LMFDB - Embedded newform 25.7.c.c.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,7,Mod(7,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	25.c (of order $4$, 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:	$5.75135209050$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{201})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 101x^{2} + 2500 $ x^4 + 101*x^2 + 2500
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$-6.58872i$ of defining polynomial
Character	$\chi$	$=$	25.7
Dual form			25.7.c.c.18.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.58872 - 4.58872i) q^{2} +(-0.411277 + 0.411277i) q^{3} -21.8872i q^{4} +3.77447 q^{6} +(-215.476 - 215.476i) q^{7} +(-394.113 + 394.113i) q^{8} +728.662i q^{9} +O(q^{10})$	\(q+(-4.58872 - 4.58872i) q^{2} +(-0.411277 + 0.411277i) q^{3} -21.8872i q^{4} +3.77447 q^{6} +(-215.476 - 215.476i) q^{7} +(-394.113 + 394.113i) q^{8} +728.662i q^{9} -1326.31 q^{11} +(9.00171 + 9.00171i) q^{12} +(-1439.89 + 1439.89i) q^{13} +1977.52i q^{14} +2216.17 q^{16} +(-1349.15 - 1349.15i) q^{17} +(3343.63 - 3343.63i) q^{18} -9191.14i q^{19} +177.240 q^{21} +(6086.06 + 6086.06i) q^{22} +(7491.20 - 7491.20i) q^{23} -324.179i q^{24} +13214.5 q^{26} +(-599.502 - 599.502i) q^{27} +(-4716.17 + 4716.17i) q^{28} +5438.74i q^{29} -32749.1 q^{31} +(15053.8 + 15053.8i) q^{32} +(545.480 - 545.480i) q^{33} +12381.7i q^{34} +15948.4 q^{36} +(-56535.1 - 56535.1i) q^{37} +(-42175.6 + 42175.6i) q^{38} -1184.39i q^{39} +17758.7 q^{41} +(-813.307 - 813.307i) q^{42} +(6394.08 - 6394.08i) q^{43} +29029.2i q^{44} -68750.1 q^{46} +(35299.9 + 35299.9i) q^{47} +(-911.457 + 911.457i) q^{48} -24789.2i q^{49} +1109.75 q^{51} +(31515.2 + 31515.2i) q^{52} +(60400.3 - 60400.3i) q^{53} +5501.90i q^{54} +169844. q^{56} +(3780.10 + 3780.10i) q^{57} +(24956.9 - 24956.9i) q^{58} -46091.2i q^{59} -75611.9 q^{61} +(150277. + 150277. i) q^{62} +(157009. - 157009. i) q^{63} -279990. i q^{64} -5006.11 q^{66} +(-154883. - 154883. i) q^{67} +(-29529.1 + 29529.1i) q^{68} +6161.91i q^{69} +184000. q^{71} +(-287175. - 287175. i) q^{72} +(-301029. + 301029. i) q^{73} +518848. i q^{74} -201169. q^{76} +(285788. + 285788. i) q^{77} +(-5434.82 + 5434.82i) q^{78} +178743. i q^{79} -530701. q^{81} +(-81489.6 - 81489.6i) q^{82} +(-565063. + 565063. i) q^{83} -3879.30i q^{84} -58681.4 q^{86} +(-2236.83 - 2236.83i) q^{87} +(522715. - 522715. i) q^{88} +249057. i q^{89} +620523. q^{91} +(-163962. - 163962. i) q^{92} +(13468.9 - 13468.9i) q^{93} -323963. i q^{94} -12382.6 q^{96} +(-30626.2 - 30626.2i) q^{97} +(-113751. + 113751. i) q^{98} -966430. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 10 q^{2} - 30 q^{3} - 552 q^{6} - 550 q^{7} - 1860 q^{8}+O(q^{10}) $ 4 * q + 10 * q^2 - 30 * q^3 - 552 * q^6 - 550 * q^7 - 1860 * q^8	$ 4 q + 10 q^{2} - 30 q^{3} - 552 q^{6} - 550 q^{7} - 1860 q^{8} - 1052 q^{11} - 3480 q^{12} - 1960 q^{13} - 776 q^{16} + 3280 q^{17} + 870 q^{18} + 3828 q^{21} + 27520 q^{22} + 39010 q^{23} + 44068 q^{26} - 31320 q^{27} + 4840 q^{28} - 33172 q^{31} + 48760 q^{32} - 22260 q^{33} - 40836 q^{36} - 146860 q^{37} - 218040 q^{38} - 213932 q^{41} + 31680 q^{42} + 72050 q^{43} + 323288 q^{46} - 830 q^{47} + 74160 q^{48} - 172212 q^{51} + 173300 q^{52} + 29620 q^{53} + 467280 q^{56} - 195840 q^{57} + 554640 q^{58} - 111052 q^{61} + 610520 q^{62} + 350130 q^{63} - 457824 q^{66} + 146930 q^{67} - 775780 q^{68} + 1310188 q^{71} - 899460 q^{72} - 553540 q^{73} - 2073840 q^{76} + 476300 q^{77} - 268200 q^{78} - 624816 q^{81} - 2554880 q^{82} - 536870 q^{83} + 1019128 q^{86} + 763440 q^{87} + 187680 q^{88} + 1131548 q^{91} + 2552680 q^{92} - 444660 q^{93} - 568992 q^{96} + 59420 q^{97} + 1892810 q^{98}+O(q^{100}) $ 4 * q + 10 * q^2 - 30 * q^3 - 552 * q^6 - 550 * q^7 - 1860 * q^8 - 1052 * q^11 - 3480 * q^12 - 1960 * q^13 - 776 * q^16 + 3280 * q^17 + 870 * q^18 + 3828 * q^21 + 27520 * q^22 + 39010 * q^23 + 44068 * q^26 - 31320 * q^27 + 4840 * q^28 - 33172 * q^31 + 48760 * q^32 - 22260 * q^33 - 40836 * q^36 - 146860 * q^37 - 218040 * q^38 - 213932 * q^41 + 31680 * q^42 + 72050 * q^43 + 323288 * q^46 - 830 * q^47 + 74160 * q^48 - 172212 * q^51 + 173300 * q^52 + 29620 * q^53 + 467280 * q^56 - 195840 * q^57 + 554640 * q^58 - 111052 * q^61 + 610520 * q^62 + 350130 * q^63 - 457824 * q^66 + 146930 * q^67 - 775780 * q^68 + 1310188 * q^71 - 899460 * q^72 - 553540 * q^73 - 2073840 * q^76 + 476300 * q^77 - 268200 * q^78 - 624816 * q^81 - 2554880 * q^82 - 536870 * q^83 + 1019128 * q^86 + 763440 * q^87 + 187680 * q^88 + 1131548 * q^91 + 2552680 * q^92 - 444660 * q^93 - 568992 * q^96 + 59420 * q^97 + 1892810 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−4.58872	−	4.58872i	−0.573590	−	0.573590i	0.359539	−	0.933130i	$-0.382934\pi$
$2$	−4.58872	−	4.58872i	−0.573590	−	0.573590i	−0.933130	+	0.359539i	$0.882934\pi$
$3$	−0.411277	+	0.411277i	−0.0152325	+	0.0152325i	−0.714682	−	0.699450i	$-0.753429\pi$
$3$	−0.411277	+	0.411277i	−0.0152325	+	0.0152325i	0.699450	+	0.714682i	$0.253429\pi$
$4$		−	21.8872i		−	0.341988i
$5$		0			0
$5$		0			0
$6$	3.77447			0.0174744
$7$	−215.476	−	215.476i	−0.628210	−	0.628210i	0.319408	−	0.947617i	$-0.396516\pi$
$7$	−215.476	−	215.476i	−0.628210	−	0.628210i	−0.947617	+	0.319408i	$0.896516\pi$
$8$	−394.113	+	394.113i	−0.769751	+	0.769751i
$9$			728.662i			0.999536i
$10$		0			0
$11$	−1326.31			−0.996475			−0.498238	−	0.867041i	$-0.666019\pi$
$11$	−1326.31			−0.996475			−0.498238	+	0.867041i	$0.666019\pi$
$12$	9.00171	+	9.00171i	0.00520932	+	0.00520932i
$13$	−1439.89	+	1439.89i	−0.655389	+	0.655389i	−0.954285	−	0.298897i	$-0.903381\pi$
$13$	−1439.89	+	1439.89i	−0.655389	+	0.655389i	0.298897	+	0.954285i	$0.403381\pi$
$14$			1977.52i			0.720670i
$15$		0			0
$16$	2216.17			0.541056
$17$	−1349.15	−	1349.15i	−0.274608	−	0.274608i	0.556344	−	0.830952i	$-0.312204\pi$
$17$	−1349.15	−	1349.15i	−0.274608	−	0.274608i	−0.830952	+	0.556344i	$0.812204\pi$
$18$	3343.63	−	3343.63i	0.573324	−	0.573324i
$19$		−	9191.14i		−	1.34001i	−0.742356	−	0.670006i	$-0.766291\pi$
$19$		−	9191.14i		−	1.34001i	0.742356	−	0.670006i	$-0.233709\pi$
$20$		0			0
$21$	177.240			0.0191384
$22$	6086.06	+	6086.06i	0.571569	+	0.571569i
$23$	7491.20	−	7491.20i	0.615698	−	0.615698i	−0.328727	−	0.944425i	$-0.606620\pi$
$23$	7491.20	−	7491.20i	0.615698	−	0.615698i	0.944425	+	0.328727i	$0.106620\pi$
$24$		−	324.179i		−	0.0234504i
$25$		0			0
$26$	13214.5			0.751849
$27$	−599.502	−	599.502i	−0.0304579	−	0.0304579i
$28$	−4716.17	+	4716.17i	−0.214840	+	0.214840i
$29$			5438.74i			0.223000i	0.993764	+	0.111500i	$0.0355655\pi$
$29$			5438.74i			0.223000i	−0.993764	+	0.111500i	$0.964435\pi$
$30$		0			0
$31$	−32749.1			−1.09929			−0.549647	−	0.835397i	$-0.685238\pi$
$31$	−32749.1			−1.09929			−0.549647	+	0.835397i	$0.685238\pi$
$32$	15053.8	+	15053.8i	0.459407	+	0.459407i
$33$	545.480	−	545.480i	0.0151788	−	0.0151788i
$34$			12381.7i			0.315025i
$35$		0			0
$36$	15948.4			0.341829
$37$	−56535.1	−	56535.1i	−1.11612	−	1.11612i	−0.992305	−	0.123820i	$-0.960485\pi$
$37$	−56535.1	−	56535.1i	−1.11612	−	1.11612i	−0.123820	−	0.992305i	$-0.539515\pi$
$38$	−42175.6	+	42175.6i	−0.768618	+	0.768618i
$39$		−	1184.39i		−	0.0199664i
$40$		0			0
$41$	17758.7			0.257667			0.128834	−	0.991666i	$-0.458877\pi$
$41$	17758.7			0.257667			0.128834	+	0.991666i	$0.458877\pi$
$42$	−813.307	−	813.307i	−0.0109776	−	0.0109776i
$43$	6394.08	−	6394.08i	0.0804216	−	0.0804216i	−0.665752	−	0.746173i	$-0.731889\pi$
$43$	6394.08	−	6394.08i	0.0804216	−	0.0804216i	0.746173	+	0.665752i	$0.231889\pi$
$44$			29029.2i			0.340783i
$45$		0			0
$46$	−68750.1			−0.706317
$47$	35299.9	+	35299.9i	0.340001	+	0.340001i	0.856368	−	0.516367i	$-0.172716\pi$
$47$	35299.9	+	35299.9i	0.340001	+	0.340001i	−0.516367	+	0.856368i	$0.672716\pi$
$48$	−911.457	+	911.457i	−0.00824162	+	0.00824162i
$49$		−	24789.2i		−	0.210705i
$50$		0			0
$51$	1109.75			0.00836592
$52$	31515.2	+	31515.2i	0.224135	+	0.224135i
