LMFDB - Embedded newform 100.6.g.a.61.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,6,Mod(21,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("100.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	100.g (of order $5$, degree $4$, 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:	$16.0383819813$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			61.7
Character	$\chi$	$=$	100.61
Dual form			100.6.g.a.41.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.438384 - 1.34921i) q^{3} +(37.4300 - 41.5210i) q^{5} -49.5774 q^{7} +(194.963 + 141.649i) q^{9} +O(q^{10})$	\(q+(0.438384 - 1.34921i) q^{3} +(37.4300 - 41.5210i) q^{5} -49.5774 q^{7} +(194.963 + 141.649i) q^{9} +(251.910 - 183.023i) q^{11} +(-717.407 - 521.227i) q^{13} +(-39.6118 - 68.7029i) q^{15} +(-221.601 - 682.017i) q^{17} +(255.896 + 787.567i) q^{19} +(-21.7339 + 66.8902i) q^{21} +(2672.86 - 1941.94i) q^{23} +(-322.994 - 3108.26i) q^{25} +(555.474 - 403.576i) q^{27} +(2538.00 - 7811.17i) q^{29} +(-1092.39 - 3362.02i) q^{31} +(-136.503 - 420.113i) q^{33} +(-1855.68 + 2058.51i) q^{35} +(-673.809 - 489.551i) q^{37} +(-1017.74 + 739.433i) q^{39} +(1507.04 + 1094.93i) q^{41} -4400.75 q^{43} +(13178.9 - 2793.15i) q^{45} +(6005.49 - 18483.0i) q^{47} -14349.1 q^{49} -1017.33 q^{51} +(-6175.13 + 19005.1i) q^{53} +(1829.66 - 17310.1i) q^{55} +1174.77 q^{57} +(42007.6 + 30520.3i) q^{59} +(1206.65 - 876.684i) q^{61} +(-9665.76 - 7022.59i) q^{63} +(-48494.4 + 10278.0i) q^{65} +(12387.5 + 38124.8i) q^{67} +(-1448.35 - 4457.55i) q^{69} +(-15071.3 + 46384.8i) q^{71} +(-17526.3 + 12733.6i) q^{73} +(-4335.28 - 926.826i) q^{75} +(-12489.0 + 9073.82i) q^{77} +(-12000.6 + 36934.0i) q^{79} +(17795.0 + 54767.5i) q^{81} +(-4290.75 - 13205.6i) q^{83} +(-36612.6 - 16326.8i) q^{85} +(-9426.26 - 6848.58i) q^{87} +(37596.8 - 27315.7i) q^{89} +(35567.2 + 25841.1i) q^{91} -5014.95 q^{93} +(42278.8 + 18853.5i) q^{95} +(34317.8 - 105619. i) q^{97} +75038.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{3} + 116 q^{5} - 42 q^{7} - 1153 q^{9}+O(q^{10}) $ 52 * q + 2 * q^3 + 116 * q^5 - 42 * q^7 - 1153 * q^9	$ 52 q + 2 q^{3} + 116 q^{5} - 42 q^{7} - 1153 q^{9} - 5 q^{11} + 1458 q^{13} + 2418 q^{15} - 2329 q^{17} + 1912 q^{19} - 4818 q^{21} + 3594 q^{23} + 934 q^{25} + 3206 q^{27} - 1458 q^{29} + 5532 q^{31} + 2435 q^{33} - 5603 q^{35} + 22043 q^{37} - 9938 q^{39} + 4567 q^{41} - 35390 q^{43} - 59359 q^{45} - 5859 q^{47} + 165974 q^{49} + 68014 q^{51} + 20151 q^{53} - 97855 q^{55} - 241368 q^{57} - 116271 q^{59} + 39134 q^{61} + 262808 q^{63} + 190502 q^{65} + 40883 q^{67} - 51844 q^{69} - 109999 q^{71} - 187802 q^{73} - 164833 q^{75} + 102220 q^{77} + 122216 q^{79} - 264922 q^{81} + 125394 q^{83} + 83764 q^{85} + 205117 q^{87} - 107222 q^{89} + 58608 q^{91} - 490158 q^{93} - 82634 q^{95} + 129683 q^{97} + 302280 q^{99}+O(q^{100}) $ 52 * q + 2 * q^3 + 116 * q^5 - 42 * q^7 - 1153 * q^9 - 5 * q^11 + 1458 * q^13 + 2418 * q^15 - 2329 * q^17 + 1912 * q^19 - 4818 * q^21 + 3594 * q^23 + 934 * q^25 + 3206 * q^27 - 1458 * q^29 + 5532 * q^31 + 2435 * q^33 - 5603 * q^35 + 22043 * q^37 - 9938 * q^39 + 4567 * q^41 - 35390 * q^43 - 59359 * q^45 - 5859 * q^47 + 165974 * q^49 + 68014 * q^51 + 20151 * q^53 - 97855 * q^55 - 241368 * q^57 - 116271 * q^59 + 39134 * q^61 + 262808 * q^63 + 190502 * q^65 + 40883 * q^67 - 51844 * q^69 - 109999 * q^71 - 187802 * q^73 - 164833 * q^75 + 102220 * q^77 + 122216 * q^79 - 264922 * q^81 + 125394 * q^83 + 83764 * q^85 + 205117 * q^87 - 107222 * q^89 + 58608 * q^91 - 490158 * q^93 - 82634 * q^95 + 129683 * q^97 + 302280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	0.438384	−	1.34921i	0.0281223	−	0.0865517i	−0.936010	−	0.351973i	$-0.885511\pi$
$3$	0.438384	−	1.34921i	0.0281223	−	0.0865517i	0.964133	+	0.265421i	$0.0855110\pi$
$4$		0			0
$5$	37.4300	−	41.5210i	0.669568	−	0.742751i
$5$	37.4300	−	41.5210i	0.669568	−	0.742751i
$6$		0			0
$7$	−49.5774			−0.382419			−0.191209	−	0.981549i	$-0.561241\pi$
$7$	−49.5774			−0.382419			−0.191209	+	0.981549i	$0.561241\pi$
$8$		0			0
$9$	194.963	+	141.649i	0.802317	+	0.582917i
$10$		0			0
$11$	251.910	−	183.023i	0.627717	−	0.456063i	−0.227892	−	0.973686i	$-0.573183\pi$
$11$	251.910	−	183.023i	0.627717	−	0.456063i	0.855608	+	0.517624i	$0.173183\pi$
$12$		0			0
$13$	−717.407	−	521.227i	−1.17735	−	0.855398i	−0.185484	−	0.982647i	$-0.559385\pi$
$13$	−717.407	−	521.227i	−1.17735	−	0.855398i	−0.991871	+	0.127249i	$0.959385\pi$
$14$		0			0
$15$	−39.6118	−	68.7029i	−0.0454565	−	0.0788401i
$16$		0			0
$17$	−221.601	−	682.017i	−0.185973	−	0.572365i	0.813991	−	0.580877i	$-0.197290\pi$
$17$	−221.601	−	682.017i	−0.185973	−	0.572365i	−0.999964	+	0.00851245i	$0.997290\pi$
$18$		0			0
$19$	255.896	+	787.567i	0.162622	+	0.500499i	0.998853	−	0.0478779i	$-0.0152458\pi$
$19$	255.896	+	787.567i	0.162622	+	0.500499i	−0.836231	+	0.548377i	$0.815246\pi$
$20$		0			0
$21$	−21.7339	+	66.8902i	−0.0107545	+	0.0330990i
$22$		0			0
$23$	2672.86	−	1941.94i	1.05355	−	0.765451i	0.0806676	−	0.996741i	$-0.474295\pi$
$23$	2672.86	−	1941.94i	1.05355	−	0.765451i	0.972885	+	0.231290i	$0.0742948\pi$
$24$		0			0
$25$	−322.994	−	3108.26i	−0.103358	−	0.994644i
$26$		0			0
$27$	555.474	−	403.576i	0.146641	−	0.106541i
$28$		0			0
$29$	2538.00	−	7811.17i	0.560399	−	1.72473i	−0.120844	−	0.992672i	$-0.538560\pi$
$29$	2538.00	−	7811.17i	0.560399	−	1.72473i	0.681242	−	0.732058i	$-0.261440\pi$
$30$		0			0
$31$	−1092.39	−	3362.02i	−0.204161	−	0.628342i	−0.999747	−	0.0225016i	$-0.992837\pi$
$31$	−1092.39	−	3362.02i	−0.204161	−	0.628342i	0.795586	−	0.605841i	$-0.207163\pi$
$32$		0			0
$33$	−136.503	−	420.113i	−0.0218201	−	0.0671555i
$34$		0			0
$35$	−1855.68	+	2058.51i	−0.256055	+	0.284042i
$36$		0			0
$37$	−673.809	−	489.551i	−0.0809157	−	0.0587887i	0.546592	−	0.837399i	$-0.315925\pi$
$37$	−673.809	−	489.551i	−0.0809157	−	0.0587887i	−0.627508	+	0.778610i	$0.715925\pi$
$38$		0			0
$39$	−1017.74	+	739.433i	−0.107146	+	0.0778462i
$40$		0			0
$41$	1507.04	+	1094.93i	0.140012	+	0.101725i	0.655586	−	0.755120i	$-0.272421\pi$
$41$	1507.04	+	1094.93i	0.140012	+	0.101725i	−0.515575	+	0.856845i	$0.672421\pi$
$42$		0			0
$43$	−4400.75			−0.362957			−0.181479	−	0.983395i	$-0.558088\pi$
$43$	−4400.75			−0.362957			−0.181479	+	0.983395i	$0.558088\pi$
$44$		0			0
$45$	13178.9	−	2793.15i	0.970168	−	0.205619i
$46$		0			0
$47$	6005.49	−	18483.0i	0.396555	−	1.22047i	−0.531188	−	0.847254i	$-0.678254\pi$
$47$	6005.49	−	18483.0i	0.396555	−	1.22047i	0.927744	−	0.373218i	$-0.121746\pi$
$48$		0			0
$49$	−14349.1			−0.853756
$50$		0			0
$51$	−1017.33			−0.0547691
$52$		0			0
$53$	−6175.13	+	19005.1i	−0.301965	+	0.929352i	0.678828	+	0.734298i	$0.262488\pi$
$53$	−6175.13	+	19005.1i	−0.301965	+	0.929352i	−0.980792	+	0.195055i	$0.937512\pi$
$54$		0			0
$55$	1829.66	−	17310.1i	0.0815576	−	0.771602i
$56$		0			0
$57$	1174.77			0.0478923
$58$		0			0
$59$	42007.6	+	30520.3i	1.57108	+	1.14145i	0.926116	+	0.377239i	$0.123126\pi$
$59$	42007.6	+	30520.3i	1.57108	+	1.14145i	0.644961	+	0.764215i	$0.276874\pi$
$60$		0			0
