LMFDB - Embedded newform 825.2.r.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(31,825)]

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, 4, 6]))

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

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

chi := DirichletCharacter("825.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.r (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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	825.31
Dual form			825.2.r.a.346.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.23607 q^{2} +(0.309017 - 0.951057i) q^{3} +3.00000 q^{4} +(1.80902 + 1.31433i) q^{5} +(0.690983 - 2.12663i) q^{6} +(-0.309017 - 0.224514i) q^{7} +2.23607 q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+2.23607 q^{2} +(0.309017 - 0.951057i) q^{3} +3.00000 q^{4} +(1.80902 + 1.31433i) q^{5} +(0.690983 - 2.12663i) q^{6} +(-0.309017 - 0.224514i) q^{7} +2.23607 q^{8} +(-0.809017 - 0.587785i) q^{9} +(4.04508 + 2.93893i) q^{10} +(-1.69098 - 2.85317i) q^{11} +(0.927051 - 2.85317i) q^{12} +(4.85410 + 3.52671i) q^{13} +(-0.690983 - 0.502029i) q^{14} +(1.80902 - 1.31433i) q^{15} -1.00000 q^{16} +(0.545085 - 1.67760i) q^{17} +(-1.80902 - 1.31433i) q^{18} +4.38197 q^{19} +(5.42705 + 3.94298i) q^{20} +(-0.309017 + 0.224514i) q^{21} +(-3.78115 - 6.37988i) q^{22} +(-1.07295 - 3.30220i) q^{23} +(0.690983 - 2.12663i) q^{24} +(1.54508 + 4.75528i) q^{25} +(10.8541 + 7.88597i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.927051 - 0.673542i) q^{28} -4.09017 q^{29} +(4.04508 - 2.93893i) q^{30} +(1.19098 - 0.865300i) q^{31} -6.70820 q^{32} +(-3.23607 + 0.726543i) q^{33} +(1.21885 - 3.75123i) q^{34} +(-0.263932 - 0.812299i) q^{35} +(-2.42705 - 1.76336i) q^{36} +(-6.35410 + 4.61653i) q^{37} +9.79837 q^{38} +(4.85410 - 3.52671i) q^{39} +(4.04508 + 2.93893i) q^{40} +(1.92705 + 5.93085i) q^{41} +(-0.690983 + 0.502029i) q^{42} -9.94427 q^{43} +(-5.07295 - 8.55951i) q^{44} +(-0.690983 - 2.12663i) q^{45} +(-2.39919 - 7.38394i) q^{46} +(-0.954915 + 2.93893i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-2.11803 - 6.51864i) q^{49} +(3.45492 + 10.6331i) q^{50} +(-1.42705 - 1.03681i) q^{51} +(14.5623 + 10.5801i) q^{52} +(-0.309017 - 0.951057i) q^{53} +(-1.80902 + 1.31433i) q^{54} +(0.690983 - 7.38394i) q^{55} +(-0.690983 - 0.502029i) q^{56} +(1.35410 - 4.16750i) q^{57} -9.14590 q^{58} +(1.38197 - 1.00406i) q^{59} +(5.42705 - 3.94298i) q^{60} +(-8.35410 + 6.06961i) q^{61} +(2.66312 - 1.93487i) q^{62} +(0.118034 + 0.363271i) q^{63} -13.0000 q^{64} +(4.14590 + 12.7598i) q^{65} +(-7.23607 + 1.62460i) q^{66} +(-0.690983 - 0.502029i) q^{67} +(1.63525 - 5.03280i) q^{68} -3.47214 q^{69} +(-0.590170 - 1.81636i) q^{70} +(1.19098 + 0.865300i) q^{71} +(-1.80902 - 1.31433i) q^{72} +(0.381966 - 1.17557i) q^{73} +(-14.2082 + 10.3229i) q^{74} +5.00000 q^{75} +13.1459 q^{76} +(-0.118034 + 1.26133i) q^{77} +(10.8541 - 7.88597i) q^{78} +(1.52786 + 4.70228i) q^{79} +(-1.80902 - 1.31433i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.30902 + 13.2618i) q^{82} +(3.57295 - 10.9964i) q^{83} +(-0.927051 + 0.673542i) q^{84} +(3.19098 - 2.31838i) q^{85} -22.2361 q^{86} +(-1.26393 + 3.88998i) q^{87} +(-3.78115 - 6.37988i) q^{88} +(-5.11803 - 15.7517i) q^{89} +(-1.54508 - 4.75528i) q^{90} +(-0.708204 - 2.17963i) q^{91} +(-3.21885 - 9.90659i) q^{92} +(-0.454915 - 1.40008i) q^{93} +(-2.13525 + 6.57164i) q^{94} +(7.92705 + 5.75934i) q^{95} +(-2.07295 + 6.37988i) q^{96} +(3.54508 + 10.9106i) q^{97} +(-4.73607 - 14.5761i) q^{98} +(-0.309017 + 3.30220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 12 q^{4} + 5 q^{5} + 5 q^{6} + q^{7} - q^{9}+O(q^{10}) $ 4 * q - q^3 + 12 * q^4 + 5 * q^5 + 5 * q^6 + q^7 - q^9	\( 4 q - q^{3} + 12 q^{4} + 5 q^{5} + 5 q^{6} + q^{7} - q^{9} + 5 q^{10} - 9 q^{11} - 3 q^{12} + 6 q^{13} - 5 q^{14} + 5 q^{15} - 4 q^{16} - 9 q^{17} - 5 q^{18} + 22 q^{19} + 15 q^{20} + q^{21} + 5 q^{22} - 11 q^{23} + 5 q^{24} - 5 q^{25} + 30 q^{26} - q^{27} + 3 q^{28} + 6 q^{29} + 5 q^{30} + 7 q^{31} - 4 q^{33} + 25 q^{34} - 10 q^{35} - 3 q^{36} - 12 q^{37} - 10 q^{38} + 6 q^{39} + 5 q^{40} + q^{41} - 5 q^{42} - 4 q^{43} - 27 q^{44} - 5 q^{45} + 15 q^{46} - 15 q^{47} + q^{48} - 4 q^{49} + 25 q^{50} + q^{51} + 18 q^{52} + q^{53} - 5 q^{54} + 5 q^{55} - 5 q^{56} - 8 q^{57} - 50 q^{58} + 10 q^{59} + 15 q^{60} - 20 q^{61} - 5 q^{62} - 4 q^{63} - 52 q^{64} + 30 q^{65} - 20 q^{66} - 5 q^{67} - 27 q^{68} + 4 q^{69} + 20 q^{70} + 7 q^{71} - 5 q^{72} + 6 q^{73} - 30 q^{74} + 20 q^{75} + 66 q^{76} + 4 q^{77} + 30 q^{78} + 24 q^{79} - 5 q^{80} - q^{81} + 15 q^{82} + 21 q^{83} + 3 q^{84} + 15 q^{85} - 80 q^{86} - 14 q^{87} + 5 q^{88} - 16 q^{89} + 5 q^{90} + 24 q^{91} - 33 q^{92} - 13 q^{93} + 25 q^{94} + 25 q^{95} - 15 q^{96} + 3 q^{97} - 10 q^{98} + q^{99}+O(q^{100}) \) 4 * q - q^3 + 12 * q^4 + 5 * q^5 + 5 * q^6 + q^7 - q^9 + 5 * q^10 - 9 * q^11 - 3 * q^12 + 6 * q^13 - 5 * q^14 + 5 * q^15 - 4 * q^16 - 9 * q^17 - 5 * q^18 + 22 * q^19 + 15 * q^20 + q^21 + 5 * q^22 - 11 * q^23 + 5 * q^24 - 5 * q^25 + 30 * q^26 - q^27 + 3 * q^28 + 6 * q^29 + 5 * q^30 + 7 * q^31 - 4 * q^33 + 25 * q^34 - 10 * q^35 - 3 * q^36 - 12 * q^37 - 10 * q^38 + 6 * q^39 + 5 * q^40 + q^41 - 5 * q^42 - 4 * q^43 - 27 * q^44 - 5 * q^45 + 15 * q^46 - 15 * q^47 + q^48 - 4 * q^49 + 25 * q^50 + q^51 + 18 * q^52 + q^53 - 5 * q^54 + 5 * q^55 - 5 * q^56 - 8 * q^57 - 50 * q^58 + 10 * q^59 + 15 * q^60 - 20 * q^61 - 5 * q^62 - 4 * q^63 - 52 * q^64 + 30 * q^65 - 20 * q^66 - 5 * q^67 - 27 * q^68 + 4 * q^69 + 20 * q^70 + 7 * q^71 - 5 * q^72 + 6 * q^73 - 30 * q^74 + 20 * q^75 + 66 * q^76 + 4 * q^77 + 30 * q^78 + 24 * q^79 - 5 * q^80 - q^81 + 15 * q^82 + 21 * q^83 + 3 * q^84 + 15 * q^85 - 80 * q^86 - 14 * q^87 + 5 * q^88 - 16 * q^89 + 5 * q^90 + 24 * q^91 - 33 * q^92 - 13 * q^93 + 25 * q^94 + 25 * q^95 - 15 * q^96 + 3 * q^97 - 10 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	2.23607			1.58114			0.790569	−	0.612372i	$-0.209785\pi$
$2$	2.23607			1.58114			0.790569	+	0.612372i	$0.209785\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	3.00000			1.50000
$5$	1.80902	+	1.31433i	0.809017	+	0.587785i
$5$	1.80902	+	1.31433i	0.809017	+	0.587785i
$6$	0.690983	−	2.12663i	0.282093	−	0.868192i
$7$	−0.309017	−	0.224514i	−0.116797	−	0.0848583i	0.527853	−	0.849336i	$-0.322997\pi$
$7$	−0.309017	−	0.224514i	−0.116797	−	0.0848583i	−0.644651	+	0.764477i	$0.722997\pi$
$8$	2.23607			0.790569
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	4.04508	+	2.93893i	1.27917	+	0.929370i
$11$	−1.69098	−	2.85317i	−0.509851	−	0.860263i
$11$	−1.69098	−	2.85317i	−0.509851	−	0.860263i
$12$	0.927051	−	2.85317i	0.267617	−	0.823639i
$13$	4.85410	+	3.52671i	1.34629	+	0.978134i	0.999187	+	0.0403050i	$0.0128330\pi$
$13$	4.85410	+	3.52671i	1.34629	+	0.978134i	0.347098	+	0.937829i	$0.387167\pi$
$14$	−0.690983	−	0.502029i	−0.184673	−	0.134173i
$15$	1.80902	−	1.31433i	0.467086	−	0.339358i
$16$	−1.00000			−0.250000
$17$	0.545085	−	1.67760i	0.132203	−	0.406878i	−0.862942	−	0.505303i	$-0.831381\pi$
$17$	0.545085	−	1.67760i	0.132203	−	0.406878i	0.995144	+	0.0984257i	$0.0313807\pi$
$18$	−1.80902	−	1.31433i	−0.426389	−	0.309790i
$19$	4.38197			1.00529			0.502646	−	0.864492i	$-0.332360\pi$
$19$	4.38197			1.00529			0.502646	+	0.864492i	$0.332360\pi$
$20$	5.42705	+	3.94298i	1.21353	+	0.881678i
$21$	−0.309017	+	0.224514i	−0.0674330	+	0.0489930i
$22$	−3.78115	−	6.37988i	−0.806145	−	1.36020i
$23$	−1.07295	−	3.30220i	−0.223725	−	0.688556i	−0.998418	−	0.0562184i	$-0.982096\pi$
$23$	−1.07295	−	3.30220i	−0.223725	−	0.688556i	0.774693	−	0.632337i	$-0.217904\pi$
$24$	0.690983	−	2.12663i	0.141046	−	0.434096i
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$	10.8541	+	7.88597i	2.12866	+	1.54657i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−0.927051	−	0.673542i	−0.175196	−	0.127287i
$29$	−4.09017			−0.759525			−0.379763	−	0.925084i	$-0.623994\pi$
$29$	−4.09017			−0.759525			−0.379763	+	0.925084i	$0.623994\pi$
$30$	4.04508	−	2.93893i	0.738528	−	0.536572i
$31$	1.19098	−	0.865300i	0.213907	−	0.155412i	−0.475673	−	0.879622i	$-0.657795\pi$
$31$	1.19098	−	0.865300i	0.213907	−	0.155412i	0.689580	+	0.724210i	$0.257795\pi$
$32$	−6.70820			−1.18585
$33$	−3.23607	+	0.726543i	−0.563327	+	0.126475i
$34$	1.21885	−	3.75123i	0.209031	−	0.643330i
$35$	−0.263932	−	0.812299i	−0.0446127	−	0.137304i
$36$	−2.42705	−	1.76336i	−0.404508	−	0.293893i
$37$	−6.35410	+	4.61653i	−1.04461	+	0.758952i	−0.971180	−	0.238348i	$-0.923394\pi$
$37$	−6.35410	+	4.61653i	−1.04461	+	0.758952i	−0.0734282	+	0.997301i	$0.523394\pi$
$38$	9.79837			1.58951
$39$	4.85410	−	3.52671i	0.777278	−	0.564726i
$40$	4.04508	+	2.93893i	0.639584	+	0.464685i
$41$	1.92705	+	5.93085i	0.300955	+	0.926244i	0.981156	+	0.193218i	$0.0618925\pi$
$41$	1.92705	+	5.93085i	0.300955	+	0.926244i	−0.680201	+	0.733026i	$0.738108\pi$
$42$	−0.690983	+	0.502029i	−0.106621	+	0.0774647i
$43$	−9.94427			−1.51649			−0.758244	−	0.651971i	$-0.773942\pi$
$43$	−9.94427			−1.51649			−0.758244	+	0.651971i	$0.773942\pi$
$44$	−5.07295	−	8.55951i	−0.764776	−	1.29039i
$45$	−0.690983	−	2.12663i	−0.103006	−	0.317019i
$46$	−2.39919	−	7.38394i	−0.353741	−	1.08870i
$47$	−0.954915	+	2.93893i	−0.139289	+	0.428686i	−0.996232	−	0.0867235i	$-0.972360\pi$
$47$	−0.954915	+	2.93893i	−0.139289	+	0.428686i	0.856944	+	0.515410i	$0.172360\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−2.11803	−	6.51864i	−0.302576	−	0.931234i
