LMFDB - Embedded newform 6023.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37815 q^{2} +0.382823 q^{3} +3.65560 q^{4} +3.62895 q^{5} -0.910412 q^{6} -2.15818 q^{7} -3.93728 q^{8} -2.85345 q^{9} +O(q^{10})$	\(q-2.37815 q^{2} +0.382823 q^{3} +3.65560 q^{4} +3.62895 q^{5} -0.910412 q^{6} -2.15818 q^{7} -3.93728 q^{8} -2.85345 q^{9} -8.63020 q^{10} -4.13952 q^{11} +1.39945 q^{12} +6.76769 q^{13} +5.13247 q^{14} +1.38925 q^{15} +2.05223 q^{16} -4.96728 q^{17} +6.78593 q^{18} -1.00000 q^{19} +13.2660 q^{20} -0.826201 q^{21} +9.84440 q^{22} -7.28337 q^{23} -1.50728 q^{24} +8.16930 q^{25} -16.0946 q^{26} -2.24084 q^{27} -7.88944 q^{28} +3.73955 q^{29} -3.30384 q^{30} +5.37967 q^{31} +2.99404 q^{32} -1.58470 q^{33} +11.8129 q^{34} -7.83193 q^{35} -10.4311 q^{36} +2.33546 q^{37} +2.37815 q^{38} +2.59083 q^{39} -14.2882 q^{40} +9.16045 q^{41} +1.96483 q^{42} +7.51653 q^{43} -15.1324 q^{44} -10.3550 q^{45} +17.3209 q^{46} +1.46743 q^{47} +0.785642 q^{48} -2.34227 q^{49} -19.4278 q^{50} -1.90159 q^{51} +24.7400 q^{52} -11.2538 q^{53} +5.32905 q^{54} -15.0221 q^{55} +8.49734 q^{56} -0.382823 q^{57} -8.89322 q^{58} -6.29114 q^{59} +5.07854 q^{60} +3.63700 q^{61} -12.7937 q^{62} +6.15824 q^{63} -11.2247 q^{64} +24.5596 q^{65} +3.76867 q^{66} +10.4776 q^{67} -18.1584 q^{68} -2.78824 q^{69} +18.6255 q^{70} -12.6529 q^{71} +11.2348 q^{72} -3.83856 q^{73} -5.55407 q^{74} +3.12740 q^{75} -3.65560 q^{76} +8.93382 q^{77} -6.16139 q^{78} -8.61876 q^{79} +7.44745 q^{80} +7.70249 q^{81} -21.7849 q^{82} -13.8507 q^{83} -3.02026 q^{84} -18.0260 q^{85} -17.8755 q^{86} +1.43159 q^{87} +16.2984 q^{88} +13.8028 q^{89} +24.6258 q^{90} -14.6059 q^{91} -26.6251 q^{92} +2.05946 q^{93} -3.48976 q^{94} -3.62895 q^{95} +1.14619 q^{96} +9.88656 q^{97} +5.57027 q^{98} +11.8119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) $ 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * 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 $

$2$	−2.37815	−1.68161	−0.840803	−	0.541341i	$-0.817917\pi$
$2$	−2.37815	−1.68161	−0.840803	+	0.541341i	$0.817917\pi$
$3$	0.382823	0.221023	0.110512	−	0.993875i	$-0.464751\pi$
$3$	0.382823	0.221023	0.110512	+	0.993875i	$0.464751\pi$
$4$	3.65560	1.82780
$5$	3.62895	1.62292	0.811458	−	0.584410i	$-0.198674\pi$
$5$	3.62895	1.62292	0.811458	+	0.584410i	$0.198674\pi$
$6$	−0.910412	−0.371674
$7$	−2.15818	−0.815715	−0.407857	−	0.913046i	$-0.633724\pi$
$7$	−2.15818	−0.815715	−0.407857	+	0.913046i	$0.633724\pi$
$8$	−3.93728	−1.39204
$9$	−2.85345	−0.951149
$10$	−8.63020	−2.72911
$11$	−4.13952	−1.24811	−0.624056	−	0.781380i	$-0.714516\pi$
$11$	−4.13952	−1.24811	−0.624056	+	0.781380i	$0.714516\pi$
$12$	1.39945	0.403987
$13$	6.76769	1.87702	0.938510	−	0.345253i	$-0.112207\pi$
$13$	6.76769	1.87702	0.938510	+	0.345253i	$0.112207\pi$
$14$	5.13247	1.37171
$15$	1.38925	0.358702
$16$	2.05223	0.513058
$17$	−4.96728	−1.20474	−0.602371	−	0.798216i	$-0.705777\pi$
$17$	−4.96728	−1.20474	−0.602371	+	0.798216i	$0.705777\pi$
$18$	6.78593	1.59946
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	13.2660	2.96637
$21$	−0.826201	−0.180292
$22$	9.84440	2.09883
$23$	−7.28337	−1.51869	−0.759343	−	0.650690i	$-0.774480\pi$
$23$	−7.28337	−1.51869	−0.759343	+	0.650690i	$0.774480\pi$
$24$	−1.50728	−0.307672
$25$	8.16930	1.63386
$26$	−16.0946	−3.15641
$27$	−2.24084	−0.431249
$28$	−7.88944	−1.49096
$29$	3.73955	0.694417	0.347209	−	0.937788i	$-0.387130\pi$
$29$	3.73955	0.694417	0.347209	+	0.937788i	$0.387130\pi$
$30$	−3.30384	−0.603196
$31$	5.37967	0.966217	0.483108	−	0.875561i	$-0.339508\pi$
$31$	5.37967	0.966217	0.483108	+	0.875561i	$0.339508\pi$
$32$	2.99404	0.529276
$33$	−1.58470	−0.275862
$34$	11.8129	2.02590
$35$	−7.83193	−1.32384
$36$	−10.4311	−1.73851
$37$	2.33546	0.383946	0.191973	−	0.981400i	$-0.438511\pi$
$37$	2.33546	0.383946	0.191973	+	0.981400i	$0.438511\pi$
$38$	2.37815	0.385787
$39$	2.59083	0.414865
$40$	−14.2882	−2.25916
$41$	9.16045	1.43062	0.715311	−	0.698807i	$-0.246285\pi$
$41$	9.16045	1.43062	0.715311	+	0.698807i	$0.246285\pi$
$42$	1.96483	0.303180
$43$	7.51653	1.14626	0.573130	−	0.819464i	$-0.305729\pi$
$43$	7.51653	1.14626	0.573130	+	0.819464i	$0.305729\pi$
$44$	−15.1324	−2.28130
$45$	−10.3550	−1.54364
$46$	17.3209	2.55383
$47$	1.46743	0.214046	0.107023	−	0.994257i	$-0.465868\pi$
$47$	1.46743	0.214046	0.107023	+	0.994257i	$0.465868\pi$
$48$	0.785642	0.113398
$49$	−2.34227	−0.334610
$50$	−19.4278	−2.74751
$51$	−1.90159	−0.266276
$52$	24.7400	3.43082
$53$	−11.2538	−1.54583	−0.772917	−	0.634508i	$-0.781203\pi$
$53$	−11.2538	−1.54583	−0.772917	+	0.634508i	$0.781203\pi$
$54$	5.32905	0.725191
$55$	−15.0221	−2.02558
$56$	8.49734	1.13551
$57$	−0.382823	−0.0507062
$58$	−8.89322	−1.16774
$59$	−6.29114	−0.819036	−0.409518	−	0.912302i	$-0.634303\pi$
$59$	−6.29114	−0.819036	−0.409518	+	0.912302i	$0.634303\pi$
$60$	5.07854	0.655637
$61$	3.63700	0.465670	0.232835	−	0.972516i	$-0.425200\pi$
$61$	3.63700	0.465670	0.232835	+	0.972516i	$0.425200\pi$
$62$	−12.7937	−1.62480
$63$	6.15824	0.775866
$64$	−11.2247	−1.40309
$65$	24.5596	3.04625
$66$	3.76867	0.463891
$67$	10.4776	1.28004	0.640022	−	0.768356i	$-0.278925\pi$
$67$	10.4776	1.28004	0.640022	+	0.768356i	$0.278925\pi$
$68$	−18.1584	−2.20203
$69$	−2.78824	−0.335665
$70$	18.6255	2.22617
$71$	−12.6529	−1.50162	−0.750811	−	0.660517i	$-0.770337\pi$
$71$	−12.6529	−1.50162	−0.750811	+	0.660517i	$0.770337\pi$
$72$	11.2348	1.32403
$73$	−3.83856	−0.449269	−0.224635	−	0.974443i	$-0.572119\pi$
