LMFDB - Embedded newform 4029.2.a.l.1.31

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:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.31
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)

$f(q)$	$=$	$q+2.67218 q^{2} -1.00000 q^{3} +5.14056 q^{4} +2.19087 q^{5} -2.67218 q^{6} +0.0367089 q^{7} +8.39213 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.67218 q^{2} -1.00000 q^{3} +5.14056 q^{4} +2.19087 q^{5} -2.67218 q^{6} +0.0367089 q^{7} +8.39213 q^{8} +1.00000 q^{9} +5.85441 q^{10} -2.40953 q^{11} -5.14056 q^{12} +3.84442 q^{13} +0.0980927 q^{14} -2.19087 q^{15} +12.1442 q^{16} -1.00000 q^{17} +2.67218 q^{18} +2.70031 q^{19} +11.2623 q^{20} -0.0367089 q^{21} -6.43869 q^{22} +2.52100 q^{23} -8.39213 q^{24} -0.200070 q^{25} +10.2730 q^{26} -1.00000 q^{27} +0.188704 q^{28} -4.94667 q^{29} -5.85441 q^{30} +6.79369 q^{31} +15.6672 q^{32} +2.40953 q^{33} -2.67218 q^{34} +0.0804245 q^{35} +5.14056 q^{36} -0.146081 q^{37} +7.21571 q^{38} -3.84442 q^{39} +18.3861 q^{40} -5.64815 q^{41} -0.0980927 q^{42} +6.67871 q^{43} -12.3863 q^{44} +2.19087 q^{45} +6.73657 q^{46} -3.17366 q^{47} -12.1442 q^{48} -6.99865 q^{49} -0.534623 q^{50} +1.00000 q^{51} +19.7625 q^{52} +11.3432 q^{53} -2.67218 q^{54} -5.27897 q^{55} +0.308066 q^{56} -2.70031 q^{57} -13.2184 q^{58} -7.01519 q^{59} -11.2623 q^{60} -14.6451 q^{61} +18.1540 q^{62} +0.0367089 q^{63} +17.5773 q^{64} +8.42265 q^{65} +6.43869 q^{66} +11.7417 q^{67} -5.14056 q^{68} -2.52100 q^{69} +0.214909 q^{70} +1.40190 q^{71} +8.39213 q^{72} +16.4756 q^{73} -0.390355 q^{74} +0.200070 q^{75} +13.8811 q^{76} -0.0884510 q^{77} -10.2730 q^{78} +1.00000 q^{79} +26.6064 q^{80} +1.00000 q^{81} -15.0929 q^{82} -13.9360 q^{83} -0.188704 q^{84} -2.19087 q^{85} +17.8467 q^{86} +4.94667 q^{87} -20.2211 q^{88} -10.6205 q^{89} +5.85441 q^{90} +0.141124 q^{91} +12.9593 q^{92} -6.79369 q^{93} -8.48060 q^{94} +5.91603 q^{95} -15.6672 q^{96} +8.20348 q^{97} -18.7017 q^{98} -2.40953 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.67218	1.88952	0.944759	−	0.327766i	$-0.106296\pi$
$2$	2.67218	1.88952	0.944759	+	0.327766i	$0.106296\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.14056	2.57028
$5$	2.19087	0.979789	0.489894	−	0.871782i	$-0.337035\pi$
$5$	2.19087	0.979789	0.489894	+	0.871782i	$0.337035\pi$
$6$	−2.67218	−1.09091
$7$	0.0367089	0.0138746	0.00693732	−	0.999976i	$-0.497792\pi$
$7$	0.0367089	0.0138746	0.00693732	+	0.999976i	$0.497792\pi$
$8$	8.39213	2.96707
$9$	1.00000	0.333333
$10$	5.85441	1.85133
$11$	−2.40953	−0.726500	−0.363250	−	0.931692i	$-0.618333\pi$
$11$	−2.40953	−0.726500	−0.363250	+	0.931692i	$0.618333\pi$
$12$	−5.14056	−1.48395
$13$	3.84442	1.06625	0.533125	−	0.846036i	$-0.321017\pi$
$13$	3.84442	1.06625	0.533125	+	0.846036i	$0.321017\pi$
$14$	0.0980927	0.0262164
$15$	−2.19087	−0.565681
$16$	12.1442	3.03605
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.67218	0.629839
$19$	2.70031	0.619493	0.309746	−	0.950819i	$-0.399756\pi$
$19$	2.70031	0.619493	0.309746	+	0.950819i	$0.399756\pi$
$20$	11.2623	2.51833
$21$	−0.0367089	−0.00801053
$22$	−6.43869	−1.37273
$23$	2.52100	0.525665	0.262832	−	0.964842i	$-0.415343\pi$
$23$	2.52100	0.525665	0.262832	+	0.964842i	$0.415343\pi$
$24$	−8.39213	−1.71304
$25$	−0.200070	−0.0400140
$26$	10.2730	2.01470
$27$	−1.00000	−0.192450
$28$	0.188704	0.0356617
$29$	−4.94667	−0.918574	−0.459287	−	0.888288i	$-0.651895\pi$
$29$	−4.94667	−0.918574	−0.459287	+	0.888288i	$0.651895\pi$
$30$	−5.85441	−1.06886
$31$	6.79369	1.22018	0.610091	−	0.792331i	$-0.291133\pi$
$31$	6.79369	1.22018	0.610091	+	0.792331i	$0.291133\pi$
$32$	15.6672	2.76960
$33$	2.40953	0.419445
$34$	−2.67218	−0.458275
$35$	0.0804245	0.0135942
$36$	5.14056	0.856759
$37$	−0.146081	−0.0240156	−0.0120078	−	0.999928i	$-0.503822\pi$
$37$	−0.146081	−0.0240156	−0.0120078	+	0.999928i	$0.503822\pi$
$38$	7.21571	1.17054
$39$	−3.84442	−0.615600
$40$	18.3861	2.90710
$41$	−5.64815	−0.882093	−0.441046	−	0.897484i	$-0.645393\pi$
$41$	−5.64815	−0.882093	−0.441046	+	0.897484i	$0.645393\pi$
$42$	−0.0980927	−0.0151360
$43$	6.67871	1.01849	0.509247	−	0.860621i	$-0.329924\pi$
$43$	6.67871	1.01849	0.509247	+	0.860621i	$0.329924\pi$
$44$	−12.3863	−1.86731
$45$	2.19087	0.326596
$46$	6.73657	0.993253
$47$	−3.17366	−0.462926	−0.231463	−	0.972844i	$-0.574351\pi$
$47$	−3.17366	−0.462926	−0.231463	+	0.972844i	$0.574351\pi$
$48$	−12.1442	−1.75286
$49$	−6.99865	−0.999807
$50$	−0.534623	−0.0756071
$51$	1.00000	0.140028
$52$	19.7625	2.74056
$53$	11.3432	1.55811	0.779057	−	0.626953i	$-0.215698\pi$
$53$	11.3432	1.55811	0.779057	+	0.626953i	$0.215698\pi$
$54$	−2.67218	−0.363638
$55$	−5.27897	−0.711816
$56$	0.308066	0.0411670
$57$	−2.70031	−0.357664
$58$	−13.2184	−1.73566
$59$	−7.01519	−0.913299	−0.456650	−	0.889647i	$-0.650951\pi$
$59$	−7.01519	−0.913299	−0.456650	+	0.889647i	$0.650951\pi$
$60$	−11.2623	−1.45396
$61$	−14.6451	−1.87511	−0.937557	−	0.347830i	$-0.886919\pi$
$61$	−14.6451	−1.87511	−0.937557	+	0.347830i	$0.886919\pi$
$62$	18.1540	2.30556
$63$	0.0367089	0.00462488
$64$	17.5773	2.19716
$65$	8.42265	1.04470
$66$	6.43869	0.792548
$67$	11.7417	1.43448	0.717240	−	0.696826i	$-0.245405\pi$
$67$	11.7417	1.43448	0.717240	+	0.696826i	$0.245405\pi$
$68$	−5.14056	−0.623384
$69$	−2.52100	−0.303493
$70$	0.214909	0.0256865
$71$	1.40190	0.166375	0.0831873	−	0.996534i	$-0.473490\pi$
$71$	1.40190	0.166375	0.0831873	+	0.996534i	$0.473490\pi$
$72$	8.39213	0.989023
$73$	16.4756	1.92832	0.964160	−	0.265323i	$-0.0854787\pi$
$73$	16.4756	1.92832	0.964160	+	0.265323i	$0.0854787\pi$
