LMFDB - Embedded newform 671.2.a.c.1.5

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			1.5
Root			$-1.62941$ 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)

$f(q)$	$=$	$q-1.62941 q^{2} -2.82994 q^{3} +0.654988 q^{4} +2.04510 q^{5} +4.61114 q^{6} -3.70972 q^{7} +2.19158 q^{8} +5.00854 q^{9} +O(q^{10})$	\(q-1.62941 q^{2} -2.82994 q^{3} +0.654988 q^{4} +2.04510 q^{5} +4.61114 q^{6} -3.70972 q^{7} +2.19158 q^{8} +5.00854 q^{9} -3.33231 q^{10} +1.00000 q^{11} -1.85358 q^{12} -5.86728 q^{13} +6.04467 q^{14} -5.78750 q^{15} -4.88097 q^{16} +0.842390 q^{17} -8.16099 q^{18} +1.22718 q^{19} +1.33952 q^{20} +10.4983 q^{21} -1.62941 q^{22} -8.32475 q^{23} -6.20203 q^{24} -0.817575 q^{25} +9.56022 q^{26} -5.68405 q^{27} -2.42983 q^{28} +4.26095 q^{29} +9.43023 q^{30} -7.99905 q^{31} +3.56995 q^{32} -2.82994 q^{33} -1.37260 q^{34} -7.58675 q^{35} +3.28054 q^{36} +2.78707 q^{37} -1.99958 q^{38} +16.6040 q^{39} +4.48200 q^{40} +8.34051 q^{41} -17.1060 q^{42} +12.1886 q^{43} +0.654988 q^{44} +10.2430 q^{45} +13.5645 q^{46} -3.69071 q^{47} +13.8128 q^{48} +6.76205 q^{49} +1.33217 q^{50} -2.38391 q^{51} -3.84300 q^{52} +3.77405 q^{53} +9.26167 q^{54} +2.04510 q^{55} -8.13016 q^{56} -3.47283 q^{57} -6.94284 q^{58} +3.44817 q^{59} -3.79074 q^{60} -1.00000 q^{61} +13.0338 q^{62} -18.5803 q^{63} +3.94500 q^{64} -11.9992 q^{65} +4.61114 q^{66} -0.830299 q^{67} +0.551756 q^{68} +23.5585 q^{69} +12.3619 q^{70} +7.22148 q^{71} +10.9766 q^{72} +12.0598 q^{73} -4.54129 q^{74} +2.31369 q^{75} +0.803786 q^{76} -3.70972 q^{77} -27.0548 q^{78} +5.50521 q^{79} -9.98205 q^{80} +1.05987 q^{81} -13.5901 q^{82} +8.50990 q^{83} +6.87625 q^{84} +1.72277 q^{85} -19.8603 q^{86} -12.0582 q^{87} +2.19158 q^{88} -7.28823 q^{89} -16.6900 q^{90} +21.7660 q^{91} -5.45261 q^{92} +22.6368 q^{93} +6.01370 q^{94} +2.50969 q^{95} -10.1027 q^{96} +11.5035 q^{97} -11.0182 q^{98} +5.00854 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.62941	−1.15217	−0.576085	−	0.817390i	$-0.695420\pi$
$2$	−1.62941	−1.15217	−0.576085	+	0.817390i	$0.695420\pi$
$3$	−2.82994	−1.63386	−0.816932	−	0.576733i	$-0.804327\pi$
$3$	−2.82994	−1.63386	−0.816932	+	0.576733i	$0.804327\pi$
$4$	0.654988	0.327494
$5$	2.04510	0.914596	0.457298	−	0.889314i	$-0.348817\pi$
$5$	2.04510	0.914596	0.457298	+	0.889314i	$0.348817\pi$
$6$	4.61114	1.88249
$7$	−3.70972	−1.40214	−0.701072	−	0.713091i	$-0.747295\pi$
$7$	−3.70972	−1.40214	−0.701072	+	0.713091i	$0.747295\pi$
$8$	2.19158	0.774841
$9$	5.00854	1.66951
$10$	−3.33231	−1.05377
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.85358	−0.535081
$13$	−5.86728	−1.62729	−0.813645	−	0.581362i	$-0.802520\pi$
$13$	−5.86728	−1.62729	−0.813645	+	0.581362i	$0.802520\pi$
$14$	6.04467	1.61551
$15$	−5.78750	−1.49433
$16$	−4.88097	−1.22024
$17$	0.842390	0.204310	0.102155	−	0.994769i	$-0.467426\pi$
$17$	0.842390	0.204310	0.102155	+	0.994769i	$0.467426\pi$
$18$	−8.16099	−1.92356
$19$	1.22718	0.281533	0.140767	−	0.990043i	$-0.455043\pi$
$19$	1.22718	0.281533	0.140767	+	0.990043i	$0.455043\pi$
$20$	1.33952	0.299525
$21$	10.4983	2.29091
$22$	−1.62941	−0.347392
$23$	−8.32475	−1.73583	−0.867915	−	0.496712i	$-0.834540\pi$
$23$	−8.32475	−1.73583	−0.867915	+	0.496712i	$0.834540\pi$
$24$	−6.20203	−1.26598
$25$	−0.817575	−0.163515
$26$	9.56022	1.87491
$27$	−5.68405	−1.09390
$28$	−2.42983	−0.459194
$29$	4.26095	0.791238	0.395619	−	0.918415i	$-0.370530\pi$
$29$	4.26095	0.791238	0.395619	+	0.918415i	$0.370530\pi$
$30$	9.43023	1.72172
$31$	−7.99905	−1.43667	−0.718336	−	0.695696i	$-0.755096\pi$
$31$	−7.99905	−1.43667	−0.718336	+	0.695696i	$0.755096\pi$
$32$	3.56995	0.631085
$33$	−2.82994	−0.492629
$34$	−1.37260	−0.235399
$35$	−7.58675	−1.28239
$36$	3.28054	0.546756
$37$	2.78707	0.458192	0.229096	−	0.973404i	$-0.426423\pi$
$37$	2.78707	0.458192	0.229096	+	0.973404i	$0.426423\pi$
$38$	−1.99958	−0.324374
$39$	16.6040	2.65877
$40$	4.48200	0.708666
$41$	8.34051	1.30257	0.651284	−	0.758834i	$-0.274230\pi$
$41$	8.34051	1.30257	0.651284	+	0.758834i	$0.274230\pi$
$42$	−17.1060	−2.63952
$43$	12.1886	1.85875	0.929373	−	0.369141i	$-0.120348\pi$
$43$	12.1886	1.85875	0.929373	+	0.369141i	$0.120348\pi$
$44$	0.654988	0.0987432
$45$	10.2430	1.52693
$46$	13.5645	1.99997
$47$	−3.69071	−0.538346	−0.269173	−	0.963092i	$-0.586750\pi$
$47$	−3.69071	−0.538346	−0.269173	+	0.963092i	$0.586750\pi$
$48$	13.8128	1.99371
$49$	6.76205	0.966006
$50$	1.33217	0.188397
$51$	−2.38391	−0.333814
$52$	−3.84300	−0.532928
$53$	3.77405	0.518405	0.259203	−	0.965823i	$-0.416540\pi$
$53$	3.77405	0.518405	0.259203	+	0.965823i	$0.416540\pi$
$54$	9.26167	1.26035
$55$	2.04510	0.275761
$56$	−8.13016	−1.08644
$57$	−3.47283	−0.459988
$58$	−6.94284	−0.911640
$59$	3.44817	0.448913	0.224456	−	0.974484i	$-0.427939\pi$
$59$	3.44817	0.448913	0.224456	+	0.974484i	$0.427939\pi$
$60$	−3.79074	−0.489383
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	13.0338	1.65529
$63$	−18.5803	−2.34090
$64$	3.94500	0.493125
$65$	−11.9992	−1.48831
$66$	4.61114	0.567592
$67$	−0.830299	−0.101437	−0.0507186	−	0.998713i	$-0.516151\pi$
$67$	−0.830299	−0.101437	−0.0507186	+	0.998713i	$0.516151\pi$
$68$	0.551756	0.0669102
$69$	23.5585	2.83611
$70$	12.3619	1.47754
$71$	7.22148	0.857032	0.428516	−	0.903534i	$-0.359037\pi$
$71$	7.22148	0.857032	0.428516	+	0.903534i	$0.359037\pi$
$72$	10.9766	1.29361
$73$	12.0598	1.41149	0.705745	−	0.708466i	$-0.250613\pi$
$73$	12.0598	1.41149	0.705745	+	0.708466i	$0.250613\pi$
$74$	−4.54129	−0.527915
$75$	2.31369	0.267162
$76$	0.803786	0.0922006
