LMFDB - Embedded newform 825.2.n.f.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	825.301
Dual form			825.2.n.f.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-1.30902 + 0.951057i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(1.30902 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-1.30902 + 0.951057i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(2.80902 + 1.76336i) q^{11} -0.618034 q^{12} +(5.04508 + 3.66547i) q^{13} +(1.50000 - 4.61653i) q^{14} +(3.92705 - 2.85317i) q^{16} +(-0.500000 + 0.363271i) q^{17} +(-0.500000 - 1.53884i) q^{18} +(-0.263932 + 0.812299i) q^{19} +3.00000 q^{21} +(2.00000 + 4.97980i) q^{22} +5.47214 q^{23} +(1.80902 + 1.31433i) q^{24} +(3.11803 + 9.59632i) q^{26} +(0.809017 - 0.587785i) q^{27} +(1.50000 - 1.08981i) q^{28} +(-1.38197 - 4.25325i) q^{29} +(3.11803 + 2.26538i) q^{31} +3.38197 q^{32} +(-2.54508 + 2.12663i) q^{33} -1.00000 q^{34} +(0.190983 - 0.587785i) q^{36} +(1.30902 + 4.02874i) q^{37} +(-1.11803 + 0.812299i) q^{38} +(-5.04508 + 3.66547i) q^{39} +(1.83688 - 5.65334i) q^{41} +(3.92705 + 2.85317i) q^{42} -1.76393 q^{43} +(-0.500000 + 1.98787i) q^{44} +(7.16312 + 5.20431i) q^{46} +(0.190983 - 0.587785i) q^{47} +(1.50000 + 4.61653i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(-0.190983 - 0.587785i) q^{51} +(-1.19098 + 3.66547i) q^{52} +(-5.97214 - 4.33901i) q^{53} +1.61803 q^{54} -6.70820 q^{56} +(-0.690983 - 0.502029i) q^{57} +(2.23607 - 6.88191i) q^{58} +(-1.64590 - 5.06555i) q^{59} +(-0.927051 + 0.673542i) q^{61} +(1.92705 + 5.93085i) q^{62} +(-0.927051 + 2.85317i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(-5.35410 + 0.363271i) q^{66} -10.5623 q^{67} +(-0.309017 - 0.224514i) q^{68} +(-1.69098 + 5.20431i) q^{69} +(-11.7812 + 8.55951i) q^{71} +(-1.80902 + 1.31433i) q^{72} +(-0.381966 - 1.17557i) q^{73} +(-2.11803 + 6.51864i) q^{74} -0.527864 q^{76} +(2.42705 - 9.64932i) q^{77} -10.0902 q^{78} +(-0.427051 - 0.310271i) q^{79} +(0.309017 + 0.951057i) q^{81} +(7.78115 - 5.65334i) q^{82} +(-10.2812 + 7.46969i) q^{83} +(0.572949 + 1.76336i) q^{84} +(-2.30902 - 1.67760i) q^{86} +4.47214 q^{87} +(5.69098 - 4.75528i) q^{88} +9.47214 q^{89} +(5.78115 - 17.7926i) q^{91} +(1.04508 + 3.21644i) q^{92} +(-3.11803 + 2.26538i) q^{93} +(0.809017 - 0.587785i) q^{94} +(-1.04508 + 3.21644i) q^{96} +(12.1631 + 8.83702i) q^{97} -3.23607 q^{98} +(-1.23607 - 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} + 9 q^{11} + 2 q^{12} + 9 q^{13} + 6 q^{14} + 9 q^{16} - 2 q^{17} - 2 q^{18} - 10 q^{19} + 12 q^{21} + 8 q^{22} + 4 q^{23} + 5 q^{24} + 8 q^{26} + q^{27} + 6 q^{28} - 10 q^{29} + 8 q^{31} + 18 q^{32} + q^{33} - 4 q^{34} + 3 q^{36} + 3 q^{37} - 9 q^{39} + 23 q^{41} + 9 q^{42} - 16 q^{43} - 2 q^{44} + 13 q^{46} + 3 q^{47} + 6 q^{48} - 2 q^{49} - 3 q^{51} - 7 q^{52} - 6 q^{53} + 2 q^{54} - 5 q^{57} - 20 q^{59} + 3 q^{61} + q^{62} + 3 q^{63} - 7 q^{64} - 8 q^{66} - 2 q^{67} + q^{68} - 9 q^{69} - 27 q^{71} - 5 q^{72} - 6 q^{73} - 4 q^{74} - 20 q^{76} + 3 q^{77} - 18 q^{78} + 5 q^{79} - q^{81} + 11 q^{82} - 21 q^{83} + 9 q^{84} - 7 q^{86} + 25 q^{88} + 20 q^{89} + 3 q^{91} - 7 q^{92} - 8 q^{93} + q^{94} + 7 q^{96} + 33 q^{97} - 4 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9 + 9 * q^11 + 2 * q^12 + 9 * q^13 + 6 * q^14 + 9 * q^16 - 2 * q^17 - 2 * q^18 - 10 * q^19 + 12 * q^21 + 8 * q^22 + 4 * q^23 + 5 * q^24 + 8 * q^26 + q^27 + 6 * q^28 - 10 * q^29 + 8 * q^31 + 18 * q^32 + q^33 - 4 * q^34 + 3 * q^36 + 3 * q^37 - 9 * q^39 + 23 * q^41 + 9 * q^42 - 16 * q^43 - 2 * q^44 + 13 * q^46 + 3 * q^47 + 6 * q^48 - 2 * q^49 - 3 * q^51 - 7 * q^52 - 6 * q^53 + 2 * q^54 - 5 * q^57 - 20 * q^59 + 3 * q^61 + q^62 + 3 * q^63 - 7 * q^64 - 8 * q^66 - 2 * q^67 + q^68 - 9 * q^69 - 27 * q^71 - 5 * q^72 - 6 * q^73 - 4 * q^74 - 20 * q^76 + 3 * q^77 - 18 * q^78 + 5 * q^79 - q^81 + 11 * q^82 - 21 * q^83 + 9 * q^84 - 7 * q^86 + 25 * q^88 + 20 * q^89 + 3 * q^91 - 7 * q^92 - 8 * q^93 + q^94 + 7 * q^96 + 33 * q^97 - 4 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	0.944915	−	0.327315i	$-0.106144\pi$
$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	−0.0193004	+	0.999814i	$0.506144\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	0.190983	+	0.587785i	0.0954915	+	0.293893i
$5$		0			0
$5$		0			0
$6$	−1.30902	+	0.951057i	−0.534404	+	0.388267i
$7$	−0.927051	−	2.85317i	−0.350392	−	1.07840i	−0.958633	−	0.284644i	$-0.908125\pi$
$7$	−0.927051	−	2.85317i	−0.350392	−	1.07840i	0.608241	−	0.793752i	$-0.291875\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	2.80902	+	1.76336i	0.846950	+	0.531672i
$11$	2.80902	+	1.76336i	0.846950	+	0.531672i
$12$	−0.618034			−0.178411
$13$	5.04508	+	3.66547i	1.39925	+	1.01662i	0.994777	+	0.102070i	$0.0325466\pi$
$13$	5.04508	+	3.66547i	1.39925	+	1.01662i	0.404478	+	0.914548i	$0.367453\pi$
$14$	1.50000	−	4.61653i	0.400892	−	1.23382i
$15$		0			0
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$	−0.500000	+	0.363271i	−0.121268	+	0.0881062i	−0.646766	−	0.762688i	$-0.723879\pi$
$17$	−0.500000	+	0.363271i	−0.121268	+	0.0881062i	0.525498	+	0.850795i	$0.323879\pi$
$18$	−0.500000	−	1.53884i	−0.117851	−	0.362708i
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	−0.976756	−	0.214353i	$-0.931236\pi$
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	0.916206	+	0.400707i	$0.131236\pi$
$20$		0			0
$21$	3.00000			0.654654
$22$	2.00000	+	4.97980i	0.426401	+	1.06170i
$23$	5.47214			1.14102			0.570510	−	0.821291i	$-0.306746\pi$
$23$	5.47214			1.14102			0.570510	+	0.821291i	$0.306746\pi$
$24$	1.80902	+	1.31433i	0.369264	+	0.268286i
$25$		0			0
$26$	3.11803	+	9.59632i	0.611497	+	1.88199i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	1.50000	−	1.08981i	0.283473	−	0.205955i
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	−0.993505	−	0.113787i	$-0.963702\pi$
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	0.736881	−	0.676023i	$-0.236298\pi$
$30$		0			0
$31$	3.11803	+	2.26538i	0.560015	+	0.406875i	0.831465	−	0.555578i	$-0.187503\pi$
$31$	3.11803	+	2.26538i	0.560015	+	0.406875i	−0.271449	+	0.962453i	$0.587503\pi$
$32$	3.38197			0.597853
$33$	−2.54508	+	2.12663i	−0.443042	+	0.370198i
$34$	−1.00000			−0.171499
$35$		0			0
$36$	0.190983	−	0.587785i	0.0318305	−	0.0979642i
$37$	1.30902	+	4.02874i	0.215201	+	0.662321i	0.999139	+	0.0414819i	$0.0132079\pi$
$37$	1.30902	+	4.02874i	0.215201	+	0.662321i	−0.783938	+	0.620839i	$0.786792\pi$
$38$	−1.11803	+	0.812299i	−0.181369	+	0.131772i
$39$	−5.04508	+	3.66547i	−0.807860	+	0.586945i
$40$		0			0
$41$	1.83688	−	5.65334i	0.286873	−	0.882903i	−0.698958	−	0.715162i	$-0.746353\pi$
$41$	1.83688	−	5.65334i	0.286873	−	0.882903i	0.985831	−	0.167741i	$-0.0536472\pi$
$42$	3.92705	+	2.85317i	0.605957	+	0.440254i
$43$	−1.76393			−0.268997			−0.134499	−	0.990914i	$-0.542942\pi$
$43$	−1.76393			−0.268997			−0.134499	+	0.990914i	$0.542942\pi$
$44$	−0.500000	+	1.98787i	−0.0753778	+	0.299683i
$45$		0			0
$46$	7.16312	+	5.20431i	1.05614	+	0.767334i
$47$	0.190983	−	0.587785i	0.0278577	−	0.0857373i	−0.936161	−	0.351572i	$-0.885647\pi$
$47$	0.190983	−	0.587785i	0.0278577	−	0.0857373i	0.964019	+	0.265834i	$0.0856474\pi$
$48$	1.50000	+	4.61653i	0.216506	+	0.666338i
$49$	−1.61803	+	1.17557i	−0.231148	+	0.167939i
$50$		0			0
$51$	−0.190983	−	0.587785i	−0.0267430	−	0.0823064i
$52$	−1.19098	+	3.66547i	−0.165160	+	0.508309i
$53$	−5.97214	−	4.33901i	−0.820336	−	0.596009i	0.0964728	−	0.995336i	$-0.469244\pi$
$53$	−5.97214	−	4.33901i	−0.820336	−	0.596009i	−0.916809	+	0.399327i	$0.869244\pi$
$54$	1.61803			0.220187
$55$		0			0
$56$	−6.70820			−0.896421
$57$	−0.690983	−	0.502029i	−0.0915229	−	0.0664953i
$58$	2.23607	−	6.88191i	0.293610	−	0.903639i
$59$	−1.64590	−	5.06555i	−0.214278	−	0.659479i	−0.999204	−	0.0398899i	$-0.987299\pi$
$59$	−1.64590	−	5.06555i	−0.214278	−	0.659479i	0.784926	−	0.619589i	$-0.212701\pi$
$60$		0			0
$61$	−0.927051	+	0.673542i	−0.118697	+	0.0862382i	−0.645550	−	0.763718i	$-0.723372\pi$
$61$	−0.927051	+	0.673542i	−0.118697	+	0.0862382i	0.526853	+	0.849956i	$0.323372\pi$
$62$	1.92705	+	5.93085i	0.244736	+	0.753219i
$63$	−0.927051	+	2.85317i	−0.116797	+	0.359466i
$64$	−3.42705	−	2.48990i	−0.428381	−	0.311237i
$65$		0			0
$66$	−5.35410	+	0.363271i	−0.659044	+	0.0447156i
$67$	−10.5623			−1.29039			−0.645196	−	0.764017i	$-0.723224\pi$
$67$	−10.5623			−1.29039			−0.645196	+	0.764017i	$0.723224\pi$
$68$	−0.309017	−	0.224514i	−0.0374738	−	0.0272263i
