LMFDB - Embedded newform 4730.2.a.bb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 22 x^{9} + 21 x^{8} + 165 x^{7} - 130 x^{6} - 535 x^{5} + 323 x^{4} + 710 x^{3} + \cdots + 128 $ x^11 - x^10 - 22x^9 + 21x^8 + 165x^7 - 130x^6 - 535x^5 + 323x^4 + 710x^3 - 343x^2 - 261*x + 128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.78036$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.78036 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.78036 q^{6} -2.23633 q^{7} -1.00000 q^{8} +4.73038 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.78036 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.78036 q^{6} -2.23633 q^{7} -1.00000 q^{8} +4.73038 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.78036 q^{12} +6.07518 q^{13} +2.23633 q^{14} +2.78036 q^{15} +1.00000 q^{16} -2.92626 q^{17} -4.73038 q^{18} +3.18904 q^{19} -1.00000 q^{20} +6.21781 q^{21} +1.00000 q^{22} +4.07518 q^{23} +2.78036 q^{24} +1.00000 q^{25} -6.07518 q^{26} -4.81108 q^{27} -2.23633 q^{28} -1.19176 q^{29} -2.78036 q^{30} +9.94427 q^{31} -1.00000 q^{32} +2.78036 q^{33} +2.92626 q^{34} +2.23633 q^{35} +4.73038 q^{36} -7.90048 q^{37} -3.18904 q^{38} -16.8912 q^{39} +1.00000 q^{40} +0.260470 q^{41} -6.21781 q^{42} +1.00000 q^{43} -1.00000 q^{44} -4.73038 q^{45} -4.07518 q^{46} +4.67376 q^{47} -2.78036 q^{48} -1.99881 q^{49} -1.00000 q^{50} +8.13606 q^{51} +6.07518 q^{52} -7.82089 q^{53} +4.81108 q^{54} +1.00000 q^{55} +2.23633 q^{56} -8.86666 q^{57} +1.19176 q^{58} -0.284247 q^{59} +2.78036 q^{60} +9.70548 q^{61} -9.94427 q^{62} -10.5787 q^{63} +1.00000 q^{64} -6.07518 q^{65} -2.78036 q^{66} +4.43505 q^{67} -2.92626 q^{68} -11.3304 q^{69} -2.23633 q^{70} +0.755828 q^{71} -4.73038 q^{72} -14.1030 q^{73} +7.90048 q^{74} -2.78036 q^{75} +3.18904 q^{76} +2.23633 q^{77} +16.8912 q^{78} -0.0896609 q^{79} -1.00000 q^{80} -0.814626 q^{81} -0.260470 q^{82} -1.36880 q^{83} +6.21781 q^{84} +2.92626 q^{85} -1.00000 q^{86} +3.31352 q^{87} +1.00000 q^{88} -0.566497 q^{89} +4.73038 q^{90} -13.5861 q^{91} +4.07518 q^{92} -27.6486 q^{93} -4.67376 q^{94} -3.18904 q^{95} +2.78036 q^{96} -9.83384 q^{97} +1.99881 q^{98} -4.73038 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * 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
$3$	−2.78036	−1.60524	−0.802620	−	0.596491i	$-0.796561\pi$
$3$	−2.78036	−1.60524	−0.802620	+	0.596491i	$0.796561\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.78036	1.13508
$7$	−2.23633	−0.845255	−0.422628	−	0.906303i	$-0.638892\pi$
$7$	−2.23633	−0.845255	−0.422628	+	0.906303i	$0.638892\pi$
$8$	−1.00000	−0.353553
$9$	4.73038	1.57679
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.78036	−0.802620
$13$	6.07518	1.68495	0.842475	−	0.538735i	$-0.181098\pi$
$13$	6.07518	1.68495	0.842475	+	0.538735i	$0.181098\pi$
$14$	2.23633	0.597686
$15$	2.78036	0.717885
$16$	1.00000	0.250000
$17$	−2.92626	−0.709723	−0.354862	−	0.934919i	$-0.615472\pi$
$17$	−2.92626	−0.709723	−0.354862	+	0.934919i	$0.615472\pi$
$18$	−4.73038	−1.11496
$19$	3.18904	0.731616	0.365808	−	0.930690i	$-0.380793\pi$
$19$	3.18904	0.731616	0.365808	+	0.930690i	$0.380793\pi$
$20$	−1.00000	−0.223607
$21$	6.21781	1.35684
$22$	1.00000	0.213201
$23$	4.07518	0.849733	0.424866	−	0.905256i	$-0.360321\pi$
$23$	4.07518	0.849733	0.424866	+	0.905256i	$0.360321\pi$
$24$	2.78036	0.567538
$25$	1.00000	0.200000
$26$	−6.07518	−1.19144
$27$	−4.81108	−0.925893
$28$	−2.23633	−0.422628
$29$	−1.19176	−0.221304	−0.110652	−	0.993859i	$-0.535294\pi$
$29$	−1.19176	−0.221304	−0.110652	+	0.993859i	$0.535294\pi$
$30$	−2.78036	−0.507621
$31$	9.94427	1.78604	0.893022	−	0.450013i	$-0.148581\pi$
$31$	9.94427	1.78604	0.893022	+	0.450013i	$0.148581\pi$
$32$	−1.00000	−0.176777
$33$	2.78036	0.483998
$34$	2.92626	0.501850
$35$	2.23633	0.378010
$36$	4.73038	0.788397
$37$	−7.90048	−1.29883	−0.649415	−	0.760434i	$-0.724986\pi$
$37$	−7.90048	−1.29883	−0.649415	+	0.760434i	$0.724986\pi$
$38$	−3.18904	−0.517330
$39$	−16.8912	−2.70475
$40$	1.00000	0.158114
$41$	0.260470	0.0406785	0.0203393	−	0.999793i	$-0.493525\pi$
$41$	0.260470	0.0406785	0.0203393	+	0.999793i	$0.493525\pi$
$42$	−6.21781	−0.959429
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	−4.73038	−0.705164
$46$	−4.07518	−0.600852
$47$	4.67376	0.681738	0.340869	−	0.940111i	$-0.389279\pi$
$47$	4.67376	0.681738	0.340869	+	0.940111i	$0.389279\pi$
$48$	−2.78036	−0.401310
$49$	−1.99881	−0.285544
$50$	−1.00000	−0.141421
$51$	8.13606	1.13928
$52$	6.07518	0.842475
$53$	−7.82089	−1.07428	−0.537141	−	0.843493i	$-0.680496\pi$
$53$	−7.82089	−1.07428	−0.537141	+	0.843493i	$0.680496\pi$
$54$	4.81108	0.654705
$55$	1.00000	0.134840
$56$	2.23633	0.298843
$57$	−8.86666	−1.17442
$58$	1.19176	0.156486
$59$	−0.284247	−0.0370059	−0.0185029	−	0.999829i	$-0.505890\pi$
$59$	−0.284247	−0.0370059	−0.0185029	+	0.999829i	$0.505890\pi$
$60$	2.78036	0.358942
$61$	9.70548	1.24266	0.621330	−	0.783549i	$-0.286593\pi$
$61$	9.70548	1.24266	0.621330	+	0.783549i	$0.286593\pi$
$62$	−9.94427	−1.26292
$63$	−10.5787	−1.33279
$64$	1.00000	0.125000
$65$	−6.07518	−0.753533
$66$	−2.78036	−0.342238
$67$	4.43505	0.541827	0.270914	−	0.962604i	$-0.412674\pi$
$67$	4.43505	0.541827	0.270914	+	0.962604i	$0.412674\pi$
$68$	−2.92626	−0.354862
$69$	−11.3304	−1.36402
$70$	−2.23633	−0.267293
$71$	0.755828	0.0897003	0.0448501	−	0.998994i	$-0.485719\pi$
$71$	0.755828	0.0897003	0.0448501	+	0.998994i	$0.485719\pi$
$72$	−4.73038	−0.557481
$73$	−14.1030	−1.65063	−0.825317	−	0.564670i	$-0.809004\pi$
$73$	−14.1030	−1.65063	−0.825317	+	0.564670i	$0.809004\pi$
