LMFDB - Embedded newform 2175.2.a.bc.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2175,2,Mod(1,2175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2175, 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("2175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2175 = 3 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2175.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:	$17.3674624396$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 12x^{6} + 23x^{5} + 36x^{4} - 62x^{3} - 15x^{2} + 14x + 2 $ x^8 - 2x^7 - 12x^6 + 23x^5 + 36x^4 - 62x^3 - 15x^2 + 14*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.485464$ of defining polynomial
Character	$\chi$	$=$	2175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.485464 q^{2} -1.00000 q^{3} -1.76432 q^{4} -0.485464 q^{6} -1.94912 q^{7} -1.82745 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.485464 q^{2} -1.00000 q^{3} -1.76432 q^{4} -0.485464 q^{6} -1.94912 q^{7} -1.82745 q^{8} +1.00000 q^{9} +5.30306 q^{11} +1.76432 q^{12} -6.00152 q^{13} -0.946227 q^{14} +2.64149 q^{16} -1.89418 q^{17} +0.485464 q^{18} -4.84040 q^{19} +1.94912 q^{21} +2.57445 q^{22} +3.19725 q^{23} +1.82745 q^{24} -2.91352 q^{26} -1.00000 q^{27} +3.43888 q^{28} +1.00000 q^{29} -4.96870 q^{31} +4.93724 q^{32} -5.30306 q^{33} -0.919558 q^{34} -1.76432 q^{36} -10.9699 q^{37} -2.34984 q^{38} +6.00152 q^{39} -0.749700 q^{41} +0.946227 q^{42} +6.21936 q^{43} -9.35633 q^{44} +1.55215 q^{46} +9.67532 q^{47} -2.64149 q^{48} -3.20094 q^{49} +1.89418 q^{51} +10.5886 q^{52} +4.44791 q^{53} -0.485464 q^{54} +3.56191 q^{56} +4.84040 q^{57} +0.485464 q^{58} +14.8542 q^{59} +15.4683 q^{61} -2.41213 q^{62} -1.94912 q^{63} -2.88613 q^{64} -2.57445 q^{66} +14.6495 q^{67} +3.34195 q^{68} -3.19725 q^{69} +5.37043 q^{71} -1.82745 q^{72} -12.5367 q^{73} -5.32550 q^{74} +8.54003 q^{76} -10.3363 q^{77} +2.91352 q^{78} -7.87855 q^{79} +1.00000 q^{81} -0.363953 q^{82} -11.1873 q^{83} -3.43888 q^{84} +3.01928 q^{86} -1.00000 q^{87} -9.69106 q^{88} +15.2850 q^{89} +11.6977 q^{91} -5.64098 q^{92} +4.96870 q^{93} +4.69702 q^{94} -4.93724 q^{96} +7.14188 q^{97} -1.55394 q^{98} +5.30306 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 8 q^{3} + 12 q^{4} + 2 q^{6} + 2 q^{7} - 3 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 8 * q^3 + 12 * q^4 + 2 * q^6 + 2 * q^7 - 3 * q^8 + 8 * q^9	$ 8 q - 2 q^{2} - 8 q^{3} + 12 q^{4} + 2 q^{6} + 2 q^{7} - 3 q^{8} + 8 q^{9} + 6 q^{11} - 12 q^{12} + 6 q^{13} + 9 q^{14} + 32 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{21} + 3 q^{22} - 14 q^{23} + 3 q^{24} + 18 q^{26} - 8 q^{27} + 14 q^{28} + 8 q^{29} + 8 q^{31} + 2 q^{32} - 6 q^{33} - 13 q^{34} + 12 q^{36} + 4 q^{37} - 26 q^{38} - 6 q^{39} + 2 q^{41} - 9 q^{42} + 2 q^{43} - 15 q^{44} + 24 q^{46} - 12 q^{47} - 32 q^{48} + 38 q^{49} + 12 q^{51} + 49 q^{52} - 4 q^{53} + 2 q^{54} + 58 q^{56} - 2 q^{58} + 18 q^{59} + 12 q^{61} + 4 q^{62} + 2 q^{63} + 21 q^{64} - 3 q^{66} + 26 q^{67} - 81 q^{68} + 14 q^{69} + 24 q^{71} - 3 q^{72} - 14 q^{73} - 22 q^{74} + 26 q^{77} - 18 q^{78} + 10 q^{79} + 8 q^{81} + 48 q^{82} - 40 q^{83} - 14 q^{84} + 8 q^{86} - 8 q^{87} - 10 q^{88} + 34 q^{89} + 26 q^{91} + 18 q^{92} - 8 q^{93} - 43 q^{94} - 2 q^{96} + 30 q^{97} - 29 q^{98} + 6 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 8 * q^3 + 12 * q^4 + 2 * q^6 + 2 * q^7 - 3 * q^8 + 8 * q^9 + 6 * q^11 - 12 * q^12 + 6 * q^13 + 9 * q^14 + 32 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^21 + 3 * q^22 - 14 * q^23 + 3 * q^24 + 18 * q^26 - 8 * q^27 + 14 * q^28 + 8 * q^29 + 8 * q^31 + 2 * q^32 - 6 * q^33 - 13 * q^34 + 12 * q^36 + 4 * q^37 - 26 * q^38 - 6 * q^39 + 2 * q^41 - 9 * q^42 + 2 * q^43 - 15 * q^44 + 24 * q^46 - 12 * q^47 - 32 * q^48 + 38 * q^49 + 12 * q^51 + 49 * q^52 - 4 * q^53 + 2 * q^54 + 58 * q^56 - 2 * q^58 + 18 * q^59 + 12 * q^61 + 4 * q^62 + 2 * q^63 + 21 * q^64 - 3 * q^66 + 26 * q^67 - 81 * q^68 + 14 * q^69 + 24 * q^71 - 3 * q^72 - 14 * q^73 - 22 * q^74 + 26 * q^77 - 18 * q^78 + 10 * q^79 + 8 * q^81 + 48 * q^82 - 40 * q^83 - 14 * q^84 + 8 * q^86 - 8 * q^87 - 10 * q^88 + 34 * q^89 + 26 * q^91 + 18 * q^92 - 8 * q^93 - 43 * q^94 - 2 * q^96 + 30 * q^97 - 29 * q^98 + 6 * q^99

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 $

$2$	0.485464	0.343275	0.171638	−	0.985160i	$-0.445094\pi$
$2$	0.485464	0.343275	0.171638	+	0.985160i	$0.445094\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.76432	−0.882162
$5$	0	0
$5$	0	0
$6$	−0.485464	−0.198190
$7$	−1.94912	−0.736697	−0.368349	−	0.929688i	$-0.620077\pi$
$7$	−1.94912	−0.736697	−0.368349	+	0.929688i	$0.620077\pi$
$8$	−1.82745	−0.646099
$9$	1.00000	0.333333
$10$	0	0
$11$	5.30306	1.59893	0.799467	−	0.600710i	$-0.205115\pi$
$11$	5.30306	1.59893	0.799467	+	0.600710i	$0.205115\pi$
$12$	1.76432	0.509317
$13$	−6.00152	−1.66452	−0.832261	−	0.554384i	$-0.812954\pi$
$13$	−6.00152	−1.66452	−0.832261	+	0.554384i	$0.812954\pi$
$14$	−0.946227	−0.252890
$15$	0	0
$16$	2.64149	0.660372
$17$	−1.89418	−0.459407	−0.229703	−	0.973261i	$-0.573776\pi$
$17$	−1.89418	−0.459407	−0.229703	+	0.973261i	$0.573776\pi$
$18$	0.485464	0.114425
$19$	−4.84040	−1.11046	−0.555232	−	0.831696i	$-0.687370\pi$
$19$	−4.84040	−1.11046	−0.555232	+	0.831696i	$0.687370\pi$
$20$	0	0
$21$	1.94912	0.425332
$22$	2.57445	0.548874
$23$	3.19725	0.666672	0.333336	−	0.942808i	$-0.391826\pi$
$23$	3.19725	0.666672	0.333336	+	0.942808i	$0.391826\pi$
$24$	1.82745	0.373026
$25$	0	0
$26$	−2.91352	−0.571389
$27$	−1.00000	−0.192450
$28$	3.43888	0.649887
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	−4.96870	−0.892406	−0.446203	−	0.894932i	$-0.647224\pi$
$31$	−4.96870	−0.892406	−0.446203	+	0.894932i	$0.647224\pi$
$32$	4.93724	0.872789
