LMFDB - Embedded newform 7595.2.a.bf.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7595,2,Mod(1,7595)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7595, 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("7595.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7595 = 5 \cdot 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7595.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:	$60.6463803352$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 1085)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	7595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44160 q^{2} +3.13328 q^{3} +3.96139 q^{4} +1.00000 q^{5} -7.65019 q^{6} -4.78892 q^{8} +6.81741 q^{9} +O(q^{10})$	\(q-2.44160 q^{2} +3.13328 q^{3} +3.96139 q^{4} +1.00000 q^{5} -7.65019 q^{6} -4.78892 q^{8} +6.81741 q^{9} -2.44160 q^{10} -4.63597 q^{11} +12.4121 q^{12} +1.08775 q^{13} +3.13328 q^{15} +3.76983 q^{16} +0.743650 q^{17} -16.6454 q^{18} -5.02179 q^{19} +3.96139 q^{20} +11.3192 q^{22} -7.70554 q^{23} -15.0050 q^{24} +1.00000 q^{25} -2.65584 q^{26} +11.9610 q^{27} -3.59212 q^{29} -7.65019 q^{30} -1.00000 q^{31} +0.373435 q^{32} -14.5258 q^{33} -1.81569 q^{34} +27.0064 q^{36} -10.0248 q^{37} +12.2612 q^{38} +3.40821 q^{39} -4.78892 q^{40} +8.57522 q^{41} +0.551184 q^{43} -18.3649 q^{44} +6.81741 q^{45} +18.8138 q^{46} +6.50147 q^{47} +11.8119 q^{48} -2.44160 q^{50} +2.33006 q^{51} +4.30899 q^{52} -5.84399 q^{53} -29.2040 q^{54} -4.63597 q^{55} -15.7347 q^{57} +8.77052 q^{58} +1.98184 q^{59} +12.4121 q^{60} -9.58016 q^{61} +2.44160 q^{62} -8.45144 q^{64} +1.08775 q^{65} +35.4660 q^{66} +3.07689 q^{67} +2.94589 q^{68} -24.1436 q^{69} +1.21839 q^{71} -32.6481 q^{72} -10.8543 q^{73} +24.4764 q^{74} +3.13328 q^{75} -19.8933 q^{76} -8.32147 q^{78} -14.0787 q^{79} +3.76983 q^{80} +17.0249 q^{81} -20.9372 q^{82} +11.3948 q^{83} +0.743650 q^{85} -1.34577 q^{86} -11.2551 q^{87} +22.2013 q^{88} +6.46297 q^{89} -16.6454 q^{90} -30.5246 q^{92} -3.13328 q^{93} -15.8740 q^{94} -5.02179 q^{95} +1.17007 q^{96} +7.82921 q^{97} -31.6053 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * 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 $

$2$	−2.44160	−1.72647	−0.863235	−	0.504803i	$-0.831565\pi$
$2$	−2.44160	−1.72647	−0.863235	+	0.504803i	$0.831565\pi$
$3$	3.13328	1.80900	0.904499	−	0.426476i	$-0.140245\pi$
$3$	3.13328	1.80900	0.904499	+	0.426476i	$0.140245\pi$
$4$	3.96139	1.98070
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−7.65019	−3.12318
$7$	0	0
$7$	0	0
$8$	−4.78892	−1.69314
$9$	6.81741	2.27247
$10$	−2.44160	−0.772100
$11$	−4.63597	−1.39780	−0.698898	−	0.715221i	$-0.746326\pi$
$11$	−4.63597	−1.39780	−0.698898	+	0.715221i	$0.746326\pi$
$12$	12.4121	3.58307
$13$	1.08775	0.301687	0.150843	−	0.988558i	$-0.451801\pi$
$13$	1.08775	0.301687	0.150843	+	0.988558i	$0.451801\pi$
$14$	0	0
$15$	3.13328	0.809008
$16$	3.76983	0.942459
$17$	0.743650	0.180362	0.0901808	−	0.995925i	$-0.471256\pi$
$17$	0.743650	0.180362	0.0901808	+	0.995925i	$0.471256\pi$
$18$	−16.6454	−3.92335
$19$	−5.02179	−1.15208	−0.576039	−	0.817422i	$-0.695402\pi$
$19$	−5.02179	−1.15208	−0.576039	+	0.817422i	$0.695402\pi$
$20$	3.96139	0.885794
$21$	0	0
$22$	11.3192	2.41325
$23$	−7.70554	−1.60672	−0.803358	−	0.595497i	$-0.796955\pi$
$23$	−7.70554	−1.60672	−0.803358	+	0.595497i	$0.796955\pi$
$24$	−15.0050	−3.06289
$25$	1.00000	0.200000
$26$	−2.65584	−0.520853
$27$	11.9610	2.30190
$28$	0	0
$29$	−3.59212	−0.667041	−0.333520	−	0.942743i	$-0.608237\pi$
$29$	−3.59212	−0.667041	−0.333520	+	0.942743i	$0.608237\pi$
$30$	−7.65019	−1.39673
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	0.373435	0.0660145
$33$	−14.5258	−2.52861
$34$	−1.81569	−0.311389
$35$	0	0
$36$	27.0064	4.50107
$37$	−10.0248	−1.64806	−0.824031	−	0.566544i	$-0.808280\pi$
$37$	−10.0248	−1.64806	−0.824031	+	0.566544i	$0.808280\pi$
$38$	12.2612	1.98903
$39$	3.40821	0.545750
$40$	−4.78892	−0.757195
$41$	8.57522	1.33922	0.669612	−	0.742711i	$-0.266460\pi$
$41$	8.57522	1.33922	0.669612	+	0.742711i	$0.266460\pi$
$42$	0	0
$43$	0.551184	0.0840548	0.0420274	−	0.999116i	$-0.486618\pi$
$43$	0.551184	0.0840548	0.0420274	+	0.999116i	$0.486618\pi$
$44$	−18.3649	−2.76861
$45$	6.81741	1.01628
$46$	18.8138	2.77394
$47$	6.50147	0.948337	0.474169	−	0.880434i	$-0.342749\pi$
$47$	6.50147	0.948337	0.474169	+	0.880434i	$0.342749\pi$
$48$	11.8119	1.70491
$49$	0	0
$50$	−2.44160	−0.345294
$51$	2.33006	0.326274
$52$	4.30899	0.597549
$53$	−5.84399	−0.802734	−0.401367	−	0.915917i	$-0.631465\pi$
$53$	−5.84399	−0.802734	−0.401367	+	0.915917i	$0.631465\pi$
$54$	−29.2040	−3.97415
$55$	−4.63597	−0.625114
$56$	0	0
$57$	−15.7347	−2.08411
$58$	8.77052	1.15163
$59$	1.98184	0.258013	0.129007	−	0.991644i	$-0.458821\pi$
$59$	1.98184	0.258013	0.129007	+	0.991644i	$0.458821\pi$
$60$	12.4121	1.60240
$61$	−9.58016	−1.22661	−0.613307	−	0.789845i	$-0.710161\pi$
$61$	−9.58016	−1.22661	−0.613307	+	0.789845i	$0.710161\pi$
$62$	2.44160	0.310083
$63$	0	0
$64$	−8.45144	−1.05643
$65$	1.08775	0.134918
$66$	35.4660	4.36557
$67$	3.07689	0.375902	0.187951	−	0.982178i	$-0.439815\pi$
$67$	3.07689	0.375902	0.187951	+	0.982178i	$0.439815\pi$
$68$	2.94589	0.357241
$69$	−24.1436	−2.90654
$70$	0	0
$71$	1.21839	0.144596	0.0722979	−	0.997383i	$-0.476967\pi$
