LMFDB - Embedded newform 1150.4.b.s.599.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,4,Mod(599,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1150.599");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1150.b (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:	$67.8521965066$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 219x^{10} + 17685x^{8} + 640366x^{6} + 10000368x^{4} + 54897345x^{2} + 95531076 $ x^12 + 219x^10 + 17685x^8 + 640366x^6 + 10000368x^4 + 54897345*x^2 + 95531076
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.2
Root			$-4.90184i$ of defining polynomial
Character	$\chi$	$=$	1150.599
Dual form			1150.4.b.s.599.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -5.90184i q^{3} -4.00000 q^{4} -11.8037 q^{6} +1.63515i q^{7} +8.00000i q^{8} -7.83172 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} -5.90184i q^{3} -4.00000 q^{4} -11.8037 q^{6} +1.63515i q^{7} +8.00000i q^{8} -7.83172 q^{9} +42.3658 q^{11} +23.6074i q^{12} -18.1952i q^{13} +3.27031 q^{14} +16.0000 q^{16} +122.548i q^{17} +15.6634i q^{18} -87.0852 q^{19} +9.65041 q^{21} -84.7316i q^{22} -23.0000i q^{23} +47.2147 q^{24} -36.3904 q^{26} -113.128i q^{27} -6.54061i q^{28} +187.490 q^{29} +167.702 q^{31} -32.0000i q^{32} -250.036i q^{33} +245.096 q^{34} +31.3269 q^{36} -405.079i q^{37} +174.170i q^{38} -107.385 q^{39} -111.070 q^{41} -19.3008i q^{42} -192.424i q^{43} -169.463 q^{44} -46.0000 q^{46} +245.437i q^{47} -94.4294i q^{48} +340.326 q^{49} +723.258 q^{51} +72.7809i q^{52} +52.0761i q^{53} -226.256 q^{54} -13.0812 q^{56} +513.963i q^{57} -374.979i q^{58} +425.068 q^{59} +669.437 q^{61} -335.404i q^{62} -12.8061i q^{63} -64.0000 q^{64} -500.072 q^{66} -661.392i q^{67} -490.191i q^{68} -135.742 q^{69} -425.237 q^{71} -62.6537i q^{72} -1109.13i q^{73} -810.158 q^{74} +348.341 q^{76} +69.2745i q^{77} +214.771i q^{78} -1195.16 q^{79} -879.121 q^{81} +222.139i q^{82} -1475.59i q^{83} -38.6016 q^{84} -384.849 q^{86} -1106.53i q^{87} +338.926i q^{88} +74.2100 q^{89} +29.7520 q^{91} +92.0000i q^{92} -989.750i q^{93} +490.874 q^{94} -188.859 q^{96} +937.166i q^{97} -680.653i q^{98} -331.797 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 48 q^{4} - 20 q^{6} - 122 q^{9}+O(q^{10}) $ 12 * q - 48 * q^4 - 20 * q^6 - 122 * q^9	$ 12 q - 48 q^{4} - 20 q^{6} - 122 q^{9} - 98 q^{11} + 168 q^{14} + 192 q^{16} + 458 q^{19} + 184 q^{21} + 80 q^{24} - 64 q^{26} + 364 q^{29} + 228 q^{31} + 700 q^{34} + 488 q^{36} + 286 q^{39} + 486 q^{41} + 392 q^{44} - 552 q^{46} - 1296 q^{49} - 2062 q^{51} + 1376 q^{54} - 672 q^{56} + 1118 q^{59} - 1376 q^{61} - 768 q^{64} - 2564 q^{66} - 230 q^{69} + 1168 q^{71} + 256 q^{74} - 1832 q^{76} + 2864 q^{79} + 68 q^{81} - 736 q^{84} - 728 q^{86} + 1182 q^{89} - 5728 q^{91} + 1992 q^{94} - 320 q^{96} + 284 q^{99}+O(q^{100}) $ 12 * q - 48 * q^4 - 20 * q^6 - 122 * q^9 - 98 * q^11 + 168 * q^14 + 192 * q^16 + 458 * q^19 + 184 * q^21 + 80 * q^24 - 64 * q^26 + 364 * q^29 + 228 * q^31 + 700 * q^34 + 488 * q^36 + 286 * q^39 + 486 * q^41 + 392 * q^44 - 552 * q^46 - 1296 * q^49 - 2062 * q^51 + 1376 * q^54 - 672 * q^56 + 1118 * q^59 - 1376 * q^61 - 768 * q^64 - 2564 * q^66 - 230 * q^69 + 1168 * q^71 + 256 * q^74 - 1832 * q^76 + 2864 * q^79 + 68 * q^81 - 736 * q^84 - 728 * q^86 + 1182 * q^89 - 5728 * q^91 + 1992 * q^94 - 320 * q^96 + 284 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 2.00000i	− 0.707107i
$2$	− 2.00000i	− 0.707107i
$3$	− 5.90184i	− 1.13581i	−0.823094	−	0.567905i	$-0.807754\pi$
$3$	− 5.90184i	− 1.13581i	0.823094	−	0.567905i	$-0.192246\pi$
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−11.8037	−0.803139
$7$	1.63515i	0.0882900i	0.999025	+	0.0441450i	$0.0140564\pi$
$7$	1.63515i	0.0882900i	−0.999025	+	0.0441450i	$0.985944\pi$
$8$	8.00000i	0.353553i
$9$	−7.83172	−0.290064
$10$	0	0
$11$	42.3658	1.16125	0.580626	−	0.814171i	$-0.302808\pi$
$11$	42.3658	1.16125	0.580626	+	0.814171i	$0.302808\pi$
$12$	23.6074i	0.567905i
$13$	− 18.1952i	− 0.388188i	−0.980983	−	0.194094i	$-0.937823\pi$
$13$	− 18.1952i	− 0.388188i	0.980983	−	0.194094i	$-0.0621767\pi$
$14$	3.27031	0.0624304
$15$	0	0
$16$	16.0000	0.250000
$17$	122.548i	1.74837i	0.485597	+	0.874183i	$0.338602\pi$
$17$	122.548i	1.74837i	−0.485597	+	0.874183i	$0.661398\pi$
$18$	15.6634i	0.205106i
$19$	−87.0852	−1.05151	−0.525756	−	0.850636i	$-0.676217\pi$
$19$	−87.0852	−1.05151	−0.525756	+	0.850636i	$0.676217\pi$
$20$	0	0
$21$	9.65041	0.100281
$22$	− 84.7316i	− 0.821129i
$23$	− 23.0000i	− 0.208514i
$23$	− 23.0000i	− 0.208514i
$24$	47.2147	0.401569
$25$	0	0
$26$	−36.3904	−0.274490
$27$	− 113.128i	− 0.806353i
$28$	− 6.54061i	− 0.0441450i
$29$	187.490	1.20055	0.600275	−	0.799793i	$-0.295058\pi$
$29$	187.490	1.20055	0.600275	+	0.799793i	$0.295058\pi$
$30$	0	0
$31$	167.702	0.971618	0.485809	−	0.874065i	$-0.338525\pi$
$31$	167.702	0.971618	0.485809	+	0.874065i	$0.338525\pi$
$32$	− 32.0000i	− 0.176777i
$33$	− 250.036i	− 1.31896i
$34$	245.096	1.23628
$35$	0	0
$36$	31.3269	0.145032
$37$	− 405.079i	− 1.79985i	−0.436042	−	0.899926i	$-0.643620\pi$
$37$	− 405.079i	− 1.79985i	0.436042	−	0.899926i	$-0.356380\pi$
$38$	174.170i	0.743531i
$39$	−107.385	−0.440908
$40$	0	0
$41$	−111.070	−0.423078	−0.211539	−	0.977370i	$-0.567847\pi$
$41$	−111.070	−0.423078	−0.211539	+	0.977370i	$0.567847\pi$
$42$	− 19.3008i	− 0.0709091i
$43$	− 192.424i	− 0.682429i	−0.939986	−	0.341214i	$-0.889162\pi$
$43$	− 192.424i	− 0.682429i	0.939986	−	0.341214i	$-0.110838\pi$
$44$	−169.463	−0.580626
$45$	0	0
$46$	−46.0000	−0.147442
$47$	245.437i	0.761716i	0.924634	+	0.380858i	$0.124371\pi$
$47$	245.437i	0.761716i	−0.924634	+	0.380858i	$0.875629\pi$
$48$	− 94.4294i	− 0.283952i
