0.255005	−	0.799901i
$145$	−4744.20			−0.225646
$146$	418.635	+	1282.37i	0.0196394	+	0.0601599i
$147$		−	4493.53i		−	0.207947i
$148$	−28791.3	+	21040.4i	−1.31443	+	0.960574i
$149$	−11974.0			−0.539346			−0.269673	−	0.962952i	$-0.586916\pi$
$149$	−11974.0			−0.539346			−0.269673	+	0.962952i	$0.586916\pi$
$150$	−4409.55	+	1439.52i	−0.195980	+	0.0639785i
$151$			42436.3i			1.86116i	0.366092	+	0.930579i	$0.380696\pi$
$151$			42436.3i			1.86116i	−0.366092	+	0.930579i	$0.619304\pi$
$152$	9460.06	−	13135.3i	0.409455	−	0.568528i
$153$	4402.82			0.188082
$154$	4406.10	+	13496.8i	0.185786	+	0.569103i
$155$		−	7440.09i		−	0.309681i
$156$	3700.19	+	5063.28i	0.152046	+	0.208057i
$157$	−8365.85			−0.339399			−0.169700	−	0.985496i	$-0.554280\pi$
$157$	−8365.85			−0.339399			−0.169700	+	0.985496i	$0.554280\pi$
$158$	−10764.8	+	3514.22i	−0.431214	+	0.140771i
$159$			11778.3i			0.465896i
$160$	−31505.9	+	218.533i	−1.23070	+	0.00853646i
$161$	3747.89			0.144589
$162$	−4434.12	−	13582.7i	−0.168958	−	0.517554i
$163$		−	31903.0i		−	1.20076i	−0.799715	−	0.600380i	$-0.795016\pi$
$163$		−	31903.0i		−	1.20076i	0.799715	−	0.600380i	$-0.204984\pi$
$164$	−16709.0	+	12210.7i	−0.621243	+	0.453999i
$165$	11586.8			0.425593
$166$	6149.36	−	2007.48i	0.223159	−	0.0728511i
$167$			4438.25i			0.159140i	0.996829	+	0.0795698i	$0.0253547\pi$
$167$			4438.25i			0.159140i	−0.996829	+	0.0795698i	$0.974645\pi$
$168$	6361.10	+	4581.29i	0.225379	+	0.162319i
$169$	−16739.3			−0.586090
$170$	−2472.79	−	7574.68i	−0.0855635	−	0.262100i
$171$		−	17200.2i		−	0.588221i
$172$	−18684.4	−	25567.4i	−0.631572	−	0.864232i
$173$	−5632.56			−0.188197			−0.0940986	−	0.995563i	$-0.529997\pi$
$173$	−5632.56			−0.188197			−0.0940986	+	0.995563i	$0.529997\pi$
$174$	2113.60	−	689.993i	0.0698110	−	0.0227901i
$175$			10930.2i			0.356904i
$176$	25479.4	+	8122.72i	0.822552	+	0.262226i
$177$	14805.0			0.472565
$178$	−6540.74	−	20035.7i	−0.206437	−	0.632360i
$179$		−	17891.7i		−	0.558401i	−0.960233	−	0.279200i	$-0.909931\pi$
$179$		−	17891.7i		−	0.558401i	0.960233	−	0.279200i	$-0.0900694\pi$
$180$	−27029.7	+	19753.1i	−0.834251	+	0.609663i
$181$	49742.6			1.51835			0.759173	−	0.650888i	$-0.225603\pi$
$181$	49742.6			1.51835			0.759173	+	0.650888i	$0.225603\pi$
$182$	14047.7	−	4585.93i	0.424094	−	0.138447i
$183$			18825.6i			0.562143i
$184$	4125.64	−	5728.45i	0.121859	−	0.169200i
$185$	68574.9			2.00365
$186$	1082.08	+	3314.65i	0.0312776	+	0.0958101i
$187$			6763.29i			0.193408i
$188$	−5832.01	−	7980.42i	−0.165007	−	0.225793i
$189$	18251.0			0.510933
$190$	−29591.5	+	9660.26i	−0.819709	+	0.267597i
$191$			14153.7i			0.387974i	0.981004	+	0.193987i	$0.0621419\pi$
$191$			14153.7i			0.387974i	−0.981004	+	0.193987i	$0.937858\pi$
$192$	14004.5	−	4679.56i	0.379896	−	0.126941i
$193$	13688.4			0.367483			0.183742	−	0.982975i	$-0.441179\pi$
$193$	13688.4			0.367483			0.183742	+	0.982975i	$0.441179\pi$
$194$	21155.0	+	64802.5i	0.562096	+	1.72182i
$195$		−	12059.7i		−	0.317151i
$196$	−16102.6	+	11767.6i	−0.419163	+	0.306320i
$197$	−59813.5			−1.54123			−0.770613	−	0.637303i	$-0.780050\pi$
$197$	−59813.5			−1.54123			−0.770613	+	0.637303i	$0.780050\pi$
$198$	27013.2	−	8818.57i	0.689042	−	0.224941i
$199$			70131.2i			1.77094i	0.464693	+	0.885472i	$0.346165\pi$
$199$			70131.2i			1.77094i	−0.464693	+	0.885472i	$0.653835\pi$
$200$	16706.2	+	12031.9i	0.417655	+	0.300796i
$201$	−10274.9			−0.254322
$202$	−8713.89	−	26692.5i	−0.213555	−	0.654165i
$203$		−	5239.09i		−	0.127135i
$204$	2203.31	+	3014.97i	0.0529438	+	0.0724474i
$205$	39797.2			0.946989
$206$	−19104.7	+	6236.80i	−0.450200	+	0.146970i
$207$		−	7501.21i		−	0.175061i
$208$	8454.24	−	26519.3i	0.195411	−	0.612964i
$209$	26421.7			0.604878
$210$	−4678.24	−	14330.5i	−0.106083	−	0.324954i
$211$		−	57004.0i		−	1.28038i	−0.768215	−	0.640192i	$-0.778855\pi$
$211$		−	57004.0i		−	1.28038i	0.768215	−	0.640192i	$-0.221145\pi$
$212$	42207.6	−	30844.9i	0.939115	−	0.686296i
$213$	−26709.1			−0.588708
$214$	−67268.8	+	21960.2i	−1.46888	+	0.479521i
$215$			60896.3i			1.31739i
$216$	20090.6	−	27895.7i	0.430611	−	0.597902i
$217$	8216.19			0.174482
$218$	21103.0	+	64643.2i	0.444050	+	1.36022i
$219$			1215.72i			0.0253482i
$220$	−30343.3	−	41521.2i	−0.626927	−	0.857875i
$221$	7039.33			0.144127
$222$	−30550.9	+	9973.47i	−0.619895	+	0.202367i
$223$		−	65219.3i		−	1.31149i	−0.754981	−	0.655747i	$-0.772354\pi$
$223$		−	65219.3i		−	1.31149i	0.754981	−	0.655747i	$-0.227646\pi$
$224$	−241.329	−	34792.4i	−0.00480965	−	0.693408i
$225$	21876.2			0.432122
$226$	9979.07	+	30568.1i	0.195377	+	0.598482i
$227$		−	90258.1i		−	1.75160i	−0.482675	−	0.875799i	$-0.660335\pi$
$227$		−	90258.1i		−	1.75160i	0.482675	−	0.875799i	$-0.339665\pi$
$228$	11778.4	−	8607.52i	0.226577	−	0.165580i
$229$	30464.1			0.580921			0.290461	−	0.956887i	$-0.406191\pi$
$229$	30464.1			0.580921			0.290461	+	0.956887i	$0.406191\pi$
$230$	−12905.2	+	4212.96i	−0.243955	+	0.0796400i
$231$			12795.4i			0.239790i
$232$	−8007.66	−	5767.14i	−0.148775	−	0.107148i
$233$	7820.36			0.144051			0.0720253	−	0.997403i	$-0.477054\pi$
$233$	7820.36			0.144051			0.0720253	+	0.997403i	$0.477054\pi$
$234$	−9178.49	−	28115.7i	−0.167625	−	0.513473i
$235$			19007.7i			0.344186i
$236$	−38771.1	−	53053.7i	−0.696120	−	0.952558i
$237$	−10205.4			−0.181690
$238$	8364.82	−	2730.73i	0.147674	−	0.0482086i
$239$			34129.7i			0.597498i	0.954332	+	0.298749i	$0.0965693\pi$
$239$			34129.7i			0.597498i	−0.954332	+	0.298749i	$0.903431\pi$
$240$	−27053.1	−	8624.42i	−0.469672	−	0.149729i
$241$	58655.5			1.00989			0.504946	−	0.863151i	$-0.331513\pi$
$241$	58655.5			1.00989			0.504946	+	0.863151i	$0.331513\pi$
$242$	−4628.06	−	14176.8i	−0.0790257	−	0.242073i
$243$		−	56385.6i		−	0.954895i
$244$	67461.5	−	49300.2i	1.13312	−	0.828074i
$245$	38352.9			0.638949
$246$	−17730.1	+	5788.08i	−0.292983	+	0.0956454i
$247$		−	27500.1i		−	0.450754i
$248$	9044.30	−	12558.0i	0.147052	−	0.204182i
$249$	5829.78			0.0940271
$250$	11584.8	+	35486.7i	0.185356	+	0.567787i
$251$			15287.9i			0.242662i	0.992612	+	0.121331i	$0.0387162\pi$
$251$			15287.9i			0.242662i	−0.992612	+	0.121331i	$0.961284\pi$
$252$	−21813.6	−	29849.3i	−0.343499	−	0.470038i
$253$	11522.8			0.180019
$254$	108349.	−	35370.9i	1.67941	−	0.548250i
$255$		−	7181.03i		−	0.110435i