$69$	−1.69098	+	5.20431i	−0.203570	+	0.626525i
$70$		0			0
$71$	−11.7812	+	8.55951i	−1.39817	+	1.01583i	−0.403253	+	0.915089i	$0.632120\pi$
$71$	−11.7812	+	8.55951i	−1.39817	+	1.01583i	−0.994913	+	0.100738i	$0.967880\pi$
$72$	−1.80902	+	1.31433i	−0.213195	+	0.154895i
$73$	−0.381966	−	1.17557i	−0.0447057	−	0.137590i	0.926212	−	0.377003i	$-0.123045\pi$
$73$	−0.381966	−	1.17557i	−0.0447057	−	0.137590i	−0.970918	+	0.239412i	$0.923045\pi$
$74$	−2.11803	+	6.51864i	−0.246216	+	0.757776i
$75$		0			0
$76$	−0.527864			−0.0605502
$77$	2.42705	−	9.64932i	0.276588	−	1.09964i
$78$	−10.0902			−1.14249
$79$	−0.427051	−	0.310271i	−0.0480470	−	0.0349082i	0.563503	−	0.826114i	$-0.309453\pi$
$79$	−0.427051	−	0.310271i	−0.0480470	−	0.0349082i	−0.611550	+	0.791206i	$0.709453\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	7.78115	−	5.65334i	0.859285	−	0.624307i
$83$	−10.2812	+	7.46969i	−1.12850	+	0.819906i	−0.985476	−	0.169813i	$-0.945684\pi$
$83$	−10.2812	+	7.46969i	−1.12850	+	0.819906i	−0.143027	+	0.989719i	$0.545684\pi$
$84$	0.572949	+	1.76336i	0.0625139	+	0.192398i
$85$		0			0
$86$	−2.30902	−	1.67760i	−0.248988	−	0.180900i
$87$	4.47214			0.479463
$88$	5.69098	−	4.75528i	0.606661	−	0.506915i
$89$	9.47214			1.00404			0.502022	−	0.864855i	$-0.332590\pi$
$89$	9.47214			1.00404			0.502022	+	0.864855i	$0.332590\pi$
$90$		0			0
$91$	5.78115	−	17.7926i	0.606029	−	1.86517i
$92$	1.04508	+	3.21644i	0.108958	+	0.335337i
$93$	−3.11803	+	2.26538i	−0.323325	+	0.234909i
$94$	0.809017	−	0.587785i	0.0834437	−	0.0606254i
$95$		0			0
$96$	−1.04508	+	3.21644i	−0.106664	+	0.328277i
$97$	12.1631	+	8.83702i	1.23498	+	0.897264i	0.997253	−	0.0740689i	$-0.0235985\pi$
$97$	12.1631	+	8.83702i	1.23498	+	0.897264i	0.237724	+	0.971333i	$0.423598\pi$
$98$	−3.23607			−0.326892
$99$	−1.23607	−	3.07768i	−0.124230	−	0.309319i
$100$		0			0
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	0.701952	−	0.712225i	$-0.252312\pi$
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	−0.460451	+	0.887685i	$0.652312\pi$
$102$	0.309017	−	0.951057i	0.0305972	−	0.0941686i
$103$	1.85410	+	5.70634i	0.182690	+	0.562262i	0.999901	−	0.0140765i	$-0.00448085\pi$
$103$	1.85410	+	5.70634i	0.182690	+	0.562262i	−0.817211	+	0.576339i	$0.804481\pi$
$104$	11.2812	−	8.19624i	1.10621	−	0.803707i
$105$		0			0
$106$	−3.69098	−	11.3597i	−0.358500	−	1.10335i
$107$	−0.0729490	+	0.224514i	−0.00705225	+	0.0217046i	−0.954521	−	0.298145i	$-0.903632\pi$
$107$	−0.0729490	+	0.224514i	−0.00705225	+	0.0217046i	0.947468	+	0.319849i	$0.103632\pi$
$108$	0.500000	+	0.363271i	0.0481125	+	0.0349558i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	−4.23607			−0.402070
$112$	−11.7812	−	8.55951i	−1.11321	−	0.808798i
$113$	3.92705	−	12.0862i	0.369426	−	1.13698i	−0.577737	−	0.816223i	$-0.696064\pi$
$113$	3.92705	−	12.0862i	0.369426	−	1.13698i	0.947163	−	0.320753i	$-0.103936\pi$
$114$	−0.427051	−	1.31433i	−0.0399970	−	0.123098i
$115$		0			0
$116$	2.23607	−	1.62460i	0.207614	−	0.150840i
$117$	−1.92705	−	5.93085i	−0.178156	−	0.548308i
$118$	2.66312	−	8.19624i	0.245160	−	0.754525i
$119$	1.50000	+	1.08981i	0.137505	+	0.0999031i
$120$		0			0
$121$	4.78115	+	9.90659i	0.434650	+	0.900599i
$122$	−1.85410			−0.167863
$123$	4.80902	+	3.49396i	0.433614	+	0.315039i
$124$	−0.736068	+	2.26538i	−0.0661009	+	0.203438i
$125$		0			0
$126$	−3.92705	+	2.85317i	−0.349850	+	0.254181i
$127$	7.85410	−	5.70634i	0.696939	−	0.506356i	−0.181995	−	0.983299i	$-0.558255\pi$
$127$	7.85410	−	5.70634i	0.696939	−	0.506356i	0.878934	+	0.476944i	$0.158255\pi$
$128$	−4.20820	−	12.9515i	−0.371956	−	1.14476i
$129$	0.545085	−	1.67760i	0.0479921	−	0.147704i
$130$		0			0
$131$	−13.8541			−1.21044			−0.605219	−	0.796059i	$-0.706915\pi$
$131$	−13.8541			−1.21044			−0.605219	+	0.796059i	$0.706915\pi$
$132$	−1.73607	−	1.08981i	−0.151105	−	0.0948561i
$133$	2.56231			0.222180
$134$	−13.8262	−	10.0453i	−1.19441	−	0.867786i
$135$		0			0
$136$	0.427051	+	1.31433i	0.0366193	+	0.112703i
$137$	−1.19098	+	0.865300i	−0.101753	+	0.0739276i	−0.637498	−	0.770452i	$-0.720031\pi$
$137$	−1.19098	+	0.865300i	−0.101753	+	0.0739276i	0.535746	+	0.844379i	$0.320031\pi$
$138$	−7.16312	+	5.20431i	−0.609765	+	0.443020i
$139$	1.80902	+	5.56758i	0.153439	+	0.472236i	0.997999	−	0.0632239i	$-0.0201382\pi$
$139$	1.80902	+	5.56758i	0.153439	+	0.472236i	−0.844561	+	0.535460i	$0.820138\pi$
$140$		0			0
$141$	0.500000	+	0.363271i	0.0421076	+	0.0305930i
$142$	−23.5623			−1.97730
$143$	7.70820	+	19.1926i	0.644592	+	1.60497i
$144$	−4.85410			−0.404508
$145$		0			0
$146$	0.618034	−	1.90211i	0.0511489	−	0.157420i
$147$	−0.618034	−	1.90211i	−0.0509746	−	0.156884i
$148$	−2.11803	+	1.53884i	−0.174101	+	0.126492i
$149$	−12.1353	+	8.81678i	−0.994159	+	0.722299i	−0.960828	−	0.277146i	$-0.910612\pi$
$149$	−12.1353	+	8.81678i	−0.994159	+	0.722299i	−0.0333309	+	0.999444i	$0.510612\pi$
$150$		0			0
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	−0.922755	−	0.385388i	$-0.874068\pi$
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	0.973050	+	0.230596i	$0.0740676\pi$
$152$	1.54508	+	1.12257i	0.125323	+	0.0910524i
$153$	0.618034			0.0499651
$154$	12.3541	−	10.3229i	0.995522	−	0.831840i
$155$		0			0
$156$	−3.11803	−	2.26538i	−0.249643	−	0.181376i
$157$	−3.00000	+	9.23305i	−0.239426	+	0.736878i	0.757077	+	0.653325i	$0.226627\pi$
$157$	−3.00000	+	9.23305i	−0.239426	+	0.736878i	−0.996503	+	0.0835524i	$0.973373\pi$
$158$	−0.263932	−	0.812299i	−0.0209973	−	0.0646231i
$159$	5.97214	−	4.33901i	0.473621	−	0.344106i
$160$		0			0
$161$	−5.07295	−	15.6129i	−0.399804	−	1.23047i
$162$	−0.500000	+	1.53884i	−0.0392837	+	0.120903i
$163$	−12.3541	−	8.97578i	−0.967648	−	0.703037i	−0.0127336	−	0.999919i	$-0.504053\pi$
$163$	−12.3541	−	8.97578i	−0.967648	−	0.703037i	−0.954914	+	0.296882i	$0.904053\pi$
$164$	3.67376			0.286873
$165$		0			0
$166$	−20.5623			−1.59594
$167$	−15.3992	−	11.1882i	−1.19162	−	0.865766i	−0.198190	−	0.980164i	$-0.563506\pi$
$167$	−15.3992	−	11.1882i	−1.19162	−	0.865766i	−0.993435	+	0.114398i	$0.963506\pi$
$168$	2.07295	−	6.37988i	0.159931	−	0.492219i
$169$	8.00000	+	24.6215i	0.615385	+	1.89396i
$170$		0			0
$171$	0.690983	−	0.502029i	0.0528408	−	0.0383911i
$172$	−0.336881	−	1.03681i	−0.0256869	−	0.0790563i
$173$	−5.44427	+	16.7557i	−0.413920	+	1.27392i	0.499293	+	0.866433i	$0.333593\pi$
$173$	−5.44427	+	16.7557i	−0.413920	+	1.27392i	−0.913213	+	0.407482i	$0.866407\pi$
$174$	5.85410	+	4.25325i	0.443798	+	0.322438i
$175$		0			0
$176$	16.0623	−	1.08981i	1.21074	−	0.0821478i
$177$	5.32624			0.400345
$178$	12.3992	+	9.00854i	0.929358	+	0.675218i
$179$	0.690983	−	2.12663i	0.0516465	−	0.158952i	−0.921907	−	0.387412i	$-0.873369\pi$
$179$	0.690983	−	2.12663i	0.0516465	−	0.158952i	0.973553	+	0.228460i	$0.0733691\pi$
$180$		0			0
$181$	6.89919	−	5.01255i	0.512813	−	0.372580i	−0.301077	−	0.953600i	$-0.597346\pi$
$181$	6.89919	−	5.01255i	0.512813	−	0.372580i	0.813889	+	0.581020i	$0.197346\pi$
$182$	24.4894	−	17.7926i	1.81527	−	1.31887i
$183$	−0.354102	−	1.08981i	−0.0261760	−	0.0805614i
$184$	3.78115	−	11.6372i	0.278750	−	0.857905i
$185$		0			0
$186$	−6.23607			−0.457251
$187$	−2.04508	+	0.138757i	−0.149551	+	0.0101469i
$188$	0.381966			0.0278577
$189$	−2.42705	−	1.76336i	−0.176542	−	0.128265i
$190$		0			0
$191$	0.454915	+	1.40008i	0.0329165	+	0.101307i	0.966165	−	0.257925i	$-0.0830388\pi$
$191$	0.454915	+	1.40008i	0.0329165	+	0.101307i	−0.933248	+	0.359232i	$0.883039\pi$
$192$	3.42705	−	2.48990i	0.247326	−	0.179693i
$193$	1.26393	−	0.918300i	0.0909798	−	0.0661007i	−0.541365	−	0.840787i	$-0.682092\pi$
$193$	1.26393	−	0.918300i	0.0909798	−	0.0661007i	0.632345	+	0.774687i	$0.282092\pi$
$194$	7.51722	+	23.1356i	0.539705	+	1.66104i
$195$		0			0
$196$	−1.00000	−	0.726543i	−0.0714286	−	0.0518959i
$197$	−26.6180			−1.89646			−0.948228	−	0.317590i	$-0.897127\pi$
$197$	−26.6180			−1.89646			−0.948228	+	0.317590i	$0.897127\pi$
$198$	1.30902	−	5.20431i	0.0930278	−	0.369854i
$199$	−3.29180			−0.233349			−0.116675	−	0.993170i	$-0.537223\pi$
$199$	−3.29180			−0.233349			−0.116675	+	0.993170i	$0.537223\pi$
$200$		0			0
$201$	3.26393	−	10.0453i	0.230220	−	0.708544i
$202$	1.50000	+	4.61653i	0.105540	+	0.324818i
$203$	−10.8541	+	7.88597i	−0.761809	+	0.553486i
$204$	0.309017	−	0.224514i	0.0216355	−	0.0157191i
$205$		0			0
$206$	−3.00000	+	9.23305i	−0.209020	+	0.643297i
$207$	−4.42705	−	3.21644i	−0.307701	−	0.223558i
$208$	30.2705			2.09888