$49$	340.326	0.992205
$50$	0	0
$51$	723.258	1.98581
$52$	72.7809i	0.194094i
$53$	52.0761i	0.134966i	0.997720	+	0.0674831i	$0.0214969\pi$
$53$	52.0761i	0.134966i	−0.997720	+	0.0674831i	$0.978503\pi$
$54$	−226.256	−0.570177
$55$	0	0
$56$	−13.0812	−0.0312152
$57$	513.963i	1.19432i
$58$	− 374.979i	− 0.848918i
$59$	425.068	0.937952	0.468976	−	0.883211i	$-0.344623\pi$
$59$	425.068	0.937952	0.468976	+	0.883211i	$0.344623\pi$
$60$	0	0
$61$	669.437	1.40513	0.702563	−	0.711622i	$-0.252039\pi$
$61$	669.437	1.40513	0.702563	+	0.711622i	$0.252039\pi$
$62$	− 335.404i	− 0.687037i
$63$	− 12.8061i	− 0.0256097i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	−500.072	−0.932646
$67$	− 661.392i	− 1.20600i	−0.797742	−	0.602999i	$-0.793972\pi$
$67$	− 661.392i	− 1.20600i	0.797742	−	0.602999i	$-0.206028\pi$
$68$	− 490.191i	− 0.874183i
$69$	−135.742	−0.236833
$70$	0	0
$71$	−425.237	−0.710793	−0.355396	−	0.934716i	$-0.615654\pi$
$71$	−425.237	−0.710793	−0.355396	+	0.934716i	$0.615654\pi$
$72$	− 62.6537i	− 0.102553i
$73$	− 1109.13i	− 1.77827i	−0.457649	−	0.889133i	$-0.651308\pi$
$73$	− 1109.13i	− 1.77827i	0.457649	−	0.889133i	$-0.348692\pi$
$74$	−810.158	−1.27269
$75$	0	0
$76$	348.341	0.525756
$77$	69.2745i	0.102527i
$78$	214.771i	0.311769i
$79$	−1195.16	−1.70210	−0.851052	−	0.525082i	$-0.824035\pi$
$79$	−1195.16	−1.70210	−0.851052	+	0.525082i	$0.824035\pi$
$80$	0	0
$81$	−879.121	−1.20593
$82$	222.139i	0.299161i
$83$	− 1475.59i	− 1.95141i	−0.219095	−	0.975704i	$-0.570310\pi$
$83$	− 1475.59i	− 1.95141i	0.219095	−	0.975704i	$-0.429690\pi$
$84$	−38.6016	−0.0501403
$85$	0	0
$86$	−384.849	−0.482550
$87$	− 1106.53i	− 1.36360i
$88$	338.926i	0.410564i
$89$	74.2100	0.0883847	0.0441924	−	0.999023i	$-0.485929\pi$
$89$	74.2100	0.0883847	0.0441924	+	0.999023i	$0.485929\pi$
$90$	0	0
$91$	29.7520	0.0342731
$92$	92.0000i	0.104257i
$93$	− 989.750i	− 1.10357i
$94$	490.874	0.538614
$95$	0	0
$96$	−188.859	−0.200785
$97$	937.166i	0.980977i	0.871448	+	0.490489i	$0.163182\pi$
$97$	937.166i	0.980977i	−0.871448	+	0.490489i	$0.836818\pi$
$98$	− 680.653i	− 0.701595i
$99$	−331.797	−0.336837
$100$	0	0
$101$	21.6198	0.0212995	0.0106497	−	0.999943i	$-0.496610\pi$
$101$	21.6198	0.0212995	0.0106497	+	0.999943i	$0.496610\pi$
$102$	− 1446.52i	− 1.40418i
$103$	− 509.165i	− 0.487083i	−0.969890	−	0.243541i	$-0.921691\pi$
$103$	− 509.165i	− 0.487083i	0.969890	−	0.243541i	$-0.0783092\pi$
$104$	145.562	0.137245
$105$	0	0
$106$	104.152	0.0954355
$107$	1269.28i	1.14678i	0.819282	+	0.573391i	$0.194372\pi$
$107$	1269.28i	1.14678i	−0.819282	+	0.573391i	$0.805628\pi$
$108$	452.513i	0.403176i
$109$	1827.07	1.60552	0.802762	−	0.596300i	$-0.203363\pi$
$109$	1827.07	1.60552	0.802762	+	0.596300i	$0.203363\pi$
$110$	0	0
$111$	−2390.71	−2.04429
$112$	26.1624i	0.0220725i
$113$	− 1175.67i	− 0.978744i	−0.872075	−	0.489372i	$-0.837226\pi$
$113$	− 1175.67i	− 0.978744i	0.872075	−	0.489372i	$-0.162774\pi$
$114$	1027.93	0.844510
$115$	0	0
$116$	−749.959	−0.600275
$117$	142.500i	0.112599i
$118$	− 850.137i	− 0.663232i
$119$	−200.384	−0.154363
$120$	0	0
$121$	463.860	0.348505
$122$	− 1338.87i	− 0.993574i
$123$	655.516i	0.480536i
$124$	−670.808	−0.485809
$125$	0	0
$126$	−25.6121	−0.0181088
$127$	1657.04i	1.15778i	0.815405	+	0.578890i	$0.196514\pi$
$127$	1657.04i	1.15778i	−0.815405	+	0.578890i	$0.803486\pi$
$128$	128.000i	0.0883883i
$129$	−1135.66	−0.775109
$130$	0	0
$131$	−1206.22	−0.804488	−0.402244	−	0.915532i	$-0.631770\pi$
$131$	−1206.22	−0.804488	−0.402244	+	0.915532i	$0.631770\pi$
$132$	1000.14i	0.659480i
$133$	− 142.398i	− 0.0928379i
$134$	−1322.78	−0.852770
$135$	0	0
$136$	−980.383	−0.618141
$137$	2091.57i	1.30434i	0.758072	+	0.652171i	$0.226142\pi$
$137$	2091.57i	1.30434i	−0.758072	+	0.652171i	$0.773858\pi$
$138$	271.485i	0.167466i
$139$	41.5499	0.0253541	0.0126770	−	0.999920i	$-0.495965\pi$
$139$	41.5499	0.0253541	0.0126770	+	0.999920i	$0.495965\pi$
$140$	0	0
$141$	1448.53	0.865164
$142$	850.473i	0.502606i
$143$	− 770.855i	− 0.450784i
$144$	−125.307	−0.0725159
$145$	0	0
$146$	−2218.25	−1.25742
$147$	− 2008.55i	− 1.12696i
$148$	1620.32i	0.899926i
$149$	−1494.41	−0.821659	−0.410829	−	0.911712i	$-0.634761\pi$
$149$	−1494.41	−0.821659	−0.410829	+	0.911712i	$0.634761\pi$
$150$	0	0
$151$	−401.577	−0.216423	−0.108211	−	0.994128i	$-0.534512\pi$
$151$	−401.577	−0.216423	−0.108211	+	0.994128i	$0.534512\pi$
$152$	− 696.682i	− 0.371766i
$153$	− 959.760i	− 0.507137i
$154$	138.549	0.0724974
$155$	0	0
$156$	429.541	0.220454
$157$	− 2631.01i	− 1.33744i	−0.743515	−	0.668719i	$-0.766843\pi$
$157$	− 2631.01i	− 1.33744i	0.743515	−	0.668719i	$-0.233157\pi$
$158$	2390.32i	1.20357i
$159$	307.345	0.153296
$160$	0	0
$161$	37.6085	0.0184097
$162$	1758.24i	0.852719i
$163$	627.170i	0.301373i	0.988582	+	0.150686i	$0.0481484\pi$
$163$	627.170i	0.301373i	−0.988582	+	0.150686i	$0.951852\pi$
$164$	444.279	0.211539
$165$	0	0
$166$	−2951.18	−1.37985
$167$	2495.88i	1.15651i	0.815856	+	0.578255i	$0.196266\pi$
$167$	2495.88i	1.15651i	−0.815856	+	0.578255i	$0.803734\pi$
$168$	77.2033i	0.0354545i
$169$	1865.93	0.849310
$170$	0	0
$171$	682.027	0.305005
$172$	769.697i	0.341214i
$173$	2853.58i	1.25407i	0.778992	+	0.627034i	$0.215731\pi$
$173$	2853.58i	1.25407i	−0.778992	+	0.627034i	$0.784269\pi$
$174$	−2213.07	−0.964209
$175$	0	0
$176$	677.853	0.290313
$177$	− 2508.68i	− 1.06534i
$178$	− 148.420i	− 0.0624974i
$179$	307.069	0.128220	0.0641101	−	0.997943i	$-0.479579\pi$
$179$	307.069	0.128220	0.0641101	+	0.997943i	$0.479579\pi$
$180$	0	0
$181$	−1733.53	−0.711889	−0.355945	−	0.934507i	$-0.615841\pi$
$181$	−1733.53	−0.711889	−0.355945	+	0.934507i	$0.615841\pi$
$182$	− 59.5039i	− 0.0242347i
$183$	− 3950.91i	− 1.59596i
$184$	184.000	0.0737210
$185$	0	0
