LMFDB - Embedded newform 825.4.c.r.199.2

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} + 83x^{8} + 2275x^{6} + 24517x^{4} + 87636x^{2} + 40000 $ x^10 + 83x^8 + 2275x^6 + 24517x^4 + 87636x^2 + 40000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.2
Root			$-6.35463i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.r.199.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.35463i q^{2} -3.00000i q^{3} -20.6721 q^{4} -16.0639 q^{6} -19.1169i q^{7} +67.8543i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-5.35463i q^{2} -3.00000i q^{3} -20.6721 q^{4} -16.0639 q^{6} -19.1169i q^{7} +67.8543i q^{8} -9.00000 q^{9} +11.0000 q^{11} +62.0162i q^{12} +37.4340i q^{13} -102.364 q^{14} +197.958 q^{16} +25.2925i q^{17} +48.1917i q^{18} +159.638 q^{19} -57.3506 q^{21} -58.9009i q^{22} +175.989i q^{23} +203.563 q^{24} +200.445 q^{26} +27.0000i q^{27} +395.185i q^{28} -65.4810 q^{29} +75.4303 q^{31} -517.159i q^{32} -33.0000i q^{33} +135.432 q^{34} +186.049 q^{36} +166.746i q^{37} -854.802i q^{38} +112.302 q^{39} +391.242 q^{41} +307.091i q^{42} +63.7652i q^{43} -227.393 q^{44} +942.357 q^{46} +385.881i q^{47} -593.875i q^{48} -22.4548 q^{49} +75.8774 q^{51} -773.838i q^{52} +89.7570i q^{53} +144.575 q^{54} +1297.16 q^{56} -478.913i q^{57} +350.627i q^{58} -281.270 q^{59} -754.718 q^{61} -403.901i q^{62} +172.052i q^{63} -1185.53 q^{64} -176.703 q^{66} +168.957i q^{67} -522.848i q^{68} +527.967 q^{69} +950.914 q^{71} -610.689i q^{72} +504.556i q^{73} +892.863 q^{74} -3300.05 q^{76} -210.286i q^{77} -601.335i q^{78} -1128.61 q^{79} +81.0000 q^{81} -2094.96i q^{82} -746.756i q^{83} +1185.56 q^{84} +341.439 q^{86} +196.443i q^{87} +746.397i q^{88} +457.199 q^{89} +715.620 q^{91} -3638.06i q^{92} -226.291i q^{93} +2066.25 q^{94} -1551.48 q^{96} -1331.18i q^{97} +120.237i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 92 q^{4} + 24 q^{6} - 90 q^{9}+O(q^{10}) $ 10 * q - 92 * q^4 + 24 * q^6 - 90 * q^9	$ 10 q - 92 q^{4} + 24 q^{6} - 90 q^{9} + 110 q^{11} - 110 q^{14} + 1268 q^{16} + 674 q^{19} - 228 q^{21} - 432 q^{24} + 718 q^{26} + 306 q^{29} + 526 q^{31} - 1034 q^{34} + 828 q^{36} - 258 q^{39} - 176 q^{41} - 1012 q^{44} + 872 q^{46} - 4762 q^{49} + 900 q^{51} - 216 q^{54} + 422 q^{56} - 820 q^{59} - 2260 q^{61} - 6340 q^{64} + 264 q^{66} + 1206 q^{69} + 2498 q^{71} + 5970 q^{74} - 5112 q^{76} - 4516 q^{79} + 810 q^{81} + 2646 q^{84} - 2870 q^{86} - 694 q^{89} - 1224 q^{91} - 1814 q^{94} + 1680 q^{96} - 990 q^{99}+O(q^{100}) $ 10 * q - 92 * q^4 + 24 * q^6 - 90 * q^9 + 110 * q^11 - 110 * q^14 + 1268 * q^16 + 674 * q^19 - 228 * q^21 - 432 * q^24 + 718 * q^26 + 306 * q^29 + 526 * q^31 - 1034 * q^34 + 828 * q^36 - 258 * q^39 - 176 * q^41 - 1012 * q^44 + 872 * q^46 - 4762 * q^49 + 900 * q^51 - 216 * q^54 + 422 * q^56 - 820 * q^59 - 2260 * q^61 - 6340 * q^64 + 264 * q^66 + 1206 * q^69 + 2498 * q^71 + 5970 * q^74 - 5112 * q^76 - 4516 * q^79 + 810 * q^81 + 2646 * q^84 - 2870 * q^86 - 694 * q^89 - 1224 * q^91 - 1814 * q^94 + 1680 * 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 $

$2$	− 5.35463i	− 1.89315i	−0.322486	−	0.946574i	$-0.604519\pi$
$2$	− 5.35463i	− 1.89315i	0.322486	−	0.946574i	$-0.395481\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	−20.6721	−2.58401
$5$	0	0
$5$	0	0
$6$	−16.0639	−1.09301
$7$	− 19.1169i	− 1.03221i	−0.856524	−	0.516107i	$-0.827381\pi$
$7$	− 19.1169i	− 1.03221i	0.856524	−	0.516107i	$-0.172619\pi$
$8$	67.8543i	2.99877i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	62.0162i	1.49188i
$13$	37.4340i	0.798639i	0.916812	+	0.399320i	$0.130754\pi$
$13$	37.4340i	0.798639i	−0.916812	+	0.399320i	$0.869246\pi$
$14$	−102.364	−1.95413
$15$	0	0
$16$	197.958	3.09310
$17$	25.2925i	0.360842i	0.983589	+	0.180421i	$0.0577461\pi$
$17$	25.2925i	0.360842i	−0.983589	+	0.180421i	$0.942254\pi$
$18$	48.1917i	0.631049i
$19$	159.638	1.92755	0.963774	−	0.266718i	$-0.0859394\pi$
$19$	159.638	1.92755	0.963774	+	0.266718i	$0.0859394\pi$
$20$	0	0
$21$	−57.3506	−0.595949
$22$	− 58.9009i	− 0.570806i
$23$	175.989i	1.59549i	0.602995	+	0.797745i	$0.293974\pi$
$23$	175.989i	1.59549i	−0.602995	+	0.797745i	$0.706026\pi$
$24$	203.563	1.73134
$25$	0	0
$26$	200.445	1.51194
$27$	27.0000i	0.192450i
$28$	395.185i	2.66725i
$29$	−65.4810	−0.419294	−0.209647	−	0.977777i	$-0.567231\pi$
$29$	−65.4810	−0.419294	−0.209647	+	0.977777i	$0.567231\pi$
$30$	0	0
$31$	75.4303	0.437022	0.218511	−	0.975834i	$-0.429880\pi$
$31$	75.4303	0.437022	0.218511	+	0.975834i	$0.429880\pi$
$32$	− 517.159i	− 2.85693i
$33$	− 33.0000i	− 0.174078i
$34$	135.432	0.683128
$35$	0	0
$36$	186.049	0.861337
$37$	166.746i	0.740888i	0.928855	+	0.370444i	$0.120794\pi$
$37$	166.746i	0.740888i	−0.928855	+	0.370444i	$0.879206\pi$
$38$	− 854.802i	− 3.64914i
$39$	112.302	0.461095
$40$	0	0
$41$	391.242	1.49029	0.745143	−	0.666904i	$-0.232381\pi$
$41$	391.242	1.49029	0.745143	+	0.666904i	$0.232381\pi$
$42$	307.091i	1.12822i
$43$	63.7652i	0.226142i	0.993587	+	0.113071i	$0.0360687\pi$
$43$	63.7652i	0.226142i	−0.993587	+	0.113071i	$0.963931\pi$
$44$	−227.393	−0.779108
$45$	0	0
$46$	942.357	3.02050
$47$	385.881i	1.19759i	0.800904	+	0.598793i	$0.204353\pi$
$47$	385.881i	1.19759i	−0.800904	+	0.598793i	$0.795647\pi$
$48$	− 593.875i	− 1.78580i
$49$	−22.4548	−0.0654658
$50$	0	0
$51$	75.8774	0.208332
$52$	− 773.838i	− 2.06369i
$53$	89.7570i	0.232624i	0.993213	+	0.116312i	$0.0371072\pi$
$53$	89.7570i	0.232624i	−0.993213	+	0.116312i	$0.962893\pi$
$54$	144.575	0.364337
$55$	0	0
$56$	1297.16	3.09537
$57$	− 478.913i	− 1.11287i
$58$	350.627i	0.793786i
$59$	−281.270	−0.620649	−0.310325	−	0.950631i	$-0.600438\pi$
