LMFDB - Embedded newform 135.5.h.a.89.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,5,Mod(44,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.44"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	135.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$13.9549450163$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.10
Character	$\chi$	$=$	135.89
Dual form			135.5.h.a.44.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.547257 + 0.947877i) q^{2} +(7.40102 + 12.8189i) q^{4} +(-6.73050 - 24.0770i) q^{5} +(16.9207 + 9.76914i) q^{7} -33.7133 q^{8} +(26.5053 + 6.79660i) q^{10} +(100.405 + 57.9690i) q^{11} +(158.728 - 91.6418i) q^{13} +(-18.5199 + 10.6925i) q^{14} +(-99.9665 + 173.147i) q^{16} +89.0232 q^{17} -52.2295 q^{19} +(258.829 - 264.472i) q^{20} +(-109.895 + 63.4480i) q^{22} +(232.002 + 401.839i) q^{23} +(-534.401 + 324.100i) q^{25} +200.607i q^{26} +289.206i q^{28} +(1255.41 + 724.811i) q^{29} +(767.942 + 1330.11i) q^{31} +(-379.121 - 656.657i) q^{32} +(-48.7186 + 84.3831i) q^{34} +(121.327 - 473.149i) q^{35} -641.462i q^{37} +(28.5830 - 49.5071i) q^{38} +(226.907 + 811.713i) q^{40} +(1195.31 - 690.111i) q^{41} +(1776.09 + 1025.43i) q^{43} +1716.12i q^{44} -507.859 q^{46} +(-589.129 + 1020.40i) q^{47} +(-1009.63 - 1748.73i) q^{49} +(-14.7527 - 683.912i) q^{50} +(2349.50 + 1356.49i) q^{52} -64.4267 q^{53} +(719.940 - 2807.62i) q^{55} +(-570.451 - 329.350i) q^{56} +(-1374.06 + 793.316i) q^{58} +(-2837.79 + 1638.40i) q^{59} +(929.409 - 1609.78i) q^{61} -1681.05 q^{62} -2369.02 q^{64} +(-3274.78 - 3204.90i) q^{65} +(-7257.38 + 4190.05i) q^{67} +(658.862 + 1141.18i) q^{68} +(382.090 + 373.937i) q^{70} -4564.71i q^{71} -8077.75i q^{73} +(608.027 + 351.045i) q^{74} +(-386.551 - 669.527i) q^{76} +(1132.62 + 1961.75i) q^{77} +(4328.70 - 7497.52i) q^{79} +(4841.68 + 1241.52i) q^{80} +1510.67i q^{82} +(1670.06 - 2892.62i) q^{83} +(-599.171 - 2143.41i) q^{85} +(-1943.96 + 1122.34i) q^{86} +(-3384.99 - 1954.33i) q^{88} -10168.3i q^{89} +3581.05 q^{91} +(-3434.10 + 5948.04i) q^{92} +(-644.811 - 1116.84i) q^{94} +(351.531 + 1257.53i) q^{95} +(11868.3 + 6852.15i) q^{97} +2210.10 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} - 6 q^{5} + 28 q^{10} - 228 q^{11} - 282 q^{14} - 1058 q^{16} - 8 q^{19} + 2196 q^{20} - 148 q^{25} - 2370 q^{29} - 1112 q^{31} - 436 q^{34} - 850 q^{40} - 1830 q^{41} - 5668 q^{46} + 5396 q^{49}+ \cdots - 58746 q^{95}+O(q^{100}) $ 44 * q - 162 * q^4 - 6 * q^5 + 28 * q^10 - 228 * q^11 - 282 * q^14 - 1058 * q^16 - 8 * q^19 + 2196 * q^20 - 148 * q^25 - 2370 * q^29 - 1112 * q^31 - 436 * q^34 - 850 * q^40 - 1830 * q^41 - 5668 * q^46 + 5396 * q^49 - 13524 * q^50 - 3072 * q^55 + 8250 * q^56 + 27348 * q^59 + 2782 * q^61 + 8348 * q^64 + 24906 * q^65 + 4782 * q^70 - 64728 * q^74 - 1776 * q^76 + 7900 * q^79 + 6766 * q^85 - 9192 * q^86 + 1560 * q^91 - 18826 * q^94 - 58746 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.547257	+	0.947877i	−0.136814	+	0.236969i	−0.926289	−	0.376814i	$-0.877020\pi$
$2$	−0.547257	+	0.947877i	−0.136814	+	0.236969i	0.789475	+	0.613783i	$0.210353\pi$
$3$		0			0
$3$		0			0
$4$	7.40102	+	12.8189i	0.462564	+	0.801184i
$5$	−6.73050	−	24.0770i	−0.269220	−	0.963079i
$5$	−6.73050	−	24.0770i	−0.269220	−	0.963079i
$6$		0			0
$7$	16.9207	+	9.76914i	0.345319	+	0.199370i	0.662622	−	0.748954i	$-0.269444\pi$
$7$	16.9207	+	9.76914i	0.345319	+	0.199370i	−0.317302	+	0.948324i	$0.602777\pi$
$8$	−33.7133			−0.526770
$9$		0			0
$10$	26.5053	+	6.79660i	0.265053	+	0.0679660i
$11$	100.405	+	57.9690i	0.829796	+	0.479083i	0.853783	−	0.520629i	$-0.174303\pi$
$11$	100.405	+	57.9690i	0.829796	+	0.479083i	−0.0239867	+	0.999712i	$0.507636\pi$
$12$		0			0
$13$	158.728	−	91.6418i	0.939220	−	0.542259i	0.0495044	−	0.998774i	$-0.484236\pi$
$13$	158.728	−	91.6418i	0.939220	−	0.542259i	0.889716	+	0.456515i	$0.150902\pi$
$14$	−18.5199	+	10.6925i	−0.0944893	+	0.0545534i
$15$		0			0
$16$	−99.9665	+	173.147i	−0.390494	+	0.676355i
$17$	89.0232			0.308039			0.154019	−	0.988068i	$-0.450778\pi$
$17$	89.0232			0.308039			0.154019	+	0.988068i	$0.450778\pi$
$18$		0			0
$19$	−52.2295			−0.144680			−0.0723400	−	0.997380i	$-0.523047\pi$
$19$	−52.2295			−0.144680			−0.0723400	+	0.997380i	$0.523047\pi$
$20$	258.829	−	264.472i	0.647072	−	0.661180i
$21$		0			0
$22$	−109.895	+	63.4480i	−0.227056	+	0.131091i
$23$	232.002	+	401.839i	0.438567	+	0.759621i	0.997579	−	0.0695388i	$-0.0221528\pi$
$23$	232.002	+	401.839i	0.438567	+	0.759621i	−0.559012	+	0.829160i	$0.688819\pi$
$24$		0			0
$25$	−534.401	+	324.100i	−0.855041	+	0.518560i
$26$			200.607i			0.296755i
$27$		0			0
$28$			289.206i			0.368886i
$29$	1255.41	+	724.811i	1.49276	+	0.861844i	0.999966	−	0.00830339i	$-0.00264308\pi$
$29$	1255.41	+	724.811i	1.49276	+	0.861844i	0.492792	+	0.870147i	$0.335976\pi$
$30$		0			0
$31$	767.942	+	1330.11i	0.799107	+	1.38409i	0.920198	+	0.391453i	$0.128027\pi$
$31$	767.942	+	1330.11i	0.799107	+	1.38409i	−0.121091	+	0.992641i	$0.538639\pi$
$32$	−379.121	−	656.657i	−0.370235	−	0.641266i
$33$		0			0
$34$	−48.7186	+	84.3831i	−0.0421441	+	0.0729957i
$35$	121.327	−	473.149i	0.0990423	−	0.386244i
$36$		0			0
$37$		−	641.462i		−	0.468562i	−0.972169	−	0.234281i	$-0.924726\pi$
$37$		−	641.462i		−	0.468562i	0.972169	−	0.234281i	$-0.0752736\pi$
$38$	28.5830	−	49.5071i	0.0197943	−	0.0342847i
$39$		0			0
$40$	226.907	+	811.713i	0.141817	+	0.507321i
$41$	1195.31	−	690.111i	0.711069	−	0.410536i	−0.100388	−	0.994948i	$-0.532008\pi$
$41$	1195.31	−	690.111i	0.711069	−	0.410536i	0.811457	+	0.584412i	$0.198675\pi$
$42$		0			0
$43$	1776.09	+	1025.43i	0.960568	+	0.554584i	0.896348	−	0.443351i	$-0.146211\pi$
$43$	1776.09	+	1025.43i	0.960568	+	0.554584i	0.0642203	+	0.997936i	$0.479544\pi$
$44$			1716.12i			0.886426i
$45$		0			0
$46$	−507.859			−0.240009
$47$	−589.129	+	1020.40i	−0.266695	+	0.461929i	−0.968006	−	0.250926i	$-0.919265\pi$
$47$	−589.129	+	1020.40i	−0.266695	+	0.461929i	0.701311	+	0.712855i	$0.252598\pi$
$48$		0			0
$49$	−1009.63	−	1748.73i	−0.420503	−	0.728333i
$50$	−14.7527	−	683.912i	−0.00590108	−	0.273565i
$51$		0			0
$52$	2349.50	+	1356.49i	0.868898	+	0.501659i
$53$	−64.4267			−0.0229358			−0.0114679	−	0.999934i	$-0.503650\pi$
$53$	−64.4267			−0.0229358			−0.0114679	+	0.999934i	$0.503650\pi$
$54$		0			0
$55$	719.940	−	2807.62i	0.237997	−	0.928138i
$56$	−570.451	−	329.350i	−0.181904	−	0.105022i
$57$		0			0
$58$	−1374.06	+	793.316i	−0.408461	+	0.235825i
$59$	−2837.79	+	1638.40i	−0.815223	+	0.470669i	−0.848766	−	0.528768i	$-0.822654\pi$
$59$	−2837.79	+	1638.40i	−0.815223	+	0.470669i	0.0335434	+	0.999437i	$0.489321\pi$
$60$		0			0
$61$	929.409	−	1609.78i	0.249774	−	0.432621i	−0.713689	−	0.700463i	$-0.752977\pi$
$61$	929.409	−	1609.78i	0.249774	−	0.432621i	0.963463	+	0.267842i	$0.0863104\pi$
$62$	−1681.05			−0.437317
$63$		0			0
$64$	−2369.02			−0.578374
$65$	−3274.78	−	3204.90i	−0.775095	−	0.758556i
$66$		0			0
$67$	−7257.38	+	4190.05i	−1.61670	+	0.933404i	−0.628938	+	0.777455i	$0.716510\pi$
$67$	−7257.38	+	4190.05i	−1.61670	+	0.933404i	−0.987765	+	0.155949i	$0.950156\pi$
$68$	658.862	+	1141.18i	0.142488	+	0.246796i
$69$		0			0
$70$	382.090	+	373.937i	0.0779777	+	0.0763137i
$71$		−	4564.71i		−	0.905517i	−0.891633	−	0.452759i	$-0.850440\pi$
$71$		−	4564.71i		−	0.905517i	0.891633	−	0.452759i	$-0.149560\pi$
