LMFDB - Embedded newform 6045.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$1$
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} - 2 x^{10} - 15 x^{9} + 29 x^{8} + 81 x^{7} - 151 x^{6} - 192 x^{5} + 345 x^{4} + 199 x^{3} + \cdots + 118 $ x^11 - 2x^10 - 15x^9 + 29x^8 + 81x^7 - 151x^6 - 192x^5 + 345x^4 + 199x^3 - 344x^2 - 70x + 118
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.45401$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.45401 q^{2} -1.00000 q^{3} +0.114145 q^{4} -1.00000 q^{5} +1.45401 q^{6} +3.05854 q^{7} +2.74205 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.45401 q^{2} -1.00000 q^{3} +0.114145 q^{4} -1.00000 q^{5} +1.45401 q^{6} +3.05854 q^{7} +2.74205 q^{8} +1.00000 q^{9} +1.45401 q^{10} -0.438814 q^{11} -0.114145 q^{12} -1.00000 q^{13} -4.44714 q^{14} +1.00000 q^{15} -4.21526 q^{16} -2.30324 q^{17} -1.45401 q^{18} +1.98206 q^{19} -0.114145 q^{20} -3.05854 q^{21} +0.638040 q^{22} +6.52136 q^{23} -2.74205 q^{24} +1.00000 q^{25} +1.45401 q^{26} -1.00000 q^{27} +0.349117 q^{28} +1.09739 q^{29} -1.45401 q^{30} -1.00000 q^{31} +0.644929 q^{32} +0.438814 q^{33} +3.34893 q^{34} -3.05854 q^{35} +0.114145 q^{36} -3.49090 q^{37} -2.88194 q^{38} +1.00000 q^{39} -2.74205 q^{40} +0.573020 q^{41} +4.44714 q^{42} -11.2767 q^{43} -0.0500886 q^{44} -1.00000 q^{45} -9.48213 q^{46} +8.21740 q^{47} +4.21526 q^{48} +2.35464 q^{49} -1.45401 q^{50} +2.30324 q^{51} -0.114145 q^{52} -10.1119 q^{53} +1.45401 q^{54} +0.438814 q^{55} +8.38666 q^{56} -1.98206 q^{57} -1.59562 q^{58} -1.03869 q^{59} +0.114145 q^{60} -1.03222 q^{61} +1.45401 q^{62} +3.05854 q^{63} +7.49279 q^{64} +1.00000 q^{65} -0.638040 q^{66} -12.0916 q^{67} -0.262904 q^{68} -6.52136 q^{69} +4.44714 q^{70} +2.55812 q^{71} +2.74205 q^{72} -12.9928 q^{73} +5.07580 q^{74} -1.00000 q^{75} +0.226243 q^{76} -1.34213 q^{77} -1.45401 q^{78} -1.52685 q^{79} +4.21526 q^{80} +1.00000 q^{81} -0.833177 q^{82} +4.80297 q^{83} -0.349117 q^{84} +2.30324 q^{85} +16.3965 q^{86} -1.09739 q^{87} -1.20325 q^{88} -7.11127 q^{89} +1.45401 q^{90} -3.05854 q^{91} +0.744383 q^{92} +1.00000 q^{93} -11.9482 q^{94} -1.98206 q^{95} -0.644929 q^{96} +3.24049 q^{97} -3.42367 q^{98} -0.438814 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9} - 2 q^{10} - 12 q^{12} - 11 q^{13} + 5 q^{14} + 11 q^{15} - 10 q^{16} - 3 q^{17} + 2 q^{18} - 8 q^{19} - 12 q^{20} - 4 q^{21} - 3 q^{22} + 11 q^{23} - 3 q^{24} + 11 q^{25} - 2 q^{26} - 11 q^{27} + 14 q^{28} - 14 q^{29} + 2 q^{30} - 11 q^{31} + 8 q^{32} - 11 q^{34} - 4 q^{35} + 12 q^{36} + 7 q^{37} + 8 q^{38} + 11 q^{39} - 3 q^{40} + 22 q^{41} - 5 q^{42} - 5 q^{43} - 13 q^{44} - 11 q^{45} - 22 q^{46} + 5 q^{47} + 10 q^{48} - 33 q^{49} + 2 q^{50} + 3 q^{51} - 12 q^{52} + 4 q^{53} - 2 q^{54} - 13 q^{56} + 8 q^{57} - 18 q^{58} - 3 q^{59} + 12 q^{60} - 28 q^{61} - 2 q^{62} + 4 q^{63} + 3 q^{64} + 11 q^{65} + 3 q^{66} - 11 q^{67} - 9 q^{68} - 11 q^{69} - 5 q^{70} + 5 q^{71} + 3 q^{72} - 3 q^{73} - 12 q^{74} - 11 q^{75} - 36 q^{76} + 18 q^{77} + 2 q^{78} - 43 q^{79} + 10 q^{80} + 11 q^{81} - 15 q^{82} - 28 q^{83} - 14 q^{84} + 3 q^{85} + 10 q^{86} + 14 q^{87} - 43 q^{88} - 25 q^{89} - 2 q^{90} - 4 q^{91} + 7 q^{92} + 11 q^{93} - 16 q^{94} + 8 q^{95} - 8 q^{96} - 6 q^{97} - 14 q^{98}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9 - 2 * q^10 - 12 * q^12 - 11 * q^13 + 5 * q^14 + 11 * q^15 - 10 * q^16 - 3 * q^17 + 2 * q^18 - 8 * q^19 - 12 * q^20 - 4 * q^21 - 3 * q^22 + 11 * q^23 - 3 * q^24 + 11 * q^25 - 2 * q^26 - 11 * q^27 + 14 * q^28 - 14 * q^29 + 2 * q^30 - 11 * q^31 + 8 * q^32 - 11 * q^34 - 4 * q^35 + 12 * q^36 + 7 * q^37 + 8 * q^38 + 11 * q^39 - 3 * q^40 + 22 * q^41 - 5 * q^42 - 5 * q^43 - 13 * q^44 - 11 * q^45 - 22 * q^46 + 5 * q^47 + 10 * q^48 - 33 * q^49 + 2 * q^50 + 3 * q^51 - 12 * q^52 + 4 * q^53 - 2 * q^54 - 13 * q^56 + 8 * q^57 - 18 * q^58 - 3 * q^59 + 12 * q^60 - 28 * q^61 - 2 * q^62 + 4 * q^63 + 3 * q^64 + 11 * q^65 + 3 * q^66 - 11 * q^67 - 9 * q^68 - 11 * q^69 - 5 * q^70 + 5 * q^71 + 3 * q^72 - 3 * q^73 - 12 * q^74 - 11 * q^75 - 36 * q^76 + 18 * q^77 + 2 * q^78 - 43 * q^79 + 10 * q^80 + 11 * q^81 - 15 * q^82 - 28 * q^83 - 14 * q^84 + 3 * q^85 + 10 * q^86 + 14 * q^87 - 43 * q^88 - 25 * q^89 - 2 * q^90 - 4 * q^91 + 7 * q^92 + 11 * q^93 - 16 * q^94 + 8 * q^95 - 8 * q^96 - 6 * q^97 - 14 * q^98

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 $

$2$	−1.45401	−1.02814	−0.514070	−	0.857748i	$-0.671863\pi$
$2$	−1.45401	−1.02814	−0.514070	+	0.857748i	$0.671863\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.114145	0.0570727
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.45401	0.593597
$7$	3.05854	1.15602	0.578009	−	0.816030i	$-0.303830\pi$
$7$	3.05854	1.15602	0.578009	+	0.816030i	$0.303830\pi$
$8$	2.74205	0.969462
$9$	1.00000	0.333333
$10$	1.45401	0.459798
$11$	−0.438814	−0.132307	−0.0661537	−	0.997809i	$-0.521073\pi$
$11$	−0.438814	−0.132307	−0.0661537	+	0.997809i	$0.521073\pi$
$12$	−0.114145	−0.0329509
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.44714	−1.18855
$15$	1.00000	0.258199
$16$	−4.21526	−1.05382
$17$	−2.30324	−0.558617	−0.279309	−	0.960201i	$-0.590105\pi$
$17$	−2.30324	−0.558617	−0.279309	+	0.960201i	$0.590105\pi$
$18$	−1.45401	−0.342713
$19$	1.98206	0.454716	0.227358	−	0.973811i	$-0.426991\pi$
$19$	1.98206	0.454716	0.227358	+	0.973811i	$0.426991\pi$
$20$	−0.114145	−0.0255237
$21$	−3.05854	−0.667427
$22$	0.638040	0.136031
$23$	6.52136	1.35980	0.679899	−	0.733306i	$-0.262024\pi$
$23$	6.52136	1.35980	0.679899	+	0.733306i	$0.262024\pi$
$24$	−2.74205	−0.559719
$25$	1.00000	0.200000
$26$	1.45401	0.285155
$27$	−1.00000	−0.192450
$28$	0.349117	0.0659770
$29$	1.09739	0.203780	0.101890	−	0.994796i	$-0.467511\pi$
$29$	1.09739	0.203780	0.101890	+	0.994796i	$0.467511\pi$
$30$	−1.45401	−0.265465
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	0.644929	0.114008
$33$	0.438814	0.0763878
$34$	3.34893	0.574337
$35$	−3.05854	−0.516987
$36$	0.114145	0.0190242
$37$	−3.49090	−0.573900	−0.286950	−	0.957946i	$-0.592641\pi$
$37$	−3.49090	−0.573900	−0.286950	+	0.957946i	$0.592641\pi$
$38$	−2.88194	−0.467512
$39$	1.00000	0.160128