$50$	3.45492	+	10.6331i	0.488599	+	1.50375i
$51$	−1.42705	−	1.03681i	−0.199827	−	0.145183i
$52$	14.5623	+	10.5801i	2.01943	+	1.46720i
$53$	−0.309017	−	0.951057i	−0.0424467	−	0.130638i	0.927587	−	0.373606i	$-0.121879\pi$
$53$	−0.309017	−	0.951057i	−0.0424467	−	0.130638i	−0.970034	+	0.242968i	$0.921879\pi$
$54$	−1.80902	+	1.31433i	−0.246176	+	0.178857i
$55$	0.690983	−	7.38394i	0.0931721	−	0.995650i
$56$	−0.690983	−	0.502029i	−0.0923365	−	0.0670864i
$57$	1.35410	−	4.16750i	0.179355	−	0.551999i
$58$	−9.14590			−1.20092
$59$	1.38197	−	1.00406i	0.179917	−	0.130717i	−0.494182	−	0.869359i	$-0.664532\pi$
$59$	1.38197	−	1.00406i	0.179917	−	0.130717i	0.674099	+	0.738641i	$0.264532\pi$
$60$	5.42705	−	3.94298i	0.700629	−	0.509037i
$61$	−8.35410	+	6.06961i	−1.06963	+	0.777134i	−0.975846	−	0.218458i	$-0.929897\pi$
$61$	−8.35410	+	6.06961i	−1.06963	+	0.777134i	−0.0937869	+	0.995592i	$0.529897\pi$
$62$	2.66312	−	1.93487i	0.338216	−	0.245729i
$63$	0.118034	+	0.363271i	0.0148709	+	0.0457679i
$64$	−13.0000			−1.62500
$65$	4.14590	+	12.7598i	0.514235	+	1.58265i
$66$	−7.23607	+	1.62460i	−0.890698	+	0.199974i
$67$	−0.690983	−	0.502029i	−0.0844170	−	0.0613325i	0.544776	−	0.838581i	$-0.316615\pi$
$67$	−0.690983	−	0.502029i	−0.0844170	−	0.0613325i	−0.629193	+	0.777249i	$0.716615\pi$
$68$	1.63525	−	5.03280i	0.198304	−	0.610316i
$69$	−3.47214			−0.417996
$70$	−0.590170	−	1.81636i	−0.0705388	−	0.217096i
$71$	1.19098	+	0.865300i	0.141344	+	0.102692i	0.656210	−	0.754578i	$-0.272158\pi$
$71$	1.19098	+	0.865300i	0.141344	+	0.102692i	−0.514866	+	0.857270i	$0.672158\pi$
$72$	−1.80902	−	1.31433i	−0.213195	−	0.154895i
$73$	0.381966	−	1.17557i	0.0447057	−	0.137590i	−0.926212	−	0.377003i	$-0.876955\pi$
$73$	0.381966	−	1.17557i	0.0447057	−	0.137590i	0.970918	+	0.239412i	$0.0769548\pi$
$74$	−14.2082	+	10.3229i	−1.65167	+	1.20001i
$75$	5.00000			0.577350
$76$	13.1459			1.50794
$77$	−0.118034	+	1.26133i	−0.0134512	+	0.143742i
$78$	10.8541	−	7.88597i	1.22899	−	0.892910i
$79$	1.52786	+	4.70228i	0.171898	+	0.529048i	0.999478	−	0.0322996i	$-0.0102831\pi$
$79$	1.52786	+	4.70228i	0.171898	+	0.529048i	−0.827580	+	0.561348i	$0.810283\pi$
$80$	−1.80902	−	1.31433i	−0.202254	−	0.146946i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	4.30902	+	13.2618i	0.475851	+	1.46452i
$83$	3.57295	−	10.9964i	0.392182	−	1.20701i	−0.538952	−	0.842336i	$-0.681180\pi$
$83$	3.57295	−	10.9964i	0.392182	−	1.20701i	0.931134	−	0.364676i	$-0.118820\pi$
$84$	−0.927051	+	0.673542i	−0.101150	+	0.0734895i
$85$	3.19098	−	2.31838i	0.346111	−	0.251464i
$86$	−22.2361			−2.39778
$87$	−1.26393	+	3.88998i	−0.135508	+	0.417050i
$88$	−3.78115	−	6.37988i	−0.403072	−	0.680098i
$89$	−5.11803	−	15.7517i	−0.542511	−	1.66968i	−0.726837	−	0.686811i	$-0.759010\pi$
$89$	−5.11803	−	15.7517i	−0.542511	−	1.66968i	0.184326	−	0.982865i	$-0.440990\pi$
$90$	−1.54508	−	4.75528i	−0.162866	−	0.501251i
$91$	−0.708204	−	2.17963i	−0.0742399	−	0.228487i
$92$	−3.21885	−	9.90659i	−0.335588	−	1.03283i
$93$	−0.454915	−	1.40008i	−0.0471725	−	0.145182i
$94$	−2.13525	+	6.57164i	−0.220235	+	0.677813i
$95$	7.92705	+	5.75934i	0.813298	+	0.590896i
$96$	−2.07295	+	6.37988i	−0.211569	+	0.651144i
$97$	3.54508	+	10.9106i	0.359949	+	1.10781i	0.953084	+	0.302706i	$0.0978899\pi$
$97$	3.54508	+	10.9106i	0.359949	+	1.10781i	−0.593135	+	0.805103i	$0.702110\pi$
$98$	−4.73607	−	14.5761i	−0.478415	−	1.47241i
$99$	−0.309017	+	3.30220i	−0.0310574	+	0.331883i
$100$	4.63525	+	14.2658i	0.463525	+	1.42658i
$101$	−5.16312	+	15.8904i	−0.513750	+	1.58116i	0.271796	+	0.962355i	$0.412382\pi$
$101$	−5.16312	+	15.8904i	−0.513750	+	1.58116i	−0.785546	+	0.618804i	$0.787618\pi$
$102$	−3.19098	−	2.31838i	−0.315954	−	0.229554i
$103$	4.70820			0.463913			0.231957	−	0.972726i	$-0.425487\pi$
$103$	4.70820			0.463913			0.231957	+	0.972726i	$0.425487\pi$
$104$	10.8541	+	7.88597i	1.06433	+	0.773283i
$105$	−0.854102			−0.0833518
$106$	−0.690983	−	2.12663i	−0.0671142	−	0.206556i
$107$	11.6631	−	8.47375i	1.12752	−	0.819189i	0.142185	−	0.989840i	$-0.454587\pi$
$107$	11.6631	−	8.47375i	1.12752	−	0.819189i	0.985331	+	0.170652i	$0.0545873\pi$
$108$	−2.42705	+	1.76336i	−0.233543	+	0.169679i
$109$	5.47214	−	16.8415i	0.524136	−	1.61312i	−0.241883	−	0.970305i	$-0.577765\pi$
$109$	5.47214	−	16.8415i	0.524136	−	1.61312i	0.766019	−	0.642818i	$-0.222235\pi$
$110$	1.54508	−	16.5110i	0.147318	−	1.57426i
$111$	2.42705	+	7.46969i	0.230365	+	0.708992i
$112$	0.309017	+	0.224514i	0.0291994	+	0.0212146i
$113$	0.454915	+	1.40008i	0.0427948	+	0.131709i	0.970171	−	0.242421i	$-0.0779415\pi$
$113$	0.454915	+	1.40008i	0.0427948	+	0.131709i	−0.927376	+	0.374130i	$0.877941\pi$
$114$	3.02786	−	9.31881i	0.283585	−	0.872786i
$115$	2.39919	−	7.38394i	0.223725	−	0.688556i
$116$	−12.2705			−1.13929
$117$	−1.85410	−	5.70634i	−0.171412	−	0.527551i
$118$	3.09017	−	2.24514i	0.284473	−	0.206682i
$119$	−0.545085	+	0.396027i	−0.0499679	+	0.0363038i
$120$	4.04508	−	2.93893i	0.369264	−	0.268286i
$121$	−5.28115	+	9.64932i	−0.480105	+	0.877211i
$122$	−18.6803	+	13.5721i	−1.69124	+	1.22876i
$123$	6.23607			0.562287
$124$	3.57295	−	2.59590i	0.320860	−	0.233119i
$125$	−3.45492	+	10.6331i	−0.309017	+	0.951057i
$126$	0.263932	+	0.812299i	0.0235129	+	0.0723654i
$127$	−11.2082	+	8.14324i	−0.994567	+	0.722595i	−0.960917	−	0.276838i	$-0.910713\pi$
$127$	−11.2082	+	8.14324i	−0.994567	+	0.722595i	−0.0336507	+	0.999434i	$0.510713\pi$
$128$	−15.6525			−1.38350
$129$	−3.07295	+	9.45756i	−0.270558	+	0.832692i
$130$	9.27051	+	28.5317i	0.813077	+	2.50240i
$131$	1.35410	+	0.983813i	0.118308	+	0.0859561i	0.645366	−	0.763873i	$-0.276705\pi$
$131$	1.35410	+	0.983813i	0.118308	+	0.0859561i	−0.527058	+	0.849830i	$0.676705\pi$
$132$	−9.70820	+	2.17963i	−0.844991	+	0.189712i
$133$	−1.35410	−	0.983813i	−0.117416	−	0.0853074i
$134$	−1.54508	−	1.12257i	−0.133475	−	0.0969753i
$135$	−2.23607			−0.192450
$136$	1.21885	−	3.75123i	0.104515	−	0.321665i
$137$	8.29180			0.708416			0.354208	−	0.935167i	$-0.384750\pi$
$137$	8.29180			0.708416			0.354208	+	0.935167i	$0.384750\pi$
$138$	−7.76393			−0.660910
$139$	3.66312	−	11.2739i	0.310702	−	0.956241i	−0.666786	−	0.745249i	$-0.732331\pi$
$139$	3.66312	−	11.2739i	0.310702	−	0.956241i	0.977488	−	0.210992i	$-0.0676695\pi$
$140$	−0.791796	−	2.43690i	−0.0669190	−	0.205955i
$141$	2.50000	+	1.81636i	0.210538	+	0.152965i
$142$	2.66312	+	1.93487i	0.223484	+	0.162371i
$143$	1.85410	−	19.8132i	0.155048	−	1.65686i
$144$	0.809017	+	0.587785i	0.0674181	+	0.0489821i
$145$	−7.39919	−	5.37582i	−0.614469	−	0.446438i
$146$	0.854102	−	2.62866i	0.0706860	−	0.217549i
$147$	−6.85410			−0.565317
$148$	−19.0623	+	13.8496i	−1.56691	+	1.13843i
$149$	−5.04508	−	15.5272i	−0.413309	−	1.27204i	−0.913754	−	0.406267i	$-0.866830\pi$
$149$	−5.04508	−	15.5272i	−0.413309	−	1.27204i	0.500445	−	0.865768i	$-0.333170\pi$
$150$	11.1803			0.912871
$151$	0.500000	−	0.363271i	0.0406894	−	0.0295626i	−0.567255	−	0.823542i	$-0.691994\pi$
$151$	0.500000	−	0.363271i	0.0406894	−	0.0295626i	0.607944	+	0.793980i	$0.291994\pi$
$152$	9.79837			0.794753
$153$	−1.42705	+	1.03681i	−0.115370	+	0.0838214i
$154$	−0.263932	+	2.82041i	−0.0212682	+	0.227275i
$155$	3.29180			0.264403
$156$	14.5623	−	10.5801i	1.16592	−	0.847089i
$157$	−3.80902	+	2.76741i	−0.303993	+	0.220864i	−0.729315	−	0.684179i	$-0.760161\pi$
$157$	−3.80902	+	2.76741i	−0.303993	+	0.220864i	0.425322	+	0.905042i	$0.360161\pi$
$158$	3.41641	+	10.5146i	0.271795	+	0.836498i
$159$	−1.00000			−0.0793052
$160$	−12.1353	−	8.81678i	−0.959376	−	0.697028i
$161$	−0.409830	+	1.26133i	−0.0322991	+	0.0994065i
$162$	0.690983	+	2.12663i	0.0542888	+	0.167084i
$163$	10.5172	+	7.64121i	0.823772	+	0.598506i	0.917791	−	0.397065i	$-0.129971\pi$
$163$	10.5172	+	7.64121i	0.823772	+	0.598506i	−0.0940182	+	0.995570i	$0.529971\pi$
$164$	5.78115	+	17.7926i	0.451432	+	1.38937i
$165$	−6.80902	−	2.93893i	−0.530081	−	0.228795i
$166$	7.98936	−	24.5887i	0.620094	−	1.90845i
$167$	−7.82624	+	5.68609i	−0.605612	+	0.440003i	−0.847867	−	0.530210i	$-0.822113\pi$
$167$	−7.82624	+	5.68609i	−0.605612	+	0.440003i	0.242254	+	0.970213i	$0.422113\pi$
$168$	−0.690983	+	0.502029i	−0.0533105	+	0.0387323i
$169$	7.10739	+	21.8743i	0.546722	+	1.68264i
$170$	7.13525	−	5.18407i	0.547249	−	0.397600i
$171$	−3.54508	−	2.57565i	−0.271099	−	0.196965i
$172$	−29.8328			−2.27473
$173$	10.7361	+	7.80021i	0.816248	+	0.593039i	0.915635	−	0.402010i	$-0.131688\pi$
$173$	10.7361	+	7.80021i	0.816248	+	0.593039i	−0.0993872	+	0.995049i	$0.531688\pi$
$174$	−2.82624	+	8.69827i	−0.214257	+	0.659414i
$175$	0.590170	−	1.81636i	0.0446127	−	0.137304i
$176$	1.69098	+	2.85317i	0.127463	+	0.215066i
$177$	−0.527864	−	1.62460i	−0.0396767	−	0.122112i
$178$	−11.4443	−	35.2218i	−0.857784	−	2.63999i
$179$	−7.00000	+	21.5438i	−0.523205	+	1.61026i	0.244635	+	0.969615i	$0.421332\pi$
$179$	−7.00000	+	21.5438i	−0.523205	+	1.61026i	−0.767839	+	0.640643i	$0.778668\pi$
$180$	−2.07295	−	6.37988i	−0.154508	−	0.475528i
$181$	−4.20820	+	12.9515i	−0.312793	+	0.962679i	0.663860	+	0.747857i	$0.268917\pi$
$181$	−4.20820	+	12.9515i	−0.312793	+	0.962679i	−0.976653	+	0.214822i	$0.931083\pi$
$182$	−1.58359	−	4.87380i	−0.117384	−	0.361270i
$183$	3.19098	+	9.82084i	0.235884	+	0.725977i
$184$	−2.39919	−	7.38394i	−0.176870	−	0.544351i
$185$	−17.5623			−1.29121
$186$	−1.01722	−	3.13068i	−0.0745863	−	0.229553i
