LMFDB - Embedded newform 925.2.o.d.174.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(174,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("925.174");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.o (of order $6$, degree $2$, 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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			174.6
Character	$\chi$	$=$	925.174
Dual form			925.2.o.d.824.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23169 + 0.711119i) q^{2} +(2.52555 + 1.45812i) q^{3} +(0.0113813 - 0.0197130i) q^{4} -4.14760 q^{6} +(4.52117 + 2.61030i) q^{7} -2.81210i q^{8} +(2.75225 + 4.76704i) q^{9} +O(q^{10})$	\(q+(-1.23169 + 0.711119i) q^{2} +(2.52555 + 1.45812i) q^{3} +(0.0113813 - 0.0197130i) q^{4} -4.14760 q^{6} +(4.52117 + 2.61030i) q^{7} -2.81210i q^{8} +(2.75225 + 4.76704i) q^{9} -2.54267 q^{11} +(0.0574879 - 0.0331906i) q^{12} +(-1.78811 - 1.03236i) q^{13} -7.42493 q^{14} +(2.02250 + 3.50308i) q^{16} +(-6.55831 + 3.78644i) q^{17} +(-6.77987 - 3.91436i) q^{18} +(-1.09671 + 1.89956i) q^{19} +(7.61227 + 13.1848i) q^{21} +(3.13180 - 1.80814i) q^{22} -3.86905i q^{23} +(4.10040 - 7.10209i) q^{24} +2.93654 q^{26} +7.30376i q^{27} +(0.102913 - 0.0594170i) q^{28} +1.70825 q^{29} +8.03194 q^{31} +(-0.111508 - 0.0643791i) q^{32} +(-6.42163 - 3.70753i) q^{33} +(5.38522 - 9.32748i) q^{34} +0.125297 q^{36} +(6.08064 + 0.160528i) q^{37} -3.11957i q^{38} +(-3.01063 - 5.21456i) q^{39} +(-4.51088 + 7.81308i) q^{41} +(-18.7520 - 10.8265i) q^{42} -0.751253i q^{43} +(-0.0289389 + 0.0501236i) q^{44} +(2.75135 + 4.76548i) q^{46} -0.0613730i q^{47} +11.7962i q^{48} +(10.1273 + 17.5410i) q^{49} -22.0844 q^{51} +(-0.0407019 + 0.0234992i) q^{52} +(1.68649 - 0.973694i) q^{53} +(-5.19385 - 8.99601i) q^{54} +(7.34042 - 12.7140i) q^{56} +(-5.53959 + 3.19829i) q^{57} +(-2.10404 + 1.21477i) q^{58} +(2.44957 + 4.24279i) q^{59} +(1.63484 - 2.83163i) q^{61} +(-9.89289 + 5.71166i) q^{62} +28.7368i q^{63} -7.90689 q^{64} +10.5460 q^{66} +(-9.42232 - 5.43998i) q^{67} +0.172378i q^{68} +(5.64155 - 9.77145i) q^{69} +(1.10115 - 1.90726i) q^{71} +(13.4054 - 7.73962i) q^{72} -9.02399i q^{73} +(-7.60365 + 4.12634i) q^{74} +(0.0249640 + 0.0432389i) q^{76} +(-11.4958 - 6.63713i) q^{77} +(7.41636 + 4.28183i) q^{78} +(3.42536 - 5.93289i) q^{79} +(-2.39304 + 4.14486i) q^{81} -12.8311i q^{82} +(7.41311 - 4.27996i) q^{83} +0.346550 q^{84} +(0.534231 + 0.925315i) q^{86} +(4.31426 + 2.49084i) q^{87} +7.15026i q^{88} +(0.806045 + 1.39611i) q^{89} +(-5.38955 - 9.33498i) q^{91} +(-0.0762703 - 0.0440347i) q^{92} +(20.2850 + 11.7116i) q^{93} +(0.0436435 + 0.0755927i) q^{94} +(-0.187746 - 0.325185i) q^{96} -1.26376i q^{97} +(-24.9475 - 14.4034i) q^{98} +(-6.99808 - 12.1210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) $ 48 * q + 22 * q^4 + 20 * q^9	$ 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) $ 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.23169	+	0.711119i	−0.870940	+	0.502837i	−0.867660	−	0.497157i	$-0.834377\pi$
$2$	−1.23169	+	0.711119i	−0.870940	+	0.502837i	−0.00327930	+	0.999995i	$0.501044\pi$
$3$	2.52555	+	1.45812i	1.45812	+	0.841848i	0.998919	−	0.0464817i	$-0.0148009\pi$
$3$	2.52555	+	1.45812i	1.45812	+	0.841848i	0.459205	+	0.888330i	$0.348134\pi$
$4$	0.0113813	−	0.0197130i	0.00569064	−	0.00985648i
$5$		0			0
$5$		0			0
$6$	−4.14760			−1.69325
$7$	4.52117	+	2.61030i	1.70884	+	0.986599i	0.936001	+	0.351996i	$0.114497\pi$
$7$	4.52117	+	2.61030i	1.70884	+	0.986599i	0.772839	+	0.634603i	$0.218836\pi$
$8$		−	2.81210i		−	0.994229i
$9$	2.75225	+	4.76704i	0.917418	+	1.58901i
$10$		0			0
$11$	−2.54267			−0.766645			−0.383322	−	0.923615i	$-0.625220\pi$
$11$	−2.54267			−0.766645			−0.383322	+	0.923615i	$0.625220\pi$
$12$	0.0574879	−	0.0331906i	0.0165953	−	0.00958131i
$13$	−1.78811	−	1.03236i	−0.495932	−	0.286326i	0.231100	−	0.972930i	$-0.425767\pi$
$13$	−1.78811	−	1.03236i	−0.495932	−	0.286326i	−0.727032	+	0.686604i	$0.759101\pi$
$14$	−7.42493			−1.98440
$15$		0			0
$16$	2.02250	+	3.50308i	0.505626	+	0.875770i
$17$	−6.55831	+	3.78644i	−1.59062	+	0.918347i	−0.597423	+	0.801926i	$0.703809\pi$
$17$	−6.55831	+	3.78644i	−1.59062	+	0.918347i	−0.993200	+	0.116421i	$0.962858\pi$
$18$	−6.77987	−	3.91436i	−1.59803	−	0.922624i
$19$	−1.09671	+	1.89956i	−0.251603	+	0.435789i	−0.963967	−	0.266021i	$-0.914291\pi$
$19$	−1.09671	+	1.89956i	−0.251603	+	0.435789i	0.712364	+	0.701810i	$0.247624\pi$
$20$		0			0
$21$	7.61227	+	13.1848i	1.66113	+	2.87717i
$22$	3.13180	−	1.80814i	0.667701	−	0.385497i
$23$		−	3.86905i		−	0.806752i	−0.915034	−	0.403376i	$-0.867837\pi$
$23$		−	3.86905i		−	0.806752i	0.915034	−	0.403376i	$-0.132163\pi$
$24$	4.10040	−	7.10209i	0.836990	−	1.44971i
$25$		0			0
$26$	2.93654			0.575902
$27$			7.30376i			1.40561i
$28$	0.102913	−	0.0594170i	0.0194488	−	0.0112288i
$29$	1.70825			0.317214			0.158607	−	0.987342i	$-0.449300\pi$
$29$	1.70825			0.317214			0.158607	+	0.987342i	$0.449300\pi$
$30$		0			0
$31$	8.03194			1.44258			0.721289	−	0.692634i	$-0.243550\pi$
$31$	8.03194			1.44258			0.721289	+	0.692634i	$0.243550\pi$
$32$	−0.111508	−	0.0643791i	−0.0197120	−	0.0113807i
$33$	−6.42163	−	3.70753i	−1.11786	−	0.645399i
$34$	5.38522	−	9.32748i	0.923558	−	1.59965i
$35$		0			0
$36$	0.125297			0.0208828
$37$	6.08064	+	0.160528i	0.999652	+	0.0263907i
$37$	6.08064	+	0.160528i	0.999652	+	0.0263907i
$38$		−	3.11957i		−	0.506062i
$39$	−3.01063	−	5.21456i	−0.482087	−	0.834999i
$40$		0			0
$41$	−4.51088	+	7.81308i	−0.704482	+	1.22020i	0.262397	+	0.964960i	$0.415487\pi$
$41$	−4.51088	+	7.81308i	−0.704482	+	1.22020i	−0.966878	+	0.255238i	$0.917846\pi$
$42$	−18.7520	−	10.8265i	−2.89350	−	1.67056i
$43$		−	0.751253i		−	0.114565i	−0.998358	−	0.0572825i	$-0.981756\pi$
$43$		−	0.751253i		−	0.114565i	0.998358	−	0.0572825i	$-0.0182436\pi$
$44$	−0.0289389	+	0.0501236i	−0.00436270	+	0.00755641i
$45$		0			0
$46$	2.75135	+	4.76548i	0.405665	+	0.702632i
$47$		−	0.0613730i		−	0.00895217i	−0.999990	−	0.00447608i	$-0.998575\pi$
$47$		−	0.0613730i		−	0.00895217i	0.999990	−	0.00447608i	$-0.00142479\pi$
$48$			11.7962i			1.70264i
$49$	10.1273	+	17.5410i	1.44676	+	2.50585i
$50$		0			0
$51$	−22.0844			−3.09244
$52$	−0.0407019	+	0.0234992i	−0.00564434	+	0.00325876i
$53$	1.68649	−	0.973694i	0.231657	−	0.133747i	−0.379679	−	0.925118i	$-0.623966\pi$
$53$	1.68649	−	0.973694i	0.231657	−	0.133747i	0.611336	+	0.791371i	$0.290632\pi$
$54$	−5.19385	−	8.99601i	−0.706793	−	1.22420i
$55$		0			0
$56$	7.34042	−	12.7140i	0.980905	−	1.69898i
$57$	−5.53959	+	3.19829i	−0.733737	+	0.423623i
$58$	−2.10404	+	1.21477i	−0.276274	+	0.159507i
$59$	2.44957	+	4.24279i	0.318907	+	0.552364i	0.980260	−	0.197711i	$-0.0633508\pi$
$59$	2.44957	+	4.24279i	0.318907	+	0.552364i	−0.661353	+	0.750075i	$0.730017\pi$
$60$		0			0
$61$	1.63484	−	2.83163i	0.209320	−	0.362553i	−0.742180	−	0.670200i	$-0.766208\pi$
$61$	1.63484	−	2.83163i	0.209320	−	0.362553i	0.951501	+	0.307647i	$0.0995416\pi$
$62$	−9.89289	+	5.71166i	−1.25640	+	0.725382i
$63$			28.7368i			3.62049i
$64$	−7.90689			−0.988361
$65$		0			0
$66$	10.5460			1.29812
$67$	−9.42232	−	5.43998i	−1.15112	−	0.664599i	−0.201959	−	0.979394i	$-0.564731\pi$
$67$	−9.42232	−	5.43998i	−1.15112	−	0.664599i	−0.949160	+	0.314795i	$0.898064\pi$
$68$			0.172378i			0.0209039i
$69$	5.64155	−	9.77145i	0.679163	−	1.17634i
$70$		0			0
$71$	1.10115	−	1.90726i	0.130683	−	0.226350i	−0.793257	−	0.608887i	$-0.791616\pi$
$71$	1.10115	−	1.90726i	0.130683	−	0.226350i	0.923940	+	0.382537i	$0.124950\pi$
$72$	13.4054	−	7.73962i	1.57984	−	0.912123i
$73$		−	9.02399i		−	1.05618i	−0.849189	−	0.528089i	$-0.822909\pi$
$73$		−	9.02399i		−	1.05618i	0.849189	−	0.528089i	$-0.177091\pi$