$186$	−1979.50	−0.780344
$187$	5191.83i	2.03029i
$188$	− 981.747i	− 0.380858i
$189$	184.982	0.0711928
$190$	0	0
$191$	2160.38	0.818427	0.409213	−	0.912439i	$-0.365803\pi$
$191$	2160.38	0.818427	0.409213	+	0.912439i	$0.365803\pi$
$192$	377.718i	0.141976i
$193$	− 3725.78i	− 1.38957i	−0.719217	−	0.694785i	$-0.755499\pi$
$193$	− 3725.78i	− 1.38957i	0.719217	−	0.694785i	$-0.244501\pi$
$194$	1874.33	0.693656
$195$	0	0
$196$	−1361.31	−0.496102
$197$	− 5267.32i	− 1.90498i	−0.304568	−	0.952491i	$-0.598512\pi$
$197$	− 5267.32i	− 1.90498i	0.304568	−	0.952491i	$-0.401488\pi$
$198$	663.594i	0.238179i
$199$	190.118	0.0677241	0.0338620	−	0.999427i	$-0.489219\pi$
$199$	190.118	0.0677241	0.0338620	+	0.999427i	$0.489219\pi$
$200$	0	0
$201$	−3903.43	−1.36978
$202$	− 43.2396i	− 0.0150610i
$203$	306.574i	0.105997i
$204$	−2893.03	−0.992905
$205$	0	0
$206$	−1018.33	−0.344420
$207$	180.129i	0.0604824i
$208$	− 291.123i	− 0.0970470i
$209$	−3689.43	−1.22107
$210$	0	0
$211$	677.866	0.221167	0.110583	−	0.993867i	$-0.464728\pi$
$211$	677.866	0.221167	0.110583	+	0.993867i	$0.464728\pi$
$212$	− 208.305i	− 0.0674831i
$213$	2509.68i	0.807325i
$214$	2538.55	0.810897
$215$	0	0
$216$	905.025	0.285089
$217$	274.218i	0.0857841i
$218$	− 3654.15i	− 1.13528i
$219$	−6545.89	−2.01977
$220$	0	0
$221$	2229.78	0.678695
$222$	4781.42i	1.44553i
$223$	− 4214.82i	− 1.26567i	−0.774285	−	0.632837i	$-0.781890\pi$
$223$	− 4214.82i	− 1.26567i	0.774285	−	0.632837i	$-0.218110\pi$
$224$	52.3249	0.0156076
$225$	0	0
$226$	−2351.35	−0.692076
$227$	3368.29i	0.984850i	0.870355	+	0.492425i	$0.163889\pi$
$227$	3368.29i	0.984850i	−0.870355	+	0.492425i	$0.836111\pi$
$228$	− 2055.85i	− 0.597159i
$229$	1138.51	0.328536	0.164268	−	0.986416i	$-0.447474\pi$
$229$	1138.51	0.328536	0.164268	+	0.986416i	$0.447474\pi$
$230$	0	0
$231$	408.847	0.116451
$232$	1499.92i	0.424459i
$233$	− 659.376i	− 0.185396i	−0.995694	−	0.0926978i	$-0.970451\pi$
$233$	− 659.376i	− 0.185396i	0.995694	−	0.0926978i	$-0.0295491\pi$
$234$	285.000	0.0796197
$235$	0	0
$236$	−1700.27	−0.468976
$237$	7053.65i	1.93327i
$238$	400.769i	0.109151i
$239$	−1401.18	−0.379224	−0.189612	−	0.981859i	$-0.560723\pi$
$239$	−1401.18	−0.379224	−0.189612	+	0.981859i	$0.560723\pi$
$240$	0	0
$241$	3668.16	0.980443	0.490221	−	0.871598i	$-0.336916\pi$
$241$	3668.16	0.980443	0.490221	+	0.871598i	$0.336916\pi$
$242$	− 927.719i	− 0.246430i
$243$	2133.97i	0.563350i
$244$	−2677.75	−0.702563
$245$	0	0
$246$	1311.03	0.339790
$247$	1584.53i	0.408184i
$248$	1341.62i	0.343519i
$249$	−8708.68	−2.21643
$250$	0	0
$251$	591.784	0.148817	0.0744085	−	0.997228i	$-0.476293\pi$
$251$	591.784	0.148817	0.0744085	+	0.997228i	$0.476293\pi$
$252$	51.2242i	0.0128048i
$253$	− 974.413i	− 0.242138i
$254$	3314.07	0.818675
$255$	0	0
$256$	256.000	0.0625000
$257$	2144.75i	0.520566i	0.965532	+	0.260283i	$0.0838159\pi$
$257$	2144.75i	0.520566i	−0.965532	+	0.260283i	$0.916184\pi$
$258$	2271.31i	0.548085i
$259$	662.366	0.158909
$260$	0	0
$261$	−1468.37	−0.348236
$262$	2412.44i	0.568859i
$263$	− 3895.49i	− 0.913333i	−0.889638	−	0.456666i	$-0.849043\pi$
$263$	− 3895.49i	− 0.913333i	0.889638	−	0.456666i	$-0.150957\pi$
$264$	2000.29	0.466323
$265$	0	0
$266$	−284.795	−0.0656463
$267$	− 437.975i	− 0.100388i
$268$	2645.57i	0.602999i
$269$	3225.65	0.731119	0.365560	−	0.930788i	$-0.380878\pi$
$269$	3225.65	0.731119	0.365560	+	0.930788i	$0.380878\pi$
$270$	0	0
$271$	−6791.74	−1.52239	−0.761197	−	0.648521i	$-0.775388\pi$
$271$	−6791.74	−1.52239	−0.761197	+	0.648521i	$0.775388\pi$
$272$	1960.77i	0.437091i
$273$	− 175.591i	− 0.0389277i
$274$	4183.14	0.922309
$275$	0	0
$276$	542.969	0.118416
$277$	− 4155.88i	− 0.901454i	−0.892662	−	0.450727i	$-0.851165\pi$
$277$	− 4155.88i	− 0.901454i	0.892662	−	0.450727i	$-0.148835\pi$
$278$	− 83.0998i	− 0.0179280i
$279$	−1313.39	−0.281831
$280$	0	0
$281$	1420.05	0.301471	0.150735	−	0.988574i	$-0.451836\pi$
$281$	1420.05	0.301471	0.150735	+	0.988574i	$0.451836\pi$
$282$	− 2897.06i	− 0.611763i
$283$	− 3809.86i	− 0.800256i	−0.916459	−	0.400128i	$-0.868966\pi$
$283$	− 3809.86i	− 0.800256i	0.916459	−	0.400128i	$-0.131034\pi$
$284$	1700.95	0.355396
$285$	0	0
$286$	−1541.71	−0.318752
$287$	− 181.616i	− 0.0373535i
$288$	250.615i	0.0512765i
$289$	−10105.0	−2.05678
$290$	0	0
$291$	5531.00	1.11420
$292$	4436.50i	0.889133i
$293$	− 4958.44i	− 0.988652i	−0.869277	−	0.494326i	$-0.835415\pi$
$293$	− 4958.44i	− 0.988652i	0.869277	−	0.494326i	$-0.164585\pi$
$294$	−4017.10	−0.796878
$295$	0	0
$296$	3240.63	0.636344
$297$	− 4792.76i	− 0.936378i
$298$	2988.83i	0.581001i
$299$	−418.490	−0.0809428
$300$	0	0
$301$	314.643	0.0602516
$302$	803.153i	0.153034i
$303$	− 127.597i	− 0.0241922i
$304$	−1393.36	−0.262878
$305$	0	0
$306$	−1919.52	−0.358600
$307$	− 6103.13i	− 1.13461i	−0.823509	−	0.567303i	$-0.807987\pi$
$307$	− 6103.13i	− 1.13461i	0.823509	−	0.567303i	$-0.192013\pi$
$308$	− 277.098i	− 0.0512634i
$309$	−3005.01	−0.553234
$310$	0	0
$311$	5156.67	0.940219	0.470110	−	0.882608i	$-0.344214\pi$
$311$	5156.67	0.940219	0.470110	+	0.882608i	$0.344214\pi$
$312$	− 859.082i	− 0.155884i
$313$	8640.79i	1.56040i	0.625528	+	0.780202i	$0.284884\pi$
$313$	8640.79i	1.56040i	−0.625528	+	0.780202i	$0.715116\pi$
$314$	−5262.03	−0.945711
$315$	0	0
$316$	4780.65	0.851052
$317$	− 88.2506i	− 0.0156361i	−0.999969	−	0.00781806i	$-0.997511\pi$
$317$	− 88.2506i	− 0.0156361i	0.999969	−	0.00781806i	$-0.00248859\pi$
$318$	− 614.690i	− 0.108397i
$319$	7943.15	1.39414
$320$	0	0
$321$	7491.07	1.30253
$322$	− 75.2170i	− 0.0130176i
$323$	− 10672.1i	− 1.83843i
$324$	3516.48	0.602963
$325$	0	0
$326$	1254.34	0.213103
$327$	− 10783.1i	− 1.82357i
$328$	− 888.558i	− 0.149580i
$329$	−401.327	−0.0672518
$330$	0	0
