LMFDB - Embedded newform 475.3.c.g.151.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,3,Mod(151,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("475.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	475.c (of order $2$, degree $1$, 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:	$12.9428125571$
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} + 30x^{10} + 329x^{8} + 1620x^{6} + 3479x^{4} + 2470x^{2} + 55 $ x^12 + 30x^10 + 329x^8 + 1620x^6 + 3479x^4 + 2470*x^2 + 55
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.11
Root			$2.84623i$ of defining polynomial
Character	$\chi$	$=$	475.151
Dual form			475.3.c.g.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.84623i q^{2} +2.18419i q^{3} -4.10101 q^{4} -6.21669 q^{6} +9.15076 q^{7} -0.287487i q^{8} +4.22932 q^{9} +O(q^{10})$	\(q+2.84623i q^{2} +2.18419i q^{3} -4.10101 q^{4} -6.21669 q^{6} +9.15076 q^{7} -0.287487i q^{8} +4.22932 q^{9} +9.89207 q^{11} -8.95737i q^{12} +12.3251i q^{13} +26.0451i q^{14} -15.5858 q^{16} +11.1895 q^{17} +12.0376i q^{18} +(18.7659 + 2.97345i) q^{19} +19.9870i q^{21} +28.1551i q^{22} -20.8666 q^{23} +0.627927 q^{24} -35.0800 q^{26} +28.8953i q^{27} -37.5273 q^{28} -10.5011i q^{29} -52.3075i q^{31} -45.5106i q^{32} +21.6061i q^{33} +31.8479i q^{34} -17.3445 q^{36} -10.5041i q^{37} +(-8.46312 + 53.4120i) q^{38} -26.9203 q^{39} +42.6288i q^{41} -56.8874 q^{42} -45.9768 q^{43} -40.5674 q^{44} -59.3912i q^{46} -4.22163 q^{47} -34.0423i q^{48} +34.7363 q^{49} +24.4400i q^{51} -50.5453i q^{52} -95.8254i q^{53} -82.2427 q^{54} -2.63073i q^{56} +(-6.49458 + 40.9882i) q^{57} +29.8886 q^{58} -6.38544i q^{59} +14.8591 q^{61} +148.879 q^{62} +38.7015 q^{63} +67.1904 q^{64} -61.4960 q^{66} -38.0693i q^{67} -45.8882 q^{68} -45.5767i q^{69} +125.169i q^{71} -1.21588i q^{72} -18.5252 q^{73} +29.8971 q^{74} +(-76.9590 - 12.1941i) q^{76} +90.5199 q^{77} -76.6214i q^{78} -137.419i q^{79} -25.0489 q^{81} -121.331 q^{82} -127.881 q^{83} -81.9667i q^{84} -130.860i q^{86} +22.9364 q^{87} -2.84385i q^{88} -19.8059i q^{89} +112.784i q^{91} +85.5743 q^{92} +114.249 q^{93} -12.0157i q^{94} +99.4037 q^{96} -42.4473i q^{97} +98.8675i q^{98} +41.8368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 28 q^{6} - 20 q^{7} - 48 q^{9}+O(q^{10}) $ 12 * q - 12 * q^4 - 28 * q^6 - 20 * q^7 - 48 * q^9	$ 12 q - 12 q^{4} - 28 q^{6} - 20 q^{7} - 48 q^{9} + 32 q^{11} - 44 q^{16} + 44 q^{17} + 8 q^{19} - 36 q^{23} + 100 q^{24} + 108 q^{26} + 36 q^{28} - 80 q^{36} + 44 q^{38} + 76 q^{39} - 100 q^{42} - 320 q^{43} - 256 q^{44} + 56 q^{47} + 72 q^{49} - 76 q^{54} - 60 q^{57} - 68 q^{58} - 296 q^{61} + 376 q^{62} + 96 q^{63} + 188 q^{64} + 152 q^{66} + 340 q^{68} + 244 q^{73} + 136 q^{74} + 248 q^{76} + 200 q^{77} - 372 q^{81} - 424 q^{82} + 160 q^{83} - 444 q^{87} - 716 q^{92} - 296 q^{93} - 44 q^{96} - 312 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 - 28 * q^6 - 20 * q^7 - 48 * q^9 + 32 * q^11 - 44 * q^16 + 44 * q^17 + 8 * q^19 - 36 * q^23 + 100 * q^24 + 108 * q^26 + 36 * q^28 - 80 * q^36 + 44 * q^38 + 76 * q^39 - 100 * q^42 - 320 * q^43 - 256 * q^44 + 56 * q^47 + 72 * q^49 - 76 * q^54 - 60 * q^57 - 68 * q^58 - 296 * q^61 + 376 * q^62 + 96 * q^63 + 188 * q^64 + 152 * q^66 + 340 * q^68 + 244 * q^73 + 136 * q^74 + 248 * q^76 + 200 * q^77 - 372 * q^81 - 424 * q^82 + 160 * q^83 - 444 * q^87 - 716 * q^92 - 296 * q^93 - 44 * q^96 - 312 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$-1$

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 $

$2$			2.84623i			1.42311i	0.702629	+	0.711557i	$0.252010\pi$
$2$			2.84623i			1.42311i	−0.702629	+	0.711557i	$0.747990\pi$
$3$			2.18419i			0.728063i	0.931387	+	0.364031i	$0.118600\pi$
$3$			2.18419i			0.728063i	−0.931387	+	0.364031i	$0.881400\pi$
$4$	−4.10101			−1.02525
$5$		0			0
$5$		0			0
$6$	−6.21669			−1.03612
$7$	9.15076			1.30725			0.653625	−	0.756818i	$-0.273247\pi$
$7$	9.15076			1.30725			0.653625	+	0.756818i	$0.273247\pi$
$8$		−	0.287487i		−	0.0359359i
$9$	4.22932			0.469925
$10$		0			0
$11$	9.89207			0.899279			0.449640	−	0.893210i	$-0.351552\pi$
$11$	9.89207			0.899279			0.449640	+	0.893210i	$0.351552\pi$
$12$		−	8.95737i		−	0.746447i
$13$			12.3251i			0.948085i	0.880502	+	0.474042i	$0.157206\pi$
$13$			12.3251i			0.948085i	−0.880502	+	0.474042i	$0.842794\pi$
$14$			26.0451i			1.86037i
$15$		0			0
$16$	−15.5858			−0.974111
$17$	11.1895			0.658206			0.329103	−	0.944294i	$-0.393254\pi$
$17$	11.1895			0.658206			0.329103	+	0.944294i	$0.393254\pi$
$18$			12.0376i			0.668756i
$19$	18.7659	+	2.97345i	0.987678	+	0.156497i
$19$	18.7659	+	2.97345i	0.987678	+	0.156497i
$20$		0			0
$21$			19.9870i			0.951760i
$22$			28.1551i			1.27978i
$23$	−20.8666			−0.907246			−0.453623	−	0.891194i	$-0.649869\pi$
$23$	−20.8666			−0.907246			−0.453623	+	0.891194i	$0.649869\pi$
$24$	0.627927			0.0261636
$25$		0			0
$26$	−35.0800			−1.34923
$27$			28.8953i			1.07020i
$28$	−37.5273			−1.34026
$29$		−	10.5011i		−	0.362107i	−0.983473	−	0.181054i	$-0.942049\pi$
$29$		−	10.5011i		−	0.362107i	0.983473	−	0.181054i	$-0.0579508\pi$
$30$		0			0
$31$		−	52.3075i		−	1.68734i	−0.536864	−	0.843669i	$-0.680391\pi$
$31$		−	52.3075i		−	1.68734i	0.536864	−	0.843669i	$-0.319609\pi$
$32$		−	45.5106i		−	1.42221i
$33$			21.6061i			0.654732i
$34$			31.8479i			0.936702i
$35$		0			0
$36$	−17.3445			−0.481791
$37$		−	10.5041i		−	0.283895i	−0.989874	−	0.141948i	$-0.954664\pi$
$37$		−	10.5041i		−	0.283895i	0.989874	−	0.141948i	$-0.0453364\pi$
$38$	−8.46312	+	53.4120i	−0.222714	+	1.40558i
$39$	−26.9203			−0.690265
$40$		0			0
$41$			42.6288i			1.03973i	0.854250	+	0.519863i	$0.174017\pi$
$41$			42.6288i			1.03973i	−0.854250	+	0.519863i	$0.825983\pi$
$42$	−56.8874			−1.35446
$43$	−45.9768			−1.06923			−0.534614	−	0.845097i	$-0.679543\pi$
$43$	−45.9768			−1.06923			−0.534614	+	0.845097i	$0.679543\pi$
$44$	−40.5674			−0.921987
$45$		0			0
$46$		−	59.3912i		−	1.29111i
$47$	−4.22163			−0.0898220			−0.0449110	−	0.998991i	$-0.514300\pi$
$47$	−4.22163			−0.0898220			−0.0449110	+	0.998991i	$0.514300\pi$
$48$		−	34.0423i		−	0.709214i
$49$	34.7363			0.708905
$50$		0			0
$51$			24.4400i			0.479215i
$52$		−	50.5453i		−	0.972025i
$53$		−	95.8254i		−	1.80803i	−0.427505	−	0.904013i	$-0.640607\pi$
$53$		−	95.8254i		−	1.80803i	0.427505	−	0.904013i	$-0.359393\pi$