$40$	−2.74205	−0.433556
$41$	0.573020	0.0894907	0.0447453	−	0.998998i	$-0.485752\pi$
$41$	0.573020	0.0894907	0.0447453	+	0.998998i	$0.485752\pi$
$42$	4.44714	0.686209
$43$	−11.2767	−1.71969	−0.859844	−	0.510558i	$-0.829439\pi$
$43$	−11.2767	−1.71969	−0.859844	+	0.510558i	$0.829439\pi$
$44$	−0.0500886	−0.00755114
$45$	−1.00000	−0.149071
$46$	−9.48213	−1.39806
$47$	8.21740	1.19863	0.599316	−	0.800513i	$-0.295439\pi$
$47$	8.21740	1.19863	0.599316	+	0.800513i	$0.295439\pi$
$48$	4.21526	0.608421
$49$	2.35464	0.336377
$50$	−1.45401	−0.205628
$51$	2.30324	0.322518
$52$	−0.114145	−0.0158291
$53$	−10.1119	−1.38897	−0.694487	−	0.719505i	$-0.744369\pi$
$53$	−10.1119	−1.38897	−0.694487	+	0.719505i	$0.744369\pi$
$54$	1.45401	0.197866
$55$	0.438814	0.0591697
$56$	8.38666	1.12071
$57$	−1.98206	−0.262530
$58$	−1.59562	−0.209515
$59$	−1.03869	−0.135226	−0.0676128	−	0.997712i	$-0.521538\pi$
$59$	−1.03869	−0.135226	−0.0676128	+	0.997712i	$0.521538\pi$
$60$	0.114145	0.0147361
$61$	−1.03222	−0.132162	−0.0660811	−	0.997814i	$-0.521050\pi$
$61$	−1.03222	−0.132162	−0.0660811	+	0.997814i	$0.521050\pi$
$62$	1.45401	0.184659
$63$	3.05854	0.385339
$64$	7.49279	0.936599
$65$	1.00000	0.124035
$66$	−0.638040	−0.0785373
$67$	−12.0916	−1.47722	−0.738610	−	0.674133i	$-0.764517\pi$
$67$	−12.0916	−1.47722	−0.738610	+	0.674133i	$0.764517\pi$
$68$	−0.262904	−0.0318818
$69$	−6.52136	−0.785080
$70$	4.44714	0.531535
$71$	2.55812	0.303593	0.151797	−	0.988412i	$-0.451494\pi$
$71$	2.55812	0.303593	0.151797	+	0.988412i	$0.451494\pi$
$72$	2.74205	0.323154
$73$	−12.9928	−1.52069	−0.760345	−	0.649519i	$-0.774970\pi$
$73$	−12.9928	−1.52069	−0.760345	+	0.649519i	$0.774970\pi$
$74$	5.07580	0.590050
$75$	−1.00000	−0.115470
$76$	0.226243	0.0259519
$77$	−1.34213	−0.152950
$78$	−1.45401	−0.164634
$79$	−1.52685	−0.171785	−0.0858923	−	0.996304i	$-0.527374\pi$
$79$	−1.52685	−0.171785	−0.0858923	+	0.996304i	$0.527374\pi$
$80$	4.21526	0.471281
$81$	1.00000	0.111111
$82$	−0.833177	−0.0920090
$83$	4.80297	0.527195	0.263597	−	0.964633i	$-0.415091\pi$
$83$	4.80297	0.527195	0.263597	+	0.964633i	$0.415091\pi$
$84$	−0.349117	−0.0380918
$85$	2.30324	0.249821
$86$	16.3965	1.76808
$87$	−1.09739	−0.117653
$88$	−1.20325	−0.128267
$89$	−7.11127	−0.753793	−0.376897	−	0.926255i	$-0.623009\pi$
$89$	−7.11127	−0.753793	−0.376897	+	0.926255i	$0.623009\pi$
$90$	1.45401	0.153266
$91$	−3.05854	−0.320622
$92$	0.744383	0.0776073
$93$	1.00000	0.103695
$94$	−11.9482	−1.23236
$95$	−1.98206	−0.203355
$96$	−0.644929	−0.0658228
$97$	3.24049	0.329022	0.164511	−	0.986375i	$-0.447395\pi$
$97$	3.24049	0.329022	0.164511	+	0.986375i	$0.447395\pi$
$98$	−3.42367	−0.345843
$99$	−0.438814	−0.0441025
$100$	0.114145	0.0114145
$101$	1.26704	0.126075	0.0630376	−	0.998011i	$-0.479921\pi$
$101$	1.26704	0.126075	0.0630376	+	0.998011i	$0.479921\pi$
$102$	−3.34893	−0.331594
$103$	14.3810	1.41700	0.708499	−	0.705712i	$-0.249373\pi$
$103$	14.3810	1.41700	0.708499	+	0.705712i	$0.249373\pi$
$104$	−2.74205	−0.268880
$105$	3.05854	0.298483
$106$	14.7028	1.42806
$107$	−1.82966	−0.176880	−0.0884400	−	0.996082i	$-0.528188\pi$
$107$	−1.82966	−0.176880	−0.0884400	+	0.996082i	$0.528188\pi$
$108$	−0.114145	−0.0109836
$109$	−11.5684	−1.10805	−0.554026	−	0.832499i	$-0.686909\pi$
$109$	−11.5684	−1.10805	−0.554026	+	0.832499i	$0.686909\pi$
$110$	−0.638040	−0.0608348
$111$	3.49090	0.331341
$112$	−12.8925	−1.21823
$113$	12.7572	1.20010	0.600050	−	0.799962i	$-0.295147\pi$
$113$	12.7572	1.20010	0.600050	+	0.799962i	$0.295147\pi$
$114$	2.88194	0.269918
$115$	−6.52136	−0.608120
$116$	0.125262	0.0116303
$117$	−1.00000	−0.0924500
$118$	1.51026	0.139031
$119$	−7.04453	−0.645771
$120$	2.74205	0.250314
$121$	−10.8074	−0.982495
$122$	1.50086	0.135881
$123$	−0.573020	−0.0516675
$124$	−0.114145	−0.0102506
$125$	−1.00000	−0.0894427
$126$	−4.44714	−0.396183
$127$	15.4979	1.37522	0.687610	−	0.726080i	$-0.258660\pi$
$127$	15.4979	1.37522	0.687610	+	0.726080i	$0.258660\pi$
$128$	−12.1844	−1.07696
$129$	11.2767	0.992862
$130$	−1.45401	−0.127525
$131$	6.18391	0.540291	0.270145	−	0.962820i	$-0.412928\pi$
$131$	6.18391	0.540291	0.270145	+	0.962820i	$0.412928\pi$
$132$	0.0500886	0.00435965
$133$	6.06221	0.525660
$134$	17.5813	1.51879
$135$	1.00000	0.0860663
$136$	−6.31560	−0.541558
$137$	−8.76829	−0.749126	−0.374563	−	0.927201i	$-0.622207\pi$
$137$	−8.76829	−0.749126	−0.374563	+	0.927201i	$0.622207\pi$
$138$	9.48213	0.807172
$139$	−4.91427	−0.416823	−0.208411	−	0.978041i	$-0.566829\pi$
$139$	−4.91427	−0.416823	−0.208411	+	0.978041i	$0.566829\pi$
$140$	−0.349117	−0.0295058
$141$	−8.21740	−0.692030
$142$	−3.71953	−0.312136
$143$	0.438814	0.0366955
$144$	−4.21526	−0.351272
$145$	−1.09739	−0.0911333
$146$	18.8916	1.56348
$147$	−2.35464	−0.194207
$148$	−0.398470	−0.0327540
$149$	15.3517	1.25766	0.628832	−	0.777541i	$-0.283533\pi$
$149$	15.3517	1.25766	0.628832	+	0.777541i	$0.283533\pi$
$150$	1.45401	0.118719
$151$	−8.59267	−0.699262	−0.349631	−	0.936887i	$-0.613693\pi$
$151$	−8.59267	−0.699262	−0.349631	+	0.936887i	$0.613693\pi$
$152$	5.43492	0.440830
$153$	−2.30324	−0.186206
$154$	1.95147	0.157254
$155$	1.00000	0.0803219
$156$	0.114145	0.00913894
$157$	−13.4190	−1.07095	−0.535477	−	0.844550i	$-0.679868\pi$
$157$	−13.4190	−1.07095	−0.535477	+	0.844550i	$0.679868\pi$
$158$	2.22006	0.176619
$159$	10.1119	0.801925
$160$	−0.644929	−0.0509861
$161$	19.9458	1.57195
$162$	−1.45401	−0.114238
$163$	23.1366	1.81219	0.906097	−	0.423069i	$-0.139047\pi$
$163$	23.1366	1.81219	0.906097	+	0.423069i	$0.139047\pi$
$164$	0.0654075	0.00510747
$165$	−0.438814	−0.0341616
$166$	−6.98357	−0.542030
$167$	−9.35233	−0.723705	−0.361853	−	0.932235i	$-0.617856\pi$
$167$	−9.35233	−0.723705	−0.361853	+	0.932235i	$0.617856\pi$
$168$	−8.38666	−0.647045
$169$	1.00000	0.0769231
$170$	−3.34893	−0.256851
$171$	1.98206	0.151572
$172$	−1.28719	−0.0981471
$173$	−2.53453	−0.192696	−0.0963482	−	0.995348i	$-0.530716\pi$
$173$	−2.53453	−0.192696	−0.0963482	+	0.995348i	$0.530716\pi$
$174$	1.59562	0.120963
$175$	3.05854	0.231204
$176$	1.84972	0.139428
$177$	1.03869	0.0780725
$178$	10.3399	0.775005
$179$	−4.92454	−0.368077	−0.184039	−	0.982919i	$-0.558917\pi$