$59$	−281.270	−0.620649	−0.310325	+	0.950631i	$0.600438\pi$
$60$	0	0
$61$	−754.718	−1.58413	−0.792064	−	0.610439i	$-0.790993\pi$
$61$	−754.718	−1.58413	−0.792064	+	0.610439i	$0.790993\pi$
$62$	− 403.901i	− 0.827347i
$63$	172.052i	0.344071i
$64$	−1185.53	−2.31549
$65$	0	0
$66$	−176.703	−0.329555
$67$	168.957i	0.308080i	0.988065	+	0.154040i	$0.0492284\pi$
$67$	168.957i	0.308080i	−0.988065	+	0.154040i	$0.950772\pi$
$68$	− 522.848i	− 0.932420i
$69$	527.967	0.921157
$70$	0	0
$71$	950.914	1.58947	0.794737	−	0.606954i	$-0.207609\pi$
$71$	950.914	1.58947	0.794737	+	0.606954i	$0.207609\pi$
$72$	− 610.689i	− 0.999588i
$73$	504.556i	0.808956i	0.914548	+	0.404478i	$0.132547\pi$
$73$	504.556i	0.808956i	−0.914548	+	0.404478i	$0.867453\pi$
$74$	892.863	1.40261
$75$	0	0
$76$	−3300.05	−4.98081
$77$	− 210.286i	− 0.311224i
$78$	− 601.335i	− 0.872920i
$79$	−1128.61	−1.60732	−0.803661	−	0.595088i	$-0.797117\pi$
$79$	−1128.61	−1.60732	−0.803661	+	0.595088i	$0.797117\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 2094.96i	− 2.82133i
$83$	− 746.756i	− 0.987556i	−0.869588	−	0.493778i	$-0.835616\pi$
$83$	− 746.756i	− 0.987556i	0.869588	−	0.493778i	$-0.164384\pi$
$84$	1185.56	1.53994
$85$	0	0
$86$	341.439	0.428120
$87$	196.443i	0.242079i
$88$	746.397i	0.904162i
$89$	457.199	0.544528	0.272264	−	0.962223i	$-0.412228\pi$
$89$	457.199	0.544528	0.272264	+	0.962223i	$0.412228\pi$
$90$	0	0
$91$	715.620	0.824367
$92$	− 3638.06i	− 4.12276i
$93$	− 226.291i	− 0.252315i
$94$	2066.25	2.26721
$95$	0	0
$96$	−1551.48	−1.64945
$97$	− 1331.18i	− 1.39341i	−0.717360	−	0.696703i	$-0.754649\pi$
$97$	− 1331.18i	− 1.39341i	0.717360	−	0.696703i	$-0.245351\pi$
$98$	120.237i	0.123936i
$99$	−99.0000	−0.100504
$100$	0	0
$101$	−997.309	−0.982535	−0.491267	−	0.871009i	$-0.663466\pi$
$101$	−997.309	−0.982535	−0.491267	+	0.871009i	$0.663466\pi$
$102$	− 406.295i	− 0.394404i
$103$	1183.84i	1.13249i	0.824236	+	0.566247i	$0.191605\pi$
$103$	1183.84i	1.13249i	−0.824236	+	0.566247i	$0.808395\pi$
$104$	−2540.06	−2.39493
$105$	0	0
$106$	480.616	0.440392
$107$	1098.71i	0.992671i	0.868131	+	0.496336i	$0.165321\pi$
$107$	1098.71i	0.992671i	−0.868131	+	0.496336i	$0.834679\pi$
$108$	− 558.146i	− 0.497293i
$109$	−1544.18	−1.35694	−0.678468	−	0.734630i	$-0.737356\pi$
$109$	−1544.18	−1.35694	−0.678468	+	0.734630i	$0.737356\pi$
$110$	0	0
$111$	500.238	0.427752
$112$	− 3784.34i	− 3.19274i
$113$	− 1101.98i	− 0.917394i	−0.888593	−	0.458697i	$-0.848316\pi$
$113$	− 1101.98i	− 0.917394i	0.888593	−	0.458697i	$-0.151684\pi$
$114$	−2564.41	−2.10683
$115$	0	0
$116$	1353.63	1.08346
$117$	− 336.906i	− 0.266213i
$118$	1506.10i	1.17498i
$119$	483.513	0.372467
$120$	0	0
$121$	121.000	0.0909091
$122$	4041.24i	2.99899i
$123$	− 1173.73i	− 0.860417i
$124$	−1559.30	−1.12927
$125$	0	0
$126$	921.274	0.651378
$127$	2217.81i	1.54960i	0.632209	+	0.774798i	$0.282148\pi$
$127$	2217.81i	1.54960i	−0.632209	+	0.774798i	$0.717852\pi$
$128$	2210.80i	1.52663i
$129$	191.296	0.130563
$130$	0	0
$131$	−2417.31	−1.61223	−0.806113	−	0.591761i	$-0.798433\pi$
$131$	−2417.31	−1.61223	−0.806113	+	0.591761i	$0.798433\pi$
$132$	682.179i	0.449818i
$133$	− 3051.78i	− 1.98964i
$134$	904.700	0.583240
$135$	0	0
$136$	−1716.20	−1.08208
$137$	1553.14i	0.968570i	0.874910	+	0.484285i	$0.160920\pi$
$137$	1553.14i	0.968570i	−0.874910	+	0.484285i	$0.839080\pi$
$138$	− 2827.07i	− 1.74389i
$139$	2314.44	1.41229	0.706144	−	0.708068i	$-0.250433\pi$
$139$	2314.44	1.41229	0.706144	+	0.708068i	$0.250433\pi$
$140$	0	0
$141$	1157.64	0.691426
$142$	− 5091.79i	− 3.00911i
$143$	411.774i	0.240799i
$144$	−1781.62	−1.03103
$145$	0	0
$146$	2701.71	1.53147
$147$	67.3643i	0.0377967i
$148$	− 3446.98i	− 1.91446i
$149$	2990.81	1.64441	0.822205	−	0.569192i	$-0.192744\pi$
$149$	2990.81	1.64441	0.822205	+	0.569192i	$0.192744\pi$
$150$	0	0
$151$	1051.84	0.566873	0.283437	−	0.958991i	$-0.408525\pi$
$151$	1051.84	0.566873	0.283437	+	0.958991i	$0.408525\pi$
$152$	10832.1i	5.78027i
$153$	− 227.632i	− 0.120281i
$154$	−1126.00	−0.589194
$155$	0	0
$156$	−2321.51	−1.19147
$157$	1387.07i	0.705096i	0.935794	+	0.352548i	$0.114685\pi$
$157$	1387.07i	0.705096i	−0.935794	+	0.352548i	$0.885315\pi$
$158$	6043.28i	3.04290i
$159$	269.271	0.134305
$160$	0	0
$161$	3364.36	1.64689
$162$	− 433.725i	− 0.210350i
$163$	− 1124.97i	− 0.540580i	−0.962779	−	0.270290i	$-0.912880\pi$
$163$	− 1124.97i	− 0.540580i	0.962779	−	0.270290i	$-0.0871195\pi$
$164$	−8087.79	−3.85092
$165$	0	0
$166$	−3998.60	−1.86959
$167$	2996.49i	1.38848i	0.719745	+	0.694238i	$0.244259\pi$
$167$	2996.49i	1.38848i	−0.719745	+	0.694238i	$0.755741\pi$
$168$	− 3891.49i	− 1.78711i
$169$	795.699	0.362175
$170$	0	0
$171$	−1436.74	−0.642516
$172$	− 1318.16i	− 0.584353i
$173$	2527.59i	1.11081i	0.831582	+	0.555403i	$0.187436\pi$
$173$	2527.59i	1.11081i	−0.831582	+	0.555403i	$0.812564\pi$
$174$	1051.88	0.458292
$175$	0	0
$176$	2177.54	0.932604
$177$	843.811i	0.358332i
$178$	− 2448.13i	− 1.03087i
$179$	−278.953	−0.116480	−0.0582399	−	0.998303i	$-0.518549\pi$
$179$	−278.953	−0.116480	−0.0582399	+	0.998303i	$0.518549\pi$
$180$	0	0
$181$	3618.53	1.48599	0.742993	−	0.669299i	$-0.233405\pi$
$181$	3618.53	1.48599	0.742993	+	0.669299i	$0.233405\pi$
$182$	− 3831.88i	− 1.56065i
$183$	2264.15i	0.914596i
$184$	−11941.6	−4.78450
$185$	0	0
$186$	−1211.70	−0.477669
$187$	278.217i	0.108798i
$188$	− 7976.96i	− 3.09457i
$189$	516.156	0.198650
$190$	0	0
$191$	−824.697	−0.312424	−0.156212	−	0.987724i	$-0.549928\pi$
$191$	−824.697	−0.312424	−0.156212	+	0.987724i	$0.549928\pi$
$192$	3556.59i	1.33685i
$193$	− 3243.48i	− 1.20969i	−0.796342	−	0.604847i	$-0.793234\pi$