$74$	−7.60365	+	4.12634i	−0.883907	+	0.479677i
$75$		0			0
$76$	0.0249640	+	0.0432389i	0.00286356	+	0.00495984i
$77$	−11.4958	−	6.63713i	−1.31007	−	0.756371i
$78$	7.41636	+	4.28183i	0.839737	+	0.484822i
$79$	3.42536	−	5.93289i	0.385383	−	0.667503i	−0.606439	−	0.795130i	$-0.707403\pi$
$79$	3.42536	−	5.93289i	0.385383	−	0.667503i	0.991822	+	0.127627i	$0.0407361\pi$
$80$		0			0
$81$	−2.39304	+	4.14486i	−0.265893	+	0.460540i
$82$		−	12.8311i		−	1.41696i
$83$	7.41311	−	4.27996i	0.813694	−	0.469787i	−0.0345430	−	0.999403i	$-0.510998\pi$
$83$	7.41311	−	4.27996i	0.813694	−	0.469787i	0.848237	+	0.529617i	$0.177664\pi$
$84$	0.346550			0.0378117
$85$		0			0
$86$	0.534231	+	0.925315i	0.0576076	+	0.0997793i
$87$	4.31426	+	2.49084i	0.462537	+	0.267046i
$88$			7.15026i			0.762220i
$89$	0.806045	+	1.39611i	0.0854406	+	0.147987i	0.905579	−	0.424178i	$-0.139437\pi$
$89$	0.806045	+	1.39611i	0.0854406	+	0.147987i	−0.820138	+	0.572165i	$0.806104\pi$
$90$		0			0
$91$	−5.38955	−	9.33498i	−0.564979	−	0.978572i
$92$	−0.0762703	−	0.0440347i	−0.00795173	−	0.00459093i
$93$	20.2850	+	11.7116i	2.10346	+	1.21443i
$94$	0.0436435	+	0.0755927i	0.00450148	+	0.00779680i
$95$		0			0
$96$	−0.187746	−	0.325185i	−0.0191617	−	0.0331890i
$97$		−	1.26376i		−	0.128315i	−0.997940	−	0.0641576i	$-0.979564\pi$
$97$		−	1.26376i		−	0.128315i	0.997940	−	0.0641576i	$-0.0204360\pi$
$98$	−24.9475	−	14.4034i	−2.52007	−	1.45497i
$99$	−6.99808	−	12.1210i	−0.703333	−	1.21821i
$100$		0			0
$101$	−6.60500			−0.657222			−0.328611	−	0.944465i	$-0.606580\pi$
$101$	−6.60500			−0.657222			−0.328611	+	0.944465i	$0.606580\pi$
$102$	27.2012	−	15.7046i	2.69332	−	1.55499i
$103$		−	12.9646i		−	1.27744i	−0.769438	−	0.638722i	$-0.779464\pi$
$103$		−	12.9646i		−	1.27744i	0.769438	−	0.638722i	$-0.220536\pi$
$104$	−2.90311	+	5.02834i	−0.284674	+	0.493069i
$105$		0			0
$106$	−1.38483	+	2.39859i	−0.134506	+	0.232971i
$107$	9.72748	+	5.61617i	0.940391	+	0.542935i	0.890083	−	0.455799i	$-0.150646\pi$
$107$	9.72748	+	5.61617i	0.940391	+	0.542935i	0.0503084	+	0.998734i	$0.483980\pi$
$108$	0.143979	+	0.0831262i	0.0138544	+	0.00799882i
$109$	4.52953	+	7.84537i	0.433850	+	0.751450i	0.997201	−	0.0747676i	$-0.0238215\pi$
$109$	4.52953	+	7.84537i	0.433850	+	0.751450i	−0.563351	+	0.826218i	$0.690488\pi$
$110$		0			0
$111$	15.1229	+	9.27176i	1.43540	+	0.880036i
$112$			21.1173i			1.99540i
$113$	2.67878	−	1.54659i	0.251998	−	0.145491i	−0.368681	−	0.929556i	$-0.620190\pi$
$113$	2.67878	−	1.54659i	0.251998	−	0.145491i	0.620679	+	0.784065i	$0.286857\pi$
$114$	4.54873	−	7.87862i	0.426027	−	0.737901i
$115$		0			0
$116$	0.0194420	−	0.0336746i	0.00180515	−	0.00312661i
$117$		−	11.3653i		−	1.05072i
$118$	−6.03426	−	3.48388i	−0.555498	−	0.320717i
$119$	−39.5349			−3.62416
$120$		0			0
$121$	−4.53482			−0.412256
$122$			4.65027i			0.421016i
$123$	−22.7849	+	13.1549i	−2.05444	+	1.18613i
$124$	0.0914137	−	0.158333i	0.00820919	−	0.0142187i
$125$		0			0
$126$	−20.4353	−	35.3949i	−1.82052	−	3.15323i
$127$	−3.58161	+	2.06785i	−0.317817	+	0.183492i	−0.650419	−	0.759576i	$-0.725407\pi$
$127$	−3.58161	+	2.06785i	−0.317817	+	0.183492i	0.332602	+	0.943067i	$0.392073\pi$
$128$	9.96189	−	5.75150i	0.880515	−	0.508366i
$129$	1.09542	−	1.89732i	0.0964464	−	0.167050i
$130$		0			0
$131$	−5.03245	−	8.71646i	−0.439687	−	0.761561i	0.557978	−	0.829856i	$-0.311577\pi$
$131$	−5.03245	−	8.71646i	−0.439687	−	0.761561i	−0.997665	+	0.0682952i	$0.978244\pi$
$132$	−0.146173	+	0.0843929i	−0.0127227	+	0.00734546i
$133$	−9.91683	+	5.72549i	−0.859899	+	0.496463i
$134$	15.4739			1.33674
$135$		0			0
$136$	10.6479	+	18.4426i	0.913047	+	1.58144i
$137$		−	15.3585i		−	1.31217i	−0.754689	−	0.656083i	$-0.772212\pi$
$137$		−	15.3585i		−	1.31217i	0.754689	−	0.656083i	$-0.227788\pi$
$138$			16.0473i			1.36603i
$139$	5.32324	+	9.22012i	0.451511	+	0.782041i	0.998480	−	0.0551123i	$-0.0175517\pi$
$139$	5.32324	+	9.22012i	0.451511	+	0.782041i	−0.546969	+	0.837153i	$0.684218\pi$
$140$		0			0
$141$	0.0894894	−	0.155000i	0.00753637	−	0.0130534i
$142$			3.13221i			0.262849i
$143$	4.54657	+	2.62496i	0.380203	+	0.219510i
$144$	−11.1329	+	19.2827i	−0.927740	+	1.60689i
$145$		0			0
$146$	6.41713	+	11.1148i	0.531086	+	0.919867i
$147$			59.0674i			4.87180i
$148$	0.0723700	−	0.118040i	0.00594878	−	0.00970286i
$149$	23.3300			1.91127			0.955634	−	0.294556i	$-0.0951716\pi$
$149$	23.3300			1.91127			0.955634	+	0.294556i	$0.0951716\pi$
$150$		0			0
$151$	−7.69709	+	13.3318i	−0.626381	+	1.08492i	0.361892	+	0.932220i	$0.382131\pi$
$151$	−7.69709	+	13.3318i	−0.626381	+	1.08492i	−0.988272	+	0.152703i	$0.951202\pi$
$152$	5.34176	+	3.08407i	0.433274	+	0.250151i
$153$	−36.1002	−	20.8425i	−2.91853	−	1.68502i
$154$	18.8792			1.52133
$155$		0			0
$156$	−0.137059			−0.0109735
$157$	4.01207	−	2.31637i	0.320198	−	0.184867i	−0.331283	−	0.943532i	$-0.607481\pi$
$157$	4.01207	−	2.31637i	0.320198	−	0.184867i	0.651481	+	0.758665i	$0.274148\pi$
$158$			9.74335i			0.775139i
$159$	5.67907			0.450379
$160$		0			0
$161$	10.0994	−	17.4926i	0.795941	−	1.37861i
$162$		−	6.80694i		−	0.534804i
$163$	12.2176	−	7.05381i	0.956952	−	0.552497i	0.0617187	−	0.998094i	$-0.480342\pi$
$163$	12.2176	−	7.05381i	0.956952	−	0.552497i	0.895234	+	0.445597i	$0.147009\pi$
$164$	0.102679	+	0.177846i	0.00801790	+	0.0138874i
$165$		0			0
$166$	−6.08712	+	10.5432i	−0.472452	+	0.818311i
$167$	−11.6369	−	6.71857i	−0.900491	−	0.519898i	−0.0231313	−	0.999732i	$-0.507364\pi$
$167$	−11.6369	−	6.71857i	−0.900491	−	0.519898i	−0.877359	+	0.479834i	$0.840697\pi$
$168$	37.0771	−	21.4065i	2.86056	−	1.65155i
$169$	−4.36845	−	7.56638i	−0.336035	−	0.582029i
$170$		0			0
$171$	−12.0737			−0.923300
$172$	−0.0148094	−	0.00855022i	−0.00112921	−	0.000651949i
$173$	9.73372	−	5.61976i	0.740041	−	0.427263i	−0.0820433	−	0.996629i	$-0.526145\pi$
$173$	9.73372	−	5.61976i	0.740041	−	0.427263i	0.822084	+	0.569366i	$0.192811\pi$
$174$	−7.08513			−0.537122
$175$		0			0
$176$	−5.14256	−	8.90718i	−0.387635	−	0.671404i
$177$			14.2871i			1.07389i
$178$	−1.98560	−	1.14639i	−0.148827	−	0.0859254i
$179$	−10.7939			−0.806775			−0.403388	−	0.915029i	$-0.632167\pi$
$179$	−10.7939			−0.806775			−0.403388	+	0.915029i	$0.632167\pi$
$180$		0			0
$181$	0.0256803	−	0.0444795i	0.00190880	−	0.00330614i	−0.865069	−	0.501652i	$-0.832726\pi$
$181$	0.0256803	−	0.0444795i	0.00190880	−	0.00330614i	0.866978	+	0.498346i	$0.166059\pi$
$182$	13.2766	+	7.66523i	0.984124	+	0.568185i
$183$	8.25774	−	4.76761i	0.610430	−	0.352432i
$184$	−10.8802			−0.802096
$185$		0			0
$186$	−33.3133			−2.44265
$187$	16.6756	−	9.62768i	1.21944	−	0.704046i
$188$	−0.00120984		0.000698503i	−8.82368e−5		5.09435e-5i
$189$	−19.0650	+	33.0215i	−1.38677	+	2.40196i
$190$		0			0
$191$	19.2370			1.39194			0.695971	−	0.718070i	$-0.254974\pi$
$191$	19.2370			1.39194			0.695971	+	0.718070i	$0.254974\pi$
$192$	−19.9692	−	11.5292i	−1.44115	−	0.832050i
$193$			22.0240i			1.58532i	0.609665	+	0.792660i	$0.291304\pi$
$193$			22.0240i			1.58532i	−0.609665	+	0.792660i	$0.708696\pi$
$194$	0.898683	+	1.55656i	0.0645216	+	0.111755i
$195$		0			0
$196$	0.461046			0.0329319
$197$	3.20462	−	1.85019i	0.228319	−	0.131820i	−0.381477	−	0.924378i	$-0.624584\pi$
$197$	3.20462	−	1.85019i	0.228319	−	0.131820i	0.609797	+	0.792558i	$0.291251\pi$
$198$	17.2390	+	9.95294i	1.22512	+	0.707324i
$199$	−8.05036			−0.570675			−0.285337	−	0.958427i	$-0.592106\pi$
$199$	−8.05036			−0.570675			−0.285337	+	0.958427i	$0.592106\pi$
$200$		0			0
$201$	−15.8643	−	27.4778i	−1.11898	−	1.93814i
$202$	8.13534	−	4.69694i	0.572401	−	0.330476i
$203$	7.72327	+	4.45903i	0.542067	+	0.312963i
$204$	−0.251349	+	0.435349i	−0.0175979	+	0.0304805i
$205$		0			0
$206$	9.21940	+	15.9685i	0.642346	+	1.11258i