$71$	1.21839	0.144596	0.0722979	+	0.997383i	$0.476967\pi$
$72$	−32.6481	−3.84761
$73$	−10.8543	−1.27040	−0.635202	−	0.772346i	$-0.719083\pi$
$73$	−10.8543	−1.27040	−0.635202	+	0.772346i	$0.719083\pi$
$74$	24.4764	2.84533
$75$	3.13328	0.361799
$76$	−19.8933	−2.28192
$77$	0	0
$78$	−8.32147	−0.942221
$79$	−14.0787	−1.58398	−0.791989	−	0.610535i	$-0.790954\pi$
$79$	−14.0787	−1.58398	−0.791989	+	0.610535i	$0.790954\pi$
$80$	3.76983	0.421480
$81$	17.0249	1.89165
$82$	−20.9372	−2.31213
$83$	11.3948	1.25075	0.625373	−	0.780326i	$-0.284947\pi$
$83$	11.3948	1.25075	0.625373	+	0.780326i	$0.284947\pi$
$84$	0	0
$85$	0.743650	0.0806601
$86$	−1.34577	−0.145118
$87$	−11.2551	−1.20668
$88$	22.2013	2.36667
$89$	6.46297	0.685074	0.342537	−	0.939504i	$-0.388714\pi$
$89$	6.46297	0.685074	0.342537	+	0.939504i	$0.388714\pi$
$90$	−16.6454	−1.75458
$91$	0	0
$92$	−30.5246	−3.18241
$93$	−3.13328	−0.324906
$94$	−15.8740	−1.63727
$95$	−5.02179	−0.515225
$96$	1.17007	0.119420
$97$	7.82921	0.794936	0.397468	−	0.917616i	$-0.369889\pi$
$97$	7.82921	0.794936	0.397468	+	0.917616i	$0.369889\pi$
$98$	0	0
$99$	−31.6053	−3.17645
$100$	3.96139	0.396139
$101$	−7.43005	−0.739318	−0.369659	−	0.929168i	$-0.620525\pi$
$101$	−7.43005	−0.739318	−0.369659	+	0.929168i	$0.620525\pi$
$102$	−5.68906	−0.563301
$103$	2.78690	0.274601	0.137300	−	0.990529i	$-0.456157\pi$
$103$	2.78690	0.274601	0.137300	+	0.990529i	$0.456157\pi$
$104$	−5.20914	−0.510798
$105$	0	0
$106$	14.2687	1.38590
$107$	1.07202	0.103636	0.0518178	−	0.998657i	$-0.483498\pi$
$107$	1.07202	0.103636	0.0518178	+	0.998657i	$0.483498\pi$
$108$	47.3822	4.55936
$109$	−14.7944	−1.41704	−0.708521	−	0.705689i	$-0.750637\pi$
$109$	−14.7944	−1.41704	−0.708521	+	0.705689i	$0.750637\pi$
$110$	11.3192	1.07924
$111$	−31.4104	−2.98134
$112$	0	0
$113$	14.5459	1.36836	0.684181	−	0.729313i	$-0.260160\pi$
$113$	14.5459	1.36836	0.684181	+	0.729313i	$0.260160\pi$
$114$	38.4177	3.59814
$115$	−7.70554	−0.718545
$116$	−14.2298	−1.32120
$117$	7.41562	0.685574
$118$	−4.83885	−0.445452
$119$	0	0
$120$	−15.0050	−1.36976
$121$	10.4922	0.953836
$122$	23.3909	2.11771
$123$	26.8685	2.42265
$124$	−3.96139	−0.355743
$125$	1.00000	0.0894427
$126$	0	0
$127$	−21.8028	−1.93468	−0.967342	−	0.253474i	$-0.918427\pi$
$127$	−21.8028	−1.93468	−0.967342	+	0.253474i	$0.918427\pi$
$128$	19.8881	1.75788
$129$	1.72701	0.152055
$130$	−2.65584	−0.232932
$131$	−13.1156	−1.14592	−0.572960	−	0.819584i	$-0.694205\pi$
$131$	−13.1156	−1.14592	−0.572960	+	0.819584i	$0.694205\pi$
$132$	−57.5422	−5.00841
$133$	0	0
$134$	−7.51252	−0.648983
$135$	11.9610	1.02944
$136$	−3.56128	−0.305377
$137$	−4.79688	−0.409825	−0.204913	−	0.978780i	$-0.565691\pi$
$137$	−4.79688	−0.409825	−0.204913	+	0.978780i	$0.565691\pi$
$138$	58.9488	5.01806
$139$	−8.06789	−0.684309	−0.342155	−	0.939644i	$-0.611157\pi$
$139$	−8.06789	−0.684309	−0.342155	+	0.939644i	$0.611157\pi$
$140$	0	0
$141$	20.3709	1.71554
$142$	−2.97481	−0.249640
$143$	−5.04276	−0.421697
$144$	25.7005	2.14171
$145$	−3.59212	−0.298310
$146$	26.5019	2.19331
$147$	0	0
$148$	−39.7120	−3.26431
$149$	17.3609	1.42226	0.711130	−	0.703060i	$-0.248184\pi$
$149$	17.3609	1.42226	0.711130	+	0.703060i	$0.248184\pi$
$150$	−7.65019	−0.624636
$151$	18.2159	1.48239	0.741193	−	0.671292i	$-0.234260\pi$
$151$	18.2159	1.48239	0.741193	+	0.671292i	$0.234260\pi$
$152$	24.0490	1.95063
$153$	5.06977	0.409866
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	13.5013	1.08097
$157$	−4.75032	−0.379117	−0.189558	−	0.981869i	$-0.560706\pi$
$157$	−4.75032	−0.379117	−0.189558	+	0.981869i	$0.560706\pi$
$158$	34.3745	2.73469
$159$	−18.3108	−1.45214
$160$	0.373435	0.0295226
$161$	0	0
$162$	−41.5679	−3.26588
$163$	−7.45852	−0.584196	−0.292098	−	0.956388i	$-0.594353\pi$
$163$	−7.45852	−0.584196	−0.292098	+	0.956388i	$0.594353\pi$
$164$	33.9698	2.65260
$165$	−14.5258	−1.13083
$166$	−27.8216	−2.15937
$167$	0.119878	0.00927648	0.00463824	−	0.999989i	$-0.498524\pi$
$167$	0.119878	0.00927648	0.00463824	+	0.999989i	$0.498524\pi$
$168$	0	0
$169$	−11.8168	−0.908985
$170$	−1.81569	−0.139257
$171$	−34.2356	−2.61806
$172$	2.18346	0.166487
$173$	−1.58661	−0.120628	−0.0603139	−	0.998179i	$-0.519210\pi$
$173$	−1.58661	−0.120628	−0.0603139	+	0.998179i	$0.519210\pi$
$174$	27.4804	2.08329
$175$	0	0
$176$	−17.4768	−1.31737
$177$	6.20965	0.466746
$178$	−15.7800	−1.18276
$179$	5.68258	0.424736	0.212368	−	0.977190i	$-0.431883\pi$
$179$	5.68258	0.424736	0.212368	+	0.977190i	$0.431883\pi$
$180$	27.0064	2.01294
$181$	−4.54925	−0.338143	−0.169072	−	0.985604i	$-0.554077\pi$
$181$	−4.54925	−0.338143	−0.169072	+	0.985604i	$0.554077\pi$
$182$	0	0
$183$	−30.0173	−2.21894
$184$	36.9012	2.72039
$185$	−10.0248	−0.737036
$186$	7.65019	0.560939
$187$	−3.44754	−0.252109
$188$	25.7549	1.87837
$189$	0	0
$190$	12.2612	0.889520
$191$	−15.3426	−1.11015	−0.555075	−	0.831800i	$-0.687310\pi$
$191$	−15.3426	−1.11015	−0.555075	+	0.831800i	$0.687310\pi$
$192$	−26.4807	−1.91108
$193$	−18.6170	−1.34008	−0.670041	−	0.742324i	$-0.733723\pi$
$193$	−18.6170	−1.34008	−0.670041	+	0.742324i	$0.733723\pi$
$194$	−19.1158	−1.37243
$195$	3.40821	0.244067
$196$	0	0
$197$	−16.6937	−1.18938	−0.594688	−	0.803956i	$-0.702725\pi$
$197$	−16.6937	−1.18938	−0.594688	+	0.803956i	$0.702725\pi$
$198$	77.1674	5.48405
