LMFDB - Embedded newform 4021.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, 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("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.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:	$32.1078466528$
Analytic rank:	$0$
Dimension:	$182$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.81003 q^{2} -0.712978 q^{3} +5.89629 q^{4} +1.47211 q^{5} +2.00349 q^{6} +1.95505 q^{7} -10.9487 q^{8} -2.49166 q^{9} +O(q^{10})$	\(q-2.81003 q^{2} -0.712978 q^{3} +5.89629 q^{4} +1.47211 q^{5} +2.00349 q^{6} +1.95505 q^{7} -10.9487 q^{8} -2.49166 q^{9} -4.13669 q^{10} -0.358376 q^{11} -4.20392 q^{12} -1.21391 q^{13} -5.49376 q^{14} -1.04958 q^{15} +18.9737 q^{16} +4.80425 q^{17} +7.00166 q^{18} +0.0546258 q^{19} +8.68001 q^{20} -1.39391 q^{21} +1.00705 q^{22} +7.56453 q^{23} +7.80619 q^{24} -2.83288 q^{25} +3.41113 q^{26} +3.91543 q^{27} +11.5276 q^{28} +4.27597 q^{29} +2.94937 q^{30} -3.73302 q^{31} -31.4192 q^{32} +0.255514 q^{33} -13.5001 q^{34} +2.87806 q^{35} -14.6916 q^{36} -3.34994 q^{37} -0.153500 q^{38} +0.865491 q^{39} -16.1177 q^{40} +4.21829 q^{41} +3.91693 q^{42} -8.81564 q^{43} -2.11309 q^{44} -3.66801 q^{45} -21.2566 q^{46} +1.60798 q^{47} -13.5278 q^{48} -3.17778 q^{49} +7.96050 q^{50} -3.42532 q^{51} -7.15757 q^{52} +2.48365 q^{53} -11.0025 q^{54} -0.527570 q^{55} -21.4053 q^{56} -0.0389470 q^{57} -12.0156 q^{58} +2.10127 q^{59} -6.18865 q^{60} +6.22165 q^{61} +10.4899 q^{62} -4.87133 q^{63} +50.3418 q^{64} -1.78701 q^{65} -0.718003 q^{66} +4.87115 q^{67} +28.3272 q^{68} -5.39334 q^{69} -8.08744 q^{70} +11.1023 q^{71} +27.2805 q^{72} +6.18677 q^{73} +9.41346 q^{74} +2.01978 q^{75} +0.322090 q^{76} -0.700643 q^{77} -2.43206 q^{78} -0.457182 q^{79} +27.9314 q^{80} +4.68337 q^{81} -11.8535 q^{82} -6.41544 q^{83} -8.21888 q^{84} +7.07239 q^{85} +24.7723 q^{86} -3.04867 q^{87} +3.92375 q^{88} -1.40786 q^{89} +10.3072 q^{90} -2.37326 q^{91} +44.6027 q^{92} +2.66156 q^{93} -4.51848 q^{94} +0.0804153 q^{95} +22.4012 q^{96} -15.1394 q^{97} +8.92966 q^{98} +0.892951 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) $ 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * 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 $

$2$	−2.81003	−1.98699	−0.993497	−	0.113858i	$-0.963679\pi$
$2$	−2.81003	−1.98699	−0.993497	+	0.113858i	$0.963679\pi$
$3$	−0.712978	−0.411638	−0.205819	−	0.978590i	$-0.565986\pi$
$3$	−0.712978	−0.411638	−0.205819	+	0.978590i	$0.565986\pi$
$4$	5.89629	2.94815
$5$	1.47211	0.658349	0.329174	−	0.944269i	$-0.393230\pi$
$5$	1.47211	0.658349	0.329174	+	0.944269i	$0.393230\pi$
$6$	2.00349	0.817922
$7$	1.95505	0.738940	0.369470	−	0.929243i	$-0.379539\pi$
$7$	1.95505	0.738940	0.369470	+	0.929243i	$0.379539\pi$
$8$	−10.9487	−3.87095
$9$	−2.49166	−0.830554
$10$	−4.13669	−1.30814
$11$	−0.358376	−0.108054	−0.0540272	−	0.998539i	$-0.517206\pi$
$11$	−0.358376	−0.108054	−0.0540272	+	0.998539i	$0.517206\pi$
$12$	−4.20392	−1.21357
$13$	−1.21391	−0.336678	−0.168339	−	0.985729i	$-0.553840\pi$
$13$	−1.21391	−0.336678	−0.168339	+	0.985729i	$0.553840\pi$
$14$	−5.49376	−1.46827
$15$	−1.04958	−0.271001
$16$	18.9737	4.74342
$17$	4.80425	1.16520	0.582600	−	0.812759i	$-0.302035\pi$
$17$	4.80425	1.16520	0.582600	+	0.812759i	$0.302035\pi$
$18$	7.00166	1.65031
$19$	0.0546258	0.0125320	0.00626601	−	0.999980i	$-0.498005\pi$
$19$	0.0546258	0.0125320	0.00626601	+	0.999980i	$0.498005\pi$
$20$	8.68001	1.94091
$21$	−1.39391	−0.304176
$22$	1.00705	0.214703
$23$	7.56453	1.57731	0.788657	−	0.614834i	$-0.210777\pi$
$23$	7.56453	1.57731	0.788657	+	0.614834i	$0.210777\pi$
$24$	7.80619	1.59343
$25$	−2.83288	−0.566577
$26$	3.41113	0.668977
$27$	3.91543	0.753525
$28$	11.5276	2.17850
$29$	4.27597	0.794028	0.397014	−	0.917813i	$-0.370046\pi$
$29$	4.27597	0.794028	0.397014	+	0.917813i	$0.370046\pi$
$30$	2.94937	0.538478
$31$	−3.73302	−0.670470	−0.335235	−	0.942135i	$-0.608816\pi$
$31$	−3.73302	−0.670470	−0.335235	+	0.942135i	$0.608816\pi$
$32$	−31.4192	−5.55419
$33$	0.255514	0.0444792
$34$	−13.5001	−2.31525
$35$	2.87806	0.486480
$36$	−14.6916	−2.44860
$37$	−3.34994	−0.550727	−0.275364	−	0.961340i	$-0.588798\pi$
$37$	−3.34994	−0.550727	−0.275364	+	0.961340i	$0.588798\pi$
$38$	−0.153500	−0.0249010
$39$	0.865491	0.138589
$40$	−16.1177	−2.54844
$41$	4.21829	0.658786	0.329393	−	0.944193i	$-0.393156\pi$
$41$	4.21829	0.658786	0.329393	+	0.944193i	$0.393156\pi$
$42$	3.91693	0.604395
$43$	−8.81564	−1.34437	−0.672186	−	0.740382i	$-0.734645\pi$
$43$	−8.81564	−1.34437	−0.672186	+	0.740382i	$0.734645\pi$
$44$	−2.11309	−0.318560
$45$	−3.66801	−0.546795
$46$	−21.2566	−3.13411
$47$	1.60798	0.234548	0.117274	−	0.993100i	$-0.462584\pi$
$47$	1.60798	0.234548	0.117274	+	0.993100i	$0.462584\pi$
$48$	−13.5278	−1.95257
$49$	−3.17778	−0.453968
$50$	7.96050	1.12578
$51$	−3.42532	−0.479641
$52$	−7.15757	−0.992576
$53$	2.48365	0.341156	0.170578	−	0.985344i	$-0.445437\pi$
$53$	2.48365	0.341156	0.170578	+	0.985344i	$0.445437\pi$
$54$	−11.0025	−1.49725
$55$	−0.527570	−0.0711375
$56$	−21.4053	−2.86040
$57$	−0.0389470	−0.00515865
$58$	−12.0156	−1.57773
$59$	2.10127	0.273562	0.136781	−	0.990601i	$-0.456324\pi$
$59$	2.10127	0.273562	0.136781	+	0.990601i	$0.456324\pi$
$60$	−6.18865	−0.798951
$61$	6.22165	0.796601	0.398300	−	0.917255i	$-0.369600\pi$
$61$	6.22165	0.796601	0.398300	+	0.917255i	$0.369600\pi$
$62$	10.4899	1.33222
$63$	−4.87133	−0.613730
$64$	50.3418	6.29272
$65$	−1.78701	−0.221652
$66$	−0.718003	−0.0883800
$67$	4.87115	0.595106	0.297553	−	0.954705i	$-0.403829\pi$
