LMFDB - Embedded newform 825.4.c.s.199.1

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 43x^{8} + 631x^{6} + 3625x^{4} + 7104x^{2} + 900 $ x^10 + 43x^8 + 631x^6 + 3625x^4 + 7104x^2 + 900
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.1
Root			$-4.08549i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.s.199.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.08549i q^{2} -3.00000i q^{3} -8.69126 q^{4} -12.2565 q^{6} -7.95915i q^{7} +2.82414i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-4.08549i q^{2} -3.00000i q^{3} -8.69126 q^{4} -12.2565 q^{6} -7.95915i q^{7} +2.82414i q^{8} -9.00000 q^{9} -11.0000 q^{11} +26.0738i q^{12} -47.2865i q^{13} -32.5171 q^{14} -57.9921 q^{16} -82.2723i q^{17} +36.7694i q^{18} +18.3225 q^{19} -23.8775 q^{21} +44.9404i q^{22} -128.333i q^{23} +8.47241 q^{24} -193.189 q^{26} +27.0000i q^{27} +69.1751i q^{28} +84.1889 q^{29} +51.0689 q^{31} +259.519i q^{32} +33.0000i q^{33} -336.123 q^{34} +78.2213 q^{36} -80.6029i q^{37} -74.8566i q^{38} -141.860 q^{39} -482.645 q^{41} +97.5512i q^{42} -223.383i q^{43} +95.6039 q^{44} -524.304 q^{46} +305.367i q^{47} +173.976i q^{48} +279.652 q^{49} -246.817 q^{51} +410.979i q^{52} +606.661i q^{53} +110.308 q^{54} +22.4777 q^{56} -54.9676i q^{57} -343.953i q^{58} -122.825 q^{59} +13.8161 q^{61} -208.642i q^{62} +71.6324i q^{63} +596.328 q^{64} +134.821 q^{66} +795.341i q^{67} +715.050i q^{68} -384.999 q^{69} -99.8975 q^{71} -25.4172i q^{72} +12.2897i q^{73} -329.303 q^{74} -159.246 q^{76} +87.5507i q^{77} +579.566i q^{78} -180.823 q^{79} +81.0000 q^{81} +1971.84i q^{82} -144.966i q^{83} +207.525 q^{84} -912.628 q^{86} -252.567i q^{87} -31.0655i q^{88} +832.167 q^{89} -376.360 q^{91} +1115.38i q^{92} -153.207i q^{93} +1247.57 q^{94} +778.558 q^{96} +1282.35i q^{97} -1142.52i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 6 q^{4} - 6 q^{6} - 90 q^{9}+O(q^{10}) $ 10 * q - 6 * q^4 - 6 * q^6 - 90 * q^9	$ 10 q - 6 q^{4} - 6 q^{6} - 90 q^{9} - 110 q^{11} - 16 q^{14} - 250 q^{16} + 114 q^{19} - 108 q^{21} - 18 q^{24} - 250 q^{26} + 214 q^{29} - 590 q^{31} - 68 q^{34} + 54 q^{36} + 186 q^{39} - 256 q^{41} + 66 q^{44} - 1154 q^{46} + 830 q^{49} - 228 q^{51} + 54 q^{54} - 264 q^{56} + 2304 q^{59} - 688 q^{61} + 1090 q^{64} + 66 q^{66} + 966 q^{69} - 1414 q^{71} + 2352 q^{74} - 3398 q^{76} + 4988 q^{79} + 810 q^{81} + 1944 q^{84} - 1598 q^{86} + 4870 q^{89} - 1608 q^{91} + 1004 q^{94} + 138 q^{96} + 990 q^{99}+O(q^{100}) $ 10 * q - 6 * q^4 - 6 * q^6 - 90 * q^9 - 110 * q^11 - 16 * q^14 - 250 * q^16 + 114 * q^19 - 108 * q^21 - 18 * q^24 - 250 * q^26 + 214 * q^29 - 590 * q^31 - 68 * q^34 + 54 * q^36 + 186 * q^39 - 256 * q^41 + 66 * q^44 - 1154 * q^46 + 830 * q^49 - 228 * q^51 + 54 * q^54 - 264 * q^56 + 2304 * q^59 - 688 * q^61 + 1090 * q^64 + 66 * q^66 + 966 * q^69 - 1414 * q^71 + 2352 * q^74 - 3398 * q^76 + 4988 * q^79 + 810 * q^81 + 1944 * q^84 - 1598 * q^86 + 4870 * q^89 - 1608 * q^91 + 1004 * q^94 + 138 * q^96 + 990 * 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 $

$2$	− 4.08549i	− 1.44444i	−0.691663	−	0.722220i	$-0.743122\pi$
$2$	− 4.08549i	− 1.44444i	0.691663	−	0.722220i	$-0.256878\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	−8.69126	−1.08641
$5$	0	0
$5$	0	0
$6$	−12.2565	−0.833948
$7$	− 7.95915i	− 0.429754i	−0.976641	−	0.214877i	$-0.931065\pi$
$7$	− 7.95915i	− 0.429754i	0.976641	−	0.214877i	$-0.0689350\pi$
$8$	2.82414i	0.124810i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	26.0738i	0.627238i
$13$	− 47.2865i	− 1.00884i	−0.863459	−	0.504420i	$-0.831706\pi$
$13$	− 47.2865i	− 1.00884i	0.863459	−	0.504420i	$-0.168294\pi$
$14$	−32.5171	−0.620754
$15$	0	0
$16$	−57.9921	−0.906126
$17$	− 82.2723i	− 1.17376i	−0.809673	−	0.586881i	$-0.800355\pi$
$17$	− 82.2723i	− 1.17376i	0.809673	−	0.586881i	$-0.199645\pi$
$18$	36.7694i	0.481480i
$19$	18.3225	0.221236	0.110618	−	0.993863i	$-0.464717\pi$
$19$	18.3225	0.221236	0.110618	+	0.993863i	$0.464717\pi$
$20$	0	0
$21$	−23.8775	−0.248118
$22$	44.9404i	0.435515i
$23$	− 128.333i	− 1.16345i	−0.813387	−	0.581724i	$-0.802379\pi$
$23$	− 128.333i	− 1.16345i	0.813387	−	0.581724i	$-0.197621\pi$
$24$	8.47241	0.0720593
$25$	0	0
$26$	−193.189	−1.45721
$27$	27.0000i	0.192450i
$28$	69.1751i	0.466888i
$29$	84.1889	0.539086	0.269543	−	0.962988i	$-0.413127\pi$
$29$	84.1889	0.539086	0.269543	+	0.962988i	$0.413127\pi$
$30$	0	0
$31$	51.0689	0.295879	0.147939	−	0.988996i	$-0.452736\pi$
$31$	51.0689	0.295879	0.147939	+	0.988996i	$0.452736\pi$
$32$	259.519i	1.43366i
$33$	33.0000i	0.174078i
$34$	−336.123	−1.69543
$35$	0	0
$36$	78.2213	0.362136
$37$	− 80.6029i	− 0.358136i	−0.983837	−	0.179068i	$-0.942692\pi$
$37$	− 80.6029i	− 0.358136i	0.983837	−	0.179068i	$-0.0573082\pi$
$38$	− 74.8566i	− 0.319562i
$39$	−141.860	−0.582454
$40$	0	0
$41$	−482.645	−1.83845	−0.919225	−	0.393732i	$-0.871184\pi$
$41$	−482.645	−1.83845	−0.919225	+	0.393732i	$0.871184\pi$
$42$	97.5512i	0.358392i
$43$	− 223.383i	− 0.792221i	−0.918203	−	0.396111i	$-0.870360\pi$
$43$	− 223.383i	− 0.792221i	0.918203	−	0.396111i	$-0.129640\pi$
$44$	95.6039	0.327564
$45$	0	0
$46$	−524.304	−1.68053
$47$	305.367i	0.947709i	0.880603	+	0.473854i	$0.157138\pi$
$47$	305.367i	0.947709i	−0.880603	+	0.473854i	$0.842862\pi$
$48$	173.976i	0.523152i
$49$	279.652	0.815312
$50$	0	0
$51$	−246.817	−0.677672
$52$	410.979i	1.09601i
$53$	606.661i	1.57229i	0.618043	+	0.786145i	$0.287926\pi$
$53$	606.661i	1.57229i	−0.618043	+	0.786145i	$0.712074\pi$
$54$	110.308	0.277983
$55$	0	0
$56$	22.4777	0.0536377
$57$	− 54.9676i	− 0.127730i
$58$	− 343.953i	− 0.778678i
$59$	−122.825	−0.271025	−0.135512	−	0.990776i	$-0.543268\pi$
