LMFDB - Embedded newform 375.2.i.c.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (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:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.1
Root			$2.53767i$ of defining polynomial
Character	$\chi$	$=$	375.49
Dual form			375.2.i.c.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49161 + 2.05302i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.37197 - 4.22249i) q^{4} +(-0.784184 + 2.41347i) q^{6} -1.04054i q^{7} +(5.88835 + 1.91324i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.49161 + 2.05302i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.37197 - 4.22249i) q^{4} +(-0.784184 + 2.41347i) q^{6} -1.04054i q^{7} +(5.88835 + 1.91324i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-2.40360 - 1.74631i) q^{11} +(-2.60964 - 3.59186i) q^{12} +(-3.33228 - 4.58650i) q^{13} +(2.13624 + 1.55207i) q^{14} +(-5.52731 + 4.01583i) q^{16} +(4.83480 + 1.57092i) q^{17} +2.53767i q^{18} +(1.65990 - 5.10866i) q^{19} +(-0.321543 - 0.989608i) q^{21} +(7.17044 - 2.32982i) q^{22} +(2.26908 - 3.12312i) q^{23} +6.19138 q^{24} +14.3866 q^{26} +(0.587785 - 0.809017i) q^{27} +(-4.39365 + 1.42758i) q^{28} +(-0.210038 - 0.646430i) q^{29} +(0.262699 - 0.808503i) q^{31} -4.95495i q^{32} +(-2.82560 - 0.918092i) q^{33} +(-10.4368 + 7.58275i) q^{34} +(-3.59186 - 2.60964i) q^{36} +(-0.950818 - 1.30869i) q^{37} +(8.01226 + 11.0279i) q^{38} +(-4.58650 - 3.33228i) q^{39} +(-0.942740 + 0.684941i) q^{41} +(2.51130 + 0.815972i) q^{42} +5.68601i q^{43} +(-4.07613 + 12.5450i) q^{44} +(3.02725 + 9.31693i) q^{46} +(3.12556 - 1.01555i) q^{47} +(-4.01583 + 5.52731i) q^{48} +5.91729 q^{49} +5.08361 q^{51} +(-14.7946 + 20.3631i) q^{52} +(-12.0652 + 3.92023i) q^{53} +(0.784184 + 2.41347i) q^{54} +(1.99080 - 6.12704i) q^{56} -5.37156i q^{57} +(1.64043 + 0.533007i) q^{58} +(2.59846 - 1.88789i) q^{59} +(4.38562 + 3.18634i) q^{61} +(1.26803 + 1.74530i) q^{62} +(-0.611611 - 0.841811i) q^{63} +(-0.881995 - 0.640807i) q^{64} +(6.09954 - 4.43157i) q^{66} +(0.883665 + 0.287120i) q^{67} -22.5702i q^{68} +(1.19292 - 3.67145i) q^{69} +(-0.436821 - 1.34440i) q^{71} +(5.88835 - 1.91324i) q^{72} +(6.65571 - 9.16080i) q^{73} +4.10501 q^{74} -23.8486 q^{76} +(-1.81710 + 2.50103i) q^{77} +(13.6825 - 4.44571i) q^{78} +(0.447171 + 1.37625i) q^{79} +(0.309017 - 0.951057i) q^{81} -2.95713i q^{82} +(-10.9140 - 3.54616i) q^{83} +(-3.73746 + 2.71542i) q^{84} +(-11.6735 - 8.48129i) q^{86} +(-0.399516 - 0.549886i) q^{87} +(-10.8121 - 14.8816i) q^{88} +(7.33961 + 5.33254i) q^{89} +(-4.77241 + 3.46736i) q^{91} +(-16.3004 - 5.29633i) q^{92} -0.850111i q^{93} +(-2.57715 + 7.93164i) q^{94} +(-1.53117 - 4.71244i) q^{96} +(-5.73419 + 1.86315i) q^{97} +(-8.82627 + 12.1483i) q^{98} -2.97101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	−1.49161	+	2.05302i	−1.05473	+	1.45171i	−0.170086	+	0.985429i	$0.554405\pi$
$2$	−1.49161	+	2.05302i	−1.05473	+	1.45171i	−0.884639	+	0.466276i	$0.845595\pi$
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$	−1.37197	−	4.22249i	−0.685985	−	2.11124i
$5$		0			0
$5$		0			0
$6$	−0.784184	+	2.41347i	−0.320142	+	0.985295i
$7$		−	1.04054i		−	0.393285i	−0.980475	−	0.196643i	$-0.936996\pi$
$7$		−	1.04054i		−	0.393285i	0.980475	−	0.196643i	$-0.0630039\pi$
$8$	5.88835	+	1.91324i	2.08185	+	0.676433i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	−2.40360	−	1.74631i	−0.724711	−	0.526533i	0.163175	−	0.986597i	$-0.447827\pi$
$11$	−2.40360	−	1.74631i	−0.724711	−	0.526533i	−0.887886	+	0.460064i	$0.847827\pi$
$12$	−2.60964	−	3.59186i	−0.753338	−	1.03688i
$13$	−3.33228	−	4.58650i	−0.924209	−	1.27207i	−0.962076	−	0.272782i	$-0.912056\pi$
$13$	−3.33228	−	4.58650i	−0.924209	−	1.27207i	0.0378663	−	0.999283i	$-0.487944\pi$
$14$	2.13624	+	1.55207i	0.570934	+	0.414808i
$15$		0			0
$16$	−5.52731	+	4.01583i	−1.38183	+	1.00396i
$17$	4.83480	+	1.57092i	1.17261	+	0.381005i	0.829617	−	0.558333i	$-0.188559\pi$
$17$	4.83480	+	1.57092i	1.17261	+	0.381005i	0.342995	+	0.939337i	$0.388559\pi$
$18$			2.53767i			0.598135i
$19$	1.65990	−	5.10866i	0.380808	−	1.17201i	−0.558668	−	0.829391i	$-0.688687\pi$
$19$	1.65990	−	5.10866i	0.380808	−	1.17201i	0.939476	−	0.342615i	$-0.111313\pi$
$20$		0			0
$21$	−0.321543	−	0.989608i	−0.0701665	−	0.215950i
$22$	7.17044	−	2.32982i	1.52874	−	0.496719i
$23$	2.26908	−	3.12312i	0.473135	−	0.651215i	−0.504032	−	0.863685i	$-0.668151\pi$
$23$	2.26908	−	3.12312i	0.473135	−	0.651215i	0.977168	+	0.212470i	$0.0681507\pi$
$24$	6.19138			1.26381
$25$		0			0
$26$	14.3866			2.82145
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	−4.39365	+	1.42758i	−0.830322	+	0.269788i
$29$	−0.210038	−	0.646430i	−0.0390030	−	0.120039i	0.929659	−	0.368421i	$-0.120101\pi$
$29$	−0.210038	−	0.646430i	−0.0390030	−	0.120039i	−0.968662	+	0.248382i	$0.920101\pi$
$30$		0			0
$31$	0.262699	−	0.808503i	0.0471821	−	0.145212i	−0.924690	−	0.380721i	$-0.875676\pi$
$31$	0.262699	−	0.808503i	0.0471821	−	0.145212i	0.971872	+	0.235509i	$0.0756759\pi$
$32$		−	4.95495i		−	0.875921i
$33$	−2.82560	−	0.918092i	−0.491873	−	0.159819i
$34$	−10.4368	+	7.58275i	−1.78989	+	1.30043i
$35$		0			0
$36$	−3.59186	−	2.60964i	−0.598644	−	0.434940i
$37$	−0.950818	−	1.30869i	−0.156313	−	0.215147i	0.723676	−	0.690139i	$-0.242451\pi$
$37$	−0.950818	−	1.30869i	−0.156313	−	0.215147i	−0.879990	+	0.474992i	$0.842451\pi$
$38$	8.01226	+	11.0279i	1.29976	+	1.78897i
$39$	−4.58650	−	3.33228i	−0.734427	−	0.533593i
$40$		0			0
$41$	−0.942740	+	0.684941i	−0.147231	+	0.106970i	−0.658962	−	0.752176i	$-0.729004\pi$
$41$	−0.942740	+	0.684941i	−0.147231	+	0.106970i	0.511731	+	0.859146i	$0.329004\pi$
$42$	2.51130	+	0.815972i	0.387502	+	0.125907i
$43$			5.68601i			0.867109i	0.901127	+	0.433554i	$0.142741\pi$
$43$			5.68601i			0.867109i	−0.901127	+	0.433554i	$0.857259\pi$
$44$	−4.07613	+	12.5450i	−0.614500	+	1.89124i
$45$		0			0
$46$	3.02725	+	9.31693i	0.446344	+	1.37371i
$47$	3.12556	−	1.01555i	0.455909	−	0.148134i	−0.0720547	−	0.997401i	$-0.522956\pi$
$47$	3.12556	−	1.01555i	0.455909	−	0.148134i	0.527964	+	0.849267i	$0.322956\pi$
$48$	−4.01583	+	5.52731i	−0.579635	+	0.797798i
$49$	5.91729			0.845327
$50$		0			0
$51$	5.08361			0.711848
$52$	−14.7946	+	20.3631i	−2.05165	+	2.82385i
$53$	−12.0652	+	3.92023i	−1.65729	+	0.538485i	−0.980301	−	0.197511i	$-0.936714\pi$
$53$	−12.0652	+	3.92023i	−1.65729	+	0.538485i	−0.676986	+	0.735996i	$0.736714\pi$
$54$	0.784184	+	2.41347i	0.106714	+	0.328432i
$55$		0			0
$56$	1.99080	−	6.12704i	0.266031	−	0.818760i
$57$		−	5.37156i		−	0.711481i
$58$	1.64043	+	0.533007i	0.215399	+	0.0699873i
$59$	2.59846	−	1.88789i	0.338290	−	0.245782i	−0.405650	−	0.914029i	$-0.632955\pi$
$59$	2.59846	−	1.88789i	0.338290	−	0.245782i	0.743940	+	0.668246i	$0.232955\pi$
$60$		0			0
$61$	4.38562	+	3.18634i	0.561521	+	0.407969i	0.832015	−	0.554753i	$-0.187187\pi$
$61$	4.38562	+	3.18634i	0.561521	+	0.407969i	−0.270494	+	0.962722i	$0.587187\pi$
$62$	1.26803	+	1.74530i	0.161040	+	0.221653i
$63$	−0.611611	−	0.841811i	−0.0770558	−	0.106058i
$64$	−0.881995	−	0.640807i	−0.110249	−	0.0801008i
$65$		0			0
$66$	6.09954	−	4.43157i	0.750801	−	0.545489i
$67$	0.883665	+	0.287120i	0.107957	+	0.0350773i	0.362497	−	0.931985i	$-0.381924\pi$
$67$	0.883665	+	0.287120i	0.107957	+	0.0350773i	−0.254540	+	0.967062i	$0.581924\pi$
$68$		−	22.5702i		−	2.73703i
$69$	1.19292	−	3.67145i	0.143611	−	0.441990i
$70$		0			0
$71$	−0.436821	−	1.34440i	−0.0518412	−	0.159551i	0.921784	−	0.387703i	$-0.126731\pi$
$71$	−0.436821	−	1.34440i	−0.0518412	−	0.159551i	−0.973625	+	0.228153i	$0.926731\pi$
$72$	5.88835	−	1.91324i	0.693949	−	0.225478i
$73$	6.65571	−	9.16080i	0.778992	−	1.07219i	−0.216400	−	0.976305i	$-0.569432\pi$
$73$	6.65571	−	9.16080i	0.778992	−	1.07219i	0.995392	−	0.0958862i	$-0.0305685\pi$
$74$	4.10501			0.477198
$75$		0			0
$76$	−23.8486			−2.73562
$77$	−1.81710	+	2.50103i	−0.207078	+	0.285018i
$78$	13.6825	−	4.44571i	1.54924	−	0.503378i
$79$	0.447171	+	1.37625i	0.0503106	+	0.154840i	0.973055	−	0.230571i	$-0.0740595\pi$