$74$	7.90048	0.918412
$75$	−2.78036	−0.321048
$76$	3.18904	0.365808
$77$	2.23633	0.254854
$78$	16.8912	1.91255
$79$	−0.0896609	−0.0100876	−0.00504382	−	0.999987i	$-0.501606\pi$
$79$	−0.0896609	−0.0100876	−0.00504382	+	0.999987i	$0.501606\pi$
$80$	−1.00000	−0.111803
$81$	−0.814626	−0.0905140
$82$	−0.260470	−0.0287641
$83$	−1.36880	−0.150245	−0.0751227	−	0.997174i	$-0.523935\pi$
$83$	−1.36880	−0.150245	−0.0751227	+	0.997174i	$0.523935\pi$
$84$	6.21781	0.678419
$85$	2.92626	0.317398
$86$	−1.00000	−0.107833
$87$	3.31352	0.355247
$88$	1.00000	0.106600
$89$	−0.566497	−0.0600486	−0.0300243	−	0.999549i	$-0.509558\pi$
$89$	−0.566497	−0.0600486	−0.0300243	+	0.999549i	$0.509558\pi$
$90$	4.73038	0.498626
$91$	−13.5861	−1.42421
$92$	4.07518	0.424866
$93$	−27.6486	−2.86703
$94$	−4.67376	−0.482062
$95$	−3.18904	−0.327188
$96$	2.78036	0.283769
$97$	−9.83384	−0.998475	−0.499237	−	0.866465i	$-0.666386\pi$
$97$	−9.83384	−0.998475	−0.499237	+	0.866465i	$0.666386\pi$
$98$	1.99881	0.201910
$99$	−4.73038	−0.475421
$100$	1.00000	0.100000
$101$	5.70831	0.567998	0.283999	−	0.958825i	$-0.408339\pi$
$101$	5.70831	0.567998	0.283999	+	0.958825i	$0.408339\pi$
$102$	−8.13606	−0.805590
$103$	13.7977	1.35953	0.679765	−	0.733430i	$-0.262082\pi$
$103$	13.7977	1.35953	0.679765	+	0.733430i	$0.262082\pi$
$104$	−6.07518	−0.595720
$105$	−6.21781	−0.606796
$106$	7.82089	0.759632
$107$	−13.2977	−1.28554	−0.642768	−	0.766061i	$-0.722214\pi$
$107$	−13.2977	−1.28554	−0.642768	+	0.766061i	$0.722214\pi$
$108$	−4.81108	−0.462947
$109$	19.6096	1.87826	0.939131	−	0.343560i	$-0.111633\pi$
$109$	19.6096	1.87826	0.939131	+	0.343560i	$0.111633\pi$
$110$	−1.00000	−0.0953463
$111$	21.9661	2.08493
$112$	−2.23633	−0.211314
$113$	−15.7306	−1.47981	−0.739906	−	0.672711i	$-0.765130\pi$
$113$	−15.7306	−1.47981	−0.739906	+	0.672711i	$0.765130\pi$
$114$	8.86666	0.830439
$115$	−4.07518	−0.380012
$116$	−1.19176	−0.110652
$117$	28.7379	2.65682
$118$	0.284247	0.0261671
$119$	6.54411	0.599897
$120$	−2.78036	−0.253811
$121$	1.00000	0.0909091
$122$	−9.70548	−0.878693
$123$	−0.724198	−0.0652988
$124$	9.94427	0.893022
$125$	−1.00000	−0.0894427
$126$	10.5787	0.942427
$127$	11.5520	1.02507	0.512536	−	0.858666i	$-0.328706\pi$
$127$	11.5520	1.02507	0.512536	+	0.858666i	$0.328706\pi$
$128$	−1.00000	−0.0883883
$129$	−2.78036	−0.244797
$130$	6.07518	0.532828
$131$	10.5776	0.924169	0.462085	−	0.886836i	$-0.347102\pi$
$131$	10.5776	0.924169	0.462085	+	0.886836i	$0.347102\pi$
$132$	2.78036	0.241999
$133$	−7.13176	−0.618402
$134$	−4.43505	−0.383130
$135$	4.81108	0.414072
$136$	2.92626	0.250925
$137$	−13.7741	−1.17680	−0.588398	−	0.808571i	$-0.700241\pi$
$137$	−13.7741	−1.17680	−0.588398	+	0.808571i	$0.700241\pi$
$138$	11.3304	0.964511
$139$	−20.5287	−1.74122	−0.870612	−	0.491971i	$-0.836277\pi$
$139$	−20.5287	−1.74122	−0.870612	+	0.491971i	$0.836277\pi$
$140$	2.23633	0.189005
$141$	−12.9947	−1.09435
$142$	−0.755828	−0.0634277
$143$	−6.07518	−0.508032
$144$	4.73038	0.394199
$145$	1.19176	0.0989704
$146$	14.1030	1.16717
$147$	5.55739	0.458366
$148$	−7.90048	−0.649415
$149$	−15.6368	−1.28101	−0.640507	−	0.767953i	$-0.721276\pi$
$149$	−15.6368	−1.28101	−0.640507	+	0.767953i	$0.721276\pi$
$150$	2.78036	0.227015
$151$	−2.68616	−0.218596	−0.109298	−	0.994009i	$-0.534860\pi$
$151$	−2.68616	−0.218596	−0.109298	+	0.994009i	$0.534860\pi$
$152$	−3.18904	−0.258665
$153$	−13.8423	−1.11909
$154$	−2.23633	−0.180209
$155$	−9.94427	−0.798743
$156$	−16.8912	−1.35237
$157$	−8.69120	−0.693633	−0.346817	−	0.937933i	$-0.612737\pi$
$157$	−8.69120	−0.693633	−0.346817	+	0.937933i	$0.612737\pi$
$158$	0.0896609	0.00713304
$159$	21.7449	1.72448
$160$	1.00000	0.0790569
$161$	−9.11346	−0.718241
$162$	0.814626	0.0640031
$163$	17.9395	1.40513	0.702566	−	0.711618i	$-0.252037\pi$
$163$	17.9395	1.40513	0.702566	+	0.711618i	$0.252037\pi$
$164$	0.260470	0.0203393
$165$	−2.78036	−0.216450
$166$	1.36880	0.106240
$167$	2.55987	0.198089	0.0990444	−	0.995083i	$-0.468421\pi$
$167$	2.55987	0.198089	0.0990444	+	0.995083i	$0.468421\pi$
$168$	−6.21781	−0.479714
$169$	23.9078	1.83906
$170$	−2.92626	−0.224434
$171$	15.0854	1.15361
$172$	1.00000	0.0762493
$173$	−5.95162	−0.452493	−0.226247	−	0.974070i	$-0.572645\pi$
$173$	−5.95162	−0.452493	−0.226247	+	0.974070i	$0.572645\pi$
$174$	−3.31352	−0.251197
$175$	−2.23633	−0.169051
$176$	−1.00000	−0.0753778
$177$	0.790309	0.0594033
$178$	0.566497	0.0424608
$179$	13.1577	0.983450	0.491725	−	0.870750i	$-0.336366\pi$
$179$	13.1577	0.983450	0.491725	+	0.870750i	$0.336366\pi$
$180$	−4.73038	−0.352582
$181$	−4.22391	−0.313961	−0.156980	−	0.987602i	$-0.550176\pi$
$181$	−4.22391	−0.313961	−0.156980	+	0.987602i	$0.550176\pi$
$182$	13.5861	1.00707
$183$	−26.9847	−1.99477
$184$	−4.07518	−0.300426
$185$	7.90048	0.580855
$186$	27.6486	2.02730
$187$	2.92626	0.213990
$188$	4.67376	0.340869
$189$	10.7592	0.782616
$190$	3.18904	0.231357
$191$	5.16411	0.373662	0.186831	−	0.982392i	$-0.440178\pi$
$191$	5.16411	0.373662	0.186831	+	0.982392i	$0.440178\pi$
$192$	−2.78036	−0.200655
$193$	−6.27237	−0.451495	−0.225747	−	0.974186i	$-0.572482\pi$
$193$	−6.27237	−0.451495	−0.225747	+	0.974186i	$0.572482\pi$
$194$	9.83384	0.706028
$195$	16.8912	1.20960
$196$	−1.99881	−0.142772
$197$	−3.22621	−0.229858	−0.114929	−	0.993374i	$-0.536664\pi$
$197$	−3.22621	−0.229858	−0.114929	+	0.993374i	$0.536664\pi$
$198$	4.73038	0.336174
$199$	−10.4621	−0.741639	−0.370820	−	0.928705i	$-0.620923\pi$
$199$	−10.4621	−0.741639	−0.370820	+	0.928705i	$0.620923\pi$
$200$	−1.00000	−0.0707107
$201$	−12.3310	−0.869763