$61$	1206.65	−	876.684i	0.0415200	−	0.0301661i	−0.566832	−	0.823834i	$-0.691831\pi$
$61$	1206.65	−	876.684i	0.0415200	−	0.0301661i	0.608352	+	0.793668i	$0.291831\pi$
$62$		0			0
$63$	−9665.76	−	7022.59i	−0.306821	−	0.222918i
$64$		0			0
$65$	−48494.4	+	10278.0i	−1.42367	+	0.301734i
$66$		0			0
$67$	12387.5	+	38124.8i	0.337130	+	1.03758i	0.965663	+	0.259796i	$0.0836554\pi$
$67$	12387.5	+	38124.8i	0.337130	+	1.03758i	−0.628534	+	0.777782i	$0.716345\pi$
$68$		0			0
$69$	−1448.35	−	4457.55i	−0.0366227	−	0.112713i
$70$		0			0
$71$	−15071.3	+	46384.8i	−0.354818	+	1.09202i	0.601296	+	0.799026i	$0.294651\pi$
$71$	−15071.3	+	46384.8i	−0.354818	+	1.09202i	−0.956115	+	0.292992i	$0.905349\pi$
$72$		0			0
$73$	−17526.3	+	12733.6i	−0.384932	+	0.279670i	−0.763376	−	0.645955i	$-0.776459\pi$
$73$	−17526.3	+	12733.6i	−0.384932	+	0.279670i	0.378443	+	0.925624i	$0.376459\pi$
$74$		0			0
$75$	−4335.28	−	926.826i	−0.0889948	−	0.0190259i
$76$		0			0
$77$	−12489.0	+	9073.82i	−0.240050	+	0.174407i
$78$		0			0
$79$	−12000.6	+	36934.0i	−0.216339	+	0.665822i	0.782717	+	0.622378i	$0.213833\pi$
$79$	−12000.6	+	36934.0i	−0.216339	+	0.665822i	−0.999056	+	0.0434446i	$0.986167\pi$
$80$		0			0
$81$	17795.0	+	54767.5i	0.301360	+	0.927492i
$82$		0			0
$83$	−4290.75	−	13205.6i	−0.0683657	−	0.210408i	0.911037	−	0.412325i	$-0.135283\pi$
$83$	−4290.75	−	13205.6i	−0.0683657	−	0.210408i	−0.979403	+	0.201917i	$0.935283\pi$
$84$		0			0
$85$	−36612.6	−	16326.8i	−0.549646	−	0.245106i
$86$		0			0
$87$	−9426.26	−	6848.58i	−0.133518	−	0.0970069i
$88$		0			0
$89$	37596.8	−	27315.7i	0.503125	−	0.365542i	−0.307084	−	0.951682i	$-0.599353\pi$
$89$	37596.8	−	27315.7i	0.503125	−	0.365542i	0.810210	+	0.586140i	$0.199353\pi$
$90$		0			0
$91$	35567.2	+	25841.1i	0.450242	+	0.327120i
$92$		0			0
$93$	−5014.95			−0.0601255
$94$		0			0
$95$	42278.8	+	18853.5i	0.480633	+	0.214330i
$96$		0			0
$97$	34317.8	−	105619.i	0.370331	−	1.13976i	−0.576244	−	0.817278i	$-0.695482\pi$
$97$	34317.8	−	105619.i	0.370331	−	1.13976i	0.946575	−	0.322484i	$-0.104518\pi$
$98$		0			0
$99$	75038.2			0.769474
$100$		0			0
$101$	−81157.6			−0.791636			−0.395818	−	0.918329i	$-0.629539\pi$
$101$	−81157.6			−0.791636			−0.395818	+	0.918329i	$0.629539\pi$
$102$		0			0
$103$	−55037.0	+	169386.i	−0.511165	+	1.57321i	0.278987	+	0.960295i	$0.410001\pi$
$103$	−55037.0	+	169386.i	−0.511165	+	1.57321i	−0.790152	+	0.612911i	$0.789999\pi$
$104$		0			0
$105$	1963.85	+	3406.11i	0.0173834	+	0.0301499i
$106$		0			0
$107$	68967.6			0.582352			0.291176	−	0.956670i	$-0.405954\pi$
$107$	68967.6			0.582352			0.291176	+	0.956670i	$0.405954\pi$
$108$		0			0
$109$	47004.5	+	34150.7i	0.378942	+	0.275318i	0.760909	−	0.648858i	$-0.224753\pi$
$109$	47004.5	+	34150.7i	0.378942	+	0.275318i	−0.381967	+	0.924176i	$0.624753\pi$
$110$		0			0
$111$	−955.892	+	694.496i	−0.00736379	+	0.00535011i
$112$		0			0
$113$	−177541.	−	128991.i	−1.30799	−	0.950308i	−0.307988	−	0.951390i	$-0.599656\pi$
$113$	−177541.	−	128991.i	−1.30799	−	0.950308i	−0.999999	+	0.00108186i	$0.999656\pi$
$114$		0			0
$115$	19413.4	−	183667.i	0.136885	−	1.29505i
$116$		0			0
$117$	−66036.6	−	203240.i	−0.445985	−	1.37260i
$118$		0			0
$119$	10986.4	+	33812.7i	0.0711194	+	0.218883i
$120$		0			0
$121$	−19806.4	+	60957.8i	−0.122982	+	0.378500i
$122$		0			0
$123$	2137.95	−	1553.31i	0.0127419	−	0.00925753i
$124$		0			0
$125$	−141148.	−	102931.i	−0.807978	−	0.589212i
$126$		0			0
$127$	278154.	−	202091.i	1.53030	−	1.11183i	0.574229	−	0.818695i	$-0.305302\pi$
$127$	278154.	−	202091.i	1.53030	−	1.11183i	0.956071	−	0.293134i	$-0.0946982\pi$
$128$		0			0
$129$	−1929.22	+	5937.52i	−0.0102072	+	0.0314146i
$130$		0			0
$131$	79389.9	+	244337.i	0.404191	+	1.24397i	0.921569	+	0.388216i	$0.126908\pi$
$131$	79389.9	+	244337.i	0.404191	+	1.24397i	−0.517377	+	0.855757i	$0.673092\pi$
$132$		0			0
$133$	−12686.7	−	39045.5i	−0.0621897	−	0.191400i
$134$		0			0
$135$	4034.50	−	38169.7i	0.0190527	−	0.180254i
$136$		0			0
$137$	124582.	+	90514.4i	0.567094	+	0.412018i	0.834049	−	0.551691i	$-0.186017\pi$
$137$	124582.	+	90514.4i	0.567094	+	0.412018i	−0.266954	+	0.963709i	$0.586017\pi$
$138$		0			0
$139$	233851.	−	169903.i	1.02660	−	0.745871i	0.0589774	−	0.998259i	$-0.481216\pi$
$139$	233851.	−	169903.i	1.02660	−	0.745871i	0.967626	+	0.252388i	$0.0812160\pi$
$140$		0			0
$141$	−22304.7	−	16205.3i	−0.0944818	−	0.0686450i
$142$		0			0
$143$	−276119.			−1.12916
$144$		0			0
$145$	−229331.	−	397752.i	−0.905820	−	1.57106i
$146$		0			0
$147$	−6290.40	+	19359.9i	−0.0240096	+	0.0738940i
$148$		0			0
$149$	262012.			0.966843			0.483422	−	0.875388i	$-0.339394\pi$
$149$	262012.			0.966843			0.483422	+	0.875388i	$0.339394\pi$
$150$		0			0
$151$	186357.			0.665124			0.332562	−	0.943081i	$-0.392087\pi$
$151$	186357.			0.665124			0.332562	+	0.943081i	$0.392087\pi$
$152$		0			0
$153$	53403.0	−	164358.i	0.184432	−	0.567624i
$154$		0			0
$155$	−180483.	−	80483.3i	−0.603401	−	0.269077i
$156$		0			0
$157$	84874.2			0.274806			0.137403	−	0.990515i	$-0.456124\pi$
$157$	84874.2			0.274806			0.137403	+	0.990515i	$0.456124\pi$
$158$		0			0
$159$	22934.7	+	16663.1i	0.0719450	+	0.0522711i
$160$		0			0
$161$	−132513.	+	96276.6i	−0.402898	+	0.292722i
$162$		0			0
$163$	195465.	+	142014.i	0.576235	+	0.418659i	0.837365	−	0.546644i	$-0.184095\pi$
$163$	195465.	+	142014.i	0.576235	+	0.418659i	−0.261130	+	0.965304i	$0.584095\pi$
$164$		0			0
$165$	−22552.8	−	10057.1i	−0.0644898	−	0.0287582i
$166$		0			0
$167$	−106364.	−	327355.i	−0.295124	−	0.908298i	−0.983180	−	0.182640i	$-0.941536\pi$
$167$	−106364.	−	327355.i	−0.295124	−	0.908298i	0.688056	−	0.725658i	$-0.258464\pi$
$168$		0			0
$169$	128260.	+	394743.i	0.345441	+	1.06316i
$170$		0			0
$171$	−61667.7	+	189794.i	−0.161275	+	0.496354i
$172$		0			0
$173$	−538316.	+	391109.i	−1.36748	+	0.993534i	−0.369554	+	0.929209i	$0.620489\pi$
$173$	−538316.	+	391109.i	−1.36748	+	0.993534i	−0.997929	+	0.0643250i	$0.979511\pi$
$174$		0			0
$175$	16013.2	+	154100.i	0.0395261	+	0.380370i
$176$		0			0
$177$	59593.6	−	43297.3i	0.142977	−	0.103879i
$178$		0			0
$179$	−87951.9	+	270688.i	−0.205169	+	0.631446i	0.794537	+	0.607216i	$0.207714\pi$
$179$	−87951.9	+	270688.i	−0.205169	+	0.631446i	−0.999706	+	0.0242306i	$0.992286\pi$
$180$		0			0
$181$	106385.	+	327419.i	0.241370	+	0.742862i	0.996212	+	0.0869548i	$0.0277136\pi$
$181$	106385.	+	327419.i	0.241370	+	0.742862i	−0.754842	+	0.655907i	$0.772286\pi$
$182$		0			0
$183$	−653.851	−	2012.35i	−0.00144328	−	0.00444197i
$184$		0			0
$185$	−45547.3	+	9653.38i	−0.0978438	+	0.0207372i
$186$		0			0
$187$	−180648.	−	131249.i	−0.377772	−	0.274468i
$188$		0			0
$189$	−27539.0	+	20008.2i	−0.0560781	+	0.0407431i
$190$		0			0
$191$	185524.	+	134791.i	0.367973	+	0.267348i	0.756370	−	0.654144i	$-0.226971\pi$
$191$	185524.	+	134791.i	0.367973	+	0.267348i	−0.388397	+	0.921492i	$0.626971\pi$
$192$		0			0
$193$	−677800.			−1.30981			−0.654905	−	0.755711i	$-0.727292\pi$
$193$	−677800.			−1.30981			−0.654905	+	0.755711i	$0.727292\pi$
$194$		0			0
$195$	−7392.03	+	69934.7i	−0.0139212	+	0.131706i
$196$		0			0