$33$	−5.30306	−0.923145
$34$	−0.919558	−0.157703
$35$	0	0
$36$	−1.76432	−0.294054
$37$	−10.9699	−1.80344	−0.901721	−	0.432319i	$-0.857695\pi$
$37$	−10.9699	−1.80344	−0.901721	+	0.432319i	$0.857695\pi$
$38$	−2.34984	−0.381194
$39$	6.00152	0.961013
$40$	0	0
$41$	−0.749700	−0.117083	−0.0585417	−	0.998285i	$-0.518645\pi$
$41$	−0.749700	−0.117083	−0.0585417	+	0.998285i	$0.518645\pi$
$42$	0.946227	0.146006
$43$	6.21936	0.948444	0.474222	−	0.880405i	$-0.342729\pi$
$43$	6.21936	0.948444	0.474222	+	0.880405i	$0.342729\pi$
$44$	−9.35633	−1.41052
$45$	0	0
$46$	1.55215	0.228852
$47$	9.67532	1.41129	0.705645	−	0.708565i	$-0.250657\pi$
$47$	9.67532	1.41129	0.705645	+	0.708565i	$0.250657\pi$
$48$	−2.64149	−0.381266
$49$	−3.20094	−0.457277
$50$	0	0
$51$	1.89418	0.265239
$52$	10.5886	1.46838
$53$	4.44791	0.610967	0.305484	−	0.952197i	$-0.401182\pi$
$53$	4.44791	0.610967	0.305484	+	0.952197i	$0.401182\pi$
$54$	−0.485464	−0.0660633
$55$	0	0
$56$	3.56191	0.475980
$57$	4.84040	0.641126
$58$	0.485464	0.0637446
$59$	14.8542	1.93385	0.966926	−	0.255056i	$-0.0820939\pi$
$59$	14.8542	1.93385	0.966926	+	0.255056i	$0.0820939\pi$
$60$	0	0
$61$	15.4683	1.98051	0.990255	−	0.139264i	$-0.0444738\pi$
$61$	15.4683	1.98051	0.990255	+	0.139264i	$0.0444738\pi$
$62$	−2.41213	−0.306341
$63$	−1.94912	−0.245566
$64$	−2.88613	−0.360766
$65$	0	0
$66$	−2.57445	−0.316893
$67$	14.6495	1.78972	0.894861	−	0.446344i	$-0.147274\pi$
$67$	14.6495	1.78972	0.894861	+	0.446344i	$0.147274\pi$
$68$	3.34195	0.405271
$69$	−3.19725	−0.384903
$70$	0	0
$71$	5.37043	0.637353	0.318676	−	0.947864i	$-0.396762\pi$
$71$	5.37043	0.637353	0.318676	+	0.947864i	$0.396762\pi$
$72$	−1.82745	−0.215366
$73$	−12.5367	−1.46731	−0.733654	−	0.679523i	$-0.762187\pi$
$73$	−12.5367	−1.46731	−0.733654	+	0.679523i	$0.762187\pi$
$74$	−5.32550	−0.619077
$75$	0	0
$76$	8.54003	0.979609
$77$	−10.3363	−1.17793
$78$	2.91352	0.329892
$79$	−7.87855	−0.886406	−0.443203	−	0.896421i	$-0.646158\pi$
$79$	−7.87855	−0.886406	−0.443203	+	0.896421i	$0.646158\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−0.363953	−0.0401918
$83$	−11.1873	−1.22797	−0.613986	−	0.789317i	$-0.710435\pi$
$83$	−11.1873	−1.22797	−0.613986	+	0.789317i	$0.710435\pi$
$84$	−3.43888	−0.375212
$85$	0	0
$86$	3.01928	0.325577
$87$	−1.00000	−0.107211
$88$	−9.69106	−1.03307
$89$	15.2850	1.62021	0.810105	−	0.586284i	$-0.199410\pi$
$89$	15.2850	1.62021	0.810105	+	0.586284i	$0.199410\pi$
$90$	0	0
$91$	11.6977	1.22625
$92$	−5.64098	−0.588113
$93$	4.96870	0.515231
$94$	4.69702	0.484461
$95$	0	0
$96$	−4.93724	−0.503905
$97$	7.14188	0.725149	0.362574	−	0.931955i	$-0.381898\pi$
$97$	7.14188	0.725149	0.362574	+	0.931955i	$0.381898\pi$
$98$	−1.55394	−0.156972
$99$	5.30306	0.532978
$100$	0	0
$101$	13.9908	1.39214	0.696069	−	0.717975i	$-0.254931\pi$
$101$	13.9908	1.39214	0.696069	+	0.717975i	$0.254931\pi$
$102$	0.919558	0.0910498
$103$	1.02871	0.101362	0.0506809	−	0.998715i	$-0.483861\pi$
$103$	1.02871	0.101362	0.0506809	+	0.998715i	$0.483861\pi$
$104$	10.9675	1.07545
$105$	0	0
$106$	2.15930	0.209730
$107$	−4.81163	−0.465158	−0.232579	−	0.972578i	$-0.574716\pi$
$107$	−4.81163	−0.465158	−0.232579	+	0.972578i	$0.574716\pi$
$108$	1.76432	0.169772
$109$	−0.502843	−0.0481636	−0.0240818	−	0.999710i	$-0.507666\pi$
$109$	−0.502843	−0.0481636	−0.0240818	+	0.999710i	$0.507666\pi$
$110$	0	0
$111$	10.9699	1.04122
$112$	−5.14857	−0.486495
$113$	19.2404	1.80999	0.904993	−	0.425427i	$-0.139876\pi$
$113$	19.2404	1.80999	0.904993	+	0.425427i	$0.139876\pi$
$114$	2.34984	0.220083
$115$	0	0
$116$	−1.76432	−0.163813
$117$	−6.00152	−0.554841
$118$	7.21119	0.663843
$119$	3.69199	0.338444
$120$	0	0
$121$	17.1225	1.55659
$122$	7.50930	0.679860
$123$	0.749700	0.0675982
$124$	8.76641	0.787246
$125$	0	0
$126$	−0.946227	−0.0842966
$127$	3.56884	0.316684	0.158342	−	0.987384i	$-0.449385\pi$
$127$	3.56884	0.316684	0.158342	+	0.987384i	$0.449385\pi$
$128$	−11.2756	−0.996631
$129$	−6.21936	−0.547585
$130$	0	0
$131$	−18.2131	−1.59128	−0.795642	−	0.605767i	$-0.792866\pi$
$131$	−18.2131	−1.59128	−0.795642	+	0.605767i	$0.792866\pi$
$132$	9.35633	0.814364
$133$	9.43450	0.818075
$134$	7.11181	0.614367
$135$	0	0
$136$	3.46152	0.296823
$137$	9.74717	0.832757	0.416379	−	0.909191i	$-0.363299\pi$
$137$	9.74717	0.832757	0.416379	+	0.909191i	$0.363299\pi$
$138$	−1.55215	−0.132128
$139$	−1.17574	−0.0997250	−0.0498625	−	0.998756i	$-0.515878\pi$
$139$	−1.17574	−0.0997250	−0.0498625	+	0.998756i	$0.515878\pi$
$140$	0	0
$141$	−9.67532	−0.814809
$142$	2.60715	0.218787
$143$	−31.8265	−2.66146
$144$	2.64149	0.220124
$145$	0	0
$146$	−6.08611	−0.503690
$147$	3.20094	0.264009
$148$	19.3545	1.59093
$149$	11.8645	0.971979	0.485989	−	0.873965i	$-0.338459\pi$
$149$	11.8645	0.971979	0.485989	+	0.873965i	$0.338459\pi$
$150$	0	0
$151$	8.03728	0.654065	0.327032	−	0.945013i	$-0.393951\pi$
$151$	8.03728	0.654065	0.327032	+	0.945013i	$0.393951\pi$
$152$	8.84556	0.717469
$153$	−1.89418	−0.153136
$154$	−5.01790	−0.404354
$155$	0	0
$156$	−10.5886	−0.847769
$157$	−2.56066	−0.204363	−0.102182	−	0.994766i	$-0.532582\pi$
$157$	−2.56066	−0.204363	−0.102182	+	0.994766i	$0.532582\pi$
$158$	−3.82475	−0.304281
$159$	−4.44791	−0.352742
$160$	0	0
$161$	−6.23181	−0.491136
$162$	0.485464	0.0381417
$163$	−1.72147	−0.134836	−0.0674180	−	0.997725i	$-0.521476\pi$
$163$	−1.72147	−0.134836	−0.0674180	+	0.997725i	$0.521476\pi$
$164$	1.32271	0.103287
$165$	0	0
$166$	−5.43106	−0.421532
$167$	0.664214	0.0513984	0.0256992	−	0.999670i	$-0.491819\pi$
$167$	0.664214	0.0513984	0.0256992	+	0.999670i	$0.491819\pi$
$168$	−3.56191	−0.274807
$169$	23.0183	1.77064
$170$	0	0
$171$	−4.84040	−0.370154
$172$	−10.9730	−0.836682
$173$	−3.59669	−0.273451	−0.136726	−	0.990609i	$-0.543658\pi$