$77$	−3.70972	−0.422762
$78$	−27.0548	−3.06335
$79$	5.50521	0.619384	0.309692	−	0.950837i	$-0.399774\pi$
$79$	5.50521	0.619384	0.309692	+	0.950837i	$0.399774\pi$
$80$	−9.98205	−1.11603
$81$	1.05987	0.117764
$82$	−13.5901	−1.50078
$83$	8.50990	0.934083	0.467042	−	0.884235i	$-0.345320\pi$
$83$	8.50990	0.934083	0.467042	+	0.884235i	$0.345320\pi$
$84$	6.87625	0.750261
$85$	1.72277	0.186861
$86$	−19.8603	−2.14159
$87$	−12.0582	−1.29278
$88$	2.19158	0.233623
$89$	−7.28823	−0.772551	−0.386275	−	0.922384i	$-0.626239\pi$
$89$	−7.28823	−0.772551	−0.386275	+	0.922384i	$0.626239\pi$
$90$	−16.6900	−1.75928
$91$	21.7660	2.28169
$92$	−5.45261	−0.568474
$93$	22.6368	2.34733
$94$	6.01370	0.620266
$95$	2.50969	0.257489
$96$	−10.1027	−1.03111
$97$	11.5035	1.16800	0.584000	−	0.811754i	$-0.301487\pi$
$97$	11.5035	1.16800	0.584000	+	0.811754i	$0.301487\pi$
$98$	−11.0182	−1.11300
$99$	5.00854	0.503377
$100$	−0.535502	−0.0535502
$101$	−2.29492	−0.228353	−0.114177	−	0.993460i	$-0.536423\pi$
$101$	−2.29492	−0.228353	−0.114177	+	0.993460i	$0.536423\pi$
$102$	3.88438	0.384611
$103$	−5.03193	−0.495811	−0.247905	−	0.968784i	$-0.579742\pi$
$103$	−5.03193	−0.495811	−0.247905	+	0.968784i	$0.579742\pi$
$104$	−12.8586	−1.26089
$105$	21.4700	2.09526
$106$	−6.14948	−0.597291
$107$	−14.2672	−1.37926	−0.689632	−	0.724160i	$-0.742228\pi$
$107$	−14.2672	−1.37926	−0.689632	+	0.724160i	$0.742228\pi$
$108$	−3.72299	−0.358244
$109$	−12.0721	−1.15630	−0.578151	−	0.815930i	$-0.696225\pi$
$109$	−12.0721	−1.15630	−0.578151	+	0.815930i	$0.696225\pi$
$110$	−3.33231	−0.317723
$111$	−7.88724	−0.748624
$112$	18.1070	1.71095
$113$	8.21424	0.772731	0.386365	−	0.922346i	$-0.373730\pi$
$113$	8.21424	0.772731	0.386365	+	0.922346i	$0.373730\pi$
$114$	5.65868	0.529984
$115$	−17.0249	−1.58758
$116$	2.79087	0.259126
$117$	−29.3865	−2.71678
$118$	−5.61849	−0.517224
$119$	−3.12503	−0.286471
$120$	−12.6838	−1.15786
$121$	1.00000	0.0909091
$122$	1.62941	0.147520
$123$	−23.6031	−2.12822
$124$	−5.23928	−0.470502
$125$	−11.8975	−1.06415
$126$	30.2750	2.69711
$127$	16.4437	1.45914	0.729572	−	0.683904i	$-0.239719\pi$
$127$	16.4437	1.45914	0.729572	+	0.683904i	$0.239719\pi$
$128$	−13.5679	−1.19925
$129$	−34.4930	−3.03694
$130$	19.5516	1.71479
$131$	14.4865	1.26569	0.632845	−	0.774279i	$-0.281887\pi$
$131$	14.4865	1.26569	0.632845	+	0.774279i	$0.281887\pi$
$132$	−1.85358	−0.161333
$133$	−4.55248	−0.394750
$134$	1.35290	0.116873
$135$	−11.6244	−1.00047
$136$	1.84617	0.158307
$137$	15.7386	1.34464	0.672321	−	0.740260i	$-0.265297\pi$
$137$	15.7386	1.34464	0.672321	+	0.740260i	$0.265297\pi$
$138$	−38.3866	−3.26768
$139$	2.29821	0.194931	0.0974657	−	0.995239i	$-0.468926\pi$
$139$	2.29821	0.194931	0.0974657	+	0.995239i	$0.468926\pi$
$140$	−4.96923	−0.419977
$141$	10.4445	0.879585
$142$	−11.7668	−0.987446
$143$	−5.86728	−0.490646
$144$	−24.4465	−2.03721
$145$	8.71405	0.723662
$146$	−19.6504	−1.62627
$147$	−19.1362	−1.57832
$148$	1.82550	0.150055
$149$	−0.675711	−0.0553564	−0.0276782	−	0.999617i	$-0.508811\pi$
$149$	−0.675711	−0.0553564	−0.0276782	+	0.999617i	$0.508811\pi$
$150$	−3.76995	−0.307815
$151$	15.1931	1.23639	0.618197	−	0.786023i	$-0.287863\pi$
$151$	15.1931	1.23639	0.618197	+	0.786023i	$0.287863\pi$
$152$	2.68945	0.218144
$153$	4.21915	0.341098
$154$	6.04467	0.487094
$155$	−16.3588	−1.31397
$156$	10.8754	0.870732
$157$	−17.1821	−1.37128	−0.685640	−	0.727940i	$-0.740478\pi$
$157$	−17.1821	−1.37128	−0.685640	+	0.727940i	$0.740478\pi$
$158$	−8.97026	−0.713636
$159$	−10.6803	−0.847004
$160$	7.30090	0.577187
$161$	30.8825	2.43388
$162$	−1.72697	−0.135684
$163$	1.84908	0.144831	0.0724156	−	0.997375i	$-0.476929\pi$
$163$	1.84908	0.144831	0.0724156	+	0.997375i	$0.476929\pi$
$164$	5.46294	0.426584
$165$	−5.78750	−0.450556
$166$	−13.8662	−1.07622
$167$	−16.2354	−1.25633	−0.628166	−	0.778080i	$-0.716194\pi$
$167$	−16.2354	−1.25633	−0.628166	+	0.778080i	$0.716194\pi$
$168$	23.0078	1.77509
$169$	21.4249	1.64807
$170$	−2.80711	−0.215295
$171$	6.14636	0.470024
$172$	7.98340	0.608729
$173$	17.4039	1.32320	0.661598	−	0.749858i	$-0.269878\pi$
$173$	17.4039	1.32320	0.661598	+	0.749858i	$0.269878\pi$
$174$	19.6478	1.48950
$175$	3.03298	0.229272
$176$	−4.88097	−0.367917
$177$	−9.75809	−0.733463
$178$	11.8755	0.890109
$179$	0.713196	0.0533068	0.0266534	−	0.999645i	$-0.491515\pi$
$179$	0.713196	0.0533068	0.0266534	+	0.999645i	$0.491515\pi$
$180$	6.70902	0.500061
$181$	−5.59547	−0.415908	−0.207954	−	0.978139i	$-0.566680\pi$
$181$	−5.59547	−0.415908	−0.207954	+	0.978139i	$0.566680\pi$
$182$	−35.4658	−2.62890
$183$	2.82994	0.209195
$184$	−18.2444	−1.34499
$185$	5.69984	0.419060
$186$	−36.8847	−2.70452
$187$	0.842390	0.0616017
$188$	−2.41738	−0.176305
$189$	21.0862	1.53380
$190$	−4.08933	−0.296671
$191$	3.56283	0.257798	0.128899	−	0.991658i	$-0.458856\pi$
$191$	3.56283	0.257798	0.128899	+	0.991658i	$0.458856\pi$
$192$	−11.1641	−0.805700
$193$	24.1275	1.73673	0.868367	−	0.495922i	$-0.165170\pi$
$193$	24.1275	1.73673	0.868367	+	0.495922i	$0.165170\pi$
$194$	−18.7439	−1.34573
$195$	33.9568	2.43170
$196$	4.42906	0.316361
$197$	−9.43477	−0.672199	−0.336100	−	0.941826i	$-0.609108\pi$
$197$	−9.43477	−0.672199	−0.336100	+	0.941826i	$0.609108\pi$
$198$	−8.16099	−0.579976
$199$	14.2921	1.01314	0.506569	−	0.862199i	$-0.330913\pi$
$199$	14.2921	1.01314	0.506569	+	0.862199i	$0.330913\pi$
$200$	−1.79178	−0.126698
$201$	2.34969	0.165735
$202$	3.73937	0.263101
$203$	−15.8069	−1.10943
$204$	−1.56143	−0.109322
$205$	17.0572	1.19132
$206$	8.19910	0.571258
