LMFDB - Embedded newform 6034.2.a.m.1.9

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:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.16337 q^{3} +1.00000 q^{4} -3.30128 q^{5} -1.16337 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.64657 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.16337 q^{3} +1.00000 q^{4} -3.30128 q^{5} -1.16337 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.64657 q^{9} -3.30128 q^{10} -2.24539 q^{11} -1.16337 q^{12} +4.49944 q^{13} +1.00000 q^{14} +3.84061 q^{15} +1.00000 q^{16} -7.24524 q^{17} -1.64657 q^{18} +8.14319 q^{19} -3.30128 q^{20} -1.16337 q^{21} -2.24539 q^{22} -3.45657 q^{23} -1.16337 q^{24} +5.89846 q^{25} +4.49944 q^{26} +5.40568 q^{27} +1.00000 q^{28} +7.71505 q^{29} +3.84061 q^{30} +0.775815 q^{31} +1.00000 q^{32} +2.61221 q^{33} -7.24524 q^{34} -3.30128 q^{35} -1.64657 q^{36} +4.79980 q^{37} +8.14319 q^{38} -5.23451 q^{39} -3.30128 q^{40} +2.03636 q^{41} -1.16337 q^{42} -10.2241 q^{43} -2.24539 q^{44} +5.43580 q^{45} -3.45657 q^{46} +2.99854 q^{47} -1.16337 q^{48} +1.00000 q^{49} +5.89846 q^{50} +8.42889 q^{51} +4.49944 q^{52} -7.07475 q^{53} +5.40568 q^{54} +7.41265 q^{55} +1.00000 q^{56} -9.47354 q^{57} +7.71505 q^{58} -0.582145 q^{59} +3.84061 q^{60} -7.45353 q^{61} +0.775815 q^{62} -1.64657 q^{63} +1.00000 q^{64} -14.8539 q^{65} +2.61221 q^{66} +8.66470 q^{67} -7.24524 q^{68} +4.02127 q^{69} -3.30128 q^{70} +0.636126 q^{71} -1.64657 q^{72} +1.38797 q^{73} +4.79980 q^{74} -6.86208 q^{75} +8.14319 q^{76} -2.24539 q^{77} -5.23451 q^{78} -3.58896 q^{79} -3.30128 q^{80} -1.34909 q^{81} +2.03636 q^{82} -3.26524 q^{83} -1.16337 q^{84} +23.9186 q^{85} -10.2241 q^{86} -8.97545 q^{87} -2.24539 q^{88} -18.4744 q^{89} +5.43580 q^{90} +4.49944 q^{91} -3.45657 q^{92} -0.902559 q^{93} +2.99854 q^{94} -26.8830 q^{95} -1.16337 q^{96} +1.99510 q^{97} +1.00000 q^{98} +3.69719 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * 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
$3$	−1.16337	−0.671672	−0.335836	−	0.941921i	$-0.609019\pi$
$3$	−1.16337	−0.671672	−0.335836	+	0.941921i	$0.609019\pi$
$4$	1.00000	0.500000
$5$	−3.30128	−1.47638	−0.738189	−	0.674594i	$-0.764319\pi$
$5$	−3.30128	−1.47638	−0.738189	+	0.674594i	$0.764319\pi$
$6$	−1.16337	−0.474944
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−1.64657	−0.548857
$10$	−3.30128	−1.04396
$11$	−2.24539	−0.677010	−0.338505	−	0.940965i	$-0.609921\pi$
$11$	−2.24539	−0.677010	−0.338505	+	0.940965i	$0.609921\pi$
$12$	−1.16337	−0.335836
$13$	4.49944	1.24792	0.623960	−	0.781456i	$-0.285523\pi$
$13$	4.49944	1.24792	0.623960	+	0.781456i	$0.285523\pi$
$14$	1.00000	0.267261
$15$	3.84061	0.991641
$16$	1.00000	0.250000
$17$	−7.24524	−1.75723	−0.878615	−	0.477532i	$-0.841532\pi$
$17$	−7.24524	−1.75723	−0.878615	+	0.477532i	$0.841532\pi$
$18$	−1.64657	−0.388101
$19$	8.14319	1.86818	0.934088	−	0.357043i	$-0.116215\pi$
$19$	8.14319	1.86818	0.934088	+	0.357043i	$0.116215\pi$
$20$	−3.30128	−0.738189
$21$	−1.16337	−0.253868
$22$	−2.24539	−0.478718
$23$	−3.45657	−0.720746	−0.360373	−	0.932808i	$-0.617351\pi$
$23$	−3.45657	−0.720746	−0.360373	+	0.932808i	$0.617351\pi$
$24$	−1.16337	−0.237472
$25$	5.89846	1.17969
$26$	4.49944	0.882413
$27$	5.40568	1.04032
$28$	1.00000	0.188982
$29$	7.71505	1.43265	0.716325	−	0.697767i	$-0.245823\pi$
$29$	7.71505	1.43265	0.716325	+	0.697767i	$0.245823\pi$
$30$	3.84061	0.701196
$31$	0.775815	0.139340	0.0696702	−	0.997570i	$-0.477805\pi$
$31$	0.775815	0.139340	0.0696702	+	0.997570i	$0.477805\pi$
$32$	1.00000	0.176777
$33$	2.61221	0.454728
$34$	−7.24524	−1.24255
$35$	−3.30128	−0.558018
$36$	−1.64657	−0.274429
$37$	4.79980	0.789083	0.394541	−	0.918878i	$-0.370903\pi$
$37$	4.79980	0.789083	0.394541	+	0.918878i	$0.370903\pi$
$38$	8.14319	1.32100
$39$	−5.23451	−0.838193
$40$	−3.30128	−0.521978
$41$	2.03636	0.318026	0.159013	−	0.987276i	$-0.449169\pi$
$41$	2.03636	0.318026	0.159013	+	0.987276i	$0.449169\pi$
$42$	−1.16337	−0.179512
$43$	−10.2241	−1.55916	−0.779579	−	0.626304i	$-0.784567\pi$
$43$	−10.2241	−1.55916	−0.779579	+	0.626304i	$0.784567\pi$
$44$	−2.24539	−0.338505
$45$	5.43580	0.810321
$46$	−3.45657	−0.509644
$47$	2.99854	0.437382	0.218691	−	0.975794i	$-0.429821\pi$
$47$	2.99854	0.437382	0.218691	+	0.975794i	$0.429821\pi$
$48$	−1.16337	−0.167918
$49$	1.00000	0.142857
$50$	5.89846	0.834168
$51$	8.42889	1.18028
$52$	4.49944	0.623960
$53$	−7.07475	−0.971792	−0.485896	−	0.874017i	$-0.661507\pi$
$53$	−7.07475	−0.971792	−0.485896	+	0.874017i	$0.661507\pi$
$54$	5.40568	0.735620
$55$	7.41265	0.999522
$56$	1.00000	0.133631
$57$	−9.47354	−1.25480
$58$	7.71505	1.01304
$59$	−0.582145	−0.0757888	−0.0378944	−	0.999282i	$-0.512065\pi$
$59$	−0.582145	−0.0757888	−0.0378944	+	0.999282i	$0.512065\pi$
$60$	3.84061	0.495821
$61$	−7.45353	−0.954327	−0.477163	−	0.878815i	$-0.658335\pi$
$61$	−7.45353	−0.954327	−0.477163	+	0.878815i	$0.658335\pi$
$62$	0.775815	0.0985286
$63$	−1.64657	−0.207449
$64$	1.00000	0.125000
$65$	−14.8539	−1.84240
$66$	2.61221	0.321541
$67$	8.66470	1.05856	0.529281	−	0.848447i	$-0.322462\pi$
$67$	8.66470	1.05856	0.529281	+	0.848447i	$0.322462\pi$
$68$	−7.24524	−0.878615
$69$	4.02127	0.484104
$70$	−3.30128	−0.394579
$71$	0.636126	0.0754943	0.0377472	−	0.999287i	$-0.487982\pi$
$71$	0.636126	0.0754943	0.0377472	+	0.999287i	$0.487982\pi$
$72$	−1.64657	−0.194050
$73$	1.38797	0.162449	0.0812245	−	0.996696i	$-0.474117\pi$
$73$	1.38797	0.162449	0.0812245	+	0.996696i	$0.474117\pi$
$74$	4.79980	0.557966
$75$	−6.86208	−0.792365
