LMFDB - Embedded newform 6034.2.a.r.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.78656 q^{3} +1.00000 q^{4} -1.18496 q^{5} -1.78656 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.191811 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.78656 q^{3} +1.00000 q^{4} -1.18496 q^{5} -1.78656 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.191811 q^{9} -1.18496 q^{10} -2.39490 q^{11} -1.78656 q^{12} -0.479746 q^{13} -1.00000 q^{14} +2.11702 q^{15} +1.00000 q^{16} +1.12610 q^{17} +0.191811 q^{18} -1.80450 q^{19} -1.18496 q^{20} +1.78656 q^{21} -2.39490 q^{22} -8.54610 q^{23} -1.78656 q^{24} -3.59586 q^{25} -0.479746 q^{26} +5.01701 q^{27} -1.00000 q^{28} +9.94648 q^{29} +2.11702 q^{30} +3.16606 q^{31} +1.00000 q^{32} +4.27864 q^{33} +1.12610 q^{34} +1.18496 q^{35} +0.191811 q^{36} +0.0228153 q^{37} -1.80450 q^{38} +0.857097 q^{39} -1.18496 q^{40} -8.29465 q^{41} +1.78656 q^{42} -11.5591 q^{43} -2.39490 q^{44} -0.227290 q^{45} -8.54610 q^{46} +1.10157 q^{47} -1.78656 q^{48} +1.00000 q^{49} -3.59586 q^{50} -2.01186 q^{51} -0.479746 q^{52} +0.735579 q^{53} +5.01701 q^{54} +2.83787 q^{55} -1.00000 q^{56} +3.22386 q^{57} +9.94648 q^{58} -11.0996 q^{59} +2.11702 q^{60} +1.57498 q^{61} +3.16606 q^{62} -0.191811 q^{63} +1.00000 q^{64} +0.568482 q^{65} +4.27864 q^{66} -4.67286 q^{67} +1.12610 q^{68} +15.2682 q^{69} +1.18496 q^{70} +15.4217 q^{71} +0.191811 q^{72} +1.64844 q^{73} +0.0228153 q^{74} +6.42423 q^{75} -1.80450 q^{76} +2.39490 q^{77} +0.857097 q^{78} +3.54102 q^{79} -1.18496 q^{80} -9.53864 q^{81} -8.29465 q^{82} +4.65603 q^{83} +1.78656 q^{84} -1.33439 q^{85} -11.5591 q^{86} -17.7700 q^{87} -2.39490 q^{88} +1.46571 q^{89} -0.227290 q^{90} +0.479746 q^{91} -8.54610 q^{92} -5.65637 q^{93} +1.10157 q^{94} +2.13827 q^{95} -1.78656 q^{96} +7.81913 q^{97} +1.00000 q^{98} -0.459368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.78656	−1.03147	−0.515737	−	0.856747i	$-0.672482\pi$
$3$	−1.78656	−1.03147	−0.515737	+	0.856747i	$0.672482\pi$
$4$	1.00000	0.500000
$5$	−1.18496	−0.529932	−0.264966	−	0.964258i	$-0.585361\pi$
$5$	−1.18496	−0.529932	−0.264966	+	0.964258i	$0.585361\pi$
$6$	−1.78656	−0.729362
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	0.191811	0.0639371
$10$	−1.18496	−0.374719
$11$	−2.39490	−0.722088	−0.361044	−	0.932549i	$-0.617580\pi$
$11$	−2.39490	−0.722088	−0.361044	+	0.932549i	$0.617580\pi$
$12$	−1.78656	−0.515737
$13$	−0.479746	−0.133058	−0.0665288	−	0.997785i	$-0.521192\pi$
$13$	−0.479746	−0.133058	−0.0665288	+	0.997785i	$0.521192\pi$
$14$	−1.00000	−0.267261
$15$	2.11702	0.546611
$16$	1.00000	0.250000
$17$	1.12610	0.273121	0.136560	−	0.990632i	$-0.456395\pi$
$17$	1.12610	0.273121	0.136560	+	0.990632i	$0.456395\pi$
$18$	0.191811	0.0452104
$19$	−1.80450	−0.413981	−0.206991	−	0.978343i	$-0.566367\pi$
$19$	−1.80450	−0.413981	−0.206991	+	0.978343i	$0.566367\pi$
$20$	−1.18496	−0.264966
$21$	1.78656	0.389860
$22$	−2.39490	−0.510594
$23$	−8.54610	−1.78199	−0.890993	−	0.454017i	$-0.849991\pi$
$23$	−8.54610	−1.78199	−0.890993	+	0.454017i	$0.849991\pi$
$24$	−1.78656	−0.364681
$25$	−3.59586	−0.719172
$26$	−0.479746	−0.0940860
$27$	5.01701	0.965524
$28$	−1.00000	−0.188982
$29$	9.94648	1.84702	0.923508	−	0.383580i	$-0.125309\pi$
$29$	9.94648	1.84702	0.923508	+	0.383580i	$0.125309\pi$
$30$	2.11702	0.386512
$31$	3.16606	0.568642	0.284321	−	0.958729i	$-0.408232\pi$
$31$	3.16606	0.568642	0.284321	+	0.958729i	$0.408232\pi$
$32$	1.00000	0.176777
$33$	4.27864	0.744815
$34$	1.12610	0.193125
$35$	1.18496	0.200296
$36$	0.191811	0.0319686
$37$	0.0228153	0.00375081	0.00187540	−	0.999998i	$-0.499403\pi$
$37$	0.0228153	0.00375081	0.00187540	+	0.999998i	$0.499403\pi$
$38$	−1.80450	−0.292729
$39$	0.857097	0.137245
$40$	−1.18496	−0.187359
$41$	−8.29465	−1.29541	−0.647703	−	0.761893i	$-0.724270\pi$
$41$	−8.29465	−1.29541	−0.647703	+	0.761893i	$0.724270\pi$
$42$	1.78656	0.275673
$43$	−11.5591	−1.76275	−0.881375	−	0.472417i	$-0.843382\pi$
$43$	−11.5591	−1.76275	−0.881375	+	0.472417i	$0.843382\pi$
$44$	−2.39490	−0.361044
$45$	−0.227290	−0.0338823
$46$	−8.54610	−1.26005
$47$	1.10157	0.160681	0.0803405	−	0.996767i	$-0.474399\pi$
$47$	1.10157	0.160681	0.0803405	+	0.996767i	$0.474399\pi$
$48$	−1.78656	−0.257868
$49$	1.00000	0.142857
$50$	−3.59586	−0.508531
$51$	−2.01186	−0.281717
$52$	−0.479746	−0.0665288
$53$	0.735579	0.101040	0.0505198	−	0.998723i	$-0.483912\pi$
$53$	0.735579	0.101040	0.0505198	+	0.998723i	$0.483912\pi$
$54$	5.01701	0.682728
$55$	2.83787	0.382658
$56$	−1.00000	−0.133631
$57$	3.22386	0.427011
$58$	9.94648	1.30604
$59$	−11.0996	−1.44505	−0.722524	−	0.691346i	$-0.757018\pi$
$59$	−11.0996	−1.44505	−0.722524	+	0.691346i	$0.757018\pi$
$60$	2.11702	0.273306
$61$	1.57498	0.201655	0.100828	−	0.994904i	$-0.467851\pi$
$61$	1.57498	0.201655	0.100828	+	0.994904i	$0.467851\pi$
$62$	3.16606	0.402090
$63$	−0.191811	−0.0241660
$64$	1.00000	0.125000
$65$	0.568482	0.0705116
$66$	4.27864	0.526664
$67$	−4.67286	−0.570881	−0.285440	−	0.958396i	$-0.592140\pi$
$67$	−4.67286	−0.570881	−0.285440	+	0.958396i	$0.592140\pi$
$68$	1.12610	0.136560
$69$	15.2682	1.83807
$70$	1.18496	0.141630
$71$	15.4217	1.83022	0.915110	−	0.403204i	$-0.132104\pi$
$71$	15.4217	1.83022	0.915110	+	0.403204i	$0.132104\pi$
$72$	0.191811	0.0226052
$73$	1.64844	0.192936	0.0964678	−	0.995336i	$-0.469246\pi$
$73$	1.64844	0.192936	0.0964678	+	0.995336i	$0.469246\pi$
$74$	0.0228153	0.00265222
$75$	6.42423	0.741806
$76$	−1.80450	−0.206991
$77$	2.39490	0.272924
$78$	0.857097	0.0970472
$79$	3.54102	0.398396	0.199198	−	0.979959i	$-0.436166\pi$
