LMFDB - Embedded newform 6005.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.36234$ of defining polynomial
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.515722 q^{2} -0.702588 q^{3} -1.73403 q^{4} -1.00000 q^{5} +0.362340 q^{6} +0.362340 q^{7} +1.92572 q^{8} -2.50637 q^{9} +O(q^{10})$	\(q-0.515722 q^{2} -0.702588 q^{3} -1.73403 q^{4} -1.00000 q^{5} +0.362340 q^{6} +0.362340 q^{7} +1.92572 q^{8} -2.50637 q^{9} +0.515722 q^{10} -1.40518 q^{11} +1.21831 q^{12} +1.51572 q^{13} -0.186866 q^{14} +0.702588 q^{15} +2.47493 q^{16} -3.17547 q^{17} +1.29259 q^{18} +5.87806 q^{19} +1.73403 q^{20} -0.254576 q^{21} +0.724680 q^{22} -4.36234 q^{23} -1.35299 q^{24} +1.00000 q^{25} -0.781690 q^{26} +3.86871 q^{27} -0.628309 q^{28} -4.80378 q^{29} -0.362340 q^{30} -5.39378 q^{31} -5.12781 q^{32} +0.987260 q^{33} +1.63766 q^{34} -0.362340 q^{35} +4.34612 q^{36} +11.1136 q^{37} -3.03144 q^{38} -1.06493 q^{39} -1.92572 q^{40} +5.50155 q^{41} +0.131290 q^{42} -9.50155 q^{43} +2.43662 q^{44} +2.50637 q^{45} +2.24975 q^{46} +6.28120 q^{47} -1.73885 q^{48} -6.86871 q^{49} -0.515722 q^{50} +2.23105 q^{51} -2.62831 q^{52} +6.18687 q^{53} -1.99518 q^{54} +1.40518 q^{55} +0.697765 q^{56} -4.12986 q^{57} +2.47741 q^{58} +9.36822 q^{59} -1.21831 q^{60} -1.64701 q^{61} +2.78169 q^{62} -0.908158 q^{63} -2.30533 q^{64} -1.51572 q^{65} -0.509151 q^{66} -1.45079 q^{67} +5.50637 q^{68} +3.06493 q^{69} +0.186866 q^{70} +10.6912 q^{71} -4.82657 q^{72} +7.18000 q^{73} -5.73154 q^{74} -0.702588 q^{75} -10.1927 q^{76} -0.509151 q^{77} +0.549206 q^{78} -1.39378 q^{79} -2.47493 q^{80} +4.80100 q^{81} -2.83727 q^{82} -12.7689 q^{83} +0.441442 q^{84} +3.17547 q^{85} +4.90015 q^{86} +3.37508 q^{87} -2.70598 q^{88} +11.9892 q^{89} -1.29259 q^{90} +0.549206 q^{91} +7.56443 q^{92} +3.78961 q^{93} -3.23935 q^{94} -5.87806 q^{95} +3.60274 q^{96} -0.0314432 q^{97} +3.54234 q^{98} +3.52189 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 7 q^{6} - 7 q^{7} + 9 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 7 * q^6 - 7 * q^7 + 9 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 7 q^{6} - 7 q^{7} + 9 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{13} - 4 q^{14} + 2 q^{15} + 6 q^{16} - q^{17} - q^{18} + 11 q^{19} - 2 q^{20} + 5 q^{21} - 14 q^{22} - 9 q^{23} + 11 q^{24} + 4 q^{25} - 8 q^{26} - 5 q^{27} - 3 q^{28} - 8 q^{29} + 7 q^{30} - 5 q^{31} + 5 q^{32} + 28 q^{33} + 15 q^{34} + 7 q^{35} - 13 q^{36} + 4 q^{37} - 4 q^{38} + 5 q^{39} - 9 q^{40} + 3 q^{41} + 21 q^{42} - 19 q^{43} - 2 q^{45} - 4 q^{46} + 4 q^{47} - 5 q^{48} - 7 q^{49} + 2 q^{50} - 20 q^{51} - 11 q^{52} + 28 q^{53} - q^{54} + 4 q^{55} - 5 q^{56} + 2 q^{57} - 9 q^{59} - 23 q^{61} + 16 q^{62} - 22 q^{63} + 21 q^{64} - 2 q^{65} + 10 q^{66} - 11 q^{67} + 10 q^{68} + 3 q^{69} + 4 q^{70} + 27 q^{71} - 38 q^{72} + 18 q^{73} - 20 q^{74} - 2 q^{75} - 6 q^{76} + 10 q^{77} - 3 q^{78} + 11 q^{79} - 6 q^{80} + 8 q^{81} + q^{82} - 2 q^{83} - q^{84} + q^{85} - 9 q^{86} - 19 q^{87} + 22 q^{88} + q^{89} + q^{90} - 3 q^{91} - 5 q^{92} - 11 q^{93} - 37 q^{94} - 11 q^{95} - 15 q^{96} + 8 q^{97} - 5 q^{98} - 22 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 7 * q^6 - 7 * q^7 + 9 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^13 - 4 * q^14 + 2 * q^15 + 6 * q^16 - q^17 - q^18 + 11 * q^19 - 2 * q^20 + 5 * q^21 - 14 * q^22 - 9 * q^23 + 11 * q^24 + 4 * q^25 - 8 * q^26 - 5 * q^27 - 3 * q^28 - 8 * q^29 + 7 * q^30 - 5 * q^31 + 5 * q^32 + 28 * q^33 + 15 * q^34 + 7 * q^35 - 13 * q^36 + 4 * q^37 - 4 * q^38 + 5 * q^39 - 9 * q^40 + 3 * q^41 + 21 * q^42 - 19 * q^43 - 2 * q^45 - 4 * q^46 + 4 * q^47 - 5 * q^48 - 7 * q^49 + 2 * q^50 - 20 * q^51 - 11 * q^52 + 28 * q^53 - q^54 + 4 * q^55 - 5 * q^56 + 2 * q^57 - 9 * q^59 - 23 * q^61 + 16 * q^62 - 22 * q^63 + 21 * q^64 - 2 * q^65 + 10 * q^66 - 11 * q^67 + 10 * q^68 + 3 * q^69 + 4 * q^70 + 27 * q^71 - 38 * q^72 + 18 * q^73 - 20 * q^74 - 2 * q^75 - 6 * q^76 + 10 * q^77 - 3 * q^78 + 11 * q^79 - 6 * q^80 + 8 * q^81 + q^82 - 2 * q^83 - q^84 + q^85 - 9 * q^86 - 19 * q^87 + 22 * q^88 + q^89 + q^90 - 3 * q^91 - 5 * q^92 - 11 * q^93 - 37 * q^94 - 11 * q^95 - 15 * q^96 + 8 * q^97 - 5 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.515722	−0.364670	−0.182335	−	0.983236i	$-0.558366\pi$
$2$	−0.515722	−0.364670	−0.182335	+	0.983236i	$0.558366\pi$
$3$	−0.702588	−0.405639	−0.202820	−	0.979216i	$-0.565011\pi$
$3$	−0.702588	−0.405639	−0.202820	+	0.979216i	$0.565011\pi$
$4$	−1.73403	−0.867016
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.362340	0.147925
$7$	0.362340	0.136952	0.0684758	−	0.997653i	$-0.478186\pi$
$7$	0.362340	0.136952	0.0684758	+	0.997653i	$0.478186\pi$
$8$	1.92572	0.680845
$9$	−2.50637	−0.835457
$10$	0.515722	0.163085
$11$	−1.40518	−0.423677	−0.211838	−	0.977305i	$-0.567945\pi$
$11$	−1.40518	−0.423677	−0.211838	+	0.977305i	$0.567945\pi$
$12$	1.21831	0.351696
$13$	1.51572	0.420386	0.210193	−	0.977660i	$-0.432591\pi$
$13$	1.51572	0.420386	0.210193	+	0.977660i	$0.432591\pi$
$14$	−0.186866	−0.0499422
$15$	0.702588	0.181407
$16$	2.47493	0.618732
$17$	−3.17547	−0.770165	−0.385083	−	0.922882i	$-0.625827\pi$
$17$	−3.17547	−0.770165	−0.385083	+	0.922882i	$0.625827\pi$
$18$	1.29259	0.304666
$19$	5.87806	1.34852	0.674260	−	0.738494i	$-0.264463\pi$
$19$	5.87806	1.34852	0.674260	+	0.738494i	$0.264463\pi$
$20$	1.73403	0.387741
$21$	−0.254576	−0.0555530
$22$	0.724680	0.154502
$23$	−4.36234	−0.909611	−0.454805	−	0.890591i	$-0.650291\pi$
$23$	−4.36234	−0.909611	−0.454805	+	0.890591i	$0.650291\pi$
$24$	−1.35299	−0.276178
$25$	1.00000	0.200000
$26$	−0.781690	−0.153302
$27$	3.86871	0.744534
$28$	−0.628309	−0.118739
$29$	−4.80378	−0.892040	−0.446020	−	0.895023i	$-0.647159\pi$
$29$	−4.80378	−0.892040	−0.446020	+	0.895023i	$0.647159\pi$
$30$	−0.362340	−0.0661539
$31$	−5.39378	−0.968752	−0.484376	−	0.874860i	$-0.660953\pi$
$31$	−5.39378	−0.968752	−0.484376	+	0.874860i	$0.660953\pi$
$32$	−5.12781	−0.906478
$33$	0.987260	0.171860
$34$	1.63766	0.280856
$35$	−0.362340	−0.0612466
$36$	4.34612	0.724354
$37$	11.1136	1.82707	0.913536	−	0.406759i	$-0.133341\pi$
$37$	11.1136	1.82707	0.913536	+	0.406759i	$0.133341\pi$
