LMFDB - Embedded newform 119.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [119,2,Mod(1,119)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(119, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("119.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	119.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:	$0.950219784053$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.453749.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 10x^{2} + x - 3 $ x^5 - 2x^4 - 5x^3 + 10*x^2 + x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.32183$ of defining polynomial
Character	$\chi$	$=$	119.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.877834 q^{2} +0.907578 q^{3} -1.22941 q^{4} +3.03818 q^{5} +0.796703 q^{6} -1.00000 q^{7} -2.83488 q^{8} -2.17630 q^{9} +2.66702 q^{10} +4.78178 q^{11} -1.11578 q^{12} -4.39933 q^{13} -0.877834 q^{14} +2.75739 q^{15} -0.0297440 q^{16} +1.00000 q^{17} -1.91043 q^{18} -2.64366 q^{19} -3.73516 q^{20} -0.907578 q^{21} +4.19761 q^{22} -8.45881 q^{23} -2.57288 q^{24} +4.23054 q^{25} -3.86188 q^{26} -4.69790 q^{27} +1.22941 q^{28} +7.04298 q^{29} +2.42053 q^{30} -3.42063 q^{31} +5.64366 q^{32} +4.33984 q^{33} +0.877834 q^{34} -3.03818 q^{35} +2.67556 q^{36} +9.66977 q^{37} -2.32069 q^{38} -3.99273 q^{39} -8.61289 q^{40} +1.33675 q^{41} -0.796703 q^{42} +2.52513 q^{43} -5.87875 q^{44} -6.61200 q^{45} -7.42544 q^{46} -5.57082 q^{47} -0.0269950 q^{48} +1.00000 q^{49} +3.71372 q^{50} +0.907578 q^{51} +5.40856 q^{52} +5.17630 q^{53} -4.12398 q^{54} +14.5279 q^{55} +2.83488 q^{56} -2.39933 q^{57} +6.18257 q^{58} +9.28732 q^{59} -3.38995 q^{60} +6.66325 q^{61} -3.00275 q^{62} +2.17630 q^{63} +5.01368 q^{64} -13.3659 q^{65} +3.80966 q^{66} +5.28251 q^{67} -1.22941 q^{68} -7.67704 q^{69} -2.66702 q^{70} -11.9310 q^{71} +6.16956 q^{72} +12.7155 q^{73} +8.48845 q^{74} +3.83955 q^{75} +3.25013 q^{76} -4.78178 q^{77} -3.50496 q^{78} +1.94051 q^{79} -0.0903677 q^{80} +2.26519 q^{81} +1.17345 q^{82} -4.58417 q^{83} +1.11578 q^{84} +3.03818 q^{85} +2.21664 q^{86} +6.39206 q^{87} -13.5558 q^{88} -13.3956 q^{89} -5.80424 q^{90} +4.39933 q^{91} +10.3993 q^{92} -3.10449 q^{93} -4.89026 q^{94} -8.03191 q^{95} +5.12206 q^{96} -15.1668 q^{97} +0.877834 q^{98} -10.4066 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - q^{6} - 5 q^{7} + 6 q^{8} + 11 q^{9} + 4 q^{10} - 2 q^{11} - 22 q^{12} + 2 q^{13} - 2 q^{14} + 8 q^{15} + 4 q^{16} + 5 q^{17} - 18 q^{18} + 6 q^{19} - 19 q^{20} + 2 q^{21}+ \cdots - 62 q^{99}+O(q^{100}) $ 5 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - q^6 - 5 * q^7 + 6 * q^8 + 11 * q^9 + 4 * q^10 - 2 * q^11 - 22 * q^12 + 2 * q^13 - 2 * q^14 + 8 * q^15 + 4 * q^16 + 5 * q^17 - 18 * q^18 + 6 * q^19 - 19 * q^20 + 2 * q^21 + 6 * q^22 - 10 * q^23 + 2 * q^24 + 21 * q^25 - 26 * q^26 - 26 * q^27 - 10 * q^28 - 8 * q^29 - 51 * q^30 + 9 * q^32 + 6 * q^33 + 2 * q^34 + 39 * q^36 + 8 * q^37 + 14 * q^38 + 14 * q^39 + 5 * q^40 + 18 * q^41 + q^42 + 8 * q^43 - 14 * q^44 + 8 * q^46 - 10 * q^47 - 27 * q^48 + 5 * q^49 + 27 * q^50 - 2 * q^51 + 4 * q^52 + 4 * q^53 + 5 * q^54 - 24 * q^55 - 6 * q^56 + 12 * q^57 + 12 * q^58 + 8 * q^59 - 7 * q^60 + 22 * q^61 + 16 * q^62 - 11 * q^63 - 16 * q^64 - 30 * q^65 + 68 * q^66 + 16 * q^67 + 10 * q^68 - 32 * q^69 - 4 * q^70 - 2 * q^71 + 9 * q^72 + 10 * q^73 - 40 * q^74 - 14 * q^75 + 24 * q^76 + 2 * q^77 + 30 * q^78 + 18 * q^79 - 4 * q^80 + 25 * q^81 - 31 * q^82 - 12 * q^83 + 22 * q^84 + 23 * q^86 - 26 * q^87 - 46 * q^88 + 20 * q^89 + 97 * q^90 - 2 * q^91 + 28 * q^92 - 28 * q^93 - 42 * q^94 - 22 * q^95 - 18 * q^96 + 12 * q^97 + 2 * q^98 - 62 * 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 $

$2$	0.877834	0.620723	0.310361	−	0.950619i	$-0.399550\pi$
$2$	0.877834	0.620723	0.310361	+	0.950619i	$0.399550\pi$
$3$	0.907578	0.523991	0.261995	−	0.965069i	$-0.415620\pi$
$3$	0.907578	0.523991	0.261995	+	0.965069i	$0.415620\pi$
$4$	−1.22941	−0.614704
$5$	3.03818	1.35872	0.679358	−	0.733807i	$-0.262258\pi$
$5$	3.03818	1.35872	0.679358	+	0.733807i	$0.262258\pi$
$6$	0.796703	0.325253
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.83488	−1.00228
$9$	−2.17630	−0.725434
$10$	2.66702	0.843385
$11$	4.78178	1.44176	0.720880	−	0.693060i	$-0.243738\pi$
$11$	4.78178	1.44176	0.720880	+	0.693060i	$0.243738\pi$
$12$	−1.11578	−0.322099
$13$	−4.39933	−1.22015	−0.610077	−	0.792342i	$-0.708861\pi$
$13$	−4.39933	−1.22015	−0.610077	+	0.792342i	$0.708861\pi$
$14$	−0.877834	−0.234611
$15$	2.75739	0.711954
$16$	−0.0297440	−0.00743600
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.91043	−0.450293
$19$	−2.64366	−0.606497	−0.303248	−	0.952912i	$-0.598071\pi$
$19$	−2.64366	−0.606497	−0.303248	+	0.952912i	$0.598071\pi$
$20$	−3.73516	−0.835207
$21$	−0.907578	−0.198050
$22$	4.19761	0.894933
$23$	−8.45881	−1.76378	−0.881892	−	0.471451i	$-0.843730\pi$
$23$	−8.45881	−1.76378	−0.881892	+	0.471451i	$0.843730\pi$
$24$	−2.57288	−0.525187
$25$	4.23054	0.846109
$26$	−3.86188	−0.757377
$27$	−4.69790	−0.904111
$28$	1.22941	0.232336
$29$	7.04298	1.30785	0.653925	−	0.756560i	$-0.273121\pi$
$29$	7.04298	1.30785	0.653925	+	0.756560i	$0.273121\pi$
$30$	2.42053	0.441926
$31$	−3.42063	−0.614364	−0.307182	−	0.951651i	$-0.599386\pi$
$31$	−3.42063	−0.614364	−0.307182	+	0.951651i	$0.599386\pi$
$32$	5.64366	0.997667
$33$	4.33984	0.755469
$34$	0.877834	0.150547
$35$	−3.03818	−0.513546
$36$	2.67556	0.445927
$37$	9.66977	1.58970	0.794850	−	0.606806i	$-0.207549\pi$
$37$	9.66977	1.58970	0.794850	+	0.606806i	$0.207549\pi$
$38$	−2.32069	−0.376466
$39$	−3.99273	−0.639349
$40$	−8.61289	−1.36182
$41$	1.33675	0.208766	0.104383	−	0.994537i	$-0.466713\pi$
$41$	1.33675	0.208766	0.104383	+	0.994537i	$0.466713\pi$
$42$	−0.796703	−0.122934
$43$	2.52513	0.385078	0.192539	−	0.981289i	$-0.438328\pi$
$43$	2.52513	0.385078	0.192539	+	0.981289i	$0.438328\pi$
$44$	−5.87875	−0.886255
$45$	−6.61200	−0.985659
$46$	−7.42544	−1.09482
$47$	−5.57082	−0.812588	−0.406294	−	0.913742i	$-0.633179\pi$