$256$	−53444.0	−	37930.3i	−0.815490	−	0.578771i
$257$	−36674.6			−0.555263			−0.277632	−	0.960688i	$-0.589549\pi$
$257$	−36674.6			−0.555263			−0.277632	+	0.960688i	$0.589549\pi$
$258$	−8856.70	−	27130.0i	−0.133055	−	0.407578i
$259$			75728.2i			1.12891i
$260$	−43215.8	+	31581.7i	−0.639287	+	0.467185i
$261$	−10485.8			−0.153928
$262$	−70550.6	+	23031.5i	−1.02777	+	0.335521i
$263$		−	13490.7i		−	0.195040i	−0.995234	−	0.0975198i	$-0.968909\pi$
$263$		−	13490.7i		−	0.195040i	0.995234	−	0.0975198i	$-0.0310909\pi$
$264$	19557.1	+	14085.1i	0.280605	+	0.202093i
$265$	−100530.			−1.43154
$266$	−10668.0	−	32678.3i	−0.150771	−	0.461845i
$267$		−	18994.4i		−	0.266443i
$268$	26907.7	+	36820.0i	0.374633	+	0.512642i
$269$	−72015.5			−0.995226			−0.497613	−	0.867399i	$-0.665790\pi$
$269$	−72015.5			−0.995226			−0.497613	+	0.867399i	$0.665790\pi$
$270$	−62844.2	+	20515.8i	−0.862061	+	0.281423i
$271$		−	29776.0i		−	0.405441i	−0.979237	−	0.202720i	$-0.935022\pi$
$271$		−	29776.0i		−	0.405441i	0.979237	−	0.202720i	$-0.0649783\pi$
$272$	5034.15	−	15791.1i	0.0680438	−	0.213440i
$273$	13317.6			0.178691
$274$	42124.8	+	129037.i	0.561095	+	1.71876i
$275$			33604.6i			0.444359i
$276$	5136.69	−	3753.84i	0.0674319	−	0.0492786i
$277$	72268.9			0.941872			0.470936	−	0.882167i	$-0.343916\pi$
$277$	72268.9			0.941872			0.470936	+	0.882167i	$0.343916\pi$
$278$	113036.	−	36901.0i	1.46260	−	0.477473i
$279$		−	16444.3i		−	0.211255i
$280$	−39101.9	+	54292.9i	−0.498749	+	0.692512i
$281$	−55660.5			−0.704911			−0.352455	−	0.935829i	$-0.614653\pi$
$281$	−55660.5			−0.704911			−0.352455	+	0.935829i	$0.614653\pi$
$282$	−2764.46	−	8468.14i	−0.0347626	−	0.106485i
$283$		−	323.584i		−	0.00404030i	−0.999998	−	0.00202015i	$-0.999357\pi$
$283$		−	323.584i		−	0.00404030i	0.999998	−	0.00202015i	$-0.000643035\pi$
$284$	69945.5	+	95712.1i	0.867207	+	1.18667i
$285$	−28053.6			−0.345382
$286$	43189.4	−	14099.3i	0.528013	−	0.172372i
$287$			43948.6i			0.533558i
$288$	−69635.2	+	483.008i	−0.839545	+	0.00582330i
$289$	−79329.4			−0.949813
$290$	5889.19	+	18039.9i	0.0700260	+	0.214505i
$291$			61434.7i			0.725484i
$292$	4356.55	−	3183.72i	0.0510948	−	0.0373396i
$293$	−107397.			−1.25100			−0.625500	−	0.780224i	$-0.715105\pi$
$293$	−107397.			−1.25100			−0.625500	+	0.780224i	$0.715105\pi$
$294$	−17086.7	+	5578.02i	−0.197680	+	0.0645335i
$295$			126363.i			1.45203i
$296$	115746.	+	83360.9i	1.32106	+	0.951434i
$297$	56112.4			0.636130
$298$	14863.9	+	45531.3i	0.167379	+	0.512717i
$299$		−	11993.1i		−	0.134150i
$300$	10947.5	+	14980.4i	0.121639	+	0.166449i
$301$	−67248.6			−0.742250
$302$	161364.	−	52678.0i	1.76927	−	0.577584i
$303$		−	25305.3i		−	0.275630i
$304$	−61690.1	−	19666.6i	−0.667527	−	0.212805i
$305$	−160679.			−1.72727
$306$	−5465.41	−	16741.7i	−0.0583687	−	0.178796i
$307$		−	50099.0i		−	0.531560i	−0.964034	−	0.265780i	$-0.914371\pi$
$307$		−	50099.0i		−	0.531560i	0.964034	−	0.265780i	$-0.0856295\pi$
$308$	45852.4	−	33508.5i	0.483348	−	0.353226i
$309$	−18111.8			−0.189690
$310$	−28291.0	+	9235.71i	−0.294391	+	0.0961052i
$311$		−	70789.5i		−	0.731894i	−0.930636	−	0.365947i	$-0.880745\pi$
$311$		−	70789.5i		−	0.731894i	0.930636	−	0.365947i	$-0.119255\pi$
$312$	14659.9	−	20355.3i	0.150599	−	0.209107i
$313$	−10735.9			−0.109585			−0.0547925	−	0.998498i	$-0.517450\pi$
$313$	−10735.9			−0.109585			−0.0547925	+	0.998498i	$0.517450\pi$
$314$	10384.9	+	31811.2i	0.105328	+	0.322642i
$315$			71094.8i			0.716501i
$316$	26725.7	+	36570.9i	0.267642	+	0.366237i
$317$	60581.5			0.602867			0.301434	−	0.953487i	$-0.402535\pi$
$317$	60581.5			0.602867			0.301434	+	0.953487i	$0.402535\pi$
$318$	44787.1	−	14620.9i	0.442893	−	0.144584i
$319$		−	16107.5i		−	0.158287i
$320$	39940.7	+	119530.i	0.390046	+	1.16729i
$321$	−63772.8			−0.618907
$322$	−4652.42	−	14251.4i	−0.0448712	−	0.137450i
$323$		−	16375.1i		−	0.156957i
$324$	−46144.0	+	33721.6i	−0.439567	+	0.321231i
$325$	34976.2			0.331135
$326$	−121311.	+	39602.6i	−1.14147	+	0.372639i
$327$			61283.7i			0.573125i
$328$	67173.0	+	48378.2i	0.624377	+	0.449679i
$329$	−20990.4			−0.193923
$330$	−14383.2	−	44058.7i	−0.132077	−	0.404580i
$331$			6457.57i			0.0589404i	0.999566	+	0.0294702i	$0.00938202\pi$
$331$			6457.57i			0.0589404i	−0.999566	+	0.0294702i	$0.990618\pi$
$332$	−15266.9	−	20891.0i	−0.138508	−	0.189532i
$333$	151566.			1.36683
$334$	16876.5	−	5509.39i	0.151282	−	0.0493868i
$335$		−	87697.4i		−	0.781443i
$336$	9524.06	−	29875.1i	0.0843614	−	0.264625i
$337$	−39775.2			−0.350229			−0.175115	−	0.984548i	$-0.556030\pi$
$337$	−39775.2			−0.350229			−0.175115	+	0.984548i	$0.556030\pi$
$338$	20779.2	+	63651.3i	0.181885	+	0.557153i
$339$			28979.4i			0.252168i
$340$	−25733.2	+	18805.6i	−0.222606	+	0.162678i
$341$	25260.5			0.217237
$342$	−65403.8	+	21351.3i	−0.559179	+	0.182546i
$343$			123934.i			1.05342i
$344$	−74026.6	+	102786.i	−0.625563	+	0.868592i
$345$	−12234.5			−0.102789
$346$	6991.94	+	21417.8i	0.0584044	+	0.178905i
$347$		−	153608.i		−	1.27572i	−0.770152	−	0.637861i	$-0.779820\pi$
$347$		−	153608.i		−	1.27572i	0.770152	−	0.637861i	$-0.220180\pi$
$348$	−5247.41	−	7180.46i	−0.0433298	−	0.0592917i
$349$	−186665.			−1.53254			−0.766268	−	0.642521i	$-0.777889\pi$
$349$	−186665.			−1.53254			−0.766268	+	0.642521i	$0.777889\pi$
$350$	41562.1	−	13568.1i	0.339283	−	0.110760i
$351$		−	58402.6i		−	0.474043i
$352$	−741.962	−	106969.i	−0.00598820	−	0.863318i
$353$	124471.			0.998889			0.499444	−	0.866346i	$-0.333538\pi$
$353$	124471.			0.998889			0.499444	+	0.866346i	$0.333538\pi$
$354$	−18378.1	−	56296.1i	−0.146654	−	0.449233i
$355$		−	227966.i		−	1.80890i
$356$	−68066.6	+	49742.4i	−0.537074	+	0.392488i
$357$	7930.10			0.0622218
$358$	−68033.4	+	22209.8i	−0.530831	+	0.173292i
$359$			108416.i			0.841207i	0.907245	+	0.420604i	$0.138182\pi$
$359$			108416.i			0.841207i	−0.907245	+	0.420604i	$0.861818\pi$
$360$	108664.	+	78260.5i	0.838460	+	0.603862i
$361$	66349.3			0.509122
$362$	−61747.6	−	189146.i	−0.471198	−	1.44338i
$363$		−	13440.0i		−	0.101997i
$364$	−34876.1	−	47723.8i	−0.263224	−	0.360190i
$365$	−10376.4			−0.0778861
$366$	71584.5	−	23369.0i	0.534388	−	0.174453i
$367$		−	13903.7i		−	0.103228i	−0.998667	−	0.0516140i	$-0.983563\pi$
$367$		−	13903.7i		−	0.103228i	0.998667	−	0.0516140i	$-0.0164366\pi$
$368$	−26903.8	−	8576.82i	−0.198663	−	0.0633331i