$207$	18.4439	−	10.6486i	1.28194	−	0.740129i
$208$		−	8.35184i		−	0.579096i
$209$	2.78858	−	4.82996i	0.192890	−	0.334095i
$210$		0			0
$211$	5.95618			0.410041			0.205020	−	0.978758i	$-0.434274\pi$
$211$	5.95618			0.410041			0.205020	+	0.978758i	$0.434274\pi$
$212$		−	0.0443275i		−	0.00304443i
$213$	5.56203	−	3.21124i	0.381104	−	0.220031i
$214$	−15.9751			−1.09203
$215$		0			0
$216$	20.5389			1.39750
$217$	36.3137	+	20.9657i	2.46514	+	1.42325i
$218$	−11.1580	−	6.44207i	−0.755714	−	0.436312i
$219$	13.1581	−	22.7905i	0.889142	−	1.54004i
$220$		0			0
$221$	15.6359			1.05179
$222$	−25.2201	−	0.665806i	−1.69266	−	0.0446860i
$223$		−	6.66192i		−	0.446115i	−0.974805	−	0.223058i	$-0.928396\pi$
$223$		−	6.66192i		−	0.446115i	0.974805	−	0.223058i	$-0.0716038\pi$
$224$	−0.336097	−	0.582137i	−0.0224564	−	0.0388957i
$225$		0			0
$226$	−2.19962	+	3.80986i	−0.146317	+	0.253428i
$227$	−19.0946	−	11.0242i	−1.26735	−	0.731705i	−0.292864	−	0.956154i	$-0.594608\pi$
$227$	−19.0946	−	11.0242i	−1.26735	−	0.731705i	−0.974486	+	0.224449i	$0.927942\pi$
$228$			0.145602i			0.00964275i
$229$	−0.666580	+	1.15455i	−0.0440489	+	0.0762948i	−0.887209	−	0.461367i	$-0.847359\pi$
$229$	−0.666580	+	1.15455i	−0.0440489	+	0.0762948i	0.843160	+	0.537662i	$0.180692\pi$
$230$		0			0
$231$	−19.3555	−	33.5247i	−1.27350	−	2.20577i
$232$		−	4.80377i		−	0.315383i
$233$			17.2068i			1.12725i	0.826029	+	0.563627i	$0.190595\pi$
$233$			17.2068i			1.12725i	−0.826029	+	0.563627i	$0.809405\pi$
$234$	8.08209	+	13.9986i	0.528343	+	0.915117i
$235$		0			0
$236$	0.111517			0.00725915
$237$	17.3018	−	9.98919i	1.12387	−	0.648868i
$238$	48.6950	−	28.1140i	3.15643	−	1.82236i
$239$	4.08531	+	7.07596i	0.264256	+	0.457706i	0.967369	−	0.253373i	$-0.0815401\pi$
$239$	4.08531	+	7.07596i	0.264256	+	0.457706i	−0.703112	+	0.711079i	$0.748207\pi$
$240$		0			0
$241$	4.25496	−	7.36980i	0.274086	−	0.474731i	−0.695818	−	0.718218i	$-0.744958\pi$
$241$	4.25496	−	7.36980i	0.274086	−	0.474731i	0.969904	+	0.243487i	$0.0782914\pi$
$242$	5.58551	−	3.22480i	0.359050	−	0.207298i
$243$	6.88829	−	3.97696i	0.441884	−	0.255122i
$244$	−0.0372132	−	0.0644552i	−0.00238233	−	0.00412632i
$245$		0			0
$246$	18.7093	−	32.4055i	1.19286	−	2.06610i
$247$	3.92208	−	2.26441i	0.249556	−	0.144081i
$248$		−	22.5866i		−	1.43425i
$249$	24.9629			1.58196
$250$		0			0
$251$	−1.83792			−0.116009			−0.0580043	−	0.998316i	$-0.518474\pi$
$251$	−1.83792			−0.116009			−0.0580043	+	0.998316i	$0.518474\pi$
$252$	0.566487	+	0.327061i	0.0356853	+	0.0206029i
$253$			9.83772i			0.618492i
$254$	2.94097	−	5.09391i	0.184533	−	0.319620i
$255$		0			0
$256$	−0.273115	+	0.473050i	−0.0170697	+	0.0295656i
$257$	16.5303	−	9.54375i	1.03113	−	0.595323i	0.113821	−	0.993501i	$-0.463691\pi$
$257$	16.5303	−	9.54375i	1.03113	−	0.595323i	0.917308	+	0.398178i	$0.130358\pi$
$258$			3.11590i			0.193987i
$259$	27.0726	+	16.5981i	1.68221	+	1.03135i
$260$		0			0
$261$	4.70153	+	8.14329i	0.291017	+	0.504057i
$262$	12.3969	+	7.15735i	0.765882	+	0.442182i
$263$	−2.62240	−	1.51405i	−0.161704	−	0.0933601i	0.416964	−	0.908923i	$-0.363094\pi$
$263$	−2.62240	−	1.51405i	−0.161704	−	0.0933601i	−0.578668	+	0.815563i	$0.696427\pi$
$264$	−10.4260	+	18.0583i	−0.641674	+	1.11141i
$265$		0			0
$266$	8.14301	−	14.1041i	0.499280	−	0.864778i
$267$			4.70126i			0.287712i
$268$	−0.214476	+	0.123828i	−0.0131012	+	0.00756398i
$269$	23.0647			1.40628			0.703140	−	0.711052i	$-0.251781\pi$
$269$	23.0647			1.40628			0.703140	+	0.711052i	$0.251781\pi$
$270$		0			0
$271$	−1.86592	−	3.23186i	−0.113346	−	0.196322i	0.803771	−	0.594939i	$-0.202824\pi$
$271$	−1.86592	−	3.23186i	−0.113346	−	0.196322i	−0.917118	+	0.398617i	$0.869490\pi$
$272$	−26.5284	−	15.3162i	−1.60852	−	0.928680i
$273$		−	31.4345i		−	1.90251i
$274$	10.9217	+	18.9170i	0.659806	+	1.14282i
$275$		0			0
$276$	−0.128416	−	0.222423i	−0.00772974	−	0.0133883i
$277$	−12.4454	−	7.18533i	−0.747769	−	0.431725i	0.0771181	−	0.997022i	$-0.475428\pi$
$277$	−12.4454	−	7.18533i	−0.747769	−	0.431725i	−0.824887	+	0.565297i	$0.808761\pi$
$278$	−13.1132	−	7.57092i	−0.786478	−	0.454074i
$279$	22.1059	+	38.2886i	1.32345	+	2.29228i
$280$		0			0
$281$	8.62432	+	14.9378i	0.514484	+	0.891112i	0.999859	+	0.0168062i	$0.00534983\pi$
$281$	8.62432	+	14.9378i	0.514484	+	0.891112i	−0.485375	+	0.874306i	$0.661317\pi$
$282$			0.254551i			0.0151583i
$283$	6.99979	+	4.04133i	0.416094	+	0.240232i	0.693405	−	0.720548i	$-0.256110\pi$
$283$	6.99979	+	4.04133i	0.416094	+	0.240232i	−0.277311	+	0.960780i	$0.589443\pi$
$284$	−0.0250651	−	0.0434140i	−0.00148734	−	0.00257615i
$285$		0			0
$286$	−7.46665			−0.441512
$287$	−40.7889	+	23.5495i	−2.40769	+	1.39008i
$288$		−	0.708751i		−	0.0417635i
$289$	20.1743	−	34.9429i	1.18672	−	2.05546i
$290$		0			0
$291$	1.84272	−	3.19168i	0.108022	−	0.187099i
$292$	−0.177889	−	0.102705i	−0.0104102	−	0.00601033i
$293$	−8.70147	−	5.02380i	−0.508345	−	0.293493i	0.223808	−	0.974633i	$-0.428151\pi$
$293$	−8.70147	−	5.02380i	−0.508345	−	0.293493i	−0.732153	+	0.681140i	$0.761485\pi$
$294$	−42.0040	−	72.7530i	−2.44972	−	4.24304i
$295$		0			0
$296$	0.451421	−	17.0994i	0.0262383	−	0.993882i
$297$		−	18.5711i		−	1.07760i
$298$	−28.7354	+	16.5904i	−1.66460	+	0.961057i
$299$	−3.99426	+	6.91827i	−0.230994	+	0.400094i
$300$		0			0
$301$	1.96099	−	3.39654i	0.113030	−	0.195773i
$302$		−	21.8942i		−	1.25987i
$303$	−16.6812	−	9.63091i	−0.958311	−	0.553281i
$304$	−8.87242			−0.508868
$305$		0			0
$306$	59.2860			3.38915
$307$			18.4310i			1.05192i	0.850511	+	0.525958i	$0.176293\pi$
$307$			18.4310i			1.05192i	−0.850511	+	0.525958i	$0.823707\pi$
$308$	−0.261675	+	0.151078i	−0.0149103	+	0.00860847i
$309$	18.9040	−	32.7428i	1.07541	−	1.86267i
$310$		0			0
$311$	−4.64667	−	8.04827i	−0.263489	−	0.456376i	0.703678	−	0.710519i	$-0.251540\pi$
$311$	−4.64667	−	8.04827i	−0.263489	−	0.456376i	−0.967167	+	0.254143i	$0.918206\pi$
$312$	−14.6639	+	8.46620i	−0.830180	+	0.479304i
$313$	−18.4048	+	10.6260i	−1.04030	+	0.600618i	−0.919918	−	0.392110i	$-0.871745\pi$
$313$	−18.4048	+	10.6260i	−1.04030	+	0.600618i	−0.120382	+	0.992728i	$0.538412\pi$
$314$	−3.29443	+	5.70613i	−0.185916	+	0.322015i
$315$		0			0
$316$	−0.0779699	−	0.135048i	−0.00438615	−	0.00759703i
$317$	5.08940	−	2.93837i	0.285849	−	0.165035i	−0.350219	−	0.936668i	$-0.613893\pi$
$317$	5.08940	−	2.93837i	0.285849	−	0.165035i	0.636068	+	0.771633i	$0.280560\pi$
$318$	−6.99488	+	4.03849i	−0.392253	+	0.226468i
$319$	−4.34351			−0.243190
$320$		0			0
$321$	16.3781	+	28.3678i	0.914138	+	1.58333i
$322$			28.7274i			1.60091i
$323$		−	16.6105i		−	0.924235i
$324$	0.0544716	+	0.0943477i	0.00302620	+	0.00524154i
$325$		0			0
$326$	−10.0322	+	17.3763i	−0.555632	+	0.962383i
$327$			26.4184i			1.46094i
$328$	21.9712	+	12.6851i	1.21316	+	0.700416i
$329$	0.160202	−	0.277477i	0.00883220	−	0.0152978i
$330$		0			0
$331$	−9.21489	−	15.9607i	−0.506496	−	0.877277i	−0.999972	−	0.00751758i	$-0.997607\pi$
$331$	−9.21489	−	15.9607i	−0.506496	−	0.877277i	0.493475	−	0.869760i	$-0.335726\pi$
$332$		−	0.194846i		−	0.0106935i
$333$	15.9702	+	29.4285i	0.875163	+	1.61267i
$334$	19.1108			1.04570
$335$		0			0
$336$	−30.7917	+	53.3328i	−1.67982	+	2.90954i
$337$	20.5550	+	11.8674i	1.11970	+	0.646461i	0.941325	−	0.337501i	$-0.109582\pi$
$337$	20.5550	+	11.8674i	1.11970	+	0.646461i	0.178378	+	0.983962i	$0.442915\pi$
$338$	10.7612	+	6.21298i	0.585332	+	0.337941i
$339$	9.02049			0.489926
$340$		0			0
$341$	−20.4226			−1.10594
$342$	14.8711	−	8.58585i	0.804139	−	0.464270i
$343$			69.1968i			3.73627i
$344$	−2.11260			−0.113904
$345$		0			0
$346$	−7.99265	+	13.8437i	−0.429687	+	0.744240i
$347$		−	20.4006i		−	1.09516i	−0.836752	−	0.547582i	$-0.815548\pi$
