LMFDB - Embedded newform 1445.2.a.r.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1445,2,Mod(1,1445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1445, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1445.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.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:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 18 x^{10} + 55 x^{9} + 114 x^{8} - 354 x^{7} - 309 x^{6} + 936 x^{5} + 396 x^{4} + \cdots + 9 $ x^12 - 3x^11 - 18x^10 + 55x^9 + 114x^8 - 354x^7 - 309x^6 + 936x^5 + 396x^4 - 899x^3 - 297x^2 + 153*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.54480$ of defining polynomial
Character	$\chi$	$=$	1445.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.54480 q^{2} -3.06453 q^{3} +4.47602 q^{4} -1.00000 q^{5} +7.79863 q^{6} -0.261390 q^{7} -6.30099 q^{8} +6.39135 q^{9} +2.54480 q^{10} +0.545043 q^{11} -13.7169 q^{12} +5.48254 q^{13} +0.665187 q^{14} +3.06453 q^{15} +7.08273 q^{16} -16.2647 q^{18} +4.34857 q^{19} -4.47602 q^{20} +0.801039 q^{21} -1.38703 q^{22} +3.75127 q^{23} +19.3096 q^{24} +1.00000 q^{25} -13.9520 q^{26} -10.3929 q^{27} -1.16999 q^{28} +2.69600 q^{29} -7.79863 q^{30} +8.95269 q^{31} -5.42218 q^{32} -1.67030 q^{33} +0.261390 q^{35} +28.6078 q^{36} -4.86119 q^{37} -11.0663 q^{38} -16.8014 q^{39} +6.30099 q^{40} -7.76968 q^{41} -2.03849 q^{42} +2.35019 q^{43} +2.43963 q^{44} -6.39135 q^{45} -9.54625 q^{46} +2.35604 q^{47} -21.7052 q^{48} -6.93168 q^{49} -2.54480 q^{50} +24.5400 q^{52} -10.8975 q^{53} +26.4479 q^{54} -0.545043 q^{55} +1.64702 q^{56} -13.3263 q^{57} -6.86078 q^{58} +6.23938 q^{59} +13.7169 q^{60} +0.633641 q^{61} -22.7828 q^{62} -1.67064 q^{63} -0.367091 q^{64} -5.48254 q^{65} +4.25059 q^{66} +8.44378 q^{67} -11.4959 q^{69} -0.665187 q^{70} +5.40706 q^{71} -40.2718 q^{72} -8.12625 q^{73} +12.3708 q^{74} -3.06453 q^{75} +19.4643 q^{76} -0.142469 q^{77} +42.7563 q^{78} -1.73147 q^{79} -7.08273 q^{80} +12.6753 q^{81} +19.7723 q^{82} -0.107006 q^{83} +3.58547 q^{84} -5.98077 q^{86} -8.26196 q^{87} -3.43431 q^{88} -16.8773 q^{89} +16.2647 q^{90} -1.43308 q^{91} +16.7908 q^{92} -27.4358 q^{93} -5.99566 q^{94} -4.34857 q^{95} +16.6164 q^{96} +7.14812 q^{97} +17.6397 q^{98} +3.48356 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{3} + 21 q^{4} - 12 q^{5} + 9 q^{6} - 6 q^{7} + 12 q^{8} + 21 q^{9} - 3 q^{10} + 6 q^{11} - 6 q^{12} + 9 q^{13} + 18 q^{14} + 3 q^{15} + 39 q^{16} - 9 q^{18} + 27 q^{19} - 21 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^3 + 21 * q^4 - 12 * q^5 + 9 * q^6 - 6 * q^7 + 12 * q^8 + 21 * q^9 - 3 * q^10 + 6 * q^11 - 6 * q^12 + 9 * q^13 + 18 * q^14 + 3 * q^15 + 39 * q^16 - 9 * q^18 + 27 * q^19 - 21 * q^20 + 6 * q^21 - 15 * q^22 - 18 * q^23 + 36 * q^24 + 12 * q^25 + 6 * q^26 - 12 * q^27 - 39 * q^28 - 9 * q^30 + 6 * q^31 + 12 * q^32 + 6 * q^35 + 48 * q^36 - 21 * q^37 - 3 * q^38 + 9 * q^39 - 12 * q^40 + 15 * q^41 + 30 * q^42 + 45 * q^43 + 42 * q^44 - 21 * q^45 + 15 * q^46 + 3 * q^47 + 63 * q^48 + 12 * q^49 + 3 * q^50 + 51 * q^52 - 12 * q^53 + 27 * q^54 - 6 * q^55 - 3 * q^56 - 6 * q^57 + 51 * q^58 + 36 * q^59 + 6 * q^60 - 3 * q^61 - 36 * q^62 - 72 * q^63 + 42 * q^64 - 9 * q^65 - 39 * q^66 + 78 * q^67 - 66 * q^69 - 18 * q^70 + 30 * q^71 - 12 * q^72 + 33 * q^73 - 9 * q^74 - 3 * q^75 + 27 * q^76 - 39 * q^77 + 24 * q^78 + 3 * q^79 - 39 * q^80 + 12 * q^81 + 51 * q^82 + 27 * q^83 + 27 * q^84 + 18 * q^86 + 24 * q^87 - 36 * q^88 + 6 * q^89 + 9 * q^90 + 24 * q^91 + 3 * q^92 - 12 * q^93 + 21 * q^94 - 27 * q^95 + 39 * q^96 + 6 * q^97 - 42 * q^98 + 6 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.54480	−1.79945	−0.899724	−	0.436460i	$-0.856232\pi$
$2$	−2.54480	−1.79945	−0.899724	+	0.436460i	$0.856232\pi$
$3$	−3.06453	−1.76931	−0.884654	−	0.466248i	$-0.845605\pi$
$3$	−3.06453	−1.76931	−0.884654	+	0.466248i	$0.845605\pi$
$4$	4.47602	2.23801
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	7.79863	3.18378
$7$	−0.261390	−0.0987963	−0.0493981	−	0.998779i	$-0.515730\pi$
$7$	−0.261390	−0.0987963	−0.0493981	+	0.998779i	$0.515730\pi$
$8$	−6.30099	−2.22774
$9$	6.39135	2.13045
$10$	2.54480	0.804737
$11$	0.545043	0.164337	0.0821683	−	0.996618i	$-0.473815\pi$
$11$	0.545043	0.164337	0.0821683	+	0.996618i	$0.473815\pi$
$12$	−13.7169	−3.95973
$13$	5.48254	1.52058	0.760291	−	0.649582i	$-0.225056\pi$
$13$	5.48254	1.52058	0.760291	+	0.649582i	$0.225056\pi$
$14$	0.665187	0.177779
$15$	3.06453	0.791259
$16$	7.08273	1.77068
$17$	0	0
$17$	0	0
$18$	−16.2647	−3.83363
$19$	4.34857	0.997631	0.498816	−	0.866708i	$-0.333768\pi$
$19$	4.34857	0.997631	0.498816	+	0.866708i	$0.333768\pi$
$20$	−4.47602	−1.00087
$21$	0.801039	0.174801
$22$	−1.38703	−0.295715
$23$	3.75127	0.782194	0.391097	−	0.920349i	$-0.372096\pi$
$23$	3.75127	0.782194	0.391097	+	0.920349i	$0.372096\pi$
$24$	19.3096	3.94155
$25$	1.00000	0.200000
$26$	−13.9520	−2.73621
$27$	−10.3929	−2.00012
$28$	−1.16999	−0.221107
$29$	2.69600	0.500634	0.250317	−	0.968164i	$-0.419465\pi$
$29$	2.69600	0.500634	0.250317	+	0.968164i	$0.419465\pi$
$30$	−7.79863	−1.42383
$31$	8.95269	1.60795	0.803975	−	0.594663i	$-0.202714\pi$
$31$	8.95269	1.60795	0.803975	+	0.594663i	$0.202714\pi$
$32$	−5.42218	−0.958514
$33$	−1.67030	−0.290762
$34$	0	0
$35$	0.261390	0.0441830
$36$	28.6078	4.76797
$37$	−4.86119	−0.799175	−0.399588	−	0.916695i	$-0.630847\pi$
$37$	−4.86119	−0.799175	−0.399588	+	0.916695i	$0.630847\pi$
$38$	−11.0663	−1.79519
$39$	−16.8014	−2.69038
$40$	6.30099	0.996274
$41$	−7.76968	−1.21342	−0.606710	−	0.794923i	$-0.707511\pi$
$41$	−7.76968	−1.21342	−0.606710	+	0.794923i	$0.707511\pi$
$42$	−2.03849	−0.314545
$43$	2.35019	0.358401	0.179200	−	0.983813i	$-0.442649\pi$
$43$	2.35019	0.358401	0.179200	+	0.983813i	$0.442649\pi$
$44$	2.43963	0.367787
$45$	−6.39135	−0.952766