$53$	60400.3	−	60400.3i	0.405706	−	0.405706i	−0.474532	−	0.880238i	$-0.657383\pi$
$53$	60400.3	−	60400.3i	0.405706	−	0.405706i	0.880238	+	0.474532i	$0.157383\pi$
$54$			5501.90i			0.0349407i
$55$		0			0
$56$	169844.			0.967131
$57$	3780.10	+	3780.10i	0.0204117	+	0.0204117i
$58$	24956.9	−	24956.9i	0.127911	−	0.127911i
$59$		−	46091.2i		−	0.224420i	−0.993685	−	0.112210i	$-0.964207\pi$
$59$		−	46091.2i		−	0.224420i	0.993685	−	0.112210i	$-0.0357930\pi$
$60$		0			0
$61$	−75611.9			−0.333120			−0.166560	−	0.986031i	$-0.553266\pi$
$61$	−75611.9			−0.333120			−0.166560	+	0.986031i	$0.553266\pi$
$62$	150277.	+	150277.i	0.630545	+	0.630545i
$63$	157009.	−	157009.i	0.627918	−	0.627918i
$64$		−	279990.i		−	1.06808i
$65$		0			0
$66$	−5006.11			−0.0174128
$67$	−154883.	−	154883.i	−0.514966	−	0.514966i	0.401078	−	0.916044i	$-0.368636\pi$
$67$	−154883.	−	154883.i	−0.514966	−	0.514966i	−0.916044	+	0.401078i	$0.868636\pi$
$68$	−29529.1	+	29529.1i	−0.0939127	+	0.0939127i
$69$			6161.91i			0.0187572i
$70$		0			0
$71$	184000.			0.514095			0.257048	−	0.966399i	$-0.417250\pi$
$71$	184000.			0.514095			0.257048	+	0.966399i	$0.417250\pi$
$72$	−287175.	−	287175.i	−0.769394	−	0.769394i
$73$	−301029.	+	301029.i	−0.773819	+	0.773819i	−0.978772	−	0.204953i	$-0.934296\pi$
$73$	−301029.	+	301029.i	−0.773819	+	0.773819i	0.204953	+	0.978772i	$0.434296\pi$
$74$			518848.i			1.28040i
$75$		0			0
$76$	−201169.			−0.458268
$77$	285788.	+	285788.i	0.625995	+	0.625995i
$78$	−5434.82	+	5434.82i	−0.0114525	+	0.0114525i
$79$			178743.i			0.362532i	0.983434	+	0.181266i	$0.0580195\pi$
$79$			178743.i			0.362532i	−0.983434	+	0.181266i	$0.941980\pi$
$80$		0			0
$81$	−530701.			−0.998608
$82$	−81489.6	−	81489.6i	−0.147795	−	0.147795i
$83$	−565063.	+	565063.i	−0.988240	+	0.988240i	−0.999932	−	0.0116912i	$-0.996278\pi$
$83$	−565063.	+	565063.i	−0.988240	+	0.988240i	0.0116912	+	0.999932i	$0.496278\pi$
$84$		−	3879.30i		−	0.00654509i
$85$		0			0
$86$	−58681.4			−0.0922582
$87$	−2236.83	−	2236.83i	−0.00339684	−	0.00339684i
$88$	522715.	−	522715.i	0.767038	−	0.767038i
$89$			249057.i			0.353289i	0.984275	+	0.176644i	$0.0565242\pi$
$89$			249057.i			0.353289i	−0.984275	+	0.176644i	$0.943476\pi$
$90$		0			0
$91$	620523.			0.823443
$92$	−163962.	−	163962.i	−0.210561	−	0.210561i
$93$	13468.9	−	13468.9i	0.0167450	−	0.0167450i
$94$		−	323963.i		−	0.390043i
$95$		0			0
$96$	−12382.6			−0.0139958
$97$	−30626.2	−	30626.2i	−0.0335567	−	0.0335567i	0.690129	−	0.723686i	$-0.257554\pi$
$97$	−30626.2	−	30626.2i	−0.0335567	−	0.0335567i	−0.723686	+	0.690129i	$0.757554\pi$
$98$	−113751.	+	113751.i	−0.120858	+	0.120858i
$99$		−	966430.i		−	0.996013i
$100$		0			0
$101$	797915.			0.774448			0.387224	−	0.921986i	$-0.373434\pi$
$101$	797915.			0.774448			0.387224	+	0.921986i	$0.373434\pi$
$102$	−5092.32	−	5092.32i	−0.00479861	−	0.00479861i
$103$	1.44814e6	−	1.44814e6i	1.32526	−	1.32526i	0.415798	−	0.909457i	$-0.363502\pi$
$103$	1.44814e6	−	1.44814e6i	1.32526	−	1.32526i	0.909457	−	0.415798i	$-0.136498\pi$
$104$		−	1.13496e6i		−	1.00897i
$105$		0			0
$106$	−554321.			−0.465418
$107$	1.50954e6	+	1.50954e6i	1.23224	+	1.23224i	0.963102	+	0.269136i	$0.0867380\pi$
$107$	1.50954e6	+	1.50954e6i	1.23224	+	1.23224i	0.269136	+	0.963102i	$0.413262\pi$
$108$	−13121.4	+	13121.4i	−0.0104162	+	0.0104162i
$109$			1.32041e6i			1.01960i	0.860294	+	0.509798i	$0.170280\pi$
$109$			1.32041e6i			1.01960i	−0.860294	+	0.509798i	$0.829720\pi$
$110$		0			0
$111$	46503.1			0.0340027
$112$	−477530.	−	477530.i	−0.339897	−	0.339897i
$113$	−783429.	+	783429.i	−0.542955	+	0.542955i	−0.924394	−	0.381439i	$-0.875429\pi$
$113$	−783429.	+	783429.i	−0.542955	+	0.542955i	0.381439	+	0.924394i	$0.375429\pi$
$114$		−	34691.7i		−	0.0234159i
$115$		0			0
$116$	119039.			0.0762632
$117$	−1.04919e6	−	1.04919e6i	−0.655085	−	0.655085i
$118$	−211500.	+	211500.i	−0.128725	+	0.128725i
$119$			581419.i			0.345023i
$120$		0			0
$121$	−12466.7			−0.00703714
$122$	346962.	+	346962.i	0.191074	+	0.191074i
$123$	−7303.72	+	7303.72i	−0.00392490	+	0.00392490i
$124$			716787.i			0.375946i
$125$		0			0
$126$	−1.44094e6			−0.720336
$127$	456295.	+	456295.i	0.222759	+	0.222759i	0.809659	−	0.586901i	$-0.199652\pi$
$127$	456295.	+	456295.i	0.222759	+	0.222759i	−0.586901	+	0.809659i	$0.699652\pi$
$128$	−321353.	+	321353.i	−0.153233	+	0.153233i
$129$			5259.47i			0.00245004i
$130$		0			0
$131$	−580402.			−0.258176			−0.129088	−	0.991633i	$-0.541205\pi$
$131$	−580402.			−0.258176			−0.129088	+	0.991633i	$0.541205\pi$
$132$	−11939.0	−	11939.0i	−0.00519096	−	0.00519096i
$133$	−1.98047e6	+	1.98047e6i	−0.841809	+	0.841809i
$134$			1.42143e6i			0.590759i
$135$		0			0
$136$	1.06343e6			0.422760
$137$	−2.50818e6	−	2.50818e6i	−0.975431	−	0.975431i	0.0242745	−	0.999705i	$-0.492272\pi$
$137$	−2.50818e6	−	2.50818e6i	−0.975431	−	0.975431i	−0.999705	+	0.0242745i	$0.992272\pi$
$138$	28275.3	−	28275.3i	0.0107589	−	0.0107589i
$139$		−	3.08650e6i		−	1.14927i	−0.818409	−	0.574636i	$-0.805144\pi$
$139$		−	3.08650e6i		−	1.14927i	0.818409	−	0.574636i	$-0.194856\pi$
$140$		0			0
$141$	−29036.1			−0.0103581
$142$	−844327.	−	844327.i	−0.294880	−	0.294880i
$143$	1.90974e6	−	1.90974e6i	0.653079	−	0.653079i
$144$			1.61484e6i			0.540805i
$145$		0			0
$146$	2.76267e6			0.887710
$147$	10195.2	+	10195.2i	0.00320956	+	0.00320956i
$148$	−1.23740e6	+	1.23740e6i	−0.381701	+	0.381701i
$149$			1.18378e6i			0.357860i	0.983862	+	0.178930i	$0.0572635\pi$
$149$			1.18378e6i			0.357860i	−0.983862	+	0.178930i	$0.942736\pi$
$150$		0			0
$151$	−3.01484e6			−0.875656			−0.437828	−	0.899059i	$-0.644252\pi$
$151$	−3.01484e6			−0.875656			−0.437828	+	0.899059i	$0.644252\pi$
$152$	3.62235e6	+	3.62235e6i	1.03148	+	1.03148i
$153$	983073.	−	983073.i	0.274481	−	0.274481i
$154$		−	2.62280e6i		−	0.718130i
$155$		0			0
$156$	−25922.9			−0.00682826
$157$	965155.	+	965155.i	0.249401	+	0.249401i	0.820725	−	0.571324i	$-0.193570\pi$
$157$	965155.	+	965155.i	0.249401	+	0.249401i	−0.571324	+	0.820725i	$0.693570\pi$
$158$	820200.	−	820200.i	0.207945	−	0.207945i
$159$			49682.5i			0.0123598i
$160$		0			0
$161$	−3.22835e6			−0.773575
$162$	2.43524e6	+	2.43524e6i	0.572792	+	0.572792i
$163$	2.59213e6	−	2.59213e6i	0.598542	−	0.598542i	−0.341383	−	0.939924i	$-0.610895\pi$
$163$	2.59213e6	−	2.59213e6i	0.598542	−	0.598542i	0.939924	+	0.341383i	$0.110895\pi$
$164$		−	388688.i		−	0.0881190i
$165$		0			0
$166$	5.18584e6			1.13369
$167$	−2.49297e6	−	2.49297e6i	−0.535263	−	0.535263i	0.386871	−	0.922134i	$-0.373556\pi$
$167$	−2.49297e6	−	2.49297e6i	−0.535263	−	0.535263i	−0.922134	+	0.386871i	$0.873556\pi$
$168$	−69852.7	+	69852.7i	−0.0147318	+	0.0147318i
$169$			680249.i			0.140931i
$170$		0			0
$171$	6.69724e6			1.33939
$172$	−139949.	−	139949.i	−0.0275032	−	0.0275032i
$173$	−1.00408e6	+	1.00408e6i	−0.193923	+	0.193923i	−0.797389	−	0.603466i	$-0.793786\pi$
$173$	−1.00408e6	+	1.00408e6i	−0.193923	+	0.193923i	0.603466	+	0.797389i	$0.293786\pi$
$174$			20528.4i			0.00389678i
$175$		0			0
$176$	−2.93932e6			−0.539149
$177$	18956.2	+	18956.2i	0.00341847	+	0.00341847i
$178$	1.14286e6	−	1.14286e6i	0.202643	−	0.202643i
$179$		−	8.39831e6i		−	1.46431i	−0.681139	−	0.732154i	$-0.738515\pi$
$179$		−	8.39831e6i		−	1.46431i	0.681139	−	0.732154i	$-0.261485\pi$
$180$		0			0
$181$	−8.17816e6			−1.37918			−0.689588	−	0.724202i	$-0.742208\pi$
$181$	−8.17816e6			−1.37918			−0.689588	+	0.724202i	$0.742208\pi$
$182$	−2.84741e6	−	2.84741e6i	−0.472319	−	0.472319i
$183$	31097.4	−	31097.4i	0.00507424	−	0.00507424i
$184$			5.90475e6i			0.947869i
$185$		0			0
$186$	−123610.			−0.0192095
$187$	1.78939e6	+	1.78939e6i	0.273640	+	0.273640i
$188$	772618.	−	772618.i	0.116276	−	0.116276i
$189$			258357.i			0.0382679i
$190$		0			0
$191$	6.45566e6			0.926489			0.463245	−	0.886230i	$-0.346685\pi$
$191$	6.45566e6			0.926489			0.463245	+	0.886230i	$0.346685\pi$
$192$	115154.	+	115154.i	0.0162695	+	0.0162695i
$193$	−6.32306e6	+	6.32306e6i	−0.879539	+	0.879539i	−0.993487	−	0.113948i	$-0.963650\pi$
$193$	−6.32306e6	+	6.32306e6i	−0.879539	+	0.879539i	0.113948	+	0.993487i	$0.463650\pi$