$38$	−3.03144	−0.491765
$39$	−1.06493	−0.170525
$40$	−1.92572	−0.304483
$41$	5.50155	0.859197	0.429599	−	0.903020i	$-0.358655\pi$
$41$	5.50155	0.859197	0.429599	+	0.903020i	$0.358655\pi$
$42$	0.131290	0.0202585
$43$	−9.50155	−1.44897	−0.724486	−	0.689289i	$-0.757923\pi$
$43$	−9.50155	−1.44897	−0.724486	+	0.689289i	$0.757923\pi$
$44$	2.43662	0.367334
$45$	2.50637	0.373628
$46$	2.24975	0.331708
$47$	6.28120	0.916207	0.458103	−	0.888899i	$-0.348529\pi$
$47$	6.28120	0.916207	0.458103	+	0.888899i	$0.348529\pi$
$48$	−1.73885	−0.250982
$49$	−6.86871	−0.981244
$50$	−0.515722	−0.0729340
$51$	2.23105	0.312409
$52$	−2.62831	−0.364481
$53$	6.18687	0.849831	0.424916	−	0.905233i	$-0.360304\pi$
$53$	6.18687	0.849831	0.424916	+	0.905233i	$0.360304\pi$
$54$	−1.99518	−0.271509
$55$	1.40518	0.189474
$56$	0.697765	0.0932428
$57$	−4.12986	−0.547013
$58$	2.47741	0.325300
$59$	9.36822	1.21964	0.609819	−	0.792541i	$-0.291242\pi$
$59$	9.36822	1.21964	0.609819	+	0.792541i	$0.291242\pi$
$60$	−1.21831	−0.157283
$61$	−1.64701	−0.210878	−0.105439	−	0.994426i	$-0.533625\pi$
$61$	−1.64701	−0.210878	−0.105439	+	0.994426i	$0.533625\pi$
$62$	2.78169	0.353275
$63$	−0.908158	−0.114417
$64$	−2.30533	−0.288166
$65$	−1.51572	−0.188002
$66$	−0.509151	−0.0626722
$67$	−1.45079	−0.177243	−0.0886213	−	0.996065i	$-0.528246\pi$
$67$	−1.45079	−0.177243	−0.0886213	+	0.996065i	$0.528246\pi$
$68$	5.50637	0.667745
$69$	3.06493	0.368974
$70$	0.186866	0.0223348
$71$	10.6912	1.26881	0.634406	−	0.773000i	$-0.281245\pi$
$71$	10.6912	1.26881	0.634406	+	0.773000i	$0.281245\pi$
$72$	−4.82657	−0.568817
$73$	7.18000	0.840356	0.420178	−	0.907442i	$-0.361968\pi$
$73$	7.18000	0.840356	0.420178	+	0.907442i	$0.361968\pi$
$74$	−5.73154	−0.666278
$75$	−0.702588	−0.0811279
$76$	−10.1927	−1.16919
$77$	−0.509151	−0.0580232
$78$	0.549206	0.0621854
$79$	−1.39378	−0.156813	−0.0784064	−	0.996921i	$-0.524983\pi$
$79$	−1.39378	−0.156813	−0.0784064	+	0.996921i	$0.524983\pi$
$80$	−2.47493	−0.276705
$81$	4.80100	0.533445
$82$	−2.83727	−0.313324
$83$	−12.7689	−1.40156	−0.700782	−	0.713375i	$-0.747166\pi$
$83$	−12.7689	−1.40156	−0.700782	+	0.713375i	$0.747166\pi$
$84$	0.441442	0.0481653
$85$	3.17547	0.344428
$86$	4.90015	0.528397
$87$	3.37508	0.361847
$88$	−2.70598	−0.288458
$89$	11.9892	1.27085	0.635427	−	0.772161i	$-0.280824\pi$
$89$	11.9892	1.27085	0.635427	+	0.772161i	$0.280824\pi$
$90$	−1.29259	−0.136251
$91$	0.549206	0.0575725
$92$	7.56443	0.788647
$93$	3.78961	0.392964
$94$	−3.23935	−0.334113
$95$	−5.87806	−0.603076
$96$	3.60274	0.367703
$97$	−0.0314432	−0.00319257	−0.00159629	−	0.999999i	$-0.500508\pi$
$97$	−0.0314432	−0.00319257	−0.00159629	+	0.999999i	$0.500508\pi$
$98$	3.54234	0.357831
$99$	3.52189	0.353963
$100$	−1.73403	−0.173403
$101$	12.7526	1.26894	0.634468	−	0.772949i	$-0.281219\pi$
$101$	12.7526	1.26894	0.634468	+	0.772949i	$0.281219\pi$
$102$	−1.15060	−0.113926
$103$	5.03144	0.495763	0.247881	−	0.968790i	$-0.420266\pi$
$103$	5.03144	0.495763	0.247881	+	0.968790i	$0.420266\pi$
$104$	2.91886	0.286217
$105$	0.254576	0.0248440
$106$	−3.19070	−0.309908
$107$	5.43005	0.524943	0.262471	−	0.964940i	$-0.415462\pi$
$107$	5.43005	0.524943	0.262471	+	0.964940i	$0.415462\pi$
$108$	−6.70846	−0.645522
$109$	−1.12533	−0.107787	−0.0538934	−	0.998547i	$-0.517163\pi$
$109$	−1.12533	−0.107787	−0.0538934	+	0.998547i	$0.517163\pi$
$110$	−0.724680	−0.0690955
$111$	−7.80831	−0.741132
$112$	0.896765	0.0847363
$113$	−7.04871	−0.663087	−0.331544	−	0.943440i	$-0.607569\pi$
$113$	−7.04871	−0.663087	−0.331544	+	0.943440i	$0.607569\pi$
$114$	2.12986	0.199479
$115$	4.36234	0.406790
$116$	8.32991	0.773413
$117$	−3.79896	−0.351214
$118$	−4.83139	−0.444766
$119$	−1.15060	−0.105475
$120$	1.35299	0.123510
$121$	−9.02548	−0.820498
$122$	0.849400	0.0769010
$123$	−3.86532	−0.348524
$124$	9.35299	0.839923
$125$	−1.00000	−0.0894427
$126$	0.468357	0.0417245
$127$	−9.29802	−0.825066	−0.412533	−	0.910943i	$-0.635356\pi$
$127$	−9.29802	−0.825066	−0.412533	+	0.910943i	$0.635356\pi$
$128$	11.4445	1.01156
$129$	6.67567	0.587760
$130$	0.781690	0.0685588
$131$	3.82897	0.334538	0.167269	−	0.985911i	$-0.446505\pi$
$131$	3.82897	0.334538	0.167269	+	0.985911i	$0.446505\pi$
$132$	−1.71194	−0.149005
$133$	2.12986	0.184682
$134$	0.748206	0.0646351
$135$	−3.86871	−0.332966
$136$	−6.11507	−0.524363
$137$	6.14712	0.525184	0.262592	−	0.964907i	$-0.415423\pi$
$137$	6.14712	0.525184	0.262592	+	0.964907i	$0.415423\pi$
$138$	−1.58065	−0.134554
$139$	−6.44936	−0.547028	−0.273514	−	0.961868i	$-0.588186\pi$
$139$	−6.44936	−0.547028	−0.273514	+	0.961868i	$0.588186\pi$
$140$	0.628309	0.0531018
$141$	−4.41309	−0.371650
$142$	−5.51368	−0.462698
$143$	−2.12986	−0.178107
$144$	−6.20308	−0.516924
$145$	4.80378	0.398932
$146$	−3.70288	−0.306453
$147$	4.82587	0.398031
$148$	−19.2714	−1.58410
$149$	19.5536	1.60190	0.800949	−	0.598733i	$-0.204329\pi$
$149$	19.5536	1.60190	0.800949	+	0.598733i	$0.204329\pi$
$150$	0.362340	0.0295849
$151$	−17.0566	−1.38805	−0.694024	−	0.719951i	$-0.744164\pi$
$151$	−17.0566	−1.38805	−0.694024	+	0.719951i	$0.744164\pi$
$152$	11.3195	0.918133
$153$	7.95891	0.643440
$154$	0.262580	0.0211593
$155$	5.39378	0.433239
$156$	1.84662	0.147848
$157$	−2.99374	−0.238927	−0.119463	−	0.992839i	$-0.538117\pi$
$157$	−2.99374	−0.238927	−0.119463	+	0.992839i	$0.538117\pi$
$158$	0.718804	0.0571850
$159$	−4.34682	−0.344725
$160$	5.12781	0.405389
$161$	−1.58065	−0.124573
$162$	−2.47598	−0.194531
$163$	19.1885	1.50296	0.751481	−	0.659755i	$-0.229340\pi$
$163$	19.1885	1.50296	0.751481	+	0.659755i	$0.229340\pi$
$164$	−9.53985	−0.744938
$165$	−0.987260	−0.0768581
$166$	6.58518	0.511109
$167$	−7.87602	−0.609465	−0.304732	−	0.952438i	$-0.598567\pi$
$167$	−7.87602	−0.609465	−0.304732	+	0.952438i	$0.598567\pi$
$168$	−0.490242	−0.0378230
$169$	−10.7026	−0.823276
$170$	−1.63766	−0.125603
$171$	−14.7326	−1.12663
$172$	16.4760	1.25628
$173$	−19.9948	−1.52018	−0.760088	−	0.649820i	$-0.774844\pi$
$173$	−19.9948	−1.52018	−0.760088	+	0.649820i	$0.774844\pi$
$174$	−1.74060	−0.131955
$175$	0.362340	0.0273903
$176$	−3.47771	−0.262142
$177$	−6.58200	−0.494733
$178$	−6.18310	−0.463443
