LMFDB - Embedded newform 825.4.c.b.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("825.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.b.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.00000i q^{2} +3.00000i q^{3} -17.0000 q^{4} +15.0000 q^{6} -3.00000i q^{7} +45.0000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-5.00000i q^{2} +3.00000i q^{3} -17.0000 q^{4} +15.0000 q^{6} -3.00000i q^{7} +45.0000i q^{8} -9.00000 q^{9} -11.0000 q^{11} -51.0000i q^{12} +32.0000i q^{13} -15.0000 q^{14} +89.0000 q^{16} -33.0000i q^{17} +45.0000i q^{18} -47.0000 q^{19} +9.00000 q^{21} +55.0000i q^{22} +113.000i q^{23} -135.000 q^{24} +160.000 q^{26} -27.0000i q^{27} +51.0000i q^{28} +54.0000 q^{29} +178.000 q^{31} -85.0000i q^{32} -33.0000i q^{33} -165.000 q^{34} +153.000 q^{36} -19.0000i q^{37} +235.000i q^{38} -96.0000 q^{39} +139.000 q^{41} -45.0000i q^{42} -308.000i q^{43} +187.000 q^{44} +565.000 q^{46} -195.000i q^{47} +267.000i q^{48} +334.000 q^{49} +99.0000 q^{51} -544.000i q^{52} +152.000i q^{53} -135.000 q^{54} +135.000 q^{56} -141.000i q^{57} -270.000i q^{58} +625.000 q^{59} +320.000 q^{61} -890.000i q^{62} +27.0000i q^{63} +287.000 q^{64} -165.000 q^{66} -200.000i q^{67} +561.000i q^{68} -339.000 q^{69} -947.000 q^{71} -405.000i q^{72} -448.000i q^{73} -95.0000 q^{74} +799.000 q^{76} +33.0000i q^{77} +480.000i q^{78} +721.000 q^{79} +81.0000 q^{81} -695.000i q^{82} +142.000i q^{83} -153.000 q^{84} -1540.00 q^{86} +162.000i q^{87} -495.000i q^{88} -404.000 q^{89} +96.0000 q^{91} -1921.00i q^{92} +534.000i q^{93} -975.000 q^{94} +255.000 q^{96} -79.0000i q^{97} -1670.00i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 34 q^{4} + 30 q^{6} - 18 q^{9}+O(q^{10}) $ 2 * q - 34 * q^4 + 30 * q^6 - 18 * q^9	$ 2 q - 34 q^{4} + 30 q^{6} - 18 q^{9} - 22 q^{11} - 30 q^{14} + 178 q^{16} - 94 q^{19} + 18 q^{21} - 270 q^{24} + 320 q^{26} + 108 q^{29} + 356 q^{31} - 330 q^{34} + 306 q^{36} - 192 q^{39} + 278 q^{41} + 374 q^{44} + 1130 q^{46} + 668 q^{49} + 198 q^{51} - 270 q^{54} + 270 q^{56} + 1250 q^{59} + 640 q^{61} + 574 q^{64} - 330 q^{66} - 678 q^{69} - 1894 q^{71} - 190 q^{74} + 1598 q^{76} + 1442 q^{79} + 162 q^{81} - 306 q^{84} - 3080 q^{86} - 808 q^{89} + 192 q^{91} - 1950 q^{94} + 510 q^{96} + 198 q^{99}+O(q^{100}) $ 2 * q - 34 * q^4 + 30 * q^6 - 18 * q^9 - 22 * q^11 - 30 * q^14 + 178 * q^16 - 94 * q^19 + 18 * q^21 - 270 * q^24 + 320 * q^26 + 108 * q^29 + 356 * q^31 - 330 * q^34 + 306 * q^36 - 192 * q^39 + 278 * q^41 + 374 * q^44 + 1130 * q^46 + 668 * q^49 + 198 * q^51 - 270 * q^54 + 270 * q^56 + 1250 * q^59 + 640 * q^61 + 574 * q^64 - 330 * q^66 - 678 * q^69 - 1894 * q^71 - 190 * q^74 + 1598 * q^76 + 1442 * q^79 + 162 * q^81 - 306 * q^84 - 3080 * q^86 - 808 * q^89 + 192 * q^91 - 1950 * q^94 + 510 * q^96 + 198 * 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 $

$2$	− 5.00000i	− 1.76777i	−0.467707	−	0.883883i	$-0.654920\pi$
$2$	− 5.00000i	− 1.76777i	0.467707	−	0.883883i	$-0.345080\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−17.0000	−2.12500
$5$	0	0
$5$	0	0
$6$	15.0000	1.02062
$7$	− 3.00000i	− 0.161985i	−0.996715	−	0.0809924i	$-0.974191\pi$
$7$	− 3.00000i	− 0.161985i	0.996715	−	0.0809924i	$-0.0258089\pi$
$8$	45.0000i	1.98874i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	− 51.0000i	− 1.22687i
$13$	32.0000i	0.682708i	0.939935	+	0.341354i	$0.110885\pi$
$13$	32.0000i	0.682708i	−0.939935	+	0.341354i	$0.889115\pi$
$14$	−15.0000	−0.286351
$15$	0	0
$16$	89.0000	1.39062
$17$	− 33.0000i	− 0.470804i	−0.971898	−	0.235402i	$-0.924359\pi$
$17$	− 33.0000i	− 0.470804i	0.971898	−	0.235402i	$-0.0756407\pi$
$18$	45.0000i	0.589256i
$19$	−47.0000	−0.567502	−0.283751	−	0.958898i	$-0.591579\pi$
$19$	−47.0000	−0.567502	−0.283751	+	0.958898i	$0.591579\pi$
$20$	0	0
$21$	9.00000	0.0935220
$22$	55.0000i	0.533002i
$23$	113.000i	1.02444i	0.858854	+	0.512220i	$0.171177\pi$
$23$	113.000i	1.02444i	−0.858854	+	0.512220i	$0.828823\pi$
$24$	−135.000	−1.14820
$25$	0	0
$26$	160.000	1.20687
$27$	− 27.0000i	− 0.192450i
$28$	51.0000i	0.344218i
$29$	54.0000	0.345778	0.172889	−	0.984941i	$-0.444690\pi$
$29$	54.0000	0.345778	0.172889	+	0.984941i	$0.444690\pi$
$30$	0	0
$31$	178.000	1.03128	0.515641	−	0.856805i	$-0.327554\pi$
$31$	178.000	1.03128	0.515641	+	0.856805i	$0.327554\pi$
$32$	− 85.0000i	− 0.469563i
$33$	− 33.0000i	− 0.174078i
$34$	−165.000	−0.832273
$35$	0	0
$36$	153.000	0.708333
$37$	− 19.0000i	− 0.0844211i	−0.999109	−	0.0422106i	$-0.986560\pi$
$37$	− 19.0000i	− 0.0844211i	0.999109	−	0.0422106i	$-0.0134400\pi$
$38$	235.000i	1.00321i
$39$	−96.0000	−0.394162
$40$	0	0
$41$	139.000	0.529467	0.264734	−	0.964322i	$-0.414716\pi$
$41$	139.000	0.529467	0.264734	+	0.964322i	$0.414716\pi$
$42$	− 45.0000i	− 0.165325i
$43$	− 308.000i	− 1.09232i	−0.837682	−	0.546158i	$-0.816090\pi$
$43$	− 308.000i	− 1.09232i	0.837682	−	0.546158i	$-0.183910\pi$
$44$	187.000	0.640712
$45$	0	0
$46$	565.000	1.81097
$47$	− 195.000i	− 0.605185i	−0.953120	−	0.302592i	$-0.902148\pi$
$47$	− 195.000i	− 0.605185i	0.953120	−	0.302592i	$-0.0978520\pi$
$48$	267.000i	0.802878i
$49$	334.000	0.973761
$50$	0	0
$51$	99.0000	0.271819
$52$	− 544.000i	− 1.45075i
$53$	152.000i	0.393940i	0.980410	+	0.196970i	$0.0631101\pi$
$53$	152.000i	0.393940i	−0.980410	+	0.196970i	$0.936890\pi$
$54$	−135.000	−0.340207
$55$	0	0
$56$	135.000	0.322145
$57$	− 141.000i	− 0.327647i
$58$	− 270.000i	− 0.611254i
$59$	625.000	1.37912	0.689560	−	0.724229i	$-0.257804\pi$
$59$	625.000	1.37912	0.689560	+	0.724229i	$0.257804\pi$
$60$	0	0
$61$	320.000	0.671669	0.335834	−	0.941921i	$-0.390982\pi$