$72$		0			0
$73$		−	8077.75i		−	1.51581i	−0.652365	−	0.757905i	$-0.726223\pi$
$73$		−	8077.75i		−	1.51581i	0.652365	−	0.757905i	$-0.273777\pi$
$74$	608.027	+	351.045i	0.111035	+	0.0641060i
$75$		0			0
$76$	−386.551	−	669.527i	−0.0669237	−	0.115915i
$77$	1132.62	+	1961.75i	0.191030	+	0.330873i
$78$		0			0
$79$	4328.70	−	7497.52i	0.693590	−	1.20133i	−0.277063	−	0.960852i	$-0.589361\pi$
$79$	4328.70	−	7497.52i	0.693590	−	1.20133i	0.970654	−	0.240482i	$-0.0773054\pi$
$80$	4841.68	+	1241.52i	0.756512	+	0.193988i
$81$		0			0
$82$			1510.67i			0.224669i
$83$	1670.06	−	2892.62i	0.242424	−	0.419890i	−0.718981	−	0.695030i	$-0.755391\pi$
$83$	1670.06	−	2892.62i	0.242424	−	0.419890i	0.961404	+	0.275140i	$0.0887243\pi$
$84$		0			0
$85$	−599.171	−	2143.41i	−0.0829302	−	0.296666i
$86$	−1943.96	+	1122.34i	−0.262839	+	0.151750i
$87$		0			0
$88$	−3384.99	−	1954.33i	−0.437112	−	0.252367i
$89$		−	10168.3i		−	1.28371i	−0.766825	−	0.641856i	$-0.778165\pi$
$89$		−	10168.3i		−	1.28371i	0.766825	−	0.641856i	$-0.221835\pi$
$90$		0			0
$91$	3581.05			0.432441
$92$	−3434.10	+	5948.04i	−0.405731	+	0.702746i
$93$		0			0
$94$	−644.811	−	1116.84i	−0.0729754	−	0.126397i
$95$	351.531	+	1257.53i	0.0389508	+	0.139338i
$96$		0			0
$97$	11868.3	+	6852.15i	1.26137	+	0.728255i	0.973340	−	0.229365i	$-0.0736649\pi$
$97$	11868.3	+	6852.15i	1.26137	+	0.728255i	0.288034	+	0.957620i	$0.406998\pi$
$98$	2210.10			0.230123
$99$		0			0
$100$	−8109.73	−	4451.78i	−0.810973	−	0.445178i
$101$	−6147.82	−	3549.45i	−0.602668	−	0.347951i	0.167422	−	0.985885i	$-0.446456\pi$
$101$	−6147.82	−	3549.45i	−0.602668	−	0.347951i	−0.770091	+	0.637935i	$0.779789\pi$
$102$		0			0
$103$	−4058.54	+	2343.20i	−0.382557	+	0.220869i	−0.678930	−	0.734203i	$-0.737556\pi$
$103$	−4058.54	+	2343.20i	−0.382557	+	0.220869i	0.296373	+	0.955072i	$0.404223\pi$
$104$	−5351.25	+	3089.54i	−0.494753	+	0.285646i
$105$		0			0
$106$	35.2580	−	61.0686i	0.00313795	−	0.00543509i
$107$	−20235.1			−1.76741			−0.883705	−	0.468044i	$-0.844959\pi$
$107$	−20235.1			−1.76741			−0.883705	+	0.468044i	$0.844959\pi$
$108$		0			0
$109$	2264.65			0.190611			0.0953053	−	0.995448i	$-0.469617\pi$
$109$	2264.65			0.190611			0.0953053	+	0.995448i	$0.469617\pi$
$110$	2267.28	+	2218.90i	0.187379	+	0.183380i
$111$		0			0
$112$	−3383.00	+	1953.17i	−0.269690	+	0.155706i
$113$	−5005.26	−	8669.36i	−0.391985	−	0.678938i	0.600726	−	0.799455i	$-0.294878\pi$
$113$	−5005.26	−	8669.36i	−0.391985	−	0.678938i	−0.992711	+	0.120517i	$0.961545\pi$
$114$		0			0
$115$	8113.58	−	8290.49i	0.613503	−	0.626880i
$116$			21457.4i			1.59463i
$117$		0			0
$118$		−	3586.50i		−	0.257577i
$119$	1506.33	+	869.680i	0.106372	+	0.0614138i
$120$		0			0
$121$	−599.679	−	1038.67i	−0.0409588	−	0.0709428i
$122$	1017.25	+	1761.93i	0.0683453	+	0.118378i
$123$		0			0
$124$	−11367.1	+	19688.4i	−0.739276	+	1.28046i
$125$	11400.1	+	10685.4i	0.729609	+	0.683865i
$126$		0			0
$127$			19581.7i			1.21406i	0.794677	+	0.607032i	$0.207640\pi$
$127$			19581.7i			1.21406i	−0.794677	+	0.607032i	$0.792360\pi$
$128$	7362.40	−	12752.0i	0.449365	−	0.778323i
$129$		0			0
$130$	4830.00	−	1350.18i	0.285799	−	0.0798925i
$131$	24663.9	−	14239.7i	1.43721	−	0.829773i	0.439553	−	0.898216i	$-0.355137\pi$
$131$	24663.9	−	14239.7i	1.43721	−	0.829773i	0.997655	+	0.0684439i	$0.0218034\pi$
$132$		0			0
$133$	−883.757	−	510.237i	−0.0499608	−	0.0288449i
$134$		−	9172.14i		−	0.510812i
$135$		0			0
$136$	−3001.26			−0.162266
$137$	−13118.2	+	22721.5i	−0.698931	+	1.21058i	0.269906	+	0.962887i	$0.413007\pi$
$137$	−13118.2	+	22721.5i	−0.698931	+	1.21058i	−0.968837	+	0.247698i	$0.920326\pi$
$138$		0			0
$139$	16654.1	+	28845.7i	0.861967	+	1.49297i	0.870027	+	0.493004i	$0.164101\pi$
$139$	16654.1	+	28845.7i	0.861967	+	1.49297i	−0.00805999	+	0.999968i	$0.502566\pi$
$140$	6963.21	−	1946.51i	0.355266	−	0.0993115i
$141$		0			0
$142$	4326.79	+	2498.07i	0.214580	+	0.123888i
$143$	21249.5			1.03915
$144$		0			0
$145$	9001.71	−	35104.8i	0.428143	−	1.66967i
$146$	7656.72	+	4420.61i	0.359201	+	0.207385i
$147$		0			0
$148$	8222.86	−	4747.47i	0.375405	−	0.216740i
$149$	4558.66	−	2631.94i	0.205336	−	0.118551i	−0.393806	−	0.919194i	$-0.628842\pi$
$149$	4558.66	−	2631.94i	0.205336	−	0.118551i	0.599142	+	0.800643i	$0.295509\pi$
$150$		0			0
$151$	−5636.90	+	9763.41i	−0.247222	+	0.428201i	−0.962754	−	0.270379i	$-0.912851\pi$
$151$	−5636.90	+	9763.41i	−0.247222	+	0.428201i	0.715532	+	0.698580i	$0.246184\pi$
$152$	1760.83			0.0762131
$153$		0			0
$154$	−2479.33			−0.104542
$155$	26856.5	−	27442.1i	1.11786	−	1.14223i
$156$		0			0
$157$	−17441.0	+	10069.5i	−0.707573	+	0.408517i	−0.810162	−	0.586207i	$-0.800621\pi$
$157$	−17441.0	+	10069.5i	−0.707573	+	0.408517i	0.102589	+	0.994724i	$0.467287\pi$
$158$	4737.82	+	8206.15i	0.189786	+	0.328719i
$159$		0			0
$160$	−13258.6	+	13547.7i	−0.517915	+	0.529208i
$161$			9065.85i			0.349749i
$162$		0			0
$163$		−	15388.7i		−	0.579197i	−0.957148	−	0.289598i	$-0.906478\pi$
$163$		−	15388.7i		−	0.579197i	0.957148	−	0.289598i	$-0.0935218\pi$
$164$	17693.0	+	10215.1i	0.657830	+	0.379798i
$165$		0			0
$166$	1827.90	+	3166.02i	0.0663340	+	0.114894i
$167$	−8523.96	−	14763.9i	−0.305639	−	0.529382i	0.671765	−	0.740765i	$-0.265537\pi$
$167$	−8523.96	−	14763.9i	−0.305639	−	0.529382i	−0.977403	+	0.211383i	$0.932203\pi$
$168$		0			0
$169$	2515.93	−	4357.72i	0.0880898	−	0.152576i
$170$	2359.59	+	605.055i	0.0816467	+	0.0209362i
$171$		0			0
$172$			30356.8i			1.02612i
$173$	−9704.36	+	16808.4i	−0.324246	+	0.561610i	−0.981359	−	0.192181i	$-0.938444\pi$
$173$	−9704.36	+	16808.4i	−0.324246	+	0.561610i	0.657114	+	0.753792i	$0.271777\pi$
$174$		0			0
$175$	−12208.6	+	263.352i	−0.398648	+	0.00859925i
$176$	−20074.3	+	11589.9i	−0.648061	+	0.374158i
$177$		0			0
$178$	9638.28	+	5564.66i	0.304200	+	0.175630i
$179$		−	6659.35i		−	0.207838i	−0.994586	−	0.103919i	$-0.966862\pi$
$179$		−	6659.35i		−	0.207838i	0.994586	−	0.103919i	$-0.0331383\pi$
$180$		0			0
$181$	−15739.8			−0.480443			−0.240221	−	0.970718i	$-0.577220\pi$
$181$	−15739.8			−0.480443			−0.240221	+	0.970718i	$0.577220\pi$
$182$	−1959.75	+	3394.39i	−0.0591642	+	0.102475i
$183$		0			0
$184$	−7821.55	−	13547.3i	−0.231024	−	0.400145i
$185$	−15444.5	+	4317.36i	−0.451262	+	0.126146i
$186$		0			0
$187$	8938.40	+	5160.59i	0.255609	+	0.147576i
$188$	−17440.6			−0.493454
$189$		0			0
$190$	−1384.36	−	354.983i	−0.0383479	−	0.00983332i
$191$	−25333.0	−	14626.0i	−0.694417	−	0.400922i	0.110847	−	0.993837i	$-0.464643\pi$
$191$	−25333.0	−	14626.0i	−0.694417	−	0.400922i	−0.805265	+	0.592915i	$0.797977\pi$
$192$		0			0
$193$	37232.0	−	21495.9i	0.999543	−	0.577086i	0.0914300	−	0.995812i	$-0.470856\pi$
$193$	37232.0	−	21495.9i	0.999543	−	0.577086i	0.908113	+	0.418725i	$0.137523\pi$
$194$	−12990.0	+	7499.78i	−0.345148	+	0.199271i
$195$		0			0
$196$	14944.5	−	25884.7i	0.389019	−	0.673800i
$197$	−48322.8			−1.24514			−0.622571	−	0.782563i	$-0.713912\pi$
$197$	−48322.8			−1.24514			−0.622571	+	0.782563i	$0.713912\pi$
$198$		0			0
$199$	10246.4			0.258740			0.129370	−	0.991596i	$-0.458705\pi$
$199$	10246.4			0.258740			0.129370	+	0.991596i	$0.458705\pi$
$200$	18016.4	−	10926.5i	0.450410	−	0.273162i
$201$		0			0
$202$	6728.88	−	3884.92i	0.164907	−	0.0952093i
$203$	14161.6	+	24528.5i	0.343652	+	0.595223i