$76$	8.14319	0.934088
$77$	−2.24539	−0.255886
$78$	−5.23451	−0.592692
$79$	−3.58896	−0.403790	−0.201895	−	0.979407i	$-0.564710\pi$
$79$	−3.58896	−0.403790	−0.201895	+	0.979407i	$0.564710\pi$
$80$	−3.30128	−0.369094
$81$	−1.34909	−0.149899
$82$	2.03636	0.224879
$83$	−3.26524	−0.358407	−0.179203	−	0.983812i	$-0.557352\pi$
$83$	−3.26524	−0.358407	−0.179203	+	0.983812i	$0.557352\pi$
$84$	−1.16337	−0.126934
$85$	23.9186	2.59433
$86$	−10.2241	−1.10249
$87$	−8.97545	−0.962270
$88$	−2.24539	−0.239359
$89$	−18.4744	−1.95828	−0.979141	−	0.203183i	$-0.934871\pi$
$89$	−18.4744	−1.95828	−0.979141	+	0.203183i	$0.934871\pi$
$90$	5.43580	0.572983
$91$	4.49944	0.471670
$92$	−3.45657	−0.360373
$93$	−0.902559	−0.0935910
$94$	2.99854	0.309276
$95$	−26.8830	−2.75813
$96$	−1.16337	−0.118736
$97$	1.99510	0.202571	0.101286	−	0.994857i	$-0.467704\pi$
$97$	1.99510	0.202571	0.101286	+	0.994857i	$0.467704\pi$
$98$	1.00000	0.101015
$99$	3.69719	0.371582
$100$	5.89846	0.589846
$101$	16.4367	1.63551	0.817754	−	0.575568i	$-0.195219\pi$
$101$	16.4367	1.63551	0.817754	+	0.575568i	$0.195219\pi$
$102$	8.42889	0.834585
$103$	−13.7185	−1.35173	−0.675864	−	0.737026i	$-0.736229\pi$
$103$	−13.7185	−1.35173	−0.675864	+	0.737026i	$0.736229\pi$
$104$	4.49944	0.441206
$105$	3.84061	0.374805
$106$	−7.07475	−0.687161
$107$	−16.1037	−1.55680	−0.778402	−	0.627767i	$-0.783969\pi$
$107$	−16.1037	−1.55680	−0.778402	+	0.627767i	$0.783969\pi$
$108$	5.40568	0.520162
$109$	−16.3177	−1.56295	−0.781474	−	0.623937i	$-0.785532\pi$
$109$	−16.3177	−1.56295	−0.781474	+	0.623937i	$0.785532\pi$
$110$	7.41265	0.706769
$111$	−5.58394	−0.530004
$112$	1.00000	0.0944911
$113$	10.2838	0.967416	0.483708	−	0.875229i	$-0.339290\pi$
$113$	10.2838	0.967416	0.483708	+	0.875229i	$0.339290\pi$
$114$	−9.47354	−0.887278
$115$	11.4111	1.06409
$116$	7.71505	0.716325
$117$	−7.40865	−0.684930
$118$	−0.582145	−0.0535908
$119$	−7.24524	−0.664170
$120$	3.84061	0.350598
$121$	−5.95824	−0.541658
$122$	−7.45353	−0.674811
$123$	−2.36904	−0.213609
$124$	0.775815	0.0696702
$125$	−2.96606	−0.265292
$126$	−1.64657	−0.146688
$127$	2.64730	0.234910	0.117455	−	0.993078i	$-0.462526\pi$
$127$	2.64730	0.234910	0.117455	+	0.993078i	$0.462526\pi$
$128$	1.00000	0.0883883
$129$	11.8944	1.04724
$130$	−14.8539	−1.30277
$131$	14.0317	1.22596	0.612978	−	0.790100i	$-0.289971\pi$
$131$	14.0317	1.22596	0.612978	+	0.790100i	$0.289971\pi$
$132$	2.61221	0.227364
$133$	8.14319	0.706104
$134$	8.66470	0.748516
$135$	−17.8457	−1.53591
$136$	−7.24524	−0.621274
$137$	−8.93369	−0.763257	−0.381628	−	0.924316i	$-0.624637\pi$
$137$	−8.93369	−0.763257	−0.381628	+	0.924316i	$0.624637\pi$
$138$	4.02127	0.342313
$139$	−5.51148	−0.467478	−0.233739	−	0.972299i	$-0.575096\pi$
$139$	−5.51148	−0.467478	−0.233739	+	0.972299i	$0.575096\pi$
$140$	−3.30128	−0.279009
$141$	−3.48841	−0.293777
$142$	0.636126	0.0533825
$143$	−10.1030	−0.844854
$144$	−1.64657	−0.137214
$145$	−25.4696	−2.11513
$146$	1.38797	0.114869
$147$	−1.16337	−0.0959531
$148$	4.79980	0.394541
$149$	−17.5882	−1.44088	−0.720442	−	0.693515i	$-0.756061\pi$
$149$	−17.5882	−1.44088	−0.720442	+	0.693515i	$0.756061\pi$
$150$	−6.86208	−0.560287
$151$	−22.1148	−1.79968	−0.899840	−	0.436220i	$-0.856317\pi$
$151$	−22.1148	−1.79968	−0.899840	+	0.436220i	$0.856317\pi$
$152$	8.14319	0.660500
$153$	11.9298	0.964468
$154$	−2.24539	−0.180938
$155$	−2.56118	−0.205719
$156$	−5.23451	−0.419096
$157$	11.8935	0.949204	0.474602	−	0.880200i	$-0.342592\pi$
$157$	11.8935	0.949204	0.474602	+	0.880200i	$0.342592\pi$
$158$	−3.58896	−0.285523
$159$	8.23055	0.652725
$160$	−3.30128	−0.260989
$161$	−3.45657	−0.272416
$162$	−1.34909	−0.105994
$163$	3.50175	0.274278	0.137139	−	0.990552i	$-0.456209\pi$
$163$	3.50175	0.274278	0.137139	+	0.990552i	$0.456209\pi$
$164$	2.03636	0.159013
$165$	−8.62365	−0.671350
$166$	−3.26524	−0.253432
$167$	−11.1263	−0.860978	−0.430489	−	0.902596i	$-0.641659\pi$
$167$	−11.1263	−0.860978	−0.430489	+	0.902596i	$0.641659\pi$
$168$	−1.16337	−0.0897559
$169$	7.24497	0.557305
$170$	23.9186	1.83447
$171$	−13.4083	−1.02536
$172$	−10.2241	−0.779579
$173$	20.6677	1.57134	0.785668	−	0.618648i	$-0.212319\pi$
$173$	20.6677	1.57134	0.785668	+	0.618648i	$0.212319\pi$
$174$	−8.97545	−0.680427
$175$	5.89846	0.445881
$176$	−2.24539	−0.169252
$177$	0.677249	0.0509052
$178$	−18.4744	−1.38471
$179$	−9.57613	−0.715754	−0.357877	−	0.933769i	$-0.616499\pi$
$179$	−9.57613	−0.715754	−0.357877	+	0.933769i	$0.616499\pi$
$180$	5.43580	0.405160
$181$	−23.3257	−1.73379	−0.866894	−	0.498492i	$-0.833887\pi$
$181$	−23.3257	−1.73379	−0.866894	+	0.498492i	$0.833887\pi$
$182$	4.49944	0.333521
$183$	8.67121	0.640994
$184$	−3.45657	−0.254822
$185$	−15.8455	−1.16498
$186$	−0.902559	−0.0661789
$187$	16.2684	1.18966
$188$	2.99854	0.218691
$189$	5.40568	0.393205
$190$	−26.8830	−1.95030
$191$	−12.3497	−0.893590	−0.446795	−	0.894636i	$-0.647435\pi$
$191$	−12.3497	−0.893590	−0.446795	+	0.894636i	$0.647435\pi$
$192$	−1.16337	−0.0839590
$193$	14.9391	1.07534	0.537671	−	0.843155i	$-0.319304\pi$
$193$	14.9391	1.07534	0.537671	+	0.843155i	$0.319304\pi$
$194$	1.99510	0.143240
$195$	17.2806	1.23749
$196$	1.00000	0.0714286
$197$	14.3426	1.02187	0.510933	−	0.859621i	$-0.329300\pi$
$197$	14.3426	1.02187	0.510933	+	0.859621i	$0.329300\pi$
$198$	3.69719	0.262748
$199$	5.76080	0.408372	0.204186	−	0.978932i	$-0.434545\pi$
$199$	5.76080	0.408372	0.204186	+	0.978932i	$0.434545\pi$
$200$	5.89846	0.417084
$201$	−10.0802	−0.711005
$202$	16.4367	1.15648
$203$	7.71505	0.541490
