LMFDB - Embedded newform 275.2.h.c.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(26,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([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("275.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (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:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} - 13 x^{13} + 53 x^{12} - 12 x^{11} + 136 x^{10} + 8 x^{9} + 300 x^{8} + \cdots + 16 $ x^16 - 4x^15 + 10x^14 - 13x^13 + 53x^12 - 12x^11 + 136x^10 + 8x^9 + 300x^8 - 256x^7 + 472x^6 - 48x^5 + 432x^4 + 88x^3 + 128x^2 + 64*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.3
Root			$-0.265939 - 0.818476i$ of defining polynomial
Character	$\chi$	$=$	275.251
Dual form			275.2.h.c.126.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0430779 + 0.132580i) q^{2} +(-2.41558 + 1.75502i) q^{3} +(1.60231 + 1.16415i) q^{4} +(-0.128623 - 0.395861i) q^{6} +(2.88786 + 2.09815i) q^{7} +(-0.448926 + 0.326164i) q^{8} +(1.82787 - 5.62561i) q^{9} +(-2.45284 + 2.23239i) q^{11} -5.91361 q^{12} +(-0.369466 + 1.13710i) q^{13} +(-0.402576 + 0.292489i) q^{14} +(1.20015 + 3.69369i) q^{16} +(-1.67964 - 5.16941i) q^{17} +(0.667104 + 0.484679i) q^{18} +(-3.88538 + 2.82290i) q^{19} -10.6581 q^{21} +(-0.190307 - 0.421365i) q^{22} -1.82203 q^{23} +(0.511992 - 1.57575i) q^{24} +(-0.134841 - 0.0979678i) q^{26} +(2.68969 + 8.27800i) q^{27} +(2.18469 + 6.72378i) q^{28} +(3.35044 + 2.43424i) q^{29} +(0.397668 - 1.22390i) q^{31} -1.65122 q^{32} +(2.00714 - 9.69730i) q^{33} +0.757717 q^{34} +(9.47786 - 6.88607i) q^{36} +(2.55724 + 1.85794i) q^{37} +(-0.206886 - 0.636730i) q^{38} +(-1.10316 - 3.39517i) q^{39} +(5.18347 - 3.76601i) q^{41} +(0.459131 - 1.41306i) q^{42} +4.23557 q^{43} +(-6.52905 + 0.721514i) q^{44} +(0.0784894 - 0.241566i) q^{46} +(5.68588 - 4.13103i) q^{47} +(-9.38157 - 6.81611i) q^{48} +(1.77436 + 5.46092i) q^{49} +(13.1297 + 9.53930i) q^{51} +(-1.91575 + 1.39187i) q^{52} +(-3.34076 + 10.2818i) q^{53} -1.21337 q^{54} -1.98078 q^{56} +(4.43121 - 13.6379i) q^{57} +(-0.467062 + 0.339340i) q^{58} +(3.24907 + 2.36059i) q^{59} +(-4.47500 - 13.7726i) q^{61} +(0.145134 + 0.105446i) q^{62} +(17.0820 - 12.4108i) q^{63} +(-2.32918 + 7.16847i) q^{64} +(1.19921 + 0.683847i) q^{66} +8.14233 q^{67} +(3.32664 - 10.2384i) q^{68} +(4.40126 - 3.19770i) q^{69} +(2.63051 + 8.09589i) q^{71} +(1.01429 + 3.12167i) q^{72} +(6.90988 + 5.02032i) q^{73} +(-0.356488 + 0.259003i) q^{74} -9.51187 q^{76} +(-11.7673 + 1.30039i) q^{77} +0.497655 q^{78} +(0.121752 - 0.374714i) q^{79} +(-6.66892 - 4.84526i) q^{81} +(0.276005 + 0.849457i) q^{82} +(-0.483189 - 1.48710i) q^{83} +(-17.0777 - 12.4077i) q^{84} +(-0.182460 + 0.561553i) q^{86} -12.3654 q^{87} +(0.373020 - 1.80221i) q^{88} -6.90425 q^{89} +(-3.45277 + 2.50858i) q^{91} +(-2.91946 - 2.12112i) q^{92} +(1.18737 + 3.65434i) q^{93} +(0.302757 + 0.931792i) q^{94} +(3.98865 - 2.89792i) q^{96} +(-2.87750 + 8.85604i) q^{97} -0.800446 q^{98} +(8.07507 + 17.8793i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} + 16 q^{8} + 8 q^{9} - 5 q^{11} - 6 q^{12} + 7 q^{13} + 3 q^{14} - 4 q^{16} + 12 q^{17} + 16 q^{18} - 13 q^{19} + 10 q^{21} + 28 q^{22} - 4 q^{23} - 43 q^{24}+ \cdots - 10 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 - 2 * q^4 - 3 * q^6 + 4 * q^7 + 16 * q^8 + 8 * q^9 - 5 * q^11 - 6 * q^12 + 7 * q^13 + 3 * q^14 - 4 * q^16 + 12 * q^17 + 16 * q^18 - 13 * q^19 + 10 * q^21 + 28 * q^22 - 4 * q^23 - 43 * q^24 - 34 * q^26 - 11 * q^27 + 47 * q^28 - 11 * q^29 - 10 * q^31 - 58 * q^32 - 34 * q^33 + 20 * q^34 + 3 * q^36 - 4 * q^37 - 36 * q^38 + 3 * q^39 + 25 * q^41 + 13 * q^42 - 28 * q^43 - q^44 + 40 * q^46 + 8 * q^47 - 106 * q^48 + 16 * q^49 + 35 * q^51 + 39 * q^52 - 22 * q^53 + 60 * q^54 - 20 * q^56 + 29 * q^57 + 6 * q^58 + 14 * q^59 + 16 * q^61 - 10 * q^62 + 73 * q^63 + 40 * q^64 - 55 * q^66 - 14 * q^67 + 83 * q^68 + 35 * q^69 - 46 * q^71 + 28 * q^72 + 7 * q^73 - 7 * q^74 - 62 * q^76 - 51 * q^77 + 34 * q^78 - 39 * q^79 - 43 * q^81 - 51 * q^82 + 28 * q^83 - 54 * q^84 + 2 * q^86 - 50 * q^87 - 76 * q^88 - 22 * q^89 - 34 * q^91 + 4 * q^92 + 3 * q^93 - 40 * q^94 + 108 * q^96 - 39 * q^97 - 52 * q^98 - 10 * q^99

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.0430779	+	0.132580i	−0.0304607	+	0.0937484i	−0.965131	−	0.261767i	$-0.915695\pi$
$2$	−0.0430779	+	0.132580i	−0.0304607	+	0.0937484i	0.934670	+	0.355516i	$0.115695\pi$
$3$	−2.41558	+	1.75502i	−1.39463	+	1.01326i	−0.399296	+	0.916822i	$0.630745\pi$
$3$	−2.41558	+	1.75502i	−1.39463	+	1.01326i	−0.995339	+	0.0964394i	$0.969255\pi$
$4$	1.60231	+	1.16415i	0.801156	+	0.582074i
$5$		0			0
$5$		0			0
$6$	−0.128623	−	0.395861i	−0.0525101	−	0.161609i
$7$	2.88786	+	2.09815i	1.09151	+	0.793026i	0.979653	−	0.200698i	$-0.0643211\pi$
$7$	2.88786	+	2.09815i	1.09151	+	0.793026i	0.111854	+	0.993725i	$0.464321\pi$
$8$	−0.448926	+	0.326164i	−0.158719	+	0.115316i