$204$		0			0
$205$	−24660.8	−	24134.6i	−0.586813	−	0.574291i
$206$		−	5129.34i		−	0.120872i
$207$		0			0
$208$			36644.4i			0.846996i
$209$	−5244.12	−	3027.69i	−0.120055	−	0.0693137i
$210$		0			0
$211$	−5566.99	−	9642.31i	−0.125042	−	0.216579i	0.796707	−	0.604365i	$-0.206573\pi$
$211$	−5566.99	−	9642.31i	−0.125042	−	0.216579i	−0.921749	+	0.387786i	$0.873240\pi$
$212$	−476.823	−	825.882i	−0.0106093	−	0.0183758i
$213$		0			0
$214$	11073.8	−	19180.4i	0.241807	−	0.418822i
$215$	12735.2	−	49664.5i	0.275504	−	1.07441i
$216$		0			0
$217$			30008.5i			0.637273i
$218$	−1239.34	+	2146.61i	−0.0260783	+	0.0451689i
$219$		0			0
$220$	41319.0	−	11550.4i	0.853698	−	0.238644i
$221$	14130.5	−	8158.24i	0.289316	−	0.167037i
$222$		0			0
$223$	−41863.5	−	24169.9i	−0.841833	−	0.486032i	0.0160539	−	0.999871i	$-0.494890\pi$
$223$	−41863.5	−	24169.9i	−0.841833	−	0.486032i	−0.857887	+	0.513839i	$0.828223\pi$
$224$		−	14814.7i		−	0.295256i
$225$		0			0
$226$	10956.7			0.214517
$227$	−9830.70	+	17027.3i	−0.190780	+	0.330441i	−0.945509	−	0.325596i	$-0.894435\pi$
$227$	−9830.70	+	17027.3i	−0.190780	+	0.330441i	0.754729	+	0.656037i	$0.227768\pi$
$228$		0			0
$229$	−41057.9	−	71114.4i	−0.782935	−	1.35608i	−0.930225	−	0.366990i	$-0.880388\pi$
$229$	−41057.9	−	71114.4i	−0.782935	−	1.35608i	0.147290	−	0.989093i	$-0.452945\pi$
$230$	3418.15	+	12227.7i	0.0646153	+	0.231148i
$231$		0			0
$232$	−42323.9	−	24435.7i	−0.786340	−	0.453993i
$233$	36907.6			0.679837			0.339918	−	0.940455i	$-0.389601\pi$
$233$	36907.6			0.679837			0.339918	+	0.940455i	$0.389601\pi$
$234$		0			0
$235$	28533.3	+	7316.63i	0.516674	+	0.132488i
$236$	−42005.1	−	24251.7i	−0.754185	−	0.435429i
$237$		0			0
$238$	−1648.70	+	951.878i	−0.0291064	+	0.0168046i
$239$	−23140.0	+	13359.9i	−0.405105	+	0.233888i	−0.688684	−	0.725061i	$-0.741811\pi$
$239$	−23140.0	+	13359.9i	−0.405105	+	0.233888i	0.283579	+	0.958949i	$0.408478\pi$
$240$		0			0
$241$	−7637.82	+	13229.1i	−0.131503	+	0.227770i	−0.924256	−	0.381773i	$-0.875314\pi$
$241$	−7637.82	+	13229.1i	−0.131503	+	0.227770i	0.792753	+	0.609543i	$0.208647\pi$
$242$	1312.71			0.0224150
$243$		0			0
$244$	27514.3			0.462145
$245$	−35308.7	+	36078.6i	−0.588234	+	0.601059i
$246$		0			0
$247$	−8290.29	+	4786.40i	−0.135886	+	0.0784540i
$248$	−25889.8	−	44842.5i	−0.420946	−	0.729099i
$249$		0			0
$250$	−16367.2	+	4958.28i	−0.261876	+	0.0793324i
$251$			17504.6i			0.277847i	0.990303	+	0.138923i	$0.0443642\pi$
$251$			17504.6i			0.277847i	−0.990303	+	0.138923i	$0.955636\pi$
$252$		0			0
$253$			53795.8i			0.840441i
$254$	−18561.0	−	10716.2i	−0.287696	−	0.166101i
$255$		0			0
$256$	−10893.9	−	18868.8i	−0.166228	−	0.287915i
$257$	28510.3	+	49381.3i	0.431654	+	0.747647i	0.997016	−	0.0771960i	$-0.0245967\pi$
$257$	28510.3	+	49381.3i	0.431654	+	0.747647i	−0.565362	+	0.824843i	$0.691263\pi$
$258$		0			0
$259$	6266.53	−	10854.0i	0.0934174	−	0.161804i
$260$	16846.7	−	65698.7i	0.249212	−	0.971874i
$261$		0			0
$262$			31171.2i			0.454099i
$263$	29717.1	−	51471.5i	0.429630	−	0.744142i	−0.567210	−	0.823573i	$-0.691977\pi$
$263$	29717.1	−	51471.5i	0.429630	−	0.744142i	0.996840	+	0.0794316i	$0.0253105\pi$
$264$		0			0
$265$	433.624	+	1551.20i	0.00617479	+	0.0220890i
$266$	967.285	−	558.462i	0.0136707	−	0.00789279i
$267$		0			0
$268$	−107424.	−	62021.3i	−1.49566	−	0.863518i
$269$			107707.i			1.48847i	0.667919	+	0.744234i	$0.267185\pi$
$269$			107707.i			1.48847i	−0.667919	+	0.744234i	$0.732815\pi$
$270$		0			0
$271$	−11971.8			−0.163012			−0.0815059	−	0.996673i	$-0.525973\pi$
$271$	−11971.8			−0.163012			−0.0815059	+	0.996673i	$0.525973\pi$
$272$	−8899.33	+	15414.1i	−0.120287	+	0.208344i
$273$		0			0
$274$	−14358.1	−	24869.0i	−0.191248	−	0.331251i
$275$	−72444.5	+	1562.70i	−0.957943	+	0.0206638i
$276$		0			0
$277$	23205.3	+	13397.6i	0.302432	+	0.174609i	0.643535	−	0.765417i	$-0.277467\pi$
$277$	23205.3	+	13397.6i	0.302432	+	0.174609i	−0.341103	+	0.940026i	$0.610800\pi$
$278$	−36456.2			−0.471718
$279$		0			0
$280$	−4090.32	+	15951.4i	−0.0521725	+	0.203462i
$281$	−37711.0	−	21772.5i	−0.477591	−	0.275737i	0.241821	−	0.970321i	$-0.422255\pi$
$281$	−37711.0	−	21772.5i	−0.477591	−	0.275737i	−0.719412	+	0.694584i	$0.755589\pi$
$282$		0			0
$283$	53849.1	−	31089.8i	0.672366	−	0.388190i	−0.124607	−	0.992206i	$-0.539767\pi$
$283$	53849.1	−	31089.8i	0.672366	−	0.388190i	0.796972	+	0.604016i	$0.206434\pi$
$284$	58514.8	−	33783.5i	0.725486	−	0.418859i
$285$		0			0
$286$	−11629.0	+	20142.0i	−0.142170	+	0.246246i
$287$	26967.2			0.327395
$288$		0			0
$289$	−75595.9			−0.905112
$290$	28348.8	+	27743.9i	0.337084	+	0.329891i
$291$		0			0
$292$	103548.	−	59783.6i	1.21444	−	0.701159i
$293$	−8608.02	−	14909.5i	−0.100269	−	0.173672i	0.811526	−	0.584316i	$-0.198637\pi$
$293$	−8608.02	−	14909.5i	−0.100269	−	0.173672i	−0.911796	+	0.410644i	$0.865304\pi$
$294$		0			0
$295$	58547.5	+	57298.1i	0.672766	+	0.658410i
$296$			21625.8i			0.246825i
$297$		0			0
$298$			5761.40i			0.0648777i
$299$	73650.6	+	42522.2i	0.823822	+	0.475634i
$300$		0			0
$301$	20035.1	+	34701.8i	0.221135	+	0.383017i
$302$	−6169.67	−	10686.2i	−0.0676470	−	0.117168i
$303$		0			0
$304$	5221.20	−	9043.38i	0.0564967	−	0.0978551i
$305$	−45014.1	−	11542.7i	−0.483892	−	0.124082i
$306$		0			0
$307$		−	107387.i		−	1.13940i	−0.821854	−	0.569698i	$-0.807060\pi$
$307$		−	107387.i		−	1.13940i	0.821854	−	0.569698i	$-0.192940\pi$
$308$	−16765.0	+	29037.9i	−0.176727	+	0.306100i
$309$		0			0
$310$	11314.3	+	40474.5i	0.117735	+	0.421171i
$311$	118121.	−	68197.1i	1.22125	−	0.705091i	0.256068	−	0.966659i	$-0.417573\pi$
$311$	118121.	−	68197.1i	1.22125	−	0.705091i	0.965185	+	0.261568i	$0.0842395\pi$
$312$		0			0
$313$	81900.2	+	47285.1i	0.835981	+	0.482654i	0.855896	−	0.517148i	$-0.173006\pi$
$313$	81900.2	+	47285.1i	0.835981	+	0.482654i	−0.0199154	+	0.999802i	$0.506340\pi$
$314$		−	22042.5i		−	0.223564i
$315$		0			0
$316$	128147.			1.28332
$317$	70757.2	−	122555.i	0.704129	−	1.21959i	−0.262876	−	0.964830i	$-0.584671\pi$
$317$	70757.2	−	122555.i	0.704129	−	1.21959i	0.967005	−	0.254758i	$-0.0819957\pi$
$318$		0			0
$319$	84033.2	+	145550.i	0.825790	+	1.43031i
$320$	15944.7	+	57038.8i	0.155710	+	0.557020i
$321$		0			0
$322$	−8593.31	−	4961.35i	−0.0828798	−	0.0478507i
$323$	−4649.64			−0.0445670
$324$		0			0
$325$	−55123.3	+	100417.i	−0.521878	+	0.950696i
$326$	14586.6	+	8421.57i	0.137252	+	0.0792424i
$327$		0			0
$328$	−40297.7	+	23265.9i	−0.374570	+	0.216258i
$329$	−19936.9	+	11510.6i	−0.184190	+	0.106342i
$330$		0			0
$331$	−41375.6	+	71664.7i	−0.377649	+	0.654108i	−0.990720	−	0.135921i	$-0.956601\pi$
$331$	−41375.6	+	71664.7i	−0.377649	+	0.654108i	0.613071	+	0.790028i	$0.289934\pi$
$332$	49440.5			0.448545
$333$		0			0
$334$	18659.2			0.167263
$335$	149730.	+	146535.i	1.33419	+	1.30572i
$336$		0			0
$337$	−72053.4	+	41600.0i	−0.634446	+	0.366297i	−0.782472	−	0.622686i	$-0.786041\pi$
$337$	−72053.4	+	41600.0i	−0.634446	+	0.366297i	0.148026	+	0.988983i	$0.452708\pi$
$338$	2753.72	+	4769.59i	0.0241039	+	0.0417491i
$339$		0			0
$340$	23041.8	−	23544.1i	0.199323	−	0.203669i
$341$			178067.i			1.53135i
$342$		0			0
$343$		−	86364.2i		−	0.734084i
$344$	−59877.8	−	34570.5i	−0.505998	−	0.292138i
$345$		0			0
$346$	−10621.6	−	18397.1i	−0.0887230	−	0.153673i