$67$	4.87115	0.595106	0.297553	+	0.954705i	$0.403829\pi$
$68$	28.3272	3.43518
$69$	−5.39334	−0.649282
$70$	−8.08744	−0.966633
$71$	11.1023	1.31760	0.658799	−	0.752319i	$-0.271065\pi$
$71$	11.1023	1.31760	0.658799	+	0.752319i	$0.271065\pi$
$72$	27.2805	3.21504
$73$	6.18677	0.724106	0.362053	−	0.932157i	$-0.382076\pi$
$73$	6.18677	0.724106	0.362053	+	0.932157i	$0.382076\pi$
$74$	9.41346	1.09429
$75$	2.01978	0.233224
$76$	0.322090	0.0369462
$77$	−0.700643	−0.0798457
$78$	−2.43206	−0.275376
$79$	−0.457182	−0.0514369	−0.0257185	−	0.999669i	$-0.508187\pi$
$79$	−0.457182	−0.0514369	−0.0257185	+	0.999669i	$0.508187\pi$
$80$	27.9314	3.12282
$81$	4.68337	0.520375
$82$	−11.8535	−1.30900
$83$	−6.41544	−0.704186	−0.352093	−	0.935965i	$-0.614530\pi$
$83$	−6.41544	−0.704186	−0.352093	+	0.935965i	$0.614530\pi$
$84$	−8.21888	−0.896754
$85$	7.07239	0.767109
$86$	24.7723	2.67126
$87$	−3.04867	−0.326852
$88$	3.92375	0.418273
$89$	−1.40786	−0.149233	−0.0746167	−	0.997212i	$-0.523773\pi$
$89$	−1.40786	−0.149233	−0.0746167	+	0.997212i	$0.523773\pi$
$90$	10.3072	1.08648
$91$	−2.37326	−0.248785
$92$	44.6027	4.65015
$93$	2.66156	0.275991
$94$	−4.51848	−0.466046
$95$	0.0804153	0.00825044
$96$	22.4012	2.28631
$97$	−15.1394	−1.53717	−0.768584	−	0.639748i	$-0.779039\pi$
$97$	−15.1394	−1.53717	−0.768584	+	0.639748i	$0.779039\pi$
$98$	8.92966	0.902032
$99$	0.892951	0.0897450
$100$	−16.7035	−1.67035
$101$	11.7654	1.17070	0.585349	−	0.810781i	$-0.300958\pi$
$101$	11.7654	1.17070	0.585349	+	0.810781i	$0.300958\pi$
$102$	9.62527	0.953043
$103$	−6.14164	−0.605154	−0.302577	−	0.953125i	$-0.597847\pi$
$103$	−6.14164	−0.605154	−0.302577	+	0.953125i	$0.597847\pi$
$104$	13.2908	1.30327
$105$	−2.05199	−0.200254
$106$	−6.97914	−0.677874
$107$	−12.3686	−1.19572	−0.597858	−	0.801602i	$-0.703981\pi$
$107$	−12.3686	−1.19572	−0.597858	+	0.801602i	$0.703981\pi$
$108$	23.0865	2.22150
$109$	4.38171	0.419692	0.209846	−	0.977734i	$-0.432704\pi$
$109$	4.38171	0.419692	0.209846	+	0.977734i	$0.432704\pi$
$110$	1.48249	0.141350
$111$	2.38844	0.226700
$112$	37.0945	3.50510
$113$	11.1815	1.05186	0.525931	−	0.850527i	$-0.323717\pi$
$113$	11.1815	1.05186	0.525931	+	0.850527i	$0.323717\pi$
$114$	0.109442	0.0102502
$115$	11.1358	1.03842
$116$	25.2124	2.34091
$117$	3.02466	0.279629
$118$	−5.90464	−0.543566
$119$	9.39255	0.861013
$120$	11.4916	1.04903
$121$	−10.8716	−0.988324
$122$	−17.4830	−1.58284
$123$	−3.00755	−0.271181
$124$	−22.0110	−1.97664
$125$	−11.5309	−1.03135
$126$	13.6886	1.21948
$127$	−8.14456	−0.722713	−0.361356	−	0.932428i	$-0.617686\pi$
$127$	−8.14456	−0.722713	−0.361356	+	0.932428i	$0.617686\pi$
$128$	−78.6237	−6.94942
$129$	6.28535	0.553395
$130$	5.02157	0.440421
$131$	6.24555	0.545676	0.272838	−	0.962060i	$-0.412038\pi$
$131$	6.24555	0.545676	0.272838	+	0.962060i	$0.412038\pi$
$132$	1.50658	0.131131
$133$	0.106796	0.00926040
$134$	−13.6881	−1.18247
$135$	5.76396	0.496083
$136$	−52.6003	−4.51044
$137$	12.1610	1.03899	0.519494	−	0.854474i	$-0.326121\pi$
$137$	12.1610	1.03899	0.519494	+	0.854474i	$0.326121\pi$
$138$	15.1555	1.29012
$139$	5.11172	0.433570	0.216785	−	0.976219i	$-0.430443\pi$
$139$	5.11172	0.433570	0.216785	+	0.976219i	$0.430443\pi$
$140$	16.9699	1.43421
$141$	−1.14645	−0.0965489
$142$	−31.1978	−2.61806
$143$	0.435036	0.0363795
$144$	−47.2760	−3.93967
$145$	6.29471	0.522748
$146$	−17.3850	−1.43879
$147$	2.26568	0.186870
$148$	−19.7522	−1.62362
$149$	2.45930	0.201473	0.100737	−	0.994913i	$-0.467880\pi$
$149$	2.45930	0.201473	0.100737	+	0.994913i	$0.467880\pi$
$150$	−5.67566	−0.463415
$151$	16.3973	1.33439	0.667197	−	0.744881i	$-0.267494\pi$
$151$	16.3973	1.33439	0.667197	+	0.744881i	$0.267494\pi$
$152$	−0.598082	−0.0485109
$153$	−11.9706	−0.967763
$154$	1.96883	0.158653
$155$	−5.49542	−0.441403
$156$	5.10319	0.408582
$157$	11.8702	0.947343	0.473672	−	0.880702i	$-0.342928\pi$
$157$	11.8702	0.947343	0.473672	+	0.880702i	$0.342928\pi$
$158$	1.28470	0.102205
$159$	−1.77079	−0.140433
$160$	−46.2527	−3.65659
$161$	14.7890	1.16554
$162$	−13.1604	−1.03398
$163$	10.9438	0.857186	0.428593	−	0.903498i	$-0.359009\pi$
$163$	10.9438	0.857186	0.428593	+	0.903498i	$0.359009\pi$
$164$	24.8723	1.94220
$165$	0.376145	0.0292829
$166$	18.0276	1.39921
$167$	2.88233	0.223041	0.111521	−	0.993762i	$-0.464428\pi$
$167$	2.88233	0.223041	0.111521	+	0.993762i	$0.464428\pi$
$168$	15.2615	1.17745
$169$	−11.5264	−0.886648
$170$	−19.8737	−1.52424
$171$	−0.136109	−0.0104085
$172$	−51.9796	−3.96341
$173$	−13.6116	−1.03487	−0.517435	−	0.855723i	$-0.673113\pi$
$173$	−13.6116	−1.03487	−0.517435	+	0.855723i	$0.673113\pi$
$174$	8.56687	0.649453
$175$	−5.53843	−0.418666
$176$	−6.79970	−0.512547
$177$	−1.49816	−0.112608
$178$	3.95615	0.296526
$179$	6.36667	0.475867	0.237933	−	0.971281i	$-0.423530\pi$
$179$	6.36667	0.475867	0.237933	+	0.971281i	$0.423530\pi$
$180$	−21.6277	−1.61203
$181$	18.0108	1.33873	0.669365	−	0.742933i	$-0.266566\pi$
$181$	18.0108	1.33873	0.669365	+	0.742933i	$0.266566\pi$
$182$	6.66893	0.494334
$183$	−4.43590	−0.327911
$184$	−82.8218	−6.10571
$185$	−4.93150	−0.362571
$186$	−7.47907	−0.548392
$187$	−1.72173	−0.125905
$188$	9.48113	0.691482
$189$	7.65487	0.556810
$190$	−0.225970	−0.0163936
$191$	21.8886	1.58381	0.791903	−	0.610648i	$-0.209091\pi$
$191$	21.8886	1.58381	0.791903	+	0.610648i	$0.209091\pi$
$192$	−35.8926	−2.59032
$193$	4.32196	0.311101	0.155551	−	0.987828i	$-0.450285\pi$
$193$	4.32196	0.311101	0.155551	+	0.987828i	$0.450285\pi$
$194$	42.5421	3.05435
$195$	1.27410	0.0912402
$196$	−18.7371	−1.33836
$197$	−7.83003	−0.557866	−0.278933	−	0.960311i	$-0.589981\pi$
