LMFDB - Embedded newform 4034.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.75660 q^{3} +1.00000 q^{4} +3.24124 q^{5} +2.75660 q^{6} +3.57367 q^{7} -1.00000 q^{8} +4.59882 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.75660 q^{3} +1.00000 q^{4} +3.24124 q^{5} +2.75660 q^{6} +3.57367 q^{7} -1.00000 q^{8} +4.59882 q^{9} -3.24124 q^{10} -0.930450 q^{11} -2.75660 q^{12} -0.743535 q^{13} -3.57367 q^{14} -8.93479 q^{15} +1.00000 q^{16} -4.18414 q^{17} -4.59882 q^{18} +0.988465 q^{19} +3.24124 q^{20} -9.85116 q^{21} +0.930450 q^{22} -7.38541 q^{23} +2.75660 q^{24} +5.50563 q^{25} +0.743535 q^{26} -4.40730 q^{27} +3.57367 q^{28} -7.63404 q^{29} +8.93479 q^{30} +10.0016 q^{31} -1.00000 q^{32} +2.56487 q^{33} +4.18414 q^{34} +11.5831 q^{35} +4.59882 q^{36} +5.43640 q^{37} -0.988465 q^{38} +2.04962 q^{39} -3.24124 q^{40} -3.06099 q^{41} +9.85116 q^{42} +11.4903 q^{43} -0.930450 q^{44} +14.9059 q^{45} +7.38541 q^{46} -12.9318 q^{47} -2.75660 q^{48} +5.77111 q^{49} -5.50563 q^{50} +11.5340 q^{51} -0.743535 q^{52} -4.43185 q^{53} +4.40730 q^{54} -3.01581 q^{55} -3.57367 q^{56} -2.72480 q^{57} +7.63404 q^{58} +5.68585 q^{59} -8.93479 q^{60} +9.86445 q^{61} -10.0016 q^{62} +16.4347 q^{63} +1.00000 q^{64} -2.40997 q^{65} -2.56487 q^{66} +8.41296 q^{67} -4.18414 q^{68} +20.3586 q^{69} -11.5831 q^{70} +16.1634 q^{71} -4.59882 q^{72} +2.94187 q^{73} -5.43640 q^{74} -15.1768 q^{75} +0.988465 q^{76} -3.32512 q^{77} -2.04962 q^{78} +12.3416 q^{79} +3.24124 q^{80} -1.64732 q^{81} +3.06099 q^{82} +8.37490 q^{83} -9.85116 q^{84} -13.5618 q^{85} -11.4903 q^{86} +21.0440 q^{87} +0.930450 q^{88} +8.59049 q^{89} -14.9059 q^{90} -2.65715 q^{91} -7.38541 q^{92} -27.5703 q^{93} +12.9318 q^{94} +3.20385 q^{95} +2.75660 q^{96} -7.28895 q^{97} -5.77111 q^{98} -4.27897 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) $ 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * 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
$3$	−2.75660	−1.59152	−0.795761	−	0.605611i	$-0.792929\pi$
$3$	−2.75660	−1.59152	−0.795761	+	0.605611i	$0.792929\pi$
$4$	1.00000	0.500000
$5$	3.24124	1.44953	0.724763	−	0.688998i	$-0.241949\pi$
$5$	3.24124	1.44953	0.724763	+	0.688998i	$0.241949\pi$
$6$	2.75660	1.12538
$7$	3.57367	1.35072	0.675360	−	0.737488i	$-0.263988\pi$
$7$	3.57367	1.35072	0.675360	+	0.737488i	$0.263988\pi$
$8$	−1.00000	−0.353553
$9$	4.59882	1.53294
$10$	−3.24124	−1.02497
$11$	−0.930450	−0.280541	−0.140271	−	0.990113i	$-0.544797\pi$
$11$	−0.930450	−0.280541	−0.140271	+	0.990113i	$0.544797\pi$
$12$	−2.75660	−0.795761
$13$	−0.743535	−0.206219	−0.103110	−	0.994670i	$-0.532879\pi$
$13$	−0.743535	−0.206219	−0.103110	+	0.994670i	$0.532879\pi$
$14$	−3.57367	−0.955103
$15$	−8.93479	−2.30695
$16$	1.00000	0.250000
$17$	−4.18414	−1.01480	−0.507401	−	0.861710i	$-0.669394\pi$
$17$	−4.18414	−1.01480	−0.507401	+	0.861710i	$0.669394\pi$
$18$	−4.59882	−1.08395
$19$	0.988465	0.226769	0.113385	−	0.993551i	$-0.463831\pi$
$19$	0.988465	0.226769	0.113385	+	0.993551i	$0.463831\pi$
$20$	3.24124	0.724763
$21$	−9.85116	−2.14970
$22$	0.930450	0.198373
$23$	−7.38541	−1.53996	−0.769982	−	0.638065i	$-0.779735\pi$
$23$	−7.38541	−1.53996	−0.769982	+	0.638065i	$0.779735\pi$
$24$	2.75660	0.562688
$25$	5.50563	1.10113
$26$	0.743535	0.145819
$27$	−4.40730	−0.848185
$28$	3.57367	0.675360
$29$	−7.63404	−1.41761	−0.708803	−	0.705406i	$-0.750765\pi$
$29$	−7.63404	−1.41761	−0.708803	+	0.705406i	$0.750765\pi$
$30$	8.93479	1.63126
$31$	10.0016	1.79633	0.898166	−	0.439656i	$-0.144899\pi$
$31$	10.0016	1.79633	0.898166	+	0.439656i	$0.144899\pi$
$32$	−1.00000	−0.176777
$33$	2.56487	0.446487
$34$	4.18414	0.717573
$35$	11.5831	1.95790
$36$	4.59882	0.766470
$37$	5.43640	0.893738	0.446869	−	0.894599i	$-0.352539\pi$
$37$	5.43640	0.893738	0.446869	+	0.894599i	$0.352539\pi$
$38$	−0.988465	−0.160350
$39$	2.04962	0.328203
$40$	−3.24124	−0.512485
$41$	−3.06099	−0.478047	−0.239023	−	0.971014i	$-0.576827\pi$
$41$	−3.06099	−0.478047	−0.239023	+	0.971014i	$0.576827\pi$
$42$	9.85116	1.52007
$43$	11.4903	1.75225	0.876127	−	0.482079i	$-0.160118\pi$
$43$	11.4903	1.75225	0.876127	+	0.482079i	$0.160118\pi$
$44$	−0.930450	−0.140271
$45$	14.9059	2.22204
$46$	7.38541	1.08892
$47$	−12.9318	−1.88630	−0.943150	−	0.332367i	$-0.892153\pi$
$47$	−12.9318	−1.88630	−0.943150	+	0.332367i	$0.892153\pi$
$48$	−2.75660	−0.397880
$49$	5.77111	0.824444
$50$	−5.50563	−0.778614
$51$	11.5340	1.61508
$52$	−0.743535	−0.103110
$53$	−4.43185	−0.608761	−0.304381	−	0.952551i	$-0.598449\pi$
$53$	−4.43185	−0.608761	−0.304381	+	0.952551i	$0.598449\pi$
$54$	4.40730	0.599757
$55$	−3.01581	−0.406652
$56$	−3.57367	−0.477552
$57$	−2.72480	−0.360908
$58$	7.63404	1.00240
$59$	5.68585	0.740234	0.370117	−	0.928985i	$-0.379318\pi$
$59$	5.68585	0.740234	0.370117	+	0.928985i	$0.379318\pi$
$60$	−8.93479	−1.15348
$61$	9.86445	1.26301	0.631507	−	0.775371i	$-0.282437\pi$
$61$	9.86445	1.26301	0.631507	+	0.775371i	$0.282437\pi$
$62$	−10.0016	−1.27020
$63$	16.4347	2.07057
$64$	1.00000	0.125000
$65$	−2.40997	−0.298920
$66$	−2.56487	−0.315714
$67$	8.41296	1.02781	0.513903	−	0.857848i	$-0.328199\pi$
$67$	8.41296	1.02781	0.513903	+	0.857848i	$0.328199\pi$
$68$	−4.18414	−0.507401
$69$	20.3586	2.45089
$70$	−11.5831	−1.38445
$71$	16.1634	1.91824	0.959119	−	0.283005i	$-0.0913311\pi$
$71$	16.1634	1.91824	0.959119	+	0.283005i	$0.0913311\pi$
$72$	−4.59882	−0.541976
$73$	2.94187	0.344320	0.172160	−	0.985069i	$-0.444925\pi$
$73$	2.94187	0.344320	0.172160	+	0.985069i	$0.444925\pi$