$347$	−51814.1	−	89744.7i	−0.430317	−	0.745332i	0.566583	−	0.824005i	$-0.308265\pi$
$347$	−51814.1	−	89744.7i	−0.430317	−	0.745332i	−0.996900	+	0.0786729i	$0.974932\pi$
$348$		0			0
$349$	−75356.4	+	130521.i	−0.618685	+	1.07159i	0.371041	+	0.928616i	$0.379001\pi$
$349$	−75356.4	+	130521.i	−0.618685	+	1.07159i	−0.989726	+	0.142977i	$0.954332\pi$
$350$	6431.61	−	11716.4i	0.0525030	−	0.0956438i
$351$		0			0
$352$		−	87909.1i		−	0.709494i
$353$	−11068.8	+	19171.8i	−0.0888286	+	0.153856i	−0.907016	−	0.421096i	$-0.861646\pi$
$353$	−11068.8	+	19171.8i	−0.0888286	+	0.153856i	0.818188	+	0.574951i	$0.194979\pi$
$354$		0			0
$355$	−109904.	+	30722.8i	−0.872084	+	0.243783i
$356$	130347.	−	75255.6i	1.02849	−	0.593798i
$357$		0			0
$358$	6312.25	+	3644.38i	0.0492513	+	0.0284353i
$359$		−	90926.7i		−	0.705509i	−0.935716	−	0.352755i	$-0.885245\pi$
$359$		−	90926.7i		−	0.705509i	0.935716	−	0.352755i	$-0.114755\pi$
$360$		0			0
$361$	−127593.			−0.979068
$362$	8613.71	−	14919.4i	0.0657314	−	0.113850i
$363$		0			0
$364$	26503.4	+	45905.2i	0.200032	+	0.346465i
$365$	−194488.	+	54367.3i	−1.45984	+	0.408087i
$366$		0			0
$367$	−17103.7	−	9874.80i	−0.126986	−	0.0733156i	0.435161	−	0.900353i	$-0.356691\pi$
$367$	−17103.7	−	9874.80i	−0.126986	−	0.0733156i	−0.562148	+	0.827037i	$0.690025\pi$
$368$	−92769.7			−0.685032
$369$		0			0
$370$	4359.76	−	17002.2i	0.0318463	−	0.124194i
$371$	−1090.14	−	629.394i	−0.00792019	−	0.00457272i
$372$		0			0
$373$	−94695.0	+	54672.2i	−0.680627	+	0.392960i	−0.800091	−	0.599878i	$-0.795216\pi$
$373$	−94695.0	+	54672.2i	−0.680627	+	0.392960i	0.119464	+	0.992839i	$0.461882\pi$
$374$	−9783.21	+	5648.34i	−0.0699420	+	0.0403811i
$375$		0			0
$376$	19861.5	−	34401.1i	0.140487	−	0.243331i
$377$	265692.			1.86937
$378$		0			0
$379$	75560.0			0.526034			0.263017	−	0.964791i	$-0.415283\pi$
$379$	75560.0			0.526034			0.263017	+	0.964791i	$0.415283\pi$
$380$	−13518.5	+	13813.2i	−0.0936183	+	0.0956595i
$381$		0			0
$382$	27727.4	−	16008.4i	0.190012	−	0.109704i
$383$	108125.	+	187277.i	0.737100	+	1.27670i	0.953796	+	0.300456i	$0.0971389\pi$
$383$	108125.	+	187277.i	0.737100	+	1.27670i	−0.216695	+	0.976239i	$0.569528\pi$
$384$		0			0
$385$	39609.9	−	40473.5i	0.267228	−	0.273055i
$386$			47055.1i			0.315815i
$387$		0			0
$388$			202852.i			1.34746i
$389$	−48977.4	−	28277.1i	−0.323666	−	0.186868i	0.329360	−	0.944205i	$-0.393167\pi$
$389$	−48977.4	−	28277.1i	−0.323666	−	0.186868i	−0.653025	+	0.757336i	$0.726500\pi$
$390$		0			0
$391$	20653.6	+	35773.0i	0.135096	+	0.233993i
$392$	34037.9	+	58955.3i	0.221508	+	0.383664i
$393$		0			0
$394$	26445.0	−	45804.0i	0.170353	−	0.295061i
$395$	−209652.	−	53759.8i	−1.34371	−	0.344559i
$396$		0			0
$397$		−	254481.i		−	1.61464i	−0.590117	−	0.807318i	$-0.700918\pi$
$397$		−	254481.i		−	1.61464i	0.590117	−	0.807318i	$-0.299082\pi$
$398$	−5607.39	+	9712.29i	−0.0353993	+	0.0613134i
$399$		0			0
$400$	−2694.85	−	124929.i	−0.0168428	−	0.780806i
$401$	−48697.9	+	28115.7i	−0.302846	+	0.174848i	−0.643721	−	0.765261i	$-0.722610\pi$
$401$	−48697.9	+	28115.7i	−0.302846	+	0.174848i	0.340875	+	0.940109i	$0.389277\pi$
$402$		0			0
$403$	243788.	+	140751.i	1.50107	+	0.866646i
$404$		−	105078.i		−	0.643797i
$405$		0			0
$406$	−31000.1			−0.188066
$407$	37184.9	−	64406.2i	0.224480	−	0.388811i
$408$		0			0
$409$	−51157.2	−	88606.9i	−0.305816	−	0.529689i	0.671627	−	0.740890i	$-0.265596\pi$
$409$	−51157.2	−	88606.9i	−0.305816	−	0.529689i	−0.977443	+	0.211201i	$0.932263\pi$
$410$	36372.4	−	10167.6i	0.216374	−	0.0604854i
$411$		0			0
$412$	−60074.7	−	34684.2i	−0.353914	−	0.204332i
$413$	−64023.0			−0.375350
$414$		0			0
$415$	−80885.9	−	20741.1i	−0.469652	−	0.120430i
$416$	−120354.	−	69486.6i	−0.695465	−	0.401527i
$417$		0			0
$418$	5739.76	−	3313.85i	0.0328505	−	0.0189662i
$419$	50586.4	−	29206.1i	0.288142	−	0.166359i	−0.348962	−	0.937137i	$-0.613466\pi$
$419$	50586.4	−	29206.1i	0.288142	−	0.166359i	0.637103	+	0.770778i	$0.280132\pi$
$420$		0			0
$421$	117518.	−	203548.i	0.663043	−	1.14842i	−0.316770	−	0.948503i	$-0.602598\pi$
$421$	117518.	−	203548.i	0.663043	−	1.14842i	0.979812	−	0.199921i	$-0.0640685\pi$
$422$	12186.3			0.0684301
$423$		0			0
$424$	2172.04			0.0120819
$425$	−47574.1	+	28852.4i	−0.263386	+	0.159737i
$426$		0			0
$427$	31452.4	−	18159.1i	0.172504	−	0.0995950i
$428$	−149760.	−	259392.i	−0.817540	−	1.41602i
$429$		0			0
$430$	40106.4	+	39250.6i	0.216909	+	0.212280i
$431$			43601.5i			0.234718i	0.993090	+	0.117359i	$0.0374429\pi$
$431$			43601.5i			0.234718i	−0.993090	+	0.117359i	$0.962557\pi$
$432$		0			0
$433$		−	102452.i		−	0.546445i	−0.961951	−	0.273222i	$-0.911910\pi$
$433$		−	102452.i		−	0.546445i	0.961951	−	0.273222i	$-0.0880895\pi$
$434$	−28444.4	−	16422.4i	−0.151014	−	0.0871880i
$435$		0			0
$436$	16760.7	+	29030.4i	0.0881696	+	0.152714i
$437$	−12117.3	−	20987.9i	−0.0634519	−	0.109902i
$438$		0			0
$439$	51232.1	−	88736.5i	0.265835	−	0.460440i	−0.701947	−	0.712229i	$-0.747686\pi$
$439$	51232.1	−	88736.5i	0.265835	−	0.460440i	0.967782	+	0.251789i	$0.0810189\pi$
$440$	−24271.5	+	94654.0i	−0.125370	+	0.488915i
$441$		0			0
$442$			17858.6i			0.0914121i
$443$	−123815.	+	214453.i	−0.630906	+	1.09276i	0.356461	+	0.934310i	$0.383983\pi$
$443$	−123815.	+	214453.i	−0.630906	+	1.09276i	−0.987367	+	0.158451i	$0.949350\pi$
$444$		0			0
$445$	−244821.	+	68437.7i	−1.23632	+	0.345601i
$446$	45820.2	−	26454.3i	0.230350	−	0.132992i
$447$		0			0
$448$	−40085.4	−	23143.3i	−0.199724	−	0.115311i
$449$		−	79287.5i		−	0.393289i	−0.980475	−	0.196645i	$-0.936995\pi$
$449$		−	79287.5i		−	0.393289i	0.980475	−	0.196645i	$-0.0630045\pi$
$450$		0			0
$451$	160020.			0.786723
$452$	74088.0	−	128324.i	0.362636	−	0.628104i
$453$		0			0
$454$	−10759.8	−	18636.6i	−0.0522029	−	0.0904180i
$455$	−24102.3	−	86220.7i	−0.116422	−	0.416475i
$456$		0			0
$457$	−101766.	−	58754.5i	−0.487270	−	0.281325i	0.236171	−	0.971711i	$-0.424107\pi$
$457$	−101766.	−	58754.5i	−0.487270	−	0.281325i	−0.723441	+	0.690386i	$0.757441\pi$
$458$	89876.9			0.428467
$459$		0			0
$460$	166324.	+	42649.5i	0.786030	+	0.201557i
$461$	−317908.	−	183544.i	−1.49589	−	0.863653i	−0.495901	−	0.868379i	$-0.665162\pi$
$461$	−317908.	−	183544.i	−1.49589	−	0.863653i	−0.999989	+	0.00472615i	$0.998496\pi$
$462$		0			0
$463$	−79996.4	+	46185.9i	−0.373171	+	0.215451i	−0.674843	−	0.737961i	$-0.735789\pi$
$463$	−79996.4	+	46185.9i	−0.373171	+	0.215451i	0.301672	+	0.953412i	$0.402455\pi$
$464$	−250998.	+	144914.i	−1.16583	+	0.673090i
$465$		0			0
$466$	−20198.0	+	34983.9i	−0.0930114	+	0.161100i
$467$	−82073.0			−0.376328			−0.188164	−	0.982138i	$-0.560254\pi$
$467$	−82073.0			−0.376328			−0.188164	+	0.982138i	$0.560254\pi$
$468$		0			0
$469$	−163733.			−0.744372
$470$	−22550.3	+	23042.0i	−0.102084	+	0.104310i
$471$		0			0
$472$	95671.2	−	55235.8i	0.429435	−	0.247934i
$473$	118886.	+	205917.i	0.531384	+	0.920384i
$474$		0			0
$475$	27911.5	−	16927.6i	0.123707	−	0.0750253i
$476$			25746.1i			0.113631i
$477$		0			0
$478$		−	29245.2i		−	0.127997i
$479$	78567.0	+	45360.7i	0.342428	+	0.197701i	0.661345	−	0.750082i	$-0.269986\pi$
$479$	78567.0	+	45360.7i	0.342428	+	0.197701i	−0.318917	+	0.947783i	$0.603319\pi$
$480$		0			0
$481$	−58784.7	−	101818.i	−0.254082	−	0.440083i
$482$	−8359.71	−	14479.4i	−0.0359830	−	0.0623243i
$483$		0			0