$197$	−7.83003	−0.557866	−0.278933	+	0.960311i	$0.589981\pi$
$198$	−2.50922	−0.178323
$199$	−9.98211	−0.707613	−0.353807	−	0.935319i	$-0.615113\pi$
$199$	−9.98211	−0.707613	−0.353807	+	0.935319i	$0.615113\pi$
$200$	31.0164	2.19319
$201$	−3.47302	−0.244968
$202$	−33.0611	−2.32617
$203$	8.35974	0.586739
$204$	−20.1967	−1.41405
$205$	6.20980	0.433711
$206$	17.2582	1.20244
$207$	−18.8483	−1.31004
$208$	−23.0323	−1.59700
$209$	−0.0195766	−0.00135414
$210$	5.76616	0.397903
$211$	2.24507	0.154557	0.0772783	−	0.997010i	$-0.475377\pi$
$211$	2.24507	0.154557	0.0772783	+	0.997010i	$0.475377\pi$
$212$	14.6443	1.00578
$213$	−7.91568	−0.542373
$214$	34.7561	2.37588
$215$	−12.9776	−0.885066
$216$	−42.8689	−2.91686
$217$	−7.29824	−0.495437
$218$	−12.3128	−0.833925
$219$	−4.41103	−0.298069
$220$	−3.11070	−0.209724
$221$	−5.83192	−0.392298
$222$	−6.71158	−0.450452
$223$	−9.27603	−0.621169	−0.310584	−	0.950546i	$-0.600525\pi$
$223$	−9.27603	−0.621169	−0.310584	+	0.950546i	$0.600525\pi$
$224$	−61.4262	−4.10421
$225$	7.05859	0.470573
$226$	−31.4203	−2.09005
$227$	−9.81070	−0.651159	−0.325580	−	0.945515i	$-0.605559\pi$
$227$	−9.81070	−0.651159	−0.325580	+	0.945515i	$0.605559\pi$
$228$	−0.229643	−0.0152085
$229$	22.6125	1.49428	0.747138	−	0.664669i	$-0.231427\pi$
$229$	22.6125	1.49428	0.747138	+	0.664669i	$0.231427\pi$
$230$	−31.2921	−2.06334
$231$	0.499543	0.0328675
$232$	−46.8164	−3.07365
$233$	16.8053	1.10095	0.550475	−	0.834851i	$-0.314447\pi$
$233$	16.8053	1.10095	0.550475	+	0.834851i	$0.314447\pi$
$234$	−8.49938	−0.555622
$235$	2.36713	0.154415
$236$	12.3897	0.806500
$237$	0.325960	0.0211734
$238$	−26.3934	−1.71083
$239$	−23.8158	−1.54052	−0.770259	−	0.637731i	$-0.779873\pi$
$239$	−23.8158	−1.54052	−0.770259	+	0.637731i	$0.779873\pi$
$240$	−19.9145	−1.28547
$241$	−20.0687	−1.29274	−0.646368	−	0.763026i	$-0.723713\pi$
$241$	−20.0687	−1.29274	−0.646368	+	0.763026i	$0.723713\pi$
$242$	30.5495	1.96379
$243$	−15.0854	−0.967731
$244$	36.6847	2.34849
$245$	−4.67804	−0.298869
$246$	8.45130	0.538835
$247$	−0.0663108	−0.00421926
$248$	40.8717	2.59536
$249$	4.57407	0.289870
$250$	32.4022	2.04929
$251$	−6.35992	−0.401435	−0.200717	−	0.979649i	$-0.564327\pi$
$251$	−6.35992	−0.401435	−0.200717	+	0.979649i	$0.564327\pi$
$252$	−28.7228	−1.80936
$253$	−2.71094	−0.170436
$254$	22.8865	1.43603
$255$	−5.04246	−0.315771
$256$	120.252	7.51573
$257$	−28.7996	−1.79647	−0.898234	−	0.439518i	$-0.855149\pi$
$257$	−28.7996	−1.79647	−0.898234	+	0.439518i	$0.855149\pi$
$258$	−17.6621	−1.09959
$259$	−6.54931	−0.406954
$260$	−10.5367	−0.653461
$261$	−10.6543	−0.659483
$262$	−17.5502	−1.08425
$263$	19.1645	1.18174	0.590868	−	0.806768i	$-0.298785\pi$
$263$	19.1645	1.18174	0.590868	+	0.806768i	$0.298785\pi$
$264$	−2.79755	−0.172177
$265$	3.65621	0.224599
$266$	−0.300101	−0.0184004
$267$	1.00378	0.0614301
$268$	28.7217	1.75446
$269$	24.2791	1.48032	0.740161	−	0.672430i	$-0.234749\pi$
$269$	24.2791	1.48032	0.740161	+	0.672430i	$0.234749\pi$
$270$	−16.1969	−0.985713
$271$	21.9136	1.33116	0.665578	−	0.746328i	$-0.268185\pi$
$271$	21.9136	1.33116	0.665578	+	0.746328i	$0.268185\pi$
$272$	91.1542	5.52704
$273$	1.69208	0.102409
$274$	−34.1729	−2.06446
$275$	1.01524	0.0612211
$276$	−31.8007	−1.91418
$277$	12.1462	0.729795	0.364897	−	0.931048i	$-0.381104\pi$
$277$	12.1462	0.729795	0.364897	+	0.931048i	$0.381104\pi$
$278$	−14.3641	−0.861502
$279$	9.30142	0.556862
$280$	−31.5110	−1.88314
$281$	2.68082	0.159924	0.0799621	−	0.996798i	$-0.474520\pi$
$281$	2.68082	0.159924	0.0799621	+	0.996798i	$0.474520\pi$
$282$	3.22158	0.191842
$283$	7.97268	0.473927	0.236963	−	0.971519i	$-0.423848\pi$
$283$	7.97268	0.473927	0.236963	+	0.971519i	$0.423848\pi$
$284$	65.4623	3.88447
$285$	−0.0573343	−0.00339619
$286$	−1.22247	−0.0722859
$287$	8.24697	0.486803
$288$	78.2862	4.61306
$289$	6.08078	0.357693
$290$	−17.6884	−1.03870
$291$	10.7940	0.632757
$292$	36.4790	2.13477
$293$	−2.42905	−0.141906	−0.0709532	−	0.997480i	$-0.522604\pi$
$293$	−2.42905	−0.141906	−0.0709532	+	0.997480i	$0.522604\pi$
$294$	−6.36665	−0.371310
$295$	3.09330	0.180099
$296$	36.6776	2.13184
$297$	−1.40320	−0.0814217
$298$	−6.91071	−0.400327
$299$	−9.18266	−0.531047
$300$	11.9092	0.687579
$301$	−17.2350	−0.993410
$302$	−46.0770	−2.65143
$303$	−8.38844	−0.481903
$304$	1.03645	0.0594446
$305$	9.15897	0.524441
$306$	33.6377	1.92294
$307$	−0.0115328	−0.000658213 0	−0.000329106	−	1.00000i	$-0.500105\pi$
$307$	−0.0115328	−0.000658213 0	−0.000329106		1.00000i	$0.500105\pi$
$308$	−4.13119	−0.235397
$309$	4.37885	0.249104
$310$	15.4423	0.877065
$311$	−10.8997	−0.618067	−0.309033	−	0.951051i	$-0.600005\pi$
$311$	−10.8997	−0.618067	−0.309033	+	0.951051i	$0.600005\pi$
$312$	−9.47601	−0.536473
$313$	28.3296	1.60128	0.800641	−	0.599144i	$-0.204492\pi$
$313$	28.3296	1.60128	0.800641	+	0.599144i	$0.204492\pi$
$314$	−33.3556	−1.88237
$315$	−7.17115	−0.404048
$316$	−2.69568	−0.151644
$317$	−27.6503	−1.55300	−0.776498	−	0.630120i	$-0.783006\pi$
$317$	−27.6503	−1.55300	−0.776498	+	0.630120i	$0.783006\pi$
$318$	4.97597	0.279039
$319$	−1.53240	−0.0857982
$320$	74.1088	4.14281
$321$	8.81852	0.492202
$322$	−41.5577	−2.31592
$323$	0.262436	0.0146023
$324$	27.6145	1.53414
$325$	3.43887	0.190754
$326$	−30.7525	−1.70322
$327$	−3.12406	−0.172761
$328$	−46.1848	−2.55013
$329$	3.14369	0.173317
$330$	−1.05698	−0.0581849
$331$	29.6595	1.63023	0.815115	−	0.579299i	$-0.196673\pi$
$331$	29.6595	1.63023	0.815115	+	0.579299i	$0.196673\pi$
$332$	−37.8273	−2.07604
$333$	8.34693	0.457409
$334$	−8.09945	−0.443182
$335$	7.17089	0.391788
$336$	−26.4475	−1.44283