$173$	−3.59669	−0.273451	−0.136726	+	0.990609i	$0.543658\pi$
$174$	−0.485464	−0.0368030
$175$	0	0
$176$	14.0080	1.05589
$177$	−14.8542	−1.11651
$178$	7.42034	0.556178
$179$	15.6539	1.17003	0.585013	−	0.811024i	$-0.301090\pi$
$179$	15.6539	1.17003	0.585013	+	0.811024i	$0.301090\pi$
$180$	0	0
$181$	−5.74977	−0.427377	−0.213689	−	0.976902i	$-0.568548\pi$
$181$	−5.74977	−0.427377	−0.213689	+	0.976902i	$0.568548\pi$
$182$	5.67880	0.420941
$183$	−15.4683	−1.14345
$184$	−5.84279	−0.430736
$185$	0	0
$186$	2.41213	0.176866
$187$	−10.0450	−0.734561
$188$	−17.0704	−1.24499
$189$	1.94912	0.141777
$190$	0	0
$191$	−15.5951	−1.12842	−0.564209	−	0.825632i	$-0.690819\pi$
$191$	−15.5951	−1.12842	−0.564209	+	0.825632i	$0.690819\pi$
$192$	2.88613	0.208288
$193$	14.7090	1.05878	0.529388	−	0.848380i	$-0.322422\pi$
$193$	14.7090	1.05878	0.529388	+	0.848380i	$0.322422\pi$
$194$	3.46713	0.248925
$195$	0	0
$196$	5.64750	0.403393
$197$	3.68654	0.262655	0.131328	−	0.991339i	$-0.458076\pi$
$197$	3.68654	0.262655	0.131328	+	0.991339i	$0.458076\pi$
$198$	2.57445	0.182958
$199$	−13.6803	−0.969774	−0.484887	−	0.874577i	$-0.661139\pi$
$199$	−13.6803	−0.969774	−0.484887	+	0.874577i	$0.661139\pi$
$200$	0	0
$201$	−14.6495	−1.03330
$202$	6.79204	0.477886
$203$	−1.94912	−0.136801
$204$	−3.34195	−0.233984
$205$	0	0
$206$	0.499402	0.0347950
$207$	3.19725	0.222224
$208$	−15.8530	−1.09920
$209$	−25.6689	−1.77556
$210$	0	0
$211$	−15.1847	−1.04536	−0.522680	−	0.852529i	$-0.675068\pi$
$211$	−15.1847	−1.04536	−0.522680	+	0.852529i	$0.675068\pi$
$212$	−7.84755	−0.538972
$213$	−5.37043	−0.367976
$214$	−2.33587	−0.159677
$215$	0	0
$216$	1.82745	0.124342
$217$	9.68459	0.657433
$218$	−0.244112	−0.0165334
$219$	12.5367	0.847151
$220$	0	0
$221$	11.3680	0.764693
$222$	5.32550	0.357424
$223$	23.8871	1.59960	0.799800	−	0.600266i	$-0.204939\pi$
$223$	23.8871	1.59960	0.799800	+	0.600266i	$0.204939\pi$
$224$	−9.62326	−0.642981
$225$	0	0
$226$	9.34053	0.621323
$227$	−23.8609	−1.58371	−0.791853	−	0.610712i	$-0.790883\pi$
$227$	−23.8609	−1.58371	−0.791853	+	0.610712i	$0.790883\pi$
$228$	−8.54003	−0.565577
$229$	−12.9027	−0.852633	−0.426317	−	0.904574i	$-0.640189\pi$
$229$	−12.9027	−0.852633	−0.426317	+	0.904574i	$0.640189\pi$
$230$	0	0
$231$	10.3363	0.680078
$232$	−1.82745	−0.119978
$233$	10.5268	0.689633	0.344816	−	0.938670i	$-0.387941\pi$
$233$	10.5268	0.689633	0.344816	+	0.938670i	$0.387941\pi$
$234$	−2.91352	−0.190463
$235$	0	0
$236$	−26.2076	−1.70597
$237$	7.87855	0.511767
$238$	1.79233	0.116179
$239$	−7.00563	−0.453156	−0.226578	−	0.973993i	$-0.572754\pi$
$239$	−7.00563	−0.453156	−0.226578	+	0.973993i	$0.572754\pi$
$240$	0	0
$241$	−14.3596	−0.924981	−0.462490	−	0.886624i	$-0.653044\pi$
$241$	−14.3596	−0.924981	−0.462490	+	0.886624i	$0.653044\pi$
$242$	8.31236	0.534339
$243$	−1.00000	−0.0641500
$244$	−27.2911	−1.74713
$245$	0	0
$246$	0.363953	0.0232048
$247$	29.0497	1.84839
$248$	9.08003	0.576583
$249$	11.1873	0.708969
$250$	0	0
$251$	21.7642	1.37375	0.686873	−	0.726778i	$-0.258983\pi$
$251$	21.7642	1.37375	0.686873	+	0.726778i	$0.258983\pi$
$252$	3.43888	0.216629
$253$	16.9552	1.06596
$254$	1.73255	0.108710
$255$	0	0
$256$	0.298356	0.0186473
$257$	−10.1732	−0.634589	−0.317295	−	0.948327i	$-0.602774\pi$
$257$	−10.1732	−0.634589	−0.317295	+	0.948327i	$0.602774\pi$
$258$	−3.01928	−0.187972
$259$	21.3816	1.32859
$260$	0	0
$261$	1.00000	0.0618984
$262$	−8.84180	−0.546248
$263$	−16.8078	−1.03642	−0.518208	−	0.855255i	$-0.673401\pi$
$263$	−16.8078	−1.03642	−0.518208	+	0.855255i	$0.673401\pi$
$264$	9.69106	0.596443
$265$	0	0
$266$	4.58011	0.280825
$267$	−15.2850	−0.935429
$268$	−25.8465	−1.57883
$269$	24.1896	1.47487	0.737434	−	0.675419i	$-0.236037\pi$
$269$	24.1896	1.47487	0.737434	+	0.675419i	$0.236037\pi$
$270$	0	0
$271$	−4.46984	−0.271523	−0.135762	−	0.990742i	$-0.543348\pi$
$271$	−4.46984	−0.271523	−0.135762	+	0.990742i	$0.543348\pi$
$272$	−5.00346	−0.303380
$273$	−11.6977	−0.707975
$274$	4.73190	0.285865
$275$	0	0
$276$	5.64098	0.339547
$277$	1.88450	0.113229	0.0566143	−	0.998396i	$-0.481969\pi$
$277$	1.88450	0.113229	0.0566143	+	0.998396i	$0.481969\pi$
$278$	−0.570780	−0.0342331
$279$	−4.96870	−0.297469
$280$	0	0
$281$	15.0159	0.895774	0.447887	−	0.894090i	$-0.352177\pi$
$281$	15.0159	0.895774	0.447887	+	0.894090i	$0.352177\pi$
$282$	−4.69702	−0.279704
$283$	20.2576	1.20419	0.602096	−	0.798424i	$-0.294333\pi$
$283$	20.2576	1.20419	0.602096	+	0.798424i	$0.294333\pi$
$284$	−9.47518	−0.562248
$285$	0	0
$286$	−15.4506	−0.913614
$287$	1.46125	0.0862551
$288$	4.93724	0.290930
$289$	−13.4121	−0.788945
$290$	0	0
$291$	−7.14188	−0.418665
$292$	22.1188	1.29440
$293$	−5.25806	−0.307179	−0.153589	−	0.988135i	$-0.549083\pi$
$293$	−5.25806	−0.307179	−0.153589	+	0.988135i	$0.549083\pi$
$294$	1.55394	0.0906277
$295$	0	0
$296$	20.0469	1.16520
$297$	−5.30306	−0.307715
$298$	5.75980	0.333656
$299$	−19.1883	−1.10969
$300$	0	0
$301$	−12.1223	−0.698716
$302$	3.90181	0.224524
$303$	−13.9908	−0.803751
$304$	−12.7859	−0.733319
$305$	0	0
$306$	−0.919558	−0.0525676
$307$	−18.0575	−1.03060	−0.515298	−	0.857011i	$-0.672319\pi$
$307$	−18.0575	−1.03060	−0.515298	+	0.857011i	$0.672319\pi$
$308$	18.2366	1.03913
$309$	−1.02871	−0.0585213
$310$	0	0
$311$	−3.28065	−0.186029	−0.0930143	−	0.995665i	$-0.529650\pi$
$311$	−3.28065	−0.186029	−0.0930143	+	0.995665i	$0.529650\pi$
$312$	−10.9675	−0.620910
$313$	−8.87479	−0.501633	−0.250816	−	0.968035i	$-0.580699\pi$
$313$	−8.87479	−0.501633	−0.250816	+	0.968035i	$0.580699\pi$
$314$	−1.24311	−0.0701528
$315$	0	0
$316$	13.9003	0.781954
$317$	18.1311	1.01835	0.509173	−	0.860664i	$-0.329951\pi$
$317$	18.1311	1.01835	0.509173	+	0.860664i	$0.329951\pi$
$318$	−2.15930	−0.121088
$319$	5.30306	0.296915
$320$	0	0
