LMFDB - Embedded newform 6034.2.a.l.1.8

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:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 36 x^{18} + 97 x^{17} + 573 x^{16} - 1292 x^{15} - 5329 x^{14} + 9121 x^{13} + \cdots - 21776 $ x^20 - 3x^19 - 36x^18 + 97x^17 + 573x^16 - 1292x^15 - 5329x^14 + 9121x^13 + 31784x^12 - 36075x^11 - 124276x^10 + 74594x^9 + 312410x^8 - 47208x^7 - 477646x^6 - 101137x^5 + 391391x^4 + 205294x^3 - 112848x^2 - 109144*x - 21776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.35617$ of defining polynomial
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.35617 q^{3} +1.00000 q^{4} +1.14574 q^{5} -1.35617 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.16079 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.35617 q^{3} +1.00000 q^{4} +1.14574 q^{5} -1.35617 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.16079 q^{9} +1.14574 q^{10} -4.90404 q^{11} -1.35617 q^{12} +3.53472 q^{13} -1.00000 q^{14} -1.55383 q^{15} +1.00000 q^{16} -2.10525 q^{17} -1.16079 q^{18} +2.64080 q^{19} +1.14574 q^{20} +1.35617 q^{21} -4.90404 q^{22} +1.73014 q^{23} -1.35617 q^{24} -3.68727 q^{25} +3.53472 q^{26} +5.64276 q^{27} -1.00000 q^{28} -1.92505 q^{29} -1.55383 q^{30} +7.14408 q^{31} +1.00000 q^{32} +6.65073 q^{33} -2.10525 q^{34} -1.14574 q^{35} -1.16079 q^{36} +11.0555 q^{37} +2.64080 q^{38} -4.79369 q^{39} +1.14574 q^{40} -7.53470 q^{41} +1.35617 q^{42} +2.28457 q^{43} -4.90404 q^{44} -1.32997 q^{45} +1.73014 q^{46} +3.23302 q^{47} -1.35617 q^{48} +1.00000 q^{49} -3.68727 q^{50} +2.85509 q^{51} +3.53472 q^{52} -13.5297 q^{53} +5.64276 q^{54} -5.61876 q^{55} -1.00000 q^{56} -3.58138 q^{57} -1.92505 q^{58} -3.53770 q^{59} -1.55383 q^{60} -0.0973943 q^{61} +7.14408 q^{62} +1.16079 q^{63} +1.00000 q^{64} +4.04988 q^{65} +6.65073 q^{66} -11.6421 q^{67} -2.10525 q^{68} -2.34637 q^{69} -1.14574 q^{70} -6.82158 q^{71} -1.16079 q^{72} -5.06332 q^{73} +11.0555 q^{74} +5.00058 q^{75} +2.64080 q^{76} +4.90404 q^{77} -4.79369 q^{78} -2.22286 q^{79} +1.14574 q^{80} -4.17018 q^{81} -7.53470 q^{82} -7.91650 q^{83} +1.35617 q^{84} -2.41208 q^{85} +2.28457 q^{86} +2.61070 q^{87} -4.90404 q^{88} +0.879303 q^{89} -1.32997 q^{90} -3.53472 q^{91} +1.73014 q^{92} -9.68861 q^{93} +3.23302 q^{94} +3.02568 q^{95} -1.35617 q^{96} -11.1767 q^{97} +1.00000 q^{98} +5.69257 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * 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
$3$	−1.35617	−0.782987	−0.391494	−	0.920181i	$-0.628041\pi$
$3$	−1.35617	−0.782987	−0.391494	+	0.920181i	$0.628041\pi$
$4$	1.00000	0.500000
$5$	1.14574	0.512392	0.256196	−	0.966625i	$-0.417531\pi$
$5$	1.14574	0.512392	0.256196	+	0.966625i	$0.417531\pi$
$6$	−1.35617	−0.553656
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−1.16079	−0.386931
$10$	1.14574	0.362316
$11$	−4.90404	−1.47862	−0.739311	−	0.673364i	$-0.764849\pi$
$11$	−4.90404	−1.47862	−0.739311	+	0.673364i	$0.764849\pi$
$12$	−1.35617	−0.391494
$13$	3.53472	0.980354	0.490177	−	0.871623i	$-0.336932\pi$
$13$	3.53472	0.980354	0.490177	+	0.871623i	$0.336932\pi$
$14$	−1.00000	−0.267261
$15$	−1.55383	−0.401196
$16$	1.00000	0.250000
$17$	−2.10525	−0.510598	−0.255299	−	0.966862i	$-0.582174\pi$
$17$	−2.10525	−0.510598	−0.255299	+	0.966862i	$0.582174\pi$
$18$	−1.16079	−0.273601
$19$	2.64080	0.605841	0.302921	−	0.953016i	$-0.402038\pi$
$19$	2.64080	0.605841	0.302921	+	0.953016i	$0.402038\pi$
$20$	1.14574	0.256196
$21$	1.35617	0.295941
$22$	−4.90404	−1.04554
$23$	1.73014	0.360759	0.180379	−	0.983597i	$-0.442267\pi$
$23$	1.73014	0.360759	0.180379	+	0.983597i	$0.442267\pi$
$24$	−1.35617	−0.276828
$25$	−3.68727	−0.737455
$26$	3.53472	0.693215
$27$	5.64276	1.08595
$28$	−1.00000	−0.188982
$29$	−1.92505	−0.357473	−0.178736	−	0.983897i	$-0.557201\pi$
$29$	−1.92505	−0.357473	−0.178736	+	0.983897i	$0.557201\pi$
$30$	−1.55383	−0.283688
$31$	7.14408	1.28311	0.641557	−	0.767075i	$-0.278289\pi$
$31$	7.14408	1.28311	0.641557	+	0.767075i	$0.278289\pi$
$32$	1.00000	0.176777
$33$	6.65073	1.15774
$34$	−2.10525	−0.361048
$35$	−1.14574	−0.193666
$36$	−1.16079	−0.193465
$37$	11.0555	1.81752	0.908758	−	0.417324i	$-0.137032\pi$
$37$	11.0555	1.81752	0.908758	+	0.417324i	$0.137032\pi$
$38$	2.64080	0.428394
$39$	−4.79369	−0.767605
$40$	1.14574	0.181158
$41$	−7.53470	−1.17672	−0.588361	−	0.808598i	$-0.700227\pi$
$41$	−7.53470	−1.17672	−0.588361	+	0.808598i	$0.700227\pi$
$42$	1.35617	0.209262
$43$	2.28457	0.348394	0.174197	−	0.984711i	$-0.444267\pi$
$43$	2.28457	0.348394	0.174197	+	0.984711i	$0.444267\pi$
$44$	−4.90404	−0.739311
$45$	−1.32997	−0.198260
$46$	1.73014	0.255095
$47$	3.23302	0.471585	0.235792	−	0.971803i	$-0.424231\pi$
$47$	3.23302	0.471585	0.235792	+	0.971803i	$0.424231\pi$
$48$	−1.35617	−0.195747
$49$	1.00000	0.142857
$50$	−3.68727	−0.521459
$51$	2.85509	0.399792
$52$	3.53472	0.490177
$53$	−13.5297	−1.85844	−0.929222	−	0.369521i	$-0.879522\pi$
$53$	−13.5297	−1.85844	−0.929222	+	0.369521i	$0.879522\pi$
$54$	5.64276	0.767882
$55$	−5.61876	−0.757634
$56$	−1.00000	−0.133631
$57$	−3.58138	−0.474366
$58$	−1.92505	−0.252771
$59$	−3.53770	−0.460569	−0.230285	−	0.973123i	$-0.573966\pi$
$59$	−3.53770	−0.460569	−0.230285	+	0.973123i	$0.573966\pi$
$60$	−1.55383	−0.200598
$61$	−0.0973943	−0.0124701	−0.00623503	−	0.999981i	$-0.501985\pi$
$61$	−0.0973943	−0.0124701	−0.00623503	+	0.999981i	$0.501985\pi$
$62$	7.14408	0.907299
$63$	1.16079	0.146246
$64$	1.00000	0.125000
$65$	4.04988	0.502325
$66$	6.65073	0.818648
$67$	−11.6421	−1.42231	−0.711155	−	0.703035i	$-0.751828\pi$
$67$	−11.6421	−1.42231	−0.711155	+	0.703035i	$0.751828\pi$