$369$	87960.8			0.646006
$370$	−85125.0	−	260757.i	−0.621805	−	1.90472i
$371$		−	111016.i		−	0.806563i
$372$	11260.7	−	8229.24i	0.0813731	−	0.0594667i
$373$	−59439.8			−0.427228			−0.213614	−	0.976918i	$-0.568523\pi$
$373$	−59439.8			−0.427228			−0.213614	+	0.976918i	$0.568523\pi$
$374$	25717.5	−	8395.57i	0.183859	−	0.0600215i
$375$			33642.4i			0.239235i
$376$	−23106.1	+	32082.7i	−0.163437	+	0.226932i
$377$	−16764.9			−0.117955
$378$	−22655.8	−	69399.7i	−0.158561	−	0.485707i
$379$		−	69097.4i		−	0.481042i	−0.970644	−	0.240521i	$-0.922682\pi$
$379$		−	69097.4i		−	0.481042i	0.970644	−	0.240521i	$-0.0773183\pi$
$380$	73466.5	+	100530.i	0.508770	+	0.696192i
$381$	102718.			0.707614
$382$	53819.5	−	17569.6i	0.368818	−	0.120402i
$383$			42761.8i			0.291514i	0.989320	+	0.145757i	$0.0465617\pi$
$383$			42761.8i			0.291514i	−0.989320	+	0.145757i	$0.953438\pi$
$384$	−35178.4	−	47443.2i	−0.238569	−	0.321745i
$385$	−109211.			−0.736790
$386$	−16992.0	−	52050.2i	−0.114043	−	0.349339i
$387$			134594.i			0.898680i
$388$	220151.	−	160884.i	1.46237	−	1.06869i
$389$	−29070.2			−0.192110			−0.0960548	−	0.995376i	$-0.530622\pi$
$389$	−29070.2			−0.192110			−0.0960548	+	0.995376i	$0.530622\pi$
$390$	−45856.9	+	14970.2i	−0.301492	+	0.0984233i
$391$		−	7141.40i		−	0.0467121i
$392$	64735.2	+	46622.5i	0.421278	+	0.303405i
$393$	−66884.0			−0.433049
$394$	74249.1	+	227441.i	0.478298	+	1.46513i
$395$		−	87104.3i		−	0.558271i
$396$	−67065.4	−	91771.1i	−0.427669	−	0.585215i
$397$	137857.			0.874674			0.437337	−	0.899298i	$-0.355922\pi$
$397$	137857.			0.874674			0.437337	+	0.899298i	$0.355922\pi$
$398$	266674.	−	87056.9i	1.68351	−	0.549588i
$399$		−	30980.0i		−	0.194597i
$400$	25013.1	−	78461.1i	0.156332	−	0.490382i
$401$	−258595.			−1.60817			−0.804083	−	0.594517i	$-0.797343\pi$
$401$	−258595.			−1.60817			−0.804083	+	0.594517i	$0.797343\pi$
$402$	12754.6	+	39070.2i	0.0789253	+	0.241765i
$403$		−	26291.5i		−	0.161884i
$404$	−90681.7	+	66269.3i	−0.555593	+	0.406022i
$405$	109905.			0.670052
$406$	−19921.7	+	6503.51i	−0.120858	+	0.0394544i
$407$			232825.i			1.40553i
$408$	8729.38	−	12120.7i	0.0524401	−	0.0728129i
$409$	210922.			1.26089			0.630444	−	0.776235i	$-0.282873\pi$
$409$	210922.			1.26089			0.630444	+	0.776235i	$0.282873\pi$
$410$	−49402.1	−	151329.i	−0.293885	−	0.900234i
$411$			122331.i			0.724192i
$412$	47431.0	+	64903.7i	0.279427	+	0.382362i
$413$	−139544.			−0.818109
$414$	−28523.4	+	9311.58i	−0.166418	+	0.0543279i
$415$			49758.0i			0.288913i
$416$	−111334.	+	772.244i	−0.643343	+	0.00446239i
$417$	107161.			0.616263
$418$	−32798.4	−	100469.i	−0.187716	−	0.575014i
$419$		−	239975.i		−	1.36690i	−0.729996	−	0.683451i	$-0.760478\pi$
$419$		−	239975.i		−	1.36690i	0.729996	−	0.683451i	$-0.239522\pi$
$420$	−48684.4	+	35578.1i	−0.275989	+	0.201690i
$421$	241037.			1.35994			0.679969	−	0.733241i	$-0.261993\pi$
$421$	241037.			1.35994			0.679969	+	0.733241i	$0.261993\pi$
$422$	−216758.	+	70761.5i	−1.21717	+	0.397349i
$423$			42011.2i			0.234793i
$424$	−169682.	−	122206.i	−0.943853	−	0.679766i
$425$	20826.9			0.115304
$426$	33155.2	+	101562.i	0.182697	+	0.559642i
$427$		−	177440.i		−	0.973187i
$428$	167007.	+	228530.i	0.911692	+	1.24754i
$429$	40944.8			0.222477
$430$	231559.	−	75593.2i	1.25234	−	0.408833i
$431$		−	137750.i		−	0.741547i	−0.928723	−	0.370773i	$-0.879093\pi$
$431$		−	137750.i		−	0.741547i	0.928723	−	0.370773i	$-0.120907\pi$
$432$	−131013.	−	41766.4i	−0.702015	−	0.223800i
$433$	72161.6			0.384885			0.192442	−	0.981308i	$-0.438359\pi$
$433$	72161.6			0.384885			0.192442	+	0.981308i	$0.438359\pi$
$434$	−10199.1	−	31242.1i	−0.0541481	−	0.165867i
$435$			17102.3i			0.0903810i
$436$	219610.	−	160489.i	1.15526	−	0.844251i
$437$	−27898.8			−0.146091
$438$	4622.80	−	1509.13i	0.0240967	−	0.00786645i
$439$			334836.i			1.73741i	0.495326	+	0.868707i	$0.335049\pi$
$439$			334836.i			1.73741i	−0.495326	+	0.868707i	$0.664951\pi$
$440$	−120218.	+	166922.i	−0.620961	+	0.862203i
$441$	84768.5			0.435871
$442$	−8738.23	−	26767.1i	−0.0447279	−	0.137011i
$443$		−	113300.i		−	0.577330i	−0.957430	−	0.288665i	$-0.906789\pi$
$443$		−	113300.i		−	0.577330i	0.957430	−	0.288665i	$-0.0932114\pi$
$444$	75848.4	+	103790.i	0.384752	+	0.526487i
$445$	162120.			0.818686
$446$	−247997.	+	80959.5i	−1.24674	+	0.407004i
$447$			43165.0i			0.216032i
$448$	−131999.	+	44107.0i	−0.657680	+	0.219762i
$449$	269612.			1.33735			0.668676	−	0.743554i	$-0.266861\pi$
$449$	269612.			1.33735			0.668676	+	0.743554i	$0.266861\pi$
$450$	−27155.9	−	83184.4i	−0.134103	−	0.410787i
$451$			135119.i			0.664299i
$452$	103848.	−	75891.0i	0.508301	−	0.371461i
$453$	152978.			0.745474
$454$	−343207.	+	112041.i	−1.66512	+	0.543584i
$455$			113668.i			0.549054i
$456$	−47351.2	−	34102.5i	−0.227720	−	0.164005i
$457$	138872.			0.664937			0.332469	−	0.943114i	$-0.392118\pi$
$457$	138872.			0.664937			0.332469	+	0.943114i	$0.392118\pi$
$458$	−37816.4	−	115840.i	−0.180281	−	0.552240i
$459$		−	34776.3i		−	0.165066i
$460$	32039.6	+	43842.4i	0.151416	+	0.207195i
$461$	−45339.2			−0.213340			−0.106670	−	0.994294i	$-0.534019\pi$
$461$	−45339.2			−0.213340			−0.106670	+	0.994294i	$0.534019\pi$
$462$	48654.6	−	15883.5i	0.227950	−	0.0744153i
$463$		−	24680.4i		−	0.115131i	−0.998342	−	0.0575653i	$-0.981666\pi$
$463$		−	24680.4i		−	0.115131i	0.998342	−	0.0575653i	$-0.0183337\pi$
$464$	−11989.3	+	37608.2i	−0.0556877	+	0.174681i
$465$	−26820.7			−0.124041
$466$	−9707.76	−	29737.0i	−0.0447041	−	0.136938i
$467$			391663.i			1.79589i	0.440111	+	0.897943i	$0.354939\pi$
$467$			391663.i			1.79589i	−0.440111	+	0.897943i	$0.645061\pi$
$468$	−95516.6	+	69802.6i	−0.436101	+	0.318698i
$469$	96845.4			0.440285
$470$	72276.8	−	23595.1i	0.327192	−	0.106813i
$471$			30158.0i			0.135944i
$472$	−153609.	+	213285.i	−0.689496	+	0.957364i
$473$	−206754.			−0.924128
$474$	12668.4	+	38806.0i	0.0563851	+	0.172720i
$475$		−	81362.9i		−	0.360611i
$476$	−20767.2	−	28417.5i	−0.0916569	−	0.125422i
$477$	−222193.			−0.976548
$478$	129778.	−	42366.7i	0.567998	−	0.185425i
$479$			329706.i			1.43699i	0.695530	+	0.718497i	$0.255170\pi$
$479$			329706.i			1.43699i	−0.695530	+	0.718497i	$0.744830\pi$
$480$	787.789	+	113575.i	0.00341922	+	0.492949i
$481$	242327.			1.04740
$482$	−72811.7	−	223038.i	−0.313406	−	0.960030i
$483$		−	13510.7i		−	0.0579142i