$61$	320.000	0.671669	0.335834	+	0.941921i	$0.390982\pi$
$62$	− 890.000i	− 1.82307i
$63$	27.0000i	0.0539949i
$64$	287.000	0.560547
$65$	0	0
$66$	−165.000	−0.307729
$67$	− 200.000i	− 0.364685i	−0.983235	−	0.182342i	$-0.941632\pi$
$67$	− 200.000i	− 0.364685i	0.983235	−	0.182342i	$-0.0583679\pi$
$68$	561.000i	1.00046i
$69$	−339.000	−0.591461
$70$	0	0
$71$	−947.000	−1.58293	−0.791466	−	0.611213i	$-0.790682\pi$
$71$	−947.000	−1.58293	−0.791466	+	0.611213i	$0.790682\pi$
$72$	− 405.000i	− 0.662913i
$73$	− 448.000i	− 0.718280i	−0.933284	−	0.359140i	$-0.883070\pi$
$73$	− 448.000i	− 0.718280i	0.933284	−	0.359140i	$-0.116930\pi$
$74$	−95.0000	−0.149237
$75$	0	0
$76$	799.000	1.20594
$77$	33.0000i	0.0488402i
$78$	480.000i	0.696786i
$79$	721.000	1.02682	0.513410	−	0.858143i	$-0.328382\pi$
$79$	721.000	1.02682	0.513410	+	0.858143i	$0.328382\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 695.000i	− 0.935975i
$83$	142.000i	0.187789i	0.995582	+	0.0938947i	$0.0299317\pi$
$83$	142.000i	0.187789i	−0.995582	+	0.0938947i	$0.970068\pi$
$84$	−153.000	−0.198734
$85$	0	0
$86$	−1540.00	−1.93096
$87$	162.000i	0.199635i
$88$	− 495.000i	− 0.599627i
$89$	−404.000	−0.481168	−0.240584	−	0.970628i	$-0.577339\pi$
$89$	−404.000	−0.481168	−0.240584	+	0.970628i	$0.577339\pi$
$90$	0	0
$91$	96.0000	0.110588
$92$	− 1921.00i	− 2.17694i
$93$	534.000i	0.595411i
$94$	−975.000	−1.06983
$95$	0	0
$96$	255.000	0.271102
$97$	− 79.0000i	− 0.0826931i	−0.999145	−	0.0413466i	$-0.986835\pi$
$97$	− 79.0000i	− 0.0826931i	0.999145	−	0.0413466i	$-0.0131648\pi$
$98$	− 1670.00i	− 1.72138i
$99$	99.0000	0.100504
$100$	0	0
$101$	−545.000	−0.536926	−0.268463	−	0.963290i	$-0.586516\pi$
$101$	−545.000	−0.536926	−0.268463	+	0.963290i	$0.586516\pi$
$102$	− 495.000i	− 0.480513i
$103$	− 1306.00i	− 1.24936i	−0.780881	−	0.624680i	$-0.785230\pi$
$103$	− 1306.00i	− 1.24936i	0.780881	−	0.624680i	$-0.214770\pi$
$104$	−1440.00	−1.35773
$105$	0	0
$106$	760.000	0.696394
$107$	− 1938.00i	− 1.75097i	−0.483247	−	0.875484i	$-0.660543\pi$
$107$	− 1938.00i	− 1.75097i	0.483247	−	0.875484i	$-0.339457\pi$
$108$	459.000i	0.408956i
$109$	576.000	0.506154	0.253077	−	0.967446i	$-0.418557\pi$
$109$	576.000	0.506154	0.253077	+	0.967446i	$0.418557\pi$
$110$	0	0
$111$	57.0000	0.0487405
$112$	− 267.000i	− 0.225260i
$113$	− 1104.00i	− 0.919076i	−0.888158	−	0.459538i	$-0.848015\pi$
$113$	− 1104.00i	− 0.919076i	0.888158	−	0.459538i	$-0.151985\pi$
$114$	−705.000	−0.579204
$115$	0	0
$116$	−918.000	−0.734777
$117$	− 288.000i	− 0.227569i
$118$	− 3125.00i	− 2.43796i
$119$	−99.0000	−0.0762632
$120$	0	0
$121$	121.000	0.0909091
$122$	− 1600.00i	− 1.18735i
$123$	417.000i	0.305688i
$124$	−3026.00	−2.19147
$125$	0	0
$126$	135.000	0.0954504
$127$	1739.00i	1.21505i	0.794301	+	0.607525i	$0.207837\pi$
$127$	1739.00i	1.21505i	−0.794301	+	0.607525i	$0.792163\pi$
$128$	− 2115.00i	− 1.46048i
$129$	924.000	0.630649
$130$	0	0
$131$	1818.00	1.21251	0.606257	−	0.795269i	$-0.292670\pi$
$131$	1818.00	1.21251	0.606257	+	0.795269i	$0.292670\pi$
$132$	561.000i	0.369915i
$133$	141.000i	0.0919267i
$134$	−1000.00	−0.644678
$135$	0	0
$136$	1485.00	0.936307
$137$	− 870.000i	− 0.542548i	−0.962502	−	0.271274i	$-0.912555\pi$
$137$	− 870.000i	− 0.542548i	0.962502	−	0.271274i	$-0.0874450\pi$
$138$	1695.00i	1.04557i
$139$	636.000	0.388092	0.194046	−	0.980992i	$-0.437839\pi$
$139$	636.000	0.388092	0.194046	+	0.980992i	$0.437839\pi$
$140$	0	0
$141$	585.000	0.349403
$142$	4735.00i	2.79826i
$143$	− 352.000i	− 0.205844i
$144$	−801.000	−0.463542
$145$	0	0
$146$	−2240.00	−1.26975
$147$	1002.00i	0.562201i
$148$	323.000i	0.179395i
$149$	239.000	0.131407	0.0657035	−	0.997839i	$-0.479071\pi$
$149$	239.000	0.131407	0.0657035	+	0.997839i	$0.479071\pi$
$150$	0	0
$151$	1208.00	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	1208.00	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	− 2115.00i	− 1.12861i
$153$	297.000i	0.156935i
$154$	165.000	0.0863382
$155$	0	0
$156$	1632.00	0.837593
$157$	1874.00i	0.952621i	0.879277	+	0.476310i	$0.158026\pi$
$157$	1874.00i	0.952621i	−0.879277	+	0.476310i	$0.841974\pi$
$158$	− 3605.00i	− 1.81518i
$159$	−456.000	−0.227441
$160$	0	0
$161$	339.000	0.165944
$162$	− 405.000i	− 0.196419i
$163$	− 1904.00i	− 0.914925i	−0.889229	−	0.457463i	$-0.848758\pi$
$163$	− 1904.00i	− 0.914925i	0.889229	−	0.457463i	$-0.151242\pi$
$164$	−2363.00	−1.12512
$165$	0	0
$166$	710.000	0.331968
$167$	1180.00i	0.546773i	0.961904	+	0.273387i	$0.0881438\pi$
$167$	1180.00i	0.546773i	−0.961904	+	0.273387i	$0.911856\pi$
$168$	405.000i	0.185991i
$169$	1173.00	0.533910
$170$	0	0
$171$	423.000	0.189167
$172$	5236.00i	2.32117i
$173$	− 3177.00i	− 1.39620i	−0.716000	−	0.698101i	$-0.754029\pi$
$173$	− 3177.00i	− 1.39620i	0.716000	−	0.698101i	$-0.245971\pi$
$174$	810.000	0.352908
$175$	0	0
$176$	−979.000	−0.419289
$177$	1875.00i	0.796235i
$178$	2020.00i	0.850592i
$179$	−1787.00	−0.746182	−0.373091	−	0.927795i	$-0.621702\pi$
$179$	−1787.00	−0.746182	−0.373091	+	0.927795i	$0.621702\pi$
$180$	0	0
$181$	−835.000	−0.342901	−0.171450	−	0.985193i	$-0.554845\pi$
$181$	−835.000	−0.342901	−0.171450	+	0.985193i	$0.554845\pi$
$182$	− 480.000i	− 0.195494i
$183$	960.000i	0.387788i
$184$	−5085.00	−2.03734
$185$	0	0
$186$	2670.00	1.05255
$187$	363.000i	0.141953i
$188$	3315.00i	1.28602i
$189$	−81.0000	−0.0311740
$190$	0	0
$191$	3613.00	1.36873	0.684365	−	0.729139i	$-0.260079\pi$
$191$	3613.00	1.36873	0.684365	+	0.729139i	$0.260079\pi$
$192$	861.000i	0.323632i
$193$	4204.00i	1.56793i	0.620805	+	0.783965i	$0.286806\pi$
$193$	4204.00i	1.56793i	−0.620805	+	0.783965i	$0.713194\pi$
$194$	−395.000	−0.146182
$195$	0	0
$196$	−5678.00	−2.06924
