LMFDB - Embedded newform 5077.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$1$
Dimension:	$205$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78060 q^{2} +0.0708990 q^{3} +5.73173 q^{4} -3.99378 q^{5} -0.197142 q^{6} +2.14019 q^{7} -10.3764 q^{8} -2.99497 q^{9} +O(q^{10})$	\(q-2.78060 q^{2} +0.0708990 q^{3} +5.73173 q^{4} -3.99378 q^{5} -0.197142 q^{6} +2.14019 q^{7} -10.3764 q^{8} -2.99497 q^{9} +11.1051 q^{10} +4.01342 q^{11} +0.406374 q^{12} +0.791985 q^{13} -5.95100 q^{14} -0.283155 q^{15} +17.3893 q^{16} -5.42755 q^{17} +8.32782 q^{18} +1.49166 q^{19} -22.8912 q^{20} +0.151737 q^{21} -11.1597 q^{22} -3.73989 q^{23} -0.735679 q^{24} +10.9502 q^{25} -2.20219 q^{26} -0.425037 q^{27} +12.2670 q^{28} +10.1964 q^{29} +0.787339 q^{30} -7.82634 q^{31} -27.5997 q^{32} +0.284547 q^{33} +15.0918 q^{34} -8.54743 q^{35} -17.1664 q^{36} +4.62333 q^{37} -4.14771 q^{38} +0.0561509 q^{39} +41.4412 q^{40} +8.31246 q^{41} -0.421920 q^{42} -8.59578 q^{43} +23.0038 q^{44} +11.9613 q^{45} +10.3991 q^{46} -13.0972 q^{47} +1.23288 q^{48} -2.41960 q^{49} -30.4482 q^{50} -0.384808 q^{51} +4.53944 q^{52} +3.74322 q^{53} +1.18186 q^{54} -16.0287 q^{55} -22.2075 q^{56} +0.105757 q^{57} -28.3522 q^{58} -3.56455 q^{59} -1.62297 q^{60} -2.27680 q^{61} +21.7619 q^{62} -6.40981 q^{63} +41.9652 q^{64} -3.16301 q^{65} -0.791212 q^{66} +9.76862 q^{67} -31.1093 q^{68} -0.265155 q^{69} +23.7670 q^{70} +9.30654 q^{71} +31.0772 q^{72} -1.45119 q^{73} -12.8556 q^{74} +0.776361 q^{75} +8.54980 q^{76} +8.58947 q^{77} -0.156133 q^{78} -3.03016 q^{79} -69.4489 q^{80} +8.95479 q^{81} -23.1136 q^{82} +4.57411 q^{83} +0.869716 q^{84} +21.6764 q^{85} +23.9014 q^{86} +0.722918 q^{87} -41.6450 q^{88} +2.71999 q^{89} -33.2594 q^{90} +1.69500 q^{91} -21.4361 q^{92} -0.554879 q^{93} +36.4182 q^{94} -5.95736 q^{95} -1.95679 q^{96} +4.90279 q^{97} +6.72793 q^{98} -12.0201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) $ 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * 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 $

$2$	−2.78060	−1.96618	−0.983090	−	0.183122i	$-0.941380\pi$
$2$	−2.78060	−1.96618	−0.983090	+	0.183122i	$0.941380\pi$
$3$	0.0708990	0.0409335	0.0204668	−	0.999791i	$-0.493485\pi$
$3$	0.0708990	0.0409335	0.0204668	+	0.999791i	$0.493485\pi$
$4$	5.73173	2.86587
$5$	−3.99378	−1.78607	−0.893035	−	0.449986i	$-0.851429\pi$
$5$	−3.99378	−1.78607	−0.893035	+	0.449986i	$0.851429\pi$
$6$	−0.197142	−0.0804827
$7$	2.14019	0.808915	0.404457	−	0.914557i	$-0.367460\pi$
$7$	2.14019	0.808915	0.404457	+	0.914557i	$0.367460\pi$
$8$	−10.3764	−3.66863
$9$	−2.99497	−0.998324
$10$	11.1051	3.51174
$11$	4.01342	1.21009	0.605045	−	0.796191i	$-0.293155\pi$
$11$	4.01342	1.21009	0.605045	+	0.796191i	$0.293155\pi$
$12$	0.406374	0.117310
$13$	0.791985	0.219657	0.109829	−	0.993951i	$-0.464970\pi$
$13$	0.791985	0.219657	0.109829	+	0.993951i	$0.464970\pi$
$14$	−5.95100	−1.59047
$15$	−0.283155	−0.0731102
$16$	17.3893	4.34732
$17$	−5.42755	−1.31637	−0.658187	−	0.752854i	$-0.728676\pi$
$17$	−5.42755	−1.31637	−0.658187	+	0.752854i	$0.728676\pi$
$18$	8.32782	1.96289
$19$	1.49166	0.342210	0.171105	−	0.985253i	$-0.445266\pi$
$19$	1.49166	0.342210	0.171105	+	0.985253i	$0.445266\pi$
$20$	−22.8912	−5.11864
$21$	0.151737	0.0331118
$22$	−11.1597	−2.37926
$23$	−3.73989	−0.779822	−0.389911	−	0.920853i	$-0.627494\pi$
$23$	−3.73989	−0.779822	−0.389911	+	0.920853i	$0.627494\pi$
$24$	−0.735679	−0.150170
$25$	10.9502	2.19005
$26$	−2.20219	−0.431885
$27$	−0.425037	−0.0817985
$28$	12.2670	2.31824
$29$	10.1964	1.89343	0.946716	−	0.322069i	$-0.104378\pi$
$29$	10.1964	1.89343	0.946716	+	0.322069i	$0.104378\pi$
$30$	0.787339	0.143748
$31$	−7.82634	−1.40565	−0.702826	−	0.711362i	$-0.748079\pi$
$31$	−7.82634	−1.40565	−0.702826	+	0.711362i	$0.748079\pi$
$32$	−27.5997	−4.87898
$33$	0.284547	0.0495333
$34$	15.0918	2.58823
$35$	−8.54743	−1.44478
$36$	−17.1664	−2.86106
$37$	4.62333	0.760070	0.380035	−	0.924972i	$-0.375912\pi$
$37$	4.62333	0.760070	0.380035	+	0.924972i	$0.375912\pi$
$38$	−4.14771	−0.672847
$39$	0.0561509	0.00899134
$40$	41.4412	6.55243
$41$	8.31246	1.29819	0.649094	−	0.760708i	$-0.275148\pi$
$41$	8.31246	1.29819	0.649094	+	0.760708i	$0.275148\pi$
$42$	−0.421920	−0.0651037
$43$	−8.59578	−1.31084	−0.655422	−	0.755263i	$-0.727509\pi$
$43$	−8.59578	−1.31084	−0.655422	+	0.755263i	$0.727509\pi$
$44$	23.0038	3.46796
$45$	11.9613	1.78308
$46$	10.3991	1.53327
$47$	−13.0972	−1.91043	−0.955215	−	0.295913i	$-0.904376\pi$
$47$	−13.0972	−1.91043	−0.955215	+	0.295913i	$0.904376\pi$
$48$	1.23288	0.177951
$49$	−2.41960	−0.345657
$50$	−30.4482	−4.30603
$51$	−0.384808	−0.0538839
$52$	4.53944	0.629507
$53$	3.74322	0.514171	0.257086	−	0.966389i	$-0.417238\pi$
$53$	3.74322	0.514171	0.257086	+	0.966389i	$0.417238\pi$
$54$	1.18186	0.160831
$55$	−16.0287	−2.16131
$56$	−22.2075	−2.96761
$57$	0.105757	0.0140079
$58$	−28.3522	−3.72283
$59$	−3.56455	−0.464065	−0.232032	−	0.972708i	$-0.574538\pi$
$59$	−3.56455	−0.464065	−0.232032	+	0.972708i	$0.574538\pi$
$60$	−1.62297	−0.209524
$61$	−2.27680	−0.291514	−0.145757	−	0.989320i	$-0.546562\pi$
$61$	−2.27680	−0.291514	−0.145757	+	0.989320i	$0.546562\pi$
$62$	21.7619	2.76377
$63$	−6.40981	−0.807560
$64$	41.9652	5.24565
$65$	−3.16301	−0.392323
$66$	−0.791212	−0.0973914
$67$	9.76862	1.19343	0.596714	−	0.802454i	$-0.296473\pi$
$67$	9.76862	1.19343	0.596714	+	0.802454i	$0.296473\pi$
$68$	−31.1093	−3.77255
$69$	−0.265155	−0.0319209
$70$	23.7670	2.84070
$71$	9.30654	1.10448	0.552242	−	0.833684i	$-0.313773\pi$
$71$	9.30654	1.10448	0.552242	+	0.833684i	$0.313773\pi$
