LMFDB - Embedded newform 275.3.q.f.249.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,3,Mod(24,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("275.24");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.q (of order $10$, degree $4$, 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:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			249.1
Character	$\chi$	$=$	275.249
Dual form			275.3.q.f.74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.85483 - 2.07416i) q^{2} +(-0.881935 - 0.286558i) q^{3} +(2.61187 + 8.03851i) q^{4} +(1.92341 + 2.64735i) q^{6} +(-1.21313 - 3.73363i) q^{7} +(4.85489 - 14.9418i) q^{8} +(-6.58546 - 4.78462i) q^{9} +(-2.87880 + 10.6166i) q^{11} -7.83789i q^{12} +(-4.65009 - 3.37849i) q^{13} +(-4.28086 + 13.1751i) q^{14} +(-17.4997 + 12.7143i) q^{16} +(-7.28252 + 5.29106i) q^{17} +(8.87634 + 27.3186i) q^{18} +(27.7487 + 9.01609i) q^{19} +3.64045i q^{21} +(30.2390 - 24.3376i) q^{22} +36.7936i q^{23} +(-8.56339 + 11.7865i) q^{24} +(6.26771 + 19.2900i) q^{26} +(9.34246 + 12.8588i) q^{27} +(26.8443 - 19.5035i) q^{28} +(24.8274 - 8.06690i) q^{29} +(-39.1642 - 28.4544i) q^{31} +13.4870 q^{32} +(5.58119 - 8.53822i) q^{33} +31.7649 q^{34} +(21.2608 - 65.4341i) q^{36} +(20.7411 - 6.73919i) q^{37} +(-60.5170 - 83.2945i) q^{38} +(3.13294 + 4.31213i) q^{39} +(40.5371 + 13.1713i) q^{41} +(7.55087 - 10.3929i) q^{42} +70.3737 q^{43} +(-92.8608 + 4.58797i) q^{44} +(76.3156 - 105.039i) q^{46} +(16.8149 + 5.46351i) q^{47} +(19.0769 - 6.19847i) q^{48} +(27.1735 - 19.7427i) q^{49} +(7.93890 - 2.57951i) q^{51} +(15.0126 - 46.2040i) q^{52} +(-36.6485 + 50.4423i) q^{53} -56.0874i q^{54} -61.6768 q^{56} +(-21.8889 - 15.9032i) q^{57} +(-87.6100 - 28.4662i) q^{58} +(12.0295 + 37.0230i) q^{59} +(26.4166 + 36.3594i) q^{61} +(52.7881 + 162.465i) q^{62} +(-9.87498 + 30.3921i) q^{63} +(31.4956 + 22.8829i) q^{64} +(-33.6430 + 12.7989i) q^{66} -36.2530i q^{67} +(-61.5533 - 44.7211i) q^{68} +(10.5435 - 32.4495i) q^{69} +(1.98595 - 1.44287i) q^{71} +(-103.462 + 75.1699i) q^{72} +(40.7610 + 125.450i) q^{73} +(-73.1905 - 23.7810i) q^{74} +246.607i q^{76} +(43.1309 - 2.13097i) q^{77} -18.8086i q^{78} +(24.9427 - 34.3307i) q^{79} +(18.0841 + 55.6573i) q^{81} +(-88.4072 - 121.682i) q^{82} +(62.4666 - 45.3846i) q^{83} +(-29.2638 + 9.50839i) q^{84} +(-200.905 - 145.966i) q^{86} -24.2077 q^{87} +(144.655 + 94.5569i) q^{88} -105.316 q^{89} +(-6.97287 + 21.4603i) q^{91} +(-295.766 + 96.1001i) q^{92} +(26.3864 + 36.3177i) q^{93} +(-36.6717 - 50.4742i) q^{94} +(-11.8946 - 3.86481i) q^{96} +(-33.2937 + 45.8248i) q^{97} -118.525 q^{98} +(69.7546 - 56.1413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 26 q^{4} + 40 q^{6} - 8 q^{9} + 24 q^{11} + 120 q^{14} - 86 q^{16} + 160 q^{19} - 420 q^{24} - 240 q^{26} - 10 q^{29} - 92 q^{31} - 20 q^{34} - 78 q^{36} + 570 q^{39} + 460 q^{41} - 976 q^{44} + 410 q^{46}+ \cdots - 1338 q^{99}+O(q^{100}) $ 24 * q - 26 * q^4 + 40 * q^6 - 8 * q^9 + 24 * q^11 + 120 * q^14 - 86 * q^16 + 160 * q^19 - 420 * q^24 - 240 * q^26 - 10 * q^29 - 92 * q^31 - 20 * q^34 - 78 * q^36 + 570 * q^39 + 460 * q^41 - 976 * q^44 + 410 * q^46 + 424 * q^49 + 720 * q^51 - 820 * q^56 + 148 * q^59 - 580 * q^61 + 14 * q^64 + 370 * q^66 + 146 * q^69 - 552 * q^71 + 200 * q^74 - 470 * q^79 - 60 * q^81 + 1160 * q^84 - 960 * q^86 + 228 * q^89 + 320 * q^91 - 750 * q^94 + 530 * q^96 - 1338 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−2.85483	−	2.07416i	−1.42742	−	1.03708i	−0.990491	−	0.137581i	$-0.956067\pi$
$2$	−2.85483	−	2.07416i	−1.42742	−	1.03708i	−0.436925	−	0.899498i	$-0.643933\pi$
$3$	−0.881935	−	0.286558i	−0.293978	−	0.0955193i	0.158315	−	0.987389i	$-0.449394\pi$
$3$	−0.881935	−	0.286558i	−0.293978	−	0.0955193i	−0.452293	+	0.891869i	$0.649394\pi$
$4$	2.61187	+	8.03851i	0.652968	+	2.00963i
$5$		0			0
$5$		0			0
$6$	1.92341	+	2.64735i	0.320568	+	0.441224i
$7$	−1.21313	−	3.73363i	−0.173304	−	0.533376i	0.826248	−	0.563307i	$-0.190471\pi$
$7$	−1.21313	−	3.73363i	−0.173304	−	0.533376i	−0.999552	+	0.0299310i	$0.990471\pi$
$8$	4.85489	−	14.9418i	0.606861	−	1.86773i
$9$	−6.58546	−	4.78462i	−0.731718	−	0.531624i
$10$		0			0
$11$	−2.87880	+	10.6166i	−0.261709	+	0.965147i
$11$	−2.87880	+	10.6166i	−0.261709	+	0.965147i
$12$		−	7.83789i		−	0.653158i
$13$	−4.65009	−	3.37849i	−0.357699	−	0.259884i	0.394393	−	0.918942i	$-0.370955\pi$
$13$	−4.65009	−	3.37849i	−0.357699	−	0.259884i	−0.752092	+	0.659058i	$0.770955\pi$
$14$	−4.28086	+	13.1751i	−0.305775	+	0.941080i
$15$		0			0
$16$	−17.4997	+	12.7143i	−1.09373	+	0.794641i
$17$	−7.28252	+	5.29106i	−0.428383	+	0.311239i	−0.781002	−	0.624528i	$-0.785291\pi$
$17$	−7.28252	+	5.29106i	−0.428383	+	0.311239i	0.352619	+	0.935767i	$0.385291\pi$
$18$	8.87634	+	27.3186i	0.493130	+	1.51770i
$19$	27.7487	+	9.01609i	1.46046	+	0.474531i	0.928210	−	0.372058i	$-0.121348\pi$
$19$	27.7487	+	9.01609i	1.46046	+	0.474531i	0.532247	+	0.846589i	$0.321348\pi$
$20$		0			0
$21$			3.64045i			0.173355i
$22$	30.2390	−	24.3376i	1.37450	−	1.10625i
$23$			36.7936i			1.59972i	0.600186	+	0.799860i	$0.295093\pi$
$23$			36.7936i			1.59972i	−0.600186	+	0.799860i	$0.704907\pi$
$24$	−8.56339	+	11.7865i	−0.356808	+	0.491104i
$25$		0			0
$26$	6.26771	+	19.2900i	0.241066	+	0.741924i
$27$	9.34246	+	12.8588i	0.346017	+	0.476252i
$28$	26.8443	−	19.5035i	0.958726	−	0.696555i
$29$	24.8274	−	8.06690i	0.856116	−	0.278169i	0.152111	−	0.988363i	$-0.451393\pi$
$29$	24.8274	−	8.06690i	0.856116	−	0.278169i	0.704006	+	0.710195i	$0.251393\pi$
$30$		0			0
$31$	−39.1642	−	28.4544i	−1.26336	−	0.917885i	−0.264442	−	0.964401i	$-0.585188\pi$
$31$	−39.1642	−	28.4544i	−1.26336	−	0.917885i	−0.998918	+	0.0465167i	$0.985188\pi$
$32$	13.4870			0.421469
$33$	5.58119	−	8.53822i	0.169127	−	0.258734i
$34$	31.7649			0.934261
$35$		0			0
$36$	21.2608	−	65.4341i	0.590579	−	1.81761i
$37$	20.7411	−	6.73919i	0.560571	−	0.182140i	−0.0150073	−	0.999887i	$-0.504777\pi$
$37$	20.7411	−	6.73919i	0.560571	−	0.182140i	0.575578	+	0.817747i	$0.304777\pi$
$38$	−60.5170	−	83.2945i	−1.59255	−	2.19196i
$39$	3.13294	+	4.31213i	0.0803319	+	0.110567i
$40$		0			0
$41$	40.5371	+	13.1713i	0.988709	+	0.321251i	0.758345	−	0.651854i	$-0.226008\pi$
$41$	40.5371	+	13.1713i	0.988709	+	0.321251i	0.230364	+	0.973105i	$0.426008\pi$
$42$	7.55087	−	10.3929i	0.179783	−	0.247450i
$43$	70.3737			1.63660			0.818298	−	0.574794i	$-0.194918\pi$
$43$	70.3737			1.63660			0.818298	+	0.574794i	$0.194918\pi$
$44$	−92.8608	+	4.58797i	−2.11047	+	0.104272i
$45$		0			0
$46$	76.3156	−	105.039i	1.65904	−	2.28347i
$47$	16.8149	+	5.46351i	0.357765	+	0.116245i	0.482384	−	0.875960i	$-0.339771\pi$
$47$	16.8149	+	5.46351i	0.357765	+	0.116245i	−0.124619	+	0.992205i	$0.539771\pi$
$48$	19.0769	−	6.19847i	0.397436	−	0.129135i
$49$	27.1735	−	19.7427i	0.554561	−	0.402912i
$50$		0			0
$51$	7.93890	−	2.57951i	0.155665	−	0.0505785i
$52$	15.0126	−	46.2040i	0.288704	−	0.888538i
$53$	−36.6485	+	50.4423i	−0.691481	+	0.951742i	0.308519	+	0.951218i	$0.400167\pi$
$53$	−36.6485	+	50.4423i	−0.691481	+	0.951742i	−1.00000		0.000523852i	$0.999833\pi$
$54$		−	56.0874i		−	1.03866i
$55$		0			0
$56$	−61.6768			−1.10137
$57$	−21.8889	−	15.9032i	−0.384016	−	0.279004i
$58$	−87.6100	−	28.4662i	−1.51052	−	0.490797i
$59$	12.0295	+	37.0230i	0.203890	+	0.627509i	0.999757	+	0.0220376i	$0.00701536\pi$
$59$	12.0295	+	37.0230i	0.203890	+	0.627509i	−0.795867	+	0.605471i	$0.792985\pi$
$60$		0			0
$61$	26.4166	+	36.3594i	0.433060	+	0.596055i	0.968652	−	0.248421i	$-0.0799117\pi$
$61$	26.4166	+	36.3594i	0.433060	+	0.596055i	−0.535593	+	0.844477i	$0.679912\pi$
$62$	52.7881	+	162.465i	0.851422	+	2.62041i
$63$	−9.87498	+	30.3921i	−0.156746	+	0.482414i
$64$	31.4956	+	22.8829i	0.492118	+	0.357545i
$65$		0			0
$66$	−33.6430	+	12.7989i	−0.509742	+	0.193923i
$67$		−	36.2530i		−	0.541090i	−0.962707	−	0.270545i	$-0.912796\pi$
$67$		−	36.2530i		−	0.541090i	0.962707	−	0.270545i	$-0.0872039\pi$
$68$	−61.5533	−	44.7211i	−0.905195	−	0.657663i
$69$	10.5435	−	32.4495i	0.152804	−	0.470283i
$70$		0			0
$71$	1.98595	−	1.44287i	0.0279711	−	0.0203222i	−0.573712	−	0.819057i	$-0.694497\pi$
