LMFDB - Embedded newform 4029.2.a.j.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.645538 q^{2} +1.00000 q^{3} -1.58328 q^{4} +2.70107 q^{5} -0.645538 q^{6} +4.18986 q^{7} +2.31314 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.645538 q^{2} +1.00000 q^{3} -1.58328 q^{4} +2.70107 q^{5} -0.645538 q^{6} +4.18986 q^{7} +2.31314 q^{8} +1.00000 q^{9} -1.74364 q^{10} +1.75152 q^{11} -1.58328 q^{12} +2.14376 q^{13} -2.70471 q^{14} +2.70107 q^{15} +1.67334 q^{16} -1.00000 q^{17} -0.645538 q^{18} -3.30108 q^{19} -4.27655 q^{20} +4.18986 q^{21} -1.13068 q^{22} +1.49590 q^{23} +2.31314 q^{24} +2.29578 q^{25} -1.38388 q^{26} +1.00000 q^{27} -6.63372 q^{28} +2.55438 q^{29} -1.74364 q^{30} +0.397194 q^{31} -5.70649 q^{32} +1.75152 q^{33} +0.645538 q^{34} +11.3171 q^{35} -1.58328 q^{36} +7.48767 q^{37} +2.13098 q^{38} +2.14376 q^{39} +6.24796 q^{40} +2.67407 q^{41} -2.70471 q^{42} +4.88703 q^{43} -2.77315 q^{44} +2.70107 q^{45} -0.965664 q^{46} +8.82045 q^{47} +1.67334 q^{48} +10.5549 q^{49} -1.48201 q^{50} -1.00000 q^{51} -3.39417 q^{52} -2.46208 q^{53} -0.645538 q^{54} +4.73099 q^{55} +9.69174 q^{56} -3.30108 q^{57} -1.64895 q^{58} +1.01706 q^{59} -4.27655 q^{60} -14.1528 q^{61} -0.256404 q^{62} +4.18986 q^{63} +0.337084 q^{64} +5.79044 q^{65} -1.13068 q^{66} -6.98258 q^{67} +1.58328 q^{68} +1.49590 q^{69} -7.30562 q^{70} -5.04070 q^{71} +2.31314 q^{72} +5.48326 q^{73} -4.83358 q^{74} +2.29578 q^{75} +5.22654 q^{76} +7.33863 q^{77} -1.38388 q^{78} -1.00000 q^{79} +4.51980 q^{80} +1.00000 q^{81} -1.72621 q^{82} -11.0764 q^{83} -6.63372 q^{84} -2.70107 q^{85} -3.15476 q^{86} +2.55438 q^{87} +4.05153 q^{88} -9.59017 q^{89} -1.74364 q^{90} +8.98204 q^{91} -2.36844 q^{92} +0.397194 q^{93} -5.69394 q^{94} -8.91646 q^{95} -5.70649 q^{96} -4.74665 q^{97} -6.81359 q^{98} +1.75152 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * 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 $

$2$	−0.645538	−0.456464	−0.228232	−	0.973607i	$-0.573295\pi$
$2$	−0.645538	−0.456464	−0.228232	+	0.973607i	$0.573295\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.58328	−0.791640
$5$	2.70107	1.20796	0.603978	−	0.797001i	$-0.293582\pi$
$5$	2.70107	1.20796	0.603978	+	0.797001i	$0.293582\pi$
$6$	−0.645538	−0.263540
$7$	4.18986	1.58362	0.791808	−	0.610769i	$-0.209140\pi$
$7$	4.18986	1.58362	0.791808	+	0.610769i	$0.209140\pi$
$8$	2.31314	0.817820
$9$	1.00000	0.333333
$10$	−1.74364	−0.551389
$11$	1.75152	0.528104	0.264052	−	0.964508i	$-0.414941\pi$
$11$	1.75152	0.528104	0.264052	+	0.964508i	$0.414941\pi$
$12$	−1.58328	−0.457054
$13$	2.14376	0.594572	0.297286	−	0.954789i	$-0.403919\pi$
$13$	2.14376	0.594572	0.297286	+	0.954789i	$0.403919\pi$
$14$	−2.70471	−0.722865
$15$	2.70107	0.697413
$16$	1.67334	0.418334
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.645538	−0.152155
$19$	−3.30108	−0.757320	−0.378660	−	0.925536i	$-0.623615\pi$
$19$	−3.30108	−0.757320	−0.378660	+	0.925536i	$0.623615\pi$
$20$	−4.27655	−0.956266
$21$	4.18986	0.914302
$22$	−1.13068	−0.241061
$23$	1.49590	0.311918	0.155959	−	0.987764i	$-0.450153\pi$
$23$	1.49590	0.311918	0.155959	+	0.987764i	$0.450153\pi$
$24$	2.31314	0.472169
$25$	2.29578	0.459156
$26$	−1.38388	−0.271401
$27$	1.00000	0.192450
$28$	−6.63372	−1.25365
$29$	2.55438	0.474336	0.237168	−	0.971469i	$-0.423781\pi$
$29$	2.55438	0.474336	0.237168	+	0.971469i	$0.423781\pi$
$30$	−1.74364	−0.318344
$31$	0.397194	0.0713382	0.0356691	−	0.999364i	$-0.488644\pi$
$31$	0.397194	0.0713382	0.0356691	+	0.999364i	$0.488644\pi$
$32$	−5.70649	−1.00877
$33$	1.75152	0.304901
$34$	0.645538	0.110709
$35$	11.3171	1.91294
$36$	−1.58328	−0.263880
$37$	7.48767	1.23097	0.615483	−	0.788150i	$-0.288961\pi$
$37$	7.48767	1.23097	0.615483	+	0.788150i	$0.288961\pi$
$38$	2.13098	0.345690
$39$	2.14376	0.343276
$40$	6.24796	0.987890
$41$	2.67407	0.417619	0.208810	−	0.977956i	$-0.433041\pi$
$41$	2.67407	0.417619	0.208810	+	0.977956i	$0.433041\pi$
$42$	−2.70471	−0.417346
$43$	4.88703	0.745265	0.372632	−	0.927979i	$-0.378455\pi$
$43$	4.88703	0.745265	0.372632	+	0.927979i	$0.378455\pi$
$44$	−2.77315	−0.418068
$45$	2.70107	0.402652
$46$	−0.965664	−0.142379
$47$	8.82045	1.28660	0.643298	−	0.765616i	$-0.277566\pi$
$47$	8.82045	1.28660	0.643298	+	0.765616i	$0.277566\pi$
$48$	1.67334	0.241525
$49$	10.5549	1.50784
$50$	−1.48201	−0.209588
$51$	−1.00000	−0.140028
$52$	−3.39417	−0.470687
$53$	−2.46208	−0.338193	−0.169097	−	0.985599i	$-0.554085\pi$
$53$	−2.46208	−0.338193	−0.169097	+	0.985599i	$0.554085\pi$
$54$	−0.645538	−0.0878466
$55$	4.73099	0.637926
$56$	9.69174	1.29511
$57$	−3.30108	−0.437239
$58$	−1.64895	−0.216517
$59$	1.01706	0.132409	0.0662047	−	0.997806i	$-0.478911\pi$
$59$	1.01706	0.132409	0.0662047	+	0.997806i	$0.478911\pi$
$60$	−4.27655	−0.552100
$61$	−14.1528	−1.81209	−0.906043	−	0.423186i	$-0.860912\pi$
$61$	−14.1528	−1.81209	−0.906043	+	0.423186i	$0.860912\pi$
$62$	−0.256404	−0.0325634
$63$	4.18986	0.527872
$64$	0.337084	0.0421356
$65$	5.79044	0.718216
$66$	−1.13068	−0.139176
$67$	−6.98258	−0.853058	−0.426529	−	0.904474i	$-0.640264\pi$
$67$	−6.98258	−0.853058	−0.426529	+	0.904474i	$0.640264\pi$
$68$	1.58328	0.192001
$69$	1.49590	0.180086
$70$	−7.30562	−0.873188
$71$	−5.04070	−0.598221	−0.299111	−	0.954218i	$-0.596690\pi$
$71$	−5.04070	−0.598221	−0.299111	+	0.954218i	$0.596690\pi$
$72$	2.31314	0.272607
$73$	5.48326	0.641767	0.320884	−	0.947119i	$-0.396020\pi$
$73$	5.48326	0.641767	0.320884	+	0.947119i	$0.396020\pi$
$74$	−4.83358	−0.561892
$75$	2.29578	0.265094
$76$	5.22654	0.599525
