LMFDB - Embedded newform 671.2.a.c.1.3

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			1.3
Root			$-2.08441$ 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)

$f(q)$	$=$	$q-2.08441 q^{2} +1.49292 q^{3} +2.34475 q^{4} +2.98183 q^{5} -3.11185 q^{6} +3.78550 q^{7} -0.718591 q^{8} -0.771187 q^{9} +O(q^{10})$	\(q-2.08441 q^{2} +1.49292 q^{3} +2.34475 q^{4} +2.98183 q^{5} -3.11185 q^{6} +3.78550 q^{7} -0.718591 q^{8} -0.771187 q^{9} -6.21535 q^{10} +1.00000 q^{11} +3.50052 q^{12} +4.41489 q^{13} -7.89053 q^{14} +4.45164 q^{15} -3.19166 q^{16} +5.30382 q^{17} +1.60747 q^{18} +0.311984 q^{19} +6.99164 q^{20} +5.65146 q^{21} -2.08441 q^{22} -5.62868 q^{23} -1.07280 q^{24} +3.89132 q^{25} -9.20243 q^{26} -5.63008 q^{27} +8.87605 q^{28} -8.30650 q^{29} -9.27902 q^{30} -6.85645 q^{31} +8.08989 q^{32} +1.49292 q^{33} -11.0553 q^{34} +11.2877 q^{35} -1.80824 q^{36} +4.98139 q^{37} -0.650300 q^{38} +6.59109 q^{39} -2.14272 q^{40} -11.9877 q^{41} -11.7799 q^{42} -0.135602 q^{43} +2.34475 q^{44} -2.29955 q^{45} +11.7324 q^{46} -10.6430 q^{47} -4.76489 q^{48} +7.33004 q^{49} -8.11109 q^{50} +7.91818 q^{51} +10.3518 q^{52} +9.36007 q^{53} +11.7354 q^{54} +2.98183 q^{55} -2.72023 q^{56} +0.465767 q^{57} +17.3141 q^{58} -7.08123 q^{59} +10.4380 q^{60} -1.00000 q^{61} +14.2916 q^{62} -2.91933 q^{63} -10.4793 q^{64} +13.1645 q^{65} -3.11185 q^{66} +3.08414 q^{67} +12.4361 q^{68} -8.40317 q^{69} -23.5282 q^{70} +4.02057 q^{71} +0.554168 q^{72} -10.7454 q^{73} -10.3832 q^{74} +5.80943 q^{75} +0.731522 q^{76} +3.78550 q^{77} -13.7385 q^{78} +15.6493 q^{79} -9.51698 q^{80} -6.09171 q^{81} +24.9873 q^{82} +10.8494 q^{83} +13.2512 q^{84} +15.8151 q^{85} +0.282649 q^{86} -12.4009 q^{87} -0.718591 q^{88} -13.6121 q^{89} +4.79319 q^{90} +16.7126 q^{91} -13.1978 q^{92} -10.2361 q^{93} +22.1844 q^{94} +0.930282 q^{95} +12.0776 q^{96} +11.5514 q^{97} -15.2788 q^{98} -0.771187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.08441	−1.47390	−0.736949	−	0.675949i	$-0.763734\pi$
$2$	−2.08441	−1.47390	−0.736949	+	0.675949i	$0.763734\pi$
$3$	1.49292	0.861938	0.430969	−	0.902367i	$-0.358172\pi$
$3$	1.49292	0.861938	0.430969	+	0.902367i	$0.358172\pi$
$4$	2.34475	1.17237
$5$	2.98183	1.33352	0.666758	−	0.745274i	$-0.267682\pi$
$5$	2.98183	1.33352	0.666758	+	0.745274i	$0.267682\pi$
$6$	−3.11185	−1.27041
$7$	3.78550	1.43079	0.715393	−	0.698722i	$-0.246248\pi$
$7$	3.78550	1.43079	0.715393	+	0.698722i	$0.246248\pi$
$8$	−0.718591	−0.254060
$9$	−0.771187	−0.257062
$10$	−6.21535	−1.96547
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.50052	1.01051
$13$	4.41489	1.22447	0.612236	−	0.790675i	$-0.290270\pi$
$13$	4.41489	1.22447	0.612236	+	0.790675i	$0.290270\pi$
$14$	−7.89053	−2.10883
$15$	4.45164	1.14941
$16$	−3.19166	−0.797914
$17$	5.30382	1.28636	0.643182	−	0.765713i	$-0.277614\pi$
$17$	5.30382	1.28636	0.643182	+	0.765713i	$0.277614\pi$
$18$	1.60747	0.378883
$19$	0.311984	0.0715739	0.0357870	−	0.999359i	$-0.488606\pi$
$19$	0.311984	0.0715739	0.0357870	+	0.999359i	$0.488606\pi$
$20$	6.99164	1.56338
$21$	5.65146	1.23325
$22$	−2.08441	−0.444397
$23$	−5.62868	−1.17366	−0.586830	−	0.809710i	$-0.699624\pi$
$23$	−5.62868	−1.17366	−0.586830	+	0.809710i	$0.699624\pi$
$24$	−1.07280	−0.218984
$25$	3.89132	0.778264
$26$	−9.20243	−1.80475
$27$	−5.63008	−1.08351
$28$	8.87605	1.67742
$29$	−8.30650	−1.54248	−0.771239	−	0.636545i	$-0.780363\pi$
$29$	−8.30650	−1.54248	−0.771239	+	0.636545i	$0.780363\pi$
$30$	−9.27902	−1.69411
$31$	−6.85645	−1.23145	−0.615727	−	0.787959i	$-0.711138\pi$
$31$	−6.85645	−1.23145	−0.615727	+	0.787959i	$0.711138\pi$
$32$	8.08989	1.43010
$33$	1.49292	0.259884
$34$	−11.0553	−1.89597
$35$	11.2877	1.90798
$36$	−1.80824	−0.301373
$37$	4.98139	0.818936	0.409468	−	0.912325i	$-0.365714\pi$
$37$	4.98139	0.818936	0.409468	+	0.912325i	$0.365714\pi$
$38$	−0.650300	−0.105493
$39$	6.59109	1.05542
$40$	−2.14272	−0.338794
$41$	−11.9877	−1.87217	−0.936085	−	0.351775i	$-0.885578\pi$
$41$	−11.9877	−1.87217	−0.936085	+	0.351775i	$0.885578\pi$
$42$	−11.7799	−1.81768
$43$	−0.135602	−0.0206791	−0.0103395	−	0.999947i	$-0.503291\pi$
$43$	−0.135602	−0.0206791	−0.0103395	+	0.999947i	$0.503291\pi$
$44$	2.34475	0.353484
$45$	−2.29955	−0.342797
$46$	11.7324	1.72986
$47$	−10.6430	−1.55245	−0.776223	−	0.630459i	$-0.782867\pi$
$47$	−10.6430	−1.55245	−0.776223	+	0.630459i	$0.782867\pi$
$48$	−4.76489	−0.687753
$49$	7.33004	1.04715
$50$	−8.11109	−1.14708
$51$	7.91818	1.10877
$52$	10.3518	1.43554
$53$	9.36007	1.28570	0.642852	−	0.765990i	$-0.277751\pi$
$53$	9.36007	1.28570	0.642852	+	0.765990i	$0.277751\pi$
$54$	11.7354	1.59698
$55$	2.98183	0.402070
$56$	−2.72023	−0.363506
$57$	0.465767	0.0616923
$58$	17.3141	2.27345
$59$	−7.08123	−0.921897	−0.460949	−	0.887427i	$-0.652491\pi$
$59$	−7.08123	−0.921897	−0.460949	+	0.887427i	$0.652491\pi$
$60$	10.4380	1.34754
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	14.2916	1.81504
$63$	−2.91933	−0.367801
$64$	−10.4793	−1.30991
$65$	13.1645	1.63285
$66$	−3.11185	−0.383043
$67$	3.08414	0.376788	0.188394	−	0.982094i	$-0.439672\pi$
$67$	3.08414	0.376788	0.188394	+	0.982094i	$0.439672\pi$
$68$	12.4361	1.50810
$69$	−8.40317	−1.01162
$70$	−23.5282	−2.81216
$71$	4.02057	0.477154	0.238577	−	0.971124i	$-0.423319\pi$
$71$	4.02057	0.477154	0.238577	+	0.971124i	$0.423319\pi$
$72$	0.554168	0.0653094
$73$	−10.7454	−1.25765	−0.628827	−	0.777545i	$-0.716465\pi$
$73$	−10.7454	−1.25765	−0.628827	+	0.777545i	$0.716465\pi$
$74$	−10.3832	−1.20703
$75$	5.80943	0.670816
