LMFDB - Embedded newform 4730.2.a.bb.1.7

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			1.7
Root			$-0.797340$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.797340 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.797340 q^{6} -1.54185 q^{7} -1.00000 q^{8} -2.36425 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.797340 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.797340 q^{6} -1.54185 q^{7} -1.00000 q^{8} -2.36425 q^{9} +1.00000 q^{10} -1.00000 q^{11} +0.797340 q^{12} -1.10794 q^{13} +1.54185 q^{14} -0.797340 q^{15} +1.00000 q^{16} -3.83917 q^{17} +2.36425 q^{18} +7.93463 q^{19} -1.00000 q^{20} -1.22938 q^{21} +1.00000 q^{22} -3.10794 q^{23} -0.797340 q^{24} +1.00000 q^{25} +1.10794 q^{26} -4.27713 q^{27} -1.54185 q^{28} -2.76882 q^{29} +0.797340 q^{30} +3.78854 q^{31} -1.00000 q^{32} -0.797340 q^{33} +3.83917 q^{34} +1.54185 q^{35} -2.36425 q^{36} +6.96120 q^{37} -7.93463 q^{38} -0.883404 q^{39} +1.00000 q^{40} -6.69318 q^{41} +1.22938 q^{42} +1.00000 q^{43} -1.00000 q^{44} +2.36425 q^{45} +3.10794 q^{46} -2.36057 q^{47} +0.797340 q^{48} -4.62269 q^{49} -1.00000 q^{50} -3.06113 q^{51} -1.10794 q^{52} +0.0407411 q^{53} +4.27713 q^{54} +1.00000 q^{55} +1.54185 q^{56} +6.32660 q^{57} +2.76882 q^{58} -14.7262 q^{59} -0.797340 q^{60} +11.6123 q^{61} -3.78854 q^{62} +3.64532 q^{63} +1.00000 q^{64} +1.10794 q^{65} +0.797340 q^{66} -9.13185 q^{67} -3.83917 q^{68} -2.47808 q^{69} -1.54185 q^{70} +15.6288 q^{71} +2.36425 q^{72} -0.994843 q^{73} -6.96120 q^{74} +0.797340 q^{75} +7.93463 q^{76} +1.54185 q^{77} +0.883404 q^{78} +2.35313 q^{79} -1.00000 q^{80} +3.68241 q^{81} +6.69318 q^{82} -15.6459 q^{83} -1.22938 q^{84} +3.83917 q^{85} -1.00000 q^{86} -2.20770 q^{87} +1.00000 q^{88} +7.56378 q^{89} -2.36425 q^{90} +1.70828 q^{91} -3.10794 q^{92} +3.02075 q^{93} +2.36057 q^{94} -7.93463 q^{95} -0.797340 q^{96} +6.65740 q^{97} +4.62269 q^{98} +2.36425 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.797340	0.460345	0.230172	−	0.973150i	$-0.426071\pi$
$3$	0.797340	0.460345	0.230172	+	0.973150i	$0.426071\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.797340	−0.325513
$7$	−1.54185	−0.582765	−0.291383	−	0.956607i	$-0.594115\pi$
$7$	−1.54185	−0.582765	−0.291383	+	0.956607i	$0.594115\pi$
$8$	−1.00000	−0.353553
$9$	−2.36425	−0.788083
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.797340	0.230172
$13$	−1.10794	−0.307287	−0.153643	−	0.988126i	$-0.549101\pi$
$13$	−1.10794	−0.307287	−0.153643	+	0.988126i	$0.549101\pi$
$14$	1.54185	0.412077
$15$	−0.797340	−0.205872
$16$	1.00000	0.250000
$17$	−3.83917	−0.931137	−0.465568	−	0.885012i	$-0.654150\pi$
$17$	−3.83917	−0.931137	−0.465568	+	0.885012i	$0.654150\pi$
$18$	2.36425	0.557259
$19$	7.93463	1.82033	0.910165	−	0.414247i	$-0.135955\pi$
$19$	7.93463	1.82033	0.910165	+	0.414247i	$0.135955\pi$
$20$	−1.00000	−0.223607
$21$	−1.22938	−0.268273
$22$	1.00000	0.213201
$23$	−3.10794	−0.648050	−0.324025	−	0.946049i	$-0.605036\pi$
$23$	−3.10794	−0.648050	−0.324025	+	0.946049i	$0.605036\pi$
$24$	−0.797340	−0.162756
$25$	1.00000	0.200000
$26$	1.10794	0.217285
$27$	−4.27713	−0.823134
$28$	−1.54185	−0.291383
$29$	−2.76882	−0.514158	−0.257079	−	0.966390i	$-0.582760\pi$
$29$	−2.76882	−0.514158	−0.257079	+	0.966390i	$0.582760\pi$
$30$	0.797340	0.145574
$31$	3.78854	0.680441	0.340221	−	0.940346i	$-0.389498\pi$
$31$	3.78854	0.680441	0.340221	+	0.940346i	$0.389498\pi$
$32$	−1.00000	−0.176777
$33$	−0.797340	−0.138799
$34$	3.83917	0.658413
$35$	1.54185	0.260621
$36$	−2.36425	−0.394041
$37$	6.96120	1.14441	0.572207	−	0.820109i	$-0.306087\pi$
$37$	6.96120	1.14441	0.572207	+	0.820109i	$0.306087\pi$
$38$	−7.93463	−1.28717
$39$	−0.883404	−0.141458
$40$	1.00000	0.158114
$41$	−6.69318	−1.04530	−0.522650	−	0.852547i	$-0.675056\pi$
$41$	−6.69318	−1.04530	−0.522650	+	0.852547i	$0.675056\pi$
$42$	1.22938	0.189698
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	2.36425	0.352441
$46$	3.10794	0.458240
$47$	−2.36057	−0.344325	−0.172162	−	0.985069i	$-0.555075\pi$
$47$	−2.36057	−0.344325	−0.172162	+	0.985069i	$0.555075\pi$
$48$	0.797340	0.115086
$49$	−4.62269	−0.660385
$50$	−1.00000	−0.141421
$51$	−3.06113	−0.428644
$52$	−1.10794	−0.153643
$53$	0.0407411	0.00559622	0.00279811	−	0.999996i	$-0.499109\pi$
$53$	0.0407411	0.00559622	0.00279811	+	0.999996i	$0.499109\pi$
$54$	4.27713	0.582044
$55$	1.00000	0.134840
$56$	1.54185	0.206039
$57$	6.32660	0.837979
$58$	2.76882	0.363565
$59$	−14.7262	−1.91719	−0.958593	−	0.284779i	$-0.908080\pi$
$59$	−14.7262	−1.91719	−0.958593	+	0.284779i	$0.908080\pi$
$60$	−0.797340	−0.102936
$61$	11.6123	1.48680	0.743402	−	0.668844i	$-0.233211\pi$
$61$	11.6123	1.48680	0.743402	+	0.668844i	$0.233211\pi$
$62$	−3.78854	−0.481144
$63$	3.64532	0.459267
$64$	1.00000	0.125000
$65$	1.10794	0.137423
$66$	0.797340	0.0981458
$67$	−9.13185	−1.11563	−0.557816	−	0.829964i	$-0.688361\pi$
$67$	−9.13185	−1.11563	−0.557816	+	0.829964i	$0.688361\pi$
$68$	−3.83917	−0.465568
$69$	−2.47808	−0.298326
$70$	−1.54185	−0.184287
$71$	15.6288	1.85480	0.927399	−	0.374073i	$-0.122039\pi$
$71$	15.6288	1.85480	0.927399	+	0.374073i	$0.122039\pi$
$72$	2.36425	0.278629
$73$	−0.994843	−0.116438	−0.0582188	−	0.998304i	$-0.518542\pi$
$73$	−0.994843	−0.116438	−0.0582188	+	0.998304i	$0.518542\pi$
$74$	−6.96120	−0.809224
$75$	0.797340	0.0920689
$76$	7.93463	0.910165
$77$	1.54185	0.175710
$78$	0.883404	0.100026
$79$	2.35313	0.264748	0.132374	−	0.991200i	$-0.457740\pi$
$79$	2.35313	0.264748	0.132374	+	0.991200i	$0.457740\pi$
$80$	−1.00000	−0.111803
