LMFDB - Embedded newform 6031.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$133$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76277 q^{2} +2.80088 q^{3} +5.63291 q^{4} -0.925460 q^{5} -7.73820 q^{6} -3.46221 q^{7} -10.0369 q^{8} +4.84493 q^{9} +O(q^{10})$	\(q-2.76277 q^{2} +2.80088 q^{3} +5.63291 q^{4} -0.925460 q^{5} -7.73820 q^{6} -3.46221 q^{7} -10.0369 q^{8} +4.84493 q^{9} +2.55683 q^{10} +0.279588 q^{11} +15.7771 q^{12} +1.46693 q^{13} +9.56531 q^{14} -2.59210 q^{15} +16.4639 q^{16} +6.09200 q^{17} -13.3854 q^{18} +3.63541 q^{19} -5.21303 q^{20} -9.69725 q^{21} -0.772438 q^{22} +4.86580 q^{23} -28.1122 q^{24} -4.14352 q^{25} -4.05280 q^{26} +5.16744 q^{27} -19.5023 q^{28} -0.941978 q^{29} +7.16139 q^{30} -4.67152 q^{31} -25.4121 q^{32} +0.783093 q^{33} -16.8308 q^{34} +3.20414 q^{35} +27.2911 q^{36} -1.00000 q^{37} -10.0438 q^{38} +4.10870 q^{39} +9.28875 q^{40} +7.80012 q^{41} +26.7913 q^{42} +2.52184 q^{43} +1.57489 q^{44} -4.48379 q^{45} -13.4431 q^{46} -7.32108 q^{47} +46.1133 q^{48} +4.98692 q^{49} +11.4476 q^{50} +17.0630 q^{51} +8.26310 q^{52} +3.60566 q^{53} -14.2765 q^{54} -0.258748 q^{55} +34.7499 q^{56} +10.1823 q^{57} +2.60247 q^{58} -1.11603 q^{59} -14.6011 q^{60} +3.93970 q^{61} +12.9063 q^{62} -16.7742 q^{63} +37.2800 q^{64} -1.35759 q^{65} -2.16351 q^{66} -2.43589 q^{67} +34.3157 q^{68} +13.6285 q^{69} -8.85230 q^{70} -0.719257 q^{71} -48.6281 q^{72} +9.67105 q^{73} +2.76277 q^{74} -11.6055 q^{75} +20.4779 q^{76} -0.967994 q^{77} -11.3514 q^{78} -12.3360 q^{79} -15.2366 q^{80} -0.0614153 q^{81} -21.5500 q^{82} +2.00912 q^{83} -54.6237 q^{84} -5.63790 q^{85} -6.96726 q^{86} -2.63837 q^{87} -2.80620 q^{88} +1.65501 q^{89} +12.3877 q^{90} -5.07883 q^{91} +27.4086 q^{92} -13.0844 q^{93} +20.2265 q^{94} -3.36442 q^{95} -71.1762 q^{96} +5.95605 q^{97} -13.7777 q^{98} +1.35459 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) $ 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.76277	−1.95357	−0.976787	−	0.214211i	$-0.931282\pi$
$2$	−2.76277	−1.95357	−0.976787	+	0.214211i	$0.931282\pi$
$3$	2.80088	1.61709	0.808545	−	0.588435i	$-0.200256\pi$
$3$	2.80088	1.61709	0.808545	+	0.588435i	$0.200256\pi$
$4$	5.63291	2.81645
$5$	−0.925460	−0.413878	−0.206939	−	0.978354i	$-0.566350\pi$
$5$	−0.925460	−0.413878	−0.206939	+	0.978354i	$0.566350\pi$
$6$	−7.73820	−3.15911
$7$	−3.46221	−1.30859	−0.654297	−	0.756238i	$-0.727035\pi$
$7$	−3.46221	−1.30859	−0.654297	+	0.756238i	$0.727035\pi$
$8$	−10.0369	−3.54858
$9$	4.84493	1.61498
$10$	2.55683	0.808542
$11$	0.279588	0.0842990	0.0421495	−	0.999111i	$-0.486579\pi$
$11$	0.279588	0.0842990	0.0421495	+	0.999111i	$0.486579\pi$
$12$	15.7771	4.55446
$13$	1.46693	0.406854	0.203427	−	0.979090i	$-0.434792\pi$
$13$	1.46693	0.406854	0.203427	+	0.979090i	$0.434792\pi$
$14$	9.56531	2.55644
$15$	−2.59210	−0.669278
$16$	16.4639	4.11596
$17$	6.09200	1.47753	0.738764	−	0.673964i	$-0.235410\pi$
$17$	6.09200	1.47753	0.738764	+	0.673964i	$0.235410\pi$
$18$	−13.3854	−3.15498
$19$	3.63541	0.834019	0.417010	−	0.908902i	$-0.363078\pi$
$19$	3.63541	0.834019	0.417010	+	0.908902i	$0.363078\pi$
$20$	−5.21303	−1.16567
$21$	−9.69725	−2.11611
$22$	−0.772438	−0.164684
$23$	4.86580	1.01459	0.507295	−	0.861773i	$-0.330646\pi$
$23$	4.86580	1.01459	0.507295	+	0.861773i	$0.330646\pi$
$24$	−28.1122	−5.73837
$25$	−4.14352	−0.828705
$26$	−4.05280	−0.794820
$27$	5.16744	0.994474
$28$	−19.5023	−3.68559
$29$	−0.941978	−0.174921	−0.0874605	−	0.996168i	$-0.527875\pi$
$29$	−0.941978	−0.174921	−0.0874605	+	0.996168i	$0.527875\pi$
$30$	7.16139	1.30748
$31$	−4.67152	−0.839030	−0.419515	−	0.907748i	$-0.637800\pi$
$31$	−4.67152	−0.839030	−0.419515	+	0.907748i	$0.637800\pi$
$32$	−25.4121	−4.49226
$33$	0.783093	0.136319
$34$	−16.8308	−2.88646
$35$	3.20414	0.541598
$36$	27.2911	4.54851
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−10.0438	−1.62932
$39$	4.10870	0.657919
$40$	9.28875	1.46868
$41$	7.80012	1.21817	0.609087	−	0.793103i	$-0.291536\pi$
$41$	7.80012	1.21817	0.609087	+	0.793103i	$0.291536\pi$
$42$	26.7913	4.13398
$43$	2.52184	0.384576	0.192288	−	0.981338i	$-0.438409\pi$
$43$	2.52184	0.384576	0.192288	+	0.981338i	$0.438409\pi$
$44$	1.57489	0.237424
$45$	−4.48379	−0.668404
$46$	−13.4431	−1.98208
$47$	−7.32108	−1.06789	−0.533945	−	0.845519i	$-0.679291\pi$
$47$	−7.32108	−1.06789	−0.533945	+	0.845519i	$0.679291\pi$
$48$	46.1133	6.65588
$49$	4.98692	0.712417
$50$	11.4476	1.61894
$51$	17.0630	2.38929
$52$	8.26310	1.14589
$53$	3.60566	0.495276	0.247638	−	0.968853i	$-0.420346\pi$
$53$	3.60566	0.495276	0.247638	+	0.968853i	$0.420346\pi$
$54$	−14.2765	−1.94278
$55$	−0.258748	−0.0348895
$56$	34.7499	4.64365
$57$	10.1823	1.34868
$58$	2.60247	0.341721
$59$	−1.11603	−0.145295	−0.0726476	−	0.997358i	$-0.523145\pi$
$59$	−1.11603	−0.145295	−0.0726476	+	0.997358i	$0.523145\pi$
$60$	−14.6011	−1.88499
$61$	3.93970	0.504427	0.252214	−	0.967672i	$-0.418841\pi$
$61$	3.93970	0.504427	0.252214	+	0.967672i	$0.418841\pi$
$62$	12.9063	1.63911
$63$	−16.7742	−2.11335
$64$	37.2800	4.66001
$65$	−1.35759	−0.168388
$66$	−2.16351	−0.266309
$67$	−2.43589	−0.297591	−0.148796	−	0.988868i	$-0.547540\pi$
$67$	−2.43589	−0.297591	−0.148796	+	0.988868i	$0.547540\pi$
$68$	34.3157	4.16139
$69$	13.6285	1.64068
$70$	−8.85230	−1.05805
$71$	−0.719257	−0.0853601	−0.0426800	−	0.999089i	$-0.513590\pi$
$71$	−0.719257	−0.0853601	−0.0426800	+	0.999089i	$0.513590\pi$
$72$	−48.6281	−5.73088
$73$	9.67105	1.13191	0.565955	−	0.824436i	$-0.308507\pi$
