LMFDB - Embedded newform 525.3.e.c.349.3

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			349.3
Character	$\chi$	$=$	525.349
Dual form			525.3.e.c.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.80460i q^{2} +1.73205 q^{3} -10.4750 q^{4} -6.58976i q^{6} +(6.55866 + 2.44621i) q^{7} +24.6348i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.80460i q^{2} +1.73205 q^{3} -10.4750 q^{4} -6.58976i q^{6} +(6.55866 + 2.44621i) q^{7} +24.6348i q^{8} +3.00000 q^{9} +14.4489 q^{11} -18.1432 q^{12} +16.9427 q^{13} +(9.30684 - 24.9531i) q^{14} +51.8255 q^{16} -13.0093 q^{17} -11.4138i q^{18} -18.6908i q^{19} +(11.3599 + 4.23695i) q^{21} -54.9723i q^{22} -10.3861i q^{23} +42.6687i q^{24} -64.4602i q^{26} +5.19615 q^{27} +(-68.7020 - 25.6240i) q^{28} +13.7269 q^{29} +42.4383i q^{31} -98.6363i q^{32} +25.0262 q^{33} +49.4951i q^{34} -31.4250 q^{36} +28.7434i q^{37} -71.1112 q^{38} +29.3456 q^{39} -28.8060i q^{41} +(16.1199 - 43.2200i) q^{42} +5.84593i q^{43} -151.352 q^{44} -39.5151 q^{46} -10.5013 q^{47} +89.7644 q^{48} +(37.0322 + 32.0877i) q^{49} -22.5327 q^{51} -177.475 q^{52} -81.9074i q^{53} -19.7693i q^{54} +(-60.2617 + 161.571i) q^{56} -32.3735i q^{57} -52.2254i q^{58} -35.1680i q^{59} -68.4826i q^{61} +161.461 q^{62} +(19.6760 + 7.33862i) q^{63} -167.970 q^{64} -95.2149i q^{66} +47.4637i q^{67} +136.272 q^{68} -17.9893i q^{69} +47.6548 q^{71} +73.9043i q^{72} -125.967 q^{73} +109.357 q^{74} +195.786i q^{76} +(94.7655 + 35.3450i) q^{77} -111.648i q^{78} +129.527 q^{79} +9.00000 q^{81} -109.595 q^{82} -42.6906 q^{83} +(-118.995 - 44.3820i) q^{84} +22.2414 q^{86} +23.7757 q^{87} +355.945i q^{88} -25.5329i q^{89} +(111.122 + 41.4453i) q^{91} +108.795i q^{92} +73.5053i q^{93} +39.9533i q^{94} -170.843i q^{96} -28.7310 q^{97} +(122.081 - 140.893i) q^{98} +43.3467 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	3.80460i		−	1.90230i	−0.308728	−	0.951150i	$-0.599903\pi$
$2$		−	3.80460i		−	1.90230i	0.308728	−	0.951150i	$-0.400097\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−10.4750			−2.61875
$5$		0			0
$5$		0			0
$6$		−	6.58976i		−	1.09829i
$7$	6.55866	+	2.44621i	0.936952	+	0.349458i
$7$	6.55866	+	2.44621i	0.936952	+	0.349458i
$8$			24.6348i			3.07935i
$9$	3.00000			0.333333
$10$		0			0
$11$	14.4489			1.31354			0.656768	−	0.754092i	$-0.271923\pi$
$11$	14.4489			1.31354			0.656768	+	0.754092i	$0.271923\pi$
$12$	−18.1432			−1.51193
$13$	16.9427			1.30329			0.651643	−	0.758526i	$-0.274080\pi$
$13$	16.9427			1.30329			0.651643	+	0.758526i	$0.274080\pi$
$14$	9.30684	−	24.9531i	0.664774	−	1.78236i
$15$		0			0
$16$	51.8255			3.23909
$17$	−13.0093			−0.765251			−0.382625	−	0.923904i	$-0.624980\pi$
$17$	−13.0093			−0.765251			−0.382625	+	0.923904i	$0.624980\pi$
$18$		−	11.4138i		−	0.634100i
$19$		−	18.6908i		−	0.983729i	−0.870672	−	0.491864i	$-0.836316\pi$
$19$		−	18.6908i		−	0.983729i	0.870672	−	0.491864i	$-0.163684\pi$
$20$		0			0
$21$	11.3599	+	4.23695i	0.540950	+	0.201760i
$22$		−	54.9723i		−	2.49874i
$23$		−	10.3861i		−	0.451570i	−0.974177	−	0.225785i	$-0.927505\pi$
$23$		−	10.3861i		−	0.451570i	0.974177	−	0.225785i	$-0.0724948\pi$
$24$			42.6687i			1.77786i
$25$		0			0
$26$		−	64.4602i		−	2.47924i
$27$	5.19615			0.192450
$28$	−68.7020	−	25.6240i	−2.45364	−	0.915142i
$29$	13.7269			0.473341			0.236671	−	0.971590i	$-0.423944\pi$
$29$	13.7269			0.473341			0.236671	+	0.971590i	$0.423944\pi$
$30$		0			0
$31$			42.4383i			1.36898i	0.729024	+	0.684488i	$0.239974\pi$
$31$			42.4383i			1.36898i	−0.729024	+	0.684488i	$0.760026\pi$
$32$		−	98.6363i		−	3.08238i
$33$	25.0262			0.758371
$34$			49.4951i			1.45574i
$35$		0			0
$36$	−31.4250			−0.872916
$37$			28.7434i			0.776850i	0.921480	+	0.388425i	$0.126981\pi$
$37$			28.7434i			0.776850i	−0.921480	+	0.388425i	$0.873019\pi$
$38$	−71.1112			−1.87135
$39$	29.3456			0.752452
$40$		0			0
$41$		−	28.8060i		−	0.702585i	−0.936266	−	0.351293i	$-0.885742\pi$
$41$		−	28.8060i		−	0.702585i	0.936266	−	0.351293i	$-0.114258\pi$
$42$	16.1199	−	43.2200i	0.383807	−	1.02905i
$43$			5.84593i			0.135952i	0.997687	+	0.0679759i	$0.0216541\pi$
$43$			5.84593i			0.135952i	−0.997687	+	0.0679759i	$0.978346\pi$
$44$	−151.352			−3.43982
$45$		0			0
$46$	−39.5151			−0.859023
$47$	−10.5013			−0.223432			−0.111716	−	0.993740i	$-0.535635\pi$
$47$	−10.5013			−0.223432			−0.111716	+	0.993740i	$0.535635\pi$
$48$	89.7644			1.87009
$49$	37.0322	+	32.0877i	0.755758	+	0.654851i
$50$		0			0
$51$	−22.5327			−0.441818
$52$	−177.475			−3.41298
$53$		−	81.9074i		−	1.54542i	−0.634757	−	0.772712i	$-0.718900\pi$
$53$		−	81.9074i		−	1.54542i	0.634757	−	0.772712i	$-0.281100\pi$
$54$		−	19.7693i		−	0.366098i
$55$		0			0
$56$	−60.2617	+	161.571i	−1.07610	+	2.88520i
$57$		−	32.3735i		−	0.567956i
$58$		−	52.2254i		−	0.900438i
$59$		−	35.1680i		−	0.596067i	−0.954555	−	0.298033i	$-0.903669\pi$
$59$		−	35.1680i		−	0.596067i	0.954555	−	0.298033i	$-0.0963307\pi$
$60$		0			0
$61$		−	68.4826i		−	1.12267i	−0.827590	−	0.561333i	$-0.810289\pi$
$61$		−	68.4826i		−	1.12267i	0.827590	−	0.561333i	$-0.189711\pi$
$62$	161.461			2.60421
$63$	19.6760	+	7.33862i	0.312317	+	0.116486i
$64$	−167.970			−2.62453
$65$		0			0
$66$		−	95.2149i		−	1.44265i
$67$			47.4637i			0.708414i	0.935167	+	0.354207i	$0.115249\pi$
$67$			47.4637i			0.708414i	−0.935167	+	0.354207i	$0.884751\pi$
$68$	136.272			2.00400
$69$		−	17.9893i		−	0.260714i
$70$		0			0
$71$	47.6548			0.671194			0.335597	−	0.942006i	$-0.391062\pi$
$71$	47.6548			0.671194			0.335597	+	0.942006i	$0.391062\pi$
$72$			73.9043i			1.02645i
$73$	−125.967			−1.72557			−0.862786	−	0.505569i	$-0.831283\pi$
$73$	−125.967			−1.72557			−0.862786	+	0.505569i	$0.831283\pi$
$74$	109.357			1.47780
$75$		0			0
$76$			195.786i			2.57614i
$77$	94.7655	+	35.3450i	1.23072	+	0.459026i
$78$		−	111.648i		−	1.43139i
$79$	129.527			1.63958			0.819790	−	0.572665i	$-0.194090\pi$
$79$	129.527			1.63958			0.819790	+	0.572665i	$0.194090\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	−109.595			−1.33653
$83$	−42.6906			−0.514345			−0.257173	−	0.966365i	$-0.582791\pi$
$83$	−42.6906			−0.514345			−0.257173	+	0.966365i	$0.582791\pi$
