LMFDB - Embedded newform 825.4.c.s.199.9

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			199.9
Root			$3.98707i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.s.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.98707i q^{2} -3.00000i q^{3} -7.89672 q^{4} +11.9612 q^{6} -12.5627i q^{7} +0.411800i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+3.98707i q^{2} -3.00000i q^{3} -7.89672 q^{4} +11.9612 q^{6} -12.5627i q^{7} +0.411800i q^{8} -9.00000 q^{9} -11.0000 q^{11} +23.6901i q^{12} +36.0726i q^{13} +50.0885 q^{14} -64.8156 q^{16} -39.7182i q^{17} -35.8836i q^{18} +148.094 q^{19} -37.6882 q^{21} -43.8578i q^{22} -35.0665i q^{23} +1.23540 q^{24} -143.824 q^{26} +27.0000i q^{27} +99.2043i q^{28} -88.2837 q^{29} -166.874 q^{31} -255.130i q^{32} +33.0000i q^{33} +158.359 q^{34} +71.0704 q^{36} -85.2847i q^{37} +590.460i q^{38} +108.218 q^{39} +329.944 q^{41} -150.265i q^{42} -278.695i q^{43} +86.8639 q^{44} +139.813 q^{46} +272.851i q^{47} +194.447i q^{48} +185.178 q^{49} -119.155 q^{51} -284.855i q^{52} +223.266i q^{53} -107.651 q^{54} +5.17334 q^{56} -444.282i q^{57} -351.993i q^{58} +467.463 q^{59} +752.249 q^{61} -665.338i q^{62} +113.065i q^{63} +498.695 q^{64} -131.573 q^{66} -733.563i q^{67} +313.643i q^{68} -105.200 q^{69} +537.226 q^{71} -3.70620i q^{72} +397.895i q^{73} +340.036 q^{74} -1169.46 q^{76} +138.190i q^{77} +431.471i q^{78} +1079.06 q^{79} +81.0000 q^{81} +1315.51i q^{82} +683.484i q^{83} +297.613 q^{84} +1111.18 q^{86} +264.851i q^{87} -4.52980i q^{88} +166.100 q^{89} +453.170 q^{91} +276.911i q^{92} +500.622i q^{93} -1087.87 q^{94} -765.390 q^{96} +694.031i q^{97} +738.317i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.98707i	1.40964i	0.709385	+	0.704821i	$0.248973\pi$
$2$	3.98707i	1.40964i	−0.709385	+	0.704821i	$0.751027\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	−7.89672	−0.987090
$5$	0	0
$5$	0	0
$6$	11.9612	0.813857
$7$	− 12.5627i	− 0.678324i	−0.940728	−	0.339162i	$-0.889857\pi$
$7$	− 12.5627i	− 0.678324i	0.940728	−	0.339162i	$-0.110143\pi$
$8$	0.411800i	0.0181992i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	23.6901i	0.569896i
$13$	36.0726i	0.769594i	0.923001	+	0.384797i	$0.125729\pi$
$13$	36.0726i	0.769594i	−0.923001	+	0.384797i	$0.874271\pi$
$14$	50.0885	0.956193
$15$	0	0
$16$	−64.8156	−1.01274
$17$	− 39.7182i	− 0.566652i	−0.959024	−	0.283326i	$-0.908562\pi$
$17$	− 39.7182i	− 0.566652i	0.959024	−	0.283326i	$-0.0914378\pi$
$18$	− 35.8836i	− 0.469881i
$19$	148.094	1.78816	0.894081	−	0.447906i	$-0.147830\pi$
$19$	148.094	1.78816	0.894081	+	0.447906i	$0.147830\pi$
$20$	0	0
$21$	−37.6882	−0.391630
$22$	− 43.8578i	− 0.425023i
$23$	− 35.0665i	− 0.317908i	−0.987286	−	0.158954i	$-0.949188\pi$
$23$	− 35.0665i	− 0.317908i	0.987286	−	0.158954i	$-0.0508121\pi$
$24$	1.23540	0.0105073
$25$	0	0
$26$	−143.824	−1.08485
$27$	27.0000i	0.192450i
$28$	99.2043i	0.669566i
$29$	−88.2837	−0.565306	−0.282653	−	0.959222i	$-0.591215\pi$
$29$	−88.2837	−0.565306	−0.282653	+	0.959222i	$0.591215\pi$
$30$	0	0
$31$	−166.874	−0.966820	−0.483410	−	0.875394i	$-0.660602\pi$
$31$	−166.874	−0.966820	−0.483410	+	0.875394i	$0.660602\pi$
$32$	− 255.130i	− 1.40941i
$33$	33.0000i	0.174078i
$34$	158.359	0.798776
$35$	0	0
$36$	71.0704	0.329030
$37$	− 85.2847i	− 0.378939i	−0.981887	−	0.189469i	$-0.939323\pi$
$37$	− 85.2847i	− 0.378939i	0.981887	−	0.189469i	$-0.0606767\pi$
$38$	590.460i	2.52067i
$39$	108.218	0.444326
$40$	0	0
$41$	329.944	1.25679	0.628397	−	0.777893i	$-0.283711\pi$
$41$	329.944	1.25679	0.628397	+	0.777893i	$0.283711\pi$
$42$	− 150.265i	− 0.552058i
$43$	− 278.695i	− 0.988386i	−0.869352	−	0.494193i	$-0.835464\pi$
$43$	− 278.695i	− 0.988386i	0.869352	−	0.494193i	$-0.164536\pi$
$44$	86.8639	0.297619
$45$	0	0
$46$	139.813	0.448136
$47$	272.851i	0.846795i	0.905944	+	0.423397i	$0.139163\pi$
$47$	272.851i	0.846795i	−0.905944	+	0.423397i	$0.860837\pi$
$48$	194.447i	0.584708i
$49$	185.178	0.539877
$50$	0	0
$51$	−119.155	−0.327157
$52$	− 284.855i	− 0.759659i
$53$	223.266i	0.578640i	0.957232	+	0.289320i	$0.0934292\pi$
$53$	223.266i	0.578640i	−0.957232	+	0.289320i	$0.906571\pi$
$54$	−107.651	−0.271286
$55$	0	0
$56$	5.17334	0.0123449
$57$	− 444.282i	− 1.03240i
$58$	− 351.993i	− 0.796879i
$59$	467.463	1.03150	0.515750	−	0.856739i	$-0.327513\pi$
$59$	467.463	1.03150	0.515750	+	0.856739i	$0.327513\pi$
$60$	0	0
$61$	752.249	1.57894	0.789472	−	0.613786i	$-0.210354\pi$
$61$	752.249	1.57894	0.789472	+	0.613786i	$0.210354\pi$
$62$	− 665.338i	− 1.36287i
$63$	113.065i	0.226108i
$64$	498.695	0.974014
$65$	0	0
$66$	−131.573	−0.245387
$67$	− 733.563i	− 1.33760i	−0.743444	−	0.668798i	$-0.766809\pi$
$67$	− 733.563i	− 1.33760i	0.743444	−	0.668798i	$-0.233191\pi$
$68$	313.643i	0.559336i
$69$	−105.200	−0.183544
$70$	0	0
$71$	537.226	0.897985	0.448993	−	0.893535i	$-0.351783\pi$
$71$	537.226	0.897985	0.448993	+	0.893535i	$0.351783\pi$
$72$	− 3.70620i	− 0.00606639i
$73$	397.895i	0.637947i	0.947764	+	0.318974i	$0.103338\pi$
$73$	397.895i	0.637947i	−0.947764	+	0.318974i	$0.896662\pi$
$74$	340.036	0.534168
$75$	0	0
$76$	−1169.46	−1.76508
$77$	138.190i	0.204522i
$78$	431.471i	0.626340i
$79$	1079.06	1.53675	0.768375	−	0.640000i	$-0.221066\pi$
$79$	1079.06	1.53675	0.768375	+	0.640000i	$0.221066\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	1315.51i	1.77163i