$187$	−5.70820	+	1.28157i	−0.417425	+	0.0937178i
$188$	−2.86475	+	8.81678i	−0.208933	+	0.643030i
$189$	0.381966			0.0277839
$190$	17.7254	+	12.8783i	1.28594	+	0.934288i
$191$	−13.4443	+	9.76784i	−0.972793	+	0.706776i	−0.956086	−	0.293085i	$-0.905318\pi$
$191$	−13.4443	+	9.76784i	−0.972793	+	0.706776i	−0.0167069	+	0.999860i	$0.505318\pi$
$192$	−4.01722	+	12.3637i	−0.289918	+	0.892276i
$193$	−1.73607	−	5.34307i	−0.124965	−	0.384602i	0.868930	−	0.494935i	$-0.164808\pi$
$193$	−1.73607	−	5.34307i	−0.124965	−	0.384602i	−0.993895	+	0.110333i	$0.964808\pi$
$194$	7.92705	+	24.3970i	0.569129	+	1.75160i
$195$	13.4164			0.960769
$196$	−6.35410	−	19.5559i	−0.453864	−	1.39685i
$197$	12.5172	−	9.09429i	0.891815	−	0.647942i	−0.0445356	−	0.999008i	$-0.514181\pi$
$197$	12.5172	−	9.09429i	0.891815	−	0.647942i	0.936351	+	0.351066i	$0.114181\pi$
$198$	−0.690983	+	7.38394i	−0.0491060	+	0.524754i
$199$	10.7984			0.765476			0.382738	−	0.923857i	$-0.374981\pi$
$199$	10.7984			0.765476			0.382738	+	0.923857i	$0.374981\pi$
$200$	3.45492	+	10.6331i	0.244299	+	0.751876i
$201$	−0.690983	+	0.502029i	−0.0487382	+	0.0354104i
$202$	−11.5451	+	35.5321i	−0.812309	+	2.50003i
$203$	1.26393	+	0.918300i	0.0887106	+	0.0644521i
$204$	−4.28115	−	3.11044i	−0.299741	−	0.217774i
$205$	−4.30902	+	13.2618i	−0.300955	+	0.926244i
$206$	10.5279			0.733511
$207$	−1.07295	+	3.30220i	−0.0745751	+	0.229519i
$208$	−4.85410	−	3.52671i	−0.336571	−	0.244533i
$209$	−7.40983	−	12.5025i	−0.512549	−	0.864815i
$210$	−1.90983			−0.131791
$211$	1.70820			0.117598			0.0587988	−	0.998270i	$-0.481273\pi$
$211$	1.70820			0.117598			0.0587988	+	0.998270i	$0.481273\pi$
$212$	−0.927051	−	2.85317i	−0.0636701	−	0.195956i
$213$	1.19098	−	0.865300i	0.0816048	−	0.0592894i
$214$	26.0795	−	18.9479i	1.78276	−	1.29525i
$215$	−17.9894	−	13.0700i	−1.22686	−	0.891369i
$216$	−1.80902	+	1.31433i	−0.123088	+	0.0894287i
$217$	−0.562306			−0.0381718
$218$	12.2361	−	37.6587i	0.828731	−	2.55057i
$219$	−1.00000	−	0.726543i	−0.0675737	−	0.0490952i
$220$	2.07295	−	22.1518i	0.139758	−	1.49348i
$221$	8.56231	−	6.22088i	0.575963	−	0.418462i
$222$	5.42705	+	16.7027i	0.364240	+	1.12101i
$223$	−1.11803	−	0.812299i	−0.0748691	−	0.0543956i	0.549721	−	0.835348i	$-0.314734\pi$
$223$	−1.11803	−	0.812299i	−0.0748691	−	0.0543956i	−0.624590	+	0.780953i	$0.714734\pi$
$224$	2.07295	+	1.50609i	0.138505	+	0.100630i
$225$	1.54508	−	4.75528i	0.103006	−	0.317019i
$226$	1.01722	+	3.13068i	0.0676645	+	0.208250i
$227$	7.01722	−	21.5968i	0.465749	−	1.43343i	−0.392288	−	0.919842i	$-0.628316\pi$
$227$	7.01722	−	21.5968i	0.465749	−	1.43343i	0.858038	−	0.513587i	$-0.171684\pi$
$228$	4.06231	−	12.5025i	0.269033	−	0.827998i
$229$	5.25329	+	16.1680i	0.347147	+	1.06841i	0.960424	+	0.278541i	$0.0898509\pi$
$229$	5.25329	+	16.1680i	0.347147	+	1.06841i	−0.613277	+	0.789868i	$0.710149\pi$
$230$	5.36475	−	16.5110i	0.353741	−	1.08870i
$231$	1.16312	+	0.502029i	0.0765276	+	0.0330311i
$232$	−9.14590			−0.600458
$233$	16.4721	−	11.9677i	1.07913	−	0.784031i	0.101595	−	0.994826i	$-0.467605\pi$
$233$	16.4721	−	11.9677i	1.07913	−	0.784031i	0.977530	+	0.210795i	$0.0676053\pi$
$234$	−4.14590	−	12.7598i	−0.271026	−	0.834132i
$235$	−5.59017	+	4.06150i	−0.364662	+	0.264943i
$236$	4.14590	−	3.01217i	0.269875	−	0.196076i
$237$	4.94427			0.321165
$238$	−1.21885	+	0.885544i	−0.0790061	+	0.0574013i
$239$	1.54508	+	1.12257i	0.0999432	+	0.0726130i	0.636635	−	0.771166i	$-0.280326\pi$
$239$	1.54508	+	1.12257i	0.0999432	+	0.0726130i	−0.536691	+	0.843779i	$0.680326\pi$
$240$	−1.80902	+	1.31433i	−0.116772	+	0.0848395i
$241$	3.44427	−	10.6004i	0.221865	−	0.682830i	−0.776730	−	0.629834i	$-0.783123\pi$
$241$	3.44427	−	10.6004i	0.221865	−	0.682830i	0.998595	−	0.0529963i	$-0.0168771\pi$
$242$	−11.8090	+	21.5765i	−0.759112	+	1.38699i
$243$	1.00000			0.0641500
$244$	−25.0623	+	18.2088i	−1.60445	+	1.16570i
$245$	4.73607	−	14.5761i	0.302576	−	0.931234i
$246$	13.9443			0.889054
$247$	21.2705	+	15.4539i	1.35341	+	0.983310i
$248$	2.66312	−	1.93487i	0.169108	−	0.122864i
$249$	−9.35410	−	6.79615i	−0.592792	−	0.430689i
$250$	−7.72542	+	23.7764i	−0.488599	+	1.50375i
$251$	8.97214	−	27.6134i	0.566316	−	1.74294i	−0.0976919	−	0.995217i	$-0.531146\pi$
$251$	8.97214	−	27.6134i	0.566316	−	1.74294i	0.664008	−	0.747725i	$-0.268854\pi$
$252$	0.354102	+	1.08981i	0.0223063	+	0.0686518i
$253$	−7.60739	+	8.64527i	−0.478273	+	0.543523i
$254$	−25.0623	+	18.2088i	−1.57255	+	1.14252i
$255$	−1.21885	−	3.75123i	−0.0763272	−	0.234911i
$256$	−9.00000			−0.562500
$257$	−9.51722	−	6.91467i	−0.593668	−	0.431325i	0.249958	−	0.968257i	$-0.419583\pi$
$257$	−9.51722	−	6.91467i	−0.593668	−	0.431325i	−0.843626	+	0.536932i	$0.819583\pi$
$258$	−6.87132	+	21.1478i	−0.427790	+	1.31660i
$259$	3.00000			0.186411
$260$	12.4377	+	38.2793i	0.771353	+	2.37398i
$261$	3.30902	+	2.40414i	0.204823	+	0.148813i
$262$	3.02786	+	2.19987i	0.187062	+	0.135909i
$263$	5.29180	−	16.2865i	0.326306	−	1.00427i	−0.644541	−	0.764569i	$-0.722952\pi$
$263$	5.29180	−	16.2865i	0.326306	−	1.00427i	0.970848	−	0.239698i	$-0.0770483\pi$
$264$	−7.23607	+	1.62460i	−0.445349	+	0.0999871i
$265$	0.690983	−	2.12663i	0.0424467	−	0.130638i
$266$	−3.02786	−	2.19987i	−0.185650	−	0.134883i
$267$	−16.5623			−1.01360
$268$	−2.07295	−	1.50609i	−0.126626	−	0.0919988i
$269$	4.21885	−	12.9843i	0.257228	−	0.791665i	−0.736155	−	0.676813i	$-0.763361\pi$
$269$	4.21885	−	12.9843i	0.257228	−	0.791665i	0.993383	−	0.114852i	$-0.0366395\pi$
$270$	−5.00000			−0.304290
$271$	−20.7984			−1.26341			−0.631706	−	0.775208i	$-0.717645\pi$
$271$	−20.7984			−1.26341			−0.631706	+	0.775208i	$0.717645\pi$
$272$	−0.545085	+	1.67760i	−0.0330506	+	0.101719i
$273$	−2.29180			−0.138706
$274$	18.5410			1.12010
$275$	10.9549	−	12.4495i	0.660606	−	0.750733i
$276$	−10.4164			−0.626994
$277$	18.3820			1.10447			0.552233	−	0.833690i	$-0.313776\pi$
$277$	18.3820			1.10447			0.552233	+	0.833690i	$0.313776\pi$
$278$	8.19098	−	25.2093i	0.491263	−	1.51195i
$279$	−1.47214			−0.0881345
$280$	−0.590170	−	1.81636i	−0.0352694	−	0.108548i
$281$	3.01722	−	9.28605i	0.179992	−	0.553959i	−0.819834	−	0.572601i	$-0.805934\pi$
$281$	3.01722	−	9.28605i	0.179992	−	0.553959i	0.999826	+	0.0186420i	$0.00593428\pi$
$282$	5.59017	+	4.06150i	0.332890	+	0.241859i
$283$	16.8885			1.00392			0.501960	−	0.864891i	$-0.332613\pi$
$283$	16.8885			1.00392			0.501960	+	0.864891i	$0.332613\pi$
$284$	3.57295	+	2.59590i	0.212016	+	0.154038i
$285$	7.92705	−	5.75934i	0.469558	−	0.341154i
$286$	4.14590	−	44.3036i	0.245152	−	2.61973i
$287$	0.736068	−	2.26538i	0.0434487	−	0.133721i
$288$	5.42705	+	3.94298i	0.319792	+	0.232343i
$289$	11.2361	+	8.16348i	0.660945	+	0.480205i
$290$	−16.5451	−	12.0207i	−0.971561	−	0.705880i
$291$	11.4721			0.672509
$292$	1.14590	−	3.52671i	0.0670586	−	0.206385i
$293$	20.0344	+	14.5559i	1.17042	+	0.850363i	0.991060	−	0.133419i	$-0.0425957\pi$
$293$	20.0344	+	14.5559i	1.17042	+	0.850363i	0.179365	+	0.983783i	$0.442596\pi$
$294$	−15.3262			−0.893844
$295$	3.81966			0.222389
$296$	−14.2082	+	10.3229i	−0.825835	+	0.600004i
$297$	3.04508	+	1.31433i	0.176694	+	0.0762650i
$298$	−11.2812	−	34.7198i	−0.653500	−	2.01127i
$299$	6.43769	−	19.8132i	0.372301	−	1.14583i
$300$	15.0000			0.866025
$301$	3.07295	+	2.23263i	0.177122	+	0.128687i
$302$	1.11803	−	0.812299i	0.0643356	−	0.0467426i
$303$	13.5172	+	9.82084i	0.776544	+	0.564192i
$304$	−4.38197			−0.251323
$305$	−23.0902			−1.32214
$306$	−3.19098	+	2.31838i	−0.182416	+	0.132533i
$307$	28.4164			1.62181			0.810905	−	0.585178i	$-0.198975\pi$
$307$	28.4164			1.62181			0.810905	+	0.585178i	$0.198975\pi$
$308$	−0.354102	+	3.78398i	−0.0201768	+	0.215612i
$309$	1.45492	−	4.47777i	0.0827672	−	0.254731i
$310$	7.36068			0.418059
$311$	−2.95492	−	2.14687i	−0.167558	−	0.121738i	0.500846	−	0.865536i	$-0.333022\pi$
$311$	−2.95492	−	2.14687i	−0.167558	−	0.121738i	−0.668404	+	0.743798i	$0.733022\pi$
$312$	10.8541	−	7.88597i	0.614493	−	0.446455i
$313$	0.416408			0.0235368			0.0117684	−	0.999931i	$-0.496254\pi$
$313$	0.416408			0.0235368			0.0117684	+	0.999931i	$0.496254\pi$
$314$	−8.51722	+	6.18812i	−0.480655	+	0.349216i
$315$	−0.263932	+	0.812299i	−0.0148709	+	0.0457679i
$316$	4.58359	+	14.1068i	0.257847	+	0.793572i
$317$	8.09017	−	5.87785i	0.454389	−	0.330133i	−0.336937	−	0.941527i	$-0.609391\pi$
$317$	8.09017	−	5.87785i	0.454389	−	0.330133i	0.791326	+	0.611394i	$0.209391\pi$
$318$	−2.23607			−0.125392
$319$	6.91641	+	11.6699i	0.387244	+	0.653392i
$320$	−23.5172	−	17.0863i	−1.31465	−	0.955151i
$321$	−4.45492	−	13.7108i	−0.248649	−	0.765263i
$322$	−0.916408	+	2.82041i	−0.0510694	+	0.157175i
$323$	2.38854	−	7.35118i	0.132902	−	0.409031i
$324$	0.927051	+	2.85317i	0.0515028	+	0.158509i
$325$	−9.27051	+	28.5317i	−0.514235	+	1.58265i
$326$	23.5172	+	17.0863i	1.30250	+	0.946320i
$327$	−14.3262	−	10.4086i	−0.792243	−	0.575598i
$328$	4.30902	+	13.2618i	0.237926	+	0.732260i
$329$	0.954915	−	0.693786i	0.0526462	−	0.0382497i
$330$	−15.2254	−	6.57164i	−0.838132	−	0.361757i
$331$	−20.1803	−	14.6619i	−1.10921	−	0.805890i	−0.126672	−	0.991945i	$-0.540430\pi$
$331$	−20.1803	−	14.6619i	−1.10921	−	0.805890i	−0.982539	+	0.186055i	$0.940430\pi$
$332$	10.7188	−	32.9892i	0.588273	−	1.81052i
$333$	7.85410			0.430402
$334$	−17.5000	+	12.7145i	−0.957557	+	0.695706i
$335$	−0.590170	−	1.81636i	−0.0322444	−	0.0992381i
$336$	0.309017	−	0.224514i	0.0168583	−	0.0122482i