$204$	8.42889	0.590140
$205$	−6.72261	−0.469527
$206$	−13.7185	−0.955816
$207$	5.69150	0.395586
$208$	4.49944	0.311980
$209$	−18.2846	−1.26477
$210$	3.84061	0.265027
$211$	−10.5878	−0.728898	−0.364449	−	0.931223i	$-0.618743\pi$
$211$	−10.5878	−0.728898	−0.364449	+	0.931223i	$0.618743\pi$
$212$	−7.07475	−0.485896
$213$	−0.740050	−0.0507074
$214$	−16.1037	−1.10083
$215$	33.7526	2.30191
$216$	5.40568	0.367810
$217$	0.775815	0.0526657
$218$	−16.3177	−1.10517
$219$	−1.61472	−0.109112
$220$	7.41265	0.499761
$221$	−32.5995	−2.19288
$222$	−5.58394	−0.374770
$223$	12.6921	0.849927	0.424964	−	0.905210i	$-0.360287\pi$
$223$	12.6921	0.849927	0.424964	+	0.905210i	$0.360287\pi$
$224$	1.00000	0.0668153
$225$	−9.71223	−0.647482
$226$	10.2838	0.684066
$227$	2.54584	0.168973	0.0844866	−	0.996425i	$-0.473075\pi$
$227$	2.54584	0.168973	0.0844866	+	0.996425i	$0.473075\pi$
$228$	−9.47354	−0.627400
$229$	6.72622	0.444481	0.222241	−	0.974992i	$-0.428663\pi$
$229$	6.72622	0.444481	0.222241	+	0.974992i	$0.428663\pi$
$230$	11.4111	0.752427
$231$	2.61221	0.171871
$232$	7.71505	0.506518
$233$	3.31773	0.217352	0.108676	−	0.994077i	$-0.465339\pi$
$233$	3.31773	0.217352	0.108676	+	0.994077i	$0.465339\pi$
$234$	−7.40865	−0.484319
$235$	−9.89902	−0.645741
$236$	−0.582145	−0.0378944
$237$	4.17529	0.271214
$238$	−7.24524	−0.469639
$239$	−24.8704	−1.60873	−0.804367	−	0.594133i	$-0.797495\pi$
$239$	−24.8704	−1.60873	−0.804367	+	0.594133i	$0.797495\pi$
$240$	3.84061	0.247910
$241$	6.92540	0.446104	0.223052	−	0.974807i	$-0.428398\pi$
$241$	6.92540	0.446104	0.223052	+	0.974807i	$0.428398\pi$
$242$	−5.95824	−0.383010
$243$	−14.6476	−0.939641
$244$	−7.45353	−0.477163
$245$	−3.30128	−0.210911
$246$	−2.36904	−0.151045
$247$	36.6398	2.33134
$248$	0.775815	0.0492643
$249$	3.79868	0.240732
$250$	−2.96606	−0.187590
$251$	17.9769	1.13469	0.567347	−	0.823479i	$-0.307970\pi$
$251$	17.9769	1.13469	0.567347	+	0.823479i	$0.307970\pi$
$252$	−1.64657	−0.103724
$253$	7.76135	0.487952
$254$	2.64730	0.166106
$255$	−27.8261	−1.74254
$256$	1.00000	0.0625000
$257$	−21.3868	−1.33407	−0.667037	−	0.745025i	$-0.732438\pi$
$257$	−21.3868	−1.33407	−0.667037	+	0.745025i	$0.732438\pi$
$258$	11.8944	0.740512
$259$	4.79980	0.298245
$260$	−14.8539	−0.921201
$261$	−12.7034	−0.786320
$262$	14.0317	0.866882
$263$	−21.7183	−1.33921	−0.669603	−	0.742719i	$-0.733536\pi$
$263$	−21.7183	−1.33921	−0.669603	+	0.742719i	$0.733536\pi$
$264$	2.61221	0.160771
$265$	23.3558	1.43473
$266$	8.14319	0.499291
$267$	21.4925	1.31532
$268$	8.66470	0.529281
$269$	−24.0206	−1.46456	−0.732280	−	0.681004i	$-0.761544\pi$
$269$	−24.0206	−1.46456	−0.732280	+	0.681004i	$0.761544\pi$
$270$	−17.8457	−1.08605
$271$	−10.7502	−0.653029	−0.326515	−	0.945192i	$-0.605874\pi$
$271$	−10.7502	−0.653029	−0.326515	+	0.945192i	$0.605874\pi$
$272$	−7.24524	−0.439307
$273$	−5.23451	−0.316807
$274$	−8.93369	−0.539704
$275$	−13.2443	−0.798662
$276$	4.02127	0.242052
$277$	−27.2538	−1.63752	−0.818761	−	0.574134i	$-0.805339\pi$
$277$	−27.2538	−1.63752	−0.818761	+	0.574134i	$0.805339\pi$
$278$	−5.51148	−0.330557
$279$	−1.27743	−0.0764780
$280$	−3.30128	−0.197289
$281$	−8.50747	−0.507513	−0.253757	−	0.967268i	$-0.581666\pi$
$281$	−8.50747	−0.507513	−0.253757	+	0.967268i	$0.581666\pi$
$282$	−3.48841	−0.207732
$283$	−2.13276	−0.126779	−0.0633897	−	0.997989i	$-0.520191\pi$
$283$	−2.13276	−0.126779	−0.0633897	+	0.997989i	$0.520191\pi$
$284$	0.636126	0.0377472
$285$	31.2748	1.85256
$286$	−10.1030	−0.597402
$287$	2.03636	0.120203
$288$	−1.64657	−0.0970252
$289$	35.4935	2.08785
$290$	−25.4696	−1.49562
$291$	−2.32103	−0.136061
$292$	1.38797	0.0812245
$293$	14.9038	0.870689	0.435345	−	0.900264i	$-0.356626\pi$
$293$	14.9038	0.870689	0.435345	+	0.900264i	$0.356626\pi$
$294$	−1.16337	−0.0678491
$295$	1.92182	0.111893
$296$	4.79980	0.278983
$297$	−12.1378	−0.704309
$298$	−17.5882	−1.01886
$299$	−15.5527	−0.899433
$300$	−6.86208	−0.396183
$301$	−10.2241	−0.589306
$302$	−22.1148	−1.27257
$303$	−19.1219	−1.09852
$304$	8.14319	0.467044
$305$	24.6062	1.40895
$306$	11.9298	0.681982
$307$	11.0478	0.630529	0.315265	−	0.949004i	$-0.397907\pi$
$307$	11.0478	0.630529	0.315265	+	0.949004i	$0.397907\pi$
$308$	−2.24539	−0.127943
$309$	15.9597	0.907917
$310$	−2.56118	−0.145465
$311$	−6.82286	−0.386889	−0.193445	−	0.981111i	$-0.561966\pi$
$311$	−6.82286	−0.386889	−0.193445	+	0.981111i	$0.561966\pi$
$312$	−5.23451	−0.296346
$313$	16.7483	0.946671	0.473335	−	0.880882i	$-0.343050\pi$
$313$	16.7483	0.946671	0.473335	+	0.880882i	$0.343050\pi$
$314$	11.8935	0.671189
$315$	5.43580	0.306272
$316$	−3.58896	−0.201895
$317$	−27.9685	−1.57087	−0.785433	−	0.618946i	$-0.787560\pi$
$317$	−27.9685	−1.57087	−0.785433	+	0.618946i	$0.787560\pi$
$318$	8.23055	0.461547
$319$	−17.3233	−0.969917
$320$	−3.30128	−0.184547
$321$	18.7346	1.04566
$322$	−3.45657	−0.192627
$323$	−58.9994	−3.28281
$324$	−1.34909	−0.0749493
$325$	26.5398	1.47216
$326$	3.50175	0.193944
$327$	18.9835	1.04979
$328$	2.03636	0.112439
$329$	2.99854	0.165315
$330$	−8.62365	−0.474716
$331$	−5.35237	−0.294193	−0.147097	−	0.989122i	$-0.546993\pi$
$331$	−5.35237	−0.294193	−0.147097	+	0.989122i	$0.546993\pi$
$332$	−3.26524	−0.179203
$333$	−7.90322	−0.433094
$334$	−11.1263	−0.608803
$335$	−28.6046	−1.56284
$336$	−1.16337	−0.0634670
$337$	−13.6096	−0.741363	−0.370681	−	0.928760i	$-0.620876\pi$
$337$	−13.6096	−0.741363	−0.370681	+	0.928760i	$0.620876\pi$
$338$	7.24497	0.394074
$339$	−11.9638	−0.649786
$340$	23.9186	1.29717
$341$	−1.74200	−0.0943348
