LMFDB - Embedded newform 325.4.c.e.51.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,4,Mod(51,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.51"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	325.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.1756207519$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 84x^{12} + 2674x^{10} + 40048x^{8} + 278769x^{6} + 727552x^{4} + 339456x^{2} + 9216 $ x^14 + 84x^12 + 2674x^10 + 40048x^8 + 278769x^6 + 727552x^4 + 339456x^2 + 9216
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.1
Root			$-5.37688i$ of defining polynomial
Character	$\chi$	$=$	325.51
Dual form			325.4.c.e.51.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.37688i q^{2} +0.936724 q^{3} -20.9108 q^{4} -5.03665i q^{6} +0.201771i q^{7} +69.4197i q^{8} -26.1225 q^{9} +10.4218i q^{11} -19.5876 q^{12} +(-39.9303 - 24.5473i) q^{13} +1.08490 q^{14} +205.975 q^{16} +54.7775 q^{17} +140.458i q^{18} +129.099i q^{19} +0.189004i q^{21} +56.0369 q^{22} +175.846 q^{23} +65.0272i q^{24} +(-131.988 + 214.700i) q^{26} -49.7612 q^{27} -4.21919i q^{28} +107.045 q^{29} +22.2028i q^{31} -552.144i q^{32} +9.76239i q^{33} -294.532i q^{34} +546.243 q^{36} -205.591i q^{37} +694.150 q^{38} +(-37.4037 - 22.9940i) q^{39} +285.238i q^{41} +1.01625 q^{42} -321.835 q^{43} -217.929i q^{44} -945.503i q^{46} +379.907i q^{47} +192.942 q^{48} +342.959 q^{49} +51.3115 q^{51} +(834.975 + 513.303i) q^{52} -506.192 q^{53} +267.560i q^{54} -14.0069 q^{56} +120.930i q^{57} -575.566i q^{58} +678.186i q^{59} -186.634 q^{61} +119.382 q^{62} -5.27077i q^{63} -1321.01 q^{64} +52.4911 q^{66} +925.768i q^{67} -1145.44 q^{68} +164.719 q^{69} -376.232i q^{71} -1813.42i q^{72} -671.223i q^{73} -1105.44 q^{74} -2699.57i q^{76} -2.10282 q^{77} +(-123.636 + 201.115i) q^{78} -593.491 q^{79} +658.696 q^{81} +1533.69 q^{82} +425.750i q^{83} -3.95222i q^{84} +1730.47i q^{86} +100.271 q^{87} -723.481 q^{88} +141.676i q^{89} +(4.95293 - 8.05678i) q^{91} -3677.08 q^{92} +20.7979i q^{93} +2042.71 q^{94} -517.206i q^{96} +551.467i q^{97} -1844.05i q^{98} -272.245i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 56 q^{4} + 158 q^{9} + 108 q^{12} + 4 q^{13} - 152 q^{14} + 280 q^{16} + 100 q^{17} - 648 q^{22} + 532 q^{23} - 344 q^{26} + 48 q^{27} + 588 q^{29} + 496 q^{36} - 148 q^{38} - 260 q^{39} + 620 q^{42}+ \cdots + 2656 q^{94}+O(q^{100}) $ 14 * q - 56 * q^4 + 158 * q^9 + 108 * q^12 + 4 * q^13 - 152 * q^14 + 280 * q^16 + 100 * q^17 - 648 * q^22 + 532 * q^23 - 344 * q^26 + 48 * q^27 + 588 * q^29 + 496 * q^36 - 148 * q^38 - 260 * q^39 + 620 * q^42 - 728 * q^43 + 2008 * q^48 - 1302 * q^49 + 176 * q^51 + 528 * q^52 - 1040 * q^53 + 512 * q^56 - 1460 * q^61 - 2964 * q^62 + 1296 * q^64 - 600 * q^66 - 1604 * q^68 + 4160 * q^69 - 5928 * q^74 + 3568 * q^77 - 2560 * q^78 - 1024 * q^79 - 2890 * q^81 + 6660 * q^82 - 5256 * q^87 - 1132 * q^88 + 916 * q^91 - 6044 * q^92 + 2656 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	5.37688i		−	1.90101i	−0.310705	−	0.950506i	$-0.600565\pi$
$2$		−	5.37688i		−	1.90101i	0.310705	−	0.950506i	$-0.399435\pi$
$3$	0.936724			0.180273			0.0901363	−	0.995929i	$-0.471270\pi$
$3$	0.936724			0.180273			0.0901363	+	0.995929i	$0.471270\pi$
$4$	−20.9108			−2.61385
$5$		0			0
$5$		0			0
$6$		−	5.03665i		−	0.342701i
$7$			0.201771i			0.0108946i	0.999985	+	0.00544731i	$0.00173394\pi$
$7$			0.201771i			0.0108946i	−0.999985	+	0.00544731i	$0.998266\pi$
$8$			69.4197i			3.06795i
$9$	−26.1225			−0.967502
$10$		0			0
$11$			10.4218i			0.285664i	0.989747	+	0.142832i	$0.0456208\pi$
$11$			10.4218i			0.285664i	−0.989747	+	0.142832i	$0.954379\pi$
$12$	−19.5876			−0.471206
$13$	−39.9303	−	24.5473i	−0.851898	−	0.523707i
$13$	−39.9303	−	24.5473i	−0.851898	−	0.523707i
$14$	1.08490			0.0207108
$15$		0			0
$16$	205.975			3.21836
$17$	54.7775			0.781500			0.390750	−	0.920497i	$-0.372216\pi$
$17$	54.7775			0.781500			0.390750	+	0.920497i	$0.372216\pi$
$18$			140.458i			1.83923i
$19$			129.099i			1.55881i	0.626521	+	0.779405i	$0.284478\pi$
$19$			129.099i			1.55881i	−0.626521	+	0.779405i	$0.715522\pi$
$20$		0			0
$21$			0.189004i			0.00196400i
$22$	56.0369			0.543050
$23$	175.846			1.59419			0.797097	−	0.603852i	$-0.206368\pi$
$23$	175.846			1.59419			0.797097	+	0.603852i	$0.206368\pi$
$24$			65.0272i			0.553067i
$25$		0			0
$26$	−131.988	+	214.700i	−0.995574	+	1.61947i
$27$	−49.7612			−0.354687
$28$		−	4.21919i		−	0.0284769i
$29$	107.045			0.685438			0.342719	−	0.939438i	$-0.388652\pi$
$29$	107.045			0.685438			0.342719	+	0.939438i	$0.388652\pi$
$30$		0			0
$31$			22.2028i			0.128637i	0.997929	+	0.0643184i	$0.0204873\pi$
$31$			22.2028i			0.128637i	−0.997929	+	0.0643184i	$0.979513\pi$
$32$		−	552.144i		−	3.05019i
$33$			9.76239i			0.0514974i
$34$		−	294.532i		−	1.48564i
$35$		0			0
$36$	546.243			2.52890
$37$		−	205.591i		−	0.913486i	−0.889599	−	0.456743i	$-0.849016\pi$
$37$		−	205.591i		−	0.913486i	0.889599	−	0.456743i	$-0.150984\pi$
$38$	694.150			2.96332
$39$	−37.4037	−	22.9940i	−0.153574	−	0.0944101i
$40$		0			0
$41$			285.238i			1.08651i	0.839569	+	0.543253i	$0.182807\pi$
$41$			285.238i			1.08651i	−0.839569	+	0.543253i	$0.817193\pi$
$42$	1.01625			0.00373359
$43$	−321.835			−1.14138			−0.570690	−	0.821166i	$-0.693324\pi$
$43$	−321.835			−1.14138			−0.570690	+	0.821166i	$0.693324\pi$
$44$		−	217.929i		−	0.746682i
$45$		0			0
$46$		−	945.503i		−	3.03058i
$47$			379.907i			1.17905i	0.807752	+	0.589523i	$0.200684\pi$
$47$			379.907i			1.17905i	−0.807752	+	0.589523i	$0.799316\pi$
$48$	192.942			0.580182
$49$	342.959			0.999881
$50$		0			0
$51$	51.3115			0.140883
$52$	834.975	+	513.303i	2.22673	+	1.36889i
$53$	−506.192			−1.31190			−0.655951	−	0.754804i	$-0.727732\pi$
$53$	−506.192			−1.31190			−0.655951	+	0.754804i	$0.727732\pi$
$54$			267.560i			0.674264i
$55$		0			0
$56$	−14.0069			−0.0334241
$57$			120.930i			0.281011i
$58$		−	575.566i		−	1.30303i
$59$			678.186i			1.49648i	0.663428	+	0.748240i	$0.269101\pi$
$59$			678.186i			1.49648i	−0.663428	+	0.748240i	$0.730899\pi$
$60$		0			0
$61$	−186.634			−0.391738			−0.195869	−	0.980630i	$-0.562753\pi$
$61$	−186.634			−0.391738			−0.195869	+	0.980630i	$0.562753\pi$
$62$	119.382			0.244540
$63$		−	5.27077i		−	0.0105406i
