LMFDB - Embedded newform 1445.2.a.j.1.3

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:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 85)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.17009$ 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)

$f(q)$	$=$	\(q+2.17009 q^{2} +0.539189 q^{3} +2.70928 q^{4} -1.00000 q^{5} +1.17009 q^{6} -4.87936 q^{7} +1.53919 q^{8} -2.70928 q^{9} -2.17009 q^{10} -3.17009 q^{11} +1.46081 q^{12} +2.63090 q^{13} -10.5886 q^{14} -0.539189 q^{15} -2.07838 q^{16} -5.87936 q^{18} -1.07838 q^{19} -2.70928 q^{20} -2.63090 q^{21} -6.87936 q^{22} +5.21953 q^{23} +0.829914 q^{24} +1.00000 q^{25} +5.70928 q^{26} -3.07838 q^{27} -13.2195 q^{28} +2.92162 q^{29} -1.17009 q^{30} -4.09171 q^{31} -7.58864 q^{32} -1.70928 q^{33} +4.87936 q^{35} -7.34017 q^{36} -5.26180 q^{37} -2.34017 q^{38} +1.41855 q^{39} -1.53919 q^{40} -5.60197 q^{41} -5.70928 q^{42} -3.36910 q^{43} -8.58864 q^{44} +2.70928 q^{45} +11.3268 q^{46} -6.78765 q^{47} -1.12064 q^{48} +16.8082 q^{49} +2.17009 q^{50} +7.12783 q^{52} -3.75872 q^{53} -6.68035 q^{54} +3.17009 q^{55} -7.51026 q^{56} -0.581449 q^{57} +6.34017 q^{58} +2.34017 q^{59} -1.46081 q^{60} +12.2557 q^{61} -8.87936 q^{62} +13.2195 q^{63} -12.3112 q^{64} -2.63090 q^{65} -3.70928 q^{66} +10.2062 q^{67} +2.81432 q^{69} +10.5886 q^{70} -4.06505 q^{71} -4.17009 q^{72} -11.0784 q^{73} -11.4186 q^{74} +0.539189 q^{75} -2.92162 q^{76} +15.4680 q^{77} +3.07838 q^{78} +6.92881 q^{79} +2.07838 q^{80} +6.46800 q^{81} -12.1568 q^{82} -8.23287 q^{83} -7.12783 q^{84} -7.31124 q^{86} +1.57531 q^{87} -4.87936 q^{88} +7.15449 q^{89} +5.87936 q^{90} -12.8371 q^{91} +14.1412 q^{92} -2.20620 q^{93} -14.7298 q^{94} +1.07838 q^{95} -4.09171 q^{96} +8.18342 q^{97} +36.4752 q^{98} +8.58864 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} + 3 q^{8} - q^{9} - q^{10} - 4 q^{11} + 6 q^{12} + 4 q^{13} - 12 q^{14} - 3 q^{16} - 5 q^{18} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} + 8 q^{24}+ \cdots + 6 q^{99}+O(q^{100}) $ 3 * q + q^2 + q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 + 3 * q^8 - q^9 - q^10 - 4 * q^11 + 6 * q^12 + 4 * q^13 - 12 * q^14 - 3 * q^16 - 5 * q^18 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 + 8 * q^24 + 3 * q^25 + 10 * q^26 - 6 * q^27 - 16 * q^28 + 12 * q^29 + 2 * q^30 - 10 * q^31 - 3 * q^32 + 2 * q^33 + 2 * q^35 - 11 * q^36 - 8 * q^37 + 4 * q^38 - 10 * q^39 - 3 * q^40 + 2 * q^41 - 10 * q^42 - 14 * q^43 - 6 * q^44 + q^45 + 22 * q^46 - 10 * q^47 - 16 * q^48 + 7 * q^49 + q^50 + 14 * q^53 + 2 * q^54 + 4 * q^55 - 6 * q^56 - 16 * q^57 + 8 * q^58 - 4 * q^59 - 6 * q^60 - 6 * q^61 - 14 * q^62 + 16 * q^63 - 11 * q^64 - 4 * q^65 - 4 * q^66 + 6 * q^67 + 12 * q^70 - 8 * q^71 - 7 * q^72 - 30 * q^73 - 20 * q^74 - 12 * q^76 + 14 * q^77 + 6 * q^78 - 10 * q^79 + 3 * q^80 - 13 * q^81 - 30 * q^82 - 2 * q^83 + 4 * q^86 - 16 * q^87 - 2 * q^88 + 2 * q^89 + 5 * q^90 - 10 * q^91 + 22 * q^92 + 18 * q^93 - 4 * q^94 - 10 * q^96 + 20 * q^97 + 43 * 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 $

$2$	2.17009	1.53448	0.767241	−	0.641358i	$-0.221629\pi$
$2$	2.17009	1.53448	0.767241	+	0.641358i	$0.221629\pi$
$3$	0.539189	0.311301	0.155650	−	0.987812i	$-0.450253\pi$
$3$	0.539189	0.311301	0.155650	+	0.987812i	$0.450253\pi$
$4$	2.70928	1.35464
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.17009	0.477686
$7$	−4.87936	−1.84423	−0.922113	−	0.386921i	$-0.873538\pi$
$7$	−4.87936	−1.84423	−0.922113	+	0.386921i	$0.873538\pi$
$8$	1.53919	0.544185
$9$	−2.70928	−0.903092
$10$	−2.17009	−0.686242
$11$	−3.17009	−0.955817	−0.477909	−	0.878410i	$-0.658605\pi$
$11$	−3.17009	−0.955817	−0.477909	+	0.878410i	$0.658605\pi$
$12$	1.46081	0.421700
$13$	2.63090	0.729680	0.364840	−	0.931070i	$-0.381124\pi$
$13$	2.63090	0.729680	0.364840	+	0.931070i	$0.381124\pi$
$14$	−10.5886	−2.82993
$15$	−0.539189	−0.139218
$16$	−2.07838	−0.519594
$17$	0	0
$17$	0	0
$18$	−5.87936	−1.38578
$19$	−1.07838	−0.247397	−0.123698	−	0.992320i	$-0.539476\pi$
$19$	−1.07838	−0.247397	−0.123698	+	0.992320i	$0.539476\pi$
$20$	−2.70928	−0.605812
$21$	−2.63090	−0.574109
$22$	−6.87936	−1.46668
$23$	5.21953	1.08835	0.544174	−	0.838972i	$-0.316843\pi$
$23$	5.21953	1.08835	0.544174	+	0.838972i	$0.316843\pi$
$24$	0.829914	0.169405
$25$	1.00000	0.200000
$26$	5.70928	1.11968
$27$	−3.07838	−0.592434
$28$	−13.2195	−2.49826
$29$	2.92162	0.542532	0.271266	−	0.962504i	$-0.412558\pi$
$29$	2.92162	0.542532	0.271266	+	0.962504i	$0.412558\pi$
$30$	−1.17009	−0.213628
$31$	−4.09171	−0.734893	−0.367446	−	0.930045i	$-0.619768\pi$
$31$	−4.09171	−0.734893	−0.367446	+	0.930045i	$0.619768\pi$
$32$	−7.58864	−1.34149
$33$	−1.70928	−0.297547
$34$	0	0
$35$	4.87936	0.824763
$36$	−7.34017	−1.22336
$37$	−5.26180	−0.865034	−0.432517	−	0.901626i	$-0.642374\pi$
$37$	−5.26180	−0.865034	−0.432517	+	0.901626i	$0.642374\pi$
$38$	−2.34017	−0.379626
$39$	1.41855	0.227150
$40$	−1.53919	−0.243367
$41$	−5.60197	−0.874880	−0.437440	−	0.899247i	$-0.644115\pi$
$41$	−5.60197	−0.874880	−0.437440	+	0.899247i	$0.644115\pi$
$42$	−5.70928	−0.880960
$43$	−3.36910	−0.513783	−0.256892	−	0.966440i	$-0.582698\pi$
$43$	−3.36910	−0.513783	−0.256892	+	0.966440i	$0.582698\pi$
$44$	−8.58864	−1.29479
$45$	2.70928	0.403875
$46$	11.3268	1.67005
$47$	−6.78765	−0.990081	−0.495040	−	0.868870i	$-0.664847\pi$
$47$	−6.78765	−0.990081	−0.495040	+	0.868870i	$0.664847\pi$
$48$	−1.12064	−0.161750
$49$	16.8082	2.40117
$50$	2.17009	0.306897
$51$	0	0
$52$	7.12783	0.988452
$53$	−3.75872	−0.516300	−0.258150	−	0.966105i	$-0.583113\pi$
$53$	−3.75872	−0.516300	−0.258150	+	0.966105i	$0.583113\pi$
$54$	−6.68035	−0.909080
$55$	3.17009	0.427454
$56$	−7.51026	−1.00360
$57$	−0.581449	−0.0770148
$58$	6.34017	0.832505
$59$	2.34017	0.304665	0.152332	−	0.988329i	$-0.451322\pi$