$321$	4.81163	0.268559
$322$	−3.02532	−0.168595
$323$	9.16860	0.510154
$324$	−1.76432	−0.0980180
$325$	0	0
$326$	−0.835712	−0.0462858
$327$	0.502843	0.0278073
$328$	1.37004	0.0756476
$329$	−18.8583	−1.03969
$330$	0	0
$331$	9.86489	0.542223	0.271112	−	0.962548i	$-0.412609\pi$
$331$	9.86489	0.542223	0.271112	+	0.962548i	$0.412609\pi$
$332$	19.7381	1.08327
$333$	−10.9699	−0.601147
$334$	0.322452	0.0176438
$335$	0	0
$336$	5.14857	0.280878
$337$	10.5463	0.574493	0.287247	−	0.957857i	$-0.407260\pi$
$337$	10.5463	0.574493	0.287247	+	0.957857i	$0.407260\pi$
$338$	11.1745	0.607815
$339$	−19.2404	−1.04500
$340$	0	0
$341$	−26.3494	−1.42690
$342$	−2.34984	−0.127065
$343$	19.8828	1.07357
$344$	−11.3655	−0.612789
$345$	0	0
$346$	−1.74606	−0.0938690
$347$	−31.1044	−1.66977	−0.834885	−	0.550425i	$-0.814466\pi$
$347$	−31.1044	−1.66977	−0.834885	+	0.550425i	$0.814466\pi$
$348$	1.76432	0.0945777
$349$	−5.00604	−0.267967	−0.133984	−	0.990984i	$-0.542777\pi$
$349$	−5.00604	−0.267967	−0.133984	+	0.990984i	$0.542777\pi$
$350$	0	0
$351$	6.00152	0.320338
$352$	26.1825	1.39553
$353$	−4.01219	−0.213548	−0.106774	−	0.994283i	$-0.534052\pi$
$353$	−4.01219	−0.213548	−0.106774	+	0.994283i	$0.534052\pi$
$354$	−7.21119	−0.383270
$355$	0	0
$356$	−26.9678	−1.42929
$357$	−3.69199	−0.195401
$358$	7.59939	0.401640
$359$	21.1999	1.11889	0.559445	−	0.828868i	$-0.311014\pi$
$359$	21.1999	1.11889	0.559445	+	0.828868i	$0.311014\pi$
$360$	0	0
$361$	4.42944	0.233128
$362$	−2.79131	−0.146708
$363$	−17.1225	−0.898698
$364$	−20.6385	−1.08175
$365$	0	0
$366$	−7.50930	−0.392517
$367$	−13.2223	−0.690196	−0.345098	−	0.938567i	$-0.612154\pi$
$367$	−13.2223	−0.690196	−0.345098	+	0.938567i	$0.612154\pi$
$368$	8.44550	0.440252
$369$	−0.749700	−0.0390278
$370$	0	0
$371$	−8.66950	−0.450098
$372$	−8.76641	−0.454517
$373$	−11.5629	−0.598702	−0.299351	−	0.954143i	$-0.596770\pi$
$373$	−11.5629	−0.598702	−0.299351	+	0.954143i	$0.596770\pi$
$374$	−4.87648	−0.252157
$375$	0	0
$376$	−17.6811	−0.911834
$377$	−6.00152	−0.309094
$378$	0.946227	0.0486687
$379$	24.3120	1.24882	0.624412	−	0.781095i	$-0.285339\pi$
$379$	24.3120	1.24882	0.624412	+	0.781095i	$0.285339\pi$
$380$	0	0
$381$	−3.56884	−0.182837
$382$	−7.57084	−0.387358
$383$	−1.27322	−0.0650586	−0.0325293	−	0.999471i	$-0.510356\pi$
$383$	−1.27322	−0.0650586	−0.0325293	+	0.999471i	$0.510356\pi$
$384$	11.2756	0.575405
$385$	0	0
$386$	7.14069	0.363451
$387$	6.21936	0.316148
$388$	−12.6006	−0.639699
$389$	28.4298	1.44145	0.720725	−	0.693221i	$-0.243809\pi$
$389$	28.4298	1.44145	0.720725	+	0.693221i	$0.243809\pi$
$390$	0	0
$391$	−6.05617	−0.306274
$392$	5.84954	0.295446
$393$	18.2131	0.918728
$394$	1.78969	0.0901631
$395$	0	0
$396$	−9.35633	−0.470173
$397$	8.89762	0.446559	0.223279	−	0.974754i	$-0.428324\pi$
$397$	8.89762	0.446559	0.223279	+	0.974754i	$0.428324\pi$
$398$	−6.64132	−0.332899
$399$	−9.43450	−0.472316
$400$	0	0
$401$	6.49653	0.324421	0.162211	−	0.986756i	$-0.448138\pi$
$401$	6.49653	0.324421	0.162211	+	0.986756i	$0.448138\pi$
$402$	−7.11181	−0.354705
$403$	29.8198	1.48543
$404$	−24.6843	−1.22809
$405$	0	0
$406$	−0.946227	−0.0469605
$407$	−58.1741	−2.88358
$408$	−3.46152	−0.171371
$409$	39.8121	1.96858	0.984291	−	0.176556i	$-0.0564956\pi$
$409$	39.8121	1.96858	0.984291	+	0.176556i	$0.0564956\pi$
$410$	0	0
$411$	−9.74717	−0.480793
$412$	−1.81498	−0.0894176
$413$	−28.9526	−1.42466
$414$	1.55215	0.0762840
$415$	0	0
$416$	−29.6309	−1.45278
$417$	1.17574	0.0575762
$418$	−12.4613	−0.609505
$419$	10.7000	0.522728	0.261364	−	0.965240i	$-0.415828\pi$
$419$	10.7000	0.522728	0.261364	+	0.965240i	$0.415828\pi$
$420$	0	0
$421$	−18.3169	−0.892711	−0.446355	−	0.894856i	$-0.647278\pi$
$421$	−18.3169	−0.892711	−0.446355	+	0.894856i	$0.647278\pi$
$422$	−7.37165	−0.358846
$423$	9.67532	0.470430
$424$	−8.12831	−0.394746
$425$	0	0
$426$	−2.60715	−0.126317
$427$	−30.1495	−1.45904
$428$	8.48927	0.410344
$429$	31.8265	1.53660
$430$	0	0
$431$	1.14956	0.0553723	0.0276861	−	0.999617i	$-0.491186\pi$
$431$	1.14956	0.0553723	0.0276861	+	0.999617i	$0.491186\pi$
$432$	−2.64149	−0.127089
$433$	26.2208	1.26009	0.630045	−	0.776559i	$-0.283036\pi$
$433$	26.2208	1.26009	0.630045	+	0.776559i	$0.283036\pi$
$434$	4.70152	0.225680
$435$	0	0
$436$	0.887178	0.0424881
$437$	−15.4759	−0.740315
$438$	6.08611	0.290806
$439$	−5.92196	−0.282640	−0.141320	−	0.989964i	$-0.545135\pi$
$439$	−5.92196	−0.282640	−0.141320	+	0.989964i	$0.545135\pi$
$440$	0	0
$441$	−3.20094	−0.152426
$442$	5.51875	0.262500
$443$	12.4000	0.589140	0.294570	−	0.955630i	$-0.404824\pi$
$443$	12.4000	0.589140	0.294570	+	0.955630i	$0.404824\pi$
$444$	−19.3545	−0.918523
$445$	0	0
$446$	11.5963	0.549103
$447$	−11.8645	−0.561172
$448$	5.62540	0.265775
$449$	−35.5492	−1.67767	−0.838835	−	0.544386i	$-0.816763\pi$
$449$	−35.5492	−1.67767	−0.838835	+	0.544386i	$0.816763\pi$
$450$	0	0
$451$	−3.97571	−0.187209
$452$	−33.9463	−1.59670
$453$	−8.03728	−0.377624
$454$	−11.5836	−0.543647
$455$	0	0
$456$	−8.84556	−0.414231
$457$	11.7868	0.551364	0.275682	−	0.961249i	$-0.411096\pi$
$457$	11.7868	0.551364	0.275682	+	0.961249i	$0.411096\pi$
$458$	−6.26379	−0.292688
$459$	1.89418	0.0884129
$460$	0	0
$461$	−8.53366	−0.397452	−0.198726	−	0.980055i	$-0.563680\pi$
$461$	−8.53366	−0.397452	−0.198726	+	0.980055i	$0.563680\pi$
$462$	5.01790	0.233454
$463$	3.75971	0.174729	0.0873643	−	0.996176i	$-0.472156\pi$
$463$	3.75971	0.174729	0.0873643	+	0.996176i	$0.472156\pi$
$464$	2.64149	0.122628
$465$	0	0
$466$	5.11038	0.236734
$467$	−1.32889	−0.0614938	−0.0307469	−	0.999527i	$-0.509789\pi$
$467$	−1.32889	−0.0614938	−0.0307469	+	0.999527i	$0.509789\pi$
$468$	10.5886	0.489460
$469$	−28.5536	−1.31848
$470$	0	0
$471$	2.56066	0.117989
$472$	−27.1452	−1.24946
