LMFDB - Embedded newform 124.5.o.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,5,Mod(13,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("124.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	124.o (of order $30$, degree $8$, 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:	$12.8178754224$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	124.13
Dual form			124.5.o.a.105.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.80107 - 8.53733i) q^{3} +(-24.2686 - 42.0344i) q^{5} +(-45.8945 - 50.9710i) q^{7} +(-4.23837 + 4.70719i) q^{9} +O(q^{10})$	\(q+(-3.80107 - 8.53733i) q^{3} +(-24.2686 - 42.0344i) q^{5} +(-45.8945 - 50.9710i) q^{7} +(-4.23837 + 4.70719i) q^{9} +(44.2757 + 208.301i) q^{11} +(90.5539 + 9.51760i) q^{13} +(-266.616 + 366.965i) q^{15} +(20.6247 - 97.0315i) q^{17} +(-39.0113 - 371.168i) q^{19} +(-260.708 + 585.560i) q^{21} +(758.181 - 246.348i) q^{23} +(-865.430 + 1498.97i) q^{25} +(-663.621 - 215.624i) q^{27} +(-289.635 - 398.648i) q^{29} +(141.149 + 950.578i) q^{31} +(1610.04 - 1169.76i) q^{33} +(-1028.74 + 3166.14i) q^{35} +(-760.660 - 439.167i) q^{37} +(-262.946 - 809.266i) q^{39} +(-1750.07 - 779.181i) q^{41} +(1503.74 - 158.050i) q^{43} +(300.723 + 63.9207i) q^{45} +(-728.371 - 529.193i) q^{47} +(-240.765 + 2290.73i) q^{49} +(-906.786 + 192.743i) q^{51} +(-181.162 - 163.119i) q^{53} +(7681.31 - 6916.28i) q^{55} +(-3020.50 + 1743.88i) q^{57} +(-1635.49 + 728.169i) q^{59} -4159.73i q^{61} +434.448 q^{63} +(-1797.55 - 4037.36i) q^{65} +(3264.05 + 5653.51i) q^{67} +(-4985.05 - 5536.46i) q^{69} +(-627.285 + 696.670i) q^{71} +(1316.95 + 6195.75i) q^{73} +(16086.7 + 1690.78i) q^{75} +(8585.30 - 11816.6i) q^{77} +(-529.184 + 2489.62i) q^{79} +(735.247 + 6995.41i) q^{81} +(2522.89 - 5666.51i) q^{83} +(-4579.20 + 1487.87i) q^{85} +(-2302.47 + 3988.00i) q^{87} +(-7317.65 - 2377.65i) q^{89} +(-3670.80 - 5052.43i) q^{91} +(7578.88 - 4818.24i) q^{93} +(-14655.1 + 10647.5i) q^{95} +(1572.91 - 4840.92i) q^{97} +(-1168.17 - 674.443i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) $ 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9	$ 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) $ 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9 - 42 * q^11 + 6 * q^13 + 665 * q^15 - 585 * q^17 - 153 * q^19 - 402 * q^21 - 1365 * q^23 - 5933 * q^25 - 9225 * q^27 - 1140 * q^29 + 117 * q^31 + 5151 * q^33 + 2898 * q^35 + 6594 * q^37 + 3173 * q^39 - 9393 * q^41 - 5322 * q^43 + 2010 * q^45 - 5112 * q^47 - 5210 * q^49 - 1829 * q^51 + 7395 * q^53 + 10585 * q^55 + 40485 * q^57 + 5625 * q^59 - 14954 * q^63 - 17094 * q^65 + 8909 * q^67 - 35370 * q^69 - 11811 * q^71 - 22105 * q^73 + 79377 * q^75 + 71490 * q^77 + 219 * q^79 - 5422 * q^81 + 10545 * q^83 - 53630 * q^85 + 13732 * q^87 - 40305 * q^89 + 42760 * q^91 - 1028 * q^93 + 62319 * q^95 + 35201 * q^97 + 16197 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{11}{30}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−3.80107	−	8.53733i	−0.422341	−	0.948593i	−0.991945	−	0.126673i	$-0.959570\pi$
$3$	−3.80107	−	8.53733i	−0.422341	−	0.948593i	0.569604	−	0.821919i	$-0.307097\pi$
$4$		0			0
$5$	−24.2686	−	42.0344i	−0.970744	−	1.68138i	−0.693320	−	0.720630i	$-0.743853\pi$
$5$	−24.2686	−	42.0344i	−0.970744	−	1.68138i	−0.277424	−	0.960747i	$-0.589481\pi$
$6$		0			0
$7$	−45.8945	−	50.9710i	−0.936622	−	1.04022i	−0.999110	−	0.0421784i	$-0.986570\pi$
$7$	−45.8945	−	50.9710i	−0.936622	−	1.04022i	0.0624881	−	0.998046i	$-0.480096\pi$
$8$		0			0
$9$	−4.23837	+	4.70719i	−0.0523256	+	0.0581134i
$10$		0			0
$11$	44.2757	+	208.301i	0.365915	+	1.72150i	0.647592	+	0.761987i	$0.275776\pi$
$11$	44.2757	+	208.301i	0.365915	+	1.72150i	−0.281677	+	0.959509i	$0.590891\pi$
$12$		0			0
$13$	90.5539	+	9.51760i	0.535822	+	0.0563172i	0.368575	−	0.929598i	$-0.379846\pi$
$13$	90.5539	+	9.51760i	0.535822	+	0.0563172i	0.167247	+	0.985915i	$0.446512\pi$
$14$		0			0
$15$	−266.616	+	366.965i	−1.18496	+	1.63095i
$16$		0			0
$17$	20.6247	−	97.0315i	0.0713656	−	0.335749i	−0.927951	−	0.372701i	$-0.878432\pi$
$17$	20.6247	−	97.0315i	0.0713656	−	0.335749i	0.999317	+	0.0369523i	$0.0117650\pi$
$18$		0			0
$19$	−39.0113	−	371.168i	−0.108065	−	1.02817i	−0.905380	−	0.424602i	$-0.860414\pi$
$19$	−39.0113	−	371.168i	−0.108065	−	1.02817i	0.797315	−	0.603563i	$-0.206253\pi$
$20$		0			0
$21$	−260.708	+	585.560i	−0.591175	+	1.32780i
$22$		0			0
$23$	758.181	−	246.348i	1.43323	−	0.465686i	0.513453	−	0.858118i	$-0.328366\pi$
$23$	758.181	−	246.348i	1.43323	−	0.465686i	0.919781	+	0.392432i	$0.128366\pi$
$24$		0			0
$25$	−865.430	+	1498.97i	−1.38469	+	2.39835i
$26$		0			0
$27$	−663.621	−	215.624i	−0.910317	−	0.295780i
$28$		0			0
$29$	−289.635	−	398.648i	−0.344393	−	0.474017i	0.601325	−	0.799005i	$-0.294640\pi$
$29$	−289.635	−	398.648i	−0.344393	−	0.474017i	−0.945718	+	0.324988i	$0.894640\pi$
$30$		0			0
$31$	141.149	+	950.578i	0.146877	+	0.989155i
$31$	141.149	+	950.578i	0.146877	+	0.989155i
$32$		0			0
$33$	1610.04	−	1169.76i	1.47846	−	1.07416i
$34$		0			0
$35$	−1028.74	+	3166.14i	−0.839790	+	2.58461i
$36$		0			0
$37$	−760.660	−	439.167i	−0.555632	−	0.320794i	0.195759	−	0.980652i	$-0.437283\pi$
$37$	−760.660	−	439.167i	−0.555632	−	0.320794i	−0.751390	+	0.659858i	$0.770616\pi$
$38$		0			0
$39$	−262.946	−	809.266i	−0.172877	−	0.532062i
$40$		0			0
$41$	−1750.07	−	779.181i	−1.04109	−	0.463522i	−0.186297	−	0.982494i	$-0.559649\pi$
$41$	−1750.07	−	779.181i	−1.04109	−	0.463522i	−0.854792	+	0.518971i	$0.826315\pi$
$42$		0			0
$43$	1503.74	−	158.050i	0.813274	−	0.0854785i	0.311245	−	0.950330i	$-0.399254\pi$
$43$	1503.74	−	158.050i	0.813274	−	0.0854785i	0.502028	+	0.864851i	$0.332587\pi$
$44$		0			0
$45$	300.723	+	63.9207i	0.148505	+	0.0315658i
$46$		0			0
$47$	−728.371	−	529.193i	−0.329729	−	0.239562i	0.410587	−	0.911822i	$-0.365324\pi$
$47$	−728.371	−	529.193i	−0.329729	−	0.239562i	−0.740316	+	0.672259i	$0.765324\pi$
$48$		0			0
$49$	−240.765	+	2290.73i	−0.100277	+	0.954072i
$50$		0			0
$51$	−906.786	+	192.743i	−0.348630	+	0.0741035i
$52$		0			0
$53$	−181.162	−	163.119i	−0.0644936	−	0.0580703i	0.636254	−	0.771480i	$-0.280483\pi$
$53$	−181.162	−	163.119i	−0.0644936	−	0.0580703i	−0.700747	+	0.713410i	$0.747150\pi$
$54$		0			0
$55$	7681.31	−	6916.28i	2.53928	−	2.28637i
$56$		0			0
$57$	−3020.50	+	1743.88i	−0.929670	+	0.536745i
$58$		0			0
$59$	−1635.49	+	728.169i	−0.469834	+	0.209184i	−0.627976	−	0.778233i	$-0.716116\pi$
$59$	−1635.49	+	728.169i	−0.469834	+	0.209184i	0.158142	+	0.987416i	$0.449450\pi$
$60$		0			0
$61$		−	4159.73i		−	1.11791i	−0.829199	−	0.558953i	$-0.811203\pi$
$61$		−	4159.73i		−	1.11791i	0.829199	−	0.558953i	$-0.188797\pi$
$62$		0			0
$63$	434.448			0.109460
$64$		0			0
$65$	−1797.55	−	4037.36i	−0.425456	−	0.955589i
$66$		0			0
$67$	3264.05	+	5653.51i	0.727123	+	1.25941i	0.958094	+	0.286453i	$0.0924762\pi$
$67$	3264.05	+	5653.51i	0.727123	+	1.25941i	−0.230972	+	0.972961i	$0.574190\pi$