$194$			281071.i			0.0384955i
$195$		0			0
$196$	−542568.			−0.0720586
$197$	−4.61427e6	−	4.61427e6i	−0.603538	−	0.603538i	0.337712	−	0.941250i	$-0.390347\pi$
$197$	−4.61427e6	−	4.61427e6i	−0.603538	−	0.603538i	−0.941250	+	0.337712i	$0.890347\pi$
$198$	−4.43468e6	+	4.43468e6i	−0.571303	+	0.571303i
$199$			9.33452e6i			1.18449i	0.805756	+	0.592247i	$0.201759\pi$
$199$			9.33452e6i			1.18449i	−0.805756	+	0.592247i	$0.798241\pi$
$200$		0			0
$201$	127399.			0.0156884
$202$	−3.66141e6	−	3.66141e6i	−0.444216	−	0.444216i
$203$	1.17192e6	−	1.17192e6i	0.140091	−	0.140091i
$204$		−	24289.3i		−	0.00286104i
$205$		0			0
$206$	−1.32902e7			−1.52031
$207$	5.45855e6	+	5.45855e6i	0.615412	+	0.615412i
$208$	−3.19103e6	+	3.19103e6i	−0.354602	+	0.354602i
$209$			1.21903e7i			1.33529i
$210$		0			0
$211$	2.21170e6			0.235439			0.117720	−	0.993047i	$-0.462442\pi$
$211$	2.21170e6			0.235439			0.117720	+	0.993047i	$0.462442\pi$
$212$	−1.32200e6	−	1.32200e6i	−0.138747	−	0.138747i
$213$	−75675.0	+	75675.0i	−0.00783094	+	0.00783094i
$214$		−	1.38538e7i		−	1.41360i
$215$		0			0
$216$	472543.			0.0468900
$217$	7.05664e6	+	7.05664e6i	0.690588	+	0.690588i
$218$	6.05898e6	−	6.05898e6i	0.584831	−	0.584831i
$219$		−	247612.i		−	0.0235743i
$220$		0			0
$221$	3.88525e6			0.359950
$222$	−213390.	−	213390.i	−0.0195036	−	0.0195036i
$223$	5.52712e6	−	5.52712e6i	0.498407	−	0.498407i	−0.412535	−	0.910942i	$-0.635356\pi$
$223$	5.52712e6	−	5.52712e6i	0.498407	−	0.498407i	0.910942	+	0.412535i	$0.135356\pi$
$224$		−	6.48748e6i		−	0.577208i
$225$		0			0
$226$	7.18988e6			0.622868
$227$	−2.23679e6	−	2.23679e6i	−0.191227	−	0.191227i	0.604999	−	0.796226i	$-0.293173\pi$
$227$	−2.23679e6	−	2.23679e6i	−0.191227	−	0.191227i	−0.796226	+	0.604999i	$0.793173\pi$
$228$	82736.0	−	82736.0i	0.00698055	−	0.00698055i
$229$		−	8.27450e6i		−	0.689025i	−0.938782	−	0.344513i	$-0.888044\pi$
$229$		−	8.27450e6i		−	0.689025i	0.938782	−	0.344513i	$-0.111956\pi$
$230$		0			0
$231$	−235075.			−0.0190709
$232$	−2.14348e6	−	2.14348e6i	−0.171654	−	0.171654i
$233$	2.68203e6	−	2.68203e6i	0.212029	−	0.212029i	−0.593100	−	0.805129i	$-0.702096\pi$
$233$	2.68203e6	−	2.68203e6i	0.212029	−	0.212029i	0.805129	+	0.593100i	$0.202096\pi$
$234$			9.62890e6i			0.751500i
$235$		0			0
$236$	−1.00881e6			−0.0767490
$237$	−73512.6	−	73512.6i	−0.00552226	−	0.00552226i
$238$	2.66797e6	−	2.66797e6i	0.197902	−	0.197902i
$239$		−	1.80178e7i		−	1.31980i	−0.751352	−	0.659902i	$-0.770598\pi$
$239$		−	1.80178e7i		−	1.31980i	0.751352	−	0.659902i	$-0.229402\pi$
$240$		0			0
$241$	2.39062e7			1.70789			0.853945	−	0.520363i	$-0.174203\pi$
$241$	2.39062e7			1.70789			0.853945	+	0.520363i	$0.174203\pi$
$242$	57206.3	+	57206.3i	0.00403644	+	0.00403644i
$243$	655302.	−	655302.i	0.0456691	−	0.0456691i
$244$			1.65494e6i			0.113923i
$245$		0			0
$246$	67029.5			0.00450258
$247$	1.32342e7	+	1.32342e7i	0.878229	+	0.878229i
$248$	1.29068e7	−	1.29068e7i	0.846184	−	0.846184i
$249$		−	464794.i		−	0.0301067i
$250$		0			0
$251$	−2.61747e7			−1.65524			−0.827620	−	0.561289i	$-0.810306\pi$
$251$	−2.61747e7			−1.65524			−0.827620	+	0.561289i	$0.810306\pi$
$252$	−3.43649e6	−	3.43649e6i	−0.214741	−	0.214741i
$253$	−9.93564e6	+	9.93564e6i	−0.613528	+	0.613528i
$254$		−	4.18762e6i		−	0.255544i
$255$		0			0
$256$	−1.49702e7			−0.892293
$257$	−6.82647e6	−	6.82647e6i	−0.402158	−	0.402158i	0.476835	−	0.878993i	$-0.341784\pi$
$257$	−6.82647e6	−	6.82647e6i	−0.402158	−	0.402158i	−0.878993	+	0.476835i	$0.841784\pi$
$258$	24134.3	−	24134.3i	0.00140532	−	0.00140532i
$259$			2.43639e7i			1.40232i
$260$		0			0
$261$	−3.96300e6			−0.222896
$262$	2.66331e6	+	2.66331e6i	0.148087	+	0.148087i
$263$	−2.01956e7	+	2.01956e7i	−1.11017	+	1.11017i	−0.117045	+	0.993127i	$0.537342\pi$
$263$	−2.01956e7	+	2.01956e7i	−1.11017	+	1.11017i	−0.993127	+	0.117045i	$0.962658\pi$
$264$			429961.i			0.0233678i
$265$		0			0
$266$	1.81757e7			0.965707
$267$	−102432.	−	102432.i	−0.00538146	−	0.00538146i
$268$	−3.38996e6	+	3.38996e6i	−0.176112	+	0.176112i
$269$			1.52094e7i			0.781368i	0.920525	+	0.390684i	$0.127762\pi$
$269$			1.52094e7i			0.781368i	−0.920525	+	0.390684i	$0.872238\pi$
$270$		0			0
$271$	1.17759e7			0.591677			0.295838	−	0.955238i	$-0.404401\pi$
$271$	1.17759e7			0.591677			0.295838	+	0.955238i	$0.404401\pi$
$272$	−2.98994e6	−	2.98994e6i	−0.148578	−	0.148578i
$273$	−255207.	+	255207.i	−0.0125431	+	0.0125431i
$274$			2.30187e7i			1.11900i
$275$		0			0
$276$	134867.			0.00641474
$277$	−1.37835e7	−	1.37835e7i	−0.648515	−	0.648515i	0.304119	−	0.952634i	$-0.401638\pi$
$277$	−1.37835e7	−	1.37835e7i	−0.648515	−	0.648515i	−0.952634	+	0.304119i	$0.901638\pi$
$278$	−1.41631e7	+	1.41631e7i	−0.659211	+	0.659211i
$279$		−	2.38630e7i		−	1.09878i
$280$		0			0
$281$	−2.56366e7			−1.15543			−0.577713	−	0.816240i	$-0.696055\pi$
$281$	−2.56366e7			−1.15543			−0.577713	+	0.816240i	$0.696055\pi$
$282$	133238.	+	133238.i	0.00594131	+	0.00594131i
$283$	1.99807e7	−	1.99807e7i	0.881559	−	0.881559i	−0.112134	−	0.993693i	$-0.535769\pi$
$283$	1.99807e7	−	1.99807e7i	0.881559	−	0.881559i	0.993693	+	0.112134i	$0.0357687\pi$
$284$		−	4.02726e6i		−	0.175814i
$285$		0			0
$286$	−1.75265e7			−0.749199
$287$	−3.82657e6	−	3.82657e6i	−0.161869	−	0.161869i
$288$	−1.09692e7	+	1.09692e7i	−0.459194	+	0.459194i
$289$		−	2.04972e7i		−	0.849181i
$290$		0			0
$291$	25191.7			0.00102230
$292$	6.58869e6	+	6.58869e6i	0.264637	+	0.264637i
$293$	5.27401e6	−	5.27401e6i	0.209671	−	0.209671i	−0.594457	−	0.804128i	$-0.702633\pi$
$293$	5.27401e6	−	5.27401e6i	0.209671	−	0.209671i	0.804128	+	0.594457i	$0.202633\pi$
$294$		−	93566.1i		−	0.00368194i
$295$		0			0
$296$	4.45624e7			1.71828
$297$	795125.	+	795125.i	0.0303505	+	0.0303505i
$298$	5.43205e6	−	5.43205e6i	0.205265	−	0.205265i
$299$			2.15730e7i			0.807043i
$300$		0			0
$301$	−2.75554e6			−0.101043
$302$	1.38343e7	+	1.38343e7i	0.502268	+	0.502268i
$303$	−328164.	+	328164.i	−0.0117968	+	0.0117968i
$304$		−	2.03691e7i		−	0.725022i
$305$		0			0
$306$	−9.02210e6			−0.314879
$307$	−3.02867e7	−	3.02867e7i	−1.04674	−	1.04674i	−0.998853	−	0.0478836i	$-0.984752\pi$
$307$	−3.02867e7	−	3.02867e7i	−1.04674	−	1.04674i	−0.0478836	−	0.998853i	$-0.515248\pi$
$308$	6.25510e6	−	6.25510e6i	0.214083	−	0.214083i
$309$			1.19117e6i			0.0403738i
$310$		0			0
$311$	1.87774e7			0.624244			0.312122	−	0.950042i	$-0.398960\pi$
$311$	1.87774e7			0.624244			0.312122	+	0.950042i	$0.398960\pi$
$312$	466781.	+	466781.i	0.0153691	+	0.0153691i
$313$	2.13347e7	−	2.13347e7i	0.695750	−	0.695750i	−0.267741	−	0.963491i	$-0.586277\pi$
$313$	2.13347e7	−	2.13347e7i	0.695750	−	0.695750i	0.963491	+	0.267741i	$0.0862772\pi$
$314$		−	8.85766e6i		−	0.286108i
$315$		0			0
$316$	3.91218e6			0.123982
$317$	4.19358e7	+	4.19358e7i	1.31646	+	1.31646i	0.916558	+	0.399901i	$0.130955\pi$
$317$	4.19358e7	+	4.19358e7i	1.31646	+	1.31646i	0.399901	+	0.916558i	$0.369045\pi$
$318$	227979.	−	227979.i	0.00708947	−	0.00708947i
$319$		−	7.21345e6i		−	0.222214i
$320$		0			0
$321$	−1.24168e6			−0.0375400
$322$	1.48140e7	+	1.48140e7i	0.443715	+	0.443715i
$323$	−1.24002e7	+	1.24002e7i	−0.367978	+	0.367978i
$324$			1.16156e7i			0.341512i
$325$		0			0
$326$	−2.37892e7			−0.686636
$327$	−543053.	−	543053.i	−0.0155310	−	0.0155310i
$328$	−6.99892e6	+	6.99892e6i	−0.198340	+	0.198340i
$329$		−	1.52126e7i		−	0.427184i
$330$		0			0
$331$	−2.36910e7			−0.653279			−0.326640	−	0.945149i	$-0.605916\pi$
$331$	−2.36910e7			−0.653279			−0.326640	+	0.945149i	$0.605916\pi$
$332$	1.23677e7	+	1.23677e7i	0.337966	+	0.337966i
$333$	4.11949e7	−	4.11949e7i	1.11561	−	1.11561i
$334$			2.28791e7i			0.614044i
$335$		0			0
$336$	392794.			0.0103549
$337$	4.12007e6	+	4.12007e6i	0.107650	+	0.107650i	0.758880	−	0.651230i	$-0.225747\pi$
$337$	4.12007e6	+	4.12007e6i	0.107650	+	0.107650i	−0.651230	+	0.758880i	$0.725747\pi$
$338$	3.12147e6	−	3.12147e6i	0.0808369	−	0.0808369i
$339$		−	644412.i		−	0.0165411i
$340$		0			0
$341$	4.34354e7			1.09542