$197$	4517.00i	1.63362i	0.576908	+	0.816809i	$0.304259\pi$
$197$	4517.00i	1.63362i	−0.576908	+	0.816809i	$0.695741\pi$
$198$	− 495.000i	− 0.177667i
$199$	−4164.00	−1.48331	−0.741654	−	0.670783i	$-0.765958\pi$
$199$	−4164.00	−1.48331	−0.741654	+	0.670783i	$0.765958\pi$
$200$	0	0
$201$	600.000	0.210551
$202$	2725.00i	0.949160i
$203$	− 162.000i	− 0.0560107i
$204$	−1683.00	−0.577616
$205$	0	0
$206$	−6530.00	−2.20858
$207$	− 1017.00i	− 0.341480i
$208$	2848.00i	0.949391i
$209$	517.000	0.171108
$210$	0	0
$211$	4660.00	1.52042	0.760208	−	0.649680i	$-0.225097\pi$
$211$	4660.00	1.52042	0.760208	+	0.649680i	$0.225097\pi$
$212$	− 2584.00i	− 0.837122i
$213$	− 2841.00i	− 0.913907i
$214$	−9690.00	−3.09530
$215$	0	0
$216$	1215.00	0.382733
$217$	− 534.000i	− 0.167052i
$218$	− 2880.00i	− 0.894762i
$219$	1344.00	0.414699
$220$	0	0
$221$	1056.00	0.321422
$222$	− 285.000i	− 0.0861619i
$223$	3560.00i	1.06904i	0.845157	+	0.534518i	$0.179507\pi$
$223$	3560.00i	1.06904i	−0.845157	+	0.534518i	$0.820493\pi$
$224$	−255.000	−0.0760621
$225$	0	0
$226$	−5520.00	−1.62471
$227$	4678.00i	1.36780i	0.729577	+	0.683898i	$0.239717\pi$
$227$	4678.00i	1.36780i	−0.729577	+	0.683898i	$0.760283\pi$
$228$	2397.00i	0.696251i
$229$	4447.00	1.28326	0.641629	−	0.767015i	$-0.278259\pi$
$229$	4447.00	1.28326	0.641629	+	0.767015i	$0.278259\pi$
$230$	0	0
$231$	−99.0000	−0.0281979
$232$	2430.00i	0.687661i
$233$	411.000i	0.115560i	0.998329	+	0.0577801i	$0.0184022\pi$
$233$	411.000i	0.115560i	−0.998329	+	0.0577801i	$0.981598\pi$
$234$	−1440.00	−0.402290
$235$	0	0
$236$	−10625.0	−2.93063
$237$	2163.00i	0.592835i
$238$	495.000i	0.134815i
$239$	6380.00	1.72673	0.863364	−	0.504582i	$-0.168353\pi$
$239$	6380.00	1.72673	0.863364	+	0.504582i	$0.168353\pi$
$240$	0	0
$241$	7282.00	1.94637	0.973184	−	0.230027i	$-0.0738813\pi$
$241$	7282.00	1.94637	0.973184	+	0.230027i	$0.0738813\pi$
$242$	− 605.000i	− 0.160706i
$243$	243.000i	0.0641500i
$244$	−5440.00	−1.42730
$245$	0	0
$246$	2085.00	0.540385
$247$	− 1504.00i	− 0.387438i
$248$	8010.00i	2.05095i
$249$	−426.000	−0.108420
$250$	0	0
$251$	−4728.00	−1.18896	−0.594480	−	0.804111i	$-0.702642\pi$
$251$	−4728.00	−1.18896	−0.594480	+	0.804111i	$0.702642\pi$
$252$	− 459.000i	− 0.114739i
$253$	− 1243.00i	− 0.308880i
$254$	8695.00	2.14792
$255$	0	0
$256$	−8279.00	−2.02124
$257$	− 5418.00i	− 1.31504i	−0.753437	−	0.657521i	$-0.771605\pi$
$257$	− 5418.00i	− 1.31504i	0.753437	−	0.657521i	$-0.228395\pi$
$258$	− 4620.00i	− 1.11484i
$259$	−57.0000	−0.0136749
$260$	0	0
$261$	−486.000	−0.115259
$262$	− 9090.00i	− 2.14344i
$263$	− 3354.00i	− 0.786375i	−0.919458	−	0.393187i	$-0.871372\pi$
$263$	− 3354.00i	− 0.786375i	0.919458	−	0.393187i	$-0.128628\pi$
$264$	1485.00	0.346195
$265$	0	0
$266$	705.000	0.162505
$267$	− 1212.00i	− 0.277802i
$268$	3400.00i	0.774955i
$269$	−1062.00	−0.240711	−0.120356	−	0.992731i	$-0.538403\pi$
$269$	−1062.00	−0.240711	−0.120356	+	0.992731i	$0.538403\pi$
$270$	0	0
$271$	−4821.00	−1.08065	−0.540323	−	0.841458i	$-0.681698\pi$
$271$	−4821.00	−1.08065	−0.540323	+	0.841458i	$0.681698\pi$
$272$	− 2937.00i	− 0.654712i
$273$	288.000i	0.0638482i
$274$	−4350.00	−0.959099
$275$	0	0
$276$	5763.00	1.25685
$277$	− 4.00000i	0 0.000867642i	−1.00000		0.000433821i	$-0.999862\pi$
$277$	− 4.00000i	0 0.000867642i	1.00000		0.000433821i	$-0.000138089\pi$
$278$	− 3180.00i	− 0.686057i
$279$	−1602.00	−0.343761
$280$	0	0
$281$	4647.00	0.986537	0.493268	−	0.869877i	$-0.335802\pi$
$281$	4647.00	0.986537	0.493268	+	0.869877i	$0.335802\pi$
$282$	− 2925.00i	− 0.617664i
$283$	− 4283.00i	− 0.899639i	−0.893119	−	0.449820i	$-0.851488\pi$
$283$	− 4283.00i	− 0.899639i	0.893119	−	0.449820i	$-0.148512\pi$
$284$	16099.0	3.36373
$285$	0	0
$286$	−1760.00	−0.363885
$287$	− 417.000i	− 0.0857656i
$288$	765.000i	0.156521i
$289$	3824.00	0.778343
$290$	0	0
$291$	237.000	0.0477429
$292$	7616.00i	1.52634i
$293$	− 6811.00i	− 1.35803i	−0.734124	−	0.679015i	$-0.762407\pi$
$293$	− 6811.00i	− 1.35803i	0.734124	−	0.679015i	$-0.237593\pi$
$294$	5010.00	0.993841
$295$	0	0
$296$	855.000	0.167891
$297$	297.000i	0.0580259i
$298$	− 1195.00i	− 0.232297i
$299$	−3616.00	−0.699394
$300$	0	0
$301$	−924.000	−0.176938
$302$	− 6040.00i	− 1.15087i
$303$	− 1635.00i	− 0.309994i
$304$	−4183.00	−0.789183
$305$	0	0
$306$	1485.00	0.277424
$307$	460.000i	0.0855166i	0.999085	+	0.0427583i	$0.0136145\pi$
$307$	460.000i	0.0855166i	−0.999085	+	0.0427583i	$0.986385\pi$
$308$	− 561.000i	− 0.103786i
$309$	3918.00	0.721318
$310$	0	0
$311$	8328.00	1.51845	0.759224	−	0.650829i	$-0.225579\pi$
$311$	8328.00	1.51845	0.759224	+	0.650829i	$0.225579\pi$
$312$	− 4320.00i	− 0.783884i
$313$	− 5929.00i	− 1.07069i	−0.844633	−	0.535346i	$-0.820181\pi$
$313$	− 5929.00i	− 1.07069i	0.844633	−	0.535346i	$-0.179819\pi$
$314$	9370.00	1.68401
$315$	0	0
$316$	−12257.0	−2.18199
$317$	− 5040.00i	− 0.892980i	−0.894789	−	0.446490i	$-0.852674\pi$
$317$	− 5040.00i	− 0.892980i	0.894789	−	0.446490i	$-0.147326\pi$
$318$	2280.00i	0.402063i
$319$	−594.000	−0.104256
$320$	0	0
$321$	5814.00	1.01092
$322$	− 1695.00i	− 0.293350i
$323$	1551.00i	0.267183i
$324$	−1377.00	−0.236111
$325$	0	0
$326$	−9520.00	−1.61737
$327$	1728.00i	0.292228i
$328$	6255.00i	1.05297i
$329$	−585.000	−0.0980307
$330$	0	0
$331$	10396.0	1.72633	0.863166	−	0.504920i	$-0.168478\pi$
$331$	10396.0	1.72633	0.863166	+	0.504920i	$0.168478\pi$
$332$	− 2414.00i	− 0.399053i
$333$	171.000i	0.0281404i
$334$	5900.00	0.966568
$335$	0	0
$336$	801.000	0.130054
$337$	7236.00i	1.16964i	0.811162	+	0.584822i	$0.198836\pi$
$337$	7236.00i	1.16964i	−0.811162	+	0.584822i	$0.801164\pi$
$338$	− 5865.00i	− 0.943828i
$339$	3312.00	0.530629