$83$	683.484i	0.903881i	0.892048	+	0.451941i	$0.149268\pi$
$83$	683.484i	0.903881i	−0.892048	+	0.451941i	$0.850732\pi$
$84$	297.613	0.386574
$85$	0	0
$86$	1111.18	1.39327
$87$	264.851i	0.326380i
$88$	− 4.52980i	− 0.00548726i
$89$	166.100	0.197826	0.0989130	−	0.995096i	$-0.468463\pi$
$89$	166.100	0.197826	0.0989130	+	0.995096i	$0.468463\pi$
$90$	0	0
$91$	453.170	0.522034
$92$	276.911i	0.313803i
$93$	500.622i	0.558194i
$94$	−1087.87	−1.19368
$95$	0	0
$96$	−765.390	−0.813721
$97$	694.031i	0.726476i	0.931696	+	0.363238i	$0.118329\pi$
$97$	694.031i	0.726476i	−0.931696	+	0.363238i	$0.881671\pi$
$98$	738.317i	0.761033i
$99$	99.0000	0.100504
$100$	0	0
$101$	447.846	0.441211	0.220605	−	0.975363i	$-0.429197\pi$
$101$	447.846	0.441211	0.220605	+	0.975363i	$0.429197\pi$
$102$	− 475.078i	− 0.461174i
$103$	− 1314.02i	− 1.25703i	−0.777797	−	0.628516i	$-0.783663\pi$
$103$	− 1314.02i	− 1.25703i	0.777797	−	0.628516i	$-0.216337\pi$
$104$	−14.8547	−0.0140060
$105$	0	0
$106$	−890.176	−0.815675
$107$	1048.81i	0.947594i	0.880634	+	0.473797i	$0.157117\pi$
$107$	1048.81i	0.947594i	−0.880634	+	0.473797i	$0.842883\pi$
$108$	− 213.211i	− 0.189965i
$109$	1240.73	1.09028	0.545140	−	0.838345i	$-0.316477\pi$
$109$	1240.73	1.09028	0.545140	+	0.838345i	$0.316477\pi$
$110$	0	0
$111$	−255.854	−0.218780
$112$	814.261i	0.686968i
$113$	1331.27i	1.10828i	0.832425	+	0.554138i	$0.186952\pi$
$113$	1331.27i	1.10828i	−0.832425	+	0.554138i	$0.813048\pi$
$114$	1771.38	1.45531
$115$	0	0
$116$	697.152	0.558008
$117$	− 324.653i	− 0.256531i
$118$	1863.81i	1.45405i
$119$	−498.969	−0.384373
$120$	0	0
$121$	121.000	0.0909091
$122$	2999.27i	2.22575i
$123$	− 989.832i	− 0.725611i
$124$	1317.76	0.954338
$125$	0	0
$126$	−450.796	−0.318731
$127$	− 1250.59i	− 0.873791i	−0.899512	−	0.436896i	$-0.856078\pi$
$127$	− 1250.59i	− 0.873791i	0.899512	−	0.436896i	$-0.143922\pi$
$128$	− 52.7060i	− 0.0363953i
$129$	−836.085	−0.570645
$130$	0	0
$131$	−168.067	−0.112092	−0.0560460	−	0.998428i	$-0.517849\pi$
$131$	−168.067	−0.112092	−0.0560460	+	0.998428i	$0.517849\pi$
$132$	− 260.592i	− 0.171830i
$133$	− 1860.46i	− 1.21295i
$134$	2924.77	1.88553
$135$	0	0
$136$	16.3560	0.0103126
$137$	1533.67i	0.956428i	0.878243	+	0.478214i	$0.158716\pi$
$137$	1533.67i	0.956428i	−0.878243	+	0.478214i	$0.841284\pi$
$138$	− 419.438i	− 0.258731i
$139$	961.259	0.586568	0.293284	−	0.956025i	$-0.405252\pi$
$139$	961.259	0.586568	0.293284	+	0.956025i	$0.405252\pi$
$140$	0	0
$141$	818.552	0.488897
$142$	2141.96i	1.26584i
$143$	− 396.798i	− 0.232041i
$144$	583.340	0.337581
$145$	0	0
$146$	−1586.44	−0.899277
$147$	− 555.534i	− 0.311698i
$148$	673.469i	0.374046i
$149$	70.0037	0.0384894	0.0192447	−	0.999815i	$-0.493874\pi$
$149$	70.0037	0.0384894	0.0192447	+	0.999815i	$0.493874\pi$
$150$	0	0
$151$	210.529	0.113461	0.0567306	−	0.998390i	$-0.481932\pi$
$151$	210.529	0.113461	0.0567306	+	0.998390i	$0.481932\pi$
$152$	60.9851i	0.0325431i
$153$	357.464i	0.188884i
$154$	−550.973	−0.288303
$155$	0	0
$156$	−854.564	−0.438589
$157$	2239.44i	1.13839i	0.822204	+	0.569193i	$0.192744\pi$
$157$	2239.44i	1.13839i	−0.822204	+	0.569193i	$0.807256\pi$
$158$	4302.27i	2.16627i
$159$	669.798	0.334078
$160$	0	0
$161$	−440.531	−0.215644
$162$	322.953i	0.156627i
$163$	− 1918.08i	− 0.921692i	−0.887480	−	0.460846i	$-0.847546\pi$
$163$	− 1918.08i	− 0.921692i	0.887480	−	0.460846i	$-0.152454\pi$
$164$	−2605.47	−1.24057
$165$	0	0
$166$	−2725.10	−1.27415
$167$	− 3036.53i	− 1.40703i	−0.710682	−	0.703513i	$-0.751614\pi$
$167$	− 3036.53i	− 1.40703i	0.710682	−	0.703513i	$-0.248386\pi$
$168$	− 15.5200i	− 0.00712735i
$169$	895.771	0.407724
$170$	0	0
$171$	−1332.84	−0.596054
$172$	2200.78i	0.975625i
$173$	− 1713.66i	− 0.753104i	−0.926396	−	0.376552i	$-0.877110\pi$
$173$	− 1713.66i	− 0.753104i	0.926396	−	0.376552i	$-0.122890\pi$
$174$	−1055.98	−0.460078
$175$	0	0
$176$	712.972	0.305354
$177$	− 1402.39i	− 0.595537i
$178$	662.250i	0.278864i
$179$	901.687	0.376510	0.188255	−	0.982120i	$-0.439717\pi$
$179$	901.687	0.376510	0.188255	+	0.982120i	$0.439717\pi$
$180$	0	0
$181$	−2970.07	−1.21969	−0.609844	−	0.792521i	$-0.708768\pi$
$181$	−2970.07	−1.21969	−0.609844	+	0.792521i	$0.708768\pi$
$182$	1806.82i	0.735881i
$183$	− 2256.75i	− 0.911604i
$184$	14.4404	0.00578566
$185$	0	0
$186$	−1996.01	−0.786854
$187$	436.900i	0.170852i
$188$	− 2154.62i	− 0.835862i
$189$	339.194	0.130543
$190$	0	0
$191$	611.910	0.231813	0.115906	−	0.993260i	$-0.463023\pi$
$191$	611.910	0.231813	0.115906	+	0.993260i	$0.463023\pi$
$192$	− 1496.09i	− 0.562348i
$193$	− 1902.58i	− 0.709589i	−0.934944	−	0.354795i	$-0.884551\pi$
$193$	− 1902.58i	− 0.709589i	0.934944	−	0.354795i	$-0.115449\pi$
$194$	−2767.15	−1.02407
$195$	0	0
$196$	−1462.30	−0.532907
$197$	268.748i	0.0971956i	0.998818	+	0.0485978i	$0.0154753\pi$
$197$	268.748i	0.0971956i	−0.998818	+	0.0485978i	$0.984525\pi$
$198$	394.720i	0.141674i
$199$	229.583	0.0817825	0.0408912	−	0.999164i	$-0.486980\pi$
$199$	229.583	0.0817825	0.0408912	+	0.999164i	$0.486980\pi$
$200$	0	0
$201$	−2200.69	−0.772262
$202$	1785.59i	0.621949i
$203$	1109.08i	0.383460i
$204$	940.930	0.322933
$205$	0	0
$206$	5239.09	1.77196
$207$	315.599i	0.105969i
$208$	− 2338.06i	− 0.779402i
$209$	−1629.03	−0.539151
$210$	0	0
$211$	−5111.79	−1.66782	−0.833910	−	0.551901i	$-0.813903\pi$
$211$	−5111.79	−1.66782	−0.833910	+	0.551901i	$0.813903\pi$