$73$	9.67105	1.13191	0.565955	+	0.824436i	$0.308507\pi$
$74$	2.76277	0.321166
$75$	−11.6055	−1.34009
$76$	20.4779	2.34898
$77$	−0.967994	−0.110313
$78$	−11.3514	−1.28529
$79$	−12.3360	−1.38791	−0.693956	−	0.720018i	$-0.744134\pi$
$79$	−12.3360	−1.38791	−0.693956	+	0.720018i	$0.744134\pi$
$80$	−15.2366	−1.70351
$81$	−0.0614153	−0.00682392
$82$	−21.5500	−2.37979
$83$	2.00912	0.220529	0.110265	−	0.993902i	$-0.464830\pi$
$83$	2.00912	0.220529	0.110265	+	0.993902i	$0.464830\pi$
$84$	−54.6237	−5.95994
$85$	−5.63790	−0.611516
$86$	−6.96726	−0.751299
$87$	−2.63837	−0.282863
$88$	−2.80620	−0.299142
$89$	1.65501	0.175431	0.0877154	−	0.996146i	$-0.472043\pi$
$89$	1.65501	0.175431	0.0877154	+	0.996146i	$0.472043\pi$
$90$	12.3877	1.30578
$91$	−5.07883	−0.532406
$92$	27.4086	2.85755
$93$	−13.0844	−1.35679
$94$	20.2265	2.08620
$95$	−3.36442	−0.345182
$96$	−71.1762	−7.26439
$97$	5.95605	0.604745	0.302373	−	0.953190i	$-0.402221\pi$
$97$	5.95605	0.604745	0.302373	+	0.953190i	$0.402221\pi$
$98$	−13.7777	−1.39176
$99$	1.35459	0.136141
$100$	−23.3401	−2.33401
$101$	14.4053	1.43338	0.716689	−	0.697393i	$-0.245657\pi$
$101$	14.4053	1.43338	0.716689	+	0.697393i	$0.245657\pi$
$102$	−47.1411	−4.66767
$103$	−2.43458	−0.239886	−0.119943	−	0.992781i	$-0.538271\pi$
$103$	−2.43458	−0.239886	−0.119943	+	0.992781i	$0.538271\pi$
$104$	−14.7235	−1.44375
$105$	8.97441	0.875813
$106$	−9.96163	−0.967559
$107$	−4.25861	−0.411696	−0.205848	−	0.978584i	$-0.565995\pi$
$107$	−4.25861	−0.411696	−0.205848	+	0.978584i	$0.565995\pi$
$108$	29.1077	2.80089
$109$	18.1659	1.73998	0.869988	−	0.493073i	$-0.164126\pi$
$109$	18.1659	1.73998	0.869988	+	0.493073i	$0.164126\pi$
$110$	0.714860	0.0681593
$111$	−2.80088	−0.265848
$112$	−57.0014	−5.38612
$113$	8.10079	0.762058	0.381029	−	0.924563i	$-0.375570\pi$
$113$	8.10079	0.762058	0.381029	+	0.924563i	$0.375570\pi$
$114$	−28.1315	−2.63475
$115$	−4.50310	−0.419916
$116$	−5.30608	−0.492657
$117$	7.10719	0.657060
$118$	3.08335	0.283845
$119$	−21.0918	−1.93348
$120$	26.0167	2.37499
$121$	−10.9218	−0.992894
$122$	−10.8845	−0.985437
$123$	21.8472	1.96990
$124$	−26.3142	−2.36309
$125$	8.46196	0.756861
$126$	46.3433	4.12859
$127$	−19.2651	−1.70950	−0.854752	−	0.519036i	$-0.826291\pi$
$127$	−19.2651	−1.70950	−0.854752	+	0.519036i	$0.826291\pi$
$128$	−52.1721	−4.61141
$129$	7.06336	0.621894
$130$	3.75070	0.328958
$131$	8.10657	0.708274	0.354137	−	0.935194i	$-0.384775\pi$
$131$	8.10657	0.708274	0.354137	+	0.935194i	$0.384775\pi$
$132$	4.41109	0.383936
$133$	−12.5865	−1.09139
$134$	6.72981	0.581367
$135$	−4.78226	−0.411591
$136$	−61.1448	−5.24313
$137$	−6.84704	−0.584982	−0.292491	−	0.956268i	$-0.594484\pi$
$137$	−6.84704	−0.584982	−0.292491	+	0.956268i	$0.594484\pi$
$138$	−37.6525	−3.20520
$139$	18.2288	1.54615	0.773074	−	0.634316i	$-0.218718\pi$
$139$	18.2288	1.54615	0.773074	+	0.634316i	$0.218718\pi$
$140$	18.0486	1.52539
$141$	−20.5055	−1.72687
$142$	1.98714	0.166757
$143$	0.410137	0.0342974
$144$	79.7663	6.64719
$145$	0.871763	0.0723960
$146$	−26.7189	−2.21127
$147$	13.9678	1.15204
$148$	−5.63291	−0.463022
$149$	5.07136	0.415462	0.207731	−	0.978186i	$-0.433392\pi$
$149$	5.07136	0.415462	0.207731	+	0.978186i	$0.433392\pi$
$150$	32.0634	2.61797
$151$	−12.0846	−0.983433	−0.491716	−	0.870755i	$-0.663630\pi$
$151$	−12.0846	−0.983433	−0.491716	+	0.870755i	$0.663630\pi$
$152$	−36.4882	−2.95958
$153$	29.5154	2.38617
$154$	2.67435	0.215505
$155$	4.32330	0.347256
$156$	23.1440	1.85300
$157$	−20.8358	−1.66288	−0.831440	−	0.555615i	$-0.812483\pi$
$157$	−20.8358	−1.66288	−0.831440	+	0.555615i	$0.812483\pi$
$158$	34.0816	2.71139
$159$	10.0990	0.800906
$160$	23.5178	1.85925
$161$	−16.8464	−1.32769
$162$	0.169676	0.0133310
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	43.9374	3.43093
$165$	−0.724721	−0.0564195
$166$	−5.55074	−0.430821
$167$	14.7279	1.13968	0.569841	−	0.821755i	$-0.307005\pi$
$167$	14.7279	1.13968	0.569841	+	0.821755i	$0.307005\pi$
$168$	97.3303	7.50920
$169$	−10.8481	−0.834470
$170$	15.5762	1.19464
$171$	17.6133	1.34692
$172$	14.2053	1.08314
$173$	9.85058	0.748926	0.374463	−	0.927242i	$-0.377827\pi$
$173$	9.85058	0.748926	0.374463	+	0.927242i	$0.377827\pi$
$174$	7.28921	0.552594
$175$	14.3458	1.08444
$176$	4.60310	0.346971
$177$	−3.12588	−0.234955
$178$	−4.57242	−0.342717
$179$	17.8678	1.33550	0.667750	−	0.744386i	$-0.267258\pi$
$179$	17.8678	1.33550	0.667750	+	0.744386i	$0.267258\pi$
$180$	−25.2568	−1.88253
$181$	19.3228	1.43625	0.718126	−	0.695913i	$-0.245000\pi$
$181$	19.3228	1.43625	0.718126	+	0.695913i	$0.245000\pi$
$182$	14.0317	1.04010
$183$	11.0346	0.815704
$184$	−48.8376	−3.60035
$185$	0.925460	0.0680412
$186$	36.1491	2.65058
$187$	1.70325	0.124554
$188$	−41.2390	−3.00766
$189$	−17.8908	−1.30136
$190$	9.29513	0.674339
$191$	0.230390	0.0166704	0.00833521	−	0.999965i	$-0.497347\pi$
$191$	0.230390	0.0166704	0.00833521	+	0.999965i	$0.497347\pi$
$192$	104.417	7.53564
$193$	−6.17498	−0.444485	−0.222243	−	0.974991i	$-0.571338\pi$
$193$	−6.17498	−0.444485	−0.222243	+	0.974991i	$0.571338\pi$
$194$	−16.4552	−1.18141
$195$	−3.80244	−0.272298
$196$	28.0909	2.00649
$197$	−9.00491	−0.641574	−0.320787	−	0.947151i	$-0.603947\pi$
$197$	−9.00491	−0.641574	−0.320787	+	0.947151i	$0.603947\pi$
$198$	−3.74241	−0.265962
$199$	13.8723	0.983382	0.491691	−	0.870770i	$-0.336379\pi$
$199$	13.8723	0.983382	0.491691	+	0.870770i	$0.336379\pi$
$200$	41.5881	2.94073
$201$	−6.82263	−0.481232
$202$	−39.7985	−2.80021
$203$	3.26133	0.228900