$193$	− 3243.48i	− 1.20969i	0.796342	−	0.604847i	$-0.206766\pi$
$194$	−7127.96	−2.63792
$195$	0	0
$196$	464.187	0.169164
$197$	2383.29i	0.861943i	0.902366	+	0.430971i	$0.141829\pi$
$197$	2383.29i	0.861943i	−0.902366	+	0.430971i	$0.858171\pi$
$198$	530.109i	0.190269i
$199$	−2071.51	−0.737918	−0.368959	−	0.929446i	$-0.620286\pi$
$199$	−2071.51	−0.737918	−0.368959	+	0.929446i	$0.620286\pi$
$200$	0	0
$201$	506.870	0.177870
$202$	5340.22i	1.86008i
$203$	1251.79i	0.432801i
$204$	−1568.54	−0.538333
$205$	0	0
$206$	6339.01	2.14398
$207$	− 1583.90i	− 0.531830i
$208$	7410.36i	2.47027i
$209$	1756.02	0.581178
$210$	0	0
$211$	3954.58	1.29026	0.645129	−	0.764074i	$-0.276804\pi$
$211$	3954.58	1.29026	0.645129	+	0.764074i	$0.276804\pi$
$212$	− 1855.46i	− 0.601103i
$213$	− 2852.74i	− 0.917684i
$214$	5883.16	1.87927
$215$	0	0
$216$	−1832.07	−0.577113
$217$	− 1441.99i	− 0.451100i
$218$	8268.53i	2.56888i
$219$	1513.67	0.467051
$220$	0	0
$221$	−946.797	−0.288183
$222$	− 2678.59i	− 0.809798i
$223$	− 2399.99i	− 0.720697i	−0.932818	−	0.360349i	$-0.882658\pi$
$223$	− 2399.99i	− 0.720697i	0.932818	−	0.360349i	$-0.117342\pi$
$224$	−9886.46	−2.94896
$225$	0	0
$226$	−5900.70	−1.73676
$227$	1233.11i	0.360547i	0.983617	+	0.180273i	$0.0576983\pi$
$227$	1233.11i	0.360547i	−0.983617	+	0.180273i	$0.942302\pi$
$228$	9900.14i	2.87567i
$229$	−895.694	−0.258468	−0.129234	−	0.991614i	$-0.541252\pi$
$229$	−895.694	−0.258468	−0.129234	+	0.991614i	$0.541252\pi$
$230$	0	0
$231$	−630.857	−0.179685
$232$	− 4443.17i	− 1.25736i
$233$	− 1518.35i	− 0.426911i	−0.976953	−	0.213456i	$-0.931528\pi$
$233$	− 1518.35i	− 0.426911i	0.976953	−	0.213456i	$-0.0684719\pi$
$234$	−1804.01	−0.503981
$235$	0	0
$236$	5814.44	1.60376
$237$	3385.83i	0.927987i
$238$	− 2589.03i	− 0.705135i
$239$	−4417.28	−1.19552	−0.597761	−	0.801674i	$-0.703943\pi$
$239$	−4417.28	−1.19552	−0.597761	+	0.801674i	$0.703943\pi$
$240$	0	0
$241$	−4131.15	−1.10419	−0.552097	−	0.833780i	$-0.686172\pi$
$241$	−4131.15	−1.10419	−0.552097	+	0.833780i	$0.686172\pi$
$242$	− 647.910i	− 0.172104i
$243$	− 243.000i	− 0.0641500i
$244$	15601.6	4.09340
$245$	0	0
$246$	−6284.87	−1.62890
$247$	5975.88i	1.53942i
$248$	5118.27i	1.31053i
$249$	−2240.27	−0.570166
$250$	0	0
$251$	1863.18	0.468538	0.234269	−	0.972172i	$-0.424730\pi$
$251$	1863.18	0.468538	0.234269	+	0.972172i	$0.424730\pi$
$252$	− 3556.67i	− 0.889084i
$253$	1935.88i	0.481058i
$254$	11875.5	2.93361
$255$	0	0
$256$	2353.79	0.574656
$257$	− 393.369i	− 0.0954774i	−0.998860	−	0.0477387i	$-0.984799\pi$
$257$	− 393.369i	− 0.0954774i	0.998860	−	0.0477387i	$-0.0152015\pi$
$258$	− 1024.32i	− 0.247175i
$259$	3187.66	0.764755
$260$	0	0
$261$	589.329	0.139765
$262$	12943.8i	3.05218i
$263$	− 5640.66i	− 1.32250i	−0.750165	−	0.661251i	$-0.770026\pi$
$263$	− 5640.66i	− 1.32250i	0.750165	−	0.661251i	$-0.229974\pi$
$264$	2239.19	0.522018
$265$	0	0
$266$	−16341.1	−3.76669
$267$	− 1371.60i	− 0.314384i
$268$	− 3492.68i	− 0.796081i
$269$	8212.42	1.86141	0.930706	−	0.365767i	$-0.119193\pi$
$269$	8212.42	1.86141	0.930706	+	0.365767i	$0.119193\pi$
$270$	0	0
$271$	−1222.44	−0.274015	−0.137007	−	0.990570i	$-0.543748\pi$
$271$	−1222.44	−0.274015	−0.137007	+	0.990570i	$0.543748\pi$
$272$	5006.85i	1.11612i
$273$	− 2146.86i	− 0.475948i
$274$	8316.52	1.83365
$275$	0	0
$276$	−10914.2	−2.38028
$277$	− 1954.53i	− 0.423958i	−0.977274	−	0.211979i	$-0.932009\pi$
$277$	− 1954.53i	− 0.423958i	0.977274	−	0.211979i	$-0.0679909\pi$
$278$	− 12393.0i	− 2.67367i
$279$	−678.873	−0.145674
$280$	0	0
$281$	8774.38	1.86276	0.931381	−	0.364047i	$-0.118605\pi$
$281$	8774.38	1.86276	0.931381	+	0.364047i	$0.118605\pi$
$282$	− 6198.75i	− 1.30897i
$283$	− 7247.33i	− 1.52229i	−0.648580	−	0.761147i	$-0.724637\pi$
$283$	− 7247.33i	− 1.52229i	0.648580	−	0.761147i	$-0.275363\pi$
$284$	−19657.4	−4.10722
$285$	0	0
$286$	2204.90	0.455868
$287$	− 7479.32i	− 1.53829i
$288$	4654.43i	0.952309i
$289$	4273.29	0.869793
$290$	0	0
$291$	−3993.53	−0.804484
$292$	− 10430.2i	− 2.09035i
$293$	− 4708.08i	− 0.938733i	−0.883003	−	0.469367i	$-0.844482\pi$
$293$	− 4708.08i	− 0.938733i	0.883003	−	0.469367i	$-0.155518\pi$
$294$	360.711	0.0715547
$295$	0	0
$296$	−11314.4	−2.22175
$297$	297.000i	0.0580259i
$298$	− 16014.7i	− 3.11311i
$299$	−6587.97	−1.27422
$300$	0	0
$301$	1218.99	0.233427
$302$	− 5632.24i	− 1.07317i
$303$	2991.93i	0.567267i
$304$	31601.6	5.96210
$305$	0	0
$306$	−1218.89	−0.227709
$307$	− 8728.67i	− 1.62271i	−0.584554	−	0.811355i	$-0.698731\pi$
$307$	− 8728.67i	− 1.62271i	0.584554	−	0.811355i	$-0.301269\pi$
$308$	4347.04i	0.804206i
$309$	3551.51	0.653846
$310$	0	0
$311$	6592.30	1.20198	0.600988	−	0.799258i	$-0.294774\pi$
$311$	6592.30	1.20198	0.600988	+	0.799258i	$0.294774\pi$
$312$	7620.17i	1.38271i
$313$	− 782.571i	− 0.141321i	−0.997500	−	0.0706606i	$-0.977489\pi$
$313$	− 782.571i	− 0.141321i	0.997500	−	0.0706606i	$-0.0225107\pi$
$314$	7427.24	1.33485
$315$	0	0
$316$	23330.7	4.15333
$317$	3615.46i	0.640582i	0.947319	+	0.320291i	$0.103781\pi$
$317$	3615.46i	0.640582i	−0.947319	+	0.320291i	$0.896219\pi$
$318$	− 1441.85i	− 0.254260i
$319$	−720.291	−0.126422
$320$	0	0
$321$	3296.12	0.573119
$322$	− 18014.9i	− 3.11780i
$323$	4037.63i	0.695541i
$324$	−1674.44	−0.287112
$325$	0	0
$326$	−6023.80	−1.02340
$327$	4632.55i	0.783427i
$328$	26547.5i	4.46902i
$329$	7376.84	1.23616
$330$	0	0
$331$	−3095.86	−0.514090	−0.257045	−	0.966399i	$-0.582749\pi$
$331$	−3095.86	−0.514090	−0.257045	+	0.966399i	$0.582749\pi$
$332$	15437.0i	2.55185i
$333$	− 1500.71i	− 0.246963i
$334$	16045.1	2.62859
$335$	0	0
$336$	−11353.0	−1.84333
$337$	− 2669.40i	− 0.431488i	−0.976450	−	0.215744i	$-0.930782\pi$
