LMFDB - Embedded newform 6011.2.a.f.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, 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("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$0$
Dimension:	$275$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60468 q^{2} -1.25355 q^{3} +4.78433 q^{4} -3.42467 q^{5} +3.26509 q^{6} -1.07098 q^{7} -7.25228 q^{8} -1.42861 q^{9} +O(q^{10})$	\(q-2.60468 q^{2} -1.25355 q^{3} +4.78433 q^{4} -3.42467 q^{5} +3.26509 q^{6} -1.07098 q^{7} -7.25228 q^{8} -1.42861 q^{9} +8.92017 q^{10} -4.14879 q^{11} -5.99740 q^{12} +0.938264 q^{13} +2.78955 q^{14} +4.29300 q^{15} +9.32118 q^{16} -2.85086 q^{17} +3.72107 q^{18} +8.06708 q^{19} -16.3848 q^{20} +1.34252 q^{21} +10.8063 q^{22} -1.20456 q^{23} +9.09110 q^{24} +6.72840 q^{25} -2.44387 q^{26} +5.55149 q^{27} -5.12391 q^{28} +4.84230 q^{29} -11.1819 q^{30} +4.16792 q^{31} -9.77407 q^{32} +5.20071 q^{33} +7.42557 q^{34} +3.66775 q^{35} -6.83496 q^{36} -1.80094 q^{37} -21.0121 q^{38} -1.17616 q^{39} +24.8367 q^{40} +7.81968 q^{41} -3.49683 q^{42} -6.76747 q^{43} -19.8492 q^{44} +4.89254 q^{45} +3.13750 q^{46} -9.97625 q^{47} -11.6846 q^{48} -5.85301 q^{49} -17.5253 q^{50} +3.57370 q^{51} +4.48897 q^{52} -1.79528 q^{53} -14.4598 q^{54} +14.2083 q^{55} +7.76703 q^{56} -10.1125 q^{57} -12.6126 q^{58} -4.67736 q^{59} +20.5391 q^{60} -6.07037 q^{61} -10.8561 q^{62} +1.53001 q^{63} +6.81593 q^{64} -3.21325 q^{65} -13.5462 q^{66} +3.73657 q^{67} -13.6395 q^{68} +1.50998 q^{69} -9.55329 q^{70} -7.66131 q^{71} +10.3607 q^{72} -3.96136 q^{73} +4.69088 q^{74} -8.43438 q^{75} +38.5956 q^{76} +4.44326 q^{77} +3.06351 q^{78} -2.42944 q^{79} -31.9220 q^{80} -2.67322 q^{81} -20.3677 q^{82} -12.1661 q^{83} +6.42307 q^{84} +9.76327 q^{85} +17.6271 q^{86} -6.07006 q^{87} +30.0882 q^{88} -4.35407 q^{89} -12.7435 q^{90} -1.00486 q^{91} -5.76303 q^{92} -5.22469 q^{93} +25.9849 q^{94} -27.6271 q^{95} +12.2523 q^{96} -14.4985 q^{97} +15.2452 q^{98} +5.92702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) $ 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * 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 $

$2$	−2.60468	−1.84178	−0.920892	−	0.389818i	$-0.872538\pi$
$2$	−2.60468	−1.84178	−0.920892	+	0.389818i	$0.872538\pi$
$3$	−1.25355	−0.723737	−0.361869	−	0.932229i	$-0.617861\pi$
$3$	−1.25355	−0.723737	−0.361869	+	0.932229i	$0.617861\pi$
$4$	4.78433	2.39217
$5$	−3.42467	−1.53156	−0.765781	−	0.643102i	$-0.777647\pi$
$5$	−3.42467	−1.53156	−0.765781	+	0.643102i	$0.777647\pi$
$6$	3.26509	1.33297
$7$	−1.07098	−0.404791	−0.202396	−	0.979304i	$-0.564873\pi$
$7$	−1.07098	−0.404791	−0.202396	+	0.979304i	$0.564873\pi$
$8$	−7.25228	−2.56407
$9$	−1.42861	−0.476205
$10$	8.92017	2.82080
$11$	−4.14879	−1.25091	−0.625454	−	0.780261i	$-0.715086\pi$
$11$	−4.14879	−1.25091	−0.625454	+	0.780261i	$0.715086\pi$
$12$	−5.99740	−1.73130
$13$	0.938264	0.260228	0.130114	−	0.991499i	$-0.458466\pi$
$13$	0.938264	0.260228	0.130114	+	0.991499i	$0.458466\pi$
$14$	2.78955	0.745538
$15$	4.29300	1.10845
$16$	9.32118	2.33029
$17$	−2.85086	−0.691436	−0.345718	−	0.938339i	$-0.612365\pi$
$17$	−2.85086	−0.691436	−0.345718	+	0.938339i	$0.612365\pi$
$18$	3.72107	0.877066
$19$	8.06708	1.85071	0.925357	−	0.379096i	$-0.123765\pi$
$19$	8.06708	1.85071	0.925357	+	0.379096i	$0.123765\pi$
$20$	−16.3848	−3.66375
$21$	1.34252	0.292962
$22$	10.8063	2.30390
$23$	−1.20456	−0.251169	−0.125584	−	0.992083i	$-0.540081\pi$
$23$	−1.20456	−0.251169	−0.125584	+	0.992083i	$0.540081\pi$
$24$	9.09110	1.85571
$25$	6.72840	1.34568
$26$	−2.44387	−0.479283
$27$	5.55149	1.06838
$28$	−5.12391	−0.968328
$29$	4.84230	0.899193	0.449596	−	0.893232i	$-0.351568\pi$
$29$	4.84230	0.899193	0.449596	+	0.893232i	$0.351568\pi$
$30$	−11.1819	−2.04152
$31$	4.16792	0.748580	0.374290	−	0.927312i	$-0.377886\pi$
$31$	4.16792	0.748580	0.374290	+	0.927312i	$0.377886\pi$
$32$	−9.77407	−1.72783
$33$	5.20071	0.905328
$34$	7.42557	1.27347
$35$	3.66775	0.619962
$36$	−6.83496	−1.13916
$37$	−1.80094	−0.296073	−0.148037	−	0.988982i	$-0.547295\pi$
$37$	−1.80094	−0.296073	−0.148037	+	0.988982i	$0.547295\pi$
$38$	−21.0121	−3.40862
$39$	−1.17616	−0.188336
$40$	24.8367	3.92703
$41$	7.81968	1.22123	0.610615	−	0.791928i	$-0.290922\pi$
$41$	7.81968	1.22123	0.610615	+	0.791928i	$0.290922\pi$
$42$	−3.49683	−0.539573
$43$	−6.76747	−1.03203	−0.516015	−	0.856580i	$-0.672585\pi$
$43$	−6.76747	−1.03203	−0.516015	+	0.856580i	$0.672585\pi$
$44$	−19.8492	−2.99238
$45$	4.89254	0.729336
$46$	3.13750	0.462599
$47$	−9.97625	−1.45519	−0.727593	−	0.686009i	$-0.759361\pi$
$47$	−9.97625	−1.45519	−0.727593	+	0.686009i	$0.759361\pi$
$48$	−11.6846	−1.68652
$49$	−5.85301	−0.836144
$50$	−17.5253	−2.47845
$51$	3.57370	0.500418
$52$	4.48897	0.622508
$53$	−1.79528	−0.246600	−0.123300	−	0.992369i	$-0.539348\pi$
$53$	−1.79528	−0.246600	−0.123300	+	0.992369i	$0.539348\pi$
$54$	−14.4598	−1.96773
$55$	14.2083	1.91584
$56$	7.76703	1.03791
$57$	−10.1125	−1.33943
$58$	−12.6126	−1.65612
$59$	−4.67736	−0.608940	−0.304470	−	0.952522i	$-0.598479\pi$
$59$	−4.67736	−0.608940	−0.304470	+	0.952522i	$0.598479\pi$
$60$	20.5391	2.65159
$61$	−6.07037	−0.777231	−0.388616	−	0.921400i	$-0.627047\pi$
$61$	−6.07037	−0.777231	−0.388616	+	0.921400i	$0.627047\pi$
$62$	−10.8561	−1.37872
$63$	1.53001	0.192763
$64$	6.81593	0.851991
$65$	−3.21325	−0.398554
$66$	−13.5462	−1.66742
$67$	3.73657	0.456494	0.228247	−	0.973603i	$-0.426701\pi$
$67$	3.73657	0.456494	0.228247	+	0.973603i	$0.426701\pi$
$68$	−13.6395	−1.65403
$69$	1.50998	0.181780