$179$	11.0193	0.823622	0.411811	−	0.911269i	$-0.364896\pi$
$179$	11.0193	0.823622	0.411811	+	0.911269i	$0.364896\pi$
$180$	−4.34612	−0.323941
$181$	−22.9793	−1.70803	−0.854017	−	0.520245i	$-0.825841\pi$
$181$	−22.9793	−1.70803	−0.854017	+	0.520245i	$0.825841\pi$
$182$	−0.283238	−0.0209950
$183$	1.15717	0.0855405
$184$	−8.40065	−0.619304
$185$	−11.1136	−0.817091
$186$	−1.95438	−0.143302
$187$	4.46210	0.326301
$188$	−10.8918	−0.794365
$189$	1.40179	0.101965
$190$	3.03144	0.219924
$191$	−2.88145	−0.208494	−0.104247	−	0.994551i	$-0.533243\pi$
$191$	−2.88145	−0.208494	−0.104247	+	0.994551i	$0.533243\pi$
$192$	1.61970	0.116892
$193$	−24.9917	−1.79894	−0.899471	−	0.436980i	$-0.856048\pi$
$193$	−24.9917	−1.79894	−0.899471	+	0.436980i	$0.856048\pi$
$194$	0.0162159	0.00116424
$195$	1.06493	0.0762611
$196$	11.9106	0.850754
$197$	16.0518	1.14364	0.571822	−	0.820378i	$-0.306237\pi$
$197$	16.0518	1.14364	0.571822	+	0.820378i	$0.306237\pi$
$198$	−1.81632	−0.129080
$199$	−5.87911	−0.416759	−0.208380	−	0.978048i	$-0.566819\pi$
$199$	−5.87911	−0.416759	−0.208380	+	0.978048i	$0.566819\pi$
$200$	1.92572	0.136169
$201$	1.01931	0.0718966
$202$	−6.57682	−0.462743
$203$	−1.74060	−0.122166
$204$	−3.86871	−0.270864
$205$	−5.50155	−0.384245
$206$	−2.59482	−0.180790
$207$	10.9336	0.759940
$208$	3.75130	0.260106
$209$	−8.25971	−0.571336
$210$	−0.131290	−0.00905988
$211$	10.9955	0.756959	0.378480	−	0.925610i	$-0.376447\pi$
$211$	10.9955	0.756959	0.378480	+	0.925610i	$0.376447\pi$
$212$	−10.7282	−0.736817
$213$	−7.51151	−0.514680
$214$	−2.80039	−0.191431
$215$	9.50155	0.648000
$216$	7.45005	0.506912
$217$	−1.95438	−0.132672
$218$	0.580355	0.0393066
$219$	−5.04458	−0.340881
$220$	−2.43662	−0.164277
$221$	−4.81313	−0.323766
$222$	4.02691	0.270269
$223$	−14.5772	−0.976160	−0.488080	−	0.872799i	$-0.662303\pi$
$223$	−14.5772	−0.976160	−0.488080	+	0.872799i	$0.662303\pi$
$224$	−1.85801	−0.124144
$225$	−2.50637	−0.167091
$226$	3.63517	0.241808
$227$	21.0131	1.39469	0.697343	−	0.716738i	$-0.254366\pi$
$227$	21.0131	1.39469	0.697343	+	0.716738i	$0.254366\pi$
$228$	7.16130	0.474269
$229$	−26.3707	−1.74263	−0.871313	−	0.490728i	$-0.836731\pi$
$229$	−26.3707	−1.74263	−0.871313	+	0.490728i	$0.836731\pi$
$230$	−2.24975	−0.148344
$231$	0.357724	0.0235365
$232$	−9.25074	−0.607341
$233$	−17.2235	−1.12835	−0.564174	−	0.825656i	$-0.690805\pi$
$233$	−17.2235	−1.12835	−0.564174	+	0.825656i	$0.690805\pi$
$234$	1.95921	0.128077
$235$	−6.28120	−0.409740
$236$	−16.2448	−1.05745
$237$	0.979255	0.0636095
$238$	0.593390	0.0384637
$239$	20.5605	1.32995	0.664974	−	0.746866i	$-0.268442\pi$
$239$	20.5605	1.32995	0.664974	+	0.746866i	$0.268442\pi$
$240$	1.73885	0.112243
$241$	−6.50049	−0.418734	−0.209367	−	0.977837i	$-0.567140\pi$
$241$	−6.50049	−0.418734	−0.209367	+	0.977837i	$0.567140\pi$
$242$	4.65463	0.299211
$243$	−14.9793	−0.960920
$244$	2.85597	0.182835
$245$	6.86871	0.438826
$246$	1.99343	0.127096
$247$	8.90950	0.566898
$248$	−10.3869	−0.659570
$249$	8.97125	0.568530
$250$	0.515722	0.0326171
$251$	27.1927	1.71639	0.858195	−	0.513323i	$-0.171586\pi$
$251$	27.1927	1.71639	0.858195	+	0.513323i	$0.171586\pi$
$252$	1.57477	0.0992014
$253$	6.12986	0.385381
$254$	4.79519	0.300877
$255$	−2.23105	−0.139714
$256$	−1.29154	−0.0807210
$257$	−23.3426	−1.45607	−0.728037	−	0.685538i	$-0.759567\pi$
$257$	−23.3426	−1.45607	−0.728037	+	0.685538i	$0.759567\pi$
$258$	−3.44279	−0.214339
$259$	4.02691	0.250220
$260$	2.62831	0.163001
$261$	12.0401	0.745261
$262$	−1.97468	−0.121996
$263$	−13.4125	−0.827049	−0.413525	−	0.910493i	$-0.635702\pi$
$263$	−13.4125	−0.827049	−0.413525	+	0.910493i	$0.635702\pi$
$264$	1.90119	0.117010
$265$	−6.18687	−0.380056
$266$	−1.09841	−0.0673480
$267$	−8.42348	−0.515509
$268$	2.51572	0.153672
$269$	−0.287453	−0.0175263	−0.00876316	−	0.999962i	$-0.502789\pi$
$269$	−0.287453	−0.0175263	−0.00876316	+	0.999962i	$0.502789\pi$
$270$	1.99518	0.121423
$271$	5.15648	0.313234	0.156617	−	0.987659i	$-0.449941\pi$
$271$	5.15648	0.313234	0.156617	+	0.987659i	$0.449941\pi$
$272$	−7.85906	−0.476526
$273$	−0.385866	−0.0233537
$274$	−3.17020	−0.191519
$275$	−1.40518	−0.0847353
$276$	−5.31468	−0.319906
$277$	2.01131	0.120848	0.0604238	−	0.998173i	$-0.480755\pi$
$277$	2.01131	0.120848	0.0604238	+	0.998173i	$0.480755\pi$
$278$	3.32607	0.199485
$279$	13.5188	0.809350
$280$	−0.697765	−0.0416994
$281$	−14.7158	−0.877869	−0.438935	−	0.898519i	$-0.644644\pi$
$281$	−14.7158	−0.877869	−0.438935	+	0.898519i	$0.644644\pi$
$282$	2.27593	0.135530
$283$	−6.77074	−0.402479	−0.201239	−	0.979542i	$-0.564497\pi$
$283$	−6.77074	−0.402479	−0.201239	+	0.979542i	$0.564497\pi$
$284$	−18.5389	−1.10008
$285$	4.12986	0.244632
$286$	1.09841	0.0649505
$287$	1.99343	0.117668
$288$	12.8522	0.757323
$289$	−6.91637	−0.406845
$290$	−2.47741	−0.145479
$291$	0.0220916	0.00129503
$292$	−12.4503	−0.728602
$293$	1.39582	0.0815449	0.0407725	−	0.999168i	$-0.487018\pi$
$293$	1.39582	0.0815449	0.0407725	+	0.999168i	$0.487018\pi$
$294$	−2.48881	−0.145150
$295$	−9.36822	−0.545439
$296$	21.4018	1.24395
$297$	−5.43622	−0.315441
$298$	−10.0842	−0.584164
$299$	−6.61209	−0.382387
$300$	1.21831	0.0703391
$301$	−3.44279	−0.198439
$302$	8.79647	0.506180
$303$	−8.95986	−0.514730
$304$	14.5478	0.834372
$305$	1.64701	0.0943076
$306$	−4.10458	−0.234643
$307$	−25.3865	−1.44888	−0.724441	−	0.689337i	$-0.757902\pi$
$307$	−25.3865	−1.44888	−0.724441	+	0.689337i	$0.757902\pi$
$308$	0.882884	0.0503070
$309$	−3.53503	−0.201101
$310$	−2.78169	−0.157989
$311$	−29.7733	−1.68829	−0.844145	−	0.536116i	$-0.819891\pi$
$311$	−29.7733	−1.68829	−0.844145	+	0.536116i	$0.819891\pi$
$312$	−2.05075	−0.116101
$313$	19.7320	1.11532	0.557659	−	0.830070i	$-0.311700\pi$
$313$	19.7320	1.11532	0.557659	+	0.830070i	$0.311700\pi$
$314$	1.54394	0.0871295
$315$	0.908158	0.0511689
$316$	2.41686	0.135959
$317$	7.59278	0.426453	0.213227	−	0.977003i	$-0.431603\pi$
$317$	7.59278	0.426453	0.213227	+	0.977003i	$0.431603\pi$
$318$	2.24175	0.125711
$319$	6.75016	0.377936
$320$	2.30533	0.128872
$321$	−3.81509	−0.212937
$322$	0.815175	0.0454279
$323$	−18.6656	−1.03858
$324$	−8.32509	−0.462505
$325$	1.51572	0.0840771