$74$	−0.390355	−0.0453779
$75$	0.200070	0.0231021
$76$	13.8811	1.59227
$77$	−0.0884510	−0.0100799
$78$	−10.2730	−1.16319
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	26.6064	2.97469
$81$	1.00000	0.111111
$82$	−15.0929	−1.66673
$83$	−13.9360	−1.52968	−0.764839	−	0.644221i	$-0.777182\pi$
$83$	−13.9360	−1.52968	−0.764839	+	0.644221i	$0.777182\pi$
$84$	−0.188704	−0.0205893
$85$	−2.19087	−0.237634
$86$	17.8467	1.92446
$87$	4.94667	0.530339
$88$	−20.2211	−2.15557
$89$	−10.6205	−1.12577	−0.562885	−	0.826535i	$-0.690309\pi$
$89$	−10.6205	−1.12577	−0.562885	+	0.826535i	$0.690309\pi$
$90$	5.85441	0.617109
$91$	0.141124	0.0147939
$92$	12.9593	1.35110
$93$	−6.79369	−0.704472
$94$	−8.48060	−0.874707
$95$	5.91603	0.606972
$96$	−15.6672	−1.59903
$97$	8.20348	0.832937	0.416468	−	0.909150i	$-0.363268\pi$
$97$	8.20348	0.832937	0.416468	+	0.909150i	$0.363268\pi$
$98$	−18.7017	−1.88915
$99$	−2.40953	−0.242167
$100$	−1.02847	−0.102847
$101$	18.5641	1.84719	0.923596	−	0.383367i	$-0.125235\pi$
$101$	18.5641	1.84719	0.923596	+	0.383367i	$0.125235\pi$
$102$	2.67218	0.264585
$103$	14.6696	1.44544	0.722718	−	0.691143i	$-0.242892\pi$
$103$	14.6696	1.44544	0.722718	+	0.691143i	$0.242892\pi$
$104$	32.2629	3.16364
$105$	−0.0804245	−0.00784863
$106$	30.3112	2.94409
$107$	−9.47113	−0.915608	−0.457804	−	0.889053i	$-0.651364\pi$
$107$	−9.47113	−0.915608	−0.457804	+	0.889053i	$0.651364\pi$
$108$	−5.14056	−0.494650
$109$	−17.1233	−1.64011	−0.820057	−	0.572281i	$-0.806059\pi$
$109$	−17.1233	−1.64011	−0.820057	+	0.572281i	$0.806059\pi$
$110$	−14.1064	−1.34499
$111$	0.146081	0.0138654
$112$	0.445800	0.0421241
$113$	−8.02009	−0.754466	−0.377233	−	0.926118i	$-0.623124\pi$
$113$	−8.02009	−0.754466	−0.377233	+	0.926118i	$0.623124\pi$
$114$	−7.21571	−0.675813
$115$	5.52319	0.515040
$116$	−25.4287	−2.36099
$117$	3.84442	0.355417
$118$	−18.7459	−1.72570
$119$	−0.0367089	−0.00336510
$120$	−18.3861	−1.67841
$121$	−5.19418	−0.472198
$122$	−39.1344	−3.54306
$123$	5.64815	0.509277
$124$	34.9233	3.13621
$125$	−11.3927	−1.01899
$126$	0.0980927	0.00873880
$127$	13.2121	1.17239	0.586193	−	0.810171i	$-0.300626\pi$
$127$	13.2121	1.17239	0.586193	+	0.810171i	$0.300626\pi$
$128$	15.6353	1.38198
$129$	−6.67871	−0.588027
$130$	22.5068	1.97398
$131$	−18.6125	−1.62618	−0.813091	−	0.582136i	$-0.802217\pi$
$131$	−18.6125	−1.62618	−0.813091	+	0.582136i	$0.802217\pi$
$132$	12.3863	1.07809
$133$	0.0991251	0.00859524
$134$	31.3760	2.71048
$135$	−2.19087	−0.188560
$136$	−8.39213	−0.719620
$137$	−9.03953	−0.772299	−0.386150	−	0.922436i	$-0.626195\pi$
$137$	−9.03953	−0.772299	−0.386150	+	0.922436i	$0.626195\pi$
$138$	−6.73657	−0.573455
$139$	9.74243	0.826342	0.413171	−	0.910653i	$-0.364421\pi$
$139$	9.74243	0.826342	0.413171	+	0.910653i	$0.364421\pi$
$140$	0.413427	0.0349409
$141$	3.17366	0.267270
$142$	3.74613	0.314368
$143$	−9.26324	−0.774631
$144$	12.1442	1.01202
$145$	−10.8375	−0.900009
$146$	44.0257	3.64359
$147$	6.99865	0.577239
$148$	−0.750938	−0.0617267
$149$	17.1426	1.40438	0.702189	−	0.711990i	$-0.252206\pi$
$149$	17.1426	1.40438	0.702189	+	0.711990i	$0.252206\pi$
$150$	0.534623	0.0436518
$151$	−23.4214	−1.90601	−0.953003	−	0.302960i	$-0.902025\pi$
$151$	−23.4214	−1.90601	−0.953003	+	0.302960i	$0.902025\pi$
$152$	22.6613	1.83808
$153$	−1.00000	−0.0808452
$154$	−0.236357	−0.0190462
$155$	14.8841	1.19552
$156$	−19.7625	−1.58226
$157$	−0.945953	−0.0754953	−0.0377476	−	0.999287i	$-0.512018\pi$
$157$	−0.945953	−0.0754953	−0.0377476	+	0.999287i	$0.512018\pi$
$158$	2.67218	0.212587
$159$	−11.3432	−0.899578
$160$	34.3249	2.71363
$161$	0.0925430	0.00729341
$162$	2.67218	0.209946
$163$	3.33829	0.261475	0.130738	−	0.991417i	$-0.458265\pi$
$163$	3.33829	0.261475	0.130738	+	0.991417i	$0.458265\pi$
$164$	−29.0346	−2.26722
$165$	5.27897	0.410967
$166$	−37.2396	−2.89035
$167$	7.13042	0.551769	0.275884	−	0.961191i	$-0.411029\pi$
$167$	7.13042	0.551769	0.275884	+	0.961191i	$0.411029\pi$
$168$	−0.308066	−0.0237678
$169$	1.77959	0.136891
$170$	−5.85441	−0.449013
$171$	2.70031	0.206498
$172$	34.3323	2.61781
$173$	−1.95195	−0.148404	−0.0742021	−	0.997243i	$-0.523641\pi$
$173$	−1.95195	−0.148404	−0.0742021	+	0.997243i	$0.523641\pi$
$174$	13.2184	1.00209
$175$	−0.00734433	−0.000555179 0
$176$	−29.2618	−2.20569
$177$	7.01519	0.527294
$178$	−28.3799	−2.12716
$179$	−8.49604	−0.635024	−0.317512	−	0.948254i	$-0.602847\pi$
$179$	−8.49604	−0.635024	−0.317512	+	0.948254i	$0.602847\pi$
$180$	11.2623	0.839443
$181$	−0.359734	−0.0267388	−0.0133694	−	0.999911i	$-0.504256\pi$
$181$	−0.359734	−0.0267388	−0.0133694	+	0.999911i	$0.504256\pi$
$182$	0.377110	0.0279532
$183$	14.6451	1.08260
$184$	21.1566	1.55968
$185$	−0.320045	−0.0235302
$186$	−18.1540	−1.33111
$187$	2.40953	0.176202
$188$	−16.3144	−1.18985
$189$	−0.0367089	−0.00267018
$190$	15.8087	1.14688
$191$	10.1504	0.734457	0.367229	−	0.930131i	$-0.380307\pi$
$191$	10.1504	0.734457	0.367229	+	0.930131i	$0.380307\pi$
$192$	−17.5773	−1.26853
$193$	−22.2169	−1.59921	−0.799605	−	0.600526i	$-0.794958\pi$
$193$	−22.2169	−1.59921	−0.799605	+	0.600526i	$0.794958\pi$
$194$	21.9212	1.57385
$195$	−8.42265	−0.603158
$196$	−35.9770	−2.56978
$197$	16.5320	1.17786	0.588929	−	0.808185i	$-0.299550\pi$
$197$	16.5320	1.17786	0.588929	+	0.808185i	$0.299550\pi$
$198$	−6.43869	−0.457578
$199$	−18.1466	−1.28638	−0.643188	−	0.765709i	$-0.722388\pi$
$199$	−18.1466	−1.28638	−0.643188	+	0.765709i	$0.722388\pi$
$200$	−1.67901	−0.118724
$201$	−11.7417	−0.828197
$202$	49.6065	3.49030
$203$	−0.181587	−0.0127449
$204$	5.14056	0.359911
$205$	−12.3744	−0.864265
