LMFDB - Embedded newform 63.7.m.c.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,7,Mod(10,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("63.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	63.m (of order $6$, degree $2$, 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:	$14.4934072681$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.2
Root			$-2.30325 - 3.98935i$ of defining polynomial
Character	$\chi$	$=$	63.10
Dual form			63.7.m.c.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80325 - 3.12332i) q^{2} +(25.4966 - 44.1614i) q^{4} +(-71.9311 + 41.5295i) q^{5} +(77.0894 + 334.225i) q^{7} -414.723 q^{8} +O(q^{10})$	\(q+(-1.80325 - 3.12332i) q^{2} +(25.4966 - 44.1614i) q^{4} +(-71.9311 + 41.5295i) q^{5} +(77.0894 + 334.225i) q^{7} -414.723 q^{8} +(259.420 + 149.776i) q^{10} +(-221.304 + 383.310i) q^{11} +696.494i q^{13} +(904.880 - 843.466i) q^{14} +(-883.932 - 1531.01i) q^{16} +(5447.24 + 3144.96i) q^{17} +(-2327.56 + 1343.82i) q^{19} +4235.44i q^{20} +1596.27 q^{22} +(7885.31 + 13657.8i) q^{23} +(-4363.11 + 7557.12i) q^{25} +(2175.37 - 1255.95i) q^{26} +(16725.3 + 5117.22i) q^{28} +23274.5 q^{29} +(41177.0 + 23773.6i) q^{31} +(-16459.0 + 28507.9i) q^{32} -22684.6i q^{34} +(-19425.3 - 20839.7i) q^{35} +(5079.89 + 8798.64i) q^{37} +(8394.35 + 4846.48i) q^{38} +(29831.5 - 17223.2i) q^{40} -38165.4i q^{41} -151197. q^{43} +(11285.0 + 19546.2i) q^{44} +(28438.4 - 49256.7i) q^{46} +(43543.1 - 25139.6i) q^{47} +(-105763. + 51530.4i) q^{49} +31471.1 q^{50} +(30758.1 + 17758.2i) q^{52} +(-99778.2 + 172821. i) q^{53} -36762.6i q^{55} +(-31970.7 - 138611. i) q^{56} +(-41969.8 - 72693.8i) q^{58} +(-335347. - 193612. i) q^{59} +(-10203.5 + 5890.98i) q^{61} -171479. i q^{62} +5575.73 q^{64} +(-28925.0 - 50099.6i) q^{65} +(192138. - 332792. i) q^{67} +(277772. - 160372. i) q^{68} +(-30060.4 + 98250.6i) q^{70} -156126. q^{71} +(325227. + 187770. i) q^{73} +(18320.6 - 31732.3i) q^{74} +137051. i q^{76} +(-145172. - 44416.2i) q^{77} +(-16591.8 - 28737.9i) q^{79} +(127164. + 73418.4i) q^{80} +(-119203. + 68821.8i) q^{82} +984986. i q^{83} -522434. q^{85} +(272646. + 472237. i) q^{86} +(91779.9 - 158967. i) q^{88} +(227430. - 131307. i) q^{89} +(-232786. + 53692.3i) q^{91} +804193. q^{92} +(-157038. - 90666.0i) q^{94} +(111616. - 193325. i) q^{95} +575147. i q^{97} +(351664. + 237411. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} - 173 q^{4} + 42 q^{5} + 748 q^{7} + 454 q^{8}+O(q^{10}) $ 8 * q + 5 * q^2 - 173 * q^4 + 42 * q^5 + 748 * q^7 + 454 * q^8	$ 8 q + 5 q^{2} - 173 q^{4} + 42 q^{5} + 748 q^{7} + 454 q^{8} + 261 q^{10} + 1070 q^{11} - 6070 q^{14} + 3911 q^{16} - 7212 q^{17} - 24606 q^{19} - 78 q^{22} + 15224 q^{23} + 22274 q^{25} + 19044 q^{26} - 3415 q^{28} - 32524 q^{29} + 40200 q^{31} - 70203 q^{32} + 242436 q^{35} - 45670 q^{37} - 503310 q^{38} - 94941 q^{40} - 445660 q^{43} + 188829 q^{44} + 525804 q^{46} - 82884 q^{47} + 24116 q^{49} + 1218884 q^{50} + 722856 q^{52} + 13034 q^{53} - 127061 q^{56} - 159501 q^{58} - 1810362 q^{59} - 392856 q^{61} - 1410446 q^{64} + 389004 q^{65} + 384094 q^{67} + 1616346 q^{68} + 406005 q^{70} - 225688 q^{71} + 903078 q^{73} - 1185530 q^{74} + 327674 q^{77} - 559592 q^{79} - 847713 q^{80} + 347634 q^{82} + 1953576 q^{85} + 2302402 q^{86} + 304887 q^{88} + 1770036 q^{89} - 2960718 q^{91} + 113064 q^{92} - 1837620 q^{94} - 1160112 q^{95} - 5732467 q^{98}+O(q^{100}) $ 8 * q + 5 * q^2 - 173 * q^4 + 42 * q^5 + 748 * q^7 + 454 * q^8 + 261 * q^10 + 1070 * q^11 - 6070 * q^14 + 3911 * q^16 - 7212 * q^17 - 24606 * q^19 - 78 * q^22 + 15224 * q^23 + 22274 * q^25 + 19044 * q^26 - 3415 * q^28 - 32524 * q^29 + 40200 * q^31 - 70203 * q^32 + 242436 * q^35 - 45670 * q^37 - 503310 * q^38 - 94941 * q^40 - 445660 * q^43 + 188829 * q^44 + 525804 * q^46 - 82884 * q^47 + 24116 * q^49 + 1218884 * q^50 + 722856 * q^52 + 13034 * q^53 - 127061 * q^56 - 159501 * q^58 - 1810362 * q^59 - 392856 * q^61 - 1410446 * q^64 + 389004 * q^65 + 384094 * q^67 + 1616346 * q^68 + 406005 * q^70 - 225688 * q^71 + 903078 * q^73 - 1185530 * q^74 + 327674 * q^77 - 559592 * q^79 - 847713 * q^80 + 347634 * q^82 + 1953576 * q^85 + 2302402 * q^86 + 304887 * q^88 + 1770036 * q^89 - 2960718 * q^91 + 113064 * q^92 - 1837620 * q^94 - 1160112 * q^95 - 5732467 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.80325	−	3.12332i	−0.225406	−	0.390415i	0.731035	−	0.682340i	$-0.239038\pi$
$2$	−1.80325	−	3.12332i	−0.225406	−	0.390415i	−0.956441	+	0.291925i	$0.905704\pi$
$3$		0			0
$3$		0			0
$4$	25.4966	−	44.1614i	0.398384	−	0.690021i
$5$	−71.9311	+	41.5295i	−0.575449	+	0.332236i	−0.759323	−	0.650714i	$-0.774470\pi$
$5$	−71.9311	+	41.5295i	−0.575449	+	0.332236i	0.183874	+	0.982950i	$0.441136\pi$
$6$		0			0
$7$	77.0894	+	334.225i	0.224750	+	0.974416i
$7$	77.0894	+	334.225i	0.224750	+	0.974416i
$8$	−414.723			−0.810006
$9$		0			0
$10$	259.420	+	149.776i	0.259420	+	0.149776i
$11$	−221.304	+	383.310i	−0.166269	+	0.287986i	−0.937105	−	0.349047i	$-0.886505\pi$
$11$	−221.304	+	383.310i	−0.166269	+	0.287986i	0.770836	+	0.637033i	$0.219839\pi$
$12$		0			0
$13$			696.494i			0.317020i	0.987357	+	0.158510i	$0.0506691\pi$
$13$			696.494i			0.317020i	−0.987357	+	0.158510i	$0.949331\pi$
$14$	904.880	−	843.466i	0.329767	−	0.307386i
$15$		0			0
$16$	−883.932	−	1531.01i	−0.215804	−	0.373783i
$17$	5447.24	+	3144.96i	1.10874	+	0.640131i	0.938503	−	0.345272i	$-0.112213\pi$
$17$	5447.24	+	3144.96i	1.10874	+	0.640131i	0.170237	+	0.985403i	$0.445547\pi$
$18$		0			0
$19$	−2327.56	+	1343.82i	−0.339344	+	0.195920i	−0.659982	−	0.751281i	$-0.729436\pi$
$19$	−2327.56	+	1343.82i	−0.339344	+	0.195920i	0.320638	+	0.947202i	$0.396103\pi$
$20$			4235.44i			0.529430i
$21$		0			0
$22$	1596.27			0.149912
$23$	7885.31	+	13657.8i	0.648090	+	1.12252i	0.983579	+	0.180480i	$0.0577652\pi$
$23$	7885.31	+	13657.8i	0.648090	+	1.12252i	−0.335489	+	0.942044i	$0.608902\pi$
$24$		0			0
$25$	−4363.11	+	7557.12i	−0.279239	+	0.483656i
$26$	2175.37	−	1255.95i	0.123770	−	0.0714584i
$27$		0			0
$28$	16725.3	+	5117.22i	0.761905	+	0.233109i
$29$	23274.5			0.954304			0.477152	−	0.878821i	$-0.341669\pi$
$29$	23274.5			0.954304			0.477152	+	0.878821i	$0.341669\pi$
$30$		0			0
$31$	41177.0	+	23773.6i	1.38220	+	0.798012i	0.992419	−	0.122897i	$-0.0392185\pi$
$31$	41177.0	+	23773.6i	1.38220	+	0.798012i	0.389778	+	0.920909i	$0.372552\pi$
$32$	−16459.0	+	28507.9i	−0.502290	+	0.869991i
$33$		0			0
$34$		−	22684.6i		−	0.577158i
$35$	−19425.3	−	20839.7i	−0.453068	−	0.486057i
$36$		0			0
$37$	5079.89	+	8798.64i	0.100288	+	0.173704i	0.911803	−	0.410627i	$-0.134690\pi$
$37$	5079.89	+	8798.64i	0.100288	+	0.173704i	−0.811515	+	0.584331i	$0.801357\pi$
$38$	8394.35	+	4846.48i	0.152981	+	0.0883234i
$39$		0			0
$40$	29831.5	−	17223.2i	0.466117	−	0.269113i
$41$		−	38165.4i		−	0.553756i	−0.960905	−	0.276878i	$-0.910700\pi$
$41$		−	38165.4i		−	0.553756i	0.960905	−	0.276878i	$-0.0892998\pi$
$42$		0			0
$43$	−151197.			−1.90168			−0.950841	−	0.309679i	$-0.899779\pi$
$43$	−151197.			−1.90168			−0.950841	+	0.309679i	$0.899779\pi$
$44$	11285.0	+	19546.2i	0.132478	+	0.229458i
$45$		0			0
$46$	28438.4	−	49256.7i	0.292167	−	0.506048i
$47$	43543.1	−	25139.6i	0.419397	−	0.242139i	−0.275422	−	0.961323i	$-0.588818\pi$
$47$	43543.1	−	25139.6i	0.419397	−	0.242139i	0.694819	+	0.719184i	$0.255484\pi$
$48$		0			0
$49$	−105763.	+	51530.4i	−0.898975	+	0.438001i
$50$	31471.1			0.251769
$51$		0			0
$52$	30758.1	+	17758.2i	0.218751	+	0.126296i
$53$	−99778.2	+	172821.i	−0.670206	+	1.16083i	0.307640	+	0.951503i	$0.400461\pi$
$53$	−99778.2	+	172821.i	−0.670206	+	1.16083i	−0.977846	+	0.209328i	$0.932873\pi$
$54$		0			0
$55$		−	36762.6i		−	0.220962i
$56$	−31970.7	−	138611.i	−0.182049	−	0.789283i
$57$		0			0
$58$	−41969.8	−	72693.8i	−0.215106	−	0.372575i
$59$	−335347.	−	193612.i	−1.63282	−	0.942708i	−0.983219	−	0.182431i	$-0.941603\pi$