$59$	−122.825	−0.271025	−0.135512	+	0.990776i	$0.543268\pi$
$60$	0	0
$61$	13.8161	0.0289995	0.0144998	−	0.999895i	$-0.495384\pi$
$61$	13.8161	0.0289995	0.0144998	+	0.999895i	$0.495384\pi$
$62$	− 208.642i	− 0.427380i
$63$	71.6324i	0.143251i
$64$	596.328	1.16470
$65$	0	0
$66$	134.821	0.251445
$67$	795.341i	1.45024i	0.688620	+	0.725122i	$0.258217\pi$
$67$	795.341i	1.45024i	−0.688620	+	0.725122i	$0.741783\pi$
$68$	715.050i	1.27518i
$69$	−384.999	−0.671716
$70$	0	0
$71$	−99.8975	−0.166981	−0.0834905	−	0.996509i	$-0.526607\pi$
$71$	−99.8975	−0.166981	−0.0834905	+	0.996509i	$0.526607\pi$
$72$	− 25.4172i	− 0.0416035i
$73$	12.2897i	0.0197041i	0.999951	+	0.00985204i	$0.00313605\pi$
$73$	12.2897i	0.0197041i	−0.999951	+	0.00985204i	$0.996864\pi$
$74$	−329.303	−0.517306
$75$	0	0
$76$	−159.246	−0.240352
$77$	87.5507i	0.129576i
$78$	579.566i	0.841320i
$79$	−180.823	−0.257521	−0.128760	−	0.991676i	$-0.541100\pi$
$79$	−180.823	−0.257521	−0.128760	+	0.991676i	$0.541100\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	1971.84i	2.65553i
$83$	− 144.966i	− 0.191712i	−0.995395	−	0.0958560i	$-0.969441\pi$
$83$	− 144.966i	− 0.191712i	0.995395	−	0.0958560i	$-0.0305588\pi$
$84$	207.525	0.269558
$85$	0	0
$86$	−912.628	−1.14432
$87$	− 252.567i	− 0.311241i
$88$	− 31.0655i	− 0.0376318i
$89$	832.167	0.991118	0.495559	−	0.868574i	$-0.334963\pi$
$89$	832.167	0.991118	0.495559	+	0.868574i	$0.334963\pi$
$90$	0	0
$91$	−376.360	−0.433553
$92$	1115.38i	1.26398i
$93$	− 153.207i	− 0.170826i
$94$	1247.57	1.36891
$95$	0	0
$96$	778.558	0.827721
$97$	1282.35i	1.34229i	0.741324	+	0.671147i	$0.234198\pi$
$97$	1282.35i	1.34229i	−0.741324	+	0.671147i	$0.765802\pi$
$98$	− 1142.52i	− 1.17767i
$99$	99.0000	0.100504
$100$	0	0
$101$	−279.370	−0.275232	−0.137616	−	0.990486i	$-0.543944\pi$
$101$	−279.370	−0.275232	−0.137616	+	0.990486i	$0.543944\pi$
$102$	1008.37i	0.978857i
$103$	420.646i	0.402403i	0.979550	+	0.201201i	$0.0644846\pi$
$103$	420.646i	0.402403i	−0.979550	+	0.201201i	$0.935515\pi$
$104$	133.544	0.125914
$105$	0	0
$106$	2478.51	2.27108
$107$	− 711.910i	− 0.643205i	−0.946875	−	0.321602i	$-0.895779\pi$
$107$	− 711.910i	− 0.643205i	0.946875	−	0.321602i	$-0.104221\pi$
$108$	− 234.664i	− 0.209079i
$109$	−761.079	−0.668790	−0.334395	−	0.942433i	$-0.608532\pi$
$109$	−761.079	−0.668790	−0.334395	+	0.942433i	$0.608532\pi$
$110$	0	0
$111$	−241.809	−0.206770
$112$	461.568i	0.389411i
$113$	− 376.790i	− 0.313676i	−0.987624	−	0.156838i	$-0.949870\pi$
$113$	− 376.790i	− 0.313676i	0.987624	−	0.156838i	$-0.0501300\pi$
$114$	−224.570	−0.184499
$115$	0	0
$116$	−731.708	−0.585667
$117$	425.579i	0.336280i
$118$	501.801i	0.391479i
$119$	−654.818	−0.504429
$120$	0	0
$121$	121.000	0.0909091
$122$	− 56.4457i	− 0.0418881i
$123$	1447.93i	1.06143i
$124$	−443.853	−0.321445
$125$	0	0
$126$	292.654	0.206918
$127$	− 499.577i	− 0.349057i	−0.984652	−	0.174529i	$-0.944160\pi$
$127$	− 499.577i	− 0.349057i	0.984652	−	0.174529i	$-0.0558401\pi$
$128$	− 360.140i	− 0.248689i
$129$	−670.148	−0.457389
$130$	0	0
$131$	−2638.09	−1.75947	−0.879737	−	0.475461i	$-0.842281\pi$
$131$	−2638.09	−1.75947	−0.879737	+	0.475461i	$0.842281\pi$
$132$	− 286.812i	− 0.189119i
$133$	− 145.832i	− 0.0950768i
$134$	3249.36	2.09479
$135$	0	0
$136$	232.348	0.146498
$137$	− 2887.01i	− 1.80039i	−0.435485	−	0.900196i	$-0.643423\pi$
$137$	− 2887.01i	− 1.80039i	0.435485	−	0.900196i	$-0.356577\pi$
$138$	1572.91i	0.970254i
$139$	2370.00	1.44619	0.723096	−	0.690747i	$-0.242718\pi$
$139$	2370.00	1.44619	0.723096	+	0.690747i	$0.242718\pi$
$140$	0	0
$141$	916.100	0.547160
$142$	408.131i	0.241194i
$143$	520.152i	0.304177i
$144$	521.929	0.302042
$145$	0	0
$146$	50.2094	0.0284614
$147$	− 838.956i	− 0.470720i
$148$	700.541i	0.389082i
$149$	1854.61	1.01970	0.509851	−	0.860263i	$-0.329701\pi$
$149$	1854.61	1.01970	0.509851	+	0.860263i	$0.329701\pi$
$150$	0	0
$151$	1423.58	0.767214	0.383607	−	0.923496i	$-0.374682\pi$
$151$	1423.58	0.767214	0.383607	+	0.923496i	$0.374682\pi$
$152$	51.7453i	0.0276125i
$153$	740.451i	0.391254i
$154$	357.688	0.187164
$155$	0	0
$156$	1232.94	0.632782
$157$	− 1332.36i	− 0.677287i	−0.940915	−	0.338643i	$-0.890032\pi$
$157$	− 1332.36i	− 0.677287i	0.940915	−	0.338643i	$-0.109968\pi$
$158$	738.750i	0.371974i
$159$	1819.98	0.907761
$160$	0	0
$161$	−1021.42	−0.499996
$162$	− 330.925i	− 0.160493i
$163$	1058.37i	0.508575i	0.967129	+	0.254288i	$0.0818410\pi$
$163$	1058.37i	0.508575i	−0.967129	+	0.254288i	$0.918159\pi$
$164$	4194.79	1.99731
$165$	0	0
$166$	−592.258	−0.276916
$167$	− 2652.65i	− 1.22915i	−0.788859	−	0.614575i	$-0.789328\pi$
$167$	− 2652.65i	− 1.22915i	0.788859	−	0.614575i	$-0.210672\pi$
$168$	− 67.4332i	− 0.0309678i
$169$	−39.0132	−0.0177575
$170$	0	0
$171$	−164.903	−0.0737452
$172$	1941.48i	0.860675i
$173$	618.618i	0.271865i	0.990718	+	0.135933i	$0.0434031\pi$
$173$	618.618i	0.271865i	−0.990718	+	0.135933i	$0.956597\pi$
$174$	−1031.86	−0.449570
$175$	0	0
$176$	637.913	0.273207
$177$	368.475i	0.156476i
$178$	− 3399.81i	− 1.43161i
$179$	−795.016	−0.331968	−0.165984	−	0.986128i	$-0.553080\pi$
$179$	−795.016	−0.331968	−0.165984	+	0.986128i	$0.553080\pi$
$180$	0	0
$181$	2478.89	1.01798	0.508989	−	0.860773i	$-0.330019\pi$
$181$	2478.89	1.01798	0.508989	+	0.860773i	$0.330019\pi$
$182$	1537.62i	0.626241i
$183$	− 41.4483i	− 0.0167429i
$184$	362.430	0.145210
$185$	0	0
$186$	−625.925	−0.246748
$187$	904.995i	0.353903i
$188$	− 2654.02i	− 1.02960i
$189$	214.897	0.0827062
$190$	0	0
$191$	−2441.39	−0.924883	−0.462442	−	0.886650i	$-0.653026\pi$
$191$	−2441.39	−0.924883	−0.462442	+	0.886650i	$0.653026\pi$
$192$	− 1788.98i	− 0.672442i
$193$	1535.55i	0.572703i	0.958125	+	0.286351i	$0.0924425\pi$