$202$	−5.70831	−0.401635
$203$	2.66518	0.187059
$204$	8.13606	0.569638
$205$	−0.260470	−0.0181920
$206$	−13.7977	−0.961333
$207$	19.2771	1.33985
$208$	6.07518	0.421238
$209$	−3.18904	−0.220590
$210$	6.21781	0.429070
$211$	5.79975	0.399271	0.199636	−	0.979870i	$-0.436024\pi$
$211$	5.79975	0.399271	0.199636	+	0.979870i	$0.436024\pi$
$212$	−7.82089	−0.537141
$213$	−2.10147	−0.143990
$214$	13.2977	0.909012
$215$	−1.00000	−0.0681994
$216$	4.81108	0.327353
$217$	−22.2387	−1.50966
$218$	−19.6096	−1.32813
$219$	39.2114	2.64966
$220$	1.00000	0.0674200
$221$	−17.7776	−1.19585
$222$	−21.9661	−1.47427
$223$	5.90132	0.395182	0.197591	−	0.980285i	$-0.436688\pi$
$223$	5.90132	0.395182	0.197591	+	0.980285i	$0.436688\pi$
$224$	2.23633	0.149421
$225$	4.73038	0.315359
$226$	15.7306	1.04638
$227$	4.86985	0.323224	0.161612	−	0.986854i	$-0.448331\pi$
$227$	4.86985	0.323224	0.161612	+	0.986854i	$0.448331\pi$
$228$	−8.86666	−0.587209
$229$	7.27039	0.480441	0.240221	−	0.970718i	$-0.422780\pi$
$229$	7.27039	0.480441	0.240221	+	0.970718i	$0.422780\pi$
$230$	4.07518	0.268709
$231$	−6.21781	−0.409102
$232$	1.19176	0.0782430
$233$	20.2797	1.32856	0.664282	−	0.747482i	$-0.268737\pi$
$233$	20.2797	1.32856	0.664282	+	0.747482i	$0.268737\pi$
$234$	−28.7379	−1.87866
$235$	−4.67376	−0.304883
$236$	−0.284247	−0.0185029
$237$	0.249289	0.0161931
$238$	−6.54411	−0.424191
$239$	−4.03204	−0.260811	−0.130405	−	0.991461i	$-0.541628\pi$
$239$	−4.03204	−0.260811	−0.130405	+	0.991461i	$0.541628\pi$
$240$	2.78036	0.179471
$241$	17.7984	1.14650	0.573248	−	0.819382i	$-0.305683\pi$
$241$	17.7984	1.14650	0.573248	+	0.819382i	$0.305683\pi$
$242$	−1.00000	−0.0642824
$243$	16.6982	1.07119
$244$	9.70548	0.621330
$245$	1.99881	0.127699
$246$	0.724198	0.0461732
$247$	19.3740	1.23274
$248$	−9.94427	−0.631462
$249$	3.80576	0.241180
$250$	1.00000	0.0632456
$251$	−12.9233	−0.815714	−0.407857	−	0.913046i	$-0.633724\pi$
$251$	−12.9233	−0.815714	−0.407857	+	0.913046i	$0.633724\pi$
$252$	−10.5787	−0.666397
$253$	−4.07518	−0.256204
$254$	−11.5520	−0.724836
$255$	−8.13606	−0.509500
$256$	1.00000	0.0625000
$257$	−4.64010	−0.289442	−0.144721	−	0.989473i	$-0.546228\pi$
$257$	−4.64010	−0.289442	−0.144721	+	0.989473i	$0.546228\pi$
$258$	2.78036	0.173097
$259$	17.6681	1.09784
$260$	−6.07518	−0.376766
$261$	−5.63749	−0.348952
$262$	−10.5776	−0.653486
$263$	23.3570	1.44025	0.720126	−	0.693843i	$-0.244084\pi$
$263$	23.3570	1.44025	0.720126	+	0.693843i	$0.244084\pi$
$264$	−2.78036	−0.171119
$265$	7.82089	0.480433
$266$	7.13176	0.437276
$267$	1.57506	0.0963924
$268$	4.43505	0.270914
$269$	25.6357	1.56304	0.781518	−	0.623882i	$-0.214446\pi$
$269$	25.6357	1.56304	0.781518	+	0.623882i	$0.214446\pi$
$270$	−4.81108	−0.292793
$271$	−22.9503	−1.39413	−0.697065	−	0.717008i	$-0.745511\pi$
$271$	−22.9503	−1.39413	−0.697065	+	0.717008i	$0.745511\pi$
$272$	−2.92626	−0.177431
$273$	37.7743	2.28620
$274$	13.7741	0.832121
$275$	−1.00000	−0.0603023
$276$	−11.3304	−0.682012
$277$	−6.32737	−0.380175	−0.190088	−	0.981767i	$-0.560877\pi$
$277$	−6.32737	−0.380175	−0.190088	+	0.981767i	$0.560877\pi$
$278$	20.5287	1.23123
$279$	47.0402	2.81622
$280$	−2.23633	−0.133647
$281$	3.92493	0.234142	0.117071	−	0.993124i	$-0.462650\pi$
$281$	3.92493	0.234142	0.117071	+	0.993124i	$0.462650\pi$
$282$	12.9947	0.773825
$283$	24.3865	1.44963	0.724814	−	0.688945i	$-0.241926\pi$
$283$	24.3865	1.44963	0.724814	+	0.688945i	$0.241926\pi$
$284$	0.755828	0.0448501
$285$	8.86666	0.525216
$286$	6.07518	0.359233
$287$	−0.582497	−0.0343837
$288$	−4.73038	−0.278740
$289$	−8.43698	−0.496293
$290$	−1.19176	−0.0699826
$291$	27.3416	1.60279
$292$	−14.1030	−0.825317
$293$	−7.85186	−0.458711	−0.229355	−	0.973343i	$-0.573662\pi$
$293$	−7.85186	−0.458711	−0.229355	+	0.973343i	$0.573662\pi$
$294$	−5.55739	−0.324114
$295$	0.284247	0.0165495
$296$	7.90048	0.459206
$297$	4.81108	0.279167
$298$	15.6368	0.905813
$299$	24.7574	1.43176
$300$	−2.78036	−0.160524
$301$	−2.23633	−0.128900
$302$	2.68616	0.154571
$303$	−15.8711	−0.911773
$304$	3.18904	0.182904
$305$	−9.70548	−0.555734
$306$	13.8423	0.791314
$307$	−17.5404	−1.00109	−0.500543	−	0.865712i	$-0.666866\pi$
$307$	−17.5404	−1.00109	−0.500543	+	0.865712i	$0.666866\pi$
$308$	2.23633	0.127427
$309$	−38.3626	−2.18237
$310$	9.94427	0.564797
$311$	4.70078	0.266557	0.133278	−	0.991079i	$-0.457450\pi$
$311$	4.70078	0.266557	0.133278	+	0.991079i	$0.457450\pi$
$312$	16.8912	0.956273
$313$	5.93044	0.335208	0.167604	−	0.985854i	$-0.446397\pi$
$313$	5.93044	0.335208	0.167604	+	0.985854i	$0.446397\pi$
$314$	8.69120	0.490473
$315$	10.5787	0.596043
$316$	−0.0896609	−0.00504382
$317$	30.5059	1.71338	0.856690	−	0.515832i	$-0.172517\pi$
$317$	30.5059	1.71338	0.856690	+	0.515832i	$0.172517\pi$
$318$	−21.7449	−1.21939
$319$	1.19176	0.0667258
$320$	−1.00000	−0.0559017
$321$	36.9723	2.06359
$322$	9.11346	0.507873
$323$	−9.33197	−0.519245
$324$	−0.814626	−0.0452570
$325$	6.07518	0.336990
$326$	−17.9395	−0.993579
$327$	−54.5218	−3.01506
$328$	−0.260470	−0.0143820
$329$	−10.4521	−0.576243
$330$	2.78036	0.153054
$331$	−33.8704	−1.86169	−0.930844	−	0.365418i	$-0.880926\pi$
$331$	−33.8704	−1.86169	−0.930844	+	0.365418i	$0.880926\pi$
$332$	−1.36880	−0.0751227
$333$	−37.3723	−2.04799
$334$	−2.55987	−0.140070
$335$	−4.43505	−0.242313
$336$	6.21781	0.339209
$337$	−14.4868	−0.789146	−0.394573	−	0.918865i	$-0.629107\pi$
$337$	−14.4868	−0.789146	−0.394573	+	0.918865i	$0.629107\pi$
$338$	−23.9078	−1.30041
$339$	43.7367	2.37545
$340$	2.92626	0.158699
$341$	−9.94427	−0.538512
$342$	−15.0854	−0.815724
$343$	20.1243	1.08661