$84$	−118.995	−	44.3820i	−1.41661	−	0.528358i
$85$		0			0
$86$	22.2414			0.258621
$87$	23.7757			0.273284
$88$			355.945i			4.04483i
$89$		−	25.5329i		−	0.286886i	−0.989659	−	0.143443i	$-0.954183\pi$
$89$		−	25.5329i		−	0.286886i	0.989659	−	0.143443i	$-0.0458174\pi$
$90$		0			0
$91$	111.122	+	41.4453i	1.22112	+	0.455443i
$92$			108.795i			1.18255i
$93$			73.5053i			0.790379i
$94$			39.9533i			0.425035i
$95$		0			0
$96$		−	170.843i		−	1.77961i
$97$	−28.7310			−0.296196			−0.148098	−	0.988973i	$-0.547315\pi$
$97$	−28.7310			−0.296196			−0.148098	+	0.988973i	$0.547315\pi$
$98$	122.081	−	140.893i	1.24572	−	1.43768i
$99$	43.3467			0.437846
$100$		0			0
$101$		−	12.4609i		−	0.123375i	−0.998096	−	0.0616875i	$-0.980352\pi$
$101$		−	12.4609i		−	0.123375i	0.998096	−	0.0616875i	$-0.0196482\pi$
$102$			85.7280i			0.840470i
$103$	−38.4795			−0.373587			−0.186794	−	0.982399i	$-0.559810\pi$
$103$	−38.4795			−0.373587			−0.186794	+	0.982399i	$0.559810\pi$
$104$			417.380i			4.01326i
$105$		0			0
$106$	−311.625			−2.93986
$107$		−	87.7985i		−	0.820547i	−0.911963	−	0.410273i	$-0.865433\pi$
$107$		−	87.7985i		−	0.820547i	0.911963	−	0.410273i	$-0.134567\pi$
$108$	−54.4297			−0.503978
$109$	−130.012			−1.19277			−0.596386	−	0.802698i	$-0.703397\pi$
$109$	−130.012			−1.19277			−0.596386	+	0.802698i	$0.703397\pi$
$110$		0			0
$111$			49.7851i			0.448515i
$112$	339.906	+	126.776i	3.03487	+	1.13193i
$113$			158.597i			1.40351i	0.712417	+	0.701757i	$0.247601\pi$
$113$			158.597i			1.40351i	−0.712417	+	0.701757i	$0.752399\pi$
$114$	−123.168			−1.08042
$115$		0			0
$116$	−143.789			−1.23956
$117$	50.8281			0.434428
$118$	−133.800			−1.13390
$119$	−85.3234	−	31.8233i	−0.717003	−	0.267423i
$120$		0			0
$121$	87.7709			0.725379
$122$	−260.549			−2.13565
$123$		−	49.8934i		−	0.405638i
$124$		−	444.541i		−	3.58501i
$125$		0			0
$126$	27.9205	−	74.8593i	0.221591	−	0.594122i
$127$			43.0643i			0.339089i	0.985523	+	0.169545i	$0.0542297\pi$
$127$			43.0643i			0.339089i	−0.985523	+	0.169545i	$0.945770\pi$
$128$			244.513i			1.91026i
$129$			10.1254i			0.0784919i
$130$		0			0
$131$		−	0.686731i		−	0.00524222i	−0.999997	−	0.00262111i	$-0.999166\pi$
$131$		−	0.686731i		−	0.00524222i	0.999997	−	0.00262111i	$-0.000834326\pi$
$132$	−262.150			−1.98598
$133$	45.7216	−	122.587i	0.343772	−	0.921707i
$134$	180.581			1.34762
$135$		0			0
$136$		−	320.480i		−	2.35647i
$137$			76.2084i			0.556266i	0.960543	+	0.278133i	$0.0897155\pi$
$137$			76.2084i			0.556266i	−0.960543	+	0.278133i	$0.910284\pi$
$138$	−68.4421			−0.495957
$139$			49.0445i			0.352838i	0.984315	+	0.176419i	$0.0564514\pi$
$139$			49.0445i			0.352838i	−0.984315	+	0.176419i	$0.943549\pi$
$140$		0			0
$141$	−18.1888			−0.128998
$142$		−	181.307i		−	1.27681i
$143$	244.804			1.71191
$144$	155.476			1.07970
$145$		0			0
$146$			479.253i			3.28256i
$147$	64.1416	+	55.5775i	0.436337	+	0.378078i
$148$		−	301.087i		−	2.03437i
$149$	242.344			1.62647			0.813236	−	0.581934i	$-0.197704\pi$
$149$	242.344			1.62647			0.813236	+	0.581934i	$0.197704\pi$
$150$		0			0
$151$	107.704			0.713271			0.356636	−	0.934244i	$-0.383924\pi$
$151$	107.704			0.713271			0.356636	+	0.934244i	$0.383924\pi$
$152$	460.445			3.02924
$153$	−39.0278			−0.255084
$154$	134.474	−	360.545i	0.873205	−	2.34120i
$155$		0			0
$156$	−307.395			−1.97048
$157$	−76.1684			−0.485149			−0.242575	−	0.970133i	$-0.577992\pi$
$157$	−76.1684			−0.485149			−0.242575	+	0.970133i	$0.577992\pi$
$158$		−	492.798i		−	3.11897i
$159$		−	141.868i		−	0.892250i
$160$		0			0
$161$	25.4066	−	68.1191i	0.157805	−	0.423100i
$162$		−	34.2414i		−	0.211367i
$163$		−	10.4287i		−	0.0639800i	−0.999488	−	0.0319900i	$-0.989816\pi$
$163$		−	10.4287i		−	0.0639800i	0.999488	−	0.0319900i	$-0.0101845\pi$
$164$			301.743i			1.83989i
$165$		0			0
$166$			162.421i			0.978439i
$167$	−75.7598			−0.453652			−0.226826	−	0.973935i	$-0.572835\pi$
$167$	−75.7598			−0.453652			−0.226826	+	0.973935i	$0.572835\pi$
$168$	−104.376	+	279.849i	−0.621287	+	1.66577i
$169$	118.055			0.698552
$170$		0			0
$171$		−	56.0725i		−	0.327910i
$172$		−	61.2361i		−	0.356024i
$173$	−325.843			−1.88349			−0.941743	−	0.336333i	$-0.890813\pi$
$173$	−325.843			−1.88349			−0.941743	+	0.336333i	$0.890813\pi$
$174$		−	90.4570i		−	0.519868i
$175$		0			0
$176$	748.822			4.25467
$177$		−	60.9127i		−	0.344139i
$178$	−97.1424			−0.545744
$179$	30.9215			0.172746			0.0863728	−	0.996263i	$-0.472472\pi$
$179$	30.9215			0.172746			0.0863728	+	0.996263i	$0.472472\pi$
$180$		0			0
$181$		−	211.403i		−	1.16797i	−0.811764	−	0.583985i	$-0.801493\pi$
$181$		−	211.403i		−	1.16797i	0.811764	−	0.583985i	$-0.198507\pi$
$182$	157.683	−	422.773i	0.866390	−	2.32293i
$183$		−	118.615i		−	0.648171i
$184$	255.860			1.39054
$185$		0			0
$186$	279.658			1.50354
$187$	−187.970			−1.00519
$188$	110.001			0.585112
$189$	34.0798	+	12.7109i	0.180317	+	0.0672532i
$190$		0			0
$191$	112.093			0.586874			0.293437	−	0.955978i	$-0.405201\pi$
$191$	112.093			0.586874			0.293437	+	0.955978i	$0.405201\pi$
$192$	−290.932			−1.51527
$193$			293.541i			1.52094i	0.649373	+	0.760470i	$0.275031\pi$
$193$			293.541i			1.52094i	−0.649373	+	0.760470i	$0.724969\pi$
$194$			109.310i			0.563453i
$195$		0			0
$196$	−387.912	−	336.118i	−1.97914	−	1.71489i
$197$		−	90.7583i		−	0.460702i	−0.973108	−	0.230351i	$-0.926013\pi$
$197$		−	90.7583i		−	0.460702i	0.973108	−	0.230351i	$-0.0739874\pi$
$198$		−	164.917i		−	0.832914i
$199$			389.421i			1.95689i	0.206505	+	0.978445i	$0.433791\pi$
$199$			389.421i			1.95689i	−0.206505	+	0.978445i	$0.566209\pi$
$200$		0			0
$201$			82.2096i			0.409003i
$202$	−47.4086			−0.234696
$203$	90.0301	+	33.5788i	0.443498	+	0.165413i
$204$	236.030			1.15701
$205$		0			0
$206$			146.399i			0.710676i
$207$		−	31.1584i		−	0.150523i
$208$	878.064			4.22146
$209$		−	270.062i		−	1.29216i
$210$		0			0
$211$	−21.1049			−0.100023			−0.0500115	−	0.998749i	$-0.515926\pi$
$211$	−21.1049			−0.100023			−0.0500115	+	0.998749i	$0.515926\pi$
$212$			857.980i			4.04707i
$213$	82.5405			0.387514
$214$	−334.038			−1.56093
$215$		0			0
$216$			128.006i			0.592620i