$326$	−9.89594	−0.548085
$327$	0.790641	0.0437226
$328$	10.5944	0.584980
$329$	2.27593	0.125476
$330$	0.509151	0.0280279
$331$	−5.79035	−0.318266	−0.159133	−	0.987257i	$-0.550870\pi$
$331$	−5.79035	−0.318266	−0.159133	+	0.987257i	$0.550870\pi$
$332$	22.1416	1.21518
$333$	−27.8549	−1.52644
$334$	4.06183	0.222254
$335$	1.45079	0.0792653
$336$	−0.630056	−0.0343724
$337$	28.3858	1.54627	0.773136	−	0.634240i	$-0.218687\pi$
$337$	28.3858	1.54627	0.773136	+	0.634240i	$0.218687\pi$
$338$	5.51956	0.300224
$339$	4.95234	0.268974
$340$	−5.50637	−0.298625
$341$	7.57922	0.410438
$342$	7.59792	0.410848
$343$	−5.02519	−0.271335
$344$	−18.2973	−0.986526
$345$	−3.06493	−0.165010
$346$	10.3117	0.554363
$347$	14.3333	0.769452	0.384726	−	0.923031i	$-0.374296\pi$
$347$	14.3333	0.769452	0.384726	+	0.923031i	$0.374296\pi$
$348$	−5.85249	−0.313727
$349$	−2.30782	−0.123535	−0.0617673	−	0.998091i	$-0.519674\pi$
$349$	−2.30782	−0.123535	−0.0617673	+	0.998091i	$0.519674\pi$
$350$	−0.186866	−0.00998843
$351$	5.86389	0.312991
$352$	7.20548	0.384053
$353$	5.21717	0.277682	0.138841	−	0.990315i	$-0.455662\pi$
$353$	5.21717	0.277682	0.138841	+	0.990315i	$0.455662\pi$
$354$	3.39448	0.180414
$355$	−10.6912	−0.567430
$356$	−20.7897	−1.10185
$357$	0.808398	0.0427850
$358$	−5.68290	−0.300350
$359$	−7.14403	−0.377047	−0.188524	−	0.982069i	$-0.560370\pi$
$359$	−7.14403	−0.377047	−0.188524	+	0.982069i	$0.560370\pi$
$360$	4.82657	0.254382
$361$	15.5516	0.818506
$362$	11.8509	0.622869
$363$	6.34119	0.332826
$364$	−0.952341	−0.0499162
$365$	−7.18000	−0.375818
$366$	−0.596778	−0.0311941
$367$	14.0541	0.733620	0.366810	−	0.930296i	$-0.380450\pi$
$367$	14.0541	0.733620	0.366810	+	0.930296i	$0.380450\pi$
$368$	−10.7965	−0.562805
$369$	−13.7889	−0.717822
$370$	5.73154	0.297969
$371$	2.24175	0.116386
$372$	−6.57130	−0.340706
$373$	14.2194	0.736251	0.368125	−	0.929776i	$-0.380000\pi$
$373$	14.2194	0.736251	0.368125	+	0.929776i	$0.380000\pi$
$374$	−2.30120	−0.118992
$375$	0.702588	0.0362815
$376$	12.0958	0.623795
$377$	−7.28120	−0.375001
$378$	−0.722932	−0.0371836
$379$	−24.1830	−1.24220	−0.621099	−	0.783732i	$-0.713313\pi$
$379$	−24.1830	−1.24220	−0.621099	+	0.783732i	$0.713313\pi$
$380$	10.1927	0.522877
$381$	6.53268	0.334679
$382$	1.48603	0.0760317
$383$	0.0618335	0.00315954	0.00157977	−	0.999999i	$-0.499497\pi$
$383$	0.0618335	0.00315954	0.00157977	+	0.999999i	$0.499497\pi$
$384$	−8.04079	−0.410330
$385$	0.509151	0.0259488
$386$	12.8888	0.656021
$387$	23.8144	1.21055
$388$	0.0545235	0.00276801
$389$	−4.05362	−0.205527	−0.102763	−	0.994706i	$-0.532768\pi$
$389$	−4.05362	−0.205527	−0.102763	+	0.994706i	$0.532768\pi$
$390$	−0.549206	−0.0278101
$391$	13.8525	0.700551
$392$	−13.2272	−0.668075
$393$	−2.69019	−0.135702
$394$	−8.27826	−0.417053
$395$	1.39378	0.0701288
$396$	−6.10707	−0.306892
$397$	−29.1510	−1.46304	−0.731522	−	0.681817i	$-0.761190\pi$
$397$	−29.1510	−1.46304	−0.731522	+	0.681817i	$0.761190\pi$
$398$	3.03199	0.151980
$399$	−1.49641	−0.0749143
$400$	2.47493	0.123746
$401$	−7.19274	−0.359188	−0.179594	−	0.983741i	$-0.557478\pi$
$401$	−7.19274	−0.359188	−0.179594	+	0.983741i	$0.557478\pi$
$402$	−0.525680	−0.0262186
$403$	−8.17547	−0.407249
$404$	−22.1135	−1.10019
$405$	−4.80100	−0.238564
$406$	0.897666	0.0445504
$407$	−15.6166	−0.774087
$408$	4.29638	0.212702
$409$	−34.4822	−1.70503	−0.852517	−	0.522700i	$-0.824925\pi$
$409$	−34.4822	−1.70503	−0.852517	+	0.522700i	$0.824925\pi$
$410$	2.83727	0.140123
$411$	−4.31890	−0.213035
$412$	−8.72468	−0.429834
$413$	3.39448	0.167031
$414$	−5.63871	−0.277128
$415$	12.7689	0.626799
$416$	−7.77234	−0.381070
$417$	4.53124	0.221896
$418$	4.25971	0.208349
$419$	−3.12676	−0.152752	−0.0763761	−	0.997079i	$-0.524335\pi$
$419$	−3.12676	−0.152752	−0.0763761	+	0.997079i	$0.524335\pi$
$420$	−0.441442	−0.0215402
$421$	13.6134	0.663478	0.331739	−	0.943371i	$-0.392365\pi$
$421$	13.6134	0.663478	0.331739	+	0.943371i	$0.392365\pi$
$422$	−5.67060	−0.276041
$423$	−15.7430	−0.765451
$424$	11.9142	0.578604
$425$	−3.17547	−0.154033
$426$	3.87385	0.187688
$427$	−0.596778	−0.0288801
$428$	−9.41587	−0.455133
$429$	1.49641	0.0722474
$430$	−4.90015	−0.236306
$431$	23.2055	1.11777	0.558884	−	0.829246i	$-0.311230\pi$
$431$	23.2055	1.11777	0.558884	+	0.829246i	$0.311230\pi$
$432$	9.57477	0.460667
$433$	5.59278	0.268772	0.134386	−	0.990929i	$-0.457094\pi$
$433$	5.59278	0.268772	0.134386	+	0.990929i	$0.457094\pi$
$434$	1.00792	0.0483816
$435$	−3.37508	−0.161823
$436$	1.95135	0.0934528
$437$	−25.6421	−1.22663
$438$	2.60160	0.124309
$439$	−35.2630	−1.68301	−0.841506	−	0.540248i	$-0.818330\pi$
$439$	−35.2630	−1.68301	−0.841506	+	0.540248i	$0.818330\pi$
$440$	2.70598	0.129002
$441$	17.2155	0.819787
$442$	2.48224	0.118068
$443$	−29.3229	−1.39317	−0.696586	−	0.717473i	$-0.745299\pi$
$443$	−29.3229	−1.39317	−0.696586	+	0.717473i	$0.745299\pi$
$444$	13.5399	0.642573
$445$	−11.9892	−0.568343
$446$	7.51776	0.355976
$447$	−13.7382	−0.649793
$448$	−0.835313	−0.0394648
$449$	−24.7806	−1.16947	−0.584734	−	0.811225i	$-0.698801\pi$
$449$	−24.7806	−1.16947	−0.584734	+	0.811225i	$0.698801\pi$
$450$	1.29259	0.0609332
$451$	−7.73064	−0.364022
$452$	12.2227	0.574907
$453$	11.9838	0.563047
$454$	−10.8369	−0.508600
$455$	−0.549206	−0.0257472
$456$	−7.95295	−0.372431
$457$	4.57657	0.214083	0.107041	−	0.994255i	$-0.465862\pi$
$457$	4.57657	0.214083	0.107041	+	0.994255i	$0.465862\pi$
$458$	13.5999	0.635483
$459$	−12.2850	−0.573414
$460$	−7.56443	−0.352694
$461$	−18.3308	−0.853751	−0.426875	−	0.904310i	$-0.640386\pi$
$461$	−18.3308	−0.853751	−0.426875	+	0.904310i	$0.640386\pi$
$462$	−0.184486	−0.00858306
$463$	−41.3896	−1.92354	−0.961768	−	0.273865i	$-0.911698\pi$
$463$	−41.3896	−1.92354	−0.961768	+	0.273865i	$0.911698\pi$
$464$	−11.8890	−0.551933
$465$	−3.78961	−0.175739
$466$	8.88253	0.411475
$467$	−3.34907	−0.154976	−0.0774882	−	0.996993i	$-0.524690\pi$
$467$	−3.34907	−0.154976	−0.0774882	+	0.996993i	$0.524690\pi$
$468$	6.58751	0.304508
$469$	−0.525680	−0.0242737
$470$	3.23935	0.149420
$471$	2.10337	0.0969181
$472$	18.0406	0.830384
$473$	13.3513	0.613896
$474$	−0.505023	−0.0231965
$475$	5.87806	0.269704