$207$	−41.6949	−2.89799
$208$	28.6380	1.98569
$209$	1.22718	0.0848855
$210$	−34.9835	−2.41409
$211$	12.7591	0.878372	0.439186	−	0.898396i	$-0.355267\pi$
$211$	12.7591	0.878372	0.439186	+	0.898396i	$0.355267\pi$
$212$	2.47196	0.169775
$213$	−20.4363	−1.40027
$214$	23.2472	1.58915
$215$	24.9269	1.70000
$216$	−12.4570	−0.847595
$217$	29.6743	2.01442
$218$	19.6705	1.33226
$219$	−34.1284	−2.30618
$220$	1.33952	0.0903101
$221$	−4.94254	−0.332471
$222$	12.8516	0.862541
$223$	−15.6489	−1.04793	−0.523964	−	0.851740i	$-0.675547\pi$
$223$	−15.6489	−1.04793	−0.523964	+	0.851740i	$0.675547\pi$
$224$	−13.2435	−0.884871
$225$	−4.09486	−0.272991
$226$	−13.3844	−0.890317
$227$	8.33236	0.553038	0.276519	−	0.961008i	$-0.410819\pi$
$227$	8.33236	0.553038	0.276519	+	0.961008i	$0.410819\pi$
$228$	−2.27466	−0.150643
$229$	12.9669	0.856875	0.428438	−	0.903571i	$-0.359064\pi$
$229$	12.9669	0.856875	0.428438	+	0.903571i	$0.359064\pi$
$230$	27.7406	1.82916
$231$	10.4983	0.690736
$232$	9.33820	0.613083
$233$	23.9727	1.57051	0.785253	−	0.619175i	$-0.212533\pi$
$233$	23.9727	1.57051	0.785253	+	0.619175i	$0.212533\pi$
$234$	47.8828	3.13019
$235$	−7.54787	−0.492369
$236$	2.25851	0.147016
$237$	−15.5794	−1.01199
$238$	5.09197	0.330064
$239$	−23.6328	−1.52868	−0.764338	−	0.644816i	$-0.776934\pi$
$239$	−23.6328	−1.52868	−0.764338	+	0.644816i	$0.776934\pi$
$240$	28.2486	1.82344
$241$	−11.4386	−0.736822	−0.368411	−	0.929663i	$-0.620098\pi$
$241$	−11.4386	−0.736822	−0.368411	+	0.929663i	$0.620098\pi$
$242$	−1.62941	−0.104743
$243$	14.0528	0.901486
$244$	−0.654988	−0.0419313
$245$	13.8290	0.883505
$246$	38.4592	2.45207
$247$	−7.20018	−0.458136
$248$	−17.5306	−1.11319
$249$	−24.0825	−1.52617
$250$	19.3860	1.22608
$251$	−3.27420	−0.206666	−0.103333	−	0.994647i	$-0.532951\pi$
$251$	−3.27420	−0.206666	−0.103333	+	0.994647i	$0.532951\pi$
$252$	−12.1699	−0.766631
$253$	−8.32475	−0.523373
$254$	−26.7936	−1.68118
$255$	−4.87533	−0.305305
$256$	14.2178	0.888612
$257$	11.6592	0.727279	0.363639	−	0.931540i	$-0.381534\pi$
$257$	11.6592	0.727279	0.363639	+	0.931540i	$0.381534\pi$
$258$	56.2034	3.49907
$259$	−10.3393	−0.642451
$260$	−7.85930	−0.487413
$261$	21.3411	1.32098
$262$	−23.6045	−1.45829
$263$	19.9066	1.22749	0.613745	−	0.789504i	$-0.289662\pi$
$263$	19.9066	1.22749	0.613745	+	0.789504i	$0.289662\pi$
$264$	−6.20203	−0.381709
$265$	7.71829	0.474131
$266$	7.41788	0.454819
$267$	20.6252	1.26224
$268$	−0.543836	−0.0332201
$269$	19.5120	1.18967	0.594834	−	0.803849i	$-0.297218\pi$
$269$	19.5120	1.18967	0.594834	+	0.803849i	$0.297218\pi$
$270$	18.9410	1.15271
$271$	−17.8472	−1.08414	−0.542070	−	0.840333i	$-0.682359\pi$
$271$	−17.8472	−1.08414	−0.542070	+	0.840333i	$0.682359\pi$
$272$	−4.11168	−0.249307
$273$	−61.5963	−3.72798
$274$	−25.6447	−1.54926
$275$	−0.817575	−0.0493016
$276$	15.4306	0.928810
$277$	−26.8305	−1.61209	−0.806045	−	0.591855i	$-0.798396\pi$
$277$	−26.8305	−1.61209	−0.806045	+	0.591855i	$0.798396\pi$
$278$	−3.74473	−0.224594
$279$	−40.0636	−2.39854
$280$	−16.6270	−0.993651
$281$	4.78416	0.285399	0.142699	−	0.989766i	$-0.454422\pi$
$281$	4.78416	0.285399	0.142699	+	0.989766i	$0.454422\pi$
$282$	−17.0184	−1.01343
$283$	−31.0123	−1.84349	−0.921743	−	0.387800i	$-0.873235\pi$
$283$	−31.0123	−1.84349	−0.921743	+	0.387800i	$0.873235\pi$
$284$	4.72999	0.280673
$285$	−7.10228	−0.420703
$286$	9.56022	0.565308
$287$	−30.9410	−1.82639
$288$	17.8803	1.05360
$289$	−16.2904	−0.958258
$290$	−14.1988	−0.833782
$291$	−32.5541	−1.90835
$292$	7.89901	0.462255
$293$	−0.528158	−0.0308553	−0.0154277	−	0.999881i	$-0.504911\pi$
$293$	−0.528158	−0.0308553	−0.0154277	+	0.999881i	$0.504911\pi$
$294$	31.1807	1.81850
$295$	7.05184	0.410574
$296$	6.10809	0.355026
$297$	−5.68405	−0.329822
$298$	1.10101	0.0637800
$299$	48.8436	2.82470
$300$	1.51544	0.0874938
$301$	−45.2164	−2.60623
$302$	−24.7558	−1.42454
$303$	6.49448	0.373098
$304$	−5.98980	−0.343539
$305$	−2.04510	−0.117102
$306$	−6.87474	−0.393002
$307$	19.1936	1.09544	0.547718	−	0.836663i	$-0.315497\pi$
$307$	19.1936	1.09544	0.547718	+	0.836663i	$0.315497\pi$
$308$	−2.42983	−0.138452
$309$	14.2400	0.810088
$310$	26.6553	1.51392
$311$	−18.1411	−1.02869	−0.514344	−	0.857584i	$-0.671965\pi$
$311$	−18.1411	−1.02869	−0.514344	+	0.857584i	$0.671965\pi$
$312$	36.3890	2.06012
$313$	24.3308	1.37526	0.687630	−	0.726062i	$-0.258651\pi$
$313$	24.3308	1.37526	0.687630	+	0.726062i	$0.258651\pi$
$314$	27.9967	1.57995
$315$	−37.9985	−2.14098
$316$	3.60585	0.202845
$317$	−7.71872	−0.433526	−0.216763	−	0.976224i	$-0.569550\pi$
$317$	−7.71872	−0.433526	−0.216763	+	0.976224i	$0.569550\pi$
$318$	17.4026	0.975892
$319$	4.26095	0.238567
$320$	8.06792	0.451010
$321$	40.3753	2.25353
$322$	−50.3204	−2.80425
$323$	1.03376	0.0575200
$324$	0.694204	0.0385669
$325$	4.79694	0.266086
$326$	−3.01292	−0.166870
$327$	34.1634	1.88924
$328$	18.2789	1.00928
$329$	13.6915	0.754838
$330$	9.43023	0.519117
$331$	33.8019	1.85792	0.928960	−	0.370181i	$-0.120704\pi$
$331$	33.8019	1.85792	0.928960	+	0.370181i	$0.120704\pi$
$332$	5.57389	0.305907
$333$	13.9592	0.764958
$334$	26.4541	1.44751
$335$	−1.69804	−0.0927740
$336$	−51.2418	−2.79547
$337$	−23.5318	−1.28186	−0.640931	−	0.767599i	$-0.721451\pi$
$337$	−23.5318	−1.28186	−0.640931	+	0.767599i	$0.721451\pi$
$338$	−34.9101	−1.89886
$339$	−23.2458	−1.26254
$340$	1.12839	0.0611958
$341$	−7.99905	−0.433173
$342$	−10.0150	−0.541547
$343$	0.882746	0.0476638
$344$	26.7123	1.44023
$345$	48.1795	2.59390
$346$	−28.3582	−1.52455