$337$	22.7533	−	16.5312i	1.23945	−	0.900514i	0.241889	−	0.970304i	$-0.422233\pi$
$337$	22.7533	−	16.5312i	1.23945	−	0.900514i	0.997562	+	0.0697904i	$0.0222330\pi$
$338$	15.8926	+	48.9124i	0.864444	+	2.66048i
$339$	1.47214			0.0799554
$340$	9.57295	−	6.95515i	0.519166	−	0.377196i
$341$	−4.48278	−	1.93487i	−0.242756	−	0.104779i
$342$	−7.92705	−	5.75934i	−0.428646	−	0.311429i
$343$	−1.63525	+	5.03280i	−0.0882955	+	0.271746i
$344$	−22.2361			−1.19889
$345$	−6.28115	−	4.56352i	−0.338166	−	0.245692i
$346$	24.0066	+	17.4418i	1.29060	+	0.937677i
$347$	−0.0450850	−	0.0327561i	−0.00242029	−	0.00175844i	0.586574	−	0.809895i	$-0.300476\pi$
$347$	−0.0450850	−	0.0327561i	−0.00242029	−	0.00175844i	−0.588995	+	0.808137i	$0.700476\pi$
$348$	−3.79180	+	11.6699i	−0.203262	+	0.625575i
$349$	−12.3992	+	9.00854i	−0.663713	+	0.482216i	−0.867915	−	0.496713i	$-0.834540\pi$
$349$	−12.3992	+	9.00854i	−0.663713	+	0.482216i	0.204202	+	0.978929i	$0.434540\pi$
$350$	1.31966	−	4.06150i	0.0705388	−	0.217096i
$351$	−6.00000			−0.320256
$352$	11.3435	+	19.1396i	0.604608	+	1.02015i
$353$	4.50000	−	3.26944i	0.239511	−	0.174015i	−0.461554	−	0.887112i	$-0.652708\pi$
$353$	4.50000	−	3.26944i	0.239511	−	0.174015i	0.701065	+	0.713097i	$0.252708\pi$
$354$	−1.18034	−	3.63271i	−0.0627344	−	0.193076i
$355$	1.01722	+	3.13068i	0.0539885	+	0.166159i
$356$	−15.3541	−	47.2551i	−0.813766	−	2.50451i
$357$	0.208204	+	0.640786i	0.0110193	+	0.0339140i
$358$	−15.6525	+	48.1734i	−0.827259	+	2.54604i
$359$	30.2705	−	21.9928i	1.59762	−	1.16074i	0.705726	−	0.708485i	$-0.250621\pi$
$359$	30.2705	−	21.9928i	1.59762	−	1.16074i	0.891891	−	0.452251i	$-0.149379\pi$
$360$	−1.54508	−	4.75528i	−0.0814331	−	0.250625i
$361$	0.201626			0.0106119
$362$	−9.40983	+	28.9605i	−0.494570	+	1.52213i
$363$	7.54508	+	8.00448i	0.396014	+	0.420126i
$364$	−2.12461	−	6.53888i	−0.111360	−	0.342731i
$365$	2.23607	−	1.62460i	0.117041	−	0.0850354i
$366$	7.13525	+	21.9601i	0.372966	+	1.14787i
$367$	9.80902	+	30.1891i	0.512027	+	1.57586i	0.788628	+	0.614871i	$0.210792\pi$
$367$	9.80902	+	30.1891i	0.512027	+	1.57586i	−0.276601	+	0.960985i	$0.589208\pi$
$368$	1.07295	+	3.30220i	0.0559313	+	0.172139i
$369$	1.92705	−	5.93085i	0.100318	−	0.308748i
$370$	−39.2705			−2.04158
$371$	−0.118034	+	0.363271i	−0.00612802	+	0.0188601i
$372$	−1.36475	−	4.20025i	−0.0707587	−	0.217773i
$373$	−10.2082	−	31.4176i	−0.528561	−	1.62674i	−0.757165	−	0.653223i	$-0.773416\pi$
$373$	−10.2082	−	31.4176i	−0.528561	−	1.62674i	0.228604	−	0.973519i	$-0.426584\pi$
$374$	−12.7639	+	2.86568i	−0.660007	+	0.148181i
$375$	9.04508	+	6.57164i	0.467086	+	0.339358i
$376$	−2.13525	+	6.57164i	−0.110117	+	0.338906i
$377$	−19.8541	−	14.4248i	−1.02254	−	0.742918i
$378$	0.854102			0.0439303
$379$	−16.2984	−	11.8415i	−0.837191	−	0.608255i	0.0843934	−	0.996433i	$-0.473105\pi$
$379$	−16.2984	−	11.8415i	−0.837191	−	0.608255i	−0.921585	+	0.388177i	$0.873105\pi$
$380$	23.7812	+	17.2780i	1.21995	+	0.886344i
$381$	4.28115	+	13.1760i	0.219330	+	0.675029i
$382$	−30.0623	+	21.8415i	−1.53812	+	1.11751i
$383$	−30.7984	+	22.3763i	−1.57372	+	1.14338i	−0.650246	+	0.759724i	$0.725334\pi$
$383$	−30.7984	+	22.3763i	−1.57372	+	1.14338i	−0.923477	+	0.383653i	$0.874666\pi$
$384$	−4.83688	+	14.8864i	−0.246831	+	0.759668i
$385$	−1.87132	+	2.12663i	−0.0953714	+	0.108383i
$386$	−3.88197	−	11.9475i	−0.197587	−	0.608110i
$387$	8.04508	+	5.84510i	0.408955	+	0.297123i
$388$	10.6353	+	32.7319i	0.539923	+	1.66171i
$389$	−6.11803	+	18.8294i	−0.310197	+	0.954687i	0.667490	+	0.744619i	$0.267369\pi$
$389$	−6.11803	+	18.8294i	−0.310197	+	0.954687i	−0.977687	+	0.210068i	$0.932631\pi$
$390$	30.0000			1.51911
$391$	−6.12461			−0.309735
$392$	−4.73607	−	14.5761i	−0.239208	−	0.736205i
$393$	1.35410	−	0.983813i	0.0683054	−	0.0496268i
$394$	27.9894	−	20.3355i	1.41008	−	1.02449i
$395$	−3.41641	+	10.5146i	−0.171898	+	0.529048i
$396$	−0.927051	+	9.90659i	−0.0465861	+	0.497825i
$397$	−19.1074	+	13.8823i	−0.958972	+	0.696734i	−0.952912	−	0.303247i	$-0.901929\pi$
$397$	−19.1074	+	13.8823i	−0.958972	+	0.696734i	−0.00606059	+	0.999982i	$0.501929\pi$
$398$	24.1459			1.21032
$399$	−1.35410	+	0.983813i	−0.0677899	+	0.0492522i
$400$	−1.54508	−	4.75528i	−0.0772542	−	0.237764i
$401$	3.21885	+	9.90659i	0.160742	+	0.494712i	0.998697	−	0.0510266i	$-0.0162493\pi$
$401$	3.21885	+	9.90659i	0.160742	+	0.494712i	−0.837956	+	0.545738i	$0.816249\pi$
$402$	−1.54508	+	1.12257i	−0.0770618	+	0.0559887i
$403$	8.83282			0.439994
$404$	−15.4894	+	47.6713i	−0.770624	+	2.37174i
$405$	−0.690983	+	2.12663i	−0.0343352	+	0.105673i
$406$	2.82624	+	2.05338i	0.140264	+	0.101908i
$407$	23.9164	+	10.3229i	1.18549	+	0.511685i
$408$	−3.19098	−	2.31838i	−0.157977	−	0.114777i
$409$	−12.8992	−	9.37181i	−0.637824	−	0.463406i	0.221278	−	0.975211i	$-0.428977\pi$
$409$	−12.8992	−	9.37181i	−0.637824	−	0.463406i	−0.859102	+	0.511805i	$0.828977\pi$
$410$	−9.63525	+	29.6543i	−0.475851	+	1.46452i
$411$	2.56231	−	7.88597i	0.126389	−	0.388986i
$412$	14.1246			0.695870
$413$	−0.652476			−0.0321062
$414$	−2.39919	+	7.38394i	−0.117914	+	0.362901i
$415$	20.9164	−	15.1967i	1.02675	−	0.745975i
$416$	−32.5623	−	23.6579i	−1.59650	−	1.15992i
$417$	−9.59017	−	6.96767i	−0.469633	−	0.341208i
$418$	−16.5689	−	27.9564i	−0.810411	−	1.36739i
$419$	−24.9443	−	18.1231i	−1.21861	−	0.885370i	−0.222624	−	0.974904i	$-0.571462\pi$
$419$	−24.9443	−	18.1231i	−1.21861	−	0.885370i	−0.995984	+	0.0895343i	$0.971462\pi$
$420$	−2.56231			−0.125028
$421$	−6.48278	+	19.9519i	−0.315951	+	0.972398i	0.659410	+	0.751784i	$0.270806\pi$
$421$	−6.48278	+	19.9519i	−0.315951	+	0.972398i	−0.975361	+	0.220614i	$0.929194\pi$
$422$	3.81966			0.185938
$423$	2.50000	−	1.81636i	0.121554	−	0.0883143i
$424$	−0.690983	−	2.12663i	−0.0335571	−	0.103278i
$425$	8.81966			0.427816
$426$	2.66312	−	1.93487i	0.129029	−	0.0937447i
$427$	3.94427			0.190877
$428$	34.9894	−	25.4213i	1.69127	−	1.22878i
$429$	−18.2705	−	7.88597i	−0.882109	−	0.380738i
$430$	−40.2254	−	29.2255i	−1.93984	−	1.40938i
$431$	−4.04508	+	2.93893i	−0.194845	+	0.141563i	−0.680930	−	0.732348i	$-0.738424\pi$
$431$	−4.04508	+	2.93893i	−0.194845	+	0.141563i	0.486085	+	0.873911i	$0.338424\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	2.18034	+	6.71040i	0.104780	+	0.322481i	0.989679	−	0.143303i	$-0.0457723\pi$
$433$	2.18034	+	6.71040i	0.104780	+	0.322481i	−0.884898	+	0.465784i	$0.845772\pi$
$434$	−1.25735			−0.0603549
$435$	−7.39919	+	5.37582i	−0.354764	+	0.257751i
$436$	16.4164	−	50.5245i	0.786203	−	2.41969i
$437$	−4.70163	−	14.4701i	−0.224909	−	0.692200i
$438$	−2.23607	−	1.62460i	−0.106843	−	0.0776263i
$439$	6.11803	+	18.8294i	0.291998	+	0.898677i	0.984213	+	0.176986i	$0.0566348\pi$
$439$	6.11803	+	18.8294i	0.291998	+	0.898677i	−0.692216	+	0.721691i	$0.743365\pi$
$440$	1.54508	−	16.5110i	0.0736590	−	0.787130i
$441$	−2.11803	+	6.51864i	−0.100859	+	0.310411i
$442$	19.1459	−	13.9103i	0.910678	−	0.661646i
$443$	9.37132	−	6.80866i	0.445245	−	0.323489i	−0.342471	−	0.939529i	$-0.611264\pi$
$443$	9.37132	−	6.80866i	0.445245	−	0.323489i	0.787716	+	0.616039i	$0.211264\pi$
$444$	7.28115	+	22.4091i	0.345548	+	1.06349i
$445$	11.4443	−	35.2218i	0.542511	−	1.66968i
$446$	−2.50000	−	1.81636i	−0.118378	−	0.0860070i
$447$	−16.3262			−0.772205
$448$	4.01722	+	2.91868i	0.189796	+	0.137895i
$449$	0.281153	−	0.865300i	0.0132684	−	0.0408360i	−0.944203	−	0.329364i	$-0.893166\pi$
$449$	0.281153	−	0.865300i	0.0132684	−	0.0408360i	0.957472	+	0.288528i	$0.0931658\pi$
$450$	3.45492	−	10.6331i	0.162866	−	0.501251i
$451$	13.6631	−	15.5272i	0.643371	−	0.731146i
$452$	1.36475	+	4.20025i	0.0641922	+	0.197563i
$453$	−0.190983	−	0.587785i	−0.00897316	−	0.0276166i
$454$	15.6910	−	48.2919i	0.736414	−	2.26645i
$455$	1.58359	−	4.87380i	0.0742399	−	0.228487i
$456$	3.02786	−	9.31881i	0.141793	−	0.436393i
$457$	9.94427	+	30.6053i	0.465173	+	1.43166i	0.858764	+	0.512371i	$0.171233\pi$
$457$	9.94427	+	30.6053i	0.465173	+	1.43166i	−0.393591	+	0.919286i	$0.628767\pi$
$458$	11.7467	+	36.1527i	0.548888	+	1.68930i
$459$	0.545085	+	1.67760i	0.0254424	+	0.0783036i
$460$	7.19756	−	22.1518i	0.335588	−	1.03283i
$461$	−4.62868	−	14.2456i	−0.215579	−	0.663484i	−0.999112	−	0.0421337i	$-0.986584\pi$
$461$	−4.62868	−	14.2456i	−0.215579	−	0.663484i	0.783533	−	0.621350i	$-0.213416\pi$
$462$	2.60081	+	1.12257i	0.121001	+	0.0522267i
$463$	1.89261	−	5.82485i	0.0879570	−	0.270704i	−0.897397	−	0.441223i	$-0.854545\pi$
$463$	1.89261	−	5.82485i	0.0879570	−	0.270704i	0.985354	+	0.170520i	$0.0545446\pi$
$464$	4.09017			0.189881
$465$	1.01722	−	3.13068i	0.0471725	−	0.145182i
$466$	36.8328	−	26.7606i	1.70625	−	1.23966i
$467$	1.40983	−	4.33901i	0.0652392	−	0.200785i	−0.913123	−	0.407683i	$-0.866337\pi$
$467$	1.40983	−	4.33901i	0.0652392	−	0.200785i	0.978363	+	0.206898i	$0.0663368\pi$
$468$	−5.56231	−	17.1190i	−0.257118	−	0.791327i
$469$	0.100813	+	0.310271i	0.00465511	+	0.0143270i
$470$	−12.5000	+	9.08178i	−0.576582	+	0.418911i
$471$	1.45492	+	4.47777i	0.0670389	+	0.206325i
$472$	3.09017	−	2.24514i	0.142237	−	0.103341i
$473$	16.8156	+	28.3727i	0.773182	+	1.30458i
$474$	11.0557			0.507806
$475$	6.77051	+	20.8375i	0.310652	+	0.956089i
$476$	−1.63525	+	1.18808i	−0.0749518	+	0.0544557i
$477$	−0.309017	+	0.951057i	−0.0141489	+	0.0435459i
$478$	3.45492	+	2.51014i	0.158024	+	0.114811i
$479$	21.1353	+	15.3557i	0.965694	+	0.701618i	0.954466	−	0.298319i	$-0.0964259\pi$
