LMFDB - Embedded newform 1183.2.c.h.337.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 96x^{8} + 266x^{6} + 332x^{4} + 141x^{2} + 1 $ x^12 + 16x^10 + 96x^8 + 266x^6 + 332x^4 + 141*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.7
Root			$2.10066i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.h.337.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.312100i q^{2} +1.10066 q^{3} +1.90259 q^{4} +1.93488i q^{5} +0.343514i q^{6} +1.00000i q^{7} +1.21800i q^{8} -1.78856 q^{9} +O(q^{10})$	\(q+0.312100i q^{2} +1.10066 q^{3} +1.90259 q^{4} +1.93488i q^{5} +0.343514i q^{6} +1.00000i q^{7} +1.21800i q^{8} -1.78856 q^{9} -0.603875 q^{10} +3.30407i q^{11} +2.09410 q^{12} -0.312100 q^{14} +2.12964i q^{15} +3.42505 q^{16} +2.68336 q^{17} -0.558208i q^{18} -3.97514i q^{19} +3.68129i q^{20} +1.10066i q^{21} -1.03120 q^{22} +0.249801 q^{23} +1.34060i q^{24} +1.25624 q^{25} -5.27055 q^{27} +1.90259i q^{28} -6.85160 q^{29} -0.664659 q^{30} +8.16283i q^{31} +3.50495i q^{32} +3.63665i q^{33} +0.837477i q^{34} -1.93488 q^{35} -3.40290 q^{36} +1.51991i q^{37} +1.24064 q^{38} -2.35668 q^{40} +1.36739i q^{41} -0.343514 q^{42} +10.5877 q^{43} +6.28630i q^{44} -3.46064i q^{45} +0.0779628i q^{46} +2.89468i q^{47} +3.76980 q^{48} -1.00000 q^{49} +0.392072i q^{50} +2.95346 q^{51} -11.3581 q^{53} -1.64494i q^{54} -6.39298 q^{55} -1.21800 q^{56} -4.37526i q^{57} -2.13838i q^{58} -13.9836i q^{59} +4.05183i q^{60} +13.7088 q^{61} -2.54762 q^{62} -1.78856i q^{63} +5.75621 q^{64} -1.13500 q^{66} +2.82526i q^{67} +5.10535 q^{68} +0.274945 q^{69} -0.603875i q^{70} -9.17197i q^{71} -2.17846i q^{72} -8.47003i q^{73} -0.474362 q^{74} +1.38269 q^{75} -7.56308i q^{76} -3.30407 q^{77} -8.68165 q^{79} +6.62706i q^{80} -0.435397 q^{81} -0.426761 q^{82} +8.89470i q^{83} +2.09410i q^{84} +5.19199i q^{85} +3.30441i q^{86} -7.54126 q^{87} -4.02435 q^{88} +7.50252i q^{89} +1.08007 q^{90} +0.475270 q^{92} +8.98447i q^{93} -0.903430 q^{94} +7.69142 q^{95} +3.85775i q^{96} -8.70065i q^{97} -0.312100i q^{98} -5.90952i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{3} - 16 q^{4}+O(q^{10}) $ 12 * q - 8 * q^3 - 16 * q^4	$ 12 q - 8 q^{3} - 16 q^{4} + 28 q^{10} + 46 q^{12} - 4 q^{14} + 46 q^{17} - 8 q^{22} + 36 q^{23} + 20 q^{25} - 20 q^{27} - 30 q^{29} - 28 q^{30} - 4 q^{35} - 44 q^{36} + 22 q^{38} - 28 q^{40} + 16 q^{42} + 36 q^{43} - 22 q^{48} - 12 q^{49} - 28 q^{51} - 50 q^{53} + 6 q^{56} + 32 q^{61} + 18 q^{62} + 14 q^{64} + 32 q^{66} - 68 q^{68} + 2 q^{69} - 28 q^{74} - 30 q^{75} + 16 q^{77} + 4 q^{79} - 12 q^{81} + 20 q^{82} + 26 q^{87} + 96 q^{88} - 64 q^{92} - 28 q^{94} + 14 q^{95}+O(q^{100}) $ 12 * q - 8 * q^3 - 16 * q^4 + 28 * q^10 + 46 * q^12 - 4 * q^14 + 46 * q^17 - 8 * q^22 + 36 * q^23 + 20 * q^25 - 20 * q^27 - 30 * q^29 - 28 * q^30 - 4 * q^35 - 44 * q^36 + 22 * q^38 - 28 * q^40 + 16 * q^42 + 36 * q^43 - 22 * q^48 - 12 * q^49 - 28 * q^51 - 50 * q^53 + 6 * q^56 + 32 * q^61 + 18 * q^62 + 14 * q^64 + 32 * q^66 - 68 * q^68 + 2 * q^69 - 28 * q^74 - 30 * q^75 + 16 * q^77 + 4 * q^79 - 12 * q^81 + 20 * q^82 + 26 * q^87 + 96 * q^88 - 64 * q^92 - 28 * q^94 + 14 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

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 $

$2$	0.312100i	0.220688i	0.993893	+	0.110344i	$0.0351952\pi$
$2$	0.312100i	0.220688i	−0.993893	+	0.110344i	$0.964805\pi$
$3$	1.10066	0.635464	0.317732	−	0.948181i	$-0.397079\pi$
$3$	1.10066	0.635464	0.317732	+	0.948181i	$0.397079\pi$
$4$	1.90259	0.951297
$5$	1.93488i	0.865305i	0.901561	+	0.432652i	$0.142422\pi$
$5$	1.93488i	0.865305i	−0.901561	+	0.432652i	$0.857578\pi$
$6$	0.343514i	0.140239i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	1.21800i	0.430627i
$9$	−1.78856	−0.596185
$10$	−0.603875	−0.190962
$11$	3.30407i	0.996215i	0.867115	+	0.498107i	$0.165971\pi$
$11$	3.30407i	0.996215i	−0.867115	+	0.498107i	$0.834029\pi$
$12$	2.09410	0.604515
$13$	0	0
$13$	0	0
$14$	−0.312100	−0.0834122
$15$	2.12964i	0.549870i
$16$	3.42505	0.856263
$17$	2.68336	0.650811	0.325406	−	0.945574i	$-0.394499\pi$
$17$	2.68336	0.650811	0.325406	+	0.945574i	$0.394499\pi$
$18$	− 0.558208i	− 0.131571i
$19$	− 3.97514i	− 0.911960i	−0.889990	−	0.455980i	$-0.849289\pi$
$19$	− 3.97514i	− 0.911960i	0.889990	−	0.455980i	$-0.150711\pi$
$20$	3.68129i	0.823162i
$21$	1.10066i	0.240183i
$22$	−1.03120	−0.219852
$23$	0.249801	0.0520871	0.0260435	−	0.999661i	$-0.491709\pi$
$23$	0.249801	0.0520871	0.0260435	+	0.999661i	$0.491709\pi$
$24$	1.34060i	0.273648i
$25$	1.25624	0.251248
$26$	0	0
$27$	−5.27055	−1.01432
$28$	1.90259i	0.359556i
$29$	−6.85160	−1.27231	−0.636155	−	0.771561i	$-0.719476\pi$
$29$	−6.85160	−1.27231	−0.636155	+	0.771561i	$0.719476\pi$
$30$	−0.664659	−0.121350
$31$	8.16283i	1.46609i	0.680181	+	0.733044i	$0.261901\pi$
$31$	8.16283i	1.46609i	−0.680181	+	0.733044i	$0.738099\pi$
$32$	3.50495i	0.619594i
$33$	3.63665i	0.633059i
$34$	0.837477i	0.143626i
$35$	−1.93488	−0.327054
$36$	−3.40290	−0.567149
$37$	1.51991i	0.249871i	0.992165	+	0.124935i	$0.0398724\pi$
$37$	1.51991i	0.249871i	−0.992165	+	0.124935i	$0.960128\pi$
$38$	1.24064	0.201258
$39$	0	0
$40$	−2.35668	−0.372624
$41$	1.36739i	0.213550i	0.994283	+	0.106775i	$0.0340525\pi$
$41$	1.36739i	0.213550i	−0.994283	+	0.106775i	$0.965948\pi$
$42$	−0.343514	−0.0530054
$43$	10.5877	1.61460	0.807302	−	0.590138i	$-0.200927\pi$
$43$	10.5877	1.61460	0.807302	+	0.590138i	$0.200927\pi$
$44$	6.28630i	0.947696i
$45$	− 3.46064i	− 0.515882i
$46$	0.0779628i	0.0114950i
$47$	2.89468i	0.422233i	0.977461	+	0.211117i	$0.0677100\pi$
$47$	2.89468i	0.422233i	−0.977461	+	0.211117i	$0.932290\pi$
$48$	3.76980	0.544124
$49$	−1.00000	−0.142857
$50$	0.392072i	0.0554474i
$51$	2.95346	0.413567
$52$	0	0
$53$	−11.3581	−1.56015	−0.780077	−	0.625683i	$-0.784820\pi$
$53$	−11.3581	−1.56015	−0.780077	+	0.625683i	$0.784820\pi$
$54$	− 1.64494i	− 0.223848i
$55$	−6.39298	−0.862029
$56$	−1.21800	−0.162762
$57$	− 4.37526i	− 0.579518i
$58$	− 2.13838i	− 0.280783i