$206$	39.1998	2.73118
$207$	2.52100	0.175222
$208$	46.6874	3.23719
$209$	−6.50646	−0.450061
$210$	−0.214909	−0.0148301
$211$	4.15343	0.285934	0.142967	−	0.989727i	$-0.454336\pi$
$211$	4.15343	0.285934	0.142967	+	0.989727i	$0.454336\pi$
$212$	58.3106	4.00479
$213$	−1.40190	−0.0960565
$214$	−25.3086	−1.73006
$215$	14.6322	0.997908
$216$	−8.39213	−0.571012
$217$	0.249388	0.0169296
$218$	−45.7566	−3.09903
$219$	−16.4756	−1.11332
$220$	−27.1368	−1.82957
$221$	−3.84442	−0.258604
$222$	0.390355	0.0261989
$223$	7.56275	0.506439	0.253220	−	0.967409i	$-0.418510\pi$
$223$	7.56275	0.506439	0.253220	+	0.967409i	$0.418510\pi$
$224$	0.575126	0.0384272
$225$	−0.200070	−0.0133380
$226$	−21.4311	−1.42558
$227$	20.6995	1.37387	0.686936	−	0.726718i	$-0.258955\pi$
$227$	20.6995	1.37387	0.686936	+	0.726718i	$0.258955\pi$
$228$	−13.8811	−0.919296
$229$	−16.7894	−1.10947	−0.554737	−	0.832026i	$-0.687181\pi$
$229$	−16.7894	−1.10947	−0.554737	+	0.832026i	$0.687181\pi$
$230$	14.7590	0.973178
$231$	0.0884510	0.00581965
$232$	−41.5132	−2.72547
$233$	−22.1371	−1.45025	−0.725125	−	0.688617i	$-0.758218\pi$
$233$	−22.1371	−1.45025	−0.725125	+	0.688617i	$0.758218\pi$
$234$	10.2730	0.671567
$235$	−6.95309	−0.453570
$236$	−36.0619	−2.34743
$237$	−1.00000	−0.0649570
$238$	−0.0980927	−0.00635841
$239$	−20.9463	−1.35490	−0.677451	−	0.735567i	$-0.736916\pi$
$239$	−20.9463	−1.35490	−0.677451	+	0.735567i	$0.736916\pi$
$240$	−26.6064	−1.71744
$241$	−6.81330	−0.438883	−0.219442	−	0.975626i	$-0.570424\pi$
$241$	−6.81330	−0.438883	−0.219442	+	0.975626i	$0.570424\pi$
$242$	−13.8798	−0.892227
$243$	−1.00000	−0.0641500
$244$	−75.2840	−4.81957
$245$	−15.3332	−0.979600
$246$	15.0929	0.962287
$247$	10.3811	0.660535
$248$	57.0135	3.62036
$249$	13.9360	0.883160
$250$	−30.4434	−1.92541
$251$	5.73363	0.361904	0.180952	−	0.983492i	$-0.442082\pi$
$251$	5.73363	0.361904	0.180952	+	0.983492i	$0.442082\pi$
$252$	0.188704	0.0118872
$253$	−6.07442	−0.381895
$254$	35.3052	2.21524
$255$	2.19087	0.137198
$256$	6.62570	0.414106
$257$	11.7429	0.732502	0.366251	−	0.930516i	$-0.380641\pi$
$257$	11.7429	0.732502	0.366251	+	0.930516i	$0.380641\pi$
$258$	−17.8467	−1.11109
$259$	−0.00536247	−0.000333208 0
$260$	43.2971	2.68517
$261$	−4.94667	−0.306191
$262$	−49.7360	−3.07270
$263$	−6.35273	−0.391726	−0.195863	−	0.980631i	$-0.562751\pi$
$263$	−6.35273	−0.391726	−0.195863	+	0.980631i	$0.562751\pi$
$264$	20.2211	1.24452
$265$	24.8516	1.52662
$266$	0.264880	0.0162409
$267$	10.6205	0.649964
$268$	60.3590	3.68701
$269$	−2.17229	−0.132447	−0.0662236	−	0.997805i	$-0.521095\pi$
$269$	−2.17229	−0.132447	−0.0662236	+	0.997805i	$0.521095\pi$
$270$	−5.85441	−0.356288
$271$	13.5878	0.825402	0.412701	−	0.910867i	$-0.364585\pi$
$271$	13.5878	0.825402	0.412701	+	0.910867i	$0.364585\pi$
$272$	−12.1442	−0.736350
$273$	−0.141124	−0.00854123
$274$	−24.1553	−1.45927
$275$	0.482073	0.0290701
$276$	−12.9593	−0.780060
$277$	21.6286	1.29954	0.649770	−	0.760131i	$-0.274865\pi$
$277$	21.6286	1.29954	0.649770	+	0.760131i	$0.274865\pi$
$278$	26.0336	1.56139
$279$	6.79369	0.406727
$280$	0.674933	0.0403350
$281$	20.6269	1.23050	0.615248	−	0.788334i	$-0.289056\pi$
$281$	20.6269	1.23050	0.615248	+	0.788334i	$0.289056\pi$
$282$	8.48060	0.505012
$283$	−9.65662	−0.574027	−0.287013	−	0.957927i	$-0.592662\pi$
$283$	−9.65662	−0.574027	−0.287013	+	0.957927i	$0.592662\pi$
$284$	7.20653	0.427629
$285$	−5.91603	−0.350435
$286$	−24.7531	−1.46368
$287$	−0.207337	−0.0122387
$288$	15.6672	0.923201
$289$	1.00000	0.0588235
$290$	−28.9599	−1.70058
$291$	−8.20348	−0.480896
$292$	84.6936	4.95632
$293$	−0.523792	−0.0306003	−0.0153001	−	0.999883i	$-0.504870\pi$
$293$	−0.523792	−0.0306003	−0.0153001	+	0.999883i	$0.504870\pi$
$294$	18.7017	1.09070
$295$	−15.3694	−0.894840
$296$	−1.22593	−0.0712559
$297$	2.40953	0.139815
$298$	45.8082	2.65360
$299$	9.69179	0.560490
$300$	1.02847	0.0593787
$301$	0.245168	0.0141312
$302$	−62.5862	−3.60143
$303$	−18.5641	−1.06648
$304$	32.7930	1.88081
$305$	−32.0856	−1.83722
$306$	−2.67218	−0.152758
$307$	14.5659	0.831318	0.415659	−	0.909521i	$-0.363551\pi$
$307$	14.5659	0.831318	0.415659	+	0.909521i	$0.363551\pi$
$308$	−0.454687	−0.0259082
$309$	−14.6696	−0.834523
$310$	39.7731	2.25896
$311$	10.5819	0.600044	0.300022	−	0.953932i	$-0.403006\pi$
$311$	10.5819	0.600044	0.300022	+	0.953932i	$0.403006\pi$
$312$	−32.2629	−1.82653
$313$	34.6390	1.95791	0.978957	−	0.204068i	$-0.0654164\pi$
$313$	34.6390	1.95791	0.978957	+	0.204068i	$0.0654164\pi$
$314$	−2.52776	−0.142650
$315$	0.0804245	0.00453141
$316$	5.14056	0.289179
$317$	−14.3489	−0.805914	−0.402957	−	0.915219i	$-0.632018\pi$
$317$	−14.3489	−0.805914	−0.402957	+	0.915219i	$0.632018\pi$
$318$	−30.3112	−1.69977
$319$	11.9191	0.667344
$320$	38.5097	2.15276
$321$	9.47113	0.528627
$322$	0.247292	0.0137810
$323$	−2.70031	−0.150249
$324$	5.14056	0.285586
$325$	−0.769153	−0.0426649
$326$	8.92052	0.494062
$327$	17.1233	0.946921
$328$	−47.4000	−2.61723
$329$	−0.116501	−0.00642293
$330$	14.1064	0.776530
$331$	7.34543	0.403741	0.201871	−	0.979412i	$-0.435298\pi$
$331$	7.34543	0.403741	0.201871	+	0.979412i	$0.435298\pi$
$332$	−71.6390	−3.93170
$333$	−0.146081	−0.00800520
$334$	19.0538	1.04258
$335$	25.7246	1.40549
$336$	−0.445800	−0.0243204
$337$	−26.4821	−1.44257	−0.721287	−	0.692636i	$-0.756449\pi$
$337$	−26.4821	−1.44257	−0.721287	+	0.692636i	$0.756449\pi$
$338$	4.75537	0.258658
$339$	8.02009	0.435591
$340$	−11.2623	−0.610785
$341$	−16.3696	−0.886462
$342$	7.21571	0.390181
$343$	−0.513875	−0.0277466
$344$	56.0486	3.02194
$345$	−5.52319	−0.297359