$54$	−82.2427			−1.52301
$55$		0			0
$56$		−	2.63073i		−	0.0469773i
$57$	−6.49458	+	40.9882i	−0.113940	+	0.719092i
$58$	29.8886			0.515320
$59$		−	6.38544i		−	0.108228i	−0.998535	−	0.0541139i	$-0.982767\pi$
$59$		−	6.38544i		−	0.108228i	0.998535	−	0.0541139i	$-0.0172334\pi$
$60$		0			0
$61$	14.8591			0.243593			0.121796	−	0.992555i	$-0.461135\pi$
$61$	14.8591			0.243593			0.121796	+	0.992555i	$0.461135\pi$
$62$	148.879			2.40127
$63$	38.7015			0.614310
$64$	67.1904			1.04985
$65$		0			0
$66$	−61.4960			−0.931757
$67$		−	38.0693i		−	0.568199i	−0.958795	−	0.284099i	$-0.908305\pi$
$67$		−	38.0693i		−	0.568199i	0.958795	−	0.284099i	$-0.0916946\pi$
$68$	−45.8882			−0.674827
$69$		−	45.5767i		−	0.660532i
$70$		0			0
$71$			125.169i			1.76295i	0.472230	+	0.881475i	$0.343449\pi$
$71$			125.169i			1.76295i	−0.472230	+	0.881475i	$0.656551\pi$
$72$		−	1.21588i		−	0.0168872i
$73$	−18.5252			−0.253769			−0.126885	−	0.991917i	$-0.540498\pi$
$73$	−18.5252			−0.253769			−0.126885	+	0.991917i	$0.540498\pi$
$74$	29.8971			0.404015
$75$		0			0
$76$	−76.9590	−	12.1941i	−1.01262	−	0.160449i
$77$	90.5199			1.17558
$78$		−	76.6214i		−	0.982325i
$79$		−	137.419i		−	1.73948i	−0.493510	−	0.869740i	$-0.664286\pi$
$79$		−	137.419i		−	1.73948i	0.493510	−	0.869740i	$-0.335714\pi$
$80$		0			0
$81$	−25.0489			−0.309246
$82$	−121.331			−1.47965
$83$	−127.881			−1.54073			−0.770365	−	0.637603i	$-0.779926\pi$
$83$	−127.881			−1.54073			−0.770365	+	0.637603i	$0.779926\pi$
$84$		−	81.9667i		−	0.975794i
$85$		0			0
$86$		−	130.860i		−	1.52163i
$87$	22.9364			0.263637
$88$		−	2.84385i		−	0.0323164i
$89$		−	19.8059i		−	0.222538i	−0.993790	−	0.111269i	$-0.964508\pi$
$89$		−	19.8059i		−	0.222538i	0.993790	−	0.111269i	$-0.0354916\pi$
$90$		0			0
$91$			112.784i			1.23938i
$92$	85.5743			0.930155
$93$	114.249			1.22849
$94$		−	12.0157i		−	0.127827i
$95$		0			0
$96$	99.4037			1.03545
$97$		−	42.4473i		−	0.437601i	−0.975770	−	0.218800i	$-0.929786\pi$
$97$		−	42.4473i		−	0.437601i	0.975770	−	0.218800i	$-0.0702143\pi$
$98$			98.8675i			1.00885i
$99$	41.8368			0.422594
$100$		0			0
$101$	−111.435			−1.10332			−0.551660	−	0.834069i	$-0.686005\pi$
$101$	−111.435			−1.10332			−0.551660	+	0.834069i	$0.686005\pi$
$102$	−69.5617			−0.681978
$103$			5.71536i			0.0554889i	0.999615	+	0.0277445i	$0.00883247\pi$
$103$			5.71536i			0.0554889i	−0.999615	+	0.0277445i	$0.991168\pi$
$104$	3.54331			0.0340703
$105$		0			0
$106$	272.741			2.57303
$107$			164.563i			1.53797i	0.639264	+	0.768987i	$0.279239\pi$
$107$			164.563i			1.53797i	−0.639264	+	0.768987i	$0.720761\pi$
$108$		−	118.500i		−	1.09722i
$109$			102.267i			0.938227i	0.883138	+	0.469113i	$0.155426\pi$
$109$			102.267i			0.938227i	−0.883138	+	0.469113i	$0.844574\pi$
$110$		0			0
$111$	22.9430			0.206693
$112$	−142.622			−1.27341
$113$		−	24.5050i		−	0.216858i	−0.994104	−	0.108429i	$-0.965418\pi$
$113$		−	24.5050i		−	0.216858i	0.994104	−	0.108429i	$-0.0345821\pi$
$114$	−116.662	−	18.4850i	−1.02335	−	0.162149i
$115$		0			0
$116$			43.0651i			0.371251i
$117$			52.1268i			0.445528i
$118$	18.1744			0.154021
$119$	102.392			0.860440
$120$		0			0
$121$	−23.1469			−0.191297
$122$			42.2925i			0.346660i
$123$	−93.1093			−0.756986
$124$			214.513i			1.72995i
$125$		0			0
$126$			110.153i			0.874232i
$127$		−	58.5427i		−	0.460966i	−0.973076	−	0.230483i	$-0.925969\pi$
$127$		−	58.5427i		−	0.460966i	0.973076	−	0.230483i	$-0.0740307\pi$
$128$			9.19667i			0.0718489i
$129$		−	100.422i		−	0.778464i
$130$		0			0
$131$	223.883			1.70903			0.854516	−	0.519425i	$-0.173854\pi$
$131$	223.883			1.70903			0.854516	+	0.519425i	$0.173854\pi$
$132$		−	88.6069i		−	0.671265i
$133$	171.722	+	27.2093i	1.29114	+	0.204581i
$134$	108.354			0.808611
$135$		0			0
$136$		−	3.21684i		−	0.0236532i
$137$	−6.24728			−0.0456006			−0.0228003	−	0.999740i	$-0.507258\pi$
$137$	−6.24728			−0.0456006			−0.0228003	+	0.999740i	$0.507258\pi$
$138$	129.722			0.940011
$139$	−204.969			−1.47460			−0.737299	−	0.675567i	$-0.763899\pi$
$139$	−204.969			−1.47460			−0.737299	+	0.675567i	$0.763899\pi$
$140$		0			0
$141$		−	9.22084i		−	0.0653960i
$142$	−356.261			−2.50888
$143$			121.921i			0.852593i
$144$	−65.9173			−0.457759
$145$		0			0
$146$		−	52.7268i		−	0.361143i
$147$			75.8707i			0.516127i
$148$			43.0775i			0.291064i
$149$	−83.5502			−0.560740			−0.280370	−	0.959892i	$-0.590457\pi$
$149$	−83.5502			−0.560740			−0.280370	+	0.959892i	$0.590457\pi$
$150$		0			0
$151$		−	189.386i		−	1.25421i	−0.778934	−	0.627106i	$-0.784239\pi$
$151$		−	189.386i		−	1.25421i	0.778934	−	0.627106i	$-0.215761\pi$
$152$	0.854830	−	5.39496i	0.00562388	−	0.0354931i
$153$	47.3240			0.309307
$154$			257.640i			1.67299i
$155$		0			0
$156$	110.400			0.707695
$157$	195.060			1.24242			0.621212	−	0.783643i	$-0.286641\pi$
$157$	195.060			1.24242			0.621212	+	0.783643i	$0.286641\pi$
$158$	391.126			2.47548
$159$	209.301			1.31636
$160$		0			0
$161$	−190.946			−1.18600
$162$		−	71.2949i		−	0.440092i
$163$	171.677			1.05323			0.526616	−	0.850103i	$-0.323461\pi$
$163$	171.677			1.05323			0.526616	+	0.850103i	$0.323461\pi$
$164$		−	174.821i		−	1.06598i
$165$		0			0
$166$		−	363.977i		−	2.19263i
$167$			40.7628i			0.244088i	0.992525	+	0.122044i	$0.0389450\pi$
$167$			40.7628i			0.244088i	−0.992525	+	0.122044i	$0.961055\pi$
$168$	5.74600			0.0342024
$169$	17.0919			0.101136
$170$		0			0
$171$	79.3670	+	12.5757i	0.464135	+	0.0735420i
$172$	188.551			1.09623
$173$			279.193i			1.61384i	0.590664	+	0.806918i	$0.298866\pi$
$173$			279.193i			1.61384i	−0.590664	+	0.806918i	$0.701134\pi$
$174$			65.2822i			0.375185i
$175$		0			0
$176$	−154.176			−0.875997
$177$	13.9470			0.0787967
$178$	56.3721			0.316697
$179$			308.777i			1.72501i	0.506048	+	0.862505i	$0.331106\pi$
$179$			308.777i			1.72501i	−0.506048	+	0.862505i	$0.668894\pi$
$180$		0			0
$181$		−	252.084i		−	1.39273i	−0.717688	−	0.696365i	$-0.754799\pi$
$181$		−	252.084i		−	1.39273i	0.717688	−	0.696365i	$-0.245201\pi$
$182$	−321.009			−1.76378
$183$			32.4552i			0.177351i
$184$			5.99890i			0.0326027i
$185$		0			0
$186$			325.180i			1.74828i
$187$	110.687			0.591911
$188$	17.3129			0.0920901
$189$			264.414i			1.39902i
$190$		0			0
$191$	210.693			1.10311			0.551553	−	0.834140i	$-0.314035\pi$
$191$	210.693			1.10311			0.551553	+	0.834140i	$0.314035\pi$
