LMFDB - Embedded newform 825.4.c.k.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(199,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("825.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.c (of order $2$, degree $1$, not 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:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.36142572544.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 53x^{4} + 632x^{2} + 484 $ x^6 + 53x^4 + 632x^2 + 484
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.4
Root			$0.906392i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.k.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.90639i q^{2} +3.00000i q^{3} +4.36567 q^{4} -5.71918 q^{6} +22.9186i q^{7} +23.5738i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+1.90639i q^{2} +3.00000i q^{3} +4.36567 q^{4} -5.71918 q^{6} +22.9186i q^{7} +23.5738i q^{8} -9.00000 q^{9} +11.0000 q^{11} +13.0970i q^{12} +66.7313i q^{13} -43.6917 q^{14} -10.0156 q^{16} +3.45588i q^{17} -17.1575i q^{18} -78.2359 q^{19} -68.7557 q^{21} +20.9703i q^{22} +12.2907i q^{23} -70.7214 q^{24} -127.216 q^{26} -27.0000i q^{27} +100.055i q^{28} +31.1827 q^{29} +247.181 q^{31} +169.497i q^{32} +33.0000i q^{33} -6.58825 q^{34} -39.2910 q^{36} -304.128i q^{37} -149.148i q^{38} -200.194 q^{39} -29.8219 q^{41} -131.075i q^{42} +269.060i q^{43} +48.0224 q^{44} -23.4309 q^{46} -225.463i q^{47} -30.0467i q^{48} -182.260 q^{49} -10.3676 q^{51} +291.327i q^{52} -16.8371i q^{53} +51.4726 q^{54} -540.278 q^{56} -234.708i q^{57} +59.4464i q^{58} -28.0701 q^{59} -853.742 q^{61} +471.224i q^{62} -206.267i q^{63} -403.252 q^{64} -62.9109 q^{66} +36.7885i q^{67} +15.0872i q^{68} -36.8722 q^{69} +23.8552 q^{71} -212.164i q^{72} +707.265i q^{73} +579.787 q^{74} -341.552 q^{76} +252.104i q^{77} -381.648i q^{78} +412.126 q^{79} +81.0000 q^{81} -56.8522i q^{82} -552.596i q^{83} -300.165 q^{84} -512.934 q^{86} +93.5480i q^{87} +259.312i q^{88} +1495.26 q^{89} -1529.39 q^{91} +53.6573i q^{92} +741.543i q^{93} +429.820 q^{94} -508.491 q^{96} -1199.45i q^{97} -347.459i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 60 q^{4} - 12 q^{6} - 54 q^{9}+O(q^{10}) $ 6 * q - 60 * q^4 - 12 * q^6 - 54 * q^9	$ 6 q - 60 q^{4} - 12 q^{6} - 54 q^{9} + 66 q^{11} + 136 q^{14} + 356 q^{16} + 116 q^{19} + 60 q^{21} - 108 q^{24} - 240 q^{26} + 440 q^{29} + 496 q^{31} + 160 q^{34} + 540 q^{36} - 684 q^{39} + 312 q^{41} - 660 q^{44} - 2512 q^{46} - 558 q^{49} - 624 q^{51} + 108 q^{54} - 3288 q^{56} - 1096 q^{59} + 828 q^{61} + 116 q^{64} - 132 q^{66} - 720 q^{69} - 1824 q^{71} + 3224 q^{74} - 5504 q^{76} + 1084 q^{79} + 486 q^{81} - 4056 q^{84} - 3096 q^{86} - 1580 q^{89} - 1544 q^{91} + 848 q^{94} - 1548 q^{96} - 594 q^{99}+O(q^{100}) $ 6 * q - 60 * q^4 - 12 * q^6 - 54 * q^9 + 66 * q^11 + 136 * q^14 + 356 * q^16 + 116 * q^19 + 60 * q^21 - 108 * q^24 - 240 * q^26 + 440 * q^29 + 496 * q^31 + 160 * q^34 + 540 * q^36 - 684 * q^39 + 312 * q^41 - 660 * q^44 - 2512 * q^46 - 558 * q^49 - 624 * q^51 + 108 * q^54 - 3288 * q^56 - 1096 * q^59 + 828 * q^61 + 116 * q^64 - 132 * q^66 - 720 * q^69 - 1824 * q^71 + 3224 * q^74 - 5504 * q^76 + 1084 * q^79 + 486 * q^81 - 4056 * q^84 - 3096 * q^86 - 1580 * q^89 - 1544 * q^91 + 848 * q^94 - 1548 * q^96 - 594 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	1.90639i	0.674011i	0.941503	+	0.337006i	$0.109414\pi$
$2$	1.90639i	0.674011i	−0.941503	+	0.337006i	$0.890586\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	4.36567	0.545709
$5$	0	0
$5$	0	0
$6$	−5.71918	−0.389141
$7$	22.9186i	1.23749i	0.785594	+	0.618743i	$0.212358\pi$
$7$	22.9186i	1.23749i	−0.785594	+	0.618743i	$0.787642\pi$
$8$	23.5738i	1.04183i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	13.0970i	0.315065i
$13$	66.7313i	1.42369i	0.702338	+	0.711844i	$0.252140\pi$
$13$	66.7313i	1.42369i	−0.702338	+	0.711844i	$0.747860\pi$
$14$	−43.6917	−0.834079
$15$	0	0
$16$	−10.0156	−0.156493
$17$	3.45588i	0.0493043i	0.999696	+	0.0246522i	$0.00784782\pi$
$17$	3.45588i	0.0493043i	−0.999696	+	0.0246522i	$0.992152\pi$
$18$	− 17.1575i	− 0.224670i
$19$	−78.2359	−0.944660	−0.472330	−	0.881422i	$-0.656587\pi$
$19$	−78.2359	−0.944660	−0.472330	+	0.881422i	$0.656587\pi$
$20$	0	0
$21$	−68.7557	−0.714463
$22$	20.9703i	0.203222i
$23$	12.2907i	0.111426i	0.998447	+	0.0557129i	$0.0177432\pi$
$23$	12.2907i	0.111426i	−0.998447	+	0.0557129i	$0.982257\pi$
$24$	−70.7214	−0.601498
$25$	0	0
$26$	−127.216	−0.959582
$27$	− 27.0000i	− 0.192450i
$28$	100.055i	0.675307i
$29$	31.1827	0.199672	0.0998358	−	0.995004i	$-0.468168\pi$
$29$	31.1827	0.199672	0.0998358	+	0.995004i	$0.468168\pi$
$30$	0	0
$31$	247.181	1.43210	0.716049	−	0.698050i	$-0.245949\pi$
$31$	247.181	1.43210	0.716049	+	0.698050i	$0.245949\pi$
$32$	169.497i	0.936347i
$33$	33.0000i	0.174078i
$34$	−6.58825	−0.0332317
$35$	0	0
$36$	−39.2910	−0.181903
$37$	− 304.128i	− 1.35131i	−0.737220	−	0.675653i	$-0.763862\pi$
$37$	− 304.128i	− 1.35131i	0.737220	−	0.675653i	$-0.236138\pi$
$38$	− 149.148i	− 0.636712i
$39$	−200.194	−0.821967
$40$	0	0
$41$	−29.8219	−0.113595	−0.0567975	−	0.998386i	$-0.518089\pi$
$41$	−29.8219	−0.113595	−0.0567975	+	0.998386i	$0.518089\pi$
$42$	− 131.075i	− 0.481556i
$43$	269.060i	0.954215i	0.878845	+	0.477108i	$0.158315\pi$
$43$	269.060i	0.954215i	−0.878845	+	0.477108i	$0.841685\pi$
$44$	48.0224	0.164537
$45$	0	0
$46$	−23.4309	−0.0751023
$47$	− 225.463i	− 0.699726i	−0.936801	−	0.349863i	$-0.886228\pi$
$47$	− 225.463i	− 0.699726i	0.936801	−	0.349863i	$-0.113772\pi$
$48$	− 30.0467i	− 0.0903514i
$49$	−182.260	−0.531371
$50$	0	0
$51$	−10.3676	−0.0284659
$52$	291.327i	0.776919i
$53$	− 16.8371i	− 0.0436369i	−0.999762	−	0.0218184i	$-0.993054\pi$