$79$	3.54102	0.398396	0.199198	+	0.979959i	$0.436166\pi$
$80$	−1.18496	−0.132483
$81$	−9.53864	−1.05985
$82$	−8.29465	−0.915990
$83$	4.65603	0.511065	0.255533	−	0.966800i	$-0.417749\pi$
$83$	4.65603	0.511065	0.255533	+	0.966800i	$0.417749\pi$
$84$	1.78656	0.194930
$85$	−1.33439	−0.144735
$86$	−11.5591	−1.24645
$87$	−17.7700	−1.90515
$88$	−2.39490	−0.255297
$89$	1.46571	0.155365	0.0776826	−	0.996978i	$-0.475248\pi$
$89$	1.46571	0.155365	0.0776826	+	0.996978i	$0.475248\pi$
$90$	−0.227290	−0.0239584
$91$	0.479746	0.0502911
$92$	−8.54610	−0.890993
$93$	−5.65637	−0.586539
$94$	1.10157	0.113619
$95$	2.13827	0.219382
$96$	−1.78656	−0.182340
$97$	7.81913	0.793912	0.396956	−	0.917838i	$-0.370067\pi$
$97$	7.81913	0.793912	0.396956	+	0.917838i	$0.370067\pi$
$98$	1.00000	0.101015
$99$	−0.459368	−0.0461682
$100$	−3.59586	−0.359586
$101$	3.41751	0.340055	0.170027	−	0.985439i	$-0.445614\pi$
$101$	3.41751	0.340055	0.170027	+	0.985439i	$0.445614\pi$
$102$	−2.01186	−0.199204
$103$	14.4262	1.42145	0.710726	−	0.703469i	$-0.248367\pi$
$103$	14.4262	1.42145	0.710726	+	0.703469i	$0.248367\pi$
$104$	−0.479746	−0.0470430
$105$	−2.11702	−0.206600
$106$	0.735579	0.0714457
$107$	−17.5047	−1.69224	−0.846119	−	0.532994i	$-0.821067\pi$
$107$	−17.5047	−1.69224	−0.846119	+	0.532994i	$0.821067\pi$
$108$	5.01701	0.482762
$109$	16.7238	1.60185	0.800925	−	0.598765i	$-0.204341\pi$
$109$	16.7238	1.60185	0.800925	+	0.598765i	$0.204341\pi$
$110$	2.83787	0.270580
$111$	−0.0407610	−0.00386886
$112$	−1.00000	−0.0944911
$113$	16.0580	1.51061	0.755306	−	0.655372i	$-0.227488\pi$
$113$	16.0580	1.51061	0.755306	+	0.655372i	$0.227488\pi$
$114$	3.22386	0.301942
$115$	10.1268	0.944332
$116$	9.94648	0.923508
$117$	−0.0920207	−0.00850732
$118$	−11.0996	−1.02180
$119$	−1.12610	−0.103230
$120$	2.11702	0.193256
$121$	−5.26447	−0.478588
$122$	1.57498	0.142592
$123$	14.8189	1.33618
$124$	3.16606	0.284321
$125$	10.1858	0.911045
$126$	−0.191811	−0.0170879
$127$	−9.81892	−0.871288	−0.435644	−	0.900119i	$-0.643479\pi$
$127$	−9.81892	−0.871288	−0.435644	+	0.900119i	$0.643479\pi$
$128$	1.00000	0.0883883
$129$	20.6511	1.81823
$130$	0.568482	0.0498592
$131$	13.1347	1.14758	0.573790	−	0.819002i	$-0.305473\pi$
$131$	13.1347	1.14758	0.573790	+	0.819002i	$0.305473\pi$
$132$	4.27864	0.372407
$133$	1.80450	0.156470
$134$	−4.67286	−0.403674
$135$	−5.94498	−0.511662
$136$	1.12610	0.0965627
$137$	−12.5461	−1.07189	−0.535943	−	0.844254i	$-0.680044\pi$
$137$	−12.5461	−1.07189	−0.535943	+	0.844254i	$0.680044\pi$
$138$	15.2682	1.29971
$139$	11.4304	0.969512	0.484756	−	0.874649i	$-0.338908\pi$
$139$	11.4304	0.969512	0.484756	+	0.874649i	$0.338908\pi$
$140$	1.18496	0.100148
$141$	−1.96803	−0.165738
$142$	15.4217	1.29416
$143$	1.14894	0.0960794
$144$	0.191811	0.0159843
$145$	−11.7862	−0.978793
$146$	1.64844	0.136426
$147$	−1.78656	−0.147353
$148$	0.0228153	0.00187540
$149$	14.7095	1.20505	0.602526	−	0.798099i	$-0.294161\pi$
$149$	14.7095	1.20505	0.602526	+	0.798099i	$0.294161\pi$
$150$	6.42423	0.524536
$151$	19.8836	1.61810	0.809051	−	0.587738i	$-0.199982\pi$
$151$	19.8836	1.61810	0.809051	+	0.587738i	$0.199982\pi$
$152$	−1.80450	−0.146365
$153$	0.216000	0.0174625
$154$	2.39490	0.192986
$155$	−3.75167	−0.301342
$156$	0.857097	0.0686227
$157$	2.22346	0.177452	0.0887259	−	0.996056i	$-0.471720\pi$
$157$	2.22346	0.177452	0.0887259	+	0.996056i	$0.471720\pi$
$158$	3.54102	0.281708
$159$	−1.31416	−0.104220
$160$	−1.18496	−0.0936797
$161$	8.54610	0.673527
$162$	−9.53864	−0.749427
$163$	−1.00030	−0.0783498	−0.0391749	−	0.999232i	$-0.512473\pi$
$163$	−1.00030	−0.0783498	−0.0391749	+	0.999232i	$0.512473\pi$
$164$	−8.29465	−0.647703
$165$	−5.07003	−0.394702
$166$	4.65603	0.361378
$167$	−1.45487	−0.112581	−0.0562904	−	0.998414i	$-0.517927\pi$
$167$	−1.45487	−0.112581	−0.0562904	+	0.998414i	$0.517927\pi$
$168$	1.78656	0.137836
$169$	−12.7698	−0.982296
$170$	−1.33439	−0.102343
$171$	−0.346124	−0.0264688
$172$	−11.5591	−0.881375
$173$	10.5036	0.798576	0.399288	−	0.916826i	$-0.369257\pi$
$173$	10.5036	0.798576	0.399288	+	0.916826i	$0.369257\pi$
$174$	−17.7700	−1.34714
$175$	3.59586	0.271821
$176$	−2.39490	−0.180522
$177$	19.8302	1.49053
$178$	1.46571	0.109860
$179$	−14.6617	−1.09587	−0.547933	−	0.836523i	$-0.684585\pi$
$179$	−14.6617	−1.09587	−0.547933	+	0.836523i	$0.684585\pi$
$180$	−0.227290	−0.0169412
$181$	−15.5550	−1.15619	−0.578095	−	0.815969i	$-0.696204\pi$
$181$	−15.5550	−1.15619	−0.578095	+	0.815969i	$0.696204\pi$
$182$	0.479746	0.0355612
$183$	−2.81380	−0.208002
$184$	−8.54610	−0.630027
$185$	−0.0270353	−0.00198768
$186$	−5.65637	−0.414745
$187$	−2.69690	−0.197217
$188$	1.10157	0.0803405
$189$	−5.01701	−0.364934
$190$	2.13827	0.155127
$191$	−11.6972	−0.846376	−0.423188	−	0.906042i	$-0.639089\pi$
$191$	−11.6972	−0.846376	−0.423188	+	0.906042i	$0.639089\pi$
$192$	−1.78656	−0.128934
$193$	−8.34211	−0.600478	−0.300239	−	0.953864i	$-0.597066\pi$
$193$	−8.34211	−0.600478	−0.300239	+	0.953864i	$0.597066\pi$
$194$	7.81913	0.561381
$195$	−1.01563	−0.0727308
$196$	1.00000	0.0714286
$197$	−2.30824	−0.164455	−0.0822276	−	0.996614i	$-0.526203\pi$
$197$	−2.30824	−0.164455	−0.0822276	+	0.996614i	$0.526203\pi$
$198$	−0.459368	−0.0326459
$199$	1.57909	0.111939	0.0559693	−	0.998432i	$-0.482175\pi$
$199$	1.57909	0.111939	0.0559693	+	0.998432i	$0.482175\pi$
$200$	−3.59586	−0.254266
$201$	8.34836	0.588848
$202$	3.41751	0.240455
$203$	−9.94648	−0.698106
$204$	−2.01186	−0.140858
$205$	9.82886	0.686478
$206$	14.4262	1.00512
$207$	−1.63924	−0.113935
$208$	−0.479746	−0.0332644
$209$	4.32160	0.298931
