LMFDB - Embedded newform 6017.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66480 q^{2} -1.17356 q^{3} +5.10118 q^{4} +4.42559 q^{5} +3.12731 q^{6} +1.20677 q^{7} -8.26404 q^{8} -1.62275 q^{9} +O(q^{10})$	\(q-2.66480 q^{2} -1.17356 q^{3} +5.10118 q^{4} +4.42559 q^{5} +3.12731 q^{6} +1.20677 q^{7} -8.26404 q^{8} -1.62275 q^{9} -11.7933 q^{10} -1.00000 q^{11} -5.98655 q^{12} +3.53290 q^{13} -3.21580 q^{14} -5.19370 q^{15} +11.8197 q^{16} -4.17739 q^{17} +4.32432 q^{18} +5.96661 q^{19} +22.5758 q^{20} -1.41622 q^{21} +2.66480 q^{22} -1.37608 q^{23} +9.69835 q^{24} +14.5859 q^{25} -9.41449 q^{26} +5.42508 q^{27} +6.15594 q^{28} -4.09416 q^{29} +13.8402 q^{30} +4.26025 q^{31} -14.9691 q^{32} +1.17356 q^{33} +11.1319 q^{34} +5.34067 q^{35} -8.27797 q^{36} +11.1171 q^{37} -15.8998 q^{38} -4.14607 q^{39} -36.5733 q^{40} +6.73017 q^{41} +3.77394 q^{42} +5.32446 q^{43} -5.10118 q^{44} -7.18165 q^{45} +3.66699 q^{46} -1.86392 q^{47} -13.8711 q^{48} -5.54371 q^{49} -38.8685 q^{50} +4.90242 q^{51} +18.0220 q^{52} -14.0322 q^{53} -14.4568 q^{54} -4.42559 q^{55} -9.97278 q^{56} -7.00218 q^{57} +10.9101 q^{58} -8.53852 q^{59} -26.4940 q^{60} -8.66438 q^{61} -11.3527 q^{62} -1.95829 q^{63} +16.2503 q^{64} +15.6352 q^{65} -3.12731 q^{66} +12.7341 q^{67} -21.3096 q^{68} +1.61492 q^{69} -14.2318 q^{70} +16.6868 q^{71} +13.4105 q^{72} +6.24979 q^{73} -29.6249 q^{74} -17.1174 q^{75} +30.4368 q^{76} -1.20677 q^{77} +11.0485 q^{78} -12.5123 q^{79} +52.3091 q^{80} -1.49840 q^{81} -17.9346 q^{82} -1.67501 q^{83} -7.22437 q^{84} -18.4874 q^{85} -14.1886 q^{86} +4.80474 q^{87} +8.26404 q^{88} -0.148598 q^{89} +19.1377 q^{90} +4.26339 q^{91} -7.01964 q^{92} -4.99967 q^{93} +4.96697 q^{94} +26.4058 q^{95} +17.5671 q^{96} +2.40260 q^{97} +14.7729 q^{98} +1.62275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) $ 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * 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 $

$2$	−2.66480	−1.88430	−0.942151	−	0.335190i	$-0.891199\pi$
$2$	−2.66480	−1.88430	−0.942151	+	0.335190i	$0.891199\pi$
$3$	−1.17356	−0.677556	−0.338778	−	0.940866i	$-0.610014\pi$
$3$	−1.17356	−0.677556	−0.338778	+	0.940866i	$0.610014\pi$
$4$	5.10118	2.55059
$5$	4.42559	1.97919	0.989593	−	0.143896i	$-0.0459631\pi$
$5$	4.42559	1.97919	0.989593	+	0.143896i	$0.0459631\pi$
$6$	3.12731	1.27672
$7$	1.20677	0.456115	0.228058	−	0.973648i	$-0.426763\pi$
$7$	1.20677	0.456115	0.228058	+	0.973648i	$0.426763\pi$
$8$	−8.26404	−2.92178
$9$	−1.62275	−0.540918
$10$	−11.7933	−3.72938
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−5.98655	−1.72817
$13$	3.53290	0.979850	0.489925	−	0.871765i	$-0.337024\pi$
$13$	3.53290	0.979850	0.489925	+	0.871765i	$0.337024\pi$
$14$	−3.21580	−0.859459
$15$	−5.19370	−1.34101
$16$	11.8197	2.95492
$17$	−4.17739	−1.01317	−0.506583	−	0.862191i	$-0.669092\pi$
$17$	−4.17739	−1.01317	−0.506583	+	0.862191i	$0.669092\pi$
$18$	4.32432	1.01925
$19$	5.96661	1.36883	0.684417	−	0.729091i	$-0.260057\pi$
$19$	5.96661	1.36883	0.684417	+	0.729091i	$0.260057\pi$
$20$	22.5758	5.04809
$21$	−1.41622	−0.309044
$22$	2.66480	0.568138
$23$	−1.37608	−0.286933	−0.143466	−	0.989655i	$-0.545825\pi$
$23$	−1.37608	−0.286933	−0.143466	+	0.989655i	$0.545825\pi$
$24$	9.69835	1.97967
$25$	14.5859	2.91718
$26$	−9.41449	−1.84633
$27$	5.42508	1.04406
$28$	6.15594	1.16336
$29$	−4.09416	−0.760266	−0.380133	−	0.924932i	$-0.624122\pi$
$29$	−4.09416	−0.760266	−0.380133	+	0.924932i	$0.624122\pi$
$30$	13.8402	2.52686
$31$	4.26025	0.765164	0.382582	−	0.923922i	$-0.375035\pi$
$31$	4.26025	0.765164	0.382582	+	0.923922i	$0.375035\pi$
$32$	−14.9691	−2.64618
$33$	1.17356	0.204291
$34$	11.1319	1.90911
$35$	5.34067	0.902737
$36$	−8.27797	−1.37966
$37$	11.1171	1.82764	0.913820	−	0.406118i	$-0.133118\pi$
$37$	11.1171	1.82764	0.913820	+	0.406118i	$0.133118\pi$
$38$	−15.8998	−2.57930
$39$	−4.14607	−0.663903
$40$	−36.5733	−5.78274
$41$	6.73017	1.05108	0.525538	−	0.850770i	$-0.323864\pi$
$41$	6.73017	1.05108	0.525538	+	0.850770i	$0.323864\pi$
$42$	3.77394	0.582331
$43$	5.32446	0.811972	0.405986	−	0.913879i	$-0.366928\pi$
$43$	5.32446	0.811972	0.405986	+	0.913879i	$0.366928\pi$
$44$	−5.10118	−0.769032
$45$	−7.18165	−1.07058
$46$	3.66699	0.540668
$47$	−1.86392	−0.271880	−0.135940	−	0.990717i	$-0.543405\pi$
$47$	−1.86392	−0.271880	−0.135940	+	0.990717i	$0.543405\pi$
$48$	−13.8711	−2.00212
$49$	−5.54371	−0.791959
$50$	−38.8685	−5.49684
$51$	4.90242	0.686477
$52$	18.0220	2.49920
$53$	−14.0322	−1.92747	−0.963735	−	0.266861i	$-0.914014\pi$
$53$	−14.0322	−1.92747	−0.963735	+	0.266861i	$0.914014\pi$
$54$	−14.4568	−1.96732
$55$	−4.42559	−0.596747
$56$	−9.97278	−1.33267
$57$	−7.00218	−0.927461
$58$	10.9101	1.43257
$59$	−8.53852	−1.11162	−0.555810	−	0.831309i	$-0.687592\pi$
$59$	−8.53852	−1.11162	−0.555810	+	0.831309i	$0.687592\pi$
$60$	−26.4940	−3.42036
$61$	−8.66438	−1.10936	−0.554680	−	0.832064i	$-0.687159\pi$
$61$	−8.66438	−1.10936	−0.554680	+	0.832064i	$0.687159\pi$
$62$	−11.3527	−1.44180
$63$	−1.95829	−0.246721
$64$	16.2503	2.03128
$65$	15.6352	1.93931
$66$	−3.12731	−0.384945
$67$	12.7341	1.55571	0.777857	−	0.628441i	$-0.216307\pi$
$67$	12.7341	1.55571	0.777857	+	0.628441i	$0.216307\pi$
$68$	−21.3096	−2.58417
$69$	1.61492	0.194413
$70$	−14.2318	−1.70103
$71$	16.6868	1.98036	0.990182	−	0.139784i	$-0.0446408\pi$
$71$	16.6868	1.98036	0.990182	+	0.139784i	$0.0446408\pi$
$72$	13.4105	1.58044
$73$	6.24979	0.731482	0.365741	−	0.930717i	$-0.380816\pi$