$479$	21.1353	+	15.3557i	0.965694	+	0.701618i	0.0112282	+	0.999937i	$0.496426\pi$
$480$	−12.1353	+	8.81678i	−0.553896	+	0.402429i
$481$	−47.1246			−2.14870
$482$	7.70163	−	23.7032i	0.350799	−	1.07965i
$483$	1.07295	+	0.779543i	0.0488209	+	0.0354704i
$484$	−15.8435	+	28.9480i	−0.720157	+	1.31582i
$485$	−7.92705	+	24.3970i	−0.359949	+	1.10781i
$486$	2.23607			0.101430
$487$	1.20820	+	3.71847i	0.0547489	+	0.168500i	0.974692	−	0.223552i	$-0.0717653\pi$
$487$	1.20820	+	3.71847i	0.0547489	+	0.168500i	−0.919943	+	0.392052i	$0.871765\pi$
$488$	−18.6803	+	13.5721i	−0.845619	+	0.614378i
$489$	10.5172	−	7.64121i	0.475605	−	0.345547i
$490$	10.5902	−	32.5932i	0.478415	−	1.47241i
$491$	−33.6074	+	24.4172i	−1.51668	+	1.10193i	−0.553578	+	0.832797i	$0.686738\pi$
$491$	−33.6074	+	24.4172i	−1.51668	+	1.10193i	−0.963102	+	0.269135i	$0.913262\pi$
$492$	18.7082			0.843431
$493$	−2.22949	+	6.86167i	−0.100411	+	0.309034i
$494$	47.5623	+	34.5560i	2.13993	+	1.55475i
$495$	−4.89919	+	5.56758i	−0.220202	+	0.250244i
$496$	−1.19098	+	0.865300i	−0.0534767	+	0.0388531i
$497$	−0.173762	−	0.534785i	−0.00779429	−	0.0239884i
$498$	−20.9164	−	15.1967i	−0.937287	−	0.680979i
$499$	−10.6631	−	7.74721i	−0.477347	−	0.346813i	0.322951	−	0.946416i	$-0.395325\pi$
$499$	−10.6631	−	7.74721i	−0.477347	−	0.346813i	−0.800298	+	0.599603i	$0.795325\pi$
$500$	−10.3647	+	31.8994i	−0.463525	+	1.42658i
$501$	2.98936	+	9.20029i	0.133555	+	0.411039i
$502$	20.0623	−	61.7454i	0.895425	−	2.75583i
$503$	1.85410	−	5.70634i	0.0826703	−	0.254433i	−0.901174	−	0.433456i	$-0.857294\pi$
$503$	1.85410	−	5.70634i	0.0826703	−	0.254433i	0.983845	+	0.179023i	$0.0572938\pi$
$504$	0.263932	+	0.812299i	0.0117565	+	0.0361827i
$505$	−30.2254	+	21.9601i	−1.34501	+	0.977210i
$506$	−17.0106	+	19.3314i	−0.756215	+	0.859386i
$507$	23.0000			1.02147
$508$	−33.6246	+	24.4297i	−1.49185	+	1.08389i
$509$	−5.38197	−	16.5640i	−0.238551	−	0.734186i	−0.996630	−	0.0820231i	$-0.973862\pi$
$509$	−5.38197	−	16.5640i	−0.238551	−	0.734186i	0.758079	−	0.652163i	$-0.226138\pi$
$510$	−2.72542	−	8.38800i	−0.120684	−	0.371427i
$511$	−0.381966	+	0.277515i	−0.0168972	+	0.0122765i
$512$	11.1803			0.494106
$513$	−3.54508	+	2.57565i	−0.156519	+	0.113718i
$514$	−21.2812	−	15.4617i	−0.938671	−	0.681985i
$515$	8.51722	+	6.18812i	0.375314	+	0.272681i
$516$	−9.21885	+	28.3727i	−0.405837	+	1.24904i
$517$	10.0000	−	2.24514i	0.439799	−	0.0987411i
$518$	6.70820			0.294742
$519$	10.7361	−	7.80021i	0.471261	−	0.342391i
$520$	9.27051	+	28.5317i	0.406539	+	1.25120i
$521$	2.47214			0.108306			0.0541531	−	0.998533i	$-0.482754\pi$
$521$	2.47214			0.108306			0.0541531	+	0.998533i	$0.482754\pi$
$522$	7.39919	+	5.37582i	0.323854	+	0.235293i
$523$	−5.82624	+	4.23301i	−0.254764	+	0.185097i	−0.707835	−	0.706377i	$-0.750328\pi$
$523$	−5.82624	+	4.23301i	−0.254764	+	0.185097i	0.453072	+	0.891474i	$0.350328\pi$
$524$	4.06231	+	2.95144i	0.177463	+	0.128934i
$525$	−1.54508	−	1.12257i	−0.0674330	−	0.0489930i
$526$	11.8328	−	36.4177i	0.515935	−	1.58789i
$527$	−0.802439	−	2.46965i	−0.0349548	−	0.107580i
$528$	3.23607	−	0.726543i	0.140832	−	0.0316187i
$529$	8.85410	−	6.43288i	0.384961	−	0.279691i
$530$	1.54508	−	4.75528i	0.0671142	−	0.206556i
$531$	−1.70820			−0.0741297
$532$	−4.06231	−	2.95144i	−0.176123	−	0.127961i
$533$	−11.5623	+	35.5851i	−0.500819	+	1.54136i
$534$	−37.0344			−1.60264
$535$	32.2361			1.39369
$536$	−1.54508	−	1.12257i	−0.0667375	−	0.0484876i
$537$	18.3262	+	13.3148i	0.790836	+	0.574576i
$538$	9.43363	−	29.0337i	0.406713	−	1.25173i
$539$	−15.0172	+	17.0660i	−0.646837	+	0.735085i
$540$	−6.70820			−0.288675
$541$	1.61803	+	1.17557i	0.0695647	+	0.0505417i	0.622024	−	0.782998i	$-0.286311\pi$
$541$	1.61803	+	1.17557i	0.0695647	+	0.0505417i	−0.552459	+	0.833540i	$0.686311\pi$
$542$	−46.5066			−1.99763
$543$	11.0172	+	8.00448i	0.472794	+	0.343505i
$544$	−3.65654	+	11.2537i	−0.156773	+	0.482497i
$545$	32.0344	−	23.2744i	1.37220	−	0.996965i
$546$	−5.12461			−0.219313
$547$	13.6697	−	42.0710i	0.584474	−	1.79883i	−0.0168983	−	0.999857i	$-0.505379\pi$
$547$	13.6697	−	42.0710i	0.584474	−	1.79883i	0.601372	−	0.798969i	$-0.294621\pi$
$548$	24.8754			1.06262
$549$	10.3262			0.440713
$550$	24.4959	−	27.8379i	1.04451	−	1.18701i
$551$	−17.9230			−0.763545
$552$	−7.76393			−0.330455
$553$	0.583592	−	1.79611i	0.0248169	−	0.0763784i
$554$	41.1033			1.74631
$555$	−5.42705	+	16.7027i	−0.230365	+	0.708992i
$556$	10.9894	−	33.8218i	0.466053	−	1.43436i
$557$	−14.7254	−	10.6986i	−0.623936	−	0.453316i	0.230358	−	0.973106i	$-0.426010\pi$
$557$	−14.7254	−	10.6986i	−0.623936	−	0.453316i	−0.854294	+	0.519790i	$0.826010\pi$
$558$	−3.29180			−0.139353
$559$	−48.2705	−	35.0706i	−2.04163	−	1.48333i
$560$	0.263932	+	0.812299i	0.0111532	+	0.0343259i
$561$	−0.545085	+	5.82485i	−0.0230135	+	0.245925i
$562$	6.74671	−	20.7642i	0.284593	−	0.875887i
$563$	34.4336	+	25.0175i	1.45120	+	1.05436i	0.985548	+	0.169396i	$0.0541817\pi$
$563$	34.4336	+	25.0175i	1.45120	+	1.05436i	0.465656	+	0.884966i	$0.345818\pi$
$564$	7.50000	+	5.44907i	0.315807	+	0.229447i
$565$	−1.01722	+	3.13068i	−0.0427948	+	0.131709i
$566$	37.7639			1.58734
$567$	0.118034	−	0.363271i	0.00495696	−	0.0152560i
$568$	2.66312	+	1.93487i	0.111742	+	0.0811853i
$569$	−33.7426			−1.41457			−0.707283	−	0.706931i	$-0.750079\pi$
$569$	−33.7426			−1.41457			−0.707283	+	0.706931i	$0.750079\pi$
$570$	17.7254	−	12.8783i	0.742436	−	0.539412i
$571$	−10.6353	+	7.72696i	−0.445072	+	0.323363i	−0.787647	−	0.616127i	$-0.788701\pi$
$571$	−10.6353	+	7.72696i	−0.445072	+	0.323363i	0.342575	+	0.939490i	$0.388701\pi$
$572$	5.56231	−	59.4396i	0.232572	−	2.48529i
$573$	5.13525	+	15.8047i	0.214528	+	0.660250i
$574$	1.64590	−	5.06555i	0.0686985	−	0.211432i
$575$	14.0451	−	10.2044i	0.585721	−	0.425551i
$576$	10.5172	+	7.64121i	0.438218	+	0.318384i
$577$	10.7082	−	7.77997i	0.445788	−	0.323884i	−0.342142	−	0.939648i	$-0.611153\pi$
$577$	10.7082	−	7.77997i	0.445788	−	0.323884i	0.787931	+	0.615764i	$0.211153\pi$
$578$	25.1246	+	18.2541i	1.04505	+	0.759270i
$579$	−5.61803			−0.233478
$580$	−22.1976	−	16.1275i	−0.921704	−	0.669657i
$581$	−3.57295	+	2.59590i	−0.148231	+	0.107696i
$582$	25.6525			1.06333
$583$	−2.19098	+	2.48990i	−0.0907412	+	0.103121i
$584$	0.854102	−	2.62866i	0.0353430	−	0.108775i
$585$	4.14590	−	12.7598i	0.171412	−	0.527551i
$586$	44.7984	+	32.5479i	1.85060	+	1.34454i
$587$	1.30902	−	0.951057i	0.0540289	−	0.0392543i	−0.560443	−	0.828193i	$-0.689369\pi$
$587$	1.30902	−	0.951057i	0.0540289	−	0.0392543i	0.614472	+	0.788939i	$0.289369\pi$
$588$	−20.5623			−0.847975
$589$	5.21885	−	3.79171i	0.215039	−	0.156235i
$590$	8.54102			0.351628
$591$	−4.78115	−	14.7149i	−0.196670	−	0.605289i
$592$	6.35410	−	4.61653i	0.261152	−	0.189738i
$593$	−7.29180			−0.299438			−0.149719	−	0.988729i	$-0.547837\pi$
$593$	−7.29180			−0.299438			−0.149719	+	0.988729i	$0.547837\pi$
$594$	6.80902	+	2.93893i	0.279377	+	0.120586i
$595$	−1.50658			−0.0617637
$596$	−15.1353	−	46.5815i	−0.619964	−	1.90805i
$597$	3.33688	−	10.2699i	0.136569	−	0.420318i
$598$	14.3951	−	44.3036i	0.588660	−	1.81171i
$599$	−13.3262	−	41.0139i	−0.544495	−	1.67578i	−0.722187	−	0.691698i	$-0.756863\pi$
$599$	−13.3262	−	41.0139i	−0.544495	−	1.67578i	0.177692	−	0.984086i	$-0.443137\pi$
$600$	11.1803			0.456435
$601$	5.35410	+	3.88998i	0.218398	+	0.158676i	0.691605	−	0.722276i	$-0.256904\pi$
$601$	5.35410	+	3.88998i	0.218398	+	0.158676i	−0.473207	+	0.880951i	$0.656904\pi$
$602$	6.87132	+	4.99231i	0.280054	+	0.203471i
$603$	0.263932	+	0.812299i	0.0107481	+	0.0330794i
$604$	1.50000	−	1.08981i	0.0610341	−	0.0443439i
$605$	−22.2361	+	10.5146i	−0.904025	+	0.427480i
$606$	30.2254	+	21.9601i	1.22782	+	0.892066i
$607$	6.54508	−	20.1437i	0.265657	−	0.817608i	−0.725885	−	0.687817i	$-0.758569\pi$
$607$	6.54508	−	20.1437i	0.265657	−	0.817608i	0.991541	−	0.129791i	$-0.0414306\pi$
$608$	−29.3951			−1.19213
$609$	1.26393	−	0.918300i	0.0512171	−	0.0372114i
$610$	−51.6312			−2.09049
$611$	−15.0000	+	10.8981i	−0.606835	+	0.440891i
$612$	−4.28115	+	3.11044i	−0.173055	+	0.125732i
$613$	11.9894	+	36.8994i	0.484246	+	1.49035i	0.833071	+	0.553167i	$0.186581\pi$
$613$	11.9894	+	36.8994i	0.484246	+	1.49035i	−0.348825	+	0.937188i	$0.613419\pi$
$614$	63.5410			2.56431
$615$	11.2812	+	8.19624i	0.454900	+	0.330504i
$616$	−0.263932	+	2.82041i	−0.0106341	+	0.113638i
$617$	34.4615	+	25.0377i	1.38737	+	1.00798i	0.996148	+	0.0876839i	$0.0279465\pi$
$617$	34.4615	+	25.0377i	1.38737	+	1.00798i	0.391219	+	0.920298i	$0.372053\pi$
$618$	3.25329	−	10.0126i	0.130866	−	0.402766i
$619$	23.1803			0.931697			0.465848	−	0.884865i	$-0.345749\pi$
$619$	23.1803			0.931697			0.465848	+	0.884865i	$0.345749\pi$
$620$	9.87539			0.396605
$621$	2.80902	+	2.04087i	0.112722	+	0.0818973i
$622$	−6.60739	−	4.80055i	−0.264932	−	0.192485i
$623$	−1.95492	+	6.01661i	−0.0783220	+	0.241050i
$624$	−4.85410	+	3.52671i	−0.194320	+	0.141181i
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$	0.931116			0.0372149
$627$	−14.1803	+	3.18368i	−0.566308	+	0.127144i
$628$	−11.4271	+	8.30224i	−0.455989	+	0.331295i
$629$	4.28115	+	13.1760i	0.170701	+	0.525363i
$630$	−0.590170	+	1.81636i	−0.0235129	+	0.0723654i
$631$	8.56231	+	26.3521i	0.340860	+	1.04906i	0.963763	+	0.266760i	$0.0859531\pi$
$631$	8.56231	+	26.3521i	0.340860	+	1.04906i	−0.622903	+	0.782299i	$0.714047\pi$
$632$	3.41641	+	10.5146i	0.135897	+	0.418249i