$68$	−2.10525	−0.255299
$69$	−2.34637	−0.282470
$70$	−1.14574	−0.136942
$71$	−6.82158	−0.809572	−0.404786	−	0.914411i	$-0.632654\pi$
$71$	−6.82158	−0.809572	−0.404786	+	0.914411i	$0.632654\pi$
$72$	−1.16079	−0.136801
$73$	−5.06332	−0.592617	−0.296309	−	0.955092i	$-0.595756\pi$
$73$	−5.06332	−0.592617	−0.296309	+	0.955092i	$0.595756\pi$
$74$	11.0555	1.28518
$75$	5.00058	0.577418
$76$	2.64080	0.302921
$77$	4.90404	0.558867
$78$	−4.79369	−0.542779
$79$	−2.22286	−0.250091	−0.125046	−	0.992151i	$-0.539908\pi$
$79$	−2.22286	−0.250091	−0.125046	+	0.992151i	$0.539908\pi$
$80$	1.14574	0.128098
$81$	−4.17018	−0.463353
$82$	−7.53470	−0.832068
$83$	−7.91650	−0.868949	−0.434475	−	0.900684i	$-0.643066\pi$
$83$	−7.91650	−0.868949	−0.434475	+	0.900684i	$0.643066\pi$
$84$	1.35617	0.147971
$85$	−2.41208	−0.261626
$86$	2.28457	0.246352
$87$	2.61070	0.279896
$88$	−4.90404	−0.522772
$89$	0.879303	0.0932059	0.0466030	−	0.998913i	$-0.485160\pi$
$89$	0.879303	0.0932059	0.0466030	+	0.998913i	$0.485160\pi$
$90$	−1.32997	−0.140191
$91$	−3.53472	−0.370539
$92$	1.73014	0.180379
$93$	−9.68861	−1.00466
$94$	3.23302	0.333461
$95$	3.02568	0.310428
$96$	−1.35617	−0.138414
$97$	−11.1767	−1.13482	−0.567409	−	0.823436i	$-0.692054\pi$
$97$	−11.1767	−1.13482	−0.567409	+	0.823436i	$0.692054\pi$
$98$	1.00000	0.101015
$99$	5.69257	0.572125
$100$	−3.68727	−0.368727
$101$	−8.30764	−0.826641	−0.413321	−	0.910586i	$-0.635631\pi$
$101$	−8.30764	−0.826641	−0.413321	+	0.910586i	$0.635631\pi$
$102$	2.85509	0.282696
$103$	3.16645	0.312000	0.156000	−	0.987757i	$-0.450140\pi$
$103$	3.16645	0.312000	0.156000	+	0.987757i	$0.450140\pi$
$104$	3.53472	0.346608
$105$	1.55383	0.151638
$106$	−13.5297	−1.31412
$107$	−7.29957	−0.705676	−0.352838	−	0.935684i	$-0.614783\pi$
$107$	−7.29957	−0.705676	−0.352838	+	0.935684i	$0.614783\pi$
$108$	5.64276	0.542975
$109$	−4.21108	−0.403348	−0.201674	−	0.979453i	$-0.564638\pi$
$109$	−4.21108	−0.403348	−0.201674	+	0.979453i	$0.564638\pi$
$110$	−5.61876	−0.535728
$111$	−14.9932	−1.42309
$112$	−1.00000	−0.0944911
$113$	−17.5188	−1.64803	−0.824014	−	0.566569i	$-0.808270\pi$
$113$	−17.5188	−1.64803	−0.824014	+	0.566569i	$0.808270\pi$
$114$	−3.58138	−0.335427
$115$	1.98229	0.184850
$116$	−1.92505	−0.178736
$117$	−4.10307	−0.379329
$118$	−3.53770	−0.325672
$119$	2.10525	0.192988
$120$	−1.55383	−0.141844
$121$	13.0496	1.18633
$122$	−0.0973943	−0.00881766
$123$	10.2184	0.921359
$124$	7.14408	0.641557
$125$	−9.95338	−0.890257
$126$	1.16079	0.103412
$127$	3.66020	0.324791	0.162395	−	0.986726i	$-0.448078\pi$
$127$	3.66020	0.324791	0.162395	+	0.986726i	$0.448078\pi$
$128$	1.00000	0.0883883
$129$	−3.09828	−0.272788
$130$	4.04988	0.355198
$131$	−10.5257	−0.919633	−0.459816	−	0.888014i	$-0.652085\pi$
$131$	−10.5257	−0.919633	−0.459816	+	0.888014i	$0.652085\pi$
$132$	6.65073	0.578871
$133$	−2.64080	−0.228986
$134$	−11.6421	−1.00573
$135$	6.46515	0.556431
$136$	−2.10525	−0.180524
$137$	1.21489	0.103795	0.0518977	−	0.998652i	$-0.483473\pi$
$137$	1.21489	0.103795	0.0518977	+	0.998652i	$0.483473\pi$
$138$	−2.34637	−0.199736
$139$	11.0518	0.937402	0.468701	−	0.883357i	$-0.344722\pi$
$139$	11.0518	0.937402	0.468701	+	0.883357i	$0.344722\pi$
$140$	−1.14574	−0.0968329
$141$	−4.38454	−0.369245
$142$	−6.82158	−0.572454
$143$	−17.3344	−1.44957
$144$	−1.16079	−0.0967327
$145$	−2.20561	−0.183166
$146$	−5.06332	−0.419044
$147$	−1.35617	−0.111855
$148$	11.0555	0.908758
$149$	−11.2710	−0.923353	−0.461677	−	0.887048i	$-0.652752\pi$
$149$	−11.2710	−0.923353	−0.461677	+	0.887048i	$0.652752\pi$
$150$	5.00058	0.408296
$151$	7.32966	0.596480	0.298240	−	0.954491i	$-0.403600\pi$
$151$	7.32966	0.596480	0.298240	+	0.954491i	$0.403600\pi$
$152$	2.64080	0.214197
$153$	2.44376	0.197566
$154$	4.90404	0.395179
$155$	8.18528	0.657457
$156$	−4.79369	−0.383802
$157$	−7.75216	−0.618689	−0.309345	−	0.950950i	$-0.600110\pi$
$157$	−7.75216	−0.618689	−0.309345	+	0.950950i	$0.600110\pi$
$158$	−2.22286	−0.176841
$159$	18.3486	1.45514
$160$	1.14574	0.0905789
$161$	−1.73014	−0.136354
$162$	−4.17018	−0.327640
$163$	−1.26861	−0.0993650	−0.0496825	−	0.998765i	$-0.515821\pi$
$163$	−1.26861	−0.0993650	−0.0496825	+	0.998765i	$0.515821\pi$
$164$	−7.53470	−0.588361
$165$	7.62002	0.593218
$166$	−7.91650	−0.614440
$167$	−11.9633	−0.925748	−0.462874	−	0.886424i	$-0.653182\pi$
$167$	−11.9633	−0.925748	−0.462874	+	0.886424i	$0.653182\pi$
$168$	1.35617	0.104631
$169$	−0.505775	−0.0389057
$170$	−2.41208	−0.184998
$171$	−3.06542	−0.234419
$172$	2.28457	0.174197
$173$	−9.93833	−0.755598	−0.377799	−	0.925888i	$-0.623319\pi$
$173$	−9.93833	−0.755598	−0.377799	+	0.925888i	$0.623319\pi$
$174$	2.61070	0.197917
$175$	3.68727	0.278732
$176$	−4.90404	−0.369656
$177$	4.79773	0.360620
$178$	0.879303	0.0659065
$179$	7.38368	0.551882	0.275941	−	0.961175i	$-0.411011\pi$
$179$	7.38368	0.551882	0.275941	+	0.961175i	$0.411011\pi$
$180$	−1.32997	−0.0991301
$181$	1.04317	0.0775384	0.0387692	−	0.999248i	$-0.487656\pi$
$181$	1.04317	0.0775384	0.0387692	+	0.999248i	$0.487656\pi$
$182$	−3.53472	−0.262011
$183$	0.132084	0.00976390
$184$	1.73014	0.127547
$185$	12.6668	0.931280
$186$	−9.68861	−0.710404
$187$	10.3242	0.754982
$188$	3.23302	0.235792
$189$	−5.64276	−0.410450
$190$	3.02568	0.219506
$191$	13.1926	0.954586	0.477293	−	0.878744i	$-0.341618\pi$
$191$	13.1926	0.954586	0.477293	+	0.878744i	$0.341618\pi$
$192$	−1.35617	−0.0978734
$193$	18.1763	1.30836	0.654180	−	0.756339i	$-0.273014\pi$
$193$	18.1763	1.30836	0.654180	+	0.756339i	$0.273014\pi$
$194$	−11.1767	−0.802437
$195$	−5.49233	−0.393314
$196$	1.00000	0.0714286