$346$	−5.21597	−0.280412
$347$	−6.98705	−0.375085	−0.187542	−	0.982257i	$-0.560052\pi$
$347$	−6.98705	−0.375085	−0.187542	+	0.982257i	$0.560052\pi$
$348$	25.4287	1.36312
$349$	−11.1009	−0.594219	−0.297110	−	0.954843i	$-0.596023\pi$
$349$	−11.1009	−0.594219	−0.297110	+	0.954843i	$0.596023\pi$
$350$	−0.0196254	−0.00104902
$351$	−3.84442	−0.205200
$352$	−37.7506	−2.01211
$353$	−19.3330	−1.02899	−0.514496	−	0.857493i	$-0.672021\pi$
$353$	−19.3330	−1.02899	−0.514496	+	0.857493i	$0.672021\pi$
$354$	18.7459	0.996331
$355$	3.07138	0.163012
$356$	−54.5952	−2.89354
$357$	0.0367089	0.00194284
$358$	−22.7030	−1.19989
$359$	6.23029	0.328822	0.164411	−	0.986392i	$-0.447428\pi$
$359$	6.23029	0.328822	0.164411	+	0.986392i	$0.447428\pi$
$360$	18.3861	0.969033
$361$	−11.7084	−0.616229
$362$	−0.961275	−0.0505235
$363$	5.19418	0.272624
$364$	0.725458	0.0380243
$365$	36.0959	1.88935
$366$	39.1344	2.04559
$367$	−8.39026	−0.437968	−0.218984	−	0.975728i	$-0.570274\pi$
$367$	−8.39026	−0.437968	−0.218984	+	0.975728i	$0.570274\pi$
$368$	30.6155	1.59594
$369$	−5.64815	−0.294031
$370$	−0.855220	−0.0444608
$371$	0.416398	0.0216183
$372$	−34.9233	−1.81069
$373$	−12.5549	−0.650068	−0.325034	−	0.945702i	$-0.605376\pi$
$373$	−12.5549	−0.650068	−0.325034	+	0.945702i	$0.605376\pi$
$374$	6.43869	0.332937
$375$	11.3927	0.588316
$376$	−26.6338	−1.37353
$377$	−19.0171	−0.979431
$378$	−0.0980927	−0.00504535
$379$	−12.1649	−0.624868	−0.312434	−	0.949939i	$-0.601144\pi$
$379$	−12.1649	−0.624868	−0.312434	+	0.949939i	$0.601144\pi$
$380$	30.4117	1.56009
$381$	−13.2121	−0.676878
$382$	27.1237	1.38777
$383$	5.63836	0.288107	0.144053	−	0.989570i	$-0.453986\pi$
$383$	5.63836	0.288107	0.144053	+	0.989570i	$0.453986\pi$
$384$	−15.6353	−0.797885
$385$	−0.193785	−0.00987620
$386$	−59.3677	−3.02174
$387$	6.67871	0.339498
$388$	42.1704	2.14088
$389$	−14.1611	−0.717997	−0.358999	−	0.933338i	$-0.616882\pi$
$389$	−14.1611	−0.717997	−0.358999	+	0.933338i	$0.616882\pi$
$390$	−22.5068	−1.13968
$391$	−2.52100	−0.127492
$392$	−58.7336	−2.96650
$393$	18.6125	0.938877
$394$	44.1766	2.22558
$395$	2.19087	0.110235
$396$	−12.3863	−0.622435
$397$	−28.0094	−1.40575	−0.702875	−	0.711314i	$-0.748101\pi$
$397$	−28.0094	−1.40575	−0.702875	+	0.711314i	$0.748101\pi$
$398$	−48.4909	−2.43063
$399$	−0.0991251	−0.00496246
$400$	−2.42969	−0.121484
$401$	4.66287	0.232853	0.116426	−	0.993199i	$-0.462856\pi$
$401$	4.66287	0.232853	0.116426	+	0.993199i	$0.462856\pi$
$402$	−31.3760	−1.56489
$403$	26.1178	1.30102
$404$	95.4296	4.74780
$405$	2.19087	0.108865
$406$	−0.485233	−0.0240817
$407$	0.351986	0.0174473
$408$	8.39213	0.415473
$409$	−0.549427	−0.0271674	−0.0135837	−	0.999908i	$-0.504324\pi$
$409$	−0.549427	−0.0271674	−0.0135837	+	0.999908i	$0.504324\pi$
$410$	−33.0666	−1.63304
$411$	9.03953	0.445887
$412$	75.4098	3.71517
$413$	−0.257519	−0.0126717
$414$	6.73657	0.331084
$415$	−30.5321	−1.49876
$416$	60.2315	2.95309
$417$	−9.74243	−0.477089
$418$	−17.3864	−0.850399
$419$	1.38066	0.0674494	0.0337247	−	0.999431i	$-0.489263\pi$
$419$	1.38066	0.0674494	0.0337247	+	0.999431i	$0.489263\pi$
$420$	−0.413427	−0.0201731
$421$	12.8147	0.624548	0.312274	−	0.949992i	$-0.398909\pi$
$421$	12.8147	0.624548	0.312274	+	0.949992i	$0.398909\pi$
$422$	11.0987	0.540277
$423$	−3.17366	−0.154309
$424$	95.1940	4.62303
$425$	0.200070	0.00970481
$426$	−3.74613	−0.181500
$427$	−0.537605	−0.0260166
$428$	−48.6869	−2.35337
$429$	9.26324	0.447233
$430$	39.0999	1.88557
$431$	1.83697	0.0884840	0.0442420	−	0.999021i	$-0.485913\pi$
$431$	1.83697	0.0884840	0.0442420	+	0.999021i	$0.485913\pi$
$432$	−12.1442	−0.584288
$433$	−15.9147	−0.764814	−0.382407	−	0.923994i	$-0.624905\pi$
$433$	−15.9147	−0.764814	−0.382407	+	0.923994i	$0.624905\pi$
$434$	0.666411	0.0319888
$435$	10.8375	0.519620
$436$	−88.0233	−4.21555
$437$	6.80747	0.325645
$438$	−44.0257	−2.10363
$439$	24.8518	1.18611	0.593055	−	0.805162i	$-0.297922\pi$
$439$	24.8518	1.18611	0.593055	+	0.805162i	$0.297922\pi$
$440$	−44.3018	−2.11201
$441$	−6.99865	−0.333269
$442$	−10.2730	−0.488637
$443$	3.52493	0.167474	0.0837372	−	0.996488i	$-0.473314\pi$
$443$	3.52493	0.167474	0.0837372	+	0.996488i	$0.473314\pi$
$444$	0.750938	0.0356380
$445$	−23.2682	−1.10302
$446$	20.2090	0.956926
$447$	−17.1426	−0.810818
$448$	0.645243	0.0304849
$449$	−32.4976	−1.53366	−0.766828	−	0.641853i	$-0.778166\pi$
$449$	−32.4976	−1.53366	−0.766828	+	0.641853i	$0.778166\pi$
$450$	−0.534623	−0.0252024
$451$	13.6094	0.640840
$452$	−41.2277	−1.93919
$453$	23.4214	1.10043
$454$	55.3127	2.59596
$455$	0.309186	0.0144949
$456$	−22.6613	−1.06121
$457$	1.12158	0.0524655	0.0262327	−	0.999656i	$-0.491649\pi$
$457$	1.12158	0.0524655	0.0262327	+	0.999656i	$0.491649\pi$
$458$	−44.8643	−2.09637
$459$	1.00000	0.0466760
$460$	28.3923	1.32380
$461$	−21.2341	−0.988970	−0.494485	−	0.869186i	$-0.664643\pi$
$461$	−21.2341	−0.988970	−0.494485	+	0.869186i	$0.664643\pi$
$462$	0.236357	0.0109963
$463$	16.6125	0.772048	0.386024	−	0.922489i	$-0.373848\pi$
$463$	16.6125	0.772048	0.386024	+	0.922489i	$0.373848\pi$
$464$	−60.0734	−2.78884
$465$	−14.8841	−0.690234
$466$	−59.1544	−2.74027
$467$	−19.6622	−0.909858	−0.454929	−	0.890528i	$-0.650335\pi$
$467$	−19.6622	−0.909858	−0.454929	+	0.890528i	$0.650335\pi$
$468$	19.7625	0.913520
$469$	0.431025	0.0199029
$470$	−18.5799	−0.857028
$471$	0.945953	0.0435872
$472$	−58.8724	−2.70982
$473$	−16.0925	−0.739935
$474$	−2.67218	−0.122737
$475$	−0.540250	−0.0247883
$476$	−0.188704	−0.00864923
$477$	11.3432	0.519372
$478$	−55.9723	−2.56011
$479$	39.0234	1.78302	0.891512	−	0.452997i	$-0.149645\pi$