$59$	2.34017	0.304665	0.152332	+	0.988329i	$0.451322\pi$
$60$	−1.46081	−0.188590
$61$	12.2557	1.56918	0.784588	−	0.620018i	$-0.212875\pi$
$61$	12.2557	1.56918	0.784588	+	0.620018i	$0.212875\pi$
$62$	−8.87936	−1.12768
$63$	13.2195	1.66550
$64$	−12.3112	−1.53891
$65$	−2.63090	−0.326323
$66$	−3.70928	−0.456580
$67$	10.2062	1.24689	0.623443	−	0.781869i	$-0.285733\pi$
$67$	10.2062	1.24689	0.623443	+	0.781869i	$0.285733\pi$
$68$	0	0
$69$	2.81432	0.338804
$70$	10.5886	1.26558
$71$	−4.06505	−0.482432	−0.241216	−	0.970471i	$-0.577546\pi$
$71$	−4.06505	−0.482432	−0.241216	+	0.970471i	$0.577546\pi$
$72$	−4.17009	−0.491449
$73$	−11.0784	−1.29663	−0.648313	−	0.761374i	$-0.724525\pi$
$73$	−11.0784	−1.29663	−0.648313	+	0.761374i	$0.724525\pi$
$74$	−11.4186	−1.32738
$75$	0.539189	0.0622602
$76$	−2.92162	−0.335133
$77$	15.4680	1.76274
$78$	3.07838	0.348558
$79$	6.92881	0.779552	0.389776	−	0.920910i	$-0.372552\pi$
$79$	6.92881	0.779552	0.389776	+	0.920910i	$0.372552\pi$
$80$	2.07838	0.232370
$81$	6.46800	0.718667
$82$	−12.1568	−1.34249
$83$	−8.23287	−0.903674	−0.451837	−	0.892100i	$-0.649231\pi$
$83$	−8.23287	−0.903674	−0.451837	+	0.892100i	$0.649231\pi$
$84$	−7.12783	−0.777710
$85$	0	0
$86$	−7.31124	−0.788392
$87$	1.57531	0.168891
$88$	−4.87936	−0.520142
$89$	7.15449	0.758374	0.379187	−	0.925320i	$-0.376204\pi$
$89$	7.15449	0.758374	0.379187	+	0.925320i	$0.376204\pi$
$90$	5.87936	0.619739
$91$	−12.8371	−1.34569
$92$	14.1412	1.47432
$93$	−2.20620	−0.228773
$94$	−14.7298	−1.51926
$95$	1.07838	0.110639
$96$	−4.09171	−0.417608
$97$	8.18342	0.830900	0.415450	−	0.909616i	$-0.363624\pi$
$97$	8.18342	0.830900	0.415450	+	0.909616i	$0.363624\pi$
$98$	36.4752	3.68455
$99$	8.58864	0.863191
$100$	2.70928	0.270928
$101$	−2.47414	−0.246186	−0.123093	−	0.992395i	$-0.539281\pi$
$101$	−2.47414	−0.246186	−0.123093	+	0.992395i	$0.539281\pi$
$102$	0	0
$103$	−19.6514	−1.93631	−0.968156	−	0.250348i	$-0.919455\pi$
$103$	−19.6514	−1.93631	−0.968156	+	0.250348i	$0.919455\pi$
$104$	4.04945	0.397081
$105$	2.63090	0.256749
$106$	−8.15676	−0.792254
$107$	12.6381	1.22177	0.610885	−	0.791719i	$-0.290814\pi$
$107$	12.6381	1.22177	0.610885	+	0.791719i	$0.290814\pi$
$108$	−8.34017	−0.802534
$109$	−8.15676	−0.781275	−0.390638	−	0.920544i	$-0.627745\pi$
$109$	−8.15676	−0.781275	−0.390638	+	0.920544i	$0.627745\pi$
$110$	6.87936	0.655921
$111$	−2.83710	−0.269286
$112$	10.1412	0.958249
$113$	17.0205	1.60116	0.800578	−	0.599229i	$-0.204526\pi$
$113$	17.0205	1.60116	0.800578	+	0.599229i	$0.204526\pi$
$114$	−1.26180	−0.118178
$115$	−5.21953	−0.486724
$116$	7.91548	0.734934
$117$	−7.12783	−0.658968
$118$	5.07838	0.467503
$119$	0	0
$120$	−0.829914	−0.0757604
$121$	−0.950552	−0.0864138
$122$	26.5958	2.40787
$123$	−3.02052	−0.272351
$124$	−11.0856	−0.995513
$125$	−1.00000	−0.0894427
$126$	28.6875	2.55569
$127$	8.04945	0.714273	0.357137	−	0.934052i	$-0.383753\pi$
$127$	8.04945	0.714273	0.357137	+	0.934052i	$0.383753\pi$
$128$	−11.5392	−1.01993
$129$	−1.81658	−0.159941
$130$	−5.70928	−0.500737
$131$	−11.6937	−1.02168	−0.510841	−	0.859675i	$-0.670666\pi$
$131$	−11.6937	−1.02168	−0.510841	+	0.859675i	$0.670666\pi$
$132$	−4.63090	−0.403068
$133$	5.26180	0.456256
$134$	22.1483	1.91333
$135$	3.07838	0.264945
$136$	0	0
$137$	1.95055	0.166647	0.0833234	−	0.996523i	$-0.473447\pi$
$137$	1.95055	0.166647	0.0833234	+	0.996523i	$0.473447\pi$
$138$	6.10731	0.519889
$139$	2.00719	0.170247	0.0851237	−	0.996370i	$-0.472871\pi$
$139$	2.00719	0.170247	0.0851237	+	0.996370i	$0.472871\pi$
$140$	13.2195	1.11725
$141$	−3.65983	−0.308213
$142$	−8.82150	−0.740284
$143$	−8.34017	−0.697440
$144$	5.63090	0.469241
$145$	−2.92162	−0.242628
$146$	−24.0410	−1.98965
$147$	9.06278	0.747485
$148$	−14.2557	−1.17181
$149$	−14.2823	−1.17005	−0.585026	−	0.811014i	$-0.698916\pi$
$149$	−14.2823	−1.17005	−0.585026	+	0.811014i	$0.698916\pi$
$150$	1.17009	0.0955372
$151$	−12.8638	−1.04684	−0.523419	−	0.852075i	$-0.675344\pi$
$151$	−12.8638	−1.04684	−0.523419	+	0.852075i	$0.675344\pi$
$152$	−1.65983	−0.134630
$153$	0	0
$154$	33.5669	2.70490
$155$	4.09171	0.328654
$156$	3.84324	0.307706
$157$	3.75872	0.299979	0.149989	−	0.988688i	$-0.452076\pi$
$157$	3.75872	0.299979	0.149989	+	0.988688i	$0.452076\pi$
$158$	15.0361	1.19621
$159$	−2.02666	−0.160725
$160$	7.58864	0.599934
$161$	−25.4680	−2.00716
$162$	14.0361	1.10278
$163$	−8.69594	−0.681119	−0.340559	−	0.940223i	$-0.610616\pi$
$163$	−8.69594	−0.681119	−0.340559	+	0.940223i	$0.610616\pi$
$164$	−15.1773	−1.18515
$165$	1.70928	0.133067
$166$	−17.8660	−1.38667
$167$	−1.37629	−0.106501	−0.0532503	−	0.998581i	$-0.516958\pi$
$167$	−1.37629	−0.106501	−0.0532503	+	0.998581i	$0.516958\pi$
$168$	−4.04945	−0.312422
$169$	−6.07838	−0.467568
$170$	0	0
$171$	2.92162	0.223422
$172$	−9.12783	−0.695990
$173$	17.3607	1.31991	0.659954	−	0.751306i	$-0.270576\pi$
$173$	17.3607	1.31991	0.659954	+	0.751306i	$0.270576\pi$
$174$	3.41855	0.259160
$175$	−4.87936	−0.368845
$176$	6.58864	0.496637
$177$	1.26180	0.0948423
$178$	15.5259	1.16371
$179$	−6.83710	−0.511029	−0.255514	−	0.966805i	$-0.582245\pi$
$179$	−6.83710	−0.511029	−0.255514	+	0.966805i	$0.582245\pi$
$180$	7.34017	0.547104
$181$	15.0205	1.11647	0.558233	−	0.829684i	$-0.311479\pi$
$181$	15.0205	1.11647	0.558233	+	0.829684i	$0.311479\pi$
$182$	−27.8576	−2.06494
$183$	6.60811	0.488486
$184$	8.03385	0.592263
$185$	5.26180	0.386855
$186$	−4.78765	−0.351048
$187$	0	0
$188$	−18.3896	−1.34120
$189$	15.0205	1.09258
$190$	2.34017	0.169774
$191$	−24.2823	−1.75701	−0.878503	−	0.477736i	$-0.841457\pi$
$191$	−24.2823	−1.75701	−0.878503	+	0.477736i	$0.841457\pi$
$192$	−6.63809	−0.479063
$193$	−11.8576	−0.853530	−0.426765	−	0.904363i	$-0.640347\pi$
$193$	−11.8576	−0.853530	−0.426765	+	0.904363i	$0.640347\pi$
$194$	17.7587	1.27500
$195$	−1.41855	−0.101585
$196$	45.5380	3.25271