$70$	−9.55329	−1.14184
$71$	−7.66131	−0.909231	−0.454615	−	0.890688i	$-0.650223\pi$
$71$	−7.66131	−0.909231	−0.454615	+	0.890688i	$0.650223\pi$
$72$	10.3607	1.22102
$73$	−3.96136	−0.463642	−0.231821	−	0.972758i	$-0.574468\pi$
$73$	−3.96136	−0.463642	−0.231821	+	0.972758i	$0.574468\pi$
$74$	4.69088	0.545303
$75$	−8.43438	−0.973918
$76$	38.5956	4.42722
$77$	4.44326	0.506356
$78$	3.06351	0.346875
$79$	−2.42944	−0.273333	−0.136666	−	0.990617i	$-0.543639\pi$
$79$	−2.42944	−0.273333	−0.136666	+	0.990617i	$0.543639\pi$
$80$	−31.9220	−3.56899
$81$	−2.67322	−0.297025
$82$	−20.3677	−2.24924
$83$	−12.1661	−1.33540	−0.667700	−	0.744431i	$-0.732721\pi$
$83$	−12.1661	−1.33540	−0.667700	+	0.744431i	$0.732721\pi$
$84$	6.42307	0.700815
$85$	9.76327	1.05898
$86$	17.6271	1.90078
$87$	−6.07006	−0.650779
$88$	30.0882	3.20741
$89$	−4.35407	−0.461530	−0.230765	−	0.973009i	$-0.574123\pi$
$89$	−4.35407	−0.461530	−0.230765	+	0.973009i	$0.574123\pi$
$90$	−12.7435	−1.34328
$91$	−1.00486	−0.105338
$92$	−5.76303	−0.600838
$93$	−5.22469	−0.541775
$94$	25.9849	2.68014
$95$	−27.6271	−2.83448
$96$	12.2523	1.25049
$97$	−14.4985	−1.47210	−0.736048	−	0.676929i	$-0.763310\pi$
$97$	−14.4985	−1.47210	−0.736048	+	0.676929i	$0.763310\pi$
$98$	15.2452	1.54000
$99$	5.92702	0.595688
$100$	32.1909	3.21909
$101$	−13.1562	−1.30909	−0.654546	−	0.756022i	$-0.727140\pi$
$101$	−13.1562	−1.30909	−0.654546	+	0.756022i	$0.727140\pi$
$102$	−9.30832	−0.921661
$103$	0.653141	0.0643559	0.0321780	−	0.999482i	$-0.489756\pi$
$103$	0.653141	0.0643559	0.0321780	+	0.999482i	$0.489756\pi$
$104$	−6.80455	−0.667241
$105$	−4.59770	−0.448690
$106$	4.67612	0.454185
$107$	−5.30169	−0.512534	−0.256267	−	0.966606i	$-0.582493\pi$
$107$	−5.30169	−0.512534	−0.256267	+	0.966606i	$0.582493\pi$
$108$	26.5602	2.55575
$109$	−13.1947	−1.26382	−0.631912	−	0.775040i	$-0.717730\pi$
$109$	−13.1947	−1.26382	−0.631912	+	0.775040i	$0.717730\pi$
$110$	−37.0079	−3.52856
$111$	2.25757	0.214279
$112$	−9.98276	−0.943282
$113$	11.8138	1.11135	0.555674	−	0.831400i	$-0.312460\pi$
$113$	11.8138	1.11135	0.555674	+	0.831400i	$0.312460\pi$
$114$	26.3397	2.46694
$115$	4.12524	0.384681
$116$	23.1672	2.15102
$117$	−1.34042	−0.123922
$118$	12.1830	1.12154
$119$	3.05321	0.279887
$120$	−31.1340	−2.84214
$121$	6.21246	0.564769
$122$	15.8113	1.43149
$123$	−9.80236	−0.883849
$124$	19.9407	1.79073
$125$	−5.91920	−0.529429
$126$	−3.98518	−0.355028
$127$	−14.0670	−1.24824	−0.624122	−	0.781327i	$-0.714543\pi$
$127$	−14.0670	−1.24824	−0.624122	+	0.781327i	$0.714543\pi$
$128$	1.79487	0.158645
$129$	8.48336	0.746919
$130$	8.36947	0.734051
$131$	−1.69197	−0.147828	−0.0739141	−	0.997265i	$-0.523549\pi$
$131$	−1.69197	−0.147828	−0.0739141	+	0.997265i	$0.523549\pi$
$132$	24.8819	2.16570
$133$	−8.63966	−0.749153
$134$	−9.73254	−0.840763
$135$	−19.0120	−1.63630
$136$	20.6753	1.77289
$137$	8.87993	0.758663	0.379332	−	0.925261i	$-0.376154\pi$
$137$	8.87993	0.758663	0.379332	+	0.925261i	$0.376154\pi$
$138$	−3.93301	−0.334800
$139$	11.8218	1.00271	0.501355	−	0.865242i	$-0.332835\pi$
$139$	11.8218	1.00271	0.501355	+	0.865242i	$0.332835\pi$
$140$	17.5477	1.48305
$141$	12.5057	1.05317
$142$	19.9552	1.67461
$143$	−3.89266	−0.325520
$144$	−13.3164	−1.10970
$145$	−16.5833	−1.37717
$146$	10.3181	0.853928
$147$	7.33704	0.605149
$148$	−8.61632	−0.708257
$149$	23.0890	1.89152	0.945761	−	0.324862i	$-0.105318\pi$
$149$	23.0890	1.89152	0.945761	+	0.324862i	$0.105318\pi$
$150$	21.9688	1.79375
$151$	−3.69794	−0.300934	−0.150467	−	0.988615i	$-0.548078\pi$
$151$	−3.69794	−0.300934	−0.150467	+	0.988615i	$0.548078\pi$
$152$	−58.5047	−4.74536
$153$	4.07278	0.329265
$154$	−11.5732	−0.932599
$155$	−14.2738	−1.14650
$156$	−5.62714	−0.450532
$157$	0.204673	0.0163347	0.00816736	−	0.999967i	$-0.497400\pi$
$157$	0.204673	0.0163347	0.00816736	+	0.999967i	$0.497400\pi$
$158$	6.32789	0.503420
$159$	2.25047	0.178474
$160$	33.4730	2.64627
$161$	1.29006	0.101671
$162$	6.96288	0.547055
$163$	−6.38595	−0.500186	−0.250093	−	0.968222i	$-0.580461\pi$
$163$	−6.38595	−0.500186	−0.250093	+	0.968222i	$0.580461\pi$
$164$	37.4120	2.92138
$165$	−17.8108	−1.38657
$166$	31.6887	2.45952
$167$	15.7286	1.21712	0.608559	−	0.793508i	$-0.291748\pi$
$167$	15.7286	1.21712	0.608559	+	0.793508i	$0.291748\pi$
$168$	−9.73635	−0.751176
$169$	−12.1197	−0.932282
$170$	−25.4302	−1.95040
$171$	−11.5247	−0.881319
$172$	−32.3778	−2.46879
$173$	−9.15947	−0.696382	−0.348191	−	0.937424i	$-0.613204\pi$
$173$	−9.15947	−0.696382	−0.348191	+	0.937424i	$0.613204\pi$
$174$	15.8105	1.19859
$175$	−7.20596	−0.544719
$176$	−38.6716	−2.91498
$177$	5.86330	0.440712
$178$	11.3409	0.850039
$179$	1.12504	0.0840894	0.0420447	−	0.999116i	$-0.486613\pi$
$179$	1.12504	0.0840894	0.0420447	+	0.999116i	$0.486613\pi$
$180$	23.4075	1.74469
$181$	−20.6763	−1.53686	−0.768428	−	0.639936i	$-0.778961\pi$
$181$	−20.6763	−1.53686	−0.768428	+	0.639936i	$0.778961\pi$
$182$	2.61733	0.194009
$183$	7.60951	0.562511
$184$	8.73584	0.644014
$185$	6.16765	0.453455
$186$	13.6086	0.997833
$187$	11.8276	0.864922
$188$	−47.7297	−3.48105
$189$	−5.94551	−0.432472
$190$	71.9597	5.22050
$191$	−10.2828	−0.744038	−0.372019	−	0.928225i	$-0.621334\pi$
$191$	−10.2828	−0.744038	−0.372019	+	0.928225i	$0.621334\pi$
$192$	−8.54410	−0.616617
$193$	−8.93621	−0.643243	−0.321621	−	0.946868i	$-0.604228\pi$
$193$	−8.93621	−0.643243	−0.321621	+	0.946868i	$0.604228\pi$
$194$	37.7638	2.71128
$195$	4.02797	0.288449
$196$	−28.0027	−2.00020
$197$	−8.19513	−0.583879	−0.291939	−	0.956437i	$-0.594301\pi$