$476$	1.99518	0.0914488
$477$	−15.5066	−0.709997
$478$	−10.6035	−0.484993
$479$	−4.87294	−0.222651	−0.111325	−	0.993784i	$-0.535510\pi$
$479$	−4.87294	−0.222651	−0.111325	+	0.993784i	$0.535510\pi$
$480$	−3.60274	−0.164442
$481$	16.8452	0.768074
$482$	3.35245	0.152700
$483$	1.11055	0.0505316
$484$	15.6505	0.711385
$485$	0.0314432	0.00142776
$486$	7.72513	0.350419
$487$	9.24885	0.419105	0.209553	−	0.977797i	$-0.432799\pi$
$487$	9.24885	0.419105	0.209553	+	0.977797i	$0.432799\pi$
$488$	−3.17168	−0.143575
$489$	−13.4816	−0.609660
$490$	−3.54234	−0.160027
$491$	−41.7190	−1.88275	−0.941377	−	0.337357i	$-0.890467\pi$
$491$	−41.7190	−1.88275	−0.941377	+	0.337357i	$0.890467\pi$
$492$	6.70259	0.302176
$493$	15.2543	0.687018
$494$	−4.59482	−0.206731
$495$	−3.52189	−0.158297
$496$	−13.3492	−0.599398
$497$	3.87385	0.173766
$498$	−4.62667	−0.207326
$499$	−10.6953	−0.478786	−0.239393	−	0.970923i	$-0.576948\pi$
$499$	−10.6953	−0.478786	−0.239393	+	0.970923i	$0.576948\pi$
$500$	1.73403	0.0775482
$501$	5.53360	0.247223
$502$	−14.0239	−0.625917
$503$	−26.9526	−1.20176	−0.600878	−	0.799341i	$-0.705182\pi$
$503$	−26.9526	−1.20176	−0.600878	+	0.799341i	$0.705182\pi$
$504$	−1.74886	−0.0779003
$505$	−12.7526	−0.567485
$506$	−3.16130	−0.140537
$507$	7.51951	0.333953
$508$	16.1231	0.715345
$509$	−38.8649	−1.72266	−0.861329	−	0.508047i	$-0.830367\pi$
$509$	−38.8649	−1.72266	−0.861329	+	0.508047i	$0.830367\pi$
$510$	1.15060	0.0509494
$511$	2.60160	0.115088
$512$	−22.2230	−0.982127
$513$	22.7405	1.00402
$514$	12.0383	0.530987
$515$	−5.03144	−0.221712
$516$	−11.5758	−0.509597
$517$	−8.82619	−0.388175
$518$	−2.07677	−0.0912479
$519$	14.0481	0.616643
$520$	−2.91886	−0.128000
$521$	33.5436	1.46957	0.734785	−	0.678300i	$-0.237283\pi$
$521$	33.5436	1.46957	0.734785	+	0.678300i	$0.237283\pi$
$522$	−6.20932	−0.271774
$523$	−34.5313	−1.50995	−0.754973	−	0.655755i	$-0.772350\pi$
$523$	−34.5313	−1.50995	−0.754973	+	0.655755i	$0.772350\pi$
$524$	−6.63955	−0.290050
$525$	−0.254576	−0.0111106
$526$	6.91711	0.301600
$527$	17.1278	0.746099
$528$	2.44340	0.106335
$529$	−3.96999	−0.172608
$530$	3.19070	0.138595
$531$	−23.4802	−1.01895
$532$	−3.69324	−0.160122
$533$	8.33881	0.361194
$534$	4.34417	0.187991
$535$	−5.43005	−0.234761
$536$	−2.79382	−0.120675
$537$	−7.74204	−0.334094
$538$	0.148246	0.00639133
$539$	9.65175	0.415730
$540$	6.70846	0.288686
$541$	−31.1980	−1.34131	−0.670654	−	0.741771i	$-0.733986\pi$
$541$	−31.1980	−1.34131	−0.670654	+	0.741771i	$0.733986\pi$
$542$	−2.65931	−0.114227
$543$	16.1450	0.692846
$544$	16.2832	0.698138
$545$	1.12533	0.0482037
$546$	0.198999	0.00851638
$547$	30.8217	1.31784	0.658919	−	0.752213i	$-0.271014\pi$
$547$	30.8217	1.31784	0.658919	+	0.752213i	$0.271014\pi$
$548$	−10.6593	−0.455343
$549$	4.12802	0.176180
$550$	0.724680	0.0309004
$551$	−28.2369	−1.20293
$552$	5.90219	0.251214
$553$	−0.505023	−0.0214758
$554$	−1.03727	−0.0440695
$555$	7.80831	0.331444
$556$	11.1834	0.474281
$557$	4.14620	0.175680	0.0878402	−	0.996135i	$-0.472004\pi$
$557$	4.14620	0.175680	0.0878402	+	0.996135i	$0.472004\pi$
$558$	−6.97195	−0.295146
$559$	−14.4017	−0.609127
$560$	−0.896765	−0.0378952
$561$	−3.13502	−0.132361
$562$	7.58924	0.320133
$563$	16.2139	0.683336	0.341668	−	0.939821i	$-0.389008\pi$
$563$	16.2139	0.683336	0.341668	+	0.939821i	$0.389008\pi$
$564$	7.65244	0.322226
$565$	7.04871	0.296542
$566$	3.49182	0.146772
$567$	1.73959	0.0730561
$568$	20.5883	0.863864
$569$	−7.43752	−0.311797	−0.155899	−	0.987773i	$-0.549827\pi$
$569$	−7.43752	−0.311797	−0.155899	+	0.987773i	$0.549827\pi$
$570$	−2.12986	−0.0892098
$571$	44.2084	1.85007	0.925033	−	0.379887i	$-0.124037\pi$
$571$	44.2084	1.85007	0.925033	+	0.379887i	$0.124037\pi$
$572$	3.69324	0.154422
$573$	2.02447	0.0845735
$574$	−1.02805	−0.0429102
$575$	−4.36234	−0.181922
$576$	5.77801	0.240750
$577$	23.1115	0.962143	0.481071	−	0.876681i	$-0.340248\pi$
$577$	23.1115	0.962143	0.481071	+	0.876681i	$0.340248\pi$
$578$	3.56692	0.148364
$579$	17.5589	0.729722
$580$	−8.32991	−0.345881
$581$	−4.62667	−0.191947
$582$	−0.0113931	−0.000472260 0
$583$	−8.69364	−0.360054
$584$	13.8267	0.572152
$585$	3.79896	0.157068
$586$	−0.719857	−0.0297370
$587$	−18.3429	−0.757094	−0.378547	−	0.925582i	$-0.623576\pi$
$587$	−18.3429	−0.757094	−0.378547	+	0.925582i	$0.623576\pi$
$588$	−8.36822	−0.345099
$589$	−31.7050	−1.30638
$590$	4.83139	0.198905
$591$	−11.2778	−0.463907
$592$	27.5054	1.13047
$593$	17.6624	0.725308	0.362654	−	0.931924i	$-0.381871\pi$
$593$	17.6624	0.725308	0.362654	+	0.931924i	$0.381871\pi$
$594$	2.80358	0.115032
$595$	1.15060	0.0471700
$596$	−33.9066	−1.38887
$597$	4.13060	0.169054
$598$	3.41000	0.139445
$599$	23.2791	0.951157	0.475578	−	0.879673i	$-0.342239\pi$
$599$	23.2791	0.951157	0.475578	+	0.879673i	$0.342239\pi$
$600$	−1.35299	−0.0552355
$601$	10.3920	0.423900	0.211950	−	0.977281i	$-0.432019\pi$
$601$	10.3920	0.423900	0.211950	+	0.977281i	$0.432019\pi$
$602$	1.77552	0.0723648
$603$	3.63623	0.148079
$604$	29.5767	1.20346
$605$	9.02548	0.366938
$606$	4.62079	0.187707
$607$	25.8446	1.04900	0.524500	−	0.851411i	$-0.324252\pi$
$607$	25.8446	1.04900	0.524500	+	0.851411i	$0.324252\pi$
$608$	−30.1416	−1.22240
$609$	1.22293	0.0495555
$610$	−0.849400	−0.0343912
$611$	9.52054	0.385160
$612$	−13.8010	−0.557872
$613$	36.9637	1.49295	0.746474	−	0.665414i	$-0.231745\pi$
$613$	36.9637	1.49295	0.746474	+	0.665414i	$0.231745\pi$
$614$	13.0924	0.528364
$615$	3.86532	0.155865
$616$	−0.980483	−0.0395048
$617$	11.5216	0.463842	0.231921	−	0.972735i	$-0.425499\pi$
$617$	11.5216	0.463842	0.231921	+	0.972735i	$0.425499\pi$
$618$	1.82309	0.0733355
$619$	28.9710	1.16444	0.582221	−	0.813031i	$-0.302184\pi$
$619$	28.9710	1.16444	0.582221	+	0.813031i	$0.302184\pi$
$620$	−9.35299	−0.375625
$621$	−16.8766	−0.677236
$622$	15.3547	0.615669
$623$	4.34417	0.174045
$624$	−2.63562	−0.105509
$625$	1.00000	0.0400000
$626$	−10.1762	−0.406723
$627$	5.80317	0.231756
$628$	5.19124	0.207153
$629$	−35.2911	−1.40715
$630$	−0.468357	−0.0186598
$631$	17.3865	0.692147	0.346074	−	0.938207i	$-0.387515\pi$
$631$	17.3865	0.692147	0.346074	+	0.938207i	$0.387515\pi$
$632$	−2.68404	−0.106765