$197$	−18.2557	−1.30066	−0.650331	−	0.759651i	$-0.725370\pi$
$197$	−18.2557	−1.30066	−0.650331	+	0.759651i	$0.725370\pi$
$198$	18.6381	1.32455
$199$	−3.72487	−0.264049	−0.132025	−	0.991246i	$-0.542148\pi$
$199$	−3.72487	−0.264049	−0.132025	+	0.991246i	$0.542148\pi$
$200$	1.53919	0.108837
$201$	5.50307	0.388157
$202$	−5.36910	−0.377769
$203$	−14.2557	−1.00055
$204$	0	0
$205$	5.60197	0.391258
$206$	−42.6453	−2.97124
$207$	−14.1412	−0.982878
$208$	−5.46800	−0.379138
$209$	3.41855	0.236466
$210$	5.70928	0.393977
$211$	−22.2485	−1.53165	−0.765824	−	0.643051i	$-0.777668\pi$
$211$	−22.2485	−1.53165	−0.765824	+	0.643051i	$0.777668\pi$
$212$	−10.1834	−0.699400
$213$	−2.19183	−0.150182
$214$	27.4257	1.87478
$215$	3.36910	0.229771
$216$	−4.73820	−0.322394
$217$	19.9649	1.35531
$218$	−17.7009	−1.19885
$219$	−5.97334	−0.403641
$220$	8.58864	0.579046
$221$	0	0
$222$	−6.15676	−0.413214
$223$	2.19183	0.146776	0.0733878	−	0.997303i	$-0.476619\pi$
$223$	2.19183	0.146776	0.0733878	+	0.997303i	$0.476619\pi$
$224$	37.0277	2.47402
$225$	−2.70928	−0.180618
$226$	36.9360	2.45695
$227$	9.55971	0.634500	0.317250	−	0.948342i	$-0.397241\pi$
$227$	9.55971	0.634500	0.317250	+	0.948342i	$0.397241\pi$
$228$	−1.57531	−0.104327
$229$	−7.36910	−0.486964	−0.243482	−	0.969905i	$-0.578290\pi$
$229$	−7.36910	−0.486964	−0.243482	+	0.969905i	$0.578290\pi$
$230$	−11.3268	−0.746870
$231$	8.34017	0.548743
$232$	4.49693	0.295238
$233$	−9.44521	−0.618776	−0.309388	−	0.950936i	$-0.600124\pi$
$233$	−9.44521	−0.618776	−0.309388	+	0.950936i	$0.600124\pi$
$234$	−15.4680	−1.01117
$235$	6.78765	0.442778
$236$	6.34017	0.412710
$237$	3.73594	0.242675
$238$	0	0
$239$	6.25565	0.404644	0.202322	−	0.979319i	$-0.435151\pi$
$239$	6.25565	0.404644	0.202322	+	0.979319i	$0.435151\pi$
$240$	1.12064	0.0723369
$241$	2.49693	0.160841	0.0804207	−	0.996761i	$-0.474374\pi$
$241$	2.49693	0.160841	0.0804207	+	0.996761i	$0.474374\pi$
$242$	−2.06278	−0.132600
$243$	12.7226	0.816156
$244$	33.2039	2.12566
$245$	−16.8082	−1.07383
$246$	−6.55479	−0.417918
$247$	−2.83710	−0.180520
$248$	−6.29791	−0.399918
$249$	−4.43907	−0.281315
$250$	−2.17009	−0.137248
$251$	−11.8166	−0.745856	−0.372928	−	0.927860i	$-0.621646\pi$
$251$	−11.8166	−0.745856	−0.372928	+	0.927860i	$0.621646\pi$
$252$	35.8154	2.25616
$253$	−16.5464	−1.04026
$254$	17.4680	1.09604
$255$	0	0
$256$	−0.418551	−0.0261594
$257$	−14.9444	−0.932207	−0.466103	−	0.884730i	$-0.654342\pi$
$257$	−14.9444	−0.932207	−0.466103	+	0.884730i	$0.654342\pi$
$258$	−3.94214	−0.245427
$259$	25.6742	1.59532
$260$	−7.12783	−0.442049
$261$	−7.91548	−0.489956
$262$	−25.3763	−1.56775
$263$	12.9444	0.798186	0.399093	−	0.916910i	$-0.369325\pi$
$263$	12.9444	0.798186	0.399093	+	0.916910i	$0.369325\pi$
$264$	−2.63090	−0.161921
$265$	3.75872	0.230897
$266$	11.4186	0.700116
$267$	3.85762	0.236083
$268$	27.6514	1.68908
$269$	7.47641	0.455845	0.227922	−	0.973679i	$-0.426807\pi$
$269$	7.47641	0.455845	0.227922	+	0.973679i	$0.426807\pi$
$270$	6.68035	0.406553
$271$	−2.15676	−0.131014	−0.0655068	−	0.997852i	$-0.520866\pi$
$271$	−2.15676	−0.131014	−0.0655068	+	0.997852i	$0.520866\pi$
$272$	0	0
$273$	−6.92162	−0.418916
$274$	4.23287	0.255717
$275$	−3.17009	−0.191163
$276$	7.62475	0.458956
$277$	−12.1568	−0.730429	−0.365214	−	0.930923i	$-0.619004\pi$
$277$	−12.1568	−0.730429	−0.365214	+	0.930923i	$0.619004\pi$
$278$	4.35577	0.261242
$279$	11.0856	0.663675
$280$	7.51026	0.448824
$281$	−13.1194	−0.782639	−0.391319	−	0.920255i	$-0.627981\pi$
$281$	−13.1194	−0.782639	−0.391319	+	0.920255i	$0.627981\pi$
$282$	−7.94214	−0.472948
$283$	−13.9577	−0.829701	−0.414851	−	0.909889i	$-0.636166\pi$
$283$	−13.9577	−0.829701	−0.414851	+	0.909889i	$0.636166\pi$
$284$	−11.0133	−0.653521
$285$	0.581449	0.0344421
$286$	−18.0989	−1.07021
$287$	27.3340	1.61348
$288$	20.5597	1.21149
$289$	0	0
$290$	−6.34017	−0.372308
$291$	4.41241	0.258660
$292$	−30.0144	−1.75646
$293$	4.73820	0.276809	0.138404	−	0.990376i	$-0.455803\pi$
$293$	4.73820	0.276809	0.138404	+	0.990376i	$0.455803\pi$
$294$	19.6670	1.14700
$295$	−2.34017	−0.136250
$296$	−8.09890	−0.470739
$297$	9.75872	0.566259
$298$	−30.9939	−1.79543
$299$	13.7321	0.794146
$300$	1.46081	0.0843400
$301$	16.4391	0.947532
$302$	−27.9155	−1.60636
$303$	−1.33403	−0.0766380
$304$	2.24128	0.128546
$305$	−12.2557	−0.701757
$306$	0	0
$307$	−21.5936	−1.23241	−0.616205	−	0.787586i	$-0.711331\pi$
$307$	−21.5936	−1.23241	−0.616205	+	0.787586i	$0.711331\pi$
$308$	41.9071	2.38788
$309$	−10.5958	−0.602775
$310$	8.87936	0.504314
$311$	−24.2628	−1.37582	−0.687910	−	0.725796i	$-0.741472\pi$
$311$	−24.2628	−1.37582	−0.687910	+	0.725796i	$0.741472\pi$
$312$	2.18342	0.123612
$313$	4.07223	0.230176	0.115088	−	0.993355i	$-0.463285\pi$
$313$	4.07223	0.230176	0.115088	+	0.993355i	$0.463285\pi$
$314$	8.15676	0.460312
$315$	−13.2195	−0.744836
$316$	18.7721	1.05601
$317$	8.05786	0.452574	0.226287	−	0.974061i	$-0.427341\pi$
$317$	8.05786	0.452574	0.226287	+	0.974061i	$0.427341\pi$
$318$	−4.39803	−0.246629
$319$	−9.26180	−0.518561
$320$	12.3112	0.688219
$321$	6.81432	0.380338
$322$	−55.2678	−3.07995
$323$	0	0
$324$	17.5236	0.973533
$325$	2.63090	0.145936
$326$	−18.8710	−1.04517
$327$	−4.39803	−0.243212
$328$	−8.62249	−0.476097
$329$	33.1194	1.82593
$330$	3.70928	0.204189
$331$	10.0722	0.553620	0.276810	−	0.960925i	$-0.410723\pi$
$331$	10.0722	0.553620	0.276810	+	0.960925i	$0.410723\pi$
$332$	−22.3051	−1.22415
$333$	14.2557	0.781205
$334$	−2.98667	−0.163423
$335$	−10.2062	−0.557624
$336$	5.46800	0.298304
$337$	11.2351	0.612017	0.306008	−	0.952029i	$-0.401006\pi$
$337$	11.2351	0.612017	0.306008	+	0.952029i	$0.401006\pi$
$338$	−13.1906	−0.717474
$339$	9.17727	0.498441
$340$	0	0
$341$	12.9711	0.702423
$342$	6.34017	0.342837
$343$	−47.8576	−2.58407
$344$	−5.18568	−0.279593
$345$	−2.81432	−0.151518