$53$	− 16.8371i	− 0.0436369i	0.999762	−	0.0218184i	$-0.00694557\pi$
$54$	51.4726	0.129714
$55$	0	0
$56$	−540.278	−1.28924
$57$	− 234.708i	− 0.545400i
$58$	59.4464i	0.134581i
$59$	−28.0701	−0.0619392	−0.0309696	−	0.999520i	$-0.509860\pi$
$59$	−28.0701	−0.0619392	−0.0309696	+	0.999520i	$0.509860\pi$
$60$	0	0
$61$	−853.742	−1.79198	−0.895988	−	0.444079i	$-0.853531\pi$
$61$	−853.742	−1.79198	−0.895988	+	0.444079i	$0.853531\pi$
$62$	471.224i	0.965250i
$63$	− 206.267i	− 0.412495i
$64$	−403.252	−0.787602
$65$	0	0
$66$	−62.9109	−0.117330
$67$	36.7885i	0.0670810i	0.999437	+	0.0335405i	$0.0106783\pi$
$67$	36.7885i	0.0670810i	−0.999437	+	0.0335405i	$0.989322\pi$
$68$	15.0872i	0.0269058i
$69$	−36.8722	−0.0643317
$70$	0	0
$71$	23.8552	0.0398746	0.0199373	−	0.999801i	$-0.493653\pi$
$71$	23.8552	0.0398746	0.0199373	+	0.999801i	$0.493653\pi$
$72$	− 212.164i	− 0.347275i
$73$	707.265i	1.13396i	0.823731	+	0.566980i	$0.191889\pi$
$73$	707.265i	1.13396i	−0.823731	+	0.566980i	$0.808111\pi$
$74$	579.787	0.910795
$75$	0	0
$76$	−341.552	−0.515509
$77$	252.104i	0.373116i
$78$	− 381.648i	− 0.554015i
$79$	412.126	0.586934	0.293467	−	0.955969i	$-0.405191\pi$
$79$	412.126	0.586934	0.293467	+	0.955969i	$0.405191\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 56.8522i	− 0.0765643i
$83$	− 552.596i	− 0.730786i	−0.930853	−	0.365393i	$-0.880935\pi$
$83$	− 552.596i	− 0.730786i	0.930853	−	0.365393i	$-0.119065\pi$
$84$	−300.165	−0.389889
$85$	0	0
$86$	−512.934	−0.643152
$87$	93.5480i	0.115280i
$88$	259.312i	0.314122i
$89$	1495.26	1.78087	0.890434	−	0.455113i	$-0.150401\pi$
$89$	1495.26	1.78087	0.890434	+	0.455113i	$0.150401\pi$
$90$	0	0
$91$	−1529.39	−1.76179
$92$	53.6573i	0.0608060i
$93$	741.543i	0.826822i
$94$	429.820	0.471623
$95$	0	0
$96$	−508.491	−0.540600
$97$	− 1199.45i	− 1.25552i	−0.778406	−	0.627761i	$-0.783971\pi$
$97$	− 1199.45i	− 1.25552i	0.778406	−	0.627761i	$-0.216029\pi$
$98$	− 347.459i	− 0.358150i
$99$	−99.0000	−0.100504
$100$	0	0
$101$	−1009.66	−0.994701	−0.497351	−	0.867550i	$-0.665694\pi$
$101$	−1009.66	−0.994701	−0.497351	+	0.867550i	$0.665694\pi$
$102$	− 19.7648i	− 0.0191863i
$103$	1156.70i	1.10653i	0.833004	+	0.553266i	$0.186619\pi$
$103$	1156.70i	1.10653i	−0.833004	+	0.553266i	$0.813381\pi$
$104$	−1573.11	−1.48323
$105$	0	0
$106$	32.0981	0.0294117
$107$	− 491.857i	− 0.444389i	−0.975002	−	0.222194i	$-0.928678\pi$
$107$	− 491.857i	− 0.444389i	0.975002	−	0.222194i	$-0.0713220\pi$
$108$	− 117.873i	− 0.105022i
$109$	−1340.77	−1.17819	−0.589093	−	0.808066i	$-0.700515\pi$
$109$	−1340.77	−1.17819	−0.589093	+	0.808066i	$0.700515\pi$
$110$	0	0
$111$	912.384	0.780177
$112$	− 229.542i	− 0.193658i
$113$	1849.21i	1.53946i	0.638371	+	0.769729i	$0.279609\pi$
$113$	1849.21i	1.53946i	−0.638371	+	0.769729i	$0.720391\pi$
$114$	447.445	0.367606
$115$	0	0
$116$	136.133	0.108963
$117$	− 600.582i	− 0.474563i
$118$	− 53.5126i	− 0.0417478i
$119$	−79.2037	−0.0610134
$120$	0	0
$121$	121.000	0.0909091
$122$	− 1627.57i	− 1.20781i
$123$	− 89.4656i	− 0.0655841i
$124$	1079.11	0.781508
$125$	0	0
$126$	393.226	0.278026
$127$	1020.24i	0.712850i	0.934324	+	0.356425i	$0.116005\pi$
$127$	1020.24i	0.712850i	−0.934324	+	0.356425i	$0.883995\pi$
$128$	587.219i	0.405495i
$129$	−807.180	−0.550917
$130$	0	0
$131$	1003.30	0.669147	0.334574	−	0.942370i	$-0.391408\pi$
$131$	1003.30	0.669147	0.334574	+	0.942370i	$0.391408\pi$
$132$	144.067i	0.0949957i
$133$	− 1793.05i	− 1.16900i
$134$	−70.1332	−0.0452134
$135$	0	0
$136$	−81.4682	−0.0513665
$137$	− 2665.14i	− 1.66203i	−0.556249	−	0.831016i	$-0.687760\pi$
$137$	− 2665.14i	− 1.66203i	0.556249	−	0.831016i	$-0.312240\pi$
$138$	− 70.2928i	− 0.0433603i
$139$	−2557.64	−1.56069	−0.780347	−	0.625347i	$-0.784957\pi$
$139$	−2557.64	−1.56069	−0.780347	+	0.625347i	$0.784957\pi$
$140$	0	0
$141$	676.388	0.403987
$142$	45.4774i	0.0268759i
$143$	734.045i	0.429258i
$144$	90.1401	0.0521644
$145$	0	0
$146$	−1348.32	−0.764303
$147$	− 546.781i	− 0.306787i
$148$	− 1327.72i	− 0.737419i
$149$	2644.66	1.45409	0.727044	−	0.686591i	$-0.240894\pi$
$149$	2644.66	1.45409	0.727044	+	0.686591i	$0.240894\pi$
$150$	0	0
$151$	−2871.44	−1.54751	−0.773757	−	0.633482i	$-0.781625\pi$
$151$	−2871.44	−1.54751	−0.773757	+	0.633482i	$0.781625\pi$
$152$	− 1844.32i	− 0.984171i
$153$	− 31.1029i	− 0.0164348i
$154$	−480.609	−0.251484
$155$	0	0
$156$	−873.981	−0.448554
$157$	− 1048.51i	− 0.532996i	−0.963835	−	0.266498i	$-0.914133\pi$
$157$	− 1048.51i	− 0.532996i	0.963835	−	0.266498i	$-0.0858666\pi$
$158$	785.674i	0.395600i
$159$	50.5113	0.0251937
$160$	0	0
$161$	−281.686	−0.137888
$162$	154.418i	0.0748901i
$163$	− 1953.90i	− 0.938905i	−0.882958	−	0.469452i	$-0.844451\pi$
$163$	− 1953.90i	− 0.938905i	0.882958	−	0.469452i	$-0.155549\pi$
$164$	−130.192	−0.0619898
$165$	0	0
$166$	1053.46	0.492558
$167$	− 2085.79i	− 0.966488i	−0.875486	−	0.483244i	$-0.839458\pi$
$167$	− 2085.79i	− 0.966488i	0.875486	−	0.483244i	$-0.160542\pi$
$168$	− 1620.83i	− 0.744345i
$169$	−2256.07	−1.02689
$170$	0	0
$171$	704.123	0.314887
$172$	1174.63i	0.520724i
$173$	− 3999.28i	− 1.75757i	−0.477218	−	0.878785i	$-0.658355\pi$
$173$	− 3999.28i	− 1.75757i	0.477218	−	0.878785i	$-0.341645\pi$
$174$	−178.339	−0.0777003
$175$	0	0
$176$	−110.171	−0.0471845
$177$	− 84.2103i	− 0.0357606i
$178$	2850.55i	1.20032i
$179$	−2046.60	−0.854580	−0.427290	−	0.904115i	$-0.640532\pi$
$179$	−2046.60	−0.854580	−0.427290	+	0.904115i	$0.640532\pi$
$180$	0	0
$181$	64.2973	0.0264043	0.0132022	−	0.999913i	$-0.495797\pi$
$181$	64.2973	0.0264043	0.0132022	+	0.999913i	$0.495797\pi$
$182$	− 2915.61i	− 1.18747i
$183$	− 2561.23i	− 1.03460i
$184$	−289.739	−0.116086
$185$	0	0
$186$	−1413.67	−0.557287
$187$	38.0146i	0.0148658i
$188$	− 984.296i	− 0.381846i