$73$	−3.83856	−0.449269	−0.224635	+	0.974443i	$0.572119\pi$
$74$	−5.55407	−0.645647
$75$	3.12740	0.361121
$76$	−3.65560	−0.419326
$77$	8.93382	1.01810
$78$	−6.16139	−0.697639
$79$	−8.61876	−0.969686	−0.484843	−	0.874601i	$-0.661123\pi$
$79$	−8.61876	−0.969686	−0.484843	+	0.874601i	$0.661123\pi$
$80$	7.44745	0.832650
$81$	7.70249	0.855833
$82$	−21.7849	−2.40574
$83$	−13.8507	−1.52031	−0.760157	−	0.649739i	$-0.774878\pi$
$83$	−13.8507	−1.52031	−0.760157	+	0.649739i	$0.774878\pi$
$84$	−3.02026	−0.329538
$85$	−18.0260	−1.95520
$86$	−17.8755	−1.92756
$87$	1.43159	0.153482
$88$	16.2984	1.73742
$89$	13.8028	1.46309	0.731546	−	0.681792i	$-0.238799\pi$
$89$	13.8028	1.46309	0.731546	+	0.681792i	$0.238799\pi$
$90$	24.6258	2.59579
$91$	−14.6059	−1.53111
$92$	−26.6251	−2.77586
$93$	2.05946	0.213556
$94$	−3.48976	−0.359941
$95$	−3.62895	−0.372323
$96$	1.14619	0.116982
$97$	9.88656	1.00383	0.501914	−	0.864918i	$-0.332629\pi$
$97$	9.88656	1.00383	0.501914	+	0.864918i	$0.332629\pi$
$98$	5.57027	0.562682
$99$	11.8119	1.18714
$100$	29.8637	2.98637
$101$	5.41077	0.538392	0.269196	−	0.963085i	$-0.413242\pi$
$101$	5.41077	0.538392	0.269196	+	0.963085i	$0.413242\pi$
$102$	4.52227	0.447772
$103$	12.6182	1.24331	0.621656	−	0.783291i	$-0.286460\pi$
$103$	12.6182	1.24331	0.621656	+	0.783291i	$0.286460\pi$
$104$	−26.6463	−2.61288
$105$	−2.99824	−0.292599
$106$	26.7633	2.59948
$107$	12.8447	1.24174	0.620871	−	0.783913i	$-0.286779\pi$
$107$	12.8447	1.24174	0.620871	+	0.783913i	$0.286779\pi$
$108$	−8.19161	−0.788238
$109$	7.90640	0.757296	0.378648	−	0.925541i	$-0.376389\pi$
$109$	7.90640	0.757296	0.378648	+	0.925541i	$0.376389\pi$
$110$	35.7249	3.40623
$111$	0.894067	0.0848611
$112$	−4.42908	−0.418509
$113$	−3.24934	−0.305672	−0.152836	−	0.988252i	$-0.548841\pi$
$113$	−3.24934	−0.305672	−0.152836	+	0.988252i	$0.548841\pi$
$114$	0.910412	0.0852679
$115$	−26.4310	−2.46470
$116$	13.6703	1.26926
$117$	−19.3112	−1.78532
$118$	14.9613	1.37730
$119$	10.7203	0.982726
$120$	−5.46985	−0.499327
$121$	6.13562	0.557783
$122$	−8.64933	−0.783073
$123$	3.50683	0.316200
$124$	19.6659	1.76605
$125$	11.5012	1.02870
$126$	−14.6452	−1.30470
$127$	−13.4192	−1.19076	−0.595381	−	0.803443i	$-0.702999\pi$
$127$	−13.4192	−1.19076	−0.595381	+	0.803443i	$0.702999\pi$
$128$	20.7060	1.83017
$129$	2.87750	0.253350
$130$	−58.4065	−5.12259
$131$	5.51163	0.481553	0.240777	−	0.970581i	$-0.422598\pi$
$131$	5.51163	0.481553	0.240777	+	0.970581i	$0.422598\pi$
$132$	−5.79305	−0.504220
$133$	2.15818	0.187138
$134$	−24.9174	−2.15253
$135$	−8.13189	−0.699881
$136$	19.5576	1.67705
$137$	11.4647	0.979494	0.489747	−	0.871865i	$-0.337089\pi$
$137$	11.4647	0.979494	0.489747	+	0.871865i	$0.337089\pi$
$138$	6.63086	0.564456
$139$	−1.99799	−0.169468	−0.0847338	−	0.996404i	$-0.527004\pi$
$139$	−1.99799	−0.169468	−0.0847338	+	0.996404i	$0.527004\pi$
$140$	−28.6304	−2.41971
$141$	0.561765	0.0473091
$142$	30.0905	2.52514
$143$	−28.0150	−2.34273
$144$	−5.85593	−0.487994
$145$	13.5707	1.12698
$146$	9.12867	0.755494
$147$	−0.896675	−0.0739565
$148$	8.53750	0.701778
$149$	3.16521	0.259304	0.129652	−	0.991560i	$-0.458614\pi$
$149$	3.16521	0.259304	0.129652	+	0.991560i	$0.458614\pi$
$150$	−7.43742	−0.607263
$151$	−5.99928	−0.488214	−0.244107	−	0.969748i	$-0.578495\pi$
$151$	−5.99928	−0.488214	−0.244107	+	0.969748i	$0.578495\pi$
$152$	3.93728	0.319355
$153$	14.1739	1.14589
$154$	−21.2460	−1.71205
$155$	19.5226	1.56809
$156$	9.47105	0.758291
$157$	7.96743	0.635871	0.317935	−	0.948112i	$-0.397011\pi$
$157$	7.96743	0.635871	0.317935	+	0.948112i	$0.397011\pi$
$158$	20.4967	1.63063
$159$	−4.30823	−0.341665
$160$	10.8652	0.858971
$161$	15.7188	1.23881
$162$	−18.3177	−1.43917
$163$	14.8872	1.16606	0.583029	−	0.812452i	$-0.301868\pi$
$163$	14.8872	1.16606	0.583029	+	0.812452i	$0.301868\pi$
$164$	33.4870	2.61489
$165$	−5.75082	−0.447700
$166$	32.9391	2.55657
$167$	24.6571	1.90803	0.954013	−	0.299765i	$-0.0969083\pi$
$167$	24.6571	1.90803	0.954013	+	0.299765i	$0.0969083\pi$
$168$	3.25298	0.250973
$169$	32.8016	2.52320
$170$	42.8686	3.28787
$171$	2.85345	0.218208
$172$	27.4775	2.09514
$173$	−24.5176	−1.86404	−0.932019	−	0.362410i	$-0.881954\pi$
$173$	−24.5176	−1.86404	−0.932019	+	0.362410i	$0.881954\pi$
$174$	−3.40453	−0.258097
$175$	−17.6308	−1.33276
$176$	−8.49525	−0.640353
$177$	−2.40839	−0.181026
$178$	−32.8251	−2.46035
$179$	24.9622	1.86576	0.932882	−	0.360183i	$-0.117286\pi$
$179$	24.9622	1.86576	0.932882	+	0.360183i	$0.117286\pi$
$180$	−37.8539	−2.82146
$181$	3.36694	0.250263	0.125131	−	0.992140i	$-0.460065\pi$
$181$	3.36694	0.250263	0.125131	+	0.992140i	$0.460065\pi$
$182$	34.7350	2.57473
$183$	1.39233	0.102924
$184$	28.6766	2.11407
$185$	8.47526	0.623113
$186$	−4.89771	−0.359118
$187$	20.5622	1.50365
$188$	5.36433	0.391234
$189$	4.83612	0.351776
$190$	8.63020	0.626100
$191$	15.4137	1.11529	0.557647	−	0.830079i	$-0.311704\pi$
$191$	15.4137	1.11529	0.557647	+	0.830079i	$0.311704\pi$
$192$	−4.29709	−0.310116
$193$	−6.17545	−0.444519	−0.222259	−	0.974988i	$-0.571343\pi$
$193$	−6.17545	−0.444519	−0.222259	+	0.974988i	$0.571343\pi$
$194$	−23.5117	−1.68804
$195$	9.40200	0.673291
$196$	−8.56240	−0.611600
$197$	11.2901	0.804388	0.402194	−	0.915555i	$-0.368248\pi$
$197$	11.2901	0.804388	0.402194	+	0.915555i	$0.368248\pi$
$198$	−28.0905	−1.99630
$199$	−6.49825	−0.460649	−0.230324	−	0.973114i	$-0.573979\pi$
$199$	−6.49825	−0.460649	−0.230324	+	0.973114i	$0.573979\pi$
$200$	−32.1648	−2.27439
$201$	4.01108	0.282920
$202$	−12.8676	−0.905364