$73$	6.24979	0.731482	0.365741	+	0.930717i	$0.380816\pi$
$74$	−29.6249	−3.44383
$75$	−17.1174	−1.97655
$76$	30.4368	3.49134
$77$	−1.20677	−0.137524
$78$	11.0485	1.25099
$79$	−12.5123	−1.40775	−0.703873	−	0.710326i	$-0.748547\pi$
$79$	−12.5123	−1.40775	−0.703873	+	0.710326i	$0.748547\pi$
$80$	52.3091	5.84834
$81$	−1.49840	−0.166489
$82$	−17.9346	−1.98054
$83$	−1.67501	−0.183856	−0.0919279	−	0.995766i	$-0.529303\pi$
$83$	−1.67501	−0.183856	−0.0919279	+	0.995766i	$0.529303\pi$
$84$	−7.22437	−0.788244
$85$	−18.4874	−2.00524
$86$	−14.1886	−1.53000
$87$	4.80474	0.515123
$88$	8.26404	0.880950
$89$	−0.148598	−0.0157513	−0.00787565	−	0.999969i	$-0.502507\pi$
$89$	−0.148598	−0.0157513	−0.00787565	+	0.999969i	$0.502507\pi$
$90$	19.1377	2.01729
$91$	4.26339	0.446925
$92$	−7.01964	−0.731848
$93$	−4.99967	−0.518441
$94$	4.96697	0.512304
$95$	26.4058	2.70918
$96$	17.5671	1.79294
$97$	2.40260	0.243947	0.121974	−	0.992533i	$-0.461078\pi$
$97$	2.40260	0.243947	0.121974	+	0.992533i	$0.461078\pi$
$98$	14.7729	1.49229
$99$	1.62275	0.163093
$100$	74.4052	7.44052
$101$	9.33560	0.928927	0.464464	−	0.885592i	$-0.346247\pi$
$101$	9.33560	0.928927	0.464464	+	0.885592i	$0.346247\pi$
$102$	−13.0640	−1.29353
$103$	−5.34343	−0.526504	−0.263252	−	0.964727i	$-0.584795\pi$
$103$	−5.34343	−0.526504	−0.263252	+	0.964727i	$0.584795\pi$
$104$	−29.1960	−2.86291
$105$	−6.26760	−0.611655
$106$	37.3930	3.63193
$107$	15.8395	1.53126	0.765630	−	0.643281i	$-0.222427\pi$
$107$	15.8395	1.53126	0.765630	+	0.643281i	$0.222427\pi$
$108$	27.6743	2.66296
$109$	−13.8658	−1.32810	−0.664052	−	0.747687i	$-0.731165\pi$
$109$	−13.8658	−1.32810	−0.664052	+	0.747687i	$0.731165\pi$
$110$	11.7933	1.12445
$111$	−13.0466	−1.23833
$112$	14.2636	1.34779
$113$	13.4483	1.26511	0.632555	−	0.774515i	$-0.282006\pi$
$113$	13.4483	1.26511	0.632555	+	0.774515i	$0.282006\pi$
$114$	18.6594	1.74762
$115$	−6.08998	−0.567893
$116$	−20.8850	−1.93913
$117$	−5.73303	−0.530019
$118$	22.7535	2.09463
$119$	−5.04114	−0.462121
$120$	42.9210	3.91813
$121$	1.00000	0.0909091
$122$	23.0889	2.09037
$123$	−7.89827	−0.712163
$124$	21.7323	1.95162
$125$	42.4232	3.79445
$126$	5.21846	0.464897
$127$	−14.4303	−1.28048	−0.640241	−	0.768174i	$-0.721165\pi$
$127$	−14.4303	−1.28048	−0.640241	+	0.768174i	$0.721165\pi$
$128$	−13.3656	−1.18137
$129$	−6.24858	−0.550156
$130$	−41.6647	−3.65424
$131$	−8.74743	−0.764267	−0.382133	−	0.924107i	$-0.624810\pi$
$131$	−8.74743	−0.764267	−0.382133	+	0.924107i	$0.624810\pi$
$132$	5.98655	0.521062
$133$	7.20031	0.624346
$134$	−33.9338	−2.93143
$135$	24.0092	2.06638
$136$	34.5221	2.96025
$137$	5.49126	0.469150	0.234575	−	0.972098i	$-0.424630\pi$
$137$	5.49126	0.469150	0.234575	+	0.972098i	$0.424630\pi$
$138$	−4.30343	−0.366332
$139$	4.37455	0.371044	0.185522	−	0.982640i	$-0.440602\pi$
$139$	4.37455	0.371044	0.185522	+	0.982640i	$0.440602\pi$
$140$	27.2437	2.30251
$141$	2.18742	0.184214
$142$	−44.4672	−3.73160
$143$	−3.53290	−0.295436
$144$	−19.1805	−1.59837
$145$	−18.1191	−1.50471
$146$	−16.6545	−1.37833
$147$	6.50588	0.536596
$148$	56.7104	4.66156
$149$	−6.21984	−0.509549	−0.254775	−	0.967000i	$-0.582001\pi$
$149$	−6.21984	−0.509549	−0.254775	+	0.967000i	$0.582001\pi$
$150$	45.6146	3.72441
$151$	−11.4140	−0.928860	−0.464430	−	0.885610i	$-0.653741\pi$
$151$	−11.4140	−0.928860	−0.464430	+	0.885610i	$0.653741\pi$
$152$	−49.3083	−3.99943
$153$	6.77888	0.548040
$154$	3.21580	0.259137
$155$	18.8542	1.51440
$156$	−21.1499	−1.69334
$157$	20.7566	1.65656	0.828279	−	0.560316i	$-0.189320\pi$
$157$	20.7566	1.65656	0.828279	+	0.560316i	$0.189320\pi$
$158$	33.3429	2.65262
$159$	16.4676	1.30597
$160$	−66.2470	−5.23729
$161$	−1.66061	−0.130874
$162$	3.99295	0.313715
$163$	−1.58768	−0.124356	−0.0621782	−	0.998065i	$-0.519805\pi$
$163$	−1.58768	−0.124356	−0.0621782	+	0.998065i	$0.519805\pi$
$164$	34.3318	2.68087
$165$	5.19370	0.404329
$166$	4.46357	0.346440
$167$	−4.64398	−0.359362	−0.179681	−	0.983725i	$-0.557507\pi$
$167$	−4.64398	−0.359362	−0.179681	+	0.983725i	$0.557507\pi$
$168$	11.7037	0.902957
$169$	−0.518618	−0.0398937
$170$	49.2654	3.77848
$171$	−9.68234	−0.740427
$172$	27.1610	2.07101
$173$	−14.7938	−1.12475	−0.562377	−	0.826881i	$-0.690113\pi$
$173$	−14.7938	−1.12475	−0.562377	+	0.826881i	$0.690113\pi$
$174$	−12.8037	−0.970646
$175$	17.6018	1.33057
$176$	−11.8197	−0.890943
$177$	10.0205	0.753184
$178$	0.395983	0.0296802
$179$	−8.85649	−0.661965	−0.330983	−	0.943637i	$-0.607380\pi$
$179$	−8.85649	−0.661965	−0.330983	+	0.943637i	$0.607380\pi$
$180$	−36.6349	−2.73061
$181$	21.6872	1.61200	0.805998	−	0.591918i	$-0.201629\pi$
$181$	21.6872	1.61200	0.805998	+	0.591918i	$0.201629\pi$
$182$	−11.3611	−0.842141
$183$	10.1682	0.751654
$184$	11.3720	0.838354
$185$	49.1998	3.61724
$186$	13.3231	0.976900
$187$	4.17739	0.305481
$188$	−9.50817	−0.693455
$189$	6.54682	0.476211
$190$	−70.3662	−5.10490
$191$	−1.27549	−0.0922915	−0.0461458	−	0.998935i	$-0.514694\pi$
$191$	−1.27549	−0.0922915	−0.0461458	+	0.998935i	$0.514694\pi$
$192$	−19.0707	−1.37631
$193$	−8.57805	−0.617461	−0.308731	−	0.951150i	$-0.599904\pi$
$193$	−8.57805	−0.617461	−0.308731	+	0.951150i	$0.599904\pi$
$194$	−6.40246	−0.459670
$195$	−18.3488	−1.31399
$196$	−28.2795	−2.01996
$197$	−0.521401	−0.0371483	−0.0185742	−	0.999827i	$-0.505913\pi$
$197$	−0.521401	−0.0371483	−0.0185742	+	0.999827i	$0.505913\pi$
$198$	−4.32432	−0.307316
$199$	6.38405	0.452553	0.226277	−	0.974063i	$-0.427345\pi$
$199$	6.38405	0.452553	0.226277	+	0.974063i	$0.427345\pi$