$193$	1535.55i	0.572703i	−0.958125	+	0.286351i	$0.907558\pi$
$194$	5239.02	1.93886
$195$	0	0
$196$	−2430.53	−0.885761
$197$	− 3650.60i	− 1.32028i	−0.751144	−	0.660138i	$-0.770498\pi$
$197$	− 3650.60i	− 1.32028i	0.751144	−	0.660138i	$-0.229502\pi$
$198$	− 404.464i	− 0.145172i
$199$	−104.337	−0.0371671	−0.0185835	−	0.999827i	$-0.505916\pi$
$199$	−104.337	−0.0371671	−0.0185835	+	0.999827i	$0.505916\pi$
$200$	0	0
$201$	2386.02	0.837299
$202$	1141.37i	0.397555i
$203$	− 670.073i	− 0.231674i
$204$	2145.15	0.736228
$205$	0	0
$206$	1718.55	0.581247
$207$	1155.00i	0.387816i
$208$	2742.24i	0.914136i
$209$	−201.548	−0.0667050
$210$	0	0
$211$	−4586.40	−1.49640	−0.748200	−	0.663473i	$-0.769082\pi$
$211$	−4586.40	−1.49640	−0.748200	+	0.663473i	$0.769082\pi$
$212$	− 5272.65i	− 1.70815i
$213$	299.693i	0.0964066i
$214$	−2908.50	−0.929071
$215$	0	0
$216$	−76.2517	−0.0240198
$217$	− 406.465i	− 0.127155i
$218$	3109.38i	0.966028i
$219$	36.8690	0.0113762
$220$	0	0
$221$	−3890.37	−1.18414
$222$	987.908i	0.298667i
$223$	4262.19i	1.27990i	0.768418	+	0.639949i	$0.221044\pi$
$223$	4262.19i	1.27990i	−0.768418	+	0.639949i	$0.778956\pi$
$224$	2065.55	0.616119
$225$	0	0
$226$	−1539.37	−0.453086
$227$	− 5729.41i	− 1.67522i	−0.546271	−	0.837609i	$-0.683953\pi$
$227$	− 5729.41i	− 1.67522i	0.546271	−	0.837609i	$-0.316047\pi$
$228$	477.738i	0.138767i
$229$	−1703.10	−0.491458	−0.245729	−	0.969339i	$-0.579027\pi$
$229$	−1703.10	−0.491458	−0.245729	+	0.969339i	$0.579027\pi$
$230$	0	0
$231$	262.652	0.0748105
$232$	237.761i	0.0672836i
$233$	− 1260.32i	− 0.354363i	−0.984178	−	0.177182i	$-0.943302\pi$
$233$	− 1260.32i	− 0.354363i	0.984178	−	0.177182i	$-0.0566980\pi$
$234$	1738.70	0.485736
$235$	0	0
$236$	1067.50	0.294443
$237$	542.468i	0.148680i
$238$	2675.25i	0.728618i
$239$	1428.65	0.386659	0.193330	−	0.981134i	$-0.438071\pi$
$239$	1428.65	0.386659	0.193330	+	0.981134i	$0.438071\pi$
$240$	0	0
$241$	−255.543	−0.0683029	−0.0341514	−	0.999417i	$-0.510873\pi$
$241$	−255.543	−0.0683029	−0.0341514	+	0.999417i	$0.510873\pi$
$242$	− 494.345i	− 0.131313i
$243$	− 243.000i	− 0.0641500i
$244$	−120.079	−0.0315053
$245$	0	0
$246$	5915.53	1.53317
$247$	− 866.408i	− 0.223191i
$248$	144.226i	0.0369288i
$249$	−434.898	−0.110685
$250$	0	0
$251$	4727.69	1.18888	0.594441	−	0.804139i	$-0.297373\pi$
$251$	4727.69	1.18888	0.594441	+	0.804139i	$0.297373\pi$
$252$	− 622.575i	− 0.155629i
$253$	1411.66i	0.350792i
$254$	−2041.02	−0.504192
$255$	0	0
$256$	3299.28	0.805487
$257$	− 3272.19i	− 0.794216i	−0.917772	−	0.397108i	$-0.870014\pi$
$257$	− 3272.19i	− 0.794216i	0.917772	−	0.397108i	$-0.129986\pi$
$258$	2737.88i	0.660671i
$259$	−641.531	−0.153910
$260$	0	0
$261$	−757.701	−0.179695
$262$	10777.9i	2.54145i
$263$	1849.13i	0.433544i	0.976222	+	0.216772i	$0.0695529\pi$
$263$	1849.13i	0.433544i	−0.976222	+	0.216772i	$0.930447\pi$
$264$	−93.1965	−0.0217267
$265$	0	0
$266$	−595.795	−0.137333
$267$	− 2496.50i	− 0.572222i
$268$	− 6912.52i	− 1.57556i
$269$	−5180.14	−1.17412	−0.587061	−	0.809543i	$-0.699715\pi$
$269$	−5180.14	−1.17412	−0.587061	+	0.809543i	$0.699715\pi$
$270$	0	0
$271$	−1688.02	−0.378375	−0.189188	−	0.981941i	$-0.560585\pi$
$271$	−1688.02	−0.378375	−0.189188	+	0.981941i	$0.560585\pi$
$272$	4771.14i	1.06358i
$273$	1129.08i	0.250312i
$274$	−11794.9	−2.60056
$275$	0	0
$276$	3346.13	0.729758
$277$	1679.85i	0.364377i	0.983264	+	0.182188i	$0.0583180\pi$
$277$	1679.85i	0.364377i	−0.983264	+	0.182188i	$0.941682\pi$
$278$	− 9682.62i	− 2.08894i
$279$	−459.620	−0.0986263
$280$	0	0
$281$	−5952.32	−1.26365	−0.631825	−	0.775111i	$-0.717694\pi$
$281$	−5952.32	−1.26365	−0.631825	+	0.775111i	$0.717694\pi$
$282$	− 3742.72i	− 0.790340i
$283$	5279.07i	1.10886i	0.832229	+	0.554432i	$0.187064\pi$
$283$	5279.07i	1.10886i	−0.832229	+	0.554432i	$0.812936\pi$
$284$	868.235	0.181409
$285$	0	0
$286$	2125.08	0.439365
$287$	3841.44i	0.790081i
$288$	− 2335.67i	− 0.477885i
$289$	−1855.73	−0.377719
$290$	0	0
$291$	3847.04	0.774974
$292$	− 106.813i	− 0.0214067i
$293$	1924.84i	0.383790i	0.981415	+	0.191895i	$0.0614632\pi$
$293$	1924.84i	0.383790i	−0.981415	+	0.191895i	$0.938537\pi$
$294$	−3427.55	−0.679927
$295$	0	0
$296$	227.634	0.0446991
$297$	− 297.000i	− 0.0580259i
$298$	− 7577.00i	− 1.47290i
$299$	−6068.42	−1.17373
$300$	0	0
$301$	−1777.94	−0.340460
$302$	− 5816.03i	− 1.10819i
$303$	838.111i	0.158905i
$304$	−1062.56	−0.200467
$305$	0	0
$306$	3025.11	0.565143
$307$	− 7215.79i	− 1.34146i	−0.741703	−	0.670728i	$-0.765982\pi$
$307$	− 7215.79i	− 1.34146i	0.741703	−	0.670728i	$-0.234018\pi$
$308$	− 760.926i	− 0.140772i
$309$	1261.94	0.232327
$310$	0	0
$311$	6267.64	1.14278	0.571391	−	0.820678i	$-0.306404\pi$
$311$	6267.64	1.14278	0.571391	+	0.820678i	$0.306404\pi$
$312$	− 400.631i	− 0.0726963i
$313$	6090.54i	1.09986i	0.835209	+	0.549932i	$0.185347\pi$
$313$	6090.54i	1.09986i	−0.835209	+	0.549932i	$0.814653\pi$
$314$	−5443.35	−0.978300
$315$	0	0
$316$	1571.58	0.279773
$317$	10386.8i	1.84032i	0.391548	+	0.920158i	$0.371940\pi$
$317$	10386.8i	1.84032i	−0.391548	+	0.920158i	$0.628060\pi$
$318$	− 7435.53i	− 1.31121i
$319$	−926.078	−0.162541
$320$	0	0
$321$	−2135.73	−0.371354
$322$	4173.01i	0.722214i
$323$	− 1507.44i	− 0.259678i
$324$	−703.992	−0.120712
$325$	0	0
$326$	4323.96	0.734607
$327$	2283.24i	0.386126i
$328$	− 1363.06i	− 0.229458i
$329$	2430.46	0.407281
$330$	0	0
$331$	−10187.5	−1.69171	−0.845854	−	0.533415i	$-0.820909\pi$
$331$	−10187.5	−1.69171	−0.845854	+	0.533415i	$0.820909\pi$
$332$	1259.94i	0.208277i
$333$	725.426i	0.119379i
$334$	−10837.4	−1.77543
$335$	0	0
$336$	1384.70	0.224827
$337$	3785.88i	0.611958i	0.952038	+	0.305979i	$0.0989838\pi$
