LMFDB - Embedded newform 3174.2.a.s.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3174,2,Mod(1,3174)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3174, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3174.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3174 = 2 \cdot 3 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3174.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,2,2,2,2,2,0,2,2,2,6,2,0,0,2,2,8,2,2,2,0,6,0,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(25)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$25.3445176016$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 138)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	3174.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} +1.00000 q^{6} -4.47214 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.23607 q^{10} +0.763932 q^{11} +1.00000 q^{12} -4.47214 q^{13} -4.47214 q^{14} +3.23607 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} +7.70820 q^{19} +3.23607 q^{20} -4.47214 q^{21} +0.763932 q^{22} +1.00000 q^{24} +5.47214 q^{25} -4.47214 q^{26} +1.00000 q^{27} -4.47214 q^{28} +4.47214 q^{29} +3.23607 q^{30} +6.47214 q^{31} +1.00000 q^{32} +0.763932 q^{33} +4.00000 q^{34} -14.4721 q^{35} +1.00000 q^{36} -6.76393 q^{37} +7.70820 q^{38} -4.47214 q^{39} +3.23607 q^{40} -2.00000 q^{41} -4.47214 q^{42} +9.23607 q^{43} +0.763932 q^{44} +3.23607 q^{45} +4.00000 q^{47} +1.00000 q^{48} +13.0000 q^{49} +5.47214 q^{50} +4.00000 q^{51} -4.47214 q^{52} -0.763932 q^{53} +1.00000 q^{54} +2.47214 q^{55} -4.47214 q^{56} +7.70820 q^{57} +4.47214 q^{58} +8.94427 q^{59} +3.23607 q^{60} -5.23607 q^{61} +6.47214 q^{62} -4.47214 q^{63} +1.00000 q^{64} -14.4721 q^{65} +0.763932 q^{66} +3.70820 q^{67} +4.00000 q^{68} -14.4721 q^{70} -8.94427 q^{71} +1.00000 q^{72} +4.47214 q^{73} -6.76393 q^{74} +5.47214 q^{75} +7.70820 q^{76} -3.41641 q^{77} -4.47214 q^{78} +4.47214 q^{79} +3.23607 q^{80} +1.00000 q^{81} -2.00000 q^{82} -8.76393 q^{83} -4.47214 q^{84} +12.9443 q^{85} +9.23607 q^{86} +4.47214 q^{87} +0.763932 q^{88} +1.52786 q^{89} +3.23607 q^{90} +20.0000 q^{91} +6.47214 q^{93} +4.00000 q^{94} +24.9443 q^{95} +1.00000 q^{96} +8.47214 q^{97} +13.0000 q^{98} +0.763932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{12} + 2 q^{15} + 2 q^{16} + 8 q^{17} + 2 q^{18} + 2 q^{19} + 2 q^{20} + 6 q^{22} + 2 q^{24} + 2 q^{25}+ \cdots + 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 + 2 * q^10 + 6 * q^11 + 2 * q^12 + 2 * q^15 + 2 * q^16 + 8 * q^17 + 2 * q^18 + 2 * q^19 + 2 * q^20 + 6 * q^22 + 2 * q^24 + 2 * q^25 + 2 * q^27 + 2 * q^30 + 4 * q^31 + 2 * q^32 + 6 * q^33 + 8 * q^34 - 20 * q^35 + 2 * q^36 - 18 * q^37 + 2 * q^38 + 2 * q^40 - 4 * q^41 + 14 * q^43 + 6 * q^44 + 2 * q^45 + 8 * q^47 + 2 * q^48 + 26 * q^49 + 2 * q^50 + 8 * q^51 - 6 * q^53 + 2 * q^54 - 4 * q^55 + 2 * q^57 + 2 * q^60 - 6 * q^61 + 4 * q^62 + 2 * q^64 - 20 * q^65 + 6 * q^66 - 6 * q^67 + 8 * q^68 - 20 * q^70 + 2 * q^72 - 18 * q^74 + 2 * q^75 + 2 * q^76 + 20 * q^77 + 2 * q^80 + 2 * q^81 - 4 * q^82 - 22 * q^83 + 8 * q^85 + 14 * q^86 + 6 * q^88 + 12 * q^89 + 2 * q^90 + 40 * q^91 + 4 * q^93 + 8 * q^94 + 32 * q^95 + 2 * q^96 + 8 * q^97 + 26 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.23607	1.44721	0.723607	−	0.690212i	$-0.242483\pi$
$5$	3.23607	1.44721	0.723607	+	0.690212i	$0.242483\pi$
$6$	1.00000	0.408248
$7$	−4.47214	−1.69031	−0.845154	−	0.534522i	$-0.820491\pi$
$7$	−4.47214	−1.69031	−0.845154	+	0.534522i	$0.820491\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.23607	1.02333
$11$	0.763932	0.230334	0.115167	−	0.993346i	$-0.463260\pi$
$11$	0.763932	0.230334	0.115167	+	0.993346i	$0.463260\pi$
$12$	1.00000	0.288675
$13$	−4.47214	−1.24035	−0.620174	−	0.784465i	$-0.712938\pi$
$13$	−4.47214	−1.24035	−0.620174	+	0.784465i	$0.712938\pi$
$14$	−4.47214	−1.19523
$15$	3.23607	0.835549
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	1.00000	0.235702
$19$	7.70820	1.76838	0.884192	−	0.467124i	$-0.154710\pi$
$19$	7.70820	1.76838	0.884192	+	0.467124i	$0.154710\pi$
$20$	3.23607	0.723607
$21$	−4.47214	−0.975900
$22$	0.763932	0.162871
$23$	0	0
$23$	0	0
$24$	1.00000	0.204124
$25$	5.47214	1.09443
$26$	−4.47214	−0.877058
$27$	1.00000	0.192450
$28$	−4.47214	−0.845154
$29$	4.47214	0.830455	0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214	0.830455	0.415227	+	0.909718i	$0.363702\pi$
$30$	3.23607	0.590822
$31$	6.47214	1.16243	0.581215	−	0.813750i	$-0.302578\pi$
$31$	6.47214	1.16243	0.581215	+	0.813750i	$0.302578\pi$
$32$	1.00000	0.176777
$33$	0.763932	0.132983
$34$	4.00000	0.685994
$35$	−14.4721	−2.44624
$36$	1.00000	0.166667
$37$	−6.76393	−1.11198	−0.555992	−	0.831188i	$-0.687661\pi$
$37$	−6.76393	−1.11198	−0.555992	+	0.831188i	$0.687661\pi$
$38$	7.70820	1.25044
$39$	−4.47214	−0.716115
$40$	3.23607	0.511667
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	−4.47214	−0.690066
$43$	9.23607	1.40849	0.704244	−	0.709958i	$-0.251286\pi$
$43$	9.23607	1.40849	0.704244	+	0.709958i	$0.251286\pi$
$44$	0.763932	0.115167
$45$	3.23607	0.482405
$46$	0	0
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	1.00000	0.144338
$49$	13.0000	1.85714
$50$	5.47214	0.773877
$51$	4.00000	0.560112
$52$	−4.47214	−0.620174
$53$	−0.763932	−0.104934	−0.0524671	−	0.998623i	$-0.516708\pi$
$53$	−0.763932	−0.104934	−0.0524671	+	0.998623i	$0.516708\pi$
$54$	1.00000	0.136083
$55$	2.47214	0.333343
$56$	−4.47214	−0.597614
$57$	7.70820	1.02098
$58$	4.47214	0.587220
$59$	8.94427	1.16445	0.582223	−	0.813029i	$-0.302183\pi$
$59$	8.94427	1.16445	0.582223	+	0.813029i	$0.302183\pi$
$60$	3.23607	0.417775
$61$	−5.23607	−0.670410	−0.335205	−	0.942145i	$-0.608806\pi$
$61$	−5.23607	−0.670410	−0.335205	+	0.942145i	$0.608806\pi$