$71$	1.98595	−	1.44287i	0.0279711	−	0.0203222i	0.601683	+	0.798735i	$0.294497\pi$
$72$	−103.462	+	75.1699i	−1.43698	+	1.04403i
$73$	40.7610	+	125.450i	0.558370	+	1.71849i	0.686873	+	0.726777i	$0.258983\pi$
$73$	40.7610	+	125.450i	0.558370	+	1.71849i	−0.128503	+	0.991709i	$0.541017\pi$
$74$	−73.1905	−	23.7810i	−0.989061	−	0.321365i
$75$		0			0
$76$			246.607i			3.24483i
$77$	43.1309	−	2.13097i	0.560142	−	0.0276749i
$78$		−	18.8086i		−	0.241136i
$79$	24.9427	−	34.3307i	0.315730	−	0.434565i	−0.621427	−	0.783472i	$-0.713447\pi$
$79$	24.9427	−	34.3307i	0.315730	−	0.434565i	0.937158	+	0.348907i	$0.113447\pi$
$80$		0			0
$81$	18.0841	+	55.6573i	0.223261	+	0.687127i
$82$	−88.4072	−	121.682i	−1.07814	−	1.48393i
$83$	62.4666	−	45.3846i	0.752609	−	0.546803i	−0.144025	−	0.989574i	$-0.546005\pi$
$83$	62.4666	−	45.3846i	0.752609	−	0.546803i	0.896635	+	0.442771i	$0.146005\pi$
$84$	−29.2638	+	9.50839i	−0.348379	+	0.113195i
$85$		0			0
$86$	−200.905	−	145.966i	−2.33610	−	1.69728i
$87$	−24.2077			−0.278250
$88$	144.655	+	94.5569i	1.64381	+	1.07451i
$89$	−105.316			−1.18332			−0.591661	−	0.806187i	$-0.701528\pi$
$89$	−105.316			−1.18332			−0.591661	+	0.806187i	$0.701528\pi$
$90$		0			0
$91$	−6.97287	+	21.4603i	−0.0766249	+	0.235827i
$92$	−295.766	+	96.1001i	−3.21484	+	1.04457i
$93$	26.3864	+	36.3177i	0.283725	+	0.390513i
$94$	−36.6717	−	50.4742i	−0.390124	−	0.536960i
$95$		0			0
$96$	−11.8946	−	3.86481i	−0.123903	−	0.0402584i
$97$	−33.2937	+	45.8248i	−0.343234	+	0.472421i	−0.945382	−	0.325963i	$-0.894311\pi$
$97$	−33.2937	+	45.8248i	−0.343234	+	0.472421i	0.602149	+	0.798384i	$0.294311\pi$
$98$	−118.525			−1.20944
$99$	69.7546	−	56.1413i	0.704592	−	0.567084i
$100$		0			0
$101$	−54.3720	+	74.8367i	−0.538337	+	0.740957i	−0.988372	−	0.152054i	$-0.951411\pi$
$101$	−54.3720	+	74.8367i	−0.538337	+	0.740957i	0.450035	+	0.893011i	$0.351411\pi$
$102$	−28.0145	−	9.10247i	−0.274652	−	0.0892399i
$103$	41.6344	−	13.5278i	0.404218	−	0.131338i	−0.0998498	−	0.995003i	$-0.531836\pi$
$103$	41.6344	−	13.5278i	0.404218	−	0.131338i	0.504068	+	0.863664i	$0.331836\pi$
$104$	−73.0564	+	53.0786i	−0.702465	+	0.510371i
$105$		0			0
$106$	209.251	−	67.9896i	1.97406	−	0.641412i
$107$	19.6680	−	60.5320i	0.183813	−	0.565719i	−0.816113	−	0.577893i	$-0.803875\pi$
$107$	19.6680	−	60.5320i	0.183813	−	0.565719i	0.999926	+	0.0121737i	$0.00387511\pi$
$108$	−78.9643	+	108.685i	−0.731151	+	1.00634i
$109$			180.853i			1.65920i	0.558358	+	0.829600i	$0.311432\pi$
$109$			180.853i			1.65920i	−0.558358	+	0.829600i	$0.688568\pi$
$110$		0			0
$111$	−20.2235			−0.182193
$112$	68.6998	+	49.9133i	0.613391	+	0.445654i
$113$	−69.2468	−	22.4996i	−0.612803	−	0.199112i	−0.0138608	−	0.999904i	$-0.504412\pi$
$113$	−69.2468	−	22.4996i	−0.612803	−	0.199112i	−0.598942	+	0.800792i	$0.704412\pi$
$114$	29.5033	+	90.8020i	0.258801	+	0.796508i
$115$		0			0
$116$	129.692	+	178.505i	1.11803	+	1.53884i
$117$	14.4582	+	44.4978i	0.123574	+	0.380323i
$118$	42.4493	−	130.646i	0.359740	−	1.10717i
$119$	28.5895	+	20.7715i	0.240248	+	0.174551i
$120$		0			0
$121$	−104.425	−	61.1262i	−0.863017	−	0.505175i
$122$		−	158.592i		−	1.29994i
$123$	−31.9767	−	23.2324i	−0.259973	−	0.188881i
$124$	126.440	−	389.141i	1.01967	−	3.13823i
$125$		0			0
$126$	91.2293	−	66.2820i	0.724042	−	0.526047i
$127$	−94.5954	+	68.7276i	−0.744846	+	0.541162i	−0.894225	−	0.447618i	$-0.852273\pi$
$127$	−94.5954	+	68.7276i	−0.744846	+	0.541162i	0.149379	+	0.988780i	$0.452273\pi$
$128$	−59.1227	−	181.961i	−0.461896	−	1.42157i
$129$	−62.0650	−	20.1661i	−0.481124	−	0.156327i
$130$		0			0
$131$			41.6464i			0.317912i	0.987286	+	0.158956i	$0.0508127\pi$
$131$			41.6464i			0.317912i	−0.987286	+	0.158956i	$0.949187\pi$
$132$	83.2119	+	22.5637i	0.630393	+	0.170937i
$133$		−	114.541i		−	0.861211i
$134$	−75.1945	+	103.496i	−0.561153	+	0.772360i
$135$		0			0
$136$	43.7022	+	134.502i	0.321340	+	0.988982i
$137$	62.3011	+	85.7502i	0.454753	+	0.625914i	0.973410	−	0.229069i	$-0.0735680\pi$
$137$	62.3011	+	85.7502i	0.454753	+	0.625914i	−0.518657	+	0.854982i	$0.673568\pi$
$138$	−97.4053	+	70.7691i	−0.705835	+	0.512819i
$139$	−31.5601	+	10.2545i	−0.227051	+	0.0737733i	−0.420333	−	0.907370i	$-0.638087\pi$
$139$	−31.5601	+	10.2545i	−0.227051	+	0.0737733i	0.193282	+	0.981143i	$0.438087\pi$
$140$		0			0
$141$	−13.2641	−	9.63691i	−0.0940714	−	0.0683469i
$142$	−8.66229			−0.0610020
$143$	49.2548	−	39.6422i	0.344439	−	0.277218i
$144$	176.076			1.22275
$145$		0			0
$146$	143.836	−	442.682i	0.985179	−	3.03207i
$147$	−29.6227	+	9.62499i	−0.201515	+	0.0654761i
$148$	108.346	+	149.126i	0.732069	+	1.00761i
$149$	−70.8877	−	97.5686i	−0.475757	−	0.654823i	0.501926	−	0.864911i	$-0.332625\pi$
$149$	−70.8877	−	97.5686i	−0.475757	−	0.654823i	−0.977683	+	0.210088i	$0.932625\pi$
$150$		0			0
$151$	−65.2872	−	21.2131i	−0.432366	−	0.140484i	0.0847449	−	0.996403i	$-0.472992\pi$
$151$	−65.2872	−	21.2131i	−0.432366	−	0.140484i	−0.517111	+	0.855919i	$0.672992\pi$
$152$	269.433	−	370.843i	1.77259	−	2.43976i
$153$	73.2744			0.478918
$154$	−127.551	−	83.3767i	−0.828256	−	0.541407i
$155$		0			0
$156$	−26.4802	+	36.4469i	−0.169745	+	0.233634i
$157$	178.042	+	57.8493i	1.13402	+	0.368467i	0.815104	−	0.579315i	$-0.196680\pi$
$157$	178.042	+	57.8493i	1.13402	+	0.368467i	0.318920	+	0.947782i	$0.396680\pi$
$158$	−142.414	+	46.2732i	−0.901356	+	0.292868i
$159$	46.7762	−	33.9849i	0.294190	−	0.213742i
$160$		0			0
$161$	137.374	−	44.6354i	0.853253	−	0.277239i
$162$	63.8147	−	196.402i	0.393918	−	1.21236i
$163$	21.2260	−	29.2151i	0.130221	−	0.179234i	−0.738928	−	0.673785i	$-0.764667\pi$
$163$	21.2260	−	29.2151i	0.130221	−	0.179234i	0.869149	+	0.494551i	$0.164667\pi$
$164$			360.259i			2.19670i
$165$		0			0
$166$	−272.466			−1.64136
$167$	124.179	+	90.2211i	0.743585	+	0.540246i	0.893832	−	0.448403i	$-0.148007\pi$
$167$	124.179	+	90.2211i	0.743585	+	0.540246i	−0.150247	+	0.988648i	$0.548007\pi$
$168$	54.3949	+	17.6740i	0.323779	+	0.105202i
$169$	−42.0147	−	129.308i	−0.248608	−	0.765136i
$170$		0			0
$171$	−139.599	−	192.142i	−0.816370	−	1.12364i
$172$	183.807	+	565.700i	1.06864	+	3.28895i
$173$	0.534955	−	1.64642i	0.00309223	−	0.00951689i	−0.949498	−	0.313772i	$-0.898407\pi$
$173$	0.534955	−	1.64642i	0.00309223	−	0.00951689i	0.952591	+	0.304255i	$0.0984074\pi$
$174$	69.1090	+	50.2107i	0.397178	+	0.288567i
$175$		0			0
$176$	−84.6043	−	222.389i	−0.480706	−	1.26357i
$177$		−	36.0990i		−	0.203949i
$178$	300.659	+	218.441i	1.68909	+	1.22720i
$179$	−26.7282	+	82.2609i	−0.149320	+	0.459558i	−0.997541	−	0.0700832i	$-0.977674\pi$
$179$	−26.7282	+	82.2609i	−0.149320	+	0.459558i	0.848222	+	0.529641i	$0.177674\pi$
$180$		0			0
$181$	−144.912	+	105.285i	−0.800619	+	0.581684i	−0.911096	−	0.412195i	$-0.864762\pi$
$181$	−144.912	+	105.285i	−0.800619	+	0.581684i	0.110477	+	0.993879i	$0.464762\pi$
$182$	64.4184	−	46.8027i	0.353947	−	0.257158i
$183$	−12.8787	−	39.6365i	−0.0703753	−	0.216593i
$184$	549.762	+	178.629i	2.98784	+	0.970808i
$185$		0			0
$186$		−	158.411i		−	0.851670i
$187$	−35.2082	−	92.5476i	−0.188279	−	0.494907i
$188$			149.437i			0.794878i
$189$	36.6764	−	50.4807i	0.194055	−	0.267094i
$190$		0			0
$191$	104.623	+	321.997i	0.547765	+	1.68585i	0.714324	+	0.699815i	$0.246734\pi$
$191$	104.623	+	321.997i	0.547765	+	1.68585i	−0.166559	+	0.986032i	$0.553266\pi$
$192$	−21.2198	−	29.2065i	−0.110520	−	0.152117i
$193$	7.19818	−	5.22978i	0.0372963	−	0.0270973i	−0.568981	−	0.822351i	$-0.692662\pi$
$193$	7.19818	−	5.22978i	0.0372963	−	0.0270973i	0.606277	+	0.795253i	$0.292662\pi$
$194$	190.096	−	61.7658i	0.979874	−	0.318381i
$195$		0			0
$196$	229.676	+	166.869i	1.17181	+	0.851373i
$197$	−199.660			−1.01350			−0.506751	−	0.862093i	$-0.669154\pi$
$197$	−199.660			−1.01350			−0.506751	+	0.862093i	$0.669154\pi$
$198$	−315.584	+	15.5920i	−1.59386	+	0.0787477i
$199$	−182.624			−0.917706			−0.458853	−	0.888512i	$-0.651740\pi$
$199$	−182.624			−0.917706			−0.458853	+	0.888512i	$0.651740\pi$
$200$		0			0
$201$	−10.3886	+	31.9728i	−0.0516845	+	0.159069i
$202$	310.446	−	100.870i	1.53686	−	0.499356i
