LMFDB - Embedded newform 4017.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59984 q^{2} +1.00000 q^{3} +4.75917 q^{4} +1.47347 q^{5} -2.59984 q^{6} +1.66117 q^{7} -7.17341 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.59984 q^{2} +1.00000 q^{3} +4.75917 q^{4} +1.47347 q^{5} -2.59984 q^{6} +1.66117 q^{7} -7.17341 q^{8} +1.00000 q^{9} -3.83079 q^{10} -6.08530 q^{11} +4.75917 q^{12} +1.00000 q^{13} -4.31877 q^{14} +1.47347 q^{15} +9.13137 q^{16} -1.80715 q^{17} -2.59984 q^{18} +3.61918 q^{19} +7.01251 q^{20} +1.66117 q^{21} +15.8208 q^{22} -2.15865 q^{23} -7.17341 q^{24} -2.82888 q^{25} -2.59984 q^{26} +1.00000 q^{27} +7.90577 q^{28} -1.25849 q^{29} -3.83079 q^{30} +5.77473 q^{31} -9.39330 q^{32} -6.08530 q^{33} +4.69831 q^{34} +2.44768 q^{35} +4.75917 q^{36} +0.863075 q^{37} -9.40929 q^{38} +1.00000 q^{39} -10.5698 q^{40} +0.164551 q^{41} -4.31877 q^{42} -8.85666 q^{43} -28.9610 q^{44} +1.47347 q^{45} +5.61214 q^{46} +4.24988 q^{47} +9.13137 q^{48} -4.24053 q^{49} +7.35463 q^{50} -1.80715 q^{51} +4.75917 q^{52} +8.47805 q^{53} -2.59984 q^{54} -8.96653 q^{55} -11.9162 q^{56} +3.61918 q^{57} +3.27186 q^{58} -1.61742 q^{59} +7.01251 q^{60} +6.25974 q^{61} -15.0134 q^{62} +1.66117 q^{63} +6.15834 q^{64} +1.47347 q^{65} +15.8208 q^{66} +8.24719 q^{67} -8.60056 q^{68} -2.15865 q^{69} -6.36358 q^{70} +12.1783 q^{71} -7.17341 q^{72} +1.64784 q^{73} -2.24386 q^{74} -2.82888 q^{75} +17.2243 q^{76} -10.1087 q^{77} -2.59984 q^{78} +9.98339 q^{79} +13.4548 q^{80} +1.00000 q^{81} -0.427807 q^{82} +6.47202 q^{83} +7.90577 q^{84} -2.66279 q^{85} +23.0259 q^{86} -1.25849 q^{87} +43.6524 q^{88} +11.9005 q^{89} -3.83079 q^{90} +1.66117 q^{91} -10.2734 q^{92} +5.77473 q^{93} -11.0490 q^{94} +5.33276 q^{95} -9.39330 q^{96} +17.8976 q^{97} +11.0247 q^{98} -6.08530 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * 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 $

$2$	−2.59984	−1.83837	−0.919183	−	0.393832i	$-0.871149\pi$
$2$	−2.59984	−1.83837	−0.919183	+	0.393832i	$0.871149\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.75917	2.37959
$5$	1.47347	0.658957	0.329478	−	0.944163i	$-0.393127\pi$
$5$	1.47347	0.658957	0.329478	+	0.944163i	$0.393127\pi$
$6$	−2.59984	−1.06138
$7$	1.66117	0.627862	0.313931	−	0.949446i	$-0.398354\pi$
$7$	1.66117	0.627862	0.313931	+	0.949446i	$0.398354\pi$
$8$	−7.17341	−2.53618
$9$	1.00000	0.333333
$10$	−3.83079	−1.21140
$11$	−6.08530	−1.83479	−0.917394	−	0.397980i	$-0.869711\pi$
$11$	−6.08530	−1.83479	−0.917394	+	0.397980i	$0.869711\pi$
$12$	4.75917	1.37385
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−4.31877	−1.15424
$15$	1.47347	0.380449
$16$	9.13137	2.28284
$17$	−1.80715	−0.438299	−0.219150	−	0.975691i	$-0.570328\pi$
$17$	−1.80715	−0.438299	−0.219150	+	0.975691i	$0.570328\pi$
$18$	−2.59984	−0.612788
$19$	3.61918	0.830297	0.415149	−	0.909754i	$-0.363730\pi$
$19$	3.61918	0.830297	0.415149	+	0.909754i	$0.363730\pi$
$20$	7.01251	1.56804
$21$	1.66117	0.362496
$22$	15.8208	3.37301
$23$	−2.15865	−0.450109	−0.225055	−	0.974346i	$-0.572256\pi$
$23$	−2.15865	−0.450109	−0.225055	+	0.974346i	$0.572256\pi$
$24$	−7.17341	−1.46427
$25$	−2.82888	−0.565776
$26$	−2.59984	−0.509871
$27$	1.00000	0.192450
$28$	7.90577	1.49405
$29$	−1.25849	−0.233695	−0.116847	−	0.993150i	$-0.537279\pi$
$29$	−1.25849	−0.233695	−0.116847	+	0.993150i	$0.537279\pi$
$30$	−3.83079	−0.699404
$31$	5.77473	1.03717	0.518586	−	0.855026i	$-0.326459\pi$
$31$	5.77473	1.03717	0.518586	+	0.855026i	$0.326459\pi$
$32$	−9.39330	−1.66052
$33$	−6.08530	−1.05932
$34$	4.69831	0.805754
$35$	2.44768	0.413734
$36$	4.75917	0.793195
$37$	0.863075	0.141889	0.0709443	−	0.997480i	$-0.477399\pi$
$37$	0.863075	0.141889	0.0709443	+	0.997480i	$0.477399\pi$
$38$	−9.40929	−1.52639
$39$	1.00000	0.160128
$40$	−10.5698	−1.67124
$41$	0.164551	0.0256986	0.0128493	−	0.999917i	$-0.495910\pi$
$41$	0.164551	0.0256986	0.0128493	+	0.999917i	$0.495910\pi$
$42$	−4.31877	−0.666400
$43$	−8.85666	−1.35063	−0.675314	−	0.737530i	$-0.735992\pi$
$43$	−8.85666	−1.35063	−0.675314	+	0.737530i	$0.735992\pi$
$44$	−28.9610	−4.36604
$45$	1.47347	0.219652
$46$	5.61214	0.827465
$47$	4.24988	0.619909	0.309954	−	0.950751i	$-0.399686\pi$
$47$	4.24988	0.619909	0.309954	+	0.950751i	$0.399686\pi$
$48$	9.13137	1.31800
$49$	−4.24053	−0.605790
$50$	7.35463	1.04010
$51$	−1.80715	−0.253052
$52$	4.75917	0.659978
$53$	8.47805	1.16455	0.582275	−	0.812992i	$-0.302163\pi$
$53$	8.47805	1.16455	0.582275	+	0.812992i	$0.302163\pi$
$54$	−2.59984	−0.353794
$55$	−8.96653	−1.20905
$56$	−11.9162	−1.59237
$57$	3.61918	0.479372
$58$	3.27186	0.429617
$59$	−1.61742	−0.210571	−0.105285	−	0.994442i	$-0.533576\pi$
$59$	−1.61742	−0.210571	−0.105285	+	0.994442i	$0.533576\pi$
$60$	7.01251	0.905311
$61$	6.25974	0.801477	0.400739	−	0.916192i	$-0.368754\pi$
$61$	6.25974	0.801477	0.400739	+	0.916192i	$0.368754\pi$
$62$	−15.0134	−1.90670
$63$	1.66117	0.209287
$64$	6.15834	0.769792
$65$	1.47347	0.182762
$66$	15.8208	1.94741
$67$	8.24719	1.00755	0.503777	−	0.863834i	$-0.331943\pi$
$67$	8.24719	1.00755	0.503777	+	0.863834i	$0.331943\pi$
$68$	−8.60056	−1.04297
$69$	−2.15865	−0.259871
$70$	−6.36358	−0.760594
$71$	12.1783	1.44529	0.722647	−	0.691217i	$-0.242925\pi$
$71$	12.1783	1.44529	0.722647	+	0.691217i	$0.242925\pi$
$72$	−7.17341	−0.845394
$73$	1.64784	0.192865	0.0964324	−	0.995340i	$-0.469257\pi$
$73$	1.64784	0.192865	0.0964324	+	0.995340i	$0.469257\pi$
$74$	−2.24386	−0.260843
$75$	−2.82888	−0.326651
