LMFDB - Embedded newform 3450.2.a.bo.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3450,2,Mod(1,3450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3450, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3450.a (trivial)

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:	yes
Analytic conductor:	$27.5483886973$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 690)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.17009$ of defining polynomial
Character	$\chi$	$=$	3450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -4.34017 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -4.34017 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.07838 q^{11} +1.00000 q^{12} +2.34017 q^{13} +4.34017 q^{14} +1.00000 q^{16} -0.921622 q^{17} -1.00000 q^{18} +2.34017 q^{19} -4.34017 q^{21} +1.07838 q^{22} -1.00000 q^{23} -1.00000 q^{24} -2.34017 q^{26} +1.00000 q^{27} -4.34017 q^{28} +10.4969 q^{29} -4.00000 q^{31} -1.00000 q^{32} -1.07838 q^{33} +0.921622 q^{34} +1.00000 q^{36} -2.58145 q^{37} -2.34017 q^{38} +2.34017 q^{39} +0.156755 q^{41} +4.34017 q^{42} -0.738205 q^{43} -1.07838 q^{44} +1.00000 q^{46} -6.83710 q^{47} +1.00000 q^{48} +11.8371 q^{49} -0.921622 q^{51} +2.34017 q^{52} +0.340173 q^{53} -1.00000 q^{54} +4.34017 q^{56} +2.34017 q^{57} -10.4969 q^{58} -8.83710 q^{59} -11.5753 q^{61} +4.00000 q^{62} -4.34017 q^{63} +1.00000 q^{64} +1.07838 q^{66} -2.58145 q^{67} -0.921622 q^{68} -1.00000 q^{69} +15.1773 q^{71} -1.00000 q^{72} +4.68035 q^{73} +2.58145 q^{74} +2.34017 q^{76} +4.68035 q^{77} -2.34017 q^{78} -11.9155 q^{79} +1.00000 q^{81} -0.156755 q^{82} -11.4186 q^{83} -4.34017 q^{84} +0.738205 q^{86} +10.4969 q^{87} +1.07838 q^{88} -4.68035 q^{89} -10.1568 q^{91} -1.00000 q^{92} -4.00000 q^{93} +6.83710 q^{94} -1.00000 q^{96} -9.02052 q^{97} -11.8371 q^{98} -1.07838 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} - 2 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 - 2 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} - 2 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{12} - 4 q^{13} + 2 q^{14} + 3 q^{16} - 6 q^{17} - 3 q^{18} - 4 q^{19} - 2 q^{21} - 3 q^{23} - 3 q^{24} + 4 q^{26} + 3 q^{27} - 2 q^{28} + 14 q^{29} - 12 q^{31} - 3 q^{32} + 6 q^{34} + 3 q^{36} - 22 q^{37} + 4 q^{38} - 4 q^{39} - 6 q^{41} + 2 q^{42} - 10 q^{43} + 3 q^{46} + 8 q^{47} + 3 q^{48} + 7 q^{49} - 6 q^{51} - 4 q^{52} - 10 q^{53} - 3 q^{54} + 2 q^{56} - 4 q^{57} - 14 q^{58} + 2 q^{59} - 14 q^{61} + 12 q^{62} - 2 q^{63} + 3 q^{64} - 22 q^{67} - 6 q^{68} - 3 q^{69} + 6 q^{71} - 3 q^{72} - 8 q^{73} + 22 q^{74} - 4 q^{76} - 8 q^{77} + 4 q^{78} - 4 q^{79} + 3 q^{81} + 6 q^{82} - 20 q^{83} - 2 q^{84} + 10 q^{86} + 14 q^{87} + 8 q^{89} - 24 q^{91} - 3 q^{92} - 12 q^{93} - 8 q^{94} - 3 q^{96} + 6 q^{97} - 7 q^{98}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 - 2 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^12 - 4 * q^13 + 2 * q^14 + 3 * q^16 - 6 * q^17 - 3 * q^18 - 4 * q^19 - 2 * q^21 - 3 * q^23 - 3 * q^24 + 4 * q^26 + 3 * q^27 - 2 * q^28 + 14 * q^29 - 12 * q^31 - 3 * q^32 + 6 * q^34 + 3 * q^36 - 22 * q^37 + 4 * q^38 - 4 * q^39 - 6 * q^41 + 2 * q^42 - 10 * q^43 + 3 * q^46 + 8 * q^47 + 3 * q^48 + 7 * q^49 - 6 * q^51 - 4 * q^52 - 10 * q^53 - 3 * q^54 + 2 * q^56 - 4 * q^57 - 14 * q^58 + 2 * q^59 - 14 * q^61 + 12 * q^62 - 2 * q^63 + 3 * q^64 - 22 * q^67 - 6 * q^68 - 3 * q^69 + 6 * q^71 - 3 * q^72 - 8 * q^73 + 22 * q^74 - 4 * q^76 - 8 * q^77 + 4 * q^78 - 4 * q^79 + 3 * q^81 + 6 * q^82 - 20 * q^83 - 2 * q^84 + 10 * q^86 + 14 * q^87 + 8 * q^89 - 24 * q^91 - 3 * q^92 - 12 * q^93 - 8 * q^94 - 3 * q^96 + 6 * q^97 - 7 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	−4.34017	−1.64043	−0.820216	−	0.572055i	$-0.806147\pi$
$7$	−4.34017	−1.64043	−0.820216	+	0.572055i	$0.806147\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.07838	−0.325143	−0.162572	−	0.986697i	$-0.551979\pi$
$11$	−1.07838	−0.325143	−0.162572	+	0.986697i	$0.551979\pi$
$12$	1.00000	0.288675
$13$	2.34017	0.649047	0.324524	−	0.945878i	$-0.394796\pi$
$13$	2.34017	0.649047	0.324524	+	0.945878i	$0.394796\pi$
$14$	4.34017	1.15996
$15$	0	0
$16$	1.00000	0.250000
$17$	−0.921622	−0.223526	−0.111763	−	0.993735i	$-0.535650\pi$
$17$	−0.921622	−0.223526	−0.111763	+	0.993735i	$0.535650\pi$
$18$	−1.00000	−0.235702
$19$	2.34017	0.536873	0.268436	−	0.963297i	$-0.413493\pi$
$19$	2.34017	0.536873	0.268436	+	0.963297i	$0.413493\pi$
$20$	0	0
$21$	−4.34017	−0.947103
$22$	1.07838	0.229911
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−2.34017	−0.458946
$27$	1.00000	0.192450
$28$	−4.34017	−0.820216
$29$	10.4969	1.94923	0.974615	−	0.223886i	$-0.0718743\pi$
$29$	10.4969	1.94923	0.974615	+	0.223886i	$0.0718743\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000	−0.176777
$33$	−1.07838	−0.187721
$34$	0.921622	0.158057
$35$	0	0
$36$	1.00000	0.166667
$37$	−2.58145	−0.424388	−0.212194	−	0.977228i	$-0.568061\pi$
$37$	−2.58145	−0.424388	−0.212194	+	0.977228i	$0.568061\pi$
$38$	−2.34017	−0.379626
$39$	2.34017	0.374728
$40$	0	0
$41$	0.156755	0.0244811	0.0122405	−	0.999925i	$-0.496104\pi$
$41$	0.156755	0.0244811	0.0122405	+	0.999925i	$0.496104\pi$
$42$	4.34017	0.669703
$43$	−0.738205	−0.112575	−0.0562876	−	0.998415i	$-0.517926\pi$
$43$	−0.738205	−0.112575	−0.0562876	+	0.998415i	$0.517926\pi$
$44$	−1.07838	−0.162572
$45$	0	0
$46$	1.00000	0.147442
$47$	−6.83710	−0.997294	−0.498647	−	0.866805i	$-0.666170\pi$
$47$	−6.83710	−0.997294	−0.498647	+	0.866805i	$0.666170\pi$
$48$	1.00000	0.144338
$49$	11.8371	1.69101
$50$	0	0
$51$	−0.921622	−0.129053
$52$	2.34017	0.324524
