LMFDB - Embedded newform 671.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, 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("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 5 x^{18} - 18 x^{17} + 122 x^{16} + 78 x^{15} - 1177 x^{14} + 387 x^{13} + 5755 x^{12} + \cdots - 43 $ x^19 - 5x^18 - 18x^17 + 122x^16 + 78x^15 - 1177x^14 + 387x^13 + 5755x^12 - 4673x^11 - 15053x^10 + 16875x^9 + 20141x^8 - 28019x^7 - 11589x^6 + 21077x^5 + 1674x^4 - 6404x^3 + 241x^2 + 643x - 43
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.21976$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21976 q^{2} -2.99078 q^{3} +2.92734 q^{4} -2.17512 q^{5} +6.63880 q^{6} +5.05675 q^{7} -2.05847 q^{8} +5.94474 q^{9} +O(q^{10})$	\(q-2.21976 q^{2} -2.99078 q^{3} +2.92734 q^{4} -2.17512 q^{5} +6.63880 q^{6} +5.05675 q^{7} -2.05847 q^{8} +5.94474 q^{9} +4.82825 q^{10} +1.00000 q^{11} -8.75501 q^{12} -3.20178 q^{13} -11.2248 q^{14} +6.50530 q^{15} -1.28537 q^{16} -5.61523 q^{17} -13.1959 q^{18} +1.25758 q^{19} -6.36732 q^{20} -15.1236 q^{21} -2.21976 q^{22} +0.955523 q^{23} +6.15641 q^{24} -0.268843 q^{25} +7.10719 q^{26} -8.80704 q^{27} +14.8028 q^{28} +2.64307 q^{29} -14.4402 q^{30} +5.28519 q^{31} +6.97015 q^{32} -2.99078 q^{33} +12.4645 q^{34} -10.9990 q^{35} +17.4022 q^{36} +7.64117 q^{37} -2.79153 q^{38} +9.57581 q^{39} +4.47742 q^{40} -3.21692 q^{41} +33.5708 q^{42} -8.70811 q^{43} +2.92734 q^{44} -12.9305 q^{45} -2.12103 q^{46} -6.21668 q^{47} +3.84426 q^{48} +18.5707 q^{49} +0.596767 q^{50} +16.7939 q^{51} -9.37269 q^{52} +2.85705 q^{53} +19.5495 q^{54} -2.17512 q^{55} -10.4091 q^{56} -3.76114 q^{57} -5.86699 q^{58} -6.34839 q^{59} +19.0432 q^{60} -1.00000 q^{61} -11.7319 q^{62} +30.0610 q^{63} -12.9013 q^{64} +6.96426 q^{65} +6.63880 q^{66} -14.1507 q^{67} -16.4377 q^{68} -2.85775 q^{69} +24.4152 q^{70} +10.5413 q^{71} -12.2370 q^{72} +4.23786 q^{73} -16.9616 q^{74} +0.804049 q^{75} +3.68136 q^{76} +5.05675 q^{77} -21.2560 q^{78} +17.1827 q^{79} +2.79584 q^{80} +8.50568 q^{81} +7.14080 q^{82} -3.89639 q^{83} -44.2719 q^{84} +12.2138 q^{85} +19.3299 q^{86} -7.90484 q^{87} -2.05847 q^{88} +9.09472 q^{89} +28.7027 q^{90} -16.1906 q^{91} +2.79714 q^{92} -15.8068 q^{93} +13.7995 q^{94} -2.73539 q^{95} -20.8462 q^{96} -6.63181 q^{97} -41.2225 q^{98} +5.94474 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) $ 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9} + 7 q^{10} + 19 q^{11} - 4 q^{12} + 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} + 9 q^{17} + 10 q^{18} + 17 q^{19} - 6 q^{20} + 18 q^{21} + 5 q^{22} - 10 q^{23} + 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} + 36 q^{28} + 27 q^{29} - 30 q^{30} + 7 q^{31} + 8 q^{32} - 5 q^{34} + 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} + 24 q^{39} + 10 q^{40} + 19 q^{41} + 21 q^{42} + 20 q^{43} + 23 q^{44} - 32 q^{45} + 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} + 36 q^{50} + 47 q^{51} - 28 q^{52} + 3 q^{53} - 33 q^{54} - 44 q^{56} + 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} - 19 q^{61} - 11 q^{62} - 32 q^{63} + 47 q^{64} + 25 q^{65} + q^{66} + 3 q^{67} + 38 q^{68} + 3 q^{70} - 19 q^{71} + 34 q^{72} + 20 q^{73} - 22 q^{74} - 50 q^{75} - 25 q^{76} + 9 q^{77} - 94 q^{78} + 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} + q^{83} - 28 q^{84} + 24 q^{85} - 27 q^{86} - 58 q^{87} + 9 q^{88} + 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} + 64 q^{94} - 3 q^{95} - 26 q^{96} + 21 q^{97} - 87 q^{98} + 29 q^{99}+O(q^{100}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9 + 7 * q^10 + 19 * q^11 - 4 * q^12 + 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 + 9 * q^17 + 10 * q^18 + 17 * q^19 - 6 * q^20 + 18 * q^21 + 5 * q^22 - 10 * q^23 + 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 + 36 * q^28 + 27 * q^29 - 30 * q^30 + 7 * q^31 + 8 * q^32 - 5 * q^34 + 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 + 24 * q^39 + 10 * q^40 + 19 * q^41 + 21 * q^42 + 20 * q^43 + 23 * q^44 - 32 * q^45 + 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 + 36 * q^50 + 47 * q^51 - 28 * q^52 + 3 * q^53 - 33 * q^54 - 44 * q^56 + 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 - 19 * q^61 - 11 * q^62 - 32 * q^63 + 47 * q^64 + 25 * q^65 + q^66 + 3 * q^67 + 38 * q^68 + 3 * q^70 - 19 * q^71 + 34 * q^72 + 20 * q^73 - 22 * q^74 - 50 * q^75 - 25 * q^76 + 9 * q^77 - 94 * q^78 + 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 + q^83 - 28 * q^84 + 24 * q^85 - 27 * q^86 - 58 * q^87 + 9 * q^88 + 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 + 64 * q^94 - 3 * q^95 - 26 * q^96 + 21 * q^97 - 87 * q^98 + 29 * 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 $

$2$	−2.21976	−1.56961	−0.784804	−	0.619744i	$-0.787236\pi$
$2$	−2.21976	−1.56961	−0.784804	+	0.619744i	$0.787236\pi$
$3$	−2.99078	−1.72672	−0.863362	−	0.504584i	$-0.831646\pi$
$3$	−2.99078	−1.72672	−0.863362	+	0.504584i	$0.831646\pi$
$4$	2.92734	1.46367
$5$	−2.17512	−0.972744	−0.486372	−	0.873752i	$-0.661680\pi$
$5$	−2.17512	−0.972744	−0.486372	+	0.873752i	$0.661680\pi$
$6$	6.63880	2.71028
$7$	5.05675	1.91127	0.955635	−	0.294552i	$-0.0951706\pi$
$7$	5.05675	1.91127	0.955635	+	0.294552i	$0.0951706\pi$
$8$	−2.05847	−0.727778
$9$	5.94474	1.98158
$10$	4.82825	1.52683
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−8.75501	−2.52735
$13$	−3.20178	−0.888014	−0.444007	−	0.896023i	$-0.646443\pi$
$13$	−3.20178	−0.888014	−0.444007	+	0.896023i	$0.646443\pi$
$14$	−11.2248	−2.99995
$15$	6.50530	1.67966
$16$	−1.28537	−0.321343
$17$	−5.61523	−1.36189	−0.680947	−	0.732333i	$-0.738432\pi$
$17$	−5.61523	−1.36189	−0.680947	+	0.732333i	$0.738432\pi$
$18$	−13.1959	−3.11030
$19$	1.25758	0.288509	0.144254	−	0.989541i	$-0.453922\pi$
$19$	1.25758	0.288509	0.144254	+	0.989541i	$0.453922\pi$
$20$	−6.36732	−1.42378
$21$	−15.1236	−3.30024
$22$	−2.21976	−0.473255
$23$	0.955523	0.199240	0.0996201	−	0.995026i	$-0.468237\pi$
$23$	0.955523	0.199240	0.0996201	+	0.995026i	$0.468237\pi$
$24$	6.15641	1.25667
$25$	−0.268843	−0.0537686
$26$	7.10719	1.39383
$27$	−8.80704	−1.69492
$28$	14.8028	2.79747