$484$	8876.46	−	15374.5i	0.0378922	−	0.0656311i
$485$	85099.6	−	331871.i	0.361779	−	1.41086i
$486$		0			0
$487$		−	240214.i		−	1.01284i	−0.862287	−	0.506421i	$-0.830968\pi$
$487$		−	240214.i		−	1.01284i	0.862287	−	0.506421i	$-0.169032\pi$
$488$	−31333.4	+	54271.1i	−0.131573	+	0.227892i
$489$		0			0
$490$	−14875.1	−	53212.6i	−0.0619538	−	0.221627i
$491$	198232.	−	114449.i	0.822264	−	0.474734i	−0.0289325	−	0.999581i	$-0.509211\pi$
$491$	198232.	−	114449.i	0.822264	−	0.474734i	0.851197	+	0.524847i	$0.175877\pi$
$492$		0			0
$493$	111761.	+	64525.0i	0.459827	+	0.265481i
$494$		−	10477.6i		−	0.0429345i
$495$		0			0
$496$	−307074.			−1.24819
$497$	44593.3	−	77237.9i	0.180533	−	0.312693i
$498$		0			0
$499$	−5232.25	−	9062.53i	−0.0210130	−	0.0363956i	0.855328	−	0.518087i	$-0.173356\pi$
$499$	−5232.25	−	9062.53i	−0.0210130	−	0.0363956i	−0.876341	+	0.481692i	$0.840022\pi$
$500$	−52602.7	+	225220.i	−0.210411	+	0.900882i
$501$		0			0
$502$	−16592.2	−	9579.54i	−0.0658412	−	0.0380134i
$503$	87312.8			0.345097			0.172549	−	0.985001i	$-0.444800\pi$
$503$	87312.8			0.345097			0.172549	+	0.985001i	$0.444800\pi$
$504$		0			0
$505$	−44081.9	+	171910.i	−0.172853	+	0.674092i
$506$	−50991.8	−	29440.1i	−0.199159	−	0.114984i
$507$		0			0
$508$	−251016.	+	144924.i	−0.972689	+	0.561582i
$509$	−211363.	+	122031.i	−0.815819	+	0.471013i	−0.848972	−	0.528437i	$-0.822778\pi$
$509$	−211363.	+	122031.i	−0.815819	+	0.471013i	0.0331537	+	0.999450i	$0.489445\pi$
$510$		0			0
$511$	78912.7	−	136681.i	0.302207	−	0.523439i
$512$	259444.			0.989700
$513$		0			0
$514$	−62409.9			−0.236226
$515$	83733.2	+	81946.5i	0.315706	+	0.308970i
$516$		0			0
$517$	−118303.	+	68302.6i	−0.442605	+	0.255538i
$518$	6858.81	+	11879.8i	0.0255617	+	0.0442741i
$519$		0			0
$520$	110403.	+	108048.i	0.408297	+	0.399584i
$521$			342391.i			1.26138i	0.776034	+	0.630692i	$0.217229\pi$
$521$			342391.i			1.26138i	−0.776034	+	0.630692i	$0.782771\pi$
$522$		0			0
$523$		−	313862.i		−	1.14746i	−0.819046	−	0.573728i	$-0.805497\pi$
$523$		−	313862.i		−	1.14746i	0.819046	−	0.573728i	$-0.194503\pi$
$524$	365076.	+	210777.i	1.32960	+	0.767645i
$525$		0			0
$526$	32525.8	+	56336.3i	0.117559	+	0.203618i
$527$	68364.6	+	118411.i	0.246156	+	0.426355i
$528$		0			0
$529$	32270.6	−	55894.3i	0.115318	−	0.199736i
$530$	−1707.65	−	437.883i	−0.00607922	−	0.00155886i
$531$		0			0
$532$		−	15105.1i		−	0.0533704i
$533$	126486.	−	219080.i	0.445234	−	0.771167i
$534$		0			0
$535$	136192.	+	487199.i	0.475823	+	1.70216i
$536$	244670.	−	141260.i	0.851631	−	0.491689i
$537$		0			0
$538$	−102093.	−	58943.5i	−0.352721	−	0.203644i
$539$		−	234109.i		−	0.805823i
$540$		0			0
$541$	81438.3			0.278249			0.139125	−	0.990275i	$-0.455571\pi$
$541$	81438.3			0.278249			0.139125	+	0.990275i	$0.455571\pi$
$542$	6551.63	−	11347.8i	0.0223024	−	0.0386288i
$543$		0			0
$544$	−33750.6	−	58457.7i	−0.114047	−	0.197535i
$545$	−15242.2	−	54525.8i	−0.0513162	−	0.183573i
$546$		0			0
$547$	345995.	+	199760.i	1.15636	+	0.667627i	0.950430	−	0.310939i	$-0.100643\pi$
$547$	345995.	+	199760.i	1.15636	+	0.667627i	0.205934	+	0.978566i	$0.433977\pi$
$548$	−388353.			−1.29320
$549$		0			0
$550$	38164.5	−	69523.7i	0.126164	−	0.229830i
$551$	−65569.4	−	37856.5i	−0.215972	−	0.124692i
$552$		0			0
$553$	146489.	−	84575.3i	0.479020	−	0.276563i
$554$	−25398.6	+	14663.9i	−0.0827541	+	0.0477781i
$555$		0			0
$556$	−246514.	+	426975.i	−0.797430	+	1.38119i
$557$	−464065.			−1.49578			−0.747892	−	0.663821i	$-0.768934\pi$
$557$	−464065.			−1.49578			−0.747892	+	0.663821i	$0.768934\pi$
$558$		0			0
$559$	375888.			1.20291
$560$	69795.8	+	68306.4i	0.222563	+	0.217814i
$561$		0			0
$562$	41275.3	−	23830.3i	0.130682	−	0.0754496i
$563$	−282361.	−	489064.i	−0.890816	−	1.54294i	−0.838899	−	0.544287i	$-0.816800\pi$
$563$	−282361.	−	489064.i	−0.890816	−	1.54294i	−0.0519165	−	0.998651i	$-0.516533\pi$
$564$		0			0
$565$	−175044.	+	178861.i	−0.548340	+	0.560296i
$566$			68056.4i			0.212440i
$567$		0			0
$568$			153891.i			0.476999i
$569$	477380.	+	275615.i	1.47448	+	0.851292i	0.999587	−	0.0287503i	$-0.00915278\pi$
$569$	477380.	+	275615.i	1.47448	+	0.851292i	0.474895	+	0.880043i	$0.342486\pi$
$570$		0			0
$571$	107836.	+	186778.i	0.330744	+	0.572865i	0.982658	−	0.185428i	$-0.0593670\pi$
$571$	107836.	+	186778.i	0.330744	+	0.572865i	−0.651914	+	0.758293i	$0.726034\pi$
$572$	157268.	+	272397.i	0.480672	+	0.832549i
$573$		0			0
$574$	−14758.0	+	25561.6i	−0.0447923	+	0.0775825i
$575$	−254218.	−	139551.i	−0.768902	−	0.422083i
$576$		0			0
$577$			302487.i			0.908562i	0.890858	+	0.454281i	$0.150104\pi$
$577$			302487.i			0.908562i	−0.890858	+	0.454281i	$0.849896\pi$
$578$	41370.4	−	71655.6i	0.123832	−	0.214484i
$579$		0			0
$580$	516628.	−	144419.i	1.53575	−	0.429307i
$581$	56516.9	−	32630.0i	0.167427	−	0.0966641i
$582$		0			0
$583$	−6468.79	−	3734.76i	−0.0190321	−	0.0109882i
$584$			272327.i			0.798483i
$585$		0			0
$586$	18843.2			0.0548731
$587$	−67877.0	+	117566.i	−0.196991	+	0.341198i	−0.947551	−	0.319603i	$-0.896450\pi$
$587$	−67877.0	+	117566.i	−0.196991	+	0.341198i	0.750560	+	0.660802i	$0.229784\pi$
$588$		0			0
$589$	−40109.2	−	69471.2i	−0.115615	−	0.200251i
$590$	−86352.1	+	24139.0i	−0.248067	+	0.0693450i
$591$		0			0
$592$	111067.	+	64124.7i	0.316915	+	0.182971i
$593$	612873.			1.74285			0.871427	−	0.490525i	$-0.163195\pi$
$593$	612873.			1.74285			0.871427	+	0.490525i	$0.163195\pi$
$594$		0			0
$595$	10800.9	−	42121.3i	0.0305089	−	0.118978i
$596$	67477.4	+	38958.1i	0.189962	+	0.109674i
$597$		0			0
$598$	−80611.6	+	46541.1i	−0.225421	+	0.130147i
$599$	152718.	−	88171.6i	0.425634	−	0.245740i	−0.271851	−	0.962339i	$-0.587636\pi$
$599$	152718.	−	88171.6i	0.425634	−	0.245740i	0.697485	+	0.716600i	$0.254303\pi$
$600$		0			0
$601$	−55051.5	+	95352.0i	−0.152412	+	0.263986i	−0.932114	−	0.362165i	$-0.882038\pi$
$601$	−55051.5	+	95352.0i	−0.152412	+	0.263986i	0.779701	+	0.626152i	$0.215371\pi$
$602$	−43857.4			−0.121018
$603$		0			0
$604$	−166875.			−0.457423
$605$	−20972.0	+	21429.2i	−0.0572966	+	0.0585458i
$606$		0			0
$607$	−189924.	+	109653.i	−0.515470	+	0.297607i	−0.735079	−	0.677981i	$-0.762855\pi$
$607$	−189924.	+	109653.i	−0.515470	+	0.297607i	0.219609	+	0.975588i	$0.429522\pi$
$608$	19801.3	+	34296.8i	0.0535656	+	0.0927784i
$609$		0			0
$610$	35575.3	−	36351.0i	0.0956069	−	0.0976915i
$611$			215955.i			0.578471i
$612$		0			0
$613$			75985.1i			0.202212i	0.994876	+	0.101106i	$0.0322382\pi$
$613$			75985.1i			0.202212i	−0.994876	+	0.101106i	$0.967762\pi$
$614$	101790.	+	58768.3i	0.270002	+	0.155886i
$615$		0			0
$616$	−38184.2	−	66137.0i	−0.100629	−	0.174294i
$617$	−242066.	−	419271.i	−0.635863	−	1.10135i	−0.986331	−	0.164773i	$-0.947311\pi$
$617$	−242066.	−	419271.i	−0.635863	−	1.10135i	0.350468	−	0.936575i	$-0.386023\pi$
$618$		0			0
$619$	−23051.5	+	39926.4i	−0.0601614	+	0.104203i	−0.894537	−	0.446993i	$-0.852495\pi$
$619$	−23051.5	+	39926.4i	−0.0601614	+	0.104203i	0.834376	+	0.551196i	$0.185828\pi$
$620$	550543.	+	141173.i	1.43221	+	0.367254i
$621$		0			0
$622$			149285.i			0.385866i
$623$	99335.4	−	172054.i	0.255934	−	0.443291i
$624$		0			0
$625$	180543.	−	346399.i	0.462190	−	0.886781i
$626$	−89640.9	+	51754.2i	−0.228748	+	0.132068i
$627$		0			0
$628$	−258162.	−	149050.i	−0.654595	−	0.377930i
$629$		−	57105.0i		−	0.144335i