$200$	−120.538	−8.52334
$201$	−14.9442	−1.05408
$202$	−24.8776	−1.75038
$203$	−4.94070	−0.346769
$204$	25.0082	1.75092
$205$	29.7850	2.08028
$206$	14.2392	0.992092
$207$	2.23304	0.155207
$208$	41.7578	2.89538
$209$	−5.96661	−0.412719
$210$	16.7019	1.15254
$211$	−0.918310	−0.0632191	−0.0316095	−	0.999500i	$-0.510063\pi$
$211$	−0.918310	−0.0632191	−0.0316095	+	0.999500i	$0.510063\pi$
$212$	−71.5808	−4.91619
$213$	−19.5830	−1.34181
$214$	−42.2091	−2.88536
$215$	23.5639	1.60704
$216$	−44.8331	−3.05051
$217$	5.14114	0.349003
$218$	36.9497	2.50255
$219$	−7.33451	−0.495620
$220$	−22.5758	−1.52206
$221$	−14.7583	−0.992751
$222$	34.7666	2.33338
$223$	15.1138	1.01210	0.506048	−	0.862505i	$-0.331106\pi$
$223$	15.1138	1.01210	0.506048	+	0.862505i	$0.331106\pi$
$224$	−18.0642	−1.20697
$225$	−23.6693	−1.57795
$226$	−35.8371	−2.38385
$227$	−13.3852	−0.888410	−0.444205	−	0.895925i	$-0.646514\pi$
$227$	−13.3852	−0.888410	−0.444205	+	0.895925i	$0.646514\pi$
$228$	−35.7194	−2.36557
$229$	24.0496	1.58924	0.794620	−	0.607108i	$-0.207670\pi$
$229$	24.0496	1.58924	0.794620	+	0.607108i	$0.207670\pi$
$230$	16.2286	1.07008
$231$	1.41622	0.0931802
$232$	33.8343	2.22133
$233$	10.2563	0.671915	0.335958	−	0.941877i	$-0.390940\pi$
$233$	10.2563	0.671915	0.335958	+	0.941877i	$0.390940\pi$
$234$	15.2774	0.998715
$235$	−8.24893	−0.538101
$236$	−43.5565	−2.83529
$237$	14.6840	0.953826
$238$	13.4337	0.870775
$239$	8.74016	0.565354	0.282677	−	0.959215i	$-0.408778\pi$
$239$	8.74016	0.565354	0.282677	+	0.959215i	$0.408778\pi$
$240$	−61.3880	−3.96258
$241$	−29.7991	−1.91953	−0.959765	−	0.280805i	$-0.909398\pi$
$241$	−29.7991	−1.91953	−0.959765	+	0.280805i	$0.909398\pi$
$242$	−2.66480	−0.171300
$243$	−14.5168	−0.931252
$244$	−44.1986	−2.82952
$245$	−24.5342	−1.56743
$246$	21.0473	1.34193
$247$	21.0794	1.34125
$248$	−35.2069	−2.23564
$249$	1.96572	0.124573
$250$	−113.050	−7.14988
$251$	18.3075	1.15556	0.577780	−	0.816192i	$-0.303919\pi$
$251$	18.3075	1.15556	0.577780	+	0.816192i	$0.303919\pi$
$252$	−9.98959	−0.629285
$253$	1.37608	0.0865135
$254$	38.4539	2.41281
$255$	21.6961	1.35866
$256$	3.11628	0.194768
$257$	23.1631	1.44487	0.722436	−	0.691438i	$-0.243023\pi$
$257$	23.1631	1.44487	0.722436	+	0.691438i	$0.243023\pi$
$258$	16.6512	1.03666
$259$	13.4158	0.833615
$260$	79.7579	4.94637
$261$	6.64382	0.411242
$262$	23.3102	1.44011
$263$	29.7571	1.83490	0.917451	−	0.397848i	$-0.130243\pi$
$263$	29.7571	1.83490	0.917451	+	0.397848i	$0.130243\pi$
$264$	−9.69835	−0.596892
$265$	−62.1008	−3.81482
$266$	−19.1874	−1.17646
$267$	0.174388	0.0106724
$268$	64.9588	3.96799
$269$	−12.0675	−0.735769	−0.367885	−	0.929871i	$-0.619918\pi$
$269$	−12.0675	−0.735769	−0.367885	+	0.929871i	$0.619918\pi$
$270$	−63.9799	−3.89369
$271$	4.76998	0.289756	0.144878	−	0.989450i	$-0.453721\pi$
$271$	4.76998	0.289756	0.144878	+	0.989450i	$0.453721\pi$
$272$	−49.3755	−2.99383
$273$	−5.00335	−0.302816
$274$	−14.6331	−0.884020
$275$	−14.5859	−0.879562
$276$	8.23797	0.495868
$277$	−4.24061	−0.254794	−0.127397	−	0.991852i	$-0.540662\pi$
$277$	−4.24061	−0.254794	−0.127397	+	0.991852i	$0.540662\pi$
$278$	−11.6573	−0.699160
$279$	−6.91335	−0.413891
$280$	−44.1355	−2.63760
$281$	−13.3372	−0.795629	−0.397814	−	0.917466i	$-0.630231\pi$
$281$	−13.3372	−0.795629	−0.397814	+	0.917466i	$0.630231\pi$
$282$	−5.82904	−0.347114
$283$	−0.407839	−0.0242435	−0.0121217	−	0.999927i	$-0.503859\pi$
$283$	−0.407839	−0.0242435	−0.0121217	+	0.999927i	$0.503859\pi$
$284$	85.1226	5.05110
$285$	−30.9888	−1.83562
$286$	9.41449	0.556690
$287$	8.12176	0.479412
$288$	24.2911	1.43137
$289$	0.450605	0.0265062
$290$	48.2838	2.83532
$291$	−2.81960	−0.165288
$292$	31.8813	1.86571
$293$	−8.75333	−0.511375	−0.255687	−	0.966760i	$-0.582302\pi$
$293$	−8.75333	−0.511375	−0.255687	+	0.966760i	$0.582302\pi$
$294$	−17.3369	−1.01111
$295$	−37.7880	−2.20010
$296$	−91.8722	−5.33996
$297$	−5.42508	−0.314795
$298$	16.5747	0.960144
$299$	−4.86156	−0.281151
$300$	−87.3190	−5.04137
$301$	6.42539	0.370353
$302$	30.4161	1.75025
$303$	−10.9559	−0.629400
$304$	70.5235	4.04480
$305$	−38.3450	−2.19563
$306$	−18.0644	−1.03267
$307$	26.1385	1.49180	0.745902	−	0.666055i	$-0.232018\pi$
$307$	26.1385	1.49180	0.745902	+	0.666055i	$0.232018\pi$
$308$	−6.15594	−0.350767
$309$	6.27084	0.356736
$310$	−50.2426	−2.85359
$311$	20.4254	1.15822	0.579108	−	0.815251i	$-0.303401\pi$
$311$	20.4254	1.15822	0.579108	+	0.815251i	$0.303401\pi$
$312$	34.2633	1.93978
$313$	−29.9494	−1.69284	−0.846421	−	0.532514i	$-0.821247\pi$
$313$	−29.9494	−1.69284	−0.846421	+	0.532514i	$0.821247\pi$
$314$	−55.3123	−3.12145
$315$	−8.66659	−0.488307
$316$	−63.8276	−3.59058
$317$	−28.6448	−1.60885	−0.804425	−	0.594054i	$-0.797526\pi$
$317$	−28.6448	−1.60885	−0.804425	+	0.594054i	$0.797526\pi$
$318$	−43.8830	−2.46084
$319$	4.09416	0.229229
$320$	71.9171	4.02029
$321$	−18.5886	−1.03751
$322$	4.42520	0.246607
$323$	−24.9249	−1.38686
$324$	−7.64362	−0.424645
$325$	51.5305	2.85840
$326$	4.23084	0.234325
$327$	16.2724	0.899864
$328$	−55.6184	−3.07101
$329$	−2.24931	−0.124009
$330$	−13.8402	−0.761878
$331$	−9.64005	−0.529865	−0.264932	−	0.964267i	$-0.585350\pi$
$331$	−9.64005	−0.529865	−0.264932	+	0.964267i	$0.585350\pi$
$332$	−8.54451	−0.468941
$333$	−18.0403	−0.988605
$334$	12.3753	0.677147
$335$	56.3558	3.07905
$336$	−16.7392	−0.913200
$337$	−2.66031	−0.144916	−0.0724581	−	0.997371i	$-0.523084\pi$
$337$	−2.66031	−0.144916	−0.0724581	+	0.997371i	$0.523084\pi$
$338$	1.38201	0.0751717
$339$	−15.7824	−0.857183