$62$	6.47214	0.821962
$63$	−4.47214	−0.563436
$64$	1.00000	0.125000
$65$	−14.4721	−1.79505
$66$	0.763932	0.0940335
$67$	3.70820	0.453029	0.226515	−	0.974008i	$-0.427267\pi$
$67$	3.70820	0.453029	0.226515	+	0.974008i	$0.427267\pi$
$68$	4.00000	0.485071
$69$	0	0
$70$	−14.4721	−1.72975
$71$	−8.94427	−1.06149	−0.530745	−	0.847532i	$-0.678088\pi$
$71$	−8.94427	−1.06149	−0.530745	+	0.847532i	$0.678088\pi$
$72$	1.00000	0.117851
$73$	4.47214	0.523424	0.261712	−	0.965146i	$-0.415713\pi$
$73$	4.47214	0.523424	0.261712	+	0.965146i	$0.415713\pi$
$74$	−6.76393	−0.786291
$75$	5.47214	0.631868
$76$	7.70820	0.884192
$77$	−3.41641	−0.389336
$78$	−4.47214	−0.506370
$79$	4.47214	0.503155	0.251577	−	0.967837i	$-0.419051\pi$
$79$	4.47214	0.503155	0.251577	+	0.967837i	$0.419051\pi$
$80$	3.23607	0.361803
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	−8.76393	−0.961967	−0.480983	−	0.876730i	$-0.659720\pi$
$83$	−8.76393	−0.961967	−0.480983	+	0.876730i	$0.659720\pi$
$84$	−4.47214	−0.487950
$85$	12.9443	1.40400
$86$	9.23607	0.995951
$87$	4.47214	0.479463
$88$	0.763932	0.0814354
$89$	1.52786	0.161953	0.0809766	−	0.996716i	$-0.474196\pi$
$89$	1.52786	0.161953	0.0809766	+	0.996716i	$0.474196\pi$
$90$	3.23607	0.341112
$91$	20.0000	2.09657
$92$	0	0
$93$	6.47214	0.671129
$94$	4.00000	0.412568
$95$	24.9443	2.55923
$96$	1.00000	0.102062
$97$	8.47214	0.860215	0.430108	−	0.902778i	$-0.358476\pi$
$97$	8.47214	0.860215	0.430108	+	0.902778i	$0.358476\pi$
$98$	13.0000	1.31320
$99$	0.763932	0.0767781
$100$	5.47214	0.547214
$101$	−4.47214	−0.444994	−0.222497	−	0.974933i	$-0.571421\pi$
$101$	−4.47214	−0.444994	−0.222497	+	0.974933i	$0.571421\pi$
$102$	4.00000	0.396059
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	−4.47214	−0.438529
$105$	−14.4721	−1.41234
$106$	−0.763932	−0.0741996
$107$	−18.6525	−1.80320	−0.901601	−	0.432568i	$-0.857608\pi$
$107$	−18.6525	−1.80320	−0.901601	+	0.432568i	$0.857608\pi$
$108$	1.00000	0.0962250
$109$	−9.23607	−0.884655	−0.442327	−	0.896854i	$-0.645847\pi$
$109$	−9.23607	−0.884655	−0.442327	+	0.896854i	$0.645847\pi$
$110$	2.47214	0.235709
$111$	−6.76393	−0.642004
$112$	−4.47214	−0.422577
$113$	14.4721	1.36142	0.680712	−	0.732551i	$-0.261671\pi$
$113$	14.4721	1.36142	0.680712	+	0.732551i	$0.261671\pi$
$114$	7.70820	0.721939
$115$	0	0
$116$	4.47214	0.415227
$117$	−4.47214	−0.413449
$118$	8.94427	0.823387
$119$	−17.8885	−1.63984
$120$	3.23607	0.295411
$121$	−10.4164	−0.946946
$122$	−5.23607	−0.474051
$123$	−2.00000	−0.180334
$124$	6.47214	0.581215
$125$	1.52786	0.136656
$126$	−4.47214	−0.398410
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	1.00000	0.0883883
$129$	9.23607	0.813190
$130$	−14.4721	−1.26929
$131$	−18.4721	−1.61392	−0.806959	−	0.590607i	$-0.798888\pi$
$131$	−18.4721	−1.61392	−0.806959	+	0.590607i	$0.798888\pi$
$132$	0.763932	0.0664917
$133$	−34.4721	−2.98911
$134$	3.70820	0.320340
$135$	3.23607	0.278516
$136$	4.00000	0.342997
$137$	−20.9443	−1.78939	−0.894695	−	0.446678i	$-0.852607\pi$
$137$	−20.9443	−1.78939	−0.894695	+	0.446678i	$0.852607\pi$
$138$	0	0
$139$	0.944272	0.0800921	0.0400460	−	0.999198i	$-0.487250\pi$
$139$	0.944272	0.0800921	0.0400460	+	0.999198i	$0.487250\pi$
$140$	−14.4721	−1.22312
$141$	4.00000	0.336861
$142$	−8.94427	−0.750587
$143$	−3.41641	−0.285694
$144$	1.00000	0.0833333
$145$	14.4721	1.20185
$146$	4.47214	0.370117
$147$	13.0000	1.07222
$148$	−6.76393	−0.555992
$149$	−1.70820	−0.139942	−0.0699708	−	0.997549i	$-0.522291\pi$
$149$	−1.70820	−0.139942	−0.0699708	+	0.997549i	$0.522291\pi$
$150$	5.47214	0.446798
$151$	−5.52786	−0.449851	−0.224926	−	0.974376i	$-0.572214\pi$
$151$	−5.52786	−0.449851	−0.224926	+	0.974376i	$0.572214\pi$
$152$	7.70820	0.625218
$153$	4.00000	0.323381
$154$	−3.41641	−0.275302
$155$	20.9443	1.68228
$156$	−4.47214	−0.358057
$157$	−24.6525	−1.96748	−0.983741	−	0.179594i	$-0.942522\pi$
$157$	−24.6525	−1.96748	−0.983741	+	0.179594i	$0.942522\pi$
$158$	4.47214	0.355784
$159$	−0.763932	−0.0605838
$160$	3.23607	0.255834
$161$	0	0
$162$	1.00000	0.0785674
$163$	6.47214	0.506937	0.253468	−	0.967344i	$-0.418429\pi$
$163$	6.47214	0.506937	0.253468	+	0.967344i	$0.418429\pi$
$164$	−2.00000	−0.156174
$165$	2.47214	0.192456
$166$	−8.76393	−0.680213
$167$	−0.944272	−0.0730700	−0.0365350	−	0.999332i	$-0.511632\pi$
$167$	−0.944272	−0.0730700	−0.0365350	+	0.999332i	$0.511632\pi$
$168$	−4.47214	−0.345033
$169$	7.00000	0.538462
$170$	12.9443	0.992780
$171$	7.70820	0.589461
$172$	9.23607	0.704244
$173$	9.41641	0.715916	0.357958	−	0.933738i	$-0.383473\pi$
$173$	9.41641	0.715916	0.357958	+	0.933738i	$0.383473\pi$
$174$	4.47214	0.339032
$175$	−24.4721	−1.84992
$176$	0.763932	0.0575835
$177$	8.94427	0.672293
$178$	1.52786	0.114518
$179$	−7.41641	−0.554328	−0.277164	−	0.960823i	$-0.589395\pi$
$179$	−7.41641	−0.554328	−0.277164	+	0.960823i	$0.589395\pi$
$180$	3.23607	0.241202
$181$	6.76393	0.502759	0.251380	−	0.967889i	$-0.419116\pi$
$181$	6.76393	0.502759	0.251380	+	0.967889i	$0.419116\pi$
$182$	20.0000	1.48250
$183$	−5.23607	−0.387061
$184$	0	0
$185$	−21.8885	−1.60928
$186$	6.47214	0.474560
$187$	3.05573	0.223457
$188$	4.00000	0.291730
$189$	−4.47214	−0.325300
$190$	24.9443	1.80965
$191$	2.47214	0.178877	0.0894387	−	0.995992i	$-0.471493\pi$
$191$	2.47214	0.178877	0.0894387	+	0.995992i	$0.471493\pi$
$192$	1.00000	0.0721688
$193$	−11.8885	−0.855756	−0.427878	−	0.903836i	$-0.640739\pi$
$193$	−11.8885	−0.855756	−0.427878	+	0.903836i	$0.640739\pi$
$194$	8.47214	0.608264
$195$	−14.4721	−1.03637
$196$	13.0000	0.928571
$197$	−14.9443	−1.06474	−0.532368	−	0.846513i	$-0.678698\pi$
$197$	−14.9443	−1.06474	−0.532368	+	0.846513i	$0.678698\pi$
$198$	0.763932	0.0542903