$72$	31.0772	3.66248
$73$	−1.45119	−0.169849	−0.0849247	−	0.996387i	$-0.527065\pi$
$73$	−1.45119	−0.169849	−0.0849247	+	0.996387i	$0.527065\pi$
$74$	−12.8556	−1.49444
$75$	0.776361	0.0896465
$76$	8.54980	0.980729
$77$	8.58947	0.978861
$78$	−0.156133	−0.0176786
$79$	−3.03016	−0.340920	−0.170460	−	0.985365i	$-0.554525\pi$
$79$	−3.03016	−0.340920	−0.170460	+	0.985365i	$0.554525\pi$
$80$	−69.4489	−7.76462
$81$	8.95479	0.994976
$82$	−23.1136	−2.55247
$83$	4.57411	0.502073	0.251037	−	0.967978i	$-0.419229\pi$
$83$	4.57411	0.502073	0.251037	+	0.967978i	$0.419229\pi$
$84$	0.869716	0.0948938
$85$	21.6764	2.35114
$86$	23.9014	2.57736
$87$	0.722918	0.0775049
$88$	−41.6450	−4.43937
$89$	2.71999	0.288319	0.144159	−	0.989554i	$-0.453952\pi$
$89$	2.71999	0.288319	0.144159	+	0.989554i	$0.453952\pi$
$90$	−33.2594	−3.50585
$91$	1.69500	0.177684
$92$	−21.4361	−2.23486
$93$	−0.554879	−0.0575383
$94$	36.4182	3.75625
$95$	−5.95736	−0.611212
$96$	−1.95679	−0.199714
$97$	4.90279	0.497803	0.248901	−	0.968529i	$-0.419930\pi$
$97$	4.90279	0.497803	0.248901	+	0.968529i	$0.419930\pi$
$98$	6.72793	0.679623
$99$	−12.0201	−1.20806
$100$	62.7638	6.27638
$101$	11.9184	1.18593	0.592963	−	0.805229i	$-0.297958\pi$
$101$	11.9184	1.18593	0.592963	+	0.805229i	$0.297958\pi$
$102$	1.07000	0.105945
$103$	4.02402	0.396499	0.198249	−	0.980152i	$-0.436474\pi$
$103$	4.02402	0.396499	0.198249	+	0.980152i	$0.436474\pi$
$104$	−8.21799	−0.805840
$105$	−0.606004	−0.0591399
$106$	−10.4084	−1.01095
$107$	−3.40228	−0.328911	−0.164455	−	0.986385i	$-0.552587\pi$
$107$	−3.40228	−0.328911	−0.164455	+	0.986385i	$0.552587\pi$
$108$	−2.43620	−0.234423
$109$	16.8668	1.61555	0.807774	−	0.589492i	$-0.200672\pi$
$109$	16.8668	1.61555	0.807774	+	0.589492i	$0.200672\pi$
$110$	44.5694	4.24952
$111$	0.327789	0.0311124
$112$	37.2163	3.51661
$113$	−11.2324	−1.05666	−0.528329	−	0.849040i	$-0.677181\pi$
$113$	−11.2324	−1.05666	−0.528329	+	0.849040i	$0.677181\pi$
$114$	−0.294068	−0.0275420
$115$	14.9363	1.39282
$116$	58.4433	5.42632
$117$	−2.37197	−0.219289
$118$	9.91158	0.912435
$119$	−11.6160	−1.06483
$120$	2.93814	0.268214
$121$	5.10752	0.464320
$122$	6.33086	0.573169
$123$	0.589345	0.0531394
$124$	−44.8585	−4.02841
$125$	−23.7639	−2.12551
$126$	17.8231	1.58781
$127$	2.97784	0.264241	0.132120	−	0.991234i	$-0.457821\pi$
$127$	2.97784	0.264241	0.132120	+	0.991234i	$0.457821\pi$
$128$	−61.4889	−5.43490
$129$	−0.609432	−0.0536575
$130$	8.79506	0.771378
$131$	−15.9243	−1.39131	−0.695655	−	0.718376i	$-0.744886\pi$
$131$	−15.9243	−1.39131	−0.695655	+	0.718376i	$0.744886\pi$
$132$	1.63095	0.141956
$133$	3.19243	0.276819
$134$	−27.1626	−2.34649
$135$	1.69750	0.146098
$136$	56.3187	4.82929
$137$	3.93124	0.335869	0.167934	−	0.985798i	$-0.446290\pi$
$137$	3.93124	0.335869	0.167934	+	0.985798i	$0.446290\pi$
$138$	0.737289	0.0627622
$139$	−6.65783	−0.564710	−0.282355	−	0.959310i	$-0.591116\pi$
$139$	−6.65783	−0.564710	−0.282355	+	0.959310i	$0.591116\pi$
$140$	−48.9916	−4.14054
$141$	−0.928581	−0.0782007
$142$	−25.8778	−2.17161
$143$	3.17856	0.265805
$144$	−52.0804	−4.34003
$145$	−40.7223	−3.38180
$146$	4.03519	0.333955
$147$	−0.171547	−0.0141489
$148$	26.4997	2.17826
$149$	2.68501	0.219965	0.109982	−	0.993934i	$-0.464921\pi$
$149$	2.68501	0.219965	0.109982	+	0.993934i	$0.464921\pi$
$150$	−2.15875	−0.176261
$151$	−21.3365	−1.73634	−0.868169	−	0.496269i	$-0.834703\pi$
$151$	−21.3365	−1.73634	−0.868169	+	0.496269i	$0.834703\pi$
$152$	−15.4781	−1.25544
$153$	16.2554	1.31417
$154$	−23.8839	−1.92462
$155$	31.2566	2.51059
$156$	0.321842	0.0257680
$157$	6.26214	0.499773	0.249886	−	0.968275i	$-0.419607\pi$
$157$	6.26214	0.499773	0.249886	+	0.968275i	$0.419607\pi$
$158$	8.42566	0.670310
$159$	0.265391	0.0210468
$160$	110.227	8.71421
$161$	−8.00407	−0.630809
$162$	−24.8997	−1.95630
$163$	11.2612	0.882047	0.441023	−	0.897496i	$-0.354616\pi$
$163$	11.2612	0.882047	0.441023	+	0.897496i	$0.354616\pi$
$164$	47.6448	3.72043
$165$	−1.13642	−0.0884700
$166$	−12.7188	−0.987167
$167$	−20.1942	−1.56268	−0.781338	−	0.624108i	$-0.785463\pi$
$167$	−20.1942	−1.56268	−0.781338	+	0.624108i	$0.785463\pi$
$168$	−1.57449	−0.121475
$169$	−12.3728	−0.951751
$170$	−60.2734	−4.62276
$171$	−4.46748	−0.341637
$172$	−49.2687	−3.75670
$173$	0.821945	0.0624913	0.0312456	−	0.999512i	$-0.490053\pi$
$173$	0.821945	0.0624913	0.0312456	+	0.999512i	$0.490053\pi$
$174$	−2.01014	−0.152389
$175$	23.4356	1.77156
$176$	69.7904	5.26065
$177$	−0.252723	−0.0189958
$178$	−7.56321	−0.566886
$179$	−3.10209	−0.231861	−0.115931	−	0.993257i	$-0.536985\pi$
$179$	−3.10209	−0.231861	−0.115931	+	0.993257i	$0.536985\pi$
$180$	68.5587	5.11006
$181$	18.3294	1.36242	0.681208	−	0.732090i	$-0.261455\pi$
$181$	18.3294	1.36242	0.681208	+	0.732090i	$0.261455\pi$
$182$	−4.71310	−0.349359
$183$	−0.161423	−0.0119327
$184$	38.8068	2.86088
$185$	−18.4645	−1.35754
$186$	1.54290	0.113131
$187$	−21.7830	−1.59293
$188$	−75.0699	−5.47503
$189$	−0.909660	−0.0661680
$190$	16.5650	1.20175
$191$	2.34954	0.170007	0.0850033	−	0.996381i	$-0.472910\pi$
$191$	2.34954	0.170007	0.0850033	+	0.996381i	$0.472910\pi$
$192$	2.97529	0.214723
$193$	23.8497	1.71674	0.858369	−	0.513033i	$-0.171478\pi$
$193$	23.8497	1.71674	0.858369	+	0.513033i	$0.171478\pi$
$194$	−13.6327	−0.978770
$195$	−0.224254	−0.0160592
$196$	−13.8685	−0.990605
$197$	−18.9533	−1.35037	−0.675183	−	0.737650i	$-0.735935\pi$
$197$	−18.9533	−1.35037	−0.675183	+	0.737650i	$0.735935\pi$
$198$	33.4230	2.37527
$199$	−1.16099	−0.0823004	−0.0411502	−	0.999153i	$-0.513102\pi$