$29$	2.64307	0.490806	0.245403	−	0.969421i	$-0.421080\pi$
$29$	2.64307	0.490806	0.245403	+	0.969421i	$0.421080\pi$
$30$	−14.4402	−2.63641
$31$	5.28519	0.949249	0.474624	−	0.880188i	$-0.342584\pi$
$31$	5.28519	0.949249	0.474624	+	0.880188i	$0.342584\pi$
$32$	6.97015	1.23216
$33$	−2.99078	−0.520627
$34$	12.4645	2.13764
$35$	−10.9990	−1.85918
$36$	17.4022	2.90037
$37$	7.64117	1.25620	0.628100	−	0.778132i	$-0.283833\pi$
$37$	7.64117	1.25620	0.628100	+	0.778132i	$0.283833\pi$
$38$	−2.79153	−0.452846
$39$	9.57581	1.53336
$40$	4.47742	0.707942
$41$	−3.21692	−0.502399	−0.251200	−	0.967935i	$-0.580825\pi$
$41$	−3.21692	−0.502399	−0.251200	+	0.967935i	$0.580825\pi$
$42$	33.5708	5.18008
$43$	−8.70811	−1.32797	−0.663987	−	0.747744i	$-0.731137\pi$
$43$	−8.70811	−1.32797	−0.663987	+	0.747744i	$0.731137\pi$
$44$	2.92734	0.441313
$45$	−12.9305	−1.92757
$46$	−2.12103	−0.312729
$47$	−6.21668	−0.906796	−0.453398	−	0.891308i	$-0.649788\pi$
$47$	−6.21668	−0.906796	−0.453398	+	0.891308i	$0.649788\pi$
$48$	3.84426	0.554871
$49$	18.5707	2.65296
$50$	0.596767	0.0843957
$51$	16.7939	2.35162
$52$	−9.37269	−1.29976
$53$	2.85705	0.392445	0.196223	−	0.980559i	$-0.437132\pi$
$53$	2.85705	0.392445	0.196223	+	0.980559i	$0.437132\pi$
$54$	19.5495	2.66035
$55$	−2.17512	−0.293293
$56$	−10.4091	−1.39098
$57$	−3.76114	−0.498175
$58$	−5.86699	−0.770373
$59$	−6.34839	−0.826491	−0.413245	−	0.910620i	$-0.635605\pi$
$59$	−6.34839	−0.826491	−0.413245	+	0.910620i	$0.635605\pi$
$60$	19.0432	2.45847
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−11.7319	−1.48995
$63$	30.0610	3.78733
$64$	−12.9013	−1.61267
$65$	6.96426	0.863811
$66$	6.63880	0.817180
$67$	−14.1507	−1.72878	−0.864391	−	0.502821i	$-0.832296\pi$
$67$	−14.1507	−1.72878	−0.864391	+	0.502821i	$0.832296\pi$
$68$	−16.4377	−1.99336
$69$	−2.85775	−0.344033
$70$	24.4152	2.91818
$71$	10.5413	1.25102	0.625511	−	0.780215i	$-0.284890\pi$
$71$	10.5413	1.25102	0.625511	+	0.780215i	$0.284890\pi$
$72$	−12.2370	−1.44215
$73$	4.23786	0.496004	0.248002	−	0.968760i	$-0.420226\pi$
$73$	4.23786	0.496004	0.248002	+	0.968760i	$0.420226\pi$
$74$	−16.9616	−1.97174
$75$	0.804049	0.0928436
$76$	3.68136	0.422281
$77$	5.05675	0.576270
$78$	−21.2560	−2.40677
$79$	17.1827	1.93320	0.966601	−	0.256288i	$-0.0824994\pi$
$79$	17.1827	1.93320	0.966601	+	0.256288i	$0.0824994\pi$
$80$	2.79584	0.312584
$81$	8.50568	0.945075
$82$	7.14080	0.788570
$83$	−3.89639	−0.427685	−0.213842	−	0.976868i	$-0.568598\pi$
$83$	−3.89639	−0.427685	−0.213842	+	0.976868i	$0.568598\pi$
$84$	−44.2719	−4.83046
$85$	12.2138	1.32477
$86$	19.3299	2.08440
$87$	−7.90484	−0.847487
$88$	−2.05847	−0.219433
$89$	9.09472	0.964039	0.482019	−	0.876161i	$-0.339904\pi$
$89$	9.09472	0.964039	0.482019	+	0.876161i	$0.339904\pi$
$90$	28.7027	3.02553
$91$	−16.1906	−1.69724
$92$	2.79714	0.291622
$93$	−15.8068	−1.63909
$94$	13.7995	1.42331
$95$	−2.73539	−0.280645
$96$	−20.8462	−2.12760
$97$	−6.63181	−0.673359	−0.336679	−	0.941619i	$-0.609304\pi$
$97$	−6.63181	−0.673359	−0.336679	+	0.941619i	$0.609304\pi$
$98$	−41.2225	−4.16410
$99$	5.94474	0.597468
$100$	−0.786995	−0.0786995
$101$	−4.51837	−0.449594	−0.224797	−	0.974406i	$-0.572172\pi$
$101$	−4.51837	−0.449594	−0.224797	+	0.974406i	$0.572172\pi$
$102$	−37.2784	−3.69111
$103$	16.3610	1.61210	0.806051	−	0.591846i	$-0.201601\pi$
$103$	16.3610	1.61210	0.806051	+	0.591846i	$0.201601\pi$
$104$	6.59076	0.646277
$105$	32.8957	3.21029
$106$	−6.34196	−0.615985
$107$	8.60049	0.831441	0.415721	−	0.909492i	$-0.363529\pi$
$107$	8.60049	0.831441	0.415721	+	0.909492i	$0.363529\pi$
$108$	−25.7812	−2.48080
$109$	18.4620	1.76834	0.884170	−	0.467165i	$-0.154724\pi$
$109$	18.4620	1.76834	0.884170	+	0.467165i	$0.154724\pi$
$110$	4.82825	0.460356
$111$	−22.8530	−2.16911
$112$	−6.49980	−0.614173
$113$	15.5049	1.45858	0.729291	−	0.684203i	$-0.239850\pi$
$113$	15.5049	1.45858	0.729291	+	0.684203i	$0.239850\pi$
$114$	8.34883	0.781940
$115$	−2.07838	−0.193810
$116$	7.73717	0.718378
$117$	−19.0337	−1.75967
$118$	14.0919	1.29727
$119$	−28.3948	−2.60295
$120$	−13.3909	−1.22242
$121$	1.00000	0.0909091
$122$	2.21976	0.200968
$123$	9.62110	0.867505
$124$	15.4715	1.38939
$125$	11.4604	1.02505
$126$	−66.7283	−5.94463
$127$	5.45540	0.484089	0.242044	−	0.970265i	$-0.422182\pi$
$127$	5.45540	0.484089	0.242044	+	0.970265i	$0.422182\pi$
$128$	14.6975	1.29909
$129$	26.0440	2.29305
$130$	−15.4590	−1.35584
$131$	15.8906	1.38836	0.694182	−	0.719799i	$-0.255766\pi$
$131$	15.8906	1.38836	0.694182	+	0.719799i	$0.255766\pi$
$132$	−8.75501	−0.762026
$133$	6.35927	0.551418
$134$	31.4111	2.71351
$135$	19.1564	1.64872
$136$	11.5588	0.991156
$137$	−2.94993	−0.252029	−0.126015	−	0.992028i	$-0.540219\pi$
$137$	−2.94993	−0.252029	−0.126015	+	0.992028i	$0.540219\pi$
$138$	6.34353	0.539997
$139$	0.637252	0.0540510	0.0270255	−	0.999635i	$-0.491396\pi$
$139$	0.637252	0.0540510	0.0270255	+	0.999635i	$0.491396\pi$
$140$	−32.1979	−2.72122
$141$	18.5927	1.56579
$142$	−23.3992	−1.96361
$143$	−3.20178	−0.267746
$144$	−7.64120	−0.636766
$145$	−5.74901	−0.477429
$146$	−9.40703	−0.778531
$147$	−55.5408	−4.58092
$148$	22.3683	1.83866
$149$	13.8076	1.13116	0.565581	−	0.824693i	$-0.308652\pi$
$149$	13.8076	1.13116	0.565581	+	0.824693i	$0.308652\pi$
$150$	−1.78480	−0.145728
$151$	−20.4624	−1.66520	−0.832602	−	0.553872i	$-0.813150\pi$
$151$	−20.4624	−1.66520	−0.832602	+	0.553872i	$0.813150\pi$
$152$	−2.58869	−0.209970
$153$	−33.3811	−2.69870
$154$	−11.2248	−0.904518
$155$	−11.4959	−0.923376
$156$	28.0316	2.24433
$157$	−0.115826	−0.00924395	−0.00462198	−	0.999989i	$-0.501471\pi$
$157$	−0.115826	−0.00924395	−0.00462198	+	0.999989i	$0.501471\pi$
$158$	−38.1414	−3.03437
$159$	−8.54478	−0.677645
$160$	−15.1609	−1.19858
$161$	4.83184	0.380802
$162$	−18.8806	−1.48340
$163$	−21.4977	−1.68383	−0.841914	−	0.539612i	$-0.818571\pi$
$163$	−21.4977	−1.68383	−0.841914	+	0.539612i	$0.818571\pi$
$164$	−9.41702	−0.735346
$165$	6.50530	0.506437
$166$	8.64906	0.671297
$167$	3.66249	0.283412	0.141706	−	0.989909i	$-0.454741\pi$
$167$	3.66249	0.283412	0.141706	+	0.989909i	$0.454741\pi$
$168$	31.1314	2.40184
$169$	−2.74860	−0.211431