$473$	32.9817	1.51650
$474$	3.82475	0.175677
$475$	0	0
$476$	−6.51386	−0.298562
$477$	4.44791	0.203656
$478$	−3.40098	−0.155557
$479$	−7.85604	−0.358952	−0.179476	−	0.983762i	$-0.557440\pi$
$479$	−7.85604	−0.358952	−0.179476	+	0.983762i	$0.557440\pi$
$480$	0	0
$481$	65.8361	3.00187
$482$	−6.97105	−0.317523
$483$	6.23181	0.283557
$484$	−30.2096	−1.37316
$485$	0	0
$486$	−0.485464	−0.0220211
$487$	−15.3505	−0.695597	−0.347798	−	0.937569i	$-0.613071\pi$
$487$	−15.3505	−0.695597	−0.347798	+	0.937569i	$0.613071\pi$
$488$	−28.2674	−1.27961
$489$	1.72147	0.0778476
$490$	0	0
$491$	−37.2963	−1.68316	−0.841579	−	0.540133i	$-0.818374\pi$
$491$	−37.2963	−1.68316	−0.841579	+	0.540133i	$0.818374\pi$
$492$	−1.32271	−0.0596326
$493$	−1.89418	−0.0853097
$494$	14.1026	0.634507
$495$	0	0
$496$	−13.1248	−0.589320
$497$	−10.4676	−0.469536
$498$	5.43106	0.243372
$499$	23.2644	1.04146	0.520730	−	0.853722i	$-0.325660\pi$
$499$	23.2644	1.04146	0.520730	+	0.853722i	$0.325660\pi$
$500$	0	0
$501$	−0.664214	−0.0296749
$502$	10.5658	0.471573
$503$	11.0584	0.493072	0.246536	−	0.969134i	$-0.420708\pi$
$503$	11.0584	0.493072	0.246536	+	0.969134i	$0.420708\pi$
$504$	3.56191	0.158660
$505$	0	0
$506$	8.23115	0.365919
$507$	−23.0183	−1.02228
$508$	−6.29660	−0.279366
$509$	−29.0128	−1.28597	−0.642984	−	0.765880i	$-0.722304\pi$
$509$	−29.0128	−1.28597	−0.642984	+	0.765880i	$0.722304\pi$
$510$	0	0
$511$	24.4355	1.08096
$512$	22.6960	1.00303
$513$	4.84040	0.213709
$514$	−4.93874	−0.217839
$515$	0	0
$516$	10.9730	0.483058
$517$	51.3088	2.25656
$518$	10.3800	0.456072
$519$	3.59669	0.157877
$520$	0	0
$521$	−17.2400	−0.755298	−0.377649	−	0.925949i	$-0.623267\pi$
$521$	−17.2400	−0.755298	−0.377649	+	0.925949i	$0.623267\pi$
$522$	0.485464	0.0212482
$523$	36.1676	1.58150	0.790750	−	0.612139i	$-0.209691\pi$
$523$	36.1676	1.58150	0.790750	+	0.612139i	$0.209691\pi$
$524$	32.1338	1.40377
$525$	0	0
$526$	−8.15961	−0.355776
$527$	9.41163	0.409977
$528$	−14.0080	−0.609619
$529$	−12.7776	−0.555548
$530$	0	0
$531$	14.8542	0.644618
$532$	−16.6455	−0.721675
$533$	4.49934	0.194888
$534$	−7.42034	−0.321110
$535$	0	0
$536$	−26.7712	−1.15634
$537$	−15.6539	−0.675514
$538$	11.7432	0.506286
$539$	−16.9748	−0.731156
$540$	0	0
$541$	−12.8146	−0.550943	−0.275471	−	0.961309i	$-0.588834\pi$
$541$	−12.8146	−0.550943	−0.275471	+	0.961309i	$0.588834\pi$
$542$	−2.16995	−0.0932072
$543$	5.74977	0.246746
$544$	−9.35203	−0.400965
$545$	0	0
$546$	−5.67880	−0.243030
$547$	−3.86645	−0.165318	−0.0826588	−	0.996578i	$-0.526341\pi$
$547$	−3.86645	−0.165318	−0.0826588	+	0.996578i	$0.526341\pi$
$548$	−17.1972	−0.734627
$549$	15.4683	0.660170
$550$	0	0
$551$	−4.84040	−0.206208
$552$	5.84279	0.248686
$553$	15.3562	0.653013
$554$	0.914857	0.0388685
$555$	0	0
$556$	2.07439	0.0879736
$557$	−27.1140	−1.14886	−0.574428	−	0.818555i	$-0.694775\pi$
$557$	−27.1140	−1.14886	−0.574428	+	0.818555i	$0.694775\pi$
$558$	−2.41213	−0.102114
$559$	−37.3257	−1.57871
$560$	0	0
$561$	10.0450	0.424099
$562$	7.28969	0.307497
$563$	11.9543	0.503816	0.251908	−	0.967751i	$-0.418942\pi$
$563$	11.9543	0.503816	0.251908	+	0.967751i	$0.418942\pi$
$564$	17.0704	0.718793
$565$	0	0
$566$	9.83436	0.413369
$567$	−1.94912	−0.0818553
$568$	−9.81416	−0.411793
$569$	44.4464	1.86329	0.931646	−	0.363368i	$-0.118373\pi$
$569$	44.4464	1.86329	0.931646	+	0.363368i	$0.118373\pi$
$570$	0	0
$571$	−14.0314	−0.587196	−0.293598	−	0.955929i	$-0.594853\pi$
$571$	−14.0314	−0.587196	−0.293598	+	0.955929i	$0.594853\pi$
$572$	56.1522	2.34784
$573$	15.5951	0.651493
$574$	0.709387	0.0296092
$575$	0	0
$576$	−2.88613	−0.120255
$577$	17.9198	0.746010	0.373005	−	0.927829i	$-0.378327\pi$
$577$	17.9198	0.746010	0.373005	+	0.927829i	$0.378327\pi$
$578$	−6.51108	−0.270825
$579$	−14.7090	−0.611285
$580$	0	0
$581$	21.8055	0.904643
$582$	−3.46713	−0.143717
$583$	23.5875	0.976896
$584$	22.9101	0.948027
$585$	0	0
$586$	−2.55260	−0.105447
$587$	13.3009	0.548988	0.274494	−	0.961589i	$-0.411490\pi$
$587$	13.3009	0.548988	0.274494	+	0.961589i	$0.411490\pi$
$588$	−5.64750	−0.232899
$589$	24.0505	0.990983
$590$	0	0
$591$	−3.68654	−0.151644
$592$	−28.9769	−1.19094
$593$	33.4113	1.37204	0.686020	−	0.727583i	$-0.259356\pi$
$593$	33.4113	1.37204	0.686020	+	0.727583i	$0.259356\pi$
$594$	−2.57445	−0.105631
$595$	0	0
$596$	−20.9328	−0.857443
$597$	13.6803	0.559899
$598$	−9.31526	−0.380929
$599$	−10.4231	−0.425875	−0.212938	−	0.977066i	$-0.568303\pi$
$599$	−10.4231	−0.425875	−0.212938	+	0.977066i	$0.568303\pi$
$600$	0	0
$601$	13.6537	0.556948	0.278474	−	0.960444i	$-0.410171\pi$
$601$	13.6537	0.556948	0.278474	+	0.960444i	$0.410171\pi$
$602$	−5.88493	−0.239852
$603$	14.6495	0.596574
$604$	−14.1804	−0.576991
$605$	0	0
$606$	−6.79204	−0.275908
$607$	−9.97305	−0.404794	−0.202397	−	0.979304i	$-0.564873\pi$
$607$	−9.97305	−0.404794	−0.202397	+	0.979304i	$0.564873\pi$
$608$	−23.8982	−0.969200
$609$	1.94912	0.0789822
$610$	0	0
$611$	−58.0666	−2.34912
$612$	3.34195	0.135090
$613$	−27.5521	−1.11282	−0.556410	−	0.830908i	$-0.687822\pi$
$613$	−27.5521	−1.11282	−0.556410	+	0.830908i	$0.687822\pi$
$614$	−8.76626	−0.353778
$615$	0	0
$616$	18.8890	0.761060
$617$	−2.82321	−0.113658	−0.0568290	−	0.998384i	$-0.518099\pi$
$617$	−2.82321	−0.113658	−0.0568290	+	0.998384i	$0.518099\pi$
$618$	−0.499402	−0.0200889
$619$	−19.7985	−0.795769	−0.397884	−	0.917436i	$-0.630256\pi$
$619$	−19.7985	−0.795769	−0.397884	+	0.917436i	$0.630256\pi$
$620$	0	0
$621$	−3.19725	−0.128301
$622$	−1.59264	−0.0638590
$623$	−29.7923	−1.19361
$624$	15.8530	0.634626
$625$	0	0
$626$	−4.30839	−0.172198
$627$	25.6689	1.02512
$628$	4.51784	0.180282
$629$	20.7790	0.828513
$630$	0	0
$631$	−21.2079	−0.844273	−0.422137	−	0.906532i	$-0.638720\pi$
$631$	−21.2079	−0.844273	−0.422137	+	0.906532i	$0.638720\pi$