$59$	−335347.	−	193612.i	−1.63282	−	0.942708i	−0.649600	−	0.760277i	$-0.725063\pi$
$60$		0			0
$61$	−10203.5	+	5890.98i	−0.0449530	+	0.0259536i	−0.522308	−	0.852757i	$-0.674929\pi$
$61$	−10203.5	+	5890.98i	−0.0449530	+	0.0259536i	0.477355	+	0.878711i	$0.341596\pi$
$62$		−	171479.i		−	0.719508i
$63$		0			0
$64$	5575.73			0.0212697
$65$	−28925.0	−	50099.6i	−0.105325	−	0.182429i
$66$		0			0
$67$	192138.	−	332792.i	0.638834	−	1.10649i	−0.346854	−	0.937919i	$-0.612750\pi$
$67$	192138.	−	332792.i	0.638834	−	1.10649i	0.985689	−	0.168575i	$-0.0539165\pi$
$68$	277772.	−	160372.i	0.883408	−	0.510036i
$69$		0			0
$70$	−30060.4	+	98250.6i	−0.0876395	+	0.286445i
$71$	−156126.			−0.436213			−0.218107	−	0.975925i	$-0.569988\pi$
$71$	−156126.			−0.436213			−0.218107	+	0.975925i	$0.569988\pi$
$72$		0			0
$73$	325227.	+	187770.i	0.836022	+	0.482677i	0.855910	−	0.517125i	$-0.172998\pi$
$73$	325227.	+	187770.i	0.836022	+	0.482677i	−0.0198883	+	0.999802i	$0.506331\pi$
$74$	18320.6	−	31732.3i	0.0452111	−	0.0783080i
$75$		0			0
$76$			137051.i			0.312206i
$77$	−145172.	−	44416.2i	−0.317988	−	0.0972902i
$78$		0			0
$79$	−16591.8	−	28737.9i	−0.0336521	−	0.0582872i	0.848709	−	0.528860i	$-0.177380\pi$
$79$	−16591.8	−	28737.9i	−0.0336521	−	0.0582872i	−0.882361	+	0.470573i	$0.844047\pi$
$80$	127164.	+	73418.4i	0.248368	+	0.143395i
$81$		0			0
$82$	−119203.	+	68821.8i	−0.216195	+	0.124820i
$83$			984986.i			1.72264i	0.508059	+	0.861322i	$0.330363\pi$
$83$			984986.i			1.72264i	−0.508059	+	0.861322i	$0.669637\pi$
$84$		0			0
$85$	−522434.			−0.850697
$86$	272646.	+	472237.i	0.428651	+	0.742446i
$87$		0			0
$88$	91779.9	−	158967.i	0.134679	−	0.233271i
$89$	227430.	−	131307.i	0.322609	−	0.186259i	−0.329946	−	0.944000i	$-0.607030\pi$
$89$	227430.	−	131307.i	0.322609	−	0.186259i	0.652555	+	0.757741i	$0.273697\pi$
$90$		0			0
$91$	−232786.	+	53692.3i	−0.308910	+	0.0712505i
$92$	804193.			1.03275
$93$		0			0
$94$	−157038.	−	90666.0i	−0.189070	−	0.109159i
$95$	111616.	−	193325.i	0.130184	−	0.225484i
$96$		0			0
$97$			575147.i			0.630179i	0.949062	+	0.315089i	$0.102034\pi$
$97$			575147.i			0.630179i	−0.949062	+	0.315089i	$0.897966\pi$
$98$	351664.	+	237411.i	0.373637	+	0.252245i
$99$		0			0
$100$	222489.	+	385362.i	0.222489	+	0.385362i
$101$	−634688.	−	366437.i	−0.616022	−	0.355661i	0.159297	−	0.987231i	$-0.449077\pi$
$101$	−634688.	−	366437.i	−0.616022	−	0.355661i	−0.775319	+	0.631570i	$0.782411\pi$
$102$		0			0
$103$	908207.	−	524353.i	0.831138	−	0.479858i	−0.0231042	−	0.999733i	$-0.507355\pi$
$103$	908207.	−	524353.i	0.831138	−	0.479858i	0.854242	+	0.519875i	$0.174022\pi$
$104$		−	288852.i		−	0.256788i
$105$		0			0
$106$	719700.			0.604274
$107$	587412.	+	1.01743e6i	0.479503	+	0.830524i	0.999724	−	0.0235083i	$-0.00748363\pi$
$107$	587412.	+	1.01743e6i	0.479503	+	0.830524i	−0.520221	+	0.854032i	$0.674150\pi$
$108$		0			0
$109$	−367045.	+	635741.i	−0.283426	+	0.490908i	−0.972226	−	0.234043i	$-0.924804\pi$
$109$	−367045.	+	635741.i	−0.283426	+	0.490908i	0.688800	+	0.724951i	$0.258138\pi$
$110$	−114821.	+	66292.1i	−0.0862669	+	0.0498062i
$111$		0			0
$112$	443561.	−	413457.i	0.315718	−	0.294291i
$113$	−2.04925e6			−1.42023			−0.710116	−	0.704085i	$-0.751357\pi$
$113$	−2.04925e6			−1.42023			−0.710116	+	0.704085i	$0.751357\pi$
$114$		0			0
$115$	−1.13440e6	−	654945.i	−0.745885	−	0.430637i
$116$	593421.	−	1.02783e6i	0.380180	−	0.658490i
$117$		0			0
$118$			1.39653e6i			0.849969i
$119$	−631201.	+	2.06304e6i	−0.374564	+	1.22424i
$120$		0			0
$121$	787829.	+	1.36456e6i	0.444709	+	0.770259i
$122$	36798.9	+	21245.8i	0.0202654	+	0.0117002i
$123$		0			0
$124$	2.09975e6	−	1.21229e6i	1.10129	−	0.635830i
$125$		−	2.02259e6i		−	1.03556i
$126$		0			0
$127$	−1.64688e6			−0.803991			−0.401995	−	0.915642i	$-0.631683\pi$
$127$	−1.64688e6			−0.803991			−0.401995	+	0.915642i	$0.631683\pi$
$128$	1.04332e6	+	1.80709e6i	0.497495	+	0.861687i
$129$		0			0
$130$	−104318.	+	180684.i	−0.0474821	+	0.0822413i
$131$	1.78472e6	−	1.03041e6i	0.793882	−	0.458348i	−0.0474457	−	0.998874i	$-0.515108\pi$
$131$	1.78472e6	−	1.03041e6i	0.793882	−	0.458348i	0.841327	+	0.540526i	$0.181775\pi$
$132$		0			0
$133$	−628568.	−	674335.i	−0.267176	−	0.286629i
$134$	−1.38589e6			−0.575989
$135$		0			0
$136$	−2.25909e6	−	1.30429e6i	−0.898085	−	0.518510i
$137$	1.61460e6	−	2.79657e6i	0.627919	−	1.08759i	−0.360050	−	0.932933i	$-0.617240\pi$
$137$	1.61460e6	−	2.79657e6i	0.627919	−	1.08759i	0.987969	−	0.154654i	$-0.0494264\pi$
$138$		0			0
$139$		−	4.06719e6i		−	1.51443i	−0.653163	−	0.757217i	$-0.726558\pi$
$139$		−	4.06719e6i		−	1.51443i	0.653163	−	0.757217i	$-0.273442\pi$
$140$	−1.41559e6	+	326507.i	−0.515885	+	0.118990i
$141$		0			0
$142$	281533.	+	487630.i	0.0983252	+	0.170304i
$143$	−266973.	−	154137.i	−0.0912976	−	0.0527107i
$144$		0			0
$145$	−1.67416e6	+	966578.i	−0.549153	+	0.317054i
$146$		−	1.35438e6i		−	0.435194i
$147$		0			0
$148$	518080.			0.159813
$149$	−1.39737e6	−	2.42031e6i	−0.422427	−	0.731666i	0.573749	−	0.819031i	$-0.305489\pi$
$149$	−1.39737e6	−	2.42031e6i	−0.422427	−	0.731666i	−0.996176	+	0.0873655i	$0.972155\pi$
$150$		0			0
$151$	−301549.	+	522299.i	−0.0875846	+	0.151701i	−0.906490	−	0.422228i	$-0.861248\pi$
$151$	−301549.	+	522299.i	−0.0875846	+	0.151701i	0.818905	+	0.573929i	$0.194581\pi$
$152$	965293.	−	557312.i	0.274871	−	0.158697i
$153$		0			0
$154$	123055.	+	533512.i	0.0336929	+	0.146077i
$155$	−3.94921e6			−1.06051
$156$		0			0
$157$	−1.23763e6	−	714546.i	−0.319810	−	0.184642i	0.331498	−	0.943456i	$-0.392446\pi$
$157$	−1.23763e6	−	714546.i	−0.319810	−	0.184642i	−0.651308	+	0.758814i	$0.725779\pi$
$158$	−59838.4	+	103643.i	−0.0151708	+	0.0262766i
$159$		0			0
$160$		−	2.73414e6i		−	0.667514i
$161$	−3.95689e6	+	3.68833e6i	−0.948148	+	0.883797i
$162$		0			0
$163$	2.78644e6	+	4.82625e6i	0.643408	+	1.11442i	0.984667	+	0.174446i	$0.0558135\pi$
$163$	2.78644e6	+	4.82625e6i	0.643408	+	1.11442i	−0.341259	+	0.939969i	$0.610853\pi$
$164$	−1.68544e6	−	973087.i	−0.382103	−	0.220607i
$165$		0			0
$166$	3.07643e6	−	1.77618e6i	0.672546	−	0.388295i
$167$		−	2.24388e6i		−	0.481781i	−0.970552	−	0.240890i	$-0.922561\pi$
$167$		−	2.24388e6i		−	0.481781i	0.970552	−	0.240890i	$-0.0774394\pi$
$168$		0			0
$169$	4.34171e6			0.899498
$170$	942080.	+	1.63173e6i	0.191752	+	0.332125i
$171$		0			0
$172$	−3.85501e6	+	6.67707e6i	−0.757600	+	1.31220i
$173$	5.95864e6	−	3.44022e6i	1.15082	−	0.664428i	0.201736	−	0.979440i	$-0.435342\pi$
$173$	5.95864e6	−	3.44022e6i	1.15082	−	0.664428i	0.949088	+	0.315012i	$0.102008\pi$
$174$		0			0
$175$	−2.86213e6	−	875685.i	−0.534041	−	0.163393i
$176$	782471.			0.143526
$177$		0			0
$178$	−820225.	−	473557.i	−0.145436	−	0.0839677i
$179$	−3.94643e6	+	6.83543e6i	−0.688091	+	1.19181i	0.284364	+	0.958716i	$0.408218\pi$
$179$	−3.94643e6	+	6.83543e6i	−0.688091	+	1.19181i	−0.972455	+	0.233092i	$0.925116\pi$
$180$		0			0
$181$			2.63639e6i			0.444604i	0.974978	+	0.222302i	$0.0713571\pi$
$181$			2.63639e6i			0.444604i	−0.974978	+	0.222302i	$0.928643\pi$
$182$	587469.	+	630243.i	0.0974475	+	0.104543i
$183$		0			0
$184$	−3.27022e6	−	5.66418e6i	−0.524956	−	0.909251i
$185$	−730805.	−	421931.i	−0.115421	−	0.0666386i
$186$		0			0
$187$	−2.41099e6	+	1.39199e6i	−0.368698	+	0.212868i
$188$		−	2.56390e6i		−	0.385858i
$189$		0			0
$190$	−805087.			−0.117377
$191$	6.17120e6	+	1.06888e7i	0.885665	+	1.53402i	0.844949	+	0.534846i	$0.179630\pi$
$191$	6.17120e6	+	1.06888e7i	0.885665	+	1.53402i	0.0407156	+	0.999171i	$0.487036\pi$
$192$		0			0
$193$	6.69614e6	−	1.15981e7i	0.931435	−	1.61329i	0.150564	−	0.988600i	$-0.451891\pi$
$193$	6.69614e6	−	1.15981e7i	0.931435	−	1.61329i	0.780871	−	0.624692i	$-0.214776\pi$
$194$	1.79637e6	−	1.03713e6i	0.246031	−	0.142046i
$195$		0			0
$196$	−420954.	+	5.98451e6i	−0.0559071	+	0.794804i
$197$	9.42468e6			1.23273			0.616365	−	0.787460i	$-0.288604\pi$
$197$	9.42468e6			1.23273			0.616365	+	0.787460i	$0.288604\pi$