$53$	0.340173	0.0467264	0.0233632	−	0.999727i	$-0.492563\pi$
$53$	0.340173	0.0467264	0.0233632	+	0.999727i	$0.492563\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	4.34017	0.579980
$57$	2.34017	0.309963
$58$	−10.4969	−1.37831
$59$	−8.83710	−1.15049	−0.575246	−	0.817980i	$-0.695094\pi$
$59$	−8.83710	−1.15049	−0.575246	+	0.817980i	$0.695094\pi$
$60$	0	0
$61$	−11.5753	−1.48207	−0.741033	−	0.671469i	$-0.765664\pi$
$61$	−11.5753	−1.48207	−0.741033	+	0.671469i	$0.765664\pi$
$62$	4.00000	0.508001
$63$	−4.34017	−0.546810
$64$	1.00000	0.125000
$65$	0	0
$66$	1.07838	0.132739
$67$	−2.58145	−0.315374	−0.157687	−	0.987489i	$-0.550404\pi$
$67$	−2.58145	−0.315374	−0.157687	+	0.987489i	$0.550404\pi$
$68$	−0.921622	−0.111763
$69$	−1.00000	−0.120386
$70$	0	0
$71$	15.1773	1.80121	0.900606	−	0.434637i	$-0.143123\pi$
$71$	15.1773	1.80121	0.900606	+	0.434637i	$0.143123\pi$
$72$	−1.00000	−0.117851
$73$	4.68035	0.547793	0.273897	−	0.961759i	$-0.411687\pi$
$73$	4.68035	0.547793	0.273897	+	0.961759i	$0.411687\pi$
$74$	2.58145	0.300087
$75$	0	0
$76$	2.34017	0.268436
$77$	4.68035	0.533375
$78$	−2.34017	−0.264972
$79$	−11.9155	−1.34060	−0.670298	−	0.742092i	$-0.733834\pi$
$79$	−11.9155	−1.34060	−0.670298	+	0.742092i	$0.733834\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−0.156755	−0.0173107
$83$	−11.4186	−1.25335	−0.626674	−	0.779281i	$-0.715584\pi$
$83$	−11.4186	−1.25335	−0.626674	+	0.779281i	$0.715584\pi$
$84$	−4.34017	−0.473552
$85$	0	0
$86$	0.738205	0.0796027
$87$	10.4969	1.12539
$88$	1.07838	0.114955
$89$	−4.68035	−0.496116	−0.248058	−	0.968745i	$-0.579792\pi$
$89$	−4.68035	−0.496116	−0.248058	+	0.968745i	$0.579792\pi$
$90$	0	0
$91$	−10.1568	−1.06472
$92$	−1.00000	−0.104257
$93$	−4.00000	−0.414781
$94$	6.83710	0.705193
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−9.02052	−0.915895	−0.457947	−	0.888979i	$-0.651415\pi$
$97$	−9.02052	−0.915895	−0.457947	+	0.888979i	$0.651415\pi$
$98$	−11.8371	−1.19573
$99$	−1.07838	−0.108381
$100$	0	0
$101$	1.50307	0.149561	0.0747806	−	0.997200i	$-0.476174\pi$
$101$	1.50307	0.149561	0.0747806	+	0.997200i	$0.476174\pi$
$102$	0.921622	0.0912542
$103$	2.49693	0.246030	0.123015	−	0.992405i	$-0.460744\pi$
$103$	2.49693	0.246030	0.123015	+	0.992405i	$0.460744\pi$
$104$	−2.34017	−0.229473
$105$	0	0
$106$	−0.340173	−0.0330405
$107$	−9.57531	−0.925680	−0.462840	−	0.886442i	$-0.653170\pi$
$107$	−9.57531	−0.925680	−0.462840	+	0.886442i	$0.653170\pi$
$108$	1.00000	0.0962250
$109$	−9.78539	−0.937270	−0.468635	−	0.883392i	$-0.655254\pi$
$109$	−9.78539	−0.937270	−0.468635	+	0.883392i	$0.655254\pi$
$110$	0	0
$111$	−2.58145	−0.245020
$112$	−4.34017	−0.410108
$113$	−8.92162	−0.839276	−0.419638	−	0.907692i	$-0.637843\pi$
$113$	−8.92162	−0.839276	−0.419638	+	0.907692i	$0.637843\pi$
$114$	−2.34017	−0.219177
$115$	0	0
$116$	10.4969	0.974615
$117$	2.34017	0.216349
$118$	8.83710	0.813521
$119$	4.00000	0.366679
$120$	0	0
$121$	−9.83710	−0.894282
$122$	11.5753	1.04798
$123$	0.156755	0.0141342
$124$	−4.00000	−0.359211
$125$	0	0
$126$	4.34017	0.386653
$127$	−17.1773	−1.52424	−0.762118	−	0.647438i	$-0.775841\pi$
$127$	−17.1773	−1.52424	−0.762118	+	0.647438i	$0.775841\pi$
$128$	−1.00000	−0.0883883
$129$	−0.738205	−0.0649953
$130$	0	0
$131$	−6.68035	−0.583665	−0.291832	−	0.956470i	$-0.594265\pi$
$131$	−6.68035	−0.583665	−0.291832	+	0.956470i	$0.594265\pi$
$132$	−1.07838	−0.0938607
$133$	−10.1568	−0.880702
$134$	2.58145	0.223003
$135$	0	0
$136$	0.921622	0.0790285
$137$	−22.2823	−1.90371	−0.951853	−	0.306554i	$-0.900824\pi$
$137$	−22.2823	−1.90371	−0.951853	+	0.306554i	$0.900824\pi$
$138$	1.00000	0.0851257
$139$	−10.5236	−0.892599	−0.446300	−	0.894884i	$-0.647258\pi$
$139$	−10.5236	−0.892599	−0.446300	+	0.894884i	$0.647258\pi$
$140$	0	0
$141$	−6.83710	−0.575788
$142$	−15.1773	−1.27365
$143$	−2.52359	−0.211033
$144$	1.00000	0.0833333
$145$	0	0
$146$	−4.68035	−0.387348
$147$	11.8371	0.976308
$148$	−2.58145	−0.212194
$149$	6.92162	0.567041	0.283521	−	0.958966i	$-0.408498\pi$
$149$	6.92162	0.567041	0.283521	+	0.958966i	$0.408498\pi$
$150$	0	0
$151$	6.15676	0.501030	0.250515	−	0.968113i	$-0.419400\pi$
$151$	6.15676	0.501030	0.250515	+	0.968113i	$0.419400\pi$
$152$	−2.34017	−0.189813
$153$	−0.921622	−0.0745087
$154$	−4.68035	−0.377153
$155$	0	0
$156$	2.34017	0.187364
$157$	−2.89496	−0.231043	−0.115521	−	0.993305i	$-0.536854\pi$
$157$	−2.89496	−0.231043	−0.115521	+	0.993305i	$0.536854\pi$
$158$	11.9155	0.947945
$159$	0.340173	0.0269775
$160$	0	0
$161$	4.34017	0.342054
$162$	−1.00000	−0.0785674
$163$	−6.52359	−0.510967	−0.255484	−	0.966813i	$-0.582235\pi$
$163$	−6.52359	−0.510967	−0.255484	+	0.966813i	$0.582235\pi$
$164$	0.156755	0.0122405
$165$	0	0
$166$	11.4186	0.886251
$167$	−5.47641	−0.423777	−0.211889	−	0.977294i	$-0.567961\pi$
$167$	−5.47641	−0.423777	−0.211889	+	0.977294i	$0.567961\pi$
$168$	4.34017	0.334852
$169$	−7.52359	−0.578738
$170$	0	0
$171$	2.34017	0.178958
$172$	−0.738205	−0.0562876
$173$	15.6742	1.19169	0.595844	−	0.803100i	$-0.296818\pi$
$173$	15.6742	1.19169	0.595844	+	0.803100i	$0.296818\pi$
$174$	−10.4969	−0.795770
$175$	0	0
$176$	−1.07838	−0.0812858
$177$	−8.83710	−0.664237
$178$	4.68035	0.350807
$179$	15.3607	1.14811	0.574056	−	0.818816i	$-0.305369\pi$
$179$	15.3607	1.14811	0.574056	+	0.818816i	$0.305369\pi$
$180$	0	0
$181$	21.6163	1.60673	0.803365	−	0.595487i	$-0.203041\pi$
$181$	21.6163	1.60673	0.803365	+	0.595487i	$0.203041\pi$
$182$	10.1568	0.752869
$183$	−11.5753	−0.855671
$184$	1.00000	0.0737210
$185$	0	0
$186$	4.00000	0.293294
$187$	0.993857	0.0726780
$188$	−6.83710	−0.498647
$189$	−4.34017	−0.315701