$203$	−8.07062	−0.566446
$204$	−6.95146	−0.486700
$205$	33.2428	2.32178
$206$	−30.0081	−2.09076
$207$	20.7827	1.44450
$208$	13.8889	0.963019
$209$	4.13952	0.286337
$210$	7.13028	0.492036
$211$	4.87494	0.335605	0.167802	−	0.985821i	$-0.446333\pi$
$211$	4.87494	0.335605	0.167802	+	0.985821i	$0.446333\pi$
$212$	−41.1396	−2.82548
$213$	−4.84382	−0.331893
$214$	−30.5466	−2.08812
$215$	27.2771	1.86029
$216$	8.82279	0.600315
$217$	−11.6103	−0.788157
$218$	−18.8026	−1.27347
$219$	−1.46949	−0.0992988
$220$	−54.9149	−3.70236
$221$	−33.6170	−2.26133
$222$	−2.12623	−0.142703
$223$	−6.01171	−0.402574	−0.201287	−	0.979532i	$-0.564512\pi$
$223$	−6.01171	−0.402574	−0.201287	+	0.979532i	$0.564512\pi$
$224$	−6.46166	−0.431738
$225$	−23.3106	−1.55404
$226$	7.72743	0.514021
$227$	−7.15309	−0.474767	−0.237383	−	0.971416i	$-0.576290\pi$
$227$	−7.15309	−0.474767	−0.237383	+	0.971416i	$0.576290\pi$
$228$	−1.39945	−0.0926809
$229$	−0.948105	−0.0626525	−0.0313263	−	0.999509i	$-0.509973\pi$
$229$	−0.948105	−0.0626525	−0.0313263	+	0.999509i	$0.509973\pi$
$230$	62.8569	4.14466
$231$	3.42007	0.225024
$232$	−14.7236	−0.966655
$233$	−2.43849	−0.159750	−0.0798752	−	0.996805i	$-0.525452\pi$
$233$	−2.43849	−0.159750	−0.0798752	+	0.996805i	$0.525452\pi$
$234$	45.9251	3.00221
$235$	5.32522	0.347379
$236$	−22.9979	−1.49704
$237$	−3.29946	−0.214323
$238$	−25.4944	−1.65256
$239$	−0.991918	−0.0641619	−0.0320809	−	0.999485i	$-0.510213\pi$
$239$	−0.991918	−0.0641619	−0.0320809	+	0.999485i	$0.510213\pi$
$240$	2.85106	0.184035
$241$	3.39251	0.218531	0.109265	−	0.994013i	$-0.465150\pi$
$241$	3.39251	0.218531	0.109265	+	0.994013i	$0.465150\pi$
$242$	−14.5914	−0.937972
$243$	9.67120	0.620408
$244$	13.2954	0.851152
$245$	−8.49998	−0.543044
$246$	−8.33978	−0.531725
$247$	−6.76769	−0.430618
$248$	−21.1812	−1.34501
$249$	−5.30238	−0.336025
$250$	−27.3516	−1.72987
$251$	−9.26235	−0.584634	−0.292317	−	0.956321i	$-0.594426\pi$
$251$	−9.26235	−0.584634	−0.292317	+	0.956321i	$0.594426\pi$
$252$	22.5121	1.41813
$253$	30.1496	1.89549
$254$	31.9129	2.00240
$255$	−6.90078	−0.432144
$256$	−26.7926	−1.67454
$257$	8.36788	0.521974	0.260987	−	0.965342i	$-0.415952\pi$
$257$	8.36788	0.521974	0.260987	+	0.965342i	$0.415952\pi$
$258$	−6.84314	−0.426035
$259$	−5.04033	−0.313191
$260$	89.7803	5.56794
$261$	−10.6706	−0.660494
$262$	−13.1075	−0.809783
$263$	30.4185	1.87569	0.937844	−	0.347058i	$-0.112819\pi$
$263$	30.4185	1.87569	0.937844	+	0.347058i	$0.112819\pi$
$264$	6.23942	0.384010
$265$	−40.8396	−2.50876
$266$	−5.13247	−0.314692
$267$	5.28403	0.323377
$268$	38.3020	2.33967
$269$	−11.3243	−0.690453	−0.345227	−	0.938519i	$-0.612198\pi$
$269$	−11.3243	−0.690453	−0.345227	+	0.938519i	$0.612198\pi$
$270$	19.3389	1.17693
$271$	18.0175	1.09449	0.547243	−	0.836974i	$-0.315677\pi$
$271$	18.0175	1.09449	0.547243	+	0.836974i	$0.315677\pi$
$272$	−10.1940	−0.618102
$273$	−5.59147	−0.338411
$274$	−27.2647	−1.64712
$275$	−33.8170	−2.03924
$276$	−10.1927	−0.613529
$277$	−16.5759	−0.995951	−0.497976	−	0.867191i	$-0.665923\pi$
$277$	−16.5759	−0.995951	−0.497976	+	0.867191i	$0.665923\pi$
$278$	4.75153	0.284978
$279$	−15.3506	−0.919016
$280$	30.8365	1.84283
$281$	21.6484	1.29144	0.645718	−	0.763576i	$-0.276558\pi$
$281$	21.6484	1.29144	0.645718	+	0.763576i	$0.276558\pi$
$282$	−1.33596	−0.0795554
$283$	−5.32445	−0.316506	−0.158253	−	0.987399i	$-0.550586\pi$
$283$	−5.32445	−0.316506	−0.158253	+	0.987399i	$0.550586\pi$
$284$	−46.2540	−2.74467
$285$	−1.38925	−0.0822919
$286$	66.6239	3.93955
$287$	−19.7699	−1.16698
$288$	−8.54332	−0.503420
$289$	7.67389	0.451405
$290$	−32.2731	−1.89514
$291$	3.78480	0.221869
$292$	−14.0322	−0.821175
$293$	22.6163	1.32126	0.660630	−	0.750712i	$-0.270289\pi$
$293$	22.6163	1.32126	0.660630	+	0.750712i	$0.270289\pi$
$294$	2.13243	0.124366
$295$	−22.8302	−1.32923
$296$	−9.19533	−0.534468
$297$	9.27598	0.538247
$298$	−7.52734	−0.436047
$299$	−49.2916	−2.85060
$300$	11.4325	0.660057
$301$	−16.2220	−0.935021
$302$	14.2672	0.820985
$303$	2.07137	0.118997
$304$	−2.05223	−0.117704
$305$	13.1985	0.755743
$306$	−33.7076	−1.92694
$307$	−26.8531	−1.53258	−0.766292	−	0.642492i	$-0.777901\pi$
$307$	−26.8531	−1.53258	−0.766292	+	0.642492i	$0.777901\pi$
$308$	32.6585	1.86089
$309$	4.83055	0.274801
$310$	−46.4276	−2.63691
$311$	−17.3409	−0.983315	−0.491657	−	0.870789i	$-0.663609\pi$
$311$	−17.3409	−0.983315	−0.491657	+	0.870789i	$0.663609\pi$
$312$	−10.2008	−0.577507
$313$	8.00850	0.452667	0.226334	−	0.974050i	$-0.427326\pi$
$313$	8.00850	0.452667	0.226334	+	0.974050i	$0.427326\pi$
$314$	−18.9478	−1.06928
$315$	22.3480	1.25917
$316$	−31.5068	−1.77239
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	10.2456	0.574546
$319$	−15.4799	−0.866711
$320$	−40.7340	−2.27710
$321$	4.91724	0.274454
$322$	−37.3817	−2.08320
$323$	4.96728	0.276387
$324$	28.1573	1.56429
$325$	55.2873	3.06679
$326$	−35.4041	−1.96085
$327$	3.02675	0.167380
$328$	−36.0672	−1.99148
$329$	−3.16697	−0.174600
$330$	13.6763	0.752856
$331$	22.1466	1.21729	0.608644	−	0.793444i	$-0.291714\pi$
$331$	22.1466	1.21729	0.608644	+	0.793444i	$0.291714\pi$
$332$	−50.6327	−2.77883
$333$	−6.66410	−0.365190
$334$	−58.6384	−3.20855
$335$	38.0228	2.07741
$336$	−1.69555	−0.0925001
$337$	−4.70467	−0.256279	−0.128140	−	0.991756i	$-0.540901\pi$
$337$	−4.70467	−0.256279	−0.128140	+	0.991756i	$0.540901\pi$
$338$	−78.0072	−4.24303
$339$	−1.24392	−0.0675607
$340$	−65.8960	−3.57371
$341$	−22.2692	−1.20595
$342$	−6.78593	−0.366941