$632$	14.3976	0.572706
$633$	15.1847	0.603539
$634$	8.80202	0.349573
$635$	0	0
$636$	7.84755	0.311176
$637$	19.2105	0.761148
$638$	2.57445	0.101923
$639$	5.37043	0.212451
$640$	0	0
$641$	20.3393	0.803352	0.401676	−	0.915782i	$-0.368428\pi$
$641$	20.3393	0.803352	0.401676	+	0.915782i	$0.368428\pi$
$642$	2.33587	0.0921896
$643$	−7.62000	−0.300504	−0.150252	−	0.988648i	$-0.548008\pi$
$643$	−7.62000	−0.300504	−0.150252	+	0.988648i	$0.548008\pi$
$644$	10.9949	0.433261
$645$	0	0
$646$	4.45103	0.175123
$647$	16.2002	0.636894	0.318447	−	0.947941i	$-0.396839\pi$
$647$	16.2002	0.636894	0.318447	+	0.947941i	$0.396839\pi$
$648$	−1.82745	−0.0717888
$649$	78.7728	3.09210
$650$	0	0
$651$	−9.68459	−0.379569
$652$	3.03723	0.118947
$653$	16.1885	0.633504	0.316752	−	0.948508i	$-0.397408\pi$
$653$	16.1885	0.633504	0.316752	+	0.948508i	$0.397408\pi$
$654$	0.244112	0.00954555
$655$	0	0
$656$	−1.98032	−0.0773187
$657$	−12.5367	−0.489103
$658$	−9.15505	−0.356901
$659$	−15.2321	−0.593360	−0.296680	−	0.954977i	$-0.595879\pi$
$659$	−15.2321	−0.593360	−0.296680	+	0.954977i	$0.595879\pi$
$660$	0	0
$661$	−24.1313	−0.938600	−0.469300	−	0.883039i	$-0.655494\pi$
$661$	−24.1313	−0.938600	−0.469300	+	0.883039i	$0.655494\pi$
$662$	4.78905	0.186132
$663$	−11.3680	−0.441496
$664$	20.4443	0.793391
$665$	0	0
$666$	−5.32550	−0.206359
$667$	3.19725	0.123798
$668$	−1.17189	−0.0453417
$669$	−23.8871	−0.923530
$670$	0	0
$671$	82.0293	3.16671
$672$	9.62326	0.371225
$673$	26.0546	1.00433	0.502166	−	0.864771i	$-0.332537\pi$
$673$	26.0546	1.00433	0.502166	+	0.864771i	$0.332537\pi$
$674$	5.11985	0.197209
$675$	0	0
$676$	−40.6117	−1.56199
$677$	−15.2415	−0.585778	−0.292889	−	0.956146i	$-0.594617\pi$
$677$	−15.2415	−0.585778	−0.292889	+	0.956146i	$0.594617\pi$
$678$	−9.34053	−0.358721
$679$	−13.9204	−0.534215
$680$	0	0
$681$	23.8609	0.914353
$682$	−12.7917	−0.489818
$683$	25.0393	0.958104	0.479052	−	0.877787i	$-0.340981\pi$
$683$	25.0393	0.958104	0.479052	+	0.877787i	$0.340981\pi$
$684$	8.54003	0.326536
$685$	0	0
$686$	9.65241	0.368531
$687$	12.9027	0.492268
$688$	16.4284	0.626326
$689$	−26.6942	−1.01697
$690$	0	0
$691$	10.0997	0.384210	0.192105	−	0.981374i	$-0.438469\pi$
$691$	10.0997	0.384210	0.192105	+	0.981374i	$0.438469\pi$
$692$	6.34573	0.241228
$693$	−10.3363	−0.392643
$694$	−15.1001	−0.573190
$695$	0	0
$696$	1.82745	0.0692691
$697$	1.42007	0.0537890
$698$	−2.43026	−0.0919865
$699$	−10.5268	−0.398160
$700$	0	0
$701$	2.30566	0.0870837	0.0435418	−	0.999052i	$-0.486136\pi$
$701$	2.30566	0.0870837	0.0435418	+	0.999052i	$0.486136\pi$
$702$	2.91352	0.109964
$703$	53.0987	2.00266
$704$	−15.3053	−0.576841
$705$	0	0
$706$	−1.94778	−0.0733055
$707$	−27.2697	−1.02558
$708$	26.2076	0.984943
$709$	−18.8911	−0.709471	−0.354736	−	0.934967i	$-0.615429\pi$
$709$	−18.8911	−0.709471	−0.354736	+	0.934967i	$0.615429\pi$
$710$	0	0
$711$	−7.87855	−0.295469
$712$	−27.9326	−1.04682
$713$	−15.8862	−0.594942
$714$	−1.79233	−0.0670762
$715$	0	0
$716$	−27.6185	−1.03215
$717$	7.00563	0.261630
$718$	10.2918	0.384087
$719$	−29.9688	−1.11765	−0.558824	−	0.829286i	$-0.688747\pi$
$719$	−29.9688	−1.11765	−0.558824	+	0.829286i	$0.688747\pi$
$720$	0	0
$721$	−2.00508	−0.0746730
$722$	2.15033	0.0800271
$723$	14.3596	0.534038
$724$	10.1445	0.377016
$725$	0	0
$726$	−8.31236	−0.308501
$727$	49.4790	1.83507	0.917537	−	0.397649i	$-0.130174\pi$
$727$	49.4790	1.83507	0.917537	+	0.397649i	$0.130174\pi$
$728$	−21.3769	−0.792279
$729$	1.00000	0.0370370
$730$	0	0
$731$	−11.7806	−0.435722
$732$	27.2911	1.00871
$733$	10.8422	0.400466	0.200233	−	0.979748i	$-0.435830\pi$
$733$	10.8422	0.400466	0.200233	+	0.979748i	$0.435830\pi$
$734$	−6.41894	−0.236927
$735$	0	0
$736$	15.7856	0.581864
$737$	77.6873	2.86165
$738$	−0.363953	−0.0133973
$739$	29.5649	1.08756	0.543782	−	0.839227i	$-0.316992\pi$
$739$	29.5649	1.08756	0.543782	+	0.839227i	$0.316992\pi$
$740$	0	0
$741$	−29.0497	−1.06717
$742$	−4.20873	−0.154507
$743$	13.0605	0.479142	0.239571	−	0.970879i	$-0.422993\pi$
$743$	13.0605	0.479142	0.239571	+	0.970879i	$0.422993\pi$
$744$	−9.08003	−0.332890
$745$	0	0
$746$	−5.61336	−0.205520
$747$	−11.1873	−0.409324
$748$	17.7226	0.648002
$749$	9.37843	0.342680
$750$	0	0
$751$	−35.6084	−1.29937	−0.649685	−	0.760204i	$-0.725099\pi$
$751$	−35.6084	−1.29937	−0.649685	+	0.760204i	$0.725099\pi$
$752$	25.5573	0.931977
$753$	−21.7642	−0.793132
$754$	−2.91352	−0.106104
$755$	0	0
$756$	−3.43888	−0.125071
$757$	14.8369	0.539256	0.269628	−	0.962964i	$-0.413099\pi$
$757$	14.8369	0.539256	0.269628	+	0.962964i	$0.413099\pi$
$758$	11.8026	0.428690
$759$	−16.9552	−0.615435
$760$	0	0
$761$	33.9733	1.23153	0.615766	−	0.787929i	$-0.288847\pi$
$761$	33.9733	1.23153	0.615766	+	0.787929i	$0.288847\pi$
$762$	−1.73255	−0.0627635
$763$	0.980100	0.0354820
$764$	27.5147	0.995449
$765$	0	0
$766$	−0.618104	−0.0223330
$767$	−89.1478	−3.21894
$768$	−0.298356	−0.0107660
$769$	−37.9334	−1.36791	−0.683957	−	0.729523i	$-0.739742\pi$
$769$	−37.9334	−1.36791	−0.683957	+	0.729523i	$0.739742\pi$
$770$	0	0
$771$	10.1732	0.366380
$772$	−25.9514	−0.934012
$773$	−6.15453	−0.221363	−0.110681	−	0.993856i	$-0.535303\pi$
$773$	−6.15453	−0.221363	−0.110681	+	0.993856i	$0.535303\pi$
$774$	3.01928	0.108526
$775$	0	0
$776$	−13.0514	−0.468518
$777$	−21.3816	−0.767062
$778$	13.8017	0.494814
$779$	3.62885	0.130017
$780$	0	0
$781$	28.4797	1.01908
$782$	−2.94006	−0.105136
$783$	−1.00000	−0.0357371
$784$	−8.45525	−0.301973
$785$	0	0
$786$	8.84180	0.315377
$787$	−51.4731	−1.83482	−0.917409	−	0.397945i	$-0.869724\pi$
$787$	−51.4731	−1.83482	−0.917409	+	0.397945i	$0.869724\pi$
$788$	−6.50426	−0.231705
$789$	16.8078	0.598375
$790$	0	0
$791$	−37.5018	−1.33341
$792$	−9.69106	−0.344357
$793$	−92.8332	−3.29660