$190$	0	0
$191$	4.36683	0.315973	0.157987	−	0.987441i	$-0.449500\pi$
$191$	4.36683	0.315973	0.157987	+	0.987441i	$0.449500\pi$
$192$	1.00000	0.0721688
$193$	8.68035	0.624825	0.312412	−	0.949947i	$-0.398863\pi$
$193$	8.68035	0.624825	0.312412	+	0.949947i	$0.398863\pi$
$194$	9.02052	0.647636
$195$	0	0
$196$	11.8371	0.845507
$197$	22.6803	1.61591	0.807954	−	0.589246i	$-0.200575\pi$
$197$	22.6803	1.61591	0.807954	+	0.589246i	$0.200575\pi$
$198$	1.07838	0.0766370
$199$	−5.44521	−0.386001	−0.193000	−	0.981199i	$-0.561822\pi$
$199$	−5.44521	−0.386001	−0.193000	+	0.981199i	$0.561822\pi$
$200$	0	0
$201$	−2.58145	−0.182081
$202$	−1.50307	−0.105756
$203$	−45.5585	−3.19758
$204$	−0.921622	−0.0645265
$205$	0	0
$206$	−2.49693	−0.173969
$207$	−1.00000	−0.0695048
$208$	2.34017	0.162262
$209$	−2.52359	−0.174560
$210$	0	0
$211$	−22.0410	−1.51737	−0.758684	−	0.651459i	$-0.774157\pi$
$211$	−22.0410	−1.51737	−0.758684	+	0.651459i	$0.774157\pi$
$212$	0.340173	0.0233632
$213$	15.1773	1.03993
$214$	9.57531	0.654554
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	17.3607	1.17852
$218$	9.78539	0.662750
$219$	4.68035	0.316268
$220$	0	0
$221$	−2.15676	−0.145079
$222$	2.58145	0.173256
$223$	−21.1773	−1.41814	−0.709068	−	0.705141i	$-0.750884\pi$
$223$	−21.1773	−1.41814	−0.709068	+	0.705141i	$0.750884\pi$
$224$	4.34017	0.289990
$225$	0	0
$226$	8.92162	0.593457
$227$	11.7854	0.782224	0.391112	−	0.920343i	$-0.372091\pi$
$227$	11.7854	0.782224	0.391112	+	0.920343i	$0.372091\pi$
$228$	2.34017	0.154982
$229$	1.78539	0.117982	0.0589908	−	0.998259i	$-0.481212\pi$
$229$	1.78539	0.117982	0.0589908	+	0.998259i	$0.481212\pi$
$230$	0	0
$231$	4.68035	0.307944
$232$	−10.4969	−0.689157
$233$	−18.3135	−1.19976	−0.599879	−	0.800091i	$-0.704785\pi$
$233$	−18.3135	−1.19976	−0.599879	+	0.800091i	$0.704785\pi$
$234$	−2.34017	−0.152982
$235$	0	0
$236$	−8.83710	−0.575246
$237$	−11.9155	−0.773994
$238$	−4.00000	−0.259281
$239$	−5.33403	−0.345030	−0.172515	−	0.985007i	$-0.555189\pi$
$239$	−5.33403	−0.345030	−0.172515	+	0.985007i	$0.555189\pi$
$240$	0	0
$241$	26.1978	1.68755	0.843774	−	0.536698i	$-0.180329\pi$
$241$	26.1978	1.68755	0.843774	+	0.536698i	$0.180329\pi$
$242$	9.83710	0.632353
$243$	1.00000	0.0641500
$244$	−11.5753	−0.741033
$245$	0	0
$246$	−0.156755	−0.00999437
$247$	5.47641	0.348456
$248$	4.00000	0.254000
$249$	−11.4186	−0.723621
$250$	0	0
$251$	27.4329	1.73155	0.865775	−	0.500433i	$-0.166826\pi$
$251$	27.4329	1.73155	0.865775	+	0.500433i	$0.166826\pi$
$252$	−4.34017	−0.273405
$253$	1.07838	0.0677970
$254$	17.1773	1.07780
$255$	0	0
$256$	1.00000	0.0625000
$257$	10.3135	0.643339	0.321670	−	0.946852i	$-0.395756\pi$
$257$	10.3135	0.643339	0.321670	+	0.946852i	$0.395756\pi$
$258$	0.738205	0.0459586
$259$	11.2039	0.696179
$260$	0	0
$261$	10.4969	0.649744
$262$	6.68035	0.412713
$263$	20.9939	1.29454	0.647268	−	0.762262i	$-0.275911\pi$
$263$	20.9939	1.29454	0.647268	+	0.762262i	$0.275911\pi$
$264$	1.07838	0.0663696
$265$	0	0
$266$	10.1568	0.622751
$267$	−4.68035	−0.286433
$268$	−2.58145	−0.157687
$269$	25.3874	1.54789	0.773947	−	0.633250i	$-0.218280\pi$
$269$	25.3874	1.54789	0.773947	+	0.633250i	$0.218280\pi$
$270$	0	0
$271$	−32.5646	−1.97816	−0.989080	−	0.147379i	$-0.952916\pi$
$271$	−32.5646	−1.97816	−0.989080	+	0.147379i	$0.952916\pi$
$272$	−0.921622	−0.0558816
$273$	−10.1568	−0.614715
$274$	22.2823	1.34612
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	−15.7009	−0.943374	−0.471687	−	0.881766i	$-0.656355\pi$
$277$	−15.7009	−0.943374	−0.471687	+	0.881766i	$0.656355\pi$
$278$	10.5236	0.631163
$279$	−4.00000	−0.239474
$280$	0	0
$281$	−9.36069	−0.558412	−0.279206	−	0.960231i	$-0.590071\pi$
$281$	−9.36069	−0.558412	−0.279206	+	0.960231i	$0.590071\pi$
$282$	6.83710	0.407143
$283$	17.4186	1.03543	0.517713	−	0.855555i	$-0.326784\pi$
$283$	17.4186	1.03543	0.517713	+	0.855555i	$0.326784\pi$
$284$	15.1773	0.900606
$285$	0	0
$286$	2.52359	0.149223
$287$	−0.680346	−0.0401596
$288$	−1.00000	−0.0589256
$289$	−16.1506	−0.950036
$290$	0	0
$291$	−9.02052	−0.528792
$292$	4.68035	0.273897
$293$	16.3402	0.954603	0.477302	−	0.878740i	$-0.341615\pi$
$293$	16.3402	0.954603	0.477302	+	0.878740i	$0.341615\pi$
$294$	−11.8371	−0.690354
$295$	0	0
$296$	2.58145	0.150044
$297$	−1.07838	−0.0625738
$298$	−6.92162	−0.400959
$299$	−2.34017	−0.135336
$300$	0	0
$301$	3.20394	0.184672
$302$	−6.15676	−0.354281
$303$	1.50307	0.0863492
$304$	2.34017	0.134218
$305$	0	0
$306$	0.921622	0.0526856
$307$	3.20394	0.182858	0.0914292	−	0.995812i	$-0.470856\pi$
$307$	3.20394	0.182858	0.0914292	+	0.995812i	$0.470856\pi$
$308$	4.68035	0.266687
$309$	2.49693	0.142045
$310$	0	0
$311$	12.6537	0.717525	0.358762	−	0.933429i	$-0.383199\pi$
$311$	12.6537	0.717525	0.358762	+	0.933429i	$0.383199\pi$
$312$	−2.34017	−0.132486
$313$	−33.2183	−1.87761	−0.938805	−	0.344449i	$-0.888066\pi$
$313$	−33.2183	−1.87761	−0.938805	+	0.344449i	$0.888066\pi$
$314$	2.89496	0.163372
$315$	0	0
$316$	−11.9155	−0.670298
$317$	6.99386	0.392814	0.196407	−	0.980522i	$-0.437073\pi$
$317$	6.99386	0.392814	0.196407	+	0.980522i	$0.437073\pi$
$318$	−0.340173	−0.0190760
$319$	−11.3197	−0.633779
$320$	0	0
$321$	−9.57531	−0.534441
$322$	−4.34017	−0.241868
$323$	−2.15676	−0.120005
$324$	1.00000	0.0555556
$325$	0	0
$326$	6.52359	0.361308
$327$	−9.78539	−0.541133
$328$	−0.156755	−0.00865537
$329$	29.6742	1.63599
$330$	0	0
$331$	−29.7275	−1.63397	−0.816986	−	0.576657i	$-0.804357\pi$
$331$	−29.7275	−1.63397	−0.816986	+	0.576657i	$0.804357\pi$
$332$	−11.4186	−0.626674
$333$	−2.58145	−0.141463
$334$	5.47641	0.299656
$335$	0	0
$336$	−4.34017	−0.236776