$344$	−1.00000	−0.0539164
$345$	11.3304	0.610010
$346$	5.95162	0.319961
$347$	−22.2669	−1.19535	−0.597676	−	0.801738i	$-0.703909\pi$
$347$	−22.2669	−1.19535	−0.597676	+	0.801738i	$0.703909\pi$
$348$	3.31352	0.177623
$349$	15.9685	0.854772	0.427386	−	0.904069i	$-0.359434\pi$
$349$	15.9685	0.854772	0.427386	+	0.904069i	$0.359434\pi$
$350$	2.23633	0.119537
$351$	−29.2282	−1.56008
$352$	1.00000	0.0533002
$353$	−3.31107	−0.176230	−0.0881152	−	0.996110i	$-0.528084\pi$
$353$	−3.31107	−0.176230	−0.0881152	+	0.996110i	$0.528084\pi$
$354$	−0.790309	−0.0420045
$355$	−0.755828	−0.0401152
$356$	−0.566497	−0.0300243
$357$	−18.1949	−0.962979
$358$	−13.1577	−0.695404
$359$	26.7424	1.41141	0.705706	−	0.708505i	$-0.250630\pi$
$359$	26.7424	1.41141	0.705706	+	0.708505i	$0.250630\pi$
$360$	4.73038	0.249313
$361$	−8.83003	−0.464739
$362$	4.22391	0.222004
$363$	−2.78036	−0.145931
$364$	−13.5861	−0.712107
$365$	14.1030	0.738186
$366$	26.9847	1.41051
$367$	16.9938	0.887067	0.443534	−	0.896258i	$-0.353725\pi$
$367$	16.9938	0.887067	0.443534	+	0.896258i	$0.353725\pi$
$368$	4.07518	0.212433
$369$	1.23212	0.0641417
$370$	−7.90048	−0.410726
$371$	17.4901	0.908042
$372$	−27.6486	−1.43351
$373$	37.3692	1.93490	0.967451	−	0.253060i	$-0.0814369\pi$
$373$	37.3692	1.93490	0.967451	+	0.253060i	$0.0814369\pi$
$374$	−2.92626	−0.151313
$375$	2.78036	0.143577
$376$	−4.67376	−0.241031
$377$	−7.24016	−0.372887
$378$	−10.7592	−0.553393
$379$	1.03658	0.0532455	0.0266227	−	0.999646i	$-0.491525\pi$
$379$	1.03658	0.0532455	0.0266227	+	0.999646i	$0.491525\pi$
$380$	−3.18904	−0.163594
$381$	−32.1186	−1.64549
$382$	−5.16411	−0.264219
$383$	27.6980	1.41530	0.707650	−	0.706563i	$-0.249755\pi$
$383$	27.6980	1.41530	0.707650	+	0.706563i	$0.249755\pi$
$384$	2.78036	0.141884
$385$	−2.23633	−0.113974
$386$	6.27237	0.319255
$387$	4.73038	0.240459
$388$	−9.83384	−0.499237
$389$	17.5667	0.890667	0.445333	−	0.895365i	$-0.353085\pi$
$389$	17.5667	0.890667	0.445333	+	0.895365i	$0.353085\pi$
$390$	−16.8912	−0.855317
$391$	−11.9250	−0.603075
$392$	1.99881	0.100955
$393$	−29.4095	−1.48351
$394$	3.22621	0.162534
$395$	0.0896609	0.00451133
$396$	−4.73038	−0.237711
$397$	−6.40764	−0.321590	−0.160795	−	0.986988i	$-0.551406\pi$
$397$	−6.40764	−0.321590	−0.160795	+	0.986988i	$0.551406\pi$
$398$	10.4621	0.524418
$399$	19.8288	0.992683
$400$	1.00000	0.0500000
$401$	10.7565	0.537153	0.268576	−	0.963258i	$-0.413447\pi$
$401$	10.7565	0.537153	0.268576	+	0.963258i	$0.413447\pi$
$402$	12.3310	0.615015
$403$	60.4132	3.00940
$404$	5.70831	0.283999
$405$	0.814626	0.0404791
$406$	−2.66518	−0.132271
$407$	7.90048	0.391612
$408$	−8.13606	−0.402795
$409$	1.88588	0.0932510	0.0466255	−	0.998912i	$-0.485153\pi$
$409$	1.88588	0.0932510	0.0466255	+	0.998912i	$0.485153\pi$
$410$	0.260470	0.0128637
$411$	38.2968	1.88904
$412$	13.7977	0.679765
$413$	0.635673	0.0312794
$414$	−19.2771	−0.947420
$415$	1.36880	0.0671918
$416$	−6.07518	−0.297860
$417$	57.0772	2.79508
$418$	3.18904	0.155981
$419$	−17.9288	−0.875877	−0.437938	−	0.899005i	$-0.644291\pi$
$419$	−17.9288	−0.875877	−0.437938	+	0.899005i	$0.644291\pi$
$420$	−6.21781	−0.303398
$421$	16.8657	0.821982	0.410991	−	0.911639i	$-0.365183\pi$
$421$	16.8657	0.821982	0.410991	+	0.911639i	$0.365183\pi$
$422$	−5.79975	−0.282327
$423$	22.1087	1.07496
$424$	7.82089	0.379816
$425$	−2.92626	−0.141945
$426$	2.10147	0.101817
$427$	−21.7047	−1.05036
$428$	−13.2977	−0.642768
$429$	16.8912	0.815513
$430$	1.00000	0.0482243
$431$	−17.1282	−0.825034	−0.412517	−	0.910950i	$-0.635350\pi$
$431$	−17.1282	−0.825034	−0.412517	+	0.910950i	$0.635350\pi$
$432$	−4.81108	−0.231473
$433$	21.8387	1.04950	0.524750	−	0.851257i	$-0.324159\pi$
$433$	21.8387	1.04950	0.524750	+	0.851257i	$0.324159\pi$
$434$	22.2387	1.06749
$435$	−3.31352	−0.158871
$436$	19.6096	0.939131
$437$	12.9959	0.621678
$438$	−39.2114	−1.87359
$439$	−19.9372	−0.951549	−0.475775	−	0.879567i	$-0.657832\pi$
$439$	−19.9372	−0.951549	−0.475775	+	0.879567i	$0.657832\pi$
$440$	−1.00000	−0.0476731
$441$	−9.45512	−0.450244
$442$	17.7776	0.845593
$443$	−0.843192	−0.0400612	−0.0200306	−	0.999799i	$-0.506376\pi$
$443$	−0.843192	−0.0400612	−0.0200306	+	0.999799i	$0.506376\pi$
$444$	21.9661	1.04247
$445$	0.566497	0.0268546
$446$	−5.90132	−0.279436
$447$	43.4758	2.05633
$448$	−2.23633	−0.105657
$449$	7.31208	0.345079	0.172539	−	0.985003i	$-0.444803\pi$
$449$	7.31208	0.345079	0.172539	+	0.985003i	$0.444803\pi$
$450$	−4.73038	−0.222992
$451$	−0.260470	−0.0122650
$452$	−15.7306	−0.739906
$453$	7.46848	0.350900
$454$	−4.86985	−0.228554
$455$	13.5861	0.636928
$456$	8.86666	0.415220
$457$	38.6073	1.80597	0.902986	−	0.429670i	$-0.141370\pi$
$457$	38.6073	1.80597	0.902986	+	0.429670i	$0.141370\pi$
$458$	−7.27039	−0.339723
$459$	14.0785	0.657128
$460$	−4.07518	−0.190006
$461$	23.3428	1.08718	0.543590	−	0.839351i	$-0.317064\pi$
$461$	23.3428	1.08718	0.543590	+	0.839351i	$0.317064\pi$
$462$	6.21781	0.289279
$463$	−8.38418	−0.389646	−0.194823	−	0.980838i	$-0.562413\pi$
$463$	−8.38418	−0.389646	−0.194823	+	0.980838i	$0.562413\pi$
$464$	−1.19176	−0.0553261
$465$	27.6486	1.28217
$466$	−20.2797	−0.939437
$467$	−11.1461	−0.515779	−0.257889	−	0.966174i	$-0.583027\pi$
$467$	−11.1461	−0.515779	−0.257889	+	0.966174i	$0.583027\pi$
$468$	28.7379	1.32841
$469$	−9.91825	−0.457982
$470$	4.67376	0.215585
$471$	24.1646	1.11345
$472$	0.284247	0.0130836
$473$	−1.00000	−0.0459800
$474$	−0.249289	−0.0114502
$475$	3.18904	0.146323
$476$	6.54411	0.299949
$477$	−36.9958	−1.69392
$478$	4.03204	0.184421
$479$	2.37394	0.108468	0.0542342	−	0.998528i	$-0.482728\pi$