$74$	−5.43640	−0.631968
$75$	−15.1768	−1.75247
$76$	0.988465	0.113385
$77$	−3.32512	−0.378933
$78$	−2.04962	−0.232074
$79$	12.3416	1.38853	0.694267	−	0.719718i	$-0.255729\pi$
$79$	12.3416	1.38853	0.694267	+	0.719718i	$0.255729\pi$
$80$	3.24124	0.362382
$81$	−1.64732	−0.183036
$82$	3.06099	0.338030
$83$	8.37490	0.919264	0.459632	−	0.888109i	$-0.347981\pi$
$83$	8.37490	0.919264	0.459632	+	0.888109i	$0.347981\pi$
$84$	−9.85116	−1.07485
$85$	−13.5618	−1.47098
$86$	−11.4903	−1.23903
$87$	21.0440	2.25615
$88$	0.930450	0.0991863
$89$	8.59049	0.910590	0.455295	−	0.890341i	$-0.349534\pi$
$89$	8.59049	0.910590	0.455295	+	0.890341i	$0.349534\pi$
$90$	−14.9059	−1.57122
$91$	−2.65715	−0.278545
$92$	−7.38541	−0.769982
$93$	−27.5703	−2.85890
$94$	12.9318	1.33382
$95$	3.20385	0.328708
$96$	2.75660	0.281344
$97$	−7.28895	−0.740081	−0.370041	−	0.929016i	$-0.620656\pi$
$97$	−7.28895	−0.740081	−0.370041	+	0.929016i	$0.620656\pi$
$98$	−5.77111	−0.582970
$99$	−4.27897	−0.430053
$100$	5.50563	0.550563
$101$	−1.87588	−0.186657	−0.0933284	−	0.995635i	$-0.529751\pi$
$101$	−1.87588	−0.186657	−0.0933284	+	0.995635i	$0.529751\pi$
$102$	−11.5340	−1.14203
$103$	−14.3673	−1.41565	−0.707827	−	0.706386i	$-0.750324\pi$
$103$	−14.3673	−1.41565	−0.707827	+	0.706386i	$0.750324\pi$
$104$	0.743535	0.0729096
$105$	−31.9300	−3.11605
$106$	4.43185	0.430459
$107$	−1.46361	−0.141493	−0.0707464	−	0.997494i	$-0.522538\pi$
$107$	−1.46361	−0.141493	−0.0707464	+	0.997494i	$0.522538\pi$
$108$	−4.40730	−0.424092
$109$	−14.9052	−1.42766	−0.713830	−	0.700319i	$-0.753041\pi$
$109$	−14.9052	−1.42766	−0.713830	+	0.700319i	$0.753041\pi$
$110$	3.01581	0.287546
$111$	−14.9859	−1.42240
$112$	3.57367	0.337680
$113$	14.5949	1.37297	0.686485	−	0.727144i	$-0.259153\pi$
$113$	14.5949	1.37297	0.686485	+	0.727144i	$0.259153\pi$
$114$	2.72480	0.255201
$115$	−23.9379	−2.23222
$116$	−7.63404	−0.708803
$117$	−3.41938	−0.316122
$118$	−5.68585	−0.523425
$119$	−14.9527	−1.37071
$120$	8.93479	0.815631
$121$	−10.1343	−0.921297
$122$	−9.86445	−0.893085
$123$	8.43791	0.760821
$124$	10.0016	0.898166
$125$	1.63888	0.146586
$126$	−16.4347	−1.46412
$127$	9.48902	0.842014	0.421007	−	0.907057i	$-0.361677\pi$
$127$	9.48902	0.842014	0.421007	+	0.907057i	$0.361677\pi$
$128$	−1.00000	−0.0883883
$129$	−31.6741	−2.78875
$130$	2.40997	0.211369
$131$	3.12043	0.272633	0.136317	−	0.990665i	$-0.456474\pi$
$131$	3.12043	0.272633	0.136317	+	0.990665i	$0.456474\pi$
$132$	2.56487	0.223244
$133$	3.53245	0.306302
$134$	−8.41296	−0.726769
$135$	−14.2851	−1.22947
$136$	4.18414	0.358787
$137$	12.7959	1.09322	0.546612	−	0.837386i	$-0.315917\pi$
$137$	12.7959	1.09322	0.546612	+	0.837386i	$0.315917\pi$
$138$	−20.3586	−1.73304
$139$	5.48519	0.465247	0.232624	−	0.972567i	$-0.425269\pi$
$139$	5.48519	0.465247	0.232624	+	0.972567i	$0.425269\pi$
$140$	11.5831	0.978952
$141$	35.6478	3.00209
$142$	−16.1634	−1.35640
$143$	0.691822	0.0578531
$144$	4.59882	0.383235
$145$	−24.7438	−2.05486
$146$	−2.94187	−0.243471
$147$	−15.9086	−1.31212
$148$	5.43640	0.446869
$149$	5.15317	0.422164	0.211082	−	0.977468i	$-0.432301\pi$
$149$	5.15317	0.422164	0.211082	+	0.977468i	$0.432301\pi$
$150$	15.1768	1.23918
$151$	−5.23676	−0.426162	−0.213081	−	0.977035i	$-0.568350\pi$
$151$	−5.23676	−0.426162	−0.213081	+	0.977035i	$0.568350\pi$
$152$	−0.988465	−0.0801751
$153$	−19.2421	−1.55563
$154$	3.32512	0.267946
$155$	32.4174	2.60383
$156$	2.04962	0.164101
$157$	−1.72612	−0.137760	−0.0688798	−	0.997625i	$-0.521942\pi$
$157$	−1.72612	−0.137760	−0.0688798	+	0.997625i	$0.521942\pi$
$158$	−12.3416	−0.981841
$159$	12.2168	0.968856
$160$	−3.24124	−0.256242
$161$	−26.3930	−2.08006
$162$	1.64732	0.129426
$163$	−14.0661	−1.10174	−0.550871	−	0.834591i	$-0.685704\pi$
$163$	−14.0661	−1.10174	−0.550871	+	0.834591i	$0.685704\pi$
$164$	−3.06099	−0.239023
$165$	8.31337	0.647195
$166$	−8.37490	−0.650018
$167$	20.5709	1.59182	0.795911	−	0.605414i	$-0.206992\pi$
$167$	20.5709	1.59182	0.795911	+	0.605414i	$0.206992\pi$
$168$	9.85116	0.760033
$169$	−12.4472	−0.957474
$170$	13.5618	1.04014
$171$	4.54577	0.347624
$172$	11.4903	0.876127
$173$	21.0515	1.60051	0.800256	−	0.599658i	$-0.204697\pi$
$173$	21.0515	1.60051	0.800256	+	0.599658i	$0.204697\pi$
$174$	−21.0440	−1.59534
$175$	19.6753	1.48731
$176$	−0.930450	−0.0701353
$177$	−15.6736	−1.17810
$178$	−8.59049	−0.643884
$179$	10.6679	0.797353	0.398677	−	0.917092i	$-0.369470\pi$
$179$	10.6679	0.797353	0.398677	+	0.917092i	$0.369470\pi$
$180$	14.9059	1.11102
$181$	10.3196	0.767049	0.383524	−	0.923531i	$-0.374710\pi$
$181$	10.3196	0.767049	0.383524	+	0.923531i	$0.374710\pi$
$182$	2.65715	0.196961
$183$	−27.1923	−2.01011
$184$	7.38541	0.544460
$185$	17.6207	1.29550
$186$	27.5703	2.02155
$187$	3.89313	0.284694
$188$	−12.9318	−0.943150
$189$	−15.7502	−1.14566
$190$	−3.20385	−0.232432
$191$	5.68469	0.411330	0.205665	−	0.978622i	$-0.434064\pi$
$191$	5.68469	0.411330	0.205665	+	0.978622i	$0.434064\pi$
$192$	−2.75660	−0.198940
$193$	6.59931	0.475029	0.237514	−	0.971384i	$-0.423667\pi$
$193$	6.59931	0.475029	0.237514	+	0.971384i	$0.423667\pi$
$194$	7.28895	0.523316
$195$	6.64332	0.475738
$196$	5.77111	0.412222
$197$	−16.3130	−1.16226	−0.581128	−	0.813812i	$-0.697389\pi$
$197$	−16.3130	−1.16226	−0.581128	+	0.813812i	$0.697389\pi$
$198$	4.27897	0.304093
$199$	16.8655	1.19556	0.597782	−	0.801659i	$-0.296049\pi$
$199$	16.8655	1.19556	0.597782	+	0.801659i	$0.296049\pi$
$200$	−5.50563	−0.389307
$201$	−23.1911	−1.63578
$202$	1.87588	0.131986
$203$	−27.2815	−1.91479