$340$	−94.3078	−5.11456
$341$	−4.26025	−0.230706
$342$	25.8016	1.39519
$343$	−15.1374	−0.817340
$344$	−44.0015	−2.37240
$345$	7.14696	0.384779
$346$	39.4227	2.11937
$347$	31.6867	1.70103	0.850514	−	0.525952i	$-0.176291\pi$
$347$	31.6867	1.70103	0.850514	+	0.525952i	$0.176291\pi$
$348$	24.5099	1.31387
$349$	−19.4782	−1.04264	−0.521321	−	0.853361i	$-0.674561\pi$
$349$	−19.4782	−1.04264	−0.521321	+	0.853361i	$0.674561\pi$
$350$	−46.9053	−2.50719
$351$	19.1663	1.02302
$352$	14.9691	0.797854
$353$	2.78124	0.148031	0.0740153	−	0.997257i	$-0.476419\pi$
$353$	2.78124	0.148031	0.0740153	+	0.997257i	$0.476419\pi$
$354$	−26.7026	−1.41923
$355$	73.8492	3.91951
$356$	−0.758023	−0.0401751
$357$	5.91609	0.313113
$358$	23.6008	1.24734
$359$	−4.11703	−0.217289	−0.108644	−	0.994081i	$-0.534651\pi$
$359$	−4.11703	−0.217289	−0.108644	+	0.994081i	$0.534651\pi$
$360$	59.3495	3.12799
$361$	16.6004	0.873706
$362$	−57.7921	−3.03749
$363$	−1.17356	−0.0615960
$364$	21.7483	1.13992
$365$	27.6590	1.44774
$366$	−27.0962	−1.41634
$367$	28.3119	1.47787	0.738934	−	0.673778i	$-0.235330\pi$
$367$	28.3119	1.47787	0.738934	+	0.673778i	$0.235330\pi$
$368$	−16.2649	−0.847864
$369$	−10.9214	−0.568546
$370$	−131.108	−6.81597
$371$	−16.9336	−0.879149
$372$	−25.5042	−1.32233
$373$	−3.30806	−0.171285	−0.0856423	−	0.996326i	$-0.527294\pi$
$373$	−3.30806	−0.171285	−0.0856423	+	0.996326i	$0.527294\pi$
$374$	−11.1319	−0.575619
$375$	−49.7862	−2.57095
$376$	15.4035	0.794373
$377$	−14.4643	−0.744947
$378$	−17.4460	−0.897325
$379$	−14.6808	−0.754102	−0.377051	−	0.926192i	$-0.623062\pi$
$379$	−14.6808	−0.754102	−0.377051	+	0.926192i	$0.623062\pi$
$380$	134.701	6.91000
$381$	16.9348	0.867598
$382$	3.39894	0.173905
$383$	0.0119913	0.000612725 0	0.000306363	−	1.00000i	$-0.499902\pi$
$383$	0.0119913	0.000612725 0	0.000306363		1.00000i	$0.499902\pi$
$384$	15.6854	0.800442
$385$	−5.34067	−0.272186
$386$	22.8588	1.16348
$387$	−8.64029	−0.439211
$388$	12.2561	0.622210
$389$	27.4932	1.39396	0.696980	−	0.717090i	$-0.254527\pi$
$389$	27.4932	1.39396	0.696980	+	0.717090i	$0.254527\pi$
$390$	48.8961	2.47595
$391$	5.74843	0.290711
$392$	45.8135	2.31393
$393$	10.2656	0.517833
$394$	1.38943	0.0699986
$395$	−55.3744	−2.78619
$396$	8.27797	0.415984
$397$	−10.9738	−0.550759	−0.275380	−	0.961336i	$-0.588804\pi$
$397$	−10.9738	−0.550759	−0.275380	+	0.961336i	$0.588804\pi$
$398$	−17.0122	−0.852746
$399$	−8.45001	−0.423029
$400$	172.401	8.62003
$401$	−22.2630	−1.11176	−0.555880	−	0.831263i	$-0.687619\pi$
$401$	−22.2630	−1.11176	−0.555880	+	0.831263i	$0.687619\pi$
$402$	39.8234	1.98621
$403$	15.0511	0.749746
$404$	47.6226	2.36931
$405$	−6.63131	−0.329513
$406$	13.1660	0.653417
$407$	−11.1171	−0.551054
$408$	−40.5138	−2.00573
$409$	19.5897	0.968647	0.484324	−	0.874889i	$-0.339066\pi$
$409$	19.5897	0.968647	0.484324	+	0.874889i	$0.339066\pi$
$410$	−79.3712	−3.91987
$411$	−6.44433	−0.317875
$412$	−27.2578	−1.34290
$413$	−10.3040	−0.507027
$414$	−5.95062	−0.292457
$415$	−7.41290	−0.363885
$416$	−52.8842	−2.59286
$417$	−5.13380	−0.251403
$418$	15.8998	0.777687
$419$	11.0588	0.540259	0.270129	−	0.962824i	$-0.412933\pi$
$419$	11.0588	0.540259	0.270129	+	0.962824i	$0.412933\pi$
$420$	−31.9721	−1.56008
$421$	6.43504	0.313625	0.156812	−	0.987628i	$-0.449878\pi$
$421$	6.43504	0.313625	0.156812	+	0.987628i	$0.449878\pi$
$422$	2.44712	0.119124
$423$	3.02468	0.147065
$424$	115.963	5.63164
$425$	−60.9309	−2.95558
$426$	52.1849	2.52837
$427$	−10.4559	−0.505997
$428$	80.8001	3.90562
$429$	4.14607	0.200174
$430$	−62.7931	−3.02815
$431$	21.6944	1.04498	0.522491	−	0.852645i	$-0.325003\pi$
$431$	21.6944	1.04498	0.522491	+	0.852645i	$0.325003\pi$
$432$	64.1228	3.08511
$433$	−10.1195	−0.486312	−0.243156	−	0.969987i	$-0.578183\pi$
$433$	−10.1195	−0.486312	−0.243156	+	0.969987i	$0.578183\pi$
$434$	−13.7001	−0.657627
$435$	21.2638	1.01952
$436$	−70.7320	−3.38745
$437$	−8.21054	−0.392763
$438$	19.5450	0.933897
$439$	14.5697	0.695374	0.347687	−	0.937611i	$-0.386967\pi$
$439$	14.5697	0.695374	0.347687	+	0.937611i	$0.386967\pi$
$440$	36.5733	1.74356
$441$	8.99608	0.428385
$442$	39.3280	1.87064
$443$	1.75637	0.0834476	0.0417238	−	0.999129i	$-0.486715\pi$
$443$	1.75637	0.0834476	0.0417238	+	0.999129i	$0.486715\pi$
$444$	−66.5531	−3.15847
$445$	−0.657632	−0.0311748
$446$	−40.2754	−1.90709
$447$	7.29936	0.345248
$448$	19.6103	0.926500
$449$	−28.2700	−1.33414	−0.667072	−	0.744994i	$-0.732453\pi$
$449$	−28.2700	−1.33414	−0.667072	+	0.744994i	$0.732453\pi$
$450$	63.0741	2.97334
$451$	−6.73017	−0.316911
$452$	68.6022	3.22678
$453$	13.3951	0.629355
$454$	35.6690	1.67403
$455$	18.8680	0.884547
$456$	57.8663	2.70984
$457$	−20.3435	−0.951629	−0.475815	−	0.879546i	$-0.657847\pi$
$457$	−20.3435	−0.951629	−0.475815	+	0.879546i	$0.657847\pi$
$458$	−64.0873	−2.99461
$459$	−22.6627	−1.05780
$460$	−31.0661	−1.44846
$461$	20.8216	0.969761	0.484880	−	0.874581i	$-0.338863\pi$
$461$	20.8216	0.969761	0.484880	+	0.874581i	$0.338863\pi$
$462$	−3.77394	−0.175579
$463$	−0.171608	−0.00797530	−0.00398765	−	0.999992i	$-0.501269\pi$
$463$	−0.171608	−0.00797530	−0.00398765	+	0.999992i	$0.501269\pi$
$464$	−48.3917	−2.24653
$465$	−22.1265	−1.02609
$466$	−27.3311	−1.26609
$467$	−15.3572	−0.710645	−0.355323	−	0.934744i	$-0.615629\pi$
$467$	−15.3572	−0.710645	−0.355323	+	0.934744i	$0.615629\pi$
$468$	−29.2452	−1.35186
$469$	15.3671	0.709585
$470$	21.9818	1.01394
$471$	−24.3592	−1.12241
$472$	70.5626	3.24791
$473$	−5.32446	−0.244819
$474$	−39.1299	−1.79730