$633$	−7.72529	−0.307053
$634$	−3.91576	−0.155515
$635$	9.29802	0.368981
$636$	7.53752	0.298882
$637$	−10.4111	−0.412501
$638$	−3.48120	−0.137822
$639$	−26.7961	−1.06004
$640$	−11.4445	−0.452385
$641$	−41.3280	−1.63236	−0.816179	−	0.577798i	$-0.803912\pi$
$641$	−41.3280	−1.63236	−0.816179	+	0.577798i	$0.803912\pi$
$642$	1.96752	0.0776519
$643$	−5.82044	−0.229536	−0.114768	−	0.993392i	$-0.536612\pi$
$643$	−5.82044	−0.229536	−0.114768	+	0.993392i	$0.536612\pi$
$644$	2.74090	0.108006
$645$	−6.67567	−0.262854
$646$	9.62627	0.378740
$647$	−29.4785	−1.15892	−0.579459	−	0.815001i	$-0.696736\pi$
$647$	−29.4785	−1.15892	−0.579459	+	0.815001i	$0.696736\pi$
$648$	9.24539	0.363193
$649$	−13.1640	−0.516732
$650$	−0.781690	−0.0306604
$651$	1.37313	0.0538170
$652$	−33.2735	−1.30309
$653$	25.0923	0.981938	0.490969	−	0.871177i	$-0.336643\pi$
$653$	25.0923	0.981938	0.490969	+	0.871177i	$0.336643\pi$
$654$	−0.407751	−0.0159443
$655$	−3.82897	−0.149610
$656$	13.6159	0.531613
$657$	−17.9957	−0.702081
$658$	−1.17374	−0.0457573
$659$	20.8221	0.811114	0.405557	−	0.914070i	$-0.367078\pi$
$659$	20.8221	0.811114	0.405557	+	0.914070i	$0.367078\pi$
$660$	1.71194	0.0666372
$661$	2.39861	0.0932950	0.0466475	−	0.998911i	$-0.485146\pi$
$661$	2.39861	0.0932950	0.0466475	+	0.998911i	$0.485146\pi$
$662$	2.98621	0.116062
$663$	3.38165	0.131332
$664$	−24.5893	−0.954248
$665$	−2.12986	−0.0825923
$666$	14.3654	0.556647
$667$	20.9557	0.811409
$668$	13.6573	0.528415
$669$	10.2417	0.395969
$670$	−0.748206	−0.0289057
$671$	2.31434	0.0893442
$672$	1.30542	0.0503575
$673$	−23.6493	−0.911614	−0.455807	−	0.890079i	$-0.650649\pi$
$673$	−23.6493	−0.911614	−0.455807	+	0.890079i	$0.650649\pi$
$674$	−14.6392	−0.563880
$675$	3.86871	0.148907
$676$	18.5586	0.713793
$677$	13.8505	0.532319	0.266160	−	0.963929i	$-0.414245\pi$
$677$	13.8505	0.532319	0.266160	+	0.963929i	$0.414245\pi$
$678$	−2.55403	−0.0980869
$679$	−0.0113931	−0.000437228 0
$680$	6.11507	0.234502
$681$	−14.7635	−0.565739
$682$	−3.90876	−0.149674
$683$	−31.7909	−1.21644	−0.608222	−	0.793767i	$-0.708117\pi$
$683$	−31.7909	−1.21644	−0.608222	+	0.793767i	$0.708117\pi$
$684$	25.5468	0.976806
$685$	−6.14712	−0.234870
$686$	2.59160	0.0989476
$687$	18.5277	0.706877
$688$	−23.5156	−0.896525
$689$	9.37757	0.357257
$690$	1.58065	0.0601743
$691$	−45.7463	−1.74027	−0.870136	−	0.492812i	$-0.835969\pi$
$691$	−45.7463	−1.74027	−0.870136	+	0.492812i	$0.835969\pi$
$692$	34.6716	1.31802
$693$	1.27612	0.0484758
$694$	−7.39199	−0.280596
$695$	6.44936	0.244638
$696$	6.49946	0.246361
$697$	−17.4700	−0.661724
$698$	1.19019	0.0450494
$699$	12.1010	0.457703
$700$	−0.628309	−0.0237478
$701$	−36.3630	−1.37341	−0.686706	−	0.726935i	$-0.740944\pi$
$701$	−36.3630	−1.37341	−0.686706	+	0.726935i	$0.740944\pi$
$702$	−3.02413	−0.114139
$703$	65.3267	2.46384
$704$	3.23939	0.122089
$705$	4.41309	0.166207
$706$	−2.69061	−0.101262
$707$	4.62079	0.173783
$708$	11.4134	0.428941
$709$	−14.0739	−0.528556	−0.264278	−	0.964446i	$-0.585134\pi$
$709$	−14.0739	−0.528556	−0.264278	+	0.964446i	$0.585134\pi$
$710$	5.51368	0.206925
$711$	3.49334	0.131010
$712$	23.0879	0.865255
$713$	23.5295	0.881187
$714$	−0.416908	−0.0156024
$715$	2.12986	0.0796521
$716$	−19.1078	−0.714093
$717$	−14.4456	−0.539480
$718$	3.68433	0.137498
$719$	−15.3298	−0.571704	−0.285852	−	0.958274i	$-0.592277\pi$
$719$	−15.3298	−0.571704	−0.285852	+	0.958274i	$0.592277\pi$
$720$	6.20308	0.231175
$721$	1.82309	0.0678955
$722$	−8.02030	−0.298485
$723$	4.56717	0.169855
$724$	39.8467	1.48089
$725$	−4.80378	−0.178408
$726$	−3.27029	−0.121372
$727$	9.40553	0.348832	0.174416	−	0.984672i	$-0.444196\pi$
$727$	9.40553	0.348832	0.174416	+	0.984672i	$0.444196\pi$
$728$	1.05762	0.0391979
$729$	−3.87876	−0.143658
$730$	3.70288	0.137050
$731$	30.1719	1.11595
$732$	−2.00657	−0.0741650
$733$	32.1173	1.18628	0.593140	−	0.805099i	$-0.297888\pi$
$733$	32.1173	1.18628	0.593140	+	0.805099i	$0.297888\pi$
$734$	−7.24802	−0.267529
$735$	−4.82587	−0.178005
$736$	22.3693	0.824542
$737$	2.03862	0.0750936
$738$	7.11124	0.261768
$739$	−4.48298	−0.164909	−0.0824545	−	0.996595i	$-0.526276\pi$
$739$	−4.48298	−0.164909	−0.0824545	+	0.996595i	$0.526276\pi$
$740$	19.2714	0.708431
$741$	−6.25971	−0.229956
$742$	−1.15612	−0.0424424
$743$	−27.8676	−1.02236	−0.511181	−	0.859473i	$-0.670792\pi$
$743$	−27.8676	−1.02236	−0.511181	+	0.859473i	$0.670792\pi$
$744$	7.29773	0.267548
$745$	−19.5536	−0.716390
$746$	−7.33323	−0.268489
$747$	32.0035	1.17095
$748$	−7.73742	−0.282908
$749$	1.96752	0.0718917
$750$	−0.362340	−0.0132308
$751$	−31.9910	−1.16737	−0.583684	−	0.811981i	$-0.698389\pi$
$751$	−31.9910	−1.16737	−0.583684	+	0.811981i	$0.698389\pi$
$752$	15.5455	0.566886
$753$	−19.1053	−0.696236
$754$	3.75507	0.136752
$755$	17.0566	0.620754
$756$	−2.43074	−0.0884053
$757$	30.2374	1.09900	0.549499	−	0.835494i	$-0.314818\pi$
$757$	30.2374	1.09900	0.549499	+	0.835494i	$0.314818\pi$
$758$	12.4717	0.452993
$759$	−4.30676	−0.156326
$760$	−11.3195	−0.410602
$761$	−22.7835	−0.825901	−0.412950	−	0.910754i	$-0.635502\pi$
$761$	−22.7835	−0.825901	−0.412950	+	0.910754i	$0.635502\pi$
$762$	−3.36904	−0.122048
$763$	−0.407751	−0.0147616
$764$	4.99652	0.180768
$765$	−7.95891	−0.287755
$766$	−0.0318889	−0.00115219
$767$	14.1996	0.512718
$768$	0.907418	0.0327436
$769$	21.8721	0.788729	0.394364	−	0.918954i	$-0.370965\pi$
$769$	21.8721	0.788729	0.394364	+	0.918954i	$0.370965\pi$
$770$	−0.262580	−0.00946274
$771$	16.4003	0.590641
$772$	43.3364	1.55971
$773$	45.8110	1.64771	0.823854	−	0.566803i	$-0.191820\pi$
$773$	45.8110	1.64771	0.823854	+	0.566803i	$0.191820\pi$
$774$	−12.2816	−0.441453
$775$	−5.39378	−0.193750
$776$	−0.0605508	−0.00217365
$777$	−2.82926	−0.101499
$778$	2.09054	0.0749495
$779$	32.3384	1.15864
$780$	−1.84662	−0.0661195
$781$	−15.0230	−0.537566
$782$	−7.14403	−0.255470
$783$	−18.5844	−0.664154
$784$	−16.9996	−0.607127
$785$	2.99374	0.106851
$786$	1.38739	0.0494865
$787$	0.881111	0.0314082	0.0157041	−	0.999877i	$-0.495001\pi$
$787$	0.881111	0.0314082	0.0157041	+	0.999877i	$0.495001\pi$
$788$	−27.8343	−0.991557
$789$	9.42345	0.335484
$790$	−0.718804	−0.0255739