$479$	2.37394	0.108468	0.0542342	+	0.998528i	$0.482728\pi$
$480$	−2.78036	−0.126905
$481$	−47.9968	−2.18847
$482$	−17.7984	−0.810695
$483$	25.3387	1.15295
$484$	1.00000	0.0454545
$485$	9.83384	0.446532
$486$	−16.6982	−0.757446
$487$	−19.6638	−0.891051	−0.445526	−	0.895269i	$-0.646983\pi$
$487$	−19.6638	−0.891051	−0.445526	+	0.895269i	$0.646983\pi$
$488$	−9.70548	−0.439346
$489$	−49.8783	−2.25557
$490$	−1.99881	−0.0902969
$491$	25.7939	1.16406	0.582031	−	0.813167i	$-0.302258\pi$
$491$	25.7939	1.16406	0.582031	+	0.813167i	$0.302258\pi$
$492$	−0.724198	−0.0326494
$493$	3.48741	0.157065
$494$	−19.3740	−0.871676
$495$	4.73038	0.212615
$496$	9.94427	0.446511
$497$	−1.69028	−0.0758196
$498$	−3.80576	−0.170540
$499$	27.9568	1.25152	0.625759	−	0.780017i	$-0.284790\pi$
$499$	27.9568	1.25152	0.625759	+	0.780017i	$0.284790\pi$
$500$	−1.00000	−0.0447214
$501$	−7.11735	−0.317980
$502$	12.9233	0.576797
$503$	−17.4342	−0.777352	−0.388676	−	0.921374i	$-0.627068\pi$
$503$	−17.4342	−0.777352	−0.388676	+	0.921374i	$0.627068\pi$
$504$	10.5787	0.471214
$505$	−5.70831	−0.254016
$506$	4.07518	0.181164
$507$	−66.4721	−2.95213
$508$	11.5520	0.512536
$509$	−9.04819	−0.401054	−0.200527	−	0.979688i	$-0.564265\pi$
$509$	−9.04819	−0.401054	−0.200527	+	0.979688i	$0.564265\pi$
$510$	8.13606	0.360271
$511$	31.5391	1.39521
$512$	−1.00000	−0.0441942
$513$	−15.3427	−0.677398
$514$	4.64010	0.204666
$515$	−13.7977	−0.608000
$516$	−2.78036	−0.122398
$517$	−4.67376	−0.205552
$518$	−17.6681	−0.776292
$519$	16.5476	0.726360
$520$	6.07518	0.266414
$521$	−23.4949	−1.02933	−0.514665	−	0.857391i	$-0.672084\pi$
$521$	−23.4949	−1.02933	−0.514665	+	0.857391i	$0.672084\pi$
$522$	5.63749	0.246746
$523$	19.5821	0.856266	0.428133	−	0.903716i	$-0.359172\pi$
$523$	19.5821	0.856266	0.428133	+	0.903716i	$0.359172\pi$
$524$	10.5776	0.462085
$525$	6.21781	0.271367
$526$	−23.3570	−1.01841
$527$	−29.0996	−1.26760
$528$	2.78036	0.120999
$529$	−6.39294	−0.277954
$530$	−7.82089	−0.339718
$531$	−1.34460	−0.0583506
$532$	−7.13176	−0.309201
$533$	1.58240	0.0685413
$534$	−1.57506	−0.0681597
$535$	13.2977	0.574909
$536$	−4.43505	−0.191565
$537$	−36.5830	−1.57867
$538$	−25.6357	−1.10523
$539$	1.99881	0.0860947
$540$	4.81108	0.207036
$541$	32.6334	1.40302	0.701510	−	0.712659i	$-0.252509\pi$
$541$	32.6334	1.40302	0.701510	+	0.712659i	$0.252509\pi$
$542$	22.9503	0.985799
$543$	11.7440	0.503982
$544$	2.92626	0.125463
$545$	−19.6096	−0.839984
$546$	−37.7743	−1.61659
$547$	16.9552	0.724953	0.362476	−	0.931993i	$-0.381931\pi$
$547$	16.9552	0.724953	0.362476	+	0.931993i	$0.381931\pi$
$548$	−13.7741	−0.588398
$549$	45.9106	1.95942
$550$	1.00000	0.0426401
$551$	−3.80057	−0.161910
$552$	11.3304	0.482256
$553$	0.200512	0.00852663
$554$	6.32737	0.268824
$555$	−21.9661	−0.932411
$556$	−20.5287	−0.870612
$557$	7.68137	0.325470	0.162735	−	0.986670i	$-0.447968\pi$
$557$	7.68137	0.325470	0.162735	+	0.986670i	$0.447968\pi$
$558$	−47.0402	−1.99137
$559$	6.07518	0.256953
$560$	2.23633	0.0945024
$561$	−8.13606	−0.343505
$562$	−3.92493	−0.165563
$563$	−4.33255	−0.182595	−0.0912977	−	0.995824i	$-0.529101\pi$
$563$	−4.33255	−0.182595	−0.0912977	+	0.995824i	$0.529101\pi$
$564$	−12.9947	−0.547177
$565$	15.7306	0.661792
$566$	−24.3865	−1.02504
$567$	1.82178	0.0765074
$568$	−0.755828	−0.0317138
$569$	42.1183	1.76569	0.882845	−	0.469664i	$-0.155625\pi$
$569$	42.1183	1.76569	0.882845	+	0.469664i	$0.155625\pi$
$570$	−8.86666	−0.371384
$571$	−27.8033	−1.16353	−0.581765	−	0.813357i	$-0.697638\pi$
$571$	−27.8033	−1.16353	−0.581765	+	0.813357i	$0.697638\pi$
$572$	−6.07518	−0.254016
$573$	−14.3581	−0.599816
$574$	0.582497	0.0243130
$575$	4.07518	0.169947
$576$	4.73038	0.197099
$577$	9.66392	0.402314	0.201157	−	0.979559i	$-0.435530\pi$
$577$	9.66392	0.402314	0.201157	+	0.979559i	$0.435530\pi$
$578$	8.43698	0.350932
$579$	17.4394	0.724757
$580$	1.19176	0.0494852
$581$	3.06110	0.126996
$582$	−27.3416	−1.13334
$583$	7.82089	0.323908
$584$	14.1030	0.583587
$585$	−28.7379	−1.18817
$586$	7.85186	0.324358
$587$	14.6392	0.604225	0.302113	−	0.953272i	$-0.402308\pi$
$587$	14.6392	0.604225	0.302113	+	0.953272i	$0.402308\pi$
$588$	5.55739	0.229183
$589$	31.7127	1.30670
$590$	−0.284247	−0.0117023
$591$	8.97002	0.368977
$592$	−7.90048	−0.324708
$593$	−41.5135	−1.70475	−0.852377	−	0.522928i	$-0.824840\pi$
$593$	−41.5135	−1.70475	−0.852377	+	0.522928i	$0.824840\pi$
$594$	−4.81108	−0.197401
$595$	−6.54411	−0.268282
$596$	−15.6368	−0.640507
$597$	29.0884	1.19051
$598$	−24.7574	−1.01241
$599$	16.8623	0.688974	0.344487	−	0.938791i	$-0.388053\pi$
$599$	16.8623	0.688974	0.344487	+	0.938791i	$0.388053\pi$
$600$	2.78036	0.113508
$601$	42.7351	1.74320	0.871600	−	0.490218i	$-0.163083\pi$
$601$	42.7351	1.74320	0.871600	+	0.490218i	$0.163083\pi$
$602$	2.23633	0.0911462
$603$	20.9795	0.854350
$604$	−2.68616	−0.109298
$605$	−1.00000	−0.0406558
$606$	15.8711	0.644721
$607$	3.01569	0.122403	0.0612015	−	0.998125i	$-0.480507\pi$
$607$	3.01569	0.122403	0.0612015	+	0.998125i	$0.480507\pi$
$608$	−3.18904	−0.129333
$609$	−7.41014	−0.300274
$610$	9.70548	0.392963
$611$	28.3939	1.14870
$612$	−13.8423	−0.559544
$613$	38.9176	1.57187	0.785934	−	0.618311i	$-0.212183\pi$
$613$	38.9176	1.57187	0.785934	+	0.618311i	$0.212183\pi$
$614$	17.5404	0.707874
$615$	0.724198	0.0292025
$616$	−2.23633	−0.0901045
$617$	0.0901936	0.00363106	0.00181553	−	0.999998i	$-0.499422\pi$
$617$	0.0901936	0.00363106	0.00181553	+	0.999998i	$0.499422\pi$
$618$	38.3626	1.54317
$619$	2.45207	0.0985570	0.0492785	−	0.998785i	$-0.484308\pi$