$337$	9.68998	0.527847	0.263923	−	0.964544i	$-0.414983\pi$
$337$	9.68998	0.527847	0.263923	+	0.964544i	$0.414983\pi$
$338$	32.3896	1.76176
$339$	−7.97213	−0.432986
$340$	41.7009	2.26155
$341$	1.33782	0.0724472
$342$	0.382471	0.0206817
$343$	−19.8981	−1.07439
$344$	96.5199	5.20400
$345$	−7.93960	−0.427454
$346$	38.2490	2.05628
$347$	−7.78858	−0.418113	−0.209056	−	0.977904i	$-0.567039\pi$
$347$	−7.78858	−0.418113	−0.209056	+	0.977904i	$0.567039\pi$
$348$	−17.9759	−0.963607
$349$	14.1668	0.758333	0.379166	−	0.925329i	$-0.376211\pi$
$349$	14.1668	0.758333	0.379166	+	0.925329i	$0.376211\pi$
$350$	15.5632	0.831887
$351$	−4.75298	−0.253695
$352$	11.2599	0.600154
$353$	−21.5699	−1.14805	−0.574025	−	0.818838i	$-0.694619\pi$
$353$	−21.5699	−1.14805	−0.574025	+	0.818838i	$0.694619\pi$
$354$	4.20987	0.223752
$355$	16.3438	0.867439
$356$	−8.30118	−0.439962
$357$	−6.69667	−0.354426
$358$	−17.8905	−0.945545
$359$	24.0299	1.26825	0.634126	−	0.773230i	$-0.281360\pi$
$359$	24.0299	1.26825	0.634126	+	0.773230i	$0.281360\pi$
$360$	40.1600	2.11662
$361$	−18.9970	−0.999843
$362$	−50.6109	−2.66005
$363$	7.75118	0.406832
$364$	−13.9934	−0.733454
$365$	9.10762	0.476715
$366$	12.4650	0.651557
$367$	14.9262	0.779140	0.389570	−	0.920997i	$-0.372624\pi$
$367$	14.9262	0.779140	0.389570	+	0.920997i	$0.372624\pi$
$368$	143.527	7.48186
$369$	−10.5106	−0.547158
$370$	13.8577	0.720426
$371$	4.85566	0.252093
$372$	15.6933	0.813661
$373$	−28.3534	−1.46809	−0.734043	−	0.679103i	$-0.762369\pi$
$373$	−28.3534	−1.46809	−0.734043	+	0.679103i	$0.762369\pi$
$374$	4.83811	0.250173
$375$	8.22127	0.424544
$376$	−17.6053	−0.907925
$377$	−5.19065	−0.267332
$378$	−21.5104	−1.10638
$379$	−9.20168	−0.472659	−0.236329	−	0.971673i	$-0.575944\pi$
$379$	−9.20168	−0.472659	−0.236329	+	0.971673i	$0.575944\pi$
$380$	0.474152	0.0243235
$381$	5.80689	0.297496
$382$	−61.5078	−3.14701
$383$	−1.17684	−0.0601340	−0.0300670	−	0.999548i	$-0.509572\pi$
$383$	−1.17684	−0.0601340	−0.0300670	+	0.999548i	$0.509572\pi$
$384$	56.0569	2.86064
$385$	−1.03143	−0.0525663
$386$	−12.1448	−0.618156
$387$	21.9656	1.11657
$388$	−89.2661	−4.53180
$389$	18.4675	0.936341	0.468170	−	0.883638i	$-0.344913\pi$
$389$	18.4675	0.936341	0.468170	+	0.883638i	$0.344913\pi$
$390$	−3.58026	−0.181294
$391$	36.3419	1.83789
$392$	34.7926	1.75729
$393$	−4.45293	−0.224621
$394$	22.0026	1.10848
$395$	−0.673023	−0.0338635
$396$	5.26510	0.264581
$397$	−1.93312	−0.0970206	−0.0485103	−	0.998823i	$-0.515447\pi$
$397$	−1.93312	−0.0970206	−0.0485103	+	0.998823i	$0.515447\pi$
$398$	28.0501	1.40602
$399$	−0.0761433	−0.00381193
$400$	−53.7502	−2.68751
$401$	−11.0825	−0.553435	−0.276718	−	0.960951i	$-0.589247\pi$
$401$	−11.0825	−0.553435	−0.276718	+	0.960951i	$0.589247\pi$
$402$	9.75931	0.486750
$403$	4.53155	0.225733
$404$	69.3720	3.45139
$405$	6.89446	0.342588
$406$	−23.4912	−1.16585
$407$	1.20054	0.0595085
$408$	37.5028	1.85667
$409$	−21.4708	−1.06166	−0.530831	−	0.847478i	$-0.678120\pi$
$409$	−21.4708	−1.06166	−0.530831	+	0.847478i	$0.678120\pi$
$410$	−17.4497	−0.861781
$411$	−8.67055	−0.427686
$412$	−36.2129	−1.78408
$413$	4.10809	0.202146
$414$	52.9642	2.60305
$415$	−9.44426	−0.463600
$416$	38.1401	1.86997
$417$	−3.64454	−0.178474
$418$	0.0550108	0.00269067
$419$	21.7035	1.06028	0.530142	−	0.847909i	$-0.322139\pi$
$419$	21.7035	1.06028	0.530142	+	0.847909i	$0.322139\pi$
$420$	−12.0991	−0.590377
$421$	32.4645	1.58222	0.791112	−	0.611672i	$-0.209503\pi$
$421$	32.4645	1.58222	0.791112	+	0.611672i	$0.209503\pi$
$422$	−6.30871	−0.307103
$423$	−4.00655	−0.194805
$424$	−27.1928	−1.32060
$425$	−13.6099	−0.660176
$426$	22.2433	1.07769
$427$	12.1636	0.588640
$428$	−72.9287	−3.52514
$429$	−0.310171	−0.0149752
$430$	36.4676	1.75862
$431$	−12.5580	−0.604899	−0.302450	−	0.953165i	$-0.597804\pi$
$431$	−12.5580	−0.604899	−0.302450	+	0.953165i	$0.597804\pi$
$432$	74.2901	3.57429
$433$	23.6638	1.13721	0.568605	−	0.822611i	$-0.307483\pi$
$433$	23.6638	1.13721	0.568605	+	0.822611i	$0.307483\pi$
$434$	20.5083	0.984430
$435$	−4.48799	−0.215183
$436$	25.8358	1.23731
$437$	0.413218	0.0197669
$438$	12.3951	0.592262
$439$	35.0646	1.67354	0.836772	−	0.547552i	$-0.184440\pi$
$439$	35.0646	1.67354	0.836772	+	0.547552i	$0.184440\pi$
$440$	5.77621	0.275370
$441$	7.91795	0.377045
$442$	16.3879	0.779493
$443$	39.9867	1.89983	0.949914	−	0.312512i	$-0.101171\pi$
$443$	39.9867	1.89983	0.949914	+	0.312512i	$0.101171\pi$
$444$	14.0829	0.668345
$445$	−2.07254	−0.0982476
$446$	26.0660	1.23426
$447$	−1.75342	−0.0829341
$448$	98.4208	4.64994
$449$	2.44205	0.115247	0.0576236	−	0.998338i	$-0.481648\pi$
$449$	2.44205	0.115247	0.0576236	+	0.998338i	$0.481648\pi$
$450$	−19.8349	−0.935025
$451$	−1.51173	−0.0711847
$452$	65.9291	3.10105
$453$	−11.6909	−0.549287
$454$	27.5684	1.29385
$455$	−3.49370	−0.163787
$456$	0.426419	0.0199689
$457$	−27.3523	−1.27949	−0.639743	−	0.768589i	$-0.720959\pi$
$457$	−27.3523	−1.27949	−0.639743	+	0.768589i	$0.720959\pi$
$458$	−63.5419	−2.96912
$459$	18.8107	0.878008
$460$	65.6602	3.06142
$461$	11.5598	0.538392	0.269196	−	0.963085i	$-0.413242\pi$
$461$	11.5598	0.538392	0.269196	+	0.963085i	$0.413242\pi$
$462$	−1.40373	−0.0653075
$463$	−1.42405	−0.0661812	−0.0330906	−	0.999452i	$-0.510535\pi$
$463$	−1.42405	−0.0661812	−0.0330906	+	0.999452i	$0.510535\pi$
$464$	81.1309	3.76641
$465$	3.91811	0.181698
$466$	−47.2234	−2.18758
$467$	−23.3856	−1.08216	−0.541078	−	0.840972i	$-0.681984\pi$
$467$	−23.3856	−1.08216	−0.541078	+	0.840972i	$0.681984\pi$
$468$	17.8342	0.824388
$469$	9.52336	0.439748
$470$	−6.65172	−0.306821
$471$	−8.46317	−0.389962
