LMFDB - Embedded newform 6023.2.a.d.1.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.50
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.926042 q^{2} +0.499387 q^{3} -1.14245 q^{4} -1.89895 q^{5} -0.462453 q^{6} -4.04075 q^{7} +2.91004 q^{8} -2.75061 q^{9} +O(q^{10})$	\(q-0.926042 q^{2} +0.499387 q^{3} -1.14245 q^{4} -1.89895 q^{5} -0.462453 q^{6} -4.04075 q^{7} +2.91004 q^{8} -2.75061 q^{9} +1.75851 q^{10} +3.71684 q^{11} -0.570523 q^{12} -1.78751 q^{13} +3.74190 q^{14} -0.948311 q^{15} -0.409923 q^{16} -1.44811 q^{17} +2.54718 q^{18} -1.00000 q^{19} +2.16945 q^{20} -2.01790 q^{21} -3.44195 q^{22} -0.752464 q^{23} +1.45324 q^{24} -1.39399 q^{25} +1.65531 q^{26} -2.87178 q^{27} +4.61634 q^{28} -4.90527 q^{29} +0.878176 q^{30} -8.79537 q^{31} -5.44047 q^{32} +1.85614 q^{33} +1.34101 q^{34} +7.67319 q^{35} +3.14243 q^{36} -7.06576 q^{37} +0.926042 q^{38} -0.892658 q^{39} -5.52602 q^{40} +7.78772 q^{41} +1.86866 q^{42} -4.91591 q^{43} -4.24629 q^{44} +5.22328 q^{45} +0.696814 q^{46} -0.748659 q^{47} -0.204710 q^{48} +9.32767 q^{49} +1.29089 q^{50} -0.723165 q^{51} +2.04213 q^{52} -9.39167 q^{53} +2.65939 q^{54} -7.05809 q^{55} -11.7587 q^{56} -0.499387 q^{57} +4.54249 q^{58} +3.54541 q^{59} +1.08340 q^{60} -4.02479 q^{61} +8.14488 q^{62} +11.1145 q^{63} +5.85795 q^{64} +3.39439 q^{65} -1.71886 q^{66} -6.88179 q^{67} +1.65438 q^{68} -0.375771 q^{69} -7.10569 q^{70} -5.63459 q^{71} -8.00438 q^{72} +7.10330 q^{73} +6.54319 q^{74} -0.696140 q^{75} +1.14245 q^{76} -15.0188 q^{77} +0.826639 q^{78} -12.8450 q^{79} +0.778424 q^{80} +6.81771 q^{81} -7.21176 q^{82} +14.0577 q^{83} +2.30534 q^{84} +2.74988 q^{85} +4.55234 q^{86} -2.44963 q^{87} +10.8161 q^{88} -4.48268 q^{89} -4.83697 q^{90} +7.22287 q^{91} +0.859650 q^{92} -4.39229 q^{93} +0.693290 q^{94} +1.89895 q^{95} -2.71690 q^{96} -16.1453 q^{97} -8.63781 q^{98} -10.2236 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) $ 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.926042	−0.654810	−0.327405	−	0.944884i	$-0.606174\pi$
$2$	−0.926042	−0.654810	−0.327405	+	0.944884i	$0.606174\pi$
$3$	0.499387	0.288321	0.144161	−	0.989554i	$-0.453952\pi$
$3$	0.499387	0.288321	0.144161	+	0.989554i	$0.453952\pi$
$4$	−1.14245	−0.571223
$5$	−1.89895	−0.849236	−0.424618	−	0.905373i	$-0.639592\pi$
$5$	−1.89895	−0.849236	−0.424618	+	0.905373i	$0.639592\pi$
$6$	−0.462453	−0.188796
$7$	−4.04075	−1.52726	−0.763630	−	0.645654i	$-0.776585\pi$
$7$	−4.04075	−1.52726	−0.763630	+	0.645654i	$0.776585\pi$
$8$	2.91004	1.02885
$9$	−2.75061	−0.916871
$10$	1.75851	0.556089
$11$	3.71684	1.12067	0.560334	−	0.828267i	$-0.310673\pi$
$11$	3.71684	1.12067	0.560334	+	0.828267i	$0.310673\pi$
$12$	−0.570523	−0.164696
$13$	−1.78751	−0.495765	−0.247883	−	0.968790i	$-0.579735\pi$
$13$	−1.78751	−0.495765	−0.247883	+	0.968790i	$0.579735\pi$
$14$	3.74190	1.00007
$15$	−0.948311	−0.244853
$16$	−0.409923	−0.102481
$17$	−1.44811	−0.351217	−0.175609	−	0.984460i	$-0.556189\pi$
$17$	−1.44811	−0.351217	−0.175609	+	0.984460i	$0.556189\pi$
$18$	2.54718	0.600377
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.16945	0.485104
$21$	−2.01790	−0.440342
$22$	−3.44195	−0.733825
$23$	−0.752464	−0.156900	−0.0784498	−	0.996918i	$-0.524997\pi$
$23$	−0.752464	−0.156900	−0.0784498	+	0.996918i	$0.524997\pi$
$24$	1.45324	0.296640
$25$	−1.39399	−0.278798
$26$	1.65531	0.324632
$27$	−2.87178	−0.552675
$28$	4.61634	0.872407
$29$	−4.90527	−0.910886	−0.455443	−	0.890265i	$-0.650519\pi$
$29$	−4.90527	−0.910886	−0.455443	+	0.890265i	$0.650519\pi$
$30$	0.878176	0.160332
$31$	−8.79537	−1.57969	−0.789847	−	0.613303i	$-0.789840\pi$
$31$	−8.79537	−1.57969	−0.789847	+	0.613303i	$0.789840\pi$
$32$	−5.44047	−0.961748
$33$	1.85614	0.323113
$34$	1.34101	0.229981
$35$	7.67319	1.29701
$36$	3.14243	0.523738
$37$	−7.06576	−1.16160	−0.580802	−	0.814045i	$-0.697261\pi$
$37$	−7.06576	−1.16160	−0.580802	+	0.814045i	$0.697261\pi$
$38$	0.926042	0.150224
$39$	−0.892658	−0.142940
$40$	−5.52602	−0.873740
$41$	7.78772	1.21624	0.608119	−	0.793846i	$-0.291924\pi$
$41$	7.78772	1.21624	0.608119	+	0.793846i	$0.291924\pi$
$42$	1.86866	0.288340
$43$	−4.91591	−0.749670	−0.374835	−	0.927092i	$-0.622301\pi$
$43$	−4.91591	−0.749670	−0.374835	+	0.927092i	$0.622301\pi$
$44$	−4.24629	−0.640152
$45$	5.22328	0.778640
$46$	0.696814	0.102740
$47$	−0.748659	−0.109203	−0.0546016	−	0.998508i	$-0.517389\pi$
$47$	−0.748659	−0.109203	−0.0546016	+	0.998508i	$0.517389\pi$
$48$	−0.204710	−0.0295474
$49$	9.32767	1.33252
$50$	1.29089	0.182560
$51$	−0.723165	−0.101263
$52$	2.04213	0.283193
$53$	−9.39167	−1.29004	−0.645022	−	0.764164i	$-0.723152\pi$
$53$	−9.39167	−1.29004	−0.645022	+	0.764164i	$0.723152\pi$
$54$	2.65939	0.361897
$55$	−7.05809	−0.951712
$56$	−11.7587	−1.57133
$57$	−0.499387	−0.0661454
$58$	4.54249	0.596458
$59$	3.54541	0.461573	0.230786	−	0.973004i	$-0.425870\pi$
$59$	3.54541	0.461573	0.230786	+	0.973004i	$0.425870\pi$
$60$	1.08340	0.139866
$61$	−4.02479	−0.515321	−0.257660	−	0.966236i	$-0.582952\pi$
$61$	−4.02479	−0.515321	−0.257660	+	0.966236i	$0.582952\pi$
$62$	8.14488	1.03440
$63$	11.1145	1.40030
$64$	5.85795	0.732243
$65$	3.39439	0.421022
$66$	−1.71886	−0.211578
$67$	−6.88179	−0.840744	−0.420372	−	0.907352i	$-0.638100\pi$
$67$	−6.88179	−0.840744	−0.420372	+	0.907352i	$0.638100\pi$
$68$	1.65438	0.200623
$69$	−0.375771	−0.0452375
$70$	−7.10569	−0.849293
$71$	−5.63459	−0.668702	−0.334351	−	0.942449i	$-0.608517\pi$
$71$	−5.63459	−0.668702	−0.334351	+	0.942449i	$0.608517\pi$
$72$	−8.00438	−0.943326