$76$	0.731522	0.0839114
$77$	3.78550	0.431398
$78$	−13.7385	−1.55558
$79$	15.6493	1.76068	0.880339	−	0.474345i	$-0.157315\pi$
$79$	15.6493	1.76068	0.880339	+	0.474345i	$0.157315\pi$
$80$	−9.51698	−1.06403
$81$	−6.09171	−0.676857
$82$	24.9873	2.75939
$83$	10.8494	1.19088	0.595440	−	0.803400i	$-0.296978\pi$
$83$	10.8494	1.19088	0.595440	+	0.803400i	$0.296978\pi$
$84$	13.2512	1.44583
$85$	15.8151	1.71539
$86$	0.282649	0.0304788
$87$	−12.4009	−1.32952
$88$	−0.718591	−0.0766021
$89$	−13.6121	−1.44288	−0.721440	−	0.692477i	$-0.756519\pi$
$89$	−13.6121	−1.44288	−0.721440	+	0.692477i	$0.756519\pi$
$90$	4.79319	0.505247
$91$	16.7126	1.75196
$92$	−13.1978	−1.37597
$93$	−10.2361	−1.06144
$94$	22.1844	2.28814
$95$	0.930282	0.0954449
$96$	12.0776	1.23266
$97$	11.5514	1.17287	0.586434	−	0.809997i	$-0.300531\pi$
$97$	11.5514	1.17287	0.586434	+	0.809997i	$0.300531\pi$
$98$	−15.2788	−1.54339
$99$	−0.771187	−0.0775072
$100$	9.12416	0.912416
$101$	−0.740757	−0.0737081	−0.0368540	−	0.999321i	$-0.511734\pi$
$101$	−0.740757	−0.0737081	−0.0368540	+	0.999321i	$0.511734\pi$
$102$	−16.5047	−1.63421
$103$	6.18245	0.609175	0.304588	−	0.952484i	$-0.401481\pi$
$103$	6.18245	0.609175	0.304588	+	0.952484i	$0.401481\pi$
$104$	−3.17251	−0.311090
$105$	16.8517	1.64456
$106$	−19.5102	−1.89500
$107$	1.63971	0.158517	0.0792583	−	0.996854i	$-0.474745\pi$
$107$	1.63971	0.158517	0.0792583	+	0.996854i	$0.474745\pi$
$108$	−13.2011	−1.27028
$109$	14.2123	1.36130	0.680648	−	0.732611i	$-0.261698\pi$
$109$	14.2123	1.36130	0.680648	+	0.732611i	$0.261698\pi$
$110$	−6.21535	−0.592610
$111$	7.43682	0.705872
$112$	−12.0820	−1.14164
$113$	−6.91858	−0.650845	−0.325423	−	0.945569i	$-0.605507\pi$
$113$	−6.91858	−0.650845	−0.325423	+	0.945569i	$0.605507\pi$
$114$	−0.970847	−0.0909281
$115$	−16.7838	−1.56509
$116$	−19.4766	−1.80836
$117$	−3.40471	−0.314765
$118$	14.7601	1.35878
$119$	20.0776	1.84051
$120$	−3.19891	−0.292019
$121$	1.00000	0.0909091
$122$	2.08441	0.188713
$123$	−17.8967	−1.61369
$124$	−16.0766	−1.44372
$125$	−3.30590	−0.295688
$126$	6.08507	0.542101
$127$	−9.92811	−0.880977	−0.440488	−	0.897758i	$-0.645195\pi$
$127$	−9.92811	−0.880977	−0.440488	+	0.897758i	$0.645195\pi$
$128$	5.66333	0.500572
$129$	−0.202443	−0.0178241
$130$	−27.4401	−2.40666
$131$	5.11152	0.446595	0.223298	−	0.974750i	$-0.428318\pi$
$131$	5.11152	0.446595	0.223298	+	0.974750i	$0.428318\pi$
$132$	3.50052	0.304681
$133$	1.18101	0.102407
$134$	−6.42861	−0.555347
$135$	−16.7880	−1.44488
$136$	−3.81128	−0.326814
$137$	8.07318	0.689739	0.344869	−	0.938651i	$-0.387923\pi$
$137$	8.07318	0.689739	0.344869	+	0.938651i	$0.387923\pi$
$138$	17.5156	1.49103
$139$	−16.6673	−1.41371	−0.706853	−	0.707360i	$-0.749886\pi$
$139$	−16.6673	−1.41371	−0.706853	+	0.707360i	$0.749886\pi$
$140$	26.4669	2.23686
$141$	−15.8892	−1.33811
$142$	−8.38051	−0.703277
$143$	4.41489	0.369192
$144$	2.46136	0.205114
$145$	−24.7686	−2.05692
$146$	22.3978	1.85365
$147$	10.9432	0.902577
$148$	11.6801	0.960098
$149$	−17.1005	−1.40093	−0.700466	−	0.713686i	$-0.747024\pi$
$149$	−17.1005	−1.40093	−0.700466	+	0.713686i	$0.747024\pi$
$150$	−12.1092	−0.988713
$151$	14.4630	1.17699	0.588493	−	0.808502i	$-0.299722\pi$
$151$	14.4630	1.17699	0.588493	+	0.808502i	$0.299722\pi$
$152$	−0.224189	−0.0181841
$153$	−4.09023	−0.330676
$154$	−7.89053	−0.635837
$155$	−20.4448	−1.64216
$156$	15.4544	1.23734
$157$	5.84286	0.466311	0.233156	−	0.972439i	$-0.425095\pi$
$157$	5.84286	0.466311	0.233156	+	0.972439i	$0.425095\pi$
$158$	−32.6194	−2.59506
$159$	13.9738	1.10820
$160$	24.1227	1.90707
$161$	−21.3074	−1.67926
$162$	12.6976	0.997617
$163$	−10.1026	−0.791294	−0.395647	−	0.918403i	$-0.629480\pi$
$163$	−10.1026	−0.791294	−0.395647	+	0.918403i	$0.629480\pi$
$164$	−28.1082	−2.19488
$165$	4.45164	0.346560
$166$	−22.6146	−1.75523
$167$	−16.1240	−1.24771	−0.623856	−	0.781540i	$-0.714435\pi$
$167$	−16.1240	−1.24771	−0.623856	+	0.781540i	$0.714435\pi$
$168$	−4.06109	−0.313320
$169$	6.49130	0.499330
$170$	−32.9651	−2.52831
$171$	−0.240598	−0.0183990
$172$	−0.317952	−0.0242436
$173$	16.5027	1.25467	0.627337	−	0.778748i	$-0.284145\pi$
$173$	16.5027	1.25467	0.627337	+	0.778748i	$0.284145\pi$
$174$	25.8486	1.95958
$175$	14.7306	1.11353
$176$	−3.19166	−0.240580
$177$	−10.5717	−0.794618
$178$	28.3731	2.12666
$179$	−18.6695	−1.39542	−0.697711	−	0.716380i	$-0.745798\pi$
$179$	−18.6695	−1.39542	−0.697711	+	0.716380i	$0.745798\pi$
$180$	−5.39186	−0.401886
$181$	19.3738	1.44004	0.720020	−	0.693954i	$-0.244133\pi$
$181$	19.3738	1.44004	0.720020	+	0.693954i	$0.244133\pi$
$182$	−34.8358	−2.58220
$183$	−1.49292	−0.110360
$184$	4.04472	0.298181
$185$	14.8537	1.09206
$186$	21.3363	1.56445
$187$	5.30382	0.387854
$188$	−24.9552	−1.82005
$189$	−21.3127	−1.55027
$190$	−1.93909	−0.140676
$191$	9.92418	0.718088	0.359044	−	0.933321i	$-0.383103\pi$
$191$	9.92418	0.718088	0.359044	+	0.933321i	$0.383103\pi$
$192$	−15.6448	−1.12906
$193$	2.24190	0.161376	0.0806879	−	0.996739i	$-0.474288\pi$
$193$	2.24190	0.161376	0.0806879	+	0.996739i	$0.474288\pi$
$194$	−24.0778	−1.72869
$195$	19.6535	1.40742
$196$	17.1871	1.22765
$197$	−1.80883	−0.128874	−0.0644368	−	0.997922i	$-0.520525\pi$
$197$	−1.80883	−0.128874	−0.0644368	+	0.997922i	$0.520525\pi$
$198$	1.60747	0.114238
$199$	−23.1528	−1.64126	−0.820629	−	0.571461i	$-0.806377\pi$
$199$	−23.1528	−1.64126	−0.820629	+	0.571461i	$0.806377\pi$
$200$	−2.79627	−0.197726
$201$	4.60438	0.324768
$202$	1.54404	0.108638
$203$	−31.4443	−2.20696
$204$	18.5661	1.29989
$205$	−35.7454	−2.49657
$206$	−12.8867	−0.897862