$337$	3785.88i	0.611958i	−0.952038	+	0.305979i	$0.901016\pi$
$338$	159.388i	0.0256497i
$339$	−1130.37	−0.181101
$340$	0	0
$341$	−561.758	−0.0892109
$342$	673.709i	0.106521i
$343$	− 4955.78i	− 0.780137i
$344$	630.863	0.0988775
$345$	0	0
$346$	2527.36	0.392693
$347$	− 2857.68i	− 0.442098i	−0.975263	−	0.221049i	$-0.929052\pi$
$347$	− 2857.68i	− 0.442098i	0.975263	−	0.221049i	$-0.0709482\pi$
$348$	2195.12i	0.338135i
$349$	−10611.4	−1.62755	−0.813773	−	0.581183i	$-0.802590\pi$
$349$	−10611.4	−1.62755	−0.813773	+	0.581183i	$0.802590\pi$
$350$	0	0
$351$	1276.74	0.194151
$352$	− 2854.71i	− 0.432263i
$353$	− 10412.0i	− 1.56989i	−0.619563	−	0.784947i	$-0.712690\pi$
$353$	− 10412.0i	− 1.56989i	0.619563	−	0.784947i	$-0.287310\pi$
$354$	1505.40	0.226020
$355$	0	0
$356$	−7232.58	−1.07676
$357$	1964.45i	0.291232i
$358$	3248.03i	0.479508i
$359$	3932.54	0.578138	0.289069	−	0.957308i	$-0.406654\pi$
$359$	3932.54	0.578138	0.289069	+	0.957308i	$0.406654\pi$
$360$	0	0
$361$	−6523.28	−0.951055
$362$	− 10127.5i	− 1.47041i
$363$	− 363.000i	− 0.0524864i
$364$	3271.05	0.471015
$365$	0	0
$366$	−169.337	−0.0241841
$367$	11067.7i	1.57419i	0.616829	+	0.787097i	$0.288417\pi$
$367$	11067.7i	1.57419i	−0.616829	+	0.787097i	$0.711583\pi$
$368$	7442.30i	1.05423i
$369$	4343.80	0.612817
$370$	0	0
$371$	4828.51	0.675697
$372$	1331.56i	0.185586i
$373$	− 12526.9i	− 1.73892i	−0.494001	−	0.869461i	$-0.664466\pi$
$373$	− 12526.9i	− 1.73892i	0.494001	−	0.869461i	$-0.335534\pi$
$374$	3697.35	0.511191
$375$	0	0
$376$	−862.398	−0.118284
$377$	− 3981.00i	− 0.543851i
$378$	− 877.961i	− 0.119464i
$379$	3298.48	0.447049	0.223525	−	0.974698i	$-0.428244\pi$
$379$	3298.48	0.447049	0.223525	+	0.974698i	$0.428244\pi$
$380$	0	0
$381$	−1498.73	−0.201528
$382$	9974.28i	1.33594i
$383$	− 10729.9i	− 1.43152i	−0.698346	−	0.715760i	$-0.746080\pi$
$383$	− 10729.9i	− 1.43152i	0.698346	−	0.715760i	$-0.253920\pi$
$384$	−1080.42	−0.143581
$385$	0	0
$386$	6273.50	0.827235
$387$	2010.44i	0.264074i
$388$	− 11145.2i	− 1.45828i
$389$	−7134.16	−0.929862	−0.464931	−	0.885347i	$-0.653921\pi$
$389$	−7134.16	−0.929862	−0.464931	+	0.885347i	$0.653921\pi$
$390$	0	0
$391$	−10558.3	−1.36561
$392$	789.775i	0.101759i
$393$	7914.27i	1.01583i
$394$	−14914.5	−1.90706
$395$	0	0
$396$	−860.435	−0.109188
$397$	− 3060.31i	− 0.386883i	−0.981112	−	0.193442i	$-0.938035\pi$
$397$	− 3060.31i	− 0.386883i	0.981112	−	0.193442i	$-0.0619650\pi$
$398$	426.268i	0.0536856i
$399$	−437.495	−0.0548926
$400$	0	0
$401$	915.088	0.113958	0.0569792	−	0.998375i	$-0.481853\pi$
$401$	915.088	0.113958	0.0569792	+	0.998375i	$0.481853\pi$
$402$	− 9748.08i	− 1.20943i
$403$	− 2414.87i	− 0.298494i
$404$	2428.08	0.299014
$405$	0	0
$406$	−2737.58	−0.334640
$407$	886.632i	0.107982i
$408$	− 697.045i	− 0.0845806i
$409$	−2081.81	−0.251684	−0.125842	−	0.992050i	$-0.540163\pi$
$409$	−2081.81	−0.251684	−0.125842	+	0.992050i	$0.540163\pi$
$410$	0	0
$411$	−8661.02	−1.03946
$412$	− 3655.94i	− 0.437173i
$413$	977.582i	0.116474i
$414$	4718.73	0.560177
$415$	0	0
$416$	12271.8	1.44633
$417$	− 7110.00i	− 0.834960i
$418$	823.422i	0.0963514i
$419$	−3971.05	−0.463004	−0.231502	−	0.972834i	$-0.574364\pi$
$419$	−3971.05	−0.463004	−0.231502	+	0.972834i	$0.574364\pi$
$420$	0	0
$421$	−8388.86	−0.971136	−0.485568	−	0.874199i	$-0.661387\pi$
$421$	−8388.86	−0.971136	−0.485568	+	0.874199i	$0.661387\pi$
$422$	18737.7i	2.16146i
$423$	− 2748.30i	− 0.315903i
$424$	−1713.29	−0.196238
$425$	0	0
$426$	1224.39	0.139254
$427$	− 109.965i	− 0.0124627i
$428$	6187.39i	0.698782i
$429$	1560.45	0.175616
$430$	0	0
$431$	−13313.3	−1.48789	−0.743944	−	0.668242i	$-0.767047\pi$
$431$	−13313.3	−1.48789	−0.743944	+	0.668242i	$0.767047\pi$
$432$	− 1565.79i	− 0.174384i
$433$	− 5946.15i	− 0.659940i	−0.943991	−	0.329970i	$-0.892961\pi$
$433$	− 5946.15i	− 0.659940i	0.943991	−	0.329970i	$-0.107039\pi$
$434$	−1660.61	−0.183668
$435$	0	0
$436$	6614.74	0.726579
$437$	− 2351.39i	− 0.257396i
$438$	− 150.628i	− 0.0164322i
$439$	15504.2	1.68559	0.842794	−	0.538236i	$-0.180909\pi$
$439$	15504.2	1.68559	0.842794	+	0.538236i	$0.180909\pi$
$440$	0	0
$441$	−2516.87	−0.271771
$442$	15894.1i	1.71042i
$443$	− 1061.40i	− 0.113835i	−0.998379	−	0.0569174i	$-0.981873\pi$
$443$	− 1061.40i	− 0.113835i	0.998379	−	0.0569174i	$-0.0181272\pi$
$444$	2101.62	0.224636
$445$	0	0
$446$	17413.1	1.84873
$447$	− 5563.83i	− 0.588725i
$448$	− 4746.27i	− 0.500536i
$449$	−11549.7	−1.21395	−0.606975	−	0.794721i	$-0.707617\pi$
$449$	−11549.7	−1.21395	−0.606975	+	0.794721i	$0.707617\pi$
$450$	0	0
$451$	5309.09	0.554314
$452$	3274.78i	0.340780i
$453$	− 4270.74i	− 0.442951i
$454$	−23407.5	−2.41975
$455$	0	0
$456$	155.236	0.0159421
$457$	1135.49i	0.116228i	0.998310	+	0.0581138i	$0.0185086\pi$
$457$	1135.49i	0.116228i	−0.998310	+	0.0581138i	$0.981491\pi$
$458$	6957.99i	0.709881i
$459$	2221.35	0.225891
$460$	0	0
$461$	−10463.7	−1.05714	−0.528572	−	0.848889i	$-0.677272\pi$
$461$	−10463.7	−1.05714	−0.528572	+	0.848889i	$0.677272\pi$
$462$	− 1073.06i	− 0.108059i
$463$	− 17541.7i	− 1.76076i	−0.474269	−	0.880380i	$-0.657288\pi$
$463$	− 17541.7i	− 1.76076i	0.474269	−	0.880380i	$-0.342712\pi$
$464$	−4882.29	−0.488480
$465$	0	0
$466$	−5149.05	−0.511856
$467$	− 12882.6i	− 1.27653i	−0.769818	−	0.638263i	$-0.779653\pi$
$467$	− 12882.6i	− 1.27653i	0.769818	−	0.638263i	$-0.220347\pi$
$468$	− 3698.81i	− 0.365337i
$469$	6330.24	0.623248
$470$	0	0
$471$	−3997.08	−0.391032
$472$	− 346.875i	− 0.0338267i
$473$	2457.21i	0.238864i
$474$	2216.25	0.214759
$475$	0	0
$476$	5691.19	0.548015
$477$	− 5459.95i	− 0.524096i
$478$	− 5836.74i	− 0.558506i
$479$	−806.687	−0.0769488	−0.0384744	−	0.999260i	$-0.512250\pi$