$342$	−13.4083	−0.725040
$343$	1.00000	0.0539949
$344$	−10.2241	−0.551245
$345$	−13.2754	−0.714721
$346$	20.6677	1.11110
$347$	−16.2608	−0.872926	−0.436463	−	0.899722i	$-0.643769\pi$
$347$	−16.2608	−0.872926	−0.436463	+	0.899722i	$0.643769\pi$
$348$	−8.97545	−0.481135
$349$	−20.1307	−1.07757	−0.538785	−	0.842443i	$-0.681116\pi$
$349$	−20.1307	−1.07757	−0.538785	+	0.842443i	$0.681116\pi$
$350$	5.89846	0.315286
$351$	24.3225	1.29824
$352$	−2.24539	−0.119680
$353$	−9.47676	−0.504397	−0.252199	−	0.967676i	$-0.581154\pi$
$353$	−9.47676	−0.504397	−0.252199	+	0.967676i	$0.581154\pi$
$354$	0.677249	0.0359954
$355$	−2.10003	−0.111458
$356$	−18.4744	−0.979141
$357$	8.42889	0.446104
$358$	−9.57613	−0.506114
$359$	13.6899	0.722523	0.361261	−	0.932465i	$-0.382346\pi$
$359$	13.6899	0.722523	0.361261	+	0.932465i	$0.382346\pi$
$360$	5.43580	0.286492
$361$	47.3116	2.49008
$362$	−23.3257	−1.22597
$363$	6.93163	0.363816
$364$	4.49944	0.235835
$365$	−4.58206	−0.239836
$366$	8.67121	0.453251
$367$	1.57660	0.0822976	0.0411488	−	0.999153i	$-0.486898\pi$
$367$	1.57660	0.0822976	0.0411488	+	0.999153i	$0.486898\pi$
$368$	−3.45657	−0.180186
$369$	−3.35302	−0.174551
$370$	−15.8455	−0.823768
$371$	−7.07475	−0.367303
$372$	−0.902559	−0.0467955
$373$	−27.6595	−1.43216	−0.716078	−	0.698021i	$-0.754064\pi$
$373$	−27.6595	−1.43216	−0.716078	+	0.698021i	$0.754064\pi$
$374$	16.2684	0.841217
$375$	3.45062	0.178189
$376$	2.99854	0.154638
$377$	34.7134	1.78783
$378$	5.40568	0.278038
$379$	−31.7924	−1.63306	−0.816532	−	0.577300i	$-0.804106\pi$
$379$	−31.7924	−1.63306	−0.816532	+	0.577300i	$0.804106\pi$
$380$	−26.8830	−1.37907
$381$	−3.07979	−0.157782
$382$	−12.3497	−0.631863
$383$	−35.7257	−1.82550	−0.912749	−	0.408520i	$-0.866045\pi$
$383$	−35.7257	−1.82550	−0.912749	+	0.408520i	$0.866045\pi$
$384$	−1.16337	−0.0593679
$385$	7.41265	0.377784
$386$	14.9391	0.760381
$387$	16.8347	0.855755
$388$	1.99510	0.101286
$389$	−25.6370	−1.29985	−0.649924	−	0.759999i	$-0.725199\pi$
$389$	−25.6370	−1.29985	−0.649924	+	0.759999i	$0.725199\pi$
$390$	17.2806	0.875037
$391$	25.0437	1.26652
$392$	1.00000	0.0505076
$393$	−16.3241	−0.823440
$394$	14.3426	0.722568
$395$	11.8482	0.596146
$396$	3.69719	0.185791
$397$	39.3181	1.97332	0.986660	−	0.162794i	$-0.0520507\pi$
$397$	39.3181	1.97332	0.986660	+	0.162794i	$0.0520507\pi$
$398$	5.76080	0.288763
$399$	−9.47354	−0.474270
$400$	5.89846	0.294923
$401$	23.1367	1.15539	0.577696	−	0.816252i	$-0.303952\pi$
$401$	23.1367	1.15539	0.577696	+	0.816252i	$0.303952\pi$
$402$	−10.0802	−0.502757
$403$	3.49073	0.173886
$404$	16.4367	0.817754
$405$	4.45372	0.221307
$406$	7.71505	0.382892
$407$	−10.7774	−0.534216
$408$	8.42889	0.417292
$409$	14.0265	0.693568	0.346784	−	0.937945i	$-0.387274\pi$
$409$	14.0265	0.693568	0.346784	+	0.937945i	$0.387274\pi$
$410$	−6.72261	−0.332006
$411$	10.3932	0.512658
$412$	−13.7185	−0.675864
$413$	−0.582145	−0.0286455
$414$	5.69150	0.279722
$415$	10.7795	0.529144
$416$	4.49944	0.220603
$417$	6.41189	0.313992
$418$	−18.2846	−0.894330
$419$	21.3241	1.04175	0.520874	−	0.853633i	$-0.325606\pi$
$419$	21.3241	1.04175	0.520874	+	0.853633i	$0.325606\pi$
$420$	3.84061	0.187403
$421$	3.24651	0.158225	0.0791125	−	0.996866i	$-0.474791\pi$
$421$	3.24651	0.158225	0.0791125	+	0.996866i	$0.474791\pi$
$422$	−10.5878	−0.515408
$423$	−4.93731	−0.240060
$424$	−7.07475	−0.343580
$425$	−42.7357	−2.07299
$426$	−0.740050	−0.0358555
$427$	−7.45353	−0.360702
$428$	−16.1037	−0.778402
$429$	11.7535	0.567464
$430$	33.7526	1.62769
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	5.40568	0.260081
$433$	−29.4910	−1.41725	−0.708623	−	0.705587i	$-0.750683\pi$
$433$	−29.4910	−1.41725	−0.708623	+	0.705587i	$0.750683\pi$
$434$	0.775815	0.0372403
$435$	29.6305	1.42067
$436$	−16.3177	−0.781474
$437$	−28.1475	−1.34648
$438$	−1.61472	−0.0771542
$439$	18.4951	0.882723	0.441362	−	0.897329i	$-0.354496\pi$
$439$	18.4951	0.882723	0.441362	+	0.897329i	$0.354496\pi$
$440$	7.41265	0.353384
$441$	−1.64657	−0.0784082
$442$	−32.5995	−1.55060
$443$	−6.27512	−0.298140	−0.149070	−	0.988827i	$-0.547628\pi$
$443$	−6.27512	−0.298140	−0.149070	+	0.988827i	$0.547628\pi$
$444$	−5.58394	−0.265002
$445$	60.9892	2.89116
$446$	12.6921	0.600989
$447$	20.4616	0.967801
$448$	1.00000	0.0472456
$449$	36.7467	1.73419	0.867093	−	0.498146i	$-0.165986\pi$
$449$	36.7467	1.73419	0.867093	+	0.498146i	$0.165986\pi$
$450$	−9.71223	−0.457839
$451$	−4.57242	−0.215307
$452$	10.2838	0.483708
$453$	25.7277	1.20879
$454$	2.54584	0.119482
$455$	−14.8539	−0.696362
$456$	−9.47354	−0.443639
$457$	20.1390	0.942063	0.471032	−	0.882116i	$-0.343882\pi$
$457$	20.1390	0.942063	0.471032	+	0.882116i	$0.343882\pi$
$458$	6.72622	0.314296
$459$	−39.1655	−1.82809
$460$	11.4111	0.532046
$461$	36.9875	1.72268	0.861339	−	0.508031i	$-0.169627\pi$
$461$	36.9875	1.72268	0.861339	+	0.508031i	$0.169627\pi$
$462$	2.61221	0.121531
$463$	20.5159	0.953456	0.476728	−	0.879051i	$-0.341823\pi$
$463$	20.5159	0.953456	0.476728	+	0.879051i	$0.341823\pi$
$464$	7.71505	0.358162
$465$	2.97960	0.138176
$466$	3.31773	0.153691
$467$	21.1092	0.976817	0.488408	−	0.872615i	$-0.337578\pi$
$467$	21.1092	0.976817	0.488408	+	0.872615i	$0.337578\pi$
$468$	−7.40865	−0.342465
$469$	8.66470	0.400098
$470$	−9.89902	−0.456608
$471$	−13.8365	−0.637554
$472$	−0.582145	−0.0267954
$473$	22.9570	1.05556
$474$	4.17529	0.191777
$475$	48.0323	2.20387
$476$	−7.24524	−0.332085
$477$	11.6491	0.533375
$478$	−24.8704	−1.13755
$479$	2.62308	0.119852	0.0599259	−	0.998203i	$-0.480914\pi$