$189$	618.801	0.238154
$190$	0	0
$191$	4816.60	1.82470	0.912348	−	0.409416i	$-0.134268\pi$
$191$	4816.60	1.82470	0.912348	+	0.409416i	$0.134268\pi$
$192$	− 1209.76i	− 0.454722i
$193$	− 295.804i	− 0.110323i	−0.998477	−	0.0551617i	$-0.982433\pi$
$193$	− 295.804i	− 0.110323i	0.998477	−	0.0551617i	$-0.0175674\pi$
$194$	2286.62	0.846237
$195$	0	0
$196$	−795.688	−0.289974
$197$	2147.97i	0.776835i	0.921483	+	0.388418i	$0.126978\pi$
$197$	2147.97i	0.776835i	−0.921483	+	0.388418i	$0.873022\pi$
$198$	− 188.733i	− 0.0677407i
$199$	876.260	0.312143	0.156071	−	0.987746i	$-0.450117\pi$
$199$	876.260	0.312143	0.156071	+	0.987746i	$0.450117\pi$
$200$	0	0
$201$	−110.365	−0.0387292
$202$	− 1924.81i	− 0.670440i
$203$	714.662i	0.247091i
$204$	−45.2616	−0.0155341
$205$	0	0
$206$	−2205.12	−0.745815
$207$	− 110.617i	− 0.0371419i
$208$	− 668.352i	− 0.222798i
$209$	−860.595	−0.284826
$210$	0	0
$211$	1413.99	0.461341	0.230670	−	0.973032i	$-0.425908\pi$
$211$	1413.99	0.461341	0.230670	+	0.973032i	$0.425908\pi$
$212$	− 73.5052i	− 0.0238130i
$213$	71.5657i	0.0230216i
$214$	937.672	0.299523
$215$	0	0
$216$	636.493	0.200499
$217$	5665.03i	1.77220i
$218$	− 2556.03i	− 0.794110i
$219$	−2121.80	−0.654693
$220$	0	0
$221$	−230.615	−0.0701939
$222$	1739.36i	0.525848i
$223$	3365.53i	1.01064i	0.862932	+	0.505320i	$0.168626\pi$
$223$	3365.53i	1.01064i	−0.862932	+	0.505320i	$0.831374\pi$
$224$	−3884.62	−1.15872
$225$	0	0
$226$	−3525.31	−1.03761
$227$	5724.31i	1.67373i	0.547411	+	0.836864i	$0.315613\pi$
$227$	5724.31i	1.67373i	−0.547411	+	0.836864i	$0.684387\pi$
$228$	− 1024.66i	− 0.297629i
$229$	−2586.74	−0.746447	−0.373224	−	0.927741i	$-0.621748\pi$
$229$	−2586.74	−0.746447	−0.373224	+	0.927741i	$0.621748\pi$
$230$	0	0
$231$	−756.312	−0.215419
$232$	735.095i	0.208023i
$233$	5571.63i	1.56656i	0.621666	+	0.783282i	$0.286456\pi$
$233$	5571.63i	1.56656i	−0.621666	+	0.783282i	$0.713544\pi$
$234$	1144.94	0.319861
$235$	0	0
$236$	−122.545	−0.0338008
$237$	1236.38i	0.338867i
$238$	− 150.993i	− 0.0411237i
$239$	1822.92	0.493369	0.246685	−	0.969096i	$-0.420659\pi$
$239$	1822.92	0.493369	0.246685	+	0.969096i	$0.420659\pi$
$240$	0	0
$241$	−2226.66	−0.595152	−0.297576	−	0.954698i	$-0.596178\pi$
$241$	−2226.66	−0.595152	−0.297576	+	0.954698i	$0.596178\pi$
$242$	230.673i	0.0612738i
$243$	243.000i	0.0641500i
$244$	−3727.16	−0.977897
$245$	0	0
$246$	170.556	0.0442044
$247$	− 5220.78i	− 1.34490i
$248$	5827.00i	1.49200i
$249$	1657.79	0.421920
$250$	0	0
$251$	7888.22	1.98367	0.991833	−	0.127543i	$-0.0407092\pi$
$251$	7888.22	1.98367	0.991833	+	0.127543i	$0.0407092\pi$
$252$	− 900.494i	− 0.225102i
$253$	135.198i	0.0335961i
$254$	−1944.98	−0.480469
$255$	0	0
$256$	−4345.49	−1.06091
$257$	4755.32i	1.15420i	0.816674	+	0.577099i	$0.195815\pi$
$257$	4755.32i	1.15420i	−0.816674	+	0.577099i	$0.804185\pi$
$258$	− 1538.80i	− 0.371324i
$259$	6970.17	1.67222
$260$	0	0
$261$	−280.644	−0.0665572
$262$	1912.67i	0.451013i
$263$	− 103.437i	− 0.0242517i	−0.999926	−	0.0121258i	$-0.996140\pi$
$263$	− 103.437i	− 0.0242517i	0.999926	−	0.0121258i	$-0.00385987\pi$
$264$	−777.936	−0.181358
$265$	0	0
$266$	3418.26	0.787921
$267$	4485.78i	1.02818i
$268$	160.606i	0.0366067i
$269$	2179.50	0.494002	0.247001	−	0.969015i	$-0.420555\pi$
$269$	2179.50	0.494002	0.247001	+	0.969015i	$0.420555\pi$
$270$	0	0
$271$	−3688.54	−0.826800	−0.413400	−	0.910550i	$-0.635659\pi$
$271$	−3688.54	−0.826800	−0.413400	+	0.910550i	$0.635659\pi$
$272$	− 34.6126i	− 0.00771579i
$273$	− 4588.16i	− 1.01717i
$274$	5080.80	1.12023
$275$	0	0
$276$	−160.972	−0.0351064
$277$	3087.18i	0.669641i	0.942282	+	0.334821i	$0.108676\pi$
$277$	3087.18i	0.669641i	−0.942282	+	0.334821i	$0.891324\pi$
$278$	− 4875.87i	− 1.05193i
$279$	−2224.63	−0.477366
$280$	0	0
$281$	3338.91	0.708836	0.354418	−	0.935087i	$-0.384679\pi$
$281$	3338.91	0.708836	0.354418	+	0.935087i	$0.384679\pi$
$282$	1289.46i	0.272292i
$283$	1483.75i	0.311661i	0.987784	+	0.155830i	$0.0498054\pi$
$283$	1483.75i	0.311661i	−0.987784	+	0.155830i	$0.950195\pi$
$284$	104.144	0.0217599
$285$	0	0
$286$	−1399.38	−0.289325
$287$	− 683.474i	− 0.140572i
$288$	− 1525.47i	− 0.312116i
$289$	4901.06	0.997569
$290$	0	0
$291$	3598.35	0.724877
$292$	3087.69i	0.618812i
$293$	− 1590.55i	− 0.317137i	−0.987348	−	0.158569i	$-0.949312\pi$
$293$	− 1590.55i	− 0.317137i	0.987348	−	0.158569i	$-0.0506879\pi$
$294$	1042.38	0.206778
$295$	0	0
$296$	7169.45	1.40782
$297$	− 297.000i	− 0.0580259i
$298$	5041.76i	0.980071i
$299$	−820.177	−0.158636
$300$	0	0
$301$	−6166.47	−1.18083
$302$	− 5474.10i	− 1.04304i
$303$	− 3028.98i	− 0.574291i
$304$	783.577	0.147833
$305$	0	0
$306$	59.2943	0.0110772
$307$	− 10175.3i	− 1.89164i	−0.324697	−	0.945818i	$-0.605262\pi$
$307$	− 10175.3i	− 1.89164i	0.324697	−	0.945818i	$-0.394738\pi$
$308$	1100.60i	0.203613i
$309$	−3470.09	−0.638857
$310$	0	0
$311$	−6258.24	−1.14107	−0.570535	−	0.821274i	$-0.693264\pi$
$311$	−6258.24	−1.14107	−0.570535	+	0.821274i	$0.693264\pi$
$312$	− 4719.34i	− 0.856346i
$313$	9592.24i	1.73222i	0.499852	+	0.866111i	$0.333388\pi$
$313$	9592.24i	1.73222i	−0.499852	+	0.866111i	$0.666612\pi$
$314$	1998.88	0.359245
$315$	0	0
$316$	1799.21	0.320295
$317$	10632.3i	1.88381i	0.335874	+	0.941907i	$0.390969\pi$
$317$	10632.3i	1.88381i	−0.335874	+	0.941907i	$0.609031\pi$
$318$	96.2943i	0.0169809i
$319$	343.009	0.0602033
$320$	0	0
$321$	1475.57	0.256568
$322$	− 537.003i	− 0.0929380i
$323$	− 270.373i	− 0.0465758i
$324$	353.619	0.0606343
$325$	0	0
$326$	3724.90	0.632832
$327$	− 4022.30i	− 0.680226i
$328$	− 703.015i	− 0.118346i
$329$	5167.28	0.865901
$330$	0	0
$331$	8222.61	1.36542	0.682712	−	0.730687i	$-0.260800\pi$
$331$	8222.61	1.36542	0.682712	+	0.730687i	$0.260800\pi$