$64$	−1321.01			−2.58009
$65$		0			0
$66$	52.4911			0.0978972
$67$			925.768i			1.68807i	0.536289	+	0.844034i	$0.319826\pi$
$67$			925.768i			1.68807i	−0.536289	+	0.844034i	$0.680174\pi$
$68$	−1145.44			−2.04272
$69$	164.719			0.287390
$70$		0			0
$71$		−	376.232i		−	0.628881i	−0.949277	−	0.314441i	$-0.898183\pi$
$71$		−	376.232i		−	0.628881i	0.949277	−	0.314441i	$-0.101817\pi$
$72$		−	1813.42i		−	2.96824i
$73$		−	671.223i		−	1.07617i	−0.842889	−	0.538087i	$-0.819147\pi$
$73$		−	671.223i		−	1.07617i	0.842889	−	0.538087i	$-0.180853\pi$
$74$	−1105.44			−1.73655
$75$		0			0
$76$		−	2699.57i		−	4.07449i
$77$	−2.10282			−0.00311220
$78$	−123.636	+	201.115i	−0.179475	+	0.291946i
$79$	−593.491			−0.845227			−0.422613	−	0.906310i	$-0.638887\pi$
$79$	−593.491			−0.845227			−0.422613	+	0.906310i	$0.638887\pi$
$80$		0			0
$81$	658.696			0.903561
$82$	1533.69			2.06546
$83$			425.750i			0.563037i	0.959556	+	0.281519i	$0.0908381\pi$
$83$			425.750i			0.563037i	−0.959556	+	0.281519i	$0.909162\pi$
$84$		−	3.95222i		−	0.00513360i
$85$		0			0
$86$			1730.47i			2.16978i
$87$	100.271			0.123566
$88$	−723.481			−0.876401
$89$			141.676i			0.168737i	0.996435	+	0.0843685i	$0.0268873\pi$
$89$			141.676i			0.168737i	−0.996435	+	0.0843685i	$0.973113\pi$
$90$		0			0
$91$	4.95293	−	8.05678i	0.00570559	−	0.00928110i
$92$	−3677.08			−4.16698
$93$			20.7979i			0.0231897i
$94$	2042.71			2.24138
$95$		0			0
$96$		−	517.206i		−	0.549866i
$97$			551.467i			0.577247i	0.957443	+	0.288623i	$0.0931976\pi$
$97$			551.467i			0.577247i	−0.957443	+	0.288623i	$0.906802\pi$
$98$		−	1844.05i		−	1.90079i
$99$		−	272.245i		−	0.276380i
$100$		0			0
$101$	−1386.39			−1.36585			−0.682924	−	0.730489i	$-0.739292\pi$
$101$	−1386.39			−1.36585			−0.682924	+	0.730489i	$0.739292\pi$
$102$		−	275.895i		−	0.267821i
$103$	−1156.61			−1.10645			−0.553223	−	0.833033i	$-0.686602\pi$
$103$	−1156.61			−1.10645			−0.553223	+	0.833033i	$0.686602\pi$
$104$	1704.07	−	2771.95i	1.60671	−	2.61358i
$105$		0			0
$106$			2721.73i			2.49394i
$107$	1145.31			1.03478			0.517390	−	0.855750i	$-0.326904\pi$
$107$	1145.31			1.03478			0.517390	+	0.855750i	$0.326904\pi$
$108$	1040.55			0.927098
$109$			2033.95i			1.78731i	0.448750	+	0.893657i	$0.351869\pi$
$109$			2033.95i			1.78731i	−0.448750	+	0.893657i	$0.648131\pi$
$110$		0			0
$111$		−	192.582i		−	0.164677i
$112$			41.5598i			0.0350628i
$113$	1218.91			1.01474			0.507370	−	0.861728i	$-0.330618\pi$
$113$	1218.91			1.01474			0.507370	+	0.861728i	$0.330618\pi$
$114$	650.227			0.534205
$115$		0			0
$116$	−2238.39			−1.79163
$117$	1043.08	+	641.238i	0.824213	+	0.506687i
$118$	3646.52			2.84483
$119$			11.0525i			0.00851414i
$120$		0			0
$121$	1222.39			0.918396
$122$			1003.51i			0.744699i
$123$			267.190i			0.195867i
$124$		−	464.278i		−	0.336237i
$125$		0			0
$126$	−28.3403			−0.0200377
$127$	1219.03			0.851746			0.425873	−	0.904783i	$-0.359967\pi$
$127$	1219.03			0.851746			0.425873	+	0.904783i	$0.359967\pi$
$128$			2685.75i			1.85460i
$129$	−301.470			−0.205760
$130$		0			0
$131$	807.392			0.538490			0.269245	−	0.963072i	$-0.413226\pi$
$131$	807.392			0.538490			0.269245	+	0.963072i	$0.413226\pi$
$132$		−	204.139i		−	0.134606i
$133$	−26.0485			−0.0169826
$134$	4977.74			3.20904
$135$		0			0
$136$			3802.64i			2.39760i
$137$		−	24.8642i		−	0.0155057i	−0.999970	−	0.00775287i	$-0.997532\pi$
$137$		−	24.8642i		−	0.0155057i	0.999970	−	0.00775287i	$-0.00246784\pi$
$138$		−	885.676i		−	0.546331i
$139$	−1351.45			−0.824665			−0.412332	−	0.911033i	$-0.635286\pi$
$139$	−1351.45			−0.824665			−0.412332	+	0.911033i	$0.635286\pi$
$140$		0			0
$141$			355.868i			0.212550i
$142$	−2022.96			−1.19551
$143$	255.828	−	416.147i	0.149604	−	0.243357i
$144$	−5380.59			−3.11377
$145$		0			0
$146$	−3609.08			−2.04582
$147$	321.258			0.180251
$148$			4299.08i			2.38772i
$149$			318.875i			0.175324i	0.996150	+	0.0876621i	$0.0279396\pi$
$149$			318.875i			0.175324i	−0.996150	+	0.0876621i	$0.972060\pi$
$150$		0			0
$151$			472.671i			0.254738i	0.991855	+	0.127369i	$0.0406533\pi$
$151$			472.671i			0.254738i	−0.991855	+	0.127369i	$0.959347\pi$
$152$	−8962.03			−4.78234
$153$	−1430.93			−0.756103
$154$			11.3066i			0.00591632i
$155$		0			0
$156$	782.141	+	480.824i	0.401419	+	0.246774i
$157$	−2157.92			−1.09695			−0.548474	−	0.836168i	$-0.684791\pi$
$157$	−2157.92			−1.09695			−0.548474	+	0.836168i	$0.684791\pi$
$158$			3191.13i			1.60679i
$159$	−474.162			−0.236500
$160$		0			0
$161$			35.4807i			0.0173681i
$162$		−	3541.73i		−	1.71768i
$163$			2482.96i			1.19313i	0.802564	+	0.596567i	$0.203469\pi$
$163$			2482.96i			1.19313i	−0.802564	+	0.596567i	$0.796531\pi$
$164$		−	5964.56i		−	2.83996i
$165$		0			0
$166$	2289.20			1.07034
$167$			1563.31i			0.724389i	0.932103	+	0.362194i	$0.117972\pi$
$167$			1563.31i			0.724389i	−0.932103	+	0.362194i	$0.882028\pi$
$168$	−13.1206			−0.00602545
$169$	991.862	+	1960.36i	0.451462	+	0.892290i
$170$		0			0
$171$		−	3372.40i		−	1.50815i
$172$	6729.82			2.98339
$173$	−2785.12			−1.22398			−0.611991	−	0.790865i	$-0.709631\pi$
$173$	−2785.12			−1.22398			−0.611991	+	0.790865i	$0.709631\pi$
$174$		−	539.147i		−	0.234900i
$175$		0			0
$176$			2146.64i			0.919368i
$177$			635.274i			0.269774i
$178$	761.772			0.320771
$179$	−3352.21			−1.39975			−0.699877	−	0.714264i	$-0.746762\pi$
$179$	−3352.21			−1.39975			−0.699877	+	0.714264i	$0.746762\pi$
$180$		0			0
$181$	3474.25			1.42674			0.713368	−	0.700789i	$-0.247169\pi$
$181$	3474.25			1.42674			0.713368	+	0.700789i	$0.247169\pi$
$182$	−43.3203	−	26.6313i	−0.0176435	−	0.0108464i
$183$	−174.825			−0.0706197
$184$			12207.2i			4.89090i
$185$		0			0
$186$	111.828			0.0440839
$187$			570.882i			0.223246i
$188$		−	7944.16i		−	3.08185i
$189$		−	10.0404i		−	0.00386418i
$190$		0			0
$191$	−823.112			−0.311824			−0.155912	−	0.987771i	$-0.549832\pi$
$191$	−823.112			−0.311824			−0.155912	+	0.987771i	$0.549832\pi$
$192$	−1237.42			−0.465121
$193$			186.060i			0.0693933i	0.999398	+	0.0346967i	$0.0110465\pi$
$193$			186.060i			0.0693933i	−0.999398	+	0.0346967i	$0.988953\pi$
$194$	2965.17			1.09735
$195$		0			0
$196$	−7171.55			−2.61354
$197$		−	3035.00i		−	1.09764i	−0.835942	−	0.548819i	$-0.815078\pi$