$479$	−806.687	−0.0769488	−0.0384744	+	0.999260i	$0.512250\pi$
$480$	0	0
$481$	−3811.43	−0.361302
$482$	1044.02i	0.0986594i
$483$	3064.27i	0.288673i
$484$	−1051.64	−0.0987643
$485$	0	0
$486$	−992.775	−0.0926609
$487$	− 511.317i	− 0.0475770i	−0.999717	−	0.0237885i	$-0.992427\pi$
$487$	− 511.317i	− 0.0475770i	0.999717	−	0.0237885i	$-0.00757282\pi$
$488$	39.0186i	0.00361945i
$489$	3175.10	0.293626
$490$	0	0
$491$	20607.7	1.89412	0.947061	−	0.321053i	$-0.104037\pi$
$491$	20607.7	1.89412	0.947061	+	0.321053i	$0.104037\pi$
$492$	− 12584.4i	− 1.15315i
$493$	− 6926.42i	− 0.632759i
$494$	−3539.71	−0.322386
$495$	0	0
$496$	−2961.59	−0.268104
$497$	795.099i	0.0717607i
$498$	1776.77i	0.159878i
$499$	19416.9	1.74192	0.870962	−	0.491351i	$-0.163497\pi$
$499$	19416.9	1.74192	0.870962	+	0.491351i	$0.163497\pi$
$500$	0	0
$501$	−7957.94	−0.709650
$502$	− 19315.0i	− 1.71727i
$503$	− 3968.14i	− 0.351750i	−0.984412	−	0.175875i	$-0.943724\pi$
$503$	− 3968.14i	− 0.351750i	0.984412	−	0.175875i	$-0.0562755\pi$
$504$	−202.300	−0.0178792
$505$	0	0
$506$	5767.34	0.506699
$507$	117.040i	0.0102523i
$508$	4341.95i	0.379218i
$509$	−12117.4	−1.05520	−0.527598	−	0.849494i	$-0.676907\pi$
$509$	−12117.4	−1.05520	−0.527598	+	0.849494i	$0.676907\pi$
$510$	0	0
$511$	97.8154	0.00846791
$512$	− 16360.3i	− 1.41217i
$513$	494.708i	0.0425768i
$514$	−13368.5	−1.14720
$515$	0	0
$516$	5824.43	0.496911
$517$	− 3359.03i	− 0.285745i
$518$	2620.97i	0.222314i
$519$	1855.86	0.156961
$520$	0	0
$521$	−6042.43	−0.508107	−0.254053	−	0.967190i	$-0.581764\pi$
$521$	−6042.43	−0.508107	−0.254053	+	0.967190i	$0.581764\pi$
$522$	3095.58i	0.259559i
$523$	− 8891.69i	− 0.743416i	−0.928350	−	0.371708i	$-0.878772\pi$
$523$	− 8891.69i	− 0.743416i	0.928350	−	0.371708i	$-0.121228\pi$
$524$	22928.3	1.91151
$525$	0	0
$526$	7554.60	0.626229
$527$	− 4201.56i	− 0.347292i
$528$	− 1913.74i	− 0.157736i
$529$	−4302.36	−0.353609
$530$	0	0
$531$	1105.42	0.0903415
$532$	1267.46i	0.103292i
$533$	22822.6i	1.85470i
$534$	−10199.4	−0.826541
$535$	0	0
$536$	−2246.15	−0.181006
$537$	2385.05i	0.191662i
$538$	21163.4i	1.69595i
$539$	−3076.17	−0.245826
$540$	0	0
$541$	2021.82	0.160675	0.0803373	−	0.996768i	$-0.474400\pi$
$541$	2021.82	0.160675	0.0803373	+	0.996768i	$0.474400\pi$
$542$	6896.38i	0.546540i
$543$	− 7436.66i	− 0.587730i
$544$	21351.3	1.68277
$545$	0	0
$546$	4612.85	0.361560
$547$	15384.9i	1.20258i	0.799031	+	0.601289i	$0.205346\pi$
$547$	15384.9i	1.20258i	−0.799031	+	0.601289i	$0.794654\pi$
$548$	25091.7i	1.95596i
$549$	−124.345	−0.00966652
$550$	0	0
$551$	1542.55	0.119265
$552$	− 1087.29i	− 0.0838372i
$553$	1439.20i	0.110671i
$554$	6863.01	0.526320
$555$	0	0
$556$	−20598.3	−1.57115
$557$	− 18366.8i	− 1.39718i	−0.715523	−	0.698589i	$-0.753812\pi$
$557$	− 18366.8i	− 1.39718i	0.715523	−	0.698589i	$-0.246188\pi$
$558$	1877.78i	0.142460i
$559$	−10563.0	−0.799224
$560$	0	0
$561$	2714.99	0.204326
$562$	24318.2i	1.82527i
$563$	19315.9i	1.44595i	0.690874	+	0.722975i	$0.257226\pi$
$563$	19315.9i	1.44595i	−0.690874	+	0.722975i	$0.742774\pi$
$564$	−7962.07	−0.594439
$565$	0	0
$566$	21567.6	1.60169
$567$	− 644.691i	− 0.0477504i
$568$	− 282.124i	− 0.0208410i
$569$	8669.00	0.638705	0.319353	−	0.947636i	$-0.396535\pi$
$569$	8669.00	0.638705	0.319353	+	0.947636i	$0.396535\pi$
$570$	0	0
$571$	6454.19	0.473029	0.236514	−	0.971628i	$-0.423995\pi$
$571$	6454.19	0.473029	0.236514	+	0.971628i	$0.423995\pi$
$572$	− 4520.77i	− 0.330460i
$573$	7324.17i	0.533982i
$574$	15694.2	1.14122
$575$	0	0
$576$	−5366.95	−0.388235
$577$	− 24828.5i	− 1.79138i	−0.444681	−	0.895689i	$-0.646683\pi$
$577$	− 24828.5i	− 1.79138i	0.444681	−	0.895689i	$-0.353317\pi$
$578$	7581.59i	0.545593i
$579$	4606.66	0.330650
$580$	0	0
$581$	−1153.81	−0.0823889
$582$	− 15717.0i	− 1.11940i
$583$	− 6673.27i	− 0.474063i
$584$	−34.7077	−0.00245928
$585$	0	0
$586$	7863.92	0.554361
$587$	973.773i	0.0684701i	0.999414	+	0.0342350i	$0.0108995\pi$
$587$	973.773i	0.0684701i	−0.999414	+	0.0342350i	$0.989101\pi$
$588$	7291.58i	0.511394i
$589$	935.712	0.0654590
$590$	0	0
$591$	−10951.8	−0.762262
$592$	4674.33i	0.324516i
$593$	− 15841.0i	− 1.09699i	−0.836155	−	0.548493i	$-0.815202\pi$
$593$	− 15841.0i	− 1.09699i	0.836155	−	0.548493i	$-0.184798\pi$
$594$	−1213.39	−0.0838149
$595$	0	0
$596$	−16118.9	−1.10781
$597$	313.011i	0.0214584i
$598$	24792.5i	1.69538i
$599$	13803.0	0.941525	0.470762	−	0.882260i	$-0.343979\pi$
$599$	13803.0	0.941525	0.470762	+	0.882260i	$0.343979\pi$
$600$	0	0
$601$	22058.6	1.49715	0.748576	−	0.663049i	$-0.230738\pi$
$601$	22058.6	1.49715	0.748576	+	0.663049i	$0.230738\pi$
$602$	7263.75i	0.491774i
$603$	− 7158.07i	− 0.483415i
$604$	−12372.7	−0.833507
$605$	0	0
$606$	3424.10	0.229529
$607$	9960.21i	0.666017i	0.942924	+	0.333009i	$0.108064\pi$
$607$	9960.21i	0.666017i	−0.942924	+	0.333009i	$0.891936\pi$
$608$	4755.05i	0.317176i
$609$	−2010.22	−0.133757
$610$	0	0
$611$	14439.7	0.956086
$612$	− 6435.45i	− 0.425062i
$613$	5722.99i	0.377079i	0.982066	+	0.188539i	$0.0603753\pi$
$613$	5722.99i	0.377079i	−0.982066	+	0.188539i	$0.939625\pi$
$614$	−29480.1	−1.93765
$615$	0	0
$616$	−247.255	−0.0161724
$617$	− 10387.5i	− 0.677774i	−0.940827	−	0.338887i	$-0.889949\pi$
$617$	− 10387.5i	− 0.677774i	0.940827	−	0.338887i	$-0.110051\pi$
$618$	− 5155.64i	− 0.335583i
$619$	24531.0	1.59286	0.796432	−	0.604728i	$-0.206718\pi$
$619$	24531.0	1.59286	0.796432	+	0.604728i	$0.206718\pi$
$620$	0	0
$621$	3464.99	0.223905
$622$	− 25606.4i	− 1.65068i
$623$	− 6623.34i	− 0.425937i
$624$	8226.73	0.527777
$625$	0	0
$626$	24882.9	1.58869
$627$	604.643i	0.0385122i
$628$	11579.9i	0.735809i
$629$	−6631.39	−0.420367
$630$	0	0
$631$	13513.5	0.852557	0.426279	−	0.904592i	$-0.359824\pi$