$217$	−103.813	+	278.338i	−0.478400	+	1.28267i
$218$			494.645i			2.26901i
$219$	−218.181			−0.996259
$220$		0			0
$221$	−220.412			−0.997340
$222$	189.413			0.853209
$223$	293.039			1.31408			0.657039	−	0.753857i	$-0.271809\pi$
$223$	293.039			1.31408			0.657039	+	0.753857i	$0.271809\pi$
$224$	241.285	−	646.922i	1.07716	−	2.88805i
$225$		0			0
$226$	603.398			2.66990
$227$	−73.9333			−0.325697			−0.162849	−	0.986651i	$-0.552068\pi$
$227$	−73.9333			−0.325697			−0.162849	+	0.986651i	$0.552068\pi$
$228$			339.112i			1.48733i
$229$			233.516i			1.01972i	0.860257	+	0.509860i	$0.170303\pi$
$229$			233.516i			1.01972i	−0.860257	+	0.509860i	$0.829697\pi$
$230$		0			0
$231$	164.139	+	61.2193i	0.710557	+	0.265019i
$232$			338.159i			1.45758i
$233$			385.429i			1.65420i	0.562054	+	0.827101i	$0.310011\pi$
$233$			385.429i			1.65420i	−0.562054	+	0.827101i	$0.689989\pi$
$234$		−	193.381i		−	0.826413i
$235$		0			0
$236$			368.384i			1.56095i
$237$	224.347			0.946611
$238$	−121.075	+	324.621i	−0.508719	+	1.36396i
$239$	−407.373			−1.70449			−0.852244	−	0.523144i	$-0.824759\pi$
$239$	−407.373			−1.70449			−0.852244	+	0.523144i	$0.824759\pi$
$240$		0			0
$241$		−	271.816i		−	1.12787i	−0.825820	−	0.563934i	$-0.809287\pi$
$241$		−	271.816i		−	1.12787i	0.825820	−	0.563934i	$-0.190713\pi$
$242$		−	333.933i		−	1.37989i
$243$	15.5885			0.0641500
$244$			717.355i			2.93998i
$245$		0			0
$246$	−189.825			−0.771645
$247$		−	316.673i		−	1.28208i
$248$	−1045.46			−4.21555
$249$	−73.9424			−0.296957
$250$		0			0
$251$		−	442.250i		−	1.76195i	−0.473162	−	0.880976i	$-0.656887\pi$
$251$		−	442.250i		−	1.76195i	0.473162	−	0.880976i	$-0.343113\pi$
$252$	−206.106	−	76.8719i	−0.817880	−	0.305047i
$253$		−	150.068i		−	0.593154i
$254$	163.843			0.645049
$255$		0			0
$256$	258.395			1.00935
$257$	390.436			1.51921			0.759604	−	0.650386i	$-0.225393\pi$
$257$	390.436			1.51921			0.759604	+	0.650386i	$0.225393\pi$
$258$	38.5233			0.149315
$259$	−70.3124	+	188.519i	−0.271476	+	0.727871i
$260$		0			0
$261$	41.1807			0.157780
$262$	−2.61274			−0.00997228
$263$			1.63279i			0.00620832i	0.999995	+	0.00310416i	$0.000988086\pi$
$263$			1.63279i			0.00620832i	−0.999995	+	0.00310416i	$0.999012\pi$
$264$			616.515i			2.33529i
$265$		0			0
$266$	−466.395	−	173.953i	−1.75336	−	0.653957i
$267$		−	44.2242i		−	0.165634i
$268$		−	497.182i		−	1.85516i
$269$		−	410.340i		−	1.52543i	−0.646737	−	0.762713i	$-0.723867\pi$
$269$		−	410.340i		−	1.52543i	0.646737	−	0.762713i	$-0.276133\pi$
$270$		0			0
$271$			470.030i			1.73443i	0.497937	+	0.867213i	$0.334091\pi$
$271$			470.030i			1.73443i	−0.497937	+	0.867213i	$0.665909\pi$
$272$	−674.211			−2.47872
$273$	192.468	+	71.7854i	0.705011	+	0.262950i
$274$	289.943			1.05818
$275$		0			0
$276$			188.438i			0.682745i
$277$			366.582i			1.32340i	0.749768	+	0.661701i	$0.230165\pi$
$277$			366.582i			1.32340i	−0.749768	+	0.661701i	$0.769835\pi$
$278$	186.595			0.671204
$279$			127.315i			0.456326i
$280$		0			0
$281$	10.1164			0.0360015			0.0180008	−	0.999838i	$-0.494270\pi$
$281$	10.1164			0.0360015			0.0180008	+	0.999838i	$0.494270\pi$
$282$			69.2011i			0.245394i
$283$	−121.896			−0.430729			−0.215364	−	0.976534i	$-0.569094\pi$
$283$	−121.896			−0.430729			−0.215364	+	0.976534i	$0.569094\pi$
$284$	−499.183			−1.75769
$285$		0			0
$286$		−	931.380i		−	3.25657i
$287$	70.4654	−	188.929i	0.245524	−	0.658289i
$288$		−	295.909i		−	1.02746i
$289$	−119.759			−0.414391
$290$		0			0
$291$	−49.7635			−0.171009
$292$	1319.50			4.51884
$293$	292.803			0.999327			0.499663	−	0.866220i	$-0.333457\pi$
$293$	292.803			0.999327			0.499663	+	0.866220i	$0.333457\pi$
$294$	211.450	−	244.033i	0.719218	−	0.830045i
$295$		0			0
$296$	−708.088			−2.39219
$297$	75.0787			0.252790
$298$		−	922.023i		−	3.09404i
$299$		−	175.969i		−	0.588525i
$300$		0			0
$301$	−14.3003	+	38.3415i	−0.0475095	+	0.127380i
$302$		−	409.771i		−	1.35686i
$303$		−	21.5829i		−	0.0712306i
$304$		−	968.662i		−	3.18639i
$305$		0			0
$306$			148.485i			0.485246i
$307$	−167.855			−0.546758			−0.273379	−	0.961906i	$-0.588141\pi$
$307$	−167.855			−0.546758			−0.273379	+	0.961906i	$0.588141\pi$
$308$	−992.668	−	370.238i	−3.22295	−	1.20207i
$309$	−66.6485			−0.215691
$310$		0			0
$311$			303.739i			0.976652i	0.872661	+	0.488326i	$0.162392\pi$
$311$			303.739i			0.976652i	−0.872661	+	0.488326i	$0.837608\pi$
$312$			722.923i			2.31706i
$313$	17.2151			0.0550004			0.0275002	−	0.999622i	$-0.491245\pi$
$313$	17.2151			0.0550004			0.0275002	+	0.999622i	$0.491245\pi$
$314$			289.790i			0.922899i
$315$		0			0
$316$	−1356.79			−4.29364
$317$			82.8657i			0.261406i	0.991422	+	0.130703i	$0.0417234\pi$
$317$			82.8657i			0.261406i	−0.991422	+	0.130703i	$0.958277\pi$
$318$	−539.750			−1.69733
$319$	198.339			0.621751
$320$		0			0
$321$		−	152.071i		−	0.473743i
$322$	−259.166	−	96.6619i	−0.804863	−	0.300192i
$323$			243.154i			0.752799i
$324$	−94.2749			−0.290972
$325$		0			0
$326$	−39.6772			−0.121709
$327$	−225.188			−0.688647
$328$	709.629			2.16350
$329$	−68.8745	−	25.6883i	−0.209345	−	0.0780800i
$330$		0			0
$331$	−451.490			−1.36402			−0.682009	−	0.731343i	$-0.738894\pi$
$331$	−451.490			−1.36402			−0.682009	+	0.731343i	$0.738894\pi$
$332$	447.184			1.34694
$333$			86.2303i			0.258950i
$334$			288.236i			0.862982i
$335$		0			0
$336$	588.734	+	219.582i	1.75219	+	0.653518i
$337$			204.157i			0.605808i	0.953021	+	0.302904i	$0.0979561\pi$
$337$			204.157i			0.605808i	−0.953021	+	0.302904i	$0.902044\pi$
$338$		−	449.153i		−	1.32886i
$339$			274.698i			0.810319i
$340$		0			0
$341$			613.187i			1.79820i
$342$	−213.334			−0.623783
$343$	164.388	+	301.041i	0.479267	+	0.877669i
$344$	−144.013			−0.418643
$345$		0			0
$346$			1239.70i			3.58296i
$347$			146.593i			0.422458i	0.977437	+	0.211229i	$0.0677465\pi$
$347$			146.593i			0.422458i	−0.977437	+	0.211229i	$0.932253\pi$
$348$	−249.050			−0.715661
$349$			11.4454i			0.0327947i	0.999866	+	0.0163974i	$0.00521968\pi$
$349$			11.4454i			0.0327947i	−0.999866	+	0.0163974i	$0.994780\pi$
$350$		0			0
$351$	88.0369			0.250817
$352$		−	1425.19i		−	4.04882i