$199$	24.0616	1.70568	0.852842	−	0.522168i	$-0.174877\pi$
$199$	24.0616	1.70568	0.852842	+	0.522168i	$0.174877\pi$
$200$	−4.78892	−0.338628
$201$	9.64074	0.680006
$202$	18.1412	1.27641
$203$	0	0
$204$	9.23027	0.646248
$205$	8.57522	0.598919
$206$	−6.80447	−0.474090
$207$	−52.5318	−3.65122
$208$	4.10063	0.284327
$209$	23.2809	1.61037
$210$	0	0
$211$	−20.9940	−1.44529	−0.722643	−	0.691221i	$-0.757073\pi$
$211$	−20.9940	−1.44529	−0.722643	+	0.691221i	$0.757073\pi$
$212$	−23.1503	−1.58997
$213$	3.81754	0.261573
$214$	−2.61743	−0.178924
$215$	0.551184	0.0375904
$216$	−57.2804	−3.89743
$217$	0	0
$218$	36.1219	2.44648
$219$	−34.0096	−2.29816
$220$	−18.3649	−1.23816
$221$	0.808903	0.0544127
$222$	76.6914	5.14719
$223$	6.70277	0.448851	0.224425	−	0.974491i	$-0.427949\pi$
$223$	6.70277	0.448851	0.224425	+	0.974491i	$0.427949\pi$
$224$	0	0
$225$	6.81741	0.454494
$226$	−35.5152	−2.36243
$227$	18.0542	1.19830	0.599149	−	0.800637i	$-0.295506\pi$
$227$	18.0542	1.19830	0.599149	+	0.800637i	$0.295506\pi$
$228$	−62.3311	−4.12798
$229$	−3.59529	−0.237583	−0.118792	−	0.992919i	$-0.537902\pi$
$229$	−3.59529	−0.237583	−0.118792	+	0.992919i	$0.537902\pi$
$230$	18.8138	1.24055
$231$	0	0
$232$	17.2024	1.12939
$233$	−11.5698	−0.757965	−0.378982	−	0.925404i	$-0.623726\pi$
$233$	−11.5698	−0.757965	−0.378982	+	0.925404i	$0.623726\pi$
$234$	−18.1060	−1.18362
$235$	6.50147	0.424109
$236$	7.85084	0.511046
$237$	−44.1125	−2.86541
$238$	0	0
$239$	−24.2920	−1.57132	−0.785661	−	0.618658i	$-0.787677\pi$
$239$	−24.2920	−1.57132	−0.785661	+	0.618658i	$0.787677\pi$
$240$	11.8119	0.762457
$241$	30.5347	1.96691	0.983456	−	0.181150i	$-0.0579818\pi$
$241$	30.5347	1.96691	0.983456	+	0.181150i	$0.0579818\pi$
$242$	−25.6177	−1.64677
$243$	17.4606	1.12010
$244$	−37.9507	−2.42955
$245$	0	0
$246$	−65.6021	−4.18264
$247$	−5.46244	−0.347567
$248$	4.78892	0.304097
$249$	35.7031	2.26259
$250$	−2.44160	−0.154420
$251$	13.2373	0.835532	0.417766	−	0.908555i	$-0.362813\pi$
$251$	13.2373	0.835532	0.417766	+	0.908555i	$0.362813\pi$
$252$	0	0
$253$	35.7226	2.24586
$254$	53.2336	3.34017
$255$	2.33006	0.145914
$256$	−31.6559	−1.97850
$257$	−20.3712	−1.27072	−0.635359	−	0.772217i	$-0.719148\pi$
$257$	−20.3712	−1.27072	−0.635359	+	0.772217i	$0.719148\pi$
$258$	−4.21666	−0.262518
$259$	0	0
$260$	4.30899	0.267232
$261$	−24.4890	−1.51583
$262$	32.0231	1.97839
$263$	−22.9708	−1.41644	−0.708221	−	0.705991i	$-0.750502\pi$
$263$	−22.9708	−1.41644	−0.708221	+	0.705991i	$0.750502\pi$
$264$	69.5628	4.28129
$265$	−5.84399	−0.358994
$266$	0	0
$267$	20.2503	1.23930
$268$	12.1888	0.744547
$269$	−12.8421	−0.782999	−0.391499	−	0.920178i	$-0.628043\pi$
$269$	−12.8421	−0.782999	−0.391499	+	0.920178i	$0.628043\pi$
$270$	−29.2040	−1.77730
$271$	24.4856	1.48740	0.743698	−	0.668516i	$-0.233070\pi$
$271$	24.4856	1.48740	0.743698	+	0.668516i	$0.233070\pi$
$272$	2.80344	0.169983
$273$	0	0
$274$	11.7120	0.707551
$275$	−4.63597	−0.279559
$276$	−95.6421	−5.75698
$277$	4.63670	0.278592	0.139296	−	0.990251i	$-0.455516\pi$
$277$	4.63670	0.278592	0.139296	+	0.990251i	$0.455516\pi$
$278$	19.6985	1.18144
$279$	−6.81741	−0.408148
$280$	0	0
$281$	−23.4463	−1.39869	−0.699345	−	0.714784i	$-0.746525\pi$
$281$	−23.4463	−1.39869	−0.699345	+	0.714784i	$0.746525\pi$
$282$	−49.7375	−2.96183
$283$	13.9668	0.830241	0.415120	−	0.909766i	$-0.363739\pi$
$283$	13.9668	0.830241	0.415120	+	0.909766i	$0.363739\pi$
$284$	4.82650	0.286400
$285$	−15.7347	−0.932041
$286$	12.3124	0.728046
$287$	0	0
$288$	2.54586	0.150016
$289$	−16.4470	−0.967470
$290$	8.77052	0.515022
$291$	24.5311	1.43804
$292$	−42.9983	−2.51628
$293$	−11.5851	−0.676807	−0.338403	−	0.941001i	$-0.609887\pi$
$293$	−11.5851	−0.676807	−0.338403	+	0.941001i	$0.609887\pi$
$294$	0	0
$295$	1.98184	0.115387
$296$	48.0079	2.79040
$297$	−55.4509	−3.21758
$298$	−42.3883	−2.45549
$299$	−8.38168	−0.484725
$300$	12.4121	0.716615
$301$	0	0
$302$	−44.4758	−2.55929
$303$	−23.2804	−1.33742
$304$	−18.9313	−1.08579
$305$	−9.58016	−0.548558
$306$	−12.3783	−0.707622
$307$	−19.6460	−1.12126	−0.560629	−	0.828067i	$-0.689440\pi$
$307$	−19.6460	−1.12126	−0.560629	+	0.828067i	$0.689440\pi$
$308$	0	0
$309$	8.73211	0.496752
$310$	2.44160	0.138673
$311$	12.2159	0.692698	0.346349	−	0.938106i	$-0.387421\pi$
$311$	12.2159	0.692698	0.346349	+	0.938106i	$0.387421\pi$
$312$	−16.3217	−0.924032
$313$	12.4881	0.705868	0.352934	−	0.935648i	$-0.385184\pi$
$313$	12.4881	0.705868	0.352934	+	0.935648i	$0.385184\pi$
$314$	11.5984	0.654533
$315$	0	0
$316$	−55.7713	−3.13738
$317$	−18.4822	−1.03806	−0.519031	−	0.854755i	$-0.673707\pi$
$317$	−18.4822	−1.03806	−0.519031	+	0.854755i	$0.673707\pi$
$318$	44.7077	2.50708
$319$	16.6530	0.932387
$320$	−8.45144	−0.472450
$321$	3.35892	0.187477
$322$	0	0
$323$	−3.73445	−0.207791
$324$	67.4422	3.74679
$325$	1.08775	0.0603373
$326$	18.2107	1.00860
$327$	−46.3548	−2.56343
$328$	−41.0661	−2.26749
$329$	0	0
$330$	35.4660	1.95234
$331$	−7.78738	−0.428033	−0.214016	−	0.976830i	$-0.568655\pi$
$331$	−7.78738	−0.428033	−0.214016	+	0.976830i	$0.568655\pi$
$332$	45.1394	2.47735
$333$	−68.3430	−3.74518
$334$	−0.292695	−0.0160155
$335$	3.07689	0.168108
$336$	0	0
$337$	17.5936	0.958385	0.479192	−	0.877710i	$-0.340930\pi$
$337$	17.5936	0.958385	0.479192	+	0.877710i	$0.340930\pi$