$197$	−8.19513	−0.583879	−0.291939	+	0.956437i	$0.594301\pi$
$198$	−15.4380	−1.09713
$199$	26.0057	1.84350	0.921748	−	0.387789i	$-0.126761\pi$
$199$	26.0057	1.84350	0.921748	+	0.387789i	$0.126761\pi$
$200$	−48.7962	−3.45042
$201$	−4.68397	−0.330382
$202$	34.2676	2.41106
$203$	−5.18599	−0.363985
$204$	17.0978	1.19708
$205$	−26.7799	−1.87039
$206$	−1.70122	−0.118530
$207$	1.72086	0.119608
$208$	8.74572	0.606407
$209$	−33.4686	−2.31507
$210$	11.9755	0.826390
$211$	−5.96987	−0.410983	−0.205491	−	0.978659i	$-0.565879\pi$
$211$	−5.96987	−0.410983	−0.205491	+	0.978659i	$0.565879\pi$
$212$	−8.58921	−0.589909
$213$	9.60384	0.658044
$214$	13.8092	0.943977
$215$	23.1764	1.58062
$216$	−40.2610	−2.73941
$217$	−4.46374	−0.303019
$218$	34.3679	2.32769
$219$	4.96576	0.335555
$220$	67.9770	4.58301
$221$	−2.67486	−0.179931
$222$	−5.88024	−0.394656
$223$	25.7368	1.72347	0.861733	−	0.507363i	$-0.169379\pi$
$223$	25.7368	1.72347	0.861733	+	0.507363i	$0.169379\pi$
$224$	10.4678	0.699409
$225$	−9.61228	−0.640819
$226$	−30.7711	−2.04686
$227$	−10.7225	−0.711680	−0.355840	−	0.934547i	$-0.615805\pi$
$227$	−10.7225	−0.711680	−0.355840	+	0.934547i	$0.615805\pi$
$228$	−48.3815	−3.20414
$229$	6.33893	0.418888	0.209444	−	0.977821i	$-0.432835\pi$
$229$	6.33893	0.418888	0.209444	+	0.977821i	$0.432835\pi$
$230$	−10.7449	−0.708498
$231$	−5.56984	−0.366469
$232$	−35.1177	−2.30559
$233$	5.21197	0.341447	0.170724	−	0.985319i	$-0.445389\pi$
$233$	5.21197	0.341447	0.170724	+	0.985319i	$0.445389\pi$
$234$	3.49135	0.228237
$235$	34.1654	2.22871
$236$	−22.3780	−1.45669
$237$	3.04542	0.197821
$238$	−7.95261	−0.515491
$239$	3.32003	0.214755	0.107377	−	0.994218i	$-0.465755\pi$
$239$	3.32003	0.214755	0.107377	+	0.994218i	$0.465755\pi$
$240$	40.0158	2.58301
$241$	−10.7845	−0.694692	−0.347346	−	0.937737i	$-0.612917\pi$
$241$	−10.7845	−0.694692	−0.347346	+	0.937737i	$0.612917\pi$
$242$	−16.1814	−1.04018
$243$	−13.3034	−0.853416
$244$	−29.0427	−1.85927
$245$	20.0447	1.28061
$246$	25.5320	1.62786
$247$	7.56905	0.481607
$248$	−30.2269	−1.91941
$249$	15.2508	0.966478
$250$	15.4176	0.975094
$251$	−8.35304	−0.527239	−0.263620	−	0.964627i	$-0.584916\pi$
$251$	−8.35304	−0.527239	−0.263620	+	0.964627i	$0.584916\pi$
$252$	7.32009	0.461122
$253$	4.99748	0.314189
$254$	36.6400	2.29900
$255$	−12.2387	−0.766420
$256$	−18.3069	−1.14418
$257$	3.24234	0.202252	0.101126	−	0.994874i	$-0.467756\pi$
$257$	3.24234	0.202252	0.101126	+	0.994874i	$0.467756\pi$
$258$	−22.0964	−1.37566
$259$	1.92877	0.119848
$260$	−15.3732	−0.953408
$261$	−6.91778	−0.428200
$262$	4.40704	0.272268
$263$	17.1960	1.06035	0.530175	−	0.847888i	$-0.322126\pi$
$263$	17.1960	1.06035	0.530175	+	0.847888i	$0.322126\pi$
$264$	−37.7170	−2.32132
$265$	6.14824	0.377684
$266$	22.5035	1.37978
$267$	5.45804	0.334027
$268$	17.8770	1.09201
$269$	20.1079	1.22600	0.613001	−	0.790082i	$-0.289962\pi$
$269$	20.1079	1.22600	0.613001	+	0.790082i	$0.289962\pi$
$270$	49.5202	3.01370
$271$	7.34203	0.445997	0.222998	−	0.974819i	$-0.428416\pi$
$271$	7.34203	0.445997	0.222998	+	0.974819i	$0.428416\pi$
$272$	−26.5734	−1.61125
$273$	1.25964	0.0762369
$274$	−23.1293	−1.39729
$275$	−27.9147	−1.68332
$276$	7.22425	0.434849
$277$	−18.0942	−1.08718	−0.543588	−	0.839352i	$-0.682934\pi$
$277$	−18.0942	−1.08718	−0.543588	+	0.839352i	$0.682934\pi$
$278$	−30.7919	−1.84677
$279$	−5.95434	−0.356477
$280$	−26.5995	−1.58963
$281$	18.3537	1.09489	0.547446	−	0.836841i	$-0.315600\pi$
$281$	18.3537	1.09489	0.547446	+	0.836841i	$0.315600\pi$
$282$	−32.5733	−1.93971
$283$	−6.91806	−0.411236	−0.205618	−	0.978632i	$-0.565920\pi$
$283$	−6.91806	−0.411236	−0.205618	+	0.978632i	$0.565920\pi$
$284$	−36.6543	−2.17503
$285$	34.6320	2.05142
$286$	10.1391	0.599538
$287$	−8.37470	−0.494343
$288$	13.9634	0.822799
$289$	−8.87259	−0.521917
$290$	43.1941	2.53645
$291$	18.1745	1.06541
$292$	−18.9525	−1.10911
$293$	−11.8488	−0.692212	−0.346106	−	0.938195i	$-0.612496\pi$
$293$	−11.8488	−0.692212	−0.346106	+	0.938195i	$0.612496\pi$
$294$	−19.1106	−1.11455
$295$	16.0184	0.932629
$296$	13.0610	0.759153
$297$	−23.0320	−1.33645
$298$	−60.1393	−3.48378
$299$	−1.13020	−0.0653611
$300$	−40.3529	−2.32977
$301$	7.24781	0.417757
$302$	9.63193	0.554255
$303$	16.4920	0.947438
$304$	75.1947	4.31271
$305$	20.7890	1.19038
$306$	−10.6083	−0.606434
$307$	12.2875	0.701287	0.350644	−	0.936509i	$-0.385963\pi$
$307$	12.2875	0.701287	0.350644	+	0.936509i	$0.385963\pi$
$308$	21.2580	1.21129
$309$	−0.818745	−0.0465768
$310$	37.1785	2.11160
$311$	7.11413	0.403405	0.201703	−	0.979447i	$-0.435353\pi$
$311$	7.11413	0.403405	0.201703	+	0.979447i	$0.435353\pi$
$312$	8.52984	0.482907
$313$	4.51945	0.255454	0.127727	−	0.991809i	$-0.459232\pi$
$313$	4.51945	0.255454	0.127727	+	0.991809i	$0.459232\pi$
$314$	−0.533108	−0.0300850
$315$	−5.23979	−0.295229
$316$	−11.6232	−0.653858
$317$	−19.3039	−1.08421	−0.542107	−	0.840310i	$-0.682373\pi$
$317$	−19.3039	−1.08421	−0.542107	+	0.840310i	$0.682373\pi$
$318$	−5.86174	−0.328710
$319$	−20.0897	−1.12481
$320$	−23.3423	−1.30488
$321$	6.64593	0.370940
$322$	−3.36019	−0.187256
$323$	−22.9981	−1.27965
$324$	−12.7896	−0.710533
$325$	6.31301	0.350183
$326$	16.6333	0.921234
$327$	16.5402	0.914676
$328$	−56.7106	−3.13132
$329$	10.6843	0.589046
$330$	46.3912	2.55375
$331$	−13.4306	−0.738212	−0.369106	−	0.929387i	$-0.620336\pi$
$331$	−13.4306	−0.738212	−0.369106	+	0.929387i	$0.620336\pi$
$332$	−58.2065	−3.19450
$333$	2.57285	0.140992
$334$	−40.9680	−2.24167
$335$	−12.7965	−0.699149
$336$	12.5139	0.682689