$73$	7.10330	0.831379	0.415689	−	0.909507i	$-0.363540\pi$
$73$	7.10330	0.831379	0.415689	+	0.909507i	$0.363540\pi$
$74$	6.54319	0.760631
$75$	−0.696140	−0.0803833
$76$	1.14245	0.131048
$77$	−15.0188	−1.71155
$78$	0.826639	0.0935984
$79$	−12.8450	−1.44518	−0.722589	−	0.691278i	$-0.757048\pi$
$79$	−12.8450	−1.44518	−0.722589	+	0.691278i	$0.757048\pi$
$80$	0.778424	0.0870304
$81$	6.81771	0.757523
$82$	−7.21176	−0.796405
$83$	14.0577	1.54304	0.771519	−	0.636207i	$-0.219497\pi$
$83$	14.0577	1.54304	0.771519	+	0.636207i	$0.219497\pi$
$84$	2.30534	0.251533
$85$	2.74988	0.298266
$86$	4.55234	0.490892
$87$	−2.44963	−0.262628
$88$	10.8161	1.15300
$89$	−4.48268	−0.475163	−0.237582	−	0.971368i	$-0.576355\pi$
$89$	−4.48268	−0.475163	−0.237582	+	0.971368i	$0.576355\pi$
$90$	−4.83697	−0.509862
$91$	7.22287	0.757163
$92$	0.859650	0.0896247
$93$	−4.39229	−0.455460
$94$	0.693290	0.0715074
$95$	1.89895	0.194828
$96$	−2.71690	−0.277292
$97$	−16.1453	−1.63931	−0.819656	−	0.572856i	$-0.805835\pi$
$97$	−16.1453	−1.63931	−0.819656	+	0.572856i	$0.805835\pi$
$98$	−8.63781	−0.872551
$99$	−10.2236	−1.02751
$100$	1.59256	0.159256
$101$	−18.8701	−1.87764	−0.938821	−	0.344406i	$-0.888080\pi$
$101$	−18.8701	−1.87764	−0.938821	+	0.344406i	$0.888080\pi$
$102$	0.669681	0.0663083
$103$	−8.96158	−0.883010	−0.441505	−	0.897259i	$-0.645555\pi$
$103$	−8.96158	−0.883010	−0.441505	+	0.897259i	$0.645555\pi$
$104$	−5.20171	−0.510070
$105$	3.83189	0.373954
$106$	8.69708	0.844735
$107$	−11.5330	−1.11493	−0.557467	−	0.830199i	$-0.688227\pi$
$107$	−11.5330	−1.11493	−0.557467	+	0.830199i	$0.688227\pi$
$108$	3.28086	0.315701
$109$	−16.9765	−1.62606	−0.813028	−	0.582225i	$-0.802182\pi$
$109$	−16.9765	−1.62606	−0.813028	+	0.582225i	$0.802182\pi$
$110$	6.53609	0.623191
$111$	−3.52855	−0.334915
$112$	1.65640	0.156515
$113$	15.0189	1.41286	0.706428	−	0.707785i	$-0.250305\pi$
$113$	15.0189	1.41286	0.706428	+	0.707785i	$0.250305\pi$
$114$	0.462453	0.0433127
$115$	1.42889	0.133245
$116$	5.60401	0.520319
$117$	4.91674	0.454553
$118$	−3.28320	−0.302243
$119$	5.85143	0.536400
$120$	−2.75962	−0.251918
$121$	2.81488	0.255898
$122$	3.72712	0.337438
$123$	3.88909	0.350667
$124$	10.0482	0.902358
$125$	12.1419	1.08600
$126$	−10.2925	−0.916931
$127$	−2.68431	−0.238194	−0.119097	−	0.992883i	$-0.538000\pi$
$127$	−2.68431	−0.238194	−0.119097	+	0.992883i	$0.538000\pi$
$128$	5.45623	0.482267
$129$	−2.45494	−0.216146
$130$	−3.14334	−0.275690
$131$	−0.910412	−0.0795430	−0.0397715	−	0.999209i	$-0.512663\pi$
$131$	−0.910412	−0.0795430	−0.0397715	+	0.999209i	$0.512663\pi$
$132$	−2.12054	−0.184569
$133$	4.04075	0.350378
$134$	6.37282	0.550528
$135$	5.45337	0.469351
$136$	−4.21404	−0.361351
$137$	13.8658	1.18463	0.592317	−	0.805705i	$-0.298213\pi$
$137$	13.8658	1.18463	0.592317	+	0.805705i	$0.298213\pi$
$138$	0.347980	0.0296220
$139$	−7.36516	−0.624705	−0.312352	−	0.949966i	$-0.601117\pi$
$139$	−7.36516	−0.624705	−0.312352	+	0.949966i	$0.601117\pi$
$140$	−8.76620	−0.740879
$141$	−0.373871	−0.0314856
$142$	5.21786	0.437873
$143$	−6.64387	−0.555588
$144$	1.12754	0.0939616
$145$	9.31486	0.773557
$146$	−6.57796	−0.544396
$147$	4.65812	0.384195
$148$	8.07226	0.663535
$149$	10.7598	0.881481	0.440740	−	0.897635i	$-0.354716\pi$
$149$	10.7598	0.881481	0.440740	+	0.897635i	$0.354716\pi$
$150$	0.644655	0.0526358
$151$	−23.0033	−1.87198	−0.935989	−	0.352029i	$-0.885492\pi$
$151$	−23.0033	−1.87198	−0.935989	+	0.352029i	$0.885492\pi$
$152$	−2.91004	−0.236035
$153$	3.98318	0.322021
$154$	13.9081	1.12074
$155$	16.7020	1.34153
$156$	1.01981	0.0816505
$157$	−2.63630	−0.210399	−0.105200	−	0.994451i	$-0.533548\pi$
$157$	−2.63630	−0.210399	−0.105200	+	0.994451i	$0.533548\pi$
$158$	11.8950	0.946318
$159$	−4.69008	−0.371947
$160$	10.3312	0.816751
$161$	3.04052	0.239627
$162$	−6.31348	−0.496034
$163$	6.14054	0.480964	0.240482	−	0.970654i	$-0.422694\pi$
$163$	6.14054	0.480964	0.240482	+	0.970654i	$0.422694\pi$
$164$	−8.89705	−0.694743
$165$	−3.52472	−0.274399
$166$	−13.0181	−1.01040
$167$	15.3070	1.18449	0.592247	−	0.805756i	$-0.298241\pi$
$167$	15.3070	1.18449	0.592247	+	0.805756i	$0.298241\pi$
$168$	−5.87216	−0.453047
$169$	−9.80482	−0.754217
$170$	−2.54650	−0.195308
$171$	2.75061	0.210345
$172$	5.61617	0.428229
$173$	−8.41329	−0.639651	−0.319825	−	0.947477i	$-0.603624\pi$
$173$	−8.41329	−0.639651	−0.319825	+	0.947477i	$0.603624\pi$
$174$	2.26846	0.171971
$175$	5.63276	0.425797
$176$	−1.52362	−0.114847
$177$	1.77053	0.133081
$178$	4.15115	0.311142
$179$	0.904197	0.0675828	0.0337914	−	0.999429i	$-0.489242\pi$
$179$	0.904197	0.0675828	0.0337914	+	0.999429i	$0.489242\pi$
$180$	−5.96731	−0.444777
$181$	−22.5882	−1.67897	−0.839485	−	0.543383i	$-0.817143\pi$
$181$	−22.5882	−1.67897	−0.839485	+	0.543383i	$0.817143\pi$
$182$	−6.68868	−0.495798
$183$	−2.00993	−0.148578
$184$	−2.18970	−0.161427
$185$	13.4175	0.986477
$186$	4.06745	0.298240
$187$	−5.38237	−0.393598
$188$	0.855303	0.0623794
$189$	11.6042	0.844078
$190$	−1.75851	−0.127576
$191$	16.7131	1.20932	0.604660	−	0.796484i	$-0.293309\pi$
$191$	16.7131	1.20932	0.604660	+	0.796484i	$0.293309\pi$
$192$	2.92538	0.211121
$193$	−25.5601	−1.83986	−0.919929	−	0.392084i	$-0.871754\pi$
$193$	−25.5601	−1.83986	−0.919929	+	0.392084i	$0.871754\pi$
$194$	14.9513	1.07344
$195$	1.69511	0.121390
$196$	−10.6564	−0.761169
$197$	3.89640	0.277607	0.138803	−	0.990320i	$-0.455674\pi$
$197$	3.89640	0.277607	0.138803	+	0.990320i	$0.455674\pi$
$198$	9.46746	0.672823
$199$	13.4867	0.956044	0.478022	−	0.878348i	$-0.341354\pi$
$199$	13.4867	0.956044	0.478022	+	0.878348i	$0.341354\pi$