$338$	28.8519	1.56933
$339$	45.5762	2.47536
$340$	2.94589	0.159763
$341$	4.63597	0.251052
$342$	83.5896	4.52001
$343$	0	0
$344$	−2.63958	−0.142317
$345$	−24.1436	−1.29985
$346$	3.87386	0.208260
$347$	−15.1100	−0.811148	−0.405574	−	0.914062i	$-0.632928\pi$
$347$	−15.1100	−0.811148	−0.405574	+	0.914062i	$0.632928\pi$
$348$	−44.5859	−2.39006
$349$	−31.1397	−1.66687	−0.833434	−	0.552619i	$-0.813628\pi$
$349$	−31.1397	−1.66687	−0.833434	+	0.552619i	$0.813628\pi$
$350$	0	0
$351$	13.0106	0.694452
$352$	−1.73123	−0.0922749
$353$	−19.4708	−1.03633	−0.518164	−	0.855281i	$-0.673384\pi$
$353$	−19.4708	−1.03633	−0.518164	+	0.855281i	$0.673384\pi$
$354$	−15.1614	−0.805822
$355$	1.21839	0.0646652
$356$	25.6024	1.35692
$357$	0	0
$358$	−13.8746	−0.733293
$359$	−12.5595	−0.662864	−0.331432	−	0.943479i	$-0.607532\pi$
$359$	−12.5595	−0.662864	−0.331432	+	0.943479i	$0.607532\pi$
$360$	−32.6481	−1.72070
$361$	6.21839	0.327284
$362$	11.1074	0.583793
$363$	32.8749	1.72549
$364$	0	0
$365$	−10.8543	−0.568142
$366$	73.2900	3.83093
$367$	−11.4574	−0.598073	−0.299037	−	0.954242i	$-0.596665\pi$
$367$	−11.4574	−0.598073	−0.299037	+	0.954242i	$0.596665\pi$
$368$	−29.0486	−1.51426
$369$	58.4608	3.04335
$370$	24.4764	1.27247
$371$	0	0
$372$	−12.4121	−0.643539
$373$	−25.7765	−1.33465	−0.667327	−	0.744765i	$-0.732562\pi$
$373$	−25.7765	−1.33465	−0.667327	+	0.744765i	$0.732562\pi$
$374$	8.41749	0.435258
$375$	3.13328	0.161802
$376$	−31.1350	−1.60567
$377$	−3.90732	−0.201237
$378$	0	0
$379$	13.9194	0.714994	0.357497	−	0.933914i	$-0.383630\pi$
$379$	13.9194	0.714994	0.357497	+	0.933914i	$0.383630\pi$
$380$	−19.8933	−1.02050
$381$	−68.3141	−3.49984
$382$	37.4604	1.91664
$383$	11.2351	0.574088	0.287044	−	0.957917i	$-0.407327\pi$
$383$	11.2351	0.574088	0.287044	+	0.957917i	$0.407327\pi$
$384$	62.3150	3.18000
$385$	0	0
$386$	45.4552	2.31361
$387$	3.75765	0.191012
$388$	31.0146	1.57453
$389$	21.0916	1.06938	0.534692	−	0.845047i	$-0.320428\pi$
$389$	21.0916	1.06938	0.534692	+	0.845047i	$0.320428\pi$
$390$	−8.32147	−0.421374
$391$	−5.73022	−0.289790
$392$	0	0
$393$	−41.0949	−2.07297
$394$	40.7593	2.05342
$395$	−14.0787	−0.708377
$396$	−125.201	−6.29159
$397$	−8.30413	−0.416773	−0.208386	−	0.978047i	$-0.566821\pi$
$397$	−8.30413	−0.416773	−0.208386	+	0.978047i	$0.566821\pi$
$398$	−58.7488	−2.94481
$399$	0	0
$400$	3.76983	0.188492
$401$	10.1814	0.508433	0.254216	−	0.967147i	$-0.418182\pi$
$401$	10.1814	0.508433	0.254216	+	0.967147i	$0.418182\pi$
$402$	−23.5388	−1.17401
$403$	−1.08775	−0.0541845
$404$	−29.4333	−1.46436
$405$	17.0249	0.845974
$406$	0	0
$407$	46.4745	2.30366
$408$	−11.1585	−0.552427
$409$	19.5976	0.969037	0.484518	−	0.874781i	$-0.338995\pi$
$409$	19.5976	0.969037	0.484518	+	0.874781i	$0.338995\pi$
$410$	−20.9372	−1.03402
$411$	−15.0299	−0.741373
$412$	11.0400	0.543901
$413$	0	0
$414$	128.262	6.30371
$415$	11.3948	0.559350
$416$	0.406202	0.0199157
$417$	−25.2789	−1.23791
$418$	−56.8425	−2.78026
$419$	36.4938	1.78284	0.891419	−	0.453180i	$-0.149710\pi$
$419$	36.4938	1.78284	0.891419	+	0.453180i	$0.149710\pi$
$420$	0	0
$421$	4.86436	0.237074	0.118537	−	0.992950i	$-0.462180\pi$
$421$	4.86436	0.237074	0.118537	+	0.992950i	$0.462180\pi$
$422$	51.2589	2.49524
$423$	44.3232	2.15507
$424$	27.9864	1.35914
$425$	0.743650	0.0360723
$426$	−9.32089	−0.451598
$427$	0	0
$428$	4.24667	0.205271
$429$	−15.8004	−0.762848
$430$	−1.34577	−0.0648987
$431$	3.84806	0.185355	0.0926773	−	0.995696i	$-0.470458\pi$
$431$	3.84806	0.185355	0.0926773	+	0.995696i	$0.470458\pi$
$432$	45.0910	2.16944
$433$	−19.7446	−0.948865	−0.474433	−	0.880292i	$-0.657347\pi$
$433$	−19.7446	−0.948865	−0.474433	+	0.880292i	$0.657347\pi$
$434$	0	0
$435$	−11.2551	−0.539641
$436$	−58.6062	−2.80673
$437$	38.6956	1.85106
$438$	83.0378	3.96770
$439$	28.9950	1.38386	0.691928	−	0.721967i	$-0.256762\pi$
$439$	28.9950	1.38386	0.691928	+	0.721967i	$0.256762\pi$
$440$	22.2013	1.05841
$441$	0	0
$442$	−1.97501	−0.0939418
$443$	23.9266	1.13679	0.568395	−	0.822756i	$-0.307565\pi$
$443$	23.9266	1.13679	0.568395	+	0.822756i	$0.307565\pi$
$444$	−124.429	−5.90513
$445$	6.46297	0.306374
$446$	−16.3655	−0.774927
$447$	54.3965	2.57286
$448$	0	0
$449$	−6.11180	−0.288434	−0.144217	−	0.989546i	$-0.546066\pi$
$449$	−6.11180	−0.288434	−0.144217	+	0.989546i	$0.546066\pi$
$450$	−16.6454	−0.784670
$451$	−39.7544	−1.87196
$452$	57.6219	2.71031
$453$	57.0753	2.68163
$454$	−44.0810	−2.06883
$455$	0	0
$456$	75.3521	3.52868
$457$	−19.0103	−0.889266	−0.444633	−	0.895713i	$-0.646666\pi$
$457$	−19.0103	−0.889266	−0.444633	+	0.895713i	$0.646666\pi$
$458$	8.77824	0.410180
$459$	8.89480	0.415174
$460$	−30.5246	−1.42322
$461$	12.9256	0.602005	0.301002	−	0.953623i	$-0.402679\pi$
$461$	12.9256	0.602005	0.301002	+	0.953623i	$0.402679\pi$
$462$	0	0
$463$	37.0401	1.72140	0.860699	−	0.509115i	$-0.170027\pi$
$463$	37.0401	1.72140	0.860699	+	0.509115i	$0.170027\pi$
$464$	−13.5417	−0.628658
$465$	−3.13328	−0.145302
$466$	28.2488	1.30860
$467$	29.4216	1.36147	0.680735	−	0.732530i	$-0.261661\pi$
$467$	29.4216	1.36147	0.680735	+	0.732530i	$0.261661\pi$
$468$	29.3762	1.35791
$469$	0	0
$470$	−15.8740	−0.732211
$471$	−14.8841	−0.685821
$472$	−9.49088	−0.436853
$473$	−2.55527	−0.117492
$474$	107.705	4.94705
$475$	−5.02179	−0.230416