$791$	−2.55403	−0.0908108
$792$	6.78218	0.240994
$793$	−2.49641	−0.0886502
$794$	15.0338	0.533529
$795$	4.34682	0.154166
$796$	10.1946	0.361337
$797$	37.5653	1.33063	0.665316	−	0.746562i	$-0.268297\pi$
$797$	37.5653	1.33063	0.665316	+	0.746562i	$0.268297\pi$
$798$	0.771732	0.0273190
$799$	−19.9458	−0.705631
$800$	−5.12781	−0.181296
$801$	−30.0494	−1.06174
$802$	3.70945	0.130985
$803$	−10.0892	−0.356039
$804$	−1.76752	−0.0623355
$805$	1.58065	0.0557106
$806$	4.21627	0.148512
$807$	0.201961	0.00710937
$808$	24.5580	0.863949
$809$	0.881896	0.0310058	0.0155029	−	0.999880i	$-0.495065\pi$
$809$	0.881896	0.0310058	0.0155029	+	0.999880i	$0.495065\pi$
$810$	2.47598	0.0869971
$811$	−10.0859	−0.354163	−0.177082	−	0.984196i	$-0.556666\pi$
$811$	−10.0859	−0.354163	−0.177082	+	0.984196i	$0.556666\pi$
$812$	3.01826	0.105920
$813$	−3.62288	−0.127060
$814$	8.05383	0.282287
$815$	−19.1885	−0.672145
$816$	5.52168	0.193298
$817$	−55.8507	−1.95397
$818$	17.7832	0.621775
$819$	−1.37651	−0.0480993
$820$	9.53985	0.333146
$821$	−35.5861	−1.24196	−0.620982	−	0.783824i	$-0.713266\pi$
$821$	−35.5861	−1.24196	−0.620982	+	0.783824i	$0.713266\pi$
$822$	2.22735	0.0776877
$823$	−2.11433	−0.0737011	−0.0368505	−	0.999321i	$-0.511733\pi$
$823$	−2.11433	−0.0737011	−0.0368505	+	0.999321i	$0.511733\pi$
$824$	9.68915	0.337538
$825$	0.987260	0.0343720
$826$	−1.75061	−0.0609114
$827$	50.4021	1.75265	0.876326	−	0.481719i	$-0.159987\pi$
$827$	50.4021	1.75265	0.876326	+	0.481719i	$0.159987\pi$
$828$	−18.9593	−0.658880
$829$	−26.9630	−0.936465	−0.468233	−	0.883605i	$-0.655109\pi$
$829$	−26.9630	−0.936465	−0.468233	+	0.883605i	$0.655109\pi$
$830$	−6.58518	−0.228575
$831$	−1.41312	−0.0490206
$832$	−3.49424	−0.121141
$833$	21.8114	0.755720
$834$	−2.33686	−0.0809188
$835$	7.87602	0.272561
$836$	14.3226	0.495357
$837$	−20.8670	−0.721268
$838$	1.61254	0.0557042
$839$	−27.4839	−0.948849	−0.474425	−	0.880296i	$-0.657344\pi$
$839$	−27.4839	−0.948849	−0.474425	+	0.880296i	$0.657344\pi$
$840$	0.490242	0.0169149
$841$	−5.92368	−0.204265
$842$	−7.02074	−0.241951
$843$	10.3391	0.356098
$844$	−19.0665	−0.656296
$845$	10.7026	0.368180
$846$	8.11901	0.279137
$847$	−3.27029	−0.112369
$848$	15.3120	0.525818
$849$	4.75704	0.163261
$850$	1.63766	0.0561713
$851$	−48.4815	−1.66192
$852$	13.0252	0.446236
$853$	−29.1025	−0.996450	−0.498225	−	0.867048i	$-0.666015\pi$
$853$	−29.1025	−0.996450	−0.498225	+	0.867048i	$0.666015\pi$
$854$	0.307771	0.0105317
$855$	14.7326	0.503844
$856$	10.4568	0.357405
$857$	6.38120	0.217978	0.108989	−	0.994043i	$-0.465239\pi$
$857$	6.38120	0.217978	0.108989	+	0.994043i	$0.465239\pi$
$858$	−0.771732	−0.0263465
$859$	−26.0159	−0.887652	−0.443826	−	0.896113i	$-0.646379\pi$
$859$	−26.0159	−0.887652	−0.443826	+	0.896113i	$0.646379\pi$
$860$	−16.4760	−0.561826
$861$	−1.40056	−0.0477310
$862$	−11.9676	−0.407617
$863$	27.4058	0.932906	0.466453	−	0.884546i	$-0.345532\pi$
$863$	27.4058	0.932906	0.466453	+	0.884546i	$0.345532\pi$
$864$	−19.8380	−0.674903
$865$	19.9948	0.679843
$866$	−2.88432	−0.0980131
$867$	4.85936	0.165032
$868$	3.38896	0.115029
$869$	1.95851	0.0664379
$870$	1.74060	0.0590119
$871$	−2.19900	−0.0745102
$872$	−2.16707	−0.0733861
$873$	0.0788082	0.00266725
$874$	13.2242	0.447315
$875$	−0.362340	−0.0122493
$876$	8.74747	0.295549
$877$	50.3187	1.69914	0.849571	−	0.527474i	$-0.176861\pi$
$877$	50.3187	1.69914	0.849571	+	0.527474i	$0.176861\pi$
$878$	18.1859	0.613744
$879$	−0.980690	−0.0330778
$880$	3.47771	0.117234
$881$	31.7762	1.07057	0.535284	−	0.844672i	$-0.320204\pi$
$881$	31.7762	1.07057	0.535284	+	0.844672i	$0.320204\pi$
$882$	−8.87842	−0.298952
$883$	−13.6878	−0.460631	−0.230316	−	0.973116i	$-0.573976\pi$
$883$	−13.6878	−0.460631	−0.230316	+	0.973116i	$0.573976\pi$
$884$	8.34612	0.280711
$885$	6.58200	0.221251
$886$	15.1224	0.508049
$887$	5.43586	0.182518	0.0912592	−	0.995827i	$-0.470911\pi$
$887$	5.43586	0.182518	0.0912592	+	0.995827i	$0.470911\pi$
$888$	−15.0366	−0.504596
$889$	−3.36904	−0.112994
$890$	6.18310	0.207258
$891$	−6.74625	−0.226008
$892$	25.2773	0.846346
$893$	36.9213	1.23552
$894$	7.08507	0.236960
$895$	−11.0193	−0.368335
$896$	4.14681	0.138535
$897$	4.64558	0.155111
$898$	12.7799	0.426470
$899$	25.9106	0.864165
$900$	4.34612	0.144871
$901$	−19.6462	−0.654511
$902$	3.98686	0.132748
$903$	2.41886	0.0804947
$904$	−13.5738	−0.451460
$905$	22.9793	0.763856
$906$	−6.18030	−0.205327
$907$	−11.7990	−0.391781	−0.195890	−	0.980626i	$-0.562760\pi$
$907$	−11.7990	−0.391781	−0.195890	+	0.980626i	$0.562760\pi$
$908$	−36.4373	−1.20921
$909$	−31.9629	−1.06014
$910$	0.283238	0.00938923
$911$	4.32282	0.143221	0.0716107	−	0.997433i	$-0.477186\pi$
$911$	4.32282	0.143221	0.0716107	+	0.997433i	$0.477186\pi$
$912$	−10.2211	−0.338454
$913$	17.9425	0.593810
$914$	−2.36023	−0.0780696
$915$	−1.15717	−0.0382549
$916$	45.7276	1.51088
$917$	1.38739	0.0458156
$918$	6.33563	0.209107
$919$	−50.5722	−1.66822	−0.834112	−	0.551595i	$-0.814019\pi$
$919$	−50.5722	−1.66822	−0.834112	+	0.551595i	$0.814019\pi$
$920$	8.40065	0.276961
$921$	17.8362	0.587724
$922$	9.45359	0.311338
$923$	16.2049	0.533390
$924$	−0.620304	−0.0204065
$925$	11.1136	0.365414
$926$	21.3455	0.701456
$927$	−12.6107	−0.414188
$928$	24.6329	0.808615
$929$	−26.0311	−0.854054	−0.427027	−	0.904239i	$-0.640439\pi$
$929$	−26.0311	−0.854054	−0.427027	+	0.904239i	$0.640439\pi$
$930$	1.95438	0.0640867
$931$	−40.3747	−1.32323
$932$	29.8661	0.978296
$933$	20.9184	0.684837
$934$	1.72719	0.0565153
$935$	−4.46210	−0.145926
$936$	−7.31573	−0.239122
$937$	−42.2583	−1.38052	−0.690260	−	0.723562i	$-0.742504\pi$
$937$	−42.2583	−1.38052	−0.690260	+	0.723562i	$0.742504\pi$
$938$	0.271105	0.00885188
$939$	−13.8635	−0.452417
$940$	10.8918	0.355251
$941$	45.0492	1.46856	0.734281	−	0.678845i	$-0.237519\pi$
$941$	45.0492	1.46856	0.734281	+	0.678845i	$0.237519\pi$
$942$	−1.08475	−0.0353431
$943$	−23.9996	−0.781535
$944$	23.1856	0.754629
$945$	−1.40179	−0.0456002
$946$	−6.88558	−0.223869
$947$	−41.4726	−1.34768	−0.673839	−	0.738878i	$-0.735356\pi$
$947$	−41.4726	−1.34768	−0.673839	+	0.738878i	$0.735356\pi$
$948$	−1.69806	−0.0551504
$949$	10.8829	0.353273