$192$			146.756i			0.764356i
$193$		−	113.346i		−	0.587285i	−0.955915	−	0.293643i	$-0.905132\pi$
$193$		−	113.346i		−	0.587285i	0.955915	−	0.293643i	$-0.0948676\pi$
$194$	120.815			0.622755
$195$		0			0
$196$	−142.454			−0.726806
$197$	206.358			1.04750			0.523752	−	0.851871i	$-0.324532\pi$
$197$	206.358			1.04750			0.523752	+	0.851871i	$0.324532\pi$
$198$			119.077i			0.601399i
$199$	181.976			0.914450			0.457225	−	0.889351i	$-0.348843\pi$
$199$	181.976			0.914450			0.457225	+	0.889351i	$0.348843\pi$
$200$		0			0
$201$	83.1505			0.413684
$202$		−	317.170i		−	1.57015i
$203$		−	96.0931i		−	0.473365i
$204$		−	100.229i		−	0.491316i
$205$		0			0
$206$	−16.2672			−0.0789670
$207$	−88.2518			−0.426337
$208$		−	192.096i		−	0.923539i
$209$	185.633	+	29.4136i	0.888199	+	0.140735i
$210$		0			0
$211$			106.729i			0.505824i	0.967489	+	0.252912i	$0.0813883\pi$
$211$			106.729i			0.505824i	−0.967489	+	0.252912i	$0.918612\pi$
$212$			392.981i			1.85368i
$213$	−273.394			−1.28354
$214$	−468.384			−2.18871
$215$		0			0
$216$	8.30704			0.0384585
$217$		−	478.653i		−	2.20577i
$218$	−291.074			−1.33520
$219$		−	40.4624i		−	0.184760i
$220$		0			0
$221$			137.912i			0.624035i
$222$			65.3009i			0.294148i
$223$		−	209.351i		−	0.938793i	−0.882987	−	0.469397i	$-0.844471\pi$
$223$		−	209.351i		−	0.938793i	0.882987	−	0.469397i	$-0.155529\pi$
$224$		−	416.456i		−	1.85918i
$225$		0			0
$226$	69.7467			0.308614
$227$		−	244.295i		−	1.07619i	−0.842885	−	0.538094i	$-0.819144\pi$
$227$		−	244.295i		−	1.07619i	0.842885	−	0.538094i	$-0.180856\pi$
$228$	26.6343	−	168.093i	0.116817	−	0.737250i
$229$	254.372			1.11079			0.555397	−	0.831586i	$-0.312566\pi$
$229$	254.372			1.11079			0.555397	+	0.831586i	$0.312566\pi$
$230$		0			0
$231$			197.713i			0.855898i
$232$	−3.01894			−0.0130127
$233$	−347.037			−1.48943			−0.744714	−	0.667384i	$-0.767414\pi$
$233$	−347.037			−1.48943			−0.744714	+	0.667384i	$0.767414\pi$
$234$	−148.365			−0.634038
$235$		0			0
$236$			26.1867i			0.110961i
$237$	300.149			1.26645
$238$			291.432i			1.22450i
$239$	0.0478766			0.000200320			0.000100160	−	1.00000i	$-0.499968\pi$
$239$	0.0478766			0.000200320			0.000100160		1.00000i	$0.499968\pi$
$240$		0			0
$241$		−	422.817i		−	1.75443i	−0.480100	−	0.877214i	$-0.659399\pi$
$241$		−	422.817i		−	1.75443i	0.480100	−	0.877214i	$-0.340601\pi$
$242$		−	65.8815i		−	0.272237i
$243$			205.346i			0.845047i
$244$	−60.9375			−0.249744
$245$		0			0
$246$		−	265.010i		−	1.07728i
$247$	−36.6481	+	231.291i	−0.148373	+	0.936403i
$248$	−15.0377			−0.0606361
$249$		−	279.315i		−	1.12175i
$250$		0			0
$251$	142.321			0.567015			0.283507	−	0.958970i	$-0.408502\pi$
$251$	142.321			0.567015			0.283507	+	0.958970i	$0.408502\pi$
$252$	−158.715			−0.629822
$253$	−206.414			−0.815867
$254$	166.626			0.656007
$255$		0			0
$256$	242.586			0.947600
$257$		−	198.179i		−	0.771123i	−0.922682	−	0.385562i	$-0.874008\pi$
$257$		−	198.179i		−	0.771123i	0.922682	−	0.385562i	$-0.125992\pi$
$258$	285.823			1.10784
$259$		−	96.1206i		−	0.371122i
$260$		0			0
$261$		−	44.4126i		−	0.170163i
$262$			637.223i			2.43215i
$263$	149.067			0.566794			0.283397	−	0.959003i	$-0.408539\pi$
$263$	149.067			0.566794			0.283397	+	0.959003i	$0.408539\pi$
$264$	6.21149			0.0235284
$265$		0			0
$266$	−77.4439	+	488.760i	−0.291143	+	1.83744i
$267$	43.2599			0.162022
$268$			156.123i			0.582547i
$269$			204.113i			0.758785i	0.925236	+	0.379392i	$0.123867\pi$
$269$			204.113i			0.758785i	−0.925236	+	0.379392i	$0.876133\pi$
$270$		0			0
$271$	−240.731			−0.888305			−0.444152	−	0.895951i	$-0.646495\pi$
$271$	−240.731			−0.888305			−0.444152	+	0.895951i	$0.646495\pi$
$272$	−174.397			−0.641166
$273$	−246.341			−0.902349
$274$		−	17.7812i		−	0.0648948i
$275$		0			0
$276$			186.910i			0.677211i
$277$	−458.745			−1.65612			−0.828059	−	0.560641i	$-0.810555\pi$
$277$	−458.745			−1.65612			−0.828059	+	0.560641i	$0.810555\pi$
$278$		−	583.388i		−	2.09852i
$279$		−	221.225i		−	0.792922i
$280$		0			0
$281$			249.476i			0.887816i	0.896072	+	0.443908i	$0.146408\pi$
$281$			249.476i			0.887816i	−0.896072	+	0.443908i	$0.853592\pi$
$282$	26.2446			0.0930659
$283$	365.612			1.29192			0.645958	−	0.763373i	$-0.276458\pi$
$283$	365.612			1.29192			0.645958	+	0.763373i	$0.276458\pi$
$284$		−	513.321i		−	1.80747i
$285$		0			0
$286$	−347.014			−1.21334
$287$			390.086i			1.35918i
$288$		−	192.479i		−	0.668330i
$289$	−163.795			−0.566765
$290$		0			0
$291$	92.7128			0.318601
$292$	75.9718			0.260177
$293$		−	173.088i		−	0.590745i	−0.955382	−	0.295373i	$-0.904556\pi$
$293$		−	173.088i		−	0.590745i	0.955382	−	0.295373i	$-0.0954438\pi$
$294$	−215.945			−0.734507
$295$		0			0
$296$	−3.01980			−0.0102020
$297$			285.835i			0.962406i
$298$		−	237.803i		−	0.797996i
$299$		−	257.184i		−	0.860146i
$300$		0			0
$301$	−420.722			−1.39775
$302$	539.036			1.78489
$303$		−	243.396i		−	0.803286i
$304$	−292.481	−	46.3435i	−0.962108	−	0.152446i
$305$		0			0
$306$			134.695i			0.440179i
$307$		−	452.211i		−	1.47300i	−0.676438	−	0.736500i	$-0.736477\pi$
$307$		−	452.211i		−	1.47300i	0.676438	−	0.736500i	$-0.263523\pi$
$308$	−371.223			−1.20527
$309$	−12.4834			−0.0403994
$310$		0			0
$311$	179.346			0.576675			0.288337	−	0.957529i	$-0.406898\pi$
$311$	179.346			0.576675			0.288337	+	0.957529i	$0.406898\pi$
$312$			7.73926i			0.0248053i
$313$	−137.714			−0.439981			−0.219990	−	0.975502i	$-0.570603\pi$
$313$	−137.714			−0.439981			−0.219990	+	0.975502i	$0.570603\pi$
$314$			555.186i			1.76811i
$315$		0			0
$316$			563.556i			1.78341i
$317$		−	602.099i		−	1.89936i	−0.313215	−	0.949682i	$-0.601406\pi$
$317$		−	602.099i		−	1.89936i	0.313215	−	0.949682i	$-0.398594\pi$
$318$			595.717i			1.87332i
$319$		−	103.878i		−	0.325636i
$320$		0			0
$321$	−359.437			−1.11974
$322$		−	543.474i		−	1.68781i
$323$	209.981	+	33.2714i	0.650096	+	0.103008i
$324$	102.726			0.317055
$325$		0			0
$326$			488.631i			1.49887i
$327$	−223.370			−0.683088
$328$	12.2552			0.0373635
$329$	−38.6311			−0.117420
$330$		0			0
$331$		−	190.514i		−	0.575571i	−0.957695	−	0.287785i	$-0.907081\pi$
$331$		−	190.514i		−	0.575571i	0.957695	−	0.287785i	$-0.0929189\pi$
$332$	524.439			1.57964
$333$		−	44.4253i		−	0.133409i
$334$	−116.020			−0.347366
$335$		0			0
$336$		−	311.512i		−	0.927120i