$343$	20.1623	1.08866
$344$	−29.5947	−1.59564
$345$	−10.1184	−0.544756
$346$	58.3065	3.13458
$347$	−26.4125	−1.41790	−0.708948	−	0.705261i	$-0.750830\pi$
$347$	−26.4125	−1.41790	−0.708948	+	0.705261i	$0.750830\pi$
$348$	5.23332	0.280535
$349$	−6.92625	−0.370754	−0.185377	−	0.982668i	$-0.559351\pi$
$349$	−6.92625	−0.370754	−0.185377	+	0.982668i	$0.559351\pi$
$350$	41.9287	2.24118
$351$	−15.1653	−0.809463
$352$	−12.3939	−0.660596
$353$	28.4447	1.51396	0.756980	−	0.653438i	$-0.226674\pi$
$353$	28.4447	1.51396	0.756980	+	0.653438i	$0.226674\pi$
$354$	5.72753	0.304415
$355$	−45.9168	−2.43701
$356$	50.4575	2.67424
$357$	4.10397	0.217205
$358$	−59.3639	−3.13748
$359$	−15.8922	−0.838760	−0.419380	−	0.907811i	$-0.637752\pi$
$359$	−15.8922	−0.838760	−0.419380	+	0.907811i	$0.637752\pi$
$360$	40.7706	2.14880
$361$	1.00000	0.0526316
$362$	−8.00709	−0.420843
$363$	2.34886	0.123283
$364$	−53.3933	−2.79857
$365$	−13.9299	−0.729126
$366$	−3.31116	−0.173077
$367$	−12.8232	−0.669364	−0.334682	−	0.942331i	$-0.608629\pi$
$367$	−12.8232	−0.669364	−0.334682	+	0.942331i	$0.608629\pi$
$368$	−14.9471	−0.779174
$369$	−26.1388	−1.36073
$370$	−20.1554	−1.04783
$371$	24.2878	1.26096
$372$	7.52858	0.390339
$373$	13.1611	0.681457	0.340728	−	0.940162i	$-0.389326\pi$
$373$	13.1611	0.681457	0.340728	+	0.940162i	$0.389326\pi$
$374$	−48.8999	−2.52855
$375$	4.40294	0.227367
$376$	−5.77766	−0.297960
$377$	25.3081	1.30343
$378$	−11.5010	−0.591549
$379$	31.2379	1.60458	0.802291	−	0.596933i	$-0.203614\pi$
$379$	31.2379	1.60458	0.802291	+	0.596933i	$0.203614\pi$
$380$	−13.2660	−0.680532
$381$	−5.13719	−0.263186
$382$	−36.6560	−1.87548
$383$	9.80364	0.500943	0.250471	−	0.968124i	$-0.419414\pi$
$383$	9.80364	0.500943	0.250471	+	0.968124i	$0.419414\pi$
$384$	7.92676	0.404511
$385$	32.4204	1.65230
$386$	14.6862	0.747506
$387$	−21.4480	−1.09026
$388$	36.1413	1.83480
$389$	−2.49449	−0.126476	−0.0632378	−	0.997998i	$-0.520143\pi$
$389$	−2.49449	−0.126476	−0.0632378	+	0.997998i	$0.520143\pi$
$390$	−22.3594	−1.13221
$391$	36.1785	1.82963
$392$	9.22216	0.465789
$393$	2.10998	0.106434
$394$	−26.8496	−1.35266
$395$	−31.2771	−1.57372
$396$	43.1796	2.16986
$397$	10.7737	0.540717	0.270359	−	0.962760i	$-0.412858\pi$
$397$	10.7737	0.540717	0.270359	+	0.962760i	$0.412858\pi$
$398$	15.4538	0.774630
$399$	0.826201	0.0413618
$400$	16.7653	0.838264
$401$	−28.7432	−1.43537	−0.717684	−	0.696369i	$-0.754798\pi$
$401$	−28.7432	−1.43537	−0.717684	+	0.696369i	$0.754798\pi$
$402$	−9.53895	−0.475759
$403$	36.4079	1.81361
$404$	19.7796	0.984074
$405$	27.9520	1.38895
$406$	19.1932	0.952540
$407$	−9.66766	−0.479208
$408$	7.48709	0.370666
$409$	−14.3407	−0.709104	−0.354552	−	0.935036i	$-0.615367\pi$
$409$	−14.3407	−0.709104	−0.354552	+	0.935036i	$0.615367\pi$
$410$	−79.0565	−3.90432
$411$	4.38895	0.216491
$412$	46.1272	2.27253
$413$	13.5774	0.668100
$414$	−49.4244	−2.42908
$415$	−50.2636	−2.46734
$416$	20.2627	0.993461
$417$	−0.764878	−0.0374563
$418$	−9.84440	−0.481505
$419$	21.9069	1.07022	0.535112	−	0.844781i	$-0.320269\pi$
$419$	21.9069	1.07022	0.535112	+	0.844781i	$0.320269\pi$
$420$	−10.9604	−0.534812
$421$	33.3762	1.62666	0.813328	−	0.581805i	$-0.197653\pi$
$421$	33.3762	1.62666	0.813328	+	0.581805i	$0.197653\pi$
$422$	−11.5934	−0.564356
$423$	−4.18722	−0.203590
$424$	44.3095	2.15186
$425$	−40.5792	−1.96838
$426$	11.5193	0.558114
$427$	−7.84929	−0.379854
$428$	46.9550	2.26966
$429$	−10.7248	−0.517798
$430$	−64.8692	−3.12827
$431$	9.34626	0.450193	0.225097	−	0.974336i	$-0.427730\pi$
$431$	9.34626	0.450193	0.225097	+	0.974336i	$0.427730\pi$
$432$	−4.59871	−0.221256
$433$	34.2874	1.64775	0.823874	−	0.566773i	$-0.191808\pi$
$433$	34.2874	1.64775	0.823874	+	0.566773i	$0.191808\pi$
$434$	27.6110	1.32537
$435$	5.19516	0.249089
$436$	28.9027	1.38419
$437$	7.28337	0.348411
$438$	3.49467	0.166982
$439$	−24.7925	−1.18328	−0.591640	−	0.806203i	$-0.701519\pi$
$439$	−24.7925	−1.18328	−0.591640	+	0.806203i	$0.701519\pi$
$440$	59.1462	2.81969
$441$	6.68354	0.318264
$442$	79.9464	3.80266
$443$	−33.7381	−1.60295	−0.801473	−	0.598031i	$-0.795950\pi$
$443$	−33.7381	−1.60295	−0.801473	+	0.598031i	$0.795950\pi$
$444$	3.26835	0.155109
$445$	50.0897	2.37448
$446$	14.2968	0.676971
$447$	1.21172	0.0573122
$448$	24.2250	1.14452
$449$	16.2541	0.767078	0.383539	−	0.923525i	$-0.374705\pi$
$449$	16.2541	0.767078	0.383539	+	0.923525i	$0.374705\pi$
$450$	55.4362	2.61329
$451$	−37.9198	−1.78558
$452$	−11.8783	−0.558709
$453$	−2.29666	−0.107907
$454$	17.0111	0.798371
$455$	−53.0040	−2.48487
$456$	1.50728	0.0705849
$457$	15.8449	0.741195	0.370597	−	0.928794i	$-0.379153\pi$
$457$	15.8449	0.741195	0.370597	+	0.928794i	$0.379153\pi$
$458$	2.25474	0.105357
$459$	11.1309	0.519544
$460$	−96.6212	−4.50499
$461$	26.5740	1.23767	0.618836	−	0.785520i	$-0.287604\pi$
$461$	26.5740	1.23767	0.618836	+	0.785520i	$0.287604\pi$
$462$	−8.13345	−0.378403
$463$	10.3668	0.481788	0.240894	−	0.970551i	$-0.422559\pi$
$463$	10.3668	0.481788	0.240894	+	0.970551i	$0.422559\pi$
$464$	7.67442	0.356276
$465$	7.47369	0.346584
$466$	5.79909	0.268637
$467$	−8.32562	−0.385264	−0.192632	−	0.981271i	$-0.561702\pi$
$467$	−8.32562	−0.385264	−0.192632	+	0.981271i	$0.561702\pi$
$468$	−70.5942	−3.26322
$469$	−22.6126	−1.04415
$470$	−12.6642	−0.584155
$471$	3.05012	0.140542
$472$	24.7699	1.14013
$473$	−31.1148	−1.43066
$474$	7.84662	0.360407
$475$	−8.16930	−0.374833
$476$	39.1891	1.79623
$477$	32.1122	1.47032
$478$	2.35893	0.107895
$479$	−31.3655	−1.43312	−0.716562	−	0.697523i	$-0.754285\pi$