$179$	−4.92454	−0.368077	−0.184039	+	0.982919i	$0.558917\pi$
$180$	−0.114145	−0.00850789
$181$	−7.57891	−0.563336	−0.281668	−	0.959512i	$-0.590888\pi$
$181$	−7.57891	−0.563336	−0.281668	+	0.959512i	$0.590888\pi$
$182$	4.44714	0.329644
$183$	1.03222	0.0763039
$184$	17.8819	1.31827
$185$	3.49090	0.256656
$186$	−1.45401	−0.106613
$187$	1.01069	0.0739092
$188$	0.937978	0.0684091
$189$	−3.05854	−0.222476
$190$	2.88194	0.209078
$191$	11.0818	0.801851	0.400926	−	0.916111i	$-0.368689\pi$
$191$	11.0818	0.801851	0.400926	+	0.916111i	$0.368689\pi$
$192$	−7.49279	−0.540745
$193$	18.5646	1.33631	0.668153	−	0.744024i	$-0.267085\pi$
$193$	18.5646	1.33631	0.668153	+	0.744024i	$0.267085\pi$
$194$	−4.71170	−0.338280
$195$	−1.00000	−0.0716115
$196$	0.268771	0.0191979
$197$	−1.31419	−0.0936324	−0.0468162	−	0.998904i	$-0.514908\pi$
$197$	−1.31419	−0.0936324	−0.0468162	+	0.998904i	$0.514908\pi$
$198$	0.638040	0.0453436
$199$	12.5948	0.892820	0.446410	−	0.894828i	$-0.352702\pi$
$199$	12.5948	0.892820	0.446410	+	0.894828i	$0.352702\pi$
$200$	2.74205	0.193892
$201$	12.0916	0.852873
$202$	−1.84229	−0.129623
$203$	3.35641	0.235574
$204$	0.262904	0.0184069
$205$	−0.573020	−0.0400214
$206$	−20.9100	−1.45687
$207$	6.52136	0.453266
$208$	4.21526	0.292276
$209$	−0.869757	−0.0601623
$210$	−4.44714	−0.306882
$211$	−12.9026	−0.888255	−0.444127	−	0.895964i	$-0.646486\pi$
$211$	−12.9026	−0.888255	−0.444127	+	0.895964i	$0.646486\pi$
$212$	−1.15422	−0.0792725
$213$	−2.55812	−0.175280
$214$	2.66034	0.181857
$215$	11.2767	0.769067
$216$	−2.74205	−0.186573
$217$	−3.05854	−0.207627
$218$	16.8206	1.13923
$219$	12.9928	0.877971
$220$	0.0500886	0.00337697
$221$	2.30324	0.154933
$222$	−5.07580	−0.340665
$223$	0.358035	0.0239758	0.0119879	−	0.999928i	$-0.496184\pi$
$223$	0.358035	0.0239758	0.0119879	+	0.999928i	$0.496184\pi$
$224$	1.97254	0.131796
$225$	1.00000	0.0666667
$226$	−18.5492	−1.23387
$227$	12.9750	0.861183	0.430591	−	0.902547i	$-0.358305\pi$
$227$	12.9750	0.861183	0.430591	+	0.902547i	$0.358305\pi$
$228$	−0.226243	−0.0149833
$229$	−9.32065	−0.615926	−0.307963	−	0.951398i	$-0.599647\pi$
$229$	−9.32065	−0.615926	−0.307963	+	0.951398i	$0.599647\pi$
$230$	9.48213	0.625233
$231$	1.34213	0.0883056
$232$	3.00910	0.197557
$233$	21.0455	1.37874	0.689369	−	0.724411i	$-0.257888\pi$
$233$	21.0455	1.37874	0.689369	+	0.724411i	$0.257888\pi$
$234$	1.45401	0.0950516
$235$	−8.21740	−0.536044
$236$	−0.118561	−0.00771768
$237$	1.52685	0.0991799
$238$	10.2428	0.663944
$239$	−15.0480	−0.973373	−0.486686	−	0.873577i	$-0.661795\pi$
$239$	−15.0480	−0.973373	−0.486686	+	0.873577i	$0.661795\pi$
$240$	−4.21526	−0.272094
$241$	7.77427	0.500785	0.250392	−	0.968144i	$-0.419440\pi$
$241$	7.77427	0.500785	0.250392	+	0.968144i	$0.419440\pi$
$242$	15.7141	1.01014
$243$	−1.00000	−0.0641500
$244$	−0.117823	−0.00754285
$245$	−2.35464	−0.150432
$246$	0.833177	0.0531214
$247$	−1.98206	−0.126116
$248$	−2.74205	−0.174120
$249$	−4.80297	−0.304376
$250$	1.45401	0.0919597
$251$	9.08161	0.573226	0.286613	−	0.958046i	$-0.407471\pi$
$251$	9.08161	0.573226	0.286613	+	0.958046i	$0.407471\pi$
$252$	0.349117	0.0219923
$253$	−2.86167	−0.179912
$254$	−22.5342	−1.41392
$255$	−2.30324	−0.144234
$256$	2.73073	0.170671
$257$	20.1520	1.25704	0.628522	−	0.777792i	$-0.283660\pi$
$257$	20.1520	1.25704	0.628522	+	0.777792i	$0.283660\pi$
$258$	−16.3965	−1.02080
$259$	−10.6770	−0.663439
$260$	0.114145	0.00707899
$261$	1.09739	0.0679268
$262$	−8.99146	−0.555495
$263$	15.1562	0.934573	0.467286	−	0.884106i	$-0.345232\pi$
$263$	15.1562	0.934573	0.467286	+	0.884106i	$0.345232\pi$
$264$	1.20325	0.0740550
$265$	10.1119	0.621168
$266$	−8.81451	−0.540452
$267$	7.11127	0.435203
$268$	−1.38020	−0.0843088
$269$	−12.1231	−0.739159	−0.369579	−	0.929199i	$-0.620498\pi$
$269$	−12.1231	−0.739159	−0.369579	+	0.929199i	$0.620498\pi$
$270$	−1.45401	−0.0884882
$271$	−29.0635	−1.76548	−0.882741	−	0.469860i	$-0.844304\pi$
$271$	−29.0635	−1.76548	−0.882741	+	0.469860i	$0.844304\pi$
$272$	9.70875	0.588679
$273$	3.05854	0.185111
$274$	12.7492	0.770207
$275$	−0.438814	−0.0264615
$276$	−0.744383	−0.0448066
$277$	2.44955	0.147179	0.0735897	−	0.997289i	$-0.476554\pi$
$277$	2.44955	0.147179	0.0735897	+	0.997289i	$0.476554\pi$
$278$	7.14539	0.428552
$279$	−1.00000	−0.0598684
$280$	−8.38666	−0.501199
$281$	−10.1014	−0.602599	−0.301299	−	0.953530i	$-0.597420\pi$
$281$	−10.1014	−0.602599	−0.301299	+	0.953530i	$0.597420\pi$
$282$	11.9482	0.711504
$283$	10.8589	0.645492	0.322746	−	0.946486i	$-0.395394\pi$
$283$	10.8589	0.645492	0.322746	+	0.946486i	$0.395394\pi$
$284$	0.291998	0.0173269
$285$	1.98206	0.117407
$286$	−0.638040	−0.0377281
$287$	1.75260	0.103453
$288$	0.644929	0.0380028
$289$	−11.6951	−0.687947
$290$	1.59562	0.0936978
$291$	−3.24049	−0.189961
$292$	−1.48307	−0.0867899
$293$	−20.0301	−1.17017	−0.585085	−	0.810972i	$-0.698939\pi$
$293$	−20.0301	−1.17017	−0.585085	+	0.810972i	$0.698939\pi$
$294$	3.42367	0.199672
$295$	1.03869	0.0604747
$296$	−9.57222	−0.556374
$297$	0.438814	0.0254626
$298$	−22.3216	−1.29305
$299$	−6.52136	−0.377140
$300$	−0.114145	−0.00659018
$301$	−34.4903	−1.98799
$302$	12.4938	0.718939
$303$	−1.26704	−0.0727895
$304$	−8.35491	−0.479187
$305$	1.03222	0.0591047
$306$	3.34893	0.191446
$307$	23.2058	1.32443	0.662213	−	0.749315i	$-0.269617\pi$
$307$	23.2058	1.32443	0.662213	+	0.749315i	$0.269617\pi$
$308$	−0.153198	−0.00872925
$309$	−14.3810	−0.818104
$310$	−1.45401	−0.0825822
$311$	−31.7056	−1.79786	−0.898928	−	0.438096i	$-0.855653\pi$
$311$	−31.7056	−1.79786	−0.898928	+	0.438096i	$0.855653\pi$
$312$	2.74205	0.155238
$313$	−23.6874	−1.33889	−0.669444	−	0.742862i	$-0.733468\pi$
$313$	−23.6874	−1.33889	−0.669444	+	0.742862i	$0.733468\pi$
$314$	19.5114	1.10109
$315$	−3.05854	−0.172329
$316$	−0.174283	−0.00980420
$317$	−13.0153	−0.731012	−0.365506	−	0.930809i	$-0.619104\pi$
$317$	−13.0153	−0.731012	−0.365506	+	0.930809i	$0.619104\pi$
$318$	−14.7028	−0.824491
$319$	−0.481551	−0.0269617
$320$	−7.49279	−0.418860
$321$	1.82966	0.102122
$322$	−29.0014	−1.61619
$323$	−4.56516	−0.254012
$324$	0.114145	0.00634141
$325$	−1.00000	−0.0554700