$81$	3.68241	0.409157
$82$	6.69318	0.739138
$83$	−15.6459	−1.71736	−0.858682	−	0.512509i	$-0.828716\pi$
$83$	−15.6459	−1.71736	−0.858682	+	0.512509i	$0.828716\pi$
$84$	−1.22938	−0.134136
$85$	3.83917	0.416417
$86$	−1.00000	−0.107833
$87$	−2.20770	−0.236690
$88$	1.00000	0.106600
$89$	7.56378	0.801759	0.400879	−	0.916131i	$-0.368705\pi$
$89$	7.56378	0.801759	0.400879	+	0.916131i	$0.368705\pi$
$90$	−2.36425	−0.249214
$91$	1.70828	0.179076
$92$	−3.10794	−0.324025
$93$	3.02075	0.313237
$94$	2.36057	0.243474
$95$	−7.93463	−0.814076
$96$	−0.797340	−0.0813782
$97$	6.65740	0.675957	0.337978	−	0.941154i	$-0.390257\pi$
$97$	6.65740	0.675957	0.337978	+	0.941154i	$0.390257\pi$
$98$	4.62269	0.466963
$99$	2.36425	0.237616
$100$	1.00000	0.100000
$101$	−1.58227	−0.157442	−0.0787208	−	0.996897i	$-0.525084\pi$
$101$	−1.58227	−0.157442	−0.0787208	+	0.996897i	$0.525084\pi$
$102$	3.06113	0.303097
$103$	−10.4974	−1.03434	−0.517169	−	0.855883i	$-0.673014\pi$
$103$	−10.4974	−1.03434	−0.517169	+	0.855883i	$0.673014\pi$
$104$	1.10794	0.108642
$105$	1.22938	0.119975
$106$	−0.0407411	−0.00395712
$107$	12.2521	1.18446	0.592229	−	0.805770i	$-0.298248\pi$
$107$	12.2521	1.18446	0.592229	+	0.805770i	$0.298248\pi$
$108$	−4.27713	−0.411567
$109$	10.4965	1.00538	0.502691	−	0.864466i	$-0.332343\pi$
$109$	10.4965	1.00538	0.502691	+	0.864466i	$0.332343\pi$
$110$	−1.00000	−0.0953463
$111$	5.55045	0.526825
$112$	−1.54185	−0.145691
$113$	14.0084	1.31780	0.658900	−	0.752231i	$-0.271022\pi$
$113$	14.0084	1.31780	0.658900	+	0.752231i	$0.271022\pi$
$114$	−6.32660	−0.592541
$115$	3.10794	0.289817
$116$	−2.76882	−0.257079
$117$	2.61944	0.242167
$118$	14.7262	1.35566
$119$	5.91944	0.542634
$120$	0.797340	0.0727869
$121$	1.00000	0.0909091
$122$	−11.6123	−1.05133
$123$	−5.33675	−0.481198
$124$	3.78854	0.340221
$125$	−1.00000	−0.0894427
$126$	−3.64532	−0.324751
$127$	8.58390	0.761698	0.380849	−	0.924637i	$-0.375632\pi$
$127$	8.58390	0.761698	0.380849	+	0.924637i	$0.375632\pi$
$128$	−1.00000	−0.0883883
$129$	0.797340	0.0702019
$130$	−1.10794	−0.0971726
$131$	20.0738	1.75385	0.876926	−	0.480625i	$-0.159590\pi$
$131$	20.0738	1.75385	0.876926	+	0.480625i	$0.159590\pi$
$132$	−0.797340	−0.0693996
$133$	−12.2340	−1.06082
$134$	9.13185	0.788871
$135$	4.27713	0.368117
$136$	3.83917	0.329207
$137$	6.88382	0.588125	0.294062	−	0.955786i	$-0.404993\pi$
$137$	6.88382	0.588125	0.294062	+	0.955786i	$0.404993\pi$
$138$	2.47808	0.210949
$139$	−8.31893	−0.705602	−0.352801	−	0.935698i	$-0.614771\pi$
$139$	−8.31893	−0.705602	−0.352801	+	0.935698i	$0.614771\pi$
$140$	1.54185	0.130310
$141$	−1.88218	−0.158508
$142$	−15.6288	−1.31154
$143$	1.10794	0.0926505
$144$	−2.36425	−0.197021
$145$	2.76882	0.229938
$146$	0.994843	0.0823338
$147$	−3.68586	−0.304005
$148$	6.96120	0.572207
$149$	14.2155	1.16458	0.582290	−	0.812981i	$-0.302157\pi$
$149$	14.2155	1.16458	0.582290	+	0.812981i	$0.302157\pi$
$150$	−0.797340	−0.0651026
$151$	2.20290	0.179269	0.0896347	−	0.995975i	$-0.471430\pi$
$151$	2.20290	0.179269	0.0896347	+	0.995975i	$0.471430\pi$
$152$	−7.93463	−0.643583
$153$	9.07676	0.733813
$154$	−1.54185	−0.124246
$155$	−3.78854	−0.304302
$156$	−0.883404	−0.0707289
$157$	11.4383	0.912879	0.456439	−	0.889755i	$-0.349125\pi$
$157$	11.4383	0.912879	0.456439	+	0.889755i	$0.349125\pi$
$158$	−2.35313	−0.187205
$159$	0.0324845	0.00257619
$160$	1.00000	0.0790569
$161$	4.79198	0.377661
$162$	−3.68241	−0.289318
$163$	9.28190	0.727015	0.363507	−	0.931591i	$-0.381579\pi$
$163$	9.28190	0.727015	0.363507	+	0.931591i	$0.381579\pi$
$164$	−6.69318	−0.522650
$165$	0.797340	0.0620729
$166$	15.6459	1.21436
$167$	−7.93432	−0.613976	−0.306988	−	0.951713i	$-0.599321\pi$
$167$	−7.93432	−0.613976	−0.306988	+	0.951713i	$0.599321\pi$
$168$	1.22938	0.0948488
$169$	−11.7725	−0.905575
$170$	−3.83917	−0.294451
$171$	−18.7594	−1.43457
$172$	1.00000	0.0762493
$173$	21.9293	1.66725	0.833627	−	0.552327i	$-0.186260\pi$
$173$	21.9293	1.66725	0.833627	+	0.552327i	$0.186260\pi$
$174$	2.20770	0.167365
$175$	−1.54185	−0.116553
$176$	−1.00000	−0.0753778
$177$	−11.7418	−0.882567
$178$	−7.56378	−0.566929
$179$	17.9201	1.33941	0.669706	−	0.742626i	$-0.266420\pi$
$179$	17.9201	1.33941	0.669706	+	0.742626i	$0.266420\pi$
$180$	2.36425	0.176221
$181$	−0.396161	−0.0294464	−0.0147232	−	0.999892i	$-0.504687\pi$
$181$	−0.396161	−0.0294464	−0.0147232	+	0.999892i	$0.504687\pi$
$182$	−1.70828	−0.126626
$183$	9.25897	0.684443
$184$	3.10794	0.229120
$185$	−6.96120	−0.511798
$186$	−3.02075	−0.221492
$187$	3.83917	0.280748
$188$	−2.36057	−0.172162
$189$	6.59470	0.479694
$190$	7.93463	0.575639
$191$	10.3449	0.748532	0.374266	−	0.927321i	$-0.377895\pi$
$191$	10.3449	0.748532	0.374266	+	0.927321i	$0.377895\pi$
$192$	0.797340	0.0575431
$193$	26.9533	1.94014	0.970069	−	0.242830i	$-0.0780756\pi$
$193$	26.9533	1.94014	0.970069	+	0.242830i	$0.0780756\pi$
$194$	−6.65740	−0.477974
$195$	0.883404	0.0632619
$196$	−4.62269	−0.330192
$197$	−15.0400	−1.07155	−0.535776	−	0.844360i	$-0.679981\pi$
$197$	−15.0400	−1.07155	−0.535776	+	0.844360i	$0.679981\pi$
$198$	−2.36425	−0.168020
$199$	−2.22430	−0.157677	−0.0788383	−	0.996887i	$-0.525121\pi$
$199$	−2.22430	−0.157677	−0.0788383	+	0.996887i	$0.525121\pi$
$200$	−1.00000	−0.0707107
$201$	−7.28119	−0.513576
$202$	1.58227	0.111328
$203$	4.26912	0.299633
$204$	−3.06113	−0.214322
$205$	6.69318	0.467472
$206$	10.4974	0.731388
$207$	7.34794	0.510717
$208$	−1.10794	−0.0768217
$209$	−7.93463	−0.548850
$210$	−1.22938	−0.0848353
$211$	9.34608	0.643411	0.321705	−	0.946840i	$-0.395744\pi$