$207$	4.34076	0.301704
$208$	−14.0908	−0.977023
$209$	0.311984	0.0215804
$210$	−35.1258	−2.42391
$211$	20.7281	1.42698	0.713490	−	0.700666i	$-0.247114\pi$
$211$	20.7281	1.42698	0.713490	+	0.700666i	$0.247114\pi$
$212$	21.9470	1.50732
$213$	6.00240	0.411278
$214$	−3.41782	−0.233637
$215$	−0.404342	−0.0275759
$216$	4.04573	0.275277
$217$	−25.9551	−1.76195
$218$	−29.6243	−2.00641
$219$	−16.0420	−1.08402
$220$	6.99164	0.471376
$221$	23.4158	1.57512
$222$	−15.5014	−1.04038
$223$	−7.99293	−0.535246	−0.267623	−	0.963524i	$-0.586238\pi$
$223$	−7.99293	−0.535246	−0.267623	+	0.963524i	$0.586238\pi$
$224$	30.6243	2.04617
$225$	−3.00093	−0.200062
$226$	14.4211	0.959279
$227$	15.2803	1.01419	0.507094	−	0.861891i	$-0.330720\pi$
$227$	15.2803	1.01419	0.507094	+	0.861891i	$0.330720\pi$
$228$	1.09210	0.0723264
$229$	6.31189	0.417102	0.208551	−	0.978012i	$-0.433125\pi$
$229$	6.31189	0.417102	0.208551	+	0.978012i	$0.433125\pi$
$230$	34.9842	2.30679
$231$	5.65146	0.371839
$232$	5.96898	0.391883
$233$	1.04962	0.0687630	0.0343815	−	0.999409i	$-0.489054\pi$
$233$	1.04962	0.0687630	0.0343815	+	0.999409i	$0.489054\pi$
$234$	7.09679	0.463932
$235$	−31.7357	−2.07021
$236$	−16.6037	−1.08081
$237$	23.3631	1.51760
$238$	−41.8499	−2.71273
$239$	−19.8108	−1.28146	−0.640728	−	0.767768i	$-0.721367\pi$
$239$	−19.8108	−1.28146	−0.640728	+	0.767768i	$0.721367\pi$
$240$	−14.2081	−0.917129
$241$	6.82853	0.439864	0.219932	−	0.975515i	$-0.429416\pi$
$241$	6.82853	0.439864	0.219932	+	0.975515i	$0.429416\pi$
$242$	−2.08441	−0.133991
$243$	7.79581	0.500101
$244$	−2.34475	−0.150107
$245$	21.8569	1.39639
$246$	37.3041	2.37842
$247$	1.37737	0.0876402
$248$	4.92699	0.312864
$249$	16.1973	1.02647
$250$	6.89083	0.435814
$251$	6.08527	0.384099	0.192049	−	0.981385i	$-0.438487\pi$
$251$	6.08527	0.384099	0.192049	+	0.981385i	$0.438487\pi$
$252$	−6.84509	−0.431200
$253$	−5.62868	−0.353872
$254$	20.6942	1.29847
$255$	23.6107	1.47856
$256$	9.15393	0.572120
$257$	4.93147	0.307617	0.153808	−	0.988101i	$-0.450846\pi$
$257$	4.93147	0.307617	0.153808	+	0.988101i	$0.450846\pi$
$258$	0.421973	0.0262709
$259$	18.8571	1.17172
$260$	30.8674	1.91431
$261$	6.40586	0.396513
$262$	−10.6545	−0.658236
$263$	−7.52597	−0.464071	−0.232035	−	0.972707i	$-0.574539\pi$
$263$	−7.52597	−0.464071	−0.232035	+	0.972707i	$0.574539\pi$
$264$	−1.07280	−0.0660263
$265$	27.9101	1.71451
$266$	−2.46171	−0.150937
$267$	−20.3218	−1.24367
$268$	7.23154	0.441736
$269$	10.0727	0.614141	0.307070	−	0.951687i	$-0.400651\pi$
$269$	10.0727	0.614141	0.307070	+	0.951687i	$0.400651\pi$
$270$	34.9929	2.12960
$271$	16.2243	0.985556	0.492778	−	0.870155i	$-0.335982\pi$
$271$	16.2243	0.985556	0.492778	+	0.870155i	$0.335982\pi$
$272$	−16.9280	−1.02641
$273$	24.9506	1.51008
$274$	−16.8278	−1.01660
$275$	3.89132	0.234655
$276$	−19.7033	−1.18600
$277$	22.1944	1.33353	0.666767	−	0.745266i	$-0.267678\pi$
$277$	22.1944	1.33353	0.666767	+	0.745266i	$0.267678\pi$
$278$	34.7415	2.08366
$279$	5.28760	0.316561
$280$	−8.11127	−0.484741
$281$	27.7353	1.65455	0.827276	−	0.561796i	$-0.189889\pi$
$281$	27.7353	1.65455	0.827276	+	0.561796i	$0.189889\pi$
$282$	33.1195	1.97224
$283$	−26.0469	−1.54833	−0.774165	−	0.632984i	$-0.781830\pi$
$283$	−26.0469	−1.54833	−0.774165	+	0.632984i	$0.781830\pi$
$284$	9.42723	0.559403
$285$	1.38884	0.0822677
$286$	−9.20243	−0.544151
$287$	−45.3796	−2.67867
$288$	−6.23882	−0.367626
$289$	11.1305	0.654734
$290$	51.6278	3.03169
$291$	17.2453	1.01094
$292$	−25.1952	−1.47444
$293$	2.89726	0.169260	0.0846300	−	0.996412i	$-0.473029\pi$
$293$	2.89726	0.169260	0.0846300	+	0.996412i	$0.473029\pi$
$294$	−22.8100	−1.33031
$295$	−21.1150	−1.22936
$296$	−3.57959	−0.208059
$297$	−5.63008	−0.326691
$298$	35.6445	2.06483
$299$	−24.8500	−1.43711
$300$	13.6216	0.786446
$301$	−0.513321	−0.0295873
$302$	−30.1468	−1.73476
$303$	−1.10589	−0.0635318
$304$	−0.995744	−0.0571099
$305$	−2.98183	−0.170739
$306$	8.52571	0.487382
$307$	−22.9909	−1.31216	−0.656081	−	0.754691i	$-0.727787\pi$
$307$	−22.9909	−1.31216	−0.656081	+	0.754691i	$0.727787\pi$
$308$	8.87605	0.505760
$309$	9.22992	0.525072
$310$	42.6152	2.42038
$311$	−3.59123	−0.203640	−0.101820	−	0.994803i	$-0.532467\pi$
$311$	−3.59123	−0.203640	−0.101820	+	0.994803i	$0.532467\pi$
$312$	−4.73630	−0.268140
$313$	−14.8121	−0.837228	−0.418614	−	0.908164i	$-0.637484\pi$
$313$	−14.8121	−0.837228	−0.418614	+	0.908164i	$0.637484\pi$
$314$	−12.1789	−0.687295
$315$	−8.70495	−0.490469
$316$	36.6935	2.06417
$317$	3.69043	0.207275	0.103638	−	0.994615i	$-0.466952\pi$
$317$	3.69043	0.207275	0.103638	+	0.994615i	$0.466952\pi$
$318$	−29.1271	−1.63337
$319$	−8.30650	−0.465075
$320$	−31.2475	−1.74679
$321$	2.44796	0.136632
$322$	44.4132	2.47505
$323$	1.65470	0.0920702
$324$	−14.2835	−0.793529
$325$	17.1798	0.952962
$326$	21.0578	1.16629
$327$	21.2179	1.17335
$328$	8.61428	0.475644
$329$	−40.2892	−2.22122
$330$	−9.27902	−0.510793
$331$	−0.830413	−0.0456437	−0.0228218	−	0.999740i	$-0.507265\pi$
$331$	−0.830413	−0.0456437	−0.0228218	+	0.999740i	$0.507265\pi$
$332$	25.4392	1.39616
$333$	−3.84158	−0.210518
$334$	33.6089	1.83900
$335$	9.19640	0.502453
$336$	−18.0375	−0.984027
$337$	−13.2432	−0.721404	−0.360702	−	0.932681i	$-0.617463\pi$
$337$	−13.2432	−0.721404	−0.360702	+	0.932681i	$0.617463\pi$
$338$	−13.5305	−0.735962
$339$	−10.3289	−0.560989
$340$	37.0824	2.01107
$341$	−6.85645	−0.371298
$342$	0.501503	0.0271182
$343$	1.24937	0.0674595
$344$	0.0974422	0.00525373
$345$	−25.0568	−1.34902
$346$	−34.3982	−1.84926