$210$	−2.11702	−0.146088
$211$	−11.3122	−0.778764	−0.389382	−	0.921076i	$-0.627311\pi$
$211$	−11.3122	−0.778764	−0.389382	+	0.921076i	$0.627311\pi$
$212$	0.735579	0.0505198
$213$	−27.5519	−1.88782
$214$	−17.5047	−1.19659
$215$	13.6972	0.934139
$216$	5.01701	0.341364
$217$	−3.16606	−0.214926
$218$	16.7238	1.13268
$219$	−2.94505	−0.199008
$220$	2.83787	0.191329
$221$	−0.540244	−0.0363408
$222$	−0.0407610	−0.00273570
$223$	16.7083	1.11887	0.559437	−	0.828873i	$-0.311018\pi$
$223$	16.7083	1.11887	0.559437	+	0.828873i	$0.311018\pi$
$224$	−1.00000	−0.0668153
$225$	−0.689726	−0.0459818
$226$	16.0580	1.06816
$227$	−15.7664	−1.04645	−0.523226	−	0.852194i	$-0.675272\pi$
$227$	−15.7664	−1.04645	−0.523226	+	0.852194i	$0.675272\pi$
$228$	3.22386	0.213505
$229$	1.06383	0.0703000	0.0351500	−	0.999382i	$-0.488809\pi$
$229$	1.06383	0.0703000	0.0351500	+	0.999382i	$0.488809\pi$
$230$	10.1268	0.667744
$231$	−4.27864	−0.281514
$232$	9.94648	0.653019
$233$	1.09089	0.0714668	0.0357334	−	0.999361i	$-0.488623\pi$
$233$	1.09089	0.0714668	0.0357334	+	0.999361i	$0.488623\pi$
$234$	−0.0920207	−0.00601558
$235$	−1.30533	−0.0851501
$236$	−11.0996	−0.722524
$237$	−6.32626	−0.410935
$238$	−1.12610	−0.0729945
$239$	13.2092	0.854429	0.427215	−	0.904150i	$-0.359495\pi$
$239$	13.2092	0.854429	0.427215	+	0.904150i	$0.359495\pi$
$240$	2.11702	0.136653
$241$	23.9670	1.54385	0.771926	−	0.635713i	$-0.219294\pi$
$241$	23.9670	1.54385	0.771926	+	0.635713i	$0.219294\pi$
$242$	−5.26447	−0.338413
$243$	1.99037	0.127682
$244$	1.57498	0.100828
$245$	−1.18496	−0.0757046
$246$	14.8189	0.944820
$247$	0.865703	0.0550834
$248$	3.16606	0.201045
$249$	−8.31829	−0.527150
$250$	10.1858	0.644206
$251$	10.0467	0.634142	0.317071	−	0.948402i	$-0.397301\pi$
$251$	10.0467	0.634142	0.317071	+	0.948402i	$0.397301\pi$
$252$	−0.191811	−0.0120830
$253$	20.4670	1.28675
$254$	−9.81892	−0.616094
$255$	2.38398	0.149291
$256$	1.00000	0.0625000
$257$	20.9859	1.30906	0.654532	−	0.756034i	$-0.272866\pi$
$257$	20.9859	1.30906	0.654532	+	0.756034i	$0.272866\pi$
$258$	20.6511	1.28568
$259$	−0.0228153	−0.00141767
$260$	0.568482	0.0352558
$261$	1.90785	0.118093
$262$	13.1347	0.811462
$263$	0.0214076	0.00132005	0.000660026	−	1.00000i	$-0.499790\pi$
$263$	0.0214076	0.00132005	0.000660026		1.00000i	$0.499790\pi$
$264$	4.27864	0.263332
$265$	−0.871635	−0.0535441
$266$	1.80450	0.110641
$267$	−2.61859	−0.160255
$268$	−4.67286	−0.285440
$269$	14.1401	0.862140	0.431070	−	0.902318i	$-0.358136\pi$
$269$	14.1401	0.862140	0.431070	+	0.902318i	$0.358136\pi$
$270$	−5.94498	−0.361800
$271$	22.5686	1.37095	0.685473	−	0.728098i	$-0.259595\pi$
$271$	22.5686	1.37095	0.685473	+	0.728098i	$0.259595\pi$
$272$	1.12610	0.0682801
$273$	−0.857097	−0.0518739
$274$	−12.5461	−0.757938
$275$	8.61171	0.519305
$276$	15.2682	0.919035
$277$	10.8302	0.650724	0.325362	−	0.945590i	$-0.394514\pi$
$277$	10.8302	0.650724	0.325362	+	0.945590i	$0.394514\pi$
$278$	11.4304	0.685548
$279$	0.607286	0.0363573
$280$	1.18496	0.0708152
$281$	23.6799	1.41262	0.706312	−	0.707901i	$-0.250358\pi$
$281$	23.6799	1.41262	0.706312	+	0.707901i	$0.250358\pi$
$282$	−1.96803	−0.117195
$283$	0.177536	0.0105534	0.00527671	−	0.999986i	$-0.498320\pi$
$283$	0.177536	0.0105534	0.00527671	+	0.999986i	$0.498320\pi$
$284$	15.4217	0.915110
$285$	−3.82016	−0.226287
$286$	1.14894	0.0679384
$287$	8.29465	0.489617
$288$	0.191811	0.0113026
$289$	−15.7319	−0.925405
$290$	−11.7862	−0.692111
$291$	−13.9694	−0.818899
$292$	1.64844	0.0964678
$293$	31.8386	1.86003	0.930015	−	0.367522i	$-0.119794\pi$
$293$	31.8386	1.86003	0.930015	+	0.367522i	$0.119794\pi$
$294$	−1.78656	−0.104195
$295$	13.1527	0.765777
$296$	0.0228153	0.00132611
$297$	−12.0152	−0.697194
$298$	14.7095	0.852101
$299$	4.09996	0.237107
$300$	6.42423	0.370903
$301$	11.5591	0.666257
$302$	19.8836	1.14417
$303$	−6.10559	−0.350757
$304$	−1.80450	−0.103495
$305$	−1.86629	−0.106864
$306$	0.216000	0.0123479
$307$	24.2873	1.38615	0.693074	−	0.720867i	$-0.256256\pi$
$307$	24.2873	1.38615	0.693074	+	0.720867i	$0.256256\pi$
$308$	2.39490	0.136462
$309$	−25.7733	−1.46619
$310$	−3.75167	−0.213081
$311$	23.7469	1.34656	0.673282	−	0.739386i	$-0.264884\pi$
$311$	23.7469	1.34656	0.673282	+	0.739386i	$0.264884\pi$
$312$	0.857097	0.0485236
$313$	−6.07796	−0.343546	−0.171773	−	0.985137i	$-0.554950\pi$
$313$	−6.07796	−0.343546	−0.171773	+	0.985137i	$0.554950\pi$
$314$	2.22346	0.125477
$315$	0.227290	0.0128063
$316$	3.54102	0.199198
$317$	4.52631	0.254223	0.127111	−	0.991888i	$-0.459429\pi$
$317$	4.52631	0.254223	0.127111	+	0.991888i	$0.459429\pi$
$318$	−1.31416	−0.0736944
$319$	−23.8208	−1.33371
$320$	−1.18496	−0.0662415
$321$	31.2732	1.74550
$322$	8.54610	0.476256
$323$	−2.03206	−0.113067
$324$	−9.53864	−0.529925
$325$	1.72510	0.0956913
$326$	−1.00030	−0.0554017
$327$	−29.8782	−1.65227
$328$	−8.29465	−0.457995
$329$	−1.10157	−0.0607317
$330$	−5.07003	−0.279096
$331$	−20.6344	−1.13417	−0.567085	−	0.823659i	$-0.691929\pi$
$331$	−20.6344	−1.13417	−0.567085	+	0.823659i	$0.691929\pi$
$332$	4.65603	0.255533
$333$	0.00437623	0.000239816 0
$334$	−1.45487	−0.0796067
$335$	5.53717	0.302528
$336$	1.78656	0.0974651
$337$	−3.06520	−0.166972	−0.0834861	−	0.996509i	$-0.526605\pi$
$337$	−3.06520	−0.166972	−0.0834861	+	0.996509i	$0.526605\pi$
$338$	−12.7698	−0.694588
$339$	−28.6887	−1.55816
$340$	−1.33439	−0.0723677
$341$	−7.58239	−0.410609
$342$	−0.346124	−0.0187162
$343$	−1.00000	−0.0539949
$344$	−11.5591	−0.623227
$345$	−18.0922	−0.974053
$346$	10.5036	0.564678
$347$	26.8993	1.44403	0.722014	−	0.691879i	$-0.243217\pi$