$211$	9.34608	0.643411	0.321705	+	0.946840i	$0.395744\pi$
$212$	0.0407411	0.00279811
$213$	12.4615	0.853847
$214$	−12.2521	−0.837538
$215$	−1.00000	−0.0681994
$216$	4.27713	0.291022
$217$	−5.84136	−0.396537
$218$	−10.4965	−0.710912
$219$	−0.793229	−0.0536014
$220$	1.00000	0.0674200
$221$	4.25357	0.286126
$222$	−5.55045	−0.372522
$223$	−16.6826	−1.11715	−0.558576	−	0.829453i	$-0.688652\pi$
$223$	−16.6826	−1.11715	−0.558576	+	0.829453i	$0.688652\pi$
$224$	1.54185	0.103019
$225$	−2.36425	−0.157617
$226$	−14.0084	−0.931825
$227$	0.426720	0.0283224	0.0141612	−	0.999900i	$-0.495492\pi$
$227$	0.426720	0.0283224	0.0141612	+	0.999900i	$0.495492\pi$
$228$	6.32660	0.418989
$229$	2.08701	0.137914	0.0689569	−	0.997620i	$-0.478033\pi$
$229$	2.08701	0.137914	0.0689569	+	0.997620i	$0.478033\pi$
$230$	−3.10794	−0.204931
$231$	1.22938	0.0808873
$232$	2.76882	0.181782
$233$	14.5553	0.953551	0.476775	−	0.879025i	$-0.341806\pi$
$233$	14.5553	0.953551	0.476775	+	0.879025i	$0.341806\pi$
$234$	−2.61944	−0.171238
$235$	2.36057	0.153987
$236$	−14.7262	−0.958593
$237$	1.87625	0.121875
$238$	−5.91944	−0.383700
$239$	17.9401	1.16045	0.580224	−	0.814457i	$-0.302965\pi$
$239$	17.9401	1.16045	0.580224	+	0.814457i	$0.302965\pi$
$240$	−0.797340	−0.0514681
$241$	−6.28095	−0.404592	−0.202296	−	0.979324i	$-0.564840\pi$
$241$	−6.28095	−0.404592	−0.202296	+	0.979324i	$0.564840\pi$
$242$	−1.00000	−0.0642824
$243$	15.7675	1.01149
$244$	11.6123	0.743402
$245$	4.62269	0.295333
$246$	5.33675	0.340258
$247$	−8.79108	−0.559363
$248$	−3.78854	−0.240572
$249$	−12.4751	−0.790579
$250$	1.00000	0.0632456
$251$	−7.46854	−0.471410	−0.235705	−	0.971825i	$-0.575740\pi$
$251$	−7.46854	−0.471410	−0.235705	+	0.971825i	$0.575740\pi$
$252$	3.64532	0.229634
$253$	3.10794	0.195394
$254$	−8.58390	−0.538602
$255$	3.06113	0.191695
$256$	1.00000	0.0625000
$257$	0.905186	0.0564639	0.0282320	−	0.999601i	$-0.491012\pi$
$257$	0.905186	0.0564639	0.0282320	+	0.999601i	$0.491012\pi$
$258$	−0.797340	−0.0496402
$259$	−10.7331	−0.666925
$260$	1.10794	0.0687114
$261$	6.54619	0.405199
$262$	−20.0738	−1.24016
$263$	−17.3546	−1.07013	−0.535065	−	0.844811i	$-0.679713\pi$
$263$	−17.3546	−1.07013	−0.535065	+	0.844811i	$0.679713\pi$
$264$	0.797340	0.0490729
$265$	−0.0407411	−0.00250270
$266$	12.2340	0.750116
$267$	6.03091	0.369086
$268$	−9.13185	−0.557816
$269$	−16.3542	−0.997132	−0.498566	−	0.866852i	$-0.666140\pi$
$269$	−16.3542	−0.997132	−0.498566	+	0.866852i	$0.666140\pi$
$270$	−4.27713	−0.260298
$271$	3.86001	0.234479	0.117239	−	0.993104i	$-0.462596\pi$
$271$	3.86001	0.234479	0.117239	+	0.993104i	$0.462596\pi$
$272$	−3.83917	−0.232784
$273$	1.36208	0.0824367
$274$	−6.88382	−0.415867
$275$	−1.00000	−0.0603023
$276$	−2.47808	−0.149163
$277$	−22.0709	−1.32611	−0.663056	−	0.748569i	$-0.730741\pi$
$277$	−22.0709	−1.32611	−0.663056	+	0.748569i	$0.730741\pi$
$278$	8.31893	0.498936
$279$	−8.95704	−0.536244
$280$	−1.54185	−0.0921433
$281$	−3.04874	−0.181872	−0.0909362	−	0.995857i	$-0.528986\pi$
$281$	−3.04874	−0.181872	−0.0909362	+	0.995857i	$0.528986\pi$
$282$	1.88218	0.112082
$283$	26.6122	1.58193	0.790967	−	0.611859i	$-0.209578\pi$
$283$	26.6122	1.58193	0.790967	+	0.611859i	$0.209578\pi$
$284$	15.6288	0.927399
$285$	−6.32660	−0.374756
$286$	−1.10794	−0.0655138
$287$	10.3199	0.609164
$288$	2.36425	0.139315
$289$	−2.26074	−0.132985
$290$	−2.76882	−0.162591
$291$	5.30822	0.311173
$292$	−0.994843	−0.0582188
$293$	−3.66988	−0.214397	−0.107198	−	0.994238i	$-0.534188\pi$
$293$	−3.66988	−0.214397	−0.107198	+	0.994238i	$0.534188\pi$
$294$	3.68586	0.214964
$295$	14.7262	0.857392
$296$	−6.96120	−0.404612
$297$	4.27713	0.248184
$298$	−14.2155	−0.823483
$299$	3.44340	0.199137
$300$	0.797340	0.0460345
$301$	−1.54185	−0.0888709
$302$	−2.20290	−0.126763
$303$	−1.26161	−0.0724774
$304$	7.93463	0.455082
$305$	−11.6123	−0.664919
$306$	−9.07676	−0.518884
$307$	25.2657	1.44199	0.720996	−	0.692940i	$-0.243685\pi$
$307$	25.2657	1.44199	0.720996	+	0.692940i	$0.243685\pi$
$308$	1.54185	0.0878552
$309$	−8.37000	−0.476152
$310$	3.78854	0.215174
$311$	2.33109	0.132184	0.0660921	−	0.997814i	$-0.478947\pi$
$311$	2.33109	0.132184	0.0660921	+	0.997814i	$0.478947\pi$
$312$	0.883404	0.0500129
$313$	−1.74866	−0.0988399	−0.0494200	−	0.998778i	$-0.515737\pi$
$313$	−1.74866	−0.0988399	−0.0494200	+	0.998778i	$0.515737\pi$
$314$	−11.4383	−0.645503
$315$	−3.64532	−0.205391
$316$	2.35313	0.132374
$317$	−15.3541	−0.862374	−0.431187	−	0.902262i	$-0.641905\pi$
$317$	−15.3541	−0.862374	−0.431187	+	0.902262i	$0.641905\pi$
$318$	−0.0324845	−0.00182164
$319$	2.76882	0.155024
$320$	−1.00000	−0.0559017
$321$	9.76912	0.545259
$322$	−4.79198	−0.267047
$323$	−30.4624	−1.69497
$324$	3.68241	0.204579
$325$	−1.10794	−0.0614574
$326$	−9.28190	−0.514077
$327$	8.36928	0.462822
$328$	6.69318	0.369569
$329$	3.63965	0.200660
$330$	−0.797340	−0.0438921
$331$	−27.6659	−1.52066	−0.760329	−	0.649538i	$-0.774962\pi$
$331$	−27.6659	−1.52066	−0.760329	+	0.649538i	$0.774962\pi$
$332$	−15.6459	−0.858682
$333$	−16.4580	−0.901894
$334$	7.93432	0.434147
$335$	9.13185	0.498926
$336$	−1.22938	−0.0670682
$337$	27.7248	1.51027	0.755133	−	0.655572i	$-0.227572\pi$
$337$	27.7248	1.51027	0.755133	+	0.655572i	$0.227572\pi$
$338$	11.7725	0.640338
$339$	11.1695	0.606642
$340$	3.83917	0.208208
$341$	−3.78854	−0.205161
$342$	18.7594	1.01439
$343$	17.9205	0.967614
$344$	−1.00000	−0.0539164
$345$	2.47808	0.133416
$346$	−21.9293	−1.17893
$347$	−0.889018	−0.0477250	−0.0238625	−	0.999715i	$-0.507596\pi$
$347$	−0.889018	−0.0477250	−0.0238625	+	0.999715i	$0.507596\pi$