$209$	−2.17376	+	1.81636i	−0.150362	+	0.125640i
$210$		0			0
$211$	−9.11803	−	6.62464i	−0.627711	−	0.456059i	0.227895	−	0.973686i	$-0.426816\pi$
$211$	−9.11803	−	6.62464i	−0.627711	−	0.456059i	−0.855607	+	0.517627i	$0.826816\pi$
$212$	1.40983	−	4.33901i	0.0968275	−	0.298004i
$213$	−4.50000	−	13.8496i	−0.308335	−	0.948957i
$214$	−0.309017	+	0.224514i	−0.0211240	+	0.0153475i
$215$		0			0
$216$	−0.690983	−	2.12663i	−0.0470154	−	0.144699i
$217$	3.57295	−	10.9964i	0.242548	−	0.746485i
$218$		0			0
$219$	1.23607			0.0835257
$220$		0			0
$221$	−3.85410			−0.259255
$222$	−5.54508	−	4.02874i	−0.372162	−	0.270391i
$223$	3.92705	−	12.0862i	0.262975	−	0.809353i	−0.729178	−	0.684324i	$-0.760097\pi$
$223$	3.92705	−	12.0862i	0.262975	−	0.809353i	0.992153	−	0.125029i	$-0.0399025\pi$
$224$	−3.13525	−	9.64932i	−0.209483	−	0.644722i
$225$		0			0
$226$	16.6353	−	12.0862i	1.10656	−	0.803963i
$227$	−3.36475	−	10.3556i	−0.223326	−	0.687327i	−0.998457	−	0.0555264i	$-0.982316\pi$
$227$	−3.36475	−	10.3556i	−0.223326	−	0.687327i	0.775131	−	0.631800i	$-0.217684\pi$
$228$	0.163119	−	0.502029i	0.0108028	−	0.0332477i
$229$	−8.09017	−	5.87785i	−0.534613	−	0.388419i	0.287467	−	0.957790i	$-0.407187\pi$
$229$	−8.09017	−	5.87785i	−0.534613	−	0.388419i	−0.822081	+	0.569371i	$0.807187\pi$
$230$		0			0
$231$	8.42705	+	5.29007i	0.554459	+	0.348061i
$232$	−10.0000			−0.656532
$233$	7.01722	+	5.09831i	0.459713	+	0.334001i	0.793419	−	0.608676i	$-0.208299\pi$
$233$	7.01722	+	5.09831i	0.459713	+	0.334001i	−0.333705	+	0.942677i	$0.608299\pi$
$234$	3.11803	−	9.59632i	0.203832	−	0.627331i
$235$		0			0
$236$	2.66312	−	1.93487i	0.173354	−	0.125949i
$237$	0.427051	−	0.310271i	0.0277399	−	0.0201542i
$238$	0.927051	+	2.85317i	0.0600918	+	0.184944i
$239$	−5.42705	+	16.7027i	−0.351047	+	1.08041i	0.607220	+	0.794534i	$0.292285\pi$
$239$	−5.42705	+	16.7027i	−0.351047	+	1.08041i	−0.958266	+	0.285877i	$0.907715\pi$
$240$		0			0
$241$	17.1246			1.10309			0.551547	−	0.834144i	$-0.314038\pi$
$241$	17.1246			1.10309			0.551547	+	0.834144i	$0.314038\pi$
$242$	−3.16312	+	17.5150i	−0.203333	+	1.12591i
$243$	−1.00000			−0.0641500
$244$	−0.572949	−	0.416272i	−0.0366793	−	0.0266491i
$245$		0			0
$246$	2.97214	+	9.14729i	0.189496	+	0.583210i
$247$	−4.30902	+	3.13068i	−0.274176	+	0.199201i
$248$	6.97214	−	5.06555i	0.442731	−	0.321663i
$249$	−3.92705	−	12.0862i	−0.248867	−	0.765933i
$250$		0			0
$251$	−13.5902	−	9.87384i	−0.857804	−	0.623231i	0.0694827	−	0.997583i	$-0.477865\pi$
$251$	−13.5902	−	9.87384i	−0.857804	−	0.623231i	−0.927287	+	0.374352i	$0.877865\pi$
$252$	−1.85410			−0.116797
$253$	15.3713	+	9.64932i	0.966387	+	0.606648i
$254$	15.7082			0.985620
$255$		0			0
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$	8.44427	+	25.9888i	0.526739	+	1.62114i	0.760851	+	0.648927i	$0.224782\pi$
$257$	8.44427	+	25.9888i	0.526739	+	1.62114i	−0.234112	+	0.972210i	$0.575218\pi$
$258$	2.30902	−	1.67760i	0.143753	−	0.104443i
$259$	10.2812	−	7.46969i	0.638840	−	0.464144i
$260$		0			0
$261$	−1.38197	+	4.25325i	−0.0855415	+	0.263270i
$262$	−18.1353	−	13.1760i	−1.12040	−	0.814018i
$263$	0.673762			0.0415459			0.0207730	−	0.999784i	$-0.493387\pi$
$263$	0.673762			0.0415459			0.0207730	+	0.999784i	$0.493387\pi$
$264$	2.76393	+	6.88191i	0.170108	+	0.423552i
$265$		0			0
$266$	3.35410	+	2.43690i	0.205653	+	0.149416i
$267$	−2.92705	+	9.00854i	−0.179133	+	0.551313i
$268$	−2.01722	−	6.20837i	−0.123221	−	0.379236i
$269$	−19.7984	+	14.3844i	−1.20713	+	0.877030i	−0.994967	−	0.100205i	$-0.968050\pi$
$269$	−19.7984	+	14.3844i	−1.20713	+	0.877030i	−0.212161	+	0.977235i	$0.568050\pi$
$270$		0			0
$271$	1.93769	+	5.96361i	0.117707	+	0.362263i	0.992502	−	0.122229i	$-0.0390043\pi$
$271$	1.93769	+	5.96361i	0.117707	+	0.362263i	−0.874795	+	0.484493i	$0.839004\pi$
$272$	−0.927051	+	2.85317i	−0.0562107	+	0.172999i
$273$	15.1353	+	10.9964i	0.916027	+	0.665533i
$274$	−2.38197			−0.143900
$275$		0			0
$276$	−3.38197			−0.203570
$277$	8.44427	+	6.13512i	0.507367	+	0.368624i	0.811824	−	0.583902i	$-0.198475\pi$
$277$	8.44427	+	6.13512i	0.507367	+	0.368624i	−0.304457	+	0.952526i	$0.598475\pi$
$278$	−2.92705	+	9.00854i	−0.175553	+	0.540296i
$279$	−1.19098	−	3.66547i	−0.0713023	−	0.219446i
$280$		0			0
$281$	4.23607	−	3.07768i	0.252703	−	0.183599i	−0.454221	−	0.890889i	$-0.650082\pi$
$281$	4.23607	−	3.07768i	0.252703	−	0.183599i	0.706924	+	0.707290i	$0.250082\pi$
$282$	0.309017	+	0.951057i	0.0184017	+	0.0566346i
$283$	6.85410	−	21.0948i	0.407434	−	1.25395i	−0.511412	−	0.859336i	$-0.670877\pi$
$283$	6.85410	−	21.0948i	0.407434	−	1.25395i	0.918846	−	0.394617i	$-0.129123\pi$
$284$	−7.28115	−	5.29007i	−0.432057	−	0.313908i
$285$		0			0
$286$	−8.16312	+	32.4544i	−0.482695	+	1.91907i
$287$	−17.8328			−1.05264
$288$	−2.73607	−	1.98787i	−0.161224	−	0.117136i
$289$	−5.13525	+	15.8047i	−0.302074	+	0.929688i
$290$		0			0
$291$	−12.1631	+	8.83702i	−0.713015	+	0.518035i
$292$	0.618034	−	0.449028i	0.0361677	−	0.0262774i
$293$	−5.54508	−	17.0660i	−0.323947	−	0.997007i	−0.971914	−	0.235338i	$-0.924380\pi$
$293$	−5.54508	−	17.0660i	−0.323947	−	0.997007i	0.647966	−	0.761669i	$-0.275620\pi$
$294$	1.00000	−	3.07768i	0.0583212	−	0.179494i
$295$		0			0
$296$	9.47214			0.550557
$297$	3.30902	−	0.224514i	0.192009	−	0.0130276i
$298$	−24.2705			−1.40595
$299$	27.6074	+	20.0579i	1.59658	+	1.15998i
$300$		0			0
$301$	1.63525	+	5.03280i	0.0942545	+	0.290086i
$302$	2.61803	−	1.90211i	0.150651	−	0.109454i
$303$	−2.42705	+	1.76336i	−0.139430	+	0.101302i
$304$	1.28115	+	3.94298i	0.0734792	+	0.226146i
$305$		0			0
$306$	0.809017	+	0.587785i	0.0462484	+	0.0336014i
$307$	19.5623			1.11648			0.558240	−	0.829680i	$-0.311477\pi$
$307$	19.5623			1.11648			0.558240	+	0.829680i	$0.311477\pi$
$308$	6.13525	−	0.416272i	0.349589	−	0.0237193i
$309$	−6.00000			−0.341328
$310$		0			0
$311$	3.54508	−	10.9106i	0.201023	−	0.618686i	−0.798830	−	0.601557i	$-0.794547\pi$
$311$	3.54508	−	10.9106i	0.201023	−	0.618686i	0.999853	−	0.0171293i	$-0.00545269\pi$
$312$	4.30902	+	13.2618i	0.243950	+	0.750801i
$313$	−22.5172	+	16.3597i	−1.27275	+	0.924706i	−0.999308	−	0.0371831i	$-0.988162\pi$
$313$	−22.5172	+	16.3597i	−1.27275	+	0.924706i	−0.273440	+	0.961889i	$0.588162\pi$
$314$	−12.7082	+	9.23305i	−0.717165	+	0.521051i
$315$		0			0
$316$	0.100813	−	0.310271i	0.00567118	−	0.0174541i
$317$	20.5172	+	14.9066i	1.15236	+	0.837240i	0.988793	−	0.149292i	$-0.0476994\pi$
$317$	20.5172	+	14.9066i	1.15236	+	0.837240i	0.163569	+	0.986532i	$0.447699\pi$
$318$	11.9443			0.669802
$319$	3.61803	−	14.3844i	0.202571	−	0.805370i
$320$		0			0
$321$	−0.190983	−	0.138757i	−0.0106596	−	0.00774468i
$322$	8.20820	−	25.2623i	0.457425	−	1.40781i
$323$	−0.163119	−	0.502029i	−0.00907618	−	0.0279336i
$324$	−0.500000	+	0.363271i	−0.0277778	+	0.0201817i
$325$		0			0
$326$	−7.63525	−	23.4989i	−0.422878	−	1.30148i
$327$		0			0
$328$	−10.7533	−	7.81272i	−0.593751	−	0.431385i
$329$	−1.85410			−0.102220
$330$		0			0
$331$	−22.5967			−1.24203			−0.621015	−	0.783799i	$-0.713279\pi$
$331$	−22.5967			−1.24203			−0.621015	+	0.783799i	$0.713279\pi$
$332$	−6.35410	−	4.61653i	−0.348727	−	0.253365i
$333$	1.30902	−	4.02874i	0.0717337	−	0.220774i
$334$	−9.51722	−	29.2910i	−0.520759	−	1.60273i
$335$		0			0
$336$	11.7812	−	8.55951i	0.642715	−	0.466959i
$337$	4.23607	+	13.0373i	0.230753	+	0.710186i	0.997656	+	0.0684228i	$0.0217967\pi$
$337$	4.23607	+	13.0373i	0.230753	+	0.710186i	−0.766903	+	0.641763i	$0.778203\pi$
$338$	−12.9443	+	39.8384i	−0.704076	+	2.16692i
$339$	10.2812	+	7.46969i	0.558396	+	0.405698i
$340$		0			0
$341$	4.76393	+	11.8617i	0.257981	+	0.642347i
$342$	1.38197			0.0747282
$343$	−12.1353	−	8.81678i	−0.655242	−	0.476061i
$344$	−1.21885	+	3.75123i	−0.0657158	+	0.202253i
$345$		0			0
$346$	−23.0623	+	16.7557i	−1.23984	+	0.900794i
$347$	−2.47214	+	1.79611i	−0.132711	+	0.0964203i	−0.652160	−	0.758081i	$-0.726137\pi$
$347$	−2.47214	+	1.79611i	−0.132711	+	0.0964203i	0.519449	+	0.854501i	$0.326137\pi$
$348$	0.854102	+	2.62866i	0.0457847	+	0.140911i
$349$	9.30902	−	28.6502i	0.498300	−	1.53361i	−0.313449	−	0.949605i	$-0.601485\pi$
$349$	9.30902	−	28.6502i	0.498300	−	1.53361i	0.811750	−	0.584006i	$-0.198515\pi$
$350$		0			0
$351$	6.23607			0.332857
$352$	9.50000	+	5.96361i	0.506352	+	0.317861i
$353$	1.52786			0.0813200			0.0406600	−	0.999173i	$-0.487054\pi$
$353$	1.52786			0.0813200			0.0406600	+	0.999173i	$0.487054\pi$
$354$	6.97214	+	5.06555i	0.370565	+	0.269231i