$76$	17.2243	1.97576
$77$	−10.1087	−1.15199
$78$	−2.59984	−0.294374
$79$	9.98339	1.12322	0.561609	−	0.827402i	$-0.310182\pi$
$79$	9.98339	1.12322	0.561609	+	0.827402i	$0.310182\pi$
$80$	13.4548	1.50430
$81$	1.00000	0.111111
$82$	−0.427807	−0.0472434
$83$	6.47202	0.710396	0.355198	−	0.934791i	$-0.384413\pi$
$83$	6.47202	0.710396	0.355198	+	0.934791i	$0.384413\pi$
$84$	7.90577	0.862591
$85$	−2.66279	−0.288820
$86$	23.0259	2.48295
$87$	−1.25849	−0.134924
$88$	43.6524	4.65336
$89$	11.9005	1.26145	0.630726	−	0.776006i	$-0.282757\pi$
$89$	11.9005	1.26145	0.630726	+	0.776006i	$0.282757\pi$
$90$	−3.83079	−0.403801
$91$	1.66117	0.174137
$92$	−10.2734	−1.07107
$93$	5.77473	0.598811
$94$	−11.0490	−1.13962
$95$	5.33276	0.547130
$96$	−9.39330	−0.958700
$97$	17.8976	1.81723	0.908613	−	0.417638i	$-0.137142\pi$
$97$	17.8976	1.81723	0.908613	+	0.417638i	$0.137142\pi$
$98$	11.0247	1.11366
$99$	−6.08530	−0.611596
$100$	−13.4631	−1.34631
$101$	−8.27886	−0.823777	−0.411889	−	0.911234i	$-0.635131\pi$
$101$	−8.27886	−0.823777	−0.411889	+	0.911234i	$0.635131\pi$
$102$	4.69831	0.465202
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−7.17341	−0.703410
$105$	2.44768	0.238869
$106$	−22.0416	−2.14087
$107$	−1.04571	−0.101093	−0.0505465	−	0.998722i	$-0.516096\pi$
$107$	−1.04571	−0.101093	−0.0505465	+	0.998722i	$0.516096\pi$
$108$	4.75917	0.457952
$109$	−5.88618	−0.563794	−0.281897	−	0.959445i	$-0.590964\pi$
$109$	−5.88618	−0.563794	−0.281897	+	0.959445i	$0.590964\pi$
$110$	23.3115	2.22267
$111$	0.863075	0.0819194
$112$	15.1687	1.43331
$113$	18.7278	1.76176	0.880880	−	0.473340i	$-0.156952\pi$
$113$	18.7278	1.76176	0.880880	+	0.473340i	$0.156952\pi$
$114$	−9.40929	−0.881261
$115$	−3.18071	−0.296603
$116$	−5.98935	−0.556097
$117$	1.00000	0.0924500
$118$	4.20504	0.387106
$119$	−3.00198	−0.275191
$120$	−10.5698	−0.964888
$121$	26.0309	2.36645
$122$	−16.2743	−1.47341
$123$	0.164551	0.0148371
$124$	27.4829	2.46804
$125$	−11.5356	−1.03178
$126$	−4.31877	−0.384746
$127$	8.85520	0.785772	0.392886	−	0.919587i	$-0.371477\pi$
$127$	8.85520	0.785772	0.392886	+	0.919587i	$0.371477\pi$
$128$	2.77590	0.245357
$129$	−8.85666	−0.779786
$130$	−3.83079	−0.335983
$131$	4.43193	0.387219	0.193610	−	0.981079i	$-0.437980\pi$
$131$	4.43193	0.387219	0.193610	+	0.981079i	$0.437980\pi$
$132$	−28.9610	−2.52073
$133$	6.01206	0.521312
$134$	−21.4414	−1.85225
$135$	1.47347	0.126816
$136$	12.9635	1.11161
$137$	9.72781	0.831103	0.415551	−	0.909570i	$-0.363589\pi$
$137$	9.72781	0.831103	0.415551	+	0.909570i	$0.363589\pi$
$138$	5.61214	0.477737
$139$	−2.52976	−0.214571	−0.107286	−	0.994228i	$-0.534216\pi$
$139$	−2.52976	−0.214571	−0.107286	+	0.994228i	$0.534216\pi$
$140$	11.6489	0.984515
$141$	4.24988	0.357905
$142$	−31.6616	−2.65698
$143$	−6.08530	−0.508879
$144$	9.13137	0.760948
$145$	−1.85434	−0.153995
$146$	−4.28411	−0.354556
$147$	−4.24053	−0.349753
$148$	4.10752	0.337636
$149$	19.5541	1.60194	0.800968	−	0.598708i	$-0.204319\pi$
$149$	19.5541	1.60194	0.800968	+	0.598708i	$0.204319\pi$
$150$	7.35463	0.600503
$151$	14.4192	1.17342	0.586708	−	0.809799i	$-0.300424\pi$
$151$	14.4192	1.17342	0.586708	+	0.809799i	$0.300424\pi$
$152$	−25.9619	−2.10578
$153$	−1.80715	−0.146100
$154$	26.2810	2.11778
$155$	8.50890	0.683451
$156$	4.75917	0.381039
$157$	−13.9811	−1.11582	−0.557908	−	0.829903i	$-0.688396\pi$
$157$	−13.9811	−1.11582	−0.557908	+	0.829903i	$0.688396\pi$
$158$	−25.9552	−2.06489
$159$	8.47805	0.672353
$160$	−13.8408	−1.09421
$161$	−3.58587	−0.282606
$162$	−2.59984	−0.204263
$163$	5.03905	0.394689	0.197345	−	0.980334i	$-0.436768\pi$
$163$	5.03905	0.394689	0.197345	+	0.980334i	$0.436768\pi$
$164$	0.783128	0.0611521
$165$	−8.96653	−0.698043
$166$	−16.8262	−1.30597
$167$	1.49573	0.115743	0.0578715	−	0.998324i	$-0.481569\pi$
$167$	1.49573	0.115743	0.0578715	+	0.998324i	$0.481569\pi$
$168$	−11.9162	−0.919356
$169$	1.00000	0.0769231
$170$	6.92284	0.530957
$171$	3.61918	0.276766
$172$	−42.1504	−3.21394
$173$	0.189693	0.0144221	0.00721105	−	0.999974i	$-0.497705\pi$
$173$	0.189693	0.0144221	0.00721105	+	0.999974i	$0.497705\pi$
$174$	3.27186	0.248039
$175$	−4.69924	−0.355229
$176$	−55.5672	−4.18853
$177$	−1.61742	−0.121573
$178$	−30.9394	−2.31901
$179$	−4.82869	−0.360914	−0.180457	−	0.983583i	$-0.557758\pi$
$179$	−4.82869	−0.360914	−0.180457	+	0.983583i	$0.557758\pi$
$180$	7.01251	0.522682
$181$	−12.7665	−0.948923	−0.474462	−	0.880276i	$-0.657357\pi$
$181$	−12.7665	−0.948923	−0.474462	+	0.880276i	$0.657357\pi$
$182$	−4.31877	−0.320128
$183$	6.25974	0.462733
$184$	15.4849	1.14156
$185$	1.27172	0.0934985
$186$	−15.0134	−1.10083
$187$	10.9971	0.804186
$188$	20.2259	1.47513
$189$	1.66117	0.120832
$190$	−13.8643	−1.00582
$191$	−3.95089	−0.285876	−0.142938	−	0.989732i	$-0.545655\pi$
$191$	−3.95089	−0.285876	−0.142938	+	0.989732i	$0.545655\pi$
$192$	6.15834	0.444440
$193$	−4.00899	−0.288574	−0.144287	−	0.989536i	$-0.546089\pi$
$193$	−4.00899	−0.288574	−0.144287	+	0.989536i	$0.546089\pi$
$194$	−46.5309	−3.34073
$195$	1.47347	0.105518
$196$	−20.1814	−1.44153
$197$	−8.43362	−0.600870	−0.300435	−	0.953802i	$-0.597132\pi$
$197$	−8.43362	−0.600870	−0.300435	+	0.953802i	$0.597132\pi$
$198$	15.8208	1.12434
$199$	10.8942	0.772270	0.386135	−	0.922442i	$-0.373810\pi$
$199$	10.8942	0.772270	0.386135	+	0.922442i	$0.373810\pi$
$200$	20.2927	1.43491
$201$	8.24719	0.581712
$202$	21.5237	1.51440
$203$	−2.09055	−0.146728
$204$	−8.60056	−0.602160
$205$	0.242462	0.0169343
$206$	−2.59984	−0.181139