$199$	−1.16099	−0.0823004	−0.0411502	+	0.999153i	$0.513102\pi$
$200$	−113.625	−8.03447
$201$	0.692586	0.0488512
$202$	−33.1403	−2.33175
$203$	21.8223	1.53163
$204$	−2.20561	−0.154424
$205$	−33.1981	−2.31865
$206$	−11.1892	−0.779588
$207$	11.2009	0.778515
$208$	13.7720	0.954919
$209$	5.98666	0.414106
$210$	1.68505	0.116280
$211$	−3.78726	−0.260726	−0.130363	−	0.991466i	$-0.541614\pi$
$211$	−3.78726	−0.260726	−0.130363	+	0.991466i	$0.541614\pi$
$212$	21.4551	1.47355
$213$	0.659824	0.0452104
$214$	9.46038	0.646698
$215$	34.3296	2.34126
$216$	4.41038	0.300088
$217$	−16.7498	−1.13705
$218$	−46.8999	−3.17646
$219$	−0.102888	−0.00695254
$220$	−91.8721	−6.19402
$221$	−4.29854	−0.289151
$222$	−0.911450	−0.0611725
$223$	−5.16562	−0.345916	−0.172958	−	0.984929i	$-0.555332\pi$
$223$	−5.16562	−0.345916	−0.172958	+	0.984929i	$0.555332\pi$
$224$	−59.0686	−3.94668
$225$	−32.7957	−2.18638
$226$	31.2329	2.07758
$227$	3.36406	0.223280	0.111640	−	0.993749i	$-0.464390\pi$
$227$	3.36406	0.223280	0.111640	+	0.993749i	$0.464390\pi$
$228$	0.606172	0.0401447
$229$	16.9123	1.11760	0.558799	−	0.829303i	$-0.311262\pi$
$229$	16.9123	1.11760	0.558799	+	0.829303i	$0.311262\pi$
$230$	−41.5318	−2.73853
$231$	0.608984	0.0400682
$232$	−105.803	−6.94630
$233$	25.8875	1.69595	0.847973	−	0.530039i	$-0.177823\pi$
$233$	25.8875	1.69595	0.847973	+	0.530039i	$0.177823\pi$
$234$	6.59551	0.431162
$235$	52.3075	3.41216
$236$	−20.4310	−1.32995
$237$	−0.214835	−0.0139551
$238$	32.2994	2.09366
$239$	0.981392	0.0634810	0.0317405	−	0.999496i	$-0.489895\pi$
$239$	0.981392	0.0634810	0.0317405	+	0.999496i	$0.489895\pi$
$240$	−4.92385	−0.317833
$241$	−23.4389	−1.50983	−0.754917	−	0.655820i	$-0.772323\pi$
$241$	−23.4389	−1.50983	−0.754917	+	0.655820i	$0.772323\pi$
$242$	−14.2020	−0.912936
$243$	1.91000	0.122526
$244$	−13.0500	−0.835440
$245$	9.66332	0.617367
$246$	−1.63873	−0.104482
$247$	1.18137	0.0751689
$248$	81.2096	5.15681
$249$	0.324299	0.0205516
$250$	66.0780	4.17914
$251$	5.09826	0.321799	0.160900	−	0.986971i	$-0.448560\pi$
$251$	5.09826	0.321799	0.160900	+	0.986971i	$0.448560\pi$
$252$	−36.7393	−2.31436
$253$	−15.0097	−0.943655
$254$	−8.28018	−0.519545
$255$	1.53684	0.0962404
$256$	87.0456	5.44035
$257$	13.5636	0.846073	0.423037	−	0.906113i	$-0.360964\pi$
$257$	13.5636	0.846073	0.423037	+	0.906113i	$0.360964\pi$
$258$	1.69459	0.105500
$259$	9.89479	0.614832
$260$	−18.1295	−1.12434
$261$	−30.5381	−1.89026
$262$	44.2790	2.73557
$263$	−15.7391	−0.970513	−0.485256	−	0.874372i	$-0.661274\pi$
$263$	−15.7391	−0.970513	−0.485256	+	0.874372i	$0.661274\pi$
$264$	−2.95259	−0.181719
$265$	−14.9496	−0.918346
$266$	−8.87688	−0.544276
$267$	0.192845	0.0118019
$268$	55.9911	3.42020
$269$	16.6678	1.01625	0.508127	−	0.861282i	$-0.330338\pi$
$269$	16.6678	1.01625	0.508127	+	0.861282i	$0.330338\pi$
$270$	−4.72008	−0.287255
$271$	−19.4885	−1.18384	−0.591920	−	0.805997i	$-0.701630\pi$
$271$	−19.4885	−1.18384	−0.591920	+	0.805997i	$0.701630\pi$
$272$	−94.3812	−5.72270
$273$	0.120173	0.00727323
$274$	−10.9312	−0.660378
$275$	43.9479	2.65016
$276$	−1.51979	−0.0914809
$277$	6.63481	0.398647	0.199324	−	0.979934i	$-0.436126\pi$
$277$	6.63481	0.398647	0.199324	+	0.979934i	$0.436126\pi$
$278$	18.5128	1.11032
$279$	23.4397	1.40330
$280$	88.6919	5.30036
$281$	9.43220	0.562678	0.281339	−	0.959608i	$-0.409221\pi$
$281$	9.43220	0.562678	0.281339	+	0.959608i	$0.409221\pi$
$282$	2.58201	0.153757
$283$	28.3112	1.68293	0.841463	−	0.540315i	$-0.181695\pi$
$283$	28.3112	1.68293	0.841463	+	0.540315i	$0.181695\pi$
$284$	53.3426	3.16530
$285$	−0.422371	−0.0250191
$286$	−8.83831	−0.522620
$287$	17.7902	1.05012
$288$	82.6604	4.87081
$289$	12.4583	0.732841
$290$	113.232	6.64924
$291$	0.347603	0.0203768
$292$	−8.31785	−0.486765
$293$	−13.9543	−0.815217	−0.407608	−	0.913157i	$-0.633637\pi$
$293$	−13.9543	−0.815217	−0.407608	+	0.913157i	$0.633637\pi$
$294$	0.477003	0.0278194
$295$	14.2360	0.828853
$296$	−47.9737	−2.78841
$297$	−1.70585	−0.0989836
$298$	−7.46595	−0.432491
$299$	−2.96194	−0.171293
$300$	4.44989	0.256915
$301$	−18.3966	−1.06036
$302$	59.3282	3.41395
$303$	0.845003	0.0485442
$304$	25.9389	1.48770
$305$	9.09302	0.520665
$306$	−45.1997	−2.58389
$307$	−26.0630	−1.48749	−0.743747	−	0.668461i	$-0.766953\pi$
$307$	−26.0630	−1.48749	−0.743747	+	0.668461i	$0.766953\pi$
$308$	49.2325	2.80528
$309$	0.285299	0.0162301
$310$	−86.9122	−4.93628
$311$	−10.0984	−0.572625	−0.286313	−	0.958136i	$-0.592430\pi$
$311$	−10.0984	−0.572625	−0.286313	+	0.958136i	$0.592430\pi$
$312$	−0.582647	−0.0329859
$313$	−22.4836	−1.27085	−0.635424	−	0.772163i	$-0.719175\pi$
$313$	−22.4836	−1.27085	−0.635424	+	0.772163i	$0.719175\pi$
$314$	−17.4125	−0.982643
$315$	25.5993	1.44236
$316$	−17.3681	−0.977030
$317$	9.45887	0.531263	0.265632	−	0.964075i	$-0.414420\pi$
$317$	9.45887	0.531263	0.265632	+	0.964075i	$0.414420\pi$
$318$	−0.737945	−0.0413819
$319$	40.9226	2.29123
$320$	−167.599	−9.36909
$321$	−0.241218	−0.0134635
$322$	22.2561	1.24029
$323$	−8.09606	−0.450477
$324$	51.3264	2.85147
$325$	8.67243	0.481060
$326$	−31.3129	−1.73426
$327$	1.19584	0.0661301
$328$	−86.2538	−4.76257
$329$	−28.0306	−1.54538
$330$	3.15992	0.173948
$331$	−5.07919	−0.279178	−0.139589	−	0.990210i	$-0.544578\pi$
$331$	−5.07919	−0.279178	−0.139589	+	0.990210i	$0.544578\pi$
$332$	26.2175	1.43887
$333$	−13.8467	−0.758797
$334$	56.1521	3.07250
$335$	−39.0137	−2.13155
$336$	2.63860	0.143947
$337$	10.6732	0.581406	0.290703	−	0.956813i	$-0.406111\pi$
$337$	10.6732	0.581406	0.290703	+	0.956813i	$0.406111\pi$
$338$	34.4037	1.87131
$339$	−0.796367	−0.0432527
$340$	124.243	6.73804