$355$		0			0
$356$	1.80902	+	5.56758i	0.0958777	+	0.295081i
$357$	−1.50000	+	1.08981i	−0.0793884	+	0.0576791i
$358$	2.92705	−	2.12663i	0.154699	−	0.112396i
$359$	−5.32624	−	16.3925i	−0.281108	−	0.865162i	−0.987538	−	0.157379i	$-0.949696\pi$
$359$	−5.32624	−	16.3925i	−0.281108	−	0.865162i	0.706430	−	0.707783i	$-0.250304\pi$
$360$		0			0
$361$	14.7812	+	10.7391i	0.777955	+	0.565218i
$362$	13.7984			0.725226
$363$	−10.8992	+	1.48584i	−0.572059	+	0.0779864i
$364$	11.5623			0.606029
$365$		0			0
$366$	0.572949	−	1.76336i	0.0299485	−	0.0921721i
$367$	4.50000	+	13.8496i	0.234898	+	0.722942i	0.997135	+	0.0756437i	$0.0241012\pi$
$367$	4.50000	+	13.8496i	0.234898	+	0.722942i	−0.762237	+	0.647298i	$0.775899\pi$
$368$	21.4894	−	15.6129i	1.12021	−	0.813880i
$369$	−4.80902	+	3.49396i	−0.250347	+	0.181888i
$370$		0			0
$371$	−6.84346	+	21.0620i	−0.355295	+	1.09348i
$372$	−1.92705	−	1.40008i	−0.0999129	−	0.0725910i
$373$	−22.4164			−1.16068			−0.580339	−	0.814375i	$-0.697080\pi$
$373$	−22.4164			−1.16068			−0.580339	+	0.814375i	$0.697080\pi$
$374$	−2.80902	−	1.76336i	−0.145251	−	0.0911810i
$375$		0			0
$376$	−1.11803	−	0.812299i	−0.0576582	−	0.0418911i
$377$	8.61803	−	26.5236i	0.443851	−	1.36603i
$378$	−1.50000	−	4.61653i	−0.0771517	−	0.237448i
$379$	−22.9894	+	16.7027i	−1.18088	+	0.857962i	−0.992271	−	0.124089i	$-0.960399\pi$
$379$	−22.9894	+	16.7027i	−1.18088	+	0.857962i	−0.188613	+	0.982052i	$0.560399\pi$
$380$		0			0
$381$	3.00000	+	9.23305i	0.153695	+	0.473024i
$382$	−0.736068	+	2.26538i	−0.0376605	+	0.115907i
$383$	−7.19098	−	5.22455i	−0.367442	−	0.266962i	0.388707	−	0.921361i	$-0.372922\pi$
$383$	−7.19098	−	5.22455i	−0.367442	−	0.266962i	−0.756149	+	0.654399i	$0.772922\pi$
$384$	13.6180			0.694942
$385$		0			0
$386$	2.52786			0.128665
$387$	1.42705	+	1.03681i	0.0725411	+	0.0527042i
$388$	−2.87132	+	8.83702i	−0.145769	+	0.448632i
$389$	−2.86475	−	8.81678i	−0.145248	−	0.447028i	0.851795	−	0.523876i	$-0.175515\pi$
$389$	−2.86475	−	8.81678i	−0.145248	−	0.447028i	−0.997043	+	0.0768476i	$0.975515\pi$
$390$		0			0
$391$	−2.73607	+	1.98787i	−0.138369	+	0.100531i
$392$	1.38197	+	4.25325i	0.0697998	+	0.214822i
$393$	4.28115	−	13.1760i	0.215956	−	0.664643i
$394$	−34.8435	−	25.3153i	−1.75539	−	1.27536i
$395$		0			0
$396$	1.57295	−	1.31433i	0.0790437	−	0.0660475i
$397$	25.2918			1.26936			0.634679	−	0.772776i	$-0.281132\pi$
$397$	25.2918			1.26936			0.634679	+	0.772776i	$0.281132\pi$
$398$	−4.30902	−	3.13068i	−0.215992	−	0.156927i
$399$	−0.791796	+	2.43690i	−0.0396394	+	0.121997i
$400$		0			0
$401$	12.0623	−	8.76378i	0.602363	−	0.437642i	−0.244354	−	0.969686i	$-0.578576\pi$
$401$	12.0623	−	8.76378i	0.602363	−	0.437642i	0.846717	+	0.532044i	$0.178576\pi$
$402$	13.8262	−	10.0453i	0.689590	−	0.501017i
$403$	7.42705	+	22.8581i	0.369968	+	1.13864i
$404$	−0.572949	+	1.76336i	−0.0285053	+	0.0877302i
$405$		0			0
$406$	−21.7082			−1.07736
$407$	−3.42705	+	13.6251i	−0.169873	+	0.675369i
$408$	−1.38197			−0.0684175
$409$	23.4164	+	17.0130i	1.15787	+	0.841240i	0.989507	−	0.144486i	$-0.0461529\pi$
$409$	23.4164	+	17.0130i	1.15787	+	0.841240i	0.168360	+	0.985726i	$0.446153\pi$
$410$		0			0
$411$	−0.454915	−	1.40008i	−0.0224393	−	0.0690611i
$412$	−3.00000	+	2.17963i	−0.147799	+	0.107383i
$413$	−12.9271	+	9.39205i	−0.636099	+	0.462153i
$414$	−2.73607	−	8.42075i	−0.134470	−	0.413857i
$415$		0			0
$416$	17.0623	+	12.3965i	0.836548	+	0.607788i
$417$	−5.85410			−0.286677
$418$	−4.57295	+	0.310271i	−0.223670	+	0.0151758i
$419$	−21.5066			−1.05067			−0.525333	−	0.850897i	$-0.676059\pi$
$419$	−21.5066			−1.05067			−0.525333	+	0.850897i	$0.676059\pi$
$420$		0			0
$421$	−1.15248	+	3.54696i	−0.0561682	+	0.172868i	−0.975205	−	0.221304i	$-0.928969\pi$
$421$	−1.15248	+	3.54696i	−0.0561682	+	0.172868i	0.919037	+	0.394172i	$0.128969\pi$
$422$	−5.63525	−	17.3435i	−0.274320	−	0.844270i
$423$	−0.500000	+	0.363271i	−0.0243108	+	0.0176629i
$424$	−13.3541	+	9.70232i	−0.648533	+	0.471186i
$425$		0			0
$426$	7.28115	−	22.4091i	0.352773	−	1.08572i
$427$	2.78115	+	2.02063i	0.134589	+	0.0977849i
$428$	−0.145898			−0.00705225
$429$	−20.6353	+	1.40008i	−0.996279	+	0.0675967i
$430$		0			0
$431$	1.20820	+	0.877812i	0.0581971	+	0.0422827i	0.616503	−	0.787352i	$-0.288549\pi$
$431$	1.20820	+	0.877812i	0.0581971	+	0.0422827i	−0.558306	+	0.829635i	$0.688549\pi$
$432$	1.50000	−	4.61653i	0.0721688	−	0.222113i
$433$	1.85410	+	5.70634i	0.0891025	+	0.274229i	0.985672	−	0.168674i	$-0.0539485\pi$
$433$	1.85410	+	5.70634i	0.0891025	+	0.274229i	−0.896569	+	0.442903i	$0.853949\pi$
$434$	15.1353	−	10.9964i	0.726515	−	0.527844i
$435$		0			0
$436$		0			0
$437$	−1.44427	+	4.44501i	−0.0690889	+	0.212634i
$438$	1.61803	+	1.17557i	0.0773127	+	0.0561709i
$439$	16.7082			0.797439			0.398720	−	0.917073i	$-0.369455\pi$
$439$	16.7082			0.797439			0.398720	+	0.917073i	$0.369455\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$	−5.04508	−	3.66547i	−0.239970	−	0.174349i
$443$	0.270510	−	0.832544i	0.0128523	−	0.0395553i	−0.944425	−	0.328728i	$-0.893380\pi$
$443$	0.270510	−	0.832544i	0.0128523	−	0.0395553i	0.957277	+	0.289172i	$0.0933801\pi$
$444$	−0.809017	−	2.48990i	−0.0383942	−	0.118165i
$445$		0			0
$446$	16.6353	−	12.0862i	0.787702	−	0.572299i
$447$	−4.63525	−	14.2658i	−0.219240	−	0.674751i
$448$	−3.92705	+	12.0862i	−0.185536	+	0.571020i
$449$	12.5623	+	9.12705i	0.592852	+	0.430732i	0.843334	−	0.537389i	$-0.180589\pi$
$449$	12.5623	+	9.12705i	0.592852	+	0.430732i	−0.250483	+	0.968121i	$0.580589\pi$
$450$		0			0
$451$	15.1287	−	12.6412i	0.712382	−	0.595253i
$452$	7.85410			0.369426
$453$	1.61803	+	1.17557i	0.0760219	+	0.0552331i
$454$	5.44427	−	16.7557i	0.255512	−	0.786386i
$455$		0			0
$456$	−1.54508	+	1.12257i	−0.0723552	+	0.0525692i
$457$	26.5344	−	19.2784i	1.24123	−	0.901806i	0.243549	−	0.969889i	$-0.421688\pi$
$457$	26.5344	−	19.2784i	1.24123	−	0.901806i	0.997680	+	0.0680830i	$0.0216883\pi$
$458$	−5.00000	−	15.3884i	−0.233635	−	0.719054i
$459$	−0.190983	+	0.587785i	−0.00891432	+	0.0274355i
$460$		0			0
$461$	−9.90983			−0.461547			−0.230773	−	0.973008i	$-0.574126\pi$
$461$	−9.90983			−0.461547			−0.230773	+	0.973008i	$0.574126\pi$
$462$	6.00000	+	14.9394i	0.279145	+	0.695043i
$463$	−8.79837			−0.408895			−0.204448	−	0.978878i	$-0.565540\pi$
$463$	−8.79837			−0.408895			−0.204448	+	0.978878i	$0.565540\pi$
$464$	−17.5623	−	12.7598i	−0.815310	−	0.592357i
$465$		0			0
$466$	4.33688	+	13.3475i	0.200902	+	0.618313i
$467$	−11.5172	+	8.36775i	−0.532953	+	0.387213i	−0.821461	−	0.570264i	$-0.806841\pi$
$467$	−11.5172	+	8.36775i	−0.532953	+	0.387213i	0.288508	+	0.957478i	$0.406841\pi$
$468$	3.11803	−	2.26538i	0.144131	−	0.104717i
$469$	9.79180	+	30.1360i	0.452143	+	1.39155i
$470$		0			0
$471$	−7.85410	−	5.70634i	−0.361898	−	0.262934i
$472$	−11.9098			−0.548194
$473$	−4.95492	−	3.11044i	−0.227827	−	0.143018i
$474$	0.854102			0.0392302
$475$		0			0
$476$	−0.354102	+	1.08981i	−0.0162302	+	0.0499515i
$477$	2.28115	+	7.02067i	0.104447	+	0.321454i
$478$	−22.9894	+	16.7027i	−1.05151	+	0.763966i
$479$	13.6803	−	9.93935i	0.625071	−	0.454140i	−0.229618	−	0.973281i	$-0.573748\pi$
$479$	13.6803	−	9.93935i	0.625071	−	0.454140i	0.854689	+	0.519140i	$0.173748\pi$
$480$		0			0
$481$	−8.16312	+	25.1235i	−0.372206	+	1.14553i
$482$	22.4164	+	16.2865i	1.02104	+	0.741829i
$483$	16.4164			0.746972
$484$	−4.90983	+	4.70228i	−0.223174	+	0.213740i
$485$		0			0
$486$	−1.30902	−	0.951057i	−0.0593782	−	0.0431408i
$487$	−12.1074	+	37.2627i	−0.548638	+	1.68853i	0.163540	+	0.986537i	$0.447709\pi$
$487$	−12.1074	+	37.2627i	−0.548638	+	1.68853i	−0.712179	+	0.701998i	$0.752291\pi$
$488$	0.791796	+	2.43690i	0.0358429	+	0.110313i
$489$	12.3541	−	8.97578i	0.558672	−	0.405899i
$490$		0			0
$491$	−8.10081	−	24.9317i	−0.365585	−	1.12515i	−0.949614	−	0.313421i	$-0.898525\pi$
$491$	−8.10081	−	24.9317i	−0.365585	−	1.12515i	0.584030	−	0.811732i	$-0.301475\pi$
$492$	−1.13525	+	3.49396i	−0.0511812	+	0.157520i
$493$	2.23607	+	1.62460i	0.100707	+	0.0731682i
$494$	−8.61803			−0.387744
$495$		0			0
$496$	18.7082			0.840023
$497$	35.3435	+	25.6785i	1.58537	+	1.15184i
$498$	6.35410	−	19.5559i	0.284734	−	0.876322i
$499$	0.791796	+	2.43690i	0.0354457	+	0.109091i	0.967214	−	0.253963i	$-0.0817342\pi$
$499$	0.791796	+	2.43690i	0.0354457	+	0.109091i	−0.931768	+	0.363054i	$0.881734\pi$
$500$		0			0
$501$	15.3992	−	11.1882i	0.687985	−	0.499850i
$502$	−8.39919	−	25.8500i	−0.374874	−	1.15374i