$59$	− 13.9836i	− 1.82052i	−0.414042	−	0.910258i	$-0.635883\pi$
$59$	− 13.9836i	− 1.82052i	0.414042	−	0.910258i	$-0.364117\pi$
$60$	4.05183i	0.523090i
$61$	13.7088	1.75523	0.877616	−	0.479365i	$-0.159133\pi$
$61$	13.7088	1.75523	0.877616	+	0.479365i	$0.159133\pi$
$62$	−2.54762	−0.323548
$63$	− 1.78856i	− 0.225337i
$64$	5.75621	0.719526
$65$	0	0
$66$	−1.13500	−0.139708
$67$	2.82526i	0.345161i	0.984995	+	0.172580i	$0.0552105\pi$
$67$	2.82526i	0.345161i	−0.984995	+	0.172580i	$0.944790\pi$
$68$	5.10535	0.619115
$69$	0.274945	0.0330995
$70$	− 0.603875i	− 0.0721769i
$71$	− 9.17197i	− 1.08851i	−0.838919	−	0.544256i	$-0.816812\pi$
$71$	− 9.17197i	− 1.08851i	0.838919	−	0.544256i	$-0.183188\pi$
$72$	− 2.17846i	− 0.256734i
$73$	− 8.47003i	− 0.991342i	−0.868510	−	0.495671i	$-0.834922\pi$
$73$	− 8.47003i	− 0.991342i	0.868510	−	0.495671i	$-0.165078\pi$
$74$	−0.474362	−0.0551435
$75$	1.38269	0.159659
$76$	− 7.56308i	− 0.867544i
$77$	−3.30407	−0.376534
$78$	0	0
$79$	−8.68165	−0.976762	−0.488381	−	0.872631i	$-0.662412\pi$
$79$	−8.68165	−0.976762	−0.488381	+	0.872631i	$0.662412\pi$
$80$	6.62706i	0.740928i
$81$	−0.435397	−0.0483775
$82$	−0.426761	−0.0471279
$83$	8.89470i	0.976320i	0.872754	+	0.488160i	$0.162332\pi$
$83$	8.89470i	0.976320i	−0.872754	+	0.488160i	$0.837668\pi$
$84$	2.09410i	0.228485i
$85$	5.19199i	0.563150i
$86$	3.30441i	0.356324i
$87$	−7.54126	−0.808508
$88$	−4.02435	−0.428997
$89$	7.50252i	0.795265i	0.917545	+	0.397633i	$0.130168\pi$
$89$	7.50252i	0.795265i	−0.917545	+	0.397633i	$0.869832\pi$
$90$	1.08007	0.113849
$91$	0	0
$92$	0.475270	0.0495503
$93$	8.98447i	0.931646i
$94$	−0.903430	−0.0931817
$95$	7.69142	0.789123
$96$	3.85775i	0.393730i
$97$	− 8.70065i	− 0.883418i	−0.897158	−	0.441709i	$-0.854372\pi$
$97$	− 8.70065i	− 0.883418i	0.897158	−	0.441709i	$-0.145628\pi$
$98$	− 0.312100i	− 0.0315268i
$99$	− 5.90952i	− 0.593929i
$100$	2.39011	0.239011
$101$	7.66968	0.763162	0.381581	−	0.924335i	$-0.375380\pi$
$101$	7.66968	0.763162	0.381581	+	0.924335i	$0.375380\pi$
$102$	0.921774i	0.0912693i
$103$	9.35776	0.922048	0.461024	−	0.887388i	$-0.347482\pi$
$103$	9.35776	0.922048	0.461024	+	0.887388i	$0.347482\pi$
$104$	0	0
$105$	−2.12964	−0.207831
$106$	− 3.54486i	− 0.344307i
$107$	9.36508	0.905357	0.452678	−	0.891674i	$-0.350469\pi$
$107$	9.36508	0.905357	0.452678	+	0.891674i	$0.350469\pi$
$108$	−10.0277	−0.964918
$109$	− 19.9277i	− 1.90872i	−0.298652	−	0.954362i	$-0.596537\pi$
$109$	− 19.9277i	− 1.90872i	0.298652	−	0.954362i	$-0.403463\pi$
$110$	− 1.99525i	− 0.190239i
$111$	1.67289i	0.158784i
$112$	3.42505i	0.323637i
$113$	−4.65777	−0.438166	−0.219083	−	0.975706i	$-0.570307\pi$
$113$	−4.65777	−0.438166	−0.219083	+	0.975706i	$0.570307\pi$
$114$	1.36552	0.127892
$115$	0.483335i	0.0450712i
$116$	−13.0358	−1.21035
$117$	0	0
$118$	4.36429	0.401766
$119$	2.68336i	0.245984i
$120$	−2.59389	−0.236789
$121$	0.0831177	0.00755616
$122$	4.27851i	0.387358i
$123$	1.50502i	0.135703i
$124$	15.5306i	1.39468i
$125$	12.1051i	1.08271i
$126$	0.558208	0.0497291
$127$	−7.56559	−0.671338	−0.335669	−	0.941980i	$-0.608962\pi$
$127$	−7.56559	−0.671338	−0.335669	+	0.941980i	$0.608962\pi$
$128$	8.80642i	0.778385i
$129$	11.6534	1.02602
$130$	0	0
$131$	20.5380	1.79441	0.897205	−	0.441615i	$-0.145594\pi$
$131$	20.5380	1.79441	0.897205	+	0.441615i	$0.145594\pi$
$132$	6.91906i	0.602227i
$133$	3.97514	0.344688
$134$	−0.881764	−0.0761728
$135$	− 10.1979i	− 0.877694i
$136$	3.26833i	0.280257i
$137$	− 10.5347i	− 0.900043i	−0.893018	−	0.450021i	$-0.851416\pi$
$137$	− 10.5347i	− 0.900043i	0.893018	−	0.450021i	$-0.148584\pi$
$138$	0.0858102i	0.00730465i
$139$	−5.42605	−0.460231	−0.230116	−	0.973163i	$-0.573910\pi$
$139$	−5.42605	−0.460231	−0.230116	+	0.973163i	$0.573910\pi$
$140$	−3.68129	−0.311126
$141$	3.18605i	0.268314i
$142$	2.86257	0.240222
$143$	0	0
$144$	−6.12590	−0.510491
$145$	− 13.2570i	− 1.10094i
$146$	2.64349	0.218777
$147$	−1.10066	−0.0907806
$148$	2.89176i	0.237701i
$149$	19.3141i	1.58227i	0.611640	+	0.791136i	$0.290510\pi$
$149$	19.3141i	1.58227i	−0.611640	+	0.791136i	$0.709490\pi$
$150$	0.431537i	0.0352348i
$151$	− 2.41011i	− 0.196132i	−0.995180	−	0.0980658i	$-0.968734\pi$
$151$	− 2.41011i	− 0.196132i	0.995180	−	0.0980658i	$-0.0312656\pi$
$152$	4.84171	0.392715
$153$	−4.79935	−0.388004
$154$	− 1.03120i	− 0.0830964i
$155$	−15.7941	−1.26861
$156$	0	0
$157$	6.27981	0.501183	0.250592	−	0.968093i	$-0.419375\pi$
$157$	6.27981	0.501183	0.250592	+	0.968093i	$0.419375\pi$
$158$	− 2.70954i	− 0.215559i
$159$	−12.5014	−0.991422
$160$	−6.78167	−0.536138
$161$	0.249801i	0.0196871i
$162$	− 0.135887i	− 0.0106763i
$163$	− 14.7792i	− 1.15760i	−0.815470	−	0.578799i	$-0.803522\pi$
$163$	− 14.7792i	− 1.15760i	0.815470	−	0.578799i	$-0.196478\pi$
$164$	2.60158i	0.203149i
$165$	−7.03647	−0.547789
$166$	−2.77603	−0.215462
$167$	− 11.6656i	− 0.902709i	−0.892345	−	0.451355i	$-0.850941\pi$
$167$	− 11.6656i	− 0.902709i	0.892345	−	0.451355i	$-0.149059\pi$
$168$	−1.34060	−0.103429
$169$	0	0
$170$	−1.62042	−0.124280
$171$	7.10976i	0.543697i
$172$	20.1440	1.53597
$173$	14.4438	1.09814	0.549072	−	0.835775i	$-0.314981\pi$
$173$	14.4438	1.09814	0.549072	+	0.835775i	$0.314981\pi$
$174$	− 2.35362i	− 0.178428i
$175$	1.25624i	0.0949628i
$176$	11.3166i	0.853021i
$177$	− 15.3912i	− 1.15687i
$178$	−2.34153	−0.175505
$179$	5.40993	0.404357	0.202179	−	0.979349i	$-0.435198\pi$
$179$	5.40993	0.404357	0.202179	+	0.979349i	$0.435198\pi$
$180$	− 6.58420i	− 0.490757i
$181$	−6.75171	−0.501851	−0.250926	−	0.968006i	$-0.580735\pi$
$181$	−6.75171	−0.501851	−0.250926	+	0.968006i	$0.580735\pi$
$182$	0	0
$183$	15.0887	1.11539
$184$	0.304257i	0.0224301i
$185$	−2.94084	−0.216215
$186$	−2.80405	−0.205603
$187$	8.86602i	0.648348i
$188$	5.50741i	0.401669i
$189$	− 5.27055i	− 0.383376i
$190$	2.40049i	0.174150i
$191$	−13.0918	−0.947290	−0.473645	−	0.880716i	$-0.657062\pi$
$191$	−13.0918	−0.947290	−0.473645	+	0.880716i	$0.657062\pi$
$192$	6.33560	0.457233