$337$	−28.3402	−1.54379	−0.771894	−	0.635751i	$-0.780690\pi$
$337$	−28.3402	−1.54379	−0.771894	+	0.635751i	$0.780690\pi$
$338$	7.52359	0.409229
$339$	−8.92162	−0.484556
$340$	0	0
$341$	4.31351	0.233590
$342$	−2.34017	−0.126542
$343$	−20.9939	−1.13356
$344$	0.738205	0.0398013
$345$	0	0
$346$	−15.6742	−0.842650
$347$	22.5236	1.20913	0.604565	−	0.796556i	$-0.293347\pi$
$347$	22.5236	1.20913	0.604565	+	0.796556i	$0.293347\pi$
$348$	10.4969	0.562694
$349$	15.6742	0.839021	0.419510	−	0.907751i	$-0.362202\pi$
$349$	15.6742	0.839021	0.419510	+	0.907751i	$0.362202\pi$
$350$	0	0
$351$	2.34017	0.124909
$352$	1.07838	0.0574777
$353$	−26.3135	−1.40053	−0.700263	−	0.713885i	$-0.746934\pi$
$353$	−26.3135	−1.40053	−0.700263	+	0.713885i	$0.746934\pi$
$354$	8.83710	0.469687
$355$	0	0
$356$	−4.68035	−0.248058
$357$	4.00000	0.211702
$358$	−15.3607	−0.811838
$359$	−0.796064	−0.0420146	−0.0210073	−	0.999779i	$-0.506687\pi$
$359$	−0.796064	−0.0420146	−0.0210073	+	0.999779i	$0.506687\pi$
$360$	0	0
$361$	−13.5236	−0.711768
$362$	−21.6163	−1.13613
$363$	−9.83710	−0.516314
$364$	−10.1568	−0.532359
$365$	0	0
$366$	11.5753	0.605051
$367$	−13.7009	−0.715179	−0.357590	−	0.933879i	$-0.616401\pi$
$367$	−13.7009	−0.715179	−0.357590	+	0.933879i	$0.616401\pi$
$368$	−1.00000	−0.0521286
$369$	0.156755	0.00816036
$370$	0	0
$371$	−1.47641	−0.0766514
$372$	−4.00000	−0.207390
$373$	−4.25565	−0.220349	−0.110175	−	0.993912i	$-0.535141\pi$
$373$	−4.25565	−0.220349	−0.110175	+	0.993912i	$0.535141\pi$
$374$	−0.993857	−0.0513911
$375$	0	0
$376$	6.83710	0.352597
$377$	24.5646	1.26514
$378$	4.34017	0.223234
$379$	−30.6537	−1.57457	−0.787287	−	0.616587i	$-0.788515\pi$
$379$	−30.6537	−1.57457	−0.787287	+	0.616587i	$0.788515\pi$
$380$	0	0
$381$	−17.1773	−0.880018
$382$	−4.36683	−0.223427
$383$	20.8781	1.06682	0.533412	−	0.845856i	$-0.320910\pi$
$383$	20.8781	1.06682	0.533412	+	0.845856i	$0.320910\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−8.68035	−0.441818
$387$	−0.738205	−0.0375251
$388$	−9.02052	−0.457947
$389$	−16.9627	−0.860041	−0.430021	−	0.902819i	$-0.641494\pi$
$389$	−16.9627	−0.860041	−0.430021	+	0.902819i	$0.641494\pi$
$390$	0	0
$391$	0.921622	0.0466084
$392$	−11.8371	−0.597864
$393$	−6.68035	−0.336979
$394$	−22.6803	−1.14262
$395$	0	0
$396$	−1.07838	−0.0541905
$397$	16.4969	0.827957	0.413979	−	0.910287i	$-0.364139\pi$
$397$	16.4969	0.827957	0.413979	+	0.910287i	$0.364139\pi$
$398$	5.44521	0.272944
$399$	−10.1568	−0.508474
$400$	0	0
$401$	−35.2039	−1.75800	−0.879000	−	0.476821i	$-0.841789\pi$
$401$	−35.2039	−1.75800	−0.879000	+	0.476821i	$0.841789\pi$
$402$	2.58145	0.128751
$403$	−9.36069	−0.466289
$404$	1.50307	0.0747806
$405$	0	0
$406$	45.5585	2.26103
$407$	2.78378	0.137987
$408$	0.921622	0.0456271
$409$	11.3607	0.561750	0.280875	−	0.959744i	$-0.409375\pi$
$409$	11.3607	0.561750	0.280875	+	0.959744i	$0.409375\pi$
$410$	0	0
$411$	−22.2823	−1.09911
$412$	2.49693	0.123015
$413$	38.3545	1.88730
$414$	1.00000	0.0491473
$415$	0	0
$416$	−2.34017	−0.114736
$417$	−10.5236	−0.515342
$418$	2.52359	0.123433
$419$	−18.1256	−0.885491	−0.442746	−	0.896647i	$-0.645996\pi$
$419$	−18.1256	−0.885491	−0.442746	+	0.896647i	$0.645996\pi$
$420$	0	0
$421$	2.58145	0.125812	0.0629061	−	0.998019i	$-0.479963\pi$
$421$	2.58145	0.125812	0.0629061	+	0.998019i	$0.479963\pi$
$422$	22.0410	1.07294
$423$	−6.83710	−0.332431
$424$	−0.340173	−0.0165203
$425$	0	0
$426$	−15.1773	−0.735341
$427$	50.2388	2.43123
$428$	−9.57531	−0.462840
$429$	−2.52359	−0.121840
$430$	0	0
$431$	−33.9877	−1.63713	−0.818565	−	0.574414i	$-0.805230\pi$
$431$	−33.9877	−1.63713	−0.818565	+	0.574414i	$0.805230\pi$
$432$	1.00000	0.0481125
$433$	8.28685	0.398241	0.199120	−	0.979975i	$-0.436192\pi$
$433$	8.28685	0.398241	0.199120	+	0.979975i	$0.436192\pi$
$434$	−17.3607	−0.833340
$435$	0	0
$436$	−9.78539	−0.468635
$437$	−2.34017	−0.111946
$438$	−4.68035	−0.223636
$439$	−28.9939	−1.38380	−0.691901	−	0.721993i	$-0.743226\pi$
$439$	−28.9939	−1.38380	−0.691901	+	0.721993i	$0.743226\pi$
$440$	0	0
$441$	11.8371	0.563671
$442$	2.15676	0.102586
$443$	3.20394	0.152224	0.0761118	−	0.997099i	$-0.475749\pi$
$443$	3.20394	0.152224	0.0761118	+	0.997099i	$0.475749\pi$
$444$	−2.58145	−0.122510
$445$	0	0
$446$	21.1773	1.00277
$447$	6.92162	0.327381
$448$	−4.34017	−0.205054
$449$	28.1568	1.32880	0.664400	−	0.747377i	$-0.268687\pi$
$449$	28.1568	1.32880	0.664400	+	0.747377i	$0.268687\pi$
$450$	0	0
$451$	−0.169042	−0.00795986
$452$	−8.92162	−0.419638
$453$	6.15676	0.289270
$454$	−11.7854	−0.553116
$455$	0	0
$456$	−2.34017	−0.109589
$457$	23.1773	1.08419	0.542094	−	0.840318i	$-0.317632\pi$
$457$	23.1773	1.08419	0.542094	+	0.840318i	$0.317632\pi$
$458$	−1.78539	−0.0834256
$459$	−0.921622	−0.0430176
$460$	0	0
$461$	−42.3279	−1.97141	−0.985703	−	0.168491i	$-0.946110\pi$
$461$	−42.3279	−1.97141	−0.985703	+	0.168491i	$0.946110\pi$
$462$	−4.68035	−0.217749
$463$	34.9048	1.62216	0.811082	−	0.584933i	$-0.198879\pi$
$463$	34.9048	1.62216	0.811082	+	0.584933i	$0.198879\pi$
$464$	10.4969	0.487308
$465$	0	0
$466$	18.3135	0.848357
$467$	37.7731	1.74793	0.873965	−	0.485988i	$-0.161540\pi$
$467$	37.7731	1.74793	0.873965	+	0.485988i	$0.161540\pi$
$468$	2.34017	0.108175
$469$	11.2039	0.517350
$470$	0	0
$471$	−2.89496	−0.133393
$472$	8.83710	0.406761
$473$	0.796064	0.0366030
$474$	11.9155	0.547296
$475$	0	0
$476$	4.00000	0.183340
$477$	0.340173	0.0155755
$478$	5.33403	0.243973
$479$	−28.1978	−1.28839	−0.644195	−	0.764861i	$-0.722807\pi$
$479$	−28.1978	−1.28839	−0.644195	+	0.764861i	$0.722807\pi$
$480$	0	0
$481$	−6.04104	−0.275448
$482$	−26.1978	−1.19328