$340$	0	0
$341$	−1958.00	−0.310943
$342$	− 2115.00i	− 0.334404i
$343$	− 2031.00i	− 0.319719i
$344$	13860.0	2.17233
$345$	0	0
$346$	−15885.0	−2.46816
$347$	− 1468.00i	− 0.227108i	−0.993532	−	0.113554i	$-0.963777\pi$
$347$	− 1468.00i	− 0.227108i	0.993532	−	0.113554i	$-0.0362234\pi$
$348$	− 2754.00i	− 0.424224i
$349$	−5690.00	−0.872718	−0.436359	−	0.899773i	$-0.643732\pi$
$349$	−5690.00	−0.872718	−0.436359	+	0.899773i	$0.643732\pi$
$350$	0	0
$351$	864.000	0.131387
$352$	935.000i	0.141579i
$353$	5376.00i	0.810582i	0.914188	+	0.405291i	$0.132830\pi$
$353$	5376.00i	0.810582i	−0.914188	+	0.405291i	$0.867170\pi$
$354$	9375.00	1.40756
$355$	0	0
$356$	6868.00	1.02248
$357$	− 297.000i	− 0.0440306i
$358$	8935.00i	1.31908i
$359$	−3734.00	−0.548950	−0.274475	−	0.961594i	$-0.588504\pi$
$359$	−3734.00	−0.548950	−0.274475	+	0.961594i	$0.588504\pi$
$360$	0	0
$361$	−4650.00	−0.677941
$362$	4175.00i	0.606169i
$363$	363.000i	0.0524864i
$364$	−1632.00	−0.235000
$365$	0	0
$366$	4800.00	0.685519
$367$	10274.0i	1.46130i	0.682750	+	0.730652i	$0.260784\pi$
$367$	10274.0i	1.46130i	−0.682750	+	0.730652i	$0.739216\pi$
$368$	10057.0i	1.42461i
$369$	−1251.00	−0.176489
$370$	0	0
$371$	456.000	0.0638122
$372$	− 9078.00i	− 1.26525i
$373$	13662.0i	1.89649i	0.317537	+	0.948246i	$0.397144\pi$
$373$	13662.0i	1.89649i	−0.317537	+	0.948246i	$0.602856\pi$
$374$	1815.00	0.250940
$375$	0	0
$376$	8775.00	1.20355
$377$	1728.00i	0.236065i
$378$	405.000i	0.0551083i
$379$	7906.00	1.07151	0.535757	−	0.844372i	$-0.320026\pi$
$379$	7906.00	1.07151	0.535757	+	0.844372i	$0.320026\pi$
$380$	0	0
$381$	−5217.00	−0.701509
$382$	− 18065.0i	− 2.41960i
$383$	− 3168.00i	− 0.422656i	−0.977415	−	0.211328i	$-0.932221\pi$
$383$	− 3168.00i	− 0.422656i	0.977415	−	0.211328i	$-0.0677788\pi$
$384$	6345.00	0.843208
$385$	0	0
$386$	21020.0	2.77174
$387$	2772.00i	0.364105i
$388$	1343.00i	0.175723i
$389$	−10770.0	−1.40375	−0.701877	−	0.712298i	$-0.747655\pi$
$389$	−10770.0	−1.40375	−0.701877	+	0.712298i	$0.747655\pi$
$390$	0	0
$391$	3729.00	0.482311
$392$	15030.0i	1.93656i
$393$	5454.00i	0.700046i
$394$	22585.0	2.88786
$395$	0	0
$396$	−1683.00	−0.213571
$397$	− 5670.00i	− 0.716799i	−0.933568	−	0.358399i	$-0.883323\pi$
$397$	− 5670.00i	− 0.716799i	0.933568	−	0.358399i	$-0.116677\pi$
$398$	20820.0i	2.62214i
$399$	−423.000	−0.0530739
$400$	0	0
$401$	832.000	0.103611	0.0518056	−	0.998657i	$-0.483502\pi$
$401$	832.000	0.103611	0.0518056	+	0.998657i	$0.483502\pi$
$402$	− 3000.00i	− 0.372205i
$403$	5696.00i	0.704064i
$404$	9265.00	1.14097
$405$	0	0
$406$	−810.000	−0.0990139
$407$	209.000i	0.0254539i
$408$	4455.00i	0.540577i
$409$	5712.00	0.690563	0.345281	−	0.938499i	$-0.387783\pi$
$409$	5712.00	0.690563	0.345281	+	0.938499i	$0.387783\pi$
$410$	0	0
$411$	2610.00	0.313240
$412$	22202.0i	2.65489i
$413$	− 1875.00i	− 0.223396i
$414$	−5085.00	−0.603657
$415$	0	0
$416$	2720.00	0.320574
$417$	1908.00i	0.224065i
$418$	− 2585.00i	− 0.302480i
$419$	4559.00	0.531555	0.265778	−	0.964034i	$-0.414371\pi$
$419$	4559.00	0.531555	0.265778	+	0.964034i	$0.414371\pi$
$420$	0	0
$421$	6855.00	0.793568	0.396784	−	0.917912i	$-0.370126\pi$
$421$	6855.00	0.793568	0.396784	+	0.917912i	$0.370126\pi$
$422$	− 23300.0i	− 2.68774i
$423$	1755.00i	0.201728i
$424$	−6840.00	−0.783443
$425$	0	0
$426$	−14205.0	−1.61557
$427$	− 960.000i	− 0.108800i
$428$	32946.0i	3.72081i
$429$	1056.00	0.118844
$430$	0	0
$431$	10770.0	1.20365	0.601824	−	0.798628i	$-0.294441\pi$
$431$	10770.0	1.20365	0.601824	+	0.798628i	$0.294441\pi$
$432$	− 2403.00i	− 0.267626i
$433$	8498.00i	0.943159i	0.881824	+	0.471579i	$0.156316\pi$
$433$	8498.00i	0.943159i	−0.881824	+	0.471579i	$0.843684\pi$
$434$	−2670.00	−0.295309
$435$	0	0
$436$	−9792.00	−1.07558
$437$	− 5311.00i	− 0.581372i
$438$	− 6720.00i	− 0.733091i
$439$	−9835.00	−1.06925	−0.534623	−	0.845091i	$-0.679546\pi$
$439$	−9835.00	−1.06925	−0.534623	+	0.845091i	$0.679546\pi$
$440$	0	0
$441$	−3006.00	−0.324587
$442$	− 5280.00i	− 0.568199i
$443$	− 10745.0i	− 1.15239i	−0.817311	−	0.576197i	$-0.804536\pi$
$443$	− 10745.0i	− 1.15239i	0.817311	−	0.576197i	$-0.195464\pi$
$444$	−969.000	−0.103574
$445$	0	0
$446$	17800.0	1.88981
$447$	717.000i	0.0758679i
$448$	− 861.000i	− 0.0908001i
$449$	−8356.00	−0.878272	−0.439136	−	0.898421i	$-0.644715\pi$
$449$	−8356.00	−0.878272	−0.439136	+	0.898421i	$0.644715\pi$
$450$	0	0
$451$	−1529.00	−0.159640
$452$	18768.0i	1.95304i
$453$	3624.00i	0.375873i
$454$	23390.0	2.41795
$455$	0	0
$456$	6345.00	0.651605
$457$	7058.00i	0.722449i	0.932479	+	0.361225i	$0.117641\pi$
$457$	7058.00i	0.722449i	−0.932479	+	0.361225i	$0.882359\pi$
$458$	− 22235.0i	− 2.26850i
$459$	−891.000	−0.0906064
$460$	0	0
$461$	646.000	0.0652651	0.0326326	−	0.999467i	$-0.489611\pi$
$461$	646.000	0.0652651	0.0326326	+	0.999467i	$0.489611\pi$
$462$	495.000i	0.0498474i
$463$	− 8982.00i	− 0.901574i	−0.892631	−	0.450787i	$-0.851143\pi$
$463$	− 8982.00i	− 0.901574i	0.892631	−	0.450787i	$-0.148857\pi$
$464$	4806.00	0.480847
$465$	0	0
$466$	2055.00	0.204283
$467$	13476.0i	1.33532i	0.744466	+	0.667661i	$0.232704\pi$
$467$	13476.0i	1.33532i	−0.744466	+	0.667661i	$0.767296\pi$
$468$	4896.00i	0.483585i
$469$	−600.000	−0.0590734
$470$	0	0
$471$	−5622.00	−0.549996
$472$	28125.0i	2.74271i
$473$	3388.00i	0.329345i
$474$	10815.0	1.04799
$475$	0	0
$476$	1683.00	0.162059
$477$	− 1368.00i	− 0.131313i
$478$	− 31900.0i	− 3.05245i
$479$	−12996.0	−1.23967	−0.619835	−	0.784732i	$-0.712801\pi$
$479$	−12996.0	−1.23967	−0.619835	+	0.784732i	$0.712801\pi$
$480$	0	0
$481$	608.000	0.0576350
$482$	− 36410.0i	− 3.44073i
$483$	1017.00i	0.0958077i
$484$	−2057.00	−0.193182