$347$		−	20.4006i		−	1.09516i	0.836752	−	0.547582i	$-0.184452\pi$
$348$	0.0982035	−	0.0566978i	0.00526426	−	0.00303932i
$349$	−13.8034	−	23.9082i	−0.738880	−	1.27978i	−0.953000	−	0.302970i	$-0.902022\pi$
$349$	−13.8034	−	23.9082i	−0.738880	−	1.27978i	0.214120	−	0.976807i	$-0.431312\pi$
$350$		0			0
$351$	7.54014	−	13.0599i	0.402463	−	0.697087i
$352$	0.283528	+	0.163695i	0.0151121	+	0.00872497i
$353$	−24.6649	+	14.2403i	−1.31278	+	0.757935i	−0.982556	−	0.185966i	$-0.940458\pi$
$353$	−24.6649	+	14.2403i	−1.31278	+	0.757935i	−0.330226	+	0.943902i	$0.607125\pi$
$354$	−10.1599	−	17.5974i	−0.539990	−	0.935291i
$355$		0			0
$356$	0.0366953			0.00194485
$357$	−99.8472	−	57.6468i	−5.28448	−	3.05099i
$358$	13.2948	−	7.67576i	0.702653	−	0.405677i
$359$	8.66371			0.457253			0.228627	−	0.973514i	$-0.426576\pi$
$359$	8.66371			0.457253			0.228627	+	0.973514i	$0.426576\pi$
$360$		0			0
$361$	7.09444	+	12.2879i	0.373392	+	0.646734i
$362$			0.0730469i			0.00383926i
$363$	−11.4529	−	6.61233i	−0.601121	−	0.347057i
$364$	−0.245360			−0.0128604
$365$		0			0
$366$	−6.78068	+	11.7445i	−0.354432	+	0.613894i
$367$	−5.40924	−	3.12302i	−0.282360	−	0.163021i	0.352131	−	0.935951i	$-0.385457\pi$
$367$	−5.40924	−	3.12302i	−0.282360	−	0.163021i	−0.634491	+	0.772930i	$0.718790\pi$
$368$	13.5536	−	7.82516i	0.706529	−	0.407915i
$369$	−49.6604			−2.58522
$370$		0			0
$371$	10.1665			0.527819
$372$	0.461739	−	0.266585i	0.0239400	−	0.0138218i
$373$	14.5373	+	8.39312i	0.752713	+	0.434579i	0.826673	−	0.562682i	$-0.190230\pi$
$373$	14.5373	+	8.39312i	0.752713	+	0.434579i	−0.0739603	+	0.997261i	$0.523564\pi$
$374$	−13.6929	+	23.7167i	−0.708041	+	1.22636i
$375$		0			0
$376$	−0.172587			−0.00890050
$377$	−3.05453	−	1.76353i	−0.157316	−	0.0908266i
$378$		−	54.2299i		−	2.78929i
$379$	1.95386	+	3.38419i	0.100363	+	0.173834i	0.911834	−	0.410558i	$-0.134666\pi$
$379$	1.95386	+	3.38419i	0.100363	+	0.173834i	−0.811471	+	0.584393i	$0.801333\pi$
$380$		0			0
$381$	−12.0607			−0.617889
$382$	−23.6941	+	13.6798i	−1.21230	+	0.699920i
$383$	−26.9239	−	15.5445i	−1.37575	−	0.794289i	−0.384104	−	0.923290i	$-0.625490\pi$
$383$	−26.9239	−	15.5445i	−1.37575	−	0.794289i	−0.991644	+	0.129001i	$0.958823\pi$
$384$	33.5456			1.71187
$385$		0			0
$386$	−15.6617	−	27.1268i	−0.797157	−	1.38072i
$387$	3.58126	−	2.06764i	0.182046	−	0.105104i
$388$	−0.0249124	−	0.0143832i	−0.00126474	−	0.000730195i
$389$	−4.12457	+	7.14396i	−0.209124	+	0.362213i	−0.951439	−	0.307838i	$-0.900395\pi$
$389$	−4.12457	+	7.14396i	−0.209124	+	0.362213i	0.742315	+	0.670051i	$0.233728\pi$
$390$		0			0
$391$	14.6499	+	25.3744i	0.740878	+	1.28324i
$392$	49.3271	−	28.4790i	2.49139	−	1.43841i
$393$		−	29.3518i		−	1.48060i
$394$	−2.63141	+	4.55773i	−0.132568	+	0.229615i
$395$		0			0
$396$	−0.318588			−0.0160097
$397$		−	32.9164i		−	1.65203i	−0.563651	−	0.826013i	$-0.690604\pi$
$397$		−	32.9164i		−	1.65203i	0.563651	−	0.826013i	$-0.309396\pi$
$398$	9.91559	−	5.72477i	0.497023	−	0.286957i
$399$	−33.3939			−1.67179
$400$		0			0
$401$	−2.71743			−0.135702			−0.0678511	−	0.997695i	$-0.521614\pi$
$401$	−2.71743			−0.135702			−0.0678511	+	0.997695i	$0.521614\pi$
$402$	39.0800	+	22.5629i	1.94913	+	1.12533i
$403$	−14.3620	−	8.29188i	−0.715420	−	0.413048i
$404$	−0.0751733	+	0.130204i	−0.00374001	+	0.00647789i
$405$		0			0
$406$	−12.6836			−0.629477
$407$	−15.4611	−	0.408170i	−0.766378	−	0.0202322i
$408$			62.1036i			3.07459i
$409$	−0.428228	−	0.741713i	−0.0211745	−	0.0366754i	0.855244	−	0.518226i	$-0.173407\pi$
$409$	−0.428228	−	0.741713i	−0.0211745	−	0.0366754i	−0.876419	+	0.481550i	$0.840074\pi$
$410$		0			0
$411$	22.3946	−	38.7886i	1.10465	−	1.91330i
$412$	−0.255571	−	0.147554i	−0.0125911	−	0.00726947i
$413$			25.5765i			1.25854i
$414$	−15.1448	+	26.2316i	−0.744329	+	1.28921i
$415$		0			0
$416$	0.132925	+	0.230234i	0.00651720	+	0.0112881i
$417$			31.0478i			1.52042i
$418$			7.93205i			0.387969i
$419$	2.80917	+	4.86563i	0.137237	+	0.237701i	0.926450	−	0.376418i	$-0.122844\pi$
$419$	2.80917	+	4.86563i	0.137237	+	0.237701i	−0.789213	+	0.614120i	$0.789511\pi$
$420$		0			0
$421$	−31.0528			−1.51342			−0.756709	−	0.653751i	$-0.773194\pi$
$421$	−31.0528			−1.51342			−0.756709	+	0.653751i	$0.773194\pi$
$422$	−7.33620	+	4.23556i	−0.357121	+	0.206184i
$423$	0.292568	−	0.168914i	0.0142251	−	0.00821288i
$424$	−2.73813	−	4.74258i	−0.132975	−	0.230320i
$425$		0			0
$426$	−4.56715	+	7.91054i	−0.221279	+	0.383267i
$427$	14.7828	−	8.53485i	0.715389	−	0.413030i
$428$	0.221422	−	0.127838i	0.0107029	−	0.00617930i
$429$	7.65505	+	13.2589i	0.369589	+	0.640147i
$430$		0			0
$431$	1.28877	−	2.23222i	0.0620780	−	0.107522i	−0.833316	−	0.552797i	$-0.813561\pi$
$431$	1.28877	−	2.23222i	0.0620780	−	0.107522i	0.895394	+	0.445275i	$0.146894\pi$
$432$	−25.5857	+	14.7719i	−1.23099	+	0.710713i
$433$		−	29.7148i		−	1.42800i	−0.700144	−	0.714002i	$-0.746881\pi$
$433$		−	29.7148i		−	1.42800i	0.700144	−	0.714002i	$-0.253119\pi$
$434$	−59.6365			−2.86265
$435$		0			0
$436$	0.206207			0.00987553
$437$	7.34949	+	4.24323i	0.351574	+	0.202981i
$438$			37.4279i			1.78837i
$439$	−7.41601	+	12.8449i	−0.353947	+	0.613054i	−0.986937	−	0.161106i	$-0.948494\pi$
$439$	−7.41601	+	12.8449i	−0.353947	+	0.613054i	0.632990	+	0.774160i	$0.281827\pi$
$440$		0			0
$441$	−55.7457	+	96.5545i	−2.65456	+	4.59783i
$442$	−19.2587	+	11.1190i	−0.916043	+	0.528878i
$443$			23.6206i			1.12225i	0.827732	+	0.561123i	$0.189631\pi$
$443$			23.6206i			1.12225i	−0.827732	+	0.561123i	$0.810369\pi$
$444$	0.354891	−	0.192592i	0.0168424	−	0.00914001i
$445$		0			0
$446$	4.73742	+	8.20545i	0.224323	+	0.388539i
$447$	58.9210	+	34.0181i	2.78687	+	1.60900i
$448$	−35.7484	−	20.6393i	−1.68895	−	0.975116i
$449$	−17.7045	+	30.6651i	−0.835528	+	1.44718i	0.0580726	+	0.998312i	$0.481505\pi$
$449$	−17.7045	+	30.6651i	−0.835528	+	1.44718i	−0.893600	+	0.448864i	$0.851829\pi$
$450$		0			0
$451$	11.4697	−	19.8661i	0.540087	−	0.935458i
$452$		−	0.0704088i		−	0.00331175i
$453$	−38.8787	+	22.4466i	−1.82668	+	1.05464i
$454$	31.3582			1.47171
$455$		0			0
$456$	8.99391	+	15.5779i	0.421178	+	0.729502i
$457$	−0.0629999	−	0.0363730i	−0.00294701	−	0.00170146i	0.498526	−	0.866875i	$-0.333875\pi$
$457$	−0.0629999	−	0.0363730i	−0.00294701	−	0.00170146i	−0.501473	+	0.865173i	$0.667208\pi$
$458$		−	1.89607i		−	0.0885976i
$459$	−27.6553	−	47.9003i	−1.29084	−	2.23580i
$460$		0			0
$461$	12.5653	+	21.7637i	0.585223	+	1.01364i	0.994848	+	0.101382i	$0.0323264\pi$
$461$	12.5653	+	21.7637i	0.585223	+	1.01364i	−0.409624	+	0.912254i	$0.634340\pi$
$462$	47.6802	+	27.5282i	2.21828	+	1.28073i
$463$	12.6741	+	7.31740i	0.589016	+	0.340068i	0.764708	−	0.644377i	$-0.222883\pi$
$463$	12.6741	+	7.31740i	0.589016	+	0.340068i	−0.175693	+	0.984445i	$0.556216\pi$
$464$	3.45494	+	5.98412i	0.160391	+	0.277806i
$465$		0			0
$466$	−12.2361	−	21.1935i	−0.566826	−	0.981771i
$467$		−	6.15983i		−	0.285043i	−0.989792	−	0.142521i	$-0.954479\pi$
$467$		−	6.15983i		−	0.285043i	0.989792	−	0.142521i	$-0.0455210\pi$
$468$	−0.224044	−	0.129352i	−0.0103564	−	0.00597929i
$469$	−28.3999	−	49.1901i	−1.31139	−	2.27139i
$470$		0			0
$471$	13.5102			0.622519
$472$	11.9312	−	6.88846i	0.549176	−	0.317067i
$473$			1.91019i			0.0878307i
$474$	−14.2070	+	24.6073i	−0.652550	+	1.13025i
$475$		0			0
$476$	−0.449958	+	0.779350i	−0.0206238	+	0.0357215i
$477$	9.28328	+	5.35971i	0.425052	+	0.245404i
$478$	−10.0637	−	5.81028i	−0.460303	−	0.265756i
$479$	5.39985	+	9.35282i	0.246726	+	0.427341i	0.962615	−	0.270872i	$-0.0873120\pi$
$479$	5.39985	+	9.35282i	0.246726	+	0.427341i	−0.715890	+	0.698213i	$0.753979\pi$
$480$		0			0
$481$	−10.7071	−	6.56448i	−0.488203	−	0.299315i
$482$			12.1031i			0.551283i