$348$	−2.20770	−0.118345
$349$	−18.5117	−0.990908	−0.495454	−	0.868634i	$-0.664998\pi$
$349$	−18.5117	−0.990908	−0.495454	+	0.868634i	$0.664998\pi$
$350$	1.54185	0.0824154
$351$	4.73880	0.252938
$352$	1.00000	0.0533002
$353$	1.26480	0.0673183	0.0336592	−	0.999433i	$-0.489284\pi$
$353$	1.26480	0.0673183	0.0336592	+	0.999433i	$0.489284\pi$
$354$	11.7418	0.624069
$355$	−15.6288	−0.829491
$356$	7.56378	0.400879
$357$	4.71981	0.249799
$358$	−17.9201	−0.947107
$359$	15.1777	0.801049	0.400524	−	0.916286i	$-0.368828\pi$
$359$	15.1777	0.801049	0.400524	+	0.916286i	$0.368828\pi$
$360$	−2.36425	−0.124607
$361$	43.9584	2.31360
$362$	0.396161	0.0208217
$363$	0.797340	0.0418495
$364$	1.70828	0.0895380
$365$	0.994843	0.0520725
$366$	−9.25897	−0.483974
$367$	22.5445	1.17681	0.588407	−	0.808565i	$-0.299755\pi$
$367$	22.5445	1.17681	0.588407	+	0.808565i	$0.299755\pi$
$368$	−3.10794	−0.162012
$369$	15.8243	0.823783
$370$	6.96120	0.361896
$371$	−0.0628167	−0.00326128
$372$	3.02075	0.156619
$373$	−32.3140	−1.67316	−0.836578	−	0.547847i	$-0.815447\pi$
$373$	−32.3140	−1.67316	−0.836578	+	0.547847i	$0.815447\pi$
$374$	−3.83917	−0.198519
$375$	−0.797340	−0.0411745
$376$	2.36057	0.121737
$377$	3.06769	0.157994
$378$	−6.59470	−0.339195
$379$	−11.6097	−0.596350	−0.298175	−	0.954511i	$-0.596378\pi$
$379$	−11.6097	−0.596350	−0.298175	+	0.954511i	$0.596378\pi$
$380$	−7.93463	−0.407038
$381$	6.84429	0.350644
$382$	−10.3449	−0.529292
$383$	−12.2737	−0.627158	−0.313579	−	0.949562i	$-0.601528\pi$
$383$	−12.2737	−0.627158	−0.313579	+	0.949562i	$0.601528\pi$
$384$	−0.797340	−0.0406891
$385$	−1.54185	−0.0785800
$386$	−26.9533	−1.37188
$387$	−2.36425	−0.120181
$388$	6.65740	0.337978
$389$	−16.1198	−0.817306	−0.408653	−	0.912690i	$-0.634001\pi$
$389$	−16.1198	−0.817306	−0.408653	+	0.912690i	$0.634001\pi$
$390$	−0.883404	−0.0447329
$391$	11.9319	0.603423
$392$	4.62269	0.233481
$393$	16.0056	0.807377
$394$	15.0400	0.757702
$395$	−2.35313	−0.118399
$396$	2.36425	0.118808
$397$	−23.7055	−1.18974	−0.594872	−	0.803821i	$-0.702797\pi$
$397$	−23.7055	−1.18974	−0.594872	+	0.803821i	$0.702797\pi$
$398$	2.22430	0.111494
$399$	−9.75468	−0.488345
$400$	1.00000	0.0500000
$401$	38.1181	1.90353	0.951765	−	0.306829i	$-0.0992679\pi$
$401$	38.1181	1.90353	0.951765	+	0.306829i	$0.0992679\pi$
$402$	7.28119	0.363153
$403$	−4.19746	−0.209091
$404$	−1.58227	−0.0787208
$405$	−3.68241	−0.182981
$406$	−4.26912	−0.211873
$407$	−6.96120	−0.345054
$408$	3.06113	0.151548
$409$	−3.03368	−0.150006	−0.0750030	−	0.997183i	$-0.523897\pi$
$409$	−3.03368	−0.150006	−0.0750030	+	0.997183i	$0.523897\pi$
$410$	−6.69318	−0.330553
$411$	5.48875	0.270740
$412$	−10.4974	−0.517169
$413$	22.7056	1.11727
$414$	−7.34794	−0.361131
$415$	15.6459	0.768028
$416$	1.10794	0.0543211
$417$	−6.63302	−0.324820
$418$	7.93463	0.388095
$419$	7.12381	0.348021	0.174010	−	0.984744i	$-0.444327\pi$
$419$	7.12381	0.348021	0.174010	+	0.984744i	$0.444327\pi$
$420$	1.22938	0.0599876
$421$	26.4911	1.29109	0.645547	−	0.763720i	$-0.276629\pi$
$421$	26.4911	1.29109	0.645547	+	0.763720i	$0.276629\pi$
$422$	−9.34608	−0.454960
$423$	5.58097	0.271356
$424$	−0.0407411	−0.00197856
$425$	−3.83917	−0.186227
$426$	−12.4615	−0.603761
$427$	−17.9045	−0.866458
$428$	12.2521	0.592229
$429$	0.883404	0.0426511
$430$	1.00000	0.0482243
$431$	25.5980	1.23301	0.616507	−	0.787350i	$-0.288547\pi$
$431$	25.5980	1.23301	0.616507	+	0.787350i	$0.288547\pi$
$432$	−4.27713	−0.205784
$433$	23.3971	1.12439	0.562196	−	0.827004i	$-0.309956\pi$
$433$	23.3971	1.12439	0.562196	+	0.827004i	$0.309956\pi$
$434$	5.84136	0.280394
$435$	2.20770	0.105851
$436$	10.4965	0.502691
$437$	−24.6603	−1.17966
$438$	0.793229	0.0379019
$439$	29.5628	1.41095	0.705477	−	0.708733i	$-0.250733\pi$
$439$	29.5628	1.41095	0.705477	+	0.708733i	$0.250733\pi$
$440$	−1.00000	−0.0476731
$441$	10.9292	0.520438
$442$	−4.25357	−0.202322
$443$	3.80670	0.180862	0.0904308	−	0.995903i	$-0.471176\pi$
$443$	3.80670	0.180862	0.0904308	+	0.995903i	$0.471176\pi$
$444$	5.55045	0.263413
$445$	−7.56378	−0.358558
$446$	16.6826	0.789946
$447$	11.3346	0.536109
$448$	−1.54185	−0.0728456
$449$	9.97857	0.470918	0.235459	−	0.971884i	$-0.424341\pi$
$449$	9.97857	0.470918	0.235459	+	0.971884i	$0.424341\pi$
$450$	2.36425	0.111452
$451$	6.69318	0.315170
$452$	14.0084	0.658900
$453$	1.75646	0.0825258
$454$	−0.426720	−0.0200270
$455$	−1.70828	−0.0800852
$456$	−6.32660	−0.296270
$457$	−8.52399	−0.398735	−0.199368	−	0.979925i	$-0.563889\pi$
$457$	−8.52399	−0.398735	−0.199368	+	0.979925i	$0.563889\pi$
$458$	−2.08701	−0.0975198
$459$	16.4207	0.766451
$460$	3.10794	0.144908
$461$	−35.0606	−1.63294	−0.816468	−	0.577391i	$-0.804071\pi$
$461$	−35.0606	−1.63294	−0.816468	+	0.577391i	$0.804071\pi$
$462$	−1.22938	−0.0571960
$463$	−4.68102	−0.217545	−0.108773	−	0.994067i	$-0.534692\pi$
$463$	−4.68102	−0.217545	−0.108773	+	0.994067i	$0.534692\pi$
$464$	−2.76882	−0.128539
$465$	−3.02075	−0.140084
$466$	−14.5553	−0.674262
$467$	−36.4304	−1.68580	−0.842899	−	0.538071i	$-0.819153\pi$
$467$	−36.4304	−1.68580	−0.842899	+	0.538071i	$0.819153\pi$
$468$	2.61944	0.121084
$469$	14.0800	0.650152
$470$	−2.36057	−0.108885
$471$	9.12025	0.420239
$472$	14.7262	0.677828
$473$	−1.00000	−0.0459800
$474$	−1.87625	−0.0861789
$475$	7.93463	0.364066
$476$	5.91944	0.271317
$477$	−0.0963220	−0.00441028
$478$	−17.9401	−0.820560
$479$	28.1107	1.28441	0.642206	−	0.766532i	$-0.278020\pi$
$479$	28.1107	1.28441	0.642206	+	0.766532i	$0.278020\pi$
$480$	0.797340	0.0363934
$481$	−7.71258	−0.351664
$482$	6.28095	0.286090
$483$	3.82084	0.173854