$950$	−3.03144	−0.0983530
$951$	−5.33460	−0.172986
$952$	−2.21573	−0.0718124
$953$	50.5968	1.63899	0.819495	−	0.573086i	$-0.194254\pi$
$953$	50.5968	1.63899	0.819495	+	0.573086i	$0.194254\pi$
$954$	7.99708	0.258915
$955$	2.88145	0.0932415
$956$	−35.6526	−1.15309
$957$	−4.74258	−0.153306
$958$	2.51308	0.0811940
$959$	2.22735	0.0719248
$960$	−1.61970	−0.0522755
$961$	−1.90710	−0.0615195
$962$	−8.68743	−0.280094
$963$	−13.6097	−0.438567
$964$	11.2721	0.363049
$965$	24.9917	0.804511
$966$	−0.572732	−0.0184274
$967$	−3.95604	−0.127218	−0.0636089	−	0.997975i	$-0.520261\pi$
$967$	−3.95604	−0.127218	−0.0636089	+	0.997975i	$0.520261\pi$
$968$	−17.3806	−0.558632
$969$	13.1142	0.421290
$970$	−0.0162159	−0.000520662 0
$971$	49.6025	1.59182	0.795910	−	0.605415i	$-0.206993\pi$
$971$	49.6025	1.59182	0.795910	+	0.605415i	$0.206993\pi$
$972$	25.9745	0.833132
$973$	−2.33686	−0.0749163
$974$	−4.76983	−0.152835
$975$	−1.06493	−0.0341050
$976$	−4.07623	−0.130477
$977$	41.8429	1.33867	0.669336	−	0.742959i	$-0.266579\pi$
$977$	41.8429	1.33867	0.669336	+	0.742959i	$0.266579\pi$
$978$	6.95277	0.222325
$979$	−16.8470	−0.538431
$980$	−11.9106	−0.380469
$981$	2.82049	0.0900512
$982$	21.5154	0.686584
$983$	17.3614	0.553742	0.276871	−	0.960907i	$-0.410703\pi$
$983$	17.3614	0.553742	0.276871	+	0.960907i	$0.410703\pi$
$984$	−7.44353	−0.237291
$985$	−16.0518	−0.511453
$986$	−7.86696	−0.250535
$987$	−1.59904	−0.0508980
$988$	−15.4494	−0.491510
$989$	41.4490	1.31800
$990$	1.81632	0.0577263
$991$	39.1446	1.24347	0.621735	−	0.783228i	$-0.286428\pi$
$991$	39.1446	1.24347	0.621735	+	0.783228i	$0.286428\pi$
$992$	27.6583	0.878152
$993$	4.06823	0.129101
$994$	−1.99783	−0.0633672
$995$	5.87911	0.186380
$996$	−15.5564	−0.492924
$997$	45.3212	1.43534	0.717669	−	0.696385i	$-0.245209\pi$
$997$	45.3212	1.43534	0.717669	+	0.696385i	$0.245209\pi$
$998$	5.51579	0.174599
$999$	42.9954	1.36032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.c.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.c.1.2	✓	4	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-0.515722 q^{2} -0.702588 q^{3} -1.73403 q^{4} -1.00000 q^{5} +0.362340 q^{6} +0.362340 q^{7} +1.92572 q^{8} -2.50637 q^{9} +O(q^{10})\)	\(q-0.515722 q^{2} -0.702588 q^{3} -1.73403 q^{4} -1.00000 q^{5} +0.362340 q^{6} +0.362340 q^{7} +1.92572 q^{8} -2.50637 q^{9} +0.515722 q^{10} -1.40518 q^{11} +1.21831 q^{12} +1.51572 q^{13} -0.186866 q^{14} +0.702588 q^{15} +2.47493 q^{16} -3.17547 q^{17} +1.29259 q^{18} +5.87806 q^{19} +1.73403 q^{20} -0.254576 q^{21} +0.724680 q^{22} -4.36234 q^{23} -1.35299 q^{24} +1.00000 q^{25} -0.781690 q^{26} +3.86871 q^{27} -0.628309 q^{28} -4.80378 q^{29} -0.362340 q^{30} -5.39378 q^{31} -5.12781 q^{32} +0.987260 q^{33} +1.63766 q^{34} -0.362340 q^{35} +4.34612 q^{36} +11.1136 q^{37} -3.03144 q^{38} -1.06493 q^{39} -1.92572 q^{40} +5.50155 q^{41} +0.131290 q^{42} -9.50155 q^{43} +2.43662 q^{44} +2.50637 q^{45} +2.24975 q^{46} +6.28120 q^{47} -1.73885 q^{48} -6.86871 q^{49} -0.515722 q^{50} +2.23105 q^{51} -2.62831 q^{52} +6.18687 q^{53} -1.99518 q^{54} +1.40518 q^{55} +0.697765 q^{56} -4.12986 q^{57} +2.47741 q^{58} +9.36822 q^{59} -1.21831 q^{60} -1.64701 q^{61} +2.78169 q^{62} -0.908158 q^{63} -2.30533 q^{64} -1.51572 q^{65} -0.509151 q^{66} -1.45079 q^{67} +5.50637 q^{68} +3.06493 q^{69} +0.186866 q^{70} +10.6912 q^{71} -4.82657 q^{72} +7.18000 q^{73} -5.73154 q^{74} -0.702588 q^{75} -10.1927 q^{76} -0.509151 q^{77} +0.549206 q^{78} -1.39378 q^{79} -2.47493 q^{80} +4.80100 q^{81} -2.83727 q^{82} -12.7689 q^{83} +0.441442 q^{84} +3.17547 q^{85} +4.90015 q^{86} +3.37508 q^{87} -2.70598 q^{88} +11.9892 q^{89} -1.29259 q^{90} +0.549206 q^{91} +7.56443 q^{92} +3.78961 q^{93} -3.23935 q^{94} -5.87806 q^{95} +3.60274 q^{96} -0.0314432 q^{97} +3.54234 q^{98} +3.52189 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 7 q^{6} - 7 q^{7} + 9 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 7 * q^6 - 7 * q^7 + 9 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 7 q^{6} - 7 q^{7} + 9 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{13} - 4 q^{14} + 2 q^{15} + 6 q^{16} - q^{17} - q^{18} + 11 q^{19} - 2 q^{20} + 5 q^{21} - 14 q^{22} - 9 q^{23} + 11 q^{24} + 4 q^{25} - 8 q^{26} - 5 q^{27} - 3 q^{28} - 8 q^{29} + 7 q^{30} - 5 q^{31} + 5 q^{32} + 28 q^{33} + 15 q^{34} + 7 q^{35} - 13 q^{36} + 4 q^{37} - 4 q^{38} + 5 q^{39} - 9 q^{40} + 3 q^{41} + 21 q^{42} - 19 q^{43} - 2 q^{45} - 4 q^{46} + 4 q^{47} - 5 q^{48} - 7 q^{49} + 2 q^{50} - 20 q^{51} - 11 q^{52} + 28 q^{53} - q^{54} + 4 q^{55} - 5 q^{56} + 2 q^{57} - 9 q^{59} - 23 q^{61} + 16 q^{62} - 22 q^{63} + 21 q^{64} - 2 q^{65} + 10 q^{66} - 11 q^{67} + 10 q^{68} + 3 q^{69} + 4 q^{70} + 27 q^{71} - 38 q^{72} + 18 q^{73} - 20 q^{74} - 2 q^{75} - 6 q^{76} + 10 q^{77} - 3 q^{78} + 11 q^{79} - 6 q^{80} + 8 q^{81} + q^{82} - 2 q^{83} - q^{84} + q^{85} - 9 q^{86} - 19 q^{87} + 22 q^{88} + q^{89} + q^{90} - 3 q^{91} - 5 q^{92} - 11 q^{93} - 37 q^{94} - 11 q^{95} - 15 q^{96} + 8 q^{97} - 5 q^{98} - 22 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 7 * q^6 - 7 * q^7 + 9 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^13 - 4 * q^14 + 2 * q^15 + 6 * q^16 - q^17 - q^18 + 11 * q^19 - 2 * q^20 + 5 * q^21 - 14 * q^22 - 9 * q^23 + 11 * q^24 + 4 * q^25 - 8 * q^26 - 5 * q^27 - 3 * q^28 - 8 * q^29 + 7 * q^30 - 5 * q^31 + 5 * q^32 + 28 * q^33 + 15 * q^34 + 7 * q^35 - 13 * q^36 + 4 * q^37 - 4 * q^38 + 5 * q^39 - 9 * q^40 + 3 * q^41 + 21 * q^42 - 19 * q^43 - 2 * q^45 - 4 * q^46 + 4 * q^47 - 5 * q^48 - 7 * q^49 + 2 * q^50 - 20 * q^51 - 11 * q^52 + 28 * q^53 - q^54 + 4 * q^55 - 5 * q^56 + 2 * q^57 - 9 * q^59 - 23 * q^61 + 16 * q^62 - 22 * q^63 + 21 * q^64 - 2 * q^65 + 10 * q^66 - 11 * q^67 + 10 * q^68 + 3 * q^69 + 4 * q^70 + 27 * q^71 - 38 * q^72 + 18 * q^73 - 20 * q^74 - 2 * q^75 - 6 * q^76 + 10 * q^77 - 3 * q^78 + 11 * q^79 - 6 * q^80 + 8 * q^81 + q^82 - 2 * q^83 - q^84 + q^85 - 9 * q^86 - 19 * q^87 + 22 * q^88 + q^89 + q^90 - 3 * q^91 - 5 * q^92 - 11 * q^93 - 37 * q^94 - 11 * q^95 - 15 * q^96 + 8 * q^97 - 5 * q^98 - 22 * q^99

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