$212$	− 1763.07i	− 0.571170i
$213$	− 1611.68i	− 0.518452i
$214$	−4181.69	−1.33577
$215$	0	0
$216$	−11.1186	−0.00350243
$217$	2096.39i	0.655817i
$218$	4946.88i	1.53690i
$219$	1193.69	0.368319
$220$	0	0
$221$	1432.74	0.436092
$222$	− 1020.11i	− 0.308402i
$223$	− 1393.60i	− 0.418486i	−0.977864	−	0.209243i	$-0.932900\pi$
$223$	− 1393.60i	− 0.418486i	0.977864	−	0.209243i	$-0.0670999\pi$
$224$	−3205.13	−0.956034
$225$	0	0
$226$	−5307.86	−1.56227
$227$	6244.88i	1.82593i	0.408032	+	0.912967i	$0.366215\pi$
$227$	6244.88i	1.82593i	−0.408032	+	0.912967i	$0.633785\pi$
$228$	3508.37i	1.01907i
$229$	−3295.16	−0.950873	−0.475437	−	0.879750i	$-0.657710\pi$
$229$	−3295.16	−0.950873	−0.475437	+	0.879750i	$0.657710\pi$
$230$	0	0
$231$	414.570	0.118081
$232$	− 36.3553i	− 0.0102881i
$233$	961.850i	0.270442i	0.990815	+	0.135221i	$0.0431744\pi$
$233$	961.850i	0.270442i	−0.990815	+	0.135221i	$0.956826\pi$
$234$	1294.41	0.361617
$235$	0	0
$236$	−3691.42	−1.01818
$237$	− 3237.17i	− 0.887242i
$238$	− 1989.42i	− 0.541829i
$239$	4738.03	1.28233	0.641166	−	0.767402i	$-0.278451\pi$
$239$	4738.03	1.28233	0.641166	+	0.767402i	$0.278451\pi$
$240$	0	0
$241$	−3928.79	−1.05011	−0.525053	−	0.851070i	$-0.675954\pi$
$241$	−3928.79	−1.05011	−0.525053	+	0.851070i	$0.675954\pi$
$242$	482.435i	0.128149i
$243$	− 243.000i	− 0.0641500i
$244$	−5940.30	−1.55856
$245$	0	0
$246$	3946.53	1.02285
$247$	5342.12i	1.37616i
$248$	− 68.7187i	− 0.0175953i
$249$	2050.45	0.521856
$250$	0	0
$251$	7733.06	1.94465	0.972324	−	0.233638i	$-0.0750632\pi$
$251$	7733.06	1.94465	0.972324	+	0.233638i	$0.0750632\pi$
$252$	− 892.839i	− 0.223189i
$253$	385.732i	0.0958528i
$254$	4986.17	1.23173
$255$	0	0
$256$	4199.71	1.02532
$257$	1574.17i	0.382079i	0.981582	+	0.191039i	$0.0611858\pi$
$257$	1574.17i	0.382079i	−0.981582	+	0.191039i	$0.938814\pi$
$258$	− 3333.53i	− 0.804405i
$259$	−1071.41	−0.257043
$260$	0	0
$261$	794.554	0.188435
$262$	− 670.093i	− 0.158009i
$263$	− 3172.64i	− 0.743853i	−0.928262	−	0.371927i	$-0.878697\pi$
$263$	− 3172.64i	− 0.743853i	0.928262	−	0.371927i	$-0.121303\pi$
$264$	−13.5894	−0.00316807
$265$	0	0
$266$	7417.79	1.70983
$267$	− 498.299i	− 0.114215i
$268$	5792.74i	1.32033i
$269$	1238.83	0.280791	0.140396	−	0.990095i	$-0.455163\pi$
$269$	1238.83	0.280791	0.140396	+	0.990095i	$0.455163\pi$
$270$	0	0
$271$	−2257.02	−0.505920	−0.252960	−	0.967477i	$-0.581404\pi$
$271$	−2257.02	−0.505920	−0.252960	+	0.967477i	$0.581404\pi$
$272$	2574.36i	0.573873i
$273$	− 1359.51i	− 0.301396i
$274$	−6114.86	−1.34822
$275$	0	0
$276$	830.732	0.181175
$277$	− 8207.95i	− 1.78039i	−0.455580	−	0.890195i	$-0.650568\pi$
$277$	− 8207.95i	− 1.78039i	0.455580	−	0.890195i	$-0.349432\pi$
$278$	3832.60i	0.826850i
$279$	1501.87	0.322273
$280$	0	0
$281$	−3499.20	−0.742864	−0.371432	−	0.928460i	$-0.621133\pi$
$281$	−3499.20	−0.742864	−0.371432	+	0.928460i	$0.621133\pi$
$282$	3263.62i	0.689170i
$283$	8614.14i	1.80939i	0.426059	+	0.904695i	$0.359901\pi$
$283$	8614.14i	1.80939i	−0.426059	+	0.904695i	$0.640099\pi$
$284$	−4242.32	−0.886392
$285$	0	0
$286$	1582.06	0.327095
$287$	− 4145.00i	− 0.852513i
$288$	2296.17i	0.469802i
$289$	3335.46	0.678906
$290$	0	0
$291$	2082.09	0.419431
$292$	− 3142.07i	− 0.629711i
$293$	− 1028.59i	− 0.205088i	−0.994728	−	0.102544i	$-0.967302\pi$
$293$	− 1028.59i	− 0.205088i	0.994728	−	0.102544i	$-0.0326983\pi$
$294$	2214.95	0.439383
$295$	0	0
$296$	35.1203	0.00689637
$297$	− 297.000i	− 0.0580259i
$298$	279.109i	0.0542563i
$299$	1264.94	0.244660
$300$	0	0
$301$	−3501.17	−0.670446
$302$	839.395i	0.159940i
$303$	− 1343.54i	− 0.254733i
$304$	−9598.79	−1.81095
$305$	0	0
$306$	−1425.23	−0.266259
$307$	− 2168.83i	− 0.403197i	−0.979468	−	0.201599i	$-0.935386\pi$
$307$	− 2168.83i	− 0.403197i	0.979468	−	0.201599i	$-0.0646136\pi$
$308$	− 1091.25i	− 0.201882i
$309$	−3942.06	−0.725748
$310$	0	0
$311$	4318.45	0.787386	0.393693	−	0.919242i	$-0.371197\pi$
$311$	4318.45	0.787386	0.393693	+	0.919242i	$0.371197\pi$
$312$	44.5641i	0.00808636i
$313$	− 4785.34i	− 0.864164i	−0.901834	−	0.432082i	$-0.857779\pi$
$313$	− 4785.34i	− 0.864164i	0.901834	−	0.432082i	$-0.142221\pi$
$314$	−8928.79	−1.60472
$315$	0	0
$316$	−8520.99	−1.51691
$317$	− 6680.52i	− 1.18364i	−0.806069	−	0.591822i	$-0.798409\pi$
$317$	− 6680.52i	− 1.18364i	0.806069	−	0.591822i	$-0.201591\pi$
$318$	2670.53i	0.470930i
$319$	971.121	0.170446
$320$	0	0
$321$	3146.44	0.547094
$322$	− 1756.43i	− 0.303981i
$323$	− 5882.02i	− 1.01326i
$324$	−639.634	−0.109677
$325$	0	0
$326$	7647.52	1.29926
$327$	− 3722.19i	− 0.629473i
$328$	135.871i	0.0228726i
$329$	3427.75	0.574401
$330$	0	0
$331$	3428.85	0.569386	0.284693	−	0.958619i	$-0.408108\pi$
$331$	3428.85	0.569386	0.284693	+	0.958619i	$0.408108\pi$
$332$	− 5397.28i	− 0.892212i
$333$	767.563i	0.126313i
$334$	12106.8	1.98340
$335$	0	0
$336$	2442.78	0.396621
$337$	7809.83i	1.26240i	0.775620	+	0.631200i	$0.217437\pi$
$337$	7809.83i	1.26240i	−0.775620	+	0.631200i	$0.782563\pi$
$338$	3571.50i	0.574745i
$339$	3993.80	0.639863
$340$	0	0
$341$	1835.61	0.291507
$342$	− 5314.14i	− 0.840222i
$343$	− 6635.35i	− 1.04453i
$344$	114.767	0.0179878
$345$	0	0
$346$	6832.47	1.06161
$347$	− 5860.34i	− 0.906627i	−0.891351	−	0.453314i	$-0.850242\pi$
$347$	− 5860.34i	− 0.906627i	0.891351	−	0.453314i	$-0.149758\pi$
$348$	− 2091.45i	− 0.322166i
$349$	−5833.65	−0.894750	−0.447375	−	0.894346i	$-0.647641\pi$