$485$	0	0
$486$	1215.00	0.113402
$487$	6026.00i	0.560707i	0.959897	+	0.280353i	$0.0904516\pi$
$487$	6026.00i	0.560707i	−0.959897	+	0.280353i	$0.909548\pi$
$488$	14400.0i	1.33577i
$489$	5712.00	0.528232
$490$	0	0
$491$	11698.0	1.07520	0.537600	−	0.843200i	$-0.319331\pi$
$491$	11698.0	1.07520	0.537600	+	0.843200i	$0.319331\pi$
$492$	− 7089.00i	− 0.649587i
$493$	− 1782.00i	− 0.162794i
$494$	−7520.00	−0.684900
$495$	0	0
$496$	15842.0	1.43413
$497$	2841.00i	0.256411i
$498$	2130.00i	0.191662i
$499$	17052.0	1.52976	0.764882	−	0.644170i	$-0.222797\pi$
$499$	17052.0	1.52976	0.764882	+	0.644170i	$0.222797\pi$
$500$	0	0
$501$	−3540.00	−0.315680
$502$	23640.0i	2.10180i
$503$	− 932.000i	− 0.0826160i	−0.999146	−	0.0413080i	$-0.986848\pi$
$503$	− 932.000i	− 0.0826160i	0.999146	−	0.0413080i	$-0.0131525\pi$
$504$	−1215.00	−0.107382
$505$	0	0
$506$	−6215.00	−0.546029
$507$	3519.00i	0.308253i
$508$	− 29563.0i	− 2.58198i
$509$	−4384.00	−0.381763	−0.190882	−	0.981613i	$-0.561135\pi$
$509$	−4384.00	−0.381763	−0.190882	+	0.981613i	$0.561135\pi$
$510$	0	0
$511$	−1344.00	−0.116350
$512$	24475.0i	2.11260i
$513$	1269.00i	0.109216i
$514$	−27090.0	−2.32469
$515$	0	0
$516$	−15708.0	−1.34013
$517$	2145.00i	0.182470i
$518$	285.000i	0.0241741i
$519$	9531.00	0.806097
$520$	0	0
$521$	−2322.00	−0.195257	−0.0976283	−	0.995223i	$-0.531126\pi$
$521$	−2322.00	−0.195257	−0.0976283	+	0.995223i	$0.531126\pi$
$522$	2430.00i	0.203751i
$523$	− 9749.00i	− 0.815094i	−0.913184	−	0.407547i	$-0.866384\pi$
$523$	− 9749.00i	− 0.815094i	0.913184	−	0.407547i	$-0.133616\pi$
$524$	−30906.0	−2.57659
$525$	0	0
$526$	−16770.0	−1.39013
$527$	− 5874.00i	− 0.485532i
$528$	− 2937.00i	− 0.242077i
$529$	−602.000	−0.0494781
$530$	0	0
$531$	−5625.00	−0.459707
$532$	− 2397.00i	− 0.195344i
$533$	4448.00i	0.361471i
$534$	−6060.00	−0.491090
$535$	0	0
$536$	9000.00	0.725263
$537$	− 5361.00i	− 0.430809i
$538$	5310.00i	0.425521i
$539$	−3674.00	−0.293600
$540$	0	0
$541$	4208.00	0.334410	0.167205	−	0.985922i	$-0.446526\pi$
$541$	4208.00	0.334410	0.167205	+	0.985922i	$0.446526\pi$
$542$	24105.0i	1.91033i
$543$	− 2505.00i	− 0.197974i
$544$	−2805.00	−0.221072
$545$	0	0
$546$	1440.00	0.112869
$547$	− 10179.0i	− 0.795654i	−0.917461	−	0.397827i	$-0.869764\pi$
$547$	− 10179.0i	− 0.795654i	0.917461	−	0.397827i	$-0.130236\pi$
$548$	14790.0i	1.15292i
$549$	−2880.00	−0.223890
$550$	0	0
$551$	−2538.00	−0.196229
$552$	− 15255.0i	− 1.17626i
$553$	− 2163.00i	− 0.166329i
$554$	−20.0000	−0.00153379
$555$	0	0
$556$	−10812.0	−0.824696
$557$	2314.00i	0.176028i	0.996119	+	0.0880138i	$0.0280519\pi$
$557$	2314.00i	0.176028i	−0.996119	+	0.0880138i	$0.971948\pi$
$558$	8010.00i	0.607689i
$559$	9856.00	0.745732
$560$	0	0
$561$	−1089.00	−0.0819565
$562$	− 23235.0i	− 1.74397i
$563$	24330.0i	1.82129i	0.413188	+	0.910646i	$0.364415\pi$
$563$	24330.0i	1.82129i	−0.413188	+	0.910646i	$0.635585\pi$
$564$	−9945.00	−0.742482
$565$	0	0
$566$	−21415.0	−1.59035
$567$	− 243.000i	− 0.0179983i
$568$	− 42615.0i	− 3.14804i
$569$	−3445.00	−0.253817	−0.126909	−	0.991914i	$-0.540505\pi$
$569$	−3445.00	−0.253817	−0.126909	+	0.991914i	$0.540505\pi$
$570$	0	0
$571$	−13056.0	−0.956877	−0.478438	−	0.878121i	$-0.658797\pi$
$571$	−13056.0	−0.956877	−0.478438	+	0.878121i	$0.658797\pi$
$572$	5984.00i	0.437419i
$573$	10839.0i	0.790237i
$574$	−2085.00	−0.151614
$575$	0	0
$576$	−2583.00	−0.186849
$577$	17347.0i	1.25159i	0.779989	+	0.625793i	$0.215225\pi$
$577$	17347.0i	1.25159i	−0.779989	+	0.625793i	$0.784775\pi$
$578$	− 19120.0i	− 1.37593i
$579$	−12612.0	−0.905245
$580$	0	0
$581$	426.000	0.0304190
$582$	− 1185.00i	− 0.0843983i
$583$	− 1672.00i	− 0.118777i
$584$	20160.0	1.42847
$585$	0	0
$586$	−34055.0	−2.40068
$587$	− 8379.00i	− 0.589162i	−0.955626	−	0.294581i	$-0.904820\pi$
$587$	− 8379.00i	− 0.589162i	0.955626	−	0.294581i	$-0.0951801\pi$
$588$	− 17034.0i	− 1.19468i
$589$	−8366.00	−0.585255
$590$	0	0
$591$	−13551.0	−0.943170
$592$	− 1691.00i	− 0.117398i
$593$	1958.00i	0.135591i	0.997699	+	0.0677955i	$0.0215965\pi$
$593$	1958.00i	0.135591i	−0.997699	+	0.0677955i	$0.978403\pi$
$594$	1485.00	0.102576
$595$	0	0
$596$	−4063.00	−0.279240
$597$	− 12492.0i	− 0.856388i
$598$	18080.0i	1.23636i
$599$	−23583.0	−1.60864	−0.804320	−	0.594196i	$-0.797470\pi$
$599$	−23583.0	−1.60864	−0.804320	+	0.594196i	$0.797470\pi$
$600$	0	0
$601$	−15328.0	−1.04034	−0.520168	−	0.854064i	$-0.674131\pi$
$601$	−15328.0	−1.04034	−0.520168	+	0.854064i	$0.674131\pi$
$602$	4620.00i	0.312786i
$603$	1800.00i	0.121562i
$604$	−20536.0	−1.38344
$605$	0	0
$606$	−8175.00	−0.547998
$607$	− 160.000i	− 0.0106988i	−0.999986	−	0.00534942i	$-0.998297\pi$
$607$	− 160.000i	− 0.0106988i	0.999986	−	0.00534942i	$-0.00170278\pi$
$608$	3995.00i	0.266478i
$609$	486.000	0.0323378
$610$	0	0
$611$	6240.00	0.413164
$612$	− 5049.00i	− 0.333486i
$613$	− 5948.00i	− 0.391904i	−0.980613	−	0.195952i	$-0.937220\pi$
$613$	− 5948.00i	− 0.391904i	0.980613	−	0.195952i	$-0.0627798\pi$
$614$	2300.00	0.151173
$615$	0	0
$616$	−1485.00	−0.0971304
$617$	− 334.000i	− 0.0217931i	−0.999941	−	0.0108965i	$-0.996531\pi$
$617$	− 334.000i	− 0.0217931i	0.999941	−	0.0108965i	$-0.00346855\pi$
$618$	− 19590.0i	− 1.27512i
$619$	7202.00	0.467646	0.233823	−	0.972279i	$-0.424876\pi$
$619$	7202.00	0.467646	0.233823	+	0.972279i	$0.424876\pi$
$620$	0	0
$621$	3051.00	0.197154
$622$	− 41640.0i	− 2.68426i
$623$	1212.00i	0.0779418i
$624$	−8544.00	−0.548131
$625$	0	0
$626$	−29645.0	−1.89274
$627$	1551.00i	0.0987894i
$628$	− 31858.0i	− 2.02432i
$629$	−627.000	−0.0397458
$630$	0	0
$631$	10306.0	0.650199	0.325099	−	0.945680i	$-0.394602\pi$
$631$	10306.0	0.650199	0.325099	+	0.945680i	$0.394602\pi$