$475$	87.0282	3.99313
$476$	−25.7158	−1.17868
$477$	22.7708	1.04260
$478$	−23.2908	−1.06530
$479$	−2.83173	−0.129385	−0.0646926	−	0.997905i	$-0.520607\pi$
$479$	−2.83173	−0.129385	−0.0646926	+	0.997905i	$0.520607\pi$
$480$	77.7449	3.54855
$481$	39.2756	1.79081
$482$	79.4088	3.61697
$483$	1.94883	0.0886747
$484$	5.10118	0.231872
$485$	10.6329	0.482817
$486$	38.6844	1.75476
$487$	10.9060	0.494198	0.247099	−	0.968990i	$-0.420523\pi$
$487$	10.9060	0.494198	0.247099	+	0.968990i	$0.420523\pi$
$488$	71.6028	3.24131
$489$	1.86323	0.0842583
$490$	65.3789	2.95352
$491$	22.7853	1.02829	0.514144	−	0.857704i	$-0.328110\pi$
$491$	22.7853	1.02829	0.514144	+	0.857704i	$0.328110\pi$
$492$	−40.2905	−1.81644
$493$	17.1029	0.770276
$494$	−56.1726	−2.52732
$495$	7.18165	0.322791
$496$	50.3549	2.26100
$497$	20.1372	0.903275
$498$	−5.23827	−0.234732
$499$	14.2476	0.637810	0.318905	−	0.947787i	$-0.396685\pi$
$499$	14.2476	0.637810	0.318905	+	0.947787i	$0.396685\pi$
$500$	216.408	9.67808
$501$	5.45000	0.243488
$502$	−48.7859	−2.17742
$503$	−15.4032	−0.686794	−0.343397	−	0.939190i	$-0.611578\pi$
$503$	−15.4032	−0.686794	−0.343397	+	0.939190i	$0.611578\pi$
$504$	16.1834	0.720865
$505$	41.3156	1.83852
$506$	−3.66699	−0.163017
$507$	0.608630	0.0270302
$508$	−73.6116	−3.26599
$509$	−4.36561	−0.193502	−0.0967510	−	0.995309i	$-0.530845\pi$
$509$	−4.36561	−0.193502	−0.0967510	+	0.995309i	$0.530845\pi$
$510$	−57.8160	−2.56013
$511$	7.54205	0.333640
$512$	18.4270	0.814366
$513$	32.3694	1.42914
$514$	−61.7250	−2.72257
$515$	−23.6478	−1.04205
$516$	−31.8751	−1.40322
$517$	1.86392	0.0819749
$518$	−35.7504	−1.57078
$519$	17.3615	0.762083
$520$	−129.210	−5.66622
$521$	−16.9197	−0.741267	−0.370634	−	0.928779i	$-0.620859\pi$
$521$	−16.9197	−0.741267	−0.370634	+	0.928779i	$0.620859\pi$
$522$	−17.7045	−0.774904
$523$	37.2713	1.62976	0.814879	−	0.579631i	$-0.196803\pi$
$523$	37.2713	1.62976	0.814879	+	0.579631i	$0.196803\pi$
$524$	−44.6222	−1.94933
$525$	−20.6568	−0.901535
$526$	−79.2969	−3.45751
$527$	−17.7968	−0.775239
$528$	13.8711	0.603663
$529$	−21.1064	−0.917670
$530$	165.486	7.18827
$531$	13.8559	0.601296
$532$	36.7301	1.59245
$533$	23.7770	1.02990
$534$	−0.464710	−0.0201100
$535$	70.0991	3.03065
$536$	−105.235	−4.54545
$537$	10.3936	0.448518
$538$	32.1576	1.38641
$539$	5.54371	0.238785
$540$	122.475	5.27050
$541$	−31.7940	−1.36693	−0.683465	−	0.729983i	$-0.739528\pi$
$541$	−31.7940	−1.36693	−0.683465	+	0.729983i	$0.739528\pi$
$542$	−12.7111	−0.545987
$543$	−25.4512	−1.09222
$544$	62.5317	2.68102
$545$	−61.3644	−2.62856
$546$	13.3329	0.570597
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	28.0119	1.19661
$549$	14.0602	0.600073
$550$	38.8685	1.65736
$551$	−24.4282	−1.04068
$552$	−13.3457	−0.568032
$553$	−15.0995	−0.642094
$554$	11.3004	0.480108
$555$	−57.7390	−2.45088
$556$	22.3154	0.946383
$557$	18.7401	0.794045	0.397022	−	0.917809i	$-0.370043\pi$
$557$	18.7401	0.794045	0.397022	+	0.917809i	$0.370043\pi$
$558$	18.4227	0.779896
$559$	18.8108	0.795611
$560$	63.1250	2.66752
$561$	−4.90242	−0.206980
$562$	35.5409	1.49920
$563$	−9.17942	−0.386866	−0.193433	−	0.981113i	$-0.561962\pi$
$563$	−9.17942	−0.386866	−0.193433	+	0.981113i	$0.561962\pi$
$564$	11.1584	0.469854
$565$	59.5167	2.50389
$566$	1.08681	0.0456821
$567$	−1.80822	−0.0759382
$568$	−137.901	−5.78619
$569$	32.1296	1.34694	0.673472	−	0.739213i	$-0.264802\pi$
$569$	32.1296	1.34694	0.673472	+	0.739213i	$0.264802\pi$
$570$	82.5791	3.45886
$571$	31.0483	1.29933	0.649665	−	0.760221i	$-0.274909\pi$
$571$	31.0483	1.29933	0.649665	+	0.760221i	$0.274909\pi$
$572$	−18.0220	−0.753536
$573$	1.49687	0.0625327
$574$	−21.6429	−0.903357
$575$	−20.0714	−0.837033
$576$	−26.3702	−1.09876
$577$	−13.6337	−0.567579	−0.283790	−	0.958887i	$-0.591592\pi$
$577$	−13.6337	−0.567579	−0.283790	+	0.958887i	$0.591592\pi$
$578$	−1.20077	−0.0499457
$579$	10.0669	0.418364
$580$	−92.4287	−3.83789
$581$	−2.02134	−0.0838595
$582$	7.51368	0.311452
$583$	14.0322	0.581154
$584$	−51.6485	−2.13723
$585$	−25.3721	−1.04901
$586$	23.3259	0.963584
$587$	31.2328	1.28911	0.644557	−	0.764556i	$-0.277042\pi$
$587$	31.2328	1.28911	0.644557	+	0.764556i	$0.277042\pi$
$588$	33.1877	1.36864
$589$	25.4193	1.04738
$590$	100.698	4.14566
$591$	0.611896	0.0251700
$592$	131.401	5.40054
$593$	5.49897	0.225815	0.112908	−	0.993605i	$-0.463984\pi$
$593$	5.49897	0.225815	0.112908	+	0.993605i	$0.463984\pi$
$594$	14.4568	0.593169
$595$	−22.3101	−0.914623
$596$	−31.7285	−1.29965
$597$	−7.49207	−0.306630
$598$	12.9551	0.529773
$599$	−34.6193	−1.41451	−0.707253	−	0.706960i	$-0.750066\pi$
$599$	−34.6193	−1.41451	−0.707253	+	0.706960i	$0.750066\pi$
$600$	141.459	5.77504
$601$	−7.94117	−0.323927	−0.161964	−	0.986797i	$-0.551783\pi$
$601$	−7.94117	−0.323927	−0.161964	+	0.986797i	$0.551783\pi$
$602$	−17.1224	−0.697857
$603$	−20.6643	−0.841514
$604$	−58.2250	−2.36914
$605$	4.42559	0.179926
$606$	29.1953	1.18598
$607$	−3.05546	−0.124017	−0.0620086	−	0.998076i	$-0.519751\pi$
$607$	−3.05546	−0.124017	−0.0620086	+	0.998076i	$0.519751\pi$
$608$	−89.3146	−3.62219
$609$	5.79821	0.234955
$610$	102.182	4.13723
$611$	−6.58503	−0.266402
$612$	34.5803	1.39783
$613$	45.1599	1.82399	0.911995	−	0.410200i	$-0.134541\pi$
$613$	45.1599	1.82399	0.911995	+	0.410200i	$0.134541\pi$
$614$	−69.6541	−2.81101
$615$	−34.9545	−1.40950
$616$	9.97278	0.401815
$617$	35.0194	1.40983	0.704915	−	0.709292i	$-0.250985\pi$
$617$	35.0194	1.40983	0.704915	+	0.709292i	$0.250985\pi$
$618$	−16.7106	−0.672197