$337$	−6.90241	−0.375998	−0.187999	−	0.982169i	$-0.560200\pi$
$337$	−6.90241	−0.375998	−0.187999	+	0.982169i	$0.560200\pi$
$338$	31.5678	1.71706
$339$	−14.8092	−0.804324
$340$	46.7108	2.53325
$341$	−17.2918	−0.936404
$342$	30.0182	1.62320
$343$	13.7653	0.743255
$344$	49.0796	2.64620
$345$	−5.17119	−0.278408
$346$	23.8574	1.28258
$347$	−34.1441	−1.83295	−0.916475	−	0.400091i	$-0.868978\pi$
$347$	−34.1441	−1.83295	−0.916475	+	0.400091i	$0.868978\pi$
$348$	−29.0412	−1.55677
$349$	−7.36378	−0.394174	−0.197087	−	0.980386i	$-0.563148\pi$
$349$	−7.36378	−0.394174	−0.197087	+	0.980386i	$0.563148\pi$
$350$	18.7692	1.00325
$351$	5.20876	0.278023
$352$	40.5506	2.16135
$353$	−35.3229	−1.88005	−0.940024	−	0.341109i	$-0.889198\pi$
$353$	−35.3229	−1.88005	−0.940024	+	0.341109i	$0.889198\pi$
$354$	−15.2720	−0.811697
$355$	26.2375	1.39254
$356$	−20.8313	−1.10406
$357$	−3.82735	−0.202565
$358$	−2.93036	−0.154874
$359$	−22.1571	−1.16941	−0.584703	−	0.811247i	$-0.698789\pi$
$359$	−22.1571	−1.16941	−0.584703	+	0.811247i	$0.698789\pi$
$360$	−35.4821	−1.87007
$361$	46.0778	2.42515
$362$	53.8550	2.83056
$363$	−7.78762	−0.408744
$364$	−4.80758	−0.251986
$365$	13.5664	0.710096
$366$	−19.8203	−1.03602
$367$	9.85621	0.514490	0.257245	−	0.966346i	$-0.417185\pi$
$367$	9.85621	0.514490	0.257245	+	0.966346i	$0.417185\pi$
$368$	−11.2280	−0.585297
$369$	−11.1713	−0.581555
$370$	−16.0647	−0.835165
$371$	1.92270	0.0998217
$372$	−24.9967	−1.29602
$373$	−25.3995	−1.31514	−0.657569	−	0.753394i	$-0.728415\pi$
$373$	−25.3995	−1.31514	−0.657569	+	0.753394i	$0.728415\pi$
$374$	−30.8071	−1.59300
$375$	7.42001	0.383168
$376$	72.3506	3.73120
$377$	4.54336	0.233995
$378$	15.4861	0.796521
$379$	−19.2728	−0.989975	−0.494988	−	0.868900i	$-0.664827\pi$
$379$	−19.2728	−0.989975	−0.494988	+	0.868900i	$0.664827\pi$
$380$	−132.177	−6.78056
$381$	17.6337	0.903401
$382$	26.7834	1.37036
$383$	−33.9012	−1.73227	−0.866135	−	0.499810i	$-0.833403\pi$
$383$	−33.9012	−1.73227	−0.866135	+	0.499810i	$0.833403\pi$
$384$	−2.24996	−0.114818
$385$	−15.2167	−0.775516
$386$	23.2759	1.18471
$387$	9.66811	0.491457
$388$	−69.3655	−3.52150
$389$	9.30050	0.471554	0.235777	−	0.971807i	$-0.424237\pi$
$389$	9.30050	0.471554	0.235777	+	0.971807i	$0.424237\pi$
$390$	−10.4915	−0.531260
$391$	3.43404	0.173667
$392$	42.4477	2.14393
$393$	2.12097	0.106989
$394$	21.3456	1.07538
$395$	8.32003	0.418626
$396$	28.3568	1.42498
$397$	9.49882	0.476732	0.238366	−	0.971175i	$-0.423388\pi$
$397$	9.49882	0.476732	0.238366	+	0.971175i	$0.423388\pi$
$398$	−67.7364	−3.39532
$399$	10.8302	0.542190
$400$	62.7166	3.13583
$401$	−26.0553	−1.30114	−0.650571	−	0.759446i	$-0.725470\pi$
$401$	−26.0553	−1.30114	−0.650571	+	0.759446i	$0.725470\pi$
$402$	12.2002	0.608492
$403$	3.91061	0.194801
$404$	−62.9437	−3.13157
$405$	9.15492	0.454912
$406$	13.5078	0.670382
$407$	7.47174	0.370360
$408$	−25.9175	−1.28311
$409$	15.3841	0.760696	0.380348	−	0.924843i	$-0.375804\pi$
$409$	15.3841	0.760696	0.380348	+	0.924843i	$0.375804\pi$
$410$	69.7529	3.44485
$411$	−11.1314	−0.549073
$412$	3.12485	0.153950
$413$	5.00934	0.246493
$414$	−4.48227	−0.220292
$415$	41.6648	2.04525
$416$	−9.17065	−0.449628
$417$	−14.8192	−0.725698
$418$	87.1749	4.26386
$419$	29.4390	1.43819	0.719094	−	0.694912i	$-0.244557\pi$
$419$	29.4390	1.43819	0.719094	+	0.694912i	$0.244557\pi$
$420$	−21.9969	−1.07334
$421$	5.42956	0.264621	0.132310	−	0.991208i	$-0.457760\pi$
$421$	5.42956	0.264621	0.132310	+	0.991208i	$0.457760\pi$
$422$	15.5496	0.756941
$423$	14.2522	0.692966
$424$	13.0199	0.632301
$425$	−19.1817	−0.930451
$426$	−25.0149	−1.21197
$427$	6.50122	0.314616
$428$	−25.3651	−1.22607
$429$	4.87964	0.235591
$430$	−60.3670	−2.91115
$431$	30.2542	1.45729	0.728647	−	0.684889i	$-0.240149\pi$
$431$	30.2542	1.45729	0.728647	+	0.684889i	$0.240149\pi$
$432$	51.7464	2.48965
$433$	−13.0222	−0.625807	−0.312903	−	0.949785i	$-0.601302\pi$
$433$	−13.0222	−0.625807	−0.312903	+	0.949785i	$0.601302\pi$
$434$	11.6266	0.558095
$435$	20.7880	0.996708
$436$	−63.1279	−3.02328
$437$	−9.71731	−0.464842
$438$	−12.9342	−0.618020
$439$	−30.0907	−1.43615	−0.718075	−	0.695966i	$-0.754977\pi$
$439$	−30.0907	−1.43615	−0.718075	+	0.695966i	$0.754977\pi$
$440$	−103.042	−4.91235
$441$	8.36169	0.398176
$442$	6.96714	0.331393
$443$	16.4811	0.783042	0.391521	−	0.920169i	$-0.371949\pi$
$443$	16.4811	0.783042	0.391521	+	0.920169i	$0.371949\pi$
$444$	10.8010	0.512592
$445$	14.9113	0.706862
$446$	−67.0361	−3.17425
$447$	−28.9432	−1.36897
$448$	−7.29970	−0.344878
$449$	25.9972	1.22688	0.613442	−	0.789740i	$-0.289785\pi$
$449$	25.9972	1.22688	0.613442	+	0.789740i	$0.289785\pi$
$450$	25.0369	1.18025
$451$	−32.4422	−1.52764
$452$	56.5211	2.65853
$453$	4.63555	0.217797
$454$	27.9288	1.31076
$455$	3.44131	0.161331
$456$	73.3386	3.43439
$457$	7.79620	0.364691	0.182345	−	0.983235i	$-0.441631\pi$
$457$	7.79620	0.364691	0.182345	+	0.983235i	$0.441631\pi$
$458$	−16.5108	−0.771501
$459$	−15.8265	−0.738719
$460$	19.7365	0.920220
$461$	38.4269	1.78972	0.894860	−	0.446347i	$-0.147275\pi$
$461$	38.4269	1.78972	0.894860	+	0.446347i	$0.147275\pi$
$462$	14.5076	0.674956
$463$	−27.7499	−1.28965	−0.644824	−	0.764331i	$-0.723070\pi$
$463$	−27.7499	−1.28965	−0.644824	+	0.764331i	$0.723070\pi$
$464$	45.1359	2.09538
$465$	17.8929	0.829762
$466$	−13.5755	−0.628872
$467$	4.95528	0.229303	0.114652	−	0.993406i	$-0.463425\pi$
$467$	4.95528	0.229303	0.114652	+	0.993406i	$0.463425\pi$
$468$	−6.41300	−0.296441
$469$	−4.00178	−0.184785
$470$	−88.9898	−4.10479
$471$	−0.256568	−0.0118220
$472$	33.9215	1.56136