$200$	−4.05656	−0.286842
$201$	−3.43668	−0.242404
$202$	17.4745	1.22950
$203$	19.8210	1.39116
$204$	0.826178	0.0578440
$205$	−14.7885	−1.03287
$206$	8.29880	0.578204
$207$	2.06974	0.143857
$208$	0.732740	0.0508064
$209$	−3.71684	−0.257099
$210$	−3.54849	−0.244869
$211$	−4.73756	−0.326147	−0.163074	−	0.986614i	$-0.552141\pi$
$211$	−4.73756	−0.326147	−0.163074	+	0.986614i	$0.552141\pi$
$212$	10.7295	0.736904
$213$	−2.81384	−0.192801
$214$	10.6800	0.730070
$215$	9.33508	0.636647
$216$	−8.35699	−0.568621
$217$	35.5399	2.41261
$218$	15.7210	1.06476
$219$	3.54730	0.239704
$220$	8.06349	0.543640
$221$	2.58850	0.174121
$222$	3.26759	0.219306
$223$	14.8798	0.996425	0.498213	−	0.867055i	$-0.333990\pi$
$223$	14.8798	0.996425	0.498213	+	0.867055i	$0.333990\pi$
$224$	21.9836	1.46884
$225$	3.83432	0.255621
$226$	−13.9081	−0.925153
$227$	10.2605	0.681016	0.340508	−	0.940242i	$-0.389401\pi$
$227$	10.2605	0.681016	0.340508	+	0.940242i	$0.389401\pi$
$228$	0.570523	0.0377838
$229$	25.2779	1.67041	0.835205	−	0.549939i	$-0.185349\pi$
$229$	25.2779	1.67041	0.835205	+	0.549939i	$0.185349\pi$
$230$	−1.32321	−0.0872502
$231$	−7.50020	−0.493477
$232$	−14.2745	−0.937168
$233$	18.5627	1.21609	0.608043	−	0.793904i	$-0.291955\pi$
$233$	18.5627	1.21609	0.608043	+	0.793904i	$0.291955\pi$
$234$	−4.55311	−0.297646
$235$	1.42167	0.0927393
$236$	−4.05044	−0.263661
$237$	−6.41464	−0.416676
$238$	−5.41867	−0.351240
$239$	10.5119	0.679957	0.339978	−	0.940433i	$-0.389580\pi$
$239$	10.5119	0.679957	0.339978	+	0.940433i	$0.389580\pi$
$240$	0.388735	0.0250927
$241$	5.05742	0.325777	0.162889	−	0.986644i	$-0.447919\pi$
$241$	5.05742	0.325777	0.162889	+	0.986644i	$0.447919\pi$
$242$	−2.60669	−0.167565
$243$	12.0200	0.771085
$244$	4.59810	0.294363
$245$	−17.7128	−1.13163
$246$	−3.60146	−0.229621
$247$	1.78751	0.113736
$248$	−25.5948	−1.62527
$249$	7.02026	0.444891
$250$	−11.2439	−0.711125
$251$	−8.11201	−0.512025	−0.256013	−	0.966673i	$-0.582409\pi$
$251$	−8.11201	−0.512025	−0.256013	+	0.966673i	$0.582409\pi$
$252$	−12.6978	−0.799884
$253$	−2.79679	−0.175833
$254$	2.48578	0.155972
$255$	1.37325	0.0859966
$256$	−16.7686	−1.04804
$257$	−24.1367	−1.50561	−0.752804	−	0.658245i	$-0.771299\pi$
$257$	−24.1367	−1.50561	−0.752804	+	0.658245i	$0.771299\pi$
$258$	2.27338	0.141535
$259$	28.5510	1.77407
$260$	−3.87790	−0.240497
$261$	13.4925	0.835165
$262$	0.843079	0.0520856
$263$	10.0639	0.620567	0.310284	−	0.950644i	$-0.399576\pi$
$263$	10.0639	0.620567	0.310284	+	0.950644i	$0.399576\pi$
$264$	5.40144	0.332436
$265$	17.8343	1.09555
$266$	−3.74190	−0.229431
$267$	−2.23859	−0.137000
$268$	7.86207	0.480252
$269$	−7.17623	−0.437542	−0.218771	−	0.975776i	$-0.570205\pi$
$269$	−7.17623	−0.437542	−0.218771	+	0.975776i	$0.570205\pi$
$270$	−5.05005	−0.307336
$271$	30.8345	1.87306	0.936532	−	0.350581i	$-0.114016\pi$
$271$	30.8345	1.87306	0.936532	+	0.350581i	$0.114016\pi$
$272$	0.593612	0.0359930
$273$	3.60701	0.218306
$274$	−12.8403	−0.775711
$275$	−5.18123	−0.312440
$276$	0.429298	0.0258407
$277$	−6.01536	−0.361428	−0.180714	−	0.983536i	$-0.557841\pi$
$277$	−6.01536	−0.361428	−0.180714	+	0.983536i	$0.557841\pi$
$278$	6.82044	0.409063
$279$	24.1926	1.44838
$280$	22.3293	1.33443
$281$	27.4265	1.63613	0.818065	−	0.575126i	$-0.195047\pi$
$281$	27.4265	1.63613	0.818065	+	0.575126i	$0.195047\pi$
$282$	0.346220	0.0206171
$283$	5.85029	0.347763	0.173882	−	0.984767i	$-0.444369\pi$
$283$	5.85029	0.347763	0.173882	+	0.984767i	$0.444369\pi$
$284$	6.43721	0.381978
$285$	0.948311	0.0561731
$286$	6.15250	0.363805
$287$	−31.4682	−1.85751
$288$	14.9646	0.881799
$289$	−14.9030	−0.876647
$290$	−8.62595	−0.506534
$291$	−8.06278	−0.472649
$292$	−8.11514	−0.474903
$293$	11.2299	0.656057	0.328028	−	0.944668i	$-0.393616\pi$
$293$	11.2299	0.656057	0.328028	+	0.944668i	$0.393616\pi$
$294$	−4.31361	−0.251575
$295$	−6.73255	−0.391984
$296$	−20.5616	−1.19512
$297$	−10.6739	−0.619365
$298$	−9.96407	−0.577203
$299$	1.34504	0.0777854
$300$	0.795302	0.0459168
$301$	19.8640	1.14494
$302$	21.3020	1.22579
$303$	−9.42347	−0.541364
$304$	0.409923	0.0235107
$305$	7.64287	0.437629
$306$	−3.68859	−0.210863
$307$	22.9019	1.30708	0.653541	−	0.756891i	$-0.273283\pi$
$307$	22.9019	1.30708	0.653541	+	0.756891i	$0.273283\pi$
$308$	17.1582	0.977679
$309$	−4.47530	−0.254591
$310$	−15.4667	−0.878451
$311$	−13.1949	−0.748212	−0.374106	−	0.927386i	$-0.622050\pi$
$311$	−13.1949	−0.748212	−0.374106	+	0.927386i	$0.622050\pi$
$312$	−2.59767	−0.147064
$313$	20.2703	1.14574	0.572872	−	0.819645i	$-0.305829\pi$
$313$	20.2703	1.14574	0.572872	+	0.819645i	$0.305829\pi$
$314$	2.44132	0.137772
$315$	−21.1060	−1.18919
$316$	14.6748	0.825520
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	4.34321	0.243555
$319$	−18.2321	−1.02080
$320$	−11.1240	−0.621848
$321$	−5.75941	−0.321459
$322$	−2.81565	−0.156910
$323$	1.44811	0.0805747
$324$	−7.78886	−0.432715
$325$	2.49176	0.138218
$326$	−5.68640	−0.314940
$327$	−8.47786	−0.468827
$328$	22.6626	1.25133
$329$	3.02515	0.166782
$330$	3.26404	0.179679
$331$	6.92028	0.380373	0.190187	−	0.981748i	$-0.439091\pi$
$331$	6.92028	0.380373	0.190187	+	0.981748i	$0.439091\pi$
$332$	−16.0602	−0.881419
$333$	19.4352	1.06504
$334$	−14.1750	−0.775620
$335$	13.0682	0.713990
$336$	0.827184	0.0451266
$337$	26.8037	1.46009	0.730045	−	0.683399i	$-0.239499\pi$
$337$	26.8037	1.46009	0.730045	+	0.683399i	$0.239499\pi$
$338$	9.07967	0.493869
$339$	7.50023	0.407357
$340$	−3.14159	−0.170377
$341$	−32.6909	−1.77031
$342$	−2.54718	−0.137736
$343$	−9.40554	−0.507852