$203$	−60.2377	−	82.9101i	−0.296737	−	0.408424i
$204$	41.4708	+	57.0796i	0.203288	+	0.279802i
$205$		0			0
$206$	−146.918	−	47.7366i	−0.713195	−	0.231731i
$207$	176.043	−	242.303i	0.850450	−	1.17054i
$208$	124.330			0.597740
$209$	−175.603	+	268.642i	−0.840207	+	1.28537i
$210$		0			0
$211$	80.0829	−	110.225i	0.379540	−	0.522392i	−0.575923	−	0.817504i	$-0.695357\pi$
$211$	80.0829	−	110.225i	0.379540	−	0.522392i	0.955463	+	0.295112i	$0.0953571\pi$
$212$	−501.202	−	162.851i	−2.36416	−	0.768163i
$213$	−2.16494	+	0.703432i	−0.0101640	+	0.00330250i
$214$	−181.702	+	132.014i	−0.849073	+	0.616888i
$215$		0			0
$216$	237.490	−	77.1653i	1.09949	−	0.357247i
$217$	−58.7271	+	180.744i	−0.270632	+	0.832920i
$218$	375.117	−	516.305i	1.72072	−	2.36837i
$219$		−	122.319i		−	0.558533i
$220$		0			0
$221$	51.7402			0.234118
$222$	57.7346	+	41.9466i	0.260066	+	0.188949i
$223$	−38.5788	−	12.5350i	−0.172999	−	0.0562108i	0.221237	−	0.975220i	$-0.428991\pi$
$223$	−38.5788	−	12.5350i	−0.172999	−	0.0562108i	−0.394236	+	0.919009i	$0.628991\pi$
$224$	−16.3615	−	50.3555i	−0.0730424	−	0.224801i
$225$		0			0
$226$	151.020	+	207.861i	0.668230	+	0.919740i
$227$	−58.8689	−	181.180i	−0.259334	−	0.798148i	−0.992945	−	0.118578i	$-0.962166\pi$
$227$	−58.8689	−	181.180i	−0.259334	−	0.798148i	0.733611	−	0.679570i	$-0.237834\pi$
$228$	70.6672	−	217.491i	0.309944	−	0.953909i
$229$	−185.982	−	135.124i	−0.812148	−	0.590060i	0.102304	−	0.994753i	$-0.467378\pi$
$229$	−185.982	−	135.124i	−0.812148	−	0.590060i	−0.914453	+	0.404693i	$0.867378\pi$
$230$		0			0
$231$	−38.6493	−	10.4801i	−0.167313	−	0.0453685i
$232$		−	410.130i		−	1.76780i
$233$	153.190	+	111.299i	0.657467	+	0.477678i	0.865807	−	0.500379i	$-0.166806\pi$
$233$	153.190	+	111.299i	0.657467	+	0.477678i	−0.208340	+	0.978057i	$0.566806\pi$
$234$	51.0197	−	157.022i	0.218033	−	0.671036i
$235$		0			0
$236$	−266.191	+	193.399i	−1.12793	+	0.819486i
$237$	−31.8355	+	23.1299i	−0.134327	+	0.0975944i
$238$	−38.5349	−	118.598i	−0.161912	−	0.498312i
$239$	106.671	+	34.6595i	0.446322	+	0.145019i	0.523551	−	0.851994i	$-0.324607\pi$
$239$	106.671	+	34.6595i	0.446322	+	0.145019i	−0.0772283	+	0.997013i	$0.524607\pi$
$240$		0			0
$241$		−	118.124i		−	0.490141i	−0.969505	−	0.245070i	$-0.921189\pi$
$241$		−	118.124i		−	0.490141i	0.969505	−	0.245070i	$-0.0788110\pi$
$242$	171.331	+	391.099i	0.707978	+	1.61611i
$243$		−	197.317i		−	0.812006i
$244$	−223.278	+	307.316i	−0.915076	+	1.25949i
$245$		0			0
$246$	43.1004	+	132.649i	0.175205	+	0.539225i
$247$	−98.5731	−	135.674i	−0.399081	−	0.549288i
$248$	−615.298	+	447.040i	−2.48104	+	1.80258i
$249$	−68.0967	+	22.1260i	−0.273481	+	0.0888593i
$250$		0			0
$251$	148.903	+	108.184i	0.593240	+	0.431014i	0.843473	−	0.537172i	$-0.180507\pi$
$251$	148.903	+	108.184i	0.593240	+	0.431014i	−0.250233	+	0.968186i	$0.580507\pi$
$252$	−270.099			−1.07182
$253$	−390.623	−	105.921i	−1.54397	−	0.418661i
$254$	412.606			1.62443
$255$		0			0
$256$	−160.509	+	493.997i	−0.626990	+	1.92968i
$257$	−381.685	+	124.017i	−1.48516	+	0.482557i	−0.935649	−	0.352932i	$-0.885185\pi$
$257$	−381.685	+	124.017i	−1.48516	+	0.482557i	−0.549507	+	0.835489i	$0.685185\pi$
$258$	135.357	+	186.303i	0.524641	+	0.722106i
$259$	−50.3234	−	69.2642i	−0.194299	−	0.267429i
$260$		0			0
$261$	−202.097	−	65.6652i	−0.774317	−	0.251591i
$262$	86.3812	−	118.894i	0.329699	−	0.453792i
$263$	72.9866			0.277516			0.138758	−	0.990326i	$-0.455689\pi$
$263$	72.9866			0.277516			0.138758	+	0.990326i	$0.455689\pi$
$264$	−100.480	−	124.845i	−0.380607	−	0.472898i
$265$		0			0
$266$	−237.576	+	326.996i	−0.893144	+	1.22931i
$267$	92.8816	+	30.1791i	0.347871	+	0.113030i
$268$	291.420	−	94.6882i	1.08739	−	0.353314i
$269$	161.917	−	117.640i	0.601923	−	0.437322i	−0.244638	−	0.969614i	$-0.578669\pi$
$269$	161.917	−	117.640i	0.601923	−	0.437322i	0.846561	+	0.532292i	$0.178669\pi$
$270$		0			0
$271$	144.974	−	47.1049i	0.534959	−	0.173819i	−0.0290645	−	0.999578i	$-0.509253\pi$
$271$	144.974	−	47.1049i	0.534959	−	0.173819i	0.564023	+	0.825759i	$0.309253\pi$
$272$	60.1698	−	185.184i	0.221213	−	0.680822i
$273$	12.2992	−	16.9284i	0.0450521	−	0.0620089i
$274$		−	374.025i		−	1.36505i
$275$		0			0
$276$	288.384			1.04487
$277$	167.719	+	121.855i	0.605485	+	0.439911i	0.847822	−	0.530281i	$-0.177914\pi$
$277$	167.719	+	121.855i	0.605485	+	0.439911i	−0.242336	+	0.970192i	$0.577914\pi$
$278$	111.368	+	36.1857i	0.400605	+	0.130164i
$279$	121.770	+	374.771i	0.436453	+	1.34327i
$280$		0			0
$281$	−72.0371	−	99.1506i	−0.256360	−	0.352849i	0.661366	−	0.750063i	$-0.269977\pi$
$281$	−72.0371	−	99.1506i	−0.256360	−	0.352849i	−0.917726	+	0.397214i	$0.869977\pi$
$282$	17.8782	+	55.0235i	0.0633980	+	0.195119i
$283$	−51.3970	+	158.184i	−0.181615	+	0.558953i	−0.999874	−	0.0158971i	$-0.994940\pi$
$283$	−51.3970	+	158.184i	−0.181615	+	0.558953i	0.818259	+	0.574850i	$0.194940\pi$
$284$	16.7856	+	12.1954i	0.0591042	+	0.0429417i
$285$		0			0
$286$	−222.838	+	11.0098i	−0.779155	+	0.0384957i
$287$		−	167.329i		−	0.583028i
$288$	−88.8181	−	64.5301i	−0.308396	−	0.224063i
$289$	−64.2661	+	197.791i	−0.222374	+	0.684397i
$290$		0			0
$291$	42.4943	−	30.8739i	0.146028	−	0.106096i
$292$	−901.965	+	655.316i	−3.08892	+	2.24423i
$293$	15.7554	+	48.4902i	0.0537728	+	0.165496i	0.974336	−	0.225097i	$-0.0722700\pi$
$293$	15.7554	+	48.4902i	0.0537728	+	0.165496i	−0.920564	+	0.390593i	$0.872270\pi$
$294$	104.531	+	33.9643i	0.355549	+	0.115525i
$295$		0			0
$296$		−	342.628i		−	1.15753i
$297$	−163.412	+	62.1675i	−0.550209	+	0.209318i
$298$			425.574i			1.42810i
$299$	124.307	−	171.093i	0.415741	−	0.572219i
$300$		0			0
$301$	−85.3725	−	262.749i	−0.283629	−	0.872922i
$302$	142.385	+	195.976i	0.471473	+	0.648927i
$303$	69.3976	−	50.4203i	0.229035	−	0.166404i
$304$	−600.226	+	195.025i	−1.97443	+	0.641530i
$305$		0			0
$306$	−209.186	−	151.983i	−0.683615	−	0.496675i
$307$	388.897			1.26676			0.633382	−	0.773839i	$-0.281666\pi$
$307$	388.897			1.26676			0.633382	+	0.773839i	$0.281666\pi$
$308$	129.782	+	341.143i	0.421371	+	1.10761i
$309$	−40.5954			−0.131377
$310$		0			0
$311$	−12.6147	+	38.8239i	−0.0405616	+	0.124836i	−0.969287	−	0.245933i	$-0.920906\pi$
$311$	−12.6147	+	38.8239i	−0.0405616	+	0.124836i	0.928725	+	0.370769i	$0.120906\pi$
$312$	79.6410	−	25.8769i	0.255260	−	0.0829389i
$313$	301.360	+	414.787i	0.962812	+	1.32520i	0.945595	+	0.325345i	$0.105480\pi$
$313$	301.360	+	414.787i	0.962812	+	1.32520i	0.0172161	+	0.999852i	$0.494520\pi$
$314$	−388.291	−	534.437i	−1.23660	−	1.70203i
$315$		0			0
$316$	341.114	+	110.835i	1.07948	+	0.350743i
$317$	−103.368	+	142.274i	−0.326083	+	0.448814i	−0.940312	−	0.340313i	$-0.889467\pi$
$317$	−103.368	+	142.274i	−0.326083	+	0.448814i	0.614230	+	0.789127i	$0.289467\pi$
$318$	−204.028			−0.641598
$319$	14.1702	+	286.806i	0.0444207	+	0.899077i
$320$		0			0
$321$	−34.6918	+	47.7492i	−0.108074	+	0.148751i
$322$	−484.760	−	157.508i	−1.50547	−	0.489155i
$323$	−249.785	+	81.1601i	−0.773328	+	0.251270i
$324$	−400.168	+	290.739i	−1.23509	+	0.897343i
$325$		0			0
$326$	−121.193	+	39.3781i	−0.371759	+	0.120792i
$327$	51.8248	−	159.500i	0.158486	−	0.487769i
$328$	393.606	−	541.752i	1.20002	−	1.65168i
$329$		−	69.4088i		−	0.210969i
$330$		0			0
$331$	−97.5050			−0.294577			−0.147289	−	0.989094i	$-0.547055\pi$
$331$	−97.5050			−0.294577			−0.147289	+	0.989094i	$0.547055\pi$
$332$	527.979	+	383.600i	1.59030	+	1.15542i
$333$	−168.834	−	54.8576i	−0.507010	−	0.164737i
$334$	−167.377	−	515.132i	−0.501127	−	1.54231i
$335$		0			0
$336$	−46.2856	−	63.7067i	−0.137755	−	0.189603i
$337$	−47.9448	−	147.559i	−0.142269	−	0.437860i	0.854380	−	0.519648i	$-0.173937\pi$
$337$	−47.9448	−	147.559i	−0.142269	−	0.437860i	−0.996650	+	0.0817878i	$0.973937\pi$
$338$	−148.260	+	456.298i	−0.438639	+	1.34999i
$339$	54.6237	+	39.6864i	0.161132	+	0.117069i
$340$		0			0
$341$	414.835	−	333.876i	1.21653	−	0.979109i
$342$			838.084i			2.45054i
$343$	−262.302	−	190.574i	−0.764729	−	0.555608i
$344$	341.656	−	1051.51i	0.993187	−	3.05671i
$345$		0			0
$346$	−4.94214	+	3.59068i	−0.0142837	+	0.0103777i