$331$	−9121.75	−1.51473	−0.757367	−	0.652990i	$-0.773515\pi$
$331$	−9121.75	−1.51473	−0.757367	+	0.652990i	$0.773515\pi$
$332$	5902.35i	0.975704i
$333$	3172.46i	0.522072i
$334$	4991.77	0.817776
$335$	0	0
$336$	154.407	0.0250701
$337$	2934.28i	0.474303i	0.971473	+	0.237152i	$0.0762138\pi$
$337$	2934.28i	0.474303i	−0.971473	+	0.237152i	$0.923786\pi$
$338$	− 3731.87i	− 0.600553i
$339$	−6938.64	−1.11167
$340$	0	0
$341$	7104.82	1.12829
$342$	− 1364.05i	− 0.215671i
$343$	1117.34i	0.175892i
$344$	1539.39	0.241275
$345$	0	0
$346$	5707.16	0.886760
$347$	− 3445.57i	− 0.533049i	−0.963828	−	0.266524i	$-0.914125\pi$
$347$	− 3445.57i	− 0.533049i	0.963828	−	0.266524i	$-0.0858753\pi$
$348$	4426.14i	0.681799i
$349$	10884.1	1.66938	0.834688	−	0.550722i	$-0.185648\pi$
$349$	10884.1	1.66938	0.834688	+	0.550722i	$0.185648\pi$
$350$	0	0
$351$	−2058.39	−0.313016
$352$	− 1355.71i	− 0.205282i
$353$	− 408.637i	− 0.0616135i	−0.999525	−	0.0308067i	$-0.990192\pi$
$353$	− 408.637i	− 0.0616135i	0.999525	−	0.0308067i	$-0.00980764\pi$
$354$	−5017.37	−0.753306
$355$	0	0
$356$	−296.840	−0.0441924
$357$	1182.64i	0.175327i
$358$	− 614.138i	− 0.0906653i
$359$	779.667	0.114622	0.0573109	−	0.998356i	$-0.481747\pi$
$359$	779.667	0.114622	0.0573109	+	0.998356i	$0.481747\pi$
$360$	0	0
$361$	724.837	0.105677
$362$	3467.05i	0.503382i
$363$	− 2737.63i	− 0.395835i
$364$	−119.008	−0.0171366
$365$	0	0
$366$	−7901.82	−1.12851
$367$	− 3815.03i	− 0.542624i	−0.962491	−	0.271312i	$-0.912543\pi$
$367$	− 3815.03i	− 0.542624i	0.962491	−	0.271312i	$-0.0874575\pi$
$368$	− 368.000i	− 0.0521286i
$369$	869.867	0.122719
$370$	0	0
$371$	−85.1524	−0.0119162
$372$	3959.00i	0.551786i
$373$	10833.2i	1.50381i	0.659272	+	0.751904i	$0.270864\pi$
$373$	10833.2i	1.50381i	−0.659272	+	0.751904i	$0.729136\pi$
$374$	10383.7	1.43563
$375$	0	0
$376$	−1963.49	−0.269307
$377$	− 3411.42i	− 0.466039i
$378$	− 369.964i	− 0.0503409i
$379$	−12700.8	−1.72136	−0.860679	−	0.509148i	$-0.829961\pi$
$379$	−12700.8	−1.72136	−0.860679	+	0.509148i	$0.829961\pi$
$380$	0	0
$381$	9779.56	1.31502
$382$	− 4320.76i	− 0.578715i
$383$	3332.12i	0.444553i	0.974984	+	0.222276i	$0.0713487\pi$
$383$	3332.12i	0.444553i	−0.974984	+	0.222276i	$0.928651\pi$
$384$	755.436	0.100392
$385$	0	0
$386$	−7451.55	−0.982575
$387$	1507.01i	0.197948i
$388$	− 3748.66i	− 0.490489i
$389$	−4267.28	−0.556195	−0.278097	−	0.960553i	$-0.589704\pi$
$389$	−4267.28	−0.556195	−0.278097	+	0.960553i	$0.589704\pi$
$390$	0	0
$391$	2818.60	0.364559
$392$	2722.61i	0.350797i
$393$	7118.92i	0.913746i
$394$	−10534.6	−1.34703
$395$	0	0
$396$	1327.19	0.168418
$397$	− 10684.1i	− 1.35068i	−0.737505	−	0.675342i	$-0.763996\pi$
$397$	− 10684.1i	− 1.35068i	0.737505	−	0.675342i	$-0.236004\pi$
$398$	− 380.236i	− 0.0478882i
$399$	−840.408	−0.105446
$400$	0	0
$401$	10178.2	1.26752	0.633760	−	0.773530i	$-0.281511\pi$
$401$	10178.2	1.26752	0.633760	+	0.773530i	$0.281511\pi$
$402$	7806.86i	0.968584i
$403$	− 3051.37i	− 0.377170i
$404$	−86.4791	−0.0106497
$405$	0	0
$406$	613.149	0.0749509
$407$	− 17161.5i	− 2.09008i
$408$	5786.06i	0.702090i
$409$	13759.6	1.66349	0.831744	−	0.555160i	$-0.187343\pi$
$409$	13759.6	1.66349	0.831744	+	0.555160i	$0.187343\pi$
$410$	0	0
$411$	12344.1	1.48148
$412$	2036.66i	0.243541i
$413$	695.052i	0.0828118i
$414$	360.259	0.0427675
$415$	0	0
$416$	−582.247	−0.0686226
$417$	− 245.221i	− 0.0287974i
$418$	7378.87i	0.863426i
$419$	737.389	0.0859757	0.0429878	−	0.999076i	$-0.486312\pi$
$419$	737.389	0.0859757	0.0429878	+	0.999076i	$0.486312\pi$
$420$	0	0
$421$	9700.13	1.12294	0.561468	−	0.827499i	$-0.310237\pi$
$421$	9700.13	1.12294	0.561468	+	0.827499i	$0.310237\pi$
$422$	− 1355.73i	− 0.156389i
$423$	− 1922.19i	− 0.220946i
$424$	−416.609	−0.0477177
$425$	0	0
$426$	5019.36	0.570865
$427$	1094.63i	0.124058i
$428$	− 5077.11i	− 0.573391i
$429$	−4549.46	−0.512005
$430$	0	0
$431$	−1036.16	−0.115800	−0.0579001	−	0.998322i	$-0.518440\pi$
$431$	−1036.16	−0.115800	−0.0579001	+	0.998322i	$0.518440\pi$
$432$	− 1810.05i	− 0.201588i
$433$	12256.9i	1.36034i	0.733053	+	0.680171i	$0.238095\pi$
$433$	12256.9i	1.36034i	−0.733053	+	0.680171i	$0.761905\pi$
$434$	548.436	0.0606585
$435$	0	0
$436$	−7308.30	−0.802762
$437$	2002.96i	0.219255i
$438$	13091.8i	1.42819i
$439$	−11855.5	−1.28891	−0.644455	−	0.764642i	$-0.722916\pi$
$439$	−11855.5	−1.28891	−0.644455	+	0.764642i	$0.722916\pi$
$440$	0	0
$441$	−2665.34	−0.287802
$442$	− 4459.57i	− 0.479910i
$443$	− 9475.12i	− 1.01620i	−0.861298	−	0.508100i	$-0.830348\pi$
$443$	− 9475.12i	− 1.01620i	0.861298	−	0.508100i	$-0.169652\pi$
$444$	9562.84	1.02215
$445$	0	0
$446$	−8429.64	−0.894967
$447$	8819.79i	0.933248i
$448$	− 104.650i	− 0.0110362i
$449$	501.444	0.0527052	0.0263526	−	0.999653i	$-0.491611\pi$
$449$	501.444	0.0527052	0.0263526	+	0.999653i	$0.491611\pi$
$450$	0	0
$451$	−4705.56	−0.491299
$452$	4702.69i	0.489372i
$453$	2370.04i	0.245815i
$454$	6736.57	0.696394
$455$	0	0
$456$	−4111.70	−0.422255
$457$	− 12951.1i	− 1.32566i	−0.748770	−	0.662829i	$-0.769355\pi$
$457$	− 12951.1i	− 1.32566i	0.748770	−	0.662829i	$-0.230645\pi$
$458$	− 2277.01i	− 0.232310i
$459$	13863.6	1.40980
$460$	0	0
$461$	−10829.4	−1.09409	−0.547044	−	0.837104i	$-0.684247\pi$
$461$	−10829.4	−1.09409	−0.547044	+	0.837104i	$0.684247\pi$
$462$	− 817.694i	− 0.0823433i
$463$	− 14228.9i	− 1.42823i	−0.700026	−	0.714117i	$-0.746828\pi$
$463$	− 14228.9i	− 1.42823i	0.700026	−	0.714117i	$-0.253172\pi$
$464$	2999.84	0.300138
$465$	0	0
$466$	−1318.75	−0.131095
$467$	− 11724.0i	− 1.16172i	−0.814003	−	0.580860i	$-0.802716\pi$
$467$	− 11724.0i	− 1.16172i	0.814003	−	0.580860i	$-0.197284\pi$
$468$	− 569.999i	− 0.0562996i
$469$	1081.48	0.106478
$470$	0	0
$471$	−15527.8	−1.51907