$633$	0.527864	−	1.62460i	0.0209807	−	0.0645720i
$634$	18.0902	−	13.1433i	0.718452	−	0.521986i
$635$	−30.9787			−1.22935
$636$	−3.00000			−0.118958
$637$	12.7082	−	39.1118i	0.503517	−	1.54967i
$638$	15.4656	+	26.0948i	0.612287	+	1.03310i
$639$	−0.454915	−	1.40008i	−0.0179962	−	0.0553865i
$640$	−28.3156	−	20.5725i	−1.11927	−	0.813199i
$641$	−0.927051	−	2.85317i	−0.0366163	−	0.112693i	0.931078	−	0.364821i	$-0.118870\pi$
$641$	−0.927051	−	2.85317i	−0.0366163	−	0.112693i	−0.967694	+	0.252127i	$0.918870\pi$
$642$	−9.96149	−	30.6583i	−0.393149	−	1.20999i
$643$	−4.38197	−	13.4863i	−0.172808	−	0.531848i	0.826719	−	0.562615i	$-0.190205\pi$
$643$	−4.38197	−	13.4863i	−0.172808	−	0.531848i	−0.999527	+	0.0307676i	$0.990205\pi$
$644$	−1.22949	+	3.78398i	−0.0484487	+	0.149110i
$645$	−17.9894	+	13.0700i	−0.708330	+	0.514632i
$646$	5.34095	−	16.4377i	0.210137	−	0.646734i
$647$	11.5279	+	35.4791i	0.453207	+	1.39483i	0.873227	+	0.487313i	$0.162023\pi$
$647$	11.5279	+	35.4791i	0.453207	+	1.39483i	−0.420020	+	0.907515i	$0.637977\pi$
$648$	0.690983	+	2.12663i	0.0271444	+	0.0835418i
$649$	−5.20163	−	2.24514i	−0.204182	−	0.0881294i
$650$	−20.7295	+	63.7988i	−0.813077	+	2.50240i
$651$	−0.173762	+	0.534785i	−0.00681027	+	0.0209599i
$652$	31.5517	+	22.9236i	1.23566	+	0.897758i
$653$	−21.0344			−0.823141			−0.411571	−	0.911378i	$-0.635020\pi$
$653$	−21.0344			−0.823141			−0.411571	+	0.911378i	$0.635020\pi$
$654$	−32.0344	−	23.2744i	−1.25265	−	0.910100i
$655$	1.15654	+	3.55947i	0.0451898	+	0.139080i
$656$	−1.92705	−	5.93085i	−0.0752387	−	0.231561i
$657$	−1.00000	+	0.726543i	−0.0390137	+	0.0283451i
$658$	2.13525	−	1.55135i	0.0832409	−	0.0604781i
$659$	−8.40983	+	25.8828i	−0.327600	+	1.00825i	0.642653	+	0.766158i	$0.277834\pi$
$659$	−8.40983	+	25.8828i	−0.327600	+	1.00825i	−0.970253	+	0.242093i	$0.922166\pi$
$660$	−20.4271	−	8.81678i	−0.795122	−	0.343193i
$661$	4.94427	+	15.2169i	0.192310	+	0.591869i	0.999997	+	0.00225826i	$0.000718826\pi$
$661$	4.94427	+	15.2169i	0.192310	+	0.591869i	−0.807688	+	0.589611i	$0.799281\pi$
$662$	−45.1246	−	32.7849i	−1.75382	−	1.27422i
$663$	−3.27051	−	10.0656i	−0.127016	−	0.390915i
$664$	7.98936	−	24.5887i	0.310047	−	0.954227i
$665$	−1.15654	−	3.55947i	−0.0448487	−	0.138030i
$666$	17.5623			0.680526
$667$	4.38854	+	13.5065i	0.169925	+	0.522976i
$668$	−23.4787	+	17.0583i	−0.908419	+	0.660005i
$669$	−1.11803	+	0.812299i	−0.0432257	+	0.0314053i
$670$	−1.31966	−	4.06150i	−0.0509829	−	0.156909i
$671$	31.4443	+	13.5721i	1.21389	+	0.523944i
$672$	2.07295	−	1.50609i	0.0799657	−	0.0580985i
$673$	−13.9098			−0.536185			−0.268092	−	0.963393i	$-0.586393\pi$
$673$	−13.9098			−0.536185			−0.268092	+	0.963393i	$0.586393\pi$
$674$	50.8779	−	36.9650i	1.95974	−	1.42384i
$675$	−4.04508	−	2.93893i	−0.155695	−	0.113119i
$676$	21.3222	+	65.6229i	0.820084	+	2.52396i
$677$	−4.04508	+	2.93893i	−0.155465	+	0.112952i	−0.662798	−	0.748798i	$-0.730631\pi$
$677$	−4.04508	+	2.93893i	−0.155465	+	0.112952i	0.507333	+	0.861750i	$0.330631\pi$
$678$	3.29180			0.126421
$679$	1.35410	−	4.16750i	0.0519657	−	0.159934i
$680$	7.13525	−	5.18407i	0.273625	−	0.198800i
$681$	−18.3713	−	13.3475i	−0.703991	−	0.511479i
$682$	−10.0238	−	4.32650i	−0.383831	−	0.165670i
$683$	13.2533	+	9.62908i	0.507123	+	0.368446i	0.811731	−	0.584031i	$-0.198525\pi$
$683$	13.2533	+	9.62908i	0.507123	+	0.368446i	−0.304608	+	0.952478i	$0.598525\pi$
$684$	−10.6353	−	7.72696i	−0.406649	−	0.295448i
$685$	15.0000	+	10.8981i	0.573121	+	0.416396i
$686$	−3.65654	+	11.2537i	−0.139607	+	0.429667i
$687$	17.0000			0.648590
$688$	9.94427			0.379122
$689$	1.85410	−	5.70634i	0.0706357	−	0.217394i
$690$	−14.0451	−	10.2044i	−0.534687	−	0.388473i
$691$	−31.8885	−	23.1684i	−1.21310	−	0.881367i	−0.217589	−	0.976040i	$-0.569819\pi$
$691$	−31.8885	−	23.1684i	−1.21310	−	0.881367i	−0.995508	+	0.0946736i	$0.969819\pi$
$692$	32.2082	+	23.4006i	1.22437	+	0.889558i
$693$	0.836881	−	0.951057i	0.0317905	−	0.0361276i
$694$	−0.100813	−	0.0732450i	−0.00382681	−	0.00278034i
$695$	21.4443	−	15.5802i	0.813428	−	0.590990i
$696$	−2.82624	+	8.69827i	−0.107128	+	0.329707i
$697$	11.0000			0.416655
$698$	−27.7254	+	20.1437i	−1.04942	+	0.762450i
$699$	−6.29180	−	19.3642i	−0.237978	−	0.732420i
$700$	1.77051	−	5.44907i	0.0669190	−	0.205955i
$701$	−16.5902	+	12.0535i	−0.626602	+	0.455253i	−0.855221	−	0.518263i	$-0.826579\pi$
$701$	−16.5902	+	12.0535i	−0.626602	+	0.455253i	0.228619	+	0.973516i	$0.426579\pi$
$702$	−13.4164			−0.506370
$703$	−27.8435	+	20.2295i	−1.05014	+	0.762968i
$704$	21.9828	+	37.0912i	0.828507	+	1.39793i
$705$	2.13525	+	6.57164i	0.0804184	+	0.247502i
$706$	10.0623	−	7.31069i	0.378700	−	0.275142i
$707$	5.16312	−	3.75123i	0.194179	−	0.141079i
$708$	−1.58359	−	4.87380i	−0.0595150	−	0.183168i
$709$	−27.4721			−1.03174			−0.515869	−	0.856668i	$-0.672531\pi$
$709$	−27.4721			−1.03174			−0.515869	+	0.856668i	$0.672531\pi$
$710$	2.27458	+	7.00042i	0.0853633	+	0.262721i
$711$	1.52786	−	4.70228i	0.0572994	−	0.176349i
$712$	−11.4443	−	35.2218i	−0.428892	−	1.31999i
$713$	−4.13525	−	3.00444i	−0.154867	−	0.112517i
$714$	0.465558	+	1.43284i	0.0174231	+	0.0536227i
$715$	29.3951	−	33.4055i	1.09932	−	1.24929i
$716$	−21.0000	+	64.6314i	−0.784807	+	2.41539i
$717$	1.54508	−	1.12257i	0.0577023	−	0.0419231i
$718$	67.6869	−	49.1774i	2.52605	−	1.83529i
$719$	−3.13525	−	9.64932i	−0.116925	−	0.359859i	0.875418	−	0.483366i	$-0.160586\pi$
$719$	−3.13525	−	9.64932i	−0.116925	−	0.359859i	−0.992344	+	0.123507i	$0.960586\pi$
$720$	0.690983	+	2.12663i	0.0257514	+	0.0792547i
$721$	−1.45492	−	1.05706i	−0.0541839	−	0.0393669i
$722$	0.450850			0.0167789
$723$	−9.01722	−	6.55139i	−0.335354	−	0.243649i
$724$	−12.6246	+	38.8546i	−0.469190	+	1.44402i
$725$	−6.31966	−	19.4499i	−0.234706	−	0.722352i
$726$	16.8713	+	17.8986i	0.626154	+	0.664278i
$727$	1.31966	+	4.06150i	0.0489435	+	0.150633i	0.972541	−	0.232730i	$-0.0747659\pi$
$727$	1.31966	+	4.06150i	0.0489435	+	0.150633i	−0.923598	+	0.383363i	$0.874766\pi$
$728$	−1.58359	−	4.87380i	−0.0586918	−	0.180635i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	5.00000	−	3.63271i	0.185058	−	0.134453i
$731$	−5.42047	+	16.6825i	−0.200483	+	0.617025i
$732$	9.57295	+	29.4625i	0.353826	+	1.08897i
$733$	−10.3713	−	31.9196i	−0.383074	−	1.17898i	−0.937868	−	0.346992i	$-0.887203\pi$
$733$	−10.3713	−	31.9196i	−0.383074	−	1.17898i	0.554795	−	0.831987i	$-0.312797\pi$
$734$	21.9336	+	67.5048i	0.809585	+	2.49165i
$735$	−12.3992	−	9.00854i	−0.457351	−	0.332285i
$736$	7.19756	+	22.1518i	0.265306	+	0.816527i
$737$	−0.263932	+	2.82041i	−0.00972206	+	0.103891i
$738$	4.30902	−	13.2618i	0.158617	−	0.488173i
$739$	−3.65248			−0.134358			−0.0671792	−	0.997741i	$-0.521400\pi$
$739$	−3.65248			−0.134358			−0.0671792	+	0.997741i	$0.521400\pi$
$740$	−52.6869			−1.93681
$741$	21.2705	−	15.4539i	0.781392	−	0.567714i
$742$	−0.263932	+	0.812299i	−0.00968925	+	0.0298204i
$743$	−3.01064	−	9.26581i	−0.110450	−	0.339929i	0.880521	−	0.474007i	$-0.157193\pi$
$743$	−3.01064	−	9.26581i	−0.110450	−	0.339929i	−0.990971	+	0.134078i	$0.957193\pi$
$744$	−1.01722	−	3.13068i	−0.0372931	−	0.114776i
$745$	11.2812	−	34.7198i	0.413309	−	1.27204i
$746$	−22.8262	−	70.2519i	−0.835728	−	2.57211i
$747$	−9.35410	+	6.79615i	−0.342249	+	0.248658i
$748$	−17.1246	+	3.84471i	−0.626138	+	0.140577i
$749$	−5.50658			−0.201206
$750$	20.2254	+	14.6946i	0.738528	+	0.536572i
$751$	3.28115	−	2.38390i	0.119731	−	0.0869896i	−0.526308	−	0.850294i	$-0.676424\pi$
$751$	3.28115	−	2.38390i	0.119731	−	0.0869896i	0.646039	+	0.763304i	$0.276424\pi$
$752$	0.954915	−	2.93893i	0.0348222	−	0.107172i
$753$	−23.4894	−	17.0660i	−0.856000	−	0.621920i
$754$	−44.3951	−	32.2549i	−1.61677	−	1.17466i
$755$	1.38197			0.0502949
$756$	1.14590			0.0416759
$757$	−13.0106	+	40.0426i	−0.472880	+	1.45537i	0.375916	+	0.926654i	$0.377328\pi$
$757$	−13.0106	+	40.0426i	−0.472880	+	1.45537i	−0.848796	+	0.528721i	$0.822672\pi$
$758$	−36.4443	−	26.4783i	−1.32372	−	0.961736i
$759$	5.87132	+	9.90659i	0.213116	+	0.359587i
$760$	17.7254	+	12.8783i	0.642969	+	0.467144i
$761$	33.6180			1.21865			0.609326	−	0.792920i	$-0.291440\pi$
$761$	33.6180			1.21865			0.609326	+	0.792920i	$0.291440\pi$
$762$	9.57295	+	29.4625i	0.346791	+	1.06731i
$763$	−5.47214	+	3.97574i	−0.198105	+	0.143931i
$764$	−40.3328	+	29.3035i	−1.45919	+	1.06016i
$765$	−3.94427			−0.142605
$766$	−68.8673	+	50.0350i	−2.48828	+	1.80784i
$767$	10.2492			0.370078
$768$	−2.78115	+	8.55951i	−0.100356	+	0.308865i
$769$	−27.1803	−	19.7477i	−0.980148	−	0.712119i	−0.0224064	−	0.999749i	$-0.507133\pi$
$769$	−27.1803	−	19.7477i	−0.980148	−	0.712119i	−0.957742	+	0.287630i	$0.907133\pi$
$770$	−4.18441	+	4.75528i	−0.150795	+	0.171368i
$771$	−9.51722	+	6.91467i	−0.342754	+	0.249026i
$772$	−5.20820	−	16.0292i	−0.187447	−	0.576904i
$773$	−23.3885	−	16.9928i	−0.841227	−	0.611188i	0.0814858	−	0.996675i	$-0.474033\pi$
$773$	−23.3885	−	16.9928i	−0.841227	−	0.611188i	−0.922713	+	0.385487i	$0.874033\pi$
$774$	17.9894	+	13.0700i	0.646614	+	0.469793i
$775$	5.95492	+	4.32650i	0.213907	+	0.155412i
$776$	7.92705	+	24.3970i	0.284565	+	0.875800i
$777$	0.927051	−	2.85317i	0.0332578	−	0.102357i
$778$	−13.6803	+	42.1038i	−0.490464	+	1.50949i
$779$	8.44427	+	25.9888i	0.302547	+	0.931145i
$780$	40.2492			1.44115
$781$	0.454915	−	4.86128i	0.0162781	−	0.173950i
$782$	−13.6950			−0.489734
$783$	3.30902	−	2.40414i	0.118255	−	0.0859170i
$784$	2.11803	+	6.51864i	0.0756441	+	0.232809i