$68$		0			0
$69$	−4985.05	−	5536.46i	−1.04706	−	1.16288i
$70$		0			0
$71$	−627.285	+	696.670i	−0.124437	+	0.138201i	−0.802144	−	0.597131i	$-0.796307\pi$
$71$	−627.285	+	696.670i	−0.124437	+	0.138201i	0.677707	+	0.735332i	$0.262974\pi$
$72$		0			0
$73$	1316.95	+	6195.75i	0.247128	+	1.16265i	0.910225	+	0.414114i	$0.135909\pi$
$73$	1316.95	+	6195.75i	0.247128	+	1.16265i	−0.663097	+	0.748534i	$0.730758\pi$
$74$		0			0
$75$	16086.7	+	1690.78i	2.85987	+	0.300584i
$76$		0			0
$77$	8585.30	−	11816.6i	1.44802	−	1.99303i
$78$		0			0
$79$	−529.184	+	2489.62i	−0.0847916	+	0.398913i	−0.999992	−	0.00408672i	$-0.998699\pi$
$79$	−529.184	+	2489.62i	−0.0847916	+	0.398913i	0.915200	+	0.403000i	$0.132032\pi$
$80$		0			0
$81$	735.247	+	6995.41i	0.112063	+	1.06621i
$82$		0			0
$83$	2522.89	−	5666.51i	0.366220	−	0.822545i	−0.632623	−	0.774460i	$-0.718022\pi$
$83$	2522.89	−	5666.51i	0.366220	−	0.822545i	0.998843	−	0.0480845i	$-0.0153117\pi$
$84$		0			0
$85$	−4579.20	+	1487.87i	−0.633799	+	0.205934i
$86$		0			0
$87$	−2302.47	+	3988.00i	−0.304198	+	0.526886i
$88$		0			0
$89$	−7317.65	−	2377.65i	−0.923829	−	0.300170i	−0.191792	−	0.981436i	$-0.561430\pi$
$89$	−7317.65	−	2377.65i	−0.923829	−	0.300170i	−0.732037	+	0.681265i	$0.761430\pi$
$90$		0			0
$91$	−3670.80	−	5052.43i	−0.443280	−	0.610123i
$92$		0			0
$93$	7578.88	−	4818.24i	0.876273	−	0.557086i
$94$		0			0
$95$	−14655.1	+	10647.5i	−1.62383	+	1.17978i
$96$		0			0
$97$	1572.91	−	4840.92i	0.167171	−	0.514499i	−0.832019	−	0.554747i	$-0.812815\pi$
$97$	1572.91	−	4840.92i	0.167171	−	0.514499i	0.999190	+	0.0402482i	$0.0128149\pi$
$98$		0			0
$99$	−1168.17	−	674.443i	−0.119189	−	0.0688136i
$100$		0			0
$101$	−4921.37	−	15146.4i	−0.482440	−	1.48480i	−0.835654	−	0.549256i	$-0.814911\pi$
$101$	−4921.37	−	15146.4i	−0.482440	−	1.48480i	0.353214	−	0.935543i	$-0.385089\pi$
$102$		0			0
$103$	8720.64	+	3882.68i	0.822004	+	0.365980i	0.774250	−	0.632879i	$-0.218127\pi$
$103$	8720.64	+	3882.68i	0.822004	+	0.365980i	0.0477537	+	0.998859i	$0.484794\pi$
$104$		0			0
$105$	30940.7	−	3252.00i	2.80642	−	0.294966i
$106$		0			0
$107$	−12841.4	−	2729.52i	−1.12162	−	0.238407i	−0.390463	−	0.920619i	$-0.627685\pi$
$107$	−12841.4	−	2729.52i	−1.12162	−	0.238407i	−0.731155	+	0.682211i	$0.761018\pi$
$108$		0			0
$109$	−3554.62	−	2582.58i	−0.299185	−	0.217371i	0.428057	−	0.903752i	$-0.359198\pi$
$109$	−3554.62	−	2582.58i	−0.299185	−	0.217371i	−0.727242	+	0.686381i	$0.759198\pi$
$110$		0			0
$111$	−857.998	+	8163.31i	−0.0696371	+	0.662552i
$112$		0			0
$113$	−12632.7	+	2685.17i	−0.989329	+	0.210288i	−0.674030	−	0.738704i	$-0.735438\pi$
$113$	−12632.7	+	2685.17i	−0.989329	+	0.210288i	−0.315299	+	0.948992i	$0.602105\pi$
$114$		0			0
$115$	−28755.1	−	25891.2i	−2.17430	−	1.95775i
$116$		0			0
$117$	−428.602	+	385.915i	−0.0313100	+	0.0281916i
$118$		0			0
$119$	−5892.35	+	3401.95i	−0.416097	+	0.240234i
$120$		0			0
$121$	−28053.8	+	12490.3i	−1.91611	+	0.853107i
$122$		0			0
$123$			17902.6i			1.18333i
$124$		0			0
$125$	53675.3			3.43522
$126$		0			0
$127$	8629.87	+	19383.0i	0.535053	+	1.20175i	0.955651	+	0.294501i	$0.0951535\pi$
$127$	8629.87	+	19383.0i	0.535053	+	1.20175i	−0.420598	+	0.907247i	$0.638180\pi$
$128$		0			0
$129$	−7065.15	−	12237.2i	−0.424563	−	0.735364i
$130$		0			0
$131$	10531.5	+	11696.5i	0.613690	+	0.681572i	0.967246	−	0.253842i	$-0.0816942\pi$
$131$	10531.5	+	11696.5i	0.613690	+	0.681572i	−0.353556	+	0.935413i	$0.615028\pi$
$132$		0			0
$133$	−17128.4	+	19023.0i	−0.968307	+	1.07541i
$134$		0			0
$135$	7041.54	+	33127.8i	0.386367	+	1.81771i
$136$		0			0
$137$	2702.39	+	284.033i	0.143982	+	0.0151331i	0.176245	−	0.984346i	$-0.443605\pi$
$137$	2702.39	+	284.033i	0.143982	+	0.0151331i	−0.0322634	+	0.999479i	$0.510272\pi$
$138$		0			0
$139$	−7706.33	+	10606.9i	−0.398858	+	0.548981i	−0.960457	−	0.278429i	$-0.910186\pi$
$139$	−7706.33	+	10606.9i	−0.398858	+	0.548981i	0.561599	+	0.827409i	$0.310186\pi$
$140$		0			0
$141$	−1749.31	+	8229.84i	−0.0879889	+	0.413955i
$142$		0			0
$143$	2026.82	+	19283.9i	0.0991157	+	0.943023i
$144$		0			0
$145$	−9727.92	+	21849.3i	−0.462684	+	1.03920i
$146$		0			0
$147$	20471.9	−	6651.71i	0.947376	−	0.307821i
$148$		0			0
$149$	−7326.95	+	12690.6i	−0.330028	+	0.571625i	−0.982517	−	0.186173i	$-0.940391\pi$
$149$	−7326.95	+	12690.6i	−0.330028	+	0.571625i	0.652489	+	0.757798i	$0.273725\pi$
$150$		0			0
$151$	5057.29	+	1643.21i	0.221801	+	0.0720676i	0.417809	−	0.908535i	$-0.362798\pi$
$151$	5057.29	+	1643.21i	0.221801	+	0.0720676i	−0.196008	+	0.980602i	$0.562798\pi$
$152$		0			0
$153$	369.330	+	508.339i	0.0157773	+	0.0217156i
$154$		0			0
$155$	36531.5	−	29002.3i	1.52056	−	1.20717i
$156$		0			0
$157$	−4365.16	+	3171.48i	−0.177093	+	0.128665i	−0.672800	−	0.739824i	$-0.734909\pi$
$157$	−4365.16	+	3171.48i	−0.177093	+	0.128665i	0.495708	+	0.868489i	$0.334909\pi$
$158$		0			0
$159$	−703.994	+	2166.67i	−0.0278468	+	0.0857036i
$160$		0			0
$161$	−47352.9	−	27339.2i	−1.82682	−	1.05471i
$162$		0			0
$163$	−12175.4	−	37472.0i	−0.458256	−	1.41037i	−0.867270	−	0.497838i	$-0.834127\pi$
$163$	−12175.4	−	37472.0i	−0.458256	−	1.41037i	0.409015	−	0.912528i	$-0.365873\pi$
$164$		0			0
$165$	−88243.7	−	39288.6i	−3.24128	−	1.44311i
$166$		0			0
$167$	−28262.7	+	2970.53i	−1.01340	+	0.106513i	−0.596644	−	0.802506i	$-0.703499\pi$
$167$	−28262.7	+	2970.53i	−1.01340	+	0.106513i	−0.416755	+	0.909019i	$0.636833\pi$
$168$		0			0
$169$	−19827.4	−	4214.45i	−0.694214	−	0.147560i
$170$		0			0
$171$	1912.50	+	1389.51i	0.0654047	+	0.0475193i
$172$		0			0
$173$	5434.96	−	51710.2i	0.181595	−	1.72776i	−0.401932	−	0.915669i	$-0.631661\pi$
$173$	5434.96	−	51710.2i	0.181595	−	1.72776i	0.583528	−	0.812093i	$-0.301672\pi$
$174$		0			0
$175$	116122.	−	24682.6i	3.79175	−	0.805961i
$176$		0			0
$177$	12433.2	+	11194.9i	0.396860	+	0.357335i
$178$		0			0
$179$	34575.0	−	31131.5i	1.07909	−	0.971615i	0.0794059	−	0.996842i	$-0.474698\pi$
$179$	34575.0	−	31131.5i	1.07909	−	0.971615i	0.999682	+	0.0252275i	$0.00803100\pi$
$180$		0			0
$181$	1785.79	−	1031.03i	0.0545097	−	0.0314712i	−0.472497	−	0.881332i	$-0.656647\pi$
$181$	1785.79	−	1031.03i	0.0545097	−	0.0314712i	0.527007	+	0.849861i	$0.323314\pi$
$182$		0			0
$183$	−35513.0	+	15811.4i	−1.06044	+	0.472137i
$184$		0			0
$185$			42631.9i			1.24564i
$186$		0			0
$187$	21124.9			0.604104
$188$		0			0
$189$	19466.0	+	43721.4i	0.544946	+	1.22397i
$190$		0			0
$191$	−1289.30	−	2233.14i	−0.0353418	−	0.0612138i	0.847813	−	0.530295i	$-0.177919\pi$
$191$	−1289.30	−	2233.14i	−0.0353418	−	0.0612138i	−0.883155	+	0.469081i	$0.844585\pi$
$192$		0			0
$193$	−2023.44	−	2247.26i	−0.0543220	−	0.0603307i	0.715371	−	0.698744i	$-0.246258\pi$
$193$	−2023.44	−	2247.26i	−0.0543220	−	0.0603307i	−0.769693	+	0.638414i	$0.779591\pi$
$194$		0			0
$195$	−27635.7	+	30692.6i	−0.726777	+	0.807168i
$196$		0			0
$197$	−5911.40	−	27811.0i	−0.152320	−	0.716611i	−0.986319	−	0.164845i	$-0.947287\pi$