$337$			394.039i			1.16926i	0.811301	+	0.584628i	$0.198760\pi$
$337$			394.039i			1.16926i	−0.811301	+	0.584628i	$0.801240\pi$
$338$			48.6475i			0.143927i
$339$	53.5235			0.157886
$340$		0			0
$341$		−	517.429i		−	1.51739i
$342$	−35.7933	+	225.896i	−0.104659	+	0.660516i
$343$	−130.523			−0.380535
$344$			13.2177i			0.0384237i
$345$		0			0
$346$	−794.648			−2.29667
$347$	−205.061			−0.590953			−0.295476	−	0.955350i	$-0.595478\pi$
$347$	−205.061			−0.590953			−0.295476	+	0.955350i	$0.595478\pi$
$348$	−94.0624			−0.270294
$349$	−488.832			−1.40066			−0.700332	−	0.713817i	$-0.746965\pi$
$349$	−488.832			−1.40066			−0.700332	+	0.713817i	$0.746965\pi$
$350$		0			0
$351$	−356.138			−1.01464
$352$		−	450.194i		−	1.27896i
$353$	−466.761			−1.32227			−0.661134	−	0.750268i	$-0.729925\pi$
$353$	−466.761			−1.32227			−0.661134	+	0.750268i	$0.729925\pi$
$354$			39.6964i			0.112137i
$355$		0			0
$356$			81.2242i			0.228158i
$357$			223.644i			0.626455i
$358$	−878.849			−2.45489
$359$	487.730			1.35858			0.679289	−	0.733871i	$-0.262288\pi$
$359$	487.730			1.35858			0.679289	+	0.733871i	$0.262288\pi$
$360$		0			0
$361$	343.317	+	111.599i	0.951017	+	0.309138i
$362$	717.489			1.98201
$363$		−	50.5573i		−	0.139276i
$364$		−	462.528i		−	1.27068i
$365$		0			0
$366$	−92.3748			−0.252390
$367$	63.0494			0.171797			0.0858983	−	0.996304i	$-0.472624\pi$
$367$	63.0494			0.171797			0.0858983	+	0.996304i	$0.472624\pi$
$368$	325.223			0.883758
$369$			180.291i			0.488593i
$370$		0			0
$371$		−	876.875i		−	2.36354i
$372$	−468.537			−1.25951
$373$			137.833i			0.369526i	0.982783	+	0.184763i	$0.0591517\pi$
$373$			137.833i			0.369526i	−0.982783	+	0.184763i	$0.940848\pi$
$374$			315.041i			0.842356i
$375$		0			0
$376$			1.21367i			0.00322784i
$377$	129.427			0.343308
$378$	−752.582			−1.99096
$379$			316.605i			0.835370i	0.908592	+	0.417685i	$0.137158\pi$
$379$			316.605i			0.835370i	−0.908592	+	0.417685i	$0.862842\pi$
$380$		0			0
$381$	127.868			0.335612
$382$			599.681i			1.56985i
$383$			197.083i			0.514577i	0.966335	+	0.257288i	$0.0828291\pi$
$383$			197.083i			0.514577i	−0.966335	+	0.257288i	$0.917171\pi$
$384$	−20.0872			−0.0523105
$385$		0			0
$386$	322.609			0.835774
$387$	−194.451			−0.502456
$388$			174.076i			0.448651i
$389$	27.8203			0.0715175			0.0357587	−	0.999360i	$-0.488615\pi$
$389$	27.8203			0.0715175			0.0357587	+	0.999360i	$0.488615\pi$
$390$		0			0
$391$	−233.487			−0.597155
$392$		−	9.98626i		−	0.0254751i
$393$			489.003i			1.24428i
$394$			587.343i			1.49072i
$395$		0			0
$396$	−171.573			−0.433265
$397$	702.745			1.77014			0.885069	−	0.465459i	$-0.154111\pi$
$397$	702.745			1.77014			0.885069	+	0.465459i	$0.154111\pi$
$398$			517.944i			1.30137i
$399$	−59.4303	+	375.073i	−0.148948	+	0.940033i
$400$		0			0
$401$		−	295.297i		−	0.736401i	−0.929746	−	0.368200i	$-0.879974\pi$
$401$		−	295.297i		−	0.736401i	0.929746	−	0.368200i	$-0.120026\pi$
$402$			236.665i			0.588720i
$403$	644.695			1.59974
$404$	456.997			1.13118
$405$		0			0
$406$	273.503			0.673652
$407$		−	103.907i		−	0.255301i
$408$	7.02619			0.0172210
$409$			371.735i			0.908887i	0.890775	+	0.454444i	$0.150162\pi$
$409$			371.735i			0.908887i	−0.890775	+	0.454444i	$0.849838\pi$
$410$		0			0
$411$		−	13.6452i		−	0.0332001i
$412$		−	23.4387i		−	0.0568901i
$413$		−	58.4316i		−	0.141481i
$414$		−	251.185i		−	0.606726i
$415$		0			0
$416$	560.923			1.34837
$417$		−	447.691i		−	1.07360i
$418$	−83.7177	+	528.355i	−0.200282	+	1.26401i
$419$	−109.242			−0.260721			−0.130360	−	0.991467i	$-0.541613\pi$
$419$	−109.242			−0.260721			−0.130360	+	0.991467i	$0.541613\pi$
$420$		0			0
$421$			762.528i			1.81123i	0.424100	+	0.905615i	$0.360591\pi$
$421$			762.528i			1.81123i	−0.424100	+	0.905615i	$0.639409\pi$
$422$	−303.774			−0.719845
$423$	−17.8546			−0.0422096
$424$	−27.5486			−0.0649731
$425$		0			0
$426$		−	778.140i		−	1.82662i
$427$	135.972			0.318437
$428$		−	674.875i		−	1.57681i
$429$	−266.298			−0.620741
$430$		0			0
$431$			131.893i			0.306016i	0.988225	+	0.153008i	$0.0488960\pi$
$431$			131.893i			0.306016i	−0.988225	+	0.153008i	$0.951104\pi$
$432$		−	450.356i		−	1.04249i
$433$		−	401.234i		−	0.926638i	−0.886191	−	0.463319i	$-0.846658\pi$
$433$		−	401.234i		−	0.926638i	0.886191	−	0.463319i	$-0.153342\pi$
$434$	1362.35			3.13907
$435$		0			0
$436$		−	419.397i		−	0.961919i
$437$	−391.581	−	62.0460i	−0.896067	−	0.141982i
$438$	115.165			0.262934
$439$		−	264.338i		−	0.602136i	−0.953603	−	0.301068i	$-0.902657\pi$
$439$		−	264.338i		−	0.602136i	0.953603	−	0.301068i	$-0.0973432\pi$
$440$		0			0
$441$	146.911			0.333132
$442$	−392.528			−0.888073
$443$	451.274			1.01868			0.509338	−	0.860566i	$-0.329890\pi$
$443$	451.274			1.01868			0.509338	+	0.860566i	$0.329890\pi$
$444$	−94.0893			−0.211913
$445$		0			0
$446$	595.860			1.33601
$447$		−	182.489i		−	0.408254i
$448$	614.843			1.37242
$449$		−	156.631i		−	0.348844i	−0.984671	−	0.174422i	$-0.944194\pi$
$449$		−	156.631i		−	0.348844i	0.984671	−	0.174422i	$-0.0558057\pi$
$450$		0			0
$451$			421.687i			0.935004i
$452$			100.495i			0.222334i
$453$	413.655			0.913145
$454$	695.318			1.53154
$455$		0			0
$456$	11.7836	+	1.86711i	0.0258412	+	0.00409454i
$457$	−906.098			−1.98271			−0.991355	−	0.131209i	$-0.958114\pi$
$457$	−906.098			−1.98271			−0.991355	+	0.131209i	$0.958114\pi$
$458$			724.000i			1.58078i
$459$			323.324i			0.704410i
$460$		0			0
$461$	−169.733			−0.368184			−0.184092	−	0.982909i	$-0.558934\pi$
$461$	−169.733			−0.368184			−0.184092	+	0.982909i	$0.558934\pi$
$462$	−562.735			−1.21804
$463$	−207.991			−0.449225			−0.224613	−	0.974448i	$-0.572112\pi$
$463$	−207.991			−0.449225			−0.224613	+	0.974448i	$0.572112\pi$
$464$			163.668i			0.352733i
$465$		0			0
$466$		−	987.745i		−	2.11962i
$467$	479.390			1.02653			0.513266	−	0.858230i	$-0.328435\pi$
$467$	479.390			1.02653			0.513266	+	0.858230i	$0.328435\pi$
$468$		−	213.772i		−	0.456779i
$469$		−	348.363i		−	0.742778i
$470$		0			0
$471$			426.049i			0.904562i
$472$	−1.83573			−0.00388927
$473$	−454.805			−0.961534
$474$			854.292i			1.80230i
$475$		0			0
$476$	−419.912			−0.882168
$477$		−	405.277i		−	0.849636i
$478$			0.136268i			0.000285079i
$479$	−712.482			−1.48744			−0.743718	−	0.668493i	$-0.766940\pi$
$479$	−712.482			−1.48744			−0.743718	+	0.668493i	$0.766940\pi$