$207$	−2.15865	−0.150036
$208$	9.13137	0.633147
$209$	−22.0238	−1.52342
$210$	−6.36358	−0.439129
$211$	17.2237	1.18573	0.592866	−	0.805301i	$-0.297996\pi$
$211$	17.2237	1.18573	0.592866	+	0.805301i	$0.297996\pi$
$212$	40.3485	2.77115
$213$	12.1783	0.834441
$214$	2.71869	0.185846
$215$	−13.0500	−0.890006
$216$	−7.17341	−0.488089
$217$	9.59278	0.651200
$218$	15.3031	1.03646
$219$	1.64784	0.111351
$220$	−42.6732	−2.87703
$221$	−1.80715	−0.121562
$222$	−2.24386	−0.150598
$223$	−10.4381	−0.698987	−0.349494	−	0.936939i	$-0.613646\pi$
$223$	−10.4381	−0.698987	−0.349494	+	0.936939i	$0.613646\pi$
$224$	−15.6038	−1.04257
$225$	−2.82888	−0.188592
$226$	−48.6892	−3.23876
$227$	−14.3370	−0.951579	−0.475790	−	0.879559i	$-0.657838\pi$
$227$	−14.3370	−0.951579	−0.475790	+	0.879559i	$0.657838\pi$
$228$	17.2243	1.14071
$229$	3.93553	0.260067	0.130034	−	0.991510i	$-0.458491\pi$
$229$	3.93553	0.260067	0.130034	+	0.991510i	$0.458491\pi$
$230$	8.26934	0.545264
$231$	−10.1087	−0.665103
$232$	9.02763	0.592693
$233$	13.4496	0.881112	0.440556	−	0.897725i	$-0.354781\pi$
$233$	13.4496	0.881112	0.440556	+	0.897725i	$0.354781\pi$
$234$	−2.59984	−0.169957
$235$	6.26208	0.408493
$236$	−7.69760	−0.501071
$237$	9.98339	0.648491
$238$	7.80468	0.505902
$239$	−4.39411	−0.284232	−0.142116	−	0.989850i	$-0.545391\pi$
$239$	−4.39411	−0.284232	−0.142116	+	0.989850i	$0.545391\pi$
$240$	13.4548	0.868505
$241$	2.50376	0.161281	0.0806405	−	0.996743i	$-0.474303\pi$
$241$	2.50376	0.161281	0.0806405	+	0.996743i	$0.474303\pi$
$242$	−67.6762	−4.35039
$243$	1.00000	0.0641500
$244$	29.7912	1.90718
$245$	−6.24830	−0.399189
$246$	−0.427807	−0.0272760
$247$	3.61918	0.230283
$248$	−41.4245	−2.63046
$249$	6.47202	0.410147
$250$	29.9908	1.89679
$251$	−5.69549	−0.359496	−0.179748	−	0.983713i	$-0.557528\pi$
$251$	−5.69549	−0.359496	−0.179748	+	0.983713i	$0.557528\pi$
$252$	7.90577	0.498017
$253$	13.1360	0.825855
$254$	−23.0221	−1.44454
$255$	−2.66279	−0.166751
$256$	−19.5336	−1.22085
$257$	−2.64830	−0.165196	−0.0825982	−	0.996583i	$-0.526322\pi$
$257$	−2.64830	−0.165196	−0.0825982	+	0.996583i	$0.526322\pi$
$258$	23.0259	1.43353
$259$	1.43371	0.0890864
$260$	7.01251	0.434897
$261$	−1.25849	−0.0778983
$262$	−11.5223	−0.711851
$263$	−15.7175	−0.969183	−0.484591	−	0.874741i	$-0.661032\pi$
$263$	−15.7175	−0.969183	−0.484591	+	0.874741i	$0.661032\pi$
$264$	43.6524	2.68662
$265$	12.4922	0.767388
$266$	−15.6304	−0.958361
$267$	11.9005	0.728299
$268$	39.2498	2.39756
$269$	−20.1989	−1.23155	−0.615773	−	0.787923i	$-0.711156\pi$
$269$	−20.1989	−1.23155	−0.615773	+	0.787923i	$0.711156\pi$
$270$	−3.83079	−0.233135
$271$	−14.1564	−0.859943	−0.429972	−	0.902842i	$-0.641476\pi$
$271$	−14.1564	−0.859943	−0.429972	+	0.902842i	$0.641476\pi$
$272$	−16.5018	−1.00057
$273$	1.66117	0.100538
$274$	−25.2908	−1.52787
$275$	17.2146	1.03808
$276$	−10.2734	−0.618385
$277$	−8.25993	−0.496291	−0.248145	−	0.968723i	$-0.579821\pi$
$277$	−8.25993	−0.496291	−0.248145	+	0.968723i	$0.579821\pi$
$278$	6.57697	0.394460
$279$	5.77473	0.345724
$280$	−17.5582	−1.04930
$281$	−24.6800	−1.47228	−0.736142	−	0.676827i	$-0.763355\pi$
$281$	−24.6800	−1.47228	−0.736142	+	0.676827i	$0.763355\pi$
$282$	−11.0490	−0.657959
$283$	−2.56780	−0.152640	−0.0763200	−	0.997083i	$-0.524317\pi$
$283$	−2.56780	−0.152640	−0.0763200	+	0.997083i	$0.524317\pi$
$284$	57.9585	3.43920
$285$	5.33276	0.315886
$286$	15.8208	0.935505
$287$	0.273347	0.0161352
$288$	−9.39330	−0.553505
$289$	−13.7342	−0.807894
$290$	4.82100	0.283099
$291$	17.8976	1.04918
$292$	7.84234	0.458938
$293$	18.8134	1.09909	0.549545	−	0.835464i	$-0.314801\pi$
$293$	18.8134	1.09909	0.549545	+	0.835464i	$0.314801\pi$
$294$	11.0247	0.642973
$295$	−2.38323	−0.138757
$296$	−6.19119	−0.359855
$297$	−6.08530	−0.353105
$298$	−50.8376	−2.94494
$299$	−2.15865	−0.124838
$300$	−13.4631	−0.777293
$301$	−14.7124	−0.848008
$302$	−37.4875	−2.15717
$303$	−8.27886	−0.475608
$304$	33.0481	1.89544
$305$	9.22355	0.528139
$306$	4.69831	0.268585
$307$	−5.98103	−0.341355	−0.170678	−	0.985327i	$-0.554596\pi$
$307$	−5.98103	−0.341355	−0.170678	+	0.985327i	$0.554596\pi$
$308$	−48.1090	−2.74127
$309$	1.00000	0.0568880
$310$	−22.1218	−1.25643
$311$	1.07875	0.0611705	0.0305852	−	0.999532i	$-0.490263\pi$
$311$	1.07875	0.0611705	0.0305852	+	0.999532i	$0.490263\pi$
$312$	−7.17341	−0.406114
$313$	17.7558	1.00362	0.501809	−	0.864979i	$-0.332668\pi$
$313$	17.7558	1.00362	0.501809	+	0.864979i	$0.332668\pi$
$314$	36.3487	2.05128
$315$	2.44768	0.137911
$316$	47.5127	2.67280
$317$	−24.3625	−1.36833	−0.684167	−	0.729325i	$-0.739834\pi$
$317$	−24.3625	−1.36833	−0.684167	+	0.729325i	$0.739834\pi$
$318$	−22.0416	−1.23603
$319$	7.65827	0.428781
$320$	9.07414	0.507260
$321$	−1.04571	−0.0583661
$322$	9.32270	0.519534
$323$	−6.54042	−0.363919
$324$	4.75917	0.264398
$325$	−2.82888	−0.156918
$326$	−13.1007	−0.725583
$327$	−5.88618	−0.325507
$328$	−1.18039	−0.0651764
$329$	7.05976	0.389217
$330$	23.3115	1.28326
$331$	28.8810	1.58744	0.793721	−	0.608282i	$-0.208141\pi$
$331$	28.8810	1.58744	0.793721	+	0.608282i	$0.208141\pi$
$332$	30.8014	1.69045
$333$	0.863075	0.0472962
$334$	−3.88866	−0.212778
$335$	12.1520	0.663935
$336$	15.1687	0.827522
$337$	22.7235	1.23783	0.618913	−	0.785459i	$-0.287573\pi$
$337$	22.7235	1.23783	0.618913	+	0.785459i	$0.287573\pi$
$338$	−2.59984	−0.141413
$339$	18.7278	1.01715
$340$	−12.6727	−0.687273
$341$	−35.1410	−1.90299
$342$	−9.40929	−0.508796
$343$	−18.6724	−1.00821
$344$	63.5324	3.42544