$346$	37.6742	2.02538
$347$	−8.74927	−0.469685	−0.234843	−	0.972033i	$-0.575457\pi$
$347$	−8.74927	−0.469685	−0.234843	+	0.972033i	$0.575457\pi$
$348$	4.26794	0.228786
$349$	26.9093	1.44042	0.720212	−	0.693754i	$-0.244045\pi$
$349$	26.9093	1.44042	0.720212	+	0.693754i	$0.244045\pi$
$350$	−10.5886	−0.565986
$351$	−8.09890	−0.432287
$352$	24.0566	1.28222
$353$	18.3135	0.974730	0.487365	−	0.873198i	$-0.337958\pi$
$353$	18.3135	0.974730	0.487365	+	0.873198i	$0.337958\pi$
$354$	2.73820	0.145534
$355$	4.06505	0.215750
$356$	19.3835	1.02732
$357$	0	0
$358$	−14.8371	−0.784165
$359$	9.57531	0.505365	0.252683	−	0.967549i	$-0.418687\pi$
$359$	9.57531	0.505365	0.252683	+	0.967549i	$0.418687\pi$
$360$	4.17009	0.219783
$361$	−17.8371	−0.938795
$362$	32.5958	1.71320
$363$	−0.512527	−0.0269007
$364$	−34.7792	−1.82293
$365$	11.0784	0.579869
$366$	14.3402	0.749573
$367$	12.1145	0.632371	0.316186	−	0.948697i	$-0.397598\pi$
$367$	12.1145	0.632371	0.316186	+	0.948697i	$0.397598\pi$
$368$	−10.8482	−0.565500
$369$	15.1773	0.790097
$370$	11.4186	0.593622
$371$	18.3402	0.952174
$372$	−5.97721	−0.309904
$373$	30.4619	1.57726	0.788628	−	0.614871i	$-0.210792\pi$
$373$	30.4619	1.57726	0.788628	+	0.614871i	$0.210792\pi$
$374$	0	0
$375$	−0.539189	−0.0278436
$376$	−10.4475	−0.538788
$377$	7.68649	0.395874
$378$	32.5958	1.67655
$379$	0.986669	0.0506818	0.0253409	−	0.999679i	$-0.491933\pi$
$379$	0.986669	0.0506818	0.0253409	+	0.999679i	$0.491933\pi$
$380$	2.92162	0.149876
$381$	4.34017	0.222354
$382$	−52.6947	−2.69610
$383$	24.9588	1.27533	0.637667	−	0.770312i	$-0.279900\pi$
$383$	24.9588	1.27533	0.637667	+	0.770312i	$0.279900\pi$
$384$	−6.22180	−0.317505
$385$	−15.4680	−0.788322
$386$	−25.7321	−1.30973
$387$	9.12783	0.463993
$388$	22.1711	1.12557
$389$	−33.8082	−1.71414	−0.857071	−	0.515198i	$-0.827718\pi$
$389$	−33.8082	−1.71414	−0.857071	+	0.515198i	$0.827718\pi$
$390$	−3.07838	−0.155880
$391$	0	0
$392$	25.8710	1.30668
$393$	−6.30510	−0.318050
$394$	−39.6163	−1.99584
$395$	−6.92881	−0.348626
$396$	23.2690	1.16931
$397$	28.5236	1.43156	0.715779	−	0.698327i	$-0.246072\pi$
$397$	28.5236	1.43156	0.715779	+	0.698327i	$0.246072\pi$
$398$	−8.08330	−0.405179
$399$	2.83710	0.142033
$400$	−2.07838	−0.103919
$401$	−33.0928	−1.65257	−0.826287	−	0.563250i	$-0.809551\pi$
$401$	−33.0928	−1.65257	−0.826287	+	0.563250i	$0.809551\pi$
$402$	11.9421	0.595620
$403$	−10.7649	−0.536236
$404$	−6.70313	−0.333493
$405$	−6.46800	−0.321397
$406$	−30.9360	−1.53533
$407$	16.6803	0.826814
$408$	0	0
$409$	−30.1978	−1.49318	−0.746592	−	0.665282i	$-0.768311\pi$
$409$	−30.1978	−1.49318	−0.746592	+	0.665282i	$0.768311\pi$
$410$	12.1568	0.600379
$411$	1.05172	0.0518773
$412$	−53.2411	−2.62300
$413$	−11.4186	−0.561870
$414$	−30.6875	−1.50821
$415$	8.23287	0.404135
$416$	−19.9649	−0.978861
$417$	1.08225	0.0529982
$418$	7.41855	0.362853
$419$	18.1639	0.887367	0.443683	−	0.896184i	$-0.353671\pi$
$419$	18.1639	0.887367	0.443683	+	0.896184i	$0.353671\pi$
$420$	7.12783	0.347802
$421$	0.760991	0.0370884	0.0185442	−	0.999828i	$-0.494097\pi$
$421$	0.760991	0.0370884	0.0185442	+	0.999828i	$0.494097\pi$
$422$	−48.2811	−2.35029
$423$	18.3896	0.894134
$424$	−5.78539	−0.280963
$425$	0	0
$426$	−4.75646	−0.230451
$427$	−59.7998	−2.89391
$428$	34.2401	1.65506
$429$	−4.49693	−0.217114
$430$	7.31124	0.352579
$431$	6.34736	0.305742	0.152871	−	0.988246i	$-0.451148\pi$
$431$	6.34736	0.305742	0.152871	+	0.988246i	$0.451148\pi$
$432$	6.39803	0.307825
$433$	−3.62475	−0.174195	−0.0870973	−	0.996200i	$-0.527759\pi$
$433$	−3.62475	−0.174195	−0.0870973	+	0.996200i	$0.527759\pi$
$434$	43.3256	2.07970
$435$	−1.57531	−0.0755302
$436$	−22.0989	−1.05835
$437$	−5.62863	−0.269254
$438$	−12.9627	−0.619380
$439$	6.40522	0.305704	0.152852	−	0.988249i	$-0.451154\pi$
$439$	6.40522	0.305704	0.152852	+	0.988249i	$0.451154\pi$
$440$	4.87936	0.232614
$441$	−45.5380	−2.16847
$442$	0	0
$443$	27.4824	1.30573	0.652864	−	0.757476i	$-0.273568\pi$
$443$	27.4824	1.30573	0.652864	+	0.757476i	$0.273568\pi$
$444$	−7.68649	−0.364785
$445$	−7.15449	−0.339155
$446$	4.75646	0.225225
$447$	−7.70086	−0.364238
$448$	60.0710	2.83809
$449$	−28.7526	−1.35692	−0.678459	−	0.734638i	$-0.737352\pi$
$449$	−28.7526	−1.35692	−0.678459	+	0.734638i	$0.737352\pi$
$450$	−5.87936	−0.277156
$451$	17.7587	0.836226
$452$	46.1133	2.16899
$453$	−6.93600	−0.325882
$454$	20.7454	0.973630
$455$	12.8371	0.601813
$456$	−0.894960	−0.0419104
$457$	31.4101	1.46930	0.734652	−	0.678444i	$-0.237345\pi$
$457$	31.4101	1.46930	0.734652	+	0.678444i	$0.237345\pi$
$458$	−15.9916	−0.747238
$459$	0	0
$460$	−14.1412	−0.659335
$461$	7.75872	0.361360	0.180680	−	0.983542i	$-0.442170\pi$
$461$	7.75872	0.361360	0.180680	+	0.983542i	$0.442170\pi$
$462$	18.0989	0.842037
$463$	24.2329	1.12620	0.563098	−	0.826390i	$-0.309609\pi$
$463$	24.2329	1.12620	0.563098	+	0.826390i	$0.309609\pi$
$464$	−6.07223	−0.281896
$465$	2.20620	0.102310
$466$	−20.4969	−0.949502
$467$	12.3174	0.569981	0.284990	−	0.958530i	$-0.408010\pi$
$467$	12.3174	0.569981	0.284990	+	0.958530i	$0.408010\pi$
$468$	−19.3112	−0.892663
$469$	−49.7998	−2.29954
$470$	14.7298	0.679435
$471$	2.02666	0.0933837
$472$	3.60197	0.165794
$473$	10.6803	0.491083
$474$	8.10731	0.372381
$475$	−1.07838	−0.0494794
$476$	0	0
$477$	10.1834	0.466267
$478$	13.5753	0.620920
$479$	−2.14957	−0.0982162	−0.0491081	−	0.998793i	$-0.515638\pi$
$479$	−2.14957	−0.0982162	−0.0491081	+	0.998793i	$0.515638\pi$
$480$	4.09171	0.186760
$481$	−13.8432	−0.631198
$482$	5.41855	0.246808
$483$	−13.7321	−0.624830
$484$	−2.57531	−0.117059
$485$	−8.18342	−0.371590
$486$	27.6092	1.25238
$487$	−40.0833	−1.81635	−0.908174	−	0.418593i	$-0.862523\pi$
$487$	−40.0833	−1.81635	−0.908174	+	0.418593i	$0.862523\pi$
$488$	18.8638	0.853922
$489$	−4.68876	−0.212033
$490$	−36.4752	−1.64778