$79$	0.447171	+	1.37625i	0.0503106	+	0.154840i	−0.922745	+	0.385412i	$0.874059\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		−	2.95713i		−	0.326560i
$83$	−10.9140	−	3.54616i	−1.19796	−	0.389242i	−0.358952	−	0.933356i	$-0.616866\pi$
$83$	−10.9140	−	3.54616i	−1.19796	−	0.389242i	−0.839011	+	0.544114i	$0.816866\pi$
$84$	−3.73746	+	2.71542i	−0.407790	+	0.296277i
$85$		0			0
$86$	−11.6735	−	8.48129i	−1.25879	−	0.914561i
$87$	−0.399516	−	0.549886i	−0.0428326	−	0.0589540i
$88$	−10.8121	−	14.8816i	−1.15257	−	1.58638i
$89$	7.33961	+	5.33254i	0.777997	+	0.565248i	0.904377	−	0.426734i	$-0.140336\pi$
$89$	7.33961	+	5.33254i	0.777997	+	0.565248i	−0.126380	+	0.991982i	$0.540336\pi$
$90$		0			0
$91$	−4.77241	+	3.46736i	−0.500285	+	0.363478i
$92$	−16.3004	−	5.29633i	−1.69944	−	0.552181i
$93$		−	0.850111i		−	0.0881524i
$94$	−2.57715	+	7.93164i	−0.265812	+	0.818086i
$95$		0			0
$96$	−1.53117	−	4.71244i	−0.156274	−	0.480962i
$97$	−5.73419	+	1.86315i	−0.582219	+	0.189174i	−0.585294	−	0.810821i	$-0.699021\pi$
$97$	−5.73419	+	1.86315i	−0.582219	+	0.189174i	0.00307549	+	0.999995i	$0.499021\pi$
$98$	−8.82627	+	12.1483i	−0.891587	+	1.22716i
$99$	−2.97101			−0.298597
$100$		0			0
$101$	−15.3408			−1.52647			−0.763236	−	0.646120i	$-0.776390\pi$
$101$	−15.3408			−1.52647			−0.763236	+	0.646120i	$0.776390\pi$
$102$	−7.58275	+	10.4368i	−0.750804	+	1.03339i
$103$	11.4688	−	3.72642i	1.13005	−	0.367175i	0.316455	−	0.948608i	$-0.397507\pi$
$103$	11.4688	−	3.72642i	1.13005	−	0.367175i	0.813595	+	0.581432i	$0.197507\pi$
$104$	−10.8466	−	33.3824i	−1.06360	−	3.27341i
$105$		0			0
$106$	9.94827	−	30.6176i	0.966261	−	2.97385i
$107$		−	6.49787i		−	0.628173i	−0.949394	−	0.314086i	$-0.898302\pi$
$107$		−	6.49787i		−	0.628173i	0.949394	−	0.314086i	$-0.101698\pi$
$108$	−4.22249	−	1.37197i	−0.406309	−	0.132018i
$109$	−1.86929	+	1.35812i	−0.179046	+	0.130084i	−0.673698	−	0.739006i	$-0.735295\pi$
$109$	−1.86929	+	1.35812i	−0.179046	+	0.130084i	0.494653	+	0.869091i	$0.335295\pi$
$110$		0			0
$111$	−1.30869	−	0.950818i	−0.124215	−	0.0902476i
$112$	4.17861	+	5.75136i	0.394841	+	0.543453i
$113$	2.27638	+	3.13317i	0.214144	+	0.294744i	0.902553	−	0.430579i	$-0.141691\pi$
$113$	2.27638	+	3.13317i	0.214144	+	0.294744i	−0.688409	+	0.725323i	$0.741691\pi$
$114$	11.0279	+	8.01226i	1.03286	+	0.750417i
$115$		0			0
$116$	−2.44138	+	1.77376i	−0.226676	+	0.164690i
$117$	−5.39175	−	1.75189i	−0.498467	−	0.161962i
$118$			8.15067i			0.750330i
$119$	1.63460	−	5.03078i	0.149844	−	0.461171i
$120$		0			0
$121$	−0.671530	−	2.06676i	−0.0610482	−	0.187887i
$122$	−13.0832	+	4.25101i	−1.18450	+	0.384868i
$123$	−0.684941	+	0.942740i	−0.0617590	+	0.0850040i
$124$	−3.77431			−0.338943
$125$		0			0
$126$	2.64054			0.235238
$127$	6.87342	−	9.46046i	0.609918	−	0.839480i	−0.386653	−	0.922225i	$-0.626369\pi$
$127$	6.87342	−	9.46046i	0.609918	−	0.839480i	0.996571	+	0.0827456i	$0.0263689\pi$
$128$	12.0561	−	3.91725i	1.06562	−	0.346239i
$129$	1.75707	+	5.40772i	0.154702	+	0.476123i
$130$		0			0
$131$	−2.46042	+	7.57241i	−0.214968	+	0.661604i	0.784188	+	0.620524i	$0.213080\pi$
$131$	−2.46042	+	7.57241i	−0.214968	+	0.661604i	−0.999156	+	0.0410805i	$0.986920\pi$
$132$			13.1906i			1.14810i
$133$	−5.31574	−	1.72719i	−0.460933	−	0.149766i
$134$	−1.90754	+	1.38591i	−0.164787	+	0.119725i
$135$		0			0
$136$	25.4635	+	18.5003i	2.18348	+	1.58639i
$137$	6.49579	+	8.94069i	0.554973	+	0.763854i	0.990676	−	0.136236i	$-0.0435004\pi$
$137$	6.49579	+	8.94069i	0.554973	+	0.763854i	−0.435704	+	0.900090i	$0.643500\pi$
$138$	5.75818	+	7.92545i	0.490169	+	0.674659i
$139$	−9.92651	−	7.21204i	−0.841956	−	0.611717i	0.0809604	−	0.996717i	$-0.474201\pi$
$139$	−9.92651	−	7.21204i	−0.841956	−	0.611717i	−0.922916	+	0.385000i	$0.874201\pi$
$140$		0			0
$141$	2.65876	−	1.93170i	0.223908	−	0.162678i
$142$	3.41164	+	1.10851i	0.286299	+	0.0930241i
$143$			16.8433i			1.40851i
$144$	−2.11124	+	6.49774i	−0.175937	+	0.541479i
$145$		0			0
$146$	8.87961	+	27.3286i	0.734882	+	2.26173i
$147$	5.62767	−	1.82854i	0.464163	−	0.150816i
$148$	−4.22143	+	5.81030i	−0.346999	+	0.477604i
$149$	4.62832			0.379167			0.189584	−	0.981865i	$-0.439286\pi$
$149$	4.62832			0.379167			0.189584	+	0.981865i	$0.439286\pi$
$150$		0			0
$151$	−4.67249			−0.380242			−0.190121	−	0.981761i	$-0.560888\pi$
$151$	−4.67249			−0.380242			−0.190121	+	0.981761i	$0.560888\pi$
$152$	19.5482	−	26.9058i	1.58557	−	2.18235i
$153$	4.83480	−	1.57092i	0.390871	−	0.127002i
$154$	−2.42426	−	7.46110i	−0.195352	−	0.601232i
$155$		0			0
$156$	−7.77800	+	23.9382i	−0.622738	+	1.91659i
$157$			14.9726i			1.19494i	0.801890	+	0.597472i	$0.203828\pi$
$157$			14.9726i			1.19494i	−0.801890	+	0.597472i	$0.796172\pi$
$158$	−3.49247	−	1.13477i	−0.277846	−	0.0902777i
$159$	−10.2633	+	7.45672i	−0.813932	+	0.591357i
$160$		0			0
$161$	−3.24972	−	2.36106i	−0.256113	−	0.186077i
$162$	1.49161	+	2.05302i	0.117192	+	0.161301i
$163$	7.00123	+	9.63637i	0.548379	+	0.754779i	0.989791	−	0.142526i	$-0.0455223\pi$
$163$	7.00123	+	9.63637i	0.548379	+	0.754779i	−0.441412	+	0.897304i	$0.645522\pi$
$164$	4.18557	+	3.04099i	0.326838	+	0.237462i
$165$		0			0
$166$	23.5597	−	17.1171i	1.82859	−	1.32855i
$167$	−10.0889	−	3.27809i	−0.780704	−	0.253666i	−0.108563	−	0.994090i	$-0.534625\pi$
$167$	−10.0889	−	3.27809i	−0.780704	−	0.253666i	−0.672141	+	0.740424i	$0.734625\pi$
$168$		−	6.44235i		−	0.497038i
$169$	−5.91461	+	18.2033i	−0.454970	+	1.40025i
$170$		0			0
$171$	−1.65990	−	5.10866i	−0.126936	−	0.390669i
$172$	24.0091	−	7.80103i	1.83068	−	0.594823i
$173$	0.736719	−	1.01401i	0.0560117	−	0.0770935i	−0.780092	−	0.625664i	$-0.784828\pi$
$173$	0.736719	−	1.01401i	0.0560117	−	0.0770935i	0.836104	+	0.548571i	$0.184828\pi$
$174$	1.72485			0.130760
$175$		0			0
$176$	20.2983			1.53004
$177$	1.88789	−	2.59846i	0.141902	−	0.195312i
$178$	−21.8956	+	7.11432i	−1.64115	+	0.533241i
$179$	6.43105	+	19.7927i	0.480679	+	1.47938i	0.838143	+	0.545451i	$0.183642\pi$
$179$	6.43105	+	19.7927i	0.480679	+	1.47938i	−0.357464	+	0.933927i	$0.616358\pi$
$180$		0			0
$181$	−2.14058	+	6.58803i	−0.159108	+	0.489684i	−0.998554	−	0.0537591i	$-0.982880\pi$
$181$	−2.14058	+	6.58803i	−0.159108	+	0.489684i	0.839446	+	0.543443i	$0.182880\pi$
$182$		−	14.9698i		−	1.10964i
$183$	5.15561	+	1.67516i	0.381113	+	0.123831i
$184$	19.3364	−	14.0487i	1.42550	−	1.03569i
$185$		0			0
$186$	1.74530	+	1.26803i	0.127971	+	0.0929766i
$187$	−8.87759	−	12.2189i	−0.649193	−	0.893538i
$188$	−8.57633	−	11.8043i	−0.625494	−	0.860918i
$189$	−0.841811	−	0.611611i	−0.0612327	−	0.0444882i
$190$		0			0
$191$	−6.60494	+	4.79877i	−0.477916	+	0.347227i	−0.800518	−	0.599308i	$-0.795442\pi$
$191$	−6.60494	+	4.79877i	−0.477916	+	0.347227i	0.322602	+	0.946535i	$0.395442\pi$
$192$	−1.03685	−	0.336892i	−0.0748280	−	0.0243131i
$193$			13.9629i			1.00507i	0.864556	+	0.502537i	$0.167600\pi$
$193$			13.9629i			1.00507i	−0.864556	+	0.502537i	$0.832400\pi$
$194$	4.72807	−	14.5515i	0.339456	−	1.04474i
$195$		0			0
$196$	−8.11834	−	24.9857i	−0.579881	−	1.78469i
$197$	−5.48046	+	1.78071i	−0.390467	+	0.126870i	−0.497669	−	0.867367i	$-0.665811\pi$
$197$	−5.48046	+	1.78071i	−0.390467	+	0.126870i	0.107203	+	0.994237i	$0.465811\pi$
$198$	4.43157	−	6.09954i	0.314938	−	0.433475i
$199$	26.5748			1.88384			0.941919	−	0.335841i	$-0.109020\pi$
$199$	26.5748			1.88384			0.941919	+	0.335841i	$0.109020\pi$
$200$		0			0
$201$	0.929140			0.0655365
$202$	22.8825	−	31.4951i	1.61001	−	2.21599i
$203$	−0.672633	+	0.218552i	−0.0472096	+	0.0153393i
$204$	−6.97456	−	21.4655i	−0.488317	−	1.50289i
$205$		0			0
$206$	−9.45644	+	29.1039i	−0.658862	+	2.02777i
$207$		−	3.86039i		−	0.268315i
$208$	36.8371	+	11.9691i	2.55420	+	0.829909i
$209$	−12.9111	+	9.38043i	−0.893076	+	0.648858i
$210$		0			0
$211$	21.4061	+	15.5525i	1.47366	+	1.07068i	0.979533	+	0.201285i	$0.0645116\pi$
$211$	21.4061	+	15.5525i	1.47366	+	1.07068i	0.494125	+	0.869391i	$0.335488\pi$
$212$	33.1063	+	45.5669i	2.27375	+	3.12954i