$353$	−177.817			−0.503730			−0.251865	−	0.967762i	$-0.581044\pi$
$353$	−177.817			−0.503730			−0.251865	+	0.967762i	$0.581044\pi$
$354$	−231.748			−0.654657
$355$		0			0
$356$			267.457i			0.751283i
$357$	−147.784	−	55.1196i	−0.413962	−	0.154397i
$358$		−	117.644i		−	0.328614i
$359$	−653.079			−1.81916			−0.909581	−	0.415526i	$-0.863598\pi$
$359$	−653.079			−1.81916			−0.909581	+	0.415526i	$0.863598\pi$
$360$		0			0
$361$	11.6523			0.0322780
$362$	−804.303			−2.22183
$363$	152.024			0.418798
$364$	−1164.00	−	434.140i	−3.19779	−	1.19269i
$365$		0			0
$366$	−451.284			−1.23302
$367$	−466.632			−1.27148			−0.635738	−	0.771905i	$-0.719304\pi$
$367$	−466.632			−1.27148			−0.635738	+	0.771905i	$0.719304\pi$
$368$		−	538.266i		−	1.46268i
$369$		−	86.4180i		−	0.234195i
$370$		0			0
$371$	200.362	−	537.203i	0.540060	−	1.44799i
$372$		−	769.967i		−	2.06980i
$373$			452.082i			1.21202i	0.795459	+	0.606008i	$0.207230\pi$
$373$			452.082i			1.21202i	−0.795459	+	0.606008i	$0.792770\pi$
$374$			715.149i			1.91216i
$375$		0			0
$376$		−	258.697i		−	0.688024i
$377$	232.571			0.616899
$378$	48.3597	−	129.660i	0.127936	−	0.343016i
$379$	−326.478			−0.861420			−0.430710	−	0.902490i	$-0.641737\pi$
$379$	−326.478			−0.861420			−0.430710	+	0.902490i	$0.641737\pi$
$380$		0			0
$381$			74.5896i			0.195773i
$382$		−	426.469i		−	1.11641i
$383$	−381.262			−0.995462			−0.497731	−	0.867331i	$-0.665833\pi$
$383$	−381.262			−0.995462			−0.497731	+	0.867331i	$0.665833\pi$
$384$			423.509i			1.10289i
$385$		0			0
$386$	1116.81			2.89329
$387$			17.5378i			0.0453173i
$388$	300.957			0.775662
$389$	68.8443			0.176978			0.0884888	−	0.996077i	$-0.471796\pi$
$389$	68.8443			0.176978			0.0884888	+	0.996077i	$0.471796\pi$
$390$		0			0
$391$			135.116i			0.345565i
$392$	−790.472	+	912.278i	−2.01651	+	2.32724i
$393$		−	1.18945i		−	0.00302660i
$394$	−345.299			−0.876394
$395$		0			0
$396$	−454.056			−1.14661
$397$	−370.531			−0.933328			−0.466664	−	0.884435i	$-0.654544\pi$
$397$	−370.531			−0.933328			−0.466664	+	0.884435i	$0.654544\pi$
$398$	1481.59			3.72259
$399$	79.1922	−	212.327i	0.198477	−	0.532148i
$400$		0			0
$401$	8.95073			0.0223210			0.0111605	−	0.999938i	$-0.496447\pi$
$401$	8.95073			0.0223210			0.0111605	+	0.999938i	$0.496447\pi$
$402$	312.775			0.778047
$403$			719.019i			1.78417i
$404$			130.528i			0.323088i
$405$		0			0
$406$	127.754	−	342.529i	0.314665	−	0.843667i
$407$			415.311i			1.02042i
$408$		−	555.088i		−	1.36051i
$409$			63.1330i			0.154359i	0.997017	+	0.0771797i	$0.0245915\pi$
$409$			63.1330i			0.154359i	−0.997017	+	0.0771797i	$0.975408\pi$
$410$		0			0
$411$			131.997i			0.321160i
$412$	403.072			0.978331
$413$	86.0280	−	230.655i	0.208300	−	0.558486i
$414$	−118.545			−0.286341
$415$		0			0
$416$		−	1671.17i		−	4.01722i
$417$			84.9475i			0.203711i
$418$	−1027.48			−2.45808
$419$			3.58774i			0.00856263i	0.999991	+	0.00428131i	$0.00136279\pi$
$419$			3.58774i			0.00856263i	−0.999991	+	0.00428131i	$0.998637\pi$
$420$		0			0
$421$	119.594			0.284071			0.142035	−	0.989862i	$-0.454635\pi$
$421$	119.594			0.284071			0.142035	+	0.989862i	$0.454635\pi$
$422$			80.2956i			0.190274i
$423$	−31.5039			−0.0744773
$424$	2017.77			4.75889
$425$		0			0
$426$		−	314.034i		−	0.737168i
$427$	167.523	−	449.154i	0.392324	−	1.05188i
$428$			919.689i			2.14881i
$429$	424.012			0.988373
$430$		0			0
$431$	−404.488			−0.938488			−0.469244	−	0.883069i	$-0.655473\pi$
$431$	−404.488			−0.938488			−0.469244	+	0.883069i	$0.655473\pi$
$432$	269.293			0.623364
$433$	−116.085			−0.268094			−0.134047	−	0.990975i	$-0.542797\pi$
$433$	−116.085			−0.268094			−0.134047	+	0.990975i	$0.542797\pi$
$434$	1058.97	+	394.966i	2.44002	+	0.910060i
$435$		0			0
$436$	1361.88			3.12357
$437$	−194.125			−0.444223
$438$			830.091i			1.89519i
$439$			58.4183i			0.133071i	0.997784	+	0.0665357i	$0.0211946\pi$
$439$			58.4183i			0.133071i	−0.997784	+	0.0665357i	$0.978805\pi$
$440$		0			0
$441$	111.096	+	96.2630i	0.251919	+	0.218284i
$442$			838.580i			1.89724i
$443$		−	267.301i		−	0.603388i	−0.953405	−	0.301694i	$-0.902448\pi$
$443$		−	267.301i		−	0.603388i	0.953405	−	0.301694i	$-0.0975520\pi$
$444$		−	521.499i		−	1.17455i
$445$		0			0
$446$		−	1114.90i		−	2.49977i
$447$	419.753			0.939044
$448$	−1101.66	−	410.888i	−2.45906	−	0.917162i
$449$	−296.478			−0.660307			−0.330154	−	0.943927i	$-0.607101\pi$
$449$	−296.478			−0.660307			−0.330154	+	0.943927i	$0.607101\pi$
$450$		0			0
$451$		−	416.215i		−	0.922872i
$452$		−	1661.30i		−	3.67545i
$453$	186.549			0.411807
$454$			281.287i			0.619574i
$455$		0			0
$456$	797.513			1.74893
$457$			12.1251i			0.0265320i	0.999912	+	0.0132660i	$0.00422282\pi$
$457$			12.1251i			0.0265320i	−0.999912	+	0.0132660i	$0.995777\pi$
$458$	888.435			1.93981
$459$	−67.5981			−0.147273
$460$		0			0
$461$			103.948i			0.225483i	0.993624	+	0.112741i	$0.0359632\pi$
$461$			103.948i			0.225483i	−0.993624	+	0.112741i	$0.964037\pi$
$462$	232.915	−	624.482i	0.504145	−	1.35169i
$463$		−	498.831i		−	1.07739i	−0.842501	−	0.538694i	$-0.818918\pi$
$463$		−	498.831i		−	1.07739i	0.842501	−	0.538694i	$-0.181082\pi$
$464$	711.403			1.53320
$465$		0			0
$466$	1466.40			3.14679
$467$	597.683			1.27983			0.639917	−	0.768444i	$-0.278969\pi$
$467$	597.683			1.27983			0.639917	+	0.768444i	$0.278969\pi$
$468$	−532.424			−1.13766
$469$	−116.106	+	311.299i	−0.247561	+	0.663750i
$470$		0			0
$471$	−131.928			−0.280101
$472$	866.354			1.83550
$473$			84.4673i			0.178578i
$474$		−	853.551i		−	1.80074i
$475$		0			0
$476$	893.762	+	333.349i	1.87765	+	0.700313i
$477$		−	245.722i		−	0.515141i
$478$			1549.89i			3.24245i
$479$		−	276.703i		−	0.577669i	−0.957379	−	0.288834i	$-0.906732\pi$
$479$		−	276.703i		−	0.577669i	0.957379	−	0.288834i	$-0.0932677\pi$
$480$		0			0
$481$			486.992i			1.01246i
$482$	−1034.15			−2.14554
$483$	44.0055	−	117.986i	0.0911087	−	0.244277i
$484$	−919.399			−1.89958
$485$		0			0
$486$		−	59.3079i		−	0.122033i
$487$		−	542.653i		−	1.11428i	−0.830420	−	0.557138i	$-0.811899\pi$
$487$		−	542.653i		−	1.11428i	0.830420	−	0.557138i	$-0.188101\pi$
$488$	1687.05			3.45708
$489$		−	18.0631i		−	0.0369389i