$46$	−9.54625	−1.40752
$47$	2.35604	0.343664	0.171832	−	0.985126i	$-0.445031\pi$
$47$	2.35604	0.343664	0.171832	+	0.985126i	$0.445031\pi$
$48$	−21.7052	−3.13288
$49$	−6.93168	−0.990239
$50$	−2.54480	−0.359889
$51$	0	0
$52$	24.5400	3.40308
$53$	−10.8975	−1.49689	−0.748445	−	0.663197i	$-0.769199\pi$
$53$	−10.8975	−1.49689	−0.748445	+	0.663197i	$0.769199\pi$
$54$	26.4479	3.59910
$55$	−0.545043	−0.0734936
$56$	1.64702	0.220092
$57$	−13.3263	−1.76512
$58$	−6.86078	−0.900864
$59$	6.23938	0.812298	0.406149	−	0.913807i	$-0.366871\pi$
$59$	6.23938	0.812298	0.406149	+	0.913807i	$0.366871\pi$
$60$	13.7169	1.77085
$61$	0.633641	0.0811294	0.0405647	−	0.999177i	$-0.487084\pi$
$61$	0.633641	0.0811294	0.0405647	+	0.999177i	$0.487084\pi$
$62$	−22.7828	−2.89342
$63$	−1.67064	−0.210481
$64$	−0.367091	−0.0458863
$65$	−5.48254	−0.680025
$66$	4.25059	0.523211
$67$	8.44378	1.03157	0.515786	−	0.856717i	$-0.327500\pi$
$67$	8.44378	1.03157	0.515786	+	0.856717i	$0.327500\pi$
$68$	0	0
$69$	−11.4959	−1.38394
$70$	−0.665187	−0.0795051
$71$	5.40706	0.641700	0.320850	−	0.947130i	$-0.396031\pi$
$71$	5.40706	0.641700	0.320850	+	0.947130i	$0.396031\pi$
$72$	−40.2718	−4.74608
$73$	−8.12625	−0.951105	−0.475553	−	0.879687i	$-0.657752\pi$
$73$	−8.12625	−0.951105	−0.475553	+	0.879687i	$0.657752\pi$
$74$	12.3708	1.43807
$75$	−3.06453	−0.353862
$76$	19.4643	2.23271
$77$	−0.142469	−0.0162359
$78$	42.7563	4.84120
$79$	−1.73147	−0.194805	−0.0974026	−	0.995245i	$-0.531053\pi$
$79$	−1.73147	−0.194805	−0.0974026	+	0.995245i	$0.531053\pi$
$80$	−7.08273	−0.791873
$81$	12.6753	1.40837
$82$	19.7723	2.18349
$83$	−0.107006	−0.0117455	−0.00587273	−	0.999983i	$-0.501869\pi$
$83$	−0.107006	−0.0117455	−0.00587273	+	0.999983i	$0.501869\pi$
$84$	3.58547	0.391207
$85$	0	0
$86$	−5.98077	−0.644923
$87$	−8.26196	−0.885775
$88$	−3.43431	−0.366099
$89$	−16.8773	−1.78899	−0.894497	−	0.447075i	$-0.852466\pi$
$89$	−16.8773	−1.78899	−0.894497	+	0.447075i	$0.852466\pi$
$90$	16.2647	1.71445
$91$	−1.43308	−0.150228
$92$	16.7908	1.75056
$93$	−27.4358	−2.84496
$94$	−5.99566	−0.618405
$95$	−4.34857	−0.446154
$96$	16.6164	1.69591
$97$	7.14812	0.725782	0.362891	−	0.931832i	$-0.381790\pi$
$97$	7.14812	0.725782	0.362891	+	0.931832i	$0.381790\pi$
$98$	17.6397	1.78188
$99$	3.48356	0.350111
$100$	4.47602	0.447602
$101$	−1.88994	−0.188056	−0.0940281	−	0.995570i	$-0.529974\pi$
$101$	−1.88994	−0.188056	−0.0940281	+	0.995570i	$0.529974\pi$
$102$	0	0
$103$	8.20152	0.808120	0.404060	−	0.914732i	$-0.367599\pi$
$103$	8.20152	0.808120	0.404060	+	0.914732i	$0.367599\pi$
$104$	−34.5454	−3.38746
$105$	−0.801039	−0.0781734
$106$	27.7320	2.69357
$107$	8.27660	0.800129	0.400065	−	0.916487i	$-0.368988\pi$
$107$	8.27660	0.800129	0.400065	+	0.916487i	$0.368988\pi$
$108$	−46.5189	−4.47628
$109$	1.38287	0.132455	0.0662276	−	0.997805i	$-0.478904\pi$
$109$	1.38287	0.132455	0.0662276	+	0.997805i	$0.478904\pi$
$110$	1.38703	0.132248
$111$	14.8973	1.41399
$112$	−1.85136	−0.174937
$113$	11.1388	1.04785	0.523925	−	0.851764i	$-0.324467\pi$
$113$	11.1388	1.04785	0.523925	+	0.851764i	$0.324467\pi$
$114$	33.9129	3.17624
$115$	−3.75127	−0.349808
$116$	12.0673	1.12042
$117$	35.0408	3.23953
$118$	−15.8780	−1.46169
$119$	0	0
$120$	−19.3096	−1.76272
$121$	−10.7029	−0.972993
$122$	−1.61249	−0.145988
$123$	23.8104	2.14692
$124$	40.0724	3.59861
$125$	−1.00000	−0.0894427
$126$	4.25144	0.378749
$127$	14.3543	1.27374	0.636870	−	0.770971i	$-0.280229\pi$
$127$	14.3543	1.27374	0.636870	+	0.770971i	$0.280229\pi$
$128$	11.7785	1.04108
$129$	−7.20223	−0.634121
$130$	13.9520	1.22367
$131$	−7.43528	−0.649623	−0.324812	−	0.945779i	$-0.605301\pi$
$131$	−7.43528	−0.649623	−0.324812	+	0.945779i	$0.605301\pi$
$132$	−7.47631	−0.650729
$133$	−1.13668	−0.0985623
$134$	−21.4878	−1.85626
$135$	10.3929	0.894479
$136$	0	0
$137$	6.86466	0.586488	0.293244	−	0.956038i	$-0.405265\pi$
$137$	6.86466	0.586488	0.293244	+	0.956038i	$0.405265\pi$
$138$	29.2548	2.49033
$139$	20.7776	1.76233	0.881167	−	0.472805i	$-0.156758\pi$
$139$	20.7776	1.76233	0.881167	+	0.472805i	$0.156758\pi$
$140$	1.16999	0.0988821
$141$	−7.22017	−0.608048
$142$	−13.7599	−1.15471
$143$	2.98822	0.249888
$144$	45.2682	3.77235
$145$	−2.69600	−0.223890
$146$	20.6797	1.71146
$147$	21.2423	1.75204
$148$	−21.7588	−1.78856
$149$	17.6157	1.44313	0.721567	−	0.692345i	$-0.243422\pi$
$149$	17.6157	1.44313	0.721567	+	0.692345i	$0.243422\pi$
$150$	7.79863	0.636755
$151$	−11.0232	−0.897058	−0.448529	−	0.893768i	$-0.648052\pi$
$151$	−11.0232	−0.897058	−0.448529	+	0.893768i	$0.648052\pi$
$152$	−27.4003	−2.22246
$153$	0	0
$154$	0.362556	0.0292156
$155$	−8.95269	−0.719097
$156$	−75.2035	−6.02110
$157$	5.27656	0.421116	0.210558	−	0.977581i	$-0.432472\pi$
$157$	5.27656	0.421116	0.210558	+	0.977581i	$0.432472\pi$
$158$	4.40624	0.350542
$159$	33.3958	2.64846
$160$	5.42218	0.428661
$161$	−0.980546	−0.0772779
$162$	−32.2562	−2.53429
$163$	−14.0791	−1.10276	−0.551381	−	0.834253i	$-0.685899\pi$
$163$	−14.0791	−1.10276	−0.551381	+	0.834253i	$0.685899\pi$
$164$	−34.7773	−2.71565
$165$	1.67030	0.130033
$166$	0.272310	0.0211353
$167$	−13.3430	−1.03251	−0.516255	−	0.856435i	$-0.672674\pi$
$167$	−13.3430	−1.03251	−0.516255	+	0.856435i	$0.672674\pi$
$168$	−5.04734	−0.389411
$169$	17.0582	1.31217
$170$	0	0
$171$	27.7933	2.12540
$172$	10.5195	0.802105
$173$	5.71831	0.434755	0.217377	−	0.976088i	$-0.430250\pi$
$173$	5.71831	0.434755	0.217377	+	0.976088i	$0.430250\pi$
$174$	21.0251	1.59391
$175$	−0.261390	−0.0197593
$176$	3.86039	0.290988
$177$	−19.1208	−1.43720
$178$	42.9495	3.21920
$179$	14.7180	1.10008	0.550038	−	0.835140i	$-0.314613\pi$
$179$	14.7180	1.10008	0.550038	+	0.835140i	$0.314613\pi$
$180$	−28.6078	−2.13230
$181$	26.3308	1.95715	0.978576	−	0.205887i	$-0.0660080\pi$
$181$	26.3308	1.95715	0.978576	+	0.205887i	$0.0660080\pi$