$198$		0			0
$199$	4.91639e6	+	2.83848e6i	0.623860	+	0.360186i	0.778370	−	0.627805i	$-0.216047\pi$
$199$	4.91639e6	+	2.83848e6i	0.623860	+	0.360186i	−0.154510	+	0.987991i	$0.549380\pi$
$200$	1.80948e6	−	3.13411e6i	0.226185	−	0.391764i
$201$		0			0
$202$			2.64311e6i			0.320672i
$203$	1.79422e6	+	7.77892e6i	0.214480	+	0.929890i
$204$		0			0
$205$	1.58499e6	+	2.74528e6i	0.183977	+	0.318658i
$206$	−3.27545e6	−	1.89108e6i	−0.374687	−	0.216326i
$207$		0			0
$208$	1.06634e6	−	615653.i	0.118497	−	0.0684142i
$209$		−	1.18957e6i		−	0.130302i
$210$		0			0
$211$	1.05196e6			0.111983			0.0559914	−	0.998431i	$-0.482168\pi$
$211$	1.05196e6			0.111983			0.0559914	+	0.998431i	$0.482168\pi$
$212$	5.08801e6	+	8.81269e6i	0.533999	+	0.924913i
$213$		0			0
$214$	2.11850e6	−	3.66935e6i	0.216166	−	0.374410i
$215$	1.08758e7	−	6.27913e6i	1.09432	−	0.631807i
$216$		0			0
$217$	−4.77141e6	+	1.55951e7i	−0.466946	+	1.52619i
$218$	2.64750e6			0.255544
$219$		0			0
$220$	−1.62348e6	−	937319.i	−0.152469	−	0.0880277i
$221$	−2.19045e6	+	3.79397e6i	−0.202935	+	0.351493i
$222$		0			0
$223$		−	9.96615e6i		−	0.898696i	−0.893357	−	0.449348i	$-0.851656\pi$
$223$		−	9.96615e6i		−	0.898696i	0.893357	−	0.449348i	$-0.148344\pi$
$224$	−1.07969e7	−	3.30336e6i	−0.960624	−	0.293908i
$225$		0			0
$226$	3.69531e6	+	6.40046e6i	0.320129	+	0.554480i
$227$	−1.59963e7	−	9.23545e6i	−1.36754	−	0.789552i	−0.376930	−	0.926242i	$-0.623020\pi$
$227$	−1.59963e7	−	9.23545e6i	−1.36754	−	0.789552i	−0.990614	+	0.136690i	$0.956354\pi$
$228$		0			0
$229$	1.17915e7	−	6.80784e6i	0.981892	−	0.566896i	0.0790512	−	0.996871i	$-0.474811\pi$
$229$	1.17915e7	−	6.80784e6i	0.981892	−	0.566896i	0.902841	+	0.429975i	$0.141478\pi$
$230$			4.72412e6i			0.388273i
$231$		0			0
$232$	−9.65248e6			−0.772992
$233$	5103.02	+	8838.68i	0.000403422	+	0.000698747i	0.866227	−	0.499651i	$-0.166538\pi$
$233$	5103.02	+	8838.68i	0.000403422	+	0.000698747i	−0.865824	+	0.500349i	$0.833205\pi$
$234$		0			0
$235$	−2.08807e6	+	3.61664e6i	−0.160895	+	0.278678i
$236$	−1.71004e7	+	9.87291e6i	−1.30098	+	0.751120i
$237$		0			0
$238$	7.58176e6	−	1.74874e6i	0.562392	−	0.129717i
$239$	−2.49567e6			−0.182807			−0.0914037	−	0.995814i	$-0.529135\pi$
$239$	−2.49567e6			−0.182807			−0.0914037	+	0.995814i	$0.529135\pi$
$240$		0			0
$241$	−4.73752e6	−	2.73521e6i	−0.338454	−	0.195407i	0.321134	−	0.947034i	$-0.395936\pi$
$241$	−4.73752e6	−	2.73521e6i	−0.338454	−	0.195407i	−0.659588	+	0.751627i	$0.729269\pi$
$242$	2.84131e6	−	4.92129e6i	0.200480	−	0.347242i
$243$		0			0
$244$			600800.i			0.0413581i
$245$	5.46766e6	−	8.09894e6i	0.371795	−	0.550719i
$246$		0			0
$247$	−935961.	−	1.62113e6i	−0.0621108	−	0.107579i
$248$	−1.70771e7	−	9.85944e6i	−1.11959	−	0.646394i
$249$		0			0
$250$	−6.31718e6	+	3.64723e6i	−0.404300	+	0.233423i
$251$		−	2.18424e6i		−	0.138127i	−0.997612	−	0.0690637i	$-0.977999\pi$
$251$		−	2.18424e6i		−	0.138127i	0.997612	−	0.0690637i	$-0.0220012\pi$
$252$		0			0
$253$	−6.98020e6			−0.431029
$254$	2.96974e6	+	5.14374e6i	0.181225	+	0.313890i
$255$		0			0
$256$	3.94117e6	−	6.82631e6i	0.234912	−	0.406880i
$257$	2.72638e7	−	1.57408e7i	1.60615	−	0.927313i	0.615933	−	0.787799i	$-0.288779\pi$
$257$	2.72638e7	−	1.57408e7i	1.60615	−	0.927313i	0.990220	−	0.139514i	$-0.0445540\pi$
$258$		0			0
$259$	−2.54912e6	+	2.37611e6i	−0.146720	+	0.136762i
$260$	−2.94996e6			−0.167840
$261$		0			0
$262$	−6.43659e6	−	3.71616e6i	−0.357892	−	0.206629i
$263$	3.28881e6	−	5.69639e6i	0.180789	−	0.313136i	−0.761360	−	0.648329i	$-0.775468\pi$
$263$	3.28881e6	−	5.69639e6i	0.180789	−	0.313136i	0.942149	+	0.335193i	$0.108802\pi$
$264$		0			0
$265$		−	1.65749e7i		−	0.890665i
$266$	−972699.	+	3.17921e6i	−0.0516813	+	0.168918i
$267$		0			0
$268$	−9.79771e6	−	1.69701e7i	−0.509003	−	0.881619i
$269$	−190420.	−	109939.i	−0.00978263	−	0.00564801i	0.495101	−	0.868836i	$-0.335131\pi$
$269$	−190420.	−	109939.i	−0.00978263	−	0.00564801i	−0.504883	+	0.863188i	$0.668464\pi$
$270$		0			0
$271$	−2.41082e7	+	1.39189e7i	−1.21132	+	0.699354i	−0.963046	−	0.269337i	$-0.913196\pi$
$271$	−2.41082e7	+	1.39189e7i	−1.21132	+	0.699354i	−0.248270	+	0.968691i	$0.579862\pi$
$272$		−	1.11197e7i		−	0.552570i
$273$		0			0
$274$	−1.16461e7			−0.566147
$275$	−1.93115e6	−	3.34485e6i	−0.0928576	−	0.160834i
$276$		0			0
$277$	2.87725e6	−	4.98354e6i	0.135375	−	0.234476i	−0.790366	−	0.612635i	$-0.790109\pi$
$277$	2.87725e6	−	4.98354e6i	0.135375	−	0.234476i	0.925741	+	0.378159i	$0.123443\pi$
$278$	−1.27032e7	+	7.33417e6i	−0.591258	+	0.341363i
$279$		0			0
$280$	8.05612e6	+	8.64270e6i	0.366988	+	0.393709i
$281$	−1.75833e7			−0.792467			−0.396233	−	0.918150i	$-0.629683\pi$
$281$	−1.75833e7			−0.792467			−0.396233	+	0.918150i	$0.629683\pi$
$282$		0			0
$283$	1.27466e7	+	7.35922e6i	0.562385	+	0.324693i	0.754102	−	0.656757i	$-0.228072\pi$
$283$	1.27466e7	+	7.35922e6i	0.562385	+	0.324693i	−0.191717	+	0.981450i	$0.561406\pi$
$284$	−3.98067e6	+	6.89472e6i	−0.173780	+	0.300997i
$285$		0			0
$286$			1.11179e6i			0.0475253i
$287$	1.27558e7	−	2.94215e6i	0.539589	−	0.124457i
$288$		0			0
$289$	7.71280e6	+	1.33590e7i	0.319535	+	0.553451i
$290$	6.03787e6	+	3.48597e6i	0.247565	+	0.142932i
$291$		0			0
$292$	1.65843e7	−	9.57497e6i	0.666115	−	0.384582i
$293$			3.49743e6i			0.139042i	0.997580	+	0.0695210i	$0.0221471\pi$
$293$			3.49743e6i			0.139042i	−0.997580	+	0.0695210i	$0.977853\pi$
$294$		0			0
$295$	3.21625e7			1.25280
$296$	−2.10675e6	−	3.64900e6i	−0.0812339	−	0.140701i
$297$		0			0
$298$	−5.03961e6	+	8.72886e6i	−0.190436	+	0.329844i
$299$	−9.51254e6	+	5.49207e6i	−0.355863	+	0.205458i
$300$		0			0
$301$	−1.16557e7	−	5.05338e7i	−0.427404	−	1.85303i
$302$	2.17508e6			0.0789685
$303$		0			0
$304$	4.11481e6	+	2.37569e6i	0.146463	+	0.0845607i
$305$	489299.	−	847490.i	0.0172455	−	0.0298700i
$306$		0			0
$307$			3.99694e7i			1.38138i	0.723152	+	0.690689i	$0.242692\pi$
$307$			3.99694e7i			1.38138i	−0.723152	+	0.690689i	$0.757308\pi$
$308$	−5.66287e6	+	5.27853e6i	−0.193814	+	0.180659i
$309$		0			0
$310$	7.12142e6	+	1.23347e7i	0.239046	+	0.414040i
$311$	2.88815e7	+	1.66747e7i	0.960148	+	0.554342i	0.896219	−	0.443613i	$-0.146303\pi$
$311$	2.88815e7	+	1.66747e7i	0.960148	+	0.554342i	0.0639296	+	0.997954i	$0.479637\pi$
$312$		0			0
$313$	1.62725e7	−	9.39495e6i	0.530667	−	0.306381i	−0.210621	−	0.977568i	$-0.567549\pi$
$313$	1.62725e7	−	9.39495e6i	0.530667	−	0.306381i	0.741288	+	0.671187i	$0.234215\pi$
$314$			5.15402e6i			0.166478i
$315$		0			0
$316$	−1.69214e6			−0.0536259
$317$	−1.01986e7	−	1.76645e7i	−0.320156	−	0.554527i	0.660364	−	0.750946i	$-0.270402\pi$
$317$	−1.01986e7	−	1.76645e7i	−0.320156	−	0.554527i	−0.980520	+	0.196419i	$0.937069\pi$
$318$		0			0
$319$	−5.15075e6	+	8.92136e6i	−0.158671	+	0.274827i
$320$	−401068.	+	231557.i	−0.0122396	+	0.00706656i
$321$		0			0
$322$	1.86551e7	+	5.70764e6i	0.558766	+	0.170958i
$323$	−1.69050e7			−0.501659
$324$		0			0
$325$	−5.26349e6	−	3.03888e6i	−0.153329	−	0.0885244i
$326$	1.00493e7	−	1.74059e7i	0.290056	−	0.502393i
$327$		0			0
$328$			1.58281e7i			0.448545i
$329$	1.17590e7	+	1.26152e7i	0.330204	+	0.354247i
$330$		0			0
$331$	1.06774e7	+	1.84939e7i	0.294431	+	0.509969i	0.974852	−	0.222852i	$-0.0715366\pi$
$331$	1.06774e7	+	1.84939e7i	0.294431	+	0.509969i	−0.680422	+	0.732821i	$0.738203\pi$
$332$	4.34983e7	+	2.51138e7i	1.18866	+	0.686274i
$333$		0			0
$334$	−7.00834e6	+	4.04627e6i	−0.188094	+	0.108596i
$335$			3.19175e7i			0.848974i
$336$		0			0
$337$	−1.98824e7			−0.519493			−0.259746	−	0.965677i	$-0.583639\pi$
$337$	−1.98824e7			−0.519493			−0.259746	+	0.965677i	$0.583639\pi$
$338$	−7.82918e6	−	1.35605e7i	−0.202753	−	0.351178i
$339$		0			0
$340$	−1.33203e7	+	2.30714e7i	−0.338904	+	0.586999i
$341$	−1.82253e7	+	1.05224e7i	−0.459633	+	0.265369i
$342$		0			0
$343$	−2.53760e7	−	3.13763e7i	−0.628840	−	0.777535i
$344$	6.27049e7			1.54037
$345$		0			0
$346$	−2.14898e7	−	1.24072e7i	−0.518806	−	0.299533i