$197$	64956.5	−	199916.i	0.119250	−	0.367013i	−0.873560	−	0.486716i	$-0.838194\pi$
$197$	64956.5	−	199916.i	0.119250	−	0.367013i	0.992810	+	0.119704i	$0.0381945\pi$
$198$		0			0
$199$	608414.			1.08910			0.544548	−	0.838730i	$-0.316701\pi$
$199$	608414.			1.08910			0.544548	+	0.838730i	$0.316701\pi$
$200$		0			0
$201$	56868.8			0.0992850
$202$		0			0
$203$	−125828.	+	387258.i	−0.214307	+	0.659569i
$204$		0			0
$205$	101871.	−	21590.7i	0.169303	−	0.0358825i
$206$		0			0
$207$	796182.			1.29148
$208$		0			0
$209$	208606.	+	151561.i	0.330340	+	0.240006i
$210$		0			0
$211$	−952730.	+	692199.i	−1.47321	+	1.07035i	−0.493537	+	0.869725i	$0.664296\pi$
$211$	−952730.	+	692199.i	−1.47321	+	1.07035i	−0.979669	+	0.200622i	$0.935704\pi$
$212$		0			0
$213$	55975.7	+	40668.7i	0.0845377	+	0.0614202i
$214$		0			0
$215$	−164720.	+	182724.i	−0.243024	+	0.269587i
$216$		0			0
$217$	54157.7	+	166680.i	0.0780749	+	0.240290i
$218$		0			0
$219$	9497.04	+	29228.9i	0.0133807	+	0.0411815i
$220$		0			0
$221$	−196508.	+	604788.i	−0.270644	+	0.832957i
$222$		0			0
$223$	7266.06	−	5279.10i	0.00978446	−	0.00710882i	−0.582882	−	0.812557i	$-0.698075\pi$
$223$	7266.06	−	5279.10i	0.00978446	−	0.00710882i	0.592667	+	0.805448i	$0.298075\pi$
$224$		0			0
$225$	377310.	−	651748.i	0.496869	−	0.858269i
$226$		0			0
$227$	−440293.	+	319892.i	−0.567123	+	0.412039i	−0.834059	−	0.551675i	$-0.813989\pi$
$227$	−440293.	+	319892.i	−0.567123	+	0.412039i	0.266936	+	0.963714i	$0.413989\pi$
$228$		0			0
$229$	225355.	−	693571.i	0.283974	−	0.873981i	−0.702731	−	0.711456i	$-0.748036\pi$
$229$	225355.	−	693571.i	0.283974	−	0.873981i	0.986704	−	0.162525i	$-0.0519638\pi$
$230$		0			0
$231$	6767.47	+	20828.1i	0.00834442	+	0.0256815i
$232$		0			0
$233$	147331.	+	453438.i	0.177789	+	0.547178i	0.999750	−	0.0223659i	$-0.00711988\pi$
$233$	147331.	+	453438.i	0.177789	+	0.547178i	−0.821961	+	0.569544i	$0.807120\pi$
$234$		0			0
$235$	−542648.	−	941172.i	−0.640986	−	1.11173i
$236$		0			0
$237$	44570.7	+	32382.5i	0.0515441	+	0.0374490i
$238$		0			0
$239$	−599739.	+	435736.i	−0.679153	+	0.493434i	−0.873077	−	0.487583i	$-0.837879\pi$
$239$	−599739.	+	435736.i	−0.679153	+	0.493434i	0.193924	+	0.981017i	$0.437879\pi$
$240$		0			0
$241$	−82578.5	−	59996.8i	−0.0915851	−	0.0665404i	0.541050	−	0.840990i	$-0.318027\pi$
$241$	−82578.5	−	59996.8i	−0.0915851	−	0.0665404i	−0.632635	+	0.774450i	$0.718027\pi$
$242$		0			0
$243$	248538.			0.270009
$244$		0			0
$245$	−537086.	+	595789.i	−0.571647	+	0.634128i
$246$		0			0
$247$	226919.	−	698386.i	0.236662	−	0.728372i
$248$		0			0
$249$	−19698.1			−0.0201338
$250$		0			0
$251$	187576.			0.187929			0.0939643	−	0.995576i	$-0.470046\pi$
$251$	187576.			0.187929			0.0939643	+	0.995576i	$0.470046\pi$
$252$		0			0
$253$	317898.	−	978390.i	0.312239	−	0.960972i
$254$		0			0
$255$	−38078.6	+	42240.5i	−0.0366716	+	0.0406798i
$256$		0			0
$257$	26825.7			0.0253349			0.0126674	−	0.999920i	$-0.495968\pi$
$257$	26825.7			0.0253349			0.0126674	+	0.999920i	$0.495968\pi$
$258$		0			0
$259$	33405.7	+	24270.7i	0.0309436	+	0.0224819i
$260$		0			0
$261$	1.60126e6	−	1.16338e6i	1.45499	−	1.05711i
$262$		0			0
$263$	−491740.	−	357270.i	−0.438375	−	0.318498i	0.346614	−	0.938008i	$-0.387331\pi$
$263$	−491740.	−	357270.i	−0.438375	−	0.318498i	−0.784989	+	0.619510i	$0.787331\pi$
$264$		0			0
$265$	557977.	+	967758.i	0.488091	+	0.846549i
$266$		0			0
$267$	−20372.7	−	62700.7i	−0.0174892	−	0.0538262i
$268$		0			0
$269$	178028.	+	547914.i	0.150006	+	0.461670i	0.997621	−	0.0689417i	$-0.0219622\pi$
$269$	178028.	+	547914.i	0.150006	+	0.461670i	−0.847615	+	0.530612i	$0.821962\pi$
$270$		0			0
$271$	606058.	−	1.86525e6i	0.501292	−	1.54282i	−0.305624	−	0.952152i	$-0.598865\pi$
$271$	606058.	−	1.86525e6i	0.501292	−	1.54282i	0.806916	−	0.590666i	$-0.201135\pi$
$272$		0			0
$273$	50457.1	−	36659.2i	0.0409747	−	0.0297698i
$274$		0			0
$275$	−650250.	−	723887.i	−0.518500	−	0.577217i
$276$		0			0
$277$	−739176.	+	537043.i	−0.578826	+	0.420542i	−0.838301	−	0.545208i	$-0.816451\pi$
$277$	−739176.	+	537043.i	−0.578826	+	0.420542i	0.259474	+	0.965750i	$0.416451\pi$
$278$		0			0
$279$	263252.	−	810205.i	0.202470	−	0.623138i
$280$		0			0
$281$	−268731.	−	827069.i	−0.203026	−	0.624850i	−0.999789	−	0.0205576i	$-0.993456\pi$
$281$	−268731.	−	827069.i	−0.203026	−	0.624850i	0.796763	−	0.604293i	$-0.206544\pi$
$282$		0			0
$283$	−226329.	−	696570.i	−0.167987	−	0.517010i	0.831257	−	0.555888i	$-0.187622\pi$
$283$	−226329.	−	696570.i	−0.167987	−	0.517010i	−0.999244	+	0.0388780i	$0.987622\pi$
$284$		0			0
$285$	43971.6	−	48777.7i	0.0320672	−	0.0355721i
$286$		0			0
$287$	−74715.1	−	54283.7i	−0.0535431	−	0.0389014i
$288$		0			0
$289$	732648.	−	532300.i	0.516001	−	0.374897i
$290$		0			0
$291$	−127458.	−	92603.6i	−0.0882336	−	0.0641055i
$292$		0			0
$293$	1.43402e6			0.975858			0.487929	−	0.872883i	$-0.337752\pi$
$293$	1.43402e6			0.975858			0.487929	+	0.872883i	$0.337752\pi$
$294$		0			0
$295$	2.83958e6	−	601825.i	1.89976	−	0.402638i
$296$		0			0
$297$	66065.7	−	203329.i	0.0434595	−	0.133755i
$298$		0			0
$299$	−2.92972e6			−1.89517
$300$		0			0
$301$	218178.			0.138802
$302$		0			0
$303$	−35578.2	+	109498.i	−0.0222627	+	0.0685174i
$304$		0			0
$305$	8764.12	−	82915.7i	0.00539459	−	0.0510373i
$306$		0			0
$307$	−1.36767e6			−0.828202			−0.414101	−	0.910231i	$-0.635904\pi$
$307$	−1.36767e6			−0.828202			−0.414101	+	0.910231i	$0.635904\pi$
$308$		0			0
$309$	204410.	+	148513.i	0.121788	+	0.0884844i
$310$		0			0
$311$	−1.85276e6	+	1.34611e6i	−1.08622	+	0.789184i	−0.978757	−	0.205025i	$-0.934272\pi$
$311$	−1.85276e6	+	1.34611e6i	−1.08622	+	0.789184i	−0.107462	+	0.994209i	$0.534272\pi$
$312$		0			0
$313$	742472.	+	539437.i	0.428370	+	0.311229i	0.780997	−	0.624535i	$-0.214711\pi$
$313$	742472.	+	539437.i	0.428370	+	0.311229i	−0.352627	+	0.935764i	$0.614711\pi$
$314$		0			0
$315$	−653374.	+	138477.i	−0.371010	+	0.0786325i
$316$		0			0
$317$	25293.1	+	77844.1i	0.0141369	+	0.0435088i	0.957876	−	0.287182i	$-0.0927184\pi$
$317$	25293.1	+	77844.1i	0.0141369	+	0.0435088i	−0.943739	+	0.330691i	$0.892718\pi$
$318$		0			0
$319$	−790278.	−	2.43222e6i	−0.434814	−	1.33822i
$320$		0			0
$321$	30234.3	−	93051.5i	0.0163771	−	0.0504035i
$322$		0			0
$323$	480427.	−	349051.i	0.256225	−	0.186158i
$324$		0			0
$325$	−1.38839e6	+	2.39824e6i	−0.729128	+	1.25946i
$326$		0			0
$327$	66682.4	−	48447.6i	0.0344859	−	0.0250555i
$328$		0			0
$329$	−297737.	+	916339.i	−0.151650	+	0.466731i
$330$		0			0
$331$	−67030.8	−	206300.i	−0.0336283	−	0.103497i	0.932833	−	0.360308i	$-0.117328\pi$
$331$	−67030.8	−	206300.i	−0.0336283	−	0.103497i	−0.966462	+	0.256811i	$0.917328\pi$
$332$		0			0
$333$	−62023.5	−	190889.i	−0.0306511	−	0.0943342i
$334$		0			0
$335$	2.04665e6	+	912669.i	0.996394	+	0.444326i
$336$		0			0
$337$	2.59051e6	+	1.88211e6i	1.24254	+	0.902757i	0.997765	−	0.0668231i	$-0.0212863\pi$
$337$	2.59051e6	+	1.88211e6i	1.24254	+	0.902757i	0.244774	+	0.969580i	$0.421286\pi$
$338$		0			0
$339$	−251867.	+	182992.i	−0.119034	+	0.0864836i
$340$		0			0
$341$	−890511.	−	646994.i	−0.414719	−	0.301311i
$342$		0			0