$332$	− 2412.45i	− 0.398796i
$333$	2737.15i	0.450435i
$334$	3976.34	0.651424
$335$	0	0
$336$	688.627	0.111809
$337$	2947.77i	0.476484i	0.971206	+	0.238242i	$0.0765711\pi$
$337$	2947.77i	0.476484i	−0.971206	+	0.238242i	$0.923429\pi$
$338$	− 4300.96i	− 0.692134i
$339$	−5547.62	−0.888806
$340$	0	0
$341$	2718.99	0.431794
$342$	1342.33i	0.212237i
$343$	3683.92i	0.579922i
$344$	−6342.77	−0.994126
$345$	0	0
$346$	7624.20	1.18462
$347$	− 3322.43i	− 0.513999i	−0.966412	−	0.256999i	$-0.917266\pi$
$347$	− 3322.43i	− 0.513999i	0.966412	−	0.256999i	$-0.0827339\pi$
$348$	408.400i	0.0629096i
$349$	9199.67	1.41102	0.705511	−	0.708699i	$-0.250717\pi$
$349$	9199.67	1.41102	0.705511	+	0.708699i	$0.250717\pi$
$350$	0	0
$351$	1801.75	0.273989
$352$	1864.47i	0.282319i
$353$	− 10105.2i	− 1.52363i	−0.647792	−	0.761817i	$-0.724307\pi$
$353$	− 10105.2i	− 1.52363i	0.647792	−	0.761817i	$-0.275693\pi$
$354$	160.538	0.0241031
$355$	0	0
$356$	6527.81	0.971835
$357$	− 237.611i	− 0.0352261i
$358$	− 3901.62i	− 0.575997i
$359$	5236.42	0.769826	0.384913	−	0.922953i	$-0.374231\pi$
$359$	5236.42	0.769826	0.384913	+	0.922953i	$0.374231\pi$
$360$	0	0
$361$	−738.148	−0.107617
$362$	122.576i	0.0177968i
$363$	363.000i	0.0524864i
$364$	−6676.79	−0.961426
$365$	0	0
$366$	4882.70	0.697330
$367$	9337.95i	1.32817i	0.747659	+	0.664083i	$0.231178\pi$
$367$	9337.95i	1.32817i	−0.747659	+	0.664083i	$0.768822\pi$
$368$	− 123.099i	− 0.0174374i
$369$	268.397	0.0378650
$370$	0	0
$371$	385.882	0.0540000
$372$	3237.33i	0.451204i
$373$	14256.1i	1.97896i	0.144659	+	0.989482i	$0.453791\pi$
$373$	14256.1i	1.97896i	−0.144659	+	0.989482i	$0.546209\pi$
$374$	−72.4708	−0.0100197
$375$	0	0
$376$	5315.02	0.728992
$377$	2080.86i	0.284270i
$378$	1179.68i	0.160519i
$379$	−1911.19	−0.259027	−0.129514	−	0.991578i	$-0.541342\pi$
$379$	−1911.19	−0.259027	−0.129514	+	0.991578i	$0.541342\pi$
$380$	0	0
$381$	−3060.73	−0.411564
$382$	9182.32i	1.22987i
$383$	1743.91i	0.232662i	0.993210	+	0.116331i	$0.0371134\pi$
$383$	1743.91i	0.232662i	−0.993210	+	0.116331i	$0.962887\pi$
$384$	−1761.66	−0.234112
$385$	0	0
$386$	563.917	0.0743592
$387$	− 2421.54i	− 0.318072i
$388$	− 5236.40i	− 0.685150i
$389$	2734.88	0.356462	0.178231	−	0.983989i	$-0.442963\pi$
$389$	2734.88	0.356462	0.178231	+	0.983989i	$0.442963\pi$
$390$	0	0
$391$	−42.4752	−0.00549377
$392$	− 4296.57i	− 0.553596i
$393$	3009.89i	0.386332i
$394$	−4094.87	−0.523596
$395$	0	0
$396$	−432.201	−0.0548458
$397$	14879.5i	1.88106i	0.339709	+	0.940530i	$0.389671\pi$
$397$	14879.5i	1.88106i	−0.339709	+	0.940530i	$0.610329\pi$
$398$	1670.50i	0.210388i
$399$	5379.16	0.674924
$400$	0	0
$401$	−11638.2	−1.44934	−0.724668	−	0.689098i	$-0.758007\pi$
$401$	−11638.2	−1.44934	−0.724668	+	0.689098i	$0.758007\pi$
$402$	− 210.400i	− 0.0261039i
$403$	16494.7i	2.03886i
$404$	−4407.84	−0.542817
$405$	0	0
$406$	−1362.43	−0.166542
$407$	− 3345.41i	− 0.407434i
$408$	− 244.405i	− 0.0296564i
$409$	−936.594	−0.113231	−0.0566157	−	0.998396i	$-0.518031\pi$
$409$	−936.594	−0.113231	−0.0566157	+	0.998396i	$0.518031\pi$
$410$	0	0
$411$	7995.42	0.959574
$412$	5049.76i	0.603845i
$413$	− 643.326i	− 0.0766489i
$414$	210.878	0.0250341
$415$	0	0
$416$	−11310.8	−1.33307
$417$	− 7672.93i	− 0.901067i
$418$	− 1640.63i	− 0.191976i
$419$	−128.037	−0.0149285	−0.00746425	−	0.999972i	$-0.502376\pi$
$419$	−128.037	−0.0149285	−0.00746425	+	0.999972i	$0.502376\pi$
$420$	0	0
$421$	−6628.97	−0.767402	−0.383701	−	0.923457i	$-0.625351\pi$
$421$	−6628.97	−0.767402	−0.383701	+	0.923457i	$0.625351\pi$
$422$	2695.61i	0.310949i
$423$	2029.16i	0.233242i
$424$	396.915	0.0454620
$425$	0	0
$426$	−136.432	−0.0155168
$427$	− 19566.5i	− 2.21754i
$428$	− 2147.29i	− 0.242507i
$429$	−2202.13	−0.247832
$430$	0	0
$431$	14677.8	1.64038	0.820192	−	0.572089i	$-0.193867\pi$
$431$	14677.8	1.64038	0.820192	+	0.572089i	$0.193867\pi$
$432$	270.420i	0.0301171i
$433$	− 1150.36i	− 0.127674i	−0.997960	−	0.0638369i	$-0.979666\pi$
$433$	− 1150.36i	− 0.127674i	0.997960	−	0.0638369i	$-0.0203337\pi$
$434$	−10799.8	−1.19448
$435$	0	0
$436$	−5853.35	−0.642946
$437$	− 961.576i	− 0.105259i
$438$	− 4044.97i	− 0.441270i
$439$	9308.30	1.01198	0.505992	−	0.862538i	$-0.331127\pi$
$439$	9308.30	1.01198	0.505992	+	0.862538i	$0.331127\pi$
$440$	0	0
$441$	1640.34	0.177124
$442$	− 439.643i	− 0.0473115i
$443$	− 5689.21i	− 0.610164i	−0.952326	−	0.305082i	$-0.901316\pi$
$443$	− 5689.21i	− 0.610164i	0.952326	−	0.305082i	$-0.0986839\pi$
$444$	3983.17	0.425749
$445$	0	0
$446$	−6416.02	−0.681183
$447$	7933.98i	0.839518i
$448$	− 9241.96i	− 0.974646i
$449$	6644.91	0.698425	0.349212	−	0.937044i	$-0.386449\pi$
$449$	6644.91	0.698425	0.349212	+	0.937044i	$0.386449\pi$
$450$	0	0
$451$	−328.041	−0.0342502
$452$	8073.02i	0.840095i
$453$	− 8614.33i	− 0.893458i
$454$	−10912.8	−1.12811
$455$	0	0
$456$	5532.95	0.568211
$457$	8355.11i	0.855220i	0.903963	+	0.427610i	$0.140644\pi$
$457$	8355.11i	0.855220i	−0.903963	+	0.427610i	$0.859356\pi$
$458$	− 4931.33i	− 0.503114i
$459$	93.3087	0.00948862
$460$	0	0
$461$	−15580.5	−1.57409	−0.787044	−	0.616897i	$-0.788389\pi$
$461$	−15580.5	−1.57409	−0.787044	+	0.616897i	$0.788389\pi$
$462$	− 1441.83i	− 0.145195i
$463$	7139.16i	0.716598i	0.933607	+	0.358299i	$0.116643\pi$
$463$	7139.16i	0.716598i	−0.933607	+	0.358299i	$0.883357\pi$
$464$	−312.312	−0.0312473
$465$	0	0
$466$	−10621.7	−1.05588
$467$	12415.1i	1.23019i	0.788451	+	0.615097i	$0.210883\pi$
$467$	12415.1i	1.23019i	−0.788451	+	0.615097i	$0.789117\pi$
$468$	− 2621.94i	− 0.258973i
$469$	−843.139	−0.0830118
$470$	0	0
$471$	3145.54	0.307726
$472$	− 661.719i	− 0.0645299i
$473$	2959.66i	0.287707i
$474$	−2357.02	−0.228400
$475$	0	0
$476$	−345.777	−0.0332955
$477$	151.534i	0.0145456i
$478$	3475.21i	0.332536i