$479$	−31.3655	−1.43312	−0.716562	+	0.697523i	$0.754285\pi$
$480$	4.15946	0.189852
$481$	15.8056	0.720675
$482$	−8.06790	−0.367483
$483$	6.01752	0.273807
$484$	22.4294	1.01952
$485$	35.8778	1.62913
$486$	−22.9996	−1.04328
$487$	32.1426	1.45652	0.728260	−	0.685301i	$-0.240329\pi$
$487$	32.1426	1.45652	0.728260	+	0.685301i	$0.240329\pi$
$488$	−14.3199	−0.648230
$489$	5.69917	0.257726
$490$	20.2142	0.913186
$491$	−15.6346	−0.705578	−0.352789	−	0.935703i	$-0.614767\pi$
$491$	−15.6346	−0.705578	−0.352789	+	0.935703i	$0.614767\pi$
$492$	12.8196	0.577952
$493$	−18.5754	−0.836594
$494$	16.0946	0.724130
$495$	42.8648	1.92663
$496$	11.0403	0.495725
$497$	27.3072	1.22490
$498$	12.6099	0.565061
$499$	19.6024	0.877525	0.438763	−	0.898603i	$-0.355417\pi$
$499$	19.6024	0.877525	0.438763	+	0.898603i	$0.355417\pi$
$500$	42.0439	1.88026
$501$	9.43933	0.421718
$502$	22.0273	0.983125
$503$	21.0389	0.938077	0.469039	−	0.883178i	$-0.344601\pi$
$503$	21.0389	0.938077	0.469039	+	0.883178i	$0.344601\pi$
$504$	−24.2467	−1.08003
$505$	19.6354	0.873766
$506$	−71.7004	−3.18747
$507$	12.5572	0.557686
$508$	−49.0553	−2.17648
$509$	−29.9429	−1.32719	−0.663597	−	0.748090i	$-0.730971\pi$
$509$	−29.9429	−1.32719	−0.663597	+	0.748090i	$0.730971\pi$
$510$	16.4111	0.726696
$511$	8.28429	0.366475
$512$	22.3049	0.985744
$513$	2.24084	0.0989353
$514$	−19.9001	−0.877755
$515$	45.7910	2.01779
$516$	10.5190	0.463074
$517$	−6.07444	−0.267153
$518$	11.9867	0.526664
$519$	−9.38590	−0.411995
$520$	−96.6980	−4.24049
$521$	11.6926	0.512262	0.256131	−	0.966642i	$-0.417552\pi$
$521$	11.6926	0.512262	0.256131	+	0.966642i	$0.417552\pi$
$522$	25.3763	1.11069
$523$	−6.79142	−0.296968	−0.148484	−	0.988915i	$-0.547439\pi$
$523$	−6.79142	−0.296968	−0.148484	+	0.988915i	$0.547439\pi$
$524$	20.1483	0.880184
$525$	−6.74948	−0.294571
$526$	−72.3399	−3.15417
$527$	−26.7223	−1.16404
$528$	−3.25218	−0.141533
$529$	30.0474	1.30641
$530$	97.1228	4.21875
$531$	17.9514	0.779025
$532$	7.88944	0.342051
$533$	61.9951	2.68530
$534$	−12.5662	−0.543794
$535$	46.6127	2.01524
$536$	−41.2533	−1.78187
$537$	9.55612	0.412377
$538$	26.9308	1.16107
$539$	9.69586	0.417630
$540$	−29.7270	−1.27924
$541$	−27.7642	−1.19368	−0.596838	−	0.802362i	$-0.703577\pi$
$541$	−27.7642	−1.19368	−0.596838	+	0.802362i	$0.703577\pi$
$542$	−42.8484	−1.84049
$543$	1.28894	0.0553138
$544$	−14.8722	−0.637641
$545$	28.6919	1.22903
$546$	13.2974	0.569075
$547$	37.6091	1.60805	0.804025	−	0.594596i	$-0.202688\pi$
$547$	37.6091	1.60805	0.804025	+	0.594596i	$0.202688\pi$
$548$	41.9103	1.79032
$549$	−10.3780	−0.442921
$550$	80.4218	3.42920
$551$	−3.73955	−0.159310
$552$	10.9781	0.467258
$553$	18.6008	0.790987
$554$	39.4201	1.67480
$555$	3.24453	0.137722
$556$	−7.30387	−0.309753
$557$	−41.0378	−1.73883	−0.869413	−	0.494085i	$-0.835503\pi$
$557$	−41.0378	−1.73883	−0.869413	+	0.494085i	$0.835503\pi$
$558$	36.5060	1.54542
$559$	50.8696	2.15155
$560$	−16.0729	−0.679205
$561$	7.87167	0.332342
$562$	−51.4832	−2.17169
$563$	−16.2428	−0.684553	−0.342277	−	0.939599i	$-0.611198\pi$
$563$	−16.2428	−0.684553	−0.342277	+	0.939599i	$0.611198\pi$
$564$	2.05359	0.0864717
$565$	−11.7917	−0.496081
$566$	12.6623	0.532238
$567$	−16.6234	−0.698115
$568$	49.8179	2.09031
$569$	1.20082	0.0503411	0.0251705	−	0.999683i	$-0.491987\pi$
$569$	1.20082	0.0503411	0.0251705	+	0.999683i	$0.491987\pi$
$570$	3.30384	0.138383
$571$	−24.2936	−1.01665	−0.508327	−	0.861164i	$-0.669736\pi$
$571$	−24.2936	−1.01665	−0.508327	+	0.861164i	$0.669736\pi$
$572$	−102.412	−4.28205
$573$	5.90071	0.246506
$574$	47.0157	1.96240
$575$	−59.5000	−2.48132
$576$	32.0292	1.33455
$577$	−12.5421	−0.522133	−0.261066	−	0.965321i	$-0.584074\pi$
$577$	−12.5421	−0.522133	−0.261066	+	0.965321i	$0.584074\pi$
$578$	−18.2497	−0.759086
$579$	−2.36411	−0.0982490
$580$	49.6089	2.05990
$581$	29.8923	1.24014
$582$	−9.00084	−0.373097
$583$	46.5855	1.92937
$584$	15.1135	0.625399
$585$	−70.0796	−2.89743
$586$	−53.7850	−2.22184
$587$	10.8949	0.449679	0.224839	−	0.974396i	$-0.427814\pi$
$587$	10.8949	0.449679	0.224839	+	0.974396i	$0.427814\pi$
$588$	−3.27789	−0.135178
$589$	−5.37967	−0.221665
$590$	54.2938	2.23524
$591$	4.32212	0.177788
$592$	4.79289	0.196987
$593$	24.9063	1.02278	0.511389	−	0.859350i	$-0.329131\pi$
$593$	24.9063	1.02278	0.511389	+	0.859350i	$0.329131\pi$
$594$	−22.0597	−0.905120
$595$	38.9034	1.59488
$596$	11.5707	0.473956
$597$	−2.48768	−0.101814
$598$	117.223	4.79360
$599$	10.0670	0.411326	0.205663	−	0.978623i	$-0.434065\pi$
$599$	10.0670	0.411326	0.205663	+	0.978623i	$0.434065\pi$
$600$	−12.3134	−0.502693
$601$	−29.2390	−1.19268	−0.596342	−	0.802730i	$-0.703380\pi$
$601$	−29.2390	−1.19268	−0.596342	+	0.802730i	$0.703380\pi$
$602$	38.5784	1.57234
$603$	−29.8973	−1.21751
$604$	−21.9310	−0.892359
$605$	22.2659	0.905236
$606$	−4.92603	−0.200106
$607$	29.6980	1.20540	0.602702	−	0.797966i	$-0.294091\pi$
$607$	29.6980	1.20540	0.602702	+	0.797966i	$0.294091\pi$
$608$	−2.99404	−0.121424
$609$	−3.08962	−0.125198
$610$	−31.3880	−1.27086
$611$	9.93108	0.401769
$612$	51.8141	2.09446
$613$	29.5530	1.19363	0.596817	−	0.802377i	$-0.296432\pi$
$613$	29.5530	1.19363	0.596817	+	0.802377i	$0.296432\pi$
$614$	63.8606	2.57721
$615$	12.7261	0.513167
$616$	−35.1749	−1.41724
$617$	3.89511	0.156811	0.0784055	−	0.996922i	$-0.475017\pi$
$617$	3.89511	0.156811	0.0784055	+	0.996922i	$0.475017\pi$
$618$	−11.4878	−0.462106
$619$	−9.31488	−0.374397	−0.187198	−	0.982322i	$-0.559941\pi$