$472$	3400.55i	0.331616i
$473$	− 8152.20i	− 0.792471i
$474$	14107.3	1.36703
$475$	0	0
$476$	801.538	0.0771816
$477$	− 407.845i	− 0.0391488i
$478$	2802.35i	0.268152i
$479$	8686.62	0.828605	0.414302	−	0.910139i	$-0.364026\pi$
$479$	8686.62	0.828605	0.414302	+	0.910139i	$0.364026\pi$
$480$	0	0
$481$	−7370.50	−0.698681
$482$	− 7336.31i	− 0.693278i
$483$	− 221.959i	− 0.0209099i
$484$	−1855.44	−0.174252
$485$	0	0
$486$	4267.94	0.398349
$487$	− 7556.93i	− 0.703156i	−0.936159	−	0.351578i	$-0.885645\pi$
$487$	− 7556.93i	− 0.703156i	0.936159	−	0.351578i	$-0.114355\pi$
$488$	5355.50i	0.496787i
$489$	3701.46	0.342302
$490$	0	0
$491$	20466.9	1.88118	0.940591	−	0.339542i	$-0.110272\pi$
$491$	20466.9	1.88118	0.940591	+	0.339542i	$0.110272\pi$
$492$	− 2622.06i	− 0.240268i
$493$	22976.5i	2.09900i
$494$	3169.07	0.288630
$495$	0	0
$496$	2683.23	0.242904
$497$	− 695.327i	− 0.0627559i
$498$	17417.4i	1.56725i
$499$	21514.4	1.93009	0.965046	−	0.262080i	$-0.0844083\pi$
$499$	21514.4	1.93009	0.965046	+	0.262080i	$0.0844083\pi$
$500$	0	0
$501$	14730.3	1.31358
$502$	− 1183.57i	− 0.105229i
$503$	10975.0i	0.972862i	0.873719	+	0.486431i	$0.161702\pi$
$503$	10975.0i	0.972862i	−0.873719	+	0.486431i	$0.838298\pi$
$504$	102.448	0.00905440
$505$	0	0
$506$	−1948.83	−0.171217
$507$	− 11012.4i	− 0.964655i
$508$	− 6628.14i	− 0.578890i
$509$	6282.97	0.547127	0.273563	−	0.961854i	$-0.411798\pi$
$509$	6282.97	0.547127	0.273563	+	0.961854i	$0.411798\pi$
$510$	0	0
$511$	1813.59	0.157003
$512$	− 512.000i	− 0.0441942i
$513$	9851.79i	0.847889i
$514$	4289.49	0.368096
$515$	0	0
$516$	4542.63	0.387554
$517$	10398.1i	0.884543i
$518$	− 1324.73i	− 0.112366i
$519$	16841.4	1.42438
$520$	0	0
$521$	−16517.6	−1.38896	−0.694481	−	0.719511i	$-0.744366\pi$
$521$	−16517.6	−1.38896	−0.694481	+	0.719511i	$0.744366\pi$
$522$	2936.73i	0.246240i
$523$	− 8149.95i	− 0.681400i	−0.940172	−	0.340700i	$-0.889336\pi$
$523$	− 8149.95i	− 0.681400i	0.940172	−	0.340700i	$-0.110664\pi$
$524$	4824.88	0.402244
$525$	0	0
$526$	−7790.99	−0.645824
$527$	20551.5i	1.69874i
$528$	− 4000.58i	− 0.329740i
$529$	−529.000	−0.0434783
$530$	0	0
$531$	−3329.01	−0.272066
$532$	569.591i	0.0464190i
$533$	2020.94i	0.164234i
$534$	−875.951	−0.0709852
$535$	0	0
$536$	5291.14	0.426385
$537$	− 1812.27i	− 0.145634i
$538$	− 6451.29i	− 0.516979i
$539$	14418.2	1.15220
$540$	0	0
$541$	6661.54	0.529394	0.264697	−	0.964332i	$-0.414728\pi$
$541$	6661.54	0.529394	0.264697	+	0.964332i	$0.414728\pi$
$542$	13583.5i	1.07650i
$543$	10231.0i	0.808571i
$544$	3921.53	0.309070
$545$	0	0
$546$	−351.183	−0.0275261
$547$	− 16232.2i	− 1.26881i	−0.773002	−	0.634403i	$-0.781246\pi$
$547$	− 16232.2i	− 1.26881i	0.773002	−	0.634403i	$-0.218754\pi$
$548$	− 8366.28i	− 0.652171i
$549$	−5242.84	−0.407576
$550$	0	0
$551$	−16327.6	−1.26239
$552$	− 1085.94i	− 0.0837330i
$553$	− 1954.27i	− 0.150279i
$554$	−8311.76	−0.637424
$555$	0	0
$556$	−166.200	−0.0126770
$557$	21238.0i	1.61559i	0.589462	+	0.807796i	$0.299340\pi$
$557$	21238.0i	1.61559i	−0.589462	+	0.807796i	$0.700660\pi$
$558$	2626.79i	0.199285i
$559$	−3501.20	−0.264911
$560$	0	0
$561$	30641.4	2.30602
$562$	− 2840.10i	− 0.213172i
$563$	15600.2i	1.16780i	0.811827	+	0.583898i	$0.198473\pi$
$563$	15600.2i	1.16780i	−0.811827	+	0.583898i	$0.801527\pi$
$564$	−5794.11	−0.432582
$565$	0	0
$566$	−7619.71	−0.565866
$567$	− 1437.50i	− 0.106471i
$568$	− 3401.89i	− 0.251303i
$569$	−678.547	−0.0499932	−0.0249966	−	0.999688i	$-0.507957\pi$
$569$	−678.547	−0.0499932	−0.0249966	+	0.999688i	$0.507957\pi$
$570$	0	0
$571$	7228.40	0.529771	0.264885	−	0.964280i	$-0.414666\pi$
$571$	7228.40	0.529771	0.264885	+	0.964280i	$0.414666\pi$
$572$	3083.42i	0.225392i
$573$	− 12750.2i	− 0.929577i
$574$	−363.232	−0.0264129
$575$	0	0
$576$	501.230	0.0362579
$577$	6170.01i	0.445166i	0.974914	+	0.222583i	$0.0714488\pi$
$577$	6170.01i	0.445166i	−0.974914	+	0.222583i	$0.928551\pi$
$578$	20209.9i	1.45436i
$579$	−21988.9	−1.57829
$580$	0	0
$581$	2412.81	0.172290
$582$	− 11062.0i	− 0.787861i
$583$	2206.25i	0.156730i
$584$	8873.01	0.628712
$585$	0	0
$586$	−9916.88	−0.699082
$587$	5074.72i	0.356825i	0.983956	+	0.178412i	$0.0570961\pi$
$587$	5074.72i	0.356825i	−0.983956	+	0.178412i	$0.942904\pi$
$588$	8034.20i	0.563478i
$589$	−14604.4	−1.02167
$590$	0	0
$591$	−31086.9	−2.16370
$592$	− 6481.26i	− 0.449963i
$593$	1668.31i	0.115530i	0.998330	+	0.0577649i	$0.0183974\pi$
$593$	1668.31i	0.115530i	−0.998330	+	0.0577649i	$0.981603\pi$
$594$	−9585.53	−0.662119
$595$	0	0
$596$	5977.66	0.410829
$597$	− 1122.04i	− 0.0769217i
$598$	836.980i	0.0572352i
$599$	3896.54	0.265790	0.132895	−	0.991130i	$-0.457573\pi$
$599$	3896.54	0.265790	0.132895	+	0.991130i	$0.457573\pi$
$600$	0	0
$601$	−6319.03	−0.428883	−0.214441	−	0.976737i	$-0.568793\pi$
$601$	−6319.03	−0.428883	−0.214441	+	0.976737i	$0.568793\pi$
$602$	− 629.286i	− 0.0426043i
$603$	5179.84i	0.349816i
$604$	1606.31	0.108211
$605$	0	0
$606$	−255.193	−0.0171064
$607$	26623.5i	1.78025i	0.455714	+	0.890126i	$0.349384\pi$
$607$	26623.5i	1.78025i	−0.455714	+	0.890126i	$0.650616\pi$
$608$	2786.73i	0.185883i
$609$	1809.35	0.120392
$610$	0	0
$611$	4465.77	0.295689
$612$	3839.04i	0.253569i
$613$	5819.80i	0.383458i	0.981448	+	0.191729i	$0.0614094\pi$
$613$	5819.80i	0.383458i	−0.981448	+	0.191729i	$0.938591\pi$
$614$	−12206.3	−0.802287
$615$	0	0
$616$	−554.196	−0.0362487
$617$	9816.46i	0.640512i	0.947331	+	0.320256i	$0.103769\pi$
$617$	9816.46i	0.640512i	−0.947331	+	0.320256i	$0.896231\pi$
$618$	6010.02i	0.391195i
$619$	14246.0	0.925029	0.462515	−	0.886612i	$-0.346947\pi$
$619$	14246.0	0.925029	0.462515	+	0.886612i	$0.346947\pi$
$620$	0	0
$621$	−2601.95	−0.168136
$622$	− 10313.3i	− 0.664835i
$623$	121.345i	0.00780348i