$9$	1.82787	−	5.62561i	0.609290	−	1.87520i
$10$		0			0
$11$	−2.45284	+	2.23239i	−0.739560	+	0.673091i
$11$	−2.45284	+	2.23239i	−0.739560	+	0.673091i
$12$	−5.91361			−1.70711
$13$	−0.369466	+	1.13710i	−0.102471	+	0.315375i	−0.989129	−	0.147053i	$-0.953021\pi$
$13$	−0.369466	+	1.13710i	−0.102471	+	0.315375i	0.886657	+	0.462427i	$0.153021\pi$
$14$	−0.402576	+	0.292489i	−0.107593	+	0.0781709i
$15$		0			0
$16$	1.20015	+	3.69369i	0.300038	+	0.923423i
$17$	−1.67964	−	5.16941i	−0.407373	−	1.25377i	−0.918897	−	0.394496i	$-0.870919\pi$
$17$	−1.67964	−	5.16941i	−0.407373	−	1.25377i	0.511524	−	0.859269i	$-0.329081\pi$
$18$	0.667104	+	0.484679i	0.157238	+	0.114240i
$19$	−3.88538	+	2.82290i	−0.891368	+	0.647617i	−0.936234	−	0.351376i	$-0.885714\pi$
$19$	−3.88538	+	2.82290i	−0.891368	+	0.647617i	0.0448661	+	0.998993i	$0.485714\pi$
$20$		0			0
$21$	−10.6581			−2.32580
$22$	−0.190307	−	0.421365i	−0.0405737	−	0.0898354i
$23$	−1.82203			−0.379920			−0.189960	−	0.981792i	$-0.560836\pi$
$23$	−1.82203			−0.379920			−0.189960	+	0.981792i	$0.560836\pi$
$24$	0.511992	−	1.57575i	0.104510	−	0.321649i
$25$		0			0
$26$	−0.134841	−	0.0979678i	−0.0264445	−	0.0192131i
$27$	2.68969	+	8.27800i	0.517630	+	1.59310i
$28$	2.18469	+	6.72378i	0.412868	+	1.27068i
$29$	3.35044	+	2.43424i	0.622161	+	0.452026i	0.853676	−	0.520805i	$-0.174368\pi$
$29$	3.35044	+	2.43424i	0.622161	+	0.452026i	−0.231515	+	0.972831i	$0.574368\pi$
$30$		0			0
$31$	0.397668	−	1.22390i	0.0714233	−	0.219818i	−0.908973	−	0.416856i	$-0.863132\pi$
$31$	0.397668	−	1.22390i	0.0714233	−	0.219818i	0.980396	+	0.197037i	$0.0631320\pi$
$32$	−1.65122			−0.291897
$33$	2.00714	−	9.69730i	0.349399	−	1.68808i
$34$	0.757717			0.129947
$35$		0			0
$36$	9.47786	−	6.88607i	1.57964	−	1.14768i
$37$	2.55724	+	1.85794i	0.420408	+	0.305444i	0.777802	−	0.628509i	$-0.216335\pi$
$37$	2.55724	+	1.85794i	0.420408	+	0.305444i	−0.357394	+	0.933954i	$0.616335\pi$
$38$	−0.206886	−	0.636730i	−0.0335614	−	0.103291i
$39$	−1.10316	−	3.39517i	−0.176647	−	0.543663i
$40$		0			0
$41$	5.18347	−	3.76601i	0.809522	−	0.588152i	−0.104170	−	0.994559i	$-0.533219\pi$
$41$	5.18347	−	3.76601i	0.809522	−	0.588152i	0.913692	+	0.406408i	$0.133219\pi$
$42$	0.459131	−	1.41306i	0.0708454	−	0.218040i
$43$	4.23557			0.645919			0.322959	−	0.946413i	$-0.395322\pi$
$43$	4.23557			0.645919			0.322959	+	0.946413i	$0.395322\pi$
$44$	−6.52905	+	0.721514i	−0.984291	+	0.108772i
$45$		0			0