$213$	−0.830884	−	1.14361i	−0.0569312	−	0.0783591i
$214$	13.3403	+	9.69227i	0.911922	+	0.662550i
$215$		0			0
$216$	5.00893	−	3.63920i	0.340815	−	0.247616i
$217$	−0.841277	−	0.273347i	−0.0571096	−	0.0185560i
$218$		−	5.86348i		−	0.397125i
$219$	3.49912	−	10.7692i	0.236448	−	0.727713i
$220$		0			0
$221$	−8.90591	−	27.4096i	−0.599076	−	1.84377i
$222$	3.90410	−	1.26852i	0.262026	−	0.0851374i
$223$	16.1321	−	22.2039i	1.08029	−	1.48689i	0.221081	−	0.975255i	$-0.429042\pi$
$223$	16.1321	−	22.2039i	1.08029	−	1.48689i	0.859205	−	0.511631i	$-0.170958\pi$
$224$	−5.15581			−0.344487
$225$		0			0
$226$	−9.82792			−0.653744
$227$	0.0765066	−	0.105302i	0.00507792	−	0.00698916i	−0.806470	−	0.591274i	$-0.798625\pi$
$227$	0.0765066	−	0.105302i	0.00507792	−	0.00698916i	0.811548	+	0.584285i	$0.198625\pi$
$228$	−22.6813	+	7.36962i	−1.50211	+	0.488065i
$229$	−0.873064	−	2.68702i	−0.0576937	−	0.177563i	0.918057	−	0.396449i	$-0.129758\pi$
$229$	−0.873064	−	2.68702i	−0.0576937	−	0.177563i	−0.975750	+	0.218886i	$0.929758\pi$
$230$		0			0
$231$	−0.955307	+	2.94013i	−0.0628546	+	0.193447i
$232$		−	4.20826i		−	0.276286i
$233$	−7.59617	−	2.46815i	−0.497642	−	0.161694i	0.0494328	−	0.998777i	$-0.484259\pi$
$233$	−7.59617	−	2.46815i	−0.497642	−	0.161694i	−0.547075	+	0.837084i	$0.684259\pi$
$234$	11.6390	−	8.45625i	0.760867	−	0.552802i
$235$		0			0
$236$	−11.5366	−	8.38182i	−0.750968	−	0.545610i
$237$	0.850569	+	1.17071i	0.0552504	+	0.0760457i
$238$	7.89012	+	10.8598i	0.511441	+	0.703938i
$239$	−15.4214	−	11.2043i	−0.997528	−	0.724747i	−0.0359713	−	0.999353i	$-0.511452\pi$
$239$	−15.4214	−	11.2043i	−0.997528	−	0.724747i	−0.961557	+	0.274606i	$0.911452\pi$
$240$		0			0
$241$	−17.0864	+	12.4140i	−1.10063	+	0.799654i	−0.981162	−	0.193184i	$-0.938118\pi$
$241$	−17.0864	+	12.4140i	−1.10063	+	0.799654i	−0.119467	+	0.992838i	$0.538118\pi$
$242$	5.24476	+	1.70413i	0.337146	+	0.109545i
$243$		−	1.00000i		−	0.0641500i
$244$	7.43735	−	22.8898i	0.476127	−	1.46537i
$245$		0			0
$246$	−0.913803	−	2.81240i	−0.0582619	−	0.179312i
$247$	−28.9621	+	9.41036i	−1.84281	+	0.598767i
$248$	3.09373	−	4.25815i	0.196452	−	0.270393i
$249$	−11.4756			−0.727238
$250$		0			0
$251$	30.2224			1.90762			0.953811	−	0.300408i	$-0.0971228\pi$
$251$	30.2224			1.90762			0.953811	+	0.300408i	$0.0971228\pi$
$252$	−2.71542	+	3.73746i	−0.171056	+	0.235438i
$253$	−10.9079	+	3.54419i	−0.685773	+	0.222821i
$254$	9.17007	+	28.2226i	0.575381	+	1.77084i
$255$		0			0
$256$	−9.26692	+	28.5207i	−0.579183	+	1.78254i
$257$			5.10215i			0.318263i	0.987257	+	0.159132i	$0.0508695\pi$
$257$			5.10215i			0.318263i	−0.987257	+	0.159132i	$0.949131\pi$
$258$	−13.7230	−	4.45888i	−0.854358	−	0.277598i
$259$	−1.36174	+	0.989360i	−0.0846142	+	0.0614758i
$260$		0			0
$261$	−0.549886	−	0.399516i	−0.0340371	−	0.0247294i
$262$	−11.8763	−	16.3464i	−0.733722	−	1.00988i
$263$	3.77088	+	5.19017i	0.232522	+	0.320040i	0.909295	−	0.416153i	$-0.136622\pi$
$263$	3.77088	+	5.19017i	0.232522	+	0.320040i	−0.676772	+	0.736192i	$0.736622\pi$
$264$	−14.8816	−	10.8121i	−0.915898	−	0.665439i
$265$		0			0
$266$	11.4749	−	8.33704i	0.703574	−	0.511177i
$267$	8.62823	+	2.80348i	0.528039	+	0.171570i
$268$		−	4.12518i		−	0.251986i
$269$	5.39518	−	16.6047i	0.328950	−	1.01240i	−0.640676	−	0.767811i	$-0.721346\pi$
$269$	5.39518	−	16.6047i	0.328950	−	1.01240i	0.969626	−	0.244592i	$-0.0786542\pi$
$270$		0			0
$271$	−0.0294140	−	0.0905270i	−0.00178677	−	0.00549912i	0.950159	−	0.311765i	$-0.100920\pi$
$271$	−0.0294140	−	0.0905270i	−0.00178677	−	0.00549912i	−0.951946	+	0.306266i	$0.900920\pi$
$272$	−33.0320	+	10.7328i	−2.00286	+	0.650769i
$273$	−3.46736	+	4.77241i	−0.209854	+	0.288840i
$274$	−28.0446			−1.69424
$275$		0			0
$276$	−17.1393			−1.03166
$277$	−10.8157	+	14.8865i	−0.649851	+	0.894443i	−0.999093	−	0.0425895i	$-0.986439\pi$
$277$	−10.8157	+	14.8865i	−0.649851	+	0.894443i	0.349242	+	0.937033i	$0.386439\pi$
$278$	29.6129	−	9.62182i	1.77606	−	0.577078i
$279$	−0.262699	−	0.808503i	−0.0157274	−	0.0484038i
$280$		0			0
$281$	5.54254	−	17.0582i	0.330640	−	1.01761i	−0.638189	−	0.769879i	$-0.720316\pi$
$281$	5.54254	−	17.0582i	0.330640	−	1.01761i	0.968830	−	0.247727i	$-0.0796837\pi$
$282$			8.33982i			0.496629i
$283$	21.1514	+	6.87252i	1.25732	+	0.408529i	0.860540	−	0.509383i	$-0.170126\pi$
$283$	21.1514	+	6.87252i	1.25732	+	0.408529i	0.396783	+	0.917912i	$0.370126\pi$
$284$	−5.07740	+	3.68895i	−0.301288	+	0.218899i
$285$		0			0
$286$	−34.5796	−	25.1236i	−2.04474	−	1.48559i
$287$	0.712705	+	0.980955i	0.0420697	+	0.0579039i
$288$	−2.91245	−	4.00864i	−0.171618	−	0.236212i
$289$	7.15424	+	5.19786i	0.420837	+	0.305756i
$290$		0			0
$291$	−4.87779	+	3.54392i	−0.285941	+	0.207749i
$292$	−47.8128	−	15.5353i	−2.79803	−	0.909136i
$293$			18.7316i			1.09431i	0.837031	+	0.547155i	$0.184289\pi$
$293$			18.7316i			1.09431i	−0.837031	+	0.547155i	$0.815711\pi$
$294$	−4.64024	+	14.2812i	−0.270624	+	0.832896i
$295$		0			0
$296$	−3.09491	−	9.52517i	−0.179888	−	0.553639i
$297$	−2.82560	+	0.918092i	−0.163958	+	0.0532731i
$298$	−6.90364	+	9.50204i	−0.399917	+	0.550439i
$299$	−21.8854			−1.26566
$300$		0			0
$301$	5.91650			0.341021
$302$	6.96952	−	9.59272i	0.401051	−	0.551999i
$303$	−14.5900	+	4.74058i	−0.838174	+	0.272339i
$304$	11.3407	+	34.9030i	0.650433	+	2.00183i
$305$		0			0
$306$	−3.98649	+	12.2692i	−0.227892	+	0.701381i
$307$		−	7.03850i		−	0.401708i	−0.979621	−	0.200854i	$-0.935628\pi$
$307$		−	7.03850i		−	0.401708i	0.979621	−	0.200854i	$-0.0643717\pi$
$308$	13.0536	+	4.24136i	0.743796	+	0.241674i
$309$	9.75590	−	7.08808i	0.554994	−	0.403227i
$310$		0			0
$311$	23.6872	+	17.2098i	1.34318	+	0.975876i	0.999321	+	0.0368546i	$0.0117338\pi$
$311$	23.6872	+	17.2098i	1.34318	+	0.975876i	0.343858	+	0.939022i	$0.388266\pi$
$312$	−20.6314	−	28.3967i	−1.16803	−	1.60765i
$313$	−9.19024	−	12.6493i	−0.519463	−	0.714980i	0.466016	−	0.884776i	$-0.345689\pi$
$313$	−9.19024	−	12.6493i	−0.519463	−	0.714980i	−0.985479	+	0.169796i	$0.945689\pi$
$314$	−30.7391	−	22.3333i	−1.73471	−	1.26034i
$315$		0			0
$316$	5.19769	−	3.77635i	0.292393	−	0.212436i
$317$	−5.93596	−	1.92871i	−0.333397	−	0.108327i	0.137535	−	0.990497i	$-0.456082\pi$
$317$	−5.93596	−	1.92871i	−0.333397	−	0.108327i	−0.470932	+	0.882170i	$0.656082\pi$
$318$		−	32.1933i		−	1.80531i
$319$	−0.624024	+	1.92055i	−0.0349386	+	0.107530i
$320$		0			0
$321$	−2.00795	−	6.17984i	−0.112073	−	0.344925i
$322$	9.69460	−	3.14997i	0.540259	−	0.175541i
$323$	16.0506	−	22.0918i	0.893080	−	1.22922i
$324$	−4.43979			−0.246655
$325$		0			0
$326$	−30.2268			−1.67411
$327$	−1.35812	+	1.86929i	−0.0751042	+	0.103372i
$328$	−6.86164	+	2.22948i	−0.378871	+	0.123103i
$329$	−1.05672	−	3.25225i	−0.0582589	−	0.179302i
$330$		0			0
$331$	6.63073	−	20.4073i	0.364458	−	1.12169i	−0.585862	−	0.810411i	$-0.699244\pi$
$331$	6.63073	−	20.4073i	0.364458	−	1.12169i	0.950320	−	0.311275i	$-0.100756\pi$
$332$			50.9493i			2.79621i
$333$	−1.53846	−	0.499875i	−0.0843068	−	0.0273930i
$334$	21.7787	−	15.8231i	1.19168	−	0.865804i
$335$		0			0
$336$	5.75136	+	4.17861i	0.313763	+	0.227962i
$337$	20.4262	+	28.1142i	1.11269	+	1.53148i	0.817399	+	0.576072i	$0.195415\pi$
$337$	20.4262	+	28.1142i	1.11269	+	1.53148i	0.295287	+	0.955409i	$0.404585\pi$
$338$	−28.5495	−	39.2950i	−1.55289	−	2.13736i
$339$	3.13317	+	2.27638i	0.170170	+	0.123636i
$340$		0			0
$341$	−2.04332	+	1.48456i	−0.110652	+	0.0803935i
$342$	12.9641	+	4.21229i	0.701019	+	0.227775i
$343$		−	13.4409i		−	0.725740i
$344$	−10.8787	+	33.4812i	−0.586541	+	1.80519i
$345$		0			0
$346$	0.982882	+	3.02500i	0.0528401	+	0.162625i
$347$	27.3182	−	8.87623i	1.46652	−	0.476501i	0.536465	−	0.843922i	$-0.319759\pi$
$347$	27.3182	−	8.87623i	1.46652	−	0.476501i	0.930055	+	0.367421i	$0.119759\pi$
$348$	−1.77376	+	2.44138i	−0.0950837	+	0.130871i
$349$	12.2834			0.657515			0.328758	−	0.944414i	$-0.393370\pi$
$349$	12.2834			0.657515			0.328758	+	0.944414i	$0.393370\pi$
$350$		0			0
$351$	−5.66922			−0.302601
$352$	−8.65291	+	11.9097i	−0.461201	+	0.634789i