$347$	26.8993	1.44403	0.722014	+	0.691879i	$0.243217\pi$
$348$	−17.7700	−0.952573
$349$	19.7912	1.05940	0.529700	−	0.848185i	$-0.322304\pi$
$349$	19.7912	1.05940	0.529700	+	0.848185i	$0.322304\pi$
$350$	3.59586	0.192207
$351$	−2.40689	−0.128470
$352$	−2.39490	−0.127648
$353$	−22.9605	−1.22206	−0.611032	−	0.791606i	$-0.709246\pi$
$353$	−22.9605	−1.22206	−0.611032	+	0.791606i	$0.709246\pi$
$354$	19.8302	1.05396
$355$	−18.2742	−0.969893
$356$	1.46571	0.0776826
$357$	2.01186	0.106479
$358$	−14.6617	−0.774894
$359$	−4.37256	−0.230775	−0.115387	−	0.993321i	$-0.536811\pi$
$359$	−4.37256	−0.230775	−0.115387	+	0.993321i	$0.536811\pi$
$360$	−0.227290	−0.0119792
$361$	−15.7438	−0.828619
$362$	−15.5550	−0.817550
$363$	9.40532	0.493651
$364$	0.479746	0.0251455
$365$	−1.95335	−0.102243
$366$	−2.81380	−0.147080
$367$	22.4321	1.17095	0.585474	−	0.810692i	$-0.300909\pi$
$367$	22.4321	1.17095	0.585474	+	0.810692i	$0.300909\pi$
$368$	−8.54610	−0.445496
$369$	−1.59101	−0.0828245
$370$	−0.0270353	−0.00140550
$371$	−0.735579	−0.0381894
$372$	−5.65637	−0.293269
$373$	30.5732	1.58302	0.791511	−	0.611155i	$-0.209295\pi$
$373$	30.5732	1.58302	0.791511	+	0.611155i	$0.209295\pi$
$374$	−2.69690	−0.139454
$375$	−18.1976	−0.939718
$376$	1.10157	0.0568093
$377$	−4.77179	−0.245760
$378$	−5.01701	−0.258047
$379$	−18.0859	−0.929008	−0.464504	−	0.885571i	$-0.653767\pi$
$379$	−18.0859	−0.929008	−0.464504	+	0.885571i	$0.653767\pi$
$380$	2.13827	0.109691
$381$	17.5421	0.898710
$382$	−11.6972	−0.598479
$383$	19.2671	0.984504	0.492252	−	0.870453i	$-0.336174\pi$
$383$	19.2671	0.984504	0.492252	+	0.870453i	$0.336174\pi$
$384$	−1.78656	−0.0911702
$385$	−2.83787	−0.144631
$386$	−8.34211	−0.424602
$387$	−2.21717	−0.112705
$388$	7.81913	0.396956
$389$	13.1537	0.666918	0.333459	−	0.942765i	$-0.391784\pi$
$389$	13.1537	0.666918	0.333459	+	0.942765i	$0.391784\pi$
$390$	−1.01563	−0.0514284
$391$	−9.62381	−0.486697
$392$	1.00000	0.0505076
$393$	−23.4659	−1.18370
$394$	−2.30824	−0.116287
$395$	−4.19598	−0.211123
$396$	−0.459368	−0.0230841
$397$	−31.9145	−1.60174	−0.800871	−	0.598837i	$-0.795630\pi$
$397$	−31.9145	−1.60174	−0.800871	+	0.598837i	$0.795630\pi$
$398$	1.57909	0.0791525
$399$	−3.22386	−0.161395
$400$	−3.59586	−0.179793
$401$	−35.3065	−1.76312	−0.881561	−	0.472069i	$-0.843507\pi$
$401$	−35.3065	−1.76312	−0.881561	+	0.472069i	$0.843507\pi$
$402$	8.34836	0.416379
$403$	−1.51891	−0.0756621
$404$	3.41751	0.170027
$405$	11.3030	0.561648
$406$	−9.94648	−0.493636
$407$	−0.0546402	−0.00270842
$408$	−2.01186	−0.0996018
$409$	15.2664	0.754873	0.377436	−	0.926036i	$-0.376806\pi$
$409$	15.2664	0.754873	0.377436	+	0.926036i	$0.376806\pi$
$410$	9.82886	0.485413
$411$	22.4144	1.10562
$412$	14.4262	0.710726
$413$	11.0996	0.546177
$414$	−1.63924	−0.0805642
$415$	−5.51723	−0.270830
$416$	−0.479746	−0.0235215
$417$	−20.4211	−1.00003
$418$	4.32160	0.211376
$419$	9.78691	0.478122	0.239061	−	0.971005i	$-0.423160\pi$
$419$	9.78691	0.478122	0.239061	+	0.971005i	$0.423160\pi$
$420$	−2.11702	−0.103300
$421$	3.73801	0.182179	0.0910896	−	0.995843i	$-0.470965\pi$
$421$	3.73801	0.182179	0.0910896	+	0.995843i	$0.470965\pi$
$422$	−11.3122	−0.550669
$423$	0.211294	0.0102735
$424$	0.735579	0.0357229
$425$	−4.04931	−0.196421
$426$	−27.5519	−1.33489
$427$	−1.57498	−0.0762185
$428$	−17.5047	−0.846119
$429$	−2.05266	−0.0991033
$430$	13.6972	0.660536
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	5.01701	0.241381
$433$	32.4534	1.55961	0.779804	−	0.626023i	$-0.215318\pi$
$433$	32.4534	1.55961	0.779804	+	0.626023i	$0.215318\pi$
$434$	−3.16606	−0.151976
$435$	21.0569	1.00960
$436$	16.7238	0.800925
$437$	15.4215	0.737709
$438$	−2.94505	−0.140720
$439$	−15.7435	−0.751398	−0.375699	−	0.926742i	$-0.622597\pi$
$439$	−15.7435	−0.751398	−0.375699	+	0.926742i	$0.622597\pi$
$440$	2.83787	0.135290
$441$	0.191811	0.00913387
$442$	−0.540244	−0.0256968
$443$	3.71705	0.176602	0.0883011	−	0.996094i	$-0.471856\pi$
$443$	3.71705	0.176602	0.0883011	+	0.996094i	$0.471856\pi$
$444$	−0.0407610	−0.00193443
$445$	−1.73682	−0.0823331
$446$	16.7083	0.791163
$447$	−26.2795	−1.24298
$448$	−1.00000	−0.0472456
$449$	24.8302	1.17181	0.585905	−	0.810380i	$-0.300739\pi$
$449$	24.8302	1.17181	0.585905	+	0.810380i	$0.300739\pi$
$450$	−0.689726	−0.0325140
$451$	19.8648	0.935398
$452$	16.0580	0.755306
$453$	−35.5233	−1.66903
$454$	−15.7664	−0.739953
$455$	−0.568482	−0.0266509
$456$	3.22386	0.150971
$457$	−38.2102	−1.78740	−0.893698	−	0.448669i	$-0.851898\pi$
$457$	−38.2102	−1.78740	−0.893698	+	0.448669i	$0.851898\pi$
$458$	1.06383	0.0497096
$459$	5.64968	0.263704
$460$	10.1268	0.472166
$461$	−20.1268	−0.937401	−0.468700	−	0.883357i	$-0.655278\pi$
$461$	−20.1268	−0.937401	−0.468700	+	0.883357i	$0.655278\pi$
$462$	−4.27864	−0.199060
$463$	−16.7340	−0.777694	−0.388847	−	0.921302i	$-0.627127\pi$
$463$	−16.7340	−0.777694	−0.388847	+	0.921302i	$0.627127\pi$
$464$	9.94648	0.461754
$465$	6.70260	0.310826
$466$	1.09089	0.0505347
$467$	−0.415953	−0.0192480	−0.00962401	−	0.999954i	$-0.503063\pi$
$467$	−0.415953	−0.0192480	−0.00962401	+	0.999954i	$0.503063\pi$
$468$	−0.0920207	−0.00425366
$469$	4.67286	0.215773
$470$	−1.30533	−0.0602102
$471$	−3.97236	−0.183037
$472$	−11.0996	−0.510901
$473$	27.6829	1.27286
$474$	−6.32626	−0.290575
$475$	6.48874	0.297724
$476$	−1.12610	−0.0516149
$477$	0.141092	0.00646017
$478$	13.2092	0.604173
$479$	−36.8549	−1.68394	−0.841972	−	0.539522i	$-0.818605\pi$
$479$	−36.8549	−1.68394	−0.841972	+	0.539522i	$0.818605\pi$
$480$	2.11702	0.0966281
$481$	−0.0109455	−0.000499074 0
$482$	23.9670	1.09167