$484$	−48162.2	+	35196.5i	−0.205596	+	0.150248i
$485$	−524354.			−2.22916
$486$	−214407.	+	69993.9i	−0.907749	+	0.296338i
$487$		−	423658.i		−	1.78631i	−0.449748	−	0.893156i	$-0.648486\pi$
$487$		−	423658.i		−	1.78631i	0.449748	−	0.893156i	$-0.351514\pi$
$488$	−271207.	−	195324.i	−1.13884	−	0.820195i
$489$	−115007.			−0.480957
$490$	−47609.2	−	145837.i	−0.198289	−	0.607402i
$491$		−	465393.i		−	1.93044i	−0.261437	−	0.965221i	$-0.584196\pi$
$491$		−	465393.i		−	1.93044i	0.261437	−	0.965221i	$-0.415804\pi$
$492$	44018.4	+	60234.0i	0.181846	+	0.248835i
$493$	−9982.79			−0.0410731
$494$	−104569.	+	34137.0i	−0.428499	+	0.139885i
$495$			218579.i			0.892070i
$496$	−58979.0	−	18802.3i	−0.239736	−	0.0764269i
$497$	251746.			1.01918
$498$	−7236.76	−	22167.8i	−0.0291800	−	0.0893847i
$499$			138927.i			0.557937i	0.960300	+	0.278968i	$0.0899925\pi$
$499$			138927.i			0.557937i	−0.960300	+	0.278968i	$0.910008\pi$
$500$	120558.	−	88102.3i	0.482231	−	0.352409i
$501$	15999.4			0.0637424
$502$	58132.5	−	18977.6i	0.230681	−	0.0753067i
$503$			257169.i			1.01644i	0.861226	+	0.508222i	$0.169697\pi$
$503$			257169.i			1.01644i	−0.861226	+	0.508222i	$0.830303\pi$
$504$	−86424.1	+	120000.i	−0.340231	+	0.472409i
$505$	215985.			0.846916
$506$	−14303.8	−	43815.6i	−0.0558663	−	0.171131i
$507$			60343.4i			0.234754i
$508$	−268996.	−	368090.i	−1.04236	−	1.42635i
$509$	−316452.			−1.22144			−0.610719	−	0.791847i	$-0.709120\pi$
$509$	−316452.			−1.22144			−0.610719	+	0.791847i	$0.709120\pi$
$510$	−27305.9	+	8914.12i	−0.104982	+	0.0342719i
$511$		−	11458.8i		−	0.0438830i
$512$	−77888.0	+	250306.i	−0.297119	+	0.954840i
$513$	−135858.			−0.516240
$514$	45525.8	+	139455.i	0.172318	+	0.527848i
$515$		−	154587.i		−	0.582852i
$516$	−92167.8	+	67355.3i	−0.346163	+	0.252972i
$517$	−64534.6			−0.241441
$518$	287957.	−	94004.7i	1.07317	−	0.350340i
$519$			20304.8i			0.0753812i
$520$	173735.	+	125125.i	0.642512	+	0.462739i
$521$	131592.			0.484791			0.242396	−	0.970177i	$-0.422067\pi$
$521$	131592.			0.484791			0.242396	+	0.970177i	$0.422067\pi$
$522$	13016.4	+	39872.2i	0.0477695	+	0.146328i
$523$		−	35937.5i		−	0.131385i	−0.997840	−	0.0656923i	$-0.979074\pi$
$523$		−	35937.5i		−	0.131385i	0.997840	−	0.0656923i	$-0.0209256\pi$
$524$	175155.	+	239679.i	0.637911	+	0.872906i
$525$	39402.1			0.142956
$526$	−51298.5	+	16746.6i	−0.185410	+	0.0605278i
$527$		−	15655.5i		−	0.0563696i
$528$	29281.5	−	91850.4i	0.105033	−	0.329468i
$529$	−12167.0			−0.0434783
$530$	124792.	+	382265.i	0.444257	+	1.36086i
$531$			279290.i			0.990527i
$532$	−111017.	+	81130.0i	−0.392252	+	0.286654i
$533$	140634.			0.495034
$534$	−72226.5	+	23578.6i	−0.253288	+	0.0826868i
$535$		−	544310.i		−	1.90169i
$536$	106607.	−	148023.i	0.371069	−	0.515228i
$537$	−64497.7			−0.223664
$538$	89396.0	+	273840.i	0.308854	+	0.946088i
$539$			130215.i			0.448213i
$540$	156023.	+	213499.i	0.535057	+	0.732162i
$541$	459002.			1.56827			0.784134	−	0.620592i	$-0.213108\pi$
$541$	459002.			1.56827			0.784134	+	0.620592i	$0.213108\pi$
$542$	−113223.	+	36962.2i	−0.385423	+	0.125823i
$543$		−	179317.i		−	0.608164i
$544$	−66295.0	+	459.839i	−0.224018	+	0.00155385i
$545$	−523065.			−1.76101
$546$	−16531.8	−	50640.4i	−0.0554542	−	0.169868i
$547$			524638.i			1.75342i	0.481022	+	0.876708i	$0.340266\pi$
$547$			524638.i			1.75342i	−0.481022	+	0.876708i	$0.659734\pi$
$548$	438374.	−	320359.i	1.45977	−	1.06678i
$549$	−355137.			−1.17829
$550$	127782.	−	41714.9i	0.422420	−	0.137901i
$551$			38999.1i			0.128455i
$552$	−20650.4	−	14872.5i	−0.0677721	−	0.0488097i
$553$	96190.4			0.314544
$554$	−89710.6	−	274803.i	−0.292297	−	0.895369i
$555$		−	247205.i		−	0.802549i
$556$	−280633.	−	384013.i	−0.907797	−	1.24221i
$557$	−335998.			−1.08299			−0.541497	−	0.840703i	$-0.682142\pi$
$557$	−335998.			−1.08299			−0.541497	+	0.840703i	$0.682142\pi$
$558$	−62529.4	+	20413.0i	−0.200824	+	0.0655599i
$559$			215193.i			0.688659i
$560$	254988.	+	81289.2i	0.813100	+	0.259213i
$561$	24380.9			0.0774684
$562$	69093.8	+	211649.i	0.218759	+	0.670107i
$563$		−	612507.i		−	1.93239i	−0.257816	−	0.966194i	$-0.583003\pi$
$563$		−	612507.i		−	1.93239i	0.257816	−	0.966194i	$-0.416997\pi$
$564$	−28768.5	+	21023.8i	−0.0904398	+	0.0660925i
$565$	−247344.			−0.774826
$566$	−1230.43	+	401.679i	−0.00384082	+	0.00125385i
$567$			121370.i			0.377524i
$568$	277120.	−	384780.i	0.858956	−	1.19266i
$569$	18735.8			0.0578693			0.0289347	−	0.999581i	$-0.490789\pi$
$569$	18735.8			0.0578693			0.0289347	+	0.999581i	$0.490789\pi$
$570$	34824.2	+	106674.i	0.107184	+	0.328329i
$571$		−	23675.7i		−	0.0726158i	−0.999341	−	0.0363079i	$-0.988440\pi$
$571$		−	23675.7i		−	0.0726158i	0.999341	−	0.0363079i	$-0.0115597\pi$
$572$	−107226.	−	146726.i	−0.327723	−	0.448450i
$573$	51022.4			0.155400
$574$	167115.	−	54555.3i	0.507214	−	0.165582i
$575$		−	35483.3i		−	0.107322i
$576$	88277.9	+	264189.i	0.266077	+	0.796287i
$577$	−350832.			−1.05378			−0.526888	−	0.849935i	$-0.676641\pi$
$577$	−350832.			−1.05378			−0.526888	+	0.849935i	$0.676641\pi$
$578$	98475.0	+	301651.i	0.294761	+	0.902918i
$579$		−	49345.1i		−	0.147193i
$580$	61286.3	−	44787.4i	0.182183	−	0.133137i
$581$	−54948.4			−0.162781
$582$	233606.	−	76261.6i	0.689665	−	0.225144i
$583$		−	341317.i		−	1.00420i
$584$	−17514.1	−	12613.7i	−0.0513526	−	0.0369843i
$585$	227500.			0.664769
$586$	133317.	+	408378.i	0.388230	+	1.18923i
$587$		−	476974.i		−	1.38426i	−0.721772	−	0.692131i	$-0.756672\pi$
$587$		−	476974.i		−	1.38426i	0.721772	−	0.692131i	$-0.243328\pi$
$588$	42420.9	+	58048.0i	0.122695	+	0.167893i
$589$	−61160.2			−0.176294
$590$	480495.	−	156860.i	1.38034	−	0.450617i
$591$			215621.i			0.617328i
$592$	173299.	−	543606.i	0.494485	−	1.55110i
$593$	−398812.			−1.13412			−0.567059	−	0.823677i	$-0.691919\pi$
$593$	−398812.			−1.13412			−0.567059	+	0.823677i	$0.691919\pi$
$594$	−69654.8	−	213368.i	−0.197414	−	0.604723i
$595$			67684.6i			0.191186i
$596$	154682.	−	113040.i	0.435459	−	0.318229i
$597$	252815.			0.709340
$598$	−45603.9	+	14887.6i	−0.127526	+	0.0416314i
$599$			506739.i			1.41231i	0.708057	+	0.706155i	$0.249572\pi$
$599$			506739.i			1.41231i	−0.708057	+	0.706155i	$0.750428\pi$
$600$	43373.5	−	60224.0i	0.120482	−	0.167289i
$601$	562074.			1.55612			0.778062	−	0.628187i	$-0.216203\pi$