$472$	−23.0062	−1.05895
$473$	3.15931	0.145265
$474$	−0.915959	−0.0420714
$475$	−0.154748	−0.00710035
$476$	55.3812	2.53839
$477$	−6.18842	−0.283348
$478$	66.9233	3.06100
$479$	−2.47290	−0.112990	−0.0564949	−	0.998403i	$-0.517992\pi$
$479$	−2.47290	−0.112990	−0.0564949	+	0.998403i	$0.517992\pi$
$480$	32.9771	1.50519
$481$	4.06653	0.185418
$482$	56.3936	2.56866
$483$	−10.5443	−0.479780
$484$	−64.1019	−2.91372
$485$	−22.2868	−1.01199
$486$	42.3906	1.92288
$487$	−15.0426	−0.681648	−0.340824	−	0.940127i	$-0.610706\pi$
$487$	−15.0426	−0.681648	−0.340824	+	0.940127i	$0.610706\pi$
$488$	−68.1190	−3.08360
$489$	−7.80270	−0.352850
$490$	13.1455	0.593852
$491$	−33.8523	−1.52773	−0.763867	−	0.645374i	$-0.776701\pi$
$491$	−33.8523	−1.52773	−0.763867	+	0.645374i	$0.776701\pi$
$492$	−17.7334	−0.799482
$493$	20.5428	0.925202
$494$	0.186336	0.00838364
$495$	1.31453	0.0590835
$496$	−70.8291	−3.18032
$497$	21.7055	0.973626
$498$	−12.8533	−0.575969
$499$	−9.25799	−0.414445	−0.207222	−	0.978294i	$-0.566442\pi$
$499$	−9.25799	−0.414445	−0.207222	+	0.978294i	$0.566442\pi$
$500$	−67.9895	−3.04058
$501$	−2.05504	−0.0918123
$502$	17.8716	0.797648
$503$	25.3263	1.12924	0.564622	−	0.825350i	$-0.309022\pi$
$503$	25.3263	1.12924	0.564622	+	0.825350i	$0.309022\pi$
$504$	53.3348	2.37572
$505$	17.3200	0.770728
$506$	7.61784	0.338654
$507$	8.21808	0.364978
$508$	−48.0227	−2.13066
$509$	29.8873	1.32473	0.662365	−	0.749181i	$-0.269553\pi$
$509$	29.8873	1.32473	0.662365	+	0.749181i	$0.269553\pi$
$510$	14.1695	0.627435
$511$	12.0954	0.535071
$512$	−180.664	−7.98429
$513$	0.213884	0.00944319
$514$	80.9278	3.56957
$515$	−9.04119	−0.398402
$516$	37.0603	1.63149
$517$	−0.576261	−0.0253439
$518$	18.4038	0.808616
$519$	9.70475	0.425991
$520$	19.5655	0.858004
$521$	−29.8932	−1.30964	−0.654822	−	0.755783i	$-0.727256\pi$
$521$	−29.8932	−1.30964	−0.654822	+	0.755783i	$0.727256\pi$
$522$	29.9389	1.31039
$523$	45.0585	1.97027	0.985135	−	0.171782i	$-0.0549526\pi$
$523$	45.0585	1.97027	0.985135	+	0.171782i	$0.0549526\pi$
$524$	36.8256	1.60873
$525$	3.94878	0.172339
$526$	−53.8530	−2.34810
$527$	−17.9343	−0.781232
$528$	4.84804	0.210984
$529$	34.2221	1.48792
$530$	−10.2741	−0.446278
$531$	−5.23565	−0.227208
$532$	0.629702	0.0273010
$533$	−5.12062	−0.221799
$534$	−2.82064	−0.122061
$535$	−18.2079	−0.787198
$536$	−53.3329	−2.30363
$537$	−4.53929	−0.195885
$538$	−68.2251	−2.94139
$539$	1.13884	0.0490532
$540$	33.9860	1.46252
$541$	2.99309	0.128683	0.0643416	−	0.997928i	$-0.479505\pi$
$541$	2.99309	0.128683	0.0643416	+	0.997928i	$0.479505\pi$
$542$	−61.5779	−2.64500
$543$	−12.8413	−0.551072
$544$	−150.946	−6.47175
$545$	6.45037	0.276304
$546$	−4.75480	−0.203487
$547$	21.0750	0.901102	0.450551	−	0.892751i	$-0.351228\pi$
$547$	21.0750	0.901102	0.450551	+	0.892751i	$0.351228\pi$
$548$	71.7050	3.06309
$549$	−15.5023	−0.661620
$550$	−2.85285	−0.121646
$551$	0.233578	0.00995077
$552$	59.0501	2.51334
$553$	−0.893813	−0.0380088
$554$	−34.1313	−1.45010
$555$	3.51605	0.149248
$556$	30.1402	1.27823
$557$	−25.1023	−1.06362	−0.531809	−	0.846865i	$-0.678487\pi$
$557$	−25.1023	−1.06362	−0.531809	+	0.846865i	$0.678487\pi$
$558$	−26.1373	−1.10648
$559$	10.7014	0.452621
$560$	54.6073	2.30758
$561$	1.22755	0.0518273
$562$	−7.53319	−0.317768
$563$	4.11003	0.173217	0.0866085	−	0.996242i	$-0.472397\pi$
$563$	4.11003	0.173217	0.0866085	+	0.996242i	$0.472397\pi$
$564$	−6.75983	−0.284640
$565$	16.4604	0.692493
$566$	−22.4035	−0.941690
$567$	9.15623	0.384526
$568$	−121.556	−5.10036
$569$	12.7354	0.533896	0.266948	−	0.963711i	$-0.413985\pi$
$569$	12.7354	0.533896	0.266948	+	0.963711i	$0.413985\pi$
$570$	0.161111	0.00674821
$571$	−11.8239	−0.494817	−0.247408	−	0.968911i	$-0.579579\pi$
$571$	−11.8239	−0.494817	−0.247408	+	0.968911i	$0.579579\pi$
$572$	2.56510	0.107252
$573$	−15.6061	−0.651954
$574$	−23.1743	−0.967275
$575$	−21.4294	−0.893669
$576$	−125.435	−5.22645
$577$	−16.6739	−0.694144	−0.347072	−	0.937839i	$-0.612824\pi$
$577$	−16.6739	−0.694144	−0.347072	+	0.937839i	$0.612824\pi$
$578$	−17.0872	−0.710734
$579$	−3.08146	−0.128061
$580$	37.1155	1.54114
$581$	−12.5425	−0.520351
$582$	−30.3316	−1.25728
$583$	−0.890080	−0.0368633
$584$	−67.7371	−2.80298
$585$	4.45263	0.184094
$586$	6.82570	0.281967
$587$	17.7420	0.732292	0.366146	−	0.930557i	$-0.380677\pi$
$587$	17.7420	0.732292	0.366146	+	0.930557i	$0.380677\pi$
$588$	13.3591	0.550921
$589$	−0.203919	−0.00840234
$590$	−8.69229	−0.357856
$591$	5.58263	0.229639
$592$	−63.5607	−2.61233
$593$	34.3335	1.40991	0.704955	−	0.709252i	$-0.250967\pi$
$593$	34.3335	1.40991	0.704955	+	0.709252i	$0.250967\pi$
$594$	3.94303	0.161784
$595$	13.8269	0.566847
$596$	14.5007	0.593973
$597$	7.11702	0.291280
$598$	25.8036	1.05519
$599$	35.4745	1.44945	0.724725	−	0.689039i	$-0.241967\pi$
$599$	35.4745	1.44945	0.724725	+	0.689039i	$0.241967\pi$
$600$	−22.1140	−0.902801
$601$	34.1037	1.39112	0.695558	−	0.718469i	$-0.255157\pi$
$601$	34.1037	1.39112	0.695558	+	0.718469i	$0.255157\pi$
$602$	48.4310	1.97390
$603$	−12.1373	−0.494268
$604$	96.6833	3.93399
$605$	−16.0042	−0.650662
$606$	23.5718	0.957539
$607$	17.2822	0.701463	0.350731	−	0.936476i	$-0.385933\pi$
$607$	17.2822	0.701463	0.350731	+	0.936476i	$0.385933\pi$
$608$	−1.71630	−0.0696052
$609$	−5.96031	−0.241524
$610$	−25.7370	−1.04206
$611$	−1.95195	−0.0789672
$612$	−70.5819	−2.85311
$613$	−31.9696	−1.29124	−0.645620	−	0.763658i	$-0.723401\pi$
$613$	−31.9696	−1.29124	−0.645620	+	0.763658i	$0.723401\pi$
$614$	0.0324076	0.00130787
$615$	−4.42745	−0.178532
$616$	7.67114	0.309079