$483$	4.34017	0.197485
$484$	−9.83710	−0.447141
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−38.2245	−1.73212	−0.866058	−	0.499944i	$-0.833354\pi$
$487$	−38.2245	−1.73212	−0.866058	+	0.499944i	$0.833354\pi$
$488$	11.5753	0.523989
$489$	−6.52359	−0.295007
$490$	0	0
$491$	11.3074	0.510294	0.255147	−	0.966902i	$-0.417876\pi$
$491$	11.3074	0.510294	0.255147	+	0.966902i	$0.417876\pi$
$492$	0.156755	0.00706708
$493$	−9.67420	−0.435704
$494$	−5.47641	−0.246395
$495$	0	0
$496$	−4.00000	−0.179605
$497$	−65.8720	−2.95476
$498$	11.4186	0.511677
$499$	−2.47027	−0.110584	−0.0552922	−	0.998470i	$-0.517609\pi$
$499$	−2.47027	−0.110584	−0.0552922	+	0.998470i	$0.517609\pi$
$500$	0	0
$501$	−5.47641	−0.244668
$502$	−27.4329	−1.22439
$503$	20.6270	0.919713	0.459857	−	0.887993i	$-0.347901\pi$
$503$	20.6270	0.919713	0.459857	+	0.887993i	$0.347901\pi$
$504$	4.34017	0.193327
$505$	0	0
$506$	−1.07838	−0.0479397
$507$	−7.52359	−0.334134
$508$	−17.1773	−0.762118
$509$	−32.2245	−1.42832	−0.714162	−	0.699981i	$-0.753192\pi$
$509$	−32.2245	−1.42832	−0.714162	+	0.699981i	$0.753192\pi$
$510$	0	0
$511$	−20.3135	−0.898617
$512$	−1.00000	−0.0441942
$513$	2.34017	0.103321
$514$	−10.3135	−0.454909
$515$	0	0
$516$	−0.738205	−0.0324977
$517$	7.37298	0.324263
$518$	−11.2039	−0.492273
$519$	15.6742	0.688021
$520$	0	0
$521$	−3.51745	−0.154102	−0.0770511	−	0.997027i	$-0.524550\pi$
$521$	−3.51745	−0.154102	−0.0770511	+	0.997027i	$0.524550\pi$
$522$	−10.4969	−0.459438
$523$	35.9421	1.57164	0.785820	−	0.618455i	$-0.212241\pi$
$523$	35.9421	1.57164	0.785820	+	0.618455i	$0.212241\pi$
$524$	−6.68035	−0.291832
$525$	0	0
$526$	−20.9939	−0.915376
$527$	3.68649	0.160586
$528$	−1.07838	−0.0469304
$529$	1.00000	0.0434783
$530$	0	0
$531$	−8.83710	−0.383498
$532$	−10.1568	−0.440351
$533$	0.366835	0.0158894
$534$	4.68035	0.202538
$535$	0	0
$536$	2.58145	0.111502
$537$	15.3607	0.662863
$538$	−25.3874	−1.09453
$539$	−12.7649	−0.549822
$540$	0	0
$541$	31.7275	1.36407	0.682036	−	0.731318i	$-0.261095\pi$
$541$	31.7275	1.36407	0.682036	+	0.731318i	$0.261095\pi$
$542$	32.5646	1.39877
$543$	21.6163	0.927646
$544$	0.921622	0.0395142
$545$	0	0
$546$	10.1568	0.434669
$547$	9.84324	0.420867	0.210433	−	0.977608i	$-0.432512\pi$
$547$	9.84324	0.420867	0.210433	+	0.977608i	$0.432512\pi$
$548$	−22.2823	−0.951853
$549$	−11.5753	−0.494022
$550$	0	0
$551$	24.5646	1.04649
$552$	1.00000	0.0425628
$553$	51.7152	2.19916
$554$	15.7009	0.667066
$555$	0	0
$556$	−10.5236	−0.446300
$557$	−26.3279	−1.11555	−0.557774	−	0.829993i	$-0.688344\pi$
$557$	−26.3279	−1.11555	−0.557774	+	0.829993i	$0.688344\pi$
$558$	4.00000	0.169334
$559$	−1.72753	−0.0730666
$560$	0	0
$561$	0.993857	0.0419607
$562$	9.36069	0.394857
$563$	30.2557	1.27512	0.637562	−	0.770399i	$-0.279943\pi$
$563$	30.2557	1.27512	0.637562	+	0.770399i	$0.279943\pi$
$564$	−6.83710	−0.287894
$565$	0	0
$566$	−17.4186	−0.732156
$567$	−4.34017	−0.182270
$568$	−15.1773	−0.636824
$569$	33.8720	1.41999	0.709994	−	0.704208i	$-0.248698\pi$
$569$	33.8720	1.41999	0.709994	+	0.704208i	$0.248698\pi$
$570$	0	0
$571$	35.1650	1.47161	0.735804	−	0.677194i	$-0.236804\pi$
$571$	35.1650	1.47161	0.735804	+	0.677194i	$0.236804\pi$
$572$	−2.52359	−0.105517
$573$	4.36683	0.182427
$574$	0.680346	0.0283971
$575$	0	0
$576$	1.00000	0.0416667
$577$	4.00000	0.166522	0.0832611	−	0.996528i	$-0.473466\pi$
$577$	4.00000	0.166522	0.0832611	+	0.996528i	$0.473466\pi$
$578$	16.1506	0.671777
$579$	8.68035	0.360743
$580$	0	0
$581$	49.5585	2.05603
$582$	9.02052	0.373913
$583$	−0.366835	−0.0151928
$584$	−4.68035	−0.193674
$585$	0	0
$586$	−16.3402	−0.675006
$587$	−9.30737	−0.384156	−0.192078	−	0.981380i	$-0.561523\pi$
$587$	−9.30737	−0.384156	−0.192078	+	0.981380i	$0.561523\pi$
$588$	11.8371	0.488154
$589$	−9.36069	−0.385701
$590$	0	0
$591$	22.6803	0.932945
$592$	−2.58145	−0.106097
$593$	−33.0349	−1.35658	−0.678290	−	0.734794i	$-0.737279\pi$
$593$	−33.0349	−1.35658	−0.678290	+	0.734794i	$0.737279\pi$
$594$	1.07838	0.0442464
$595$	0	0
$596$	6.92162	0.283521
$597$	−5.44521	−0.222858
$598$	2.34017	0.0956968
$599$	13.6475	0.557623	0.278812	−	0.960346i	$-0.410059\pi$
$599$	13.6475	0.557623	0.278812	+	0.960346i	$0.410059\pi$
$600$	0	0
$601$	1.68649	0.0687933	0.0343967	−	0.999408i	$-0.489049\pi$
$601$	1.68649	0.0687933	0.0343967	+	0.999408i	$0.489049\pi$
$602$	−3.20394	−0.130583
$603$	−2.58145	−0.105125
$604$	6.15676	0.250515
$605$	0	0
$606$	−1.50307	−0.0610581
$607$	47.2183	1.91653	0.958266	−	0.285878i	$-0.0922851\pi$
$607$	47.2183	1.91653	0.958266	+	0.285878i	$0.0922851\pi$
$608$	−2.34017	−0.0949065
$609$	−45.5585	−1.84612
$610$	0	0
$611$	−16.0000	−0.647291
$612$	−0.921622	−0.0372544
$613$	7.45959	0.301290	0.150645	−	0.988588i	$-0.451865\pi$
$613$	7.45959	0.301290	0.150645	+	0.988588i	$0.451865\pi$
$614$	−3.20394	−0.129300
$615$	0	0
$616$	−4.68035	−0.188577
$617$	−15.8120	−0.636569	−0.318285	−	0.947995i	$-0.603107\pi$
$617$	−15.8120	−0.636569	−0.318285	+	0.947995i	$0.603107\pi$
$618$	−2.49693	−0.100441
$619$	−26.3402	−1.05870	−0.529350	−	0.848403i	$-0.677564\pi$
$619$	−26.3402	−1.05870	−0.529350	+	0.848403i	$0.677564\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	−12.6537	−0.507367
$623$	20.3135	0.813844
$624$	2.34017	0.0936819
$625$	0	0
$626$	33.2183	1.32767
$627$	−2.52359	−0.100782
$628$	−2.89496	−0.115521
$629$	2.37912	0.0948618
$630$	0	0
$631$	−14.4391	−0.574810	−0.287405	−	0.957809i	$-0.592793\pi$
$631$	−14.4391	−0.574810	−0.287405	+	0.957809i	$0.592793\pi$
$632$	11.9155	0.473972
$633$	−22.0410	−0.876053
$634$	−6.99386	−0.277762
$635$	0	0
$636$	0.340173	0.0134887
$637$	27.7009	1.09755