$785$	−10.5279			−0.375756
$786$	3.02786	−	2.19987i	0.108000	−	0.0784668i
$787$	5.85410			0.208676			0.104338	−	0.994542i	$-0.466728\pi$
$787$	5.85410			0.208676			0.104338	+	0.994542i	$0.466728\pi$
$788$	37.5517	−	27.2829i	1.33772	−	0.971912i
$789$	−13.8541	−	10.0656i	−0.493219	−	0.358345i
$790$	−7.63932	+	23.5114i	−0.271795	+	0.836498i
$791$	0.173762	−	0.534785i	0.00617827	−	0.0190148i
$792$	−0.690983	+	7.38394i	−0.0245530	+	0.262377i
$793$	−61.9574			−2.20017
$794$	−42.7254	+	31.0418i	−1.51627	+	1.10163i
$795$	−1.80902	−	1.31433i	−0.0641592	−	0.0466144i
$796$	32.3951			1.14821
$797$	−25.6525	−	18.6376i	−0.908657	−	0.660178i	0.0320176	−	0.999487i	$-0.489807\pi$
$797$	−25.6525	−	18.6376i	−0.908657	−	0.660178i	−0.940675	+	0.339309i	$0.889807\pi$
$798$	−3.02786	+	2.19987i	−0.107185	+	0.0778746i
$799$	4.40983	+	3.20393i	0.156009	+	0.113347i
$800$	−10.3647	−	31.8994i	−0.366449	−	1.12781i
$801$	−5.11803	+	15.7517i	−0.180837	+	0.556559i
$802$	7.19756	+	22.1518i	0.254155	+	0.782208i
$803$	−4.00000	+	0.898056i	−0.141157	+	0.0316917i
$804$	−2.07295	+	1.50609i	−0.0731073	+	0.0531155i
$805$	−2.39919	+	1.74311i	−0.0845602	+	0.0614366i
$806$	19.7508			0.695691
$807$	−11.0451	−	8.02472i	−0.388805	−	0.282484i
$808$	−11.5451	+	35.5321i	−0.406155	+	1.25002i
$809$	38.7082			1.36091			0.680454	−	0.732791i	$-0.261783\pi$
$809$	38.7082			1.36091			0.680454	+	0.732791i	$0.261783\pi$
$810$	−1.54508	+	4.75528i	−0.0542888	+	0.167084i
$811$	9.80902	+	7.12667i	0.344441	+	0.250251i	0.746533	−	0.665348i	$-0.231717\pi$
$811$	9.80902	+	7.12667i	0.344441	+	0.250251i	−0.402092	+	0.915599i	$0.631717\pi$
$812$	3.79180	+	2.75490i	0.133066	+	0.0966781i
$813$	−6.42705	+	19.7804i	−0.225407	+	0.693730i
$814$	53.4787	+	23.0826i	1.87443	+	0.809046i
$815$	8.98278	+	27.6462i	0.314653	+	0.968402i
$816$	1.42705	+	1.03681i	0.0499568	+	0.0362957i
$817$	−43.5755			−1.52451
$818$	−28.8435	−	20.9560i	−1.00849	−	0.732709i
$819$	−0.708204	+	2.17963i	−0.0247466	+	0.0761624i
$820$	−12.9271	+	39.7854i	−0.451432	+	1.38937i
$821$	−36.3050			−1.26705			−0.633526	−	0.773722i	$-0.718393\pi$
$821$	−36.3050			−1.26705			−0.633526	+	0.773722i	$0.718393\pi$
$822$	5.72949	−	17.6336i	0.199839	−	0.615041i
$823$	30.0557			1.04768			0.523838	−	0.851818i	$-0.324500\pi$
$823$	30.0557			1.04768			0.523838	+	0.851818i	$0.324500\pi$
$824$	10.5279			0.366756
$825$	−8.45492	−	14.2658i	−0.294362	−	0.496673i
$826$	−1.45898			−0.0507644
$827$	−1.94427			−0.0676090			−0.0338045	−	0.999428i	$-0.510762\pi$
$827$	−1.94427			−0.0676090			−0.0338045	+	0.999428i	$0.510762\pi$
$828$	−3.21885	+	9.90659i	−0.111863	+	0.344278i
$829$	40.7082			1.41385			0.706927	−	0.707286i	$-0.250081\pi$
$829$	40.7082			1.41385			0.706927	+	0.707286i	$0.250081\pi$
$830$	46.7705	−	33.9808i	1.62343	−	1.17949i
$831$	5.68034	−	17.4823i	0.197049	−	0.606454i
$832$	−63.1033	−	45.8472i	−2.18771	−	1.58947i
$833$	−12.0902			−0.418900
$834$	−21.4443	−	15.5802i	−0.742554	−	0.539497i
$835$	−21.6312			−0.748578
$836$	−22.2295	−	37.5075i	−0.768823	−	1.29722i
$837$	−0.454915	+	1.40008i	−0.0157242	+	0.0483940i
$838$	−55.7771	−	40.5244i	−1.92679	−	1.39989i
$839$	−26.8713	−	19.5232i	−0.927701	−	0.674014i	0.0177278	−	0.999843i	$-0.494357\pi$
$839$	−26.8713	−	19.5232i	−0.927701	−	0.674014i	−0.945429	+	0.325829i	$0.894357\pi$
$840$	−1.90983			−0.0658954
$841$	−12.2705			−0.423121
$842$	−14.4959	+	44.6139i	−0.499563	+	1.53750i
$843$	−7.89919	−	5.73910i	−0.272062	−	0.197665i
$844$	5.12461			0.176396
$845$	−15.8926	+	48.9124i	−0.546722	+	1.68264i
$846$	5.59017	−	4.06150i	0.192194	−	0.139637i
$847$	3.79837	−	1.79611i	0.130514	−	0.0617151i
$848$	0.309017	+	0.951057i	0.0106117	+	0.0326594i
$849$	5.21885	−	16.0620i	0.179110	−	0.551245i
$850$	19.7214			0.676437
$851$	22.0623	+	16.0292i	0.756286	+	0.549474i
$852$	3.57295	−	2.59590i	0.122407	−	0.0889340i
$853$	4.09017	+	2.97168i	0.140045	+	0.101748i	0.655602	−	0.755107i	$-0.272415\pi$
$853$	4.09017	+	2.97168i	0.140045	+	0.101748i	−0.515557	+	0.856855i	$0.672415\pi$
$854$	8.81966			0.301803
$855$	−3.02786	−	9.31881i	−0.103551	−	0.318696i
$856$	26.0795	−	18.9479i	0.891380	−	0.647625i
$857$	−34.2705			−1.17066			−0.585329	−	0.810796i	$-0.699035\pi$
$857$	−34.2705			−1.17066			−0.585329	+	0.810796i	$0.699035\pi$
$858$	−40.8541	−	17.6336i	−1.39474	−	0.602000i
$859$	−7.78115	+	23.9479i	−0.265490	+	0.817093i	0.726091	+	0.687599i	$0.241335\pi$
$859$	−7.78115	+	23.9479i	−0.265490	+	0.817093i	−0.991580	+	0.129494i	$0.958665\pi$
$860$	−53.9681	−	39.2101i	−1.84030	−	1.33705i
$861$	−1.92705	−	1.40008i	−0.0656737	−	0.0477148i
$862$	−9.04508	+	6.57164i	−0.308077	+	0.223831i
$863$	−31.7984			−1.08243			−0.541215	−	0.840884i	$-0.682035\pi$
$863$	−31.7984			−1.08243			−0.541215	+	0.840884i	$0.682035\pi$
$864$	5.42705	−	3.94298i	0.184632	−	0.134143i
$865$	9.16970	+	28.2214i	0.311779	+	0.959557i
$866$	4.87539	+	15.0049i	0.165672	+	0.509887i
$867$	11.2361	−	8.16348i	0.381597	−	0.277246i
$868$	−1.68692			−0.0572577
$869$	10.8328	−	12.3107i	0.367478	−	0.417613i
$870$	−16.5451	+	12.0207i	−0.560931	+	0.407540i
$871$	−1.58359	−	4.87380i	−0.0536580	−	0.165142i
$872$	12.2361	−	37.6587i	0.414366	−	1.27529i
$873$	3.54508	−	10.9106i	0.119983	−	0.369270i
$874$	−10.5132	−	32.3562i	−0.355613	−	1.09446i
$875$	3.45492	−	2.51014i	0.116797	−	0.0848583i
$876$	−3.00000	−	2.17963i	−0.101361	−	0.0736428i
$877$	−33.3435	−	24.2254i	−1.12593	−	0.818035i	−0.140831	−	0.990034i	$-0.544978\pi$
$877$	−33.3435	−	24.2254i	−1.12593	−	0.818035i	−0.985097	+	0.171999i	$0.944978\pi$
$878$	13.6803	+	42.1038i	0.461689	+	1.42093i
$879$	20.0344	−	14.5559i	0.675745	−	0.490957i
$880$	−0.690983	+	7.38394i	−0.0232930	+	0.248913i
$881$	4.73607	+	3.44095i	0.159562	+	0.115929i	0.664701	−	0.747109i	$-0.268559\pi$
$881$	4.73607	+	3.44095i	0.159562	+	0.115929i	−0.505139	+	0.863038i	$0.668559\pi$
$882$	−4.73607	+	14.5761i	−0.159472	+	0.490803i
$883$	−38.8328			−1.30683			−0.653414	−	0.757001i	$-0.726664\pi$
$883$	−38.8328			−1.30683			−0.653414	+	0.757001i	$0.726664\pi$
$884$	25.6869	−	18.6626i	0.863945	−	0.627692i
$885$	1.18034	−	3.63271i	0.0396767	−	0.122112i
$886$	20.9549	−	15.2246i	0.703994	−	0.511482i
$887$	−30.1697	+	21.9196i	−1.01300	+	0.735987i	−0.964836	−	0.262852i	$-0.915337\pi$
$887$	−30.1697	+	21.9196i	−1.01300	+	0.735987i	−0.0481632	+	0.998839i	$0.515337\pi$
$888$	5.42705	+	16.7027i	0.182120	+	0.560507i
$889$	5.29180			0.177481
$890$	25.5902	−	78.7584i	0.857784	−	2.63999i
$891$	2.19098	−	2.48990i	0.0734007	−	0.0834147i
$892$	−3.35410	−	2.43690i	−0.112304	−	0.0815934i
$893$	−4.18441	+	12.8783i	−0.140026	+	0.430955i
$894$	−36.5066			−1.22096
$895$	−40.9787	+	29.7728i	−1.36977	+	0.995194i
$896$	4.83688	+	3.51420i	0.161589	+	0.117401i
$897$	−16.8541	−	12.2452i	−0.562742	−	0.408856i
$898$	0.628677	−	1.93487i	0.0209792	−	0.0645674i
$899$	−4.87132	+	3.53922i	−0.162468	+	0.118040i
$900$	4.63525	−	14.2658i	0.154508	−	0.475528i
$901$	−1.76393			−0.0587651
$902$	30.5517	−	34.7198i	1.01726	−	1.15604i
$903$	3.07295	−	2.23263i	0.102261	−	0.0742972i
$904$	1.01722	+	3.13068i	0.0338323	+	0.104125i
$905$	−24.6353	+	17.8986i	−0.818904	+	0.594968i
$906$	−0.427051	−	1.31433i	−0.0141878	−	0.0436656i
$907$	14.2467	+	43.8469i	0.473054	+	1.45591i	0.848564	+	0.529093i	$0.177468\pi$
$907$	14.2467	+	43.8469i	0.473054	+	1.45591i	−0.375510	+	0.926818i	$0.622532\pi$
$908$	21.0517	−	64.7904i	0.698624	−	2.15014i
$909$	13.5172	−	9.82084i	0.448338	−	0.325737i
$910$	3.54102	−	10.8981i	0.117384	−	0.361270i
$911$	19.0689			0.631780			0.315890	−	0.948796i	$-0.397697\pi$
$911$	19.0689			0.631780			0.315890	+	0.948796i	$0.397697\pi$
$912$	−1.35410	+	4.16750i	−0.0448388	+	0.138000i
$913$	−37.4164	+	8.40051i	−1.23830	+	0.278016i
$914$	22.2361	+	68.4356i	0.735504	+	2.26365i
$915$	−7.13525	+	21.9601i	−0.235884	+	0.725977i
$916$	15.7599	+	48.5039i	0.520721	+	1.60261i
$917$	−0.197561	−	0.608030i	−0.00652403	−	0.0200789i
$918$	1.21885	+	3.75123i	0.0402279	+	0.123809i
$919$	5.45492	−	16.7885i	0.179941	−	0.553802i	−0.819884	−	0.572530i	$-0.805962\pi$
$919$	5.45492	−	16.7885i	0.179941	−	0.553802i	0.999825	+	0.0187287i	$0.00596188\pi$
$920$	5.36475	−	16.5110i	0.176870	−	0.544351i
$921$	8.78115	−	27.0256i	0.289349	−	0.890524i
$922$	−10.3500	−	31.8541i	−0.340860	−	1.04906i
$923$	2.72949	+	8.40051i	0.0898423	+	0.276506i
$924$	3.48936	+	1.50609i	0.114791	+	0.0495466i
$925$	−31.7705	−	23.0826i	−1.04461	−	0.758952i
$926$	4.23200	−	13.0248i	0.139072	−	0.428020i
$927$	−3.80902	−	2.76741i	−0.125105	−	0.0908938i
$928$	27.4377			0.900686
$929$	40.5967	+	29.4953i	1.33194	+	0.967708i	0.999700	+	0.0245121i	$0.00780323\pi$
$929$	40.5967	+	29.4953i	1.33194	+	0.967708i	0.332237	+	0.943196i	$0.392197\pi$
$930$	2.27458	−	7.00042i	0.0745863	−	0.229553i
$931$	−9.28115	−	28.5645i	−0.304178	−	0.936162i
$932$	49.4164	−	35.9031i	1.61869	−	1.17605i
$933$	−2.95492	+	2.14687i	−0.0967396	+	0.0702854i
$934$	3.15248	−	9.70232i	0.103152	−	0.317470i
$935$	−12.0106	−	5.18407i	−0.392790	−	0.169537i
$936$	−4.14590	−	12.7598i	−0.135513	−	0.417066i
$937$	−14.9271	−	10.8451i	−0.487645	−	0.354295i	0.316633	−	0.948548i	$-0.397448\pi$
$937$	−14.9271	−	10.8451i	−0.487645	−	0.354295i	−0.804278	+	0.594253i	$0.797448\pi$
$938$	0.225425	+	0.693786i	0.00736038	+	0.0226529i
$939$	0.128677	−	0.396027i	0.00419922	−	0.0129239i
$940$	−16.7705	+	12.1845i	−0.546994	+	0.397414i