$170$	−27.1117	−2.07938
$171$	7.47598	0.571703
$172$	−25.4916	−1.94371
$173$	16.7593	1.27419	0.637095	−	0.770785i	$-0.280136\pi$
$173$	16.7593	1.27419	0.637095	+	0.770785i	$0.280136\pi$
$174$	17.5468	1.33022
$175$	−1.35947	−0.102766
$176$	−1.28537	−0.0968885
$177$	18.9866	1.42712
$178$	−20.1881	−1.51316
$179$	16.8397	1.25866	0.629329	−	0.777139i	$-0.283330\pi$
$179$	16.8397	1.25866	0.629329	+	0.777139i	$0.283330\pi$
$180$	−37.8520	−2.82132
$181$	13.3009	0.988645	0.494323	−	0.869279i	$-0.335416\pi$
$181$	13.3009	0.988645	0.494323	+	0.869279i	$0.335416\pi$
$182$	35.9392	2.66399
$183$	2.99078	0.221084
$184$	−1.96691	−0.145003
$185$	−16.6205	−1.22196
$186$	35.0874	2.57273
$187$	−5.61523	−0.410626
$188$	−18.1983	−1.32725
$189$	−44.5350	−3.23944
$190$	6.07191	0.440503
$191$	−20.8693	−1.51005	−0.755024	−	0.655698i	$-0.772375\pi$
$191$	−20.8693	−1.51005	−0.755024	+	0.655698i	$0.772375\pi$
$192$	38.5850	2.78463
$193$	−2.99802	−0.215802	−0.107901	−	0.994162i	$-0.534413\pi$
$193$	−2.99802	−0.215802	−0.107901	+	0.994162i	$0.534413\pi$
$194$	14.7210	1.05691
$195$	−20.8285	−1.49156
$196$	54.3627	3.88305
$197$	16.0388	1.14272	0.571360	−	0.820699i	$-0.306416\pi$
$197$	16.0388	1.14272	0.571360	+	0.820699i	$0.306416\pi$
$198$	−13.1959	−0.937791
$199$	0.533497	0.0378186	0.0189093	−	0.999821i	$-0.493981\pi$
$199$	0.533497	0.0378186	0.0189093	+	0.999821i	$0.493981\pi$
$200$	0.553405	0.0391316
$201$	42.3215	2.98513
$202$	10.0297	0.705687
$203$	13.3654	0.938064
$204$	49.1614	3.44199
$205$	6.99720	0.488706
$206$	−36.3176	−2.53037
$207$	5.68033	0.394810
$208$	4.11548	0.285357
$209$	1.25758	0.0869887
$210$	−73.0205	−5.03889
$211$	−5.67278	−0.390530	−0.195265	−	0.980750i	$-0.562557\pi$
$211$	−5.67278	−0.390530	−0.195265	+	0.980750i	$0.562557\pi$
$212$	8.36354	0.574410
$213$	−31.5267	−2.16017
$214$	−19.0910	−1.30504
$215$	18.9412	1.29178
$216$	18.1290	1.23352
$217$	26.7259	1.81427
$218$	−40.9813	−2.77560
$219$	−12.6745	−0.856462
$220$	−6.36732	−0.429284
$221$	17.9787	1.20938
$222$	50.7282	3.40466
$223$	14.2351	0.953255	0.476627	−	0.879105i	$-0.341859\pi$
$223$	14.2351	0.953255	0.476627	+	0.879105i	$0.341859\pi$
$224$	35.2463	2.35499
$225$	−1.59820	−0.106547
$226$	−34.4173	−2.28940
$227$	−3.30880	−0.219613	−0.109806	−	0.993953i	$-0.535023\pi$
$227$	−3.30880	−0.219613	−0.109806	+	0.993953i	$0.535023\pi$
$228$	−11.0101	−0.729163
$229$	−3.72809	−0.246359	−0.123180	−	0.992384i	$-0.539309\pi$
$229$	−3.72809	−0.246359	−0.123180	+	0.992384i	$0.539309\pi$
$230$	4.61350	0.304205
$231$	−15.1236	−0.995059
$232$	−5.44068	−0.357198
$233$	11.3017	0.740402	0.370201	−	0.928952i	$-0.379289\pi$
$233$	11.3017	0.740402	0.370201	+	0.928952i	$0.379289\pi$
$234$	42.2503	2.76199
$235$	13.5220	0.882081
$236$	−18.5839	−1.20971
$237$	−51.3895	−3.33811
$238$	63.0297	4.08561
$239$	2.35225	0.152155	0.0760773	−	0.997102i	$-0.475760\pi$
$239$	2.35225	0.152155	0.0760773	+	0.997102i	$0.475760\pi$
$240$	−8.36173	−0.539747
$241$	7.75854	0.499771	0.249886	−	0.968275i	$-0.419607\pi$
$241$	7.75854	0.499771	0.249886	+	0.968275i	$0.419607\pi$
$242$	−2.21976	−0.142692
$243$	0.982565	0.0630315
$244$	−2.92734	−0.187404
$245$	−40.3935	−2.58065
$246$	−21.3565	−1.36164
$247$	−4.02650	−0.256200
$248$	−10.8794	−0.690842
$249$	11.6532	0.738493
$250$	−25.4393	−1.60892
$251$	−4.26673	−0.269314	−0.134657	−	0.990892i	$-0.542993\pi$
$251$	−4.26673	−0.269314	−0.134657	+	0.990892i	$0.542993\pi$
$252$	87.9987	5.54340
$253$	0.955523	0.0600732
$254$	−12.1097	−0.759829
$255$	−36.5288	−2.28752
$256$	−6.82239	−0.426399
$257$	4.14948	0.258838	0.129419	−	0.991590i	$-0.458689\pi$
$257$	4.14948	0.258838	0.129419	+	0.991590i	$0.458689\pi$
$258$	−57.8114	−3.59918
$259$	38.6395	2.40094
$260$	20.3867	1.26433
$261$	15.7124	0.972571
$262$	−35.2732	−2.17919
$263$	11.8060	0.727990	0.363995	−	0.931401i	$-0.381412\pi$
$263$	11.8060	0.727990	0.363995	+	0.931401i	$0.381412\pi$
$264$	6.15641	0.378901
$265$	−6.21442	−0.381749
$266$	−14.1160	−0.865511
$267$	−27.2003	−1.66463
$268$	−41.4238	−2.53036
$269$	−27.5004	−1.67673	−0.838363	−	0.545112i	$-0.816487\pi$
$269$	−27.5004	−1.67673	−0.838363	+	0.545112i	$0.816487\pi$
$270$	−42.5226	−2.58784
$271$	19.8308	1.20463	0.602317	−	0.798257i	$-0.294244\pi$
$271$	19.8308	1.20463	0.602317	+	0.798257i	$0.294244\pi$
$272$	7.21766	0.437635
$273$	48.4224	2.93066
$274$	6.54814	0.395587
$275$	−0.268843	−0.0162119
$276$	−8.36561	−0.503550
$277$	9.78672	0.588027	0.294013	−	0.955801i	$-0.405009\pi$
$277$	9.78672	0.588027	0.294013	+	0.955801i	$0.405009\pi$
$278$	−1.41455	−0.0848389
$279$	31.4191	1.88101
$280$	22.6412	1.35307
$281$	7.31594	0.436432	0.218216	−	0.975900i	$-0.429976\pi$
$281$	7.31594	0.436432	0.218216	+	0.975900i	$0.429976\pi$
$282$	−41.2713	−2.45767
$283$	14.1525	0.841279	0.420640	−	0.907228i	$-0.361806\pi$
$283$	14.1525	0.841279	0.420640	+	0.907228i	$0.361806\pi$
$284$	30.8579	1.83108
$285$	8.18094	0.484597
$286$	7.10719	0.420257
$287$	−16.2672	−0.960221
$288$	41.4357	2.44162
$289$	14.5308	0.854755
$290$	12.7614	0.749376
$291$	19.8343	1.16271
$292$	12.4056	0.725985
$293$	−15.8736	−0.927347	−0.463673	−	0.886006i	$-0.653469\pi$
$293$	−15.8736	−0.927347	−0.463673	+	0.886006i	$0.653469\pi$
$294$	123.287	7.19025
$295$	13.8085	0.803964
$296$	−15.7291	−0.914235
$297$	−8.80704	−0.511036
$298$	−30.6496	−1.77548
$299$	−3.05937	−0.176928
$300$	2.35372	0.135892
$301$	−44.0347	−2.53812
$302$	45.4216	2.61372
$303$	13.5134	0.776326
$304$	−1.61646	−0.0927103
$305$	2.17512	0.124547
$306$	74.0980	4.23590
$307$	−22.3977	−1.27830	−0.639151	−	0.769081i	$-0.720714\pi$
$307$	−22.3977	−1.27830	−0.639151	+	0.769081i	$0.720714\pi$
$308$	14.8028	0.843468
$309$	−48.9322	−2.78366
$310$	25.5182	1.44934
$311$	−11.6603	−0.661194	−0.330597	−	0.943772i	$-0.607250\pi$
$311$	−11.6603	−0.661194	−0.330597	+	0.943772i	$0.607250\pi$
$312$	−19.7115	−1.11594
$313$	1.19268	0.0674142	0.0337071	−	0.999432i	$-0.489269\pi$
$313$	1.19268	0.0674142	0.0337071	+	0.999432i	$0.489269\pi$
$314$	0.257107	0.0145094
$315$	−65.3864	−3.68411
$316$	50.2995	2.82957
$317$	13.3231	0.748300	0.374150	−	0.927368i	$-0.377935\pi$
$317$	13.3231	0.748300	0.374150	+	0.927368i	$0.377935\pi$