$630$		0			0
$631$	240096.			0.603013			0.301507	−	0.953464i	$-0.402510\pi$
$631$	240096.			0.603013			0.301507	+	0.953464i	$0.402510\pi$
$632$	−145935.	+	252766.i	−0.365362	+	0.632826i
$633$		0			0
$634$	77444.8	+	134138.i	0.192670	+	0.333714i
$635$	471467.	−	131794.i	1.16924	−	0.326851i
$636$		0			0
$637$	−320513.	−	185048.i	−0.789890	−	0.456043i
$638$	−183951.			−0.451919
$639$		0			0
$640$	−356583.	−	91436.5i	−0.870565	−	0.223234i
$641$	−480663.	−	277511.i	−1.16984	−	0.675405i	−0.216195	−	0.976350i	$-0.569365\pi$
$641$	−480663.	−	277511.i	−1.16984	−	0.675405i	−0.953641	+	0.300945i	$0.902698\pi$
$642$		0			0
$643$	560077.	−	323360.i	1.35465	−	0.782105i	0.365749	−	0.930713i	$-0.380813\pi$
$643$	560077.	−	323360.i	1.35465	−	0.782105i	0.988896	+	0.148609i	$0.0474794\pi$
$644$	−116215.	+	67096.5i	−0.280213	+	0.161781i
$645$		0			0
$646$	2544.55	−	4407.28i	0.00609741	−	0.0105610i
$647$	347688.			0.830579			0.415289	−	0.909689i	$-0.363680\pi$
$647$	347688.			0.830579			0.415289	+	0.909689i	$0.363680\pi$
$648$		0			0
$649$	−379906.			−0.901959
$650$	−65016.6	−	107204.i	−0.153885	−	0.253738i
$651$		0			0
$652$	197267.	−	113892.i	0.464043	−	0.267915i
$653$	304539.	+	527478.i	0.714196	+	1.23702i	0.963269	+	0.268538i	$0.0865406\pi$
$653$	304539.	+	527478.i	0.714196	+	1.23702i	−0.249073	+	0.968485i	$0.580126\pi$
$654$		0			0
$655$	−508850.	−	497992.i	−1.18606	−	1.16075i
$656$			275952.i			0.641247i
$657$		0			0
$658$		−	25197.0i		−	0.0581965i
$659$	−540048.	−	311797.i	−1.24354	−	0.717961i	−0.273731	−	0.961806i	$-0.588258\pi$
$659$	−540048.	−	311797.i	−1.24354	−	0.717961i	−0.969814	+	0.243845i	$0.921591\pi$
$660$		0			0
$661$	−184642.	−	319810.i	−0.422598	−	0.731962i	0.573594	−	0.819140i	$-0.305549\pi$
$661$	−184642.	−	319810.i	−0.422598	−	0.731962i	−0.996193	+	0.0871775i	$0.972215\pi$
$662$	−45286.2	−	78438.0i	−0.103336	−	0.178983i
$663$		0			0
$664$	−56303.1	+	97519.8i	−0.127701	+	0.221185i
$665$	−6336.84	+	24712.3i	−0.0143294	+	0.0558818i
$666$		0			0
$667$			672630.i			1.51191i
$668$	126172.	−	218536.i	0.282755	−	0.489746i
$669$		0			0
$670$	−220837.	+	61733.2i	−0.491952	+	0.137521i
$671$	186635.	−	107754.i	0.414523	−	0.239325i
$672$		0			0
$673$	−130097.	−	75111.4i	−0.287234	−	0.165835i	0.349460	−	0.936951i	$-0.386365\pi$
$673$	−130097.	−	75111.4i	−0.287234	−	0.165835i	−0.636694	+	0.771117i	$0.719699\pi$
$674$		−	91063.7i		−	0.200459i
$675$		0			0
$676$	74481.8			0.162988
$677$	−290147.	+	502550.i	−0.633055	+	1.09648i	0.353869	+	0.935295i	$0.384866\pi$
$677$	−290147.	+	502550.i	−0.633055	+	1.09648i	−0.986924	+	0.161188i	$0.948467\pi$
$678$		0			0
$679$	133879.	+	231886.i	0.290385	+	0.502961i
$680$	20200.0	+	72261.3i	0.0436852	+	0.156274i
$681$		0			0
$682$	−168786.	−	97448.7i	−0.362884	−	0.209511i
$683$	11404.6			0.0244477			0.0122238	−	0.999925i	$-0.496109\pi$
$683$	11404.6			0.0244477			0.0122238	+	0.999925i	$0.496109\pi$
$684$		0			0
$685$	635356.	+	162921.i	1.35405	+	0.347212i
$686$	81862.7	+	47263.4i	0.173955	+	0.100433i
$687$		0			0
$688$	−355099.	+	205017.i	−0.750192	+	0.433124i
$689$	−10226.3	+	5904.18i	−0.0215418	+	0.0124372i
$690$		0			0
$691$	50403.6	−	87301.6i	0.105562	−	0.182838i	−0.808406	−	0.588625i	$-0.799669\pi$
$691$	50403.6	−	87301.6i	0.105562	−	0.182838i	0.913967	+	0.405787i	$0.133003\pi$
$692$	−287289.			−0.599938
$693$		0			0
$694$	113423.			0.235494
$695$	582427.	−	595126.i	1.20579	−	1.23208i
$696$		0			0
$697$	106410.	−	61435.9i	0.219037	−	0.126461i
$698$	−82478.7	−	142857.i	−0.169290	−	0.293219i
$699$		0			0
$700$	−93731.9	−	154552.i	−0.191290	−	0.315412i
$701$		−	220659.i		−	0.449040i	−0.974469	−	0.224520i	$-0.927919\pi$
$701$		−	220659.i		−	0.449040i	0.974469	−	0.224520i	$-0.0720814\pi$
$702$		0			0
$703$			33503.2i			0.0677916i
$704$	−237862.	−	137330.i	−0.479933	−	0.277089i
$705$		0			0
$706$	−12115.0	−	20983.8i	−0.0243060	−	0.0420993i
$707$	−69350.1	−	120118.i	−0.138742	−	0.240308i
$708$		0			0
$709$	64731.1	−	112118.i	0.128772	−	0.223039i	−0.794429	−	0.607357i	$-0.792230\pi$
$709$	64731.1	−	112118.i	0.128772	−	0.223039i	0.923201	+	0.384318i	$0.125563\pi$
$710$	31024.5	−	120989.i	0.0615444	−	0.240010i
$711$		0			0
$712$			342806.i			0.676221i
$713$	−356328.	+	617179.i	−0.700924	+	1.21404i
$714$		0			0
$715$	−143020.	−	511625.i	−0.279760	−	1.00078i
$716$	85365.8	−	49286.0i	0.166517	−	0.0961385i
$717$		0			0
$718$	86187.4	+	49760.3i	0.167184	+	0.0965238i
$719$		−	354459.i		−	0.685659i	−0.939398	−	0.342829i	$-0.888615\pi$
$719$		−	354459.i		−	0.685659i	0.939398	−	0.342829i	$-0.111385\pi$
$720$		0			0
$721$	−91564.3			−0.176139
$722$	69826.2	−	120943.i	0.133950	−	0.232009i
$723$		0			0
$724$	−116490.	−	201767.i	−0.222235	−	0.384923i
$725$	−905803.	+	19539.1i	−1.72329	+	0.0371731i
$726$		0			0
$727$	−173161.	−	99974.6i	−0.327628	−	0.189156i	0.327159	−	0.944969i	$-0.393909\pi$
$727$	−173161.	−	99974.6i	−0.327628	−	0.189156i	−0.654788	+	0.755813i	$0.727242\pi$
$728$	−120729.			−0.227797
$729$		0			0
$730$	54901.3	−	214103.i	0.103024	−	0.401770i
$731$	158113.	+	91286.7i	0.295892	+	0.170833i
$732$		0			0
$733$	746774.	−	431150.i	1.38989	−	0.802455i	0.396590	−	0.917996i	$-0.370193\pi$
$733$	746774.	−	431150.i	1.38989	−	0.802455i	0.993303	+	0.115541i	$0.0368600\pi$
$734$	18720.2	−	10808.1i	0.0347471	−	0.0200612i
$735$		0			0
$736$	175914.	−	304691.i	0.324746	−	0.562477i
$737$	−971573.			−1.78871
$738$		0			0
$739$	684605.			1.25358			0.626789	−	0.779189i	$-0.284369\pi$
$739$	684605.			1.25358			0.626789	+	0.779189i	$0.284369\pi$
$740$	−169649.	−	166029.i	−0.309804	−	0.303193i
$741$		0			0
$742$	1193.18	−	688.881i	0.00216719	−	0.00125123i
$743$	400928.	+	694427.i	0.726254	+	1.25791i	0.958456	+	0.285241i	$0.0920737\pi$
$743$	400928.	+	694427.i	0.726254	+	1.25791i	−0.232202	+	0.972668i	$0.574593\pi$
$744$		0			0
$745$	−94051.3	−	92044.4i	−0.169454	−	0.165838i
$746$		−	119679.i		−	0.215050i
$747$		0			0
$748$			152775.i			0.273053i
$749$	−342391.	−	197679.i	−0.610321	−	0.352369i
$750$		0			0
$751$	−254539.	−	440875.i	−0.451310	−	0.781692i	0.547158	−	0.837030i	$-0.315710\pi$
$751$	−254539.	−	440875.i	−0.451310	−	0.781692i	−0.998468	+	0.0553377i	$0.982376\pi$
$752$	−117786.	−	204012.i	−0.208286	−	0.360761i
$753$		0			0
$754$	−145402.	+	251843.i	−0.255757	+	0.442983i
$755$	273012.	+	70006.9i	0.478948	+	0.122814i
$756$		0			0
$757$			766769.i			1.33805i	0.743239	+	0.669026i	$0.233288\pi$
$757$			766769.i			1.33805i	−0.743239	+	0.669026i	$0.766712\pi$
$758$	−41350.8	+	71621.6i	−0.0719689	+	0.124654i
$759$		0			0
$760$	−11851.3	−	42395.4i	−0.0205181	−	0.0733992i
$761$	−283879.	+	163898.i	−0.490190	+	0.283011i	−0.724653	−	0.689114i	$-0.758000\pi$
$761$	−283879.	+	163898.i	−0.490190	+	0.283011i	0.234463	+	0.972125i	$0.424667\pi$
$762$		0			0
$763$	38319.3	+	22123.6i	0.0658216	+	0.0380021i
$764$		−	432990.i		−	0.741808i
$765$		0			0
$766$	−236688.			−0.403384
$767$	−300292.	+	520120.i	−0.510449	+	0.884124i
$768$		0			0
$769$	−197438.	−	341972.i	−0.333870	−	0.578280i	0.649397	−	0.760449i	$-0.275021\pi$
$769$	−197438.	−	341972.i	−0.333870	−	0.578280i	−0.983267	+	0.182170i	$0.941688\pi$
$770$	16687.1	+	59694.7i	0.0281449	+	0.100683i
$771$		0			0
$772$	551109.	+	318183.i	0.924705	+	0.533878i
$773$	121076.			0.202628			0.101314	−	0.994855i	$-0.467695\pi$