$941$	−6.23607			−0.203290			−0.101645	−	0.994821i	$-0.532411\pi$
$941$	−6.23607			−0.203290			−0.101645	+	0.994821i	$0.532411\pi$
$942$	3.25329	+	10.0126i	0.105998	+	0.326228i
$943$	17.5172	−	12.7270i	0.570439	−	0.414448i
$944$	−1.38197	+	1.00406i	−0.0449792	+	0.0326793i
$945$	0.690983	+	0.502029i	0.0224777	+	0.0163310i
$946$	37.6008	+	63.4433i	1.22251	+	2.06272i
$947$	−17.5451	+	12.7473i	−0.570139	+	0.414230i	−0.835156	−	0.550014i	$-0.814622\pi$
$947$	−17.5451	+	12.7473i	−0.570139	+	0.414230i	0.265017	+	0.964244i	$0.414622\pi$
$948$	14.8328			0.481747
$949$	6.00000	−	4.35926i	0.194768	−	0.141507i
$950$	15.1393	+	46.5940i	0.491184	+	1.51171i
$951$	−3.09017	−	9.51057i	−0.100206	−	0.308401i
$952$	−1.21885	+	0.885544i	−0.0395031	+	0.0287007i
$953$	16.2705			0.527054			0.263527	−	0.964652i	$-0.415114\pi$
$953$	16.2705			0.527054			0.263527	+	0.964652i	$0.415114\pi$
$954$	−0.690983	+	2.12663i	−0.0223714	+	0.0688521i
$955$	−37.1591			−1.20244
$956$	4.63525	+	3.36771i	0.149915	+	0.108920i
$957$	13.2361	−	2.97168i	0.427861	−	0.0960608i
$958$	47.2599	+	34.3363i	1.52690	+	1.10936i
$959$	−2.56231	−	1.86162i	−0.0827412	−	0.0601150i
$960$	−23.5172	+	17.0863i	−0.759015	+	0.551457i
$961$	−8.90983	+	27.4216i	−0.287414	+	0.884569i
$962$	−105.374			−3.39739
$963$	−14.4164			−0.464562
$964$	10.3328	−	31.8011i	0.332798	−	1.02425i
$965$	3.88197	−	11.9475i	0.124965	−	0.384602i
$966$	2.39919	+	1.74311i	0.0771926	+	0.0560837i
$967$	−6.57295	−	4.77553i	−0.211372	−	0.153571i	0.477062	−	0.878869i	$-0.341702\pi$
$967$	−6.57295	−	4.77553i	−0.211372	−	0.153571i	−0.688434	+	0.725299i	$0.741702\pi$
$968$	−11.8090	+	21.5765i	−0.379556	+	0.693496i
$969$	−6.25329	−	4.54328i	−0.200885	−	0.145951i
$970$	−17.7254	+	54.5532i	−0.569129	+	1.75160i
$971$	−11.1631	+	34.3565i	−0.358242	+	1.10255i	0.595864	+	0.803085i	$0.296810\pi$
$971$	−11.1631	+	34.3565i	−0.358242	+	1.10255i	−0.954106	+	0.299469i	$0.903190\pi$
$972$	3.00000			0.0962250
$973$	−3.66312	+	2.66141i	−0.117434	+	0.0853209i
$974$	2.70163	+	8.31475i	0.0865657	+	0.266422i
$975$	24.2705	+	17.6336i	0.777278	+	0.564726i
$976$	8.35410	−	6.06961i	0.267408	−	0.194283i
$977$	−32.6525			−1.04465			−0.522323	−	0.852748i	$-0.674934\pi$
$977$	−32.6525			−1.04465			−0.522323	+	0.852748i	$0.674934\pi$
$978$	23.5172	−	17.0863i	0.751998	−	0.546358i
$979$	−36.2877	+	41.2385i	−1.15976	+	1.31799i
$980$	14.2082	−	43.7284i	0.453864	−	1.39685i
$981$	−14.3262	+	10.4086i	−0.457402	+	0.332322i
$982$	−75.1484	+	54.5985i	−2.39808	+	1.74231i
$983$	2.76393	+	8.50651i	0.0881557	+	0.271315i	0.985410	−	0.170199i	$-0.0544412\pi$
$983$	2.76393	+	8.50651i	0.0881557	+	0.271315i	−0.897254	+	0.441515i	$0.854441\pi$
$984$	13.9443			0.444527
$985$	34.5967			1.10234
$986$	−4.98529	+	15.3431i	−0.158764	+	0.488625i
$987$	−0.364745	−	1.12257i	−0.0116100	−	0.0357318i
$988$	63.8115	+	46.3618i	2.03012	+	1.47497i
$989$	10.6697	+	32.8380i	0.339277	+	1.04419i
$990$	−10.9549	+	12.4495i	−0.348170	+	0.395671i
$991$	−4.43363	+	13.6453i	−0.140839	+	0.433457i	−0.996452	−	0.0841576i	$-0.973180\pi$
$991$	−4.43363	+	13.6453i	−0.140839	+	0.433457i	0.855614	+	0.517615i	$0.173180\pi$
$992$	−7.98936	+	5.80461i	−0.253662	+	0.184296i
$993$	−20.1803	+	14.6619i	−0.640404	+	0.465281i
$994$	−0.388544	−	1.19581i	−0.0123239	−	0.0379289i
$995$	19.5344	+	14.1926i	0.619283	+	0.449936i
$996$	−28.0623	−	20.3885i	−0.889188	−	0.646033i
$997$	26.3820			0.835525			0.417763	−	0.908556i	$-0.362814\pi$
$997$	26.3820			0.835525			0.417763	+	0.908556i	$0.362814\pi$
$998$	−23.8435	−	17.3233i	−0.754752	−	0.548359i
$999$	2.42705	−	7.46969i	0.0767885	−	0.236331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.r.a.31.1	yes	4
11.5	even	5		825.2.p.a.181.1	✓	4
25.21	even	5		825.2.p.a.196.1	yes	4
275.71	even	5	inner	825.2.r.a.346.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.p.a.181.1	✓	4	11.5	even	5
825.2.p.a.196.1	yes	4	25.21	even	5
825.2.r.a.31.1	yes	4	1.1	even	1	trivial
825.2.r.a.346.1	yes	4	275.71	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+2.23607 q^{2} +(0.309017 - 0.951057i) q^{3} +3.00000 q^{4} +(1.80902 + 1.31433i) q^{5} +(0.690983 - 2.12663i) q^{6} +(-0.309017 - 0.224514i) q^{7} +2.23607 q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+2.23607 q^{2} +(0.309017 - 0.951057i) q^{3} +3.00000 q^{4} +(1.80902 + 1.31433i) q^{5} +(0.690983 - 2.12663i) q^{6} +(-0.309017 - 0.224514i) q^{7} +2.23607 q^{8} +(-0.809017 - 0.587785i) q^{9} +(4.04508 + 2.93893i) q^{10} +(-1.69098 - 2.85317i) q^{11} +(0.927051 - 2.85317i) q^{12} +(4.85410 + 3.52671i) q^{13} +(-0.690983 - 0.502029i) q^{14} +(1.80902 - 1.31433i) q^{15} -1.00000 q^{16} +(0.545085 - 1.67760i) q^{17} +(-1.80902 - 1.31433i) q^{18} +4.38197 q^{19} +(5.42705 + 3.94298i) q^{20} +(-0.309017 + 0.224514i) q^{21} +(-3.78115 - 6.37988i) q^{22} +(-1.07295 - 3.30220i) q^{23} +(0.690983 - 2.12663i) q^{24} +(1.54508 + 4.75528i) q^{25} +(10.8541 + 7.88597i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.927051 - 0.673542i) q^{28} -4.09017 q^{29} +(4.04508 - 2.93893i) q^{30} +(1.19098 - 0.865300i) q^{31} -6.70820 q^{32} +(-3.23607 + 0.726543i) q^{33} +(1.21885 - 3.75123i) q^{34} +(-0.263932 - 0.812299i) q^{35} +(-2.42705 - 1.76336i) q^{36} +(-6.35410 + 4.61653i) q^{37} +9.79837 q^{38} +(4.85410 - 3.52671i) q^{39} +(4.04508 + 2.93893i) q^{40} +(1.92705 + 5.93085i) q^{41} +(-0.690983 + 0.502029i) q^{42} -9.94427 q^{43} +(-5.07295 - 8.55951i) q^{44} +(-0.690983 - 2.12663i) q^{45} +(-2.39919 - 7.38394i) q^{46} +(-0.954915 + 2.93893i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-2.11803 - 6.51864i) q^{49} +(3.45492 + 10.6331i) q^{50} +(-1.42705 - 1.03681i) q^{51} +(14.5623 + 10.5801i) q^{52} +(-0.309017 - 0.951057i) q^{53} +(-1.80902 + 1.31433i) q^{54} +(0.690983 - 7.38394i) q^{55} +(-0.690983 - 0.502029i) q^{56} +(1.35410 - 4.16750i) q^{57} -9.14590 q^{58} +(1.38197 - 1.00406i) q^{59} +(5.42705 - 3.94298i) q^{60} +(-8.35410 + 6.06961i) q^{61} +(2.66312 - 1.93487i) q^{62} +(0.118034 + 0.363271i) q^{63} -13.0000 q^{64} +(4.14590 + 12.7598i) q^{65} +(-7.23607 + 1.62460i) q^{66} +(-0.690983 - 0.502029i) q^{67} +(1.63525 - 5.03280i) q^{68} -3.47214 q^{69} +(-0.590170 - 1.81636i) q^{70} +(1.19098 + 0.865300i) q^{71} +(-1.80902 - 1.31433i) q^{72} +(0.381966 - 1.17557i) q^{73} +(-14.2082 + 10.3229i) q^{74} +5.00000 q^{75} +13.1459 q^{76} +(-0.118034 + 1.26133i) q^{77} +(10.8541 - 7.88597i) q^{78} +(1.52786 + 4.70228i) q^{79} +(-1.80902 - 1.31433i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.30902 + 13.2618i) q^{82} +(3.57295 - 10.9964i) q^{83} +(-0.927051 + 0.673542i) q^{84} +(3.19098 - 2.31838i) q^{85} -22.2361 q^{86} +(-1.26393 + 3.88998i) q^{87} +(-3.78115 - 6.37988i) q^{88} +(-5.11803 - 15.7517i) q^{89} +(-1.54508 - 4.75528i) q^{90} +(-0.708204 - 2.17963i) q^{91} +(-3.21885 - 9.90659i) q^{92} +(-0.454915 - 1.40008i) q^{93} +(-2.13525 + 6.57164i) q^{94} +(7.92705 + 5.75934i) q^{95} +(-2.07295 + 6.37988i) q^{96} +(3.54508 + 10.9106i) q^{97} +(-4.73607 - 14.5761i) q^{98} +(-0.309017 + 3.30220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 12 q^{4} + 5 q^{5} + 5 q^{6} + q^{7} - q^{9}+O(q^{10}) \) 4 * q - q^3 + 12 * q^4 + 5 * q^5 + 5 * q^6 + q^7 - q^9	\( 4 q - q^{3} + 12 q^{4} + 5 q^{5} + 5 q^{6} + q^{7} - q^{9} + 5 q^{10} - 9 q^{11} - 3 q^{12} + 6 q^{13} - 5 q^{14} + 5 q^{15} - 4 q^{16} - 9 q^{17} - 5 q^{18} + 22 q^{19} + 15 q^{20} + q^{21} + 5 q^{22} - 11 q^{23} + 5 q^{24} - 5 q^{25} + 30 q^{26} - q^{27} + 3 q^{28} + 6 q^{29} + 5 q^{30} + 7 q^{31} - 4 q^{33} + 25 q^{34} - 10 q^{35} - 3 q^{36} - 12 q^{37} - 10 q^{38} + 6 q^{39} + 5 q^{40} + q^{41} - 5 q^{42} - 4 q^{43} - 27 q^{44} - 5 q^{45} + 15 q^{46} - 15 q^{47} + q^{48} - 4 q^{49} + 25 q^{50} + q^{51} + 18 q^{52} + q^{53} - 5 q^{54} + 5 q^{55} - 5 q^{56} - 8 q^{57} - 50 q^{58} + 10 q^{59} + 15 q^{60} - 20 q^{61} - 5 q^{62} - 4 q^{63} - 52 q^{64} + 30 q^{65} - 20 q^{66} - 5 q^{67} - 27 q^{68} + 4 q^{69} + 20 q^{70} + 7 q^{71} - 5 q^{72} + 6 q^{73} - 30 q^{74} + 20 q^{75} + 66 q^{76} + 4 q^{77} + 30 q^{78} + 24 q^{79} - 5 q^{80} - q^{81} + 15 q^{82} + 21 q^{83} + 3 q^{84} + 15 q^{85} - 80 q^{86} - 14 q^{87} + 5 q^{88} - 16 q^{89} + 5 q^{90} + 24 q^{91} - 33 q^{92} - 13 q^{93} + 25 q^{94} + 25 q^{95} - 15 q^{96} + 3 q^{97} - 10 q^{98} + q^{99}+O(q^{100}) \) 4 * q - q^3 + 12 * q^4 + 5 * q^5 + 5 * q^6 + q^7 - q^9 + 5 * q^10 - 9 * q^11 - 3 * q^12 + 6 * q^13 - 5 * q^14 + 5 * q^15 - 4 * q^16 - 9 * q^17 - 5 * q^18 + 22 * q^19 + 15 * q^20 + q^21 + 5 * q^22 - 11 * q^23 + 5 * q^24 - 5 * q^25 + 30 * q^26 - q^27 + 3 * q^28 + 6 * q^29 + 5 * q^30 + 7 * q^31 - 4 * q^33 + 25 * q^34 - 10 * q^35 - 3 * q^36 - 12 * q^37 - 10 * q^38 + 6 * q^39 + 5 * q^40 + q^41 - 5 * q^42 - 4 * q^43 - 27 * q^44 - 5 * q^45 + 15 * q^46 - 15 * q^47 + q^48 - 4 * q^49 + 25 * q^50 + q^51 + 18 * q^52 + q^53 - 5 * q^54 + 5 * q^55 - 5 * q^56 - 8 * q^57 - 50 * q^58 + 10 * q^59 + 15 * q^60 - 20 * q^61 - 5 * q^62 - 4 * q^63 - 52 * q^64 + 30 * q^65 - 20 * q^66 - 5 * q^67 - 27 * q^68 + 4 * q^69 + 20 * q^70 + 7 * q^71 - 5 * q^72 + 6 * q^73 - 30 * q^74 + 20 * q^75 + 66 * q^76 + 4 * q^77 + 30 * q^78 + 24 * q^79 - 5 * q^80 - q^81 + 15 * q^82 + 21 * q^83 + 3 * q^84 + 15 * q^85 - 80 * q^86 - 14 * q^87 + 5 * q^88 - 16 * q^89 + 5 * q^90 + 24 * q^91 - 33 * q^92 - 13 * q^93 + 25 * q^94 + 25 * q^95 - 15 * q^96 + 3 * q^97 - 10 * q^98 + q^99

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