$182$	3.64691	0.270327
$183$	−1.94181	−0.143543
$184$	−23.6367	−1.74252
$185$	4.86119	0.357402
$186$	69.8187	5.11935
$187$	0	0
$188$	10.5457	0.769124
$189$	2.71661	0.197604
$190$	11.0663	0.802831
$191$	−7.69096	−0.556498	−0.278249	−	0.960509i	$-0.589754\pi$
$191$	−7.69096	−0.556498	−0.278249	+	0.960509i	$0.589754\pi$
$192$	1.12496	0.0811870
$193$	4.56393	0.328519	0.164259	−	0.986417i	$-0.447477\pi$
$193$	4.56393	0.328519	0.164259	+	0.986417i	$0.447477\pi$
$194$	−18.1906	−1.30601
$195$	16.8014	1.20317
$196$	−31.0263	−2.21617
$197$	20.5420	1.46356	0.731779	−	0.681542i	$-0.238690\pi$
$197$	20.5420	1.46356	0.731779	+	0.681542i	$0.238690\pi$
$198$	−8.86498	−0.630007
$199$	−22.5698	−1.59993	−0.799967	−	0.600044i	$-0.795150\pi$
$199$	−22.5698	−1.59993	−0.799967	+	0.600044i	$0.795150\pi$
$200$	−6.30099	−0.445547
$201$	−25.8762	−1.82517
$202$	4.80953	0.338397
$203$	−0.704707	−0.0494608
$204$	0	0
$205$	7.76968	0.542658
$206$	−20.8713	−1.45417
$207$	23.9757	1.66643
$208$	38.8314	2.69247
$209$	2.37016	0.163947
$210$	2.03849	0.140669
$211$	−15.3824	−1.05897	−0.529485	−	0.848320i	$-0.677615\pi$
$211$	−15.3824	−1.05897	−0.529485	+	0.848320i	$0.677615\pi$
$212$	−48.7775	−3.35006
$213$	−16.5701	−1.13537
$214$	−21.0623	−1.43979
$215$	−2.35019	−0.160282
$216$	65.4856	4.45573
$217$	−2.34015	−0.158860
$218$	−3.51914	−0.238346
$219$	24.9031	1.68280
$220$	−2.43963	−0.164480
$221$	0	0
$222$	−37.9106	−2.54439
$223$	23.5213	1.57510	0.787552	−	0.616248i	$-0.211348\pi$
$223$	23.5213	1.57510	0.787552	+	0.616248i	$0.211348\pi$
$224$	1.41730	0.0946977
$225$	6.39135	0.426090
$226$	−28.3460	−1.88555
$227$	−18.9590	−1.25835	−0.629177	−	0.777262i	$-0.716608\pi$
$227$	−18.9590	−1.25835	−0.629177	+	0.777262i	$0.716608\pi$
$228$	−59.6490	−3.95035
$229$	−22.3030	−1.47382	−0.736912	−	0.675989i	$-0.763717\pi$
$229$	−22.3030	−1.47382	−0.736912	+	0.675989i	$0.763717\pi$
$230$	9.54625	0.629461
$231$	0.436601	0.0287262
$232$	−16.9874	−1.11528
$233$	−10.9844	−0.719611	−0.359805	−	0.933027i	$-0.617157\pi$
$233$	−10.9844	−0.719611	−0.359805	+	0.933027i	$0.617157\pi$
$234$	−89.1720	−5.82936
$235$	−2.35604	−0.153691
$236$	27.9276	1.81793
$237$	5.30613	0.344670
$238$	0	0
$239$	−2.54775	−0.164800	−0.0824002	−	0.996599i	$-0.526259\pi$
$239$	−2.54775	−0.164800	−0.0824002	+	0.996599i	$0.526259\pi$
$240$	21.7052	1.40107
$241$	−7.02833	−0.452734	−0.226367	−	0.974042i	$-0.572685\pi$
$241$	−7.02833	−0.452734	−0.226367	+	0.974042i	$0.572685\pi$
$242$	27.2368	1.75085
$243$	−7.66521	−0.491724
$244$	2.83619	0.181568
$245$	6.93168	0.442848
$246$	−60.5929	−3.86326
$247$	23.8412	1.51698
$248$	−56.4108	−3.58209
$249$	0.327924	0.0207813
$250$	2.54480	0.160947
$251$	−26.3557	−1.66356	−0.831779	−	0.555106i	$-0.812678\pi$
$251$	−26.3557	−1.66356	−0.831779	+	0.555106i	$0.812678\pi$
$252$	−7.47781	−0.471058
$253$	2.04461	0.128543
$254$	−36.5289	−2.29203
$255$	0	0
$256$	−29.2398	−1.82749
$257$	18.4413	1.15034	0.575168	−	0.818035i	$-0.304937\pi$
$257$	18.4413	1.15034	0.575168	+	0.818035i	$0.304937\pi$
$258$	18.3283	1.14107
$259$	1.27067	0.0789555
$260$	−24.5400	−1.52190
$261$	17.2311	1.06658
$262$	18.9213	1.16896
$263$	−13.6689	−0.842862	−0.421431	−	0.906860i	$-0.638472\pi$
$263$	−13.6689	−0.842862	−0.421431	+	0.906860i	$0.638472\pi$
$264$	10.5246	0.647741
$265$	10.8975	0.669429
$266$	2.89262	0.177358
$267$	51.7211	3.16528
$268$	37.7946	2.30867
$269$	20.9142	1.27516	0.637580	−	0.770384i	$-0.279936\pi$
$269$	20.9142	1.27516	0.637580	+	0.770384i	$0.279936\pi$
$270$	−26.4479	−1.60957
$271$	−4.92778	−0.299341	−0.149671	−	0.988736i	$-0.547821\pi$
$271$	−4.92778	−0.299341	−0.149671	+	0.988736i	$0.547821\pi$
$272$	0	0
$273$	4.39173	0.265799
$274$	−17.4692	−1.05535
$275$	0.545043	0.0328673
$276$	−51.4559	−3.09728
$277$	23.6010	1.41805	0.709024	−	0.705185i	$-0.249136\pi$
$277$	23.6010	1.41805	0.709024	+	0.705185i	$0.249136\pi$
$278$	−52.8749	−3.17123
$279$	57.2198	3.42566
$280$	−1.64702	−0.0984281
$281$	−2.81808	−0.168112	−0.0840562	−	0.996461i	$-0.526788\pi$
$281$	−2.81808	−0.168112	−0.0840562	+	0.996461i	$0.526788\pi$
$282$	18.3739	1.09415
$283$	−11.7242	−0.696931	−0.348466	−	0.937322i	$-0.613297\pi$
$283$	−11.7242	−0.696931	−0.348466	+	0.937322i	$0.613297\pi$
$284$	24.2021	1.43613
$285$	13.3263	0.789384
$286$	−7.60443	−0.449660
$287$	2.03092	0.119881
$288$	−34.6550	−2.04207
$289$	0	0
$290$	6.86078	0.402879
$291$	−21.9056	−1.28413
$292$	−36.3733	−2.12858
$293$	−25.8626	−1.51091	−0.755453	−	0.655202i	$-0.772583\pi$
$293$	−25.8626	−1.51091	−0.755453	+	0.655202i	$0.772583\pi$
$294$	−54.0576	−3.15270
$295$	−6.23938	−0.363271
$296$	30.6303	1.78035
$297$	−5.66458	−0.328692
$298$	−44.8284	−2.59684
$299$	20.5665	1.18939
$300$	−13.7169	−0.791946
$301$	−0.614317	−0.0354087
$302$	28.0520	1.61421
$303$	5.79179	0.332729
$304$	30.7998	1.76649
$305$	−0.633641	−0.0362822
$306$	0	0
$307$	5.85905	0.334393	0.167197	−	0.985924i	$-0.446529\pi$
$307$	5.85905	0.334393	0.167197	+	0.985924i	$0.446529\pi$
$308$	−0.637695	−0.0363360
$309$	−25.1338	−1.42981
$310$	22.7828	1.29398
$311$	10.6794	0.605576	0.302788	−	0.953058i	$-0.402083\pi$
$311$	10.6794	0.605576	0.302788	+	0.953058i	$0.402083\pi$
$312$	105.866	5.99346
$313$	−24.3627	−1.37706	−0.688530	−	0.725208i	$-0.741744\pi$
$313$	−24.3627	−1.37706	−0.688530	+	0.725208i	$0.741744\pi$
$314$	−13.4278	−0.757775
$315$	1.67064	0.0941298
$316$	−7.75008	−0.435976
$317$	−7.36660	−0.413750	−0.206875	−	0.978367i	$-0.566329\pi$
$317$	−7.36660	−0.413750	−0.206875	+	0.978367i	$0.566329\pi$
$318$	−84.9857	−4.76576
$319$	1.46943	0.0822725
$320$	0.367091	0.0205210
$321$	−25.3639	−1.41567
$322$	2.49530	0.139057
$323$	0	0
$324$	56.7350	3.15195
$325$	5.48254	0.304117
$326$	35.8286	1.98436
$327$	−4.23786	−0.234354
$328$	48.9567	2.70318
$329$	−0.615847	−0.0339527
$330$	−4.25059	−0.233987