$344$	−14.3055	−0.771300
$345$	0.713571	0.0384173
$346$	7.79106	0.418850
$347$	12.3485	0.662902	0.331451	−	0.943472i	$-0.392462\pi$
$347$	12.3485	0.662902	0.331451	+	0.943472i	$0.392462\pi$
$348$	2.79857	0.150019
$349$	12.9779	0.694690	0.347345	−	0.937737i	$-0.387083\pi$
$349$	12.9779	0.694690	0.347345	+	0.937737i	$0.387083\pi$
$350$	−5.21617	−0.278816
$351$	5.13333	0.273997
$352$	−20.2213	−1.07780
$353$	−12.3788	−0.658854	−0.329427	−	0.944181i	$-0.606856\pi$
$353$	−12.3788	−0.658854	−0.329427	+	0.944181i	$0.606856\pi$
$354$	−1.63959	−0.0871430
$355$	10.6998	0.567886
$356$	5.12122	0.271424
$357$	2.92213	0.154656
$358$	−0.837324	−0.0442540
$359$	−26.4639	−1.39671	−0.698356	−	0.715751i	$-0.746085\pi$
$359$	−26.4639	−1.39671	−0.698356	+	0.715751i	$0.746085\pi$
$360$	15.1999	0.801106
$361$	1.00000	0.0526316
$362$	20.9176	1.09941
$363$	1.40571	0.0737808
$364$	−8.25174	−0.432509
$365$	−13.4888	−0.706037
$366$	1.86128	0.0972904
$367$	17.4003	0.908288	0.454144	−	0.890928i	$-0.349945\pi$
$367$	17.4003	0.908288	0.454144	+	0.890928i	$0.349945\pi$
$368$	0.308453	0.0160792
$369$	−21.4210	−1.11513
$370$	−12.4252	−0.645955
$371$	37.9494	1.97023
$372$	5.01796	0.260169
$373$	−8.25358	−0.427354	−0.213677	−	0.976904i	$-0.568544\pi$
$373$	−8.25358	−0.427354	−0.213677	+	0.976904i	$0.568544\pi$
$374$	4.98430	0.257732
$375$	6.06349	0.313117
$376$	−2.17863	−0.112354
$377$	8.76821	0.451586
$378$	−10.7459	−0.552711
$379$	−28.1630	−1.44664	−0.723318	−	0.690515i	$-0.757384\pi$
$379$	−28.1630	−1.44664	−0.723318	+	0.690515i	$0.757384\pi$
$380$	−2.16945	−0.111290
$381$	−1.34051	−0.0686763
$382$	−15.4771	−0.791875
$383$	30.5910	1.56313	0.781564	−	0.623825i	$-0.214422\pi$
$383$	30.5910	1.56313	0.781564	+	0.623825i	$0.214422\pi$
$384$	2.72477	0.139048
$385$	28.5200	1.45351
$386$	23.6698	1.20476
$387$	13.5218	0.687350
$388$	18.4452	0.936413
$389$	−5.70701	−0.289357	−0.144678	−	0.989479i	$-0.546215\pi$
$389$	−5.70701	−0.289357	−0.144678	+	0.989479i	$0.546215\pi$
$390$	−1.56975	−0.0794872
$391$	1.08965	0.0551059
$392$	27.1439	1.37097
$393$	−0.454648	−0.0229340
$394$	−3.60823	−0.181780
$395$	24.3921	1.22730
$396$	11.6799	0.586937
$397$	−27.2320	−1.36674	−0.683368	−	0.730074i	$-0.739486\pi$
$397$	−27.2320	−1.36674	−0.683368	+	0.730074i	$0.739486\pi$
$398$	−12.4892	−0.626028
$399$	2.01790	0.101021
$400$	0.571428	0.0285714
$401$	11.2786	0.563227	0.281614	−	0.959528i	$-0.409130\pi$
$401$	11.2786	0.563227	0.281614	+	0.959528i	$0.409130\pi$
$402$	3.18251	0.158729
$403$	15.7218	0.783158
$404$	21.5580	1.07255
$405$	−12.9465	−0.643316
$406$	−18.3551	−0.910946
$407$	−26.2623	−1.30177
$408$	−2.10444	−0.104185
$409$	−26.3147	−1.30118	−0.650589	−	0.759430i	$-0.725478\pi$
$409$	−26.3147	−1.30118	−0.650589	+	0.759430i	$0.725478\pi$
$410$	13.6948	0.676336
$411$	6.92440	0.341555
$412$	10.2381	0.504396
$413$	−14.3261	−0.704942
$414$	−1.91666	−0.0941989
$415$	−26.6949	−1.31040
$416$	9.72487	0.476801
$417$	−3.67807	−0.180116
$418$	3.44195	0.168351
$419$	−29.3379	−1.43325	−0.716626	−	0.697458i	$-0.754314\pi$
$419$	−29.3379	−1.43325	−0.716626	+	0.697458i	$0.754314\pi$
$420$	−4.37773	−0.213611
$421$	−10.2654	−0.500303	−0.250152	−	0.968207i	$-0.580480\pi$
$421$	−10.2654	−0.500303	−0.250152	+	0.968207i	$0.580480\pi$
$422$	4.38718	0.213564
$423$	2.05927	0.100125
$424$	−27.3301	−1.32727
$425$	2.01864	0.0979185
$426$	2.60573	0.126248
$427$	16.2632	0.787029
$428$	13.1758	0.636876
$429$	−3.31786	−0.160188
$430$	−8.64467	−0.416883
$431$	−12.1300	−0.584280	−0.292140	−	0.956376i	$-0.594367\pi$
$431$	−12.1300	−0.584280	−0.292140	+	0.956376i	$0.594367\pi$
$432$	1.17721	0.0566385
$433$	21.0189	1.01010	0.505052	−	0.863089i	$-0.331473\pi$
$433$	21.0189	1.01010	0.505052	+	0.863089i	$0.331473\pi$
$434$	−32.9114	−1.57980
$435$	4.65172	0.223033
$436$	19.3948	0.928841
$437$	0.752464	0.0359953
$438$	−3.28495	−0.156961
$439$	1.94852	0.0929976	0.0464988	−	0.998918i	$-0.485194\pi$
$439$	1.94852	0.0929976	0.0464988	+	0.998918i	$0.485194\pi$
$440$	−20.5393	−0.979173
$441$	−25.6568	−1.22175
$442$	−2.39706	−0.114016
$443$	−2.51886	−0.119675	−0.0598373	−	0.998208i	$-0.519058\pi$
$443$	−2.51886	−0.119675	−0.0598373	+	0.998208i	$0.519058\pi$
$444$	4.03118	0.191311
$445$	8.51239	0.403526
$446$	−13.7793	−0.652470
$447$	5.37333	0.254150
$448$	−23.6705	−1.11833
$449$	23.5677	1.11223	0.556115	−	0.831106i	$-0.312292\pi$
$449$	23.5677	1.11223	0.556115	+	0.831106i	$0.312292\pi$
$450$	−3.55074	−0.167384
$451$	28.9457	1.36300
$452$	−17.1583	−0.807056
$453$	−11.4875	−0.539731
$454$	−9.50169	−0.445936
$455$	−13.7159	−0.643010
$456$	−1.45324	−0.0680540
$457$	−7.77421	−0.363662	−0.181831	−	0.983330i	$-0.558202\pi$
$457$	−7.77421	−0.363662	−0.181831	+	0.983330i	$0.558202\pi$
$458$	−23.4084	−1.09380
$459$	4.15864	0.194109
$460$	−1.63243	−0.0761126
$461$	−0.549185	−0.0255781	−0.0127891	−	0.999918i	$-0.504071\pi$
$461$	−0.549185	−0.0255781	−0.0127891	+	0.999918i	$0.504071\pi$
$462$	6.94550	0.323134
$463$	−32.5445	−1.51247	−0.756235	−	0.654300i	$-0.772963\pi$
$463$	−32.5445	−1.51247	−0.756235	+	0.654300i	$0.772963\pi$
$464$	2.01078	0.0933483
$465$	8.34075	0.386793
$466$	−17.1899	−0.796306
$467$	6.93404	0.320869	0.160435	−	0.987046i	$-0.448710\pi$
$467$	6.93404	0.320869	0.160435	+	0.987046i	$0.448710\pi$
$468$	−5.61711	−0.259651
$469$	27.8076	1.28403
$470$	−1.31652	−0.0607267
$471$	−1.31653	−0.0606626
$472$	10.3173	0.474891
$473$	−18.2717	−0.840131
$474$	5.94023	0.272844
$475$	1.39399	0.0639606
$476$	−6.68495	−0.306404
$477$	25.8328	1.18280
$478$	−9.73443	−0.445243