$491$	2.25565	0.101796	0.0508981	−	0.998704i	$-0.483792\pi$
$491$	2.25565	0.101796	0.0508981	+	0.998704i	$0.483792\pi$
$492$	−8.18342	−0.368937
$493$	0	0
$494$	−6.15676	−0.277006
$495$	−8.58864	−0.386031
$496$	8.50412	0.381846
$497$	19.8348	0.889714
$498$	−9.63317	−0.431672
$499$	−42.5452	−1.90458	−0.952291	−	0.305190i	$-0.901280\pi$
$499$	−42.5452	−1.90458	−0.952291	+	0.305190i	$0.901280\pi$
$500$	−2.70928	−0.121162
$501$	−0.742080	−0.0331537
$502$	−25.6430	−1.14450
$503$	−9.55971	−0.426246	−0.213123	−	0.977025i	$-0.568364\pi$
$503$	−9.55971	−0.426246	−0.213123	+	0.977025i	$0.568364\pi$
$504$	20.3474	0.906343
$505$	2.47414	0.110098
$506$	−35.9071	−1.59626
$507$	−3.27739	−0.145554
$508$	21.8082	0.967581
$509$	28.3545	1.25679	0.628397	−	0.777893i	$-0.283712\pi$
$509$	28.3545	1.25679	0.628397	+	0.777893i	$0.283712\pi$
$510$	0	0
$511$	54.0554	2.39127
$512$	22.1701	0.979789
$513$	3.31965	0.146566
$514$	−32.4307	−1.43046
$515$	19.6514	0.865945
$516$	−4.92162	−0.216662
$517$	21.5174	0.946336
$518$	55.7152	2.44799
$519$	9.36069	0.410889
$520$	−4.04945	−0.177580
$521$	15.1050	0.661764	0.330882	−	0.943672i	$-0.392654\pi$
$521$	15.1050	0.661764	0.330882	+	0.943672i	$0.392654\pi$
$522$	−17.1773	−0.751829
$523$	−10.8865	−0.476036	−0.238018	−	0.971261i	$-0.576498\pi$
$523$	−10.8865	−0.476036	−0.238018	+	0.971261i	$0.576498\pi$
$524$	−31.6814	−1.38401
$525$	−2.63090	−0.114822
$526$	28.0905	1.22480
$527$	0	0
$528$	3.55252	0.154604
$529$	4.24354	0.184502
$530$	8.15676	0.354307
$531$	−6.34017	−0.275140
$532$	14.2557	0.618061
$533$	−14.7382	−0.638383
$534$	8.37137	0.362265
$535$	−12.6381	−0.546392
$536$	15.7093	0.678537
$537$	−3.68649	−0.159084
$538$	16.2245	0.699486
$539$	−53.2834	−2.29508
$540$	8.34017	0.358904
$541$	−6.86830	−0.295291	−0.147646	−	0.989040i	$-0.547170\pi$
$541$	−6.86830	−0.295291	−0.147646	+	0.989040i	$0.547170\pi$
$542$	−4.68035	−0.201038
$543$	8.09890	0.347557
$544$	0	0
$545$	8.15676	0.349397
$546$	−15.0205	−0.642819
$547$	5.89988	0.252261	0.126130	−	0.992014i	$-0.459744\pi$
$547$	5.89988	0.252261	0.126130	+	0.992014i	$0.459744\pi$
$548$	5.28458	0.225746
$549$	−33.2039	−1.41711
$550$	−6.87936	−0.293337
$551$	−3.15061	−0.134221
$552$	4.33176	0.184372
$553$	−33.8082	−1.43767
$554$	−26.3812	−1.12083
$555$	2.83710	0.120428
$556$	5.43802	0.230624
$557$	−17.7359	−0.751496	−0.375748	−	0.926722i	$-0.622614\pi$
$557$	−17.7359	−0.751496	−0.375748	+	0.926722i	$0.622614\pi$
$558$	24.0566	1.01840
$559$	−8.86376	−0.374897
$560$	−10.1412	−0.428542
$561$	0	0
$562$	−28.4703	−1.20095
$563$	38.8020	1.63531	0.817655	−	0.575708i	$-0.195274\pi$
$563$	38.8020	1.63531	0.817655	+	0.575708i	$0.195274\pi$
$564$	−9.91548	−0.417517
$565$	−17.0205	−0.716059
$566$	−30.2895	−1.27316
$567$	−31.5597	−1.32538
$568$	−6.25687	−0.262533
$569$	−12.1568	−0.509638	−0.254819	−	0.966989i	$-0.582016\pi$
$569$	−12.1568	−0.509638	−0.254819	+	0.966989i	$0.582016\pi$
$570$	1.26180	0.0528508
$571$	−15.4569	−0.646853	−0.323426	−	0.946253i	$-0.604835\pi$
$571$	−15.4569	−0.646853	−0.323426	+	0.946253i	$0.604835\pi$
$572$	−22.5958	−0.944779
$573$	−13.0928	−0.546958
$574$	59.3172	2.47585
$575$	5.21953	0.217670
$576$	33.3545	1.38977
$577$	−2.36296	−0.0983713	−0.0491856	−	0.998790i	$-0.515663\pi$
$577$	−2.36296	−0.0983713	−0.0491856	+	0.998790i	$0.515663\pi$
$578$	0	0
$579$	−6.39350	−0.265705
$580$	−7.91548	−0.328672
$581$	40.1711	1.66658
$582$	9.57531	0.396909
$583$	11.9155	0.493489
$584$	−17.0517	−0.705605
$585$	7.12783	0.294699
$586$	10.2823	0.424758
$587$	3.65142	0.150710	0.0753550	−	0.997157i	$-0.475991\pi$
$587$	3.65142	0.150710	0.0753550	+	0.997157i	$0.475991\pi$
$588$	24.5536	1.01257
$589$	4.41241	0.181810
$590$	−5.07838	−0.209074
$591$	−9.84324	−0.404897
$592$	10.9360	0.449467
$593$	1.38735	0.0569718	0.0284859	−	0.999594i	$-0.490931\pi$
$593$	1.38735	0.0569718	0.0284859	+	0.999594i	$0.490931\pi$
$594$	21.1773	0.868914
$595$	0	0
$596$	−38.6947	−1.58500
$597$	−2.00841	−0.0821988
$598$	29.7998	1.21860
$599$	−0.451356	−0.0184419	−0.00922095	−	0.999957i	$-0.502935\pi$
$599$	−0.451356	−0.0184419	−0.00922095	+	0.999957i	$0.502935\pi$
$600$	0.829914	0.0338811
$601$	22.1301	0.902705	0.451353	−	0.892346i	$-0.350942\pi$
$601$	22.1301	0.902705	0.451353	+	0.892346i	$0.350942\pi$
$602$	35.6742	1.45397
$603$	−27.6514	−1.12605
$604$	−34.8515	−1.41809
$605$	0.950552	0.0386454
$606$	−2.89496	−0.117600
$607$	−10.2667	−0.416713	−0.208357	−	0.978053i	$-0.566811\pi$
$607$	−10.2667	−0.416713	−0.208357	+	0.978053i	$0.566811\pi$
$608$	8.18342	0.331881
$609$	−7.68649	−0.311472
$610$	−26.5958	−1.07683
$611$	−17.8576	−0.722442
$612$	0	0
$613$	−9.05172	−0.365595	−0.182798	−	0.983151i	$-0.558515\pi$
$613$	−9.05172	−0.365595	−0.182798	+	0.983151i	$0.558515\pi$
$614$	−46.8599	−1.89111
$615$	3.02052	0.121799
$616$	23.8082	0.959259
$617$	−17.8166	−0.717269	−0.358634	−	0.933478i	$-0.616757\pi$
$617$	−17.8166	−0.717269	−0.358634	+	0.933478i	$0.616757\pi$
$618$	−22.9939	−0.924949
$619$	38.3884	1.54296	0.771480	−	0.636254i	$-0.219517\pi$
$619$	38.3884	1.54296	0.771480	+	0.636254i	$0.219517\pi$
$620$	11.0856	0.445207
$621$	−16.0677	−0.644775
$622$	−52.6525	−2.11117
$623$	−34.9093	−1.39861
$624$	−2.94828	−0.118026
$625$	1.00000	0.0400000
$626$	8.83710	0.353202
$627$	1.84324	0.0736121
$628$	10.1834	0.406363
$629$	0	0
$630$	−28.6875	−1.14294
$631$	27.4863	1.09421	0.547105	−	0.837064i	$-0.315730\pi$
$631$	27.4863	1.09421	0.547105	+	0.837064i	$0.315730\pi$
$632$	10.6647	0.424221
$633$	−11.9961	−0.476803
$634$	17.4863	0.694468
$635$	−8.04945	−0.319433
$636$	−5.49079	−0.217724
$637$	44.2206	1.75208
$638$	−20.0989	−0.795723
$639$	11.0133	0.435681
$640$	11.5392	0.456126
$641$	−9.79976	−0.387067	−0.193534	−	0.981094i	$-0.561995\pi$
$641$	−9.79976	−0.387067	−0.193534	+	0.981094i	$0.561995\pi$
$642$	14.7877	0.583622