$473$	28.0768	1.29097
$474$	−7.93233	−0.364344
$475$	54.2785	2.49047
$476$	14.6076	0.669536
$477$	2.56476	0.117432
$478$	−8.64760	−0.395532
$479$	1.40344	0.0641248	0.0320624	−	0.999486i	$-0.489792\pi$
$479$	1.40344	0.0641248	0.0320624	+	0.999486i	$0.489792\pi$
$480$	−41.9601	−1.91521
$481$	−1.68976	−0.0770465
$482$	28.0902	1.27947
$483$	−1.61715	−0.0735831
$484$	29.7225	1.35102
$485$	49.6525	2.25461
$486$	34.6511	1.57181
$487$	12.8286	0.581317	0.290659	−	0.956827i	$-0.406126\pi$
$487$	12.8286	0.581317	0.290659	+	0.956827i	$0.406126\pi$
$488$	44.0240	1.99287
$489$	8.00510	0.362003
$490$	−52.2098	−2.35860
$491$	9.41215	0.424765	0.212382	−	0.977187i	$-0.431878\pi$
$491$	9.41215	0.424765	0.212382	+	0.977187i	$0.431878\pi$
$492$	−46.8978	−2.11431
$493$	−13.8047	−0.621734
$494$	−19.7149	−0.887016
$495$	−20.2981	−0.912332
$496$	38.8499	1.74441
$497$	8.20509	0.368049
$498$	−39.7233	−1.78004
$499$	−7.70355	−0.344858	−0.172429	−	0.985022i	$-0.555162\pi$
$499$	−7.70355	−0.344858	−0.172429	+	0.985022i	$0.555162\pi$
$500$	−28.3194	−1.26648
$501$	−19.7166	−0.880874
$502$	21.7570	0.971061
$503$	−31.6912	−1.41304	−0.706521	−	0.707692i	$-0.749736\pi$
$503$	−31.6912	−1.41304	−0.706521	+	0.707692i	$0.749736\pi$
$504$	−11.0961	−0.494259
$505$	45.0557	2.00495
$506$	−13.0168	−0.578668
$507$	15.1926	0.674727
$508$	−67.3012	−2.98601
$509$	10.0473	0.445340	0.222670	−	0.974894i	$-0.428523\pi$
$509$	10.0473	0.445340	0.222670	+	0.974894i	$0.428523\pi$
$510$	31.8780	1.41158
$511$	4.24252	0.187678
$512$	44.0938	1.94869
$513$	44.7843	1.97727
$514$	−8.44525	−0.372504
$515$	−2.23680	−0.0985650
$516$	40.5872	1.78675
$517$	41.3894	1.82030
$518$	−5.02382	−0.220734
$519$	11.4819	0.503997
$520$	23.3034	1.02192
$521$	12.2090	0.534884	0.267442	−	0.963574i	$-0.413822\pi$
$521$	12.2090	0.534884	0.267442	+	0.963574i	$0.413822\pi$
$522$	18.0186	0.788651
$523$	−17.3968	−0.760707	−0.380353	−	0.924841i	$-0.624198\pi$
$523$	−17.3968	−0.760707	−0.380353	+	0.924841i	$0.624198\pi$
$524$	−8.09496	−0.353630
$525$	9.03303	0.394234
$526$	−44.7900	−1.95293
$527$	−11.8822	−0.517595
$528$	48.4768	2.10968
$529$	−21.5490	−0.936914
$530$	−16.0142	−0.695611
$531$	6.68213	0.289980
$532$	−41.3350	−1.79210
$533$	7.33693	0.317798
$534$	−14.2164	−0.615205
$535$	18.1566	0.784977
$536$	−27.0986	−1.17048
$537$	−1.41029	−0.0608586
$538$	−52.3746	−2.25803
$539$	24.2829	1.04594
$540$	−90.9599	−3.91429
$541$	−31.6246	−1.35965	−0.679823	−	0.733376i	$-0.737944\pi$
$541$	−31.6246	−1.35965	−0.679823	+	0.733376i	$0.737944\pi$
$542$	−19.1236	−0.821429
$543$	25.9188	1.11228
$544$	27.8645	1.19468
$545$	45.1876	1.93562
$546$	−3.28095	−0.140412
$547$	4.11485	0.175938	0.0879691	−	0.996123i	$-0.471962\pi$
$547$	4.11485	0.175938	0.0879691	+	0.996123i	$0.471962\pi$
$548$	42.4845	1.81485
$549$	8.67221	0.370121
$550$	72.7088	3.10031
$551$	39.0632	1.66415
$552$	−10.9508	−0.466097
$553$	2.60187	0.110643
$554$	47.1295	2.00234
$555$	−7.73145	−0.328182
$556$	56.5593	2.39865
$557$	−4.90157	−0.207686	−0.103843	−	0.994594i	$-0.533114\pi$
$557$	−4.90157	−0.207686	−0.103843	+	0.994594i	$0.533114\pi$
$558$	15.5091	0.656554
$559$	−6.34968	−0.268563
$560$	34.1877	1.44469
$561$	−14.8265	−0.625976
$562$	−47.8055	−2.01655
$563$	−10.0324	−0.422815	−0.211408	−	0.977398i	$-0.567805\pi$
$563$	−10.0324	−0.422815	−0.211408	+	0.977398i	$0.567805\pi$
$564$	59.8315	2.51936
$565$	−40.4584	−1.70210
$566$	18.0193	0.757408
$567$	2.86296	0.120233
$568$	55.5620	2.33133
$569$	−39.3104	−1.64798	−0.823988	−	0.566607i	$-0.808256\pi$
$569$	−39.3104	−1.64798	−0.823988	+	0.566607i	$0.808256\pi$
$570$	−90.2050	−3.77827
$571$	−23.6115	−0.988110	−0.494055	−	0.869431i	$-0.664486\pi$
$571$	−23.6115	−0.988110	−0.494055	+	0.869431i	$0.664486\pi$
$572$	−18.6238	−0.778699
$573$	12.8900	0.538488
$574$	21.8134	0.910473
$575$	−8.10478	−0.337993
$576$	−9.73732	−0.405722
$577$	1.06419	0.0443030	0.0221515	−	0.999755i	$-0.492948\pi$
$577$	1.06419	0.0443030	0.0221515	+	0.999755i	$0.492948\pi$
$578$	23.1102	0.961258
$579$	11.2020	0.465539
$580$	−79.3401	−3.29442
$581$	13.0296	0.540558
$582$	−47.3388	−1.96226
$583$	7.44823	0.308474
$584$	28.7289	1.18881
$585$	4.59049	0.189793
$586$	30.8622	1.27490
$587$	22.8690	0.943905	0.471952	−	0.881624i	$-0.343549\pi$
$587$	22.8690	0.943905	0.471952	+	0.881624i	$0.343549\pi$
$588$	35.1028	1.44762
$589$	33.6229	1.38541
$590$	−41.7228	−1.71770
$591$	10.2730	0.422575
$592$	−16.7869	−0.689938
$593$	−10.5438	−0.432983	−0.216492	−	0.976284i	$-0.569461\pi$
$593$	−10.5438	−0.432983	−0.216492	+	0.976284i	$0.569461\pi$
$594$	59.9908	2.46145
$595$	−10.4562	−0.428664
$596$	110.465	4.52484
$597$	−32.5995	−1.33421
$598$	2.94380	0.120381
$599$	−27.5646	−1.12626	−0.563129	−	0.826369i	$-0.690403\pi$
$599$	−27.5646	−1.12626	−0.563129	+	0.826369i	$0.690403\pi$
$600$	61.1685	2.49719
$601$	10.0022	0.407998	0.203999	−	0.978971i	$-0.434606\pi$
$601$	10.0022	0.407998	0.203999	+	0.978971i	$0.434606\pi$
$602$	−18.8782	−0.769417
$603$	−5.33811	−0.217385
$604$	−17.6922	−0.719884
$605$	−21.2756	−0.864978
$606$	−42.9562	−1.74498
$607$	−11.3156	−0.459286	−0.229643	−	0.973275i	$-0.573756\pi$
$607$	−11.3156	−0.459286	−0.229643	+	0.973275i	$0.573756\pi$
$608$	−78.8482	−3.19772
$609$	6.50090	0.263430
$610$	−54.1487	−2.19242
$611$	−9.36035	−0.378679
$612$	19.4855	0.787656
$613$	22.5524	0.910882	0.455441	−	0.890266i	$-0.349482\pi$
$613$	22.5524	0.910882	0.455441	+	0.890266i	$0.349482\pi$
$614$	−32.0051	−1.29162
$615$	33.5699	1.35367
$616$	−32.2238	−1.29833
$617$	30.2174	1.21651	0.608254	−	0.793742i	$-0.291870\pi$