$479$	2.62246	0.119823	0.0599117	−	0.998204i	$-0.480918\pi$
$479$	2.62246	0.119823	0.0599117	+	0.998204i	$0.480918\pi$
$480$	5.15926	0.235487
$481$	12.6301	0.575883
$482$	−4.68339	−0.213322
$483$	1.51840	0.0690895
$484$	−3.21585	−0.146175
$485$	30.6592	1.39216
$486$	−11.1310	−0.504914
$487$	−27.7509	−1.25752	−0.628758	−	0.777601i	$-0.716436\pi$
$487$	−27.7509	−1.25752	−0.628758	+	0.777601i	$0.716436\pi$
$488$	−11.7123	−0.530190
$489$	3.06651	0.138672
$490$	16.4028	0.741002
$491$	12.8149	0.578329	0.289165	−	0.957279i	$-0.406622\pi$
$491$	12.8149	0.578329	0.289165	+	0.957279i	$0.406622\pi$
$492$	−4.44307	−0.200309
$493$	7.10335	0.319919
$494$	−1.65531	−0.0744757
$495$	19.4141	0.872597
$496$	3.60542	0.161888
$497$	22.7680	1.02128
$498$	−6.50105	−0.291319
$499$	30.8233	1.37984	0.689921	−	0.723885i	$-0.257645\pi$
$499$	30.8233	1.37984	0.689921	+	0.723885i	$0.257645\pi$
$500$	−13.8714	−0.620349
$501$	7.64414	0.341515
$502$	7.51206	0.335280
$503$	22.7442	1.01411	0.507057	−	0.861912i	$-0.330733\pi$
$503$	22.7442	1.01411	0.507057	+	0.861912i	$0.330733\pi$
$504$	32.3437	1.44070
$505$	35.8333	1.59456
$506$	2.58994	0.115137
$507$	−4.89640	−0.217457
$508$	3.06668	0.136062
$509$	−18.9086	−0.838110	−0.419055	−	0.907961i	$-0.637639\pi$
$509$	−18.9086	−0.838110	−0.419055	+	0.907961i	$0.637639\pi$
$510$	−1.27169	−0.0563114
$511$	−28.7027	−1.26973
$512$	4.61596	0.203998
$513$	2.87178	0.126792
$514$	22.3516	0.985888
$515$	17.0176	0.749885
$516$	2.80464	0.123468
$517$	−2.78264	−0.122381
$518$	−26.4394	−1.16168
$519$	−4.20149	−0.184425
$520$	9.87779	0.433170
$521$	−11.0084	−0.482289	−0.241144	−	0.970489i	$-0.577523\pi$
$521$	−11.0084	−0.482289	−0.241144	+	0.970489i	$0.577523\pi$
$522$	−12.4946	−0.546875
$523$	−21.8533	−0.955578	−0.477789	−	0.878475i	$-0.658562\pi$
$523$	−21.8533	−0.955578	−0.477789	+	0.878475i	$0.658562\pi$
$524$	1.04010	0.0454368
$525$	2.81293	0.122766
$526$	−9.31960	−0.406354
$527$	12.7366	0.554816
$528$	−0.760875	−0.0331128
$529$	−22.4338	−0.975382
$530$	−16.5153	−0.717379
$531$	−9.75204	−0.423203
$532$	−4.61634	−0.200144
$533$	−13.9206	−0.602968
$534$	2.07303	0.0897088
$535$	21.9005	0.946842
$536$	−20.0263	−0.865002
$537$	0.451544	0.0194856
$538$	6.64549	0.286507
$539$	34.6694	1.49332
$540$	−6.23018	−0.268104
$541$	−2.63120	−0.113124	−0.0565622	−	0.998399i	$-0.518014\pi$
$541$	−2.63120	−0.113124	−0.0565622	+	0.998399i	$0.518014\pi$
$542$	−28.5541	−1.22650
$543$	−11.2803	−0.484083
$544$	7.87837	0.337782
$545$	32.2376	1.38091
$546$	−3.34024	−0.142949
$547$	−16.1783	−0.691732	−0.345866	−	0.938284i	$-0.612415\pi$
$547$	−16.1783	−0.691732	−0.345866	+	0.938284i	$0.612415\pi$
$548$	−15.8409	−0.676690
$549$	11.0706	0.472483
$550$	4.79803	0.204589
$551$	4.90527	0.208972
$552$	−1.09351	−0.0465428
$553$	51.9036	2.20716
$554$	5.57048	0.236667
$555$	6.70054	0.284422
$556$	8.41430	0.356846
$557$	−0.535012	−0.0226692	−0.0113346	−	0.999936i	$-0.503608\pi$
$557$	−0.535012	−0.0226692	−0.0113346	+	0.999936i	$0.503608\pi$
$558$	−22.4034	−0.948412
$559$	8.78723	0.371660
$560$	−3.14542	−0.132918
$561$	−2.68789	−0.113483
$562$	−25.3981	−1.07135
$563$	−20.2752	−0.854499	−0.427250	−	0.904134i	$-0.640517\pi$
$563$	−20.2752	−0.854499	−0.427250	+	0.904134i	$0.640517\pi$
$564$	0.427127	0.0179853
$565$	−28.5201	−1.19985
$566$	−5.41761	−0.227719
$567$	−27.5487	−1.15693
$568$	−16.3969	−0.687997
$569$	−42.6860	−1.78949	−0.894746	−	0.446575i	$-0.852643\pi$
$569$	−42.6860	−1.78949	−0.894746	+	0.446575i	$0.852643\pi$
$570$	−0.878176	−0.0367827
$571$	8.83290	0.369645	0.184823	−	0.982772i	$-0.440829\pi$
$571$	8.83290	0.369645	0.184823	+	0.982772i	$0.440829\pi$
$572$	7.59027	0.317365
$573$	8.34632	0.348673
$574$	29.1409	1.21632
$575$	1.04893	0.0437433
$576$	−16.1129	−0.671373
$577$	30.2330	1.25862	0.629309	−	0.777156i	$-0.283338\pi$
$577$	30.2330	1.25862	0.629309	+	0.777156i	$0.283338\pi$
$578$	13.8008	0.574037
$579$	−12.7644	−0.530470
$580$	−10.6417	−0.441874
$581$	−56.8038	−2.35662
$582$	7.46647	0.309495
$583$	−34.9073	−1.44571
$584$	20.6709	0.855367
$585$	−9.33664	−0.386023
$586$	−10.3993	−0.429593
$587$	−16.9189	−0.698317	−0.349159	−	0.937064i	$-0.613533\pi$
$587$	−16.9189	−0.698317	−0.349159	+	0.937064i	$0.613533\pi$
$588$	−5.32165	−0.219461
$589$	8.79537	0.362407
$590$	6.23463	0.256675
$591$	1.94581	0.0800400
$592$	2.89642	0.119042
$593$	−26.4459	−1.08600	−0.543002	−	0.839731i	$-0.682712\pi$
$593$	−26.4459	−1.08600	−0.543002	+	0.839731i	$0.682712\pi$
$594$	9.88452	0.405567
$595$	−11.1116	−0.455530
$596$	−12.2925	−0.503522
$597$	6.73507	0.275648
$598$	−1.24556	−0.0509347
$599$	29.8324	1.21892	0.609460	−	0.792817i	$-0.291386\pi$
$599$	29.8324	1.21892	0.609460	+	0.792817i	$0.291386\pi$
$600$	−2.02579	−0.0827026
$601$	25.8802	1.05568	0.527838	−	0.849345i	$-0.323003\pi$
$601$	25.8802	1.05568	0.527838	+	0.849345i	$0.323003\pi$
$602$	−18.3949	−0.749720
$603$	18.9291	0.770854
$604$	26.2800	1.06932
$605$	−5.34531	−0.217318
$606$	8.72653	0.354491
$607$	22.5801	0.916497	0.458248	−	0.888824i	$-0.348477\pi$
$607$	22.5801	0.916497	0.458248	+	0.888824i	$0.348477\pi$
$608$	5.44047	0.220640
$609$	9.89834	0.401101
$610$	−7.07761	−0.286564
$611$	1.33823	0.0541391
$612$	−4.55057	−0.183946
$613$	−20.6803	−0.835268	−0.417634	−	0.908615i	$-0.637141\pi$
$613$	−20.6803	−0.835268	−0.417634	+	0.908615i	$0.637141\pi$
$614$	−21.2081	−0.855891
$615$	−7.38518	−0.297799
$616$	−43.7053	−1.76094
$617$	−21.9625	−0.884175	−0.442087	−	0.896972i	$-0.645762\pi$
$617$	−21.9625	−0.884175	−0.442087	+	0.896972i	$0.645762\pi$
$618$	4.14431	0.166709