$484$	1.00000	0.0454545
$485$	−6.65740	−0.302297
$486$	−15.7675	−0.715230
$487$	−40.7399	−1.84610	−0.923049	−	0.384681i	$-0.874311\pi$
$487$	−40.7399	−1.84610	−0.923049	+	0.384681i	$0.874311\pi$
$488$	−11.6123	−0.525665
$489$	7.40084	0.334677
$490$	−4.62269	−0.208832
$491$	22.4611	1.01366	0.506829	−	0.862047i	$-0.330818\pi$
$491$	22.4611	1.01366	0.506829	+	0.862047i	$0.330818\pi$
$492$	−5.33675	−0.240599
$493$	10.6300	0.478751
$494$	8.79108	0.395529
$495$	−2.36425	−0.106265
$496$	3.78854	0.170110
$497$	−24.0973	−1.08091
$498$	12.4751	0.559024
$499$	−22.3880	−1.00222	−0.501111	−	0.865383i	$-0.667075\pi$
$499$	−22.3880	−1.00222	−0.501111	+	0.865383i	$0.667075\pi$
$500$	−1.00000	−0.0447214
$501$	−6.32635	−0.282641
$502$	7.46854	0.333337
$503$	−33.3956	−1.48904	−0.744518	−	0.667603i	$-0.767320\pi$
$503$	−33.3956	−1.48904	−0.744518	+	0.667603i	$0.767320\pi$
$504$	−3.64532	−0.162375
$505$	1.58227	0.0704100
$506$	−3.10794	−0.138165
$507$	−9.38667	−0.416877
$508$	8.58390	0.380849
$509$	−1.62579	−0.0720617	−0.0360309	−	0.999351i	$-0.511471\pi$
$509$	−1.62579	−0.0720617	−0.0360309	+	0.999351i	$0.511471\pi$
$510$	−3.06113	−0.135549
$511$	1.53390	0.0678558
$512$	−1.00000	−0.0441942
$513$	−33.9375	−1.49838
$514$	−0.905186	−0.0399260
$515$	10.4974	0.462570
$516$	0.797340	0.0351010
$517$	2.36057	0.103818
$518$	10.7331	0.471587
$519$	17.4851	0.767512
$520$	−1.10794	−0.0485863
$521$	39.1274	1.71420	0.857101	−	0.515149i	$-0.172263\pi$
$521$	39.1274	1.71420	0.857101	+	0.515149i	$0.172263\pi$
$522$	−6.54619	−0.286519
$523$	3.34218	0.146143	0.0730717	−	0.997327i	$-0.476720\pi$
$523$	3.34218	0.146143	0.0730717	+	0.997327i	$0.476720\pi$
$524$	20.0738	0.876926
$525$	−1.22938	−0.0536546
$526$	17.3546	0.756696
$527$	−14.5448	−0.633584
$528$	−0.797340	−0.0346998
$529$	−13.3407	−0.580031
$530$	0.0407411	0.00176968
$531$	34.8164	1.51090
$532$	−12.2340	−0.530412
$533$	7.41563	0.321207
$534$	−6.03091	−0.260983
$535$	−12.2521	−0.529706
$536$	9.13185	0.394436
$537$	14.2884	0.616591
$538$	16.3542	0.705079
$539$	4.62269	0.199113
$540$	4.27713	0.184058
$541$	0.335401	0.0144200	0.00721001	−	0.999974i	$-0.497705\pi$
$541$	0.335401	0.0144200	0.00721001	+	0.999974i	$0.497705\pi$
$542$	−3.86001	−0.165802
$543$	−0.315875	−0.0135555
$544$	3.83917	0.164603
$545$	−10.4965	−0.449620
$546$	−1.36208	−0.0582916
$547$	3.32579	0.142201	0.0711003	−	0.997469i	$-0.477349\pi$
$547$	3.32579	0.142201	0.0711003	+	0.997469i	$0.477349\pi$
$548$	6.88382	0.294062
$549$	−27.4544	−1.17173
$550$	1.00000	0.0426401
$551$	−21.9696	−0.935937
$552$	2.47808	0.105474
$553$	−3.62818	−0.154286
$554$	22.0709	0.937703
$555$	−5.55045	−0.235603
$556$	−8.31893	−0.352801
$557$	−9.00032	−0.381356	−0.190678	−	0.981653i	$-0.561069\pi$
$557$	−9.00032	−0.381356	−0.190678	+	0.981653i	$0.561069\pi$
$558$	8.95704	0.379182
$559$	−1.10794	−0.0468608
$560$	1.54185	0.0651551
$561$	3.06113	0.129241
$562$	3.04874	0.128603
$563$	7.90272	0.333060	0.166530	−	0.986036i	$-0.446744\pi$
$563$	7.90272	0.333060	0.166530	+	0.986036i	$0.446744\pi$
$564$	−1.88218	−0.0792540
$565$	−14.0084	−0.589338
$566$	−26.6122	−1.11860
$567$	−5.67774	−0.238443
$568$	−15.6288	−0.655770
$569$	−43.8015	−1.83625	−0.918127	−	0.396286i	$-0.870299\pi$
$569$	−43.8015	−1.83625	−0.918127	+	0.396286i	$0.870299\pi$
$570$	6.32660	0.264992
$571$	29.5061	1.23479	0.617396	−	0.786652i	$-0.288188\pi$
$571$	29.5061	1.23479	0.617396	+	0.786652i	$0.288188\pi$
$572$	1.10794	0.0463252
$573$	8.24842	0.344583
$574$	−10.3199	−0.430744
$575$	−3.10794	−0.129610
$576$	−2.36425	−0.0985103
$577$	−25.2189	−1.04988	−0.524938	−	0.851140i	$-0.675912\pi$
$577$	−25.2189	−1.04988	−0.524938	+	0.851140i	$0.675912\pi$
$578$	2.26074	0.0940343
$579$	21.4909	0.893132
$580$	2.76882	0.114969
$581$	24.1237	1.00082
$582$	−5.30822	−0.220033
$583$	−0.0407411	−0.00168732
$584$	0.994843	0.0411669
$585$	−2.61944	−0.108301
$586$	3.66988	0.151601
$587$	−19.9248	−0.822385	−0.411192	−	0.911549i	$-0.634888\pi$
$587$	−19.9248	−0.822385	−0.411192	+	0.911549i	$0.634888\pi$
$588$	−3.68586	−0.152002
$589$	30.0606	1.23863
$590$	−14.7262	−0.606268
$591$	−11.9920	−0.493284
$592$	6.96120	0.286104
$593$	45.6001	1.87257	0.936286	−	0.351239i	$-0.114239\pi$
$593$	45.6001	1.87257	0.936286	+	0.351239i	$0.114239\pi$
$594$	−4.27713	−0.175493
$595$	−5.91944	−0.242673
$596$	14.2155	0.582290
$597$	−1.77353	−0.0725856
$598$	−3.44340	−0.140811
$599$	−22.2320	−0.908375	−0.454188	−	0.890906i	$-0.650070\pi$
$599$	−22.2320	−0.908375	−0.454188	+	0.890906i	$0.650070\pi$
$600$	−0.797340	−0.0325513
$601$	6.91402	0.282029	0.141014	−	0.990008i	$-0.454964\pi$
$601$	6.91402	0.282029	0.141014	+	0.990008i	$0.454964\pi$
$602$	1.54185	0.0628412
$603$	21.5900	0.879211
$604$	2.20290	0.0896347
$605$	−1.00000	−0.0406558
$606$	1.26161	0.0512493
$607$	−21.9576	−0.891233	−0.445617	−	0.895224i	$-0.647016\pi$
$607$	−21.9576	−0.891233	−0.445617	+	0.895224i	$0.647016\pi$
$608$	−7.93463	−0.321792
$609$	3.40394	0.137935
$610$	11.6123	0.470169
$611$	2.61537	0.105806
$612$	9.07676	0.366906
$613$	29.5738	1.19447	0.597237	−	0.802064i	$-0.296265\pi$
$613$	29.5738	1.19447	0.597237	+	0.802064i	$0.296265\pi$
$614$	−25.2657	−1.01964
$615$	5.33675	0.215198
$616$	−1.54185	−0.0621230
$617$	−30.8554	−1.24219	−0.621095	−	0.783735i	$-0.713312\pi$
$617$	−30.8554	−1.24219	−0.621095	+	0.783735i	$0.713312\pi$
$618$	8.37000	0.336691
$619$	41.7274	1.67717	0.838584	−	0.544773i	$-0.183384\pi$
$619$	41.7274	1.67717	0.838584	+	0.544773i	$0.183384\pi$
$620$	−3.78854	−0.152151
$621$	13.2931	0.533432
$622$	−2.33109	−0.0934684