$601$	562074.			1.55612			0.778062	+	0.628187i	$0.216203\pi$
$602$	83478.6	+	255713.i	0.230347	+	0.705602i
$603$		−	193831.i		−	0.533075i
$604$	−400617.	−	548197.i	−1.09813	−	1.50267i
$605$	114712.			0.313400
$606$	−96223.7	+	31412.6i	−0.262021	+	0.0855380i
$607$			380072.i			1.03155i	0.856725	+	0.515773i	$0.172495\pi$
$607$			380072.i			1.03155i	−0.856725	+	0.515773i	$0.827505\pi$
$608$	1796.42	+	258990.i	0.00485961	+	0.700610i
$609$	−18886.3			−0.0509229
$610$	199458.	+	610984.i	0.536034	+	1.64199i
$611$			67168.5i			0.179922i
$612$	−56876.2	+	41564.5i	−0.151854	+	0.110974i
$613$	247239.			0.657955			0.328978	−	0.944338i	$-0.393296\pi$
$613$	247239.			0.657955			0.328978	+	0.944338i	$0.393296\pi$
$614$	−190502.	+	62190.1i	−0.505315	+	0.164962i
$615$		−	143465.i		−	0.379310i
$616$	−184335.	−	132758.i	−0.485787	−	0.349865i
$617$	−94172.5			−0.247374			−0.123687	−	0.992321i	$-0.539472\pi$
$617$	−94172.5			−0.247374			−0.123687	+	0.992321i	$0.539472\pi$
$618$	22483.0	+	68870.3i	0.0588677	+	0.180325i
$619$			106928.i			0.279069i	0.990217	+	0.139534i	$0.0445606\pi$
$619$			106928.i			0.279069i	−0.990217	+	0.139534i	$0.955439\pi$
$620$	70237.7	+	96112.0i	0.182720	+	0.250031i
$621$	−59249.4			−0.153639
$622$	−269178.	+	87874.1i	−0.695758	+	0.227133i
$623$			179032.i			0.461268i
$624$	−95599.1	−	30476.6i	−0.245519	−	0.0782704i
$625$	−488197.			−1.24978
$626$	13327.0	+	40823.5i	0.0340082	+	0.104175i
$627$		−	95247.3i		−	0.242280i
$628$	108071.	−	78977.4i	0.274025	−	0.200255i
$629$	144296.			0.364714
$630$	270338.	−	88253.1i	0.681125	−	0.222356i
$631$		−	176805.i		−	0.444055i	−0.975040	−	0.222028i	$-0.928733\pi$
$631$		−	176805.i		−	0.444055i	0.975040	−	0.222028i	$-0.0712675\pi$
$632$	105885.	−	147022.i	0.265095	−	0.368084i
$633$	−205493.			−0.512849
$634$	−75202.5	−	230362.i	−0.187091	−	0.573102i
$635$			876713.i			2.17425i
$636$	−111192.	−	152154.i	−0.274891	−	0.376156i
$637$	135530.			0.334008
$638$	−61248.8	+	19994.9i	−0.150472	+	0.0491222i
$639$		−	503856.i		−	1.23397i
$640$	404935.	−	300253.i	0.988610	−	0.733040i
$641$	356149.			0.866794			0.433397	−	0.901203i	$-0.357315\pi$
$641$	356149.			0.866794			0.433397	+	0.901203i	$0.357315\pi$
$642$	79164.0	+	242497.i	0.192069	+	0.588350i
$643$		−	76843.8i		−	0.185860i	−0.995673	−	0.0929302i	$-0.970377\pi$
$643$		−	76843.8i		−	0.185860i	0.995673	−	0.0929302i	$-0.0296233\pi$
$644$	−48415.7	+	35381.8i	−0.116739	+	0.0853115i
$645$	219524.			0.527671
$646$	−62266.6	+	20327.2i	−0.149207	+	0.0487093i
$647$		−	725754.i		−	1.73373i	−0.498545	−	0.866864i	$-0.666132\pi$
$647$		−	725754.i		−	1.73373i	0.498545	−	0.866864i	$-0.333868\pi$
$648$	185507.	+	133603.i	0.441785	+	0.318175i
$649$	−429025.			−1.01858
$650$	−43417.5	−	132997.i	−0.102763	−	0.314786i
$651$		−	29618.5i		−	0.0698877i
$652$	301178.	+	412127.i	0.708482	+	0.969473i
$653$	45577.6			0.106887			0.0534435	−	0.998571i	$-0.482980\pi$
$653$	45577.6			0.106887			0.0534435	+	0.998571i	$0.482980\pi$
$654$	233032.	−	76074.1i	0.544828	−	0.177861i
$655$		−	570865.i		−	1.33061i
$656$	100574.	−	315480.i	0.233710	−	0.733101i
$657$	−22934.1			−0.0531314
$658$	26056.3	+	79816.2i	0.0601813	+	0.184348i
$659$			164180.i			0.378050i	0.981972	+	0.189025i	$0.0605327\pi$
$659$			164180.i			0.378050i	−0.981972	+	0.189025i	$0.939467\pi$
$660$	−149679.	+	109384.i	−0.343616	+	0.251111i
$661$	−140067.			−0.320576			−0.160288	−	0.987070i	$-0.551242\pi$
$661$	−140067.			−0.320576			−0.160288	+	0.987070i	$0.551242\pi$
$662$	24555.0	−	8016.07i	0.0560304	−	0.0182913i
$663$		−	25376.0i		−	0.0577293i
$664$	−60486.7	+	83985.6i	−0.137190	+	0.190488i
$665$	264419.			0.597928
$666$	−188145.	−	576330.i	−0.424175	−	1.29934i
$667$			17008.0i			0.0382297i
$668$	−41899.0	−	57333.8i	−0.0938968	−	0.128487i
$669$	−235108.			−0.525310
$670$	−333470.	+	108863.i	−0.742861	+	0.242510i
$671$		−	545536.i		−	1.21165i
$672$	−125423.	+	869.965i	−0.277740	+	0.00192648i
$673$	100807.			0.222568			0.111284	−	0.993789i	$-0.464504\pi$
$673$	100807.			0.222568			0.111284	+	0.993789i	$0.464504\pi$
$674$	49374.7	+	151245.i	0.108689	+	0.332937i
$675$		−	172792.i		−	0.379243i
$676$	216240.	−	158026.i	0.473199	−	0.345809i
$677$	392318.			0.855974			0.427987	−	0.903785i	$-0.359223\pi$
$677$	392318.			0.855974			0.427987	+	0.903785i	$0.359223\pi$
$678$	110195.	−	35973.5i	0.239718	−	0.0782569i
$679$		−	579051.i		−	1.25596i
$680$	103452.	+	74506.5i	0.223729	+	0.161130i
$681$	−325371.			−0.701591
$682$	−31357.0	−	96053.2i	−0.0674164	−	0.206511i
$683$		−	141613.i		−	0.303573i	−0.988413	−	0.151786i	$-0.951497\pi$
$683$		−	141613.i		−	0.303573i	0.988413	−	0.151786i	$-0.0485025\pi$
$684$	162377.	+	222194.i	0.347067	+	0.474920i
$685$	−1.04411e6			−2.22519
$686$	471261.	−	153845.i	1.00141	−	0.326916i
$687$		−	109820.i		−	0.232684i
$688$	482736.	+	153894.i	1.01984	+	0.325121i
$689$	−355247.			−0.748329
$690$	15187.2	+	46521.9i	0.0318993	+	0.0977145i
$691$			575255.i			1.20477i	0.798205	+	0.602385i	$0.205783\pi$
$691$			575255.i			1.20477i	−0.798205	+	0.602385i	$0.794217\pi$
$692$	72762.1	−	53173.8i	0.151947	−	0.111042i
$693$	−241380.			−0.502614
$694$	−584097.	+	190681.i	−1.21274	+	0.395902i
$695$			914638.i			1.89356i
$696$	−20789.9	+	28866.7i	−0.0429175	+	0.0595908i
$697$	83741.6			0.172376
$698$	231715.	+	709793.i	0.475601	+	1.45687i
$699$		−	28191.5i		−	0.0576985i
$700$	−103186.	−	141198.i	−0.210583	−	0.288158i
$701$	469781.			0.956003			0.478002	−	0.878359i	$-0.341361\pi$
$701$	469781.			0.956003			0.478002	+	0.878359i	$0.341361\pi$
$702$	−222076.	+	72497.7i	−0.450638	+	0.147113i
$703$		−	563710.i		−	1.14063i
$704$	−405828.	+	135606.i	−0.818835	+	0.273611i
$705$	68520.6			0.137861
$706$	−154511.	−	473300.i	−0.309991	−	0.949571i
$707$			238515.i			0.477173i
$708$	−191253.	+	139766.i	−0.381541	+	0.278826i
$709$	−604441.			−1.20243			−0.601217	−	0.799085i	$-0.705317\pi$
$709$	−604441.			−1.20243			−0.601217	+	0.799085i	$0.705317\pi$
$710$	−866843.	+	282984.i	−1.71959	+	0.561366i
$711$		−	192520.i		−	0.380835i
$712$	273640.	+	197076.i	0.539783	+	0.388754i
$713$	−26672.7			−0.0524672
$714$	−9843.98	−	30154.3i	−0.0193097	−	0.0591497i
$715$			349470.i			0.683593i
$716$	168906.	+	231128.i	0.329472	+	0.450844i
$717$	123034.			0.239324
$718$	412251.	−	134581.i	0.799674	−	0.261057i