$349$	−5833.65	−0.894750	−0.447375	+	0.894346i	$0.647641\pi$
$350$	0	0
$351$	−973.959	−0.148109
$352$	2806.43i	0.424952i
$353$	− 4532.47i	− 0.683397i	−0.939810	−	0.341699i	$-0.888998\pi$
$353$	− 4532.47i	− 0.683397i	0.939810	−	0.341699i	$-0.111002\pi$
$354$	5591.42	0.839494
$355$	0	0
$356$	−1311.64	−0.195272
$357$	1496.91i	0.221918i
$358$	3595.09i	0.530744i
$359$	8727.48	1.28306	0.641530	−	0.767098i	$-0.278300\pi$
$359$	8727.48	1.28306	0.641530	+	0.767098i	$0.278300\pi$
$360$	0	0
$361$	15072.8	2.19752
$362$	− 11841.9i	− 1.71932i
$363$	− 363.000i	− 0.0524864i
$364$	−3578.55	−0.515294
$365$	0	0
$366$	8997.80	1.28503
$367$	− 11397.8i	− 1.62114i	−0.585639	−	0.810572i	$-0.699156\pi$
$367$	− 11397.8i	− 1.62114i	0.585639	−	0.810572i	$-0.300844\pi$
$368$	2272.86i	0.321959i
$369$	−2969.50	−0.418932
$370$	0	0
$371$	2804.83	0.392505
$372$	− 3953.27i	− 0.550988i
$373$	− 10698.2i	− 1.48507i	−0.669807	−	0.742535i	$-0.733623\pi$
$373$	− 10698.2i	− 1.48507i	0.669807	−	0.742535i	$-0.266377\pi$
$374$	−1741.95	−0.240840
$375$	0	0
$376$	−112.360	−0.0154110
$377$	− 3184.62i	− 0.435056i
$378$	1352.39i	0.184019i
$379$	−6055.57	−0.820723	−0.410361	−	0.911923i	$-0.634597\pi$
$379$	−6055.57	−0.820723	−0.410361	+	0.911923i	$0.634597\pi$
$380$	0	0
$381$	−3751.76	−0.504484
$382$	2439.73i	0.326773i
$383$	13989.5i	1.86640i	0.359363	+	0.933198i	$0.382994\pi$
$383$	13989.5i	1.86640i	−0.359363	+	0.933198i	$0.617006\pi$
$384$	−158.118	−0.0210128
$385$	0	0
$386$	7585.72	1.00027
$387$	2508.26i	0.329462i
$388$	− 5480.56i	− 0.717097i
$389$	−4223.88	−0.550538	−0.275269	−	0.961367i	$-0.588767\pi$
$389$	−4223.88	−0.550538	−0.275269	+	0.961367i	$0.588767\pi$
$390$	0	0
$391$	−1392.78	−0.180143
$392$	76.2563i	0.00982532i
$393$	504.200i	0.0647163i
$394$	−1071.52	−0.137011
$395$	0	0
$396$	−781.775	−0.0992062
$397$	3341.86i	0.422476i	0.977435	+	0.211238i	$0.0677495\pi$
$397$	3341.86i	0.422476i	−0.977435	+	0.211238i	$0.932250\pi$
$398$	915.364i	0.115284i
$399$	−5581.39	−0.700298
$400$	0	0
$401$	−7167.91	−0.892639	−0.446320	−	0.894874i	$-0.647266\pi$
$401$	−7167.91	−0.892639	−0.446320	+	0.894874i	$0.647266\pi$
$402$	− 8774.30i	− 1.08861i
$403$	− 6019.57i	− 0.744060i
$404$	−3536.51	−0.435515
$405$	0	0
$406$	−4422.00	−0.540542
$407$	938.132i	0.114254i
$408$	− 49.0679i	− 0.00595398i
$409$	10360.7	1.25257	0.626287	−	0.779592i	$-0.284574\pi$
$409$	10360.7	1.25257	0.626287	+	0.779592i	$0.284574\pi$
$410$	0	0
$411$	4601.02	0.552194
$412$	10376.4i	1.24080i
$413$	− 5872.61i	− 0.699691i
$414$	−1258.31	−0.149379
$415$	0	0
$416$	9203.19	1.08467
$417$	− 2883.78i	− 0.338655i
$418$	− 6495.06i	− 0.760009i
$419$	7640.60	0.890853	0.445427	−	0.895318i	$-0.353052\pi$
$419$	7640.60	0.890853	0.445427	+	0.895318i	$0.353052\pi$
$420$	0	0
$421$	−1013.65	−0.117345	−0.0586724	−	0.998277i	$-0.518687\pi$
$421$	−1013.65	−0.117345	−0.0586724	+	0.998277i	$0.518687\pi$
$422$	− 20381.0i	− 2.35103i
$423$	− 2455.66i	− 0.282265i
$424$	−91.9410	−0.0105308
$425$	0	0
$426$	6425.87	0.730831
$427$	− 9450.30i	− 1.07104i
$428$	− 8282.18i	− 0.935360i
$429$	−1190.39	−0.133969
$430$	0	0
$431$	−13161.9	−1.47097	−0.735485	−	0.677541i	$-0.763046\pi$
$431$	−13161.9	−1.47097	−0.735485	+	0.677541i	$0.763046\pi$
$432$	− 1750.02i	− 0.194903i
$433$	− 3886.06i	− 0.431298i	−0.976471	−	0.215649i	$-0.930813\pi$
$433$	− 3886.06i	− 0.431298i	0.976471	−	0.215649i	$-0.0691867\pi$
$434$	−8358.46	−0.924467
$435$	0	0
$436$	−9797.70	−1.07620
$437$	− 5193.14i	− 0.568470i
$438$	4759.31i	0.519198i
$439$	384.942	0.0418503	0.0209252	−	0.999781i	$-0.493339\pi$
$439$	384.942	0.0418503	0.0209252	+	0.999781i	$0.493339\pi$
$440$	0	0
$441$	−1666.60	−0.179959
$442$	5712.42i	0.614734i
$443$	− 13324.7i	− 1.42907i	−0.699601	−	0.714533i	$-0.746639\pi$
$443$	− 13324.7i	− 1.42907i	0.699601	−	0.714533i	$-0.253361\pi$
$444$	2020.41	0.215956
$445$	0	0
$446$	5556.38	0.589915
$447$	− 210.011i	− 0.0222219i
$448$	− 6264.97i	− 0.660697i
$449$	3242.44	0.340802	0.170401	−	0.985375i	$-0.445494\pi$
$449$	3242.44	0.340802	0.170401	+	0.985375i	$0.445494\pi$
$450$	0	0
$451$	−3629.38	−0.378938
$452$	− 10512.6i	− 1.09397i
$453$	− 631.588i	− 0.0655068i
$454$	−24898.8	−2.57391
$455$	0	0
$456$	182.955	0.0187887
$457$	3686.70i	0.377366i	0.982038	+	0.188683i	$0.0604219\pi$
$457$	3686.70i	0.377366i	−0.982038	+	0.188683i	$0.939578\pi$
$458$	− 13138.0i	− 1.34039i
$459$	1072.39	0.109052
$460$	0	0
$461$	−19219.2	−1.94171	−0.970856	−	0.239664i	$-0.922963\pi$
$461$	−19219.2	−1.94171	−0.970856	+	0.239664i	$0.922963\pi$
$462$	1652.92i	0.166452i
$463$	− 1346.60i	− 0.135166i	−0.997714	−	0.0675832i	$-0.978471\pi$
$463$	− 1346.60i	− 0.135166i	0.997714	−	0.0675832i	$-0.0215288\pi$
$464$	5722.16	0.572510
$465$	0	0
$466$	−3834.96	−0.381226
$467$	8913.27i	0.883205i	0.897211	+	0.441603i	$0.145590\pi$
$467$	8913.27i	0.883205i	−0.897211	+	0.441603i	$0.854410\pi$
$468$	2563.69i	0.253220i
$469$	−9215.55	−0.907323
$470$	0	0
$471$	6718.31	0.657247
$472$	192.501i	0.0187725i
$473$	3065.65i	0.298010i
$474$	12906.8	1.25069
$475$	0	0
$476$	3940.22	0.379411
$477$	− 2009.39i	− 0.192880i
$478$	18890.8i	1.80763i
$479$	11726.8	1.11860	0.559300	−	0.828965i	$-0.311070\pi$
$479$	11726.8	1.11860	0.559300	+	0.828965i	$0.311070\pi$
$480$	0	0
$481$	3076.44	0.291629
$482$	− 15664.3i	− 1.48027i
$483$	1321.59i	0.124502i
$484$	−955.503	−0.0897354