$197$	16.3826	1.16721	0.583606	−	0.812037i	$-0.301641\pi$
$197$	16.3826	1.16721	0.583606	+	0.812037i	$0.301641\pi$
$198$	5.69257	0.404553
$199$	−5.79459	−0.410767	−0.205384	−	0.978682i	$-0.565844\pi$
$199$	−5.79459	−0.410767	−0.205384	+	0.978682i	$0.565844\pi$
$200$	−3.68727	−0.260730
$201$	15.7887	1.11365
$202$	−8.30764	−0.584523
$203$	1.92505	0.135112
$204$	2.85509	0.199896
$205$	−8.63282	−0.602943
$206$	3.16645	0.220617
$207$	−2.00833	−0.139589
$208$	3.53472	0.245089
$209$	−12.9506	−0.895811
$210$	1.55383	0.107224
$211$	9.91695	0.682711	0.341355	−	0.939934i	$-0.389114\pi$
$211$	9.91695	0.682711	0.341355	+	0.939934i	$0.389114\pi$
$212$	−13.5297	−0.929222
$213$	9.25124	0.633885
$214$	−7.29957	−0.498988
$215$	2.61753	0.178514
$216$	5.64276	0.383941
$217$	−7.14408	−0.484972
$218$	−4.21108	−0.285210
$219$	6.86675	0.464012
$220$	−5.61876	−0.378817
$221$	−7.44147	−0.500567
$222$	−14.9932	−1.00628
$223$	−8.88501	−0.594984	−0.297492	−	0.954724i	$-0.596150\pi$
$223$	−8.88501	−0.594984	−0.297492	+	0.954724i	$0.596150\pi$
$224$	−1.00000	−0.0668153
$225$	4.28016	0.285344
$226$	−17.5188	−1.16533
$227$	−19.6178	−1.30208	−0.651040	−	0.759043i	$-0.725667\pi$
$227$	−19.6178	−1.30208	−0.651040	+	0.759043i	$0.725667\pi$
$228$	−3.58138	−0.237183
$229$	−9.04766	−0.597886	−0.298943	−	0.954271i	$-0.596634\pi$
$229$	−9.04766	−0.597886	−0.298943	+	0.954271i	$0.596634\pi$
$230$	1.98229	0.130709
$231$	−6.65073	−0.437586
$232$	−1.92505	−0.126386
$233$	−12.4968	−0.818693	−0.409346	−	0.912379i	$-0.634243\pi$
$233$	−12.4968	−0.818693	−0.409346	+	0.912379i	$0.634243\pi$
$234$	−4.10307	−0.268226
$235$	3.70421	0.241636
$236$	−3.53770	−0.230285
$237$	3.01459	0.195818
$238$	2.10525	0.136463
$239$	−20.7502	−1.34222	−0.671109	−	0.741359i	$-0.734182\pi$
$239$	−20.7502	−1.34222	−0.671109	+	0.741359i	$0.734182\pi$
$240$	−1.55383	−0.100299
$241$	8.41356	0.541965	0.270982	−	0.962584i	$-0.412651\pi$
$241$	8.41356	0.541965	0.270982	+	0.962584i	$0.412651\pi$
$242$	13.0496	0.838859
$243$	−11.2728	−0.723149
$244$	−0.0973943	−0.00623503
$245$	1.14574	0.0731988
$246$	10.2184	0.651499
$247$	9.33448	0.593939
$248$	7.14408	0.453650
$249$	10.7362	0.680376
$250$	−9.95338	−0.629507
$251$	28.7022	1.81167	0.905834	−	0.423633i	$-0.139245\pi$
$251$	28.7022	1.81167	0.905834	+	0.423633i	$0.139245\pi$
$252$	1.16079	0.0731231
$253$	−8.48466	−0.533426
$254$	3.66020	0.229662
$255$	3.27119	0.204850
$256$	1.00000	0.0625000
$257$	−26.6139	−1.66013	−0.830065	−	0.557667i	$-0.811697\pi$
$257$	−26.6139	−1.66013	−0.830065	+	0.557667i	$0.811697\pi$
$258$	−3.09828	−0.192890
$259$	−11.0555	−0.686956
$260$	4.04988	0.251163
$261$	2.23458	0.138317
$262$	−10.5257	−0.650279
$263$	−11.6978	−0.721320	−0.360660	−	0.932697i	$-0.617448\pi$
$263$	−11.6978	−0.721320	−0.360660	+	0.932697i	$0.617448\pi$
$264$	6.65073	0.409324
$265$	−15.5015	−0.952252
$266$	−2.64080	−0.161918
$267$	−1.19249	−0.0729790
$268$	−11.6421	−0.711155
$269$	16.0908	0.981074	0.490537	−	0.871420i	$-0.336801\pi$
$269$	16.0908	0.981074	0.490537	+	0.871420i	$0.336801\pi$
$270$	6.46515	0.393456
$271$	2.84989	0.173118	0.0865591	−	0.996247i	$-0.472413\pi$
$271$	2.84989	0.173118	0.0865591	+	0.996247i	$0.472413\pi$
$272$	−2.10525	−0.127650
$273$	4.79369	0.290127
$274$	1.21489	0.0733944
$275$	18.0825	1.09042
$276$	−2.34637	−0.141235
$277$	8.72327	0.524131	0.262065	−	0.965050i	$-0.415596\pi$
$277$	8.72327	0.524131	0.262065	+	0.965050i	$0.415596\pi$
$278$	11.0518	0.662843
$279$	−8.29280	−0.496477
$280$	−1.14574	−0.0684712
$281$	−23.6016	−1.40796	−0.703978	−	0.710222i	$-0.748595\pi$
$281$	−23.6016	−1.40796	−0.703978	+	0.710222i	$0.748595\pi$
$282$	−4.38454	−0.261096
$283$	29.8859	1.77653	0.888265	−	0.459332i	$-0.151911\pi$
$283$	29.8859	1.77653	0.888265	+	0.459332i	$0.151911\pi$
$284$	−6.82158	−0.404786
$285$	−4.10334	−0.243061
$286$	−17.3344	−1.02500
$287$	7.53470	0.444759
$288$	−1.16079	−0.0684004
$289$	−12.5679	−0.739289
$290$	−2.20561	−0.129518
$291$	15.1575	0.888548
$292$	−5.06332	−0.296309
$293$	23.3294	1.36292	0.681458	−	0.731857i	$-0.261346\pi$
$293$	23.3294	1.36292	0.681458	+	0.731857i	$0.261346\pi$
$294$	−1.35617	−0.0790937
$295$	−4.05329	−0.235992
$296$	11.0555	0.642589
$297$	−27.6723	−1.60571
$298$	−11.2710	−0.652909
$299$	6.11555	0.353671
$300$	5.00058	0.288709
$301$	−2.28457	−0.131681
$302$	7.32966	0.421775
$303$	11.2666	0.647249
$304$	2.64080	0.151460
$305$	−0.111589	−0.00638955
$306$	2.44376	0.139700
$307$	−11.0714	−0.631877	−0.315939	−	0.948780i	$-0.602319\pi$
$307$	−11.0714	−0.631877	−0.315939	+	0.948780i	$0.602319\pi$
$308$	4.90404	0.279433
$309$	−4.29426	−0.244292
$310$	8.18528	0.464893
$311$	−20.0417	−1.13646	−0.568231	−	0.822869i	$-0.692372\pi$
$311$	−20.0417	−1.13646	−0.568231	+	0.822869i	$0.692372\pi$
$312$	−4.79369	−0.271389
$313$	−14.6082	−0.825705	−0.412853	−	0.910798i	$-0.635468\pi$
$313$	−14.6082	−0.825705	−0.412853	+	0.910798i	$0.635468\pi$
$314$	−7.75216	−0.437479
$315$	1.32997	0.0749353
$316$	−2.22286	−0.125046
$317$	−4.45017	−0.249947	−0.124973	−	0.992160i	$-0.539885\pi$
$317$	−4.45017	−0.249947	−0.124973	+	0.992160i	$0.539885\pi$
$318$	18.3486	1.02894
$319$	9.44051	0.528567
$320$	1.14574	0.0640490
$321$	9.89948	0.552535
$322$	−1.73014	−0.0964168
$323$	−5.55955	−0.309342
$324$	−4.17018	−0.231677
$325$	−13.0335	−0.722967
$326$	−1.26861	−0.0702617
$327$	5.71095	0.315816
$328$	−7.53470	−0.416034
$329$	−3.23302	−0.178242
$330$	7.62002	0.419468
$331$	33.9755	1.86746	0.933730	−	0.357978i	$-0.116534\pi$
$331$	33.9755	1.86746	0.933730	+	0.357978i	$0.116534\pi$
$332$	−7.91650	−0.434475
$333$	−12.8332	−0.703253