$341$	−31.4104	−1.70097
$342$	12.4223	0.671720
$343$	−20.1597	−1.08852
$344$	89.1936	4.80900
$345$	1.05897	0.0570129
$346$	−2.28550	−0.122869
$347$	6.85888	0.368204	0.184102	−	0.982907i	$-0.441062\pi$
$347$	6.85888	0.368204	0.184102	+	0.982907i	$0.441062\pi$
$348$	4.14357	0.222119
$349$	−35.7383	−1.91302	−0.956512	−	0.291692i	$-0.905782\pi$
$349$	−35.7383	−1.91302	−0.956512	+	0.291692i	$0.905782\pi$
$350$	−65.1649	−3.48321
$351$	−0.336623	−0.0179676
$352$	−110.769	−5.90401
$353$	9.25438	0.492561	0.246280	−	0.969199i	$-0.420792\pi$
$353$	9.25438	0.492561	0.246280	+	0.969199i	$0.420792\pi$
$354$	0.702721	0.0373492
$355$	−37.1682	−1.97269
$356$	15.5903	0.826282
$357$	−0.823561	−0.0435875
$358$	8.62568	0.455881
$359$	−21.5975	−1.13987	−0.569937	−	0.821689i	$-0.693032\pi$
$359$	−21.5975	−1.13987	−0.569937	+	0.821689i	$0.693032\pi$
$360$	−124.115	−6.54145
$361$	−16.7749	−0.882892
$362$	−50.9668	−2.67875
$363$	0.362118	0.0190062
$364$	9.71526	0.509218
$365$	5.79574	0.303363
$366$	0.448852	0.0234619
$367$	−27.9177	−1.45729	−0.728647	−	0.684890i	$-0.759850\pi$
$367$	−27.9177	−1.45729	−0.728647	+	0.684890i	$0.759850\pi$
$368$	−65.0340	−3.39013
$369$	−24.8956	−1.29601
$370$	51.3425	2.66917
$371$	8.01120	0.415921
$372$	−3.18042	−0.164897
$373$	31.0184	1.60607	0.803037	−	0.595930i	$-0.203216\pi$
$373$	31.0184	1.60607	0.803037	+	0.595930i	$0.203216\pi$
$374$	60.5698	3.13199
$375$	−1.68484	−0.0870047
$376$	135.903	7.00866
$377$	8.07543	0.415906
$378$	2.52940	0.130098
$379$	−37.7660	−1.93991	−0.969954	−	0.243289i	$-0.921774\pi$
$379$	−37.7660	−1.93991	−0.969954	+	0.243289i	$0.921774\pi$
$380$	−34.1460	−1.75165
$381$	0.211126	0.0108163
$382$	−6.53312	−0.334264
$383$	−21.5427	−1.10078	−0.550389	−	0.834908i	$-0.685521\pi$
$383$	−21.5427	−1.10078	−0.550389	+	0.834908i	$0.685521\pi$
$384$	−4.35950	−0.222470
$385$	−34.3044	−1.74831
$386$	−66.3164	−3.37542
$387$	25.7441	1.30865
$388$	28.1015	1.42664
$389$	13.8606	0.702762	0.351381	−	0.936233i	$-0.385712\pi$
$389$	13.8606	0.702762	0.351381	+	0.936233i	$0.385712\pi$
$390$	0.623561	0.0315752
$391$	20.2985	1.02654
$392$	25.1068	1.26809
$393$	−1.12901	−0.0569513
$394$	52.7015	2.65506
$395$	12.1018	0.608907
$396$	−68.8958	−3.46215
$397$	6.15475	0.308898	0.154449	−	0.988001i	$-0.450640\pi$
$397$	6.15475	0.308898	0.154449	+	0.988001i	$0.450640\pi$
$398$	3.22825	0.161817
$399$	0.226340	0.0113312
$400$	190.417	9.52084
$401$	31.0064	1.54839	0.774193	−	0.632949i	$-0.218156\pi$
$401$	31.0064	1.54839	0.774193	+	0.632949i	$0.218156\pi$
$402$	−1.92580	−0.0960503
$403$	−6.19834	−0.308761
$404$	68.3131	3.39871
$405$	−35.7634	−1.77710
$406$	−60.6791	−3.01145
$407$	18.5553	0.919754
$408$	3.99294	0.197680
$409$	−34.9753	−1.72942	−0.864708	−	0.502275i	$-0.832497\pi$
$409$	−34.9753	−1.72942	−0.864708	+	0.502275i	$0.832497\pi$
$410$	92.3106	4.55889
$411$	0.278721	0.0137483
$412$	23.0646	1.13631
$413$	−7.62881	−0.375389
$414$	−31.1452	−1.53070
$415$	−18.2680	−0.896739
$416$	−21.8585	−1.07170
$417$	−0.472034	−0.0231156
$418$	−16.6465	−0.814206
$419$	29.4206	1.43729	0.718646	−	0.695376i	$-0.244762\pi$
$419$	29.4206	1.43729	0.718646	+	0.695376i	$0.244762\pi$
$420$	−3.47345	−0.169487
$421$	−20.6152	−1.00472	−0.502361	−	0.864658i	$-0.667535\pi$
$421$	−20.6152	−1.00472	−0.502361	+	0.864658i	$0.667535\pi$
$422$	10.5308	0.512634
$423$	39.2259	1.90723
$424$	−38.8413	−1.88630
$425$	−59.4330	−2.88292
$426$	−1.83471	−0.0888918
$427$	−4.87278	−0.235810
$428$	−19.5010	−0.942614
$429$	0.225357	0.0108803
$430$	−95.4569	−4.60334
$431$	15.8951	0.765640	0.382820	−	0.923823i	$-0.374953\pi$
$431$	15.8951	0.765640	0.382820	+	0.923823i	$0.374953\pi$
$432$	−7.39109	−0.355604
$433$	−9.68692	−0.465524	−0.232762	−	0.972534i	$-0.574776\pi$
$433$	−9.68692	−0.465524	−0.232762	+	0.972534i	$0.574776\pi$
$434$	46.5746	2.23565
$435$	−2.88717	−0.138429
$436$	96.6760	4.62994
$437$	−5.57865	−0.266863
$438$	0.286091	0.0136699
$439$	30.3328	1.44771	0.723853	−	0.689954i	$-0.242369\pi$
$439$	30.3328	1.44771	0.723853	+	0.689954i	$0.242369\pi$
$440$	166.321	7.92903
$441$	7.24662	0.345077
$442$	11.9525	0.568523
$443$	−27.6728	−1.31478	−0.657388	−	0.753552i	$-0.728339\pi$
$443$	−27.6728	−1.31478	−0.657388	+	0.753552i	$0.728339\pi$
$444$	1.87880	0.0891639
$445$	−10.8630	−0.514957
$446$	14.3635	0.680133
$447$	0.190365	0.00900394
$448$	89.8133	4.24328
$449$	7.51165	0.354497	0.177248	−	0.984166i	$-0.443280\pi$
$449$	7.51165	0.354497	0.177248	+	0.984166i	$0.443280\pi$
$450$	91.1917	4.29882
$451$	33.3614	1.57092
$452$	−64.3812	−3.02824
$453$	−1.51273	−0.0710745
$454$	−9.35409	−0.439009
$455$	−6.76943	−0.317356
$456$	−1.09738	−0.0513897
$457$	−41.2959	−1.93174	−0.965871	−	0.259023i	$-0.916599\pi$
$457$	−41.2959	−1.93174	−0.965871	+	0.259023i	$0.916599\pi$
$458$	−47.0264	−2.19740
$459$	2.30691	0.107677
$460$	85.6108	3.99162
$461$	−4.54452	−0.211660	−0.105830	−	0.994384i	$-0.533750\pi$
$461$	−4.54452	−0.211660	−0.105830	+	0.994384i	$0.533750\pi$
$462$	−1.69334	−0.0787814
$463$	−17.1992	−0.799316	−0.399658	−	0.916664i	$-0.630871\pi$
$463$	−17.1992	−0.799316	−0.399658	+	0.916664i	$0.630871\pi$
$464$	177.309	8.23135
$465$	2.21606	0.102768
$466$	−71.9827	−3.33454
$467$	−15.8421	−0.733084	−0.366542	−	0.930402i	$-0.619458\pi$
$467$	−15.8421	−0.733084	−0.366542	+	0.930402i	$0.619458\pi$
$468$	−13.5955	−0.628453
$469$	20.9067	0.965381
$470$	−145.446	−6.70893
$471$	0.443979	0.0204575
$472$	36.9874	1.70248
$473$	−34.4984	−1.58624
$474$	0.597371	0.0274382
$475$	16.3340	0.749457
$476$	−66.5797	−3.05167
$477$	−11.2109	−0.513310
$478$	−2.72886	−0.124815