$193$	8.06247i	0.580350i	0.956974	+	0.290175i	$0.0937134\pi$
$193$	8.06247i	0.580350i	−0.956974	+	0.290175i	$0.906287\pi$
$194$	2.71547	0.194960
$195$	0	0
$196$	−1.90259	−0.135900
$197$	− 14.9630i	− 1.06607i	−0.846094	−	0.533033i	$-0.821052\pi$
$197$	− 14.9630i	− 1.06607i	0.846094	−	0.533033i	$-0.178948\pi$
$198$	1.84436	0.131073
$199$	−10.2781	−0.728597	−0.364299	−	0.931282i	$-0.618691\pi$
$199$	−10.2781	−0.728597	−0.364299	+	0.931282i	$0.618691\pi$
$200$	1.53010i	0.108194i
$201$	3.10964i	0.219337i
$202$	2.39370i	0.168420i
$203$	− 6.85160i	− 0.480888i
$204$	5.61924	0.393425
$205$	−2.64573	−0.184786
$206$	2.92056i	0.203485i
$207$	−0.446783	−0.0310536
$208$	0	0
$209$	13.1341	0.908508
$210$	− 0.664659i	− 0.0458658i
$211$	−7.19246	−0.495150	−0.247575	−	0.968869i	$-0.579634\pi$
$211$	−7.19246	−0.495150	−0.247575	+	0.968869i	$0.579634\pi$
$212$	−21.6098	−1.48417
$213$	− 10.0952i	− 0.691711i
$214$	2.92284i	0.199801i
$215$	20.4859i	1.39713i
$216$	− 6.41953i	− 0.436793i
$217$	−8.16283	−0.554129
$218$	6.21942	0.421232
$219$	− 9.32259i	− 0.629962i
$220$	−12.1632	−0.820046
$221$	0	0
$222$	−0.522110	−0.0350417
$223$	− 29.7080i	− 1.98939i	−0.102851	−	0.994697i	$-0.532797\pi$
$223$	− 29.7080i	− 1.98939i	0.102851	−	0.994697i	$-0.467203\pi$
$224$	−3.50495	−0.234185
$225$	−2.24686	−0.149790
$226$	− 1.45369i	− 0.0966980i
$227$	12.8350i	0.851891i	0.904749	+	0.425946i	$0.140059\pi$
$227$	12.8350i	0.851891i	−0.904749	+	0.425946i	$0.859941\pi$
$228$	− 8.32435i	− 0.551293i
$229$	− 12.9893i	− 0.858360i	−0.903219	−	0.429180i	$-0.858803\pi$
$229$	− 12.9893i	− 0.858360i	0.903219	−	0.429180i	$-0.141197\pi$
$230$	−0.150849	−0.00994667
$231$	−3.63665	−0.239274
$232$	− 8.34524i	− 0.547892i
$233$	−20.7043	−1.35638	−0.678192	−	0.734884i	$-0.737236\pi$
$233$	−20.7043	−1.35638	−0.678192	+	0.734884i	$0.737236\pi$
$234$	0	0
$235$	−5.60087	−0.365360
$236$	− 26.6052i	− 1.73185i
$237$	−9.55551	−0.620697
$238$	−0.837477	−0.0542856
$239$	14.2812i	0.923772i	0.886939	+	0.461886i	$0.152827\pi$
$239$	14.2812i	0.923772i	−0.886939	+	0.461886i	$0.847173\pi$
$240$	7.29412i	0.470833i
$241$	− 12.8333i	− 0.826665i	−0.910580	−	0.413332i	$-0.864365\pi$
$241$	− 12.8333i	− 0.826665i	0.910580	−	0.413332i	$-0.135635\pi$
$242$	0.0259410i	0.00166755i
$243$	15.3324	0.983576
$244$	26.0823	1.66975
$245$	− 1.93488i	− 0.123615i
$246$	−0.469717	−0.0299481
$247$	0	0
$248$	−9.94232	−0.631338
$249$	9.79000i	0.620416i
$250$	−3.77799	−0.238941
$251$	15.1961	0.959168	0.479584	−	0.877496i	$-0.340788\pi$
$251$	15.1961	0.959168	0.479584	+	0.877496i	$0.340788\pi$
$252$	− 3.40290i	− 0.214362i
$253$	0.825360i	0.0518899i
$254$	− 2.36122i	− 0.148156i
$255$	5.71459i	0.357862i
$256$	8.76393	0.547746
$257$	30.4182	1.89744	0.948718	−	0.316125i	$-0.102382\pi$
$257$	30.4182	1.89744	0.948718	+	0.316125i	$0.102382\pi$
$258$	3.63702i	0.226431i
$259$	−1.51991	−0.0944424
$260$	0	0
$261$	12.2545	0.758533
$262$	6.40989i	0.396004i
$263$	4.87591	0.300662	0.150331	−	0.988636i	$-0.451966\pi$
$263$	4.87591	0.300662	0.150331	+	0.988636i	$0.451966\pi$
$264$	−4.42943	−0.272612
$265$	− 21.9766i	− 1.35001i
$266$	1.24064i	0.0760685i
$267$	8.25769i	0.505362i
$268$	5.37533i	0.328350i
$269$	−6.89823	−0.420592	−0.210296	−	0.977638i	$-0.567443\pi$
$269$	−6.89823	−0.420592	−0.210296	+	0.977638i	$0.567443\pi$
$270$	3.18276	0.193696
$271$	2.14946i	0.130570i	0.997867	+	0.0652851i	$0.0207957\pi$
$271$	2.14946i	0.130570i	−0.997867	+	0.0652851i	$0.979204\pi$
$272$	9.19066	0.557266
$273$	0	0
$274$	3.28789	0.198629
$275$	4.15071i	0.250297i
$276$	0.523108	0.0314874
$277$	−27.8905	−1.67577	−0.837887	−	0.545843i	$-0.816209\pi$
$277$	−27.8905	−1.67577	−0.837887	+	0.545843i	$0.816209\pi$
$278$	− 1.69347i	− 0.101567i
$279$	− 14.5997i	− 0.874060i
$280$	− 2.35668i	− 0.140839i
$281$	1.76846i	0.105498i	0.998608	+	0.0527488i	$0.0167982\pi$
$281$	1.76846i	0.105498i	−0.998608	+	0.0527488i	$0.983202\pi$
$282$	−0.994366	−0.0592136
$283$	−18.6963	−1.11138	−0.555690	−	0.831390i	$-0.687546\pi$
$283$	−18.6963	−1.11138	−0.555690	+	0.831390i	$0.687546\pi$
$284$	− 17.4505i	− 1.03550i
$285$	8.46561	0.501459
$286$	0	0
$287$	−1.36739	−0.0807143
$288$	− 6.26881i	− 0.369393i
$289$	−9.79956	−0.576444
$290$	4.13751	0.242963
$291$	− 9.57643i	− 0.561380i
$292$	− 16.1150i	− 0.943061i
$293$	− 9.71217i	− 0.567391i	−0.958914	−	0.283695i	$-0.908440\pi$
$293$	− 9.71217i	− 0.567391i	0.958914	−	0.283695i	$-0.0915605\pi$
$294$	− 0.343514i	− 0.0200342i
$295$	27.0567	1.57530
$296$	−1.85124	−0.107601
$297$	− 17.4143i	− 1.01048i
$298$	−6.02792	−0.349188
$299$	0	0
$300$	2.63069	0.151883
$301$	10.5877i	0.610263i
$302$	0.752193	0.0432839
$303$	8.44168	0.484962
$304$	− 13.6151i	− 0.780877i
$305$	26.5249i	1.51881i
$306$	− 1.49788i	− 0.0856278i
$307$	− 3.92435i	− 0.223975i	−0.993710	−	0.111987i	$-0.964278\pi$
$307$	− 3.92435i	− 0.223975i	0.993710	−	0.111987i	$-0.0357216\pi$
$308$	−6.28630	−0.358195
$309$	10.2997	0.585928
$310$	− 4.92933i	− 0.279967i
$311$	−22.5407	−1.27817	−0.639084	−	0.769137i	$-0.720686\pi$
$311$	−22.5407	−1.27817	−0.639084	+	0.769137i	$0.720686\pi$
$312$	0	0
$313$	33.2674	1.88038	0.940191	−	0.340647i	$-0.110646\pi$
$313$	33.2674	1.88038	0.940191	+	0.340647i	$0.110646\pi$
$314$	1.95993i	0.110605i
$315$	3.46064	0.194985
$316$	−16.5177	−0.929191
$317$	− 16.5373i	− 0.928827i	−0.885618	−	0.464413i	$-0.846265\pi$
$317$	− 16.5373i	− 0.928827i	0.885618	−	0.464413i	$-0.153735\pi$
$318$	− 3.90167i	− 0.218795i
$319$	− 22.6382i	− 1.26749i
$320$	11.1376i	0.622609i
$321$	10.3077	0.575322
$322$	−0.0779628	−0.00434470
$323$	− 10.6667i	− 0.593514i
$324$	−0.828384	−0.0460214
$325$	0	0
$326$	4.61259	0.255468
$327$	− 21.9335i	− 1.21293i
$328$	−1.66548	−0.0919605
$329$	−2.89468	−0.159589
$330$	− 2.19608i	− 0.120890i
$331$	− 10.3115i	− 0.566769i	−0.959006	−	0.283384i	$-0.908543\pi$
$331$	− 10.3115i	− 0.566769i	0.959006	−	0.283384i	$-0.0914572\pi$
$332$	16.9230i	0.928770i
$333$	− 2.71844i	− 0.148969i
$334$	3.64082	0.199217
$335$	−5.46654	−0.298669