$199$	9.41641	0.667511	0.333756	−	0.942660i	$-0.391684\pi$
$199$	9.41641	0.667511	0.333756	+	0.942660i	$0.391684\pi$
$200$	5.47214	0.386938
$201$	3.70820	0.261557
$202$	−4.47214	−0.314658
$203$	−20.0000	−1.40372
$204$	4.00000	0.280056
$205$	−6.47214	−0.452034
$206$	6.00000	0.418040
$207$	0	0
$208$	−4.47214	−0.310087
$209$	5.88854	0.407319
$210$	−14.4721	−0.998672
$211$	3.41641	0.235195	0.117598	−	0.993061i	$-0.462481\pi$
$211$	3.41641	0.235195	0.117598	+	0.993061i	$0.462481\pi$
$212$	−0.763932	−0.0524671
$213$	−8.94427	−0.612851
$214$	−18.6525	−1.27506
$215$	29.8885	2.03838
$216$	1.00000	0.0680414
$217$	−28.9443	−1.96487
$218$	−9.23607	−0.625545
$219$	4.47214	0.302199
$220$	2.47214	0.166671
$221$	−17.8885	−1.20331
$222$	−6.76393	−0.453965
$223$	−7.41641	−0.496639	−0.248320	−	0.968678i	$-0.579878\pi$
$223$	−7.41641	−0.496639	−0.248320	+	0.968678i	$0.579878\pi$
$224$	−4.47214	−0.298807
$225$	5.47214	0.364809
$226$	14.4721	0.962672
$227$	4.76393	0.316193	0.158097	−	0.987424i	$-0.449464\pi$
$227$	4.76393	0.316193	0.158097	+	0.987424i	$0.449464\pi$
$228$	7.70820	0.510488
$229$	−4.29180	−0.283610	−0.141805	−	0.989895i	$-0.545291\pi$
$229$	−4.29180	−0.283610	−0.141805	+	0.989895i	$0.545291\pi$
$230$	0	0
$231$	−3.41641	−0.224783
$232$	4.47214	0.293610
$233$	−15.8885	−1.04089	−0.520447	−	0.853894i	$-0.674235\pi$
$233$	−15.8885	−1.04089	−0.520447	+	0.853894i	$0.674235\pi$
$234$	−4.47214	−0.292353
$235$	12.9443	0.844391
$236$	8.94427	0.582223
$237$	4.47214	0.290496
$238$	−17.8885	−1.15954
$239$	12.9443	0.837295	0.418648	−	0.908149i	$-0.362504\pi$
$239$	12.9443	0.837295	0.418648	+	0.908149i	$0.362504\pi$
$240$	3.23607	0.208887
$241$	3.52786	0.227250	0.113625	−	0.993524i	$-0.463754\pi$
$241$	3.52786	0.227250	0.113625	+	0.993524i	$0.463754\pi$
$242$	−10.4164	−0.669592
$243$	1.00000	0.0641500
$244$	−5.23607	−0.335205
$245$	42.0689	2.68768
$246$	−2.00000	−0.127515
$247$	−34.4721	−2.19341
$248$	6.47214	0.410981
$249$	−8.76393	−0.555392
$250$	1.52786	0.0966306
$251$	6.29180	0.397135	0.198567	−	0.980087i	$-0.436371\pi$
$251$	6.29180	0.397135	0.198567	+	0.980087i	$0.436371\pi$
$252$	−4.47214	−0.281718
$253$	0	0
$254$	−4.00000	−0.250982
$255$	12.9443	0.810602
$256$	1.00000	0.0625000
$257$	23.8885	1.49013	0.745063	−	0.666994i	$-0.232419\pi$
$257$	23.8885	1.49013	0.745063	+	0.666994i	$0.232419\pi$
$258$	9.23607	0.575012
$259$	30.2492	1.87960
$260$	−14.4721	−0.897524
$261$	4.47214	0.276818
$262$	−18.4721	−1.14121
$263$	−7.05573	−0.435075	−0.217537	−	0.976052i	$-0.569802\pi$
$263$	−7.05573	−0.435075	−0.217537	+	0.976052i	$0.569802\pi$
$264$	0.763932	0.0470168
$265$	−2.47214	−0.151862
$266$	−34.4721	−2.11362
$267$	1.52786	0.0935038
$268$	3.70820	0.226515
$269$	−30.9443	−1.88671	−0.943353	−	0.331791i	$-0.892347\pi$
$269$	−30.9443	−1.88671	−0.943353	+	0.331791i	$0.892347\pi$
$270$	3.23607	0.196941
$271$	0.944272	0.0573604	0.0286802	−	0.999589i	$-0.490870\pi$
$271$	0.944272	0.0573604	0.0286802	+	0.999589i	$0.490870\pi$
$272$	4.00000	0.242536
$273$	20.0000	1.21046
$274$	−20.9443	−1.26529
$275$	4.18034	0.252084
$276$	0	0
$277$	−11.5279	−0.692642	−0.346321	−	0.938116i	$-0.612569\pi$
$277$	−11.5279	−0.692642	−0.346321	+	0.938116i	$0.612569\pi$
$278$	0.944272	0.0566337
$279$	6.47214	0.387477
$280$	−14.4721	−0.864876
$281$	22.4721	1.34058	0.670288	−	0.742101i	$-0.266171\pi$
$281$	22.4721	1.34058	0.670288	+	0.742101i	$0.266171\pi$
$282$	4.00000	0.238197
$283$	26.1803	1.55626	0.778130	−	0.628103i	$-0.216169\pi$
$283$	26.1803	1.55626	0.778130	+	0.628103i	$0.216169\pi$
$284$	−8.94427	−0.530745
$285$	24.9443	1.47757
$286$	−3.41641	−0.202016
$287$	8.94427	0.527964
$288$	1.00000	0.0589256
$289$	−1.00000	−0.0588235
$290$	14.4721	0.849833
$291$	8.47214	0.496645
$292$	4.47214	0.261712
$293$	−13.7082	−0.800842	−0.400421	−	0.916331i	$-0.631136\pi$
$293$	−13.7082	−0.800842	−0.400421	+	0.916331i	$0.631136\pi$
$294$	13.0000	0.758175
$295$	28.9443	1.68520
$296$	−6.76393	−0.393146
$297$	0.763932	0.0443278
$298$	−1.70820	−0.0989536
$299$	0	0
$300$	5.47214	0.315934
$301$	−41.3050	−2.38078
$302$	−5.52786	−0.318093
$303$	−4.47214	−0.256917
$304$	7.70820	0.442096
$305$	−16.9443	−0.970226
$306$	4.00000	0.228665
$307$	−11.4164	−0.651569	−0.325784	−	0.945444i	$-0.605628\pi$
$307$	−11.4164	−0.651569	−0.325784	+	0.945444i	$0.605628\pi$
$308$	−3.41641	−0.194668
$309$	6.00000	0.341328
$310$	20.9443	1.18955
$311$	−3.05573	−0.173274	−0.0866372	−	0.996240i	$-0.527612\pi$
$311$	−3.05573	−0.173274	−0.0866372	+	0.996240i	$0.527612\pi$
$312$	−4.47214	−0.253185
$313$	−24.4721	−1.38325	−0.691623	−	0.722258i	$-0.743104\pi$
$313$	−24.4721	−1.38325	−0.691623	+	0.722258i	$0.743104\pi$
$314$	−24.6525	−1.39122
$315$	−14.4721	−0.815412
$316$	4.47214	0.251577
$317$	28.4721	1.59915	0.799577	−	0.600563i	$-0.205057\pi$
$317$	28.4721	1.59915	0.799577	+	0.600563i	$0.205057\pi$
$318$	−0.763932	−0.0428392
$319$	3.41641	0.191282
$320$	3.23607	0.180902
$321$	−18.6525	−1.04108
$322$	0	0
$323$	30.8328	1.71558
$324$	1.00000	0.0555556
$325$	−24.4721	−1.35747
$326$	6.47214	0.358458
$327$	−9.23607	−0.510756
$328$	−2.00000	−0.110432
$329$	−17.8885	−0.986227
$330$	2.47214	0.136087
$331$	−1.52786	−0.0839790	−0.0419895	−	0.999118i	$-0.513370\pi$
$331$	−1.52786	−0.0839790	−0.0419895	+	0.999118i	$0.513370\pi$
$332$	−8.76393	−0.480983
$333$	−6.76393	−0.370661
$334$	−0.944272	−0.0516683
$335$	12.0000	0.655630
$336$	−4.47214	−0.243975
$337$	−15.8885	−0.865504	−0.432752	−	0.901513i	$-0.642457\pi$
$337$	−15.8885	−0.865504	−0.432752	+	0.901513i	$0.642457\pi$
$338$	7.00000	0.380750
$339$	14.4721	0.786019
$340$	12.9443	0.702002
$341$	4.94427	0.267747
$342$	7.70820	0.416812
$343$	−26.8328	−1.44884
$344$	9.23607	0.497975
$345$	0	0
$346$	9.41641	0.506229