$197$	−5911.40	−	27811.0i	−0.152320	−	0.716611i	0.833999	−	0.551766i	$-0.186046\pi$
$198$		0			0
$199$	−14278.8	−	1500.76i	−0.360567	−	0.0378971i	−0.0774869	−	0.996993i	$-0.524690\pi$
$199$	−14278.8	−	1500.76i	−0.360567	−	0.0378971i	−0.283080	+	0.959096i	$0.591356\pi$
$200$		0			0
$201$	35859.0	−	49355.7i	0.887577	−	1.22164i
$202$		0			0
$203$	−7026.85	+	33058.7i	−0.170517	+	0.802221i
$204$		0			0
$205$	9719.29	+	92472.8i	0.231274	+	2.20042i
$206$		0			0
$207$	−2053.85	+	4613.01i	−0.0479322	+	0.107657i
$208$		0			0
$209$	75587.4	−	24559.8i	1.73044	−	0.562254i
$210$		0			0
$211$	10790.7	−	18690.1i	0.242374	−	0.419804i	−0.719016	−	0.694993i	$-0.755407\pi$
$211$	10790.7	−	18690.1i	0.242374	−	0.419804i	0.961390	+	0.275189i	$0.0887406\pi$
$212$		0			0
$213$	8332.05	+	2707.25i	0.183651	+	0.0596718i
$214$		0			0
$215$	−43137.3	−	59373.3i	−0.933202	−	1.28444i
$216$		0			0
$217$	41973.9	−	50820.8i	0.891375	−	1.07925i
$218$		0			0
$219$	47889.4	−	34793.7i	0.998507	−	0.725458i
$220$		0			0
$221$	2791.15	−	8590.28i	0.0571477	−	0.175883i
$222$		0			0
$223$	12226.6	+	7059.02i	0.245864	+	0.141950i	0.617869	−	0.786281i	$-0.287996\pi$
$223$	12226.6	+	7059.02i	0.245864	+	0.141950i	−0.372005	+	0.928231i	$0.621330\pi$
$224$		0			0
$225$	−3387.91	−	10426.9i	−0.0669217	−	0.205964i
$226$		0			0
$227$	21684.0	+	9654.33i	0.420811	+	0.187357i	0.606207	−	0.795307i	$-0.292690\pi$
$227$	21684.0	+	9654.33i	0.420811	+	0.187357i	−0.185396	+	0.982664i	$0.559357\pi$
$228$		0			0
$229$	78850.5	−	8287.52i	1.50360	−	0.158035i	0.683374	−	0.730069i	$-0.260512\pi$
$229$	78850.5	−	8287.52i	1.50360	−	0.158035i	0.820230	+	0.572034i	$0.193845\pi$
$230$		0			0
$231$	−133516.	−	28379.7i	−2.50213	−	0.531843i
$232$		0			0
$233$	−64238.8	−	46672.2i	−1.18327	−	0.859699i	−0.190737	−	0.981641i	$-0.561088\pi$
$233$	−64238.8	−	46672.2i	−1.18327	−	0.859699i	−0.992537	+	0.121942i	$0.961088\pi$
$234$		0			0
$235$	−4567.77	+	43459.4i	−0.0827120	+	0.786952i
$236$		0			0
$237$	23266.2	−	4945.37i	0.414217	−	0.0880445i
$238$		0			0
$239$	−40431.5	−	36404.7i	−0.707822	−	0.637325i	0.234468	−	0.972124i	$-0.424665\pi$
$239$	−40431.5	−	36404.7i	−0.707822	−	0.637325i	−0.942290	+	0.334798i	$0.891332\pi$
$240$		0			0
$241$	−61343.7	+	55234.1i	−1.05618	+	0.950985i	−0.998877	−	0.0473723i	$-0.984915\pi$
$241$	−61343.7	+	55234.1i	−1.05618	+	0.950985i	−0.0572983	+	0.998357i	$0.518249\pi$
$242$		0			0
$243$	7980.02	−	4607.27i	0.135142	−	0.0780245i
$244$		0			0
$245$	102132.	−	45472.3i	1.70150	−	0.757556i
$246$		0			0
$247$		−	33982.0i		−	0.557000i
$248$		0			0
$249$	−57966.6			−0.934929
$250$		0			0
$251$	−28686.5	−	64430.9i	−0.455334	−	1.02270i	−0.984693	−	0.174299i	$-0.944234\pi$
$251$	−28686.5	−	64430.9i	−0.455334	−	1.02270i	0.529359	−	0.848398i	$-0.322433\pi$
$252$		0			0
$253$	84883.6	+	147023.i	1.32612	+	2.29691i
$254$		0			0
$255$	30108.3	+	33438.6i	0.463026	+	0.514242i
$256$		0			0
$257$	37360.0	−	41492.4i	0.565640	−	0.628207i	−0.390681	−	0.920526i	$-0.627760\pi$
$257$	37360.0	−	41492.4i	0.565640	−	0.628207i	0.956321	+	0.292319i	$0.0944270\pi$
$258$		0			0
$259$	12525.3	+	58926.9i	0.186719	+	0.878444i
$260$		0			0
$261$	3104.09	+	326.253i	0.0455673	+	0.00478932i
$262$		0			0
$263$	50624.5	−	69678.7i	0.731896	−	1.00737i	−0.267148	−	0.963656i	$-0.586081\pi$
$263$	50624.5	−	69678.7i	0.731896	−	1.00737i	0.999044	−	0.0437134i	$-0.0139188\pi$
$264$		0			0
$265$	−2460.07	+	11573.7i	−0.0350313	+	0.164809i
$266$		0			0
$267$	7516.09	+	71510.8i	0.105431	+	1.00311i
$268$		0			0
$269$	−43408.8	+	97497.9i	−0.599893	+	1.34738i	0.317068	+	0.948403i	$0.397302\pi$
$269$	−43408.8	+	97497.9i	−0.599893	+	1.34738i	−0.916960	+	0.398978i	$0.869365\pi$
$270$		0			0
$271$	−20832.2	+	6768.78i	−0.283658	+	0.0921662i	−0.447391	−	0.894339i	$-0.647647\pi$
$271$	−20832.2	+	6768.78i	−0.283658	+	0.0921662i	0.163732	+	0.986505i	$0.447647\pi$
$272$		0			0
$273$	−29181.3	+	50543.5i	−0.391543	+	0.678172i
$274$		0			0
$275$	−350554.	−	113902.i	−4.63543	−	1.50614i
$276$		0			0
$277$	−17705.0	−	24368.9i	−0.230748	−	0.317597i	0.677905	−	0.735149i	$-0.262888\pi$
$277$	−17705.0	−	24368.9i	−0.230748	−	0.317597i	−0.908653	+	0.417552i	$0.862888\pi$
$278$		0			0
$279$	−5072.79	−	3364.49i	−0.0651686	−	0.0432226i
$280$		0			0
$281$	−17735.6	+	12885.6i	−0.224612	+	0.163190i	−0.694400	−	0.719589i	$-0.744330\pi$
$281$	−17735.6	+	12885.6i	−0.224612	+	0.163190i	0.469788	+	0.882779i	$0.344330\pi$
$282$		0			0
$283$	16557.5	−	50958.7i	0.206739	−	0.636276i	−0.792899	−	0.609353i	$-0.791429\pi$
$283$	16557.5	−	50958.7i	0.206739	−	0.636276i	0.999638	−	0.0269230i	$-0.00857091\pi$
$284$		0			0
$285$	146606.	+	84643.3i	1.80494	+	1.04208i
$286$		0			0
$287$	40602.9	+	124963.i	0.492939	+	1.51711i
$288$		0			0
$289$	67310.5	+	29968.6i	0.805911	+	0.358815i
$290$		0			0
$291$	−47307.3	+	4972.20i	−0.558653	+	0.0587168i
$292$		0			0
$293$	78831.4	+	16756.1i	0.918257	+	0.195181i	0.642713	−	0.766107i	$-0.277809\pi$
$293$	78831.4	+	16756.1i	0.918257	+	0.195181i	0.275544	+	0.961289i	$0.411142\pi$
$294$		0			0
$295$	70299.3	+	51075.4i	0.807806	+	0.586905i
$296$		0			0
$297$	15532.3	−	147780.i	0.176085	−	1.67534i
$298$		0			0
$299$	71000.9	−	15091.7i	0.794185	−	0.168809i
$300$		0			0
$301$	−77069.4	−	69393.6i	−0.850647	−	0.765926i
$302$		0			0
$303$	−110604.	+	99588.0i	−1.20471	+	1.08473i
$304$		0			0
$305$	−174852.	+	100951.i	−1.87962	+	1.08520i
$306$		0			0
$307$	−82451.3	+	36709.7i	−0.874825	+	0.389497i	−0.794495	−	0.607271i	$-0.792264\pi$
$307$	−82451.3	+	36709.7i	−0.874825	+	0.389497i	−0.0803300	+	0.996768i	$0.525597\pi$
$308$		0			0
$309$		−	89209.3i		−	0.934315i
$310$		0			0
$311$	52490.7			0.542702			0.271351	−	0.962480i	$-0.412530\pi$
$311$	52490.7			0.542702			0.271351	+	0.962480i	$0.412530\pi$
$312$		0			0
$313$	−6598.52	−	14820.5i	−0.0673532	−	0.151278i	0.876732	−	0.480979i	$-0.159719\pi$
$313$	−6598.52	−	14820.5i	−0.0673532	−	0.151278i	−0.944085	+	0.329701i	$0.893052\pi$
$314$		0			0
$315$	−10543.4	−	18261.8i	−0.106258	−	0.184044i
$316$		0			0
$317$	−98409.2	−	109294.i	−0.979303	−	1.08763i	−0.996141	−	0.0877682i	$-0.972027\pi$
$317$	−98409.2	−	109294.i	−0.979303	−	1.08763i	0.0168377	−	0.999858i	$-0.494640\pi$
$318$		0			0
$319$	70215.0	−	77981.7i	0.689999	−	0.766322i
$320$		0			0
$321$	25508.2	+	120006.i	0.247553	+	1.16465i
$322$		0			0
$323$	−36819.5	−	3869.89i	−0.352918	−	0.0370931i
$324$		0			0
$325$	−92634.6	+	127501.i	−0.877014	+	1.20711i
$326$		0			0
$327$	−8537.03	+	40163.6i	−0.0798383	+	0.375610i
$328$		0			0
$329$	6454.75	+	61412.8i	0.0596331	+	0.567371i
$330$		0			0
$331$	−9813.15	+	22040.7i	−0.0895679	+	0.201173i	−0.952775	−	0.303677i	$-0.901786\pi$
$331$	−9813.15	+	22040.7i	−0.0895679	+	0.201173i	0.863207	+	0.504850i	$0.168452\pi$
$332$		0			0
$333$	5291.20	−	1719.21i	0.0477162	−	0.0155039i
$334$		0			0
$335$	158428.	−	274405.i	1.41170	−	2.44514i
$336$		0			0
$337$	134809.	+	43802.1i	1.18702	+	0.385687i	0.834972	−	0.550293i	$-0.185484\pi$