$342$	−3.07318e7	−	3.07318e7i	−0.768262	−	0.768262i
$343$	−3.06920e7	+	3.06920e7i	−0.760577	+	0.760577i
$344$			5.03998e6i			0.123809i
$345$		0			0
$346$	9.21487e6			0.222465
$347$	−3.58847e7	−	3.58847e7i	−0.858857	−	0.858857i	0.132347	−	0.991203i	$-0.457749\pi$
$347$	−3.58847e7	−	3.58847e7i	−0.858857	−	0.858857i	−0.991203	+	0.132347i	$0.957749\pi$
$348$	−48957.9	+	48957.9i	−0.00116168	+	0.00116168i
$349$		−	5.38706e7i		−	1.26729i	−0.773624	−	0.633645i	$-0.781558\pi$
$349$		−	5.38706e7i		−	1.26729i	0.773624	−	0.633645i	$-0.218442\pi$
$350$		0			0
$351$	1.72643e6			0.0399235
$352$	−1.99660e7	−	1.99660e7i	−0.457788	−	0.457788i
$353$	−9.94346e6	+	9.94346e6i	−0.226055	+	0.226055i	−0.811042	−	0.584988i	$-0.801099\pi$
$353$	−9.94346e6	+	9.94346e6i	−0.226055	+	0.226055i	0.584988	+	0.811042i	$0.301099\pi$
$354$		−	173970.i		−	0.00392161i
$355$		0			0
$356$	5.45118e6			0.120820
$357$	−239124.	−	239124.i	−0.00525555	−	0.00525555i
$358$	−3.85375e7	+	3.85375e7i	−0.839913	+	0.839913i
$359$			8.32978e7i			1.80032i	0.435556	+	0.900162i	$0.356552\pi$
$359$			8.32978e7i			1.80032i	−0.435556	+	0.900162i	$0.643448\pi$
$360$		0			0
$361$	−3.74313e7			−0.795633
$362$	3.75273e7	+	3.75273e7i	0.791082	+	0.791082i
$363$	5127.27	−	5127.27i	0.000107193	−	0.000107193i
$364$		−	1.35815e7i		−	0.281608i
$365$		0			0
$366$	−285395.			−0.00582107
$367$	−6.36276e6	−	6.36276e6i	−0.128720	−	0.128720i	0.639811	−	0.768532i	$-0.279012\pi$
$367$	−6.36276e6	−	6.36276e6i	−0.128720	−	0.128720i	−0.768532	+	0.639811i	$0.779012\pi$
$368$	1.66017e7	−	1.66017e7i	0.333127	−	0.333127i
$369$			1.29401e7i			0.257547i
$370$		0			0
$371$	−2.60296e7			−0.509737
$372$	−294798.	−	294798.i	−0.00572658	−	0.00572658i
$373$	4.79779e6	−	4.79779e6i	0.0924517	−	0.0924517i	−0.659368	−	0.751820i	$-0.729176\pi$
$373$	4.79779e6	−	4.79779e6i	0.0924517	−	0.0924517i	0.751820	+	0.659368i	$0.229176\pi$
$374$		−	1.64220e7i		−	0.313915i
$375$		0			0
$376$	−2.78243e7			−0.523432
$377$	−7.83118e6	−	7.83118e6i	−0.146152	−	0.146152i
$378$	1.18553e6	−	1.18553e6i	0.0219501	−	0.0219501i
$379$			1.31093e6i			0.0240803i	0.999928	+	0.0120401i	$0.00383259\pi$
$379$			1.31093e6i			0.0240803i	−0.999928	+	0.0120401i	$0.996167\pi$
$380$		0			0
$381$	−375327.			−0.00678632
$382$	−2.96232e7	−	2.96232e7i	−0.531425	−	0.531425i
$383$	−5.50901e7	+	5.50901e7i	−0.980566	+	0.980566i	−0.999815	−	0.0192483i	$-0.993873\pi$
$383$	−5.50901e7	+	5.50901e7i	−0.980566	+	0.980566i	0.0192483	+	0.999815i	$0.493873\pi$
$384$		−	264330.i		−	0.00466823i
$385$		0			0
$386$	5.80295e7			1.00899
$387$	4.65912e6	+	4.65912e6i	0.0803843	+	0.0803843i
$388$	−670324.	+	670324.i	−0.0114760	+	0.0114760i
$389$			3.10657e7i			0.527755i	0.964556	+	0.263877i	$0.0850014\pi$
$389$			3.10657e7i			0.527755i	−0.964556	+	0.263877i	$0.914999\pi$
$390$		0			0
$391$	−2.02135e7			−0.338151
$392$	9.76975e6	+	9.76975e6i	0.162190	+	0.162190i
$393$	238706.	−	238706.i	0.00393265	−	0.00393265i
$394$			4.23472e7i			0.692367i
$395$		0			0
$396$	−2.11525e7			−0.340624
$397$	2.74272e7	+	2.74272e7i	0.438339	+	0.438339i	0.891453	−	0.453114i	$-0.149687\pi$
$397$	2.74272e7	+	2.74272e7i	0.438339	+	0.438339i	−0.453114	+	0.891453i	$0.649687\pi$
$398$	4.28335e7	−	4.28335e7i	0.679414	−	0.679414i
$399$		−	1.62904e6i		−	0.0256456i
$400$		0			0
$401$	5.39359e7			0.836459			0.418230	−	0.908341i	$-0.362651\pi$
$401$	5.39359e7			0.836459			0.418230	+	0.908341i	$0.362651\pi$
$402$	−584600.	−	584600.i	−0.00899872	−	0.00899872i
$403$	4.71551e7	−	4.71551e7i	0.720465	−	0.720465i
$404$		−	1.74642e7i		−	0.264852i
$405$		0			0
$406$	−1.07552e7			−0.160709
$407$	7.49829e7	+	7.49829e7i	1.11219	+	1.11219i
$408$	−437365.	+	437365.i	−0.00643968	+	0.00643968i
$409$		−	8.00992e7i		−	1.17073i	−0.810769	−	0.585367i	$-0.800951\pi$
$409$		−	8.00992e7i		−	1.17073i	0.810769	−	0.585367i	$-0.199049\pi$
$410$		0			0
$411$	2.06311e6			0.0297164
$412$	−3.16958e7	−	3.16958e7i	−0.453221	−	0.453221i
$413$	−9.93154e6	+	9.93154e6i	−0.140983	+	0.140983i
$414$		−	5.00955e7i		−	0.705989i
$415$		0			0
$416$	−4.33517e7			−0.602180
$417$	1.26941e6	+	1.26941e6i	0.0175062	+	0.0175062i
$418$	5.59379e7	−	5.59379e7i	0.765909	−	0.765909i
$419$		−	7.63894e7i		−	1.03846i	−0.854634	−	0.519231i	$-0.826218\pi$
$419$		−	7.63894e7i		−	1.03846i	0.854634	−	0.519231i	$-0.173782\pi$
$420$		0			0
$421$	8.62618e7			1.15604			0.578019	−	0.816023i	$-0.303826\pi$
$421$	8.62618e7			1.15604			0.578019	+	0.816023i	$0.303826\pi$
$422$	−1.01489e7	−	1.01489e7i	−0.135046	−	0.135046i
$423$	−2.57217e7	+	2.57217e7i	−0.339843	+	0.339843i
$424$			4.76091e7i			0.624586i
$425$		0			0
$426$	694504.			0.00898350
$427$	1.62925e7	+	1.62925e7i	0.209269	+	0.209269i
$428$	3.30398e7	−	3.30398e7i	0.421411	−	0.421411i
$429$			1.57086e6i			0.0198960i
$430$		0			0
$431$	1.52887e7			0.190959			0.0954795	−	0.995431i	$-0.469562\pi$
$431$	1.52887e7			0.190959			0.0954795	+	0.995431i	$0.469562\pi$
$432$	−1.32860e6	−	1.32860e6i	−0.0164794	−	0.0164794i
$433$	3.40552e7	−	3.40552e7i	0.419489	−	0.419489i	−0.465539	−	0.885028i	$-0.654139\pi$
$433$	3.40552e7	−	3.40552e7i	0.419489	−	0.419489i	0.885028	+	0.465539i	$0.154139\pi$
$434$		−	6.47620e7i		−	0.792229i
$435$		0			0
$436$	2.89001e7			0.348690
$437$	−6.88527e7	−	6.88527e7i	−0.825043	−	0.825043i
$438$	−1.13622e6	+	1.13622e6i	−0.0135220	+	0.0135220i
$439$			7.90801e7i			0.934703i	0.884072	+	0.467351i	$0.154792\pi$
$439$			7.90801e7i			0.934703i	−0.884072	+	0.467351i	$0.845208\pi$
$440$		0			0
$441$	1.80630e7			0.210607
$442$	−1.78283e7	−	1.78283e7i	−0.206464	−	0.206464i
$443$	−5.21596e7	+	5.21596e7i	−0.599961	+	0.599961i	−0.940302	−	0.340341i	$-0.889458\pi$
$443$	−5.21596e7	+	5.21596e7i	−0.599961	+	0.599961i	0.340341	+	0.940302i	$0.389458\pi$
$444$		−	1.01782e6i		−	0.0116285i
$445$		0			0
$446$	−5.07249e7			−0.571763
$447$	−486862.	−	486862.i	−0.00545108	−	0.00545108i
$448$	−6.03312e7	+	6.03312e7i	−0.670978	+	0.670978i
$449$			7.16826e7i			0.791908i	0.918270	+	0.395954i	$0.129586\pi$
$449$			7.16826e7i			0.791908i	−0.918270	+	0.395954i	$0.870414\pi$
$450$		0			0
$451$	−2.35535e7			−0.256759
$452$	1.71471e7	+	1.71471e7i	0.185684	+	0.185684i
$453$	1.23993e6	−	1.23993e6i	0.0133384	−	0.0133384i
$454$			2.05281e7i			0.219372i
$455$		0			0
$456$	−2.97957e6			−0.0314239
$457$	9.43530e7	+	9.43530e7i	0.988570	+	0.988570i	0.999935	−	0.0113658i	$-0.00361792\pi$
$457$	9.43530e7	+	9.43530e7i	0.988570	+	0.988570i	−0.0113658	+	0.999935i	$0.503618\pi$
$458$	−3.79694e7	+	3.79694e7i	−0.395218	+	0.395218i
$459$			1.61764e6i			0.0167279i
$460$		0			0
$461$	−1.52870e8			−1.56034			−0.780168	−	0.625570i	$-0.784867\pi$
$461$	−1.52870e8			−1.56034			−0.780168	+	0.625570i	$0.784867\pi$
$462$	1.07870e6	+	1.07870e6i	0.0109389	+	0.0109389i
$463$	8.33930e6	−	8.33930e6i	0.0840207	−	0.0840207i	−0.663847	−	0.747868i	$-0.731078\pi$
$463$	8.33930e6	−	8.33930e6i	0.0840207	−	0.0840207i	0.747868	+	0.663847i	$0.231078\pi$
$464$			1.20532e7i			0.120655i
$465$		0			0
$466$	−2.46142e7			−0.243236
$467$	−9.10189e7	−	9.10189e7i	−0.893678	−	0.893678i	0.101189	−	0.994867i	$-0.467735\pi$
$467$	−9.10189e7	−	9.10189e7i	−0.893678	−	0.893678i	−0.994867	+	0.101189i	$0.967735\pi$
$468$	−2.29639e7	+	2.29639e7i	−0.224031	+	0.224031i
$469$			6.67470e7i			0.647014i
$470$		0			0
$471$	−793891.			−0.00759798
$472$	1.81651e7	+	1.81651e7i	0.172748	+	0.172748i
$473$	−8.48053e6	+	8.48053e6i	−0.0801382	+	0.0801382i
$474$			674658.i			0.00633503i
$475$		0			0
$476$	1.27256e7			0.117994
$477$	4.40114e7	+	4.40114e7i	0.405518	+	0.405518i
$478$	−8.26789e7	+	8.26789e7i	−0.757027	+	0.757027i
$479$			1.10830e8i			1.00845i	0.863574	+	0.504223i	$0.168221\pi$
$479$			1.10830e8i			1.00845i	−0.863574	+	0.504223i	$0.831779\pi$
$480$		0			0
$481$	1.62808e8			1.46299
$482$	−1.09699e8	−	1.09699e8i	−0.979630	−	0.979630i
$483$	1.32774e6	−	1.32774e6i	0.0117835	−	0.0117835i
$484$			272862.i			0.00240662i
$485$		0			0
$486$	−6.01400e6			−0.0523907
$487$	−4.44091e7	−	4.44091e7i	−0.384490	−	0.384490i	0.488227	−	0.872717i	$-0.337644\pi$