$347$	21.5279	1.15568	0.577838	−	0.816151i	$-0.303896\pi$
$347$	21.5279	1.15568	0.577838	+	0.816151i	$0.303896\pi$
$348$	4.47214	0.239732
$349$	−31.8885	−1.70695	−0.853477	−	0.521130i	$-0.825511\pi$
$349$	−31.8885	−1.70695	−0.853477	+	0.521130i	$0.825511\pi$
$350$	−24.4721	−1.30809
$351$	−4.47214	−0.238705
$352$	0.763932	0.0407177
$353$	31.8885	1.69726	0.848628	−	0.528990i	$-0.177429\pi$
$353$	31.8885	1.69726	0.848628	+	0.528990i	$0.177429\pi$
$354$	8.94427	0.475383
$355$	−28.9443	−1.53620
$356$	1.52786	0.0809766
$357$	−17.8885	−0.946762
$358$	−7.41641	−0.391969
$359$	33.3050	1.75777	0.878884	−	0.477035i	$-0.158289\pi$
$359$	33.3050	1.75777	0.878884	+	0.477035i	$0.158289\pi$
$360$	3.23607	0.170556
$361$	40.4164	2.12718
$362$	6.76393	0.355504
$363$	−10.4164	−0.546720
$364$	20.0000	1.04828
$365$	14.4721	0.757506
$366$	−5.23607	−0.273694
$367$	17.4164	0.909129	0.454565	−	0.890714i	$-0.349795\pi$
$367$	17.4164	0.909129	0.454565	+	0.890714i	$0.349795\pi$
$368$	0	0
$369$	−2.00000	−0.104116
$370$	−21.8885	−1.13793
$371$	3.41641	0.177371
$372$	6.47214	0.335565
$373$	−13.5967	−0.704013	−0.352006	−	0.935998i	$-0.614500\pi$
$373$	−13.5967	−0.704013	−0.352006	+	0.935998i	$0.614500\pi$
$374$	3.05573	0.158008
$375$	1.52786	0.0788986
$376$	4.00000	0.206284
$377$	−20.0000	−1.03005
$378$	−4.47214	−0.230022
$379$	−0.291796	−0.0149886	−0.00749428	−	0.999972i	$-0.502386\pi$
$379$	−0.291796	−0.0149886	−0.00749428	+	0.999972i	$0.502386\pi$
$380$	24.9443	1.27961
$381$	−4.00000	−0.204926
$382$	2.47214	0.126485
$383$	−24.9443	−1.27459	−0.637296	−	0.770619i	$-0.719947\pi$
$383$	−24.9443	−1.27459	−0.637296	+	0.770619i	$0.719947\pi$
$384$	1.00000	0.0510310
$385$	−11.0557	−0.563452
$386$	−11.8885	−0.605111
$387$	9.23607	0.469496
$388$	8.47214	0.430108
$389$	−10.2918	−0.521815	−0.260907	−	0.965364i	$-0.584022\pi$
$389$	−10.2918	−0.521815	−0.260907	+	0.965364i	$0.584022\pi$
$390$	−14.4721	−0.732825
$391$	0	0
$392$	13.0000	0.656599
$393$	−18.4721	−0.931796
$394$	−14.9443	−0.752882
$395$	14.4721	0.728172
$396$	0.763932	0.0383890
$397$	9.05573	0.454494	0.227247	−	0.973837i	$-0.427028\pi$
$397$	9.05573	0.454494	0.227247	+	0.973837i	$0.427028\pi$
$398$	9.41641	0.472002
$399$	−34.4721	−1.72577
$400$	5.47214	0.273607
$401$	8.94427	0.446656	0.223328	−	0.974743i	$-0.428308\pi$
$401$	8.94427	0.446656	0.223328	+	0.974743i	$0.428308\pi$
$402$	3.70820	0.184948
$403$	−28.9443	−1.44182
$404$	−4.47214	−0.222497
$405$	3.23607	0.160802
$406$	−20.0000	−0.992583
$407$	−5.16718	−0.256128
$408$	4.00000	0.198030
$409$	−0.111456	−0.00551115	−0.00275558	−	0.999996i	$-0.500877\pi$
$409$	−0.111456	−0.00551115	−0.00275558	+	0.999996i	$0.500877\pi$
$410$	−6.47214	−0.319636
$411$	−20.9443	−1.03310
$412$	6.00000	0.295599
$413$	−40.0000	−1.96827
$414$	0	0
$415$	−28.3607	−1.39217
$416$	−4.47214	−0.219265
$417$	0.944272	0.0462412
$418$	5.88854	0.288018
$419$	30.0689	1.46896	0.734481	−	0.678630i	$-0.237426\pi$
$419$	30.0689	1.46896	0.734481	+	0.678630i	$0.237426\pi$
$420$	−14.4721	−0.706168
$421$	5.23607	0.255190	0.127595	−	0.991826i	$-0.459274\pi$
$421$	5.23607	0.255190	0.127595	+	0.991826i	$0.459274\pi$
$422$	3.41641	0.166308
$423$	4.00000	0.194487
$424$	−0.763932	−0.0370998
$425$	21.8885	1.06175
$426$	−8.94427	−0.433351
$427$	23.4164	1.13320
$428$	−18.6525	−0.901601
$429$	−3.41641	−0.164946
$430$	29.8885	1.44135
$431$	−3.41641	−0.164563	−0.0822813	−	0.996609i	$-0.526221\pi$
$431$	−3.41641	−0.164563	−0.0822813	+	0.996609i	$0.526221\pi$
$432$	1.00000	0.0481125
$433$	−5.41641	−0.260296	−0.130148	−	0.991495i	$-0.541545\pi$
$433$	−5.41641	−0.260296	−0.130148	+	0.991495i	$0.541545\pi$
$434$	−28.9443	−1.38937
$435$	14.4721	0.693886
$436$	−9.23607	−0.442327
$437$	0	0
$438$	4.47214	0.213687
$439$	36.9443	1.76325	0.881627	−	0.471947i	$-0.156449\pi$
$439$	36.9443	1.76325	0.881627	+	0.471947i	$0.156449\pi$
$440$	2.47214	0.117854
$441$	13.0000	0.619048
$442$	−17.8885	−0.850871
$443$	−32.9443	−1.56523	−0.782615	−	0.622506i	$-0.786115\pi$
$443$	−32.9443	−1.56523	−0.782615	+	0.622506i	$0.786115\pi$
$444$	−6.76393	−0.321002
$445$	4.94427	0.234381
$446$	−7.41641	−0.351177
$447$	−1.70820	−0.0807953
$448$	−4.47214	−0.211289
$449$	−19.8885	−0.938598	−0.469299	−	0.883039i	$-0.655493\pi$
$449$	−19.8885	−0.938598	−0.469299	+	0.883039i	$0.655493\pi$
$450$	5.47214	0.257959
$451$	−1.52786	−0.0719443
$452$	14.4721	0.680712
$453$	−5.52786	−0.259722
$454$	4.76393	0.223582
$455$	64.7214	3.03418
$456$	7.70820	0.360970
$457$	−36.4721	−1.70609	−0.853047	−	0.521834i	$-0.825248\pi$
$457$	−36.4721	−1.70609	−0.853047	+	0.521834i	$0.825248\pi$
$458$	−4.29180	−0.200542
$459$	4.00000	0.186704
$460$	0	0
$461$	22.0000	1.02464	0.512321	−	0.858794i	$-0.328786\pi$
$461$	22.0000	1.02464	0.512321	+	0.858794i	$0.328786\pi$
$462$	−3.41641	−0.158946
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	4.47214	0.207614
$465$	20.9443	0.971267
$466$	−15.8885	−0.736023
$467$	40.1803	1.85932	0.929662	−	0.368413i	$-0.120099\pi$
$467$	40.1803	1.85932	0.929662	+	0.368413i	$0.120099\pi$
$468$	−4.47214	−0.206725
$469$	−16.5836	−0.765759
$470$	12.9443	0.597075
$471$	−24.6525	−1.13593
$472$	8.94427	0.411693
$473$	7.05573	0.324423
$474$	4.47214	0.205412
$475$	42.1803	1.93537
$476$	−17.8885	−0.819920
$477$	−0.763932	−0.0349780
$478$	12.9443	0.592057
$479$	11.0557	0.505149	0.252575	−	0.967577i	$-0.418723\pi$
$479$	11.0557	0.505149	0.252575	+	0.967577i	$0.418723\pi$
$480$	3.23607	0.147706
$481$	30.2492	1.37925
$482$	3.52786	0.160690
$483$	0	0
$484$	−10.4164	−0.473473
$485$	27.4164	1.24491
$486$	1.00000	0.0453609
$487$	−25.8885	−1.17312	−0.586561	−	0.809905i	$-0.699519\pi$
$487$	−25.8885	−1.17312	−0.586561	+	0.809905i	$0.699519\pi$
$488$	−5.23607	−0.237026