$353$	25.6575	−	8.33663i	1.36561	−	0.443714i	0.467699	−	0.883888i	$-0.345083\pi$
$353$	25.6575	−	8.33663i	1.36561	−	0.443714i	0.897913	+	0.440174i	$0.145083\pi$
$354$	2.51870	+	7.75175i	0.133867	+	0.412001i
$355$		0			0
$356$	12.4469	−	38.3075i	0.659682	−	2.03029i
$357$		−	5.28968i		−	0.279960i
$358$	−50.2275	−	16.3199i	−2.65461	−	0.862533i
$359$	13.2875	−	9.65393i	0.701287	−	0.509515i	−0.179064	−	0.983837i	$-0.557307\pi$
$359$	13.2875	−	9.65393i	0.701287	−	0.509515i	0.880351	+	0.474322i	$0.157307\pi$
$360$		0			0
$361$	−7.97178	−	5.79184i	−0.419567	−	0.304834i
$362$	−10.3325	−	14.2214i	−0.543062	−	0.747460i
$363$	−1.27733	−	1.75809i	−0.0670423	−	0.0922758i
$364$	21.1885	+	15.3943i	1.11058	+	0.806883i
$365$		0			0
$366$	−11.1293	+	8.08589i	−0.581737	+	0.422656i
$367$	28.4321	+	9.23816i	1.48415	+	0.482228i	0.935349	−	0.353727i	$-0.115086\pi$
$367$	28.4321	+	9.23816i	1.48415	+	0.482228i	0.548797	+	0.835956i	$0.315086\pi$
$368$			26.3747i			1.37487i
$369$	−0.360095	+	1.10826i	−0.0187458	+	0.0576936i
$370$		0			0
$371$	4.07914	+	12.5543i	0.211778	+	0.651787i
$372$	−3.58958	+	1.16633i	−0.186111	+	0.0604712i
$373$	−14.5951	+	20.0885i	−0.755706	+	1.04014i	0.241853	+	0.970313i	$0.422245\pi$
$373$	−14.5951	+	20.0885i	−0.755706	+	1.04014i	−0.997559	+	0.0698276i	$0.977755\pi$
$374$	38.3276			1.98187
$375$		0			0
$376$	20.3474			1.04934
$377$	−2.26494	+	3.11742i	−0.116650	+	0.160556i
$378$	2.51130	−	0.815972i	0.129167	−	0.0419690i
$379$	−5.99389	−	18.4473i	−0.307885	−	0.947574i	−0.978585	−	0.205845i	$-0.934006\pi$
$379$	−5.99389	−	18.4473i	−0.307885	−	0.947574i	0.670699	−	0.741729i	$-0.265994\pi$
$380$		0			0
$381$	3.61357	−	11.1214i	0.185129	−	0.569768i
$382$		−	20.7179i		−	1.06002i
$383$	−10.7002	−	3.47670i	−0.546754	−	0.177651i	0.0225986	−	0.999745i	$-0.492806\pi$
$383$	−10.7002	−	3.47670i	−0.546754	−	0.177651i	−0.569353	+	0.822094i	$0.692806\pi$
$384$	10.2555	−	7.45106i	0.523349	−	0.380235i
$385$		0			0
$386$	−28.6662	−	20.8272i	−1.45907	−	1.06008i
$387$	3.34215	+	4.60008i	0.169891	+	0.233835i
$388$	15.7343	+	21.6564i	0.798786	+	1.09944i
$389$	12.0558	+	8.75903i	0.611252	+	0.444100i	0.849855	−	0.527017i	$-0.176690\pi$
$389$	12.0558	+	8.75903i	0.611252	+	0.444100i	−0.238603	+	0.971117i	$0.576690\pi$
$390$		0			0
$391$	15.8767	−	11.5351i	0.802920	−	0.583356i
$392$	34.8431	+	11.3212i	1.75984	+	0.571807i
$393$			7.96210i			0.401635i
$394$	4.51886	−	13.9076i	0.227657	−	0.700656i
$395$		0			0
$396$	4.07613	+	12.5450i	0.204833	+	0.630412i
$397$	22.9172	−	7.44626i	1.15018	−	0.373717i	0.328971	−	0.944340i	$-0.393298\pi$
$397$	22.9172	−	7.44626i	1.15018	−	0.373717i	0.821212	+	0.570623i	$0.193298\pi$
$398$	−39.6392	+	54.5586i	−1.98693	+	2.73478i
$399$	−5.58930			−0.279815
$400$		0			0
$401$	13.4580			0.672059			0.336030	−	0.941851i	$-0.390916\pi$
$401$	13.4580			0.672059			0.336030	+	0.941851i	$0.390916\pi$
$402$	−1.38591	+	1.90754i	−0.0691230	+	0.0951397i
$403$	−4.58358	+	1.48930i	−0.228325	+	0.0741872i
$404$	21.0472	+	64.7765i	1.04714	+	3.22275i
$405$		0			0
$406$	0.554613	−	1.70692i	0.0275250	−	0.0847132i
$407$			4.80598i			0.238224i
$408$	29.9341	+	9.72618i	1.48196	+	0.481518i
$409$	−28.6988	+	20.8509i	−1.41906	+	1.03101i	−0.427140	+	0.904186i	$0.640479\pi$
$409$	−28.6988	+	20.8509i	−1.41906	+	1.03101i	−0.991925	+	0.126825i	$0.959521\pi$
$410$		0			0
$411$	8.94069	+	6.49579i	0.441012	+	0.320414i
$412$	−31.4696	−	43.3141i	−1.55039	−	2.13393i
$413$	−1.96441	−	2.70379i	−0.0966625	−	0.133045i
$414$	7.92545	+	5.75818i	0.389515	+	0.282999i
$415$		0			0
$416$	−22.7259	+	16.5113i	−1.11423	+	0.809534i
$417$	−11.6693	−	3.79159i	−0.571449	−	0.185675i
$418$		−	40.4986i		−	1.98085i
$419$	−4.88617	+	15.0381i	−0.238705	+	0.734659i	0.757903	+	0.652367i	$0.226224\pi$
$419$	−4.88617	+	15.0381i	−0.238705	+	0.734659i	−0.996608	+	0.0822916i	$0.973776\pi$
$420$		0			0
$421$	3.70244	+	11.3949i	0.180446	+	0.555355i	0.999840	−	0.0178752i	$-0.00569015\pi$
$421$	3.70244	+	11.3949i	0.180446	+	0.555355i	−0.819394	+	0.573230i	$0.805690\pi$
$422$	−63.8590	+	20.7491i	−3.10861	+	1.01005i
$423$	1.93170	−	2.65876i	0.0939225	−	0.129273i
$424$	−78.5447			−3.81447
$425$		0			0
$426$	3.58721			0.173801
$427$	3.31550	−	4.56340i	0.160448	−	0.220838i
$428$	−27.4372	+	8.91488i	−1.32623	+	0.430917i
$429$	5.20486	+	16.0189i	0.251293	+	0.773401i
$430$		0			0
$431$	4.52486	−	13.9261i	0.217955	−	0.670797i	−0.780976	−	0.624562i	$-0.785278\pi$
$431$	4.52486	−	13.9261i	0.217955	−	0.670797i	0.998931	−	0.0462350i	$-0.0147223\pi$
$432$			6.83213i			0.328711i
$433$	−4.06380	−	1.32041i	−0.195294	−	0.0634547i	0.209737	−	0.977758i	$-0.432739\pi$
$433$	−4.06380	−	1.32041i	−0.195294	−	0.0634547i	−0.405031	+	0.914303i	$0.632739\pi$
$434$	1.81604	−	1.31943i	0.0871728	−	0.0633347i
$435$		0			0
$436$	8.29926	+	6.02976i	0.397462	+	0.288773i
$437$	−12.1885	−	16.7760i	−0.583055	−	0.802506i
$438$	16.8900	+	23.2471i	0.807037	+	1.11079i
$439$	−16.4289	−	11.9363i	−0.784111	−	0.569690i	0.122099	−	0.992518i	$-0.461037\pi$
$439$	−16.4289	−	11.9363i	−0.784111	−	0.569690i	−0.906210	+	0.422828i	$0.861037\pi$
$440$		0			0
$441$	4.78718	−	3.47809i	0.227961	−	0.165623i
$442$	69.5565	+	22.6003i	3.30847	+	1.07499i
$443$		−	19.0543i		−	0.905299i	−0.891689	−	0.452649i	$-0.850479\pi$
$443$		−	19.0543i		−	0.905299i	0.891689	−	0.452649i	$-0.149521\pi$
$444$	−2.21934	+	6.83041i	−0.105325	+	0.324157i
$445$		0			0
$446$	21.5224	+	66.2391i	1.01912	+	3.13651i
$447$	4.40180	−	1.43023i	0.208198	−	0.0676476i
$448$	−0.666782	+	0.917747i	−0.0315025	+	0.0433595i
$449$	−29.4793			−1.39122			−0.695608	−	0.718421i	$-0.744865\pi$
$449$	−29.4793			−1.39122			−0.695608	+	0.718421i	$0.744865\pi$
$450$		0			0
$451$	3.46209			0.163023
$452$	10.1066	−	13.9106i	0.475376	−	0.654299i
$453$	−4.44380	+	1.44388i	−0.208788	+	0.0678394i
$454$	0.102070	+	0.314139i	0.00479038	+	0.0147433i
$455$		0			0
$456$	10.2771	−	31.6296i	0.481269	−	1.48119i
$457$			28.3015i			1.32389i	0.749553	+	0.661945i	$0.230269\pi$
$457$			28.3015i			1.32389i	−0.749553	+	0.661945i	$0.769731\pi$
$458$	6.81877	+	2.21555i	0.318620	+	0.103526i
$459$	4.11273	−	2.98807i	0.191966	−	0.139471i
$460$		0			0
$461$	13.3953	+	9.73223i	0.623879	+	0.453275i	0.854274	−	0.519822i	$-0.174002\pi$
$461$	13.3953	+	9.73223i	0.623879	+	0.453275i	−0.230395	+	0.973097i	$0.574002\pi$
$462$	−4.61121	−	6.34679i	−0.214533	−	0.295279i
$463$	5.41311	+	7.45051i	0.251569	+	0.346254i	0.916060	−	0.401042i	$-0.131352\pi$
$463$	5.41311	+	7.45051i	0.251569	+	0.346254i	−0.664491	+	0.747296i	$0.731352\pi$
$464$	3.75689	+	2.72954i	0.174409	+	0.126716i
$465$		0			0
$466$	16.3977	−	11.9136i	0.759607	−	0.551887i
$467$	10.0929	+	3.27938i	0.467043	+	0.151752i	0.533079	−	0.846066i	$-0.321035\pi$
$467$	10.0929	+	3.27938i	0.467043	+	0.151752i	−0.0660353	+	0.997817i	$0.521035\pi$
$468$			25.1701i			1.16349i
$469$	0.298759	−	0.919485i	0.0137954	−	0.0424579i
$470$		0			0
$471$	4.62679	+	14.2398i	0.213191	+	0.656135i
$472$	18.9126	−	6.14508i	0.870524	−	0.282850i
$473$	9.92956	−	13.6669i	0.456562	−	0.628403i
$474$	−3.67220			−0.168670
$475$		0			0
$476$	−23.4850			−1.07644
$477$	−7.45672	+	10.2633i	−0.341420	+	0.469924i
$478$	46.0054	−	14.9480i	2.10424	−	0.683708i
$479$	−10.3849	−	31.9613i	−0.474496	−	1.46035i	−0.846636	−	0.532172i	$-0.821376\pi$
$479$	−10.3849	−	31.9613i	−0.474496	−	1.46035i	0.372140	−	0.928177i	$-0.378624\pi$
$480$		0			0
$481$	−2.83390	+	8.72184i	−0.129215	+	0.397682i
$482$		−	53.5954i		−	2.44120i
$483$	−3.82027	−	1.24128i	−0.173828	−	0.0564802i
$484$	−7.80554	+	5.67106i	−0.354797	+	0.257775i
$485$		0			0
$486$	2.05302	+	1.49161i	0.0931269	+	0.0676607i
$487$	−17.1919	−	23.6626i	−0.779039	−	1.07226i	−0.995387	−	0.0959389i	$-0.969415\pi$
$487$	−17.1919	−	23.6626i	−0.779039	−	1.07226i	0.216348	−	0.976316i	$-0.430585\pi$
$488$	19.7279	+	27.1531i	0.893038	+	1.22916i
$489$	9.63637	+	7.00123i	0.435772	+	0.316607i
$490$		0			0
$491$	−11.2898	+	8.20251i	−0.509501	+	0.370174i	−0.812634	−	0.582774i	$-0.801967\pi$