$617$	5.33907	0.214943	0.107471	−	0.994208i	$-0.465725\pi$
$617$	5.33907	0.214943	0.107471	+	0.994208i	$0.465725\pi$
$618$	−12.3047	−0.494969
$619$	9.10747	0.366060	0.183030	−	0.983107i	$-0.441409\pi$
$619$	9.10747	0.366060	0.183030	+	0.983107i	$0.441409\pi$
$620$	−32.4026	−1.30132
$621$	29.6184	1.18855
$622$	30.6286	1.22809
$623$	−2.75245	−0.110274
$624$	16.4215	0.657388
$625$	−2.81036	−0.112414
$626$	−79.6071	−3.18174
$627$	0.0139576	0.000557415 0
$628$	69.9900	2.79291
$629$	−16.0940	−0.641708
$630$	20.1512	0.802842
$631$	33.5007	1.33364	0.666820	−	0.745219i	$-0.267655\pi$
$631$	33.5007	1.33364	0.666820	+	0.745219i	$0.267655\pi$
$632$	5.00555	0.199110
$633$	−1.60068	−0.0636214
$634$	77.6983	3.08579
$635$	−11.9897	−0.475797
$636$	−10.4411	−0.414016
$637$	3.85753	0.152841
$638$	4.30611	0.170480
$639$	−27.6631	−1.09434
$640$	−115.743	−4.57514
$641$	6.76452	0.267183	0.133591	−	0.991037i	$-0.457349\pi$
$641$	6.76452	0.267183	0.133591	+	0.991037i	$0.457349\pi$
$642$	−24.7803	−0.978002
$643$	24.3056	0.958519	0.479259	−	0.877673i	$-0.340905\pi$
$643$	24.3056	0.958519	0.479259	+	0.877673i	$0.340905\pi$
$644$	87.2005	3.43618
$645$	9.25275	0.364327
$646$	−0.737453	−0.0290147
$647$	35.2819	1.38707	0.693537	−	0.720421i	$-0.256052\pi$
$647$	35.2819	1.38707	0.693537	+	0.720421i	$0.256052\pi$
$648$	−51.2769	−2.01435
$649$	−0.753044	−0.0295595
$650$	−9.66333	−0.379027
$651$	5.20348	0.203941
$652$	64.5279	2.52711
$653$	4.98327	0.195010	0.0975051	−	0.995235i	$-0.468914\pi$
$653$	4.98327	0.195010	0.0975051	+	0.995235i	$0.468914\pi$
$654$	8.77872	0.343275
$655$	9.19415	0.359245
$656$	80.0364	3.12490
$657$	−15.4153	−0.601410
$658$	−8.83386	−0.344380
$659$	−7.54480	−0.293904	−0.146952	−	0.989144i	$-0.546946\pi$
$659$	−7.54480	−0.293904	−0.146952	+	0.989144i	$0.546946\pi$
$660$	2.21786	0.0863302
$661$	−2.83729	−0.110358	−0.0551789	−	0.998476i	$-0.517573\pi$
$661$	−2.83729	−0.110358	−0.0551789	+	0.998476i	$0.517573\pi$
$662$	−83.3441	−3.23926
$663$	4.15803	0.161485
$664$	70.2408	2.72587
$665$	0.157216	0.00609658
$666$	−23.4552	−0.908869
$667$	32.3457	1.25243
$668$	16.9951	0.657559
$669$	6.61360	0.255697
$670$	−20.1504	−0.778480
$671$	−2.22969	−0.0860761
$672$	43.7955	1.68945
$673$	−23.7746	−0.916444	−0.458222	−	0.888838i	$-0.651514\pi$
$673$	−23.7746	−0.916444	−0.458222	+	0.888838i	$0.651514\pi$
$674$	−27.2292	−1.04883
$675$	−11.0920	−0.426930
$676$	−67.9631	−2.61397
$677$	−2.24261	−0.0861903	−0.0430952	−	0.999071i	$-0.513722\pi$
$677$	−2.24261	−0.0861903	−0.0430952	+	0.999071i	$0.513722\pi$
$678$	22.4019	0.860342
$679$	−29.5982	−1.13588
$680$	−77.4336	−2.96944
$681$	6.99481	0.268042
$682$	−3.75933	−0.143952
$683$	9.17124	0.350928	0.175464	−	0.984486i	$-0.443857\pi$
$683$	9.17124	0.350928	0.175464	+	0.984486i	$0.443857\pi$
$684$	−0.802539	−0.0306858
$685$	17.9024	0.684016
$686$	55.9143	2.13482
$687$	−16.1222	−0.615101
$688$	−167.265	−6.37692
$689$	−3.01493	−0.114860
$690$	22.3106	0.849348
$691$	6.24835	0.237698	0.118849	−	0.992912i	$-0.462079\pi$
$691$	6.24835	0.237698	0.118849	+	0.992912i	$0.462079\pi$
$692$	−80.2578	−3.05095
$693$	1.74577	0.0663162
$694$	21.8862	0.830788
$695$	7.52503	0.285441
$696$	33.3790	1.26523
$697$	20.2657	0.767618
$698$	−39.8093	−1.50680
$699$	−11.9818	−0.453193
$700$	−32.6562	−1.23429
$701$	18.3346	0.692490	0.346245	−	0.938144i	$-0.387457\pi$
$701$	18.3346	0.692490	0.346245	+	0.938144i	$0.387457\pi$
$702$	13.3560	0.504091
$703$	−0.182993	−0.00690172
$704$	−18.0413	−0.679956
$705$	−1.68771	−0.0635629
$706$	60.6122	2.28117
$707$	23.0019	0.865075
$708$	−8.83357	−0.331986
$709$	37.7846	1.41903	0.709516	−	0.704689i	$-0.248914\pi$
$709$	37.7846	1.41903	0.709516	+	0.704689i	$0.248914\pi$
$710$	−45.9267	−1.72360
$711$	1.13914	0.0427212
$712$	15.4143	0.577675
$713$	−28.2385	−1.05754
$714$	18.8179	0.704242
$715$	0.640422	0.0239504
$716$	37.5397	1.40293
$717$	16.9802	0.634136
$718$	−67.5249	−2.52001
$719$	3.06554	0.114325	0.0571626	−	0.998365i	$-0.481795\pi$
$719$	3.06554	0.114325	0.0571626	+	0.998365i	$0.481795\pi$
$720$	−69.5956	−2.59368
$721$	−12.0072	−0.447172
$722$	53.3823	1.98668
$723$	14.3085	0.532139
$724$	106.197	3.94677
$725$	−12.1133	−0.449878
$726$	−21.7811	−0.808372
$727$	−13.0427	−0.483727	−0.241864	−	0.970310i	$-0.577759\pi$
$727$	−13.0427	−0.483727	−0.241864	+	0.970310i	$0.577759\pi$
$728$	25.9841	0.963035
$729$	−3.29454	−0.122020
$730$	−25.5927	−0.947229
$731$	−42.3525	−1.56646
$732$	−26.1553	−0.966729
$733$	−11.4835	−0.424153	−0.212077	−	0.977253i	$-0.568023\pi$
$733$	−11.4835	−0.424153	−0.212077	+	0.977253i	$0.568023\pi$
$734$	−41.9430	−1.54815
$735$	3.33534	0.123026
$736$	−237.672	−8.76070
$737$	−1.74570	−0.0643038
$738$	29.5350	1.08720
$739$	42.3651	1.55843	0.779214	−	0.626758i	$-0.215619\pi$
$739$	42.3651	1.55843	0.779214	+	0.626758i	$0.215619\pi$
$740$	−29.0775	−1.06891
$741$	0.0472781	0.00173680
$742$	−13.6446	−0.500908
$743$	5.94491	0.218098	0.109049	−	0.994036i	$-0.465219\pi$
$743$	5.94491	0.218098	0.109049	+	0.994036i	$0.465219\pi$
$744$	−29.1406	−1.06835
$745$	3.62036	0.132640
$746$	79.6741	2.91708
$747$	15.9851	0.584865
$748$	−10.1518	−0.371186
$749$	−24.1812	−0.883562
$750$	−23.1020	−0.843567
$751$	−17.4577	−0.637040	−0.318520	−	0.947916i	$-0.603186\pi$
$751$	−17.4577	−0.637040	−0.318520	+	0.947916i	$0.603186\pi$
$752$	30.5093	1.11256
$753$	4.53448	0.165246
$754$	14.5859	0.531187
$755$	24.1387	0.878497
$756$	45.1353	1.64156
$757$	14.9130	0.542023	0.271012	−	0.962576i	$-0.412642\pi$
$757$	14.9130	0.542023	0.271012	+	0.962576i	$0.412642\pi$
$758$	25.8570	0.939170
$759$	1.93284	0.0701577