$487$	−4.44091e7	−	4.44091e7i	−0.384490	−	0.384490i	−0.872717	+	0.488227i	$0.837644\pi$
$488$	2.97996e7	−	2.97996e7i	0.256420	−	0.256420i
$489$			2.13217e6i			0.0182345i
$490$		0			0
$491$	−4.56855e7			−0.385953			−0.192976	−	0.981203i	$-0.561814\pi$
$491$	−4.56855e7			−0.385953			−0.192976	+	0.981203i	$0.561814\pi$
$492$	159858.	+	159858.i	0.00134227	+	0.00134227i
$493$	7.33767e6	−	7.33767e6i	0.0612375	−	0.0612375i
$494$		−	1.21456e8i		−	1.00749i
$495$		0			0
$496$	−7.25774e7			−0.594780
$497$	−3.96477e7	−	3.96477e7i	−0.322960	−	0.322960i
$498$	−2.13281e6	+	2.13281e6i	−0.0172689	+	0.0172689i
$499$		−	1.98876e8i		−	1.60059i	−0.599604	−	0.800297i	$-0.704675\pi$
$499$		−	1.98876e8i		−	1.60059i	0.599604	−	0.800297i	$-0.295325\pi$
$500$		0			0
$501$	2.05060e6			0.0163068
$502$	1.20109e8	+	1.20109e8i	0.949430	+	0.949430i
$503$	1.40471e8	−	1.40471e8i	1.10378	−	1.10378i	0.109831	−	0.993950i	$-0.464969\pi$
$503$	1.40471e8	−	1.40471e8i	1.10378	−	1.10378i	0.993950	−	0.109831i	$-0.0350309\pi$
$504$			1.23759e8i			0.966682i
$505$		0			0
$506$	9.11838e7			0.703827
$507$	−279770.	−	279770.i	−0.00214673	−	0.00214673i
$508$	9.98703e6	−	9.98703e6i	0.0761807	−	0.0761807i
$509$		−	2.05461e8i		−	1.55803i	−0.627005	−	0.779015i	$-0.715719\pi$
$509$		−	2.05461e8i		−	1.55803i	0.627005	−	0.779015i	$-0.284281\pi$
$510$		0			0
$511$	1.29729e8			0.972241
$512$	8.92607e7	+	8.92607e7i	0.665044	+	0.665044i
$513$	−5.51011e6	+	5.51011e6i	−0.0408139	+	0.0408139i
$514$			6.26496e7i			0.461348i
$515$		0			0
$516$	115115.			0.000837884
$517$	−4.68186e7	−	4.68186e7i	−0.338802	−	0.338802i
$518$	1.11799e8	−	1.11799e8i	0.804358	−	0.804358i
$519$		−	825908.i		−	0.00590785i
$520$		0			0
$521$	−2.38512e8			−1.68654			−0.843271	−	0.537488i	$-0.819373\pi$
$521$	−2.38512e8			−1.68654			−0.843271	+	0.537488i	$0.819373\pi$
$522$	1.81851e7	+	1.81851e7i	0.127851	+	0.127851i
$523$	−5.77184e7	+	5.77184e7i	−0.403468	+	0.403468i	−0.879453	−	0.475985i	$-0.842092\pi$
$523$	−5.77184e7	+	5.77184e7i	−0.403468	+	0.403468i	0.475985	+	0.879453i	$0.342092\pi$
$524$			1.27034e7i			0.0882930i
$525$		0			0
$526$	1.85344e8			1.27357
$527$	4.41834e7	+	4.41834e7i	0.301875	+	0.301875i
$528$	1.20887e6	−	1.20887e6i	0.00821257	−	0.00821257i
$529$			3.57998e7i			0.241832i
$530$		0			0
$531$	3.35849e7			0.224316
$532$	4.33470e7	+	4.33470e7i	0.287889	+	0.287889i
$533$	−2.55705e7	+	2.55705e7i	−0.168872	+	0.168872i
$534$			940060.i			0.00617350i
$535$		0			0
$536$	1.22083e8			0.792792
$537$	3.45403e6	+	3.45403e6i	0.0223050	+	0.0223050i
$538$	6.97918e7	−	6.97918e7i	0.448185	−	0.448185i
$539$			3.28782e7i			0.209962i
$540$		0			0
$541$	−1.95129e8			−1.23234			−0.616169	−	0.787614i	$-0.711316\pi$
$541$	−1.95129e8			−1.23234			−0.616169	+	0.787614i	$0.711316\pi$
$542$	−5.40361e7	−	5.40361e7i	−0.339380	−	0.339380i
$543$	3.36348e6	−	3.36348e6i	0.0210083	−	0.0210083i
$544$		−	4.06198e7i		−	0.252314i
$545$		0			0
$546$	2.34214e6			0.0143892
$547$	−3.48848e7	−	3.48848e7i	−0.213145	−	0.213145i	0.592457	−	0.805602i	$-0.298158\pi$
$547$	−3.48848e7	−	3.48848e7i	−0.213145	−	0.213145i	−0.805602	+	0.592457i	$0.798158\pi$
$548$	−5.48971e7	+	5.48971e7i	−0.333586	+	0.333586i
$549$		−	5.50955e7i		−	0.332965i
$550$		0			0
$551$	4.99883e7			0.298822
$552$	−2.42849e6	−	2.42849e6i	−0.0144384	−	0.0144384i
$553$	3.85147e7	−	3.85147e7i	0.227746	−	0.227746i
$554$			1.26497e8i			0.743964i
$555$		0			0
$556$	−6.75551e7			−0.393037
$557$	−2.29154e7	−	2.29154e7i	−0.132606	−	0.132606i	0.637689	−	0.770294i	$-0.279891\pi$
$557$	−2.29154e7	−	2.29154e7i	−0.132606	−	0.132606i	−0.770294	+	0.637689i	$0.779891\pi$
$558$	−1.09501e8	+	1.09501e8i	−0.630252	+	0.630252i
$559$			1.84135e7i			0.105415i
$560$		0			0
$561$	−1.47187e6			−0.00833643
$562$	1.17639e8	+	1.17639e8i	0.662741	+	0.662741i
$563$	7.98554e7	−	7.98554e7i	0.447486	−	0.447486i	−0.447032	−	0.894518i	$-0.647519\pi$
$563$	7.98554e7	−	7.98554e7i	0.447486	−	0.447486i	0.894518	+	0.447032i	$0.147519\pi$
$564$			635519.i			0.00354235i
$565$		0			0
$566$	−1.83372e8			−1.01131
$567$	1.14353e8	+	1.14353e8i	0.627335	+	0.627335i
$568$	−7.25169e7	+	7.25169e7i	−0.395726	+	0.395726i
$569$			6.42351e7i			0.348687i	0.984685	+	0.174343i	$0.0557803\pi$
$569$			6.42351e7i			0.348687i	−0.984685	+	0.174343i	$0.944220\pi$
$570$		0			0
$571$	−1.63954e8			−0.880672			−0.440336	−	0.897833i	$-0.645141\pi$
$571$	−1.63954e8			−0.880672			−0.440336	+	0.897833i	$0.645141\pi$
$572$	−4.17989e7	−	4.17989e7i	−0.223345	−	0.223345i
$573$	−2.65506e6	+	2.65506e6i	−0.0141127	+	0.0141127i
$574$			3.51181e7i			0.185693i
$575$		0			0
$576$	2.04018e8			1.06758
$577$	−2.43201e8	−	2.43201e8i	−1.26601	−	1.26601i	−0.948130	−	0.317884i	$-0.897028\pi$
$577$	−2.43201e8	−	2.43201e8i	−1.26601	−	1.26601i	−0.317884	−	0.948130i	$-0.602972\pi$
$578$	−9.40558e7	+	9.40558e7i	−0.487082	+	0.487082i
$579$		−	5.20105e6i		−	0.0267951i
$580$		0			0
$581$	2.43515e8			1.24164
$582$	−115598.	−	115598.i	−0.000586382	−	0.000586382i
$583$	−8.01094e7	+	8.01094e7i	−0.404276	+	0.404276i
$584$		−	2.37278e8i		−	1.19130i
$585$		0			0
$586$	−4.84019e7			−0.240530
$587$	−1.89685e8	−	1.89685e8i	−0.937819	−	0.937819i	0.0603574	−	0.998177i	$-0.480776\pi$
$587$	−1.89685e8	−	1.89685e8i	−0.937819	−	0.937819i	−0.998177	+	0.0603574i	$0.980776\pi$
$588$	223145.	−	223145.i	0.00109763	−	0.00109763i
$589$			3.01002e8i			1.47307i
$590$		0			0
$591$	3.79548e6			0.0183867
$592$	−1.25291e8	−	1.25291e8i	−0.603886	−	0.603886i
$593$	−1.53385e8	+	1.53385e8i	−0.735561	+	0.735561i	−0.971715	−	0.236155i	$-0.924113\pi$
$593$	−1.53385e8	+	1.53385e8i	−0.735561	+	0.735561i	0.236155	+	0.971715i	$0.424113\pi$
$594$		−	7.29721e6i		−	0.0348175i
$595$		0			0
$596$	2.59097e7			0.122384
$597$	−3.83907e6	−	3.83907e6i	−0.0180428	−	0.0180428i
$598$	9.89925e7	−	9.89925e7i	0.462912	−	0.462912i
$599$		−	1.58011e8i		−	0.735201i	−0.929984	−	0.367601i	$-0.880179\pi$
$599$		−	1.58011e8i		−	0.735201i	0.929984	−	0.367601i	$-0.119821\pi$
$600$		0			0
$601$	−6.50644e7			−0.299723			−0.149861	−	0.988707i	$-0.547883\pi$
$601$	−6.50644e7			−0.299723			−0.149861	+	0.988707i	$0.547883\pi$
$602$	1.26444e7	+	1.26444e7i	0.0579575	+	0.0579575i
$603$	1.12857e8	−	1.12857e8i	0.514727	−	0.514727i
$604$			6.59865e7i			0.299464i
$605$		0			0
$606$	3.01171e6			0.0135330
$607$	2.99149e8	+	2.99149e8i	1.33759	+	1.33759i	0.898393	+	0.439192i	$0.144735\pi$
$607$	2.99149e8	+	2.99149e8i	1.33759	+	1.33759i	0.439192	+	0.898393i	$0.355265\pi$
$608$	1.38362e8	−	1.38362e8i	0.615611	−	0.615611i
$609$			963965.i			0.00426785i
$610$		0			0
$611$	−1.01656e8			−0.445666
$612$	−2.15168e7	−	2.15168e7i	−0.0938691	−	0.0938691i
$613$	−1.98366e8	+	1.98366e8i	−0.861164	+	0.861164i	−0.991473	−	0.130310i	$-0.958403\pi$
$613$	−1.98366e8	+	1.98366e8i	−0.861164	+	0.861164i	0.130310	+	0.991473i	$0.458403\pi$
$614$			2.77955e8i			1.20080i
$615$		0			0
$616$	−2.25265e8			−0.963722
$617$	2.29329e8	+	2.29329e8i	0.976347	+	0.976347i	0.999727	−	0.0233799i	$-0.00744274\pi$
$617$	2.29329e8	+	2.29329e8i	0.976347	+	0.976347i	−0.0233799	+	0.999727i	$0.507443\pi$
$618$	5.46597e6	−	5.46597e6i	0.0231580	−	0.0231580i
$619$		−	2.71801e8i		−	1.14598i	−0.819561	−	0.572992i	$-0.805783\pi$
$619$		−	2.71801e8i		−	1.14598i	0.819561	−	0.572992i	$-0.194217\pi$
$620$		0			0
$621$	−8.98198e6			−0.0375057
$622$	−8.61643e7	−	8.61643e7i	−0.358060	−	0.358060i
$623$	5.36659e7	−	5.36659e7i	0.221939	−	0.221939i
$624$		−	2.62479e6i		−	0.0108029i
$625$		0			0
$626$	−1.95798e8			−0.798151
$627$	−5.01358e6	−	5.01358e6i	−0.0203397	−	0.0203397i
$628$	2.11246e7	−	2.11246e7i	0.0852922	−	0.0852922i
$629$			1.52549e8i			0.612994i
$630$		0			0
$631$	4.20768e8			1.67477			0.837384	−	0.546615i	$-0.184084\pi$
$631$	4.20768e8			1.67477			0.837384	+	0.546615i	$0.184084\pi$
$632$	−7.04447e7	−	7.04447e7i	−0.279060	−	0.279060i
$633$	−909620.	+	909620.i	−0.00358632	+	0.00358632i
$634$		−	3.84864e8i		−	1.51022i
$635$		0			0
$636$	1.08741e6			0.00422691
$637$	3.56937e7	+	3.56937e7i	0.138094	+	0.138094i
$638$	−3.31005e7	+	3.31005e7i	−0.127460	+	0.127460i