$326$	−33.6408	−1.86319
$327$	11.5684	0.639735
$328$	1.57125	0.0867578
$329$	25.1332	1.38564
$330$	0.638040	0.0351230
$331$	−6.43786	−0.353857	−0.176928	−	0.984224i	$-0.556616\pi$
$331$	−6.43786	−0.353857	−0.176928	+	0.984224i	$0.556616\pi$
$332$	0.548237	0.0300884
$333$	−3.49090	−0.191300
$334$	13.5984	0.744070
$335$	12.0916	0.660633
$336$	12.8925	0.703345
$337$	−34.6318	−1.88652	−0.943258	−	0.332061i	$-0.892256\pi$
$337$	−34.6318	−1.88652	−0.943258	+	0.332061i	$0.892256\pi$
$338$	−1.45401	−0.0790877
$339$	−12.7572	−0.692879
$340$	0.262904	0.0142580
$341$	0.438814	0.0237631
$342$	−2.88194	−0.155837
$343$	−14.2080	−0.767160
$344$	−30.9214	−1.66717
$345$	6.52136	0.351098
$346$	3.68523	0.198119
$347$	−19.2309	−1.03237	−0.516184	−	0.856478i	$-0.672648\pi$
$347$	−19.2309	−1.03237	−0.516184	+	0.856478i	$0.672648\pi$
$348$	−0.125262	−0.00671475
$349$	−29.6567	−1.58749	−0.793745	−	0.608251i	$-0.791871\pi$
$349$	−29.6567	−1.58749	−0.793745	+	0.608251i	$0.791871\pi$
$350$	−4.44714	−0.237710
$351$	1.00000	0.0533761
$352$	−0.283004	−0.0150842
$353$	19.0954	1.01634	0.508172	−	0.861256i	$-0.330321\pi$
$353$	19.0954	1.01634	0.508172	+	0.861256i	$0.330321\pi$
$354$	−1.51026	−0.0802695
$355$	−2.55812	−0.135771
$356$	−0.811718	−0.0430210
$357$	7.04453	0.372836
$358$	7.16033	0.378435
$359$	−28.9754	−1.52927	−0.764633	−	0.644466i	$-0.777080\pi$
$359$	−28.9754	−1.52927	−0.764633	+	0.644466i	$0.777080\pi$
$360$	−2.74205	−0.144519
$361$	−15.0714	−0.793233
$362$	11.0198	0.579189
$363$	10.8074	0.567244
$364$	−0.349117	−0.0182987
$365$	12.9928	0.680074
$366$	−1.50086	−0.0784511
$367$	−10.9836	−0.573339	−0.286670	−	0.958030i	$-0.592548\pi$
$367$	−10.9836	−0.573339	−0.286670	+	0.958030i	$0.592548\pi$
$368$	−27.4893	−1.43298
$369$	0.573020	0.0298302
$370$	−5.07580	−0.263878
$371$	−30.9276	−1.60568
$372$	0.114145	0.00591816
$373$	11.4915	0.595009	0.297504	−	0.954720i	$-0.403846\pi$
$373$	11.4915	0.595009	0.297504	+	0.954720i	$0.403846\pi$
$374$	−1.46956	−0.0759891
$375$	1.00000	0.0516398
$376$	22.5325	1.16203
$377$	−1.09739	−0.0565185
$378$	4.44714	0.228736
$379$	12.4912	0.641629	0.320815	−	0.947142i	$-0.396043\pi$
$379$	12.4912	0.641629	0.320815	+	0.947142i	$0.396043\pi$
$380$	−0.226243	−0.0116060
$381$	−15.4979	−0.793984
$382$	−16.1131	−0.824416
$383$	−11.0619	−0.565236	−0.282618	−	0.959233i	$-0.591203\pi$
$383$	−11.0619	−0.565236	−0.282618	+	0.959233i	$0.591203\pi$
$384$	12.1844	0.621785
$385$	1.34213	0.0684012
$386$	−26.9931	−1.37391
$387$	−11.2767	−0.573229
$388$	0.369886	0.0187781
$389$	−9.31362	−0.472220	−0.236110	−	0.971726i	$-0.575872\pi$
$389$	−9.31362	−0.472220	−0.236110	+	0.971726i	$0.575872\pi$
$390$	1.45401	0.0736267
$391$	−15.0202	−0.759607
$392$	6.45654	0.326105
$393$	−6.18391	−0.311937
$394$	1.91085	0.0962673
$395$	1.52685	0.0768244
$396$	−0.0500886	−0.00251705
$397$	−32.5330	−1.63279	−0.816393	−	0.577496i	$-0.804030\pi$
$397$	−32.5330	−1.63279	−0.816393	+	0.577496i	$0.804030\pi$
$398$	−18.3129	−0.917945
$399$	−6.06221	−0.303490
$400$	−4.21526	−0.210763
$401$	−4.56009	−0.227720	−0.113860	−	0.993497i	$-0.536322\pi$
$401$	−4.56009	−0.227720	−0.113860	+	0.993497i	$0.536322\pi$
$402$	−17.5813	−0.876873
$403$	1.00000	0.0498135
$404$	0.144627	0.00719544
$405$	−1.00000	−0.0496904
$406$	−4.88025	−0.242203
$407$	1.53186	0.0759313
$408$	6.31560	0.312669
$409$	36.6540	1.81242	0.906212	−	0.422823i	$-0.138961\pi$
$409$	36.6540	1.81242	0.906212	+	0.422823i	$0.138961\pi$
$410$	0.833177	0.0411477
$411$	8.76829	0.432508
$412$	1.64152	0.0808718
$413$	−3.17686	−0.156323
$414$	−9.48213	−0.466021
$415$	−4.80297	−0.235769
$416$	−0.644929	−0.0316203
$417$	4.91427	0.240653
$418$	1.26464	0.0618553
$419$	1.15519	0.0564345	0.0282172	−	0.999602i	$-0.491017\pi$
$419$	1.15519	0.0564345	0.0282172	+	0.999602i	$0.491017\pi$
$420$	0.349117	0.0170352
$421$	−22.4520	−1.09424	−0.547121	−	0.837054i	$-0.684276\pi$
$421$	−22.4520	−1.09424	−0.547121	+	0.837054i	$0.684276\pi$
$422$	18.7606	0.913251
$423$	8.21740	0.399544
$424$	−27.7273	−1.34656
$425$	−2.30324	−0.111723
$426$	3.71953	0.180212
$427$	−3.15708	−0.152782
$428$	−0.208847	−0.0100950
$429$	−0.438814	−0.0211862
$430$	−16.3965	−0.790709
$431$	38.7768	1.86781	0.933907	−	0.357516i	$-0.116376\pi$
$431$	38.7768	1.86781	0.933907	+	0.357516i	$0.116376\pi$
$432$	4.21526	0.202807
$433$	19.7105	0.947228	0.473614	−	0.880732i	$-0.342949\pi$
$433$	19.7105	0.947228	0.473614	+	0.880732i	$0.342949\pi$
$434$	4.44714	0.213470
$435$	1.09739	0.0526158
$436$	−1.32048	−0.0632395
$437$	12.9257	0.618322
$438$	−18.8916	−0.902678
$439$	−34.2710	−1.63567	−0.817834	−	0.575454i	$-0.804825\pi$
$439$	−34.2710	−1.63567	−0.817834	+	0.575454i	$0.804825\pi$
$440$	1.20325	0.0573628
$441$	2.35464	0.112126
$442$	−3.34893	−0.159292
$443$	−26.8560	−1.27597	−0.637983	−	0.770051i	$-0.720231\pi$
$443$	−26.8560	−1.27597	−0.637983	+	0.770051i	$0.720231\pi$
$444$	0.398470	0.0189105
$445$	7.11127	0.337107
$446$	−0.520586	−0.0246505
$447$	−15.3517	−0.726112
$448$	22.9170	1.08272
$449$	−19.6346	−0.926615	−0.463308	−	0.886198i	$-0.653337\pi$
$449$	−19.6346	−0.926615	−0.463308	+	0.886198i	$0.653337\pi$
$450$	−1.45401	−0.0685427
$451$	−0.251449	−0.0118403
$452$	1.45618	0.0684929
$453$	8.59267	0.403719
$454$	−18.8658	−0.885417
$455$	3.05854	0.143386
$456$	−5.43492	−0.254513
$457$	−12.1821	−0.569852	−0.284926	−	0.958549i	$-0.591969\pi$
$457$	−12.1821	−0.569852	−0.284926	+	0.958549i	$0.591969\pi$
$458$	13.5523	0.633258
$459$	2.30324	0.107506
$460$	−0.744383	−0.0347070
$461$	−3.73620	−0.174012	−0.0870062	−	0.996208i	$-0.527730\pi$
$461$	−3.73620	−0.174012	−0.0870062	+	0.996208i	$0.527730\pi$
$462$	−1.95147	−0.0907906
$463$	2.14417	0.0996480	0.0498240	−	0.998758i	$-0.484134\pi$
$463$	2.14417	0.0996480	0.0498240	+	0.998758i	$0.484134\pi$
$464$	−4.62579	−0.214747
$465$	−1.00000	−0.0463739
$466$	−30.6004	−1.41754
$467$	−3.61262	−0.167172	−0.0835860	−	0.996501i	$-0.526637\pi$
$467$	−3.61262	−0.167172	−0.0835860	+	0.996501i	$0.526637\pi$
$468$	−0.114145	−0.00527637
$469$	−36.9825	−1.70769
$470$	11.9482	0.551129
$471$	13.4190	0.618316
$472$	−2.84813	−0.131096
$473$	4.94840	0.227527
$474$	−2.22006	−0.101971