$619$	2.45207	0.0985570	0.0492785	+	0.998785i	$0.484308\pi$
$620$	−9.94427	−0.399372
$621$	−19.6060	−0.786762
$622$	−4.70078	−0.188484
$623$	1.26688	0.0507564
$624$	−16.8912	−0.676187
$625$	1.00000	0.0400000
$626$	−5.93044	−0.237028
$627$	8.86666	0.354100
$628$	−8.69120	−0.346817
$629$	23.1189	0.921810
$630$	−10.5787	−0.421466
$631$	−26.5739	−1.05789	−0.528946	−	0.848656i	$-0.677413\pi$
$631$	−26.5739	−1.05789	−0.528946	+	0.848656i	$0.677413\pi$
$632$	0.0896609	0.00356652
$633$	−16.1254	−0.640926
$634$	−30.5059	−1.21154
$635$	−11.5520	−0.458426
$636$	21.7449	0.862240
$637$	−12.1431	−0.481127
$638$	−1.19176	−0.0471823
$639$	3.57536	0.141439
$640$	1.00000	0.0395285
$641$	19.5523	0.772269	0.386134	−	0.922443i	$-0.373810\pi$
$641$	19.5523	0.772269	0.386134	+	0.922443i	$0.373810\pi$
$642$	−36.9723	−1.45918
$643$	4.33884	0.171107	0.0855536	−	0.996334i	$-0.472734\pi$
$643$	4.33884	0.171107	0.0855536	+	0.996334i	$0.472734\pi$
$644$	−9.11346	−0.359121
$645$	2.78036	0.109476
$646$	9.33197	0.367161
$647$	16.2937	0.640571	0.320285	−	0.947321i	$-0.396221\pi$
$647$	16.2937	0.640571	0.320285	+	0.947321i	$0.396221\pi$
$648$	0.814626	0.0320015
$649$	0.284247	0.0111577
$650$	−6.07518	−0.238288
$651$	61.8316	2.42337
$652$	17.9395	0.702566
$653$	−0.332094	−0.0129959	−0.00649793	−	0.999979i	$-0.502068\pi$
$653$	−0.332094	−0.0129959	−0.00649793	+	0.999979i	$0.502068\pi$
$654$	54.5218	2.13197
$655$	−10.5776	−0.413301
$656$	0.260470	0.0101696
$657$	−66.7127	−2.60271
$658$	10.4521	0.407465
$659$	−33.0075	−1.28579	−0.642894	−	0.765955i	$-0.722267\pi$
$659$	−33.0075	−1.28579	−0.642894	+	0.765955i	$0.722267\pi$
$660$	−2.78036	−0.108225
$661$	−20.2264	−0.786717	−0.393359	−	0.919385i	$-0.628687\pi$
$661$	−20.2264	−0.786717	−0.393359	+	0.919385i	$0.628687\pi$
$662$	33.8704	1.31641
$663$	49.4280	1.91962
$664$	1.36880	0.0531198
$665$	7.13176	0.276558
$666$	37.3723	1.44815
$667$	−4.85664	−0.188050
$668$	2.55987	0.0990444
$669$	−16.4078	−0.634362
$670$	4.43505	0.171341
$671$	−9.70548	−0.374676
$672$	−6.21781	−0.239857
$673$	−39.1340	−1.50851	−0.754253	−	0.656584i	$-0.772001\pi$
$673$	−39.1340	−1.50851	−0.754253	+	0.656584i	$0.772001\pi$
$674$	14.4868	0.558010
$675$	−4.81108	−0.185179
$676$	23.9078	0.919529
$677$	37.5404	1.44279	0.721397	−	0.692522i	$-0.243500\pi$
$677$	37.5404	1.44279	0.721397	+	0.692522i	$0.243500\pi$
$678$	−43.7367	−1.67970
$679$	21.9918	0.843966
$680$	−2.92626	−0.112217
$681$	−13.5399	−0.518851
$682$	9.94427	0.380786
$683$	25.0783	0.959593	0.479797	−	0.877380i	$-0.340710\pi$
$683$	25.0783	0.959593	0.479797	+	0.877380i	$0.340710\pi$
$684$	15.0854	0.576804
$685$	13.7741	0.526280
$686$	−20.1243	−0.768351
$687$	−20.2143	−0.771223
$688$	1.00000	0.0381246
$689$	−47.5133	−1.81011
$690$	−11.3304	−0.431343
$691$	12.3002	0.467923	0.233962	−	0.972246i	$-0.424831\pi$
$691$	12.3002	0.467923	0.233962	+	0.972246i	$0.424831\pi$
$692$	−5.95162	−0.226247
$693$	10.5787	0.401852
$694$	22.2669	0.845241
$695$	20.5287	0.778699
$696$	−3.31352	−0.125599
$697$	−0.762203	−0.0288705
$698$	−15.9685	−0.604415
$699$	−56.3847	−2.13266
$700$	−2.23633	−0.0845255
$701$	−21.2307	−0.801873	−0.400937	−	0.916106i	$-0.631315\pi$
$701$	−21.2307	−0.801873	−0.400937	+	0.916106i	$0.631315\pi$
$702$	29.2282	1.10315
$703$	−25.1949	−0.950245
$704$	−1.00000	−0.0376889
$705$	12.9947	0.489410
$706$	3.31107	0.124614
$707$	−12.7657	−0.480103
$708$	0.790309	0.0297016
$709$	−6.08228	−0.228425	−0.114212	−	0.993456i	$-0.536434\pi$
$709$	−6.08228	−0.228425	−0.114212	+	0.993456i	$0.536434\pi$
$710$	0.755828	0.0283657
$711$	−0.424131	−0.0159061
$712$	0.566497	0.0212304
$713$	40.5247	1.51766
$714$	18.1949	0.680929
$715$	6.07518	0.227199
$716$	13.1577	0.491725
$717$	11.2105	0.418664
$718$	−26.7424	−0.998019
$719$	1.07483	0.0400845	0.0200422	−	0.999799i	$-0.493620\pi$
$719$	1.07483	0.0400845	0.0200422	+	0.999799i	$0.493620\pi$
$720$	−4.73038	−0.176291
$721$	−30.8563	−1.14915
$722$	8.83003	0.328620
$723$	−49.4859	−1.84040
$724$	−4.22391	−0.156980
$725$	−1.19176	−0.0442609
$726$	2.78036	0.103189
$727$	−17.9217	−0.664681	−0.332340	−	0.943160i	$-0.607838\pi$
$727$	−17.9217	−0.664681	−0.332340	+	0.943160i	$0.607838\pi$
$728$	13.5861	0.503535
$729$	−43.9831	−1.62900
$730$	−14.1030	−0.521976
$731$	−2.92626	−0.108232
$732$	−26.9847	−0.997383
$733$	−8.14994	−0.301025	−0.150512	−	0.988608i	$-0.548092\pi$
$733$	−8.14994	−0.301025	−0.150512	+	0.988608i	$0.548092\pi$
$734$	−16.9938	−0.627251
$735$	−5.55739	−0.204988
$736$	−4.07518	−0.150213
$737$	−4.43505	−0.163367
$738$	−1.23212	−0.0453550
$739$	−7.03166	−0.258664	−0.129332	−	0.991601i	$-0.541283\pi$
$739$	−7.03166	−0.258664	−0.129332	+	0.991601i	$0.541283\pi$
$740$	7.90048	0.290427
$741$	−53.8665	−1.97884
$742$	−17.4901	−0.642083
$743$	−30.6577	−1.12472	−0.562362	−	0.826891i	$-0.690107\pi$
$743$	−30.6577	−1.12472	−0.562362	+	0.826891i	$0.690107\pi$
$744$	27.6486	1.01365
$745$	15.6368	0.572887
$746$	−37.3692	−1.36818
$747$	−6.47496	−0.236906
$748$	2.92626	0.106995
$749$	29.7381	1.08661
$750$	−2.78036	−0.101524
$751$	−16.3040	−0.594942	−0.297471	−	0.954731i	$-0.596143\pi$
$751$	−16.3040	−0.594942	−0.297471	+	0.954731i	$0.596143\pi$
$752$	4.67376	0.170435
$753$	35.9315	1.30942
$754$	7.24016	0.263671
$755$	2.68616	0.0977593
$756$	10.7592	0.391308
$757$	9.87049	0.358749	0.179375	−	0.983781i	$-0.442593\pi$
$757$	9.87049	0.358749	0.179375	+	0.983781i	$0.442593\pi$
$758$	−1.03658	−0.0376502
$759$	11.3304	0.411269
$760$	3.18904	0.115679
$761$	−11.4904	−0.416528	−0.208264	−	0.978073i	$-0.566781\pi$