$331$	−0.194810	−0.0107077	−0.00535385	−	0.999986i	$-0.501704\pi$
$331$	−0.194810	−0.0107077	−0.00535385	+	0.999986i	$0.501704\pi$
$332$	−0.478962	−0.0262865
$333$	−31.0696	−1.70260
$334$	33.9553	1.85795
$335$	−8.44378	−0.461333
$336$	5.67354	0.309517
$337$	2.27890	0.124140	0.0620699	−	0.998072i	$-0.480230\pi$
$337$	2.27890	0.124140	0.0620699	+	0.998072i	$0.480230\pi$
$338$	−43.4099	−2.36119
$339$	−34.1352	−1.85397
$340$	0	0
$341$	4.87960	0.264245
$342$	−70.7284	−3.82455
$343$	3.64161	0.196628
$344$	−14.8085	−0.798422
$345$	11.4959	0.618918
$346$	−14.5520	−0.782318
$347$	18.1468	0.974170	0.487085	−	0.873355i	$-0.338060\pi$
$347$	18.1468	0.974170	0.487085	+	0.873355i	$0.338060\pi$
$348$	−36.9807	−1.98238
$349$	21.3369	1.14214	0.571068	−	0.820903i	$-0.306529\pi$
$349$	21.3369	1.14214	0.571068	+	0.820903i	$0.306529\pi$
$350$	0.665187	0.0355557
$351$	−56.9795	−3.04134
$352$	−2.95532	−0.157519
$353$	−0.596667	−0.0317574	−0.0158787	−	0.999874i	$-0.505055\pi$
$353$	−0.596667	−0.0317574	−0.0158787	+	0.999874i	$0.505055\pi$
$354$	48.6586	2.58617
$355$	−5.40706	−0.286977
$356$	−75.5433	−4.00379
$357$	0	0
$358$	−37.4544	−1.97953
$359$	6.66904	0.351979	0.175989	−	0.984392i	$-0.443688\pi$
$359$	6.66904	0.351979	0.175989	+	0.984392i	$0.443688\pi$
$360$	40.2718	2.12251
$361$	−0.0898986	−0.00473151
$362$	−67.0066	−3.52179
$363$	32.7995	1.72153
$364$	−6.41451	−0.336212
$365$	8.12625	0.425347
$366$	4.94153	0.258298
$367$	−9.36845	−0.489029	−0.244514	−	0.969646i	$-0.578629\pi$
$367$	−9.36845	−0.489029	−0.244514	+	0.969646i	$0.578629\pi$
$368$	26.5692	1.38502
$369$	−49.6588	−2.58513
$370$	−12.3708	−0.643126
$371$	2.84851	0.147887
$372$	−122.803	−6.36705
$373$	−19.2804	−0.998301	−0.499151	−	0.866515i	$-0.666355\pi$
$373$	−19.2804	−0.998301	−0.499151	+	0.866515i	$0.666355\pi$
$374$	0	0
$375$	3.06453	0.158252
$376$	−14.8454	−0.765593
$377$	14.7809	0.761255
$378$	−6.91322	−0.355578
$379$	35.6049	1.82890	0.914452	−	0.404695i	$-0.132622\pi$
$379$	35.6049	1.82890	0.914452	+	0.404695i	$0.132622\pi$
$380$	−19.4643	−0.998498
$381$	−43.9893	−2.25364
$382$	19.5720	1.00139
$383$	8.31885	0.425074	0.212537	−	0.977153i	$-0.431827\pi$
$383$	8.31885	0.425074	0.212537	+	0.977153i	$0.431827\pi$
$384$	−36.0957	−1.84200
$385$	0.142469	0.00726089
$386$	−11.6143	−0.591153
$387$	15.0209	0.763555
$388$	31.9952	1.62431
$389$	2.79890	0.141910	0.0709550	−	0.997480i	$-0.477395\pi$
$389$	2.79890	0.141910	0.0709550	+	0.997480i	$0.477395\pi$
$390$	−42.7563	−2.16505
$391$	0	0
$392$	43.6764	2.20599
$393$	22.7856	1.14938
$394$	−52.2754	−2.63360
$395$	1.73147	0.0871195
$396$	15.5925	0.783553
$397$	−6.88625	−0.345611	−0.172805	−	0.984956i	$-0.555283\pi$
$397$	−6.88625	−0.345611	−0.172805	+	0.984956i	$0.555283\pi$
$398$	57.4358	2.87900
$399$	3.48338	0.174387
$400$	7.08273	0.354137
$401$	10.2317	0.510949	0.255475	−	0.966816i	$-0.417768\pi$
$401$	10.2317	0.510949	0.255475	+	0.966816i	$0.417768\pi$
$402$	65.8499	3.28430
$403$	49.0835	2.44502
$404$	−8.45942	−0.420872
$405$	−12.6753	−0.629842
$406$	1.79334	0.0890020
$407$	−2.64956	−0.131334
$408$	0	0
$409$	−3.30625	−0.163484	−0.0817419	−	0.996654i	$-0.526048\pi$
$409$	−3.30625	−0.163484	−0.0817419	+	0.996654i	$0.526048\pi$
$410$	−19.7723	−0.976485
$411$	−21.0370	−1.03768
$412$	36.7102	1.80858
$413$	−1.63091	−0.0802520
$414$	−61.0134	−2.99865
$415$	0.107006	0.00525273
$416$	−29.7273	−1.45750
$417$	−63.6737	−3.11811
$418$	−6.03159	−0.295015
$419$	−2.45289	−0.119832	−0.0599159	−	0.998203i	$-0.519083\pi$
$419$	−2.45289	−0.119832	−0.0599159	+	0.998203i	$0.519083\pi$
$420$	−3.58547	−0.174953
$421$	30.8040	1.50130	0.750648	−	0.660702i	$-0.229741\pi$
$421$	30.8040	1.50130	0.750648	+	0.660702i	$0.229741\pi$
$422$	39.1452	1.90556
$423$	15.0583	0.732159
$424$	68.6652	3.33468
$425$	0	0
$426$	42.1677	2.04303
$427$	−0.165628	−0.00801528
$428$	37.0462	1.79070
$429$	−9.15750	−0.442128
$430$	5.98077	0.288418
$431$	26.0142	1.25306	0.626530	−	0.779397i	$-0.284474\pi$
$431$	26.0142	1.25306	0.626530	+	0.779397i	$0.284474\pi$
$432$	−73.6101	−3.54157
$433$	2.26911	0.109046	0.0545232	−	0.998513i	$-0.482636\pi$
$433$	2.26911	0.109046	0.0545232	+	0.998513i	$0.482636\pi$
$434$	5.95521	0.285859
$435$	8.26196	0.396131
$436$	6.18977	0.296436
$437$	16.3127	0.780342
$438$	−63.3736	−3.02811
$439$	4.19666	0.200296	0.100148	−	0.994973i	$-0.468068\pi$
$439$	4.19666	0.200296	0.100148	+	0.994973i	$0.468068\pi$
$440$	3.43431	0.163724
$441$	−44.3028	−2.10966
$442$	0	0
$443$	3.35324	0.159317	0.0796586	−	0.996822i	$-0.474617\pi$
$443$	3.35324	0.159317	0.0796586	+	0.996822i	$0.474617\pi$
$444$	66.6805	3.16452
$445$	16.8773	0.800062
$446$	−59.8571	−2.83432
$447$	−53.9838	−2.55335
$448$	0.0959539	0.00453340
$449$	16.4196	0.774888	0.387444	−	0.921893i	$-0.373358\pi$
$449$	16.4196	0.774888	0.387444	+	0.921893i	$0.373358\pi$
$450$	−16.2647	−0.766727
$451$	−4.23481	−0.199410
$452$	49.8575	2.34510
$453$	33.7810	1.58717
$454$	48.2469	2.26434
$455$	1.43308	0.0671840
$456$	83.9691	3.93222
$457$	8.28442	0.387529	0.193764	−	0.981048i	$-0.437930\pi$
$457$	8.28442	0.387529	0.193764	+	0.981048i	$0.437930\pi$
$458$	56.7568	2.65207
$459$	0	0
$460$	−16.7908	−0.782874
$461$	40.2762	1.87585	0.937925	−	0.346837i	$-0.112744\pi$
$461$	40.2762	1.87585	0.937925	+	0.346837i	$0.112744\pi$
$462$	−1.11106	−0.0516913
$463$	−22.3596	−1.03914	−0.519568	−	0.854429i	$-0.673907\pi$
$463$	−22.3596	−1.03914	−0.519568	+	0.854429i	$0.673907\pi$
$464$	19.0950	0.886464
$465$	27.4358	1.27230
$466$	27.9531	1.29490
$467$	30.4655	1.40977	0.704887	−	0.709320i	$-0.250998\pi$
$467$	30.4655	1.40977	0.704887	+	0.709320i	$0.250998\pi$
$468$	156.844	7.25010
$469$	−2.20712	−0.101916
$470$	5.99566	0.276559
$471$	−16.1702	−0.745083
$472$	−39.3142	−1.80958
$473$	1.28096	0.0588984
$474$	−13.5031	−0.620216
$475$	4.34857	0.199526
$476$	0	0