$347$	18.6321	1.00023	0.500113	−	0.865960i	$-0.333292\pi$
$347$	18.6321	1.00023	0.500113	+	0.865960i	$0.333292\pi$
$348$	−29.0771	−1.55870
$349$	4.87651	0.261034	0.130517	−	0.991446i	$-0.458336\pi$
$349$	4.87651	0.261034	0.130517	+	0.991446i	$0.458336\pi$
$350$	−30.7046	−1.64123
$351$	−24.8562	−1.32673
$352$	8.08989	0.431193
$353$	22.1701	1.17999	0.589997	−	0.807406i	$-0.299129\pi$
$353$	22.1701	1.17999	0.589997	+	0.807406i	$0.299129\pi$
$354$	22.0357	1.17119
$355$	11.9887	0.636293
$356$	−31.9169	−1.69159
$357$	29.9743	1.58641
$358$	38.9147	2.05671
$359$	3.41958	0.180478	0.0902392	−	0.995920i	$-0.471237\pi$
$359$	3.41958	0.180478	0.0902392	+	0.995920i	$0.471237\pi$
$360$	1.65244	0.0870910
$361$	−18.9027	−0.994877
$362$	−40.3828	−2.12247
$363$	1.49292	0.0783580
$364$	39.1868	2.05395
$365$	−32.0410	−1.67710
$366$	3.11185	0.162659
$367$	17.0313	0.889025	0.444512	−	0.895773i	$-0.353377\pi$
$367$	17.0313	0.889025	0.444512	+	0.895773i	$0.353377\pi$
$368$	17.9648	0.936481
$369$	9.24478	0.481264
$370$	−30.9611	−1.60959
$371$	35.4326	1.83957
$372$	−24.0011	−1.24440
$373$	19.9234	1.03160	0.515798	−	0.856710i	$-0.327496\pi$
$373$	19.9234	1.03160	0.515798	+	0.856710i	$0.327496\pi$
$374$	−11.0553	−0.571656
$375$	−4.93544	−0.254865
$376$	7.64799	0.394415
$377$	−36.6723	−1.88872
$378$	44.4243	2.28494
$379$	8.27906	0.425267	0.212633	−	0.977132i	$-0.431796\pi$
$379$	8.27906	0.425267	0.212633	+	0.977132i	$0.431796\pi$
$380$	2.18128	0.111897
$381$	−14.8219	−0.759348
$382$	−20.6860	−1.05839
$383$	−22.9227	−1.17129	−0.585647	−	0.810566i	$-0.699160\pi$
$383$	−22.9227	−1.17129	−0.585647	+	0.810566i	$0.699160\pi$
$384$	8.45490	0.431462
$385$	11.2877	0.575276
$386$	−4.67304	−0.237851
$387$	0.104574	0.00531581
$388$	27.0851	1.37504
$389$	−16.2780	−0.825327	−0.412663	−	0.910884i	$-0.635401\pi$
$389$	−16.2780	−0.825327	−0.412663	+	0.910884i	$0.635401\pi$
$390$	−40.9659	−2.07439
$391$	−29.8535	−1.50976
$392$	−5.26730	−0.266039
$393$	7.63109	0.384938
$394$	3.77033	0.189946
$395$	46.6634	2.34789
$396$	−1.80824	−0.0908674
$397$	11.0033	0.552239	0.276119	−	0.961123i	$-0.410952\pi$
$397$	11.0033	0.552239	0.276119	+	0.961123i	$0.410952\pi$
$398$	48.2598	2.41905
$399$	1.76316	0.0882685
$400$	−12.4198	−0.620988
$401$	29.1596	1.45616	0.728080	−	0.685492i	$-0.240413\pi$
$401$	29.1596	1.45616	0.728080	+	0.685492i	$0.240413\pi$
$402$	−9.59740	−0.478675
$403$	−30.2705	−1.50788
$404$	−1.73689	−0.0864134
$405$	−18.1645	−0.902599
$406$	65.5426	3.25283
$407$	4.98139	0.246918
$408$	−5.68994	−0.281694
$409$	−19.0595	−0.942433	−0.471216	−	0.882018i	$-0.656185\pi$
$409$	−19.0595	−0.942433	−0.471216	+	0.882018i	$0.656185\pi$
$410$	74.5079	3.67968
$411$	12.0526	0.594512
$412$	14.4963	0.714181
$413$	−26.8060	−1.31904
$414$	−9.04791	−0.444681
$415$	32.3512	1.58806
$416$	35.7160	1.75112
$417$	−24.8830	−1.21853
$418$	−0.650300	−0.0318072
$419$	−19.6633	−0.960616	−0.480308	−	0.877100i	$-0.659475\pi$
$419$	−19.6633	−0.960616	−0.480308	+	0.877100i	$0.659475\pi$
$420$	39.5130	1.92803
$421$	−18.0228	−0.878380	−0.439190	−	0.898394i	$-0.644734\pi$
$421$	−18.0228	−0.878380	−0.439190	+	0.898394i	$0.644734\pi$
$422$	−43.2057	−2.10322
$423$	8.20776	0.399075
$424$	−6.72606	−0.326646
$425$	20.6389	1.00113
$426$	−12.5114	−0.606181
$427$	−3.78550	−0.183193
$428$	3.84470	0.185841
$429$	6.59109	0.318221
$430$	0.842812	0.0406440
$431$	22.5762	1.08746	0.543728	−	0.839261i	$-0.317012\pi$
$431$	22.5762	1.08746	0.543728	+	0.839261i	$0.317012\pi$
$432$	17.9693	0.864548
$433$	8.30030	0.398887	0.199444	−	0.979909i	$-0.436087\pi$
$433$	8.30030	0.398887	0.199444	+	0.979909i	$0.436087\pi$
$434$	54.1010	2.59693
$435$	−36.9775	−1.77294
$436$	33.3244	1.59595
$437$	−1.75605	−0.0840035
$438$	33.4381	1.59773
$439$	6.53799	0.312041	0.156021	−	0.987754i	$-0.450133\pi$
$439$	6.53799	0.312041	0.156021	+	0.987754i	$0.450133\pi$
$440$	−2.14272	−0.102150
$441$	−5.65283	−0.269182
$442$	−48.8080	−2.32156
$443$	6.53605	0.310537	0.155269	−	0.987872i	$-0.450376\pi$
$443$	6.53605	0.310537	0.155269	+	0.987872i	$0.450376\pi$
$444$	17.4375	0.827546
$445$	−40.5890	−1.92410
$446$	16.6605	0.788898
$447$	−25.5298	−1.20752
$448$	−39.6694	−1.87420
$449$	−32.0478	−1.51243	−0.756215	−	0.654323i	$-0.772954\pi$
$449$	−32.0478	−1.51243	−0.756215	+	0.654323i	$0.772954\pi$
$450$	6.25517	0.294871
$451$	−11.9877	−0.564480
$452$	−16.2223	−0.763034
$453$	21.5922	1.01449
$454$	−31.8503	−1.49481
$455$	49.8342	2.33626
$456$	−0.334696	−0.0156736
$457$	−12.5441	−0.586788	−0.293394	−	0.955992i	$-0.594785\pi$
$457$	−12.5441	−0.586788	−0.293394	+	0.955992i	$0.594785\pi$
$458$	−13.1565	−0.614765
$459$	−29.8609	−1.39379
$460$	−39.3537	−1.83488
$461$	32.6919	1.52261	0.761307	−	0.648392i	$-0.224558\pi$
$461$	32.6919	1.52261	0.761307	+	0.648392i	$0.224558\pi$
$462$	−11.7799	−0.548052
$463$	−10.4702	−0.486593	−0.243297	−	0.969952i	$-0.578229\pi$
$463$	−10.4702	−0.486593	−0.243297	+	0.969952i	$0.578229\pi$
$464$	26.5115	1.23077
$465$	−30.5224	−1.41544
$466$	−2.18784	−0.101350
$467$	−6.16377	−0.285225	−0.142613	−	0.989779i	$-0.545550\pi$
$467$	−6.16377	−0.285225	−0.142613	+	0.989779i	$0.545550\pi$
$468$	−7.98318	−0.369023
$469$	11.6750	0.539103
$470$	66.1501	3.05128
$471$	8.72294	0.401932
$472$	5.08851	0.234218
$473$	−0.135602	−0.00623497
$474$	−48.6982	−2.23678
$475$	1.21403	0.0557034
$476$	47.0769	2.15777
$477$	−7.21836	−0.330506
$478$	41.2938	1.88873
$479$	−14.8725	−0.679541	−0.339770	−	0.940508i	$-0.610349\pi$
$479$	−14.8725	−0.679541	−0.339770	+	0.940508i	$0.610349\pi$
$480$	36.0133	1.64377