$483$	−15.2682	−0.694725
$484$	−5.26447	−0.239294
$485$	−9.26539	−0.420720
$486$	1.99037	0.0902850
$487$	−26.6668	−1.20839	−0.604194	−	0.796837i	$-0.706505\pi$
$487$	−26.6668	−1.20839	−0.604194	+	0.796837i	$0.706505\pi$
$488$	1.57498	0.0712959
$489$	1.78711	0.0808157
$490$	−1.18496	−0.0535313
$491$	14.3522	0.647707	0.323853	−	0.946107i	$-0.395022\pi$
$491$	14.3522	0.647707	0.323853	+	0.946107i	$0.395022\pi$
$492$	14.8189	0.668088
$493$	11.2008	0.504458
$494$	0.865703	0.0389498
$495$	0.544335	0.0244660
$496$	3.16606	0.142160
$497$	−15.4217	−0.691758
$498$	−8.31829	−0.372751
$499$	−33.4327	−1.49665	−0.748326	−	0.663331i	$-0.769142\pi$
$499$	−33.4327	−1.49665	−0.748326	+	0.663331i	$0.769142\pi$
$500$	10.1858	0.455522
$501$	2.59921	0.116124
$502$	10.0467	0.448406
$503$	−31.7718	−1.41664	−0.708318	−	0.705893i	$-0.750546\pi$
$503$	−31.7718	−1.41664	−0.708318	+	0.705893i	$0.750546\pi$
$504$	−0.191811	−0.00854395
$505$	−4.04963	−0.180206
$506$	20.4670	0.909871
$507$	22.8141	1.01321
$508$	−9.81892	−0.435644
$509$	26.6934	1.18317	0.591583	−	0.806244i	$-0.298503\pi$
$509$	26.6934	1.18317	0.591583	+	0.806244i	$0.298503\pi$
$510$	2.38398	0.105564
$511$	−1.64844	−0.0729228
$512$	1.00000	0.0441942
$513$	−9.05321	−0.399709
$514$	20.9859	0.925649
$515$	−17.0945	−0.753273
$516$	20.6511	0.909115
$517$	−2.63816	−0.116026
$518$	−0.0228153	−0.00100245
$519$	−18.7654	−0.823710
$520$	0.568482	0.0249296
$521$	−17.9110	−0.784695	−0.392347	−	0.919817i	$-0.628337\pi$
$521$	−17.9110	−0.784695	−0.392347	+	0.919817i	$0.628337\pi$
$522$	1.90785	0.0835042
$523$	1.92026	0.0839670	0.0419835	−	0.999118i	$-0.486632\pi$
$523$	1.92026	0.0839670	0.0419835	+	0.999118i	$0.486632\pi$
$524$	13.1347	0.573790
$525$	−6.42423	−0.280376
$526$	0.0214076	0.000933418 0
$527$	3.56532	0.155308
$528$	4.27864	0.186204
$529$	50.0359	2.17547
$530$	−0.871635	−0.0378614
$531$	−2.12903	−0.0923921
$532$	1.80450	0.0782351
$533$	3.97932	0.172364
$534$	−2.61859	−0.113317
$535$	20.7424	0.896772
$536$	−4.67286	−0.201837
$537$	26.1940	1.13036
$538$	14.1401	0.609625
$539$	−2.39490	−0.103155
$540$	−5.94498	−0.255831
$541$	5.79893	0.249315	0.124658	−	0.992200i	$-0.460217\pi$
$541$	5.79893	0.249315	0.124658	+	0.992200i	$0.460217\pi$
$542$	22.5686	0.969405
$543$	27.7899	1.19258
$544$	1.12610	0.0482813
$545$	−19.8171	−0.848872
$546$	−0.857097	−0.0366804
$547$	0.839364	0.0358886	0.0179443	−	0.999839i	$-0.494288\pi$
$547$	0.839364	0.0358886	0.0179443	+	0.999839i	$0.494288\pi$
$548$	−12.5461	−0.535943
$549$	0.302099	0.0128933
$550$	8.61171	0.367204
$551$	−17.9485	−0.764630
$552$	15.2682	0.649856
$553$	−3.54102	−0.150579
$554$	10.8302	0.460131
$555$	0.0483003	0.00205023
$556$	11.4304	0.484756
$557$	−28.8853	−1.22391	−0.611954	−	0.790893i	$-0.709616\pi$
$557$	−28.8853	−1.22391	−0.611954	+	0.790893i	$0.709616\pi$
$558$	0.607286	0.0257085
$559$	5.54545	0.234548
$560$	1.18496	0.0500739
$561$	4.81819	0.203424
$562$	23.6799	0.998876
$563$	28.3623	1.19533	0.597664	−	0.801747i	$-0.296096\pi$
$563$	28.3623	1.19533	0.597664	+	0.801747i	$0.296096\pi$
$564$	−1.96803	−0.0828691
$565$	−19.0282	−0.800523
$566$	0.177536	0.00746239
$567$	9.53864	0.400585
$568$	15.4217	0.647080
$569$	16.1802	0.678309	0.339154	−	0.940731i	$-0.389859\pi$
$569$	16.1802	0.678309	0.339154	+	0.940731i	$0.389859\pi$
$570$	−3.82016	−0.160009
$571$	10.9799	0.459496	0.229748	−	0.973250i	$-0.426210\pi$
$571$	10.9799	0.459496	0.229748	+	0.973250i	$0.426210\pi$
$572$	1.14894	0.0480397
$573$	20.8977	0.873015
$574$	8.29465	0.346212
$575$	30.7306	1.28155
$576$	0.191811	0.00799214
$577$	−20.4099	−0.849674	−0.424837	−	0.905270i	$-0.639669\pi$
$577$	−20.4099	−0.849674	−0.424837	+	0.905270i	$0.639669\pi$
$578$	−15.7319	−0.654360
$579$	14.9037	0.619377
$580$	−11.7862	−0.489397
$581$	−4.65603	−0.193165
$582$	−13.9694	−0.579049
$583$	−1.76163	−0.0729595
$584$	1.64844	0.0682130
$585$	0.109041	0.00450830
$586$	31.8386	1.31524
$587$	−12.0415	−0.497007	−0.248504	−	0.968631i	$-0.579939\pi$
$587$	−12.0415	−0.497007	−0.248504	+	0.968631i	$0.579939\pi$
$588$	−1.78656	−0.0736767
$589$	−5.71317	−0.235407
$590$	13.1527	0.541486
$591$	4.12382	0.169631
$592$	0.0228153	0.000937702 0
$593$	4.80823	0.197450	0.0987252	−	0.995115i	$-0.468524\pi$
$593$	4.80823	0.197450	0.0987252	+	0.995115i	$0.468524\pi$
$594$	−12.0152	−0.492990
$595$	1.33439	0.0547048
$596$	14.7095	0.602526
$597$	−2.82114	−0.115462
$598$	4.09996	0.167660
$599$	−16.9255	−0.691556	−0.345778	−	0.938316i	$-0.612385\pi$
$599$	−16.9255	−0.691556	−0.345778	+	0.938316i	$0.612385\pi$
$600$	6.42423	0.262268
$601$	−16.8610	−0.687776	−0.343888	−	0.939011i	$-0.611744\pi$
$601$	−16.8610	−0.687776	−0.343888	+	0.939011i	$0.611744\pi$
$602$	11.5591	0.471115
$603$	−0.896307	−0.0365005
$604$	19.8836	0.809051
$605$	6.23821	0.253619
$606$	−6.10559	−0.248023
$607$	−35.3340	−1.43416	−0.717082	−	0.696989i	$-0.754523\pi$
$607$	−35.3340	−1.43416	−0.717082	+	0.696989i	$0.754523\pi$
$608$	−1.80450	−0.0731823
$609$	17.7700	0.720078
$610$	−1.86629	−0.0755640
$611$	−0.528476	−0.0213798
$612$	0.216000	0.00873127
$613$	−3.22803	−0.130379	−0.0651895	−	0.997873i	$-0.520765\pi$
$613$	−3.22803	−0.130379	−0.0651895	+	0.997873i	$0.520765\pi$
$614$	24.2873	0.980154
$615$	−17.5599	−0.708083
$616$	2.39490	0.0964931
$617$	33.3584	1.34296	0.671480	−	0.741023i	$-0.265659\pi$
$617$	33.3584	1.34296	0.671480	+	0.741023i	$0.265659\pi$
$618$	−25.7733	−1.03675
$619$	−2.61118	−0.104952	−0.0524761	−	0.998622i	$-0.516711\pi$
$619$	−2.61118	−0.104952	−0.0524761	+	0.998622i	$0.516711\pi$
$620$	−3.75167	−0.150671
$621$	−42.8759	−1.72055