$480$		0			0
$481$	129.464			0.269157
$482$	1203.43			2.49675
$483$		−	417.061i		−	0.863480i
$484$	94.9258			0.196128
$485$		0			0
$486$	−584.462			−1.20260
$487$			34.4191i			0.0706757i	0.999375	+	0.0353379i	$0.0112507\pi$
$487$			34.4191i			0.0706757i	−0.999375	+	0.0353379i	$0.988749\pi$
$488$		−	4.27182i		−	0.00875373i
$489$			374.975i			0.766819i
$490$		0			0
$491$	361.608			0.736472			0.368236	−	0.929732i	$-0.379962\pi$
$491$	361.608			0.736472			0.368236	+	0.929732i	$0.379962\pi$
$492$	381.842			0.776101
$493$		−	117.502i		−	0.238341i
$494$	−658.308	−	104.309i	−1.33261	−	0.211151i
$495$		0			0
$496$			815.252i			1.64365i
$497$			1145.40i			2.30462i
$498$	794.994			1.59637
$499$	−189.977			−0.380715			−0.190358	−	0.981715i	$-0.560965\pi$
$499$	−189.977			−0.380715			−0.190358	+	0.981715i	$0.560965\pi$
$500$		0			0
$501$	−89.0336			−0.177712
$502$			405.077i			0.806926i
$503$	687.468			1.36674			0.683368	−	0.730074i	$-0.260514\pi$
$503$	687.468			1.36674			0.683368	+	0.730074i	$0.260514\pi$
$504$		−	11.1262i		−	0.0220758i
$505$		0			0
$506$		−	587.502i		−	1.16107i
$507$			37.3319i			0.0736330i
$508$			240.084i			0.472607i
$509$		−	348.233i		−	0.684151i	−0.939672	−	0.342076i	$-0.888870\pi$
$509$		−	348.233i		−	0.684151i	0.939672	−	0.342076i	$-0.111130\pi$
$510$		0			0
$511$	−169.519			−0.331740
$512$			727.241i			1.42039i
$513$	−85.9189	+	542.247i	−0.167483	+	1.05701i
$514$	564.061			1.09740
$515$		0			0
$516$			411.831i			0.798122i
$517$	−41.7607			−0.0807750
$518$	273.581			0.528149
$519$	−609.811			−1.17497
$520$		0			0
$521$			222.778i			0.427597i	0.976878	+	0.213798i	$0.0685835\pi$
$521$			222.778i			0.427597i	−0.976878	+	0.213798i	$0.931416\pi$
$522$	126.408			0.242162
$523$			45.6247i			0.0872365i	0.999048	+	0.0436182i	$0.0138885\pi$
$523$			45.6247i			0.0872365i	−0.999048	+	0.0436182i	$0.986111\pi$
$524$	−918.147			−1.75219
$525$		0			0
$526$			424.278i			0.806612i
$527$		−	585.295i		−	1.11062i
$528$		−	336.748i		−	0.637781i
$529$	−93.5830			−0.176905
$530$		0			0
$531$		−	27.0061i		−	0.0508590i
$532$	−704.233	−	111.586i	−1.32375	−	0.209747i
$533$	−525.404			−0.985749
$534$			123.127i			0.230576i
$535$		0			0
$536$	−10.9444			−0.0204187
$537$	−674.427			−1.25592
$538$	−580.952			−1.07984
$539$	343.614			0.637503
$540$		0			0
$541$	671.919			1.24199			0.620997	−	0.783813i	$-0.286728\pi$
$541$	671.919			1.24199			0.620997	+	0.783813i	$0.286728\pi$
$542$		−	685.174i		−	1.26416i
$543$	550.599			1.01399
$544$		−	509.241i		−	0.936105i
$545$		0			0
$546$		−	701.143i		−	1.28415i
$547$			910.710i			1.66492i	0.554087	+	0.832459i	$0.313068\pi$
$547$			910.710i			1.66492i	−0.554087	+	0.832459i	$0.686932\pi$
$548$	25.6201			0.0467520
$549$	62.8441			0.114470
$550$		0			0
$551$	31.2246	−	197.063i	0.0566689	−	0.357646i
$552$	−13.1027			−0.0237368
$553$		−	1257.49i		−	2.27394i
$554$		−	1305.69i		−	2.35684i
$555$		0			0
$556$	840.579			1.51183
$557$	246.347			0.442275			0.221138	−	0.975243i	$-0.429023\pi$
$557$	246.347			0.442275			0.221138	+	0.975243i	$0.429023\pi$
$558$	629.657			1.12842
$559$		−	566.668i		−	1.01372i
$560$		0			0
$561$			241.762i			0.430948i
$562$	−710.066			−1.26346
$563$			772.769i			1.37259i	0.727322	+	0.686296i	$0.240765\pi$
$563$			772.769i			1.37259i	−0.727322	+	0.686296i	$0.759235\pi$
$564$			37.8147i			0.0670474i
$565$		0			0
$566$			1040.61i			1.83854i
$567$	−229.217			−0.404262
$568$	35.9847			0.0633533
$569$		−	123.962i		−	0.217860i	−0.994049	−	0.108930i	$-0.965258\pi$
$569$		−	123.962i		−	0.217860i	0.994049	−	0.108930i	$-0.0347424\pi$
$570$		0			0
$571$	535.555			0.937925			0.468963	−	0.883218i	$-0.344628\pi$
$571$	535.555			0.937925			0.468963	+	0.883218i	$0.344628\pi$
$572$		−	499.998i		−	0.874122i
$573$			460.194i			0.803131i
$574$	−1110.27			−1.93427
$575$		0			0
$576$	284.170			0.493350
$577$	210.295			0.364463			0.182231	−	0.983256i	$-0.441668\pi$
$577$	210.295			0.364463			0.182231	+	0.983256i	$0.441668\pi$
$578$		−	466.198i		−	0.806570i
$579$	247.569			0.427580
$580$		0			0
$581$	−1170.20			−2.01412
$582$			263.882i			0.453405i
$583$		−	947.912i		−	1.62592i
$584$			5.32575i			0.00911944i
$585$		0			0
$586$	492.649			0.840697
$587$	508.069			0.865534			0.432767	−	0.901506i	$-0.357537\pi$
$587$	508.069			0.865534			0.432767	+	0.901506i	$0.357537\pi$
$588$		−	311.146i		−	0.529160i
$589$	155.534	−	981.596i	0.264064	−	1.66655i
$590$		0			0
$591$			450.726i			0.762649i
$592$			163.715i			0.276545i
$593$	32.8735			0.0554358			0.0277179	−	0.999616i	$-0.491176\pi$
$593$	32.8735			0.0554358			0.0277179	+	0.999616i	$0.491176\pi$
$594$	−813.550			−1.36961
$595$		0			0
$596$	342.640			0.574899
$597$			397.469i			0.665777i
$598$	732.003			1.22408
$599$		−	225.201i		−	0.375961i	−0.982173	−	0.187981i	$-0.939806\pi$
$599$		−	225.201i		−	0.375961i	0.982173	−	0.187981i	$-0.0601942\pi$
$600$		0			0
$601$		−	169.930i		−	0.282746i	−0.989956	−	0.141373i	$-0.954848\pi$
$601$		−	169.930i		−	0.282746i	0.989956	−	0.141373i	$-0.0451517\pi$
$602$		−	1197.47i		−	1.98915i
$603$		−	161.007i		−	0.267011i
$604$			776.674i			1.28588i
$605$		0			0
$606$	692.760			1.14317
$607$		−	522.217i		−	0.860325i	−0.902752	−	0.430162i	$-0.858456\pi$
$607$		−	522.217i		−	0.860325i	0.902752	−	0.430162i	$-0.141544\pi$
$608$	135.324	−	854.047i	0.222572	−	1.40468i
$609$	209.885			0.344640
$610$		0			0
$611$		−	52.0320i		−	0.0851588i
$612$	−194.076			−0.317118
$613$	639.666			1.04350			0.521750	−	0.853098i	$-0.325279\pi$
$613$	639.666			1.04350			0.521750	+	0.853098i	$0.325279\pi$
$614$	1287.09			2.09625
$615$		0			0
$616$		−	26.0233i		−	0.0422457i
$617$	−200.342			−0.324704			−0.162352	−	0.986733i	$-0.551908\pi$
$617$	−200.342			−0.324704			−0.162352	+	0.986733i	$0.551908\pi$
$618$		−	35.5306i		−	0.0574929i
$619$	−347.156			−0.560833			−0.280417	−	0.959878i	$-0.590473\pi$
$619$	−347.156			−0.560833			−0.280417	+	0.959878i	$0.590473\pi$
$620$		0			0
$621$		−	602.949i		−	0.970932i
$622$			510.459i			0.820674i
$623$		−	181.239i		−	0.290914i
$624$	419.574			0.672395
$625$		0			0
$626$		−	391.965i		−	0.626143i
$627$	−64.2448	+	405.458i	−0.102464	+	0.646664i
$628$	−799.944			−1.27380
$629$		−	117.536i		−	0.186861i
$630$		0			0
$631$	204.105			0.323463			0.161732	−	0.986835i	$-0.448292\pi$