$197$		−	3035.00i		−	1.09764i	0.835942	−	0.548819i	$-0.184922\pi$
$198$	−1463.83			−0.525402
$199$	2690.11			0.958276			0.479138	−	0.877740i	$-0.340949\pi$
$199$	2690.11			0.958276			0.479138	+	0.877740i	$0.340949\pi$
$200$		0			0
$201$			867.190i			0.304313i
$202$			7454.43i			2.59650i
$203$			21.5985i			0.00746758i
$204$	−1072.96			−0.368247
$205$		0			0
$206$			6218.93i			2.10337i
$207$	−4593.55			−1.54239
$208$	−8224.64	−	5056.12i	−2.74171	−	1.68548i
$209$	−1345.45			−0.445295
$210$		0			0
$211$	1411.57			0.460554			0.230277	−	0.973125i	$-0.426037\pi$
$211$	1411.57			0.460554			0.230277	+	0.973125i	$0.426037\pi$
$212$	10584.9			3.42911
$213$		−	352.426i		−	0.113370i
$214$		−	6158.20i		−	1.96713i
$215$		0			0
$216$		−	3454.41i		−	1.08816i
$217$	−4.47988			−0.00140145
$218$	10936.3			3.39771
$219$		−	628.751i		−	0.194005i
$220$		0			0
$221$	−2187.28	−	1344.64i	−0.665759	−	0.409277i
$222$	−1035.49			−0.313052
$223$		−	474.236i		−	0.142409i	−0.997462	−	0.0712044i	$-0.977316\pi$
$223$		−	474.236i		−	0.142409i	0.997462	−	0.0712044i	$-0.0226843\pi$
$224$	111.407			0.0332307
$225$		0			0
$226$		−	6553.94i		−	1.92903i
$227$		−	1561.74i		−	0.456635i	−0.973587	−	0.228318i	$-0.926678\pi$
$227$		−	1561.74i		−	0.456635i	0.973587	−	0.228318i	$-0.0733225\pi$
$228$		−	2528.75i		−	0.734520i
$229$		−	2928.82i		−	0.845162i	−0.906325	−	0.422581i	$-0.861124\pi$
$229$		−	2928.82i		−	0.845162i	0.906325	−	0.422581i	$-0.138876\pi$
$230$		0			0
$231$	−1.96977			−0.000561044
$232$			7431.01i			2.10289i
$233$	−2785.91			−0.783310			−0.391655	−	0.920112i	$-0.628097\pi$
$233$	−2785.91			−0.783310			−0.391655	+	0.920112i	$0.628097\pi$
$234$	3447.85	−	5608.52i	0.963219	−	1.56684i
$235$		0			0
$236$		−	14181.4i		−	3.91157i
$237$	−555.937			−0.152371
$238$	59.4280			0.0161855
$239$			2488.61i			0.673534i	0.941588	+	0.336767i	$0.109333\pi$
$239$			2488.61i			0.673534i	−0.941588	+	0.336767i	$0.890667\pi$
$240$		0			0
$241$			4840.64i			1.29383i	0.762562	+	0.646915i	$0.223941\pi$
$241$			4840.64i			1.29383i	−0.762562	+	0.646915i	$0.776059\pi$
$242$		−	6572.61i		−	1.74588i
$243$	1960.57			0.517574
$244$	3902.66			1.02394
$245$		0			0
$246$	1436.65			0.372346
$247$	3169.03	−	5154.97i	0.816359	−	1.32795i
$248$	−1541.31			−0.394651
$249$			398.810i			0.101500i
$250$		0			0
$251$	8.77945			0.00220779			0.00110389	−	0.999999i	$-0.499649\pi$
$251$	8.77945			0.00220779			0.00110389	+	0.999999i	$0.499649\pi$
$252$			110.216i			0.0275514i
$253$			1832.64i			0.455403i
$254$		−	6554.59i		−	1.61918i
$255$		0			0
$256$	3872.87			0.945525
$257$	−1600.04			−0.388357			−0.194179	−	0.980966i	$-0.562204\pi$
$257$	−1600.04			−0.388357			−0.194179	+	0.980966i	$0.562204\pi$
$258$			1620.97i			0.391152i
$259$	41.4824			0.00995208
$260$		0			0
$261$	−2796.28			−0.663162
$262$		−	4341.25i		−	1.02368i
$263$	3050.24			0.715155			0.357578	−	0.933883i	$-0.383603\pi$
$263$	3050.24			0.715155			0.357578	+	0.933883i	$0.383603\pi$
$264$	−677.702			−0.157991
$265$		0			0
$266$			140.059i			0.0322842i
$267$			132.711i			0.0304187i
$268$		−	19358.6i		−	4.41236i
$269$	−6168.58			−1.39816			−0.699080	−	0.715043i	$-0.746407\pi$
$269$	−6168.58			−1.39816			−0.699080	+	0.715043i	$0.746407\pi$
$270$		0			0
$271$		−	2424.93i		−	0.543556i	−0.962360	−	0.271778i	$-0.912388\pi$
$271$		−	2424.93i		−	0.543556i	0.962360	−	0.271778i	$-0.0876117\pi$
$272$	11282.8			2.51515
$273$	4.63953	−	7.54699i	0.00102856	−	0.00167313i
$274$	−133.691			−0.0294766
$275$		0			0
$276$	−3444.41			−0.751193
$277$	−4442.72			−0.963673			−0.481836	−	0.876261i	$-0.660030\pi$
$277$	−4442.72			−0.963673			−0.481836	+	0.876261i	$0.660030\pi$
$278$			7266.57i			1.56770i
$279$		−	579.993i		−	0.124456i
$280$		0			0
$281$		−	357.622i		−	0.0759215i	−0.999279	−	0.0379608i	$-0.987914\pi$
$281$		−	357.622i		−	0.0759215i	0.999279	−	0.0379608i	$-0.0120862\pi$
$282$	1913.46			0.404060
$283$	−1573.71			−0.330556			−0.165278	−	0.986247i	$-0.552852\pi$
$283$	−1573.71			−0.330556			−0.165278	+	0.986247i	$0.552852\pi$
$284$			7867.32i			1.64380i
$285$		0			0
$286$	−2237.57	−	1375.55i	−0.462624	−	0.284399i
$287$	−57.5528			−0.0118371
$288$			14423.4i			2.95107i
$289$	−1912.42			−0.389257
$290$		0			0
$291$			516.572i			0.104062i
$292$			14035.8i			2.81296i
$293$		−	4370.32i		−	0.871389i	−0.900095	−	0.435694i	$-0.856503\pi$
$293$		−	4370.32i		−	0.871389i	0.900095	−	0.435694i	$-0.143497\pi$
$294$		−	1727.37i		−	0.342660i
$295$		0			0
$296$	14272.1			2.80253
$297$		−	518.603i		−	0.101321i
$298$	1714.55			0.333293
$299$	−7021.59	−	4316.54i	−1.35809	−	0.834890i
$300$		0			0
$301$		−	64.9369i		−	0.0124349i
$302$	2541.50			0.484260
$303$	−1298.66			−0.246225
$304$			26591.2i			5.01680i
$305$		0			0
$306$			7693.93i			1.43736i
$307$		−	3998.97i		−	0.743430i	−0.928347	−	0.371715i	$-0.878770\pi$
$307$		−	3998.97i		−	0.743430i	0.928347	−	0.371715i	$-0.121230\pi$
$308$	43.9717			0.00813481
$309$	−1083.42			−0.199462
$310$		0			0
$311$	2116.08			0.385825			0.192913	−	0.981216i	$-0.438207\pi$
$311$	2116.08			0.385825			0.192913	+	0.981216i	$0.438207\pi$
$312$	1596.24	−	2596.56i	0.289645	−	0.471157i
$313$	−1729.75			−0.312368			−0.156184	−	0.987728i	$-0.549919\pi$
$313$	−1729.75			−0.312368			−0.156184	+	0.987728i	$0.549919\pi$
$314$			11602.9i			2.08531i
$315$		0			0
$316$	12410.4			2.20930
$317$		−	4636.84i		−	0.821548i	−0.911737	−	0.410774i	$-0.865259\pi$
$317$		−	4636.84i		−	0.821548i	0.911737	−	0.410774i	$-0.134741\pi$
$318$			2549.51i			0.449590i
$319$			1115.60i			0.195805i
$320$		0			0
$321$	1072.84			0.186543
$322$	190.775			0.0330170
$323$			7071.73i			1.21821i
$324$	−13773.9			−2.36177
$325$		0			0
$326$	13350.6			2.26816
$327$			1905.25i			0.322204i
$328$	−19801.2			−3.33334
$329$	−76.6543			−0.0128453
$330$		0			0
$331$		−	2278.33i		−	0.378333i	−0.981945	−	0.189167i	$-0.939421\pi$
$331$		−	2278.33i		−	0.378333i	0.981945	−	0.189167i	$-0.0605787\pi$
$332$		−	8902.76i		−	1.47169i
$333$			5370.57i			0.883800i
$334$	8405.75			1.37707
$335$		0			0
$336$			38.9301i			0.00632086i
$337$	419.703			0.0678418			0.0339209	−	0.999425i	$-0.489201\pi$
$337$	419.703			0.0678418			0.0339209	+	0.999425i	$0.489201\pi$
$338$	10540.6	−	5333.12i	1.69626	−	0.858235i
$339$	1141.79			0.182930
$340$		0			0