$477$	−69.6499	−3.18905
$478$	6.48353	0.296550
$479$	−3.49412	−0.159650	−0.0798252	−	0.996809i	$-0.525436\pi$
$479$	−3.49412	−0.159650	−0.0798252	+	0.996809i	$0.525436\pi$
$480$	−16.6164	−0.758433
$481$	−26.6517	−1.21521
$482$	17.8857	0.814671
$483$	3.00492	0.136728
$484$	−47.9065	−2.17757
$485$	−7.14812	−0.324580
$486$	19.5065	0.884831
$487$	27.3202	1.23800	0.618998	−	0.785392i	$-0.287539\pi$
$487$	27.3202	1.23800	0.618998	+	0.785392i	$0.287539\pi$
$488$	−3.99256	−0.180735
$489$	43.1459	1.95113
$490$	−17.6397	−0.796883
$491$	23.2568	1.04956	0.524782	−	0.851237i	$-0.324147\pi$
$491$	23.2568	1.04956	0.524782	+	0.851237i	$0.324147\pi$
$492$	106.576	4.80482
$493$	0	0
$494$	−60.6712	−2.72973
$495$	−3.48356	−0.156574
$496$	63.4095	2.84717
$497$	−1.41335	−0.0633976
$498$	−0.834501	−0.0373949
$499$	13.2790	0.594449	0.297225	−	0.954808i	$-0.403939\pi$
$499$	13.2790	0.594449	0.297225	+	0.954808i	$0.403939\pi$
$500$	−4.47602	−0.200174
$501$	40.8900	1.82683
$502$	67.0701	2.99349
$503$	9.94397	0.443380	0.221690	−	0.975117i	$-0.428843\pi$
$503$	9.94397	0.443380	0.221690	+	0.975117i	$0.428843\pi$
$504$	10.5267	0.468895
$505$	1.88994	0.0841013
$506$	−5.20312	−0.231307
$507$	−52.2755	−2.32164
$508$	64.2503	2.85064
$509$	17.4610	0.773943	0.386972	−	0.922092i	$-0.373521\pi$
$509$	17.4610	0.773943	0.386972	+	0.922092i	$0.373521\pi$
$510$	0	0
$511$	2.12412	0.0939657
$512$	50.8526	2.24739
$513$	−45.1943	−1.99538
$514$	−46.9295	−2.06997
$515$	−8.20152	−0.361402
$516$	−32.2374	−1.41917
$517$	1.28414	0.0564766
$518$	−3.23360	−0.142076
$519$	−17.5239	−0.769215
$520$	34.5454	1.51492
$521$	−21.6384	−0.947994	−0.473997	−	0.880526i	$-0.657189\pi$
$521$	−21.6384	−0.947994	−0.473997	+	0.880526i	$0.657189\pi$
$522$	−43.8496	−1.91925
$523$	−35.4255	−1.54905	−0.774525	−	0.632544i	$-0.782011\pi$
$523$	−35.4255	−1.54905	−0.774525	+	0.632544i	$0.782011\pi$
$524$	−33.2805	−1.45386
$525$	0.801039	0.0349602
$526$	34.7847	1.51669
$527$	0	0
$528$	−11.8303	−0.514848
$529$	−8.92796	−0.388172
$530$	−27.7320	−1.20460
$531$	39.8781	1.73056
$532$	−5.08779	−0.220583
$533$	−42.5976	−1.84511
$534$	−131.620	−5.69575
$535$	−8.27660	−0.357829
$536$	−53.2042	−2.29807
$537$	−45.1038	−1.94637
$538$	−53.2225	−2.29458
$539$	−3.77806	−0.162733
$540$	46.5189	2.00185
$541$	−2.53781	−0.109109	−0.0545544	−	0.998511i	$-0.517374\pi$
$541$	−2.53781	−0.109109	−0.0545544	+	0.998511i	$0.517374\pi$
$542$	12.5402	0.538649
$543$	−80.6915	−3.46280
$544$	0	0
$545$	−1.38287	−0.0592357
$546$	−11.1761	−0.478292
$547$	−21.7700	−0.930820	−0.465410	−	0.885095i	$-0.654093\pi$
$547$	−21.7700	−0.930820	−0.465410	+	0.885095i	$0.654093\pi$
$548$	30.7264	1.31257
$549$	4.04982	0.172842
$550$	−1.38703	−0.0591431
$551$	11.7237	0.499448
$552$	72.4355	3.08306
$553$	0.452589	0.0192460
$554$	−60.0599	−2.55170
$555$	−14.8973	−0.632354
$556$	93.0011	3.94412
$557$	−9.99564	−0.423529	−0.211764	−	0.977321i	$-0.567921\pi$
$557$	−9.99564	−0.423529	−0.211764	+	0.977321i	$0.567921\pi$
$558$	−145.613	−6.16429
$559$	12.8850	0.544978
$560$	1.85136	0.0782341
$561$	0	0
$562$	7.17145	0.302509
$563$	−44.8779	−1.89138	−0.945689	−	0.325072i	$-0.894611\pi$
$563$	−44.8779	−1.89138	−0.945689	+	0.325072i	$0.894611\pi$
$564$	−32.3176	−1.36082
$565$	−11.1388	−0.468613
$566$	29.8358	1.25409
$567$	−3.31321	−0.139142
$568$	−34.0698	−1.42954
$569$	26.9590	1.13018	0.565091	−	0.825029i	$-0.308841\pi$
$569$	26.9590	1.13018	0.565091	+	0.825029i	$0.308841\pi$
$570$	−33.9129	−1.42046
$571$	15.1296	0.633155	0.316577	−	0.948567i	$-0.397466\pi$
$571$	15.1296	0.633155	0.316577	+	0.948567i	$0.397466\pi$
$572$	13.3753	0.559251
$573$	23.5692	0.984616
$574$	−5.16829	−0.215720
$575$	3.75127	0.156439
$576$	−2.34620	−0.0977585
$577$	−19.0447	−0.792839	−0.396420	−	0.918069i	$-0.629747\pi$
$577$	−19.0447	−0.792839	−0.396420	+	0.918069i	$0.629747\pi$
$578$	0	0
$579$	−13.9863	−0.581251
$580$	−12.0673	−0.501069
$581$	0.0279704	0.00116041
$582$	55.7456	2.31073
$583$	−5.93962	−0.245994
$584$	51.2034	2.11881
$585$	−35.0408	−1.44876
$586$	65.8151	2.71880
$587$	19.7756	0.816227	0.408114	−	0.912931i	$-0.366187\pi$
$587$	19.7756	0.816227	0.408114	+	0.912931i	$0.366187\pi$
$588$	95.0812	3.92108
$589$	38.9314	1.60414
$590$	15.8780	0.653686
$591$	−62.9516	−2.58948
$592$	−34.4305	−1.41509
$593$	−38.1146	−1.56518	−0.782590	−	0.622538i	$-0.786102\pi$
$593$	−38.1146	−1.56518	−0.782590	+	0.622538i	$0.786102\pi$
$594$	14.4152	0.591465
$595$	0	0
$596$	78.8482	3.22975
$597$	69.1660	2.83078
$598$	−52.3377	−2.14025
$599$	−26.2354	−1.07195	−0.535974	−	0.844234i	$-0.680056\pi$
$599$	−26.2354	−1.07195	−0.535974	+	0.844234i	$0.680056\pi$
$600$	19.3096	0.788310
$601$	34.9489	1.42560	0.712798	−	0.701369i	$-0.247428\pi$
$601$	34.9489	1.42560	0.712798	+	0.701369i	$0.247428\pi$
$602$	1.56332	0.0637160
$603$	53.9672	2.19771
$604$	−49.3402	−2.00763
$605$	10.7029	0.435136
$606$	−14.7390	−0.598729
$607$	2.52460	0.102470	0.0512352	−	0.998687i	$-0.483684\pi$
$607$	2.52460	0.102470	0.0512352	+	0.998687i	$0.483684\pi$
$608$	−23.5787	−0.956244
$609$	2.15960	0.0875113
$610$	1.61249	0.0652878
$611$	12.9171	0.522570
$612$	0	0
$613$	−10.2713	−0.414852	−0.207426	−	0.978251i	$-0.566509\pi$
$613$	−10.2713	−0.414852	−0.207426	+	0.978251i	$0.566509\pi$
$614$	−14.9101	−0.601723
$615$	−23.8104	−0.960130
$616$	0.897696	0.0361692
$617$	29.7313	1.19694	0.598469	−	0.801146i	$-0.295776\pi$
$617$	29.7313	1.19694	0.598469	+	0.801146i	$0.295776\pi$
$618$	63.9606	2.57287
$619$	−9.54519	−0.383653	−0.191827	−	0.981429i	$-0.561441\pi$
$619$	−9.54519	−0.383653	−0.191827	+	0.981429i	$0.561441\pi$
$620$	−40.0724	−1.60935
$621$	−38.9866	−1.56448
$622$	−27.1771	−1.08970
$623$	4.41157	0.176746
$624$	−119.000	−4.76381
$625$	1.00000	0.0400000
$626$	61.9982	2.47795
$627$	−7.26343	−0.290074
$628$	23.6180	0.942461
$629$	0	0