$479$	39.0234	1.78302	0.891512	+	0.452997i	$0.149645\pi$
$480$	−34.3249	−1.56671
$481$	−0.561598	−0.0256067
$482$	−18.2064	−0.829277
$483$	−0.0925430	−0.00421085
$484$	−26.7010	−1.21368
$485$	17.9728	0.816102
$486$	−2.67218	−0.121213
$487$	−37.5203	−1.70021	−0.850103	−	0.526616i	$-0.823461\pi$
$487$	−37.5203	−1.70021	−0.850103	+	0.526616i	$0.823461\pi$
$488$	−122.904	−5.56359
$489$	−3.33829	−0.150963
$490$	−40.9730	−1.85097
$491$	−15.7304	−0.709903	−0.354952	−	0.934885i	$-0.615503\pi$
$491$	−15.7304	−0.709903	−0.354952	+	0.934885i	$0.615503\pi$
$492$	29.0346	1.30898
$493$	4.94667	0.222787
$494$	27.7402	1.24809
$495$	−5.27897	−0.237272
$496$	82.5039	3.70453
$497$	0.0514621	0.00230839
$498$	37.2396	1.66875
$499$	−24.9080	−1.11503	−0.557517	−	0.830166i	$-0.688246\pi$
$499$	−24.9080	−1.11503	−0.557517	+	0.830166i	$0.688246\pi$
$500$	−58.5648	−2.61910
$501$	−7.13042	−0.318564
$502$	15.3213	0.683823
$503$	22.4943	1.00297	0.501486	−	0.865166i	$-0.332787\pi$
$503$	22.4943	1.00297	0.501486	+	0.865166i	$0.332787\pi$
$504$	0.308066	0.0137223
$505$	40.6715	1.80986
$506$	−16.2319	−0.721598
$507$	−1.77959	−0.0790341
$508$	67.9176	3.01336
$509$	−16.4372	−0.728564	−0.364282	−	0.931289i	$-0.618686\pi$
$509$	−16.4372	−0.728564	−0.364282	+	0.931289i	$0.618686\pi$
$510$	5.85441	0.259238
$511$	0.604799	0.0267547
$512$	−13.5655	−0.599515
$513$	−2.70031	−0.119221
$514$	31.3792	1.38408
$515$	32.1392	1.41622
$516$	−34.3323	−1.51139
$517$	7.64702	0.336316
$518$	−0.0143295	−0.000629602 0
$519$	1.95195	0.0856811
$520$	70.6840	3.09970
$521$	−12.4312	−0.544623	−0.272311	−	0.962209i	$-0.587788\pi$
$521$	−12.4312	−0.544623	−0.272311	+	0.962209i	$0.587788\pi$
$522$	−13.2184	−0.578554
$523$	−9.54913	−0.417554	−0.208777	−	0.977963i	$-0.566948\pi$
$523$	−9.54913	−0.417554	−0.208777	+	0.977963i	$0.566948\pi$
$524$	−95.6786	−4.17974
$525$	0.00734433	0.000320533 0
$526$	−16.9756	−0.740173
$527$	−6.79369	−0.295938
$528$	29.2618	1.27346
$529$	−16.6446	−0.723677
$530$	66.4081	2.88458
$531$	−7.01519	−0.304433
$532$	0.509558	0.0220921
$533$	−21.7139	−0.940532
$534$	28.3799	1.22812
$535$	−20.7500	−0.897103
$536$	98.5381	4.25620
$537$	8.49604	0.366631
$538$	−5.80476	−0.250261
$539$	16.8634	0.726360
$540$	−11.2623	−0.484653
$541$	−19.4008	−0.834105	−0.417052	−	0.908882i	$-0.636937\pi$
$541$	−19.4008	−0.834105	−0.417052	+	0.908882i	$0.636937\pi$
$542$	36.3092	1.55961
$543$	0.359734	0.0154377
$544$	−15.6672	−0.671727
$545$	−37.5150	−1.60697
$546$	−0.377110	−0.0161388
$547$	3.86624	0.165309	0.0826543	−	0.996578i	$-0.473660\pi$
$547$	3.86624	0.165309	0.0826543	+	0.996578i	$0.473660\pi$
$548$	−46.4682	−1.98502
$549$	−14.6451	−0.625038
$550$	1.28819	0.0549285
$551$	−13.3575	−0.569050
$552$	−21.1566	−0.900483
$553$	0.0367089	0.00156102
$554$	57.7957	2.45550
$555$	0.320045	0.0135852
$556$	50.0815	2.12393
$557$	−10.9716	−0.464882	−0.232441	−	0.972610i	$-0.574671\pi$
$557$	−10.9716	−0.464882	−0.232441	+	0.972610i	$0.574671\pi$
$558$	18.1540	0.768519
$559$	25.6758	1.08597
$560$	0.976691	0.0412727
$561$	−2.40953	−0.101730
$562$	55.1188	2.32504
$563$	−27.9787	−1.17916	−0.589581	−	0.807709i	$-0.700707\pi$
$563$	−27.9787	−1.17916	−0.589581	+	0.807709i	$0.700707\pi$
$564$	16.3144	0.686959
$565$	−17.5710	−0.739218
$566$	−25.8043	−1.08463
$567$	0.0367089	0.00154163
$568$	11.7649	0.493645
$569$	−10.0267	−0.420341	−0.210171	−	0.977665i	$-0.567402\pi$
$569$	−10.0267	−0.420341	−0.210171	+	0.977665i	$0.567402\pi$
$570$	−15.8087	−0.662154
$571$	20.0104	0.837410	0.418705	−	0.908122i	$-0.362484\pi$
$571$	20.0104	0.837410	0.418705	+	0.908122i	$0.362484\pi$
$572$	−47.6182	−1.99102
$573$	−10.1504	−0.424039
$574$	−0.554042	−0.0231253
$575$	−0.504376	−0.0210339
$576$	17.5773	0.732388
$577$	−45.1796	−1.88085	−0.940426	−	0.339998i	$-0.889574\pi$
$577$	−45.1796	−1.88085	−0.940426	+	0.339998i	$0.889574\pi$
$578$	2.67218	0.111148
$579$	22.2169	0.923305
$580$	−55.7110	−2.31327
$581$	−0.511576	−0.0212237
$582$	−21.9212	−0.908662
$583$	−27.3319	−1.13197
$584$	138.265	5.72145
$585$	8.42265	0.348234
$586$	−1.39967	−0.0578198
$587$	9.64935	0.398271	0.199136	−	0.979972i	$-0.436187\pi$
$587$	9.64935	0.398271	0.199136	+	0.979972i	$0.436187\pi$
$588$	35.9770	1.48366
$589$	18.3450	0.755894
$590$	−41.0698	−1.69082
$591$	−16.5320	−0.680037
$592$	−1.77404	−0.0729125
$593$	36.9110	1.51575	0.757876	−	0.652399i	$-0.226237\pi$
$593$	36.9110	1.51575	0.757876	+	0.652399i	$0.226237\pi$
$594$	6.43869	0.264183
$595$	−0.0804245	−0.00329708
$596$	88.1226	3.60964
$597$	18.1466	0.742689
$598$	25.8982	1.05906
$599$	14.0186	0.572785	0.286392	−	0.958112i	$-0.407544\pi$
$599$	14.0186	0.572785	0.286392	+	0.958112i	$0.407544\pi$
$600$	1.67901	0.0685454
$601$	22.8533	0.932204	0.466102	−	0.884731i	$-0.345658\pi$
$601$	22.8533	0.932204	0.466102	+	0.884731i	$0.345658\pi$
$602$	0.655133	0.0267012
$603$	11.7417	0.478160
$604$	−120.399	−4.89897
$605$	−11.3798	−0.462655
$606$	−49.6065	−2.01513
$607$	19.9737	0.810706	0.405353	−	0.914160i	$-0.367149\pi$
$607$	19.9737	0.810706	0.405353	+	0.914160i	$0.367149\pi$
$608$	42.3063	1.71575
$609$	0.181587	0.00735827
$610$	−85.7386	−3.47145
$611$	−12.2009	−0.493595
$612$	−5.14056	−0.207795
$613$	−41.8181	−1.68902	−0.844508	−	0.535543i	$-0.820107\pi$
$613$	−41.8181	−1.68902	−0.844508	+	0.535543i	$0.820107\pi$
$614$	38.9226	1.57079
$615$	12.3744	0.498983
$616$	−0.742292	−0.0299078
$617$	10.4599	0.421098	0.210549	−	0.977583i	$-0.432475\pi$
$617$	10.4599	0.421098	0.210549	+	0.977583i	$0.432475\pi$
$618$	−39.1998	−1.57685
$619$	10.2998	0.413983	0.206991	−	0.978343i	$-0.433633\pi$