$503$	9.29180	−	28.5972i	0.414301	−	1.27509i	−0.498574	−	0.866847i	$-0.666143\pi$
$503$	9.29180	−	28.5972i	0.414301	−	1.27509i	0.912875	−	0.408239i	$-0.133857\pi$
$504$	5.42705	+	3.94298i	0.241740	+	0.175634i
$505$		0			0
$506$	10.9443	+	27.2501i	0.486532	+	1.21142i
$507$	−25.8885			−1.14975
$508$	4.85410	+	3.52671i	0.215366	+	0.156473i
$509$	6.60739	−	20.3355i	0.292867	−	0.901353i	−0.691062	−	0.722796i	$-0.742857\pi$
$509$	6.60739	−	20.3355i	0.292867	−	0.901353i	0.983929	−	0.178558i	$-0.0571432\pi$
$510$		0			0
$511$	−3.00000	+	2.17963i	−0.132712	+	0.0964210i
$512$	−4.28115	+	3.11044i	−0.189202	+	0.137463i
$513$	0.263932	+	0.812299i	0.0116529	+	0.0358639i
$514$	−13.6631	+	42.0508i	−0.602654	+	1.85478i
$515$		0			0
$516$	1.09017			0.0479921
$517$	1.57295	−	1.31433i	0.0691782	−	0.0578041i
$518$	20.5623			0.903456
$519$	−14.2533	−	10.3556i	−0.625650	−	0.454561i
$520$		0			0
$521$	12.0000	+	36.9322i	0.525730	+	1.61803i	0.762869	+	0.646553i	$0.223790\pi$
$521$	12.0000	+	36.9322i	0.525730	+	1.61803i	−0.237139	+	0.971476i	$0.576210\pi$
$522$	−5.85410	+	4.25325i	−0.256227	+	0.186160i
$523$	28.2984	−	20.5600i	1.23740	−	0.899025i	0.239979	−	0.970778i	$-0.422859\pi$
$523$	28.2984	−	20.5600i	1.23740	−	0.899025i	0.997422	+	0.0717533i	$0.0228594\pi$
$524$	−2.64590	−	8.14324i	−0.115587	−	0.355739i
$525$		0			0
$526$	0.881966	+	0.640786i	0.0384555	+	0.0279396i
$527$	−2.38197			−0.103760
$528$	−3.92705	+	15.6129i	−0.170903	+	0.679466i
$529$	6.94427			0.301925
$530$		0			0
$531$	−1.64590	+	5.06555i	−0.0714259	+	0.219826i
$532$	0.489357	+	1.50609i	0.0212163	+	0.0652971i
$533$	29.9894	−	21.7885i	1.29898	−	0.943767i
$534$	−12.3992	+	9.00854i	−0.536565	+	0.389838i
$535$		0			0
$536$	−7.29837	+	22.4621i	−0.315242	+	0.970214i
$537$	1.80902	+	1.31433i	0.0780648	+	0.0567174i
$538$	−39.5967			−1.70714
$539$	−6.61803	+	0.449028i	−0.285059	+	0.0193410i
$540$		0			0
$541$	0.454915	+	0.330515i	0.0195583	+	0.0142100i	0.597521	−	0.801853i	$-0.296152\pi$
$541$	0.454915	+	0.330515i	0.0195583	+	0.0142100i	−0.577963	+	0.816063i	$0.696152\pi$
$542$	−3.13525	+	9.64932i	−0.134671	+	0.414474i
$543$	2.63525	+	8.11048i	0.113090	+	0.348054i
$544$	−1.69098	+	1.22857i	−0.0725003	+	0.0526745i
$545$		0			0
$546$	9.35410	+	28.7890i	0.400319	+	1.23205i
$547$	−5.98936	+	18.4333i	−0.256086	+	0.788153i	0.737527	+	0.675317i	$0.235993\pi$
$547$	−5.98936	+	18.4333i	−0.256086	+	0.788153i	−0.993614	+	0.112836i	$0.964007\pi$
$548$	−0.736068	−	0.534785i	−0.0314433	−	0.0228449i
$549$	1.14590			0.0489057
$550$		0			0
$551$	3.81966			0.162723
$552$	9.89919	+	7.19218i	0.421337	+	0.306120i
$553$	−0.489357	+	1.50609i	−0.0208096	+	0.0640453i
$554$	5.21885	+	16.0620i	0.221728	+	0.682407i
$555$		0			0
$556$	−2.92705	+	2.12663i	−0.124135	+	0.0901891i
$557$	−8.06231	−	24.8132i	−0.341611	−	1.05137i	−0.963373	−	0.268164i	$-0.913583\pi$
$557$	−8.06231	−	24.8132i	−0.341611	−	1.05137i	0.621762	−	0.783206i	$-0.286417\pi$
$558$	1.92705	−	5.93085i	0.0815786	−	0.251073i
$559$	−8.89919	−	6.46564i	−0.376396	−	0.273467i
$560$		0			0
$561$	0.500000	−	1.98787i	0.0211100	−	0.0839279i
$562$	8.47214			0.357375
$563$	21.7533	+	15.8047i	0.916792	+	0.666088i	0.942723	−	0.333575i	$-0.108255\pi$
$563$	21.7533	+	15.8047i	0.916792	+	0.666088i	−0.0259316	+	0.999664i	$0.508255\pi$
$564$	−0.118034	+	0.363271i	−0.00497013	+	0.0152965i
$565$		0			0
$566$	29.0344	−	21.0948i	1.22041	−	0.886679i
$567$	2.42705	−	1.76336i	0.101927	−	0.0740540i
$568$	10.0623	+	30.9686i	0.422205	+	1.29941i
$569$	10.5279	−	32.4014i	0.441351	−	1.35834i	−0.445085	−	0.895488i	$-0.646827\pi$
$569$	10.5279	−	32.4014i	0.441351	−	1.35834i	0.886436	−	0.462851i	$-0.153173\pi$
$570$		0			0
$571$	−25.6869			−1.07496			−0.537482	−	0.843275i	$-0.680624\pi$
$571$	−25.6869			−1.07496			−0.537482	+	0.843275i	$0.680624\pi$
$572$	−9.80902	+	8.19624i	−0.410136	+	0.342702i
$573$	−1.47214			−0.0614994
$574$	−23.3435	−	16.9600i	−0.974337	−	0.707897i
$575$		0			0
$576$	1.30902	+	4.02874i	0.0545424	+	0.167864i
$577$	12.3262	−	8.95554i	0.513148	−	0.372824i	−0.300868	−	0.953666i	$-0.597277\pi$
$577$	12.3262	−	8.95554i	0.513148	−	0.372824i	0.814016	+	0.580842i	$0.197277\pi$
$578$	−21.7533	+	15.8047i	−0.904818	+	0.657388i
$579$	0.482779	+	1.48584i	0.0200636	+	0.0617495i
$580$		0			0
$581$	30.8435	+	22.4091i	1.27960	+	0.929685i
$582$	−24.3262			−1.00836
$583$	−9.12461	−	22.7194i	−0.377903	−	0.940940i
$584$	−2.76393			−0.114372
$585$		0			0
$586$	8.97214	−	27.6134i	0.370636	−	1.14070i
$587$	−7.51064	−	23.1154i	−0.309997	−	0.954074i	−0.977765	−	0.209704i	$-0.932750\pi$
$587$	−7.51064	−	23.1154i	−0.309997	−	0.954074i	0.667767	−	0.744370i	$-0.267250\pi$
$588$	1.00000	−	0.726543i	0.0412393	−	0.0299621i
$589$	−2.66312	+	1.93487i	−0.109732	+	0.0797249i
$590$		0			0
$591$	8.22542	−	25.3153i	0.338349	−	1.04133i
$592$	16.6353	+	12.0862i	0.683705	+	0.496741i
$593$	29.2148			1.19971			0.599854	−	0.800110i	$-0.295225\pi$
$593$	29.2148			1.19971			0.599854	+	0.800110i	$0.295225\pi$
$594$	4.54508	+	2.85317i	0.186487	+	0.117067i
$595$		0			0
$596$	−7.50000	−	5.44907i	−0.307212	−	0.223203i
$597$	1.01722	−	3.13068i	0.0416321	−	0.128130i
$598$	17.0623	+	52.5124i	0.697730	+	2.14739i
$599$	17.5623	−	12.7598i	0.717576	−	0.521350i	−0.168033	−	0.985781i	$-0.553741\pi$
$599$	17.5623	−	12.7598i	0.717576	−	0.521350i	0.885609	+	0.464432i	$0.153741\pi$
$600$		0			0
$601$	−6.12868	−	18.8621i	−0.249994	−	0.769402i	−0.994775	−	0.102093i	$-0.967446\pi$
$601$	−6.12868	−	18.8621i	−0.249994	−	0.769402i	0.744781	−	0.667309i	$-0.232554\pi$
$602$	−2.64590	+	8.14324i	−0.107839	+	0.331894i
$603$	8.54508	+	6.20837i	0.347983	+	0.252824i
$604$	1.23607			0.0502949
$605$		0			0
$606$	−4.85410			−0.197184
$607$	−1.88197	−	1.36733i	−0.0763866	−	0.0554981i	0.548937	−	0.835864i	$-0.315033\pi$
$607$	−1.88197	−	1.36733i	−0.0763866	−	0.0554981i	−0.625323	+	0.780366i	$0.715033\pi$
$608$	−0.892609	+	2.74717i	−0.0362001	+	0.111412i
$609$	−4.14590	−	12.7598i	−0.168000	−	0.517052i
$610$		0			0
$611$	3.11803	−	2.26538i	0.126142	−	0.0916476i
$612$	0.118034	+	0.363271i	0.00477124	+	0.0146844i
$613$	−1.03444	+	3.18368i	−0.0417807	+	0.128588i	−0.969771	−	0.244016i	$-0.921535\pi$
$613$	−1.03444	+	3.18368i	−0.0417807	+	0.128588i	0.927990	+	0.372604i	$0.121535\pi$
$614$	25.6074	+	18.6049i	1.03343	+	0.750831i
$615$		0			0
$616$	−18.8435	−	11.8290i	−0.759225	−	0.476602i
$617$	−46.4164			−1.86865			−0.934327	−	0.356417i	$-0.883998\pi$
$617$	−46.4164			−1.86865			−0.934327	+	0.356417i	$0.883998\pi$
$618$	−7.85410	−	5.70634i	−0.315938	−	0.229543i
$619$	−9.63525	+	29.6543i	−0.387274	+	1.19191i	0.547544	+	0.836777i	$0.315563\pi$
$619$	−9.63525	+	29.6543i	−0.387274	+	1.19191i	−0.934817	+	0.355129i	$0.884437\pi$
$620$		0			0
$621$	4.42705	−	3.21644i	0.177651	−	0.129071i
$622$	15.0172	−	10.9106i	0.602136	−	0.437477i
$623$	−8.78115	−	27.0256i	−0.351809	−	1.08276i
$624$	−9.35410	+	28.7890i	−0.374464	+	1.15248i
$625$		0			0
$626$	−45.0344			−1.79994
$627$	−1.05573	−	2.62866i	−0.0421617	−	0.104978i
$628$	−6.00000			−0.239426
$629$	−2.11803	−	1.53884i	−0.0844515	−	0.0613576i
$630$		0			0
$631$	3.93363	+	12.1065i	0.156595	+	0.481951i	0.998319	−	0.0579577i	$-0.0184589\pi$
$631$	3.93363	+	12.1065i	0.156595	+	0.481951i	−0.841724	+	0.539908i	$0.818459\pi$
$632$	−0.954915	+	0.693786i	−0.0379845	+	0.0275973i
$633$	9.11803	−	6.62464i	0.362409	−	0.263306i
$634$	12.6803	+	39.0261i	0.503601	+	1.54992i
$635$		0			0
$636$	3.69098	+	2.68166i	0.146357	+	0.106335i
$637$	−12.4721			−0.494164
$638$	18.4164	−	15.3884i	0.729113	−	0.609233i
$639$	14.5623			0.576076
$640$		0			0
$641$	−2.08359	+	6.41264i	−0.0822969	+	0.253284i	−0.983736	−	0.179623i	$-0.942512\pi$
$641$	−2.08359	+	6.41264i	−0.0822969	+	0.253284i	0.901439	+	0.432907i	$0.142512\pi$
$642$	−0.118034	−	0.363271i	−0.00465843	−	0.0143372i
$643$	−14.9164	+	10.8374i	−0.588246	+	0.427386i	−0.841687	−	0.539965i	$-0.818437\pi$
$643$	−14.9164	+	10.8374i	−0.588246	+	0.427386i	0.253442	+	0.967351i	$0.418437\pi$
$644$	8.20820	−	5.96361i	0.323449	−	0.234999i
$645$		0			0
$646$	0.263932	−	0.812299i	0.0103843	−	0.0319595i
$647$	2.59017	+	1.88187i	0.101830	+	0.0739839i	0.637535	−	0.770421i	$-0.279954\pi$
$647$	2.59017	+	1.88187i	0.101830	+	0.0739839i	−0.535705	+	0.844405i	$0.679954\pi$
$648$	2.23607			0.0878410
$649$	4.30902	−	17.1315i	0.169144	−	0.672471i
$650$		0			0
$651$	9.35410	+	6.79615i	0.366616	+	0.266362i
$652$	2.91641	−	8.97578i	0.114215	−	0.351519i