$77$	7.33863	0.836315
$78$	−1.38388	−0.156693
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	4.51980	0.505329
$81$	1.00000	0.111111
$82$	−1.72621	−0.190628
$83$	−11.0764	−1.21580	−0.607899	−	0.794015i	$-0.707987\pi$
$83$	−11.0764	−1.21580	−0.607899	+	0.794015i	$0.707987\pi$
$84$	−6.63372	−0.723798
$85$	−2.70107	−0.292972
$86$	−3.15476	−0.340187
$87$	2.55438	0.273858
$88$	4.05153	0.431894
$89$	−9.59017	−1.01656	−0.508278	−	0.861193i	$-0.669718\pi$
$89$	−9.59017	−1.01656	−0.508278	+	0.861193i	$0.669718\pi$
$90$	−1.74364	−0.183796
$91$	8.98204	0.941574
$92$	−2.36844	−0.246927
$93$	0.397194	0.0411871
$94$	−5.69394	−0.587285
$95$	−8.91646	−0.914809
$96$	−5.70649	−0.582416
$97$	−4.74665	−0.481950	−0.240975	−	0.970531i	$-0.577467\pi$
$97$	−4.74665	−0.481950	−0.240975	+	0.970531i	$0.577467\pi$
$98$	−6.81359	−0.688277
$99$	1.75152	0.176035
$100$	−3.63486	−0.363486
$101$	−8.51306	−0.847081	−0.423540	−	0.905877i	$-0.639213\pi$
$101$	−8.51306	−0.847081	−0.423540	+	0.905877i	$0.639213\pi$
$102$	0.645538	0.0639178
$103$	−6.43439	−0.633999	−0.317000	−	0.948426i	$-0.602675\pi$
$103$	−6.43439	−0.633999	−0.317000	+	0.948426i	$0.602675\pi$
$104$	4.95882	0.486253
$105$	11.3171	1.10444
$106$	1.58937	0.154373
$107$	−5.33094	−0.515361	−0.257680	−	0.966230i	$-0.582958\pi$
$107$	−5.33094	−0.515361	−0.257680	+	0.966230i	$0.582958\pi$
$108$	−1.58328	−0.152351
$109$	3.01191	0.288488	0.144244	−	0.989542i	$-0.453925\pi$
$109$	3.01191	0.288488	0.144244	+	0.989542i	$0.453925\pi$
$110$	−3.05403	−0.291191
$111$	7.48767	0.710699
$112$	7.01104	0.662481
$113$	−3.16223	−0.297477	−0.148739	−	0.988877i	$-0.547521\pi$
$113$	−3.16223	−0.297477	−0.148739	+	0.988877i	$0.547521\pi$
$114$	2.13098	0.199584
$115$	4.04054	0.376783
$116$	−4.04429	−0.375503
$117$	2.14376	0.198191
$118$	−0.656549	−0.0604402
$119$	−4.18986	−0.384084
$120$	6.24796	0.570359
$121$	−7.93217	−0.721106
$122$	9.13620	0.827153
$123$	2.67407	0.241113
$124$	−0.628870	−0.0564742
$125$	−7.30429	−0.653316
$126$	−2.70471	−0.240955
$127$	−3.67173	−0.325813	−0.162907	−	0.986641i	$-0.552087\pi$
$127$	−3.67173	−0.325813	−0.162907	+	0.986641i	$0.552087\pi$
$128$	11.1954	0.989541
$129$	4.88703	0.430279
$130$	−3.73795	−0.327840
$131$	−10.3584	−0.905017	−0.452508	−	0.891760i	$-0.649471\pi$
$131$	−10.3584	−0.905017	−0.452508	+	0.891760i	$0.649471\pi$
$132$	−2.77315	−0.241372
$133$	−13.8311	−1.19931
$134$	4.50752	0.389391
$135$	2.70107	0.232471
$136$	−2.31314	−0.198351
$137$	7.28757	0.622619	0.311309	−	0.950309i	$-0.399232\pi$
$137$	7.28757	0.622619	0.311309	+	0.950309i	$0.399232\pi$
$138$	−0.965664	−0.0822028
$139$	8.55695	0.725791	0.362896	−	0.931830i	$-0.381788\pi$
$139$	8.55695	0.725791	0.362896	+	0.931830i	$0.381788\pi$
$140$	−17.9181	−1.51436
$141$	8.82045	0.742816
$142$	3.25397	0.273067
$143$	3.75484	0.313996
$144$	1.67334	0.139445
$145$	6.89955	0.572976
$146$	−3.53966	−0.292944
$147$	10.5549	0.870553
$148$	−11.8551	−0.974482
$149$	17.2234	1.41100	0.705500	−	0.708710i	$-0.250723\pi$
$149$	17.2234	1.41100	0.705500	+	0.708710i	$0.250723\pi$
$150$	−1.48201	−0.121006
$151$	13.8791	1.12946	0.564732	−	0.825275i	$-0.308980\pi$
$151$	13.8791	1.12946	0.564732	+	0.825275i	$0.308980\pi$
$152$	−7.63588	−0.619352
$153$	−1.00000	−0.0808452
$154$	−4.73737	−0.381748
$155$	1.07285	0.0861733
$156$	−3.39417	−0.271751
$157$	18.9172	1.50976	0.754879	−	0.655864i	$-0.227696\pi$
$157$	18.9172	1.50976	0.754879	+	0.655864i	$0.227696\pi$
$158$	0.645538	0.0513563
$159$	−2.46208	−0.195256
$160$	−15.4136	−1.21855
$161$	6.26763	0.493958
$162$	−0.645538	−0.0507183
$163$	−8.83972	−0.692380	−0.346190	−	0.938164i	$-0.612525\pi$
$163$	−8.83972	−0.692380	−0.346190	+	0.938164i	$0.612525\pi$
$164$	−4.23380	−0.330604
$165$	4.73099	0.368307
$166$	7.15027	0.554968
$167$	17.5342	1.35684	0.678418	−	0.734676i	$-0.262666\pi$
$167$	17.5342	1.35684	0.678418	+	0.734676i	$0.262666\pi$
$168$	9.69174	0.747734
$169$	−8.40430	−0.646485
$170$	1.74364	0.133731
$171$	−3.30108	−0.252440
$172$	−7.73754	−0.589982
$173$	−7.76339	−0.590240	−0.295120	−	0.955460i	$-0.595360\pi$
$173$	−7.76339	−0.590240	−0.295120	+	0.955460i	$0.595360\pi$
$174$	−1.64895	−0.125006
$175$	9.61898	0.727127
$176$	2.93089	0.220924
$177$	1.01706	0.0764466
$178$	6.19082	0.464022
$179$	18.7067	1.39821	0.699103	−	0.715021i	$-0.253583\pi$
$179$	18.7067	1.39821	0.699103	+	0.715021i	$0.253583\pi$
$180$	−4.27655	−0.318755
$181$	7.22304	0.536885	0.268442	−	0.963296i	$-0.413491\pi$
$181$	7.22304	0.536885	0.268442	+	0.963296i	$0.413491\pi$
$182$	−5.79825	−0.429795
$183$	−14.1528	−1.04621
$184$	3.46024	0.255093
$185$	20.2247	1.48695
$186$	−0.256404	−0.0188005
$187$	−1.75152	−0.128084
$188$	−13.9652	−1.01852
$189$	4.18986	0.304767
$190$	5.75591	0.417578
$191$	−13.2987	−0.962258	−0.481129	−	0.876650i	$-0.659773\pi$
$191$	−13.2987	−0.962258	−0.481129	+	0.876650i	$0.659773\pi$
$192$	0.337084	0.0243270
$193$	−9.01830	−0.649152	−0.324576	−	0.945860i	$-0.605222\pi$
$193$	−9.01830	−0.649152	−0.324576	+	0.945860i	$0.605222\pi$
$194$	3.06415	0.219993
$195$	5.79044	0.414662
$196$	−16.7114	−1.19367
$197$	−1.86022	−0.132535	−0.0662677	−	0.997802i	$-0.521109\pi$
$197$	−1.86022	−0.132535	−0.0662677	+	0.997802i	$0.521109\pi$
$198$	−1.13068	−0.0803536
$199$	−27.0985	−1.92096	−0.960481	−	0.278344i	$-0.910214\pi$
$199$	−27.0985	−1.92096	−0.960481	+	0.278344i	$0.910214\pi$
$200$	5.31047	0.375507
$201$	−6.98258	−0.492513
$202$	5.49550	0.386662
$203$	10.7025	0.751166
$204$	1.58328	0.110852
$205$	7.22285	0.504466
$206$	4.15365	0.289398
$207$	1.49590	0.103973