$347$	−9.71525	−0.521542	−0.260771	−	0.965401i	$-0.583977\pi$
$347$	−9.71525	−0.521542	−0.260771	+	0.965401i	$0.583977\pi$
$348$	−7.89799	−0.423376
$349$	17.4388	0.933480	0.466740	−	0.884395i	$-0.345428\pi$
$349$	17.4388	0.933480	0.466740	+	0.884395i	$0.345428\pi$
$350$	−4.94198	−0.264160
$351$	33.3499	1.78008
$352$	3.56995	0.190279
$353$	−20.9705	−1.11615	−0.558073	−	0.829792i	$-0.688459\pi$
$353$	−20.9705	−1.11615	−0.558073	+	0.829792i	$0.688459\pi$
$354$	15.9000	0.845074
$355$	14.7686	0.783838
$356$	−4.77371	−0.253006
$357$	8.84365	0.468056
$358$	−1.16209	−0.0614184
$359$	28.6526	1.51223	0.756114	−	0.654440i	$-0.227096\pi$
$359$	28.6526	1.51223	0.756114	+	0.654440i	$0.227096\pi$
$360$	22.4483	1.18313
$361$	−17.4940	−0.920739
$362$	9.11734	0.479197
$363$	−2.82994	−0.148533
$364$	14.2565	0.747241
$365$	24.6634	1.29094
$366$	−4.61114	−0.241028
$367$	−18.7030	−0.976289	−0.488144	−	0.872763i	$-0.662326\pi$
$367$	−18.7030	−0.976289	−0.488144	+	0.872763i	$0.662326\pi$
$368$	40.6328	2.11813
$369$	41.7738	2.17466
$370$	−9.28739	−0.482828
$371$	−14.0007	−0.726878
$372$	14.8268	0.768736
$373$	4.61310	0.238857	0.119429	−	0.992843i	$-0.461894\pi$
$373$	4.61310	0.238857	0.119429	+	0.992843i	$0.461894\pi$
$374$	−1.37260	−0.0709756
$375$	33.6692	1.73867
$376$	−8.08850	−0.417132
$377$	−25.0001	−1.28757
$378$	−34.3582	−1.76720
$379$	31.5508	1.62066	0.810328	−	0.585976i	$-0.199289\pi$
$379$	31.5508	1.62066	0.810328	+	0.585976i	$0.199289\pi$
$380$	1.64382	0.0843262
$381$	−46.5347	−2.38405
$382$	−5.80533	−0.297026
$383$	11.5891	0.592177	0.296089	−	0.955160i	$-0.404318\pi$
$383$	11.5891	0.592177	0.296089	+	0.955160i	$0.404318\pi$
$384$	38.3964	1.95941
$385$	−7.58675	−0.386656
$386$	−39.3136	−2.00101
$387$	61.0472	3.10320
$388$	7.53464	0.382513
$389$	9.72680	0.493169	0.246584	−	0.969121i	$-0.420692\pi$
$389$	9.72680	0.493169	0.246584	+	0.969121i	$0.420692\pi$
$390$	−55.3297	−2.80173
$391$	−7.01269	−0.354647
$392$	14.8196	0.748501
$393$	−40.9958	−2.06797
$394$	15.3731	0.774488
$395$	11.2587	0.566486
$396$	3.28054	0.164853
$397$	−28.3728	−1.42399	−0.711996	−	0.702184i	$-0.752208\pi$
$397$	−28.3728	−1.42399	−0.711996	+	0.702184i	$0.752208\pi$
$398$	−23.2877	−1.16731
$399$	12.8832	0.644969
$400$	3.99056	0.199528
$401$	−2.73591	−0.136625	−0.0683123	−	0.997664i	$-0.521761\pi$
$401$	−2.73591	−0.136625	−0.0683123	+	0.997664i	$0.521761\pi$
$402$	−3.82862	−0.190954
$403$	46.9326	2.33788
$404$	−1.50315	−0.0747843
$405$	2.16754	0.107706
$406$	25.7560	1.27825
$407$	2.78707	0.138150
$408$	−5.22453	−0.258653
$409$	−27.8825	−1.37870	−0.689350	−	0.724429i	$-0.742104\pi$
$409$	−27.8825	−1.37870	−0.689350	+	0.724429i	$0.742104\pi$
$410$	−27.7932	−1.37261
$411$	−44.5393	−2.19696
$412$	−3.29586	−0.162375
$413$	−12.7917	−0.629440
$414$	67.9382	3.33898
$415$	17.4036	0.854308
$416$	−20.9459	−1.02696
$417$	−6.50378	−0.318492
$418$	−1.99958	−0.0978025
$419$	−19.2186	−0.938890	−0.469445	−	0.882962i	$-0.655546\pi$
$419$	−19.2186	−0.938890	−0.469445	+	0.882962i	$0.655546\pi$
$420$	14.0626	0.686185
$421$	−12.8399	−0.625780	−0.312890	−	0.949789i	$-0.601297\pi$
$421$	−12.8399	−0.625780	−0.312890	+	0.949789i	$0.601297\pi$
$422$	−20.7898	−1.01203
$423$	−18.4851	−0.898776
$424$	8.27113	0.401681
$425$	−0.688717	−0.0334077
$426$	33.2992	1.61335
$427$	3.70972	0.179526
$428$	−9.34487	−0.451701
$429$	16.6040	0.801650
$430$	−40.6162	−1.95869
$431$	6.21870	0.299544	0.149772	−	0.988721i	$-0.452146\pi$
$431$	6.21870	0.299544	0.149772	+	0.988721i	$0.452146\pi$
$432$	27.7437	1.33482
$433$	31.5577	1.51657	0.758284	−	0.651924i	$-0.226038\pi$
$433$	31.5577	1.51657	0.758284	+	0.651924i	$0.226038\pi$
$434$	−48.3516	−2.32095
$435$	−24.6602	−1.18237
$436$	−7.90711	−0.378682
$437$	−10.2159	−0.488694
$438$	55.6093	2.65711
$439$	−11.0969	−0.529625	−0.264813	−	0.964300i	$-0.585310\pi$
$439$	−11.0969	−0.529625	−0.264813	+	0.964300i	$0.585310\pi$
$440$	4.48200	0.213671
$441$	33.8680	1.61276
$442$	8.05343	0.383063
$443$	−29.8872	−1.41999	−0.709993	−	0.704209i	$-0.751302\pi$
$443$	−29.8872	−1.41999	−0.709993	+	0.704209i	$0.751302\pi$
$444$	−5.16605	−0.245170
$445$	−14.9051	−0.706571
$446$	25.4985	1.20739
$447$	1.91222	0.0904449
$448$	−14.6349	−0.691433
$449$	−39.4981	−1.86403	−0.932015	−	0.362420i	$-0.881951\pi$
$449$	−39.4981	−1.86403	−0.932015	+	0.362420i	$0.881951\pi$
$450$	6.67222	0.314532
$451$	8.34051	0.392739
$452$	5.38023	0.253065
$453$	−42.9954	−2.02010
$454$	−13.5769	−0.637194
$455$	44.5135	2.08683
$456$	−7.61098	−0.356417
$457$	−1.55255	−0.0726253	−0.0363127	−	0.999340i	$-0.511561\pi$
$457$	−1.55255	−0.0726253	−0.0363127	+	0.999340i	$0.511561\pi$
$458$	−21.1284	−0.987266
$459$	−4.78819	−0.223493
$460$	−11.1511	−0.519924
$461$	−20.3456	−0.947588	−0.473794	−	0.880636i	$-0.657116\pi$
$461$	−20.3456	−0.947588	−0.473794	+	0.880636i	$0.657116\pi$
$462$	−17.1060	−0.795845
$463$	31.5576	1.46661	0.733303	−	0.679902i	$-0.237978\pi$
$463$	31.5576	1.46661	0.733303	+	0.679902i	$0.237978\pi$
$464$	−20.7975	−0.965501
$465$	46.2945	2.14686
$466$	−39.0615	−1.80949
$467$	−4.95928	−0.229488	−0.114744	−	0.993395i	$-0.536605\pi$
$467$	−4.95928	−0.229488	−0.114744	+	0.993395i	$0.536605\pi$
$468$	−19.2478	−0.889731
$469$	3.08018	0.142230
$470$	12.2986	0.567292
$471$	48.6243	2.24049
$472$	7.55693	0.347836
$473$	12.1886	0.560433
$474$	25.3853	1.16598
$475$	−1.00331	−0.0460350
$476$	−2.04686	−0.0938177
$477$	18.9025	0.865485
$478$	38.5075	1.76129
$479$	23.8074	1.08779	0.543894	−	0.839154i	$-0.316949\pi$
$479$	23.8074	1.08779	0.543894	+	0.839154i	$0.316949\pi$