$336$	3.76980i	0.205660i
$337$	27.0447	1.47322	0.736610	−	0.676318i	$-0.236425\pi$
$337$	27.0447	1.47322	0.736610	+	0.676318i	$0.236425\pi$
$338$	0	0
$339$	−5.12660	−0.278439
$340$	9.87824i	0.535723i
$341$	−26.9706	−1.46054
$342$	−2.21895	−0.119987
$343$	− 1.00000i	− 0.0539949i
$344$	12.8958i	0.695293i
$345$	0.531985i	0.0286411i
$346$	4.50792i	0.242347i
$347$	−28.3496	−1.52189	−0.760943	−	0.648818i	$-0.775264\pi$
$347$	−28.3496	−1.52189	−0.760943	+	0.648818i	$0.775264\pi$
$348$	−14.3479	−0.769131
$349$	18.6769i	0.999751i	0.866097	+	0.499876i	$0.166621\pi$
$349$	18.6769i	0.999751i	−0.866097	+	0.499876i	$0.833379\pi$
$350$	−0.392072	−0.0209571
$351$	0	0
$352$	−11.5806	−0.617249
$353$	− 18.8456i	− 1.00305i	−0.865142	−	0.501526i	$-0.832772\pi$
$353$	− 18.8456i	− 1.00305i	0.865142	−	0.501526i	$-0.167228\pi$
$354$	4.80358	0.255308
$355$	17.7467	0.941895
$356$	14.2742i	0.756533i
$357$	2.95346i	0.156314i
$358$	1.68844i	0.0892368i
$359$	− 3.46550i	− 0.182902i	−0.995810	−	0.0914509i	$-0.970850\pi$
$359$	− 3.46550i	− 0.182902i	0.995810	−	0.0914509i	$-0.0291505\pi$
$360$	4.21506	0.222153
$361$	3.19826	0.168330
$362$	− 2.10721i	− 0.110752i
$363$	0.0914840	0.00480167
$364$	0	0
$365$	16.3885	0.857813
$366$	4.70917i	0.246152i
$367$	31.0976	1.62328	0.811640	−	0.584158i	$-0.198575\pi$
$367$	31.0976	1.62328	0.811640	+	0.584158i	$0.198575\pi$
$368$	0.855581	0.0446002
$369$	− 2.44565i	− 0.127315i
$370$	− 0.917834i	− 0.0477159i
$371$	− 11.3581i	− 0.589683i
$372$	17.0938i	0.886272i
$373$	−10.8655	−0.562597	−0.281298	−	0.959620i	$-0.590765\pi$
$373$	−10.8655	−0.562597	−0.281298	+	0.959620i	$0.590765\pi$
$374$	−2.76708	−0.143083
$375$	13.3235i	0.688024i
$376$	−3.52572	−0.181825
$377$	0	0
$378$	1.64494	0.0846065
$379$	1.88019i	0.0965786i	0.998833	+	0.0482893i	$0.0153769\pi$
$379$	1.88019i	0.0965786i	−0.998833	+	0.0482893i	$0.984623\pi$
$380$	14.6336	0.750690
$381$	−8.32712	−0.426611
$382$	− 4.08595i	− 0.209055i
$383$	− 35.2053i	− 1.79891i	−0.437016	−	0.899454i	$-0.643965\pi$
$383$	− 35.2053i	− 1.79891i	0.437016	−	0.899454i	$-0.356035\pi$
$384$	9.69284i	0.494636i
$385$	− 6.39298i	− 0.325816i
$386$	−2.51630	−0.128076
$387$	−18.9366	−0.962604
$388$	− 16.5538i	− 0.840392i
$389$	14.7871	0.749738	0.374869	−	0.927078i	$-0.377688\pi$
$389$	14.7871	0.749738	0.374869	+	0.927078i	$0.377688\pi$
$390$	0	0
$391$	0.670307	0.0338989
$392$	− 1.21800i	− 0.0615182i
$393$	22.6052	1.14028
$394$	4.66994	0.235268
$395$	− 16.7980i	− 0.845197i
$396$	− 11.2434i	− 0.565003i
$397$	29.0277i	1.45686i	0.685122	+	0.728428i	$0.259749\pi$
$397$	29.0277i	1.45686i	−0.685122	+	0.728428i	$0.740251\pi$
$398$	− 3.20780i	− 0.160792i
$399$	4.37526	0.219037
$400$	4.30268	0.215134
$401$	20.5046i	1.02395i	0.859001	+	0.511974i	$0.171086\pi$
$401$	20.5046i	1.02395i	−0.859001	+	0.511974i	$0.828914\pi$
$402$	−0.970518	−0.0484051
$403$	0	0
$404$	14.5923	0.725993
$405$	− 0.842442i	− 0.0418613i
$406$	2.13838	0.106126
$407$	−5.02188	−0.248925
$408$	3.59731i	0.178093i
$409$	2.31717i	0.114576i	0.998358	+	0.0572882i	$0.0182454\pi$
$409$	2.31717i	0.114576i	−0.998358	+	0.0572882i	$0.981755\pi$
$410$	− 0.825732i	− 0.0407800i
$411$	− 11.5951i	− 0.571945i
$412$	17.8040	0.877141
$413$	13.9836	0.688090
$414$	− 0.139441i	− 0.00685314i
$415$	−17.2102	−0.844814
$416$	0	0
$417$	−5.97221	−0.292460
$418$	4.09916i	0.200497i
$419$	−10.1990	−0.498254	−0.249127	−	0.968471i	$-0.580144\pi$
$419$	−10.1990	−0.498254	−0.249127	+	0.968471i	$0.580144\pi$
$420$	−4.05183	−0.197709
$421$	8.80131i	0.428950i	0.976730	+	0.214475i	$0.0688040\pi$
$421$	8.80131i	0.428950i	−0.976730	+	0.214475i	$0.931196\pi$
$422$	− 2.24477i	− 0.109274i
$423$	− 5.17731i	− 0.251729i
$424$	− 13.8341i	− 0.671845i
$425$	3.37095	0.163515
$426$	3.15070	0.152652
$427$	13.7088i	0.663415i
$428$	17.8179	0.861263
$429$	0	0
$430$	−6.39364	−0.308328
$431$	15.7687i	0.759552i	0.925078	+	0.379776i	$0.123999\pi$
$431$	15.7687i	0.759552i	−0.925078	+	0.379776i	$0.876001\pi$
$432$	−18.0519	−0.868523
$433$	−20.9710	−1.00780	−0.503901	−	0.863761i	$-0.668102\pi$
$433$	−20.9710	−1.00780	−0.503901	+	0.863761i	$0.668102\pi$
$434$	− 2.54762i	− 0.122290i
$435$	− 14.5914i	− 0.699605i
$436$	− 37.9142i	− 1.81576i
$437$	− 0.992994i	− 0.0475013i
$438$	2.90958	0.139025
$439$	−22.2439	−1.06164	−0.530822	−	0.847483i	$-0.678117\pi$
$439$	−22.2439	−1.06164	−0.530822	+	0.847483i	$0.678117\pi$
$440$	− 7.78664i	− 0.371213i
$441$	1.78856	0.0851693
$442$	0	0
$443$	−22.6025	−1.07388	−0.536939	−	0.843621i	$-0.680419\pi$
$443$	−22.6025	−1.07388	−0.536939	+	0.843621i	$0.680419\pi$
$444$	3.18284i	0.151051i
$445$	−14.5165	−0.688147
$446$	9.27185	0.439035
$447$	21.2582i	1.00548i
$448$	5.75621i	0.271955i
$449$	33.6781i	1.58937i	0.607022	+	0.794685i	$0.292364\pi$
$449$	33.6781i	1.58937i	−0.607022	+	0.794685i	$0.707636\pi$
$450$	− 0.701243i	− 0.0330569i
$451$	−4.51794	−0.212742
$452$	−8.86185	−0.416826
$453$	− 2.65270i	− 0.124635i
$454$	−4.00581	−0.188002
$455$	0	0
$456$	5.32906	0.249556
$457$	29.9328i	1.40020i	0.714046	+	0.700099i	$0.246861\pi$
$457$	29.9328i	1.40020i	−0.714046	+	0.700099i	$0.753139\pi$
$458$	4.05397	0.189430
$459$	−14.1428	−0.660130
$460$	0.919590i	0.0428761i
$461$	11.8887i	0.553714i	0.960911	+	0.276857i	$0.0892928\pi$
$461$	11.8887i	0.553714i	−0.960911	+	0.276857i	$0.910707\pi$
$462$	− 1.13500i	− 0.0528048i
$463$	− 17.1606i	− 0.797522i	−0.917055	−	0.398761i	$-0.869440\pi$
$463$	− 17.1606i	− 0.797522i	0.917055	−	0.398761i	$-0.130560\pi$
$464$	−23.4671	−1.08943
$465$	−17.3839	−0.806158
$466$	− 6.46181i	− 0.299338i
$467$	5.83855	0.270176	0.135088	−	0.990834i	$-0.456868\pi$
$467$	5.83855	0.270176	0.135088	+	0.990834i	$0.456868\pi$
$468$	0	0
$469$	−2.82526	−0.130459
$470$	− 1.74803i	− 0.0806306i
$471$	6.91191	0.318484
$472$	17.0321	0.783964
$473$	34.9824i	1.60849i
$474$	− 2.98227i	− 0.136980i
$475$	− 4.99373i	− 0.229128i
$476$	5.10535i	0.234003i
$477$	20.3146	0.930141
$478$	−4.45715	−0.203865
$479$	15.9848i	0.730364i	0.930936	+	0.365182i	$0.118993\pi$