$345$	−3.18071	−0.171244
$346$	−0.493172	−0.0265131
$347$	11.4211	0.613118	0.306559	−	0.951852i	$-0.400822\pi$
$347$	11.4211	0.613118	0.306559	+	0.951852i	$0.400822\pi$
$348$	−5.98935	−0.321063
$349$	10.1505	0.543345	0.271673	−	0.962390i	$-0.412423\pi$
$349$	10.1505	0.543345	0.271673	+	0.962390i	$0.412423\pi$
$350$	12.2173	0.653040
$351$	1.00000	0.0533761
$352$	57.1611	3.04670
$353$	16.3691	0.871239	0.435620	−	0.900131i	$-0.356529\pi$
$353$	16.3691	0.871239	0.435620	+	0.900131i	$0.356529\pi$
$354$	4.20504	0.223496
$355$	17.9444	0.952387
$356$	56.6366	3.00173
$357$	−3.00198	−0.158882
$358$	12.5538	0.663491
$359$	9.70525	0.512223	0.256112	−	0.966647i	$-0.417559\pi$
$359$	9.70525	0.512223	0.256112	+	0.966647i	$0.417559\pi$
$360$	−10.5698	−0.557078
$361$	−5.90153	−0.310607
$362$	33.1908	1.74447
$363$	26.0309	1.36627
$364$	7.90577	0.414375
$365$	2.42804	0.127090
$366$	−16.2743	−0.850672
$367$	23.5884	1.23131	0.615653	−	0.788017i	$-0.288892\pi$
$367$	23.5884	1.23131	0.615653	+	0.788017i	$0.288892\pi$
$368$	−19.7114	−1.02753
$369$	0.164551	0.00856620
$370$	−3.30626	−0.171884
$371$	14.0834	0.731176
$372$	27.4829	1.42492
$373$	−23.6425	−1.22416	−0.612082	−	0.790794i	$-0.709668\pi$
$373$	−23.6425	−1.22416	−0.612082	+	0.790794i	$0.709668\pi$
$374$	−28.5907	−1.47839
$375$	−11.5356	−0.595698
$376$	−30.4861	−1.57220
$377$	−1.25849	−0.0648153
$378$	−4.31877	−0.222133
$379$	−13.8804	−0.712986	−0.356493	−	0.934298i	$-0.616028\pi$
$379$	−13.8804	−0.712986	−0.356493	+	0.934298i	$0.616028\pi$
$380$	25.3795	1.30194
$381$	8.85520	0.453666
$382$	10.2717	0.525545
$383$	17.5461	0.896561	0.448281	−	0.893893i	$-0.352037\pi$
$383$	17.5461	0.896561	0.448281	+	0.893893i	$0.352037\pi$
$384$	2.77590	0.141657
$385$	−14.8949	−0.759114
$386$	10.4227	0.530504
$387$	−8.85666	−0.450209
$388$	85.1778	4.32425
$389$	28.9906	1.46988	0.734942	−	0.678130i	$-0.237209\pi$
$389$	28.9906	1.46988	0.734942	+	0.678130i	$0.237209\pi$
$390$	−3.83079	−0.193980
$391$	3.90101	0.197283
$392$	30.4190	1.53639
$393$	4.43193	0.223561
$394$	21.9261	1.10462
$395$	14.7102	0.740153
$396$	−28.9610	−1.45535
$397$	−16.4268	−0.824439	−0.412220	−	0.911084i	$-0.635246\pi$
$397$	−16.4268	−0.824439	−0.412220	+	0.911084i	$0.635246\pi$
$398$	−28.3232	−1.41972
$399$	6.01206	0.300979
$400$	−25.8315	−1.29158
$401$	4.94652	0.247017	0.123509	−	0.992343i	$-0.460585\pi$
$401$	4.94652	0.247017	0.123509	+	0.992343i	$0.460585\pi$
$402$	−21.4414	−1.06940
$403$	5.77473	0.287660
$404$	−39.4005	−1.96025
$405$	1.47347	0.0732174
$406$	5.43511	0.269740
$407$	−5.25207	−0.260336
$408$	12.9635	0.641787
$409$	−35.1831	−1.73969	−0.869846	−	0.493324i	$-0.835782\pi$
$409$	−35.1831	−1.73969	−0.869846	+	0.493324i	$0.835782\pi$
$410$	−0.630363	−0.0311314
$411$	9.72781	0.479837
$412$	4.75917	0.234468
$413$	−2.68681	−0.132209
$414$	5.61214	0.275822
$415$	9.53634	0.468120
$416$	−9.39330	−0.460544
$417$	−2.52976	−0.123883
$418$	57.2584	2.80060
$419$	−13.2050	−0.645105	−0.322553	−	0.946551i	$-0.604541\pi$
$419$	−13.2050	−0.645105	−0.322553	+	0.946551i	$0.604541\pi$
$420$	11.6489	0.568410
$421$	−6.82496	−0.332628	−0.166314	−	0.986073i	$-0.553187\pi$
$421$	−6.82496	−0.332628	−0.166314	+	0.986073i	$0.553187\pi$
$422$	−44.7790	−2.17981
$423$	4.24988	0.206636
$424$	−60.8165	−2.95351
$425$	5.11222	0.247979
$426$	−31.6616	−1.53401
$427$	10.3985	0.503217
$428$	−4.97673	−0.240560
$429$	−6.08530	−0.293801
$430$	33.9280	1.63616
$431$	−6.92164	−0.333404	−0.166702	−	0.986007i	$-0.553312\pi$
$431$	−6.92164	−0.333404	−0.166702	+	0.986007i	$0.553312\pi$
$432$	9.13137	0.439333
$433$	5.25047	0.252321	0.126161	−	0.992010i	$-0.459735\pi$
$433$	5.25047	0.252321	0.126161	+	0.992010i	$0.459735\pi$
$434$	−24.9397	−1.19714
$435$	−1.85434	−0.0889090
$436$	−28.0133	−1.34160
$437$	−7.81254	−0.373725
$438$	−4.28411	−0.204703
$439$	−5.57232	−0.265952	−0.132976	−	0.991119i	$-0.542453\pi$
$439$	−5.57232	−0.265952	−0.132976	+	0.991119i	$0.542453\pi$
$440$	64.3206	3.06636
$441$	−4.24053	−0.201930
$442$	4.69831	0.223476
$443$	10.0410	0.477064	0.238532	−	0.971135i	$-0.423334\pi$
$443$	10.0410	0.477064	0.238532	+	0.971135i	$0.423334\pi$
$444$	4.10752	0.194934
$445$	17.5351	0.831242
$446$	27.1374	1.28499
$447$	19.5541	0.924878
$448$	10.2300	0.483323
$449$	−15.8640	−0.748668	−0.374334	−	0.927294i	$-0.622129\pi$
$449$	−15.8640	−0.748668	−0.374334	+	0.927294i	$0.622129\pi$
$450$	7.35463	0.346701
$451$	−1.00135	−0.0471515
$452$	89.1286	4.19226
$453$	14.4192	0.677472
$454$	37.2739	1.74935
$455$	2.44768	0.114749
$456$	−25.9619	−1.21578
$457$	−29.6074	−1.38497	−0.692487	−	0.721430i	$-0.743485\pi$
$457$	−29.6074	−1.38497	−0.692487	+	0.721430i	$0.743485\pi$
$458$	−10.2318	−0.478099
$459$	−1.80715	−0.0843508
$460$	−15.1375	−0.705792
$461$	−3.15363	−0.146879	−0.0734395	−	0.997300i	$-0.523398\pi$
$461$	−3.15363	−0.146879	−0.0734395	+	0.997300i	$0.523398\pi$
$462$	26.2810	1.22270
$463$	35.5818	1.65363	0.826813	−	0.562477i	$-0.190151\pi$
$463$	35.5818	1.65363	0.826813	+	0.562477i	$0.190151\pi$
$464$	−11.4917	−0.533489
$465$	8.50890	0.394591
$466$	−34.9668	−1.61981
$467$	−16.4053	−0.759148	−0.379574	−	0.925161i	$-0.623930\pi$
$467$	−16.4053	−0.759148	−0.379574	+	0.925161i	$0.623930\pi$
$468$	4.75917	0.219993
$469$	13.6999	0.632605
$470$	−16.2804	−0.750960
$471$	−13.9811	−0.644217
$472$	11.6024	0.534045
$473$	53.8955	2.47812
$474$	−25.9552	−1.19216
$475$	−10.2382	−0.469762
$476$	−14.2870	−0.654842
$477$	8.47805	0.388183
$478$	11.4240	0.522521
$479$	−1.34279	−0.0613537	−0.0306768	−	0.999529i	$-0.509766\pi$