$480$	−20.6611	−0.943046
$481$	−16.3525	−0.745611
$482$	18.6381	0.848944
$483$	−87.3956	−3.97664
$484$	0.654988	0.0297722
$485$	23.5257	1.06825
$486$	−22.8978	−1.03866
$487$	7.35139	0.333123	0.166562	−	0.986031i	$-0.446734\pi$
$487$	7.35139	0.333123	0.166562	+	0.986031i	$0.446734\pi$
$488$	−2.19158	−0.0992082
$489$	−5.23279	−0.236635
$490$	−22.5332	−1.01795
$491$	11.8781	0.536053	0.268026	−	0.963412i	$-0.413629\pi$
$491$	11.8781	0.536053	0.268026	+	0.963412i	$0.413629\pi$
$492$	−15.4598	−0.696980
$493$	3.58938	0.161658
$494$	11.7321	0.527851
$495$	10.2430	0.460387
$496$	39.0431	1.75309
$497$	−26.7897	−1.20168
$498$	39.2403	1.75840
$499$	−32.0488	−1.43470	−0.717352	−	0.696711i	$-0.754646\pi$
$499$	−32.0488	−1.43470	−0.717352	+	0.696711i	$0.754646\pi$
$500$	−7.79273	−0.348502
$501$	45.9451	2.05268
$502$	5.33502	0.238114
$503$	30.2006	1.34658	0.673290	−	0.739379i	$-0.264881\pi$
$503$	30.2006	1.34658	0.673290	+	0.739379i	$0.264881\pi$
$504$	−40.7202	−1.81382
$505$	−4.69333	−0.208851
$506$	13.5645	0.603014
$507$	−60.6312	−2.69272
$508$	10.7704	0.477861
$509$	−10.4632	−0.463774	−0.231887	−	0.972743i	$-0.574490\pi$
$509$	−10.4632	−0.463774	−0.231887	+	0.972743i	$0.574490\pi$
$510$	7.94393	0.351763
$511$	−44.7384	−1.97911
$512$	3.96924	0.175417
$513$	−6.97533	−0.307968
$514$	−18.9976	−0.837948
$515$	−10.2908	−0.453466
$516$	−22.5925	−0.994580
$517$	−3.69071	−0.162317
$518$	16.8469	0.740212
$519$	−49.2520	−2.16192
$520$	−26.2971	−1.15320
$521$	−14.4603	−0.633516	−0.316758	−	0.948506i	$-0.602594\pi$
$521$	−14.4603	−0.633516	−0.316758	+	0.948506i	$0.602594\pi$
$522$	−34.7735	−1.52200
$523$	4.64270	0.203011	0.101506	−	0.994835i	$-0.467634\pi$
$523$	4.64270	0.203011	0.101506	+	0.994835i	$0.467634\pi$
$524$	9.48848	0.414506
$525$	−8.58314	−0.374599
$526$	−32.4360	−1.41428
$527$	−6.73832	−0.293526
$528$	13.8128	0.601126
$529$	46.3015	2.01311
$530$	−12.5763	−0.546279
$531$	17.2703	0.749467
$532$	−2.98182	−0.129278
$533$	−48.9361	−2.11966
$534$	−33.6070	−1.45432
$535$	−29.1779	−1.26147
$536$	−1.81967	−0.0785977
$537$	−2.01830	−0.0870960
$538$	−31.7931	−1.37070
$539$	6.76205	0.291262
$540$	−7.61387	−0.327649
$541$	4.08267	0.175528	0.0877639	−	0.996141i	$-0.472028\pi$
$541$	4.08267	0.175528	0.0877639	+	0.996141i	$0.472028\pi$
$542$	29.0805	1.24911
$543$	15.8348	0.679538
$544$	3.00729	0.128937
$545$	−24.6887	−1.05755
$546$	100.366	4.29526
$547$	26.3937	1.12851	0.564257	−	0.825599i	$-0.309163\pi$
$547$	26.3937	1.12851	0.564257	+	0.825599i	$0.309163\pi$
$548$	10.3086	0.440362
$549$	−5.00854	−0.213759
$550$	1.33217	0.0568038
$551$	5.22893	0.222760
$552$	51.6304	2.19754
$553$	−20.4228	−0.868466
$554$	43.7180	1.85740
$555$	−16.1302	−0.684688
$556$	1.50530	0.0638389
$557$	−10.9278	−0.463027	−0.231513	−	0.972832i	$-0.574368\pi$
$557$	−10.9278	−0.463027	−0.231513	+	0.972832i	$0.574368\pi$
$558$	65.2801	2.76353
$559$	−71.5140	−3.02472
$560$	37.0307	1.56483
$561$	−2.38391	−0.100649
$562$	−7.79537	−0.328828
$563$	−2.39070	−0.100756	−0.0503780	−	0.998730i	$-0.516043\pi$
$563$	−2.39070	−0.100756	−0.0503780	+	0.998730i	$0.516043\pi$
$564$	6.84102	0.288059
$565$	16.7989	0.706736
$566$	50.5318	2.12401
$567$	−3.93183	−0.165121
$568$	15.8265	0.664063
$569$	32.1605	1.34824	0.674120	−	0.738622i	$-0.264523\pi$
$569$	32.1605	1.34824	0.674120	+	0.738622i	$0.264523\pi$
$570$	11.5725	0.484721
$571$	−29.9967	−1.25532	−0.627661	−	0.778487i	$-0.715988\pi$
$571$	−29.9967	−1.25532	−0.627661	+	0.778487i	$0.715988\pi$
$572$	−3.84300	−0.160684
$573$	−10.0826	−0.421206
$574$	50.4157	2.10431
$575$	6.80611	0.283834
$576$	19.7587	0.823280
$577$	16.1830	0.673709	0.336854	−	0.941557i	$-0.390637\pi$
$577$	16.1830	0.673709	0.336854	+	0.941557i	$0.390637\pi$
$578$	26.5438	1.10407
$579$	−68.2792	−2.83759
$580$	5.70760	0.236995
$581$	−31.5694	−1.30972
$582$	53.0441	2.19875
$583$	3.77405	0.156305
$584$	26.4300	1.09368
$585$	−60.0983	−2.48476
$586$	0.860588	0.0355506
$587$	−21.9789	−0.907166	−0.453583	−	0.891214i	$-0.649854\pi$
$587$	−21.9789	−0.907166	−0.453583	+	0.891214i	$0.649854\pi$
$588$	−12.5340	−0.516892
$589$	−9.81624	−0.404471
$590$	−11.4904	−0.473051
$591$	26.6998	1.09828
$592$	−13.6036	−0.559105
$593$	−4.51554	−0.185431	−0.0927154	−	0.995693i	$-0.529555\pi$
$593$	−4.51554	−0.185431	−0.0927154	+	0.995693i	$0.529555\pi$
$594$	9.26167	0.380011
$595$	−6.39100	−0.262005
$596$	−0.442583	−0.0181289
$597$	−40.4457	−1.65533
$598$	−79.5864	−3.25453
$599$	23.7222	0.969264	0.484632	−	0.874718i	$-0.338953\pi$
$599$	23.7222	0.969264	0.484632	+	0.874718i	$0.338953\pi$
$600$	5.07063	0.207008
$601$	−1.41494	−0.0577167	−0.0288584	−	0.999584i	$-0.509187\pi$
$601$	−1.41494	−0.0577167	−0.0288584	+	0.999584i	$0.509187\pi$
$602$	73.6762	3.00282
$603$	−4.15859	−0.169351
$604$	9.95129	0.404912
$605$	2.04510	0.0831450
$606$	−10.5822	−0.429872
$607$	−14.3746	−0.583446	−0.291723	−	0.956503i	$-0.594229\pi$
$607$	−14.3746	−0.583446	−0.291723	+	0.956503i	$0.594229\pi$
$608$	4.38096	0.177671
$609$	44.7326	1.81266
$610$	3.33231	0.134921
$611$	21.6544	0.876045
$612$	2.76349	0.111708
$613$	−10.7279	−0.433294	−0.216647	−	0.976250i	$-0.569512\pi$
$613$	−10.7279	−0.433294	−0.216647	+	0.976250i	$0.569512\pi$
$614$	−31.2743	−1.26213
$615$	−48.2707	−1.94646
$616$	−8.13016	−0.327573
$617$	−33.7414	−1.35838	−0.679188	−	0.733964i	$-0.737668\pi$
$617$	−33.7414	−1.35838	−0.679188	+	0.733964i	$0.737668\pi$
$618$	−23.2029	−0.933358
$619$	14.4543	0.580968	0.290484	−	0.956880i	$-0.406184\pi$
$619$	14.4543	0.580968	0.290484	+	0.956880i	$0.406184\pi$