$479$	0.278071	0.0127054	0.00635269	−	0.999980i	$-0.497978\pi$
$479$	0.278071	0.0127054	0.00635269	+	0.999980i	$0.497978\pi$
$480$	7.81498	0.356704
$481$	3.66160	0.166955
$482$	65.1743	2.96861
$483$	−0.567481	−0.0258213
$484$	29.2749	1.33068
$485$	−19.5806	−0.889111
$486$	−5.31094	−0.240909
$487$	10.9506	0.496217	0.248109	−	0.968732i	$-0.420191\pi$
$487$	10.9506	0.496217	0.248109	+	0.968732i	$0.420191\pi$
$488$	23.6251	1.06946
$489$	0.798409	0.0361053
$490$	−26.8698	−1.21385
$491$	41.6594	1.88006	0.940030	−	0.341091i	$-0.110797\pi$
$491$	41.6594	1.88006	0.940030	+	0.341091i	$0.110797\pi$
$492$	3.37796	0.152290
$493$	−55.3417	−2.49247
$494$	−3.28492	−0.147796
$495$	48.0055	2.15769
$496$	−136.094	−6.11082
$497$	19.9177	0.893433
$498$	−0.901747	−0.0404082
$499$	−7.35928	−0.329447	−0.164723	−	0.986340i	$-0.552673\pi$
$499$	−7.35928	−0.329447	−0.164723	+	0.986340i	$0.552673\pi$
$500$	−136.208	−6.09143
$501$	−1.43175	−0.0639659
$502$	−14.1762	−0.632715
$503$	−6.07811	−0.271009	−0.135505	−	0.990777i	$-0.543266\pi$
$503$	−6.07811	−0.271009	−0.135505	+	0.990777i	$0.543266\pi$
$504$	66.5110	2.96264
$505$	−47.5995	−2.11815
$506$	41.7361	1.85540
$507$	−0.877216	−0.0389585
$508$	17.0682	0.757278
$509$	5.53298	0.245245	0.122622	−	0.992453i	$-0.460870\pi$
$509$	5.53298	0.245245	0.122622	+	0.992453i	$0.460870\pi$
$510$	−4.27332	−0.189226
$511$	−3.10583	−0.137394
$512$	−119.061	−5.26181
$513$	−0.634012	−0.0279923
$514$	−37.7149	−1.66353
$515$	−16.0710	−0.708175
$516$	−3.49310	−0.153775
$517$	−52.5647	−2.31179
$518$	−27.5134	−1.20887
$519$	0.0582750	0.00255799
$520$	32.8208	1.43929
$521$	15.8425	0.694073	0.347037	−	0.937852i	$-0.387188\pi$
$521$	15.8425	0.694073	0.347037	+	0.937852i	$0.387188\pi$
$522$	84.9142	3.71659
$523$	−6.44151	−0.281668	−0.140834	−	0.990033i	$-0.544978\pi$
$523$	−6.44151	−0.281668	−0.140834	+	0.990033i	$0.544978\pi$
$524$	−91.2737	−3.98731
$525$	1.66156	0.0725164
$526$	43.7640	1.90820
$527$	42.4779	1.85036
$528$	4.94807	0.215337
$529$	−9.01320	−0.391878
$530$	41.5688	1.80563
$531$	10.6757	0.463287
$532$	18.2982	0.793326
$533$	6.58334	0.285156
$534$	−0.536224	−0.0232047
$535$	13.5879	0.587458
$536$	−101.364	−4.37824
$537$	−0.219935	−0.00949091
$538$	−46.3464	−1.99814
$539$	−9.71085	−0.418276
$540$	9.72964	0.418697
$541$	−26.2298	−1.12771	−0.563853	−	0.825875i	$-0.690682\pi$
$541$	−26.2298	−1.12771	−0.563853	+	0.825875i	$0.690682\pi$
$542$	54.1896	2.32764
$543$	1.29954	0.0557685
$544$	149.799	6.42257
$545$	−67.3623	−2.88548
$546$	−0.334154	−0.0143005
$547$	−18.5969	−0.795145	−0.397573	−	0.917571i	$-0.630147\pi$
$547$	−18.5969	−0.795145	−0.397573	+	0.917571i	$0.630147\pi$
$548$	22.5328	0.962554
$549$	6.81895	0.291026
$550$	−122.201	−5.21069
$551$	15.2096	0.647952
$552$	2.75136	0.117106
$553$	−6.48511	−0.275775
$554$	−18.4487	−0.783812
$555$	−1.30912	−0.0555689
$556$	−38.1609	−1.61838
$557$	−17.3050	−0.733237	−0.366619	−	0.930371i	$-0.619485\pi$
$557$	−17.3050	−0.733237	−0.366619	+	0.930371i	$0.619485\pi$
$558$	−65.1763	−2.75913
$559$	−6.80773	−0.287936
$560$	−148.634	−6.28092
$561$	−1.54439	−0.0652044
$562$	−26.2272	−1.10633
$563$	−7.76718	−0.327348	−0.163674	−	0.986515i	$-0.552334\pi$
$563$	−7.76718	−0.327348	−0.163674	+	0.986515i	$0.552334\pi$
$564$	−5.32238	−0.224113
$565$	44.8598	1.88726
$566$	−78.7221	−3.30894
$567$	19.1649	0.804851
$568$	−96.5688	−4.05194
$569$	−17.5237	−0.734631	−0.367316	−	0.930096i	$-0.619723\pi$
$569$	−17.5237	−0.734631	−0.367316	+	0.930096i	$0.619723\pi$
$570$	1.17444	0.0491920
$571$	−7.06989	−0.295866	−0.147933	−	0.988997i	$-0.547262\pi$
$571$	−7.06989	−0.295866	−0.147933	+	0.988997i	$0.547262\pi$
$572$	18.2187	0.761761
$573$	0.166580	0.00695897
$574$	−49.4675	−2.06473
$575$	−40.9527	−1.70785
$576$	−125.685	−5.23686
$577$	−13.1000	−0.545360	−0.272680	−	0.962105i	$-0.587910\pi$
$577$	−13.1000	−0.545360	−0.272680	+	0.962105i	$0.587910\pi$
$578$	−34.6415	−1.44090
$579$	1.69092	0.0702721
$580$	−233.409	−9.69180
$581$	9.78945	0.406135
$582$	−0.966544	−0.0400645
$583$	15.0231	0.622194
$584$	15.0582	0.623114
$585$	9.47313	0.391666
$586$	38.8012	1.60286
$587$	−30.6674	−1.26578	−0.632889	−	0.774243i	$-0.718131\pi$
$587$	−30.6674	−1.26578	−0.632889	+	0.774243i	$0.718131\pi$
$588$	−0.983260	−0.0405490
$589$	−11.6742	−0.481029
$590$	−39.5846	−1.62967
$591$	−1.34377	−0.0552753
$592$	80.3963	3.30427
$593$	−16.0949	−0.660939	−0.330469	−	0.943817i	$-0.607207\pi$
$593$	−16.0949	−0.660939	−0.330469	+	0.943817i	$0.607207\pi$
$594$	4.74329	0.194620
$595$	46.3916	1.90187
$596$	15.3898	0.630390
$597$	−0.0823130	−0.00336885
$598$	8.23596	0.336794
$599$	−5.36921	−0.219380	−0.109690	−	0.993966i	$-0.534986\pi$
$599$	−5.36921	−0.219380	−0.109690	+	0.993966i	$0.534986\pi$
$600$	−8.05587	−0.328879
$601$	−0.0840415	−0.00342812	−0.00171406	−	0.999999i	$-0.500546\pi$
$601$	−0.0840415	−0.00342812	−0.00171406	+	0.999999i	$0.500546\pi$
$602$	51.1535	2.08486
$603$	−29.2568	−1.19143
$604$	−122.295	−4.97611
$605$	−20.3983	−0.829308
$606$	−2.34962	−0.0954466
$607$	5.97281	0.242429	0.121214	−	0.992626i	$-0.461321\pi$
$607$	5.97281	0.242429	0.121214	+	0.992626i	$0.461321\pi$
$608$	−41.1694	−1.66964
$609$	1.54718	0.0626949
$610$	−25.2840	−1.02372
$611$	−10.3728	−0.419639
$612$	93.1714	3.76623
$613$	−5.28497	−0.213458	−0.106729	−	0.994288i	$-0.534038\pi$
$613$	−5.28497	−0.213458	−0.106729	+	0.994288i	$0.534038\pi$
$614$	72.4708	2.92468
$615$	−2.35371	−0.0949108
$616$	−89.1281	−3.59107
$617$	−46.0603	−1.85432	−0.927159	−	0.374668i	$-0.877757\pi$
$617$	−46.0603	−1.85432	−0.927159	+	0.374668i	$0.877757\pi$