$631$	13513.5	0.852557	0.426279	+	0.904592i	$0.359824\pi$
$632$	− 510.668i	− 0.0321413i
$633$	13759.2i	0.863947i
$634$	42435.1	2.65823
$635$	0	0
$636$	−15817.9	−0.986199
$637$	− 13223.8i	− 0.822519i
$638$	3783.49i	0.234780i
$639$	899.078	0.0556603
$640$	0	0
$641$	11006.8	0.678224	0.339112	−	0.940746i	$-0.389873\pi$
$641$	11006.8	0.678224	0.339112	+	0.940746i	$0.389873\pi$
$642$	8725.51i	0.536399i
$643$	− 11265.9i	− 0.690952i	−0.938428	−	0.345476i	$-0.887717\pi$
$643$	− 11265.9i	− 0.690952i	0.938428	−	0.345476i	$-0.112283\pi$
$644$	8877.44	0.543199
$645$	0	0
$646$	−6158.62	−0.375089
$647$	16468.0i	1.00066i	0.865835	+	0.500329i	$0.166788\pi$
$647$	16468.0i	1.00066i	−0.865835	+	0.500329i	$0.833212\pi$
$648$	228.755i	0.0138678i
$649$	1351.07	0.0817170
$650$	0	0
$651$	−1219.40	−0.0734130
$652$	− 9198.55i	− 0.552520i
$653$	6767.28i	0.405550i	0.979225	+	0.202775i	$0.0649960\pi$
$653$	6767.28i	0.405550i	−0.979225	+	0.202775i	$0.935004\pi$
$654$	9328.15	0.557736
$655$	0	0
$656$	27989.6	1.66587
$657$	− 110.607i	− 0.00656803i
$658$	− 9929.63i	− 0.588294i
$659$	−15799.0	−0.933901	−0.466950	−	0.884284i	$-0.654647\pi$
$659$	−15799.0	−0.933901	−0.466950	+	0.884284i	$0.654647\pi$
$660$	0	0
$661$	−8401.65	−0.494382	−0.247191	−	0.968967i	$-0.579507\pi$
$661$	−8401.65	−0.494382	−0.247191	+	0.968967i	$0.579507\pi$
$662$	41620.9i	2.44357i
$663$	11671.1i	0.683663i
$664$	409.404	0.0239277
$665$	0	0
$666$	2963.72	0.172435
$667$	− 10804.2i	− 0.627198i
$668$	23054.8i	1.33536i
$669$	12786.6	0.738949
$670$	0	0
$671$	−151.977	−0.00874369
$672$	− 6196.66i	− 0.355716i
$673$	− 21097.3i	− 1.20838i	−0.796838	−	0.604192i	$-0.793496\pi$
$673$	− 21097.3i	− 1.20838i	0.796838	−	0.604192i	$-0.206504\pi$
$674$	15467.2	0.883937
$675$	0	0
$676$	339.074	0.0192919
$677$	21730.8i	1.23365i	0.787099	+	0.616827i	$0.211582\pi$
$677$	21730.8i	1.23365i	−0.787099	+	0.616827i	$0.788418\pi$
$678$	4618.11i	0.261589i
$679$	10206.4	0.576856
$680$	0	0
$681$	−17188.2	−0.967187
$682$	2295.06i	0.128860i
$683$	6117.84i	0.342742i	0.985207	+	0.171371i	$0.0548197\pi$
$683$	6117.84i	0.342742i	−0.985207	+	0.171371i	$0.945180\pi$
$684$	1433.21	0.0801173
$685$	0	0
$686$	−20246.8	−1.12686
$687$	5109.29i	0.283743i
$688$	12954.4i	0.717853i
$689$	28686.9	1.58619
$690$	0	0
$691$	−11919.3	−0.656199	−0.328099	−	0.944643i	$-0.606408\pi$
$691$	−11919.3	−0.656199	−0.328099	+	0.944643i	$0.606408\pi$
$692$	− 5376.57i	− 0.295356i
$693$	− 787.956i	− 0.0431919i
$694$	−11675.0	−0.638585
$695$	0	0
$696$	713.283	0.0388462
$697$	39708.3i	2.15790i
$698$	43352.7i	2.35089i
$699$	−3780.97	−0.204592
$700$	0	0
$701$	3713.44	0.200078	0.100039	−	0.994984i	$-0.468103\pi$
$701$	3713.44	0.200078	0.100039	+	0.994984i	$0.468103\pi$
$702$	− 5216.10i	− 0.280440i
$703$	− 1476.85i	− 0.0792324i
$704$	−6559.61	−0.351171
$705$	0	0
$706$	−42538.0	−2.26762
$707$	2223.55i	0.118282i
$708$	− 3202.51i	− 0.169997i
$709$	30476.7	1.61435	0.807177	−	0.590310i	$-0.200994\pi$
$709$	30476.7	1.61435	0.807177	+	0.590310i	$0.200994\pi$
$710$	0	0
$711$	1627.40	0.0858403
$712$	2350.15i	0.123702i
$713$	− 6553.83i	− 0.344240i
$714$	8025.76	0.420668
$715$	0	0
$716$	6909.69	0.360653
$717$	− 4285.95i	− 0.223238i
$718$	− 16066.4i	− 0.835085i
$719$	2677.22	0.138864	0.0694321	−	0.997587i	$-0.477881\pi$
$719$	2677.22	0.138864	0.0694321	+	0.997587i	$0.477881\pi$
$720$	0	0
$721$	3347.99	0.172934
$722$	26650.8i	1.37374i
$723$	766.630i	0.0394347i
$724$	−21544.6	−1.10594
$725$	0	0
$726$	−1483.03	−0.0758134
$727$	11069.1i	0.564692i	0.959313	+	0.282346i	$0.0911127\pi$
$727$	11069.1i	0.564692i	−0.959313	+	0.282346i	$0.908887\pi$
$728$	− 1062.89i	− 0.0541119i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−18378.2	−0.929880
$732$	360.238i	0.0181896i
$733$	26621.6i	1.34146i	0.741701	+	0.670730i	$0.234019\pi$
$733$	26621.6i	1.34146i	−0.741701	+	0.670730i	$0.765981\pi$
$734$	45217.0	2.27383
$735$	0	0
$736$	33304.9	1.66798
$737$	− 8748.75i	− 0.437265i
$738$	− 17746.6i	− 0.885177i
$739$	−15047.5	−0.749030	−0.374515	−	0.927221i	$-0.622191\pi$
$739$	−15047.5	−0.749030	−0.374515	+	0.927221i	$0.622191\pi$
$740$	0	0
$741$	−2599.22	−0.128860
$742$	− 19726.8i	− 0.976004i
$743$	− 31715.1i	− 1.56597i	−0.622042	−	0.782984i	$-0.713697\pi$
$743$	− 31715.1i	− 1.56597i	0.622042	−	0.782984i	$-0.286303\pi$
$744$	432.677	0.0213208
$745$	0	0
$746$	−51178.6	−2.51177
$747$	1304.69i	0.0639040i
$748$	− 7865.55i	− 0.384483i
$749$	−5666.20	−0.276420
$750$	0	0
$751$	−26978.9	−1.31088	−0.655442	−	0.755245i	$-0.727518\pi$
$751$	−26978.9	−1.31088	−0.655442	+	0.755245i	$0.727518\pi$
$752$	− 17708.9i	− 0.858744i
$753$	− 14183.1i	− 0.686401i
$754$	−16264.4	−0.785561
$755$	0	0
$756$	−1867.73	−0.0898526
$757$	21875.5i	1.05030i	0.851008	+	0.525152i	$0.175992\pi$
$757$	21875.5i	1.05030i	−0.851008	+	0.525152i	$0.824008\pi$
$758$	− 13475.9i	− 0.645736i
$759$	4234.99	0.202530
$760$	0	0
$761$	26746.8	1.27407	0.637037	−	0.770833i	$-0.280160\pi$
$761$	26746.8	1.27407	0.637037	+	0.770833i	$0.280160\pi$
$762$	6123.05i	0.291096i
$763$	6057.54i	0.287415i
$764$	21218.7	1.00480
$765$	0	0
$766$	−43836.9	−2.06775
$767$	5807.96i	0.273420i
$768$	− 9897.83i	− 0.465048i
$769$	5964.06	0.279674	0.139837	−	0.990175i	$-0.455342\pi$
$769$	5964.06	0.279674	0.139837	+	0.990175i	$0.455342\pi$
$770$	0	0
$771$	−9816.57	−0.458541
$772$	− 13345.9i	− 0.622189i
$773$	− 38290.9i	− 1.78167i	−0.454329	−	0.890834i	$-0.650121\pi$
$773$	− 38290.9i	− 1.78167i	0.454329	−	0.890834i	$-0.349879\pi$
$774$	8213.65	0.381439
$775$	0	0
$776$	−3621.52	−0.167532
$777$	1924.59i	0.0888602i
$778$	29146.6i	1.34313i
$779$	−8843.27	−0.406731
$780$	0	0
$781$	1098.87	0.0503467