$343$	1.54464e6			0.708911
$344$		0			0
$345$	−239294.	−	106709.i	−0.108239	−	0.0482674i
$346$		0			0
$347$	−686412.	+	2.11256e6i	−0.306028	+	0.941858i	0.673263	+	0.739403i	$0.264892\pi$
$347$	−686412.	+	2.11256e6i	−0.306028	+	0.941858i	−0.979292	+	0.202455i	$0.935108\pi$
$348$		0			0
$349$	449590.			0.197585			0.0987923	−	0.995108i	$-0.468502\pi$
$349$	449590.			0.197585			0.0987923	+	0.995108i	$0.468502\pi$
$350$		0			0
$351$	−608856.			−0.263783
$352$		0			0
$353$	229772.	−	707165.i	0.0981431	−	0.302053i	−0.889917	−	0.456123i	$-0.849238\pi$
$353$	229772.	−	707165.i	0.0981431	−	0.302053i	0.988060	+	0.154069i	$0.0492378\pi$
$354$		0			0
$355$	1.36183e6	+	2.36196e6i	0.573523	+	0.994722i
$356$		0			0
$357$	50436.5			0.0209447
$358$		0			0
$359$	−2.63609e6	−	1.91523e6i	−1.07950	−	0.784304i	−0.101906	−	0.994794i	$-0.532494\pi$
$359$	−2.63609e6	−	1.91523e6i	−1.07950	−	0.784304i	−0.977596	+	0.210490i	$0.932494\pi$
$360$		0			0
$361$	1.44843e6	−	1.05234e6i	0.584963	−	0.425001i
$362$		0			0
$363$	73561.9	+	53445.8i	0.0293013	+	0.0212886i
$364$		0			0
$365$	−127297.	+	1.20433e6i	−0.0500133	+	0.473167i
$366$		0			0
$367$	−513970.	−	1.58184e6i	−0.199192	−	0.613051i	−0.999902	−	0.0139986i	$-0.995544\pi$
$367$	−513970.	−	1.58184e6i	−0.199192	−	0.613051i	0.800710	−	0.599053i	$-0.204456\pi$
$368$		0			0
$369$	138721.	+	426941.i	0.0530369	+	0.163231i
$370$		0			0
$371$	306147.	−	942224.i	0.115477	−	0.355402i
$372$		0			0
$373$	2.40825e6	−	1.74969e6i	0.896249	−	0.651163i	−0.0412505	−	0.999149i	$-0.513134\pi$
$373$	2.40825e6	−	1.74969e6i	0.896249	−	0.651163i	0.937500	+	0.347986i	$0.113134\pi$
$374$		0			0
$375$	−200752.	+	145314.i	−0.0737195	+	0.0533618i
$376$		0			0
$377$	−5.89217e6	+	4.28091e6i	−2.13512	+	1.55125i
$378$		0			0
$379$	−1.44523e6	+	4.44796e6i	−0.516820	+	1.59061i	0.263127	+	0.964761i	$0.415246\pi$
$379$	−1.44523e6	+	4.44796e6i	−0.516820	+	1.59061i	−0.779947	+	0.625846i	$0.784754\pi$
$380$		0			0
$381$	−150724.	−	463881.i	−0.0531950	−	0.163717i
$382$		0			0
$383$	1.10578e6	+	3.40323e6i	0.385186	+	1.18548i	0.936345	+	0.351080i	$0.114186\pi$
$383$	1.10578e6	+	3.40323e6i	0.385186	+	1.18548i	−0.551160	+	0.834400i	$0.685814\pi$
$384$		0			0
$385$	−90710.1	+	858191.i	−0.0311892	+	0.295075i
$386$		0			0
$387$	−857983.	−	623361.i	−0.291207	−	0.211574i
$388$		0			0
$389$	−727923.	+	528867.i	−0.243900	+	0.177203i	−0.703019	−	0.711171i	$-0.748165\pi$
$389$	−727923.	+	528867.i	−0.243900	+	0.177203i	0.459119	+	0.888375i	$0.348165\pi$
$390$		0			0
$391$	−1.91675e6	−	1.39260e6i	−0.634049	−	0.460663i
$392$		0			0
$393$	364464.			0.119035
$394$		0			0
$395$	1.08436e6	+	1.88071e6i	0.349687	+	0.606499i
$396$		0			0
$397$	−1.30629e6	+	4.02035e6i	−0.415971	+	1.28023i	0.495408	+	0.868660i	$0.335018\pi$
$397$	−1.30629e6	+	4.02035e6i	−0.415971	+	1.28023i	−0.911379	+	0.411567i	$0.864982\pi$
$398$		0			0
$399$	−58242.1			−0.0183149
$400$		0			0
$401$	4.36081e6			1.35427			0.677136	−	0.735858i	$-0.263221\pi$
$401$	4.36081e6			1.35427			0.677136	+	0.735858i	$0.263221\pi$
$402$		0			0
$403$	−968690.	+	2.98132e6i	−0.297113	+	0.914421i
$404$		0			0
$405$	2.94007e6	+	1.31108e6i	0.890677	+	0.397183i
$406$		0			0
$407$	−259338.			−0.0776034
$408$		0			0
$409$	−3.09899e6	−	2.25155e6i	−0.916034	−	0.665538i	0.0264997	−	0.999649i	$-0.491564\pi$
$409$	−3.09899e6	−	2.25155e6i	−0.916034	−	0.665538i	−0.942534	+	0.334111i	$0.891564\pi$
$410$		0			0
$411$	176738.	−	128407.i	0.0516089	−	0.0374960i
$412$		0			0
$413$	−2.08263e6	−	1.51312e6i	−0.600809	−	0.436513i
$414$		0			0
$415$	−708912.	−	316128.i	−0.202056	−	0.0901037i
$416$		0			0
$417$	−126718.	−	389996.i	−0.0356859	−	0.109830i
$418$		0			0
$419$	−493353.	−	1.51839e6i	−0.137285	−	0.422520i	0.858653	−	0.512557i	$-0.171302\pi$
$419$	−493353.	−	1.51839e6i	−0.137285	−	0.422520i	−0.995938	+	0.0900368i	$0.971302\pi$
$420$		0			0
$421$	1.87890e6	−	5.78267e6i	0.516653	−	1.59010i	−0.263600	−	0.964632i	$-0.584910\pi$
$421$	1.87890e6	−	5.78267e6i	0.516653	−	1.59010i	0.780254	−	0.625463i	$-0.215090\pi$
$422$		0			0
$423$	3.78894e6	−	2.75283e6i	1.02960	−	0.748046i
$424$		0			0
$425$	−2.04831e6	+	909081.i	−0.550078	+	0.244135i
$426$		0			0
$427$	−59822.7	+	43463.8i	−0.0158780	+	0.0115361i
$428$		0			0
$429$	−121046.	+	372541.i	−0.0317546	+	0.0977307i
$430$		0			0
$431$	218231.	+	671647.i	0.0565879	+	0.174160i	0.975356	−	0.220639i	$-0.0708143\pi$
$431$	218231.	+	671647.i	0.0565879	+	0.174160i	−0.918768	+	0.394799i	$0.870814\pi$
$432$		0			0
$433$	−1.59826e6	−	4.91893e6i	−0.409663	−	1.26081i	−0.916938	−	0.399029i	$-0.869347\pi$
$433$	−1.59826e6	−	4.91893e6i	−0.409663	−	1.26081i	0.507275	−	0.861784i	$-0.330653\pi$
$434$		0			0
$435$	−637185.	+	135046.i	−0.161452	+	0.0342183i
$436$		0			0
$437$	2.21338e6	+	1.60812e6i	0.554438	+	0.402823i
$438$		0			0
$439$	160737.	−	116782.i	0.0398064	−	0.0289211i	−0.567704	−	0.823233i	$-0.692168\pi$
$439$	160737.	−	116782.i	0.0398064	−	0.0289211i	0.607511	+	0.794312i	$0.292168\pi$
$440$		0			0
$441$	−2.79754e6	−	2.03253e6i	−0.684983	−	0.497669i
$442$		0			0
$443$	4.04379e6			0.978991			0.489496	−	0.872006i	$-0.337181\pi$
$443$	4.04379e6			0.978991			0.489496	+	0.872006i	$0.337181\pi$
$444$		0			0
$445$	273072.	−	2.58349e6i	0.0653698	−	0.618452i
$446$		0			0
$447$	114862.	−	353509.i	0.0271899	−	0.0836819i
$448$		0			0
$449$	247339.			0.0578998			0.0289499	−	0.999581i	$-0.490784\pi$
$449$	247339.			0.0578998			0.0289499	+	0.999581i	$0.490784\pi$
$450$		0			0
$451$	580035.			0.134281
$452$		0			0
$453$	81695.8	−	251434.i	0.0187049	−	0.0575676i
$454$		0			0
$455$	2.40423e6	−	509556.i	0.544437	−	0.115389i
$456$		0			0
$457$	6.03841e6			1.35248			0.676242	−	0.736679i	$-0.263607\pi$
$457$	6.03841e6			1.35248			0.676242	+	0.736679i	$0.263607\pi$
$458$		0			0
$459$	−398339.	−	289410.i	−0.0882513	−	0.0641183i
$460$		0			0
$461$	−3.64452e6	+	2.64790e6i	−0.798709	+	0.580296i	−0.910535	−	0.413432i	$-0.864330\pi$
$461$	−3.64452e6	+	2.64790e6i	−0.798709	+	0.580296i	0.111826	+	0.993728i	$0.464330\pi$
$462$		0			0
$463$	5.31936e6	+	3.86474e6i	1.15321	+	0.837853i	0.988904	−	0.148558i	$-0.0474631\pi$
$463$	5.31936e6	+	3.86474e6i	1.15321	+	0.837853i	0.164301	+	0.986410i	$0.447463\pi$
$464$		0			0
$465$	−187709.	+	208226.i	−0.0402581	+	0.0446583i
$466$		0			0
$467$	−1.93958e6	−	5.96940e6i	−0.411543	−	1.26660i	−0.915307	−	0.402757i	$-0.868052\pi$
$467$	−1.93958e6	−	5.96940e6i	−0.411543	−	1.26660i	0.503765	−	0.863841i	$-0.331948\pi$
$468$		0			0
$469$	−614141.	−	1.89013e6i	−0.128925	−	0.396789i
$470$		0			0
$471$	37207.5	−	114513.i	0.00772819	−	0.0237849i
$472$		0			0
$473$	−1.10859e6	+	805440.i	−0.227834	+	0.165531i
$474$		0			0
$475$	2.36531e6	−	1.04977e6i	0.481010	−	0.213482i
$476$		0			0
$477$	−3.89597e6	+	2.83059e6i	−0.784007	+	0.569614i
$478$		0			0
$479$	2.27504e6	−	7.00184e6i	0.453054	−	1.39436i	−0.420351	−	0.907361i	$-0.638093\pi$
$479$	2.27504e6	−	7.00184e6i	0.453054	−	1.39436i	0.873405	−	0.486995i	$-0.161907\pi$
$480$		0			0
$481$	228228.	+	702415.i	0.0449787	+	0.138430i
$482$		0			0
$483$	71805.3	+	220994.i	0.0140052	+	0.0431035i
$484$		0			0