$485$	0	0
$486$	968.858	0.0904286
$487$	8115.91i	0.755168i	0.925975	+	0.377584i	$0.123245\pi$
$487$	8115.91i	0.755168i	−0.925975	+	0.377584i	$0.876755\pi$
$488$	309.776i	0.0287355i
$489$	−5754.25	−0.532139
$490$	0	0
$491$	−12161.5	−1.11780	−0.558901	−	0.829235i	$-0.688777\pi$
$491$	−12161.5	−1.11780	−0.558901	+	0.829235i	$0.688777\pi$
$492$	7816.42i	0.716243i
$493$	3506.47i	0.320332i
$494$	−21299.4	−1.93989
$495$	0	0
$496$	10816.0	0.979141
$497$	− 6749.02i	− 0.609125i
$498$	8175.30i	0.735630i
$499$	−5696.54	−0.511046	−0.255523	−	0.966803i	$-0.582248\pi$
$499$	−5696.54	−0.511046	−0.255523	+	0.966803i	$0.582248\pi$
$500$	0	0
$501$	−9109.58	−0.812347
$502$	30832.2i	2.74126i
$503$	− 9287.58i	− 0.823286i	−0.911345	−	0.411643i	$-0.864955\pi$
$503$	− 9287.58i	− 0.823286i	0.911345	−	0.411643i	$-0.135045\pi$
$504$	−46.5600	−0.00411498
$505$	0	0
$506$	−1537.94	−0.135118
$507$	− 2687.31i	− 0.235400i
$508$	9875.52i	0.862510i
$509$	8316.30	0.724192	0.362096	−	0.932141i	$-0.382061\pi$
$509$	8316.30	0.724192	0.362096	+	0.932141i	$0.382061\pi$
$510$	0	0
$511$	4998.65	0.432735
$512$	16322.9i	1.40894i
$513$	3998.53i	0.344132i
$514$	−6276.34	−0.538594
$515$	0	0
$516$	6602.33	0.563278
$517$	− 3001.36i	− 0.255318i
$518$	− 4271.78i	− 0.362338i
$519$	−5140.97	−0.434805
$520$	0	0
$521$	−4349.68	−0.365764	−0.182882	−	0.983135i	$-0.558543\pi$
$521$	−4349.68	−0.365764	−0.182882	+	0.983135i	$0.558543\pi$
$522$	3167.94i	0.265626i
$523$	− 6877.36i	− 0.575002i	−0.957780	−	0.287501i	$-0.907176\pi$
$523$	− 6877.36i	− 0.575002i	0.957780	−	0.287501i	$-0.0928245\pi$
$524$	1327.17	0.110645
$525$	0	0
$526$	12649.5	1.04857
$527$	6627.93i	0.547851i
$528$	− 2138.91i	− 0.176296i
$529$	10937.3	0.898935
$530$	0	0
$531$	−4207.17	−0.343833
$532$	14691.5i	1.19729i
$533$	11901.9i	0.967222i
$534$	1986.75	0.161002
$535$	0	0
$536$	302.081	0.0243432
$537$	− 2705.06i	− 0.217378i
$538$	4939.30i	0.395815i
$539$	−2036.96	−0.162779
$540$	0	0
$541$	9908.33	0.787417	0.393708	−	0.919235i	$-0.371192\pi$
$541$	9908.33	0.787417	0.393708	+	0.919235i	$0.371192\pi$
$542$	− 8998.90i	− 0.713166i
$543$	8910.21i	0.704187i
$544$	−10133.3	−0.798643
$545$	0	0
$546$	5420.46	0.424861
$547$	8052.99i	0.629472i	0.949179	+	0.314736i	$0.101916\pi$
$547$	8052.99i	0.629472i	−0.949179	+	0.314736i	$0.898084\pi$
$548$	− 12111.0i	− 0.944080i
$549$	−6770.24	−0.526315
$550$	0	0
$551$	−13074.3	−1.01086
$552$	− 43.3212i	− 0.00334035i
$553$	− 13555.9i	− 1.04241i
$554$	32725.7	2.50971
$555$	0	0
$556$	−7590.79	−0.578995
$557$	22805.4i	1.73482i	0.497591	+	0.867412i	$0.334218\pi$
$557$	22805.4i	1.73482i	−0.497591	+	0.867412i	$0.665782\pi$
$558$	5988.04i	0.454290i
$559$	10053.2	0.760656
$560$	0	0
$561$	1310.70	0.0986414
$562$	− 13951.5i	− 1.04717i
$563$	21527.6i	1.61151i	0.592251	+	0.805754i	$0.298240\pi$
$563$	21527.6i	1.61151i	−0.592251	+	0.805754i	$0.701760\pi$
$564$	−6463.87	−0.482585
$565$	0	0
$566$	−34345.2	−2.55059
$567$	− 1017.58i	− 0.0753693i
$568$	221.230i	0.0163426i
$569$	287.375	0.0211729	0.0105865	−	0.999944i	$-0.496630\pi$
$569$	287.375	0.0211729	0.0105865	+	0.999944i	$0.496630\pi$
$570$	0	0
$571$	−14297.5	−1.04787	−0.523934	−	0.851759i	$-0.675536\pi$
$571$	−14297.5	−1.04787	−0.523934	+	0.851759i	$0.675536\pi$
$572$	3133.40i	0.229046i
$573$	− 1835.73i	− 0.133837i
$574$	16526.4	1.20174
$575$	0	0
$576$	−4488.26	−0.324671
$577$	16408.0i	1.18383i	0.805999	+	0.591917i	$0.201629\pi$
$577$	16408.0i	1.18383i	−0.805999	+	0.591917i	$0.798371\pi$
$578$	13298.7i	0.957014i
$579$	−5707.74	−0.409681
$580$	0	0
$581$	8586.43	0.613124
$582$	8301.45i	0.591247i
$583$	− 2455.92i	− 0.174467i
$584$	−163.853	−0.0116101
$585$	0	0
$586$	4101.06	0.289101
$587$	7700.65i	0.541465i	0.962655	+	0.270732i	$0.0872658\pi$
$587$	7700.65i	0.541465i	−0.962655	+	0.270732i	$0.912734\pi$
$588$	4386.89i	0.307674i
$589$	−24713.0	−1.72883
$590$	0	0
$591$	806.245	0.0561159
$592$	5527.78i	0.383768i
$593$	13161.1i	0.911402i	0.890133	+	0.455701i	$0.150611\pi$
$593$	13161.1i	0.911402i	−0.890133	+	0.455701i	$0.849389\pi$
$594$	1184.16	0.0817957
$595$	0	0
$596$	−552.799	−0.0379925
$597$	− 688.749i	− 0.0472171i
$598$	5043.40i	0.344883i
$599$	−11115.0	−0.758175	−0.379088	−	0.925361i	$-0.623762\pi$
$599$	−11115.0	−0.758175	−0.379088	+	0.925361i	$0.623762\pi$
$600$	0	0
$601$	−12069.2	−0.819155	−0.409578	−	0.912275i	$-0.634324\pi$
$601$	−12069.2	−0.819155	−0.409578	+	0.912275i	$0.634324\pi$
$602$	− 13959.4i	− 0.945088i
$603$	6602.07i	0.445866i
$604$	−1662.49	−0.111996
$605$	0	0
$606$	5356.77	0.359083
$607$	− 249.659i	− 0.0166941i	−0.999965	−	0.00834706i	$-0.997343\pi$
$607$	− 249.659i	− 0.0166941i	0.999965	−	0.00834706i	$-0.00265698\pi$
$608$	− 37783.2i	− 2.52025i
$609$	3327.25	0.221391
$610$	0	0
$611$	−9842.42	−0.651689
$612$	− 2822.79i	− 0.186445i
$613$	19136.0i	1.26084i	0.776253	+	0.630421i	$0.217118\pi$
$613$	19136.0i	1.26084i	−0.776253	+	0.630421i	$0.782882\pi$
$614$	8647.26	0.568363
$615$	0	0
$616$	−56.9067	−0.00372214
$617$	− 22119.6i	− 1.44327i	−0.692272	−	0.721637i	$-0.743390\pi$
$617$	− 22119.6i	− 1.44327i	0.692272	−	0.721637i	$-0.256610\pi$
$618$	− 15717.3i	− 1.02304i
$619$	−19523.8	−1.26773	−0.633867	−	0.773442i	$-0.718533\pi$
$619$	−19523.8	−1.26773	−0.633867	+	0.773442i	$0.718533\pi$
$620$	0	0
$621$	946.797	0.0611814
$622$	17218.0i	1.10993i
$623$	− 2086.66i	− 0.134190i
$624$	−7014.19	−0.449988