$481$	21.9923	1.00276
$482$	−14.2334	−0.648315
$483$	−31.8102	−1.44742
$484$	2.34475	0.106579
$485$	34.4444	1.56404
$486$	−16.2496	−0.737098
$487$	11.9464	0.541342	0.270671	−	0.962672i	$-0.412755\pi$
$487$	11.9464	0.541342	0.270671	+	0.962672i	$0.412755\pi$
$488$	0.718591	0.0325291
$489$	−15.0823	−0.682047
$490$	−45.5587	−2.05813
$491$	−10.7791	−0.486453	−0.243227	−	0.969969i	$-0.578206\pi$
$491$	−10.7791	−0.486453	−0.243227	+	0.969969i	$0.578206\pi$
$492$	−41.9633	−1.89185
$493$	−44.0562	−1.98419
$494$	−2.87101	−0.129173
$495$	−2.29955	−0.103357
$496$	21.8834	0.982595
$497$	15.2199	0.682706
$498$	−33.7618	−1.51290
$499$	−3.60513	−0.161388	−0.0806940	−	0.996739i	$-0.525714\pi$
$499$	−3.60513	−0.161388	−0.0806940	+	0.996739i	$0.525714\pi$
$500$	−7.75149	−0.346657
$501$	−24.0718	−1.07545
$502$	−12.6842	−0.566122
$503$	−36.2506	−1.61634	−0.808168	−	0.588952i	$-0.799541\pi$
$503$	−36.2506	−1.61634	−0.808168	+	0.588952i	$0.799541\pi$
$504$	2.09781	0.0934437
$505$	−2.20881	−0.0982909
$506$	11.7324	0.521571
$507$	9.69099	0.430392
$508$	−23.2789	−1.03283
$509$	12.8068	0.567652	0.283826	−	0.958876i	$-0.408396\pi$
$509$	12.8068	0.567652	0.283826	+	0.958876i	$0.408396\pi$
$510$	−49.2142	−2.17924
$511$	−40.6767	−1.79943
$512$	−30.4071	−1.34382
$513$	−1.75649	−0.0775511
$514$	−10.2792	−0.453395
$515$	18.4350	0.812345
$516$	−0.474677	−0.0208965
$517$	−10.6430	−0.468080
$518$	−39.3058	−1.72700
$519$	24.6372	1.08145
$520$	−9.45988	−0.414843
$521$	7.62484	0.334050	0.167025	−	0.985953i	$-0.446584\pi$
$521$	7.62484	0.334050	0.167025	+	0.985953i	$0.446584\pi$
$522$	−13.3524	−0.584419
$523$	7.28355	0.318487	0.159244	−	0.987239i	$-0.449094\pi$
$523$	7.28355	0.318487	0.159244	+	0.987239i	$0.449094\pi$
$524$	11.9852	0.523576
$525$	21.9916	0.959793
$526$	15.6872	0.683993
$527$	−36.3654	−1.58410
$528$	−4.76489	−0.207365
$529$	8.68202	0.377479
$530$	−58.1760	−2.52701
$531$	5.46095	0.236985
$532$	2.76918	0.120059
$533$	−52.9246	−2.29242
$534$	42.3589	1.83305
$535$	4.88934	0.211384
$536$	−2.21624	−0.0957270
$537$	−27.8720	−1.20277
$538$	−20.9955	−0.905180
$539$	7.33004	0.315727
$540$	−39.3635	−1.69394
$541$	−13.0431	−0.560765	−0.280383	−	0.959888i	$-0.590461\pi$
$541$	−13.0431	−0.560765	−0.280383	+	0.959888i	$0.590461\pi$
$542$	−33.8180	−1.45261
$543$	28.9235	1.24123
$544$	42.9073	1.83964
$545$	42.3788	1.81531
$546$	−52.0072	−2.22570
$547$	5.68800	0.243201	0.121601	−	0.992579i	$-0.461197\pi$
$547$	5.68800	0.243201	0.121601	+	0.992579i	$0.461197\pi$
$548$	18.9296	0.808631
$549$	0.771187	0.0329135
$550$	−8.11109	−0.345858
$551$	−2.59149	−0.110401
$552$	6.03845	0.257013
$553$	59.2403	2.51915
$554$	−46.2622	−1.96549
$555$	22.1754	0.941292
$556$	−39.0807	−1.65739
$557$	34.6291	1.46728	0.733641	−	0.679538i	$-0.237820\pi$
$557$	34.6291	1.46728	0.733641	+	0.679538i	$0.237820\pi$
$558$	−11.0215	−0.466578
$559$	−0.598667	−0.0253209
$560$	−36.0266	−1.52240
$561$	7.91818	0.334306
$562$	−57.8117	−2.43864
$563$	26.7927	1.12918	0.564588	−	0.825373i	$-0.309035\pi$
$563$	26.7927	1.12918	0.564588	+	0.825373i	$0.309035\pi$
$564$	−37.2561	−1.56877
$565$	−20.6300	−0.867913
$566$	54.2924	2.28208
$567$	−23.0602	−0.968437
$568$	−2.88915	−0.121226
$569$	26.8823	1.12696	0.563482	−	0.826129i	$-0.309462\pi$
$569$	26.8823	1.12696	0.563482	+	0.826129i	$0.309462\pi$
$570$	−2.89490	−0.121254
$571$	11.6787	0.488740	0.244370	−	0.969682i	$-0.421419\pi$
$571$	11.6787	0.488740	0.244370	+	0.969682i	$0.421419\pi$
$572$	10.3518	0.432831
$573$	14.8160	0.618948
$574$	94.5895	3.94809
$575$	−21.9030	−0.913418
$576$	8.08150	0.336729
$577$	−14.5191	−0.604438	−0.302219	−	0.953238i	$-0.597727\pi$
$577$	−14.5191	−0.604438	−0.302219	+	0.953238i	$0.597727\pi$
$578$	−23.2004	−0.965011
$579$	3.34698	0.139096
$580$	−58.0761	−2.41148
$581$	41.0706	1.70389
$582$	−35.9463	−1.49002
$583$	9.36007	0.387654
$584$	7.72155	0.319520
$585$	−10.1523	−0.419745
$586$	−6.03907	−0.249472
$587$	42.4867	1.75361	0.876806	−	0.480844i	$-0.159670\pi$
$587$	42.4867	1.75361	0.876806	+	0.480844i	$0.159670\pi$
$588$	25.6590	1.05816
$589$	−2.13910	−0.0881400
$590$	44.0123	1.81196
$591$	−2.70044	−0.111081
$592$	−15.8989	−0.653441
$593$	26.9749	1.10772	0.553862	−	0.832608i	$-0.313153\pi$
$593$	26.9749	1.10772	0.553862	+	0.832608i	$0.313153\pi$
$594$	11.7354	0.481508
$595$	59.8681	2.45435
$596$	−40.0964	−1.64241
$597$	−34.5653	−1.41466
$598$	51.7975	2.11816
$599$	0.252191	0.0103042	0.00515212	−	0.999987i	$-0.498360\pi$
$599$	0.252191	0.0103042	0.00515212	+	0.999987i	$0.498360\pi$
$600$	−4.17461	−0.170428
$601$	10.0959	0.411821	0.205910	−	0.978571i	$-0.433984\pi$
$601$	10.0959	0.411821	0.205910	+	0.978571i	$0.433984\pi$
$602$	1.06997	0.0436087
$603$	−2.37845	−0.0968581
$604$	33.9122	1.37987
$605$	2.98183	0.121229
$606$	2.30513	0.0936394
$607$	−28.8159	−1.16960	−0.584801	−	0.811177i	$-0.698827\pi$
$607$	−28.8159	−1.16960	−0.584801	+	0.811177i	$0.698827\pi$
$608$	2.52391	0.102358
$609$	−46.9438	−1.90226
$610$	6.21535	0.251652
$611$	−46.9879	−1.90092
$612$	−9.59056	−0.387676
$613$	−19.4842	−0.786961	−0.393481	−	0.919333i	$-0.628729\pi$
$613$	−19.4842	−0.786961	−0.393481	+	0.919333i	$0.628729\pi$
$614$	47.9224	1.93399
$615$	−53.3651	−2.15189
$616$	−2.72023	−0.109601
$617$	13.6018	0.547589	0.273794	−	0.961788i	$-0.411721\pi$
$617$	13.6018	0.547589	0.273794	+	0.961788i	$0.411721\pi$
$618$	−19.2389	−0.773902
$619$	−28.6157	−1.15016	−0.575081	−	0.818097i	$-0.695029\pi$
$619$	−28.6157	−1.15016	−0.575081	+	0.818097i	$0.695029\pi$
$620$	−47.9378	−1.92523
$621$	31.6899	1.27167