$491$	−11.2898	+	8.20251i	−0.509501	+	0.370174i	0.303133	+	0.952948i	$0.401967\pi$
$492$	4.92043	+	1.59874i	0.221830	+	0.0720769i
$493$		−	3.45531i		−	0.155619i
$494$	23.8804	−	73.4964i	1.07443	−	3.30676i
$495$		0			0
$496$	1.79479	+	5.52380i	0.0805885	+	0.248026i
$497$	−1.39889	+	0.454528i	−0.0627490	+	0.0203884i
$498$	17.1171	−	23.5597i	0.767036	−	1.05573i
$499$	35.7533			1.60054			0.800268	−	0.599642i	$-0.204690\pi$
$499$	35.7533			1.60054			0.800268	+	0.599642i	$0.204690\pi$
$500$		0			0
$501$	−10.6081			−0.473936
$502$	−45.0800	+	62.0472i	−2.01202	+	2.76930i
$503$	−11.0744	+	3.59828i	−0.493782	+	0.160439i	−0.545314	−	0.838232i	$-0.683590\pi$
$503$	−11.0744	+	3.59828i	−0.493782	+	0.160439i	0.0515323	+	0.998671i	$0.483590\pi$
$504$	−1.99080	−	6.12704i	−0.0886771	−	0.272920i
$505$		0			0
$506$	8.99399	−	27.6807i	0.399832	−	1.23056i
$507$			19.1401i			0.850040i
$508$	−49.3768	−	16.0435i	−2.19074	−	0.711815i
$509$	−6.90384	+	5.01594i	−0.306007	+	0.222327i	−0.730181	−	0.683253i	$-0.760564\pi$
$509$	−6.90384	+	5.01594i	−0.306007	+	0.222327i	0.424174	+	0.905581i	$0.360564\pi$
$510$		0			0
$511$	−9.53214	−	6.92551i	−0.421677	−	0.306366i
$512$	−29.8288	−	41.0558i	−1.31826	−	1.81443i
$513$	−3.15732	−	4.34568i	−0.139399	−	0.191867i
$514$	−10.4748	−	7.61040i	−0.462025	−	0.335681i
$515$		0			0
$516$	20.4234	−	14.8384i	0.899089	−	0.653226i
$517$	−9.28605	−	3.01722i	−0.408400	−	0.132697i
$518$		−	4.27141i		−	0.187675i
$519$	0.387316	−	1.19204i	0.0170013	−	0.0523246i
$520$		0			0
$521$	0.390998	+	1.20337i	0.0171299	+	0.0527205i	0.959256	−	0.282538i	$-0.0911763\pi$
$521$	0.390998	+	1.20337i	0.0171299	+	0.0527205i	−0.942126	+	0.335259i	$0.891176\pi$
$522$	1.64043	−	0.533007i	0.0717996	−	0.0233291i
$523$	−15.9998	+	22.0218i	−0.699621	+	0.962946i	0.300337	+	0.953833i	$0.402901\pi$
$523$	−15.9998	+	22.0218i	−0.699621	+	0.962946i	−0.999958	+	0.00911285i	$0.997099\pi$
$524$	35.3500			1.54427
$525$		0			0
$526$	−16.2802			−0.709850
$527$	2.54019	−	3.49628i	0.110653	−	0.152300i
$528$	19.3048	−	6.27252i	0.840135	−	0.272976i
$529$	2.50224	+	7.70110i	0.108793	+	0.334831i
$530$		0			0
$531$	0.992522	−	3.05467i	0.0430718	−	0.132561i
$532$			24.8153i			1.07588i
$533$	6.28296	+	2.04146i	0.272145	+	0.0884253i
$534$	−18.6255	+	13.5322i	−0.806005	+	0.585597i
$535$		0			0
$536$	4.65400	+	3.38133i	0.201022	+	0.146051i
$537$	12.2326	+	16.8367i	0.527875	+	0.726557i
$538$	26.0422	+	35.8440i	1.12276	+	1.54535i
$539$	−14.2228	−	10.3334i	−0.612618	−	0.445093i
$540$		0			0
$541$	−24.5804	+	17.8587i	−1.05679	+	0.767805i	−0.973492	−	0.228719i	$-0.926546\pi$
$541$	−24.5804	+	17.8587i	−1.05679	+	0.767805i	−0.0833007	+	0.996524i	$0.526546\pi$
$542$	0.229728	+	0.0746431i	0.00986766	+	0.00320620i
$543$			6.92706i			0.297269i
$544$	7.78385	−	23.9562i	0.333730	−	1.02711i
$545$		0			0
$546$	−4.62592	−	14.2371i	−0.197971	−	0.609293i
$547$	−10.8200	+	3.51564i	−0.462631	+	0.150318i	−0.531053	−	0.847339i	$-0.678203\pi$
$547$	−10.8200	+	3.51564i	−0.462631	+	0.150318i	0.0684223	+	0.997656i	$0.478203\pi$
$548$	28.8399	−	39.6947i	1.23198	−	1.69568i
$549$	5.42093			0.231360
$550$		0			0
$551$	−3.65103			−0.155539
$552$	14.0487	−	19.3364i	0.597954	−	0.823012i
$553$	1.43204	−	0.465297i	0.0608964	−	0.0197864i
$554$	−14.4296	−	44.4096i	−0.613053	−	1.88678i
$555$		0			0
$556$	−16.8339	+	51.8093i	−0.713914	+	2.19720i
$557$		−	45.7532i		−	1.93862i	−0.245833	−	0.969312i	$-0.579062\pi$
$557$		−	45.7532i		−	1.93862i	0.245833	−	0.969312i	$-0.420938\pi$
$558$	2.05172	+	0.666643i	0.0868561	+	0.0282213i
$559$	26.0789	−	18.9474i	1.10302	−	0.801390i
$560$		0			0
$561$	−12.2189	−	8.87759i	−0.515884	−	0.374812i
$562$	26.7535	+	36.8231i	1.12853	+	1.55329i
$563$	5.25650	+	7.23495i	0.221535	+	0.304917i	0.905289	−	0.424796i	$-0.139654\pi$
$563$	5.25650	+	7.23495i	0.221535	+	0.304917i	−0.683754	+	0.729712i	$0.739654\pi$
$564$	−11.8043	−	8.57633i	−0.497051	−	0.361129i
$565$		0			0
$566$	−45.6591	+	33.1733i	−1.91919	+	1.39438i
$567$	−0.989608	−	0.321543i	−0.0415596	−	0.0135035i
$568$		−	8.75203i		−	0.367227i
$569$	0.707365	−	2.17704i	0.0296543	−	0.0912665i	−0.935134	−	0.354294i	$-0.884721\pi$
$569$	0.707365	−	2.17704i	0.0296543	−	0.0912665i	0.964788	+	0.263028i	$0.0847211\pi$
$570$		0			0
$571$	−9.50522	−	29.2541i	−0.397781	−	1.22424i	−0.926774	−	0.375618i	$-0.877430\pi$
$571$	−9.50522	−	29.2541i	−0.397781	−	1.22424i	0.528993	−	0.848626i	$-0.322570\pi$
$572$	71.1206	−	23.1085i	2.97370	−	0.966214i
$573$	−4.79877	+	6.60494i	−0.200471	+	0.275925i
$574$	−3.07700			−0.128431
$575$		0			0
$576$	−1.09021			−0.0454252
$577$	3.87484	−	5.33326i	0.161312	−	0.222027i	−0.720708	−	0.693238i	$-0.756183\pi$
$577$	3.87484	−	5.33326i	0.161312	−	0.222027i	0.882020	+	0.471212i	$0.156183\pi$
$578$	−21.3426	+	6.93464i	−0.887736	+	0.288443i
$579$	4.31479	+	13.2795i	0.179316	+	0.551879i
$580$		0			0
$581$	−3.68991	+	11.3564i	−0.153083	+	0.471141i
$582$		−	15.3004i		−	0.634220i
$583$	35.8459	+	11.6470i	1.48458	+	0.482371i
$584$	56.7180	−	41.2081i	2.34701	−	1.70520i
$585$		0			0
$586$	−38.4563	−	27.9401i	−1.58861	−	1.15420i
$587$	−3.25499	−	4.48010i	−0.134348	−	0.184914i	0.736543	−	0.676391i	$-0.236457\pi$
$587$	−3.25499	−	4.48010i	−0.134348	−	0.184914i	−0.870890	+	0.491477i	$0.836457\pi$
$588$	−15.4420	−	21.2541i	−0.636817	−	0.876503i
$589$	−3.69431	−	2.68408i	−0.152222	−	0.110595i
$590$		0			0
$591$	−4.66196	+	3.38711i	−0.191767	+	0.139327i
$592$	10.5109	+	3.41521i	0.431997	+	0.140364i
$593$		−	1.88122i		−	0.0772524i	−0.999254	−	0.0386262i	$-0.987702\pi$
$593$		−	1.88122i		−	0.0772524i	0.999254	−	0.0386262i	$-0.0122982\pi$
$594$	2.32982	−	7.17044i	0.0955935	−	0.294207i
$595$		0			0
$596$	−6.34992	−	19.5430i	−0.260103	−	0.800514i
$597$	25.2741	−	8.21206i	1.03440	−	0.336097i
$598$	32.6444	−	44.9311i	1.33493	−	1.83737i
$599$	−17.8272			−0.728400			−0.364200	−	0.931321i	$-0.618658\pi$
$599$	−17.8272			−0.728400			−0.364200	+	0.931321i	$0.618658\pi$
$600$		0			0
$601$	33.0994			1.35015			0.675077	−	0.737747i	$-0.264110\pi$
$601$	33.0994			1.35015			0.675077	+	0.737747i	$0.264110\pi$
$602$	−8.82509	+	12.1467i	−0.359684	+	0.495062i
$603$	0.883665	−	0.287120i	0.0359856	−	0.0116924i
$604$	6.41052	+	19.7295i	0.260840	+	0.802784i
$605$		0			0
$606$	12.0300	−	37.0247i	0.488687	−	1.50402i
$607$			23.4603i			0.952226i	0.879384	+	0.476113i	$0.157955\pi$
$607$			23.4603i			0.952226i	−0.879384	+	0.476113i	$0.842045\pi$
$608$	−25.3132	−	8.22475i	−1.02658	−	0.333558i
$609$	−0.572176	+	0.415710i	−0.0231857	+	0.0168454i
$610$		0			0
$611$	−15.0731	−	10.9512i	−0.609792	−	0.443039i
$612$	−13.2664	−	18.2596i	−0.536263	−	0.738102i
$613$	−27.7600	−	38.2083i	−1.12121	−	1.54322i	−0.803769	−	0.594942i	$-0.797175\pi$
$613$	−27.7600	−	38.2083i	−1.12121	−	1.54322i	−0.317445	−	0.948277i	$-0.602825\pi$
$614$	14.4502	+	10.4987i	0.583162	+	0.423692i
$615$		0			0
$616$	−15.4848	+	11.2504i	−0.623901	+	0.453290i
$617$	−15.4735	−	5.02765i	−0.622941	−	0.202406i	−0.0194952	−	0.999810i	$-0.506206\pi$
$617$	−15.4735	−	5.02765i	−0.622941	−	0.202406i	−0.603446	+	0.797404i	$0.706206\pi$
$618$			30.6017i			1.23098i
$619$	−10.9577	+	33.7244i	−0.440428	+	1.35550i	0.446993	+	0.894537i	$0.352495\pi$
$619$	−10.9577	+	33.7244i	−0.440428	+	1.35550i	−0.887421	+	0.460960i	$0.847505\pi$
$620$		0			0
$621$	−1.19292	−	3.67145i	−0.0478704	−	0.147330i
$622$	−70.6640	+	22.9601i	−2.83337	+	0.920617i
$623$	5.54869	−	7.63712i	0.222304	−	0.305975i
$624$	38.7329			1.55056
$625$		0			0
$626$	39.6775			1.58583
$627$	−9.38043	+	12.9111i	−0.374618	+	0.515618i
$628$	63.2217	−	20.5420i	2.52282	−	0.819714i
$629$	−2.54117	−	7.82091i	−0.101323	−	0.311840i
$630$		0			0
$631$	−9.03453	+	27.8054i	−0.359659	+	1.10692i	0.593599	+	0.804761i	$0.297706\pi$
$631$	−9.03453	+	27.8054i	−0.359659	+	1.10692i	−0.953258	+	0.302156i	$0.902294\pi$
$632$			8.95939i			0.356385i
$633$	25.1644	+	8.17641i	1.00020	+	0.324983i
$634$	12.8138	−	9.30978i	0.508901	−	0.369738i
$635$		0			0
$636$	45.5669	+	33.1063i	1.80684	+	1.31275i