$334$	−11.9633	−0.654602
$335$	−13.3389	−0.728780
$336$	1.35617	0.0739853
$337$	−19.5007	−1.06227	−0.531136	−	0.847286i	$-0.678235\pi$
$337$	−19.5007	−1.06227	−0.531136	+	0.847286i	$0.678235\pi$
$338$	−0.505775	−0.0275105
$339$	23.7585	1.29039
$340$	−2.41208	−0.130813
$341$	−35.0348	−1.89724
$342$	−3.06542	−0.165759
$343$	−1.00000	−0.0539949
$344$	2.28457	0.123176
$345$	−2.68833	−0.144735
$346$	−9.93833	−0.534288
$347$	22.6747	1.21724	0.608620	−	0.793462i	$-0.291723\pi$
$347$	22.6747	1.21724	0.608620	+	0.793462i	$0.291723\pi$
$348$	2.61070	0.139948
$349$	2.46440	0.131916	0.0659582	−	0.997822i	$-0.478990\pi$
$349$	2.46440	0.131916	0.0659582	+	0.997822i	$0.478990\pi$
$350$	3.68727	0.197093
$351$	19.9456	1.06461
$352$	−4.90404	−0.261386
$353$	14.1125	0.751135	0.375567	−	0.926795i	$-0.377448\pi$
$353$	14.1125	0.751135	0.375567	+	0.926795i	$0.377448\pi$
$354$	4.79773	0.254997
$355$	−7.81577	−0.414818
$356$	0.879303	0.0466030
$357$	−2.85509	−0.151107
$358$	7.38368	0.390240
$359$	25.0089	1.31992	0.659960	−	0.751301i	$-0.270573\pi$
$359$	25.0089	1.31992	0.659960	+	0.751301i	$0.270573\pi$
$360$	−1.32997	−0.0700956
$361$	−12.0262	−0.632956
$362$	1.04317	0.0548279
$363$	−17.6975	−0.928878
$364$	−3.53472	−0.185270
$365$	−5.80126	−0.303652
$366$	0.132084	0.00690412
$367$	−19.9683	−1.04234	−0.521170	−	0.853453i	$-0.674504\pi$
$367$	−19.9683	−1.04234	−0.521170	+	0.853453i	$0.674504\pi$
$368$	1.73014	0.0901897
$369$	8.74622	0.455310
$370$	12.6668	0.658514
$371$	13.5297	0.702426
$372$	−9.68861	−0.502331
$373$	−13.6918	−0.708934	−0.354467	−	0.935069i	$-0.615338\pi$
$373$	−13.6918	−0.708934	−0.354467	+	0.935069i	$0.615338\pi$
$374$	10.3242	0.533853
$375$	13.4985	0.697060
$376$	3.23302	0.166730
$377$	−6.80450	−0.350450
$378$	−5.64276	−0.290232
$379$	4.21371	0.216444	0.108222	−	0.994127i	$-0.465484\pi$
$379$	4.21371	0.216444	0.108222	+	0.994127i	$0.465484\pi$
$380$	3.02568	0.155214
$381$	−4.96387	−0.254307
$382$	13.1926	0.674994
$383$	18.0865	0.924179	0.462089	−	0.886833i	$-0.347100\pi$
$383$	18.0865	0.924179	0.462089	+	0.886833i	$0.347100\pi$
$384$	−1.35617	−0.0692070
$385$	5.61876	0.286359
$386$	18.1763	0.925150
$387$	−2.65191	−0.134804
$388$	−11.1767	−0.567409
$389$	25.5220	1.29402	0.647008	−	0.762483i	$-0.276020\pi$
$389$	25.5220	1.29402	0.647008	+	0.762483i	$0.276020\pi$
$390$	−5.49233	−0.278115
$391$	−3.64238	−0.184203
$392$	1.00000	0.0505076
$393$	14.2746	0.720061
$394$	16.3826	0.825344
$395$	−2.54683	−0.128145
$396$	5.69257	0.286062
$397$	−17.1808	−0.862278	−0.431139	−	0.902285i	$-0.641888\pi$
$397$	−17.1808	−0.862278	−0.431139	+	0.902285i	$0.641888\pi$
$398$	−5.79459	−0.290456
$399$	3.58138	0.179293
$400$	−3.68727	−0.184364
$401$	15.8302	0.790520	0.395260	−	0.918569i	$-0.370654\pi$
$401$	15.8302	0.790520	0.395260	+	0.918569i	$0.370654\pi$
$402$	15.7887	0.787470
$403$	25.2523	1.25791
$404$	−8.30764	−0.413321
$405$	−4.77795	−0.237418
$406$	1.92505	0.0955386
$407$	−54.2166	−2.68742
$408$	2.85509	0.141348
$409$	−26.5689	−1.31375	−0.656874	−	0.754000i	$-0.728122\pi$
$409$	−26.5689	−1.31375	−0.656874	+	0.754000i	$0.728122\pi$
$410$	−8.63282	−0.426345
$411$	−1.64761	−0.0812705
$412$	3.16645	0.156000
$413$	3.53770	0.174079
$414$	−2.00833	−0.0987041
$415$	−9.07028	−0.445242
$416$	3.53472	0.173304
$417$	−14.9882	−0.733974
$418$	−12.9506	−0.633434
$419$	2.73493	0.133610	0.0668049	−	0.997766i	$-0.478719\pi$
$419$	2.73493	0.133610	0.0668049	+	0.997766i	$0.478719\pi$
$420$	1.55383	0.0758189
$421$	−16.8138	−0.819455	−0.409728	−	0.912208i	$-0.634376\pi$
$421$	−16.8138	−0.819455	−0.409728	+	0.912208i	$0.634376\pi$
$422$	9.91695	0.482750
$423$	−3.75287	−0.182471
$424$	−13.5297	−0.657059
$425$	7.76264	0.376543
$426$	9.25124	0.448224
$427$	0.0973943	0.00471324
$428$	−7.29957	−0.352838
$429$	23.5084	1.13500
$430$	2.61753	0.126229
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	5.64276	0.271487
$433$	11.5140	0.553329	0.276664	−	0.960967i	$-0.410771\pi$
$433$	11.5140	0.553329	0.276664	+	0.960967i	$0.410771\pi$
$434$	−7.14408	−0.342927
$435$	2.99119	0.143417
$436$	−4.21108	−0.201674
$437$	4.56895	0.218563
$438$	6.86675	0.328106
$439$	−9.27411	−0.442629	−0.221314	−	0.975203i	$-0.571035\pi$
$439$	−9.27411	−0.442629	−0.221314	+	0.975203i	$0.571035\pi$
$440$	−5.61876	−0.267864
$441$	−1.16079	−0.0552758
$442$	−7.44147	−0.353955
$443$	29.7255	1.41230	0.706151	−	0.708061i	$-0.250430\pi$
$443$	29.7255	1.41230	0.706151	+	0.708061i	$0.250430\pi$
$444$	−14.9932	−0.711546
$445$	1.00745	0.0477579
$446$	−8.88501	−0.420717
$447$	15.2854	0.722974
$448$	−1.00000	−0.0472456
$449$	13.5470	0.639323	0.319661	−	0.947532i	$-0.396431\pi$
$449$	13.5470	0.639323	0.319661	+	0.947532i	$0.396431\pi$
$450$	4.28016	0.201769
$451$	36.9504	1.73993
$452$	−17.5188	−0.824014
$453$	−9.94030	−0.467036
$454$	−19.6178	−0.920710
$455$	−4.04988	−0.189861
$456$	−3.58138	−0.167714
$457$	−4.06347	−0.190081	−0.0950406	−	0.995473i	$-0.530298\pi$
$457$	−4.06347	−0.190081	−0.0950406	+	0.995473i	$0.530298\pi$
$458$	−9.04766	−0.422769
$459$	−11.8794	−0.554484
$460$	1.98229	0.0924249
$461$	−28.8537	−1.34385	−0.671925	−	0.740619i	$-0.734532\pi$
$461$	−28.8537	−1.34385	−0.671925	+	0.740619i	$0.734532\pi$
$462$	−6.65073	−0.309420
$463$	2.43037	0.112949	0.0564744	−	0.998404i	$-0.482014\pi$
$463$	2.43037	0.112949	0.0564744	+	0.998404i	$0.482014\pi$
$464$	−1.92505	−0.0893681
$465$	−11.1007	−0.514781
$466$	−12.4968	−0.578903
$467$	3.04652	0.140976	0.0704880	−	0.997513i	$-0.477544\pi$
$467$	3.04652	0.140976	0.0704880	+	0.997513i	$0.477544\pi$
$468$	−4.10307	−0.189665
$469$	11.6421	0.537583
$470$	3.70421	0.170863