$619$	23.1479	0.930394	0.465197	−	0.885207i	$-0.345984\pi$
$619$	23.1479	0.930394	0.465197	+	0.885207i	$0.345984\pi$
$620$	96.1784	3.86262
$621$	−7.46536	−0.299574
$622$	−54.4296	−2.18243
$623$	−0.179323	−0.00718441
$624$	−49.0053	−1.96178
$625$	114.818	4.59274
$626$	79.8094	3.18982
$627$	7.00218	0.279640
$628$	105.883	4.22520
$629$	−46.4405	−1.85170
$630$	23.0948	0.920118
$631$	−30.3057	−1.20645	−0.603225	−	0.797571i	$-0.706118\pi$
$631$	−30.3057	−1.20645	−0.603225	+	0.797571i	$0.706118\pi$
$632$	103.402	4.11312
$633$	1.07769	0.0428344
$634$	76.3327	3.03156
$635$	−63.8626	−2.53431
$636$	84.0044	3.33099
$637$	−19.5854	−0.776001
$638$	−10.9101	−0.431936
$639$	−27.0787	−1.07122
$640$	−59.1509	−2.33814
$641$	−32.3153	−1.27638	−0.638188	−	0.769880i	$-0.720316\pi$
$641$	−32.3153	−1.27638	−0.638188	+	0.769880i	$0.720316\pi$
$642$	49.5350	1.95499
$643$	20.2927	0.800267	0.400134	−	0.916457i	$-0.368964\pi$
$643$	20.2927	0.800267	0.400134	+	0.916457i	$0.368964\pi$
$644$	−8.47108	−0.333807
$645$	−27.6537	−1.08886
$646$	66.4199	2.61326
$647$	22.7686	0.895125	0.447563	−	0.894253i	$-0.352292\pi$
$647$	22.7686	0.895125	0.447563	+	0.894253i	$0.352292\pi$
$648$	12.3828	0.486444
$649$	8.53852	0.335166
$650$	−137.319	−5.38608
$651$	−6.03344	−0.236469
$652$	−8.09902	−0.317182
$653$	−42.9788	−1.68189	−0.840946	−	0.541119i	$-0.818001\pi$
$653$	−42.9788	−1.68189	−0.840946	+	0.541119i	$0.818001\pi$
$654$	−43.3627	−1.69562
$655$	−38.7126	−1.51263
$656$	79.5485	3.10585
$657$	−10.1419	−0.395672
$658$	5.99398	0.233670
$659$	12.5276	0.488006	0.244003	−	0.969775i	$-0.421539\pi$
$659$	12.5276	0.488006	0.244003	+	0.969775i	$0.421539\pi$
$660$	26.4940	1.03128
$661$	37.3192	1.45155	0.725775	−	0.687932i	$-0.241481\pi$
$661$	37.3192	1.45155	0.725775	+	0.687932i	$0.241481\pi$
$662$	25.6888	0.998425
$663$	17.3198	0.672644
$664$	13.8423	0.537186
$665$	31.8657	1.23570
$666$	48.0740	1.86283
$667$	5.63389	0.218145
$668$	−23.6898	−0.916586
$669$	−17.7370	−0.685751
$670$	−150.177	−5.80185
$671$	8.66438	0.334485
$672$	21.1994	0.817786
$673$	−16.2948	−0.628120	−0.314060	−	0.949403i	$-0.601689\pi$
$673$	−16.2948	−0.628120	−0.314060	+	0.949403i	$0.601689\pi$
$674$	7.08920	0.273066
$675$	79.1296	3.04570
$676$	−2.64556	−0.101752
$677$	−31.5661	−1.21318	−0.606591	−	0.795014i	$-0.707463\pi$
$677$	−31.5661	−1.21318	−0.606591	+	0.795014i	$0.707463\pi$
$678$	42.0570	1.61519
$679$	2.89938	0.111268
$680$	152.781	5.85888
$681$	15.7084	0.601947
$682$	11.3527	0.434719
$683$	33.4557	1.28015	0.640074	−	0.768314i	$-0.278904\pi$
$683$	33.4557	1.28015	0.640074	+	0.768314i	$0.278904\pi$
$684$	−49.3914	−1.88853
$685$	24.3021	0.928536
$686$	40.3381	1.54011
$687$	−28.2236	−1.07680
$688$	62.9334	2.39931
$689$	−49.5743	−1.88863
$690$	−19.0452	−0.725040
$691$	−31.5598	−1.20059	−0.600295	−	0.799778i	$-0.704950\pi$
$691$	−31.5598	−1.20059	−0.600295	+	0.799778i	$0.704950\pi$
$692$	−75.4660	−2.86879
$693$	1.95829	0.0743892
$694$	−84.4387	−3.20525
$695$	19.3600	0.734366
$696$	−39.7066	−1.50507
$697$	−28.1146	−1.06492
$698$	51.9055	1.96465
$699$	−12.0364	−0.455260
$700$	89.7898	3.39374
$701$	−26.8933	−1.01575	−0.507874	−	0.861432i	$-0.669568\pi$
$701$	−26.8933	−1.01575	−0.507874	+	0.861432i	$0.669568\pi$
$702$	−51.0744	−1.92768
$703$	66.3314	2.50174
$704$	−16.2503	−0.612455
$705$	9.68062	0.364593
$706$	−7.41147	−0.278934
$707$	11.2659	0.423698
$708$	51.1162	1.92107
$709$	−31.9901	−1.20141	−0.600706	−	0.799470i	$-0.705114\pi$
$709$	−31.9901	−1.20141	−0.600706	+	0.799470i	$0.705114\pi$
$710$	−196.794	−7.38553
$711$	20.3044	0.761475
$712$	1.22802	0.0460218
$713$	−5.86246	−0.219551
$714$	−15.7652	−0.589998
$715$	−15.6352	−0.584723
$716$	−45.1786	−1.68840
$717$	−10.2571	−0.383059
$718$	10.9711	0.409437
$719$	−21.4311	−0.799243	−0.399622	−	0.916680i	$-0.630859\pi$
$719$	−21.4311	−0.799243	−0.399622	+	0.916680i	$0.630859\pi$
$720$	−84.8849	−3.16347
$721$	−6.44828	−0.240147
$722$	−44.2369	−1.64633
$723$	34.9711	1.30059
$724$	110.630	4.11154
$725$	−59.7169	−2.21783
$726$	3.12731	0.116065
$727$	16.8462	0.624789	0.312395	−	0.949952i	$-0.398869\pi$
$727$	16.8462	0.624789	0.312395	+	0.949952i	$0.398869\pi$
$728$	−35.2328	−1.30582
$729$	21.5315	0.797464
$730$	−73.7059	−2.72798
$731$	−22.2424	−0.822663
$732$	51.8697	1.91716
$733$	10.1001	0.373057	0.186529	−	0.982450i	$-0.440276\pi$
$733$	10.1001	0.373057	0.186529	+	0.982450i	$0.440276\pi$
$734$	−75.4456	−2.78475
$735$	28.7924	1.06202
$736$	20.5987	0.759277
$737$	−12.7341	−0.469066
$738$	29.1034	1.07131
$739$	39.0134	1.43513	0.717566	−	0.696491i	$-0.245256\pi$
$739$	39.0134	1.43513	0.717566	+	0.696491i	$0.245256\pi$
$740$	250.977	9.22610
$741$	−24.7380	−0.908773
$742$	45.1247	1.65658
$743$	−4.19798	−0.154009	−0.0770044	−	0.997031i	$-0.524536\pi$
$743$	−4.19798	−0.154009	−0.0770044	+	0.997031i	$0.524536\pi$
$744$	41.3175	1.51477
$745$	−27.5265	−1.00849
$746$	8.81532	0.322752
$747$	2.71813	0.0994510
$748$	21.3096	0.779157
$749$	19.1146	0.698432
$750$	132.671	4.84444
$751$	−7.95253	−0.290192	−0.145096	−	0.989418i	$-0.546349\pi$
$751$	−7.95253	−0.290192	−0.145096	+	0.989418i	$0.546349\pi$
$752$	−22.0309	−0.803384
$753$	−21.4850	−0.782956
$754$	38.5444	1.40370
$755$	−50.5138	−1.83839
$756$	33.3965	1.21462
$757$	0.550226	0.0199983	0.00999915	−	0.999950i	$-0.496817\pi$
$757$	0.550226	0.0199983	0.00999915	+	0.999950i	$0.496817\pi$
$758$	39.1215	1.42096
$759$	−1.61492	−0.0586177
$760$	−218.218	−7.91562
$761$	−23.7224	−0.859937	−0.429968	−	0.902844i	$-0.641475\pi$