$622$	7.48558	0.300145
$623$	−51.5287	−2.06445
$624$	−21.0365	−0.842134
$625$	−29.3142	−1.17257
$626$	30.8744	1.23399
$627$	0.465767	0.0186009
$628$	13.7000	0.546691
$629$	26.4204	1.05345
$630$	18.1447	0.722900
$631$	0.321585	0.0128021	0.00640104	−	0.999980i	$-0.497962\pi$
$631$	0.321585	0.0128021	0.00640104	+	0.999980i	$0.497962\pi$
$632$	−11.2454	−0.447319
$633$	30.9454	1.22997
$634$	−7.69235	−0.305502
$635$	−29.6039	−1.17480
$636$	32.7651	1.29922
$637$	32.3614	1.28220
$638$	17.3141	0.685472
$639$	−3.10061	−0.122658
$640$	16.8871	0.667521
$641$	−41.8152	−1.65160	−0.825800	−	0.563963i	$-0.809276\pi$
$641$	−41.8152	−1.65160	−0.825800	+	0.563963i	$0.809276\pi$
$642$	−5.10253	−0.201381
$643$	−20.5122	−0.808923	−0.404461	−	0.914555i	$-0.632541\pi$
$643$	−20.5122	−0.808923	−0.404461	+	0.914555i	$0.632541\pi$
$644$	−49.9604	−1.96872
$645$	−0.603650	−0.0237687
$646$	−3.44907	−0.135702
$647$	−29.8808	−1.17474	−0.587368	−	0.809320i	$-0.699836\pi$
$647$	−29.8808	−1.17474	−0.587368	+	0.809320i	$0.699836\pi$
$648$	4.37745	0.171962
$649$	−7.08123	−0.277962
$650$	−35.8096	−1.40457
$651$	−38.7489	−1.51869
$652$	−23.6880	−0.927692
$653$	34.4146	1.34675	0.673373	−	0.739303i	$-0.264845\pi$
$653$	34.4146	1.34675	0.673373	+	0.739303i	$0.264845\pi$
$654$	−44.2267	−1.72940
$655$	15.2417	0.595542
$656$	38.2607	1.49383
$657$	8.28671	0.323295
$658$	83.9791	3.27385
$659$	1.74540	0.0679911	0.0339955	−	0.999422i	$-0.489177\pi$
$659$	1.74540	0.0679911	0.0339955	+	0.999422i	$0.489177\pi$
$660$	10.4380	0.406297
$661$	−21.6073	−0.840425	−0.420212	−	0.907426i	$-0.638044\pi$
$661$	−21.6073	−0.840425	−0.420212	+	0.907426i	$0.638044\pi$
$662$	1.73092	0.0672741
$663$	34.9579	1.35765
$664$	−7.79631	−0.302555
$665$	3.52159	0.136561
$666$	8.00742	0.310281
$667$	46.7546	1.81035
$668$	−37.8066	−1.46278
$669$	−11.9328	−0.461349
$670$	−19.1690	−0.740564
$671$	−1.00000	−0.0386046
$672$	45.7197	1.76367
$673$	35.8905	1.38348	0.691738	−	0.722149i	$-0.256845\pi$
$673$	35.8905	1.38348	0.691738	+	0.722149i	$0.256845\pi$
$674$	27.6043	1.06328
$675$	−21.9085	−0.843257
$676$	15.2204	0.585402
$677$	−16.5765	−0.637088	−0.318544	−	0.947908i	$-0.603194\pi$
$677$	−16.5765	−0.637088	−0.318544	+	0.947908i	$0.603194\pi$
$678$	21.5296	0.826840
$679$	43.7279	1.67812
$680$	−11.3646	−0.435812
$681$	22.8122	0.874167
$682$	14.2916	0.547254
$683$	29.9616	1.14645	0.573224	−	0.819399i	$-0.305693\pi$
$683$	29.9616	1.14645	0.573224	+	0.819399i	$0.305693\pi$
$684$	−0.564140	−0.0215704
$685$	24.0729	0.919777
$686$	−2.60419	−0.0994283
$687$	9.42316	0.359516
$688$	0.432794	0.0165001
$689$	41.3237	1.57431
$690$	52.2286	1.98831
$691$	−9.35132	−0.355741	−0.177871	−	0.984054i	$-0.556921\pi$
$691$	−9.35132	−0.355741	−0.177871	+	0.984054i	$0.556921\pi$
$692$	38.6945	1.47095
$693$	−2.91933	−0.110896
$694$	−38.8370	−1.47423
$695$	−49.6992	−1.88520
$696$	8.91122	0.337779
$697$	−63.5808	−2.40829
$698$	−10.1646	−0.384737
$699$	1.56700	0.0592695
$700$	34.5395	1.30547
$701$	−11.0613	−0.417779	−0.208890	−	0.977939i	$-0.566985\pi$
$701$	−11.0613	−0.417779	−0.208890	+	0.977939i	$0.566985\pi$
$702$	51.8105	1.95546
$703$	1.55411	0.0586144
$704$	−10.4793	−0.394953
$705$	−47.3789	−1.78439
$706$	−46.2114	−1.73919
$707$	−2.80414	−0.105460
$708$	−24.7880	−0.931589
$709$	4.66820	0.175318	0.0876589	−	0.996151i	$-0.472061\pi$
$709$	4.66820	0.175318	0.0876589	+	0.996151i	$0.472061\pi$
$710$	−24.9893	−0.937830
$711$	−12.0685	−0.452604
$712$	9.78154	0.366579
$713$	38.5927	1.44531
$714$	−62.4786	−2.33820
$715$	13.1645	0.492323
$716$	−43.7752	−1.63595
$717$	−29.5760	−1.10454
$718$	−7.12779	−0.266007
$719$	30.4581	1.13589	0.567947	−	0.823065i	$-0.307738\pi$
$719$	30.4581	1.13589	0.567947	+	0.823065i	$0.307738\pi$
$720$	7.33937	0.273522
$721$	23.4037	0.871600
$722$	39.4008	1.46635
$723$	10.1945	0.379136
$724$	45.4265	1.68826
$725$	−32.3232	−1.20046
$726$	−3.11185	−0.115492
$727$	40.3806	1.49763	0.748816	−	0.662778i	$-0.230623\pi$
$727$	40.3806	1.49763	0.748816	+	0.662778i	$0.230623\pi$
$728$	−12.0095	−0.445103
$729$	29.9137	1.10791
$730$	66.7864	2.47187
$731$	−0.719207	−0.0266008
$732$	−3.50052	−0.129383
$733$	30.9302	1.14243	0.571217	−	0.820799i	$-0.306472\pi$
$733$	30.9302	1.14243	0.571217	+	0.820799i	$0.306472\pi$
$734$	−35.5001	−1.31033
$735$	32.6307	1.20360
$736$	−45.5354	−1.67846
$737$	3.08414	0.113606
$738$	−19.2699	−0.709334
$739$	29.5134	1.08567	0.542834	−	0.839840i	$-0.317351\pi$
$739$	29.5134	1.08567	0.542834	+	0.839840i	$0.317351\pi$
$740$	34.8281	1.28031
$741$	2.05631	0.0755405
$742$	−73.8558	−2.71133
$743$	−12.2720	−0.450216	−0.225108	−	0.974334i	$-0.572273\pi$
$743$	−12.2720	−0.450216	−0.225108	+	0.974334i	$0.572273\pi$
$744$	7.35560	0.269669
$745$	−50.9909	−1.86816
$746$	−41.5285	−1.52047
$747$	−8.36694	−0.306130
$748$	12.4361	0.454709
$749$	6.20713	0.226803
$750$	10.2875	0.375645
$751$	8.28527	0.302334	0.151167	−	0.988508i	$-0.451697\pi$
$751$	8.28527	0.302334	0.151167	+	0.988508i	$0.451697\pi$
$752$	33.9689	1.23872
$753$	9.08483	0.331070
$754$	76.4400	2.78378
$755$	43.1264	1.56953
$756$	−49.9729	−1.81750
$757$	−3.05443	−0.111015	−0.0555076	−	0.998458i	$-0.517678\pi$
$757$	−3.05443	−0.111015	−0.0555076	+	0.998458i	$0.517678\pi$
$758$	−17.2569	−0.626799
$759$	−8.40317	−0.305016
$760$	−0.668493	−0.0242488
$761$	43.7061	1.58434	0.792172	−	0.610298i	$-0.208950\pi$
$761$	43.7061	1.58434	0.792172	+	0.610298i	$0.208950\pi$
$762$	30.8948	1.11920
$763$	53.8009	1.94772
$764$	23.2697	0.841867
$765$	−12.1964	−0.440961
$766$	47.7802	1.72637