$625$	0	0
$626$	19079.5	1.21816
$627$	4887.10i	0.311279i
$628$	− 17684.2i	− 1.12369i
$629$	−3387.36	−0.214726
$630$	0	0
$631$	13656.2	0.861562	0.430781	−	0.902457i	$-0.358238\pi$
$631$	13656.2	0.861562	0.430781	+	0.902457i	$0.358238\pi$
$632$	444.355i	0.0279676i
$633$	15335.4i	0.962916i
$634$	26635.7	1.66851
$635$	0	0
$636$	−5289.20	−0.329765
$637$	6679.84i	0.415486i
$638$	3871.93i	0.240268i
$639$	−4835.03	−0.299328
$640$	0	0
$641$	−27823.7	−1.71446	−0.857230	−	0.514934i	$-0.827816\pi$
$641$	−27823.7	−1.71446	−0.857230	+	0.514934i	$0.827816\pi$
$642$	12545.1i	0.771206i
$643$	− 29045.0i	− 1.78137i	−0.454618	−	0.890687i	$-0.650224\pi$
$643$	− 29045.0i	− 1.78137i	0.454618	−	0.890687i	$-0.349776\pi$
$644$	3478.75	0.212860
$645$	0	0
$646$	23452.0	1.42834
$647$	− 7596.84i	− 0.461612i	−0.973000	−	0.230806i	$-0.925864\pi$
$647$	− 7596.84i	− 0.461612i	0.973000	−	0.230806i	$-0.0741362\pi$
$648$	33.3558i	0.00202213i
$649$	−5142.10	−0.311009
$650$	0	0
$651$	6289.17	0.378636
$652$	15146.5i	0.909792i
$653$	4744.20i	0.284310i	0.989844	+	0.142155i	$0.0454032\pi$
$653$	4744.20i	0.284310i	−0.989844	+	0.142155i	$0.954597\pi$
$654$	14840.6	0.887332
$655$	0	0
$656$	−21385.5	−1.27281
$657$	− 3581.06i	− 0.212649i
$658$	13666.7i	0.809699i
$659$	−25736.9	−1.52135	−0.760674	−	0.649134i	$-0.775132\pi$
$659$	−25736.9	−1.52135	−0.760674	+	0.649134i	$0.775132\pi$
$660$	0	0
$661$	14548.4	0.856080	0.428040	−	0.903760i	$-0.359204\pi$
$661$	14548.4	0.856080	0.428040	+	0.903760i	$0.359204\pi$
$662$	13671.1i	0.802630i
$663$	− 4298.21i	− 0.251778i
$664$	−281.459	−0.0164499
$665$	0	0
$666$	−3060.33	−0.178056
$667$	3095.81i	0.179715i
$668$	23978.6i	1.38886i
$669$	−4180.80	−0.241613
$670$	0	0
$671$	−8274.74	−0.476070
$672$	9615.38i	0.551966i
$673$	− 2228.16i	− 0.127621i	−0.997962	−	0.0638106i	$-0.979675\pi$
$673$	− 2228.16i	− 0.127621i	0.997962	−	0.0638106i	$-0.0203254\pi$
$674$	−31138.3	−1.77953
$675$	0	0
$676$	−7073.65	−0.402461
$677$	− 1975.02i	− 0.112121i	−0.998427	−	0.0560606i	$-0.982146\pi$
$677$	− 1975.02i	− 0.112121i	0.998427	−	0.0560606i	$-0.0178540\pi$
$678$	15923.6i	0.901978i
$679$	8718.92	0.492786
$680$	0	0
$681$	18734.6	1.05420
$682$	7318.71i	0.410921i
$683$	14600.7i	0.817980i	0.912539	+	0.408990i	$0.134119\pi$
$683$	14600.7i	0.817980i	−0.912539	+	0.408990i	$0.865881\pi$
$684$	10525.1	0.588358
$685$	0	0
$686$	26455.6	1.47242
$687$	9885.47i	0.548987i
$688$	18063.8i	1.00098i
$689$	−8053.77	−0.445318
$690$	0	0
$691$	−27053.0	−1.48936	−0.744678	−	0.667423i	$-0.767397\pi$
$691$	−27053.0	−1.48936	−0.744678	+	0.667423i	$0.767397\pi$
$692$	13532.3i	0.743381i
$693$	− 1243.71i	− 0.0681741i
$694$	23365.6	1.27802
$695$	0	0
$696$	−109.066	−0.00593984
$697$	− 13104.8i	− 0.712165i
$698$	− 23259.1i	− 1.26128i
$699$	2885.55	0.156140
$700$	0	0
$701$	−25541.0	−1.37613	−0.688067	−	0.725647i	$-0.741541\pi$
$701$	−25541.0	−1.37613	−0.688067	+	0.725647i	$0.741541\pi$
$702$	− 3883.24i	− 0.208780i
$703$	− 12630.1i	− 0.677603i
$704$	−5485.65	−0.293676
$705$	0	0
$706$	18071.3	0.963345
$707$	− 5626.16i	− 0.299284i
$708$	11074.3i	0.587848i
$709$	−10650.6	−0.564161	−0.282081	−	0.959391i	$-0.591025\pi$
$709$	−10650.6	−0.564161	−0.282081	+	0.959391i	$0.591025\pi$
$710$	0	0
$711$	−9711.50	−0.512250
$712$	68.3998i	0.00360027i
$713$	5851.69i	0.307360i
$714$	−5968.27	−0.312825
$715$	0	0
$716$	−7120.36	−0.371649
$717$	− 14214.1i	− 0.740355i
$718$	34797.0i	1.80866i
$719$	26425.6	1.37066	0.685332	−	0.728231i	$-0.259657\pi$
$719$	26425.6	1.37066	0.685332	+	0.728231i	$0.259657\pi$
$720$	0	0
$721$	−16507.7	−0.852675
$722$	60096.2i	3.09772i
$723$	11786.4i	0.606279i
$724$	23453.8	1.20394
$725$	0	0
$726$	1447.31	0.0739870
$727$	− 5323.81i	− 0.271594i	−0.990737	−	0.135797i	$-0.956640\pi$
$727$	− 5323.81i	− 0.271594i	0.990737	−	0.135797i	$-0.0433596\pi$
$728$	186.615i	0.00950059i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−11069.3	−0.560071
$732$	17820.9i	0.899835i
$733$	9265.08i	0.466867i	0.972373	+	0.233434i	$0.0749962\pi$
$733$	9265.08i	0.466867i	−0.972373	+	0.233434i	$0.925004\pi$
$734$	45443.8	2.28523
$735$	0	0
$736$	−8946.52	−0.448061
$737$	8069.19i	0.403301i
$738$	− 11839.6i	− 0.590543i
$739$	31074.1	1.54679	0.773396	−	0.633923i	$-0.218557\pi$
$739$	31074.1	1.54679	0.773396	+	0.633923i	$0.218557\pi$
$740$	0	0
$741$	16026.4	0.794526
$742$	11183.0i	0.553292i
$743$	5376.26i	0.265459i	0.991152	+	0.132729i	$0.0423741\pi$
$743$	5376.26i	0.265459i	−0.991152	+	0.132729i	$0.957626\pi$
$744$	−206.156	−0.0101587
$745$	0	0
$746$	42654.4	2.09342
$747$	− 6151.36i	− 0.301294i
$748$	− 3450.08i	− 0.168646i
$749$	13176.0	0.642776
$750$	0	0
$751$	16857.3	0.819082	0.409541	−	0.912292i	$-0.365689\pi$
$751$	16857.3	0.819082	0.409541	+	0.912292i	$0.365689\pi$
$752$	− 17685.0i	− 0.857586i
$753$	− 23199.2i	− 1.12274i
$754$	12697.3	0.613274
$755$	0	0
$756$	−2678.52	−0.128858
$757$	− 27458.7i	− 1.31837i	−0.751982	−	0.659183i	$-0.770902\pi$
$757$	− 27458.7i	− 1.31837i	0.751982	−	0.659183i	$-0.229098\pi$
$758$	− 24144.0i	− 1.15692i
$759$	1157.20	0.0553406
$760$	0	0
$761$	−35829.9	−1.70675	−0.853373	−	0.521300i	$-0.825447\pi$
$761$	−35829.9	−1.70675	−0.853373	+	0.521300i	$0.825447\pi$
$762$	− 14958.5i	− 0.711141i
$763$	− 15587.0i	− 0.739562i
$764$	−4832.08	−0.228820
$765$	0	0
$766$	−55777.1	−2.63095
$767$	16862.6i	0.793837i
$768$	− 12599.1i	− 0.591968i