$208$	3.58723	0.248730
$209$	−5.78192	−0.399944
$210$	−7.30562	−0.504136
$211$	−3.24541	−0.223424	−0.111712	−	0.993741i	$-0.535633\pi$
$211$	−3.24541	−0.223424	−0.111712	+	0.993741i	$0.535633\pi$
$212$	3.89817	0.267727
$213$	−5.04070	−0.345383
$214$	3.44132	0.235244
$215$	13.2002	0.900247
$216$	2.31314	0.157390
$217$	1.66419	0.112972
$218$	−1.94430	−0.131685
$219$	5.48326	0.370525
$220$	−7.49048	−0.505008
$221$	−2.14376	−0.144205
$222$	−4.83358	−0.324409
$223$	5.80430	0.388685	0.194342	−	0.980934i	$-0.437743\pi$
$223$	5.80430	0.388685	0.194342	+	0.980934i	$0.437743\pi$
$224$	−23.9094	−1.59751
$225$	2.29578	0.153052
$226$	2.04134	0.135788
$227$	0.436340	0.0289609	0.0144804	−	0.999895i	$-0.495391\pi$
$227$	0.436340	0.0289609	0.0144804	+	0.999895i	$0.495391\pi$
$228$	5.22654	0.346136
$229$	−12.3716	−0.817540	−0.408770	−	0.912638i	$-0.634042\pi$
$229$	−12.3716	−0.817540	−0.408770	+	0.912638i	$0.634042\pi$
$230$	−2.60833	−0.171988
$231$	7.33863	0.482846
$232$	5.90864	0.387921
$233$	1.61241	0.105632	0.0528162	−	0.998604i	$-0.483180\pi$
$233$	1.61241	0.105632	0.0528162	+	0.998604i	$0.483180\pi$
$234$	−1.38388	−0.0904670
$235$	23.8247	1.55415
$236$	−1.61028	−0.104821
$237$	−1.00000	−0.0649570
$238$	2.70471	0.175320
$239$	−5.69763	−0.368549	−0.184275	−	0.982875i	$-0.558994\pi$
$239$	−5.69763	−0.368549	−0.184275	+	0.982875i	$0.558994\pi$
$240$	4.51980	0.291752
$241$	−18.0250	−1.16109	−0.580547	−	0.814227i	$-0.697161\pi$
$241$	−18.0250	−1.16109	−0.580547	+	0.814227i	$0.697161\pi$
$242$	5.12052	0.329159
$243$	1.00000	0.0641500
$244$	22.4079	1.43452
$245$	28.5095	1.82141
$246$	−1.72621	−0.110059
$247$	−7.07673	−0.450281
$248$	0.918768	0.0583418
$249$	−11.0764	−0.701941
$250$	4.71520	0.298215
$251$	5.00283	0.315776	0.157888	−	0.987457i	$-0.449532\pi$
$251$	5.00283	0.315776	0.157888	+	0.987457i	$0.449532\pi$
$252$	−6.63372	−0.417885
$253$	2.62011	0.164725
$254$	2.37024	0.148722
$255$	−2.70107	−0.169148
$256$	−7.90122	−0.493826
$257$	10.2621	0.640134	0.320067	−	0.947395i	$-0.396295\pi$
$257$	10.2621	0.640134	0.320067	+	0.947395i	$0.396295\pi$
$258$	−3.15476	−0.196407
$259$	31.3723	1.94938
$260$	−9.16789	−0.568569
$261$	2.55438	0.158112
$262$	6.68674	0.413108
$263$	14.5781	0.898922	0.449461	−	0.893300i	$-0.351616\pi$
$263$	14.5781	0.898922	0.449461	+	0.893300i	$0.351616\pi$
$264$	4.05153	0.249354
$265$	−6.65026	−0.408522
$266$	8.92848	0.547440
$267$	−9.59017	−0.586909
$268$	11.0554	0.675315
$269$	19.5641	1.19284	0.596421	−	0.802671i	$-0.296589\pi$
$269$	19.5641	1.19284	0.596421	+	0.802671i	$0.296589\pi$
$270$	−1.74364	−0.106115
$271$	11.3523	0.689605	0.344802	−	0.938675i	$-0.387946\pi$
$271$	11.3523	0.689605	0.344802	+	0.938675i	$0.387946\pi$
$272$	−1.67334	−0.101461
$273$	8.98204	0.543618
$274$	−4.70440	−0.284203
$275$	4.02111	0.242482
$276$	−2.36844	−0.142563
$277$	24.0581	1.44551	0.722757	−	0.691103i	$-0.242875\pi$
$277$	24.0581	1.44551	0.722757	+	0.691103i	$0.242875\pi$
$278$	−5.52384	−0.331298
$279$	0.397194	0.0237794
$280$	26.1781	1.56444
$281$	3.36479	0.200727	0.100363	−	0.994951i	$-0.467999\pi$
$281$	3.36479	0.200727	0.100363	+	0.994951i	$0.467999\pi$
$282$	−5.69394	−0.339069
$283$	3.29052	0.195601	0.0978005	−	0.995206i	$-0.468819\pi$
$283$	3.29052	0.195601	0.0978005	+	0.995206i	$0.468819\pi$
$284$	7.98084	0.473576
$285$	−8.91646	−0.528165
$286$	−2.42389	−0.143328
$287$	11.2040	0.661349
$288$	−5.70649	−0.336258
$289$	1.00000	0.0588235
$290$	−4.45392	−0.261543
$291$	−4.74665	−0.278254
$292$	−8.68154	−0.508049
$293$	21.2141	1.23934	0.619671	−	0.784862i	$-0.287266\pi$
$293$	21.2141	1.23934	0.619671	+	0.784862i	$0.287266\pi$
$294$	−6.81359	−0.397377
$295$	2.74714	0.159945
$296$	17.3201	1.00671
$297$	1.75152	0.101634
$298$	−11.1184	−0.644071
$299$	3.20686	0.185457
$300$	−3.63486	−0.209859
$301$	20.4759	1.18021
$302$	−8.95948	−0.515560
$303$	−8.51306	−0.489062
$304$	−5.52383	−0.316813
$305$	−38.2278	−2.18892
$306$	0.645538	0.0369030
$307$	4.83788	0.276112	0.138056	−	0.990424i	$-0.455915\pi$
$307$	4.83788	0.276112	0.138056	+	0.990424i	$0.455915\pi$
$308$	−11.6191	−0.662060
$309$	−6.43439	−0.366040
$310$	−0.692565	−0.0393351
$311$	16.8242	0.954015	0.477008	−	0.878899i	$-0.341721\pi$
$311$	16.8242	0.954015	0.477008	+	0.878899i	$0.341721\pi$
$312$	4.95882	0.280738
$313$	−16.4134	−0.927742	−0.463871	−	0.885903i	$-0.653540\pi$
$313$	−16.4134	−0.927742	−0.463871	+	0.885903i	$0.653540\pi$
$314$	−12.2118	−0.689151
$315$	11.3171	0.637646
$316$	1.58328	0.0890665
$317$	−6.85414	−0.384967	−0.192483	−	0.981300i	$-0.561654\pi$
$317$	−6.85414	−0.384967	−0.192483	+	0.981300i	$0.561654\pi$
$318$	1.58937	0.0891274
$319$	4.47405	0.250499
$320$	0.910489	0.0508979
$321$	−5.33094	−0.297544
$322$	−4.04599	−0.225474
$323$	3.30108	0.183677
$324$	−1.58328	−0.0879600
$325$	4.92159	0.273001
$326$	5.70638	0.316047
$327$	3.01191	0.166559
$328$	6.18551	0.341538
$329$	36.9564	2.03747
$330$	−3.05403	−0.168119
$331$	−15.8581	−0.871641	−0.435821	−	0.900034i	$-0.643542\pi$
$331$	−15.8581	−0.871641	−0.435821	+	0.900034i	$0.643542\pi$
$332$	17.5371	0.962474
$333$	7.48767	0.410322
$334$	−11.3190	−0.619348
$335$	−18.8604	−1.03046
$336$	7.01104	0.382484
$337$	3.14101	0.171101	0.0855507	−	0.996334i	$-0.472735\pi$
$337$	3.14101	0.171101	0.0855507	+	0.996334i	$0.472735\pi$
$338$	5.42530	0.295097
$339$	−3.16223	−0.171749
$340$	4.27655	0.231929
$341$	0.695695	0.0376740
$342$	2.13098	0.115230
$343$	14.8945	0.804228
$344$	11.3044	0.609493
$345$	4.04054	0.217536
$346$	5.01157	0.269423
$347$	32.4571	1.74239	0.871195	−	0.490938i	$-0.163346\pi$
