LMFDB - Embedded newform 525.3.e.c.349.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(349,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("525.349");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.e (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.7
Character	$\chi$	$=$	525.349
Dual form			525.3.e.c.349.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79155i q^{2} -1.73205 q^{3} -3.79273 q^{4} +4.83510i q^{6} +(5.63139 + 4.15782i) q^{7} -0.578591i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-2.79155i q^{2} -1.73205 q^{3} -3.79273 q^{4} +4.83510i q^{6} +(5.63139 + 4.15782i) q^{7} -0.578591i q^{8} +3.00000 q^{9} -18.9690 q^{11} +6.56921 q^{12} -10.9807 q^{13} +(11.6068 - 15.7203i) q^{14} -16.7861 q^{16} +22.3060 q^{17} -8.37464i q^{18} +19.6057i q^{19} +(-9.75385 - 7.20156i) q^{21} +52.9528i q^{22} +31.9991i q^{23} +1.00215i q^{24} +30.6530i q^{26} -5.19615 q^{27} +(-21.3583 - 15.7695i) q^{28} -39.9967 q^{29} +36.6641i q^{31} +44.5448i q^{32} +32.8553 q^{33} -62.2683i q^{34} -11.3782 q^{36} +8.94699i q^{37} +54.7302 q^{38} +19.0191 q^{39} -37.6320i q^{41} +(-20.1035 + 27.2283i) q^{42} +18.8702i q^{43} +71.9443 q^{44} +89.3269 q^{46} +49.3786 q^{47} +29.0744 q^{48} +(14.4250 + 46.8286i) q^{49} -38.6352 q^{51} +41.6468 q^{52} -49.2398i q^{53} +14.5053i q^{54} +(2.40568 - 3.25827i) q^{56} -33.9580i q^{57} +111.653i q^{58} -35.2173i q^{59} +63.4723i q^{61} +102.349 q^{62} +(16.8942 + 12.4735i) q^{63} +57.2046 q^{64} -91.7170i q^{66} +21.3544i q^{67} -84.6008 q^{68} -55.4240i q^{69} +36.2998 q^{71} -1.73577i q^{72} -6.66818 q^{73} +24.9759 q^{74} -74.3591i q^{76} +(-106.822 - 78.8697i) q^{77} -53.0926i q^{78} +16.2015 q^{79} +9.00000 q^{81} -105.052 q^{82} -36.7822 q^{83} +(36.9937 + 27.3136i) q^{84} +52.6770 q^{86} +69.2763 q^{87} +10.9753i q^{88} +88.0954i q^{89} +(-61.8364 - 45.6557i) q^{91} -121.364i q^{92} -63.5040i q^{93} -137.843i q^{94} -77.1539i q^{96} -133.810 q^{97} +(130.724 - 40.2681i) q^{98} -56.9070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 88 q^{4} + 72 q^{9}+O(q^{10}) $ 24 * q - 88 * q^4 + 72 * q^9	$ 24 q - 88 q^{4} + 72 q^{9} - 32 q^{11} + 80 q^{14} + 184 q^{16} + 72 q^{21} - 208 q^{29} - 264 q^{36} + 48 q^{39} - 384 q^{44} + 400 q^{46} - 120 q^{49} + 48 q^{51} - 736 q^{56} + 40 q^{64} + 64 q^{71} - 368 q^{74} - 240 q^{79} + 216 q^{81} - 216 q^{84} + 800 q^{86} + 48 q^{91} - 96 q^{99}+O(q^{100}) $ 24 * q - 88 * q^4 + 72 * q^9 - 32 * q^11 + 80 * q^14 + 184 * q^16 + 72 * q^21 - 208 * q^29 - 264 * q^36 + 48 * q^39 - 384 * q^44 + 400 * q^46 - 120 * q^49 + 48 * q^51 - 736 * q^56 + 40 * q^64 + 64 * q^71 - 368 * q^74 - 240 * q^79 + 216 * q^81 - 216 * q^84 + 800 * q^86 + 48 * q^91 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	2.79155i		−	1.39577i	−0.716208	−	0.697887i	$-0.754124\pi$
$2$		−	2.79155i		−	1.39577i	0.716208	−	0.697887i	$-0.245876\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−3.79273			−0.948184
$5$		0			0
$5$		0			0
$6$			4.83510i			0.805850i
$7$	5.63139	+	4.15782i	0.804484	+	0.593975i
$7$	5.63139	+	4.15782i	0.804484	+	0.593975i
$8$		−	0.578591i		−	0.0723239i
$9$	3.00000			0.333333
$10$		0			0
$11$	−18.9690			−1.72445			−0.862227	−	0.506522i	$-0.830931\pi$
$11$	−18.9690			−1.72445			−0.862227	+	0.506522i	$0.830931\pi$
$12$	6.56921			0.547434
$13$	−10.9807			−0.844667			−0.422333	−	0.906441i	$-0.638789\pi$
$13$	−10.9807			−0.844667			−0.422333	+	0.906441i	$0.638789\pi$
$14$	11.6068	−	15.7203i	0.829054	−	1.12288i
$15$		0			0
$16$	−16.7861			−1.04913
$17$	22.3060			1.31212			0.656060	−	0.754709i	$-0.272222\pi$
$17$	22.3060			1.31212			0.656060	+	0.754709i	$0.272222\pi$
$18$		−	8.37464i		−	0.465258i
$19$			19.6057i			1.03188i	0.856625	+	0.515939i	$0.172557\pi$
$19$			19.6057i			1.03188i	−0.856625	+	0.515939i	$0.827443\pi$
$20$		0			0
$21$	−9.75385	−	7.20156i	−0.464469	−	0.342932i
$22$			52.9528i			2.40695i
$23$			31.9991i			1.39126i	0.718399	+	0.695632i	$0.244875\pi$
$23$			31.9991i			1.39126i	−0.718399	+	0.695632i	$0.755125\pi$
$24$			1.00215i			0.0417562i
$25$		0			0
$26$			30.6530i			1.17896i
$27$	−5.19615			−0.192450
$28$	−21.3583	−	15.7695i	−0.762798	−	0.563197i
$29$	−39.9967			−1.37920			−0.689598	−	0.724192i	$-0.742213\pi$
$29$	−39.9967			−1.37920			−0.689598	+	0.724192i	$0.742213\pi$
$30$		0			0
$31$			36.6641i			1.18271i	0.806411	+	0.591356i	$0.201407\pi$
$31$			36.6641i			1.18271i	−0.806411	+	0.591356i	$0.798593\pi$
$32$			44.5448i			1.39203i
$33$	32.8553			0.995614
$34$		−	62.2683i		−	1.83142i
$35$		0			0
$36$	−11.3782			−0.316061
$37$			8.94699i			0.241810i	0.992664	+	0.120905i	$0.0385797\pi$
$37$			8.94699i			0.241810i	−0.992664	+	0.120905i	$0.961420\pi$
$38$	54.7302			1.44027
$39$	19.0191			0.487669
$40$		0			0
$41$		−	37.6320i		−	0.917854i	−0.888474	−	0.458927i	$-0.848234\pi$
$41$		−	37.6320i		−	0.917854i	0.888474	−	0.458927i	$-0.151766\pi$
$42$	−20.1035	+	27.2283i	−0.478655	+	0.648293i
$43$			18.8702i			0.438841i	0.975630	+	0.219421i	$0.0704167\pi$
$43$			18.8702i			0.438841i	−0.975630	+	0.219421i	$0.929583\pi$
$44$	71.9443			1.63510
$45$		0			0
$46$	89.3269			1.94189
$47$	49.3786			1.05061			0.525304	−	0.850914i	$-0.323952\pi$
$47$	49.3786			1.05061			0.525304	+	0.850914i	$0.323952\pi$
$48$	29.0744			0.605716
$49$	14.4250	+	46.8286i	0.294388	+	0.955686i
$50$		0			0
$51$	−38.6352			−0.757552
$52$	41.6468			0.800899
$53$		−	49.2398i		−	0.929052i	−0.885559	−	0.464526i	$-0.846225\pi$
$53$		−	49.2398i		−	0.929052i	0.885559	−	0.464526i	$-0.153775\pi$
$54$			14.5053i			0.268617i
$55$		0			0
$56$	2.40568	−	3.25827i	0.0429586	−	0.0581834i
$57$		−	33.9580i		−	0.595755i
$58$			111.653i			1.92505i
$59$		−	35.2173i		−	0.596903i	−0.954425	−	0.298452i	$-0.903530\pi$
$59$		−	35.2173i		−	0.596903i	0.954425	−	0.298452i	$-0.0964701\pi$
$60$		0			0
$61$			63.4723i			1.04053i	0.854005	+	0.520265i	$0.174167\pi$
$61$			63.4723i			1.04053i	−0.854005	+	0.520265i	$0.825833\pi$
$62$	102.349			1.65080
$63$	16.8942	+	12.4735i	0.268161	+	0.197992i
$64$	57.2046			0.893821
$65$		0			0
$66$		−	91.7170i		−	1.38965i
$67$			21.3544i			0.318723i	0.987220	+	0.159361i	$0.0509435\pi$
$67$			21.3544i			0.318723i	−0.987220	+	0.159361i	$0.949057\pi$
$68$	−84.6008			−1.24413
$69$		−	55.4240i		−	0.803246i
$70$		0			0
$71$	36.2998			0.511265			0.255632	−	0.966774i	$-0.417716\pi$