$337$	− 2669.40i	− 0.431488i	0.976450	−	0.215744i	$-0.0692177\pi$
$338$	− 4260.67i	− 0.685651i
$339$	−3305.94	−0.529658
$340$	0	0
$341$	829.733	0.131767
$342$	7693.22i	1.21638i
$343$	− 6127.82i	− 0.964639i
$344$	−4326.74	−0.678146
$345$	0	0
$346$	13534.3	2.10292
$347$	1549.86i	0.239772i	0.992788	+	0.119886i	$0.0382529\pi$
$347$	1549.86i	0.239772i	−0.992788	+	0.119886i	$0.961747\pi$
$348$	− 4060.89i	− 0.625536i
$349$	−8764.29	−1.34425	−0.672123	−	0.740440i	$-0.734617\pi$
$349$	−8764.29	−1.34425	−0.672123	+	0.740440i	$0.734617\pi$
$350$	0	0
$351$	−1010.72	−0.153698
$352$	− 5688.75i	− 0.861396i
$353$	6099.45i	0.919663i	0.888006	+	0.459831i	$0.152090\pi$
$353$	6099.45i	0.919663i	−0.888006	+	0.459831i	$0.847910\pi$
$354$	4518.30	0.678375
$355$	0	0
$356$	−9451.26	−1.40707
$357$	− 1450.54i	− 0.215044i
$358$	1493.69i	0.220514i
$359$	8806.15	1.29463	0.647313	−	0.762224i	$-0.275893\pi$
$359$	8806.15	1.29463	0.647313	+	0.762224i	$0.275893\pi$
$360$	0	0
$361$	18625.2	2.71545
$362$	− 19375.9i	− 2.81319i
$363$	− 363.000i	− 0.0524864i
$364$	−14793.4	−2.13017
$365$	0	0
$366$	12123.7	1.73147
$367$	8910.67i	1.26739i	0.773582	+	0.633697i	$0.218463\pi$
$367$	8910.67i	1.26739i	−0.773582	+	0.633697i	$0.781537\pi$
$368$	34838.5i	4.93501i
$369$	−3521.18	−0.496762
$370$	0	0
$371$	1715.87	0.240118
$372$	4677.90i	0.651984i
$373$	4676.39i	0.649153i	0.945859	+	0.324577i	$0.105222\pi$
$373$	4676.39i	0.649153i	−0.945859	+	0.324577i	$0.894778\pi$
$374$	1489.75	0.205971
$375$	0	0
$376$	−26183.7	−3.59128
$377$	− 2451.21i	− 0.334865i
$378$	− 2763.82i	− 0.376073i
$379$	−9494.21	−1.28677	−0.643384	−	0.765544i	$-0.722470\pi$
$379$	−9494.21	−1.28677	−0.643384	+	0.765544i	$0.722470\pi$
$380$	0	0
$381$	6653.43	0.894660
$382$	4415.95i	0.591465i
$383$	− 1858.80i	− 0.247990i	−0.992283	−	0.123995i	$-0.960429\pi$
$383$	− 1858.80i	− 0.247990i	0.992283	−	0.123995i	$-0.0395708\pi$
$384$	6632.40	0.881402
$385$	0	0
$386$	−17367.6	−2.29013
$387$	− 573.887i	− 0.0753806i
$388$	27518.2i	3.60058i
$389$	4941.27	0.644042	0.322021	−	0.946732i	$-0.395638\pi$
$389$	4941.27	0.644042	0.322021	+	0.946732i	$0.395638\pi$
$390$	0	0
$391$	−4451.20	−0.575721
$392$	− 1523.65i	− 0.196317i
$393$	7251.94i	0.930819i
$394$	12761.7	1.63179
$395$	0	0
$396$	2046.54	0.259703
$397$	2156.94i	0.272680i	0.990662	+	0.136340i	$0.0435339\pi$
$397$	2156.94i	0.272680i	−0.990662	+	0.136340i	$0.956466\pi$
$398$	11092.2i	1.39699i
$399$	−9155.33	−1.14872
$400$	0	0
$401$	−5003.77	−0.623132	−0.311566	−	0.950224i	$-0.600854\pi$
$401$	−5003.77	−0.623132	−0.311566	+	0.950224i	$0.600854\pi$
$402$	− 2714.10i	− 0.336734i
$403$	2823.65i	0.349023i
$404$	20616.5	2.53888
$405$	0	0
$406$	6702.89	0.819357
$407$	1834.20i	0.223386i
$408$	5148.61i	0.624740i
$409$	−10852.2	−1.31200	−0.655999	−	0.754762i	$-0.727752\pi$
$409$	−10852.2	−1.31200	−0.655999	+	0.754762i	$0.727752\pi$
$410$	0	0
$411$	4659.43	0.559204
$412$	− 24472.4i	− 2.92637i
$413$	5377.01i	0.640643i
$414$	−8481.21	−1.00683
$415$	0	0
$416$	19359.3	2.28165
$417$	− 6943.31i	− 0.815385i
$418$	− 9402.82i	− 1.10026i
$419$	7610.64	0.887360	0.443680	−	0.896185i	$-0.353673\pi$
$419$	7610.64	0.887360	0.443680	+	0.896185i	$0.353673\pi$
$420$	0	0
$421$	−8352.07	−0.966877	−0.483438	−	0.875378i	$-0.660612\pi$
$421$	−8352.07	−0.966877	−0.483438	+	0.875378i	$0.660612\pi$
$422$	− 21175.3i	− 2.44265i
$423$	− 3472.93i	− 0.399195i
$424$	−6090.40	−0.697585
$425$	0	0
$426$	−15275.4	−1.73731
$427$	14427.8i	1.63516i
$428$	− 22712.5i	− 2.56507i
$429$	1235.32	0.139025
$430$	0	0
$431$	3267.36	0.365158	0.182579	−	0.983191i	$-0.441556\pi$
$431$	3267.36	0.365158	0.182579	+	0.983191i	$0.441556\pi$
$432$	5344.87i	0.595267i
$433$	− 3548.85i	− 0.393873i	−0.980416	−	0.196937i	$-0.936901\pi$
$433$	− 3548.85i	− 0.393873i	0.980416	−	0.196937i	$-0.0630993\pi$
$434$	−7721.33	−0.853999
$435$	0	0
$436$	31921.5	3.50633
$437$	28094.5i	3.07539i
$438$	− 8105.13i	− 0.884197i
$439$	−4394.99	−0.477817	−0.238908	−	0.971042i	$-0.576790\pi$
$439$	−4394.99	−0.477817	−0.238908	+	0.971042i	$0.576790\pi$
$440$	0	0
$441$	202.093	0.0218219
$442$	5069.75i	0.545573i
$443$	10779.0i	1.15604i	0.816024	+	0.578018i	$0.196174\pi$
$443$	10779.0i	1.15604i	−0.816024	+	0.578018i	$0.803826\pi$
$444$	−10341.0	−1.10532
$445$	0	0
$446$	−12851.1	−1.36439
$447$	− 8972.44i	− 0.949400i
$448$	22663.6i	2.39008i
$449$	−12770.5	−1.34227	−0.671134	−	0.741336i	$-0.734193\pi$
$449$	−12770.5	−1.34227	−0.671134	+	0.741336i	$0.734193\pi$
$450$	0	0
$451$	4303.66	0.449338
$452$	22780.2i	2.37056i
$453$	− 3155.53i	− 0.327284i
$454$	6602.83	0.682569
$455$	0	0
$456$	32496.3	3.33724
$457$	− 8842.49i	− 0.905108i	−0.891737	−	0.452554i	$-0.850513\pi$
$457$	− 8842.49i	− 0.905108i	0.891737	−	0.452554i	$-0.149487\pi$
$458$	4796.11i	0.489318i
$459$	−682.896	−0.0694442
$460$	0	0
$461$	4939.24	0.499009	0.249505	−	0.968374i	$-0.419732\pi$
$461$	4939.24	0.499009	0.249505	+	0.968374i	$0.419732\pi$
$462$	3378.01i	0.340171i
$463$	8626.71i	0.865912i	0.901415	+	0.432956i	$0.142529\pi$
$463$	8626.71i	0.865912i	−0.901415	+	0.432956i	$0.857471\pi$
$464$	−12962.5	−1.29692
$465$	0	0
$466$	−8130.20	−0.808207
$467$	− 5683.16i	− 0.563138i	−0.959541	−	0.281569i	$-0.909145\pi$
$467$	− 5683.16i	− 0.563138i	0.959541	−	0.281569i	$-0.0908548\pi$
$468$	6964.54i	0.687897i
$469$	3229.92	0.318004
$470$	0	0
$471$	4161.21	0.407088
$472$	− 19085.4i	− 1.86118i
$473$	701.417i	0.0681843i
$474$	18129.8	1.75682
$475$	0	0
$476$	−9995.21	−0.962457
$477$	− 807.813i	− 0.0775413i
$478$	23652.9i	2.26330i
$479$	12243.9	1.16793	0.583963	−	0.811780i	$-0.301501\pi$
$479$	12243.9	1.16793	0.583963	+	0.811780i	$0.301501\pi$