$479$	14151.0	1.34985	0.674925	−	0.737887i	$-0.264176\pi$
$479$	14151.0	1.34985	0.674925	+	0.737887i	$0.264176\pi$
$480$	0	0
$481$	20294.9	1.92384
$482$	− 4244.88i	− 0.401139i
$483$	− 845.057i	− 0.0796096i
$484$	528.246	0.0496099
$485$	0	0
$486$	−463.253	−0.0432378
$487$	76.6358i	0.00713080i	0.999994	+	0.00356540i	$0.00113490\pi$
$487$	76.6358i	0.00713080i	−0.999994	+	0.00356540i	$0.998865\pi$
$488$	− 20126.0i	− 1.86693i
$489$	5861.71	0.542077
$490$	0	0
$491$	−1707.54	−0.156945	−0.0784725	−	0.996916i	$-0.525004\pi$
$491$	−1707.54	−0.156945	−0.0784725	+	0.996916i	$0.525004\pi$
$492$	− 390.577i	− 0.0357898i
$493$	107.763i	0.00984467i
$494$	9952.86	0.906479
$495$	0	0
$496$	−2475.66	−0.224114
$497$	546.728i	0.0493443i
$498$	3160.39i	0.284379i
$499$	13168.5	1.18137	0.590686	−	0.806902i	$-0.298857\pi$
$499$	13168.5	1.18137	0.590686	+	0.806902i	$0.298857\pi$
$500$	0	0
$501$	6257.38	0.558002
$502$	15038.0i	1.33701i
$503$	− 1525.32i	− 0.135210i	−0.997712	−	0.0676052i	$-0.978464\pi$
$503$	− 1525.32i	− 0.135210i	0.997712	−	0.0676052i	$-0.0215358\pi$
$504$	4862.50	0.429748
$505$	0	0
$506$	−257.740	−0.0226442
$507$	− 6768.22i	− 0.592874i
$508$	4454.05i	0.389009i
$509$	−9006.01	−0.784253	−0.392126	−	0.919911i	$-0.628260\pi$
$509$	−9006.01	−0.784253	−0.392126	+	0.919911i	$0.628260\pi$
$510$	0	0
$511$	−16209.5	−1.40326
$512$	− 3586.45i	− 0.309571i
$513$	2112.37i	0.181800i
$514$	−9065.51	−0.777942
$515$	0	0
$516$	−3523.88	−0.300640
$517$	− 2480.09i	− 0.210975i
$518$	13287.9i	1.12710i
$519$	11997.8	1.01473
$520$	0	0
$521$	21707.8	1.82541	0.912703	−	0.408623i	$-0.133991\pi$
$521$	21707.8	1.82541	0.912703	+	0.408623i	$0.133991\pi$
$522$	− 535.018i	− 0.0448603i
$523$	− 14015.0i	− 1.17177i	−0.810396	−	0.585883i	$-0.800748\pi$
$523$	− 14015.0i	− 1.17177i	0.810396	−	0.585883i	$-0.199252\pi$
$524$	4380.06	0.365160
$525$	0	0
$526$	197.191	0.0163459
$527$	854.227i	0.0706086i
$528$	− 330.514i	− 0.0272420i
$529$	12015.9	0.987584
$530$	0	0
$531$	252.631	0.0206464
$532$	− 7827.88i	− 0.637935i
$533$	− 1990.05i	− 0.161724i
$534$	−8551.65	−0.693008
$535$	0	0
$536$	−867.244	−0.0698867
$537$	− 6139.79i	− 0.493392i
$538$	4154.98i	0.332963i
$539$	−2004.86	−0.160214
$540$	0	0
$541$	14444.9	1.14793	0.573967	−	0.818878i	$-0.305404\pi$
$541$	14444.9	1.14793	0.573967	+	0.818878i	$0.305404\pi$
$542$	− 7031.80i	− 0.557273i
$543$	192.892i	0.0152445i
$544$	−585.760	−0.0461659
$545$	0	0
$546$	8746.83	0.685585
$547$	− 20286.4i	− 1.58571i	−0.609412	−	0.792854i	$-0.708594\pi$
$547$	− 20286.4i	− 1.58571i	0.609412	−	0.792854i	$-0.291406\pi$
$548$	− 11635.1i	− 0.906985i
$549$	7683.68	0.597325
$550$	0	0
$551$	−2439.60	−0.188622
$552$	− 869.218i	− 0.0670224i
$553$	9445.34i	0.726323i
$554$	−5885.38	−0.451346
$555$	0	0
$556$	−11165.8	−0.851684
$557$	24482.4i	1.86239i	0.364520	+	0.931196i	$0.381233\pi$
$557$	24482.4i	1.86239i	−0.364520	+	0.931196i	$0.618767\pi$
$558$	− 4241.02i	− 0.321750i
$559$	−17954.7	−1.35851
$560$	0	0
$561$	−114.044	−0.00858278
$562$	6365.27i	0.477763i
$563$	− 20383.5i	− 1.52587i	−0.646478	−	0.762933i	$-0.723759\pi$
$563$	− 20383.5i	− 1.52587i	0.646478	−	0.762933i	$-0.276241\pi$
$564$	2952.89	0.220459
$565$	0	0
$566$	−2828.62	−0.210063
$567$	1856.40i	0.137498i
$568$	562.359i	0.0415424i
$569$	−3297.74	−0.242967	−0.121484	−	0.992593i	$-0.538765\pi$
$569$	−3297.74	−0.242967	−0.121484	+	0.992593i	$0.538765\pi$
$570$	0	0
$571$	−7213.03	−0.528644	−0.264322	−	0.964434i	$-0.585148\pi$
$571$	−7213.03	−0.528644	−0.264322	+	0.964434i	$0.585148\pi$
$572$	3204.60i	0.234250i
$573$	14449.8i	1.05349i
$574$	1302.97	0.0947472
$575$	0	0
$576$	3629.27	0.262534
$577$	18080.4i	1.30450i	0.758003	+	0.652251i	$0.226175\pi$
$577$	18080.4i	1.30450i	−0.758003	+	0.652251i	$0.773825\pi$
$578$	9343.34i	0.672373i
$579$	887.411	0.0636952
$580$	0	0
$581$	12664.7	0.904337
$582$	6859.87i	0.488575i
$583$	− 185.208i	− 0.0131570i
$584$	−16672.9	−1.18139
$585$	0	0
$586$	3032.22	0.213754
$587$	− 13457.5i	− 0.946250i	−0.880995	−	0.473125i	$-0.843126\pi$
$587$	− 13457.5i	− 0.946250i	0.880995	−	0.473125i	$-0.156874\pi$
$588$	− 2387.06i	− 0.167416i
$589$	−19338.4	−1.35285
$590$	0	0
$591$	−6443.91	−0.448506
$592$	3046.01i	0.211470i
$593$	− 10262.3i	− 0.710665i	−0.934740	−	0.355332i	$-0.884368\pi$
$593$	− 10262.3i	− 0.710665i	0.934740	−	0.355332i	$-0.115632\pi$
$594$	566.198	0.0391101
$595$	0	0
$596$	11545.7	0.793508
$597$	2628.78i	0.180216i
$598$	− 1563.58i	− 0.106922i
$599$	−23153.3	−1.57933	−0.789665	−	0.613538i	$-0.789746\pi$
$599$	−23153.3	−1.57933	−0.789665	+	0.613538i	$0.789746\pi$
$600$	0	0
$601$	14414.8	0.978357	0.489178	−	0.872184i	$-0.337297\pi$
$601$	14414.8	0.978357	0.489178	+	0.872184i	$0.337297\pi$
$602$	− 11755.7i	− 0.795891i
$603$	− 331.096i	− 0.0223603i
$604$	−12535.8	−0.844492
$605$	0	0
$606$	5774.42	0.387079
$607$	− 10808.8i	− 0.722757i	−0.932419	−	0.361379i	$-0.882306\pi$
$607$	− 10808.8i	− 0.722757i	0.932419	−	0.361379i	$-0.117694\pi$
$608$	− 13260.7i	− 0.884530i
$609$	−2143.99	−0.142658
$610$	0	0
$611$	15045.4	0.996191
$612$	− 135.785i	− 0.00896860i
$613$	12072.8i	0.795455i	0.917504	+	0.397727i	$0.130201\pi$
$613$	12072.8i	0.795455i	−0.917504	+	0.397727i	$0.869799\pi$
$614$	19398.0	1.27498
$615$	0	0
$616$	−5943.06	−0.388722
$617$	− 11593.5i	− 0.756462i	−0.925711	−	0.378231i	$-0.876532\pi$
$617$	− 11593.5i	− 0.756462i	0.925711	−	0.378231i	$-0.123468\pi$
$618$	− 6615.36i	− 0.430597i
$619$	−4037.96	−0.262196	−0.131098	−	0.991369i	$-0.541850\pi$
$619$	−4037.96	−0.262196	−0.131098	+	0.991369i	$0.541850\pi$
$620$	0	0
$621$	331.850	0.0214439
$622$	− 11930.7i	− 0.769094i
$623$	34269.2i	2.20380i
$624$	2005.06	0.128632
$625$	0	0
$626$	−18286.6	−1.16754
$627$	− 2581.78i	− 0.164444i