$71$	36.2998			0.511265			0.255632	+	0.966774i	$0.417716\pi$
$72$		−	1.73577i		−	0.0241080i
$73$	−6.66818			−0.0913449			−0.0456725	−	0.998956i	$-0.514543\pi$
$73$	−6.66818			−0.0913449			−0.0456725	+	0.998956i	$0.514543\pi$
$74$	24.9759			0.337513
$75$		0			0
$76$		−	74.3591i		−	0.978409i
$77$	−106.822	−	78.8697i	−1.38729	−	1.02428i
$78$		−	53.0926i		−	0.680675i
$79$	16.2015			0.205082			0.102541	−	0.994729i	$-0.467303\pi$
$79$	16.2015			0.205082			0.102541	+	0.994729i	$0.467303\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	−105.052			−1.28112
$83$	−36.7822			−0.443159			−0.221579	−	0.975142i	$-0.571121\pi$
$83$	−36.7822			−0.443159			−0.221579	+	0.975142i	$0.571121\pi$
$84$	36.9937	+	27.3136i	0.440402	+	0.325162i
$85$		0			0
$86$	52.6770			0.612523
$87$	69.2763			0.796279
$88$			10.9753i			0.124719i
$89$			88.0954i			0.989836i	0.868940	+	0.494918i	$0.164802\pi$
$89$			88.0954i			0.989836i	−0.868940	+	0.494918i	$0.835198\pi$
$90$		0			0
$91$	−61.8364	−	45.6557i	−0.679520	−	0.501711i
$92$		−	121.364i		−	1.31917i
$93$		−	63.5040i		−	0.682839i
$94$		−	137.843i		−	1.46641i
$95$		0			0
$96$		−	77.1539i		−	0.803687i
$97$	−133.810			−1.37948			−0.689742	−	0.724055i	$-0.742276\pi$
$97$	−133.810			−1.37948			−0.689742	+	0.724055i	$0.742276\pi$
$98$	130.724	−	40.2681i	1.33392	−	0.410899i
$99$	−56.9070			−0.574818
$100$		0			0
$101$			194.903i			1.92973i	0.262743	+	0.964866i	$0.415373\pi$
$101$			194.903i			1.92973i	−0.262743	+	0.964866i	$0.584627\pi$
$102$			107.852i			1.05737i
$103$	−41.2629			−0.400610			−0.200305	−	0.979734i	$-0.564193\pi$
$103$	−41.2629			−0.400610			−0.200305	+	0.979734i	$0.564193\pi$
$104$			6.35332i			0.0610896i
$105$		0			0
$106$	−137.455			−1.29675
$107$			29.7031i			0.277599i	0.990321	+	0.138799i	$0.0443243\pi$
$107$			29.7031i			0.277599i	−0.990321	+	0.138799i	$0.955676\pi$
$108$	19.7076			0.182478
$109$	−91.7028			−0.841310			−0.420655	−	0.907221i	$-0.638200\pi$
$109$	−91.7028			−0.841310			−0.420655	+	0.907221i	$0.638200\pi$
$110$		0			0
$111$		−	15.4966i		−	0.139609i
$112$	−94.5290	−	69.7937i	−0.844009	−	0.623158i
$113$		−	2.98301i		−	0.0263983i	−0.999913	−	0.0131992i	$-0.995798\pi$
$113$		−	2.98301i		−	0.0263983i	0.999913	−	0.0131992i	$-0.00420155\pi$
$114$	−94.7954			−0.831539
$115$		0			0
$116$	151.697			1.30773
$117$	−32.9420			−0.281556
$118$	−98.3107			−0.833142
$119$	125.614	+	92.7445i	1.05558	+	0.779366i
$120$		0			0
$121$	238.823			1.97374
$122$	177.186			1.45234
$123$			65.1806i			0.529923i
$124$		−	139.057i		−	1.12143i
$125$		0			0
$126$	34.8203	−	47.1608i	0.276351	−	0.374292i
$127$			104.651i			0.824023i	0.911179	+	0.412012i	$0.135174\pi$
$127$			104.651i			0.824023i	−0.911179	+	0.412012i	$0.864826\pi$
$128$			18.4901i			0.144454i
$129$		−	32.6841i		−	0.253365i
$130$		0			0
$131$		−	70.8051i		−	0.540497i	−0.962791	−	0.270249i	$-0.912894\pi$
$131$		−	70.8051i		−	0.540497i	0.962791	−	0.270249i	$-0.0871059\pi$
$132$	−124.611			−0.944025
$133$	−81.5169	+	110.407i	−0.612909	+	0.830129i
$134$	59.6118			0.444864
$135$		0			0
$136$		−	12.9061i		−	0.0948976i
$137$		−	158.673i		−	1.15820i	−0.815256	−	0.579100i	$-0.803404\pi$
$137$		−	158.673i		−	1.15820i	0.815256	−	0.579100i	$-0.196596\pi$
$138$	−154.719			−1.12115
$139$		−	54.4253i		−	0.391549i	−0.980649	−	0.195774i	$-0.937278\pi$
$139$		−	54.4253i		−	0.391549i	0.980649	−	0.195774i	$-0.0627220\pi$
$140$		0			0
$141$	−85.5262			−0.606569
$142$		−	101.333i		−	0.713610i
$143$	208.292			1.45659
$144$	−50.3583			−0.349710
$145$		0			0
$146$			18.6145i			0.127497i
$147$	−24.9848	−	81.1095i	−0.169965	−	0.551766i
$148$		−	33.9335i		−	0.229281i
$149$	−229.102			−1.53760			−0.768799	−	0.639490i	$-0.779146\pi$
$149$	−229.102			−1.53760			−0.768799	+	0.639490i	$0.779146\pi$
$150$		0			0
$151$	−197.735			−1.30950			−0.654750	−	0.755845i	$-0.727226\pi$
$151$	−197.735			−1.30950			−0.654750	+	0.755845i	$0.727226\pi$
$152$	11.3437			0.0746294
$153$	66.9181			0.437373
$154$	−220.169	+	298.198i	−1.42967	+	1.93635i
$155$		0			0
$156$	−72.1343			−0.462399
$157$	211.036			1.34418			0.672089	−	0.740470i	$-0.265397\pi$
$157$	211.036			1.34418			0.672089	+	0.740470i	$0.265397\pi$
$158$		−	45.2271i		−	0.286248i
$159$			85.2858i			0.536389i
$160$		0			0
$161$	−133.046	+	180.199i	−0.826375	+	1.11925i
$162$		−	25.1239i		−	0.155086i
$163$		−	181.823i		−	1.11548i	−0.830015	−	0.557741i	$-0.811668\pi$
$163$		−	181.823i		−	1.11548i	0.830015	−	0.557741i	$-0.188332\pi$
$164$			142.728i			0.870295i
$165$		0			0
$166$			102.679i			0.618549i
$167$	101.160			0.605751			0.302876	−	0.953030i	$-0.402053\pi$
$167$	101.160			0.605751			0.302876	+	0.953030i	$0.402053\pi$
$168$	−4.16676	+	5.64349i	−0.0248021	+	0.0335922i
$169$	−48.4250			−0.286538
$170$		0			0
$171$			58.8170i			0.343959i
$172$		−	71.5696i		−	0.416102i
$173$	−109.976			−0.635702			−0.317851	−	0.948141i	$-0.602961\pi$
$173$	−109.976			−0.635702			−0.317851	+	0.948141i	$0.602961\pi$
$174$		−	193.388i		−	1.11143i
$175$		0			0
$176$	318.415			1.80918
$177$			60.9981i			0.344622i
$178$	245.922			1.38159
$179$	−91.8832			−0.513314			−0.256657	−	0.966503i	$-0.582621\pi$
$179$	−91.8832			−0.513314			−0.256657	+	0.966503i	$0.582621\pi$
$180$		0			0
$181$		−	62.8649i		−	0.347320i	−0.984806	−	0.173660i	$-0.944441\pi$
$181$		−	62.8649i		−	0.347320i	0.984806	−	0.173660i	$-0.0555594\pi$
$182$	−127.450	+	172.619i	−0.700275	+	0.948457i
$183$		−	109.937i		−	0.600750i
$184$	18.5144			0.100622
$185$		0			0
$186$	−177.274			−0.953088
$187$	−423.123			−2.26269
$188$	−187.280			−0.996170
$189$	−29.2615	−	21.6047i	−0.154823	−	0.114311i
$190$		0			0
$191$	−75.9925			−0.397866			−0.198933	−	0.980013i	$-0.563748\pi$
$191$	−75.9925			−0.397866			−0.198933	+	0.980013i	$0.563748\pi$
$192$	−99.0812			−0.516048
$193$		−	22.7530i		−	0.117891i	−0.998261	−	0.0589456i	$-0.981226\pi$
$193$		−	22.7530i		−	0.117891i	0.998261	−	0.0589456i	$-0.0187738\pi$
$194$			373.537i			1.92545i
$195$		0			0
$196$	−54.7102	−	177.609i	−0.279134	−	0.906166i
$197$		−	137.485i		−	0.697891i	−0.937143	−	0.348946i	$-0.886540\pi$
$197$		−	137.485i		−	0.697891i	0.937143	−	0.348946i	$-0.113460\pi$
$198$			158.858i			0.802316i
$199$			267.299i			1.34321i	0.740909	+	0.671606i	$0.234395\pi$
$199$			267.299i			1.34321i	−0.740909	+	0.671606i	$0.765605\pi$