$347$	−1.66198e7	+	2.87863e7i	−0.397774	+	0.688965i	−0.993451	−	0.114259i	$-0.963551\pi$
$347$	−1.66198e7	+	2.87863e7i	−0.397774	+	0.688965i	0.595677	+	0.803224i	$0.296884\pi$
$348$		0			0
$349$		−	2.57850e7i		−	0.606584i	−0.952898	−	0.303292i	$-0.901914\pi$
$349$		−	2.57850e7i		−	0.606584i	0.952898	−	0.303292i	$-0.0980858\pi$
$350$	2.42609e6	+	1.05184e7i	0.0565851	+	0.245328i
$351$		0			0
$352$	−7.28490e6	−	1.26178e7i	−0.167030	−	0.289305i
$353$	4.82036e7	+	2.78303e7i	1.09586	+	0.632695i	0.935130	−	0.354304i	$-0.115282\pi$
$353$	4.82036e7	+	2.78303e7i	1.09586	+	0.632695i	0.160729	+	0.986999i	$0.448615\pi$
$354$		0			0
$355$	1.12303e7	−	6.48381e6i	0.251019	−	0.144926i
$356$		−	1.33915e7i		−	0.296810i
$357$		0			0
$358$	2.84656e7			0.620400
$359$	−8.08714e6	−	1.40073e7i	−0.174788	−	0.302742i	0.765300	−	0.643674i	$-0.222591\pi$
$359$	−8.08714e6	−	1.40073e7i	−0.174788	−	0.302742i	−0.940088	+	0.340932i	$0.889257\pi$
$360$		0			0
$361$	−1.99112e7	+	3.44873e7i	−0.423230	+	0.733056i
$362$	8.23428e6	−	4.75406e6i	0.173580	−	0.100217i
$363$		0			0
$364$	−3.56411e6	+	1.16491e7i	−0.0739004	+	0.241539i
$365$	−3.11919e7			−0.641451
$366$		0			0
$367$	9.72318e6	+	5.61368e6i	0.196703	+	0.113566i	0.595117	−	0.803639i	$-0.297106\pi$
$367$	9.72318e6	+	5.61368e6i	0.196703	+	0.113566i	−0.398414	+	0.917206i	$0.630439\pi$
$368$	1.39401e7	−	2.41450e7i	0.279720	−	0.484490i
$369$		0			0
$370$			3.04339e6i			0.0600830i
$371$	−6.54529e7	−	2.00257e7i	−1.28176	−	0.392162i
$372$		0			0
$373$	−1.99988e7	−	3.46389e7i	−0.385369	−	0.667479i	0.606451	−	0.795121i	$-0.292593\pi$
$373$	−1.99988e7	−	3.46389e7i	−0.385369	−	0.667479i	−0.991820	+	0.127642i	$0.959259\pi$
$374$	8.69524e6	+	5.02020e6i	0.166214	+	0.0959635i
$375$		0			0
$376$	−1.80583e7	+	1.04260e7i	−0.339714	+	0.196134i
$377$			1.62106e7i			0.302534i
$378$		0			0
$379$	2.92098e7			0.536551			0.268276	−	0.963342i	$-0.413546\pi$
$379$	2.92098e7			0.536551			0.268276	+	0.963342i	$0.413546\pi$
$380$	−5.69166e6	−	9.85824e6i	−0.103726	−	0.179659i
$381$		0			0
$382$	2.22564e7	−	3.85493e7i	0.399269	−	0.691554i
$383$	−3.97181e7	+	2.29312e7i	−0.706955	+	0.408161i	−0.809933	−	0.586523i	$-0.800496\pi$
$383$	−3.97181e7	+	2.29312e7i	−0.706955	+	0.408161i	0.102978	+	0.994684i	$0.467163\pi$
$384$		0			0
$385$	1.22870e7	−	2.83400e6i	0.215309	−	0.0496613i
$386$	−4.82993e7			−0.839805
$387$		0			0
$388$	2.53993e7	+	1.46643e7i	0.434837	+	0.251053i
$389$	7.72431e6	−	1.33789e7i	0.131223	−	0.227285i	−0.792925	−	0.609319i	$-0.791443\pi$
$389$	7.72431e6	−	1.33789e7i	0.131223	−	0.227285i	0.924148	+	0.382034i	$0.124776\pi$
$390$		0			0
$391$			9.91960e7i			1.65945i
$392$	4.38625e7	−	2.13708e7i	0.728174	−	0.354783i
$393$		0			0
$394$	−1.69951e7	−	2.94363e7i	−0.277865	−	0.481277i
$395$	2.38693e6	+	1.37810e6i	0.0387302	+	0.0223609i
$396$		0			0
$397$	2.54737e7	−	1.47073e7i	0.407118	−	0.235050i	−0.282433	−	0.959287i	$-0.591141\pi$
$397$	2.54737e7	−	1.47073e7i	0.407118	−	0.235050i	0.689551	+	0.724237i	$0.257808\pi$
$398$		−	2.04740e7i		−	0.324753i
$399$		0			0
$400$	1.54268e7			0.241043
$401$	−5.70055e7	−	9.87364e7i	−0.884064	−	1.53124i	−0.846783	−	0.531939i	$-0.821464\pi$
$401$	−5.70055e7	−	9.87364e7i	−0.884064	−	1.53124i	−0.0372810	−	0.999305i	$-0.511870\pi$
$402$		0			0
$403$	−1.65581e7	+	2.86796e7i	−0.252986	+	0.438185i
$404$	−3.23648e7	+	1.86858e7i	−0.490827	+	0.283379i
$405$		0			0
$406$	2.10607e7	−	1.96313e7i	0.314698	−	0.293339i
$407$	−4.49681e6			−0.0666992
$408$		0			0
$409$	2.99288e7	+	1.72794e7i	0.437442	+	0.252557i	0.702512	−	0.711672i	$-0.252062\pi$
$409$	2.99288e7	+	1.72794e7i	0.437442	+	0.252557i	−0.265070	+	0.964229i	$0.585395\pi$
$410$	5.71626e6	−	9.90086e6i	0.0829393	−	0.143655i
$411$		0			0
$412$		−	5.34769e7i		−	0.764671i
$413$	3.88584e7	−	1.27007e8i	0.551614	−	1.80292i
$414$		0			0
$415$	−4.09059e7	−	7.08511e7i	−0.572324	−	0.991294i
$416$	−1.98556e7	−	1.14636e7i	−0.275805	−	0.159236i
$417$		0			0
$418$	−3.71541e6	+	2.14509e6i	−0.0508719	+	0.0293709i
$419$			3.73902e7i			0.508294i	0.967166	+	0.254147i	$0.0817948\pi$
$419$			3.73902e7i			0.508294i	−0.967166	+	0.254147i	$0.918205\pi$
$420$		0			0
$421$	−5.93910e7			−0.795929			−0.397965	−	0.917401i	$-0.630283\pi$
$421$	−5.93910e7			−0.795929			−0.397965	+	0.917401i	$0.630283\pi$
$422$	−1.89694e6	−	3.28560e6i	−0.0252416	−	0.0437198i
$423$		0			0
$424$	4.13803e7	−	7.16728e7i	0.542870	−	0.940279i
$425$	−4.75338e7	+	2.74436e7i	−0.619206	+	0.357499i
$426$		0			0
$427$	−2.75549e6	−	2.95612e6i	−0.0353929	−	0.0379699i
$428$	5.99080e7			0.764105
$429$		0			0
$430$	−3.92235e7	−	2.26457e7i	−0.493334	−	0.284826i
$431$	−2.97697e7	+	5.15627e7i	−0.371829	+	0.644026i	−0.989847	−	0.142137i	$-0.954603\pi$
$431$	−2.97697e7	+	5.15627e7i	−0.371829	+	0.644026i	0.618018	+	0.786164i	$0.287936\pi$
$432$		0			0
$433$		−	6.40730e7i		−	0.789244i	−0.918843	−	0.394622i	$-0.870876\pi$
$433$		−	6.40730e7i		−	0.789244i	0.918843	−	0.394622i	$-0.129124\pi$
$434$	5.73125e7	−	1.32192e7i	0.701100	−	0.161710i
$435$		0			0
$436$	1.87168e7	+	3.24184e7i	0.225825	+	0.391140i
$437$	−3.67071e7	−	2.11928e7i	−0.439851	−	0.253948i
$438$		0			0
$439$	−1.31778e8	+	7.60819e7i	−1.55757	+	0.899265i	−0.560084	+	0.828436i	$0.689231\pi$
$439$	−1.31778e8	+	7.60819e7i	−1.55757	+	0.899265i	−0.997488	+	0.0708286i	$0.977436\pi$
$440$			1.52463e7i			0.178980i
$441$		0			0
$442$	1.57997e7			0.182971
$443$	1.72920e7	+	2.99506e7i	0.198899	+	0.344504i	0.948172	−	0.317758i	$-0.102930\pi$
$443$	1.72920e7	+	2.99506e7i	0.198899	+	0.344504i	−0.749273	+	0.662262i	$0.769597\pi$
$444$		0			0
$445$	−1.09062e7	+	1.88901e7i	−0.123763	+	0.214365i
$446$	−3.11275e7	+	1.79715e7i	−0.350864	+	0.202572i
$447$		0			0
$448$	429829.	+	1.86355e6i	0.00478037	+	0.0207255i
$449$	1.33795e8			1.47809			0.739047	−	0.673654i	$-0.235276\pi$
$449$	1.33795e8			1.47809			0.739047	+	0.673654i	$0.235276\pi$
$450$		0			0
$451$	1.46292e7	+	8.44616e6i	0.159474	+	0.0920724i
$452$	−5.22488e7	+	9.04976e7i	−0.565798	+	0.979990i
$453$		0			0
$454$			6.66153e7i			0.711880i
$455$	1.45147e7	−	1.35296e7i	0.154090	−	0.143632i
$456$		0			0
$457$	−7.62638e6	−	1.32093e7i	−0.0799043	−	0.138398i	0.823304	−	0.567600i	$-0.192128\pi$
$457$	−7.62638e6	−	1.32093e7i	−0.0799043	−	0.138398i	−0.903208	+	0.429202i	$0.858795\pi$
$458$	−4.25262e7	−	2.45525e7i	−0.442649	−	0.255564i
$459$		0			0
$460$	−5.78465e7	+	3.33977e7i	−0.594298	+	0.343118i
$461$			3.05013e7i			0.311326i	0.987810	+	0.155663i	$0.0497514\pi$
$461$			3.05013e7i			0.311326i	−0.987810	+	0.155663i	$0.950249\pi$
$462$		0			0
$463$	−1.61661e8			−1.62878			−0.814388	−	0.580320i	$-0.802927\pi$
$463$	−1.61661e8			−1.62878			−0.814388	+	0.580320i	$0.802927\pi$
$464$	−2.05731e7	−	3.56336e7i	−0.205942	−	0.356703i
$465$		0			0
$466$	18404.0	−	31876.7i	0.000181868	−	0.000315004i
$467$	−5.70833e7	+	3.29570e7i	−0.560478	+	0.323592i	−0.753337	−	0.657635i	$-0.771557\pi$
$467$	−5.70833e7	+	3.29570e7i	−0.560478	+	0.323592i	0.192860	+	0.981226i	$0.438224\pi$
$468$		0			0
$469$	1.26039e8	+	3.85624e7i	1.22176	+	0.373806i
$470$	1.50612e7			0.145067
$471$		0			0
$472$	1.39076e8	+	8.02955e7i	1.32259	+	0.763599i
$473$	3.34605e7	−	5.79553e7i	0.316191	−	0.547659i
$474$		0			0
$475$		−	2.34529e7i		−	0.218834i
$476$	7.50134e7	+	8.04753e7i	0.695534	+	0.746176i
$477$		0			0
$478$	4.50032e6	+	7.79479e6i	0.0412060	+	0.0713708i
$479$	7.96535e7	+	4.59880e7i	0.724767	+	0.418444i	0.816505	−	0.577339i	$-0.195909\pi$
$479$	7.96535e7	+	4.59880e7i	0.724767	+	0.418444i	−0.0917379	+	0.995783i	$0.529242\pi$
$480$		0			0
$481$	−6.12820e6	+	3.53812e6i	−0.0550678	+	0.0317934i
$482$			1.97291e7i			0.176183i
$483$		0			0
$484$	8.03478e7			0.708660
$485$	−2.38855e7	−	4.13710e7i	−0.209368	−	0.362636i
$486$		0			0
$487$	9.53763e7	−	1.65197e8i	0.825759	−	1.43026i	−0.0755785	−	0.997140i	$-0.524080\pi$
$487$	9.53763e7	−	1.65197e8i	0.825759	−	1.43026i	0.901338	−	0.433117i	$-0.142586\pi$