$47$	−5.57082	−0.812588	−0.406294	+	0.913742i	$0.633179\pi$
$48$	−0.0269950	−0.00389639
$49$	1.00000	0.142857
$50$	3.71372	0.525199
$51$	0.907578	0.127086
$52$	5.40856	0.750033
$53$	5.17630	0.711020	0.355510	−	0.934673i	$-0.384307\pi$
$53$	5.17630	0.711020	0.355510	+	0.934673i	$0.384307\pi$
$54$	−4.12398	−0.561202
$55$	14.5279	1.95894
$56$	2.83488	0.378827
$57$	−2.39933	−0.317799
$58$	6.18257	0.811812
$59$	9.28732	1.20911	0.604553	−	0.796565i	$-0.293352\pi$
$59$	9.28732	1.20911	0.604553	+	0.796565i	$0.293352\pi$
$60$	−3.38995	−0.437641
$61$	6.66325	0.853141	0.426571	−	0.904454i	$-0.359722\pi$
$61$	6.66325	0.853141	0.426571	+	0.904454i	$0.359722\pi$
$62$	−3.00275	−0.381350
$63$	2.17630	0.274188
$64$	5.01368	0.626710
$65$	−13.3659	−1.65784
$66$	3.80966	0.468937
$67$	5.28251	0.645362	0.322681	−	0.946508i	$-0.395416\pi$
$67$	5.28251	0.645362	0.322681	+	0.946508i	$0.395416\pi$
$68$	−1.22941	−0.149088
$69$	−7.67704	−0.924206
$70$	−2.66702	−0.318770
$71$	−11.9310	−1.41595	−0.707973	−	0.706239i	$-0.750390\pi$
$71$	−11.9310	−1.41595	−0.707973	+	0.706239i	$0.750390\pi$
$72$	6.16956	0.727090
$73$	12.7155	1.48823	0.744116	−	0.668050i	$-0.232871\pi$
$73$	12.7155	1.48823	0.744116	+	0.668050i	$0.232871\pi$
$74$	8.48845	0.986763
$75$	3.83955	0.443353
$76$	3.25013	0.372816
$77$	−4.78178	−0.544934
$78$	−3.50496	−0.396858
$79$	1.94051	0.218325	0.109162	−	0.994024i	$-0.465183\pi$
$79$	1.94051	0.218325	0.109162	+	0.994024i	$0.465183\pi$
$80$	−0.0903677	−0.0101034
$81$	2.26519	0.251688
$82$	1.17345	0.129586
$83$	−4.58417	−0.503178	−0.251589	−	0.967834i	$-0.580953\pi$
$83$	−4.58417	−0.503178	−0.251589	+	0.967834i	$0.580953\pi$
$84$	1.11578	0.121742
$85$	3.03818	0.329537
$86$	2.21664	0.239027
$87$	6.39206	0.685301
$88$	−13.5558	−1.44505
$89$	−13.3956	−1.41993	−0.709965	−	0.704237i	$-0.751289\pi$
$89$	−13.3956	−1.41993	−0.709965	+	0.704237i	$0.751289\pi$
$90$	−5.80424	−0.611820
$91$	4.39933	0.461175
$92$	10.3993	1.08420
$93$	−3.10449	−0.321921
$94$	−4.89026	−0.504392
$95$	−8.03191	−0.824057
$96$	5.12206	0.522768
$97$	−15.1668	−1.53995	−0.769976	−	0.638073i	$-0.779732\pi$
$97$	−15.1668	−1.53995	−0.769976	+	0.638073i	$0.779732\pi$
$98$	0.877834	0.0886746
$99$	−10.4066	−1.04590
$100$	−5.20106	−0.520106
$101$	3.24786	0.323174	0.161587	−	0.986858i	$-0.448339\pi$
$101$	3.24786	0.323174	0.161587	+	0.986858i	$0.448339\pi$
$102$	0.796703	0.0788854
$103$	−12.7031	−1.25168	−0.625839	−	0.779952i	$-0.715243\pi$
$103$	−12.7031	−1.25168	−0.625839	+	0.779952i	$0.715243\pi$
$104$	12.4716	1.22294
$105$	−2.75739	−0.269093
$106$	4.54393	0.441346
$107$	3.91410	0.378390	0.189195	−	0.981940i	$-0.439412\pi$
$107$	3.91410	0.378390	0.189195	+	0.981940i	$0.439412\pi$
$108$	5.77563	0.555760
$109$	−3.56356	−0.341327	−0.170663	−	0.985329i	$-0.554591\pi$
$109$	−3.56356	−0.341327	−0.170663	+	0.985329i	$0.554591\pi$
$110$	12.7531	1.21596
$111$	8.77607	0.832988
$112$	0.0297440	0.00281054
$113$	0.966622	0.0909322	0.0454661	−	0.998966i	$-0.485523\pi$
$113$	0.966622	0.0909322	0.0454661	+	0.998966i	$0.485523\pi$
$114$	−2.10621	−0.197265
$115$	−25.6994	−2.39648
$116$	−8.65869	−0.803940
$117$	9.57426	0.885141
$118$	8.15272	0.750519
$119$	−1.00000	−0.0916698
$120$	−7.81687	−0.713579
$121$	11.8654	1.07867
$122$	5.84923	0.529564
$123$	1.21321	0.109391
$124$	4.20535	0.377652
$125$	−2.33775	−0.209095
$126$	1.91043	0.170195
$127$	−5.55875	−0.493260	−0.246630	−	0.969110i	$-0.579323\pi$
$127$	−5.55875	−0.493260	−0.246630	+	0.969110i	$0.579323\pi$
$128$	−6.88613	−0.608654
$129$	2.29175	0.201777
$130$	−11.7331	−1.02906
$131$	−3.51134	−0.306787	−0.153393	−	0.988165i	$-0.549020\pi$
$131$	−3.51134	−0.306787	−0.153393	+	0.988165i	$0.549020\pi$
$132$	−5.33543	−0.464389
$133$	2.64366	0.229234
$134$	4.63717	0.400590
$135$	−14.2731	−1.22843
$136$	−2.83488	−0.243089
$137$	−1.93780	−0.165557	−0.0827786	−	0.996568i	$-0.526379\pi$
$137$	−1.93780	−0.165557	−0.0827786	+	0.996568i	$0.526379\pi$
$138$	−6.73916	−0.573676
$139$	4.69834	0.398508	0.199254	−	0.979948i	$-0.436148\pi$
$139$	4.69834	0.398508	0.199254	+	0.979948i	$0.436148\pi$
$140$	3.73516	0.315679
$141$	−5.05596	−0.425789
$142$	−10.4734	−0.878910
$143$	−21.0366	−1.75917
$144$	0.0647319	0.00539433
$145$	21.3979	1.77700
$146$	11.1621	0.923780
$147$	0.907578	0.0748558
$148$	−11.8881	−0.977194
$149$	4.24162	0.347487	0.173743	−	0.984791i	$-0.444414\pi$
$149$	4.24162	0.347487	0.173743	+	0.984791i	$0.444414\pi$
$150$	3.37049	0.275199
$151$	12.4584	1.01385	0.506924	−	0.861991i	$-0.330783\pi$
$151$	12.4584	1.01385	0.506924	+	0.861991i	$0.330783\pi$
$152$	7.49446	0.607881
$153$	−2.17630	−0.175944
$154$	−4.19761	−0.338253
$155$	−10.3925	−0.834746
$156$	4.90869	0.393010
$157$	−17.6472	−1.40840	−0.704199	−	0.710002i	$-0.748694\pi$
$157$	−17.6472	−1.40840	−0.704199	+	0.710002i	$0.748694\pi$
$158$	1.70345	0.135519
$159$	4.69790	0.372568
$160$	17.1465	1.35555
$161$	8.45881	0.666648
$162$	1.98847	0.156229
$163$	−2.67557	−0.209567	−0.104783	−	0.994495i	$-0.533415\pi$
$163$	−2.67557	−0.209567	−0.104783	+	0.994495i	$0.533415\pi$
$164$	−1.64341	−0.128329
$165$	13.1852	1.02647
$166$	−4.02414	−0.312334
$167$	−1.95783	−0.151501	−0.0757507	−	0.997127i	$-0.524135\pi$
$167$	−1.95783	−0.151501	−0.0757507	+	0.997127i	$0.524135\pi$
$168$	2.57288	0.198502
$169$	6.35407	0.488775
$170$	2.66702	0.204551
$171$	5.75340	0.439973
$172$	−3.10441	−0.236709
$173$	6.01732	0.457488	0.228744	−	0.973487i	$-0.426538\pi$
$173$	6.01732	0.457488	0.228744	+	0.973487i	$0.426538\pi$
$174$	5.61117	0.425382
$175$	−4.23054	−0.319799
$176$	−0.142229	−0.0107209
$177$	8.42897	0.633560
$178$	−11.7591	−0.881382
$179$	1.75112	0.130885	0.0654423	−	0.997856i	$-0.479154\pi$
$179$	1.75112	0.130885	0.0654423	+	0.997856i	$0.479154\pi$
$180$	8.12884	0.605888
$181$	2.76491	0.205514	0.102757	−	0.994707i	$-0.467234\pi$
$181$	2.76491	0.205514	0.102757	+	0.994707i	$0.467234\pi$
$182$	3.86188	0.286262
$183$	6.04742	0.447038
$184$	23.9798	1.76781
$185$	29.3785	2.15995
$186$	−2.72523	−0.199824
$187$	4.78178	0.349678
$188$	6.84881	0.499501