$761$	−23.7224	−0.859937	−0.429968	+	0.902844i	$0.641475\pi$
$762$	−45.1280	−1.63482
$763$	−16.7328	−0.605769
$764$	−6.50653	−0.235398
$765$	30.0006	1.08467
$766$	−0.0319544	−0.00115456
$767$	−30.1657	−1.08922
$768$	−3.65715	−0.131966
$769$	34.7491	1.25309	0.626543	−	0.779387i	$-0.284469\pi$
$769$	34.7491	1.25309	0.626543	+	0.779387i	$0.284469\pi$
$770$	14.2318	0.512879
$771$	−27.1833	−0.978981
$772$	−43.7582	−1.57489
$773$	2.54252	0.0914480	0.0457240	−	0.998954i	$-0.485441\pi$
$773$	2.54252	0.0914480	0.0457240	+	0.998954i	$0.485441\pi$
$774$	23.0247	0.827605
$775$	62.1395	2.23212
$776$	−19.8552	−0.712760
$777$	−15.7442	−0.564821
$778$	−73.2640	−2.62664
$779$	40.1563	1.43875
$780$	−93.6007	−3.35144
$781$	−16.6868	−0.597102
$782$	−15.3184	−0.547786
$783$	−22.2112	−0.793762
$784$	−65.5249	−2.34018
$785$	91.8603	3.27864
$786$	−27.3559	−0.975754
$787$	−40.1959	−1.43283	−0.716415	−	0.697674i	$-0.754218\pi$
$787$	−40.1959	−1.43283	−0.716415	+	0.697674i	$0.754218\pi$
$788$	−2.65976	−0.0947501
$789$	−34.9218	−1.24325
$790$	147.562	5.25002
$791$	16.2290	0.577036
$792$	−13.4105	−0.476522
$793$	−30.6104	−1.08701
$794$	29.2430	1.03780
$795$	72.8791	2.58475
$796$	32.5662	1.15428
$797$	19.4966	0.690605	0.345302	−	0.938491i	$-0.387776\pi$
$797$	19.4966	0.690605	0.345302	+	0.938491i	$0.387776\pi$
$798$	22.5176	0.797115
$799$	7.78631	0.275460
$800$	−218.337	−7.71938
$801$	0.241137	0.00852017
$802$	59.3265	2.09489
$803$	−6.24979	−0.220550
$804$	−76.2331	−2.68853
$805$	−7.34919	−0.259025
$806$	−40.1081	−1.41275
$807$	14.1620	0.498525
$808$	−77.1498	−2.71412
$809$	−24.8823	−0.874815	−0.437408	−	0.899263i	$-0.644103\pi$
$809$	−24.8823	−0.874815	−0.437408	+	0.899263i	$0.644103\pi$
$810$	17.6712	0.620901
$811$	−25.2285	−0.885891	−0.442945	−	0.896549i	$-0.646066\pi$
$811$	−25.2285	−0.885891	−0.442945	+	0.896549i	$0.646066\pi$
$812$	−25.2034	−0.884466
$813$	−5.59786	−0.196326
$814$	29.6249	1.03835
$815$	−7.02641	−0.246124
$816$	57.9451	2.02848
$817$	31.7690	1.11146
$818$	−52.2027	−1.82522
$819$	−6.91844	−0.241750
$820$	151.939	5.30593
$821$	−9.15930	−0.319662	−0.159831	−	0.987144i	$-0.551095\pi$
$821$	−9.15930	−0.319662	−0.159831	+	0.987144i	$0.551095\pi$
$822$	17.1729	0.598973
$823$	−34.0908	−1.18833	−0.594166	−	0.804343i	$-0.702518\pi$
$823$	−34.0908	−1.18833	−0.594166	+	0.804343i	$0.702518\pi$
$824$	44.1583	1.53833
$825$	17.1174	0.595952
$826$	27.4582	0.955392
$827$	48.8108	1.69732	0.848659	−	0.528940i	$-0.177410\pi$
$827$	48.8108	1.69732	0.848659	+	0.528940i	$0.177410\pi$
$828$	11.3912	0.395870
$829$	−46.7178	−1.62258	−0.811289	−	0.584645i	$-0.801234\pi$
$829$	−46.7178	−1.62258	−0.811289	+	0.584645i	$0.801234\pi$
$830$	19.7539	0.685669
$831$	4.97662	0.172637
$832$	57.4106	1.99035
$833$	23.1583	0.802386
$834$	13.6806	0.473720
$835$	−20.5524	−0.711245
$836$	−30.4368	−1.05268
$837$	23.1122	0.798876
$838$	−29.4696	−1.01801
$839$	11.9581	0.412839	0.206420	−	0.978464i	$-0.433819\pi$
$839$	11.9581	0.412839	0.206420	+	0.978464i	$0.433819\pi$
$840$	51.7957	1.78712
$841$	−12.2379	−0.421995
$842$	−17.1481	−0.590964
$843$	15.6520	0.539083
$844$	−4.68447	−0.161246
$845$	−2.29519	−0.0789570
$846$	−8.06017	−0.277115
$847$	1.20677	0.0414650
$848$	−165.856	−5.69552
$849$	0.478624	0.0164263
$850$	162.369	5.56921
$851$	−15.2980	−0.524410
$852$	−99.8966	−3.42240
$853$	7.71211	0.264058	0.132029	−	0.991246i	$-0.457851\pi$
$853$	7.71211	0.264058	0.132029	+	0.991246i	$0.457851\pi$
$854$	27.8629	0.953450
$855$	−42.8501	−1.46544
$856$	−130.898	−4.47401
$857$	−10.3856	−0.354764	−0.177382	−	0.984142i	$-0.556763\pi$
$857$	−10.3856	−0.354764	−0.177382	+	0.984142i	$0.556763\pi$
$858$	−11.0485	−0.377189
$859$	7.95340	0.271367	0.135683	−	0.990752i	$-0.456677\pi$
$859$	7.95340	0.271367	0.135683	+	0.990752i	$0.456677\pi$
$860$	120.204	4.09891
$861$	−9.53138	−0.324828
$862$	−57.8113	−1.96906
$863$	41.6337	1.41723	0.708614	−	0.705596i	$-0.249321\pi$
$863$	41.6337	1.41723	0.708614	+	0.705596i	$0.249321\pi$
$864$	−81.2085	−2.76277
$865$	−65.4715	−2.22610
$866$	26.9665	0.916357
$867$	−0.528813	−0.0179594
$868$	26.2259	0.890164
$869$	12.5123	0.424451
$870$	−56.6640	−1.92109
$871$	44.9882	1.52437
$872$	114.588	3.88043
$873$	−3.89884	−0.131956
$874$	21.8795	0.740084
$875$	51.1950	1.73071
$876$	−37.4147	−1.26412
$877$	−48.9084	−1.65152	−0.825759	−	0.564023i	$-0.809253\pi$
$877$	−48.9084	−1.65152	−0.825759	+	0.564023i	$0.809253\pi$
$878$	−38.8254	−1.31029
$879$	10.2726	0.346485
$880$	−52.3091	−1.76334
$881$	−38.8566	−1.30911	−0.654556	−	0.756014i	$-0.727144\pi$
$881$	−38.8566	−1.30911	−0.654556	+	0.756014i	$0.727144\pi$
$882$	−23.9728	−0.807206
$883$	25.6894	0.864519	0.432259	−	0.901749i	$-0.357716\pi$
$883$	25.6894	0.864519	0.432259	+	0.901749i	$0.357716\pi$
$884$	−75.2848	−2.53210
$885$	44.3465	1.49069
$886$	−4.68038	−0.157240
$887$	44.4514	1.49253	0.746266	−	0.665648i	$-0.231845\pi$
$887$	44.4514	1.49253	0.746266	+	0.665648i	$0.231845\pi$
$888$	107.818	3.61812
$889$	−17.4140	−0.584048
$890$	1.75246	0.0587426
$891$	1.49840	0.0501983
$892$	77.0983	2.58144
$893$	−11.1213	−0.372159
$894$	−19.4514	−0.650551
$895$	−39.1952	−1.31015
$896$	−16.1292	−0.538840
$897$	5.70533	0.190496
$898$	75.3340	2.51393
$899$	−17.4422	−0.581728
$900$	−120.741	−4.02471
$901$	58.6180	1.95285
$902$	17.9346	0.597157
$903$	−7.54058	−0.250935
$904$	−111.137	−3.69637
$905$	95.9787	3.19044
$906$	−35.6952	−1.18589
$907$	16.9032	0.561263	0.280631	−	0.959816i	$-0.409456\pi$