$638$	11.3197	0.448149
$639$	15.1773	0.600404
$640$	0	0
$641$	−5.78992	−0.228688	−0.114344	−	0.993441i	$-0.536477\pi$
$641$	−5.78992	−0.228688	−0.114344	+	0.993441i	$0.536477\pi$
$642$	9.57531	0.377907
$643$	−23.4063	−0.923053	−0.461526	−	0.887126i	$-0.652698\pi$
$643$	−23.4063	−0.923053	−0.461526	+	0.887126i	$0.652698\pi$
$644$	4.34017	0.171027
$645$	0	0
$646$	2.15676	0.0848564
$647$	−25.9877	−1.02168	−0.510841	−	0.859675i	$-0.670666\pi$
$647$	−25.9877	−1.02168	−0.510841	+	0.859675i	$0.670666\pi$
$648$	−1.00000	−0.0392837
$649$	9.52973	0.374075
$650$	0	0
$651$	17.3607	0.680419
$652$	−6.52359	−0.255484
$653$	0.325797	0.0127494	0.00637471	−	0.999980i	$-0.497971\pi$
$653$	0.325797	0.0127494	0.00637471	+	0.999980i	$0.497971\pi$
$654$	9.78539	0.382639
$655$	0	0
$656$	0.156755	0.00612027
$657$	4.68035	0.182598
$658$	−29.6742	−1.15682
$659$	−3.11942	−0.121515	−0.0607576	−	0.998153i	$-0.519352\pi$
$659$	−3.11942	−0.121515	−0.0607576	+	0.998153i	$0.519352\pi$
$660$	0	0
$661$	24.1399	0.938935	0.469467	−	0.882950i	$-0.344446\pi$
$661$	24.1399	0.938935	0.469467	+	0.882950i	$0.344446\pi$
$662$	29.7275	1.15539
$663$	−2.15676	−0.0837614
$664$	11.4186	0.443126
$665$	0	0
$666$	2.58145	0.100029
$667$	−10.4969	−0.406443
$668$	−5.47641	−0.211889
$669$	−21.1773	−0.818761
$670$	0	0
$671$	12.4826	0.481884
$672$	4.34017	0.167426
$673$	45.6742	1.76061	0.880306	−	0.474407i	$-0.157338\pi$
$673$	45.6742	1.76061	0.880306	+	0.474407i	$0.157338\pi$
$674$	28.3402	1.09162
$675$	0	0
$676$	−7.52359	−0.289369
$677$	−9.38735	−0.360785	−0.180393	−	0.983595i	$-0.557737\pi$
$677$	−9.38735	−0.360785	−0.180393	+	0.983595i	$0.557737\pi$
$678$	8.92162	0.342633
$679$	39.1506	1.50246
$680$	0	0
$681$	11.7854	0.451617
$682$	−4.31351	−0.165173
$683$	−20.9939	−0.803308	−0.401654	−	0.915792i	$-0.631564\pi$
$683$	−20.9939	−0.803308	−0.401654	+	0.915792i	$0.631564\pi$
$684$	2.34017	0.0894788
$685$	0	0
$686$	20.9939	0.801549
$687$	1.78539	0.0681167
$688$	−0.738205	−0.0281438
$689$	0.796064	0.0303276
$690$	0	0
$691$	−44.1445	−1.67933	−0.839667	−	0.543101i	$-0.817250\pi$
$691$	−44.1445	−1.67933	−0.839667	+	0.543101i	$0.817250\pi$
$692$	15.6742	0.595844
$693$	4.68035	0.177792
$694$	−22.5236	−0.854984
$695$	0	0
$696$	−10.4969	−0.397885
$697$	−0.144469	−0.00547217
$698$	−15.6742	−0.593277
$699$	−18.3135	−0.692681
$700$	0	0
$701$	−27.7998	−1.04998	−0.524991	−	0.851108i	$-0.675931\pi$
$701$	−27.7998	−1.04998	−0.524991	+	0.851108i	$0.675931\pi$
$702$	−2.34017	−0.0883241
$703$	−6.04104	−0.227842
$704$	−1.07838	−0.0406429
$705$	0	0
$706$	26.3135	0.990322
$707$	−6.52359	−0.245345
$708$	−8.83710	−0.332119
$709$	4.30898	0.161827	0.0809135	−	0.996721i	$-0.474216\pi$
$709$	4.30898	0.161827	0.0809135	+	0.996721i	$0.474216\pi$
$710$	0	0
$711$	−11.9155	−0.446865
$712$	4.68035	0.175403
$713$	4.00000	0.149801
$714$	−4.00000	−0.149696
$715$	0	0
$716$	15.3607	0.574056
$717$	−5.33403	−0.199203
$718$	0.796064	0.0297088
$719$	15.9733	0.595705	0.297852	−	0.954612i	$-0.403730\pi$
$719$	15.9733	0.595705	0.297852	+	0.954612i	$0.403730\pi$
$720$	0	0
$721$	−10.8371	−0.403595
$722$	13.5236	0.503296
$723$	26.1978	0.974306
$724$	21.6163	0.803365
$725$	0	0
$726$	9.83710	0.365089
$727$	0.340173	0.0126163	0.00630816	−	0.999980i	$-0.497992\pi$
$727$	0.340173	0.0126163	0.00630816	+	0.999980i	$0.497992\pi$
$728$	10.1568	0.376434
$729$	1.00000	0.0370370
$730$	0	0
$731$	0.680346	0.0251635
$732$	−11.5753	−0.427836
$733$	19.2618	0.711451	0.355725	−	0.934591i	$-0.384234\pi$
$733$	19.2618	0.711451	0.355725	+	0.934591i	$0.384234\pi$
$734$	13.7009	0.505708
$735$	0	0
$736$	1.00000	0.0368605
$737$	2.78378	0.102542
$738$	−0.156755	−0.00577025
$739$	25.5585	0.940184	0.470092	−	0.882617i	$-0.344221\pi$
$739$	25.5585	0.940184	0.470092	+	0.882617i	$0.344221\pi$
$740$	0	0
$741$	5.47641	0.201181
$742$	1.47641	0.0542007
$743$	36.8781	1.35293	0.676464	−	0.736476i	$-0.263511\pi$
$743$	36.8781	1.35293	0.676464	+	0.736476i	$0.263511\pi$
$744$	4.00000	0.146647
$745$	0	0
$746$	4.25565	0.155810
$747$	−11.4186	−0.417783
$748$	0.993857	0.0363390
$749$	41.5585	1.51851
$750$	0	0
$751$	18.1256	0.661411	0.330706	−	0.943734i	$-0.392713\pi$
$751$	18.1256	0.661411	0.330706	+	0.943734i	$0.392713\pi$
$752$	−6.83710	−0.249323
$753$	27.4329	0.999711
$754$	−24.5646	−0.894591
$755$	0	0
$756$	−4.34017	−0.157851
$757$	17.4186	0.633088	0.316544	−	0.948578i	$-0.397478\pi$
$757$	17.4186	0.633088	0.316544	+	0.948578i	$0.397478\pi$
$758$	30.6537	1.11339
$759$	1.07838	0.0391426
$760$	0	0
$761$	−23.4140	−0.848757	−0.424379	−	0.905485i	$-0.639507\pi$
$761$	−23.4140	−0.848757	−0.424379	+	0.905485i	$0.639507\pi$
$762$	17.1773	0.622267
$763$	42.4703	1.53753
$764$	4.36683	0.157987
$765$	0	0
$766$	−20.8781	−0.754358
$767$	−20.6803	−0.746724
$768$	1.00000	0.0360844
$769$	−29.7152	−1.07156	−0.535779	−	0.844358i	$-0.679982\pi$
$769$	−29.7152	−1.07156	−0.535779	+	0.844358i	$0.679982\pi$
$770$	0	0
$771$	10.3135	0.371432
$772$	8.68035	0.312412
$773$	−15.3463	−0.551969	−0.275984	−	0.961162i	$-0.589004\pi$
$773$	−15.3463	−0.551969	−0.275984	+	0.961162i	$0.589004\pi$
$774$	0.738205	0.0265342
$775$	0	0
$776$	9.02052	0.323818
$777$	11.2039	0.401939
$778$	16.9627	0.608141
$779$	0.366835	0.0131432
$780$	0	0
$781$	−16.3668	−0.585651
$782$	−0.921622	−0.0329571
$783$	10.4969	0.375130
$784$	11.8371	0.422754
$785$	0	0
$786$	6.68035	0.238280
$787$	22.8950	0.816117	0.408059	−	0.912956i	$-0.366206\pi$
$787$	22.8950	0.816117	0.408059	+	0.912956i	$0.366206\pi$
$788$	22.6803	0.807954
$789$	20.9939	0.747401
$790$	0	0
$791$	38.7214	1.37677
$792$	1.07838	0.0383185
$793$	−27.0882	−0.961931