$471$	10.5133	0.484426
$472$	−3.53770	−0.162836
$473$	−11.2036	−0.515143
$474$	3.01459	0.138464
$475$	−9.73736	−0.446781
$476$	2.10525	0.0964940
$477$	15.7052	0.719090
$478$	−20.7502	−0.949091
$479$	−27.7072	−1.26597	−0.632986	−	0.774163i	$-0.718171\pi$
$479$	−27.7072	−1.26597	−0.632986	+	0.774163i	$0.718171\pi$
$480$	−1.55383	−0.0709221
$481$	39.0781	1.78181
$482$	8.41356	0.383227
$483$	2.34637	0.106763
$484$	13.0496	0.593163
$485$	−12.8056	−0.581471
$486$	−11.2728	−0.511344
$487$	5.29140	0.239776	0.119888	−	0.992787i	$-0.461746\pi$
$487$	5.29140	0.239776	0.119888	+	0.992787i	$0.461746\pi$
$488$	−0.0973943	−0.00440883
$489$	1.72045	0.0778016
$490$	1.14574	0.0517594
$491$	3.44552	0.155494	0.0777472	−	0.996973i	$-0.475227\pi$
$491$	3.44552	0.155494	0.0777472	+	0.996973i	$0.475227\pi$
$492$	10.2184	0.460679
$493$	4.05271	0.182525
$494$	9.33448	0.419978
$495$	6.52222	0.293152
$496$	7.14408	0.320779
$497$	6.82158	0.305989
$498$	10.7362	0.481099
$499$	−11.1979	−0.501289	−0.250645	−	0.968079i	$-0.580643\pi$
$499$	−11.1979	−0.501289	−0.250645	+	0.968079i	$0.580643\pi$
$500$	−9.95338	−0.445129
$501$	16.2243	0.724849
$502$	28.7022	1.28104
$503$	8.65536	0.385923	0.192962	−	0.981206i	$-0.438191\pi$
$503$	8.65536	0.385923	0.192962	+	0.981206i	$0.438191\pi$
$504$	1.16079	0.0517058
$505$	−9.51842	−0.423564
$506$	−8.48466	−0.377189
$507$	0.685918	0.0304627
$508$	3.66020	0.162395
$509$	−26.7644	−1.18631	−0.593157	−	0.805087i	$-0.702118\pi$
$509$	−26.7644	−1.18631	−0.593157	+	0.805087i	$0.702118\pi$
$510$	3.27119	0.144851
$511$	5.06332	0.223988
$512$	1.00000	0.0441942
$513$	14.9014	0.657913
$514$	−26.6139	−1.17389
$515$	3.62794	0.159866
$516$	−3.09828	−0.136394
$517$	−15.8549	−0.697296
$518$	−11.0555	−0.485751
$519$	13.4781	0.591623
$520$	4.04988	0.177599
$521$	−12.1340	−0.531602	−0.265801	−	0.964028i	$-0.585636\pi$
$521$	−12.1340	−0.531602	−0.265801	+	0.964028i	$0.585636\pi$
$522$	2.23458	0.0978050
$523$	−34.4822	−1.50780	−0.753901	−	0.656988i	$-0.771830\pi$
$523$	−34.4822	−1.50780	−0.753901	+	0.656988i	$0.771830\pi$
$524$	−10.5257	−0.459816
$525$	−5.00058	−0.218243
$526$	−11.6978	−0.510050
$527$	−15.0401	−0.655156
$528$	6.65073	0.289436
$529$	−20.0066	−0.869853
$530$	−15.5015	−0.673344
$531$	4.10654	0.178208
$532$	−2.64080	−0.114493
$533$	−26.6330	−1.15360
$534$	−1.19249	−0.0516040
$535$	−8.36343	−0.361582
$536$	−11.6421	−0.502863
$537$	−10.0136	−0.432117
$538$	16.0908	0.693724
$539$	−4.90404	−0.211232
$540$	6.46515	0.278216
$541$	40.3882	1.73643	0.868213	−	0.496192i	$-0.165269\pi$
$541$	40.3882	1.73643	0.868213	+	0.496192i	$0.165269\pi$
$542$	2.84989	0.122413
$543$	−1.41472	−0.0607116
$544$	−2.10525	−0.0902619
$545$	−4.82481	−0.206672
$546$	4.79369	0.205151
$547$	29.2613	1.25112	0.625562	−	0.780175i	$-0.284870\pi$
$547$	29.2613	1.25112	0.625562	+	0.780175i	$0.284870\pi$
$548$	1.21489	0.0518977
$549$	0.113055	0.00482505
$550$	18.0825	0.771042
$551$	−5.08367	−0.216572
$552$	−2.34637	−0.0998681
$553$	2.22286	0.0945257
$554$	8.72327	0.370616
$555$	−17.1783	−0.729180
$556$	11.0518	0.468701
$557$	−15.1914	−0.643681	−0.321841	−	0.946794i	$-0.604302\pi$
$557$	−15.1914	−0.643681	−0.321841	+	0.946794i	$0.604302\pi$
$558$	−8.29280	−0.351062
$559$	8.07531	0.341549
$560$	−1.14574	−0.0484165
$561$	−14.0014	−0.591142
$562$	−23.6016	−0.995575
$563$	−29.1446	−1.22830	−0.614149	−	0.789190i	$-0.710501\pi$
$563$	−29.1446	−1.22830	−0.614149	+	0.789190i	$0.710501\pi$
$564$	−4.38454	−0.184622
$565$	−20.0720	−0.844436
$566$	29.8859	1.25620
$567$	4.17018	0.175131
$568$	−6.82158	−0.286227
$569$	20.7375	0.869363	0.434682	−	0.900584i	$-0.356861\pi$
$569$	20.7375	0.869363	0.434682	+	0.900584i	$0.356861\pi$
$570$	−4.10334	−0.171870
$571$	30.7830	1.28823	0.644114	−	0.764929i	$-0.277226\pi$
$571$	30.7830	1.28823	0.644114	+	0.764929i	$0.277226\pi$
$572$	−17.3344	−0.724787
$573$	−17.8915	−0.747429
$574$	7.53470	0.314492
$575$	−6.37949	−0.266043
$576$	−1.16079	−0.0483664
$577$	13.2893	0.553240	0.276620	−	0.960979i	$-0.410786\pi$
$577$	13.2893	0.553240	0.276620	+	0.960979i	$0.410786\pi$
$578$	−12.5679	−0.522756
$579$	−24.6502	−1.02443
$580$	−2.20561	−0.0915830
$581$	7.91650	0.328432
$582$	15.1575	0.628298
$583$	66.3501	2.74794
$584$	−5.06332	−0.209522
$585$	−4.70107	−0.194365
$586$	23.3294	0.963728
$587$	9.51557	0.392750	0.196375	−	0.980529i	$-0.437083\pi$
$587$	9.51557	0.392750	0.196375	+	0.980529i	$0.437083\pi$
$588$	−1.35617	−0.0559277
$589$	18.8661	0.777364
$590$	−4.05329	−0.166871
$591$	−22.2177	−0.913913
$592$	11.0555	0.454379
$593$	−25.1462	−1.03263	−0.516316	−	0.856398i	$-0.672697\pi$
$593$	−25.1462	−1.03263	−0.516316	+	0.856398i	$0.672697\pi$
$594$	−27.6723	−1.13541
$595$	2.41208	0.0988855
$596$	−11.2710	−0.461677
$597$	7.85847	0.321626
$598$	6.11555	0.250083
$599$	29.9202	1.22251	0.611253	−	0.791436i	$-0.290666\pi$
$599$	29.9202	1.22251	0.611253	+	0.791436i	$0.290666\pi$
$600$	5.00058	0.204148
$601$	32.4455	1.32348	0.661739	−	0.749734i	$-0.269819\pi$
$601$	32.4455	1.32348	0.661739	+	0.749734i	$0.269819\pi$
$602$	−2.28457	−0.0931122
$603$	13.5141	0.550336
$604$	7.32966	0.298240
$605$	14.9515	0.607863
$606$	11.2666	0.457674
$607$	−22.3150	−0.905736	−0.452868	−	0.891577i	$-0.649599\pi$
$607$	−22.3150	−0.905736	−0.452868	+	0.891577i	$0.649599\pi$
$608$	2.64080	0.107099
$609$	−2.61070	−0.105791
$610$	−0.111589	−0.00451810
$611$	11.4278	0.462320
$612$	2.44376	0.0987832
$613$	−38.9110	−1.57160	−0.785799	−	0.618481i	$-0.787748\pi$
$613$	−38.9110	−1.57160	−0.785799	+	0.618481i	$0.787748\pi$
$614$	−11.0714	−0.446805
$615$	11.7076	0.472096
$616$	4.90404	0.197589