$46$	0.0784894	−	0.241566i	0.0115726	−	0.0356169i
$47$	5.68588	−	4.13103i	0.829371	−	0.602573i	−0.0900107	−	0.995941i	$-0.528690\pi$
$47$	5.68588	−	4.13103i	0.829371	−	0.602573i	0.919381	+	0.393368i	$0.128690\pi$
$48$	−9.38157	−	6.81611i	−1.35411	−	0.983821i
$49$	1.77436	+	5.46092i	0.253480	+	0.780131i
$50$		0			0
$51$	13.1297	+	9.53930i	1.83853	+	1.33577i
$52$	−1.91575	+	1.39187i	−0.265667	+	0.193018i
$53$	−3.34076	+	10.2818i	−0.458889	+	1.41232i	0.407618	+	0.913152i	$0.366359\pi$
$53$	−3.34076	+	10.2818i	−0.458889	+	1.41232i	−0.866508	+	0.499164i	$0.833641\pi$
$54$	−1.21337			−0.165118
$55$		0			0
$56$	−1.98078			−0.264692
$57$	4.43121	−	13.6379i	0.586928	−	1.80638i
$58$	−0.467062	+	0.339340i	−0.0613282	+	0.0445575i
$59$	3.24907	+	2.36059i	0.422993	+	0.307323i	0.778841	−	0.627221i	$-0.215808\pi$
$59$	3.24907	+	2.36059i	0.422993	+	0.307323i	−0.355848	+	0.934544i	$0.615808\pi$
$60$		0			0
$61$	−4.47500	−	13.7726i	−0.572964	−	1.76340i	−0.643008	−	0.765859i	$-0.722314\pi$
$61$	−4.47500	−	13.7726i	−0.572964	−	1.76340i	0.0700436	−	0.997544i	$-0.477686\pi$
$62$	0.145134	+	0.105446i	0.0184320	+	0.0133916i
$63$	17.0820	−	12.4108i	2.15213	−	1.56361i
$64$	−2.32918	+	7.16847i	−0.291147	+	0.896058i
$65$		0			0
$66$	1.19921	+	0.683847i	0.147612	+	0.0841758i
$67$	8.14233			0.994744			0.497372	−	0.867537i	$-0.334298\pi$
$67$	8.14233			0.994744			0.497372	+	0.867537i	$0.334298\pi$
$68$	3.32664	−	10.2384i	0.403415	−	1.24158i
$69$	4.40126	−	3.19770i	0.529850	−	0.384958i
$70$		0			0
$71$	2.63051	+	8.09589i	0.312185	+	0.960806i	0.976898	+	0.213707i	$0.0685538\pi$
$71$	2.63051	+	8.09589i	0.312185	+	0.960806i	−0.664713	+	0.747099i	$0.731446\pi$
$72$	1.01429	+	3.12167i	0.119535	+	0.367892i
$73$	6.90988	+	5.02032i	0.808740	+	0.587584i	0.913465	−	0.406917i	$-0.133396\pi$
$73$	6.90988	+	5.02032i	0.808740	+	0.587584i	−0.104725	+	0.994501i	$0.533396\pi$
$74$	−0.356488	+	0.259003i	−0.0414408	+	0.0301085i
$75$		0			0
$76$	−9.51187			−1.09109
$77$	−11.7673	+	1.30039i	−1.34101	+	0.148193i
$78$	0.497655			0.0563483
$79$	0.121752	−	0.374714i	0.0136982	−	0.0421586i	−0.943974	−	0.330020i	$-0.892944\pi$
$79$	0.121752	−	0.374714i	0.0136982	−	0.0421586i	0.957672	+	0.287862i	$0.0929444\pi$
$80$		0			0
$81$	−6.66892	−	4.84526i	−0.740992	−	0.538362i
$82$	0.276005	+	0.849457i	0.0304797	+	0.0938069i
$83$	−0.483189	−	1.48710i	−0.0530369	−	0.163231i	0.921030	−	0.389492i	$-0.127350\pi$