$489$	6.47214	0.292680
$490$	42.0689	1.90048
$491$	−33.3050	−1.50303	−0.751516	−	0.659715i	$-0.770677\pi$
$491$	−33.3050	−1.50303	−0.751516	+	0.659715i	$0.770677\pi$
$492$	−2.00000	−0.0901670
$493$	17.8885	0.805659
$494$	−34.4721	−1.55097
$495$	2.47214	0.111114
$496$	6.47214	0.290607
$497$	40.0000	1.79425
$498$	−8.76393	−0.392721
$499$	27.4164	1.22733	0.613663	−	0.789568i	$-0.289695\pi$
$499$	27.4164	1.22733	0.613663	+	0.789568i	$0.289695\pi$
$500$	1.52786	0.0683282
$501$	−0.944272	−0.0421870
$502$	6.29180	0.280817
$503$	−1.52786	−0.0681241	−0.0340620	−	0.999420i	$-0.510844\pi$
$503$	−1.52786	−0.0681241	−0.0340620	+	0.999420i	$0.510844\pi$
$504$	−4.47214	−0.199205
$505$	−14.4721	−0.644002
$506$	0	0
$507$	7.00000	0.310881
$508$	−4.00000	−0.177471
$509$	−6.58359	−0.291813	−0.145906	−	0.989298i	$-0.546610\pi$
$509$	−6.58359	−0.291813	−0.145906	+	0.989298i	$0.546610\pi$
$510$	12.9443	0.573182
$511$	−20.0000	−0.884748
$512$	1.00000	0.0441942
$513$	7.70820	0.340326
$514$	23.8885	1.05368
$515$	19.4164	0.855589
$516$	9.23607	0.406595
$517$	3.05573	0.134391
$518$	30.2492	1.32907
$519$	9.41641	0.413334
$520$	−14.4721	−0.634645
$521$	−16.0000	−0.700973	−0.350486	−	0.936568i	$-0.613984\pi$
$521$	−16.0000	−0.700973	−0.350486	+	0.936568i	$0.613984\pi$
$522$	4.47214	0.195740
$523$	−12.2918	−0.537483	−0.268741	−	0.963212i	$-0.586608\pi$
$523$	−12.2918	−0.537483	−0.268741	+	0.963212i	$0.586608\pi$
$524$	−18.4721	−0.806959
$525$	−24.4721	−1.06805
$526$	−7.05573	−0.307644
$527$	25.8885	1.12772
$528$	0.763932	0.0332459
$529$	0	0
$530$	−2.47214	−0.107383
$531$	8.94427	0.388148
$532$	−34.4721	−1.49456
$533$	8.94427	0.387419
$534$	1.52786	0.0661171
$535$	−60.3607	−2.60962
$536$	3.70820	0.160170
$537$	−7.41641	−0.320042
$538$	−30.9443	−1.33410
$539$	9.93112	0.427763
$540$	3.23607	0.139258
$541$	43.8885	1.88692	0.943458	−	0.331492i	$-0.107552\pi$
$541$	43.8885	1.88692	0.943458	+	0.331492i	$0.107552\pi$
$542$	0.944272	0.0405600
$543$	6.76393	0.290268
$544$	4.00000	0.171499
$545$	−29.8885	−1.28028
$546$	20.0000	0.855921
$547$	−21.3050	−0.910934	−0.455467	−	0.890253i	$-0.650528\pi$
$547$	−21.3050	−0.910934	−0.455467	+	0.890253i	$0.650528\pi$
$548$	−20.9443	−0.894695
$549$	−5.23607	−0.223470
$550$	4.18034	0.178250
$551$	34.4721	1.46856
$552$	0	0
$553$	−20.0000	−0.850487
$554$	−11.5279	−0.489772
$555$	−21.8885	−0.929117
$556$	0.944272	0.0400460
$557$	−25.1246	−1.06456	−0.532282	−	0.846567i	$-0.678665\pi$
$557$	−25.1246	−1.06456	−0.532282	+	0.846567i	$0.678665\pi$
$558$	6.47214	0.273987
$559$	−41.3050	−1.74701
$560$	−14.4721	−0.611559
$561$	3.05573	0.129013
$562$	22.4721	0.947930
$563$	6.65248	0.280368	0.140184	−	0.990125i	$-0.455231\pi$
$563$	6.65248	0.280368	0.140184	+	0.990125i	$0.455231\pi$
$564$	4.00000	0.168430
$565$	46.8328	1.97027
$566$	26.1803	1.10044
$567$	−4.47214	−0.187812
$568$	−8.94427	−0.375293
$569$	−20.0000	−0.838444	−0.419222	−	0.907884i	$-0.637697\pi$
$569$	−20.0000	−0.838444	−0.419222	+	0.907884i	$0.637697\pi$
$570$	24.9443	1.04480
$571$	27.7082	1.15955	0.579776	−	0.814776i	$-0.303140\pi$
$571$	27.7082	1.15955	0.579776	+	0.814776i	$0.303140\pi$
$572$	−3.41641	−0.142847
$573$	2.47214	0.103275
$574$	8.94427	0.373327
$575$	0	0
$576$	1.00000	0.0416667
$577$	10.3607	0.431321	0.215660	−	0.976468i	$-0.430810\pi$
$577$	10.3607	0.431321	0.215660	+	0.976468i	$0.430810\pi$
$578$	−1.00000	−0.0415945
$579$	−11.8885	−0.494071
$580$	14.4721	0.600923
$581$	39.1935	1.62602
$582$	8.47214	0.351181
$583$	−0.583592	−0.0241699
$584$	4.47214	0.185058
$585$	−14.4721	−0.598349
$586$	−13.7082	−0.566281
$587$	−2.47214	−0.102036	−0.0510180	−	0.998698i	$-0.516247\pi$
$587$	−2.47214	−0.102036	−0.0510180	+	0.998698i	$0.516247\pi$
$588$	13.0000	0.536111
$589$	49.8885	2.05562
$590$	28.9443	1.19162
$591$	−14.9443	−0.614725
$592$	−6.76393	−0.277996
$593$	−37.7771	−1.55132	−0.775660	−	0.631152i	$-0.782583\pi$
$593$	−37.7771	−1.55132	−0.775660	+	0.631152i	$0.782583\pi$
$594$	0.763932	0.0313445
$595$	−57.8885	−2.37320
$596$	−1.70820	−0.0699708
$597$	9.41641	0.385388
$598$	0	0
$599$	−1.88854	−0.0771638	−0.0385819	−	0.999255i	$-0.512284\pi$
$599$	−1.88854	−0.0771638	−0.0385819	+	0.999255i	$0.512284\pi$
$600$	5.47214	0.223399
$601$	34.3607	1.40160	0.700801	−	0.713357i	$-0.252826\pi$
$601$	34.3607	1.40160	0.700801	+	0.713357i	$0.252826\pi$
$602$	−41.3050	−1.68346
$603$	3.70820	0.151010
$604$	−5.52786	−0.224926
$605$	−33.7082	−1.37043
$606$	−4.47214	−0.181668
$607$	−26.4721	−1.07447	−0.537235	−	0.843432i	$-0.680531\pi$
$607$	−26.4721	−1.07447	−0.537235	+	0.843432i	$0.680531\pi$
$608$	7.70820	0.312609
$609$	−20.0000	−0.810441
$610$	−16.9443	−0.686054
$611$	−17.8885	−0.723693
$612$	4.00000	0.161690
$613$	−15.1246	−0.610877	−0.305439	−	0.952212i	$-0.598803\pi$
$613$	−15.1246	−0.610877	−0.305439	+	0.952212i	$0.598803\pi$
$614$	−11.4164	−0.460729
$615$	−6.47214	−0.260982
$616$	−3.41641	−0.137651
$617$	24.3607	0.980724	0.490362	−	0.871519i	$-0.336865\pi$
$617$	24.3607	0.980724	0.490362	+	0.871519i	$0.336865\pi$
$618$	6.00000	0.241355
$619$	−31.7082	−1.27446	−0.637230	−	0.770674i	$-0.719920\pi$
$619$	−31.7082	−1.27446	−0.637230	+	0.770674i	$0.719920\pi$
$620$	20.9443	0.841142
$621$	0	0
$622$	−3.05573	−0.122524
$623$	−6.83282	−0.273751
$624$	−4.47214	−0.179029
$625$	−22.4164	−0.896656
$626$	−24.4721	−0.978103
$627$	5.88854	0.235166
$628$	−24.6525	−0.983741
$629$	−27.0557	−1.07878
$630$	−14.4721	−0.576584
$631$	6.00000	0.238856	0.119428	−	0.992843i	$-0.461894\pi$
$631$	6.00000	0.238856	0.119428	+	0.992843i	$0.461894\pi$
$632$	4.47214	0.177892
$633$	3.41641	0.135790
$634$	28.4721	1.13077
$635$	−12.9443	−0.513678
$636$	−0.763932	−0.0302919
$637$	−58.1378	−2.30350
$638$	3.41641	0.135257
$639$	−8.94427	−0.353830