$204$	96.1142	6.72934
$205$	−7.21870	−0.504176
$206$	6.72618	0.468635
$207$	23.5745	1.63854
$208$	24.1514	1.67460
$209$	1.01642	0.0703070
$210$	−24.7943	−1.71097
$211$	12.2595	0.843976	0.421988	−	0.906602i	$-0.361333\pi$
$211$	12.2595	0.843976	0.421988	+	0.906602i	$0.361333\pi$
$212$	20.3104	1.39492
$213$	−2.01455	−0.138035
$214$	11.7656	0.804278
$215$	−2.33386	−0.159168
$216$	−51.8651	−3.52897
$217$	16.1738	1.09795
$218$	−50.1882	−3.39917
$219$	27.0875	1.83040
$220$	−1.45750	−0.0982647
$221$	8.93656	0.601138
$222$	7.73820	0.519354
$223$	−16.4273	−1.10005	−0.550025	−	0.835148i	$-0.685382\pi$
$223$	−16.4273	−1.10005	−0.550025	+	0.835148i	$0.685382\pi$
$224$	87.9820	5.87854
$225$	−20.0751	−1.33834
$226$	−22.3806	−1.48874
$227$	23.8493	1.58294	0.791468	−	0.611211i	$-0.209317\pi$
$227$	23.8493	1.58294	0.791468	+	0.611211i	$0.209317\pi$
$228$	57.3562	3.79851
$229$	−14.7790	−0.976627	−0.488314	−	0.872668i	$-0.662388\pi$
$229$	−14.7790	−0.976627	−0.488314	+	0.872668i	$0.662388\pi$
$230$	12.4410	0.820338
$231$	−2.71123	−0.178386
$232$	9.45454	0.620721
$233$	24.1164	1.57992	0.789959	−	0.613159i	$-0.210102\pi$
$233$	24.1164	1.57992	0.789959	+	0.613159i	$0.210102\pi$
$234$	−19.6356	−1.28362
$235$	6.77537	0.441976
$236$	−6.28651	−0.409217
$237$	−34.5517	−2.24438
$238$	58.2719	3.77720
$239$	−3.54125	−0.229064	−0.114532	−	0.993420i	$-0.536537\pi$
$239$	−3.54125	−0.229064	−0.114532	+	0.993420i	$0.536537\pi$
$240$	−42.6760	−2.75472
$241$	3.02102	0.194601	0.0973006	−	0.995255i	$-0.468979\pi$
$241$	3.02102	0.194601	0.0973006	+	0.995255i	$0.468979\pi$
$242$	30.1745	1.93969
$243$	−15.6743	−1.00551
$244$	22.1920	1.42070
$245$	−4.61519	−0.294854
$246$	−60.3589	−3.84834
$247$	5.33289	0.339324
$248$	46.8876	2.97736
$249$	5.62730	0.356616
$250$	−23.3785	−1.47858
$251$	13.6806	0.863514	0.431757	−	0.901990i	$-0.357894\pi$
$251$	13.6806	0.863514	0.431757	+	0.901990i	$0.357894\pi$
$252$	−94.4875	−5.95215
$253$	1.36042	0.0855289
$254$	53.2252	3.33964
$255$	−15.7911	−0.988877
$256$	69.5796	4.34873
$257$	0.487370	0.0304013	0.0152007	−	0.999884i	$-0.495161\pi$
$257$	0.487370	0.0304013	0.0152007	+	0.999884i	$0.495161\pi$
$258$	−19.5145	−1.21492
$259$	3.46221	0.215131
$260$	−7.64716	−0.474257
$261$	−4.56382	−0.282494
$262$	−22.3966	−1.38367
$263$	−3.69832	−0.228048	−0.114024	−	0.993478i	$-0.536374\pi$
$263$	−3.69832	−0.228048	−0.114024	+	0.993478i	$0.536374\pi$
$264$	−7.85983	−0.483739
$265$	−3.33690	−0.204984
$266$	34.7738	2.13212
$267$	4.63549	0.283687
$268$	−13.7211	−0.838152
$269$	5.63716	0.343704	0.171852	−	0.985123i	$-0.445025\pi$
$269$	5.63716	0.343704	0.171852	+	0.985123i	$0.445025\pi$
$270$	13.2123	0.804074
$271$	−10.2208	−0.620872	−0.310436	−	0.950594i	$-0.600475\pi$
$271$	−10.2208	−0.620872	−0.310436	+	0.950594i	$0.600475\pi$
$272$	100.298	6.08145
$273$	−14.2252	−0.860949
$274$	18.9168	1.14281
$275$	−1.15848	−0.0698590
$276$	76.7683	4.62091
$277$	29.7247	1.78598	0.892991	−	0.450074i	$-0.148602\pi$
$277$	29.7247	1.78598	0.892991	+	0.450074i	$0.148602\pi$
$278$	−50.3621	−3.02052
$279$	−22.6332	−1.35501
$280$	−32.1596	−1.92190
$281$	15.2856	0.911864	0.455932	−	0.890015i	$-0.349306\pi$
$281$	15.2856	0.911864	0.455932	+	0.890015i	$0.349306\pi$
$282$	56.6520	3.37358
$283$	25.6100	1.52235	0.761177	−	0.648544i	$-0.224622\pi$
$283$	25.6100	1.52235	0.761177	+	0.648544i	$0.224622\pi$
$284$	−4.05151	−0.240413
$285$	−9.42334	−0.558191
$286$	−1.13311	−0.0670025
$287$	−27.0057	−1.59410
$288$	−123.120	−7.25490
$289$	20.1125	1.18309
$290$	−2.40848	−0.141431
$291$	16.6822	0.977927
$292$	54.4761	3.18798
$293$	−5.94313	−0.347201	−0.173601	−	0.984816i	$-0.555540\pi$
$293$	−5.94313	−0.347201	−0.173601	+	0.984816i	$0.555540\pi$
$294$	−38.5898	−2.25060
$295$	1.03284	0.0601345
$296$	10.0369	0.583383
$297$	1.44476	0.0838332
$298$	−14.0110	−0.811637
$299$	7.13780	0.412790
$300$	−65.3728	−3.77430
$301$	−8.73113	−0.503254
$302$	33.3871	1.92121
$303$	40.3475	2.31790
$304$	59.8528	3.43279
$305$	−3.64604	−0.208771
$306$	−81.5442	−4.66157
$307$	−24.2638	−1.38481	−0.692403	−	0.721511i	$-0.743448\pi$
$307$	−24.2638	−1.38481	−0.692403	+	0.721511i	$0.743448\pi$
$308$	−5.45262	−0.310692
$309$	−6.81896	−0.387917
$310$	−11.9443	−0.678391
$311$	−16.4318	−0.931761	−0.465880	−	0.884848i	$-0.654262\pi$
$311$	−16.4318	−0.931761	−0.465880	+	0.884848i	$0.654262\pi$
$312$	−41.2386	−2.33468
$313$	−12.3122	−0.695928	−0.347964	−	0.937508i	$-0.613127\pi$
$313$	−12.3122	−0.695928	−0.347964	+	0.937508i	$0.613127\pi$
$314$	57.5646	3.24856
$315$	15.5238	0.874669
$316$	−69.4877	−3.90899
$317$	9.91096	0.556655	0.278327	−	0.960486i	$-0.410220\pi$
$317$	9.91096	0.556655	0.278327	+	0.960486i	$0.410220\pi$
$318$	−27.9013	−1.56463
$319$	−0.263366	−0.0147457
$320$	−34.5012	−1.92867
$321$	−11.9279	−0.665749
$322$	46.5429	2.59373
$323$	22.1469	1.23229
$324$	−0.345947	−0.0192193
$325$	−6.07827	−0.337162
$326$	−2.76277	−0.153016
$327$	50.8805	2.81370
$328$	−78.2890	−4.32279
$329$	25.3472	1.39743
$330$	2.00224	0.110220
$331$	−9.06596	−0.498310	−0.249155	−	0.968464i	$-0.580153\pi$
$331$	−9.06596	−0.498310	−0.249155	+	0.968464i	$0.580153\pi$
$332$	11.3172	0.621111
$333$	−4.84493	−0.265501
$334$	−40.6899	−2.22645
$335$	2.25432	0.123166
$336$	−159.654	−8.70984
$337$	7.85340	0.427802	0.213901	−	0.976855i	$-0.431383\pi$
$337$	7.85340	0.427802	0.213901	+	0.976855i	$0.431383\pi$
$338$	29.9709	1.63020
$339$	22.6894	1.23232
$340$	−31.7578	−1.72231
$341$	−1.30610	−0.0707293
$342$	−48.6615	−2.63131
$343$	6.96972	0.376329