$628$	− 4577.46i	− 0.290861i
$629$	1051.03	0.0666252
$630$	0	0
$631$	2896.22	0.182721	0.0913604	−	0.995818i	$-0.470878\pi$
$631$	2896.22	0.182721	0.0913604	+	0.995818i	$0.470878\pi$
$632$	9715.39i	0.611483i
$633$	4241.96i	0.266355i
$634$	−20269.3	−1.26971
$635$	0	0
$636$	220.516	0.0137484
$637$	− 12162.5i	− 0.756506i
$638$	653.910i	0.0405777i
$639$	−214.697	−0.0132915
$640$	0	0
$641$	13371.2	0.823916	0.411958	−	0.911203i	$-0.364845\pi$
$641$	13371.2	0.823916	0.411958	+	0.911203i	$0.364845\pi$
$642$	2813.02i	0.172930i
$643$	14063.6i	0.862544i	0.902222	+	0.431272i	$0.141935\pi$
$643$	14063.6i	0.862544i	−0.902222	+	0.431272i	$0.858065\pi$
$644$	−1229.75	−0.0752466
$645$	0	0
$646$	515.438	0.0313926
$647$	− 20899.7i	− 1.26994i	−0.772536	−	0.634971i	$-0.781012\pi$
$647$	− 20899.7i	− 1.26994i	0.772536	−	0.634971i	$-0.218988\pi$
$648$	1909.48i	0.115758i
$649$	−308.771	−0.0186754
$650$	0	0
$651$	−16995.1	−1.02318
$652$	− 8530.09i	− 0.512368i
$653$	− 1607.80i	− 0.0963523i	−0.998839	−	0.0481761i	$-0.984659\pi$
$653$	− 1607.80i	− 0.0963523i	0.998839	−	0.0481761i	$-0.0153409\pi$
$654$	7668.08	0.458480
$655$	0	0
$656$	298.683	0.0177768
$657$	− 6365.39i	− 0.377987i
$658$	9850.86i	0.583627i
$659$	−14733.1	−0.870896	−0.435448	−	0.900214i	$-0.643410\pi$
$659$	−14733.1	−0.870896	−0.435448	+	0.900214i	$0.643410\pi$
$660$	0	0
$661$	−16442.2	−0.967518	−0.483759	−	0.875201i	$-0.660729\pi$
$661$	−16442.2	−0.967518	−0.483759	+	0.875201i	$0.660729\pi$
$662$	15675.5i	0.920312i
$663$	− 691.846i	− 0.0405265i
$664$	13026.8	0.761351
$665$	0	0
$666$	−5218.08	−0.303598
$667$	383.258i	0.0222486i
$668$	− 9105.88i	− 0.527421i
$669$	−10096.6	−0.583493
$670$	0	0
$671$	−9391.16	−0.540301
$672$	− 11653.9i	− 0.668985i
$673$	− 25246.6i	− 1.44604i	−0.690826	−	0.723021i	$-0.742753\pi$
$673$	− 25246.6i	− 1.44604i	0.690826	−	0.723021i	$-0.257247\pi$
$674$	−5619.60	−0.321156
$675$	0	0
$676$	−9849.26	−0.560381
$677$	− 24582.6i	− 1.39555i	−0.716318	−	0.697774i	$-0.754174\pi$
$677$	− 24582.6i	− 1.39555i	0.716318	−	0.697774i	$-0.245826\pi$
$678$	− 10575.9i	− 0.599065i
$679$	27489.7	1.55369
$680$	0	0
$681$	−17172.9	−0.966327
$682$	5183.46i	0.291034i
$683$	11459.5i	0.642000i	0.947079	+	0.321000i	$0.104019\pi$
$683$	11459.5i	0.642000i	−0.947079	+	0.321000i	$0.895981\pi$
$684$	3073.97	0.171836
$685$	0	0
$686$	−7023.00	−0.390874
$687$	− 7760.21i	− 0.430961i
$688$	− 2694.79i	− 0.149328i
$689$	1123.56	0.0621253
$690$	0	0
$691$	−15683.8	−0.863445	−0.431723	−	0.902006i	$-0.642094\pi$
$691$	−15683.8	−0.863445	−0.431723	+	0.902006i	$0.642094\pi$
$692$	− 17459.5i	− 0.959121i
$693$	− 2268.94i	− 0.124372i
$694$	6333.86	0.346441
$695$	0	0
$696$	−2205.28	−0.120102
$697$	− 103.061i	− 0.00560072i
$698$	17538.2i	0.951045i
$699$	−16714.9	−0.904457
$700$	0	0
$701$	6185.65	0.333279	0.166640	−	0.986018i	$-0.446708\pi$
$701$	6185.65	0.333279	0.166640	+	0.986018i	$0.446708\pi$
$702$	3434.83i	0.184672i
$703$	23793.7i	1.27652i
$704$	−4435.77	−0.237471
$705$	0	0
$706$	19264.4	1.02695
$707$	− 23139.9i	− 1.23093i
$708$	− 367.634i	− 0.0195149i
$709$	28031.2	1.48481	0.742407	−	0.669950i	$-0.233684\pi$
$709$	28031.2	1.48481	0.742407	+	0.669950i	$0.233684\pi$
$710$	0	0
$711$	−3709.14	−0.195645
$712$	35249.0i	1.85535i
$713$	3038.03i	0.159573i
$714$	452.980	0.0237428
$715$	0	0
$716$	−8934.77	−0.466352
$717$	5468.77i	0.284847i
$718$	9982.67i	0.518872i
$719$	−23313.0	−1.20922	−0.604610	−	0.796522i	$-0.706671\pi$
$719$	−23313.0	−1.20922	−0.604610	+	0.796522i	$0.706671\pi$
$720$	0	0
$721$	−26509.9	−1.36932
$722$	− 1407.20i	− 0.0725354i
$723$	− 6679.98i	− 0.343611i
$724$	280.701	0.0144091
$725$	0	0
$726$	−692.020	−0.0353764
$727$	69.6810i	0.00355478i	0.999998	+	0.00177739i	$0.000565761\pi$
$727$	69.6810i	0.00355478i	−0.999998	+	0.00177739i	$0.999434\pi$
$728$	− 36053.5i	− 1.83548i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−929.838	−0.0470469
$732$	− 11181.5i	− 0.564589i
$733$	15152.9i	0.763552i	0.924255	+	0.381776i	$0.124687\pi$
$733$	15152.9i	0.763552i	−0.924255	+	0.381776i	$0.875313\pi$
$734$	−17801.8	−0.895199
$735$	0	0
$736$	−2083.24	−0.104333
$737$	404.673i	0.0202257i
$738$	511.669i	0.0255214i
$739$	31557.9	1.57087	0.785437	−	0.618941i	$-0.212438\pi$
$739$	31557.9	1.57087	0.785437	+	0.618941i	$0.212438\pi$
$740$	0	0
$741$	15662.4	0.776479
$742$	735.642i	0.0363966i
$743$	6925.00i	0.341929i	0.985277	+	0.170965i	$0.0546884\pi$
$743$	6925.00i	0.341929i	−0.985277	+	0.170965i	$0.945312\pi$
$744$	−17481.0	−0.861404
$745$	0	0
$746$	−27177.7	−1.33384
$747$	4973.36i	0.243595i
$748$	165.959i	0.00811240i
$749$	11272.7	0.549925
$750$	0	0
$751$	−22202.1	−1.07878	−0.539392	−	0.842055i	$-0.681346\pi$
$751$	−22202.1	−1.07878	−0.539392	+	0.842055i	$0.681346\pi$
$752$	2258.14i	0.109502i
$753$	23664.7i	1.14527i
$754$	−3966.94	−0.191601
$755$	0	0
$756$	2701.48	0.129963
$757$	− 18928.6i	− 0.908813i	−0.890795	−	0.454406i	$-0.849851\pi$
$757$	− 18928.6i	− 0.908813i	0.890795	−	0.454406i	$-0.150149\pi$
$758$	− 3643.48i	− 0.174587i
$759$	−405.594	−0.0193967
$760$	0	0
$761$	−22883.3	−1.09004	−0.545019	−	0.838423i	$-0.683478\pi$
$761$	−22883.3	−1.09004	−0.545019	+	0.838423i	$0.683478\pi$
$762$	− 5834.95i	− 0.277399i
$763$	− 30728.4i	− 1.45799i
$764$	21027.7	0.995752
$765$	0	0
$766$	−3324.57	−0.156817
$767$	− 1873.16i	− 0.0881822i
$768$	− 13036.5i	− 0.612516i
$769$	−8903.82	−0.417529	−0.208765	−	0.977966i	$-0.566944\pi$
$769$	−8903.82	−0.417529	−0.208765	+	0.977966i	$0.566944\pi$
$770$	0	0
$771$	−14266.0	−0.666376
$772$	− 1291.38i	− 0.0602044i
$773$	24691.9i	1.14891i	0.818537	+	0.574454i	$0.194786\pi$
$773$	24691.9i	1.14891i	−0.818537	+	0.574454i	$0.805214\pi$
$774$	4616.40	0.214384
$775$	0	0
$776$	28275.6	1.30804