$640$	3.23607	0.127917
$641$	−4.00000	−0.157991	−0.0789953	−	0.996875i	$-0.525171\pi$
$641$	−4.00000	−0.157991	−0.0789953	+	0.996875i	$0.525171\pi$
$642$	−18.6525	−0.736155
$643$	−34.5410	−1.36216	−0.681082	−	0.732207i	$-0.738490\pi$
$643$	−34.5410	−1.36216	−0.681082	+	0.732207i	$0.738490\pi$
$644$	0	0
$645$	29.8885	1.17686
$646$	30.8328	1.21310
$647$	−4.94427	−0.194379	−0.0971897	−	0.995266i	$-0.530985\pi$
$647$	−4.94427	−0.194379	−0.0971897	+	0.995266i	$0.530985\pi$
$648$	1.00000	0.0392837
$649$	6.83282	0.268211
$650$	−24.4721	−0.959876
$651$	−28.9443	−1.13442
$652$	6.47214	0.253468
$653$	−17.4164	−0.681557	−0.340778	−	0.940144i	$-0.610691\pi$
$653$	−17.4164	−0.681557	−0.340778	+	0.940144i	$0.610691\pi$
$654$	−9.23607	−0.361159
$655$	−59.7771	−2.33568
$656$	−2.00000	−0.0780869
$657$	4.47214	0.174475
$658$	−17.8885	−0.697368
$659$	1.34752	0.0524921	0.0262460	−	0.999656i	$-0.491645\pi$
$659$	1.34752	0.0524921	0.0262460	+	0.999656i	$0.491645\pi$
$660$	2.47214	0.0962278
$661$	−26.1803	−1.01830	−0.509149	−	0.860679i	$-0.670040\pi$
$661$	−26.1803	−1.01830	−0.509149	+	0.860679i	$0.670040\pi$
$662$	−1.52786	−0.0593821
$663$	−17.8885	−0.694733
$664$	−8.76393	−0.340107
$665$	−111.554	−4.32589
$666$	−6.76393	−0.262097
$667$	0	0
$668$	−0.944272	−0.0365350
$669$	−7.41641	−0.286735
$670$	12.0000	0.463600
$671$	−4.00000	−0.154418
$672$	−4.47214	−0.172516
$673$	−4.47214	−0.172388	−0.0861941	−	0.996278i	$-0.527471\pi$
$673$	−4.47214	−0.172388	−0.0861941	+	0.996278i	$0.527471\pi$
$674$	−15.8885	−0.612004
$675$	5.47214	0.210623
$676$	7.00000	0.269231
$677$	21.1246	0.811885	0.405942	−	0.913899i	$-0.366943\pi$
$677$	21.1246	0.811885	0.405942	+	0.913899i	$0.366943\pi$
$678$	14.4721	0.555799
$679$	−37.8885	−1.45403
$680$	12.9443	0.496390
$681$	4.76393	0.182554
$682$	4.94427	0.189326
$683$	5.52786	0.211518	0.105759	−	0.994392i	$-0.466273\pi$
$683$	5.52786	0.211518	0.105759	+	0.994392i	$0.466273\pi$
$684$	7.70820	0.294731
$685$	−67.7771	−2.58963
$686$	−26.8328	−1.02448
$687$	−4.29180	−0.163742
$688$	9.23607	0.352122
$689$	3.41641	0.130155
$690$	0	0
$691$	43.4164	1.65164	0.825819	−	0.563935i	$-0.190713\pi$
$691$	43.4164	1.65164	0.825819	+	0.563935i	$0.190713\pi$
$692$	9.41641	0.357958
$693$	−3.41641	−0.129779
$694$	21.5279	0.817187
$695$	3.05573	0.115910
$696$	4.47214	0.169516
$697$	−8.00000	−0.303022
$698$	−31.8885	−1.20700
$699$	−15.8885	−0.600960
$700$	−24.4721	−0.924960
$701$	−37.1246	−1.40218	−0.701089	−	0.713074i	$-0.747302\pi$
$701$	−37.1246	−1.40218	−0.701089	+	0.713074i	$0.747302\pi$
$702$	−4.47214	−0.168790
$703$	−52.1378	−1.96641
$704$	0.763932	0.0287918
$705$	12.9443	0.487509
$706$	31.8885	1.20014
$707$	20.0000	0.752177
$708$	8.94427	0.336146
$709$	41.0132	1.54028	0.770141	−	0.637874i	$-0.220186\pi$
$709$	41.0132	1.54028	0.770141	+	0.637874i	$0.220186\pi$
$710$	−28.9443	−1.08626
$711$	4.47214	0.167718
$712$	1.52786	0.0572591
$713$	0	0
$714$	−17.8885	−0.669462
$715$	−11.0557	−0.413461
$716$	−7.41641	−0.277164
$717$	12.9443	0.483413
$718$	33.3050	1.24293
$719$	−20.9443	−0.781090	−0.390545	−	0.920584i	$-0.627713\pi$
$719$	−20.9443	−0.781090	−0.390545	+	0.920584i	$0.627713\pi$
$720$	3.23607	0.120601
$721$	−26.8328	−0.999306
$722$	40.4164	1.50414
$723$	3.52786	0.131203
$724$	6.76393	0.251380
$725$	24.4721	0.908872
$726$	−10.4164	−0.386589
$727$	−43.3050	−1.60609	−0.803046	−	0.595917i	$-0.796789\pi$
$727$	−43.3050	−1.60609	−0.803046	+	0.595917i	$0.796789\pi$
$728$	20.0000	0.741249
$729$	1.00000	0.0370370
$730$	14.4721	0.535638
$731$	36.9443	1.36643
$732$	−5.23607	−0.193531
$733$	8.29180	0.306264	0.153132	−	0.988206i	$-0.451064\pi$
$733$	8.29180	0.306264	0.153132	+	0.988206i	$0.451064\pi$
$734$	17.4164	0.642851
$735$	42.0689	1.55173
$736$	0	0
$737$	2.83282	0.104348
$738$	−2.00000	−0.0736210
$739$	−15.0557	−0.553834	−0.276917	−	0.960894i	$-0.589313\pi$
$739$	−15.0557	−0.553834	−0.276917	+	0.960894i	$0.589313\pi$
$740$	−21.8885	−0.804639
$741$	−34.4721	−1.26637
$742$	3.41641	0.125420
$743$	4.00000	0.146746	0.0733729	−	0.997305i	$-0.476624\pi$
$743$	4.00000	0.146746	0.0733729	+	0.997305i	$0.476624\pi$
$744$	6.47214	0.237280
$745$	−5.52786	−0.202525
$746$	−13.5967	−0.497812
$747$	−8.76393	−0.320656
$748$	3.05573	0.111728
$749$	83.4164	3.04797
$750$	1.52786	0.0557897
$751$	18.0000	0.656829	0.328415	−	0.944534i	$-0.393486\pi$
$751$	18.0000	0.656829	0.328415	+	0.944534i	$0.393486\pi$
$752$	4.00000	0.145865
$753$	6.29180	0.229286
$754$	−20.0000	−0.728357
$755$	−17.8885	−0.651031
$756$	−4.47214	−0.162650
$757$	32.6525	1.18677	0.593387	−	0.804917i	$-0.297790\pi$
$757$	32.6525	1.18677	0.593387	+	0.804917i	$0.297790\pi$
$758$	−0.291796	−0.0105985
$759$	0	0
$760$	24.9443	0.904824
$761$	−22.9443	−0.831729	−0.415865	−	0.909427i	$-0.636521\pi$
$761$	−22.9443	−0.831729	−0.415865	+	0.909427i	$0.636521\pi$
$762$	−4.00000	−0.144905
$763$	41.3050	1.49534
$764$	2.47214	0.0894387
$765$	12.9443	0.468001
$766$	−24.9443	−0.901273
$767$	−40.0000	−1.44432
$768$	1.00000	0.0360844
$769$	−3.52786	−0.127218	−0.0636090	−	0.997975i	$-0.520261\pi$
$769$	−3.52786	−0.127218	−0.0636090	+	0.997975i	$0.520261\pi$
$770$	−11.0557	−0.398421
$771$	23.8885	0.860325
$772$	−11.8885	−0.427878
$773$	15.8197	0.568994	0.284497	−	0.958677i	$-0.408173\pi$
$773$	15.8197	0.568994	0.284497	+	0.958677i	$0.408173\pi$
$774$	9.23607	0.331984
$775$	35.4164	1.27219
$776$	8.47214	0.304132
$777$	30.2492	1.08518
$778$	−10.2918	−0.368979
$779$	−15.4164	−0.552350
$780$	−14.4721	−0.518186
$781$	−6.83282	−0.244497
$782$	0	0
$783$	4.47214	0.159821
$784$	13.0000	0.464286
$785$	−79.7771	−2.84737
$786$	−18.4721	−0.658879
$787$	−30.7639	−1.09662	−0.548308	−	0.836277i	$-0.684728\pi$
$787$	−30.7639	−1.09662	−0.548308	+	0.836277i	$0.684728\pi$