$475$	1.98206	0.0909432
$476$	−0.804100	−0.0368559
$477$	−10.1119	−0.462991
$478$	21.8799	1.00076
$479$	27.8784	1.27380	0.636898	−	0.770948i	$-0.280217\pi$
$479$	27.8784	1.27380	0.636898	+	0.770948i	$0.280217\pi$
$480$	0.644929	0.0294369
$481$	3.49090	0.159171
$482$	−11.3039	−0.514877
$483$	−19.9458	−0.907566
$484$	−1.23362	−0.0560736
$485$	−3.24049	−0.147143
$486$	1.45401	0.0659552
$487$	−23.9857	−1.08690	−0.543448	−	0.839443i	$-0.682882\pi$
$487$	−23.9857	−1.08690	−0.543448	+	0.839443i	$0.682882\pi$
$488$	−2.83040	−0.128126
$489$	−23.1366	−1.04627
$490$	3.42367	0.154666
$491$	13.6901	0.617825	0.308912	−	0.951091i	$-0.400035\pi$
$491$	13.6901	0.617825	0.308912	+	0.951091i	$0.400035\pi$
$492$	−0.0654075	−0.00294880
$493$	−2.52755	−0.113835
$494$	2.88194	0.129664
$495$	0.438814	0.0197232
$496$	4.21526	0.189271
$497$	7.82410	0.350959
$498$	6.98357	0.312941
$499$	12.8186	0.573838	0.286919	−	0.957955i	$-0.407369\pi$
$499$	12.8186	0.573838	0.286919	+	0.957955i	$0.407369\pi$
$500$	−0.114145	−0.00510473
$501$	9.35233	0.417831
$502$	−13.2048	−0.589357
$503$	23.6613	1.05501	0.527504	−	0.849553i	$-0.323128\pi$
$503$	23.6613	1.05501	0.527504	+	0.849553i	$0.323128\pi$
$504$	8.38666	0.373572
$505$	−1.26704	−0.0563825
$506$	4.16089	0.184974
$507$	−1.00000	−0.0444116
$508$	1.76902	0.0784875
$509$	27.3800	1.21360	0.606799	−	0.794855i	$-0.292453\pi$
$509$	27.3800	1.21360	0.606799	+	0.794855i	$0.292453\pi$
$510$	3.34893	0.148293
$511$	−39.7389	−1.75795
$512$	20.3984	0.901490
$513$	−1.98206	−0.0875102
$514$	−29.3011	−1.29242
$515$	−14.3810	−0.633700
$516$	1.28719	0.0566653
$517$	−3.60591	−0.158588
$518$	15.5245	0.682108
$519$	2.53453	0.111253
$520$	2.74205	0.120247
$521$	−23.2933	−1.02050	−0.510249	−	0.860027i	$-0.670447\pi$
$521$	−23.2933	−1.02050	−0.510249	+	0.860027i	$0.670447\pi$
$522$	−1.59562	−0.0698382
$523$	29.2178	1.27761	0.638803	−	0.769370i	$-0.279430\pi$
$523$	29.2178	1.27761	0.638803	+	0.769370i	$0.279430\pi$
$524$	0.705864	0.0308358
$525$	−3.05854	−0.133485
$526$	−22.0373	−0.960872
$527$	2.30324	0.100331
$528$	−1.84972	−0.0804986
$529$	19.5282	0.849051
$530$	−14.7028	−0.638648
$531$	−1.03869	−0.0450752
$532$	0.691972	0.0300008
$533$	−0.573020	−0.0248202
$534$	−10.3399	−0.447450
$535$	1.82966	0.0791031
$536$	−33.1557	−1.43211
$537$	4.92454	0.212510
$538$	17.6271	0.759959
$539$	−1.03325	−0.0445052
$540$	0.114145	0.00491203
$541$	−7.37513	−0.317082	−0.158541	−	0.987352i	$-0.550679\pi$
$541$	−7.37513	−0.317082	−0.158541	+	0.987352i	$0.550679\pi$
$542$	42.2586	1.81516
$543$	7.57891	0.325242
$544$	−1.48543	−0.0636871
$545$	11.5684	0.495536
$546$	−4.44714	−0.190320
$547$	−12.9415	−0.553337	−0.276669	−	0.960965i	$-0.589230\pi$
$547$	−12.9415	−0.553337	−0.276669	+	0.960965i	$0.589230\pi$
$548$	−1.00086	−0.0427546
$549$	−1.03222	−0.0440541
$550$	0.638040	0.0272061
$551$	2.17510	0.0926622
$552$	−17.8819	−0.761105
$553$	−4.66994	−0.198586
$554$	−3.56168	−0.151321
$555$	−3.49090	−0.148180
$556$	−0.560940	−0.0237892
$557$	−29.4166	−1.24642	−0.623210	−	0.782055i	$-0.714172\pi$
$557$	−29.4166	−1.24642	−0.623210	+	0.782055i	$0.714172\pi$
$558$	1.45401	0.0615532
$559$	11.2767	0.476955
$560$	12.8925	0.544809
$561$	−1.01069	−0.0426715
$562$	14.6875	0.619556
$563$	13.0646	0.550607	0.275303	−	0.961357i	$-0.411222\pi$
$563$	13.0646	0.550607	0.275303	+	0.961357i	$0.411222\pi$
$564$	−0.937978	−0.0394960
$565$	−12.7572	−0.536701
$566$	−15.7889	−0.663656
$567$	3.05854	0.128446
$568$	7.01450	0.294322
$569$	−34.1748	−1.43268	−0.716342	−	0.697750i	$-0.754185\pi$
$569$	−34.1748	−1.43268	−0.716342	+	0.697750i	$0.754185\pi$
$570$	−2.88194	−0.120711
$571$	20.3749	0.852663	0.426331	−	0.904567i	$-0.359806\pi$
$571$	20.3749	0.852663	0.426331	+	0.904567i	$0.359806\pi$
$572$	0.0500886	0.00209431
$573$	−11.0818	−0.462949
$574$	−2.54830	−0.106364
$575$	6.52136	0.271960
$576$	7.49279	0.312200
$577$	−12.8593	−0.535341	−0.267671	−	0.963510i	$-0.586254\pi$
$577$	−12.8593	−0.535341	−0.267671	+	0.963510i	$0.586254\pi$
$578$	17.0048	0.707306
$579$	−18.5646	−0.771517
$580$	−0.125262	−0.00520122
$581$	14.6901	0.609446
$582$	4.71170	0.195306
$583$	4.43724	0.183772
$584$	−35.6269	−1.47425
$585$	1.00000	0.0413449
$586$	29.1239	1.20310
$587$	−35.1357	−1.45021	−0.725103	−	0.688640i	$-0.758208\pi$
$587$	−35.1357	−1.45021	−0.725103	+	0.688640i	$0.758208\pi$
$588$	−0.268771	−0.0110839
$589$	−1.98206	−0.0816694
$590$	−1.51026	−0.0621765
$591$	1.31419	0.0540587
$592$	14.7150	0.604785
$593$	−15.4160	−0.633060	−0.316530	−	0.948582i	$-0.602518\pi$
$593$	−15.4160	−0.633060	−0.316530	+	0.948582i	$0.602518\pi$
$594$	−0.638040	−0.0261791
$595$	7.04453	0.288798
$596$	1.75233	0.0717782
$597$	−12.5948	−0.515470
$598$	9.48213	0.387753
$599$	35.0848	1.43352	0.716762	−	0.697318i	$-0.245623\pi$
$599$	35.0848	1.43352	0.716762	+	0.697318i	$0.245623\pi$
$600$	−2.74205	−0.111944
$601$	2.36043	0.0962839	0.0481420	−	0.998841i	$-0.484670\pi$
$601$	2.36043	0.0962839	0.0481420	+	0.998841i	$0.484670\pi$
$602$	50.1493	2.04393
$603$	−12.0916	−0.492407
$604$	−0.980814	−0.0399087
$605$	10.8074	0.439385
$606$	1.84229	0.0748378
$607$	0.842804	0.0342084	0.0171042	−	0.999854i	$-0.494555\pi$
$607$	0.842804	0.0342084	0.0171042	+	0.999854i	$0.494555\pi$
$608$	1.27829	0.0518415
$609$	−3.35641	−0.136008
$610$	−1.50086	−0.0607680
$611$	−8.21740	−0.332441
$612$	−0.262904	−0.0106273
$613$	24.4305	0.986738	0.493369	−	0.869820i	$-0.335765\pi$
$613$	24.4305	0.986738	0.493369	+	0.869820i	$0.335765\pi$
$614$	−33.7415	−1.36170
$615$	0.573020	0.0231064
$616$	−3.68019	−0.148279
$617$	−15.9730	−0.643047	−0.321524	−	0.946902i	$-0.604195\pi$
$617$	−15.9730	−0.643047	−0.321524	+	0.946902i	$0.604195\pi$
$618$	20.9100	0.841125
$619$	−41.9556	−1.68634	−0.843169	−	0.537649i	$-0.819312\pi$
$619$	−41.9556	−1.68634	−0.843169	+	0.537649i	$0.819312\pi$
$620$	0.114145	0.00458419
$621$	−6.52136	−0.261693
$622$	46.1002	1.84845
$623$	−21.7501	−0.871398
$624$	−4.21526	−0.168746
$625$	1.00000	0.0400000
$626$	34.4417	1.37657
$627$	0.869757	0.0347347
$628$	−1.53172	−0.0611222
$629$	8.04037	0.320590
$630$	4.44714	0.177178
$631$	2.76105	0.109916	0.0549578	−	0.998489i	$-0.482498\pi$