$619$	−9.31488	−0.374397	−0.187198	+	0.982322i	$0.559941\pi$
$620$	71.3667	2.86616
$621$	16.3208	0.654932
$622$	41.2394	1.65355
$623$	−29.7889	−1.19347
$624$	5.31698	0.212850
$625$	0.890914	0.0356366
$626$	−19.0454	−0.761208
$627$	1.58470	0.0632870
$628$	29.1258	1.16225
$629$	−11.6009	−0.462557
$630$	−53.1469	−2.11742
$631$	27.9312	1.11193	0.555963	−	0.831207i	$-0.312350\pi$
$631$	27.9312	1.11193	0.555963	+	0.831207i	$0.312350\pi$
$632$	33.9344	1.34984
$633$	1.86624	0.0741764
$634$	−2.37815	−0.0944485
$635$	−48.6977	−1.93251
$636$	−15.7492	−0.624496
$637$	−15.8517	−0.628069
$638$	36.8137	1.45747
$639$	36.1044	1.42827
$640$	75.1412	2.97022
$641$	−28.0834	−1.10923	−0.554614	−	0.832108i	$-0.687134\pi$
$641$	−28.0834	−1.10923	−0.554614	+	0.832108i	$0.687134\pi$
$642$	−11.6939	−0.461523
$643$	19.9594	0.787123	0.393562	−	0.919298i	$-0.371243\pi$
$643$	19.9594	0.787123	0.393562	+	0.919298i	$0.371243\pi$
$644$	57.4617	2.26431
$645$	10.4423	0.411166
$646$	−11.8129	−0.464774
$647$	−15.5299	−0.610543	−0.305271	−	0.952265i	$-0.598747\pi$
$647$	−15.5299	−0.610543	−0.305271	+	0.952265i	$0.598747\pi$
$648$	−30.3268	−1.19135
$649$	26.0423	1.02225
$650$	−131.481	−5.15713
$651$	−4.44469	−0.174201
$652$	54.4218	2.13132
$653$	47.3148	1.85157	0.925786	−	0.378047i	$-0.123404\pi$
$653$	47.3148	1.85157	0.925786	+	0.378047i	$0.123404\pi$
$654$	−7.19808	−0.281467
$655$	20.0014	0.781521
$656$	18.7993	0.733991
$657$	10.9531	0.427322
$658$	7.53152	0.293609
$659$	−28.6759	−1.11705	−0.558526	−	0.829487i	$-0.688633\pi$
$659$	−28.6759	−1.11705	−0.558526	+	0.829487i	$0.688633\pi$
$660$	−21.0227	−0.818308
$661$	36.5788	1.42275	0.711375	−	0.702812i	$-0.248073\pi$
$661$	36.5788	1.42275	0.711375	+	0.702812i	$0.248073\pi$
$662$	−52.6680	−2.04700
$663$	−12.8694	−0.499805
$664$	54.5341	2.11633
$665$	7.83193	0.303709
$666$	15.8482	0.614106
$667$	−27.2365	−1.05460
$668$	90.1367	3.48749
$669$	−2.30142	−0.0889782
$670$	−90.4239	−3.49338
$671$	−15.0554	−0.581208
$672$	−2.47368	−0.0954241
$673$	41.5032	1.59983	0.799915	−	0.600113i	$-0.204878\pi$
$673$	41.5032	1.59983	0.799915	+	0.600113i	$0.204878\pi$
$674$	11.1884	0.430961
$675$	−18.3061	−0.704600
$676$	119.910	4.61191
$677$	12.1213	0.465858	0.232929	−	0.972494i	$-0.425169\pi$
$677$	12.1213	0.465858	0.232929	+	0.972494i	$0.425169\pi$
$678$	2.95824	0.113611
$679$	−21.3369	−0.818837
$680$	70.9734	2.72171
$681$	−2.73837	−0.104934
$682$	52.9596	2.02793
$683$	1.11162	0.0425351	0.0212675	−	0.999774i	$-0.493230\pi$
$683$	1.11162	0.0425351	0.0212675	+	0.999774i	$0.493230\pi$
$684$	10.4311	0.398842
$685$	41.6048	1.58964
$686$	−47.9489	−1.83070
$687$	−0.362957	−0.0138477
$688$	15.4257	0.588098
$689$	−76.1625	−2.90156
$690$	24.0631	0.916066
$691$	21.1130	0.803177	0.401588	−	0.915820i	$-0.368458\pi$
$691$	21.1130	0.803177	0.401588	+	0.915820i	$0.368458\pi$
$692$	−89.6266	−3.40709
$693$	−25.4922	−0.968368
$694$	62.8128	2.38434
$695$	−7.25062	−0.275032
$696$	−5.63656	−0.213653
$697$	−45.5025	−1.72353
$698$	16.4717	0.623462
$699$	−0.933509	−0.0353086
$700$	−64.4512	−2.43603
$701$	−17.3808	−0.656463	−0.328231	−	0.944597i	$-0.606453\pi$
$701$	−17.3808	−0.656463	−0.328231	+	0.944597i	$0.606453\pi$
$702$	36.0653	1.36120
$703$	−2.33546	−0.0880834
$704$	46.4650	1.75122
$705$	2.03862	0.0767788
$706$	−67.6459	−2.54589
$707$	−11.6774	−0.439174
$708$	−8.80413	−0.330880
$709$	−7.16784	−0.269194	−0.134597	−	0.990900i	$-0.542974\pi$
$709$	−7.16784	−0.269194	−0.134597	+	0.990900i	$0.542974\pi$
$710$	109.197	4.09809
$711$	24.5932	0.922315
$712$	−54.3454	−2.03668
$713$	−39.1821	−1.46738
$714$	−9.75987	−0.365254
$715$	−101.665	−3.80206
$716$	91.2520	3.41025
$717$	−0.379729	−0.0141813
$718$	37.7941	1.41046
$719$	21.9674	0.819244	0.409622	−	0.912255i	$-0.365661\pi$
$719$	21.9674	0.819244	0.409622	+	0.912255i	$0.365661\pi$
$720$	−21.2509	−0.791974
$721$	−27.2324	−1.01419
$722$	−2.37815	−0.0885056
$723$	1.29873	0.0483003
$724$	12.3082	0.457431
$725$	30.5495	1.13458
$726$	−5.58594	−0.207314
$727$	−19.1339	−0.709639	−0.354819	−	0.934935i	$-0.615458\pi$
$727$	−19.1339	−0.709639	−0.354819	+	0.934935i	$0.615458\pi$
$728$	57.5074	2.13137
$729$	−19.4051	−0.718708
$730$	33.1275	1.22610
$731$	−37.3367	−1.38095
$732$	5.08980	0.188124
$733$	−40.6482	−1.50138	−0.750688	−	0.660657i	$-0.770278\pi$
$733$	−40.6482	−1.50138	−0.750688	+	0.660657i	$0.770278\pi$
$734$	30.4955	1.12561
$735$	−3.25399	−0.120025
$736$	−21.8067	−0.803804
$737$	−43.3723	−1.59764
$738$	62.1621	2.28822
$739$	38.1595	1.40372	0.701860	−	0.712315i	$-0.252353\pi$
$739$	38.1595	1.40372	0.701860	+	0.712315i	$0.252353\pi$
$740$	30.9822	1.13893
$741$	−2.59083	−0.0951765
$742$	−57.7600	−2.12044
$743$	11.4083	0.418530	0.209265	−	0.977859i	$-0.432893\pi$
$743$	11.4083	0.418530	0.209265	+	0.977859i	$0.432893\pi$
$744$	−8.10867	−0.297278
$745$	11.4864	0.420829
$746$	−31.2991	−1.14594
$747$	39.5223	1.44604
$748$	75.1671	2.74838
$749$	−27.7211	−1.01291
$750$	−10.4708	−0.382341
$751$	38.4796	1.40414	0.702070	−	0.712108i	$-0.252259\pi$
$751$	38.4796	1.40414	0.702070	+	0.712108i	$0.252259\pi$
$752$	3.01150	0.109818
$753$	−3.54584	−0.129218
$754$	−60.1866	−2.19187
$755$	−21.7711	−0.792331
$756$	17.6789	0.642977
$757$	−0.0509774	−0.00185280	−0.000926402	−	1.00000i	$-0.500295\pi$
$757$	−0.0509774	−0.00185280	−0.000926402		1.00000i	$0.500295\pi$
$758$	−74.2884	−2.69828
$759$	11.5420	0.418947
$760$	14.2882	0.518287
$761$	−19.0982	−0.692308	−0.346154	−	0.938178i	$-0.612512\pi$
$761$	−19.0982	−0.692308	−0.346154	+	0.938178i	$0.612512\pi$