$653$	−6.78773	−	20.8905i	−0.265624	−	0.817508i	−0.991549	−	0.129734i	$-0.958588\pi$
$653$	−6.78773	−	20.8905i	−0.265624	−	0.817508i	0.725924	−	0.687774i	$-0.241412\pi$
$654$		0			0
$655$		0			0
$656$	−8.91641	−	27.4419i	−0.348127	−	1.07143i
$657$	−0.381966	+	1.17557i	−0.0149019	+	0.0458634i
$658$	−2.42705	−	1.76336i	−0.0946163	−	0.0687428i
$659$	20.6525			0.804506			0.402253	−	0.915528i	$-0.368227\pi$
$659$	20.6525			0.804506			0.402253	+	0.915528i	$0.368227\pi$
$660$		0			0
$661$	−21.0902			−0.820313			−0.410156	−	0.912015i	$-0.634526\pi$
$661$	−21.0902			−0.820313			−0.410156	+	0.912015i	$0.634526\pi$
$662$	−29.5795	−	21.4908i	−1.14964	−	0.835263i
$663$	1.19098	−	3.66547i	0.0462539	−	0.142355i
$664$	8.78115	+	27.0256i	0.340775	+	1.04880i
$665$		0			0
$666$	5.54508	−	4.02874i	0.214868	−	0.156111i
$667$	−7.56231	−	23.2744i	−0.292814	−	0.901188i
$668$	3.63525	−	11.1882i	0.140652	−	0.432883i
$669$	10.2812	+	7.46969i	0.397492	+	0.288795i
$670$		0			0
$671$	−3.79180	+	0.257270i	−0.146381	+	0.00993180i
$672$	10.1459			0.391387
$673$	−11.6631	−	8.47375i	−0.449580	−	0.326639i	0.339850	−	0.940480i	$-0.389624\pi$
$673$	−11.6631	−	8.47375i	−0.449580	−	0.326639i	−0.789430	+	0.613841i	$0.789624\pi$
$674$	−6.85410	+	21.0948i	−0.264010	+	0.812540i
$675$		0			0
$676$	−12.9443	+	9.40456i	−0.497857	+	0.361714i
$677$	18.1803	−	13.2088i	0.698727	−	0.507655i	−0.180790	−	0.983522i	$-0.557866\pi$
$677$	18.1803	−	13.2088i	0.698727	−	0.507655i	0.879517	+	0.475867i	$0.157866\pi$
$678$	6.35410	+	19.5559i	0.244028	+	0.751040i
$679$	13.9377	−	42.8958i	0.534880	−	1.64619i
$680$		0			0
$681$	10.8885			0.417250
$682$	−5.04508	+	20.0579i	−0.193186	+	0.768058i
$683$	38.8885			1.48803			0.744014	−	0.668164i	$-0.232919\pi$
$683$	38.8885			1.48803			0.744014	+	0.668164i	$0.232919\pi$
$684$	0.427051	+	0.310271i	0.0163287	+	0.0118635i
$685$		0			0
$686$	−7.50000	−	23.0826i	−0.286351	−	0.881299i
$687$	8.09017	−	5.87785i	0.308659	−	0.224254i
$688$	−6.92705	+	5.03280i	−0.264091	+	0.191874i
$689$	−14.2254	−	43.7814i	−0.541946	−	1.66794i
$690$		0			0
$691$	32.1246	+	23.3399i	1.22208	+	0.887892i	0.996271	−	0.0862806i	$-0.0274981\pi$
$691$	32.1246	+	23.3399i	1.22208	+	0.887892i	0.225807	+	0.974172i	$0.427498\pi$
$692$	−10.8885			−0.413920
$693$	−7.63525	+	6.37988i	−0.290039	+	0.242352i
$694$	−4.94427			−0.187682
$695$		0			0
$696$	3.09017	−	9.51057i	0.117133	−	0.360497i
$697$	1.13525	+	3.49396i	0.0430008	+	0.132343i
$698$	39.4336	−	28.6502i	1.49258	−	1.08443i
$699$	−7.01722	+	5.09831i	−0.265416	+	0.192836i
$700$		0			0
$701$	15.3541	−	47.2551i	0.579916	−	1.78480i	−0.0388752	−	0.999244i	$-0.512377\pi$
$701$	15.3541	−	47.2551i	0.579916	−	1.78480i	0.618792	−	0.785555i	$-0.287623\pi$
$702$	8.16312	+	5.93085i	0.308097	+	0.223846i
$703$	−3.61803			−0.136457
$704$	−5.23607	−	13.0373i	−0.197342	−	0.491361i
$705$		0			0
$706$	2.00000	+	1.45309i	0.0752710	+	0.0546876i
$707$	2.78115	−	8.55951i	0.104596	−	0.321913i
$708$	1.01722	+	3.13068i	0.0382295	+	0.117658i
$709$	−5.06231	+	3.67798i	−0.190119	+	0.138129i	−0.678773	−	0.734348i	$-0.737488\pi$
$709$	−5.06231	+	3.67798i	−0.190119	+	0.138129i	0.488654	+	0.872478i	$0.337488\pi$
$710$		0			0
$711$	0.163119	+	0.502029i	0.00611744	+	0.0188275i
$712$	6.54508	−	20.1437i	0.245287	−	0.754917i
$713$	17.0623	+	12.3965i	0.638988	+	0.464252i
$714$	−3.00000			−0.112272
$715$		0			0
$716$	1.38197			0.0516465
$717$	−14.2082	−	10.3229i	−0.530615	−	0.385514i
$718$	8.61803	−	26.5236i	0.321622	−	0.989851i
$719$	−8.78115	−	27.0256i	−0.327482	−	1.00789i	−0.970308	−	0.241873i	$-0.922238\pi$
$719$	−8.78115	−	27.0256i	−0.327482	−	1.00789i	0.642826	−	0.766012i	$-0.277762\pi$
$720$		0			0
$721$	14.5623	−	10.5801i	0.542329	−	0.394025i
$722$	9.13525	+	28.1154i	0.339979	+	1.04635i
$723$	−5.29180	+	16.2865i	−0.196804	+	0.605700i
$724$	4.26393	+	3.09793i	0.158468	+	0.115134i
$725$		0			0
$726$	−15.6803	−	8.42075i	−0.581952	−	0.312523i
$727$	−32.1459			−1.19223			−0.596113	−	0.802901i	$-0.703289\pi$
$727$	−32.1459			−1.19223			−0.596113	+	0.802901i	$0.703289\pi$
$728$	−33.8435	−	24.5887i	−1.25432	−	0.911318i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	0.881966	−	0.640786i	0.0326207	−	0.0237003i
$732$	0.572949	−	0.416272i	0.0211768	−	0.0153858i
$733$	7.50658	+	23.1029i	0.277262	+	0.853324i	0.988612	+	0.150486i	$0.0480840\pi$
$733$	7.50658	+	23.1029i	0.277262	+	0.853324i	−0.711350	+	0.702838i	$0.751916\pi$
$734$	−7.28115	+	22.4091i	−0.268752	+	0.827134i
$735$		0			0
$736$	18.5066			0.682162
$737$	−29.6697	−	18.6251i	−1.09290	−	0.686064i
$738$	−9.61803			−0.354045
$739$	20.2254	+	14.6946i	0.744004	+	0.540551i	0.893963	−	0.448142i	$-0.147914\pi$
$739$	20.2254	+	14.6946i	0.744004	+	0.540551i	−0.149958	+	0.988692i	$0.547914\pi$
$740$		0			0
$741$	−1.64590	−	5.06555i	−0.0604636	−	0.186088i
$742$	−28.9894	+	21.0620i	−1.06423	+	0.773210i
$743$	10.3713	−	7.53521i	0.380487	−	0.276440i	−0.381059	−	0.924551i	$-0.624441\pi$
$743$	10.3713	−	7.53521i	0.380487	−	0.276440i	0.761546	+	0.648111i	$0.224441\pi$
$744$	2.66312	+	8.19624i	0.0976347	+	0.300489i
$745$		0			0
$746$	−29.3435	−	21.3193i	−1.07434	−	0.780554i
$747$	12.7082			0.464969
$748$	−0.472136	−	1.17557i	−0.0172630	−	0.0429831i
$749$	0.708204			0.0258772
$750$		0			0
$751$	−16.3541	+	50.3328i	−0.596770	+	1.83667i	−0.0510571	+	0.998696i	$0.516259\pi$
$751$	−16.3541	+	50.3328i	−0.596770	+	1.83667i	−0.545713	+	0.837972i	$0.683741\pi$
$752$	−0.927051	−	2.85317i	−0.0338061	−	0.104044i
$753$	13.5902	−	9.87384i	0.495253	−	0.359823i
$754$	36.5066	−	26.5236i	1.32949	−	0.965932i
$755$		0			0
$756$	0.572949	−	1.76336i	0.0208380	−	0.0641326i
$757$	−12.8992	−	9.37181i	−0.468829	−	0.340624i	0.328156	−	0.944624i	$-0.393573\pi$
$757$	−12.8992	−	9.37181i	−0.468829	−	0.340624i	−0.796985	+	0.603999i	$0.793573\pi$
$758$	−45.9787			−1.67002
$759$	−13.9271	+	11.6372i	−0.505520	+	0.422403i
$760$		0			0
$761$	−3.95492	−	2.87341i	−0.143366	−	0.104161i	0.513791	−	0.857916i	$-0.328241\pi$
$761$	−3.95492	−	2.87341i	−0.143366	−	0.104161i	−0.657156	+	0.753754i	$0.728241\pi$
$762$	−4.85410	+	14.9394i	−0.175846	+	0.541197i
$763$		0			0
$764$	−0.736068	+	0.534785i	−0.0266300	+	0.0193478i
$765$		0			0
$766$	−4.44427	−	13.6781i	−0.160578	−	0.494208i
$767$	10.2639	−	31.5891i	0.370609	−	1.14062i
$768$	10.9721	+	7.97172i	0.395923	+	0.287655i
$769$	−47.6869			−1.71963			−0.859817	−	0.510602i	$-0.829423\pi$
$769$	−47.6869			−1.71963			−0.859817	+	0.510602i	$0.829423\pi$
$770$		0			0
$771$	−27.3262			−0.984130
$772$	0.781153	+	0.567541i	0.0281143	+	0.0204262i
$773$	−15.2188	+	46.8388i	−0.547384	+	1.68467i	0.167870	+	0.985809i	$0.446311\pi$
$773$	−15.2188	+	46.8388i	−0.547384	+	1.68467i	−0.715253	+	0.698865i	$0.753689\pi$
$774$	0.881966	+	2.71441i	0.0317016	+	0.0975675i
$775$		0			0
$776$	27.1976	−	19.7602i	0.976336	−	0.709349i
$777$	3.92705	+	12.0862i	0.140882	+	0.433591i
$778$	4.63525	−	14.2658i	0.166182	−	0.511455i
$779$	4.10739	+	2.98419i	0.147163	+	0.106920i
$780$		0			0
$781$	−48.1869	+	3.26944i	−1.72426	+	0.116990i
$782$	−5.47214			−0.195683
$783$	−3.61803	−	2.62866i	−0.129298	−	0.0939405i
$784$	−3.00000	+	9.23305i	−0.107143	+	0.329752i
$785$		0			0
$786$	18.1353	−	13.1760i	0.646863	−	0.469974i
$787$	−19.1803	+	13.9353i	−0.683705	+	0.496741i	−0.874585	−	0.484873i	$-0.838866\pi$
$787$	−19.1803	+	13.9353i	−0.683705	+	0.496741i	0.190880	+	0.981613i	$0.438866\pi$
$788$	−5.08359	−	15.6457i	−0.181095	−	0.557355i
$789$	−0.208204	+	0.640786i	−0.00741226	+	0.0228126i
$790$		0			0
$791$	−38.1246			−1.35556
$792$	−7.39919	+	0.502029i	−0.262919	+	0.0178388i
$793$	−7.14590			−0.253758
$794$	33.1074	+	24.0539i	1.17494	+	0.853642i
$795$		0			0
$796$	−0.628677	−	1.93487i	−0.0222829	−	0.0685796i
$797$	12.3262	−	8.95554i	0.436618	−	0.317221i	−0.347672	−	0.937616i	$-0.613028\pi$
$797$	12.3262	−	8.95554i	0.436618	−	0.317221i	0.784290	+	0.620395i	$0.213028\pi$
$798$	−3.35410	+	2.43690i	−0.118734	+	0.0862652i
$799$	0.118034	+	0.363271i	0.00417574	+	0.0128516i
$800$		0			0
$801$	−7.66312	−	5.56758i	−0.270763	−	0.196721i
$802$	24.1246			0.851870
$803$	1.00000	−	3.97574i	0.0352892	−	0.140301i
$804$	6.52786			0.230220
$805$		0			0
$806$	−12.0172	+	36.9852i	−0.423289	+	1.30275i
$807$	−7.56231	−	23.2744i	−0.266206	−	0.819297i
$808$	5.42705	−	3.94298i	0.190923	−	0.138714i
$809$	−20.4894	+	14.8864i	−0.720367	+	0.523378i	−0.886502	−	0.462726i	$-0.846872\pi$