$623$	−11.6622	−0.467237
$624$	−0.883404	−0.0353645
$625$	1.00000	0.0400000
$626$	1.74866	0.0698904
$627$	−6.32660	−0.252660
$628$	11.4383	0.456439
$629$	−26.7253	−1.06561
$630$	3.64532	0.145233
$631$	12.5749	0.500599	0.250300	−	0.968168i	$-0.419471\pi$
$631$	12.5749	0.500599	0.250300	+	0.968168i	$0.419471\pi$
$632$	−2.35313	−0.0936026
$633$	7.45201	0.296191
$634$	15.3541	0.609791
$635$	−8.58390	−0.340642
$636$	0.0324845	0.00128809
$637$	5.12166	0.202927
$638$	−2.76882	−0.109619
$639$	−36.9504	−1.46173
$640$	1.00000	0.0395285
$641$	38.1618	1.50730	0.753651	−	0.657275i	$-0.228291\pi$
$641$	38.1618	1.50730	0.753651	+	0.657275i	$0.228291\pi$
$642$	−9.76912	−0.385556
$643$	20.0564	0.790947	0.395473	−	0.918477i	$-0.370581\pi$
$643$	20.0564	0.790947	0.395473	+	0.918477i	$0.370581\pi$
$644$	4.79198	0.188830
$645$	−0.797340	−0.0313952
$646$	30.4624	1.19853
$647$	37.6532	1.48030	0.740149	−	0.672443i	$-0.234755\pi$
$647$	37.6532	1.48030	0.740149	+	0.672443i	$0.234755\pi$
$648$	−3.68241	−0.144659
$649$	14.7262	0.578053
$650$	1.10794	0.0434569
$651$	−4.65755	−0.182544
$652$	9.28190	0.363507
$653$	−42.4118	−1.65970	−0.829850	−	0.557986i	$-0.811574\pi$
$653$	−42.4118	−1.65970	−0.829850	+	0.557986i	$0.811574\pi$
$654$	−8.36928	−0.327265
$655$	−20.0738	−0.784346
$656$	−6.69318	−0.261325
$657$	2.35206	0.0917625
$658$	−3.63965	−0.141888
$659$	45.9687	1.79069	0.895343	−	0.445377i	$-0.146930\pi$
$659$	45.9687	1.79069	0.895343	+	0.445377i	$0.146930\pi$
$660$	0.797340	0.0310364
$661$	−3.82044	−0.148598	−0.0742989	−	0.997236i	$-0.523672\pi$
$661$	−3.82044	−0.148598	−0.0742989	+	0.997236i	$0.523672\pi$
$662$	27.6659	1.07527
$663$	3.39154	0.131717
$664$	15.6459	0.607180
$665$	12.2340	0.474415
$666$	16.4580	0.637735
$667$	8.60534	0.333200
$668$	−7.93432	−0.306988
$669$	−13.3017	−0.514275
$670$	−9.13185	−0.352794
$671$	−11.6123	−0.448289
$672$	1.22938	0.0474244
$673$	0.352240	0.0135779	0.00678894	−	0.999977i	$-0.497839\pi$
$673$	0.352240	0.0135779	0.00678894	+	0.999977i	$0.497839\pi$
$674$	−27.7248	−1.06792
$675$	−4.27713	−0.164627
$676$	−11.7725	−0.452787
$677$	−3.16612	−0.121684	−0.0608419	−	0.998147i	$-0.519379\pi$
$677$	−3.16612	−0.121684	−0.0608419	+	0.998147i	$0.519379\pi$
$678$	−11.1695	−0.428961
$679$	−10.2647	−0.393924
$680$	−3.83917	−0.147226
$681$	0.340241	0.0130381
$682$	3.78854	0.145071
$683$	6.41970	0.245643	0.122821	−	0.992429i	$-0.460806\pi$
$683$	6.41970	0.245643	0.122821	+	0.992429i	$0.460806\pi$
$684$	−18.7594	−0.717285
$685$	−6.88382	−0.263017
$686$	−17.9205	−0.684207
$687$	1.66406	0.0634879
$688$	1.00000	0.0381246
$689$	−0.0451386	−0.00171964
$690$	−2.47808	−0.0943391
$691$	40.2445	1.53097	0.765486	−	0.643453i	$-0.222499\pi$
$691$	40.2445	1.53097	0.765486	+	0.643453i	$0.222499\pi$
$692$	21.9293	0.833627
$693$	−3.64532	−0.138474
$694$	0.889018	0.0337467
$695$	8.31893	0.315555
$696$	2.20770	0.0836825
$697$	25.6963	0.973317
$698$	18.5117	0.700678
$699$	11.6055	0.438962
$700$	−1.54185	−0.0582765
$701$	−21.6765	−0.818712	−0.409356	−	0.912375i	$-0.634247\pi$
$701$	−21.6765	−0.818712	−0.409356	+	0.912375i	$0.634247\pi$
$702$	−4.73880	−0.178854
$703$	55.2346	2.08321
$704$	−1.00000	−0.0376889
$705$	1.88218	0.0708869
$706$	−1.26480	−0.0476012
$707$	2.43962	0.0917515
$708$	−11.7418	−0.441283
$709$	23.8119	0.894274	0.447137	−	0.894465i	$-0.352444\pi$
$709$	23.8119	0.894274	0.447137	+	0.894465i	$0.352444\pi$
$710$	15.6288	0.586539
$711$	−5.56339	−0.208643
$712$	−7.56378	−0.283465
$713$	−11.7745	−0.440960
$714$	−4.71981	−0.176634
$715$	−1.10794	−0.0414345
$716$	17.9201	0.669706
$717$	14.3043	0.534206
$718$	−15.1777	−0.566427
$719$	−35.9884	−1.34214	−0.671071	−	0.741393i	$-0.734165\pi$
$719$	−35.9884	−1.34214	−0.671071	+	0.741393i	$0.734165\pi$
$720$	2.36425	0.0881103
$721$	16.1854	0.602777
$722$	−43.9584	−1.63596
$723$	−5.00806	−0.186252
$724$	−0.396161	−0.0147232
$725$	−2.76882	−0.102832
$726$	−0.797340	−0.0295921
$727$	1.77159	0.0657046	0.0328523	−	0.999460i	$-0.489541\pi$
$727$	1.77159	0.0657046	0.0328523	+	0.999460i	$0.489541\pi$
$728$	−1.70828	−0.0633129
$729$	1.52485	0.0564759
$730$	−0.994843	−0.0368208
$731$	−3.83917	−0.141997
$732$	9.25897	0.342221
$733$	−34.4755	−1.27338	−0.636691	−	0.771119i	$-0.719697\pi$
$733$	−34.4755	−1.27338	−0.636691	+	0.771119i	$0.719697\pi$
$734$	−22.5445	−0.832133
$735$	3.68586	0.135955
$736$	3.10794	0.114560
$737$	9.13185	0.336376
$738$	−15.8243	−0.582502
$739$	37.1542	1.36674	0.683370	−	0.730072i	$-0.260513\pi$
$739$	37.1542	1.36674	0.683370	+	0.730072i	$0.260513\pi$
$740$	−6.96120	−0.255899
$741$	−7.00948	−0.257500
$742$	0.0628167	0.00230607
$743$	−19.8144	−0.726919	−0.363460	−	0.931610i	$-0.618405\pi$
$743$	−19.8144	−0.726919	−0.363460	+	0.931610i	$0.618405\pi$
$744$	−3.02075	−0.110746
$745$	−14.2155	−0.520816
$746$	32.3140	1.18310
$747$	36.9909	1.35342
$748$	3.83917	0.140374
$749$	−18.8910	−0.690261
$750$	0.797340	0.0291148
$751$	−6.87619	−0.250916	−0.125458	−	0.992099i	$-0.540040\pi$
$751$	−6.87619	−0.250916	−0.125458	+	0.992099i	$0.540040\pi$
$752$	−2.36057	−0.0860811
$753$	−5.95497	−0.217011
$754$	−3.06769	−0.111719
$755$	−2.20290	−0.0801718
$756$	6.59470	0.239847
$757$	14.6193	0.531346	0.265673	−	0.964063i	$-0.414406\pi$
$757$	14.6193	0.531346	0.265673	+	0.964063i	$0.414406\pi$
$758$	11.6097	0.421683
$759$	2.47808	0.0899488
$760$	7.93463	0.287819
$761$	16.9298	0.613707	0.306853	−	0.951757i	$-0.400724\pi$
$761$	16.9298	0.613707	0.306853	+	0.951757i	$0.400724\pi$
$762$	−6.84429	−0.247943
$763$	−16.1840	−0.585901
$764$	10.3449	0.374266