$762$	12.2170	0.442576
$763$	−17.0634	−0.617737
$764$	56.3462	2.03853
$765$	51.4363	1.85968
$766$	−23.3145	−0.842389
$767$	−42.5765	−1.53735
$768$	−10.2568	−0.370112
$769$	−38.1097	−1.37427	−0.687136	−	0.726529i	$-0.741132\pi$
$769$	−38.1097	−1.37427	−0.687136	+	0.726529i	$0.741132\pi$
$770$	−77.1006	−2.77851
$771$	3.20342	0.115368
$772$	−22.5750	−0.812493
$773$	−36.5750	−1.31551	−0.657757	−	0.753231i	$-0.728494\pi$
$773$	−36.5750	−1.31551	−0.657757	+	0.753231i	$0.728494\pi$
$774$	51.0066	1.83340
$775$	43.9481	1.57866
$776$	−38.9261	−1.39737
$777$	−1.92956	−0.0692224
$778$	5.93227	0.212682
$779$	−9.16045	−0.328207
$780$	34.3700	1.23064
$781$	52.3769	1.87419
$782$	−86.0380	−3.07671
$783$	−8.37972	−0.299467
$784$	−4.80687	−0.171674
$785$	28.9134	1.03196
$786$	−5.01785	−0.178981
$787$	−21.3578	−0.761323	−0.380662	−	0.924714i	$-0.624304\pi$
$787$	−21.3578	−0.761323	−0.380662	+	0.924714i	$0.624304\pi$
$788$	41.2722	1.47026
$789$	11.6449	0.414570
$790$	74.3816	2.64638
$791$	7.01266	0.249341
$792$	−46.5067	−1.65254
$793$	24.6141	0.874071
$794$	−25.6215	−0.909274
$795$	−15.6344	−0.554494
$796$	−23.7550	−0.841975
$797$	28.7877	1.01971	0.509857	−	0.860259i	$-0.329698\pi$
$797$	28.7877	1.01971	0.509857	+	0.860259i	$0.329698\pi$
$798$	−1.96483	−0.0695543
$799$	−7.28912	−0.257870
$800$	24.4592	0.864762
$801$	−39.3855	−1.39162
$802$	68.3557	2.41372
$803$	15.8898	0.560738
$804$	14.6629	0.517121
$805$	57.0428	2.01049
$806$	−86.5836	−3.04978
$807$	−4.33520	−0.152606
$808$	−21.3037	−0.749462
$809$	−15.8475	−0.557170	−0.278585	−	0.960412i	$-0.589865\pi$
$809$	−15.8475	−0.557170	−0.278585	+	0.960412i	$0.589865\pi$
$810$	−66.4741	−2.33566
$811$	20.3349	0.714056	0.357028	−	0.934094i	$-0.383790\pi$
$811$	20.3349	0.714056	0.357028	+	0.934094i	$0.383790\pi$
$812$	−29.5030	−1.03535
$813$	6.89752	0.241907
$814$	22.9912	0.805840
$815$	54.0250	1.89241
$816$	−3.90250	−0.136615
$817$	−7.51653	−0.262970
$818$	34.1044	1.19243
$819$	41.6771	1.45632
$820$	121.523	4.24375
$821$	32.6809	1.14057	0.570286	−	0.821446i	$-0.306832\pi$
$821$	32.6809	1.14057	0.570286	+	0.821446i	$0.306832\pi$
$822$	−10.4376	−0.364052
$823$	−43.4992	−1.51629	−0.758143	−	0.652089i	$-0.773893\pi$
$823$	−43.4992	−1.51629	−0.758143	+	0.652089i	$0.773893\pi$
$824$	−49.6814	−1.73074
$825$	−12.9459	−0.450719
$826$	−32.2891	−1.12348
$827$	10.0762	0.350383	0.175191	−	0.984534i	$-0.443946\pi$
$827$	10.0762	0.350383	0.175191	+	0.984534i	$0.443946\pi$
$828$	75.9733	2.64025
$829$	−51.3659	−1.78401	−0.892006	−	0.452023i	$-0.850702\pi$
$829$	−51.3659	−1.78401	−0.892006	+	0.452023i	$0.850702\pi$
$830$	119.534	4.14910
$831$	−6.34565	−0.220128
$832$	−75.9655	−2.63363
$833$	11.6347	0.403119
$834$	1.81900	0.0629867
$835$	89.4796	3.09657
$836$	15.1324	0.523366
$837$	−12.0550	−0.416680
$838$	−52.0980	−1.79970
$839$	−0.419602	−0.0144863	−0.00724314	−	0.999974i	$-0.502306\pi$
$839$	−0.419602	−0.0144863	−0.00724314	+	0.999974i	$0.502306\pi$
$840$	11.8049	0.407308
$841$	−15.0158	−0.517785
$842$	−79.3737	−2.73540
$843$	8.28751	0.285437
$844$	17.8209	0.613419
$845$	119.036	4.09495
$846$	9.95784	0.342358
$847$	−13.2418	−0.454992
$848$	−23.0955	−0.793101
$849$	−2.03832	−0.0699551
$850$	96.5035	3.31004
$851$	−17.0100	−0.583094
$852$	−17.7071	−0.606635
$853$	39.8333	1.36387	0.681933	−	0.731414i	$-0.261139\pi$
$853$	39.8333	1.36387	0.681933	+	0.731414i	$0.261139\pi$
$854$	18.6668	0.638764
$855$	10.3550	0.354134
$856$	−50.5730	−1.72855
$857$	45.3441	1.54892	0.774462	−	0.632620i	$-0.218020\pi$
$857$	45.3441	1.54892	0.774462	+	0.632620i	$0.218020\pi$
$858$	25.5052	0.870732
$859$	−34.5736	−1.17964	−0.589818	−	0.807536i	$-0.700801\pi$
$859$	−34.5736	−1.17964	−0.589818	+	0.807536i	$0.700801\pi$
$860$	99.7144	3.40023
$861$	−7.56837	−0.257929
$862$	−22.2268	−0.757048
$863$	1.20679	0.0410796	0.0205398	−	0.999789i	$-0.493462\pi$
$863$	1.20679	0.0410796	0.0205398	+	0.999789i	$0.493462\pi$
$864$	−6.70914	−0.228250
$865$	−88.9731	−3.02518
$866$	−81.5407	−2.77086
$867$	2.93774	0.0997710
$868$	−42.4426	−1.44060
$869$	35.6775	1.21028
$870$	−12.3549	−0.418870
$871$	70.9093	2.40267
$872$	−31.1297	−1.05418
$873$	−28.2108	−0.954790
$874$	−17.3209	−0.585890
$875$	−24.8217	−0.839126
$876$	−5.37187	−0.181499
$877$	39.3106	1.32742	0.663712	−	0.747988i	$-0.268980\pi$
$877$	39.3106	1.32742	0.663712	+	0.747988i	$0.268980\pi$
$878$	58.9602	1.98981
$879$	8.65806	0.292029
$880$	−30.8288	−1.03924
$881$	−6.62074	−0.223058	−0.111529	−	0.993761i	$-0.535575\pi$
$881$	−6.62074	−0.223058	−0.111529	+	0.993761i	$0.535575\pi$
$882$	−15.8945	−0.535194
$883$	33.7871	1.13703	0.568513	−	0.822675i	$-0.307519\pi$
$883$	33.7871	1.13703	0.568513	+	0.822675i	$0.307519\pi$
$884$	−122.891	−4.13326
$885$	−8.73995	−0.293790
$886$	80.2343	2.69552
$887$	−8.84972	−0.297144	−0.148572	−	0.988902i	$-0.547468\pi$
$887$	−8.84972	−0.297144	−0.148572	+	0.988902i	$0.547468\pi$
$888$	−3.52019	−0.118130
$889$	28.9611	0.971323
$890$	−119.121	−3.99294
$891$	−31.8846	−1.06818
$892$	−21.9764	−0.735826
$893$	−1.46743	−0.0491055
$894$	−2.88164	−0.0963765
$895$	90.5867	3.02798
$896$	−44.6873	−1.49290
$897$	−18.8700	−0.630050
$898$	−38.6547	−1.28992
$899$	20.1175	0.670958
$900$	−85.2145	−2.84048
$901$	55.9010	1.86233
$902$	90.1791	3.00264
$903$	−6.21017	−0.206661
$904$	12.7936	0.425507
$905$	12.2185	0.406156
$906$	5.46181	0.181457
$907$	9.04011	0.300172	0.150086	−	0.988673i	$-0.452045\pi$
$907$	9.04011	0.300172	0.150086	+	0.988673i	$0.452045\pi$