$200$		0			0
$201$		−	36.9869i		−	0.184015i
$202$	544.081			2.69347
$203$	−225.237	−	166.299i	−1.10954	−	0.819208i
$204$	146.533			0.718299
$205$		0			0
$206$			115.187i			0.559161i
$207$			95.9972i			0.463754i
$208$	184.323			0.886166
$209$		−	371.900i		−	1.77943i
$210$		0			0
$211$	−366.610			−1.73749			−0.868744	−	0.495261i	$-0.835073\pi$
$211$	−366.610			−1.73749			−0.868744	+	0.495261i	$0.835073\pi$
$212$			186.753i			0.880912i
$213$	−62.8731			−0.295179
$214$	82.9175			0.387465
$215$		0			0
$216$			3.00645i			0.0139187i
$217$	−152.443	+	206.469i	−0.702501	+	0.951472i
$218$			255.993i			1.17428i
$219$	11.5496			0.0527380
$220$		0			0
$221$	−244.935			−1.10830
$222$	−43.2596			−0.194863
$223$	−282.872			−1.26848			−0.634242	−	0.773134i	$-0.718688\pi$
$223$	−282.872			−1.26848			−0.634242	+	0.773134i	$0.718688\pi$
$224$	−185.210	+	250.849i	−0.826828	+	1.11986i
$225$		0			0
$226$	−8.32722			−0.0368461
$227$	210.777			0.928534			0.464267	−	0.885695i	$-0.346318\pi$
$227$	210.777			0.928534			0.464267	+	0.885695i	$0.346318\pi$
$228$			128.794i			0.564885i
$229$			137.506i			0.600464i	0.953866	+	0.300232i	$0.0970641\pi$
$229$			137.506i			0.600464i	−0.953866	+	0.300232i	$0.902936\pi$
$230$		0			0
$231$	185.021	+	136.606i	0.800955	+	0.591370i
$232$			23.1417i			0.0997488i
$233$			77.7682i			0.333769i	0.985976	+	0.166884i	$0.0533707\pi$
$233$			77.7682i			0.333769i	−0.985976	+	0.166884i	$0.946629\pi$
$234$			91.9591i			0.392988i
$235$		0			0
$236$			133.570i			0.565974i
$237$	−28.0618			−0.118404
$238$	258.901	−	350.657i	1.08782	−	1.47335i
$239$	123.843			0.518173			0.259086	−	0.965854i	$-0.416579\pi$
$239$	123.843			0.518173			0.259086	+	0.965854i	$0.416579\pi$
$240$		0			0
$241$		−	155.802i		−	0.646481i	−0.946317	−	0.323240i	$-0.895228\pi$
$241$		−	155.802i		−	0.646481i	0.946317	−	0.323240i	$-0.104772\pi$
$242$		−	666.684i		−	2.75489i
$243$	−15.5885			−0.0641500
$244$		−	240.734i		−	0.986613i
$245$		0			0
$246$	181.955			0.739653
$247$		−	215.283i		−	0.871593i
$248$	21.2135			0.0855383
$249$	63.7086			0.255858
$250$		0			0
$251$			278.340i			1.10892i	0.832210	+	0.554461i	$0.187076\pi$
$251$			278.340i			1.10892i	−0.832210	+	0.554461i	$0.812924\pi$
$252$	−64.0750	−	47.3086i	−0.254266	−	0.187732i
$253$		−	606.990i		−	2.39917i
$254$	292.138			1.15015
$255$		0			0
$256$	280.434			1.09545
$257$	−220.802			−0.859151			−0.429575	−	0.903031i	$-0.641337\pi$
$257$	−220.802			−0.859151			−0.429575	+	0.903031i	$0.641337\pi$
$258$	−91.2392			−0.353640
$259$	−37.2000	+	50.3839i	−0.143629	+	0.194533i
$260$		0			0
$261$	−119.990			−0.459732
$262$	−197.656			−0.754412
$263$			17.3477i			0.0659609i	0.999456	+	0.0329804i	$0.0104999\pi$
$263$			17.3477i			0.0659609i	−0.999456	+	0.0329804i	$0.989500\pi$
$264$		−	19.0098i		−	0.0720067i
$265$		0			0
$266$	308.207	+	227.558i	1.15867	+	0.855483i
$267$		−	152.586i		−	0.571482i
$268$		−	80.9916i		−	0.302207i
$269$		−	499.213i		−	1.85581i	−0.372816	−	0.927905i	$-0.621608\pi$
$269$		−	499.213i		−	1.85581i	0.372816	−	0.927905i	$-0.378392\pi$
$270$		0			0
$271$		−	330.005i		−	1.21773i	−0.793273	−	0.608866i	$-0.791625\pi$
$271$		−	330.005i		−	1.21773i	0.793273	−	0.608866i	$-0.208375\pi$
$272$	−374.431			−1.37659
$273$	107.104	+	79.0780i	0.392321	+	0.289663i
$274$	−442.944			−1.61659
$275$		0			0
$276$			210.209i			0.761625i
$277$			147.766i			0.533452i	0.963772	+	0.266726i	$0.0859418\pi$
$277$			147.766i			0.533452i	−0.963772	+	0.266726i	$0.914058\pi$
$278$	−151.931			−0.546513
$279$			109.992i			0.394237i
$280$		0			0
$281$	353.405			1.25767			0.628834	−	0.777540i	$-0.283533\pi$
$281$	353.405			1.25767			0.628834	+	0.777540i	$0.283533\pi$
$282$			238.751i			0.846633i
$283$	428.203			1.51308			0.756542	−	0.653945i	$-0.226887\pi$
$283$	428.203			1.51308			0.756542	+	0.653945i	$0.226887\pi$
$284$	−137.675			−0.484773
$285$		0			0
$286$		−	581.457i		−	2.03307i
$287$	156.467	−	211.920i	0.545182	−	0.738399i
$288$			133.634i			0.464009i
$289$	208.559			0.721657
$290$		0			0
$291$	231.766			0.796446
$292$	25.2906			0.0866117
$293$	−402.632			−1.37417			−0.687085	−	0.726577i	$-0.741110\pi$
$293$	−402.632			−1.37417			−0.687085	+	0.726577i	$0.741110\pi$
$294$	−226.421	+	69.7463i	−0.770140	+	0.237232i
$295$		0			0
$296$	5.17665			0.0174887
$297$	98.5658			0.331871
$298$			639.550i			2.14614i
$299$		−	351.371i		−	1.17515i
$300$		0			0
$301$	−78.4589	+	106.265i	−0.260661	+	0.353041i
$302$			551.986i			1.82777i
$303$		−	337.582i		−	1.11413i
$304$		−	329.103i		−	1.08258i
$305$		0			0
$306$		−	186.805i		−	0.610474i
$307$	92.7330			0.302062			0.151031	−	0.988529i	$-0.451741\pi$
$307$	92.7330			0.302062			0.151031	+	0.988529i	$0.451741\pi$
$308$	405.146	+	299.132i	1.31541	+	0.971207i
$309$	71.4694			0.231292
$310$		0			0
$311$		−	218.118i		−	0.701343i	−0.936498	−	0.350672i	$-0.885953\pi$
$311$		−	218.118i		−	0.701343i	0.936498	−	0.350672i	$-0.114047\pi$
$312$		−	11.0043i		−	0.0352701i
$313$	293.684			0.938288			0.469144	−	0.883122i	$-0.344562\pi$
$313$	293.684			0.938288			0.469144	+	0.883122i	$0.344562\pi$
$314$		−	589.117i		−	1.87617i
$315$		0			0
$316$	−61.4479			−0.194455
$317$			109.074i			0.344081i	0.985090	+	0.172041i	$0.0550361\pi$
$317$			109.074i			0.344081i	−0.985090	+	0.172041i	$0.944964\pi$
$318$	238.079			0.748677
$319$	758.697			2.37836
$320$		0			0
$321$		−	51.4472i		−	0.160272i
$322$	503.034	+	371.405i	1.56222	+	1.15343i
$323$			437.325i			1.35395i
$324$	−34.1346			−0.105354
$325$		0			0
$326$	−507.569			−1.55696
$327$	158.834			0.485731
$328$	−21.7736			−0.0663828
$329$	278.070	+	205.308i	0.845197	+	0.624035i
$330$		0			0
$331$	408.913			1.23539			0.617694	−	0.786419i	$-0.288067\pi$
$331$	408.913			1.23539			0.617694	+	0.786419i	$0.288067\pi$
$332$	139.505			0.420196
$333$			26.8410i			0.0806035i
$334$		−	282.394i		−	0.845492i
$335$		0			0
$336$	163.729	+	120.886i	0.487289	+	0.359780i
$337$		−	299.269i		−	0.888040i	−0.896017	−	0.444020i	$-0.853552\pi$
$337$		−	299.269i		−	0.888040i	0.896017	−	0.444020i	$-0.146448\pi$
$338$			135.181i			0.399942i
$339$			5.16673i			0.0152411i
$340$		0			0
$341$		−	695.480i		−	2.03953i
$342$	164.190			0.480089
$343$	−113.472	+	323.687i	−0.330823	+	0.943693i
$344$	10.9181			0.0317387
$345$		0			0
$346$			307.004i			0.887296i