$479$	2.62308	0.119852	0.0599259	+	0.998203i	$0.480914\pi$
$480$	3.84061	0.175299
$481$	21.5964	0.984712
$482$	6.92540	0.315443
$483$	4.02127	0.182974
$484$	−5.95824	−0.270829
$485$	−6.58637	−0.299072
$486$	−14.6476	−0.664426
$487$	19.7643	0.895606	0.447803	−	0.894132i	$-0.352207\pi$
$487$	19.7643	0.895606	0.447803	+	0.894132i	$0.352207\pi$
$488$	−7.45353	−0.337405
$489$	−4.07383	−0.184225
$490$	−3.30128	−0.149137
$491$	30.1121	1.35894	0.679471	−	0.733703i	$-0.262209\pi$
$491$	30.1121	1.35894	0.679471	+	0.733703i	$0.262209\pi$
$492$	−2.36904	−0.106805
$493$	−55.8974	−2.51749
$494$	36.6398	1.64850
$495$	−12.2055	−0.548595
$496$	0.775815	0.0348351
$497$	0.636126	0.0285342
$498$	3.79868	0.170223
$499$	−17.7862	−0.796220	−0.398110	−	0.917338i	$-0.630334\pi$
$499$	−17.7862	−0.796220	−0.398110	+	0.917338i	$0.630334\pi$
$500$	−2.96606	−0.132646
$501$	12.9440	0.578295
$502$	17.9769	0.802349
$503$	10.8163	0.482275	0.241138	−	0.970491i	$-0.422479\pi$
$503$	10.8163	0.482275	0.241138	+	0.970491i	$0.422479\pi$
$504$	−1.64657	−0.0733441
$505$	−54.2620	−2.41463
$506$	7.76135	0.345034
$507$	−8.42858	−0.374326
$508$	2.64730	0.117455
$509$	−44.5234	−1.97346	−0.986732	−	0.162357i	$-0.948090\pi$
$509$	−44.5234	−1.97346	−0.986732	+	0.162357i	$0.948090\pi$
$510$	−27.8261	−1.23216
$511$	1.38797	0.0614000
$512$	1.00000	0.0441942
$513$	44.0195	1.94351
$514$	−21.3868	−0.943332
$515$	45.2888	1.99566
$516$	11.8944	0.523621
$517$	−6.73288	−0.296112
$518$	4.79980	0.210891
$519$	−24.0442	−1.05542
$520$	−14.8539	−0.651387
$521$	−35.9166	−1.57354	−0.786768	−	0.617248i	$-0.788247\pi$
$521$	−35.9166	−1.57354	−0.786768	+	0.617248i	$0.788247\pi$
$522$	−12.7034	−0.556012
$523$	−27.5637	−1.20528	−0.602639	−	0.798014i	$-0.705884\pi$
$523$	−27.5637	−1.20528	−0.602639	+	0.798014i	$0.705884\pi$
$524$	14.0317	0.612978
$525$	−6.86208	−0.299486
$526$	−21.7183	−0.946962
$527$	−5.62097	−0.244853
$528$	2.61221	0.113682
$529$	−11.0521	−0.480526
$530$	23.3558	1.01451
$531$	0.958543	0.0415972
$532$	8.14319	0.353052
$533$	9.16250	0.396872
$534$	21.4925	0.930073
$535$	53.1628	2.29843
$536$	8.66470	0.374258
$537$	11.1406	0.480752
$538$	−24.0206	−1.03560
$539$	−2.24539	−0.0967156
$540$	−17.8457	−0.767955
$541$	−32.4303	−1.39429	−0.697144	−	0.716931i	$-0.745546\pi$
$541$	−32.4303	−1.39429	−0.697144	+	0.716931i	$0.745546\pi$
$542$	−10.7502	−0.461761
$543$	27.1364	1.16454
$544$	−7.24524	−0.310637
$545$	53.8692	2.30750
$546$	−5.23451	−0.224016
$547$	−11.5754	−0.494930	−0.247465	−	0.968897i	$-0.579598\pi$
$547$	−11.5754	−0.494930	−0.247465	+	0.968897i	$0.579598\pi$
$548$	−8.93369	−0.381628
$549$	12.2728	0.523789
$550$	−13.2443	−0.564740
$551$	62.8251	2.67644
$552$	4.02127	0.171157
$553$	−3.58896	−0.152618
$554$	−27.2538	−1.15790
$555$	18.4342	0.782487
$556$	−5.51148	−0.233739
$557$	−5.73597	−0.243041	−0.121520	−	0.992589i	$-0.538777\pi$
$557$	−5.73597	−0.243041	−0.121520	+	0.992589i	$0.538777\pi$
$558$	−1.27743	−0.0540781
$559$	−46.0026	−1.94570
$560$	−3.30128	−0.139505
$561$	−18.9261	−0.799061
$562$	−8.50747	−0.358866
$563$	−29.7173	−1.25243	−0.626217	−	0.779649i	$-0.715397\pi$
$563$	−29.7173	−1.25243	−0.626217	+	0.779649i	$0.715397\pi$
$564$	−3.48841	−0.146888
$565$	−33.9496	−1.42827
$566$	−2.13276	−0.0896466
$567$	−1.34909	−0.0566563
$568$	0.636126	0.0266913
$569$	−26.7587	−1.12178	−0.560892	−	0.827889i	$-0.689542\pi$
$569$	−26.7587	−1.12178	−0.560892	+	0.827889i	$0.689542\pi$
$570$	31.2748	1.30996
$571$	−2.73248	−0.114351	−0.0571753	−	0.998364i	$-0.518209\pi$
$571$	−2.73248	−0.114351	−0.0571753	+	0.998364i	$0.518209\pi$
$572$	−10.1030	−0.422427
$573$	14.3672	0.600199
$574$	2.03636	0.0849962
$575$	−20.3885	−0.850257
$576$	−1.64657	−0.0686071
$577$	−13.0745	−0.544298	−0.272149	−	0.962255i	$-0.587734\pi$
$577$	−13.0745	−0.544298	−0.272149	+	0.962255i	$0.587734\pi$
$578$	35.4935	1.47634
$579$	−17.3797	−0.722276
$580$	−25.4696	−1.05757
$581$	−3.26524	−0.135465
$582$	−2.32103	−0.0962100
$583$	15.8856	0.657913
$584$	1.38797	0.0574344
$585$	24.4580	1.01122
$586$	14.9038	0.615670
$587$	−44.9897	−1.85692	−0.928462	−	0.371428i	$-0.878868\pi$
$587$	−44.9897	−1.85692	−0.928462	+	0.371428i	$0.878868\pi$
$588$	−1.16337	−0.0479765
$589$	6.31761	0.260313
$590$	1.92182	0.0791202
$591$	−16.6857	−0.686358
$592$	4.79980	0.197271
$593$	20.7562	0.852356	0.426178	−	0.904639i	$-0.359860\pi$
$593$	20.7562	0.852356	0.426178	+	0.904639i	$0.359860\pi$
$594$	−12.1378	−0.498022
$595$	23.9186	0.980566
$596$	−17.5882	−0.720442
$597$	−6.70194	−0.274292
$598$	−15.5527	−0.635995
$599$	−2.69564	−0.110141	−0.0550704	−	0.998482i	$-0.517538\pi$
$599$	−2.69564	−0.110141	−0.0550704	+	0.998482i	$0.517538\pi$
$600$	−6.86208	−0.280143
$601$	−23.4735	−0.957505	−0.478752	−	0.877950i	$-0.658911\pi$
$601$	−23.4735	−0.957505	−0.478752	+	0.877950i	$0.658911\pi$
$602$	−10.2241	−0.416702
$603$	−14.2670	−0.580999
$604$	−22.1148	−0.899840
$605$	19.6698	0.799692
$606$	−19.1219	−0.776774
$607$	26.1318	1.06066	0.530329	−	0.847792i	$-0.322068\pi$
$607$	26.1318	1.06066	0.530329	+	0.847792i	$0.322068\pi$
$608$	8.14319	0.330250
$609$	−8.97545	−0.363704
$610$	24.6062	0.996276
$611$	13.4917	0.545817
$612$	11.9298	0.482234
$613$	9.86554	0.398465	0.199233	−	0.979952i	$-0.436155\pi$
$613$	9.86554	0.398465	0.199233	+	0.979952i	$0.436155\pi$
$614$	11.0478	0.445852
$615$	7.82088	0.315368
$616$	−2.24539	−0.0904692
$617$	1.91911	0.0772605	0.0386302	−	0.999254i	$-0.487701\pi$
$617$	1.91911	0.0772605	0.0386302	+	0.999254i	$0.487701\pi$
$618$	15.9597	0.641994