$337$	134809.	+	43802.1i	1.18702	+	0.385687i	0.352052	+	0.935980i	$0.385484\pi$
$338$		0			0
$339$	70942.1	+	97643.4i	0.617312	+	0.849657i
$340$		0			0
$341$	−191757.	+	71488.9i	−1.64908	+	0.614795i
$342$		0			0
$343$	−5418.83	+	3937.01i	−0.0460593	+	0.0334641i
$344$		0			0
$345$	−111742.	+	343906.i	−0.938809	+	2.88936i
$346$		0			0
$347$	64855.1	+	37444.1i	0.538623	+	0.310974i	0.744521	−	0.667599i	$-0.232678\pi$
$347$	64855.1	+	37444.1i	0.538623	+	0.310974i	−0.205897	+	0.978574i	$0.566011\pi$
$348$		0			0
$349$	−13321.6	−	40999.7i	−0.109372	−	0.336613i	0.881360	−	0.472446i	$-0.156629\pi$
$349$	−13321.6	−	40999.7i	−0.109372	−	0.336613i	−0.990732	+	0.135833i	$0.956629\pi$
$350$		0			0
$351$	−58041.3	−	25841.7i	−0.471111	−	0.209752i
$352$		0			0
$353$	128684.	−	13525.2i	1.03270	−	0.108541i	0.427014	−	0.904245i	$-0.359566\pi$
$353$	128684.	−	13525.2i	1.03270	−	0.108541i	0.605686	+	0.795704i	$0.292899\pi$
$354$		0			0
$355$	44507.5	+	9460.35i	0.353164	+	0.0750673i
$356$		0			0
$357$	51440.8	+	37373.9i	0.403618	+	0.293246i
$358$		0			0
$359$	−5719.37	+	54416.2i	−0.0443771	+	0.422220i	0.949669	+	0.313256i	$0.101420\pi$
$359$	−5719.37	+	54416.2i	−0.0443771	+	0.422220i	−0.994046	+	0.108964i	$0.965247\pi$
$360$		0			0
$361$	−8770.38	+	1864.20i	−0.0672983	+	0.0143047i
$362$		0			0
$363$	213268.	+	192028.i	1.61850	+	1.45731i
$364$		0			0
$365$	228474.	−	205719.i	1.71495	−	1.54415i
$366$		0			0
$367$	−50435.2	+	29118.8i	−0.374457	+	0.216193i	−0.675404	−	0.737448i	$-0.736031\pi$
$367$	−50435.2	+	29118.8i	−0.374457	+	0.216193i	0.300947	+	0.953641i	$0.402697\pi$
$368$		0			0
$369$	11085.2	−	4935.45i	0.0814124	−	0.0362471i
$370$		0			0
$371$			16720.3i			0.121478i
$372$		0			0
$373$	186368.			1.33954			0.669769	−	0.742570i	$-0.266393\pi$
$373$	186368.			1.33954			0.669769	+	0.742570i	$0.266393\pi$
$374$		0			0
$375$	−204023.	−	458244.i	−1.45083	−	3.25862i
$376$		0			0
$377$	−22433.4	−	38855.8i	−0.157838	−	0.273384i
$378$		0			0
$379$	−155548.	−	172754.i	−1.08289	−	1.20268i	−0.978090	−	0.208183i	$-0.933245\pi$
$379$	−155548.	−	172754.i	−1.08289	−	1.20268i	−0.104804	−	0.994493i	$-0.533421\pi$
$380$		0			0
$381$	132676.	−	147352.i	0.913995	−	1.01509i
$382$		0			0
$383$	−1866.60	−	8781.67i	−0.0127249	−	0.0598659i	0.971327	−	0.237747i	$-0.0764090\pi$
$383$	−1866.60	−	8781.67i	−0.0127249	−	0.0598659i	−0.984052	+	0.177881i	$0.943076\pi$
$384$		0			0
$385$	−705059.	−	74104.7i	−4.75668	−	0.499947i
$386$		0			0
$387$	−5629.45	+	7748.27i	−0.0375875	+	0.0517348i
$388$		0			0
$389$	−26907.4	+	126589.i	−0.177817	+	0.836562i	0.795294	+	0.606224i	$0.207317\pi$
$389$	−26907.4	+	126589.i	−0.177817	+	0.836562i	−0.973111	+	0.230338i	$0.926017\pi$
$390$		0			0
$391$	−8266.26	−	78648.2i	−0.0540699	−	0.514441i
$392$		0			0
$393$	59825.5	−	134370.i	0.387348	−	0.869997i
$394$		0			0
$395$	117492.	−	38175.5i	0.753035	−	0.244676i
$396$		0			0
$397$	12673.8	−	21951.6i	0.0804127	−	0.139279i	−0.823015	−	0.568020i	$-0.807710\pi$
$397$	12673.8	−	21951.6i	0.0804127	−	0.139279i	0.903427	+	0.428741i	$0.141043\pi$
$398$		0			0
$399$	227512.	+	73923.0i	1.42908	+	0.464338i
$400$		0			0
$401$	23860.5	+	32841.2i	0.148385	+	0.204235i	0.876739	−	0.480966i	$-0.159714\pi$
$401$	23860.5	+	32841.2i	0.148385	+	0.204235i	−0.728354	+	0.685201i	$0.759714\pi$
$402$		0			0
$403$	3734.34	+	87421.9i	0.0229934	+	0.538283i
$404$		0			0
$405$	276205.	−	200675.i	1.68392	−	1.22344i
$406$		0			0
$407$	57800.2	−	177891.i	0.348932	−	1.07390i
$408$		0			0
$409$	−36441.2	−	21039.3i	−0.217844	−	0.125772i	0.387108	−	0.922035i	$-0.373474\pi$
$409$	−36441.2	−	21039.3i	−0.217844	−	0.125772i	−0.604952	+	0.796262i	$0.706808\pi$
$410$		0			0
$411$	−7847.09	−	24150.9i	−0.0464542	−	0.142971i
$412$		0			0
$413$	112176.	+	49943.8i	0.657655	+	0.292807i
$414$		0			0
$415$	−299416.	+	31469.9i	−1.73851	+	0.182725i
$416$		0			0
$417$	119846.	+	25474.2i	0.689213	+	0.146497i
$418$		0			0
$419$	−67489.2	−	49033.8i	−0.384420	−	0.279298i	0.378745	−	0.925501i	$-0.376356\pi$
$419$	−67489.2	−	49033.8i	−0.384420	−	0.279298i	−0.763165	+	0.646204i	$0.776356\pi$
$420$		0			0
$421$	23045.6	−	219264.i	0.130024	−	1.23709i	−0.713752	−	0.700399i	$-0.753006\pi$
$421$	23045.6	−	219264.i	0.130024	−	1.23709i	0.843776	−	0.536696i	$-0.180328\pi$
$422$		0			0
$423$	5578.11	−	1185.66i	0.0311750	−	0.00662645i
$424$		0			0
$425$	127598.	+	114890.i	0.706424	+	0.636067i
$426$		0			0
$427$	−212025.	+	190909.i	−1.16287	+	1.04706i
$428$		0			0
$429$	156929.	−	90602.9i	0.852684	−	0.492297i
$430$		0			0
$431$	82758.0	−	36846.2i	0.445508	−	0.198353i	−0.171706	−	0.985148i	$-0.554928\pi$
$431$	82758.0	−	36846.2i	0.445508	−	0.198353i	0.617214	+	0.786795i	$0.288261\pi$
$432$		0			0
$433$		−	116978.i		−	0.623919i	−0.950095	−	0.311960i	$-0.899015\pi$
$433$		−	116978.i		−	0.623919i	0.950095	−	0.311960i	$-0.100985\pi$
$434$		0			0
$435$	223511.			1.18119
$436$		0			0
$437$	−121014.	−	271802.i	−0.633684	−	1.42328i
$438$		0			0
$439$	−55333.8	−	95840.9i	−0.287119	−	0.497304i	0.686002	−	0.727600i	$-0.259364\pi$
$439$	−55333.8	−	95840.9i	−0.287119	−	0.497304i	−0.973121	+	0.230295i	$0.926031\pi$
$440$		0			0
$441$	−9762.42	−	10842.3i	−0.0501973	−	0.0557498i
$442$		0			0
$443$	−160896.	+	178693.i	−0.819855	+	0.910541i	−0.997288	−	0.0735916i	$-0.976554\pi$
$443$	−160896.	+	178693.i	−0.819855	+	0.910541i	0.177433	+	0.984133i	$0.443221\pi$
$444$		0			0
$445$	77646.0	+	365295.i	0.392102	+	1.84469i
$446$		0			0
$447$	136194.	+	14314.6i	0.681623	+	0.0716415i
$448$		0			0
$449$	−148609.	+	204543.i	−0.737144	+	1.01459i	0.261634	+	0.965167i	$0.415739\pi$
$449$	−148609.	+	204543.i	−0.737144	+	1.01459i	−0.998778	+	0.0494247i	$0.984261\pi$
$450$		0			0
$451$	84818.6	−	399040.i	0.417002	−	1.96184i
$452$		0			0
$453$	−5194.43	−	49421.7i	−0.0253129	−	0.240836i
$454$		0			0
$455$	−123291.	+	276916.i	−0.595536	+	1.33759i
$456$		0			0
$457$	87095.1	−	28298.9i	0.417024	−	0.135499i	−0.0929865	−	0.995667i	$-0.529641\pi$
$457$	87095.1	−	28298.9i	0.417024	−	0.135499i	0.510011	+	0.860168i	$0.329641\pi$
$458$		0			0
$459$	−34609.3	+	59945.0i	−0.164273	+	0.284530i
$460$		0			0
$461$	109486.	+	35574.2i	0.515178	+	0.167391i	0.555056	−	0.831813i	$-0.312697\pi$
$461$	109486.	+	35574.2i	0.515178	+	0.167391i	−0.0398781	+	0.999205i	$0.512697\pi$
$462$		0			0
$463$	201547.	+	277405.i	0.940187	+	1.29406i	0.955751	+	0.294177i	$0.0950455\pi$
$463$	201547.	+	277405.i	0.940187	+	1.29406i	−0.0155644	+	0.999879i	$0.504954\pi$
$464$		0			0
$465$	−386461.	−	201642.i	−1.78731	−	0.932557i
$466$		0			0
$467$	−43483.0	+	31592.2i	−0.199382	+	0.144859i	−0.682997	−	0.730422i	$-0.739324\pi$
$467$	−43483.0	+	31592.2i	−0.199382	+	0.144859i	0.483615	+	0.875281i	$0.339324\pi$
$468$		0			0
$469$	138363.	−	425837.i	0.629033	−	1.93597i
$470$		0			0
$471$	43668.2	+	25211.8i	0.196845	+	0.113648i
$472$		0			0
$473$	99501.3	+	306233.i	0.444740	+	1.36877i
$474$		0			0