$618$	−0.793302	−0.0319113
$619$	−11.7204	−0.471082	−0.235541	−	0.971864i	$-0.575686\pi$
$619$	−11.7204	−0.471082	−0.235541	+	0.971864i	$0.575686\pi$
$620$	179.155	7.19502
$621$	1.58959	0.0637882
$622$	28.0795	1.12588
$623$	5.82129	0.233225
$624$	0.976424	0.0390882
$625$	40.1566	1.60626
$626$	62.5179	2.49872
$627$	0.424448	0.0169508
$628$	35.8929	1.43228
$629$	−25.0933	−1.00054
$630$	−71.1815	−2.83594
$631$	4.67135	0.185963	0.0929817	−	0.995668i	$-0.470360\pi$
$631$	4.67135	0.185963	0.0929817	+	0.995668i	$0.470360\pi$
$632$	31.4423	1.25071
$633$	−0.268513	−0.0106724
$634$	−26.3013	−1.04456
$635$	−11.8928	−0.471952
$636$	1.52115	0.0603174
$637$	−1.91628	−0.0759259
$638$	−113.789	−4.50496
$639$	−27.8728	−1.10263
$640$	245.573	9.70712
$641$	−37.2225	−1.47020	−0.735100	−	0.677959i	$-0.762865\pi$
$641$	−37.2225	−1.47020	−0.735100	+	0.677959i	$0.762865\pi$
$642$	0.670731	0.0264716
$643$	−14.5639	−0.574344	−0.287172	−	0.957879i	$-0.592715\pi$
$643$	−14.5639	−0.574344	−0.287172	+	0.957879i	$0.592715\pi$
$644$	−45.8772	−1.80781
$645$	2.43393	0.0958361
$646$	22.5119	0.885719
$647$	−46.1536	−1.81448	−0.907242	−	0.420609i	$-0.861816\pi$
$647$	−46.1536	−1.81448	−0.907242	+	0.420609i	$0.861816\pi$
$648$	−92.9188	−3.65020
$649$	−14.3060	−0.561561
$650$	−24.1145	−0.945850
$651$	−1.18755	−0.0465436
$652$	64.5463	2.52783
$653$	49.4900	1.93669	0.968347	−	0.249609i	$-0.0803022\pi$
$653$	49.4900	1.93669	0.968347	+	0.249609i	$0.0803022\pi$
$654$	−3.32515	−0.130024
$655$	63.5980	2.48498
$656$	144.548	5.64363
$657$	4.34629	0.169565
$658$	77.9418	3.03849
$659$	−33.6003	−1.30888	−0.654440	−	0.756114i	$-0.727096\pi$
$659$	−33.6003	−1.30888	−0.654440	+	0.756114i	$0.727096\pi$
$660$	−6.51364	−0.253543
$661$	15.5172	0.603548	0.301774	−	0.953379i	$-0.402421\pi$
$661$	15.5172	0.603548	0.301774	+	0.953379i	$0.402421\pi$
$662$	14.1232	0.548914
$663$	−0.304762	−0.0118360
$664$	−47.4630	−1.84192
$665$	−12.7499	−0.494419
$666$	38.5022	1.49193
$667$	−38.1336	−1.47654
$668$	−115.748	−4.47842
$669$	−0.366237	−0.0141596
$670$	108.481	4.19100
$671$	−9.13774	−0.352759
$672$	−4.18790	−0.161552
$673$	0.369119	0.0142285	0.00711424	−	0.999975i	$-0.497735\pi$
$673$	0.369119	0.0142285	0.00711424	+	0.999975i	$0.497735\pi$
$674$	−29.6779	−1.14315
$675$	−4.65426	−0.179143
$676$	−70.9173	−2.72759
$677$	1.81638	0.0698093	0.0349046	−	0.999391i	$-0.488887\pi$
$677$	1.81638	0.0698093	0.0349046	+	0.999391i	$0.488887\pi$
$678$	2.21438	0.0850427
$679$	10.4929	0.402680
$680$	−224.924	−8.62545
$681$	0.238508	0.00913965
$682$	87.3396	3.34441
$683$	4.02931	0.154177	0.0770886	−	0.997024i	$-0.475438\pi$
$683$	4.02931	0.154177	0.0770886	+	0.997024i	$0.475438\pi$
$684$	−25.6064	−0.979086
$685$	−15.7005	−0.599885
$686$	56.0561	2.14023
$687$	1.19907	0.0457473
$688$	−149.474	−5.69866
$689$	2.96457	0.112941
$690$	−2.94457	−0.112098
$691$	−28.5537	−1.08623	−0.543116	−	0.839657i	$-0.682756\pi$
$691$	−28.5537	−1.08623	−0.543116	+	0.839657i	$0.682756\pi$
$692$	4.71117	0.179092
$693$	−25.7252	−0.977220
$694$	−19.0718	−0.723955
$695$	26.5899	1.00861
$696$	−7.50132	−0.284337
$697$	−45.1163	−1.70890
$698$	99.3737	3.76135
$699$	1.83540	0.0694211
$700$	134.326	5.07706
$701$	−26.6060	−1.00490	−0.502448	−	0.864608i	$-0.667567\pi$
$701$	−26.6060	−1.00490	−0.502448	+	0.864608i	$0.667567\pi$
$702$	0.936014	0.0353276
$703$	6.89643	0.260104
$704$	168.424	6.34771
$705$	3.70855	0.139672
$706$	−25.7327	−0.968463
$707$	25.5076	0.959314
$708$	−1.44854	−0.0544395
$709$	−27.3699	−1.02790	−0.513950	−	0.857820i	$-0.671818\pi$
$709$	−27.3699	−1.02790	−0.513950	+	0.857820i	$0.671818\pi$
$710$	103.350	3.87866
$711$	9.07525	0.340349
$712$	−28.2239	−1.05773
$713$	29.2697	1.09616
$714$	2.28999	0.0857008
$715$	−12.6945	−0.474746
$716$	−17.7804	−0.664484
$717$	0.0695797	0.00259850
$718$	60.0540	2.24120
$719$	−12.5425	−0.467758	−0.233879	−	0.972266i	$-0.575142\pi$
$719$	−12.5425	−0.467758	−0.233879	+	0.972266i	$0.575142\pi$
$720$	207.997	7.75161
$721$	8.61216	0.320734
$722$	46.6444	1.73593
$723$	−1.66180	−0.0618029
$724$	105.059	3.90450
$725$	111.654	4.14671
$726$	−1.00690	−0.0373697
$727$	−33.8157	−1.25416	−0.627078	−	0.778956i	$-0.715749\pi$
$727$	−33.8157	−1.25416	−0.627078	+	0.778956i	$0.715749\pi$
$728$	−17.5880	−0.651856
$729$	−26.7289	−0.989961
$730$	−16.1156	−0.596466
$731$	46.6540	1.72556
$732$	−0.925231	−0.0341975
$733$	−36.3928	−1.34420	−0.672100	−	0.740461i	$-0.734607\pi$
$733$	−36.3928	−1.34420	−0.672100	+	0.740461i	$0.734607\pi$
$734$	77.6280	2.86530
$735$	0.685120	0.0252710
$736$	103.220	3.80474
$737$	39.2056	1.44416
$738$	69.2246	2.54819
$739$	−14.7221	−0.541562	−0.270781	−	0.962641i	$-0.587282\pi$
$739$	−14.7221	−0.541562	−0.270781	+	0.962641i	$0.587282\pi$
$740$	−105.834	−3.89052
$741$	0.0837581	0.00307693
$742$	−22.2759	−0.817775
$743$	−12.1121	−0.444350	−0.222175	−	0.975007i	$-0.571316\pi$
$743$	−12.1121	−0.444350	−0.222175	+	0.975007i	$0.571316\pi$
$744$	5.75768	0.211087
$745$	−10.7233	−0.392873
$746$	−86.2498	−3.15783
$747$	−13.6993	−0.501232
$748$	−124.854	−4.56513
$749$	−7.28152	−0.266061
$750$	4.68486	0.171067
$751$	−22.1161	−0.807027	−0.403513	−	0.914974i	$-0.632211\pi$
$751$	−22.1161	−0.807027	−0.403513	+	0.914974i	$0.632211\pi$
$752$	−227.752	−8.30525
$753$	0.361461	0.0131724
$754$	−22.4545	−0.817746
$755$	85.2131	3.10122
$756$	−5.21393	−0.189629
$757$	19.5875	0.711919	0.355960	−	0.934501i	$-0.384154\pi$
$757$	19.5875	0.711919	0.355960	+	0.934501i	$0.384154\pi$
$758$	105.012	3.81421
$759$	−1.06418	−0.0386271
$760$	61.8162	2.24231
$761$	−33.5539	−1.21633	−0.608164	−	0.793811i	$-0.708094\pi$