$341$	−231.394			−0.0367469
$342$	−18133.0			−2.86701
$343$			138.407i			0.0217879i
$344$		−	22341.7i		−	3.50169i
$345$		0			0
$346$			14975.3i			2.32681i
$347$	495.311			0.0766273			0.0383137	−	0.999266i	$-0.487801\pi$
$347$	495.311			0.0766273			0.0383137	+	0.999266i	$0.487801\pi$
$348$	−2096.75			−0.322982
$349$		−	4453.77i		−	0.683109i	−0.939862	−	0.341554i	$-0.889047\pi$
$349$		−	4453.77i		−	0.683109i	0.939862	−	0.341554i	$-0.110953\pi$
$350$		0			0
$351$	1986.98	+	1221.50i	0.302157	+	0.185752i
$352$	5754.35			0.871329
$353$			11893.7i			1.79330i	0.442736	+	0.896652i	$0.354008\pi$
$353$			11893.7i			1.79330i	−0.442736	+	0.896652i	$0.645992\pi$
$354$	3415.79			0.512845
$355$		0			0
$356$		−	2962.55i		−	0.441053i
$357$			10.3532i			0.00153487i
$358$			18024.4i			2.66095i
$359$		−	5141.43i		−	0.755861i	−0.925834	−	0.377931i	$-0.876636\pi$
$359$		−	5141.43i		−	0.755861i	0.925834	−	0.377931i	$-0.123364\pi$
$360$		0			0
$361$	−9807.58			−1.42989
$362$		−	18680.6i		−	2.71224i
$363$	1145.04			0.165562
$364$	−103.570	+	168.474i	−0.0149135	+	0.0242594i
$365$		0			0
$366$			940.010i			0.134249i
$367$	−9410.74			−1.33852			−0.669260	−	0.743028i	$-0.733389\pi$
$367$	−9410.74			−1.33852			−0.669260	+	0.743028i	$0.733389\pi$
$368$	36219.9			5.13068
$369$		−	7451.15i		−	1.05120i
$370$		0			0
$371$		−	102.135i		−	0.0142927i
$372$		−	434.900i		−	0.0606143i
$373$	4992.80			0.693076			0.346538	−	0.938036i	$-0.387357\pi$
$373$	4992.80			0.693076			0.346538	+	0.938036i	$0.387357\pi$
$374$	3069.56			0.424394
$375$		0			0
$376$	−26373.1			−3.61725
$377$	−4274.33	−	2627.66i	−0.583923	−	0.358969i
$378$	−53.9858			−0.00734585
$379$			2436.78i			0.330261i	0.986272	+	0.165131i	$0.0528046\pi$
$379$			2436.78i			0.330261i	−0.986272	+	0.165131i	$0.947195\pi$
$380$		0			0
$381$	1141.90			0.153547
$382$			4425.77i			0.592781i
$383$		−	10395.4i		−	1.38690i	−0.720506	−	0.693449i	$-0.756090\pi$
$383$		−	10395.4i		−	1.38690i	0.720506	−	0.693449i	$-0.243910\pi$
$384$			2515.81i			0.334334i
$385$		0			0
$386$	1000.42			0.131918
$387$	8407.14			1.10429
$388$		−	11531.6i		−	1.50884i
$389$	13872.3			1.80811			0.904056	−	0.427413i	$-0.140575\pi$
$389$	13872.3			1.80811			0.904056	+	0.427413i	$0.140575\pi$
$390$		0			0
$391$	9632.42			1.24586
$392$			23808.1i			3.06758i
$393$	756.304			0.0970750
$394$	−16318.8			−2.08662
$395$		0			0
$396$			5692.86i			0.722416i
$397$			2216.16i			0.280166i	0.990140	+	0.140083i	$0.0447369\pi$
$397$			2216.16i			0.280166i	−0.990140	+	0.140083i	$0.955263\pi$
$398$		−	14464.4i		−	1.82169i
$399$	−24.4002			−0.00306150
$400$		0			0
$401$		−	12127.7i		−	1.51030i	−0.655554	−	0.755148i	$-0.727565\pi$
$401$		−	12127.7i		−	1.51030i	0.655554	−	0.755148i	$-0.272435\pi$
$402$	4662.77			0.578502
$403$	545.018	−	886.565i	0.0673680	−	0.109585i
$404$	28990.5			3.57012
$405$		0			0
$406$	116.133			0.0141960
$407$	2142.64			0.260950
$408$			3562.03i			0.432222i
$409$			2755.96i			0.333187i	0.986026	+	0.166594i	$0.0532768\pi$
$409$			2755.96i			0.333187i	−0.986026	+	0.166594i	$0.946723\pi$
$410$		0			0
$411$		−	23.2909i		−	0.00279526i
$412$	24185.6			2.89208
$413$	−136.838			−0.0163036
$414$			24698.9i			2.93209i
$415$		0			0
$416$	−13553.6	+	22047.3i	−1.59741	+	2.59845i
$417$	−1265.94			−0.148665
$418$			7234.32i			0.846512i
$419$	417.932			0.0487287			0.0243643	−	0.999703i	$-0.492244\pi$
$419$	417.932			0.0487287			0.0243643	+	0.999703i	$0.492244\pi$
$420$		0			0
$421$			7623.50i			0.882534i	0.897376	+	0.441267i	$0.145471\pi$
$421$			7623.50i			0.882534i	−0.897376	+	0.441267i	$0.854529\pi$
$422$		−	7589.86i		−	0.875518i
$423$		−	9924.15i		−	1.14073i
$424$		−	35139.7i		−	4.02484i
$425$		0			0
$426$	−1894.95			−0.215518
$427$		−	37.6573i		−	0.00426783i
$428$	−23949.4			−2.70476
$429$	239.640	−	389.815i	0.0269695	−	0.0438705i
$430$		0			0
$431$			6348.22i			0.709473i	0.934966	+	0.354736i	$0.115429\pi$
$431$			6348.22i			0.709473i	−0.934966	+	0.354736i	$0.884571\pi$
$432$	−10249.6			−1.14151
$433$	4286.27			0.475716			0.237858	−	0.971300i	$-0.423555\pi$
$433$	4286.27			0.475716			0.237858	+	0.971300i	$0.423555\pi$
$434$			24.0878i			0.00266417i
$435$		0			0
$436$		−	42531.6i		−	4.67177i
$437$			22701.6i			2.48504i
$438$	−3380.72			−0.368806
$439$	−898.674			−0.0977024			−0.0488512	−	0.998806i	$-0.515556\pi$
$439$	−898.674			−0.0977024			−0.0488512	+	0.998806i	$0.515556\pi$
$440$		0			0
$441$	−8958.97			−0.967387
$442$	−7229.96	+	11760.8i	−0.778041	+	1.26562i
$443$	−4981.83			−0.534297			−0.267149	−	0.963655i	$-0.586081\pi$
$443$	−4981.83			−0.534297			−0.267149	+	0.963655i	$0.586081\pi$
$444$			4027.05i			0.430440i
$445$		0			0
$446$	−2549.91			−0.270721
$447$			298.698i			0.0316062i
$448$		−	266.541i		−	0.0281091i
$449$		−	4494.76i		−	0.472429i	−0.971701	−	0.236215i	$-0.924093\pi$
$449$		−	4494.76i		−	0.472429i	0.971701	−	0.236215i	$-0.0759068\pi$
$450$		0			0
$451$	−2972.71			−0.310375
$452$	−25488.4			−2.65238
$453$			442.763i			0.0459223i
$454$	−8397.27			−0.868069
$455$		0			0
$456$	−8394.95			−0.862126
$457$		−	2924.71i		−	0.299370i	−0.988734	−	0.149685i	$-0.952174\pi$
$457$		−	2924.71i		−	0.299370i	0.988734	−	0.149685i	$-0.0478259\pi$
$458$	−15747.9			−1.60666
$459$	−2725.80			−0.277188
$460$		0			0
$461$		−	10122.2i		−	1.02264i	−0.859390	−	0.511320i	$-0.829157\pi$
$461$		−	10122.2i		−	1.02264i	0.859390	−	0.511320i	$-0.170843\pi$
$462$			10.5912i			0.00106655i
$463$			5225.27i			0.524490i	0.965001	+	0.262245i	$0.0844628\pi$
$463$			5225.27i			0.524490i	−0.965001	+	0.262245i	$0.915537\pi$
$464$	22048.5			2.20598
$465$		0			0
$466$			14979.5i			1.48908i
$467$	5596.68			0.554569			0.277284	−	0.960788i	$-0.410566\pi$
$467$	5596.68			0.554569			0.277284	+	0.960788i	$0.410566\pi$
$468$	−21811.7	−	13408.8i	−2.15437	−	1.32440i
$469$	−186.793			−0.0183909
$470$		0			0
$471$	−2021.38			−0.197750
$472$	−47079.5			−4.59112
$473$		−	3354.11i		−	0.326051i
$474$			2989.21i			0.289660i
$475$		0			0
$476$		−	231.117i		−	0.0222547i
$477$	13223.0			1.26927
$478$	13380.9			1.28040
$479$			14342.8i			1.36814i	0.729418	+	0.684069i	$0.239791\pi$
$479$			14342.8i			1.36814i	−0.729418	+	0.684069i	$0.760209\pi$
$480$		0			0
$481$	−5046.71	+	8209.33i	−0.478399	+	0.778198i
$482$	26027.5			2.45959