$619$	37.5433	1.50899	0.754495	−	0.656305i	$-0.227882\pi$
$619$	37.5433	1.50899	0.754495	+	0.656305i	$0.227882\pi$
$620$	−2.56118	−0.102860
$621$	−18.6851	−0.749809
$622$	−6.82286	−0.273572
$623$	−18.4744	−0.740161
$624$	−5.23451	−0.209548
$625$	−19.7005	−0.788020
$626$	16.7483	0.669397
$627$	21.2718	0.849512
$628$	11.8935	0.474602
$629$	−34.7757	−1.38660
$630$	5.43580	0.216567
$631$	10.7557	0.428178	0.214089	−	0.976814i	$-0.431322\pi$
$631$	10.7557	0.428178	0.214089	+	0.976814i	$0.431322\pi$
$632$	−3.58896	−0.142761
$633$	12.3176	0.489580
$634$	−27.9685	−1.11077
$635$	−8.73947	−0.346815
$636$	8.23055	0.326363
$637$	4.49944	0.178274
$638$	−17.3233	−0.685835
$639$	−1.04743	−0.0414356
$640$	−3.30128	−0.130495
$641$	−13.5746	−0.536164	−0.268082	−	0.963396i	$-0.586390\pi$
$641$	−13.5746	−0.536164	−0.268082	+	0.963396i	$0.586390\pi$
$642$	18.7346	0.739394
$643$	−0.600095	−0.0236654	−0.0118327	−	0.999930i	$-0.503767\pi$
$643$	−0.600095	−0.0236654	−0.0118327	+	0.999930i	$0.503767\pi$
$644$	−3.45657	−0.136208
$645$	−39.2667	−1.54612
$646$	−58.9994	−2.32130
$647$	−31.4898	−1.23799	−0.618996	−	0.785394i	$-0.712460\pi$
$647$	−31.4898	−1.23799	−0.618996	+	0.785394i	$0.712460\pi$
$648$	−1.34909	−0.0529972
$649$	1.30714	0.0513097
$650$	26.5398	1.04097
$651$	−0.902559	−0.0353741
$652$	3.50175	0.137139
$653$	37.2279	1.45684	0.728420	−	0.685131i	$-0.240255\pi$
$653$	37.2279	1.45684	0.728420	+	0.685131i	$0.240255\pi$
$654$	18.9835	0.742312
$655$	−46.3226	−1.80997
$656$	2.03636	0.0795066
$657$	−2.28538	−0.0891613
$658$	2.99854	0.116895
$659$	18.2721	0.711780	0.355890	−	0.934528i	$-0.384178\pi$
$659$	18.2721	0.711780	0.355890	+	0.934528i	$0.384178\pi$
$660$	−8.62365	−0.335675
$661$	−24.7441	−0.962433	−0.481216	−	0.876602i	$-0.659805\pi$
$661$	−24.7441	−0.962433	−0.481216	+	0.876602i	$0.659805\pi$
$662$	−5.35237	−0.208026
$663$	37.9253	1.47290
$664$	−3.26524	−0.126716
$665$	−26.8830	−1.04248
$666$	−7.90322	−0.306243
$667$	−26.6676	−1.03258
$668$	−11.1263	−0.430489
$669$	−14.7656	−0.570872
$670$	−28.6046	−1.10509
$671$	16.7361	0.646088
$672$	−1.16337	−0.0448780
$673$	−0.299621	−0.0115495	−0.00577476	−	0.999983i	$-0.501838\pi$
$673$	−0.299621	−0.0115495	−0.00577476	+	0.999983i	$0.501838\pi$
$674$	−13.6096	−0.524223
$675$	31.8852	1.22726
$676$	7.24497	0.278653
$677$	8.86823	0.340834	0.170417	−	0.985372i	$-0.445489\pi$
$677$	8.86823	0.340834	0.170417	+	0.985372i	$0.445489\pi$
$678$	−11.9638	−0.459468
$679$	1.99510	0.0765648
$680$	23.9186	0.917236
$681$	−2.96175	−0.113495
$682$	−1.74200	−0.0667048
$683$	15.4225	0.590126	0.295063	−	0.955478i	$-0.404659\pi$
$683$	15.4225	0.590126	0.295063	+	0.955478i	$0.404659\pi$
$684$	−13.4083	−0.512681
$685$	29.4926	1.12685
$686$	1.00000	0.0381802
$687$	−7.82508	−0.298546
$688$	−10.2241	−0.389789
$689$	−31.8324	−1.21272
$690$	−13.2754	−0.505384
$691$	4.22371	0.160678	0.0803388	−	0.996768i	$-0.474400\pi$
$691$	4.22371	0.160678	0.0803388	+	0.996768i	$0.474400\pi$
$692$	20.6677	0.785668
$693$	3.69719	0.140445
$694$	−16.2608	−0.617252
$695$	18.1950	0.690174
$696$	−8.97545	−0.340214
$697$	−14.7539	−0.558845
$698$	−20.1307	−0.761957
$699$	−3.85974	−0.145989
$700$	5.89846	0.222941
$701$	18.5466	0.700494	0.350247	−	0.936657i	$-0.386098\pi$
$701$	18.5466	0.700494	0.350247	+	0.936657i	$0.386098\pi$
$702$	24.3225	0.917995
$703$	39.0857	1.47415
$704$	−2.24539	−0.0846262
$705$	11.5162	0.433726
$706$	−9.47676	−0.356663
$707$	16.4367	0.618164
$708$	0.677249	0.0254526
$709$	22.8641	0.858680	0.429340	−	0.903143i	$-0.358746\pi$
$709$	22.8641	0.858680	0.429340	+	0.903143i	$0.358746\pi$
$710$	−2.10003	−0.0788128
$711$	5.90948	0.221623
$712$	−18.4744	−0.692357
$713$	−2.68166	−0.100429
$714$	8.42889	0.315443
$715$	33.3528	1.24732
$716$	−9.57613	−0.357877
$717$	28.9335	1.08054
$718$	13.6899	0.510901
$719$	43.2283	1.61214	0.806071	−	0.591819i	$-0.201590\pi$
$719$	43.2283	1.61214	0.806071	+	0.591819i	$0.201590\pi$
$720$	5.43580	0.202580
$721$	−13.7185	−0.510905
$722$	47.3116	1.76075
$723$	−8.05680	−0.299636
$724$	−23.3257	−0.866894
$725$	45.5069	1.69008
$726$	6.93163	0.257257
$727$	14.4355	0.535382	0.267691	−	0.963505i	$-0.413739\pi$
$727$	14.4355	0.535382	0.267691	+	0.963505i	$0.413739\pi$
$728$	4.49944	0.166760
$729$	21.0878	0.781029
$730$	−4.58206	−0.169590
$731$	74.0759	2.73980
$732$	8.67121	0.320497
$733$	13.8291	0.510791	0.255396	−	0.966837i	$-0.417794\pi$
$733$	13.8291	0.510791	0.255396	+	0.966837i	$0.417794\pi$
$734$	1.57660	0.0581932
$735$	3.84061	0.141663
$736$	−3.45657	−0.127411
$737$	−19.4556	−0.716656
$738$	−3.35302	−0.123426
$739$	6.25624	0.230140	0.115070	−	0.993357i	$-0.463291\pi$
$739$	6.25624	0.230140	0.115070	+	0.993357i	$0.463291\pi$
$740$	−15.8455	−0.582492
$741$	−42.6256	−1.56589
$742$	−7.07475	−0.259722
$743$	31.1682	1.14345	0.571726	−	0.820445i	$-0.306274\pi$
$743$	31.1682	1.14345	0.571726	+	0.820445i	$0.306274\pi$
$744$	−0.902559	−0.0330894
$745$	58.0637	2.12729
$746$	−27.6595	−1.01269
$747$	5.37646	0.196714
$748$	16.2684	0.594830
$749$	−16.1037	−0.588416
$750$	3.45062	0.125999
$751$	32.2874	1.17818	0.589092	−	0.808066i	$-0.299485\pi$
$751$	32.2874	1.17818	0.589092	+	0.808066i	$0.299485\pi$
$752$	2.99854	0.109345
$753$	−20.9138	−0.762141
$754$	34.7134	1.26419
$755$	73.0073	2.65701
$756$	5.40568	0.196603
$757$	−33.2637	−1.20899	−0.604494	−	0.796610i	$-0.706625\pi$
$757$	−33.2637	−1.20899	−0.604494	+	0.796610i	$0.706625\pi$
$758$	−31.7924	−1.15475
$759$	−9.02931	−0.327743
$760$	−26.8830	−0.975148
$761$	50.1458	1.81778	0.908892	−	0.417033i	$-0.136930\pi$