$476$	0	0
$477$	−39.8409	−1.82419
$478$	59.3113	2.71284
$479$	37.2293	1.70105	0.850524	−	0.525936i	$-0.176285\pi$
$479$	37.2293	1.70105	0.850524	+	0.525936i	$0.176285\pi$
$480$	1.17007	0.0534063
$481$	−10.9044	−0.497199
$482$	−74.5533	−3.39581
$483$	0	0
$484$	41.5637	1.88926
$485$	7.82921	0.355506
$486$	−42.6318	−1.93382
$487$	−18.7987	−0.851852	−0.425926	−	0.904758i	$-0.640052\pi$
$487$	−18.7987	−0.851852	−0.425926	+	0.904758i	$0.640052\pi$
$488$	45.8786	2.07683
$489$	−23.3696	−1.05681
$490$	0	0
$491$	13.6021	0.613855	0.306928	−	0.951733i	$-0.400699\pi$
$491$	13.6021	0.613855	0.306928	+	0.951733i	$0.400699\pi$
$492$	106.437	4.79854
$493$	−2.67128	−0.120308
$494$	13.3371	0.600063
$495$	−31.6053	−1.42055
$496$	−3.76983	−0.169271
$497$	0	0
$498$	−87.1726	−3.90630
$499$	−16.4669	−0.737158	−0.368579	−	0.929597i	$-0.620156\pi$
$499$	−16.4669	−0.737158	−0.368579	+	0.929597i	$0.620156\pi$
$500$	3.96139	0.177159
$501$	0.375612	0.0167811
$502$	−32.3202	−1.44252
$503$	26.9925	1.20354	0.601768	−	0.798671i	$-0.294463\pi$
$503$	26.9925	1.20354	0.601768	+	0.798671i	$0.294463\pi$
$504$	0	0
$505$	−7.43005	−0.330633
$506$	−87.2202	−3.87741
$507$	−37.0253	−1.64435
$508$	−86.3694	−3.83202
$509$	4.57806	0.202919	0.101459	−	0.994840i	$-0.467649\pi$
$509$	4.57806	0.202919	0.101459	+	0.994840i	$0.467649\pi$
$510$	−5.68906	−0.251916
$511$	0	0
$512$	37.5147	1.65793
$513$	−60.0657	−2.65197
$514$	49.7382	2.19386
$515$	2.78690	0.122805
$516$	6.84137	0.301174
$517$	−30.1406	−1.32558
$518$	0	0
$519$	−4.97129	−0.218215
$520$	−5.20914	−0.228436
$521$	17.3092	0.758328	0.379164	−	0.925329i	$-0.376212\pi$
$521$	17.3092	0.758328	0.379164	+	0.925329i	$0.376212\pi$
$522$	59.7922	2.61704
$523$	−25.5525	−1.11733	−0.558666	−	0.829393i	$-0.688687\pi$
$523$	−25.5525	−1.11733	−0.558666	+	0.829393i	$0.688687\pi$
$524$	−51.9562	−2.26972
$525$	0	0
$526$	56.0855	2.44544
$527$	−0.743650	−0.0323939
$528$	−54.7597	−2.38311
$529$	36.3753	1.58154
$530$	14.2687	0.619791
$531$	13.5110	0.586328
$532$	0	0
$533$	9.32767	0.404026
$534$	−49.4430	−2.13961
$535$	1.07202	0.0463473
$536$	−14.7350	−0.636455
$537$	17.8051	0.768346
$538$	31.3553	1.35182
$539$	0	0
$540$	47.3822	2.03901
$541$	39.1932	1.68505	0.842524	−	0.538659i	$-0.181069\pi$
$541$	39.1932	1.68505	0.842524	+	0.538659i	$0.181069\pi$
$542$	−59.7840	−2.56794
$543$	−14.2540	−0.611700
$544$	0.277705	0.0119065
$545$	−14.7944	−0.633721
$546$	0	0
$547$	−2.44091	−0.104366	−0.0521829	−	0.998638i	$-0.516618\pi$
$547$	−2.44091	−0.104366	−0.0521829	+	0.998638i	$0.516618\pi$
$548$	−19.0023	−0.811739
$549$	−65.3119	−2.78744
$550$	11.3192	0.482651
$551$	18.0389	0.768483
$552$	115.622	4.92119
$553$	0	0
$554$	−11.3209	−0.480981
$555$	−31.4104	−1.33330
$556$	−31.9601	−1.35541
$557$	38.8067	1.64429	0.822147	−	0.569275i	$-0.192776\pi$
$557$	38.8067	1.64429	0.822147	+	0.569275i	$0.192776\pi$
$558$	16.6454	0.704655
$559$	0.599549	0.0253582
$560$	0	0
$561$	−10.8021	−0.456064
$562$	57.2464	2.41480
$563$	8.71114	0.367131	0.183565	−	0.983008i	$-0.441236\pi$
$563$	8.71114	0.367131	0.183565	+	0.983008i	$0.441236\pi$
$564$	80.6971	3.39796
$565$	14.5459	0.611950
$566$	−34.1013	−1.43339
$567$	0	0
$568$	−5.83476	−0.244821
$569$	−1.18351	−0.0496153	−0.0248076	−	0.999692i	$-0.507897\pi$
$569$	−1.18351	−0.0496153	−0.0248076	+	0.999692i	$0.507897\pi$
$570$	38.4177	1.60914
$571$	−16.6507	−0.696809	−0.348404	−	0.937344i	$-0.613276\pi$
$571$	−16.6507	−0.696809	−0.348404	+	0.937344i	$0.613276\pi$
$572$	−19.9763	−0.835253
$573$	−48.0725	−2.00826
$574$	0	0
$575$	−7.70554	−0.321343
$576$	−57.6170	−2.40071
$577$	−18.0179	−0.750096	−0.375048	−	0.927005i	$-0.622374\pi$
$577$	−18.0179	−0.750096	−0.375048	+	0.927005i	$0.622374\pi$
$578$	40.1569	1.67031
$579$	−58.3322	−2.42420
$580$	−14.2298	−0.590861
$581$	0	0
$582$	−59.8950	−2.48273
$583$	27.0926	1.12206
$584$	51.9806	2.15097
$585$	7.41562	0.306598
$586$	28.2860	1.16849
$587$	18.4562	0.761769	0.380885	−	0.924623i	$-0.375619\pi$
$587$	18.4562	0.761769	0.380885	+	0.924623i	$0.375619\pi$
$588$	0	0
$589$	5.02179	0.206919
$590$	−4.83885	−0.199212
$591$	−52.3060	−2.15158
$592$	−37.7917	−1.55323
$593$	25.5224	1.04808	0.524040	−	0.851694i	$-0.324424\pi$
$593$	25.5224	1.04808	0.524040	+	0.851694i	$0.324424\pi$
$594$	135.389	5.55506
$595$	0	0
$596$	68.7733	2.81706
$597$	75.3918	3.08558
$598$	20.4647	0.836862
$599$	20.3656	0.832118	0.416059	−	0.909338i	$-0.363411\pi$
$599$	20.3656	0.832118	0.416059	+	0.909338i	$0.363411\pi$
$600$	−15.0050	−0.612577
$601$	8.04905	0.328327	0.164164	−	0.986433i	$-0.447507\pi$
$601$	8.04905	0.328327	0.164164	+	0.986433i	$0.447507\pi$
$602$	0	0
$603$	20.9764	0.854226
$604$	72.1601	2.93615
$605$	10.4922	0.426568
$606$	56.8413	2.30902
$607$	0.967309	0.0392618	0.0196309	−	0.999807i	$-0.493751\pi$
$607$	0.967309	0.0392618	0.0196309	+	0.999807i	$0.493751\pi$
$608$	−1.87531	−0.0760539
$609$	0	0
$610$	23.3909	0.947069
$611$	7.07196	0.286101
$612$	20.0833	0.811820
$613$	−31.1978	−1.26007	−0.630034	−	0.776568i	$-0.716959\pi$
$613$	−31.1978	−1.26007	−0.630034	+	0.776568i	$0.716959\pi$
$614$	47.9676	1.93582
$615$	26.8685	1.08344
$616$	0	0
$617$	5.08139	0.204569	0.102284	−	0.994755i	$-0.467385\pi$
$617$	5.08139	0.204569	0.102284	+	0.994755i	$0.467385\pi$
$618$	−21.3203	−0.857628