$631$	2.76105	0.109916	0.0549578	+	0.998489i	$0.482498\pi$
$632$	−4.18672	−0.166539
$633$	12.9026	0.512834
$634$	18.9244	0.751583
$635$	−15.4979	−0.615017
$636$	1.15422	0.0457680
$637$	−2.35464	−0.0932942
$638$	0.700179	0.0277204
$639$	2.55812	0.101198
$640$	12.1844	0.481633
$641$	34.8568	1.37676	0.688381	−	0.725349i	$-0.258322\pi$
$641$	34.8568	1.37676	0.688381	+	0.725349i	$0.258322\pi$
$642$	−2.66034	−0.104995
$643$	33.7857	1.33238	0.666190	−	0.745782i	$-0.267924\pi$
$643$	33.7857	1.33238	0.666190	+	0.745782i	$0.267924\pi$
$644$	2.27672	0.0897154
$645$	−11.2767	−0.444021
$646$	6.63779	0.261160
$647$	−0.460684	−0.0181114	−0.00905568	−	0.999959i	$-0.502883\pi$
$647$	−0.460684	−0.0181114	−0.00905568	+	0.999959i	$0.502883\pi$
$648$	2.74205	0.107718
$649$	0.455791	0.0178914
$650$	1.45401	0.0570310
$651$	3.05854	0.119873
$652$	2.64093	0.103427
$653$	50.7272	1.98511	0.992554	−	0.121808i	$-0.0388691\pi$
$653$	50.7272	1.98511	0.992554	+	0.121808i	$0.0388691\pi$
$654$	−16.8206	−0.657737
$655$	−6.18391	−0.241625
$656$	−2.41543	−0.0943066
$657$	−12.9928	−0.506897
$658$	−36.5440	−1.42463
$659$	−48.5924	−1.89289	−0.946445	−	0.322866i	$-0.895354\pi$
$659$	−48.5924	−1.89289	−0.946445	+	0.322866i	$0.895354\pi$
$660$	−0.0500886	−0.00194970
$661$	−0.880607	−0.0342516	−0.0171258	−	0.999853i	$-0.505452\pi$
$661$	−0.880607	−0.0342516	−0.0171258	+	0.999853i	$0.505452\pi$
$662$	9.36072	0.363815
$663$	−2.30324	−0.0894503
$664$	13.1700	0.511095
$665$	−6.06221	−0.235082
$666$	5.07580	0.196683
$667$	7.15648	0.277100
$668$	−1.06752	−0.0413038
$669$	−0.358035	−0.0138424
$670$	−17.5813	−0.679223
$671$	0.452953	0.0174860
$672$	−1.97254	−0.0760923
$673$	−17.2644	−0.665493	−0.332747	−	0.943016i	$-0.607975\pi$
$673$	−17.2644	−0.665493	−0.332747	+	0.943016i	$0.607975\pi$
$674$	50.3550	1.93960
$675$	−1.00000	−0.0384900
$676$	0.114145	0.00439020
$677$	20.0703	0.771365	0.385682	−	0.922632i	$-0.373966\pi$
$677$	20.0703	0.771365	0.385682	+	0.922632i	$0.373966\pi$
$678$	18.5492	0.712376
$679$	9.91114	0.380355
$680$	6.31560	0.242192
$681$	−12.9750	−0.497204
$682$	−0.638040	−0.0244318
$683$	14.5334	0.556105	0.278053	−	0.960566i	$-0.410311\pi$
$683$	14.5334	0.556105	0.278053	+	0.960566i	$0.410311\pi$
$684$	0.226243	0.00865062
$685$	8.76829	0.335019
$686$	20.6586	0.788748
$687$	9.32065	0.355605
$688$	47.5344	1.81223
$689$	10.1119	0.385232
$690$	−9.48213	−0.360978
$691$	−47.1134	−1.79228	−0.896140	−	0.443772i	$-0.853640\pi$
$691$	−47.1134	−1.79228	−0.896140	+	0.443772i	$0.853640\pi$
$692$	−0.289304	−0.0109977
$693$	−1.34213	−0.0509833
$694$	27.9619	1.06142
$695$	4.91427	0.186409
$696$	−3.00910	−0.114060
$697$	−1.31980	−0.0499910
$698$	43.1212	1.63216
$699$	−21.0455	−0.796015
$700$	0.349117	0.0131954
$701$	−28.9888	−1.09489	−0.547445	−	0.836841i	$-0.684400\pi$
$701$	−28.9888	−1.09489	−0.547445	+	0.836841i	$0.684400\pi$
$702$	−1.45401	−0.0548781
$703$	−6.91917	−0.260962
$704$	−3.28794	−0.123919
$705$	8.21740	0.309485
$706$	−27.7649	−1.04494
$707$	3.87529	0.145745
$708$	0.118561	0.00445581
$709$	−40.6511	−1.52668	−0.763342	−	0.645995i	$-0.776443\pi$
$709$	−40.6511	−1.52668	−0.763342	+	0.645995i	$0.776443\pi$
$710$	3.71953	0.139592
$711$	−1.52685	−0.0572615
$712$	−19.4995	−0.730774
$713$	−6.52136	−0.244227
$714$	−10.2428	−0.383328
$715$	−0.438814	−0.0164107
$716$	−0.562113	−0.0210071
$717$	15.0480	0.561977
$718$	42.1306	1.57230
$719$	−34.2219	−1.27626	−0.638131	−	0.769928i	$-0.720292\pi$
$719$	−34.2219	−1.27626	−0.638131	+	0.769928i	$0.720292\pi$
$720$	4.21526	0.157094
$721$	43.9847	1.63807
$722$	21.9140	0.815555
$723$	−7.77427	−0.289128
$724$	−0.865098	−0.0321511
$725$	1.09739	0.0407561
$726$	−15.7141	−0.583206
$727$	−16.1494	−0.598949	−0.299474	−	0.954104i	$-0.596811\pi$
$727$	−16.1494	−0.598949	−0.299474	+	0.954104i	$0.596811\pi$
$728$	−8.38666	−0.310830
$729$	1.00000	0.0370370
$730$	−18.8916	−0.699211
$731$	25.9730	0.960647
$732$	0.117823	0.00435486
$733$	−37.1316	−1.37149	−0.685744	−	0.727843i	$-0.740523\pi$
$733$	−37.1316	−1.37149	−0.685744	+	0.727843i	$0.740523\pi$
$734$	15.9703	0.589473
$735$	2.35464	0.0868522
$736$	4.20582	0.155029
$737$	5.30595	0.195447
$738$	−0.833177	−0.0306697
$739$	−9.24991	−0.340264	−0.170132	−	0.985421i	$-0.554419\pi$
$739$	−9.24991	−0.340264	−0.170132	+	0.985421i	$0.554419\pi$
$740$	0.398470	0.0146480
$741$	1.98206	0.0728129
$742$	44.9690	1.65086
$743$	−6.63187	−0.243300	−0.121650	−	0.992573i	$-0.538818\pi$
$743$	−6.63187	−0.243300	−0.121650	+	0.992573i	$0.538818\pi$
$744$	2.74205	0.100528
$745$	−15.3517	−0.562444
$746$	−16.7088	−0.611753
$747$	4.80297	0.175732
$748$	0.115366	0.00421820
$749$	−5.59608	−0.204476
$750$	−1.45401	−0.0530929
$751$	9.80311	0.357721	0.178860	−	0.983874i	$-0.442759\pi$
$751$	9.80311	0.357721	0.178860	+	0.983874i	$0.442759\pi$
$752$	−34.6385	−1.26314
$753$	−9.08161	−0.330952
$754$	1.59562	0.0581089
$755$	8.59267	0.312719
$756$	−0.349117	−0.0126973
$757$	16.6427	0.604891	0.302445	−	0.953167i	$-0.402197\pi$
$757$	16.6427	0.604891	0.302445	+	0.953167i	$0.402197\pi$
$758$	−18.1623	−0.659685
$759$	2.86167	0.103872
$760$	−5.43492	−0.197145
$761$	46.9656	1.70250	0.851250	−	0.524760i	$-0.175845\pi$
$761$	46.9656	1.70250	0.851250	+	0.524760i	$0.175845\pi$
$762$	22.5342	0.816327
$763$	−35.3824	−1.28093
$764$	1.26494	0.0457638
$765$	2.30324	0.0832737
$766$	16.0841	0.581142
$767$	1.03869	0.0375048
$768$	−2.73073	−0.0985369
$769$	−9.32964	−0.336435	−0.168218	−	0.985750i	$-0.553801\pi$
$769$	−9.32964	−0.336435	−0.168218	+	0.985750i	$0.553801\pi$
$770$	−1.95147	−0.0703261
$771$	−20.1520	−0.725755
$772$	2.11906	0.0762666
$773$	−1.40330	−0.0504732	−0.0252366	−	0.999682i	$-0.508034\pi$
$773$	−1.40330	−0.0504732	−0.0252366	+	0.999682i	$0.508034\pi$
$774$	16.3965	0.589360
$775$	−1.00000	−0.0359211
$776$	8.88558	0.318974
$777$	10.6770	0.383037
$778$	13.5421	0.485508
$779$	1.13576	0.0406928
$780$	−0.114145	−0.00408706
$781$	−1.12254	−0.0401676
$782$	21.8396	0.780982
$783$	−1.09739	−0.0392175
$784$	−9.92542	−0.354479
$785$	13.4190	0.478946
$786$	8.99146	0.320715
$787$	−5.46433	−0.194782	−0.0973911	−	0.995246i	$-0.531050\pi$