$485$	−3.10091e6	−	5.37824e6i	−0.598597	−	1.03821i
$486$		0			0
$487$	790706.	+	574482.i	0.151075	+	0.109762i	0.660755	−	0.750602i	$-0.270236\pi$
$487$	790706.	+	574482.i	0.151075	+	0.109762i	−0.509680	+	0.860364i	$0.670236\pi$
$488$		0			0
$489$	277294.	−	201466.i	0.0524407	−	0.0381004i
$490$		0			0
$491$	−3.63382e6	−	2.64012e6i	−0.680236	−	0.494220i	0.193200	−	0.981159i	$-0.438113\pi$
$491$	−3.63382e6	−	2.64012e6i	−0.680236	−	0.494220i	−0.873436	+	0.486939i	$0.838113\pi$
$492$		0			0
$493$	−5.88977e6			−1.09139
$494$		0			0
$495$	2.80868e6	−	3.11566e6i	0.515215	−	0.571528i
$496$		0			0
$497$	747198.	−	2.29964e6i	0.135689	−	0.417608i
$498$		0			0
$499$	−5.66461e6			−1.01840			−0.509201	−	0.860648i	$-0.670059\pi$
$499$	−5.66461e6			−1.01840			−0.509201	+	0.860648i	$0.670059\pi$
$500$		0			0
$501$	−488299.			−0.0869143
$502$		0			0
$503$	2.25762e6	−	6.94825e6i	0.397861	−	1.22449i	−0.528850	−	0.848716i	$-0.677376\pi$
$503$	2.25762e6	−	6.94825e6i	0.397861	−	1.22449i	0.926711	−	0.375775i	$-0.122624\pi$
$504$		0			0
$505$	−3.03773e6	+	3.36975e6i	−0.530054	+	0.587989i
$506$		0			0
$507$	588817.			0.101733
$508$		0			0
$509$	7.42190e6	+	5.39233e6i	1.26976	+	0.922533i	0.999193	−	0.0401689i	$-0.0127896\pi$
$509$	7.42190e6	+	5.39233e6i	1.26976	+	0.922533i	0.270565	+	0.962702i	$0.412790\pi$
$510$		0			0
$511$	868911.	−	631301.i	0.147205	−	0.106951i
$512$		0			0
$513$	459986.	+	334200.i	0.0771705	+	0.0560677i
$514$		0			0
$515$	4.97307e6	+	8.62532e6i	0.826240	+	1.43304i
$516$		0			0
$517$	−1.86998e6	−	5.75519e6i	−0.307687	−	0.946964i
$518$		0			0
$519$	291698.	+	897755.i	0.0475352	+	0.146298i
$520$		0			0
$521$	2.87897e6	−	8.86056e6i	0.464668	−	1.43010i	−0.394731	−	0.918797i	$-0.629162\pi$
$521$	2.87897e6	−	8.86056e6i	0.464668	−	1.43010i	0.859399	−	0.511305i	$-0.170838\pi$
$522$		0			0
$523$	−7.99870e6	+	5.81140e6i	−1.27869	+	0.929023i	−0.999513	−	0.0312171i	$-0.990062\pi$
$523$	−7.99870e6	+	5.81140e6i	−1.27869	+	0.929023i	−0.279177	+	0.960240i	$0.590062\pi$
$524$		0			0
$525$	214932.	+	45949.7i	0.0340332	+	0.00727586i
$526$		0			0
$527$	−2.05088e6	+	1.49005e6i	−0.321673	+	0.233709i
$528$		0			0
$529$	1.38408e6	−	4.25975e6i	0.215041	−	0.661828i
$530$		0			0
$531$	3.86676e6	+	1.19006e7i	0.595128	+	1.83162i
$532$		0			0
$533$	−510455.	−	1.57102e6i	−0.0778286	−	0.239532i
$534$		0			0
$535$	2.58145e6	−	2.86361e6i	0.389924	−	0.432542i
$536$		0			0
$537$	326657.	+	237330.i	0.0488829	+	0.0355155i
$538$		0			0
$539$	−3.61468e6	+	2.62622e6i	−0.535917	+	0.389366i
$540$		0			0
$541$	−962554.	−	699337.i	−0.141394	−	0.102729i	0.514840	−	0.857287i	$-0.327852\pi$
$541$	−962554.	−	699337.i	−0.141394	−	0.102729i	−0.656234	+	0.754558i	$0.727852\pi$
$542$		0			0
$543$	488394.			0.0710838
$544$		0			0
$545$	3.17735e6	−	673413.i	0.458220	−	0.0971159i
$546$		0			0
$547$	914842.	−	2.81559e6i	0.130731	−	0.402348i	−0.864171	−	0.503199i	$-0.832156\pi$
$547$	914842.	−	2.81559e6i	0.130731	−	0.402348i	0.994902	+	0.100851i	$0.0321564\pi$
$548$		0			0
$549$	359434.			0.0508965
$550$		0			0
$551$	6.80128e6			0.954359
$552$		0			0
$553$	594958.	−	1.83109e6i	0.0827320	−	0.254623i
$554$		0			0
$555$	−6942.81	+	65684.6i	−0.000956759	+	0.00905172i
$556$		0			0
$557$	2.80221e6			0.382704			0.191352	−	0.981521i	$-0.438713\pi$
$557$	2.80221e6			0.382704			0.191352	+	0.981521i	$0.438713\pi$
$558$		0			0
$559$	3.15713e6	+	2.29379e6i	0.427329	+	0.310473i
$560$		0			0
$561$	−256275.	+	186195.i	−0.0343795	+	0.0249782i
$562$		0			0
$563$	1.01068e6	+	734305.i	0.134383	+	0.0976350i	0.652946	−	0.757404i	$-0.273533\pi$
$563$	1.01068e6	+	734305.i	0.134383	+	0.0976350i	−0.518563	+	0.855039i	$0.673533\pi$
$564$		0			0
$565$	−1.20012e7	+	2.54356e6i	−1.58163	+	0.335213i
$566$		0			0
$567$	−882232.	−	2.71523e6i	−0.115246	−	0.354690i
$568$		0			0
$569$	3.48443e6	+	1.07240e7i	0.451181	+	1.38859i	0.875560	+	0.483109i	$0.160492\pi$
$569$	3.48443e6	+	1.07240e7i	0.451181	+	1.38859i	−0.424379	+	0.905485i	$0.639508\pi$
$570$		0			0
$571$	−4.11856e6	+	1.26756e7i	−0.528634	+	1.62697i	0.228382	+	0.973572i	$0.426656\pi$
$571$	−4.11856e6	+	1.26756e7i	−0.528634	+	1.62697i	−0.757016	+	0.653396i	$0.773344\pi$
$572$		0			0
$573$	263192.	−	191220.i	0.0334877	−	0.0243302i
$574$		0			0
$575$	−6.89939e6	−	7.68071e6i	−0.870244	−	0.968794i
$576$		0			0
$577$	−1.04802e7	+	7.61430e6i	−1.31048	+	0.952118i	−0.310479	+	0.950580i	$0.600489\pi$
$577$	−1.04802e7	+	7.61430e6i	−1.31048	+	0.952118i	−0.999999	+	0.00153767i	$0.999511\pi$
$578$		0			0
$579$	−297137.	+	914493.i	−0.0368349	+	0.113366i
$580$		0			0
$581$	212724.	+	654699.i	0.0261443	+	0.0804639i
$582$		0			0
$583$	1.92280e6	+	5.91777e6i	0.234295	+	0.721085i
$584$		0			0
$585$	−1.09105e7	−	4.86535e6i	−1.31812	−	0.587793i
$586$		0			0
$587$	8.09908e6	+	5.88432e6i	0.970153	+	0.704857i	0.955486	−	0.295035i	$-0.0953313\pi$
$587$	8.09908e6	+	5.88432e6i	0.970153	+	0.704857i	0.0146666	+	0.999892i	$0.495331\pi$
$588$		0			0
$589$	2.36828e6	−	1.72066e6i	0.281284	−	0.204365i
$590$		0			0
$591$	−241252.	−	175280.i	−0.0284120	−	0.0206425i
$592$		0			0
$593$	−6.74376e6			−0.787527			−0.393763	−	0.919212i	$-0.628827\pi$
$593$	−6.74376e6			−0.787527			−0.393763	+	0.919212i	$0.628827\pi$
$594$		0			0
$595$	1.81516e6	+	809440.i	0.210195	+	0.0937329i
$596$		0			0
$597$	266719.	−	820876.i	0.0306279	−	0.0942631i
$598$		0			0
$599$	1.03252e7			1.17579			0.587897	−	0.808936i	$-0.299956\pi$
$599$	1.03252e7			1.17579			0.587897	+	0.808936i	$0.299956\pi$
$600$		0			0
$601$	−1.57943e6			−0.178367			−0.0891836	−	0.996015i	$-0.528426\pi$
$601$	−1.57943e6			−0.178367			−0.0891836	+	0.996015i	$0.528426\pi$
$602$		0			0
$603$	−2.98524e6	+	9.18761e6i	−0.334338	+	1.02899i
$604$		0			0
$605$	1.78968e6	+	3.10403e6i	0.198786	+	0.344777i
$606$		0			0
$607$	1.68898e7			1.86060			0.930299	−	0.366801i	$-0.119547\pi$
$607$	1.68898e7			1.86060			0.930299	+	0.366801i	$0.119547\pi$
$608$		0			0
$609$	467330.	+	339535.i	0.0510599	+	0.0370972i
$610$		0			0
$611$	−1.39422e7	+	1.01296e7i	−1.51088	+	1.09772i
$612$		0			0
$613$	−7.20241e6	−	5.23286e6i	−0.774153	−	0.562455i	0.129065	−	0.991636i	$-0.458802\pi$
$613$	−7.20241e6	−	5.23286e6i	−0.774153	−	0.562455i	−0.903219	+	0.429181i	$0.858802\pi$
$614$		0			0
$615$	15528.3	−	146910.i	0.00165552	−	0.0156626i
$616$		0			0
$617$	−1.41115e6	−	4.34307e6i	−0.149231	−	0.459287i	0.848300	−	0.529517i	$-0.177627\pi$
$617$	−1.41115e6	−	4.34307e6i	−0.149231	−	0.459287i	−0.997531	+	0.0702299i	$0.977627\pi$
$618$		0			0
$619$	431712.	+	1.32867e6i	0.0452864	+	0.139377i	0.971143	−	0.238498i	$-0.0766550\pi$
$619$	431712.	+	1.32867e6i	0.0452864	+	0.139377i	−0.925857	+	0.377875i	$0.876655\pi$
$620$		0			0
$621$	700982.	−	2.15740e6i	0.0729420	−	0.224492i
$622$		0			0
$623$	−1.86395e6	+	1.35424e6i	−0.192404	+	0.139790i
$624$		0			0
$625$	−9.55697e6	+	2.00790e6i	−0.978634	+	0.205609i
$626$		0			0
$627$	295937.	−	215010.i	0.0300628	−	0.0218419i
$628$		0			0
$629$	−184565.	+	568034.i	−0.0186005	+	0.0572464i
$630$		0			0
$631$	3.99356e6	+	1.22909e7i	0.399288	+	1.22888i	0.925571	+	0.378573i	$0.123585\pi$