$318$	18.9674	1.06364
$319$	2.64307	0.147984
$320$	28.0620	1.56871
$321$	−25.7221	−1.43567
$322$	−10.7255	−0.597710
$323$	−7.06161	−0.392918
$324$	24.8990	1.38328
$325$	0.860777	0.0477473
$326$	47.7197	2.64295
$327$	−55.2157	−3.05344
$328$	6.62193	0.365635
$329$	−31.4362	−1.73313
$330$	−14.4402	−0.794908
$331$	23.8884	1.31303	0.656514	−	0.754314i	$-0.272030\pi$
$331$	23.8884	1.31303	0.656514	+	0.754314i	$0.272030\pi$
$332$	−11.4061	−0.625988
$333$	45.4247	2.48926
$334$	−8.12985	−0.444845
$335$	30.7795	1.68166
$336$	19.4394	1.06051
$337$	7.52823	0.410089	0.205044	−	0.978753i	$-0.434266\pi$
$337$	7.52823	0.410089	0.205044	+	0.978753i	$0.434266\pi$
$338$	6.10124	0.331864
$339$	−46.3718	−2.51857
$340$	35.7540	1.93903
$341$	5.28519	0.286209
$342$	−16.5949	−0.897349
$343$	58.5100	3.15925
$344$	17.9253	0.966470
$345$	6.21596	0.334656
$346$	−37.2017	−1.99998
$347$	12.0728	0.648102	0.324051	−	0.946040i	$-0.394955\pi$
$347$	12.0728	0.648102	0.324051	+	0.946040i	$0.394955\pi$
$348$	−23.1401	−1.24044
$349$	−13.4052	−0.717564	−0.358782	−	0.933421i	$-0.616808\pi$
$349$	−13.4052	−0.717564	−0.358782	+	0.933421i	$0.616808\pi$
$350$	3.01770	0.161303
$351$	28.1982	1.50511
$352$	6.97015	0.371510
$353$	26.2962	1.39961	0.699804	−	0.714335i	$-0.253271\pi$
$353$	26.2962	1.39961	0.699804	+	0.714335i	$0.253271\pi$
$354$	−42.1457	−2.24002
$355$	−22.9286	−1.21692
$356$	26.6233	1.41103
$357$	84.9225	4.49457
$358$	−37.3801	−1.97560
$359$	4.55740	0.240530	0.120265	−	0.992742i	$-0.461626\pi$
$359$	4.55740	0.240530	0.120265	+	0.992742i	$0.461626\pi$
$360$	26.6171	1.40284
$361$	−17.4185	−0.916763
$362$	−29.5247	−1.55179
$363$	−2.99078	−0.156975
$364$	−47.3953	−2.48419
$365$	−9.21786	−0.482485
$366$	−6.63880	−0.347016
$367$	−14.5909	−0.761638	−0.380819	−	0.924650i	$-0.624358\pi$
$367$	−14.5909	−0.761638	−0.380819	+	0.924650i	$0.624358\pi$
$368$	−1.22820	−0.0640244
$369$	−19.1238	−0.995543
$370$	36.8935	1.91800
$371$	14.4474	0.750069
$372$	−46.2719	−2.39909
$373$	−27.5057	−1.42419	−0.712097	−	0.702081i	$-0.752254\pi$
$373$	−27.5057	−1.42419	−0.712097	+	0.702081i	$0.752254\pi$
$374$	12.4645	0.644522
$375$	−34.2754	−1.76997
$376$	12.7968	0.659946
$377$	−8.46254	−0.435843
$378$	98.8570	5.08466
$379$	−9.32525	−0.479006	−0.239503	−	0.970896i	$-0.576984\pi$
$379$	−9.32525	−0.479006	−0.239503	+	0.970896i	$0.576984\pi$
$380$	−8.00741	−0.410772
$381$	−16.3159	−0.835888
$382$	46.3248	2.37018
$383$	26.5579	1.35704	0.678522	−	0.734581i	$-0.262621\pi$
$383$	26.5579	1.35704	0.678522	+	0.734581i	$0.262621\pi$
$384$	−43.9570	−2.24317
$385$	−10.9990	−0.560563
$386$	6.65488	0.338724
$387$	−51.7674	−2.63149
$388$	−19.4136	−0.985574
$389$	22.2104	1.12611	0.563055	−	0.826419i	$-0.309626\pi$
$389$	22.2104	1.12611	0.563055	+	0.826419i	$0.309626\pi$
$390$	46.2344	2.34117
$391$	−5.36548	−0.271344
$392$	−38.2271	−1.93076
$393$	−47.5251	−2.39732
$394$	−35.6024	−1.79362
$395$	−37.3744	−1.88051
$396$	17.4022	0.874496
$397$	19.9200	0.999754	0.499877	−	0.866096i	$-0.333378\pi$
$397$	19.9200	0.999754	0.499877	+	0.866096i	$0.333378\pi$
$398$	−1.18424	−0.0593604
$399$	−19.0191	−0.952148
$400$	0.345563	0.0172782
$401$	−37.7336	−1.88433	−0.942163	−	0.335154i	$-0.891212\pi$
$401$	−37.7336	−1.88433	−0.942163	+	0.335154i	$0.891212\pi$
$402$	−93.9436	−4.68548
$403$	−16.9220	−0.842946
$404$	−13.2268	−0.658057
$405$	−18.5009	−0.919316
$406$	−29.6679	−1.47239
$407$	7.64117	0.378759
$408$	−34.5697	−1.71145
$409$	6.44752	0.318809	0.159405	−	0.987213i	$-0.449043\pi$
$409$	6.44752	0.318809	0.159405	+	0.987213i	$0.449043\pi$
$410$	−15.5321	−0.767076
$411$	8.82258	0.435186
$412$	47.8943	2.35958
$413$	−32.1022	−1.57965
$414$	−12.6090	−0.619697
$415$	8.47513	0.416028
$416$	−22.3169	−1.09418
$417$	−1.90588	−0.0933312
$418$	−2.79153	−0.136538
$419$	−17.0964	−0.835212	−0.417606	−	0.908628i	$-0.637131\pi$
$419$	−17.0964	−0.835212	−0.417606	+	0.908628i	$0.637131\pi$
$420$	96.2967	4.69880
$421$	19.2338	0.937400	0.468700	−	0.883357i	$-0.344723\pi$
$421$	19.2338	0.937400	0.468700	+	0.883357i	$0.344723\pi$
$422$	12.5922	0.612980
$423$	−36.9565	−1.79689
$424$	−5.88113	−0.285613
$425$	1.50962	0.0732272
$426$	69.9816	3.39062
$427$	−5.05675	−0.244713
$428$	25.1765	1.21695
$429$	9.57581	0.462324
$430$	−42.0449	−2.02759
$431$	−15.0711	−0.725951	−0.362976	−	0.931799i	$-0.618239\pi$
$431$	−15.0711	−0.725951	−0.362976	+	0.931799i	$0.618239\pi$
$432$	11.3203	0.544649
$433$	−1.16749	−0.0561058	−0.0280529	−	0.999606i	$-0.508931\pi$
$433$	−1.16749	−0.0561058	−0.0280529	+	0.999606i	$0.508931\pi$
$434$	−59.3251	−2.84769
$435$	17.1940	0.824389
$436$	54.0446	2.58826
$437$	1.20165	0.0574826
$438$	28.1343	1.34431
$439$	16.3226	0.779035	0.389518	−	0.921019i	$-0.372642\pi$
$439$	16.3226	0.779035	0.389518	+	0.921019i	$0.372642\pi$
$440$	4.47742	0.213452
$441$	110.398	5.25704
$442$	−39.9085	−1.89825
$443$	4.47718	0.212717	0.106359	−	0.994328i	$-0.466081\pi$
$443$	4.47718	0.212717	0.106359	+	0.994328i	$0.466081\pi$
$444$	−66.8985	−3.17486
$445$	−19.7821	−0.937763
$446$	−31.5986	−1.49624
$447$	−41.2954	−1.95321
$448$	−65.2387	−3.08224
$449$	−26.7590	−1.26284	−0.631418	−	0.775442i	$-0.717527\pi$
$449$	−26.7590	−1.26284	−0.631418	+	0.775442i	$0.717527\pi$
$450$	3.54762	0.167237
$451$	−3.21692	−0.151479
$452$	45.3882	2.13488
$453$	61.1983	2.87535
$454$	7.34475	0.344706
$455$	35.2165	1.65098
$456$	7.74218	0.362561
$457$	6.98309	0.326655	0.163328	−	0.986572i	$-0.447777\pi$
$457$	6.98309	0.326655	0.163328	+	0.986572i	$0.447777\pi$
$458$	8.27547	0.386687
$459$	49.4536	2.30830
$460$	−6.08411	−0.283673
$461$	−0.637167	−0.0296758	−0.0148379	−	0.999890i	$-0.504723\pi$
$461$	−0.637167	−0.0296758	−0.0148379	+	0.999890i	$0.504723\pi$
$462$	33.5708	1.56185
$463$	18.7279	0.870361	0.435180	−	0.900343i	$-0.356685\pi$
$463$	18.7279	0.870361	0.435180	+	0.900343i	$0.356685\pi$
$464$	−3.39733	−0.157717
$465$	34.3818	1.59442
$466$	−25.0872	−1.16214
$467$	−10.7986	−0.499698	−0.249849	−	0.968285i	$-0.580381\pi$
$467$	−10.7986	−0.499698	−0.249849	+	0.968285i	$0.580381\pi$
$468$	−55.7182	−2.57557
$469$	−71.5564	−3.30417
$470$	−30.0157	−1.38452
$471$	0.346411	0.0159618