$809$	−20.4894	+	14.8864i	−0.720367	+	0.523378i	0.166134	+	0.986103i	$0.446872\pi$
$810$		0			0
$811$	14.1353	−	43.5038i	0.496356	−	1.52763i	−0.318477	−	0.947931i	$-0.603171\pi$
$811$	14.1353	−	43.5038i	0.496356	−	1.52763i	0.814833	−	0.579696i	$-0.196829\pi$
$812$	−6.70820	−	4.87380i	−0.235412	−	0.171037i
$813$	−6.27051			−0.219916
$814$	−17.4443	+	14.5761i	−0.611421	+	0.510893i
$815$		0			0
$816$	−2.42705	−	1.76336i	−0.0849638	−	0.0617298i
$817$	0.465558	−	1.43284i	0.0162878	−	0.0501287i
$818$	14.4721	+	44.5407i	0.506006	+	1.55733i
$819$	−15.1353	+	10.9964i	−0.528869	+	0.384246i
$820$		0			0
$821$	4.19756	+	12.9188i	0.146496	+	0.450868i	0.997200	−	0.0747763i	$-0.0238243\pi$
$821$	4.19756	+	12.9188i	0.146496	+	0.450868i	−0.850704	+	0.525644i	$0.823824\pi$
$822$	0.736068	−	2.26538i	0.0256733	−	0.0790144i
$823$	−21.4615	−	15.5927i	−0.748101	−	0.543527i	0.147137	−	0.989116i	$-0.452994\pi$
$823$	−21.4615	−	15.5927i	−0.748101	−	0.543527i	−0.895238	+	0.445589i	$0.852994\pi$
$824$	13.4164			0.467383
$825$		0			0
$826$	−25.8541			−0.899579
$827$	10.4164	+	7.56796i	0.362214	+	0.263164i	0.753975	−	0.656903i	$-0.228134\pi$
$827$	10.4164	+	7.56796i	0.362214	+	0.263164i	−0.391761	+	0.920067i	$0.628134\pi$
$828$	1.04508	−	3.21644i	0.0363192	−	0.111779i
$829$	−13.1910	−	40.5977i	−0.458142	−	1.41002i	−0.867407	−	0.497600i	$-0.834215\pi$
$829$	−13.1910	−	40.5977i	−0.458142	−	1.41002i	0.409265	−	0.912416i	$-0.365785\pi$
$830$		0			0
$831$	−8.44427	+	6.13512i	−0.292929	+	0.212825i
$832$	−8.16312	−	25.1235i	−0.283005	−	0.871001i
$833$	0.381966	−	1.17557i	0.0132343	−	0.0407311i
$834$	−7.66312	−	5.56758i	−0.265352	−	0.192790i
$835$		0			0
$836$	−1.48278	−	0.930812i	−0.0512830	−	0.0321928i
$837$	3.85410			0.133217
$838$	−28.1525	−	20.4540i	−0.972511	−	0.706571i
$839$	−7.19756	+	22.1518i	−0.248487	+	0.764766i	0.746556	+	0.665323i	$0.231706\pi$
$839$	−7.19756	+	22.1518i	−0.248487	+	0.764766i	−0.995043	+	0.0994428i	$0.968294\pi$
$840$		0			0
$841$	7.28115	−	5.29007i	0.251074	−	0.182416i
$842$	−4.88197	+	3.54696i	−0.168244	+	0.122236i
$843$	1.61803	+	4.97980i	0.0557281	+	0.171513i
$844$	2.15248	−	6.62464i	0.0740913	−	0.228029i
$845$		0			0
$846$	−1.00000			−0.0343807
$847$	23.8328	−	22.8254i	0.818905	−	0.784289i
$848$	−35.8328			−1.23050
$849$	17.9443	+	13.0373i	0.615846	+	0.447438i
$850$		0			0
$851$	7.16312	+	22.0458i	0.245549	+	0.755721i
$852$	7.28115	−	5.29007i	0.249448	−	0.181235i
$853$	6.42705	−	4.66953i	0.220058	−	0.159882i	−0.472295	−	0.881441i	$-0.656574\pi$
$853$	6.42705	−	4.66953i	0.220058	−	0.159882i	0.692353	+	0.721559i	$0.256574\pi$
$854$	1.71885	+	5.29007i	0.0588177	+	0.181022i
$855$		0			0
$856$	0.427051	+	0.310271i	0.0145963	+	0.0106048i
$857$	41.7214			1.42517			0.712587	−	0.701584i	$-0.247523\pi$
$857$	41.7214			1.42517			0.712587	+	0.701584i	$0.247523\pi$
$858$	−28.3435	−	17.7926i	−0.967630	−	0.607428i
$859$	42.8885			1.46334			0.731669	−	0.681660i	$-0.238742\pi$
$859$	42.8885			1.46334			0.731669	+	0.681660i	$0.238742\pi$
$860$		0			0
$861$	5.51064	−	16.9600i	0.187802	−	0.577996i
$862$	0.746711	+	2.29814i	0.0254331	+	0.0782750i
$863$	−19.3262	+	14.0413i	−0.657873	+	0.477973i	−0.865944	−	0.500141i	$-0.833281\pi$
$863$	−19.3262	+	14.0413i	−0.657873	+	0.477973i	0.208071	+	0.978114i	$0.433281\pi$
$864$	2.73607	−	1.98787i	0.0930829	−	0.0676287i
$865$		0			0
$866$	−3.00000	+	9.23305i	−0.101944	+	0.313752i
$867$	−13.4443	−	9.76784i	−0.456591	−	0.331733i
$868$	7.14590			0.242548
$869$	−0.652476	−	1.62460i	−0.0221337	−	0.0551107i
$870$		0			0
$871$	−53.2877	−	38.7158i	−1.80559	−	1.31183i
$872$		0			0
$873$	−4.64590	−	14.2986i	−0.157240	−	0.483934i
$874$	−6.11803	+	4.44501i	−0.206946	+	0.150355i
$875$		0			0
$876$	0.236068	+	0.726543i	0.00797600	+	0.0245476i
$877$	6.30902	−	19.4172i	0.213040	−	0.655671i	−0.786247	−	0.617913i	$-0.787978\pi$
$877$	6.30902	−	19.4172i	0.213040	−	0.655671i	0.999287	−	0.0377579i	$-0.0120216\pi$
$878$	21.8713	+	15.8904i	0.738121	+	0.536277i
$879$	17.9443			0.605245
$880$		0			0
$881$	25.0902			0.845309			0.422655	−	0.906291i	$-0.361098\pi$
$881$	25.0902			0.845309			0.422655	+	0.906291i	$0.361098\pi$
$882$	2.61803	+	1.90211i	0.0881538	+	0.0640475i
$883$	−11.5623	+	35.5851i	−0.389103	+	1.19753i	0.544358	+	0.838853i	$0.316774\pi$
$883$	−11.5623	+	35.5851i	−0.389103	+	1.19753i	−0.933460	+	0.358681i	$0.883226\pi$
$884$	−0.736068	−	2.26538i	−0.0247566	−	0.0761931i
$885$		0			0
$886$	1.14590	−	0.832544i	0.0384972	−	0.0279699i
$887$	−0.927051	−	2.85317i	−0.0311273	−	0.0958001i	0.934286	−	0.356525i	$-0.116038\pi$
$887$	−0.927051	−	2.85317i	−0.0311273	−	0.0958001i	−0.965413	+	0.260725i	$0.916038\pi$
$888$	−2.92705	+	9.00854i	−0.0982254	+	0.302307i
$889$	−23.5623	−	17.1190i	−0.790254	−	0.574153i
$890$		0			0
$891$	−0.809017	+	3.21644i	−0.0271031	+	0.107755i
$892$	7.85410			0.262975
$893$	0.427051	+	0.310271i	0.0142907	+	0.0103828i
$894$	7.50000	−	23.0826i	0.250838	−	0.771999i
$895$		0			0
$896$	−33.0517	+	24.0134i	−1.10418	+	0.802233i
$897$	−27.6074	+	20.0579i	−0.921784	+	0.669715i
$898$	7.76393	+	23.8949i	0.259086	+	0.797384i
$899$	5.32624	−	16.3925i	0.177640	−	0.546720i
$900$		0			0
$901$	4.56231			0.151992
$902$	31.8262	−	2.15938i	1.05970	−	0.0718996i
$903$	−5.29180			−0.176100
$904$	−22.9894	−	16.7027i	−0.764615	−	0.555525i
$905$		0			0
$906$	1.00000	+	3.07768i	0.0332228	+	0.102249i
$907$	3.21885	−	2.33863i	0.106880	−	0.0776529i	−0.533061	−	0.846077i	$-0.678959\pi$
$907$	3.21885	−	2.33863i	0.106880	−	0.0776529i	0.639942	+	0.768424i	$0.278959\pi$
$908$	5.44427	−	3.95550i	0.180675	−	0.131268i
$909$	−0.927051	−	2.85317i	−0.0307483	−	0.0946337i
$910$		0			0
$911$	−29.0795	−	21.1275i	−0.963448	−	0.699986i	−0.00949880	−	0.999955i	$-0.503024\pi$
$911$	−29.0795	−	21.1275i	−0.963448	−	0.699986i	−0.953949	+	0.299969i	$0.903024\pi$
$912$	−4.14590			−0.137284
$913$	−42.0517	+	2.85317i	−1.39171	+	0.0944261i
$914$	53.0689			1.75536
$915$		0			0
$916$	1.90983	−	5.87785i	0.0631026	−	0.194210i
$917$	12.8435	+	39.5281i	0.424128	+	1.30533i
$918$	−0.809017	+	0.587785i	−0.0267015	+	0.0193998i
$919$	37.9894	−	27.6009i	1.25315	−	0.910469i	0.254753	−	0.967006i	$-0.418006\pi$
$919$	37.9894	−	27.6009i	1.25315	−	0.910469i	0.998400	+	0.0565371i	$0.0180059\pi$
$920$		0			0
$921$	−6.04508	+	18.6049i	−0.199192	+	0.613051i
$922$	−12.9721	−	9.42481i	−0.427215	−	0.310390i
$923$	−90.8115			−2.98910
$924$	−1.50000	+	5.96361i	−0.0493464	+	0.196188i
$925$		0			0
$926$	−11.5172	−	8.36775i	−0.378479	−	0.274981i
$927$	1.85410	−	5.70634i	0.0608967	−	0.187421i
$928$	−4.67376	−	14.3844i	−0.153424	−	0.472190i
$929$	−2.33688	+	1.69784i	−0.0766706	+	0.0557044i	−0.625460	−	0.780256i	$-0.715089\pi$
$929$	−2.33688	+	1.69784i	−0.0766706	+	0.0557044i	0.548790	+	0.835960i	$0.315089\pi$
$930$		0			0
$931$	−0.527864	−	1.62460i	−0.0173000	−	0.0532441i
$932$	−1.65654	+	5.09831i	−0.0542618	+	0.167001i
$933$	9.28115	+	6.74315i	0.303851	+	0.220761i
$934$	−23.0344			−0.753710
$935$		0			0
$936$	−13.9443			−0.455783
$937$	26.3713	+	19.1599i	0.861514	+	0.625926i	0.928296	−	0.371841i	$-0.121273\pi$
$937$	26.3713	+	19.1599i	0.861514	+	0.625926i	−0.0667827	+	0.997768i	$0.521273\pi$
$938$	−15.8435	+	48.7612i	−0.517307	+	1.59211i
$939$	−8.60081	−	26.4706i	−0.280677	−	0.863835i
$940$		0			0
$941$	−27.2082	+	19.7679i	−0.886962	+	0.644416i	−0.935084	−	0.354426i	$-0.884676\pi$
$941$	−27.2082	+	19.7679i	−0.886962	+	0.644416i	0.0481221	+	0.998841i	$0.484676\pi$
$942$	−4.85410	−	14.9394i	−0.158155	−	0.486752i
$943$	10.0517	−	30.9358i	0.327327	−	1.00741i
$944$	−20.9164	−	15.1967i	−0.680771	−	0.494609i
$945$		0			0
$946$	−3.52786	−	8.78402i	−0.114701	−	0.285593i
$947$	−2.67376			−0.0868856			−0.0434428	−	0.999056i	$-0.513833\pi$
$947$	−2.67376			−0.0868856			−0.0434428	+	0.999056i	$0.513833\pi$
$948$	0.263932	+	0.191758i	0.00857211	+	0.00622801i
$949$	2.38197	−	7.33094i	0.0773219	−	0.237972i
$950$		0			0
$951$	−20.5172	+	14.9066i	−0.665316	+	0.483381i
$952$	3.35410	−	2.43690i	0.108707	−	0.0789803i
$953$	−18.5967	−	57.2349i	−0.602408	−	1.85402i	−0.513714	−	0.857961i	$-0.671731\pi$
$953$	−18.5967	−	57.2349i	−0.602408	−	1.85402i	−0.0886937	−	0.996059i	$-0.528269\pi$
$954$	−3.69098	+	11.3597i	−0.119500	+	0.367783i
$955$		0			0
$956$	−10.8541			−0.351047
$957$	12.5623	+	7.88597i	0.406082	+	0.254917i
$958$	27.3607			0.883983
$959$	3.57295	+	2.59590i	0.115377	+	0.0838260i
$960$		0			0
$961$	−4.98936	−	15.3557i	−0.160947	−	0.495344i
$962$	−34.5795	+	25.1235i	−1.11489	+	0.810014i