$617$	30.2174	1.21651	0.608254	+	0.793742i	$0.291870\pi$
$618$	2.13256	0.0857843
$619$	21.9989	0.884211	0.442105	−	0.896963i	$-0.354232\pi$
$619$	21.9989	0.884211	0.442105	+	0.896963i	$0.354232\pi$
$620$	−68.2904	−2.74261
$621$	−6.68712	−0.268345
$622$	−18.5300	−0.742985
$623$	4.66311	0.186823
$624$	−10.9632	−0.438879
$625$	−13.3707	−0.534826
$626$	−11.7717	−0.470491
$627$	41.9546	1.67550
$628$	0.979226	0.0390754
$629$	5.13424	0.204716
$630$	13.6480	0.543748
$631$	−27.0888	−1.07839	−0.539193	−	0.842182i	$-0.681271\pi$
$631$	−27.0888	−1.07839	−0.539193	+	0.842182i	$0.681271\pi$
$632$	17.6190	0.700844
$633$	7.48353	0.297443
$634$	50.2803	1.99689
$635$	48.1749	1.91176
$636$	10.7670	0.426939
$637$	−5.49167	−0.217588
$638$	52.3271	2.07165
$639$	10.9451	0.432980
$640$	−6.14684	−0.242975
$641$	32.9422	1.30114	0.650568	−	0.759448i	$-0.274531\pi$
$641$	32.9422	1.30114	0.650568	+	0.759448i	$0.274531\pi$
$642$	−17.3105	−0.683191
$643$	20.0769	0.791756	0.395878	−	0.918303i	$-0.370440\pi$
$643$	20.0769	0.791756	0.395878	+	0.918303i	$0.370440\pi$
$644$	6.17208	0.243214
$645$	−29.0528	−1.14395
$646$	59.9027	2.35684
$647$	26.5617	1.04425	0.522123	−	0.852870i	$-0.325140\pi$
$647$	26.5617	1.04425	0.522123	+	0.852870i	$0.325140\pi$
$648$	19.3870	0.761592
$649$	19.4054	0.761727
$650$	−16.4433	−0.644961
$651$	5.59552	0.219306
$652$	−30.5525	−1.19653
$653$	−37.4045	−1.46375	−0.731876	−	0.681438i	$-0.761355\pi$
$653$	−37.4045	−1.46375	−0.731876	+	0.681438i	$0.761355\pi$
$654$	−43.0819	−1.68464
$655$	5.79445	0.226408
$656$	72.8886	2.84582
$657$	5.65925	0.220788
$658$	−27.8292	−1.08490
$659$	11.2209	0.437104	0.218552	−	0.975825i	$-0.429867\pi$
$659$	11.2209	0.437104	0.218552	+	0.975825i	$0.429867\pi$
$660$	−85.2126	−3.31689
$661$	43.6888	1.69930	0.849648	−	0.527350i	$-0.176814\pi$
$661$	43.6888	1.69930	0.849648	+	0.527350i	$0.176814\pi$
$662$	34.9823	1.35963
$663$	3.35307	0.130222
$664$	88.2318	3.42406
$665$	29.5880	1.14737
$666$	−6.70145	−0.259676
$667$	−5.83286	−0.225849
$668$	75.2510	2.91155
$669$	−32.2624	−1.24734
$670$	33.3308	1.28768
$671$	25.1847	0.972244
$672$	−13.1219	−0.506189
$673$	11.1009	0.427910	0.213955	−	0.976844i	$-0.431365\pi$
$673$	11.1009	0.427910	0.213955	+	0.976844i	$0.431365\pi$
$674$	17.9785	0.692508
$675$	37.3526	1.43770
$676$	−57.9845	−2.23017
$677$	−7.46986	−0.287090	−0.143545	−	0.989644i	$-0.545850\pi$
$677$	−7.46986	−0.287090	−0.143545	+	0.989644i	$0.545850\pi$
$678$	38.5731	1.48139
$679$	15.5275	0.595891
$680$	−70.8060	−2.71529
$681$	13.4412	0.515070
$682$	45.0396	1.72465
$683$	−22.8821	−0.875561	−0.437780	−	0.899082i	$-0.644235\pi$
$683$	−22.8821	−0.875561	−0.437780	+	0.899082i	$0.644235\pi$
$684$	−55.1382	−2.10826
$685$	−30.4109	−1.16194
$686$	−35.8541	−1.36891
$687$	−7.94616	−0.303165
$688$	−63.0808	−2.40493
$689$	−1.68444	−0.0641722
$690$	13.4693	0.512767
$691$	19.1052	0.726797	0.363398	−	0.931634i	$-0.381616\pi$
$691$	19.1052	0.726797	0.363398	+	0.931634i	$0.381616\pi$
$692$	−43.8220	−1.66586
$693$	−6.34770	−0.241129
$694$	88.9343	3.37590
$695$	−40.4857	−1.53571
$696$	44.0218	1.66864
$697$	−22.2928	−0.844401
$698$	19.1803	0.725984
$699$	−6.53346	−0.247118
$700$	−34.4757	−1.30306
$701$	26.9406	1.01753	0.508765	−	0.860905i	$-0.330102\pi$
$701$	26.9406	1.01753	0.508765	+	0.860905i	$0.330102\pi$
$702$	−13.5671	−0.512058
$703$	−14.5284	−0.547948
$704$	−28.2778	−1.06576
$705$	−42.8280	−1.61300
$706$	92.0046	3.46264
$707$	14.0900	0.529909
$708$	28.0520	1.05426
$709$	43.4337	1.63119	0.815594	−	0.578624i	$-0.196410\pi$
$709$	43.4337	1.63119	0.815594	+	0.578624i	$0.196410\pi$
$710$	−68.3402	−2.56476
$711$	3.47073	0.130162
$712$	31.5769	1.18340
$713$	−5.02052	−0.188020
$714$	9.96899	0.373080
$715$	13.3311	0.498555
$716$	5.38256	0.201156
$717$	−4.16182	−0.155426
$718$	57.7120	2.15379
$719$	35.6046	1.32783	0.663913	−	0.747810i	$-0.268894\pi$
$719$	35.6046	1.32783	0.663913	+	0.747810i	$0.268894\pi$
$720$	45.6042	1.69957
$721$	−0.699499	−0.0260507
$722$	−120.018	−4.46659
$723$	13.5189	0.502774
$724$	−98.9223	−3.67642
$725$	32.5809	1.21003
$726$	20.2842	0.752818
$727$	9.49711	0.352228	0.176114	−	0.984370i	$-0.443647\pi$
$727$	9.49711	0.352228	0.176114	+	0.984370i	$0.443647\pi$
$728$	7.28752	0.270093
$729$	24.6962	0.914674
$730$	−35.3360	−1.30784
$731$	19.2931	0.713582
$732$	36.4064	1.34562
$733$	−28.6171	−1.05700	−0.528499	−	0.848934i	$-0.677245\pi$
$733$	−28.6171	−1.05700	−0.528499	+	0.848934i	$0.677245\pi$
$734$	−25.6722	−0.947579
$735$	−25.1270	−0.926822
$736$	11.7735	0.433977
$737$	−15.5022	−0.571032
$738$	29.0976	1.07110
$739$	22.5835	0.830749	0.415374	−	0.909651i	$-0.363651\pi$
$739$	22.5835	0.830749	0.415374	+	0.909651i	$0.363651\pi$
$740$	29.5081	1.08474
$741$	−9.48818	−0.348557
$742$	−5.00801	−0.183850
$743$	−20.1898	−0.740691	−0.370346	−	0.928894i	$-0.620761\pi$
$743$	−20.1898	−0.740691	−0.370346	+	0.928894i	$0.620761\pi$
$744$	37.8909	1.38915
$745$	−79.0722	−2.89698
$746$	66.1575	2.42220
$747$	17.3806	0.635923
$748$	56.5873	2.06904
$749$	5.67799	0.207469
$750$	−19.3267	−0.705712
$751$	−3.87231	−0.141303	−0.0706514	−	0.997501i	$-0.522508\pi$
$751$	−3.87231	−0.141303	−0.0706514	+	0.997501i	$0.522508\pi$
$752$	−92.9904	−3.39101
$753$	10.4710	0.381583
$754$	−11.8340	−0.430968
$755$	12.6642	0.460899
$756$	−28.4453	−1.03455
$757$	32.0935	1.16646	0.583229	−	0.812307i	$-0.301789\pi$
$757$	32.0935	1.16646	0.583229	+	0.812307i	$0.301789\pi$
$758$	50.1993	1.82332
$759$	−6.26459	−0.227390
$760$	200.360	7.26781
$761$	8.08052	0.292918	0.146459	−	0.989217i	$-0.453212\pi$