$472$	13.0680	0.601501
$473$	−8.70811	−0.400399
$474$	114.072	5.23952
$475$	−0.338092	−0.0155127
$476$	−83.1212	−3.80985
$477$	16.9844	0.777661
$478$	−5.22144	−0.238823
$479$	−37.6783	−1.72157	−0.860783	−	0.508972i	$-0.830026\pi$
$479$	−37.6783	−1.72157	−0.860783	+	0.508972i	$0.830026\pi$
$480$	45.3429	2.06961
$481$	−24.4654	−1.11552
$482$	−17.2221	−0.784445
$483$	−14.4509	−0.657540
$484$	2.92734	0.133061
$485$	14.4250	0.655006
$486$	−2.18106	−0.0989348
$487$	9.34251	0.423349	0.211675	−	0.977340i	$-0.432108\pi$
$487$	9.34251	0.423349	0.211675	+	0.977340i	$0.432108\pi$
$488$	2.05847	0.0931824
$489$	64.2947	2.90751
$490$	89.6639	4.05060
$491$	41.6005	1.87741	0.938703	−	0.344728i	$-0.112029\pi$
$491$	41.6005	1.87741	0.938703	+	0.344728i	$0.112029\pi$
$492$	28.1642	1.26974
$493$	−14.8415	−0.668426
$494$	8.93786	0.402133
$495$	−12.9305	−0.581184
$496$	−6.79344	−0.305034
$497$	53.3047	2.39104
$498$	−25.8674	−1.15915
$499$	−9.80103	−0.438755	−0.219377	−	0.975640i	$-0.570403\pi$
$499$	−9.80103	−0.438755	−0.219377	+	0.975640i	$0.570403\pi$
$500$	33.5484	1.50033
$501$	−10.9537	−0.489374
$502$	9.47113	0.422717
$503$	36.9840	1.64904	0.824518	−	0.565836i	$-0.191446\pi$
$503$	36.9840	1.64904	0.824518	+	0.565836i	$0.191446\pi$
$504$	−61.8796	−2.75634
$505$	9.82800	0.437340
$506$	−2.12103	−0.0942913
$507$	8.22045	0.365083
$508$	15.9698	0.708545
$509$	27.0976	1.20108	0.600540	−	0.799594i	$-0.294952\pi$
$509$	27.0976	1.20108	0.600540	+	0.799594i	$0.294952\pi$
$510$	81.0851	3.59051
$511$	21.4298	0.947997
$512$	−14.2510	−0.629812
$513$	−11.0756	−0.488998
$514$	−9.21086	−0.406274
$515$	−35.5873	−1.56816
$516$	76.2396	3.35626
$517$	−6.21668	−0.273409
$518$	−85.7704	−3.76853
$519$	−50.1234	−2.20017
$520$	−14.3357	−0.628662
$521$	29.9679	1.31292	0.656459	−	0.754361i	$-0.272053\pi$
$521$	29.9679	1.31292	0.656459	+	0.754361i	$0.272053\pi$
$522$	−34.8777	−1.52656
$523$	29.1056	1.27270	0.636348	−	0.771402i	$-0.280444\pi$
$523$	29.1056	1.27270	0.636348	+	0.771402i	$0.280444\pi$
$524$	46.5170	2.03211
$525$	4.06587	0.177449
$526$	−26.2065	−1.14266
$527$	−29.6776	−1.29278
$528$	3.84426	0.167300
$529$	−22.0870	−0.960303
$530$	13.7945	0.599196
$531$	−37.7395	−1.63776
$532$	18.6157	0.807094
$533$	10.2999	0.446138
$534$	60.3781	2.61282
$535$	−18.7071	−0.808780
$536$	29.1287	1.25817
$537$	−50.3637	−2.17335
$538$	61.0442	2.63180
$539$	18.5707	0.799896
$540$	56.0772	2.41318
$541$	42.6909	1.83543	0.917713	−	0.397245i	$-0.130034\pi$
$541$	42.6909	1.83543	0.917713	+	0.397245i	$0.130034\pi$
$542$	−44.0196	−1.89080
$543$	−39.7799	−1.70712
$544$	−39.1390	−1.67807
$545$	−40.1571	−1.72014
$546$	−107.486	−4.59998
$547$	−27.5597	−1.17837	−0.589184	−	0.807999i	$-0.700551\pi$
$547$	−27.5597	−1.17837	−0.589184	+	0.807999i	$0.700551\pi$
$548$	−8.63544	−0.368888
$549$	−5.94474	−0.253715
$550$	0.596767	0.0254462
$551$	3.32388	0.141602
$552$	5.88259	0.250380
$553$	86.8884	3.69487
$554$	−21.7242	−0.922971
$555$	49.7081	2.10999
$556$	1.86545	0.0791127
$557$	0.987301	0.0418333	0.0209166	−	0.999781i	$-0.493342\pi$
$557$	0.987301	0.0418333	0.0209166	+	0.999781i	$0.493342\pi$
$558$	−69.7428	−2.95245
$559$	27.8815	1.17926
$560$	14.1379	0.597434
$561$	16.7939	0.709039
$562$	−16.2396	−0.685028
$563$	−42.4725	−1.79000	−0.895001	−	0.446064i	$-0.852825\pi$
$563$	−42.4725	−1.79000	−0.895001	+	0.446064i	$0.852825\pi$
$564$	54.4271	2.29179
$565$	−33.7252	−1.41883
$566$	−31.4152	−1.32048
$567$	43.0110	1.80629
$568$	−21.6989	−0.910466
$569$	25.8404	1.08329	0.541643	−	0.840609i	$-0.317802\pi$
$569$	25.8404	1.08329	0.541643	+	0.840609i	$0.317802\pi$
$570$	−18.1597	−0.760627
$571$	−7.75510	−0.324541	−0.162270	−	0.986746i	$-0.551882\pi$
$571$	−7.75510	−0.324541	−0.162270	+	0.986746i	$0.551882\pi$
$572$	−9.37269	−0.391892
$573$	62.4153	2.60744
$574$	36.1092	1.50717
$575$	−0.256886	−0.0107129
$576$	−76.6949	−3.19562
$577$	−17.0522	−0.709893	−0.354946	−	0.934887i	$-0.615501\pi$
$577$	−17.0522	−0.709893	−0.354946	+	0.934887i	$0.615501\pi$
$578$	−32.2550	−1.34163
$579$	8.96639	0.372630
$580$	−16.8293	−0.698798
$581$	−19.7031	−0.817421
$582$	−44.0273	−1.82499
$583$	2.85705	0.118327
$584$	−8.72349	−0.360980
$585$	41.4007	1.71171
$586$	35.2356	1.45557
$587$	18.5551	0.765852	0.382926	−	0.923779i	$-0.374916\pi$
$587$	18.5551	0.765852	0.382926	+	0.923779i	$0.374916\pi$
$588$	−162.587	−6.70495
$589$	6.64656	0.273867
$590$	−30.6516	−1.26191
$591$	−47.9686	−1.97316
$592$	−9.82174	−0.403671
$593$	−15.3999	−0.632399	−0.316199	−	0.948693i	$-0.602407\pi$
$593$	−15.3999	−0.632399	−0.316199	+	0.948693i	$0.602407\pi$
$594$	19.5495	0.802127
$595$	61.7622	2.53200
$596$	40.4195	1.65565
$597$	−1.59557	−0.0653023
$598$	6.79108	0.277708
$599$	−30.4897	−1.24578	−0.622888	−	0.782311i	$-0.714041\pi$
$599$	−30.4897	−1.24578	−0.622888	+	0.782311i	$0.714041\pi$
$600$	−1.65511	−0.0675695
$601$	−8.97417	−0.366064	−0.183032	−	0.983107i	$-0.558591\pi$
$601$	−8.97417	−0.366064	−0.183032	+	0.983107i	$0.558591\pi$
$602$	97.7465	3.98385
$603$	−84.1221	−3.42572
$604$	−59.9003	−2.43731
$605$	−2.17512	−0.0884313
$606$	−29.9966	−1.21853
$607$	−4.13601	−0.167875	−0.0839376	−	0.996471i	$-0.526750\pi$
$607$	−4.13601	−0.167875	−0.0839376	+	0.996471i	$0.526750\pi$
$608$	8.76553	0.355489
$609$	−39.9728	−1.61978
$610$	−4.82825	−0.195490
$611$	19.9044	0.805248
$612$	−97.7176	−3.95000
$613$	36.6287	1.47942	0.739710	−	0.672926i	$-0.234963\pi$
$613$	36.6287	1.47942	0.739710	+	0.672926i	$0.234963\pi$
$614$	49.7175	2.00643
$615$	−20.9271	−0.843860
$616$	−10.4091	−0.419396
$617$	8.24763	0.332037	0.166019	−	0.986123i	$-0.446909\pi$
$617$	8.24763	0.332037	0.166019	+	0.986123i	$0.446909\pi$
$618$	108.618	4.36925
$619$	11.4400	0.459811	0.229906	−	0.973213i	$-0.426158\pi$
$619$	11.4400	0.459811	0.229906	+	0.973213i	$0.426158\pi$
$620$	−33.6525	−1.35152
$621$	−8.41533	−0.337695
$622$	25.8830	1.03781
$623$	45.9897	1.84254
$624$	−12.3085	−0.492733
$625$	−23.5835	−0.943340
$626$	−2.64746	−0.105814
$627$	−3.76114	−0.150205
$628$	−0.339063	−0.0135301
$629$	−42.9069	−1.71081
$630$	145.142	5.78260
$631$	−37.8435	−1.50653	−0.753263	−	0.657719i	$-0.771521\pi$