$483$	51.0128	−	29.4522i	2.32116	−	1.34012i
$484$	−0.0516120	+	0.0893946i	−0.00234600	+	0.00406339i
$485$		0			0
$486$	−5.65618	+	9.79679i	−0.256570	+	0.444391i
$487$			8.17898i			0.370625i	0.982680	+	0.185312i	$0.0593297\pi$
$487$			8.17898i			0.370625i	−0.982680	+	0.185312i	$0.940670\pi$
$488$	−7.96284	−	4.59735i	−0.360461	−	0.208112i
$489$	41.1413			1.86047
$490$		0			0
$491$	−6.05519			−0.273267			−0.136634	−	0.990622i	$-0.543628\pi$
$491$	−6.05519			−0.273267			−0.136634	+	0.990622i	$0.543628\pi$
$492$			0.598876i			0.0269994i
$493$	−11.2032	+	6.46818i	−0.504567	+	0.291312i
$494$	−3.22053	+	5.57813i	−0.144899	+	0.250972i
$495$		0			0
$496$	16.2446	+	28.1365i	0.729405	+	1.26337i
$497$	9.95700	−	5.74868i	0.446633	−	0.257864i
$498$	−30.7466	+	17.7516i	−1.37779	+	0.795467i
$499$	8.85042	−	15.3294i	0.396199	−	0.686238i	−0.597054	−	0.802201i	$-0.703662\pi$
$499$	8.85042	−	15.3294i	0.396199	−	0.686238i	0.993253	+	0.115963i	$0.0369956\pi$
$500$		0			0
$501$	−19.5930	−	33.9361i	−0.875351	−	1.51615i
$502$	2.26376	−	1.30698i	0.101037	−	0.0583335i
$503$	3.88804	−	2.24476i	0.173359	−	0.100089i	−0.410810	−	0.911721i	$-0.634754\pi$
$503$	3.88804	−	2.24476i	0.173359	−	0.100089i	0.584169	+	0.811632i	$0.301421\pi$
$504$	80.8108			3.59960
$505$		0			0
$506$	−6.99579	−	12.1171i	−0.311001	−	0.538669i
$507$		−	25.4790i		−	1.13156i
$508$			0.0941389i			0.00417674i
$509$	−17.9265	−	31.0496i	−0.794577	−	1.37625i	−0.923107	−	0.384542i	$-0.874359\pi$
$509$	−17.9265	−	31.0496i	−0.794577	−	1.37625i	0.128530	−	0.991706i	$-0.458974\pi$
$510$		0			0
$511$	23.5553	−	40.7989i	1.04202	−	1.80484i
$512$			22.2291i			0.982398i
$513$	−13.8739	−	8.01013i	−0.612550	−	0.353656i
$514$	−13.5735	+	23.5100i	−0.598701	+	1.03698i
$515$		0			0
$516$	−0.0249346	−	0.0431880i	−0.00109768	−	0.00190124i
$517$			0.156051i			0.00686313i
$518$	−45.1483	−	1.19191i	−1.98370	−	0.0523695i
$519$	32.7773			1.43876
$520$		0			0
$521$	−2.11178	+	3.65772i	−0.0925189	+	0.160247i	−0.908570	−	0.417732i	$-0.862825\pi$
$521$	−2.11178	+	3.65772i	−0.0925189	+	0.160247i	0.816051	+	0.577979i	$0.196159\pi$
$522$	−11.5817	−	6.68670i	−0.506917	−	0.292669i
$523$	4.90434	+	2.83152i	0.214452	+	0.123814i	0.603379	−	0.797455i	$-0.293821\pi$
$523$	4.90434	+	2.83152i	0.214452	+	0.123814i	−0.388927	+	0.921269i	$0.627154\pi$
$524$	−0.229103			−0.0100084
$525$		0			0
$526$	4.30667			0.187780
$527$	−52.6759	+	30.4125i	−2.29460	+	1.32479i
$528$		−	29.9940i		−	1.30532i
$529$	8.03048			0.349151
$530$		0			0
$531$	−13.4837	+	23.3544i	−0.585143	+	1.01350i
$532$			0.260653i			0.0113008i
$533$	16.1319	−	9.31375i	0.698750	−	0.403423i
$534$	−3.34315	−	5.79051i	−0.144672	−	0.250580i
$535$		0			0
$536$	−15.2978	+	26.4965i	−0.660763	+	1.14448i
$537$	−27.2605	−	15.7389i	−1.17638	−	0.679183i
$538$	−28.4087	+	16.4017i	−1.22478	+	0.707129i
$539$	−25.7504	−	44.6010i	−1.10915	−	1.92110i
$540$		0			0
$541$	−38.6546			−1.66189			−0.830945	−	0.556354i	$-0.812200\pi$
$541$	−38.6546			−1.66189			−0.830945	+	0.556354i	$0.812200\pi$
$542$	4.59648	+	2.65378i	0.197436	+	0.113990i
$543$	0.129713	−	0.0748900i	0.00556653	−	0.00321384i
$544$	0.975071			0.0418058
$545$		0			0
$546$	22.3537	+	38.7178i	0.956651	+	1.65697i
$547$		−	33.4404i		−	1.42981i	−0.699222	−	0.714905i	$-0.746470\pi$
$547$		−	33.4404i		−	1.42981i	0.699222	−	0.714905i	$-0.253530\pi$
$548$	−0.302762	−	0.174800i	−0.0129333	−	0.00746706i
$549$	17.9980			0.768136
$550$		0			0
$551$	−1.87346	+	3.24492i	−0.0798119	+	0.138238i
$552$	−27.4783	−	15.8646i	−1.16956	−	0.675243i
$553$	30.9732	−	17.8824i	1.31711	−	0.760437i
$554$	20.4385			0.868349
$555$		0			0
$556$	0.242341			0.0102776
$557$	4.26675	−	2.46341i	0.180788	−	0.104378i	−0.406875	−	0.913484i	$-0.633381\pi$
$557$	4.26675	−	2.46341i	0.180788	−	0.104378i	0.587663	+	0.809106i	$0.300048\pi$
$558$	−54.4555	−	31.4399i	−2.30529	−	1.33096i
$559$	−0.775567	+	1.34332i	−0.0328030	+	0.0568164i
$560$		0			0
$561$	56.1534			2.37080
$562$	−21.2451	−	12.2658i	−0.896169	−	0.517403i
$563$		−	16.4011i		−	0.691222i	−0.938378	−	0.345611i	$-0.887672\pi$
$563$		−	16.4011i		−	0.691222i	0.938378	−	0.345611i	$-0.112328\pi$
$564$	−0.00203701	−	0.00352820i	−8.57735e−5	−	0.000148564i
$565$		0			0
$566$	−11.4955			−0.483191
$567$	−21.6386	+	12.4931i	−0.908737	+	0.524660i
$568$	−5.36340	−	3.09656i	−0.225043	−	0.129929i
$569$	−30.4363			−1.27595			−0.637977	−	0.770055i	$-0.720229\pi$
$569$	−30.4363			−1.27595			−0.637977	+	0.770055i	$0.720229\pi$
$570$		0			0
$571$	7.01364	+	12.1480i	0.293512	+	0.508377i	0.974638	−	0.223789i	$-0.0718427\pi$
$571$	7.01364	+	12.1480i	0.293512	+	0.508377i	−0.681126	+	0.732166i	$0.738509\pi$
$572$	0.103492	−	0.0597509i	0.00432720	−	0.00249831i
$573$	48.5840	+	28.0500i	2.02962	+	1.17180i
$574$	33.4930	−	58.0116i	1.39797	−	2.42136i
$575$		0			0
$576$	−21.7618	−	37.6925i	−0.906740	−	1.57052i
$577$	−28.3701	+	16.3795i	−1.18106	+	0.681887i	−0.956260	−	0.292517i	$-0.905507\pi$
$577$	−28.3701	+	16.3795i	−1.18106	+	0.681887i	−0.224803	+	0.974404i	$0.572174\pi$
$578$			57.3852i			2.38691i
$579$	−32.1137	+	55.6225i	−1.33460	+	2.31159i
$580$		0			0
$581$	44.6878			1.85396
$582$			5.24156i			0.217270i
$583$	−4.28819	+	2.47578i	−0.177598	+	0.102537i
$584$	−25.3764			−1.05008
$585$		0			0
$586$	14.2901			0.590318
$587$	27.5329	+	15.8961i	1.13641	+	0.656104i	0.945538	−	0.325512i	$-0.105537\pi$
$587$	27.5329	+	15.8961i	1.13641	+	0.656104i	0.190867	+	0.981616i	$0.438870\pi$
$588$	1.16439	+	0.672262i	0.0480187	+	0.0277236i
$589$	−8.80872	+	15.2572i	−0.362957	+	0.628660i
$590$		0			0
$591$	10.7912			0.443891
$592$	11.7358	+	21.6256i	0.482338	+	0.888808i
$593$		−	13.5235i		−	0.555345i	−0.960676	−	0.277672i	$-0.910437\pi$
$593$		−	13.5235i		−	0.555345i	0.960676	−	0.277672i	$-0.0895630\pi$
$594$	13.2063	+	22.8739i	0.541859	+	0.938528i
$595$		0			0
$596$	0.265525	−	0.459903i	0.0108763	−	0.0188384i
$597$	−20.3316	−	11.7384i	−0.832115	−	0.480422i
$598$		−	11.3616i		−	0.464610i
$599$	3.09266	−	5.35664i	0.126362	−	0.218866i	−0.795902	−	0.605425i	$-0.793003\pi$
$599$	3.09266	−	5.35664i	0.126362	−	0.218866i	0.922265	+	0.386559i	$0.126336\pi$
$600$		0			0
$601$	−9.55743	−	16.5540i	−0.389856	−	0.675250i	0.602574	−	0.798063i	$-0.294142\pi$
$601$	−9.55743	−	16.5540i	−0.389856	−	0.675250i	−0.992430	+	0.122813i	$0.960808\pi$
$602$			5.57800i			0.227342i
$603$		−	59.8888i		−	2.43886i
$604$	0.175206	+	0.303465i	0.00712901	+	0.0123478i
$605$		0			0
$606$	27.3949			1.11284
$607$	−29.0872	+	16.7935i	−1.18061	+	0.681627i	−0.956156	−	0.292857i	$-0.905394\pi$
$607$	−29.0872	+	16.7935i	−1.18061	+	0.681627i	−0.224457	+	0.974484i	$0.572061\pi$
$608$	0.244584	−	0.141211i	0.00991920	−	0.00572685i
$609$	13.0036	+	22.5230i	0.526934	+	0.912677i
$610$		0			0
$611$	−0.0633592	+	0.109741i	−0.00256324	+	0.00443966i
$612$	−0.821734	+	0.474428i	−0.0332166	+	0.0191776i
$613$	−18.0710	+	10.4333i	−0.729879	+	0.421396i	−0.818378	−	0.574680i	$-0.805126\pi$
$613$	−18.0710	+	10.4333i	−0.729879	+	0.421396i	0.0884989	+	0.996076i	$0.471793\pi$
$614$	−13.1067	−	22.7014i	−0.528942	−	0.916155i
$615$		0			0
$616$	−18.6643	+	32.3275i	−0.752006	+	1.30251i
$617$	−13.9659	+	8.06321i	−0.562245	+	0.324612i	−0.754046	−	0.656821i	$-0.771901\pi$
$617$	−13.9659	+	8.06321i	−0.562245	+	0.324612i	0.191801	+	0.981434i	$0.438567\pi$
$618$			53.7721i			2.16303i
$619$	22.4003			0.900344			0.450172	−	0.892942i	$-0.351363\pi$
$619$	22.4003			0.900344			0.450172	+	0.892942i	$0.351363\pi$
$620$		0			0
$621$	28.2586			1.13398
$622$	11.4466	+	6.60868i	0.458965	+	0.264984i
$623$			8.41606i			0.337183i
$624$	12.1780	−	21.0930i	0.487511	−	0.844394i
$625$		0			0
$626$	15.1127	−	26.1760i	0.604026	−	1.04620i