$620$	−10.7148	−0.430319
$621$	47.3183	1.89882
$622$	29.5594	1.18522
$623$	27.0373	1.08323
$624$	−81.0437	−3.24434
$625$	−20.2437	−0.809748
$626$	−39.6450	−1.58453
$627$	−3.47283	−0.138691
$628$	−11.2541	−0.449087
$629$	2.34780	0.0936130
$630$	61.9153	2.46677
$631$	47.8394	1.90446	0.952229	−	0.305385i	$-0.0987852\pi$
$631$	47.8394	1.90446	0.952229	+	0.305385i	$0.0987852\pi$
$632$	12.0651	0.479924
$633$	−36.1074	−1.43514
$634$	12.5770	0.499496
$635$	33.6290	1.33453
$636$	−6.99548	−0.277389
$637$	−39.6748	−1.57197
$638$	−6.94284	−0.274870
$639$	36.1691	1.43083
$640$	−27.7478	−1.09683
$641$	−2.81818	−0.111311	−0.0556557	−	0.998450i	$-0.517725\pi$
$641$	−2.81818	−0.111311	−0.0556557	+	0.998450i	$0.517725\pi$
$642$	−65.7881	−2.59645
$643$	−28.3812	−1.11924	−0.559622	−	0.828748i	$-0.689054\pi$
$643$	−28.3812	−1.11924	−0.559622	+	0.828748i	$0.689054\pi$
$644$	20.2277	0.797083
$645$	−70.5416	−2.77757
$646$	−1.68442	−0.0662728
$647$	8.31411	0.326861	0.163431	−	0.986555i	$-0.447744\pi$
$647$	8.31411	0.326861	0.163431	+	0.986555i	$0.447744\pi$
$648$	2.32279	0.0912480
$649$	3.44817	0.135352
$650$	−7.81620	−0.306576
$651$	−83.9763	−3.29129
$652$	1.21113	0.0474314
$653$	−4.95285	−0.193820	−0.0969100	−	0.995293i	$-0.530896\pi$
$653$	−4.95285	−0.193820	−0.0969100	+	0.995293i	$0.530896\pi$
$654$	−55.6663	−2.17672
$655$	29.6263	1.15759
$656$	−40.7098	−1.58945
$657$	60.4019	2.35650
$658$	−22.3092	−0.869702
$659$	−11.6767	−0.454861	−0.227430	−	0.973794i	$-0.573032\pi$
$659$	−11.6767	−0.454861	−0.227430	+	0.973794i	$0.573032\pi$
$660$	−3.79074	−0.147554
$661$	44.8723	1.74533	0.872665	−	0.488319i	$-0.162390\pi$
$661$	44.8723	1.74533	0.872665	+	0.488319i	$0.162390\pi$
$662$	−55.0772	−2.14064
$663$	13.9871	0.543213
$664$	18.6501	0.723766
$665$	−9.31027	−0.361037
$666$	−22.7453	−0.881361
$667$	−35.4713	−1.37345
$668$	−10.6340	−0.411441
$669$	44.2854	1.71217
$670$	2.76681	0.106891
$671$	−1.00000	−0.0386046
$672$	37.4784	1.44576
$673$	48.3940	1.86545	0.932725	−	0.360588i	$-0.117424\pi$
$673$	48.3940	1.86545	0.932725	+	0.360588i	$0.117424\pi$
$674$	38.3431	1.47692
$675$	4.64714	0.178868
$676$	14.0331	0.539734
$677$	5.80458	0.223088	0.111544	−	0.993759i	$-0.464420\pi$
$677$	5.80458	0.223088	0.111544	+	0.993759i	$0.464420\pi$
$678$	37.8770	1.45466
$679$	−42.6747	−1.63770
$680$	3.77559	0.144787
$681$	−23.5801	−0.903590
$682$	13.0338	0.499088
$683$	17.6874	0.676788	0.338394	−	0.941004i	$-0.390116\pi$
$683$	17.6874	0.676788	0.338394	+	0.941004i	$0.390116\pi$
$684$	4.02580	0.153930
$685$	32.1870	1.22980
$686$	−1.43836	−0.0549168
$687$	−36.6954	−1.40002
$688$	−59.4922	−2.26812
$689$	−22.1434	−0.843595
$690$	−78.5043	−2.98861
$691$	−3.50483	−0.133330	−0.0666650	−	0.997775i	$-0.521236\pi$
$691$	−3.50483	−0.133330	−0.0666650	+	0.997775i	$0.521236\pi$
$692$	11.3994	0.433339
$693$	−18.5803	−0.705807
$694$	15.8302	0.600904
$695$	4.70006	0.178283
$696$	−26.4265	−1.00169
$697$	7.02596	0.266127
$698$	−28.4151	−1.07553
$699$	−67.8413	−2.56599
$700$	1.98657	0.0750851
$701$	15.9491	0.602390	0.301195	−	0.953563i	$-0.402614\pi$
$701$	15.9491	0.602390	0.301195	+	0.953563i	$0.402614\pi$
$702$	−54.3407	−2.05096
$703$	3.42023	0.128996
$704$	3.94500	0.148683
$705$	21.3600	0.804464
$706$	34.1696	1.28599
$707$	8.51352	0.320184
$708$	−6.39144	−0.240205
$709$	3.20638	0.120418	0.0602091	−	0.998186i	$-0.480823\pi$
$709$	3.20638	0.120418	0.0602091	+	0.998186i	$0.480823\pi$
$710$	−24.0642	−0.903114
$711$	27.5731	1.03407
$712$	−15.9727	−0.598604
$713$	66.5901	2.49382
$714$	−14.4100	−0.539279
$715$	−11.9992	−0.448743
$716$	0.467135	0.0174577
$717$	66.8792	2.49765
$718$	−46.6870	−1.74234
$719$	−24.5734	−0.916435	−0.458217	−	0.888840i	$-0.651512\pi$
$719$	−24.5734	−0.916435	−0.458217	+	0.888840i	$0.651512\pi$
$720$	−49.9955	−1.86322
$721$	18.6671	0.695198
$722$	28.5050	1.06085
$723$	32.3704	1.20387
$724$	−3.66497	−0.136208
$725$	−3.48364	−0.129379
$726$	4.61114	0.171135
$727$	25.3486	0.940129	0.470064	−	0.882632i	$-0.344231\pi$
$727$	25.3486	0.940129	0.470064	+	0.882632i	$0.344231\pi$
$728$	47.7019	1.76795
$729$	−42.9481	−1.59067
$730$	−40.1869	−1.48738
$731$	10.2676	0.379760
$732$	1.85358	0.0685101
$733$	−12.7238	−0.469966	−0.234983	−	0.971999i	$-0.575503\pi$
$733$	−12.7238	−0.469966	−0.234983	+	0.971999i	$0.575503\pi$
$734$	30.4749	1.12485
$735$	−39.1353	−1.44353
$736$	−29.7190	−1.09546
$737$	−0.830299	−0.0305845
$738$	−68.0668	−2.50557
$739$	−37.3988	−1.37574	−0.687869	−	0.725835i	$-0.741454\pi$
$739$	−37.3988	−1.37574	−0.687869	+	0.725835i	$0.741454\pi$
$740$	3.73333	0.137240
$741$	20.3760	0.748533
$742$	22.8129	0.837487
$743$	−8.48274	−0.311201	−0.155601	−	0.987820i	$-0.549731\pi$
$743$	−8.48274	−0.311201	−0.155601	+	0.987820i	$0.549731\pi$
$744$	49.6104	1.81880
$745$	−1.38190	−0.0506287
$746$	−7.51665	−0.275204
$747$	42.6222	1.55947
$748$	0.551756	0.0201742
$749$	52.9274	1.93393
$750$	−54.8611	−2.00324
$751$	33.1605	1.21004	0.605021	−	0.796209i	$-0.293165\pi$
$751$	33.1605	1.21004	0.605021	+	0.796209i	$0.293165\pi$
$752$	18.0143	0.656912
$753$	9.26577	0.337664
$754$	40.7356	1.48350
$755$	31.0713	1.13080
$756$	13.8112	0.502310
$757$	1.51228	0.0549647	0.0274823	−	0.999622i	$-0.491251\pi$
$757$	1.51228	0.0549647	0.0274823	+	0.999622i	$0.491251\pi$
$758$	−51.4093	−1.86727
$759$	23.5585	0.855120
$760$	5.50020	0.199513
$761$	−18.2273	−0.660738	−0.330369	−	0.943852i	$-0.607173\pi$
$761$	−18.2273	−0.660738	−0.330369	+	0.943852i	$0.607173\pi$
$762$	75.8243	2.74682
$763$	44.7843	1.62130
$764$	2.33361	0.0844272