$719$			251213.i			0.485942i	0.970034	+	0.242971i	$0.0781219\pi$
$719$			251213.i			0.485942i	−0.970034	+	0.242971i	$0.921878\pi$
$720$	162696.	−	510345.i	0.313843	−	0.984463i
$721$	170712.			0.328394
$722$	−82362.4	−	252294.i	−0.157999	−	0.483986i
$723$		−	211447.i		−	0.404505i
$724$	−642581.	+	469592.i	−1.22589	+	0.895867i
$725$	−49601.3			−0.0943663
$726$	−51105.7	+	16683.6i	−0.0969607	+	0.0316532i
$727$			323010.i			0.611148i	0.952168	+	0.305574i	$0.0988484\pi$
$727$			323010.i			0.611148i	−0.952168	+	0.305574i	$0.901152\pi$
$728$	−138177.	+	191858.i	−0.260719	+	0.362007i
$729$	86070.7			0.161957
$730$	12880.7	+	39456.3i	0.0241709	+	0.0740407i
$731$			128138.i			0.239797i
$732$	−177722.	−	243191.i	−0.331680	−	0.453865i
$733$	−306118.			−0.569745			−0.284873	−	0.958565i	$-0.591951\pi$
$733$	−306118.			−0.569745			−0.284873	+	0.958565i	$0.591951\pi$
$734$	−52868.8	+	17259.3i	−0.0981313	+	0.0320354i
$735$		−	138258.i		−	0.255927i
$736$	783.441	+	112949.i	0.00144627	+	0.208509i
$737$	297749.			0.548171
$738$	−109190.	−	334472.i	−0.200479	−	0.614111i
$739$			508237.i			0.930631i	0.885145	+	0.465315i	$0.154059\pi$
$739$			508237.i			0.930631i	−0.885145	+	0.465315i	$0.845941\pi$
$740$	−885859.	+	647377.i	−1.61771	+	1.18221i
$741$	−99134.7			−0.180547
$742$	−422140.	+	137809.i	−0.766741	+	0.250306i
$743$			336681.i			0.609876i	0.952372	+	0.304938i	$0.0986357\pi$
$743$			336681.i			0.609876i	−0.952372	+	0.304938i	$0.901364\pi$
$744$	−45270.2	−	32603.7i	−0.0817836	−	0.0589008i
$745$	−368420.			−0.663790
$746$	73785.2	+	226020.i	0.132584	+	0.406134i
$747$			109976.i			0.197087i
$748$	−63848.5	−	87369.1i	−0.114116	−	0.156155i
$749$	601089.			1.07146
$750$	127926.	−	41761.8i	0.227423	−	0.0742432i
$751$			303171.i			0.537537i	0.963205	+	0.268768i	$0.0866166\pi$
$751$			303171.i			0.537537i	−0.963205	+	0.268768i	$0.913383\pi$
$752$	150677.	+	48035.3i	0.266448	+	0.0849425i
$753$	55111.3			0.0971965
$754$	20811.0	+	63748.6i	0.0366058	+	0.112132i
$755$			1.30569e6i			2.29058i
$756$	−235769.	+	172298.i	−0.412519	+	0.301465i
$757$	843629.			1.47218			0.736088	−	0.676886i	$-0.236671\pi$
$757$	843629.			1.47218			0.736088	+	0.676886i	$0.236671\pi$
$758$	−262743.	+	85773.6i	−0.457292	+	0.149285i
$759$		−	41538.5i		−	0.0721053i
$760$	291070.	−	404149.i	0.503929	−	0.699704i
$761$	539703.			0.931934			0.465967	−	0.884802i	$-0.345706\pi$
$761$	539703.			0.931934			0.465967	+	0.884802i	$0.345706\pi$
$762$	−127508.	−	390586.i	−0.219598	−	0.672677i
$763$		−	577627.i		−	0.992199i
$764$	−133617.	−	182839.i	−0.228915	−	0.313244i
$765$	135467.			0.231479
$766$	162602.	−	53082.2i	0.277121	−	0.0904672i
$767$			446535.i			0.759041i
$768$	−136735.	+	192660.i	−0.231823	+	0.326639i
$769$	439096.			0.742518			0.371259	−	0.928529i	$-0.378926\pi$
$769$	439096.			0.742518			0.371259	+	0.928529i	$0.378926\pi$
$770$	135568.	+	415274.i	0.228652	+	0.700412i
$771$			132208.i			0.222407i
$772$	−176828.	+	129224.i	−0.296700	+	0.216825i
$773$	−81700.0			−0.136730			−0.0683648	−	0.997660i	$-0.521778\pi$
$773$	−81700.0			−0.136730			−0.0683648	+	0.997660i	$0.521778\pi$
$774$	511796.	−	167078.i	0.854309	−	0.278893i
$775$		−	77787.1i		−	0.129510i
$776$	−885048.	−	637414.i	−1.46975	−	1.05852i
$777$	272992.			0.452176
$778$	36086.2	+	110540.i	0.0596186	+	0.182625i
$779$		−	327148.i		−	0.539099i
$780$	113849.	+	155788.i	0.187128	+	0.256062i
$781$	773988.			1.26891
$782$	−27155.2	+	8864.93i	−0.0444058	+	0.0144965i
$783$			82823.3i			0.135092i
$784$	96923.7	−	304031.i	0.157688	−	0.494635i
$785$	−257403.			−0.417709
$786$	83026.1	+	254327.i	0.134391	+	0.411668i
$787$			1.08194e6i			1.74685i	0.486963	+	0.873423i	$0.338105\pi$
$787$			1.08194e6i			1.74685i	−0.486963	+	0.873423i	$0.661895\pi$
$788$	772678.	−	564665.i	1.24436	−	0.909366i
$789$	−48632.5			−0.0781218
$790$	−331215.	+	108126.i	−0.530708	+	0.173252i
$791$		−	273145.i		−	0.436556i
$792$	−265709.	+	368936.i	−0.423600	+	0.588167i
$793$	−567801.			−0.902922
$794$	−171127.	−	524200.i	−0.271443	−	0.831489i
$795$			362398.i			0.573392i
$796$	−662069.	−	905963.i	−1.04491	−	1.42983i
$797$	701652.			1.10460			0.552300	−	0.833645i	$-0.313750\pi$
$797$	701652.			1.10460			0.552300	+	0.833645i	$0.313750\pi$
$798$	−117802.	+	38456.8i	−0.184989	+	0.0603904i
$799$			39996.1i			0.0626504i
$800$	−329399.	+	2284.79i	−0.514686	+	0.00356999i
$801$	358322.			0.558481
$802$	321005.	+	983308.i	0.499072	+	1.52877i
$803$		−	35229.8i		−	0.0546360i
$804$	132732.	−	96999.2i	0.205335	−	0.150057i
$805$	115316.			0.177950
$806$	−99973.6	+	32636.8i	−0.153892	+	0.0502386i
$807$			259608.i			0.398631i
$808$	364557.	+	262555.i	0.558396	+	0.402158i
$809$	902290.			1.37863			0.689317	−	0.724459i	$-0.257911\pi$
$809$	902290.			1.37863			0.689317	+	0.724459i	$0.257911\pi$
$810$	−136430.	−	417916.i	−0.207941	−	0.636969i
$811$			683466.i			1.03914i	0.854427	+	0.519571i	$0.173908\pi$
$811$			683466.i			1.03914i	−0.854427	+	0.519571i	$0.826092\pi$
$812$	49459.3	+	67679.2i	0.0750129	+	0.102646i
$813$	−107339.			−0.162397
$814$	885317.	−	289015.i	1.33613	−	0.436187i
$815$		−	981600.i		−	1.47781i
$816$	−56925.3	−	18147.6i	−0.0854919	−	0.0272545i
$817$	500589.			0.749959
$818$	−261827.	−	802034.i	−0.391299	−	1.19863i
$819$			251232.i			0.374547i
$820$	−514106.	+	375703.i	−0.764583	+	0.558750i
$821$	1.05149e6			1.55997			0.779987	−	0.625796i	$-0.215226\pi$
$821$	1.05149e6			1.55997			0.779987	+	0.625796i	$0.215226\pi$
$822$	465165.	−	151855.i	0.688436	−	0.224743i
$823$		−	1.02055e6i		−	1.50673i	−0.657601	−	0.753366i	$-0.728429\pi$
$823$		−	1.02055e6i		−	1.50673i	0.657601	−	0.753366i	$-0.271571\pi$
$824$	187919.	−	260925.i	0.276768	−	0.384291i
$825$	121141.			0.177985
$826$	173222.	+	530617.i	0.253889	+	0.777716i
$827$		−	327743.i		−	0.479206i	−0.970871	−	0.239603i	$-0.922983\pi$
$827$		−	327743.i		−	0.479206i	0.970871	−	0.239603i	$-0.0770173\pi$
$828$	70814.7	+	96901.5i	0.103291	+	0.141342i
$829$	−1.17863e6			−1.71502			−0.857508	−	0.514471i	$-0.827988\pi$
$829$	−1.17863e6			−1.71502			−0.857508	+	0.514471i	$0.827988\pi$
$830$	189205.	−	61766.8i	0.274648	−	0.0896600i
$831$		−	260521.i		−	0.377261i
$832$	141141.	+	422391.i	0.203895	+	0.610195i
$833$	80702.5			0.116305
$834$	−133024.	−	407482.i	−0.191249	−	0.585836i
$835$			136557.i			0.195858i
$836$	−341319.	+	249432.i	−0.488369	+	0.356895i