$631$	−37.8435	−1.50653	−0.753263	+	0.657719i	$0.771521\pi$
$632$	−35.3699	−1.40694
$633$	16.9660	0.674339
$634$	−29.5741	−1.17454
$635$	−11.8662	−0.470895
$636$	−25.0135	−0.991848
$637$	−59.4593	−2.35586
$638$	−5.86699	−0.232276
$639$	62.6653	2.47900
$640$	−31.9690	−1.26368
$641$	−26.7866	−1.05801	−0.529003	−	0.848620i	$-0.677434\pi$
$641$	−26.7866	−1.05801	−0.529003	+	0.848620i	$0.677434\pi$
$642$	57.0970	2.25344
$643$	−25.8395	−1.01901	−0.509505	−	0.860468i	$-0.670172\pi$
$643$	−25.8395	−1.01901	−0.509505	+	0.860468i	$0.670172\pi$
$644$	14.1444	0.557368
$645$	−56.6489	−2.23055
$646$	15.6751	0.616728
$647$	30.5070	1.19935	0.599677	−	0.800242i	$-0.295296\pi$
$647$	30.5070	1.19935	0.599677	+	0.800242i	$0.295296\pi$
$648$	−17.5086	−0.687805
$649$	−6.34839	−0.249196
$650$	−1.91072	−0.0749445
$651$	−79.9311	−3.13275
$652$	−62.9309	−2.46457
$653$	1.47873	0.0578672	0.0289336	−	0.999581i	$-0.490789\pi$
$653$	1.47873	0.0578672	0.0289336	+	0.999581i	$0.490789\pi$
$654$	122.566	4.79270
$655$	−34.5639	−1.35052
$656$	4.13494	0.161442
$657$	25.1929	0.982870
$658$	69.7808	2.72034
$659$	−4.68280	−0.182416	−0.0912080	−	0.995832i	$-0.529073\pi$
$659$	−4.68280	−0.182416	−0.0912080	+	0.995832i	$0.529073\pi$
$660$	19.0432	0.741256
$661$	14.5913	0.567536	0.283768	−	0.958893i	$-0.408415\pi$
$661$	14.5913	0.567536	0.283768	+	0.958893i	$0.408415\pi$
$662$	−53.0266	−2.06094
$663$	−53.7704	−2.08827
$664$	8.02059	0.311259
$665$	−13.8322	−0.536389
$666$	−100.832	−3.90716
$667$	2.52552	0.0977884
$668$	10.7213	0.414821
$669$	−42.5741	−1.64601
$670$	−68.3231	−2.63955
$671$	−1.00000	−0.0386046
$672$	−105.414	−4.06642
$673$	−2.33640	−0.0900616	−0.0450308	−	0.998986i	$-0.514339\pi$
$673$	−2.33640	−0.0900616	−0.0450308	+	0.998986i	$0.514339\pi$
$674$	−16.7109	−0.643679
$675$	2.36771	0.0911333
$676$	−8.04608	−0.309465
$677$	0.867708	0.0333487	0.0166744	−	0.999861i	$-0.494692\pi$
$677$	0.867708	0.0333487	0.0166744	+	0.999861i	$0.494692\pi$
$678$	102.934	3.95317
$679$	−33.5354	−1.28697
$680$	−25.1417	−0.964141
$681$	9.89588	0.379211
$682$	−11.7319	−0.449236
$683$	−2.82033	−0.107917	−0.0539585	−	0.998543i	$-0.517184\pi$
$683$	−2.82033	−0.107917	−0.0539585	+	0.998543i	$0.517184\pi$
$684$	21.8847	0.836783
$685$	6.41646	0.245160
$686$	−129.878	−4.95878
$687$	11.1499	0.425394
$688$	11.1932	0.426735
$689$	−9.14763	−0.348497
$690$	−13.7979	−0.525279
$691$	−35.0428	−1.33309	−0.666545	−	0.745465i	$-0.732227\pi$
$691$	−35.0428	−1.33309	−0.666545	+	0.745465i	$0.732227\pi$
$692$	49.0603	1.86499
$693$	30.0610	1.14192
$694$	−26.7987	−1.01727
$695$	−1.38610	−0.0525778
$696$	16.2718	0.616782
$697$	18.0638	0.684214
$698$	29.7563	1.12629
$699$	−33.8010	−1.27847
$700$	−3.97963	−0.150416
$701$	46.6126	1.76053	0.880267	−	0.474478i	$-0.157363\pi$
$701$	46.6126	1.76053	0.880267	+	0.474478i	$0.157363\pi$
$702$	−62.5933	−2.36243
$703$	9.60939	0.362425
$704$	−12.9013	−0.486237
$705$	−40.4414	−1.52311
$706$	−58.3714	−2.19684
$707$	−22.8482	−0.859296
$708$	55.5802	2.08883
$709$	14.6994	0.552049	0.276025	−	0.961151i	$-0.410983\pi$
$709$	14.6994	0.552049	0.276025	+	0.961151i	$0.410983\pi$
$710$	50.8960	1.91009
$711$	102.146	3.83079
$712$	−18.7212	−0.701606
$713$	5.05012	0.189129
$714$	−188.508	−7.05472
$715$	6.96426	0.260449
$716$	49.2954	1.84226
$717$	−7.03506	−0.262729
$718$	−10.1163	−0.377538
$719$	7.93574	0.295953	0.147977	−	0.988991i	$-0.452724\pi$
$719$	7.93574	0.295953	0.147977	+	0.988991i	$0.452724\pi$
$720$	16.6205	0.619411
$721$	82.7337	3.08116
$722$	38.6649	1.43896
$723$	−23.2040	−0.862968
$724$	38.9361	1.44705
$725$	−0.710572	−0.0263900
$726$	6.63880	0.246389
$727$	−44.4043	−1.64686	−0.823432	−	0.567415i	$-0.807944\pi$
$727$	−44.4043	−1.64686	−0.823432	+	0.567415i	$0.807944\pi$
$728$	33.3278	1.23521
$729$	−28.4557	−1.05391
$730$	20.4614	0.757312
$731$	48.8980	1.80856
$732$	8.75501	0.323594
$733$	−27.4350	−1.01333	−0.506667	−	0.862142i	$-0.669122\pi$
$733$	−27.4350	−1.01333	−0.506667	+	0.862142i	$0.669122\pi$
$734$	32.3883	1.19547
$735$	120.808	4.45607
$736$	6.66014	0.245496
$737$	−14.1507	−0.521247
$738$	42.4502	1.56261
$739$	−4.73622	−0.174225	−0.0871124	−	0.996198i	$-0.527764\pi$
$739$	−4.73622	−0.174225	−0.0871124	+	0.996198i	$0.527764\pi$
$740$	−48.6538	−1.78855
$741$	12.0423	0.442387
$742$	−32.0697	−1.17731
$743$	−23.6033	−0.865920	−0.432960	−	0.901413i	$-0.642531\pi$
$743$	−23.6033	−0.865920	−0.432960	+	0.901413i	$0.642531\pi$
$744$	32.5378	1.19289
$745$	−30.0332	−1.10033
$746$	61.0562	2.23543
$747$	−23.1630	−0.847490
$748$	−16.4377	−0.601021
$749$	43.4905	1.58911
$750$	76.0832	2.77817
$751$	−41.3633	−1.50937	−0.754684	−	0.656089i	$-0.772210\pi$
$751$	−41.3633	−1.50937	−0.754684	+	0.656089i	$0.772210\pi$
$752$	7.99075	0.291393
$753$	12.7608	0.465031
$754$	18.7848	0.684102
$755$	44.5082	1.61982
$756$	−130.369	−4.74147
$757$	−9.70134	−0.352601	−0.176301	−	0.984336i	$-0.556413\pi$
$757$	−9.70134	−0.352601	−0.176301	+	0.984336i	$0.556413\pi$
$758$	20.6998	0.751851
$759$	−2.85775	−0.103730
$760$	5.63071	0.204247
$761$	32.7697	1.18790	0.593951	−	0.804501i	$-0.297567\pi$
$761$	32.7697	1.18790	0.593951	+	0.804501i	$0.297567\pi$
$762$	36.2174	1.31202
$763$	93.3578	3.37978
$764$	−61.0914	−2.21021
$765$	72.6079	2.62514
$766$	−58.9521	−2.13003
$767$	20.3262	0.733935
$768$	20.4042	0.736274
$769$	−13.2509	−0.477840	−0.238920	−	0.971039i	$-0.576793\pi$
$769$	−13.2509	−0.477840	−0.238920	+	0.971039i	$0.576793\pi$
$770$	24.4152	0.879864
$771$	−12.4102	−0.446941
$772$	−8.77620	−0.315862
$773$	−24.4785	−0.880430	−0.440215	−	0.897892i	$-0.645098\pi$
$773$	−24.4785	−0.880430	−0.440215	+	0.897892i	$0.645098\pi$
$774$	114.911	4.13040
$775$	−1.42089	−0.0510398
$776$	13.6514	0.490055
$777$	−115.562	−4.14576
$778$	−49.3017	−1.76755
$779$	−4.04554	−0.144947
$780$	−60.9722	−2.18315
$781$	10.5413	0.377197
$782$	11.9101	0.425904
$783$	−23.2777	−0.831875
$784$	−23.8702	−0.852508
$785$	0.251937	0.00899200
$786$	105.494	3.76286
$787$	−7.47104	−0.266314	−0.133157	−	0.991095i	$-0.542511\pi$
$787$	−7.47104	−0.266314	−0.133157	+	0.991095i	$0.542511\pi$
$788$	46.9511	1.67256
$789$	−35.3092	−1.25704
$790$	82.9622	2.95166