$963$	0.190983	−	0.138757i	0.00615434	−	0.00447139i
$964$	3.27051	+	10.0656i	0.105336	+	0.324191i
$965$		0			0
$966$	21.4894	+	15.6129i	0.691409	+	0.502338i
$967$	−25.6869			−0.826036			−0.413018	−	0.910723i	$-0.635525\pi$
$967$	−25.6869			−0.826036			−0.413018	+	0.910723i	$0.635525\pi$
$968$	24.3713	−	3.32244i	0.783324	−	0.106787i
$969$	0.527864			0.0169574
$970$		0			0
$971$	−10.4377	+	32.1239i	−0.334962	+	1.03091i	0.631779	+	0.775148i	$0.282325\pi$
$971$	−10.4377	+	32.1239i	−0.334962	+	1.03091i	−0.966741	+	0.255757i	$0.917675\pi$
$972$	−0.190983	−	0.587785i	−0.00612578	−	0.0188532i
$973$	14.2082	−	10.3229i	0.455494	−	0.330936i
$974$	−51.2877	+	37.2627i	−1.64336	+	1.19397i
$975$		0			0
$976$	−1.71885	+	5.29007i	−0.0550190	+	0.169331i
$977$	−39.9336	−	29.0135i	−1.27759	−	0.928223i	−0.278113	−	0.960548i	$-0.589709\pi$
$977$	−39.9336	−	29.0135i	−1.27759	−	0.928223i	−0.999477	+	0.0323250i	$0.989709\pi$
$978$	24.7082			0.790081
$979$	26.6074	+	16.7027i	0.850376	+	0.533822i
$980$		0			0
$981$		0			0
$982$	13.1074	−	40.3404i	0.418274	−	1.28731i
$983$	−10.9098	−	33.5770i	−0.347970	−	1.07094i	−0.959975	−	0.280086i	$-0.909637\pi$
$983$	−10.9098	−	33.5770i	−0.347970	−	1.07094i	0.612005	−	0.790854i	$-0.290363\pi$
$984$	10.7533	−	7.81272i	0.342802	−	0.249060i
$985$		0			0
$986$	1.38197	+	4.25325i	0.0440108	+	0.135451i
$987$	0.572949	−	1.76336i	0.0182372	−	0.0561282i
$988$	−2.66312	−	1.93487i	−0.0847251	−	0.0615564i
$989$	−9.65248			−0.306931
$990$		0			0
$991$	−12.2705			−0.389786			−0.194893	−	0.980825i	$-0.562436\pi$
$991$	−12.2705			−0.389786			−0.194893	+	0.980825i	$0.562436\pi$
$992$	10.5451	+	7.66145i	0.334807	+	0.243251i
$993$	6.98278	−	21.4908i	0.221592	−	0.681989i
$994$	21.8435	+	67.2273i	0.692832	+	2.13232i
$995$		0			0
$996$	6.35410	−	4.61653i	0.201337	−	0.146280i
$997$	−10.5000	−	32.3157i	−0.332538	−	1.02345i	−0.967922	−	0.251251i	$-0.919158\pi$
$997$	−10.5000	−	32.3157i	−0.332538	−	1.02345i	0.635384	−	0.772197i	$-0.280842\pi$
$998$	−1.28115	+	3.94298i	−0.0405542	+	0.124813i
$999$	3.42705	+	2.48990i	0.108427	+	0.0787769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.f.301.1		4
5.2	odd	4		825.2.bx.b.499.1		8
5.3	odd	4		825.2.bx.b.499.2		8
5.4	even	2		33.2.e.a.4.1	✓	4
11.3	even	5	inner	825.2.n.f.751.1		4
11.5	even	5		9075.2.a.x.1.1		2
11.6	odd	10		9075.2.a.bv.1.2		2
15.14	odd	2		99.2.f.b.37.1		4
20.19	odd	2		528.2.y.f.433.1		4
45.4	even	6		891.2.n.d.136.1		8
45.14	odd	6		891.2.n.a.136.1		8
45.29	odd	6		891.2.n.a.433.1		8
45.34	even	6		891.2.n.d.433.1		8
55.3	odd	20		825.2.bx.b.124.1		8
55.4	even	10		363.2.e.h.130.1		4
55.9	even	10		363.2.e.h.148.1		4
55.14	even	10		33.2.e.a.25.1	yes	4
55.19	odd	10		363.2.e.j.124.1		4
55.24	odd	10		363.2.e.c.148.1		4
55.29	odd	10		363.2.e.c.130.1		4
55.39	odd	10		363.2.a.e.1.1		2
55.47	odd	20		825.2.bx.b.124.2		8
55.49	even	10		363.2.a.h.1.2		2
55.54	odd	2		363.2.e.j.202.1		4
165.14	odd	10		99.2.f.b.91.1		4
165.104	odd	10		1089.2.a.m.1.1		2
165.149	even	10		1089.2.a.s.1.2		2
220.39	even	10		5808.2.a.bm.1.2		2
220.159	odd	10		5808.2.a.bl.1.2		2
220.179	odd	10		528.2.y.f.289.1		4
495.14	odd	30		891.2.n.a.784.1		8
495.124	even	30		891.2.n.d.190.1		8
495.344	odd	30		891.2.n.a.190.1		8
495.454	even	30		891.2.n.d.784.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.4.1	✓	4	5.4	even	2
33.2.e.a.25.1	yes	4	55.14	even	10
99.2.f.b.37.1		4	15.14	odd	2
99.2.f.b.91.1		4	165.14	odd	10
363.2.a.e.1.1		2	55.39	odd	10
363.2.a.h.1.2		2	55.49	even	10
363.2.e.c.130.1		4	55.29	odd	10
363.2.e.c.148.1		4	55.24	odd	10
363.2.e.h.130.1		4	55.4	even	10
363.2.e.h.148.1		4	55.9	even	10
363.2.e.j.124.1		4	55.19	odd	10
363.2.e.j.202.1		4	55.54	odd	2
528.2.y.f.289.1		4	220.179	odd	10
528.2.y.f.433.1		4	20.19	odd	2
825.2.n.f.301.1		4	1.1	even	1	trivial
825.2.n.f.751.1		4	11.3	even	5	inner
825.2.bx.b.124.1		8	55.3	odd	20
825.2.bx.b.124.2		8	55.47	odd	20
825.2.bx.b.499.1		8	5.2	odd	4
825.2.bx.b.499.2		8	5.3	odd	4
891.2.n.a.136.1		8	45.14	odd	6
891.2.n.a.190.1		8	495.344	odd	30
891.2.n.a.433.1		8	45.29	odd	6
891.2.n.a.784.1		8	495.14	odd	30
891.2.n.d.136.1		8	45.4	even	6
891.2.n.d.190.1		8	495.124	even	30
891.2.n.d.433.1		8	45.34	even	6
891.2.n.d.784.1		8	495.454	even	30
1089.2.a.m.1.1		2	165.104	odd	10
1089.2.a.s.1.2		2	165.149	even	10
5808.2.a.bl.1.2		2	220.159	odd	10
5808.2.a.bm.1.2		2	220.39	even	10
9075.2.a.x.1.1		2	11.5	even	5
9075.2.a.bv.1.2		2	11.6	odd	10

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30902 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-1.30902 + 0.951057i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.30902 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-1.30902 + 0.951057i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(2.80902 + 1.76336i) q^{11} -0.618034 q^{12} +(5.04508 + 3.66547i) q^{13} +(1.50000 - 4.61653i) q^{14} +(3.92705 - 2.85317i) q^{16} +(-0.500000 + 0.363271i) q^{17} +(-0.500000 - 1.53884i) q^{18} +(-0.263932 + 0.812299i) q^{19} +3.00000 q^{21} +(2.00000 + 4.97980i) q^{22} +5.47214 q^{23} +(1.80902 + 1.31433i) q^{24} +(3.11803 + 9.59632i) q^{26} +(0.809017 - 0.587785i) q^{27} +(1.50000 - 1.08981i) q^{28} +(-1.38197 - 4.25325i) q^{29} +(3.11803 + 2.26538i) q^{31} +3.38197 q^{32} +(-2.54508 + 2.12663i) q^{33} -1.00000 q^{34} +(0.190983 - 0.587785i) q^{36} +(1.30902 + 4.02874i) q^{37} +(-1.11803 + 0.812299i) q^{38} +(-5.04508 + 3.66547i) q^{39} +(1.83688 - 5.65334i) q^{41} +(3.92705 + 2.85317i) q^{42} -1.76393 q^{43} +(-0.500000 + 1.98787i) q^{44} +(7.16312 + 5.20431i) q^{46} +(0.190983 - 0.587785i) q^{47} +(1.50000 + 4.61653i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(-0.190983 - 0.587785i) q^{51} +(-1.19098 + 3.66547i) q^{52} +(-5.97214 - 4.33901i) q^{53} +1.61803 q^{54} -6.70820 q^{56} +(-0.690983 - 0.502029i) q^{57} +(2.23607 - 6.88191i) q^{58} +(-1.64590 - 5.06555i) q^{59} +(-0.927051 + 0.673542i) q^{61} +(1.92705 + 5.93085i) q^{62} +(-0.927051 + 2.85317i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(-5.35410 + 0.363271i) q^{66} -10.5623 q^{67} +(-0.309017 - 0.224514i) q^{68} +(-1.69098 + 5.20431i) q^{69} +(-11.7812 + 8.55951i) q^{71} +(-1.80902 + 1.31433i) q^{72} +(-0.381966 - 1.17557i) q^{73} +(-2.11803 + 6.51864i) q^{74} -0.527864 q^{76} +(2.42705 - 9.64932i) q^{77} -10.0902 q^{78} +(-0.427051 - 0.310271i) q^{79} +(0.309017 + 0.951057i) q^{81} +(7.78115 - 5.65334i) q^{82} +(-10.2812 + 7.46969i) q^{83} +(0.572949 + 1.76336i) q^{84} +(-2.30902 - 1.67760i) q^{86} +4.47214 q^{87} +(5.69098 - 4.75528i) q^{88} +9.47214 q^{89} +(5.78115 - 17.7926i) q^{91} +(1.04508 + 3.21644i) q^{92} +(-3.11803 + 2.26538i) q^{93} +(0.809017 - 0.587785i) q^{94} +(-1.04508 + 3.21644i) q^{96} +(12.1631 + 8.83702i) q^{97} -3.23607 q^{98} +(-1.23607 - 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} + 9 q^{11} + 2 q^{12} + 9 q^{13} + 6 q^{14} + 9 q^{16} - 2 q^{17} - 2 q^{18} - 10 q^{19} + 12 q^{21} + 8 q^{22} + 4 q^{23} + 5 q^{24} + 8 q^{26} + q^{27} + 6 q^{28} - 10 q^{29} + 8 q^{31} + 18 q^{32} + q^{33} - 4 q^{34} + 3 q^{36} + 3 q^{37} - 9 q^{39} + 23 q^{41} + 9 q^{42} - 16 q^{43} - 2 q^{44} + 13 q^{46} + 3 q^{47} + 6 q^{48} - 2 q^{49} - 3 q^{51} - 7 q^{52} - 6 q^{53} + 2 q^{54} - 5 q^{57} - 20 q^{59} + 3 q^{61} + q^{62} + 3 q^{63} - 7 q^{64} - 8 q^{66} - 2 q^{67} + q^{68} - 9 q^{69} - 27 q^{71} - 5 q^{72} - 6 q^{73} - 4 q^{74} - 20 q^{76} + 3 q^{77} - 18 q^{78} + 5 q^{79} - q^{81} + 11 q^{82} - 21 q^{83} + 9 q^{84} - 7 q^{86} + 25 q^{88} + 20 q^{89} + 3 q^{91} - 7 q^{92} - 8 q^{93} + q^{94} + 7 q^{96} + 33 q^{97} - 4 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9 + 9 * q^11 + 2 * q^12 + 9 * q^13 + 6 * q^14 + 9 * q^16 - 2 * q^17 - 2 * q^18 - 10 * q^19 + 12 * q^21 + 8 * q^22 + 4 * q^23 + 5 * q^24 + 8 * q^26 + q^27 + 6 * q^28 - 10 * q^29 + 8 * q^31 + 18 * q^32 + q^33 - 4 * q^34 + 3 * q^36 + 3 * q^37 - 9 * q^39 + 23 * q^41 + 9 * q^42 - 16 * q^43 - 2 * q^44 + 13 * q^46 + 3 * q^47 + 6 * q^48 - 2 * q^49 - 3 * q^51 - 7 * q^52 - 6 * q^53 + 2 * q^54 - 5 * q^57 - 20 * q^59 + 3 * q^61 + q^62 + 3 * q^63 - 7 * q^64 - 8 * q^66 - 2 * q^67 + q^68 - 9 * q^69 - 27 * q^71 - 5 * q^72 - 6 * q^73 - 4 * q^74 - 20 * q^76 + 3 * q^77 - 18 * q^78 + 5 * q^79 - q^81 + 11 * q^82 - 21 * q^83 + 9 * q^84 - 7 * q^86 + 25 * q^88 + 20 * q^89 + 3 * q^91 - 7 * q^92 - 8 * q^93 + q^94 + 7 * q^96 + 33 * q^97 - 4 * q^98 + 4 * q^99

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