$787$	−5.46433	−0.194782	−0.0973911	+	0.995246i	$0.531050\pi$
$788$	−0.150009	−0.00534385
$789$	−15.1562	−0.539576
$790$	−2.22006	−0.0789863
$791$	39.0185	1.38734
$792$	−1.20325	−0.0427557
$793$	1.03222	0.0366552
$794$	47.3034	1.67873
$795$	−10.1119	−0.358632
$796$	1.43764	0.0509556
$797$	−45.5228	−1.61250	−0.806251	−	0.591574i	$-0.798507\pi$
$797$	−45.5228	−1.61250	−0.806251	+	0.591574i	$0.798507\pi$
$798$	8.81451	0.312030
$799$	−18.9266	−0.669576
$800$	0.644929	0.0228017
$801$	−7.11127	−0.251264
$802$	6.63042	0.234128
$803$	5.70142	0.201199
$804$	1.38020	0.0486757
$805$	−19.9458	−0.702998
$806$	−1.45401	−0.0512153
$807$	12.1231	0.426754
$808$	3.47429	0.122225
$809$	−29.7773	−1.04691	−0.523457	−	0.852052i	$-0.675358\pi$
$809$	−29.7773	−1.04691	−0.523457	+	0.852052i	$0.675358\pi$
$810$	1.45401	0.0510887
$811$	23.3942	0.821482	0.410741	−	0.911752i	$-0.365270\pi$
$811$	23.3942	0.821482	0.410741	+	0.911752i	$0.365270\pi$
$812$	0.383118	0.0134448
$813$	29.0635	1.01930
$814$	−2.22733	−0.0780680
$815$	−23.1366	−0.810438
$816$	−9.70875	−0.339874
$817$	−22.3512	−0.781969
$818$	−53.2953	−1.86343
$819$	−3.05854	−0.106874
$820$	−0.0654075	−0.00228413
$821$	−8.55599	−0.298606	−0.149303	−	0.988791i	$-0.547703\pi$
$821$	−8.55599	−0.298606	−0.149303	+	0.988791i	$0.547703\pi$
$822$	−12.7492	−0.444679
$823$	29.6899	1.03493	0.517463	−	0.855705i	$-0.326876\pi$
$823$	29.6899	1.03493	0.517463	+	0.855705i	$0.326876\pi$
$824$	39.4333	1.37372
$825$	0.438814	0.0152776
$826$	4.61919	0.160722
$827$	4.17583	0.145208	0.0726039	−	0.997361i	$-0.476869\pi$
$827$	4.17583	0.145208	0.0726039	+	0.997361i	$0.476869\pi$
$828$	0.744383	0.0258691
$829$	18.6802	0.648791	0.324395	−	0.945922i	$-0.394839\pi$
$829$	18.6802	0.648791	0.324395	+	0.945922i	$0.394839\pi$
$830$	6.98357	0.242403
$831$	−2.44955	−0.0849741
$832$	−7.49279	−0.259766
$833$	−5.42329	−0.187906
$834$	−7.14539	−0.247425
$835$	9.35233	0.323651
$836$	−0.0992787	−0.00343362
$837$	1.00000	0.0345651
$838$	−1.67965	−0.0580226
$839$	−39.7249	−1.37145	−0.685727	−	0.727859i	$-0.740516\pi$
$839$	−39.7249	−1.37145	−0.685727	+	0.727859i	$0.740516\pi$
$840$	8.38666	0.289367
$841$	−27.7957	−0.958474
$842$	32.6454	1.12503
$843$	10.1014	0.347911
$844$	−1.47278	−0.0506951
$845$	−1.00000	−0.0344010
$846$	−11.9482	−0.410787
$847$	−33.0549	−1.13578
$848$	42.6242	1.46372
$849$	−10.8589	−0.372675
$850$	3.34893	0.114867
$851$	−22.7654	−0.780388
$852$	−0.291998	−0.0100037
$853$	−18.0810	−0.619082	−0.309541	−	0.950886i	$-0.600175\pi$
$853$	−18.0810	−0.619082	−0.309541	+	0.950886i	$0.600175\pi$
$854$	4.59043	0.157081
$855$	−1.98206	−0.0677851
$856$	−5.01702	−0.171478
$857$	8.68877	0.296803	0.148401	−	0.988927i	$-0.452587\pi$
$857$	8.68877	0.296803	0.148401	+	0.988927i	$0.452587\pi$
$858$	0.638040	0.0217823
$859$	−31.7036	−1.08171	−0.540857	−	0.841115i	$-0.681900\pi$
$859$	−31.7036	−1.08171	−0.540857	+	0.841115i	$0.681900\pi$
$860$	1.28719	0.0438927
$861$	−1.75260	−0.0597285
$862$	−56.3819	−1.92038
$863$	36.8631	1.25483	0.627417	−	0.778684i	$-0.284112\pi$
$863$	36.8631	1.25483	0.627417	+	0.778684i	$0.284112\pi$
$864$	−0.644929	−0.0219409
$865$	2.53453	0.0861764
$866$	−28.6593	−0.973884
$867$	11.6951	0.397186
$868$	−0.349117	−0.0118498
$869$	0.670006	0.0227284
$870$	−1.59562	−0.0540965
$871$	12.0916	0.409707
$872$	−31.7212	−1.07421
$873$	3.24049	0.109674
$874$	−18.7942	−0.635722
$875$	−3.05854	−0.103397
$876$	1.48307	0.0501082
$877$	−3.29780	−0.111359	−0.0556793	−	0.998449i	$-0.517732\pi$
$877$	−3.29780	−0.111359	−0.0556793	+	0.998449i	$0.517732\pi$
$878$	49.8304	1.68170
$879$	20.0301	0.675598
$880$	−1.84972	−0.0623539
$881$	21.7018	0.731152	0.365576	−	0.930781i	$-0.380872\pi$
$881$	21.7018	0.731152	0.365576	+	0.930781i	$0.380872\pi$
$882$	−3.42367	−0.115281
$883$	7.80426	0.262634	0.131317	−	0.991340i	$-0.458079\pi$
$883$	7.80426	0.262634	0.131317	+	0.991340i	$0.458079\pi$
$884$	0.262904	0.00884241
$885$	−1.03869	−0.0349151
$886$	39.0488	1.31187
$887$	7.78187	0.261290	0.130645	−	0.991429i	$-0.458295\pi$
$887$	7.78187	0.261290	0.130645	+	0.991429i	$0.458295\pi$
$888$	9.57222	0.321223
$889$	47.4010	1.58978
$890$	−10.3399	−0.346593
$891$	−0.438814	−0.0147008
$892$	0.0408680	0.00136836
$893$	16.2874	0.545037
$894$	22.3216	0.746545
$895$	4.92454	0.164609
$896$	−37.2666	−1.24499
$897$	6.52136	0.217742
$898$	28.5489	0.952691
$899$	−1.09739	−0.0366000
$900$	0.114145	0.00380484
$901$	23.2901	0.775905
$902$	0.365610	0.0121735
$903$	34.4903	1.14777
$904$	34.9810	1.16345
$905$	7.57891	0.251932
$906$	−12.4938	−0.415080
$907$	−45.9486	−1.52570	−0.762849	−	0.646577i	$-0.776200\pi$
$907$	−45.9486	−1.52570	−0.762849	+	0.646577i	$0.776200\pi$
$908$	1.48104	0.0491500
$909$	1.26704	0.0420250
$910$	−4.44714	−0.147421
$911$	5.48582	0.181753	0.0908767	−	0.995862i	$-0.471033\pi$
$911$	5.48582	0.181753	0.0908767	+	0.995862i	$0.471033\pi$
$912$	8.35491	0.276659
$913$	−2.10761	−0.0697518
$914$	17.7128	0.585888
$915$	−1.03222	−0.0341241
$916$	−1.06391	−0.0351525
$917$	18.9137	0.624586
$918$	−3.34893	−0.110531
$919$	−34.5608	−1.14006	−0.570028	−	0.821625i	$-0.693068\pi$
$919$	−34.5608	−1.14006	−0.570028	+	0.821625i	$0.693068\pi$
$920$	−17.8819	−0.589549
$921$	−23.2058	−0.764658
$922$	5.43248	0.178909
$923$	−2.55812	−0.0842016
$924$	0.153198	0.00503984
$925$	−3.49090	−0.114780
$926$	−3.11764	−0.102452
$927$	14.3810	0.472332
$928$	0.707739	0.0232327
$929$	10.9427	0.359019	0.179510	−	0.983756i	$-0.442549\pi$
$929$	10.9427	0.359019	0.179510	+	0.983756i	$0.442549\pi$
$930$	1.45401	0.0476789
$931$	4.66704	0.152956
$932$	2.40225	0.0786882
$933$	31.7056	1.03799
$934$	5.25278	0.171876
$935$	−1.01069	−0.0330532
$936$	−2.74205	−0.0896268
$937$	−44.5543	−1.45553	−0.727764	−	0.685828i	$-0.759440\pi$
$937$	−44.5543	−1.45553	−0.727764	+	0.685828i	$0.759440\pi$
$938$	53.7729	1.75575
$939$	23.6874	0.773008
$940$	−0.937978	−0.0305935
$941$	−9.91571	−0.323243	−0.161621	−	0.986853i	$-0.551672\pi$
$941$	−9.91571	−0.323243	−0.161621	+	0.986853i	$0.551672\pi$
$942$	−19.5114	−0.635716
$943$	3.73687	0.121689
$944$	4.37834	0.142503
$945$	3.05854	0.0994942
$946$	−7.19502	−0.233930
$947$	14.0820	0.457603	0.228802	−	0.973473i	$-0.426519\pi$