$475$	590130.	+	262743.i	2.61553	+	1.16451i
$476$		0			0
$477$	1535.67	−	161.405i	0.00674932	−	0.000709383i
$478$		0			0
$479$	−25691.6	−	5460.92i	−0.111975	−	0.0238010i	0.151583	−	0.988444i	$-0.451563\pi$
$479$	−25691.6	−	5460.92i	−0.111975	−	0.0238010i	−0.263558	+	0.964643i	$0.584896\pi$
$480$		0			0
$481$	−64700.9	−	47008.0i	−0.279654	−	0.203180i
$482$		0			0
$483$	−53412.5	+	508186.i	−0.228954	+	2.17835i
$484$		0			0
$485$	−241658.	+	51366.0i	−1.02735	+	0.218370i
$486$		0			0
$487$	9869.19	+	8886.26i	0.0416125	+	0.0374681i	0.689675	−	0.724119i	$-0.257754\pi$
$487$	9869.19	+	8886.26i	0.0416125	+	0.0374681i	−0.648062	+	0.761588i	$0.724420\pi$
$488$		0			0
$489$	−273632.	+	246379.i	−1.14432	+	1.03035i
$490$		0			0
$491$	345480.	−	199463.i	1.43305	−	0.827370i	0.435694	−	0.900095i	$-0.356503\pi$
$491$	345480.	−	199463.i	1.43305	−	0.827370i	0.997352	+	0.0727249i	$0.0231695\pi$
$492$		0			0
$493$	−44655.0	+	19881.7i	−0.183729	+	0.0818012i
$494$		0			0
$495$			65471.1i			0.267202i
$496$		0			0
$497$	64298.9			0.260310
$498$		0			0
$499$	−54005.5	−	121298.i	−0.216889	−	0.487140i	0.772032	−	0.635583i	$-0.219240\pi$
$499$	−54005.5	−	121298.i	−0.216889	−	0.487140i	−0.988921	+	0.148444i	$0.952574\pi$
$500$		0			0
$501$	132789.	+	229997.i	0.529037	+	0.916318i
$502$		0			0
$503$	−148499.	−	164925.i	−0.586931	−	0.651853i	0.374394	−	0.927270i	$-0.377851\pi$
$503$	−148499.	−	164925.i	−0.586931	−	0.651853i	−0.961325	+	0.275417i	$0.911184\pi$
$504$		0			0
$505$	−517237.	+	574450.i	−2.02818	+	2.25252i
$506$		0			0
$507$	39385.2	+	185293.i	0.153221	+	0.720847i
$508$		0			0
$509$	−281439.	−	29580.4i	−1.08630	−	0.114174i	−0.455585	−	0.890192i	$-0.650570\pi$
$509$	−281439.	−	29580.4i	−1.08630	−	0.114174i	−0.630711	+	0.776018i	$0.717237\pi$
$510$		0			0
$511$	255363.	−	351477.i	0.977948	−	1.34603i
$512$		0			0
$513$	−54143.8	+	254727.i	−0.205738	+	0.967920i
$514$		0			0
$515$	−48431.5	−	460795.i	−0.182605	−	1.73737i
$516$		0			0
$517$	77982.2	−	175151.i	0.291752	−	0.655286i
$518$		0			0
$519$	−462126.	+	150154.i	−1.71564	+	0.557444i
$520$		0			0
$521$	147992.	−	256330.i	0.545210	−	0.944331i	−0.453384	−	0.891315i	$-0.649783\pi$
$521$	147992.	−	256330.i	0.545210	−	0.944331i	0.998594	−	0.0530158i	$-0.0168834\pi$
$522$		0			0
$523$	−97898.8	−	31809.2i	−0.357910	−	0.116292i	0.124542	−	0.992214i	$-0.460254\pi$
$523$	−97898.8	−	31809.2i	−0.357910	−	0.116292i	−0.482452	+	0.875922i	$0.660254\pi$
$524$		0			0
$525$	−652112.	−	897555.i	−2.36594	−	3.25643i
$526$		0			0
$527$	95147.1	+	5909.50i	0.342590	+	0.0212779i
$528$		0			0
$529$	287755.	−	209066.i	1.02828	−	0.747089i
$530$		0			0
$531$	3504.20	−	10784.8i	0.0124280	−	0.0382493i
$532$		0			0
$533$	−151060.	−	87214.4i	−0.531734	−	0.306997i
$534$		0			0
$535$	196909.	+	606023.i	0.687951	+	2.11730i
$536$		0			0
$537$	−397202.	−	176846.i	−1.37741	−	0.613262i
$538$		0			0
$539$	−487821.	+	51272.0i	−1.67912	+	0.176483i
$540$		0			0
$541$	455702.	+	96862.5i	1.55699	+	0.330949i	0.904375	−	0.426739i	$-0.140338\pi$
$541$	455702.	+	96862.5i	1.55699	+	0.330949i	0.652617	+	0.757688i	$0.273671\pi$
$542$		0			0
$543$	−15590.1	−	11326.9i	−0.0528750	−	0.0384159i
$544$		0			0
$545$	−22291.8	+	212092.i	−0.0750502	+	0.714055i
$546$		0			0
$547$	−559134.	+	118848.i	−1.86871	+	0.397206i	−0.995869	−	0.0908031i	$-0.971057\pi$
$547$	−559134.	+	118848.i	−1.86871	+	0.397206i	−0.872839	+	0.488009i	$0.837723\pi$
$548$		0			0
$549$	19580.6	+	17630.5i	0.0649653	+	0.0584950i
$550$		0			0
$551$	−136666.	+	123055.i	−0.450151	+	0.405318i
$552$		0			0
$553$	151185.	−	87286.6i	0.494377	−	0.285429i
$554$		0			0
$555$	363963.	−	162047.i	1.18160	−	0.526083i
$556$		0			0
$557$		−	95299.6i		−	0.307171i	−0.988135	−	0.153586i	$-0.950918\pi$
$557$		−	95299.6i		−	0.307171i	0.988135	−	0.153586i	$-0.0490821\pi$
$558$		0			0
$559$	137674.			0.440584
$560$		0			0
$561$	−80297.2	−	180351.i	−0.255138	−	0.573049i
$562$		0			0
$563$	298397.	+	516838.i	0.941406	+	1.63056i	0.762792	+	0.646644i	$0.223828\pi$
$563$	298397.	+	516838.i	0.941406	+	1.63056i	0.178615	+	0.983919i	$0.442838\pi$
$564$		0			0
$565$	419449.	+	465845.i	1.31396	+	1.45930i
$566$		0			0
$567$	322819.	−	358527.i	1.00414	−	1.11521i
$568$		0			0
$569$	−51593.4	−	242728.i	−0.159356	−	0.749713i	−0.983147	−	0.182818i	$-0.941478\pi$
$569$	−51593.4	−	242728.i	−0.159356	−	0.749713i	0.823790	−	0.566895i	$-0.191855\pi$
$570$		0			0
$571$	−85241.4	−	8959.23i	−0.261444	−	0.0274789i	−0.0271004	−	0.999633i	$-0.508627\pi$
$571$	−85241.4	−	8959.23i	−0.261444	−	0.0274789i	−0.234344	+	0.972154i	$0.575294\pi$
$572$		0			0
$573$	−14164.3	+	19495.5i	−0.0431407	+	0.0593780i
$574$		0			0
$575$	−286885.	+	1.34969e6i	−0.867704	+	4.08223i
$576$		0			0
$577$	−1056.55	−	10052.4i	−0.00317350	−	0.0301939i	0.992821	−	0.119613i	$-0.0381655\pi$
$577$	−1056.55	−	10052.4i	−0.00317350	−	0.0301939i	−0.995994	+	0.0894195i	$0.971499\pi$
$578$		0			0
$579$	−11494.4	+	25816.7i	−0.0342868	+	0.0770095i
$580$		0			0
$581$	−404614.	+	131467.i	−1.19864	+	0.389462i
$582$		0			0
$583$	25956.8	−	44958.6i	0.0763686	−	0.132274i
$584$		0			0
$585$	26623.3	+	8650.43i	0.0777947	+	0.0252770i
$586$		0			0
$587$	−236170.	−	325060.i	−0.685407	−	0.943381i	0.314576	−	0.949232i	$-0.398138\pi$
$587$	−236170.	−	325060.i	−0.685407	−	0.943381i	−0.999983	+	0.00585090i	$0.998138\pi$
$588$		0			0
$589$	347317.	−	89473.1i	1.00114	−	0.257906i
$590$		0			0
$591$	−214962.	+	156179.i	−0.615441	+	0.447144i
$592$		0			0
$593$	−91427.4	+	281384.i	−0.259996	+	0.800186i	0.732808	+	0.680435i	$0.238209\pi$
$593$	−91427.4	+	281384.i	−0.259996	+	0.800186i	−0.992804	+	0.119750i	$0.961791\pi$
$594$		0			0
$595$	285998.	+	165121.i	0.807847	+	0.466411i
$596$		0			0
$597$	41462.2	+	127608.i	0.116333	+	0.358037i
$598$		0			0
$599$	−489895.	−	218115.i	−1.36537	−	0.607901i	−0.412408	−	0.910999i	$-0.635312\pi$
$599$	−489895.	−	218115.i	−1.36537	−	0.607901i	−0.952959	+	0.303098i	$0.901979\pi$
$600$		0			0
$601$	245247.	−	25776.5i	0.678978	−	0.0713634i	0.241239	−	0.970466i	$-0.422446\pi$
$601$	245247.	−	25776.5i	0.678978	−	0.0713634i	0.437739	+	0.899102i	$0.355780\pi$
$602$		0			0
$603$	−40446.4	−	8597.14i	−0.111236	−	0.0236439i
$604$		0			0
$605$	1.20585e6	+	876101.i	3.29445	+	2.39356i
$606$		0			0
$607$	7705.28	−	73310.9i	0.0209128	−	0.198972i	−0.979077	−	0.203490i	$-0.934772\pi$
$607$	7705.28	−	73310.9i	0.0209128	−	0.198972i	0.999990	+	0.00451839i	$0.00143825\pi$
$608$		0			0
$609$	308943.	−	65667.8i	0.832997	−	0.177059i
$610$		0			0
$611$	−60920.2	−	54852.8i	−0.163185	−	0.146932i
$612$		0			0
$613$	299562.	−	269726.i	0.797196	−	0.717798i	−0.166138	−	0.986102i	$-0.553130\pi$
$613$	299562.	−	269726.i	0.797196	−	0.717798i	0.963334	+	0.268304i	$0.0864632\pi$
$614$		0			0
$615$	752528.	−	434472.i	1.98963	−	1.14871i
$616$		0			0
$617$	−260412.	+	115943.i	−0.684055	+	0.304561i	−0.719182	−	0.694822i	$-0.755483\pi$
$617$	−260412.	+	115943.i	−0.684055	+	0.304561i	0.0351265	+	0.999383i	$0.488817\pi$