$344$	−25.3114	−1.36470
$345$	−12.6127	−0.679042
$346$	−27.2149	−1.46308
$347$	−3.72324	−0.199874	−0.0999369	−	0.994994i	$-0.531864\pi$
$347$	−3.72324	−0.199874	−0.0999369	+	0.994994i	$0.531864\pi$
$348$	−14.8617	−0.796670
$349$	36.9960	1.98035	0.990175	−	0.139837i	$-0.0446577\pi$
$349$	36.9960	1.98035	0.990175	+	0.139837i	$0.0446577\pi$
$350$	−39.6341	−2.11853
$351$	7.58029	0.404606
$352$	−7.10491	−0.378693
$353$	−13.0029	−0.692073	−0.346036	−	0.938221i	$-0.612473\pi$
$353$	−13.0029	−0.692073	−0.346036	+	0.938221i	$0.612473\pi$
$354$	8.63608	0.459003
$355$	0.665643	0.0353287
$356$	9.32253	0.494093
$357$	−59.0757	−3.12662
$358$	−49.3646	−2.60900
$359$	16.1855	0.854240	0.427120	−	0.904195i	$-0.359528\pi$
$359$	16.1855	0.854240	0.427120	+	0.904195i	$0.359528\pi$
$360$	45.0034	2.37189
$361$	−5.78383	−0.304412
$362$	−53.3845	−2.80583
$363$	−30.5907	−1.60560
$364$	−28.6086	−1.49950
$365$	−8.95017	−0.468473
$366$	−30.4862	−1.59354
$367$	−30.6822	−1.60160	−0.800799	−	0.598933i	$-0.795592\pi$
$367$	−30.6822	−1.60160	−0.800799	+	0.598933i	$0.795592\pi$
$368$	80.1098	4.17601
$369$	37.7911	1.96732
$370$	−2.55683	−0.132923
$371$	−12.4836	−0.648115
$372$	−73.7031	−3.82133
$373$	33.1004	1.71387	0.856937	−	0.515421i	$-0.172364\pi$
$373$	33.1004	1.71387	0.856937	+	0.515421i	$0.172364\pi$
$374$	−4.70570	−0.243326
$375$	23.7010	1.22391
$376$	73.4810	3.78949
$377$	−1.38182	−0.0711673
$378$	49.4282	2.54231
$379$	−10.2943	−0.528784	−0.264392	−	0.964415i	$-0.585171\pi$
$379$	−10.2943	−0.528784	−0.264392	+	0.964415i	$0.585171\pi$
$380$	−18.9515	−0.972190
$381$	−53.9593	−2.76442
$382$	−0.636514	−0.0325669
$383$	29.9566	1.53071	0.765354	−	0.643609i	$-0.222564\pi$
$383$	29.9566	1.53071	0.765354	+	0.643609i	$0.222564\pi$
$384$	−146.128	−7.45706
$385$	0.895839	0.0456562
$386$	17.0601	0.868335
$387$	12.2181	0.621083
$388$	33.5499	1.70324
$389$	20.0836	1.01828	0.509139	−	0.860684i	$-0.329964\pi$
$389$	20.0836	1.01828	0.509139	+	0.860684i	$0.329964\pi$
$390$	10.5053	0.531955
$391$	29.6425	1.49908
$392$	−50.0532	−2.52807
$393$	22.7055	1.14534
$394$	24.8785	1.25336
$395$	11.4165	0.574426
$396$	7.63026	0.383435
$397$	−4.25426	−0.213515	−0.106758	−	0.994285i	$-0.534047\pi$
$397$	−4.25426	−0.213515	−0.106758	+	0.994285i	$0.534047\pi$
$398$	−38.3260	−1.92111
$399$	−35.2534	−1.76488
$400$	−68.2184	−3.41092
$401$	25.6003	1.27842	0.639208	−	0.769034i	$-0.279262\pi$
$401$	25.6003	1.27842	0.639208	+	0.769034i	$0.279262\pi$
$402$	18.8494	0.940122
$403$	−6.85280	−0.341362
$404$	81.1436	4.03705
$405$	0.0568374	0.00282427
$406$	−9.01031	−0.447174
$407$	−0.279588	−0.0138587
$408$	−171.259	−8.47860
$409$	−10.6323	−0.525733	−0.262866	−	0.964832i	$-0.584668\pi$
$409$	−10.6323	−0.525733	−0.262866	+	0.964832i	$0.584668\pi$
$410$	19.9436	0.984945
$411$	−19.1777	−0.945968
$412$	−13.7137	−0.675628
$413$	3.86394	0.190132
$414$	−65.1309	−3.20101
$415$	−1.85936	−0.0912723
$416$	−37.2778	−1.82769
$417$	51.0567	2.50026
$418$	−2.80813	−0.137350
$419$	23.6313	1.15447	0.577233	−	0.816579i	$-0.304132\pi$
$419$	23.6313	1.15447	0.577233	+	0.816579i	$0.304132\pi$
$420$	50.5520	2.46669
$421$	27.4994	1.34024	0.670118	−	0.742254i	$-0.266243\pi$
$421$	27.4994	1.34024	0.670118	+	0.742254i	$0.266243\pi$
$422$	−33.8701	−1.64877
$423$	−35.4702	−1.72462
$424$	−36.1897	−1.75753
$425$	−25.2424	−1.22443
$426$	5.56575	0.269661
$427$	−13.6401	−0.660090
$428$	−23.9884	−1.15952
$429$	1.14874	0.0554619
$430$	6.44792	0.310946
$431$	−37.1287	−1.78843	−0.894214	−	0.447640i	$-0.852264\pi$
$431$	−37.1287	−1.78843	−0.894214	+	0.447640i	$0.852264\pi$
$432$	85.0760	4.09322
$433$	−37.2597	−1.79059	−0.895293	−	0.445477i	$-0.853034\pi$
$433$	−37.2597	−1.79059	−0.895293	+	0.445477i	$0.853034\pi$
$434$	−44.6845	−2.14492
$435$	2.44170	0.117071
$436$	102.327	4.90056
$437$	17.6892	0.846187
$438$	−74.8365	−3.57582
$439$	−12.3615	−0.589983	−0.294991	−	0.955500i	$-0.595317\pi$
$439$	−12.3615	−0.589983	−0.294991	+	0.955500i	$0.595317\pi$
$440$	2.59702	0.123808
$441$	24.1613	1.15054
$442$	−24.6897	−1.17437
$443$	9.18189	0.436245	0.218122	−	0.975921i	$-0.430007\pi$
$443$	9.18189	0.436245	0.218122	+	0.975921i	$0.430007\pi$
$444$	−15.7771	−0.748748
$445$	−1.53165	−0.0726070
$446$	45.3848	2.14903
$447$	14.2043	0.671840
$448$	−129.071	−6.09805
$449$	20.0323	0.945382	0.472691	−	0.881228i	$-0.343283\pi$
$449$	20.0323	0.945382	0.472691	+	0.881228i	$0.343283\pi$
$450$	55.4629	2.61455
$451$	2.18082	0.102691
$452$	45.6310	2.14630
$453$	−33.8476	−1.59030
$454$	−65.8903	−3.09238
$455$	4.70026	0.220351
$456$	−102.199	−4.78591
$457$	10.0055	0.468037	0.234018	−	0.972232i	$-0.424812\pi$
$457$	10.0055	0.468037	0.234018	+	0.972232i	$0.424812\pi$
$458$	40.8311	1.90791
$459$	31.4801	1.46936
$460$	−25.3656	−1.18268
$461$	−27.2196	−1.26774	−0.633872	−	0.773438i	$-0.718535\pi$
$461$	−27.2196	−1.26774	−0.633872	+	0.773438i	$0.718535\pi$
$462$	7.49052	0.348491
$463$	−6.96503	−0.323693	−0.161846	−	0.986816i	$-0.551745\pi$
$463$	−6.96503	−0.323693	−0.161846	+	0.986816i	$0.551745\pi$
$464$	−15.5086	−0.719968
$465$	12.1091	0.561544
$466$	−66.6282	−3.08649
$467$	−10.6868	−0.494528	−0.247264	−	0.968948i	$-0.579531\pi$
$467$	−10.6868	−0.494528	−0.247264	+	0.968948i	$0.579531\pi$
$468$	40.0342	1.85058
$469$	8.43357	0.389426
$470$	−18.7188	−0.863434
$471$	−58.3586	−2.68902
$472$	11.2015	0.515591
$473$	0.705075	0.0324194
$474$	95.4586	4.38456
$475$	−15.0634	−0.691156
$476$	−118.808	−5.44557
$477$	17.4692	0.799860
$478$	9.78366	0.447494