$837$	−129888.			−0.185403
$838$	−912505.	+	297891.i	−1.29941	+	0.424199i
$839$		−	738323.i		−	1.04887i	−0.851450	−	0.524436i	$-0.824276\pi$
$839$		−	738323.i		−	1.04887i	0.851450	−	0.524436i	$-0.175724\pi$
$840$	195720.	+	140958.i	0.277381	+	0.199771i
$841$	−683506.			−0.966385
$842$	−299210.	−	916545.i	−0.422038	−	1.29279i
$843$			200650.i			0.282347i
$844$	538143.	+	736385.i	0.755462	+	1.03376i
$845$	−515039.			−0.721318
$846$	159748.	−	52150.4i	0.223200	−	0.0728646i
$847$			126678.i			0.176577i
$848$	−254054.	+	796917.i	−0.353292	+	1.10821i
$849$	−1166.48			−0.00161832
$850$	−25853.3	−	79194.3i	−0.0357831	−	0.109611i
$851$		−	245841.i		−	0.339465i
$852$	345032.	−	252146.i	0.475313	−	0.347354i
$853$	−705779.			−0.969997			−0.484999	−	0.874515i	$-0.661180\pi$
$853$	−705779.			−0.969997			−0.484999	+	0.874515i	$0.661180\pi$
$854$	−674718.	+	220264.i	−0.925137	+	0.302015i
$855$		−	529220.i		−	0.723942i
$856$	661673.	−	918731.i	0.903017	−	1.25384i
$857$	−219749.			−0.299203			−0.149601	−	0.988746i	$-0.547799\pi$
$857$	−219749.			−0.299203			−0.149601	+	0.988746i	$0.547799\pi$
$858$	−50826.6	−	155693.i	−0.0690425	−	0.211492i
$859$		−	959328.i		−	1.30011i	−0.759886	−	0.650056i	$-0.774745\pi$
$859$		−	959328.i		−	1.30011i	0.759886	−	0.650056i	$-0.225255\pi$
$860$	−574888.	−	786666.i	−0.777295	−	1.06364i
$861$	158430.			0.213713
$862$	−523797.	+	170996.i	−0.704934	+	0.230129i
$863$		−	1.35441e6i		−	1.81856i	−0.416181	−	0.909282i	$-0.636632\pi$
$863$		−	1.35441e6i		−	1.81856i	0.416181	−	0.909282i	$-0.363368\pi$
$864$	3815.11	+	550024.i	0.00511069	+	0.736808i
$865$	−173304.			−0.231620
$866$	−89577.4	−	274395.i	−0.119444	−	0.365882i
$867$			285974.i			0.380442i
$868$	−106138.	+	77564.4i	−0.140874	+	0.102949i
$869$	295735.			0.391619
$870$	65031.8	−	21229.9i	0.0859186	−	0.0280485i
$871$		−	309902.i		−	0.408496i
$872$	−882872.	−	635847.i	−1.16109	−	0.836218i
$873$	−1.15894e6			−1.52066
$874$	34632.0	+	106085.i	0.0453372	+	0.138878i
$875$		−	317096.i		−	0.414166i
$876$	−11477.0	−	15704.9i	−0.0149561	−	0.0204657i
$877$	428963.			0.557725			0.278863	−	0.960331i	$-0.410043\pi$
$877$	428963.			0.557725			0.278863	+	0.960331i	$0.410043\pi$
$878$	1.27322e6	−	415647.i	1.65163	−	0.539182i
$879$			387155.i			0.501080i
$880$	783956.	+	249922.i	1.01234	+	0.322730i
$881$	−266986.			−0.343983			−0.171991	−	0.985098i	$-0.555020\pi$
$881$	−266986.			−0.343983			−0.171991	+	0.985098i	$0.555020\pi$
$882$	−105227.	−	322333.i	−0.135266	−	0.414350i
$883$			1.02496e6i			1.31458i	0.753638	+	0.657290i	$0.228297\pi$
$883$			1.02496e6i			1.31458i	−0.753638	+	0.657290i	$0.771703\pi$
$884$	−90935.0	+	66454.4i	−0.116366	+	0.0850392i
$885$	455524.			0.581600
$886$	−430826.	+	140645.i	−0.548825	+	0.179166i
$887$			825747.i			1.04954i	0.851244	+	0.524771i	$0.175849\pi$
$887$			825747.i			1.04954i	−0.851244	+	0.524771i	$0.824151\pi$
$888$	300507.	−	417253.i	0.381091	−	0.529143i
$889$	−968165.			−1.22503
$890$	−201247.	−	616464.i	−0.254068	−	0.778265i
$891$			373149.i			0.470031i
$892$	615699.	+	842511.i	0.773817	+	1.05888i
$893$	156250.			0.195937
$894$	164135.	−	53582.7i	0.205365	−	0.0670424i
$895$		−	550497.i		−	0.687241i
$896$	331573.	+	447175.i	0.413013	+	0.557008i
$897$	−43233.8			−0.0537327
$898$	−334681.	−	1.02520e6i	−0.415029	−	1.27132i
$899$			37285.1i			0.0461335i
$900$	−282600.	+	206521.i	−0.348888	+	0.254964i
$901$	−211535.			−0.260575
$902$	513791.	−	167729.i	0.631500	−	0.206156i
$903$			242424.i			0.297303i
$904$	−417487.	−	300675.i	−0.510865	−	0.367927i
$905$	1.53049e6			1.86868
$906$	−189898.	−	581700.i	−0.231348	−	0.708668i
$907$		−	1.30607e6i		−	1.58765i	−0.608149	−	0.793823i	$-0.708088\pi$
$907$		−	1.30607e6i		−	1.58765i	0.608149	−	0.793823i	$-0.291912\pi$
$908$	852077.	+	1.16597e6i	1.03349	+	1.41421i
$909$	477374.			0.577739
$910$	432223.	−	141101.i	0.521946	−	0.170391i
$911$		−	165146.i		−	0.198991i	−0.995038	−	0.0994953i	$-0.968277\pi$
$911$		−	165146.i		−	0.198991i	0.995038	−	0.0994953i	$-0.0317228\pi$
$912$	−70895.8	+	222386.i	−0.0852375	+	0.267373i
$913$	−168938.			−0.202668
$914$	−172387.	−	528060.i	−0.206354	−	0.632107i
$915$			579231.i			0.691846i
$916$	−393539.	+	287595.i	−0.469026	+	0.342760i
$917$	630414.			0.749699
$918$	−132237.	+	43169.4i	−0.156916	+	0.0512260i
$919$			1.36219e6i			1.61289i	0.591307	+	0.806447i	$0.298612\pi$
$919$			1.36219e6i			1.61289i	−0.591307	+	0.806447i	$0.701388\pi$
$920$	126939.	−	176254.i	0.149975	−	0.208240i
$921$	−180601.			−0.212913
$922$	56281.6	+	172403.i	0.0662071	+	0.202807i
$923$		−	805577.i		−	0.945592i
$924$	−120794.	−	165293.i	−0.141482	−	0.193602i
$925$	716959.			0.837937
$926$	−93847.5	+	30636.9i	−0.109446	+	0.0357291i
$927$		−	341672.i		−	0.397603i
$928$	157888.	−	1095.15i	0.183339	−	0.00127168i
$929$	−189961.			−0.220106			−0.110053	−	0.993926i	$-0.535102\pi$
$929$	−189961.			−0.220106			−0.110053	+	0.993926i	$0.535102\pi$
$930$	33293.7	+	101986.i	0.0384943	+	0.117916i
$931$		−	315275.i		−	0.363739i
$932$	−101024.	+	73827.6i	−0.116304	+	0.0849938i
$933$	−255188.			−0.293155
$934$	1.48930e6	−	486189.i	1.70722	−	0.557328i
$935$			208095.i			0.238033i
$936$	383994.	+	276554.i	0.438301	+	0.315666i
$937$	895024.			1.01943			0.509713	−	0.860345i	$-0.329752\pi$
$937$	895024.			1.01943			0.509713	+	0.860345i	$0.329752\pi$
$938$	−120219.	−	368255.i	−0.136636	−	0.418546i
$939$			38701.9i			0.0438936i
$940$	−179441.	−	245544.i	−0.203079	−	0.277890i
$941$	−881205.			−0.995171			−0.497586	−	0.867415i	$-0.665780\pi$
$941$	−881205.			−0.995171			−0.497586	+	0.867415i	$0.665780\pi$
$942$	114676.	−	37436.4i	0.129232	−	0.0421884i
$943$		−	142673.i		−	0.160442i
$944$	1.00170e6	+	319338.i	1.12407	+	0.358349i
$945$	561553.			0.628821
$946$	256653.	+	786185.i	0.286790	+	0.878501i
$947$		−	810727.i		−	0.904013i	−0.892015	−	0.452006i	$-0.850708\pi$
$947$		−	810727.i		−	0.904013i	0.892015	−	0.452006i	$-0.149292\pi$
$948$	131834.	−	96343.1i	0.146694	−	0.107202i
$949$	−36667.6			−0.0407146
$950$	−309383.	+	100999.i	−0.342807	+	0.111911i
$951$		−	218390.i		−	0.241475i
$952$	−82278.6	+	114244.i	−0.0907847	+	0.126054i
$953$	−935492.			−1.03004			−0.515020	−	0.857178i	$-0.672216\pi$
$953$	−935492.			−1.03004			−0.515020	+	0.857178i	$0.672216\pi$
$954$	275818.	+	844890.i	0.303058	+	0.928333i