$773$	121076.			0.202628			0.101314	+	0.994855i	$0.467695\pi$
$774$		0			0
$775$	−841479.	−	461924.i	−1.40101	−	0.769072i
$776$	−400118.	−	231008.i	−0.664454	−	0.383623i
$777$		0			0
$778$	53606.5	−	30949.7i	0.0885642	−	0.0511326i
$779$	−62430.3	+	36044.1i	−0.102878	+	0.0593964i
$780$		0			0
$781$	264612.	−	458321.i	0.433818	−	0.751395i
$782$	−45211.3			−0.0739321
$783$		0			0
$784$	403716.			0.656816
$785$	359830.	+	352152.i	0.583927	+	0.571467i
$786$		0			0
$787$	−523274.	+	302112.i	−0.844849	+	0.487774i	−0.858910	−	0.512127i	$-0.828858\pi$
$787$	−523274.	+	302112.i	−0.844849	+	0.487774i	0.0140603	+	0.999901i	$0.495524\pi$
$788$	−357638.	−	619446.i	−0.575958	−	0.997588i
$789$		0			0
$790$	165691.	−	169304.i	0.265488	−	0.271277i
$791$		−	195588.i		−	0.312601i
$792$		0			0
$793$		−	340691.i		−	0.541769i
$794$	241217.	+	139267.i	0.382619	+	0.220905i
$795$		0			0
$796$	75833.5	+	131347.i	0.119684	+	0.207298i
$797$	444851.	+	770505.i	0.700322	+	1.21299i	0.968353	+	0.249584i	$0.0802937\pi$
$797$	444851.	+	770505.i	0.700322	+	1.21299i	−0.268031	+	0.963410i	$0.586373\pi$
$798$		0			0
$799$	−52446.2	+	90839.5i	−0.0821524	+	0.142292i
$800$	415425.	+	228045.i	0.649102	+	0.356320i
$801$		0			0
$802$		−	61546.2i		−	0.0956868i
$803$	468260.	−	811049.i	0.726199	−	1.25781i
$804$		0			0
$805$	218278.	−	61017.7i	0.336836	−	0.0941595i
$806$	−266830.	+	154054.i	−0.410737	+	0.237139i
$807$		0			0
$808$	207263.	+	119663.i	0.317468	+	0.183290i
$809$			351052.i			0.536382i	0.963366	+	0.268191i	$0.0864258\pi$
$809$			351052.i			0.536382i	−0.963366	+	0.268191i	$0.913574\pi$
$810$		0			0
$811$	−316054.			−0.480529			−0.240264	−	0.970707i	$-0.577234\pi$
$811$	−316054.			−0.480529			−0.240264	+	0.970707i	$0.577234\pi$
$812$	−209620.	+	363072.i	−0.317922	+	0.550657i
$813$		0			0
$814$	40699.4	+	70493.5i	0.0614242	+	0.106390i
$815$	−370513.	+	103574.i	−0.557812	+	0.155932i
$816$		0			0
$817$	−92764.3	−	53557.5i	−0.138975	−	0.0802373i
$818$	111985.			0.167360
$819$		0			0
$820$	126865.	−	494746.i	0.188674	−	0.735791i
$821$	853848.	+	492970.i	1.26676	+	0.731364i	0.974374	−	0.224936i	$-0.0722172\pi$
$821$	853848.	+	492970.i	1.26676	+	0.731364i	0.292387	+	0.956300i	$0.405551\pi$
$822$		0			0
$823$	−547461.	+	316077.i	−0.808264	+	0.466651i	−0.846353	−	0.532623i	$-0.821206\pi$
$823$	−547461.	+	316077.i	−0.808264	+	0.466651i	0.0380887	+	0.999274i	$0.487873\pi$
$824$	136827.	−	78997.0i	0.201519	−	0.116347i
$825$		0			0
$826$	35037.1	−	60686.0i	0.0513532	−	0.0889464i
$827$	−309027.			−0.451840			−0.225920	−	0.974146i	$-0.572539\pi$
$827$	−309027.			−0.451840			−0.225920	+	0.974146i	$0.572539\pi$
$828$		0			0
$829$	−832364.			−1.21117			−0.605584	−	0.795782i	$-0.707060\pi$
$829$	−832364.			−1.21117			−0.605584	+	0.795782i	$0.707060\pi$
$830$	63925.4	−	65319.2i	0.0927934	−	0.0948166i
$831$		0			0
$832$	−376030.	+	217101.i	−0.543221	+	0.313629i
$833$	−89880.3	−	155677.i	−0.129531	−	0.224355i
$834$		0			0
$835$	−298100.	+	304600.i	−0.427552	+	0.436875i
$836$		−	89632.1i		−	0.128248i
$837$		0			0
$838$			63933.0i			0.0910410i
$839$	−718506.	−	414830.i	−1.02072	−	0.589313i	−0.106407	−	0.994323i	$-0.533935\pi$
$839$	−718506.	−	414830.i	−1.02072	−	0.589313i	−0.914312	+	0.405010i	$0.867268\pi$
$840$		0			0
$841$	697061.	+	1.20734e6i	0.985550	+	1.70702i
$842$	128626.	+	222786.i	0.181427	+	0.314241i
$843$		0			0
$844$	82402.8	−	142726.i	0.115680	−	0.200363i
$845$	−121854.	−	31246.3i	−0.170658	−	0.0437608i
$846$		0			0
$847$		−	23433.4i		−	0.0326639i
$848$	6440.51	−	11155.3i	0.00895630	−	0.0155128i
$849$		0			0
$850$	−1313.33	−	60884.1i	−0.00181776	−	0.0842686i
$851$	257765.	−	148820.i	0.355930	−	0.205496i
$852$		0			0
$853$	−607611.	−	350804.i	−0.835079	−	0.482133i	0.0205095	−	0.999790i	$-0.493471\pi$
$853$	−607611.	−	350804.i	−0.835079	−	0.482133i	−0.855588	+	0.517657i	$0.826805\pi$
$854$			39750.7i			0.0545041i
$855$		0			0
$856$	682191.			0.931019
$857$	542612.	−	939831.i	0.738801	−	1.27964i	−0.214234	−	0.976782i	$-0.568726\pi$
$857$	542612.	−	939831.i	0.738801	−	1.27964i	0.953035	−	0.302859i	$-0.0979411\pi$
$858$		0			0
$859$	442391.	+	766243.i	0.599542	+	1.03844i	0.992889	+	0.119047i	$0.0379839\pi$
$859$	442391.	+	766243.i	0.599542	+	1.03844i	−0.393347	+	0.919390i	$0.628683\pi$
$860$	730900.	−	204317.i	0.988236	−	0.276253i
$861$		0			0
$862$	−41328.9	−	23861.2i	−0.0556210	−	0.0321128i
$863$	848540.			1.13933			0.569667	−	0.821876i	$-0.307072\pi$
$863$	848540.			1.13933			0.569667	+	0.821876i	$0.307072\pi$
$864$		0			0
$865$	470011.	+	120522.i	0.628169	+	0.161077i
$866$	97112.3	+	56067.8i	0.129491	+	0.0747615i
$867$		0			0
$868$	−384678.	+	222094.i	−0.510573	+	0.294779i
$869$	869248.	−	501861.i	1.15108	−	0.664575i
$870$		0			0
$871$	−767967.	+	1.33016e6i	−1.01229	+	1.75334i
$872$	−76348.6			−0.100408
$873$		0			0
$874$	26525.2			0.0347245
$875$	88510.7	+	292173.i	0.115606	+	0.381614i
$876$		0			0
$877$	445046.	−	256947.i	0.578636	−	0.334076i	−0.181955	−	0.983307i	$-0.558243\pi$
$877$	445046.	−	256947.i	0.578636	−	0.334076i	0.760591	+	0.649231i	$0.224909\pi$
$878$	56074.2	+	97123.4i	0.0727402	+	0.125990i
$879$		0			0
$880$	414161.	+	405323.i	0.534815	+	0.523403i
$881$		−	222212.i		−	0.286297i	−0.989701	−	0.143148i	$-0.954277\pi$
$881$		−	222212.i		−	0.286297i	0.989701	−	0.143148i	$-0.0457226\pi$
$882$		0			0
$883$		−	248366.i		−	0.318545i	−0.987235	−	0.159272i	$-0.949085\pi$
$883$		−	248366.i		−	0.318545i	0.987235	−	0.159272i	$-0.0509148\pi$
$884$	209160.	+	120759.i	0.267654	+	0.154530i
$885$		0			0
$886$	−135517.	−	234722.i	−0.172634	−	0.299011i
$887$	−432263.	−	748702.i	−0.549415	−	0.951616i	−0.998315	−	0.0580331i	$-0.981517\pi$
$887$	−432263.	−	748702.i	−0.549415	−	0.951616i	0.448899	−	0.893582i	$-0.351816\pi$
$888$		0			0
$889$	−191296.	+	331334.i	−0.242048	+	0.419240i
$890$	69109.7	−	269514.i	0.0872488	−	0.340252i
$891$		0			0
$892$		−	715528.i		−	0.899284i
$893$	30769.9	−	53295.1i	0.0385855	−	0.0668320i
$894$		0			0
$895$	−160337.	+	44820.8i	−0.200165	+	0.0559543i
$896$	249153.	−	143849.i	0.310349	−	0.179180i
$897$		0			0
$898$	75154.8	+	43390.7i	0.0931975	+	0.0538076i
$899$			2.22645e6i			2.75482i
$900$		0			0
$901$	−5735.47			−0.00706512
$902$	−87572.3	+	151680.i	−0.107635	+	0.186429i
$903$		0			0
$904$	168744.	+	292272.i	0.206486	+	0.357644i
$905$	105937.	+	378966.i	0.129345	+	0.462704i
$906$		0			0
$907$	929719.	+	536773.i	1.13015	+	0.652494i	0.943973	−	0.330022i	$-0.107056\pi$
$907$	929719.	+	536773.i	1.13015	+	0.652494i	0.186179	+	0.982516i	$0.440390\pi$
$908$	−291029.			−0.352992
$909$		0			0
$910$	94916.8	+	24338.9i	0.114620	+	0.0293913i
$911$	872700.	+	503854.i	1.05155	+	0.607110i	0.923082	−	0.384604i	$-0.125662\pi$
$911$	872700.	+	503854.i	1.05155	+	0.607110i	0.128464	+	0.991714i	$0.458995\pi$
$912$		0			0
$913$	335365.	−	193623.i	0.402324	−	0.232282i
$914$	111384.	−	64307.7i	0.133331	−	0.0769787i
$915$		0			0
$916$	607741.	−	1.05264e6i	0.724315	−	1.25455i
$917$	556440.			0.661728
$918$		0			0
$919$	−576271.			−0.682332			−0.341166	−	0.940003i	$-0.610822\pi$
$919$	−576271.			−0.682332			−0.341166	+	0.940003i	$0.610822\pi$
$920$	−273535.	+	279500.i	−0.323175	+	0.330222i
$921$		0			0
$922$	347955.	−	200892.i	0.409318	−	0.236320i
$923$	−418318.	−	724549.i	−0.491025	−	0.850480i
$924$		0			0