$632$	32445.0i	2.04208i
$633$	13980.0i	0.877812i
$634$	−25200.0	−1.57858
$635$	0	0
$636$	7752.00	0.483313
$637$	10688.0i	0.664794i
$638$	2970.00i	0.184300i
$639$	8523.00	0.527644
$640$	0	0
$641$	−1228.00	−0.0756678	−0.0378339	−	0.999284i	$-0.512046\pi$
$641$	−1228.00	−0.0756678	−0.0378339	+	0.999284i	$0.512046\pi$
$642$	− 29070.0i	− 1.78707i
$643$	− 18454.0i	− 1.13181i	−0.824470	−	0.565906i	$-0.808527\pi$
$643$	− 18454.0i	− 1.13181i	0.824470	−	0.565906i	$-0.191473\pi$
$644$	−5763.00	−0.352630
$645$	0	0
$646$	7755.00	0.472316
$647$	− 17647.0i	− 1.07230i	−0.844124	−	0.536148i	$-0.819879\pi$
$647$	− 17647.0i	− 1.07230i	0.844124	−	0.536148i	$-0.180121\pi$
$648$	3645.00i	0.220971i
$649$	−6875.00	−0.415820
$650$	0	0
$651$	1602.00	0.0964475
$652$	32368.0i	1.94422i
$653$	25918.0i	1.55322i	0.629984	+	0.776608i	$0.283061\pi$
$653$	25918.0i	1.55322i	−0.629984	+	0.776608i	$0.716939\pi$
$654$	8640.00	0.516591
$655$	0	0
$656$	12371.0	0.736290
$657$	4032.00i	0.239427i
$658$	2925.00i	0.173295i
$659$	−12864.0	−0.760410	−0.380205	−	0.924902i	$-0.624147\pi$
$659$	−12864.0	−0.760410	−0.380205	+	0.924902i	$0.624147\pi$
$660$	0	0
$661$	−11419.0	−0.671933	−0.335966	−	0.941874i	$-0.609063\pi$
$661$	−11419.0	−0.671933	−0.335966	+	0.941874i	$0.609063\pi$
$662$	− 51980.0i	− 3.05175i
$663$	3168.00i	0.185573i
$664$	−6390.00	−0.373464
$665$	0	0
$666$	855.000	0.0497456
$667$	6102.00i	0.354228i
$668$	− 20060.0i	− 1.16189i
$669$	−10680.0	−0.617209
$670$	0	0
$671$	−3520.00	−0.202516
$672$	− 765.000i	− 0.0439145i
$673$	15784.0i	0.904054i	0.892004	+	0.452027i	$0.149299\pi$
$673$	15784.0i	0.904054i	−0.892004	+	0.452027i	$0.850701\pi$
$674$	36180.0	2.06766
$675$	0	0
$676$	−19941.0	−1.13456
$677$	26050.0i	1.47885i	0.673238	+	0.739426i	$0.264903\pi$
$677$	26050.0i	1.47885i	−0.673238	+	0.739426i	$0.735097\pi$
$678$	− 16560.0i	− 0.938028i
$679$	−237.000	−0.0133950
$680$	0	0
$681$	−14034.0	−0.789698
$682$	9790.00i	0.549675i
$683$	− 15095.0i	− 0.845672i	−0.906206	−	0.422836i	$-0.861035\pi$
$683$	− 15095.0i	− 0.845672i	0.906206	−	0.422836i	$-0.138965\pi$
$684$	−7191.00	−0.401981
$685$	0	0
$686$	−10155.0	−0.565189
$687$	13341.0i	0.740889i
$688$	− 27412.0i	− 1.51900i
$689$	−4864.00	−0.268946
$690$	0	0
$691$	15896.0	0.875126	0.437563	−	0.899188i	$-0.355842\pi$
$691$	15896.0	0.875126	0.437563	+	0.899188i	$0.355842\pi$
$692$	54009.0i	2.96693i
$693$	− 297.000i	− 0.0162801i
$694$	−7340.00	−0.401473
$695$	0	0
$696$	−7290.00	−0.397021
$697$	− 4587.00i	− 0.249275i
$698$	28450.0i	1.54276i
$699$	−1233.00	−0.0667187
$700$	0	0
$701$	10529.0	0.567296	0.283648	−	0.958928i	$-0.408455\pi$
$701$	10529.0	0.567296	0.283648	+	0.958928i	$0.408455\pi$
$702$	− 4320.00i	− 0.232262i
$703$	893.000i	0.0479092i
$704$	−3157.00	−0.169011
$705$	0	0
$706$	26880.0	1.43292
$707$	1635.00i	0.0869738i
$708$	− 31875.0i	− 1.69200i
$709$	16087.0	0.852130	0.426065	−	0.904693i	$-0.359900\pi$
$709$	16087.0	0.852130	0.426065	+	0.904693i	$0.359900\pi$
$710$	0	0
$711$	−6489.00	−0.342274
$712$	− 18180.0i	− 0.956916i
$713$	20114.0i	1.05649i
$714$	−1485.00	−0.0778358
$715$	0	0
$716$	30379.0	1.58564
$717$	19140.0i	0.996927i
$718$	18670.0i	0.970415i
$719$	−24336.0	−1.26228	−0.631140	−	0.775669i	$-0.717413\pi$
$719$	−24336.0	−1.26228	−0.631140	+	0.775669i	$0.717413\pi$
$720$	0	0
$721$	−3918.00	−0.202377
$722$	23250.0i	1.19844i
$723$	21846.0i	1.12374i
$724$	14195.0	0.728664
$725$	0	0
$726$	1815.00	0.0927837
$727$	− 13960.0i	− 0.712170i	−0.934454	−	0.356085i	$-0.884111\pi$
$727$	− 13960.0i	− 0.712170i	0.934454	−	0.356085i	$-0.115889\pi$
$728$	4320.00i	0.219931i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−10164.0	−0.514267
$732$	− 16320.0i	− 0.824050i
$733$	9252.00i	0.466208i	0.972452	+	0.233104i	$0.0748882\pi$
$733$	9252.00i	0.466208i	−0.972452	+	0.233104i	$0.925112\pi$
$734$	51370.0	2.58324
$735$	0	0
$736$	9605.00	0.481039
$737$	2200.00i	0.109957i
$738$	6255.00i	0.311992i
$739$	−28453.0	−1.41632	−0.708160	−	0.706052i	$-0.750474\pi$
$739$	−28453.0	−1.41632	−0.708160	+	0.706052i	$0.750474\pi$
$740$	0	0
$741$	4512.00	0.223688
$742$	− 2280.00i	− 0.112805i
$743$	512.000i	0.0252806i	0.999920	+	0.0126403i	$0.00402363\pi$
$743$	512.000i	0.0252806i	−0.999920	+	0.0126403i	$0.995976\pi$
$744$	−24030.0	−1.18412
$745$	0	0
$746$	68310.0	3.35256
$747$	− 1278.00i	− 0.0625965i
$748$	− 6171.00i	− 0.301650i
$749$	−5814.00	−0.283630
$750$	0	0
$751$	772.000	0.0375109	0.0187554	−	0.999824i	$-0.494030\pi$
$751$	772.000	0.0375109	0.0187554	+	0.999824i	$0.494030\pi$
$752$	− 17355.0i	− 0.841585i
$753$	− 14184.0i	− 0.686446i
$754$	8640.00	0.417308
$755$	0	0
$756$	1377.00	0.0662447
$757$	− 8058.00i	− 0.386886i	−0.981111	−	0.193443i	$-0.938034\pi$
$757$	− 8058.00i	− 0.386886i	0.981111	−	0.193443i	$-0.0619655\pi$
$758$	− 39530.0i	− 1.89419i
$759$	3729.00	0.178332
$760$	0	0
$761$	18650.0	0.888386	0.444193	−	0.895931i	$-0.353490\pi$
$761$	18650.0	0.888386	0.444193	+	0.895931i	$0.353490\pi$
$762$	26085.0i	1.24010i
$763$	− 1728.00i	− 0.0819893i
$764$	−61421.0	−2.90855
$765$	0	0
$766$	−15840.0	−0.747157
$767$	20000.0i	0.941536i
$768$	− 24837.0i	− 1.16696i
$769$	7144.00	0.335005	0.167503	−	0.985872i	$-0.446430\pi$
$769$	7144.00	0.335005	0.167503	+	0.985872i	$0.446430\pi$
$770$	0	0
$771$	16254.0	0.759239
$772$	− 71468.0i	− 3.33185i
$773$	− 1904.00i	− 0.0885927i	−0.999018	−	0.0442963i	$-0.985895\pi$
$773$	− 1904.00i	− 0.0885927i	0.999018	−	0.0442963i	$-0.0141046\pi$
$774$	13860.0	0.643653
$775$	0	0
$776$	3555.00	0.164455
$777$	− 171.000i	− 0.00789523i
$778$	53850.0i	2.48151i
$779$	−6533.00	−0.300474
$780$	0	0
$781$	10417.0	0.477272
$782$	− 18645.0i	− 0.852614i