$777$	20910.5i	0.965457i
$778$	5213.75i	0.240259i
$779$	2333.14	0.107309
$780$	0	0
$781$	262.408	0.0120226
$782$	− 80.9744i	− 0.00370286i
$783$	− 841.932i	− 0.0384268i
$784$	1825.44	0.0831559
$785$	0	0
$786$	−5738.02	−0.260392
$787$	7418.83i	0.336026i	0.985785	+	0.168013i	$0.0537351\pi$
$787$	7418.83i	0.336026i	−0.985785	+	0.168013i	$0.946265\pi$
$788$	9377.33i	0.423926i
$789$	310.311	0.0140017
$790$	0	0
$791$	−42381.1	−1.90506
$792$	− 2333.81i	− 0.104707i
$793$	− 56971.4i	− 2.55121i
$794$	−28366.2	−1.26786
$795$	0	0
$796$	3825.46	0.170339
$797$	27971.2i	1.24315i	0.783354	+	0.621576i	$0.213507\pi$
$797$	27971.2i	1.24315i	−0.783354	+	0.621576i	$0.786493\pi$
$798$	10254.8i	0.454907i
$799$	779.171	0.0344995
$800$	0	0
$801$	−13457.3	−0.593622
$802$	− 22187.0i	− 0.976869i
$803$	7779.92i	0.341902i
$804$	−481.819	−0.0211349
$805$	0	0
$806$	−31445.4	−1.37421
$807$	6538.51i	0.285212i
$808$	− 23801.5i	− 1.03630i
$809$	10670.0	0.463704	0.231852	−	0.972751i	$-0.425521\pi$
$809$	10670.0	0.463704	0.231852	+	0.972751i	$0.425521\pi$
$810$	0	0
$811$	40618.3	1.75869	0.879346	−	0.476182i	$-0.157980\pi$
$811$	40618.3	1.75869	0.879346	+	0.476182i	$0.157980\pi$
$812$	3119.98i	0.134840i
$813$	− 11065.6i	− 0.477353i
$814$	6377.66	0.274615
$815$	0	0
$816$	103.838	0.00445471
$817$	− 21050.1i	− 0.901409i
$818$	− 1785.52i	− 0.0763192i
$819$	13764.5	0.587265
$820$	0	0
$821$	16710.5	0.710355	0.355178	−	0.934799i	$-0.384420\pi$
$821$	16710.5	0.710355	0.355178	+	0.934799i	$0.384420\pi$
$822$	15242.4i	0.646764i
$823$	− 16920.5i	− 0.716661i	−0.933595	−	0.358331i	$-0.883346\pi$
$823$	− 16920.5i	− 0.716661i	0.933595	−	0.358331i	$-0.116654\pi$
$824$	−27267.8	−1.15281
$825$	0	0
$826$	1226.43	0.0516623
$827$	9478.39i	0.398544i	0.979944	+	0.199272i	$0.0638577\pi$
$827$	9478.39i	0.398544i	−0.979944	+	0.199272i	$0.936142\pi$
$828$	− 482.915i	− 0.0202687i
$829$	31908.1	1.33681	0.668405	−	0.743798i	$-0.266977\pi$
$829$	31908.1	1.33681	0.668405	+	0.743798i	$0.266977\pi$
$830$	0	0
$831$	−9261.54	−0.386618
$832$	− 26909.6i	− 1.12130i
$833$	− 629.869i	− 0.0261989i
$834$	14627.6	0.607329
$835$	0	0
$836$	−3757.07	−0.155432
$837$	− 6673.89i	− 0.275607i
$838$	− 244.090i	− 0.0100620i
$839$	−25195.7	−1.03677	−0.518386	−	0.855147i	$-0.673467\pi$
$839$	−25195.7	−1.03677	−0.518386	+	0.855147i	$0.673467\pi$
$840$	0	0
$841$	−23416.6	−0.960131
$842$	− 12637.4i	− 0.517238i
$843$	10016.7i	0.409246i
$844$	6173.00	0.251758
$845$	0	0
$846$	−3868.38	−0.157208
$847$	2773.15i	0.112499i
$848$	168.633i	0.00682887i
$849$	−4451.26	−0.179938
$850$	0	0
$851$	3737.95	0.150570
$852$	312.432i	0.0125631i
$853$	8239.19i	0.330720i	0.986233	+	0.165360i	$0.0528786\pi$
$853$	8239.19i	0.330720i	−0.986233	+	0.165360i	$0.947121\pi$
$854$	37301.5	1.49465
$855$	0	0
$856$	11594.9	0.462976
$857$	− 12912.8i	− 0.514694i	−0.966319	−	0.257347i	$-0.917152\pi$
$857$	− 12912.8i	− 0.514694i	0.966319	−	0.257347i	$-0.0828484\pi$
$858$	− 4198.13i	− 0.167042i
$859$	−18534.6	−0.736196	−0.368098	−	0.929787i	$-0.619991\pi$
$859$	−18534.6	−0.736196	−0.368098	+	0.929787i	$0.619991\pi$
$860$	0	0
$861$	2050.42	0.0811594
$862$	27981.7i	1.10564i
$863$	− 18743.4i	− 0.739318i	−0.929168	−	0.369659i	$-0.879475\pi$
$863$	− 18743.4i	− 0.739318i	0.929168	−	0.369659i	$-0.120525\pi$
$864$	4576.42	0.180200
$865$	0	0
$866$	2193.04	0.0860536
$867$	14703.2i	0.575947i
$868$	24731.7i	0.967105i
$869$	4533.39	0.176967
$870$	0	0
$871$	−2454.94	−0.0955024
$872$	− 31607.0i	− 1.22746i
$873$	10795.1i	0.418508i
$874$	1833.14	0.0709461
$875$	0	0
$876$	−9263.06	−0.357272
$877$	− 25629.7i	− 0.986833i	−0.869793	−	0.493417i	$-0.835748\pi$
$877$	− 25629.7i	− 0.986833i	0.869793	−	0.493417i	$-0.164252\pi$
$878$	17745.3i	0.682088i
$879$	4771.66	0.183099
$880$	0	0
$881$	14336.5	0.548250	0.274125	−	0.961694i	$-0.411612\pi$
$881$	14336.5	0.548250	0.274125	+	0.961694i	$0.411612\pi$
$882$	3127.13i	0.119383i
$883$	1012.36i	0.0385827i	0.999814	+	0.0192914i	$0.00614102\pi$
$883$	1012.36i	0.0385827i	−0.999814	+	0.0192914i	$0.993859\pi$
$884$	−1006.79	−0.0383054
$885$	0	0
$886$	10845.9	0.411258
$887$	2586.40i	0.0979061i	0.998801	+	0.0489530i	$0.0155885\pi$
$887$	2586.40i	0.0979061i	−0.998801	+	0.0489530i	$0.984412\pi$
$888$	21508.4i	0.812808i
$889$	−23382.5	−0.882142
$890$	0	0
$891$	891.000	0.0335013
$892$	14692.8i	0.551515i
$893$	17639.3i	0.661003i
$894$	−15125.3	−0.565844
$895$	0	0
$896$	−13458.2	−0.501794
$897$	− 2460.53i	− 0.0915883i
$898$	12667.8i	0.470746i
$899$	7707.77	0.285949
$900$	0	0
$901$	58.1869	0.00215148
$902$	− 625.374i	− 0.0230850i
$903$	− 18499.4i	− 0.681751i
$904$	−43592.8	−1.60385
$905$	0	0
$906$	16422.3	0.602201
$907$	− 43346.1i	− 1.58686i	−0.608660	−	0.793431i	$-0.708293\pi$
$907$	− 43346.1i	− 1.58686i	0.608660	−	0.793431i	$-0.291707\pi$
$908$	24990.5i	0.913368i
$909$	9086.93	0.331567
$910$	0	0
$911$	−5218.71	−0.189796	−0.0948978	−	0.995487i	$-0.530252\pi$
$911$	−5218.71	−0.189796	−0.0948978	+	0.995487i	$0.530252\pi$
$912$	2350.73i	0.0853514i
$913$	− 6078.55i	− 0.220340i
$914$	−15928.1	−0.576428
$915$	0	0
$916$	−11292.8	−0.407343
$917$	22994.1i	0.828060i
$918$	177.883i	0.00639544i
$919$	29209.5	1.04846	0.524230	−	0.851577i	$-0.324353\pi$
$919$	29209.5	1.04846	0.524230	+	0.851577i	$0.324353\pi$
$920$	0	0
$921$	30525.8	1.09214
$922$	− 29702.5i	− 1.06095i
$923$	1591.89i	0.0567690i
$924$	−3301.81	−0.117556
$925$	0	0
$926$	−13610.0	−0.482995
$927$	− 10410.3i	− 0.368844i
$928$	5285.37i	0.186962i
$929$	39401.0	1.39150	0.695751	−	0.718283i	$-0.255072\pi$
$929$	39401.0	1.39150	0.695751	+	0.718283i	$0.255072\pi$
$930$	0	0
$931$	14259.3	0.501965
$932$	24323.9i	0.854888i
$933$	− 18774.7i	− 0.658797i
$934$	−23668.0	−0.829165
$935$	0	0
$936$	14158.0	0.494411