$189$	4.69790	0.341722
$190$	−7.05069	−0.511511
$191$	18.8461	1.36365	0.681827	−	0.731514i	$-0.261186\pi$
$191$	18.8461	1.36365	0.681827	+	0.731514i	$0.261186\pi$
$192$	4.55031	0.328390
$193$	11.9107	0.857348	0.428674	−	0.903459i	$-0.358981\pi$
$193$	11.9107	0.857348	0.428674	+	0.903459i	$0.358981\pi$
$194$	−13.3139	−0.955883
$195$	−12.1306	−0.868693
$196$	−1.22941	−0.0878148
$197$	−17.2682	−1.23031	−0.615153	−	0.788408i	$-0.710906\pi$
$197$	−17.2682	−1.23031	−0.615153	+	0.788408i	$0.710906\pi$
$198$	−9.13526	−0.649215
$199$	−15.2451	−1.08070	−0.540350	−	0.841440i	$-0.681708\pi$
$199$	−15.2451	−1.08070	−0.540350	+	0.841440i	$0.681708\pi$
$200$	−11.9931	−0.848040
$201$	4.79429	0.338163
$202$	2.85108	0.200601
$203$	−7.04298	−0.494321
$204$	−1.11578	−0.0781204
$205$	4.06130	0.283653
$206$	−11.1513	−0.776945
$207$	18.4089	1.27951
$208$	0.130854	0.00907306
$209$	−12.6414	−0.874423
$210$	−2.42053	−0.167032
$211$	8.51331	0.586080	0.293040	−	0.956100i	$-0.405333\pi$
$211$	8.51331	0.586080	0.293040	+	0.956100i	$0.405333\pi$
$212$	−6.36378	−0.437066
$213$	−10.8283	−0.741942
$214$	3.43593	0.234875
$215$	7.67179	0.523212
$216$	13.3180	0.906175
$217$	3.42063	0.232208
$218$	−3.12821	−0.211869
$219$	11.5403	0.779820
$220$	−17.8607	−1.20417
$221$	−4.39933	−0.295931
$222$	7.70394	0.517054
$223$	−2.49093	−0.166805	−0.0834027	−	0.996516i	$-0.526579\pi$
$223$	−2.49093	−0.166805	−0.0834027	+	0.996516i	$0.526579\pi$
$224$	−5.64366	−0.377083
$225$	−9.20694	−0.613796
$226$	0.848534	0.0564437
$227$	−16.9842	−1.12728	−0.563640	−	0.826020i	$-0.690600\pi$
$227$	−16.9842	−1.12728	−0.563640	+	0.826020i	$0.690600\pi$
$228$	2.94975	0.195352
$229$	−16.3303	−1.07914	−0.539568	−	0.841942i	$-0.681413\pi$
$229$	−16.3303	−1.07914	−0.539568	+	0.841942i	$0.681413\pi$
$230$	−22.5598	−1.48755
$231$	−4.33984	−0.285540
$232$	−19.9660	−1.31083
$233$	−5.77825	−0.378546	−0.189273	−	0.981925i	$-0.560613\pi$
$233$	−5.77825	−0.378546	−0.189273	+	0.981925i	$0.560613\pi$
$234$	8.40461	0.549427
$235$	−16.9252	−1.10408
$236$	−11.4179	−0.743241
$237$	1.76117	0.114400
$238$	−0.877834	−0.0569015
$239$	7.44275	0.481432	0.240716	−	0.970596i	$-0.422618\pi$
$239$	7.44275	0.481432	0.240716	+	0.970596i	$0.422618\pi$
$240$	−0.0820157	−0.00529409
$241$	21.9036	1.41093	0.705467	−	0.708743i	$-0.250737\pi$
$241$	21.9036	1.41093	0.705467	+	0.708743i	$0.250737\pi$
$242$	10.4159	0.669557
$243$	16.1495	1.03599
$244$	−8.19184	−0.524429
$245$	3.03818	0.194102
$246$	1.06500	0.0679016
$247$	11.6303	0.740019
$248$	9.69710	0.615766
$249$	−4.16049	−0.263661
$250$	−2.05216	−0.129790
$251$	16.5769	1.04632	0.523162	−	0.852233i	$-0.324752\pi$
$251$	16.5769	1.04632	0.523162	+	0.852233i	$0.324752\pi$
$252$	−2.67556	−0.168544
$253$	−40.4482	−2.54296
$254$	−4.87966	−0.306177
$255$	2.75739	0.172674
$256$	−16.0723	−1.00452
$257$	12.1158	0.755764	0.377882	−	0.925854i	$-0.376653\pi$
$257$	12.1158	0.755764	0.377882	+	0.925854i	$0.376653\pi$
$258$	2.01178	0.125248
$259$	−9.66977	−0.600850
$260$	16.4322	1.01908
$261$	−15.3277	−0.948758
$262$	−3.08237	−0.190430
$263$	3.20135	0.197404	0.0987018	−	0.995117i	$-0.468531\pi$
$263$	3.20135	0.197404	0.0987018	+	0.995117i	$0.468531\pi$
$264$	−12.3029	−0.757193
$265$	15.7265	0.966074
$266$	2.32069	0.142291
$267$	−12.1575	−0.744030
$268$	−6.49436	−0.396706
$269$	15.4400	0.941396	0.470698	−	0.882294i	$-0.344002\pi$
$269$	15.4400	0.941396	0.470698	+	0.882294i	$0.344002\pi$
$270$	−12.5294	−0.762514
$271$	−24.8878	−1.51182	−0.755912	−	0.654673i	$-0.772806\pi$
$271$	−24.8878	−1.51182	−0.755912	+	0.654673i	$0.772806\pi$
$272$	−0.0297440	−0.00180349
$273$	3.99273	0.241651
$274$	−1.70106	−0.102765
$275$	20.2295	1.21989
$276$	9.43820	0.568113
$277$	−11.2870	−0.678172	−0.339086	−	0.940755i	$-0.610118\pi$
$277$	−11.2870	−0.678172	−0.339086	+	0.940755i	$0.610118\pi$
$278$	4.12437	0.247363
$279$	7.44433	0.445680
$280$	8.61289	0.514719
$281$	13.0332	0.777495	0.388747	−	0.921344i	$-0.372908\pi$
$281$	13.0332	0.777495	0.388747	+	0.921344i	$0.372908\pi$
$282$	−4.43829	−0.264297
$283$	21.7190	1.29106	0.645531	−	0.763734i	$-0.276636\pi$
$283$	21.7190	1.29106	0.645531	+	0.763734i	$0.276636\pi$
$284$	14.6680	0.870387
$285$	−7.28959	−0.431798
$286$	−18.4667	−1.09196
$287$	−1.33675	−0.0789061
$288$	−12.2823	−0.723742
$289$	1.00000	0.0588235
$290$	18.7838	1.10302
$291$	−13.7650	−0.806920
$292$	−15.6325	−0.914822
$293$	−28.9400	−1.69069	−0.845346	−	0.534219i	$-0.820606\pi$
$293$	−28.9400	−1.69069	−0.845346	+	0.534219i	$0.820606\pi$
$294$	0.796703	0.0464647
$295$	28.2165	1.64283
$296$	−27.4127	−1.59333
$297$	−22.4643	−1.30351
$298$	3.72344	0.215693
$299$	37.2131	2.15209
$300$	−4.72037	−0.272531
$301$	−2.52513	−0.145546
$302$	10.9364	0.629318
$303$	2.94769	0.169340
$304$	0.0786330	0.00450991
$305$	20.2441	1.15918
$306$	−1.91043	−0.109212
$307$	−11.5836	−0.661110	−0.330555	−	0.943787i	$-0.607236\pi$
$307$	−11.5836	−0.661110	−0.330555	+	0.943787i	$0.607236\pi$
$308$	5.87875	0.334973
$309$	−11.5291	−0.655867
$310$	−9.12289	−0.518146
$311$	−15.7999	−0.895932	−0.447966	−	0.894051i	$-0.647851\pi$
$311$	−15.7999	−0.895932	−0.447966	+	0.894051i	$0.647851\pi$
$312$	11.3189	0.640808
$313$	20.2658	1.14549	0.572745	−	0.819733i	$-0.305878\pi$
$313$	20.2658	1.14549	0.572745	+	0.819733i	$0.305878\pi$
$314$	−15.4913	−0.874225
$315$	6.61200	0.372544
$316$	−2.38568	−0.134205
$317$	6.36537	0.357515	0.178757	−	0.983893i	$-0.442792\pi$
$317$	6.36537	0.357515	0.178757	+	0.983893i	$0.442792\pi$
$318$	4.12398	0.231261
$319$	33.6780	1.88561
$320$	15.2325	0.851521
$321$	3.55235	0.198273
$322$	7.42544	0.413803
$323$	−2.64366	−0.147097
$324$	−2.78485	−0.154714
$325$	−18.6115	−1.03238
$326$	−2.34871	−0.130083
$327$	−3.23421	−0.178852
$328$	−3.78954	−0.209242
$329$	5.57082	0.307130
$330$	11.5744	0.637151
$331$	24.5910	1.35165	0.675823	−	0.737064i	$-0.263788\pi$
$331$	24.5910	1.35165	0.675823	+	0.737064i	$0.263788\pi$
$332$	5.63581	0.309305
$333$	−21.0443	−1.15322
$334$	−1.71865	−0.0940403
$335$	16.0492	0.876863