$619$	6.89525	0.277143	0.138572	−	0.990352i	$-0.455749\pi$
$619$	6.89525	0.277143	0.138572	+	0.990352i	$0.455749\pi$
$620$	−19.0811	−0.766315
$621$	2.16091	0.0867145
$622$	12.2190	0.489937
$623$	18.1134	0.725698
$624$	0.365921	0.0146486
$625$	−16.0869	−0.643474
$626$	−18.7711	−0.750246
$627$	−1.85614	−0.0741271
$628$	3.01183	0.120185
$629$	10.2320	0.407975
$630$	19.5450	0.778692
$631$	−39.5533	−1.57459	−0.787297	−	0.616574i	$-0.788520\pi$
$631$	−39.5533	−1.57459	−0.787297	+	0.616574i	$0.788520\pi$
$632$	−37.3795	−1.48688
$633$	−2.36588	−0.0940351
$634$	−0.926042	−0.0367778
$635$	5.09737	0.202283
$636$	5.35816	0.212465
$637$	−16.6733	−0.660619
$638$	16.8837	0.668431
$639$	15.4986	0.613114
$640$	−10.3611	−0.409559
$641$	−6.20500	−0.245083	−0.122541	−	0.992463i	$-0.539104\pi$
$641$	−6.20500	−0.245083	−0.122541	+	0.992463i	$0.539104\pi$
$642$	5.33346	0.210495
$643$	−5.77985	−0.227935	−0.113968	−	0.993484i	$-0.536356\pi$
$643$	−5.77985	−0.227935	−0.113968	+	0.993484i	$0.536356\pi$
$644$	−3.47363	−0.136880
$645$	4.66182	0.183559
$646$	−1.34101	−0.0527612
$647$	−21.1779	−0.832591	−0.416295	−	0.909229i	$-0.636672\pi$
$647$	−21.1779	−0.832591	−0.416295	+	0.909229i	$0.636672\pi$
$648$	19.8398	0.779380
$649$	13.1777	0.517270
$650$	−2.30748	−0.0905067
$651$	17.7482	0.695606
$652$	−7.01524	−0.274738
$653$	−8.48162	−0.331911	−0.165956	−	0.986133i	$-0.553071\pi$
$653$	−8.48162	−0.331911	−0.165956	+	0.986133i	$0.553071\pi$
$654$	7.85085	0.306993
$655$	1.72883	0.0675508
$656$	−3.19237	−0.124641
$657$	−19.5384	−0.762267
$658$	−2.80141	−0.109210
$659$	11.0409	0.430091	0.215046	−	0.976604i	$-0.431010\pi$
$659$	11.0409	0.430091	0.215046	+	0.976604i	$0.431010\pi$
$660$	4.02680	0.156743
$661$	−38.7087	−1.50559	−0.752797	−	0.658252i	$-0.771296\pi$
$661$	−38.7087	−1.50559	−0.752797	+	0.658252i	$0.771296\pi$
$662$	−6.40847	−0.249072
$663$	1.29266	0.0502029
$664$	40.9085	1.58756
$665$	−7.67319	−0.297553
$666$	−17.9978	−0.697400
$667$	3.69104	0.142918
$668$	−17.4875	−0.676611
$669$	7.43078	0.287291
$670$	−12.1017	−0.467528
$671$	−14.9595	−0.577504
$672$	10.9783	0.423498
$673$	−44.6041	−1.71936	−0.859681	−	0.510831i	$-0.829338\pi$
$673$	−44.6041	−1.71936	−0.859681	+	0.510831i	$0.829338\pi$
$674$	−24.8213	−0.956082
$675$	4.00323	0.154084
$676$	11.2015	0.430826
$677$	26.6821	1.02548	0.512738	−	0.858545i	$-0.328631\pi$
$677$	26.6821	1.02548	0.512738	+	0.858545i	$0.328631\pi$
$678$	−6.94553	−0.266741
$679$	65.2393	2.50366
$680$	8.00225	0.306872
$681$	5.12398	0.196351
$682$	30.2732	1.15922
$683$	−0.338807	−0.0129641	−0.00648204	−	0.999979i	$-0.502063\pi$
$683$	−0.338807	−0.0129641	−0.00648204	+	0.999979i	$0.502063\pi$
$684$	−3.14243	−0.120154
$685$	−26.3304	−1.00603
$686$	8.70993	0.332547
$687$	12.6234	0.481615
$688$	2.01515	0.0768268
$689$	16.7877	0.639559
$690$	−0.660796	−0.0251561
$691$	19.2444	0.732090	0.366045	−	0.930597i	$-0.380712\pi$
$691$	19.2444	0.732090	0.366045	+	0.930597i	$0.380712\pi$
$692$	9.61173	0.365383
$693$	41.3109	1.56927
$694$	−11.4352	−0.434075
$695$	13.9861	0.530522
$696$	−7.12851	−0.270206
$697$	−11.2774	−0.427164
$698$	−12.0181	−0.454890
$699$	9.27000	0.350623
$700$	−6.43513	−0.243225
$701$	−36.8451	−1.39162	−0.695810	−	0.718226i	$-0.744954\pi$
$701$	−36.8451	−1.39162	−0.695810	+	0.718226i	$0.744954\pi$
$702$	−4.75368	−0.179416
$703$	7.06576	0.266490
$704$	21.7730	0.820602
$705$	0.709962	0.0267387
$706$	11.4632	0.431425
$707$	76.2492	2.86765
$708$	−2.02274	−0.0760191
$709$	45.3741	1.70406	0.852030	−	0.523493i	$-0.175372\pi$
$709$	45.3741	1.70406	0.852030	+	0.523493i	$0.175372\pi$
$710$	−9.90846	−0.371858
$711$	35.3317	1.32504
$712$	−13.0448	−0.488873
$713$	6.61820	0.247854
$714$	−2.70602	−0.101270
$715$	12.6164	0.471826
$716$	−1.03300	−0.0386049
$717$	5.24949	0.196046
$718$	24.5067	0.914581
$719$	14.7665	0.550699	0.275350	−	0.961344i	$-0.411206\pi$
$719$	14.7665	0.550699	0.275350	+	0.961344i	$0.411206\pi$
$720$	−2.14114	−0.0797956
$721$	36.2115	1.34859
$722$	−0.926042	−0.0344637
$723$	2.52561	0.0939285
$724$	25.8058	0.959066
$725$	6.83789	0.253953
$726$	−1.30175	−0.0483125
$727$	6.48352	0.240461	0.120230	−	0.992746i	$-0.461637\pi$
$727$	6.48352	0.240461	0.120230	+	0.992746i	$0.461637\pi$
$728$	21.0188	0.779009
$729$	−14.4505	−0.535203
$730$	12.4912	0.462320
$731$	7.11876	0.263297
$732$	2.29623	0.0848712
$733$	12.1807	0.449903	0.224952	−	0.974370i	$-0.427778\pi$
$733$	12.1807	0.449903	0.224952	+	0.974370i	$0.427778\pi$
$734$	−16.1134	−0.594756
$735$	−8.84554	−0.326273
$736$	4.09376	0.150898
$737$	−25.5785	−0.942195
$738$	19.8367	0.730201
$739$	−35.3927	−1.30194	−0.650970	−	0.759103i	$-0.725638\pi$
$739$	−35.3927	−1.30194	−0.650970	+	0.759103i	$0.725638\pi$
$740$	−15.3288	−0.563498
$741$	0.892658	0.0327926
$742$	−35.1427	−1.29013
$743$	47.8963	1.75714	0.878572	−	0.477610i	$-0.158497\pi$
$743$	47.8963	1.75714	0.878572	+	0.477610i	$0.158497\pi$
$744$	−12.7817	−0.468601
$745$	−20.4324	−0.748586
$746$	7.64316	0.279836
$747$	−38.6674	−1.41477
$748$	6.14907	0.224832
$749$	46.6018	1.70279
$750$	−5.61505	−0.205033
$751$	−19.6445	−0.716839	−0.358420	−	0.933561i	$-0.616684\pi$
$751$	−19.6445	−0.716839	−0.358420	+	0.933561i	$0.616684\pi$
$752$	0.306893	0.0111912
$753$	−4.05103	−0.147628
$754$	−8.11973	−0.295703
$755$	43.6820	1.58975
$756$	−13.2571	−0.482157
$757$	45.1320	1.64035	0.820176	−	0.572112i	$-0.193876\pi$
$757$	45.1320	1.64035	0.820176	+	0.572112i	$0.193876\pi$
$758$	26.0801	0.947273
$759$	−1.39668	−0.0506963
$760$	5.52602	0.200450
$761$	50.7340	1.83910	0.919552	−	0.392967i	$-0.128551\pi$