$204$	11.5340	0.807539
$205$	−9.92141	−0.692941
$206$	14.3673	1.00102
$207$	−33.9642	−2.36067
$208$	−0.743535	−0.0515549
$209$	−0.919718	−0.0636182
$210$	31.9300	2.20338
$211$	−7.56575	−0.520847	−0.260424	−	0.965494i	$-0.583862\pi$
$211$	−7.56575	−0.520847	−0.260424	+	0.965494i	$0.583862\pi$
$212$	−4.43185	−0.304381
$213$	−44.5558	−3.05292
$214$	1.46361	0.100050
$215$	37.2428	2.53994
$216$	4.40730	0.299879
$217$	35.7423	2.42634
$218$	14.9052	1.00951
$219$	−8.10954	−0.547992
$220$	−3.01581	−0.203326
$221$	3.11105	0.209272
$222$	14.9859	1.00579
$223$	12.7020	0.850588	0.425294	−	0.905055i	$-0.360171\pi$
$223$	12.7020	0.850588	0.425294	+	0.905055i	$0.360171\pi$
$224$	−3.57367	−0.238776
$225$	25.3194	1.68796
$226$	−14.5949	−0.970837
$227$	−24.4118	−1.62027	−0.810133	−	0.586246i	$-0.800605\pi$
$227$	−24.4118	−1.62027	−0.810133	+	0.586246i	$0.800605\pi$
$228$	−2.72480	−0.180454
$229$	23.9272	1.58115	0.790577	−	0.612362i	$-0.209781\pi$
$229$	23.9272	1.58115	0.790577	+	0.612362i	$0.209781\pi$
$230$	23.9379	1.57842
$231$	9.16601	0.603079
$232$	7.63404	0.501200
$233$	17.2361	1.12917	0.564586	−	0.825374i	$-0.309036\pi$
$233$	17.2361	1.12917	0.564586	+	0.825374i	$0.309036\pi$
$234$	3.41938	0.223532
$235$	−41.9151	−2.73424
$236$	5.68585	0.370117
$237$	−34.0207	−2.20988
$238$	14.9527	0.969241
$239$	2.98527	0.193101	0.0965504	−	0.995328i	$-0.469219\pi$
$239$	2.98527	0.193101	0.0965504	+	0.995328i	$0.469219\pi$
$240$	−8.93479	−0.576738
$241$	6.70522	0.431921	0.215961	−	0.976402i	$-0.430712\pi$
$241$	6.70522	0.431921	0.215961	+	0.976402i	$0.430712\pi$
$242$	10.1343	0.651455
$243$	17.7629	1.13949
$244$	9.86445	0.631507
$245$	18.7055	1.19505
$246$	−8.43791	−0.537982
$247$	−0.734958	−0.0467643
$248$	−10.0016	−0.635100
$249$	−23.0862	−1.46303
$250$	−1.63888	−0.103652
$251$	16.3283	1.03063	0.515316	−	0.857000i	$-0.327674\pi$
$251$	16.3283	1.03063	0.515316	+	0.857000i	$0.327674\pi$
$252$	16.4347	1.03529
$253$	6.87176	0.432024
$254$	−9.48902	−0.595394
$255$	37.3844	2.34110
$256$	1.00000	0.0625000
$257$	−1.01726	−0.0634550	−0.0317275	−	0.999497i	$-0.510101\pi$
$257$	−1.01726	−0.0634550	−0.0317275	+	0.999497i	$0.510101\pi$
$258$	31.6741	1.97194
$259$	19.4279	1.20719
$260$	−2.40997	−0.149460
$261$	−35.1076	−2.17311
$262$	−3.12043	−0.192781
$263$	13.0642	0.805571	0.402786	−	0.915294i	$-0.368042\pi$
$263$	13.0642	0.805571	0.402786	+	0.915294i	$0.368042\pi$
$264$	−2.56487	−0.157857
$265$	−14.3647	−0.882415
$266$	−3.53245	−0.216588
$267$	−23.6805	−1.44922
$268$	8.41296	0.513903
$269$	−18.2309	−1.11156	−0.555779	−	0.831330i	$-0.687580\pi$
$269$	−18.2309	−1.11156	−0.555779	+	0.831330i	$0.687580\pi$
$270$	14.2851	0.869364
$271$	24.4264	1.48380	0.741898	−	0.670513i	$-0.233926\pi$
$271$	24.4264	1.48380	0.741898	+	0.670513i	$0.233926\pi$
$272$	−4.18414	−0.253700
$273$	7.32468	0.443310
$274$	−12.7959	−0.773026
$275$	−5.12272	−0.308912
$276$	20.3586	1.22544
$277$	−0.191506	−0.0115065	−0.00575325	−	0.999983i	$-0.501831\pi$
$277$	−0.191506	−0.0115065	−0.00575325	+	0.999983i	$0.501831\pi$
$278$	−5.48519	−0.328980
$279$	45.9954	2.75367
$280$	−11.5831	−0.692224
$281$	16.9264	1.00975	0.504873	−	0.863194i	$-0.331539\pi$
$281$	16.9264	1.00975	0.504873	+	0.863194i	$0.331539\pi$
$282$	−35.6478	−2.12280
$283$	3.08809	0.183568	0.0917839	−	0.995779i	$-0.470743\pi$
$283$	3.08809	0.183568	0.0917839	+	0.995779i	$0.470743\pi$
$284$	16.1634	0.959119
$285$	−8.83172	−0.523146
$286$	−0.691822	−0.0409083
$287$	−10.9390	−0.645707
$288$	−4.59882	−0.270988
$289$	0.506993	0.0298231
$290$	24.7438	1.45300
$291$	20.0927	1.17785
$292$	2.94187	0.172160
$293$	−11.8723	−0.693585	−0.346792	−	0.937942i	$-0.612729\pi$
$293$	−11.8723	−0.693585	−0.346792	+	0.937942i	$0.612729\pi$
$294$	15.9086	0.927809
$295$	18.4292	1.07299
$296$	−5.43640	−0.315984
$297$	4.10077	0.237951
$298$	−5.15317	−0.298515
$299$	5.49131	0.317571
$300$	−15.1768	−0.876233
$301$	41.0625	2.36681
$302$	5.23676	0.301342
$303$	5.17103	0.297068
$304$	0.988465	0.0566924
$305$	31.9730	1.83077
$306$	19.2421	1.10000
$307$	−12.2861	−0.701202	−0.350601	−	0.936525i	$-0.614023\pi$
$307$	−12.2861	−0.701202	−0.350601	+	0.936525i	$0.614023\pi$
$308$	−3.32512	−0.189466
$309$	39.6049	2.25304
$310$	−32.4174	−1.84119
$311$	−15.7994	−0.895904	−0.447952	−	0.894058i	$-0.647846\pi$
$311$	−15.7994	−0.895904	−0.447952	+	0.894058i	$0.647846\pi$
$312$	−2.04962	−0.116037
$313$	1.02244	0.0577917	0.0288959	−	0.999582i	$-0.490801\pi$
$313$	1.02244	0.0577917	0.0288959	+	0.999582i	$0.490801\pi$
$314$	1.72612	0.0974107
$315$	53.2687	3.00135
$316$	12.3416	0.694267
$317$	−12.3496	−0.693620	−0.346810	−	0.937935i	$-0.612735\pi$
$317$	−12.3496	−0.693620	−0.346810	+	0.937935i	$0.612735\pi$
$318$	−12.2168	−0.685085
$319$	7.10310	0.397697
$320$	3.24124	0.181191
$321$	4.03459	0.225189
$322$	26.3930	1.47083
$323$	−4.13587	−0.230126
$324$	−1.64732	−0.0915178
$325$	−4.09363	−0.227074
$326$	14.0661	0.779049
$327$	41.0876	2.27215
$328$	3.06099	0.169015
$329$	−46.2141	−2.54786
$330$	−8.31337	−0.457636
$331$	20.1146	1.10560	0.552798	−	0.833315i	$-0.313560\pi$
$331$	20.1146	1.10560	0.552798	+	0.833315i	$0.313560\pi$
$332$	8.37490	0.459632
$333$	25.0010	1.37005
$334$	−20.5709	−1.12559
$335$	27.2684	1.48983
$336$	−9.85116	−0.537425
$337$	17.3116	0.943024	0.471512	−	0.881860i	$-0.343708\pi$
$337$	17.3116	0.943024	0.471512	+	0.881860i	$0.343708\pi$
$338$	12.4472	0.677036
$339$	−40.2322	−2.18511
$340$	−13.5618	−0.735491
$341$	−9.30595	−0.503946
$342$	−4.54577	−0.245807
$343$	−4.39165	−0.237127