$488$	4.23162e6	−	2.44313e6i	0.0364122	−	0.0210226i
$489$		0			0
$490$	−3.51551e7	−	2.47284e6i	−0.298814	−	0.0210188i
$491$	−8.85504e7			−0.748077			−0.374038	−	0.927413i	$-0.622027\pi$
$491$	−8.85504e7			−0.748077			−0.374038	+	0.927413i	$0.622027\pi$
$492$		0			0
$493$	1.26782e8	+	7.31975e7i	1.05807	+	0.610880i
$494$	−3.37554e6	+	5.84661e6i	−0.0280003	+	0.0484980i
$495$		0			0
$496$		−	8.40569e7i		−	0.688856i
$497$	−1.20356e7	−	5.21810e7i	−0.0980391	−	0.425053i
$498$		0			0
$499$	2.61754e7	+	4.53371e7i	0.210665	+	0.364882i	0.951923	−	0.306338i	$-0.0991038\pi$
$499$	2.61754e7	+	4.53371e7i	0.210665	+	0.364882i	−0.741258	+	0.671220i	$0.765770\pi$
$500$	−8.93202e7	−	5.15690e7i	−0.714561	−	0.412552i
$501$		0			0
$502$	−6.82210e6	+	3.93874e6i	−0.0539271	+	0.0311348i
$503$			1.34114e8i			1.05383i	0.849919	+	0.526914i	$0.176651\pi$
$503$			1.34114e8i			1.05383i	−0.849919	+	0.526914i	$0.823349\pi$
$504$		0			0
$505$	6.08718e7			0.472653
$506$	1.25871e7	+	2.18014e7i	0.0971566	+	0.168280i
$507$		0			0
$508$	−4.19898e7	+	7.27285e7i	−0.320297	+	0.554771i
$509$	1.62222e8	−	9.36588e7i	1.23014	−	0.710224i	0.263084	−	0.964773i	$-0.415260\pi$
$509$	1.62222e8	−	9.36588e7i	1.23014	−	0.710224i	0.967060	+	0.254549i	$0.0819269\pi$
$510$		0			0
$511$	−3.76858e7	+	1.23174e8i	−0.282432	+	0.923115i
$512$	1.05118e8			0.783188
$513$		0			0
$514$	−9.83269e7	−	5.67690e7i	−0.724074	−	0.418044i
$515$	−4.35522e7	+	7.54347e7i	−0.318852	+	0.552267i
$516$		0			0
$517$			2.22540e7i			0.161041i
$518$	1.20180e7	+	3.67699e6i	0.0864658	+	0.0264547i
$519$		0			0
$520$	1.19959e7	+	2.07774e7i	0.0853142	+	0.147769i
$521$	3.89027e7	+	2.24605e7i	0.275085	+	0.158820i	0.631196	−	0.775623i	$-0.282564\pi$
$521$	3.89027e7	+	2.24605e7i	0.275085	+	0.158820i	−0.356111	+	0.934444i	$0.615898\pi$
$522$		0			0
$523$	1.43752e8	−	8.29951e7i	1.00487	−	0.580160i	0.0951815	−	0.995460i	$-0.469657\pi$
$523$	1.43752e8	−	8.29951e7i	1.00487	−	0.580160i	0.909684	+	0.415300i	$0.136324\pi$
$524$		−	1.05087e8i		−	0.730394i
$525$		0			0
$526$	−2.37222e7			−0.163004
$527$	1.49534e8	+	2.59000e8i	1.02166	+	1.76957i
$528$		0			0
$529$	−5.03382e7	+	8.71883e7i	−0.340041	+	0.588967i
$530$	−5.17689e7	+	2.98888e7i	−0.347729	+	0.200761i
$531$		0			0
$532$	−4.58059e7	+	1.05652e7i	−0.304219	+	0.0701685i
$533$	2.65820e7			0.175552
$534$		0			0
$535$	−8.45064e7	−	4.87898e7i	−0.551859	−	0.318616i
$536$	−7.96839e7	+	1.38017e8i	−0.517459	+	0.896266i
$537$		0			0
$538$			792991.i			0.00509238i
$539$	3.65378e6	−	5.19441e7i	0.0233333	−	0.331718i
$540$		0			0
$541$	−6.31514e7	−	1.09381e8i	−0.398833	−	0.690799i	0.594749	−	0.803911i	$-0.297251\pi$
$541$	−6.31514e7	−	1.09381e8i	−0.398833	−	0.690799i	−0.993582	+	0.113112i	$0.963918\pi$
$542$	8.69464e7	+	5.01985e7i	0.546077	+	0.315278i
$543$		0			0
$544$	−1.79312e8	+	1.03526e8i	−1.11382	+	0.643062i
$545$		−	6.09727e7i		−	0.376657i
$546$		0			0
$547$	2.31931e8			1.41709			0.708545	−	0.705666i	$-0.249352\pi$
$547$	2.31931e8			1.41709			0.708545	+	0.705666i	$0.249352\pi$
$548$	−8.23336e7	−	1.42606e8i	−0.500306	−	0.866555i
$549$		0			0
$550$	−6.96468e6	+	1.20632e7i	−0.0418614	+	0.0725060i
$551$	−5.41729e7	+	3.12767e7i	−0.323838	+	0.186968i
$552$		0			0
$553$	8.32585e6	−	7.76078e6i	0.0492327	−	0.0458912i
$554$	−2.07536e7			−0.122057
$555$		0			0
$556$	−1.79613e8	−	1.03700e8i	−1.04499	−	0.603326i
$557$	1.20538e8	−	2.08779e8i	0.697525	−	1.20815i	−0.271797	−	0.962355i	$-0.587618\pi$
$557$	1.20538e8	−	2.08779e8i	0.697525	−	1.20815i	0.969322	−	0.245794i	$-0.0790488\pi$
$558$		0			0
$559$		−	1.05308e8i		−	0.602872i
$560$	−1.47352e7	+	4.81613e7i	−0.0839060	+	0.274242i
$561$		0			0
$562$	3.17071e7	+	5.49182e7i	0.178627	+	0.309391i
$563$	1.01477e8	+	5.85878e7i	0.568647	+	0.328308i	0.756609	−	0.653868i	$-0.226855\pi$
$563$	1.01477e8	+	5.85878e7i	0.568647	+	0.328308i	−0.187962	+	0.982176i	$0.560188\pi$
$564$		0			0
$565$	1.47405e8	−	8.51042e7i	0.817271	−	0.471852i
$566$		−	5.30821e7i		−	0.292751i
$567$		0			0
$568$	6.47488e7			0.353335
$569$	−6.04302e7	−	1.04668e8i	−0.328033	−	0.568170i	0.654088	−	0.756418i	$-0.273052\pi$
$569$	−6.04302e7	−	1.04668e8i	−0.328033	−	0.568170i	−0.982121	+	0.188248i	$0.939719\pi$
$570$		0			0
$571$	−5.39062e7	+	9.33683e7i	−0.289555	+	0.501523i	−0.973703	−	0.227819i	$-0.926841\pi$
$571$	−5.39062e7	+	9.33683e7i	−0.289555	+	0.501523i	0.684149	+	0.729342i	$0.260174\pi$
$572$	−1.36138e7	+	7.85993e6i	−0.0727430	+	0.0419982i
$573$		0			0
$574$	−3.21912e7	−	3.45351e7i	−0.170217	−	0.182610i
$575$	−1.37618e8			−0.723887
$576$		0			0
$577$	−6.79444e7	−	3.92277e7i	−0.353693	−	0.204205i	0.312618	−	0.949879i	$-0.398794\pi$
$577$	−6.79444e7	−	3.92277e7i	−0.353693	−	0.204205i	−0.666310	+	0.745674i	$0.732127\pi$
$578$	2.78162e7	−	4.81791e7i	0.144050	−	0.249503i
$579$		0			0
$580$			9.85778e7i			0.505237i
$581$	−3.29207e8	+	7.59319e7i	−1.67857	+	0.387165i
$582$		0			0
$583$	−4.41627e7	−	7.64920e7i	−0.222869	−	0.386020i
$584$	−1.34879e8	−	7.78724e7i	−0.677182	−	0.390971i
$585$		0			0
$586$	1.09236e7	−	6.30674e6i	0.0542841	−	0.0313410i
$587$		−	1.98030e8i		−	0.979075i	−0.871982	−	0.489538i	$-0.837166\pi$
$587$		−	1.98030e8i		−	0.979075i	0.871982	−	0.489538i	$-0.162834\pi$
$588$		0			0
$589$	−1.27789e8			−0.625387
$590$	−5.79970e7	−	1.00454e8i	−0.282390	−	0.489114i
$591$		0			0
$592$	8.98056e6	−	1.55548e7i	0.0432851	−	0.0749720i
$593$	3.26564e6	−	1.88542e6i	0.0156605	−	0.00904157i	−0.492149	−	0.870511i	$-0.663789\pi$
$593$	3.26564e6	−	1.88542e6i	0.0156605	−	0.00904157i	0.507810	+	0.861469i	$0.330455\pi$
$594$		0			0
$595$	−4.02742e7	−	1.74611e8i	−0.191195	−	0.828933i
$596$	−1.42512e8			−0.673153
$597$		0			0
$598$	3.43070e7	+	1.98071e7i	0.160428	+	0.0926229i
$599$	1.33653e8	−	2.31493e8i	0.621867	−	1.07710i	−0.367271	−	0.930114i	$-0.619708\pi$
$599$	1.33653e8	−	2.31493e8i	0.621867	−	1.07710i	0.989138	−	0.146991i	$-0.0469588\pi$
$600$		0			0
$601$			9.26866e7i			0.426966i	0.976947	+	0.213483i	$0.0684809\pi$
$601$			9.26866e7i			0.426966i	−0.976947	+	0.213483i	$0.931519\pi$
$602$	−1.36815e8	+	1.27530e8i	−0.627112	+	0.584550i
$603$		0			0
$604$	1.53770e7	+	2.66337e7i	0.0697846	+	0.120870i
$605$	−1.13339e8	−	6.54363e7i	−0.511815	−	0.295497i
$606$		0			0
$607$	1.38921e8	−	8.02061e7i	0.621158	−	0.358625i	−0.156162	−	0.987731i	$-0.549912\pi$
$607$	1.38921e8	−	8.02061e7i	0.621158	−	0.358625i	0.777320	+	0.629106i	$0.216579\pi$
$608$		−	8.84718e7i		−	0.393635i
$609$		0			0
$610$	−3.52931e6			−0.0155489
$611$	1.75096e7	+	3.03275e7i	0.0767631	+	0.132958i
$612$		0			0
$613$	−3.60980e7	+	6.25236e7i	−0.156712	+	0.271433i	−0.933681	−	0.358106i	$-0.883423\pi$
$613$	−3.60980e7	+	6.25236e7i	−0.156712	+	0.271433i	0.776969	+	0.629539i	$0.216756\pi$
$614$	1.24837e8	−	7.20748e7i	0.539311	−	0.311371i
$615$		0			0
$616$	6.02061e7	+	1.84204e7i	0.257572	+	0.0788056i
$617$	−3.16720e6			−0.0134841			−0.00674203	−	0.999977i	$-0.502146\pi$
$617$	−3.16720e6			−0.0134841			−0.00674203	+	0.999977i	$0.502146\pi$
$618$		0			0
$619$	1.20117e8	+	6.93494e7i	0.506444	+	0.292396i	0.731371	−	0.681980i	$-0.238881\pi$
$619$	1.20117e8	+	6.93494e7i	0.506444	+	0.292396i	−0.224927	+	0.974376i	$0.572214\pi$
$620$	−1.00691e8	+	1.74403e8i	−0.422491	+	0.731776i
$621$		0			0
$622$		−	1.20275e8i		−	0.499809i
$623$	6.14183e7	+	6.58903e7i	0.254000	+	0.272494i
$624$		0			0
$625$	1.58233e7	+	2.74068e7i	0.0648124	+	0.112258i
$626$	−5.86869e7	−	3.38829e7i	−0.239231	−	0.138120i
$627$		0			0
$628$	−6.31107e7	+	3.64370e7i	−0.254814	+	0.147117i
$629$			6.39043e7i			0.256790i
$630$		0			0
$631$	−1.98716e8			−0.790944			−0.395472	−	0.918478i	$-0.629419\pi$
$631$	−1.98716e8			−0.790944			−0.395472	+	0.918478i	$0.629419\pi$
$632$	6.88100e6	+	1.19182e7i	0.0272584	+	0.0472129i
$633$		0			0
$634$	−3.67812e7	+	6.37069e7i	−0.144331	+	0.249988i
$635$	1.18462e8	−	6.83941e7i	0.462656	−	0.267114i
$636$		0			0
$637$	−3.58906e7	−	7.36636e7i	−0.138855	−	0.284993i