$483$			33.2356i			0.00313100i
$484$	−25561.0			−2.40055
$485$		0			0
$486$		−	10541.7i		−	0.983915i
$487$		−	19369.6i		−	1.80230i	−0.433512	−	0.901148i	$-0.642726\pi$
$487$		−	19369.6i		−	1.80230i	0.433512	−	0.901148i	$-0.357274\pi$
$488$		−	12956.1i		−	1.20183i
$489$			2325.85i			0.215089i
$490$		0			0
$491$	12486.5			1.14768			0.573838	−	0.818969i	$-0.305454\pi$
$491$	12486.5			1.14768			0.573838	+	0.818969i	$0.305454\pi$
$492$		−	5587.15i		−	0.511967i
$493$	5863.64			0.535670
$494$	−27717.6	−	17039.5i	−2.52444	−	1.55191i
$495$		0			0
$496$			4573.22i			0.413999i
$497$	75.9128			0.00685142
$498$	2144.35			0.192953
$499$			15364.4i			1.37837i	0.724585	+	0.689186i	$0.242032\pi$
$499$			15364.4i			1.37837i	−0.724585	+	0.689186i	$0.757968\pi$
$500$		0			0
$501$			1464.40i			0.130588i
$502$		−	47.2060i		−	0.00419703i
$503$	−15778.4			−1.39866			−0.699328	−	0.714800i	$-0.746517\pi$
$503$	−15778.4			−1.39866			−0.699328	+	0.714800i	$0.746517\pi$
$504$	365.896			0.0323379
$505$		0			0
$506$	9853.87			0.865727
$507$	929.101	+	1836.32i	0.0813863	+	0.160856i
$508$	−25491.0			−2.22634
$509$		−	6252.54i		−	0.544478i	−0.962230	−	0.272239i	$-0.912236\pi$
$509$		−	6252.54i		−	0.544478i	0.962230	−	0.272239i	$-0.0877641\pi$
$510$		0			0
$511$	135.433			0.0117245
$512$			662.049i			0.0571459i
$513$		−	6424.13i		−	0.552889i
$514$			8603.22i			0.738272i
$515$		0			0
$516$	6303.99			0.537825
$517$	−3959.33			−0.336811
$518$		−	223.046i		−	0.0189190i
$519$	−2608.89			−0.220651
$520$		0			0
$521$	−13016.7			−1.09457			−0.547287	−	0.836945i	$-0.684340\pi$
$521$	−13016.7			−1.09457			−0.547287	+	0.836945i	$0.684340\pi$
$522$			15035.2i			1.26068i
$523$	16344.2			1.36650			0.683251	−	0.730183i	$-0.260565\pi$
$523$	16344.2			1.36650			0.683251	+	0.730183i	$0.260565\pi$
$524$	−16883.2			−1.40753
$525$		0			0
$526$		−	16400.8i		−	1.35952i
$527$			1216.21i			0.100530i
$528$			2010.81i			0.165737i
$529$	18754.9			1.54145
$530$		0			0
$531$		−	17715.9i		−	1.44785i
$532$	544.694			0.0443900
$533$	7001.82	−	11389.7i	0.569010	−	0.925592i
$534$	713.571			0.0578263
$535$		0			0
$536$	−64266.6			−5.17891
$537$	−3140.10			−0.252337
$538$			33167.7i			2.65792i
$539$			3574.26i			0.285630i
$540$		0			0
$541$			21385.8i			1.69953i	0.527158	+	0.849767i	$0.323258\pi$
$541$			21385.8i			1.69953i	−0.527158	+	0.849767i	$0.676742\pi$
$542$	−13038.5			−1.03331
$543$	3254.42			0.257202
$544$		−	30245.1i		−	2.38373i
$545$		0			0
$546$	−40.5792	−	24.9462i	−0.00318064	−	0.00195531i
$547$	22836.7			1.78505			0.892527	−	0.450993i	$-0.148930\pi$
$547$	22836.7			1.78505			0.892527	+	0.450993i	$0.148930\pi$
$548$			519.929i			0.0405297i
$549$	4875.35			0.379007
$550$		0			0
$551$			13819.4i			1.06847i
$552$			11434.8i			0.881696i
$553$		−	119.749i		−	0.00920842i
$554$			23888.0i			1.83195i
$555$		0			0
$556$	28259.9			2.15555
$557$			14375.7i			1.09357i	0.837274	+	0.546784i	$0.184148\pi$
$557$			14375.7i			1.09357i	−0.837274	+	0.546784i	$0.815852\pi$
$558$	−3118.55			−0.236593
$559$	12851.0	+	7900.17i	0.972340	+	0.597749i
$560$		0			0
$561$			534.760i			0.0402452i
$562$	−1922.89			−0.144328
$563$	−2088.93			−0.156373			−0.0781866	−	0.996939i	$-0.524913\pi$
$563$	−2088.93			−0.156373			−0.0781866	+	0.996939i	$0.524913\pi$
$564$		−	7441.49i		−	0.555573i
$565$		0			0
$566$			8461.65i			0.628392i
$567$			132.906i			0.00984395i
$568$	26118.0			1.92937
$569$	7775.20			0.572853			0.286426	−	0.958102i	$-0.407533\pi$
$569$	7775.20			0.572853			0.286426	+	0.958102i	$0.407533\pi$
$570$		0			0
$571$	21491.9			1.57515			0.787573	−	0.616221i	$-0.211337\pi$
$571$	21491.9			1.57515			0.787573	+	0.616221i	$0.211337\pi$
$572$	−5349.56	+	8701.97i	−0.391043	+	0.636097i
$573$	−771.029			−0.0562133
$574$			309.454i			0.0225024i
$575$		0			0
$576$	34508.1			2.49625
$577$			4348.75i			0.313762i	0.987617	+	0.156881i	$0.0501440\pi$
$577$			4348.75i			0.313762i	−0.987617	+	0.156881i	$0.949856\pi$
$578$			10282.9i			0.739983i
$579$			174.287i			0.0125097i
$580$		0			0
$581$	−85.9040			−0.00613407
$582$	2777.55			0.197823
$583$		−	5275.45i		−	0.374763i
$584$	46596.1			3.30165
$585$		0			0
$586$	−23498.7			−1.65652
$587$			5800.67i			0.407870i	0.978984	+	0.203935i	$0.0653731\pi$
$587$			5800.67i			0.407870i	−0.978984	+	0.203935i	$0.934627\pi$
$588$	−6717.77			−0.471150
$589$	−2866.36			−0.200520
$590$		0			0
$591$		−	2842.95i		−	0.197874i
$592$		−	42346.6i		−	2.93993i
$593$		−	4577.14i		−	0.316966i	−0.987362	−	0.158483i	$-0.949340\pi$
$593$		−	4577.14i		−	0.316966i	0.987362	−	0.158483i	$-0.0506603\pi$
$594$	−2788.46			−0.192613
$595$		0			0
$596$		−	6667.94i		−	0.458271i
$597$	2519.89			0.172751
$598$	−23209.5	+	37754.2i	−1.58714	+	2.58175i
$599$	17537.7			1.19628			0.598140	−	0.801392i	$-0.295907\pi$
$599$	17537.7			1.19628			0.598140	+	0.801392i	$0.295907\pi$
$600$		0			0
$601$	13316.0			0.903780			0.451890	−	0.892074i	$-0.350750\pi$
$601$	13316.0			0.903780			0.451890	+	0.892074i	$0.350750\pi$
$602$	−349.158			−0.0236389
$603$		−	24183.4i		−	1.63321i
$604$		−	9883.94i		−	0.665847i
$605$		0			0
$606$			6982.75i			0.468077i
$607$	−2103.20			−0.140636			−0.0703182	−	0.997525i	$-0.522401\pi$
$607$	−2103.20			−0.140636			−0.0703182	+	0.997525i	$0.522401\pi$
$608$	71281.3			4.75467
$609$			20.2319i			0.00134620i
$610$		0			0
$611$	9325.69	−	15169.8i	0.617475	−	1.00443i
$612$	29921.9			1.97634
$613$		−	6984.21i		−	0.460178i	−0.973170	−	0.230089i	$-0.926098\pi$
$613$		−	6984.21i		−	0.460178i	0.973170	−	0.230089i	$-0.0739018\pi$
$614$	−21502.0			−1.41327
$615$		0			0
$616$		−	145.977i		−	0.00954805i
$617$			13605.0i			0.887713i	0.896098	+	0.443856i	$0.146390\pi$
$617$			13605.0i			0.887713i	−0.896098	+	0.443856i	$0.853610\pi$
$618$			5825.43i			0.379180i
$619$		−	24505.8i		−	1.59123i	−0.605801	−	0.795616i	$-0.707147\pi$
$619$		−	24505.8i		−	1.59123i	0.605801	−	0.795616i	$-0.292853\pi$
$620$		0			0
$621$	−8750.31			−0.565439
$622$		−	11377.9i		−	0.733458i
$623$	−28.5860			−0.00183832
$624$	−7704.23	−	4736.19i	−0.494256	−	0.303845i
$625$		0			0
$626$			9300.65i			0.593816i
$627$	−1260.32			−0.0802746
$628$	45123.8			2.86726
$629$		−	11261.8i		−	0.713890i
$630$		0			0
$631$			18694.2i			1.17940i	0.807621	+	0.589702i	$0.200755\pi$