$347$			567.731i			1.63611i	0.575138	+	0.818056i	$0.304948\pi$
$347$			567.731i			1.63611i	−0.575138	+	0.818056i	$0.695052\pi$
$348$	−262.747			−0.755019
$349$			141.703i			0.406025i	0.979176	+	0.203012i	$0.0650732\pi$
$349$			141.703i			0.406025i	−0.979176	+	0.203012i	$0.934927\pi$
$350$		0			0
$351$	57.0572			0.162556
$352$		−	844.970i		−	2.40048i
$353$	−452.435			−1.28169			−0.640843	−	0.767672i	$-0.721415\pi$
$353$	−452.435			−1.28169			−0.640843	+	0.767672i	$0.721415\pi$
$354$	170.279			0.481015
$355$		0			0
$356$		−	334.123i		−	0.938546i
$357$	−217.570	−	160.638i	−0.609439	−	0.449967i
$358$			256.496i			0.716470i
$359$	−174.670			−0.486546			−0.243273	−	0.969958i	$-0.578221\pi$
$359$	−174.670			−0.486546			−0.243273	+	0.969958i	$0.578221\pi$
$360$		0			0
$361$	−23.3825			−0.0647714
$362$	−175.490			−0.484780
$363$	−413.653			−1.13954
$364$	234.529	+	173.160i	0.644310	+	0.475714i
$365$		0			0
$366$	−306.895			−0.838511
$367$	−121.147			−0.330101			−0.165051	−	0.986285i	$-0.552779\pi$
$367$	−121.147			−0.330101			−0.165051	+	0.986285i	$0.552779\pi$
$368$		−	537.139i		−	1.45962i
$369$		−	112.896i		−	0.305951i
$370$		0			0
$371$	204.730	−	277.288i	0.551834	−	0.747407i
$372$			240.854i			0.647456i
$373$			90.9075i			0.243720i	0.992547	+	0.121860i	$0.0388859\pi$
$373$			90.9075i			0.243720i	−0.992547	+	0.121860i	$0.961114\pi$
$374$			1181.17i			3.15820i
$375$		0			0
$376$		−	28.5700i		−	0.0759841i
$377$	439.190			1.16496
$378$	−60.3105	+	81.6850i	−0.159552	+	0.216098i
$379$	638.344			1.68429			0.842143	−	0.539254i	$-0.181294\pi$
$379$	638.344			1.68429			0.842143	+	0.539254i	$0.181294\pi$
$380$		0			0
$381$		−	181.261i		−	0.475750i
$382$			212.137i			0.555331i
$383$	176.395			0.460561			0.230281	−	0.973124i	$-0.426036\pi$
$383$	176.395			0.460561			0.230281	+	0.973124i	$0.426036\pi$
$384$		−	32.0257i		−	0.0834003i
$385$		0			0
$386$	−63.5160			−0.164549
$387$			56.6105i			0.146280i
$388$	507.506			1.30800
$389$	−249.521			−0.641442			−0.320721	−	0.947174i	$-0.603925\pi$
$389$	−249.521			−0.641442			−0.320721	+	0.947174i	$0.603925\pi$
$390$		0			0
$391$			713.772i			1.82550i
$392$	27.0946	−	8.34618i	0.0691189	−	0.0212913i
$393$			122.638i			0.312056i
$394$	−383.795			−0.974098
$395$		0			0
$396$	215.833			0.545033
$397$	186.071			0.468694			0.234347	−	0.972153i	$-0.424705\pi$
$397$	186.071			0.468694			0.234347	+	0.972153i	$0.424705\pi$
$398$	746.178			1.87482
$399$	141.191	−	191.231i	0.353863	−	0.479275i
$400$		0			0
$401$	−188.067			−0.468996			−0.234498	−	0.972117i	$-0.575345\pi$
$401$	−188.067			−0.468996			−0.234498	+	0.972117i	$0.575345\pi$
$402$	−103.251			−0.256843
$403$		−	402.596i		−	0.998997i
$404$		−	739.215i		−	1.82974i
$405$		0			0
$406$	−464.232	+	628.759i	−1.14343	+	1.54867i
$407$		−	169.715i		−	0.416991i
$408$			22.3540i			0.0547891i
$409$			512.173i			1.25226i	0.779720	+	0.626128i	$0.215361\pi$
$409$			512.173i			1.25226i	−0.779720	+	0.626128i	$0.784639\pi$
$410$		0			0
$411$			274.831i			0.668687i
$412$	156.499			0.379852
$413$	146.427	−	198.322i	0.354545	−	0.480199i
$414$	267.981			0.647296
$415$		0			0
$416$		−	489.132i		−	1.17580i
$417$			94.2673i			0.226061i
$418$	−1038.18			−2.48367
$419$		−	323.661i		−	0.772461i	−0.922402	−	0.386231i	$-0.873777\pi$
$419$		−	323.661i		−	0.772461i	0.922402	−	0.386231i	$-0.126223\pi$
$420$		0			0
$421$	−503.872			−1.19685			−0.598423	−	0.801180i	$-0.704206\pi$
$421$	−503.872			−1.19685			−0.598423	+	0.801180i	$0.704206\pi$
$422$			1023.41i			2.42514i
$423$	148.136			0.350203
$424$	−28.4897			−0.0671927
$425$		0			0
$426$			175.513i			0.412003i
$427$	−263.907	+	357.437i	−0.618049	+	0.837089i
$428$		−	112.656i		−	0.263215i
$429$	−360.773			−0.840962
$430$		0			0
$431$	317.731			0.737195			0.368597	−	0.929589i	$-0.379838\pi$
$431$	317.731			0.737195			0.368597	+	0.929589i	$0.379838\pi$
$432$	87.2231			0.201905
$433$	−261.387			−0.603665			−0.301833	−	0.953361i	$-0.597598\pi$
$433$	−261.387			−0.603665			−0.301833	+	0.953361i	$0.597598\pi$
$434$	576.369	+	425.551i	1.32804	+	0.980532i
$435$		0			0
$436$	347.805			0.797717
$437$	−627.363			−1.43561
$438$		−	32.2413i		−	0.0736103i
$439$		−	789.513i		−	1.79844i	−0.437501	−	0.899218i	$-0.644137\pi$
$439$		−	789.513i		−	1.79844i	0.437501	−	0.899218i	$-0.355863\pi$
$440$		0			0
$441$	43.2750	+	140.486i	0.0981293	+	0.318562i
$442$			683.748i			1.54694i
$443$		−	585.242i		−	1.32109i	−0.750787	−	0.660544i	$-0.770326\pi$
$443$		−	585.242i		−	1.32109i	0.750787	−	0.660544i	$-0.229674\pi$
$444$			58.7746i			0.132375i
$445$		0			0
$446$			789.651i			1.77052i
$447$	396.817			0.887733
$448$	322.141	+	237.847i	0.719065	+	0.530907i
$449$	−528.147			−1.17627			−0.588137	−	0.808761i	$-0.700138\pi$
$449$	−528.147			−1.17627			−0.588137	+	0.808761i	$0.700138\pi$
$450$		0			0
$451$			713.842i			1.58280i
$452$			11.3138i			0.0250305i
$453$	342.486			0.756041
$454$		−	588.395i		−	1.29602i
$455$		0			0
$456$	−19.6478			−0.0430873
$457$		−	164.041i		−	0.358953i	−0.983762	−	0.179476i	$-0.942560\pi$
$457$		−	164.041i		−	0.358953i	0.983762	−	0.179476i	$-0.0574404\pi$
$458$	383.855			0.838112
$459$	−115.906			−0.252517
$460$		0			0
$461$			399.626i			0.866867i	0.901186	+	0.433434i	$0.142698\pi$
$461$			399.626i			0.866867i	−0.901186	+	0.433434i	$0.857302\pi$
$462$	381.343	−	516.494i	0.825418	−	1.11795i
$463$			680.267i			1.46926i	0.678468	+	0.734630i	$0.262644\pi$
$463$			680.267i			1.46926i	−0.678468	+	0.734630i	$0.737356\pi$
$464$	671.388			1.44696
$465$		0			0
$466$	217.093			0.465866
$467$	725.217			1.55293			0.776464	−	0.630162i	$-0.217011\pi$
$467$	725.217			1.55293			0.776464	+	0.630162i	$0.217011\pi$
$468$	124.940			0.266966
$469$	−88.7879	+	120.255i	−0.189313	+	0.256407i
$470$		0			0
$471$	−365.525			−0.776062
$472$	−20.3764			−0.0431704
$473$		−	357.948i		−	0.756762i
$474$			78.3357i			0.165265i
$475$		0			0
$476$	−476.420	−	351.755i	−1.00088	−	0.738982i
$477$		−	147.719i		−	0.309684i
$478$		−	345.714i		−	0.723252i
$479$			317.103i			0.662010i	0.943629	+	0.331005i	$0.107388\pi$
$479$			317.103i			0.662010i	−0.943629	+	0.331005i	$0.892612\pi$
$480$		0			0
$481$		−	98.2439i		−	0.204249i
$482$	−434.928			−0.902341
$483$	230.443	−	312.114i	0.477108	−	0.646198i
$484$	−905.791			−1.87147
$485$		0			0
$486$			43.5159i			0.0895389i