$624$	−1718.16	−0.110227
$625$	0	0
$626$	17281.6	1.10337
$627$	21774.4i	1.38690i
$628$	10524.1i	0.668719i
$629$	49641.5	3.14680
$630$	0	0
$631$	−7637.96	−0.481874	−0.240937	−	0.970541i	$-0.577455\pi$
$631$	−7637.96	−0.481874	−0.240937	+	0.970541i	$0.577455\pi$
$632$	− 9561.29i	− 0.601785i
$633$	− 4000.66i	− 0.251204i
$634$	−176.501	−0.0110564
$635$	0	0
$636$	−1229.38	−0.0766479
$637$	− 6192.31i	− 0.385162i
$638$	− 15886.3i	− 0.985807i
$639$	3330.33	0.206175
$640$	0	0
$641$	−15541.7	−0.957663	−0.478831	−	0.877907i	$-0.658940\pi$
$641$	−15541.7	−0.957663	−0.478831	+	0.877907i	$0.658940\pi$
$642$	− 14982.1i	− 0.921025i
$643$	− 7899.02i	− 0.484459i	−0.970219	−	0.242229i	$-0.922121\pi$
$643$	− 7899.02i	− 0.484459i	0.970219	−	0.242229i	$-0.0778787\pi$
$644$	−150.434	−0.00920486
$645$	0	0
$646$	−21344.2	−1.29996
$647$	− 23848.3i	− 1.44911i	−0.689219	−	0.724553i	$-0.742046\pi$
$647$	− 23848.3i	− 1.44911i	0.689219	−	0.724553i	$-0.257954\pi$
$648$	− 7032.96i	− 0.426359i
$649$	18008.4	1.08920
$650$	0	0
$651$	1618.39	0.0974344
$652$	− 2508.68i	− 0.150686i
$653$	− 6308.32i	− 0.378046i	−0.981973	−	0.189023i	$-0.939468\pi$
$653$	− 6308.32i	− 0.378046i	0.981973	−	0.189023i	$-0.0605320\pi$
$654$	−21566.2	−1.28946
$655$	0	0
$656$	−1777.12	−0.105769
$657$	8686.36i	0.515810i
$658$	802.653i	0.0475542i
$659$	−16683.7	−0.986196	−0.493098	−	0.869974i	$-0.664136\pi$
$659$	−16683.7	−0.986196	−0.493098	+	0.869974i	$0.664136\pi$
$660$	0	0
$661$	1994.62	0.117370	0.0586850	−	0.998277i	$-0.481309\pi$
$661$	1994.62	0.117370	0.0586850	+	0.998277i	$0.481309\pi$
$662$	18243.5i	1.07108i
$663$	− 13159.8i	− 0.770868i
$664$	11804.7	0.689927
$665$	0	0
$666$	6344.92	0.369160
$667$	− 4312.26i	− 0.250332i
$668$	− 9983.53i	− 0.578255i
$669$	−24875.2	−1.43756
$670$	0	0
$671$	28361.2	1.63170
$672$	− 308.813i	− 0.0177273i
$673$	19202.9i	1.09988i	0.835205	+	0.549939i	$0.185349\pi$
$673$	19202.9i	1.09988i	−0.835205	+	0.549939i	$0.814651\pi$
$674$	5868.55	0.335383
$675$	0	0
$676$	−7463.74	−0.424655
$677$	− 9478.33i	− 0.538083i	−0.963129	−	0.269041i	$-0.913293\pi$
$677$	− 9478.33i	− 0.538083i	0.963129	−	0.269041i	$-0.0867068\pi$
$678$	13877.3i	0.786067i
$679$	−1532.41	−0.0866104
$680$	0	0
$681$	19879.1	1.11860
$682$	− 14209.6i	− 0.797823i
$683$	− 12019.1i	− 0.673348i	−0.941621	−	0.336674i	$-0.890698\pi$
$683$	− 12019.1i	− 0.673348i	0.941621	−	0.336674i	$-0.109302\pi$
$684$	−2728.11	−0.152503
$685$	0	0
$686$	2234.69	0.124374
$687$	− 6719.29i	− 0.373154i
$688$	− 3078.79i	− 0.170607i
$689$	947.536	0.0523923
$690$	0	0
$691$	9605.96	0.528839	0.264420	−	0.964408i	$-0.414820\pi$
$691$	9605.96	0.528839	0.264420	+	0.964408i	$0.414820\pi$
$692$	− 11414.3i	− 0.627034i
$693$	− 542.538i	− 0.0297393i
$694$	−6891.14	−0.376922
$695$	0	0
$696$	8852.28	0.482104
$697$	− 13611.4i	− 0.739694i
$698$	− 21768.2i	− 1.18043i
$699$	−3891.53	−0.210574
$700$	0	0
$701$	1557.50	0.0839170	0.0419585	−	0.999119i	$-0.486640\pi$
$701$	1557.50	0.0839170	0.0419585	+	0.999119i	$0.486640\pi$
$702$	4116.78i	0.221336i
$703$	35276.4i	1.89257i
$704$	−2711.41	−0.145156
$705$	0	0
$706$	−817.274	−0.0435673
$707$	35.3517i	0.00188053i
$708$	10034.7i	0.532668i
$709$	29539.5	1.56471	0.782354	−	0.622834i	$-0.214019\pi$
$709$	29539.5	1.56471	0.782354	+	0.622834i	$0.214019\pi$
$710$	0	0
$711$	9360.17	0.493718
$712$	593.680i	0.0312487i
$713$	− 3857.14i	− 0.202596i
$714$	2365.27	0.123975
$715$	0	0
$716$	−1228.28	−0.0641101
$717$	8269.52i	0.430727i
$718$	− 1559.33i	− 0.0810499i
$719$	20393.6	1.05780	0.528898	−	0.848686i	$-0.322606\pi$
$719$	20393.6	1.05780	0.528898	+	0.848686i	$0.322606\pi$
$720$	0	0
$721$	832.563	0.0430045
$722$	− 1449.67i	− 0.0747248i
$723$	− 21648.9i	− 1.11360i
$724$	6934.10	0.355945
$725$	0	0
$726$	−5475.25	−0.279898
$727$	27602.9i	1.40816i	0.710119	+	0.704082i	$0.248641\pi$
$727$	27602.9i	1.40816i	−0.710119	+	0.704082i	$0.751359\pi$
$728$	238.016i	0.0121174i
$729$	−11141.9	−0.566068
$730$	0	0
$731$	23581.2	1.19313
$732$	15803.6i	0.797978i
$733$	28300.4i	1.42606i	0.701136	+	0.713028i	$0.252677\pi$
$733$	28300.4i	1.42606i	−0.701136	+	0.713028i	$0.747323\pi$
$734$	−7630.06	−0.383693
$735$	0	0
$736$	−736.000	−0.0368605
$737$	− 28020.4i	− 1.40047i
$738$	− 1739.73i	− 0.0867757i
$739$	643.235	0.0320187	0.0160093	−	0.999872i	$-0.494904\pi$
$739$	643.235	0.0320187	0.0160093	+	0.999872i	$0.494904\pi$
$740$	0	0
$741$	9351.67	0.463620
$742$	170.305i	0.00842600i
$743$	27212.6i	1.34365i	0.740709	+	0.671826i	$0.234490\pi$
$743$	27212.6i	1.34365i	−0.740709	+	0.671826i	$0.765510\pi$
$744$	7918.00	0.390172
$745$	0	0
$746$	21666.4	1.06335
$747$	11556.4i	0.566032i
$748$	− 20767.3i	− 1.01515i
$749$	−2075.46	−0.101249
$750$	0	0
$751$	−6331.75	−0.307655	−0.153827	−	0.988098i	$-0.549160\pi$
$751$	−6331.75	−0.307655	−0.153827	+	0.988098i	$0.549160\pi$
$752$	3926.99i	0.190429i
$753$	− 3492.61i	− 0.169028i
$754$	−6822.83	−0.329540
$755$	0	0
$756$	−739.927	−0.0355964
$757$	13949.1i	0.669734i	0.942265	+	0.334867i	$0.108691\pi$
$757$	13949.1i	0.669734i	−0.942265	+	0.334867i	$0.891309\pi$
$758$	25401.5i	1.21718i
$759$	−5750.83	−0.275022
$760$	0	0
$761$	16217.5	0.772517	0.386258	−	0.922391i	$-0.373767\pi$
$761$	16217.5	0.772517	0.386258	+	0.922391i	$0.373767\pi$
$762$	− 19559.1i	− 0.929859i
$763$	2987.55i	0.141752i
$764$	−8641.52	−0.409213
$765$	0	0
$766$	6664.25	0.314346
$767$	− 7734.21i	− 0.364102i
$768$	− 1510.87i	− 0.0709881i
$769$	−2419.50	−0.113458	−0.0567291	−	0.998390i	$-0.518067\pi$
$769$	−2419.50	−0.113458	−0.0567291	+	0.998390i	$0.518067\pi$
$770$	0	0
$771$	12657.9	0.591264
$772$	14903.1i	0.694785i
$773$	− 20853.3i	− 0.970299i	−0.874431	−	0.485150i	$-0.838765\pi$
$773$	− 20853.3i	− 0.970299i	0.874431	−	0.485150i	$-0.161235\pi$