$955$			435484.i			0.477491i
$956$	−322199.	−	440892.i	−0.352540	−	0.482410i
$957$	−58065.7			−0.0634009
$958$	1.25371e6	−	409278.i	1.36605	−	0.445951i
$959$		−	1.15303e6i		−	1.25373i
$960$	430894.	−	143982.i	0.467550	−	0.156230i
$961$	865049.			0.936685
$962$	−300811.	−	921451.i	−0.325045	−	0.995685i
$963$		−	1.20305e6i		−	1.29727i
$964$	−757719.	+	553734.i	−0.815369	+	0.595864i
$965$	421168.			0.452273
$966$	−51374.7	+	16771.5i	−0.0550548	+	0.0179729i
$967$		−	179856.i		−	0.192341i	−0.995365	−	0.0961704i	$-0.969341\pi$
$967$		−	179856.i		−	0.192341i	0.995365	−	0.0961704i	$-0.0306594\pi$
$968$	193621.	+	139446.i	0.206634	+	0.148818i
$969$	−59030.6			−0.0628680
$970$	650904.	+	1.99386e6i	0.691789	+	2.11910i
$971$			1.18891e6i			1.26099i	0.776193	+	0.630495i	$0.217148\pi$
$971$			1.18891e6i			1.26099i	−0.776193	+	0.630495i	$0.782852\pi$
$972$	532305.	+	728397.i	0.563415	+	0.770966i
$973$	−1.01005e6			−1.06688
$974$	−1.61096e6	+	525905.i	−1.69812	+	0.554357i
$975$		−	126085.i		−	0.132634i
$976$	−406061.	+	1.27373e6i	−0.426277	+	1.33715i
$977$	461739.			0.483735			0.241867	−	0.970309i	$-0.422240\pi$
$977$	461739.			0.483735			0.241867	+	0.970309i	$0.422240\pi$
$978$	142763.	+	437314.i	0.149258	+	0.457210i
$979$			550429.i			0.574296i
$980$	−495448.	+	362068.i	−0.515877	+	0.376998i
$981$	−1.15609e6			−1.20131
$982$	−1.76966e6	+	577712.i	−1.83513	+	0.599085i
$983$			1.34200e6i			1.38882i	0.719579	+	0.694410i	$0.244335\pi$
$983$			1.34200e6i			1.38882i	−0.719579	+	0.694410i	$0.755665\pi$
$984$	174398.	−	242151.i	0.180116	−	0.250090i
$985$	−1.84036e6			−1.89683
$986$	12392.1	+	37959.6i	0.0127465	+	0.0390452i
$987$			75668.2i			0.0776746i
$988$	259613.	+	355249.i	0.265957	+	0.363931i
$989$	218313.			0.223196
$990$	831150.	−	271332.i	0.848025	−	0.276841i
$991$			1.73102e6i			1.76261i	0.472549	+	0.881304i	$0.343334\pi$
$991$			1.73102e6i			1.76261i	−0.472549	+	0.881304i	$0.656666\pi$
$992$	1717.47	+	247608.i	0.00174529	+	0.251618i
$993$	23278.8			0.0236082
$994$	−312503.	−	957266.i	−0.316287	−	0.968858i
$995$			2.15781e6i			2.17956i
$996$	−75309.8	+	55035.7i	−0.0759159	+	0.0554786i
$997$	−1.38355e6			−1.39189			−0.695945	−	0.718095i	$-0.745014\pi$
$997$	−1.38355e6			−1.39189			−0.695945	+	0.718095i	$0.745014\pi$
$998$	528270.	−	172456.i	0.530390	−	0.173148i
$999$		−	1.19717e6i		−	1.19956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.c.a.47.17	✓	44
4.3	odd	2	inner	92.5.c.a.47.18	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.c.a.47.17	✓	44	1.1	even	1	trivial
92.5.c.a.47.18	yes	44	4.3	odd	2	inner

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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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24134 - 3.80251i) q^{2} -3.60489i q^{3} +(-12.9181 + 9.44044i) q^{4} +30.7683 q^{5} +(-13.7076 + 4.47491i) q^{6} +33.9778i q^{7} +(51.9332 + 37.4025i) q^{8} +68.0048 q^{9} +(-38.1940 - 116.997i) q^{10} +104.464i q^{11} +(34.0318 + 46.5684i) q^{12} +108.728 q^{13} +(129.201 - 42.1781i) q^{14} -110.916i q^{15} +(77.7561 - 243.906i) q^{16} +64.7428 q^{17} +(-84.4173 - 258.589i) q^{18} -252.926i q^{19} +(-397.468 + 290.466i) q^{20} +122.486 q^{21} +(397.225 - 129.676i) q^{22} -110.304i q^{23} +(134.832 - 187.213i) q^{24} +321.686 q^{25} +(-134.968 - 413.438i) q^{26} -537.146i q^{27} +(-320.765 - 438.930i) q^{28} -154.191 q^{29} +(-421.760 + 137.685i) q^{30} -241.810i q^{31} +(-1023.98 + 7.10256i) q^{32} +376.581 q^{33} +(-80.3681 - 246.185i) q^{34} +1045.44i q^{35} +(-878.494 + 641.995i) q^{36} +2228.75 q^{37} +(-961.754 + 313.968i) q^{38} -391.951i q^{39} +(1597.89 + 1150.81i) q^{40} +1293.45 q^{41} +(-152.048 - 465.755i) q^{42} +1979.19i q^{43} +(-986.187 - 1349.48i) q^{44} +2092.39 q^{45} +(-419.432 + 136.925i) q^{46} +617.769i q^{47} +(-879.253 - 280.302i) q^{48} +1246.51 q^{49} +(-399.323 - 1223.21i) q^{50} -233.391i q^{51} +(-1404.56 + 1026.44i) q^{52} -3267.31 q^{53} +(-2042.50 + 666.783i) q^{54} +3214.18i q^{55} +(-1270.85 + 1764.58i) q^{56} -911.771 q^{57} +(191.405 + 586.314i) q^{58} +4106.92i q^{59} +(1047.10 + 1432.83i) q^{60} -5222.24 q^{61} +(-919.486 + 300.170i) q^{62} +2310.65i q^{63} +(1298.11 + 3884.86i) q^{64} +3345.36 q^{65} +(-467.467 - 1431.95i) q^{66} -2850.26i q^{67} +(-836.356 + 611.200i) q^{68} -397.634 q^{69} +(3975.29 - 1297.75i) q^{70} -7409.13i q^{71} +(3531.70 + 2543.54i) q^{72} -337.243 q^{73} +(-2766.65 - 8474.85i) q^{74} -1159.64i q^{75} +(2387.73 + 3267.33i) q^{76} -3549.46 q^{77} +(-1490.40 + 486.546i) q^{78} -2830.98i q^{79} +(2392.42 - 7504.56i) q^{80} +3572.03 q^{81} +(-1605.62 - 4918.36i) q^{82} +1617.19i q^{83} +(-1582.29 + 1156.32i) q^{84} +1992.02 q^{85} +(7525.89 - 2456.86i) q^{86} +555.843i q^{87} +(-3907.21 + 5425.15i) q^{88} +5269.08 q^{89} +(-2597.37 - 7956.32i) q^{90} +3694.33i q^{91} +(1041.32 + 1424.92i) q^{92} -871.700 q^{93} +(2349.07 - 766.864i) q^{94} -7782.10i q^{95} +(25.6039 + 3691.32i) q^{96} -17042.0 q^{97} +(-1547.35 - 4739.86i) q^{98} +7104.05i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 24 q^{5} + 33 q^{6} - 27 q^{8} - 1300 q^{9} - 46 q^{10} + 145 q^{12} + 472 q^{13} - 264 q^{14} + 272 q^{16} - 648 q^{17} + 1313 q^{18} + 324 q^{20} - 288 q^{21} + 796 q^{22} - 1028 q^{24} + 5604 q^{25}+ \cdots + 57204 q^{98}+O(q^{100}) \) 44 * q + 24 * q^5 + 33 * q^6 - 27 * q^8 - 1300 * q^9 - 46 * q^10 + 145 * q^12 + 472 * q^13 - 264 * q^14 + 272 * q^16 - 648 * q^17 + 1313 * q^18 + 324 * q^20 - 288 * q^21 + 796 * q^22 - 1028 * q^24 + 5604 * q^25 - 3015 * q^26 - 510 * q^28 - 840 * q^29 + 1390 * q^30 + 4200 * q^32 + 320 * q^33 - 4302 * q^34 - 3741 * q^36 - 680 * q^37 + 5940 * q^38 - 626 * q^40 + 7320 * q^41 + 1320 * q^42 - 378 * q^44 - 3240 * q^45 - 8813 * q^48 - 19444 * q^49 - 6960 * q^50 + 1519 * q^52 + 4152 * q^53 - 14405 * q^54 + 13026 * q^56 + 3840 * q^57 + 6771 * q^58 - 180 * q^60 + 6360 * q^61 + 9309 * q^62 - 12765 * q^64 - 15792 * q^65 - 5610 * q^66 - 5484 * q^68 + 4236 * q^70 + 39063 * q^72 - 2888 * q^73 + 43854 * q^74 - 13712 * q^76 + 4320 * q^77 + 18907 * q^78 + 12174 * q^80 + 31628 * q^81 - 31507 * q^82 - 16642 * q^84 - 1904 * q^85 - 25470 * q^86 + 540 * q^88 - 9768 * q^89 - 42044 * q^90 - 11136 * q^93 - 2219 * q^94 + 24435 * q^96 - 3752 * q^97 + 57204 * q^98

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