$761$	−11.4904	−0.416528	−0.208264	+	0.978073i	$0.566781\pi$
$762$	32.1186	1.16353
$763$	−43.8537	−1.58761
$764$	5.16411	0.186831
$765$	13.8423	0.500471
$766$	−27.6980	−1.00077
$767$	−1.72685	−0.0623531
$768$	−2.78036	−0.100327
$769$	28.1250	1.01421	0.507107	−	0.861883i	$-0.330715\pi$
$769$	28.1250	1.01421	0.507107	+	0.861883i	$0.330715\pi$
$770$	2.23633	0.0805919
$771$	12.9011	0.464623
$772$	−6.27237	−0.225747
$773$	23.9790	0.862464	0.431232	−	0.902241i	$-0.358079\pi$
$773$	23.9790	0.862464	0.431232	+	0.902241i	$0.358079\pi$
$774$	−4.73038	−0.170030
$775$	9.94427	0.357209
$776$	9.83384	0.353014
$777$	−49.1237	−1.76230
$778$	−17.5667	−0.629796
$779$	0.830648	0.0297610
$780$	16.8912	0.604800
$781$	−0.755828	−0.0270457
$782$	11.9250	0.426439
$783$	5.73366	0.204904
$784$	−1.99881	−0.0713859
$785$	8.69120	0.310202
$786$	29.4095	1.04900
$787$	26.1714	0.932908	0.466454	−	0.884545i	$-0.345531\pi$
$787$	26.1714	0.932908	0.466454	+	0.884545i	$0.345531\pi$
$788$	−3.22621	−0.114929
$789$	−64.9407	−2.31195
$790$	−0.0896609	−0.00318999
$791$	35.1789	1.25082
$792$	4.73038	0.168087
$793$	58.9625	2.09382
$794$	6.40764	0.227398
$795$	−21.7449	−0.771211
$796$	−10.4621	−0.370820
$797$	37.7124	1.33584	0.667921	−	0.744232i	$-0.267184\pi$
$797$	37.7124	1.33584	0.667921	+	0.744232i	$0.267184\pi$
$798$	−19.8288	−0.701933
$799$	−13.6767	−0.483846
$800$	−1.00000	−0.0353553
$801$	−2.67975	−0.0946843
$802$	−10.7565	−0.379824
$803$	14.1030	0.497685
$804$	−12.3310	−0.434881
$805$	9.11346	0.321207
$806$	−60.4132	−2.12796
$807$	−71.2764	−2.50905
$808$	−5.70831	−0.200818
$809$	−42.1131	−1.48062	−0.740309	−	0.672267i	$-0.765321\pi$
$809$	−42.1131	−1.48062	−0.740309	+	0.672267i	$0.765321\pi$
$810$	−0.814626	−0.0286230
$811$	−46.4013	−1.62937	−0.814684	−	0.579905i	$-0.803090\pi$
$811$	−46.4013	−1.62937	−0.814684	+	0.579905i	$0.803090\pi$
$812$	2.66518	0.0935294
$813$	63.8100	2.23791
$814$	−7.90048	−0.276912
$815$	−17.9395	−0.628394
$816$	8.13606	0.284819
$817$	3.18904	0.111570
$818$	−1.88588	−0.0659384
$819$	−64.2676	−2.24569
$820$	−0.260470	−0.00909599
$821$	−24.1105	−0.841463	−0.420731	−	0.907185i	$-0.638226\pi$
$821$	−24.1105	−0.841463	−0.420731	+	0.907185i	$0.638226\pi$
$822$	−38.2968	−1.33575
$823$	9.31660	0.324756	0.162378	−	0.986729i	$-0.448084\pi$
$823$	9.31660	0.324756	0.162378	+	0.986729i	$0.448084\pi$
$824$	−13.7977	−0.480666
$825$	2.78036	0.0967996
$826$	−0.635673	−0.0221179
$827$	12.6945	0.441431	0.220715	−	0.975338i	$-0.429161\pi$
$827$	12.6945	0.441431	0.220715	+	0.975338i	$0.429161\pi$
$828$	19.2771	0.669927
$829$	41.3858	1.43739	0.718695	−	0.695326i	$-0.244740\pi$
$829$	41.3858	1.43739	0.718695	+	0.695326i	$0.244740\pi$
$830$	−1.36880	−0.0475118
$831$	17.5924	0.610272
$832$	6.07518	0.210619
$833$	5.84903	0.202657
$834$	−57.0772	−1.97642
$835$	−2.55987	−0.0885880
$836$	−3.18904	−0.110295
$837$	−47.8427	−1.65369
$838$	17.9288	0.619339
$839$	3.92581	0.135534	0.0677671	−	0.997701i	$-0.478413\pi$
$839$	3.92581	0.135534	0.0677671	+	0.997701i	$0.478413\pi$
$840$	6.21781	0.214535
$841$	−27.5797	−0.951024
$842$	−16.8657	−0.581229
$843$	−10.9127	−0.375853
$844$	5.79975	0.199636
$845$	−23.9078	−0.822452
$846$	−22.1087	−0.760112
$847$	−2.23633	−0.0768414
$848$	−7.82089	−0.268570
$849$	−67.8032	−2.32700
$850$	2.92626	0.100370
$851$	−32.1958	−1.10366
$852$	−2.10147	−0.0719952
$853$	−31.4017	−1.07517	−0.537587	−	0.843208i	$-0.680664\pi$
$853$	−31.4017	−1.07517	−0.537587	+	0.843208i	$0.680664\pi$
$854$	21.7047	0.742720
$855$	−15.0854	−0.515909
$856$	13.2977	0.454506
$857$	−43.8245	−1.49701	−0.748507	−	0.663126i	$-0.769229\pi$
$857$	−43.8245	−1.49701	−0.748507	+	0.663126i	$0.769229\pi$
$858$	−16.8912	−0.576655
$859$	−40.9094	−1.39581	−0.697905	−	0.716191i	$-0.745884\pi$
$859$	−40.9094	−1.39581	−0.697905	+	0.716191i	$0.745884\pi$
$860$	−1.00000	−0.0340997
$861$	1.61955	0.0551941
$862$	17.1282	0.583387
$863$	16.9259	0.576165	0.288082	−	0.957606i	$-0.406982\pi$
$863$	16.9259	0.576165	0.288082	+	0.957606i	$0.406982\pi$
$864$	4.81108	0.163676
$865$	5.95162	0.202361
$866$	−21.8387	−0.742108
$867$	23.4578	0.796669
$868$	−22.2387	−0.754831
$869$	0.0896609	0.00304154
$870$	3.31352	0.112339
$871$	26.9437	0.912952
$872$	−19.6096	−0.664066
$873$	−46.5178	−1.57439
$874$	−12.9959	−0.439593
$875$	2.23633	0.0756019
$876$	39.2114	1.32483
$877$	28.5771	0.964979	0.482489	−	0.875902i	$-0.339733\pi$
$877$	28.5771	0.964979	0.482489	+	0.875902i	$0.339733\pi$
$878$	19.9372	0.672847
$879$	21.8310	0.736341
$880$	1.00000	0.0337100
$881$	−22.4892	−0.757681	−0.378840	−	0.925462i	$-0.623677\pi$
$881$	−22.4892	−0.757681	−0.378840	+	0.925462i	$0.623677\pi$
$882$	9.45512	0.318370
$883$	37.3828	1.25803	0.629015	−	0.777393i	$-0.283458\pi$
$883$	37.3828	1.25803	0.629015	+	0.777393i	$0.283458\pi$
$884$	−17.7776	−0.597924
$885$	−0.790309	−0.0265660
$886$	0.843192	0.0283276
$887$	−30.7267	−1.03170	−0.515852	−	0.856678i	$-0.672524\pi$
$887$	−30.7267	−1.03170	−0.515852	+	0.856678i	$0.672524\pi$
$888$	−21.9661	−0.737136
$889$	−25.8341	−0.866448
$890$	−0.566497	−0.0189890
$891$	0.814626	0.0272910
$892$	5.90132	0.197591
$893$	14.9048	0.498771
$894$	−43.4758	−1.45405
$895$	−13.1577	−0.439812
$896$	2.23633	0.0747107
$897$	−68.8344	−2.29831
$898$	−7.31208	−0.244007
$899$	−11.8512	−0.395260
$900$	4.73038	0.157679
$901$	22.8860	0.762443
$902$	0.260470	0.00867269
$903$	6.21781	0.206916
$904$	15.7306	0.523192
$905$	4.22391	0.140407
$906$	−7.46848	−0.248124
$907$	44.2721	1.47003	0.735015	−	0.678051i	$-0.237175\pi$
$907$	44.2721	1.47003	0.735015	+	0.678051i	$0.237175\pi$
$908$	4.86985	0.161612