$791$	78.4046	2.78775
$792$	−12.2370	−0.434824
$793$	3.20178	0.113699
$794$	−44.2176	−1.56922
$795$	18.5859	0.659175
$796$	1.56173	0.0553539
$797$	4.02337	0.142515	0.0712576	−	0.997458i	$-0.477299\pi$
$797$	4.02337	0.142515	0.0712576	+	0.997458i	$0.477299\pi$
$798$	42.2179	1.49450
$799$	34.9081	1.23496
$800$	−1.87388	−0.0662516
$801$	54.0657	1.91032
$802$	83.7596	2.95765
$803$	4.23786	0.149551
$804$	123.889	4.36924
$805$	−10.5098	−0.370423
$806$	37.5629	1.32310
$807$	82.2474	2.89524
$808$	9.30091	0.327205
$809$	−35.2530	−1.23943	−0.619715	−	0.784827i	$-0.712752\pi$
$809$	−35.2530	−1.23943	−0.619715	+	0.784827i	$0.712752\pi$
$810$	41.0675	1.44297
$811$	41.0721	1.44224	0.721118	−	0.692812i	$-0.243628\pi$
$811$	41.0721	1.44224	0.721118	+	0.692812i	$0.243628\pi$
$812$	39.1249	1.37301
$813$	−59.3094	−2.08007
$814$	−16.9616	−0.594503
$815$	46.7601	1.63793
$816$	−21.5864	−0.755675
$817$	−10.9511	−0.383132
$818$	−14.3119	−0.500405
$819$	−96.2488	−3.36321
$820$	20.4832	0.715303
$821$	21.1227	0.737189	0.368594	−	0.929590i	$-0.379839\pi$
$821$	21.1227	0.737189	0.368594	+	0.929590i	$0.379839\pi$
$822$	−19.5840	−0.683071
$823$	39.4675	1.37575	0.687875	−	0.725829i	$-0.258544\pi$
$823$	39.4675	1.37575	0.687875	+	0.725829i	$0.258544\pi$
$824$	−33.6787	−1.17325
$825$	0.804049	0.0279934
$826$	71.2592	2.47943
$827$	35.0703	1.21951	0.609757	−	0.792588i	$-0.291267\pi$
$827$	35.0703	1.21951	0.609757	+	0.792588i	$0.291267\pi$
$828$	16.6282	0.577871
$829$	16.4013	0.569642	0.284821	−	0.958581i	$-0.408066\pi$
$829$	16.4013	0.569642	0.284821	+	0.958581i	$0.408066\pi$
$830$	−18.8128	−0.653000
$831$	−29.2699	−1.01536
$832$	41.3072	1.43207
$833$	−104.279	−3.61304
$834$	4.23059	0.146493
$835$	−7.96636	−0.275687
$836$	3.68136	0.127323
$837$	−46.5469	−1.60890
$838$	37.9498	1.31095
$839$	−12.1840	−0.420639	−0.210319	−	0.977633i	$-0.567450\pi$
$839$	−12.1840	−0.420639	−0.210319	+	0.977633i	$0.567450\pi$
$840$	−67.7146	−2.33638
$841$	−22.0142	−0.759109
$842$	−42.6945	−1.47135
$843$	−21.8803	−0.753599
$844$	−16.6061	−0.571607
$845$	5.97854	0.205668
$846$	82.0346	2.82041
$847$	5.05675	0.173752
$848$	−3.67237	−0.126110
$849$	−42.3270	−1.45266
$850$	−3.35099	−0.114938
$851$	7.30131	0.250286
$852$	−92.2892	−3.16177
$853$	49.9463	1.71013	0.855065	−	0.518521i	$-0.173517\pi$
$853$	49.9463	1.71013	0.855065	+	0.518521i	$0.173517\pi$
$854$	11.2248	0.384104
$855$	−16.2612	−0.556121
$856$	−17.7038	−0.605104
$857$	−27.5472	−0.940994	−0.470497	−	0.882402i	$-0.655925\pi$
$857$	−27.5472	−0.940994	−0.470497	+	0.882402i	$0.655925\pi$
$858$	−21.2560	−0.725668
$859$	−23.6340	−0.806383	−0.403192	−	0.915116i	$-0.632099\pi$
$859$	−23.6340	−0.806383	−0.403192	+	0.915116i	$0.632099\pi$
$860$	55.4473	1.89074
$861$	48.6514	1.65804
$862$	33.4543	1.13946
$863$	19.1966	0.653461	0.326731	−	0.945118i	$-0.394053\pi$
$863$	19.1966	0.653461	0.326731	+	0.945118i	$0.394053\pi$
$864$	−61.3864	−2.08841
$865$	−36.4536	−1.23946
$866$	2.59154	0.0880641
$867$	−43.4584	−1.47593
$868$	78.2357	2.65549
$869$	17.1827	0.582882
$870$	−38.1665	−1.29397
$871$	45.3074	1.53518
$872$	−38.0034	−1.28696
$873$	−39.4244	−1.33431
$874$	−2.66737	−0.0902251
$875$	57.9522	1.95914
$876$	−37.1025	−1.25358
$877$	−33.6570	−1.13652	−0.568259	−	0.822850i	$-0.692383\pi$
$877$	−33.6570	−1.13652	−0.568259	+	0.822850i	$0.692383\pi$
$878$	−36.2323	−1.22278
$879$	47.4744	1.60127
$880$	2.79584	0.0942478
$881$	−9.88462	−0.333021	−0.166511	−	0.986040i	$-0.553250\pi$
$881$	−9.88462	−0.333021	−0.166511	+	0.986040i	$0.553250\pi$
$882$	−245.057	−8.25149
$883$	−30.6737	−1.03225	−0.516126	−	0.856513i	$-0.672626\pi$
$883$	−30.6737	−1.03225	−0.516126	+	0.856513i	$0.672626\pi$
$884$	52.6298	1.77013
$885$	−41.2982	−1.38822
$886$	−9.93827	−0.333883
$887$	−5.63849	−0.189322	−0.0946610	−	0.995510i	$-0.530177\pi$
$887$	−5.63849	−0.189322	−0.0946610	+	0.995510i	$0.530177\pi$
$888$	47.0422	1.57863
$889$	27.5866	0.925225
$890$	43.9116	1.47192
$891$	8.50568	0.284951
$892$	41.6710	1.39525
$893$	−7.81798	−0.261619
$894$	91.6660	3.06577
$895$	−36.6284	−1.22435
$896$	74.3218	2.48292
$897$	9.14990	0.305506
$898$	59.3986	1.98216
$899$	13.9692	0.465897
$900$	−4.67847	−0.155949
$901$	−16.0430	−0.534469
$902$	7.14080	0.237763
$903$	131.698	4.38263
$904$	−31.9164	−1.06152
$905$	−28.9310	−0.961699
$906$	−135.846	−4.51317
$907$	6.27594	0.208389	0.104195	−	0.994557i	$-0.466774\pi$
$907$	6.27594	0.208389	0.104195	+	0.994557i	$0.466774\pi$
$908$	−9.68598	−0.321440
$909$	−26.8605	−0.890906
$910$	−78.1722	−2.59138
$911$	15.6434	0.518290	0.259145	−	0.965838i	$-0.416559\pi$
$911$	15.6434	0.518290	0.259145	+	0.965838i	$0.416559\pi$
$912$	4.83446	0.160085
$913$	−3.89639	−0.128952
$914$	−15.5008	−0.512720
$915$	−6.50530	−0.215059
$916$	−10.9134	−0.360588
$917$	80.3545	2.65354
$918$	−109.775	−3.62312
$919$	−37.8167	−1.24746	−0.623728	−	0.781641i	$-0.714383\pi$
$919$	−37.8167	−1.24746	−0.623728	+	0.781641i	$0.714383\pi$
$920$	4.27827	0.141050
$921$	66.9864	2.20728
$922$	1.41436	0.0465794
$923$	−33.7509	−1.11093
$924$	−44.2719	−1.45644
$925$	−2.05428	−0.0675442
$926$	−41.5715	−1.36613
$927$	97.2621	3.19451
$928$	18.4226	0.604752
$929$	28.9770	0.950705	0.475352	−	0.879796i	$-0.342321\pi$
$929$	28.9770	0.950705	0.475352	+	0.879796i	$0.342321\pi$
$930$	−76.3193	−2.50261
$931$	23.3541	0.765401
$932$	33.0840	1.08370
$933$	34.8733	1.14170
$934$	23.9702	0.784331
$935$	12.2138	0.399434
$936$	39.1803	1.28065
$937$	53.8625	1.75961	0.879805	−	0.475334i	$-0.157673\pi$
$937$	53.8625	1.75961	0.879805	+	0.475334i	$0.157673\pi$
$938$	158.838	5.18625
$939$	−3.56703	−0.116406
$940$	39.5836	1.29107
$941$	17.7491	0.578603	0.289301	−	0.957238i	$-0.406577\pi$
$941$	17.7491	0.578603	0.289301	+	0.957238i	$0.406577\pi$
$942$	−0.768949	−0.0250537
$943$	−3.07384	−0.100098
$944$	8.16005	0.265587
$945$	96.8690	3.15115
$946$	19.3299	0.628470
$947$	−36.6133	−1.18977	−0.594886	−	0.803810i	$-0.702803\pi$
$947$	−36.6133	−1.18977	−0.594886	+	0.803810i	$0.702803\pi$
$948$	−150.434	−4.88588
$949$	−13.5687	−0.440458
$950$	0.750483	0.0243489
$951$	−39.8464	−1.29211
$952$	58.4498	1.89437
$953$	4.57686	0.148259	0.0741295	−	0.997249i	$-0.476382\pi$