$631$			18694.2i			1.17940i	−0.807621	+	0.589702i	$0.799245\pi$
$632$		−	41200.0i		−	2.59311i
$633$	1322.26			0.0830252
$634$	−24931.7			−1.56177
$635$		0			0
$636$	9915.11			0.618175
$637$	−13694.5	−	8418.72i	−0.851797	−	0.523645i
$638$	5998.45			0.372227
$639$			9828.15i			0.608444i
$640$		0			0
$641$	−22658.3			−1.39617			−0.698087	−	0.716013i	$-0.745965\pi$
$641$	−22658.3			−1.39617			−0.698087	+	0.716013i	$0.745965\pi$
$642$		−	5768.53i		−	0.354620i
$643$			18187.4i			1.11546i	0.830022	+	0.557730i	$0.188328\pi$
$643$			18187.4i			1.11546i	−0.830022	+	0.557730i	$0.811672\pi$
$644$		−	741.929i		−	0.0453976i
$645$		0			0
$646$	38023.8			2.31583
$647$	−4755.08			−0.288936			−0.144468	−	0.989509i	$-0.546147\pi$
$647$	−4755.08			−0.288936			−0.144468	+	0.989509i	$0.546147\pi$
$648$			45726.5i			2.77208i
$649$	−7067.94			−0.427490
$650$		0			0
$651$	−4.19641			−0.000252643
$652$		−	51920.7i		−	3.11867i
$653$	−731.494			−0.0438370			−0.0219185	−	0.999760i	$-0.506977\pi$
$653$	−731.494			−0.0438370			−0.0219185	+	0.999760i	$0.506977\pi$
$654$	10244.3			0.612514
$655$		0			0
$656$			58751.9i			3.49676i
$657$			17534.1i			1.04120i
$658$			412.161i			0.0244190i
$659$	16005.3			0.946099			0.473050	−	0.881036i	$-0.343153\pi$
$659$	16005.3			0.946099			0.473050	+	0.881036i	$0.343153\pi$
$660$		0			0
$661$			12332.1i			0.725664i	0.931855	+	0.362832i	$0.118190\pi$
$661$			12332.1i			0.725664i	−0.931855	+	0.362832i	$0.881810\pi$
$662$	−12250.3			−0.719217
$663$	−2048.88	−	1259.56i	−0.120018	−	0.0737815i
$664$	−29555.4			−1.72737
$665$		0			0
$666$	28876.9			1.68011
$667$	18823.4			1.09272
$668$		−	32690.2i		−	1.89344i
$669$		−	444.228i		−	0.0256724i
$670$		0			0
$671$		−	1945.07i		−	0.111905i
$672$	104.357			0.00599058
$673$	−12183.0			−0.697799			−0.348899	−	0.937160i	$-0.613444\pi$
$673$	−12183.0			−0.697799			−0.348899	+	0.937160i	$0.613444\pi$
$674$		−	2256.69i		−	0.128968i
$675$		0			0
$676$	−20740.6	−	40992.7i	−1.18005	−	2.33231i
$677$	−25830.0			−1.46637			−0.733183	−	0.680032i	$-0.761966\pi$
$677$	−25830.0			−1.46637			−0.733183	+	0.680032i	$0.761966\pi$
$678$		−	6139.24i		−	0.347752i
$679$	−111.270			−0.00628888
$680$		0			0
$681$		−	1462.92i		−	0.0823189i
$682$			1244.18i			0.0698562i
$683$			6832.74i			0.382793i	0.981513	+	0.191396i	$0.0613016\pi$
$683$			6832.74i			0.382793i	−0.981513	+	0.191396i	$0.938698\pi$
$684$			70519.5i			3.94208i
$685$		0			0
$686$	744.196			0.0414191
$687$		−	2743.50i		−	0.152360i
$688$	−66289.9			−3.67337
$689$	20212.4	+	12425.6i	1.11761	+	0.687052i
$690$		0			0
$691$		−	26068.7i		−	1.43517i	−0.696472	−	0.717584i	$-0.745248\pi$
$691$		−	26068.7i		−	1.43517i	0.696472	−	0.717584i	$-0.254752\pi$
$692$	58239.1			3.19930
$693$	54.9311			0.00301106
$694$		−	2663.23i		−	0.145670i
$695$		0			0
$696$			6960.81i			0.379093i
$697$			15624.6i			0.849104i
$698$	−23947.4			−1.29860
$699$	−2609.63			−0.141209
$700$		0			0
$701$	−31003.6			−1.67045			−0.835227	−	0.549905i	$-0.814664\pi$
$701$	−31003.6			−1.67045			−0.835227	+	0.549905i	$0.814664\pi$
$702$	6567.86	−	10683.7i	0.353117	−	0.574405i
$703$	26541.7			1.42395
$704$		−	13767.3i		−	0.737039i
$705$		0			0
$706$	63950.8			3.40909
$707$		−	279.733i		−	0.0148804i
$708$		−	13284.1i		−	0.705150i
$709$			19868.2i			1.05242i	0.850355	+	0.526209i	$0.176387\pi$
$709$			19868.2i			1.05242i	−0.850355	+	0.526209i	$0.823613\pi$
$710$		0			0
$711$	15503.5			0.817759
$712$	−9835.08			−0.517676
$713$			3904.27i			0.205072i
$714$	55.6677			0.00291780
$715$		0			0
$716$	70097.4			3.65874
$717$			2331.14i			0.121420i
$718$	−27644.8			−1.43690
$719$	2878.38			0.149298			0.0746491	−	0.997210i	$-0.476216\pi$
$719$	2878.38			0.149298			0.0746491	+	0.997210i	$0.476216\pi$
$720$		0			0
$721$		−	233.370i		−	0.0120543i
$722$			52734.2i			2.71823i
$723$			4534.35i			0.233242i
$724$	−72649.4			−3.72927
$725$		0			0
$726$		−	6156.73i		−	0.314735i
$727$	22798.9			1.16309			0.581543	−	0.813516i	$-0.302449\pi$
$727$	22798.9			1.16309			0.581543	+	0.813516i	$0.302449\pi$
$728$	559.300	+	343.831i	0.0284739	+	0.0175044i
$729$	−15948.3			−0.810257
$730$		0			0
$731$	−17629.3			−0.891989
$732$	3655.72			0.184589
$733$			27940.5i			1.40792i	0.710240	+	0.703960i	$0.248586\pi$
$733$			27940.5i			1.40792i	−0.710240	+	0.703960i	$0.751414\pi$
$734$			50600.4i			2.54454i
$735$		0			0
$736$		−	97092.3i		−	4.86259i
$737$	−9648.21			−0.482220
$738$	−40063.9			−1.99834
$739$		−	30468.8i		−	1.51666i	−0.651871	−	0.758330i	$-0.726016\pi$
$739$		−	30468.8i		−	1.51666i	0.651871	−	0.758330i	$-0.273984\pi$
$740$		0			0
$741$	2968.51	−	4828.79i	0.147167	−	0.239393i
$742$	−549.166			−0.0271705
$743$		−	17528.7i		−	0.865501i	−0.901514	−	0.432750i	$-0.857543\pi$
$743$		−	17528.7i		−	0.865501i	0.901514	−	0.432750i	$-0.142457\pi$
$744$	−1443.78			−0.0711447
$745$		0			0
$746$		−	26845.7i		−	1.31755i
$747$		−	11121.7i		−	0.544740i
$748$		−	11937.6i		−	0.583532i
$749$			231.091i			0.0112735i
$750$		0			0
$751$	−4371.31			−0.212399			−0.106199	−	0.994345i	$-0.533868\pi$
$751$	−4371.31			−0.212399			−0.106199	+	0.994345i	$0.533868\pi$
$752$			78251.4i			3.79459i
$753$	8.22393			0.000398003
$754$	−14128.6	+	22982.5i	−0.682404	+	1.11005i
$755$		0			0
$756$			209.952i			0.0101004i
$757$	−2920.51			−0.140221			−0.0701107	−	0.997539i	$-0.522335\pi$
$757$	−2920.51			−0.140221			−0.0701107	+	0.997539i	$0.522335\pi$
$758$	13102.3			0.627831
$759$			1716.68i			0.0820968i
$760$		0			0
$761$			40352.4i			1.92217i	0.276246	+	0.961087i	$0.410909\pi$
$761$			40352.4i			1.92217i	−0.276246	+	0.961087i	$0.589091\pi$
$762$		−	6139.85i		−	0.291894i
$763$	−410.393			−0.0194721
$764$	17211.9			0.815060
$765$		0			0
$766$	−55895.0			−2.63651
$767$	16647.6	−	27080.2i	0.783717	−	1.27485i
$768$	3627.81			0.170452
$769$		−	27282.1i		−	1.27935i	−0.768646	−	0.639674i	$-0.779069\pi$
$769$		−	27282.1i		−	1.27935i	0.768646	−	0.639674i	$-0.220931\pi$
$770$		0			0
$771$	−1498.80			−0.0700102
$772$		−	3890.67i		−	0.181384i
$773$		−	10121.3i		−	0.470942i	−0.971881	−	0.235471i	$-0.924337\pi$
$773$		−	10121.3i		−	0.470942i	0.971881	−	0.235471i	$-0.0756633\pi$
$774$		−	45204.2i		−	2.09926i
$775$		0			0
$776$	−38282.7			−1.77096
$777$	38.8575			0.00179409
$778$		−	74589.9i		−	3.43725i