$347$	40.6288	−	29.5186i	0.117086	−	0.0850680i	−0.527701	−	0.849430i	$-0.676946\pi$
$347$	40.6288	−	29.5186i	0.117086	−	0.0850680i	0.644787	+	0.764362i	$0.276946\pi$
$348$	−63.2275	−	194.594i	−0.181688	−	0.559179i
$349$	146.948	+	47.7462i	0.421053	+	0.136809i	0.511878	−	0.859058i	$-0.328950\pi$
$349$	146.948	+	47.7462i	0.421053	+	0.136809i	−0.0908242	+	0.995867i	$0.528950\pi$
$350$		0			0
$351$		−	91.3580i		−	0.260279i
$352$	−38.8263	+	143.186i	−0.110302	+	0.406779i
$353$		−	559.143i		−	1.58397i	−0.610538	−	0.791987i	$-0.709047\pi$
$353$		−	559.143i		−	1.58397i	0.610538	−	0.791987i	$-0.290953\pi$
$354$	−74.8751	+	103.057i	−0.211511	+	0.291121i
$355$		0			0
$356$	−275.071	−	846.582i	−0.772672	−	2.37804i
$357$	−19.2619	−	26.5117i	−0.0539548	−	0.0742624i
$358$	246.927	−	179.403i	0.689739	−	0.501125i
$359$	646.648	−	210.109i	1.80125	−	0.585261i	0.801331	−	0.598221i	$-0.204126\pi$
$359$	646.648	−	210.109i	1.80125	−	0.585261i	0.999916	+	0.0129603i	$0.00412551\pi$
$360$		0			0
$361$	396.644	+	288.179i	1.09874	+	0.798279i
$362$	632.077			1.74607
$363$	74.5799	+	83.8331i	0.205454	+	0.230945i
$364$	−190.721			−0.523959
$365$		0			0
$366$	−45.4458	+	139.868i	−0.124169	+	0.382153i
$367$	428.051	−	139.082i	1.16635	−	0.378970i	0.339071	−	0.940761i	$-0.389887\pi$
$367$	428.051	−	139.082i	1.16635	−	0.378970i	0.827279	+	0.561791i	$0.189887\pi$
$368$	−467.803	−	643.875i	−1.27120	−	1.74966i
$369$	−203.936	−	280.693i	−0.552671	−	0.760686i
$370$		0			0
$371$	232.793	+	75.6389i	0.627473	+	0.203878i
$372$	−223.023	+	306.965i	−0.599524	+	0.825173i
$373$	−396.273			−1.06239			−0.531197	−	0.847248i	$-0.678258\pi$
$373$	−396.273			−1.06239			−0.531197	+	0.847248i	$0.678258\pi$
$374$	−91.4446	+	337.235i	−0.244504	+	0.901699i
$375$		0			0
$376$	163.269	−	224.721i	0.434227	−	0.597662i
$377$	−142.703	−	46.3672i	−0.378524	−	0.122990i
$378$	−209.410	+	68.0414i	−0.553995	+	0.180004i
$379$	429.812	−	312.277i	1.13407	−	0.823950i	0.147787	−	0.989019i	$-0.452785\pi$
$379$	429.812	−	312.277i	1.13407	−	0.823950i	0.986282	+	0.165069i	$0.0527848\pi$
$380$		0			0
$381$	103.121	−	33.5062i	0.270660	−	0.0879427i
$382$	369.190	−	1136.25i	0.966467	−	2.97448i
$383$	−363.276	+	500.006i	−0.948500	+	1.30550i	0.00368998	+	0.999993i	$0.498825\pi$
$383$	−363.276	+	500.006i	−0.948500	+	1.30550i	−0.952190	+	0.305506i	$0.901175\pi$
$384$			177.420i			0.462031i
$385$		0			0
$386$	−31.3970			−0.0813393
$387$	−463.443	−	336.711i	−1.19753	−	0.870054i
$388$	−455.322	−	147.943i	−1.17351	−	0.381297i
$389$	−3.92137	−	12.0687i	−0.0100806	−	0.0310250i	0.945890	−	0.324488i	$-0.105192\pi$
$389$	−3.92137	−	12.0687i	−0.0100806	−	0.0310250i	−0.955970	+	0.293463i	$0.905192\pi$
$390$		0			0
$391$	−194.677	−	267.950i	−0.497895	−	0.685294i
$392$	−163.067	−	501.870i	−0.415988	−	1.28028i
$393$	11.9341	−	36.7294i	0.0303667	−	0.0934591i
$394$	569.995	+	414.126i	1.44669	+	1.05108i
$395$		0			0
$396$	633.483	+	414.090i	1.59970	+	1.04568i
$397$			240.779i			0.606497i	0.952911	+	0.303249i	$0.0980713\pi$
$397$			240.779i			0.606497i	−0.952911	+	0.303249i	$0.901929\pi$
$398$	521.359	+	378.790i	1.30995	+	0.951733i
$399$	−32.8227	+	101.018i	−0.0822623	+	0.253177i
$400$		0			0
$401$	581.860	−	422.746i	1.45102	−	1.05423i	0.465431	−	0.885084i	$-0.345899\pi$
$401$	581.860	−	422.746i	1.45102	−	1.05423i	0.985591	−	0.169145i	$-0.0541008\pi$
$402$	95.9743	−	69.7294i	0.238742	−	0.173456i
$403$	85.9839	+	264.631i	0.213360	+	0.656653i
$404$	−743.588	−	241.606i	−1.84056	−	0.598036i
$405$		0			0
$406$			361.637i			0.890731i
$407$	11.8380	+	239.601i	0.0290859	+	0.588701i
$408$		−	131.145i		−	0.321433i
$409$	62.9642	−	86.6628i	0.153947	−	0.211890i	−0.725077	−	0.688668i	$-0.758196\pi$
$409$	62.9642	−	86.6628i	0.153947	−	0.211890i	0.879023	+	0.476779i	$0.158196\pi$
$410$		0			0
$411$	−30.3731	−	93.4789i	−0.0739006	−	0.227443i
$412$	217.488	+	299.346i	0.527882	+	0.726568i
$413$	123.637	−	89.8276i	0.299363	−	0.217500i
$414$	−1005.15	+	326.592i	−2.42789	+	0.788870i
$415$		0			0
$416$	−62.7158	−	45.5657i	−0.150759	−	0.109533i
$417$	30.7724			0.0737948
$418$	1058.52	−	402.698i	2.53235	−	0.963392i
$419$	−29.4752			−0.0703464			−0.0351732	−	0.999381i	$-0.511198\pi$
$419$	−29.4752			−0.0703464			−0.0351732	+	0.999381i	$0.511198\pi$
$420$		0			0
$421$	−127.694	+	393.002i	−0.303311	+	0.933496i	0.676991	+	0.735991i	$0.263284\pi$
$421$	−127.694	+	393.002i	−0.303311	+	0.933496i	−0.980302	+	0.197504i	$0.936716\pi$
$422$	−457.247	+	148.568i	−1.08352	+	0.352058i
$423$	−84.5934	−	116.433i	−0.199984	−	0.275255i
$424$	575.775	+	792.487i	1.35796	+	1.86907i
$425$		0			0
$426$	7.63957	+	2.48225i	0.0179333	+	0.00582687i
$427$	103.706	−	142.739i	0.242871	−	0.334283i
$428$	537.957			1.25691
$429$	−54.7993	+	20.8475i	−0.127737	+	0.0485956i
$430$		0			0
$431$	115.324	−	158.730i	0.267574	−	0.368284i	−0.653995	−	0.756499i	$-0.726908\pi$
$431$	115.324	−	158.730i	0.267574	−	0.368284i	0.921569	+	0.388215i	$0.126908\pi$
$432$	−326.980	−	106.242i	−0.756898	−	0.245931i
$433$	79.8895	−	25.9577i	0.184502	−	0.0599484i	−0.215309	−	0.976546i	$-0.569076\pi$
$433$	79.8895	−	25.9577i	0.184502	−	0.0599484i	0.399811	+	0.916598i	$0.369076\pi$
$434$	542.547	−	394.183i	1.25011	−	0.908256i
$435$		0			0
$436$	−1453.79	+	472.364i	−3.33438	+	1.08340i
$437$	−331.734	+	1020.97i	−0.759117	+	2.33632i
$438$	−253.708	+	349.199i	−0.579242	+	0.797258i
$439$		−	139.738i		−	0.318309i	−0.987254	−	0.159154i	$-0.949123\pi$
$439$		−	139.738i		−	0.318309i	0.987254	−	0.159154i	$-0.0508768\pi$
$440$		0			0
$441$	−273.411			−0.619980
$442$	−147.709	−	107.317i	−0.334184	−	0.242799i
$443$	281.315	+	91.4047i	0.635022	+	0.206331i	0.608799	−	0.793325i	$-0.291652\pi$
$443$	281.315	+	91.4047i	0.635022	+	0.206331i	0.0262237	+	0.999656i	$0.491652\pi$
$444$	−52.8211	−	162.567i	−0.118966	−	0.366141i
$445$		0			0
$446$	84.1364	+	115.804i	0.188647	+	0.259650i
$447$	34.5593	+	106.363i	0.0773139	+	0.237948i
$448$	47.2280	−	145.353i	0.105420	−	0.324448i
$449$	532.550	+	386.920i	1.18608	+	0.861737i	0.992844	−	0.119415i	$-0.0381021\pi$
$449$	532.550	+	386.920i	1.18608	+	0.861737i	0.193235	+	0.981153i	$0.438102\pi$
$450$		0			0
$451$	−256.532	+	392.449i	−0.568808	+	0.870175i
$452$		−	615.407i		−	1.36152i
$453$	51.5003	+	37.4171i	0.113687	+	0.0825986i
$454$	−207.734	+	639.341i	−0.457565	+	1.40824i
$455$		0			0
$456$	−343.891	+	249.851i	−0.754146	+	0.547919i
$457$	120.056	−	87.2258i	0.262705	−	0.190866i	−0.448634	−	0.893716i	$-0.648089\pi$
$457$	120.056	−	87.2258i	0.262705	−	0.190866i	0.711339	+	0.702849i	$0.248089\pi$
$458$	250.679	+	771.512i	0.547335	+	1.68452i
$459$	−136.073	−	44.2129i	−0.296456	−	0.0963244i
$460$		0			0
$461$			500.817i			1.08637i	0.839613	+	0.543185i	$0.182782\pi$
$461$			500.817i			1.08637i	−0.839613	+	0.543185i	$0.817218\pi$
$462$	88.5998	+	110.084i	0.191774	+	0.238276i
$463$		−	398.770i		−	0.861275i	−0.902525	−	0.430638i	$-0.858289\pi$
$463$		−	398.770i		−	0.861275i	0.902525	−	0.430638i	$-0.141711\pi$
$464$	−331.906	+	456.830i	−0.715315	+	0.984547i
$465$		0			0
$466$	−206.480	−	635.479i	−0.443090	−	1.36369i
$467$	−369.661	−	508.794i	−0.791564	−	1.08949i	−0.993912	−	0.110181i	$-0.964857\pi$
$467$	−369.661	−	508.794i	−0.791564	−	1.08949i	0.202347	−	0.979314i	$-0.435143\pi$
$468$	−319.933	+	232.445i	−0.683618	+	0.496677i
$469$	−135.356	+	43.9797i	−0.288604	+	0.0937733i
$470$		0			0
$471$	−140.444	−	102.039i	−0.298183	−	0.216642i
$472$	611.593			1.29575
$473$	−202.592	+	747.130i	−0.428312	+	1.57956i
$474$	138.860			0.292954
$475$		0			0
$476$	−92.2999	+	284.070i	−0.193907	+	0.596785i
$477$	482.694	−	156.837i	1.01194	−	0.328799i
$478$	−232.639	−	320.200i	−0.486692	−	0.669874i
$479$	56.6925	+	78.0306i	0.118356	+	0.162903i	0.864084	−	0.503347i	$-0.167898\pi$
$479$	56.6925	+	78.0306i	0.118356	+	0.162903i	−0.745728	+	0.666250i	$0.767898\pi$
$480$		0			0
$481$	−119.216	−	38.7357i	−0.247851	−	0.0805317i
$482$	−245.007	+	337.224i	−0.508314	+	0.699634i
$483$	−133.945			−0.277319
$484$	218.619	−	999.076i	0.451692	−	2.06421i
$485$		0			0
$486$	−409.267	+	563.308i	−0.842114	+	1.15907i