$761$	8.08052	0.292918	0.146459	+	0.989217i	$0.453212\pi$
$762$	−45.9300	−1.66387
$763$	14.1312	0.511585
$764$	−49.1964	−1.77986
$765$	−13.9479	−0.504289
$766$	88.3016	3.19047
$767$	−4.38859	−0.158463
$768$	22.9486	0.828086
$769$	−3.63624	−0.131126	−0.0655632	−	0.997848i	$-0.520884\pi$
$769$	−3.63624	−0.131126	−0.0655632	+	0.997848i	$0.520884\pi$
$770$	39.6346	1.42833
$771$	−4.06443	−0.146377
$772$	−42.7538	−1.53874
$773$	0.750376	0.0269891	0.0134946	−	0.999909i	$-0.495704\pi$
$773$	0.750376	0.0269891	0.0134946	+	0.999909i	$0.495704\pi$
$774$	−25.1823	−0.905158
$775$	28.0434	1.00735
$776$	105.147	3.77456
$777$	−2.41781	−0.0867384
$778$	−24.2248	−0.868500
$779$	63.0820	2.26015
$780$	19.2711	0.690017
$781$	31.7852	1.13736
$782$	−8.94457	−0.319857
$783$	26.8820	0.960683
$784$	−54.5569	−1.94846
$785$	−0.700940	−0.0250176
$786$	−5.52444	−0.197050
$787$	3.91278	0.139476	0.0697378	−	0.997565i	$-0.477784\pi$
$787$	3.91278	0.139476	0.0697378	+	0.997565i	$0.477784\pi$
$788$	−39.2082	−1.39674
$789$	−21.5560	−0.767414
$790$	−21.6710	−0.771019
$791$	−12.6523	−0.449864
$792$	−42.9844	−1.52738
$793$	−5.69561	−0.202257
$794$	−24.7413	−0.878037
$795$	−7.70713	−0.273344
$796$	124.420	4.40995
$797$	52.3906	1.85577	0.927885	−	0.372867i	$-0.121625\pi$
$797$	52.3906	1.85577	0.927885	+	0.372867i	$0.121625\pi$
$798$	−28.2092	−0.998596
$799$	28.4409	1.00617
$800$	−65.7638	−2.32510
$801$	6.22028	0.219783
$802$	67.8657	2.39642
$803$	16.4348	0.579973
$804$	−22.4097	−0.790328
$805$	−4.41804	−0.155715
$806$	−10.1859	−0.358782
$807$	−25.2063	−0.887303
$808$	95.4125	3.35660
$809$	−18.3787	−0.646161	−0.323080	−	0.946371i	$-0.604718\pi$
$809$	−18.3787	−0.646161	−0.323080	+	0.946371i	$0.604718\pi$
$810$	−23.8456	−0.837849
$811$	21.8104	0.765865	0.382933	−	0.923776i	$-0.374914\pi$
$811$	21.8104	0.765865	0.382933	+	0.923776i	$0.374914\pi$
$812$	−24.8115	−0.870713
$813$	−9.20360	−0.322784
$814$	−19.4615	−0.682124
$815$	21.8698	0.766066
$816$	33.3111	1.16612
$817$	−54.5938	−1.90999
$818$	−40.0707	−1.40104
$819$	1.43555	0.0501623
$820$	−128.124	−4.47428
$821$	−2.79094	−0.0974046	−0.0487023	−	0.998813i	$-0.515509\pi$
$821$	−2.79094	−0.0974046	−0.0487023	+	0.998813i	$0.515509\pi$
$822$	28.9938	1.01127
$823$	−22.5975	−0.787699	−0.393850	−	0.919175i	$-0.628857\pi$
$823$	−22.5975	−0.787699	−0.393850	+	0.919175i	$0.628857\pi$
$824$	−4.73677	−0.165013
$825$	34.9925	1.21828
$826$	−13.0477	−0.453988
$827$	−29.0631	−1.01062	−0.505312	−	0.862937i	$-0.668622\pi$
$827$	−29.0631	−1.01062	−0.505312	+	0.862937i	$0.668622\pi$
$828$	8.23315	0.286122
$829$	−31.7032	−1.10110	−0.550548	−	0.834803i	$-0.685581\pi$
$829$	−31.7032	−1.10110	−0.550548	+	0.834803i	$0.685581\pi$
$830$	−108.523	−3.76690
$831$	22.6820	0.786829
$832$	6.39514	0.221711
$833$	16.6861	0.578140
$834$	38.5991	1.33658
$835$	−53.8655	−1.86409
$836$	−160.125	−5.53804
$837$	23.1381	0.799771
$838$	−76.6790	−2.64883
$839$	29.0140	1.00168	0.500838	−	0.865541i	$-0.333025\pi$
$839$	29.0140	1.00168	0.500838	+	0.865541i	$0.333025\pi$
$840$	33.3438	1.15047
$841$	−5.55212	−0.191452
$842$	−14.1422	−0.487374
$843$	−23.0073	−0.792414
$844$	−28.5618	−0.983139
$845$	41.5059	1.42785
$846$	−37.1224	−1.27629
$847$	−6.65340	−0.228613
$848$	−16.7341	−0.574651
$849$	8.67213	0.297627
$850$	49.9622	1.71369
$851$	2.16935	0.0743644
$852$	45.9479	1.57415
$853$	54.7218	1.87364	0.936819	−	0.349814i	$-0.113755\pi$
$853$	54.7218	1.87364	0.936819	+	0.349814i	$0.113755\pi$
$854$	−16.9336	−0.579455
$855$	39.4685	1.34979
$856$	38.4494	1.31417
$857$	−47.9423	−1.63768	−0.818840	−	0.574022i	$-0.805382\pi$
$857$	−47.9423	−1.63768	−0.818840	+	0.574022i	$0.805382\pi$
$858$	−12.7099	−0.433908
$859$	−22.2564	−0.759378	−0.379689	−	0.925114i	$-0.623969\pi$
$859$	−22.2564	−0.759378	−0.379689	+	0.925114i	$0.623969\pi$
$860$	110.884	3.78110
$861$	10.4981	0.357774
$862$	−78.8024	−2.68402
$863$	15.1082	0.514289	0.257145	−	0.966373i	$-0.417218\pi$
$863$	15.1082	0.514289	0.257145	+	0.966373i	$0.417218\pi$
$864$	−54.2606	−1.84598
$865$	31.3682	1.06655
$866$	33.9186	1.15260
$867$	11.1222	0.377731
$868$	−21.3560	−0.724871
$869$	10.0792	0.341914
$870$	−54.1460	−1.83572
$871$	3.50588	0.118792
$872$	95.6917	3.24053
$873$	20.7127	0.701019
$874$	25.3104	0.856138
$875$	6.33933	0.214308
$876$	23.7578	0.802703
$877$	22.9897	0.776306	0.388153	−	0.921595i	$-0.373113\pi$
$877$	22.9897	0.776306	0.388153	+	0.921595i	$0.373113\pi$
$878$	78.3765	2.64508
$879$	14.8530	0.500979
$880$	132.438	4.46447
$881$	−34.2255	−1.15309	−0.576543	−	0.817067i	$-0.695599\pi$
$881$	−34.2255	−1.15309	−0.576543	+	0.817067i	$0.695599\pi$
$882$	−21.7795	−0.733353
$883$	−35.9790	−1.21079	−0.605395	−	0.795925i	$-0.706985\pi$
$883$	−35.9790	−1.21079	−0.605395	+	0.795925i	$0.706985\pi$
$884$	−12.7974	−0.430424
$885$	−20.0799	−0.674978
$886$	−42.9280	−1.44219
$887$	−58.7062	−1.97116	−0.985581	−	0.169206i	$-0.945880\pi$
$887$	−58.7062	−1.97116	−0.985581	+	0.169206i	$0.945880\pi$
$888$	−16.3726	−0.549427
$889$	15.0654	0.505278
$890$	−38.8390	−1.30189
$891$	11.0906	0.371550
$892$	123.134	4.12282
$893$	−80.4792	−2.69313
$894$	75.3876	2.52134
$895$	−3.85289	−0.128788
$896$	−1.92226	−0.0642183
$897$	1.41676	0.0473042
$898$	−67.7142	−2.25965
$899$	20.1823	0.673118
$900$	−45.9884	−1.53295
$901$	5.11809	0.170508
$902$	84.5015	2.81359
$903$	−9.08549	−0.302346
$904$	−85.6769	−2.84957
$905$	70.8096	2.35379
$906$	−12.0741	−0.401135
$907$	24.5285	0.814455	0.407227	−	0.913327i	$-0.366496\pi$
$907$	24.5285	0.814455	0.407227	+	0.913327i	$0.366496\pi$