$619$	10.2998	0.413983	0.206991	+	0.978343i	$0.433633\pi$
$620$	76.5126	3.07282
$621$	−2.52100	−0.101164
$622$	28.2767	1.13379
$623$	−0.389866	−0.0156197
$624$	−46.6874	−1.86899
$625$	−23.9596	−0.958385
$626$	92.5618	3.69951
$627$	6.50646	0.259843
$628$	−4.86272	−0.194044
$629$	0.146081	0.00582464
$630$	0.214909	0.00856217
$631$	2.56593	0.102148	0.0510740	−	0.998695i	$-0.483736\pi$
$631$	2.56593	0.102148	0.0510740	+	0.998695i	$0.483736\pi$
$632$	8.39213	0.333821
$633$	−4.15343	−0.165084
$634$	−38.3428	−1.52279
$635$	28.9461	1.14869
$636$	−58.3106	−2.31216
$637$	−26.9058	−1.06605
$638$	31.8501	1.26096
$639$	1.40190	0.0554582
$640$	34.2549	1.35405
$641$	−24.5032	−0.967816	−0.483908	−	0.875119i	$-0.660783\pi$
$641$	−24.5032	−0.967816	−0.483908	+	0.875119i	$0.660783\pi$
$642$	25.3086	0.998850
$643$	−14.8770	−0.586692	−0.293346	−	0.956006i	$-0.594769\pi$
$643$	−14.8770	−0.586692	−0.293346	+	0.956006i	$0.594769\pi$
$644$	0.475722	0.0187461
$645$	−14.6322	−0.576143
$646$	−7.21571	−0.283898
$647$	35.0656	1.37857	0.689285	−	0.724491i	$-0.257925\pi$
$647$	35.0656	1.37857	0.689285	+	0.724491i	$0.257925\pi$
$648$	8.39213	0.329674
$649$	16.9033	0.663512
$650$	−2.05532	−0.0806161
$651$	−0.249388	−0.00977430
$652$	17.1607	0.672064
$653$	37.4176	1.46426	0.732132	−	0.681163i	$-0.238525\pi$
$653$	37.4176	1.46426	0.732132	+	0.681163i	$0.238525\pi$
$654$	45.7566	1.78922
$655$	−40.7777	−1.59332
$656$	−68.5923	−2.67808
$657$	16.4756	0.642773
$658$	−0.311313	−0.0121362
$659$	11.0216	0.429341	0.214671	−	0.976686i	$-0.431132\pi$
$659$	11.0216	0.429341	0.214671	+	0.976686i	$0.431132\pi$
$660$	27.1368	1.05630
$661$	40.5016	1.57533	0.787666	−	0.616103i	$-0.211290\pi$
$661$	40.5016	1.57533	0.787666	+	0.616103i	$0.211290\pi$
$662$	19.6283	0.762876
$663$	3.84442	0.149305
$664$	−116.953	−4.53866
$665$	0.217171	0.00842152
$666$	−0.390355	−0.0151260
$667$	−12.4706	−0.482862
$668$	36.6543	1.41820
$669$	−7.56275	−0.292393
$670$	68.7409	2.65569
$671$	35.2878	1.36227
$672$	−0.575126	−0.0221860
$673$	−9.02560	−0.347911	−0.173956	−	0.984753i	$-0.555655\pi$
$673$	−9.02560	−0.347911	−0.173956	+	0.984753i	$0.555655\pi$
$674$	−70.7651	−2.72577
$675$	0.200070	0.00770069
$676$	9.14806	0.351848
$677$	−21.9720	−0.844452	−0.422226	−	0.906490i	$-0.638751\pi$
$677$	−21.9720	−0.844452	−0.422226	+	0.906490i	$0.638751\pi$
$678$	21.4311	0.823058
$679$	0.301140	0.0115567
$680$	−18.3861	−0.705075
$681$	−20.6995	−0.793205
$682$	−43.7425	−1.67499
$683$	10.7219	0.410261	0.205130	−	0.978735i	$-0.434238\pi$
$683$	10.7219	0.410261	0.205130	+	0.978735i	$0.434238\pi$
$684$	13.8811	0.530756
$685$	−19.8045	−0.756690
$686$	−1.37317	−0.0524277
$687$	16.7894	0.640555
$688$	81.1075	3.09220
$689$	43.6082	1.66134
$690$	−14.7590	−0.561865
$691$	44.1952	1.68127	0.840633	−	0.541605i	$-0.182183\pi$
$691$	44.1952	1.68127	0.840633	+	0.541605i	$0.182183\pi$
$692$	−10.0341	−0.381440
$693$	−0.0884510	−0.00335997
$694$	−18.6707	−0.708729
$695$	21.3444	0.809641
$696$	41.5132	1.57355
$697$	5.64815	0.213939
$698$	−29.6637	−1.12279
$699$	22.1371	0.837302
$700$	−0.0377539	−0.00142697
$701$	13.9207	0.525776	0.262888	−	0.964826i	$-0.415325\pi$
$701$	13.9207	0.525776	0.262888	+	0.964826i	$0.415325\pi$
$702$	−10.2730	−0.387729
$703$	−0.394464	−0.0148775
$704$	−42.3530	−1.59624
$705$	6.95309	0.261869
$706$	−51.6613	−1.94430
$707$	0.681465	0.0256291
$708$	36.0619	1.35529
$709$	−27.2559	−1.02362	−0.511808	−	0.859100i	$-0.671024\pi$
$709$	−27.2559	−1.02362	−0.511808	+	0.859100i	$0.671024\pi$
$710$	8.20729	0.308014
$711$	1.00000	0.0375029
$712$	−89.1286	−3.34024
$713$	17.1269	0.641407
$714$	0.0980927	0.00367103
$715$	−20.2946	−0.758975
$716$	−43.6744	−1.63219
$717$	20.9463	0.782254
$718$	16.6485	0.621315
$719$	20.8464	0.777440	0.388720	−	0.921356i	$-0.372917\pi$
$719$	20.8464	0.777440	0.388720	+	0.921356i	$0.372917\pi$
$720$	26.6064	0.991562
$721$	0.538503	0.0200549
$722$	−31.2868	−1.16438
$723$	6.81330	0.253389
$724$	−1.84923	−0.0687262
$725$	0.989680	0.0367558
$726$	13.8798	0.515128
$727$	45.6645	1.69360	0.846800	−	0.531911i	$-0.178526\pi$
$727$	45.6645	1.69360	0.846800	+	0.531911i	$0.178526\pi$
$728$	1.18433	0.0438944
$729$	1.00000	0.0370370
$730$	96.4548	3.56995
$731$	−6.67871	−0.247021
$732$	75.2840	2.78258
$733$	33.7532	1.24670	0.623351	−	0.781942i	$-0.285771\pi$
$733$	33.7532	1.24670	0.623351	+	0.781942i	$0.285771\pi$
$734$	−22.4203	−0.827548
$735$	15.3332	0.565572
$736$	39.4971	1.45588
$737$	−28.2920	−1.04215
$738$	−15.0929	−0.555577
$739$	2.88934	0.106286	0.0531431	−	0.998587i	$-0.483076\pi$
$739$	2.88934	0.106286	0.0531431	+	0.998587i	$0.483076\pi$
$740$	−1.64521	−0.0604792
$741$	−10.3811	−0.381360
$742$	1.11269	0.0408481
$743$	25.5338	0.936745	0.468373	−	0.883531i	$-0.344841\pi$
$743$	25.5338	0.936745	0.468373	+	0.883531i	$0.344841\pi$
$744$	−57.0135	−2.09022
$745$	37.5573	1.37599
$746$	−33.5490	−1.22832
$747$	−13.9360	−0.509893
$748$	12.3863	0.452888
$749$	−0.347674	−0.0127037
$750$	30.4434	1.11163
$751$	34.6434	1.26416	0.632079	−	0.774904i	$-0.282202\pi$
$751$	34.6434	1.26416	0.632079	+	0.774904i	$0.282202\pi$
$752$	−38.5416	−1.40547
$753$	−5.73363	−0.208945
$754$	−50.8172	−1.85065
$755$	−51.3133	−1.86748
$756$	−0.188704	−0.00686309
$757$	−0.784297	−0.0285058	−0.0142529	−	0.999898i	$-0.504537\pi$
$757$	−0.784297	−0.0285058	−0.0142529	+	0.999898i	$0.504537\pi$
$758$	−32.5068	−1.18070
$759$	6.07442	0.220487
$760$	49.6481	1.80093
$761$	22.5795	0.818506	0.409253	−	0.912421i	$-0.365789\pi$
$761$	22.5795	0.818506	0.409253	+	0.912421i	$0.365789\pi$