$479$	−1.34279	−0.0613537	−0.0306768	+	0.999529i	$0.509766\pi$
$480$	−13.8408	−0.631742
$481$	0.863075	0.0393528
$482$	−6.50937	−0.296494
$483$	−3.58587	−0.163163
$484$	123.886	5.63116
$485$	26.3716	1.19747
$486$	−2.59984	−0.117931
$487$	−10.6934	−0.484566	−0.242283	−	0.970206i	$-0.577896\pi$
$487$	−10.6934	−0.484566	−0.242283	+	0.970206i	$0.577896\pi$
$488$	−44.9036	−2.03269
$489$	5.03905	0.227874
$490$	16.2446	0.733856
$491$	14.5719	0.657619	0.328810	−	0.944396i	$-0.393353\pi$
$491$	14.5719	0.657619	0.328810	+	0.944396i	$0.393353\pi$
$492$	0.783128	0.0353062
$493$	2.27428	0.102428
$494$	−9.40929	−0.423344
$495$	−8.96653	−0.403015
$496$	52.7312	2.36770
$497$	20.2301	0.907445
$498$	−16.8262	−0.754001
$499$	−20.0712	−0.898511	−0.449256	−	0.893403i	$-0.648311\pi$
$499$	−20.0712	−0.898511	−0.449256	+	0.893403i	$0.648311\pi$
$500$	−54.9001	−2.45521
$501$	1.49573	0.0668243
$502$	14.8074	0.660885
$503$	−19.5365	−0.871088	−0.435544	−	0.900167i	$-0.643444\pi$
$503$	−19.5365	−0.871088	−0.435544	+	0.900167i	$0.643444\pi$
$504$	−11.9162	−0.530791
$505$	−12.1987	−0.542834
$506$	−34.1516	−1.51822
$507$	1.00000	0.0444116
$508$	42.1434	1.86981
$509$	27.2397	1.20738	0.603689	−	0.797220i	$-0.293697\pi$
$509$	27.2397	1.20738	0.603689	+	0.797220i	$0.293697\pi$
$510$	6.92284	0.306548
$511$	2.73733	0.121092
$512$	45.2324	1.99901
$513$	3.61918	0.159791
$514$	6.88516	0.303691
$515$	1.47347	0.0649290
$516$	−42.1504	−1.85557
$517$	−25.8618	−1.13740
$518$	−3.72742	−0.163773
$519$	0.189693	0.00832660
$520$	−10.5698	−0.463517
$521$	8.30435	0.363820	0.181910	−	0.983315i	$-0.441772\pi$
$521$	8.30435	0.363820	0.181910	+	0.983315i	$0.441772\pi$
$522$	3.27186	0.143206
$523$	31.3435	1.37055	0.685277	−	0.728283i	$-0.259681\pi$
$523$	31.3435	1.37055	0.685277	+	0.728283i	$0.259681\pi$
$524$	21.0923	0.921422
$525$	−4.69924	−0.205091
$526$	40.8630	1.78171
$527$	−10.4358	−0.454592
$528$	−55.5672	−2.41825
$529$	−18.3402	−0.797401
$530$	−32.4777	−1.41074
$531$	−1.61742	−0.0701902
$532$	28.6124	1.24051
$533$	0.164551	0.00712751
$534$	−30.9394	−1.33888
$535$	−1.54083	−0.0666160
$536$	−59.1604	−2.55534
$537$	−4.82869	−0.208374
$538$	52.5139	2.26403
$539$	25.8049	1.11150
$540$	7.01251	0.301770
$541$	−34.5606	−1.48588	−0.742938	−	0.669361i	$-0.766568\pi$
$541$	−34.5606	−1.48588	−0.742938	+	0.669361i	$0.766568\pi$
$542$	36.8045	1.58089
$543$	−12.7665	−0.547861
$544$	16.9751	0.727803
$545$	−8.67313	−0.371516
$546$	−4.31877	−0.184826
$547$	29.3054	1.25301	0.626505	−	0.779417i	$-0.284485\pi$
$547$	29.3054	1.25301	0.626505	+	0.779417i	$0.284485\pi$
$548$	46.2963	1.97768
$549$	6.25974	0.267159
$550$	−44.7552	−1.90837
$551$	−4.55469	−0.194036
$552$	15.4849	0.659080
$553$	16.5841	0.705226
$554$	21.4745	0.912364
$555$	1.27172	0.0539814
$556$	−12.0396	−0.510591
$557$	21.3452	0.904426	0.452213	−	0.891910i	$-0.350635\pi$
$557$	21.3452	0.904426	0.452213	+	0.891910i	$0.350635\pi$
$558$	−15.0134	−0.635567
$559$	−8.85666	−0.374597
$560$	22.3507	0.944489
$561$	10.9971	0.464297
$562$	64.1640	2.70660
$563$	5.52270	0.232754	0.116377	−	0.993205i	$-0.462872\pi$
$563$	5.52270	0.232754	0.116377	+	0.993205i	$0.462872\pi$
$564$	20.2259	0.851665
$565$	27.5948	1.16092
$566$	6.67587	0.280608
$567$	1.66117	0.0697624
$568$	−87.3597	−3.66553
$569$	8.48789	0.355831	0.177916	−	0.984046i	$-0.443065\pi$
$569$	8.48789	0.355831	0.177916	+	0.984046i	$0.443065\pi$
$570$	−13.8643	−0.580713
$571$	−6.62038	−0.277054	−0.138527	−	0.990359i	$-0.544237\pi$
$571$	−6.62038	−0.277054	−0.138527	+	0.990359i	$0.544237\pi$
$572$	−28.9610	−1.21092
$573$	−3.95089	−0.165051
$574$	−0.710659	−0.0296623
$575$	6.10656	0.254661
$576$	6.15834	0.256597
$577$	−17.8999	−0.745183	−0.372591	−	0.927996i	$-0.621531\pi$
$577$	−17.8999	−0.745183	−0.372591	+	0.927996i	$0.621531\pi$
$578$	35.7067	1.48520
$579$	−4.00899	−0.166608
$580$	−8.82514	−0.366444
$581$	10.7511	0.446030
$582$	−46.5309	−1.92877
$583$	−51.5915	−2.13670
$584$	−11.8206	−0.489140
$585$	1.47347	0.0609206
$586$	−48.9118	−2.02053
$587$	42.7757	1.76554	0.882770	−	0.469805i	$-0.155676\pi$
$587$	42.7757	1.76554	0.882770	+	0.469805i	$0.155676\pi$
$588$	−20.1814	−0.832267
$589$	20.8998	0.861160
$590$	6.19602	0.255086
$591$	−8.43362	−0.346913
$592$	7.88106	0.323909
$593$	−31.3712	−1.28826	−0.644131	−	0.764916i	$-0.722781\pi$
$593$	−31.3712	−1.28826	−0.644131	+	0.764916i	$0.722781\pi$
$594$	15.8208	0.649136
$595$	−4.42334	−0.181339
$596$	93.0614	3.81194
$597$	10.8942	0.445871
$598$	5.61214	0.229498
$599$	5.17377	0.211395	0.105697	−	0.994398i	$-0.466293\pi$
$599$	5.17377	0.211395	0.105697	+	0.994398i	$0.466293\pi$
$600$	20.2927	0.828446
$601$	−17.1969	−0.701475	−0.350738	−	0.936474i	$-0.614069\pi$
$601$	−17.1969	−0.701475	−0.350738	+	0.936474i	$0.614069\pi$
$602$	38.2499	1.55895
$603$	8.24719	0.335851
$604$	68.6233	2.79224
$605$	38.3558	1.55939
$606$	21.5237	0.874341
$607$	30.0175	1.21837	0.609186	−	0.793028i	$-0.291496\pi$
$607$	30.0175	1.21837	0.609186	+	0.793028i	$0.291496\pi$
$608$	−33.9961	−1.37872
$609$	−2.09055	−0.0847135
$610$	−23.9798	−0.970912
$611$	4.24988	0.171932
$612$	−8.60056	−0.347657
$613$	−18.4302	−0.744391	−0.372195	−	0.928154i	$-0.621395\pi$
$613$	−18.4302	−0.744391	−0.372195	+	0.928154i	$0.621395\pi$
$614$	15.5497	0.627535
$615$	0.242462	0.00977701
$616$	72.5138	2.92166
$617$	9.53255	0.383766	0.191883	−	0.981418i	$-0.438541\pi$
$617$	9.53255	0.383766	0.191883	+	0.981418i	$0.438541\pi$
$618$	−2.59984	−0.104581