$347$	32.4571	1.74239	0.871195	+	0.490938i	$0.163346\pi$
$348$	−4.04429	−0.216797
$349$	−17.0497	−0.912650	−0.456325	−	0.889813i	$-0.650834\pi$
$349$	−17.0497	−0.912650	−0.456325	+	0.889813i	$0.650834\pi$
$350$	−6.20942	−0.331907
$351$	2.14376	0.114425
$352$	−9.99505	−0.532738
$353$	−3.72748	−0.198394	−0.0991968	−	0.995068i	$-0.531627\pi$
$353$	−3.72748	−0.198394	−0.0991968	+	0.995068i	$0.531627\pi$
$354$	−0.656549	−0.0348952
$355$	−13.6153	−0.722624
$356$	15.1839	0.804747
$357$	−4.18986	−0.221751
$358$	−12.0759	−0.638231
$359$	−24.5783	−1.29719	−0.648596	−	0.761133i	$-0.724644\pi$
$359$	−24.5783	−1.29719	−0.648596	+	0.761133i	$0.724644\pi$
$360$	6.24796	0.329297
$361$	−8.10285	−0.426466
$362$	−4.66275	−0.245069
$363$	−7.93217	−0.416331
$364$	−14.2211	−0.745388
$365$	14.8107	0.775226
$366$	9.13620	0.477557
$367$	−0.633618	−0.0330746	−0.0165373	−	0.999863i	$-0.505264\pi$
$367$	−0.633618	−0.0330746	−0.0165373	+	0.999863i	$0.505264\pi$
$368$	2.50315	0.130486
$369$	2.67407	0.139206
$370$	−13.0558	−0.678741
$371$	−10.3158	−0.535568
$372$	−0.628870	−0.0326054
$373$	−30.4210	−1.57514	−0.787570	−	0.616225i	$-0.788661\pi$
$373$	−30.4210	−1.57514	−0.787570	+	0.616225i	$0.788661\pi$
$374$	1.13068	0.0584658
$375$	−7.30429	−0.377192
$376$	20.4030	1.05220
$377$	5.47597	0.282027
$378$	−2.70471	−0.139115
$379$	−15.5492	−0.798710	−0.399355	−	0.916796i	$-0.630766\pi$
$379$	−15.5492	−0.798710	−0.399355	+	0.916796i	$0.630766\pi$
$380$	14.1172	0.724200
$381$	−3.67173	−0.188108
$382$	8.58480	0.439237
$383$	7.87525	0.402407	0.201203	−	0.979550i	$-0.435515\pi$
$383$	7.87525	0.402407	0.201203	+	0.979550i	$0.435515\pi$
$384$	11.1954	0.571312
$385$	19.8222	1.01023
$386$	5.82166	0.296315
$387$	4.88703	0.248422
$388$	7.51528	0.381531
$389$	25.2585	1.28065	0.640327	−	0.768102i	$-0.278799\pi$
$389$	25.2585	1.28065	0.640327	+	0.768102i	$0.278799\pi$
$390$	−3.73795	−0.189279
$391$	−1.49590	−0.0756512
$392$	24.4150	1.23314
$393$	−10.3584	−0.522512
$394$	1.20084	0.0604977
$395$	−2.70107	−0.135906
$396$	−2.77315	−0.139356
$397$	16.9412	0.850252	0.425126	−	0.905134i	$-0.360230\pi$
$397$	16.9412	0.850252	0.425126	+	0.905134i	$0.360230\pi$
$398$	17.4931	0.876851
$399$	−13.8311	−0.692419
$400$	3.84161	0.192081
$401$	16.0078	0.799391	0.399696	−	0.916648i	$-0.369116\pi$
$401$	16.0078	0.799391	0.399696	+	0.916648i	$0.369116\pi$
$402$	4.50752	0.224815
$403$	0.851489	0.0424157
$404$	13.4786	0.670583
$405$	2.70107	0.134217
$406$	−6.90885	−0.342881
$407$	13.1148	0.650078
$408$	−2.31314	−0.114518
$409$	−28.3475	−1.40169	−0.700847	−	0.713312i	$-0.747194\pi$
$409$	−28.3475	−1.40169	−0.700847	+	0.713312i	$0.747194\pi$
$410$	−4.66262	−0.230271
$411$	7.28757	0.359469
$412$	10.1874	0.501899
$413$	4.26132	0.209686
$414$	−0.965664	−0.0474598
$415$	−29.9182	−1.46863
$416$	−12.2333	−0.599789
$417$	8.55695	0.419036
$418$	3.73245	0.182560
$419$	−21.0445	−1.02809	−0.514045	−	0.857763i	$-0.671854\pi$
$419$	−21.0445	−1.02809	−0.514045	+	0.857763i	$0.671854\pi$
$420$	−17.9181	−0.874315
$421$	−16.9137	−0.824324	−0.412162	−	0.911111i	$-0.635226\pi$
$421$	−16.9137	−0.824324	−0.412162	+	0.911111i	$0.635226\pi$
$422$	2.09504	0.101985
$423$	8.82045	0.428865
$424$	−5.69515	−0.276581
$425$	−2.29578	−0.111362
$426$	3.25397	0.157655
$427$	−59.2984	−2.86965
$428$	8.44037	0.407980
$429$	3.75484	0.181286
$430$	−8.52124	−0.410931
$431$	−10.5419	−0.507786	−0.253893	−	0.967232i	$-0.581711\pi$
$431$	−10.5419	−0.507786	−0.253893	+	0.967232i	$0.581711\pi$
$432$	1.67334	0.0805085
$433$	−26.3218	−1.26494	−0.632472	−	0.774584i	$-0.717959\pi$
$433$	−26.3218	−1.26494	−0.632472	+	0.774584i	$0.717959\pi$
$434$	−1.07430	−0.0515679
$435$	6.89955	0.330808
$436$	−4.76869	−0.228379
$437$	−4.93811	−0.236222
$438$	−3.53966	−0.169131
$439$	6.00289	0.286502	0.143251	−	0.989686i	$-0.454244\pi$
$439$	6.00289	0.286502	0.143251	+	0.989686i	$0.454244\pi$
$440$	10.9435	0.521709
$441$	10.5549	0.502614
$442$	1.38388	0.0658244
$443$	−20.0004	−0.950249	−0.475124	−	0.879919i	$-0.657597\pi$
$443$	−20.0004	−0.950249	−0.475124	+	0.879919i	$0.657597\pi$
$444$	−11.8551	−0.562618
$445$	−25.9037	−1.22795
$446$	−3.74690	−0.177421
$447$	17.2234	0.814641
$448$	1.41234	0.0667266
$449$	−8.33078	−0.393154	−0.196577	−	0.980488i	$-0.562983\pi$
$449$	−8.33078	−0.393154	−0.196577	+	0.980488i	$0.562983\pi$
$450$	−1.48201	−0.0698627
$451$	4.68369	0.220547
$452$	5.00669	0.235495
$453$	13.8791	0.652096
$454$	−0.281674	−0.0132196
$455$	24.2611	1.13738
$456$	−7.63588	−0.357583
$457$	13.4672	0.629970	0.314985	−	0.949097i	$-0.398001\pi$
$457$	13.4672	0.629970	0.314985	+	0.949097i	$0.398001\pi$
$458$	7.98635	0.373178
$459$	−1.00000	−0.0466760
$460$	−6.39731	−0.298276
$461$	−10.9713	−0.510983	−0.255492	−	0.966811i	$-0.582237\pi$
$461$	−10.9713	−0.510983	−0.255492	+	0.966811i	$0.582237\pi$
$462$	−4.73737	−0.220402
$463$	22.7856	1.05894	0.529468	−	0.848330i	$-0.322391\pi$
$463$	22.7856	1.05894	0.529468	+	0.848330i	$0.322391\pi$
$464$	4.27433	0.198431
$465$	1.07285	0.0497522
$466$	−1.04087	−0.0482174
$467$	−3.13758	−0.145190	−0.0725950	−	0.997362i	$-0.523128\pi$
$467$	−3.13758	−0.145190	−0.0725950	+	0.997362i	$0.523128\pi$
$468$	−3.39417	−0.156896
$469$	−29.2560	−1.35092
$470$	−15.3797	−0.709414
$471$	18.9172	0.871659
$472$	2.35260	0.108287
$473$	8.55974	0.393577
$474$	0.645538	0.0296506
$475$	−7.57855	−0.347728
$476$	6.63372	0.304056
$477$	−2.46208	−0.112731
$478$	3.67804	0.168230
$479$	18.2172	0.832367	0.416184	−	0.909281i	$-0.363367\pi$
$479$	18.2172	0.832367	0.416184	+	0.909281i	$0.363367\pi$