$638$	3.71523e7			0.143062
$639$		0			0
$640$	−1.50095e8	−	8.66573e7i	−0.572567	−	0.330571i
$641$	7.21736e7	−	1.25008e8i	0.274034	−	0.474641i	−0.695857	−	0.718180i	$-0.744975\pi$
$641$	7.21736e7	−	1.25008e8i	0.274034	−	0.474641i	0.969891	+	0.243540i	$0.0783086\pi$
$642$		0			0
$643$			2.68271e8i			1.00911i	0.863378	+	0.504557i	$0.168344\pi$
$643$			2.68271e8i			1.00911i	−0.863378	+	0.504557i	$0.831656\pi$
$644$	6.19948e7	+	2.68781e8i	0.232112	+	1.00633i
$645$		0			0
$646$	3.04840e7	+	5.27999e7i	0.113077	+	0.195855i
$647$	3.38971e8	+	1.95705e8i	1.25155	+	0.722585i	0.971418	−	0.237375i	$-0.0762871\pi$
$647$	3.38971e8	+	1.95705e8i	1.25155	+	0.722585i	0.280136	+	0.959960i	$0.409620\pi$
$648$		0			0
$649$	1.48427e8	−	8.56944e7i	0.542974	−	0.313486i
$650$			2.19194e7i			0.0798158i
$651$		0			0
$652$	2.84179e8			1.02529
$653$	2.30591e8	+	3.99396e8i	0.828139	+	1.43438i	0.899496	+	0.436929i	$0.143934\pi$
$653$	2.30591e8	+	3.99396e8i	0.828139	+	1.43438i	−0.0713566	+	0.997451i	$0.522733\pi$
$654$		0			0
$655$	−8.55845e7	+	1.48237e8i	−0.304559	+	0.527512i
$656$	−5.84318e7	+	3.37356e7i	−0.206984	+	0.119503i
$657$		0			0
$658$	1.81969e7	−	5.94754e7i	0.0638732	−	0.208766i
$659$	−2.90612e8			−1.01545			−0.507724	−	0.861520i	$-0.669513\pi$
$659$	−2.90612e8			−1.01545			−0.507724	+	0.861520i	$0.669513\pi$
$660$		0			0
$661$	−2.43164e8	−	1.40391e8i	−0.841965	−	0.486109i	0.0159666	−	0.999873i	$-0.494917\pi$
$661$	−2.43164e8	−	1.40391e8i	−0.841965	−	0.486109i	−0.857932	+	0.513764i	$0.828251\pi$
$662$	3.85082e7	−	6.66981e7i	0.132733	−	0.229900i
$663$		0			0
$664$		−	4.08496e8i		−	1.39535i
$665$	7.32183e7	+	2.24016e7i	0.248975	+	0.0761752i
$666$		0			0
$667$	1.83527e8	+	3.17878e8i	0.618475	+	1.07123i
$668$	−9.90926e7	−	5.72111e7i	−0.332439	−	0.191934i
$669$		0			0
$670$	9.96886e7	−	5.75553e7i	0.331452	−	0.191364i
$671$		−	5.21480e6i		−	0.0172611i
$672$		0			0
$673$	−2.35293e8			−0.771904			−0.385952	−	0.922519i	$-0.626127\pi$
$673$	−2.35293e8			−0.771904			−0.385952	+	0.922519i	$0.626127\pi$
$674$	3.58530e7	+	6.20992e7i	0.117097	+	0.202818i
$675$		0			0
$676$	1.10699e8	−	1.91736e8i	0.358346	−	0.620673i
$677$	5.35332e8	−	3.09074e8i	1.72527	−	0.996085i	0.818435	−	0.574599i	$-0.194842\pi$
$677$	5.35332e8	−	3.09074e8i	1.72527	−	0.996085i	0.906835	−	0.421486i	$-0.138491\pi$
$678$		0			0
$679$	−1.92228e8	+	4.43377e7i	−0.614056	+	0.141633i
$680$	2.16665e8			0.689069
$681$		0			0
$682$	6.57295e7	+	3.79490e7i	0.207208	+	0.119632i
$683$	6.53722e6	−	1.13228e7i	0.0205178	−	0.0355379i	−0.855584	−	0.517664i	$-0.826802\pi$
$683$	6.53722e6	−	1.13228e7i	0.0205178	−	0.0355379i	0.876102	+	0.482126i	$0.160135\pi$
$684$		0			0
$685$			2.68214e8i			0.834468i
$686$	−5.22391e7	+	1.35837e8i	−0.161817	+	0.420770i
$687$		0			0
$688$	1.33648e8	+	2.31485e8i	0.410390	+	0.710817i
$689$	−1.20369e8	−	6.94949e7i	−0.368007	−	0.212469i
$690$		0			0
$691$	2.37346e8	−	1.37032e8i	0.719362	−	0.415324i	−0.0951555	−	0.995462i	$-0.530335\pi$
$691$	2.37346e8	−	1.37032e8i	0.719362	−	0.415324i	0.814518	+	0.580138i	$0.197002\pi$
$692$		−	3.50855e8i		−	1.05879i
$693$		0			0
$694$	1.19878e8			0.358643
$695$	1.68908e8	+	2.92558e8i	0.503149	+	0.871480i
$696$		0			0
$697$	1.20029e8	−	2.07896e8i	0.354476	−	0.613971i
$698$	−8.05349e7	+	4.64968e7i	−0.236820	+	0.136728i
$699$		0			0
$700$	−1.11646e8	+	1.04069e8i	−0.325498	+	0.303407i
$701$	−4.35624e8			−1.26461			−0.632307	−	0.774718i	$-0.717892\pi$
$701$	−4.35624e8			−1.26461			−0.632307	+	0.774718i	$0.717892\pi$
$702$		0			0
$703$	−2.36475e7	−	1.36529e7i	−0.0680644	−	0.0392970i
$704$	−1.23393e6	+	2.13723e6i	−0.00353649	+	0.00612539i
$705$		0			0
$706$		−	2.00740e8i		−	0.570454i
$707$	7.35448e7	−	2.40377e8i	0.208110	−	0.680197i
$708$		0			0
$709$	1.80906e8	+	3.13339e8i	0.507592	+	0.879176i	0.999961	+	0.00878924i	$0.00279774\pi$
$709$	1.80906e8	+	3.13339e8i	0.507592	+	0.879176i	−0.492369	+	0.870387i	$0.663869\pi$
$710$	−4.05020e7	−	2.33839e7i	−0.113162	−	0.0653343i
$711$		0			0
$712$	−9.43202e7	+	5.44558e7i	−0.261315	+	0.150870i
$713$			7.49848e8i			2.06873i
$714$		0			0
$715$	2.56049e7			0.0700495
$716$	2.01241e8	+	3.48560e8i	0.548249	+	0.949595i
$717$		0			0
$718$	−2.91663e7	+	5.05174e7i	−0.0787966	+	0.136480i
$719$	2.12503e8	−	1.22689e8i	0.571713	−	0.330079i	−0.186120	−	0.982527i	$-0.559591\pi$
$719$	2.12503e8	−	1.22689e8i	0.571713	−	0.330079i	0.757833	+	0.652448i	$0.226258\pi$
$720$		0			0
$721$	2.45265e8	+	2.63123e8i	0.654380	+	0.702026i
$722$	1.43620e8			0.381595
$723$		0			0
$724$	1.16426e8	+	6.72188e7i	0.306786	+	0.177123i
$725$	−1.01549e8	+	1.75888e8i	−0.266479	+	0.461555i
$726$		0			0
$727$			2.59949e8i			0.676526i	0.941052	+	0.338263i	$0.109839\pi$
$727$			2.59949e8i			0.676526i	−0.941052	+	0.338263i	$0.890161\pi$
$728$	9.65415e7	−	2.22674e7i	0.250219	−	0.0577133i
$729$		0			0
$730$	5.62468e7	+	9.74223e7i	0.144587	+	0.250432i
$731$	−8.23606e8	−	4.75509e8i	−2.10847	−	1.21733i
$732$		0			0
$733$	−1.08280e8	+	6.25152e7i	−0.274938	+	0.158735i	−0.631129	−	0.775678i	$-0.717408\pi$
$733$	−1.08280e8	+	6.25152e7i	−0.274938	+	0.158735i	0.356192	+	0.934413i	$0.384075\pi$
$734$		−	4.04915e7i		−	0.102394i
$735$		0			0
$736$	−5.19138e8			−1.30212
$737$	8.50418e7	+	1.47297e8i	0.212437	+	0.367951i
$738$		0			0
$739$	2.82361e8	−	4.89063e8i	0.699634	−	1.21180i	−0.268960	−	0.963151i	$-0.586680\pi$
$739$	2.82361e8	−	4.89063e8i	0.699634	−	1.21180i	0.968593	−	0.248650i	$-0.0799869\pi$
$740$	−3.72661e7	+	2.15156e7i	−0.0919641	+	0.0530955i
$741$		0			0
$742$	5.54813e7	+	2.40542e8i	0.135811	+	0.588815i
$743$	−2.68677e8			−0.655035			−0.327518	−	0.944845i	$-0.606212\pi$
$743$	−2.68677e8			−0.655035			−0.327518	+	0.944845i	$0.606212\pi$
$744$		0			0
$745$	2.01029e8	+	1.16064e8i	0.486171	+	0.280691i
$746$	−7.21256e7	+	1.24925e8i	−0.173729	+	0.300908i
$747$		0			0
$748$			1.41964e8i			0.339213i
$749$	−2.94766e8	+	2.74760e8i	−0.701507	+	0.653896i
$750$		0			0
$751$	−1.95480e8	−	3.38581e8i	−0.461512	−	0.799362i	0.537525	−	0.843248i	$-0.319359\pi$
$751$	−1.95480e8	−	3.38581e8i	−0.461512	−	0.799362i	−0.999037	+	0.0438862i	$0.986026\pi$
$752$	−7.69783e7	−	4.44434e7i	−0.181015	−	0.104509i
$753$		0			0
$754$	5.06308e7	−	2.92317e7i	0.118114	−	0.0681930i
$755$		−	5.00927e7i		−	0.116395i
$756$		0			0
$757$	−5.67872e8			−1.30907			−0.654535	−	0.756031i	$-0.727136\pi$
$757$	−5.67872e8			−1.30907			−0.654535	+	0.756031i	$0.727136\pi$
$758$	−5.26726e7	−	9.12317e7i	−0.120942	−	0.209478i
$759$		0			0
$760$	−4.62897e7	+	8.01762e7i	−0.105449	+	0.182644i
$761$	1.66316e8	−	9.60225e7i	0.377381	−	0.217881i	−0.299297	−	0.954160i	$-0.596752\pi$
$761$	1.66316e8	−	9.60225e7i	0.377381	−	0.217881i	0.676678	+	0.736279i	$0.263419\pi$
$762$		0			0
$763$	−2.40776e8	−	7.36667e7i	−0.542049	−	0.165843i
$764$	6.29378e8			1.41134
$765$		0			0
$766$	1.43243e8	+	8.27015e7i	0.318704	+	0.184004i
$767$	1.34850e8	−	2.33567e8i	0.298858	−	0.517637i
$768$		0			0
$769$		−	7.75766e8i		−	1.70589i	−0.521999	−	0.852946i	$-0.674813\pi$
$769$		−	7.75766e8i		−	1.70589i	0.521999	−	0.852946i	$-0.325187\pi$
$770$	−3.10080e7	−	3.32657e7i	−0.0679205	−	0.0728659i
$771$		0			0
$772$	−3.41457e8	−	5.91421e8i	−0.742138	−	1.28542i
$773$	−2.34180e7	−	1.35204e7i	−0.0507005	−	0.0292719i	0.474436	−	0.880290i	$-0.342652\pi$
$773$	−2.34180e7	−	1.35204e7i	−0.0507005	−	0.0292719i	−0.525136	+	0.851018i	$0.675986\pi$
$774$		0			0
$775$	−3.59320e8	+	2.07453e8i	−0.771926	+	0.445672i
$776$		−	2.38527e8i		−	0.510448i
$777$		0			0
$778$	−5.57154e7			−0.118314
$779$	5.12874e7	+	8.88323e7i	0.108492	+	0.187914i
$780$		0			0
$781$	3.45512e7	−	5.98445e7i	0.0725288	−	0.125624i
$782$	3.09821e8	−	1.78875e8i	0.647874	−	0.374050i
$783$		0			0
$784$	1.72381e8	+	1.16376e8i	0.357719	+	0.241499i
$785$	1.18699e8			0.245379
$786$		0			0
$787$	−3.68573e8	−	2.12796e8i	−0.756136	−	0.436555i	0.0717707	−	0.997421i	$-0.477135\pi$
$787$	−3.68573e8	−	2.12796e8i	−0.756136	−	0.436555i	−0.827907	+	0.560866i	$0.810468\pi$