$336$	0.0269950	0.00147270
$337$	7.11956	0.387827	0.193913	−	0.981019i	$-0.437882\pi$
$337$	7.11956	0.387827	0.193913	+	0.981019i	$0.437882\pi$
$338$	5.57782	0.303393
$339$	0.877285	0.0476476
$340$	−3.73516	−0.202568
$341$	−16.3567	−0.885766
$342$	5.05053	0.273101
$343$	−1.00000	−0.0539949
$344$	−7.15844	−0.385957
$345$	−23.3242	−1.25573
$346$	5.28221	0.283973
$347$	1.51477	0.0813173	0.0406586	−	0.999173i	$-0.487054\pi$
$347$	1.51477	0.0813173	0.0406586	+	0.999173i	$0.487054\pi$
$348$	−7.85844	−0.421257
$349$	24.7937	1.32717	0.663587	−	0.748099i	$-0.269033\pi$
$349$	24.7937	1.32717	0.663587	+	0.748099i	$0.269033\pi$
$350$	−3.71372	−0.198506
$351$	20.6676	1.10315
$352$	26.9867	1.43840
$353$	−11.8416	−0.630267	−0.315133	−	0.949047i	$-0.602049\pi$
$353$	−11.8416	−0.630267	−0.315133	+	0.949047i	$0.602049\pi$
$354$	7.39923	0.393265
$355$	−36.2485	−1.92387
$356$	16.4686	0.872836
$357$	−0.907578	−0.0480341
$358$	1.53719	0.0812430
$359$	−26.6743	−1.40781	−0.703907	−	0.710292i	$-0.748563\pi$
$359$	−26.6743	−1.40781	−0.703907	+	0.710292i	$0.748563\pi$
$360$	18.7442	0.987909
$361$	−12.0111	−0.632162
$362$	2.42713	0.127567
$363$	10.7688	0.565215
$364$	−5.40856	−0.283486
$365$	38.6319	2.02209
$366$	5.30863	0.277487
$367$	−28.6897	−1.49759	−0.748796	−	0.662801i	$-0.769368\pi$
$367$	−28.6897	−1.49759	−0.748796	+	0.662801i	$0.769368\pi$
$368$	0.251599	0.0131155
$369$	−2.90918	−0.151446
$370$	25.7895	1.34073
$371$	−5.17630	−0.268740
$372$	3.81668	0.197886
$373$	−26.8946	−1.39255	−0.696275	−	0.717775i	$-0.745161\pi$
$373$	−26.8946	−1.39255	−0.696275	+	0.717775i	$0.745161\pi$
$374$	4.19761	0.217053
$375$	−2.12169	−0.109564
$376$	15.7926	0.814443
$377$	−30.9844	−1.59578
$378$	4.12398	0.212114
$379$	0.960453	0.0493351	0.0246676	−	0.999696i	$-0.492147\pi$
$379$	0.960453	0.0493351	0.0246676	+	0.999696i	$0.492147\pi$
$380$	9.87449	0.506551
$381$	−5.04500	−0.258463
$382$	16.5437	0.846451
$383$	−10.9913	−0.561627	−0.280814	−	0.959762i	$-0.590604\pi$
$383$	−10.9913	−0.561627	−0.280814	+	0.959762i	$0.590604\pi$
$384$	−6.24970	−0.318929
$385$	−14.5279	−0.740411
$386$	10.4556	0.532175
$387$	−5.49544	−0.279349
$388$	18.6461	0.946614
$389$	−25.4239	−1.28904	−0.644520	−	0.764587i	$-0.722943\pi$
$389$	−25.4239	−1.28904	−0.644520	+	0.764587i	$0.722943\pi$
$390$	−10.6487	−0.539218
$391$	−8.45881	−0.427781
$392$	−2.83488	−0.143183
$393$	−3.18681	−0.160753
$394$	−15.1586	−0.763679
$395$	5.89563	0.296641
$396$	12.7939	0.642920
$397$	−15.0140	−0.753533	−0.376767	−	0.926308i	$-0.622964\pi$
$397$	−15.0140	−0.753533	−0.376767	+	0.926308i	$0.622964\pi$
$398$	−13.3827	−0.670815
$399$	2.39933	0.120117
$400$	−0.125833	−0.00629166
$401$	−11.0656	−0.552588	−0.276294	−	0.961073i	$-0.589106\pi$
$401$	−11.0656	−0.552588	−0.276294	+	0.961073i	$0.589106\pi$
$402$	4.20859	0.209906
$403$	15.0485	0.749618
$404$	−3.99294	−0.198656
$405$	6.88207	0.341973
$406$	−6.18257	−0.306836
$407$	46.2387	2.29197
$408$	−2.57288	−0.127376
$409$	28.5650	1.41245	0.706225	−	0.707988i	$-0.250397\pi$
$409$	28.5650	1.41245	0.706225	+	0.707988i	$0.250397\pi$
$410$	3.56515	0.176070
$411$	−1.75870	−0.0867504
$412$	15.6173	0.769411
$413$	−9.28732	−0.456999
$414$	16.1600	0.794220
$415$	−13.9275	−0.683676
$416$	−24.8283	−1.21731
$417$	4.26411	0.208815
$418$	−11.0970	−0.542774
$419$	−1.98566	−0.0970057	−0.0485029	−	0.998823i	$-0.515445\pi$
$419$	−1.98566	−0.0970057	−0.0485029	+	0.998823i	$0.515445\pi$
$420$	3.38995	0.165413
$421$	25.1984	1.22810	0.614048	−	0.789269i	$-0.289540\pi$
$421$	25.1984	1.22810	0.614048	+	0.789269i	$0.289540\pi$
$422$	7.47327	0.363793
$423$	12.1238	0.589479
$424$	−14.6742	−0.712643
$425$	4.23054	0.205211
$426$	−9.50544	−0.460540
$427$	−6.66325	−0.322457
$428$	−4.81202	−0.232598
$429$	−19.0924	−0.921788
$430$	6.73456	0.324769
$431$	−27.4984	−1.32455	−0.662275	−	0.749261i	$-0.730409\pi$
$431$	−27.4984	−1.32455	−0.662275	+	0.749261i	$0.730409\pi$
$432$	0.139734	0.00672297
$433$	28.1977	1.35509	0.677547	−	0.735480i	$-0.263043\pi$
$433$	28.1977	1.35509	0.677547	+	0.735480i	$0.263043\pi$
$434$	3.00275	0.144137
$435$	19.4202	0.931129
$436$	4.38106	0.209815
$437$	22.3622	1.06973
$438$	10.1305	0.484052
$439$	6.31298	0.301302	0.150651	−	0.988587i	$-0.451863\pi$
$439$	6.31298	0.301302	0.150651	+	0.988587i	$0.451863\pi$
$440$	−41.1849	−1.96341
$441$	−2.17630	−0.103633
$442$	−3.86188	−0.183691
$443$	26.4557	1.25695	0.628473	−	0.777831i	$-0.283680\pi$
$443$	26.4557	1.25695	0.628473	+	0.777831i	$0.283680\pi$
$444$	−10.7894	−0.512041
$445$	−40.6982	−1.92928
$446$	−2.18663	−0.103540
$447$	3.84960	0.182080
$448$	−5.01368	−0.236874
$449$	−34.5555	−1.63077	−0.815387	−	0.578916i	$-0.803476\pi$
$449$	−34.5555	−1.63077	−0.815387	+	0.578916i	$0.803476\pi$
$450$	−8.08216	−0.380997
$451$	6.39206	0.300990
$452$	−1.18837	−0.0558963
$453$	11.3069	0.531247
$454$	−14.9093	−0.699728
$455$	13.3659	0.626605
$456$	6.80181	0.318524
$457$	26.5922	1.24393	0.621965	−	0.783045i	$-0.286334\pi$
$457$	26.5922	1.24393	0.621965	+	0.783045i	$0.286334\pi$
$458$	−14.3353	−0.669844
$459$	−4.69790	−0.219279
$460$	31.5950	1.47313
$461$	−0.310199	−0.0144474	−0.00722371	−	0.999974i	$-0.502299\pi$
$461$	−0.310199	−0.0144474	−0.00722371	+	0.999974i	$0.502299\pi$
$462$	−3.80966	−0.177241
$463$	22.4654	1.04406	0.522028	−	0.852928i	$-0.325175\pi$
$463$	22.4654	1.04406	0.522028	+	0.852928i	$0.325175\pi$
$464$	−0.209487	−0.00972517
$465$	−9.43201	−0.437399
$466$	−5.07235	−0.234972
$467$	−11.6126	−0.537365	−0.268682	−	0.963229i	$-0.586588\pi$
$467$	−11.6126	−0.537365	−0.268682	+	0.963229i	$0.586588\pi$
$468$	−11.7707	−0.544099
$469$	−5.28251	−0.243924
$470$	−14.8575	−0.685325
$471$	−16.0162	−0.737988
$472$	−26.3285	−1.21187
$473$	12.0746	0.555190
$474$	1.54601	0.0710107
$475$	−11.1841	−0.513162
$476$	1.22941	0.0563498
$477$	−11.2652	−0.515798
$478$	6.53350	0.298836
$479$	31.7976	1.45287	0.726435	−	0.687235i	$-0.241176\pi$
$479$	31.7976	1.45287	0.726435	+	0.687235i	$0.241176\pi$
$480$	15.5617	0.710293
$481$	−42.5405	−1.93968