$490$		0			0
$491$	574.817			1.17071			0.585353	−	0.810778i	$-0.300956\pi$
$491$	574.817			1.17071			0.585353	+	0.810778i	$0.300956\pi$
$492$			522.633i			1.06226i
$493$	−178.577			−0.362225
$494$	−1204.82			−2.43890
$495$		0			0
$496$			2199.38i			4.43424i
$497$	312.552	+	116.573i	0.628877	+	0.234554i
$498$			281.321i			0.564902i
$499$	549.967			1.10214			0.551070	−	0.834459i	$-0.314220\pi$
$499$	549.967			1.10214			0.551070	+	0.834459i	$0.314220\pi$
$500$		0			0
$501$	−131.220			−0.261916
$502$	−1682.58			−3.35176
$503$	−397.053			−0.789369			−0.394685	−	0.918817i	$-0.629146\pi$
$503$	−397.053			−0.789369			−0.394685	+	0.918817i	$0.629146\pi$
$504$	−180.785	+	484.713i	−0.358701	+	0.961733i
$505$		0			0
$506$	−570.949			−1.12836
$507$	204.478			0.403309
$508$		−	451.098i		−	0.887989i
$509$			557.813i			1.09590i	0.836511	+	0.547950i	$0.184592\pi$
$509$			557.813i			1.09590i	−0.836511	+	0.547950i	$0.815408\pi$
$510$		0			0
$511$	−826.174	−	308.141i	−1.61678	−	0.603015i
$512$		−	5.03806i		−	0.00983995i
$513$		−	97.1205i		−	0.189319i
$514$		−	1485.45i		−	2.88999i
$515$		0			0
$516$		−	106.064i		−	0.205550i
$517$	−151.732			−0.293486
$518$	717.238	+	267.511i	1.38463	+	0.516430i
$519$	−564.377			−1.08743
$520$		0			0
$521$			287.300i			0.551439i	0.961238	+	0.275719i	$0.0889161\pi$
$521$			287.300i			0.551439i	−0.961238	+	0.275719i	$0.911084\pi$
$522$		−	156.676i		−	0.300146i
$523$	−1012.28			−1.93553			−0.967766	−	0.251853i	$-0.918960\pi$
$523$	−1012.28			−1.93553			−0.967766	+	0.251853i	$0.918960\pi$
$524$			7.19350i			0.0137281i
$525$		0			0
$526$	6.21211			0.0118101
$527$		−	552.091i		−	1.04761i
$528$	1297.00			2.45643
$529$	421.128			0.796084
$530$		0			0
$531$		−	105.504i		−	0.198689i
$532$	−478.934	+	1284.10i	−0.900252	+	2.41372i
$533$		−	488.051i		−	0.915669i
$534$	−168.256			−0.315085
$535$		0			0
$536$	−1169.26			−2.18145
$537$	53.5575			0.0997347
$538$	−1561.18			−2.90182
$539$	535.074	+	463.632i	0.992716	+	0.860170i
$540$		0			0
$541$	526.853			0.973851			0.486925	−	0.873444i	$-0.338118\pi$
$541$	526.853			0.973851			0.486925	+	0.873444i	$0.338118\pi$
$542$	1788.28			3.29940
$543$		−	366.160i		−	0.674328i
$544$			1283.19i			2.35880i
$545$		0			0
$546$	273.115	−	732.265i	0.500211	−	1.34114i
$547$		−	250.549i		−	0.458042i	−0.973421	−	0.229021i	$-0.926447\pi$
$547$		−	250.549i		−	0.458042i	0.973421	−	0.229021i	$-0.0735525\pi$
$548$		−	798.282i		−	1.45672i
$549$		−	205.448i		−	0.374222i
$550$		0			0
$551$		−	256.567i		−	0.465640i
$552$	443.162			0.802829
$553$	849.522	+	316.849i	1.53621	+	0.572964i
$554$	1394.70			2.51751
$555$		0			0
$556$		−	513.741i		−	0.923994i
$557$		−	64.1496i		−	0.115170i	−0.998341	−	0.0575849i	$-0.981660\pi$
$557$		−	64.1496i		−	0.115170i	0.998341	−	0.0575849i	$-0.0183400\pi$
$558$	484.382			0.868069
$559$			99.0459i			0.177184i
$560$		0			0
$561$	−325.573			−0.580344
$562$		−	38.4890i		−	0.0684857i
$563$	17.3869			0.0308826			0.0154413	−	0.999881i	$-0.495085\pi$
$563$	17.3869			0.0308826			0.0154413	+	0.999881i	$0.495085\pi$
$564$	190.527			0.337814
$565$		0			0
$566$			463.767i			0.819376i
$567$	59.0280	+	22.0158i	0.104106	+	0.0388287i
$568$			1173.96i			2.06684i
$569$	−174.914			−0.307405			−0.153703	−	0.988117i	$-0.549120\pi$
$569$	−174.914			−0.307405			−0.153703	+	0.988117i	$0.549120\pi$
$570$		0			0
$571$	−376.637			−0.659609			−0.329805	−	0.944049i	$-0.606983\pi$
$571$	−376.637			−0.659609			−0.329805	+	0.944049i	$0.606983\pi$
$572$	−2564.32			−4.48307
$573$	194.151			0.338832
$574$	−718.799	−	268.093i	−1.25226	−	0.467060i
$575$		0			0
$576$	−503.909			−0.874842
$577$	448.775			0.777773			0.388886	−	0.921286i	$-0.372860\pi$
$577$	448.775			0.777773			0.388886	+	0.921286i	$0.372860\pi$
$578$			455.636i			0.788297i
$579$			508.429i			0.878115i
$580$		0			0
$581$	−279.994	−	104.430i	−0.481917	−	0.179742i
$582$			189.330i			0.325310i
$583$		−	1183.47i		−	2.02997i
$584$		−	3103.16i		−	5.31363i
$585$		0			0
$586$		−	1114.00i		−	1.90102i
$587$	275.916			0.470044			0.235022	−	0.971990i	$-0.424484\pi$
$587$	275.916			0.470044			0.235022	+	0.971990i	$0.424484\pi$
$588$	−671.883	−	582.174i	−1.14266	−	0.990091i
$589$	793.207			1.34670
$590$		0			0
$591$		−	157.198i		−	0.265986i
$592$			1489.64i			2.51629i
$593$	−893.938			−1.50748			−0.753742	−	0.657171i	$-0.771753\pi$
$593$	−893.938			−1.50748			−0.753742	+	0.657171i	$0.771753\pi$
$594$		−	285.645i		−	0.480883i
$595$		0			0
$596$	−2538.55			−4.25932
$597$			674.497i			1.12981i
$598$	−669.492			−1.11955
$599$	122.407			0.204352			0.102176	−	0.994766i	$-0.467419\pi$
$599$	122.407			0.204352			0.102176	+	0.994766i	$0.467419\pi$
$600$		0			0
$601$			594.921i			0.989885i	0.868926	+	0.494943i	$0.164811\pi$
$601$			594.921i			0.989885i	−0.868926	+	0.494943i	$0.835189\pi$
$602$	145.874	+	54.4071i	0.242316	+	0.0903773i
$603$			142.391i			0.236138i
$604$	−1128.20			−1.86788
$605$		0			0
$606$	−82.1142			−0.135502
$607$	−539.772			−0.889246			−0.444623	−	0.895718i	$-0.646662\pi$
$607$	−539.772			−0.889246			−0.444623	+	0.895718i	$0.646662\pi$
$608$	−1843.60			−3.03223
$609$	155.937	+	58.1602i	0.256054	+	0.0955012i
$610$		0			0
$611$	−177.920			−0.291195
$612$	408.816			0.668000
$613$		−	1180.07i		−	1.92508i	−0.271140	−	0.962540i	$-0.587401\pi$
$613$		−	1180.07i		−	1.92508i	0.271140	−	0.962540i	$-0.412599\pi$
$614$			638.620i			1.04010i
$615$		0			0
$616$	−870.715	+	2334.53i	−1.41350	+	3.78982i
$617$		−	777.688i		−	1.26043i	−0.776419	−	0.630217i	$-0.782966\pi$
$617$		−	777.688i		−	1.26043i	0.776419	−	0.630217i	$-0.217034\pi$
$618$			253.571i			0.410309i
$619$			285.107i			0.460592i	0.973121	+	0.230296i	$0.0739695\pi$
$619$			285.107i			0.460592i	−0.973121	+	0.230296i	$0.926030\pi$
$620$		0			0
$621$		−	53.9679i		−	0.0869048i
$622$	1155.60			1.85789
$623$	62.4586	−	167.462i	0.100255	−	0.268799i
$624$	1520.85			2.43726
$625$		0			0
$626$		−	65.4967i		−	0.104627i
$627$		−	467.762i		−	0.746031i
$628$	797.863			1.27048
$629$		−	373.931i		−	0.594485i
$630$		0			0
$631$	506.946			0.803401			0.401700	−	0.915771i	$-0.368419\pi$
$631$	506.946			0.803401			0.401700	+	0.915771i	$0.368419\pi$