$783$	− 1458.00i	− 0.0665449i
$784$	29726.0	1.35414
$785$	0	0
$786$	27270.0	1.23752
$787$	− 7555.00i	− 0.342194i	−0.985254	−	0.171097i	$-0.945269\pi$
$787$	− 7555.00i	− 0.342194i	0.985254	−	0.171097i	$-0.0547311\pi$
$788$	− 76789.0i	− 3.47144i
$789$	10062.0	0.454014
$790$	0	0
$791$	−3312.00	−0.148876
$792$	4455.00i	0.199876i
$793$	10240.0i	0.458554i
$794$	−28350.0	−1.26713
$795$	0	0
$796$	70788.0	3.15203
$797$	− 24950.0i	− 1.10888i	−0.832225	−	0.554438i	$-0.812933\pi$
$797$	− 24950.0i	− 1.10888i	0.832225	−	0.554438i	$-0.187067\pi$
$798$	2115.00i	0.0938223i
$799$	−6435.00	−0.284924
$800$	0	0
$801$	3636.00	0.160389
$802$	− 4160.00i	− 0.183160i
$803$	4928.00i	0.216570i
$804$	−10200.0	−0.447421
$805$	0	0
$806$	28480.0	1.24462
$807$	− 3186.00i	− 0.138975i
$808$	− 24525.0i	− 1.06781i
$809$	−19893.0	−0.864525	−0.432262	−	0.901748i	$-0.642285\pi$
$809$	−19893.0	−0.864525	−0.432262	+	0.901748i	$0.642285\pi$
$810$	0	0
$811$	34503.0	1.49391	0.746957	−	0.664872i	$-0.231514\pi$
$811$	34503.0	1.49391	0.746957	+	0.664872i	$0.231514\pi$
$812$	2754.00i	0.119023i
$813$	− 14463.0i	− 0.623911i
$814$	1045.00	0.0449966
$815$	0	0
$816$	8811.00	0.377998
$817$	14476.0i	0.619891i
$818$	− 28560.0i	− 1.22075i
$819$	−864.000	−0.0368628
$820$	0	0
$821$	16890.0	0.717984	0.358992	−	0.933341i	$-0.383120\pi$
$821$	16890.0	0.717984	0.358992	+	0.933341i	$0.383120\pi$
$822$	− 13050.0i	− 0.553736i
$823$	34692.0i	1.46936i	0.678411	+	0.734682i	$0.262669\pi$
$823$	34692.0i	1.46936i	−0.678411	+	0.734682i	$0.737331\pi$
$824$	58770.0	2.48465
$825$	0	0
$826$	−9375.00	−0.394913
$827$	− 41424.0i	− 1.74178i	−0.491476	−	0.870891i	$-0.663543\pi$
$827$	− 41424.0i	− 1.74178i	0.491476	−	0.870891i	$-0.336457\pi$
$828$	17289.0i	0.725645i
$829$	18494.0	0.774817	0.387408	−	0.921908i	$-0.373370\pi$
$829$	18494.0	0.774817	0.387408	+	0.921908i	$0.373370\pi$
$830$	0	0
$831$	12.0000	0.000500933 0
$832$	9184.00i	0.382690i
$833$	− 11022.0i	− 0.458451i
$834$	9540.00	0.396095
$835$	0	0
$836$	−8789.00	−0.363605
$837$	− 4806.00i	− 0.198470i
$838$	− 22795.0i	− 0.939666i
$839$	−6680.00	−0.274874	−0.137437	−	0.990511i	$-0.543886\pi$
$839$	−6680.00	−0.274874	−0.137437	+	0.990511i	$0.543886\pi$
$840$	0	0
$841$	−21473.0	−0.880438
$842$	− 34275.0i	− 1.40284i
$843$	13941.0i	0.569577i
$844$	−79220.0	−3.23088
$845$	0	0
$846$	8775.00	0.356608
$847$	− 363.000i	− 0.0147259i
$848$	13528.0i	0.547822i
$849$	12849.0	0.519407
$850$	0	0
$851$	2147.00	0.0864844
$852$	48297.0i	1.94205i
$853$	43358.0i	1.74039i	0.492711	+	0.870193i	$0.336006\pi$
$853$	43358.0i	1.74039i	−0.492711	+	0.870193i	$0.663994\pi$
$854$	−4800.00	−0.192333
$855$	0	0
$856$	87210.0	3.48222
$857$	− 15585.0i	− 0.621206i	−0.950540	−	0.310603i	$-0.899469\pi$
$857$	− 15585.0i	− 0.621206i	0.950540	−	0.310603i	$-0.100531\pi$
$858$	− 5280.00i	− 0.210089i
$859$	17036.0	0.676672	0.338336	−	0.941025i	$-0.390136\pi$
$859$	17036.0	0.676672	0.338336	+	0.941025i	$0.390136\pi$
$860$	0	0
$861$	1251.00	0.0495168
$862$	− 53850.0i	− 2.12777i
$863$	28064.0i	1.10696i	0.832861	+	0.553482i	$0.186701\pi$
$863$	28064.0i	1.10696i	−0.832861	+	0.553482i	$0.813299\pi$
$864$	−2295.00	−0.0903675
$865$	0	0
$866$	42490.0	1.66729
$867$	11472.0i	0.449377i
$868$	9078.00i	0.354985i
$869$	−7931.00	−0.309598
$870$	0	0
$871$	6400.00	0.248973
$872$	25920.0i	1.00661i
$873$	711.000i	0.0275644i
$874$	−26555.0	−1.02773
$875$	0	0
$876$	−22848.0	−0.881236
$877$	22654.0i	0.872259i	0.899884	+	0.436130i	$0.143651\pi$
$877$	22654.0i	0.872259i	−0.899884	+	0.436130i	$0.856349\pi$
$878$	49175.0i	1.89018i
$879$	20433.0	0.784059
$880$	0	0
$881$	−22380.0	−0.855847	−0.427924	−	0.903815i	$-0.640755\pi$
$881$	−22380.0	−0.855847	−0.427924	+	0.903815i	$0.640755\pi$
$882$	15030.0i	0.573794i
$883$	35174.0i	1.34054i	0.742116	+	0.670271i	$0.233822\pi$
$883$	35174.0i	1.34054i	−0.742116	+	0.670271i	$0.766178\pi$
$884$	−17952.0	−0.683022
$885$	0	0
$886$	−53725.0	−2.03716
$887$	− 30868.0i	− 1.16848i	−0.811579	−	0.584242i	$-0.801392\pi$
$887$	− 30868.0i	− 1.16848i	0.811579	−	0.584242i	$-0.198608\pi$
$888$	2565.00i	0.0969322i
$889$	5217.00	0.196820
$890$	0	0
$891$	−891.000	−0.0335013
$892$	− 60520.0i	− 2.27170i
$893$	9165.00i	0.343443i
$894$	3585.00	0.134117
$895$	0	0
$896$	−6345.00	−0.236575
$897$	− 10848.0i	− 0.403795i
$898$	41780.0i	1.55258i
$899$	9612.00	0.356594
$900$	0	0
$901$	5016.00	0.185469
$902$	7645.00i	0.282207i
$903$	− 2772.00i	− 0.102155i
$904$	49680.0	1.82780
$905$	0	0
$906$	18120.0	0.664455
$907$	− 10070.0i	− 0.368654i	−0.982865	−	0.184327i	$-0.940990\pi$
$907$	− 10070.0i	− 0.368654i	0.982865	−	0.184327i	$-0.0590105\pi$
$908$	− 79526.0i	− 2.90657i
$909$	4905.00	0.178975
$910$	0	0
$911$	1885.00	0.0685542	0.0342771	−	0.999412i	$-0.489087\pi$
$911$	1885.00	0.0685542	0.0342771	+	0.999412i	$0.489087\pi$
$912$	− 12549.0i	− 0.455635i
$913$	− 1562.00i	− 0.0566207i
$914$	35290.0	1.27712
$915$	0	0
$916$	−75599.0	−2.72692
$917$	− 5454.00i	− 0.196409i
$918$	4455.00i	0.160171i
$919$	−23703.0	−0.850805	−0.425403	−	0.905004i	$-0.639867\pi$
$919$	−23703.0	−0.850805	−0.425403	+	0.905004i	$0.639867\pi$
$920$	0	0
$921$	−1380.00	−0.0493730
$922$	− 3230.00i	− 0.115374i
$923$	− 30304.0i	− 1.08068i
$924$	1683.00	0.0599206
$925$	0	0
$926$	−44910.0	−1.59377
$927$	11754.0i	0.416453i
$928$	− 4590.00i	− 0.162364i
$929$	−53804.0	−1.90016	−0.950082	−	0.312001i	$-0.899001\pi$
$929$	−53804.0	−1.90016	−0.950082	+	0.312001i	$0.899001\pi$
$930$	0	0
$931$	−15698.0	−0.552611
$932$	− 6987.00i	− 0.245565i
$933$	24984.0i	0.876677i
$934$	67380.0	2.36054
$935$	0	0
$936$	12960.0	0.452576
$937$	− 1326.00i	− 0.0462311i	−0.999733	−	0.0231155i	$-0.992641\pi$