$925$	207898.	+	342798.i	0.242978	+	0.400640i
$926$		−	101102.i		−	0.117907i
$927$		0			0
$928$		−	1.09916e6i		−	1.27634i
$929$	889734.	+	513688.i	1.03093	+	0.595207i	0.917251	−	0.398310i	$-0.130403\pi$
$929$	889734.	+	513688.i	1.03093	+	0.595207i	0.113679	+	0.993518i	$0.463737\pi$
$930$		0			0
$931$	52732.3	+	91335.1i	0.0608384	+	0.105375i
$932$	273154.	+	473117.i	0.314468	+	0.544674i
$933$		0			0
$934$	44915.0	−	77795.1i	0.0514870	−	0.0891782i
$935$	64091.4	−	249943.i	0.0733122	−	0.285902i
$936$		0			0
$937$			358312.i			0.408115i	0.978959	+	0.204057i	$0.0654129\pi$
$937$			358312.i			0.408115i	−0.978959	+	0.204057i	$0.934587\pi$
$938$	89604.0	−	155199.i	0.101841	−	0.176393i
$939$		0			0
$940$	117384.	+	419918.i	0.132848	+	0.475235i
$941$	−634781.	+	366491.i	−0.716877	+	0.413889i	−0.813602	−	0.581422i	$-0.802497\pi$
$941$	−634781.	+	366491.i	−0.716877	+	0.413889i	0.0967250	+	0.995311i	$0.469163\pi$
$942$		0			0
$943$	554628.	+	320214.i	0.623703	+	0.360095i
$944$		−	655140.i		−	0.735174i
$945$		0			0
$946$	−260245.			−0.290804
$947$	−361257.	+	625716.i	−0.402825	+	0.697713i	−0.994066	−	0.108782i	$-0.965305\pi$
$947$	−361257.	+	625716.i	−0.402825	+	0.697713i	0.591241	+	0.806495i	$0.298638\pi$
$948$		0			0
$949$	−740260.	−	1.28217e6i	−0.821962	−	1.42368i
$950$	770.526	+	35720.4i	0.000853768	+	0.0395794i
$951$		0			0
$952$	−50783.3	−	29319.8i	−0.0560335	−	0.0323509i
$953$	−686812.			−0.756227			−0.378113	−	0.925759i	$-0.623427\pi$
$953$	−686812.			−0.756227			−0.378113	+	0.925759i	$0.623427\pi$
$954$		0			0
$955$	−181646.	+	708383.i	−0.199168	+	0.776715i
$956$	−342519.	−	197754.i	−0.374774	−	0.216376i
$957$		0			0
$958$	−85992.7	+	49647.9i	−0.0936980	+	0.0540966i
$959$	−443938.	+	256308.i	−0.482709	+	0.278692i
$960$		0			0
$961$	−717709.	+	1.24311e6i	−0.777144	+	1.34605i
$962$	128681.			0.139048
$963$		0			0
$964$	−226111.			−0.243314
$965$	−768146.	−	751755.i	−0.824877	−	0.807275i
$966$		0			0
$967$	−217686.	+	125681.i	−0.232797	+	0.134406i	−0.611862	−	0.790965i	$-0.709579\pi$
$967$	−217686.	+	125681.i	−0.232797	+	0.134406i	0.379064	+	0.925370i	$0.376246\pi$
$968$	20217.1	+	35017.1i	0.0215759	+	0.0373705i
$969$		0			0
$970$	268001.	+	262282.i	0.284835	+	0.278757i
$971$		−	299319.i		−	0.317465i	−0.987322	−	0.158733i	$-0.949259\pi$
$971$		−	299319.i		−	0.317465i	0.987322	−	0.158733i	$-0.0507408\pi$
$972$		0			0
$973$			650784.i			0.687403i
$974$	227694.	+	131459.i	0.240012	+	0.138571i
$975$		0			0
$976$	185819.	+	321849.i	0.195070	+	0.337872i
$977$	−352133.	−	609912.i	−0.368907	−	0.638966i	0.620488	−	0.784216i	$-0.286935\pi$
$977$	−352133.	−	609912.i	−0.368907	−	0.638966i	−0.989395	+	0.145250i	$0.953601\pi$
$978$		0			0
$979$	589446.	−	1.02095e6i	0.615004	−	1.06522i
$980$	−723810.	−	185602.i	−0.753654	−	0.193255i
$981$		0			0
$982$			250533.i			0.259802i
$983$	−343643.	+	595207.i	−0.355632	+	0.615972i	−0.987226	−	0.159327i	$-0.949068\pi$
$983$	−343643.	+	595207.i	−0.355632	+	0.615972i	0.631594	+	0.775299i	$0.282401\pi$
$984$		0			0
$985$	325237.	+	1.16347e6i	0.335218	+	1.19917i
$986$	−122323.	+	70623.5i	−0.125822	+	0.0726433i
$987$		0			0
$988$	−122713.	−	70848.5i	−0.125712	−	0.0725800i
$989$			951604.i			0.972890i
$990$		0			0
$991$	315848.			0.321611			0.160806	−	0.986986i	$-0.448591\pi$
$991$	315848.			0.321611			0.160806	+	0.986986i	$0.448591\pi$
$992$	582286.	−	1.00855e6i	0.591715	−	1.02488i
$993$		0			0
$994$	48808.0	+	84538.0i	0.0493990	+	0.0855617i
$995$	−68963.1	−	246701.i	−0.0696580	−	0.249187i
$996$		0			0
$997$	−458423.	−	264671.i	−0.461186	−	0.266266i	0.251357	−	0.967895i	$-0.419123\pi$
$997$	−458423.	−	264671.i	−0.461186	−	0.266266i	−0.712543	+	0.701629i	$0.752457\pi$
$998$	11453.6			0.0114995
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.5.h.a.89.10		44
3.2	odd	2		45.5.h.a.29.13	yes	44
5.4	even	2	inner	135.5.h.a.89.13		44
9.2	odd	6		405.5.d.a.404.19		44
9.4	even	3		45.5.h.a.14.10	✓	44
9.5	odd	6	inner	135.5.h.a.44.13		44
9.7	even	3		405.5.d.a.404.25		44
15.14	odd	2		45.5.h.a.29.10	yes	44
45.4	even	6		45.5.h.a.14.13	yes	44
45.14	odd	6	inner	135.5.h.a.44.10		44
45.29	odd	6		405.5.d.a.404.26		44
45.34	even	6		405.5.d.a.404.20		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.10	✓	44	9.4	even	3
45.5.h.a.14.13	yes	44	45.4	even	6
45.5.h.a.29.10	yes	44	15.14	odd	2
45.5.h.a.29.13	yes	44	3.2	odd	2
135.5.h.a.44.10		44	45.14	odd	6	inner
135.5.h.a.44.13		44	9.5	odd	6	inner
135.5.h.a.89.10		44	1.1	even	1	trivial
135.5.h.a.89.13		44	5.4	even	2	inner
405.5.d.a.404.19		44	9.2	odd	6
405.5.d.a.404.20		44	45.34	even	6
405.5.d.a.404.25		44	9.7	even	3
405.5.d.a.404.26		44	45.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	135.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.547257 + 0.947877i) q^{2} +(7.40102 + 12.8189i) q^{4} +(-6.73050 - 24.0770i) q^{5} +(16.9207 + 9.76914i) q^{7} -33.7133 q^{8} +(26.5053 + 6.79660i) q^{10} +(100.405 + 57.9690i) q^{11} +(158.728 - 91.6418i) q^{13} +(-18.5199 + 10.6925i) q^{14} +(-99.9665 + 173.147i) q^{16} +89.0232 q^{17} -52.2295 q^{19} +(258.829 - 264.472i) q^{20} +(-109.895 + 63.4480i) q^{22} +(232.002 + 401.839i) q^{23} +(-534.401 + 324.100i) q^{25} +200.607i q^{26} +289.206i q^{28} +(1255.41 + 724.811i) q^{29} +(767.942 + 1330.11i) q^{31} +(-379.121 - 656.657i) q^{32} +(-48.7186 + 84.3831i) q^{34} +(121.327 - 473.149i) q^{35} -641.462i q^{37} +(28.5830 - 49.5071i) q^{38} +(226.907 + 811.713i) q^{40} +(1195.31 - 690.111i) q^{41} +(1776.09 + 1025.43i) q^{43} +1716.12i q^{44} -507.859 q^{46} +(-589.129 + 1020.40i) q^{47} +(-1009.63 - 1748.73i) q^{49} +(-14.7527 - 683.912i) q^{50} +(2349.50 + 1356.49i) q^{52} -64.4267 q^{53} +(719.940 - 2807.62i) q^{55} +(-570.451 - 329.350i) q^{56} +(-1374.06 + 793.316i) q^{58} +(-2837.79 + 1638.40i) q^{59} +(929.409 - 1609.78i) q^{61} -1681.05 q^{62} -2369.02 q^{64} +(-3274.78 - 3204.90i) q^{65} +(-7257.38 + 4190.05i) q^{67} +(658.862 + 1141.18i) q^{68} +(382.090 + 373.937i) q^{70} -4564.71i q^{71} -8077.75i q^{73} +(608.027 + 351.045i) q^{74} +(-386.551 - 669.527i) q^{76} +(1132.62 + 1961.75i) q^{77} +(4328.70 - 7497.52i) q^{79} +(4841.68 + 1241.52i) q^{80} +1510.67i q^{82} +(1670.06 - 2892.62i) q^{83} +(-599.171 - 2143.41i) q^{85} +(-1943.96 + 1122.34i) q^{86} +(-3384.99 - 1954.33i) q^{88} -10168.3i q^{89} +3581.05 q^{91} +(-3434.10 + 5948.04i) q^{92} +(-644.811 - 1116.84i) q^{94} +(351.531 + 1257.53i) q^{95} +(11868.3 + 6852.15i) q^{97} +2210.10 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} - 6 q^{5} + 28 q^{10} - 228 q^{11} - 282 q^{14} - 1058 q^{16} - 8 q^{19} + 2196 q^{20} - 148 q^{25} - 2370 q^{29} - 1112 q^{31} - 436 q^{34} - 850 q^{40} - 1830 q^{41} - 5668 q^{46} + 5396 q^{49}+ \cdots - 58746 q^{95}+O(q^{100}) \) 44 * q - 162 * q^4 - 6 * q^5 + 28 * q^10 - 228 * q^11 - 282 * q^14 - 1058 * q^16 - 8 * q^19 + 2196 * q^20 - 148 * q^25 - 2370 * q^29 - 1112 * q^31 - 436 * q^34 - 850 * q^40 - 1830 * q^41 - 5668 * q^46 + 5396 * q^49 - 13524 * q^50 - 3072 * q^55 + 8250 * q^56 + 27348 * q^59 + 2782 * q^61 + 8348 * q^64 + 24906 * q^65 + 4782 * q^70 - 64728 * q^74 - 1776 * q^76 + 7900 * q^79 + 6766 * q^85 - 9192 * q^86 + 1560 * q^91 - 18826 * q^94 - 58746 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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