$479$	15.9848i	0.730364i	−0.930936	+	0.365182i	$0.881007\pi$
$480$	−7.46428	−0.340696
$481$	0	0
$482$	4.00527	0.182435
$483$	0.274945i	0.0125104i
$484$	0.158139	0.00718815
$485$	16.8347	0.764425
$486$	4.78525i	0.217063i
$487$	16.9216i	0.766790i	0.923585	+	0.383395i	$0.125245\pi$
$487$	16.9216i	0.766790i	−0.923585	+	0.383395i	$0.874755\pi$
$488$	16.6973i	0.755851i
$489$	− 16.2668i	− 0.735612i
$490$	0.603875	0.0272803
$491$	6.03131	0.272189	0.136095	−	0.990696i	$-0.456545\pi$
$491$	6.03131	0.272189	0.136095	+	0.990696i	$0.456545\pi$
$492$	2.86345i	0.129094i
$493$	−18.3853	−0.828034
$494$	0	0
$495$	11.4342	0.513929
$496$	27.9581i	1.25536i
$497$	9.17197	0.411419
$498$	−3.05546	−0.136918
$499$	− 20.3622i	− 0.911537i	−0.890098	−	0.455768i	$-0.849365\pi$
$499$	− 20.3622i	− 0.911537i	0.890098	−	0.455768i	$-0.150635\pi$
$500$	23.0310i	1.02998i
$501$	− 12.8398i	− 0.573639i
$502$	4.74269i	0.211677i
$503$	−14.7571	−0.657986	−0.328993	−	0.944332i	$-0.606709\pi$
$503$	−14.7571	−0.657986	−0.328993	+	0.944332i	$0.606709\pi$
$504$	2.17846	0.0970363
$505$	14.8399i	0.660367i
$506$	−0.257595	−0.0114515
$507$	0	0
$508$	−14.3943	−0.638642
$509$	− 8.19735i	− 0.363341i	−0.983359	−	0.181670i	$-0.941850\pi$
$509$	− 8.19735i	− 0.363341i	0.983359	−	0.181670i	$-0.0581504\pi$
$510$	−1.78352	−0.0789757
$511$	8.47003	0.374692
$512$	20.3481i	0.899266i
$513$	20.9512i	0.925018i
$514$	9.49351i	0.418741i
$515$	18.1061i	0.797852i
$516$	22.1717	0.976053
$517$	−9.56424	−0.420635
$518$	− 0.474362i	− 0.0208423i
$519$	15.8977	0.697831
$520$	0	0
$521$	−36.4358	−1.59628	−0.798141	−	0.602471i	$-0.794183\pi$
$521$	−36.4358	−1.59628	−0.798141	+	0.602471i	$0.794183\pi$
$522$	3.82462i	0.167399i
$523$	3.12730	0.136747	0.0683737	−	0.997660i	$-0.478219\pi$
$523$	3.12730	0.136747	0.0683737	+	0.997660i	$0.478219\pi$
$524$	39.0754	1.70702
$525$	1.38269i	0.0603454i
$526$	1.52177i	0.0663523i
$527$	21.9038i	0.954147i
$528$	12.4557i	0.542064i
$529$	−22.9376	−0.997287
$530$	6.85888	0.297931
$531$	25.0105i	1.08536i
$532$	7.56308	0.327901
$533$	0	0
$534$	−2.57722	−0.111527
$535$	18.1203i	0.783409i
$536$	−3.44117	−0.148636
$537$	5.95448	0.256955
$538$	− 2.15294i	− 0.0928196i
$539$	− 3.30407i	− 0.142316i
$540$	− 19.4024i	− 0.834948i
$541$	40.2086i	1.72870i	0.502889	+	0.864351i	$0.332270\pi$
$541$	40.2086i	1.72870i	−0.502889	+	0.864351i	$0.667730\pi$
$542$	−0.670845	−0.0288153
$543$	−7.43132	−0.318908
$544$	9.40507i	0.403239i
$545$	38.5576	1.65163
$546$	0	0
$547$	−32.0924	−1.37217	−0.686086	−	0.727521i	$-0.740673\pi$
$547$	−32.0924	−1.37217	−0.686086	+	0.727521i	$0.740673\pi$
$548$	− 20.0433i	− 0.856208i
$549$	−24.5190	−1.04644
$550$	−1.29543	−0.0552375
$551$	27.2361i	1.16030i
$552$	0.334882i	0.0142535i
$553$	− 8.68165i	− 0.369181i
$554$	− 8.70460i	− 0.369823i
$555$	−3.23685	−0.137397
$556$	−10.3236	−0.437817
$557$	− 24.3334i	− 1.03104i	−0.856877	−	0.515520i	$-0.827599\pi$
$557$	− 24.3334i	− 1.03104i	0.856877	−	0.515520i	$-0.172401\pi$
$558$	4.55656	0.192894
$559$	0	0
$560$	−6.62706	−0.280044
$561$	9.75844i	0.412002i
$562$	−0.551936	−0.0232820
$563$	25.0355	1.05512	0.527559	−	0.849518i	$-0.323107\pi$
$563$	25.0355	1.05512	0.527559	+	0.849518i	$0.323107\pi$
$564$	6.06176i	0.255246i
$565$	− 9.01223i	− 0.379147i
$566$	− 5.83511i	− 0.245268i
$567$	− 0.435397i	− 0.0182850i
$568$	11.1714	0.468744
$569$	21.6212	0.906407	0.453203	−	0.891407i	$-0.350281\pi$
$569$	21.6212	0.906407	0.453203	+	0.891407i	$0.350281\pi$
$570$	2.64211i	0.110666i
$571$	−16.6372	−0.696246	−0.348123	−	0.937449i	$-0.613181\pi$
$571$	−16.6372	−0.696246	−0.348123	+	0.937449i	$0.613181\pi$
$572$	0	0
$573$	−14.4096	−0.601969
$574$	− 0.426761i	− 0.0178127i
$575$	0.313810	0.0130868
$576$	−10.2953	−0.428971
$577$	0.909053i	0.0378444i	0.999821	+	0.0189222i	$0.00602348\pi$
$577$	0.909053i	0.0378444i	−0.999821	+	0.0189222i	$0.993977\pi$
$578$	− 3.05844i	− 0.127214i
$579$	8.87401i	0.368791i
$580$	− 25.2227i	− 1.04732i
$581$	−8.89470	−0.369014
$582$	2.98880	0.123890
$583$	− 37.5280i	− 1.55425i
$584$	10.3165	0.426899
$585$	0	0
$586$	3.03116	0.125216
$587$	− 41.1599i	− 1.69885i	−0.527710	−	0.849424i	$-0.676949\pi$
$587$	− 41.1599i	− 1.69885i	0.527710	−	0.849424i	$-0.323051\pi$
$588$	−2.09410	−0.0863593
$589$	32.4484	1.33701
$590$	8.44438i	0.347650i
$591$	− 16.4691i	− 0.677447i
$592$	5.20575i	0.213955i
$593$	7.37079i	0.302682i	0.988482	+	0.151341i	$0.0483591\pi$
$593$	7.37079i	0.302682i	−0.988482	+	0.151341i	$0.951641\pi$
$594$	5.43499	0.223000
$595$	−5.19199	−0.212851
$596$	36.7469i	1.50521i
$597$	−11.3127	−0.462997
$598$	0	0
$599$	−14.4698	−0.591220	−0.295610	−	0.955309i	$-0.595523\pi$
$599$	−14.4698	−0.591220	−0.295610	+	0.955309i	$0.595523\pi$
$600$	1.68411i	0.0687536i
$601$	4.85844	0.198180	0.0990900	−	0.995078i	$-0.468407\pi$
$601$	4.85844	0.198180	0.0990900	+	0.995078i	$0.468407\pi$
$602$	−3.30441	−0.134678
$603$	− 5.05314i	− 0.205780i
$604$	− 4.58545i	− 0.186579i
$605$	0.160823i	0.00653838i
$606$	2.63465i	0.107025i
$607$	11.4226	0.463628	0.231814	−	0.972760i	$-0.425534\pi$
$607$	11.4226	0.463628	0.231814	+	0.972760i	$0.425534\pi$
$608$	13.9327	0.565045
$609$	− 7.54126i	− 0.305587i
$610$	−8.27841	−0.335183
$611$	0	0
$612$	−9.13121	−0.369107
$613$	31.2929i	1.26391i	0.775005	+	0.631955i	$0.217747\pi$
$613$	31.2929i	1.26391i	−0.775005	+	0.631955i	$0.782253\pi$
$614$	1.22479	0.0494285
$615$	−2.91204	−0.117425
$616$	− 4.02435i	− 0.162146i
$617$	− 20.5067i	− 0.825567i	−0.910829	−	0.412784i	$-0.864557\pi$
$617$	− 20.5067i	− 0.825567i	0.910829	−	0.412784i	$-0.135443\pi$
$618$	3.21453i	0.129307i
$619$	15.1362i	0.608373i	0.952612	+	0.304187i	$0.0983846\pi$
$619$	15.1362i	0.608373i	−0.952612	+	0.304187i	$0.901615\pi$
$620$	−30.0498	−1.20683
$621$	−1.31659	−0.0528329
$622$	− 7.03495i	− 0.282076i
$623$	−7.50252	−0.300582
$624$	0	0
$625$	−17.1407	−0.685626
$626$	10.3827i	0.414977i
$627$	14.4562	0.577324
$628$	11.9479	0.476774
$629$	4.07846i	0.162619i
$630$	1.08007i	0.0430308i