$480$	0	0
$481$	−6241.96	−0.591702
$482$	22120.8i	2.09040i
$483$	− 10093.1i	− 0.950831i
$484$	−2501.32	−0.234910
$485$	0	0
$486$	−1301.18	−0.121446
$487$	12738.9i	1.18533i	0.805451	+	0.592663i	$0.201923\pi$
$487$	12738.9i	1.18533i	−0.805451	+	0.592663i	$0.798077\pi$
$488$	− 51210.9i	− 4.75043i
$489$	−3374.91	−0.312104
$490$	0	0
$491$	15699.7	1.44301	0.721506	−	0.692408i	$-0.243450\pi$
$491$	15699.7	1.44301	0.721506	+	0.692408i	$0.243450\pi$
$492$	24263.4i	2.22333i
$493$	− 1656.18i	− 0.151299i
$494$	31998.6	2.91434
$495$	0	0
$496$	14932.0	1.35175
$497$	− 18178.5i	− 1.64068i
$498$	11995.8i	1.07941i
$499$	6526.03	0.585461	0.292731	−	0.956195i	$-0.405436\pi$
$499$	6526.03	0.585461	0.292731	+	0.956195i	$0.405436\pi$
$500$	0	0
$501$	8989.48	0.801638
$502$	− 9976.65i	− 0.887011i
$503$	13164.5i	1.16695i	0.812131	+	0.583475i	$0.198307\pi$
$503$	13164.5i	1.16695i	−0.812131	+	0.583475i	$0.801693\pi$
$504$	−11674.5	−1.03179
$505$	0	0
$506$	10365.9	0.910715
$507$	− 2387.10i	− 0.209102i
$508$	− 45846.7i	− 4.00417i
$509$	5635.08	0.490708	0.245354	−	0.969434i	$-0.421096\pi$
$509$	5635.08	0.490708	0.245354	+	0.969434i	$0.421096\pi$
$510$	0	0
$511$	9645.53	0.835016
$512$	5082.72i	0.438724i
$513$	4310.22i	0.370957i
$514$	−2106.35	−0.180753
$515$	0	0
$516$	−3954.48	−0.337376
$517$	4244.69i	0.361086i
$518$	− 17068.7i	− 1.44779i
$519$	7582.78	0.641324
$520$	0	0
$521$	−5117.05	−0.430292	−0.215146	−	0.976582i	$-0.569023\pi$
$521$	−5117.05	−0.430292	−0.215146	+	0.976582i	$0.569023\pi$
$522$	− 3155.64i	− 0.264595i
$523$	17121.2i	1.43146i	0.698375	+	0.715732i	$0.253907\pi$
$523$	17121.2i	1.43146i	−0.698375	+	0.715732i	$0.746093\pi$
$524$	49970.9	4.16601
$525$	0	0
$526$	−30203.6	−2.50369
$527$	1907.82i	0.157696i
$528$	− 6532.62i	− 0.538439i
$529$	−18805.2	−1.54559
$530$	0	0
$531$	2531.43	0.206883
$532$	63086.6i	5.14126i
$533$	14645.7i	1.19020i
$534$	−7344.40	−0.595175
$535$	0	0
$536$	−11464.4	−0.923859
$537$	836.858i	0.0672497i
$538$	− 43974.5i	− 3.52393i
$539$	−247.002	−0.0197387
$540$	0	0
$541$	13850.5	1.10070	0.550350	−	0.834934i	$-0.314494\pi$
$541$	13850.5	1.10070	0.550350	+	0.834934i	$0.314494\pi$
$542$	6545.72i	0.518750i
$543$	− 10855.6i	− 0.857935i
$544$	13080.2	1.03090
$545$	0	0
$546$	−11495.6	−0.901041
$547$	− 23854.8i	− 1.86464i	−0.361636	−	0.932319i	$-0.617782\pi$
$547$	− 23854.8i	− 1.86464i	0.361636	−	0.932319i	$-0.382218\pi$
$548$	− 32106.7i	− 2.50280i
$549$	6792.46	0.528042
$550$	0	0
$551$	−10453.3	−0.808210
$552$	35824.9i	2.76233i
$553$	21575.5i	1.65910i
$554$	−10465.8	−0.802616
$555$	0	0
$556$	−47844.2	−3.64937
$557$	9375.37i	0.713190i	0.934259	+	0.356595i	$0.116062\pi$
$557$	9375.37i	0.713190i	−0.934259	+	0.356595i	$0.883938\pi$
$558$	3635.11i	0.275782i
$559$	−2386.98	−0.180606
$560$	0	0
$561$	834.651	0.0628146
$562$	− 46983.6i	− 3.52648i
$563$	3751.35i	0.280818i	0.990094	+	0.140409i	$0.0448417\pi$
$563$	3751.35i	0.280818i	−0.990094	+	0.140409i	$0.955158\pi$
$564$	−23930.9	−1.78665
$565$	0	0
$566$	−38806.8	−2.88193
$567$	− 1548.47i	− 0.114690i
$568$	64523.6i	4.76646i
$569$	22294.2	1.64257	0.821286	−	0.570517i	$-0.193257\pi$
$569$	22294.2	1.64257	0.821286	+	0.570517i	$0.193257\pi$
$570$	0	0
$571$	16413.4	1.20294	0.601470	−	0.798896i	$-0.294582\pi$
$571$	16413.4	1.20294	0.601470	+	0.798896i	$0.294582\pi$
$572$	− 8512.21i	− 0.622227i
$573$	2474.09i	0.180378i
$574$	−40049.0	−2.91222
$575$	0	0
$576$	10669.8	0.771829
$577$	− 8727.05i	− 0.629657i	−0.949149	−	0.314828i	$-0.898053\pi$
$577$	− 8727.05i	− 0.629657i	0.949149	−	0.314828i	$-0.101947\pi$
$578$	− 22881.9i	− 1.64665i
$579$	−9730.44	−0.698417
$580$	0	0
$581$	−14275.6	−1.01937
$582$	21383.9i	1.52301i
$583$	987.327i	0.0701388i
$584$	−34236.3	−2.42587
$585$	0	0
$586$	−25210.0	−1.77716
$587$	15343.2i	1.07885i	0.842035	+	0.539423i	$0.181357\pi$
$587$	15343.2i	1.07885i	−0.842035	+	0.539423i	$0.818643\pi$
$588$	− 1392.56i	− 0.0976670i
$589$	12041.5	0.842381
$590$	0	0
$591$	7149.88	0.497643
$592$	33008.7i	2.29164i
$593$	− 7630.64i	− 0.528420i	−0.964465	−	0.264210i	$-0.914889\pi$
$593$	− 7630.64i	− 0.528420i	0.964465	−	0.264210i	$-0.0851112\pi$
$594$	1590.33	0.109852
$595$	0	0
$596$	−61826.3	−4.24917
$597$	6214.54i	0.426037i
$598$	35276.2i	2.41229i
$599$	−19244.4	−1.31270	−0.656349	−	0.754457i	$-0.727900\pi$
$599$	−19244.4	−1.31270	−0.656349	+	0.754457i	$0.727900\pi$
$600$	0	0
$601$	−20720.7	−1.40635	−0.703174	−	0.711018i	$-0.748234\pi$
$601$	−20720.7	−1.40635	−0.703174	+	0.711018i	$0.748234\pi$
$602$	− 6527.24i	− 0.441911i
$603$	− 1520.61i	− 0.102693i
$604$	−21743.8	−1.46481
$605$	0	0
$606$	16020.7	1.07392
$607$	− 775.664i	− 0.0518670i	−0.999664	−	0.0259335i	$-0.991744\pi$
$607$	− 775.664i	− 0.0518670i	0.999664	−	0.0259335i	$-0.00825581\pi$
$608$	− 82558.1i	− 5.50686i
$609$	3755.38	0.249878
$610$	0	0
$611$	−14445.1	−0.956439
$612$	4705.63i	0.310807i
$613$	1407.53i	0.0927400i	0.998924	+	0.0463700i	$0.0147653\pi$
$613$	1407.53i	0.0927400i	−0.998924	+	0.0463700i	$0.985235\pi$
$614$	−46738.8	−3.07203
$615$	0	0
$616$	14268.8	0.933288
$617$	17442.5i	1.13810i	0.822303	+	0.569050i	$0.192689\pi$
$617$	17442.5i	1.13810i	−0.822303	+	0.569050i	$0.807311\pi$
$618$	− 19017.0i	− 1.23783i
$619$	−17656.0	−1.14645	−0.573227	−	0.819397i	$-0.694309\pi$
$619$	−17656.0	−1.14645	−0.573227	+	0.819397i	$0.694309\pi$
$620$	0	0
$621$	−4751.71	−0.307052
$622$	− 35299.3i	− 2.27552i
$623$	− 8740.22i	− 0.562070i
$624$	22231.1	1.42621
$625$	0	0
$626$	−4190.38	−0.267542
$627$	− 5268.05i	− 0.335543i
$628$	− 28673.6i	− 1.82198i
$629$	−4217.41	−0.267344
$630$	0	0
$631$	502.123	0.0316786	0.0158393	−	0.999875i	$-0.494958\pi$