$479$	21.0355	0.961137	0.480568	−	0.876957i	$-0.340430\pi$
$479$	21.0355	0.961137	0.480568	+	0.876957i	$0.340430\pi$
$480$	65.8707	3.00657
$481$	−1.46693	−0.0668864
$482$	−8.34640	−0.380168
$483$	−47.1849	−2.14699
$484$	−61.5217	−2.79644
$485$	−5.51208	−0.250291
$486$	43.3046	1.96434
$487$	31.6628	1.43478	0.717388	−	0.696674i	$-0.245337\pi$
$487$	31.6628	1.43478	0.717388	+	0.696674i	$0.245337\pi$
$488$	−39.5424	−1.79000
$489$	2.80088	0.126660
$490$	12.7507	0.576019
$491$	−3.45732	−0.156027	−0.0780133	−	0.996952i	$-0.524858\pi$
$491$	−3.45732	−0.156027	−0.0780133	+	0.996952i	$0.524858\pi$
$492$	123.063	5.54813
$493$	−5.73854	−0.258451
$494$	−14.7336	−0.662895
$495$	−1.25361	−0.0563458
$496$	−76.9112	−3.45341
$497$	2.49022	0.111702
$498$	−15.5470	−0.696676
$499$	22.3240	0.999361	0.499681	−	0.866210i	$-0.333451\pi$
$499$	22.3240	0.999361	0.499681	+	0.866210i	$0.333451\pi$
$500$	47.6655	2.13166
$501$	41.2512	1.84297
$502$	−37.7965	−1.68694
$503$	−29.9701	−1.33630	−0.668151	−	0.744026i	$-0.732914\pi$
$503$	−29.9701	−1.33630	−0.668151	+	0.744026i	$0.732914\pi$
$504$	168.361	7.49939
$505$	−13.3315	−0.593244
$506$	−3.75853	−0.167087
$507$	−30.3843	−1.34941
$508$	−108.519	−4.81474
$509$	38.2400	1.69496	0.847480	−	0.530828i	$-0.178119\pi$
$509$	38.2400	1.69496	0.847480	+	0.530828i	$0.178119\pi$
$510$	43.6272	1.93184
$511$	−33.4832	−1.48121
$512$	−87.8884	−3.88415
$513$	18.7857	0.829411
$514$	−1.34649	−0.0593912
$515$	2.25310	0.0992835
$516$	39.7873	1.75154
$517$	−2.04689	−0.0900220
$518$	−9.56531	−0.420275
$519$	27.5903	1.21108
$520$	13.6260	0.597538
$521$	29.6578	1.29933	0.649666	−	0.760220i	$-0.274909\pi$
$521$	29.6578	1.29933	0.649666	+	0.760220i	$0.274909\pi$
$522$	12.6088	0.551872
$523$	9.41652	0.411755	0.205878	−	0.978578i	$-0.433995\pi$
$523$	9.41652	0.411755	0.205878	+	0.978578i	$0.433995\pi$
$524$	45.6636	1.99482
$525$	40.1808	1.75363
$526$	10.2176	0.445509
$527$	−28.4589	−1.23969
$528$	12.8927	0.561084
$529$	0.676015	0.0293920
$530$	9.21909	0.400452
$531$	−5.40711	−0.234648
$532$	−70.8989	−3.07386
$533$	11.4423	0.495619
$534$	−12.8068	−0.554205
$535$	3.94118	0.170392
$536$	24.4488	1.05603
$537$	50.0455	2.15962
$538$	−15.5742	−0.671451
$539$	1.39428	0.0600560
$540$	−26.9380	−1.15923
$541$	10.6419	0.457533	0.228766	−	0.973481i	$-0.426531\pi$
$541$	10.6419	0.457533	0.228766	+	0.973481i	$0.426531\pi$
$542$	28.2378	1.21292
$543$	54.1208	2.32255
$544$	−154.810	−6.63744
$545$	−16.8118	−0.720138
$546$	39.3010	1.68193
$547$	7.69953	0.329208	0.164604	−	0.986360i	$-0.447365\pi$
$547$	7.69953	0.329208	0.164604	+	0.986360i	$0.447365\pi$
$548$	−38.5688	−1.64758
$549$	19.0876	0.814639
$550$	3.20062	0.136475
$551$	−3.42447	−0.145887
$552$	−136.788	−5.82209
$553$	42.7099	1.81621
$554$	−82.1225	−3.48905
$555$	2.59210	0.110029
$556$	102.681	4.35466
$557$	14.4475	0.612162	0.306081	−	0.952005i	$-0.400982\pi$
$557$	14.4475	0.612162	0.306081	+	0.952005i	$0.400982\pi$
$558$	62.5304	2.64712
$559$	3.69936	0.156466
$560$	52.7525	2.22920
$561$	4.77061	0.201415
$562$	−42.2307	−1.78139
$563$	−46.7664	−1.97097	−0.985484	−	0.169768i	$-0.945698\pi$
$563$	−46.7664	−1.97097	−0.985484	+	0.169768i	$0.945698\pi$
$564$	−115.506	−4.86366
$565$	−7.49696	−0.315399
$566$	−70.7545	−2.97403
$567$	0.212633	0.00892974
$568$	7.21911	0.302907
$569$	−11.4600	−0.480430	−0.240215	−	0.970720i	$-0.577218\pi$
$569$	−11.4600	−0.480430	−0.240215	+	0.970720i	$0.577218\pi$
$570$	26.0345	1.09047
$571$	9.31625	0.389873	0.194936	−	0.980816i	$-0.437550\pi$
$571$	9.31625	0.389873	0.194936	+	0.980816i	$0.437550\pi$
$572$	2.31026	0.0965970
$573$	0.645294	0.0269575
$574$	74.6105	3.11418
$575$	−20.1616	−0.840795
$576$	180.619	7.52581
$577$	−0.851880	−0.0354642	−0.0177321	−	0.999843i	$-0.505645\pi$
$577$	−0.851880	−0.0354642	−0.0177321	+	0.999843i	$0.505645\pi$
$578$	−55.5663	−2.31125
$579$	−17.2954	−0.718772
$580$	4.91056	0.203900
$581$	−6.95600	−0.288583
$582$	−46.0891	−1.91045
$583$	1.00810	0.0417513
$584$	−97.0674	−4.01668
$585$	−6.57742	−0.271943
$586$	16.4195	0.678283
$587$	−27.2441	−1.12448	−0.562241	−	0.826973i	$-0.690061\pi$
$587$	−27.2441	−1.12448	−0.562241	+	0.826973i	$0.690061\pi$
$588$	78.6792	3.24467
$589$	−16.9829	−0.699767
$590$	−2.85351	−0.117477
$591$	−25.2217	−1.03748
$592$	−16.4639	−0.676660
$593$	−11.8585	−0.486972	−0.243486	−	0.969904i	$-0.578291\pi$
$593$	−11.8585	−0.486972	−0.243486	+	0.969904i	$0.578291\pi$
$594$	−3.99153	−0.163774
$595$	19.5196	0.800227
$596$	28.5665	1.17013
$597$	38.8547	1.59022
$598$	−19.7201	−0.806416
$599$	33.8588	1.38343	0.691717	−	0.722169i	$-0.256855\pi$
$599$	33.8588	1.38343	0.691717	+	0.722169i	$0.256855\pi$
$600$	116.483	4.75542
$601$	23.9307	0.976155	0.488078	−	0.872800i	$-0.337698\pi$
$601$	23.9307	0.976155	0.488078	+	0.872800i	$0.337698\pi$
$602$	24.1221	0.983145
$603$	−11.8017	−0.480603
$604$	−68.0716	−2.76979
$605$	10.1077	0.410937
$606$	−111.471	−4.52819
$607$	−39.9833	−1.62287	−0.811435	−	0.584442i	$-0.801313\pi$
$607$	−39.9833	−1.62287	−0.811435	+	0.584442i	$0.801313\pi$
$608$	−92.3831	−3.74663
$609$	9.13460	0.370153
$610$	10.0732	0.407851
$611$	−10.7395	−0.434475
$612$	166.257	6.72055
$613$	23.3360	0.942533	0.471266	−	0.881991i	$-0.343797\pi$
$613$	23.3360	0.942533	0.471266	+	0.881991i	$0.343797\pi$
$614$	67.0352	2.70532
$615$	−20.2187	−0.815297
$616$	9.71566	0.391455
$617$	6.91326	0.278317	0.139159	−	0.990270i	$-0.455560\pi$
$617$	6.91326	0.278317	0.139159	+	0.990270i	$0.455560\pi$
$618$	18.8392	0.757825
$619$	17.2422	0.693023	0.346512	−	0.938046i	$-0.387366\pi$