$907$	16.9032	0.561263	0.280631	+	0.959816i	$0.409456\pi$
$908$	−68.2805	−2.26597
$909$	−15.1494	−0.502474
$910$	−50.2796	−1.66675
$911$	20.9836	0.695219	0.347610	−	0.937639i	$-0.386993\pi$
$911$	20.9836	0.695219	0.347610	+	0.937639i	$0.386993\pi$
$912$	−82.7636	−2.74058
$913$	1.67501	0.0554346
$914$	54.2115	1.79316
$915$	45.0002	1.48766
$916$	122.681	4.05350
$917$	−10.5561	−0.348594
$918$	60.3917	1.99322
$919$	40.3059	1.32957	0.664784	−	0.747035i	$-0.268523\pi$
$919$	40.3059	1.32957	0.664784	+	0.747035i	$0.268523\pi$
$920$	50.3278	1.65926
$921$	−30.6752	−1.01078
$922$	−55.4856	−1.82732
$923$	58.9530	1.94046
$924$	7.22437	0.237664
$925$	162.153	5.33155
$926$	0.457302	0.0150279
$927$	8.67108	0.284796
$928$	61.2858	2.01180
$929$	−7.17121	−0.235280	−0.117640	−	0.993056i	$-0.537533\pi$
$929$	−7.17121	−0.235280	−0.117640	+	0.993056i	$0.537533\pi$
$930$	58.9628	1.93347
$931$	−33.0772	−1.08406
$932$	52.3195	1.71378
$933$	−23.9704	−0.784756
$934$	40.9239	1.33907
$935$	18.4874	0.604604
$936$	47.3780	1.54860
$937$	−27.8906	−0.911145	−0.455573	−	0.890199i	$-0.650565\pi$
$937$	−27.8906	−0.911145	−0.455573	+	0.890199i	$0.650565\pi$
$938$	−40.9502	−1.33707
$939$	35.1475	1.14699
$940$	−42.0793	−1.37248
$941$	43.1463	1.40653	0.703264	−	0.710929i	$-0.251725\pi$
$941$	43.1463	1.40653	0.703264	+	0.710929i	$0.251725\pi$
$942$	64.9124	2.11496
$943$	−9.26126	−0.301588
$944$	−100.923	−3.28475
$945$	28.9736	0.942510
$946$	14.1886	0.461312
$947$	−47.0670	−1.52947	−0.764736	−	0.644344i	$-0.777131\pi$
$947$	−47.0670	−1.52947	−0.764736	+	0.644344i	$0.777131\pi$
$948$	74.9056	2.43282
$949$	22.0799	0.716743
$950$	−231.913	−7.52426
$951$	33.6164	1.09009
$952$	41.6602	1.35022
$953$	3.32097	0.107577	0.0537884	−	0.998552i	$-0.482870\pi$
$953$	3.32097	0.107577	0.0537884	+	0.998552i	$0.482870\pi$
$954$	−60.6798	−1.96458
$955$	−5.64482	−0.182662
$956$	44.5851	1.44199
$957$	−4.80474	−0.155315
$958$	7.54601	0.243801
$959$	6.62668	0.213987
$960$	−84.3991	−2.72397
$961$	−12.8502	−0.414524
$962$	−104.662	−3.37443
$963$	−25.7036	−0.828287
$964$	−152.011	−4.89593
$965$	−37.9629	−1.22207
$966$	−5.19324	−0.167090
$967$	10.3820	0.333864	0.166932	−	0.985968i	$-0.446614\pi$
$967$	10.3820	0.333864	0.166932	+	0.985968i	$0.446614\pi$
$968$	−8.26404	−0.265616
$969$	29.2508	0.939673
$970$	−28.3347	−0.909773
$971$	−20.9803	−0.673289	−0.336645	−	0.941632i	$-0.609292\pi$
$971$	−20.9803	−0.673289	−0.336645	+	0.941632i	$0.609292\pi$
$972$	−74.0528	−2.37524
$973$	5.27907	0.169239
$974$	−29.0624	−0.931219
$975$	−60.4741	−1.93672
$976$	−102.410	−3.27807
$977$	44.5462	1.42516	0.712579	−	0.701592i	$-0.247527\pi$
$977$	44.5462	1.42516	0.712579	+	0.701592i	$0.247527\pi$
$978$	−4.96515	−0.158768
$979$	0.148598	0.00474920
$980$	−125.153	−3.99788
$981$	22.5008	0.718396
$982$	−60.7185	−1.93760
$983$	−22.1515	−0.706522	−0.353261	−	0.935525i	$-0.614927\pi$
$983$	−22.1515	−0.706522	−0.353261	+	0.935525i	$0.614927\pi$
$984$	65.2716	2.08078
$985$	−2.30751	−0.0735234
$986$	−45.5759	−1.45143
$987$	2.63971	0.0840228
$988$	107.530	3.42099
$989$	−7.32689	−0.232981
$990$	−19.1377	−0.608236
$991$	−6.07060	−0.192839	−0.0964195	−	0.995341i	$-0.530739\pi$
$991$	−6.07060	−0.192839	−0.0964195	+	0.995341i	$0.530739\pi$
$992$	−63.7720	−2.02476
$993$	11.3132	0.359013
$994$	−53.6616	−1.70204
$995$	28.2532	0.895687
$996$	10.0275	0.317734
$997$	21.2719	0.673689	0.336844	−	0.941560i	$-0.390640\pi$
$997$	21.2719	0.673689	0.336844	+	0.941560i	$0.390640\pi$
$998$	−37.9670	−1.20183
$999$	60.3112	1.90816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.6	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.6	✓	121	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66480 q^{2} -1.17356 q^{3} +5.10118 q^{4} +4.42559 q^{5} +3.12731 q^{6} +1.20677 q^{7} -8.26404 q^{8} -1.62275 q^{9} +O(q^{10})\)	\(q-2.66480 q^{2} -1.17356 q^{3} +5.10118 q^{4} +4.42559 q^{5} +3.12731 q^{6} +1.20677 q^{7} -8.26404 q^{8} -1.62275 q^{9} -11.7933 q^{10} -1.00000 q^{11} -5.98655 q^{12} +3.53290 q^{13} -3.21580 q^{14} -5.19370 q^{15} +11.8197 q^{16} -4.17739 q^{17} +4.32432 q^{18} +5.96661 q^{19} +22.5758 q^{20} -1.41622 q^{21} +2.66480 q^{22} -1.37608 q^{23} +9.69835 q^{24} +14.5859 q^{25} -9.41449 q^{26} +5.42508 q^{27} +6.15594 q^{28} -4.09416 q^{29} +13.8402 q^{30} +4.26025 q^{31} -14.9691 q^{32} +1.17356 q^{33} +11.1319 q^{34} +5.34067 q^{35} -8.27797 q^{36} +11.1171 q^{37} -15.8998 q^{38} -4.14607 q^{39} -36.5733 q^{40} +6.73017 q^{41} +3.77394 q^{42} +5.32446 q^{43} -5.10118 q^{44} -7.18165 q^{45} +3.66699 q^{46} -1.86392 q^{47} -13.8711 q^{48} -5.54371 q^{49} -38.8685 q^{50} +4.90242 q^{51} +18.0220 q^{52} -14.0322 q^{53} -14.4568 q^{54} -4.42559 q^{55} -9.97278 q^{56} -7.00218 q^{57} +10.9101 q^{58} -8.53852 q^{59} -26.4940 q^{60} -8.66438 q^{61} -11.3527 q^{62} -1.95829 q^{63} +16.2503 q^{64} +15.6352 q^{65} -3.12731 q^{66} +12.7341 q^{67} -21.3096 q^{68} +1.61492 q^{69} -14.2318 q^{70} +16.6868 q^{71} +13.4105 q^{72} +6.24979 q^{73} -29.6249 q^{74} -17.1174 q^{75} +30.4368 q^{76} -1.20677 q^{77} +11.0485 q^{78} -12.5123 q^{79} +52.3091 q^{80} -1.49840 q^{81} -17.9346 q^{82} -1.67501 q^{83} -7.22437 q^{84} -18.4874 q^{85} -14.1886 q^{86} +4.80474 q^{87} +8.26404 q^{88} -0.148598 q^{89} +19.1377 q^{90} +4.26339 q^{91} -7.01964 q^{92} -4.99967 q^{93} +4.96697 q^{94} +26.4058 q^{95} +17.5671 q^{96} +2.40260 q^{97} +14.7729 q^{98} +1.62275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * q^99

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