$627$	14.0854	−	8.13219i	0.562515	−	0.324768i
$628$		−	0.105453i		−	0.00420804i
$629$	−40.4866	+	21.9712i	−1.61431	+	0.876049i
$630$		0			0
$631$	20.5465	+	35.5876i	0.817945	+	1.41672i	0.907194	+	0.420712i	$0.138220\pi$
$631$	20.5465	+	35.5876i	0.817945	+	1.41672i	−0.0892495	+	0.996009i	$0.528447\pi$
$632$	−16.6839	−	9.63246i	−0.663650	−	0.383159i
$633$	15.0426	+	8.68486i	0.597890	+	0.345192i
$634$	−4.17906	+	7.23834i	−0.165972	+	0.287471i
$635$		0			0
$636$	0.0646351	−	0.111951i	0.00256295	−	0.00443915i
$637$		−	41.8202i		−	1.65698i
$638$	5.34988	−	3.08876i	0.211804	−	0.122285i
$639$	12.1226			0.479564
$640$		0			0
$641$	0.0233381	+	0.0404228i	0.000921800	+	0.00159660i	0.866486	−	0.499201i	$-0.166373\pi$
$641$	0.0233381	+	0.0404228i	0.000921800	+	0.00159660i	−0.865564	+	0.500798i	$0.833040\pi$
$642$	−40.3457	−	23.2936i	−1.59232	−	0.919326i
$643$		−	24.4497i		−	0.964203i	−0.876115	−	0.482101i	$-0.839874\pi$
$643$		−	24.4497i		−	0.964203i	0.876115	−	0.482101i	$-0.160126\pi$
$644$	−0.229887	−	0.398176i	−0.00905882	−	0.0156903i
$645$		0			0
$646$	11.8121	+	20.4591i	0.464740	+	0.804953i
$647$	−7.96200	−	4.59686i	−0.313018	−	0.180721i	0.335258	−	0.942126i	$-0.391177\pi$
$647$	−7.96200	−	4.59686i	−0.313018	−	0.180721i	−0.648276	+	0.761405i	$0.724510\pi$
$648$	11.6558	+	6.72947i	0.457882	+	0.264358i
$649$	−6.22846	−	10.7880i	−0.244489	−	0.423467i
$650$		0			0
$651$	61.1413	+	105.900i	2.39632	+	4.15054i
$652$		−	0.321125i		−	0.0125762i
$653$	29.5298	+	17.0490i	1.15559	+	0.667180i	0.950243	−	0.311509i	$-0.100834\pi$
$653$	29.5298	+	17.0490i	1.15559	+	0.667180i	0.205347	+	0.978689i	$0.434168\pi$
$654$	−18.7867	−	32.5395i	−0.734617	−	1.27239i
$655$		0			0
$656$	−36.4931			−1.42482
$657$	43.0177	−	24.8363i	1.67828	−	0.968957i
$658$			0.455690i			0.0177646i
$659$	3.32960	−	5.76703i	0.129703	−	0.224652i	−0.793859	−	0.608102i	$-0.791931\pi$
$659$	3.32960	−	5.76703i	0.129703	−	0.224652i	0.923561	+	0.383451i	$0.125264\pi$
$660$		0			0
$661$	−20.0326	+	34.6975i	−0.779179	+	1.34958i	0.153237	+	0.988190i	$0.451030\pi$
$661$	−20.0326	+	34.6975i	−0.779179	+	1.34958i	−0.932416	+	0.361388i	$0.882303\pi$
$662$	22.6999	+	13.1058i	0.882255	+	0.509370i
$663$	39.4893	+	22.7991i	1.53364	+	0.885446i
$664$	−12.0357	−	20.8464i	−0.467075	−	0.808998i
$665$		0			0
$666$	−40.5976	−	24.8902i	−1.57313	−	0.964475i
$667$		−	6.60929i		−	0.255913i
$668$	−0.264886	+	0.152932i	−0.0102487	+	0.00591711i
$669$	9.71391	−	16.8250i	0.375561	−	0.650491i
$670$		0			0
$671$	−4.15687	+	7.19991i	−0.160474	+	0.277949i
$672$		−	1.96029i		−	0.0756197i
$673$	4.21118	+	2.43133i	0.162329	+	0.0937208i	0.578964	−	0.815353i	$-0.303457\pi$
$673$	4.21118	+	2.43133i	0.162329	+	0.0937208i	−0.416635	+	0.909074i	$0.636791\pi$
$674$	−33.7567			−1.30026
$675$		0			0
$676$	−0.198874			−0.00764901
$677$		−	38.7791i		−	1.49040i	−0.666840	−	0.745201i	$-0.732354\pi$
$677$		−	38.7791i		−	1.49040i	0.666840	−	0.745201i	$-0.267646\pi$
$678$	−11.1105	+	6.41465i	−0.426696	+	0.246353i
$679$	3.29878	−	5.71366i	0.126596	−	0.219270i
$680$		0			0
$681$	−32.1494	−	55.6845i	−1.23197	−	2.13383i
$682$	25.1544	−	14.5229i	0.963211	−	0.556110i
$683$	34.4076	−	19.8652i	1.31657	−	0.760121i	0.333394	−	0.942788i	$-0.391806\pi$
$683$	34.4076	−	19.8652i	1.31657	−	0.760121i	0.983175	+	0.182666i	$0.0584729\pi$
$684$	−0.137414	+	0.238009i	−0.00525417	+	0.00910049i
$685$		0			0
$686$	−49.2071	−	85.2293i	−1.87874	−	3.25407i
$687$	−3.36696	+	1.94391i	−0.128457	+	0.0741649i
$688$	2.63170	−	1.51941i	0.100333	−	0.0579271i
$689$	−4.02083			−0.153181
$690$		0			0
$691$	−17.8563	−	30.9280i	−0.679284	−	1.17655i	−0.975197	−	0.221340i	$-0.928957\pi$
$691$	−17.8563	−	30.9280i	−0.679284	−	1.17655i	0.295912	−	0.955215i	$-0.404376\pi$
$692$		−	0.255840i		−	0.00972559i
$693$		−	73.0682i		−	2.77563i
$694$	14.5073	+	25.1274i	0.550689	+	0.953822i
$695$		0			0
$696$	7.00449	−	12.1321i	0.265505	−	0.459867i
$697$		−	68.3208i		−	2.58783i
$698$	34.0032	+	19.6318i	1.28704	+	0.743073i
$699$	−25.0897	+	43.4566i	−0.948978	+	1.64368i
$700$		0			0
$701$	11.8641	+	20.5492i	0.448101	+	0.776134i	0.998262	−	0.0589243i	$-0.0187671\pi$
$701$	11.8641	+	20.5492i	0.448101	+	0.776134i	−0.550161	+	0.835058i	$0.685434\pi$
$702$			21.4478i			0.809494i
$703$	−6.97365	+	11.3745i	−0.263016	+	0.428997i
$704$	20.1046			0.757722
$705$		0			0
$706$	20.2531	−	35.0794i	0.762236	−	1.32023i
$707$	−29.8623	−	17.2410i	−1.12309	−	0.648414i
$708$	0.281642	+	0.162606i	0.0105847	+	0.00611110i
$709$	5.55537			0.208636			0.104318	−	0.994544i	$-0.466734\pi$
$709$	5.55537			0.208636			0.104318	+	0.994544i	$0.466734\pi$
$710$		0			0
$711$	37.7098			1.41423
$712$	3.92601	−	2.26668i	0.147133	−	0.0849475i
$713$		−	31.0759i		−	1.16380i
$714$	163.975			6.13661
$715$		0			0
$716$	−0.122849	+	0.212780i	−0.00459107	+	0.00795196i
$717$			23.8275i			0.889856i
$718$	−10.6711	+	6.16093i	−0.398240	+	0.229924i
$719$	8.26595	+	14.3170i	0.308268	+	0.533936i	0.977984	−	0.208682i	$-0.0669173\pi$
$719$	8.26595	+	14.3170i	0.308268	+	0.533936i	−0.669716	+	0.742618i	$0.733584\pi$
$720$		0			0
$721$	33.8415	−	58.6152i	1.26032	−	2.18295i
$722$	−17.4764	−	10.0900i	−0.650404	−	0.375511i
$723$	21.4922	−	12.4085i	0.799303	−	0.461478i
$724$	−0.000584548	−	0.00101247i	−2.17246e−5	−	3.76281e-5i
$725$		0			0
$726$	18.8086			0.698053
$727$	15.0764	+	8.70439i	0.559154	+	0.322828i	0.752806	−	0.658243i	$-0.228700\pi$
$727$	15.0764	+	8.70439i	0.559154	+	0.322828i	−0.193652	+	0.981070i	$0.562033\pi$
$728$	−26.2509	+	15.1560i	−0.972924	+	0.561718i
$729$	37.5538			1.39088
$730$		0			0
$731$	2.84458	+	4.92695i	0.105210	+	0.182230i
$732$		−	0.217046i		−	0.00802225i
$733$	19.4852	+	11.2498i	0.719701	+	0.415519i	0.814643	−	0.579963i	$-0.196933\pi$
$733$	19.4852	+	11.2498i	0.719701	+	0.415519i	−0.0949417	+	0.995483i	$0.530266\pi$
$734$	8.88337			0.327891
$735$		0			0
$736$	−0.249086	+	0.431429i	−0.00918142	+	0.0159027i
$737$	23.9579	+	13.8321i	0.882499	+	0.509511i
$738$	61.1664	−	35.3145i	2.25157	−	1.29994i
$739$	−49.9011			−1.83564			−0.917822	−	0.396993i	$-0.870054\pi$
$739$	−49.9011			−1.83564			−0.917822	+	0.396993i	$0.870054\pi$
$740$		0			0
$741$	13.2072			0.485178
$742$	−12.5220	+	7.22961i	−0.459699	+	0.265407i
$743$	−28.5047	−	16.4572i	−1.04573	−	0.603755i	−0.124283	−	0.992247i	$-0.539663\pi$
$743$	−28.5047	−	16.4572i	−1.04573	−	0.603755i	−0.921452	+	0.388492i	$0.872996\pi$
$744$	32.9341	−	57.0436i	1.20742	−	2.09132i
$745$		0			0
$746$	−23.8740			−0.874090
$747$	40.8055	+	23.5591i	1.49299	+	0.861981i
$748$		−	0.438301i		−	0.0160259i
$749$	29.3197	+	50.7832i	1.07132	+	1.85558i
$750$		0			0
$751$	−37.5840			−1.37146			−0.685729	−	0.727857i	$-0.740517\pi$
$751$	−37.5840			−1.37146			−0.685729	+	0.727857i	$0.740517\pi$
$752$	0.214994	−	0.124127i	0.00784004	−	0.00452645i
$753$	−4.64176	−	2.67992i	−0.169155	−	0.0976617i
$754$	5.01633			0.182684
$755$		0			0
$756$	0.433968	+	0.751654i	0.0157833	+	0.0273374i
$757$	−25.0888	+	14.4850i	−0.911867	+	0.526467i	−0.881031	−	0.473058i	$-0.843150\pi$
$757$	−25.0888	+	14.4850i	−0.911867	+	0.526467i	−0.0308358	+	0.999524i	$0.509817\pi$
$758$	−4.81313	−	2.77886i	−0.174821	−	0.100933i
$759$	−14.3446	+	24.8456i	−0.520677	+	0.901838i
$760$		0			0
$761$	−20.3309	−	35.2142i	−0.736996	−	1.27651i	−0.953842	−	0.300309i	$-0.902910\pi$
$761$	−20.3309	−	35.2142i	−0.736996	−	1.27651i	0.216846	−	0.976206i	$-0.430423\pi$
$762$	14.8551	−	8.57660i	0.538144	−	0.310697i
$763$			47.2936i			1.71214i
$764$	0.218942	−	0.379218i	0.00792104	−	0.0137196i
$765$		0			0
$766$	44.2161			1.59759
$767$		−	10.1154i		−	0.365246i
$768$	−1.37953	+	0.796473i	−0.0497795	+	0.0287402i
$769$	−9.87409			−0.356069			−0.178034	−	0.984024i	$-0.556974\pi$