$619$	33.5405	1.34811	0.674054	−	0.738682i	$-0.264552\pi$
$619$	33.5405	1.34811	0.674054	+	0.738682i	$0.264552\pi$
$620$	40.4953	1.62633
$621$	−2.15865	−0.0866236
$622$	−2.80459	−0.112454
$623$	19.7687	0.792017
$624$	9.13137	0.365547
$625$	−2.85306	−0.114122
$626$	−46.1623	−1.84502
$627$	−22.0238	−0.879546
$628$	−66.5386	−2.65518
$629$	−1.55971	−0.0621897
$630$	−6.36358	−0.253531
$631$	−3.96377	−0.157795	−0.0788976	−	0.996883i	$-0.525140\pi$
$631$	−3.96377	−0.157795	−0.0788976	+	0.996883i	$0.525140\pi$
$632$	−71.6149	−2.84869
$633$	17.2237	0.684582
$634$	63.3386	2.51550
$635$	13.0479	0.517790
$636$	40.3485	1.59992
$637$	−4.24053	−0.168016
$638$	−19.9103	−0.788255
$639$	12.1783	0.481765
$640$	4.09021	0.161680
$641$	7.96743	0.314695	0.157347	−	0.987543i	$-0.449706\pi$
$641$	7.96743	0.314695	0.157347	+	0.987543i	$0.449706\pi$
$642$	2.71869	0.107298
$643$	49.8118	1.96438	0.982192	−	0.187880i	$-0.0601615\pi$
$643$	49.8118	1.96438	0.982192	+	0.187880i	$0.0601615\pi$
$644$	−17.0658	−0.672486
$645$	−13.0500	−0.513845
$646$	17.0041	0.669015
$647$	−40.9330	−1.60924	−0.804621	−	0.593789i	$-0.797631\pi$
$647$	−40.9330	−1.60924	−0.804621	+	0.593789i	$0.797631\pi$
$648$	−7.17341	−0.281798
$649$	9.84251	0.386352
$650$	7.35463	0.288472
$651$	9.59278	0.375971
$652$	23.9817	0.939197
$653$	−4.13211	−0.161702	−0.0808509	−	0.996726i	$-0.525764\pi$
$653$	−4.13211	−0.161702	−0.0808509	+	0.996726i	$0.525764\pi$
$654$	15.3031	0.598400
$655$	6.53033	0.255161
$656$	1.50258	0.0586659
$657$	1.64784	0.0642882
$658$	−18.3542	−0.715523
$659$	−27.8676	−1.08557	−0.542783	−	0.839873i	$-0.682629\pi$
$659$	−27.8676	−1.08557	−0.542783	+	0.839873i	$0.682629\pi$
$660$	−42.6732	−1.66105
$661$	24.9830	0.971725	0.485862	−	0.874035i	$-0.338506\pi$
$661$	24.9830	0.971725	0.485862	+	0.874035i	$0.338506\pi$
$662$	−75.0860	−2.91830
$663$	−1.80715	−0.0701841
$664$	−46.4264	−1.80169
$665$	8.85860	0.343522
$666$	−2.24386	−0.0869477
$667$	2.71663	0.105188
$668$	7.11844	0.275421
$669$	−10.4381	−0.403560
$670$	−31.5933	−1.22055
$671$	−38.0924	−1.47054
$672$	−15.6038	−0.601931
$673$	−50.0516	−1.92935	−0.964673	−	0.263451i	$-0.915139\pi$
$673$	−50.0516	−1.92935	−0.964673	+	0.263451i	$0.915139\pi$
$674$	−59.0774	−2.27558
$675$	−2.82888	−0.108884
$676$	4.75917	0.183045
$677$	32.9355	1.26582	0.632908	−	0.774227i	$-0.281861\pi$
$677$	32.9355	1.26582	0.632908	+	0.774227i	$0.281861\pi$
$678$	−48.6892	−1.86990
$679$	29.7309	1.14097
$680$	19.1013	0.732501
$681$	−14.3370	−0.549395
$682$	91.3609	3.49839
$683$	43.5202	1.66525	0.832627	−	0.553834i	$-0.186836\pi$
$683$	43.5202	1.66525	0.832627	+	0.553834i	$0.186836\pi$
$684$	17.2243	0.658588
$685$	14.3337	0.547661
$686$	48.5452	1.85346
$687$	3.93553	0.150150
$688$	−80.8735	−3.08327
$689$	8.47805	0.322988
$690$	8.26934	0.314808
$691$	40.4584	1.53911	0.769556	−	0.638580i	$-0.220478\pi$
$691$	40.4584	1.53911	0.769556	+	0.638580i	$0.220478\pi$
$692$	0.902782	0.0343186
$693$	−10.1087	−0.383998
$694$	−29.6931	−1.12713
$695$	−3.72753	−0.141393
$696$	9.02763	0.342191
$697$	−0.297370	−0.0112637
$698$	−26.3897	−0.998867
$699$	13.4496	0.508710
$700$	−22.3645	−0.845298
$701$	−23.9810	−0.905750	−0.452875	−	0.891574i	$-0.649602\pi$
$701$	−23.9810	−0.905750	−0.452875	+	0.891574i	$0.649602\pi$
$702$	−2.59984	−0.0981247
$703$	3.12362	0.117810
$704$	−37.4754	−1.41241
$705$	6.26208	0.235844
$706$	−42.5570	−1.60166
$707$	−13.7526	−0.517218
$708$	−7.69760	−0.289293
$709$	−36.7533	−1.38030	−0.690150	−	0.723667i	$-0.742455\pi$
$709$	−36.7533	−1.38030	−0.690150	+	0.723667i	$0.742455\pi$
$710$	−46.6525	−1.75084
$711$	9.98339	0.374406
$712$	−85.3672	−3.19927
$713$	−12.4656	−0.466841
$714$	7.80468	0.292083
$715$	−8.96653	−0.335329
$716$	−22.9806	−0.858825
$717$	−4.39411	−0.164101
$718$	−25.2321	−0.941653
$719$	−20.5850	−0.767691	−0.383846	−	0.923397i	$-0.625400\pi$
$719$	−20.5850	−0.767691	−0.383846	+	0.923397i	$0.625400\pi$
$720$	13.4548	0.501432
$721$	1.66117	0.0618650
$722$	15.3430	0.571009
$723$	2.50376	0.0931157
$724$	−60.7578	−2.25804
$725$	3.56010	0.132219
$726$	−67.6762	−2.51170
$727$	−18.3682	−0.681239	−0.340619	−	0.940201i	$-0.610637\pi$
$727$	−18.3682	−0.681239	−0.340619	+	0.940201i	$0.610637\pi$
$728$	−11.9162	−0.441644
$729$	1.00000	0.0370370
$730$	−6.31252	−0.233637
$731$	16.0054	0.591980
$732$	29.7912	1.10111
$733$	−42.7628	−1.57948	−0.789740	−	0.613441i	$-0.789785\pi$
$733$	−42.7628	−1.57948	−0.789740	+	0.613441i	$0.789785\pi$
$734$	−61.3262	−2.26359
$735$	−6.24830	−0.230472
$736$	20.2768	0.747414
$737$	−50.1866	−1.84865
$738$	−0.427807	−0.0157478
$739$	−16.0770	−0.591401	−0.295701	−	0.955281i	$-0.595553\pi$
$739$	−16.0770	−0.591401	−0.295701	+	0.955281i	$0.595553\pi$
$740$	6.05232	0.222488
$741$	3.61918	0.132954
$742$	−36.6147	−1.34417
$743$	3.52142	0.129188	0.0645942	−	0.997912i	$-0.479425\pi$
$743$	3.52142	0.129188	0.0645942	+	0.997912i	$0.479425\pi$
$744$	−41.4245	−1.51869
$745$	28.8124	1.05561
$746$	61.4668	2.25046
$747$	6.47202	0.236799
$748$	52.3370	1.91363
$749$	−1.73710	−0.0634724
$750$	29.9908	1.09511
$751$	21.5784	0.787407	0.393703	−	0.919238i	$-0.371194\pi$
$751$	21.5784	0.787407	0.393703	+	0.919238i	$0.371194\pi$
$752$	38.8072	1.41515
$753$	−5.69549	−0.207555
$754$	3.27186	0.119154
$755$	21.2462	0.773230
$756$	7.90577	0.287530
$757$	−25.3788	−0.922407	−0.461203	−	0.887294i	$-0.652582\pi$
$757$	−25.3788	−0.922407	−0.461203	+	0.887294i	$0.652582\pi$
$758$	36.0867	1.31073
$759$	13.1360	0.476808
$760$	−38.2541	−1.38762