$480$	−15.4136	−0.703533
$481$	16.0518	0.731898
$482$	11.6358	0.529998
$483$	6.26763	0.285187
$484$	12.5588	0.570857
$485$	−12.8210	−0.582174
$486$	−0.645538	−0.0292822
$487$	2.90336	0.131564	0.0657819	−	0.997834i	$-0.479046\pi$
$487$	2.90336	0.131564	0.0657819	+	0.997834i	$0.479046\pi$
$488$	−32.7376	−1.48196
$489$	−8.83972	−0.399746
$490$	−18.4040	−0.831407
$491$	−4.95726	−0.223718	−0.111859	−	0.993724i	$-0.535681\pi$
$491$	−4.95726	−0.223718	−0.111859	+	0.993724i	$0.535681\pi$
$492$	−4.23380	−0.190874
$493$	−2.55438	−0.115043
$494$	4.56830	0.205537
$495$	4.73099	0.212642
$496$	0.664640	0.0298432
$497$	−21.1198	−0.947353
$498$	7.15027	0.320411
$499$	−0.586279	−0.0262455	−0.0131227	−	0.999914i	$-0.504177\pi$
$499$	−0.586279	−0.0262455	−0.0131227	+	0.999914i	$0.504177\pi$
$500$	11.5647	0.517191
$501$	17.5342	0.783370
$502$	−3.22952	−0.144141
$503$	15.8923	0.708602	0.354301	−	0.935131i	$-0.384719\pi$
$503$	15.8923	0.708602	0.354301	+	0.935131i	$0.384719\pi$
$504$	9.69174	0.431705
$505$	−22.9944	−1.02324
$506$	−1.69138	−0.0751911
$507$	−8.40430	−0.373248
$508$	5.81338	0.257927
$509$	12.1723	0.539530	0.269765	−	0.962926i	$-0.413054\pi$
$509$	12.1723	0.539530	0.269765	+	0.962926i	$0.413054\pi$
$510$	1.74364	0.0772099
$511$	22.9741	1.01631
$512$	−17.2902	−0.764127
$513$	−3.30108	−0.145746
$514$	−6.62460	−0.292198
$515$	−17.3797	−0.765843
$516$	−7.73754	−0.340626
$517$	15.4492	0.679456
$518$	−20.2520	−0.889822
$519$	−7.76339	−0.340775
$520$	13.3941	0.587371
$521$	32.1106	1.40679	0.703396	−	0.710798i	$-0.251666\pi$
$521$	32.1106	1.40679	0.703396	+	0.710798i	$0.251666\pi$
$522$	−1.64895	−0.0721725
$523$	11.2898	0.493669	0.246835	−	0.969058i	$-0.420610\pi$
$523$	11.2898	0.493669	0.246835	+	0.969058i	$0.420610\pi$
$524$	16.4002	0.716448
$525$	9.61898	0.419807
$526$	−9.41069	−0.410326
$527$	−0.397194	−0.0173021
$528$	2.93089	0.127551
$529$	−20.7623	−0.902707
$530$	4.29300	0.186476
$531$	1.01706	0.0441365
$532$	21.8985	0.949418
$533$	5.73256	0.248305
$534$	6.19082	0.267903
$535$	−14.3992	−0.622533
$536$	−16.1517	−0.697648
$537$	18.7067	0.807255
$538$	−12.6294	−0.544490
$539$	18.4871	0.796298
$540$	−4.27655	−0.184033
$541$	−14.6885	−0.631510	−0.315755	−	0.948841i	$-0.602258\pi$
$541$	−14.6885	−0.631510	−0.315755	+	0.948841i	$0.602258\pi$
$542$	−7.32836	−0.314780
$543$	7.22304	0.309970
$544$	5.70649	0.244664
$545$	8.13537	0.348481
$546$	−5.79825	−0.248142
$547$	8.36702	0.357748	0.178874	−	0.983872i	$-0.442755\pi$
$547$	8.36702	0.357748	0.178874	+	0.983872i	$0.442755\pi$
$548$	−11.5383	−0.492890
$549$	−14.1528	−0.604029
$550$	−2.59578	−0.110684
$551$	−8.43221	−0.359224
$552$	3.46024	0.147278
$553$	−4.18986	−0.178171
$554$	−15.5304	−0.659825
$555$	20.2247	0.858492
$556$	−13.5481	−0.574565
$557$	14.9918	0.635225	0.317612	−	0.948221i	$-0.397119\pi$
$557$	14.9918	0.635225	0.317612	+	0.948221i	$0.397119\pi$
$558$	−0.256404	−0.0108545
$559$	10.4766	0.443113
$560$	18.9373	0.800248
$561$	−1.75152	−0.0739494
$562$	−2.17210	−0.0916246
$563$	−23.2174	−0.978495	−0.489248	−	0.872145i	$-0.662729\pi$
$563$	−23.2174	−0.978495	−0.489248	+	0.872145i	$0.662729\pi$
$564$	−13.9652	−0.588043
$565$	−8.54139	−0.359339
$566$	−2.12416	−0.0892849
$567$	4.18986	0.175957
$568$	−11.6599	−0.489237
$569$	14.3598	0.601996	0.300998	−	0.953625i	$-0.402680\pi$
$569$	14.3598	0.601996	0.300998	+	0.953625i	$0.402680\pi$
$570$	5.75591	0.241089
$571$	−32.3425	−1.35349	−0.676745	−	0.736218i	$-0.736610\pi$
$571$	−32.3425	−1.35349	−0.676745	+	0.736218i	$0.736610\pi$
$572$	−5.94497	−0.248572
$573$	−13.2987	−0.555560
$574$	−7.23259	−0.301882
$575$	3.43427	0.143219
$576$	0.337084	0.0140452
$577$	14.0437	0.584647	0.292323	−	0.956320i	$-0.405572\pi$
$577$	14.0437	0.584647	0.292323	+	0.956320i	$0.405572\pi$
$578$	−0.645538	−0.0268509
$579$	−9.01830	−0.374788
$580$	−10.9239	−0.453591
$581$	−46.4087	−1.92536
$582$	3.06415	0.127013
$583$	−4.31240	−0.178601
$584$	12.6836	0.524850
$585$	5.79044	0.239405
$586$	−13.6945	−0.565715
$587$	−11.4422	−0.472271	−0.236136	−	0.971720i	$-0.575881\pi$
$587$	−11.4422	−0.472271	−0.236136	+	0.971720i	$0.575881\pi$
$588$	−16.7114	−0.689165
$589$	−1.31117	−0.0540259
$590$	−1.77338	−0.0730090
$591$	−1.86022	−0.0765193
$592$	12.5294	0.514955
$593$	5.14778	0.211394	0.105697	−	0.994398i	$-0.466293\pi$
$593$	5.14778	0.211394	0.105697	+	0.994398i	$0.466293\pi$
$594$	−1.13068	−0.0463922
$595$	−11.3171	−0.463956
$596$	−27.2695	−1.11700
$597$	−27.0985	−1.10907
$598$	−2.07015	−0.0846547
$599$	20.2858	0.828857	0.414429	−	0.910082i	$-0.363981\pi$
$599$	20.2858	0.828857	0.414429	+	0.910082i	$0.363981\pi$
$600$	5.31047	0.216799
$601$	18.1783	0.741507	0.370753	−	0.928731i	$-0.379099\pi$
$601$	18.1783	0.741507	0.370753	+	0.928731i	$0.379099\pi$
$602$	−13.2180	−0.538726
$603$	−6.98258	−0.284353
$604$	−21.9745	−0.894128
$605$	−21.4253	−0.871064
$606$	5.49550	0.223240
$607$	28.8273	1.17006	0.585032	−	0.811010i	$-0.301082\pi$
$607$	28.8273	1.17006	0.585032	+	0.811010i	$0.301082\pi$
$608$	18.8376	0.763966
$609$	10.7025	0.433686
$610$	24.6775	0.999163
$611$	18.9089	0.764973
$612$	1.58328	0.0640003
$613$	18.8664	0.762008	0.381004	−	0.924573i	$-0.375578\pi$
$613$	18.8664	0.762008	0.381004	+	0.924573i	$0.375578\pi$
$614$	−3.12303	−0.126035
$615$	7.22285	0.291253
$616$	16.9753	0.683955
$617$	26.1779	1.05388	0.526941	−	0.849902i	$-0.323339\pi$
$617$	26.1779	1.05388	0.526941	+	0.849902i	$0.323339\pi$
$618$	4.15365	0.167084
$619$	13.4375	0.540098	0.270049	−	0.962847i	$-0.412960\pi$