$769$	−9.87409			−0.356069			−0.178034	+	0.984024i	$0.556974\pi$
$770$		0			0
$771$	55.6639			2.00469
$772$	0.434157	+	0.250661i	0.0156257	+	0.00902148i
$773$	−22.8259	−	13.1785i	−0.820989	−	0.473998i	0.0297685	−	0.999557i	$-0.490523\pi$
$773$	−22.8259	−	13.1785i	−0.820989	−	0.473998i	−0.850757	+	0.525559i	$0.823856\pi$
$774$	−2.94068	+	5.09340i	−0.105700	+	0.183079i
$775$		0			0
$776$	−3.55382			−0.127575
$777$	44.1710	+	81.3943i	1.58463	+	2.92000i
$778$		−	11.7322i		−	0.420621i
$779$	−9.89428	−	17.1374i	−0.354499	−	0.614011i
$780$		0			0
$781$	−2.79988	+	4.84953i	−0.100187	+	0.173530i
$782$	−36.0884	−	20.8357i	−1.29052	−	0.745082i
$783$			12.4766i			0.445879i
$784$	−40.9650	+	70.9534i	−1.46303	+	2.53405i
$785$		0			0
$786$	20.8726	+	36.1524i	0.744501	+	1.28951i
$787$		−	36.6680i		−	1.30707i	−0.756895	−	0.653537i	$-0.773285\pi$
$787$		−	36.6680i		−	1.30707i	0.756895	−	0.653537i	$-0.226715\pi$
$788$		−	0.0842299i		−	0.00300057i
$789$	−4.41533	−	7.64758i	−0.157190	−	0.272261i
$790$		0			0
$791$	16.1482			0.574166
$792$	−34.0856	+	19.6793i	−1.21118	+	0.699274i
$793$	−5.84655	+	3.37551i	−0.207617	+	0.119868i
$794$	23.4075	+	40.5429i	0.830700	+	1.43881i
$795$		0			0
$796$	−0.0916234	+	0.158696i	−0.00324751	+	0.00562484i
$797$	−9.82734	+	5.67382i	−0.348102	+	0.200977i	−0.663849	−	0.747867i	$-0.731078\pi$
$797$	−9.82734	+	5.67382i	−0.348102	+	0.200977i	0.315747	+	0.948843i	$0.397745\pi$
$798$	41.1311	−	23.7470i	1.45602	−	0.840636i
$799$	0.232385	+	0.402503i	0.00822119	+	0.0142395i
$800$		0			0
$801$	−4.43688	+	7.68490i	−0.156769	+	0.271533i
$802$	3.34705	−	1.93242i	0.118188	−	0.0682361i
$803$			22.9450i			0.809713i
$804$	−0.722225			−0.0254709
$805$		0			0
$806$	23.5861			0.830784
$807$	58.2509	+	33.6312i	2.05053	+	1.18387i
$808$			18.5739i			0.653429i
$809$	−0.170408	+	0.295156i	−0.00599123	+	0.0103771i	−0.869005	−	0.494802i	$-0.835240\pi$
$809$	−0.170408	+	0.295156i	−0.00599123	+	0.0103771i	0.863014	+	0.505180i	$0.168574\pi$
$810$		0			0
$811$	16.1418	−	27.9584i	0.566815	−	0.981752i	−0.430064	−	0.902798i	$-0.641509\pi$
$811$	16.1418	−	27.9584i	0.566815	−	0.981752i	0.996878	−	0.0789530i	$-0.0251577\pi$
$812$	0.175801	−	0.101499i	0.00616942	−	0.00356191i
$813$		−	10.8830i		−	0.381682i
$814$	19.3336	−	10.4919i	0.677642	−	0.367742i
$815$		0			0
$816$	−44.6658	−	77.3634i	−1.56362	−	2.70826i
$817$	1.42705	+	0.823909i	0.0499262	+	0.0288249i
$818$	1.05489	+	0.609043i	0.0368835	+	0.0212947i
$819$	29.6668	−	51.3844i	1.03664	−	1.79552i
$820$		0			0
$821$	−14.4962	+	25.1081i	−0.505920	+	0.876279i	0.494056	+	0.869430i	$0.335514\pi$
$821$	−14.4962	+	25.1081i	−0.505920	+	0.876279i	−0.999977	+	0.00684945i	$0.997820\pi$
$822$			63.7010i			2.22183i
$823$	31.3226	−	18.0841i	1.09184	−	0.630372i	0.157771	−	0.987476i	$-0.449569\pi$
$823$	31.3226	−	18.0841i	1.09184	−	0.630372i	0.934065	+	0.357104i	$0.116236\pi$
$824$	−36.4579			−1.27007
$825$		0			0
$826$	−18.1879	−	31.5024i	−0.632838	−	1.09611i
$827$	14.1808	+	8.18727i	0.493114	+	0.284699i	0.725865	−	0.687837i	$-0.241440\pi$
$827$	14.1808	+	8.18727i	0.493114	+	0.284699i	−0.232752	+	0.972536i	$0.574773\pi$
$828$		−	0.484779i		−	0.0168472i
$829$	−0.924433	−	1.60116i	−0.0321069	−	0.0556107i	0.849525	−	0.527548i	$-0.176888\pi$
$829$	−0.924433	−	1.60116i	−0.0321069	−	0.0556107i	−0.881632	+	0.471937i	$0.843555\pi$
$830$		0			0
$831$	−20.9542	−	36.2938i	−0.726894	−	1.25902i
$832$	14.1384	+	8.16279i	0.490160	+	0.282994i
$833$	−132.836	−	76.6928i	−4.60249	−	2.65725i
$834$	−22.0787	−	38.2414i	−0.764522	−	1.32419i
$835$		0			0
$836$	−0.0634752	−	0.109942i	−0.00219534	−	0.00380243i
$837$			58.6634i			2.02770i
$838$	−6.92008	−	3.99531i	−0.239050	−	0.138016i
$839$	27.4399	+	47.5273i	0.947330	+	1.64082i	0.751018	+	0.660282i	$0.229563\pi$
$839$	27.4399	+	47.5273i	0.947330	+	1.64082i	0.196312	+	0.980542i	$0.437104\pi$
$840$		0			0
$841$	−26.0819			−0.899376
$842$	38.2475	−	22.0822i	1.31810	−	0.761003i
$843$			50.3013i			1.73247i
$844$	0.0677890	−	0.117414i	0.00233339	−	0.00404156i
$845$		0			0
$846$	−0.240236	+	0.416101i	−0.00825948	+	0.0143058i
$847$	−20.5027	−	11.8372i	−0.704480	−	0.406732i
$848$	6.82185	+	3.93860i	0.234263	+	0.135252i
$849$	11.7855	+	20.4131i	0.404478	+	0.700577i
$850$		0			0
$851$	0.621091	−	23.5263i	0.0212907	−	0.806471i
$852$		−	0.146192i		−	0.00500846i
$853$	24.2573	−	14.0050i	0.830555	−	0.479521i	−0.0234877	−	0.999724i	$-0.507477\pi$
$853$	24.2573	−	14.0050i	0.830555	−	0.479521i	0.854043	+	0.520203i	$0.174144\pi$
$854$	−12.1386	+	21.0247i	−0.415374	+	0.719449i
$855$		0			0
$856$	15.7932	−	27.3547i	0.539802	−	0.934964i
$857$			31.6094i			1.07976i	0.841744	+	0.539878i	$0.181529\pi$
$857$			31.6094i			1.07976i	−0.841744	+	0.539878i	$0.818471\pi$
$858$	−18.8574	−	10.8873i	−0.643780	−	0.371686i
$859$	−12.7732			−0.435817			−0.217909	−	0.975969i	$-0.569923\pi$
$859$	−12.7732			−0.435817			−0.217909	+	0.975969i	$0.569923\pi$
$860$		0			0
$861$	−137.352			−4.68095
$862$			3.66588i			0.124861i
$863$	−15.1014	+	8.71880i	−0.514058	+	0.296791i	−0.734500	−	0.678609i	$-0.762583\pi$
$863$	−15.1014	+	8.71880i	−0.514058	+	0.296791i	0.220442	+	0.975400i	$0.429250\pi$
$864$	0.470210	−	0.814427i	0.0159969	−	0.0277074i
$865$		0			0
$866$	21.1308	+	36.5996i	0.718053	+	1.24370i
$867$	101.902	−	58.8332i	3.46078	−	1.99808i
$868$	0.826593	−	0.477234i	0.0280564	−	0.0161984i
$869$	−8.70956	+	15.0854i	−0.295452	+	0.511737i
$870$		0			0
$871$	11.2321	+	19.4545i	0.380584	+	0.659191i
$872$	22.0620	−	12.7375i	0.747113	−	0.431346i
$873$	6.02439	−	3.47818i	0.203895	−	0.117719i
$874$	−12.0698			−0.408266
$875$		0			0
$876$	−0.299512	−	0.518770i	−0.0101196	−	0.0175276i
$877$			40.6356i			1.37217i	0.727522	+	0.686084i	$0.240672\pi$
$877$			40.6356i			1.37217i	−0.727522	+	0.686084i	$0.759328\pi$
$878$		−	21.0947i		−	0.711911i
$879$	−14.6506	−	25.3757i	−0.494154	−	0.855900i
$880$		0			0
$881$	−5.75546	+	9.96876i	−0.193907	+	0.335856i	−0.946542	−	0.322582i	$-0.895449\pi$
$881$	−5.75546	+	9.96876i	−0.193907	+	0.335856i	0.752635	+	0.658438i	$0.228783\pi$
$882$		−	158.567i		−	5.33924i
$883$	43.7332	+	25.2494i	1.47174	+	0.849709i	0.999496	−	0.0317599i	$-0.0101112\pi$
$883$	43.7332	+	25.2494i	1.47174	+	0.849709i	0.472243	+	0.881468i	$0.343445\pi$
$884$	0.177957	−	0.308231i	0.00598534	−	0.0103669i
$885$		0			0
$886$	−16.7970	−	29.0933i	−0.564308	−	0.977409i
$887$			9.59970i			0.322326i	0.986928	+	0.161163i	$0.0515245\pi$
$887$			9.59970i			0.322326i	−0.986928	+	0.161163i	$0.948475\pi$
$888$	26.0731	−	42.5271i	0.874957	−	1.42712i
$889$	−21.5908			−0.724131
$890$		0			0
$891$	6.08471	−	10.5390i	0.203845	−	0.353071i
$892$	−0.131326	−	0.0758212i	−0.00439712	−	0.00253868i
$893$	0.116582	+	0.0673085i	0.00390126	+	0.00225239i
$894$	−96.7636			−3.23626
$895$		0			0
$896$	60.0525			2.00621
$897$	−20.1754	+	11.6483i	−0.673637	+	0.388924i
$898$		−	50.3601i		−	1.68054i
$899$	13.7205			0.457605
$900$		0			0
$901$	−7.37367	+	12.7716i	−0.245653	+	0.425483i
$902$			32.6253i			1.08630i
$903$	9.90516	−	5.71875i	0.329623	−	0.190308i
$904$	−4.34918	−	7.53299i	−0.144651	−	0.250544i
$905$		0			0
$906$	31.9245	−	55.2948i	1.06062	−	1.83705i
$907$	14.0403	+	8.10615i	0.466199	+	0.269160i	0.714647	−	0.699485i	$-0.246587\pi$
$907$	14.0403	+	8.10615i	0.466199	+	0.269160i	−0.248448	+	0.968645i	$0.579920\pi$
$908$	−0.434641	+	0.250940i	−0.0144241	+	0.00832774i
$909$	−18.1786	−	31.4863i	−0.602947	−	1.04433i
$910$		0			0
$911$	−35.3959			−1.17272			−0.586360	−	0.810051i	$-0.699439\pi$
$911$	−35.3959			−1.17272			−0.586360	+	0.810051i	$0.699439\pi$
$912$	−22.4077	−	12.9371i	−0.741993	−	0.428390i
$913$	−18.8491	+	10.8825i	−0.623814	+	0.360159i
$914$	0.103462			0.00342223