$782$	43135.7i	1.97254i
$783$	2273.10i	0.103747i
$784$	−16217.6	−0.738775
$785$	0	0
$786$	32333.7	1.46731
$787$	− 1526.51i	− 0.0691415i	−0.999402	−	0.0345707i	$-0.988994\pi$
$787$	− 1526.51i	− 0.0691415i	0.999402	−	0.0345707i	$-0.0110064\pi$
$788$	31728.3i	1.43436i
$789$	5547.39	0.250307
$790$	0	0
$791$	−2998.93	−0.134803
$792$	279.590i	0.0125439i
$793$	− 653.316i	− 0.0292559i
$794$	−12502.9	−0.558830
$795$	0	0
$796$	906.819	0.0403786
$797$	− 37456.2i	− 1.66470i	−0.554250	−	0.832350i	$-0.686995\pi$
$797$	− 37456.2i	− 1.66470i	0.554250	−	0.832350i	$-0.313005\pi$
$798$	1787.38i	0.0792891i
$799$	25123.2	1.11239
$800$	0	0
$801$	−7489.50	−0.330373
$802$	− 3738.58i	− 0.164606i
$803$	− 135.186i	− 0.00594101i
$804$	−20737.6	−0.909648
$805$	0	0
$806$	−9865.94	−0.431157
$807$	15540.4i	0.677880i
$808$	− 788.980i	− 0.0343518i
$809$	−17521.5	−0.761462	−0.380731	−	0.924686i	$-0.624328\pi$
$809$	−17521.5	−0.761462	−0.380731	+	0.924686i	$0.624328\pi$
$810$	0	0
$811$	−15602.5	−0.675557	−0.337778	−	0.941226i	$-0.609675\pi$
$811$	−15602.5	−0.675557	−0.337778	+	0.941226i	$0.609675\pi$
$812$	5823.78i	0.251693i
$813$	5064.05i	0.218455i
$814$	3622.33	0.155974
$815$	0	0
$816$	14313.4	0.614057
$817$	− 4092.93i	− 0.175268i
$818$	8505.21i	0.363542i
$819$	3387.24	0.144518
$820$	0	0
$821$	−2564.03	−0.108995	−0.0544977	−	0.998514i	$-0.517356\pi$
$821$	−2564.03	−0.108995	−0.0544977	+	0.998514i	$0.517356\pi$
$822$	35384.6i	1.50143i
$823$	− 27211.2i	− 1.15252i	−0.817267	−	0.576259i	$-0.804512\pi$
$823$	− 27211.2i	− 1.15252i	0.817267	−	0.576259i	$-0.195488\pi$
$824$	−1187.96	−0.0502241
$825$	0	0
$826$	3993.91	0.168239
$827$	20153.5i	0.847409i	0.905801	+	0.423704i	$0.139270\pi$
$827$	20153.5i	0.847409i	−0.905801	+	0.423704i	$0.860730\pi$
$828$	− 10038.4i	− 0.421326i
$829$	−25373.7	−1.06304	−0.531522	−	0.847044i	$-0.678380\pi$
$829$	−25373.7	−1.06304	−0.531522	+	0.847044i	$0.678380\pi$
$830$	0	0
$831$	5039.54	0.210373
$832$	− 28198.3i	− 1.17500i
$833$	− 23007.6i	− 0.956983i
$834$	−29047.9	−1.20605
$835$	0	0
$836$	1751.70	0.0724689
$837$	1378.86i	0.0569419i
$838$	16223.7i	0.668781i
$839$	−5793.53	−0.238397	−0.119198	−	0.992870i	$-0.538032\pi$
$839$	−5793.53	−0.238397	−0.119198	+	0.992870i	$0.538032\pi$
$840$	0	0
$841$	−17301.2	−0.709386
$842$	34272.7i	1.40275i
$843$	17857.0i	0.729569i
$844$	39861.6	1.62570
$845$	0	0
$846$	−11228.2	−0.456303
$847$	− 963.057i	− 0.0390685i
$848$	− 35181.5i	− 1.42469i
$849$	15837.2	0.640203
$850$	0	0
$851$	−10344.0	−0.416672
$852$	− 2604.71i	− 0.104737i
$853$	− 37798.8i	− 1.51724i	−0.651532	−	0.758621i	$-0.725873\pi$
$853$	− 37798.8i	− 1.51724i	0.651532	−	0.758621i	$-0.274127\pi$
$854$	−449.260	−0.0180016
$855$	0	0
$856$	2010.53	0.0802787
$857$	− 23963.4i	− 0.955162i	−0.878588	−	0.477581i	$-0.841514\pi$
$857$	− 23963.4i	− 0.955162i	0.878588	−	0.477581i	$-0.158486\pi$
$858$	− 6375.23i	− 0.253667i
$859$	17816.5	0.707674	0.353837	−	0.935307i	$-0.384877\pi$
$859$	17816.5	0.707674	0.353837	+	0.935307i	$0.384877\pi$
$860$	0	0
$861$	11524.3	0.456153
$862$	54391.5i	2.14917i
$863$	8223.53i	0.324371i	0.986760	+	0.162186i	$0.0518543\pi$
$863$	8223.53i	0.324371i	−0.986760	+	0.162186i	$0.948146\pi$
$864$	−7007.02	−0.275907
$865$	0	0
$866$	−24293.0	−0.953243
$867$	5567.20i	0.218076i
$868$	3532.70i	0.138142i
$869$	1989.05	0.0776455
$870$	0	0
$871$	37608.9	1.46306
$872$	− 2149.39i	− 0.0834720i
$873$	− 11541.1i	− 0.447431i
$874$	−9606.57	−0.371793
$875$	0	0
$876$	−320.438	−0.0123591
$877$	− 27307.6i	− 1.05144i	−0.850658	−	0.525719i	$-0.823796\pi$
$877$	− 27307.6i	− 1.05144i	0.850658	−	0.525719i	$-0.176204\pi$
$878$	− 63342.1i	− 2.43473i
$879$	5774.52	0.221581
$880$	0	0
$881$	−6102.15	−0.233356	−0.116678	−	0.993170i	$-0.537225\pi$
$881$	−6102.15	−0.233356	−0.116678	+	0.993170i	$0.537225\pi$
$882$	10282.6i	0.392556i
$883$	− 3244.93i	− 0.123670i	−0.998086	−	0.0618349i	$-0.980305\pi$
$883$	− 3244.93i	− 0.123670i	0.998086	−	0.0618349i	$-0.0196952\pi$
$884$	33812.2	1.28646
$885$	0	0
$886$	−4336.36	−0.164428
$887$	− 21820.4i	− 0.825996i	−0.910732	−	0.412998i	$-0.864482\pi$
$887$	− 21820.4i	− 0.825996i	0.910732	−	0.412998i	$-0.135518\pi$
$888$	− 682.901i	− 0.0258070i
$889$	−3976.21	−0.150009
$890$	0	0
$891$	−891.000	−0.0335013
$892$	− 37043.8i	− 1.39049i
$893$	5595.09i	0.209667i
$894$	−22731.0	−0.850378
$895$	0	0
$896$	−2866.41	−0.106875
$897$	18205.3i	0.677654i
$898$	47186.1i	1.75348i
$899$	4299.44	0.159504
$900$	0	0
$901$	49911.4	1.84549
$902$	− 21690.3i	− 0.800673i
$903$	5333.81i	0.196565i
$904$	1064.11	0.0391500
$905$	0	0
$906$	−17448.1	−0.639817
$907$	3406.10i	0.124694i	0.998055	+	0.0623471i	$0.0198586\pi$
$907$	3406.10i	0.124694i	−0.998055	+	0.0623471i	$0.980141\pi$
$908$	49795.8i	1.81997i
$909$	2514.33	0.0917438
$910$	0	0
$911$	−26473.4	−0.962791	−0.481396	−	0.876503i	$-0.659870\pi$
$911$	−26473.4	−0.962791	−0.481396	+	0.876503i	$0.659870\pi$
$912$	3187.68i	0.115740i
$913$	1594.63i	0.0578033i
$914$	4639.04	0.167884
$915$	0	0
$916$	14802.1	0.533923
$917$	20997.0i	0.756141i
$918$	− 9075.32i	− 0.326286i
$919$	17741.4	0.636816	0.318408	−	0.947954i	$-0.396852\pi$
$919$	17741.4	0.636816	0.318408	+	0.947954i	$0.396852\pi$
$920$	0	0
$921$	−21647.4	−0.774490
$922$	42749.4i	1.52698i
$923$	4723.80i	0.168457i
$924$	−2282.78	−0.0812747
$925$	0	0
$926$	−71666.5	−2.54331
$927$	− 3785.81i	− 0.134134i
$928$	21848.7i	0.772864i
$929$	−47535.4	−1.67878	−0.839390	−	0.543530i	$-0.817087\pi$
$929$	−47535.4	−1.67878	−0.839390	+	0.543530i	$0.817087\pi$
$930$	0	0
$931$	5123.93	0.180376
$932$	10953.8i	0.384983i
$933$	− 18802.9i	− 0.659786i
$934$	−52632.0	−1.84387
$935$	0	0
$936$	−1201.89	−0.0419712
$937$	51569.2i	1.79796i	0.437986	+	0.898982i	$0.355692\pi$