$619$	17.2422	0.693023	0.346512	+	0.938046i	$0.387366\pi$
$620$	24.3528	0.978031
$621$	25.1437	1.00898
$622$	45.3973	1.82026
$623$	−5.73000	−0.229568
$624$	67.6451	2.70797
$625$	12.8864	0.515457
$626$	34.0158	1.35955
$627$	2.84686	0.113693
$628$	−117.366	−4.68342
$629$	−6.09200	−0.242904
$630$	−42.8888	−1.70873
$631$	22.6982	0.903601	0.451801	−	0.892119i	$-0.350782\pi$
$631$	22.6982	0.903601	0.451801	+	0.892119i	$0.350782\pi$
$632$	123.815	4.92512
$633$	34.3373	1.36478
$634$	−27.3817	−1.08747
$635$	17.8291	0.707526
$636$	56.8870	2.25571
$637$	7.31547	0.289850
$638$	0.727620	0.0288068
$639$	−3.48475	−0.137855
$640$	48.2832	1.90856
$641$	4.06360	0.160502	0.0802512	−	0.996775i	$-0.474428\pi$
$641$	4.06360	0.160502	0.0802512	+	0.996775i	$0.474428\pi$
$642$	32.9540	1.30059
$643$	24.1741	0.953334	0.476667	−	0.879084i	$-0.341845\pi$
$643$	24.1741	0.953334	0.476667	+	0.879084i	$0.341845\pi$
$644$	−94.8945	−3.73937
$645$	−6.53686	−0.257389
$646$	−61.1868	−2.40736
$647$	39.6516	1.55887	0.779433	−	0.626486i	$-0.215507\pi$
$647$	39.6516	1.55887	0.779433	+	0.626486i	$0.215507\pi$
$648$	0.616419	0.0242152
$649$	−0.312030	−0.0122482
$650$	16.7929	0.658671
$651$	45.3009	1.77548
$652$	5.63291	0.220602
$653$	−25.7095	−1.00609	−0.503046	−	0.864260i	$-0.667787\pi$
$653$	−25.7095	−1.00609	−0.503046	+	0.864260i	$0.667787\pi$
$654$	−140.571	−5.49677
$655$	−7.50230	−0.293139
$656$	128.420	5.01396
$657$	46.8556	1.82801
$658$	−70.0284	−2.72999
$659$	−6.13647	−0.239043	−0.119521	−	0.992832i	$-0.538136\pi$
$659$	−6.13647	−0.239043	−0.119521	+	0.992832i	$0.538136\pi$
$660$	−4.08229	−0.158903
$661$	−10.5010	−0.408442	−0.204221	−	0.978925i	$-0.565466\pi$
$661$	−10.5010	−0.408442	−0.204221	+	0.978925i	$0.565466\pi$
$662$	25.0472	0.973486
$663$	25.0302	0.972094
$664$	−20.1653	−0.782567
$665$	11.6483	0.451703
$666$	13.3854	0.518676
$667$	−4.58348	−0.177473
$668$	82.9612	3.20986
$669$	−46.0108	−1.77888
$670$	−6.22816	−0.240615
$671$	1.10149	0.0425227
$672$	246.427	9.50613
$673$	−5.79030	−0.223200	−0.111600	−	0.993753i	$-0.535597\pi$
$673$	−5.79030	−0.223200	−0.111600	+	0.993753i	$0.535597\pi$
$674$	−21.6972	−0.835744
$675$	−21.4114	−0.824126
$676$	−61.1064	−2.35025
$677$	8.12218	0.312161	0.156080	−	0.987744i	$-0.450114\pi$
$677$	8.12218	0.312161	0.156080	+	0.987744i	$0.450114\pi$
$678$	−62.6855	−2.40742
$679$	−20.6211	−0.791365
$680$	56.5871	2.17002
$681$	66.7991	2.55975
$682$	3.60846	0.138175
$683$	−30.1228	−1.15262	−0.576308	−	0.817233i	$-0.695507\pi$
$683$	−30.1228	−1.15262	−0.576308	+	0.817233i	$0.695507\pi$
$684$	99.2141	3.79355
$685$	6.33666	0.242111
$686$	−19.2557	−0.735188
$687$	−41.3944	−1.57929
$688$	41.5191	1.58290
$689$	5.28927	0.201505
$690$	34.8459	1.32656
$691$	37.6736	1.43317	0.716586	−	0.697499i	$-0.245704\pi$
$691$	37.6736	1.43317	0.716586	+	0.697499i	$0.245704\pi$
$692$	55.4874	2.10932
$693$	−4.68987	−0.178153
$694$	10.2865	0.390468
$695$	−16.8700	−0.639917
$696$	26.4811	1.00376
$697$	47.5184	1.79989
$698$	−102.211	−3.86876
$699$	67.5472	2.55487
$700$	80.8084	3.05427
$701$	14.9423	0.564364	0.282182	−	0.959361i	$-0.408942\pi$
$701$	14.9423	0.564364	0.282182	+	0.959361i	$0.408942\pi$
$702$	−20.9426	−0.790428
$703$	−3.63541	−0.137112
$704$	10.4231	0.392834
$705$	18.9770	0.714715
$706$	35.9239	1.35202
$707$	−49.8741	−1.87571
$708$	−17.6078	−0.661741
$709$	−22.8546	−0.858322	−0.429161	−	0.903228i	$-0.641191\pi$
$709$	−22.8546	−0.858322	−0.429161	+	0.903228i	$0.641191\pi$
$710$	−1.83902	−0.0690172
$711$	−59.7672	−2.24145
$712$	−16.6112	−0.622531
$713$	−22.7307	−0.851271
$714$	163.213	6.10808
$715$	−0.379565	−0.0141949
$716$	100.648	3.76138
$717$	−9.91861	−0.370417
$718$	−44.7170	−1.66882
$719$	33.5019	1.24941	0.624705	−	0.780861i	$-0.285219\pi$
$719$	33.5019	1.24941	0.624705	+	0.780861i	$0.285219\pi$
$720$	−73.8205	−2.75113
$721$	8.42902	0.313913
$722$	15.9794	0.594692
$723$	8.46153	0.314688
$724$	108.844	4.04514
$725$	3.90311	0.144958
$726$	84.5153	3.13666
$727$	−20.1723	−0.748148	−0.374074	−	0.927399i	$-0.622039\pi$
$727$	−20.1723	−0.748148	−0.374074	+	0.927399i	$0.622039\pi$
$728$	50.9757	1.88929
$729$	−43.7177	−1.61917
$730$	24.7273	0.915197
$731$	15.3630	0.568222
$732$	62.1571	2.29739
$733$	−9.63131	−0.355741	−0.177870	−	0.984054i	$-0.556921\pi$
$733$	−9.63131	−0.355741	−0.177870	+	0.984054i	$0.556921\pi$
$734$	84.7680	3.12884
$735$	−12.9266	−0.476805
$736$	−123.650	−4.55780
$737$	−0.681046	−0.0250866
$738$	−104.408	−3.84332
$739$	43.2283	1.59018	0.795090	−	0.606492i	$-0.207424\pi$
$739$	43.2283	1.59018	0.795090	+	0.606492i	$0.207424\pi$
$740$	5.21303	0.191635
$741$	14.9368	0.548717
$742$	34.4893	1.26614
$743$	50.7456	1.86167	0.930837	−	0.365434i	$-0.119079\pi$
$743$	50.7456	1.86167	0.930837	+	0.365434i	$0.119079\pi$
$744$	131.327	4.81466
$745$	−4.69334	−0.171951
$746$	−91.4489	−3.34818
$747$	9.73405	0.356150
$748$	9.59426	0.350801
$749$	14.7442	0.538742
$750$	−65.4803	−2.39100
$751$	38.1525	1.39220	0.696102	−	0.717943i	$-0.254916\pi$
$751$	38.1525	1.39220	0.696102	+	0.717943i	$0.254916\pi$
$752$	−120.533	−4.39539
$753$	38.3178	1.39638
$754$	3.81765	0.139031
$755$	11.1838	0.407021
$756$	−100.777	−3.66523
$757$	−17.5113	−0.636460	−0.318230	−	0.948014i	$-0.603088\pi$
$757$	−17.5113	−0.636460	−0.318230	+	0.948014i	$0.603088\pi$
$758$	28.4409	1.03302
$759$	3.81037	0.138308
$760$	33.7684	1.22491
$761$	−24.2784	−0.880091	−0.440045	−	0.897976i	$-0.645038\pi$
$761$	−24.2784	−0.880091	−0.440045	+	0.897976i	$0.645038\pi$