$630$	−4.25144	−0.169382
$631$	−25.5337	−1.01648	−0.508240	−	0.861215i	$-0.669704\pi$
$631$	−25.5337	−1.01648	−0.508240	+	0.861215i	$0.669704\pi$
$632$	10.9100	0.433975
$633$	47.1399	1.87364
$634$	18.7466	0.744521
$635$	−14.3543	−0.569634
$636$	149.480	5.92728
$637$	−38.0032	−1.50574
$638$	−3.73942	−0.148045
$639$	34.5584	1.36711
$640$	−11.7785	−0.465587
$641$	−15.0694	−0.595206	−0.297603	−	0.954690i	$-0.596187\pi$
$641$	−15.0694	−0.595206	−0.297603	+	0.954690i	$0.596187\pi$
$642$	64.5461	2.54743
$643$	35.8483	1.41372	0.706860	−	0.707353i	$-0.250111\pi$
$643$	35.8483	1.41372	0.706860	+	0.707353i	$0.250111\pi$
$644$	−4.38895	−0.172949
$645$	7.20223	0.283588
$646$	0	0
$647$	9.80515	0.385480	0.192740	−	0.981250i	$-0.438263\pi$
$647$	9.80515	0.385480	0.192740	+	0.981250i	$0.438263\pi$
$648$	−79.8671	−3.13747
$649$	3.40073	0.133490
$650$	−13.9520	−0.547242
$651$	7.17145	0.281071
$652$	−63.0185	−2.46800
$653$	14.3262	0.560627	0.280314	−	0.959908i	$-0.409562\pi$
$653$	14.3262	0.560627	0.280314	+	0.959908i	$0.409562\pi$
$654$	10.7845	0.421708
$655$	7.43528	0.290520
$656$	−55.0306	−2.14858
$657$	−51.9377	−2.02628
$658$	1.56721	0.0610962
$659$	9.77178	0.380655	0.190327	−	0.981721i	$-0.439045\pi$
$659$	9.77178	0.380655	0.190327	+	0.981721i	$0.439045\pi$
$660$	7.47631	0.291015
$661$	−14.3439	−0.557914	−0.278957	−	0.960304i	$-0.589989\pi$
$661$	−14.3439	−0.557914	−0.278957	+	0.960304i	$0.589989\pi$
$662$	0.495752	0.0192679
$663$	0	0
$664$	0.674245	0.0261658
$665$	1.13668	0.0440784
$666$	79.0660	3.06374
$667$	10.1134	0.391593
$668$	−59.7235	−2.31077
$669$	−72.0818	−2.78684
$670$	21.4878	0.830145
$671$	0.345362	0.0133325
$672$	−4.34337	−0.167549
$673$	35.5082	1.36874	0.684370	−	0.729135i	$-0.260078\pi$
$673$	35.5082	1.36874	0.684370	+	0.729135i	$0.260078\pi$
$674$	−5.79936	−0.223383
$675$	−10.3929	−0.400023
$676$	76.3531	2.93666
$677$	17.8589	0.686372	0.343186	−	0.939267i	$-0.388494\pi$
$677$	17.8589	0.686372	0.343186	+	0.939267i	$0.388494\pi$
$678$	86.8673	3.33612
$679$	−1.86845	−0.0717045
$680$	0	0
$681$	58.1005	2.22641
$682$	−12.4176	−0.475495
$683$	2.40521	0.0920328	0.0460164	−	0.998941i	$-0.485347\pi$
$683$	2.40521	0.0920328	0.0460164	+	0.998941i	$0.485347\pi$
$684$	124.403	4.75668
$685$	−6.86466	−0.262285
$686$	−9.26717	−0.353822
$687$	68.3483	2.60765
$688$	16.6458	0.634614
$689$	−59.7461	−2.27614
$690$	−29.2548	−1.11371
$691$	23.8153	0.905976	0.452988	−	0.891517i	$-0.350358\pi$
$691$	23.8153	0.905976	0.452988	+	0.891517i	$0.350358\pi$
$692$	25.5953	0.972986
$693$	−0.910570	−0.0345897
$694$	−46.1800	−1.75297
$695$	−20.7776	−0.788140
$696$	52.0585	1.97327
$697$	0	0
$698$	−54.2981	−2.05521
$699$	33.6620	1.27321
$700$	−1.16999	−0.0442214
$701$	16.5171	0.623843	0.311921	−	0.950108i	$-0.399027\pi$
$701$	16.5171	0.623843	0.311921	+	0.950108i	$0.399027\pi$
$702$	145.002	5.47273
$703$	−21.1393	−0.797282
$704$	−0.200080	−0.00754081
$705$	7.22017	0.271927
$706$	1.51840	0.0571457
$707$	0.494013	0.0185793
$708$	−85.5850	−3.21648
$709$	7.88357	0.296074	0.148037	−	0.988982i	$-0.452705\pi$
$709$	7.88357	0.296074	0.148037	+	0.988982i	$0.452705\pi$
$710$	13.7599	0.516400
$711$	−11.0664	−0.415023
$712$	106.344	3.98540
$713$	33.5840	1.25773
$714$	0	0
$715$	−2.98822	−0.111753
$716$	65.8782	2.46198
$717$	7.80767	0.291583
$718$	−16.9714	−0.633367
$719$	15.4100	0.574695	0.287347	−	0.957826i	$-0.407227\pi$
$719$	15.4100	0.574695	0.287347	+	0.957826i	$0.407227\pi$
$720$	−45.2682	−1.68705
$721$	−2.14380	−0.0798393
$722$	0.228774	0.00851410
$723$	21.5385	0.801026
$724$	117.857	4.38013
$725$	2.69600	0.100127
$726$	−83.4682	−3.09779
$727$	−31.1724	−1.15612	−0.578060	−	0.815994i	$-0.696190\pi$
$727$	−31.1724	−1.15612	−0.578060	+	0.815994i	$0.696190\pi$
$728$	9.02984	0.334668
$729$	−14.5357	−0.538359
$730$	−20.6797	−0.765390
$731$	0	0
$732$	−8.69159	−0.321251
$733$	−51.2681	−1.89363	−0.946816	−	0.321776i	$-0.895720\pi$
$733$	−51.2681	−1.89363	−0.946816	+	0.321776i	$0.895720\pi$
$734$	23.8409	0.879982
$735$	−21.2423	−0.783535
$736$	−20.3401	−0.749744
$737$	4.60223	0.169525
$738$	126.372	4.65181
$739$	4.59844	0.169156	0.0845782	−	0.996417i	$-0.473046\pi$
$739$	4.59844	0.169156	0.0845782	+	0.996417i	$0.473046\pi$
$740$	21.7588	0.799869
$741$	−73.0622	−2.68401
$742$	−7.24889	−0.266115
$743$	−23.0541	−0.845775	−0.422887	−	0.906182i	$-0.638983\pi$
$743$	−23.0541	−0.845775	−0.422887	+	0.906182i	$0.638983\pi$
$744$	172.873	6.33782
$745$	−17.6157	−0.645389
$746$	49.0648	1.79639
$747$	−0.683914	−0.0250231
$748$	0	0
$749$	−2.16342	−0.0790498
$750$	−7.79863	−0.284766
$751$	0.480334	0.0175276	0.00876382	−	0.999962i	$-0.497210\pi$
$751$	0.480334	0.0175276	0.00876382	+	0.999962i	$0.497210\pi$
$752$	16.6872	0.608520
$753$	80.7680	2.94335
$754$	−37.6145	−1.36984
$755$	11.0232	0.401176
$756$	12.1596	0.442240
$757$	−27.2363	−0.989919	−0.494959	−	0.868916i	$-0.664817\pi$
$757$	−27.2363	−0.989919	−0.494959	+	0.868916i	$0.664817\pi$
$758$	−90.6076	−3.29102
$759$	−6.26576	−0.227433
$760$	27.4003	0.993914
$761$	46.2606	1.67695	0.838473	−	0.544943i	$-0.183449\pi$
$761$	46.2606	1.67695	0.838473	+	0.544943i	$0.183449\pi$
$762$	111.944	4.05530
$763$	−0.361470	−0.0130861
$764$	−34.4249	−1.24545
$765$	0	0
$766$	−21.1698	−0.764898
$767$	34.2076	1.23517
$768$	89.6064	3.23339
$769$	1.59752	0.0576081	0.0288041	−	0.999585i	$-0.490830\pi$
$769$	1.59752	0.0576081	0.0288041	+	0.999585i	$0.490830\pi$
$770$	−0.362556	−0.0130656
$771$	−56.5139	−2.03530
$772$	20.4283	0.735229
$773$	−0.694799	−0.0249902	−0.0124951	−	0.999922i	$-0.503977\pi$
$773$	−0.694799	−0.0249902	−0.0124951	+	0.999922i	$0.503977\pi$
$774$	−38.2252	−1.37398
$775$	8.95269	0.321590
$776$	−45.0402	−1.61685
$777$	−3.89400	−0.139697
$778$	−7.12266	−0.255360
$779$	−33.7871	−1.21055
$780$	75.2035	2.69272
$781$	2.94708	0.105455
$782$	0	0