$344$	−11.4903	−0.619516
$345$	65.9871	3.55262
$346$	−21.0515	−1.13173
$347$	−17.8973	−0.960778	−0.480389	−	0.877056i	$-0.659504\pi$
$347$	−17.8973	−0.960778	−0.480389	+	0.877056i	$0.659504\pi$
$348$	21.0440	1.12808
$349$	−25.0116	−1.33884	−0.669421	−	0.742884i	$-0.733458\pi$
$349$	−25.0116	−1.33884	−0.669421	+	0.742884i	$0.733458\pi$
$350$	−19.6753	−1.05169
$351$	3.27698	0.174912
$352$	0.930450	0.0495932
$353$	−18.6890	−0.994713	−0.497357	−	0.867546i	$-0.665696\pi$
$353$	−18.6890	−0.994713	−0.497357	+	0.867546i	$0.665696\pi$
$354$	15.6736	0.833041
$355$	52.3893	2.78054
$356$	8.59049	0.455295
$357$	41.2186	2.18152
$358$	−10.6679	−0.563814
$359$	−0.324952	−0.0171503	−0.00857517	−	0.999963i	$-0.502730\pi$
$359$	−0.324952	−0.0171503	−0.00857517	+	0.999963i	$0.502730\pi$
$360$	−14.9059	−0.785609
$361$	−18.0229	−0.948576
$362$	−10.3196	−0.542385
$363$	27.9361	1.46626
$364$	−2.65715	−0.139272
$365$	9.53530	0.499101
$366$	27.1923	1.42136
$367$	−1.18666	−0.0619430	−0.0309715	−	0.999520i	$-0.509860\pi$
$367$	−1.18666	−0.0619430	−0.0309715	+	0.999520i	$0.509860\pi$
$368$	−7.38541	−0.384991
$369$	−14.0769	−0.732816
$370$	−17.6207	−0.916055
$371$	−15.8380	−0.822266
$372$	−27.5703	−1.42945
$373$	16.7231	0.865891	0.432945	−	0.901420i	$-0.357474\pi$
$373$	16.7231	0.865891	0.432945	+	0.901420i	$0.357474\pi$
$374$	−3.89313	−0.201309
$375$	−4.51773	−0.233294
$376$	12.9318	0.666908
$377$	5.67618	0.292338
$378$	15.7502	0.810104
$379$	−16.3639	−0.840558	−0.420279	−	0.907395i	$-0.638068\pi$
$379$	−16.3639	−0.840558	−0.420279	+	0.907395i	$0.638068\pi$
$380$	3.20385	0.164354
$381$	−26.1574	−1.34008
$382$	−5.68469	−0.290854
$383$	12.2040	0.623595	0.311797	−	0.950149i	$-0.399069\pi$
$383$	12.2040	0.623595	0.311797	+	0.950149i	$0.399069\pi$
$384$	2.75660	0.140672
$385$	−10.7775	−0.549273
$386$	−6.59931	−0.335896
$387$	52.8418	2.68610
$388$	−7.28895	−0.370041
$389$	−10.6498	−0.539965	−0.269983	−	0.962865i	$-0.587018\pi$
$389$	−10.6498	−0.539965	−0.269983	+	0.962865i	$0.587018\pi$
$390$	−6.64332	−0.336398
$391$	30.9016	1.56276
$392$	−5.77111	−0.291485
$393$	−8.60177	−0.433902
$394$	16.3130	0.821839
$395$	40.0019	2.01272
$396$	−4.27897	−0.215026
$397$	−28.9568	−1.45330	−0.726650	−	0.687008i	$-0.758924\pi$
$397$	−28.9568	−1.45330	−0.726650	+	0.687008i	$0.758924\pi$
$398$	−16.8655	−0.845391
$399$	−9.73753	−0.487486
$400$	5.50563	0.275282
$401$	36.0269	1.79910	0.899549	−	0.436820i	$-0.143895\pi$
$401$	36.0269	1.79910	0.899549	+	0.436820i	$0.143895\pi$
$402$	23.1911	1.15667
$403$	−7.43651	−0.370439
$404$	−1.87588	−0.0933284
$405$	−5.33936	−0.265315
$406$	27.2815	1.35396
$407$	−5.05830	−0.250730
$408$	−11.5340	−0.571017
$409$	−26.5409	−1.31236	−0.656181	−	0.754604i	$-0.727829\pi$
$409$	−26.5409	−1.31236	−0.656181	+	0.754604i	$0.727829\pi$
$410$	9.92141	0.489983
$411$	−35.2730	−1.73989
$412$	−14.3673	−0.707827
$413$	20.3193	0.999849
$414$	33.9642	1.66925
$415$	27.1450	1.33250
$416$	0.743535	0.0364548
$417$	−15.1204	−0.740451
$418$	0.919718	0.0449849
$419$	−35.3655	−1.72772	−0.863858	−	0.503735i	$-0.831959\pi$
$419$	−35.3655	−1.72772	−0.863858	+	0.503735i	$0.831959\pi$
$420$	−31.9300	−1.55802
$421$	36.3696	1.77255	0.886274	−	0.463162i	$-0.153285\pi$
$421$	36.3696	1.77255	0.886274	+	0.463162i	$0.153285\pi$
$422$	7.56575	0.368295
$423$	−59.4711	−2.89158
$424$	4.43185	0.215230
$425$	−23.0363	−1.11743
$426$	44.5558	2.15874
$427$	35.2523	1.70598
$428$	−1.46361	−0.0707464
$429$	−1.90707	−0.0920744
$430$	−37.2428	−1.79601
$431$	32.7091	1.57554	0.787771	−	0.615968i	$-0.211235\pi$
$431$	32.7091	1.57554	0.787771	+	0.615968i	$0.211235\pi$
$432$	−4.40730	−0.212046
$433$	15.2787	0.734246	0.367123	−	0.930172i	$-0.380343\pi$
$433$	15.2787	0.734246	0.367123	+	0.930172i	$0.380343\pi$
$434$	−35.7423	−1.71568
$435$	68.2086	3.27035
$436$	−14.9052	−0.713830
$437$	−7.30022	−0.349217
$438$	8.10954	0.387489
$439$	−29.0334	−1.38569	−0.692845	−	0.721087i	$-0.743643\pi$
$439$	−29.0334	−1.38569	−0.692845	+	0.721087i	$0.743643\pi$
$440$	3.01581	0.143773
$441$	26.5403	1.26382
$442$	−3.11105	−0.147978
$443$	24.4160	1.16004	0.580020	−	0.814602i	$-0.303045\pi$
$443$	24.4160	1.16004	0.580020	+	0.814602i	$0.303045\pi$
$444$	−14.9859	−0.711202
$445$	27.8438	1.31992
$446$	−12.7020	−0.601456
$447$	−14.2052	−0.671883
$448$	3.57367	0.168840
$449$	−23.9333	−1.12948	−0.564741	−	0.825268i	$-0.691024\pi$
$449$	−23.9333	−1.12948	−0.564741	+	0.825268i	$0.691024\pi$
$450$	−25.3194	−1.19357
$451$	2.84810	0.134112
$452$	14.5949	0.686485
$453$	14.4356	0.678245
$454$	24.4118	1.14570
$455$	−8.61245	−0.403758
$456$	2.72480	0.127600
$457$	−24.1773	−1.13097	−0.565483	−	0.824760i	$-0.691310\pi$
$457$	−24.1773	−1.13097	−0.565483	+	0.824760i	$0.691310\pi$
$458$	−23.9272	−1.11805
$459$	18.4407	0.860740
$460$	−23.9379	−1.11611
$461$	9.39792	0.437705	0.218852	−	0.975758i	$-0.429769\pi$
$461$	9.39792	0.437705	0.218852	+	0.975758i	$0.429769\pi$
$462$	−9.16601	−0.426442
$463$	11.4014	0.529867	0.264933	−	0.964267i	$-0.414650\pi$
$463$	11.4014	0.529867	0.264933	+	0.964267i	$0.414650\pi$
$464$	−7.63404	−0.354402
$465$	−89.3618	−4.14405
$466$	−17.2361	−0.798445
$467$	−32.0694	−1.48399	−0.741997	−	0.670403i	$-0.766121\pi$
$467$	−32.0694	−1.48399	−0.741997	+	0.670403i	$0.766121\pi$
$468$	−3.41938	−0.158061
$469$	30.0651	1.38828
$470$	41.9151	1.93340
$471$	4.75822	0.219247
$472$	−5.68585	−0.261712
$473$	−10.6912	−0.491580
$474$	34.0207	1.56262
$475$	5.44213	0.249702
$476$	−14.9527	−0.685357
$477$	−20.3813	−0.933194
$478$	−2.98527	−0.136543