$761$	50.1458	1.81778	0.908892	+	0.417033i	$0.136930\pi$
$762$	−3.07979	−0.111569
$763$	−16.3177	−0.590739
$764$	−12.3497	−0.446795
$765$	−39.3837	−1.42392
$766$	−35.7257	−1.29082
$767$	−2.61933	−0.0945784
$768$	−1.16337	−0.0419795
$769$	−19.3154	−0.696533	−0.348266	−	0.937396i	$-0.613230\pi$
$769$	−19.3154	−0.696533	−0.348266	+	0.937396i	$0.613230\pi$
$770$	7.41265	0.267133
$771$	24.8808	0.896059
$772$	14.9391	0.537671
$773$	−15.9277	−0.572879	−0.286440	−	0.958098i	$-0.592472\pi$
$773$	−15.9277	−0.572879	−0.286440	+	0.958098i	$0.592472\pi$
$774$	16.8347	0.605110
$775$	4.57611	0.164379
$776$	1.99510	0.0716198
$777$	−5.58394	−0.200323
$778$	−25.6370	−0.919132
$779$	16.5825	0.594129
$780$	17.2806	0.618745
$781$	−1.42835	−0.0511104
$782$	25.0437	0.895561
$783$	41.7051	1.49042
$784$	1.00000	0.0357143
$785$	−39.2638	−1.40138
$786$	−16.3241	−0.582260
$787$	−15.3326	−0.546549	−0.273274	−	0.961936i	$-0.588107\pi$
$787$	−15.3326	−0.546549	−0.273274	+	0.961936i	$0.588107\pi$
$788$	14.3426	0.510933
$789$	25.2664	0.899507
$790$	11.8482	0.421539
$791$	10.2838	0.365649
$792$	3.69719	0.131374
$793$	−33.5367	−1.19092
$794$	39.3181	1.39535
$795$	−27.1714	−0.963669
$796$	5.76080	0.204186
$797$	−4.28029	−0.151616	−0.0758078	−	0.997122i	$-0.524154\pi$
$797$	−4.28029	−0.151616	−0.0758078	+	0.997122i	$0.524154\pi$
$798$	−9.47354	−0.335360
$799$	−21.7251	−0.768580
$800$	5.89846	0.208542
$801$	30.4194	1.07482
$802$	23.1367	0.816985
$803$	−3.11652	−0.109980
$804$	−10.0802	−0.355503
$805$	11.4111	0.402189
$806$	3.49073	0.122956
$807$	27.9448	0.983703
$808$	16.4367	0.578239
$809$	−40.3837	−1.41981	−0.709907	−	0.704295i	$-0.751263\pi$
$809$	−40.3837	−1.41981	−0.709907	+	0.704295i	$0.751263\pi$
$810$	4.45372	0.156488
$811$	32.8287	1.15277	0.576386	−	0.817177i	$-0.304462\pi$
$811$	32.8287	1.15277	0.576386	+	0.817177i	$0.304462\pi$
$812$	7.71505	0.270745
$813$	12.5065	0.438621
$814$	−10.7774	−0.377748
$815$	−11.5603	−0.404939
$816$	8.42889	0.295070
$817$	−83.2566	−2.91278
$818$	14.0265	0.490427
$819$	−7.40865	−0.258879
$820$	−6.72261	−0.234764
$821$	−17.6348	−0.615460	−0.307730	−	0.951474i	$-0.599569\pi$
$821$	−17.6348	−0.615460	−0.307730	+	0.951474i	$0.599569\pi$
$822$	10.3932	0.362504
$823$	10.0401	0.349976	0.174988	−	0.984571i	$-0.444011\pi$
$823$	10.0401	0.349976	0.174988	+	0.984571i	$0.444011\pi$
$824$	−13.7185	−0.477908
$825$	15.4080	0.536439
$826$	−0.582145	−0.0202554
$827$	−32.2671	−1.12204	−0.561019	−	0.827803i	$-0.689591\pi$
$827$	−32.2671	−1.12204	−0.561019	+	0.827803i	$0.689591\pi$
$828$	5.69150	0.197793
$829$	−44.7432	−1.55399	−0.776997	−	0.629504i	$-0.783258\pi$
$829$	−44.7432	−1.55399	−0.776997	+	0.629504i	$0.783258\pi$
$830$	10.7795	0.374161
$831$	31.7063	1.09988
$832$	4.49944	0.155990
$833$	−7.24524	−0.251033
$834$	6.41189	0.222026
$835$	36.7310	1.27113
$836$	−18.2846	−0.632387
$837$	4.19381	0.144959
$838$	21.3241	0.736627
$839$	40.8134	1.40903	0.704517	−	0.709687i	$-0.251164\pi$
$839$	40.8134	1.40903	0.704517	+	0.709687i	$0.251164\pi$
$840$	3.84061	0.132514
$841$	30.5220	1.05248
$842$	3.24651	0.111882
$843$	9.89733	0.340882
$844$	−10.5878	−0.364449
$845$	−23.9177	−0.822793
$846$	−4.93731	−0.169748
$847$	−5.95824	−0.204728
$848$	−7.07475	−0.242948
$849$	2.48119	0.0851542
$850$	−42.7357	−1.46582
$851$	−16.5909	−0.568728
$852$	−0.740050	−0.0253537
$853$	32.9102	1.12682	0.563412	−	0.826176i	$-0.309488\pi$
$853$	32.9102	1.12682	0.563412	+	0.826176i	$0.309488\pi$
$854$	−7.45353	−0.255055
$855$	44.2647	1.51382
$856$	−16.1037	−0.550413
$857$	30.4380	1.03974	0.519871	−	0.854245i	$-0.325980\pi$
$857$	30.4380	1.03974	0.519871	+	0.854245i	$0.325980\pi$
$858$	11.7535	0.401258
$859$	47.7798	1.63023	0.815113	−	0.579301i	$-0.196675\pi$
$859$	47.7798	1.63023	0.815113	+	0.579301i	$0.196675\pi$
$860$	33.7526	1.15095
$861$	−2.36904	−0.0807368
$862$	−1.00000	−0.0340601
$863$	21.5401	0.733232	0.366616	−	0.930372i	$-0.380516\pi$
$863$	21.5401	0.733232	0.366616	+	0.930372i	$0.380516\pi$
$864$	5.40568	0.183905
$865$	−68.2299	−2.31989
$866$	−29.4910	−1.00214
$867$	−41.2921	−1.40235
$868$	0.775815	0.0263329
$869$	8.05861	0.273370
$870$	29.6305	1.00457
$871$	38.9863	1.32100
$872$	−16.3177	−0.552586
$873$	−3.28507	−0.111183
$874$	−28.1475	−0.952105
$875$	−2.96606	−0.100271
$876$	−1.61472	−0.0545562
$877$	−25.4377	−0.858971	−0.429486	−	0.903074i	$-0.641305\pi$
$877$	−25.4377	−0.858971	−0.429486	+	0.903074i	$0.641305\pi$
$878$	18.4951	0.624180
$879$	−17.3386	−0.584817
$880$	7.41265	0.249880
$881$	−40.9227	−1.37872	−0.689360	−	0.724419i	$-0.742108\pi$
$881$	−40.9227	−1.37872	−0.689360	+	0.724419i	$0.742108\pi$
$882$	−1.64657	−0.0554429
$883$	−37.9994	−1.27878	−0.639391	−	0.768881i	$-0.720814\pi$
$883$	−37.9994	−1.27878	−0.639391	+	0.768881i	$0.720814\pi$
$884$	−32.5995	−1.09644
$885$	−2.23579	−0.0751553
$886$	−6.27512	−0.210817
$887$	1.22523	0.0411393	0.0205696	−	0.999788i	$-0.493452\pi$
$887$	1.22523	0.0411393	0.0205696	+	0.999788i	$0.493452\pi$
$888$	−5.58394	−0.187385
$889$	2.64730	0.0887875
$890$	60.9892	2.04436
$891$	3.02922	0.101483
$892$	12.6921	0.424964
$893$	24.4177	0.817106
$894$	20.4616	0.684338
$895$	31.6135	1.05672
$896$	1.00000	0.0334077
$897$	18.0935	0.604124
$898$	36.7467	1.22625
$899$	5.98545	0.199626
$900$	−9.71223	−0.323741
$901$	51.2583	1.70766
$902$	−4.57242	−0.152245
$903$	11.8944	0.395820
$904$	10.2838	0.342033
$905$	77.0048	2.55973
$906$	25.7277	0.854746
$907$	31.1390	1.03395	0.516977	−	0.855999i	$-0.327057\pi$
$907$	31.1390	1.03395	0.516977	+	0.855999i	$0.327057\pi$