$631$	− 14.0749i	− 0.560313i	−0.959954	−	0.280157i	$-0.909614\pi$
$631$	− 14.0749i	− 0.560313i	0.959954	−	0.280157i	$-0.0903864\pi$
$632$	− 10.5742i	− 0.420621i
$633$	−7.91643	−0.314650
$634$	5.16129	0.204981
$635$	− 14.6385i	− 0.580912i
$636$	−23.7850	−0.943137
$637$	0	0
$638$	7.06537	0.279721
$639$	16.4046i	0.648955i
$640$	−17.0394	−0.673540
$641$	−5.65089	−0.223197	−0.111598	−	0.993753i	$-0.535597\pi$
$641$	−5.65089	−0.223197	−0.111598	+	0.993753i	$0.535597\pi$
$642$	3.21704i	0.126966i
$643$	− 13.5494i	− 0.534335i	−0.963650	−	0.267167i	$-0.913912\pi$
$643$	− 13.5494i	− 0.534335i	0.963650	−	0.267167i	$-0.0860877\pi$
$644$	0.475270i	0.0187283i
$645$	22.5479i	0.887823i
$646$	3.32909	0.130981
$647$	29.6278	1.16479	0.582395	−	0.812906i	$-0.302116\pi$
$647$	29.6278	1.16479	0.582395	+	0.812906i	$0.302116\pi$
$648$	− 0.530313i	− 0.0208327i
$649$	46.2029	1.81362
$650$	0	0
$651$	−8.98447	−0.352129
$652$	− 28.1189i	− 1.10122i
$653$	−16.6538	−0.651714	−0.325857	−	0.945419i	$-0.605653\pi$
$653$	−16.6538	−0.651714	−0.325857	+	0.945419i	$0.605653\pi$
$654$	6.84544	0.267678
$655$	39.7385i	1.55271i
$656$	4.68337i	0.182855i
$657$	15.1491i	0.591024i
$658$	− 0.903430i	− 0.0352194i
$659$	−14.5002	−0.564850	−0.282425	−	0.959289i	$-0.591139\pi$
$659$	−14.5002	−0.564850	−0.282425	+	0.959289i	$0.591139\pi$
$660$	−13.3875	−0.521110
$661$	32.7213i	1.27271i	0.771396	+	0.636355i	$0.219559\pi$
$661$	32.7213i	1.27271i	−0.771396	+	0.636355i	$0.780441\pi$
$662$	3.21820	0.125079
$663$	0	0
$664$	−10.8337	−0.420430
$665$	7.69142i	0.298260i
$666$	0.848423	0.0328757
$667$	−1.71154	−0.0662710
$668$	− 22.1948i	− 0.858744i
$669$	− 32.6983i	− 1.26419i
$670$	− 1.70611i	− 0.0659127i
$671$	45.2948i	1.74859i
$672$	−3.85775	−0.148816
$673$	14.6250	0.563751	0.281875	−	0.959451i	$-0.409044\pi$
$673$	14.6250	0.563751	0.281875	+	0.959451i	$0.409044\pi$
$674$	8.44065i	0.325122i
$675$	−6.62108	−0.254845
$676$	0	0
$677$	−41.1507	−1.58155	−0.790774	−	0.612108i	$-0.790322\pi$
$677$	−41.1507	−1.58155	−0.790774	+	0.612108i	$0.790322\pi$
$678$	− 1.60001i	− 0.0614481i
$679$	8.70065	0.333900
$680$	−6.32383	−0.242508
$681$	14.1270i	0.541346i
$682$	− 8.41751i	− 0.322323i
$683$	− 31.0900i	− 1.18963i	−0.803864	−	0.594813i	$-0.797226\pi$
$683$	− 31.0900i	− 1.18963i	0.803864	−	0.594813i	$-0.202774\pi$
$684$	13.5270i	0.517217i
$685$	20.3834	0.778811
$686$	0.312100	0.0119160
$687$	− 14.2968i	− 0.545457i
$688$	36.2633	1.38253
$689$	0	0
$690$	−0.166032	−0.00632075
$691$	10.4806i	0.398700i	0.979928	+	0.199350i	$0.0638831\pi$
$691$	10.4806i	0.398700i	−0.979928	+	0.199350i	$0.936117\pi$
$692$	27.4808	1.04466
$693$	5.90952	0.224484
$694$	− 8.84790i	− 0.335862i
$695$	− 10.4987i	− 0.398240i
$696$	− 9.18524i	− 0.348166i
$697$	3.66920i	0.138981i
$698$	−5.82905	−0.220633
$699$	−22.7883	−0.861934
$700$	2.39011i	0.0903378i
$701$	−30.9900	−1.17047	−0.585237	−	0.810862i	$-0.698999\pi$
$701$	−30.9900	−1.17047	−0.585237	+	0.810862i	$0.698999\pi$
$702$	0	0
$703$	6.04184	0.227872
$704$	19.0189i	0.716802i
$705$	−6.16463	−0.232173
$706$	5.88172	0.221362
$707$	7.66968i	0.288448i
$708$	− 29.2832i	− 1.10053i
$709$	− 9.26922i	− 0.348113i	−0.984736	−	0.174056i	$-0.944312\pi$
$709$	− 9.26922i	− 0.348113i	0.984736	−	0.174056i	$-0.0556875\pi$
$710$	5.53873i	0.207865i
$711$	15.5276	0.582331
$712$	−9.13805	−0.342463
$713$	2.03908i	0.0763643i
$714$	−0.921774	−0.0344965
$715$	0	0
$716$	10.2929	0.384664
$717$	15.7187i	0.587024i
$718$	1.08158	0.0403642
$719$	−12.6772	−0.472779	−0.236389	−	0.971658i	$-0.575964\pi$
$719$	−12.6772	−0.472779	−0.236389	+	0.971658i	$0.575964\pi$
$720$	− 11.8529i	− 0.441730i
$721$	9.35776i	0.348501i
$722$	0.998177i	0.0371483i
$723$	− 14.1250i	− 0.525316i
$724$	−12.8458	−0.477409
$725$	−8.60726	−0.319665
$726$	0.0285521i	0.00105967i
$727$	20.4565	0.758691	0.379345	−	0.925255i	$-0.376149\pi$
$727$	20.4565	0.758691	0.379345	+	0.925255i	$0.376149\pi$
$728$	0	0
$729$	18.1819	0.673405
$730$	5.11484i	0.189309i
$731$	28.4106	1.05080
$732$	28.7076	1.06106
$733$	1.20844i	0.0446347i	0.999751	+	0.0223174i	$0.00710443\pi$
$733$	1.20844i	0.0446347i	−0.999751	+	0.0223174i	$0.992896\pi$
$734$	9.70554i	0.358238i
$735$	− 2.12964i	− 0.0785529i
$736$	0.875541i	0.0322729i
$737$	−9.33487	−0.343854
$738$	0.763286	0.0280970
$739$	27.7387i	1.02038i	0.860061	+	0.510192i	$0.170426\pi$
$739$	27.7387i	1.02038i	−0.860061	+	0.510192i	$0.829574\pi$
$740$	−5.59521	−0.205684
$741$	0	0
$742$	3.54486	0.130136
$743$	0.529188i	0.0194140i	0.999953	+	0.00970702i	$0.00308989\pi$
$743$	0.529188i	0.0194140i	−0.999953	+	0.00970702i	$0.996910\pi$
$744$	−10.9431	−0.401192
$745$	−37.3704	−1.36915
$746$	− 3.39113i	− 0.124158i
$747$	− 15.9087i	− 0.582068i
$748$	16.8684i	0.616771i
$749$	9.36508i	0.342193i
$750$	−4.15827	−0.151838
$751$	11.7927	0.430323	0.215161	−	0.976578i	$-0.430972\pi$
$751$	11.7927	0.430323	0.215161	+	0.976578i	$0.430972\pi$
$752$	9.91444i	0.361542i
$753$	16.7257	0.609517
$754$	0	0
$755$	4.66326	0.169714
$756$	− 10.0277i	− 0.364705i
$757$	−30.2288	−1.09868	−0.549342	−	0.835598i	$-0.685121\pi$
$757$	−30.2288	−1.09868	−0.549342	+	0.835598i	$0.685121\pi$
$758$	−0.586805	−0.0213137
$759$	0.908437i	0.0329742i
$760$	9.36814i	0.339818i
$761$	16.9978i	0.616170i	0.951359	+	0.308085i	$0.0996882\pi$
$761$	16.9978i	0.616170i	−0.951359	+	0.308085i	$0.900312\pi$
$762$	− 2.59889i	− 0.0941479i
$763$	19.9277	0.721430
$764$	−24.9084	−0.901154
$765$	− 9.28616i	− 0.335742i
$766$	10.9876	0.396997
$767$	0	0
$768$	9.64607	0.348073
$769$	− 2.13537i	− 0.0770035i	−0.999259	−	0.0385017i	$-0.987741\pi$
$769$	− 2.13537i	− 0.0770035i	0.999259	−	0.0385017i	$-0.0122585\pi$
$770$	1.99525	0.0719037
$771$	33.4800	1.20575
$772$	15.3396i	0.552085i
$773$	41.9443i	1.50863i	0.656512	+	0.754316i	$0.272031\pi$
$773$	41.9443i	1.50863i	−0.656512	+	0.754316i	$0.727969\pi$
$774$	− 5.91012i	− 0.212435i
$775$	10.2545i	0.368352i
$776$	10.5974	0.380424
$777$	−1.67289	−0.0600147
$778$	4.61506i	0.165458i