$769$	−21200.9	−0.994177	−0.497089	−	0.867700i	$-0.665598\pi$
$769$	−21200.9	−0.994177	−0.497089	+	0.867700i	$0.665598\pi$
$770$	0	0
$771$	4722.52	0.220593
$772$	15024.1i	0.700428i
$773$	− 29661.6i	− 1.38015i	−0.723739	−	0.690074i	$-0.757578\pi$
$773$	− 29661.6i	− 1.38015i	0.723739	−	0.690074i	$-0.242422\pi$
$774$	−10000.6	−0.464423
$775$	0	0
$776$	−285.802	−0.0132213
$777$	3214.23i	0.148404i
$778$	− 16840.9i	− 0.776061i
$779$	48862.7	2.24735
$780$	0	0
$781$	−5909.48	−0.270753
$782$	− 5553.11i	− 0.253937i
$783$	− 2383.66i	− 0.108793i
$784$	−12002.4	−0.546757
$785$	0	0
$786$	−2010.28	−0.0912268
$787$	340.379i	0.0154170i	0.999970	+	0.00770852i	$0.00245372\pi$
$787$	340.379i	0.0154170i	−0.999970	+	0.00770852i	$0.997546\pi$
$788$	− 2122.23i	− 0.0959407i
$789$	−9517.92	−0.429464
$790$	0	0
$791$	16724.4	0.751769
$792$	40.7682i	0.00182909i
$793$	27135.5i	1.21515i
$794$	−13324.2	−0.595540
$795$	0	0
$796$	−1812.95	−0.0807266
$797$	− 37442.3i	− 1.66408i	−0.554715	−	0.832041i	$-0.687173\pi$
$797$	− 37442.3i	− 1.66408i	0.554715	−	0.832041i	$-0.312827\pi$
$798$	− 22253.4i	− 0.987169i
$799$	10837.1	0.479838
$800$	0	0
$801$	−1494.90	−0.0659420
$802$	− 28578.9i	− 1.25830i
$803$	− 4376.85i	− 0.192348i
$804$	17378.2	0.762292
$805$	0	0
$806$	24000.4	1.04886
$807$	− 3716.49i	− 0.162115i
$808$	184.423i	0.00802967i
$809$	23629.8	1.02692	0.513461	−	0.858113i	$-0.328363\pi$
$809$	23629.8	1.02692	0.513461	+	0.858113i	$0.328363\pi$
$810$	0	0
$811$	−40325.2	−1.74601	−0.873003	−	0.487715i	$-0.837830\pi$
$811$	−40325.2	−1.74601	−0.873003	+	0.487715i	$0.837830\pi$
$812$	− 8758.13i	− 0.378510i
$813$	6771.06i	0.292093i
$814$	−3740.40	−0.161058
$815$	0	0
$816$	7723.08	0.331326
$817$	− 41273.0i	− 1.76739i
$818$	41308.8i	1.76568i
$819$	−4078.53	−0.174011
$820$	0	0
$821$	20710.8	0.880403	0.440201	−	0.897899i	$-0.354907\pi$
$821$	20710.8	0.880403	0.440201	+	0.897899i	$0.354907\pi$
$822$	18344.6i	0.778395i
$823$	14546.6i	0.616116i	0.951368	+	0.308058i	$0.0996791\pi$
$823$	14546.6i	0.616116i	−0.951368	+	0.308058i	$0.900321\pi$
$824$	541.114	0.0228769
$825$	0	0
$826$	23414.5	0.986314
$827$	− 39477.0i	− 1.65992i	−0.557826	−	0.829958i	$-0.688364\pi$
$827$	− 39477.0i	− 1.65992i	0.557826	−	0.829958i	$-0.311636\pi$
$828$	− 2492.19i	− 0.104601i
$829$	37344.7	1.56458	0.782289	−	0.622915i	$-0.214052\pi$
$829$	37344.7	1.56458	0.782289	+	0.622915i	$0.214052\pi$
$830$	0	0
$831$	−24623.9	−1.02791
$832$	17989.2i	0.749596i
$833$	− 7354.93i	− 0.305922i
$834$	11497.8	0.477382
$835$	0	0
$836$	12864.0	0.532190
$837$	− 4505.60i	− 0.186065i
$838$	30463.6i	1.25578i
$839$	28412.4	1.16914	0.584568	−	0.811345i	$-0.301264\pi$
$839$	28412.4	1.16914	0.584568	+	0.811345i	$0.301264\pi$
$840$	0	0
$841$	−16595.0	−0.680429
$842$	− 4041.48i	− 0.165414i
$843$	10497.6i	0.428892i
$844$	40366.3	1.64629
$845$	0	0
$846$	9790.87	0.397892
$847$	− 1520.09i	− 0.0616658i
$848$	− 14471.1i	− 0.586014i
$849$	25842.4	1.04465
$850$	0	0
$851$	−2990.64	−0.120468
$852$	12727.0i	0.511759i
$853$	31070.6i	1.24717i	0.781756	+	0.623585i	$0.214324\pi$
$853$	31070.6i	1.24717i	−0.781756	+	0.623585i	$0.785676\pi$
$854$	37679.0	1.50978
$855$	0	0
$856$	−431.902	−0.0172454
$857$	28889.1i	1.15150i	0.817626	+	0.575749i	$0.195290\pi$
$857$	28889.1i	1.15150i	−0.817626	+	0.575749i	$0.804710\pi$
$858$	− 4746.18i	− 0.188849i
$859$	−17190.9	−0.682825	−0.341413	−	0.939913i	$-0.610905\pi$
$859$	−17190.9	−0.682825	−0.341413	+	0.939913i	$0.610905\pi$
$860$	0	0
$861$	−12435.0	−0.492199
$862$	− 52477.5i	− 2.07354i
$863$	39878.7i	1.57298i	0.617600	+	0.786492i	$0.288105\pi$
$863$	39878.7i	1.57298i	−0.617600	+	0.786492i	$0.711895\pi$
$864$	6888.51	0.271240
$865$	0	0
$866$	15494.0	0.607976
$867$	− 10006.4i	− 0.391966i
$868$	− 16554.6i	− 0.647350i
$869$	−11869.6	−0.463347
$870$	0	0
$871$	26461.5	1.02941
$872$	510.933i	0.0198422i
$873$	− 6246.28i	− 0.242159i
$874$	20705.4	0.801339
$875$	0	0
$876$	−9426.20	−0.363564
$877$	− 28622.5i	− 1.10207i	−0.834483	−	0.551034i	$-0.814233\pi$
$877$	− 28622.5i	− 1.10207i	0.834483	−	0.551034i	$-0.185767\pi$
$878$	1534.79i	0.0589939i
$879$	−3085.77	−0.118408
$880$	0	0
$881$	34427.7	1.31657	0.658286	−	0.752768i	$-0.271282\pi$
$881$	34427.7	1.31657	0.658286	+	0.752768i	$0.271282\pi$
$882$	− 6644.85i	− 0.253678i
$883$	14049.2i	0.535441i	0.963497	+	0.267721i	$0.0862704\pi$
$883$	14049.2i	0.535441i	−0.963497	+	0.267721i	$0.913730\pi$
$884$	−11313.9	−0.430462
$885$	0	0
$886$	53126.6	2.01447
$887$	29052.4i	1.09976i	0.835245	+	0.549878i	$0.185326\pi$
$887$	29052.4i	1.09976i	−0.835245	+	0.549878i	$0.814674\pi$
$888$	− 105.361i	− 0.00398162i
$889$	−15710.8	−0.592713
$890$	0	0
$891$	−891.000	−0.0335013
$892$	11004.9i	0.413083i
$893$	40407.5i	1.51421i
$894$	837.328	0.0313249
$895$	0	0
$896$	−662.132	−0.0246878
$897$	− 3794.82i	− 0.141255i
$898$	12927.8i	0.480409i
$899$	14732.3	0.546550
$900$	0	0
$901$	8867.72	0.327888
$902$	− 14470.6i	− 0.534167i
$903$	10503.5i	0.387082i
$904$	−548.216	−0.0201697
$905$	0	0
$906$	2518.18	0.0923411
$907$	39504.2i	1.44621i	0.690736	+	0.723107i	$0.257287\pi$
$907$	39504.2i	1.44621i	−0.690736	+	0.723107i	$0.742713\pi$
$908$	− 49314.0i	− 1.80236i
$909$	−4030.61	−0.147070
$910$	0	0
$911$	−45484.2	−1.65418	−0.827090	−	0.562070i	$-0.810005\pi$
$911$	−45484.2	−1.65418	−0.827090	+	0.562070i	$0.810005\pi$
$912$	28796.4i	1.04555i
$913$	− 7518.33i	− 0.272530i