$794$	−16.4969	−0.585454
$795$	0	0
$796$	−5.44521	−0.193000
$797$	7.60650	0.269436	0.134718	−	0.990884i	$-0.456987\pi$
$797$	7.60650	0.269436	0.134718	+	0.990884i	$0.456987\pi$
$798$	10.1568	0.359545
$799$	6.30122	0.222921
$800$	0	0
$801$	−4.68035	−0.165372
$802$	35.2039	1.24309
$803$	−5.04718	−0.178111
$804$	−2.58145	−0.0910407
$805$	0	0
$806$	9.36069	0.329716
$807$	25.3874	0.893677
$808$	−1.50307	−0.0528779
$809$	43.7275	1.53738	0.768689	−	0.639623i	$-0.220909\pi$
$809$	43.7275	1.53738	0.768689	+	0.639623i	$0.220909\pi$
$810$	0	0
$811$	−4.79606	−0.168413	−0.0842063	−	0.996448i	$-0.526835\pi$
$811$	−4.79606	−0.168413	−0.0842063	+	0.996448i	$0.526835\pi$
$812$	−45.5585	−1.59879
$813$	−32.5646	−1.14209
$814$	−2.78378	−0.0975713
$815$	0	0
$816$	−0.921622	−0.0322632
$817$	−1.72753	−0.0604385
$818$	−11.3607	−0.397217
$819$	−10.1568	−0.354906
$820$	0	0
$821$	−12.2245	−0.426636	−0.213318	−	0.976983i	$-0.568427\pi$
$821$	−12.2245	−0.426636	−0.213318	+	0.976983i	$0.568427\pi$
$822$	22.2823	0.777185
$823$	37.5441	1.30871	0.654353	−	0.756189i	$-0.272941\pi$
$823$	37.5441	1.30871	0.654353	+	0.756189i	$0.272941\pi$
$824$	−2.49693	−0.0869846
$825$	0	0
$826$	−38.3545	−1.33453
$827$	38.3090	1.33213	0.666067	−	0.745892i	$-0.267977\pi$
$827$	38.3090	1.33213	0.666067	+	0.745892i	$0.267977\pi$
$828$	−1.00000	−0.0347524
$829$	−31.4140	−1.09105	−0.545527	−	0.838093i	$-0.683670\pi$
$829$	−31.4140	−1.09105	−0.545527	+	0.838093i	$0.683670\pi$
$830$	0	0
$831$	−15.7009	−0.544657
$832$	2.34017	0.0811309
$833$	−10.9093	−0.377986
$834$	10.5236	0.364402
$835$	0	0
$836$	−2.52359	−0.0872802
$837$	−4.00000	−0.138260
$838$	18.1256	0.626137
$839$	23.1506	0.799248	0.399624	−	0.916679i	$-0.369141\pi$
$839$	23.1506	0.799248	0.399624	+	0.916679i	$0.369141\pi$
$840$	0	0
$841$	81.1855	2.79950
$842$	−2.58145	−0.0889626
$843$	−9.36069	−0.322399
$844$	−22.0410	−0.758684
$845$	0	0
$846$	6.83710	0.235064
$847$	42.6947	1.46701
$848$	0.340173	0.0116816
$849$	17.4186	0.597803
$850$	0	0
$851$	2.58145	0.0884909
$852$	15.1773	0.519965
$853$	32.4969	1.11267	0.556337	−	0.830957i	$-0.312206\pi$
$853$	32.4969	1.11267	0.556337	+	0.830957i	$0.312206\pi$
$854$	−50.2388	−1.71914
$855$	0	0
$856$	9.57531	0.327277
$857$	−37.8310	−1.29228	−0.646140	−	0.763219i	$-0.723618\pi$
$857$	−37.8310	−1.29228	−0.646140	+	0.763219i	$0.723618\pi$
$858$	2.52359	0.0861540
$859$	−28.1978	−0.962096	−0.481048	−	0.876694i	$-0.659744\pi$
$859$	−28.1978	−0.962096	−0.481048	+	0.876694i	$0.659744\pi$
$860$	0	0
$861$	−0.680346	−0.0231861
$862$	33.9877	1.15763
$863$	−32.0288	−1.09027	−0.545136	−	0.838348i	$-0.683522\pi$
$863$	−32.0288	−1.09027	−0.545136	+	0.838348i	$0.683522\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−8.28685	−0.281599
$867$	−16.1506	−0.548504
$868$	17.3607	0.589260
$869$	12.8494	0.435886
$870$	0	0
$871$	−6.04104	−0.204693
$872$	9.78539	0.331375
$873$	−9.02052	−0.305298
$874$	2.34017	0.0791575
$875$	0	0
$876$	4.68035	0.158134
$877$	−27.7009	−0.935392	−0.467696	−	0.883889i	$-0.654916\pi$
$877$	−27.7009	−0.935392	−0.467696	+	0.883889i	$0.654916\pi$
$878$	28.9939	0.978495
$879$	16.3402	0.551140
$880$	0	0
$881$	12.3135	0.414853	0.207426	−	0.978251i	$-0.433491\pi$
$881$	12.3135	0.414853	0.207426	+	0.978251i	$0.433491\pi$
$882$	−11.8371	−0.398576
$883$	−7.15061	−0.240637	−0.120319	−	0.992735i	$-0.538392\pi$
$883$	−7.15061	−0.240637	−0.120319	+	0.992735i	$0.538392\pi$
$884$	−2.15676	−0.0725395
$885$	0	0
$886$	−3.20394	−0.107638
$887$	−9.19165	−0.308625	−0.154313	−	0.988022i	$-0.549316\pi$
$887$	−9.19165	−0.308625	−0.154313	+	0.988022i	$0.549316\pi$
$888$	2.58145	0.0866278
$889$	74.5523	2.50041
$890$	0	0
$891$	−1.07838	−0.0361270
$892$	−21.1773	−0.709068
$893$	−16.0000	−0.535420
$894$	−6.92162	−0.231494
$895$	0	0
$896$	4.34017	0.144995
$897$	−2.34017	−0.0781361
$898$	−28.1568	−0.939603
$899$	−41.9877	−1.40037
$900$	0	0
$901$	−0.313511	−0.0104446
$902$	0.169042	0.00562847
$903$	3.20394	0.106620
$904$	8.92162	0.296729
$905$	0	0
$906$	−6.15676	−0.204545
$907$	14.0989	0.468146	0.234073	−	0.972219i	$-0.424794\pi$
$907$	14.0989	0.468146	0.234073	+	0.972219i	$0.424794\pi$
$908$	11.7854	0.391112
$909$	1.50307	0.0498537
$910$	0	0
$911$	−20.9939	−0.695558	−0.347779	−	0.937577i	$-0.613064\pi$
$911$	−20.9939	−0.695558	−0.347779	+	0.937577i	$0.613064\pi$
$912$	2.34017	0.0774909
$913$	12.3135	0.407518
$914$	−23.1773	−0.766636
$915$	0	0
$916$	1.78539	0.0589908
$917$	28.9939	0.957462
$918$	0.921622	0.0304181
$919$	−1.92777	−0.0635911	−0.0317956	−	0.999494i	$-0.510123\pi$
$919$	−1.92777	−0.0635911	−0.0317956	+	0.999494i	$0.510123\pi$
$920$	0	0
$921$	3.20394	0.105573
$922$	42.3279	1.39399
$923$	35.5174	1.16907
$924$	4.68035	0.153972
$925$	0	0
$926$	−34.9048	−1.14704
$927$	2.49693	0.0820099
$928$	−10.4969	−0.344579
$929$	18.5646	0.609086	0.304543	−	0.952499i	$-0.401496\pi$
$929$	18.5646	0.609086	0.304543	+	0.952499i	$0.401496\pi$
$930$	0	0
$931$	27.7009	0.907859
$932$	−18.3135	−0.599879
$933$	12.6537	0.414263
$934$	−37.7731	−1.23597
$935$	0	0
$936$	−2.34017	−0.0764909
$937$	−22.3279	−0.729420	−0.364710	−	0.931121i	$-0.618832\pi$
$937$	−22.3279	−0.729420	−0.364710	+	0.931121i	$0.618832\pi$
$938$	−11.2039	−0.365821
$939$	−33.2183	−1.08404
$940$	0	0
$941$	−11.0661	−0.360744	−0.180372	−	0.983598i	$-0.557730\pi$
$941$	−11.0661	−0.360744	−0.180372	+	0.983598i	$0.557730\pi$
$942$	2.89496	0.0943229
$943$	−0.156755	−0.00510466
$944$	−8.83710	−0.287623
$945$	0	0
$946$	−0.796064	−0.0258823
$947$	−8.05332	−0.261698	−0.130849	−	0.991402i	$-0.541770\pi$
$947$	−8.05332	−0.261698	−0.130849	+	0.991402i	$0.541770\pi$