$779$	5.43556	0.194749
$780$	0	0
$781$	30.3048	1.08439
$782$	0.209203i	0.00748107i
$783$	36.1117	1.29053
$784$	−3.42505	−0.122323
$785$	12.1507i	0.433676i
$786$	7.05508i	0.251646i
$787$	5.31182i	0.189346i	0.995508	+	0.0946729i	$0.0301805\pi$
$787$	5.31182i	0.189346i	−0.995508	+	0.0946729i	$0.969819\pi$
$788$	− 28.4684i	− 1.01415i
$789$	5.36670	0.191060
$790$	5.24264	0.186525
$791$	− 4.65777i	− 0.165611i
$792$	7.19778	0.255762
$793$	0	0
$794$	−9.05953	−0.321511
$795$	− 24.1886i	− 0.857882i
$796$	−19.5551	−0.693112
$797$	−1.28506	−0.0455191	−0.0227596	−	0.999741i	$-0.507245\pi$
$797$	−1.28506	−0.0455191	−0.0227596	+	0.999741i	$0.507245\pi$
$798$	1.36552i	0.0483388i
$799$	7.76749i	0.274794i
$800$	4.40306i	0.155672i
$801$	− 13.4187i	− 0.474126i
$802$	−6.39947	−0.225973
$803$	27.9856	0.987590
$804$	5.91639i	0.208655i
$805$	−0.483335	−0.0170353
$806$	0	0
$807$	−7.59258	−0.267271
$808$	9.34166i	0.328638i
$809$	−7.67690	−0.269905	−0.134953	−	0.990852i	$-0.543088\pi$
$809$	−7.67690	−0.269905	−0.134953	+	0.990852i	$0.543088\pi$
$810$	0.262926	0.00923827
$811$	− 9.69738i	− 0.340521i	−0.985399	−	0.170261i	$-0.945539\pi$
$811$	− 9.69738i	− 0.340521i	0.985399	−	0.170261i	$-0.0544610\pi$
$812$	− 13.0358i	− 0.457467i
$813$	2.36581i	0.0829727i
$814$	− 1.56733i	− 0.0549348i
$815$	28.5960	1.00167
$816$	10.1158	0.354122
$817$	− 42.0875i	− 1.47245i
$818$	−0.723187	−0.0252856
$819$	0	0
$820$	−5.03375	−0.175786
$821$	28.7275i	1.00260i	0.865275	+	0.501298i	$0.167144\pi$
$821$	28.7275i	1.00260i	−0.865275	+	0.501298i	$0.832856\pi$
$822$	3.61883	0.126221
$823$	2.15032	0.0749553	0.0374777	−	0.999297i	$-0.488068\pi$
$823$	2.15032	0.0749553	0.0374777	+	0.999297i	$0.488068\pi$
$824$	11.3977i	0.397059i
$825$	4.56850i	0.159055i
$826$	4.36429i	0.151853i
$827$	− 38.5500i	− 1.34051i	−0.742129	−	0.670257i	$-0.766184\pi$
$827$	− 38.5500i	− 1.34051i	0.742129	−	0.670257i	$-0.233816\pi$
$828$	−0.850047	−0.0295412
$829$	−8.11579	−0.281873	−0.140936	−	0.990019i	$-0.545011\pi$
$829$	−8.11579	−0.281873	−0.140936	+	0.990019i	$0.545011\pi$
$830$	− 5.37129i	− 0.186440i
$831$	−30.6978	−1.06489
$832$	0	0
$833$	−2.68336	−0.0929731
$834$	− 1.86393i	− 0.0645425i
$835$	22.5715	0.781118
$836$	24.9889	0.864261
$837$	− 43.0226i	− 1.48708i
$838$	− 3.18311i	− 0.109959i
$839$	19.0949i	0.659228i	0.944116	+	0.329614i	$0.106919\pi$
$839$	19.0949i	0.659228i	−0.944116	+	0.329614i	$0.893081\pi$
$840$	− 2.59389i	− 0.0894979i
$841$	17.9445	0.618774
$842$	−2.74689	−0.0946640
$843$	1.94647i	0.0670399i
$844$	−13.6843	−0.471034
$845$	0	0
$846$	1.61584	0.0555536
$847$	0.0831177i	0.00285596i
$848$	−38.9021	−1.33590
$849$	−20.5782	−0.706242
$850$	1.05207i	0.0360858i
$851$	0.379674i	0.0130151i
$852$	− 19.2070i	− 0.658022i
$853$	49.0402i	1.67910i	0.543280	+	0.839551i	$0.317182\pi$
$853$	49.0402i	1.67910i	−0.543280	+	0.839551i	$0.682818\pi$
$854$	−4.27851	−0.146408
$855$	−13.7565	−0.470464
$856$	11.4067i	0.389871i
$857$	50.1325	1.71249	0.856247	−	0.516566i	$-0.172790\pi$
$857$	50.1325	1.71249	0.856247	+	0.516566i	$0.172790\pi$
$858$	0	0
$859$	34.5583	1.17912	0.589558	−	0.807726i	$-0.299302\pi$
$859$	34.5583	1.17912	0.589558	+	0.807726i	$0.299302\pi$
$860$	38.9763i	1.32908i
$861$	−1.50502	−0.0512910
$862$	−4.92141	−0.167624
$863$	− 8.86279i	− 0.301693i	−0.988557	−	0.150846i	$-0.951800\pi$
$863$	− 8.86279i	− 0.301693i	0.988557	−	0.150846i	$-0.0481999\pi$
$864$	− 18.4730i	− 0.628466i
$865$	27.9471i	0.950230i
$866$	− 6.54504i	− 0.222410i
$867$	−10.7859	−0.366310
$868$	−15.5306	−0.527141
$869$	− 28.6848i	− 0.973065i
$870$	4.55398	0.154394
$871$	0	0
$872$	24.2719	0.821949
$873$	15.5616i	0.526681i
$874$	0.309913	0.0104830
$875$	−12.1051	−0.409226
$876$	− 17.7371i	− 0.599281i
$877$	10.2278i	0.345367i	0.984977	+	0.172683i	$0.0552438\pi$
$877$	10.2278i	0.345367i	−0.984977	+	0.172683i	$0.944756\pi$
$878$	− 6.94232i	− 0.234292i
$879$	− 10.6898i	− 0.360557i
$880$	−21.8963	−0.738123
$881$	−28.8841	−0.973131	−0.486565	−	0.873644i	$-0.661750\pi$
$881$	−28.8841	−0.973131	−0.486565	+	0.873644i	$0.661750\pi$
$882$	0.558208i	0.0187958i
$883$	3.42325	0.115202	0.0576008	−	0.998340i	$-0.481655\pi$
$883$	3.42325	0.115202	0.0576008	+	0.998340i	$0.481655\pi$
$884$	0	0
$885$	29.7801	1.00105
$886$	− 7.05423i	− 0.236992i
$887$	6.79837	0.228267	0.114133	−	0.993465i	$-0.463591\pi$
$887$	6.79837	0.228267	0.114133	+	0.993465i	$0.463591\pi$
$888$	−2.03758	−0.0683768
$889$	− 7.56559i	− 0.253742i
$890$	− 4.53059i	− 0.151866i
$891$	− 1.43858i	− 0.0481944i
$892$	− 56.5222i	− 1.89250i
$893$	11.5068	0.385060
$894$	−6.63467	−0.221897
$895$	10.4676i	0.349892i
$896$	−8.80642	−0.294202
$897$	0	0
$898$	−10.5109	−0.350755
$899$	− 55.9285i	− 1.86532i
$900$	−4.27485	−0.142495
$901$	−30.4779	−1.01537
$902$	− 1.41005i	− 0.0469495i
$903$	11.6534i	0.387800i
$904$	− 5.67316i	− 0.188686i
$905$	− 13.0638i	− 0.434254i
$906$	0.827906	0.0275053
$907$	−50.9386	−1.69139	−0.845694	−	0.533668i	$-0.820813\pi$
$907$	−50.9386	−1.69139	−0.845694	+	0.533668i	$0.820813\pi$
$908$	24.4199i	0.810402i
$909$	−13.7177	−0.454986
$910$	0	0
$911$	−28.4847	−0.943742	−0.471871	−	0.881668i	$-0.656421\pi$
$911$	−28.4847	−0.943742	−0.471871	+	0.881668i	$0.656421\pi$
$912$	− 14.9855i	− 0.496219i
$913$	−29.3887	−0.972624
$914$	−9.34202	−0.309007
$915$	29.1948i	0.965149i
$916$	− 24.7134i	− 0.816555i
$917$	20.5380i	0.678223i
$918$	− 4.41397i	− 0.145683i
$919$	44.6522	1.47294	0.736470	−	0.676470i	$-0.236491\pi$
$919$	44.6522	1.47294	0.736470	+	0.676470i	$0.236491\pi$
$920$	−0.588701	−0.0194089
$921$	− 4.31936i	− 0.142328i
$922$	−3.71047	−0.122198
$923$	0	0
$924$	−6.91906	−0.227620
$925$	1.90937i	0.0627796i
$926$	5.35583	0.176003
$927$	−16.7369	−0.549712
$928$	− 24.0146i	− 0.788316i
$929$	35.6955i	1.17113i	0.810625	+	0.585565i	$0.199127\pi$
$929$	35.6955i	1.17113i	−0.810625	+	0.585565i	$0.800873\pi$
$930$	− 5.42550i	− 0.177909i
$931$	3.97514i	0.130280i
$932$	−39.3919	−1.29032
$933$	−24.8096	−0.812229
$934$	1.82221i	0.0596245i