$618$		0			0
$619$			233499.i			0.609402i	0.952448	+	0.304701i	$0.0985565\pi$
$619$			233499.i			0.609402i	−0.952448	+	0.304701i	$0.901443\pi$
$620$		0			0
$621$	−556264.			−1.44244
$622$		0			0
$623$	214649.	+	482109.i	0.553034	+	1.24214i
$624$		0			0
$625$	−761731.	−	1.31936e6i	−1.95003	−	3.37755i
$626$		0			0
$627$	−496988.	−	551961.i	−1.26419	−	1.40402i
$628$		0			0
$629$	−58301.4	+	64750.2i	−0.147359	+	0.163659i
$630$		0			0
$631$	125390.	+	589916.i	0.314924	+	1.48160i	0.796201	+	0.605032i	$0.206840\pi$
$631$	125390.	+	589916.i	0.314924	+	1.48160i	−0.481277	+	0.876568i	$0.659827\pi$
$632$		0			0
$633$	−200580.	−	21081.8i	−0.500587	−	0.0526138i
$634$		0			0
$635$	605319.	−	833150.i	1.50119	−	2.06622i
$636$		0			0
$637$	−43604.4	+	205143.i	−0.107461	+	0.505565i
$638$		0			0
$639$	−620.692	−	5905.49i	−0.00152011	−	0.0144629i
$640$		0			0
$641$	145903.	−	327703.i	0.355097	−	0.797562i	−0.644363	−	0.764720i	$-0.722877\pi$
$641$	145903.	−	327703.i	0.355097	−	0.797562i	0.999461	−	0.0328421i	$-0.0104558\pi$
$642$		0			0
$643$	186522.	−	60604.5i	0.451136	−	0.146583i	−0.0746319	−	0.997211i	$-0.523778\pi$
$643$	186522.	−	60604.5i	0.451136	−	0.146583i	0.525768	+	0.850628i	$0.323778\pi$
$644$		0			0
$645$	−342922.	+	593959.i	−0.824283	+	1.42770i
$646$		0			0
$647$	−121701.	−	39543.1i	−0.290728	−	0.0944632i	0.160022	−	0.987113i	$-0.448843\pi$
$647$	−121701.	−	39543.1i	−0.290728	−	0.0944632i	−0.450750	+	0.892650i	$0.648843\pi$
$648$		0			0
$649$	−224091.	−	308435.i	−0.532029	−	0.732275i
$650$		0			0
$651$	−593419.	−	165172.i	−1.40023	−	0.389741i
$652$		0			0
$653$	643345.	−	467417.i	1.50875	−	1.09617i	0.542022	−	0.840364i	$-0.317659\pi$
$653$	643345.	−	467417.i	1.50875	−	1.09617i	0.966728	−	0.255807i	$-0.0823412\pi$
$654$		0			0
$655$	236068.	−	726544.i	0.550244	−	1.69348i
$656$		0			0
$657$	−34746.3	−	20060.8i	−0.0804966	−	0.0464747i
$658$		0			0
$659$	74436.6	+	229092.i	0.171402	+	0.527521i	0.999451	−	0.0331350i	$-0.0105491\pi$
$659$	74436.6	+	229092.i	0.171402	+	0.527521i	−0.828049	+	0.560656i	$0.810549\pi$
$660$		0			0
$661$	−743096.	−	330848.i	−1.70076	−	0.757226i	−0.998995	−	0.0448134i	$-0.985731\pi$
$661$	−743096.	−	330848.i	−1.70076	−	0.757226i	−0.701761	−	0.712412i	$-0.747603\pi$
$662$		0			0
$663$	−83947.4	+	8823.23i	−0.190977	+	0.0200725i
$664$		0			0
$665$	1.21530e6	+	258321.i	2.74815	+	0.584138i
$666$		0			0
$667$	−317802.	−	230896.i	−0.714339	−	0.518998i
$668$		0			0
$669$	13791.2	−	131214.i	0.0308141	−	0.293176i
$670$		0			0
$671$	866476.	−	184175.i	1.92447	−	0.409059i
$672$		0			0
$673$	−470909.	−	424008.i	−1.03970	−	0.936147i	−0.0416818	−	0.999131i	$-0.513272\pi$
$673$	−470909.	−	424008.i	−1.03970	−	0.936147i	−0.998015	+	0.0629842i	$0.979938\pi$
$674$		0			0
$675$	897531.	−	808140.i	1.96989	−	1.77370i
$676$		0			0
$677$	−158015.	+	91230.3i	−0.344764	+	0.199050i	−0.662377	−	0.749171i	$-0.730452\pi$
$677$	−158015.	+	91230.3i	−0.344764	+	0.199050i	0.317613	+	0.948221i	$0.397119\pi$
$678$		0			0
$679$	−318935.	+	141999.i	−0.691770	+	0.307996i
$680$		0			0
$681$		−	221820.i		−	0.478307i
$682$		0			0
$683$	124046.			0.265913			0.132957	−	0.991122i	$-0.457553\pi$
$683$	124046.			0.265913			0.132957	+	0.991122i	$0.457553\pi$
$684$		0			0
$685$	−53644.1	−	120487.i	−0.114325	−	0.256778i
$686$		0			0
$687$	−370469.	−	641671.i	−0.784944	−	1.35956i
$688$		0			0
$689$	−14852.5	−	16495.3i	−0.0312867	−	0.0347474i
$690$		0			0
$691$	−558986.	+	620817.i	−1.17070	+	1.30019i	−0.225295	+	0.974291i	$0.572335\pi$
$691$	−558986.	+	620817.i	−1.17070	+	1.30019i	−0.945404	+	0.325902i	$0.894332\pi$
$692$		0			0
$693$	19235.5	+	90495.9i	0.0400532	+	0.188435i
$694$		0			0
$695$	632875.	+	66517.8i	1.31023	+	0.137711i
$696$		0			0
$697$	−111700.	+	153741.i	−0.229925	+	0.316465i
$698$		0			0
$699$	−154280.	+	725832.i	−0.315759	+	1.48553i
$700$		0			0
$701$	−48547.3	−	461897.i	−0.0987937	−	0.939959i	−0.925863	−	0.377859i	$-0.876660\pi$
$701$	−48547.3	−	461897.i	−0.0987937	−	0.939959i	0.827069	−	0.562100i	$-0.190006\pi$
$702$		0			0
$703$	−133330.	+	299465.i	−0.269785	+	0.605948i
$704$		0			0
$705$	388390.	−	126196.i	0.781430	−	0.253902i
$706$		0			0
$707$	−546165.	+	945985.i	−1.09266	+	1.89254i
$708$		0			0
$709$	62550.1	+	20323.8i	0.124433	+	0.0404307i	0.370572	−	0.928804i	$-0.379162\pi$
$709$	62550.1	+	20323.8i	0.124433	+	0.0404307i	−0.246139	+	0.969235i	$0.579162\pi$
$710$		0			0
$711$	−9476.21	−	13042.9i	−0.0187454	−	0.0258009i
$712$		0			0
$713$	341189.	+	685938.i	0.671144	+	1.34929i
$714$		0			0
$715$	761399.	−	553189.i	1.48936	−	1.08208i
$716$		0			0
$717$	−157116.	+	483554.i	−0.305620	+	0.940603i
$718$		0			0
$719$	−242585.	−	140056.i	−0.469252	−	0.270922i	0.246675	−	0.969098i	$-0.420662\pi$
$719$	−242585.	−	140056.i	−0.469252	−	0.270922i	−0.715926	+	0.698176i	$0.753995\pi$
$720$		0			0
$721$	−202325.	−	622693.i	−0.389206	−	1.19785i
$722$		0			0
$723$	704724.	+	313763.i	1.34816	+	0.600241i
$724$		0			0
$725$	848219.	−	89151.5i	1.61374	−	0.169610i
$726$		0			0
$727$	−367667.	−	78150.1i	−0.695643	−	0.147863i	−0.153499	−	0.988149i	$-0.549054\pi$
$727$	−367667.	−	78150.1i	−0.695643	−	0.147863i	−0.542144	+	0.840285i	$0.682387\pi$
$728$		0			0
$729$	391271.	+	284275.i	0.736245	+	0.534913i
$730$		0			0
$731$	15678.4	−	149170.i	0.0293405	−	0.279156i
$732$		0			0
$733$	−551624.	+	117251.i	−1.02668	+	0.218227i	−0.690318	−	0.723506i	$-0.742530\pi$
$733$	−551624.	+	117251.i	−1.02668	+	0.218227i	−0.336361	+	0.941733i	$0.609196\pi$
$734$		0			0
$735$	−776424.	−	699095.i	−1.43722	−	1.29408i
$736$		0			0
$737$	−1.03311e6	+	930219.i	−1.90201	+	1.71258i
$738$		0			0
$739$	739369.	−	426875.i	1.35386	−	0.781649i	0.365068	−	0.930981i	$-0.381046\pi$
$739$	739369.	−	426875.i	1.35386	−	0.781649i	0.988787	+	0.149332i	$0.0477124\pi$
$740$		0			0
$741$	−290115.	+	129168.i	−0.528366	+	0.235244i
$742$		0			0
$743$			515122.i			0.933109i	0.884493	+	0.466554i	$0.154505\pi$
$743$			515122.i			0.933109i	−0.884493	+	0.466554i	$0.845495\pi$
$744$		0			0
$745$	711259.			1.28149
$746$		0			0
$747$	15980.4	+	35892.5i	0.0286382	+	0.0643224i
$748$		0			0
$749$	450223.	+	779809.i	0.802535	+	1.39003i
$750$		0			0
$751$	−208576.	−	231647.i	−0.369815	−	0.410721i	0.529299	−	0.848435i	$-0.322455\pi$
$751$	−208576.	−	231647.i	−0.369815	−	0.410721i	−0.899114	+	0.437714i	$0.855788\pi$
$752$		0			0
$753$	−441029.	+	489812.i	−0.777817	+	0.863853i
$754$		0			0
$755$	−53661.8	−	252459.i	−0.0941393	−	0.442891i
$756$		0			0
$757$	59073.5	+	6208.87i	0.103086	+	0.0108348i	0.155931	−	0.987768i	$-0.450162\pi$
$757$	59073.5	+	6208.87i	0.103086	+	0.0108348i	−0.0528449	+	0.998603i	$0.516829\pi$
$758$		0			0
$759$	932533.	−	1.28352e6i	1.61875	−	2.22802i
$760$		0			0
$761$	212089.	−	997801.i	0.366226	−	1.72296i	−0.280165	−	0.959952i	$-0.590389\pi$
$761$	212089.	−	997801.i	0.366226	−	1.72296i	0.646391	−	0.763006i	$-0.276277\pi$
$762$		0			0
$763$	31500.7	+	299709.i	0.0541092	+	0.514814i