$761$	50.7340	1.83910	0.919552	+	0.392967i	$0.128551\pi$
$762$	1.24137	0.0449700
$763$	68.5979	2.48341
$764$	−19.0939	−0.690792
$765$	−7.56385	−0.273472
$766$	−28.3286	−1.02355
$767$	−6.33744	−0.228832
$768$	−8.37402	−0.302171
$769$	−44.6437	−1.60989	−0.804947	−	0.593346i	$-0.797806\pi$
$769$	−44.6437	−1.60989	−0.804947	+	0.593346i	$0.797806\pi$
$770$	−26.4107	−0.951775
$771$	−12.0536	−0.434099
$772$	29.2011	1.05097
$773$	−44.0034	−1.58269	−0.791347	−	0.611367i	$-0.790620\pi$
$773$	−44.0034	−1.58269	−0.791347	+	0.611367i	$0.790620\pi$
$774$	−12.5217	−0.450084
$775$	12.2606	0.440415
$776$	−46.9836	−1.68661
$777$	14.2580	0.511503
$778$	5.28493	0.189474
$779$	−7.78772	−0.279024
$780$	−1.93658	−0.0693405
$781$	−20.9428	−0.749394
$782$	−1.00906	−0.0360839
$783$	14.0869	0.503424
$784$	−3.82363	−0.136558
$785$	5.00619	0.178679
$786$	0.421023	0.0150174
$787$	−53.1421	−1.89431	−0.947156	−	0.320773i	$-0.896057\pi$
$787$	−53.1421	−1.89431	−0.947156	+	0.320773i	$0.896057\pi$
$788$	−4.45143	−0.158575
$789$	5.02579	0.178923
$790$	−22.5881	−0.803648
$791$	−60.6875	−2.15780
$792$	−29.7510	−1.05716
$793$	7.19433	0.255478
$794$	25.2180	0.894953
$795$	8.90623	0.315871
$796$	−15.4078	−0.546115
$797$	−27.3475	−0.968699	−0.484350	−	0.874875i	$-0.660944\pi$
$797$	−27.3475	−0.968699	−0.484350	+	0.874875i	$0.660944\pi$
$798$	−1.86866	−0.0661498
$799$	1.08414	0.0383540
$800$	7.58395	0.268133
$801$	12.3301	0.435663
$802$	−10.4445	−0.368807
$803$	26.4018	0.931700
$804$	3.92622	0.138467
$805$	−5.77380	−0.203500
$806$	−14.5590	−0.512820
$807$	−3.58372	−0.126153
$808$	−54.9126	−1.93182
$809$	−35.2113	−1.23796	−0.618982	−	0.785405i	$-0.712454\pi$
$809$	−35.2113	−1.23796	−0.618982	+	0.785405i	$0.712454\pi$
$810$	11.9890	0.421250
$811$	−32.3809	−1.13705	−0.568523	−	0.822667i	$-0.692485\pi$
$811$	−32.3809	−1.13705	−0.568523	+	0.822667i	$0.692485\pi$
$812$	−22.6444	−0.794663
$813$	15.3984	0.540045
$814$	24.3200	0.852415
$815$	−11.6606	−0.408452
$816$	0.296442	0.0103776
$817$	4.91591	0.171986
$818$	24.3685	0.852025
$819$	−19.8673	−0.694220
$820$	16.8951	0.590001
$821$	1.80952	0.0631527	0.0315763	−	0.999501i	$-0.489947\pi$
$821$	1.80952	0.0631527	0.0315763	+	0.999501i	$0.489947\pi$
$822$	−6.41228	−0.223654
$823$	16.1204	0.561923	0.280962	−	0.959719i	$-0.409347\pi$
$823$	16.1204	0.561923	0.280962	+	0.959719i	$0.409347\pi$
$824$	−26.0785	−0.908488
$825$	−2.58744	−0.0900830
$826$	13.2666	0.461603
$827$	33.9952	1.18213	0.591065	−	0.806624i	$-0.298708\pi$
$827$	33.9952	1.18213	0.591065	+	0.806624i	$0.298708\pi$
$828$	−2.36456	−0.0821743
$829$	18.7607	0.651587	0.325794	−	0.945441i	$-0.394369\pi$
$829$	18.7607	0.651587	0.325794	+	0.945441i	$0.394369\pi$
$830$	24.7206	0.858066
$831$	−3.00399	−0.104207
$832$	−10.4711	−0.363021
$833$	−13.5075	−0.468005
$834$	3.40604	0.117942
$835$	−29.0673	−1.00592
$836$	4.24629	0.146861
$837$	25.2584	0.873057
$838$	27.1681	0.938508
$839$	6.63636	0.229113	0.114556	−	0.993417i	$-0.463455\pi$
$839$	6.63636	0.229113	0.114556	+	0.993417i	$0.463455\pi$
$840$	11.1509	0.384744
$841$	−4.93832	−0.170287
$842$	9.50616	0.327604
$843$	13.6965	0.471731
$844$	5.41241	0.186303
$845$	18.6189	0.640508
$846$	−1.90697	−0.0655630
$847$	−11.3742	−0.390823
$848$	3.84986	0.132205
$849$	2.92156	0.100268
$850$	−1.86935	−0.0641181
$851$	5.31674	0.182255
$852$	3.21466	0.110132
$853$	50.0507	1.71370	0.856852	−	0.515563i	$-0.172417\pi$
$853$	50.0507	1.71370	0.856852	+	0.515563i	$0.172417\pi$
$854$	−15.0604	−0.515355
$855$	−5.22328	−0.178632
$856$	−33.5613	−1.14710
$857$	−28.2030	−0.963395	−0.481698	−	0.876337i	$-0.659980\pi$
$857$	−28.2030	−0.963395	−0.481698	+	0.876337i	$0.659980\pi$
$858$	3.07248	0.104893
$859$	−17.9545	−0.612600	−0.306300	−	0.951935i	$-0.599091\pi$
$859$	−17.9545	−0.612600	−0.306300	+	0.951935i	$0.599091\pi$
$860$	−10.6648	−0.363668
$861$	−15.7148	−0.535560
$862$	11.2328	0.382592
$863$	−14.6201	−0.497675	−0.248837	−	0.968545i	$-0.580048\pi$
$863$	−14.6201	−0.497675	−0.248837	+	0.968545i	$0.580048\pi$
$864$	15.6238	0.531534
$865$	15.9764	0.543215
$866$	−19.4644	−0.661427
$867$	−7.44236	−0.252756
$868$	−40.6024	−1.37814
$869$	−47.7429	−1.61957
$870$	−4.30769	−0.146044
$871$	12.3012	0.416812
$872$	−49.4023	−1.67297
$873$	44.4096	1.50304
$874$	−0.696814	−0.0235701
$875$	−49.0623	−1.65861
$876$	−4.05260	−0.136925
$877$	55.1749	1.86312	0.931561	−	0.363585i	$-0.118447\pi$
$877$	55.1749	1.86312	0.931561	+	0.363585i	$0.118447\pi$
$878$	−1.80441	−0.0608958
$879$	5.60806	0.189155
$880$	2.89327	0.0975322
$881$	−47.2331	−1.59132	−0.795661	−	0.605742i	$-0.792876\pi$
$881$	−47.2331	−1.59132	−0.795661	+	0.605742i	$0.792876\pi$
$882$	23.7593	0.800017
$883$	12.0723	0.406265	0.203133	−	0.979151i	$-0.434888\pi$
$883$	12.0723	0.406265	0.203133	+	0.979151i	$0.434888\pi$
$884$	−2.95722	−0.0994621
$885$	−3.36215	−0.113017
$886$	2.33257	0.0783642
$887$	25.8593	0.868270	0.434135	−	0.900848i	$-0.357054\pi$
$887$	25.8593	0.868270	0.434135	+	0.900848i	$0.357054\pi$
$888$	−10.2682	−0.344579
$889$	10.8466	0.363784
$890$	−7.88283	−0.264233
$891$	25.3403	0.848932
$892$	−16.9994	−0.569181
$893$	0.748659	0.0250529
$894$	−4.97593	−0.166420
$895$	−1.71702	−0.0573938
$896$	−22.0473	−0.736548
$897$	0.671693	0.0224272
$898$	−21.8247	−0.728299
$899$	43.1437	1.43892
$900$	−4.38051	−0.146017
$901$	13.6001	0.453086
$902$	−26.8049	−0.892506
$903$	9.91982	0.330111
$904$	43.7055	1.45362
$905$	42.8939	1.42584
$906$	10.6379	0.353422
$907$	−9.11687	−0.302721	−0.151360	−	0.988479i	$-0.548365\pi$
$907$	−9.11687	−0.302721	−0.151360	+	0.988479i	$0.548365\pi$