$788$	2.40297e8	−	4.16207e8i	0.491100	−	0.850610i
$789$		0			0
$790$		−	9.94022e6i		−	0.0201611i
$791$	−1.57975e8	−	6.84910e8i	−0.319198	−	1.38390i
$792$		0			0
$793$	−4.10303e6	−	7.10666e6i	−0.00822783	−	0.0142510i
$794$	−9.18709e7	−	5.30417e7i	−0.183534	−	0.105963i
$795$		0			0
$796$	2.50702e8	−	1.44743e8i	0.497072	−	0.286985i
$797$		−	7.51386e7i		−	0.148419i	−0.997243	−	0.0742093i	$-0.976357\pi$
$797$		−	7.51386e7i		−	0.148419i	0.997243	−	0.0742093i	$-0.0236433\pi$
$798$		0			0
$799$	3.16253e8			0.620003
$800$	−1.43625e8	−	2.48766e8i	−0.280518	−	0.485871i
$801$		0			0
$802$	−2.05590e8	+	3.56093e8i	−0.398547	+	0.690304i
$803$	−1.43948e8	+	8.31084e7i	−0.278009	+	0.160509i
$804$		0			0
$805$	1.31449e8	−	4.29633e8i	0.251982	−	0.823589i
$806$	1.19434e8			0.228099
$807$		0			0
$808$	2.63220e8	+	1.51970e8i	0.498981	+	0.288087i
$809$	−3.91158e8	+	6.77506e8i	−0.738766	+	1.27958i	0.214285	+	0.976771i	$0.431258\pi$
$809$	−3.91158e8	+	6.77506e8i	−0.738766	+	1.27958i	−0.953051	+	0.302810i	$0.902075\pi$
$810$		0			0
$811$			8.00635e8i			1.50097i	0.660888	+	0.750485i	$0.270180\pi$
$811$			8.00635e8i			1.50097i	−0.660888	+	0.750485i	$0.729820\pi$
$812$	3.89274e8	+	1.19101e8i	0.727089	+	0.222457i
$813$		0			0
$814$	8.10887e6	+	1.40450e7i	0.0150344	+	0.0260404i
$815$	−4.00863e8	−	2.31439e8i	−0.740497	−	0.427526i
$816$		0			0
$817$	3.51921e8	−	2.03181e8i	0.645325	−	0.372579i
$818$		−	1.24637e8i		−	0.227712i
$819$		0			0
$820$	1.61647e8			0.293175
$821$	−1.37831e8	−	2.38730e8i	−0.249067	−	0.431397i	0.714200	−	0.699942i	$-0.246791\pi$
$821$	−1.37831e8	−	2.38730e8i	−0.249067	−	0.431397i	−0.963267	+	0.268544i	$0.913457\pi$
$822$		0			0
$823$	3.78952e8	−	6.56364e8i	0.679806	−	1.17746i	−0.295233	−	0.955425i	$-0.595397\pi$
$823$	3.78952e8	−	6.56364e8i	0.679806	−	1.17746i	0.975039	−	0.222033i	$-0.0712693\pi$
$824$	−3.76654e8	+	2.17461e8i	−0.673226	+	0.388687i
$825$		0			0
$826$	−4.66754e8	+	1.07657e8i	−0.828224	+	0.191031i
$827$	−3.06595e8			−0.542061			−0.271030	−	0.962571i	$-0.587364\pi$
$827$	−3.06595e8			−0.542061			−0.271030	+	0.962571i	$0.587364\pi$
$828$		0			0
$829$	1.07092e8	+	6.18296e7i	0.187972	+	0.108526i	0.591033	−	0.806647i	$-0.298720\pi$
$829$	1.07092e8	+	6.18296e7i	0.187972	+	0.108526i	−0.403061	+	0.915173i	$0.632054\pi$
$830$	−1.47527e8	+	2.55525e8i	−0.258011	+	0.446888i
$831$		0			0
$832$			3.88346e6i			0.00674293i
$833$	−7.38180e8	−	5.19240e7i	−1.27711	−	0.0898325i
$834$		0			0
$835$	9.31869e7	+	1.61405e8i	0.160065	+	0.277240i
$836$	−5.25330e7	−	3.03300e7i	−0.0899112	−	0.0519102i
$837$		0			0
$838$	1.16781e8	−	6.74238e7i	0.198446	−	0.114573i
$839$		−	2.04720e8i		−	0.346637i	−0.984866	−	0.173318i	$-0.944551\pi$
$839$		−	2.04720e8i		−	0.346637i	0.984866	−	0.173318i	$-0.0554489\pi$
$840$		0			0
$841$	−5.31198e7			−0.0893035
$842$	1.07097e8	+	1.85497e8i	0.179407	+	0.310743i
$843$		0			0
$844$	2.68213e7	−	4.64559e7i	0.0446121	−	0.0772705i
$845$	−3.12304e8	+	1.80309e8i	−0.517615	+	0.298845i
$846$		0			0
$847$	−3.95337e8	+	3.68505e8i	−0.650604	+	0.606448i
$848$	3.52789e8			0.578532
$849$		0			0
$850$	1.71430e8	+	9.89754e7i	0.279146	+	0.161165i
$851$	−8.01131e7	+	1.38760e8i	−0.129991	+	0.225152i
$852$		0			0
$853$		−	1.81851e8i		−	0.293001i	−0.989211	−	0.146500i	$-0.953199\pi$
$853$		−	1.81851e8i		−	0.293001i	0.989211	−	0.146500i	$-0.0468010\pi$
$854$	−4.26408e6	+	1.39369e7i	−0.00684624	+	0.0223766i
$855$		0			0
$856$	−2.43613e8	−	4.21950e8i	−0.388400	−	0.672729i
$857$	5.32176e8	+	3.07252e8i	0.845499	+	0.488149i	0.859130	−	0.511758i	$-0.171006\pi$
$857$	5.32176e8	+	3.07252e8i	0.845499	+	0.488149i	−0.0136307	+	0.999907i	$0.504339\pi$
$858$		0			0
$859$	−1.89532e8	+	1.09426e8i	−0.299022	+	0.172640i	−0.642003	−	0.766702i	$-0.721897\pi$
$859$	−1.89532e8	+	1.09426e8i	−0.299022	+	0.172640i	0.342981	+	0.939342i	$0.388563\pi$
$860$		−	6.40386e8i		−	1.00681i
$861$		0			0
$862$	2.14729e8			0.335250
$863$	−3.29715e8	−	5.71084e8i	−0.512988	−	0.888521i	−0.999887	−	0.0150623i	$-0.995205\pi$
$863$	−3.29715e8	−	5.71084e8i	−0.512988	−	0.888521i	0.486899	−	0.873458i	$-0.338128\pi$
$864$		0			0
$865$	−2.85741e8	+	4.94918e8i	−0.441494	+	0.764689i
$866$	−2.00121e8	+	1.15540e8i	−0.308133	+	0.177901i
$867$		0			0
$868$	5.67045e8	+	6.08333e8i	0.867079	+	0.930212i
$869$	1.46873e7			0.0223812
$870$		0			0
$871$	2.31788e8	+	1.33823e8i	0.350781	+	0.202524i
$872$	1.52222e8	−	2.63656e8i	0.229577	−	0.397639i
$873$		0			0
$874$			1.52864e8i			0.228966i
$875$	6.75998e8	−	1.55920e8i	1.00907	−	0.232743i
$876$		0			0
$877$	−8.11828e7	−	1.40613e8i	−0.120355	−	0.208462i	0.799552	−	0.600596i	$-0.205070\pi$
$877$	−8.11828e7	−	1.40613e8i	−0.120355	−	0.208462i	−0.919908	+	0.392135i	$0.871737\pi$
$878$	4.75256e8	+	2.74389e8i	0.702173	+	0.405400i
$879$		0			0
$880$	−5.62840e7	+	3.24956e7i	−0.0825918	+	0.0476844i
$881$			8.48365e8i			1.24067i	0.784338	+	0.620333i	$0.213003\pi$
$881$			8.48365e8i			1.24067i	−0.784338	+	0.620333i	$0.786997\pi$
$882$		0			0
$883$	3.14592e8			0.456947			0.228473	−	0.973550i	$-0.426627\pi$
$883$	3.14592e8			0.456947			0.228473	+	0.973550i	$0.426627\pi$
$884$	1.11698e8	+	1.93466e8i	0.161692	+	0.280058i
$885$		0			0
$886$	6.23635e7	−	1.08017e8i	0.0896663	−	0.155307i
$887$	7.25058e8	−	4.18612e8i	1.03897	−	0.599848i	0.119426	−	0.992843i	$-0.461894\pi$
$887$	7.25058e8	−	4.18612e8i	1.03897	−	0.599848i	0.919540	+	0.392995i	$0.128561\pi$
$888$		0			0
$889$	−1.26957e8	−	5.50429e8i	−0.180697	−	0.783422i
$890$	7.86663e7			0.111588
$891$		0			0
$892$	−4.40119e8	−	2.54103e8i	−0.620119	−	0.358026i
$893$	−6.75662e7	+	1.17028e8i	−0.0948800	+	0.164337i
$894$		0			0
$895$		−	6.55573e8i		−	0.914433i
$896$	−5.23545e8	+	4.88012e8i	−0.727830	+	0.678432i
$897$		0			0
$898$	−2.41267e8	−	4.17886e8i	−0.333172	−	0.577070i
$899$	9.58376e8	+	5.53319e8i	1.31904	+	0.761546i
$900$		0			0
$901$	−1.08703e9	+	6.27598e8i	−1.48617	+	0.858039i
$902$		−	6.09222e7i		−	0.0830148i
$903$		0			0
$904$	8.49870e8			1.15040
$905$	−1.09488e8	−	1.89638e8i	−0.147713	−	0.255847i
$906$		0			0
$907$	−3.44024e8	+	5.95867e8i	−0.461070	+	0.798596i	−0.999015	−	0.0443839i	$-0.985868\pi$
$907$	−3.44024e8	+	5.95867e8i	−0.461070	+	0.798596i	0.537945	+	0.842980i	$0.319201\pi$
$908$	−8.15700e8	+	4.70945e8i	−1.08962	+	0.629090i
$909$		0			0
$910$	−6.84310e7	−	2.09369e7i	−0.0908089	−	0.0277835i
$911$	−2.31613e8			−0.306343			−0.153171	−	0.988200i	$-0.548949\pi$
$911$	−2.31613e8			−0.306343			−0.153171	+	0.988200i	$0.548949\pi$
$912$		0			0
$913$	−3.77555e8	−	2.17981e8i	−0.496098	−	0.286422i
$914$	−2.75045e7	+	4.76393e7i	−0.0360218	+	0.0623917i
$915$		0			0
$916$		−	6.94307e8i		−	0.903369i
$917$	4.81971e8	+	5.17064e8i	0.625047	+	0.670557i
$918$		0			0
$919$	5.62582e8	+	9.74420e8i	0.724835	+	1.25545i	0.959042	+	0.283264i	$0.0914174\pi$
$919$	5.62582e8	+	9.74420e8i	0.724835	+	1.25545i	−0.234207	+	0.972187i	$0.575249\pi$
$920$	4.70461e8	+	2.71621e8i	0.604171	+	0.348818i
$921$		0			0
$922$	9.52653e7	−	5.50014e7i	0.121546	−	0.0701748i
$923$		−	1.08740e8i		−	0.138289i
$924$		0			0
$925$	−8.86565e7			−0.112017
$926$	2.91515e8	+	5.04918e8i	0.367136	+	0.635899i
$927$		0			0
$928$	−3.83076e8	+	6.63507e8i	−0.479337	+	0.830237i
$929$	5.93421e8	−	3.42612e8i	0.740143	−	0.427322i	−0.0819782	−	0.996634i	$-0.526124\pi$
$929$	5.93421e8	−	3.42612e8i	0.740143	−	0.427322i	0.822121	+	0.569312i	$0.192790\pi$
$930$		0			0
$931$	1.76923e8	−	2.62067e8i	0.219248	−	0.324761i
$932$	520438.			0.000642867
$933$		0			0
$934$	2.05871e8	+	1.18860e8i	0.252670	+	0.145879i
$935$	1.15617e8	−	2.00254e8i	0.141445	−	0.244989i
$936$		0			0
$937$			7.87984e8i			0.957852i	0.877855	+	0.478926i	$0.158974\pi$
$937$			7.87984e8i			0.957852i	−0.877855	+	0.478926i	$0.841026\pi$
$938$	−1.06837e8	−	4.63199e8i	−0.129454	−	0.561253i
$939$		0			0
$940$	1.06477e8	+	1.84424e8i	0.128196	+	0.222041i
$941$	−1.79551e8	−	1.03664e8i	−0.215486	−	0.124411i	0.388372	−	0.921503i	$-0.373037\pi$