$937$	51569.2i	1.79796i	−0.437986	+	0.898982i	$0.644308\pi$
$938$	− 25862.2i	− 0.900245i
$939$	18271.6	0.635007
$940$	0	0
$941$	47734.4	1.65366	0.826832	−	0.562450i	$-0.190141\pi$
$941$	47734.4	1.65366	0.826832	+	0.562450i	$0.190141\pi$
$942$	16330.1i	0.564822i
$943$	61939.3i	2.13894i
$944$	7122.87	0.245582
$945$	0	0
$946$	10038.9	0.345024
$947$	46776.1i	1.60509i	0.596591	+	0.802545i	$0.296521\pi$
$947$	46776.1i	1.60509i	−0.596591	+	0.802545i	$0.703479\pi$
$948$	− 4714.73i	− 0.161527i
$949$	581.136	0.0198783
$950$	0	0
$951$	31160.4	1.06251
$952$	− 1849.30i	− 0.0629580i
$953$	− 53486.0i	− 1.81803i	−0.416763	−	0.909015i	$-0.636836\pi$
$953$	− 53486.0i	− 1.81803i	0.416763	−	0.909015i	$-0.363164\pi$
$954$	−22306.6	−0.757026
$955$	0	0
$956$	−12416.8	−0.420070
$957$	2778.24i	0.0938428i
$958$	3295.72i	0.111148i
$959$	−22978.1	−0.773725
$960$	0	0
$961$	−27183.0	−0.912456
$962$	15571.6i	0.521879i
$963$	6407.19i	0.214402i
$964$	2220.99	0.0742047
$965$	0	0
$966$	12519.0	0.416970
$967$	28794.3i	0.957560i	0.877935	+	0.478780i	$0.158921\pi$
$967$	28794.3i	0.957560i	−0.877935	+	0.478780i	$0.841079\pi$
$968$	341.721i	0.0113464i
$969$	−4522.31	−0.149925
$970$	0	0
$971$	26657.3	0.881025	0.440512	−	0.897747i	$-0.354797\pi$
$971$	26657.3	0.881025	0.440512	+	0.897747i	$0.354797\pi$
$972$	2111.98i	0.0696931i
$973$	− 18863.2i	− 0.621507i
$974$	−2088.98	−0.0687221
$975$	0	0
$976$	−801.225	−0.0262773
$977$	− 41980.5i	− 1.37469i	−0.726330	−	0.687346i	$-0.758775\pi$
$977$	− 41980.5i	− 1.37469i	0.726330	−	0.687346i	$-0.241225\pi$
$978$	− 12971.9i	− 0.424125i
$979$	−9153.84	−0.298833
$980$	0	0
$981$	6849.71	0.222930
$982$	− 84192.8i	− 2.73595i
$983$	− 2922.30i	− 0.0948189i	−0.998876	−	0.0474095i	$-0.984903\pi$
$983$	− 2922.30i	− 0.0948189i	0.998876	−	0.0474095i	$-0.0150966\pi$
$984$	−4089.17	−0.132478
$985$	0	0
$986$	−28297.8	−0.913983
$987$	− 7291.38i	− 0.235144i
$988$	7530.18i	0.242477i
$989$	−28667.4	−0.921708
$990$	0	0
$991$	10790.0	0.345869	0.172934	−	0.984933i	$-0.444675\pi$
$991$	10790.0	0.345869	0.172934	+	0.984933i	$0.444675\pi$
$992$	13253.4i	0.424189i
$993$	30562.5i	0.976708i
$994$	3248.37	0.103654
$995$	0	0
$996$	3779.81	0.120249
$997$	− 12761.8i	− 0.405386i	−0.979242	−	0.202693i	$-0.935031\pi$
$997$	− 12761.8i	− 0.405386i	0.979242	−	0.202693i	$-0.0649693\pi$
$998$	− 79327.6i	− 2.51610i
$999$	2176.28	0.0689233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.s.199.1		10
5.2	odd	4		825.4.a.y.1.5	yes	5
5.3	odd	4		825.4.a.x.1.1	✓	5
5.4	even	2	inner	825.4.c.s.199.10		10
15.2	even	4		2475.4.a.bi.1.1		5
15.8	even	4		2475.4.a.bj.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.4.a.x.1.1	✓	5	5.3	odd	4
825.4.a.y.1.5	yes	5	5.2	odd	4
825.4.c.s.199.1		10	1.1	even	1	trivial
825.4.c.s.199.10		10	5.4	even	2	inner
2475.4.a.bi.1.1		5	15.2	even	4
2475.4.a.bj.1.5		5	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)

\(f(q)\)	\(=\)	\(q-4.08549i q^{2} -3.00000i q^{3} -8.69126 q^{4} -12.2565 q^{6} -7.95915i q^{7} +2.82414i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-4.08549i q^{2} -3.00000i q^{3} -8.69126 q^{4} -12.2565 q^{6} -7.95915i q^{7} +2.82414i q^{8} -9.00000 q^{9} -11.0000 q^{11} +26.0738i q^{12} -47.2865i q^{13} -32.5171 q^{14} -57.9921 q^{16} -82.2723i q^{17} +36.7694i q^{18} +18.3225 q^{19} -23.8775 q^{21} +44.9404i q^{22} -128.333i q^{23} +8.47241 q^{24} -193.189 q^{26} +27.0000i q^{27} +69.1751i q^{28} +84.1889 q^{29} +51.0689 q^{31} +259.519i q^{32} +33.0000i q^{33} -336.123 q^{34} +78.2213 q^{36} -80.6029i q^{37} -74.8566i q^{38} -141.860 q^{39} -482.645 q^{41} +97.5512i q^{42} -223.383i q^{43} +95.6039 q^{44} -524.304 q^{46} +305.367i q^{47} +173.976i q^{48} +279.652 q^{49} -246.817 q^{51} +410.979i q^{52} +606.661i q^{53} +110.308 q^{54} +22.4777 q^{56} -54.9676i q^{57} -343.953i q^{58} -122.825 q^{59} +13.8161 q^{61} -208.642i q^{62} +71.6324i q^{63} +596.328 q^{64} +134.821 q^{66} +795.341i q^{67} +715.050i q^{68} -384.999 q^{69} -99.8975 q^{71} -25.4172i q^{72} +12.2897i q^{73} -329.303 q^{74} -159.246 q^{76} +87.5507i q^{77} +579.566i q^{78} -180.823 q^{79} +81.0000 q^{81} +1971.84i q^{82} -144.966i q^{83} +207.525 q^{84} -912.628 q^{86} -252.567i q^{87} -31.0655i q^{88} +832.167 q^{89} -376.360 q^{91} +1115.38i q^{92} -153.207i q^{93} +1247.57 q^{94} +778.558 q^{96} +1282.35i q^{97} -1142.52i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 6 q^{4} - 6 q^{6} - 90 q^{9}+O(q^{10}) \) 10 * q - 6 * q^4 - 6 * q^6 - 90 * q^9	\( 10 q - 6 q^{4} - 6 q^{6} - 90 q^{9} - 110 q^{11} - 16 q^{14} - 250 q^{16} + 114 q^{19} - 108 q^{21} - 18 q^{24} - 250 q^{26} + 214 q^{29} - 590 q^{31} - 68 q^{34} + 54 q^{36} + 186 q^{39} - 256 q^{41} + 66 q^{44} - 1154 q^{46} + 830 q^{49} - 228 q^{51} + 54 q^{54} - 264 q^{56} + 2304 q^{59} - 688 q^{61} + 1090 q^{64} + 66 q^{66} + 966 q^{69} - 1414 q^{71} + 2352 q^{74} - 3398 q^{76} + 4988 q^{79} + 810 q^{81} + 1944 q^{84} - 1598 q^{86} + 4870 q^{89} - 1608 q^{91} + 1004 q^{94} + 138 q^{96} + 990 q^{99}+O(q^{100}) \) 10 * q - 6 * q^4 - 6 * q^6 - 90 * q^9 - 110 * q^11 - 16 * q^14 - 250 * q^16 + 114 * q^19 - 108 * q^21 - 18 * q^24 - 250 * q^26 + 214 * q^29 - 590 * q^31 - 68 * q^34 + 54 * q^36 + 186 * q^39 - 256 * q^41 + 66 * q^44 - 1154 * q^46 + 830 * q^49 - 228 * q^51 + 54 * q^54 - 264 * q^56 + 2304 * q^59 - 688 * q^61 + 1090 * q^64 + 66 * q^66 + 966 * q^69 - 1414 * q^71 + 2352 * q^74 - 3398 * q^76 + 4988 * q^79 + 810 * q^81 + 1944 * q^84 - 1598 * q^86 + 4870 * q^89 - 1608 * q^91 + 1004 * q^94 + 138 * q^96 + 990 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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