$937$	− 1326.00i	− 0.0462311i	0.999733	−	0.0231155i	$-0.00735856\pi$
$938$	3000.00i	0.104428i
$939$	17787.0	0.618165
$940$	0	0
$941$	−27109.0	−0.939137	−0.469569	−	0.882896i	$-0.655591\pi$
$941$	−27109.0	−0.939137	−0.469569	+	0.882896i	$0.655591\pi$
$942$	28110.0i	0.972265i
$943$	15707.0i	0.542408i
$944$	55625.0	1.91784
$945$	0	0
$946$	16940.0	0.582206
$947$	− 31143.0i	− 1.06865i	−0.845279	−	0.534325i	$-0.820566\pi$
$947$	− 31143.0i	− 1.06865i	0.845279	−	0.534325i	$-0.179434\pi$
$948$	− 36771.0i	− 1.25977i
$949$	14336.0	0.490375
$950$	0	0
$951$	15120.0	0.515562
$952$	− 4455.00i	− 0.151667i
$953$	− 879.000i	− 0.0298779i	−0.999888	−	0.0149389i	$-0.995245\pi$
$953$	− 879.000i	− 0.0298779i	0.999888	−	0.0149389i	$-0.00475539\pi$
$954$	−6840.00	−0.232131
$955$	0	0
$956$	−108460.	−3.66930
$957$	− 1782.00i	− 0.0601921i
$958$	64980.0i	2.19145i
$959$	−2610.00	−0.0878846
$960$	0	0
$961$	1893.00	0.0635427
$962$	− 3040.00i	− 0.101885i
$963$	17442.0i	0.583656i
$964$	−123794.	−4.13603
$965$	0	0
$966$	5085.00	0.169366
$967$	14824.0i	0.492976i	0.969146	+	0.246488i	$0.0792766\pi$
$967$	14824.0i	0.492976i	−0.969146	+	0.246488i	$0.920723\pi$
$968$	5445.00i	0.180794i
$969$	−4653.00	−0.154258
$970$	0	0
$971$	34089.0	1.12664	0.563320	−	0.826239i	$-0.309524\pi$
$971$	34089.0	1.12664	0.563320	+	0.826239i	$0.309524\pi$
$972$	− 4131.00i	− 0.136319i
$973$	− 1908.00i	− 0.0628650i
$974$	30130.0	0.991199
$975$	0	0
$976$	28480.0	0.934040
$977$	− 33446.0i	− 1.09522i	−0.836733	−	0.547611i	$-0.815537\pi$
$977$	− 33446.0i	− 1.09522i	0.836733	−	0.547611i	$-0.184463\pi$
$978$	− 28560.0i	− 0.933792i
$979$	4444.00	0.145077
$980$	0	0
$981$	−5184.00	−0.168718
$982$	− 58490.0i	− 1.90070i
$983$	− 52025.0i	− 1.68804i	−0.536315	−	0.844018i	$-0.680184\pi$
$983$	− 52025.0i	− 1.68804i	0.536315	−	0.844018i	$-0.319816\pi$
$984$	−18765.0	−0.607933
$985$	0	0
$986$	−8910.00	−0.287781
$987$	− 1755.00i	− 0.0565980i
$988$	25568.0i	0.823306i
$989$	34804.0	1.11901
$990$	0	0
$991$	−41260.0	−1.32257	−0.661285	−	0.750135i	$-0.729989\pi$
$991$	−41260.0	−1.32257	−0.661285	+	0.750135i	$0.729989\pi$
$992$	− 15130.0i	− 0.484252i
$993$	31188.0i	0.996698i
$994$	14205.0	0.453275
$995$	0	0
$996$	7242.00	0.230393
$997$	190.000i	0.00603547i	0.999995	+	0.00301773i	$0.000960576\pi$
$997$	190.000i	0.00603547i	−0.999995	+	0.00301773i	$0.999039\pi$
$998$	− 85260.0i	− 2.70427i
$999$	−513.000	−0.0162468

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.b.199.1		2
5.2	odd	4		825.4.a.j.1.1	yes	1
5.3	odd	4		825.4.a.a.1.1	✓	1
5.4	even	2	inner	825.4.c.b.199.2		2
15.2	even	4		2475.4.a.a.1.1		1
15.8	even	4		2475.4.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.4.a.a.1.1	✓	1	5.3	odd	4
825.4.a.j.1.1	yes	1	5.2	odd	4
825.4.c.b.199.1		2	1.1	even	1	trivial
825.4.c.b.199.2		2	5.4	even	2	inner
2475.4.a.a.1.1		1	15.2	even	4
2475.4.a.k.1.1		1	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-5.00000i q^{2} +3.00000i q^{3} -17.0000 q^{4} +15.0000 q^{6} -3.00000i q^{7} +45.0000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-5.00000i q^{2} +3.00000i q^{3} -17.0000 q^{4} +15.0000 q^{6} -3.00000i q^{7} +45.0000i q^{8} -9.00000 q^{9} -11.0000 q^{11} -51.0000i q^{12} +32.0000i q^{13} -15.0000 q^{14} +89.0000 q^{16} -33.0000i q^{17} +45.0000i q^{18} -47.0000 q^{19} +9.00000 q^{21} +55.0000i q^{22} +113.000i q^{23} -135.000 q^{24} +160.000 q^{26} -27.0000i q^{27} +51.0000i q^{28} +54.0000 q^{29} +178.000 q^{31} -85.0000i q^{32} -33.0000i q^{33} -165.000 q^{34} +153.000 q^{36} -19.0000i q^{37} +235.000i q^{38} -96.0000 q^{39} +139.000 q^{41} -45.0000i q^{42} -308.000i q^{43} +187.000 q^{44} +565.000 q^{46} -195.000i q^{47} +267.000i q^{48} +334.000 q^{49} +99.0000 q^{51} -544.000i q^{52} +152.000i q^{53} -135.000 q^{54} +135.000 q^{56} -141.000i q^{57} -270.000i q^{58} +625.000 q^{59} +320.000 q^{61} -890.000i q^{62} +27.0000i q^{63} +287.000 q^{64} -165.000 q^{66} -200.000i q^{67} +561.000i q^{68} -339.000 q^{69} -947.000 q^{71} -405.000i q^{72} -448.000i q^{73} -95.0000 q^{74} +799.000 q^{76} +33.0000i q^{77} +480.000i q^{78} +721.000 q^{79} +81.0000 q^{81} -695.000i q^{82} +142.000i q^{83} -153.000 q^{84} -1540.00 q^{86} +162.000i q^{87} -495.000i q^{88} -404.000 q^{89} +96.0000 q^{91} -1921.00i q^{92} +534.000i q^{93} -975.000 q^{94} +255.000 q^{96} -79.0000i q^{97} -1670.00i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 34 q^{4} + 30 q^{6} - 18 q^{9}+O(q^{10}) \) 2 * q - 34 * q^4 + 30 * q^6 - 18 * q^9	\( 2 q - 34 q^{4} + 30 q^{6} - 18 q^{9} - 22 q^{11} - 30 q^{14} + 178 q^{16} - 94 q^{19} + 18 q^{21} - 270 q^{24} + 320 q^{26} + 108 q^{29} + 356 q^{31} - 330 q^{34} + 306 q^{36} - 192 q^{39} + 278 q^{41} + 374 q^{44} + 1130 q^{46} + 668 q^{49} + 198 q^{51} - 270 q^{54} + 270 q^{56} + 1250 q^{59} + 640 q^{61} + 574 q^{64} - 330 q^{66} - 678 q^{69} - 1894 q^{71} - 190 q^{74} + 1598 q^{76} + 1442 q^{79} + 162 q^{81} - 306 q^{84} - 3080 q^{86} - 808 q^{89} + 192 q^{91} - 1950 q^{94} + 510 q^{96} + 198 q^{99}+O(q^{100}) \) 2 * q - 34 * q^4 + 30 * q^6 - 18 * q^9 - 22 * q^11 - 30 * q^14 + 178 * q^16 - 94 * q^19 + 18 * q^21 - 270 * q^24 + 320 * q^26 + 108 * q^29 + 356 * q^31 - 330 * q^34 + 306 * q^36 - 192 * q^39 + 278 * q^41 + 374 * q^44 + 1130 * q^46 + 668 * q^49 + 198 * q^51 - 270 * q^54 + 270 * q^56 + 1250 * q^59 + 640 * q^61 + 574 * q^64 - 330 * q^66 - 678 * q^69 - 1894 * q^71 - 190 * q^74 + 1598 * q^76 + 1442 * q^79 + 162 * q^81 - 306 * q^84 - 3080 * q^86 - 808 * q^89 + 192 * q^91 - 1950 * q^94 + 510 * q^96 + 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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