$632$			3190.86i			5.04883i
$633$	−36.5547			−0.0577483
$634$	315.271			0.497273
$635$		0			0
$636$			1486.06i			2.33658i
$637$	627.425	+	543.652i	0.984969	+	0.853457i
$638$		−	754.600i		−	1.18276i
$639$	142.964			0.223731
$640$		0			0
$641$	537.896			0.839152			0.419576	−	0.907720i	$-0.362179\pi$
$641$	537.896			0.839152			0.419576	+	0.907720i	$0.362179\pi$
$642$	−578.571			−0.901202
$643$	673.330			1.04717			0.523585	−	0.851973i	$-0.324594\pi$
$643$	673.330			1.04717			0.523585	+	0.851973i	$0.324594\pi$
$644$	−266.134	+	713.547i	−0.413251	+	1.10799i
$645$		0			0
$646$	925.104			1.43205
$647$	−1082.21			−1.67266			−0.836332	−	0.548224i	$-0.815304\pi$
$647$	−1082.21			−1.67266			−0.836332	+	0.548224i	$0.815304\pi$
$648$			221.713i			0.342149i
$649$		−	508.138i		−	0.782956i
$650$		0			0
$651$	−179.809	+	482.096i	−0.276204	+	0.740547i
$652$			109.241i			0.167547i
$653$			491.429i			0.752571i	0.926504	+	0.376285i	$0.122799\pi$
$653$			491.429i			0.752571i	−0.926504	+	0.376285i	$0.877201\pi$
$654$			856.749i			1.31001i
$655$		0			0
$656$		−	1492.88i		−	2.27574i
$657$	−377.900			−0.575191
$658$	−97.7339	+	262.040i	−0.148532	+	0.398237i
$659$	−248.373			−0.376893			−0.188447	−	0.982083i	$-0.560345\pi$
$659$	−248.373			−0.376893			−0.188447	+	0.982083i	$0.560345\pi$
$660$		0			0
$661$		−	681.545i		−	1.03108i	−0.856865	−	0.515541i	$-0.827591\pi$
$661$		−	681.545i		−	1.03108i	0.856865	−	0.515541i	$-0.172409\pi$
$662$			1717.74i			2.59477i
$663$	−381.765			−0.575814
$664$		−	1051.67i		−	1.58385i
$665$		0			0
$666$	328.072			0.492601
$667$		−	142.569i		−	0.213747i
$668$	793.584			1.18800
$669$	507.559			0.758683
$670$		0			0
$671$		−	989.499i		−	1.47466i
$672$	417.917	−	1120.50i	0.621900	−	1.66741i
$673$		−	86.1498i		−	0.128009i	−0.997950	−	0.0640043i	$-0.979613\pi$
$673$		−	86.1498i		−	0.128009i	0.997950	−	0.0640043i	$-0.0203871\pi$
$674$	776.737			1.15243
$675$		0			0
$676$	−1236.63			−1.82933
$677$	−793.846			−1.17259			−0.586297	−	0.810096i	$-0.699415\pi$
$677$	−793.846			−1.17259			−0.586297	+	0.810096i	$0.699415\pi$
$678$	1045.12			1.54147
$679$	−188.437	−	70.2819i	−0.277521	−	0.103508i
$680$		0			0
$681$	−128.056			−0.188041
$682$	2332.93			3.42072
$683$			186.736i			0.273406i	0.990612	+	0.136703i	$0.0436506\pi$
$683$			186.736i			0.273406i	−0.990612	+	0.136703i	$0.956349\pi$
$684$			587.359i			0.858712i
$685$		0			0
$686$	1145.34	−	625.433i	1.66959	−	0.911709i
$687$			404.461i			0.588736i
$688$			302.968i			0.440361i
$689$		−	1387.73i		−	2.01413i
$690$		0			0
$691$			1030.46i			1.49126i	0.666361	+	0.745630i	$0.267851\pi$
$691$			1030.46i			1.49126i	−0.666361	+	0.745630i	$0.732149\pi$
$692$	3413.20			4.93238
$693$	284.297	+	106.035i	0.410240	+	0.153009i
$694$	557.727			0.803642
$695$		0			0
$696$			585.709i			0.841535i
$697$			374.745i			0.537654i
$698$	43.5450			0.0623854
$699$			667.582i			0.955054i
$700$		0			0
$701$	−1143.88			−1.63179			−0.815893	−	0.578203i	$-0.803754\pi$
$701$	−1143.88			−1.63179			−0.815893	+	0.578203i	$0.803754\pi$
$702$		−	334.945i		−	0.477130i
$703$	537.239			0.764210
$704$	−2426.98			−3.44741
$705$		0			0
$706$			676.521i			0.958246i
$707$	30.4818	−	81.7267i	0.0431143	−	0.115596i
$708$			638.060i			0.901214i
$709$	316.757			0.446766			0.223383	−	0.974731i	$-0.428290\pi$
$709$	316.757			0.446766			0.223383	+	0.974731i	$0.428290\pi$
$710$		0			0
$711$	388.580			0.546526
$712$	628.996			0.883422
$713$	440.769			0.618190
$714$	−209.708	+	562.261i	−0.293709	+	0.787480i
$715$		0			0
$716$	−323.902			−0.452377
$717$	−705.590			−0.984087
$718$			2484.71i			3.46059i
$719$		−	1145.95i		−	1.59381i	−0.604104	−	0.796906i	$-0.706469\pi$
$719$		−	1145.95i		−	1.59381i	0.604104	−	0.796906i	$-0.293531\pi$
$720$		0			0
$721$	−252.374	−	94.1288i	−0.350034	−	0.130553i
$722$		−	44.3325i		−	0.0614024i
$723$		−	470.799i		−	0.651174i
$724$			2214.44i			3.05862i
$725$		0			0
$726$		−	578.389i		−	0.796679i
$727$	−149.829			−0.206093			−0.103046	−	0.994677i	$-0.532859\pi$
$727$	−149.829			−0.206093			−0.103046	+	0.994677i	$0.532859\pi$
$728$	−1021.00	+	2737.45i	−1.40247	+	3.76024i
$729$	27.0000			0.0370370
$730$		0			0
$731$		−	76.0512i		−	0.104037i
$732$			1242.49i			1.69740i
$733$	70.3231			0.0959388			0.0479694	−	0.998849i	$-0.484725\pi$
$733$	70.3231			0.0959388			0.0479694	+	0.998849i	$0.484725\pi$
$734$			1775.35i			2.41873i
$735$		0			0
$736$	−1024.45			−1.39191
$737$			685.799i			0.930528i
$738$	−328.786			−0.445509
$739$	−774.145			−1.04756			−0.523779	−	0.851854i	$-0.675478\pi$
$739$	−774.145			−1.04756			−0.523779	+	0.851854i	$0.675478\pi$
$740$		0			0
$741$		−	548.495i		−	0.740209i
$742$	−2043.84	−	762.299i	−2.75451	−	1.02736i
$743$		−	1071.79i		−	1.44252i	−0.692665	−	0.721260i	$-0.743563\pi$
$743$		−	1071.79i		−	1.44252i	0.692665	−	0.721260i	$-0.256437\pi$
$744$	−1810.78			−2.43385
$745$		0			0
$746$	1719.99			2.30562
$747$	−128.072			−0.171448
$748$	1968.98			2.63233
$749$	214.773	−	575.841i	0.286747	−	0.768813i
$750$		0			0
$751$	361.789			0.481742			0.240871	−	0.970557i	$-0.422567\pi$
$751$	361.789			0.481742			0.240871	+	0.970557i	$0.422567\pi$
$752$	−544.235			−0.723717
$753$		−	765.999i		−	1.01726i
$754$		−	884.839i		−	1.17353i
$755$		0			0
$756$	−356.986	−	133.146i	−0.472203	−	0.176119i
$757$			812.552i			1.07338i	0.843778	+	0.536692i	$0.180326\pi$
$757$			812.552i			1.07338i	−0.843778	+	0.536692i	$0.819674\pi$
$758$			1242.12i			1.63868i
$759$		−	259.926i		−	0.342458i
$760$		0			0
$761$			728.812i			0.957703i	0.877896	+	0.478851i	$0.158947\pi$
$761$			728.812i			0.957703i	−0.877896	+	0.478851i	$0.841053\pi$
$762$	283.784			0.372419
$763$	−852.706	−	318.036i	−1.11757	−	0.416824i
$764$	−1174.17			−1.53688
$765$		0			0
$766$			1450.55i			1.89367i
$767$		−	595.840i		−	0.776845i
$768$	447.553			0.582751
$769$		−	624.378i		−	0.811935i	−0.913888	−	0.405967i	$-0.866935\pi$
$769$		−	624.378i		−	0.811935i	0.913888	−	0.405967i	$-0.133065\pi$
$770$		0			0
$771$	676.255			0.877115
$772$		−	3074.84i		−	3.98296i
$773$	−34.6106			−0.0447744			−0.0223872	−	0.999749i	$-0.507127\pi$