$760$	−0.880444	−0.0319371
$761$	−5.92628	−0.214828	−0.107414	−	0.994214i	$-0.534257\pi$
$761$	−5.92628	−0.214828	−0.107414	+	0.994214i	$0.534257\pi$
$762$	−16.3176	−0.591123
$763$	8.56647	0.310127
$764$	129.062	4.66929
$765$	−17.6220	−0.637126
$766$	3.30697	0.119486
$767$	−2.55075	−0.0921023
$768$	−85.7367	−3.09376
$769$	−1.38975	−0.0501155	−0.0250578	−	0.999686i	$-0.507977\pi$
$769$	−1.38975	−0.0501155	−0.0250578	+	0.999686i	$0.507977\pi$
$770$	2.89834	0.104449
$771$	20.5334	0.739494
$772$	25.4835	0.917172
$773$	46.1485	1.65985	0.829924	−	0.557877i	$-0.188384\pi$
$773$	46.1485	1.65985	0.829924	+	0.557877i	$0.188384\pi$
$774$	−61.7241	−2.21863
$775$	10.5752	0.379873
$776$	165.756	5.95031
$777$	4.66951	0.167518
$778$	−51.8944	−1.86050
$779$	0.230427	0.00825592
$780$	7.51247	0.268989
$781$	−3.97879	−0.142372
$782$	−102.122	−3.65187
$783$	16.7423	0.598320
$784$	−60.2941	−2.15336
$785$	17.4742	0.623682
$786$	12.5129	0.446320
$787$	−17.3371	−0.618002	−0.309001	−	0.951062i	$-0.599995\pi$
$787$	−17.3371	−0.618002	−0.309001	+	0.951062i	$0.599995\pi$
$788$	−46.1681	−1.64467
$789$	−13.6639	−0.486447
$790$	1.89122	0.0672865
$791$	21.8603	0.777263
$792$	−9.77667	−0.347399
$793$	−7.55252	−0.268198
$794$	5.43214	0.192779
$795$	−2.60680	−0.0924536
$796$	−58.8575	−2.08615
$797$	45.9843	1.62885	0.814424	−	0.580270i	$-0.197053\pi$
$797$	45.9843	1.62885	0.814424	+	0.580270i	$0.197053\pi$
$798$	0.213965	0.00757429
$799$	7.72514	0.273296
$800$	89.0070	3.14687
$801$	3.50792	0.123946
$802$	31.1423	1.09967
$803$	−2.21719	−0.0782428
$804$	−20.4780	−0.722202
$805$	21.7711	0.767332
$806$	−12.7338	−0.448529
$807$	−17.3104	−0.609357
$808$	−128.816	−4.53172
$809$	−13.3983	−0.471060	−0.235530	−	0.971867i	$-0.575683\pi$
$809$	−13.3983	−0.471060	−0.235530	+	0.971867i	$0.575683\pi$
$810$	−19.3737	−0.680721
$811$	32.7045	1.14841	0.574205	−	0.818712i	$-0.305311\pi$
$811$	32.7045	1.14841	0.574205	+	0.818712i	$0.305311\pi$
$812$	49.2915	1.72979
$813$	−15.6239	−0.547954
$814$	−3.37355	−0.118243
$815$	16.1105	0.564328
$816$	−64.9909	−2.27514
$817$	−0.481561	−0.0168477
$818$	60.3336	2.10952
$819$	5.91335	0.206629
$820$	36.6148	1.27864
$821$	27.1013	0.945843	0.472921	−	0.881105i	$-0.343199\pi$
$821$	27.1013	0.945843	0.472921	+	0.881105i	$0.343199\pi$
$822$	24.3645	0.849811
$823$	6.48435	0.226030	0.113015	−	0.993593i	$-0.463949\pi$
$823$	6.48435	0.226030	0.113015	+	0.993593i	$0.463949\pi$
$824$	67.2431	2.34252
$825$	−0.723841	−0.0252009
$826$	−11.5439	−0.401662
$827$	25.8867	0.900170	0.450085	−	0.892986i	$-0.351394\pi$
$827$	25.8867	0.900170	0.450085	+	0.892986i	$0.351394\pi$
$828$	−111.135	−3.86220
$829$	−39.8078	−1.38258	−0.691291	−	0.722576i	$-0.742958\pi$
$829$	−39.8078	−1.38258	−0.691291	+	0.722576i	$0.742958\pi$
$830$	26.5387	0.921171
$831$	−8.65997	−0.300411
$832$	−61.1104	−2.11862
$833$	−15.2668	−0.528964
$834$	10.2413	0.354627
$835$	4.24312	0.146839
$836$	−0.115429	−0.00399220
$837$	−14.6164	−0.505216
$838$	−60.9875	−2.10678
$839$	−2.04513	−0.0706057	−0.0353028	−	0.999377i	$-0.511240\pi$
$839$	−2.04513	−0.0706057	−0.0353028	+	0.999377i	$0.511240\pi$
$840$	22.4666	0.775173
$841$	−10.7161	−0.369519
$842$	−91.2264	−3.14387
$843$	−1.91136	−0.0658308
$844$	13.2376	0.455656
$845$	−16.9682	−0.583724
$846$	11.2585	0.387076
$847$	−21.2545	−0.730312
$848$	47.1240	1.61824
$849$	−5.68434	−0.195086
$850$	38.2442	1.31177
$851$	−25.3407	−0.868670
$852$	−46.6731	−1.59900
$853$	−3.45008	−0.118128	−0.0590642	−	0.998254i	$-0.518812\pi$
$853$	−3.45008	−0.118128	−0.0590642	+	0.998254i	$0.518812\pi$
$854$	−34.1802	−1.16962
$855$	−0.200368	−0.00685244
$856$	135.420	4.62856
$857$	34.6538	1.18375	0.591876	−	0.806029i	$-0.298387\pi$
$857$	34.6538	1.18375	0.591876	+	0.806029i	$0.298387\pi$
$858$	0.871591	0.0297556
$859$	−20.2761	−0.691810	−0.345905	−	0.938269i	$-0.612428\pi$
$859$	−20.2761	−0.691810	−0.345905	+	0.938269i	$0.612428\pi$
$860$	−76.5198	−2.60930
$861$	−5.87990	−0.200387
$862$	35.2885	1.20193
$863$	9.75541	0.332078	0.166039	−	0.986119i	$-0.446902\pi$
$863$	9.75541	0.332078	0.166039	+	0.986119i	$0.446902\pi$
$864$	−123.020	−4.18522
$865$	−20.0378	−0.681305
$866$	−66.4961	−2.25963
$867$	−4.33546	−0.147240
$868$	−43.0326	−1.46062
$869$	0.163843	0.00555798
$870$	12.6114	0.427567
$871$	−5.91314	−0.200359
$872$	−47.9741	−1.62461
$873$	37.7222	1.27670
$874$	−1.16116	−0.0392767
$875$	−22.5435	−0.762109
$876$	−26.0087	−0.878752
$877$	−55.0888	−1.86022	−0.930109	−	0.367284i	$-0.880288\pi$
$877$	−55.0888	−1.86022	−0.930109	+	0.367284i	$0.880288\pi$
$878$	−98.5328	−3.32532
$879$	1.73186	0.0584140
$880$	−10.0099	−0.337435
$881$	−50.0595	−1.68655	−0.843273	−	0.537485i	$-0.819375\pi$
$881$	−50.0595	−1.68655	−0.843273	+	0.537485i	$0.819375\pi$
$882$	−22.2497	−0.749186
$883$	−6.12297	−0.206054	−0.103027	−	0.994679i	$-0.532853\pi$
$883$	−6.12297	−0.206054	−0.103027	+	0.994679i	$0.532853\pi$
$884$	−34.3867	−1.15655
$885$	−2.20546	−0.0741356
$886$	−112.364	−3.77495
$887$	16.4725	0.553094	0.276547	−	0.961000i	$-0.410810\pi$
$887$	16.4725	0.553094	0.276547	+	0.961000i	$0.410810\pi$
$888$	−26.1503	−0.877546
$889$	−15.9230	−0.534041
$890$	5.82390	0.195217
$891$	−1.67841	−0.0562288
$892$	−54.6942	−1.83130
$893$	0.0878373	0.00293936
$894$	4.92718	0.164790
$895$	9.37245	0.313287
$896$	−153.713	−5.13520
$897$	6.54703	0.218599
$898$	−6.86223	−0.228996
$899$	−15.9623	−0.532372
$900$	41.6195	1.38732
$901$	11.9321	0.397515
$902$	4.24802	0.141444
$903$	12.2882	0.408925
$904$	−122.423	−4.07171
$905$	26.5139	0.881352
$906$	32.8519	1.09143
$907$	−44.1853	−1.46715	−0.733574	−	0.679609i	$-0.762149\pi$