$487$	−760.849	−	247.215i	−1.56232	−	0.507628i	−0.604892	−	0.796307i	$-0.706784\pi$
$487$	−760.849	−	247.215i	−1.56232	−	0.507628i	−0.957426	+	0.288680i	$0.906784\pi$
$488$	671.525	−	218.192i	1.37607	−	0.447114i
$489$	−27.0918	+	19.6833i	−0.0554024	+	0.0402522i
$490$		0			0
$491$	−800.353	+	260.050i	−1.63005	+	0.529634i	−0.974282	−	0.225332i	$-0.927653\pi$
$491$	−800.353	+	260.050i	−1.63005	+	0.529634i	−0.655764	+	0.754966i	$0.727653\pi$
$492$	103.235	−	317.725i	0.209828	−	0.645783i
$493$	−138.123	+	190.110i	−0.280169	+	0.385620i
$494$			591.783i			1.19794i
$495$		0			0
$496$	1047.14			2.11116
$497$	−7.79638	−	5.66440i	−0.0156869	−	0.0113972i
$498$	240.298	+	78.0774i	0.482525	+	0.156782i
$499$	220.886	+	679.818i	0.442658	+	1.36236i	0.885032	+	0.465530i	$0.154136\pi$
$499$	220.886	+	679.818i	0.442658	+	1.36236i	−0.442374	+	0.896830i	$0.645864\pi$
$500$		0			0
$501$	−83.6639	−	115.153i	−0.166994	−	0.229847i
$502$	−200.702	−	617.697i	−0.399805	−	1.23047i
$503$	214.625	−	660.549i	0.426690	−	1.31322i	−0.474676	−	0.880161i	$-0.657435\pi$
$503$	214.625	−	660.549i	0.426690	−	1.31322i	0.901366	−	0.433057i	$-0.142565\pi$
$504$	406.170	+	295.100i	0.805894	+	0.585516i
$505$		0			0
$506$	895.466	+	1112.60i	1.76970	+	2.19882i
$507$			126.081i			0.248680i
$508$	−799.539	−	580.899i	−1.57390	−	1.14350i
$509$	7.78172	−	23.9497i	0.0152883	−	0.0470524i	−0.943121	−	0.332449i	$-0.892125\pi$
$509$	7.78172	−	23.9497i	0.0152883	−	0.0470524i	0.958410	+	0.285396i	$0.0921252\pi$
$510$		0			0
$511$	418.934	−	304.373i	0.819832	−	0.595643i
$512$	863.714	−	627.525i	1.68694	−	1.22563i
$513$	143.305	+	441.047i	0.279347	+	0.859741i
$514$	1346.88	+	437.627i	2.62038	+	0.851415i
$515$		0			0
$516$		−	551.581i		−	1.06896i
$517$	−106.411	+	162.789i	−0.205824	+	0.314873i
$518$			302.116i			0.583236i
$519$	−0.943590	+	1.29874i	−0.00181809	+	0.00250239i
$520$		0			0
$521$	144.330	+	444.202i	0.277025	+	0.852596i	0.988676	+	0.150063i	$0.0479476\pi$
$521$	144.330	+	444.202i	0.277025	+	0.852596i	−0.711651	+	0.702533i	$0.752052\pi$
$522$	440.752	+	606.643i	0.844353	+	1.16215i
$523$	646.608	−	469.788i	1.23634	−	0.898257i	0.238995	−	0.971021i	$-0.423182\pi$
$523$	646.608	−	469.788i	1.23634	−	0.898257i	0.997349	+	0.0727642i	$0.0231820\pi$
$524$	−334.775	+	108.775i	−0.638884	+	0.207586i
$525$		0			0
$526$	−208.365	−	151.386i	−0.396130	−	0.287806i
$527$	435.768			0.826884
$528$	10.8881	+	220.377i	0.0206215	+	0.417380i
$529$	−824.767			−1.55911
$530$		0			0
$531$	97.9211	−	301.370i	0.184409	−	0.567552i
$532$	920.740	−	299.167i	1.73071	−	0.562343i
$533$	−144.002	−	198.202i	−0.270172	−	0.371860i
$534$	−202.565	−	278.807i	−0.379336	−	0.522111i
$535$		0			0
$536$	−541.686	−	176.004i	−1.01061	−	0.328366i
$537$	47.1450	−	64.8896i	0.0877934	−	0.120837i
$538$	−706.250			−1.31273
$539$	131.374	+	345.326i	0.243736	+	0.640679i
$540$		0			0
$541$	631.800	−	869.598i	1.16784	−	1.60739i	0.491272	−	0.871006i	$-0.336532\pi$
$541$	631.800	−	869.598i	1.16784	−	1.60739i	0.676564	−	0.736383i	$-0.263468\pi$
$542$	−511.579	−	166.222i	−0.943872	−	0.306683i
$543$	157.973	−	51.3286i	0.290927	−	0.0945278i
$544$	−98.2193	+	71.3605i	−0.180550	+	0.131177i
$545$		0			0
$546$	−70.2245	+	22.8173i	−0.128616	+	0.0417899i
$547$	104.930	−	322.941i	0.191828	−	0.590386i	−0.808171	−	0.588948i	$-0.799542\pi$
$547$	104.930	−	322.941i	0.191828	−	0.590386i	0.999999	−	0.00143823i	$-0.000457802\pi$
$548$	−526.581	+	724.777i	−0.960915	+	1.32259i
$549$		−	365.837i		−	0.666369i
$550$		0			0
$551$	761.659			1.38232
$552$	−433.667	−	315.078i	−0.785629	−	0.570793i
$553$	−158.437	−	51.4792i	−0.286504	−	0.0930909i
$554$	−226.064	−	695.753i	−0.408057	−	1.25587i
$555$		0			0
$556$	−164.862	−	226.913i	−0.296514	−	0.408116i
$557$	−128.015	−	393.990i	−0.229830	−	0.707344i	−0.997765	−	0.0668164i	$-0.978716\pi$
$557$	−128.015	−	393.990i	−0.229830	−	0.707344i	0.767935	−	0.640527i	$-0.221284\pi$
$558$	429.700	−	1322.48i	0.770071	−	2.37003i
$559$	−327.244	−	237.757i	−0.585409	−	0.425325i
$560$		0			0
$561$	4.53112	+	91.7101i	0.00807686	+	0.163476i
$562$			432.475i			0.769528i
$563$	−649.518	−	471.902i	−1.15367	−	0.838193i	−0.164708	−	0.986342i	$-0.552668\pi$
$563$	−649.518	−	471.902i	−1.15367	−	0.838193i	−0.988965	+	0.148150i	$0.952668\pi$
$564$	42.8224	−	131.794i	0.0759262	−	0.233677i
$565$		0			0
$566$	474.827	−	344.982i	0.838918	−	0.609509i
$567$	185.865	−	135.039i	0.327805	−	0.238164i
$568$	−11.9176	−	36.6786i	−0.0209817	−	0.0645750i
$569$	−436.517	−	141.833i	−0.767165	−	0.249267i	−0.100814	−	0.994905i	$-0.532145\pi$
$569$	−436.517	−	141.833i	−0.767165	−	0.249267i	−0.666351	+	0.745638i	$0.732145\pi$
$570$		0			0
$571$			203.201i			0.355869i	0.984042	+	0.177935i	$0.0569416\pi$
$571$			203.201i			0.355869i	−0.984042	+	0.177935i	$0.943058\pi$
$572$	447.312	+	292.395i	0.782014	+	0.511180i
$573$		−	313.961i		−	0.547924i
$574$	−347.067	+	477.696i	−0.604646	+	0.832223i
$575$		0			0
$576$	−97.9271	−	301.388i	−0.170012	−	0.523244i
$577$	476.608	+	655.994i	0.826010	+	1.13690i	0.988653	+	0.150220i	$0.0479981\pi$
$577$	476.608	+	655.994i	0.826010	+	1.13690i	−0.162643	+	0.986685i	$0.552002\pi$
$578$	593.718	−	431.362i	1.02719	−	0.746300i
$579$	−7.84696	+	2.54963i	−0.0135526	+	0.00440351i
$580$		0			0
$581$	−245.230	−	178.170i	−0.422082	−	0.306661i
$582$	−185.351			−0.318473
$583$	−430.023	−	534.296i	−0.737604	−	0.916460i
$584$	2072.33			3.54851
$585$		0			0
$586$	55.5972	−	171.111i	0.0948758	−	0.291998i
$587$	56.4895	−	18.3545i	0.0962342	−	0.0312684i	−0.260504	−	0.965473i	$-0.583889\pi$
$587$	56.4895	−	18.3545i	0.0962342	−	0.0312684i	0.356738	+	0.934204i	$0.383889\pi$
$588$	−154.741	−	212.983i	−0.263165	−	0.362216i
$589$	−830.206	−	1142.68i	−1.40952	−	1.94003i
$590$		0			0
$591$	176.087	+	57.2141i	0.297947	+	0.0968090i
$592$	−277.279	+	381.641i	−0.468376	+	0.644665i
$593$	1164.75			1.96416			0.982081	−	0.188457i	$-0.0603486\pi$
$593$	1164.75			1.96416			0.982081	+	0.188457i	$0.0603486\pi$
$594$	595.459	+	161.464i	1.00246	+	0.271826i
$595$		0			0
$596$	599.157	−	824.669i	1.00530	−	1.38367i
$597$	161.062	+	52.3322i	0.269786	+	0.0876586i
$598$	−709.749	+	230.612i	−1.18687	+	0.385638i
$599$	196.571	−	142.817i	0.328165	−	0.238426i	−0.411487	−	0.911416i	$-0.634990\pi$
$599$	196.571	−	142.817i	0.328165	−	0.238426i	0.739651	+	0.672990i	$0.234990\pi$
$600$		0			0
$601$	−572.415	+	185.989i	−0.952438	+	0.309466i	−0.743706	−	0.668507i	$-0.766934\pi$
$601$	−572.415	+	185.989i	−0.952438	+	0.309466i	−0.208732	+	0.977973i	$0.566934\pi$
$602$	−301.260	+	927.181i	−0.500431	+	1.54017i
$603$	−173.457	+	238.743i	−0.287656	+	0.395925i
$604$		−	580.218i		−	0.960626i
$605$		0			0
$606$	−302.698			−0.499502
$607$	−186.849	−	135.753i	−0.307823	−	0.223646i	0.423139	−	0.906065i	$-0.360928\pi$
$607$	−186.849	−	135.753i	−0.307823	−	0.223646i	−0.730962	+	0.682418i	$0.760928\pi$
$608$	374.246	+	121.600i	0.615537	+	0.200000i
$609$	29.3672	+	90.3829i	0.0482220	+	0.148412i
$610$		0			0
$611$	−59.7326	−	82.2149i	−0.0977621	−	0.134558i
$612$	191.383	+	589.017i	0.312718	+	0.962447i
$613$	−217.900	+	670.628i	−0.355465	+	1.09401i	0.600274	+	0.799794i	$0.295058\pi$
$613$	−217.900	+	670.628i	−0.355465	+	1.09401i	−0.955739	+	0.294215i	$0.904942\pi$
$614$	−1110.23	−	806.633i	−1.80820	−	1.31373i
$615$		0			0
$616$	177.555	−	654.799i	0.288239	−	1.06299i
$617$			181.458i			0.294097i	0.989129	+	0.147049i	$0.0469774\pi$
$617$			181.458i			0.294097i	−0.989129	+	0.147049i	$0.953023\pi$
$618$	115.893	+	84.2011i	0.187529	+	0.136248i
$619$	−323.645	+	996.077i	−0.522852	+	1.60917i	0.245674	+	0.969352i	$0.420991\pi$
$619$	−323.645	+	996.077i	−0.522852	+	1.60917i	−0.768526	+	0.639819i	$0.779009\pi$
$620$		0			0
$621$	−473.121	+	343.743i	−0.761870	+	0.553531i
$622$	116.540	−	84.6710i	0.187363	−	0.136127i
$623$	127.762	+	393.210i	0.205075	+	0.631156i
$624$	−109.651	−	35.6277i	−0.175723	−	0.0570958i
$625$		0			0
$626$		−	1809.21i		−	2.89012i
$627$	231.852	−	186.604i	0.369780	−	0.297614i
$628$			1582.29i			2.51956i
$629$	−115.390	+	158.821i	−0.183450	+	0.252497i
$630$		0			0