$953$	4.57686	0.148259	0.0741295	+	0.997249i	$0.476382\pi$
$954$	−37.7013	−1.22062
$955$	45.3932	1.46889
$956$	6.88584	0.222704
$957$	−7.90484	−0.255527
$958$	83.6368	2.70218
$959$	−14.9170	−0.481697
$960$	−83.9270	−2.70873
$961$	−3.06672	−0.0989265
$962$	54.3072	1.75094
$963$	51.1277	1.64757
$964$	22.7119	0.731500
$965$	6.52105	0.209920
$966$	32.0776	1.03208
$967$	22.2757	0.716340	0.358170	−	0.933656i	$-0.383401\pi$
$967$	22.2757	0.716340	0.358170	+	0.933656i	$0.383401\pi$
$968$	−2.05847	−0.0661616
$969$	21.1197	0.678462
$970$	−32.0201	−1.02810
$971$	−25.4408	−0.816435	−0.408217	−	0.912885i	$-0.633849\pi$
$971$	−25.4408	−0.816435	−0.408217	+	0.912885i	$0.633849\pi$
$972$	2.87630	0.0922573
$973$	3.22242	0.103306
$974$	−20.7381	−0.664493
$975$	−2.57439	−0.0824465
$976$	1.28537	0.0411437
$977$	31.8193	1.01799	0.508995	−	0.860770i	$-0.330017\pi$
$977$	31.8193	1.01799	0.508995	+	0.860770i	$0.330017\pi$
$978$	−142.719	−4.56365
$979$	9.09472	0.290669
$980$	−118.245	−3.77721
$981$	109.752	3.50411
$982$	−92.3432	−2.94679
$983$	2.49700	0.0796418	0.0398209	−	0.999207i	$-0.487321\pi$
$983$	2.49700	0.0796418	0.0398209	+	0.999207i	$0.487321\pi$
$984$	−19.8047	−0.631351
$985$	−34.8864	−1.11157
$986$	32.9445	1.04917
$987$	94.0186	2.99264
$988$	−11.7869	−0.374992
$989$	−8.32079	−0.264586
$990$	28.7027	0.912231
$991$	37.7292	1.19851	0.599253	−	0.800560i	$-0.295464\pi$
$991$	37.7292	1.19851	0.599253	+	0.800560i	$0.295464\pi$
$992$	36.8386	1.16963
$993$	−71.4450	−2.26724
$994$	−118.324	−3.75300
$995$	−1.16042	−0.0367878
$996$	34.1129	1.08091
$997$	−33.8874	−1.07322	−0.536612	−	0.843829i	$-0.680296\pi$
$997$	−33.8874	−1.07322	−0.536612	+	0.843829i	$0.680296\pi$
$998$	21.7559	0.688672
$999$	−67.2961	−2.12915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.c.1.2	✓	19
3.2	odd	2		6039.2.a.k.1.18		19
11.10	odd	2		7381.2.a.i.1.18		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.c.1.2	✓	19	1.1	even	1	trivial
6039.2.a.k.1.18		19	3.2	odd	2
7381.2.a.i.1.18		19	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21976 q^{2} -2.99078 q^{3} +2.92734 q^{4} -2.17512 q^{5} +6.63880 q^{6} +5.05675 q^{7} -2.05847 q^{8} +5.94474 q^{9} +O(q^{10})\)	\(q-2.21976 q^{2} -2.99078 q^{3} +2.92734 q^{4} -2.17512 q^{5} +6.63880 q^{6} +5.05675 q^{7} -2.05847 q^{8} +5.94474 q^{9} +4.82825 q^{10} +1.00000 q^{11} -8.75501 q^{12} -3.20178 q^{13} -11.2248 q^{14} +6.50530 q^{15} -1.28537 q^{16} -5.61523 q^{17} -13.1959 q^{18} +1.25758 q^{19} -6.36732 q^{20} -15.1236 q^{21} -2.21976 q^{22} +0.955523 q^{23} +6.15641 q^{24} -0.268843 q^{25} +7.10719 q^{26} -8.80704 q^{27} +14.8028 q^{28} +2.64307 q^{29} -14.4402 q^{30} +5.28519 q^{31} +6.97015 q^{32} -2.99078 q^{33} +12.4645 q^{34} -10.9990 q^{35} +17.4022 q^{36} +7.64117 q^{37} -2.79153 q^{38} +9.57581 q^{39} +4.47742 q^{40} -3.21692 q^{41} +33.5708 q^{42} -8.70811 q^{43} +2.92734 q^{44} -12.9305 q^{45} -2.12103 q^{46} -6.21668 q^{47} +3.84426 q^{48} +18.5707 q^{49} +0.596767 q^{50} +16.7939 q^{51} -9.37269 q^{52} +2.85705 q^{53} +19.5495 q^{54} -2.17512 q^{55} -10.4091 q^{56} -3.76114 q^{57} -5.86699 q^{58} -6.34839 q^{59} +19.0432 q^{60} -1.00000 q^{61} -11.7319 q^{62} +30.0610 q^{63} -12.9013 q^{64} +6.96426 q^{65} +6.63880 q^{66} -14.1507 q^{67} -16.4377 q^{68} -2.85775 q^{69} +24.4152 q^{70} +10.5413 q^{71} -12.2370 q^{72} +4.23786 q^{73} -16.9616 q^{74} +0.804049 q^{75} +3.68136 q^{76} +5.05675 q^{77} -21.2560 q^{78} +17.1827 q^{79} +2.79584 q^{80} +8.50568 q^{81} +7.14080 q^{82} -3.89639 q^{83} -44.2719 q^{84} +12.2138 q^{85} +19.3299 q^{86} -7.90484 q^{87} -2.05847 q^{88} +9.09472 q^{89} +28.7027 q^{90} -16.1906 q^{91} +2.79714 q^{92} -15.8068 q^{93} +13.7995 q^{94} -2.73539 q^{95} -20.8462 q^{96} -6.63181 q^{97} -41.2225 q^{98} +5.94474 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9} + 7 q^{10} + 19 q^{11} - 4 q^{12} + 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} + 9 q^{17} + 10 q^{18} + 17 q^{19} - 6 q^{20} + 18 q^{21} + 5 q^{22} - 10 q^{23} + 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} + 36 q^{28} + 27 q^{29} - 30 q^{30} + 7 q^{31} + 8 q^{32} - 5 q^{34} + 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} + 24 q^{39} + 10 q^{40} + 19 q^{41} + 21 q^{42} + 20 q^{43} + 23 q^{44} - 32 q^{45} + 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} + 36 q^{50} + 47 q^{51} - 28 q^{52} + 3 q^{53} - 33 q^{54} - 44 q^{56} + 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} - 19 q^{61} - 11 q^{62} - 32 q^{63} + 47 q^{64} + 25 q^{65} + q^{66} + 3 q^{67} + 38 q^{68} + 3 q^{70} - 19 q^{71} + 34 q^{72} + 20 q^{73} - 22 q^{74} - 50 q^{75} - 25 q^{76} + 9 q^{77} - 94 q^{78} + 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} + q^{83} - 28 q^{84} + 24 q^{85} - 27 q^{86} - 58 q^{87} + 9 q^{88} + 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} + 64 q^{94} - 3 q^{95} - 26 q^{96} + 21 q^{97} - 87 q^{98} + 29 q^{99}+O(q^{100}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9 + 7 * q^10 + 19 * q^11 - 4 * q^12 + 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 + 9 * q^17 + 10 * q^18 + 17 * q^19 - 6 * q^20 + 18 * q^21 + 5 * q^22 - 10 * q^23 + 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 + 36 * q^28 + 27 * q^29 - 30 * q^30 + 7 * q^31 + 8 * q^32 - 5 * q^34 + 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 + 24 * q^39 + 10 * q^40 + 19 * q^41 + 21 * q^42 + 20 * q^43 + 23 * q^44 - 32 * q^45 + 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 + 36 * q^50 + 47 * q^51 - 28 * q^52 + 3 * q^53 - 33 * q^54 - 44 * q^56 + 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 - 19 * q^61 - 11 * q^62 - 32 * q^63 + 47 * q^64 + 25 * q^65 + q^66 + 3 * q^67 + 38 * q^68 + 3 * q^70 - 19 * q^71 + 34 * q^72 + 20 * q^73 - 22 * q^74 - 50 * q^75 - 25 * q^76 + 9 * q^77 - 94 * q^78 + 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 + q^83 - 28 * q^84 + 24 * q^85 - 27 * q^86 - 58 * q^87 + 9 * q^88 + 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 + 64 * q^94 - 3 * q^95 - 26 * q^96 + 21 * q^97 - 87 * q^98 + 29 * q^99

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