$774$	3014.02	0.139970
$775$	0	0
$776$	−7497.33	−0.346828
$777$	− 3909.18i	− 0.180490i
$778$	8534.56i	0.393289i
$779$	9672.53	0.444871
$780$	0	0
$781$	−18015.5	−0.825409
$782$	− 5637.20i	− 0.257782i
$783$	− 21210.4i	− 0.968067i
$784$	5445.22	0.248051
$785$	0	0
$786$	14237.8	0.646116
$787$	− 9499.10i	− 0.430249i	−0.976587	−	0.215125i	$-0.930984\pi$
$787$	− 9499.10i	− 0.430249i	0.976587	−	0.215125i	$-0.0690158\pi$
$788$	21069.3i	0.952491i
$789$	−22990.6	−1.03737
$790$	0	0
$791$	1922.41	0.0864132
$792$	− 2654.37i	− 0.119090i
$793$	− 12180.6i	− 0.545453i
$794$	−21368.3	−0.955078
$795$	0	0
$796$	−760.471	−0.0338620
$797$	19087.7i	0.848334i	0.905584	+	0.424167i	$0.139433\pi$
$797$	19087.7i	0.848334i	−0.905584	+	0.424167i	$0.860567\pi$
$798$	1680.82i	0.0745617i
$799$	−30077.7	−1.33176
$800$	0	0
$801$	−581.191	−0.0256372
$802$	− 20356.4i	− 0.896272i
$803$	− 46989.0i	− 2.06501i
$804$	15613.7	0.684892
$805$	0	0
$806$	−6102.74	−0.266700
$807$	− 19037.2i	− 0.830412i
$808$	172.958i	0.00753051i
$809$	−34482.0	−1.49855	−0.749273	−	0.662262i	$-0.769597\pi$
$809$	−34482.0	−1.49855	−0.749273	+	0.662262i	$0.769597\pi$
$810$	0	0
$811$	−17807.0	−0.771009	−0.385505	−	0.922706i	$-0.625973\pi$
$811$	−17807.0	−0.771009	−0.385505	+	0.922706i	$0.625973\pi$
$812$	− 1226.30i	− 0.0529983i
$813$	40083.8i	1.72915i
$814$	−34323.0	−1.47791
$815$	0	0
$816$	11572.1	0.496453
$817$	16757.3i	0.717582i
$818$	− 27519.1i	− 1.17626i
$819$	−233.009	−0.00994138
$820$	0	0
$821$	15030.8	0.638950	0.319475	−	0.947595i	$-0.396493\pi$
$821$	15030.8	0.638950	0.319475	+	0.947595i	$0.396493\pi$
$822$	− 24688.2i	− 1.04757i
$823$	21668.9i	0.917775i	0.888494	+	0.458888i	$0.151752\pi$
$823$	21668.9i	0.917775i	−0.888494	+	0.458888i	$0.848248\pi$
$824$	4073.32	0.172210
$825$	0	0
$826$	1390.10	0.0585568
$827$	8174.05i	0.343699i	0.985123	+	0.171850i	$0.0549743\pi$
$827$	8174.05i	0.343699i	−0.985123	+	0.171850i	$0.945026\pi$
$828$	− 720.518i	− 0.0302412i
$829$	−22775.9	−0.954211	−0.477106	−	0.878846i	$-0.658314\pi$
$829$	−22775.9	−0.954211	−0.477106	+	0.878846i	$0.658314\pi$
$830$	0	0
$831$	−24527.3	−1.02388
$832$	1164.49i	0.0485235i
$833$	41706.2i	1.73474i
$834$	−490.442	−0.0203628
$835$	0	0
$836$	14757.7	0.610535
$837$	− 18971.8i	− 0.783467i
$838$	− 1474.78i	− 0.0607940i
$839$	4543.66	0.186966	0.0934831	−	0.995621i	$-0.470200\pi$
$839$	4543.66	0.186966	0.0934831	+	0.995621i	$0.470200\pi$
$840$	0	0
$841$	10763.4	0.441322
$842$	− 19400.3i	− 0.794035i
$843$	− 8380.92i	− 0.342413i
$844$	−2711.46	−0.110583
$845$	0	0
$846$	−3844.38	−0.156232
$847$	758.481i	0.0307695i
$848$	833.218i	0.0337415i
$849$	−22485.2	−0.908938
$850$	0	0
$851$	−9316.81	−0.375295
$852$	− 10038.7i	− 0.403663i
$853$	− 13198.5i	− 0.529785i	−0.964278	−	0.264892i	$-0.914664\pi$
$853$	− 13198.5i	− 0.529785i	0.964278	−	0.264892i	$-0.0853364\pi$
$854$	2189.26	0.0877226
$855$	0	0
$856$	−10154.2	−0.405449
$857$	− 8209.19i	− 0.327212i	−0.986526	−	0.163606i	$-0.947687\pi$
$857$	− 8209.19i	− 0.327212i	0.986526	−	0.163606i	$-0.0523125\pi$
$858$	9098.92i	0.362042i
$859$	2296.20	0.0912055	0.0456027	−	0.998960i	$-0.485479\pi$
$859$	2296.20	0.0912055	0.0456027	+	0.998960i	$0.485479\pi$
$860$	0	0
$861$	−1071.87	−0.0424265
$862$	2072.31i	0.0818831i
$863$	− 35083.8i	− 1.38385i	−0.721967	−	0.691927i	$-0.756762\pi$
$863$	− 35083.8i	− 1.38385i	0.721967	−	0.691927i	$-0.243238\pi$
$864$	−3620.10	−0.142544
$865$	0	0
$866$	24513.8	0.961908
$867$	59637.9i	2.33611i
$868$	− 1096.87i	− 0.0428920i
$869$	−50634.0	−1.97657
$870$	0	0
$871$	−12034.2	−0.468154
$872$	14616.6i	0.567638i
$873$	− 7339.62i	− 0.284546i
$874$	4005.92	0.155037
$875$	0	0
$876$	26183.5	1.00989
$877$	13761.2i	0.529854i	0.964268	+	0.264927i	$0.0853479\pi$
$877$	13761.2i	0.529854i	−0.964268	+	0.264927i	$0.914652\pi$
$878$	23711.0i	0.911397i
$879$	−29263.9	−1.12292
$880$	0	0
$881$	35260.1	1.34840	0.674202	−	0.738547i	$-0.264488\pi$
$881$	35260.1	1.34840	0.674202	+	0.738547i	$0.264488\pi$
$882$	5330.68i	0.203507i
$883$	− 21770.3i	− 0.829704i	−0.909889	−	0.414852i	$-0.863833\pi$
$883$	− 21770.3i	− 0.829704i	0.909889	−	0.414852i	$-0.136167\pi$
$884$	−8919.14	−0.339347
$885$	0	0
$886$	−18950.2	−0.718562
$887$	− 6289.26i	− 0.238075i	−0.992890	−	0.119038i	$-0.962019\pi$
$887$	− 6289.26i	− 0.238075i	0.992890	−	0.119038i	$-0.0379809\pi$
$888$	− 19125.7i	− 0.722766i
$889$	−2709.51	−0.102220
$890$	0	0
$891$	−37244.6	−1.40038
$892$	16859.3i	0.632837i
$893$	− 21373.9i	− 0.800953i
$894$	17639.6	0.659906
$895$	0	0
$896$	−209.300	−0.00780380
$897$	2469.86i	0.0919356i
$898$	− 1002.89i	− 0.0372682i
$899$	31442.4	1.16648
$900$	0	0
$901$	−6381.82	−0.235970
$902$	9411.11i	0.347401i
$903$	− 1856.97i	− 0.0684343i
$904$	9405.39	0.346038
$905$	0	0
$906$	4740.08	0.173818
$907$	− 19725.0i	− 0.722115i	−0.932543	−	0.361058i	$-0.882416\pi$
$907$	− 19725.0i	− 0.722115i	0.932543	−	0.361058i	$-0.117584\pi$
$908$	− 13473.1i	− 0.492425i
$909$	−169.320	−0.00617821
$910$	0	0
$911$	−13617.4	−0.495241	−0.247620	−	0.968857i	$-0.579649\pi$
$911$	−13617.4	−0.495241	−0.247620	+	0.968857i	$0.579649\pi$
$912$	8223.41i	0.298579i
$913$	− 62514.4i	− 2.26607i
$914$	−25902.2	−0.937382
$915$	0	0
$916$	−4554.03	−0.164268
$917$	− 1972.35i	− 0.0710282i
$918$	− 27727.2i	− 0.996878i
$919$	12440.7	0.446553	0.223276	−	0.974755i	$-0.428325\pi$
$919$	12440.7	0.446553	0.223276	+	0.974755i	$0.428325\pi$
$920$	0	0
$921$	−36019.7	−1.28870
$922$	21658.7i	0.773636i
$923$	7737.27i	0.275921i
$924$	−1635.39	−0.0582255
$925$	0	0
$926$	−28457.8	−1.00991
$927$	3987.64i	0.141285i
$928$	− 5999.67i	− 0.212229i
$929$	6881.48	0.243029	0.121515	−	0.992590i	$-0.461225\pi$
$929$	6881.48	0.243029	0.121515	+	0.992590i	$0.461225\pi$
$930$	0	0
$931$	−29637.4	−1.04332