$631$	3.99356e6	+	1.22909e7i	0.399288	+	1.22888i	−0.526283	+	0.850309i	$0.676415\pi$
$632$		0			0
$633$	516258.	+	1.58888e6i	0.0512103	+	0.157609i
$634$		0			0
$635$	2.02028e6	−	1.91135e7i	0.198828	−	1.88108i
$636$		0			0
$637$	1.02941e7	+	7.47912e6i	1.00517	+	0.730302i
$638$		0			0
$639$	−9.50871e6	+	6.90848e6i	−0.921233	+	0.669315i
$640$		0			0
$641$	1.17880e7	+	8.56445e6i	1.13317	+	0.823293i	0.986152	−	0.165841i	$-0.0530339\pi$
$641$	1.17880e7	+	8.56445e6i	1.13317	+	0.823293i	0.147014	+	0.989134i	$0.453034\pi$
$642$		0			0
$643$	−1.07431e7			−1.02472			−0.512358	−	0.858772i	$-0.671228\pi$
$643$	−1.07431e7			−1.02472			−0.512358	+	0.858772i	$0.671228\pi$
$644$		0			0
$645$	174322.	+	302344.i	0.0164988	+	0.0286156i
$646$		0			0
$647$	5.70200e6	−	1.75490e7i	0.535509	−	1.64813i	−0.207038	−	0.978333i	$-0.566383\pi$
$647$	5.70200e6	−	1.75490e7i	0.535509	−	1.64813i	0.742547	−	0.669794i	$-0.233617\pi$
$648$		0			0
$649$	1.61680e7			1.50677
$650$		0			0
$651$	248628.			0.0229931
$652$		0			0
$653$	−1.03257e6	+	3.17793e6i	−0.0947628	+	0.291650i	−0.987192	−	0.159538i	$-0.949000\pi$
$653$	−1.03257e6	+	3.17793e6i	−0.0947628	+	0.291650i	0.892429	+	0.451188i	$0.149000\pi$
$654$		0			0
$655$	1.31167e7	+	5.84918e6i	1.19460	+	0.532711i
$656$		0			0
$657$	−5.22069e6			−0.471862
$658$		0			0
$659$	−8.40387e6	−	6.10577e6i	−0.753817	−	0.547680i	0.143191	−	0.989695i	$-0.454264\pi$
$659$	−8.40387e6	−	6.10577e6i	−0.753817	−	0.547680i	−0.897008	+	0.442015i	$0.854264\pi$
$660$		0			0
$661$	−4.78446e6	+	3.47611e6i	−0.425921	+	0.309450i	−0.780016	−	0.625760i	$-0.784789\pi$
$661$	−4.78446e6	+	3.47611e6i	−0.425921	+	0.309450i	0.354095	+	0.935210i	$0.384789\pi$
$662$		0			0
$663$	729839.	+	530259.i	0.0644827	+	0.0468494i
$664$		0			0
$665$	−2.09607e6	−	934710.i	−0.183803	−	0.0819639i
$666$		0			0
$667$	−8.38514e6	−	2.58068e7i	−0.729786	−	2.24605i
$668$		0			0
$669$	−3937.27	−	12117.7i	−0.000340119	−	0.00104678i
$670$		0			0
$671$	143514.	−	441691.i	0.0123052	−	0.0378715i
$672$		0			0
$673$	−6.32371e6	+	4.59444e6i	−0.538188	+	0.391017i	−0.823412	−	0.567444i	$-0.807932\pi$
$673$	−6.32371e6	+	4.59444e6i	−0.538188	+	0.391017i	0.285224	+	0.958461i	$0.407932\pi$
$674$		0			0
$675$	−1.43383e6	−	1.59621e6i	−0.121127	−	0.134843i
$676$		0			0
$677$	6.30575e6	−	4.58139e6i	0.528768	−	0.384172i	−0.291129	−	0.956684i	$-0.594031\pi$
$677$	6.30575e6	−	4.58139e6i	0.528768	−	0.384172i	0.819897	+	0.572512i	$0.194031\pi$
$678$		0			0
$679$	−1.70139e6	+	5.23633e6i	−0.141621	+	0.435866i
$680$		0			0
$681$	238583.	+	734282.i	0.0197138	+	0.0606730i
$682$		0			0
$683$	1.21016e6	+	3.72448e6i	0.0992636	+	0.305502i	0.988341	−	0.152254i	$-0.0486533\pi$
$683$	1.21016e6	+	3.72448e6i	0.0992636	+	0.305502i	−0.889078	+	0.457756i	$0.848653\pi$
$684$		0			0
$685$	8.42137e6	−	1.78484e6i	0.685735	−	0.145336i
$686$		0			0
$687$	−836978.	−	608100.i	−0.0676585	−	0.0491568i
$688$		0			0
$689$	1.43360e7	−	1.04157e7i	1.15049	−	0.835877i
$690$		0			0
$691$	−1.83201e7	−	1.33103e7i	−1.45960	−	1.06046i	−0.983468	−	0.181083i	$-0.942040\pi$
$691$	−1.83201e7	−	1.33103e7i	−1.45960	−	1.06046i	−0.476128	−	0.879376i	$-0.657960\pi$
$692$		0			0
$693$	−3.72020e6			−0.294261
$694$		0			0
$695$	1.69850e6	−	1.60692e7i	0.133384	−	1.26192i
$696$		0			0
$697$	412798.	−	1.27046e6i	0.0321852	−	0.0990558i
$698$		0			0
$699$	676370.			0.0523590
$700$		0			0
$701$	2.43172e7			1.86904			0.934520	−	0.355911i	$-0.115829\pi$
$701$	2.43172e7			1.86904			0.934520	+	0.355911i	$0.115829\pi$
$702$		0			0
$703$	213129.	−	655944.i	0.0162650	−	0.0500585i
$704$		0			0
$705$	−1.50772e6	+	319550.i	−0.114248	+	0.0242139i
$706$		0			0
$707$	4.02358e6			0.302736
$708$		0			0
$709$	1.33372e7	+	9.69003e6i	0.996434	+	0.723951i	0.961321	−	0.275432i	$-0.0888209\pi$
$709$	1.33372e7	+	9.69003e6i	0.996434	+	0.723951i	0.0351130	+	0.999383i	$0.488821\pi$
$710$		0			0
$711$	−7.57132e6	+	5.50089e6i	−0.561691	+	0.408093i
$712$		0			0
$713$	−9.44865e6	−	6.86485e6i	−0.696059	−	0.505717i
$714$		0			0
$715$	−1.03351e7	+	1.14647e7i	−0.756049	+	0.838685i
$716$		0			0
$717$	324982.	+	1.00019e6i	0.0236081	+	0.0726583i
$718$		0			0
$719$	−3.31516e6	−	1.02030e7i	−0.239156	−	0.736048i	−0.996543	−	0.0830808i	$-0.973524\pi$
$719$	−3.31516e6	−	1.02030e7i	−0.239156	−	0.736048i	0.757386	−	0.652967i	$-0.226476\pi$
$720$		0			0
$721$	2.72859e6	−	8.39774e6i	0.195479	−	0.601623i
$722$		0			0
$723$	−117149.	+	85113.9i	−0.00833477	+	0.00605557i
$724$		0			0
$725$	−2.50989e7	−	5.36582e6i	−1.77341	−	0.379132i
$726$		0			0
$727$	−1.48769e7	+	1.08087e7i	−1.04394	+	0.758466i	−0.971051	−	0.238874i	$-0.923222\pi$
$727$	−1.48769e7	+	1.08087e7i	−1.04394	+	0.758466i	−0.0728884	+	0.997340i	$0.523222\pi$
$728$		0			0
$729$	−4.21524e6	+	1.29732e7i	−0.293767	+	0.904122i
$730$		0			0
$731$	975209.	+	3.00139e6i	0.0675001	+	0.207744i
$732$		0			0
$733$	−5.24280e6	−	1.61357e7i	−0.360416	−	1.10925i	−0.952802	−	0.303591i	$-0.901814\pi$
$733$	−5.24280e6	−	1.61357e7i	−0.360416	−	1.10925i	0.592387	−	0.805654i	$-0.298186\pi$
$734$		0			0
$735$	568392.	+	985824.i	0.0388088	+	0.0673102i
$736$		0			0
$737$	1.00983e7	+	7.33682e6i	0.684823	+	0.497553i
$738$		0			0
$739$	2.26459e7	−	1.64532e7i	1.52538	−	1.10825i	0.566641	−	0.823964i	$-0.308242\pi$
$739$	2.26459e7	−	1.64532e7i	1.52538	−	1.10825i	0.958739	−	0.284289i	$-0.0917575\pi$
$740$		0			0
$741$	−842789.	−	612322.i	−0.0563863	−	0.0409670i
$742$		0			0
$743$	1.91330e7			1.27149			0.635743	−	0.771901i	$-0.280694\pi$
$743$	1.91330e7			1.27149			0.635743	+	0.771901i	$0.280694\pi$
$744$		0			0
$745$	9.80711e6	−	1.08790e7i	0.647367	−	0.718124i
$746$		0			0
$747$	1.03402e6	−	3.18238e6i	0.0677995	−	0.208665i
$748$		0			0
$749$	−3.41923e6			−0.222702
$750$		0			0
$751$	1.31957e6			0.0853752			0.0426876	−	0.999088i	$-0.486408\pi$
$751$	1.31957e6			0.0853752			0.0426876	+	0.999088i	$0.486408\pi$
$752$		0			0
$753$	82230.2	−	253079.i	0.00528499	−	0.0162655i
$754$		0			0
$755$	6.97533e6	−	7.73773e6i	0.445346	−	0.494022i
$756$		0			0
$757$	1.40025e7			0.888109			0.444055	−	0.896000i	$-0.353540\pi$
$757$	1.40025e7			0.888109			0.444055	+	0.896000i	$0.353540\pi$
$758$		0			0
$759$	−1.18069e6	−	857821.i	−0.0743928	−	0.0540496i
$760$		0			0
$761$	−6.90341e6	+	5.01562e6i	−0.432118	+	0.313952i	−0.782495	−	0.622657i	$-0.786053\pi$
$761$	−6.90341e6	+	5.01562e6i	−0.432118	+	0.313952i	0.350377	+	0.936609i	$0.386053\pi$
$762$		0			0
$763$	−2.33036e6	−	1.69311e6i	−0.144914	−	0.105287i
$764$		0			0
$765$	−4.82542e6	−	8.36925e6i	−0.298114	−	0.517050i
$766$		0			0
$767$	−1.42285e7	−	4.37909e7i	−0.873317	−	2.68779i
$768$		0			0
$769$	−847052.	−	2.60696e6i	−0.0516529	−	0.158971i	0.921903	−	0.387421i	$-0.126634\pi$
$769$	−847052.	−	2.60696e6i	−0.0516529	−	0.158971i	−0.973556	+	0.228450i	$0.926634\pi$
$770$		0			0
$771$	11760.0	−	36193.4i	0.000712475	−	0.00219277i
$772$		0			0
$773$	8.52646e6	−	6.19483e6i	0.513239	−	0.372890i	−0.300812	−	0.953684i	$-0.597258\pi$
$773$	8.52646e6	−	6.19483e6i	0.513239	−	0.372890i	0.814051	+	0.580793i	$0.197258\pi$
$774$		0			0
$775$	−1.00972e7	+	4.48134e6i	−0.603875	+	0.268012i