$617$	23.5506	0.948113	0.474057	−	0.880494i	$-0.342789\pi$
$617$	23.5506	0.948113	0.474057	+	0.880494i	$0.342789\pi$
$618$	−4.29426	−0.172741
$619$	−20.8450	−0.837829	−0.418915	−	0.908026i	$-0.637589\pi$
$619$	−20.8450	−0.837829	−0.418915	+	0.908026i	$0.637589\pi$
$620$	8.18528	0.328729
$621$	9.76275	0.391766
$622$	−20.0417	−0.803600
$623$	−0.879303	−0.0352285
$624$	−4.79369	−0.191901
$625$	7.03236	0.281294
$626$	−14.6082	−0.583862
$627$	17.5632	0.701408
$628$	−7.75216	−0.309345
$629$	−23.2746	−0.928020
$630$	1.32997	0.0529873
$631$	−29.1169	−1.15913	−0.579563	−	0.814928i	$-0.696777\pi$
$631$	−29.1169	−1.15913	−0.579563	+	0.814928i	$0.696777\pi$
$632$	−2.22286	−0.0884207
$633$	−13.4491	−0.534554
$634$	−4.45017	−0.176739
$635$	4.19365	0.166420
$636$	18.3486	0.727569
$637$	3.53472	0.140051
$638$	9.44051	0.373753
$639$	7.91844	0.313248
$640$	1.14574	0.0452894
$641$	−43.4277	−1.71529	−0.857645	−	0.514242i	$-0.828073\pi$
$641$	−43.4277	−1.71529	−0.857645	+	0.514242i	$0.828073\pi$
$642$	9.89948	0.390701
$643$	−2.95223	−0.116425	−0.0582123	−	0.998304i	$-0.518540\pi$
$643$	−2.95223	−0.116425	−0.0582123	+	0.998304i	$0.518540\pi$
$644$	−1.73014	−0.0681770
$645$	−3.54983	−0.139774
$646$	−5.55955	−0.218738
$647$	15.2926	0.601213	0.300607	−	0.953748i	$-0.402811\pi$
$647$	15.2926	0.601213	0.300607	+	0.953748i	$0.402811\pi$
$648$	−4.17018	−0.163820
$649$	17.3490	0.681008
$650$	−13.0335	−0.511215
$651$	9.68861	0.379727
$652$	−1.26861	−0.0496825
$653$	31.9240	1.24928	0.624640	−	0.780913i	$-0.285246\pi$
$653$	31.9240	1.24928	0.624640	+	0.780913i	$0.285246\pi$
$654$	5.71095	0.223316
$655$	−12.0597	−0.471212
$656$	−7.53470	−0.294181
$657$	5.87747	0.229302
$658$	−3.23302	−0.126036
$659$	−31.4421	−1.22481	−0.612406	−	0.790544i	$-0.709798\pi$
$659$	−31.4421	−1.22481	−0.612406	+	0.790544i	$0.709798\pi$
$660$	7.62002	0.296609
$661$	7.09662	0.276027	0.138013	−	0.990430i	$-0.455928\pi$
$661$	7.09662	0.276027	0.138013	+	0.990430i	$0.455928\pi$
$662$	33.9755	1.32049
$663$	10.0919	0.391938
$664$	−7.91650	−0.307220
$665$	−3.02568	−0.117331
$666$	−12.8332	−0.497275
$667$	−3.33060	−0.128961
$668$	−11.9633	−0.462874
$669$	12.0496	0.465865
$670$	−13.3389	−0.515325
$671$	0.477625	0.0184385
$672$	1.35617	0.0523155
$673$	−31.2657	−1.20520	−0.602602	−	0.798042i	$-0.705869\pi$
$673$	−31.2657	−1.20520	−0.602602	+	0.798042i	$0.705869\pi$
$674$	−19.5007	−0.751140
$675$	−20.8064	−0.800839
$676$	−0.505775	−0.0194529
$677$	29.0329	1.11582	0.557912	−	0.829900i	$-0.311603\pi$
$677$	29.0329	1.11582	0.557912	+	0.829900i	$0.311603\pi$
$678$	23.7585	0.912440
$679$	11.1767	0.428921
$680$	−2.41208	−0.0924989
$681$	26.6052	1.01951
$682$	−35.0348	−1.34155
$683$	−44.7310	−1.71159	−0.855793	−	0.517319i	$-0.826930\pi$
$683$	−44.7310	−1.71159	−0.855793	+	0.517319i	$0.826930\pi$
$684$	−3.06542	−0.117209
$685$	1.39196	0.0531839
$686$	−1.00000	−0.0381802
$687$	12.2702	0.468137
$688$	2.28457	0.0870985
$689$	−47.8236	−1.82193
$690$	−2.68833	−0.102343
$691$	8.20859	0.312270	0.156135	−	0.987736i	$-0.450097\pi$
$691$	8.20859	0.312270	0.156135	+	0.987736i	$0.450097\pi$
$692$	−9.93833	−0.377799
$693$	−5.69257	−0.216243
$694$	22.6747	0.860719
$695$	12.6625	0.480317
$696$	2.61070	0.0989583
$697$	15.8624	0.600833
$698$	2.46440	0.0932790
$699$	16.9478	0.641026
$700$	3.68727	0.139366
$701$	−11.0094	−0.415819	−0.207910	−	0.978148i	$-0.566666\pi$
$701$	−11.0094	−0.415819	−0.207910	+	0.978148i	$0.566666\pi$
$702$	19.9456	0.752796
$703$	29.1954	1.10113
$704$	−4.90404	−0.184828
$705$	−5.02355	−0.189198
$706$	14.1125	0.531133
$707$	8.30764	0.312441
$708$	4.79773	0.180310
$709$	−52.0900	−1.95628	−0.978141	−	0.207943i	$-0.933323\pi$
$709$	−52.0900	−1.95628	−0.978141	+	0.207943i	$0.933323\pi$
$710$	−7.81577	−0.293321
$711$	2.58028	0.0967681
$712$	0.879303	0.0329533
$713$	12.3602	0.462895
$714$	−2.85509	−0.106849
$715$	−19.8607	−0.742750
$716$	7.38368	0.275941
$717$	28.1409	1.05094
$718$	25.0089	0.933325
$719$	−9.74203	−0.363316	−0.181658	−	0.983362i	$-0.558146\pi$
$719$	−9.74203	−0.363316	−0.181658	+	0.983362i	$0.558146\pi$
$720$	−1.32997	−0.0495650
$721$	−3.16645	−0.117925
$722$	−12.0262	−0.447568
$723$	−11.4102	−0.424352
$724$	1.04317	0.0387692
$725$	7.09818	0.263620
$726$	−17.6975	−0.656816
$727$	18.2819	0.678038	0.339019	−	0.940779i	$-0.389905\pi$
$727$	18.2819	0.678038	0.339019	+	0.940779i	$0.389905\pi$
$728$	−3.53472	−0.131005
$729$	27.7984	1.02957
$730$	−5.80126	−0.214714
$731$	−4.80960	−0.177889
$732$	0.132084	0.00488195
$733$	−13.6652	−0.504736	−0.252368	−	0.967631i	$-0.581209\pi$
$733$	−13.6652	−0.504736	−0.252368	+	0.967631i	$0.581209\pi$
$734$	−19.9683	−0.737045
$735$	−1.55383	−0.0573137
$736$	1.73014	0.0637737
$737$	57.0934	2.10306
$738$	8.74622	0.321953
$739$	46.1911	1.69917	0.849584	−	0.527453i	$-0.176853\pi$
$739$	46.1911	1.69917	0.849584	+	0.527453i	$0.176853\pi$
$740$	12.6668	0.465640
$741$	−12.6592	−0.465047
$742$	13.5297	0.496690
$743$	2.73788	0.100443	0.0502215	−	0.998738i	$-0.484007\pi$
$743$	2.73788	0.100443	0.0502215	+	0.998738i	$0.484007\pi$
$744$	−9.68861	−0.355202
$745$	−12.9136	−0.473119
$746$	−13.6918	−0.501292
$747$	9.18942	0.336223
$748$	10.3242	0.377491
$749$	7.29957	0.266720
$750$	13.4985	0.492896
$751$	15.9346	0.581463	0.290732	−	0.956805i	$-0.406101\pi$
$751$	15.9346	0.581463	0.290732	+	0.956805i	$0.406101\pi$
$752$	3.23302	0.117896
$753$	−38.9252	−1.41851
$754$	−6.80450	−0.247805
$755$	8.39791	0.305631
$756$	−5.64276	−0.205225
$757$	37.2259	1.35300	0.676500	−	0.736443i	$-0.263496\pi$
$757$	37.2259	1.35300	0.676500	+	0.736443i	$0.263496\pi$
$758$	4.21371	0.153049