$932$	2637.51i	0.0926978i
$933$	− 30433.9i	− 1.06791i
$934$	−23448.1	−0.821461
$935$	0	0
$936$	−1140.00	−0.0398098
$937$	44549.4i	1.55322i	0.629983	+	0.776609i	$0.283062\pi$
$937$	44549.4i	1.55322i	−0.629983	+	0.776609i	$0.716938\pi$
$938$	− 2162.95i	− 0.0752910i
$939$	50996.5	1.77232
$940$	0	0
$941$	−53673.0	−1.85939	−0.929697	−	0.368324i	$-0.879932\pi$
$941$	−53673.0	−1.85939	−0.929697	+	0.368324i	$0.879932\pi$
$942$	31055.6i	1.07415i
$943$	2554.60i	0.0882178i
$944$	6801.09	0.234488
$945$	0	0
$946$	−16304.4	−0.560362
$947$	15772.6i	0.541226i	0.962688	+	0.270613i	$0.0872263\pi$
$947$	15772.6i	0.541226i	−0.962688	+	0.270613i	$0.912774\pi$
$948$	− 28214.6i	− 0.966633i
$949$	−20180.8	−0.690302
$950$	0	0
$951$	−520.841	−0.0177596
$952$	− 1603.08i	− 0.0545756i
$953$	33796.2i	1.14876i	0.818589	+	0.574379i	$0.194756\pi$
$953$	33796.2i	1.14876i	−0.818589	+	0.574379i	$0.805244\pi$
$954$	−815.691	−0.0276824
$955$	0	0
$956$	5604.71	0.189612
$957$	− 46879.2i	− 1.58348i
$958$	− 17373.2i	− 0.585912i
$959$	−3420.04	−0.115160
$960$	0	0
$961$	−1667.08	−0.0559591
$962$	14741.0i	0.494042i
$963$	− 9940.62i	− 0.332640i
$964$	−14672.6	−0.490221
$965$	0	0
$966$	−443.919	−0.0147856
$967$	− 36502.1i	− 1.21389i	−0.794745	−	0.606944i	$-0.792395\pi$
$967$	− 36502.1i	− 1.21389i	0.794745	−	0.606944i	$-0.207605\pi$
$968$	3710.88i	0.123215i
$969$	−62985.1	−2.08810
$970$	0	0
$971$	−23238.4	−0.768029	−0.384014	−	0.923327i	$-0.625459\pi$
$971$	−23238.4	−0.768029	−0.384014	+	0.923327i	$0.625459\pi$
$972$	− 8535.88i	− 0.281675i
$973$	67.9404i	0.00223851i
$974$	−15113.9	−0.497207
$975$	0	0
$976$	10711.0	0.351281
$977$	4074.86i	0.133435i	0.997772	+	0.0667177i	$0.0212527\pi$
$977$	4074.86i	0.133435i	−0.997772	+	0.0667177i	$0.978747\pi$
$978$	− 7402.91i	− 0.242044i
$979$	3143.96	0.102637
$980$	0	0
$981$	−14309.1	−0.465704
$982$	− 40933.9i	− 1.33020i
$983$	− 41839.4i	− 1.35755i	−0.734347	−	0.678775i	$-0.762511\pi$
$983$	− 41839.4i	− 1.35755i	0.734347	−	0.678775i	$-0.237489\pi$
$984$	−5244.13	−0.169895
$985$	0	0
$986$	45952.9	1.48422
$987$	2368.57i	0.0763853i
$988$	− 6338.14i	− 0.204092i
$989$	−4425.76	−0.142296
$990$	0	0
$991$	−30214.8	−0.968521	−0.484260	−	0.874924i	$-0.660911\pi$
$991$	−30214.8	−0.968521	−0.484260	+	0.874924i	$0.660911\pi$
$992$	− 5366.46i	− 0.171759i
$993$	53835.1i	1.72045i
$994$	−1390.65	−0.0443751
$995$	0	0
$996$	34834.7	1.10821
$997$	23509.3i	0.746788i	0.927673	+	0.373394i	$0.121806\pi$
$997$	23509.3i	0.746788i	−0.927673	+	0.373394i	$0.878194\pi$
$998$	− 43028.8i	− 1.36478i
$999$	−45825.8	−1.45132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.b.s.599.2		12
5.2	odd	4		1150.4.a.x.1.2	yes	6
5.3	odd	4		1150.4.a.w.1.5	✓	6
5.4	even	2	inner	1150.4.b.s.599.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.4.a.w.1.5	✓	6	5.3	odd	4
1150.4.a.x.1.2	yes	6	5.2	odd	4
1150.4.b.s.599.2		12	1.1	even	1	trivial
1150.4.b.s.599.11		12	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -5.90184i q^{3} -4.00000 q^{4} -11.8037 q^{6} +1.63515i q^{7} +8.00000i q^{8} -7.83172 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} -5.90184i q^{3} -4.00000 q^{4} -11.8037 q^{6} +1.63515i q^{7} +8.00000i q^{8} -7.83172 q^{9} +42.3658 q^{11} +23.6074i q^{12} -18.1952i q^{13} +3.27031 q^{14} +16.0000 q^{16} +122.548i q^{17} +15.6634i q^{18} -87.0852 q^{19} +9.65041 q^{21} -84.7316i q^{22} -23.0000i q^{23} +47.2147 q^{24} -36.3904 q^{26} -113.128i q^{27} -6.54061i q^{28} +187.490 q^{29} +167.702 q^{31} -32.0000i q^{32} -250.036i q^{33} +245.096 q^{34} +31.3269 q^{36} -405.079i q^{37} +174.170i q^{38} -107.385 q^{39} -111.070 q^{41} -19.3008i q^{42} -192.424i q^{43} -169.463 q^{44} -46.0000 q^{46} +245.437i q^{47} -94.4294i q^{48} +340.326 q^{49} +723.258 q^{51} +72.7809i q^{52} +52.0761i q^{53} -226.256 q^{54} -13.0812 q^{56} +513.963i q^{57} -374.979i q^{58} +425.068 q^{59} +669.437 q^{61} -335.404i q^{62} -12.8061i q^{63} -64.0000 q^{64} -500.072 q^{66} -661.392i q^{67} -490.191i q^{68} -135.742 q^{69} -425.237 q^{71} -62.6537i q^{72} -1109.13i q^{73} -810.158 q^{74} +348.341 q^{76} +69.2745i q^{77} +214.771i q^{78} -1195.16 q^{79} -879.121 q^{81} +222.139i q^{82} -1475.59i q^{83} -38.6016 q^{84} -384.849 q^{86} -1106.53i q^{87} +338.926i q^{88} +74.2100 q^{89} +29.7520 q^{91} +92.0000i q^{92} -989.750i q^{93} +490.874 q^{94} -188.859 q^{96} +937.166i q^{97} -680.653i q^{98} -331.797 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 48 q^{4} - 20 q^{6} - 122 q^{9}+O(q^{10}) \) 12 * q - 48 * q^4 - 20 * q^6 - 122 * q^9	\( 12 q - 48 q^{4} - 20 q^{6} - 122 q^{9} - 98 q^{11} + 168 q^{14} + 192 q^{16} + 458 q^{19} + 184 q^{21} + 80 q^{24} - 64 q^{26} + 364 q^{29} + 228 q^{31} + 700 q^{34} + 488 q^{36} + 286 q^{39} + 486 q^{41} + 392 q^{44} - 552 q^{46} - 1296 q^{49} - 2062 q^{51} + 1376 q^{54} - 672 q^{56} + 1118 q^{59} - 1376 q^{61} - 768 q^{64} - 2564 q^{66} - 230 q^{69} + 1168 q^{71} + 256 q^{74} - 1832 q^{76} + 2864 q^{79} + 68 q^{81} - 736 q^{84} - 728 q^{86} + 1182 q^{89} - 5728 q^{91} + 1992 q^{94} - 320 q^{96} + 284 q^{99}+O(q^{100}) \) 12 * q - 48 * q^4 - 20 * q^6 - 122 * q^9 - 98 * q^11 + 168 * q^14 + 192 * q^16 + 458 * q^19 + 184 * q^21 + 80 * q^24 - 64 * q^26 + 364 * q^29 + 228 * q^31 + 700 * q^34 + 488 * q^36 + 286 * q^39 + 486 * q^41 + 392 * q^44 - 552 * q^46 - 1296 * q^49 - 2062 * q^51 + 1376 * q^54 - 672 * q^56 + 1118 * q^59 - 1376 * q^61 - 768 * q^64 - 2564 * q^66 - 230 * q^69 + 1168 * q^71 + 256 * q^74 - 1832 * q^76 + 2864 * q^79 + 68 * q^81 - 736 * q^84 - 728 * q^86 + 1182 * q^89 - 5728 * q^91 + 1992 * q^94 - 320 * q^96 + 284 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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