$619$	18.8675	0.758349	0.379174	−	0.925325i	$-0.376208\pi$
$619$	18.8675	0.758349	0.379174	+	0.925325i	$0.376208\pi$
$620$	−3.96139	−0.159093
$621$	−92.1660	−3.69849
$622$	−29.8262	−1.19592
$623$	0	0
$624$	12.8484	0.514347
$625$	1.00000	0.0400000
$626$	−30.4908	−1.21866
$627$	72.9454	2.91316
$628$	−18.8179	−0.750915
$629$	−7.45492	−0.297247
$630$	0	0
$631$	30.6298	1.21935	0.609677	−	0.792650i	$-0.291299\pi$
$631$	30.6298	1.21935	0.609677	+	0.792650i	$0.291299\pi$
$632$	67.4218	2.68190
$633$	−65.7800	−2.61452
$634$	45.1260	1.79218
$635$	−21.8028	−0.865217
$636$	−72.5364	−2.87625
$637$	0	0
$638$	−40.6598	−1.60974
$639$	8.30624	0.328590
$640$	19.8881	0.786148
$641$	−40.8222	−1.61238	−0.806190	−	0.591656i	$-0.798474\pi$
$641$	−40.8222	−1.61238	−0.806190	+	0.591656i	$0.798474\pi$
$642$	−8.20112	−0.323673
$643$	21.0943	0.831876	0.415938	−	0.909393i	$-0.363453\pi$
$643$	21.0943	0.831876	0.415938	+	0.909393i	$0.363453\pi$
$644$	0	0
$645$	1.72701	0.0680010
$646$	9.11803	0.358744
$647$	−23.5580	−0.926162	−0.463081	−	0.886316i	$-0.653256\pi$
$647$	−23.5580	−0.926162	−0.463081	+	0.886316i	$0.653256\pi$
$648$	−81.5309	−3.20284
$649$	−9.18774	−0.360650
$650$	−2.65584	−0.104171
$651$	0	0
$652$	−29.5461	−1.15712
$653$	16.2138	0.634496	0.317248	−	0.948343i	$-0.397241\pi$
$653$	16.2138	0.634496	0.317248	+	0.948343i	$0.397241\pi$
$654$	113.180	4.42568
$655$	−13.1156	−0.512471
$656$	32.3272	1.26216
$657$	−73.9985	−2.88696
$658$	0	0
$659$	22.2816	0.867967	0.433983	−	0.900921i	$-0.357108\pi$
$659$	22.2816	0.867967	0.433983	+	0.900921i	$0.357108\pi$
$660$	−57.5422	−2.23983
$661$	34.2028	1.33033	0.665167	−	0.746695i	$-0.268360\pi$
$661$	34.2028	1.33033	0.665167	+	0.746695i	$0.268360\pi$
$662$	19.0136	0.738986
$663$	2.53451	0.0984324
$664$	−54.5690	−2.11769
$665$	0	0
$666$	166.866	6.46593
$667$	27.6793	1.07174
$668$	0.474885	0.0183739
$669$	21.0016	0.811970
$670$	−7.51252	−0.290234
$671$	44.4133	1.71456
$672$	0	0
$673$	28.1381	1.08464	0.542321	−	0.840171i	$-0.317546\pi$
$673$	28.1381	1.08464	0.542321	+	0.840171i	$0.317546\pi$
$674$	−42.9565	−1.65462
$675$	11.9610	0.460379
$676$	−46.8110	−1.80042
$677$	−38.4413	−1.47742	−0.738709	−	0.674025i	$-0.764564\pi$
$677$	−38.4413	−1.47742	−0.738709	+	0.674025i	$0.764564\pi$
$678$	−111.279	−4.27364
$679$	0	0
$680$	−3.56128	−0.136569
$681$	56.5688	2.16772
$682$	−11.3192	−0.433433
$683$	23.7751	0.909730	0.454865	−	0.890560i	$-0.349687\pi$
$683$	23.7751	0.909730	0.454865	+	0.890560i	$0.349687\pi$
$684$	−135.621	−5.18559
$685$	−4.79688	−0.183279
$686$	0	0
$687$	−11.2650	−0.429788
$688$	2.07787	0.0792181
$689$	−6.35679	−0.242174
$690$	58.9488	2.24414
$691$	−15.2253	−0.579199	−0.289599	−	0.957148i	$-0.593522\pi$
$691$	−15.2253	−0.579199	−0.289599	+	0.957148i	$0.593522\pi$
$692$	−6.28518	−0.238927
$693$	0	0
$694$	36.8926	1.40042
$695$	−8.06789	−0.306032
$696$	53.8999	2.04307
$697$	6.37696	0.241545
$698$	76.0305	2.87780
$699$	−36.2515	−1.37116
$700$	0	0
$701$	−23.7757	−0.897995	−0.448997	−	0.893533i	$-0.648219\pi$
$701$	−23.7757	−0.897995	−0.448997	+	0.893533i	$0.648219\pi$
$702$	−31.7665	−1.19895
$703$	50.3423	1.89870
$704$	39.1806	1.47668
$705$	20.3709	0.767212
$706$	47.5399	1.78919
$707$	0	0
$708$	24.5988	0.924481
$709$	13.0482	0.490036	0.245018	−	0.969518i	$-0.421206\pi$
$709$	13.0482	0.490036	0.245018	+	0.969518i	$0.421206\pi$
$710$	−2.97481	−0.111642
$711$	−95.9804	−3.59955
$712$	−30.9507	−1.15993
$713$	7.70554	0.288575
$714$	0	0
$715$	−5.04276	−0.188589
$716$	22.5109	0.841272
$717$	−76.1137	−2.84252
$718$	30.6652	1.14441
$719$	10.8180	0.403443	0.201722	−	0.979443i	$-0.435346\pi$
$719$	10.8180	0.403443	0.201722	+	0.979443i	$0.435346\pi$
$720$	25.7005	0.957802
$721$	0	0
$722$	−15.1828	−0.565045
$723$	95.6735	3.55814
$724$	−18.0214	−0.669758
$725$	−3.59212	−0.133408
$726$	−80.2673	−2.97900
$727$	−8.83203	−0.327562	−0.163781	−	0.986497i	$-0.552369\pi$
$727$	−8.83203	−0.327562	−0.163781	+	0.986497i	$0.552369\pi$
$728$	0	0
$729$	3.63434	0.134605
$730$	26.5019	0.980879
$731$	0.409888	0.0151602
$732$	−118.910	−4.39505
$733$	−44.1777	−1.63174	−0.815870	−	0.578235i	$-0.803742\pi$
$733$	−44.1777	−1.63174	−0.815870	+	0.578235i	$0.803742\pi$
$734$	27.9744	1.03256
$735$	0	0
$736$	−2.87751	−0.106067
$737$	−14.2644	−0.525435
$738$	−142.738	−5.25425
$739$	−8.70441	−0.320197	−0.160098	−	0.987101i	$-0.551181\pi$
$739$	−8.70441	−0.320197	−0.160098	+	0.987101i	$0.551181\pi$
$740$	−39.7120	−1.45984
$741$	−17.1153	−0.628747
$742$	0	0
$743$	−37.7843	−1.38617	−0.693085	−	0.720856i	$-0.743749\pi$
$743$	−37.7843	−1.38617	−0.693085	+	0.720856i	$0.743749\pi$
$744$	15.0050	0.550111
$745$	17.3609	0.636054
$746$	62.9357	2.30424
$747$	77.6833	2.84228
$748$	−13.6570	−0.499351
$749$	0	0
$750$	−7.65019	−0.279346
$751$	17.9964	0.656698	0.328349	−	0.944556i	$-0.393508\pi$
$751$	17.9964	0.656698	0.328349	+	0.944556i	$0.393508\pi$
$752$	24.5095	0.893768
$753$	41.4762	1.51148
$754$	9.54010	0.347430
$755$	18.2159	0.662943
$756$	0	0
$757$	7.33099	0.266450	0.133225	−	0.991086i	$-0.457467\pi$
$757$	7.33099	0.266450	0.133225	+	0.991086i	$0.457467\pi$
$758$	−33.9856	−1.23441
$759$	111.929	4.06276
$760$	24.0490	0.872348
$761$	−3.68358	−0.133530	−0.0667648	−	0.997769i	$-0.521268\pi$
$761$	−3.68358	−0.133530	−0.0667648	+	0.997769i	$0.521268\pi$