$637$	−19.7181	−	27.1396i	−0.781259	−	1.07531i
$638$	−3.01213	−	4.14583i	−0.119251	−	0.164135i
$639$	−1.14361	−	0.830884i	−0.0452406	−	0.0328692i
$640$		0			0
$641$	12.7145	−	9.23764i	0.502194	−	0.364865i	−0.307661	−	0.951496i	$-0.599546\pi$
$641$	12.7145	−	9.23764i	0.502194	−	0.364865i	0.809854	+	0.586631i	$0.199546\pi$
$642$	15.6824	+	5.09553i	0.618936	+	0.201104i
$643$			8.08055i			0.318666i	0.987225	+	0.159333i	$0.0509343\pi$
$643$			8.08055i			0.318666i	−0.987225	+	0.159333i	$0.949066\pi$
$644$	−5.51102	+	16.9612i	−0.217165	+	0.668364i
$645$		0			0
$646$	21.4137	+	65.9045i	0.842510	+	2.59298i
$647$	−10.4800	+	3.40516i	−0.412011	+	0.133870i	−0.507686	−	0.861542i	$-0.669499\pi$
$647$	−10.4800	+	3.40516i	−0.412011	+	0.133870i	0.0956751	+	0.995413i	$0.469499\pi$
$648$	3.63920	−	5.00893i	0.142961	−	0.196769i
$649$	−9.54248			−0.374575
$650$		0			0
$651$	−0.884570			−0.0346691
$652$	31.0840	−	42.7834i	1.21734	−	1.67553i
$653$	−29.5646	+	9.60613i	−1.15695	+	0.375917i	−0.823758	−	0.566941i	$-0.808127\pi$
$653$	−29.5646	+	9.60613i	−1.15695	+	0.375917i	−0.333195	+	0.942858i	$0.608127\pi$
$654$	−1.81191	−	5.57650i	−0.0708515	−	0.218058i
$655$		0			0
$656$	2.46021	−	7.57176i	0.0960552	−	0.295628i
$657$		−	11.3234i		−	0.441767i
$658$	8.25315	+	2.68161i	0.321741	+	0.104540i
$659$	26.2325	−	19.0590i	1.02187	−	0.742435i	0.0552080	−	0.998475i	$-0.482418\pi$
$659$	26.2325	−	19.0590i	1.02187	−	0.742435i	0.966666	+	0.256040i	$0.0824178\pi$
$660$		0			0
$661$	−12.6268	−	9.17394i	−0.491128	−	0.356825i	0.314490	−	0.949261i	$-0.398166\pi$
$661$	−12.6268	−	9.17394i	−0.491128	−	0.356825i	−0.805618	+	0.592436i	$0.798166\pi$
$662$	32.0061	+	44.0527i	1.24395	+	1.71216i
$663$	−16.9400	−	23.3160i	−0.657897	−	0.905517i
$664$	−57.4806	−	41.7621i	−2.23068	−	1.62068i
$665$		0			0
$666$	3.32102	−	2.41287i	0.128687	−	0.0934966i
$667$	−2.49547	−	0.810827i	−0.0966249	−	0.0313953i
$668$			47.0978i			1.82227i
$669$	8.48115	−	26.1023i	0.327900	−	1.00917i
$670$		0			0
$671$	−4.97691	−	15.3173i	−0.192131	−	0.591320i
$672$	−4.90346	+	1.59323i	−0.189155	+	0.0614602i
$673$	−18.2373	+	25.1014i	−0.702995	+	0.967589i	0.296925	+	0.954901i	$0.404039\pi$
$673$	−18.2373	+	25.1014i	−0.702995	+	0.967589i	−0.999919	+	0.0126883i	$0.995961\pi$
$674$	−88.1870			−3.39684
$675$		0			0
$676$	84.9778			3.26838
$677$	−13.5716	+	18.6796i	−0.521597	+	0.717917i	−0.985821	−	0.167801i	$-0.946333\pi$
$677$	−13.5716	+	18.6796i	−0.521597	+	0.717917i	0.464224	+	0.885718i	$0.346333\pi$
$678$	−9.34691	+	3.03700i	−0.358966	+	0.116635i
$679$	1.93868	+	5.96663i	0.0743995	+	0.228978i
$680$		0			0
$681$	0.0402219	−	0.123790i	0.00154131	−	0.00474365i
$682$		−	6.40936i		−	0.245427i
$683$	39.3301	+	12.7791i	1.50492	+	0.488979i	0.941449	−	0.337154i	$-0.109464\pi$
$683$	39.3301	+	12.7791i	1.50492	+	0.488979i	0.563474	+	0.826134i	$0.309464\pi$
$684$	−19.2939	+	14.0178i	−0.737721	+	0.535986i
$685$		0			0
$686$	27.5944	+	20.0485i	1.05356	+	0.765457i
$687$	−1.66067	−	2.28571i	−0.0633584	−	0.0872053i
$688$	−22.8340	−	31.4283i	−0.870539	−	1.19819i
$689$	58.1849	+	42.2738i	2.21667	+	1.61050i
$690$		0			0
$691$	−3.61557	+	2.62686i	−0.137543	+	0.0999306i	−0.654429	−	0.756123i	$-0.727091\pi$
$691$	−3.61557	+	2.62686i	−0.137543	+	0.0999306i	0.516886	+	0.856054i	$0.327091\pi$
$692$	−5.29239	−	1.71960i	−0.201186	−	0.0653694i
$693$			3.09144i			0.117434i
$694$	−22.5250	+	69.3248i	−0.855037	+	2.63153i
$695$		0			0
$696$	−1.30042	−	4.00229i	−0.0492924	−	0.151707i
$697$	−5.63395	+	1.83058i	−0.213401	+	0.0693382i
$698$	−18.3220	+	25.2181i	−0.693498	+	0.954518i
$699$	−7.98709			−0.302099
$700$		0			0
$701$	−25.2265			−0.952791			−0.476396	−	0.879231i	$-0.658057\pi$
$701$	−25.2265			−0.952791			−0.476396	+	0.879231i	$0.658057\pi$
$702$	8.45625	−	11.6390i	0.319161	−	0.439287i
$703$	−8.26391	+	2.68511i	−0.311679	+	0.101271i
$704$	1.00091	+	3.08048i	0.0377231	+	0.116100i
$705$		0			0
$706$	−21.1556	+	65.1104i	−0.796203	+	2.45046i
$707$			15.9627i			0.600339i
$708$	−13.5621	−	4.40658i	−0.509694	−	0.165610i
$709$	1.26199	−	0.916889i	0.0473950	−	0.0344345i	−0.563836	−	0.825887i	$-0.690675\pi$
$709$	1.26199	−	0.916889i	0.0473950	−	0.0344345i	0.611231	+	0.791453i	$0.290675\pi$
$710$		0			0
$711$	1.17071	+	0.850569i	0.0439050	+	0.0318988i
$712$	33.0158	+	45.4423i	1.23732	+	1.70302i
$713$	−1.92897	−	2.65500i	−0.0722404	−	0.0994304i
$714$	10.8598	+	7.89012i	0.406419	+	0.295280i
$715$		0			0
$716$	74.7514	−	54.3100i	2.79359	−	2.02966i
$717$	−18.1290	−	5.89045i	−0.677038	−	0.219983i
$718$			41.6794i			1.55546i
$719$	−8.94304	+	27.5238i	−0.333519	+	1.02647i	0.633928	+	0.773392i	$0.281442\pi$
$719$	−8.94304	+	27.5238i	−0.333519	+	1.02647i	−0.967447	+	0.253074i	$0.918558\pi$
$720$		0			0
$721$	−3.87748	−	11.9336i	−0.144405	−	0.444432i
$722$	23.7815	−	7.72709i	0.885057	−	0.287572i
$723$	−12.4140	+	17.0864i	−0.461680	+	0.635448i
$724$	30.7547			1.14299
$725$		0			0
$726$	5.51466			0.204668
$727$	21.7242	−	29.9008i	0.805707	−	1.10896i	−0.186265	−	0.982500i	$-0.559638\pi$
$727$	21.7242	−	29.9008i	0.805707	−	1.10896i	0.991972	−	0.126461i	$-0.0403618\pi$
$728$	−34.7355	+	11.2863i	−1.28739	+	0.418297i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	−8.93229	+	27.4907i	−0.330372	+	1.01678i
$732$		−	24.0678i		−	0.889570i
$733$	−3.95793	−	1.28601i	−0.146189	−	0.0474998i	0.235008	−	0.971993i	$-0.424488\pi$
$733$	−3.95793	−	1.28601i	−0.146189	−	0.0474998i	−0.381198	+	0.924494i	$0.624488\pi$
$734$	−61.3757	+	44.5921i	−2.26542	+	1.64592i
$735$		0			0
$736$	−15.4749	−	11.2432i	−0.570413	−	0.414429i
$737$	−1.62257	−	2.23328i	−0.0597682	−	0.0822638i
$738$	−1.73816	−	2.39237i	−0.0639824	−	0.0880642i
$739$	15.3371	+	11.1431i	0.564184	+	0.409904i	0.832988	−	0.553291i	$-0.186628\pi$
$739$	15.3371	+	11.1431i	0.564184	+	0.409904i	−0.268804	+	0.963195i	$0.586628\pi$
$740$		0			0
$741$	−24.6366	+	17.8996i	−0.905050	+	0.657557i
$742$	−31.8587	−	10.3515i	−1.16957	−	0.380016i
$743$		−	11.7060i		−	0.429452i	−0.976674	−	0.214726i	$-0.931114\pi$
$743$		−	11.7060i		−	0.429452i	0.976674	−	0.214726i	$-0.0688859\pi$
$744$	1.62647	−	5.00575i	0.0596292	−	0.183520i
$745$		0			0
$746$	−19.4718	−	59.9281i	−0.712915	−	2.19413i
$747$	−10.9140	+	3.54616i	−0.399321	+	0.129747i
$748$	−39.4146	+	54.2495i	−1.44114	+	1.98356i
$749$	−6.76126			−0.247051
$750$		0			0
$751$	−4.95672			−0.180873			−0.0904367	−	0.995902i	$-0.528826\pi$
$751$	−4.95672			−0.180873			−0.0904367	+	0.995902i	$0.528826\pi$
$752$	−13.1976	+	18.1650i	−0.481268	+	0.662408i
$753$	28.7432	−	9.33924i	1.04746	−	0.340341i
$754$	−3.02174	−	9.29995i	−0.110045	−	0.338684i
$755$		0			0
$756$	−1.42758	+	4.39365i	−0.0519207	+	0.159795i
$757$		−	18.6020i		−	0.676101i	−0.941128	−	0.338051i	$-0.890232\pi$
$757$		−	18.6020i		−	0.676101i	0.941128	−	0.338051i	$-0.109768\pi$
$758$	46.8132	+	15.2105i	1.70033	+	0.552472i
$759$	−9.27881	+	6.74145i	−0.336799	+	0.244699i
$760$		0			0
$761$	9.18925	+	6.67638i	0.333110	+	0.242019i	0.741749	−	0.670677i	$-0.233997\pi$
$761$	9.18925	+	6.67638i	0.333110	+	0.242019i	−0.408639	+	0.912696i	$0.633997\pi$
$762$	17.4425	+	24.0075i	0.631875	+	0.869702i
$763$	1.41317	+	1.94507i	0.0511603	+	0.0704161i
$764$	29.3245	+	21.3055i	1.06092	+	0.770806i
$765$		0			0
$766$	23.0982	−	16.7818i	0.834572	−	0.606352i
$767$	−17.3176	−	5.62682i	−0.625302	−	0.203173i
$768$			29.9884i			1.08211i
$769$	−2.24803	+	6.91872i	−0.0810660	+	0.249495i	−0.983373	−	0.181599i	$-0.941873\pi$
$769$	−2.24803	+	6.91872i	−0.0810660	+	0.249495i	0.902307	+	0.431095i	$0.141873\pi$
$770$		0			0
$771$	1.57665	+	4.85243i	0.0567817	+	0.174756i
$772$	58.9584	−	19.1567i	2.12196	−	0.689466i
$773$	5.47985	−	7.54237i	0.197097	−	0.271280i	−0.699017	−	0.715105i	$-0.746379\pi$
$773$	5.47985	−	7.54237i	0.197097	−	0.271280i	0.896114	+	0.443825i	$0.146379\pi$
$774$	−14.4292			−0.518648
$775$		0			0
$776$	−37.3296			−1.34005
$777$	−0.989360	+	1.36174i	−0.0354931	+	0.0488520i
$778$	−35.9649	+	11.6857i	−1.28941	+	0.418953i