$794$	4.31948	0.153293
$795$	0	0
$796$	24.1366	0.855498
$797$	34.9078	1.23650	0.618249	−	0.785982i	$-0.287842\pi$
$797$	34.9078	1.23650	0.618249	+	0.785982i	$0.287842\pi$
$798$	−4.58011	−0.162134
$799$	−18.3268	−0.648356
$800$	0	0
$801$	15.2850	0.540070
$802$	3.15384	0.111366
$803$	−66.4828	−2.34613
$804$	25.8465	0.911535
$805$	0	0
$806$	14.4764	0.509911
$807$	−24.1896	−0.851516
$808$	−25.5674	−0.899460
$809$	−5.72847	−0.201402	−0.100701	−	0.994917i	$-0.532109\pi$
$809$	−5.72847	−0.201402	−0.100701	+	0.994917i	$0.532109\pi$
$810$	0	0
$811$	−4.09859	−0.143921	−0.0719605	−	0.997407i	$-0.522926\pi$
$811$	−4.09859	−0.143921	−0.0719605	+	0.997407i	$0.522926\pi$
$812$	3.43888	0.120681
$813$	4.46984	0.156764
$814$	−28.2415	−0.989863
$815$	0	0
$816$	5.00346	0.175156
$817$	−30.1042	−1.05321
$818$	19.3273	0.675765
$819$	11.6977	0.408750
$820$	0	0
$821$	26.9013	0.938862	0.469431	−	0.882969i	$-0.344459\pi$
$821$	26.9013	0.938862	0.469431	+	0.882969i	$0.344459\pi$
$822$	−4.73190	−0.165044
$823$	−14.7883	−0.515489	−0.257744	−	0.966213i	$-0.582979\pi$
$823$	−14.7883	−0.515489	−0.257744	+	0.966213i	$0.582979\pi$
$824$	−1.87991	−0.0654898
$825$	0	0
$826$	−14.0555	−0.489052
$827$	20.3841	0.708826	0.354413	−	0.935089i	$-0.384681\pi$
$827$	20.3841	0.708826	0.354413	+	0.935089i	$0.384681\pi$
$828$	−5.64098	−0.196038
$829$	10.9727	0.381097	0.190548	−	0.981678i	$-0.438973\pi$
$829$	10.9727	0.381097	0.190548	+	0.981678i	$0.438973\pi$
$830$	0	0
$831$	−1.88450	−0.0653725
$832$	17.3211	0.600503
$833$	6.06317	0.210076
$834$	0.570780	0.0197645
$835$	0	0
$836$	45.2883	1.56633
$837$	4.96870	0.171744
$838$	5.19445	0.179439
$839$	−52.7098	−1.81974	−0.909872	−	0.414889i	$-0.863821\pi$
$839$	−52.7098	−1.81974	−0.909872	+	0.414889i	$0.863821\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−8.89220	−0.306445
$843$	−15.0159	−0.517175
$844$	26.7908	0.922178
$845$	0	0
$846$	4.69702	0.161487
$847$	−33.3738	−1.14674
$848$	11.7491	0.403466
$849$	−20.2576	−0.695240
$850$	0	0
$851$	−35.0735	−1.20230
$852$	9.47518	0.324614
$853$	−39.8561	−1.36465	−0.682324	−	0.731050i	$-0.739031\pi$
$853$	−39.8561	−1.36465	−0.682324	+	0.731050i	$0.739031\pi$
$854$	−14.6365	−0.500851
$855$	0	0
$856$	8.79299	0.300538
$857$	30.1101	1.02854	0.514271	−	0.857628i	$-0.328062\pi$
$857$	30.1101	1.02854	0.514271	+	0.857628i	$0.328062\pi$
$858$	15.4506	0.527475
$859$	19.8331	0.676697	0.338349	−	0.941021i	$-0.390132\pi$
$859$	19.8331	0.676697	0.338349	+	0.941021i	$0.390132\pi$
$860$	0	0
$861$	−1.46125	−0.0497994
$862$	0.558069	0.0190079
$863$	19.8047	0.674161	0.337080	−	0.941476i	$-0.390561\pi$
$863$	19.8047	0.674161	0.337080	+	0.941476i	$0.390561\pi$
$864$	−4.93724	−0.167968
$865$	0	0
$866$	12.7292	0.432557
$867$	13.4121	0.455498
$868$	−17.0868	−0.579962
$869$	−41.7804	−1.41730
$870$	0	0
$871$	−87.9194	−2.97903
$872$	0.918918	0.0311185
$873$	7.14188	0.241716
$874$	−7.51302	−0.254132
$875$	0	0
$876$	−22.1188	−0.747324
$877$	−9.17766	−0.309908	−0.154954	−	0.987922i	$-0.549523\pi$
$877$	−9.17766	−0.309908	−0.154954	+	0.987922i	$0.549523\pi$
$878$	−2.87490	−0.0970231
$879$	5.25806	0.177350
$880$	0	0
$881$	−19.0970	−0.643393	−0.321697	−	0.946843i	$-0.604253\pi$
$881$	−19.0970	−0.643393	−0.321697	+	0.946843i	$0.604253\pi$
$882$	−1.55394	−0.0523239
$883$	20.3991	0.686484	0.343242	−	0.939247i	$-0.388475\pi$
$883$	20.3991	0.686484	0.343242	+	0.939247i	$0.388475\pi$
$884$	−20.0568	−0.674583
$885$	0	0
$886$	6.01974	0.202237
$887$	51.3290	1.72346	0.861730	−	0.507367i	$-0.169381\pi$
$887$	51.3290	1.72346	0.861730	+	0.507367i	$0.169381\pi$
$888$	−20.0469	−0.672730
$889$	−6.95610	−0.233300
$890$	0	0
$891$	5.30306	0.177659
$892$	−42.1446	−1.41111
$893$	−46.8324	−1.56719
$894$	−5.75980	−0.192636
$895$	0	0
$896$	21.9775	0.734215
$897$	19.1883	0.640680
$898$	−17.2579	−0.575902
$899$	−4.96870	−0.165716
$900$	0	0
$901$	−8.42515	−0.280683
$902$	−1.93006	−0.0642641
$903$	12.1223	0.403404
$904$	−35.1608	−1.16943
$905$	0	0
$906$	−3.90181	−0.129629
$907$	5.19249	0.172414	0.0862068	−	0.996277i	$-0.472525\pi$
$907$	5.19249	0.172414	0.0862068	+	0.996277i	$0.472525\pi$
$908$	42.0984	1.39709
$909$	13.9908	0.464046
$910$	0	0
$911$	35.9052	1.18959	0.594795	−	0.803877i	$-0.297233\pi$
$911$	35.9052	1.18959	0.594795	+	0.803877i	$0.297233\pi$
$912$	12.7859	0.423382
$913$	−59.3272	−1.96344
$914$	5.72208	0.189269
$915$	0	0
$916$	22.7645	0.752161
$917$	35.4994	1.17229
$918$	0.919558	0.0303499
$919$	−16.2745	−0.536845	−0.268423	−	0.963301i	$-0.586502\pi$
$919$	−16.2745	−0.536845	−0.268423	+	0.963301i	$0.586502\pi$
$920$	0	0
$921$	18.0575	0.595014
$922$	−4.14279	−0.136435
$923$	−32.2307	−1.06089
$924$	−18.2366	−0.599940
$925$	0	0
$926$	1.82521	0.0599800
$927$	1.02871	0.0337873
$928$	4.93724	0.162073
$929$	44.8694	1.47212	0.736059	−	0.676918i	$-0.236685\pi$
$929$	44.8694	1.47212	0.736059	+	0.676918i	$0.236685\pi$
$930$	0	0
$931$	15.4938	0.507789
$932$	−18.5727	−0.608368
$933$	3.28065	0.107404
$934$	−0.645130	−0.0211093
$935$	0	0
$936$	10.9675	0.358482
$937$	42.5002	1.38842	0.694210	−	0.719772i	$-0.255754\pi$
$937$	42.5002	1.38842	0.694210	+	0.719772i	$0.255754\pi$
$938$	−13.8618	−0.452603
$939$	8.87479	0.289618
$940$	0	0
$941$	16.3907	0.534323	0.267161	−	0.963652i	$-0.413914\pi$
$941$	16.3907	0.534323	0.267161	+	0.963652i	$0.413914\pi$
$942$	1.24311	0.0405027
$943$	−2.39698	−0.0780563
$944$	39.2372	1.27706
$945$	0	0
$946$	16.0114	0.520577
$947$	−6.23282	−0.202539	−0.101270	−	0.994859i	$-0.532291\pi$
$947$	−6.23282	−0.202539	−0.101270	+	0.994859i	$0.532291\pi$
$948$	−13.9003	−0.451461
$949$	75.2392	2.44237
$950$	0	0
$951$	−18.1311	−0.587943
$952$	−6.74690	−0.218668
$953$	32.3834	1.04900	0.524500	−	0.851410i	$-0.324252\pi$