$479$	1.70651	0.0779724	0.0389862	−	0.999240i	$-0.487587\pi$
$479$	1.70651	0.0779724	0.0389862	+	0.999240i	$0.487587\pi$
$480$	8.93479	0.407815
$481$	−4.04215	−0.184306
$482$	−6.70522	−0.305414
$483$	72.7549	3.31046
$484$	−10.1343	−0.460648
$485$	−23.6252	−1.07277
$486$	−17.7629	−0.805741
$487$	2.31154	0.104746	0.0523729	−	0.998628i	$-0.483322\pi$
$487$	2.31154	0.104746	0.0523729	+	0.998628i	$0.483322\pi$
$488$	−9.86445	−0.446543
$489$	38.7745	1.75344
$490$	−18.7055	−0.845030
$491$	5.24741	0.236813	0.118406	−	0.992965i	$-0.462221\pi$
$491$	5.24741	0.236813	0.118406	+	0.992965i	$0.462221\pi$
$492$	8.43791	0.380411
$493$	31.9419	1.43859
$494$	0.734958	0.0330673
$495$	−13.8692	−0.623373
$496$	10.0016	0.449083
$497$	57.7625	2.59100
$498$	23.0862	1.03452
$499$	−6.90416	−0.309072	−0.154536	−	0.987987i	$-0.549388\pi$
$499$	−6.90416	−0.309072	−0.154536	+	0.987987i	$0.549388\pi$
$500$	1.63888	0.0732929
$501$	−56.7056	−2.53342
$502$	−16.3283	−0.728767
$503$	28.8310	1.28551	0.642756	−	0.766071i	$-0.277791\pi$
$503$	28.8310	1.28551	0.642756	+	0.766071i	$0.277791\pi$
$504$	−16.4347	−0.732058
$505$	−6.08017	−0.270564
$506$	−6.87176	−0.305487
$507$	34.3118	1.52384
$508$	9.48902	0.421007
$509$	12.3528	0.547529	0.273765	−	0.961797i	$-0.411731\pi$
$509$	12.3528	0.547529	0.273765	+	0.961797i	$0.411731\pi$
$510$	−37.3844	−1.65541
$511$	10.5133	0.465079
$512$	−1.00000	−0.0441942
$513$	−4.35646	−0.192342
$514$	1.01726	0.0448695
$515$	−46.5679	−2.05203
$516$	−31.6741	−1.39438
$517$	12.0324	0.529185
$518$	−19.4279	−0.853612
$519$	−58.0304	−2.54725
$520$	2.40997	0.105684
$521$	38.9757	1.70756	0.853778	−	0.520637i	$-0.174306\pi$
$521$	38.9757	1.70756	0.853778	+	0.520637i	$0.174306\pi$
$522$	35.1076	1.53662
$523$	−19.1979	−0.839466	−0.419733	−	0.907648i	$-0.637876\pi$
$523$	−19.1979	−0.839466	−0.419733	+	0.907648i	$0.637876\pi$
$524$	3.12043	0.136317
$525$	−54.2369	−2.36709
$526$	−13.0642	−0.569625
$527$	−41.8479	−1.82292
$528$	2.56487	0.111622
$529$	31.5443	1.37149
$530$	14.3647	0.623962
$531$	26.1482	1.13473
$532$	3.53245	0.153151
$533$	2.27595	0.0985825
$534$	23.6805	1.02476
$535$	−4.74392	−0.205097
$536$	−8.41296	−0.363384
$537$	−29.4070	−1.26900
$538$	18.2309	0.785990
$539$	−5.36973	−0.231291
$540$	−14.2851	−0.614733
$541$	4.04754	0.174017	0.0870087	−	0.996208i	$-0.472269\pi$
$541$	4.04754	0.174017	0.0870087	+	0.996208i	$0.472269\pi$
$542$	−24.4264	−1.04920
$543$	−28.4469	−1.22077
$544$	4.18414	0.179393
$545$	−48.3113	−2.06943
$546$	−7.32468	−0.313467
$547$	−21.4660	−0.917819	−0.458909	−	0.888483i	$-0.651760\pi$
$547$	−21.4660	−0.917819	−0.458909	+	0.888483i	$0.651760\pi$
$548$	12.7959	0.546612
$549$	45.3648	1.93612
$550$	5.12272	0.218433
$551$	−7.54599	−0.321470
$552$	−20.3586	−0.866519
$553$	44.1046	1.87552
$554$	0.191506	0.00813633
$555$	−48.5730	−2.06181
$556$	5.48519	0.232624
$557$	3.90359	0.165400	0.0827002	−	0.996574i	$-0.473646\pi$
$557$	3.90359	0.165400	0.0827002	+	0.996574i	$0.473646\pi$
$558$	−45.9954	−1.94714
$559$	−8.54344	−0.361349
$560$	11.5831	0.489476
$561$	−10.7318	−0.453096
$562$	−16.9264	−0.713998
$563$	−28.6985	−1.20950	−0.604748	−	0.796417i	$-0.706726\pi$
$563$	−28.6985	−1.20950	−0.604748	+	0.796417i	$0.706726\pi$
$564$	35.6478	1.50104
$565$	47.3055	1.99016
$566$	−3.08809	−0.129802
$567$	−5.88698	−0.247230
$568$	−16.1634	−0.678199
$569$	26.2343	1.09980	0.549899	−	0.835231i	$-0.314666\pi$
$569$	26.2343	1.09980	0.549899	+	0.835231i	$0.314666\pi$
$570$	8.83172	0.369920
$571$	−5.96481	−0.249620	−0.124810	−	0.992181i	$-0.539832\pi$
$571$	−5.96481	−0.249620	−0.124810	+	0.992181i	$0.539832\pi$
$572$	0.691822	0.0289265
$573$	−15.6704	−0.654640
$574$	10.9390	0.456584
$575$	−40.6614	−1.69570
$576$	4.59882	0.191617
$577$	−18.8772	−0.785868	−0.392934	−	0.919567i	$-0.628540\pi$
$577$	−18.8772	−0.785868	−0.392934	+	0.919567i	$0.628540\pi$
$578$	−0.506993	−0.0210881
$579$	−18.1916	−0.756019
$580$	−24.7438	−1.02743
$581$	29.9291	1.24167
$582$	−20.0927	−0.832869
$583$	4.12361	0.170783
$584$	−2.94187	−0.121735
$585$	−11.0830	−0.458227
$586$	11.8723	0.490438
$587$	−16.0266	−0.661490	−0.330745	−	0.943720i	$-0.607300\pi$
$587$	−16.0266	−0.661490	−0.330745	+	0.943720i	$0.607300\pi$
$588$	−15.9086	−0.656060
$589$	9.88619	0.407353
$590$	−18.4292	−0.758718
$591$	44.9685	1.84976
$592$	5.43640	0.223435
$593$	16.4506	0.675546	0.337773	−	0.941228i	$-0.390326\pi$
$593$	16.4506	0.675546	0.337773	+	0.941228i	$0.390326\pi$
$594$	−4.10077	−0.168257
$595$	−48.4653	−1.98688
$596$	5.15317	0.211082
$597$	−46.4914	−1.90277
$598$	−5.49131	−0.224556
$599$	37.0823	1.51514	0.757571	−	0.652753i	$-0.226386\pi$
$599$	37.0823	1.51514	0.757571	+	0.652753i	$0.226386\pi$
$600$	15.1768	0.619590
$601$	36.0729	1.47144	0.735721	−	0.677284i	$-0.236843\pi$
$601$	36.0729	1.47144	0.735721	+	0.677284i	$0.236843\pi$
$602$	−41.0625	−1.67358
$603$	38.6897	1.57556
$604$	−5.23676	−0.213081
$605$	−32.8476	−1.33544
$606$	−5.17103	−0.210059
$607$	30.7786	1.24926	0.624632	−	0.780919i	$-0.285249\pi$
$607$	30.7786	1.24926	0.624632	+	0.780919i	$0.285249\pi$
$608$	−0.988465	−0.0400876
$609$	75.2042	3.04743
$610$	−31.9730	−1.29455
$611$	9.61526	0.388992
$612$	−19.2421	−0.777815
$613$	−28.4065	−1.14733	−0.573664	−	0.819091i	$-0.694478\pi$
$613$	−28.4065	−1.14733	−0.573664	+	0.819091i	$0.694478\pi$
$614$	12.2861	0.495825
$615$	27.3493	1.10283
$616$	3.32512	0.133973
$617$	12.9583	0.521683	0.260841	−	0.965382i	$-0.416000\pi$
$617$	12.9583	0.521683	0.260841	+	0.965382i	$0.416000\pi$
$618$	−39.6049	−1.59314