$639$			1.34074e8i			0.513857i
$640$		0			0
$641$	2.64309e8			1.00355			0.501773	−	0.864999i	$-0.332681\pi$
$641$	2.64309e8			1.00355			0.501773	+	0.864999i	$0.332681\pi$
$642$	5.69773e6	+	5.69773e6i	0.0215326	+	0.0215326i
$643$	2.46084e8	−	2.46084e8i	0.925659	−	0.925659i	−0.0717631	−	0.997422i	$-0.522863\pi$
$643$	2.46084e8	−	2.46084e8i	0.925659	−	0.925659i	0.997422	+	0.0717631i	$0.0228626\pi$
$644$			7.06596e7i			0.264553i
$645$		0			0
$646$	1.13802e8			0.422138
$647$	2.80240e8	+	2.80240e8i	1.03471	+	1.03471i	0.999376	+	0.0353306i	$0.0112484\pi$
$647$	2.80240e8	+	2.80240e8i	1.03471	+	1.03471i	0.0353306	+	0.999376i	$0.488752\pi$
$648$	2.09156e8	−	2.09156e8i	0.768680	−	0.768680i
$649$			6.11311e7i			0.223629i
$650$		0			0
$651$	−5.80446e6			−0.0210387
$652$	−5.67346e7	−	5.67346e7i	−0.204694	−	0.204694i
$653$	−6.29176e7	+	6.29176e7i	−0.225961	+	0.225961i	−0.811003	−	0.585042i	$-0.801078\pi$
$653$	−6.29176e7	+	6.29176e7i	−0.225961	+	0.225961i	0.585042	+	0.811003i	$0.301078\pi$
$654$			4.98384e6i			0.0178168i
$655$		0			0
$656$	3.93562e7			0.139412
$657$	−2.19348e8	−	2.19348e8i	−0.773460	−	0.773460i
$658$	−6.98063e7	+	6.98063e7i	−0.245029	+	0.245029i
$659$		−	1.20587e8i		−	0.421351i	−0.977556	−	0.210676i	$-0.932434\pi$
$659$		−	1.20587e8i		−	0.421351i	0.977556	−	0.210676i	$-0.0675664\pi$
$660$		0			0
$661$	−7.06531e7			−0.244640			−0.122320	−	0.992491i	$-0.539033\pi$
$661$	−7.06531e7			−0.244640			−0.122320	+	0.992491i	$0.539033\pi$
$662$	1.08711e8	+	1.08711e8i	0.374715	+	0.374715i
$663$	−1.59791e6	+	1.59791e6i	−0.00548293	+	0.00548293i
$664$		−	4.45397e8i		−	1.52140i
$665$		0			0
$666$	−3.78064e8			−1.27980
$667$	4.07427e7	+	4.07427e7i	0.137300	+	0.137300i
$668$	−5.45642e7	+	5.45642e7i	−0.183054	+	0.183054i
$669$			4.54635e6i			0.0151839i
$670$		0			0
$671$	1.00285e8			0.331946
$672$	2.66815e6	+	2.66815e6i	0.00879230	+	0.00879230i
$673$	3.05643e7	−	3.05643e7i	0.100270	−	0.100270i	−0.655192	−	0.755462i	$-0.727412\pi$
$673$	3.05643e7	−	3.05643e7i	0.100270	−	0.100270i	0.755462	+	0.655192i	$0.227412\pi$
$674$		−	3.78117e7i		−	0.123494i
$675$		0			0
$676$	1.48888e7			0.0481968
$677$	−3.25627e7	−	3.25627e7i	−0.104943	−	0.104943i	0.652686	−	0.757629i	$-0.273642\pi$
$677$	−3.25627e7	−	3.25627e7i	−0.104943	−	0.104943i	−0.757629	+	0.652686i	$0.773642\pi$
$678$	−2.95703e6	+	2.95703e6i	−0.00948782	+	0.00948782i
$679$			1.31984e7i			0.0421612i
$680$		0			0
$681$	1.83988e6			0.00582571
$682$	−1.99313e8	−	1.99313e8i	−0.628323	−	0.628323i
$683$	3.30544e8	−	3.30544e8i	1.03745	−	1.03745i	0.0381800	−	0.999271i	$-0.487844\pi$
$683$	3.30544e8	−	3.30544e8i	1.03745	−	1.03745i	0.999271	−	0.0381800i	$-0.0121560\pi$
$684$		−	1.46584e8i		−	0.458056i
$685$		0			0
$686$	2.81674e8			0.872519
$687$	3.40311e6	+	3.40311e6i	0.0104956	+	0.0104956i
$688$	1.41703e7	−	1.41703e7i	0.0435126	−	0.0435126i
$689$			1.73939e8i			0.531790i
$690$		0			0
$691$	−1.82764e8			−0.553931			−0.276965	−	0.960880i	$-0.589329\pi$
$691$	−1.82764e8			−0.553931			−0.276965	+	0.960880i	$0.589329\pi$
$692$	2.19765e7	+	2.19765e7i	0.0663193	+	0.0663193i
$693$	−2.08242e8	+	2.08242e8i	−0.625705	+	0.625705i
$694$			3.29330e8i			0.985264i
$695$		0			0
$696$	1.76312e6			0.00522944
$697$	−2.39591e7	−	2.39591e7i	−0.0707574	−	0.0707574i
$698$	−2.47197e8	+	2.47197e8i	−0.726905	+	0.726905i
$699$			2.20611e6i			0.00645945i
$700$		0			0
$701$	9.24516e7			0.268386			0.134193	−	0.990955i	$-0.457156\pi$
$701$	9.24516e7			0.268386			0.134193	+	0.990955i	$0.457156\pi$
$702$	−7.92212e6	−	7.92212e6i	−0.0228997	−	0.0228997i
$703$	−5.19622e8	+	5.19622e8i	−1.49562	+	1.49562i
$704$			3.71354e8i			1.06431i
$705$		0			0
$706$	9.12556e7			0.259326
$707$	−1.71931e8	−	1.71931e8i	−0.486516	−	0.486516i
$708$	414899.	−	414899.i	0.00116908	−	0.00116908i
$709$			3.04366e8i			0.853999i	0.904252	+	0.427000i	$0.140429\pi$
$709$			3.04366e8i			0.853999i	−0.904252	+	0.427000i	$0.859571\pi$
$710$		0			0
$711$	−1.30243e8			−0.362364
$712$	−9.81567e7	−	9.81567e7i	−0.271944	−	0.271944i
$713$	−2.45330e8	+	2.45330e8i	−0.676834	+	0.676834i
$714$			2.19455e6i			0.00602907i
$715$		0			0
$716$	−1.83816e8			−0.500776
$717$	7.41032e6	+	7.41032e6i	0.0201039	+	0.0201039i
$718$	3.82231e8	−	3.82231e8i	1.03265	−	1.03265i
$719$		−	7.55310e7i		−	0.203207i	−0.994825	−	0.101604i	$-0.967603\pi$
$719$		−	7.55310e7i		−	0.203207i	0.994825	−	0.101604i	$-0.0323973\pi$
$720$		0			0
$721$	−6.24080e8			−1.66508
$722$	1.71762e8	+	1.71762e8i	0.456368	+	0.456368i
$723$	−9.83207e6	+	9.83207e6i	−0.0260154	+	0.0260154i
$724$			1.78997e8i			0.471662i
$725$		0			0
$726$	−47055.2			−0.000122970
$727$	7.46010e7	+	7.46010e7i	0.194152	+	0.194152i	0.797487	−	0.603336i	$-0.206162\pi$
$727$	7.46010e7	+	7.46010e7i	0.194152	+	0.194152i	−0.603336	+	0.797487i	$0.706162\pi$
$728$	−2.44556e8	+	2.44556e8i	−0.633847	+	0.633847i
$729$		−	3.86342e8i		−	0.997217i
$730$		0			0
$731$	−1.72531e7			−0.0441689
$732$	−680636.	−	680636.i	−0.00173533	−	0.00173533i
$733$	4.35999e8	−	4.35999e8i	1.10707	−	1.10707i	0.113531	−	0.993534i	$-0.463784\pi$
$733$	4.35999e8	−	4.35999e8i	1.10707	−	1.10707i	0.993534	−	0.113531i	$-0.0362162\pi$
$734$			5.83939e7i			0.147666i
$735$		0			0
$736$	2.25543e8			0.565712
$737$	2.05422e8	+	2.05422e8i	0.513151	+	0.513151i
$738$	5.93784e7	−	5.93784e7i	0.147727	−	0.147727i
$739$			3.93731e8i			0.975587i	0.872959	+	0.487794i	$0.162198\pi$
$739$			3.93731e8i			0.975587i	−0.872959	+	0.487794i	$0.837802\pi$
$740$		0			0
$741$	−1.08859e7			−0.0267552
$742$	1.19443e8	+	1.19443e8i	0.292380	+	0.292380i
$743$	−3.05130e8	+	3.05130e8i	−0.743906	+	0.743906i	−0.973327	−	0.229421i	$-0.926317\pi$
$743$	−3.05130e8	+	3.05130e8i	−0.743906	+	0.743906i	0.229421	+	0.973327i	$0.426317\pi$
$744$			1.06166e7i			0.0257789i
$745$		0			0
$746$	−4.40315e7			−0.106059
$747$	−4.11740e8	−	4.11740e8i	−0.987782	−	0.987782i
$748$	3.91648e7	−	3.91648e7i	0.0935816	−	0.0935816i
$749$		−	6.50541e8i		−	1.54821i
$750$		0			0
$751$	3.96683e8			0.936534			0.468267	−	0.883587i	$-0.344879\pi$
$751$	3.96683e8			0.936534			0.468267	+	0.883587i	$0.344879\pi$
$752$	7.82305e7	+	7.82305e7i	0.183960	+	0.183960i
$753$	1.07651e7	−	1.07651e7i	0.0252134	−	0.0252134i
$754$			7.18703e7i			0.167662i
$755$		0			0
$756$	5.65471e6			0.0130871
$757$	−1.91605e8	−	1.91605e8i	−0.441691	−	0.441691i	0.450889	−	0.892580i	$-0.351107\pi$
$757$	−1.91605e8	−	1.91605e8i	−0.441691	−	0.441691i	−0.892580	+	0.450889i	$0.851107\pi$
$758$	6.01549e6	−	6.01549e6i	0.0138122	−	0.0138122i
$759$		−	8.17259e6i		−	0.0186911i
$760$		0			0
$761$	5.82598e7			0.132195			0.0660975	−	0.997813i	$-0.478945\pi$
$761$	5.82598e7			0.132195			0.0660975	+	0.997813i	$0.478945\pi$
$762$	1.72227e6	+	1.72227e6i	0.00389257	+	0.00389257i
$763$	2.84516e8	−	2.84516e8i	0.640521	−	0.640521i
$764$		−	1.41296e8i		−	0.316848i
$765$		0			0
$766$	5.05586e8			1.12489
$767$	6.63662e7	+	6.63662e7i	0.147082	+	0.147082i
$768$	6.15689e6	−	6.15689e6i	0.0135918	−	0.0135918i
$769$		−	3.41834e8i		−	0.751687i	−0.926683	−	0.375843i	$-0.877353\pi$
$769$		−	3.41834e8i		−	0.751687i	0.926683	−	0.375843i	$-0.122647\pi$
$770$		0			0
$771$	5.61513e6			0.0122517
$772$	1.38394e8	+	1.38394e8i	0.300792	+	0.300792i
$773$	3.94613e8	−	3.94613e8i	0.854344	−	0.854344i	−0.136321	−	0.990665i	$-0.543528\pi$
$773$	3.94613e8	−	3.94613e8i	0.854344	−	0.854344i	0.990665	+	0.136321i	$0.0435277\pi$
$774$		−	4.27589e7i		−	0.0922153i
$775$		0			0
$776$	2.41404e7			0.0516606
$777$	−1.00203e7	−	1.00203e7i	−0.0213608	−	0.0213608i
$778$	1.42552e8	−	1.42552e8i	0.302715	−	0.302715i
$779$		−	1.63223e8i		−	0.345277i
$780$		0			0
$781$	−2.44041e8			−0.512283
$782$	9.27541e7	+	9.27541e7i	0.193960	+	0.193960i
$783$	3.26054e6	−	3.26054e6i	0.00679210	−	0.00679210i
$784$		−	5.49370e7i		−	0.114003i
$785$		0			0
$786$	−2.19071e6			−0.00451146
$787$	1.24249e7	+	1.24249e7i	0.0254899	+	0.0254899i	0.719737	−	0.694247i	$-0.244262\pi$
$787$	1.24249e7	+	1.24249e7i	0.0254899	+	0.0254899i	−0.694247	+	0.719737i	$0.744262\pi$
$788$	−1.00994e8	+	1.00994e8i	−0.206403	+	0.206403i