$631$	502.123	0.0316786	0.0158393	+	0.999875i	$0.494958\pi$
$632$	− 76581.0i	− 4.81998i
$633$	− 11863.7i	− 0.744931i
$634$	19359.5	1.21272
$635$	0	0
$636$	−5566.39	−0.347047
$637$	− 840.571i	− 0.0522835i
$638$	3856.90i	0.239335i
$639$	−8558.22	−0.529825
$640$	0	0
$641$	12329.8	0.759749	0.379875	−	0.925038i	$-0.375967\pi$
$641$	12329.8	0.759749	0.379875	+	0.925038i	$0.375967\pi$
$642$	− 17649.5i	− 1.08500i
$643$	4512.87i	0.276781i	0.990378	+	0.138391i	$0.0441929\pi$
$643$	4512.87i	0.276781i	−0.990378	+	0.138391i	$0.955807\pi$
$644$	−69548.4	−4.25557
$645$	0	0
$646$	21620.0	1.31676
$647$	− 20528.4i	− 1.24738i	−0.781673	−	0.623689i	$-0.785633\pi$
$647$	− 20528.4i	− 1.24738i	0.781673	−	0.623689i	$-0.214367\pi$
$648$	5496.20i	0.333196i
$649$	−3093.97	−0.187133
$650$	0	0
$651$	−4325.97	−0.260443
$652$	23255.5i	1.39686i
$653$	− 15846.4i	− 0.949644i	−0.880082	−	0.474822i	$-0.842512\pi$
$653$	− 15846.4i	− 0.949644i	0.880082	−	0.474822i	$-0.157488\pi$
$654$	24805.6	1.48314
$655$	0	0
$656$	77449.6	4.60960
$657$	− 4541.00i	− 0.269652i
$658$	− 39500.2i	− 2.34024i
$659$	2380.49	0.140714	0.0703571	−	0.997522i	$-0.477586\pi$
$659$	2380.49	0.140714	0.0703571	+	0.997522i	$0.477586\pi$
$660$	0	0
$661$	−26393.8	−1.55310	−0.776552	−	0.630054i	$-0.783033\pi$
$661$	−26393.8	−1.55310	−0.776552	+	0.630054i	$0.783033\pi$
$662$	16577.2i	0.973248i
$663$	2840.39i	0.166383i
$664$	50670.6	2.96145
$665$	0	0
$666$	−8035.77	−0.467537
$667$	− 11524.0i	− 0.668979i
$668$	− 61943.8i	− 3.58784i
$669$	−7199.98	−0.416095
$670$	0	0
$671$	−8301.90	−0.477632
$672$	29659.4i	1.70258i
$673$	27228.9i	1.55958i	0.626041	+	0.779790i	$0.284674\pi$
$673$	27228.9i	1.55958i	−0.626041	+	0.779790i	$0.715326\pi$
$674$	−14293.7	−0.816871
$675$	0	0
$676$	−16448.8	−0.935864
$677$	15485.8i	0.879124i	0.898212	+	0.439562i	$0.144866\pi$
$677$	15485.8i	0.879124i	−0.898212	+	0.439562i	$0.855134\pi$
$678$	17702.1i	1.00272i
$679$	−25447.9	−1.43829
$680$	0	0
$681$	3699.32	0.208162
$682$	− 4442.92i	− 0.249455i
$683$	19953.7i	1.11787i	0.829210	+	0.558937i	$0.188791\pi$
$683$	19953.7i	1.11787i	−0.829210	+	0.558937i	$0.811209\pi$
$684$	29700.4	1.66027
$685$	0	0
$686$	−32812.2	−1.82621
$687$	2687.08i	0.149226i
$688$	12622.8i	0.699479i
$689$	−3359.96	−0.185783
$690$	0	0
$691$	−19224.3	−1.05836	−0.529180	−	0.848510i	$-0.677500\pi$
$691$	−19224.3	−1.05836	−0.529180	+	0.848510i	$0.677500\pi$
$692$	− 52250.6i	− 2.87033i
$693$	1892.57i	0.103741i
$694$	8298.93	0.453924
$695$	0	0
$696$	−13329.5	−0.725940
$697$	9895.47i	0.537759i
$698$	46929.5i	2.54485i
$699$	−4555.05	−0.246477
$700$	0	0
$701$	−4428.72	−0.238617	−0.119308	−	0.992857i	$-0.538068\pi$
$701$	−4428.72	−0.238617	−0.119308	+	0.992857i	$0.538068\pi$
$702$	5412.02i	0.290973i
$703$	26619.0i	1.42810i
$704$	−13040.8	−0.698145
$705$	0	0
$706$	32660.3	1.74106
$707$	19065.4i	1.01419i
$708$	− 17443.3i	− 0.925933i
$709$	25751.5	1.36406	0.682029	−	0.731325i	$-0.261098\pi$
$709$	25751.5	1.36406	0.682029	+	0.731325i	$0.261098\pi$
$710$	0	0
$711$	10157.5	0.535774
$712$	31022.9i	1.63291i
$713$	13274.9i	0.697264i
$714$	−7767.10	−0.407110
$715$	0	0
$716$	5766.53	0.300985
$717$	13251.8i	0.690235i
$718$	− 47153.7i	− 2.45092i
$719$	−33521.7	−1.73873	−0.869367	−	0.494167i	$-0.835473\pi$
$719$	−33521.7	−1.73873	−0.869367	+	0.494167i	$0.835473\pi$
$720$	0	0
$721$	22631.2	1.16898
$722$	− 99731.3i	− 5.14074i
$723$	12393.4i	0.637506i
$724$	−74802.6	−3.83980
$725$	0	0
$726$	−1943.73	−0.0993645
$727$	13092.7i	0.667923i	0.942587	+	0.333961i	$0.108385\pi$
$727$	13092.7i	0.667923i	−0.942587	+	0.333961i	$0.891615\pi$
$728$	48557.9i	2.47208i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−1612.78	−0.0816016
$732$	− 46804.8i	− 2.36333i
$733$	− 8040.40i	− 0.405156i	−0.979266	−	0.202578i	$-0.935068\pi$
$733$	− 8040.40i	− 0.405156i	0.979266	−	0.202578i	$-0.0649319\pi$
$734$	47713.4	2.39936
$735$	0	0
$736$	91014.3	4.55820
$737$	1858.52i	0.0928895i
$738$	18854.6i	0.940444i
$739$	−12152.5	−0.604920	−0.302460	−	0.953162i	$-0.597808\pi$
$739$	−12152.5	−0.604920	−0.302460	+	0.953162i	$0.597808\pi$
$740$	0	0
$741$	17927.6	0.888783
$742$	− 9187.87i	− 0.454578i
$743$	− 28733.5i	− 1.41875i	−0.704833	−	0.709373i	$-0.748978\pi$
$743$	− 28733.5i	− 1.41875i	0.704833	−	0.709373i	$-0.251022\pi$
$744$	15354.8	0.756633
$745$	0	0
$746$	25040.3	1.22894
$747$	6720.80i	0.329185i
$748$	− 5751.32i	− 0.281135i
$749$	21003.8	1.02465
$750$	0	0
$751$	31463.0	1.52876	0.764382	−	0.644763i	$-0.223044\pi$
$751$	31463.0	1.52876	0.764382	+	0.644763i	$0.223044\pi$
$752$	76388.3i	3.70425i
$753$	− 5589.54i	− 0.270510i
$754$	−13125.4	−0.633948
$755$	0	0
$756$	−10670.0	−0.513313
$757$	− 2850.61i	− 0.136865i	−0.997656	−	0.0684327i	$-0.978200\pi$
$757$	− 2850.61i	− 0.136865i	0.997656	−	0.0684327i	$-0.0217999\pi$
$758$	50838.0i	2.43604i
$759$	5807.64	0.277739
$760$	0	0
$761$	−15856.8	−0.755333	−0.377667	−	0.925942i	$-0.623273\pi$
$761$	−15856.8	−0.755333	−0.377667	+	0.925942i	$0.623273\pi$
$762$	− 35626.6i	− 1.69372i
$763$	29520.0i	1.40065i
$764$	17048.2	0.807306
$765$	0	0
$766$	−9953.20	−0.469483
$767$	− 10529.1i	− 0.495675i
$768$	− 7061.38i	− 0.331778i
$769$	−8835.57	−0.414329	−0.207164	−	0.978306i	$-0.566424\pi$
$769$	−8835.57	−0.414329	−0.207164	+	0.978306i	$0.566424\pi$
$770$	0	0
$771$	−1180.11	−0.0551239
$772$	67049.5i	3.12586i
$773$	1207.49i	0.0561844i	0.999605	+	0.0280922i	$0.00894320\pi$
$773$	1207.49i	0.0561844i	−0.999605	+	0.0280922i	$0.991057\pi$
$774$	−3072.95	−0.142707
$775$	0	0
$776$	90326.0	4.17850
$777$	− 9562.98i	− 0.441531i
$778$	− 26458.7i	− 1.21927i
$779$	62457.0	2.87260
$780$	0	0
$781$	10460.1	0.479245
$782$	23834.5i	1.08992i