$482$	19.2277	0.875799
$483$	7.67704	0.349317
$484$	−14.5874	−0.663064
$485$	−46.0794	−2.09236
$486$	14.1766	0.643064
$487$	−23.0166	−1.04298	−0.521490	−	0.853257i	$-0.674624\pi$
$487$	−23.0166	−1.04298	−0.521490	+	0.853257i	$0.674624\pi$
$488$	−18.8895	−0.855089
$489$	−2.42829	−0.109811
$490$	2.66702	0.120484
$491$	−33.3176	−1.50360	−0.751802	−	0.659389i	$-0.770815\pi$
$491$	−33.3176	−1.50360	−0.751802	+	0.659389i	$0.770815\pi$
$492$	−1.49153	−0.0672432
$493$	7.04298	0.317200
$494$	10.2095	0.459347
$495$	−31.6171	−1.42108
$496$	0.101743	0.00456841
$497$	11.9310	0.535177
$498$	−3.65222	−0.163660
$499$	37.0236	1.65741	0.828703	−	0.559689i	$-0.189079\pi$
$499$	37.0236	1.65741	0.828703	+	0.559689i	$0.189079\pi$
$500$	2.87405	0.128531
$501$	−1.77688	−0.0793853
$502$	14.5518	0.649477
$503$	−12.4172	−0.553654	−0.276827	−	0.960920i	$-0.589283\pi$
$503$	−12.4172	−0.553654	−0.276827	+	0.960920i	$0.589283\pi$
$504$	−6.16956	−0.274814
$505$	9.86759	0.439102
$506$	−35.5068	−1.57847
$507$	5.76682	0.256113
$508$	6.83397	0.303208
$509$	11.9257	0.528597	0.264299	−	0.964441i	$-0.414860\pi$
$509$	11.9257	0.528597	0.264299	+	0.964441i	$0.414860\pi$
$510$	2.42053	0.107183
$511$	−12.7155	−0.562499
$512$	−0.336507	−0.0148716
$513$	12.4196	0.548340
$514$	10.6357	0.469120
$515$	−38.5945	−1.70067
$516$	−2.81749	−0.124033
$517$	−26.6385	−1.17156
$518$	−8.48845	−0.372961
$519$	5.46119	0.239719
$520$	37.8909	1.66163
$521$	26.3980	1.15652	0.578259	−	0.815853i	$-0.303732\pi$
$521$	26.3980	1.15652	0.578259	+	0.815853i	$0.303732\pi$
$522$	−13.4551	−0.588916
$523$	13.6272	0.595874	0.297937	−	0.954586i	$-0.403701\pi$
$523$	13.6272	0.595874	0.297937	+	0.954586i	$0.403701\pi$
$524$	4.31686	0.188583
$525$	−3.83955	−0.167572
$526$	2.81025	0.122533
$527$	−3.42063	−0.149005
$528$	−0.129084	−0.00561767
$529$	48.5515	2.11094
$530$	13.8053	0.599664
$531$	−20.2120	−0.877126
$532$	−3.25013	−0.140911
$533$	−5.88081	−0.254726
$534$	−10.6723	−0.461836
$535$	11.8917	0.514125
$536$	−14.9753	−0.646835
$537$	1.58927	0.0685823
$538$	13.5538	0.584346
$539$	4.78178	0.205966
$540$	17.5474	0.755120
$541$	26.3358	1.13226	0.566132	−	0.824314i	$-0.308439\pi$
$541$	26.3358	1.13226	0.566132	+	0.824314i	$0.308439\pi$
$542$	−21.8473	−0.938424
$543$	2.50937	0.107687
$544$	5.64366	0.241970
$545$	−10.8267	−0.463766
$546$	3.50496	0.149998
$547$	−2.25139	−0.0962624	−0.0481312	−	0.998841i	$-0.515327\pi$
$547$	−2.25139	−0.0962624	−0.0481312	+	0.998841i	$0.515327\pi$
$548$	2.38234	0.101769
$549$	−14.5012	−0.618898
$550$	17.7582	0.757211
$551$	−18.6192	−0.793206
$552$	21.7635	0.926316
$553$	−1.94051	−0.0825190
$554$	−9.90815	−0.420957
$555$	26.6633	1.13179
$556$	−5.77618	−0.244964
$557$	30.3355	1.28536	0.642679	−	0.766136i	$-0.277823\pi$
$557$	30.3355	1.28536	0.642679	+	0.766136i	$0.277823\pi$
$558$	6.53489	0.276644
$559$	−11.1089	−0.469854
$560$	0.0903677	0.00381873
$561$	4.33984	0.183228
$562$	11.4410	0.482608
$563$	10.9867	0.463035	0.231518	−	0.972831i	$-0.425631\pi$
$563$	10.9867	0.463035	0.231518	+	0.972831i	$0.425631\pi$
$564$	6.21583	0.261734
$565$	2.93677	0.123551
$566$	19.0657	0.801391
$567$	−2.26519	−0.0951292
$568$	33.8229	1.41918
$569$	−28.8479	−1.20937	−0.604684	−	0.796465i	$-0.706701\pi$
$569$	−28.8479	−1.20937	−0.604684	+	0.796465i	$0.706701\pi$
$570$	−6.39905	−0.268027
$571$	−10.5165	−0.440100	−0.220050	−	0.975489i	$-0.570622\pi$
$571$	−10.5165	−0.440100	−0.220050	+	0.975489i	$0.570622\pi$
$572$	25.8626	1.08137
$573$	17.1043	0.714542
$574$	−1.17345	−0.0489788
$575$	−35.7854	−1.49235
$576$	−10.9113	−0.454637
$577$	−36.8288	−1.53320	−0.766601	−	0.642123i	$-0.778054\pi$
$577$	−36.8288	−1.53320	−0.766601	+	0.642123i	$0.778054\pi$
$578$	0.877834	0.0365131
$579$	10.8099	0.449242
$580$	−26.3067	−1.09233
$581$	4.58417	0.190183
$582$	−12.0834	−0.500873
$583$	24.7519	1.02512
$584$	−36.0469	−1.49163
$585$	29.0883	1.20265
$586$	−25.4045	−1.04945
$587$	30.1420	1.24409	0.622047	−	0.782980i	$-0.286301\pi$
$587$	30.1420	1.24409	0.622047	+	0.782980i	$0.286301\pi$
$588$	−1.11578	−0.0460141
$589$	9.04298	0.372610
$590$	24.7694	1.01974
$591$	−15.6722	−0.644669
$592$	−0.287618	−0.0118210
$593$	−7.88925	−0.323973	−0.161986	−	0.986793i	$-0.551790\pi$
$593$	−7.88925	−0.323973	−0.161986	+	0.986793i	$0.551790\pi$
$594$	−19.7199	−0.809119
$595$	−3.03818	−0.124553
$596$	−5.21467	−0.213601
$597$	−13.8362	−0.566276
$598$	32.6669	1.33585
$599$	29.8059	1.21783	0.608917	−	0.793234i	$-0.291604\pi$
$599$	29.8059	1.21783	0.608917	+	0.793234i	$0.291604\pi$
$600$	−10.8847	−0.444365
$601$	11.9432	0.487175	0.243587	−	0.969879i	$-0.421676\pi$
$601$	11.9432	0.487175	0.243587	+	0.969879i	$0.421676\pi$
$602$	−2.21664	−0.0903436
$603$	−11.4963	−0.468167
$604$	−15.3164	−0.623216
$605$	36.0493	1.46561
$606$	2.58758	0.105113
$607$	−4.67281	−0.189664	−0.0948318	−	0.995493i	$-0.530231\pi$
$607$	−4.67281	−0.189664	−0.0948318	+	0.995493i	$0.530231\pi$
$608$	−14.9199	−0.605082
$609$	−6.39206	−0.259019
$610$	17.7710	0.719527
$611$	24.5079	0.991483
$612$	2.67556	0.108153
$613$	42.3894	1.71209	0.856046	−	0.516900i	$-0.172914\pi$
$613$	42.3894	1.71209	0.856046	+	0.516900i	$0.172914\pi$
$614$	−10.1685	−0.410366
$615$	3.68595	0.148632
$616$	13.5558	0.546178
$617$	−23.2809	−0.937255	−0.468628	−	0.883396i	$-0.655251\pi$
$617$	−23.2809	−0.937255	−0.468628	+	0.883396i	$0.655251\pi$
$618$	−10.1206	−0.407112
$619$	−43.2201	−1.73716	−0.868582	−	0.495545i	$-0.834968\pi$
$619$	−43.2201	−1.73716	−0.868582	+	0.495545i	$0.834968\pi$
$620$	12.7766	0.513121
$621$	39.7387	1.59466
$622$	−13.8697	−0.556125
$623$	13.3956	0.536683
$624$	0.118760	0.00475420
$625$	−28.2552	−1.13021
$626$	17.7900	0.711032
$627$	−11.4730	−0.458189
$628$	21.6956	0.865748
$629$	9.66977	0.385559
$630$	5.80424	0.231246
$631$	30.6825	1.22145	0.610725	−	0.791843i	$-0.290878\pi$
$631$	30.6825	1.22145	0.610725	+	0.791843i	$0.290878\pi$
$632$	−5.50113	−0.218823
$633$	7.72649	0.307100
$634$	5.58774	0.221917
$635$	−16.8885	−0.670200
$636$	−5.77563	−0.229019