$776$		0			0
$777$	47390.7	−	34431.4i	0.00281605	−	0.00204598i
$778$		0			0
$779$	−476684.	+	1.46708e6i	−0.0281441	+	0.0866185i
$780$		0			0
$781$	4.69288e6	+	1.44432e7i	0.275304	+	0.847298i
$782$		0			0
$783$	−1.74260e6	−	5.36318e6i	−0.101577	−	0.312621i
$784$		0			0
$785$	3.17684e6	−	3.52406e6i	0.184001	−	0.204112i
$786$		0			0
$787$	2.03408e7	+	1.47784e7i	1.17066	+	0.850533i	0.991088	−	0.133212i	$-0.0425291\pi$
$787$	2.03408e7	+	1.47784e7i	1.17066	+	0.850533i	0.179571	+	0.983745i	$0.442529\pi$
$788$		0			0
$789$	−697601.	+	506837.i	−0.0398947	+	0.0289852i
$790$		0			0
$791$	8.80205e6	+	6.39506e6i	0.500199	+	0.363416i
$792$		0			0
$793$	−1.32261e6			−0.0746878
$794$		0			0
$795$	1.55031e6	−	328576.i	0.0869965	−	0.0184382i
$796$		0			0
$797$	−8.43301e6	+	2.59541e7i	−0.470259	+	1.44731i	0.381988	+	0.924167i	$0.375239\pi$
$797$	−8.43301e6	+	2.59541e7i	−0.470259	+	1.44731i	−0.852247	+	0.523140i	$0.824761\pi$
$798$		0			0
$799$	−1.39365e7			−0.772303
$800$		0			0
$801$	1.11992e7			0.616747
$802$		0			0
$803$	−2.08451e6	+	6.41546e6i	−0.114081	+	0.351107i
$804$		0			0
$805$	−962467.	+	9.10572e6i	−0.0523475	+	0.495250i
$806$		0			0
$807$	817294.			0.0441768
$808$		0			0
$809$	1.37767e7	+	1.00094e7i	0.740072	+	0.537694i	0.892734	−	0.450585i	$-0.148785\pi$
$809$	1.37767e7	+	1.00094e7i	0.740072	+	0.537694i	−0.152662	+	0.988278i	$0.548785\pi$
$810$		0			0
$811$	−1.24348e7	+	9.03444e6i	−0.663877	+	0.482335i	−0.867970	−	0.496616i	$-0.834576\pi$
$811$	−1.24348e7	+	9.03444e6i	−0.663877	+	0.482335i	0.204093	+	0.978952i	$0.434576\pi$
$812$		0			0
$813$	−2.25093e6	−	1.63539e6i	−0.119436	−	0.0867753i
$814$		0			0
$815$	1.32128e7	−	2.80034e6i	0.696788	−	0.147678i
$816$		0			0
$817$	−1.12613e6	−	3.46588e6i	−0.0590249	−	0.181660i
$818$		0			0
$819$	3.27393e6	+	1.00761e7i	0.170553	+	0.524908i
$820$		0			0
$821$	3.79517e6	−	1.16803e7i	0.196505	−	0.604780i	−0.803451	−	0.595371i	$-0.797005\pi$
$821$	3.79517e6	−	1.16803e7i	0.196505	−	0.604780i	0.999956	−	0.00940861i	$-0.00299490\pi$
$822$		0			0
$823$	−2.33299e7	+	1.69502e7i	−1.20064	+	0.872318i	−0.994348	−	0.106171i	$-0.966141\pi$
$823$	−2.33299e7	+	1.69502e7i	−1.20064	+	0.872318i	−0.206295	+	0.978490i	$0.566141\pi$
$824$		0			0
$825$	−1.26173e6	+	559981.i	−0.0645405	+	0.0286443i
$826$		0			0
$827$	−2.29449e7	+	1.66704e7i	−1.16660	+	0.847585i	−0.990598	−	0.136805i	$-0.956317\pi$
$827$	−2.29449e7	+	1.66704e7i	−1.16660	+	0.847585i	−0.176002	+	0.984390i	$0.556317\pi$
$828$		0			0
$829$	4.25366e6	−	1.30914e7i	0.214969	−	0.661607i	−0.784187	−	0.620525i	$-0.786920\pi$
$829$	4.25366e6	−	1.30914e7i	0.214969	−	0.661607i	0.999156	−	0.0410818i	$-0.0130804\pi$
$830$		0			0
$831$	400539.	+	1.23273e6i	0.0201207	+	0.0619250i
$832$		0			0
$833$	3.17977e6	+	9.78632e6i	0.158775	+	0.488660i
$834$		0			0
$835$	−1.75734e7	−	7.83655e6i	−0.872245	−	0.388963i
$836$		0			0
$837$	−1.96362e6	−	1.42666e6i	−0.0968823	−	0.0703891i
$838$		0			0
$839$	−2.48757e7	+	1.80733e7i	−1.22003	+	0.886404i	−0.996103	−	0.0882011i	$-0.971888\pi$
$839$	−2.48757e7	+	1.80733e7i	−1.22003	+	0.886404i	−0.223928	+	0.974606i	$0.571888\pi$
$840$		0			0
$841$	−3.79790e7	−	2.75934e7i	−1.85163	−	1.34529i
$842$		0			0
$843$	−1.23369e6			−0.0597914
$844$		0			0
$845$	2.11909e7	+	9.44974e6i	1.02096	+	0.455280i
$846$		0			0
$847$	981950.	−	3.02213e6i	0.0470307	−	0.144745i
$848$		0			0
$849$	−1.03904e6			−0.0494722
$850$		0			0
$851$	−2.75168e6			−0.130249
$852$		0			0
$853$	−5.85803e6	+	1.80292e7i	−0.275663	+	0.848404i	0.713380	+	0.700777i	$0.247163\pi$
$853$	−5.85803e6	+	1.80292e7i	−0.275663	+	0.848404i	−0.989043	+	0.147627i	$0.952837\pi$
$854$		0			0
$855$	5.57221e6	+	9.66448e6i	0.260683	+	0.452130i
$856$		0			0
$857$	2.77971e7			1.29285			0.646424	−	0.762978i	$-0.276264\pi$
$857$	2.77971e7			1.29285			0.646424	+	0.762978i	$0.276264\pi$
$858$		0			0
$859$	−5.92918e6	−	4.30780e6i	−0.274165	−	0.199192i	0.442204	−	0.896915i	$-0.354197\pi$
$859$	−5.92918e6	−	4.30780e6i	−0.274165	−	0.199192i	−0.716368	+	0.697722i	$0.754197\pi$
$860$		0			0
$861$	−105994.	+	77009.0i	−0.00487274	+	0.00354025i
$862$		0			0
$863$	3.40726e6	+	2.47552e6i	0.155732	+	0.113146i	0.662923	−	0.748688i	$-0.269316\pi$
$863$	3.40726e6	+	2.47552e6i	0.155732	+	0.113146i	−0.507190	+	0.861834i	$0.669316\pi$
$864$		0			0
$865$	−3.90988e6	+	3.69906e7i	−0.177674	+	1.68094i
$866$		0			0
$867$	−397002.	−	1.22185e6i	−0.0179368	−	0.0552037i
$868$		0			0
$869$	3.73671e6	+	1.15004e7i	0.167857	+	0.516612i
$870$		0			0
$871$	1.09848e7	−	3.38077e7i	0.490622	−	1.50998i
$872$		0			0
$873$	2.16515e7	−	1.57308e7i	0.961509	−	0.698577i
$874$		0			0
$875$	6.99776e6	+	5.10306e6i	0.308986	+	0.225326i
$876$		0			0
$877$	−2.63512e7	+	1.91453e7i	−1.15692	+	0.840549i	−0.989385	−	0.145318i	$-0.953580\pi$
$877$	−2.63512e7	+	1.91453e7i	−1.15692	+	0.840549i	−0.167532	+	0.985867i	$0.553580\pi$
$878$		0			0
$879$	628652.	−	1.93479e6i	0.0274434	−	0.0844621i
$880$		0			0
$881$	7.75717e6	+	2.38741e7i	0.336716	+	1.03631i	0.965871	+	0.259025i	$0.0834012\pi$
$881$	7.75717e6	+	2.38741e7i	0.336716	+	1.03631i	−0.629155	+	0.777280i	$0.716599\pi$
$882$		0			0
$883$	9.34538e6	+	2.87621e7i	0.403362	+	1.24142i	0.922255	+	0.386582i	$0.126344\pi$
$883$	9.34538e6	+	2.87621e7i	0.403362	+	1.24142i	−0.518893	+	0.854839i	$0.673656\pi$
$884$		0			0
$885$	432838.	−	4.09501e6i	0.0185767	−	0.175750i
$886$		0			0
$887$	−1.17617e7	−	8.54535e6i	−0.501949	−	0.364687i	0.307812	−	0.951447i	$-0.400403\pi$
$887$	−1.17617e7	−	8.54535e6i	−0.501949	−	0.364687i	−0.809761	+	0.586760i	$0.800403\pi$
$888$		0			0
$889$	−1.37902e7	+	1.00192e7i	−0.585215	+	0.425184i
$890$		0			0
$891$	1.45065e7	+	1.05396e7i	0.612163	+	0.444763i
$892$		0			0
$893$	1.60934e7			0.675334
$894$		0			0
$895$	7.94721e6	+	1.37837e7i	0.331633	+	0.575186i
$896$		0			0
$897$	−1.28434e6	+	3.95280e6i	−0.0532966	+	0.164030i
$898$		0			0
$899$	−2.90338e7			−1.19813
$900$		0			0
$901$	1.43302e7			0.588086
$902$		0			0
$903$	95645.6	−	294367.i	0.00390342	−	0.0120135i
$904$		0			0
$905$	1.75768e7	+	7.83808e6i	0.713375	+	0.318118i
$906$		0			0
$907$	1.76853e7			0.713828			0.356914	−	0.934137i	$-0.383829\pi$
$907$	1.76853e7			0.713828			0.356914	+	0.934137i	$0.383829\pi$
$908$		0			0
$909$	−1.58227e7	−	1.14959e7i	−0.635143	−	0.461458i
$910$		0			0
$911$	−3.68913e6	+	2.68031e6i	−0.147274	+	0.107001i	−0.658983	−	0.752158i	$-0.729013\pi$
$911$	−3.68913e6	+	2.68031e6i	−0.147274	+	0.107001i	0.511708	+	0.859159i	$0.329013\pi$
$912$		0			0
$913$	−3.49781e6	−	2.54131e6i	−0.138874	−	0.100898i
$914$		0			0
$915$	−108028.	−	48173.5i	−0.00426565	−	0.00190220i
$916$		0			0
$917$	−3.93595e6	−	1.21136e7i	−0.154570	−	0.475718i
$918$		0			0
$919$	−1.15900e7	−	3.56703e7i	−0.452682	−	1.39321i	−0.873835	−	0.486223i	$-0.838374\pi$
$919$	−1.15900e7	−	3.56703e7i	−0.452682	−	1.39321i	0.421152	−	0.906990i	$-0.361626\pi$
$920$		0			0
$921$	−599566.	+	1.84527e6i	−0.0232910	+	0.0716823i
$922$		0			0
$923$	3.49893e7	−	2.54212e7i	1.35186	−	0.982182i
$924$		0			0
$925$	−1.30402e6	+	2.25250e6i	−0.0501105	+	0.0865586i
$926$		0			0
$927$	−3.47236e7	+	2.52281e7i	−1.32717	+	0.964242i