$761$	−33.5539	−1.21633	−0.608164	+	0.793811i	$0.708094\pi$
$762$	−0.587056	−0.0212668
$763$	36.0982	1.30684
$764$	13.4669	0.487216
$765$	−64.9203	−2.34720
$766$	59.9015	2.16433
$767$	−2.82307	−0.101935
$768$	6.17144	0.222693
$769$	44.4903	1.60436	0.802180	−	0.597082i	$-0.203673\pi$
$769$	44.4903	1.60436	0.802180	+	0.597082i	$0.203673\pi$
$770$	95.3868	3.43750
$771$	0.961644	0.0346328
$772$	136.700	4.91994
$773$	27.8465	1.00157	0.500785	−	0.865572i	$-0.333045\pi$
$773$	27.8465	1.00157	0.500785	+	0.865572i	$0.333045\pi$
$774$	−71.5841	−2.57304
$775$	−85.7003	−3.07845
$776$	−50.8735	−1.82625
$777$	0.701530	0.0251673
$778$	−38.5408	−1.38176
$779$	12.3994	0.444253
$780$	−1.28536	−0.0460234
$781$	37.3510	1.33653
$782$	−56.4419	−2.01836
$783$	−4.33387	−0.154880
$784$	−42.0750	−1.50268
$785$	−25.0096	−0.892630
$786$	3.13934	0.111976
$787$	1.78391	0.0635897	0.0317948	−	0.999494i	$-0.489878\pi$
$787$	1.78391	0.0635897	0.0317948	+	0.999494i	$0.489878\pi$
$788$	−108.635	−3.86997
$789$	−1.11588	−0.0397265
$790$	−33.6502	−1.19722
$791$	−24.0395	−0.854746
$792$	124.726	4.43193
$793$	−1.80319	−0.0640331
$794$	−17.1139	−0.607349
$795$	−1.05991	−0.0375912
$796$	−6.65448	−0.235862
$797$	−47.4296	−1.68004	−0.840021	−	0.542554i	$-0.817458\pi$
$797$	−47.4296	−1.68004	−0.840021	+	0.542554i	$0.817458\pi$
$798$	−0.629362	−0.0222792
$799$	71.0860	2.51484
$800$	−302.223	−10.6852
$801$	−8.14630	−0.287835
$802$	−86.2164	−3.04441
$803$	−5.82425	−0.205533
$804$	3.96971	0.140001
$805$	31.9665	1.12667
$806$	17.2351	0.607081
$807$	1.18173	0.0415988
$808$	−123.671	−4.35072
$809$	−23.3012	−0.819226	−0.409613	−	0.912259i	$-0.634336\pi$
$809$	−23.3012	−0.819226	−0.409613	+	0.912259i	$0.634336\pi$
$810$	99.4437	3.49409
$811$	38.0175	1.33498	0.667488	−	0.744621i	$-0.267370\pi$
$811$	38.0175	1.33498	0.667488	+	0.744621i	$0.267370\pi$
$812$	125.080	4.38943
$813$	−1.38171	−0.0484588
$814$	−51.5950	−1.80840
$815$	−44.9748	−1.57540
$816$	−6.69153	−0.234250
$817$	−12.8220	−0.448584
$818$	97.2522	3.40034
$819$	−5.07647	−0.177386
$820$	−190.282	−6.64495
$821$	−7.32751	−0.255732	−0.127866	−	0.991791i	$-0.540813\pi$
$821$	−7.32751	−0.255732	−0.127866	+	0.991791i	$0.540813\pi$
$822$	−0.775012	−0.0270316
$823$	19.2426	0.670753	0.335377	−	0.942084i	$-0.391136\pi$
$823$	19.2426	0.670753	0.335377	+	0.942084i	$0.391136\pi$
$824$	−41.7551	−1.45461
$825$	3.11586	0.108480
$826$	21.2127	0.738082
$827$	−34.3984	−1.19615	−0.598074	−	0.801441i	$-0.704067\pi$
$827$	−34.3984	−1.19615	−0.598074	+	0.801441i	$0.704067\pi$
$828$	64.2004	2.23112
$829$	1.04321	0.0362321	0.0181160	−	0.999836i	$-0.494233\pi$
$829$	1.04321	0.0362321	0.0181160	+	0.999836i	$0.494233\pi$
$830$	50.7959	1.76315
$831$	0.470401	0.0163180
$832$	33.2358	1.15224
$833$	13.1325	0.455013
$834$	1.31254	0.0454494
$835$	80.6512	2.79105
$836$	34.3139	1.18677
$837$	3.32649	0.114980
$838$	−81.8070	−2.82598
$839$	10.2665	0.354437	0.177219	−	0.984172i	$-0.443290\pi$
$839$	10.2665	0.354437	0.177219	+	0.984172i	$0.443290\pi$
$840$	6.28817	0.216962
$841$	74.9675	2.58509
$842$	57.3225	1.97546
$843$	0.668733	0.0230324
$844$	−21.7075	−0.747205
$845$	49.4140	1.69989
$846$	−109.072	−3.74996
$847$	10.9310	0.375595
$848$	65.0919	2.23527
$849$	2.00723	0.0688881
$850$	165.259	5.66835
$851$	−17.2907	−0.592719
$852$	3.78194	0.129567
$853$	7.89786	0.270418	0.135209	−	0.990817i	$-0.456829\pi$
$853$	7.89786	0.270418	0.135209	+	0.990817i	$0.456829\pi$
$854$	13.5492	0.463645
$855$	17.8421	0.610188
$856$	35.3036	1.20665
$857$	−6.10413	−0.208513	−0.104257	−	0.994550i	$-0.533246\pi$
$857$	−6.10413	−0.208513	−0.104257	+	0.994550i	$0.533246\pi$
$858$	−0.626627	−0.0213927
$859$	−31.2915	−1.06765	−0.533827	−	0.845594i	$-0.679247\pi$
$859$	−31.2915	−1.06765	−0.533827	+	0.845594i	$0.679247\pi$
$860$	196.768	6.70974
$861$	1.26131	0.0429853
$862$	−44.1979	−1.50539
$863$	43.5121	1.48117	0.740584	−	0.671964i	$-0.234549\pi$
$863$	43.5121	1.48117	0.740584	+	0.671964i	$0.234549\pi$
$864$	11.7309	0.399094
$865$	−3.28266	−0.111614
$866$	26.9354	0.915304
$867$	0.883281	0.0299978
$868$	−96.0056	−3.25864
$869$	−12.1613	−0.412544
$870$	8.02806	0.272177
$871$	7.73660	0.262145
$872$	−175.018	−5.92684
$873$	−14.6837	−0.496969
$874$	15.5120	0.524701
$875$	−50.8593	−1.71936
$876$	−0.589727	−0.0199250
$877$	26.9666	0.910596	0.455298	−	0.890339i	$-0.349533\pi$
$877$	26.9666	0.910596	0.455298	+	0.890339i	$0.349533\pi$
$878$	−84.3434	−2.84645
$879$	−0.989343	−0.0333697
$880$	−278.727	−9.39589
$881$	21.0805	0.710221	0.355110	−	0.934824i	$-0.384443\pi$
$881$	21.0805	0.710221	0.355110	+	0.934824i	$0.384443\pi$
$882$	−20.1500	−0.678484
$883$	−44.5868	−1.50046	−0.750232	−	0.661175i	$-0.770058\pi$
$883$	−44.5868	−1.50046	−0.750232	+	0.661175i	$0.770058\pi$
$884$	−24.6381	−0.828667
$885$	1.00932	0.0339279
$886$	76.9471	2.58509
$887$	40.4562	1.35839	0.679193	−	0.733960i	$-0.262330\pi$
$887$	40.4562	1.35839	0.679193	+	0.733960i	$0.262330\pi$
$888$	−3.40129	−0.114140
$889$	6.37314	0.213748
$890$	30.2058	1.01250
$891$	35.9393	1.20401
$892$	−29.6080	−0.991348
$893$	−19.5366	−0.653769
$894$	−0.529328	−0.0177034
$895$	12.3891	0.414121
$896$	−131.598	−4.39637
$897$	−0.209998	−0.00701164
$898$	−20.8869	−0.697004
$899$	−79.8009	−2.66151
$900$	−187.976	−6.26587
$901$	−20.3165	−0.676842
$902$	−92.7645	−3.08872
$903$	−1.30430	−0.0434044
$904$	116.553	3.87648
$905$	−73.2036	−2.43337
$906$	4.20631	0.139745
$907$	−6.07553	−0.201735	−0.100867	−	0.994900i	$-0.532162\pi$
$907$	−6.07553	−0.201735	−0.100867	+	0.994900i	$0.532162\pi$
$908$	19.2819	0.639891