$83$	−0.483189	−	1.48710i	−0.0530369	−	0.163231i	−0.974067	+	0.226262i	$0.927350\pi$
$84$	−17.0777	−	12.4077i	−1.86333	−	1.35379i
$85$		0			0
$86$	−0.182460	+	0.561553i	−0.0196751	+	0.0605538i
$87$	−12.3654			−1.32571
$88$	0.373020	−	1.80221i	0.0397641	−	0.192116i
$89$	−6.90425			−0.731849			−0.365925	−	0.930645i	$-0.619247\pi$
$89$	−6.90425			−0.731849			−0.365925	+	0.930645i	$0.619247\pi$
$90$		0			0
$91$	−3.45277	+	2.50858i	−0.361949	+	0.262971i
$92$	−2.91946	−	2.12112i	−0.304375	−	0.221142i
$93$	1.18737	+	3.65434i	0.123124	+	0.378937i
$94$	0.302757	+	0.931792i	0.0312270	+	0.0961070i
$95$		0			0
$96$	3.98865	−	2.89792i	0.407089	−	0.295768i
$97$	−2.87750	+	8.85604i	−0.292166	+	0.899195i	0.691993	+	0.721905i	$0.256733\pi$
$97$	−2.87750	+	8.85604i	−0.292166	+	0.899195i	−0.984159	+	0.177290i	$0.943267\pi$
$98$	−0.800446			−0.0808572
$99$	8.07507	+	17.8793i	0.811575	+	1.79693i
$100$		0			0
$101$	−0.810256	+	2.49371i	−0.0806235	+	0.248134i	−0.983241	−	0.182309i	$-0.941643\pi$
$101$	−0.810256	+	2.49371i	−0.0806235	+	0.248134i	0.902618	+	0.430443i	$0.141643\pi$
$102$	−1.83032	+	1.32981i	−0.181229	+	0.131671i
$103$	−5.34404	−	3.88267i	−0.526564	−	0.382571i	0.292507	−	0.956263i	$-0.405510\pi$
$103$	−5.34404	−	3.88267i	−0.526564	−	0.382571i	−0.819071	+	0.573692i	$0.805510\pi$
$104$	−0.205018	−	0.630980i	−0.0201037	−	0.0618727i
$105$		0			0
$106$	−1.21925	−	0.885839i	−0.118424	−	0.0860403i
$107$	11.3766	−	8.26556i	1.09981	−	0.799062i	0.118785	−	0.992920i	$-0.462100\pi$
$107$	11.3766	−	8.26556i	1.09981	−	0.799062i	0.981030	+	0.193858i	$0.0621001\pi$
$108$	−5.32710	+	16.3951i	−0.512601	+	1.57762i
$109$	12.3514			1.18305			0.591525	−	0.806286i	$-0.298526\pi$
$109$	12.3514			1.18305			0.591525	+	0.806286i	$0.298526\pi$
$110$		0			0
$111$	−9.43795			−0.895810
$112$	−4.28405	+	13.1850i	−0.404805	+	1.24586i
$113$	2.88710	−	2.09760i	0.271596	−	0.197326i	−0.443648	−	0.896201i	$-0.646316\pi$
$113$	2.88710	−	2.09760i	0.271596	−	0.197326i	0.715243	+	0.698875i	$0.246316\pi$
$114$	1.61722	+	1.17498i	0.151467	+	0.110047i
$115$		0			0
$116$	2.53464	+	7.80081i	0.235335	+	0.724287i
$117$	5.72154	+	4.15694i	0.528956	+	0.384309i
$118$	−0.452931	+	0.329074i	−0.0416957	+	0.0302937i
$119$	5.99563	−	18.4526i	0.549618	−	1.69155i
$120$		0			0
$121$	1.03287	−	10.9514i	0.0938974	−	0.995582i
$122$	2.01875			0.182769
$123$	−5.91165	+	18.1942i	−0.533035	+	1.64051i
$124$	2.06199	−	1.49812i	0.185172	−	0.134535i
$125$		0			0
$126$	0.909570	+	2.79937i	0.0810309	+	0.249388i