$631$	−104.631	−	322.020i	−0.165817	−	0.510333i	0.833278	−	0.552854i	$-0.186461\pi$
$631$	−104.631	−	322.020i	−0.165817	−	0.510333i	−0.999096	+	0.0425205i	$0.986461\pi$
$632$	−391.868	−	539.360i	−0.620044	−	0.853418i
$633$	−102.214	+	74.2626i	−0.161475	+	0.117318i
$634$	590.197	−	191.767i	0.930911	−	0.302471i
$635$		0			0
$636$	395.362	+	287.247i	0.621638	+	0.451646i
$637$	−193.060			−0.303076
$638$	554.426	−	848.173i	0.869007	−	1.32942i
$639$	−19.9820			−0.0312707
$640$		0			0
$641$	−218.541	+	672.600i	−0.340937	+	1.04930i	0.622786	+	0.782393i	$0.286001\pi$
$641$	−218.541	+	672.600i	−0.340937	+	1.04930i	−0.963723	+	0.266905i	$0.913999\pi$
$642$	198.079	−	64.3596i	0.308534	−	0.100249i
$643$	576.696	+	793.754i	0.896884	+	1.23445i	0.971451	+	0.237238i	$0.0762422\pi$
$643$	576.696	+	793.754i	0.896884	+	1.23445i	−0.0745679	+	0.997216i	$0.523758\pi$
$644$	717.605	+	987.698i	1.11429	+	1.53369i
$645$		0			0
$646$	881.433	+	286.395i	1.36445	+	0.443336i
$647$	−203.966	+	280.736i	−0.315250	+	0.433904i	−0.937009	−	0.349304i	$-0.886418\pi$
$647$	−203.966	+	280.736i	−0.315250	+	0.433904i	0.621760	+	0.783208i	$0.286418\pi$
$648$	919.417			1.41885
$649$	−427.690	+	21.1309i	−0.658998	+	0.0325591i
$650$		0			0
$651$	103.587	−	142.575i	0.159120	−	0.219010i
$652$	290.286	+	94.3195i	0.445223	+	0.144662i
$653$	−1060.87	+	344.696i	−1.62460	+	0.527866i	−0.973022	−	0.230712i	$-0.925894\pi$
$653$	−1060.87	+	344.696i	−1.62460	+	0.527866i	−0.651582	+	0.758578i	$0.725894\pi$
$654$	−478.780	+	347.854i	−0.732079	+	0.531887i
$655$		0			0
$656$	−876.848	+	284.905i	−1.33666	+	0.434307i
$657$	331.798	−	1021.17i	0.505019	−	1.55429i
$658$	−143.965	+	198.150i	−0.218791	+	0.301141i
$659$		−	68.8178i		−	0.104428i	−0.998636	−	0.0522138i	$-0.983372\pi$
$659$		−	68.8178i		−	0.104428i	0.998636	−	0.0522138i	$-0.0166277\pi$
$660$		0			0
$661$	−56.9620			−0.0861754			−0.0430877	−	0.999071i	$-0.513719\pi$
$661$	−56.9620			−0.0861754			−0.0430877	+	0.999071i	$0.513719\pi$
$662$	278.360	+	202.241i	0.420484	+	0.305500i
$663$	−45.6314	−	14.8266i	−0.0688257	−	0.0223628i
$664$	−374.860	−	1153.70i	−0.564548	−	1.73750i
$665$		0			0
$666$	368.210	+	506.798i	0.552868	+	0.760958i
$667$	296.810	+	913.487i	0.444993	+	1.36955i
$668$	−400.905	+	1233.86i	−0.600157	+	1.84709i
$669$	30.4320	+	22.1101i	0.0454888	+	0.0330495i
$670$		0			0
$671$	−462.062	+	175.784i	−0.688617	+	0.261973i
$672$			49.0988i			0.0730637i
$673$	303.417	+	220.445i	0.450842	+	0.327556i	0.789928	−	0.613199i	$-0.210118\pi$
$673$	303.417	+	220.445i	0.450842	+	0.327556i	−0.339086	+	0.940755i	$0.610118\pi$
$674$	−169.186	+	520.701i	−0.251018	+	0.772554i
$675$		0			0
$676$	929.707	−	675.472i	1.37531	−	0.999218i
$677$	−470.259	+	341.663i	−0.694621	+	0.504672i	−0.878176	−	0.478338i	$-0.841240\pi$
$677$	−470.259	+	341.663i	−0.694621	+	0.504672i	0.183555	+	0.983009i	$0.441240\pi$
$678$	−73.6255	−	226.596i	−0.108592	−	0.334212i
$679$	211.483	+	68.7149i	0.311462	+	0.101200i
$680$		0			0
$681$			176.658i			0.259410i
$682$	−1876.80	+	92.7269i	−2.75190	+	0.135963i
$683$		−	688.418i		−	1.00793i	−0.863723	−	0.503966i	$-0.831874\pi$
$683$		−	688.418i		−	1.00793i	0.863723	−	0.503966i	$-0.168126\pi$
$684$	1179.92	−	1624.02i	1.72503	−	2.37430i
$685$		0			0
$686$	353.549	+	1088.11i	0.515377	+	1.58617i
$687$	125.303	+	172.465i	0.182392	+	0.251041i
$688$	−1231.52	+	894.749i	−1.78999	+	1.30051i
$689$	340.838	−	110.745i	0.494685	−	0.160733i
$690$		0			0
$691$	−479.696	−	348.519i	−0.694205	−	0.504369i	0.183835	−	0.982957i	$-0.441149\pi$
$691$	−479.696	−	348.519i	−0.694205	−	0.504369i	−0.878040	+	0.478588i	$0.841149\pi$
$692$	14.6320			0.0211445
$693$	−294.233	−	192.331i	−0.424578	−	0.277535i
$694$	−177.215			−0.255353
$695$		0			0
$696$	−117.526	+	361.707i	−0.168859	+	0.519695i
$697$	−364.902	+	118.564i	−0.523532	+	0.170106i
$698$	−320.478	−	441.100i	−0.459137	−	0.631948i
$699$	−103.210	−	142.056i	−0.147654	−	0.203228i
$700$		0			0
$701$	−563.333	−	183.038i	−0.803613	−	0.261110i	−0.121723	−	0.992564i	$-0.538842\pi$
$701$	−563.333	−	183.038i	−0.803613	−	0.261110i	−0.681890	+	0.731455i	$0.738842\pi$
$702$	−189.491	+	260.812i	−0.269930	+	0.371527i
$703$	636.300			0.905120
$704$	−333.608	+	268.501i	−0.473875	+	0.381394i
$705$		0			0
$706$	−1159.75	+	1596.26i	−1.64270	+	2.26099i
$707$	345.373	+	112.219i	0.488505	+	0.158725i
$708$	290.183	−	94.2860i	0.409862	−	0.133172i
$709$	−238.019	+	172.931i	−0.335711	+	0.243909i	−0.742850	−	0.669458i	$-0.766527\pi$
$709$	−238.019	+	172.931i	−0.335711	+	0.243909i	0.407139	+	0.913366i	$0.366527\pi$
$710$		0			0
$711$	−328.518	+	106.742i	−0.462051	+	0.150129i
$712$	−511.296	+	1573.61i	−0.718112	+	2.21012i
$713$	1046.94	−	1440.99i	1.46836	−	2.02102i
$714$			115.638i			0.161959i
$715$		0			0
$716$	−731.066			−1.02104
$717$	−84.1449	−	61.1349i	−0.117357	−	0.0852648i
$718$	−2281.87	−	741.424i	−3.17809	−	1.03262i
$719$	−184.687	−	568.407i	−0.256866	−	0.790552i	−0.993456	−	0.114213i	$-0.963565\pi$
$719$	−184.687	−	568.407i	−0.256866	−	0.790552i	0.736590	−	0.676339i	$-0.236435\pi$
$720$		0			0
$721$	−101.016	−	139.037i	−0.140105	−	0.192839i
$722$	−534.624	−	1645.40i	−0.740477	−	2.27895i
$723$	−33.8493	+	104.178i	−0.0468179	+	0.144091i
$724$	−1224.82	−	889.887i	−1.69175	−	1.22913i
$725$		0			0
$726$	−39.0299	−	394.020i	−0.0537602	−	0.542727i
$727$		−	165.031i		−	0.227003i	−0.993538	−	0.113502i	$-0.963793\pi$
$727$		−	165.031i		−	0.227003i	0.993538	−	0.113502i	$-0.0362067\pi$
$728$	286.803	+	208.375i	0.393960	+	0.286229i
$729$	106.214	−	326.894i	0.145699	−	0.448415i
$730$		0			0
$731$	−512.498	+	372.351i	−0.701091	+	0.509372i
$732$	284.981	−	207.051i	0.389318	−	0.282856i
$733$	−11.4769	−	35.3224i	−0.0156575	−	0.0481888i	0.942923	−	0.333012i	$-0.108065\pi$
$733$	−11.4769	−	35.3224i	−0.0156575	−	0.0481888i	−0.958580	+	0.284823i	$0.908065\pi$
$734$	−1510.49	−	490.788i	−2.05789	−	0.668649i
$735$		0			0
$736$			496.235i			0.674232i
$737$	384.884	+	104.365i	0.522231	+	0.141608i
$738$			1224.33i			1.65898i
$739$	152.133	−	209.393i	0.205864	−	0.283347i	−0.693584	−	0.720376i	$-0.743969\pi$
$739$	152.133	−	209.393i	0.205864	−	0.283347i	0.899447	+	0.437029i	$0.143969\pi$
$740$		0			0
$741$	48.0565	+	147.903i	0.0648536	+	0.199599i
$742$	−507.697	−	698.785i	−0.684228	−	0.941758i
$743$	453.181	−	329.255i	0.609933	−	0.443143i	−0.239457	−	0.970907i	$-0.576970\pi$
$743$	453.181	−	329.255i	0.609933	−	0.443143i	0.849391	+	0.527764i	$0.176970\pi$
$744$	670.756	−	217.942i	0.901553	−	0.292932i
$745$		0			0
$746$	1131.29	+	821.932i	1.51648	+	1.10179i
$747$	−628.519			−0.841391
$748$	651.986	−	524.744i	0.871639	−	0.701530i
$749$	−249.864			−0.333597
$750$		0			0
$751$	−231.599	+	712.788i	−0.308387	+	0.949119i	0.670004	+	0.742358i	$0.266292\pi$
$751$	−231.599	+	712.788i	−0.308387	+	0.949119i	−0.978391	+	0.206761i	$0.933708\pi$
$752$	−363.720	+	118.180i	−0.483671	+	0.157154i
$753$	−100.322	−	138.081i	−0.133229	−	0.183374i
$754$	311.222	+	428.360i	0.412761	+	0.568116i
$755$		0			0
$756$	501.584	+	162.975i	0.663471	+	0.215575i
$757$	−503.392	+	692.859i	−0.664982	+	0.915270i	−0.999633	−	0.0270725i	$-0.991382\pi$
$757$	−503.392	+	692.859i	−0.664982	+	0.915270i	0.334651	+	0.942342i	$0.391382\pi$
$758$	−1874.75			−2.47329
$759$	314.151	+	205.352i	0.413902	+	0.270556i
$760$		0			0
$761$	−94.4945	+	130.061i	−0.124172	+	0.170907i	−0.866577	−	0.499043i	$-0.833685\pi$
$761$	−94.4945	+	130.061i	−0.124172	+	0.170907i	0.742405	+	0.669951i	$0.233685\pi$
$762$	−363.891	−	118.235i	−0.477548	−	0.155165i
$763$	675.238	−	219.398i	0.884978	−	0.287547i
$764$	−2315.11	+	1682.03i	−3.03025	+	2.20161i
$765$		0			0
$766$	2074.18	−	673.942i	2.70781	−	0.879820i
$767$	69.1436	−	212.802i	0.0901481	−	0.277447i
$768$	283.118	−	389.678i	0.368643	−	0.507393i
$769$		−	81.4227i		−	0.105881i	−0.998598	−	0.0529407i	$-0.983141\pi$
$769$		−	81.4227i		−	0.105881i	0.998598	−	0.0529407i	$-0.0168594\pi$
$770$		0			0
$771$	372.159			0.482697
$772$	60.8404	+	44.2031i	0.0788088	+	0.0572579i
$773$	433.209	+	140.758i	0.560426	+	0.182094i	0.575513	−	0.817793i	$-0.304802\pi$
$773$	433.209	+	140.758i	0.560426	+	0.182094i	−0.0150867	+	0.999886i	$0.504802\pi$