$619$	13.4375	0.540098	0.270049	+	0.962847i	$0.412960\pi$
$620$	−1.69862	−0.0682183
$621$	1.49590	0.0600286
$622$	−10.8607	−0.435474
$623$	−40.1815	−1.60984
$624$	3.58723	0.143604
$625$	−31.2083	−1.24833
$626$	10.5955	0.423481
$627$	−5.78192	−0.230908
$628$	−29.9513	−1.19519
$629$	−7.48767	−0.298553
$630$	−7.30562	−0.291063
$631$	−39.5028	−1.57258	−0.786291	−	0.617856i	$-0.788001\pi$
$631$	−39.5028	−1.57258	−0.786291	+	0.617856i	$0.788001\pi$
$632$	−2.31314	−0.0920120
$633$	−3.24541	−0.128994
$634$	4.42461	0.175724
$635$	−9.91760	−0.393568
$636$	3.89817	0.154572
$637$	22.6272	0.896521
$638$	−2.88817	−0.114344
$639$	−5.04070	−0.199407
$640$	30.2395	1.19532
$641$	−27.8963	−1.10184	−0.550919	−	0.834559i	$-0.685723\pi$
$641$	−27.8963	−1.10184	−0.550919	+	0.834559i	$0.685723\pi$
$642$	3.44132	0.135818
$643$	−31.6712	−1.24899	−0.624496	−	0.781028i	$-0.714696\pi$
$643$	−31.6712	−1.24899	−0.624496	+	0.781028i	$0.714696\pi$
$644$	−9.92341	−0.391037
$645$	13.2002	0.519758
$646$	−2.13098	−0.0838421
$647$	28.1241	1.10567	0.552837	−	0.833290i	$-0.313545\pi$
$647$	28.1241	1.10567	0.552837	+	0.833290i	$0.313545\pi$
$648$	2.31314	0.0908689
$649$	1.78140	0.0699259
$650$	−3.17708	−0.124615
$651$	1.66419	0.0652246
$652$	13.9958	0.548116
$653$	28.7952	1.12684	0.563422	−	0.826169i	$-0.309485\pi$
$653$	28.7952	1.12684	0.563422	+	0.826169i	$0.309485\pi$
$654$	−1.94430	−0.0760282
$655$	−27.9787	−1.09322
$656$	4.47462	0.174705
$657$	5.48326	0.213922
$658$	−23.8568	−0.930035
$659$	−40.4800	−1.57688	−0.788438	−	0.615114i	$-0.789110\pi$
$659$	−40.4800	−1.57688	−0.788438	+	0.615114i	$0.789110\pi$
$660$	−7.49048	−0.291566
$661$	−8.36809	−0.325481	−0.162741	−	0.986669i	$-0.552033\pi$
$661$	−8.36809	−0.325481	−0.162741	+	0.986669i	$0.552033\pi$
$662$	10.2370	0.397873
$663$	−2.14376	−0.0832567
$664$	−25.6214	−0.994303
$665$	−37.3587	−1.44871
$666$	−4.83358	−0.187297
$667$	3.82110	0.147954
$668$	−27.7615	−1.07413
$669$	5.80430	0.224407
$670$	12.1751	0.470366
$671$	−24.7890	−0.956970
$672$	−23.9094	−0.922325
$673$	−16.7327	−0.645000	−0.322500	−	0.946569i	$-0.604523\pi$
$673$	−16.7327	−0.645000	−0.322500	+	0.946569i	$0.604523\pi$
$674$	−2.02764	−0.0781017
$675$	2.29578	0.0883645
$676$	13.3064	0.511783
$677$	4.26450	0.163898	0.0819490	−	0.996637i	$-0.473886\pi$
$677$	4.26450	0.163898	0.0819490	+	0.996637i	$0.473886\pi$
$678$	2.04134	0.0783971
$679$	−19.8878	−0.763224
$680$	−6.24796	−0.239599
$681$	0.436340	0.0167206
$682$	−0.449098	−0.0171968
$683$	46.0793	1.76318	0.881588	−	0.472020i	$-0.156475\pi$
$683$	46.0793	1.76318	0.881588	+	0.472020i	$0.156475\pi$
$684$	5.22654	0.199842
$685$	19.6842	0.752096
$686$	−9.61498	−0.367102
$687$	−12.3716	−0.472007
$688$	8.17765	0.311770
$689$	−5.27811	−0.201080
$690$	−2.60833	−0.0992972
$691$	−25.1151	−0.955423	−0.477711	−	0.878517i	$-0.658534\pi$
$691$	−25.1151	−0.955423	−0.477711	+	0.878517i	$0.658534\pi$
$692$	12.2916	0.467257
$693$	7.33863	0.278772
$694$	−20.9523	−0.795339
$695$	23.1129	0.876723
$696$	5.90864	0.223966
$697$	−2.67407	−0.101288
$698$	11.0062	0.416592
$699$	1.61241	0.0609868
$700$	−15.2295	−0.575623
$701$	−13.9902	−0.528401	−0.264201	−	0.964468i	$-0.585108\pi$
$701$	−13.9902	−0.528401	−0.264201	+	0.964468i	$0.585108\pi$
$702$	−1.38388	−0.0522311
$703$	−24.7174	−0.932236
$704$	0.590411	0.0222520
$705$	23.8247	0.897289
$706$	2.40623	0.0905597
$707$	−35.6685	−1.34145
$708$	−1.61028	−0.0605182
$709$	−24.4212	−0.917159	−0.458580	−	0.888653i	$-0.651642\pi$
$709$	−24.4212	−0.917159	−0.458580	+	0.888653i	$0.651642\pi$
$710$	8.78919	0.329852
$711$	−1.00000	−0.0375029
$712$	−22.1835	−0.831360
$713$	0.594165	0.0222516
$714$	2.70471	0.101221
$715$	10.1421	0.379293
$716$	−29.6180	−1.10688
$717$	−5.69763	−0.212782
$718$	15.8662	0.592122
$719$	15.1878	0.566410	0.283205	−	0.959059i	$-0.408602\pi$
$719$	15.1878	0.566410	0.283205	+	0.959059i	$0.408602\pi$
$720$	4.51980	0.168443
$721$	−26.9592	−1.00401
$722$	5.23070	0.194667
$723$	−18.0250	−0.670358
$724$	−11.4361	−0.425019
$725$	5.86428	0.217794
$726$	5.12052	0.190040
$727$	49.5396	1.83732	0.918662	−	0.395045i	$-0.129271\pi$
$727$	49.5396	1.83732	0.918662	+	0.395045i	$0.129271\pi$
$728$	20.7768	0.770038
$729$	1.00000	0.0370370
$730$	−9.56086	−0.353863
$731$	−4.88703	−0.180753
$732$	22.4079	0.828220
$733$	0.859068	0.0317304	0.0158652	−	0.999874i	$-0.494950\pi$
$733$	0.859068	0.0317304	0.0158652	+	0.999874i	$0.494950\pi$
$734$	0.409025	0.0150974
$735$	28.5095	1.05159
$736$	−8.53637	−0.314655
$737$	−12.2301	−0.450503
$738$	−1.72621	−0.0635428
$739$	−1.10959	−0.0408170	−0.0204085	−	0.999792i	$-0.506497\pi$
$739$	−1.10959	−0.0408170	−0.0204085	+	0.999792i	$0.506497\pi$
$740$	−32.0214	−1.17713
$741$	−7.07673	−0.259970
$742$	6.65923	0.244468
$743$	27.9369	1.02490	0.512452	−	0.858716i	$-0.328737\pi$
$743$	27.9369	1.02490	0.512452	+	0.858716i	$0.328737\pi$
$744$	0.918768	0.0336837
$745$	46.5217	1.70442
$746$	19.6379	0.718996
$747$	−11.0764	−0.405266
$748$	2.77315	0.101396
$749$	−22.3359	−0.816134
$750$	4.71520	0.172175
$751$	−43.2880	−1.57960	−0.789800	−	0.613365i	$-0.789816\pi$
$751$	−43.2880	−1.57960	−0.789800	+	0.613365i	$0.789816\pi$
$752$	14.7596	0.538227
$753$	5.00283	0.182313
$754$	−3.53495	−0.128735
$755$	37.4884	1.36434
$756$	−6.63372	−0.241266
$757$	32.5579	1.18334	0.591669	−	0.806181i	$-0.298469\pi$
$757$	32.5579	1.18334	0.591669	+	0.806181i	$0.298469\pi$
$758$	10.0376	0.364583
$759$	2.62011	0.0951040
$760$	−20.6251	−0.748149
$761$	11.0289	0.399799	0.199899	−	0.979816i	$-0.435938\pi$
$761$	11.0289	0.399799	0.199899	+	0.979816i	$0.435938\pi$