$762$	166.796	6.04236
$763$	0	0
$764$	−60.7780	−2.19887
$765$	5.06977	0.183298
$766$	−27.4317	−0.991146
$767$	2.15574	0.0778392
$768$	−99.1867	−3.57909
$769$	6.27690	0.226351	0.113175	−	0.993575i	$-0.463898\pi$
$769$	6.27690	0.226351	0.113175	+	0.993575i	$0.463898\pi$
$770$	0	0
$771$	−63.8285	−2.29873
$772$	−73.7492	−2.65429
$773$	9.89475	0.355890	0.177945	−	0.984040i	$-0.443055\pi$
$773$	9.89475	0.355890	0.177945	+	0.984040i	$0.443055\pi$
$774$	−9.17466	−0.329776
$775$	−1.00000	−0.0359211
$776$	−37.4935	−1.34594
$777$	0	0
$778$	−51.4971	−1.84626
$779$	−43.0630	−1.54289
$780$	13.5013	0.483422
$781$	−5.64840	−0.202116
$782$	13.9909	0.500313
$783$	−42.9654	−1.53546
$784$	0	0
$785$	−4.75032	−0.169546
$786$	100.337	3.57891
$787$	31.8871	1.13665	0.568326	−	0.822803i	$-0.307591\pi$
$787$	31.8871	1.13665	0.568326	+	0.822803i	$0.307591\pi$
$788$	−66.1303	−2.35579
$789$	−71.9739	−2.56234
$790$	34.3745	1.22299
$791$	0	0
$792$	151.355	5.37818
$793$	−10.4208	−0.370053
$794$	20.2753	0.719545
$795$	−18.3108	−0.649419
$796$	95.3176	3.37844
$797$	−32.3146	−1.14464	−0.572322	−	0.820029i	$-0.693957\pi$
$797$	−32.3146	−1.14464	−0.572322	+	0.820029i	$0.693957\pi$
$798$	0	0
$799$	4.83482	0.171044
$800$	0.373435	0.0132029
$801$	44.0608	1.55681
$802$	−24.8588	−0.877794
$803$	50.3204	1.77577
$804$	38.1908	1.34688
$805$	0	0
$806$	2.65584	0.0935479
$807$	−40.2379	−1.41644
$808$	35.5820	1.25177
$809$	21.8679	0.768834	0.384417	−	0.923159i	$-0.374402\pi$
$809$	21.8679	0.768834	0.384417	+	0.923159i	$0.374402\pi$
$810$	−41.5679	−1.46055
$811$	15.5147	0.544796	0.272398	−	0.962185i	$-0.412183\pi$
$811$	15.5147	0.544796	0.272398	+	0.962185i	$0.412183\pi$
$812$	0	0
$813$	76.7202	2.69069
$814$	−113.472	−3.97719
$815$	−7.45852	−0.261261
$816$	8.78394	0.307499
$817$	−2.76793	−0.0968377
$818$	−47.8493	−1.67301
$819$	0	0
$820$	33.9698	1.18628
$821$	19.0783	0.665839	0.332919	−	0.942955i	$-0.391966\pi$
$821$	19.0783	0.665839	0.332919	+	0.942955i	$0.391966\pi$
$822$	36.6971	1.27996
$823$	13.0211	0.453887	0.226943	−	0.973908i	$-0.427127\pi$
$823$	13.0211	0.453887	0.226943	+	0.973908i	$0.427127\pi$
$824$	−13.3462	−0.464938
$825$	−14.5258	−0.505722
$826$	0	0
$827$	−29.7588	−1.03481	−0.517407	−	0.855740i	$-0.673103\pi$
$827$	−29.7588	−1.03481	−0.517407	+	0.855740i	$0.673103\pi$
$828$	−208.099	−7.23194
$829$	−23.6007	−0.819688	−0.409844	−	0.912156i	$-0.634417\pi$
$829$	−23.6007	−0.819688	−0.409844	+	0.912156i	$0.634417\pi$
$830$	−27.8216	−0.965701
$831$	14.5280	0.503972
$832$	−9.19303	−0.318711
$833$	0	0
$834$	61.7209	2.13722
$835$	0.119878	0.00414857
$836$	92.2246	3.18965
$837$	−11.9610	−0.413433
$838$	−89.1031	−3.07802
$839$	−23.0352	−0.795263	−0.397632	−	0.917545i	$-0.630168\pi$
$839$	−23.0352	−0.795263	−0.397632	+	0.917545i	$0.630168\pi$
$840$	0	0
$841$	−16.0966	−0.555057
$842$	−11.8768	−0.409301
$843$	−73.4638	−2.53023
$844$	−83.1654	−2.86267
$845$	−11.8168	−0.406511
$846$	−108.219	−3.72066
$847$	0	0
$848$	−22.0309	−0.756544
$849$	43.7619	1.50190
$850$	−1.81569	−0.0622777
$851$	77.2463	2.64797
$852$	15.1228	0.518097
$853$	18.0517	0.618079	0.309040	−	0.951049i	$-0.399992\pi$
$853$	18.0517	0.618079	0.309040	+	0.951049i	$0.399992\pi$
$854$	0	0
$855$	−34.2356	−1.17083
$856$	−5.13380	−0.175470
$857$	−5.75909	−0.196727	−0.0983634	−	0.995151i	$-0.531361\pi$
$857$	−5.75909	−0.196727	−0.0983634	+	0.995151i	$0.531361\pi$
$858$	38.5781	1.31703
$859$	−10.2034	−0.348137	−0.174068	−	0.984734i	$-0.555691\pi$
$859$	−10.2034	−0.348137	−0.174068	+	0.984734i	$0.555691\pi$
$860$	2.18346	0.0744552
$861$	0	0
$862$	−9.39541	−0.320009
$863$	19.9748	0.679949	0.339974	−	0.940435i	$-0.389582\pi$
$863$	19.9748	0.679949	0.339974	+	0.940435i	$0.389582\pi$
$864$	4.46666	0.151959
$865$	−1.58661	−0.0539463
$866$	48.2084	1.63819
$867$	−51.5329	−1.75015
$868$	0	0
$869$	65.2684	2.21408
$870$	27.4804	0.931674
$871$	3.34688	0.113405
$872$	70.8491	2.39925
$873$	53.3750	1.80647
$874$	−94.4790	−3.19580
$875$	0	0
$876$	−134.725	−4.55195
$877$	−14.3581	−0.484839	−0.242419	−	0.970172i	$-0.577941\pi$
$877$	−14.3581	−0.484839	−0.242419	+	0.970172i	$0.577941\pi$
$878$	−70.7941	−2.38918
$879$	−36.2992	−1.22434
$880$	−17.4768	−0.589144
$881$	−2.30125	−0.0775312	−0.0387656	−	0.999248i	$-0.512343\pi$
$881$	−2.30125	−0.0775312	−0.0387656	+	0.999248i	$0.512343\pi$
$882$	0	0
$883$	−16.1943	−0.544982	−0.272491	−	0.962158i	$-0.587848\pi$
$883$	−16.1943	−0.544982	−0.272491	+	0.962158i	$0.587848\pi$
$884$	3.20438	0.107775
$885$	6.20965	0.208735
$886$	−58.4192	−1.96263
$887$	−31.4195	−1.05496	−0.527482	−	0.849566i	$-0.676864\pi$
$887$	−31.4195	−1.05496	−0.527482	+	0.849566i	$0.676864\pi$
$888$	150.422	5.04783
$889$	0	0
$890$	−15.7800	−0.528946
$891$	−78.9268	−2.64415
$892$	26.5523	0.889037
$893$	−32.6490	−1.09256
$894$	−132.814	−4.44197
$895$	5.68258	0.189948
$896$	0	0
$897$	−26.2621	−0.876866
$898$	14.9225	0.497972
$899$	3.59212	0.119804
$900$	27.0064	0.900215
$901$	−4.34588	−0.144782
$902$	97.0643	3.23189
$903$	0	0
$904$	−69.6591	−2.31683
$905$	−4.54925	−0.151222
$906$	−139.355	−4.62975
$907$	−29.9141	−0.993281	−0.496640	−	0.867956i	$-0.665433\pi$
$907$	−29.9141	−0.993281	−0.496640	+	0.867956i	$0.665433\pi$
$908$	71.5197	2.37346
$909$	−50.6537	−1.68008
$910$	0	0
$911$	29.7343	0.985142	0.492571	−	0.870272i	$-0.336057\pi$