$767$	−31.2629	−1.12884
$768$	13.6661	0.493133
$769$	−13.1128	−0.472861	−0.236431	−	0.971648i	$-0.575978\pi$
$769$	−13.1128	−0.472861	−0.236431	+	0.971648i	$0.575978\pi$
$770$	−23.5282	−0.847898
$771$	7.36229	0.265147
$772$	5.25669	0.189193
$773$	46.5477	1.67420	0.837102	−	0.547048i	$-0.184248\pi$
$773$	46.5477	1.67420	0.837102	+	0.547048i	$0.184248\pi$
$774$	−0.217975	−0.00783496
$775$	−26.6806	−0.958397
$776$	−8.30075	−0.297979
$777$	28.1521	1.00995
$778$	33.9299	1.21645
$779$	−3.73997	−0.133999
$780$	46.0825	1.65002
$781$	4.02057	0.143867
$782$	62.2268	2.22522
$783$	46.7663	1.67129
$784$	−23.3950	−0.835535
$785$	17.4224	0.621834
$786$	−15.9063	−0.567359
$787$	30.5629	1.08945	0.544725	−	0.838615i	$-0.316634\pi$
$787$	30.5629	1.08945	0.544725	+	0.838615i	$0.316634\pi$
$788$	−4.24124	−0.151088
$789$	−11.2357	−0.400001
$790$	−97.2655	−3.46055
$791$	−26.1903	−0.931220
$792$	0.554168	0.0196915
$793$	−4.41489	−0.156778
$794$	−22.9353	−0.813943
$795$	41.6676	1.47780
$796$	−54.2875	−1.92417
$797$	3.15070	0.111603	0.0558017	−	0.998442i	$-0.482229\pi$
$797$	3.15070	0.111603	0.0558017	+	0.998442i	$0.482229\pi$
$798$	−3.67514	−0.130099
$799$	−56.4487	−1.99701
$800$	31.4804	1.11300
$801$	10.4975	0.370910
$802$	−60.7804	−2.14623
$803$	−10.7454	−0.379197
$804$	10.7961	0.380750
$805$	−63.5350	−2.23932
$806$	63.0960	2.22246
$807$	15.0377	0.529351
$808$	0.532302	0.0187263
$809$	7.42365	0.261002	0.130501	−	0.991448i	$-0.458341\pi$
$809$	7.42365	0.261002	0.130501	+	0.991448i	$0.458341\pi$
$810$	37.8621	1.33034
$811$	−47.6535	−1.67334	−0.836670	−	0.547708i	$-0.815501\pi$
$811$	−47.6535	−1.67334	−0.836670	+	0.547708i	$0.815501\pi$
$812$	−73.7289	−2.58738
$813$	24.2216	0.849488
$814$	−10.3832	−0.363932
$815$	−30.1242	−1.05520
$816$	−25.2721	−0.884701
$817$	−0.0423055	−0.00148008
$818$	39.7278	1.38905
$819$	−12.8885	−0.450362
$820$	−83.8139	−2.92691
$821$	−43.3269	−1.51212	−0.756059	−	0.654503i	$-0.772878\pi$
$821$	−43.3269	−1.51212	−0.756059	+	0.654503i	$0.772878\pi$
$822$	−25.1226	−0.876250
$823$	−29.7284	−1.03627	−0.518133	−	0.855300i	$-0.673373\pi$
$823$	−29.7284	−1.03627	−0.518133	+	0.855300i	$0.673373\pi$
$824$	−4.44266	−0.154767
$825$	5.80943	0.202259
$826$	55.8746	1.94413
$827$	20.1947	0.702240	0.351120	−	0.936330i	$-0.385801\pi$
$827$	20.1947	0.702240	0.351120	+	0.936330i	$0.385801\pi$
$828$	10.1780	0.353710
$829$	−29.4893	−1.02421	−0.512103	−	0.858924i	$-0.671134\pi$
$829$	−29.4893	−1.02421	−0.512103	+	0.858924i	$0.671134\pi$
$830$	−67.4330	−2.34063
$831$	33.1345	1.14942
$832$	−46.2650	−1.60395
$833$	38.8772	1.34701
$834$	51.8663	1.79598
$835$	−48.0790	−1.66384
$836$	0.731522	0.0253002
$837$	38.6024	1.33429
$838$	40.9863	1.41585
$839$	−34.6484	−1.19619	−0.598097	−	0.801424i	$-0.704076\pi$
$839$	−34.6484	−1.19619	−0.598097	+	0.801424i	$0.704076\pi$
$840$	−12.1095	−0.417817
$841$	39.9979	1.37924
$842$	37.5669	1.29464
$843$	41.4067	1.42612
$844$	48.6021	1.67295
$845$	19.3559	0.665865
$846$	−17.1083	−0.588196
$847$	3.78550	0.130071
$848$	−29.8741	−1.02588
$849$	−38.8860	−1.33456
$850$	−43.0197	−1.47556
$851$	−28.0387	−0.961153
$852$	14.0741	0.482171
$853$	0.382697	0.0131033	0.00655165	−	0.999979i	$-0.497915\pi$
$853$	0.382697	0.0131033	0.00655165	+	0.999979i	$0.497915\pi$
$854$	7.89053	0.270008
$855$	−0.717421	−0.0245353
$856$	−1.17828	−0.0402728
$857$	27.0449	0.923835	0.461917	−	0.886923i	$-0.347162\pi$
$857$	27.0449	0.923835	0.461917	+	0.886923i	$0.347162\pi$
$858$	−13.7385	−0.469025
$859$	−35.5906	−1.21434	−0.607168	−	0.794573i	$-0.707695\pi$
$859$	−35.5906	−1.21434	−0.607168	+	0.794573i	$0.707695\pi$
$860$	−0.948078	−0.0323292
$861$	−67.7482	−2.30885
$862$	−47.0579	−1.60280
$863$	−19.7203	−0.671285	−0.335643	−	0.941989i	$-0.608953\pi$
$863$	−19.7203	−0.671285	−0.335643	+	0.941989i	$0.608953\pi$
$864$	−45.5468	−1.54953
$865$	49.2081	1.67313
$866$	−17.3012	−0.587919
$867$	16.6169	0.564341
$868$	−60.8582	−2.06566
$869$	15.6493	0.530865
$870$	77.0762	2.61313
$871$	13.6162	0.461366
$872$	−10.2129	−0.345851
$873$	−8.90830	−0.301500
$874$	3.66033	0.123813
$875$	−12.5145	−0.423067
$876$	−37.6145	−1.27088
$877$	−21.3828	−0.722045	−0.361022	−	0.932557i	$-0.617572\pi$
$877$	−21.3828	−0.722045	−0.361022	+	0.932557i	$0.617572\pi$
$878$	−13.6278	−0.459917
$879$	4.32539	0.145892
$880$	−9.51698	−0.320817
$881$	−34.7349	−1.17025	−0.585124	−	0.810944i	$-0.698954\pi$
$881$	−34.7349	−1.17025	−0.585124	+	0.810944i	$0.698954\pi$
$882$	11.7828	0.396747
$883$	−23.9852	−0.807167	−0.403583	−	0.914943i	$-0.632235\pi$
$883$	−23.9852	−0.807167	−0.403583	+	0.914943i	$0.632235\pi$
$884$	54.9041	1.84662
$885$	−31.5231	−1.05964
$886$	−13.6238	−0.457700
$887$	−37.2407	−1.25042	−0.625211	−	0.780456i	$-0.714987\pi$
$887$	−37.2407	−1.25042	−0.625211	+	0.780456i	$0.714987\pi$
$888$	−5.34404	−0.179334
$889$	−37.5829	−1.26049
$890$	84.6039	2.83593
$891$	−6.09171	−0.204080
$892$	−18.7414	−0.627508
$893$	−3.32045	−0.111115
$894$	53.2144	1.77976
$895$	−55.6692	−1.86082
$896$	21.4385	0.716212
$897$	−37.0991	−1.23870
$898$	66.8006	2.22917
$899$	56.9531	1.89949
$900$	−7.03643	−0.234548
$901$	49.6441	1.65388
$902$	24.9873	0.831986
$903$	−0.766347	−0.0255024
$904$	4.97163	0.165354
$905$	57.7693	1.92032
$906$	−45.0069	−1.49525
$907$	8.37749	0.278170	0.139085	−	0.990280i	$-0.455584\pi$
$907$	8.37749	0.278170	0.139085	+	0.990280i	$0.455584\pi$
$908$	35.8284	1.18901
$909$	0.571262	0.0189476
$910$	−103.875	−3.44341
$911$	−3.99772	−0.132450	−0.0662252	−	0.997805i	$-0.521096\pi$
$911$	−3.99772	−0.132450	−0.0662252	+	0.997805i	$0.521096\pi$