$631$	204.105			0.323463			0.161732	+	0.986835i	$0.448292\pi$
$632$	−39.5062			−0.0625099
$633$	−233.116			−0.368271
$634$	1713.71			2.70301
$635$		0			0
$636$	−858.343			−1.34960
$637$			428.129i			0.672102i
$638$	295.660			0.463416
$639$			529.382i			0.828454i
$640$		0			0
$641$			334.435i			0.521740i	0.965374	+	0.260870i	$0.0840094\pi$
$641$			334.435i			0.521740i	−0.965374	+	0.260870i	$0.915991\pi$
$642$		−	1023.04i		−	1.59352i
$643$	22.8316			0.0355079			0.0177540	−	0.999842i	$-0.494348\pi$
$643$	22.8316			0.0355079			0.0177540	+	0.999842i	$0.494348\pi$
$644$	783.069			1.21595
$645$		0			0
$646$	−94.6981	+	597.653i	−0.146591	+	0.925160i
$647$	−280.968			−0.434263			−0.217131	−	0.976142i	$-0.569670\pi$
$647$	−280.968			−0.434263			−0.217131	+	0.976142i	$0.569670\pi$
$648$			7.20125i			0.0111130i
$649$		−	63.1653i		−	0.0973271i
$650$		0			0
$651$	1045.47			1.60594
$652$	−704.048			−1.07983
$653$	−891.423			−1.36512			−0.682559	−	0.730830i	$-0.739133\pi$
$653$	−891.423			−1.36512			−0.682559	+	0.730830i	$0.739133\pi$
$654$		−	635.761i		−	0.972112i
$655$		0			0
$656$		−	664.402i		−	1.01281i
$657$	−78.3489			−0.119253
$658$		−	109.953i		−	0.167102i
$659$			734.584i			1.11470i	0.830279	+	0.557348i	$0.188181\pi$
$659$			734.584i			1.11470i	−0.830279	+	0.557348i	$0.811819\pi$
$660$		0			0
$661$			968.622i			1.46539i	0.680558	+	0.732694i	$0.261737\pi$
$661$			968.622i			1.46539i	−0.680558	+	0.732694i	$0.738263\pi$
$662$	542.246			0.819102
$663$	−301.225			−0.454337
$664$			36.7641i			0.0553676i
$665$		0			0
$666$	126.445			0.189857
$667$			219.123i			0.328520i
$668$		−	167.168i		−	0.250252i
$669$	457.262			0.683500
$670$		0			0
$671$	146.988			0.219058
$672$	909.619			1.35360
$673$			948.399i			1.40921i	0.709599	+	0.704606i	$0.248876\pi$
$673$			948.399i			1.40921i	−0.709599	+	0.704606i	$0.751124\pi$
$674$	−1121.53			−1.66398
$675$		0			0
$676$	−70.0940			−0.103689
$677$			82.3399i			0.121625i	0.998149	+	0.0608123i	$0.0193691\pi$
$677$			82.3399i			0.121625i	−0.998149	+	0.0608123i	$0.980631\pi$
$678$			152.340i			0.224690i
$679$		−	388.425i		−	0.572054i
$680$		0			0
$681$	533.586			0.783533
$682$	1472.72			2.15941
$683$		−	10.8842i		−	0.0159359i	−0.999968	−	0.00796796i	$-0.997464\pi$
$683$		−	10.8842i		−	0.0159359i	0.999968	−	0.00796796i	$-0.00253631\pi$
$684$	−325.485	−	51.5730i	−0.475855	−	0.0753991i
$685$		0			0
$686$		−	371.499i		−	0.541544i
$687$			555.596i			0.808727i
$688$	716.583			1.04155
$689$	1181.06			1.71416
$690$		0			0
$691$	188.047			0.272138			0.136069	−	0.990699i	$-0.456553\pi$
$691$	188.047			0.272138			0.136069	+	0.990699i	$0.456553\pi$
$692$		−	1144.97i		−	1.65459i
$693$	382.838			0.552436
$694$		−	583.649i		−	0.840993i
$695$		0			0
$696$		−	6.59393i		−	0.00947404i
$697$			476.995i			0.684354i
$698$		−	1391.33i		−	1.99330i
$699$		−	757.993i		−	1.08440i
$700$		0			0
$701$	−1184.52			−1.68976			−0.844879	−	0.534957i	$-0.820328\pi$
$701$	−1184.52			−1.68976			−0.844879	+	0.534957i	$0.820328\pi$
$702$		−	1013.65i		−	1.44394i
$703$	31.2335	−	197.119i	0.0444289	−	0.280397i
$704$	664.652			0.944108
$705$		0			0
$706$		−	1328.51i		−	1.88174i
$707$	−1019.72			−1.44232
$708$	−57.1968			−0.0807864
$709$	−541.289			−0.763455			−0.381727	−	0.924275i	$-0.624671\pi$
$709$	−541.289			−0.763455			−0.381727	+	0.924275i	$0.624671\pi$
$710$		0			0
$711$		−	581.189i		−	0.817425i
$712$	−5.69395			−0.00799713
$713$			1091.48i			1.53083i
$714$	−636.542			−0.891516
$715$		0			0
$716$		−	1266.30i		−	1.76857i
$717$			0.104571i			0.000145846i
$718$			1388.19i			1.93341i
$719$	−388.854			−0.540826			−0.270413	−	0.962744i	$-0.587160\pi$
$719$	−388.854			−0.540826			−0.270413	+	0.962744i	$0.587160\pi$
$720$		0			0
$721$			52.2998i			0.0725379i
$722$	−317.636	+	977.159i	−0.439939	+	1.35341i
$723$	923.512			1.27733
$724$			1033.80i			1.42790i
$725$		0			0
$726$	143.897			0.198206
$727$	−1450.46			−1.99513			−0.997565	−	0.0697458i	$-0.977781\pi$
$727$	−1450.46			−1.99513			−0.997565	+	0.0697458i	$0.977781\pi$
$728$	32.4240			0.0445384
$729$	−673.955			−0.924493
$730$		0			0
$731$	−514.457			−0.703772
$732$		−	133.099i		−	0.181829i
$733$	−873.057			−1.19107			−0.595537	−	0.803328i	$-0.703061\pi$
$733$	−873.057			−1.19107			−0.595537	+	0.803328i	$0.703061\pi$
$734$			179.453i			0.244486i
$735$		0			0
$736$			949.653i			1.29029i
$737$		−	376.584i		−	0.510969i
$738$	−513.149			−0.695323
$739$	−456.992			−0.618393			−0.309196	−	0.950998i	$-0.600060\pi$
$739$	−456.992			−0.618393			−0.309196	+	0.950998i	$0.600060\pi$
$740$		0			0
$741$	−505.184	−	80.0463i	−0.681760	−	0.108025i
$742$	2495.78			3.36359
$743$		−	60.6398i		−	0.0816148i	−0.999167	−	0.0408074i	$-0.987007\pi$
$743$		−	60.6398i		−	0.0816148i	0.999167	−	0.0408074i	$-0.0129930\pi$
$744$		−	32.8453i		−	0.0441468i
$745$		0			0
$746$	−392.304			−0.525877
$747$	−540.848			−0.724027
$748$	−453.930			−0.606858
$749$			1505.88i			2.01052i
$750$		0			0
$751$			1177.72i			1.56821i	0.620629	+	0.784104i	$0.286877\pi$
$751$			1177.72i			1.56821i	−0.620629	+	0.784104i	$0.713123\pi$
$752$	65.7974			0.0874965
$753$			310.855i			0.412822i
$754$			368.379i			0.488567i
$755$		0			0
$756$		−	1084.36i		−	1.43434i
$757$	112.664			0.148830			0.0744151	−	0.997227i	$-0.476291\pi$
$757$	112.664			0.148830			0.0744151	+	0.997227i	$0.476291\pi$
$758$	−901.130			−1.18883
$759$		−	450.848i		−	0.594002i
$760$		0			0
$761$	−857.698			−1.12707			−0.563534	−	0.826093i	$-0.690558\pi$
$761$	−857.698			−1.12707			−0.563534	+	0.826093i	$0.690558\pi$
$762$			363.942i			0.477615i
$763$			935.818i			1.22650i
$764$	−864.055			−1.13096
$765$		0			0
$766$	−560.943			−0.732301
$767$	78.7012			0.102609
$768$			529.853i			0.689912i
$769$	−146.990			−0.191144			−0.0955719	−	0.995423i	$-0.530468\pi$
$769$	−146.990			−0.191144			−0.0955719	+	0.995423i	$0.530468\pi$
$770$		0			0
$771$	432.859			0.561426
$772$			464.833i			0.602115i
$773$		−	624.217i		−	0.807525i	−0.914864	−	0.403762i	$-0.867702\pi$
$773$		−	624.217i		−	0.807525i	0.914864	−	0.403762i	$-0.132298\pi$
$774$		−	553.451i		−	0.715052i
$775$		0			0
$776$	−12.2031			−0.0157256
$777$	209.946			0.270200
$778$			79.1829i			0.101778i
$779$	−126.755	+	799.967i	−0.162715	+	1.02692i
$780$		0			0
$781$			1238.19i			1.58538i
$782$		−	664.558i		−	0.849819i
$783$	303.433			0.387526