$907$	−44.1853	−1.46715	−0.733574	+	0.679609i	$0.762149\pi$
$908$	−57.8468	−1.91971
$909$	−29.3153	−0.972328
$910$	9.81742	0.325444
$911$	56.0612	1.85739	0.928695	−	0.370844i	$-0.120931\pi$
$911$	56.0612	1.85739	0.928695	+	0.370844i	$0.120931\pi$
$912$	−0.738967	−0.0244696
$913$	2.29914	0.0760904
$914$	76.8609	2.54233
$915$	−6.53014	−0.215880
$916$	133.330	4.40534
$917$	12.2104	0.403222
$918$	−52.8587	−1.74460
$919$	−40.8237	−1.34665	−0.673325	−	0.739346i	$-0.735135\pi$
$919$	−40.8237	−1.34665	−0.673325	+	0.739346i	$0.735135\pi$
$920$	−121.923	−4.01969
$921$	0.00822264	0.000270945 0
$922$	−32.4833	−1.06978
$923$	−13.4772	−0.443606
$924$	2.94545	0.0968981
$925$	9.49000	0.312029
$926$	4.00163	0.131502
$927$	15.3029	0.502613
$928$	−134.348	−4.41018
$929$	25.5732	0.839031	0.419516	−	0.907748i	$-0.362200\pi$
$929$	25.5732	0.839031	0.419516	+	0.907748i	$0.362200\pi$
$930$	−11.0100	−0.361033
$931$	−0.173588	−0.00568913
$932$	99.0888	3.24576
$933$	7.77126	0.254420
$934$	65.7144	2.15024
$935$	−2.53457	−0.0828894
$936$	−33.1161	−1.08243
$937$	−29.0170	−0.947944	−0.473972	−	0.880540i	$-0.657180\pi$
$937$	−29.0170	−0.947944	−0.473972	+	0.880540i	$0.657180\pi$
$938$	−26.7610	−0.873776
$939$	−20.1983	−0.659148
$940$	13.9573	0.455237
$941$	−21.5930	−0.703913	−0.351956	−	0.936016i	$-0.614483\pi$
$941$	−21.5930	−0.703913	−0.351956	+	0.936016i	$0.614483\pi$
$942$	23.7818	0.774853
$943$	31.9094	1.03911
$944$	39.8688	1.29762
$945$	11.2688	0.366575
$946$	−8.87777	−0.288641
$947$	45.5580	1.48044	0.740218	−	0.672367i	$-0.234722\pi$
$947$	45.5580	1.48044	0.740218	+	0.672367i	$0.234722\pi$
$948$	1.92196	0.0624222
$949$	−7.51018	−0.243791
$950$	0.434848	0.0141083
$951$	19.7140	0.639271
$952$	−102.836	−3.33294
$953$	−57.7839	−1.87180	−0.935902	−	0.352261i	$-0.885413\pi$
$953$	−57.7839	−1.87180	−0.935902	+	0.352261i	$0.885413\pi$
$954$	17.3897	0.563011
$955$	32.2225	1.04270
$956$	−140.425	−4.54167
$957$	1.09257	0.0353178
$958$	6.94894	0.224510
$959$	23.7754	0.767749
$960$	−52.8379	−1.70534
$961$	−17.0646	−0.550470
$962$	−11.4271	−0.368424
$963$	30.8183	0.993107
$964$	−118.331	−3.81117
$965$	6.36241	0.204813
$966$	29.6297	0.953320
$967$	−28.2883	−0.909691	−0.454845	−	0.890570i	$-0.650306\pi$
$967$	−28.2883	−0.909691	−0.454845	+	0.890570i	$0.650306\pi$
$968$	119.030	3.82576
$969$	−0.187111	−0.00601086
$970$	62.6268	2.01083
$971$	16.4125	0.526701	0.263350	−	0.964700i	$-0.415172\pi$
$971$	16.4125	0.526701	0.263350	+	0.964700i	$0.415172\pi$
$972$	−88.9481	−2.85301
$973$	9.99367	0.320382
$974$	42.2704	1.35443
$975$	−2.45183	−0.0785215
$976$	118.048	3.77861
$977$	25.4787	0.815135	0.407568	−	0.913175i	$-0.366377\pi$
$977$	25.4787	0.815135	0.407568	+	0.913175i	$0.366377\pi$
$978$	21.9258	0.701111
$979$	0.504544	0.0161253
$980$	−27.5831	−0.881110
$981$	−10.9177	−0.348577
$982$	95.1261	3.03560
$983$	16.3739	0.522248	0.261124	−	0.965305i	$-0.415907\pi$
$983$	16.3739	0.522248	0.261124	+	0.965305i	$0.415907\pi$
$984$	32.9287	1.04973
$985$	−11.5267	−0.367271
$986$	−57.7260	−1.83837
$987$	−2.24138	−0.0713438
$988$	−0.390988	−0.0124390
$989$	−66.6862	−2.12050
$990$	−3.69386	−0.117399
$991$	14.1922	0.450831	0.225415	−	0.974263i	$-0.427626\pi$
$991$	14.1922	0.450831	0.225415	+	0.974263i	$0.427626\pi$
$992$	117.289	3.72392
$993$	−21.1465	−0.671065
$994$	−60.9933	−1.93459
$995$	−14.6948	−0.465856
$996$	26.9700	0.854578
$997$	2.92078	0.0925019	0.0462510	−	0.998930i	$-0.485273\pi$
$997$	2.92078	0.0925019	0.0462510	+	0.998930i	$0.485273\pi$
$998$	26.0153	0.823499
$999$	−13.1165	−0.414987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.1	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.1	✓	182	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.81003 q^{2} -0.712978 q^{3} +5.89629 q^{4} +1.47211 q^{5} +2.00349 q^{6} +1.95505 q^{7} -10.9487 q^{8} -2.49166 q^{9} +O(q^{10})\)	\(q-2.81003 q^{2} -0.712978 q^{3} +5.89629 q^{4} +1.47211 q^{5} +2.00349 q^{6} +1.95505 q^{7} -10.9487 q^{8} -2.49166 q^{9} -4.13669 q^{10} -0.358376 q^{11} -4.20392 q^{12} -1.21391 q^{13} -5.49376 q^{14} -1.04958 q^{15} +18.9737 q^{16} +4.80425 q^{17} +7.00166 q^{18} +0.0546258 q^{19} +8.68001 q^{20} -1.39391 q^{21} +1.00705 q^{22} +7.56453 q^{23} +7.80619 q^{24} -2.83288 q^{25} +3.41113 q^{26} +3.91543 q^{27} +11.5276 q^{28} +4.27597 q^{29} +2.94937 q^{30} -3.73302 q^{31} -31.4192 q^{32} +0.255514 q^{33} -13.5001 q^{34} +2.87806 q^{35} -14.6916 q^{36} -3.34994 q^{37} -0.153500 q^{38} +0.865491 q^{39} -16.1177 q^{40} +4.21829 q^{41} +3.91693 q^{42} -8.81564 q^{43} -2.11309 q^{44} -3.66801 q^{45} -21.2566 q^{46} +1.60798 q^{47} -13.5278 q^{48} -3.17778 q^{49} +7.96050 q^{50} -3.42532 q^{51} -7.15757 q^{52} +2.48365 q^{53} -11.0025 q^{54} -0.527570 q^{55} -21.4053 q^{56} -0.0389470 q^{57} -12.0156 q^{58} +2.10127 q^{59} -6.18865 q^{60} +6.22165 q^{61} +10.4899 q^{62} -4.87133 q^{63} +50.3418 q^{64} -1.78701 q^{65} -0.718003 q^{66} +4.87115 q^{67} +28.3272 q^{68} -5.39334 q^{69} -8.08744 q^{70} +11.1023 q^{71} +27.2805 q^{72} +6.18677 q^{73} +9.41346 q^{74} +2.01978 q^{75} +0.322090 q^{76} -0.700643 q^{77} -2.43206 q^{78} -0.457182 q^{79} +27.9314 q^{80} +4.68337 q^{81} -11.8535 q^{82} -6.41544 q^{83} -8.21888 q^{84} +7.07239 q^{85} +24.7723 q^{86} -3.04867 q^{87} +3.92375 q^{88} -1.40786 q^{89} +10.3072 q^{90} -2.37326 q^{91} +44.6027 q^{92} +2.66156 q^{93} -4.51848 q^{94} +0.0804153 q^{95} +22.4012 q^{96} -15.1394 q^{97} +8.92966 q^{98} +0.892951 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * q^99

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