$643$	−16.9372	−0.667939	−0.333969	−	0.942584i	$-0.608388\pi$
$643$	−16.9372	−0.667939	−0.333969	+	0.942584i	$0.608388\pi$
$644$	−68.9998	−2.71897
$645$	1.81658	0.0715279
$646$	0	0
$647$	−2.98545	−0.117370	−0.0586850	−	0.998277i	$-0.518691\pi$
$647$	−2.98545	−0.117370	−0.0586850	+	0.998277i	$0.518691\pi$
$648$	9.95547	0.391088
$649$	−7.41855	−0.291204
$650$	5.70928	0.223936
$651$	10.7649	0.421908
$652$	−23.5597	−0.922669
$653$	40.1978	1.57306	0.786531	−	0.617551i	$-0.211875\pi$
$653$	40.1978	1.57306	0.786531	+	0.617551i	$0.211875\pi$
$654$	−9.54411	−0.373204
$655$	11.6937	0.456910
$656$	11.6430	0.454583
$657$	30.0144	1.17097
$658$	71.8720	2.80186
$659$	43.9832	1.71334	0.856671	−	0.515864i	$-0.172529\pi$
$659$	43.9832	1.71334	0.856671	+	0.515864i	$0.172529\pi$
$660$	4.63090	0.180257
$661$	−26.1133	−1.01569	−0.507844	−	0.861449i	$-0.669557\pi$
$661$	−26.1133	−1.01569	−0.507844	+	0.861449i	$0.669557\pi$
$662$	21.8576	0.849521
$663$	0	0
$664$	−12.6719	−0.491766
$665$	−5.26180	−0.204044
$666$	30.9360	1.19875
$667$	15.2495	0.590463
$668$	−3.72875	−0.144270
$669$	1.18181	0.0456914
$670$	−22.1483	−0.855665
$671$	−38.8515	−1.49984
$672$	19.9649	0.770164
$673$	−13.3340	−0.513989	−0.256995	−	0.966413i	$-0.582732\pi$
$673$	−13.3340	−0.513989	−0.256995	+	0.966413i	$0.582732\pi$
$674$	24.3812	0.939129
$675$	−3.07838	−0.118487
$676$	−16.4680	−0.633385
$677$	26.5113	1.01891	0.509456	−	0.860497i	$-0.329847\pi$
$677$	26.5113	1.01891	0.509456	+	0.860497i	$0.329847\pi$
$678$	19.9155	0.764849
$679$	−39.9299	−1.53237
$680$	0	0
$681$	5.15449	0.197520
$682$	28.1483	1.07786
$683$	−5.71646	−0.218734	−0.109367	−	0.994001i	$-0.534882\pi$
$683$	−5.71646	−0.218734	−0.109367	+	0.994001i	$0.534882\pi$
$684$	7.91548	0.302656
$685$	−1.95055	−0.0745267
$686$	−103.855	−3.96521
$687$	−3.97334	−0.151592
$688$	7.00227	0.266959
$689$	−9.88882	−0.376734
$690$	−6.10731	−0.232501
$691$	−43.8504	−1.66815	−0.834075	−	0.551652i	$-0.813998\pi$
$691$	−43.8504	−1.66815	−0.834075	+	0.551652i	$0.813998\pi$
$692$	47.0349	1.78800
$693$	−41.9071	−1.59192
$694$	−18.9867	−0.720724
$695$	−2.00719	−0.0761370
$696$	2.42469	0.0919078
$697$	0	0
$698$	58.3956	2.21031
$699$	−5.09275	−0.192626
$700$	−13.2195	−0.499651
$701$	0.0806452	0.00304593	0.00152296	−	0.999999i	$-0.499515\pi$
$701$	0.0806452	0.00304593	0.00152296	+	0.999999i	$0.499515\pi$
$702$	−17.5753	−0.663337
$703$	5.67420	0.214007
$704$	39.0277	1.47091
$705$	3.65983	0.137837
$706$	39.7419	1.49571
$707$	12.0722	0.454023
$708$	3.41855	0.128477
$709$	10.8227	0.406456	0.203228	−	0.979131i	$-0.434857\pi$
$709$	10.8227	0.406456	0.203228	+	0.979131i	$0.434857\pi$
$710$	8.82150	0.331065
$711$	−18.7721	−0.704007
$712$	11.0121	0.412696
$713$	−21.3568	−0.799819
$714$	0	0
$715$	8.34017	0.311905
$716$	−18.5236	−0.692259
$717$	3.37298	0.125966
$718$	20.7792	0.775474
$719$	43.7659	1.63219	0.816097	−	0.577916i	$-0.196134\pi$
$719$	43.7659	1.63219	0.816097	+	0.577916i	$0.196134\pi$
$720$	−5.63090	−0.209851
$721$	95.8864	3.57100
$722$	−38.7081	−1.44056
$723$	1.34632	0.0500700
$724$	40.6947	1.51241
$725$	2.92162	0.108506
$726$	−1.11223	−0.0412786
$727$	−3.59809	−0.133446	−0.0667229	−	0.997772i	$-0.521254\pi$
$727$	−3.59809	−0.133446	−0.0667229	+	0.997772i	$0.521254\pi$
$728$	−19.7587	−0.732307
$729$	−12.5441	−0.464597
$730$	24.0410	0.889799
$731$	0	0
$732$	17.9032	0.661721
$733$	39.8264	1.47102	0.735511	−	0.677513i	$-0.236942\pi$
$733$	39.8264	1.47102	0.735511	+	0.677513i	$0.236942\pi$
$734$	26.2895	0.970363
$735$	−9.06278	−0.334286
$736$	−39.6092	−1.46001
$737$	−32.3545	−1.19180
$738$	32.9360	1.21239
$739$	−13.7587	−0.506123	−0.253061	−	0.967450i	$-0.581437\pi$
$739$	−13.7587	−0.506123	−0.253061	+	0.967450i	$0.581437\pi$
$740$	14.2557	0.524048
$741$	−1.52973	−0.0561962
$742$	39.7998	1.46110
$743$	9.34963	0.343005	0.171502	−	0.985184i	$-0.445138\pi$
$743$	9.34963	0.343005	0.171502	+	0.985184i	$0.445138\pi$
$744$	−3.39576	−0.124495
$745$	14.2823	0.523264
$746$	66.1049	2.42027
$747$	22.3051	0.816101
$748$	0	0
$749$	−61.6658	−2.25322
$750$	−1.17009	−0.0427255
$751$	−53.7392	−1.96097	−0.980487	−	0.196586i	$-0.937014\pi$
$751$	−53.7392	−1.96097	−0.980487	+	0.196586i	$0.937014\pi$
$752$	14.1073	0.514441
$753$	−6.37137	−0.232186
$754$	16.6803	0.607462
$755$	12.8638	0.468160
$756$	40.6947	1.48005
$757$	41.5136	1.50884	0.754418	−	0.656394i	$-0.227919\pi$
$757$	41.5136	1.50884	0.754418	+	0.656394i	$0.227919\pi$
$758$	2.14116	0.0777703
$759$	−8.92162	−0.323834
$760$	1.65983	0.0602083
$761$	−18.0372	−0.653847	−0.326923	−	0.945051i	$-0.606012\pi$
$761$	−18.0372	−0.653847	−0.326923	+	0.945051i	$0.606012\pi$
$762$	9.41855	0.341198
$763$	39.7998	1.44085
$764$	−65.7875	−2.38011
$765$	0	0
$766$	54.1627	1.95698
$767$	6.15676	0.222308
$768$	−0.225678	−0.00814345
$769$	−23.0843	−0.832443	−0.416221	−	0.909263i	$-0.636646\pi$
$769$	−23.0843	−0.832443	−0.416221	+	0.909263i	$0.636646\pi$
$770$	−33.5669	−1.20967
$771$	−8.05786	−0.290197
$772$	−32.1256	−1.15622
$773$	27.4101	0.985874	0.492937	−	0.870065i	$-0.335923\pi$
$773$	27.4101	0.985874	0.492937	+	0.870065i	$0.335923\pi$
$774$	19.8082	0.711990
$775$	−4.09171	−0.146979
$776$	12.5958	0.452164
$777$	13.8432	0.496624
$778$	−73.3667	−2.63032
$779$	6.04104	0.216443
$780$	−3.84324	−0.137610
$781$	12.8865	0.461117
$782$	0	0
$783$	−8.99386	−0.321414
$784$	−34.9337	−1.24763
$785$	−3.75872	−0.134155
$786$	−13.6826	−0.488043
$787$	−30.6069	−1.09102	−0.545509	−	0.838105i	$-0.683664\pi$
$787$	−30.6069	−1.09102	−0.545509	+	0.838105i	$0.683664\pi$
$788$	−49.4596	−1.76192
$789$	6.97948	0.248476
$790$	−15.0361	−0.534961
$791$	−83.0493	−2.95289
$792$	13.2195	0.469736
$793$	32.2434	1.14500
$794$	61.8987	2.19670
$795$	2.02666	0.0718783
$796$	−10.0917	−0.357691
$797$	−22.9770	−0.813888	−0.406944	−	0.913453i	$-0.633406\pi$