$779$	1.93427	+	5.95307i	0.0693024	+	0.213291i
$780$		0			0
$781$	−1.29780	+	3.99421i	−0.0464389	+	0.142924i
$782$			49.8011i			1.78088i
$783$	−0.646430	−	0.210038i	−0.0231015	−	0.00750614i
$784$	−32.7067	+	23.7628i	−1.16810	+	0.848671i
$785$		0			0
$786$	−16.3464	−	11.8763i	−0.583055	−	0.423615i
$787$	−8.73787	−	12.0266i	−0.311471	−	0.428704i	0.624368	−	0.781130i	$-0.285357\pi$
$787$	−8.73787	−	12.0266i	−0.311471	−	0.428704i	−0.935839	+	0.352427i	$0.885357\pi$
$788$	15.0381	+	20.6981i	0.535708	+	0.737339i
$789$	5.19017	+	3.77088i	0.184775	+	0.134247i
$790$		0			0
$791$	3.26017	−	2.36865i	0.115918	−	0.0842196i
$792$	−17.4943	−	5.68426i	−0.621634	−	0.201981i
$793$		−	30.7324i		−	1.09134i
$794$	−18.8962	+	58.1565i	−0.670600	+	2.06390i
$795$		0			0
$796$	−36.4598	−	112.212i	−1.29228	−	3.97724i
$797$	9.10680	−	2.95898i	0.322580	−	0.104812i	−0.143251	−	0.989686i	$-0.545756\pi$
$797$	9.10680	−	2.95898i	0.322580	−	0.104812i	0.465831	+	0.884874i	$0.345756\pi$
$798$	8.33704	−	11.4749i	0.295128	−	0.406209i
$799$	16.7068			0.591044
$800$		0			0
$801$	9.07225			0.320552
$802$	−20.0740	+	27.6295i	−0.708838	+	0.975632i
$803$	−31.9953	+	10.3959i	−1.12909	+	0.366863i
$804$	−1.27475	−	3.92328i	−0.0449570	−	0.138364i
$805$		0			0
$806$	3.77935	−	11.6316i	0.133122	−	0.409707i
$807$		−	17.4592i		−	0.614592i
$808$	−90.3323	−	29.3508i	−3.17788	−	1.03256i
$809$	33.2859	−	24.1836i	1.17027	−	0.850250i	0.179228	−	0.983808i	$-0.442640\pi$
$809$	33.2859	−	24.1836i	1.17027	−	0.850250i	0.991041	+	0.133557i	$0.0426400\pi$
$810$		0			0
$811$	−35.1435	−	25.5333i	−1.23406	−	0.896594i	−0.236868	−	0.971542i	$-0.576121\pi$
$811$	−35.1435	−	25.5333i	−1.23406	−	0.896594i	−0.997187	+	0.0749479i	$0.976121\pi$
$812$	1.84566	+	2.54034i	0.0647701	+	0.0891484i
$813$	−0.0559488	−	0.0770069i	−0.00196221	−	0.00270075i
$814$	−9.86679	−	7.16864i	−0.345831	−	0.251261i
$815$		0			0
$816$	−28.0987	+	20.4149i	−0.983651	+	0.714665i
$817$	29.0479	+	9.43823i	1.01626	+	0.330202i
$818$		−	90.0206i		−	3.14750i
$819$	−1.82290	+	5.61031i	−0.0636973	+	0.196040i
$820$		0			0
$821$	5.39595	+	16.6070i	0.188320	+	0.579589i	0.999990	−	0.00452746i	$-0.00144114\pi$
$821$	5.39595	+	16.6070i	0.188320	+	0.579589i	−0.811670	+	0.584116i	$0.801441\pi$
$822$	−26.6720	+	8.66625i	−0.930292	+	0.302270i
$823$	1.30756	−	1.79970i	0.0455787	−	0.0627337i	−0.785619	−	0.618710i	$-0.787656\pi$
$823$	1.30756	−	1.79970i	0.0455787	−	0.0627337i	0.831198	+	0.555976i	$0.187656\pi$
$824$	74.6616			2.60096
$825$		0			0
$826$	8.48106			0.295094
$827$	18.4888	−	25.4476i	0.642918	−	0.884900i	−0.355849	−	0.934543i	$-0.615808\pi$
$827$	18.4888	−	25.4476i	0.642918	−	0.884900i	0.998767	+	0.0496432i	$0.0158084\pi$
$828$	−16.3004	+	5.29633i	−0.566479	+	0.184060i
$829$	−16.4690	−	50.6862i	−0.571990	−	1.76041i	−0.646206	−	0.763163i	$-0.723645\pi$
$829$	−16.4690	−	50.6862i	−0.571990	−	1.76041i	0.0742155	−	0.997242i	$-0.476355\pi$
$830$		0			0
$831$	−5.68614	+	17.5001i	−0.197250	+	0.607073i
$832$			6.18061i			0.214274i
$833$	28.6089	+	9.29560i	0.991240	+	0.322073i
$834$	25.1903	−	18.3018i	0.872267	−	0.633739i
$835$		0			0
$836$	57.3223	+	41.6471i	1.98253	+	1.44040i
$837$	−0.499683	−	0.687754i	−0.0172716	−	0.0237723i
$838$	−23.5853	−	32.4623i	−0.814739	−	1.12139i
$839$	−6.77415	−	4.92171i	−0.233870	−	0.169916i	0.464678	−	0.885480i	$-0.346170\pi$
$839$	−6.77415	−	4.92171i	−0.233870	−	0.169916i	−0.698548	+	0.715563i	$0.746170\pi$
$840$		0			0
$841$	23.0877	−	16.7742i	0.796129	−	0.578421i
$842$	−28.9166	−	9.39558i	−0.996532	−	0.323793i
$843$		−	17.9361i		−	0.617750i
$844$	36.3015	−	111.725i	1.24955	−	3.84572i
$845$		0			0
$846$	2.57715	+	7.93164i	0.0886041	+	0.272695i
$847$	−2.15054	+	0.698751i	−0.0738933	+	0.0240094i
$848$	50.9453	−	70.1202i	1.74947	−	2.40794i
$849$	22.2399			0.763273
$850$		0			0
$851$	−6.24467			−0.214064
$852$	−3.68895	+	5.07740i	−0.126381	+	0.173949i
$853$	−1.16381	+	0.378146i	−0.0398482	+	0.0129475i	−0.328873	−	0.944374i	$-0.606669\pi$
$853$	−1.16381	+	0.378146i	−0.0398482	+	0.0129475i	0.289025	+	0.957322i	$0.406669\pi$
$854$	4.42332	+	13.6136i	0.151363	+	0.465847i
$855$		0			0
$856$	12.4320	−	38.2618i	0.424917	−	1.30776i
$857$		−	14.3684i		−	0.490816i	−0.969420	−	0.245408i	$-0.921078\pi$
$857$		−	14.3684i		−	0.490816i	0.969420	−	0.245408i	$-0.0789219\pi$
$858$	−40.6508	−	13.2082i	−1.38780	−	0.450922i
$859$	−8.34015	+	6.05947i	−0.284562	+	0.206747i	−0.720905	−	0.693034i	$-0.756274\pi$
$859$	−8.34015	+	6.05947i	−0.284562	+	0.206747i	0.436343	+	0.899781i	$0.356274\pi$
$860$		0			0
$861$	0.980955	+	0.712705i	0.0334308	+	0.0242889i
$862$	21.8413	+	30.0619i	0.743916	+	1.02391i
$863$	17.7937	+	24.4909i	0.605703	+	0.833679i	0.996215	−	0.0869190i	$-0.0277021\pi$
$863$	17.7937	+	24.4909i	0.605703	+	0.833679i	−0.390512	+	0.920598i	$0.627702\pi$
$864$	−4.00864	−	2.91245i	−0.136377	−	0.0990835i
$865$		0			0
$866$	8.77241	−	6.37353i	0.298099	−	0.216581i
$867$	8.41031	+	2.73268i	0.285629	+	0.0928065i
$868$			3.92730i			0.133301i
$869$	1.32855	−	4.08885i	0.0450679	−	0.138705i
$870$		0			0
$871$	−1.62775	−	5.00969i	−0.0551541	−	0.169747i
$872$	−13.6055	+	4.42068i	−0.460739	+	0.149703i
$873$	−3.54392	+	4.87779i	−0.119944	+	0.165088i
$874$	52.6220			1.77996
$875$		0			0
$876$	−50.2734			−1.69858
$877$	18.0065	−	24.7839i	0.608037	−	0.836892i	−0.388377	−	0.921501i	$-0.626964\pi$
$877$	18.0065	−	24.7839i	0.608037	−	0.836892i	0.996414	+	0.0846091i	$0.0269641\pi$
$878$	49.0111	−	15.9247i	1.65404	−	0.537431i
$879$	5.78837	+	17.8148i	0.195237	+	0.600877i
$880$		0			0
$881$	4.70359	−	14.4762i	0.158468	−	0.487714i	−0.840028	−	0.542543i	$-0.817461\pi$
$881$	4.70359	−	14.4762i	0.158468	−	0.487714i	0.998496	+	0.0548293i	$0.0174615\pi$
$882$			15.0161i			0.505620i
$883$	−38.2310	−	12.4220i	−1.28658	−	0.418034i	−0.415684	−	0.909509i	$-0.636458\pi$
$883$	−38.2310	−	12.4220i	−1.28658	−	0.418034i	−0.870892	+	0.491475i	$0.836458\pi$
$884$	−103.518	+	75.2102i	−3.48169	+	2.52959i
$885$		0			0
$886$	39.1189	+	28.4216i	1.31423	+	0.954842i
$887$	18.7169	+	25.7617i	0.628453	+	0.864992i	0.997934	−	0.0642465i	$-0.0204644\pi$
$887$	18.7169	+	25.7617i	0.628453	+	0.864992i	−0.369481	+	0.929238i	$0.620464\pi$
$888$	−5.88688	−	8.10259i	−0.197551	−	0.271905i
$889$	−9.84394	−	7.15204i	−0.330155	−	0.239872i
$890$		0			0
$891$	−2.40360	+	1.74631i	−0.0805235	+	0.0585037i
$892$	−115.889	−	37.6545i	−3.88024	−	1.26077i
$893$		−	17.6531i		−	0.590739i
$894$	−3.62946	+	11.1703i	−0.121387	+	0.373591i
$895$		0			0
$896$	−4.07604	−	12.5448i	−0.136171	−	0.419091i
$897$	−20.8142	+	6.76296i	−0.694967	+	0.225809i
$898$	43.9716	−	60.5217i	1.46735	−	2.01964i
$899$	−0.577817			−0.0192713
$900$		0			0
$901$	−64.4914			−2.14852
$902$	−5.16407	+	7.10774i	−0.171945	+	0.236662i
$903$	5.62692	−	1.82830i	0.187252	−	0.0608419i
$904$	7.40962	+	22.8045i	0.246440	+	0.758465i
$905$		0			0
$906$	3.66409	−	11.2769i	0.121731	−	0.374651i
$907$		−	28.8507i		−	0.957970i	−0.877823	−	0.478985i	$-0.841005\pi$
$907$		−	28.8507i		−	0.957970i	0.877823	−	0.478985i	$-0.158995\pi$
$908$	−0.549602	−	0.178577i	−0.0182392	−	0.00592627i
$909$	−12.4110	+	9.01712i	−0.411647	+	0.299079i
$910$		0			0
$911$	−39.1370	−	28.4347i	−1.29667	−	0.942084i	−0.296750	−	0.954955i	$-0.595903\pi$
$911$	−39.1370	−	28.4347i	−1.29667	−	0.942084i	−0.999917	+	0.0128711i	$0.995903\pi$
$912$	21.5713	+	29.6903i	0.714296	+	0.983143i
$913$	20.0400	+	27.5827i	0.663228	+	0.912855i
$914$	−58.1036	−	42.2148i	−1.92190	−	1.39634i
$915$		0			0
$916$	−10.1481	+	7.37301i	−0.335302	+	0.243611i
$917$	7.87936	+	2.56016i	0.260199	+	0.0845439i
$918$			12.9006i			0.425782i
$919$	2.58963	−	7.97006i	0.0854240	−	0.262908i	−0.899216	−	0.437505i	$-0.855862\pi$
$919$	2.58963	−	7.97006i	0.0854240	−	0.262908i	0.984640	+	0.174597i	$0.0558622\pi$
$920$		0			0
$921$	−2.17501	−	6.69401i	−0.0716692	−	0.220575i
$922$	−39.9609	+	12.9841i	−1.31604	+	0.427608i
$923$	−4.71046	+	6.48340i	−0.155047	+	0.213404i
$924$	13.7253			0.451530
$925$		0			0
$926$	−23.3703			−0.767995