$774$	624.660	+	1922.51i	0.807055	+	2.48386i
$775$		0			0
$776$	523.068	+	719.942i	0.674057	+	0.927760i
$777$	24.5337	+	75.5070i	0.0315749	+	0.0971776i
$778$	−13.8376	+	42.5877i	−0.0177861	+	0.0547400i
$779$	1006.10	+	730.972i	1.29152	+	0.938346i
$780$		0			0
$781$	9.60130	+	25.2378i	0.0122936	+	0.0323147i
$782$			1168.74i			1.49456i
$783$	335.679	+	243.885i	0.428709	+	0.311476i
$784$	−224.514	+	690.982i	−0.286369	+	0.881354i
$785$		0			0
$786$	−110.252	+	80.1031i	−0.140270	+	0.101912i
$787$	96.6224	−	70.2003i	0.122773	−	0.0891999i	−0.524704	−	0.851285i	$-0.675824\pi$
$787$	96.6224	−	70.2003i	0.122773	−	0.0891999i	0.647477	+	0.762085i	$0.275824\pi$
$788$	−521.486	−	1604.97i	−0.661784	−	2.03676i
$789$	−64.3694	−	20.9149i	−0.0815836	−	0.0265081i
$790$		0			0
$791$			285.837i			0.361362i
$792$	−500.202	−	1314.82i	−0.631568	−	1.66013i
$793$		−	258.323i		−	0.325754i
$794$	499.414	−	687.385i	0.628985	−	0.865724i
$795$		0			0
$796$	−476.989	−	1468.02i	−0.599233	−	1.84425i
$797$	−806.080	−	1109.47i	−1.01139	−	1.39206i	−0.918066	−	0.396427i	$-0.870250\pi$
$797$	−806.080	−	1109.47i	−1.01139	−	1.39206i	−0.0933265	−	0.995636i	$-0.529750\pi$
$798$	303.230	−	220.309i	0.379987	−	0.276077i
$799$	−151.363	+	49.1808i	−0.189440	+	0.0615529i
$800$		0			0
$801$	693.553	+	503.895i	0.865858	+	0.629083i
$802$	−2537.95			−3.16453
$803$	−1449.19	+	71.6002i	−1.80472	+	0.0891659i
$804$	−284.147			−0.353417
$805$		0			0
$806$	303.417	−	933.822i	0.376448	−	1.15859i
$807$	−176.511	+	57.3519i	−0.218725	+	0.0710680i
$808$	854.225	+	1175.74i	1.05721	+	1.45512i
$809$	7.99326	+	11.0018i	0.00988042	+	0.0135992i	0.813929	−	0.580965i	$-0.197325\pi$
$809$	7.99326	+	11.0018i	0.00988042	+	0.0135992i	−0.804048	+	0.594564i	$0.797325\pi$
$810$		0			0
$811$	−203.261	−	66.0435i	−0.250630	−	0.0814346i	0.181008	−	0.983482i	$-0.442064\pi$
$811$	−203.261	−	66.0435i	−0.250630	−	0.0814346i	−0.431638	+	0.902047i	$0.642064\pi$
$812$	509.141	−	700.772i	0.627020	−	0.863020i
$813$	−141.356			−0.173869
$814$	463.175	−	708.575i	0.569011	−	0.870485i
$815$		0			0
$816$	−106.132	+	146.078i	−0.130063	+	0.179017i
$817$	1952.78	+	634.495i	2.39018	+	0.776616i
$818$	−359.505	+	116.810i	−0.439492	+	0.142800i
$819$	148.599	−	107.963i	0.181439	−	0.131823i
$820$		0			0
$821$	1240.59	−	403.092i	1.51107	−	0.490977i	0.567848	−	0.823134i	$-0.307776\pi$
$821$	1240.59	−	403.092i	1.51107	−	0.490977i	0.943224	+	0.332157i	$0.107776\pi$
$822$	−107.180	+	329.865i	−0.130389	+	0.401296i
$823$	168.077	−	231.338i	0.204225	−	0.281091i	−0.694603	−	0.719393i	$-0.744420\pi$
$823$	168.077	−	231.338i	0.204225	−	0.281091i	0.898828	+	0.438302i	$0.144420\pi$
$824$		−	687.770i		−	0.834672i
$825$		0			0
$826$	−539.279			−0.652881
$827$	452.602	+	328.834i	0.547282	+	0.397623i	0.826782	−	0.562522i	$-0.190169\pi$
$827$	452.602	+	328.834i	0.547282	+	0.397623i	−0.279501	+	0.960146i	$0.590169\pi$
$828$	2407.55	+	782.262i	2.90767	+	0.944761i
$829$	279.385	+	859.857i	0.337014	+	1.03722i	0.965721	+	0.259580i	$0.0835843\pi$
$829$	279.385	+	859.857i	0.337014	+	1.03722i	−0.628707	+	0.777642i	$0.716416\pi$
$830$		0			0
$831$	−112.999	−	155.530i	−0.135980	−	0.187160i
$832$	−69.1477	−	212.815i	−0.0831103	−	0.255787i
$833$	−93.4317	+	287.553i	−0.112163	+	0.345202i
$834$	−87.8501	−	63.8268i	−0.105336	−	0.0765310i
$835$		0			0
$836$	−2618.13	−	709.932i	−3.13174	−	0.849201i
$837$		−	769.439i		−	0.919281i
$838$	84.1466	+	61.1361i	0.100414	+	0.0729548i
$839$	49.7340	−	153.066i	0.0592778	−	0.182438i	−0.917033	−	0.398811i	$-0.869423\pi$
$839$	49.7340	−	153.066i	0.0592778	−	0.182438i	0.976311	+	0.216373i	$0.0694228\pi$
$840$		0			0
$841$	−129.060	+	93.7676i	−0.153460	+	0.111495i
$842$	1179.69	−	857.096i	1.40106	−	1.01793i
$843$	35.1196	+	108.087i	0.0416603	+	0.128217i
$844$	1095.21	+	355.855i	1.29764	+	0.421629i
$845$		0			0
$846$			507.856i			0.600303i
$847$	−101.542	+	464.039i	−0.119884	+	0.547862i
$848$		−	1348.68i		−	1.59043i
$849$	90.6575	−	124.779i	0.106782	−	0.146972i
$850$		0			0
$851$	247.959	+	763.139i	0.291374	+	0.896756i
$852$	−11.3091	−	15.5656i	−0.0132736	−	0.0182695i
$853$	−1183.22	+	859.656i	−1.38712	+	1.00780i	−0.390948	+	0.920413i	$0.627853\pi$
$853$	−1183.22	+	859.656i	−1.38712	+	1.00780i	−0.996174	+	0.0873903i	$0.972147\pi$
$854$	−592.125	+	192.393i	−0.693355	+	0.225285i
$855$		0			0
$856$	−808.971	−	587.752i	−0.945059	−	0.686626i
$857$	874.204			1.02007			0.510037	−	0.860152i	$-0.329632\pi$
$857$	874.204			1.02007			0.510037	+	0.860152i	$0.329632\pi$
$858$	199.684	+	54.1462i	0.232732	+	0.0631075i
$859$	−984.004			−1.14552			−0.572761	−	0.819722i	$-0.694128\pi$
$859$	−984.004			−1.14552			−0.572761	+	0.819722i	$0.694128\pi$
$860$		0			0
$861$	−47.9494	+	147.573i	−0.0556904	+	0.171397i
$862$	−658.463	+	213.948i	−0.763878	+	0.248199i
$863$	806.939	+	1110.66i	0.935039	+	1.28697i	0.957861	+	0.287232i	$0.0927350\pi$
$863$	806.939	+	1110.66i	0.935039	+	1.28697i	−0.0228217	+	0.999740i	$0.507265\pi$
$864$	126.002	+	173.427i	0.145835	+	0.200725i
$865$		0			0
$866$	−281.911	−	91.5985i	−0.325533	−	0.105772i
$867$	113.357	−	156.023i	0.130746	−	0.179957i
$868$	−1606.30			−1.85057
$869$	292.670	+	363.638i	0.336790	+	0.418456i
$870$		0			0
$871$	−122.480	+	168.580i	−0.140620	+	0.193547i
$872$	2702.27	+	878.020i	3.09893	+	1.00690i
$873$	438.508	−	142.480i	0.502300	−	0.163207i
$874$	3064.70	−	2226.64i	3.50653	−	2.54764i
$875$		0			0
$876$	983.260	−	319.481i	1.12244	−	0.364704i
$877$	−250.622	+	771.335i	−0.285772	+	0.879516i	0.700394	+	0.713756i	$0.253008\pi$
$877$	−250.622	+	771.335i	−0.285772	+	0.879516i	−0.986166	+	0.165760i	$0.946992\pi$
$878$	−289.838	+	398.927i	−0.330111	+	0.454359i
$879$		−	47.2800i		−	0.0537884i
$880$		0			0
$881$	−348.997			−0.396137			−0.198069	−	0.980188i	$-0.563467\pi$
$881$	−348.997			−0.396137			−0.198069	+	0.980188i	$0.563467\pi$
$882$	780.543	+	567.098i	0.884970	+	0.642968i
$883$	929.644	+	302.060i	1.05282	+	0.342084i	0.783776	−	0.621043i	$-0.213291\pi$
$883$	929.644	+	302.060i	1.05282	+	0.342084i	0.269049	+	0.963127i	$0.413291\pi$
$884$	135.139	+	415.914i	0.152872	+	0.470491i
$885$		0			0
$886$	−613.519	−	844.436i	−0.692459	−	0.953088i
$887$	−4.68686	−	14.4247i	−0.00528395	−	0.0162623i	0.948380	−	0.317137i	$-0.102721\pi$
$887$	−4.68686	−	14.4247i	−0.00528395	−	0.0162623i	−0.953664	+	0.300875i	$0.902721\pi$
$888$	−98.1827	+	302.175i	−0.110566	+	0.340287i
$889$	371.360	+	269.809i	0.417728	+	0.303497i
$890$		0			0
$891$	−642.952	+	31.7663i	−0.721608	+	0.0356525i
$892$		−	342.856i		−	0.384368i
$893$	417.333	+	303.210i	0.467338	+	0.339541i
$894$	121.952	−	375.329i	0.136411	−	0.419831i
$895$		0			0
$896$	−607.652	+	441.485i	−0.678184	+	0.492729i
$897$	−158.659	+	115.272i	−0.176877	+	0.128509i
$898$	−717.807	−	2209.18i	−0.799340	−	2.46011i
$899$	−1201.88	−	390.515i	−1.33691	−	0.434388i
$900$		0			0
$901$		−	561.257i		−	0.622926i
$902$	1546.36	−	588.287i	1.71437	−	0.652203i
$903$			256.192i			0.283712i
$904$	−672.370	+	925.438i	−0.743773	+	1.02372i
$905$		0			0
$906$	−69.4156	−	213.639i	−0.0766177	−	0.235805i
$907$	327.095	+	450.207i	0.360634	+	0.496369i	0.950325	−	0.311259i	$-0.100751\pi$
$907$	327.095	+	450.207i	0.360634	+	0.496369i	−0.589692	+	0.807629i	$0.700751\pi$
$908$	1302.66	−	946.436i	1.43464	−	1.04233i
$909$	716.130	−	232.685i	0.787821	−	0.255979i
$910$		0			0
$911$	264.619	+	192.257i	0.290471	+	0.211039i	0.723472	−	0.690354i	$-0.242545\pi$
$911$	264.619	+	192.257i	0.290471	+	0.211039i	−0.433001	+	0.901394i	$0.642545\pi$
$912$	585.246			0.641717
$913$	302.002	+	793.837i	0.330780	+	0.869482i
$914$	−523.660			−0.572932
$915$		0			0
$916$	600.434	−	1847.94i	0.655495	−	2.01741i
$917$	155.492	−	50.5226i	0.169567	−	0.0550955i
$918$	296.762	+	408.458i	0.323270	+	0.444943i
$919$	−312.999	−	430.806i	−0.340586	−	0.468776i	0.604026	−	0.796964i	$-0.293562\pi$
$919$	−312.999	−	430.806i	−0.340586	−	0.468776i	−0.944612	+	0.328188i	$0.893562\pi$
$920$		0			0
$921$	−342.981	−	111.441i	−0.372401	−	0.121000i
$922$	1038.77	−	1429.75i	1.12665	−	1.55070i
$923$	−14.1096			−0.0152866