$759$	11.5067	0.417666
$760$	3.02568	0.109753
$761$	48.6629	1.76403	0.882015	−	0.471221i	$-0.156187\pi$
$761$	48.6629	1.76403	0.882015	+	0.471221i	$0.156187\pi$
$762$	−4.96387	−0.179822
$763$	4.21108	0.152451
$764$	13.1926	0.477293
$765$	2.79992	0.101231
$766$	18.0865	0.653493
$767$	−12.5048	−0.451521
$768$	−1.35617	−0.0489367
$769$	23.3698	0.842736	0.421368	−	0.906890i	$-0.361550\pi$
$769$	23.3698	0.842736	0.421368	+	0.906890i	$0.361550\pi$
$770$	5.61876	0.202486
$771$	36.0931	1.29986
$772$	18.1763	0.654180
$773$	−7.11128	−0.255775	−0.127887	−	0.991789i	$-0.540820\pi$
$773$	−7.11128	−0.255775	−0.127887	+	0.991789i	$0.540820\pi$
$774$	−2.65191	−0.0953211
$775$	−26.3422	−0.946239
$776$	−11.1767	−0.401219
$777$	14.9932	0.537878
$778$	25.5220	0.915008
$779$	−19.8976	−0.712907
$780$	−5.49233	−0.196657
$781$	33.4533	1.19705
$782$	−3.64238	−0.130251
$783$	−10.8626	−0.388197
$784$	1.00000	0.0357143
$785$	−8.88197	−0.317011
$786$	14.2746	0.509160
$787$	1.24229	0.0442829	0.0221414	−	0.999755i	$-0.492952\pi$
$787$	1.24229	0.0442829	0.0221414	+	0.999755i	$0.492952\pi$
$788$	16.3826	0.583606
$789$	15.8643	0.564784
$790$	−2.54683	−0.0906120
$791$	17.5188	0.622896
$792$	5.69257	0.202277
$793$	−0.344261	−0.0122251
$794$	−17.1808	−0.609723
$795$	21.0228	0.745601
$796$	−5.79459	−0.205384
$797$	−40.4081	−1.43133	−0.715663	−	0.698445i	$-0.753876\pi$
$797$	−40.4081	−1.43133	−0.715663	+	0.698445i	$0.753876\pi$
$798$	3.58138	0.126780
$799$	−6.80632	−0.240790
$800$	−3.68727	−0.130365
$801$	−1.02069	−0.0360643
$802$	15.8302	0.558982
$803$	24.8307	0.876257
$804$	15.7887	0.556826
$805$	−1.98229	−0.0698666
$806$	25.2523	0.889475
$807$	−21.8219	−0.768169
$808$	−8.30764	−0.292262
$809$	42.1841	1.48312	0.741558	−	0.670889i	$-0.234087\pi$
$809$	42.1841	1.48312	0.741558	+	0.670889i	$0.234087\pi$
$810$	−4.77795	−0.167880
$811$	−44.2422	−1.55355	−0.776776	−	0.629777i	$-0.783146\pi$
$811$	−44.2422	−1.55355	−0.776776	+	0.629777i	$0.783146\pi$
$812$	1.92505	0.0675560
$813$	−3.86494	−0.135549
$814$	−54.2166	−1.90029
$815$	−1.45350	−0.0509138
$816$	2.85509	0.0999480
$817$	6.03310	0.211071
$818$	−26.5689	−0.928960
$819$	4.10307	0.143373
$820$	−8.63282	−0.301471
$821$	−7.90394	−0.275850	−0.137925	−	0.990443i	$-0.544043\pi$
$821$	−7.90394	−0.275850	−0.137925	+	0.990443i	$0.544043\pi$
$822$	−1.64761	−0.0574669
$823$	−22.5714	−0.786789	−0.393394	−	0.919370i	$-0.628699\pi$
$823$	−22.5714	−0.786789	−0.393394	+	0.919370i	$0.628699\pi$
$824$	3.16645	0.110309
$825$	−24.5231	−0.853783
$826$	3.53770	0.123092
$827$	−14.5987	−0.507648	−0.253824	−	0.967250i	$-0.581688\pi$
$827$	−14.5987	−0.507648	−0.253824	+	0.967250i	$0.581688\pi$
$828$	−2.00833	−0.0697944
$829$	−37.1226	−1.28932	−0.644660	−	0.764469i	$-0.723001\pi$
$829$	−37.1226	−1.28932	−0.644660	+	0.764469i	$0.723001\pi$
$830$	−9.07028	−0.314834
$831$	−11.8303	−0.410388
$832$	3.53472	0.122544
$833$	−2.10525	−0.0729426
$834$	−14.9882	−0.518998
$835$	−13.7069	−0.474345
$836$	−12.9506	−0.447905
$837$	40.3123	1.39340
$838$	2.73493	0.0944765
$839$	44.5317	1.53740	0.768702	−	0.639607i	$-0.220903\pi$
$839$	44.5317	1.53740	0.768702	+	0.639607i	$0.220903\pi$
$840$	1.55383	0.0536121
$841$	−25.2942	−0.872213
$842$	−16.8138	−0.579442
$843$	32.0079	1.10241
$844$	9.91695	0.341355
$845$	−0.579488	−0.0199350
$846$	−3.75287	−0.129026
$847$	−13.0496	−0.448389
$848$	−13.5297	−0.464611
$849$	−40.5304	−1.39100
$850$	7.76264	0.266256
$851$	19.1276	0.655685
$852$	9.25124	0.316942
$853$	28.3695	0.971352	0.485676	−	0.874139i	$-0.338574\pi$
$853$	28.3695	0.971352	0.485676	+	0.874139i	$0.338574\pi$
$854$	0.0973943	0.00333276
$855$	−3.51219	−0.120114
$856$	−7.29957	−0.249494
$857$	44.9274	1.53469	0.767346	−	0.641233i	$-0.221577\pi$
$857$	44.9274	1.53469	0.767346	+	0.641233i	$0.221577\pi$
$858$	23.5084	0.802565
$859$	9.47658	0.323337	0.161668	−	0.986845i	$-0.448312\pi$
$859$	9.47658	0.323337	0.161668	+	0.986845i	$0.448312\pi$
$860$	2.61753	0.0892570
$861$	−10.2184	−0.348241
$862$	1.00000	0.0340601
$863$	53.9640	1.83696	0.918478	−	0.395472i	$-0.129419\pi$
$863$	53.9640	1.83696	0.918478	+	0.395472i	$0.129419\pi$
$864$	5.64276	0.191971
$865$	−11.3868	−0.387162
$866$	11.5140	0.391263
$867$	17.0443	0.578854
$868$	−7.14408	−0.242486
$869$	10.9010	0.369791
$870$	2.99119	0.101411
$871$	−41.1516	−1.39437
$872$	−4.21108	−0.142605
$873$	12.9738	0.439096
$874$	4.56895	0.154547
$875$	9.95338	0.336486
$876$	6.86675	0.232006
$877$	−52.3417	−1.76745	−0.883726	−	0.468004i	$-0.844973\pi$
$877$	−52.3417	−1.76745	−0.883726	+	0.468004i	$0.844973\pi$
$878$	−9.27411	−0.312986
$879$	−31.6387	−1.06715
$880$	−5.61876	−0.189408
$881$	−49.3253	−1.66181	−0.830907	−	0.556412i	$-0.812178\pi$
$881$	−49.3253	−1.66181	−0.830907	+	0.556412i	$0.812178\pi$
$882$	−1.16079	−0.0390859
$883$	−15.2043	−0.511665	−0.255833	−	0.966721i	$-0.582350\pi$
$883$	−15.2043	−0.511665	−0.255833	+	0.966721i	$0.582350\pi$
$884$	−7.44147	−0.250284
$885$	5.49697	0.184779
$886$	29.7255	0.998648
$887$	7.79135	0.261608	0.130804	−	0.991408i	$-0.458244\pi$
$887$	7.79135	0.261608	0.130804	+	0.991408i	$0.458244\pi$
$888$	−14.9932	−0.503139
$889$	−3.66020	−0.122759
$890$	1.00745	0.0337700
$891$	20.4507	0.685125
$892$	−8.88501	−0.297492
$893$	8.53777	0.285706
$894$	15.2854	0.511220
$895$	8.45980	0.282780
$896$	−1.00000	−0.0334077
$897$	−8.29375	−0.276920
$898$	13.5470	0.452070
$899$	−13.7527	−0.458678
$900$	4.28016	0.142672
$901$	28.4834	0.948919
$902$	36.9504	1.23032
$903$	3.09828	0.103104
$904$	−17.5188	−0.582666
$905$	1.19521	0.0397300
$906$	−9.94030	−0.330244
$907$	26.0447	0.864799	0.432400	−	0.901682i	$-0.357667\pi$