$622$	23.7469	0.952164
$623$	−1.46571	−0.0587225
$624$	0.857097	0.0343114
$625$	5.90949	0.236380
$626$	−6.07796	−0.242924
$627$	−7.72081	−0.308339
$628$	2.22346	0.0887259
$629$	0.0256924	0.00102442
$630$	0.227290	0.00905544
$631$	−3.63757	−0.144809	−0.0724046	−	0.997375i	$-0.523067\pi$
$631$	−3.63757	−0.144809	−0.0724046	+	0.997375i	$0.523067\pi$
$632$	3.54102	0.140854
$633$	20.2100	0.803274
$634$	4.52631	0.179763
$635$	11.6351	0.461724
$636$	−1.31416	−0.0521098
$637$	−0.479746	−0.0190082
$638$	−23.8208	−0.943074
$639$	2.95806	0.117019
$640$	−1.18496	−0.0468398
$641$	15.9511	0.630029	0.315014	−	0.949087i	$-0.397991\pi$
$641$	15.9511	0.630029	0.315014	+	0.949087i	$0.397991\pi$
$642$	31.2732	1.23425
$643$	31.6684	1.24888	0.624440	−	0.781073i	$-0.285327\pi$
$643$	31.6684	1.24888	0.624440	+	0.781073i	$0.285327\pi$
$644$	8.54610	0.336764
$645$	−24.4709	−0.963539
$646$	−2.03206	−0.0799503
$647$	48.3023	1.89896	0.949480	−	0.313829i	$-0.101612\pi$
$647$	48.3023	1.89896	0.949480	+	0.313829i	$0.101612\pi$
$648$	−9.53864	−0.374713
$649$	26.5824	1.04345
$650$	1.72510	0.0676640
$651$	5.65637	0.221691
$652$	−1.00030	−0.0391749
$653$	22.3991	0.876545	0.438273	−	0.898842i	$-0.355590\pi$
$653$	22.3991	0.876545	0.438273	+	0.898842i	$0.355590\pi$
$654$	−29.8782	−1.16833
$655$	−15.5641	−0.608140
$656$	−8.29465	−0.323851
$657$	0.316190	0.0123357
$658$	−1.10157	−0.0429438
$659$	18.8899	0.735846	0.367923	−	0.929856i	$-0.380069\pi$
$659$	18.8899	0.735846	0.367923	+	0.929856i	$0.380069\pi$
$660$	−5.07003	−0.197351
$661$	0.942451	0.0366571	0.0183285	−	0.999832i	$-0.494166\pi$
$661$	0.942451	0.0366571	0.0183285	+	0.999832i	$0.494166\pi$
$662$	−20.6344	−0.801979
$663$	0.965181	0.0374845
$664$	4.65603	0.180689
$665$	−2.13827	−0.0829187
$666$	0.00437623	0.000169575 0
$667$	−85.0037	−3.29136
$668$	−1.45487	−0.0562904
$669$	−29.8505	−1.15409
$670$	5.53717	0.213920
$671$	−3.77191	−0.145613
$672$	1.78656	0.0689182
$673$	−32.4311	−1.25013	−0.625064	−	0.780574i	$-0.714927\pi$
$673$	−32.4311	−1.25013	−0.625064	+	0.780574i	$0.714927\pi$
$674$	−3.06520	−0.118067
$675$	−18.0405	−0.694377
$676$	−12.7698	−0.491148
$677$	−36.0529	−1.38562	−0.692812	−	0.721118i	$-0.743629\pi$
$677$	−36.0529	−1.38562	−0.692812	+	0.721118i	$0.743629\pi$
$678$	−28.6887	−1.10178
$679$	−7.81913	−0.300071
$680$	−1.33439	−0.0511717
$681$	28.1677	1.07939
$682$	−7.58239	−0.290345
$683$	−24.8967	−0.952647	−0.476323	−	0.879270i	$-0.658031\pi$
$683$	−24.8967	−0.952647	−0.476323	+	0.879270i	$0.658031\pi$
$684$	−0.346124	−0.0132344
$685$	14.8667	0.568027
$686$	−1.00000	−0.0381802
$687$	−1.90061	−0.0725126
$688$	−11.5591	−0.440688
$689$	−0.352891	−0.0134441
$690$	−18.0922	−0.688760
$691$	−28.5310	−1.08537	−0.542685	−	0.839936i	$-0.682592\pi$
$691$	−28.5310	−1.08537	−0.542685	+	0.839936i	$0.682592\pi$
$692$	10.5036	0.399288
$693$	0.459368	0.0174500
$694$	26.8993	1.02108
$695$	−13.5446	−0.513776
$696$	−17.7700	−0.673571
$697$	−9.34064	−0.353802
$698$	19.7912	0.749109
$699$	−1.94895	−0.0737161
$700$	3.59586	0.135911
$701$	13.6395	0.515158	0.257579	−	0.966257i	$-0.417075\pi$
$701$	13.6395	0.515158	0.257579	+	0.966257i	$0.417075\pi$
$702$	−2.40689	−0.0908423
$703$	−0.0411702	−0.00155276
$704$	−2.39490	−0.0902610
$705$	2.33205	0.0878301
$706$	−22.9605	−0.864130
$707$	−3.41751	−0.128529
$708$	19.8302	0.745264
$709$	44.7843	1.68191	0.840955	−	0.541105i	$-0.181994\pi$
$709$	44.7843	1.68191	0.840955	+	0.541105i	$0.181994\pi$
$710$	−18.2742	−0.685818
$711$	0.679208	0.0254723
$712$	1.46571	0.0549299
$713$	−27.0575	−1.01331
$714$	2.01186	0.0752919
$715$	−1.36146	−0.0509156
$716$	−14.6617	−0.547933
$717$	−23.5990	−0.881321
$718$	−4.37256	−0.163183
$719$	−22.8717	−0.852972	−0.426486	−	0.904494i	$-0.640249\pi$
$719$	−22.8717	−0.852972	−0.426486	+	0.904494i	$0.640249\pi$
$720$	−0.227290	−0.00847059
$721$	−14.4262	−0.537258
$722$	−15.7438	−0.585922
$723$	−42.8186	−1.59244
$724$	−15.5550	−0.578095
$725$	−35.7661	−1.32832
$726$	9.40532	0.349064
$727$	−40.2307	−1.49207	−0.746037	−	0.665905i	$-0.768046\pi$
$727$	−40.2307	−1.49207	−0.746037	+	0.665905i	$0.768046\pi$
$728$	0.479746	0.0177806
$729$	25.0600	0.928148
$730$	−1.95335	−0.0722966
$731$	−13.0168	−0.481443
$732$	−2.81380	−0.104001
$733$	−14.2993	−0.528157	−0.264078	−	0.964501i	$-0.585068\pi$
$733$	−14.2993	−0.528157	−0.264078	+	0.964501i	$0.585068\pi$
$734$	22.4321	0.827985
$735$	2.11702	0.0780873
$736$	−8.54610	−0.315014
$737$	11.1910	0.412226
$738$	−1.59101	−0.0585658
$739$	11.2734	0.414700	0.207350	−	0.978267i	$-0.433516\pi$
$739$	11.2734	0.414700	0.207350	+	0.978267i	$0.433516\pi$
$740$	−0.0270353	−0.000993838 0
$741$	−1.54663	−0.0568170
$742$	−0.735579	−0.0270039
$743$	2.36812	0.0868781	0.0434390	−	0.999056i	$-0.486169\pi$
$743$	2.36812	0.0868781	0.0434390	+	0.999056i	$0.486169\pi$
$744$	−5.65637	−0.207373
$745$	−17.4303	−0.638596
$746$	30.5732	1.11937
$747$	0.893078	0.0326760
$748$	−2.69690	−0.0986086
$749$	17.5047	0.639606
$750$	−18.1976	−0.664481
$751$	−24.7882	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$751$	−24.7882	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$752$	1.10157	0.0401703
$753$	−17.9491	−0.654100
$754$	−4.77179	−0.173778
$755$	−23.5613	−0.857485
$756$	−5.01701	−0.182467
$757$	4.62921	0.168251	0.0841257	−	0.996455i	$-0.473190\pi$
$757$	4.62921	0.168251	0.0841257	+	0.996455i	$0.473190\pi$
$758$	−18.0859	−0.656908
$759$	−36.5657	−1.32725
$760$	2.13827	0.0775633
$761$	−2.24990	−0.0815587	−0.0407793	−	0.999168i	$-0.512984\pi$
$761$	−2.24990	−0.0815587	−0.0407793	+	0.999168i	$0.512984\pi$
$762$	17.5421	0.635484