$765$	−9.07676	−0.328171
$766$	12.2737	0.443468
$767$	16.3157	0.589126
$768$	0.797340	0.0287715
$769$	32.5040	1.17212	0.586061	−	0.810267i	$-0.300678\pi$
$769$	32.5040	1.17212	0.586061	+	0.810267i	$0.300678\pi$
$770$	1.54185	0.0555645
$771$	0.721741	0.0259929
$772$	26.9533	0.970069
$773$	0.0944775	0.00339812	0.00169906	−	0.999999i	$-0.499459\pi$
$773$	0.0944775	0.00339812	0.00169906	+	0.999999i	$0.499459\pi$
$774$	2.36425	0.0849811
$775$	3.78854	0.136088
$776$	−6.65740	−0.238987
$777$	−8.55797	−0.307015
$778$	16.1198	0.577923
$779$	−53.1079	−1.90279
$780$	0.883404	0.0316309
$781$	−15.6288	−0.559243
$782$	−11.9319	−0.426685
$783$	11.8426	0.423221
$784$	−4.62269	−0.165096
$785$	−11.4383	−0.408252
$786$	−16.0056	−0.570901
$787$	17.6027	0.627467	0.313733	−	0.949511i	$-0.398420\pi$
$787$	17.6027	0.627467	0.313733	+	0.949511i	$0.398420\pi$
$788$	−15.0400	−0.535776
$789$	−13.8375	−0.492628
$790$	2.35313	0.0837207
$791$	−21.5989	−0.767968
$792$	−2.36425	−0.0840099
$793$	−12.8657	−0.456875
$794$	23.7055	0.841276
$795$	−0.0324845	−0.00115211
$796$	−2.22430	−0.0788383
$797$	−27.3366	−0.968311	−0.484156	−	0.874982i	$-0.660873\pi$
$797$	−27.3366	−0.968311	−0.484156	+	0.874982i	$0.660873\pi$
$798$	9.75468	0.345312
$799$	9.06264	0.320613
$800$	−1.00000	−0.0353553
$801$	−17.8827	−0.631852
$802$	−38.1181	−1.34600
$803$	0.994843	0.0351073
$804$	−7.28119	−0.256788
$805$	−4.79198	−0.168895
$806$	4.19746	0.147849
$807$	−13.0399	−0.459025
$808$	1.58227	0.0556640
$809$	24.5666	0.863714	0.431857	−	0.901942i	$-0.357858\pi$
$809$	24.5666	0.863714	0.431857	+	0.901942i	$0.357858\pi$
$810$	3.68241	0.129387
$811$	9.74512	0.342197	0.171099	−	0.985254i	$-0.445268\pi$
$811$	9.74512	0.342197	0.171099	+	0.985254i	$0.445268\pi$
$812$	4.26912	0.149817
$813$	3.07774	0.107941
$814$	6.96120	0.243990
$815$	−9.28190	−0.325131
$816$	−3.06113	−0.107161
$817$	7.93463	0.277598
$818$	3.03368	0.106070
$819$	−4.03879	−0.141127
$820$	6.69318	0.233736
$821$	46.5085	1.62316	0.811579	−	0.584243i	$-0.198608\pi$
$821$	46.5085	1.62316	0.811579	+	0.584243i	$0.198608\pi$
$822$	−5.48875	−0.191442
$823$	−33.6425	−1.17270	−0.586351	−	0.810057i	$-0.699436\pi$
$823$	−33.6425	−1.17270	−0.586351	+	0.810057i	$0.699436\pi$
$824$	10.4974	0.365694
$825$	−0.797340	−0.0277598
$826$	−22.7056	−0.790029
$827$	14.4250	0.501606	0.250803	−	0.968038i	$-0.419305\pi$
$827$	14.4250	0.501606	0.250803	+	0.968038i	$0.419305\pi$
$828$	7.34794	0.255358
$829$	−23.6766	−0.822322	−0.411161	−	0.911563i	$-0.634877\pi$
$829$	−23.6766	−0.822322	−0.411161	+	0.911563i	$0.634877\pi$
$830$	−15.6459	−0.543078
$831$	−17.5980	−0.610469
$832$	−1.10794	−0.0384108
$833$	17.7473	0.614908
$834$	6.63302	0.229683
$835$	7.93432	0.274578
$836$	−7.93463	−0.274425
$837$	−16.2041	−0.560094
$838$	−7.12381	−0.246088
$839$	47.5625	1.64204	0.821020	−	0.570899i	$-0.193405\pi$
$839$	47.5625	1.64204	0.821020	+	0.570899i	$0.193405\pi$
$840$	−1.22938	−0.0424177
$841$	−21.3336	−0.735642
$842$	−26.4911	−0.912942
$843$	−2.43088	−0.0837240
$844$	9.34608	0.321705
$845$	11.7725	0.404985
$846$	−5.58097	−0.191878
$847$	−1.54185	−0.0529787
$848$	0.0407411	0.00139905
$849$	21.2190	0.728235
$850$	3.83917	0.131683
$851$	−21.6350	−0.741638
$852$	12.4615	0.426923
$853$	7.72737	0.264580	0.132290	−	0.991211i	$-0.457767\pi$
$853$	7.72737	0.264580	0.132290	+	0.991211i	$0.457767\pi$
$854$	17.9045	0.612678
$855$	18.7594	0.641559
$856$	−12.2521	−0.418769
$857$	−30.0118	−1.02518	−0.512591	−	0.858633i	$-0.671314\pi$
$857$	−30.0118	−1.02518	−0.512591	+	0.858633i	$0.671314\pi$
$858$	−0.883404	−0.0301589
$859$	1.29093	0.0440460	0.0220230	−	0.999757i	$-0.492989\pi$
$859$	1.29093	0.0440460	0.0220230	+	0.999757i	$0.492989\pi$
$860$	−1.00000	−0.0340997
$861$	8.22847	0.280426
$862$	−25.5980	−0.871872
$863$	−1.94837	−0.0663233	−0.0331616	−	0.999450i	$-0.510558\pi$
$863$	−1.94837	−0.0663233	−0.0331616	+	0.999450i	$0.510558\pi$
$864$	4.27713	0.145511
$865$	−21.9293	−0.745619
$866$	−23.3971	−0.795066
$867$	−1.80258	−0.0612188
$868$	−5.84136	−0.198269
$869$	−2.35313	−0.0798246
$870$	−2.20770	−0.0748479
$871$	10.1175	0.342819
$872$	−10.4965	−0.355456
$873$	−15.7398	−0.532710
$874$	24.6603	0.834148
$875$	1.54185	0.0521241
$876$	−0.793229	−0.0268007
$877$	−1.92327	−0.0649443	−0.0324722	−	0.999473i	$-0.510338\pi$
$877$	−1.92327	−0.0649443	−0.0324722	+	0.999473i	$0.510338\pi$
$878$	−29.5628	−0.997695
$879$	−2.92614	−0.0986964
$880$	1.00000	0.0337100
$881$	19.6557	0.662216	0.331108	−	0.943593i	$-0.392578\pi$
$881$	19.6557	0.662216	0.331108	+	0.943593i	$0.392578\pi$
$882$	−10.9292	−0.368005
$883$	6.59115	0.221810	0.110905	−	0.993831i	$-0.464625\pi$
$883$	6.59115	0.221810	0.110905	+	0.993831i	$0.464625\pi$
$884$	4.25357	0.143063
$885$	11.7418	0.394696
$886$	−3.80670	−0.127888
$887$	0.548999	0.0184336	0.00921680	−	0.999958i	$-0.497066\pi$
$887$	0.548999	0.0184336	0.00921680	+	0.999958i	$0.497066\pi$
$888$	−5.55045	−0.186261
$889$	−13.2351	−0.443891
$890$	7.56378	0.253538
$891$	−3.68241	−0.123366
$892$	−16.6826	−0.558576
$893$	−18.7302	−0.626784
$894$	−11.3346	−0.379086
$895$	−17.9201	−0.599003
$896$	1.54185	0.0515097
$897$	2.74556	0.0916717
$898$	−9.97857	−0.332989
$899$	−10.4898	−0.349854
$900$	−2.36425	−0.0788083
$901$	−0.156412	−0.00521084
$902$	−6.69318	−0.222859
$903$	−1.22938	−0.0409112
$904$	−14.0084	−0.465912
$905$	0.396161	0.0131688
$906$	−1.75646	−0.0583545
$907$	−43.7416	−1.45241	−0.726207	−	0.687476i	$-0.758719\pi$
$907$	−43.7416	−1.45241	−0.726207	+	0.687476i	$0.758719\pi$
$908$	0.426720	0.0141612
$909$	3.74088	0.124077
$910$	1.70828	0.0566288