$779$	−36824.0			−1.69365
$780$		0			0
$781$	3921.03			0.179649
$782$		−	51792.3i		−	2.36840i
$783$	−5326.67			−0.243116
$784$	70641.0			3.21798
$785$		0			0
$786$		−	4066.55i		−	0.184541i
$787$			17973.2i			0.814072i	0.913412	+	0.407036i	$0.133438\pi$
$787$			17973.2i			0.814072i	−0.913412	+	0.407036i	$0.866562\pi$
$788$			63464.2i			2.86906i
$789$	2857.23			0.128923
$790$		0			0
$791$			245.941i			0.0110552i
$792$	18899.2			0.847920
$793$	7452.35	+	4581.36i	0.333721	+	0.205156i
$794$	11916.0			0.532598
$795$		0			0
$796$	−56252.3			−2.50479
$797$	1050.61			0.0466931			0.0233465	−	0.999727i	$-0.492568\pi$
$797$	1050.61			0.0466931			0.0233465	+	0.999727i	$0.492568\pi$
$798$			131.197i			0.00581996i
$799$			20810.4i			0.921425i
$800$		0			0
$801$		−	3700.93i		−	0.163253i
$802$	−65209.2			−2.87109
$803$	6995.38			0.307424
$804$		−	18133.6i		−	0.795428i
$805$		0			0
$806$	−4766.95	−	2930.49i	−0.208323	−	0.128067i
$807$	−5778.26			−0.252050
$808$		−	96242.6i		−	4.19035i
$809$	−10131.7			−0.440310			−0.220155	−	0.975465i	$-0.570656\pi$
$809$	−10131.7			−0.440310			−0.220155	+	0.975465i	$0.570656\pi$
$810$		0			0
$811$			3463.42i			0.149959i	0.997185	+	0.0749797i	$0.0238892\pi$
$811$			3463.42i			0.149959i	−0.997185	+	0.0749797i	$0.976111\pi$
$812$		−	451.642i		−	0.0195191i
$813$		−	2271.49i		−	0.0979884i
$814$		−	11520.7i		−	0.496069i
$815$		0			0
$816$	10568.9			0.453412
$817$		−	41548.6i		−	1.77919i
$818$	14818.5			0.633393
$819$	−129.383	+	210.464i	−0.00552016	+	0.00897948i
$820$		0			0
$821$		−	9876.00i		−	0.419823i	−0.977720	−	0.209912i	$-0.932682\pi$
$821$		−	9876.00i		−	0.419823i	0.977720	−	0.209912i	$-0.0673176\pi$
$822$	−125.232			−0.00531383
$823$	7199.95			0.304951			0.152475	−	0.988307i	$-0.451276\pi$
$823$	7199.95			0.304951			0.152475	+	0.988307i	$0.451276\pi$
$824$		−	80291.3i		−	3.39452i
$825$		0			0
$826$			735.763i			0.0309933i
$827$			16864.4i			0.709110i	0.935035	+	0.354555i	$0.115368\pi$
$827$			16864.4i			0.709110i	−0.935035	+	0.354555i	$0.884632\pi$
$828$	96054.7			4.03156
$829$	26061.1			1.09184			0.545922	−	0.837836i	$-0.316180\pi$
$829$	26061.1			1.09184			0.545922	+	0.837836i	$0.316180\pi$
$830$		0			0
$831$	−4161.61			−0.173724
$832$	52748.3	+	32427.2i	2.19798	+	1.35121i
$833$	18786.5			0.781407
$834$			6806.78i			0.282613i
$835$		0			0
$836$	28134.4			1.16393
$837$		−	1104.84i		−	0.0456258i
$838$		−	2247.17i		−	0.0926338i
$839$		−	35491.9i		−	1.46045i	−0.683208	−	0.730224i	$-0.739416\pi$
$839$		−	35491.9i		−	1.46045i	0.683208	−	0.730224i	$-0.260584\pi$
$840$		0			0
$841$	−12930.4			−0.530175
$842$	40990.6			1.67771
$843$		−	334.993i		−	0.0136866i
$844$	−29517.1			−1.20382
$845$		0			0
$846$	−53360.9			−2.16854
$847$			246.642i			0.0100056i
$848$	−104263.			−4.22217
$849$	−1474.13			−0.0595903
$850$		0			0
$851$		−	36152.4i		−	1.45627i
$852$			7369.51i			0.296332i
$853$			10763.1i			0.432029i	0.976390	+	0.216014i	$0.0693058\pi$
$853$			10763.1i			0.432029i	−0.976390	+	0.216014i	$0.930694\pi$
$854$	−202.479			−0.00811321
$855$		0			0
$856$			79507.2i			3.17465i
$857$	3344.32			0.133302			0.0666511	−	0.997776i	$-0.478769\pi$
$857$	3344.32			0.133302			0.0666511	+	0.997776i	$0.478769\pi$
$858$	−2095.99	−	1288.51i	−0.0833984	−	0.0512694i
$859$	−31361.2			−1.24567			−0.622836	−	0.782353i	$-0.714020\pi$
$859$	−31361.2			−1.24567			−0.622836	+	0.782353i	$0.714020\pi$
$860$		0			0
$861$	−53.9111			−0.00213390
$862$	34133.6			1.34872
$863$		−	9576.65i		−	0.377744i	−0.982002	−	0.188872i	$-0.939517\pi$
$863$		−	9576.65i		−	0.377744i	0.982002	−	0.188872i	$-0.0604831\pi$
$864$			27475.3i			1.08186i
$865$		0			0
$866$		−	23046.8i		−	0.904342i
$867$	−1791.41			−0.0701725
$868$	93.6778			0.00366317
$869$		−	6185.26i		−	0.241451i
$870$		0			0
$871$	22725.1	−	36966.2i	0.884054	−	1.43806i
$872$	−141196.			−5.48339
$873$		−	14405.7i		−	0.558487i
$874$	122064.			4.72410
$875$		0			0
$876$			13147.7i			0.507100i
$877$		−	28993.5i		−	1.11635i	−0.829722	−	0.558177i	$-0.811501\pi$
$877$		−	28993.5i		−	1.11635i	0.829722	−	0.558177i	$-0.188499\pi$
$878$			4832.06i			0.185734i
$879$		−	4093.79i		−	0.157088i
$880$		0			0
$881$	23068.0			0.882156			0.441078	−	0.897469i	$-0.354596\pi$
$881$	23068.0			0.882156			0.441078	+	0.897469i	$0.354596\pi$
$882$			48171.3i			1.83901i
$883$	29675.0			1.13097			0.565483	−	0.824760i	$-0.308690\pi$
$883$	29675.0			1.13097			0.565483	+	0.824760i	$0.308690\pi$
$884$	45737.9	+	28117.5i	1.74019	+	1.06979i
$885$		0			0
$886$			26786.7i			1.01571i
$887$	5118.12			0.193742			0.0968712	−	0.995297i	$-0.469117\pi$
$887$	5118.12			0.193742			0.0968712	+	0.995297i	$0.469117\pi$
$888$	13369.0			0.505219
$889$			245.966i			0.00927944i
$890$		0			0
$891$			6864.82i			0.258115i
$892$			9916.64i			0.372235i
$893$	−49045.7			−1.83791
$894$	1606.06			0.0600837
$895$		0			0
$896$	−541.906			−0.0202052
$897$	−6577.30	−	4043.41i	−0.244827	−	0.150508i
$898$	−24167.8			−0.898094
$899$			2376.69i			0.0881725i
$900$		0			0
$901$	−27727.9			−1.02525
$902$			15983.9i			0.590027i
$903$		−	60.8280i		−	0.00224167i
$904$			84616.6i			3.11317i
$905$		0			0
$906$	2380.68			0.0872989
$907$	−37154.2			−1.36018			−0.680091	−	0.733128i	$-0.738060\pi$
$907$	−37154.2			−1.36018			−0.680091	+	0.733128i	$0.738060\pi$
$908$			32657.2i			1.19358i
$909$	36216.0			1.32146
$910$		0			0
$911$	7888.56			0.286893			0.143447	−	0.989658i	$-0.454181\pi$
$911$	7888.56			0.286893			0.143447	+	0.989658i	$0.454181\pi$
$912$			24908.6i			0.904393i
$913$	−4437.09			−0.160839
$914$	−15725.8			−0.569106
$915$		0			0
$916$			61244.1i			2.20913i
$917$			162.908i			0.00586664i
$918$			14656.3i			0.526938i
$919$	−32292.7			−1.15913			−0.579563	−	0.814927i	$-0.696777\pi$
$919$	−32292.7			−1.15913			−0.579563	+	0.814927i	$0.696777\pi$
$920$		0			0
$921$		−	3745.93i		−	0.134020i
$922$	−54425.7			−1.94405
$923$	−9235.48	+	15023.1i	−0.329350	+	0.535743i
$924$	41.1894			0.00146648
$925$		0			0
$926$	28095.6			0.997062
$927$	30213.5			1.07049
$928$		−	59104.0i		−	2.09072i
$929$		−	7931.61i		−	0.280116i	−0.990143	−	0.140058i	$-0.955271\pi$
$929$		−	7931.61i		−	0.280116i	0.990143	−	0.140058i	$-0.0447289\pi$
$930$		0			0
$931$			44275.7i			1.55862i
$932$	58255.6			2.04745