$763$	−16.7238	−0.605442
$764$	−11.6972	−0.423188
$765$	−0.255952	−0.00925396
$766$	19.2671	0.696149
$767$	5.32500	0.192275
$768$	−1.78656	−0.0644671
$769$	−31.0134	−1.11837	−0.559185	−	0.829043i	$-0.688886\pi$
$769$	−31.0134	−1.11837	−0.559185	+	0.829043i	$0.688886\pi$
$770$	−2.83787	−0.102270
$771$	−37.4927	−1.35027
$772$	−8.34211	−0.300239
$773$	−4.84413	−0.174231	−0.0871157	−	0.996198i	$-0.527765\pi$
$773$	−4.84413	−0.174231	−0.0871157	+	0.996198i	$0.527765\pi$
$774$	−2.21717	−0.0796946
$775$	−11.3847	−0.408951
$776$	7.81913	0.280690
$777$	0.0407610	0.00146229
$778$	13.1537	0.471582
$779$	14.9677	0.536274
$780$	−1.01563	−0.0363654
$781$	−36.9334	−1.32158
$782$	−9.62381	−0.344147
$783$	49.9016	1.78334
$784$	1.00000	0.0357143
$785$	−2.63473	−0.0940374
$786$	−23.4659	−0.837001
$787$	53.9346	1.92256	0.961281	−	0.275571i	$-0.0888670\pi$
$787$	53.9346	1.92256	0.961281	+	0.275571i	$0.0888670\pi$
$788$	−2.30824	−0.0822276
$789$	−0.0382461	−0.00136160
$790$	−4.19598	−0.149286
$791$	−16.0580	−0.570958
$792$	−0.459368	−0.0163229
$793$	−0.755590	−0.0268318
$794$	−31.9145	−1.13260
$795$	1.55723	0.0552293
$796$	1.57909	0.0559693
$797$	−7.58425	−0.268648	−0.134324	−	0.990937i	$-0.542886\pi$
$797$	−7.58425	−0.268648	−0.134324	+	0.990937i	$0.542886\pi$
$798$	−3.22386	−0.114123
$799$	1.24049	0.0438853
$800$	−3.59586	−0.127133
$801$	0.281140	0.00993360
$802$	−35.3065	−1.24672
$803$	−3.94785	−0.139317
$804$	8.34836	0.294424
$805$	−10.1268	−0.356924
$806$	−1.51891	−0.0535012
$807$	−25.2623	−0.889274
$808$	3.41751	0.120227
$809$	29.2595	1.02871	0.514354	−	0.857578i	$-0.328032\pi$
$809$	29.2595	1.02871	0.514354	+	0.857578i	$0.328032\pi$
$810$	11.3030	0.397145
$811$	−0.981512	−0.0344656	−0.0172328	−	0.999852i	$-0.505486\pi$
$811$	−0.981512	−0.0344656	−0.0172328	+	0.999852i	$0.505486\pi$
$812$	−9.94648	−0.349053
$813$	−40.3203	−1.41409
$814$	−0.0546402	−0.00191514
$815$	1.18532	0.0415201
$816$	−2.01186	−0.0704291
$817$	20.8585	0.729746
$818$	15.2664	0.533776
$819$	0.0920207	0.00321547
$820$	9.82886	0.343239
$821$	−7.87553	−0.274858	−0.137429	−	0.990512i	$-0.543884\pi$
$821$	−7.87553	−0.274858	−0.137429	+	0.990512i	$0.543884\pi$
$822$	22.4144	0.781793
$823$	0.375662	0.0130947	0.00654737	−	0.999979i	$-0.497916\pi$
$823$	0.375662	0.0130947	0.00654737	+	0.999979i	$0.497916\pi$
$824$	14.4262	0.502559
$825$	−15.3854	−0.535650
$826$	11.0996	0.386205
$827$	−1.31704	−0.0457978	−0.0228989	−	0.999738i	$-0.507290\pi$
$827$	−1.31704	−0.0457978	−0.0228989	+	0.999738i	$0.507290\pi$
$828$	−1.63924	−0.0569675
$829$	−7.70355	−0.267555	−0.133778	−	0.991011i	$-0.542711\pi$
$829$	−7.70355	−0.267555	−0.133778	+	0.991011i	$0.542711\pi$
$830$	−5.51723	−0.191506
$831$	−19.3488	−0.671204
$832$	−0.479746	−0.0166322
$833$	1.12610	0.0390172
$834$	−20.4211	−0.707125
$835$	1.72396	0.0596603
$836$	4.32160	0.149466
$837$	15.8842	0.549037
$838$	9.78691	0.338083
$839$	23.6826	0.817615	0.408808	−	0.912621i	$-0.365945\pi$
$839$	23.6826	0.817615	0.408808	+	0.912621i	$0.365945\pi$
$840$	−2.11702	−0.0730440
$841$	69.9325	2.41147
$842$	3.73801	0.128820
$843$	−42.3056	−1.45708
$844$	−11.3122	−0.389382
$845$	15.1318	0.520550
$846$	0.211294	0.00726445
$847$	5.26447	0.180889
$848$	0.735579	0.0252599
$849$	−0.317179	−0.0108856
$850$	−4.04931	−0.138890
$851$	−0.194982	−0.00668389
$852$	−27.5519	−0.943911
$853$	15.8365	0.542232	0.271116	−	0.962547i	$-0.412607\pi$
$853$	15.8365	0.542232	0.271116	+	0.962547i	$0.412607\pi$
$854$	−1.57498	−0.0538946
$855$	0.410145	0.0140267
$856$	−17.5047	−0.598297
$857$	−41.4670	−1.41649	−0.708243	−	0.705968i	$-0.750512\pi$
$857$	−41.4670	−1.41649	−0.708243	+	0.705968i	$0.750512\pi$
$858$	−2.05266	−0.0700766
$859$	−4.78156	−0.163145	−0.0815724	−	0.996667i	$-0.525994\pi$
$859$	−4.78156	−0.163145	−0.0815724	+	0.996667i	$0.525994\pi$
$860$	13.6972	0.467069
$861$	−14.8189	−0.505027
$862$	−1.00000	−0.0340601
$863$	3.02701	0.103040	0.0515202	−	0.998672i	$-0.483593\pi$
$863$	3.02701	0.103040	0.0515202	+	0.998672i	$0.483593\pi$
$864$	5.01701	0.170682
$865$	−12.4464	−0.423191
$866$	32.4534	1.10281
$867$	28.1060	0.954531
$868$	−3.16606	−0.107463
$869$	−8.48037	−0.287677
$870$	21.0569	0.713894
$871$	2.24179	0.0759601
$872$	16.7238	0.566340
$873$	1.49980	0.0507604
$874$	15.4215	0.521639
$875$	−10.1858	−0.344343
$876$	−2.94505	−0.0995039
$877$	49.4975	1.67141	0.835706	−	0.549177i	$-0.185059\pi$
$877$	49.4975	1.67141	0.835706	+	0.549177i	$0.185059\pi$
$878$	−15.7435	−0.531318
$879$	−56.8817	−1.91857
$880$	2.83787	0.0956645
$881$	43.7617	1.47437	0.737184	−	0.675692i	$-0.236155\pi$
$881$	43.7617	1.47437	0.737184	+	0.675692i	$0.236155\pi$
$882$	0.191811	0.00645862
$883$	15.2996	0.514874	0.257437	−	0.966295i	$-0.417122\pi$
$883$	15.2996	0.514874	0.257437	+	0.966295i	$0.417122\pi$
$884$	−0.540244	−0.0181704
$885$	−23.4981	−0.789879
$886$	3.71705	0.124877
$887$	8.63427	0.289911	0.144955	−	0.989438i	$-0.453696\pi$
$887$	8.63427	0.289911	0.144955	+	0.989438i	$0.453696\pi$
$888$	−0.0407610	−0.00136785
$889$	9.81892	0.329316
$890$	−1.73682	−0.0582183
$891$	22.8441	0.765305
$892$	16.7083	0.559437
$893$	−1.98779	−0.0665190
$894$	−26.2795	−0.878919
$895$	17.3736	0.580734
$896$	−1.00000	−0.0334077
$897$	−7.32484	−0.244569
$898$	24.8302	0.828595
$899$	31.4912	1.05029
$900$	−0.689726	−0.0229909
$901$	0.828339	0.0275960
$902$	19.8648	0.661426
$903$	−20.6511	−0.687226
$904$	16.0580	0.534082
$905$	18.4321	0.612703
$906$	−35.5233	−1.18018
$907$	4.48743	0.149003	0.0745013	−	0.997221i	$-0.476264\pi$
$907$	4.48743	0.149003	0.0745013	+	0.997221i	$0.476264\pi$