$127$	1.94047	+	5.97215i	0.172189	+	0.529943i	0.999494	−	0.0318100i	$-0.0101271\pi$
$127$	1.94047	+	5.97215i	0.172189	+	0.529943i	−0.827305	+	0.561753i	$0.810127\pi$
$128$	−3.52179	−	2.55873i	−0.311285	−	0.226162i
$129$	−10.2314	+	7.43352i	−0.900821	+	0.654485i
$130$		0			0
$131$	18.4755			1.61421			0.807105	−	0.590408i	$-0.201033\pi$
$131$	18.4755			1.61421			0.807105	+	0.590408i	$0.201033\pi$
$132$	14.5052	−	13.2015i	1.26251	−	1.14904i
$133$	−17.1433			−1.48651
$134$	−0.350755	+	1.07951i	−0.0303006	+	0.0932557i
$135$		0			0
$136$	2.44011	+	1.77284i	0.209238	+	0.152020i
$137$	−1.29063	−	3.97216i	−0.110266	−	0.339364i	0.880664	−	0.473741i	$-0.157097\pi$
$137$	−1.29063	−	3.97216i	−0.110266	−	0.339364i	−0.990930	+	0.134377i	$0.957097\pi$
$138$	0.234355	+	0.721271i	0.0199496	+	0.0613987i
$139$	2.20927	+	1.60513i	0.187388	+	0.136145i	0.677524	−	0.735501i	$-0.263053\pi$
$139$	2.20927	+	1.60513i	0.187388	+	0.136145i	−0.490136	+	0.871646i	$0.663053\pi$
$140$		0			0
$141$	−6.48464	+	19.9577i	−0.546105	+	1.68074i
$142$	−1.18667			−0.0995834
$143$	−1.63221	−	3.61392i	−0.136492	−	0.302211i
$144$	22.9730			1.91442
$145$		0			0
$146$	−0.963258	+	0.699848i	−0.0797198	+	0.0579199i
$147$	−13.8701	−	10.0772i	−1.14399	−	0.831156i
$148$	1.93458	+	5.95401i	0.159021	+	0.489417i
$149$	−5.48466	−	16.8800i	−0.449321	−	1.38287i	−0.877675	−	0.479256i	$-0.840906\pi$
$149$	−5.48466	−	16.8800i	−0.449321	−	1.38287i	0.428354	−	0.903611i	$-0.359094\pi$
$150$		0			0
$151$	1.17615	−	0.854522i	0.0957136	−	0.0695400i	−0.538899	−	0.842370i	$-0.681160\pi$
$151$	1.17615	−	0.854522i	0.0957136	−	0.0695400i	0.634613	+	0.772830i	$0.281160\pi$
$152$	0.823524	−	2.53455i	0.0667966	−	0.205579i
$153$	−32.1512			−2.59927
$154$	0.334507	−	1.61614i	0.0269554	−	0.130232i
$155$		0			0
$156$	2.18488	−	6.72437i	0.174930	−	0.538380i
$157$	−2.71585	+	1.97318i	−0.216749	+	0.157477i	−0.690862	−	0.722987i	$-0.742769\pi$
$157$	−2.71585	+	1.97318i	−0.216749	+	0.157477i	0.474113	+	0.880464i	$0.342769\pi$
$158$	0.0444348	+	0.0322838i	0.00353504	+	0.00256836i
$159$	−9.97492	−	30.6996i	−0.791062	−	2.43464i
$160$		0			0
$161$	−5.26177	−	3.82290i	−0.414685	−	0.301287i
$162$	0.929669	−	0.675444i	0.0730417	−	0.0530679i
$163$	2.10431	−	6.47640i	0.164822	−	0.507271i	−0.834201	−	0.551461i	$-0.814071\pi$
$163$	2.10431	−	6.47640i	0.164822	−	0.507271i	0.999023	+	0.0441897i	$0.0140706\pi$
$164$	12.6897			0.990901
$165$		0			0