$953$	32.3834	1.04900	0.524500	+	0.851410i	$0.324252\pi$
$954$	2.15930	0.0699099
$955$	0	0
$956$	12.3602	0.399757
$957$	−5.30306	−0.171424
$958$	−3.81383	−0.123219
$959$	−18.9984	−0.613490
$960$	0	0
$961$	−6.31198	−0.203612
$962$	31.9611	1.03047
$963$	−4.81163	−0.155053
$964$	25.3349	0.815983
$965$	0	0
$966$	3.02532	0.0973381
$967$	−47.7887	−1.53678	−0.768390	−	0.639981i	$-0.778942\pi$
$967$	−47.7887	−1.53678	−0.768390	+	0.639981i	$0.778942\pi$
$968$	−31.2904	−1.00571
$969$	−9.16860	−0.294538
$970$	0	0
$971$	20.9352	0.671843	0.335921	−	0.941890i	$-0.390952\pi$
$971$	20.9352	0.671843	0.335921	+	0.941890i	$0.390952\pi$
$972$	1.76432	0.0565907
$973$	2.29166	0.0734671
$974$	−7.45211	−0.238781
$975$	0	0
$976$	40.8593	1.30787
$977$	42.3745	1.35568	0.677840	−	0.735210i	$-0.262916\pi$
$977$	42.3745	1.35568	0.677840	+	0.735210i	$0.262916\pi$
$978$	0.835712	0.0267231
$979$	81.0575	2.59061
$980$	0	0
$981$	−0.502843	−0.0160545
$982$	−18.1060	−0.577787
$983$	48.3116	1.54090	0.770451	−	0.637499i	$-0.220031\pi$
$983$	48.3116	1.54090	0.770451	+	0.637499i	$0.220031\pi$
$984$	−1.37004	−0.0436751
$985$	0	0
$986$	−0.919558	−0.0292847
$987$	18.8583	0.600267
$988$	−51.2532	−1.63058
$989$	19.8848	0.632301
$990$	0	0
$991$	41.7003	1.32465	0.662327	−	0.749215i	$-0.269569\pi$
$991$	41.7003	1.32465	0.662327	+	0.749215i	$0.269569\pi$
$992$	−24.5317	−0.778882
$993$	−9.86489	−0.313053
$994$	−5.08164	−0.161180
$995$	0	0
$996$	−19.7381	−0.625426
$997$	12.2642	0.388411	0.194206	−	0.980961i	$-0.437787\pi$
$997$	12.2642	0.388411	0.194206	+	0.980961i	$0.437787\pi$
$998$	11.2941	0.357507
$999$	10.9699	0.347072

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2175.2.a.bc.1.6	✓	8
3.2	odd	2		6525.2.a.bz.1.3		8
5.2	odd	4		2175.2.c.p.349.10		16
5.3	odd	4		2175.2.c.p.349.7		16
5.4	even	2		2175.2.a.bd.1.3	yes	8
15.14	odd	2		6525.2.a.by.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2175.2.a.bc.1.6	✓	8	1.1	even	1	trivial
2175.2.a.bd.1.3	yes	8	5.4	even	2
2175.2.c.p.349.7		16	5.3	odd	4
2175.2.c.p.349.10		16	5.2	odd	4
6525.2.a.by.1.6		8	15.14	odd	2
6525.2.a.bz.1.3		8	3.2	odd	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:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2175.a (trivial)

\(f(q)\)	\(=\)	\(q+0.485464 q^{2} -1.00000 q^{3} -1.76432 q^{4} -0.485464 q^{6} -1.94912 q^{7} -1.82745 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.485464 q^{2} -1.00000 q^{3} -1.76432 q^{4} -0.485464 q^{6} -1.94912 q^{7} -1.82745 q^{8} +1.00000 q^{9} +5.30306 q^{11} +1.76432 q^{12} -6.00152 q^{13} -0.946227 q^{14} +2.64149 q^{16} -1.89418 q^{17} +0.485464 q^{18} -4.84040 q^{19} +1.94912 q^{21} +2.57445 q^{22} +3.19725 q^{23} +1.82745 q^{24} -2.91352 q^{26} -1.00000 q^{27} +3.43888 q^{28} +1.00000 q^{29} -4.96870 q^{31} +4.93724 q^{32} -5.30306 q^{33} -0.919558 q^{34} -1.76432 q^{36} -10.9699 q^{37} -2.34984 q^{38} +6.00152 q^{39} -0.749700 q^{41} +0.946227 q^{42} +6.21936 q^{43} -9.35633 q^{44} +1.55215 q^{46} +9.67532 q^{47} -2.64149 q^{48} -3.20094 q^{49} +1.89418 q^{51} +10.5886 q^{52} +4.44791 q^{53} -0.485464 q^{54} +3.56191 q^{56} +4.84040 q^{57} +0.485464 q^{58} +14.8542 q^{59} +15.4683 q^{61} -2.41213 q^{62} -1.94912 q^{63} -2.88613 q^{64} -2.57445 q^{66} +14.6495 q^{67} +3.34195 q^{68} -3.19725 q^{69} +5.37043 q^{71} -1.82745 q^{72} -12.5367 q^{73} -5.32550 q^{74} +8.54003 q^{76} -10.3363 q^{77} +2.91352 q^{78} -7.87855 q^{79} +1.00000 q^{81} -0.363953 q^{82} -11.1873 q^{83} -3.43888 q^{84} +3.01928 q^{86} -1.00000 q^{87} -9.69106 q^{88} +15.2850 q^{89} +11.6977 q^{91} -5.64098 q^{92} +4.96870 q^{93} +4.69702 q^{94} -4.93724 q^{96} +7.14188 q^{97} -1.55394 q^{98} +5.30306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{3} + 12 q^{4} + 2 q^{6} + 2 q^{7} - 3 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 8 * q^3 + 12 * q^4 + 2 * q^6 + 2 * q^7 - 3 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} - 8 q^{3} + 12 q^{4} + 2 q^{6} + 2 q^{7} - 3 q^{8} + 8 q^{9} + 6 q^{11} - 12 q^{12} + 6 q^{13} + 9 q^{14} + 32 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{21} + 3 q^{22} - 14 q^{23} + 3 q^{24} + 18 q^{26} - 8 q^{27} + 14 q^{28} + 8 q^{29} + 8 q^{31} + 2 q^{32} - 6 q^{33} - 13 q^{34} + 12 q^{36} + 4 q^{37} - 26 q^{38} - 6 q^{39} + 2 q^{41} - 9 q^{42} + 2 q^{43} - 15 q^{44} + 24 q^{46} - 12 q^{47} - 32 q^{48} + 38 q^{49} + 12 q^{51} + 49 q^{52} - 4 q^{53} + 2 q^{54} + 58 q^{56} - 2 q^{58} + 18 q^{59} + 12 q^{61} + 4 q^{62} + 2 q^{63} + 21 q^{64} - 3 q^{66} + 26 q^{67} - 81 q^{68} + 14 q^{69} + 24 q^{71} - 3 q^{72} - 14 q^{73} - 22 q^{74} + 26 q^{77} - 18 q^{78} + 10 q^{79} + 8 q^{81} + 48 q^{82} - 40 q^{83} - 14 q^{84} + 8 q^{86} - 8 q^{87} - 10 q^{88} + 34 q^{89} + 26 q^{91} + 18 q^{92} - 8 q^{93} - 43 q^{94} - 2 q^{96} + 30 q^{97} - 29 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^3 + 12 * q^4 + 2 * q^6 + 2 * q^7 - 3 * q^8 + 8 * q^9 + 6 * q^11 - 12 * q^12 + 6 * q^13 + 9 * q^14 + 32 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^21 + 3 * q^22 - 14 * q^23 + 3 * q^24 + 18 * q^26 - 8 * q^27 + 14 * q^28 + 8 * q^29 + 8 * q^31 + 2 * q^32 - 6 * q^33 - 13 * q^34 + 12 * q^36 + 4 * q^37 - 26 * q^38 - 6 * q^39 + 2 * q^41 - 9 * q^42 + 2 * q^43 - 15 * q^44 + 24 * q^46 - 12 * q^47 - 32 * q^48 + 38 * q^49 + 12 * q^51 + 49 * q^52 - 4 * q^53 + 2 * q^54 + 58 * q^56 - 2 * q^58 + 18 * q^59 + 12 * q^61 + 4 * q^62 + 2 * q^63 + 21 * q^64 - 3 * q^66 + 26 * q^67 - 81 * q^68 + 14 * q^69 + 24 * q^71 - 3 * q^72 - 14 * q^73 - 22 * q^74 + 26 * q^77 - 18 * q^78 + 10 * q^79 + 8 * q^81 + 48 * q^82 - 40 * q^83 - 14 * q^84 + 8 * q^86 - 8 * q^87 - 10 * q^88 + 34 * q^89 + 26 * q^91 + 18 * q^92 - 8 * q^93 - 43 * q^94 - 2 * q^96 + 30 * q^97 - 29 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more