$908$	−26.1488	−0.867780
$909$	−15.4394	−0.512091
$910$	126.052	4.17857
$911$	−25.9588	−0.860053	−0.430027	−	0.902816i	$-0.641496\pi$
$911$	−25.9588	−0.860053	−0.430027	+	0.902816i	$0.641496\pi$
$912$	−0.785642	−0.0260152
$913$	57.3353	1.89752
$914$	−37.6817	−1.24640
$915$	5.05269	0.167037
$916$	−3.46590	−0.114516
$917$	−11.8951	−0.392810
$918$	−26.4709	−0.873669
$919$	−25.9809	−0.857032	−0.428516	−	0.903534i	$-0.640963\pi$
$919$	−25.9809	−0.857032	−0.428516	+	0.903534i	$0.640963\pi$
$920$	104.066	3.43096
$921$	−10.2800	−0.338737
$922$	−63.1969	−2.08128
$923$	−85.6309	−2.81857
$924$	12.5024	0.411300
$925$	19.0790	0.627314
$926$	−24.6539	−0.810179
$927$	−36.0054	−1.18257
$928$	11.1964	0.367538
$929$	−38.1369	−1.25123	−0.625615	−	0.780132i	$-0.715152\pi$
$929$	−38.1369	−1.25123	−0.625615	+	0.780132i	$0.715152\pi$
$930$	−17.7736	−0.582818
$931$	2.34227	0.0767647
$932$	−8.91413	−0.291992
$933$	−6.63852	−0.217335
$934$	19.7996	0.647862
$935$	74.6191	2.44031
$936$	76.0337	2.48524
$937$	21.7392	0.710190	0.355095	−	0.934830i	$-0.384449\pi$
$937$	21.7392	0.710190	0.355095	+	0.934830i	$0.384449\pi$
$938$	53.7761	1.75585
$939$	3.06584	0.100050
$940$	19.4669	0.634940
$941$	−23.4821	−0.765494	−0.382747	−	0.923853i	$-0.625022\pi$
$941$	−23.4821	−0.765494	−0.382747	+	0.923853i	$0.625022\pi$
$942$	−7.25365	−0.236337
$943$	−66.7189	−2.17267
$944$	−12.9109	−0.420213
$945$	17.5501	0.570903
$946$	73.9958	2.40581
$947$	25.8666	0.840550	0.420275	−	0.907397i	$-0.361934\pi$
$947$	25.8666	0.840550	0.420275	+	0.907397i	$0.361934\pi$
$948$	−12.0615	−0.391740
$949$	−25.9782	−0.843287
$950$	19.4278	0.630322
$951$	0.382823	0.0124139
$952$	−42.2087	−1.36799
$953$	−17.4872	−0.566466	−0.283233	−	0.959051i	$-0.591407\pi$
$953$	−17.4872	−0.566466	−0.283233	+	0.959051i	$0.591407\pi$
$954$	−76.3677	−2.47250
$955$	55.9354	1.81003
$956$	−3.62606	−0.117275
$957$	−5.92608	−0.191563
$958$	74.5918	2.40995
$959$	−24.7428	−0.798987
$960$	−15.5939	−0.503292
$961$	−2.05917	−0.0664250
$962$	−37.5882	−1.21189
$963$	−36.6516	−1.18108
$964$	12.4017	0.399431
$965$	−22.4104	−0.721417
$966$	−14.3106	−0.460435
$967$	−47.1401	−1.51592	−0.757962	−	0.652299i	$-0.773805\pi$
$967$	−47.1401	−1.51592	−0.757962	+	0.652299i	$0.773805\pi$
$968$	−24.1576	−0.776455
$969$	1.90159	0.0610879
$970$	−85.3229	−2.73955
$971$	−57.1317	−1.83344	−0.916722	−	0.399526i	$-0.869175\pi$
$971$	−57.1317	−1.83344	−0.916722	+	0.399526i	$0.869175\pi$
$972$	35.3541	1.13398
$973$	4.31202	0.138237
$974$	−76.4399	−2.44929
$975$	21.1653	0.677831
$976$	7.46396	0.238915
$977$	35.7075	1.14238	0.571191	−	0.820817i	$-0.306481\pi$
$977$	35.7075	1.14238	0.571191	+	0.820817i	$0.306481\pi$
$978$	−13.5535	−0.433393
$979$	−57.1369	−1.82610
$980$	−31.0726	−0.992576
$981$	−22.5605	−0.720301
$982$	37.1814	1.18650
$983$	2.21413	0.0706199	0.0353099	−	0.999376i	$-0.488758\pi$
$983$	2.21413	0.0706199	0.0353099	+	0.999376i	$0.488758\pi$
$984$	−13.8074	−0.440163
$985$	40.9713	1.30545
$986$	44.1751	1.40682
$987$	−1.21239	−0.0385908
$988$	−24.7400	−0.787084
$989$	−54.7457	−1.74081
$990$	−101.939	−3.23983
$991$	7.73689	0.245770	0.122885	−	0.992421i	$-0.460785\pi$
$991$	7.73689	0.245770	0.122885	+	0.992421i	$0.460785\pi$
$992$	16.1069	0.511395
$993$	8.47824	0.269049
$994$	−64.9407	−2.05979
$995$	−23.5819	−0.747595
$996$	−19.3834	−0.614186
$997$	22.5369	0.713751	0.356875	−	0.934152i	$-0.383842\pi$
$997$	22.5369	0.713751	0.356875	+	0.934152i	$0.383842\pi$
$998$	−46.6175	−1.47565
$999$	−5.23337	−0.165577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.16	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.16	✓	140	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37815 q^{2} +0.382823 q^{3} +3.65560 q^{4} +3.62895 q^{5} -0.910412 q^{6} -2.15818 q^{7} -3.93728 q^{8} -2.85345 q^{9} +O(q^{10})\)	\(q-2.37815 q^{2} +0.382823 q^{3} +3.65560 q^{4} +3.62895 q^{5} -0.910412 q^{6} -2.15818 q^{7} -3.93728 q^{8} -2.85345 q^{9} -8.63020 q^{10} -4.13952 q^{11} +1.39945 q^{12} +6.76769 q^{13} +5.13247 q^{14} +1.38925 q^{15} +2.05223 q^{16} -4.96728 q^{17} +6.78593 q^{18} -1.00000 q^{19} +13.2660 q^{20} -0.826201 q^{21} +9.84440 q^{22} -7.28337 q^{23} -1.50728 q^{24} +8.16930 q^{25} -16.0946 q^{26} -2.24084 q^{27} -7.88944 q^{28} +3.73955 q^{29} -3.30384 q^{30} +5.37967 q^{31} +2.99404 q^{32} -1.58470 q^{33} +11.8129 q^{34} -7.83193 q^{35} -10.4311 q^{36} +2.33546 q^{37} +2.37815 q^{38} +2.59083 q^{39} -14.2882 q^{40} +9.16045 q^{41} +1.96483 q^{42} +7.51653 q^{43} -15.1324 q^{44} -10.3550 q^{45} +17.3209 q^{46} +1.46743 q^{47} +0.785642 q^{48} -2.34227 q^{49} -19.4278 q^{50} -1.90159 q^{51} +24.7400 q^{52} -11.2538 q^{53} +5.32905 q^{54} -15.0221 q^{55} +8.49734 q^{56} -0.382823 q^{57} -8.89322 q^{58} -6.29114 q^{59} +5.07854 q^{60} +3.63700 q^{61} -12.7937 q^{62} +6.15824 q^{63} -11.2247 q^{64} +24.5596 q^{65} +3.76867 q^{66} +10.4776 q^{67} -18.1584 q^{68} -2.78824 q^{69} +18.6255 q^{70} -12.6529 q^{71} +11.2348 q^{72} -3.83856 q^{73} -5.55407 q^{74} +3.12740 q^{75} -3.65560 q^{76} +8.93382 q^{77} -6.16139 q^{78} -8.61876 q^{79} +7.44745 q^{80} +7.70249 q^{81} -21.7849 q^{82} -13.8507 q^{83} -3.02026 q^{84} -18.0260 q^{85} -17.8755 q^{86} +1.43159 q^{87} +16.2984 q^{88} +13.8028 q^{89} +24.6258 q^{90} -14.6059 q^{91} -26.6251 q^{92} +2.05946 q^{93} -3.48976 q^{94} -3.62895 q^{95} +1.14619 q^{96} +9.88656 q^{97} +5.57027 q^{98} +11.8119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

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