$487$			353.125i			0.725103i	0.931964	+	0.362551i	$0.118094\pi$
$487$			353.125i			0.725103i	−0.931964	+	0.362551i	$0.881906\pi$
$488$	36.7245			0.0752552
$489$			314.927i			0.644023i
$490$		0			0
$491$	−343.280			−0.699145			−0.349572	−	0.936909i	$-0.613673\pi$
$491$	−343.280			−0.699145			−0.349572	+	0.936909i	$0.613673\pi$
$492$		−	247.213i		−	0.502465i
$493$	−892.167			−1.80967
$494$	−600.974			−1.21655
$495$		0			0
$496$		−	615.447i		−	1.24082i
$497$	204.418	+	150.928i	0.411304	+	0.303678i
$498$		−	177.846i		−	0.357120i
$499$	420.584			0.842853			0.421427	−	0.906863i	$-0.361530\pi$
$499$	420.584			0.842853			0.421427	+	0.906863i	$0.361530\pi$
$500$		0			0
$501$	−175.215			−0.349731
$502$	776.998			1.54780
$503$	−183.030			−0.363876			−0.181938	−	0.983310i	$-0.558237\pi$
$503$	−183.030			−0.363876			−0.181938	+	0.983310i	$0.558237\pi$
$504$	7.21704	−	9.77481i	0.0143195	−	0.0193945i
$505$		0			0
$506$	−1694.44			−3.34870
$507$	83.8745			0.165433
$508$		−	396.913i		−	0.781326i
$509$			261.854i			0.514448i	0.966352	+	0.257224i	$0.0828079\pi$
$509$			261.854i			0.514448i	−0.966352	+	0.257224i	$0.917192\pi$
$510$		0			0
$511$	−37.5511	−	27.7251i	−0.0734855	−	0.0542566i
$512$		−	708.885i		−	1.38454i
$513$		−	101.874i		−	0.198585i
$514$			616.378i			1.19918i
$515$		0			0
$516$			123.962i			0.240237i
$517$	−936.662			−1.81173
$518$	140.649	+	103.846i	0.271523	+	0.200474i
$519$	190.485			0.367023
$520$		0			0
$521$			477.677i			0.916846i	0.888734	+	0.458423i	$0.151586\pi$
$521$			477.677i			0.916846i	−0.888734	+	0.458423i	$0.848414\pi$
$522$			334.958i			0.641682i
$523$	770.784			1.47377			0.736887	−	0.676016i	$-0.236295\pi$
$523$	770.784			1.47377			0.736887	+	0.676016i	$0.236295\pi$
$524$			268.545i			0.512491i
$525$		0			0
$526$	48.4269			0.0920664
$527$			817.829i			1.55186i
$528$	−551.512			−1.04453
$529$	−494.940			−0.935614
$530$		0			0
$531$		−	105.652i		−	0.198968i
$532$	309.172	−	418.745i	0.581151	−	0.787114i
$533$			413.225i			0.775281i
$534$	−425.950			−0.797660
$535$		0			0
$536$	12.3555			0.0230513
$537$	159.146			0.296362
$538$	−1393.58			−2.59029
$539$	−273.628	−	888.292i	−0.507658	−	1.64804i
$540$		0			0
$541$	1054.53			1.94922			0.974609	−	0.223912i	$-0.0718828\pi$
$541$	1054.53			1.94922			0.974609	+	0.223912i	$0.0718828\pi$
$542$	−921.225			−1.69968
$543$			108.885i			0.200525i
$544$			993.618i			1.82650i
$545$		0			0
$546$	220.750	−	298.985i	0.404304	−	0.547592i
$547$			697.821i			1.27572i	0.770151	+	0.637862i	$0.220181\pi$
$547$			697.821i			1.27572i	−0.770151	+	0.637862i	$0.779819\pi$
$548$			601.806i			1.09819i
$549$			190.417i			0.346843i
$550$		0			0
$551$		−	784.162i		−	1.42316i
$552$	−32.0678			−0.0580939
$553$	91.2367	+	67.3628i	0.164985	+	0.121813i
$554$	412.496			0.744578
$555$		0			0
$556$			206.421i			0.371260i
$557$		−	941.244i		−	1.68985i	−0.534888	−	0.844923i	$-0.679646\pi$
$557$		−	941.244i		−	1.68985i	0.534888	−	0.844923i	$-0.320354\pi$
$558$	307.048			0.550266
$559$		−	207.207i		−	0.370675i
$560$		0			0
$561$	732.870			1.30636
$562$		−	986.545i		−	1.75542i
$563$	768.996			1.36589			0.682945	−	0.730470i	$-0.260699\pi$
$563$	768.996			1.36589			0.682945	+	0.730470i	$0.260699\pi$
$564$	324.378			0.575139
$565$		0			0
$566$		−	1195.35i		−	2.11192i
$567$	50.6825	+	37.4204i	0.0893871	+	0.0659972i
$568$		−	21.0027i		−	0.0369766i
$569$	46.4935			0.0817108			0.0408554	−	0.999165i	$-0.486992\pi$
$569$	46.4935			0.0817108			0.0408554	+	0.999165i	$0.486992\pi$
$570$		0			0
$571$	774.153			1.35578			0.677892	−	0.735161i	$-0.262894\pi$
$571$	774.153			1.35578			0.677892	+	0.735161i	$0.262894\pi$
$572$	−789.997			−1.38111
$573$	131.623			0.229708
$574$	−591.586	−	436.786i	−1.03064	−	0.760951i
$575$		0			0
$576$	171.614			0.297940
$577$	66.7246			0.115641			0.0578203	−	0.998327i	$-0.481585\pi$
$577$	66.7246			0.115641			0.0578203	+	0.998327i	$0.481585\pi$
$578$		−	582.202i		−	1.00727i
$579$			39.4093i			0.0680645i
$580$		0			0
$581$	−207.135	−	152.934i	−0.356514	−	0.263225i
$582$		−	646.985i		−	1.11166i
$583$			934.029i			1.60211i
$584$			3.85815i			0.00660642i
$585$		0			0
$586$			1123.97i			1.91803i
$587$	−678.789			−1.15637			−0.578185	−	0.815906i	$-0.696239\pi$
$587$	−678.789			−1.15637			−0.578185	+	0.815906i	$0.696239\pi$
$588$	94.7608	+	307.627i	0.161158	+	0.523175i
$589$	−718.823			−1.22041
$590$		0			0
$591$			238.130i			0.402928i
$592$		−	150.185i		−	0.253691i
$593$	289.610			0.488381			0.244190	−	0.969727i	$-0.421478\pi$
$593$	289.610			0.488381			0.244190	+	0.969727i	$0.421478\pi$
$594$		−	275.151i		−	0.463217i
$595$		0			0
$596$	868.924			1.45793
$597$		−	462.976i		−	0.775503i
$598$	−980.869			−1.64025
$599$	−384.076			−0.641195			−0.320598	−	0.947216i	$-0.603884\pi$
$599$	−384.076			−0.641195			−0.320598	+	0.947216i	$0.603884\pi$
$600$		0			0
$601$		−	37.4083i		−	0.0622434i	−0.999516	−	0.0311217i	$-0.990092\pi$
$601$		−	37.4083i		−	0.0622434i	0.999516	−	0.0311217i	$-0.00990794\pi$
$602$	296.644	+	219.022i	0.492765	+	0.363823i
$603$			64.0632i			0.106241i
$604$	749.955			1.24165
$605$		0			0
$606$	−942.375			−1.55507
$607$	876.691			1.44430			0.722150	−	0.691736i	$-0.243154\pi$
$607$	876.691			1.44430			0.722150	+	0.691736i	$0.243154\pi$
$608$	−873.331			−1.43640
$609$	390.121	+	288.039i	0.640594	+	0.472970i
$610$		0			0
$611$	−542.210			−0.887414
$612$	−253.803			−0.414710
$613$			591.071i			0.964226i	0.876109	+	0.482113i	$0.160131\pi$
$613$			591.071i			0.964226i	−0.876109	+	0.482113i	$0.839869\pi$
$614$		−	258.868i		−	0.421610i
$615$		0			0
$616$	−45.6333	+	61.8061i	−0.0740801	+	0.100335i
$617$		−	744.668i		−	1.20692i	−0.797394	−	0.603459i	$-0.793789\pi$
$617$		−	744.668i		−	1.20692i	0.797394	−	0.603459i	$-0.206211\pi$
$618$		−	199.510i		−	0.322832i
$619$			851.811i			1.37611i	0.725659	+	0.688054i	$0.241535\pi$
$619$			851.811i			1.37611i	−0.725659	+	0.688054i	$0.758465\pi$
$620$		0			0
$621$		−	166.272i		−	0.267749i
$622$	−608.886			−0.978917
$623$	−366.285	+	496.099i	−0.587938	+	0.796307i
$624$	−319.256			−0.511628
$625$		0			0
$626$		−	819.833i		−	1.30964i
$627$			644.149i			1.02735i
$628$	−800.404			−1.27453
$629$			199.572i			0.317284i
$630$		0			0
$631$	316.625			0.501783			0.250891	−	0.968015i	$-0.419276\pi$
$631$	316.625			0.501783			0.250891	+	0.968015i	$0.419276\pi$