$773$	−34.6106			−0.0447744			−0.0223872	+	0.999749i	$0.507127\pi$
$774$	66.7243			0.0862071
$775$		0			0
$776$		−	707.781i		−	0.912089i
$777$	−121.785	+	326.524i	−0.156737	+	0.420237i
$778$		−	261.925i		−	0.336665i
$779$	−538.408			−0.691153
$780$		0			0
$781$	688.559			0.881638
$782$	514.062			0.657368
$783$	71.3271			0.0910946
$784$	1919.21	+	1662.96i	2.44797	+	2.12112i
$785$		0			0
$786$	−4.52539			−0.00575750
$787$	563.953			0.716586			0.358293	−	0.933609i	$-0.383359\pi$
$787$	563.953			0.716586			0.358293	+	0.933609i	$0.383359\pi$
$788$			950.692i			1.20646i
$789$			2.82807i			0.00358437i
$790$		0			0
$791$	−387.961	+	1040.18i	−0.490469	+	1.31502i
$792$			1067.84i			1.34828i
$793$		−	1160.28i		−	1.46315i
$794$			1409.72i			1.77547i
$795$		0			0
$796$		−	4079.18i		−	5.12460i
$797$	887.777			1.11390			0.556949	−	0.830546i	$-0.311972\pi$
$797$	887.777			1.11390			0.556949	+	0.830546i	$0.311972\pi$
$798$	−807.819	−	301.295i	−1.01230	−	0.377562i
$799$	136.614			0.170981
$800$		0			0
$801$		−	76.5986i		−	0.0956287i
$802$		−	34.0540i		−	0.0424613i
$803$	−1820.08			−2.26660
$804$		−	861.145i		−	1.07108i
$805$		0			0
$806$	2735.58			3.39402
$807$		−	710.729i		−	0.880706i
$808$	306.971			0.379914
$809$	1338.15			1.65408			0.827041	−	0.562142i	$-0.190023\pi$
$809$	1338.15			1.65408			0.827041	+	0.562142i	$0.190023\pi$
$810$		0			0
$811$		−	1002.03i		−	1.23555i	−0.786353	−	0.617777i	$-0.788033\pi$
$811$		−	1002.03i		−	1.23555i	0.786353	−	0.617777i	$-0.211967\pi$
$812$	−943.065	−	351.738i	−1.16141	−	0.433175i
$813$			814.115i			1.00137i
$814$	1580.09			1.94115
$815$		0			0
$816$	−1167.77			−1.43109
$817$	109.265			0.133740
$818$	240.196			0.293638
$819$	333.365	+	124.336i	0.407039	+	0.151814i
$820$		0			0
$821$	−519.980			−0.633349			−0.316675	−	0.948534i	$-0.602566\pi$
$821$	−519.980			−0.633349			−0.316675	+	0.948534i	$0.602566\pi$
$822$	502.195			0.610943
$823$			35.2676i			0.0428524i	0.999770	+	0.0214262i	$0.00682070\pi$
$823$			35.2676i			0.0428524i	−0.999770	+	0.0214262i	$0.993179\pi$
$824$		−	947.933i		−	1.15040i
$825$		0			0
$826$	−877.550	−	327.302i	−1.06241	−	0.396250i
$827$		−	1047.83i		−	1.26703i	−0.773731	−	0.633514i	$-0.781612\pi$
$827$		−	1047.83i		−	1.26703i	0.773731	−	0.633514i	$-0.218388\pi$
$828$			326.384i			0.394183i
$829$		−	125.947i		−	0.151926i	−0.997111	−	0.0759632i	$-0.975797\pi$
$829$		−	125.947i		−	0.151926i	0.997111	−	0.0759632i	$-0.0242031\pi$
$830$		0			0
$831$			634.939i			0.764067i
$832$	−2845.86			−3.42051
$833$	−481.761	−	417.437i	−0.578345	−	0.501125i
$834$	323.192			0.387520
$835$		0			0
$836$			2828.90i			3.38385i
$837$			220.516i			0.263460i
$838$	13.6499			0.0162887
$839$		−	456.709i		−	0.544349i	−0.962248	−	0.272174i	$-0.912257\pi$
$839$		−	456.709i		−	0.544349i	0.962248	−	0.272174i	$-0.0877427\pi$
$840$		0			0
$841$	−652.572			−0.775948
$842$		−	455.007i		−	0.540388i
$843$	17.5222			0.0207855
$844$	221.073			0.261935
$845$		0			0
$846$			119.860i			0.141678i
$847$	575.660	+	214.706i	0.679645	+	0.253489i
$848$		−	4244.89i		−	5.00577i
$849$	−211.131			−0.248681
$850$		0			0
$851$	298.533			0.350802
$852$	−864.611			−1.01480
$853$	815.418			0.955941			0.477971	−	0.878376i	$-0.341373\pi$
$853$	815.418			0.955941			0.477971	+	0.878376i	$0.341373\pi$
$854$	−1708.85	−	637.356i	−2.00100	−	0.746319i
$855$		0			0
$856$	2162.90			2.52675
$857$	−609.807			−0.711560			−0.355780	−	0.934570i	$-0.615785\pi$
$857$	−609.807			−0.711560			−0.355780	+	0.934570i	$0.615785\pi$
$858$		−	1613.20i		−	1.88018i
$859$			136.971i			0.159454i	0.996817	+	0.0797272i	$0.0254049\pi$
$859$			136.971i			0.159454i	−0.996817	+	0.0797272i	$0.974595\pi$
$860$		0			0
$861$	122.050	−	327.234i	0.141753	−	0.380063i
$862$			1538.92i			1.78529i
$863$		−	305.240i		−	0.353696i	−0.984238	−	0.176848i	$-0.943410\pi$
$863$		−	305.240i		−	0.353696i	0.984238	−	0.176848i	$-0.0565902\pi$
$864$		−	512.529i		−	0.593205i
$865$		0			0
$866$			441.657i			0.509996i
$867$	−207.429			−0.239249
$868$	1087.44	−	2915.59i	1.25281	−	3.35898i
$869$	1871.52			2.15365
$870$		0			0
$871$			804.164i			0.923266i
$872$		−	3202.82i		−	3.67296i
$873$	−86.1929			−0.0987319
$874$			738.570i			0.845045i
$875$		0			0
$876$	2285.44			2.60895
$877$			621.320i			0.708461i	0.935158	+	0.354231i	$0.115257\pi$
$877$			621.320i			0.708461i	−0.935158	+	0.354231i	$0.884743\pi$
$878$	222.258			0.253142
$879$	507.149			0.576962
$880$		0			0
$881$		−	739.549i		−	0.839443i	−0.907653	−	0.419721i	$-0.862128\pi$
$881$		−	739.549i		−	0.839443i	0.907653	−	0.419721i	$-0.137872\pi$
$882$	366.242	−	422.678i	0.415241	−	0.479227i
$883$		−	643.821i		−	0.729129i	−0.931178	−	0.364564i	$-0.881218\pi$
$883$		−	643.821i		−	0.729129i	0.931178	−	0.364564i	$-0.118782\pi$
$884$	2308.82			2.61178
$885$		0			0
$886$	−1016.97			−1.14782
$887$	−926.753			−1.04482			−0.522409	−	0.852695i	$-0.674966\pi$
$887$	−926.753			−1.04482			−0.522409	+	0.852695i	$0.674966\pi$
$888$	−1226.44			−1.38113
$889$	−105.344	+	282.444i	−0.118497	+	0.317710i
$890$		0			0
$891$	130.040			0.145949
$892$	−3069.58			−3.44124
$893$			196.278i			0.219796i
$894$		−	1596.99i		−	1.78634i
$895$		0			0
$896$	−598.128	+	1603.68i	−0.667554	+	1.78982i
$897$		−	304.787i		−	0.339785i
$898$			1127.98i			1.25610i
$899$			582.546i			0.647994i
$900$		0			0
$901$			1065.56i			1.18264i
$902$	−1583.53			−1.75558
$903$	−24.7689	+	66.4094i	−0.0274296	+	0.0735431i
$904$	−3907.00			−4.32190
$905$		0			0
$906$		−	709.744i		−	0.783382i
$907$		−	1540.97i		−	1.69898i	−0.527607	−	0.849489i	$-0.676910\pi$
$907$		−	1540.97i		−	1.69898i	0.527607	−	0.849489i	$-0.323090\pi$
$908$	774.450			0.852919
$909$		−	37.3826i		−	0.0411250i
$910$		0			0
$911$	−1187.49			−1.30350			−0.651748	−	0.758435i	$-0.725964\pi$
$911$	−1187.49			−1.30350			−0.651748	+	0.758435i	$0.725964\pi$
$912$		−	1677.77i		−	1.83966i
$913$	−616.833			−0.675611
$914$	46.1312			0.0504718
$915$		0			0
$916$		−	2446.08i		−	2.67039i
$917$	1.67988	−	4.50404i	0.00183194	−	0.00491171i
$918$			257.184i			0.280157i
$919$	−223.009			−0.242665			−0.121333	−	0.992612i	$-0.538717\pi$
$919$	−223.009			−0.242665			−0.121333	+	0.992612i	$0.538717\pi$