$619$	29.1063	1.16988	0.584941	−	0.811076i	$-0.301118\pi$
$619$	29.1063	1.16988	0.584941	+	0.811076i	$0.301118\pi$
$620$	32.4174	1.30192
$621$	32.5497	1.30617
$622$	15.7994	0.633500
$623$	30.6996	1.22995
$624$	2.04962	0.0820506
$625$	−22.2162	−0.888647
$626$	−1.02244	−0.0408649
$627$	2.53529	0.101250
$628$	−1.72612	−0.0688798
$629$	−22.7466	−0.906967
$630$	−53.2687	−2.12227
$631$	−33.5590	−1.33596	−0.667982	−	0.744177i	$-0.732842\pi$
$631$	−33.5590	−1.33596	−0.667982	+	0.744177i	$0.732842\pi$
$632$	−12.3416	−0.490921
$633$	20.8557	0.828940
$634$	12.3496	0.490464
$635$	30.7562	1.22052
$636$	12.2168	0.484428
$637$	−4.29102	−0.170016
$638$	−7.10310	−0.281214
$639$	74.3323	2.94054
$640$	−3.24124	−0.128121
$641$	37.0901	1.46497	0.732485	−	0.680783i	$-0.238360\pi$
$641$	37.0901	1.46497	0.732485	+	0.680783i	$0.238360\pi$
$642$	−4.03459	−0.159232
$643$	−21.9744	−0.866585	−0.433293	−	0.901253i	$-0.642648\pi$
$643$	−21.9744	−0.866585	−0.433293	+	0.901253i	$0.642648\pi$
$644$	−26.3930	−1.04003
$645$	−102.663	−4.04237
$646$	4.13587	0.162724
$647$	14.8706	0.584625	0.292313	−	0.956323i	$-0.405575\pi$
$647$	14.8706	0.584625	0.292313	+	0.956323i	$0.405575\pi$
$648$	1.64732	0.0647129
$649$	−5.29040	−0.207666
$650$	4.09363	0.160565
$651$	−98.5269	−3.86158
$652$	−14.0661	−0.550871
$653$	−22.5882	−0.883943	−0.441972	−	0.897029i	$-0.645721\pi$
$653$	−22.5882	−0.883943	−0.441972	+	0.897029i	$0.645721\pi$
$654$	−41.0876	−1.60665
$655$	10.1141	0.395189
$656$	−3.06099	−0.119512
$657$	13.5291	0.527821
$658$	46.2141	1.80161
$659$	16.8168	0.655088	0.327544	−	0.944836i	$-0.393779\pi$
$659$	16.8168	0.655088	0.327544	+	0.944836i	$0.393779\pi$
$660$	8.31337	0.323598
$661$	−10.9836	−0.427213	−0.213607	−	0.976920i	$-0.568521\pi$
$661$	−10.9836	−0.427213	−0.213607	+	0.976920i	$0.568521\pi$
$662$	−20.1146	−0.781774
$663$	−8.57591	−0.333061
$664$	−8.37490	−0.325009
$665$	11.4495	0.443993
$666$	−25.0010	−0.968769
$667$	56.3806	2.18306
$668$	20.5709	0.795911
$669$	−35.0142	−1.35373
$670$	−27.2684	−1.05347
$671$	−9.17838	−0.354327
$672$	9.85116	0.380017
$673$	−49.9583	−1.92575	−0.962875	−	0.269948i	$-0.912994\pi$
$673$	−49.9583	−1.92575	−0.962875	+	0.269948i	$0.912994\pi$
$674$	−17.3116	−0.666818
$675$	−24.2650	−0.933959
$676$	−12.4472	−0.478737
$677$	3.55233	0.136527	0.0682636	−	0.997667i	$-0.478254\pi$
$677$	3.55233	0.136527	0.0682636	+	0.997667i	$0.478254\pi$
$678$	40.2322	1.54511
$679$	−26.0483	−0.999642
$680$	13.5618	0.520071
$681$	67.2934	2.57869
$682$	9.30595	0.356343
$683$	9.94736	0.380625	0.190313	−	0.981724i	$-0.439050\pi$
$683$	9.94736	0.380625	0.190313	+	0.981724i	$0.439050\pi$
$684$	4.54577	0.173812
$685$	41.4744	1.58466
$686$	4.39165	0.167674
$687$	−65.9576	−2.51644
$688$	11.4903	0.438064
$689$	3.29523	0.125538
$690$	−65.9871	−2.51208
$691$	7.03341	0.267563	0.133782	−	0.991011i	$-0.457288\pi$
$691$	7.03341	0.267563	0.133782	+	0.991011i	$0.457288\pi$
$692$	21.0515	0.800256
$693$	−15.2916	−0.580881
$694$	17.8973	0.679372
$695$	17.7788	0.674388
$696$	−21.0440	−0.797670
$697$	12.8076	0.485123
$698$	25.0116	0.946704
$699$	−47.5129	−1.79710
$700$	19.6753	0.743657
$701$	−30.1261	−1.13785	−0.568924	−	0.822390i	$-0.692640\pi$
$701$	−30.1261	−1.13785	−0.568924	+	0.822390i	$0.692640\pi$
$702$	−3.27698	−0.123682
$703$	5.37369	0.202673
$704$	−0.930450	−0.0350677
$705$	115.543	4.35160
$706$	18.6890	0.703369
$707$	−6.70376	−0.252121
$708$	−15.6736	−0.589049
$709$	−38.2147	−1.43518	−0.717591	−	0.696465i	$-0.754755\pi$
$709$	−38.2147	−1.43518	−0.717591	+	0.696465i	$0.754755\pi$
$710$	−52.3893	−1.96614
$711$	56.7566	2.12854
$712$	−8.59049	−0.321942
$713$	−73.8656	−2.76629
$714$	−41.2186	−1.54257
$715$	2.24236	0.0838595
$716$	10.6679	0.398677
$717$	−8.22917	−0.307324
$718$	0.324952	0.0121271
$719$	49.1806	1.83413	0.917063	−	0.398741i	$-0.130553\pi$
$719$	49.1806	1.83413	0.917063	+	0.398741i	$0.130553\pi$
$720$	14.9059	0.555509
$721$	−51.3440	−1.91215
$722$	18.0229	0.670744
$723$	−18.4836	−0.687412
$724$	10.3196	0.383524
$725$	−42.0303	−1.56096
$726$	−27.9361	−1.03680
$727$	−3.72979	−0.138330	−0.0691651	−	0.997605i	$-0.522034\pi$
$727$	−3.72979	−0.138330	−0.0691651	+	0.997605i	$0.522034\pi$
$728$	2.65715	0.0984804
$729$	−44.0231	−1.63049
$730$	−9.53530	−0.352917
$731$	−48.0770	−1.77819
$732$	−27.1923	−1.00506
$733$	44.0526	1.62712	0.813560	−	0.581480i	$-0.197526\pi$
$733$	44.0526	1.62712	0.813560	+	0.581480i	$0.197526\pi$
$734$	1.18666	0.0438003
$735$	−51.5636	−1.90195
$736$	7.38541	0.272230
$737$	−7.82784	−0.288342
$738$	14.0769	0.518179
$739$	18.9928	0.698663	0.349331	−	0.936999i	$-0.386409\pi$
$739$	18.9928	0.698663	0.349331	+	0.936999i	$0.386409\pi$
$740$	17.6207	0.647749
$741$	2.02598	0.0744263
$742$	15.8380	0.581430
$743$	−37.2349	−1.36602	−0.683008	−	0.730411i	$-0.739328\pi$
$743$	−37.2349	−1.36602	−0.683008	+	0.730411i	$0.739328\pi$
$744$	27.5703	1.01077
$745$	16.7026	0.611938
$746$	−16.7231	−0.612277
$747$	38.5146	1.40918
$748$	3.89313	0.142347
$749$	−5.23047	−0.191117
$750$	4.51773	0.164964
$751$	20.7354	0.756644	0.378322	−	0.925674i	$-0.376501\pi$
$751$	20.7354	0.756644	0.378322	+	0.925674i	$0.376501\pi$
$752$	−12.9318	−0.471575
$753$	−45.0105	−1.64027
$754$	−5.67618	−0.206714
$755$	−16.9736	−0.617733
$756$	−15.7502	−0.572830
$757$	−17.7095	−0.643663	−0.321832	−	0.946797i	$-0.604298\pi$
$757$	−17.7095	−0.643663	−0.321832	+	0.946797i	$0.604298\pi$
$758$	16.3639	0.594364
$759$	−18.9427	−0.687575
$760$	−3.20385	−0.116216
$761$	25.3327	0.918309	0.459154	−	0.888356i	$-0.348152\pi$