$797$	−22.9770	−0.813888	−0.406944	+	0.913453i	$0.633406\pi$
$798$	6.15676	0.217947
$799$	0	0
$800$	−7.58864	−0.268299
$801$	−19.3835	−0.684882
$802$	−71.8141	−2.53585
$803$	35.1194	1.23934
$804$	14.9093	0.525812
$805$	25.4680	0.897629
$806$	−23.3607	−0.822845
$807$	4.03120	0.141905
$808$	−3.80817	−0.133971
$809$	42.7670	1.50361	0.751803	−	0.659388i	$-0.229184\pi$
$809$	42.7670	1.50361	0.751803	+	0.659388i	$0.229184\pi$
$810$	−14.0361	−0.493179
$811$	−9.41136	−0.330478	−0.165239	−	0.986254i	$-0.552839\pi$
$811$	−9.41136	−0.330478	−0.165239	+	0.986254i	$0.552839\pi$
$812$	−38.6225	−1.35538
$813$	−1.16290	−0.0407846
$814$	36.1978	1.26873
$815$	8.69594	0.304606
$816$	0	0
$817$	3.63317	0.127108
$818$	−65.5318	−2.29127
$819$	34.7792	1.21529
$820$	15.1773	0.530013
$821$	32.6681	1.14012	0.570062	−	0.821602i	$-0.306919\pi$
$821$	32.6681	1.14012	0.570062	+	0.821602i	$0.306919\pi$
$822$	2.28231	0.0796048
$823$	−15.9265	−0.555164	−0.277582	−	0.960702i	$-0.589533\pi$
$823$	−15.9265	−0.555164	−0.277582	+	0.960702i	$0.589533\pi$
$824$	−30.2472	−1.05371
$825$	−1.70928	−0.0595093
$826$	−24.7792	−0.862180
$827$	−6.01560	−0.209183	−0.104591	−	0.994515i	$-0.533353\pi$
$827$	−6.01560	−0.209183	−0.104591	+	0.994515i	$0.533353\pi$
$828$	−38.3123	−1.33144
$829$	11.0472	0.383684	0.191842	−	0.981426i	$-0.438554\pi$
$829$	11.0472	0.383684	0.191842	+	0.981426i	$0.438554\pi$
$830$	17.8660	0.620139
$831$	−6.55479	−0.227383
$832$	−32.3896	−1.12291
$833$	0	0
$834$	2.34858	0.0813248
$835$	1.37629	0.0476285
$836$	9.26180	0.320326
$837$	12.5958	0.435375
$838$	39.4173	1.36165
$839$	−35.9805	−1.24219	−0.621093	−	0.783737i	$-0.713311\pi$
$839$	−35.9805	−1.24219	−0.621093	+	0.783737i	$0.713311\pi$
$840$	4.04945	0.139719
$841$	−20.4641	−0.705659
$842$	1.65142	0.0569116
$843$	−7.07384	−0.243636
$844$	−60.2772	−2.07483
$845$	6.07838	0.209103
$846$	39.9071	1.37203
$847$	4.63809	0.159367
$848$	7.81205	0.268267
$849$	−7.52586	−0.258287
$850$	0	0
$851$	−27.4641	−0.941458
$852$	−5.93827	−0.203442
$853$	28.7792	0.985382	0.492691	−	0.870204i	$-0.336013\pi$
$853$	28.7792	0.985382	0.492691	+	0.870204i	$0.336013\pi$
$854$	−129.771	−4.44066
$855$	−2.92162	−0.0999174
$856$	19.4524	0.664869
$857$	−17.0661	−0.582967	−0.291483	−	0.956576i	$-0.594149\pi$
$857$	−17.0661	−0.582967	−0.291483	+	0.956576i	$0.594149\pi$
$858$	−9.75872	−0.333157
$859$	18.9360	0.646088	0.323044	−	0.946384i	$-0.395294\pi$
$859$	18.9360	0.646088	0.323044	+	0.946384i	$0.395294\pi$
$860$	9.12783	0.311256
$861$	14.7382	0.502277
$862$	13.7743	0.469155
$863$	30.8332	1.04958	0.524788	−	0.851233i	$-0.324145\pi$
$863$	30.8332	1.04958	0.524788	+	0.851233i	$0.324145\pi$
$864$	23.3607	0.794747
$865$	−17.3607	−0.590281
$866$	−7.86603	−0.267299
$867$	0	0
$868$	54.0905	1.83595
$869$	−21.9649	−0.745109
$870$	−3.41855	−0.115900
$871$	26.8515	0.909828
$872$	−12.5548	−0.425159
$873$	−22.1711	−0.750379
$874$	−12.2146	−0.413165
$875$	4.87936	0.164953
$876$	−16.1834	−0.546787
$877$	4.30898	0.145504	0.0727519	−	0.997350i	$-0.476822\pi$
$877$	4.30898	0.145504	0.0727519	+	0.997350i	$0.476822\pi$
$878$	13.8999	0.469098
$879$	2.55479	0.0861708
$880$	−6.58864	−0.222103
$881$	12.2245	0.411852	0.205926	−	0.978568i	$-0.433979\pi$
$881$	12.2245	0.411852	0.205926	+	0.978568i	$0.433979\pi$
$882$	−98.8213	−3.32749
$883$	−28.2329	−0.950112	−0.475056	−	0.879956i	$-0.657572\pi$
$883$	−28.2329	−0.950112	−0.475056	+	0.879956i	$0.657572\pi$
$884$	0	0
$885$	−1.26180	−0.0424148
$886$	59.6391	2.00362
$887$	−5.17396	−0.173725	−0.0868623	−	0.996220i	$-0.527684\pi$
$887$	−5.17396	−0.173725	−0.0868623	+	0.996220i	$0.527684\pi$
$888$	−4.36683	−0.146541
$889$	−39.2762	−1.31728
$890$	−15.5259	−0.520428
$891$	−20.5041	−0.686914
$892$	5.93827	0.198828
$893$	7.31965	0.244943
$894$	−16.7115	−0.558918
$895$	6.83710	0.228539
$896$	56.3039	1.88098
$897$	7.40417	0.247218
$898$	−62.3956	−2.08217
$899$	−11.9544	−0.398702
$900$	−7.34017	−0.244672
$901$	0	0
$902$	38.5380	1.28317
$903$	8.86376	0.294968
$904$	26.1978	0.871326
$905$	−15.0205	−0.499299
$906$	−15.0517	−0.500060
$907$	−6.32457	−0.210004	−0.105002	−	0.994472i	$-0.533485\pi$
$907$	−6.32457	−0.210004	−0.105002	+	0.994472i	$0.533485\pi$
$908$	25.8999	0.859518
$909$	6.70313	0.222329
$910$	27.8576	0.923471
$911$	27.6526	0.916173	0.458086	−	0.888908i	$-0.348535\pi$
$911$	27.6526	0.916173	0.458086	+	0.888908i	$0.348535\pi$
$912$	1.20847	0.0400165
$913$	26.0989	0.863747
$914$	68.1627	2.25462
$915$	−6.60811	−0.218457
$916$	−19.9649	−0.659660
$917$	57.0577	1.88421
$918$	0	0
$919$	−47.5318	−1.56793	−0.783965	−	0.620805i	$-0.786806\pi$
$919$	−47.5318	−1.56793	−0.783965	+	0.620805i	$0.786806\pi$
$920$	−8.03385	−0.264868
$921$	−11.6430	−0.383650
$922$	16.8371	0.554500
$923$	−10.6947	−0.352021
$924$	22.5958	0.743348
$925$	−5.26180	−0.173007
$926$	52.5874	1.72813
$927$	53.2411	1.74867
$928$	−22.1711	−0.727803
$929$	−43.7875	−1.43662	−0.718310	−	0.695723i	$-0.755084\pi$
$929$	−43.7875	−1.43662	−0.718310	+	0.695723i	$0.755084\pi$
$930$	4.78765	0.156993
$931$	−18.1256	−0.594041
$932$	−25.5897	−0.838218
$933$	−13.0823	−0.428294
$934$	26.7298	0.874626
$935$	0	0
$936$	−10.9711	−0.358601
$937$	−14.2367	−0.465094	−0.232547	−	0.972585i	$-0.574706\pi$
$937$	−14.2367	−0.465094	−0.232547	+	0.972585i	$0.574706\pi$
$938$	−108.070	−3.52860
$939$	2.19570	0.0716541
$940$	18.3896	0.599803
$941$	35.2183	1.14808	0.574042	−	0.818826i	$-0.305375\pi$
$941$	35.2183	1.14808	0.574042	+	0.818826i	$0.305375\pi$
$942$	4.39803	0.143296
$943$	−29.2397	−0.952175
$944$	−4.86376	−0.158302
$945$	−15.0205	−0.488618
$946$	23.1773	0.753558
$947$	−49.1227	−1.59627	−0.798137	−	0.602476i	$-0.794181\pi$
$947$	−49.1227	−1.59627	−0.798137	+	0.602476i	$0.794181\pi$
$948$	10.1217	0.328737
$949$	−29.1461	−0.946122
$950$	−2.34017	−0.0759252
$951$	4.34471	0.140887