$784$	−541.392			−0.690552
$785$		0			0
$786$	−1391.81			−1.77076
$787$		−	551.370i		−	0.700597i	−0.936638	−	0.350298i	$-0.886080\pi$
$787$		−	551.370i		−	0.700597i	0.936638	−	0.350298i	$-0.113920\pi$
$788$	−846.277			−1.07396
$789$			325.590i			0.412661i
$790$		0			0
$791$		−	224.239i		−	0.283488i
$792$		−	12.0275i		−	0.0151863i
$793$			183.140i			0.230946i
$794$			2000.17i			2.51911i
$795$		0			0
$796$	−746.283			−0.937541
$797$		−	202.295i		−	0.253821i	−0.991914	−	0.126911i	$-0.959494\pi$
$797$		−	202.295i		−	0.253821i	0.991914	−	0.126911i	$-0.0405061\pi$
$798$	−1067.54	−	169.152i	−1.33777	−	0.211970i
$799$	−47.2380			−0.0591214
$800$		0			0
$801$		−	83.7656i		−	0.104576i
$802$	840.481			1.04798
$803$	−183.252			−0.228209
$804$	−341.001			−0.424130
$805$		0			0
$806$			1834.95i			2.27661i
$807$	−445.821			−0.552443
$808$			32.0363i			0.0396489i
$809$	−1164.20			−1.43906			−0.719531	−	0.694461i	$-0.755643\pi$
$809$	−1164.20			−1.43906			−0.719531	+	0.694461i	$0.755643\pi$
$810$		0			0
$811$		−	617.970i		−	0.761985i	−0.924578	−	0.380993i	$-0.875582\pi$
$811$		−	617.970i		−	0.761985i	0.924578	−	0.380993i	$-0.124418\pi$
$812$			394.079i			0.485318i
$813$		−	525.801i		−	0.646741i
$814$	295.744			0.363322
$815$		0			0
$816$		−	380.916i		−	0.466809i
$817$	−862.795	−	136.710i	−1.05605	−	0.167331i
$818$	−1058.04			−1.29345
$819$			477.000i			0.582417i
$820$		0			0
$821$	255.141			0.310769			0.155384	−	0.987854i	$-0.450338\pi$
$821$	255.141			0.310769			0.155384	+	0.987854i	$0.450338\pi$
$822$	38.8374			0.0472474
$823$	658.923			0.800636			0.400318	−	0.916376i	$-0.368900\pi$
$823$	658.923			0.800636			0.400318	+	0.916376i	$0.368900\pi$
$824$	1.64309			0.00199405
$825$		0			0
$826$	166.310			0.201343
$827$			633.264i			0.765736i	0.923803	+	0.382868i	$0.125064\pi$
$827$			633.264i			0.765736i	−0.923803	+	0.382868i	$0.874936\pi$
$828$	361.921			0.437103
$829$			459.961i			0.554838i	0.960749	+	0.277419i	$0.0894790\pi$
$829$			459.961i			0.554838i	−0.960749	+	0.277419i	$0.910521\pi$
$830$		0			0
$831$		−	1001.98i		−	1.20576i
$832$			828.128i			0.995346i
$833$	388.682			0.466605
$834$	1274.23			1.52785
$835$		0			0
$836$	−761.284	−	120.625i	−0.910627	−	0.144289i
$837$	1511.44			1.80578
$838$		−	310.927i		−	0.371035i
$839$			1033.89i			1.23228i	0.787635	+	0.616142i	$0.211305\pi$
$839$			1033.89i			1.23228i	−0.787635	+	0.616142i	$0.788695\pi$
$840$		0			0
$841$	730.727			0.868878
$842$	−2170.33			−2.57759
$843$	−544.903			−0.646386
$844$		−	437.696i		−	0.518597i
$845$		0			0
$846$		−	50.8184i		−	0.0600690i
$847$	−211.812			−0.250073
$848$			1493.51i			1.76122i
$849$			798.565i			0.940595i
$850$		0			0
$851$			219.186i			0.257563i
$852$	1121.19			1.31595
$853$	333.243			0.390671			0.195336	−	0.980736i	$-0.437420\pi$
$853$	333.243			0.390671			0.195336	+	0.980736i	$0.437420\pi$
$854$			387.008i			0.453171i
$855$		0			0
$856$	47.3099			0.0552685
$857$			55.2946i			0.0645211i	0.999479	+	0.0322605i	$0.0102706\pi$
$857$			55.2946i			0.0645211i	−0.999479	+	0.0322605i	$0.989729\pi$
$858$		−	757.944i		−	0.883385i
$859$	417.893			0.486488			0.243244	−	0.969965i	$-0.421788\pi$
$859$	417.893			0.486488			0.243244	+	0.969965i	$0.421788\pi$
$860$		0			0
$861$	−852.020			−0.989570
$862$	−375.396			−0.435495
$863$			1042.76i			1.20830i	0.796871	+	0.604150i	$0.206487\pi$
$863$			1042.76i			1.20830i	−0.796871	+	0.604150i	$0.793513\pi$
$864$	1315.04			1.52204
$865$		0			0
$866$	1142.00			1.31871
$867$		−	357.759i		−	0.412640i
$868$			1962.96i			2.26147i
$869$		−	1359.36i		−	1.56428i
$870$		0			0
$871$	469.208			0.538700
$872$	29.4004			0.0337161
$873$		−	179.523i		−	0.205639i
$874$	176.597	−	1114.53i	0.202056	−	1.27520i
$875$		0			0
$876$			165.937i			0.189425i
$877$			143.302i			0.163400i	0.996657	+	0.0817002i	$0.0260350\pi$
$877$			143.302i			0.163400i	−0.996657	+	0.0817002i	$0.973965\pi$
$878$	752.366			0.856908
$879$	378.057			0.430099
$880$		0			0
$881$	−944.916			−1.07255			−0.536275	−	0.844043i	$-0.680169\pi$
$881$	−944.916			−1.07255			−0.536275	+	0.844043i	$0.680169\pi$
$882$			418.142i			0.474084i
$883$	1406.88			1.59329			0.796646	−	0.604446i	$-0.206605\pi$
$883$	1406.88			1.59329			0.796646	+	0.604446i	$0.206605\pi$
$884$		−	565.577i		−	0.639793i
$885$		0			0
$886$			1284.43i			1.44969i
$887$			437.734i			0.493500i	0.969079	+	0.246750i	$0.0793626\pi$
$887$			437.734i			0.493500i	−0.969079	+	0.246750i	$0.920637\pi$
$888$		−	6.59582i		−	0.00742772i
$889$		−	535.710i		−	0.602599i
$890$		0			0
$891$	−247.786			−0.278098
$892$			858.549i			0.962499i
$893$	−79.2227	−	12.5528i	−0.0887152	−	0.0140569i
$894$	519.406			0.580991
$895$		0			0
$896$			84.1564i			0.0939246i
$897$	561.737			0.626240
$898$	445.807			0.496445
$899$	−549.287			−0.610998
$900$		0			0
$901$		−	1072.24i		−	1.19005i
$902$	−1200.22			−1.33062
$903$		−	918.936i		−	1.01765i
$904$	−7.04488			−0.00779300
$905$		0			0
$906$			1177.36i			1.29951i
$907$		−	174.898i		−	0.192832i	−0.995341	−	0.0964158i	$-0.969262\pi$
$907$		−	174.898i		−	0.192832i	0.995341	−	0.0964158i	$-0.0307378\pi$
$908$			1001.85i			1.10336i
$909$	−471.296			−0.518478
$910$		0			0
$911$		−	475.064i		−	0.521476i	−0.965410	−	0.260738i	$-0.916034\pi$
$911$		−	475.064i		−	0.521476i	0.965410	−	0.260738i	$-0.0839658\pi$
$912$	101.223	−	638.833i	0.110990	−	0.700475i
$913$	−1265.00			−1.38555
$914$		−	2578.96i		−	2.82162i
$915$		0			0
$916$	−1043.18			−1.13884
$917$	2048.70			2.23413
$918$	−920.254			−1.00246
$919$	456.862			0.497130			0.248565	−	0.968615i	$-0.420041\pi$
$919$	456.862			0.497130			0.248565	+	0.968615i	$0.420041\pi$
$920$		0			0
$921$	987.714			1.07244
$922$		−	483.098i		−	0.523967i
$923$	−1542.73			−1.67143
$924$		−	810.820i		−	0.877511i
$925$		0			0
$926$		−	591.991i		−	0.639299i
$927$			24.1721i			0.0260756i
$928$	−477.912			−0.514991
$929$	714.272			0.768861			0.384430	−	0.923154i	$-0.374398\pi$
$929$	714.272			0.768861			0.384430	+	0.923154i	$0.374398\pi$
$930$		0			0
$931$	651.858	+	103.287i	0.700170	+	0.110942i
$932$	1423.20			1.52704
$933$			391.725i			0.419855i
$934$			1364.45i			1.46087i
$935$		0			0
$936$	14.9858			0.0160105
$937$	−711.794			−0.759652			−0.379826	−	0.925058i	$-0.624016\pi$
$937$	−711.794			−0.759652			−0.379826	+	0.925058i	$0.624016\pi$
$938$	991.520			1.05706