$761$	25.3327	0.918309	0.459154	+	0.888356i	$0.348152\pi$
$762$	26.1574	0.947582
$763$	−53.2663	−1.92837
$764$	5.68469	0.205665
$765$	−62.3682	−2.25493
$766$	−12.2040	−0.440948
$767$	−4.22762	−0.152651
$768$	−2.75660	−0.0994701
$769$	−41.0723	−1.48111	−0.740553	−	0.671998i	$-0.765436\pi$
$769$	−41.0723	−1.48111	−0.740553	+	0.671998i	$0.765436\pi$
$770$	10.7775	0.388395
$771$	2.80418	0.100990
$772$	6.59931	0.237514
$773$	28.1197	1.01140	0.505698	−	0.862711i	$-0.331235\pi$
$773$	28.1197	1.01140	0.505698	+	0.862711i	$0.331235\pi$
$774$	−52.8418	−1.89936
$775$	55.0649	1.97799
$776$	7.28895	0.261658
$777$	−53.5548	−1.92127
$778$	10.6498	0.381813
$779$	−3.02568	−0.108406
$780$	6.64332	0.237869
$781$	−15.0392	−0.538145
$782$	−30.9016	−1.10504
$783$	33.6455	1.20239
$784$	5.77111	0.206111
$785$	−5.59478	−0.199686
$786$	8.60177	0.306815
$787$	−47.7555	−1.70230	−0.851150	−	0.524922i	$-0.824094\pi$
$787$	−47.7555	−1.70230	−0.851150	+	0.524922i	$0.824094\pi$
$788$	−16.3130	−0.581128
$789$	−36.0126	−1.28208
$790$	−40.0019	−1.42320
$791$	52.1572	1.85450
$792$	4.27897	0.152047
$793$	−7.33456	−0.260458
$794$	28.9568	1.02764
$795$	39.5976	1.40438
$796$	16.8655	0.597782
$797$	−44.0244	−1.55942	−0.779711	−	0.626139i	$-0.784634\pi$
$797$	−44.0244	−1.55942	−0.779711	+	0.626139i	$0.784634\pi$
$798$	9.73753	0.344705
$799$	54.1085	1.91422
$800$	−5.50563	−0.194654
$801$	39.5061	1.39588
$802$	−36.0269	−1.27215
$803$	−2.73726	−0.0965959
$804$	−23.1911	−0.817888
$805$	−85.5461	−3.01510
$806$	7.43651	0.261940
$807$	50.2553	1.76907
$808$	1.87588	0.0659931
$809$	−19.1439	−0.673062	−0.336531	−	0.941672i	$-0.609254\pi$
$809$	−19.1439	−0.673062	−0.336531	+	0.941672i	$0.609254\pi$
$810$	5.33936	0.187606
$811$	16.8717	0.592447	0.296223	−	0.955119i	$-0.404273\pi$
$811$	16.8717	0.592447	0.296223	+	0.955119i	$0.404273\pi$
$812$	−27.2815	−0.957395
$813$	−67.3336	−2.36149
$814$	5.05830	0.177293
$815$	−45.5916	−1.59700
$816$	11.5340	0.403770
$817$	11.3578	0.397358
$818$	26.5409	0.927980
$819$	−12.2197	−0.426992
$820$	−9.92141	−0.346471
$821$	26.5570	0.926847	0.463423	−	0.886137i	$-0.346621\pi$
$821$	26.5570	0.926847	0.463423	+	0.886137i	$0.346621\pi$
$822$	35.2730	1.23029
$823$	−53.9648	−1.88110	−0.940548	−	0.339662i	$-0.889687\pi$
$823$	−53.9648	−1.88110	−0.940548	+	0.339662i	$0.889687\pi$
$824$	14.3673	0.500509
$825$	14.1213	0.491639
$826$	−20.3193	−0.707000
$827$	38.7447	1.34728	0.673642	−	0.739058i	$-0.264729\pi$
$827$	38.7447	1.34728	0.673642	+	0.739058i	$0.264729\pi$
$828$	−33.9642	−1.18034
$829$	−23.5507	−0.817948	−0.408974	−	0.912546i	$-0.634113\pi$
$829$	−23.5507	−0.817948	−0.408974	+	0.912546i	$0.634113\pi$
$830$	−27.1450	−0.942218
$831$	0.527906	0.0183128
$832$	−0.743535	−0.0257774
$833$	−24.1471	−0.836647
$834$	15.1204	0.523578
$835$	66.6751	2.30739
$836$	−0.919718	−0.0318091
$837$	−44.0798	−1.52362
$838$	35.3655	1.22168
$839$	44.1311	1.52357	0.761787	−	0.647828i	$-0.224322\pi$
$839$	44.1311	1.52357	0.761787	+	0.647828i	$0.224322\pi$
$840$	31.9300	1.10169
$841$	29.2786	1.00961
$842$	−36.3696	−1.25338
$843$	−46.6593	−1.60703
$844$	−7.56575	−0.260424
$845$	−40.3442	−1.38788
$846$	59.4711	2.04466
$847$	−36.2165	−1.24441
$848$	−4.43185	−0.152190
$849$	−8.51262	−0.292152
$850$	23.0363	0.790139
$851$	−40.1500	−1.37633
$852$	−44.5558	−1.52646
$853$	16.9476	0.580273	0.290137	−	0.956985i	$-0.406299\pi$
$853$	16.9476	0.580273	0.290137	+	0.956985i	$0.406299\pi$
$854$	−35.2523	−1.20631
$855$	14.7339	0.503890
$856$	1.46361	0.0500252
$857$	−0.809344	−0.0276467	−0.0138233	−	0.999904i	$-0.504400\pi$
$857$	−0.809344	−0.0276467	−0.0138233	+	0.999904i	$0.504400\pi$
$858$	1.90707	0.0651064
$859$	36.1338	1.23287	0.616435	−	0.787406i	$-0.288576\pi$
$859$	36.1338	1.23287	0.616435	+	0.787406i	$0.288576\pi$
$860$	37.2428	1.26997
$861$	30.1543	1.02766
$862$	−32.7091	−1.11408
$863$	−3.80396	−0.129488	−0.0647441	−	0.997902i	$-0.520623\pi$
$863$	−3.80396	−0.129488	−0.0647441	+	0.997902i	$0.520623\pi$
$864$	4.40730	0.149939
$865$	68.2328	2.31999
$866$	−15.2787	−0.519190
$867$	−1.39757	−0.0474641
$868$	35.7423	1.21317
$869$	−11.4832	−0.389541
$870$	−68.2086	−2.31249
$871$	−6.25532	−0.211954
$872$	14.9052	0.504754
$873$	−33.5206	−1.13450
$874$	7.30022	0.246934
$875$	5.85681	0.197996
$876$	−8.10954	−0.273996
$877$	39.6698	1.33955	0.669777	−	0.742563i	$-0.266390\pi$
$877$	39.6698	1.33955	0.669777	+	0.742563i	$0.266390\pi$
$878$	29.0334	0.979831
$879$	32.7270	1.10385
$880$	−3.01581	−0.101663
$881$	57.1385	1.92505	0.962523	−	0.271202i	$-0.0874210\pi$
$881$	57.1385	1.92505	0.962523	+	0.271202i	$0.0874210\pi$
$882$	−26.5403	−0.893658
$883$	−15.6500	−0.526666	−0.263333	−	0.964705i	$-0.584822\pi$
$883$	−15.6500	−0.526666	−0.263333	+	0.964705i	$0.584822\pi$
$884$	3.11105	0.104636
$885$	−50.8018	−1.70768
$886$	−24.4160	−0.820273
$887$	−55.6511	−1.86858	−0.934290	−	0.356515i	$-0.883965\pi$
$887$	−55.6511	−1.86858	−0.934290	+	0.356515i	$0.883965\pi$
$888$	14.9859	0.502895
$889$	33.9106	1.13733
$890$	−27.8438	−0.933327
$891$	1.53275	0.0513491
$892$	12.7020	0.425294
$893$	−12.7827	−0.427755
$894$	14.2052	0.475093
$895$	34.5771	1.15578
$896$	−3.57367	−0.119388
$897$	−15.1373	−0.505420
$898$	23.9333	0.798664
$899$	−76.3523	−2.54649
$900$	25.3194	0.843980
$901$	18.5435	0.617772
$902$	−2.84810	−0.0948314
$903$	−113.193	−3.76682
$904$	−14.5949	−0.485418
$905$	33.4483	1.11186
$906$	−14.4356	−0.479592
$907$	25.6520	0.851762	0.425881	−	0.904779i	$-0.359964\pi$
$907$	25.6520	0.851762	0.425881	+	0.904779i	$0.359964\pi$