$761$	−9.57213	−0.346989	−0.173495	−	0.984835i	$-0.555506\pi$
$761$	−9.57213	−0.346989	−0.173495	+	0.984835i	$0.555506\pi$
$762$	−23.0221	−0.834003
$763$	−9.77792	−0.353985
$764$	−18.8030	−0.680267
$765$	−2.66279	−0.0962735
$766$	−45.6169	−1.64821
$767$	−1.61742	−0.0584018
$768$	−19.5336	−0.704857
$769$	38.4150	1.38528	0.692639	−	0.721284i	$-0.256448\pi$
$769$	38.4150	1.38528	0.692639	+	0.721284i	$0.256448\pi$
$770$	38.7243	1.39553
$771$	−2.64830	−0.0953762
$772$	−19.0795	−0.686686
$773$	40.3523	1.45137	0.725685	−	0.688027i	$-0.241523\pi$
$773$	40.3523	1.45137	0.725685	+	0.688027i	$0.241523\pi$
$774$	23.0259	0.827649
$775$	−16.3360	−0.586806
$776$	−128.387	−4.60882
$777$	1.43371	0.0514341
$778$	−75.3710	−2.70218
$779$	0.595541	0.0213375
$780$	7.01251	0.251088
$781$	−74.1085	−2.65181
$782$	−10.1420	−0.362678
$783$	−1.25849	−0.0449746
$784$	−38.7218	−1.38292
$785$	−20.6008	−0.735275
$786$	−11.5223	−0.410987
$787$	43.8649	1.56361	0.781807	−	0.623521i	$-0.214298\pi$
$787$	43.8649	1.56361	0.781807	+	0.623521i	$0.214298\pi$
$788$	−40.1370	−1.42982
$789$	−15.7175	−0.559558
$790$	−38.2443	−1.36067
$791$	31.1099	1.10614
$792$	43.6524	1.55112
$793$	6.25974	0.222290
$794$	42.7072	1.51562
$795$	12.4922	0.443052
$796$	51.8474	1.83768
$797$	26.6206	0.942950	0.471475	−	0.881879i	$-0.343722\pi$
$797$	26.6206	0.942950	0.471475	+	0.881879i	$0.343722\pi$
$798$	−15.6304	−0.553310
$799$	−7.68019	−0.271706
$800$	26.5725	0.939480
$801$	11.9005	0.420484
$802$	−12.8602	−0.454108
$803$	−10.0276	−0.353866
$804$	39.2498	1.38423
$805$	−5.28369	−0.186225
$806$	−15.0134	−0.528823
$807$	−20.1989	−0.711034
$808$	59.3876	2.08925
$809$	7.55345	0.265565	0.132783	−	0.991145i	$-0.457609\pi$
$809$	7.55345	0.265565	0.132783	+	0.991145i	$0.457609\pi$
$810$	−3.83079	−0.134600
$811$	−22.1737	−0.778623	−0.389311	−	0.921106i	$-0.627287\pi$
$811$	−22.1737	−0.778623	−0.389311	+	0.921106i	$0.627287\pi$
$812$	−9.94930	−0.349152
$813$	−14.1564	−0.496488
$814$	13.6545	0.478592
$815$	7.42491	0.260083
$816$	−16.5018	−0.577679
$817$	−32.0539	−1.12142
$818$	91.4704	3.19819
$819$	1.66117	0.0580458
$820$	1.15392	0.0402966
$821$	−46.8972	−1.63672	−0.818361	−	0.574705i	$-0.805117\pi$
$821$	−46.8972	−1.63672	−0.818361	+	0.574705i	$0.805117\pi$
$822$	−25.2908	−0.882116
$823$	−15.5312	−0.541384	−0.270692	−	0.962666i	$-0.587252\pi$
$823$	−15.5312	−0.541384	−0.270692	+	0.962666i	$0.587252\pi$
$824$	−7.17341	−0.249897
$825$	17.2146	0.599335
$826$	6.98527	0.243049
$827$	−30.1584	−1.04871	−0.524356	−	0.851499i	$-0.675694\pi$
$827$	−30.1584	−1.04871	−0.524356	+	0.851499i	$0.675694\pi$
$828$	−10.2734	−0.357025
$829$	9.88855	0.343444	0.171722	−	0.985145i	$-0.445067\pi$
$829$	9.88855	0.343444	0.171722	+	0.985145i	$0.445067\pi$
$830$	−24.7930	−0.860576
$831$	−8.25993	−0.286534
$832$	6.15834	0.213502
$833$	7.66329	0.265517
$834$	6.57697	0.227742
$835$	2.20392	0.0762697
$836$	−104.815	−3.62511
$837$	5.77473	0.199604
$838$	34.3308	1.18594
$839$	9.03825	0.312035	0.156018	−	0.987754i	$-0.450134\pi$
$839$	9.03825	0.312035	0.156018	+	0.987754i	$0.450134\pi$
$840$	−17.5582	−0.605816
$841$	−27.4162	−0.945387
$842$	17.7438	0.611492
$843$	−24.6800	−0.850024
$844$	81.9708	2.82155
$845$	1.47347	0.0506890
$846$	−11.0490	−0.379873
$847$	43.2417	1.48580
$848$	77.4162	2.65848
$849$	−2.56780	−0.0881267
$850$	−13.2910	−0.455876
$851$	−1.86308	−0.0638654
$852$	57.9585	1.98563
$853$	38.1506	1.30625	0.653126	−	0.757250i	$-0.273457\pi$
$853$	38.1506	1.30625	0.653126	+	0.757250i	$0.273457\pi$
$854$	−27.0343	−0.925096
$855$	5.33276	0.182377
$856$	7.50133	0.256390
$857$	45.6200	1.55835	0.779175	−	0.626806i	$-0.215638\pi$
$857$	45.6200	1.55835	0.779175	+	0.626806i	$0.215638\pi$
$858$	15.8208	0.540114
$859$	−8.39910	−0.286574	−0.143287	−	0.989681i	$-0.545767\pi$
$859$	−8.39910	−0.286574	−0.143287	+	0.989681i	$0.545767\pi$
$860$	−62.1074	−2.11785
$861$	0.273347	0.00931565
$862$	17.9952	0.612918
$863$	44.2199	1.50526	0.752631	−	0.658443i	$-0.228784\pi$
$863$	44.2199	1.50526	0.752631	+	0.658443i	$0.228784\pi$
$864$	−9.39330	−0.319567
$865$	0.279508	0.00950354
$866$	−13.6504	−0.463859
$867$	−13.7342	−0.466438
$868$	45.6537	1.54959
$869$	−60.7519	−2.06087
$870$	4.82100	0.163447
$871$	8.24719	0.279445
$872$	42.2240	1.42988
$873$	17.8976	0.605742
$874$	20.3114	0.687042
$875$	−19.1626	−0.647814
$876$	7.84234	0.264968
$877$	−16.3550	−0.552271	−0.276135	−	0.961119i	$-0.589054\pi$
$877$	−16.3550	−0.552271	−0.276135	+	0.961119i	$0.589054\pi$
$878$	14.4871	0.488918
$879$	18.8134	0.634560
$880$	−81.8767	−2.76006
$881$	5.88936	0.198418	0.0992088	−	0.995067i	$-0.468369\pi$
$881$	5.88936	0.198418	0.0992088	+	0.995067i	$0.468369\pi$
$882$	11.0247	0.371221
$883$	−8.51362	−0.286506	−0.143253	−	0.989686i	$-0.545756\pi$
$883$	−8.51362	−0.286506	−0.143253	+	0.989686i	$0.545756\pi$
$884$	−8.60056	−0.289268
$885$	−2.38323	−0.0801114
$886$	−26.1051	−0.877017
$887$	49.7867	1.67167	0.835836	−	0.548979i	$-0.184983\pi$
$887$	49.7867	1.67167	0.835836	+	0.548979i	$0.184983\pi$
$888$	−6.19119	−0.207763
$889$	14.7100	0.493356
$890$	−45.5884	−1.52813
$891$	−6.08530	−0.203865
$892$	−49.6767	−1.66330
$893$	15.3811	0.514708
$894$	−50.8376	−1.70026
$895$	−7.11495	−0.237827
$896$	4.61123	0.154050
$897$	−2.15865	−0.0720752
$898$	41.2438	1.37632
$899$	−7.26741	−0.242382
$900$	−13.4631	−0.448771
$901$	−15.3212	−0.510422
$902$	2.60334	0.0866817
$903$	−14.7124	−0.489597
$904$	−134.342	−4.46814
$905$	−18.8110	−0.625300
$906$	−37.4875	−1.24544