$920$		0			0
$921$	−290.733			−0.315671
$922$	395.479			0.428936
$923$	807.401			0.874757
$924$	−1719.35	−	641.272i	−1.86077	−	0.694017i
$925$		0			0
$926$	−1897.85			−2.04952
$927$	−115.439			−0.124529
$928$		−	1353.97i		−	1.45902i
$929$			1482.17i			1.59545i	0.603024	+	0.797723i	$0.293962\pi$
$929$			1482.17i			1.59545i	−0.603024	+	0.797723i	$0.706038\pi$
$930$		0			0
$931$	599.746	−	692.162i	0.644195	−	0.743461i
$932$		−	4037.36i		−	4.33194i
$933$			526.091i			0.563870i
$934$		−	2273.95i		−	2.43463i
$935$		0			0
$936$			1252.14i			1.33775i
$937$	836.508			0.892751			0.446376	−	0.894846i	$-0.352715\pi$
$937$	836.508			0.892751			0.446376	+	0.894846i	$0.352715\pi$
$938$	1184.37	+	441.737i	1.26265	+	0.470935i
$939$	29.8175			0.0317545
$940$		0			0
$941$		−	1637.85i		−	1.74055i	−0.492569	−	0.870273i	$-0.663942\pi$
$941$		−	1637.85i		−	1.74055i	0.492569	−	0.870273i	$-0.336058\pi$
$942$			501.932i			0.532836i
$943$	−299.183			−0.317267
$944$		−	1822.60i		−	1.93072i
$945$		0			0
$946$	321.364			0.339709
$947$			748.381i			0.790265i	0.918624	+	0.395133i	$0.129301\pi$
$947$			748.381i			0.790265i	−0.918624	+	0.395133i	$0.870699\pi$
$948$	−2350.03			−2.47894
$949$	−2134.22			−2.24891
$950$		0			0
$951$			143.528i			0.150923i
$952$	783.960	−	2101.92i	0.823487	−	2.20790i
$953$			942.124i			0.988588i	0.869295	+	0.494294i	$0.164573\pi$
$953$			942.124i			0.988588i	−0.869295	+	0.494294i	$0.835427\pi$
$954$	−934.875			−0.979953
$955$		0			0
$956$	4267.23			4.46362
$957$	343.533			0.358968
$958$	−1052.75			−1.09890
$959$	−186.421	+	499.825i	−0.194391	+	0.521194i
$960$		0			0
$961$	−840.008			−0.874098
$962$	1852.81			1.92600
$963$		−	263.396i		−	0.273516i
$964$			2847.27i			2.95360i
$965$		0			0
$966$	−448.889	−	167.423i	−0.464688	−	0.173316i
$967$		−	1654.90i		−	1.71138i	−0.517489	−	0.855690i	$-0.673133\pi$
$967$		−	1654.90i		−	1.71138i	0.517489	−	0.855690i	$-0.326867\pi$
$968$			2162.21i			2.23369i
$969$			421.155i			0.434629i
$970$		0			0
$971$			354.436i			0.365022i	0.983204	+	0.182511i	$0.0584224\pi$
$971$			354.436i			0.365022i	−0.983204	+	0.182511i	$0.941578\pi$
$972$	−163.289			−0.167993
$973$	−119.973	+	321.666i	−0.123302	+	0.330592i
$974$	−2064.58			−2.11969
$975$		0			0
$976$		−	3549.14i		−	3.63642i
$977$			1726.63i			1.76727i	0.468173	+	0.883637i	$0.344912\pi$
$977$			1726.63i			1.76727i	−0.468173	+	0.883637i	$0.655088\pi$
$978$	−68.7229			−0.0702688
$979$		−	368.922i		−	0.376836i
$980$		0			0
$981$	−390.037			−0.397591
$982$		−	2186.95i		−	2.22704i
$983$	−1635.34			−1.66362			−0.831809	−	0.555062i	$-0.812694\pi$
$983$	−1635.34			−1.66362			−0.831809	+	0.555062i	$0.812694\pi$
$984$	1229.11			1.24910
$985$		0			0
$986$			679.414i			0.689061i
$987$	−119.294	−	44.4935i	−0.120865	−	0.0450795i
$988$			3317.15i			3.35744i
$989$	60.7165			0.0613919
$990$		0			0
$991$	−313.579			−0.316427			−0.158213	−	0.987405i	$-0.550573\pi$
$991$	−313.579			−0.316427			−0.158213	+	0.987405i	$0.550573\pi$
$992$	4185.95			4.21971
$993$	−782.004			−0.787517
$994$	443.515	−	1189.13i	0.446192	−	1.19631i
$995$		0			0
$996$	774.546			0.777656
$997$	17.3708			0.0174231			0.00871155	−	0.999962i	$-0.497227\pi$
$997$	17.3708			0.0174231			0.00871155	+	0.999962i	$0.497227\pi$
$998$		−	2092.41i		−	2.09660i
$999$			149.355i			0.149505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.e.c.349.3		24
5.2	odd	4		525.3.h.d.76.11		12
5.3	odd	4		105.3.h.a.76.2	yes	12
5.4	even	2	inner	525.3.e.c.349.12		24
7.6	odd	2	inner	525.3.e.c.349.11		24
15.8	even	4		315.3.h.d.181.11		12
20.3	even	4		1680.3.s.c.1441.5		12
35.13	even	4		105.3.h.a.76.1	✓	12
35.27	even	4		525.3.h.d.76.12		12
35.34	odd	2	inner	525.3.e.c.349.4		24
105.83	odd	4		315.3.h.d.181.12		12
140.83	odd	4		1680.3.s.c.1441.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.1	✓	12	35.13	even	4
105.3.h.a.76.2	yes	12	5.3	odd	4
315.3.h.d.181.11		12	15.8	even	4
315.3.h.d.181.12		12	105.83	odd	4
525.3.e.c.349.3		24	1.1	even	1	trivial
525.3.e.c.349.4		24	35.34	odd	2	inner
525.3.e.c.349.11		24	7.6	odd	2	inner
525.3.e.c.349.12		24	5.4	even	2	inner
525.3.h.d.76.11		12	5.2	odd	4
525.3.h.d.76.12		12	35.27	even	4
1680.3.s.c.1441.5		12	20.3	even	4
1680.3.s.c.1441.8		12	140.83	odd	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)

\(f(q)\)	\(=\)	\(q-3.80460i q^{2} +1.73205 q^{3} -10.4750 q^{4} -6.58976i q^{6} +(6.55866 + 2.44621i) q^{7} +24.6348i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.80460i q^{2} +1.73205 q^{3} -10.4750 q^{4} -6.58976i q^{6} +(6.55866 + 2.44621i) q^{7} +24.6348i q^{8} +3.00000 q^{9} +14.4489 q^{11} -18.1432 q^{12} +16.9427 q^{13} +(9.30684 - 24.9531i) q^{14} +51.8255 q^{16} -13.0093 q^{17} -11.4138i q^{18} -18.6908i q^{19} +(11.3599 + 4.23695i) q^{21} -54.9723i q^{22} -10.3861i q^{23} +42.6687i q^{24} -64.4602i q^{26} +5.19615 q^{27} +(-68.7020 - 25.6240i) q^{28} +13.7269 q^{29} +42.4383i q^{31} -98.6363i q^{32} +25.0262 q^{33} +49.4951i q^{34} -31.4250 q^{36} +28.7434i q^{37} -71.1112 q^{38} +29.3456 q^{39} -28.8060i q^{41} +(16.1199 - 43.2200i) q^{42} +5.84593i q^{43} -151.352 q^{44} -39.5151 q^{46} -10.5013 q^{47} +89.7644 q^{48} +(37.0322 + 32.0877i) q^{49} -22.5327 q^{51} -177.475 q^{52} -81.9074i q^{53} -19.7693i q^{54} +(-60.2617 + 161.571i) q^{56} -32.3735i q^{57} -52.2254i q^{58} -35.1680i q^{59} -68.4826i q^{61} +161.461 q^{62} +(19.6760 + 7.33862i) q^{63} -167.970 q^{64} -95.2149i q^{66} +47.4637i q^{67} +136.272 q^{68} -17.9893i q^{69} +47.6548 q^{71} +73.9043i q^{72} -125.967 q^{73} +109.357 q^{74} +195.786i q^{76} +(94.7655 + 35.3450i) q^{77} -111.648i q^{78} +129.527 q^{79} +9.00000 q^{81} -109.595 q^{82} -42.6906 q^{83} +(-118.995 - 44.3820i) q^{84} +22.2414 q^{86} +23.7757 q^{87} +355.945i q^{88} -25.5329i q^{89} +(111.122 + 41.4453i) q^{91} +108.795i q^{92} +73.5053i q^{93} +39.9533i q^{94} -170.843i q^{96} -28.7310 q^{97} +(122.081 - 140.893i) q^{98} +43.3467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 88 q^{4} + 72 q^{9}+O(q^{10}) \) 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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