$783$	− 1767.99i	− 0.0806932i
$784$	−4445.10	−0.202492
$785$	0	0
$786$	38831.5	1.76218
$787$	− 17365.3i	− 0.786537i	−0.919424	−	0.393269i	$-0.871344\pi$
$787$	− 17365.3i	− 0.786537i	0.919424	−	0.393269i	$-0.128656\pi$
$788$	− 49267.7i	− 2.22727i
$789$	−16922.0	−0.763546
$790$	0	0
$791$	−21066.4	−0.946947
$792$	− 6717.58i	− 0.301387i
$793$	− 28252.1i	− 1.26515i
$794$	11549.6	0.516223
$795$	0	0
$796$	42822.5	1.90679
$797$	− 24361.2i	− 1.08271i	−0.840795	−	0.541354i	$-0.817912\pi$
$797$	− 24361.2i	− 1.08271i	0.840795	−	0.541354i	$-0.182088\pi$
$798$	49023.4i	2.17470i
$799$	−9759.88	−0.432140
$800$	0	0
$801$	−4114.79	−0.181509
$802$	26793.3i	1.17968i
$803$	5550.11i	0.243909i
$804$	−10478.1	−0.459618
$805$	0	0
$806$	15119.6	0.660752
$807$	− 24637.3i	− 1.07469i
$808$	− 67671.8i	− 2.94639i
$809$	−1788.32	−0.0777182	−0.0388591	−	0.999245i	$-0.512372\pi$
$809$	−1788.32	−0.0777182	−0.0388591	+	0.999245i	$0.512372\pi$
$810$	0	0
$811$	−3415.43	−0.147882	−0.0739409	−	0.997263i	$-0.523558\pi$
$811$	−3415.43	−0.147882	−0.0739409	+	0.997263i	$0.523558\pi$
$812$	− 25877.2i	− 1.11836i
$813$	3667.32i	0.158202i
$814$	9821.49	0.422903
$815$	0	0
$816$	15020.5	0.644393
$817$	10179.3i	0.435899i
$818$	58109.6i	2.48381i
$819$	−6440.58	−0.274789
$820$	0	0
$821$	21040.6	0.894422	0.447211	−	0.894429i	$-0.352417\pi$
$821$	21040.6	0.894422	0.447211	+	0.894429i	$0.352417\pi$
$822$	− 24949.6i	− 1.05866i
$823$	− 27736.0i	− 1.17474i	−0.809317	−	0.587372i	$-0.800162\pi$
$823$	− 27736.0i	− 1.17474i	0.809317	−	0.587372i	$-0.199838\pi$
$824$	−80328.4	−3.39608
$825$	0	0
$826$	28791.9	1.21283
$827$	17795.0i	0.748236i	0.927381	+	0.374118i	$0.122055\pi$
$827$	17795.0i	0.748236i	−0.927381	+	0.374118i	$0.877945\pi$
$828$	32742.6i	1.37425i
$829$	7362.92	0.308474	0.154237	−	0.988034i	$-0.450708\pi$
$829$	7362.92	0.308474	0.154237	+	0.988034i	$0.450708\pi$
$830$	0	0
$831$	−5863.60	−0.244773
$832$	− 44379.0i	− 1.84924i
$833$	− 567.936i	− 0.0236228i
$834$	−37178.9	−1.54364
$835$	0	0
$836$	−36300.5	−1.50177
$837$	2036.62i	0.0841049i
$838$	− 40752.1i	− 1.67990i
$839$	14025.2	0.577121	0.288561	−	0.957462i	$-0.406823\pi$
$839$	14025.2	0.577121	0.288561	+	0.957462i	$0.406823\pi$
$840$	0	0
$841$	−20101.2	−0.824193
$842$	44722.3i	1.83044i
$843$	− 26323.2i	− 1.07547i
$844$	−81749.4	−3.33404
$845$	0	0
$846$	−18596.3	−0.755736
$847$	− 2313.14i	− 0.0938376i
$848$	17768.1i	0.719528i
$849$	−21742.0	−0.878896
$850$	0	0
$851$	−29345.5	−1.18208
$852$	58972.1i	2.37130i
$853$	− 5752.48i	− 0.230904i	−0.993313	−	0.115452i	$-0.963168\pi$
$853$	− 5752.48i	− 0.230904i	0.993313	−	0.115452i	$-0.0368316\pi$
$854$	77255.8	3.09560
$855$	0	0
$856$	−74551.9	−2.97679
$857$	22891.0i	0.912416i	0.889873	+	0.456208i	$0.150793\pi$
$857$	22891.0i	0.912416i	−0.889873	+	0.456208i	$0.849207\pi$
$858$	− 6614.69i	− 0.263195i
$859$	−43090.2	−1.71154	−0.855772	−	0.517353i	$-0.826918\pi$
$859$	−43090.2	−1.71154	−0.855772	+	0.517353i	$0.826918\pi$
$860$	0	0
$861$	−22438.0	−0.888135
$862$	− 17495.5i	− 0.691298i
$863$	42168.9i	1.66332i	0.555283	+	0.831661i	$0.312610\pi$
$863$	42168.9i	1.66332i	−0.555283	+	0.831661i	$0.687390\pi$
$864$	13963.3	0.549816
$865$	0	0
$866$	−19002.8	−0.745660
$867$	− 12819.9i	− 0.502175i
$868$	29809.0i	1.16565i
$869$	−12414.7	−0.484626
$870$	0	0
$871$	−6324.72	−0.246045
$872$	− 104780.i	− 4.06913i
$873$	11980.6i	0.464469i
$874$	150436.	5.82216
$875$	0	0
$876$	−31290.6	−1.20686
$877$	− 41301.0i	− 1.59024i	−0.606455	−	0.795118i	$-0.707409\pi$
$877$	− 41301.0i	− 1.59024i	0.606455	−	0.795118i	$-0.292591\pi$
$878$	23533.6i	0.904578i
$879$	−14124.2	−0.541978
$880$	0	0
$881$	706.595	0.0270213	0.0135107	−	0.999909i	$-0.495699\pi$
$881$	706.595	0.0270213	0.0135107	+	0.999909i	$0.495699\pi$
$882$	− 1082.13i	− 0.0413121i
$883$	17503.2i	0.667080i	0.942736	+	0.333540i	$0.108243\pi$
$883$	17503.2i	0.667080i	−0.942736	+	0.333540i	$0.891757\pi$
$884$	19572.3	0.744668
$885$	0	0
$886$	57717.3	2.18855
$887$	− 27501.8i	− 1.04106i	−0.853843	−	0.520531i	$-0.825734\pi$
$887$	− 27501.8i	− 1.04106i	0.853843	−	0.520531i	$-0.174266\pi$
$888$	33943.3i	1.28273i
$889$	42397.6	1.59951
$890$	0	0
$891$	891.000	0.0335013
$892$	49612.9i	1.86229i
$893$	61601.2i	2.30841i
$894$	−48044.1	−1.79736
$895$	0	0
$896$	42263.6	1.57581
$897$	19763.9i	0.735672i
$898$	68381.5i	2.54111i
$899$	−4939.25	−0.183241
$900$	0	0
$901$	−2270.17	−0.0839406
$902$	− 23044.5i	− 0.850664i
$903$	− 3656.97i	− 0.134769i
$904$	74774.1	2.75105
$905$	0	0
$906$	−16896.7	−0.619598
$907$	− 42636.9i	− 1.56090i	−0.625219	−	0.780449i	$-0.714990\pi$
$907$	− 42636.9i	− 1.56090i	0.625219	−	0.780449i	$-0.285010\pi$
$908$	− 25490.9i	− 0.931657i
$909$	8975.79	0.327512
$910$	0	0
$911$	−16290.8	−0.592468	−0.296234	−	0.955115i	$-0.595731\pi$
$911$	−16290.8	−0.592468	−0.296234	+	0.955115i	$0.595731\pi$
$912$	− 94804.9i	− 3.44222i
$913$	− 8214.32i	− 0.297759i
$914$	−47348.3	−1.71350
$915$	0	0
$916$	18515.9	0.667883
$917$	46211.5i	1.66416i
$918$	3656.66i	0.131468i
$919$	−21323.4	−0.765389	−0.382695	−	0.923875i	$-0.625004\pi$
$919$	−21323.4	−0.765389	−0.382695	+	0.923875i	$0.625004\pi$
$920$	0	0
$921$	−26186.0	−0.936871
$922$	− 26447.8i	− 0.944698i
$923$	35596.5i	1.26942i
$924$	13041.1	0.464309
$925$	0	0
$926$	46192.9	1.63930
$927$	− 10654.5i	− 0.377498i
$928$	33864.1i	1.19789i
$929$	9989.50	0.352793	0.176397	−	0.984319i	$-0.443556\pi$
$929$	9989.50	0.352793	0.176397	+	0.984319i	$0.443556\pi$
$930$	0	0
$931$	−3584.63	−0.126188
$932$	31387.4i	1.10314i
$933$	− 19776.9i	− 0.693962i
$934$	−30431.3	−1.06610
$935$	0	0
$936$	22860.5	0.798311
$937$	25688.0i	0.895613i	0.894131	+	0.447806i	$0.147795\pi$