$764$		0			0
$765$	12404.6	−	27861.3i	0.0211964	−	0.0476078i
$766$		0			0
$767$	−155031.	+	50372.6i	−0.263528	+	0.0856255i
$768$		0			0
$769$	−218236.	+	377996.i	−0.369040	+	0.639197i	−0.989416	−	0.145108i	$-0.953647\pi$
$769$	−218236.	+	377996.i	−0.369040	+	0.639197i	0.620375	+	0.784305i	$0.286980\pi$
$770$		0			0
$771$	−496242.	−	161239.i	−0.834805	−	0.271245i
$772$		0			0
$773$	−118388.	−	162947.i	−0.198129	−	0.272701i	0.698380	−	0.715727i	$-0.253905\pi$
$773$	−118388.	−	162947.i	−0.198129	−	0.272701i	−0.896508	+	0.443027i	$0.853905\pi$
$774$		0			0
$775$	−1.54704e6	−	611081.i	−2.57572	−	1.01741i
$776$		0			0
$777$	455469.	−	330918.i	0.754427	−	0.548123i
$778$		0			0
$779$	−220934.	+	679966.i	−0.364073	+	1.12050i
$780$		0			0
$781$	−172891.	−	99818.4i	−0.283445	−	0.163647i
$782$		0			0
$783$	106250.	+	327004.i	0.173303	+	0.533371i
$784$		0			0
$785$	239248.	+	106520.i	0.388247	+	0.172859i
$786$		0			0
$787$	302859.	−	31831.7i	0.488979	−	0.0513938i	0.143169	−	0.989698i	$-0.454271\pi$
$787$	302859.	−	31831.7i	0.488979	−	0.0513938i	0.345810	+	0.938304i	$0.387604\pi$
$788$		0			0
$789$	−787297.	−	167345.i	−1.26469	−	0.268819i
$790$		0			0
$791$	716639.	+	520669.i	1.14537	+	0.832163i
$792$		0			0
$793$	39590.6	−	376680.i	0.0629573	−	0.598999i
$794$		0			0
$795$	108160.	−	22990.1i	0.171132	−	0.0363753i
$796$		0			0
$797$	−457273.	−	411731.i	−0.719879	−	0.648182i	0.225467	−	0.974251i	$-0.427609\pi$
$797$	−457273.	−	411731.i	−0.719879	−	0.648182i	−0.945346	+	0.326069i	$0.894276\pi$
$798$		0			0
$799$	−66370.7	+	59760.5i	−0.103964	+	0.0936096i
$800$		0			0
$801$	42206.9	−	24368.2i	0.0657838	−	0.0379803i
$802$		0			0
$803$	−1.23227e6	+	548643.i	−1.91107	+	0.850861i
$804$		0			0
$805$			2.65394e6i			4.09543i
$806$		0			0
$807$	997372.			1.53147
$808$		0			0
$809$	−155647.	−	349590.i	−0.237818	−	0.534148i	0.754725	−	0.656041i	$-0.227770\pi$
$809$	−155647.	−	349590.i	−0.237818	−	0.534148i	−0.992543	+	0.121893i	$0.961104\pi$
$810$		0			0
$811$	−591578.	−	1.02464e6i	−0.899436	−	1.55787i	−0.828217	−	0.560407i	$-0.810645\pi$
$811$	−591578.	−	1.02464e6i	−0.899436	−	1.55787i	−0.0712184	−	0.997461i	$-0.522689\pi$
$812$		0			0
$813$	136972.	+	152122.i	0.207229	+	0.230151i
$814$		0			0
$815$	−1.27964e6	+	1.42118e6i	−1.92651	+	2.13960i
$816$		0			0
$817$	−117326.	−	551975.i	−0.175772	−	0.826942i
$818$		0			0
$819$	39340.9	+	4134.90i	0.0586512	+	0.00616449i
$820$		0			0
$821$	535243.	−	736699.i	0.794081	−	1.09296i	−0.199507	−	0.979896i	$-0.563934\pi$
$821$	535243.	−	736699.i	0.794081	−	1.09296i	0.993588	−	0.113062i	$-0.0360658\pi$
$822$		0			0
$823$	142368.	−	669789.i	0.210190	−	0.988868i	−0.738888	−	0.673828i	$-0.764649\pi$
$823$	142368.	−	669789.i	0.210190	−	0.988868i	0.949078	−	0.315040i	$-0.102018\pi$
$824$		0			0
$825$	360060.	+	3.42575e6i	0.529014	+	5.03324i
$826$		0			0
$827$	327138.	−	734765.i	0.478322	−	1.07433i	−0.499770	−	0.866158i	$-0.666582\pi$
$827$	327138.	−	734765.i	0.478322	−	1.07433i	0.978092	−	0.208171i	$-0.0667510\pi$
$828$		0			0
$829$	−505914.	+	164381.i	−0.736152	+	0.239190i	−0.653012	−	0.757347i	$-0.726495\pi$
$829$	−505914.	+	164381.i	−0.736152	+	0.239190i	−0.0831402	+	0.996538i	$0.526495\pi$
$830$		0			0
$831$	−140747.	+	243782.i	−0.203816	+	0.353020i
$832$		0			0
$833$	217307.	+	70607.3i	0.313172	+	0.101756i
$834$		0			0
$835$	810760.	+	1.11592e6i	1.16284	+	1.60051i
$836$		0			0
$837$	111298.	−	661259.i	0.158868	−	0.943888i
$838$		0			0
$839$	−143375.	+	104168.i	−0.203681	+	0.147983i	−0.684950	−	0.728590i	$-0.740176\pi$
$839$	−143375.	+	104168.i	−0.203681	+	0.147983i	0.481269	+	0.876573i	$0.340176\pi$
$840$		0			0
$841$	143530.	−	441739.i	0.202932	−	0.624560i
$842$		0			0
$843$	177423.	+	102435.i	0.249664	+	0.144143i
$844$		0			0
$845$	304032.	+	935714.i	0.425800	+	1.31048i
$846$		0			0
$847$	1.92416e6	+	856690.i	2.68209	+	1.19414i
$848$		0			0
$849$	−497988.	+	52340.6i	−0.690881	+	0.0726145i
$850$		0			0
$851$	−684906.	−	145581.i	−0.945740	−	0.201023i
$852$		0			0
$853$	331314.	+	240714.i	0.455346	+	0.330828i	0.791703	−	0.610906i	$-0.209195\pi$
$853$	331314.	+	240714.i	0.455346	+	0.330828i	−0.336357	+	0.941735i	$0.609195\pi$
$854$		0			0
$855$	11993.7	−	114112.i	0.0164067	−	0.156099i
$856$		0			0
$857$	142472.	−	30283.4i	0.193985	−	0.0412328i	−0.109894	−	0.993943i	$-0.535051\pi$
$857$	142472.	−	30283.4i	0.193985	−	0.0412328i	0.303880	+	0.952710i	$0.401718\pi$
$858$		0			0
$859$	762820.	+	686846.i	1.03380	+	0.930836i	0.997650	−	0.0685104i	$-0.0218246\pi$
$859$	762820.	+	686846.i	1.03380	+	0.930836i	0.0361477	+	0.999346i	$0.488491\pi$
$860$		0			0
$861$	912515.	−	821632.i	1.23093	−	1.10834i
$862$		0			0
$863$	−755896.	+	436417.i	−1.01494	+	0.585976i	−0.912634	−	0.408777i	$-0.865955\pi$
$863$	−755896.	+	436417.i	−1.01494	+	0.585976i	−0.102306	+	0.994753i	$0.532622\pi$
$864$		0			0
$865$	−2.30551e6	+	1.02648e6i	−3.08130	+	1.37188i
$866$		0			0
$867$		−	688565.i		−	0.916023i
$868$		0			0
$869$	−542020.			−0.717754
$870$		0			0
$871$	241765.	+	543013.i	0.318682	+	0.715771i
$872$		0			0
$873$	16120.5	+	27921.6i	0.0211520	+	0.0366363i
$874$		0			0
$875$	−2.46340e6	−	2.73588e6i	−3.21750	−	3.57340i
$876$		0			0
$877$	−5505.90	+	6114.92i	−0.00715861	+	0.00795045i	−0.746714	−	0.665146i	$-0.768369\pi$
$877$	−5505.90	+	6114.92i	−0.00715861	+	0.00795045i	0.739555	+	0.673096i	$0.235036\pi$
$878$		0			0
$879$	−156591.	−	736701.i	−0.202669	−	0.953484i
$880$		0			0
$881$	680933.	+	71569.0i	0.877309	+	0.0922089i	0.532466	−	0.846451i	$-0.321265\pi$
$881$	680933.	+	71569.0i	0.877309	+	0.0922089i	0.344843	+	0.938660i	$0.387932\pi$
$882$		0			0
$883$	126907.	−	174672.i	0.162766	−	0.224028i	−0.719842	−	0.694138i	$-0.755786\pi$
$883$	126907.	−	174672.i	0.162766	−	0.224028i	0.882608	+	0.470110i	$0.155786\pi$
$884$		0			0
$885$	168836.	−	794310.i	0.215565	−	1.01415i
$886$		0			0
$887$	−12332.6	−	117337.i	−0.0156751	−	0.149138i	0.983885	−	0.178803i	$-0.0572226\pi$
$887$	−12332.6	−	117337.i	−0.0156751	−	0.149138i	−0.999560	+	0.0296651i	$0.990556\pi$
$888$		0			0
$889$	591907.	−	1.32945e6i	0.748945	−	1.68216i
$890$		0			0
$891$	−1.42460e6	+	462880.i	−1.79447	+	0.583060i
$892$		0			0
$893$	−168004.	+	290992.i	−0.210677	+	0.364904i
$894$		0			0
$895$	−2.14768e6	−	697825.i	−2.68117	−	0.871165i
$896$		0			0
$897$	−398722.	−	548794.i	−0.495548	−	0.682063i
$898$		0			0
$899$	338065.	−	331589.i	0.418293	−	0.410280i
$900$		0			0
$901$	−19564.1	+	14214.2i	−0.0240997	+	0.0175094i
$902$		0			0
$903$	−299491.	+	921737.i	−0.367289	+	1.13040i
$904$		0			0
$905$	−86677.3	−	50043.2i	−0.105830	−	0.0611009i
$906$		0			0
$907$	−462488.	−	1.42339e6i	−0.562193	−	1.73025i	−0.676147	−	0.736767i	$-0.736352\pi$
$907$	−462488.	−	1.42339e6i	−0.562193	−	1.73025i	0.113954	−	0.993486i	$-0.463648\pi$
$908$		0			0
$909$	92155.7	+	41030.3i	0.111531	+	0.0496567i
$910$		0			0
$911$	109645.	−	11524.1i	0.132115	−	0.0138858i	−0.0382403	−	0.999269i	$-0.512175\pi$