$915$		0			0
$916$	0.0151731	+	0.0262805i	0.000501332	+	0.000868333i
$917$		−	52.5447i		−	1.73518i
$918$	68.1257	+	39.3324i	2.24848	+	1.29816i
$919$	−8.57769			−0.282952			−0.141476	−	0.989942i	$-0.545185\pi$
$919$	−8.57769			−0.282952			−0.141476	+	0.989942i	$0.545185\pi$
$920$		0			0
$921$	−26.8748	+	46.5484i	−0.885553	+	1.53382i
$922$	−30.9532	−	17.8708i	−1.01939	−	0.588544i
$923$	−3.93796	+	2.27359i	−0.129620	+	0.0748360i
$924$	−0.881162			−0.0289881
$925$		0			0
$926$	−20.8142			−0.683996
$927$	61.8030	−	35.6820i	2.02988	−	1.17195i
$928$	−0.190483	−	0.109975i	−0.00625291	−	0.00361012i
$929$	8.94046	−	15.4853i	0.293327	−	0.508057i	−0.681267	−	0.732035i	$-0.738571\pi$
$929$	8.94046	−	15.4853i	0.293327	−	0.508057i	0.974594	+	0.223977i	$0.0719042\pi$
$930$		0			0
$931$	−44.4269			−1.45603
$932$	0.339197	+	0.195835i	0.0111108	+	0.00641480i
$933$		−	27.1017i		−	0.887270i
$934$	4.38037	+	7.58703i	0.143330	+	0.248255i
$935$		0			0
$936$	−31.9604			−1.04466
$937$	−45.2922	+	26.1494i	−1.47963	+	0.854265i	−0.999734	−	0.0230606i	$-0.992659\pi$
$937$	−45.2922	+	26.1494i	−1.47963	+	0.854265i	−0.479896	+	0.877325i	$0.659326\pi$
$938$	69.9600	+	40.3914i	2.28428	+	1.31883i
$939$	−61.9762			−2.02252
$940$		0			0
$941$	17.0997	+	29.6175i	0.557433	+	0.965503i	0.997710	+	0.0676403i	$0.0215470\pi$
$941$	17.0997	+	29.6175i	0.557433	+	0.965503i	−0.440277	+	0.897862i	$0.645120\pi$
$942$	−16.6405	+	9.60739i	−0.542176	+	0.313026i
$943$	30.2292	+	17.4528i	0.984397	+	0.568342i
$944$	−9.90854	+	17.1621i	−0.322496	+	0.558579i
$945$		0			0
$946$	−1.35837	−	2.35277i	−0.0441645	−	0.0764952i
$947$	7.55604	−	4.36248i	0.245538	−	0.141762i	−0.372181	−	0.928160i	$-0.621390\pi$
$947$	7.55604	−	4.36248i	0.245538	−	0.141762i	0.617720	+	0.786398i	$0.288057\pi$
$948$		−	0.454759i		−	0.0147699i
$949$	−9.31604	+	16.1359i	−0.302412	+	0.523792i
$950$		0			0
$951$	17.1380			0.555738
$952$			111.176i			3.60324i
$953$	−25.5611	+	14.7577i	−0.828006	+	0.478050i	−0.853169	−	0.521634i	$-0.825323\pi$
$953$	−25.5611	+	14.7577i	−0.828006	+	0.478050i	0.0251634	+	0.999683i	$0.491989\pi$
$954$	−15.2456			−0.493593
$955$		0			0
$956$	0.185984			0.00601515
$957$	−10.9697	−	6.33338i	−0.354601	−	0.204729i
$958$	−13.3019	−	7.67988i	−0.429766	−	0.248126i
$959$	40.0903	−	69.4384i	1.29458	−	2.24228i
$960$		0			0
$961$	33.5120			1.08103
$962$	17.8560	+	0.471396i	0.575702	+	0.0151984i
$963$			61.8284i			1.99239i
$964$	−0.0968537	−	0.167756i	−0.00311945	−	0.00540304i
$965$		0			0
$966$	−41.8881	+	72.5523i	−1.34773	+	2.33433i
$967$	−13.4916	−	7.78938i	−0.433861	−	0.250490i	0.267129	−	0.963661i	$-0.413925\pi$
$967$	−13.4916	−	7.78938i	−0.433861	−	0.250490i	−0.700990	+	0.713171i	$0.747258\pi$
$968$			12.7524i			0.409877i
$969$	24.2202	−	41.9507i	0.778066	−	1.34765i
$970$		0			0
$971$	22.5294	+	39.0221i	0.723003	+	1.25228i	0.959791	+	0.280716i	$0.0905719\pi$
$971$	22.5294	+	39.0221i	0.723003	+	1.25228i	−0.236788	+	0.971561i	$0.576095\pi$
$972$		−	0.181051i		−	0.00580722i
$973$			55.5809i			1.78184i
$974$	−5.81623	−	10.0740i	−0.186364	−	0.322792i
$975$		0			0
$976$	13.2259			0.423351
$977$	43.1239	−	24.8976i	1.37966	−	0.796544i	0.387538	−	0.921854i	$-0.373326\pi$
$977$	43.1239	−	24.8976i	1.37966	−	0.796544i	0.992118	+	0.125309i	$0.0399923\pi$
$978$	−50.6735	+	29.2564i	−1.62036	+	0.935516i
$979$	−2.04951	−	3.54985i	−0.0655026	−	0.113454i
$980$		0			0
$981$	−24.9328	+	43.1849i	−0.796043	+	1.37879i
$982$	7.45815	−	4.30597i	0.237999	−	0.137409i
$983$	−5.52642	+	3.19068i	−0.176265	+	0.101767i	−0.585537	−	0.810646i	$-0.699116\pi$
$983$	−5.52642	+	3.19068i	−0.176265	+	0.101767i	0.409271	+	0.912413i	$0.365783\pi$
$984$	36.9928	+	64.0735i	1.17929	+	2.04259i
$985$		0			0
$986$	9.19929	−	15.9336i	0.292965	−	0.507430i
$987$	0.809193	−	0.467188i	0.0257569	−	0.0148707i
$988$		−	0.103088i		−	0.00327965i
$989$	−2.90663			−0.0924256
$990$		0			0
$991$	−18.6469			−0.592337			−0.296169	−	0.955136i	$-0.595709\pi$
$991$	−18.6469			−0.592337			−0.296169	+	0.955136i	$0.595709\pi$
$992$	−0.895624	−	0.517089i	−0.0284361	−	0.0164176i
$993$		−	53.7458i		−	1.70557i
$994$	−8.17599	+	14.1612i	−0.259327	+	0.449167i
$995$		0			0
$996$	0.284109	−	0.492091i	0.00900234	−	0.0155925i
$997$	−21.9173	+	12.6539i	−0.694127	+	0.400754i	−0.805156	−	0.593063i	$-0.797919\pi$
$997$	−21.9173	+	12.6539i	−0.694127	+	0.400754i	0.111029	+	0.993817i	$0.464585\pi$
$998$			25.1748i			0.796895i
$999$	−1.17246	+	44.4116i	−0.0370950	+	1.40512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.o.d.174.6		48
5.2	odd	4		925.2.e.d.26.4	✓	24
5.3	odd	4		925.2.e.e.26.9	yes	24
5.4	even	2	inner	925.2.o.d.174.19		48
37.10	even	3	inner	925.2.o.d.824.19		48
185.47	odd	12		925.2.e.d.676.4	yes	24
185.84	even	6	inner	925.2.o.d.824.6		48
185.158	odd	12		925.2.e.e.676.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.e.d.26.4	✓	24	5.2	odd	4
925.2.e.d.676.4	yes	24	185.47	odd	12
925.2.e.e.26.9	yes	24	5.3	odd	4
925.2.e.e.676.9	yes	24	185.158	odd	12
925.2.o.d.174.6		48	1.1	even	1	trivial
925.2.o.d.174.19		48	5.4	even	2	inner
925.2.o.d.824.6		48	185.84	even	6	inner
925.2.o.d.824.19		48	37.10	even	3	inner

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.23169 + 0.711119i) q^{2} +(2.52555 + 1.45812i) q^{3} +(0.0113813 - 0.0197130i) q^{4} -4.14760 q^{6} +(4.52117 + 2.61030i) q^{7} -2.81210i q^{8} +(2.75225 + 4.76704i) q^{9} +O(q^{10})\)	\(q+(-1.23169 + 0.711119i) q^{2} +(2.52555 + 1.45812i) q^{3} +(0.0113813 - 0.0197130i) q^{4} -4.14760 q^{6} +(4.52117 + 2.61030i) q^{7} -2.81210i q^{8} +(2.75225 + 4.76704i) q^{9} -2.54267 q^{11} +(0.0574879 - 0.0331906i) q^{12} +(-1.78811 - 1.03236i) q^{13} -7.42493 q^{14} +(2.02250 + 3.50308i) q^{16} +(-6.55831 + 3.78644i) q^{17} +(-6.77987 - 3.91436i) q^{18} +(-1.09671 + 1.89956i) q^{19} +(7.61227 + 13.1848i) q^{21} +(3.13180 - 1.80814i) q^{22} -3.86905i q^{23} +(4.10040 - 7.10209i) q^{24} +2.93654 q^{26} +7.30376i q^{27} +(0.102913 - 0.0594170i) q^{28} +1.70825 q^{29} +8.03194 q^{31} +(-0.111508 - 0.0643791i) q^{32} +(-6.42163 - 3.70753i) q^{33} +(5.38522 - 9.32748i) q^{34} +0.125297 q^{36} +(6.08064 + 0.160528i) q^{37} -3.11957i q^{38} +(-3.01063 - 5.21456i) q^{39} +(-4.51088 + 7.81308i) q^{41} +(-18.7520 - 10.8265i) q^{42} -0.751253i q^{43} +(-0.0289389 + 0.0501236i) q^{44} +(2.75135 + 4.76548i) q^{46} -0.0613730i q^{47} +11.7962i q^{48} +(10.1273 + 17.5410i) q^{49} -22.0844 q^{51} +(-0.0407019 + 0.0234992i) q^{52} +(1.68649 - 0.973694i) q^{53} +(-5.19385 - 8.99601i) q^{54} +(7.34042 - 12.7140i) q^{56} +(-5.53959 + 3.19829i) q^{57} +(-2.10404 + 1.21477i) q^{58} +(2.44957 + 4.24279i) q^{59} +(1.63484 - 2.83163i) q^{61} +(-9.89289 + 5.71166i) q^{62} +28.7368i q^{63} -7.90689 q^{64} +10.5460 q^{66} +(-9.42232 - 5.43998i) q^{67} +0.172378i q^{68} +(5.64155 - 9.77145i) q^{69} +(1.10115 - 1.90726i) q^{71} +(13.4054 - 7.73962i) q^{72} -9.02399i q^{73} +(-7.60365 + 4.12634i) q^{74} +(0.0249640 + 0.0432389i) q^{76} +(-11.4958 - 6.63713i) q^{77} +(7.41636 + 4.28183i) q^{78} +(3.42536 - 5.93289i) q^{79} +(-2.39304 + 4.14486i) q^{81} -12.8311i q^{82} +(7.41311 - 4.27996i) q^{83} +0.346550 q^{84} +(0.534231 + 0.925315i) q^{86} +(4.31426 + 2.49084i) q^{87} +7.15026i q^{88} +(0.806045 + 1.39611i) q^{89} +(-5.38955 - 9.33498i) q^{91} +(-0.0762703 - 0.0440347i) q^{92} +(20.2850 + 11.7116i) q^{93} +(0.0436435 + 0.0755927i) q^{94} +(-0.187746 - 0.325185i) q^{96} -1.26376i q^{97} +(-24.9475 - 14.4034i) q^{98} +(-6.99808 - 12.1210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) \) 48 * q + 22 * q^4 + 20 * q^9	\( 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Introduction

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