$789$		−	1.66120e7i		−	0.0338213i
$790$		0			0
$791$	3.37620e8			0.682180
$792$	3.80882e8	+	3.80882e8i	0.766682	+	0.766682i
$793$	1.08873e8	−	1.08873e8i	0.218323	−	0.218323i
$794$		−	2.51712e8i		−	0.502854i
$795$		0			0
$796$	2.04307e8			0.405083
$797$	2.16052e8	+	2.16052e8i	0.426760	+	0.426760i	0.887523	−	0.460763i	$-0.152424\pi$
$797$	2.16052e8	+	2.16052e8i	0.426760	+	0.426760i	−0.460763	+	0.887523i	$0.652424\pi$
$798$	−7.47522e6	+	7.47522e6i	−0.0147101	+	0.0147101i
$799$		−	9.52497e7i		−	0.186734i
$800$		0			0
$801$	−1.81479e8			−0.353125
$802$	−2.47497e8	−	2.47497e8i	−0.479785	−	0.479785i
$803$	3.99257e8	−	3.99257e8i	0.771091	−	0.771091i
$804$		−	2.78842e6i		−	0.00536525i
$805$		0			0
$806$	−4.32763e8			−0.826504
$807$	−6.25528e6	−	6.25528e6i	−0.0119022	−	0.0119022i
$808$	−3.14468e8	+	3.14468e8i	−0.596133	+	0.596133i
$809$			7.65363e8i			1.44551i	0.691102	+	0.722757i	$0.257125\pi$
$809$			7.65363e8i			1.44551i	−0.691102	+	0.722757i	$0.742875\pi$
$810$		0			0
$811$	−7.53196e8			−1.41203			−0.706017	−	0.708195i	$-0.749510\pi$
$811$	−7.53196e8			−1.41203			−0.706017	+	0.708195i	$0.749510\pi$
$812$	−2.56500e7	−	2.56500e7i	−0.0479093	−	0.0479093i
$813$	−4.84313e6	+	4.84313e6i	−0.00901269	+	0.00901269i
$814$		−	6.88152e8i		−	1.27588i
$815$		0			0
$816$	2.45938e6			0.00452643
$817$	−5.87689e7	−	5.87689e7i	−0.107766	−	0.107766i
$818$	−3.67553e8	+	3.67553e8i	−0.671521	+	0.671521i
$819$			4.52151e8i			0.823061i
$820$		0			0
$821$	3.57195e8			0.645469			0.322734	−	0.946490i	$-0.395398\pi$
$821$	3.57195e8			0.645469			0.322734	+	0.946490i	$0.395398\pi$
$822$	−9.46704e6	−	9.46704e6i	−0.0170451	−	0.0170451i
$823$	−3.47845e8	+	3.47845e8i	−0.624002	+	0.624002i	−0.946552	−	0.322550i	$-0.895460\pi$
$823$	−3.47845e8	+	3.47845e8i	−0.624002	+	0.624002i	0.322550	+	0.946552i	$0.395460\pi$
$824$			1.14146e9i			2.04023i
$825$		0			0
$826$	9.11462e7			0.161733
$827$	−4.91730e8	−	4.91730e8i	−0.869380	−	0.869380i	0.123023	−	0.992404i	$-0.460741\pi$
$827$	−4.91730e8	−	4.91730e8i	−0.869380	−	0.869380i	−0.992404	+	0.123023i	$0.960741\pi$
$828$	1.19473e8	−	1.19473e8i	0.210464	−	0.210464i
$829$			8.41407e7i			0.147687i	0.997270	+	0.0738435i	$0.0235265\pi$
$829$			8.41407e7i			0.147687i	−0.997270	+	0.0738435i	$0.976473\pi$
$830$		0			0
$831$	1.13377e7			0.0197570
$832$	4.03155e8	+	4.03155e8i	0.700007	+	0.700007i
$833$	−3.34444e7	+	3.34444e7i	−0.0578613	+	0.0578613i
$834$		−	1.16499e7i		−	0.0200828i
$835$		0			0
$836$	2.66812e8			0.456653
$837$	1.96332e7	+	1.96332e7i	0.0334822	+	0.0334822i
$838$	−3.50530e8	+	3.50530e8i	−0.595652	+	0.595652i
$839$		−	1.92325e8i		−	0.325650i	−0.986655	−	0.162825i	$-0.947939\pi$
$839$		−	1.92325e8i		−	0.325650i	0.986655	−	0.162825i	$-0.0520605\pi$
$840$		0			0
$841$	5.65243e8			0.950271
$842$	−3.95831e8	−	3.95831e8i	−0.663092	−	0.663092i
$843$	1.05438e7	−	1.05438e7i	0.0176000	−	0.0176000i
$844$		−	4.84080e7i		−	0.0805174i
$845$		0			0
$846$	2.36060e8			0.389862
$847$	2.68628e6	+	2.68628e6i	0.00442080	+	0.00442080i
$848$	1.33857e8	−	1.33857e8i	0.219510	−	0.219510i
$849$			1.64352e7i			0.0268566i
$850$		0			0
$851$	−8.47031e8			−1.37439
$852$	1.65632e6	+	1.65632e6i	0.00267809	+	0.00267809i
$853$	−4.32334e8	+	4.32334e8i	−0.696582	+	0.696582i	−0.963672	−	0.267090i	$-0.913938\pi$
$853$	−4.32334e8	+	4.32334e8i	−0.696582	+	0.696582i	0.267090	+	0.963672i	$0.413938\pi$
$854$		−	1.49524e8i		−	0.240070i
$855$		0			0
$856$	−1.18986e9			−1.89703
$857$	1.34271e8	+	1.34271e8i	0.213323	+	0.213323i	0.805678	−	0.592354i	$-0.201801\pi$
$857$	1.34271e8	+	1.34271e8i	0.213323	+	0.213323i	−0.592354	+	0.805678i	$0.701801\pi$
$858$	7.20824e6	−	7.20824e6i	0.0114122	−	0.0114122i
$859$		−	2.62687e8i		−	0.414438i	−0.978295	−	0.207219i	$-0.933559\pi$
$859$		−	2.62687e8i		−	0.414438i	0.978295	−	0.207219i	$-0.0664413\pi$
$860$		0			0
$861$	3.14755e6			0.00493133
$862$	−7.01558e7	−	7.01558e7i	−0.109532	−	0.109532i
$863$	1.09116e8	−	1.09116e8i	0.169769	−	0.169769i	−0.617109	−	0.786878i	$-0.711696\pi$
$863$	1.09116e8	−	1.09116e8i	0.169769	−	0.169769i	0.786878	+	0.617109i	$0.211696\pi$
$864$		−	1.80496e7i		−	0.0279851i
$865$		0			0
$866$	−3.12540e8			−0.481230
$867$	8.43000e6	+	8.43000e6i	0.0129351	+	0.0129351i
$868$	1.54450e8	−	1.54450e8i	0.236173	−	0.236173i
$869$		−	2.37068e8i		−	0.361254i
$870$		0			0
$871$	4.46028e8			0.675006
$872$	−5.20389e8	−	5.20389e8i	−0.784836	−	0.784836i
$873$	2.23162e7	−	2.23162e7i	0.0335411	−	0.0335411i
$874$			6.31892e8i			0.946473i
$875$		0			0
$876$	−5.41954e6			−0.00806214
$877$	−3.07353e7	−	3.07353e7i	−0.0455658	−	0.0455658i	0.683957	−	0.729523i	$-0.260258\pi$
$877$	−3.07353e7	−	3.07353e7i	−0.0455658	−	0.0455658i	−0.729523	+	0.683957i	$0.760258\pi$
$878$	3.62877e8	−	3.62877e8i	0.536137	−	0.536137i
$879$			4.33815e6i			0.00638760i
$880$		0			0
$881$	6.97712e8			1.02035			0.510174	−	0.860071i	$-0.329581\pi$
$881$	6.97712e8			1.02035			0.510174	+	0.860071i	$0.329581\pi$
$882$	−8.28859e7	−	8.28859e7i	−0.120802	−	0.120802i
$883$	−7.66490e8	+	7.66490e8i	−1.11333	+	1.11333i	−0.120635	+	0.992697i	$0.538493\pi$
$883$	−7.66490e8	+	7.66490e8i	−1.11333	+	1.11333i	−0.992697	+	0.120635i	$0.961507\pi$
$884$		−	8.50374e7i		−	0.123099i
$885$		0			0
$886$	4.78692e8			0.688264
$887$	1.80718e8	+	1.80718e8i	0.258959	+	0.258959i	0.824631	−	0.565672i	$-0.191383\pi$
$887$	1.80718e8	+	1.80718e8i	0.258959	+	0.258959i	−0.565672	+	0.824631i	$0.691383\pi$
$888$	−1.83275e7	+	1.83275e7i	−0.0261736	+	0.0261736i
$889$		−	1.96641e8i		−	0.279878i
$890$		0			0
$891$	7.03874e8			0.995088
$892$	−1.20973e8	−	1.20973e8i	−0.170449	−	0.170449i
$893$	3.24447e8	−	3.24447e8i	0.455605	−	0.455605i
$894$			4.46815e6i			0.00625338i
$895$		0			0
$896$	1.38488e8			0.192525
$897$	−8.87246e6	−	8.87246e6i	−0.0122933	−	0.0122933i
$898$	3.28932e8	−	3.28932e8i	0.454231	−	0.454231i
$899$		−	1.78114e8i		−	0.245142i
$900$		0			0
$901$	−1.62978e8			−0.222820
$902$	1.08080e8	+	1.08080e8i	0.147274	+	0.147274i
$903$	1.13329e6	−	1.13329e6i	0.00153914	−	0.00153914i
$904$		−	6.17519e8i		−	0.835882i
$905$		0			0
$906$	−1.13794e7			−0.0153016
$907$	2.51326e8	+	2.51326e8i	0.336834	+	0.336834i	0.855174	−	0.518341i	$-0.173450\pi$
$907$	2.51326e8	+	2.51326e8i	0.336834	+	0.336834i	−0.518341	+	0.855174i	$0.673450\pi$
$908$	−4.89572e7	+	4.89572e7i	−0.0653972	+	0.0653972i
$909$			5.81410e8i			0.774089i
$910$		0			0
$911$	−1.32793e9			−1.75639			−0.878193	−	0.478306i	$-0.841251\pi$
$911$	−1.32793e9			−1.75639			−0.878193	+	0.478306i	$0.841251\pi$
$912$	8.37733e6	+	8.37733e6i	0.0110439	+	0.0110439i
$913$	7.49448e8	−	7.49448e8i	0.984757	−	0.984757i
$914$		−	8.65920e8i		−	1.13407i
$915$		0			0
$916$	−1.81106e8			−0.235638
$917$	1.25063e8	+	1.25063e8i	0.162188	+	0.162188i
$918$	7.42288e6	−	7.42288e6i	0.00959499	−	0.00959499i
$919$			1.31280e9i			1.69143i	0.533638	+	0.845713i	$0.320825\pi$
$919$			1.31280e9i			1.69143i	−0.533638	+	0.845713i	$0.679175\pi$
$920$		0			0
$921$	2.49125e7			0.0318888
$922$	7.01476e8	+	7.01476e8i	0.894994	+	0.894994i
$923$	−2.64940e8	+	2.64940e8i	−0.336932	+	0.336932i
$924$			5.14515e6i			0.00652202i
$925$		0			0
$926$	−7.65334e7			−0.0963870
$927$	1.05521e9	+	1.05521e9i	1.32464	+	1.32464i
$928$	−8.18740e7	+	8.18740e7i	−0.102448	+	0.102448i
$929$		−	1.28584e9i		−	1.60377i	−0.597481	−	0.801883i	$-0.703832\pi$
$929$		−	1.28584e9i		−	1.60377i	0.597481	−	0.801883i	$-0.296168\pi$
$930$		0			0
$931$	−2.27841e8			−0.282347
$932$	−5.87022e7	−	5.87022e7i	−0.0725114	−	0.0725114i
$933$	−7.72270e6	+	7.72270e6i	−0.00950877	+	0.00950877i
$934$			8.35322e8i			1.02521i
$935$		0			0
$936$	8.27000e8			1.00850
$937$	−1.61452e8	−	1.61452e8i	−0.196256	−	0.196256i	0.602137	−	0.798393i	$-0.294316\pi$
$937$	−1.61452e8	−	1.61452e8i	−0.196256	−	0.196256i	−0.798393	+	0.602137i	$0.794316\pi$
$938$	3.06284e8	−	3.06284e8i	0.371121	−	0.371121i
$939$			1.75489e7i			0.0211960i
$940$		0			0
$941$	7.40996e8			0.889297			0.444649	−	0.895705i	$-0.353329\pi$
$941$	7.40996e8			0.889297			0.444649	+	0.895705i	$0.353329\pi$