$632$		−	9.37402i		−	0.0148323i
$633$	634.987			1.00314
$634$	304.485			0.480260
$635$		0			0
$636$		−	323.466i		−	0.508595i
$637$	−158.396	−	514.209i	−0.248660	−	0.807236i
$638$		−	2117.94i		−	3.31965i
$639$	108.899			0.170422
$640$		0			0
$641$	173.979			0.271418			0.135709	−	0.990749i	$-0.456669\pi$
$641$	173.979			0.271418			0.135709	+	0.990749i	$0.456669\pi$
$642$	−143.617			−0.223703
$643$	926.785			1.44135			0.720673	−	0.693275i	$-0.243833\pi$
$643$	926.785			1.44135			0.720673	+	0.693275i	$0.243833\pi$
$644$	504.610	−	683.447i	0.783556	−	1.06125i
$645$		0			0
$646$	1220.81			1.88980
$647$	−429.625			−0.664027			−0.332013	−	0.943275i	$-0.607728\pi$
$647$	−429.625			−0.664027			−0.332013	+	0.943275i	$0.607728\pi$
$648$		−	5.20732i		−	0.00803599i
$649$			668.036i			1.02933i
$650$		0			0
$651$	264.038	−	357.615i	0.405589	−	0.549333i
$652$			689.608i			1.05768i
$653$			927.100i			1.41976i	0.704325	+	0.709878i	$0.251250\pi$
$653$			927.100i			1.41976i	−0.704325	+	0.709878i	$0.748750\pi$
$654$		−	443.392i		−	0.677970i
$655$		0			0
$656$			631.695i			0.962950i
$657$	−20.0045			−0.0304483
$658$	573.126	−	776.245i	0.871012	−	1.17970i
$659$	−692.153			−1.05031			−0.525154	−	0.851007i	$-0.675992\pi$
$659$	−692.153			−1.05031			−0.525154	+	0.851007i	$0.675992\pi$
$660$		0			0
$661$		−	1101.42i		−	1.66629i	−0.553053	−	0.833146i	$-0.686537\pi$
$661$		−	1101.42i		−	1.66629i	0.553053	−	0.833146i	$-0.313463\pi$
$662$		−	1141.50i		−	1.72432i
$663$	424.240			0.639879
$664$			21.2818i			0.0320510i
$665$		0			0
$666$	74.9278			0.112504
$667$		−	1279.86i		−	1.91882i
$668$	−383.675			−0.574364
$669$	489.949			0.732360
$670$		0			0
$671$		−	1204.01i		−	1.79435i
$672$	320.792	−	434.483i	0.477370	−	0.646553i
$673$		−	701.861i		−	1.04288i	−0.853287	−	0.521442i	$-0.825394\pi$
$673$		−	701.861i		−	1.04288i	0.853287	−	0.521442i	$-0.174606\pi$
$674$	−835.424			−1.23950
$675$		0			0
$676$	183.663			0.271691
$677$	404.920			0.598110			0.299055	−	0.954236i	$-0.403329\pi$
$677$	404.920			0.598110			0.299055	+	0.954236i	$0.403329\pi$
$678$	14.4232			0.0212731
$679$	−753.535	−	556.358i	−1.10977	−	0.819379i
$680$		0			0
$681$	−365.077			−0.536090
$682$	−1941.47			−2.84672
$683$			766.177i			1.12178i	0.827890	+	0.560891i	$0.189541\pi$
$683$			766.177i			1.12178i	−0.827890	+	0.560891i	$0.810459\pi$
$684$		−	223.077i		−	0.326136i
$685$		0			0
$686$	903.586	+	316.764i	1.31718	+	0.461754i
$687$		−	238.168i		−	0.346678i
$688$		−	316.757i		−	0.460402i
$689$			540.686i			0.784740i
$690$		0			0
$691$			162.333i			0.234925i	0.993077	+	0.117462i	$0.0374760\pi$
$691$			162.333i			0.234925i	−0.993077	+	0.117462i	$0.962524\pi$
$692$	417.111			0.602762
$693$	−320.465	−	236.609i	−0.462432	−	0.341427i
$694$	1584.85			2.28364
$695$		0			0
$696$		−	40.0826i		−	0.0575900i
$697$		−	839.421i		−	1.20433i
$698$	395.570			0.566719
$699$		−	134.698i		−	0.192702i
$700$		0			0
$701$	−69.5098			−0.0991581			−0.0495790	−	0.998770i	$-0.515788\pi$
$701$	−69.5098			−0.0991581			−0.0495790	+	0.998770i	$0.515788\pi$
$702$		−	159.278i		−	0.226892i
$703$	−175.412			−0.249519
$704$	−1085.11			−1.54135
$705$		0			0
$706$			1262.99i			1.78894i
$707$	−810.372	+	1097.57i	−1.14621	+	1.55244i
$708$		−	231.350i		−	0.326765i
$709$	−134.839			−0.190182			−0.0950912	−	0.995469i	$-0.530314\pi$
$709$	−134.839			−0.190182			−0.0950912	+	0.995469i	$0.530314\pi$
$710$		0			0
$711$	48.6044			0.0683606
$712$	50.9712			0.0715888
$713$	−1173.22			−1.64546
$714$	−448.429	+	607.356i	−0.628052	+	0.850638i
$715$		0			0
$716$	348.489			0.486716
$717$	−214.503			−0.299167
$718$			487.600i			0.679109i
$719$		−	638.863i		−	0.888544i	−0.895892	−	0.444272i	$-0.853462\pi$
$719$		−	638.863i		−	0.888544i	0.895892	−	0.444272i	$-0.146538\pi$
$720$		0			0
$721$	−232.367	−	171.564i	−0.322284	−	0.237952i
$722$			65.2732i			0.0904062i
$723$			269.857i			0.373246i
$724$			238.430i			0.329323i
$725$		0			0
$726$			1154.73i			1.59054i
$727$	704.430			0.968955			0.484477	−	0.874804i	$-0.339010\pi$
$727$	704.430			0.968955			0.484477	+	0.874804i	$0.339010\pi$
$728$	−26.4160	+	35.7780i	−0.0362857	+	0.0491456i
$729$	27.0000			0.0370370
$730$		0			0
$731$			420.919i			0.575812i
$732$			416.963i			0.569622i
$733$	275.472			0.375815			0.187907	−	0.982187i	$-0.439830\pi$
$733$	275.472			0.375815			0.187907	+	0.982187i	$0.439830\pi$
$734$			338.188i			0.460747i
$735$		0			0
$736$	−1425.39			−1.93667
$737$		−	405.072i		−	0.549622i
$738$	−315.155			−0.427039
$739$	−238.655			−0.322943			−0.161471	−	0.986877i	$-0.551624\pi$
$739$	−238.655			−0.322943			−0.161471	+	0.986877i	$0.551624\pi$
$740$		0			0
$741$			372.882i			0.503214i
$742$	−774.063	−	571.514i	−1.04321	−	0.770235i
$743$		−	221.162i		−	0.297661i	−0.988863	−	0.148831i	$-0.952449\pi$
$743$		−	221.162i		−	0.297661i	0.988863	−	0.148831i	$-0.0475509\pi$
$744$	−36.7429			−0.0493856
$745$		0			0
$746$	253.773			0.340178
$747$	−110.347			−0.147720
$748$	1604.79			2.14544
$749$	−123.500	+	167.269i	−0.164887	+	0.223324i
$750$		0			0
$751$	−496.682			−0.661361			−0.330680	−	0.943743i	$-0.607278\pi$
$751$	−496.682			−0.661361			−0.330680	+	0.943743i	$0.607278\pi$
$752$	−828.874			−1.10223
$753$		−	482.098i		−	0.640237i
$754$		−	1226.02i		−	1.62602i
$755$		0			0
$756$	110.981	+	81.9408i	0.146801	+	0.108387i
$757$			866.706i			1.14492i	0.819932	+	0.572461i	$0.194011\pi$
$757$			866.706i			1.14492i	−0.819932	+	0.572461i	$0.805989\pi$
$758$		−	1781.97i		−	2.35088i
$759$			1051.34i			1.38516i
$760$		0			0
$761$		−	621.621i		−	0.816847i	−0.912793	−	0.408424i	$-0.866079\pi$
$761$		−	621.621i		−	0.816847i	0.912793	−	0.408424i	$-0.133921\pi$
$762$	−505.998			−0.664039
$763$	−516.414	−	381.284i	−0.676820	−	0.499717i
$764$	288.219			0.377250
$765$		0			0
$766$		−	492.415i		−	0.642839i
$767$			386.709i			0.504184i
$768$	−485.726			−0.632456
$769$		−	316.574i		−	0.411669i	−0.978587	−	0.205835i	$-0.934009\pi$
$769$		−	316.574i		−	0.411669i	0.978587	−	0.205835i	$-0.0659909\pi$
$770$		0			0
$771$	382.440			0.496031
$772$			86.2961i			0.111782i
$773$	710.993			0.919784			0.459892	−	0.887975i	$-0.347888\pi$
$773$	710.993			0.919784			0.459892	+	0.887975i	$0.347888\pi$
$774$	158.031			0.204174
$775$		0			0
$776$			77.4213i			0.0997697i
$777$	64.4323	−	87.2675i	0.0829244	−	0.112313i