$937$	− 6099.66i	− 0.212665i	−0.994331	−	0.106332i	$-0.966089\pi$
$937$	− 6099.66i	− 0.212665i	0.994331	−	0.106332i	$-0.0339108\pi$
$938$	− 1607.35i	− 0.0559509i
$939$	−28776.7	−1.00010
$940$	0	0
$941$	11534.4	0.399587	0.199793	−	0.979838i	$-0.435973\pi$
$941$	11534.4	0.399587	0.199793	+	0.979838i	$0.435973\pi$
$942$	5996.63i	0.207410i
$943$	− 366.532i	− 0.0126574i
$944$	281.138	0.00969307
$945$	0	0
$946$	−5642.27	−0.193918
$947$	16680.4i	0.572376i	0.958174	+	0.286188i	$0.0923881\pi$
$947$	16680.4i	0.572376i	−0.958174	+	0.286188i	$0.907612\pi$
$948$	5397.62i	0.184923i
$949$	−47196.8	−1.61441
$950$	0	0
$951$	−31896.9	−1.08762
$952$	− 1867.13i	− 0.0635653i
$953$	− 17114.4i	− 0.581733i	−0.956764	−	0.290866i	$-0.906057\pi$
$953$	− 17114.4i	− 0.581733i	0.956764	−	0.290866i	$-0.0939435\pi$
$954$	−288.883	−0.00980391
$955$	0	0
$956$	7958.29	0.269236
$957$	1029.03i	0.0347584i
$958$	26977.4i	0.909814i
$959$	61081.2	2.05674
$960$	0	0
$961$	31307.5	1.05090
$962$	38690.0i	1.29669i
$963$	4426.71i	0.148130i
$964$	−9720.86	−0.324780
$965$	0	0
$966$	1611.01	0.0536578
$967$	35200.4i	1.17060i	0.810817	+	0.585299i	$0.199023\pi$
$967$	35200.4i	1.17060i	−0.810817	+	0.585299i	$0.800977\pi$
$968$	2852.43i	0.0947114i
$969$	811.120	0.0268906
$970$	0	0
$971$	−43502.6	−1.43776	−0.718881	−	0.695134i	$-0.755345\pi$
$971$	−43502.6	−1.43776	−0.718881	+	0.695134i	$0.755345\pi$
$972$	1060.86i	0.0350072i
$973$	− 58617.5i	− 1.93134i
$974$	−146.098	−0.00480624
$975$	0	0
$976$	8550.71	0.280432
$977$	5365.50i	0.175699i	0.996134	+	0.0878494i	$0.0279994\pi$
$977$	5365.50i	0.175699i	−0.996134	+	0.0878494i	$0.972001\pi$
$978$	11174.7i	0.365366i
$979$	16447.9	0.536952
$980$	0	0
$981$	12066.9	0.392728
$982$	− 3255.23i	− 0.105783i
$983$	42459.0i	1.37765i	0.724926	+	0.688826i	$0.241874\pi$
$983$	42459.0i	1.37765i	−0.724926	+	0.688826i	$0.758126\pi$
$984$	2109.05	0.0683271
$985$	0	0
$986$	−205.439	−0.00663542
$987$	15501.8i	0.499928i
$988$	− 22792.2i	− 0.733924i
$989$	−3306.94	−0.106324
$990$	0	0
$991$	−6881.29	−0.220576	−0.110288	−	0.993900i	$-0.535177\pi$
$991$	−6881.29	−0.220576	−0.110288	+	0.993900i	$0.535177\pi$
$992$	41896.4i	1.34094i
$993$	24667.8i	0.788328i
$994$	−1042.28	−0.0332586
$995$	0	0
$996$	7237.35	0.230245
$997$	3166.87i	0.100597i	0.998734	+	0.0502987i	$0.0160173\pi$
$997$	3166.87i	0.100597i	−0.998734	+	0.0502987i	$0.983983\pi$
$998$	25104.4i	0.796258i
$999$	−8211.45	−0.260059

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.k.199.4		6
5.2	odd	4		165.4.a.e.1.2	✓	3
5.3	odd	4		825.4.a.r.1.2		3
5.4	even	2	inner	825.4.c.k.199.3		6
15.2	even	4		495.4.a.k.1.2		3
15.8	even	4		2475.4.a.t.1.2		3
55.32	even	4		1815.4.a.r.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.e.1.2	✓	3	5.2	odd	4
495.4.a.k.1.2		3	15.2	even	4
825.4.a.r.1.2		3	5.3	odd	4
825.4.c.k.199.3		6	5.4	even	2	inner
825.4.c.k.199.4		6	1.1	even	1	trivial
1815.4.a.r.1.2		3	55.32	even	4
2475.4.a.t.1.2		3	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.90639i q^{2} +3.00000i q^{3} +4.36567 q^{4} -5.71918 q^{6} +22.9186i q^{7} +23.5738i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+1.90639i q^{2} +3.00000i q^{3} +4.36567 q^{4} -5.71918 q^{6} +22.9186i q^{7} +23.5738i q^{8} -9.00000 q^{9} +11.0000 q^{11} +13.0970i q^{12} +66.7313i q^{13} -43.6917 q^{14} -10.0156 q^{16} +3.45588i q^{17} -17.1575i q^{18} -78.2359 q^{19} -68.7557 q^{21} +20.9703i q^{22} +12.2907i q^{23} -70.7214 q^{24} -127.216 q^{26} -27.0000i q^{27} +100.055i q^{28} +31.1827 q^{29} +247.181 q^{31} +169.497i q^{32} +33.0000i q^{33} -6.58825 q^{34} -39.2910 q^{36} -304.128i q^{37} -149.148i q^{38} -200.194 q^{39} -29.8219 q^{41} -131.075i q^{42} +269.060i q^{43} +48.0224 q^{44} -23.4309 q^{46} -225.463i q^{47} -30.0467i q^{48} -182.260 q^{49} -10.3676 q^{51} +291.327i q^{52} -16.8371i q^{53} +51.4726 q^{54} -540.278 q^{56} -234.708i q^{57} +59.4464i q^{58} -28.0701 q^{59} -853.742 q^{61} +471.224i q^{62} -206.267i q^{63} -403.252 q^{64} -62.9109 q^{66} +36.7885i q^{67} +15.0872i q^{68} -36.8722 q^{69} +23.8552 q^{71} -212.164i q^{72} +707.265i q^{73} +579.787 q^{74} -341.552 q^{76} +252.104i q^{77} -381.648i q^{78} +412.126 q^{79} +81.0000 q^{81} -56.8522i q^{82} -552.596i q^{83} -300.165 q^{84} -512.934 q^{86} +93.5480i q^{87} +259.312i q^{88} +1495.26 q^{89} -1529.39 q^{91} +53.6573i q^{92} +741.543i q^{93} +429.820 q^{94} -508.491 q^{96} -1199.45i q^{97} -347.459i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 60 q^{4} - 12 q^{6} - 54 q^{9}+O(q^{10}) \) 6 * q - 60 * q^4 - 12 * q^6 - 54 * q^9	\( 6 q - 60 q^{4} - 12 q^{6} - 54 q^{9} + 66 q^{11} + 136 q^{14} + 356 q^{16} + 116 q^{19} + 60 q^{21} - 108 q^{24} - 240 q^{26} + 440 q^{29} + 496 q^{31} + 160 q^{34} + 540 q^{36} - 684 q^{39} + 312 q^{41} - 660 q^{44} - 2512 q^{46} - 558 q^{49} - 624 q^{51} + 108 q^{54} - 3288 q^{56} - 1096 q^{59} + 828 q^{61} + 116 q^{64} - 132 q^{66} - 720 q^{69} - 1824 q^{71} + 3224 q^{74} - 5504 q^{76} + 1084 q^{79} + 486 q^{81} - 4056 q^{84} - 3096 q^{86} - 1580 q^{89} - 1544 q^{91} + 848 q^{94} - 1548 q^{96} - 594 q^{99}+O(q^{100}) \) 6 * q - 60 * q^4 - 12 * q^6 - 54 * q^9 + 66 * q^11 + 136 * q^14 + 356 * q^16 + 116 * q^19 + 60 * q^21 - 108 * q^24 - 240 * q^26 + 440 * q^29 + 496 * q^31 + 160 * q^34 + 540 * q^36 - 684 * q^39 + 312 * q^41 - 660 * q^44 - 2512 * q^46 - 558 * q^49 - 624 * q^51 + 108 * q^54 - 3288 * q^56 - 1096 * q^59 + 828 * q^61 + 116 * q^64 - 132 * q^66 - 720 * q^69 - 1824 * q^71 + 3224 * q^74 - 5504 * q^76 + 1084 * q^79 + 486 * q^81 - 4056 * q^84 - 3096 * q^86 - 1580 * q^89 - 1544 * q^91 + 848 * q^94 - 1548 * q^96 - 594 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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