$927$	7.08808	−	9.75590i	0.232803	−	0.320426i
$928$	−3.20303	+	1.04073i	−0.105145	+	0.0341636i
$929$	−4.42283	−	13.6121i	−0.145108	−	0.446597i	0.851917	−	0.523677i	$-0.175440\pi$
$929$	−4.42283	−	13.6121i	−0.145108	−	0.446597i	−0.997025	+	0.0770801i	$0.975440\pi$
$930$		0			0
$931$	9.82212	−	30.2294i	0.321907	−	0.990728i
$932$			35.4610i			1.16156i
$933$	27.8460	+	9.04771i	0.911637	+	0.296209i
$934$	−21.7873	+	15.8294i	−0.712901	+	0.517953i
$935$		0			0
$936$	−28.3967	−	20.6314i	−0.928177	−	0.674360i
$937$	12.8869	+	17.7372i	0.420996	+	0.579451i	0.965857	−	0.259075i	$-0.0834178\pi$
$937$	12.8869	+	17.7372i	0.420996	+	0.579451i	−0.544862	+	0.838526i	$0.683418\pi$
$938$	1.44209	+	1.98487i	0.0470859	+	0.0648082i
$939$	−12.6493	−	9.19024i	−0.412794	−	0.299912i
$940$		0			0
$941$	−18.1167	+	13.1625i	−0.590586	+	0.429086i	−0.842525	−	0.538657i	$-0.818932\pi$
$941$	−18.1167	+	13.1625i	−0.590586	+	0.429086i	0.251939	+	0.967743i	$0.418932\pi$
$942$	−36.1360	−	11.7413i	−1.17737	−	0.382552i
$943$			4.49847i			0.146490i
$944$	−6.78104	+	20.8699i	−0.220704	+	0.679257i
$945$		0			0
$946$	13.2474	+	40.7712i	0.430709	+	1.32559i
$947$	−41.4316	+	13.4619i	−1.34635	+	0.437454i	−0.891462	−	0.453096i	$-0.850319\pi$
$947$	−41.4316	+	13.4619i	−1.34635	+	0.437454i	−0.454884	+	0.890550i	$0.650319\pi$
$948$	3.77635	−	5.19769i	0.122650	−	0.168813i
$949$	−64.1947			−2.08385
$950$		0			0
$951$	−6.24144			−0.202393
$952$	19.2502	−	26.4957i	0.623903	−	0.858729i
$953$	2.25561	−	0.732893i	0.0730664	−	0.0237407i	−0.272256	−	0.962225i	$-0.587770\pi$
$953$	2.25561	−	0.732893i	0.0730664	−	0.0237407i	0.345322	+	0.938484i	$0.387770\pi$
$954$	−9.94827	−	30.6176i	−0.322087	−	0.991282i
$955$		0			0
$956$	−26.1524	+	80.4887i	−0.845828	+	2.60319i
$957$			2.01938i			0.0652774i
$958$	81.1073	+	26.3534i	2.62046	+	0.851439i
$959$	9.30310	−	6.75910i	0.300413	−	0.218263i
$960$		0			0
$961$	24.4949	+	17.7966i	0.790157	+	0.574082i
$962$	−13.6791	−	18.8276i	−0.441031	−	0.607027i
$963$	−3.81935	−	5.25689i	−0.123077	−	0.169401i
$964$	75.8598	+	55.1154i	2.44328	+	1.77515i
$965$		0			0
$966$	8.24672	−	5.99159i	0.265334	−	0.192776i
$967$	−18.8174	−	6.11413i	−0.605125	−	0.196617i	−0.00960036	−	0.999954i	$-0.503056\pi$
$967$	−18.8174	−	6.11413i	−0.605125	−	0.196617i	−0.595525	+	0.803337i	$0.703056\pi$
$968$		−	13.4546i		−	0.432447i
$969$	8.43831	−	25.9704i	0.271077	−	0.834291i
$970$		0			0
$971$	15.2604	+	46.9668i	0.489731	+	1.50724i	0.825010	+	0.565118i	$0.191169\pi$
$971$	15.2604	+	46.9668i	0.489731	+	1.50724i	−0.335279	+	0.942119i	$0.608831\pi$
$972$	−4.22249	+	1.37197i	−0.135436	+	0.0440059i
$973$	−7.50438	+	10.3289i	−0.240579	+	0.331129i
$974$	74.2234			2.37827
$975$		0			0
$976$	−37.0365			−1.18551
$977$	−28.0757	+	38.6429i	−0.898221	+	1.23630i	0.0728110	+	0.997346i	$0.476803\pi$
$977$	−28.0757	+	38.6429i	−0.898221	+	1.23630i	−0.971032	+	0.238949i	$0.923197\pi$
$978$	−28.7474	+	9.34058i	−0.919239	+	0.298679i
$979$	−8.32916	−	25.6345i	−0.266201	−	0.819283i
$980$		0			0
$981$	−0.714006	+	2.19749i	−0.0227965	+	0.0701603i
$982$		−	35.4131i		−	1.13008i
$983$	−49.3867	−	16.0467i	−1.57519	−	0.511810i	−0.614379	−	0.789011i	$-0.710593\pi$
$983$	−49.3867	−	16.0467i	−1.57519	−	0.511810i	−0.960812	+	0.277201i	$0.910593\pi$
$984$	−5.83686	+	4.24073i	−0.186072	+	0.135190i
$985$		0			0
$986$	7.09383	+	5.15397i	0.225914	+	0.164136i
$987$	−2.01000	−	2.76653i	−0.0639791	−	0.0880596i
$988$	79.4703	+	109.381i	2.52829	+	3.47989i
$989$	17.7581	+	12.9020i	0.564674	+	0.410260i
$990$		0			0
$991$	13.2509	−	9.62734i	0.420929	−	0.305823i	−0.357083	−	0.934073i	$-0.616229\pi$
$991$	13.2509	−	9.62734i	0.420929	−	0.305823i	0.778011	+	0.628250i	$0.216229\pi$
$992$	−4.00610	−	1.30166i	−0.127194	−	0.0413277i
$993$		−	21.4575i		−	0.680933i
$994$	1.15344	−	3.54994i	0.0365850	−	0.112597i
$995$		0			0
$996$	15.7442	+	48.4557i	0.498874	+	1.53538i
$997$	21.1625	−	6.87610i	0.670222	−	0.217768i	0.0459126	−	0.998945i	$-0.485380\pi$
$997$	21.1625	−	6.87610i	0.670222	−	0.217768i	0.624309	+	0.781177i	$0.285380\pi$
$998$	−53.3299	+	73.4022i	−1.68813	+	2.32351i
$999$	−1.61763			−0.0511795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.c.49.1		16
5.2	odd	4		375.2.g.d.76.1		16
5.3	odd	4		375.2.g.e.76.4		16
5.4	even	2		75.2.i.a.34.4	✓	16
15.14	odd	2		225.2.m.b.109.1		16
25.2	odd	20		375.2.g.d.301.1		16
25.6	even	5		1875.2.b.h.1249.1		16
25.8	odd	20		1875.2.a.m.1.1		8
25.11	even	5		75.2.i.a.64.4	yes	16
25.14	even	10	inner	375.2.i.c.199.1		16
25.17	odd	20		1875.2.a.p.1.8		8
25.19	even	10		1875.2.b.h.1249.16		16
25.23	odd	20		375.2.g.e.301.4		16
75.8	even	20		5625.2.a.bd.1.8		8
75.11	odd	10		225.2.m.b.64.1		16
75.17	even	20		5625.2.a.t.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.4	✓	16	5.4	even	2
75.2.i.a.64.4	yes	16	25.11	even	5
225.2.m.b.64.1		16	75.11	odd	10
225.2.m.b.109.1		16	15.14	odd	2
375.2.g.d.76.1		16	5.2	odd	4
375.2.g.d.301.1		16	25.2	odd	20
375.2.g.e.76.4		16	5.3	odd	4
375.2.g.e.301.4		16	25.23	odd	20
375.2.i.c.49.1		16	1.1	even	1	trivial
375.2.i.c.199.1		16	25.14	even	10	inner
1875.2.a.m.1.1		8	25.8	odd	20
1875.2.a.p.1.8		8	25.17	odd	20
1875.2.b.h.1249.1		16	25.6	even	5
1875.2.b.h.1249.16		16	25.19	even	10
5625.2.a.t.1.1		8	75.17	even	20
5625.2.a.bd.1.8		8	75.8	even	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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.49161 + 2.05302i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.37197 - 4.22249i) q^{4} +(-0.784184 + 2.41347i) q^{6} -1.04054i q^{7} +(5.88835 + 1.91324i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.49161 + 2.05302i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.37197 - 4.22249i) q^{4} +(-0.784184 + 2.41347i) q^{6} -1.04054i q^{7} +(5.88835 + 1.91324i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-2.40360 - 1.74631i) q^{11} +(-2.60964 - 3.59186i) q^{12} +(-3.33228 - 4.58650i) q^{13} +(2.13624 + 1.55207i) q^{14} +(-5.52731 + 4.01583i) q^{16} +(4.83480 + 1.57092i) q^{17} +2.53767i q^{18} +(1.65990 - 5.10866i) q^{19} +(-0.321543 - 0.989608i) q^{21} +(7.17044 - 2.32982i) q^{22} +(2.26908 - 3.12312i) q^{23} +6.19138 q^{24} +14.3866 q^{26} +(0.587785 - 0.809017i) q^{27} +(-4.39365 + 1.42758i) q^{28} +(-0.210038 - 0.646430i) q^{29} +(0.262699 - 0.808503i) q^{31} -4.95495i q^{32} +(-2.82560 - 0.918092i) q^{33} +(-10.4368 + 7.58275i) q^{34} +(-3.59186 - 2.60964i) q^{36} +(-0.950818 - 1.30869i) q^{37} +(8.01226 + 11.0279i) q^{38} +(-4.58650 - 3.33228i) q^{39} +(-0.942740 + 0.684941i) q^{41} +(2.51130 + 0.815972i) q^{42} +5.68601i q^{43} +(-4.07613 + 12.5450i) q^{44} +(3.02725 + 9.31693i) q^{46} +(3.12556 - 1.01555i) q^{47} +(-4.01583 + 5.52731i) q^{48} +5.91729 q^{49} +5.08361 q^{51} +(-14.7946 + 20.3631i) q^{52} +(-12.0652 + 3.92023i) q^{53} +(0.784184 + 2.41347i) q^{54} +(1.99080 - 6.12704i) q^{56} -5.37156i q^{57} +(1.64043 + 0.533007i) q^{58} +(2.59846 - 1.88789i) q^{59} +(4.38562 + 3.18634i) q^{61} +(1.26803 + 1.74530i) q^{62} +(-0.611611 - 0.841811i) q^{63} +(-0.881995 - 0.640807i) q^{64} +(6.09954 - 4.43157i) q^{66} +(0.883665 + 0.287120i) q^{67} -22.5702i q^{68} +(1.19292 - 3.67145i) q^{69} +(-0.436821 - 1.34440i) q^{71} +(5.88835 - 1.91324i) q^{72} +(6.65571 - 9.16080i) q^{73} +4.10501 q^{74} -23.8486 q^{76} +(-1.81710 + 2.50103i) q^{77} +(13.6825 - 4.44571i) q^{78} +(0.447171 + 1.37625i) q^{79} +(0.309017 - 0.951057i) q^{81} -2.95713i q^{82} +(-10.9140 - 3.54616i) q^{83} +(-3.73746 + 2.71542i) q^{84} +(-11.6735 - 8.48129i) q^{86} +(-0.399516 - 0.549886i) q^{87} +(-10.8121 - 14.8816i) q^{88} +(7.33961 + 5.33254i) q^{89} +(-4.77241 + 3.46736i) q^{91} +(-16.3004 - 5.29633i) q^{92} -0.850111i q^{93} +(-2.57715 + 7.93164i) q^{94} +(-1.53117 - 4.71244i) q^{96} +(-5.73419 + 1.86315i) q^{97} +(-8.82627 + 12.1483i) q^{98} -2.97101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Introduction

L-functions

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Database

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