$907$	−28.3370	−0.940913	−0.470457	−	0.882423i	$-0.655911\pi$
$907$	−28.3370	−0.940913	−0.470457	+	0.882423i	$0.655911\pi$
$908$	−68.2322	−2.26436
$909$	−8.27886	−0.274592
$910$	−6.36358	−0.210951
$911$	−9.06633	−0.300381	−0.150190	−	0.988657i	$-0.547989\pi$
$911$	−9.06633	−0.300381	−0.150190	+	0.988657i	$0.547989\pi$
$912$	33.0481	1.09433
$913$	−39.3842	−1.30343
$914$	76.9745	2.54609
$915$	9.22355	0.304921
$916$	18.7299	0.618852
$917$	7.36217	0.243120
$918$	4.69831	0.155067
$919$	−47.9551	−1.58189	−0.790946	−	0.611886i	$-0.790411\pi$
$919$	−47.9551	−1.58189	−0.790946	+	0.611886i	$0.790411\pi$
$920$	22.8165	0.752239
$921$	−5.98103	−0.197081
$922$	8.19892	0.270017
$923$	12.1783	0.400853
$924$	−48.1090	−1.58267
$925$	−2.44153	−0.0802771
$926$	−92.5070	−3.03997
$927$	1.00000	0.0328443
$928$	11.8213	0.388054
$929$	5.32977	0.174864	0.0874320	−	0.996170i	$-0.472134\pi$
$929$	5.32977	0.174864	0.0874320	+	0.996170i	$0.472134\pi$
$930$	−22.1218	−0.725402
$931$	−15.3472	−0.502985
$932$	64.0089	2.09668
$933$	1.07875	0.0353168
$934$	42.6513	1.39559
$935$	16.2039	0.529924
$936$	−7.17341	−0.234470
$937$	25.5327	0.834117	0.417059	−	0.908880i	$-0.363061\pi$
$937$	25.5327	0.834117	0.417059	+	0.908880i	$0.363061\pi$
$938$	−35.6177	−1.16296
$939$	17.7558	0.579439
$940$	29.8023	0.972045
$941$	−34.6693	−1.13019	−0.565094	−	0.825027i	$-0.691160\pi$
$941$	−34.6693	−1.13019	−0.565094	+	0.825027i	$0.691160\pi$
$942$	36.3487	1.18431
$943$	−0.355209	−0.0115672
$944$	−14.7693	−0.480700
$945$	2.44768	0.0796231
$946$	−140.120	−4.55568
$947$	38.1269	1.23896	0.619478	−	0.785014i	$-0.287344\pi$
$947$	38.1269	1.23896	0.619478	+	0.785014i	$0.287344\pi$
$948$	47.5127	1.54314
$949$	1.64784	0.0534911
$950$	26.6177	0.863594
$951$	−24.3625	−0.790008
$952$	21.5344	0.697936
$953$	7.00686	0.226974	0.113487	−	0.993539i	$-0.463798\pi$
$953$	7.00686	0.226974	0.113487	+	0.993539i	$0.463798\pi$
$954$	−22.0416	−0.713623
$955$	−5.82153	−0.188380
$956$	−20.9123	−0.676353
$957$	7.65827	0.247557
$958$	3.49104	0.112790
$959$	16.1595	0.521818
$960$	9.07414	0.292867
$961$	2.34746	0.0757245
$962$	−2.24386	−0.0723448
$963$	−1.04571	−0.0336977
$964$	11.9158	0.383782
$965$	−5.90714	−0.190158
$966$	9.32270	0.299953
$967$	−43.6602	−1.40402	−0.702009	−	0.712168i	$-0.747713\pi$
$967$	−43.6602	−1.40402	−0.702009	+	0.712168i	$0.747713\pi$
$968$	−186.730	−6.00174
$969$	−6.54042	−0.210109
$970$	−68.5621	−2.20139
$971$	−57.9623	−1.86010	−0.930049	−	0.367435i	$-0.880236\pi$
$971$	−57.9623	−1.86010	−0.930049	+	0.367435i	$0.880236\pi$
$972$	4.75917	0.152651
$973$	−4.20235	−0.134721
$974$	27.8013	0.890810
$975$	−2.82888	−0.0905966
$976$	57.1600	1.82965
$977$	29.1329	0.932044	0.466022	−	0.884773i	$-0.345687\pi$
$977$	29.1329	0.932044	0.466022	+	0.884773i	$0.345687\pi$
$978$	−13.1007	−0.418915
$979$	−72.4182	−2.31450
$980$	−29.7367	−0.949906
$981$	−5.88618	−0.187931
$982$	−37.8845	−1.20894
$983$	−41.1617	−1.31285	−0.656427	−	0.754389i	$-0.727933\pi$
$983$	−41.1617	−1.31285	−0.656427	+	0.754389i	$0.727933\pi$
$984$	−1.18039	−0.0376296
$985$	−12.4267	−0.395948
$986$	−5.91276	−0.188301
$987$	7.05976	0.224715
$988$	17.2243	0.547978
$989$	19.1184	0.607930
$990$	23.3115	0.740890
$991$	38.8382	1.23374	0.616869	−	0.787066i	$-0.288401\pi$
$991$	38.8382	1.23374	0.616869	+	0.787066i	$0.288401\pi$
$992$	−54.2437	−1.72224
$993$	28.8810	0.916510
$994$	−52.5951	−1.66822
$995$	16.0523	0.508893
$996$	30.8014	0.975981
$997$	−40.6308	−1.28679	−0.643394	−	0.765535i	$-0.722474\pi$
$997$	−40.6308	−1.28679	−0.643394	+	0.765535i	$0.722474\pi$
$998$	52.1820	1.65179
$999$	0.863075	0.0273065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.2	✓	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59984 q^{2} +1.00000 q^{3} +4.75917 q^{4} +1.47347 q^{5} -2.59984 q^{6} +1.66117 q^{7} -7.17341 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.59984 q^{2} +1.00000 q^{3} +4.75917 q^{4} +1.47347 q^{5} -2.59984 q^{6} +1.66117 q^{7} -7.17341 q^{8} +1.00000 q^{9} -3.83079 q^{10} -6.08530 q^{11} +4.75917 q^{12} +1.00000 q^{13} -4.31877 q^{14} +1.47347 q^{15} +9.13137 q^{16} -1.80715 q^{17} -2.59984 q^{18} +3.61918 q^{19} +7.01251 q^{20} +1.66117 q^{21} +15.8208 q^{22} -2.15865 q^{23} -7.17341 q^{24} -2.82888 q^{25} -2.59984 q^{26} +1.00000 q^{27} +7.90577 q^{28} -1.25849 q^{29} -3.83079 q^{30} +5.77473 q^{31} -9.39330 q^{32} -6.08530 q^{33} +4.69831 q^{34} +2.44768 q^{35} +4.75917 q^{36} +0.863075 q^{37} -9.40929 q^{38} +1.00000 q^{39} -10.5698 q^{40} +0.164551 q^{41} -4.31877 q^{42} -8.85666 q^{43} -28.9610 q^{44} +1.47347 q^{45} +5.61214 q^{46} +4.24988 q^{47} +9.13137 q^{48} -4.24053 q^{49} +7.35463 q^{50} -1.80715 q^{51} +4.75917 q^{52} +8.47805 q^{53} -2.59984 q^{54} -8.96653 q^{55} -11.9162 q^{56} +3.61918 q^{57} +3.27186 q^{58} -1.61742 q^{59} +7.01251 q^{60} +6.25974 q^{61} -15.0134 q^{62} +1.66117 q^{63} +6.15834 q^{64} +1.47347 q^{65} +15.8208 q^{66} +8.24719 q^{67} -8.60056 q^{68} -2.15865 q^{69} -6.36358 q^{70} +12.1783 q^{71} -7.17341 q^{72} +1.64784 q^{73} -2.24386 q^{74} -2.82888 q^{75} +17.2243 q^{76} -10.1087 q^{77} -2.59984 q^{78} +9.98339 q^{79} +13.4548 q^{80} +1.00000 q^{81} -0.427807 q^{82} +6.47202 q^{83} +7.90577 q^{84} -2.66279 q^{85} +23.0259 q^{86} -1.25849 q^{87} +43.6524 q^{88} +11.9005 q^{89} -3.83079 q^{90} +1.66117 q^{91} -10.2734 q^{92} +5.77473 q^{93} -11.0490 q^{94} +5.33276 q^{95} -9.39330 q^{96} +17.8976 q^{97} +11.0247 q^{98} -6.08530 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more