$939$		−	300.793i		−	0.320334i
$940$		0			0
$941$			1055.43i			1.12161i	0.827950	+	0.560803i	$0.189507\pi$
$941$			1055.43i			1.12161i	−0.827950	+	0.560803i	$0.810493\pi$
$942$	−1212.63			−1.28729
$943$		−	889.520i		−	0.943287i
$944$			99.5221i			0.105426i
$945$		0			0
$946$		−	1294.48i		−	1.36837i
$947$	611.188			0.645394			0.322697	−	0.946502i	$-0.395411\pi$
$947$	611.188			0.645394			0.322697	+	0.946502i	$0.395411\pi$
$948$	−1230.91			−1.29843
$949$		−	228.324i		−	0.240595i
$950$		0			0
$951$	1315.10			1.38286
$952$		−	29.4365i		−	0.0309207i
$953$		−	847.554i		−	0.889354i	−0.895691	−	0.444677i	$-0.853318\pi$
$953$		−	847.554i		−	0.889354i	0.895691	−	0.444677i	$-0.146682\pi$
$954$	1153.51			1.20913
$955$		0			0
$956$	−0.196342			−0.000205379
$957$	226.889			0.237083
$958$		−	2027.89i		−	2.11679i
$959$	−57.1673			−0.0596114
$960$		0			0
$961$	−1775.07			−1.84711
$962$			368.485i			0.383040i
$963$			695.991i			0.722732i
$964$			1733.98i			1.79873i
$965$		0			0
$966$	1187.05			1.22883
$967$	293.882			0.303911			0.151955	−	0.988387i	$-0.451443\pi$
$967$	293.882			0.303911			0.151955	+	0.988387i	$0.451443\pi$
$968$			6.65446i			0.00687444i
$969$	−72.6711	+	458.638i	−0.0749960	+	0.473311i
$970$		0			0
$971$		−	1289.96i		−	1.32849i	−0.747517	−	0.664243i	$-0.768754\pi$
$971$		−	1289.96i		−	1.32849i	0.747517	−	0.664243i	$-0.231246\pi$
$972$		−	842.127i		−	0.866386i
$973$	−1875.62			−1.92767
$974$	−97.9645			−0.100580
$975$		0			0
$976$	−231.591			−0.237286
$977$			362.429i			0.370961i	0.982648	+	0.185481i	$0.0593842\pi$
$977$			362.429i			0.370961i	−0.982648	+	0.185481i	$0.940616\pi$
$978$	−1067.26			−1.09127
$979$		−	195.922i		−	0.200124i
$980$		0			0
$981$			432.519i			0.440896i
$982$			1029.22i			1.04808i
$983$		−	236.553i		−	0.240644i	−0.992735	−	0.120322i	$-0.961607\pi$
$983$		−	236.553i		−	0.240644i	0.992735	−	0.120322i	$-0.0383927\pi$
$984$			26.7677i			0.0272030i
$985$		0			0
$986$	334.438			0.339187
$987$		−	84.3776i		−	0.0854890i
$988$	150.294	−	948.528i	0.152119	−	0.960048i
$989$	959.381			0.970052
$990$		0			0
$991$		−	328.650i		−	0.331635i	−0.986156	−	0.165817i	$-0.946974\pi$
$991$		−	328.650i		−	0.331635i	0.986156	−	0.165817i	$-0.0530262\pi$
$992$	−2380.54			−2.39974
$993$	416.118			0.419051
$994$	−3260.06			−3.27973
$995$		0			0
$996$			1145.47i			1.15007i
$997$	537.051			0.538667			0.269333	−	0.963047i	$-0.413197\pi$
$997$	537.051			0.538667			0.269333	+	0.963047i	$0.413197\pi$
$998$		−	540.718i		−	0.541801i
$999$	303.520			0.303824

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.3.c.g.151.11		12
5.2	odd	4		475.3.d.c.474.3		24
5.3	odd	4		475.3.d.c.474.22		24
5.4	even	2		95.3.c.a.56.2	✓	12
15.14	odd	2		855.3.e.a.721.11		12
19.18	odd	2	inner	475.3.c.g.151.2		12
20.19	odd	2		1520.3.h.a.721.8		12
95.18	even	4		475.3.d.c.474.4		24
95.37	even	4		475.3.d.c.474.21		24
95.94	odd	2		95.3.c.a.56.11	yes	12
285.284	even	2		855.3.e.a.721.2		12
380.379	even	2		1520.3.h.a.721.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.3.c.a.56.2	✓	12	5.4	even	2
95.3.c.a.56.11	yes	12	95.94	odd	2
475.3.c.g.151.2		12	19.18	odd	2	inner
475.3.c.g.151.11		12	1.1	even	1	trivial
475.3.d.c.474.3		24	5.2	odd	4
475.3.d.c.474.4		24	95.18	even	4
475.3.d.c.474.21		24	95.37	even	4
475.3.d.c.474.22		24	5.3	odd	4
855.3.e.a.721.2		12	285.284	even	2
855.3.e.a.721.11		12	15.14	odd	2
1520.3.h.a.721.5		12	380.379	even	2
1520.3.h.a.721.8		12	20.19	odd	2

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	475.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.84623i q^{2} +2.18419i q^{3} -4.10101 q^{4} -6.21669 q^{6} +9.15076 q^{7} -0.287487i q^{8} +4.22932 q^{9} +O(q^{10})\)	\(q+2.84623i q^{2} +2.18419i q^{3} -4.10101 q^{4} -6.21669 q^{6} +9.15076 q^{7} -0.287487i q^{8} +4.22932 q^{9} +9.89207 q^{11} -8.95737i q^{12} +12.3251i q^{13} +26.0451i q^{14} -15.5858 q^{16} +11.1895 q^{17} +12.0376i q^{18} +(18.7659 + 2.97345i) q^{19} +19.9870i q^{21} +28.1551i q^{22} -20.8666 q^{23} +0.627927 q^{24} -35.0800 q^{26} +28.8953i q^{27} -37.5273 q^{28} -10.5011i q^{29} -52.3075i q^{31} -45.5106i q^{32} +21.6061i q^{33} +31.8479i q^{34} -17.3445 q^{36} -10.5041i q^{37} +(-8.46312 + 53.4120i) q^{38} -26.9203 q^{39} +42.6288i q^{41} -56.8874 q^{42} -45.9768 q^{43} -40.5674 q^{44} -59.3912i q^{46} -4.22163 q^{47} -34.0423i q^{48} +34.7363 q^{49} +24.4400i q^{51} -50.5453i q^{52} -95.8254i q^{53} -82.2427 q^{54} -2.63073i q^{56} +(-6.49458 + 40.9882i) q^{57} +29.8886 q^{58} -6.38544i q^{59} +14.8591 q^{61} +148.879 q^{62} +38.7015 q^{63} +67.1904 q^{64} -61.4960 q^{66} -38.0693i q^{67} -45.8882 q^{68} -45.5767i q^{69} +125.169i q^{71} -1.21588i q^{72} -18.5252 q^{73} +29.8971 q^{74} +(-76.9590 - 12.1941i) q^{76} +90.5199 q^{77} -76.6214i q^{78} -137.419i q^{79} -25.0489 q^{81} -121.331 q^{82} -127.881 q^{83} -81.9667i q^{84} -130.860i q^{86} +22.9364 q^{87} -2.84385i q^{88} -19.8059i q^{89} +112.784i q^{91} +85.5743 q^{92} +114.249 q^{93} -12.0157i q^{94} +99.4037 q^{96} -42.4473i q^{97} +98.8675i q^{98} +41.8368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 28 q^{6} - 20 q^{7} - 48 q^{9}+O(q^{10}) \) 12 * q - 12 * q^4 - 28 * q^6 - 20 * q^7 - 48 * q^9	\( 12 q - 12 q^{4} - 28 q^{6} - 20 q^{7} - 48 q^{9} + 32 q^{11} - 44 q^{16} + 44 q^{17} + 8 q^{19} - 36 q^{23} + 100 q^{24} + 108 q^{26} + 36 q^{28} - 80 q^{36} + 44 q^{38} + 76 q^{39} - 100 q^{42} - 320 q^{43} - 256 q^{44} + 56 q^{47} + 72 q^{49} - 76 q^{54} - 60 q^{57} - 68 q^{58} - 296 q^{61} + 376 q^{62} + 96 q^{63} + 188 q^{64} + 152 q^{66} + 340 q^{68} + 244 q^{73} + 136 q^{74} + 248 q^{76} + 200 q^{77} - 372 q^{81} - 424 q^{82} + 160 q^{83} - 444 q^{87} - 716 q^{92} - 296 q^{93} - 44 q^{96} - 312 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 - 28 * q^6 - 20 * q^7 - 48 * q^9 + 32 * q^11 - 44 * q^16 + 44 * q^17 + 8 * q^19 - 36 * q^23 + 100 * q^24 + 108 * q^26 + 36 * q^28 - 80 * q^36 + 44 * q^38 + 76 * q^39 - 100 * q^42 - 320 * q^43 - 256 * q^44 + 56 * q^47 + 72 * q^49 - 76 * q^54 - 60 * q^57 - 68 * q^58 - 296 * q^61 + 376 * q^62 + 96 * q^63 + 188 * q^64 + 152 * q^66 + 340 * q^68 + 244 * q^73 + 136 * q^74 + 248 * q^76 + 200 * q^77 - 372 * q^81 - 424 * q^82 + 160 * q^83 - 444 * q^87 - 716 * q^92 - 296 * q^93 - 44 * q^96 - 312 * q^99

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