$788$	−14.9443	−0.532368
$789$	−7.05573	−0.251191
$790$	14.4721	0.514895
$791$	−64.7214	−2.30123
$792$	0.763932	0.0271451
$793$	23.4164	0.831541
$794$	9.05573	0.321376
$795$	−2.47214	−0.0876776
$796$	9.41641	0.333756
$797$	7.59675	0.269091	0.134545	−	0.990907i	$-0.457043\pi$
$797$	7.59675	0.269091	0.134545	+	0.990907i	$0.457043\pi$
$798$	−34.4721	−1.22030
$799$	16.0000	0.566039
$800$	5.47214	0.193469
$801$	1.52786	0.0539844
$802$	8.94427	0.315833
$803$	3.41641	0.120562
$804$	3.70820	0.130778
$805$	0	0
$806$	−28.9443	−1.01952
$807$	−30.9443	−1.08929
$808$	−4.47214	−0.157329
$809$	25.0557	0.880912	0.440456	−	0.897774i	$-0.354817\pi$
$809$	25.0557	0.880912	0.440456	+	0.897774i	$0.354817\pi$
$810$	3.23607	0.113704
$811$	−21.3050	−0.748118	−0.374059	−	0.927405i	$-0.622034\pi$
$811$	−21.3050	−0.748118	−0.374059	+	0.927405i	$0.622034\pi$
$812$	−20.0000	−0.701862
$813$	0.944272	0.0331171
$814$	−5.16718	−0.181110
$815$	20.9443	0.733646
$816$	4.00000	0.140028
$817$	71.1935	2.49075
$818$	−0.111456	−0.00389697
$819$	20.0000	0.698857
$820$	−6.47214	−0.226017
$821$	48.4721	1.69169	0.845845	−	0.533429i	$-0.179097\pi$
$821$	48.4721	1.69169	0.845845	+	0.533429i	$0.179097\pi$
$822$	−20.9443	−0.730515
$823$	−7.63932	−0.266290	−0.133145	−	0.991097i	$-0.542508\pi$
$823$	−7.63932	−0.266290	−0.133145	+	0.991097i	$0.542508\pi$
$824$	6.00000	0.209020
$825$	4.18034	0.145541
$826$	−40.0000	−1.39178
$827$	−27.5967	−0.959633	−0.479816	−	0.877369i	$-0.659297\pi$
$827$	−27.5967	−0.959633	−0.479816	+	0.877369i	$0.659297\pi$
$828$	0	0
$829$	−6.00000	−0.208389	−0.104194	−	0.994557i	$-0.533226\pi$
$829$	−6.00000	−0.208389	−0.104194	+	0.994557i	$0.533226\pi$
$830$	−28.3607	−0.984414
$831$	−11.5279	−0.399897
$832$	−4.47214	−0.155043
$833$	52.0000	1.80169
$834$	0.944272	0.0326975
$835$	−3.05573	−0.105748
$836$	5.88854	0.203660
$837$	6.47214	0.223710
$838$	30.0689	1.03871
$839$	10.1115	0.349086	0.174543	−	0.984650i	$-0.444155\pi$
$839$	10.1115	0.349086	0.174543	+	0.984650i	$0.444155\pi$
$840$	−14.4721	−0.499336
$841$	−9.00000	−0.310345
$842$	5.23607	0.180447
$843$	22.4721	0.773981
$844$	3.41641	0.117598
$845$	22.6525	0.779269
$846$	4.00000	0.137523
$847$	46.5836	1.60063
$848$	−0.763932	−0.0262335
$849$	26.1803	0.898507
$850$	21.8885	0.750771
$851$	0	0
$852$	−8.94427	−0.306426
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	23.4164	0.801293
$855$	24.9443	0.853076
$856$	−18.6525	−0.637528
$857$	−22.0000	−0.751506	−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000	−0.751506	−0.375753	+	0.926720i	$0.622616\pi$
$858$	−3.41641	−0.116634
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	29.8885	1.01919
$861$	8.94427	0.304820
$862$	−3.41641	−0.116363
$863$	−38.8328	−1.32188	−0.660942	−	0.750437i	$-0.729843\pi$
$863$	−38.8328	−1.32188	−0.660942	+	0.750437i	$0.729843\pi$
$864$	1.00000	0.0340207
$865$	30.4721	1.03608
$866$	−5.41641	−0.184057
$867$	−1.00000	−0.0339618
$868$	−28.9443	−0.982433
$869$	3.41641	0.115894
$870$	14.4721	0.490651
$871$	−16.5836	−0.561914
$872$	−9.23607	−0.312773
$873$	8.47214	0.286738
$874$	0	0
$875$	−6.83282	−0.230991
$876$	4.47214	0.151099
$877$	32.2492	1.08898	0.544489	−	0.838768i	$-0.316723\pi$
$877$	32.2492	1.08898	0.544489	+	0.838768i	$0.316723\pi$
$878$	36.9443	1.24681
$879$	−13.7082	−0.462366
$880$	2.47214	0.0833357
$881$	−12.5836	−0.423952	−0.211976	−	0.977275i	$-0.567990\pi$
$881$	−12.5836	−0.423952	−0.211976	+	0.977275i	$0.567990\pi$
$882$	13.0000	0.437733
$883$	22.4721	0.756248	0.378124	−	0.925755i	$-0.376569\pi$
$883$	22.4721	0.756248	0.378124	+	0.925755i	$0.376569\pi$
$884$	−17.8885	−0.601657
$885$	28.9443	0.972951
$886$	−32.9443	−1.10678
$887$	0.944272	0.0317055	0.0158528	−	0.999874i	$-0.494954\pi$
$887$	0.944272	0.0317055	0.0158528	+	0.999874i	$0.494954\pi$
$888$	−6.76393	−0.226983
$889$	17.8885	0.599963
$890$	4.94427	0.165732
$891$	0.763932	0.0255927
$892$	−7.41641	−0.248320
$893$	30.8328	1.03178
$894$	−1.70820	−0.0571309
$895$	−24.0000	−0.802232
$896$	−4.47214	−0.149404
$897$	0	0
$898$	−19.8885	−0.663689
$899$	28.9443	0.965346
$900$	5.47214	0.182405
$901$	−3.05573	−0.101801
$902$	−1.52786	−0.0508723
$903$	−41.3050	−1.37454
$904$	14.4721	0.481336
$905$	21.8885	0.727600
$906$	−5.52786	−0.183651
$907$	18.1803	0.603668	0.301834	−	0.953360i	$-0.402401\pi$
$907$	18.1803	0.603668	0.301834	+	0.953360i	$0.402401\pi$
$908$	4.76393	0.158097
$909$	−4.47214	−0.148331
$910$	64.7214	2.14549
$911$	−43.4164	−1.43845	−0.719225	−	0.694777i	$-0.755503\pi$
$911$	−43.4164	−1.43845	−0.719225	+	0.694777i	$0.755503\pi$
$912$	7.70820	0.255244
$913$	−6.69505	−0.221574
$914$	−36.4721	−1.20639
$915$	−16.9443	−0.560160
$916$	−4.29180	−0.141805
$917$	82.6099	2.72802
$918$	4.00000	0.132020
$919$	7.52786	0.248321	0.124161	−	0.992262i	$-0.460376\pi$
$919$	7.52786	0.248321	0.124161	+	0.992262i	$0.460376\pi$
$920$	0	0
$921$	−11.4164	−0.376183
$922$	22.0000	0.724531
$923$	40.0000	1.31662
$924$	−3.41641	−0.112392
$925$	−37.0132	−1.21699
$926$	24.0000	0.788689
$927$	6.00000	0.197066
$928$	4.47214	0.146805
$929$	28.8328	0.945974	0.472987	−	0.881069i	$-0.343176\pi$
$929$	28.8328	0.945974	0.472987	+	0.881069i	$0.343176\pi$
$930$	20.9443	0.686790
$931$	100.207	3.28414
$932$	−15.8885	−0.520447
$933$	−3.05573	−0.100040
$934$	40.1803	1.31474
$935$	9.88854	0.323390
$936$	−4.47214	−0.146176
$937$	30.0000	0.980057	0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000	0.980057	0.490029	+	0.871706i	$0.336986\pi$
$938$	−16.5836	−0.541473
$939$	−24.4721	−0.798618
$940$	12.9443	0.422196
$941$	−15.8197	−0.515706	−0.257853	−	0.966184i	$-0.583015\pi$
$941$	−15.8197	−0.515706	−0.257853	+	0.966184i	$0.583015\pi$
$942$	−24.6525	−0.803221
$943$	0	0