$908$	−24.4118	−0.810133
$909$	−8.62682	−0.286134
$910$	8.61245	0.285500
$911$	−50.1286	−1.66084	−0.830418	−	0.557141i	$-0.811898\pi$
$911$	−50.1286	−1.66084	−0.830418	+	0.557141i	$0.811898\pi$
$912$	−2.72480	−0.0902271
$913$	−7.79242	−0.257892
$914$	24.1773	0.799713
$915$	−88.1367	−2.91371
$916$	23.9272	0.790577
$917$	11.1514	0.368251
$918$	−18.4407	−0.608635
$919$	32.1130	1.05931	0.529655	−	0.848213i	$-0.322321\pi$
$919$	32.1130	1.05931	0.529655	+	0.848213i	$0.322321\pi$
$920$	23.9379	0.789209
$921$	33.8677	1.11598
$922$	−9.39792	−0.309504
$923$	−12.0180	−0.395578
$924$	9.16601	0.301540
$925$	29.9308	0.984119
$926$	−11.4014	−0.374672
$927$	−66.0727	−2.17011
$928$	7.63404	0.250600
$929$	18.3862	0.603231	0.301615	−	0.953430i	$-0.402474\pi$
$929$	18.3862	0.603231	0.301615	+	0.953430i	$0.402474\pi$
$930$	89.3618	2.93029
$931$	5.70454	0.186959
$932$	17.2361	0.564586
$933$	43.5527	1.42585
$934$	32.0694	1.04934
$935$	12.6186	0.412671
$936$	3.41938	0.111766
$937$	−17.4224	−0.569165	−0.284582	−	0.958652i	$-0.591855\pi$
$937$	−17.4224	−0.569165	−0.284582	+	0.958652i	$0.591855\pi$
$938$	−30.0651	−0.981661
$939$	−2.81845	−0.0919768
$940$	−41.9151	−1.36712
$941$	−0.990306	−0.0322831	−0.0161415	−	0.999870i	$-0.505138\pi$
$941$	−0.990306	−0.0322831	−0.0161415	+	0.999870i	$0.505138\pi$
$942$	−4.75822	−0.155031
$943$	22.6067	0.736175
$944$	5.68585	0.185059
$945$	−51.0502	−1.66066
$946$	10.6912	0.347599
$947$	−2.36277	−0.0767798	−0.0383899	−	0.999263i	$-0.512223\pi$
$947$	−2.36277	−0.0767798	−0.0383899	+	0.999263i	$0.512223\pi$
$948$	−34.0207	−1.10494
$949$	−2.18738	−0.0710054
$950$	−5.44213	−0.176566
$951$	34.0427	1.10391
$952$	14.9527	0.484620
$953$	10.1113	0.327538	0.163769	−	0.986499i	$-0.447635\pi$
$953$	10.1113	0.327538	0.163769	+	0.986499i	$0.447635\pi$
$954$	20.3813	0.659868
$955$	18.4255	0.596234
$956$	2.98527	0.0965504
$957$	−19.5804	−0.632943
$958$	−1.70651	−0.0551348
$959$	45.7282	1.47664
$960$	−8.93479	−0.288369
$961$	69.0312	2.22681
$962$	4.04215	0.130324
$963$	−6.73089	−0.216900
$964$	6.70522	0.215961
$965$	21.3900	0.688567
$966$	−72.7549	−2.34085
$967$	45.0242	1.44788	0.723940	−	0.689863i	$-0.242329\pi$
$967$	45.0242	1.44788	0.723940	+	0.689863i	$0.242329\pi$
$968$	10.1343	0.325728
$969$	11.4009	0.366251
$970$	23.6252	0.758561
$971$	0.539912	0.0173266	0.00866330	−	0.999962i	$-0.497242\pi$
$971$	0.539912	0.0173266	0.00866330	+	0.999962i	$0.497242\pi$
$972$	17.7629	0.569745
$973$	19.6022	0.628419
$974$	−2.31154	−0.0740665
$975$	11.2845	0.361393
$976$	9.86445	0.315753
$977$	37.7103	1.20646	0.603230	−	0.797567i	$-0.293880\pi$
$977$	37.7103	1.20646	0.603230	+	0.797567i	$0.293880\pi$
$978$	−38.7745	−1.23987
$979$	−7.99302	−0.255458
$980$	18.7055	0.597527
$981$	−68.5463	−2.18852
$982$	−5.24741	−0.167452
$983$	−10.4394	−0.332966	−0.166483	−	0.986044i	$-0.553241\pi$
$983$	−10.4394	−0.332966	−0.166483	+	0.986044i	$0.553241\pi$
$984$	−8.43791	−0.268991
$985$	−52.8745	−1.68472
$986$	−31.9419	−1.01724
$987$	127.393	4.05498
$988$	−0.734958	−0.0233821
$989$	−84.8606	−2.69841
$990$	13.8692	0.440791
$991$	9.99274	0.317430	0.158715	−	0.987324i	$-0.449265\pi$
$991$	9.99274	0.317430	0.158715	+	0.987324i	$0.449265\pi$
$992$	−10.0016	−0.317550
$993$	−55.4477	−1.75958
$994$	−57.7625	−1.83211
$995$	54.6651	1.73300
$996$	−23.0862	−0.731514
$997$	−53.7608	−1.70262	−0.851311	−	0.524661i	$-0.824192\pi$
$997$	−53.7608	−1.70262	−0.851311	+	0.524661i	$0.824192\pi$
$998$	6.90416	0.218547
$999$	−23.9598	−0.758055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.5	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.5	✓	49	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.75660 q^{3} +1.00000 q^{4} +3.24124 q^{5} +2.75660 q^{6} +3.57367 q^{7} -1.00000 q^{8} +4.59882 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.75660 q^{3} +1.00000 q^{4} +3.24124 q^{5} +2.75660 q^{6} +3.57367 q^{7} -1.00000 q^{8} +4.59882 q^{9} -3.24124 q^{10} -0.930450 q^{11} -2.75660 q^{12} -0.743535 q^{13} -3.57367 q^{14} -8.93479 q^{15} +1.00000 q^{16} -4.18414 q^{17} -4.59882 q^{18} +0.988465 q^{19} +3.24124 q^{20} -9.85116 q^{21} +0.930450 q^{22} -7.38541 q^{23} +2.75660 q^{24} +5.50563 q^{25} +0.743535 q^{26} -4.40730 q^{27} +3.57367 q^{28} -7.63404 q^{29} +8.93479 q^{30} +10.0016 q^{31} -1.00000 q^{32} +2.56487 q^{33} +4.18414 q^{34} +11.5831 q^{35} +4.59882 q^{36} +5.43640 q^{37} -0.988465 q^{38} +2.04962 q^{39} -3.24124 q^{40} -3.06099 q^{41} +9.85116 q^{42} +11.4903 q^{43} -0.930450 q^{44} +14.9059 q^{45} +7.38541 q^{46} -12.9318 q^{47} -2.75660 q^{48} +5.77111 q^{49} -5.50563 q^{50} +11.5340 q^{51} -0.743535 q^{52} -4.43185 q^{53} +4.40730 q^{54} -3.01581 q^{55} -3.57367 q^{56} -2.72480 q^{57} +7.63404 q^{58} +5.68585 q^{59} -8.93479 q^{60} +9.86445 q^{61} -10.0016 q^{62} +16.4347 q^{63} +1.00000 q^{64} -2.40997 q^{65} -2.56487 q^{66} +8.41296 q^{67} -4.18414 q^{68} +20.3586 q^{69} -11.5831 q^{70} +16.1634 q^{71} -4.59882 q^{72} +2.94187 q^{73} -5.43640 q^{74} -15.1768 q^{75} +0.988465 q^{76} -3.32512 q^{77} -2.04962 q^{78} +12.3416 q^{79} +3.24124 q^{80} -1.64732 q^{81} +3.06099 q^{82} +8.37490 q^{83} -9.85116 q^{84} -13.5618 q^{85} -11.4903 q^{86} +21.0440 q^{87} +0.930450 q^{88} +8.59049 q^{89} -14.9059 q^{90} -2.65715 q^{91} -7.38541 q^{92} -27.5703 q^{93} +12.9318 q^{94} +3.20385 q^{95} +2.75660 q^{96} -7.28895 q^{97} -5.77111 q^{98} -4.27897 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

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