$166$	0.217975			0.0169182
$167$	−6.06962	+	18.6804i	−0.469681	+	1.44553i	0.383318	+	0.923616i	$0.374781\pi$
$167$	−6.06962	+	18.6804i	−0.469681	+	1.44553i	−0.852999	+	0.521913i	$0.825219\pi$
$168$	4.78472	−	3.47630i	0.369149	−	0.268203i
$169$	9.36073	+	6.80097i	0.720056	+	0.523152i
$170$		0			0
$171$	8.77853	+	27.0175i	0.671311	+	2.06608i
$172$	6.78671	+	4.93083i	0.517482	+	0.375972i
$173$	−0.189438	+	0.137634i	−0.0144027	+	0.0104642i	−0.594963	−	0.803753i	$-0.702833\pi$
$173$	−0.189438	+	0.137634i	−0.0144027	+	0.0104642i	0.580561	+	0.814217i	$0.302833\pi$
$174$	0.532675	−	1.63941i	0.0403820	−	0.124283i
$175$		0			0
$176$	−11.1895	−	6.38084i	−0.843444	−	0.480974i
$177$	−11.9913			−0.901319
$178$	0.297421	−	0.915367i	0.0222926	−	0.0686097i
$179$	−13.7416	+	9.98383i	−1.02709	+	0.746227i	−0.967725	−	0.252010i	$-0.918909\pi$
$179$	−13.7416	+	9.98383i	−1.02709	+	0.746227i	−0.0593679	+	0.998236i	$0.518909\pi$
$180$		0			0
$181$	−5.36003	−	16.4965i	−0.398408	−	1.22617i	−0.926275	−	0.376847i	$-0.877008\pi$
$181$	−5.36003	−	16.4965i	−0.398408	−	1.22617i	0.527867	−	0.849327i	$-0.322992\pi$
$182$	−0.183851	−	0.565834i	−0.0136279	−	0.0419424i
$183$	34.9809	+	25.4151i	2.58586	+	1.87874i
$184$	0.817958	−	0.594282i	0.0603007	−	0.0438110i
$185$		0			0
$186$	−0.535642			−0.0392752
$187$	15.6600	+	8.93012i	1.14517	+	0.653035i
$188$	13.9197			1.01520
$189$	−9.60107	+	29.5490i	−0.698375	+	2.14938i
$190$		0			0
$191$	−16.8029	−	12.2080i	−1.21582	−	0.883342i	−0.220070	−	0.975484i	$-0.570629\pi$
$191$	−16.8029	−	12.2080i	−1.21582	−	0.883342i	−0.995746	+	0.0921420i	$0.970629\pi$
$192$	−6.95450	−	21.4037i	−0.501898	−	1.54468i
$193$	−2.63050	−	8.09586i	−0.189348	−	0.582752i	0.810648	−	0.585533i	$-0.199115\pi$
$193$	−2.63050	−	8.09586i	−0.189348	−	0.582752i	−0.999996	+	0.00278083i	$0.999115\pi$
$194$	−1.05018	−	0.763000i	−0.0753985	−	0.0547802i
$195$		0			0
$196$	−3.51424	+	10.8157i	−0.251017	+	0.772551i
$197$	2.60251			0.185421			0.0927106	−	0.995693i	$-0.470447\pi$
$197$	2.60251			0.185421			0.0927106	+	0.995693i	$0.470447\pi$
$198$	−2.71829	+	0.300394i	−0.193181	+	0.0213481i
$199$	−8.77731			−0.622207			−0.311104	−	0.950376i	$-0.600699\pi$
$199$	−8.77731			−0.622207			−0.311104	+	0.950376i	$0.600699\pi$
$200$		0			0
$201$	−19.6684	+	14.2900i	−1.38730	+	1.00794i
$202$	−0.295713	−	0.214848i	−0.0208063	−	0.0151167i
$203$	4.56819	+	14.0594i	0.320624	+	0.986780i
$204$	9.93275	+	30.5699i	0.695432	+	2.14032i