$762$	−35.3052	−1.27897
$763$	−0.628577	−0.0227560
$764$	52.1787	1.88776
$765$	−2.19087	−0.0792112
$766$	15.0667	0.544383
$767$	−26.9693	−0.973806
$768$	−6.62570	−0.239084
$769$	11.0831	0.399666	0.199833	−	0.979830i	$-0.435960\pi$
$769$	11.0831	0.399666	0.199833	+	0.979830i	$0.435960\pi$
$770$	−0.517829	−0.0186612
$771$	−11.7429	−0.422910
$772$	−114.207	−4.11041
$773$	−6.48098	−0.233105	−0.116552	−	0.993185i	$-0.537184\pi$
$773$	−6.48098	−0.233105	−0.116552	+	0.993185i	$0.537184\pi$
$774$	17.8467	0.641487
$775$	−1.35921	−0.0488243
$776$	68.8447	2.47138
$777$	0.00536247	0.000192378 0
$778$	−37.8411	−1.35667
$779$	−15.2517	−0.546450
$780$	−43.2971	−1.55028
$781$	−3.37791	−0.120871
$782$	−6.73657	−0.240899
$783$	4.94667	0.176780
$784$	−84.9930	−3.03547
$785$	−2.07246	−0.0739694
$786$	49.7360	1.77402
$787$	−25.2440	−0.899851	−0.449925	−	0.893066i	$-0.648549\pi$
$787$	−25.2440	−0.899851	−0.449925	+	0.893066i	$0.648549\pi$
$788$	84.9838	3.02742
$789$	6.35273	0.226163
$790$	5.85441	0.208291
$791$	−0.294408	−0.0104680
$792$	−20.2211	−0.718525
$793$	−56.3020	−1.99934
$794$	−74.8461	−2.65619
$795$	−24.8516	−0.881396
$796$	−93.2834	−3.30634
$797$	−20.9355	−0.741575	−0.370787	−	0.928718i	$-0.620912\pi$
$797$	−20.9355	−0.741575	−0.370787	+	0.928718i	$0.620912\pi$
$798$	−0.264880	−0.00937666
$799$	3.17366	0.112276
$800$	−3.13454	−0.110823
$801$	−10.6205	−0.375257
$802$	12.4600	0.439979
$803$	−39.6983	−1.40092
$804$	−60.3590	−2.12870
$805$	0.202750	0.00714600
$806$	69.7915	2.45830
$807$	2.17229	0.0764684
$808$	155.792	5.48075
$809$	38.8870	1.36719	0.683596	−	0.729860i	$-0.260415\pi$
$809$	38.8870	1.36719	0.683596	+	0.729860i	$0.260415\pi$
$810$	5.85441	0.205703
$811$	−33.6524	−1.18169	−0.590847	−	0.806783i	$-0.701206\pi$
$811$	−33.6524	−1.18169	−0.590847	+	0.806783i	$0.701206\pi$
$812$	−0.933457	−0.0327579
$813$	−13.5878	−0.476546
$814$	0.940572	0.0329670
$815$	7.31378	0.256190
$816$	12.1442	0.425132
$817$	18.0345	0.630949
$818$	−1.46817	−0.0513333
$819$	0.141124	0.00493128
$820$	−63.6112	−2.22140
$821$	−5.49895	−0.191915	−0.0959574	−	0.995385i	$-0.530591\pi$
$821$	−5.49895	−0.191915	−0.0959574	+	0.995385i	$0.530591\pi$
$822$	24.1553	0.842512
$823$	17.1080	0.596349	0.298175	−	0.954511i	$-0.403622\pi$
$823$	17.1080	0.596349	0.298175	+	0.954511i	$0.403622\pi$
$824$	123.109	4.28871
$825$	−0.482073	−0.0167836
$826$	−0.688139	−0.0239434
$827$	−51.7187	−1.79844	−0.899218	−	0.437500i	$-0.855864\pi$
$827$	−51.7187	−1.79844	−0.899218	+	0.437500i	$0.855864\pi$
$828$	12.9593	0.450368
$829$	19.2961	0.670182	0.335091	−	0.942186i	$-0.391233\pi$
$829$	19.2961	0.670182	0.335091	+	0.942186i	$0.391233\pi$
$830$	−81.5873	−2.83194
$831$	−21.6286	−0.750289
$832$	67.5746	2.34273
$833$	6.99865	0.242489
$834$	−26.0336	−0.901468
$835$	15.6219	0.540617
$836$	−33.4468	−1.15678
$837$	−6.79369	−0.234824
$838$	3.68936	0.127447
$839$	−20.6871	−0.714196	−0.357098	−	0.934067i	$-0.616234\pi$
$839$	−20.6871	−0.714196	−0.357098	+	0.934067i	$0.616234\pi$
$840$	−0.674933	−0.0232874
$841$	−4.53041	−0.156221
$842$	34.2431	1.18009
$843$	−20.6269	−0.710427
$844$	21.3509	0.734929
$845$	3.89885	0.134124
$846$	−8.48060	−0.291569
$847$	−0.190672	−0.00655158
$848$	137.755	4.73051
$849$	9.65662	0.331414
$850$	0.534623	0.0183374
$851$	−0.368270	−0.0126241
$852$	−7.20653	−0.246892
$853$	32.4637	1.11153	0.555767	−	0.831338i	$-0.312424\pi$
$853$	32.4637	1.11153	0.555767	+	0.831338i	$0.312424\pi$
$854$	−1.43658	−0.0491587
$855$	5.91603	0.202324
$856$	−79.4830	−2.71667
$857$	−28.1159	−0.960420	−0.480210	−	0.877154i	$-0.659439\pi$
$857$	−28.1159	−0.960420	−0.480210	+	0.877154i	$0.659439\pi$
$858$	24.7531	0.845055
$859$	2.13646	0.0728952	0.0364476	−	0.999336i	$-0.488396\pi$
$859$	2.13646	0.0728952	0.0364476	+	0.999336i	$0.488396\pi$
$860$	75.2177	2.56490
$861$	0.207337	0.00706603
$862$	4.90873	0.167192
$863$	0.598649	0.0203783	0.0101891	−	0.999948i	$-0.496757\pi$
$863$	0.598649	0.0203783	0.0101891	+	0.999948i	$0.496757\pi$
$864$	−15.6672	−0.533010
$865$	−4.27648	−0.145405
$866$	−42.5271	−1.44513
$867$	−1.00000	−0.0339618
$868$	1.28199	0.0435137
$869$	−2.40953	−0.0817376
$870$	28.9599	0.981832
$871$	45.1402	1.52952
$872$	−143.701	−4.86633
$873$	8.20348	0.277646
$874$	18.1908	0.615313
$875$	−0.418213	−0.0141382
$876$	−84.6936	−2.86153
$877$	1.66164	0.0561096	0.0280548	−	0.999606i	$-0.491069\pi$
$877$	1.66164	0.0561096	0.0280548	+	0.999606i	$0.491069\pi$
$878$	66.4084	2.24118
$879$	0.523792	0.0176671
$880$	−64.1089	−2.16111
$881$	−2.40612	−0.0810641	−0.0405321	−	0.999178i	$-0.512905\pi$
$881$	−2.40612	−0.0810641	−0.0405321	+	0.999178i	$0.512905\pi$
$882$	−18.7017	−0.629718
$883$	13.5115	0.454699	0.227350	−	0.973813i	$-0.426994\pi$
$883$	13.5115	0.454699	0.227350	+	0.973813i	$0.426994\pi$
$884$	−19.7625	−0.664684
$885$	15.3694	0.516636
$886$	9.41925	0.316446
$887$	13.3168	0.447133	0.223567	−	0.974689i	$-0.428230\pi$
$887$	13.3168	0.447133	0.223567	+	0.974689i	$0.428230\pi$
$888$	1.22593	0.0411396
$889$	0.485002	0.0162664
$890$	−62.1768	−2.08417
$891$	−2.40953	−0.0807222
$892$	38.8767	1.30169
$893$	−8.56985	−0.286779
$894$	−45.8082	−1.53206
$895$	−18.6138	−0.622190
$896$	0.573953	0.0191744
$897$	−9.69179	−0.323599
$898$	−86.8394	−2.89787
$899$	−33.6062	−1.12083
$900$	−1.02847	−0.0342823
$901$	−11.3432	−0.377898
$902$	36.3667	1.21088
$903$	−0.245168	−0.00815867
$904$	−67.3057	−2.23855
$905$	−0.788132	−0.0261984
$906$	62.5862	2.07929
$907$	−10.5685	−0.350920	−0.175460	−	0.984487i	$-0.556141\pi$
$907$	−10.5685	−0.350920	−0.175460	+	0.984487i	$0.556141\pi$