$908$	−51.3002	−1.70246
$909$	18.7951	0.623395
$910$	−8.96351	−0.297137
$911$	−56.5584	−1.87386	−0.936932	−	0.349510i	$-0.886348\pi$
$911$	−56.5584	−1.87386	−0.936932	+	0.349510i	$0.886348\pi$
$912$	−94.2602	−3.12127
$913$	50.4745	1.67046
$914$	−20.3066	−0.671681
$915$	−26.0601	−0.861520
$916$	30.3275	1.00205
$917$	1.81206	0.0598396
$918$	41.2229	1.36056
$919$	−4.46222	−0.147195	−0.0735975	−	0.997288i	$-0.523448\pi$
$919$	−4.46222	−0.147195	−0.0735975	+	0.997288i	$0.523448\pi$
$920$	−29.9174	−0.986348
$921$	−15.4030	−0.507548
$922$	−100.090	−3.29628
$923$	−7.18833	−0.236607
$924$	−26.6480	−0.876654
$925$	−12.1175	−0.398420
$926$	72.2796	2.37525
$927$	−0.933086	−0.0306466
$928$	−47.3290	−1.55365
$929$	−16.4030	−0.538165	−0.269082	−	0.963117i	$-0.586720\pi$
$929$	−16.4030	−0.538165	−0.269082	+	0.963117i	$0.586720\pi$
$930$	−46.6051	−1.52824
$931$	−47.2167	−1.54746
$932$	24.9358	0.816799
$933$	−8.91792	−0.291959
$934$	−12.9069	−0.422327
$935$	−40.5058	−1.32468
$936$	9.72108	0.317743
$937$	−40.5928	−1.32611	−0.663054	−	0.748571i	$-0.730740\pi$
$937$	−40.5928	−1.32611	−0.663054	+	0.748571i	$0.730740\pi$
$938$	10.4233	0.340334
$939$	−5.66535	−0.184882
$940$	163.459	5.33143
$941$	−43.9057	−1.43128	−0.715642	−	0.698467i	$-0.753866\pi$
$941$	−43.9057	−1.43128	−0.715642	+	0.698467i	$0.753866\pi$
$942$	0.668277	0.0217736
$943$	−9.41931	−0.306735
$944$	−43.5985	−1.41901
$945$	20.3614	0.662358
$946$	−73.1310	−2.37769
$947$	25.9322	0.842683	0.421342	−	0.906902i	$-0.361559\pi$
$947$	25.9322	0.842683	0.421342	+	0.906902i	$0.361559\pi$
$948$	14.5703	0.473221
$949$	−3.71680	−0.120652
$950$	−141.378	−4.58691
$951$	24.1984	0.784686
$952$	−22.1427	−0.717650
$953$	−15.2764	−0.494850	−0.247425	−	0.968907i	$-0.579584\pi$
$953$	−15.2764	−0.494850	−0.247425	+	0.968907i	$0.579584\pi$
$954$	−6.68036	−0.216285
$955$	35.2153	1.13954
$956$	15.8841	0.513730
$957$	25.1834	0.814064
$958$	−3.65550	−0.118104
$959$	−9.51019	−0.307100
$960$	29.2608	0.944387
$961$	−13.6285	−0.439628
$962$	4.40128	0.141903
$963$	7.57407	0.244071
$964$	−51.5967	−1.66182
$965$	30.6036	0.985165
$966$	4.21216	0.135524
$967$	−23.2682	−0.748255	−0.374127	−	0.927377i	$-0.622058\pi$
$967$	−23.2682	−0.748255	−0.374127	+	0.927377i	$0.622058\pi$
$968$	−45.0545	−1.44811
$969$	28.8293	0.926130
$970$	−129.329	−4.15249
$971$	−23.9730	−0.769329	−0.384665	−	0.923056i	$-0.625683\pi$
$971$	−23.9730	−0.769329	−0.384665	+	0.923056i	$0.625683\pi$
$972$	−63.6481	−2.04151
$973$	−12.6608	−0.405888
$974$	−33.4142	−1.07066
$975$	−7.91367	−0.253440
$976$	−56.5830	−1.81118
$977$	−42.6030	−1.36299	−0.681495	−	0.731823i	$-0.738670\pi$
$977$	−42.6030	−1.36299	−0.681495	+	0.731823i	$0.738670\pi$
$978$	−20.8507	−0.666732
$979$	18.0641	0.577332
$980$	95.9003	3.06342
$981$	18.8501	0.601839
$982$	−24.5156	−0.782324
$983$	−50.3368	−1.60549	−0.802747	−	0.596320i	$-0.796629\pi$
$983$	−50.3368	−1.60549	−0.802747	+	0.596320i	$0.796629\pi$
$984$	71.0895	2.26625
$985$	28.0657	0.894246
$986$	35.9568	1.14510
$987$	−13.3933	−0.426315
$988$	36.2128	1.15208
$989$	8.15185	0.259214
$990$	52.8700	1.68032
$991$	−35.8680	−1.13939	−0.569693	−	0.821858i	$-0.692938\pi$
$991$	−35.8680	−1.13939	−0.569693	+	0.821858i	$0.692938\pi$
$992$	−40.7375	−1.29342
$993$	16.8359	0.534272
$994$	−21.3716	−0.677866
$995$	−89.0611	−2.82343
$996$	72.9648	2.31198
$997$	22.1166	0.700441	0.350220	−	0.936667i	$-0.386107\pi$
$997$	22.1166	0.700441	0.350220	+	0.936667i	$0.386107\pi$
$998$	20.0653	0.635155
$999$	−9.99792	−0.316320

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.f.1.16	✓	275

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.f.1.16	✓	275	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60468 q^{2} -1.25355 q^{3} +4.78433 q^{4} -3.42467 q^{5} +3.26509 q^{6} -1.07098 q^{7} -7.25228 q^{8} -1.42861 q^{9} +O(q^{10})\)	\(q-2.60468 q^{2} -1.25355 q^{3} +4.78433 q^{4} -3.42467 q^{5} +3.26509 q^{6} -1.07098 q^{7} -7.25228 q^{8} -1.42861 q^{9} +8.92017 q^{10} -4.14879 q^{11} -5.99740 q^{12} +0.938264 q^{13} +2.78955 q^{14} +4.29300 q^{15} +9.32118 q^{16} -2.85086 q^{17} +3.72107 q^{18} +8.06708 q^{19} -16.3848 q^{20} +1.34252 q^{21} +10.8063 q^{22} -1.20456 q^{23} +9.09110 q^{24} +6.72840 q^{25} -2.44387 q^{26} +5.55149 q^{27} -5.12391 q^{28} +4.84230 q^{29} -11.1819 q^{30} +4.16792 q^{31} -9.77407 q^{32} +5.20071 q^{33} +7.42557 q^{34} +3.66775 q^{35} -6.83496 q^{36} -1.80094 q^{37} -21.0121 q^{38} -1.17616 q^{39} +24.8367 q^{40} +7.81968 q^{41} -3.49683 q^{42} -6.76747 q^{43} -19.8492 q^{44} +4.89254 q^{45} +3.13750 q^{46} -9.97625 q^{47} -11.6846 q^{48} -5.85301 q^{49} -17.5253 q^{50} +3.57370 q^{51} +4.48897 q^{52} -1.79528 q^{53} -14.4598 q^{54} +14.2083 q^{55} +7.76703 q^{56} -10.1125 q^{57} -12.6126 q^{58} -4.67736 q^{59} +20.5391 q^{60} -6.07037 q^{61} -10.8561 q^{62} +1.53001 q^{63} +6.81593 q^{64} -3.21325 q^{65} -13.5462 q^{66} +3.73657 q^{67} -13.6395 q^{68} +1.50998 q^{69} -9.55329 q^{70} -7.66131 q^{71} +10.3607 q^{72} -3.96136 q^{73} +4.69088 q^{74} -8.43438 q^{75} +38.5956 q^{76} +4.44326 q^{77} +3.06351 q^{78} -2.42944 q^{79} -31.9220 q^{80} -2.67322 q^{81} -20.3677 q^{82} -12.1661 q^{83} +6.42307 q^{84} +9.76327 q^{85} +17.6271 q^{86} -6.07006 q^{87} +30.0882 q^{88} -4.35407 q^{89} -12.7435 q^{90} -1.00486 q^{91} -5.76303 q^{92} -5.22469 q^{93} +25.9849 q^{94} -27.6271 q^{95} +12.2523 q^{96} -14.4985 q^{97} +15.2452 q^{98} +5.92702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * q^99

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