$911$	29.7343	0.985142	0.492571	+	0.870272i	$0.336057\pi$
$912$	−59.3170	−1.96418
$913$	−52.8261	−1.74829
$914$	46.4156	1.53529
$915$	−30.0173	−0.992340
$916$	−14.2423	−0.470580
$917$	0	0
$918$	−21.7175	−0.716785
$919$	−47.4170	−1.56414	−0.782072	−	0.623188i	$-0.785837\pi$
$919$	−47.4170	−1.56414	−0.782072	+	0.623188i	$0.785837\pi$
$920$	36.9012	1.21660
$921$	−61.5564	−2.02835
$922$	−31.5591	−1.03934
$923$	1.32530	0.0436226
$924$	0	0
$925$	−10.0248	−0.329613
$926$	−90.4369	−2.97194
$927$	18.9994	0.624023
$928$	−1.34142	−0.0440344
$929$	−38.8466	−1.27452	−0.637258	−	0.770651i	$-0.719931\pi$
$929$	−38.8466	−1.27452	−0.637258	+	0.770651i	$0.719931\pi$
$930$	7.65019	0.250860
$931$	0	0
$932$	−45.8326	−1.50130
$933$	38.2756	1.25309
$934$	−71.8357	−2.35053
$935$	−3.44754	−0.112746
$936$	−35.5128	−1.16077
$937$	−35.1843	−1.14942	−0.574710	−	0.818357i	$-0.694885\pi$
$937$	−35.1843	−1.14942	−0.574710	+	0.818357i	$0.694885\pi$
$938$	0	0
$939$	39.1286	1.27691
$940$	25.7549	0.840031
$941$	−36.9162	−1.20343	−0.601717	−	0.798710i	$-0.705516\pi$
$941$	−36.9162	−1.20343	−0.601717	+	0.798710i	$0.705516\pi$
$942$	36.3408	1.18405
$943$	−66.0767	−2.15175
$944$	7.47120	0.243167
$945$	0	0
$946$	6.23894	0.202845
$947$	−15.4686	−0.502663	−0.251331	−	0.967901i	$-0.580868\pi$
$947$	−15.4686	−0.502663	−0.251331	+	0.967901i	$0.580868\pi$
$948$	−174.747	−5.67551
$949$	−11.8068	−0.383264
$950$	12.2612	0.397805
$951$	−57.9098	−1.87785
$952$	0	0
$953$	−14.2766	−0.462464	−0.231232	−	0.972899i	$-0.574276\pi$
$953$	−14.2766	−0.462464	−0.231232	+	0.972899i	$0.574276\pi$
$954$	97.2754	3.14941
$955$	−15.3426	−0.496474
$956$	−96.2303	−3.11231
$957$	52.1783	1.68669
$958$	−90.8988	−2.93681
$959$	0	0
$960$	−26.4807	−0.854661
$961$	1.00000	0.0322581
$962$	26.6242	0.858398
$963$	7.30837	0.235509
$964$	120.960	3.89585
$965$	−18.6170	−0.599303
$966$	0	0
$967$	16.3898	0.527060	0.263530	−	0.964651i	$-0.415113\pi$
$967$	16.3898	0.527060	0.263530	+	0.964651i	$0.415113\pi$
$968$	−50.2463	−1.61498
$969$	−11.7011	−0.375893
$970$	−19.1158	−0.613771
$971$	30.5030	0.978887	0.489444	−	0.872035i	$-0.337200\pi$
$971$	30.5030	0.978887	0.489444	+	0.872035i	$0.337200\pi$
$972$	69.1684	2.21858
$973$	0	0
$974$	45.8989	1.47070
$975$	3.40821	0.109150
$976$	−36.1156	−1.15603
$977$	−15.3543	−0.491226	−0.245613	−	0.969368i	$-0.578989\pi$
$977$	−15.3543	−0.491226	−0.245613	+	0.969368i	$0.578989\pi$
$978$	57.0591	1.82455
$979$	−29.9621	−0.957594
$980$	0	0
$981$	−100.859	−3.22019
$982$	−33.2109	−1.05980
$983$	1.08449	0.0345899	0.0172949	−	0.999850i	$-0.494495\pi$
$983$	1.08449	0.0345899	0.0172949	+	0.999850i	$0.494495\pi$
$984$	−128.671	−4.10189
$985$	−16.6937	−0.531905
$986$	6.52219	0.207709
$987$	0	0
$988$	−21.6389	−0.688424
$989$	−4.24717	−0.135052
$990$	77.1674	2.45254
$991$	19.3985	0.616213	0.308106	−	0.951352i	$-0.400305\pi$
$991$	19.3985	0.616213	0.308106	+	0.951352i	$0.400305\pi$
$992$	−0.373435	−0.0118566
$993$	−24.4000	−0.774310
$994$	0	0
$995$	24.0616	0.762806
$996$	141.434	4.48151
$997$	−38.5907	−1.22218	−0.611091	−	0.791561i	$-0.709269\pi$
$997$	−38.5907	−1.22218	−0.611091	+	0.791561i	$0.709269\pi$
$998$	40.2054	1.27268
$999$	−119.906	−3.79367

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.bf.1.3		21
7.3	odd	6		1085.2.j.d.156.19	✓	42
7.5	odd	6		1085.2.j.d.466.19	yes	42
7.6	odd	2		7595.2.a.bg.1.3		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1085.2.j.d.156.19	✓	42	7.3	odd	6
1085.2.j.d.466.19	yes	42	7.5	odd	6
7595.2.a.bf.1.3		21	1.1	even	1	trivial
7595.2.a.bg.1.3		21	7.6	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:	\( N \)	\(=\)	\( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7595.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44160 q^{2} +3.13328 q^{3} +3.96139 q^{4} +1.00000 q^{5} -7.65019 q^{6} -4.78892 q^{8} +6.81741 q^{9} +O(q^{10})\)	\(q-2.44160 q^{2} +3.13328 q^{3} +3.96139 q^{4} +1.00000 q^{5} -7.65019 q^{6} -4.78892 q^{8} +6.81741 q^{9} -2.44160 q^{10} -4.63597 q^{11} +12.4121 q^{12} +1.08775 q^{13} +3.13328 q^{15} +3.76983 q^{16} +0.743650 q^{17} -16.6454 q^{18} -5.02179 q^{19} +3.96139 q^{20} +11.3192 q^{22} -7.70554 q^{23} -15.0050 q^{24} +1.00000 q^{25} -2.65584 q^{26} +11.9610 q^{27} -3.59212 q^{29} -7.65019 q^{30} -1.00000 q^{31} +0.373435 q^{32} -14.5258 q^{33} -1.81569 q^{34} +27.0064 q^{36} -10.0248 q^{37} +12.2612 q^{38} +3.40821 q^{39} -4.78892 q^{40} +8.57522 q^{41} +0.551184 q^{43} -18.3649 q^{44} +6.81741 q^{45} +18.8138 q^{46} +6.50147 q^{47} +11.8119 q^{48} -2.44160 q^{50} +2.33006 q^{51} +4.30899 q^{52} -5.84399 q^{53} -29.2040 q^{54} -4.63597 q^{55} -15.7347 q^{57} +8.77052 q^{58} +1.98184 q^{59} +12.4121 q^{60} -9.58016 q^{61} +2.44160 q^{62} -8.45144 q^{64} +1.08775 q^{65} +35.4660 q^{66} +3.07689 q^{67} +2.94589 q^{68} -24.1436 q^{69} +1.21839 q^{71} -32.6481 q^{72} -10.8543 q^{73} +24.4764 q^{74} +3.13328 q^{75} -19.8933 q^{76} -8.32147 q^{78} -14.0787 q^{79} +3.76983 q^{80} +17.0249 q^{81} -20.9372 q^{82} +11.3948 q^{83} +0.743650 q^{85} -1.34577 q^{86} -11.2551 q^{87} +22.2013 q^{88} +6.46297 q^{89} -16.6454 q^{90} -30.5246 q^{92} -3.13328 q^{93} -15.8740 q^{94} -5.02179 q^{95} +1.17007 q^{96} +7.82921 q^{97} -31.6053 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more