$952$	0	0
$953$	−17.0556	−0.552485	−0.276242	−	0.961088i	$-0.589089\pi$
$953$	−17.0556	−0.552485	−0.276242	+	0.961088i	$0.589089\pi$
$954$	22.0989	0.715478
$955$	24.2823	0.785757
$956$	16.9483	0.548147
$957$	−4.99386	−0.161428
$958$	−4.66475	−0.150711
$959$	−9.51745	−0.307334
$960$	6.63809	0.214243
$961$	−14.2579	−0.459933
$962$	−30.0410	−0.968562
$963$	−34.2401	−1.10337
$964$	6.76487	0.217882
$965$	11.8576	0.381710
$966$	−29.7998	−0.958792
$967$	25.1955	0.810233	0.405117	−	0.914265i	$-0.367231\pi$
$967$	25.1955	0.810233	0.405117	+	0.914265i	$0.367231\pi$
$968$	−1.46308	−0.0470251
$969$	0	0
$970$	−17.7587	−0.570198
$971$	−1.67420	−0.0537277	−0.0268639	−	0.999639i	$-0.508552\pi$
$971$	−1.67420	−0.0537277	−0.0268639	+	0.999639i	$0.508552\pi$
$972$	34.4690	1.10560
$973$	−9.79380	−0.313975
$974$	−86.9842	−2.78715
$975$	1.41855	0.0454300
$976$	−25.4719	−0.815335
$977$	39.9109	1.27686	0.638432	−	0.769678i	$-0.279583\pi$
$977$	39.9109	1.27686	0.638432	+	0.769678i	$0.279583\pi$
$978$	−10.1750	−0.325361
$979$	−22.6803	−0.724867
$980$	−45.5380	−1.45466
$981$	22.0989	0.705563
$982$	4.89496	0.156204
$983$	5.46081	0.174173	0.0870864	−	0.996201i	$-0.472244\pi$
$983$	5.46081	0.174173	0.0870864	+	0.996201i	$0.472244\pi$
$984$	−4.64915	−0.148209
$985$	18.2557	0.581673
$986$	0	0
$987$	17.8576	0.568414
$988$	−7.68649	−0.244540
$989$	−17.5851	−0.559175
$990$	−18.6381	−0.592357
$991$	42.0749	1.33655	0.668276	−	0.743913i	$-0.267032\pi$
$991$	42.0749	1.33655	0.668276	+	0.743913i	$0.267032\pi$
$992$	31.0505	0.985854
$993$	5.43084	0.172342
$994$	43.0433	1.36525
$995$	3.72487	0.118086
$996$	−12.0267	−0.381079
$997$	−54.6681	−1.73135	−0.865677	−	0.500602i	$-0.833112\pi$
$997$	−54.6681	−1.73135	−0.865677	+	0.500602i	$0.833112\pi$
$998$	−92.3267	−2.92255
$999$	16.1978	0.512476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.a.j.1.3		3
5.4	even	2		7225.2.a.q.1.1		3
17.4	even	4		85.2.d.a.16.1	✓	6
17.13	even	4		85.2.d.a.16.2	yes	6
17.16	even	2		1445.2.a.k.1.3		3
51.38	odd	4		765.2.g.b.271.5		6
51.47	odd	4		765.2.g.b.271.6		6
68.47	odd	4		1360.2.c.f.1121.3		6
68.55	odd	4		1360.2.c.f.1121.4		6
85.4	even	4		425.2.d.c.101.6		6
85.13	odd	4		425.2.c.b.424.6		6
85.38	odd	4		425.2.c.a.424.6		6
85.47	odd	4		425.2.c.a.424.1		6
85.64	even	4		425.2.d.c.101.5		6
85.72	odd	4		425.2.c.b.424.1		6
85.84	even	2		7225.2.a.r.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.d.a.16.1	✓	6	17.4	even	4
85.2.d.a.16.2	yes	6	17.13	even	4
425.2.c.a.424.1		6	85.47	odd	4
425.2.c.a.424.6		6	85.38	odd	4
425.2.c.b.424.1		6	85.72	odd	4
425.2.c.b.424.6		6	85.13	odd	4
425.2.d.c.101.5		6	85.64	even	4
425.2.d.c.101.6		6	85.4	even	4
765.2.g.b.271.5		6	51.38	odd	4
765.2.g.b.271.6		6	51.47	odd	4
1360.2.c.f.1121.3		6	68.47	odd	4
1360.2.c.f.1121.4		6	68.55	odd	4
1445.2.a.j.1.3		3	1.1	even	1	trivial
1445.2.a.k.1.3		3	17.16	even	2
7225.2.a.q.1.1		3	5.4	even	2
7225.2.a.r.1.1		3	85.84	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)

\(f(q)\)	\(=\)	\(q+2.17009 q^{2} +0.539189 q^{3} +2.70928 q^{4} -1.00000 q^{5} +1.17009 q^{6} -4.87936 q^{7} +1.53919 q^{8} -2.70928 q^{9} -2.17009 q^{10} -3.17009 q^{11} +1.46081 q^{12} +2.63090 q^{13} -10.5886 q^{14} -0.539189 q^{15} -2.07838 q^{16} -5.87936 q^{18} -1.07838 q^{19} -2.70928 q^{20} -2.63090 q^{21} -6.87936 q^{22} +5.21953 q^{23} +0.829914 q^{24} +1.00000 q^{25} +5.70928 q^{26} -3.07838 q^{27} -13.2195 q^{28} +2.92162 q^{29} -1.17009 q^{30} -4.09171 q^{31} -7.58864 q^{32} -1.70928 q^{33} +4.87936 q^{35} -7.34017 q^{36} -5.26180 q^{37} -2.34017 q^{38} +1.41855 q^{39} -1.53919 q^{40} -5.60197 q^{41} -5.70928 q^{42} -3.36910 q^{43} -8.58864 q^{44} +2.70928 q^{45} +11.3268 q^{46} -6.78765 q^{47} -1.12064 q^{48} +16.8082 q^{49} +2.17009 q^{50} +7.12783 q^{52} -3.75872 q^{53} -6.68035 q^{54} +3.17009 q^{55} -7.51026 q^{56} -0.581449 q^{57} +6.34017 q^{58} +2.34017 q^{59} -1.46081 q^{60} +12.2557 q^{61} -8.87936 q^{62} +13.2195 q^{63} -12.3112 q^{64} -2.63090 q^{65} -3.70928 q^{66} +10.2062 q^{67} +2.81432 q^{69} +10.5886 q^{70} -4.06505 q^{71} -4.17009 q^{72} -11.0784 q^{73} -11.4186 q^{74} +0.539189 q^{75} -2.92162 q^{76} +15.4680 q^{77} +3.07838 q^{78} +6.92881 q^{79} +2.07838 q^{80} +6.46800 q^{81} -12.1568 q^{82} -8.23287 q^{83} -7.12783 q^{84} -7.31124 q^{86} +1.57531 q^{87} -4.87936 q^{88} +7.15449 q^{89} +5.87936 q^{90} -12.8371 q^{91} +14.1412 q^{92} -2.20620 q^{93} -14.7298 q^{94} +1.07838 q^{95} -4.09171 q^{96} +8.18342 q^{97} +36.4752 q^{98} +8.58864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} + 3 q^{8} - q^{9} - q^{10} - 4 q^{11} + 6 q^{12} + 4 q^{13} - 12 q^{14} - 3 q^{16} - 5 q^{18} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} + 8 q^{24}+ \cdots + 6 q^{99}+O(q^{100}) \) 3 * q + q^2 + q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 + 3 * q^8 - q^9 - q^10 - 4 * q^11 + 6 * q^12 + 4 * q^13 - 12 * q^14 - 3 * q^16 - 5 * q^18 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 + 8 * q^24 + 3 * q^25 + 10 * q^26 - 6 * q^27 - 16 * q^28 + 12 * q^29 + 2 * q^30 - 10 * q^31 - 3 * q^32 + 2 * q^33 + 2 * q^35 - 11 * q^36 - 8 * q^37 + 4 * q^38 - 10 * q^39 - 3 * q^40 + 2 * q^41 - 10 * q^42 - 14 * q^43 - 6 * q^44 + q^45 + 22 * q^46 - 10 * q^47 - 16 * q^48 + 7 * q^49 + q^50 + 14 * q^53 + 2 * q^54 + 4 * q^55 - 6 * q^56 - 16 * q^57 + 8 * q^58 - 4 * q^59 - 6 * q^60 - 6 * q^61 - 14 * q^62 + 16 * q^63 - 11 * q^64 - 4 * q^65 - 4 * q^66 + 6 * q^67 + 12 * q^70 - 8 * q^71 - 7 * q^72 - 30 * q^73 - 20 * q^74 - 12 * q^76 + 14 * q^77 + 6 * q^78 - 10 * q^79 + 3 * q^80 - 13 * q^81 - 30 * q^82 - 2 * q^83 + 4 * q^86 - 16 * q^87 - 2 * q^88 + 2 * q^89 + 5 * q^90 - 10 * q^91 + 22 * q^92 + 18 * q^93 - 4 * q^94 - 10 * q^96 + 20 * q^97 + 43 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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