$911$	109645.	−	11524.1i	0.132115	−	0.0138858i	0.170355	+	0.985383i	$0.445509\pi$
$912$		0			0
$913$	1.29204e6	+	274632.i	1.55001	+	0.329465i
$914$		0			0
$915$	1.52647e6	+	1.10905e6i	1.82325	+	1.32467i
$916$		0			0
$917$	112840.	−	1.07361e6i	0.134192	−	1.27675i
$918$		0			0
$919$	1.19556e6	−	254123.i	1.41559	−	0.300894i	0.564295	−	0.825573i	$-0.309148\pi$
$919$	1.19556e6	−	254123.i	1.41559	−	0.300894i	0.851300	+	0.524679i	$0.175815\pi$
$920$		0			0
$921$	626806.	+	564379.i	0.738948	+	0.665352i
$922$		0			0
$923$	−63433.7	+	57116.0i	−0.0744589	+	0.0670431i
$924$		0			0
$925$	1.31660e6	−	760137.i	1.53875	−	0.888399i
$926$		0			0
$927$	−55237.8	+	24593.5i	−0.0642802	+	0.0286194i
$928$		0			0
$929$			539235.i			0.624808i	0.949949	+	0.312404i	$0.101134\pi$
$929$			539235.i			0.624808i	−0.949949	+	0.312404i	$0.898866\pi$
$930$		0			0
$931$	859636.			0.991780
$932$		0			0
$933$	−199521.	−	448130.i	−0.229205	−	0.514803i
$934$		0			0
$935$	−512672.	−	887974.i	−0.586431	−	1.01573i
$936$		0			0
$937$	651861.	+	723965.i	0.742464	+	0.824590i	0.989518	−	0.144412i	$-0.0461290\pi$
$937$	651861.	+	723965.i	0.742464	+	0.824590i	−0.247053	+	0.969002i	$0.579462\pi$
$938$		0			0
$939$	−101446.	+	112668.i	−0.115055	+	0.127781i
$940$		0			0
$941$	232735.	+	1.09493e6i	0.262834	+	1.23654i	0.889386	+	0.457158i	$0.151133\pi$
$941$	232735.	+	1.09493e6i	0.262834	+	1.23654i	−0.626551	+	0.779380i	$0.715534\pi$
$942$		0			0
$943$	−1.51882e6	−	159634.i	−1.70798	−	0.179516i
$944$		0			0
$945$	1.36539e6	−	1.87930e6i	1.52895	−	2.10442i
$946$		0			0
$947$	−200520.	+	943374.i	−0.223593	+	1.05192i	0.712908	+	0.701258i	$0.247378\pi$
$947$	−200520.	+	943374.i	−0.223593	+	1.05192i	−0.936501	+	0.350665i	$0.885956\pi$
$948$		0			0
$949$	60286.1	+	573584.i	0.0669398	+	0.636890i
$950$		0			0
$951$	−559024.	+	1.25559e6i	−0.618115	+	1.38831i
$952$		0			0
$953$	502431.	−	163250.i	0.553211	−	0.179749i	−0.0190531	−	0.999818i	$-0.506065\pi$
$953$	502431.	−	163250.i	0.553211	−	0.179749i	0.572264	+	0.820069i	$0.306065\pi$
$954$		0			0
$955$	−62579.2	+	108390.i	−0.0686157	+	0.118846i
$956$		0			0
$957$	−932647.	−	303036.i	−1.01834	−	0.330879i
$958$		0			0
$959$	−109547.	−	150779.i	−0.119115	−	0.163947i
$960$		0			0
$961$	−883675.	+	268345.i	−0.956854	+	0.290568i
$962$		0			0
$963$	67275.0	−	48878.1i	0.0725439	−	0.0527063i
$964$		0			0
$965$	−45356.2	+	139592.i	−0.0487059	+	0.149901i
$966$		0			0
$967$	525299.	+	303281.i	0.561763	+	0.324334i	0.753853	−	0.657043i	$-0.228193\pi$
$967$	525299.	+	303281.i	0.561763	+	0.324334i	−0.192090	+	0.981377i	$0.561526\pi$
$968$		0			0
$969$	106915.	+	329050.i	0.113865	+	0.350441i
$970$		0			0
$971$	−1.11357e6	−	495792.i	−1.18108	−	0.525849i	−0.280208	−	0.959939i	$-0.590403\pi$
$971$	−1.11357e6	−	495792.i	−1.18108	−	0.525849i	−0.900870	+	0.434090i	$0.857070\pi$
$972$		0			0
$973$	894320.	−	93996.8i	0.944642	−	0.0992858i
$974$		0			0
$975$	1.44063e6	+	306214.i	1.51545	+	0.322119i
$976$		0			0
$977$	1.13854e6	+	827195.i	1.19277	+	0.866600i	0.993555	−	0.113355i	$-0.0361597\pi$
$977$	1.13854e6	+	827195.i	1.19277	+	0.866600i	0.199218	+	0.979955i	$0.436160\pi$
$978$		0			0
$979$	171272.	−	1.62955e6i	0.178699	−	1.70020i
$980$		0			0
$981$	27222.5	−	5786.32i	0.0282872	−	0.00601263i
$982$		0			0
$983$	−388287.	−	349615.i	−0.401833	−	0.361812i	0.443295	−	0.896376i	$-0.353809\pi$
$983$	−388287.	−	349615.i	−0.401833	−	0.361812i	−0.845128	+	0.534564i	$0.820476\pi$
$984$		0			0
$985$	−1.02556e6	+	923416.i	−1.05703	+	0.951754i
$986$		0			0
$987$	499767.	−	288540.i	0.513018	−	0.296191i
$988$		0			0
$989$	1.10117e6	−	490274.i	1.12581	−	0.501241i
$990$		0			0
$991$			230383.i			0.234586i	0.993097	+	0.117293i	$0.0374217\pi$
$991$			230383.i			0.234586i	−0.993097	+	0.117293i	$0.962578\pi$
$992$		0			0
$993$	225469.			0.228659
$994$		0			0
$995$	283443.	+	636624.i	0.286299	+	0.643038i
$996$		0			0
$997$	363181.	+	629047.i	0.365370	+	0.632839i	0.988835	−	0.149012i	$-0.0476093\pi$
$997$	363181.	+	629047.i	0.365370	+	0.632839i	−0.623466	+	0.781851i	$0.714276\pi$
$998$		0			0
$999$	410095.	+	455457.i	0.410917	+	0.456369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.o.a.13.3	✓	88
31.12	odd	30	inner	124.5.o.a.105.3	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.o.a.13.3	✓	88	1.1	even	1	trivial
124.5.o.a.105.3	yes	88	31.12	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.o (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.80107 - 8.53733i) q^{3} +(-24.2686 - 42.0344i) q^{5} +(-45.8945 - 50.9710i) q^{7} +(-4.23837 + 4.70719i) q^{9} +O(q^{10})\)	\(q+(-3.80107 - 8.53733i) q^{3} +(-24.2686 - 42.0344i) q^{5} +(-45.8945 - 50.9710i) q^{7} +(-4.23837 + 4.70719i) q^{9} +(44.2757 + 208.301i) q^{11} +(90.5539 + 9.51760i) q^{13} +(-266.616 + 366.965i) q^{15} +(20.6247 - 97.0315i) q^{17} +(-39.0113 - 371.168i) q^{19} +(-260.708 + 585.560i) q^{21} +(758.181 - 246.348i) q^{23} +(-865.430 + 1498.97i) q^{25} +(-663.621 - 215.624i) q^{27} +(-289.635 - 398.648i) q^{29} +(141.149 + 950.578i) q^{31} +(1610.04 - 1169.76i) q^{33} +(-1028.74 + 3166.14i) q^{35} +(-760.660 - 439.167i) q^{37} +(-262.946 - 809.266i) q^{39} +(-1750.07 - 779.181i) q^{41} +(1503.74 - 158.050i) q^{43} +(300.723 + 63.9207i) q^{45} +(-728.371 - 529.193i) q^{47} +(-240.765 + 2290.73i) q^{49} +(-906.786 + 192.743i) q^{51} +(-181.162 - 163.119i) q^{53} +(7681.31 - 6916.28i) q^{55} +(-3020.50 + 1743.88i) q^{57} +(-1635.49 + 728.169i) q^{59} -4159.73i q^{61} +434.448 q^{63} +(-1797.55 - 4037.36i) q^{65} +(3264.05 + 5653.51i) q^{67} +(-4985.05 - 5536.46i) q^{69} +(-627.285 + 696.670i) q^{71} +(1316.95 + 6195.75i) q^{73} +(16086.7 + 1690.78i) q^{75} +(8585.30 - 11816.6i) q^{77} +(-529.184 + 2489.62i) q^{79} +(735.247 + 6995.41i) q^{81} +(2522.89 - 5666.51i) q^{83} +(-4579.20 + 1487.87i) q^{85} +(-2302.47 + 3988.00i) q^{87} +(-7317.65 - 2377.65i) q^{89} +(-3670.80 - 5052.43i) q^{91} +(7578.88 - 4818.24i) q^{93} +(-14655.1 + 10647.5i) q^{95} +(1572.91 - 4840.92i) q^{97} +(-1168.17 - 674.443i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \) 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) \) 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9 - 42 * q^11 + 6 * q^13 + 665 * q^15 - 585 * q^17 - 153 * q^19 - 402 * q^21 - 1365 * q^23 - 5933 * q^25 - 9225 * q^27 - 1140 * q^29 + 117 * q^31 + 5151 * q^33 + 2898 * q^35 + 6594 * q^37 + 3173 * q^39 - 9393 * q^41 - 5322 * q^43 + 2010 * q^45 - 5112 * q^47 - 5210 * q^49 - 1829 * q^51 + 7395 * q^53 + 10585 * q^55 + 40485 * q^57 + 5625 * q^59 - 14954 * q^63 - 17094 * q^65 + 8909 * q^67 - 35370 * q^69 - 11811 * q^71 - 22105 * q^73 + 79377 * q^75 + 71490 * q^77 + 219 * q^79 - 5422 * q^81 + 10545 * q^83 - 53630 * q^85 + 13732 * q^87 - 40305 * q^89 + 42760 * q^91 - 1028 * q^93 + 62319 * q^95 + 35201 * q^97 + 16197 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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