$909$	−35.6953	−1.18394
$910$	18.8231	0.623979
$911$	−58.9986	−1.95471	−0.977355	−	0.211608i	$-0.932130\pi$
$911$	−58.9986	−1.95471	−0.977355	+	0.211608i	$0.932130\pi$
$912$	1.83904	0.0608967
$913$	18.3578	0.607554
$914$	114.827	3.79815
$915$	0.644686	0.0213127
$916$	96.9370	3.20289
$917$	−34.0809	−1.12545
$918$	−6.41460	−0.211713
$919$	35.9459	1.18575	0.592873	−	0.805296i	$-0.297994\pi$
$919$	35.9459	1.18575	0.592873	+	0.805296i	$0.297994\pi$
$920$	−154.986	−5.10973
$921$	−1.84784	−0.0608884
$922$	12.6365	0.416161
$923$	7.37064	0.242608
$924$	3.49053	0.114830
$925$	50.6266	1.66459
$926$	47.8242	1.57160
$927$	−12.0518	−0.395834
$928$	−281.419	−9.23803
$929$	−18.9122	−0.620488	−0.310244	−	0.950657i	$-0.600411\pi$
$929$	−18.9122	−0.620488	−0.310244	+	0.950657i	$0.600411\pi$
$930$	−6.16199	−0.202059
$931$	−3.60922	−0.118287
$932$	148.380	4.86035
$933$	−0.715963	−0.0234396
$934$	44.0504	1.44137
$935$	86.9965	2.84509
$936$	24.6127	0.804490
$937$	1.85381	0.0605612	0.0302806	−	0.999541i	$-0.490360\pi$
$937$	1.85381	0.0605612	0.0302806	+	0.999541i	$0.490360\pi$
$938$	−58.1331	−1.89811
$939$	−1.59406	−0.0520203
$940$	299.812	9.77880
$941$	5.10940	0.166562	0.0832809	−	0.996526i	$-0.473460\pi$
$941$	5.10940	0.166562	0.0832809	+	0.996526i	$0.473460\pi$
$942$	−1.23453	−0.0402231
$943$	−31.0877	−1.01235
$944$	−61.9849	−2.01744
$945$	3.63298	0.118181
$946$	95.9264	3.11883
$947$	−3.25064	−0.105632	−0.0528158	−	0.998604i	$-0.516820\pi$
$947$	−3.25064	−0.105632	−0.0528158	+	0.998604i	$0.516820\pi$
$948$	−1.23138	−0.0399933
$949$	−1.14932	−0.0373086
$950$	−45.4184	−1.47357
$951$	0.670624	0.0217465
$952$	120.533	3.90648
$953$	−0.276349	−0.00895181	−0.00447590	−	0.999990i	$-0.501425\pi$
$953$	−0.276349	−0.00895181	−0.00447590	+	0.999990i	$0.501425\pi$
$954$	31.1729	1.00926
$955$	−9.38353	−0.303644
$956$	5.62507	0.181928
$957$	2.90137	0.0937880
$958$	−0.773203	−0.0249811
$959$	8.41360	0.271689
$960$	−11.8826	−0.383510
$961$	30.2516	0.975858
$962$	−10.1815	−0.328263
$963$	10.1897	0.328360
$964$	−134.346	−4.32698
$965$	−95.2503	−3.06621
$966$	1.57794	0.0507693
$967$	−42.7378	−1.37435	−0.687177	−	0.726490i	$-0.741150\pi$
$967$	−42.7378	−1.37435	−0.687177	+	0.726490i	$0.741150\pi$
$968$	−52.9979	−1.70342
$969$	−0.574003	−0.0184396
$970$	54.4459	1.74815
$971$	−10.7882	−0.346209	−0.173105	−	0.984903i	$-0.555380\pi$
$971$	−10.7882	−0.346209	−0.173105	+	0.984903i	$0.555380\pi$
$972$	10.9476	0.351144
$973$	−14.2490	−0.456803
$974$	−30.4491	−0.975652
$975$	0.614866	0.0196915
$976$	−39.5919	−1.26730
$977$	21.7484	0.695793	0.347896	−	0.937533i	$-0.386896\pi$
$977$	21.7484	0.695793	0.347896	+	0.937533i	$0.386896\pi$
$978$	−2.22006	−0.0709895
$979$	10.9165	0.348892
$980$	55.3876	1.76929
$981$	−50.5157	−1.61284
$982$	−115.838	−3.69654
$983$	−51.7503	−1.65058	−0.825289	−	0.564711i	$-0.808988\pi$
$983$	−51.7503	−1.65058	−0.825289	+	0.564711i	$0.808988\pi$
$984$	−6.11530	−0.194949
$985$	75.6952	2.41185
$986$	153.883	4.90064
$987$	−1.98734	−0.0632577
$988$	6.77131	0.215424
$989$	32.1473	1.02222
$990$	−133.484	−4.24240
$991$	56.3721	1.79072	0.895360	−	0.445343i	$-0.146918\pi$
$991$	56.3721	1.79072	0.895360	+	0.445343i	$0.146918\pi$
$992$	216.005	6.85815
$993$	−0.360110	−0.0114277
$994$	−55.3833	−1.75665
$995$	4.63673	0.146994
$996$	1.85880	0.0588982
$997$	−17.5627	−0.556218	−0.278109	−	0.960550i	$-0.589708\pi$
$997$	−17.5627	−0.556218	−0.278109	+	0.960550i	$0.589708\pi$
$998$	20.4632	0.647751
$999$	−1.96509	−0.0621726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.b.1.3	✓	205

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.b.1.3	✓	205	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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78060 q^{2} +0.0708990 q^{3} +5.73173 q^{4} -3.99378 q^{5} -0.197142 q^{6} +2.14019 q^{7} -10.3764 q^{8} -2.99497 q^{9} +O(q^{10})\)	\(q-2.78060 q^{2} +0.0708990 q^{3} +5.73173 q^{4} -3.99378 q^{5} -0.197142 q^{6} +2.14019 q^{7} -10.3764 q^{8} -2.99497 q^{9} +11.1051 q^{10} +4.01342 q^{11} +0.406374 q^{12} +0.791985 q^{13} -5.95100 q^{14} -0.283155 q^{15} +17.3893 q^{16} -5.42755 q^{17} +8.32782 q^{18} +1.49166 q^{19} -22.8912 q^{20} +0.151737 q^{21} -11.1597 q^{22} -3.73989 q^{23} -0.735679 q^{24} +10.9502 q^{25} -2.20219 q^{26} -0.425037 q^{27} +12.2670 q^{28} +10.1964 q^{29} +0.787339 q^{30} -7.82634 q^{31} -27.5997 q^{32} +0.284547 q^{33} +15.0918 q^{34} -8.54743 q^{35} -17.1664 q^{36} +4.62333 q^{37} -4.14771 q^{38} +0.0561509 q^{39} +41.4412 q^{40} +8.31246 q^{41} -0.421920 q^{42} -8.59578 q^{43} +23.0038 q^{44} +11.9613 q^{45} +10.3991 q^{46} -13.0972 q^{47} +1.23288 q^{48} -2.41960 q^{49} -30.4482 q^{50} -0.384808 q^{51} +4.53944 q^{52} +3.74322 q^{53} +1.18186 q^{54} -16.0287 q^{55} -22.2075 q^{56} +0.105757 q^{57} -28.3522 q^{58} -3.56455 q^{59} -1.62297 q^{60} -2.27680 q^{61} +21.7619 q^{62} -6.40981 q^{63} +41.9652 q^{64} -3.16301 q^{65} -0.791212 q^{66} +9.76862 q^{67} -31.1093 q^{68} -0.265155 q^{69} +23.7670 q^{70} +9.30654 q^{71} +31.0772 q^{72} -1.45119 q^{73} -12.8556 q^{74} +0.776361 q^{75} +8.54980 q^{76} +8.58947 q^{77} -0.156133 q^{78} -3.03016 q^{79} -69.4489 q^{80} +8.95479 q^{81} -23.1136 q^{82} +4.57411 q^{83} +0.869716 q^{84} +21.6764 q^{85} +23.9014 q^{86} +0.722918 q^{87} -41.6450 q^{88} +2.71999 q^{89} -33.2594 q^{90} +1.69500 q^{91} -21.4361 q^{92} -0.554879 q^{93} +36.4182 q^{94} -5.95736 q^{95} -1.95679 q^{96} +4.90279 q^{97} +6.72793 q^{98} -12.0201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * q^99

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