$762$	149.077	5.40050
$763$	−62.8942	−2.27692
$764$	1.29776	0.0469515
$765$	−27.3153	−0.987586
$766$	−82.7631	−2.99035
$767$	−1.63715	−0.0591139
$768$	194.884	7.03228
$769$	40.7553	1.46967	0.734837	−	0.678244i	$-0.237259\pi$
$769$	40.7553	1.46967	0.734837	+	0.678244i	$0.237259\pi$
$770$	−2.47500	−0.0891928
$771$	1.36507	0.0491616
$772$	−34.7831	−1.25187
$773$	−28.9542	−1.04141	−0.520705	−	0.853737i	$-0.674331\pi$
$773$	−28.9542	−1.04141	−0.520705	+	0.853737i	$0.674331\pi$
$774$	−33.7559	−1.21333
$775$	19.3566	0.695308
$776$	−59.7803	−2.14599
$777$	9.69725	0.347887
$778$	−55.4864	−1.98928
$779$	28.3566	1.01598
$780$	−21.4188	−0.766916
$781$	−0.201096	−0.00719577
$782$	−81.8954	−2.92857
$783$	−4.86762	−0.173954
$784$	82.1039	2.93228
$785$	19.2827	0.688229
$786$	−62.7302	−2.23751
$787$	16.4020	0.584667	0.292334	−	0.956316i	$-0.405568\pi$
$787$	16.4020	0.584667	0.292334	+	0.956316i	$0.405568\pi$
$788$	−50.7239	−1.80696
$789$	−10.3585	−0.368774
$790$	−31.5412	−1.12218
$791$	−28.0467	−0.997225
$792$	−13.5958	−0.483107
$793$	5.77928	0.205228
$794$	11.7536	0.417118
$795$	−9.34625	−0.331477
$796$	78.1415	2.76965
$797$	−8.03704	−0.284687	−0.142343	−	0.989817i	$-0.545464\pi$
$797$	−8.03704	−0.284687	−0.142343	+	0.989817i	$0.545464\pi$
$798$	97.3972	3.44782
$799$	−44.6001	−1.57784
$800$	105.296	3.72276
$801$	8.01842	0.283317
$802$	−70.7277	−2.49748
$803$	2.70391	0.0954189
$804$	−38.4313	−1.35537
$805$	15.5907	0.549500
$806$	18.9327	0.666877
$807$	15.7890	0.555800
$808$	−144.584	−5.08646
$809$	4.75154	0.167055	0.0835276	−	0.996505i	$-0.473381\pi$
$809$	4.75154	0.167055	0.0835276	+	0.996505i	$0.473381\pi$
$810$	−0.157029	−0.00551743
$811$	−42.5501	−1.49414	−0.747068	−	0.664748i	$-0.768539\pi$
$811$	−42.5501	−1.49414	−0.747068	+	0.664748i	$0.768539\pi$
$812$	18.3708	0.644688
$813$	−28.6273	−1.00400
$814$	0.772438	0.0270739
$815$	−0.925460	−0.0324174
$816$	280.922	9.83425
$817$	9.16790	0.320744
$818$	29.3746	1.02706
$819$	−24.6066	−0.859825
$820$	−40.6623	−1.41999
$821$	−18.4415	−0.643613	−0.321806	−	0.946806i	$-0.604290\pi$
$821$	−18.4415	−0.643613	−0.321806	+	0.946806i	$0.604290\pi$
$822$	52.9837	1.84802
$823$	21.9806	0.766194	0.383097	−	0.923708i	$-0.374858\pi$
$823$	21.9806	0.766194	0.383097	+	0.923708i	$0.374858\pi$
$824$	24.4356	0.851254
$825$	−3.24476	−0.112968
$826$	−10.6752	−0.371438
$827$	17.4815	0.607893	0.303946	−	0.952689i	$-0.401696\pi$
$827$	17.4815	0.607893	0.303946	+	0.952689i	$0.401696\pi$
$828$	132.793	4.61487
$829$	16.6670	0.578869	0.289434	−	0.957198i	$-0.406533\pi$
$829$	16.6670	0.578869	0.289434	+	0.957198i	$0.406533\pi$
$830$	5.13699	0.178307
$831$	83.2553	2.88809
$832$	54.6873	1.89594
$833$	30.3803	1.05262
$834$	−141.058	−4.88444
$835$	−13.6301	−0.471690
$836$	5.72538	0.198016
$837$	−24.1398	−0.834394
$838$	−65.2880	−2.25534
$839$	−26.0078	−0.897891	−0.448945	−	0.893559i	$-0.648200\pi$
$839$	−26.0078	−0.897891	−0.448945	+	0.893559i	$0.648200\pi$
$840$	−90.0753	−3.10789
$841$	−28.1127	−0.969403
$842$	−75.9745	−2.61825
$843$	42.8132	1.47457
$844$	69.0564	2.37702
$845$	10.0395	0.345369
$846$	97.9960	3.36917
$847$	37.8137	1.29929
$848$	59.3631	2.03854
$849$	71.7304	2.46178
$850$	69.7389	2.39202
$851$	−4.86580	−0.166797
$852$	−11.3478	−0.388769
$853$	−41.7091	−1.42809	−0.714046	−	0.700099i	$-0.753139\pi$
$853$	−41.7091	−1.42809	−0.714046	+	0.700099i	$0.753139\pi$
$854$	37.6845	1.28954
$855$	−16.3004	−0.557462
$856$	42.7433	1.46094
$857$	−49.7046	−1.69788	−0.848939	−	0.528491i	$-0.822758\pi$
$857$	−49.7046	−1.69788	−0.848939	+	0.528491i	$0.822758\pi$
$858$	−3.17372	−0.108349
$859$	25.1831	0.859235	0.429618	−	0.903011i	$-0.358648\pi$
$859$	25.1831	0.859235	0.429618	+	0.903011i	$0.358648\pi$
$860$	−13.1464	−0.448289
$861$	−75.6397	−2.57779
$862$	102.578	3.49383
$863$	−31.8707	−1.08489	−0.542445	−	0.840091i	$-0.682501\pi$
$863$	−31.8707	−1.08489	−0.542445	+	0.840091i	$0.682501\pi$
$864$	−131.315	−4.46744
$865$	−9.11632	−0.309964
$866$	102.940	3.49805
$867$	56.3327	1.91316
$868$	91.1055	3.09232
$869$	−3.44901	−0.117000
$870$	−6.74587	−0.228707
$871$	−3.57328	−0.121076
$872$	−182.329	−6.17445
$873$	28.8567	0.976650
$874$	−48.8711	−1.65309
$875$	−29.2971	−0.990423
$876$	152.581	5.15524
$877$	−22.0466	−0.744459	−0.372230	−	0.928141i	$-0.621407\pi$
$877$	−22.0466	−0.744459	−0.372230	+	0.928141i	$0.621407\pi$
$878$	34.1520	1.15258
$879$	−16.6460	−0.561455
$880$	−4.25998	−0.143604
$881$	−37.3081	−1.25694	−0.628470	−	0.777833i	$-0.716319\pi$
$881$	−37.3081	−1.25694	−0.628470	+	0.777833i	$0.716319\pi$
$882$	−66.7521	−2.24766
$883$	43.0393	1.44839	0.724193	−	0.689597i	$-0.242212\pi$
$883$	43.0393	1.44839	0.724193	+	0.689597i	$0.242212\pi$
$884$	50.3388	1.69308
$885$	2.89287	0.0972428
$886$	−25.3675	−0.852237
$887$	−41.9923	−1.40996	−0.704982	−	0.709226i	$-0.749045\pi$
$887$	−41.9923	−1.40996	−0.704982	+	0.709226i	$0.749045\pi$
$888$	28.1122	0.943382
$889$	66.7000	2.23705
$890$	4.23159	0.141843
$891$	−0.0171710	−0.000575250 0
$892$	−92.5332	−3.09824
$893$	−26.6151	−0.890641
$894$	−39.2432	−1.31249
$895$	−16.5359	−0.552734
$896$	180.631	6.03446
$897$	19.9921	0.667518
$898$	−55.3446	−1.84687
$899$	4.40047	0.146764
$900$	−113.081	−3.76937
$901$	21.9657	0.731784
$902$	−6.02511	−0.200614
$903$	−24.4549	−0.813807
$904$	−81.3068	−2.70423
$905$	−17.8825	−0.594433
$906$	93.5132	3.10677
$907$	−38.3250	−1.27256	−0.636281	−	0.771458i	$-0.719528\pi$
$907$	−38.3250	−1.27256	−0.636281	+	0.771458i	$0.719528\pi$
$908$	134.341	4.45827