$765$	8.62857	0.311967
$766$	−18.8835	−0.682289
$767$	−20.2313	−0.730511
$768$	−40.2355	−1.45187
$769$	5.80897	0.209477	0.104738	−	0.994500i	$-0.466599\pi$
$769$	5.80897	0.209477	0.104738	+	0.994500i	$0.466599\pi$
$770$	12.3619	0.445494
$771$	−32.9947	−1.18827
$772$	15.8032	0.568770
$773$	−14.5476	−0.523242	−0.261621	−	0.965171i	$-0.584257\pi$
$773$	−14.5476	−0.523242	−0.261621	+	0.965171i	$0.584257\pi$
$774$	−99.4711	−3.57542
$775$	6.53983	0.234917
$776$	25.2108	0.905014
$777$	29.2595	1.04968
$778$	−15.8490	−0.568214
$779$	10.2353	0.366717
$780$	22.2413	0.796368
$781$	7.22148	0.258405
$782$	11.4266	0.408613
$783$	−24.2194	−0.865532
$784$	−33.0053	−1.17876
$785$	−35.1391	−1.25417
$786$	66.7992	2.38265
$787$	3.62056	0.129059	0.0645294	−	0.997916i	$-0.479445\pi$
$787$	3.62056	0.129059	0.0645294	+	0.997916i	$0.479445\pi$
$788$	−6.17966	−0.220141
$789$	−56.3343	−2.00555
$790$	−18.3451	−0.652688
$791$	−30.4726	−1.08348
$792$	10.9766	0.390037
$793$	5.86728	0.208353
$794$	46.2311	1.64068
$795$	−21.8423	−0.774666
$796$	9.36115	0.331797
$797$	47.4911	1.68222	0.841110	−	0.540864i	$-0.181902\pi$
$797$	47.4911	1.68222	0.841110	+	0.540864i	$0.181902\pi$
$798$	−20.9921	−0.743113
$799$	−3.10902	−0.109989
$800$	−2.91871	−0.103192
$801$	−36.5034	−1.28978
$802$	4.45792	0.157415
$803$	12.0598	0.425580
$804$	1.53902	0.0542771
$805$	63.1578	2.22602
$806$	−76.4727	−2.69363
$807$	−55.2177	−1.94376
$808$	−5.02950	−0.176937
$809$	−23.2766	−0.818361	−0.409180	−	0.912453i	$-0.634185\pi$
$809$	−23.2766	−0.818361	−0.409180	+	0.912453i	$0.634185\pi$
$810$	−3.53182	−0.124096
$811$	7.21348	0.253300	0.126650	−	0.991947i	$-0.459578\pi$
$811$	7.21348	0.253300	0.126650	+	0.991947i	$0.459578\pi$
$812$	−10.3534	−0.363331
$813$	50.5064	1.77134
$814$	−4.54129	−0.159172
$815$	3.78155	0.132462
$816$	11.6358	0.407334
$817$	14.9576	0.523299
$818$	45.4321	1.58849
$819$	109.016	3.80932
$820$	11.1722	0.390152
$821$	−11.2201	−0.391585	−0.195793	−	0.980645i	$-0.562728\pi$
$821$	−11.2201	−0.391585	−0.195793	+	0.980645i	$0.562728\pi$
$822$	72.5730	2.53127
$823$	28.8015	1.00396	0.501978	−	0.864880i	$-0.332606\pi$
$823$	28.8015	1.00396	0.501978	+	0.864880i	$0.332606\pi$
$824$	−11.0279	−0.384174
$825$	2.31369	0.0805522
$826$	20.8430	0.725222
$827$	28.9189	1.00561	0.502804	−	0.864401i	$-0.332302\pi$
$827$	28.9189	1.00561	0.502804	+	0.864401i	$0.332302\pi$
$828$	−27.3097	−0.949076
$829$	6.08709	0.211413	0.105707	−	0.994397i	$-0.466290\pi$
$829$	6.08709	0.211413	0.105707	+	0.994397i	$0.466290\pi$
$830$	−28.3576	−0.984308
$831$	75.9287	2.63394
$832$	−23.1464	−0.802458
$833$	5.69628	0.197364
$834$	10.5974	0.366956
$835$	−33.2029	−1.14903
$836$	0.803786	0.0277995
$837$	45.4670	1.57157
$838$	31.3150	1.08176
$839$	12.5318	0.432647	0.216324	−	0.976322i	$-0.430593\pi$
$839$	12.5318	0.432647	0.216324	+	0.976322i	$0.430593\pi$
$840$	47.0533	1.62349
$841$	−10.8443	−0.373943
$842$	20.9216	0.721004
$843$	−13.5389	−0.466303
$844$	8.35706	0.287662
$845$	43.8161	1.50732
$846$	30.1199	1.03554
$847$	−3.70972	−0.127468
$848$	−18.4210	−0.632580
$849$	87.7627	3.01201
$850$	1.12221	0.0384913
$851$	−23.2017	−0.795344
$852$	−13.3856	−0.458582
$853$	29.0662	0.995208	0.497604	−	0.867404i	$-0.334213\pi$
$853$	29.0662	0.995208	0.497604	+	0.867404i	$0.334213\pi$
$854$	−6.04467	−0.206844
$855$	12.5699	0.429882
$856$	−31.2678	−1.06871
$857$	−48.6893	−1.66319	−0.831597	−	0.555380i	$-0.812573\pi$
$857$	−48.6893	−1.66319	−0.831597	+	0.555380i	$0.812573\pi$
$858$	−27.0548	−0.923636
$859$	7.94731	0.271159	0.135579	−	0.990766i	$-0.456710\pi$
$859$	7.94731	0.271159	0.135579	+	0.990766i	$0.456710\pi$
$860$	16.3268	0.556741
$861$	87.5610	2.98407
$862$	−10.1328	−0.345126
$863$	26.5544	0.903921	0.451961	−	0.892038i	$-0.350725\pi$
$863$	26.5544	0.903921	0.451961	+	0.892038i	$0.350725\pi$
$864$	−20.2918	−0.690341
$865$	35.5928	1.21019
$866$	−51.4206	−1.74734
$867$	46.1007	1.56566
$868$	19.4363	0.659711
$869$	5.50521	0.186751
$870$	40.1817	1.36229
$871$	4.87159	0.165068
$872$	−26.4571	−0.895949
$873$	57.6156	1.94999
$874$	16.6460	0.563059
$875$	44.1365	1.49208
$876$	−22.3537	−0.755261
$877$	17.1293	0.578415	0.289207	−	0.957266i	$-0.406608\pi$
$877$	17.1293	0.578415	0.289207	+	0.957266i	$0.406608\pi$
$878$	18.0814	0.610218
$879$	1.49465	0.0504134
$880$	−9.98205	−0.336495
$881$	−35.1571	−1.18447	−0.592236	−	0.805764i	$-0.701755\pi$
$881$	−35.1571	−1.18447	−0.592236	+	0.805764i	$0.701755\pi$
$882$	−55.1850	−1.85817
$883$	6.10683	0.205511	0.102756	−	0.994707i	$-0.467234\pi$
$883$	6.10683	0.205511	0.102756	+	0.994707i	$0.467234\pi$
$884$	−3.23730	−0.108882
$885$	−19.9563	−0.670822
$886$	48.6987	1.63606
$887$	58.6731	1.97005	0.985025	−	0.172410i	$-0.0551555\pi$
$887$	58.6731	1.97005	0.985025	+	0.172410i	$0.0551555\pi$
$888$	−17.2855	−0.580064
$889$	−61.0017	−2.04593
$890$	24.2866	0.814090
$891$	1.05987	0.0355070
$892$	−10.2499	−0.343190
$893$	−4.52916	−0.151562
$894$	−3.11580	−0.104208
$895$	1.45856	0.0487541
$896$	50.3333	1.68152
$897$	−138.224	−4.61518
$898$	64.3587	2.14768
$899$	−34.0835	−1.13675
$900$	−2.68209	−0.0894029
$901$	3.17922	0.105915
$902$	−13.5901	−0.452502
$903$	127.960	4.25823
$904$	18.0022	0.598743
$905$	−11.4433	−0.380388
$906$	70.0573	2.32750
$907$	24.7438	0.821606	0.410803	−	0.911724i	$-0.365248\pi$
$907$	24.7438	0.821606	0.410803	+	0.911724i	$0.365248\pi$
$908$	5.45760	0.181117
$909$	−11.4942	−0.381239
$910$	−72.5309	−2.40438
$911$	−0.347652	−0.0115182	−0.00575912	−	0.999983i	$-0.501833\pi$
$911$	−0.347652	−0.0115182	−0.00575912	+	0.999983i	$0.501833\pi$