$783$	−28.0192	−1.00133
$784$	−49.0952	−1.75340
$785$	−5.27656	−0.188329
$786$	−57.9850	−2.06825
$787$	−40.0524	−1.42771	−0.713857	−	0.700292i	$-0.753053\pi$
$787$	−40.0524	−1.42771	−0.713857	+	0.700292i	$0.753053\pi$
$788$	91.9465	3.27546
$789$	41.8889	1.49128
$790$	−4.40624	−0.156767
$791$	−2.91157	−0.103524
$792$	−21.9499	−0.779955
$793$	3.47396	0.123364
$794$	17.5241	0.621909
$795$	−33.3958	−1.18443
$796$	−101.023	−3.58067
$797$	−2.90280	−0.102822	−0.0514112	−	0.998678i	$-0.516372\pi$
$797$	−2.90280	−0.102822	−0.0514112	+	0.998678i	$0.516372\pi$
$798$	−8.86451	−0.313800
$799$	0	0
$800$	−5.42218	−0.191703
$801$	−107.869	−3.81136
$802$	−26.0378	−0.919426
$803$	−4.42916	−0.156301
$804$	−115.823	−4.08475
$805$	0.980546	0.0345597
$806$	−124.908	−4.39969
$807$	−64.0922	−2.25615
$808$	11.9085	0.418940
$809$	12.6728	0.445551	0.222775	−	0.974870i	$-0.428488\pi$
$809$	12.6728	0.445551	0.222775	+	0.974870i	$0.428488\pi$
$810$	32.2562	1.13337
$811$	−11.4213	−0.401055	−0.200528	−	0.979688i	$-0.564266\pi$
$811$	−11.4213	−0.401055	−0.200528	+	0.979688i	$0.564266\pi$
$812$	−3.15429	−0.110694
$813$	15.1013	0.529627
$814$	6.74261	0.236328
$815$	14.0791	0.493171
$816$	0	0
$817$	10.2200	0.357552
$818$	8.41376	0.294180
$819$	−9.15934	−0.320053
$820$	34.7773	1.21448
$821$	25.1443	0.877543	0.438771	−	0.898599i	$-0.355414\pi$
$821$	25.1443	0.877543	0.438771	+	0.898599i	$0.355414\pi$
$822$	53.5349	1.86725
$823$	3.15241	0.109886	0.0549430	−	0.998489i	$-0.482502\pi$
$823$	3.15241	0.109886	0.0549430	+	0.998489i	$0.482502\pi$
$824$	−51.6777	−1.80028
$825$	−1.67030	−0.0581524
$826$	4.15035	0.144409
$827$	51.5648	1.79308	0.896542	−	0.442959i	$-0.146071\pi$
$827$	51.5648	1.79308	0.896542	+	0.442959i	$0.146071\pi$
$828$	107.316	3.72948
$829$	−23.5779	−0.818896	−0.409448	−	0.912334i	$-0.634279\pi$
$829$	−23.5779	−0.818896	−0.409448	+	0.912334i	$0.634279\pi$
$830$	−0.272310	−0.00945200
$831$	−72.3260	−2.50896
$832$	−2.01259	−0.0697740
$833$	0	0
$834$	162.037	5.61088
$835$	13.3430	0.461753
$836$	10.6089	0.366916
$837$	−93.0444	−3.21609
$838$	6.24213	0.215631
$839$	−3.47286	−0.119896	−0.0599482	−	0.998201i	$-0.519094\pi$
$839$	−3.47286	−0.119896	−0.0599482	+	0.998201i	$0.519094\pi$
$840$	5.04734	0.174150
$841$	−21.7316	−0.749366
$842$	−78.3902	−2.70150
$843$	8.63608	0.297443
$844$	−68.8520	−2.36999
$845$	−17.0582	−0.586821
$846$	−38.3204	−1.31748
$847$	2.79764	0.0961281
$848$	−77.1842	−2.65052
$849$	35.9292	1.23309
$850$	0	0
$851$	−18.2357	−0.625110
$852$	−74.1682	−2.54096
$853$	40.1266	1.37391	0.686954	−	0.726701i	$-0.258947\pi$
$853$	40.1266	1.37391	0.686954	+	0.726701i	$0.258947\pi$
$854$	0.421490	0.0144231
$855$	−27.7933	−0.950510
$856$	−52.1508	−1.78248
$857$	−26.1935	−0.894754	−0.447377	−	0.894346i	$-0.647642\pi$
$857$	−26.1935	−0.894754	−0.447377	+	0.894346i	$0.647642\pi$
$858$	23.3040	0.795586
$859$	16.1653	0.551554	0.275777	−	0.961222i	$-0.411065\pi$
$859$	16.1653	0.551554	0.275777	+	0.961222i	$0.411065\pi$
$860$	−10.5195	−0.358712
$861$	−6.22382	−0.212107
$862$	−66.2011	−2.25482
$863$	45.4960	1.54870	0.774351	−	0.632756i	$-0.218077\pi$
$863$	45.4960	1.54870	0.774351	+	0.632756i	$0.218077\pi$
$864$	56.3522	1.91714
$865$	−5.71831	−0.194428
$866$	−5.77443	−0.196223
$867$	0	0
$868$	−10.4745	−0.355529
$869$	−0.943724	−0.0320136
$870$	−21.0251	−0.712817
$871$	46.2934	1.56859
$872$	−8.71346	−0.295075
$873$	45.6862	1.54624
$874$	−41.5126	−1.40418
$875$	0.261390	0.00883661
$876$	111.467	3.76612
$877$	3.40809	0.115083	0.0575416	−	0.998343i	$-0.481674\pi$
$877$	3.40809	0.115083	0.0575416	+	0.998343i	$0.481674\pi$
$878$	−10.6797	−0.360422
$879$	79.2566	2.67326
$880$	−3.86039	−0.130134
$881$	−55.0205	−1.85369	−0.926843	−	0.375449i	$-0.877489\pi$
$881$	−55.0205	−1.85369	−0.926843	+	0.375449i	$0.877489\pi$
$882$	112.742	3.79621
$883$	4.42759	0.149000	0.0745001	−	0.997221i	$-0.476264\pi$
$883$	4.42759	0.149000	0.0745001	+	0.997221i	$0.476264\pi$
$884$	0	0
$885$	19.1208	0.642738
$886$	−8.53333	−0.286683
$887$	10.0231	0.336544	0.168272	−	0.985741i	$-0.446181\pi$
$887$	10.0231	0.336544	0.168272	+	0.985741i	$0.446181\pi$
$888$	−93.8676	−3.14999
$889$	−3.75208	−0.125841
$890$	−42.9495	−1.43967
$891$	6.90860	0.231447
$892$	105.282	3.52510
$893$	10.2454	0.342850
$894$	137.378	4.59461
$895$	−14.7180	−0.491969
$896$	−3.07879	−0.102855
$897$	−63.0267	−2.10440
$898$	−41.7846	−1.39437
$899$	24.1364	0.804994
$900$	28.6078	0.953594
$901$	0	0
$902$	10.7768	0.358827
$903$	1.88259	0.0626488
$904$	−70.1854	−2.33433
$905$	−26.3308	−0.875265
$906$	−85.9661	−2.85603
$907$	9.52472	0.316263	0.158132	−	0.987418i	$-0.449453\pi$
$907$	9.52472	0.316263	0.158132	+	0.987418i	$0.449453\pi$
$908$	−84.8609	−2.81621
$909$	−12.0793	−0.400645
$910$	−3.64691	−0.120894
$911$	13.4872	0.446851	0.223426	−	0.974721i	$-0.428276\pi$
$911$	13.4872	0.446851	0.223426	+	0.974721i	$0.428276\pi$
$912$	−94.3869	−3.12546
$913$	−0.0583230	−0.00193021
$914$	−21.0822	−0.697337
$915$	1.94181	0.0641943
$916$	−99.8287	−3.29843
$917$	1.94351	0.0641803
$918$	0	0
$919$	21.8423	0.720511	0.360256	−	0.932854i	$-0.382690\pi$
$919$	21.8423	0.720511	0.360256	+	0.932854i	$0.382690\pi$
$920$	23.6367	0.779280
$921$	−17.9552	−0.591645
$922$	−102.495	−3.37549
$923$	29.6444	0.975758
$924$	1.95423	0.0642896
$925$	−4.86119	−0.159835
$926$	56.9007	1.86987
$927$	52.4188	1.72166
$928$	−14.6182	−0.479865
$929$	−5.82188	−0.191010	−0.0955049	−	0.995429i	$-0.530447\pi$
$929$	−5.82188	−0.191010	−0.0955049	+	0.995429i	$0.530447\pi$
$930$	−69.8187	−2.28945
$931$	−30.1429	−0.987894
$932$	−49.1663	−1.61050
$933$	−32.7275	−1.07145
$934$	−77.5286	−2.53681
$935$	0	0
$936$	−220.792	−7.21681
$937$	−5.54471	−0.181138	−0.0905690	−	0.995890i	$-0.528869\pi$
$937$	−5.54471	−0.181138	−0.0905690	+	0.995890i	$0.528869\pi$
$938$	5.61669	0.183392