$909$	27.0025	0.895616
$910$	−13.5861	−0.450376
$911$	−35.5107	−1.17652	−0.588261	−	0.808671i	$-0.700187\pi$
$911$	−35.5107	−1.17652	−0.588261	+	0.808671i	$0.700187\pi$
$912$	−8.86666	−0.293605
$913$	1.36880	0.0453007
$914$	−38.6073	−1.27701
$915$	26.9847	0.892087
$916$	7.27039	0.240221
$917$	−23.6551	−0.781159
$918$	−14.0785	−0.464660
$919$	−20.4651	−0.675080	−0.337540	−	0.941311i	$-0.609595\pi$
$919$	−20.4651	−0.675080	−0.337540	+	0.941311i	$0.609595\pi$
$920$	4.07518	0.134355
$921$	48.7686	1.60698
$922$	−23.3428	−0.768753
$923$	4.59179	0.151141
$924$	−6.21781	−0.204551
$925$	−7.90048	−0.259766
$926$	8.38418	0.275521
$927$	65.2685	2.14370
$928$	1.19176	0.0391215
$929$	−14.6723	−0.481382	−0.240691	−	0.970602i	$-0.577374\pi$
$929$	−14.6723	−0.481382	−0.240691	+	0.970602i	$0.577374\pi$
$930$	−27.6486	−0.906634
$931$	−6.37427	−0.208908
$932$	20.2797	0.664282
$933$	−13.0698	−0.427887
$934$	11.1461	0.364711
$935$	−2.92626	−0.0956991
$936$	−28.7379	−0.939328
$937$	−28.0827	−0.917422	−0.458711	−	0.888586i	$-0.651689\pi$
$937$	−28.0827	−0.917422	−0.458711	+	0.888586i	$0.651689\pi$
$938$	9.91825	0.323842
$939$	−16.4887	−0.538089
$940$	−4.67376	−0.152441
$941$	−50.3679	−1.64195	−0.820974	−	0.570966i	$-0.806569\pi$
$941$	−50.3679	−1.64195	−0.820974	+	0.570966i	$0.806569\pi$
$942$	−24.1646	−0.787326
$943$	1.06146	0.0345659
$944$	−0.284247	−0.00925147
$945$	−10.7592	−0.349996
$946$	1.00000	0.0325128
$947$	−55.6353	−1.80790	−0.903951	−	0.427635i	$-0.859347\pi$
$947$	−55.6353	−1.80790	−0.903951	+	0.427635i	$0.859347\pi$
$948$	0.249289	0.00809654
$949$	−85.6783	−2.78124
$950$	−3.18904	−0.103466
$951$	−84.8172	−2.75038
$952$	−6.54411	−0.212096
$953$	−40.6791	−1.31772	−0.658862	−	0.752264i	$-0.728962\pi$
$953$	−40.6791	−1.31772	−0.658862	+	0.752264i	$0.728962\pi$
$954$	36.9958	1.19778
$955$	−5.16411	−0.167107
$956$	−4.03204	−0.130405
$957$	−3.31352	−0.107111
$958$	−2.37394	−0.0766987
$959$	30.8034	0.994694
$960$	2.78036	0.0897356
$961$	67.8885	2.18995
$962$	47.9968	1.54748
$963$	−62.9032	−2.02703
$964$	17.7984	0.573248
$965$	6.27237	0.201915
$966$	−25.3387	−0.815258
$967$	61.0806	1.96422	0.982110	−	0.188310i	$-0.0603010\pi$
$967$	61.0806	1.96422	0.982110	+	0.188310i	$0.0603010\pi$
$968$	−1.00000	−0.0321412
$969$	25.9462	0.833512
$970$	−9.83384	−0.315745
$971$	−18.0646	−0.579719	−0.289860	−	0.957069i	$-0.593609\pi$
$971$	−18.0646	−0.579719	−0.289860	+	0.957069i	$0.593609\pi$
$972$	16.6982	0.535595
$973$	45.9091	1.47178
$974$	19.6638	0.630068
$975$	−16.8912	−0.540950
$976$	9.70548	0.310665
$977$	24.8109	0.793771	0.396885	−	0.917868i	$-0.370091\pi$
$977$	24.8109	0.793771	0.396885	+	0.917868i	$0.370091\pi$
$978$	49.8783	1.59493
$979$	0.566497	0.0181053
$980$	1.99881	0.0638495
$981$	92.7611	2.96163
$982$	−25.7939	−0.823116
$983$	−43.9925	−1.40314	−0.701571	−	0.712599i	$-0.747518\pi$
$983$	−43.9925	−1.40314	−0.701571	+	0.712599i	$0.747518\pi$
$984$	0.724198	0.0230866
$985$	3.22621	0.102796
$986$	−3.48741	−0.111062
$987$	29.0606	0.925008
$988$	19.3740	0.616368
$989$	4.07518	0.129583
$990$	−4.73038	−0.150341
$991$	−60.1570	−1.91095	−0.955476	−	0.295070i	$-0.904657\pi$
$991$	−60.1570	−1.91095	−0.955476	+	0.295070i	$0.904657\pi$
$992$	−9.94427	−0.315731
$993$	94.1719	2.98845
$994$	1.69028	0.0536126
$995$	10.4621	0.331671
$996$	3.80576	0.120590
$997$	−23.9534	−0.758612	−0.379306	−	0.925271i	$-0.623837\pi$
$997$	−23.9534	−0.758612	−0.379306	+	0.925271i	$0.623837\pi$
$998$	−27.9568	−0.884956
$999$	38.0098	1.20258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bb.1.2	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bb.1.2	✓	11	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.78036 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.78036 q^{6} -2.23633 q^{7} -1.00000 q^{8} +4.73038 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.78036 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.78036 q^{6} -2.23633 q^{7} -1.00000 q^{8} +4.73038 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.78036 q^{12} +6.07518 q^{13} +2.23633 q^{14} +2.78036 q^{15} +1.00000 q^{16} -2.92626 q^{17} -4.73038 q^{18} +3.18904 q^{19} -1.00000 q^{20} +6.21781 q^{21} +1.00000 q^{22} +4.07518 q^{23} +2.78036 q^{24} +1.00000 q^{25} -6.07518 q^{26} -4.81108 q^{27} -2.23633 q^{28} -1.19176 q^{29} -2.78036 q^{30} +9.94427 q^{31} -1.00000 q^{32} +2.78036 q^{33} +2.92626 q^{34} +2.23633 q^{35} +4.73038 q^{36} -7.90048 q^{37} -3.18904 q^{38} -16.8912 q^{39} +1.00000 q^{40} +0.260470 q^{41} -6.21781 q^{42} +1.00000 q^{43} -1.00000 q^{44} -4.73038 q^{45} -4.07518 q^{46} +4.67376 q^{47} -2.78036 q^{48} -1.99881 q^{49} -1.00000 q^{50} +8.13606 q^{51} +6.07518 q^{52} -7.82089 q^{53} +4.81108 q^{54} +1.00000 q^{55} +2.23633 q^{56} -8.86666 q^{57} +1.19176 q^{58} -0.284247 q^{59} +2.78036 q^{60} +9.70548 q^{61} -9.94427 q^{62} -10.5787 q^{63} +1.00000 q^{64} -6.07518 q^{65} -2.78036 q^{66} +4.43505 q^{67} -2.92626 q^{68} -11.3304 q^{69} -2.23633 q^{70} +0.755828 q^{71} -4.73038 q^{72} -14.1030 q^{73} +7.90048 q^{74} -2.78036 q^{75} +3.18904 q^{76} +2.23633 q^{77} +16.8912 q^{78} -0.0896609 q^{79} -1.00000 q^{80} -0.814626 q^{81} -0.260470 q^{82} -1.36880 q^{83} +6.21781 q^{84} +2.92626 q^{85} -1.00000 q^{86} +3.31352 q^{87} +1.00000 q^{88} -0.566497 q^{89} +4.73038 q^{90} -13.5861 q^{91} +4.07518 q^{92} -27.6486 q^{93} -4.67376 q^{94} -3.18904 q^{95} +2.78036 q^{96} -9.83384 q^{97} +1.99881 q^{98} -4.73038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * q^99

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