$944$	8.94427	0.291111
$945$	−14.4721	−0.470779
$946$	7.05573	0.229402
$947$	51.1935	1.66357	0.831783	−	0.555102i	$-0.187321\pi$
$947$	51.1935	1.66357	0.831783	+	0.555102i	$0.187321\pi$
$948$	4.47214	0.145248
$949$	−20.0000	−0.649227
$950$	42.1803	1.36851
$951$	28.4721	0.923272
$952$	−17.8885	−0.579771
$953$	−23.7771	−0.770215	−0.385108	−	0.922872i	$-0.625836\pi$
$953$	−23.7771	−0.770215	−0.385108	+	0.922872i	$0.625836\pi$
$954$	−0.763932	−0.0247332
$955$	8.00000	0.258874
$956$	12.9443	0.418648
$957$	3.41641	0.110437
$958$	11.0557	0.357194
$959$	93.6656	3.02462
$960$	3.23607	0.104444
$961$	10.8885	0.351243
$962$	30.2492	0.975274
$963$	−18.6525	−0.601068
$964$	3.52786	0.113625
$965$	−38.4721	−1.23846
$966$	0	0
$967$	−11.4164	−0.367127	−0.183563	−	0.983008i	$-0.558763\pi$
$967$	−11.4164	−0.367127	−0.183563	+	0.983008i	$0.558763\pi$
$968$	−10.4164	−0.334796
$969$	30.8328	0.990493
$970$	27.4164	0.880288
$971$	−21.1246	−0.677921	−0.338961	−	0.940801i	$-0.610075\pi$
$971$	−21.1246	−0.677921	−0.338961	+	0.940801i	$0.610075\pi$
$972$	1.00000	0.0320750
$973$	−4.22291	−0.135380
$974$	−25.8885	−0.829522
$975$	−24.4721	−0.783736
$976$	−5.23607	−0.167602
$977$	−54.8328	−1.75426	−0.877129	−	0.480256i	$-0.840544\pi$
$977$	−54.8328	−1.75426	−0.877129	+	0.480256i	$0.840544\pi$
$978$	6.47214	0.206956
$979$	1.16718	0.0373034
$980$	42.0689	1.34384
$981$	−9.23607	−0.294885
$982$	−33.3050	−1.06280
$983$	−27.4164	−0.874448	−0.437224	−	0.899353i	$-0.644038\pi$
$983$	−27.4164	−0.874448	−0.437224	+	0.899353i	$0.644038\pi$
$984$	−2.00000	−0.0637577
$985$	−48.3607	−1.54090
$986$	17.8885	0.569687
$987$	−17.8885	−0.569399
$988$	−34.4721	−1.09670
$989$	0	0
$990$	2.47214	0.0785696
$991$	−1.52786	−0.0485342	−0.0242671	−	0.999706i	$-0.507725\pi$
$991$	−1.52786	−0.0485342	−0.0242671	+	0.999706i	$0.507725\pi$
$992$	6.47214	0.205491
$993$	−1.52786	−0.0484853
$994$	40.0000	1.26872
$995$	30.4721	0.966032
$996$	−8.76393	−0.277696
$997$	22.9443	0.726652	0.363326	−	0.931662i	$-0.381641\pi$
$997$	22.9443	0.726652	0.363326	+	0.931662i	$0.381641\pi$
$998$	27.4164	0.867851
$999$	−6.76393	−0.214001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3174.2.a.s.1.2		2
3.2	odd	2		9522.2.a.q.1.1		2
23.22	odd	2		138.2.a.d.1.1	✓	2
69.68	even	2		414.2.a.f.1.2		2
92.91	even	2		1104.2.a.j.1.1		2
115.22	even	4		3450.2.d.x.2899.4		4
115.68	even	4		3450.2.d.x.2899.1		4
115.114	odd	2		3450.2.a.be.1.1		2
161.160	even	2		6762.2.a.cb.1.2		2
184.45	odd	2		4416.2.a.bh.1.2		2
184.91	even	2		4416.2.a.bl.1.2		2
276.275	odd	2		3312.2.a.bc.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.a.d.1.1	✓	2	23.22	odd	2
414.2.a.f.1.2		2	69.68	even	2
1104.2.a.j.1.1		2	92.91	even	2
3174.2.a.s.1.2		2	1.1	even	1	trivial
3312.2.a.bc.1.2		2	276.275	odd	2
3450.2.a.be.1.1		2	115.114	odd	2
3450.2.d.x.2899.1		4	115.68	even	4
3450.2.d.x.2899.4		4	115.22	even	4
4416.2.a.bh.1.2		2	184.45	odd	2
4416.2.a.bl.1.2		2	184.91	even	2
6762.2.a.cb.1.2		2	161.160	even	2
9522.2.a.q.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3174 = 2 \cdot 3 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3174.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} +1.00000 q^{6} -4.47214 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.23607 q^{10} +0.763932 q^{11} +1.00000 q^{12} -4.47214 q^{13} -4.47214 q^{14} +3.23607 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} +7.70820 q^{19} +3.23607 q^{20} -4.47214 q^{21} +0.763932 q^{22} +1.00000 q^{24} +5.47214 q^{25} -4.47214 q^{26} +1.00000 q^{27} -4.47214 q^{28} +4.47214 q^{29} +3.23607 q^{30} +6.47214 q^{31} +1.00000 q^{32} +0.763932 q^{33} +4.00000 q^{34} -14.4721 q^{35} +1.00000 q^{36} -6.76393 q^{37} +7.70820 q^{38} -4.47214 q^{39} +3.23607 q^{40} -2.00000 q^{41} -4.47214 q^{42} +9.23607 q^{43} +0.763932 q^{44} +3.23607 q^{45} +4.00000 q^{47} +1.00000 q^{48} +13.0000 q^{49} +5.47214 q^{50} +4.00000 q^{51} -4.47214 q^{52} -0.763932 q^{53} +1.00000 q^{54} +2.47214 q^{55} -4.47214 q^{56} +7.70820 q^{57} +4.47214 q^{58} +8.94427 q^{59} +3.23607 q^{60} -5.23607 q^{61} +6.47214 q^{62} -4.47214 q^{63} +1.00000 q^{64} -14.4721 q^{65} +0.763932 q^{66} +3.70820 q^{67} +4.00000 q^{68} -14.4721 q^{70} -8.94427 q^{71} +1.00000 q^{72} +4.47214 q^{73} -6.76393 q^{74} +5.47214 q^{75} +7.70820 q^{76} -3.41641 q^{77} -4.47214 q^{78} +4.47214 q^{79} +3.23607 q^{80} +1.00000 q^{81} -2.00000 q^{82} -8.76393 q^{83} -4.47214 q^{84} +12.9443 q^{85} +9.23607 q^{86} +4.47214 q^{87} +0.763932 q^{88} +1.52786 q^{89} +3.23607 q^{90} +20.0000 q^{91} +6.47214 q^{93} +4.00000 q^{94} +24.9443 q^{95} +1.00000 q^{96} +8.47214 q^{97} +13.0000 q^{98} +0.763932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{12} + 2 q^{15} + 2 q^{16} + 8 q^{17} + 2 q^{18} + 2 q^{19} + 2 q^{20} + 6 q^{22} + 2 q^{24} + 2 q^{25}+ \cdots + 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 + 2 * q^10 + 6 * q^11 + 2 * q^12 + 2 * q^15 + 2 * q^16 + 8 * q^17 + 2 * q^18 + 2 * q^19 + 2 * q^20 + 6 * q^22 + 2 * q^24 + 2 * q^25 + 2 * q^27 + 2 * q^30 + 4 * q^31 + 2 * q^32 + 6 * q^33 + 8 * q^34 - 20 * q^35 + 2 * q^36 - 18 * q^37 + 2 * q^38 + 2 * q^40 - 4 * q^41 + 14 * q^43 + 6 * q^44 + 2 * q^45 + 8 * q^47 + 2 * q^48 + 26 * q^49 + 2 * q^50 + 8 * q^51 - 6 * q^53 + 2 * q^54 - 4 * q^55 + 2 * q^57 + 2 * q^60 - 6 * q^61 + 4 * q^62 + 2 * q^64 - 20 * q^65 + 6 * q^66 - 6 * q^67 + 8 * q^68 - 20 * q^70 + 2 * q^72 - 18 * q^74 + 2 * q^75 + 2 * q^76 + 20 * q^77 + 2 * q^80 + 2 * q^81 - 4 * q^82 - 22 * q^83 + 8 * q^85 + 14 * q^86 + 6 * q^88 + 12 * q^89 + 2 * q^90 + 40 * q^91 + 4 * q^93 + 8 * q^94 + 32 * q^95 + 2 * q^96 + 8 * q^97 + 26 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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