$914$	−14699.1	−0.531951
$915$	0	0
$916$	26020.9	0.938597
$917$	2111.37i	0.0760346i
$918$	4275.70i	0.153725i
$919$	14765.8	0.530011	0.265005	−	0.964247i	$-0.414626\pi$
$919$	14765.8	0.530011	0.265005	+	0.964247i	$0.414626\pi$
$920$	0	0
$921$	−6506.48	−0.232786
$922$	− 76628.4i	− 2.73712i
$923$	19379.1i	0.691084i
$924$	−3273.74	−0.116556
$925$	0	0
$926$	5369.01	0.190536
$927$	11826.2i	0.419011i
$928$	22523.8i	0.796746i
$929$	−31598.4	−1.11594	−0.557971	−	0.829861i	$-0.688420\pi$
$929$	−31598.4	−1.11594	−0.557971	+	0.829861i	$0.688420\pi$
$930$	0	0
$931$	27423.7	0.965387
$932$	− 7595.46i	− 0.266950i
$933$	− 12955.4i	− 0.454597i
$934$	−35537.8	−1.24500
$935$	0	0
$936$	133.692	0.00466866
$937$	− 14121.9i	− 0.492363i	−0.969224	−	0.246181i	$-0.920824\pi$
$937$	− 14121.9i	− 0.492363i	0.969224	−	0.246181i	$-0.0791759\pi$
$938$	− 36743.0i	− 1.27900i
$939$	−14356.0	−0.498925
$940$	0	0
$941$	39525.5	1.36928	0.684641	−	0.728880i	$-0.259959\pi$
$941$	39525.5	1.36928	0.684641	+	0.728880i	$0.259959\pi$
$942$	26786.4i	0.926483i
$943$	− 11570.0i	− 0.399545i
$944$	−30298.9	−1.04465
$945$	0	0
$946$	−12222.9	−0.420087
$947$	39575.6i	1.35801i	0.734135	+	0.679004i	$0.237588\pi$
$947$	39575.6i	1.35801i	−0.734135	+	0.679004i	$0.762412\pi$
$948$	25563.0i	0.875788i
$949$	−14353.1	−0.490961
$950$	0	0
$951$	−20041.5	−0.683377
$952$	− 205.476i	− 0.00699528i
$953$	− 18421.4i	− 0.626158i	−0.949727	−	0.313079i	$-0.898640\pi$
$953$	− 18421.4i	− 0.626158i	0.949727	−	0.313079i	$-0.101360\pi$
$954$	8011.59	0.271892
$955$	0	0
$956$	−37414.8	−1.26578
$957$	− 2913.36i	− 0.0984072i
$958$	46755.4i	1.57682i
$959$	19267.1	0.648767
$960$	0	0
$961$	−1944.10	−0.0652581
$962$	12266.0i	0.411092i
$963$	− 9439.32i	− 0.315865i
$964$	31024.5	1.03655
$965$	0	0
$966$	−5269.29	−0.175504
$967$	− 50038.2i	− 1.66403i	−0.554752	−	0.832016i	$-0.687187\pi$
$967$	− 50038.2i	− 1.66403i	0.554752	−	0.832016i	$-0.312813\pi$
$968$	49.8278i	0.00165447i
$969$	−17646.1	−0.585009
$970$	0	0
$971$	53444.3	1.76633	0.883166	−	0.469060i	$-0.155407\pi$
$971$	53444.3	1.76633	0.883166	+	0.469060i	$0.155407\pi$
$972$	1918.90i	0.0633218i
$973$	− 12076.0i	− 0.397883i
$974$	−32358.7	−1.06452
$975$	0	0
$976$	−48757.5	−1.59907
$977$	− 20163.0i	− 0.660256i	−0.943936	−	0.330128i	$-0.892908\pi$
$977$	− 20163.0i	− 0.660256i	0.943936	−	0.330128i	$-0.107092\pi$
$978$	− 22942.6i	− 0.750125i
$979$	−1827.09	−0.0596468
$980$	0	0
$981$	−11166.6	−0.363427
$982$	− 48488.7i	− 1.57570i
$983$	40813.1i	1.32425i	0.749395	+	0.662124i	$0.230345\pi$
$983$	40813.1i	1.32425i	−0.749395	+	0.662124i	$0.769655\pi$
$984$	407.613	0.0132055
$985$	0	0
$986$	−13980.5	−0.451553
$987$	− 10283.2i	− 0.331631i
$988$	− 42185.2i	− 1.35839i
$989$	−9772.87	−0.314216
$990$	0	0
$991$	36663.8	1.17524	0.587620	−	0.809137i	$-0.300065\pi$
$991$	36663.8	1.17524	0.587620	+	0.809137i	$0.300065\pi$
$992$	42574.5i	1.36264i
$993$	− 10286.6i	− 0.328735i
$994$	26908.8	0.858647
$995$	0	0
$996$	−16191.8	−0.515119
$997$	− 1330.33i	− 0.0422587i	−0.999777	−	0.0211294i	$-0.993274\pi$
$997$	− 1330.33i	− 0.0422587i	0.999777	−	0.0211294i	$-0.00672619\pi$
$998$	− 22712.5i	− 0.720392i
$999$	2302.69	0.0729268

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.s.199.9		10
5.2	odd	4		825.4.a.y.1.1	yes	5
5.3	odd	4		825.4.a.x.1.5	✓	5
5.4	even	2	inner	825.4.c.s.199.2		10
15.2	even	4		2475.4.a.bi.1.5		5
15.8	even	4		2475.4.a.bj.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.4.a.x.1.5	✓	5	5.3	odd	4
825.4.a.y.1.1	yes	5	5.2	odd	4
825.4.c.s.199.2		10	5.4	even	2	inner
825.4.c.s.199.9		10	1.1	even	1	trivial
2475.4.a.bi.1.5		5	15.2	even	4
2475.4.a.bj.1.1		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)

\(f(q)\)	\(=\)	\(q+3.98707i q^{2} -3.00000i q^{3} -7.89672 q^{4} +11.9612 q^{6} -12.5627i q^{7} +0.411800i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+3.98707i q^{2} -3.00000i q^{3} -7.89672 q^{4} +11.9612 q^{6} -12.5627i q^{7} +0.411800i q^{8} -9.00000 q^{9} -11.0000 q^{11} +23.6901i q^{12} +36.0726i q^{13} +50.0885 q^{14} -64.8156 q^{16} -39.7182i q^{17} -35.8836i q^{18} +148.094 q^{19} -37.6882 q^{21} -43.8578i q^{22} -35.0665i q^{23} +1.23540 q^{24} -143.824 q^{26} +27.0000i q^{27} +99.2043i q^{28} -88.2837 q^{29} -166.874 q^{31} -255.130i q^{32} +33.0000i q^{33} +158.359 q^{34} +71.0704 q^{36} -85.2847i q^{37} +590.460i q^{38} +108.218 q^{39} +329.944 q^{41} -150.265i q^{42} -278.695i q^{43} +86.8639 q^{44} +139.813 q^{46} +272.851i q^{47} +194.447i q^{48} +185.178 q^{49} -119.155 q^{51} -284.855i q^{52} +223.266i q^{53} -107.651 q^{54} +5.17334 q^{56} -444.282i q^{57} -351.993i q^{58} +467.463 q^{59} +752.249 q^{61} -665.338i q^{62} +113.065i q^{63} +498.695 q^{64} -131.573 q^{66} -733.563i q^{67} +313.643i q^{68} -105.200 q^{69} +537.226 q^{71} -3.70620i q^{72} +397.895i q^{73} +340.036 q^{74} -1169.46 q^{76} +138.190i q^{77} +431.471i q^{78} +1079.06 q^{79} +81.0000 q^{81} +1315.51i q^{82} +683.484i q^{83} +297.613 q^{84} +1111.18 q^{86} +264.851i q^{87} -4.52980i q^{88} +166.100 q^{89} +453.170 q^{91} +276.911i q^{92} +500.622i q^{93} -1087.87 q^{94} -765.390 q^{96} +694.031i q^{97} +738.317i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 6 q^{4} - 6 q^{6} - 90 q^{9}+O(q^{10}) \) 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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