$942$	3.64295e6	+	3.64295e6i	0.00435813	+	0.00435813i
$943$	1.33034e8	−	1.33034e8i	0.158645	−	0.158645i
$944$		−	1.02146e8i		−	0.121424i
$945$		0			0
$946$	7.78296e7			0.0919330
$947$	−4.84666e8	−	4.84666e8i	−0.570680	−	0.570680i	0.361639	−	0.932318i	$-0.382217\pi$
$947$	−4.84666e8	−	4.84666e8i	−0.570680	−	0.570680i	−0.932318	+	0.361639i	$0.882217\pi$
$948$	−1.60899e6	+	1.60899e6i	−0.00188855	+	0.00188855i
$949$		−	8.66896e8i		−	1.01430i
$950$		0			0
$951$	−3.44944e7			−0.0401058
$952$	−2.29144e8	−	2.29144e8i	−0.265582	−	0.265582i
$953$	6.04027e8	−	6.04027e8i	0.697876	−	0.697876i	−0.266076	−	0.963952i	$-0.585727\pi$
$953$	6.04027e8	−	6.04027e8i	0.697876	−	0.697876i	0.963952	+	0.266076i	$0.0857274\pi$
$954$		−	4.03912e8i		−	0.465202i
$955$		0			0
$956$	−3.94361e8			−0.451357
$957$	2.96672e6	+	2.96672e6i	0.00338486	+	0.00338486i
$958$	5.08570e8	−	5.08570e8i	0.578435	−	0.578435i
$959$			1.08090e9i			1.22555i
$960$		0			0
$961$	1.85000e8			0.208449
$962$	−7.47083e8	−	7.47083e8i	−0.839158	−	0.839158i
$963$	−1.09995e9	+	1.09995e9i	−1.23167	+	1.23167i
$964$		−	5.23241e8i		−	0.584078i
$965$		0			0
$966$	−1.21853e7			−0.0135178
$967$	−9.16779e8	−	9.16779e8i	−1.01388	−	1.01388i	−0.999902	−	0.0139747i	$-0.995552\pi$
$967$	−9.16779e8	−	9.16779e8i	−1.01388	−	1.01388i	−0.0139747	−	0.999902i	$-0.504448\pi$
$968$	4.91329e6	−	4.91329e6i	0.00541685	−	0.00541685i
$969$		−	1.01998e7i		−	0.0112104i
$970$		0			0
$971$	4.28954e8			0.468547			0.234273	−	0.972171i	$-0.424729\pi$
$971$	4.28954e8			0.468547			0.234273	+	0.972171i	$0.424729\pi$
$972$	−1.43427e7	−	1.43427e7i	−0.0156183	−	0.0156183i
$973$	−6.65068e8	+	6.65068e8i	−0.721983	+	0.721983i
$974$			4.07562e8i			0.441080i
$975$		0			0
$976$	−1.67568e8			−0.180237
$977$	9.78728e8	+	9.78728e8i	1.04949	+	1.04949i	0.998710	+	0.0507801i	$0.0161708\pi$
$977$	9.78728e8	+	9.78728e8i	1.04949	+	1.04949i	0.0507801	+	0.998710i	$0.483829\pi$
$978$	9.78393e6	−	9.78393e6i	0.0104592	−	0.0104592i
$979$		−	3.30327e8i		−	0.352043i
$980$		0			0
$981$	−9.62130e8			−1.01912
$982$	2.09638e8	+	2.09638e8i	0.221379	+	0.221379i
$983$	−1.22302e6	+	1.22302e6i	−0.00128758	+	0.00128758i	−0.707750	−	0.706463i	$-0.750290\pi$
$983$	−1.22302e6	+	1.22302e6i	−0.00128758	+	0.00128758i	0.706463	+	0.707750i	$0.250290\pi$
$984$		−	5.75698e6i		−	0.00604240i
$985$		0			0
$986$	−6.73411e7			−0.0702505
$987$	6.25657e6	+	6.25657e6i	0.00650706	+	0.00650706i
$988$	2.89661e8	−	2.89661e8i	0.300344	−	0.300344i
$989$		−	9.57987e7i		−	0.0990309i
$990$		0			0
$991$	1.28005e9			1.31524			0.657620	−	0.753349i	$-0.271563\pi$
$991$	1.28005e9			1.31524			0.657620	+	0.753349i	$0.271563\pi$
$992$	−4.93000e8	−	4.93000e8i	−0.505024	−	0.505024i
$993$	9.74354e6	−	9.74354e6i	0.00995105	−	0.00995105i
$994$			3.63864e8i			0.370493i
$995$		0			0
$996$	−1.01731e7			−0.0102961
$997$	6.11907e8	+	6.11907e8i	0.617447	+	0.617447i	0.944876	−	0.327429i	$-0.106182\pi$
$997$	6.11907e8	+	6.11907e8i	0.617447	+	0.617447i	−0.327429	+	0.944876i	$0.606182\pi$
$998$	−9.12587e8	+	9.12587e8i	−0.918085	+	0.918085i
$999$			6.77858e7i			0.0679896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.7.c.c.7.1		4
3.2	odd	2		225.7.g.c.82.2		4
5.2	odd	4		5.7.c.a.3.2	yes	4
5.3	odd	4	inner	25.7.c.c.18.1		4
5.4	even	2		5.7.c.a.2.2	✓	4
15.2	even	4		45.7.g.a.28.1		4
15.8	even	4		225.7.g.c.118.2		4
15.14	odd	2		45.7.g.a.37.1		4
20.7	even	4		80.7.p.b.33.2		4
20.19	odd	2		80.7.p.b.17.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.7.c.a.2.2	✓	4	5.4	even	2
5.7.c.a.3.2	yes	4	5.2	odd	4
25.7.c.c.7.1		4	1.1	even	1	trivial
25.7.c.c.18.1		4	5.3	odd	4	inner
45.7.g.a.28.1		4	15.2	even	4
45.7.g.a.37.1		4	15.14	odd	2
80.7.p.b.17.2		4	20.19	odd	2
80.7.p.b.33.2		4	20.7	even	4
225.7.g.c.82.2		4	3.2	odd	2
225.7.g.c.118.2		4	15.8	even	4

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.58872 - 4.58872i) q^{2} +(-0.411277 + 0.411277i) q^{3} -21.8872i q^{4} +3.77447 q^{6} +(-215.476 - 215.476i) q^{7} +(-394.113 + 394.113i) q^{8} +728.662i q^{9} +O(q^{10})\)	\(q+(-4.58872 - 4.58872i) q^{2} +(-0.411277 + 0.411277i) q^{3} -21.8872i q^{4} +3.77447 q^{6} +(-215.476 - 215.476i) q^{7} +(-394.113 + 394.113i) q^{8} +728.662i q^{9} -1326.31 q^{11} +(9.00171 + 9.00171i) q^{12} +(-1439.89 + 1439.89i) q^{13} +1977.52i q^{14} +2216.17 q^{16} +(-1349.15 - 1349.15i) q^{17} +(3343.63 - 3343.63i) q^{18} -9191.14i q^{19} +177.240 q^{21} +(6086.06 + 6086.06i) q^{22} +(7491.20 - 7491.20i) q^{23} -324.179i q^{24} +13214.5 q^{26} +(-599.502 - 599.502i) q^{27} +(-4716.17 + 4716.17i) q^{28} +5438.74i q^{29} -32749.1 q^{31} +(15053.8 + 15053.8i) q^{32} +(545.480 - 545.480i) q^{33} +12381.7i q^{34} +15948.4 q^{36} +(-56535.1 - 56535.1i) q^{37} +(-42175.6 + 42175.6i) q^{38} -1184.39i q^{39} +17758.7 q^{41} +(-813.307 - 813.307i) q^{42} +(6394.08 - 6394.08i) q^{43} +29029.2i q^{44} -68750.1 q^{46} +(35299.9 + 35299.9i) q^{47} +(-911.457 + 911.457i) q^{48} -24789.2i q^{49} +1109.75 q^{51} +(31515.2 + 31515.2i) q^{52} +(60400.3 - 60400.3i) q^{53} +5501.90i q^{54} +169844. q^{56} +(3780.10 + 3780.10i) q^{57} +(24956.9 - 24956.9i) q^{58} -46091.2i q^{59} -75611.9 q^{61} +(150277. + 150277. i) q^{62} +(157009. - 157009. i) q^{63} -279990. i q^{64} -5006.11 q^{66} +(-154883. - 154883. i) q^{67} +(-29529.1 + 29529.1i) q^{68} +6161.91i q^{69} +184000. q^{71} +(-287175. - 287175. i) q^{72} +(-301029. + 301029. i) q^{73} +518848. i q^{74} -201169. q^{76} +(285788. + 285788. i) q^{77} +(-5434.82 + 5434.82i) q^{78} +178743. i q^{79} -530701. q^{81} +(-81489.6 - 81489.6i) q^{82} +(-565063. + 565063. i) q^{83} -3879.30i q^{84} -58681.4 q^{86} +(-2236.83 - 2236.83i) q^{87} +(522715. - 522715. i) q^{88} +249057. i q^{89} +620523. q^{91} +(-163962. - 163962. i) q^{92} +(13468.9 - 13468.9i) q^{93} -323963. i q^{94} -12382.6 q^{96} +(-30626.2 - 30626.2i) q^{97} +(-113751. + 113751. i) q^{98} -966430. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 10 q^{2} - 30 q^{3} - 552 q^{6} - 550 q^{7} - 1860 q^{8}+O(q^{10}) \) 4 * q + 10 * q^2 - 30 * q^3 - 552 * q^6 - 550 * q^7 - 1860 * q^8	\( 4 q + 10 q^{2} - 30 q^{3} - 552 q^{6} - 550 q^{7} - 1860 q^{8} - 1052 q^{11} - 3480 q^{12} - 1960 q^{13} - 776 q^{16} + 3280 q^{17} + 870 q^{18} + 3828 q^{21} + 27520 q^{22} + 39010 q^{23} + 44068 q^{26} - 31320 q^{27} + 4840 q^{28} - 33172 q^{31} + 48760 q^{32} - 22260 q^{33} - 40836 q^{36} - 146860 q^{37} - 218040 q^{38} - 213932 q^{41} + 31680 q^{42} + 72050 q^{43} + 323288 q^{46} - 830 q^{47} + 74160 q^{48} - 172212 q^{51} + 173300 q^{52} + 29620 q^{53} + 467280 q^{56} - 195840 q^{57} + 554640 q^{58} - 111052 q^{61} + 610520 q^{62} + 350130 q^{63} - 457824 q^{66} + 146930 q^{67} - 775780 q^{68} + 1310188 q^{71} - 899460 q^{72} - 553540 q^{73} - 2073840 q^{76} + 476300 q^{77} - 268200 q^{78} - 624816 q^{81} - 2554880 q^{82} - 536870 q^{83} + 1019128 q^{86} + 763440 q^{87} + 187680 q^{88} + 1131548 q^{91} + 2552680 q^{92} - 444660 q^{93} - 568992 q^{96} + 59420 q^{97} + 1892810 q^{98}+O(q^{100}) \) 4 * q + 10 * q^2 - 30 * q^3 - 552 * q^6 - 550 * q^7 - 1860 * q^8 - 1052 * q^11 - 3480 * q^12 - 1960 * q^13 - 776 * q^16 + 3280 * q^17 + 870 * q^18 + 3828 * q^21 + 27520 * q^22 + 39010 * q^23 + 44068 * q^26 - 31320 * q^27 + 4840 * q^28 - 33172 * q^31 + 48760 * q^32 - 22260 * q^33 - 40836 * q^36 - 146860 * q^37 - 218040 * q^38 - 213932 * q^41 + 31680 * q^42 + 72050 * q^43 + 323288 * q^46 - 830 * q^47 + 74160 * q^48 - 172212 * q^51 + 173300 * q^52 + 29620 * q^53 + 467280 * q^56 - 195840 * q^57 + 554640 * q^58 - 111052 * q^61 + 610520 * q^62 + 350130 * q^63 - 457824 * q^66 + 146930 * q^67 - 775780 * q^68 + 1310188 * q^71 - 899460 * q^72 - 553540 * q^73 - 2073840 * q^76 + 476300 * q^77 - 268200 * q^78 - 624816 * q^81 - 2554880 * q^82 - 536870 * q^83 + 1019128 * q^86 + 763440 * q^87 + 187680 * q^88 + 1131548 * q^91 + 2552680 * q^92 - 444660 * q^93 - 568992 * q^96 + 59420 * q^97 + 1892810 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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