$911$	−13.9346	−0.461675	−0.230837	−	0.972992i	$-0.574147\pi$
$911$	−13.9346	−0.461675	−0.230837	+	0.972992i	$0.574147\pi$
$912$	6.32660	0.209495
$913$	15.6459	0.517805
$914$	8.52399	0.281948
$915$	−9.25897	−0.306092
$916$	2.08701	0.0689569
$917$	−30.9508	−1.02208
$918$	−16.4207	−0.541962
$919$	−22.8133	−0.752540	−0.376270	−	0.926510i	$-0.622794\pi$
$919$	−22.8133	−0.752540	−0.376270	+	0.926510i	$0.622794\pi$
$920$	−3.10794	−0.102466
$921$	20.1454	0.663813
$922$	35.0606	1.15466
$923$	−17.3158	−0.569955
$924$	1.22938	0.0404437
$925$	6.96120	0.228883
$926$	4.68102	0.153828
$927$	24.8184	0.815145
$928$	2.76882	0.0908911
$929$	−14.1156	−0.463119	−0.231559	−	0.972821i	$-0.574383\pi$
$929$	−14.1156	−0.463119	−0.231559	+	0.972821i	$0.574383\pi$
$930$	3.02075	0.0990544
$931$	−36.6794	−1.20212
$932$	14.5553	0.476775
$933$	1.85868	0.0608503
$934$	36.4304	1.19204
$935$	−3.83917	−0.125554
$936$	−2.61944	−0.0856191
$937$	15.2763	0.499055	0.249528	−	0.968368i	$-0.419725\pi$
$937$	15.2763	0.499055	0.249528	+	0.968368i	$0.419725\pi$
$938$	−14.0800	−0.459727
$939$	−1.39428	−0.0455004
$940$	2.36057	0.0769933
$941$	−8.03056	−0.261789	−0.130894	−	0.991396i	$-0.541785\pi$
$941$	−8.03056	−0.261789	−0.130894	+	0.991396i	$0.541785\pi$
$942$	−9.12025	−0.297154
$943$	20.8020	0.677406
$944$	−14.7262	−0.479297
$945$	−6.59470	−0.214526
$946$	1.00000	0.0325128
$947$	−33.0870	−1.07518	−0.537591	−	0.843205i	$-0.680666\pi$
$947$	−33.0870	−1.07518	−0.537591	+	0.843205i	$0.680666\pi$
$948$	1.87625	0.0609377
$949$	1.10222	0.0357797
$950$	−7.93463	−0.257433
$951$	−12.2425	−0.396990
$952$	−5.91944	−0.191850
$953$	28.7463	0.931183	0.465591	−	0.885000i	$-0.345842\pi$
$953$	28.7463	0.931183	0.465591	+	0.885000i	$0.345842\pi$
$954$	0.0963220	0.00311854
$955$	−10.3449	−0.334754
$956$	17.9401	0.580224
$957$	2.20770	0.0713647
$958$	−28.1107	−0.908216
$959$	−10.6138	−0.342739
$960$	−0.797340	−0.0257341
$961$	−16.6470	−0.537000
$962$	7.71258	0.248664
$963$	−28.9671	−0.933451
$964$	−6.28095	−0.202296
$965$	−26.9533	−0.867656
$966$	−3.82084	−0.122933
$967$	−45.0894	−1.44998	−0.724988	−	0.688761i	$-0.758155\pi$
$967$	−45.0894	−1.44998	−0.724988	+	0.688761i	$0.758155\pi$
$968$	−1.00000	−0.0321412
$969$	−24.2889	−0.780273
$970$	6.65740	0.213756
$971$	−46.8478	−1.50342	−0.751709	−	0.659495i	$-0.770770\pi$
$971$	−46.8478	−1.50342	−0.751709	+	0.659495i	$0.770770\pi$
$972$	15.7675	0.505744
$973$	12.8266	0.411200
$974$	40.7399	1.30539
$975$	−0.883404	−0.0282916
$976$	11.6123	0.371701
$977$	−52.7059	−1.68621	−0.843105	−	0.537749i	$-0.819275\pi$
$977$	−52.7059	−1.68621	−0.843105	+	0.537749i	$0.819275\pi$
$978$	−7.40084	−0.236653
$979$	−7.56378	−0.241739
$980$	4.62269	0.147667
$981$	−24.8163	−0.792324
$982$	−22.4611	−0.716764
$983$	40.4769	1.29101	0.645507	−	0.763755i	$-0.276646\pi$
$983$	40.4769	1.29101	0.645507	+	0.763755i	$0.276646\pi$
$984$	5.33675	0.170129
$985$	15.0400	0.479213
$986$	−10.6300	−0.338528
$987$	2.90204	0.0923729
$988$	−8.79108	−0.279682
$989$	−3.10794	−0.0988267
$990$	2.36425	0.0751407
$991$	−30.3799	−0.965050	−0.482525	−	0.875882i	$-0.660280\pi$
$991$	−30.3799	−0.965050	−0.482525	+	0.875882i	$0.660280\pi$
$992$	−3.78854	−0.120286
$993$	−22.0592	−0.700027
$994$	24.0973	0.764320
$995$	2.22430	0.0705151
$996$	−12.4751	−0.395290
$997$	51.8876	1.64330	0.821649	−	0.569994i	$-0.193054\pi$
$997$	51.8876	1.64330	0.821649	+	0.569994i	$0.193054\pi$
$998$	22.3880	0.708678
$999$	−29.7740	−0.942007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bb.1.7	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bb.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.797340 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.797340 q^{6} -1.54185 q^{7} -1.00000 q^{8} -2.36425 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.797340 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.797340 q^{6} -1.54185 q^{7} -1.00000 q^{8} -2.36425 q^{9} +1.00000 q^{10} -1.00000 q^{11} +0.797340 q^{12} -1.10794 q^{13} +1.54185 q^{14} -0.797340 q^{15} +1.00000 q^{16} -3.83917 q^{17} +2.36425 q^{18} +7.93463 q^{19} -1.00000 q^{20} -1.22938 q^{21} +1.00000 q^{22} -3.10794 q^{23} -0.797340 q^{24} +1.00000 q^{25} +1.10794 q^{26} -4.27713 q^{27} -1.54185 q^{28} -2.76882 q^{29} +0.797340 q^{30} +3.78854 q^{31} -1.00000 q^{32} -0.797340 q^{33} +3.83917 q^{34} +1.54185 q^{35} -2.36425 q^{36} +6.96120 q^{37} -7.93463 q^{38} -0.883404 q^{39} +1.00000 q^{40} -6.69318 q^{41} +1.22938 q^{42} +1.00000 q^{43} -1.00000 q^{44} +2.36425 q^{45} +3.10794 q^{46} -2.36057 q^{47} +0.797340 q^{48} -4.62269 q^{49} -1.00000 q^{50} -3.06113 q^{51} -1.10794 q^{52} +0.0407411 q^{53} +4.27713 q^{54} +1.00000 q^{55} +1.54185 q^{56} +6.32660 q^{57} +2.76882 q^{58} -14.7262 q^{59} -0.797340 q^{60} +11.6123 q^{61} -3.78854 q^{62} +3.64532 q^{63} +1.00000 q^{64} +1.10794 q^{65} +0.797340 q^{66} -9.13185 q^{67} -3.83917 q^{68} -2.47808 q^{69} -1.54185 q^{70} +15.6288 q^{71} +2.36425 q^{72} -0.994843 q^{73} -6.96120 q^{74} +0.797340 q^{75} +7.93463 q^{76} +1.54185 q^{77} +0.883404 q^{78} +2.35313 q^{79} -1.00000 q^{80} +3.68241 q^{81} +6.69318 q^{82} -15.6459 q^{83} -1.22938 q^{84} +3.83917 q^{85} -1.00000 q^{86} -2.20770 q^{87} +1.00000 q^{88} +7.56378 q^{89} -2.36425 q^{90} +1.70828 q^{91} -3.10794 q^{92} +3.02075 q^{93} +2.36057 q^{94} -7.93463 q^{95} -0.797340 q^{96} +6.65740 q^{97} +4.62269 q^{98} +2.36425 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 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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