$762$	2.37024	0.0858648
$763$	12.6195	0.456855
$764$	21.0555	0.761762
$765$	−2.70107	−0.0976574
$766$	−5.08378	−0.183684
$767$	2.18032	0.0787269
$768$	−7.90122	−0.285111
$769$	−18.0775	−0.651891	−0.325946	−	0.945388i	$-0.605683\pi$
$769$	−18.0775	−0.651891	−0.325946	+	0.945388i	$0.605683\pi$
$770$	−12.7960	−0.461134
$771$	10.2621	0.369582
$772$	14.2785	0.513895
$773$	23.5581	0.847326	0.423663	−	0.905820i	$-0.360744\pi$
$773$	23.5581	0.847326	0.423663	+	0.905820i	$0.360744\pi$
$774$	−3.15476	−0.113396
$775$	0.911870	0.0327553
$776$	−10.9797	−0.394148
$777$	31.3723	1.12547
$778$	−16.3053	−0.584573
$779$	−8.82732	−0.316272
$780$	−9.16789	−0.328263
$781$	−8.82890	−0.315923
$782$	0.965664	0.0345321
$783$	2.55438	0.0912859
$784$	17.6619	0.630782
$785$	51.0967	1.82372
$786$	6.68674	0.238508
$787$	5.67868	0.202423	0.101212	−	0.994865i	$-0.467728\pi$
$787$	5.67868	0.202423	0.101212	+	0.994865i	$0.467728\pi$
$788$	2.94525	0.104920
$789$	14.5781	0.518993
$790$	1.74364	0.0620361
$791$	−13.2493	−0.471090
$792$	4.05153	0.143965
$793$	−30.3403	−1.07741
$794$	−10.9362	−0.388110
$795$	−6.65026	−0.235860
$796$	42.9045	1.52071
$797$	16.0034	0.566869	0.283434	−	0.958992i	$-0.408526\pi$
$797$	16.0034	0.566869	0.283434	+	0.958992i	$0.408526\pi$
$798$	8.92848	0.316065
$799$	−8.82045	−0.312045
$800$	−13.1008	−0.463185
$801$	−9.59017	−0.338852
$802$	−10.3336	−0.364894
$803$	9.60406	0.338920
$804$	11.0554	0.389893
$805$	16.9293	0.596679
$806$	−0.549669	−0.0193612
$807$	19.5641	0.688688
$808$	−19.6919	−0.692760
$809$	−46.1328	−1.62194	−0.810971	−	0.585086i	$-0.801061\pi$
$809$	−46.1328	−1.62194	−0.810971	+	0.585086i	$0.801061\pi$
$810$	−1.74364	−0.0612654
$811$	43.5244	1.52835	0.764173	−	0.645011i	$-0.223147\pi$
$811$	43.5244	1.52835	0.764173	+	0.645011i	$0.223147\pi$
$812$	−16.9450	−0.594653
$813$	11.3523	0.398144
$814$	−8.46613	−0.296738
$815$	−23.8767	−0.836364
$816$	−1.67334	−0.0585785
$817$	−16.1325	−0.564404
$818$	18.2994	0.639823
$819$	8.98204	0.313858
$820$	−11.4358	−0.399355
$821$	30.7502	1.07319	0.536595	−	0.843840i	$-0.319710\pi$
$821$	30.7502	1.07319	0.536595	+	0.843840i	$0.319710\pi$
$822$	−4.70440	−0.164085
$823$	−29.3837	−1.02425	−0.512126	−	0.858910i	$-0.671142\pi$
$823$	−29.3837	−1.02425	−0.512126	+	0.858910i	$0.671142\pi$
$824$	−14.8837	−0.518497
$825$	4.02111	0.139997
$826$	−2.75084	−0.0957141
$827$	−17.8546	−0.620865	−0.310432	−	0.950595i	$-0.600474\pi$
$827$	−17.8546	−0.620865	−0.310432	+	0.950595i	$0.600474\pi$
$828$	−2.36844	−0.0823089
$829$	−10.1143	−0.351284	−0.175642	−	0.984454i	$-0.556200\pi$
$829$	−10.1143	−0.351284	−0.175642	+	0.984454i	$0.556200\pi$
$830$	19.3134	0.670377
$831$	24.0581	0.834567
$832$	0.722628	0.0250526
$833$	−10.5549	−0.365706
$834$	−5.52384	−0.191275
$835$	47.3611	1.63900
$836$	9.15441	0.316612
$837$	0.397194	0.0137290
$838$	13.5850	0.469287
$839$	50.7262	1.75126	0.875632	−	0.482979i	$-0.160445\pi$
$839$	50.7262	1.75126	0.875632	+	0.482979i	$0.160445\pi$
$840$	26.1781	0.903229
$841$	−22.4752	−0.775006
$842$	10.9184	0.376274
$843$	3.36479	0.115890
$844$	5.13840	0.176871
$845$	−22.7006	−0.780924
$846$	−5.69394	−0.195762
$847$	−33.2346	−1.14196
$848$	−4.11990	−0.141478
$849$	3.29052	0.112930
$850$	1.48201	0.0508326
$851$	11.2008	0.383960
$852$	7.98084	0.273419
$853$	43.2485	1.48080	0.740400	−	0.672166i	$-0.234636\pi$
$853$	43.2485	1.48080	0.740400	+	0.672166i	$0.234636\pi$
$854$	38.2794	1.30989
$855$	−8.91646	−0.304936
$856$	−12.3312	−0.421473
$857$	−8.61089	−0.294142	−0.147071	−	0.989126i	$-0.546985\pi$
$857$	−8.61089	−0.294142	−0.147071	+	0.989126i	$0.546985\pi$
$858$	−2.42389	−0.0827504
$859$	−15.3554	−0.523919	−0.261960	−	0.965079i	$-0.584369\pi$
$859$	−15.3554	−0.523919	−0.261960	+	0.965079i	$0.584369\pi$
$860$	−20.8996	−0.712671
$861$	11.2040	0.381830
$862$	6.80521	0.231786
$863$	5.84394	0.198930	0.0994650	−	0.995041i	$-0.468287\pi$
$863$	5.84394	0.198930	0.0994650	+	0.995041i	$0.468287\pi$
$864$	−5.70649	−0.194139
$865$	−20.9695	−0.712983
$866$	16.9917	0.577402
$867$	1.00000	0.0339618
$868$	−2.63487	−0.0894335
$869$	−1.75152	−0.0594164
$870$	−4.45392	−0.151002
$871$	−14.9690	−0.507204
$872$	6.96697	0.235932
$873$	−4.74665	−0.160650
$874$	3.18774	0.107827
$875$	−30.6039	−1.03460
$876$	−8.68154	−0.293322
$877$	37.9840	1.28263	0.641314	−	0.767279i	$-0.278390\pi$
$877$	37.9840	1.28263	0.641314	+	0.767279i	$0.278390\pi$
$878$	−3.87509	−0.130778
$879$	21.2141	0.715534
$880$	7.91654	0.266866
$881$	38.9662	1.31280	0.656402	−	0.754411i	$-0.272078\pi$
$881$	38.9662	1.31280	0.656402	+	0.754411i	$0.272078\pi$
$882$	−6.81359	−0.229426
$883$	−36.0132	−1.21194	−0.605970	−	0.795488i	$-0.707215\pi$
$883$	−36.0132	−1.21194	−0.605970	+	0.795488i	$0.707215\pi$
$884$	3.39417	0.114158
$885$	2.74714	0.0923441
$886$	12.9110	0.433755
$887$	−29.7395	−0.998555	−0.499278	−	0.866442i	$-0.666401\pi$
$887$	−29.7395	−0.998555	−0.499278	+	0.866442i	$0.666401\pi$
$888$	17.3201	0.581224
$889$	−15.3840	−0.515964
$890$	16.7218	0.560518
$891$	1.75152	0.0586782
$892$	−9.18984	−0.307698
$893$	−29.1170	−0.974365
$894$	−11.1184	−0.371855
$895$	50.5282	1.68897
$896$	46.9071	1.56705
$897$	3.20686	0.107074
$898$	5.37784	0.179461
$899$	1.01458	0.0338383
$900$	−3.63486	−0.121162
$901$	2.46208	0.0820239
$902$	−3.02350	−0.100672
$903$	20.4759	0.681397
$904$	−7.31469	−0.243283
$905$	19.5099	0.648532
$906$	−8.95948	−0.297659
$907$	25.1956	0.836607	0.418303	−	0.908307i	$-0.362625\pi$
$907$	25.1956	0.836607	0.418303	+	0.908307i	$0.362625\pi$
$908$	−0.690848	−0.0229266