$908$	2.54584	0.0844866
$909$	−27.0641	−0.897660
$910$	−14.8539	−0.492403
$911$	−39.6831	−1.31476	−0.657380	−	0.753559i	$-0.728336\pi$
$911$	−39.6831	−1.31476	−0.657380	+	0.753559i	$0.728336\pi$
$912$	−9.47354	−0.313700
$913$	7.33173	0.242645
$914$	20.1390	0.666139
$915$	−28.6261	−0.946350
$916$	6.72622	0.222241
$917$	14.0317	0.463368
$918$	−39.1655	−1.29265
$919$	34.0902	1.12453	0.562266	−	0.826956i	$-0.309930\pi$
$919$	34.0902	1.12453	0.562266	+	0.826956i	$0.309930\pi$
$920$	11.4111	0.376214
$921$	−12.8526	−0.423509
$922$	36.9875	1.21812
$923$	2.86221	0.0942109
$924$	2.61221	0.0859355
$925$	28.3114	0.930874
$926$	20.5159	0.674195
$927$	22.5886	0.741906
$928$	7.71505	0.253259
$929$	−6.39827	−0.209920	−0.104960	−	0.994476i	$-0.533472\pi$
$929$	−6.39827	−0.209920	−0.104960	+	0.994476i	$0.533472\pi$
$930$	2.97960	0.0977050
$931$	8.14319	0.266882
$932$	3.31773	0.108676
$933$	7.93751	0.259862
$934$	21.1092	0.690714
$935$	−53.7065	−1.75639
$936$	−7.40865	−0.242159
$937$	13.1515	0.429641	0.214821	−	0.976653i	$-0.431083\pi$
$937$	13.1515	0.429641	0.214821	+	0.976653i	$0.431083\pi$
$938$	8.66470	0.282912
$939$	−19.4845	−0.635852
$940$	−9.89902	−0.322870
$941$	−19.0528	−0.621102	−0.310551	−	0.950557i	$-0.600514\pi$
$941$	−19.0528	−0.621102	−0.310551	+	0.950557i	$0.600514\pi$
$942$	−13.8365	−0.450819
$943$	−7.03884	−0.229216
$944$	−0.582145	−0.0189472
$945$	−17.8457	−0.580520
$946$	22.9570	0.746397
$947$	3.97876	0.129292	0.0646462	−	0.997908i	$-0.479408\pi$
$947$	3.97876	0.129292	0.0646462	+	0.997908i	$0.479408\pi$
$948$	4.17529	0.135607
$949$	6.24507	0.202724
$950$	48.0323	1.55837
$951$	32.5377	1.05511
$952$	−7.24524	−0.234820
$953$	24.9091	0.806884	0.403442	−	0.915005i	$-0.367814\pi$
$953$	24.9091	0.806884	0.403442	+	0.915005i	$0.367814\pi$
$954$	11.6491	0.377153
$955$	40.7697	1.31928
$956$	−24.8704	−0.804367
$957$	20.1534	0.651466
$958$	2.62308	0.0847480
$959$	−8.93369	−0.288484
$960$	3.84061	0.123955
$961$	−30.3981	−0.980584
$962$	21.5964	0.696297
$963$	26.5159	0.854463
$964$	6.92540	0.223052
$965$	−49.3182	−1.58761
$966$	4.02127	0.129382
$967$	19.3218	0.621346	0.310673	−	0.950517i	$-0.399446\pi$
$967$	19.3218	0.621346	0.310673	+	0.950517i	$0.399446\pi$
$968$	−5.95824	−0.191505
$969$	68.6381	2.20497
$970$	−6.58637	−0.211476
$971$	−46.6160	−1.49598	−0.747989	−	0.663711i	$-0.768981\pi$
$971$	−46.6160	−1.49598	−0.747989	+	0.663711i	$0.768981\pi$
$972$	−14.6476	−0.469820
$973$	−5.51148	−0.176690
$974$	19.7643	0.633289
$975$	−30.8755	−0.988809
$976$	−7.45353	−0.238582
$977$	32.8643	1.05142	0.525711	−	0.850663i	$-0.323799\pi$
$977$	32.8643	1.05142	0.525711	+	0.850663i	$0.323799\pi$
$978$	−4.07383	−0.130267
$979$	41.4821	1.32578
$980$	−3.30128	−0.105456
$981$	26.8682	0.857836
$982$	30.1121	0.960917
$983$	−9.94410	−0.317168	−0.158584	−	0.987346i	$-0.550693\pi$
$983$	−9.94410	−0.317168	−0.158584	+	0.987346i	$0.550693\pi$
$984$	−2.36904	−0.0755223
$985$	−47.3488	−1.50866
$986$	−55.8974	−1.78014
$987$	−3.48841	−0.111037
$988$	36.6398	1.16567
$989$	35.3403	1.12376
$990$	−12.2055	−0.387915
$991$	−52.3674	−1.66351	−0.831753	−	0.555146i	$-0.812662\pi$
$991$	−52.3674	−1.66351	−0.831753	+	0.555146i	$0.812662\pi$
$992$	0.775815	0.0246321
$993$	6.22679	0.197601
$994$	0.636126	0.0201767
$995$	−19.0180	−0.602912
$996$	3.79868	0.120366
$997$	−16.5124	−0.522952	−0.261476	−	0.965210i	$-0.584209\pi$
$997$	−16.5124	−0.522952	−0.261476	+	0.965210i	$0.584209\pi$
$998$	−17.7862	−0.563013
$999$	25.9462	0.820901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.9	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.9	✓	21	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.16337 q^{3} +1.00000 q^{4} -3.30128 q^{5} -1.16337 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.64657 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.16337 q^{3} +1.00000 q^{4} -3.30128 q^{5} -1.16337 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.64657 q^{9} -3.30128 q^{10} -2.24539 q^{11} -1.16337 q^{12} +4.49944 q^{13} +1.00000 q^{14} +3.84061 q^{15} +1.00000 q^{16} -7.24524 q^{17} -1.64657 q^{18} +8.14319 q^{19} -3.30128 q^{20} -1.16337 q^{21} -2.24539 q^{22} -3.45657 q^{23} -1.16337 q^{24} +5.89846 q^{25} +4.49944 q^{26} +5.40568 q^{27} +1.00000 q^{28} +7.71505 q^{29} +3.84061 q^{30} +0.775815 q^{31} +1.00000 q^{32} +2.61221 q^{33} -7.24524 q^{34} -3.30128 q^{35} -1.64657 q^{36} +4.79980 q^{37} +8.14319 q^{38} -5.23451 q^{39} -3.30128 q^{40} +2.03636 q^{41} -1.16337 q^{42} -10.2241 q^{43} -2.24539 q^{44} +5.43580 q^{45} -3.45657 q^{46} +2.99854 q^{47} -1.16337 q^{48} +1.00000 q^{49} +5.89846 q^{50} +8.42889 q^{51} +4.49944 q^{52} -7.07475 q^{53} +5.40568 q^{54} +7.41265 q^{55} +1.00000 q^{56} -9.47354 q^{57} +7.71505 q^{58} -0.582145 q^{59} +3.84061 q^{60} -7.45353 q^{61} +0.775815 q^{62} -1.64657 q^{63} +1.00000 q^{64} -14.8539 q^{65} +2.61221 q^{66} +8.66470 q^{67} -7.24524 q^{68} +4.02127 q^{69} -3.30128 q^{70} +0.636126 q^{71} -1.64657 q^{72} +1.38797 q^{73} +4.79980 q^{74} -6.86208 q^{75} +8.14319 q^{76} -2.24539 q^{77} -5.23451 q^{78} -3.58896 q^{79} -3.30128 q^{80} -1.34909 q^{81} +2.03636 q^{82} -3.26524 q^{83} -1.16337 q^{84} +23.9186 q^{85} -10.2241 q^{86} -8.97545 q^{87} -2.24539 q^{88} -18.4744 q^{89} +5.43580 q^{90} +4.49944 q^{91} -3.45657 q^{92} -0.902559 q^{93} +2.99854 q^{94} -26.8830 q^{95} -1.16337 q^{96} +1.99510 q^{97} +1.00000 q^{98} +3.69719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

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