$637$	−4.39933	−0.174308
$638$	29.5637	1.17044
$639$	25.9654	1.02718
$640$	−20.9213	−0.826988
$641$	−21.3561	−0.843517	−0.421758	−	0.906708i	$-0.638587\pi$
$641$	−21.3561	−0.843517	−0.421758	+	0.906708i	$0.638587\pi$
$642$	3.11838	0.123072
$643$	22.7013	0.895253	0.447626	−	0.894221i	$-0.352269\pi$
$643$	22.7013	0.895253	0.447626	+	0.894221i	$0.352269\pi$
$644$	−10.3993	−0.409791
$645$	6.96275	0.274158
$646$	−2.32069	−0.0913065
$647$	35.2630	1.38633	0.693165	−	0.720779i	$-0.256216\pi$
$647$	35.2630	1.38633	0.693165	+	0.720779i	$0.256216\pi$
$648$	−6.42156	−0.252263
$649$	44.4099	1.74324
$650$	−16.3378	−0.640823
$651$	3.10449	0.121675
$652$	3.28936	0.128821
$653$	−30.0593	−1.17631	−0.588155	−	0.808748i	$-0.700146\pi$
$653$	−30.0593	−1.17631	−0.588155	+	0.808748i	$0.700146\pi$
$654$	−2.83910	−0.111018
$655$	−10.6681	−0.416836
$656$	−0.0397604	−0.00155238
$657$	−27.6727	−1.07961
$658$	4.89026	0.190642
$659$	−18.9747	−0.739148	−0.369574	−	0.929201i	$-0.620496\pi$
$659$	−18.9747	−0.739148	−0.369574	+	0.929201i	$0.620496\pi$
$660$	−16.2100	−0.630973
$661$	25.8038	1.00365	0.501825	−	0.864969i	$-0.332662\pi$
$661$	25.8038	1.00365	0.501825	+	0.864969i	$0.332662\pi$
$662$	21.5869	0.838997
$663$	−3.99273	−0.155065
$664$	12.9956	0.504327
$665$	8.03191	0.311464
$666$	−18.4734	−0.715831
$667$	−59.5753	−2.30676
$668$	2.40697	0.0931284
$669$	−2.26072	−0.0874044
$670$	14.0886	0.544289
$671$	31.8622	1.23003
$672$	−5.12206	−0.197588
$673$	4.38401	0.168991	0.0844956	−	0.996424i	$-0.473072\pi$
$673$	4.38401	0.168991	0.0844956	+	0.996424i	$0.473072\pi$
$674$	6.24979	0.240733
$675$	−19.8747	−0.764976
$676$	−7.81174	−0.300452
$677$	−32.1115	−1.23415	−0.617073	−	0.786906i	$-0.711682\pi$
$677$	−32.1115	−1.23415	−0.617073	+	0.786906i	$0.711682\pi$
$678$	0.770111	0.0295759
$679$	15.1668	0.582047
$680$	−8.61289	−0.330289
$681$	−15.4145	−0.590684
$682$	−14.3585	−0.549815
$683$	−18.7093	−0.715892	−0.357946	−	0.933742i	$-0.616523\pi$
$683$	−18.7093	−0.715892	−0.357946	+	0.933742i	$0.616523\pi$
$684$	−7.07327	−0.270453
$685$	−5.88738	−0.224945
$686$	−0.877834	−0.0335159
$687$	−14.8210	−0.565457
$688$	−0.0751073	−0.00286344
$689$	−22.7722	−0.867553
$690$	−20.4748	−0.779462
$691$	−40.9131	−1.55641	−0.778205	−	0.628011i	$-0.783869\pi$
$691$	−40.9131	−1.55641	−0.778205	+	0.628011i	$0.783869\pi$
$692$	−7.39773	−0.281220
$693$	10.4066	0.395314
$694$	1.32972	0.0504755
$695$	14.2744	0.541459
$696$	−18.1207	−0.686865
$697$	1.33675	0.0506331
$698$	21.7647	0.823807
$699$	−5.24421	−0.198354
$700$	5.20106	0.196582
$701$	−17.6240	−0.665649	−0.332825	−	0.942989i	$-0.608002\pi$
$701$	−17.6240	−0.665649	−0.332825	+	0.942989i	$0.608002\pi$
$702$	18.1427	0.684753
$703$	−25.5636	−0.964148
$704$	23.9743	0.903566
$705$	−15.3609	−0.578526
$706$	−10.3950	−0.391221
$707$	−3.24786	−0.122148
$708$	−10.3626	−0.389451
$709$	−8.18690	−0.307466	−0.153733	−	0.988112i	$-0.549130\pi$
$709$	−8.18690	−0.307466	−0.153733	+	0.988112i	$0.549130\pi$
$710$	−31.8201	−1.19419
$711$	−4.22314	−0.158380
$712$	37.9749	1.42317
$713$	28.9345	1.08361
$714$	−0.796703	−0.0298159
$715$	−63.9130	−2.39021
$716$	−2.15283	−0.0804552
$717$	6.75488	0.252266
$718$	−23.4156	−0.873862
$719$	42.6093	1.58906	0.794530	−	0.607225i	$-0.207717\pi$
$719$	42.6093	1.58906	0.794530	+	0.607225i	$0.207717\pi$
$720$	0.196667	0.00732936
$721$	12.7031	0.473090
$722$	−10.5437	−0.392397
$723$	19.8792	0.739316
$724$	−3.39919	−0.126330
$725$	29.7956	1.10658
$726$	9.45321	0.350841
$727$	−10.5470	−0.391166	−0.195583	−	0.980687i	$-0.562660\pi$
$727$	−10.5470	−0.391166	−0.195583	+	0.980687i	$0.562660\pi$
$728$	−12.4716	−0.462227
$729$	7.86138	0.291162
$730$	33.9124	1.25515
$731$	2.52513	0.0933951
$732$	−7.43474	−0.274796
$733$	6.61491	0.244327	0.122164	−	0.992510i	$-0.461017\pi$
$733$	6.61491	0.244327	0.122164	+	0.992510i	$0.461017\pi$
$734$	−25.1848	−0.929589
$735$	2.75739	0.101708
$736$	−47.7387	−1.75967
$737$	25.2598	0.930457
$738$	−2.55378	−0.0940058
$739$	−0.834376	−0.0306930	−0.0153465	−	0.999882i	$-0.504885\pi$
$739$	−0.834376	−0.0306930	−0.0153465	+	0.999882i	$0.504885\pi$
$740$	−36.1181	−1.32773
$741$	10.5554	0.387763
$742$	−4.54393	−0.166813
$743$	52.9082	1.94101	0.970506	−	0.241077i	$-0.0775006\pi$
$743$	52.9082	1.94101	0.970506	+	0.241077i	$0.0775006\pi$
$744$	8.80088	0.322656
$745$	12.8868	0.472136
$746$	−23.6090	−0.864387
$747$	9.97654	0.365022
$748$	−5.87875	−0.214948
$749$	−3.91410	−0.143018
$750$	−1.86249	−0.0680086
$751$	35.3681	1.29060	0.645300	−	0.763929i	$-0.276732\pi$
$751$	35.3681	1.29060	0.645300	+	0.763929i	$0.276732\pi$
$752$	0.165699	0.00604241
$753$	15.0448	0.548264
$754$	−27.1992	−0.990535
$755$	37.8508	1.37753
$756$	−5.77563	−0.210058
$757$	−19.6550	−0.714372	−0.357186	−	0.934033i	$-0.616264\pi$
$757$	−19.6550	−0.714372	−0.357186	+	0.934033i	$0.616264\pi$
$758$	0.843118	0.0306234
$759$	−36.7099	−1.33248
$760$	22.7695	0.825938
$761$	−6.80776	−0.246781	−0.123390	−	0.992358i	$-0.539377\pi$
$761$	−6.80776	−0.246781	−0.123390	+	0.992358i	$0.539377\pi$
$762$	−4.42868	−0.160434
$763$	3.56356	0.129009
$764$	−23.1695	−0.838243
$765$	−6.61200	−0.239057
$766$	−9.64851	−0.348615
$767$	−40.8579	−1.47529
$768$	−14.5868	−0.526357
$769$	44.3645	1.59983	0.799913	−	0.600116i	$-0.204879\pi$
$769$	44.3645	1.59983	0.799913	+	0.600116i	$0.204879\pi$
$770$	−12.7531	−0.459590
$771$	10.9961	0.396013
$772$	−14.6431	−0.527015
$773$	−25.6974	−0.924270	−0.462135	−	0.886810i	$-0.652916\pi$
$773$	−25.6974	−0.924270	−0.462135	+	0.886810i	$0.652916\pi$
$774$	−4.82408	−0.173398
$775$	−14.4711	−0.519819
$776$	42.9960	1.54347
$777$	−8.77607	−0.314840
$778$	−22.3179	−0.800137
$779$	−3.53392	−0.126616
$780$	14.9135	0.533989
$781$	−57.0513	−2.04146
$782$	−7.42544	−0.265533
$783$	−33.0872	−1.18244
$784$	−0.0297440	−0.00106229
$785$	−53.6153	−1.91361
$786$	−2.79749	−0.0997833
$787$	25.6566	0.914558	0.457279	−	0.889323i	$-0.348824\pi$
$787$	25.6566	0.914558	0.457279	+	0.889323i	$0.348824\pi$
$788$	21.2296	0.756274
$789$	2.90547	0.103438