$908$	−15.7664	−0.523226
$909$	0.655516	0.0217421
$910$	−0.568482	−0.0188450
$911$	26.2290	0.869007	0.434503	−	0.900670i	$-0.356924\pi$
$911$	26.2290	0.869007	0.434503	+	0.900670i	$0.356924\pi$
$912$	3.22386	0.106753
$913$	−11.1507	−0.369034
$914$	−38.2102	−1.26388
$915$	3.33425	0.110227
$916$	1.06383	0.0351500
$917$	−13.1347	−0.433744
$918$	5.64968	0.186467
$919$	41.3218	1.36308	0.681539	−	0.731781i	$-0.261311\pi$
$919$	41.3218	1.36308	0.681539	+	0.731781i	$0.261311\pi$
$920$	10.1268	0.333872
$921$	−43.3908	−1.42977
$922$	−20.1268	−0.662842
$923$	−7.39851	−0.243525
$924$	−4.27864	−0.140757
$925$	−0.0820405	−0.00269748
$926$	−16.7340	−0.549913
$927$	2.76710	0.0908835
$928$	9.94648	0.326509
$929$	−52.7469	−1.73057	−0.865285	−	0.501280i	$-0.832863\pi$
$929$	−52.7469	−1.73057	−0.865285	+	0.501280i	$0.832863\pi$
$930$	6.70260	0.219787
$931$	−1.80450	−0.0591402
$932$	1.09089	0.0357334
$933$	−42.4254	−1.38894
$934$	−0.415953	−0.0136104
$935$	3.19574	0.104512
$936$	−0.0920207	−0.00300779
$937$	28.8435	0.942276	0.471138	−	0.882060i	$-0.343843\pi$
$937$	28.8435	0.942276	0.471138	+	0.882060i	$0.343843\pi$
$938$	4.67286	0.152574
$939$	10.8587	0.354359
$940$	−1.30533	−0.0425751
$941$	5.65008	0.184187	0.0920937	−	0.995750i	$-0.470644\pi$
$941$	5.65008	0.184187	0.0920937	+	0.995750i	$0.470644\pi$
$942$	−3.97236	−0.129426
$943$	70.8869	2.30840
$944$	−11.0996	−0.361262
$945$	5.94498	0.193390
$946$	27.6829	0.900049
$947$	−58.0164	−1.88528	−0.942640	−	0.333812i	$-0.891665\pi$
$947$	−58.0164	−1.88528	−0.942640	+	0.333812i	$0.891665\pi$
$948$	−6.32626	−0.205467
$949$	−0.790834	−0.0256716
$950$	6.48874	0.210522
$951$	−8.08654	−0.262224
$952$	−1.12610	−0.0364973
$953$	−46.3437	−1.50122	−0.750610	−	0.660745i	$-0.770240\pi$
$953$	−46.3437	−1.50122	−0.750610	+	0.660745i	$0.770240\pi$
$954$	0.141092	0.00456803
$955$	13.8607	0.448522
$956$	13.2092	0.427215
$957$	42.5574	1.37568
$958$	−36.8549	−1.19073
$959$	12.5461	0.405135
$960$	2.11702	0.0683264
$961$	−20.9761	−0.676647
$962$	−0.0109455	−0.000352898 0
$963$	−3.35759	−0.108197
$964$	23.9670	0.771926
$965$	9.88510	0.318213
$966$	−15.2682	−0.491245
$967$	−40.9876	−1.31807	−0.659036	−	0.752112i	$-0.729035\pi$
$967$	−40.9876	−1.31807	−0.659036	+	0.752112i	$0.729035\pi$
$968$	−5.26447	−0.169207
$969$	3.63040	0.116625
$970$	−9.26539	−0.297494
$971$	6.46133	0.207354	0.103677	−	0.994611i	$-0.466939\pi$
$971$	6.46133	0.207354	0.103677	+	0.994611i	$0.466939\pi$
$972$	1.99037	0.0638411
$973$	−11.4304	−0.366441
$974$	−26.6668	−0.854459
$975$	−3.08200	−0.0987030
$976$	1.57498	0.0504138
$977$	40.5805	1.29828	0.649142	−	0.760667i	$-0.275128\pi$
$977$	40.5805	1.29828	0.649142	+	0.760667i	$0.275128\pi$
$978$	1.78711	0.0571453
$979$	−3.51023	−0.112187
$980$	−1.18496	−0.0378523
$981$	3.20782	0.102418
$982$	14.3522	0.457998
$983$	−48.8633	−1.55850	−0.779249	−	0.626714i	$-0.784399\pi$
$983$	−48.8633	−1.55850	−0.779249	+	0.626714i	$0.784399\pi$
$984$	14.8189	0.472410
$985$	2.73518	0.0871502
$986$	11.2008	0.356706
$987$	1.96803	0.0626432
$988$	0.865703	0.0275417
$989$	98.7855	3.14120
$990$	0.544335	0.0173001
$991$	−39.7925	−1.26405	−0.632024	−	0.774948i	$-0.717776\pi$
$991$	−39.7925	−1.26405	−0.632024	+	0.774948i	$0.717776\pi$
$992$	3.16606	0.100523
$993$	36.8647	1.16987
$994$	−15.4217	−0.489147
$995$	−1.87116	−0.0593199
$996$	−8.31829	−0.263575
$997$	−39.4197	−1.24843	−0.624217	−	0.781251i	$-0.714582\pi$
$997$	−39.4197	−1.24843	−0.624217	+	0.781251i	$0.714582\pi$
$998$	−33.4327	−1.05829
$999$	0.114464	0.00362150

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.r.1.7	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.r.1.7	✓	31	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.78656 q^{3} +1.00000 q^{4} -1.18496 q^{5} -1.78656 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.191811 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.78656 q^{3} +1.00000 q^{4} -1.18496 q^{5} -1.78656 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.191811 q^{9} -1.18496 q^{10} -2.39490 q^{11} -1.78656 q^{12} -0.479746 q^{13} -1.00000 q^{14} +2.11702 q^{15} +1.00000 q^{16} +1.12610 q^{17} +0.191811 q^{18} -1.80450 q^{19} -1.18496 q^{20} +1.78656 q^{21} -2.39490 q^{22} -8.54610 q^{23} -1.78656 q^{24} -3.59586 q^{25} -0.479746 q^{26} +5.01701 q^{27} -1.00000 q^{28} +9.94648 q^{29} +2.11702 q^{30} +3.16606 q^{31} +1.00000 q^{32} +4.27864 q^{33} +1.12610 q^{34} +1.18496 q^{35} +0.191811 q^{36} +0.0228153 q^{37} -1.80450 q^{38} +0.857097 q^{39} -1.18496 q^{40} -8.29465 q^{41} +1.78656 q^{42} -11.5591 q^{43} -2.39490 q^{44} -0.227290 q^{45} -8.54610 q^{46} +1.10157 q^{47} -1.78656 q^{48} +1.00000 q^{49} -3.59586 q^{50} -2.01186 q^{51} -0.479746 q^{52} +0.735579 q^{53} +5.01701 q^{54} +2.83787 q^{55} -1.00000 q^{56} +3.22386 q^{57} +9.94648 q^{58} -11.0996 q^{59} +2.11702 q^{60} +1.57498 q^{61} +3.16606 q^{62} -0.191811 q^{63} +1.00000 q^{64} +0.568482 q^{65} +4.27864 q^{66} -4.67286 q^{67} +1.12610 q^{68} +15.2682 q^{69} +1.18496 q^{70} +15.4217 q^{71} +0.191811 q^{72} +1.64844 q^{73} +0.0228153 q^{74} +6.42423 q^{75} -1.80450 q^{76} +2.39490 q^{77} +0.857097 q^{78} +3.54102 q^{79} -1.18496 q^{80} -9.53864 q^{81} -8.29465 q^{82} +4.65603 q^{83} +1.78656 q^{84} -1.33439 q^{85} -11.5591 q^{86} -17.7700 q^{87} -2.39490 q^{88} +1.46571 q^{89} -0.227290 q^{90} +0.479746 q^{91} -8.54610 q^{92} -5.65637 q^{93} +1.10157 q^{94} +2.13827 q^{95} -1.78656 q^{96} +7.81913 q^{97} +1.00000 q^{98} -0.459368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * q^99

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