$947$	14.0820	0.457603	0.228802	+	0.973473i	$0.426519\pi$
$948$	0.174283	0.00566046
$949$	12.9928	0.421764
$950$	−2.88194	−0.0935024
$951$	13.0153	0.422050
$952$	−19.3165	−0.626051
$953$	9.28236	0.300685	0.150343	−	0.988634i	$-0.451962\pi$
$953$	9.28236	0.300685	0.150343	+	0.988634i	$0.451962\pi$
$954$	14.7028	0.476020
$955$	−11.0818	−0.358599
$956$	−1.71766	−0.0555530
$957$	0.481551	0.0155663
$958$	−40.5355	−1.30964
$959$	−26.8181	−0.866003
$960$	7.49279	0.241829
$961$	1.00000	0.0322581
$962$	−5.07580	−0.163650
$963$	−1.82966	−0.0589600
$964$	0.887396	0.0285811
$965$	−18.5646	−0.597614
$966$	29.0014	0.933106
$967$	50.7033	1.63051	0.815254	−	0.579103i	$-0.196597\pi$
$967$	50.7033	1.63051	0.815254	+	0.579103i	$0.196597\pi$
$968$	−29.6346	−0.952491
$969$	4.56516	0.146654
$970$	4.71170	0.151284
$971$	−2.40570	−0.0772025	−0.0386013	−	0.999255i	$-0.512290\pi$
$971$	−2.40570	−0.0772025	−0.0386013	+	0.999255i	$0.512290\pi$
$972$	−0.114145	−0.00366121
$973$	−15.0305	−0.481854
$974$	34.8755	1.11748
$975$	1.00000	0.0320256
$976$	4.35108	0.139275
$977$	20.3614	0.651418	0.325709	−	0.945470i	$-0.394397\pi$
$977$	20.3614	0.651418	0.325709	+	0.945470i	$0.394397\pi$
$978$	33.6408	1.07571
$979$	3.12053	0.0997325
$980$	−0.268771	−0.00858558
$981$	−11.5684	−0.369351
$982$	−19.9055	−0.635211
$983$	13.8169	0.440690	0.220345	−	0.975422i	$-0.429282\pi$
$983$	13.8169	0.440690	0.220345	+	0.975422i	$0.429282\pi$
$984$	−1.57125	−0.0500896
$985$	1.31419	0.0418737
$986$	3.67508	0.117039
$987$	−25.1332	−0.799999
$988$	−0.226243	−0.00719775
$989$	−73.5397	−2.33843
$990$	−0.638040	−0.0202783
$991$	−32.0759	−1.01892	−0.509462	−	0.860493i	$-0.670155\pi$
$991$	−32.0759	−1.01892	−0.509462	+	0.860493i	$0.670155\pi$
$992$	−0.644929	−0.0204765
$993$	6.43786	0.204299
$994$	−11.3763	−0.360835
$995$	−12.5948	−0.399281
$996$	−0.548237	−0.0173715
$997$	45.4253	1.43864	0.719318	−	0.694681i	$-0.244455\pi$
$997$	45.4253	1.43864	0.719318	+	0.694681i	$0.244455\pi$
$998$	−18.6383	−0.589986
$999$	3.49090	0.110447

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.w.1.3	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.w.1.3	✓	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-1.45401 q^{2} -1.00000 q^{3} +0.114145 q^{4} -1.00000 q^{5} +1.45401 q^{6} +3.05854 q^{7} +2.74205 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.45401 q^{2} -1.00000 q^{3} +0.114145 q^{4} -1.00000 q^{5} +1.45401 q^{6} +3.05854 q^{7} +2.74205 q^{8} +1.00000 q^{9} +1.45401 q^{10} -0.438814 q^{11} -0.114145 q^{12} -1.00000 q^{13} -4.44714 q^{14} +1.00000 q^{15} -4.21526 q^{16} -2.30324 q^{17} -1.45401 q^{18} +1.98206 q^{19} -0.114145 q^{20} -3.05854 q^{21} +0.638040 q^{22} +6.52136 q^{23} -2.74205 q^{24} +1.00000 q^{25} +1.45401 q^{26} -1.00000 q^{27} +0.349117 q^{28} +1.09739 q^{29} -1.45401 q^{30} -1.00000 q^{31} +0.644929 q^{32} +0.438814 q^{33} +3.34893 q^{34} -3.05854 q^{35} +0.114145 q^{36} -3.49090 q^{37} -2.88194 q^{38} +1.00000 q^{39} -2.74205 q^{40} +0.573020 q^{41} +4.44714 q^{42} -11.2767 q^{43} -0.0500886 q^{44} -1.00000 q^{45} -9.48213 q^{46} +8.21740 q^{47} +4.21526 q^{48} +2.35464 q^{49} -1.45401 q^{50} +2.30324 q^{51} -0.114145 q^{52} -10.1119 q^{53} +1.45401 q^{54} +0.438814 q^{55} +8.38666 q^{56} -1.98206 q^{57} -1.59562 q^{58} -1.03869 q^{59} +0.114145 q^{60} -1.03222 q^{61} +1.45401 q^{62} +3.05854 q^{63} +7.49279 q^{64} +1.00000 q^{65} -0.638040 q^{66} -12.0916 q^{67} -0.262904 q^{68} -6.52136 q^{69} +4.44714 q^{70} +2.55812 q^{71} +2.74205 q^{72} -12.9928 q^{73} +5.07580 q^{74} -1.00000 q^{75} +0.226243 q^{76} -1.34213 q^{77} -1.45401 q^{78} -1.52685 q^{79} +4.21526 q^{80} +1.00000 q^{81} -0.833177 q^{82} +4.80297 q^{83} -0.349117 q^{84} +2.30324 q^{85} +16.3965 q^{86} -1.09739 q^{87} -1.20325 q^{88} -7.11127 q^{89} +1.45401 q^{90} -3.05854 q^{91} +0.744383 q^{92} +1.00000 q^{93} -11.9482 q^{94} -1.98206 q^{95} -0.644929 q^{96} +3.24049 q^{97} -3.42367 q^{98} -0.438814 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9} - 2 q^{10} - 12 q^{12} - 11 q^{13} + 5 q^{14} + 11 q^{15} - 10 q^{16} - 3 q^{17} + 2 q^{18} - 8 q^{19} - 12 q^{20} - 4 q^{21} - 3 q^{22} + 11 q^{23} - 3 q^{24} + 11 q^{25} - 2 q^{26} - 11 q^{27} + 14 q^{28} - 14 q^{29} + 2 q^{30} - 11 q^{31} + 8 q^{32} - 11 q^{34} - 4 q^{35} + 12 q^{36} + 7 q^{37} + 8 q^{38} + 11 q^{39} - 3 q^{40} + 22 q^{41} - 5 q^{42} - 5 q^{43} - 13 q^{44} - 11 q^{45} - 22 q^{46} + 5 q^{47} + 10 q^{48} - 33 q^{49} + 2 q^{50} + 3 q^{51} - 12 q^{52} + 4 q^{53} - 2 q^{54} - 13 q^{56} + 8 q^{57} - 18 q^{58} - 3 q^{59} + 12 q^{60} - 28 q^{61} - 2 q^{62} + 4 q^{63} + 3 q^{64} + 11 q^{65} + 3 q^{66} - 11 q^{67} - 9 q^{68} - 11 q^{69} - 5 q^{70} + 5 q^{71} + 3 q^{72} - 3 q^{73} - 12 q^{74} - 11 q^{75} - 36 q^{76} + 18 q^{77} + 2 q^{78} - 43 q^{79} + 10 q^{80} + 11 q^{81} - 15 q^{82} - 28 q^{83} - 14 q^{84} + 3 q^{85} + 10 q^{86} + 14 q^{87} - 43 q^{88} - 25 q^{89} - 2 q^{90} - 4 q^{91} + 7 q^{92} + 11 q^{93} - 16 q^{94} + 8 q^{95} - 8 q^{96} - 6 q^{97} - 14 q^{98}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9 - 2 * q^10 - 12 * q^12 - 11 * q^13 + 5 * q^14 + 11 * q^15 - 10 * q^16 - 3 * q^17 + 2 * q^18 - 8 * q^19 - 12 * q^20 - 4 * q^21 - 3 * q^22 + 11 * q^23 - 3 * q^24 + 11 * q^25 - 2 * q^26 - 11 * q^27 + 14 * q^28 - 14 * q^29 + 2 * q^30 - 11 * q^31 + 8 * q^32 - 11 * q^34 - 4 * q^35 + 12 * q^36 + 7 * q^37 + 8 * q^38 + 11 * q^39 - 3 * q^40 + 22 * q^41 - 5 * q^42 - 5 * q^43 - 13 * q^44 - 11 * q^45 - 22 * q^46 + 5 * q^47 + 10 * q^48 - 33 * q^49 + 2 * q^50 + 3 * q^51 - 12 * q^52 + 4 * q^53 - 2 * q^54 - 13 * q^56 + 8 * q^57 - 18 * q^58 - 3 * q^59 + 12 * q^60 - 28 * q^61 - 2 * q^62 + 4 * q^63 + 3 * q^64 + 11 * q^65 + 3 * q^66 - 11 * q^67 - 9 * q^68 - 11 * q^69 - 5 * q^70 + 5 * q^71 + 3 * q^72 - 3 * q^73 - 12 * q^74 - 11 * q^75 - 36 * q^76 + 18 * q^77 + 2 * q^78 - 43 * q^79 + 10 * q^80 + 11 * q^81 - 15 * q^82 - 28 * q^83 - 14 * q^84 + 3 * q^85 + 10 * q^86 + 14 * q^87 - 43 * q^88 - 25 * q^89 - 2 * q^90 - 4 * q^91 + 7 * q^92 + 11 * q^93 - 16 * q^94 + 8 * q^95 - 8 * q^96 - 6 * q^97 - 14 * q^98

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