$778$			696.550i			0.895308i
$779$	737.801			0.947113
$780$		0			0
$781$	−688.570			−0.881652
$782$	1992.53			2.54799
$783$	207.829			0.265426
$784$	−242.140	−	786.070i	−0.308851	−	1.00264i
$785$		0			0
$786$	342.350			0.435560
$787$	845.181			1.07393			0.536964	−	0.843605i	$-0.319571\pi$
$787$	845.181			1.07393			0.536964	+	0.843605i	$0.319571\pi$
$788$			521.443i			0.661729i
$789$		−	30.0471i		−	0.0380825i
$790$		0			0
$791$	12.4028	−	16.7985i	0.0156799	−	0.0212370i
$792$			32.9259i			0.0415731i
$793$		−	696.968i		−	0.878901i
$794$		−	519.427i		−	0.654190i
$795$		0			0
$796$		−	1013.79i		−	1.27361i
$797$	−541.537			−0.679469			−0.339734	−	0.940521i	$-0.610337\pi$
$797$	−541.537			−0.679469			−0.339734	+	0.940521i	$0.610337\pi$
$798$	−533.830	−	394.143i	−0.668959	−	0.493913i
$799$	1101.44			1.37852
$800$		0			0
$801$			264.286i			0.329945i
$802$			524.999i			0.654612i
$803$	126.489			0.157520
$804$			140.282i			0.174480i
$805$		0			0
$806$	−1123.86			−1.39437
$807$			864.662i			1.07145i
$808$	112.769			0.139566
$809$	363.991			0.449927			0.224963	−	0.974367i	$-0.427774\pi$
$809$	363.991			0.449927			0.224963	+	0.974367i	$0.427774\pi$
$810$		0			0
$811$			882.216i			1.08781i	0.839146	+	0.543906i	$0.183055\pi$
$811$			882.216i			1.08781i	−0.839146	+	0.543906i	$0.816945\pi$
$812$	854.263	+	630.729i	1.05205	+	0.776759i
$813$			571.586i			0.703057i
$814$	−473.768			−0.582025
$815$		0			0
$816$	648.534			0.794772
$817$	−369.963			−0.452831
$818$	1429.76			1.74787
$819$	−185.509	−	136.967i	−0.226507	−	0.167237i
$820$		0			0
$821$	681.271			0.829806			0.414903	−	0.909866i	$-0.363815\pi$
$821$	681.271			0.829806			0.414903	+	0.909866i	$0.363815\pi$
$822$	767.202			0.933336
$823$			360.544i			0.438085i	0.975715	+	0.219042i	$0.0702933\pi$
$823$			360.544i			0.438085i	−0.975715	+	0.219042i	$0.929707\pi$
$824$			23.8743i			0.0289737i
$825$		0			0
$826$	−553.626	−	408.759i	−0.670249	−	0.494865i
$827$		−	770.095i		−	0.931191i	−0.884998	−	0.465596i	$-0.845840\pi$
$827$		−	770.095i		−	0.931191i	0.884998	−	0.465596i	$-0.154160\pi$
$828$		−	364.092i		−	0.439724i
$829$			128.381i			0.154862i	0.996998	+	0.0774312i	$0.0246718\pi$
$829$			128.381i			0.154862i	−0.996998	+	0.0774312i	$0.975328\pi$
$830$		0			0
$831$		−	255.938i		−	0.307988i
$832$	−628.144			−0.754981
$833$	321.764	+	1044.56i	0.386272	+	1.25397i
$834$	263.152			0.315530
$835$		0			0
$836$			1410.52i			1.68722i
$837$		−	190.512i		−	0.227613i
$838$	−903.515			−1.07818
$839$			1367.14i			1.62949i	0.579823	+	0.814743i	$0.303122\pi$
$839$			1367.14i			1.62949i	−0.579823	+	0.814743i	$0.696878\pi$
$840$		0			0
$841$	758.735			0.902182
$842$			1406.58i			1.67053i
$843$	−612.115			−0.726115
$844$	1390.46			1.64746
$845$		0			0
$846$		−	413.528i		−	0.488804i
$847$	1344.90	+	992.982i	1.58784	+	1.17235i
$848$			826.544i			0.974698i
$849$	−741.669			−0.873580
$850$		0			0
$851$	−286.295			−0.336422
$852$	238.461			0.279884
$853$	797.415			0.934836			0.467418	−	0.884036i	$-0.345184\pi$
$853$	797.415			0.934836			0.467418	+	0.884036i	$0.345184\pi$
$854$	997.803	+	736.708i	1.16839	+	0.862656i
$855$		0			0
$856$	17.1859			0.0200770
$857$	898.781			1.04875			0.524377	−	0.851486i	$-0.324298\pi$
$857$	898.781			1.04875			0.524377	+	0.851486i	$0.324298\pi$
$858$			1007.11i			1.17379i
$859$			915.157i			1.06537i	0.846312	+	0.532687i	$0.178818\pi$
$859$			915.157i			1.06537i	−0.846312	+	0.532687i	$0.821182\pi$
$860$		0			0
$861$	−271.009	+	367.057i	−0.314761	+	0.426315i
$862$		−	886.961i		−	1.02896i
$863$			1357.85i			1.57341i	0.617332	+	0.786703i	$0.288214\pi$
$863$			1357.85i			1.57341i	−0.617332	+	0.786703i	$0.711786\pi$
$864$		−	231.462i		−	0.267896i
$865$		0			0
$866$			729.674i			0.842580i
$867$	−361.235			−0.416649
$868$	578.175	−	783.084i	0.666100	−	0.902170i
$869$	−307.325			−0.353654
$870$		0			0
$871$		−	234.486i		−	0.269214i
$872$			53.0584i			0.0608468i
$873$	−401.430			−0.459828
$874$			1751.31i			2.00379i
$875$		0			0
$876$	−43.8047			−0.0500053
$877$			1513.27i			1.72550i	0.505627	+	0.862752i	$0.331261\pi$
$877$			1513.27i			1.72550i	−0.505627	+	0.862752i	$0.668739\pi$
$878$	−2203.96			−2.51021
$879$	697.379			0.793377
$880$		0			0
$881$			677.970i			0.769546i	0.923011	+	0.384773i	$0.125720\pi$
$881$			677.970i			0.769546i	−0.923011	+	0.384773i	$0.874280\pi$
$882$	392.173	−	120.804i	0.444640	−	0.136966i
$883$		−	155.548i		−	0.176159i	−0.996113	−	0.0880793i	$-0.971927\pi$
$883$		−	155.548i		−	0.176159i	0.996113	−	0.0880793i	$-0.0280729\pi$
$884$	928.974			1.05088
$885$		0			0
$886$	−1633.73			−1.84394
$887$	−871.417			−0.982432			−0.491216	−	0.871038i	$-0.663447\pi$
$887$	−871.417			−0.982432			−0.491216	+	0.871038i	$0.663447\pi$
$888$	−8.96622			−0.0100971
$889$	−435.120	+	589.330i	−0.489449	+	0.662913i
$890$		0			0
$891$	−170.721			−0.191606
$892$	1072.86			1.20276
$893$			968.101i			1.08410i
$894$		−	1107.73i		−	1.23907i
$895$		0			0
$896$	−76.8784	+	104.125i	−0.0858018	+	0.116211i
$897$			608.592i			0.678475i
$898$			1474.35i			1.64181i
$899$		−	1466.44i		−	1.63119i
$900$		0			0
$901$		−	1098.34i		−	1.21903i
$902$	1992.72			2.20923
$903$	135.895	−	184.057i	0.150493	−	0.203828i
$904$	−1.72594			−0.00190923
$905$		0			0
$906$		−	956.067i		−	1.05526i
$907$		−	473.129i		−	0.521642i	−0.965387	−	0.260821i	$-0.916007\pi$
$907$		−	473.129i		−	0.521642i	0.965387	−	0.260821i	$-0.0839932\pi$
$908$	−799.422			−0.880421
$909$			584.709i			0.643244i
$910$		0			0
$911$	−676.153			−0.742210			−0.371105	−	0.928591i	$-0.621021\pi$
$911$	−676.153			−0.742210			−0.371105	+	0.928591i	$0.621021\pi$
$912$			570.023i			0.625025i
$913$	697.721			0.764207
$914$	−457.929			−0.501017
$915$		0			0
$916$		−	521.525i		−	0.569350i
$917$	294.395	−	398.731i	0.321042	−	0.434821i
$918$			323.556i			0.352457i
$919$	−1204.50			−1.31066			−0.655331	−	0.755342i	$-0.727471\pi$
$919$	−1204.50			−1.31066			−0.655331	+	0.755342i	$0.727471\pi$
$920$		0			0
$921$	−160.618			−0.174395
$922$	1115.57			1.20995
$923$	−398.596			−0.431848
$924$	−701.734	−	518.112i	−0.759452	−	0.560727i
$925$		0			0
$926$	1899.00			2.05075
$927$	−123.789			−0.133537
$928$		−	1781.65i		−	1.91988i
$929$		−	586.143i		−	0.630940i	−0.948936	−	0.315470i	$-0.897838\pi$
$929$		−	586.143i		−	0.630940i	0.948936	−	0.315470i	$-0.102162\pi$