$790$	5.17538	0.184132
$791$	−0.966622	−0.0343691
$792$	29.5015	1.04829
$793$	−29.3138	−1.04096
$794$	−13.1798	−0.467735
$795$	14.2731	0.506213
$796$	18.7425	0.664310
$797$	20.3683	0.721483	0.360741	−	0.932666i	$-0.382524\pi$
$797$	20.3683	0.721483	0.360741	+	0.932666i	$0.382524\pi$
$798$	2.10621	0.0745590
$799$	−5.57082	−0.197082
$800$	23.8757	0.844135
$801$	29.1528	1.03006
$802$	−9.71373	−0.343004
$803$	60.8026	2.14568
$804$	−5.89414	−0.207870
$805$	25.6994	0.905785
$806$	13.2101	0.465305
$807$	14.0130	0.493282
$808$	−9.20731	−0.323912
$809$	−36.5480	−1.28496	−0.642480	−	0.766303i	$-0.722094\pi$
$809$	−36.5480	−1.28496	−0.642480	+	0.766303i	$0.722094\pi$
$810$	6.04132	0.212270
$811$	7.33037	0.257404	0.128702	−	0.991683i	$-0.458919\pi$
$811$	7.33037	0.257404	0.128702	+	0.991683i	$0.458919\pi$
$812$	8.65869	0.303861
$813$	−22.5876	−0.792182
$814$	40.5899	1.42268
$815$	−8.12886	−0.284742
$816$	−0.0269950	−0.000945014 0
$817$	−6.67557	−0.233549
$818$	25.0754	0.876739
$819$	−9.57426	−0.334552
$820$	−4.99299	−0.174363
$821$	1.76321	0.0615366	0.0307683	−	0.999527i	$-0.490205\pi$
$821$	1.76321	0.0615366	0.0307683	+	0.999527i	$0.490205\pi$
$822$	−1.54385	−0.0538479
$823$	0.636323	0.0221808	0.0110904	−	0.999938i	$-0.496470\pi$
$823$	0.636323	0.0221808	0.0110904	+	0.999938i	$0.496470\pi$
$824$	36.0119	1.25454
$825$	18.3599	0.639209
$826$	−8.15272	−0.283670
$827$	−6.81869	−0.237109	−0.118554	−	0.992948i	$-0.537826\pi$
$827$	−6.81869	−0.237109	−0.118554	+	0.992948i	$0.537826\pi$
$828$	−22.6321	−0.786519
$829$	50.9480	1.76950	0.884749	−	0.466068i	$-0.154330\pi$
$829$	50.9480	1.76950	0.884749	+	0.466068i	$0.154330\pi$
$830$	−12.2261	−0.424373
$831$	−10.2439	−0.355356
$832$	−22.0568	−0.764683
$833$	1.00000	0.0346479
$834$	3.74318	0.129616
$835$	−5.94824	−0.205847
$836$	15.5414	0.537511
$837$	16.0698	0.555453
$838$	−1.74308	−0.0602137
$839$	2.95064	0.101867	0.0509336	−	0.998702i	$-0.483780\pi$
$839$	2.95064	0.101867	0.0509336	+	0.998702i	$0.483780\pi$
$840$	7.81687	0.269708
$841$	20.6036	0.710470
$842$	22.1200	0.762307
$843$	11.8286	0.407400
$844$	−10.4663	−0.360266
$845$	19.3048	0.664106
$846$	10.6427	0.365903
$847$	−11.8654	−0.407700
$848$	−0.153964	−0.00528714
$849$	19.7117	0.676504
$850$	3.71372	0.127379
$851$	−81.7948	−2.80389
$852$	13.3124	0.456075
$853$	−28.8764	−0.988709	−0.494355	−	0.869260i	$-0.664596\pi$
$853$	−28.8764	−0.988709	−0.494355	+	0.869260i	$0.664596\pi$
$854$	−5.84923	−0.200156
$855$	17.4799	0.597799
$856$	−11.0960	−0.379254
$857$	−9.83977	−0.336120	−0.168060	−	0.985777i	$-0.553750\pi$
$857$	−9.83977	−0.336120	−0.168060	+	0.985777i	$0.553750\pi$
$858$	−16.7599	−0.572175
$859$	−11.1344	−0.379900	−0.189950	−	0.981794i	$-0.560833\pi$
$859$	−11.1344	−0.379900	−0.189950	+	0.981794i	$0.560833\pi$
$860$	−9.43175	−0.321620
$861$	−1.21321	−0.0413460
$862$	−24.1390	−0.822178
$863$	22.7030	0.772818	0.386409	−	0.922328i	$-0.373715\pi$
$863$	22.7030	0.772818	0.386409	+	0.922328i	$0.373715\pi$
$864$	−26.5133	−0.902002
$865$	18.2817	0.621596
$866$	24.7529	0.841137
$867$	0.907578	0.0308230
$868$	−4.20535	−0.142739
$869$	9.27910	0.314772
$870$	17.0477	0.577973
$871$	−23.2395	−0.787440
$872$	10.1023	0.342106
$873$	33.0075	1.11713
$874$	19.6303	0.664005
$875$	2.33775	0.0790304
$876$	−14.1877	−0.479358
$877$	1.55717	0.0525819	0.0262910	−	0.999654i	$-0.491630\pi$
$877$	1.55717	0.0525819	0.0262910	+	0.999654i	$0.491630\pi$
$878$	5.54175	0.187025
$879$	−26.2653	−0.885907
$880$	−0.432118	−0.0145667
$881$	−10.3326	−0.348113	−0.174056	−	0.984736i	$-0.555687\pi$
$881$	−10.3326	−0.348113	−0.174056	+	0.984736i	$0.555687\pi$
$882$	−1.91043	−0.0643276
$883$	23.6160	0.794743	0.397371	−	0.917658i	$-0.369922\pi$
$883$	23.6160	0.794743	0.397371	+	0.917658i	$0.369922\pi$
$884$	5.40856	0.181910
$885$	25.6087	0.860828
$886$	23.2237	0.780215
$887$	13.9260	0.467588	0.233794	−	0.972286i	$-0.424886\pi$
$887$	13.9260	0.467588	0.233794	+	0.972286i	$0.424886\pi$
$888$	−24.8791	−0.834889
$889$	5.55875	0.186435
$890$	−35.7263	−1.19755
$891$	10.8317	0.362874
$892$	3.06237	0.102536
$893$	14.7274	0.492832
$894$	3.37931	0.113021
$895$	5.32021	0.177835
$896$	6.88613	0.230050
$897$	33.7738	1.12767
$898$	−30.3340	−1.01226
$899$	−24.0915	−0.803495
$900$	11.3191	0.377302
$901$	5.17630	0.172448
$902$	5.61117	0.186831
$903$	−2.29175	−0.0762646
$904$	−2.74026	−0.0911398
$905$	8.40028	0.279235
$906$	9.92562	0.329757
$907$	11.3628	0.377295	0.188648	−	0.982045i	$-0.439590\pi$
$907$	11.3628	0.377295	0.188648	+	0.982045i	$0.439590\pi$
$908$	20.8805	0.692943
$909$	−7.06832	−0.234442
$910$	11.7331	0.388948
$911$	4.75507	0.157543	0.0787713	−	0.996893i	$-0.474900\pi$
$911$	4.75507	0.157543	0.0787713	+	0.996893i	$0.474900\pi$
$912$	0.0713656	0.00236315
$913$	−21.9205	−0.725462
$914$	23.3435	0.772136
$915$	18.3731	0.607398
$916$	20.0766	0.663349
$917$	3.51134	0.115955
$918$	−4.12398	−0.136111
$919$	−32.6303	−1.07637	−0.538187	−	0.842825i	$-0.680891\pi$
$919$	−32.6303	−1.07637	−0.538187	+	0.842825i	$0.680891\pi$
$920$	72.8548	2.40195
$921$	−10.5130	−0.346416
$922$	−0.272303	−0.00896784
$923$	52.4882	1.72767
$924$	5.33543	0.175523
$925$	40.9084	1.34506
$926$	19.7209	0.648070
$927$	27.6459	0.908010
$928$	39.7482	1.30480
$929$	−47.3546	−1.55365	−0.776827	−	0.629714i	$-0.783172\pi$
$929$	−47.3546	−1.55365	−0.776827	+	0.629714i	$0.783172\pi$
$930$	−8.27974	−0.271503
$931$	−2.64366	−0.0866424
$932$	7.10382	0.232693
$933$	−14.3397	−0.469460
$934$	−10.1939	−0.333554
$935$	14.5279	0.475113
$936$	−27.1419	−0.887161
$937$	−51.6525	−1.68741	−0.843707	−	0.536803i	$-0.819632\pi$
$937$	−51.6525	−1.68741	−0.843707	+	0.536803i	$0.819632\pi$
$938$	−4.63717	−0.151409
$939$	18.3928	0.600226
$940$	20.8079	0.678680
$941$	−54.7240	−1.78395	−0.891975	−	0.452084i	$-0.850681\pi$
$941$	−54.7240	−1.78395	−0.891975	+	0.452084i	$0.850681\pi$
$942$	−14.0596	−0.458086
$943$	−11.3073	−0.368218
$944$	−0.276242	−0.00899091
$945$	14.2731	0.464303
$946$	10.5995	0.344619
$947$	−36.9728	−1.20145	−0.600727	−	0.799454i	$-0.705122\pi$