$939$	74.6602	2.43644
$940$	−10.5457	−0.343963
$941$	38.7292	1.26253	0.631267	−	0.775565i	$-0.282535\pi$
$941$	38.7292	1.26253	0.631267	+	0.775565i	$0.282535\pi$
$942$	41.1500	1.34074
$943$	−29.1462	−0.949131
$944$	44.1918	1.43832
$945$	−2.71661	−0.0883712
$946$	−3.25978	−0.105985
$947$	−40.9411	−1.33041	−0.665204	−	0.746662i	$-0.731655\pi$
$947$	−40.9411	−1.33041	−0.665204	+	0.746662i	$0.731655\pi$
$948$	23.7504	0.771376
$949$	−44.5525	−1.44623
$950$	−11.0663	−0.359037
$951$	22.5752	0.732051
$952$	0	0
$953$	38.4819	1.24655	0.623276	−	0.782002i	$-0.285801\pi$
$953$	38.4819	1.24655	0.623276	+	0.782002i	$0.285801\pi$
$954$	177.245	5.73853
$955$	7.69096	0.248873
$956$	−11.4038	−0.368825
$957$	−4.50313	−0.145565
$958$	8.89184	0.287282
$959$	−1.79436	−0.0579428
$960$	−1.12496	−0.0363079
$961$	49.1506	1.58550
$962$	67.8233	2.18671
$963$	52.8987	1.70464
$964$	−31.4589	−1.01322
$965$	−4.56393	−0.146918
$966$	−7.64692	−0.246036
$967$	40.8040	1.31217	0.656084	−	0.754688i	$-0.272212\pi$
$967$	40.8040	1.31217	0.656084	+	0.754688i	$0.272212\pi$
$968$	67.4390	2.16757
$969$	0	0
$970$	18.1906	0.584064
$971$	33.3847	1.07137	0.535683	−	0.844419i	$-0.320054\pi$
$971$	33.3847	1.07137	0.535683	+	0.844419i	$0.320054\pi$
$972$	−34.3097	−1.10048
$973$	−5.43107	−0.174112
$974$	−69.5245	−2.22771
$975$	−16.8014	−0.538076
$976$	4.48791	0.143654
$977$	1.71392	0.0548333	0.0274167	−	0.999624i	$-0.491272\pi$
$977$	1.71392	0.0548333	0.0274167	+	0.999624i	$0.491272\pi$
$978$	−109.798	−3.51095
$979$	−9.19887	−0.293997
$980$	31.0263	0.991100
$981$	8.83842	0.282189
$982$	−59.1839	−1.88864
$983$	−28.3798	−0.905174	−0.452587	−	0.891720i	$-0.649499\pi$
$983$	−28.3798	−0.905174	−0.452587	+	0.891720i	$0.649499\pi$
$984$	−150.029	−4.78276
$985$	−20.5420	−0.654523
$986$	0	0
$987$	1.88728	0.0600728
$988$	106.714	3.39502
$989$	8.81621	0.280339
$990$	8.86498	0.281748
$991$	12.4374	0.395087	0.197544	−	0.980294i	$-0.436704\pi$
$991$	12.4374	0.395087	0.197544	+	0.980294i	$0.436704\pi$
$992$	−48.5431	−1.54124
$993$	0.597000	0.0189452
$994$	3.59671	0.114081
$995$	22.5698	0.715512
$996$	1.46779	0.0465088
$997$	−13.3607	−0.423138	−0.211569	−	0.977363i	$-0.567857\pi$
$997$	−13.3607	−0.423138	−0.211569	+	0.977363i	$0.567857\pi$
$998$	−33.7924	−1.06968
$999$	50.5219	1.59844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.a.r.1.2	✓	12
5.4	even	2		7225.2.a.bo.1.11		12
17.4	even	4		1445.2.d.i.866.21		24
17.13	even	4		1445.2.d.i.866.22		24
17.16	even	2		1445.2.a.s.1.2	yes	12
85.84	even	2		7225.2.a.bn.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1445.2.a.r.1.2	✓	12	1.1	even	1	trivial
1445.2.a.s.1.2	yes	12	17.16	even	2
1445.2.d.i.866.21		24	17.4	even	4
1445.2.d.i.866.22		24	17.13	even	4
7225.2.a.bn.1.11		12	85.84	even	2
7225.2.a.bo.1.11		12	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:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54480 q^{2} -3.06453 q^{3} +4.47602 q^{4} -1.00000 q^{5} +7.79863 q^{6} -0.261390 q^{7} -6.30099 q^{8} +6.39135 q^{9} +2.54480 q^{10} +0.545043 q^{11} -13.7169 q^{12} +5.48254 q^{13} +0.665187 q^{14} +3.06453 q^{15} +7.08273 q^{16} -16.2647 q^{18} +4.34857 q^{19} -4.47602 q^{20} +0.801039 q^{21} -1.38703 q^{22} +3.75127 q^{23} +19.3096 q^{24} +1.00000 q^{25} -13.9520 q^{26} -10.3929 q^{27} -1.16999 q^{28} +2.69600 q^{29} -7.79863 q^{30} +8.95269 q^{31} -5.42218 q^{32} -1.67030 q^{33} +0.261390 q^{35} +28.6078 q^{36} -4.86119 q^{37} -11.0663 q^{38} -16.8014 q^{39} +6.30099 q^{40} -7.76968 q^{41} -2.03849 q^{42} +2.35019 q^{43} +2.43963 q^{44} -6.39135 q^{45} -9.54625 q^{46} +2.35604 q^{47} -21.7052 q^{48} -6.93168 q^{49} -2.54480 q^{50} +24.5400 q^{52} -10.8975 q^{53} +26.4479 q^{54} -0.545043 q^{55} +1.64702 q^{56} -13.3263 q^{57} -6.86078 q^{58} +6.23938 q^{59} +13.7169 q^{60} +0.633641 q^{61} -22.7828 q^{62} -1.67064 q^{63} -0.367091 q^{64} -5.48254 q^{65} +4.25059 q^{66} +8.44378 q^{67} -11.4959 q^{69} -0.665187 q^{70} +5.40706 q^{71} -40.2718 q^{72} -8.12625 q^{73} +12.3708 q^{74} -3.06453 q^{75} +19.4643 q^{76} -0.142469 q^{77} +42.7563 q^{78} -1.73147 q^{79} -7.08273 q^{80} +12.6753 q^{81} +19.7723 q^{82} -0.107006 q^{83} +3.58547 q^{84} -5.98077 q^{86} -8.26196 q^{87} -3.43431 q^{88} -16.8773 q^{89} +16.2647 q^{90} -1.43308 q^{91} +16.7908 q^{92} -27.4358 q^{93} -5.99566 q^{94} -4.34857 q^{95} +16.6164 q^{96} +7.14812 q^{97} +17.6397 q^{98} +3.48356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{3} + 21 q^{4} - 12 q^{5} + 9 q^{6} - 6 q^{7} + 12 q^{8} + 21 q^{9} - 3 q^{10} + 6 q^{11} - 6 q^{12} + 9 q^{13} + 18 q^{14} + 3 q^{15} + 39 q^{16} - 9 q^{18} + 27 q^{19} - 21 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 + 21 * q^4 - 12 * q^5 + 9 * q^6 - 6 * q^7 + 12 * q^8 + 21 * q^9 - 3 * q^10 + 6 * q^11 - 6 * q^12 + 9 * q^13 + 18 * q^14 + 3 * q^15 + 39 * q^16 - 9 * q^18 + 27 * q^19 - 21 * q^20 + 6 * q^21 - 15 * q^22 - 18 * q^23 + 36 * q^24 + 12 * q^25 + 6 * q^26 - 12 * q^27 - 39 * q^28 - 9 * q^30 + 6 * q^31 + 12 * q^32 + 6 * q^35 + 48 * q^36 - 21 * q^37 - 3 * q^38 + 9 * q^39 - 12 * q^40 + 15 * q^41 + 30 * q^42 + 45 * q^43 + 42 * q^44 - 21 * q^45 + 15 * q^46 + 3 * q^47 + 63 * q^48 + 12 * q^49 + 3 * q^50 + 51 * q^52 - 12 * q^53 + 27 * q^54 - 6 * q^55 - 3 * q^56 - 6 * q^57 + 51 * q^58 + 36 * q^59 + 6 * q^60 - 3 * q^61 - 36 * q^62 - 72 * q^63 + 42 * q^64 - 9 * q^65 - 39 * q^66 + 78 * q^67 - 66 * q^69 - 18 * q^70 + 30 * q^71 - 12 * q^72 + 33 * q^73 - 9 * q^74 - 3 * q^75 + 27 * q^76 - 39 * q^77 + 24 * q^78 + 3 * q^79 - 39 * q^80 + 12 * q^81 + 51 * q^82 + 27 * q^83 + 27 * q^84 + 18 * q^86 + 24 * q^87 - 36 * q^88 + 6 * q^89 + 9 * q^90 + 24 * q^91 + 3 * q^92 - 12 * q^93 + 21 * q^94 - 27 * q^95 + 39 * q^96 + 6 * q^97 - 42 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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