$941$	−1.79551e8	−	1.03664e8i	−0.215486	−	0.124411i	−0.603859	+	0.797092i	$0.706371\pi$
$942$		0			0
$943$	5.21254e8	−	3.00946e8i	0.621604	−	0.358883i
$944$			6.84561e8i			0.813759i
$945$		0			0
$946$	−2.41351e8			−0.285086
$947$	−1.77030e8	−	3.06624e8i	−0.208447	−	0.361041i	0.742778	−	0.669537i	$-0.233508\pi$
$947$	−1.77030e8	−	3.06624e8i	−0.208447	−	0.361041i	−0.951226	+	0.308496i	$0.900174\pi$
$948$		0			0
$949$	−1.30780e8	+	2.26518e8i	−0.153019	+	0.265036i
$950$	−7.32509e7	+	4.22914e7i	−0.0854363	+	0.0493267i
$951$		0			0
$952$	2.61773e8	−	8.55592e8i	0.303399	−	0.991644i
$953$	4.28652e8			0.495252			0.247626	−	0.968856i	$-0.420350\pi$
$953$	4.28652e8			0.495252			0.247626	+	0.968856i	$0.420350\pi$
$954$		0			0
$955$	−8.87803e8	−	5.12573e8i	−1.01931	−	0.588499i
$956$	−6.36311e7	+	1.10212e8i	−0.0728276	+	0.126141i
$957$		0			0
$958$		−	3.31711e8i		−	0.377280i
$959$	1.05915e9	+	3.24054e8i	1.20089	+	0.367419i
$960$		0			0
$961$	6.86614e8	+	1.18925e9i	0.773646	+	1.33999i
$962$	2.21013e7	+	1.27602e7i	0.0248252	+	0.0143329i
$963$		0			0
$964$	−2.41581e8	+	1.39477e8i	−0.269669	+	0.155694i
$965$			1.11235e9i			1.23782i
$966$		0			0
$967$	1.16972e9			1.29361			0.646805	−	0.762655i	$-0.276105\pi$
$967$	1.16972e9			1.29361			0.646805	+	0.762655i	$0.276105\pi$
$968$	−3.26731e8	−	5.65915e8i	−0.360217	−	0.623914i
$969$		0			0
$970$	−8.61432e7	+	1.49204e8i	−0.0943856	+	0.163481i
$971$	−6.09512e8	+	3.51902e8i	−0.665770	+	0.384383i	−0.794472	−	0.607301i	$-0.792252\pi$
$971$	−6.09512e8	+	3.51902e8i	−0.665770	+	0.384383i	0.128702	+	0.991683i	$0.458919\pi$
$972$		0			0
$973$	1.35936e9	−	3.13537e8i	1.47569	−	0.340370i
$974$	−6.87949e8			−0.744525
$975$		0			0
$976$	1.80384e7	+	1.04145e7i	0.0194021	+	0.0112018i
$977$	2.21206e8	−	3.83140e8i	0.237199	−	0.410841i	−0.722710	−	0.691151i	$-0.757104\pi$
$977$	2.21206e8	−	3.83140e8i	0.237199	−	0.410841i	0.959910	+	0.280310i	$0.0904372\pi$
$978$		0			0
$979$			1.16235e8i			0.123876i
$980$	−2.18254e8	−	4.47954e8i	−0.231891	−	0.475944i
$981$		0			0
$982$	1.59679e8	+	2.76571e8i	0.168621	+	0.292061i
$983$	1.01182e9	+	5.84175e8i	1.06523	+	0.615011i	0.926874	−	0.375372i	$-0.122485\pi$
$983$	1.01182e9	+	5.84175e8i	1.06523	+	0.615011i	0.138355	+	0.990383i	$0.455818\pi$
$984$		0			0
$985$	−6.77928e8	+	3.91402e8i	−0.709374	+	0.409557i
$986$		−	5.27974e8i		−	0.550784i
$987$		0			0
$988$	−9.54552e7			−0.0989758
$989$	−1.19224e9	−	2.06501e9i	−1.23246	−	2.13468i
$990$		0			0
$991$	5.01818e8	−	8.69174e8i	0.515615	−	0.893071i	−0.484221	−	0.874946i	$-0.660897\pi$
$991$	5.01818e8	−	8.69174e8i	0.515615	−	0.893071i	0.999836	−	0.0181249i	$-0.00576967\pi$
$992$	−1.35547e9	+	7.82580e8i	−1.38853	+	0.801666i
$993$		0			0
$994$	−1.41275e8	+	1.31687e8i	−0.143849	+	0.134086i
$995$	−4.71522e8			−0.478666
$996$		0			0
$997$	1.60115e9	+	9.24424e8i	1.61565	+	0.932794i	0.988028	+	0.154274i	$0.0493037\pi$
$997$	1.60115e9	+	9.24424e8i	1.61565	+	0.932794i	0.627619	+	0.778521i	$0.284030\pi$
$998$	9.44016e7	−	1.63508e8i	0.0949703	−	0.164493i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.7.m.c.10.2		8
3.2	odd	2		21.7.f.b.10.3	✓	8
7.3	odd	6		441.7.d.d.244.6		8
7.4	even	3		441.7.d.d.244.5		8
7.5	odd	6	inner	63.7.m.c.19.2		8
12.11	even	2		336.7.bh.b.241.3		8
21.2	odd	6		147.7.f.a.19.3		8
21.5	even	6		21.7.f.b.19.3	yes	8
21.11	odd	6		147.7.d.a.97.3		8
21.17	even	6		147.7.d.a.97.4		8
21.20	even	2		147.7.f.a.31.3		8
84.47	odd	6		336.7.bh.b.145.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.3	✓	8	3.2	odd	2
21.7.f.b.19.3	yes	8	21.5	even	6
63.7.m.c.10.2		8	1.1	even	1	trivial
63.7.m.c.19.2		8	7.5	odd	6	inner
147.7.d.a.97.3		8	21.11	odd	6
147.7.d.a.97.4		8	21.17	even	6
147.7.f.a.19.3		8	21.2	odd	6
147.7.f.a.31.3		8	21.20	even	2
336.7.bh.b.145.3		8	84.47	odd	6
336.7.bh.b.241.3		8	12.11	even	2
441.7.d.d.244.5		8	7.4	even	3
441.7.d.d.244.6		8	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	63.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80325 - 3.12332i) q^{2} +(25.4966 - 44.1614i) q^{4} +(-71.9311 + 41.5295i) q^{5} +(77.0894 + 334.225i) q^{7} -414.723 q^{8} +O(q^{10})\)	\(q+(-1.80325 - 3.12332i) q^{2} +(25.4966 - 44.1614i) q^{4} +(-71.9311 + 41.5295i) q^{5} +(77.0894 + 334.225i) q^{7} -414.723 q^{8} +(259.420 + 149.776i) q^{10} +(-221.304 + 383.310i) q^{11} +696.494i q^{13} +(904.880 - 843.466i) q^{14} +(-883.932 - 1531.01i) q^{16} +(5447.24 + 3144.96i) q^{17} +(-2327.56 + 1343.82i) q^{19} +4235.44i q^{20} +1596.27 q^{22} +(7885.31 + 13657.8i) q^{23} +(-4363.11 + 7557.12i) q^{25} +(2175.37 - 1255.95i) q^{26} +(16725.3 + 5117.22i) q^{28} +23274.5 q^{29} +(41177.0 + 23773.6i) q^{31} +(-16459.0 + 28507.9i) q^{32} -22684.6i q^{34} +(-19425.3 - 20839.7i) q^{35} +(5079.89 + 8798.64i) q^{37} +(8394.35 + 4846.48i) q^{38} +(29831.5 - 17223.2i) q^{40} -38165.4i q^{41} -151197. q^{43} +(11285.0 + 19546.2i) q^{44} +(28438.4 - 49256.7i) q^{46} +(43543.1 - 25139.6i) q^{47} +(-105763. + 51530.4i) q^{49} +31471.1 q^{50} +(30758.1 + 17758.2i) q^{52} +(-99778.2 + 172821. i) q^{53} -36762.6i q^{55} +(-31970.7 - 138611. i) q^{56} +(-41969.8 - 72693.8i) q^{58} +(-335347. - 193612. i) q^{59} +(-10203.5 + 5890.98i) q^{61} -171479. i q^{62} +5575.73 q^{64} +(-28925.0 - 50099.6i) q^{65} +(192138. - 332792. i) q^{67} +(277772. - 160372. i) q^{68} +(-30060.4 + 98250.6i) q^{70} -156126. q^{71} +(325227. + 187770. i) q^{73} +(18320.6 - 31732.3i) q^{74} +137051. i q^{76} +(-145172. - 44416.2i) q^{77} +(-16591.8 - 28737.9i) q^{79} +(127164. + 73418.4i) q^{80} +(-119203. + 68821.8i) q^{82} +984986. i q^{83} -522434. q^{85} +(272646. + 472237. i) q^{86} +(91779.9 - 158967. i) q^{88} +(227430. - 131307. i) q^{89} +(-232786. + 53692.3i) q^{91} +804193. q^{92} +(-157038. - 90666.0i) q^{94} +(111616. - 193325. i) q^{95} +575147. i q^{97} +(351664. + 237411. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} - 173 q^{4} + 42 q^{5} + 748 q^{7} + 454 q^{8}+O(q^{10}) \) 8 * q + 5 * q^2 - 173 * q^4 + 42 * q^5 + 748 * q^7 + 454 * q^8	\( 8 q + 5 q^{2} - 173 q^{4} + 42 q^{5} + 748 q^{7} + 454 q^{8} + 261 q^{10} + 1070 q^{11} - 6070 q^{14} + 3911 q^{16} - 7212 q^{17} - 24606 q^{19} - 78 q^{22} + 15224 q^{23} + 22274 q^{25} + 19044 q^{26} - 3415 q^{28} - 32524 q^{29} + 40200 q^{31} - 70203 q^{32} + 242436 q^{35} - 45670 q^{37} - 503310 q^{38} - 94941 q^{40} - 445660 q^{43} + 188829 q^{44} + 525804 q^{46} - 82884 q^{47} + 24116 q^{49} + 1218884 q^{50} + 722856 q^{52} + 13034 q^{53} - 127061 q^{56} - 159501 q^{58} - 1810362 q^{59} - 392856 q^{61} - 1410446 q^{64} + 389004 q^{65} + 384094 q^{67} + 1616346 q^{68} + 406005 q^{70} - 225688 q^{71} + 903078 q^{73} - 1185530 q^{74} + 327674 q^{77} - 559592 q^{79} - 847713 q^{80} + 347634 q^{82} + 1953576 q^{85} + 2302402 q^{86} + 304887 q^{88} + 1770036 q^{89} - 2960718 q^{91} + 113064 q^{92} - 1837620 q^{94} - 1160112 q^{95} - 5732467 q^{98}+O(q^{100}) \) 8 * q + 5 * q^2 - 173 * q^4 + 42 * q^5 + 748 * q^7 + 454 * q^8 + 261 * q^10 + 1070 * q^11 - 6070 * q^14 + 3911 * q^16 - 7212 * q^17 - 24606 * q^19 - 78 * q^22 + 15224 * q^23 + 22274 * q^25 + 19044 * q^26 - 3415 * q^28 - 32524 * q^29 + 40200 * q^31 - 70203 * q^32 + 242436 * q^35 - 45670 * q^37 - 503310 * q^38 - 94941 * q^40 - 445660 * q^43 + 188829 * q^44 + 525804 * q^46 - 82884 * q^47 + 24116 * q^49 + 1218884 * q^50 + 722856 * q^52 + 13034 * q^53 - 127061 * q^56 - 159501 * q^58 - 1810362 * q^59 - 392856 * q^61 - 1410446 * q^64 + 389004 * q^65 + 384094 * q^67 + 1616346 * q^68 + 406005 * q^70 - 225688 * q^71 + 903078 * q^73 - 1185530 * q^74 + 327674 * q^77 - 559592 * q^79 - 847713 * q^80 + 347634 * q^82 + 1953576 * q^85 + 2302402 * q^86 + 304887 * q^88 + 1770036 * q^89 - 2960718 * q^91 + 113064 * q^92 - 1837620 * q^94 - 1160112 * q^95 - 5732467 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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