$948$	−11.9155	−0.386997
$949$	10.9528	0.355544
$950$	0	0
$951$	6.99386	0.226791
$952$	−4.00000	−0.129641
$953$	−39.5897	−1.28244	−0.641218	−	0.767359i	$-0.721570\pi$
$953$	−39.5897	−1.28244	−0.641218	+	0.767359i	$0.721570\pi$
$954$	−0.340173	−0.0110135
$955$	0	0
$956$	−5.33403	−0.172515
$957$	−11.3197	−0.365912
$958$	28.1978	0.911029
$959$	96.7091	3.12290
$960$	0	0
$961$	−15.0000	−0.483871
$962$	6.04104	0.194771
$963$	−9.57531	−0.308560
$964$	26.1978	0.843774
$965$	0	0
$966$	−4.34017	−0.139643
$967$	−48.2655	−1.55211	−0.776057	−	0.630663i	$-0.782783\pi$
$967$	−48.2655	−1.55211	−0.776057	+	0.630663i	$0.782783\pi$
$968$	9.83710	0.316176
$969$	−2.15676	−0.0692850
$970$	0	0
$971$	18.0722	0.579966	0.289983	−	0.957032i	$-0.406350\pi$
$971$	18.0722	0.579966	0.289983	+	0.957032i	$0.406350\pi$
$972$	1.00000	0.0320750
$973$	45.6742	1.46425
$974$	38.2245	1.22479
$975$	0	0
$976$	−11.5753	−0.370517
$977$	45.9442	1.46989	0.734943	−	0.678129i	$-0.237209\pi$
$977$	45.9442	1.46989	0.734943	+	0.678129i	$0.237209\pi$
$978$	6.52359	0.208601
$979$	5.04718	0.161309
$980$	0	0
$981$	−9.78539	−0.312423
$982$	−11.3074	−0.360833
$983$	−1.78992	−0.0570896	−0.0285448	−	0.999593i	$-0.509087\pi$
$983$	−1.78992	−0.0570896	−0.0285448	+	0.999593i	$0.509087\pi$
$984$	−0.156755	−0.00499718
$985$	0	0
$986$	9.67420	0.308089
$987$	29.6742	0.944540
$988$	5.47641	0.174228
$989$	0.738205	0.0234735
$990$	0	0
$991$	7.68649	0.244169	0.122085	−	0.992520i	$-0.461042\pi$
$991$	7.68649	0.244169	0.122085	+	0.992520i	$0.461042\pi$
$992$	4.00000	0.127000
$993$	−29.7275	−0.943375
$994$	65.8720	2.08933
$995$	0	0
$996$	−11.4186	−0.361811
$997$	21.4908	0.680620	0.340310	−	0.940313i	$-0.389468\pi$
$997$	21.4908	0.680620	0.340310	+	0.940313i	$0.389468\pi$
$998$	2.47027	0.0781949
$999$	−2.58145	−0.0816734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.a.bo.1.1		3
5.2	odd	4		690.2.d.c.139.2	✓	6
5.3	odd	4		690.2.d.c.139.5	yes	6
5.4	even	2		3450.2.a.bt.1.3		3
15.2	even	4		2070.2.d.e.829.5		6
15.8	even	4		2070.2.d.e.829.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.d.c.139.2	✓	6	5.2	odd	4
690.2.d.c.139.5	yes	6	5.3	odd	4
2070.2.d.e.829.2		6	15.8	even	4
2070.2.d.e.829.5		6	15.2	even	4
3450.2.a.bo.1.1		3	1.1	even	1	trivial
3450.2.a.bt.1.3		3	5.4	even	2

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:	\( N \)	\(=\)	\( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3450.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -4.34017 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -4.34017 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.07838 q^{11} +1.00000 q^{12} +2.34017 q^{13} +4.34017 q^{14} +1.00000 q^{16} -0.921622 q^{17} -1.00000 q^{18} +2.34017 q^{19} -4.34017 q^{21} +1.07838 q^{22} -1.00000 q^{23} -1.00000 q^{24} -2.34017 q^{26} +1.00000 q^{27} -4.34017 q^{28} +10.4969 q^{29} -4.00000 q^{31} -1.00000 q^{32} -1.07838 q^{33} +0.921622 q^{34} +1.00000 q^{36} -2.58145 q^{37} -2.34017 q^{38} +2.34017 q^{39} +0.156755 q^{41} +4.34017 q^{42} -0.738205 q^{43} -1.07838 q^{44} +1.00000 q^{46} -6.83710 q^{47} +1.00000 q^{48} +11.8371 q^{49} -0.921622 q^{51} +2.34017 q^{52} +0.340173 q^{53} -1.00000 q^{54} +4.34017 q^{56} +2.34017 q^{57} -10.4969 q^{58} -8.83710 q^{59} -11.5753 q^{61} +4.00000 q^{62} -4.34017 q^{63} +1.00000 q^{64} +1.07838 q^{66} -2.58145 q^{67} -0.921622 q^{68} -1.00000 q^{69} +15.1773 q^{71} -1.00000 q^{72} +4.68035 q^{73} +2.58145 q^{74} +2.34017 q^{76} +4.68035 q^{77} -2.34017 q^{78} -11.9155 q^{79} +1.00000 q^{81} -0.156755 q^{82} -11.4186 q^{83} -4.34017 q^{84} +0.738205 q^{86} +10.4969 q^{87} +1.07838 q^{88} -4.68035 q^{89} -10.1568 q^{91} -1.00000 q^{92} -4.00000 q^{93} +6.83710 q^{94} -1.00000 q^{96} -9.02052 q^{97} -11.8371 q^{98} -1.07838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} - 2 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 - 2 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} - 2 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{12} - 4 q^{13} + 2 q^{14} + 3 q^{16} - 6 q^{17} - 3 q^{18} - 4 q^{19} - 2 q^{21} - 3 q^{23} - 3 q^{24} + 4 q^{26} + 3 q^{27} - 2 q^{28} + 14 q^{29} - 12 q^{31} - 3 q^{32} + 6 q^{34} + 3 q^{36} - 22 q^{37} + 4 q^{38} - 4 q^{39} - 6 q^{41} + 2 q^{42} - 10 q^{43} + 3 q^{46} + 8 q^{47} + 3 q^{48} + 7 q^{49} - 6 q^{51} - 4 q^{52} - 10 q^{53} - 3 q^{54} + 2 q^{56} - 4 q^{57} - 14 q^{58} + 2 q^{59} - 14 q^{61} + 12 q^{62} - 2 q^{63} + 3 q^{64} - 22 q^{67} - 6 q^{68} - 3 q^{69} + 6 q^{71} - 3 q^{72} - 8 q^{73} + 22 q^{74} - 4 q^{76} - 8 q^{77} + 4 q^{78} - 4 q^{79} + 3 q^{81} + 6 q^{82} - 20 q^{83} - 2 q^{84} + 10 q^{86} + 14 q^{87} + 8 q^{89} - 24 q^{91} - 3 q^{92} - 12 q^{93} - 8 q^{94} - 3 q^{96} + 6 q^{97} - 7 q^{98}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 - 2 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^12 - 4 * q^13 + 2 * q^14 + 3 * q^16 - 6 * q^17 - 3 * q^18 - 4 * q^19 - 2 * q^21 - 3 * q^23 - 3 * q^24 + 4 * q^26 + 3 * q^27 - 2 * q^28 + 14 * q^29 - 12 * q^31 - 3 * q^32 + 6 * q^34 + 3 * q^36 - 22 * q^37 + 4 * q^38 - 4 * q^39 - 6 * q^41 + 2 * q^42 - 10 * q^43 + 3 * q^46 + 8 * q^47 + 3 * q^48 + 7 * q^49 - 6 * q^51 - 4 * q^52 - 10 * q^53 - 3 * q^54 + 2 * q^56 - 4 * q^57 - 14 * q^58 + 2 * q^59 - 14 * q^61 + 12 * q^62 - 2 * q^63 + 3 * q^64 - 22 * q^67 - 6 * q^68 - 3 * q^69 + 6 * q^71 - 3 * q^72 - 8 * q^73 + 22 * q^74 - 4 * q^76 - 8 * q^77 + 4 * q^78 - 4 * q^79 + 3 * q^81 + 6 * q^82 - 20 * q^83 - 2 * q^84 + 10 * q^86 + 14 * q^87 + 8 * q^89 - 24 * q^91 - 3 * q^92 - 12 * q^93 - 8 * q^94 - 3 * q^96 + 6 * q^97 - 7 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more