$930$		0			0
$931$	−918.107	+	282.812i	−0.986151	+	0.303772i
$932$		−	294.954i		−	0.316474i
$933$			377.791i			0.404921i
$934$		−	2024.48i		−	2.16754i
$935$		0			0
$936$			19.0599i			0.0203632i
$937$	−449.053			−0.479245			−0.239623	−	0.970866i	$-0.577024\pi$
$937$	−449.053			−0.479245			−0.239623	+	0.970866i	$0.577024\pi$
$938$	335.697	+	247.856i	0.357886	+	0.264238i
$939$	−508.676			−0.541721
$940$		0			0
$941$			904.538i			0.961252i	0.876926	+	0.480626i	$0.159591\pi$
$941$			904.538i			0.961252i	−0.876926	+	0.480626i	$0.840409\pi$
$942$			1020.38i			1.08321i
$943$	1204.19			1.27698
$944$			591.161i			0.626230i
$945$		0			0
$946$	−999.229			−1.05627
$947$			1631.56i			1.72288i	0.507861	+	0.861439i	$0.330436\pi$
$947$			1631.56i			1.72288i	−0.507861	+	0.861439i	$0.669564\pi$
$948$	106.431			0.112269
$949$	73.2210			0.0771560
$950$		0			0
$951$		−	188.921i		−	0.198656i
$952$	53.6612	−	72.6791i	0.0563668	−	0.0763435i
$953$		−	1547.14i		−	1.62344i	−0.584046	−	0.811721i	$-0.698531\pi$
$953$		−	1547.14i		−	1.62344i	0.584046	−	0.811721i	$-0.301469\pi$
$954$	−412.365			−0.432249
$955$		0			0
$956$	−469.705			−0.491323
$957$	−1314.10			−1.37315
$958$	885.207			0.924015
$959$	659.736	−	893.552i	0.687942	−	0.931753i
$960$		0			0
$961$	−383.253			−0.398806
$962$	−274.252			−0.285086
$963$			89.1092i			0.0925329i
$964$			590.915i			0.612982i
$965$		0			0
$966$	−871.281	−	643.293i	−0.901947	−	0.665935i
$967$			282.618i			0.292263i	0.989265	+	0.146131i	$0.0466822\pi$
$967$			282.618i			0.292263i	−0.989265	+	0.146131i	$0.953318\pi$
$968$		−	138.181i		−	0.142749i
$969$		−	757.469i		−	0.781701i
$970$		0			0
$971$			586.935i			0.604465i	0.953234	+	0.302232i	$0.0977319\pi$
$971$			586.935i			0.604465i	−0.953234	+	0.302232i	$0.902268\pi$
$972$	59.1229			0.0608260
$973$	226.291	−	306.490i	0.232570	−	0.314994i
$974$	985.765			1.01208
$975$		0			0
$976$		−	1065.45i		−	1.09165i
$977$		−	651.703i		−	0.667045i	−0.942742	−	0.333523i	$-0.891763\pi$
$977$		−	651.703i		−	0.667045i	0.942742	−	0.333523i	$-0.108237\pi$
$978$	879.135			0.898911
$979$		−	1671.08i		−	1.70693i
$980$		0			0
$981$	−275.109			−0.280437
$982$			958.283i			0.975848i
$983$	−583.048			−0.593131			−0.296565	−	0.955013i	$-0.595841\pi$
$983$	−583.048			−0.593131			−0.296565	+	0.955013i	$0.595841\pi$
$984$	37.7129			0.0383261
$985$		0			0
$986$			2490.53i			2.52589i
$987$	−481.631	−	355.603i	−0.487975	−	0.360287i
$988$			816.513i			0.826430i
$989$	−603.828			−0.610544
$990$		0			0
$991$	377.146			0.380572			0.190286	−	0.981729i	$-0.439059\pi$
$991$	377.146			0.380572			0.190286	+	0.981729i	$0.439059\pi$
$992$	−1633.19			−1.64636
$993$	−708.259			−0.713251
$994$	421.323	−	570.643i	0.423866	−	0.574087i
$995$		0			0
$996$	−241.630			−0.242600
$997$	1586.82			1.59159			0.795795	−	0.605565i	$-0.207053\pi$
$997$	1586.82			1.59159			0.795795	+	0.605565i	$0.207053\pi$
$998$		−	1174.08i		−	1.17643i
$999$		−	46.4899i		−	0.0465364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.e.c.349.7		24
5.2	odd	4		525.3.h.d.76.10		12
5.3	odd	4		105.3.h.a.76.3	✓	12
5.4	even	2	inner	525.3.e.c.349.22		24
7.6	odd	2	inner	525.3.e.c.349.21		24
15.8	even	4		315.3.h.d.181.9		12
20.3	even	4		1680.3.s.c.1441.10		12
35.13	even	4		105.3.h.a.76.4	yes	12
35.27	even	4		525.3.h.d.76.9		12
35.34	odd	2	inner	525.3.e.c.349.8		24
105.83	odd	4		315.3.h.d.181.10		12
140.83	odd	4		1680.3.s.c.1441.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.3	✓	12	5.3	odd	4
105.3.h.a.76.4	yes	12	35.13	even	4
315.3.h.d.181.9		12	15.8	even	4
315.3.h.d.181.10		12	105.83	odd	4
525.3.e.c.349.7		24	1.1	even	1	trivial
525.3.e.c.349.8		24	35.34	odd	2	inner
525.3.e.c.349.21		24	7.6	odd	2	inner
525.3.e.c.349.22		24	5.4	even	2	inner
525.3.h.d.76.9		12	35.27	even	4
525.3.h.d.76.10		12	5.2	odd	4
1680.3.s.c.1441.1		12	140.83	odd	4
1680.3.s.c.1441.10		12	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.79155i q^{2} -1.73205 q^{3} -3.79273 q^{4} +4.83510i q^{6} +(5.63139 + 4.15782i) q^{7} -0.578591i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-2.79155i q^{2} -1.73205 q^{3} -3.79273 q^{4} +4.83510i q^{6} +(5.63139 + 4.15782i) q^{7} -0.578591i q^{8} +3.00000 q^{9} -18.9690 q^{11} +6.56921 q^{12} -10.9807 q^{13} +(11.6068 - 15.7203i) q^{14} -16.7861 q^{16} +22.3060 q^{17} -8.37464i q^{18} +19.6057i q^{19} +(-9.75385 - 7.20156i) q^{21} +52.9528i q^{22} +31.9991i q^{23} +1.00215i q^{24} +30.6530i q^{26} -5.19615 q^{27} +(-21.3583 - 15.7695i) q^{28} -39.9967 q^{29} +36.6641i q^{31} +44.5448i q^{32} +32.8553 q^{33} -62.2683i q^{34} -11.3782 q^{36} +8.94699i q^{37} +54.7302 q^{38} +19.0191 q^{39} -37.6320i q^{41} +(-20.1035 + 27.2283i) q^{42} +18.8702i q^{43} +71.9443 q^{44} +89.3269 q^{46} +49.3786 q^{47} +29.0744 q^{48} +(14.4250 + 46.8286i) q^{49} -38.6352 q^{51} +41.6468 q^{52} -49.2398i q^{53} +14.5053i q^{54} +(2.40568 - 3.25827i) q^{56} -33.9580i q^{57} +111.653i q^{58} -35.2173i q^{59} +63.4723i q^{61} +102.349 q^{62} +(16.8942 + 12.4735i) q^{63} +57.2046 q^{64} -91.7170i q^{66} +21.3544i q^{67} -84.6008 q^{68} -55.4240i q^{69} +36.2998 q^{71} -1.73577i q^{72} -6.66818 q^{73} +24.9759 q^{74} -74.3591i q^{76} +(-106.822 - 78.8697i) q^{77} -53.0926i q^{78} +16.2015 q^{79} +9.00000 q^{81} -105.052 q^{82} -36.7822 q^{83} +(36.9937 + 27.3136i) q^{84} +52.6770 q^{86} +69.2763 q^{87} +10.9753i q^{88} +88.0954i q^{89} +(-61.8364 - 45.6557i) q^{91} -121.364i q^{92} -63.5040i q^{93} -137.843i q^{94} -77.1539i q^{96} -133.810 q^{97} +(130.724 - 40.2681i) q^{98} -56.9070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 88 q^{4} + 72 q^{9}+O(q^{10}) \) 24 * q - 88 * q^4 + 72 * q^9	\( 24 q - 88 q^{4} + 72 q^{9} - 32 q^{11} + 80 q^{14} + 184 q^{16} + 72 q^{21} - 208 q^{29} - 264 q^{36} + 48 q^{39} - 384 q^{44} + 400 q^{46} - 120 q^{49} + 48 q^{51} - 736 q^{56} + 40 q^{64} + 64 q^{71} - 368 q^{74} - 240 q^{79} + 216 q^{81} - 216 q^{84} + 800 q^{86} + 48 q^{91} - 96 q^{99}+O(q^{100}) \) 24 * q - 88 * q^4 + 72 * q^9 - 32 * q^11 + 80 * q^14 + 184 * q^16 + 72 * q^21 - 208 * q^29 - 264 * q^36 + 48 * q^39 - 384 * q^44 + 400 * q^46 - 120 * q^49 + 48 * q^51 - 736 * q^56 + 40 * q^64 + 64 * q^71 - 368 * q^74 - 240 * q^79 + 216 * q^81 - 216 * q^84 + 800 * q^86 + 48 * q^91 - 96 * q^99

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