$908$	106.407	3.53123
$909$	18.5641	0.615731
$910$	0.826200	0.0273883
$911$	−58.0289	−1.92258	−0.961292	−	0.275530i	$-0.911147\pi$
$911$	−58.0289	−1.92258	−0.961292	+	0.275530i	$0.911147\pi$
$912$	−32.7930	−1.08589
$913$	33.5792	1.11131
$914$	2.99708	0.0991345
$915$	32.0856	1.06072
$916$	−86.3067	−2.85166
$917$	−0.683244	−0.0225627
$918$	2.67218	0.0881951
$919$	27.9010	0.920368	0.460184	−	0.887824i	$-0.347783\pi$
$919$	27.9010	0.920368	0.460184	+	0.887824i	$0.347783\pi$
$920$	46.3514	1.52816
$921$	−14.5659	−0.479961
$922$	−56.7413	−1.86868
$923$	5.38949	0.177397
$924$	0.454687	0.0149581
$925$	0.0292264	0.000960959 0
$926$	44.3916	1.45880
$927$	14.6696	0.481812
$928$	−77.5007	−2.54409
$929$	−45.5010	−1.49284	−0.746419	−	0.665476i	$-0.768229\pi$
$929$	−45.5010	−1.49284	−0.746419	+	0.665476i	$0.768229\pi$
$930$	−39.7731	−1.30421
$931$	−18.8985	−0.619373
$932$	−113.797	−3.72754
$933$	−10.5819	−0.346436
$934$	−52.5410	−1.71919
$935$	5.27897	0.172641
$936$	32.2629	1.05455
$937$	30.6476	1.00121	0.500607	−	0.865675i	$-0.333110\pi$
$937$	30.6476	1.00121	0.500607	+	0.865675i	$0.333110\pi$
$938$	1.15178	0.0376069
$939$	−34.6390	−1.13040
$940$	−35.7427	−1.16580
$941$	10.0679	0.328203	0.164101	−	0.986443i	$-0.447528\pi$
$941$	10.0679	0.328203	0.164101	+	0.986443i	$0.447528\pi$
$942$	2.52776	0.0823588
$943$	−14.2390	−0.463685
$944$	−85.1938	−2.77282
$945$	−0.0804245	−0.00261621
$946$	−43.0021	−1.39812
$947$	−32.5830	−1.05881	−0.529403	−	0.848370i	$-0.677584\pi$
$947$	−32.5830	−1.05881	−0.529403	+	0.848370i	$0.677584\pi$
$948$	−5.14056	−0.166957
$949$	63.3390	2.05607
$950$	−1.44364	−0.0468380
$951$	14.3489	0.465295
$952$	−0.308066	−0.00998447
$953$	−45.9981	−1.49002	−0.745012	−	0.667051i	$-0.767556\pi$
$953$	−45.9981	−1.49002	−0.745012	+	0.667051i	$0.767556\pi$
$954$	30.3112	0.981362
$955$	22.2383	0.719613
$956$	−107.676	−3.48248
$957$	−11.9191	−0.385291
$958$	104.278	3.36905
$959$	−0.331831	−0.0107154
$960$	−38.5097	−1.24289
$961$	15.1542	0.488844
$962$	−1.50069	−0.0483842
$963$	−9.47113	−0.305203
$964$	−35.0241	−1.12805
$965$	−48.6745	−1.56689
$966$	−0.247292	−0.00795648
$967$	−56.6450	−1.82158	−0.910790	−	0.412870i	$-0.864527\pi$
$967$	−56.6450	−1.82158	−0.910790	+	0.412870i	$0.864527\pi$
$968$	−43.5903	−1.40104
$969$	2.70031	0.0867463
$970$	48.0266	1.54204
$971$	26.4384	0.848448	0.424224	−	0.905557i	$-0.360547\pi$
$971$	26.4384	0.848448	0.424224	+	0.905557i	$0.360547\pi$
$972$	−5.14056	−0.164883
$973$	0.357634	0.0114652
$974$	−100.261	−3.21257
$975$	0.769153	0.0246326
$976$	−177.853	−5.69294
$977$	−13.4335	−0.429775	−0.214888	−	0.976639i	$-0.568939\pi$
$977$	−13.4335	−0.429775	−0.214888	+	0.976639i	$0.568939\pi$
$978$	−8.92052	−0.285247
$979$	25.5904	0.817871
$980$	−78.8210	−2.51784
$981$	−17.1233	−0.546705
$982$	−42.0345	−1.34138
$983$	−25.5528	−0.815009	−0.407505	−	0.913203i	$-0.633601\pi$
$983$	−25.5528	−0.815009	−0.407505	+	0.913203i	$0.633601\pi$
$984$	47.4000	1.51106
$985$	36.2196	1.15405
$986$	13.2184	0.420960
$987$	0.116501	0.00370828
$988$	53.3647	1.69776
$989$	16.8370	0.535386
$990$	−14.1064	−0.448330
$991$	−44.8254	−1.42393	−0.711963	−	0.702217i	$-0.752194\pi$
$991$	−44.8254	−1.42393	−0.711963	+	0.702217i	$0.752194\pi$
$992$	106.438	3.37942
$993$	−7.34543	−0.233100
$994$	0.137516	0.00436174
$995$	−39.7568	−1.26038
$996$	71.6390	2.26997
$997$	24.6269	0.779941	0.389970	−	0.920827i	$-0.372485\pi$
$997$	24.6269	0.779941	0.389970	+	0.920827i	$0.372485\pi$
$998$	−66.5586	−2.10688
$999$	0.146081	0.00462180

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.31	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.31	✓	32	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)

\(f(q)\)	\(=\)	\(q+2.67218 q^{2} -1.00000 q^{3} +5.14056 q^{4} +2.19087 q^{5} -2.67218 q^{6} +0.0367089 q^{7} +8.39213 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.67218 q^{2} -1.00000 q^{3} +5.14056 q^{4} +2.19087 q^{5} -2.67218 q^{6} +0.0367089 q^{7} +8.39213 q^{8} +1.00000 q^{9} +5.85441 q^{10} -2.40953 q^{11} -5.14056 q^{12} +3.84442 q^{13} +0.0980927 q^{14} -2.19087 q^{15} +12.1442 q^{16} -1.00000 q^{17} +2.67218 q^{18} +2.70031 q^{19} +11.2623 q^{20} -0.0367089 q^{21} -6.43869 q^{22} +2.52100 q^{23} -8.39213 q^{24} -0.200070 q^{25} +10.2730 q^{26} -1.00000 q^{27} +0.188704 q^{28} -4.94667 q^{29} -5.85441 q^{30} +6.79369 q^{31} +15.6672 q^{32} +2.40953 q^{33} -2.67218 q^{34} +0.0804245 q^{35} +5.14056 q^{36} -0.146081 q^{37} +7.21571 q^{38} -3.84442 q^{39} +18.3861 q^{40} -5.64815 q^{41} -0.0980927 q^{42} +6.67871 q^{43} -12.3863 q^{44} +2.19087 q^{45} +6.73657 q^{46} -3.17366 q^{47} -12.1442 q^{48} -6.99865 q^{49} -0.534623 q^{50} +1.00000 q^{51} +19.7625 q^{52} +11.3432 q^{53} -2.67218 q^{54} -5.27897 q^{55} +0.308066 q^{56} -2.70031 q^{57} -13.2184 q^{58} -7.01519 q^{59} -11.2623 q^{60} -14.6451 q^{61} +18.1540 q^{62} +0.0367089 q^{63} +17.5773 q^{64} +8.42265 q^{65} +6.43869 q^{66} +11.7417 q^{67} -5.14056 q^{68} -2.52100 q^{69} +0.214909 q^{70} +1.40190 q^{71} +8.39213 q^{72} +16.4756 q^{73} -0.390355 q^{74} +0.200070 q^{75} +13.8811 q^{76} -0.0884510 q^{77} -10.2730 q^{78} +1.00000 q^{79} +26.6064 q^{80} +1.00000 q^{81} -15.0929 q^{82} -13.9360 q^{83} -0.188704 q^{84} -2.19087 q^{85} +17.8467 q^{86} +4.94667 q^{87} -20.2211 q^{88} -10.6205 q^{89} +5.85441 q^{90} +0.141124 q^{91} +12.9593 q^{92} -6.79369 q^{93} -8.48060 q^{94} +5.91603 q^{95} -15.6672 q^{96} +8.20348 q^{97} -18.7017 q^{98} -2.40953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

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