$912$	16.9508	0.561296
$913$	8.50990	0.281637
$914$	2.52975	0.0836767
$915$	5.78750	0.191329
$916$	8.49315	0.280622
$917$	−53.7408	−1.77468
$918$	7.80194	0.257502
$919$	49.0824	1.61908	0.809539	−	0.587066i	$-0.199717\pi$
$919$	49.0824	1.61908	0.809539	+	0.587066i	$0.199717\pi$
$920$	−37.3115	−1.23012
$921$	−54.3167	−1.78979
$922$	33.1514	1.09178
$923$	−42.3704	−1.39464
$924$	6.87625	0.226212
$925$	−2.27864	−0.0749213
$926$	−51.4204	−1.68978
$927$	−25.2026	−0.827763
$928$	15.2114	0.499338
$929$	14.0877	0.462203	0.231102	−	0.972930i	$-0.425767\pi$
$929$	14.0877	0.462203	0.231102	+	0.972930i	$0.425767\pi$
$930$	−75.4329	−2.47354
$931$	8.29822	0.271963
$932$	15.7019	0.514331
$933$	51.3382	1.68074
$934$	8.08073	0.264409
$935$	1.72277	0.0563406
$936$	−64.4029	−2.10507
$937$	−5.75906	−0.188140	−0.0940702	−	0.995566i	$-0.529988\pi$
$937$	−5.75906	−0.188140	−0.0940702	+	0.995566i	$0.529988\pi$
$938$	−5.01889	−0.163872
$939$	−68.8547	−2.24699
$940$	−4.94377	−0.161248
$941$	10.0022	0.326064	0.163032	−	0.986621i	$-0.447873\pi$
$941$	10.0022	0.326064	0.163032	+	0.986621i	$0.447873\pi$
$942$	−79.2290	−2.58142
$943$	−69.4327	−2.26104
$944$	−16.8304	−0.547782
$945$	43.1234	1.40281
$946$	−19.8603	−0.645714
$947$	−33.1385	−1.07686	−0.538428	−	0.842672i	$-0.680982\pi$
$947$	−33.1385	−1.07686	−0.538428	+	0.842672i	$0.680982\pi$
$948$	−10.2043	−0.331421
$949$	−70.7580	−2.29690
$950$	1.63480	0.0530401
$951$	21.8435	0.708323
$952$	−6.84876	−0.221970
$953$	30.3018	0.981571	0.490786	−	0.871280i	$-0.336710\pi$
$953$	30.3018	0.981571	0.490786	+	0.871280i	$0.336710\pi$
$954$	−30.7999	−0.997185
$955$	7.28634	0.235781
$956$	−15.4792	−0.500632
$957$	−12.0582	−0.389786
$958$	−38.7921	−1.25332
$959$	−58.3860	−1.88538
$960$	−22.8317	−0.736890
$961$	32.9848	1.06403
$962$	26.6450	0.859070
$963$	−71.4580	−2.30270
$964$	−7.49212	−0.241305
$965$	49.3431	1.58841
$966$	142.404	4.58176
$967$	13.3429	0.429078	0.214539	−	0.976715i	$-0.431175\pi$
$967$	13.3429	0.429078	0.214539	+	0.976715i	$0.431175\pi$
$968$	2.19158	0.0704401
$969$	−2.92548	−0.0939799
$970$	−38.3331	−1.23080
$971$	−56.3617	−1.80873	−0.904366	−	0.426757i	$-0.859656\pi$
$971$	−56.3617	−1.80873	−0.904366	+	0.426757i	$0.859656\pi$
$972$	9.20441	0.295231
$973$	−8.52572	−0.273322
$974$	−11.9785	−0.383814
$975$	−13.5750	−0.434749
$976$	4.88097	0.156236
$977$	40.0682	1.28190	0.640948	−	0.767584i	$-0.278541\pi$
$977$	40.0682	1.28190	0.640948	+	0.767584i	$0.278541\pi$
$978$	8.52637	0.272643
$979$	−7.28823	−0.232933
$980$	9.05786	0.289343
$981$	−60.4638	−1.93046
$982$	−19.3544	−0.617623
$983$	14.0465	0.448015	0.224007	−	0.974587i	$-0.428086\pi$
$983$	14.0465	0.448015	0.224007	+	0.974587i	$0.428086\pi$
$984$	−51.7281	−1.64903
$985$	−19.2950	−0.614791
$986$	−5.84858	−0.186257
$987$	−38.7462	−1.23330
$988$	−4.71603	−0.150037
$989$	−101.467	−3.22647
$990$	−16.6900	−0.530444
$991$	34.4743	1.09511	0.547556	−	0.836769i	$-0.315558\pi$
$991$	34.4743	1.09511	0.547556	+	0.836769i	$0.315558\pi$
$992$	−28.5562	−0.906661
$993$	−95.6572	−3.03559
$994$	43.6515	1.38454
$995$	29.2287	0.926612
$996$	−15.7737	−0.499810
$997$	−15.3004	−0.484569	−0.242284	−	0.970205i	$-0.577897\pi$
$997$	−15.3004	−0.484569	−0.242284	+	0.970205i	$0.577897\pi$
$998$	52.2208	1.65302
$999$	−15.8419	−0.501214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.c.1.5	✓	19
3.2	odd	2		6039.2.a.k.1.15		19
11.10	odd	2		7381.2.a.i.1.15		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.c.1.5	✓	19	1.1	even	1	trivial
6039.2.a.k.1.15		19	3.2	odd	2
7381.2.a.i.1.15		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)

\(f(q)\)	\(=\)	\(q-1.62941 q^{2} -2.82994 q^{3} +0.654988 q^{4} +2.04510 q^{5} +4.61114 q^{6} -3.70972 q^{7} +2.19158 q^{8} +5.00854 q^{9} +O(q^{10})\)	\(q-1.62941 q^{2} -2.82994 q^{3} +0.654988 q^{4} +2.04510 q^{5} +4.61114 q^{6} -3.70972 q^{7} +2.19158 q^{8} +5.00854 q^{9} -3.33231 q^{10} +1.00000 q^{11} -1.85358 q^{12} -5.86728 q^{13} +6.04467 q^{14} -5.78750 q^{15} -4.88097 q^{16} +0.842390 q^{17} -8.16099 q^{18} +1.22718 q^{19} +1.33952 q^{20} +10.4983 q^{21} -1.62941 q^{22} -8.32475 q^{23} -6.20203 q^{24} -0.817575 q^{25} +9.56022 q^{26} -5.68405 q^{27} -2.42983 q^{28} +4.26095 q^{29} +9.43023 q^{30} -7.99905 q^{31} +3.56995 q^{32} -2.82994 q^{33} -1.37260 q^{34} -7.58675 q^{35} +3.28054 q^{36} +2.78707 q^{37} -1.99958 q^{38} +16.6040 q^{39} +4.48200 q^{40} +8.34051 q^{41} -17.1060 q^{42} +12.1886 q^{43} +0.654988 q^{44} +10.2430 q^{45} +13.5645 q^{46} -3.69071 q^{47} +13.8128 q^{48} +6.76205 q^{49} +1.33217 q^{50} -2.38391 q^{51} -3.84300 q^{52} +3.77405 q^{53} +9.26167 q^{54} +2.04510 q^{55} -8.13016 q^{56} -3.47283 q^{57} -6.94284 q^{58} +3.44817 q^{59} -3.79074 q^{60} -1.00000 q^{61} +13.0338 q^{62} -18.5803 q^{63} +3.94500 q^{64} -11.9992 q^{65} +4.61114 q^{66} -0.830299 q^{67} +0.551756 q^{68} +23.5585 q^{69} +12.3619 q^{70} +7.22148 q^{71} +10.9766 q^{72} +12.0598 q^{73} -4.54129 q^{74} +2.31369 q^{75} +0.803786 q^{76} -3.70972 q^{77} -27.0548 q^{78} +5.50521 q^{79} -9.98205 q^{80} +1.05987 q^{81} -13.5901 q^{82} +8.50990 q^{83} +6.87625 q^{84} +1.72277 q^{85} -19.8603 q^{86} -12.0582 q^{87} +2.19158 q^{88} -7.28823 q^{89} -16.6900 q^{90} +21.7660 q^{91} -5.45261 q^{92} +22.6368 q^{93} +6.01370 q^{94} +2.50969 q^{95} -10.1027 q^{96} +11.5035 q^{97} -11.0182 q^{98} +5.00854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) \) 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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