$909$	−8.51306	−0.282360
$910$	−15.6615	−0.519173
$911$	8.05581	0.266901	0.133450	−	0.991055i	$-0.457394\pi$
$911$	8.05581	0.266901	0.133450	+	0.991055i	$0.457394\pi$
$912$	−5.52383	−0.182912
$913$	−19.4006	−0.642067
$914$	−8.69360	−0.287559
$915$	−38.2278	−1.26377
$916$	19.5877	0.647197
$917$	−43.4002	−1.43320
$918$	0.645538	0.0213059
$919$	−39.2632	−1.29517	−0.647586	−	0.761992i	$-0.724221\pi$
$919$	−39.2632	−1.29517	−0.647586	+	0.761992i	$0.724221\pi$
$920$	9.34636	0.308140
$921$	4.83788	0.159413
$922$	7.08238	0.233246
$923$	−10.8060	−0.355685
$924$	−11.6191	−0.382241
$925$	17.1900	0.565205
$926$	−14.7090	−0.483367
$927$	−6.43439	−0.211333
$928$	−14.5765	−0.478498
$929$	−9.08104	−0.297939	−0.148970	−	0.988842i	$-0.547596\pi$
$929$	−9.08104	−0.297939	−0.148970	+	0.988842i	$0.547596\pi$
$930$	−0.692565	−0.0227101
$931$	−34.8426	−1.14192
$932$	−2.55289	−0.0836228
$933$	16.8242	0.550801
$934$	2.02543	0.0662741
$935$	−4.73099	−0.154720
$936$	4.95882	0.162084
$937$	26.1695	0.854921	0.427460	−	0.904034i	$-0.359408\pi$
$937$	26.1695	0.854921	0.427460	+	0.904034i	$0.359408\pi$
$938$	18.8859	0.616645
$939$	−16.4134	−0.535632
$940$	−37.7211	−1.23033
$941$	−26.9447	−0.878374	−0.439187	−	0.898396i	$-0.644733\pi$
$941$	−26.9447	−0.878374	−0.439187	+	0.898396i	$0.644733\pi$
$942$	−12.2118	−0.397881
$943$	4.00015	0.130263
$944$	1.70188	0.0553914
$945$	11.3171	0.368145
$946$	−5.52564	−0.179654
$947$	5.97189	0.194060	0.0970302	−	0.995281i	$-0.469066\pi$
$947$	5.97189	0.194060	0.0970302	+	0.995281i	$0.469066\pi$
$948$	1.58328	0.0514226
$949$	11.7548	0.381577
$950$	4.89225	0.158725
$951$	−6.85414	−0.222261
$952$	−9.69174	−0.314111
$953$	−36.2594	−1.17456	−0.587278	−	0.809385i	$-0.699800\pi$
$953$	−36.2594	−1.17456	−0.587278	+	0.809385i	$0.699800\pi$
$954$	1.58937	0.0514577
$955$	−35.9206	−1.16236
$956$	9.02095	0.291758
$957$	4.47405	0.144625
$958$	−11.7599	−0.379946
$959$	30.5339	0.985990
$960$	0.910489	0.0293859
$961$	−30.8422	−0.994911
$962$	−10.3620	−0.334085
$963$	−5.33094	−0.171787
$964$	28.5387	0.919168
$965$	−24.3591	−0.784146
$966$	−4.04599	−0.130178
$967$	−8.39361	−0.269920	−0.134960	−	0.990851i	$-0.543091\pi$
$967$	−8.39361	−0.269920	−0.134960	+	0.990851i	$0.543091\pi$
$968$	−18.3482	−0.589735
$969$	3.30108	0.106046
$970$	8.27648	0.265742
$971$	5.53491	0.177624	0.0888119	−	0.996048i	$-0.471693\pi$
$971$	5.53491	0.177624	0.0888119	+	0.996048i	$0.471693\pi$
$972$	−1.58328	−0.0507837
$973$	35.8524	1.14937
$974$	−1.87423	−0.0600542
$975$	4.92159	0.157617
$976$	−23.6825	−0.758058
$977$	−50.8053	−1.62540	−0.812702	−	0.582679i	$-0.802004\pi$
$977$	−50.8053	−1.62540	−0.812702	+	0.582679i	$0.802004\pi$
$978$	5.70638	0.182470
$979$	−16.7974	−0.536848
$980$	−45.1386	−1.44190
$981$	3.01191	0.0961628
$982$	3.20010	0.102119
$983$	53.2975	1.69993	0.849963	−	0.526842i	$-0.176624\pi$
$983$	53.2975	1.69993	0.849963	+	0.526842i	$0.176624\pi$
$984$	6.18551	0.197187
$985$	−5.02459	−0.160097
$986$	1.64895	0.0525132
$987$	36.9564	1.17634
$988$	11.2044	0.356461
$989$	7.31053	0.232461
$990$	−3.05403	−0.0970635
$991$	−4.36103	−0.138533	−0.0692663	−	0.997598i	$-0.522066\pi$
$991$	−4.36103	−0.138533	−0.0692663	+	0.997598i	$0.522066\pi$
$992$	−2.26659	−0.0719642
$993$	−15.8581	−0.503242
$994$	13.6336	0.432433
$995$	−73.1950	−2.32044
$996$	17.5371	0.555685
$997$	−6.74573	−0.213639	−0.106820	−	0.994278i	$-0.534067\pi$
$997$	−6.74573	−0.213639	−0.106820	+	0.994278i	$0.534067\pi$
$998$	0.378466	0.0119801
$999$	7.48767	0.236900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.j.1.10	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.j.1.10	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-0.645538 q^{2} +1.00000 q^{3} -1.58328 q^{4} +2.70107 q^{5} -0.645538 q^{6} +4.18986 q^{7} +2.31314 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.645538 q^{2} +1.00000 q^{3} -1.58328 q^{4} +2.70107 q^{5} -0.645538 q^{6} +4.18986 q^{7} +2.31314 q^{8} +1.00000 q^{9} -1.74364 q^{10} +1.75152 q^{11} -1.58328 q^{12} +2.14376 q^{13} -2.70471 q^{14} +2.70107 q^{15} +1.67334 q^{16} -1.00000 q^{17} -0.645538 q^{18} -3.30108 q^{19} -4.27655 q^{20} +4.18986 q^{21} -1.13068 q^{22} +1.49590 q^{23} +2.31314 q^{24} +2.29578 q^{25} -1.38388 q^{26} +1.00000 q^{27} -6.63372 q^{28} +2.55438 q^{29} -1.74364 q^{30} +0.397194 q^{31} -5.70649 q^{32} +1.75152 q^{33} +0.645538 q^{34} +11.3171 q^{35} -1.58328 q^{36} +7.48767 q^{37} +2.13098 q^{38} +2.14376 q^{39} +6.24796 q^{40} +2.67407 q^{41} -2.70471 q^{42} +4.88703 q^{43} -2.77315 q^{44} +2.70107 q^{45} -0.965664 q^{46} +8.82045 q^{47} +1.67334 q^{48} +10.5549 q^{49} -1.48201 q^{50} -1.00000 q^{51} -3.39417 q^{52} -2.46208 q^{53} -0.645538 q^{54} +4.73099 q^{55} +9.69174 q^{56} -3.30108 q^{57} -1.64895 q^{58} +1.01706 q^{59} -4.27655 q^{60} -14.1528 q^{61} -0.256404 q^{62} +4.18986 q^{63} +0.337084 q^{64} +5.79044 q^{65} -1.13068 q^{66} -6.98258 q^{67} +1.58328 q^{68} +1.49590 q^{69} -7.30562 q^{70} -5.04070 q^{71} +2.31314 q^{72} +5.48326 q^{73} -4.83358 q^{74} +2.29578 q^{75} +5.22654 q^{76} +7.33863 q^{77} -1.38388 q^{78} -1.00000 q^{79} +4.51980 q^{80} +1.00000 q^{81} -1.72621 q^{82} -11.0764 q^{83} -6.63372 q^{84} -2.70107 q^{85} -3.15476 q^{86} +2.55438 q^{87} +4.05153 q^{88} -9.59017 q^{89} -1.74364 q^{90} +8.98204 q^{91} -2.36844 q^{92} +0.397194 q^{93} -5.69394 q^{94} -8.91646 q^{95} -5.70649 q^{96} -4.74665 q^{97} -6.81359 q^{98} +1.75152 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * q^99

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