$908$	−11.7221	−0.389012
$909$	51.9042	1.72155
$910$	12.7015	0.421050
$911$	21.3205	0.706380	0.353190	−	0.935552i	$-0.385097\pi$
$911$	21.3205	0.706380	0.353190	+	0.935552i	$0.385097\pi$
$912$	0.204710	0.00677864
$913$	52.2503	1.72923
$914$	7.19925	0.238130
$915$	3.81675	0.126178
$916$	−28.8786	−0.954177
$917$	3.67875	0.121483
$918$	−3.85108	−0.127105
$919$	−25.2942	−0.834377	−0.417189	−	0.908820i	$-0.636985\pi$
$919$	−25.2942	−0.834377	−0.417189	+	0.908820i	$0.636985\pi$
$920$	4.15813	0.137089
$921$	11.4369	0.376860
$922$	0.508569	0.0167488
$923$	10.0719	0.331519
$924$	8.56858	0.281886
$925$	9.84959	0.323853
$926$	30.1375	0.990381
$927$	24.6498	0.809606
$928$	26.6870	0.876043
$929$	16.0922	0.527968	0.263984	−	0.964527i	$-0.414963\pi$
$929$	16.0922	0.527968	0.263984	+	0.964527i	$0.414963\pi$
$930$	−7.72388	−0.253276
$931$	−9.32767	−0.305702
$932$	−21.2069	−0.694656
$933$	−6.58934	−0.215725
$934$	−6.42121	−0.210108
$935$	10.2209	0.334258
$936$	14.3079	0.467668
$937$	−19.1322	−0.625023	−0.312512	−	0.949914i	$-0.601170\pi$
$937$	−19.1322	−0.625023	−0.312512	+	0.949914i	$0.601170\pi$
$938$	−25.7510	−0.840800
$939$	10.1227	0.330343
$940$	−1.62418	−0.0529748
$941$	−35.0362	−1.14215	−0.571074	−	0.820898i	$-0.693473\pi$
$941$	−35.0362	−1.14215	−0.571074	+	0.820898i	$0.693473\pi$
$942$	1.21916	0.0397225
$943$	−5.85998	−0.190827
$944$	−1.45334	−0.0473023
$945$	−22.0357	−0.716822
$946$	16.9203	0.550127
$947$	−53.1184	−1.72612	−0.863058	−	0.505106i	$-0.831454\pi$
$947$	−53.1184	−1.72612	−0.863058	+	0.505106i	$0.831454\pi$
$948$	7.32839	0.238015
$949$	−12.6972	−0.412169
$950$	−1.29089	−0.0418820
$951$	0.499387	0.0161937
$952$	17.0279	0.551877
$953$	54.7357	1.77306	0.886531	−	0.462668i	$-0.153108\pi$
$953$	54.7357	1.77306	0.886531	+	0.462668i	$0.153108\pi$
$954$	−23.9223	−0.774513
$955$	−31.7374	−1.02700
$956$	−12.0093	−0.388407
$957$	−9.10487	−0.294319
$958$	−2.42851	−0.0784616
$959$	−56.0282	−1.80924
$960$	−5.55516	−0.179292
$961$	46.3585	1.49544
$962$	−11.6960	−0.377094
$963$	31.7227	1.02225
$964$	−5.77783	−0.186092
$965$	48.5374	1.56247
$966$	−1.40610	−0.0452405
$967$	29.4524	0.947125	0.473563	−	0.880760i	$-0.342968\pi$
$967$	29.4524	0.947125	0.473563	+	0.880760i	$0.342968\pi$
$968$	8.19140	0.263281
$969$	0.723165	0.0232314
$970$	−28.3917	−0.911603
$971$	−25.7782	−0.827261	−0.413631	−	0.910445i	$-0.635739\pi$
$971$	−25.7782	−0.827261	−0.413631	+	0.910445i	$0.635739\pi$
$972$	−13.7322	−0.440462
$973$	29.7608	0.954087
$974$	25.6985	0.823434
$975$	1.24435	0.0398512
$976$	1.64985	0.0528105
$977$	13.8989	0.444666	0.222333	−	0.974971i	$-0.428633\pi$
$977$	13.8989	0.444666	0.222333	+	0.974971i	$0.428633\pi$
$978$	−2.83971	−0.0908040
$979$	−16.6614	−0.532501
$980$	20.2359	0.646412
$981$	46.6958	1.49088
$982$	−11.8672	−0.378696
$983$	−15.3870	−0.490770	−0.245385	−	0.969426i	$-0.578914\pi$
$983$	−15.3870	−0.490770	−0.245385	+	0.969426i	$0.578914\pi$
$984$	11.3174	0.360785
$985$	−7.39907	−0.235754
$986$	−6.57800	−0.209486
$987$	1.51072	0.0480867
$988$	−2.04213	−0.0649688
$989$	3.69905	0.117623
$990$	−17.9782	−0.571386
$991$	−29.2466	−0.929047	−0.464524	−	0.885561i	$-0.653774\pi$
$991$	−29.2466	−0.929047	−0.464524	+	0.885561i	$0.653774\pi$
$992$	47.8509	1.51927
$993$	3.45590	0.109670
$994$	−21.0841	−0.668747
$995$	−25.6105	−0.811907
$996$	−8.02027	−0.254132
$997$	55.7556	1.76580	0.882899	−	0.469563i	$-0.155589\pi$
$997$	55.7556	1.76580	0.882899	+	0.469563i	$0.155589\pi$
$998$	−28.5437	−0.903535
$999$	20.2913	0.641989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.50	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.50	✓	140	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-0.926042 q^{2} +0.499387 q^{3} -1.14245 q^{4} -1.89895 q^{5} -0.462453 q^{6} -4.04075 q^{7} +2.91004 q^{8} -2.75061 q^{9} +O(q^{10})\)	\(q-0.926042 q^{2} +0.499387 q^{3} -1.14245 q^{4} -1.89895 q^{5} -0.462453 q^{6} -4.04075 q^{7} +2.91004 q^{8} -2.75061 q^{9} +1.75851 q^{10} +3.71684 q^{11} -0.570523 q^{12} -1.78751 q^{13} +3.74190 q^{14} -0.948311 q^{15} -0.409923 q^{16} -1.44811 q^{17} +2.54718 q^{18} -1.00000 q^{19} +2.16945 q^{20} -2.01790 q^{21} -3.44195 q^{22} -0.752464 q^{23} +1.45324 q^{24} -1.39399 q^{25} +1.65531 q^{26} -2.87178 q^{27} +4.61634 q^{28} -4.90527 q^{29} +0.878176 q^{30} -8.79537 q^{31} -5.44047 q^{32} +1.85614 q^{33} +1.34101 q^{34} +7.67319 q^{35} +3.14243 q^{36} -7.06576 q^{37} +0.926042 q^{38} -0.892658 q^{39} -5.52602 q^{40} +7.78772 q^{41} +1.86866 q^{42} -4.91591 q^{43} -4.24629 q^{44} +5.22328 q^{45} +0.696814 q^{46} -0.748659 q^{47} -0.204710 q^{48} +9.32767 q^{49} +1.29089 q^{50} -0.723165 q^{51} +2.04213 q^{52} -9.39167 q^{53} +2.65939 q^{54} -7.05809 q^{55} -11.7587 q^{56} -0.499387 q^{57} +4.54249 q^{58} +3.54541 q^{59} +1.08340 q^{60} -4.02479 q^{61} +8.14488 q^{62} +11.1145 q^{63} +5.85795 q^{64} +3.39439 q^{65} -1.71886 q^{66} -6.88179 q^{67} +1.65438 q^{68} -0.375771 q^{69} -7.10569 q^{70} -5.63459 q^{71} -8.00438 q^{72} +7.10330 q^{73} +6.54319 q^{74} -0.696140 q^{75} +1.14245 q^{76} -15.0188 q^{77} +0.826639 q^{78} -12.8450 q^{79} +0.778424 q^{80} +6.81771 q^{81} -7.21176 q^{82} +14.0577 q^{83} +2.30534 q^{84} +2.74988 q^{85} +4.55234 q^{86} -2.44963 q^{87} +10.8161 q^{88} -4.48268 q^{89} -4.83697 q^{90} +7.22287 q^{91} +0.859650 q^{92} -4.39229 q^{93} +0.693290 q^{94} +1.89895 q^{95} -2.71690 q^{96} -16.1453 q^{97} -8.63781 q^{98} -10.2236 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

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