$935$	−17.1547	−0.561018
$936$	0	0
$937$	−8.92893	−0.291695	−0.145848	−	0.989307i	$-0.546591\pi$
$937$	−8.92893	−0.291695	−0.145848	+	0.989307i	$0.546591\pi$
$938$	− 0.881764i	− 0.0287906i
$939$	36.6159	1.19492
$940$	−10.6562	−0.347566
$941$	10.5470i	0.343821i	0.985113	+	0.171911i	$0.0549940\pi$
$941$	10.5470i	0.343821i	−0.985113	+	0.171911i	$0.945006\pi$
$942$	2.15721i	0.0702856i
$943$	0.341575i	0.0111232i
$944$	− 47.8947i	− 1.55884i
$945$	10.1979	0.331737
$946$	−10.9180	−0.354975
$947$	9.84312i	0.319858i	0.987128	+	0.159929i	$0.0511266\pi$
$947$	9.84312i	0.319858i	−0.987128	+	0.159929i	$0.948873\pi$
$948$	−18.1803	−0.590467
$949$	0	0
$950$	1.55854	0.0505658
$951$	− 18.2019i	− 0.590236i
$952$	−3.26833	−0.105927
$953$	10.8735	0.352226	0.176113	−	0.984370i	$-0.443648\pi$
$953$	10.8735	0.352226	0.176113	+	0.984370i	$0.443648\pi$
$954$	6.34018i	0.205271i
$955$	− 25.3311i	− 0.819695i
$956$	27.1713i	0.878781i
$957$	− 24.9168i	− 0.805447i
$958$	−4.98885	−0.161183
$959$	10.5347	0.340184
$960$	12.2586i	0.395646i
$961$	−35.6318	−1.14941
$962$	0	0
$963$	−16.7500	−0.539761
$964$	− 24.4165i	− 0.786404i
$965$	−15.5999	−0.502179
$966$	−0.0858102	−0.00276090
$967$	− 33.7702i	− 1.08598i	−0.839741	−	0.542988i	$-0.817293\pi$
$967$	− 33.7702i	− 1.08598i	0.839741	−	0.542988i	$-0.182707\pi$
$968$	0.101237i	0.00325389i
$969$	− 11.7404i	− 0.377157i
$970$	5.25411i	0.168699i
$971$	44.4037	1.42498	0.712492	−	0.701680i	$-0.247567\pi$
$971$	44.4037	1.42498	0.712492	+	0.701680i	$0.247567\pi$
$972$	29.1714	0.935673
$973$	− 5.42605i	− 0.173951i
$974$	−5.28122	−0.169221
$975$	0	0
$976$	46.9533	1.50294
$977$	− 7.28864i	− 0.233184i	−0.993180	−	0.116592i	$-0.962803\pi$
$977$	− 7.28864i	− 0.233184i	0.993180	−	0.116592i	$-0.0371970\pi$
$978$	5.07688	0.162341
$979$	−24.7888	−0.792255
$980$	− 3.68129i	− 0.117595i
$981$	35.6417i	1.13795i
$982$	1.88237i	0.0600689i
$983$	7.27754i	0.232118i	0.993242	+	0.116059i	$0.0370261\pi$
$983$	7.27754i	0.232118i	−0.993242	+	0.116059i	$0.962974\pi$
$984$	−1.83312	−0.0584376
$985$	28.9515	0.922473
$986$	− 5.73806i	− 0.182737i
$987$	−3.18605	−0.101413
$988$	0	0
$989$	2.64481	0.0841001
$990$	3.56861i	0.113418i
$991$	−2.38406	−0.0757320	−0.0378660	−	0.999283i	$-0.512056\pi$
$991$	−2.38406	−0.0757320	−0.0378660	+	0.999283i	$0.512056\pi$
$992$	−28.6103	−0.908379
$993$	− 11.3494i	− 0.360161i
$994$	2.86257i	0.0907952i
$995$	− 19.8869i	− 0.630458i
$996$	18.6264i	0.590200i
$997$	−7.64905	−0.242248	−0.121124	−	0.992637i	$-0.538650\pi$
$997$	−7.64905	−0.242248	−0.121124	+	0.992637i	$0.538650\pi$
$998$	6.35503	0.201165
$999$	− 8.01074i	− 0.253449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.h.337.7		12
13.5	odd	4		1183.2.a.o.1.3	yes	6
13.8	odd	4		1183.2.a.n.1.4	✓	6
13.12	even	2	inner	1183.2.c.h.337.6		12
91.34	even	4		8281.2.a.cb.1.4		6
91.83	even	4		8281.2.a.cg.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.n.1.4	✓	6	13.8	odd	4
1183.2.a.o.1.3	yes	6	13.5	odd	4
1183.2.c.h.337.6		12	13.12	even	2	inner
1183.2.c.h.337.7		12	1.1	even	1	trivial
8281.2.a.cb.1.4		6	91.34	even	4
8281.2.a.cg.1.3		6	91.83	even	4

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.312100i q^{2} +1.10066 q^{3} +1.90259 q^{4} +1.93488i q^{5} +0.343514i q^{6} +1.00000i q^{7} +1.21800i q^{8} -1.78856 q^{9} +O(q^{10})\)	\(q+0.312100i q^{2} +1.10066 q^{3} +1.90259 q^{4} +1.93488i q^{5} +0.343514i q^{6} +1.00000i q^{7} +1.21800i q^{8} -1.78856 q^{9} -0.603875 q^{10} +3.30407i q^{11} +2.09410 q^{12} -0.312100 q^{14} +2.12964i q^{15} +3.42505 q^{16} +2.68336 q^{17} -0.558208i q^{18} -3.97514i q^{19} +3.68129i q^{20} +1.10066i q^{21} -1.03120 q^{22} +0.249801 q^{23} +1.34060i q^{24} +1.25624 q^{25} -5.27055 q^{27} +1.90259i q^{28} -6.85160 q^{29} -0.664659 q^{30} +8.16283i q^{31} +3.50495i q^{32} +3.63665i q^{33} +0.837477i q^{34} -1.93488 q^{35} -3.40290 q^{36} +1.51991i q^{37} +1.24064 q^{38} -2.35668 q^{40} +1.36739i q^{41} -0.343514 q^{42} +10.5877 q^{43} +6.28630i q^{44} -3.46064i q^{45} +0.0779628i q^{46} +2.89468i q^{47} +3.76980 q^{48} -1.00000 q^{49} +0.392072i q^{50} +2.95346 q^{51} -11.3581 q^{53} -1.64494i q^{54} -6.39298 q^{55} -1.21800 q^{56} -4.37526i q^{57} -2.13838i q^{58} -13.9836i q^{59} +4.05183i q^{60} +13.7088 q^{61} -2.54762 q^{62} -1.78856i q^{63} +5.75621 q^{64} -1.13500 q^{66} +2.82526i q^{67} +5.10535 q^{68} +0.274945 q^{69} -0.603875i q^{70} -9.17197i q^{71} -2.17846i q^{72} -8.47003i q^{73} -0.474362 q^{74} +1.38269 q^{75} -7.56308i q^{76} -3.30407 q^{77} -8.68165 q^{79} +6.62706i q^{80} -0.435397 q^{81} -0.426761 q^{82} +8.89470i q^{83} +2.09410i q^{84} +5.19199i q^{85} +3.30441i q^{86} -7.54126 q^{87} -4.02435 q^{88} +7.50252i q^{89} +1.08007 q^{90} +0.475270 q^{92} +8.98447i q^{93} -0.903430 q^{94} +7.69142 q^{95} +3.85775i q^{96} -8.70065i q^{97} -0.312100i q^{98} -5.90952i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{3} - 16 q^{4}+O(q^{10}) \) 12 * q - 8 * q^3 - 16 * q^4	\( 12 q - 8 q^{3} - 16 q^{4} + 28 q^{10} + 46 q^{12} - 4 q^{14} + 46 q^{17} - 8 q^{22} + 36 q^{23} + 20 q^{25} - 20 q^{27} - 30 q^{29} - 28 q^{30} - 4 q^{35} - 44 q^{36} + 22 q^{38} - 28 q^{40} + 16 q^{42} + 36 q^{43} - 22 q^{48} - 12 q^{49} - 28 q^{51} - 50 q^{53} + 6 q^{56} + 32 q^{61} + 18 q^{62} + 14 q^{64} + 32 q^{66} - 68 q^{68} + 2 q^{69} - 28 q^{74} - 30 q^{75} + 16 q^{77} + 4 q^{79} - 12 q^{81} + 20 q^{82} + 26 q^{87} + 96 q^{88} - 64 q^{92} - 28 q^{94} + 14 q^{95}+O(q^{100}) \) 12 * q - 8 * q^3 - 16 * q^4 + 28 * q^10 + 46 * q^12 - 4 * q^14 + 46 * q^17 - 8 * q^22 + 36 * q^23 + 20 * q^25 - 20 * q^27 - 30 * q^29 - 28 * q^30 - 4 * q^35 - 44 * q^36 + 22 * q^38 - 28 * q^40 + 16 * q^42 + 36 * q^43 - 22 * q^48 - 12 * q^49 - 28 * q^51 - 50 * q^53 + 6 * q^56 + 32 * q^61 + 18 * q^62 + 14 * q^64 + 32 * q^66 - 68 * q^68 + 2 * q^69 - 28 * q^74 - 30 * q^75 + 16 * q^77 + 4 * q^79 - 12 * q^81 + 20 * q^82 + 26 * q^87 + 96 * q^88 - 64 * q^92 - 28 * q^94 + 14 * q^95

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