$933$	1982.18			0.0695537
$934$		−	30092.7i		−	1.05424i
$935$		0			0
$936$	−44514.5	+	72410.5i	−1.55449	+	2.52864i
$937$	−35368.6			−1.23313			−0.616565	−	0.787304i	$-0.711476\pi$
$937$	−35368.6			−1.23313			−0.616565	+	0.787304i	$0.711476\pi$
$938$			1004.36i			0.0349613i
$939$	−1620.30			−0.0563115
$940$		0			0
$941$			21319.4i			0.738569i	0.929316	+	0.369285i	$0.120397\pi$
$941$			21319.4i			0.738569i	−0.929316	+	0.369285i	$0.879603\pi$
$942$			10868.7i			0.375925i
$943$			50158.0i			1.73210i
$944$			139689.i			4.81621i
$945$		0			0
$946$	−18034.6			−0.619827
$947$		−	16623.5i		−	0.570422i	−0.958465	−	0.285211i	$-0.907936\pi$
$947$		−	16623.5i		−	0.570422i	0.958465	−	0.285211i	$-0.0920637\pi$
$948$	11625.1			0.398276
$949$	−16476.7	+	26802.2i	−0.563600	+	0.916792i
$950$		0			0
$951$		−	4343.44i		−	0.148103i
$952$	−767.263			−0.0261209
$953$	−25047.2			−0.851374			−0.425687	−	0.904870i	$-0.639968\pi$
$953$	−25047.2			−0.851374			−0.425687	+	0.904870i	$0.639968\pi$
$954$		−	71098.5i		−	2.41289i
$955$		0			0
$956$		−	52038.8i		−	1.76052i
$957$			1045.01i			0.0352982i
$958$	77119.3			2.60085
$959$	5.01687			0.000168929
$960$		0			0
$961$	29298.0			0.983453
$962$	44140.5	+	27135.5i	1.47936	+	0.909443i
$963$	−29918.4			−1.00115
$964$		−	101222.i		−	3.38188i
$965$		0			0
$966$	178.704			0.00595207
$967$		−	13656.8i		−	0.454161i	−0.973876	−	0.227081i	$-0.927082\pi$
$967$		−	13656.8i		−	0.454161i	0.973876	−	0.227081i	$-0.0729181\pi$
$968$			84857.7i			2.81759i
$969$			6624.26i			0.219610i
$970$		0			0
$971$	2265.67			0.0748803			0.0374401	−	0.999299i	$-0.488080\pi$
$971$	2265.67			0.0748803			0.0374401	+	0.999299i	$0.488080\pi$
$972$	−40997.0			−1.35286
$973$		−	272.683i		−	0.00898440i
$974$	−104148.			−3.42619
$975$		0			0
$976$	−38441.9			−1.26075
$977$		−	20144.9i		−	0.659666i	−0.944039	−	0.329833i	$-0.893008\pi$
$977$		−	20144.9i		−	0.659666i	0.944039	−	0.329833i	$-0.106992\pi$
$978$	12505.8			0.408888
$979$	−1476.52			−0.0482020
$980$		0			0
$981$		−	53132.0i		−	1.72923i
$982$		−	67138.5i		−	2.18175i
$983$		−	10526.6i		−	0.341552i	−0.985310	−	0.170776i	$-0.945373\pi$
$983$		−	10526.6i		−	0.341552i	0.985310	−	0.170776i	$-0.0546274\pi$
$984$	−18548.2			−0.600910
$985$		0			0
$986$		−	31528.1i		−	1.01831i
$987$	−71.8039			−0.00231565
$988$	−66267.0	+	107795.i	−2.13384	+	3.47105i
$989$	−56593.4			−1.81958
$990$		0			0
$991$	55992.7			1.79482			0.897410	−	0.441198i	$-0.145446\pi$
$991$	55992.7			1.79482			0.897410	+	0.441198i	$0.145446\pi$
$992$	12259.1			0.392367
$993$		−	2134.17i		−	0.0682032i
$994$		−	408.174i		−	0.0130246i
$995$		0			0
$996$		−	8339.43i		−	0.265306i
$997$	−48578.5			−1.54312			−0.771562	−	0.636154i	$-0.780524\pi$
$997$	−48578.5			−1.54312			−0.771562	+	0.636154i	$0.780524\pi$
$998$	82612.7			2.62030
$999$			10230.5i			0.324002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.4.c.e.51.1		14
5.2	odd	4		325.4.d.d.324.13		14
5.3	odd	4		325.4.d.c.324.2		14
5.4	even	2		65.4.c.a.51.14	yes	14
13.12	even	2	inner	325.4.c.e.51.14		14
15.14	odd	2		585.4.b.e.181.1		14
20.19	odd	2		1040.4.k.d.961.8		14
65.12	odd	4		325.4.d.c.324.1		14
65.34	odd	4		845.4.a.i.1.1		7
65.38	odd	4		325.4.d.d.324.14		14
65.44	odd	4		845.4.a.l.1.7		7
65.64	even	2		65.4.c.a.51.1	✓	14
195.194	odd	2		585.4.b.e.181.14		14
260.259	odd	2		1040.4.k.d.961.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.c.a.51.1	✓	14	65.64	even	2
65.4.c.a.51.14	yes	14	5.4	even	2
325.4.c.e.51.1		14	1.1	even	1	trivial
325.4.c.e.51.14		14	13.12	even	2	inner
325.4.d.c.324.1		14	65.12	odd	4
325.4.d.c.324.2		14	5.3	odd	4
325.4.d.d.324.13		14	5.2	odd	4
325.4.d.d.324.14		14	65.38	odd	4
585.4.b.e.181.1		14	15.14	odd	2
585.4.b.e.181.14		14	195.194	odd	2
845.4.a.i.1.1		7	65.34	odd	4
845.4.a.l.1.7		7	65.44	odd	4
1040.4.k.d.961.7		14	260.259	odd	2
1040.4.k.d.961.8		14	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	325.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.37688i q^{2} +0.936724 q^{3} -20.9108 q^{4} -5.03665i q^{6} +0.201771i q^{7} +69.4197i q^{8} -26.1225 q^{9} +10.4218i q^{11} -19.5876 q^{12} +(-39.9303 - 24.5473i) q^{13} +1.08490 q^{14} +205.975 q^{16} +54.7775 q^{17} +140.458i q^{18} +129.099i q^{19} +0.189004i q^{21} +56.0369 q^{22} +175.846 q^{23} +65.0272i q^{24} +(-131.988 + 214.700i) q^{26} -49.7612 q^{27} -4.21919i q^{28} +107.045 q^{29} +22.2028i q^{31} -552.144i q^{32} +9.76239i q^{33} -294.532i q^{34} +546.243 q^{36} -205.591i q^{37} +694.150 q^{38} +(-37.4037 - 22.9940i) q^{39} +285.238i q^{41} +1.01625 q^{42} -321.835 q^{43} -217.929i q^{44} -945.503i q^{46} +379.907i q^{47} +192.942 q^{48} +342.959 q^{49} +51.3115 q^{51} +(834.975 + 513.303i) q^{52} -506.192 q^{53} +267.560i q^{54} -14.0069 q^{56} +120.930i q^{57} -575.566i q^{58} +678.186i q^{59} -186.634 q^{61} +119.382 q^{62} -5.27077i q^{63} -1321.01 q^{64} +52.4911 q^{66} +925.768i q^{67} -1145.44 q^{68} +164.719 q^{69} -376.232i q^{71} -1813.42i q^{72} -671.223i q^{73} -1105.44 q^{74} -2699.57i q^{76} -2.10282 q^{77} +(-123.636 + 201.115i) q^{78} -593.491 q^{79} +658.696 q^{81} +1533.69 q^{82} +425.750i q^{83} -3.95222i q^{84} +1730.47i q^{86} +100.271 q^{87} -723.481 q^{88} +141.676i q^{89} +(4.95293 - 8.05678i) q^{91} -3677.08 q^{92} +20.7979i q^{93} +2042.71 q^{94} -517.206i q^{96} +551.467i q^{97} -1844.05i q^{98} -272.245i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 56 q^{4} + 158 q^{9} + 108 q^{12} + 4 q^{13} - 152 q^{14} + 280 q^{16} + 100 q^{17} - 648 q^{22} + 532 q^{23} - 344 q^{26} + 48 q^{27} + 588 q^{29} + 496 q^{36} - 148 q^{38} - 260 q^{39} + 620 q^{42}+ \cdots + 2656 q^{94}+O(q^{100}) \) 14 * q - 56 * q^4 + 158 * q^9 + 108 * q^12 + 4 * q^13 - 152 * q^14 + 280 * q^16 + 100 * q^17 - 648 * q^22 + 532 * q^23 - 344 * q^26 + 48 * q^27 + 588 * q^29 + 496 * q^36 - 148 * q^38 - 260 * q^39 + 620 * q^42 - 728 * q^43 + 2008 * q^48 - 1302 * q^49 + 176 * q^51 + 528 * q^52 - 1040 * q^53 + 512 * q^56 - 1460 * q^61 - 2964 * q^62 + 1296 * q^64 - 600 * q^66 - 1604 * q^68 + 4160 * q^69 - 5928 * q^74 + 3568 * q^77 - 2560 * q^78 - 1024 * q^79 - 2890 * q^81 + 6660 * q^82 - 5256 * q^87 - 1132 * q^88 + 916 * q^91 - 6044 * q^92 + 2656 * q^94

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