$912$	−1.48657	−0.0492252
$913$	10.8494	0.359064
$914$	26.1470	0.864865
$915$	−4.45164	−0.147167
$916$	14.7998	0.488999
$917$	19.3497	0.638982
$918$	62.2423	2.05430
$919$	9.13809	0.301438	0.150719	−	0.988577i	$-0.451841\pi$
$919$	9.13809	0.301438	0.150719	+	0.988577i	$0.451841\pi$
$920$	12.0607	0.397629
$921$	−34.3236	−1.13100
$922$	−68.1432	−2.24418
$923$	17.7504	0.584262
$924$	13.2512	0.435934
$925$	19.3842	0.637348
$926$	21.8242	0.717189
$927$	−4.76783	−0.156596
$928$	−67.1987	−2.20590
$929$	51.7590	1.69816	0.849079	−	0.528267i	$-0.177158\pi$
$929$	51.7590	1.69816	0.849079	+	0.528267i	$0.177158\pi$
$930$	63.6211	2.08622
$931$	2.28685	0.0749485
$932$	2.46110	0.0806159
$933$	−5.36143	−0.175525
$934$	12.8478	0.420393
$935$	15.8151	0.517209
$936$	2.44659	0.0799694
$937$	−27.9536	−0.913203	−0.456601	−	0.889671i	$-0.650933\pi$
$937$	−27.9536	−0.913203	−0.456601	+	0.889671i	$0.650933\pi$
$938$	−24.3355	−0.794583
$939$	−22.1133	−0.721639
$940$	−74.4122	−2.42706
$941$	47.4243	1.54599	0.772994	−	0.634414i	$-0.218758\pi$
$941$	47.4243	1.54599	0.772994	+	0.634414i	$0.218758\pi$
$942$	−18.1821	−0.592406
$943$	67.4751	2.19729
$944$	22.6008	0.735595
$945$	−63.5509	−2.06731
$946$	0.282649	0.00918971
$947$	19.9896	0.649574	0.324787	−	0.945787i	$-0.394707\pi$
$947$	19.9896	0.649574	0.324787	+	0.945787i	$0.394707\pi$
$948$	54.7805	1.77919
$949$	−47.4398	−1.53996
$950$	−2.53053	−0.0821011
$951$	5.50952	0.178658
$952$	−14.4276	−0.467601
$953$	−14.9169	−0.483206	−0.241603	−	0.970375i	$-0.577673\pi$
$953$	−14.9169	−0.483206	−0.241603	+	0.970375i	$0.577673\pi$
$954$	15.0460	0.487132
$955$	29.5922	0.957582
$956$	−46.4513	−1.50234
$957$	−12.4009	−0.400866
$958$	31.0003	1.00157
$959$	30.5611	0.986868
$960$	−46.6501	−1.50562
$961$	16.0109	0.516481
$962$	−45.8409	−1.47797
$963$	−1.26452	−0.0407487
$964$	16.0112	0.515685
$965$	6.68498	0.215197
$966$	66.3054	2.13334
$967$	28.9409	0.930675	0.465338	−	0.885133i	$-0.345933\pi$
$967$	28.9409	0.930675	0.465338	+	0.885133i	$0.345933\pi$
$968$	−0.718591	−0.0230964
$969$	2.47034	0.0793588
$970$	−71.7960	−2.30523
$971$	7.32733	0.235145	0.117573	−	0.993064i	$-0.462489\pi$
$971$	7.32733	0.235145	0.117573	+	0.993064i	$0.462489\pi$
$972$	18.2792	0.586306
$973$	−63.0943	−2.02271
$974$	−24.9011	−0.797882
$975$	25.6480	0.821395
$976$	3.19166	0.102162
$977$	5.07070	0.162226	0.0811131	−	0.996705i	$-0.474153\pi$
$977$	5.07070	0.162226	0.0811131	+	0.996705i	$0.474153\pi$
$978$	31.4377	1.00527
$979$	−13.6121	−0.435045
$980$	51.2490	1.63709
$981$	−10.9604	−0.349938
$982$	22.4680	0.716982
$983$	1.61384	0.0514735	0.0257368	−	0.999669i	$-0.491807\pi$
$983$	1.61384	0.0514735	0.0257368	+	0.999669i	$0.491807\pi$
$984$	12.8604	0.409976
$985$	−5.39362	−0.171855
$986$	91.8309	2.92449
$987$	−60.1486	−1.91455
$988$	3.22959	0.102747
$989$	0.763258	0.0242702
$990$	4.79319	0.152338
$991$	−23.6526	−0.751350	−0.375675	−	0.926752i	$-0.622589\pi$
$991$	−23.6526	−0.751350	−0.375675	+	0.926752i	$0.622589\pi$
$992$	−55.4679	−1.76111
$993$	−1.23974	−0.0393420
$994$	−31.7244	−1.00624
$995$	−69.0378	−2.18864
$996$	37.9787	1.20340
$997$	3.40590	0.107866	0.0539330	−	0.998545i	$-0.482824\pi$
$997$	3.40590	0.107866	0.0539330	+	0.998545i	$0.482824\pi$
$998$	7.51456	0.237869
$999$	−28.0457	−0.887325

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.c.1.3	✓	19
3.2	odd	2		6039.2.a.k.1.17		19
11.10	odd	2		7381.2.a.i.1.17		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.c.1.3	✓	19	1.1	even	1	trivial
6039.2.a.k.1.17		19	3.2	odd	2
7381.2.a.i.1.17		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)

\(f(q)\)	\(=\)	\(q-2.08441 q^{2} +1.49292 q^{3} +2.34475 q^{4} +2.98183 q^{5} -3.11185 q^{6} +3.78550 q^{7} -0.718591 q^{8} -0.771187 q^{9} +O(q^{10})\)	\(q-2.08441 q^{2} +1.49292 q^{3} +2.34475 q^{4} +2.98183 q^{5} -3.11185 q^{6} +3.78550 q^{7} -0.718591 q^{8} -0.771187 q^{9} -6.21535 q^{10} +1.00000 q^{11} +3.50052 q^{12} +4.41489 q^{13} -7.89053 q^{14} +4.45164 q^{15} -3.19166 q^{16} +5.30382 q^{17} +1.60747 q^{18} +0.311984 q^{19} +6.99164 q^{20} +5.65146 q^{21} -2.08441 q^{22} -5.62868 q^{23} -1.07280 q^{24} +3.89132 q^{25} -9.20243 q^{26} -5.63008 q^{27} +8.87605 q^{28} -8.30650 q^{29} -9.27902 q^{30} -6.85645 q^{31} +8.08989 q^{32} +1.49292 q^{33} -11.0553 q^{34} +11.2877 q^{35} -1.80824 q^{36} +4.98139 q^{37} -0.650300 q^{38} +6.59109 q^{39} -2.14272 q^{40} -11.9877 q^{41} -11.7799 q^{42} -0.135602 q^{43} +2.34475 q^{44} -2.29955 q^{45} +11.7324 q^{46} -10.6430 q^{47} -4.76489 q^{48} +7.33004 q^{49} -8.11109 q^{50} +7.91818 q^{51} +10.3518 q^{52} +9.36007 q^{53} +11.7354 q^{54} +2.98183 q^{55} -2.72023 q^{56} +0.465767 q^{57} +17.3141 q^{58} -7.08123 q^{59} +10.4380 q^{60} -1.00000 q^{61} +14.2916 q^{62} -2.91933 q^{63} -10.4793 q^{64} +13.1645 q^{65} -3.11185 q^{66} +3.08414 q^{67} +12.4361 q^{68} -8.40317 q^{69} -23.5282 q^{70} +4.02057 q^{71} +0.554168 q^{72} -10.7454 q^{73} -10.3832 q^{74} +5.80943 q^{75} +0.731522 q^{76} +3.78550 q^{77} -13.7385 q^{78} +15.6493 q^{79} -9.51698 q^{80} -6.09171 q^{81} +24.9873 q^{82} +10.8494 q^{83} +13.2512 q^{84} +15.8151 q^{85} +0.282649 q^{86} -12.4009 q^{87} -0.718591 q^{88} -13.6121 q^{89} +4.79319 q^{90} +16.7126 q^{91} -13.1978 q^{92} -10.2361 q^{93} +22.1844 q^{94} +0.930282 q^{95} +12.0776 q^{96} +11.5514 q^{97} -15.2788 q^{98} -0.771187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) \) 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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