$928$		0			0
$929$	1.55014e6	−	4.77084e6i	0.0589294	−	0.181366i	−0.917259	−	0.398292i	$-0.869603\pi$
$929$	1.55014e6	−	4.77084e6i	0.0589294	−	0.181366i	0.976188	+	0.216926i	$0.0696031\pi$
$930$		0			0
$931$	−3.67187e6	−	1.13009e7i	−0.138840	−	0.427304i
$932$		0			0
$933$	1.00396e6	+	3.08986e6i	0.0377582	+	0.116208i
$934$		0			0
$935$	−1.22113e7	+	2.58807e6i	−0.456805	+	0.0968161i
$936$		0			0
$937$	1.69330e7	+	1.23026e7i	0.630066	+	0.457769i	0.856423	−	0.516275i	$-0.172682\pi$
$937$	1.69330e7	+	1.23026e7i	0.630066	+	0.457769i	−0.226357	+	0.974044i	$0.572682\pi$
$938$		0			0
$939$	1.05330e6	−	765267.i	0.0389842	−	0.0283237i
$940$		0			0
$941$	−3.66957e7	−	2.66610e7i	−1.35096	−	0.981526i	−0.998963	−	0.0455233i	$-0.985504\pi$
$941$	−3.66957e7	−	2.66610e7i	−1.35096	−	0.981526i	−0.351992	−	0.936003i	$-0.614496\pi$
$942$		0			0
$943$	6.15439e6			0.225375
$944$		0			0
$945$	−200020.	+	1.89236e6i	−0.00728609	+	0.0689324i
$946$		0			0
$947$	−89250.8	+	274686.i	−0.00323398	+	0.00995316i	−0.952660	−	0.304036i	$-0.901666\pi$
$947$	−89250.8	+	274686.i	−0.00323398	+	0.00995316i	0.949427	+	0.313989i	$0.101666\pi$
$948$		0			0
$949$	1.92106e7			0.692431
$950$		0			0
$951$	116116.			0.00416332
$952$		0			0
$953$	1.19252e7	−	3.67021e7i	0.425338	−	1.30906i	−0.477332	−	0.878723i	$-0.658396\pi$
$953$	1.19252e7	−	3.67021e7i	0.425338	−	1.30906i	0.902670	−	0.430333i	$-0.141604\pi$
$954$		0			0
$955$	1.25408e7	−	2.65792e6i	0.444956	−	0.0943048i
$956$		0			0
$957$	−3.62802e6			−0.128053
$958$		0			0
$959$	−6.17647e6	−	4.48747e6i	−0.216867	−	0.157563i
$960$		0			0
$961$	1.30516e7	−	9.48253e6i	0.455885	−	0.331220i
$962$		0			0
$963$	1.34461e7	+	9.76918e6i	0.467231	+	0.339463i
$964$		0			0
$965$	−2.53701e7	+	2.81430e7i	−0.877007	+	0.972863i
$966$		0			0
$967$	1.52065e7	+	4.68009e7i	0.522955	+	1.60949i	0.768325	+	0.640060i	$0.221090\pi$
$967$	1.52065e7	+	4.68009e7i	0.522955	+	1.60949i	−0.245371	+	0.969429i	$0.578910\pi$
$968$		0			0
$969$	−260330.	−	801214.i	−0.00890666	−	0.0274119i
$970$		0			0
$971$	4.61408e6	−	1.42007e7i	0.157050	−	0.483349i	−0.841313	−	0.540548i	$-0.818217\pi$
$971$	4.61408e6	−	1.42007e7i	0.157050	−	0.483349i	0.998363	+	0.0571991i	$0.0182170\pi$
$972$		0			0
$973$	−1.15937e7	+	8.42335e6i	−0.392592	+	0.285235i
$974$		0			0
$975$	2.62708e6	+	2.92458e6i	0.0885037	+	0.0985262i
$976$		0			0
$977$	−4.61891e7	+	3.35584e7i	−1.54812	+	1.12477i	−0.603138	+	0.797637i	$0.706083\pi$
$977$	−4.61891e7	+	3.35584e7i	−1.54812	+	1.12477i	−0.944978	+	0.327135i	$0.893917\pi$
$978$		0			0
$979$	4.47161e6	−	1.37622e7i	0.149110	−	0.458914i
$980$		0			0
$981$	4.32671e6	+	1.33163e7i	0.143544	+	0.441784i
$982$		0			0
$983$	−1.45229e7	−	4.46970e7i	−0.479370	−	1.47535i	−0.839973	−	0.542629i	$-0.817429\pi$
$983$	−1.45229e7	−	4.46970e7i	−0.479370	−	1.47535i	0.360603	−	0.932719i	$-0.382571\pi$
$984$		0			0
$985$	−5.86938e6	−	1.01799e7i	−0.192753	−	0.334313i
$986$		0			0
$987$	1.10581e6	+	803417.i	0.0361316	+	0.0262511i
$988$		0			0
$989$	−1.17626e7	+	8.54601e6i	−0.382394	+	0.277826i
$990$		0			0
$991$	−1.36643e7	−	9.92768e6i	−0.441980	−	0.321117i	0.344441	−	0.938808i	$-0.388068\pi$
$991$	−1.36643e7	−	9.92768e6i	−0.441980	−	0.321117i	−0.786421	+	0.617691i	$0.788068\pi$
$992$		0			0
$993$	−307726.			−0.00990355
$994$		0			0
$995$	2.27729e7	−	2.52620e7i	0.729224	−	0.808927i
$996$		0			0
$997$	2.67753e6	−	8.24060e6i	0.0853094	−	0.262555i	−0.899298	−	0.437337i	$-0.855922\pi$
$997$	2.67753e6	−	8.24060e6i	0.0853094	−	0.262555i	0.984607	+	0.174781i	$0.0559218\pi$
$998$		0			0
$999$	−571854.			−0.0181289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.6.g.a.61.7	yes	52
25.16	even	5	inner	100.6.g.a.41.7	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.6.g.a.41.7	✓	52	25.16	even	5	inner
100.6.g.a.61.7	yes	52	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	100.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.438384 - 1.34921i) q^{3} +(37.4300 - 41.5210i) q^{5} -49.5774 q^{7} +(194.963 + 141.649i) q^{9} +O(q^{10})\)	\(q+(0.438384 - 1.34921i) q^{3} +(37.4300 - 41.5210i) q^{5} -49.5774 q^{7} +(194.963 + 141.649i) q^{9} +(251.910 - 183.023i) q^{11} +(-717.407 - 521.227i) q^{13} +(-39.6118 - 68.7029i) q^{15} +(-221.601 - 682.017i) q^{17} +(255.896 + 787.567i) q^{19} +(-21.7339 + 66.8902i) q^{21} +(2672.86 - 1941.94i) q^{23} +(-322.994 - 3108.26i) q^{25} +(555.474 - 403.576i) q^{27} +(2538.00 - 7811.17i) q^{29} +(-1092.39 - 3362.02i) q^{31} +(-136.503 - 420.113i) q^{33} +(-1855.68 + 2058.51i) q^{35} +(-673.809 - 489.551i) q^{37} +(-1017.74 + 739.433i) q^{39} +(1507.04 + 1094.93i) q^{41} -4400.75 q^{43} +(13178.9 - 2793.15i) q^{45} +(6005.49 - 18483.0i) q^{47} -14349.1 q^{49} -1017.33 q^{51} +(-6175.13 + 19005.1i) q^{53} +(1829.66 - 17310.1i) q^{55} +1174.77 q^{57} +(42007.6 + 30520.3i) q^{59} +(1206.65 - 876.684i) q^{61} +(-9665.76 - 7022.59i) q^{63} +(-48494.4 + 10278.0i) q^{65} +(12387.5 + 38124.8i) q^{67} +(-1448.35 - 4457.55i) q^{69} +(-15071.3 + 46384.8i) q^{71} +(-17526.3 + 12733.6i) q^{73} +(-4335.28 - 926.826i) q^{75} +(-12489.0 + 9073.82i) q^{77} +(-12000.6 + 36934.0i) q^{79} +(17795.0 + 54767.5i) q^{81} +(-4290.75 - 13205.6i) q^{83} +(-36612.6 - 16326.8i) q^{85} +(-9426.26 - 6848.58i) q^{87} +(37596.8 - 27315.7i) q^{89} +(35567.2 + 25841.1i) q^{91} -5014.95 q^{93} +(42278.8 + 18853.5i) q^{95} +(34317.8 - 105619. i) q^{97} +75038.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{3} + 116 q^{5} - 42 q^{7} - 1153 q^{9}+O(q^{10}) \) 52 * q + 2 * q^3 + 116 * q^5 - 42 * q^7 - 1153 * q^9	\( 52 q + 2 q^{3} + 116 q^{5} - 42 q^{7} - 1153 q^{9} - 5 q^{11} + 1458 q^{13} + 2418 q^{15} - 2329 q^{17} + 1912 q^{19} - 4818 q^{21} + 3594 q^{23} + 934 q^{25} + 3206 q^{27} - 1458 q^{29} + 5532 q^{31} + 2435 q^{33} - 5603 q^{35} + 22043 q^{37} - 9938 q^{39} + 4567 q^{41} - 35390 q^{43} - 59359 q^{45} - 5859 q^{47} + 165974 q^{49} + 68014 q^{51} + 20151 q^{53} - 97855 q^{55} - 241368 q^{57} - 116271 q^{59} + 39134 q^{61} + 262808 q^{63} + 190502 q^{65} + 40883 q^{67} - 51844 q^{69} - 109999 q^{71} - 187802 q^{73} - 164833 q^{75} + 102220 q^{77} + 122216 q^{79} - 264922 q^{81} + 125394 q^{83} + 83764 q^{85} + 205117 q^{87} - 107222 q^{89} + 58608 q^{91} - 490158 q^{93} - 82634 q^{95} + 129683 q^{97} + 302280 q^{99}+O(q^{100}) \) 52 * q + 2 * q^3 + 116 * q^5 - 42 * q^7 - 1153 * q^9 - 5 * q^11 + 1458 * q^13 + 2418 * q^15 - 2329 * q^17 + 1912 * q^19 - 4818 * q^21 + 3594 * q^23 + 934 * q^25 + 3206 * q^27 - 1458 * q^29 + 5532 * q^31 + 2435 * q^33 - 5603 * q^35 + 22043 * q^37 - 9938 * q^39 + 4567 * q^41 - 35390 * q^43 - 59359 * q^45 - 5859 * q^47 + 165974 * q^49 + 68014 * q^51 + 20151 * q^53 - 97855 * q^55 - 241368 * q^57 - 116271 * q^59 + 39134 * q^61 + 262808 * q^63 + 190502 * q^65 + 40883 * q^67 - 51844 * q^69 - 109999 * q^71 - 187802 * q^73 - 164833 * q^75 + 102220 * q^77 + 122216 * q^79 - 264922 * q^81 + 125394 * q^83 + 83764 * q^85 + 205117 * q^87 - 107222 * q^89 + 58608 * q^91 - 490158 * q^93 - 82634 * q^95 + 129683 * q^97 + 302280 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more