$947$	−36.9728	−1.20145	−0.600727	+	0.799454i	$0.705122\pi$
$948$	−2.16519	−0.0703221
$949$	−55.9395	−1.81587
$950$	−9.81779	−0.318531
$951$	5.77707	0.187334
$952$	2.83488	0.0918791
$953$	−7.91313	−0.256331	−0.128166	−	0.991753i	$-0.540909\pi$
$953$	−7.91313	−0.256331	−0.128166	+	0.991753i	$0.540909\pi$
$954$	−9.88897	−0.320167
$955$	57.2578	1.85282
$956$	−9.15017	−0.295938
$957$	30.5654	0.988039
$958$	27.9130	0.901830
$959$	1.93780	0.0625747
$960$	13.8247	0.446189
$961$	−19.2993	−0.622557
$962$	−37.3435	−1.20400
$963$	−8.51826	−0.274497
$964$	−26.9284	−0.867306
$965$	36.1867	1.16489
$966$	6.73916	0.216829
$967$	8.05906	0.259162	0.129581	−	0.991569i	$-0.458637\pi$
$967$	8.05906	0.259162	0.129581	+	0.991569i	$0.458637\pi$
$968$	−33.6371	−1.08114
$969$	−2.39933	−0.0770775
$970$	−40.4500	−1.29877
$971$	−1.81193	−0.0581476	−0.0290738	−	0.999577i	$-0.509256\pi$
$971$	−1.81193	−0.0581476	−0.0290738	+	0.999577i	$0.509256\pi$
$972$	−19.8544	−0.636829
$973$	−4.69834	−0.150622
$974$	−20.2047	−0.647401
$975$	−16.8914	−0.540959
$976$	−0.198192	−0.00634396
$977$	15.1934	0.486079	0.243040	−	0.970016i	$-0.421855\pi$
$977$	15.1934	0.486079	0.243040	+	0.970016i	$0.421855\pi$
$978$	−2.13163	−0.0681621
$979$	−64.0547	−2.04720
$980$	−3.73516	−0.119315
$981$	7.75538	0.247610
$982$	−29.2474	−0.933321
$983$	11.6472	0.371488	0.185744	−	0.982598i	$-0.440530\pi$
$983$	11.6472	0.371488	0.185744	+	0.982598i	$0.440530\pi$
$984$	−3.43930	−0.109641
$985$	−52.4638	−1.67164
$986$	6.18257	0.196893
$987$	5.05596	0.160933
$988$	−14.2984	−0.454892
$989$	−21.3596	−0.679195
$990$	−27.7546	−0.882099
$991$	−47.1759	−1.49859	−0.749296	−	0.662235i	$-0.769608\pi$
$991$	−47.1759	−1.49859	−0.749296	+	0.662235i	$0.769608\pi$
$992$	−19.3049	−0.612931
$993$	22.3183	0.708249
$994$	10.4734	0.332197
$995$	−46.3175	−1.46836
$996$	5.11494	0.162073
$997$	39.7574	1.25913	0.629564	−	0.776949i	$-0.283234\pi$
$997$	39.7574	1.25913	0.629564	+	0.776949i	$0.283234\pi$
$998$	32.5006	1.02879
$999$	−45.4276	−1.43727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.2.a.b.1.3	✓	5
3.2	odd	2		1071.2.a.m.1.3		5
4.3	odd	2		1904.2.a.t.1.2		5
5.4	even	2		2975.2.a.m.1.3		5
7.2	even	3		833.2.e.i.18.3		10
7.3	odd	6		833.2.e.h.324.3		10
7.4	even	3		833.2.e.i.324.3		10
7.5	odd	6		833.2.e.h.18.3		10
7.6	odd	2		833.2.a.g.1.3		5
8.3	odd	2		7616.2.a.bq.1.4		5
8.5	even	2		7616.2.a.bt.1.2		5
17.16	even	2		2023.2.a.j.1.3		5
21.20	even	2		7497.2.a.br.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.a.b.1.3	✓	5	1.1	even	1	trivial
833.2.a.g.1.3		5	7.6	odd	2
833.2.e.h.18.3		10	7.5	odd	6
833.2.e.h.324.3		10	7.3	odd	6
833.2.e.i.18.3		10	7.2	even	3
833.2.e.i.324.3		10	7.4	even	3
1071.2.a.m.1.3		5	3.2	odd	2
1904.2.a.t.1.2		5	4.3	odd	2
2023.2.a.j.1.3		5	17.16	even	2
2975.2.a.m.1.3		5	5.4	even	2
7497.2.a.br.1.3		5	21.20	even	2
7616.2.a.bq.1.4		5	8.3	odd	2
7616.2.a.bt.1.2		5	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	119.a (trivial)

\(f(q)\)	\(=\)	\(q+0.877834 q^{2} +0.907578 q^{3} -1.22941 q^{4} +3.03818 q^{5} +0.796703 q^{6} -1.00000 q^{7} -2.83488 q^{8} -2.17630 q^{9} +2.66702 q^{10} +4.78178 q^{11} -1.11578 q^{12} -4.39933 q^{13} -0.877834 q^{14} +2.75739 q^{15} -0.0297440 q^{16} +1.00000 q^{17} -1.91043 q^{18} -2.64366 q^{19} -3.73516 q^{20} -0.907578 q^{21} +4.19761 q^{22} -8.45881 q^{23} -2.57288 q^{24} +4.23054 q^{25} -3.86188 q^{26} -4.69790 q^{27} +1.22941 q^{28} +7.04298 q^{29} +2.42053 q^{30} -3.42063 q^{31} +5.64366 q^{32} +4.33984 q^{33} +0.877834 q^{34} -3.03818 q^{35} +2.67556 q^{36} +9.66977 q^{37} -2.32069 q^{38} -3.99273 q^{39} -8.61289 q^{40} +1.33675 q^{41} -0.796703 q^{42} +2.52513 q^{43} -5.87875 q^{44} -6.61200 q^{45} -7.42544 q^{46} -5.57082 q^{47} -0.0269950 q^{48} +1.00000 q^{49} +3.71372 q^{50} +0.907578 q^{51} +5.40856 q^{52} +5.17630 q^{53} -4.12398 q^{54} +14.5279 q^{55} +2.83488 q^{56} -2.39933 q^{57} +6.18257 q^{58} +9.28732 q^{59} -3.38995 q^{60} +6.66325 q^{61} -3.00275 q^{62} +2.17630 q^{63} +5.01368 q^{64} -13.3659 q^{65} +3.80966 q^{66} +5.28251 q^{67} -1.22941 q^{68} -7.67704 q^{69} -2.66702 q^{70} -11.9310 q^{71} +6.16956 q^{72} +12.7155 q^{73} +8.48845 q^{74} +3.83955 q^{75} +3.25013 q^{76} -4.78178 q^{77} -3.50496 q^{78} +1.94051 q^{79} -0.0903677 q^{80} +2.26519 q^{81} +1.17345 q^{82} -4.58417 q^{83} +1.11578 q^{84} +3.03818 q^{85} +2.21664 q^{86} +6.39206 q^{87} -13.5558 q^{88} -13.3956 q^{89} -5.80424 q^{90} +4.39933 q^{91} +10.3993 q^{92} -3.10449 q^{93} -4.89026 q^{94} -8.03191 q^{95} +5.12206 q^{96} -15.1668 q^{97} +0.877834 q^{98} -10.4066 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - q^{6} - 5 q^{7} + 6 q^{8} + 11 q^{9} + 4 q^{10} - 2 q^{11} - 22 q^{12} + 2 q^{13} - 2 q^{14} + 8 q^{15} + 4 q^{16} + 5 q^{17} - 18 q^{18} + 6 q^{19} - 19 q^{20} + 2 q^{21}+ \cdots - 62 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - q^6 - 5 * q^7 + 6 * q^8 + 11 * q^9 + 4 * q^10 - 2 * q^11 - 22 * q^12 + 2 * q^13 - 2 * q^14 + 8 * q^15 + 4 * q^16 + 5 * q^17 - 18 * q^18 + 6 * q^19 - 19 * q^20 + 2 * q^21 + 6 * q^22 - 10 * q^23 + 2 * q^24 + 21 * q^25 - 26 * q^26 - 26 * q^27 - 10 * q^28 - 8 * q^29 - 51 * q^30 + 9 * q^32 + 6 * q^33 + 2 * q^34 + 39 * q^36 + 8 * q^37 + 14 * q^38 + 14 * q^39 + 5 * q^40 + 18 * q^41 + q^42 + 8 * q^43 - 14 * q^44 + 8 * q^46 - 10 * q^47 - 27 * q^48 + 5 * q^49 + 27 * q^50 - 2 * q^51 + 4 * q^52 + 4 * q^53 + 5 * q^54 - 24 * q^55 - 6 * q^56 + 12 * q^57 + 12 * q^58 + 8 * q^59 - 7 * q^60 + 22 * q^61 + 16 * q^62 - 11 * q^63 - 16 * q^64 - 30 * q^65 + 68 * q^66 + 16 * q^67 + 10 * q^68 - 32 * q^69 - 4 * q^70 - 2 * q^71 + 9 * q^72 + 10 * q^73 - 40 * q^74 - 14 * q^75 + 24 * q^76 + 2 * q^77 + 30 * q^78 + 18 * q^79 - 4 * q^80 + 25 * q^81 - 31 * q^82 - 12 * q^83 + 22 * q^84 + 23 * q^86 - 26 * q^87 - 46 * q^88 + 20 * q^89 + 97 * q^90 - 2 * q^91 + 28 * q^92 - 28 * q^93 - 42 * q^94 - 22 * q^95 - 18 * q^96 + 12 * q^97 + 2 * q^98 - 62 * q^99

Introduction

L-functions

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