$937$	25688.0i	0.895613i	−0.894131	+	0.447806i	$0.852205\pi$
$938$	− 17295.0i	− 0.602029i
$939$	−2347.71	−0.0815918
$940$	0	0
$941$	38860.6	1.34625	0.673123	−	0.739530i	$-0.264952\pi$
$941$	38860.6	1.34625	0.673123	+	0.739530i	$0.264952\pi$
$942$	− 22281.7i	− 0.770677i
$943$	68854.4i	2.37774i
$944$	−55679.8	−1.91973
$945$	0	0
$946$	3755.83	0.129083
$947$	− 12733.5i	− 0.436941i	−0.975844	−	0.218471i	$-0.929893\pi$
$947$	− 12733.5i	− 0.436941i	0.975844	−	0.218471i	$-0.0701068\pi$
$948$	− 69992.1i	− 2.39793i
$949$	−18887.5	−0.646064
$950$	0	0
$951$	10846.4	0.369840
$952$	32808.4i	1.11694i
$953$	31381.9i	1.06669i	0.845896	+	0.533347i	$0.179066\pi$
$953$	31381.9i	1.06669i	−0.845896	+	0.533347i	$0.820934\pi$
$954$	−4325.54	−0.146797
$955$	0	0
$956$	91314.3	3.08924
$957$	2160.87i	0.0729897i
$958$	− 65561.4i	− 2.21106i
$959$	29691.3	0.999772
$960$	0	0
$961$	−24101.3	−0.809012
$962$	33423.4i	1.12018i
$963$	− 9888.35i	− 0.330890i
$964$	85399.4	2.85325
$965$	0	0
$966$	−54044.8	−1.80006
$967$	− 16365.9i	− 0.544254i	−0.962261	−	0.272127i	$-0.912273\pi$
$967$	− 16365.9i	− 0.544254i	0.962261	−	0.272127i	$-0.0877270\pi$
$968$	8210.37i	0.272615i
$969$	12112.9	0.401571
$970$	0	0
$971$	2733.69	0.0903485	0.0451742	−	0.998979i	$-0.485616\pi$
$971$	2733.69	0.0903485	0.0451742	+	0.998979i	$0.485616\pi$
$972$	5023.32i	0.165764i
$973$	− 44244.8i	− 1.45778i
$974$	68212.0	2.24400
$975$	0	0
$976$	−149403.	−4.89986
$977$	32538.0i	1.06549i	0.846276	+	0.532745i	$0.178840\pi$
$977$	32538.0i	1.06549i	−0.846276	+	0.532745i	$0.821160\pi$
$978$	18071.4i	0.590859i
$979$	5029.19	0.164181
$980$	0	0
$981$	13897.6	0.452312
$982$	− 84066.3i	− 2.73184i
$983$	20393.6i	0.661705i	0.943682	+	0.330853i	$0.107336\pi$
$983$	20393.6i	0.661705i	−0.943682	+	0.330853i	$0.892664\pi$
$984$	79642.4	2.58019
$985$	0	0
$986$	−8868.21	−0.286432
$987$	− 22130.5i	− 0.713700i
$988$	− 123534.i	− 3.97787i
$989$	−11222.0	−0.360807
$990$	0	0
$991$	−41403.3	−1.32716	−0.663582	−	0.748103i	$-0.730965\pi$
$991$	−41403.3	−1.32716	−0.663582	+	0.748103i	$0.730965\pi$
$992$	− 39009.4i	− 1.24854i
$993$	9287.57i	0.296810i
$994$	−97339.1	−3.10605
$995$	0	0
$996$	46311.0	1.47331
$997$	29979.8i	0.952328i	0.879357	+	0.476164i	$0.157973\pi$
$997$	29979.8i	0.952328i	−0.879357	+	0.476164i	$0.842027\pi$
$998$	− 34944.5i	− 1.10837i
$999$	−4502.14	−0.142584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.r.199.2		10
5.2	odd	4		825.4.a.w.1.5	✓	5
5.3	odd	4		825.4.a.z.1.1	yes	5
5.4	even	2	inner	825.4.c.r.199.9		10
15.2	even	4		2475.4.a.bm.1.1		5
15.8	even	4		2475.4.a.bf.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.4.a.w.1.5	✓	5	5.2	odd	4
825.4.a.z.1.1	yes	5	5.3	odd	4
825.4.c.r.199.2		10	1.1	even	1	trivial
825.4.c.r.199.9		10	5.4	even	2	inner
2475.4.a.bf.1.5		5	15.8	even	4
2475.4.a.bm.1.1		5	15.2	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)

\(f(q)\)	\(=\)	\(q-5.35463i q^{2} -3.00000i q^{3} -20.6721 q^{4} -16.0639 q^{6} -19.1169i q^{7} +67.8543i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-5.35463i q^{2} -3.00000i q^{3} -20.6721 q^{4} -16.0639 q^{6} -19.1169i q^{7} +67.8543i q^{8} -9.00000 q^{9} +11.0000 q^{11} +62.0162i q^{12} +37.4340i q^{13} -102.364 q^{14} +197.958 q^{16} +25.2925i q^{17} +48.1917i q^{18} +159.638 q^{19} -57.3506 q^{21} -58.9009i q^{22} +175.989i q^{23} +203.563 q^{24} +200.445 q^{26} +27.0000i q^{27} +395.185i q^{28} -65.4810 q^{29} +75.4303 q^{31} -517.159i q^{32} -33.0000i q^{33} +135.432 q^{34} +186.049 q^{36} +166.746i q^{37} -854.802i q^{38} +112.302 q^{39} +391.242 q^{41} +307.091i q^{42} +63.7652i q^{43} -227.393 q^{44} +942.357 q^{46} +385.881i q^{47} -593.875i q^{48} -22.4548 q^{49} +75.8774 q^{51} -773.838i q^{52} +89.7570i q^{53} +144.575 q^{54} +1297.16 q^{56} -478.913i q^{57} +350.627i q^{58} -281.270 q^{59} -754.718 q^{61} -403.901i q^{62} +172.052i q^{63} -1185.53 q^{64} -176.703 q^{66} +168.957i q^{67} -522.848i q^{68} +527.967 q^{69} +950.914 q^{71} -610.689i q^{72} +504.556i q^{73} +892.863 q^{74} -3300.05 q^{76} -210.286i q^{77} -601.335i q^{78} -1128.61 q^{79} +81.0000 q^{81} -2094.96i q^{82} -746.756i q^{83} +1185.56 q^{84} +341.439 q^{86} +196.443i q^{87} +746.397i q^{88} +457.199 q^{89} +715.620 q^{91} -3638.06i q^{92} -226.291i q^{93} +2066.25 q^{94} -1551.48 q^{96} -1331.18i q^{97} +120.237i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 92 q^{4} + 24 q^{6} - 90 q^{9}+O(q^{10}) \) 10 * q - 92 * q^4 + 24 * q^6 - 90 * q^9	\( 10 q - 92 q^{4} + 24 q^{6} - 90 q^{9} + 110 q^{11} - 110 q^{14} + 1268 q^{16} + 674 q^{19} - 228 q^{21} - 432 q^{24} + 718 q^{26} + 306 q^{29} + 526 q^{31} - 1034 q^{34} + 828 q^{36} - 258 q^{39} - 176 q^{41} - 1012 q^{44} + 872 q^{46} - 4762 q^{49} + 900 q^{51} - 216 q^{54} + 422 q^{56} - 820 q^{59} - 2260 q^{61} - 6340 q^{64} + 264 q^{66} + 1206 q^{69} + 2498 q^{71} + 5970 q^{74} - 5112 q^{76} - 4516 q^{79} + 810 q^{81} + 2646 q^{84} - 2870 q^{86} - 694 q^{89} - 1224 q^{91} - 1814 q^{94} + 1680 q^{96} - 990 q^{99}+O(q^{100}) \) 10 * q - 92 * q^4 + 24 * q^6 - 90 * q^9 + 110 * q^11 - 110 * q^14 + 1268 * q^16 + 674 * q^19 - 228 * q^21 - 432 * q^24 + 718 * q^26 + 306 * q^29 + 526 * q^31 - 1034 * q^34 + 828 * q^36 - 258 * q^39 - 176 * q^41 - 1012 * q^44 + 872 * q^46 - 4762 * q^49 + 900 * q^51 - 216 * q^54 + 422 * q^56 - 820 * q^59 - 2260 * q^61 - 6340 * q^64 + 264 * q^66 + 1206 * q^69 + 2498 * q^71 + 5970 * q^74 - 5112 * q^76 - 4516 * q^79 + 810 * q^81 + 2646 * q^84 - 2870 * q^86 - 694 * q^89 - 1224 * q^91 - 1814 * q^94 + 1680 * q^96 - 990 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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