$907$	26.0447	0.864799	0.432400	+	0.901682i	$0.357667\pi$
$908$	−19.6178	−0.651040
$909$	9.64345	0.319853
$910$	−4.04988	−0.134252
$911$	30.4713	1.00956	0.504779	−	0.863248i	$-0.331574\pi$
$911$	30.4713	1.00956	0.504779	+	0.863248i	$0.331574\pi$
$912$	−3.58138	−0.118591
$913$	38.8228	1.28485
$914$	−4.06347	−0.134408
$915$	0.151334	0.00500294
$916$	−9.04766	−0.298943
$917$	10.5257	0.347589
$918$	−11.8794	−0.392079
$919$	−26.8941	−0.887155	−0.443578	−	0.896236i	$-0.646291\pi$
$919$	−26.8941	−0.887155	−0.443578	+	0.896236i	$0.646291\pi$
$920$	1.98229	0.0653543
$921$	15.0147	0.494752
$922$	−28.8537	−0.950245
$923$	−24.1123	−0.793667
$924$	−6.65073	−0.218793
$925$	−40.7647	−1.34034
$926$	2.43037	0.0798669
$927$	−3.67560	−0.120722
$928$	−1.92505	−0.0631928
$929$	45.3528	1.48798	0.743988	−	0.668193i	$-0.232932\pi$
$929$	45.3528	1.48798	0.743988	+	0.668193i	$0.232932\pi$
$930$	−11.1007	−0.364005
$931$	2.64080	0.0865488
$932$	−12.4968	−0.409346
$933$	27.1801	0.889835
$934$	3.04652	0.0996851
$935$	11.8289	0.386847
$936$	−4.10307	−0.134113
$937$	−30.3138	−0.990308	−0.495154	−	0.868805i	$-0.664888\pi$
$937$	−30.3138	−0.990308	−0.495154	+	0.868805i	$0.664888\pi$
$938$	11.6421	0.380129
$939$	19.8113	0.646517
$940$	3.70421	0.120818
$941$	−49.2076	−1.60412	−0.802061	−	0.597241i	$-0.796263\pi$
$941$	−49.2076	−1.60412	−0.802061	+	0.597241i	$0.796263\pi$
$942$	10.5133	0.342541
$943$	−13.0361	−0.424513
$944$	−3.53770	−0.115142
$945$	−6.46515	−0.210311
$946$	−11.2036	−0.364261
$947$	15.8750	0.515867	0.257934	−	0.966163i	$-0.416958\pi$
$947$	15.8750	0.515867	0.257934	+	0.966163i	$0.416958\pi$
$948$	3.01459	0.0979092
$949$	−17.8974	−0.580975
$950$	−9.73736	−0.315922
$951$	6.03521	0.195705
$952$	2.10525	0.0682316
$953$	27.9330	0.904838	0.452419	−	0.891806i	$-0.350561\pi$
$953$	27.9330	0.904838	0.452419	+	0.891806i	$0.350561\pi$
$954$	15.7052	0.508473
$955$	15.1154	0.489122
$956$	−20.7502	−0.671109
$957$	−12.8030	−0.413861
$958$	−27.7072	−0.895177
$959$	−1.21489	−0.0392310
$960$	−1.55383	−0.0501495
$961$	20.0379	0.646384
$962$	39.0781	1.25993
$963$	8.47329	0.273048
$964$	8.41356	0.270982
$965$	20.8254	0.670393
$966$	2.34637	0.0754932
$967$	12.3904	0.398448	0.199224	−	0.979954i	$-0.436158\pi$
$967$	12.3904	0.398448	0.199224	+	0.979954i	$0.436158\pi$
$968$	13.0496	0.419429
$969$	7.53971	0.242211
$970$	−12.8056	−0.411162
$971$	−11.8212	−0.379359	−0.189680	−	0.981846i	$-0.560745\pi$
$971$	−11.8212	−0.379359	−0.189680	+	0.981846i	$0.560745\pi$
$972$	−11.2728	−0.361575
$973$	−11.0518	−0.354305
$974$	5.29140	0.169547
$975$	17.6757	0.566074
$976$	−0.0973943	−0.00311752
$977$	56.8405	1.81849	0.909245	−	0.416261i	$-0.136660\pi$
$977$	56.8405	1.81849	0.909245	+	0.416261i	$0.136660\pi$
$978$	1.72045	0.0550140
$979$	−4.31213	−0.137816
$980$	1.14574	0.0365994
$981$	4.88819	0.156068
$982$	3.44552	0.109951
$983$	5.39585	0.172101	0.0860504	−	0.996291i	$-0.472575\pi$
$983$	5.39585	0.172101	0.0860504	+	0.996291i	$0.472575\pi$
$984$	10.2184	0.325749
$985$	18.7703	0.598070
$986$	4.05271	0.129065
$987$	4.38454	0.139561
$988$	9.33448	0.296969
$989$	3.95262	0.125686
$990$	6.52222	0.207290
$991$	−44.6814	−1.41935	−0.709676	−	0.704528i	$-0.751159\pi$
$991$	−44.6814	−1.41935	−0.709676	+	0.704528i	$0.751159\pi$
$992$	7.14408	0.226825
$993$	−46.0766	−1.46220
$994$	6.82158	0.216367
$995$	−6.63910	−0.210474
$996$	10.7362	0.340188
$997$	17.0680	0.540548	0.270274	−	0.962783i	$-0.412886\pi$
$997$	17.0680	0.540548	0.270274	+	0.962783i	$0.412886\pi$
$998$	−11.1979	−0.354465
$999$	62.3836	1.97373

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.l.1.8	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.l.1.8	✓	20	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.35617 q^{3} +1.00000 q^{4} +1.14574 q^{5} -1.35617 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.16079 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.35617 q^{3} +1.00000 q^{4} +1.14574 q^{5} -1.35617 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.16079 q^{9} +1.14574 q^{10} -4.90404 q^{11} -1.35617 q^{12} +3.53472 q^{13} -1.00000 q^{14} -1.55383 q^{15} +1.00000 q^{16} -2.10525 q^{17} -1.16079 q^{18} +2.64080 q^{19} +1.14574 q^{20} +1.35617 q^{21} -4.90404 q^{22} +1.73014 q^{23} -1.35617 q^{24} -3.68727 q^{25} +3.53472 q^{26} +5.64276 q^{27} -1.00000 q^{28} -1.92505 q^{29} -1.55383 q^{30} +7.14408 q^{31} +1.00000 q^{32} +6.65073 q^{33} -2.10525 q^{34} -1.14574 q^{35} -1.16079 q^{36} +11.0555 q^{37} +2.64080 q^{38} -4.79369 q^{39} +1.14574 q^{40} -7.53470 q^{41} +1.35617 q^{42} +2.28457 q^{43} -4.90404 q^{44} -1.32997 q^{45} +1.73014 q^{46} +3.23302 q^{47} -1.35617 q^{48} +1.00000 q^{49} -3.68727 q^{50} +2.85509 q^{51} +3.53472 q^{52} -13.5297 q^{53} +5.64276 q^{54} -5.61876 q^{55} -1.00000 q^{56} -3.58138 q^{57} -1.92505 q^{58} -3.53770 q^{59} -1.55383 q^{60} -0.0973943 q^{61} +7.14408 q^{62} +1.16079 q^{63} +1.00000 q^{64} +4.04988 q^{65} +6.65073 q^{66} -11.6421 q^{67} -2.10525 q^{68} -2.34637 q^{69} -1.14574 q^{70} -6.82158 q^{71} -1.16079 q^{72} -5.06332 q^{73} +11.0555 q^{74} +5.00058 q^{75} +2.64080 q^{76} +4.90404 q^{77} -4.79369 q^{78} -2.22286 q^{79} +1.14574 q^{80} -4.17018 q^{81} -7.53470 q^{82} -7.91650 q^{83} +1.35617 q^{84} -2.41208 q^{85} +2.28457 q^{86} +2.61070 q^{87} -4.90404 q^{88} +0.879303 q^{89} -1.32997 q^{90} -3.53472 q^{91} +1.73014 q^{92} -9.68861 q^{93} +3.23302 q^{94} +3.02568 q^{95} -1.35617 q^{96} -11.1767 q^{97} +1.00000 q^{98} +5.69257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * q^99

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