$909$	69.7926	2.31488
$910$	−12.9857	−0.430473
$911$	−18.5491	−0.614560	−0.307280	−	0.951619i	$-0.599419\pi$
$911$	−18.5491	−0.614560	−0.307280	+	0.951619i	$0.599419\pi$
$912$	167.640	5.55113
$913$	0.561726	0.0185904
$914$	−27.6429	−0.914345
$915$	−10.2121	−0.337602
$916$	−83.2490	−2.75063
$917$	−28.0667	−0.926843
$918$	−86.9723	−2.87051
$919$	−45.8441	−1.51226	−0.756128	−	0.654424i	$-0.772911\pi$
$919$	−45.8441	−1.51226	−0.756128	+	0.654424i	$0.772911\pi$
$920$	45.1972	1.49011
$921$	−67.9599	−2.23935
$922$	75.2016	2.47663
$923$	−1.05510	−0.0347291
$924$	−15.2721	−0.502417
$925$	4.14352	0.136238
$926$	19.2428	0.632358
$927$	−11.7954	−0.387411
$928$	23.9376	0.785791
$929$	−0.883078	−0.0289729	−0.0144864	−	0.999895i	$-0.504611\pi$
$929$	−0.883078	−0.0289729	−0.0144864	+	0.999895i	$0.504611\pi$
$930$	−33.4546	−1.09702
$931$	18.1295	0.594169
$932$	135.846	4.44977
$933$	−46.0235	−1.50674
$934$	29.5253	0.966097
$935$	−1.57629	−0.0515502
$936$	−71.3342	−2.33163
$937$	−23.2564	−0.759754	−0.379877	−	0.925037i	$-0.624034\pi$
$937$	−23.2564	−0.759754	−0.379877	+	0.925037i	$0.624034\pi$
$938$	−23.3000	−0.760773
$939$	−34.4851	−1.12538
$940$	38.1650	1.24481
$941$	−34.1110	−1.11199	−0.555994	−	0.831186i	$-0.687662\pi$
$941$	−34.1110	−1.11199	−0.555994	+	0.831186i	$0.687662\pi$
$942$	161.232	5.25321
$943$	37.9538	1.23595
$944$	−18.3742	−0.598029
$945$	16.5572	0.538606
$946$	−1.94796	−0.0633337
$947$	−10.4363	−0.339133	−0.169566	−	0.985519i	$-0.554237\pi$
$947$	−10.4363	−0.339133	−0.169566	+	0.985519i	$0.554237\pi$
$948$	−194.627	−6.32119
$949$	14.1868	0.460522
$950$	41.6167	1.35022
$951$	27.7594	0.900160
$952$	211.696	6.86112
$953$	−20.8007	−0.673799	−0.336900	−	0.941541i	$-0.609378\pi$
$953$	−20.8007	−0.673799	−0.336900	+	0.941541i	$0.609378\pi$
$954$	−48.2634	−1.56259
$955$	−0.213216	−0.00689952
$956$	−19.9475	−0.645149
$957$	−0.737657	−0.0238451
$958$	−58.1163	−1.87765
$959$	23.7059	0.765504
$960$	−96.6337	−3.11884
$961$	−9.17691	−0.296029
$962$	4.05280	0.130668
$963$	−20.6327	−0.664880
$964$	17.0172	0.548086
$965$	5.71470	0.183963
$966$	130.361	4.19430
$967$	1.65042	0.0530739	0.0265369	−	0.999648i	$-0.491552\pi$
$967$	1.65042	0.0530739	0.0265369	+	0.999648i	$0.491552\pi$
$968$	109.621	3.52336
$969$	62.0308	1.99272
$970$	15.2286	0.488962
$971$	6.14448	0.197186	0.0985929	−	0.995128i	$-0.468566\pi$
$971$	6.14448	0.197186	0.0985929	+	0.995128i	$0.468566\pi$
$972$	−88.2921	−2.83197
$973$	−63.1120	−2.02328
$974$	−87.4770	−2.80294
$975$	−17.0245	−0.545221
$976$	64.8627	2.07620
$977$	−7.58908	−0.242796	−0.121398	−	0.992604i	$-0.538738\pi$
$977$	−7.58908	−0.242796	−0.121398	+	0.992604i	$0.538738\pi$
$978$	−7.73820	−0.247440
$979$	0.462722	0.0147886
$980$	−25.9970	−0.830442
$981$	88.0125	2.81002
$982$	9.55179	0.304810
$983$	−7.43141	−0.237025	−0.118513	−	0.992953i	$-0.537813\pi$
$983$	−7.43141	−0.237025	−0.118513	+	0.992953i	$0.537813\pi$
$984$	−219.278	−6.99034
$985$	8.33369	0.265533
$986$	15.8543	0.504903
$987$	70.9944	2.25978
$988$	30.0397	0.955690
$989$	12.2708	0.390187
$990$	3.46345	0.110076
$991$	22.6255	0.718722	0.359361	−	0.933199i	$-0.382995\pi$
$991$	22.6255	0.718722	0.359361	+	0.933199i	$0.382995\pi$
$992$	118.713	3.76914
$993$	−25.3927	−0.805812
$994$	−6.87991	−0.218217
$995$	−12.8383	−0.407000
$996$	31.6981	1.00439
$997$	45.5353	1.44212	0.721058	−	0.692874i	$-0.243656\pi$
$997$	45.5353	1.44212	0.721058	+	0.692874i	$0.243656\pi$
$998$	−61.6762	−1.95233
$999$	−5.16744	−0.163491

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.1	✓	133

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.d.1.1	✓	133	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76277 q^{2} +2.80088 q^{3} +5.63291 q^{4} -0.925460 q^{5} -7.73820 q^{6} -3.46221 q^{7} -10.0369 q^{8} +4.84493 q^{9} +O(q^{10})\)	\(q-2.76277 q^{2} +2.80088 q^{3} +5.63291 q^{4} -0.925460 q^{5} -7.73820 q^{6} -3.46221 q^{7} -10.0369 q^{8} +4.84493 q^{9} +2.55683 q^{10} +0.279588 q^{11} +15.7771 q^{12} +1.46693 q^{13} +9.56531 q^{14} -2.59210 q^{15} +16.4639 q^{16} +6.09200 q^{17} -13.3854 q^{18} +3.63541 q^{19} -5.21303 q^{20} -9.69725 q^{21} -0.772438 q^{22} +4.86580 q^{23} -28.1122 q^{24} -4.14352 q^{25} -4.05280 q^{26} +5.16744 q^{27} -19.5023 q^{28} -0.941978 q^{29} +7.16139 q^{30} -4.67152 q^{31} -25.4121 q^{32} +0.783093 q^{33} -16.8308 q^{34} +3.20414 q^{35} +27.2911 q^{36} -1.00000 q^{37} -10.0438 q^{38} +4.10870 q^{39} +9.28875 q^{40} +7.80012 q^{41} +26.7913 q^{42} +2.52184 q^{43} +1.57489 q^{44} -4.48379 q^{45} -13.4431 q^{46} -7.32108 q^{47} +46.1133 q^{48} +4.98692 q^{49} +11.4476 q^{50} +17.0630 q^{51} +8.26310 q^{52} +3.60566 q^{53} -14.2765 q^{54} -0.258748 q^{55} +34.7499 q^{56} +10.1823 q^{57} +2.60247 q^{58} -1.11603 q^{59} -14.6011 q^{60} +3.93970 q^{61} +12.9063 q^{62} -16.7742 q^{63} +37.2800 q^{64} -1.35759 q^{65} -2.16351 q^{66} -2.43589 q^{67} +34.3157 q^{68} +13.6285 q^{69} -8.85230 q^{70} -0.719257 q^{71} -48.6281 q^{72} +9.67105 q^{73} +2.76277 q^{74} -11.6055 q^{75} +20.4779 q^{76} -0.967994 q^{77} -11.3514 q^{78} -12.3360 q^{79} -15.2366 q^{80} -0.0614153 q^{81} -21.5500 q^{82} +2.00912 q^{83} -54.6237 q^{84} -5.63790 q^{85} -6.96726 q^{86} -2.63837 q^{87} -2.80620 q^{88} +1.65501 q^{89} +12.3877 q^{90} -5.07883 q^{91} +27.4086 q^{92} -13.0844 q^{93} +20.2265 q^{94} -3.36442 q^{95} -71.1762 q^{96} +5.95605 q^{97} -13.7777 q^{98} +1.35459 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * q^99

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