$924$	−16.7023	−	338.056i	−0.0180761	−	0.365861i
$925$		0			0
$926$	−827.113	+	1138.42i	−0.893210	+	1.22940i
$927$	−338.907	−	110.118i	−0.365596	−	0.118789i
$928$	334.847	−	108.798i	0.360826	−	0.117240i
$929$	617.340	−	448.524i	0.664521	−	0.482803i	−0.203666	−	0.979041i	$-0.565286\pi$
$929$	617.340	−	448.524i	0.664521	−	0.482803i	0.868187	+	0.496238i	$0.165286\pi$
$930$		0			0
$931$	932.031	−	302.835i	1.00111	−	0.325279i
$932$	−494.566	+	1522.12i	−0.530650	+	1.63317i
$933$	22.2506	−	30.6253i	0.0238484	−	0.0328246i
$934$			2219.26i			2.37608i
$935$		0			0
$936$	735.071			0.785332
$937$	−1280.72	−	930.495i	−1.36683	−	0.993058i	−0.997977	−	0.0635691i	$-0.979752\pi$
$937$	−1280.72	−	930.495i	−1.36683	−	0.993058i	−0.368850	−	0.929489i	$-0.620248\pi$
$938$	477.638	+	155.194i	0.509209	+	0.165452i
$939$	−146.919	−	452.172i	−0.156464	−	0.481546i
$940$		0			0
$941$	−325.495	−	448.005i	−0.345903	−	0.476094i	0.600251	−	0.799812i	$-0.295067\pi$
$941$	−325.495	−	448.005i	−0.345903	−	0.476094i	−0.946154	+	0.323717i	$0.895067\pi$
$942$	189.300	+	582.606i	0.200956	+	0.618477i
$943$	−484.619	+	1491.50i	−0.513912	+	1.58166i
$944$	−681.233	−	494.945i	−0.721645	−	0.524306i
$945$		0			0
$946$	2128.03	−	1712.72i	2.24950	−	1.81049i
$947$		−	945.630i		−	0.998553i	−0.866443	−	0.499276i	$-0.833599\pi$
$947$		−	945.630i		−	0.998553i	0.866443	−	0.499276i	$-0.166401\pi$
$948$	−269.080	−	195.498i	−0.283840	−	0.206222i
$949$	234.287	−	721.062i	0.246878	−	0.759813i
$950$		0			0
$951$	131.934	−	95.8555i	0.138732	−	0.100794i
$952$	449.163	−	326.336i	0.471810	−	0.342790i
$953$	−195.755	−	602.472i	−0.205409	−	0.632185i	−0.999696	−	0.0246421i	$-0.992155\pi$
$953$	−195.755	−	602.472i	−0.205409	−	0.632185i	0.794287	−	0.607543i	$-0.207845\pi$
$954$	−1703.32	−	553.441i	−1.78545	−	0.580127i
$955$		0			0
$956$			948.003i			0.991635i
$957$	69.6892	−	257.004i	0.0728205	−	0.268552i
$958$		−	340.353i		−	0.355275i
$959$	244.580	−	336.636i	0.255037	−	0.351028i
$960$		0			0
$961$	427.212	+	1314.82i	0.444549	+	1.36818i
$962$	259.999	+	357.857i	0.270269	+	0.371993i
$963$	−419.145	+	304.527i	−0.435249	+	0.316227i
$964$	949.540	−	308.524i	0.985000	−	0.320046i
$965$		0			0
$966$	382.391	+	277.823i	0.395850	+	0.287602i
$967$	855.136			0.884318			0.442159	−	0.896937i	$-0.354213\pi$
$967$	855.136			0.884318			0.442159	+	0.896937i	$0.354213\pi$
$968$	−1420.31	+	1263.54i	−1.46726	+	1.30531i
$969$	243.551			0.251343
$970$		0			0
$971$	306.329	−	942.784i	0.315478	−	0.970942i	−0.660079	−	0.751196i	$-0.729477\pi$
$971$	306.329	−	942.784i	0.315478	−	0.970942i	0.975557	−	0.219746i	$-0.0705227\pi$
$972$	1586.14	−	515.368i	1.63183	−	0.530214i
$973$	76.5730	+	105.394i	0.0786979	+	0.108318i
$974$	1659.33	+	2283.88i	1.70363	+	2.34484i
$975$		0			0
$976$	−924.565	−	300.409i	−0.947300	−	0.307796i
$977$	−33.7732	+	46.4848i	−0.0345682	+	0.0475791i	−0.825951	−	0.563742i	$-0.809361\pi$
$977$	−33.7732	+	46.4848i	−0.0345682	+	0.0475791i	0.791383	+	0.611321i	$0.209361\pi$
$978$	118.169			0.120827
$979$	303.183	−	1118.10i	0.309686	−	1.14208i
$980$		0			0
$981$	865.312	−	1191.00i	0.882071	−	1.21407i
$982$	2824.26	+	917.657i	2.87603	+	0.934477i
$983$	−673.476	+	218.826i	−0.685123	+	0.222610i	−0.630837	−	0.775915i	$-0.717288\pi$
$983$	−673.476	+	218.826i	−0.685123	+	0.222610i	−0.0542862	+	0.998525i	$0.517288\pi$
$984$	−502.378	+	364.999i	−0.510546	+	0.370934i
$985$		0			0
$986$	788.638	−	256.244i	0.799835	−	0.259882i
$987$	−19.8896	+	61.2140i	−0.0201516	+	0.0620203i
$988$	833.159	−	1146.74i	0.843278	−	1.16067i
$989$			2589.30i			2.61810i
$990$		0			0
$991$	1006.83			1.01598			0.507989	−	0.861363i	$-0.330389\pi$
$991$	1006.83			1.01598			0.507989	+	0.861363i	$0.330389\pi$
$992$	−528.207	−	383.765i	−0.532467	−	0.386860i
$993$	85.9930	+	27.9408i	0.0865992	+	0.0281378i
$994$	10.5085	+	32.3418i	0.0105719	+	0.0325370i
$995$		0			0
$996$	−355.720	−	489.606i	−0.357148	−	0.491573i
$997$	−174.686	−	537.627i	−0.175211	−	0.539245i	0.824432	−	0.565961i	$-0.191495\pi$
$997$	−174.686	−	537.627i	−0.175211	−	0.539245i	−0.999643	+	0.0267164i	$0.991495\pi$
$998$	779.456	−	2398.92i	0.781018	−	2.40373i
$999$	280.431	+	203.745i	0.280712	+	0.203949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.q.f.249.1		24
5.2	odd	4		55.3.i.d.51.3	yes	12
5.3	odd	4		275.3.x.f.51.1		12
5.4	even	2	inner	275.3.q.f.249.6		24
11.8	odd	10	inner	275.3.q.f.74.6		24
55.8	even	20		275.3.x.f.151.1		12
55.17	even	20		605.3.c.d.241.2		12
55.19	odd	10	inner	275.3.q.f.74.1		24
55.27	odd	20		605.3.c.d.241.11		12
55.52	even	20		55.3.i.d.41.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.d.41.3	✓	12	55.52	even	20
55.3.i.d.51.3	yes	12	5.2	odd	4
275.3.q.f.74.1		24	55.19	odd	10	inner
275.3.q.f.74.6		24	11.8	odd	10	inner
275.3.q.f.249.1		24	1.1	even	1	trivial
275.3.q.f.249.6		24	5.4	even	2	inner
275.3.x.f.51.1		12	5.3	odd	4
275.3.x.f.151.1		12	55.8	even	20
605.3.c.d.241.2		12	55.17	even	20
605.3.c.d.241.11		12	55.27	odd	20

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.q (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.85483 - 2.07416i) q^{2} +(-0.881935 - 0.286558i) q^{3} +(2.61187 + 8.03851i) q^{4} +(1.92341 + 2.64735i) q^{6} +(-1.21313 - 3.73363i) q^{7} +(4.85489 - 14.9418i) q^{8} +(-6.58546 - 4.78462i) q^{9} +(-2.87880 + 10.6166i) q^{11} -7.83789i q^{12} +(-4.65009 - 3.37849i) q^{13} +(-4.28086 + 13.1751i) q^{14} +(-17.4997 + 12.7143i) q^{16} +(-7.28252 + 5.29106i) q^{17} +(8.87634 + 27.3186i) q^{18} +(27.7487 + 9.01609i) q^{19} +3.64045i q^{21} +(30.2390 - 24.3376i) q^{22} +36.7936i q^{23} +(-8.56339 + 11.7865i) q^{24} +(6.26771 + 19.2900i) q^{26} +(9.34246 + 12.8588i) q^{27} +(26.8443 - 19.5035i) q^{28} +(24.8274 - 8.06690i) q^{29} +(-39.1642 - 28.4544i) q^{31} +13.4870 q^{32} +(5.58119 - 8.53822i) q^{33} +31.7649 q^{34} +(21.2608 - 65.4341i) q^{36} +(20.7411 - 6.73919i) q^{37} +(-60.5170 - 83.2945i) q^{38} +(3.13294 + 4.31213i) q^{39} +(40.5371 + 13.1713i) q^{41} +(7.55087 - 10.3929i) q^{42} +70.3737 q^{43} +(-92.8608 + 4.58797i) q^{44} +(76.3156 - 105.039i) q^{46} +(16.8149 + 5.46351i) q^{47} +(19.0769 - 6.19847i) q^{48} +(27.1735 - 19.7427i) q^{49} +(7.93890 - 2.57951i) q^{51} +(15.0126 - 46.2040i) q^{52} +(-36.6485 + 50.4423i) q^{53} -56.0874i q^{54} -61.6768 q^{56} +(-21.8889 - 15.9032i) q^{57} +(-87.6100 - 28.4662i) q^{58} +(12.0295 + 37.0230i) q^{59} +(26.4166 + 36.3594i) q^{61} +(52.7881 + 162.465i) q^{62} +(-9.87498 + 30.3921i) q^{63} +(31.4956 + 22.8829i) q^{64} +(-33.6430 + 12.7989i) q^{66} -36.2530i q^{67} +(-61.5533 - 44.7211i) q^{68} +(10.5435 - 32.4495i) q^{69} +(1.98595 - 1.44287i) q^{71} +(-103.462 + 75.1699i) q^{72} +(40.7610 + 125.450i) q^{73} +(-73.1905 - 23.7810i) q^{74} +246.607i q^{76} +(43.1309 - 2.13097i) q^{77} -18.8086i q^{78} +(24.9427 - 34.3307i) q^{79} +(18.0841 + 55.6573i) q^{81} +(-88.4072 - 121.682i) q^{82} +(62.4666 - 45.3846i) q^{83} +(-29.2638 + 9.50839i) q^{84} +(-200.905 - 145.966i) q^{86} -24.2077 q^{87} +(144.655 + 94.5569i) q^{88} -105.316 q^{89} +(-6.97287 + 21.4603i) q^{91} +(-295.766 + 96.1001i) q^{92} +(26.3864 + 36.3177i) q^{93} +(-36.6717 - 50.4742i) q^{94} +(-11.8946 - 3.86481i) q^{96} +(-33.2937 + 45.8248i) q^{97} -118.525 q^{98} +(69.7546 - 56.1413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 26 q^{4} + 40 q^{6} - 8 q^{9} + 24 q^{11} + 120 q^{14} - 86 q^{16} + 160 q^{19} - 420 q^{24} - 240 q^{26} - 10 q^{29} - 92 q^{31} - 20 q^{34} - 78 q^{36} + 570 q^{39} + 460 q^{41} - 976 q^{44} + 410 q^{46}+ \cdots - 1338 q^{99}+O(q^{100}) \) 24 * q - 26 * q^4 + 40 * q^6 - 8 * q^9 + 24 * q^11 + 120 * q^14 - 86 * q^16 + 160 * q^19 - 420 * q^24 - 240 * q^26 - 10 * q^29 - 92 * q^31 - 20 * q^34 - 78 * q^36 + 570 * q^39 + 460 * q^41 - 976 * q^44 + 410 * q^46 + 424 * q^49 + 720 * q^51 - 820 * q^56 + 148 * q^59 - 580 * q^61 + 14 * q^64 + 370 * q^66 + 146 * q^69 - 552 * q^71 + 200 * q^74 - 470 * q^79 - 60 * q^81 + 1160 * q^84 - 960 * q^86 + 228 * q^89 + 320 * q^91 - 750 * q^94 + 530 * q^96 - 1338 * q^99

Introduction

L-functions

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