$205$		0			0
$206$	0.744976	−	0.541256i	0.0519049	−	0.0377111i
$207$	−3.33044	+	10.2500i	−0.231482	+	0.712427i
$208$	−4.64351			−0.321970
$209$	3.22843	−	15.5978i	0.223315	−	1.07892i
$210$		0			0
$211$	3.34024	−	10.2802i	0.229952	−	0.707718i	−0.767799	−	0.640690i	$-0.778648\pi$
$211$	3.34024	−	10.2802i	0.229952	−	0.707718i	0.997751	−	0.0670281i	$-0.0213517\pi$
$212$	−17.3225	+	12.5855i	−1.18971	+	0.864378i
$213$	−20.5627	−	14.9397i	−1.40893	−	1.02365i
$214$	0.605771	+	1.86437i	0.0414097	+	0.127446i
$215$		0			0
$216$	−3.90746	−	2.83893i	−0.265869	−	0.193165i
$217$	3.71633	−	2.70007i	0.252281	−	0.183293i
$218$	−0.532073	+	1.63755i	−0.0360366	+	0.110909i
$219$	−25.5021			−1.72327
$220$		0			0
$221$	6.49870			0.437150
$222$	0.406567	−	1.25129i	0.0272870	−	0.0839808i
$223$	6.51146	−	4.73085i	0.436040	−	0.316801i	−0.348020	−	0.937487i	$-0.613146\pi$
$223$	6.51146	−	4.73085i	0.436040	−	0.316801i	0.784059	+	0.620686i	$0.213146\pi$
$224$	−4.76848	−	3.46450i	−0.318607	−	0.231482i
$225$		0			0
$226$	0.153730	+	0.473133i	0.0102260	+	0.0314724i
$227$	−16.7624	−	12.1786i	−1.11256	−	0.808323i	−0.129496	−	0.991580i	$-0.541336\pi$
$227$	−16.7624	−	12.1786i	−1.11256	−	0.808323i	−0.983065	+	0.183257i	$0.941336\pi$
$228$	22.9767	−	16.6935i	1.52167	−	1.10556i
$229$	2.47597	−	7.62024i	0.163616	−	0.503560i	−0.835315	−	0.549771i	$-0.814715\pi$
$229$	2.47597	−	7.62024i	0.163616	−	0.503560i	0.998932	+	0.0462117i	$0.0147149\pi$
$230$		0			0
$231$	26.1427	−	23.7931i	1.72007	−	1.56547i
$232$	−2.29806			−0.150875
$233$	7.86737	−	24.2133i	0.515408	−	1.58626i	−0.267129	−	0.963661i	$-0.586075\pi$
$233$	7.86737	−	24.2133i	0.515408	−	1.58626i	0.782538	−	0.622603i	$-0.213925\pi$
$234$	−0.797601	+	0.579491i	−0.0521408	+	0.0378825i
$235$		0			0
$236$	2.45795	+	7.56480i	0.159999	+	0.492427i
$237$	0.363529	+	1.11883i	0.0236137	+	0.0726756i
$238$	2.18818	+	1.58980i	0.141838	+	0.103052i
$239$	−0.442580	+	0.321553i	−0.0286281	+	0.0207995i	−0.602007	−	0.798491i	$-0.705632\pi$
$239$	−0.442580	+	0.321553i	−0.0286281	+	0.0207995i	0.573379	+	0.819290i	$0.305632\pi$
$240$		0			0
$241$	21.9600			1.41457			0.707285	−	0.706929i	$-0.249920\pi$
$241$	21.9600			1.41457			0.707285	+	0.706929i	$0.249920\pi$
$242$	1.40745	+	0.608702i	0.0904740	+	0.0391289i
$243$	−1.49919			−0.0961728
$244$	8.86303	−	27.2776i	0.567397	−	1.74627i
$245$		0			0
$246$	−2.15753	−	1.56754i	−0.137559	−	0.0999424i
$247$	−1.77440	−	5.46103i	−0.112902	−	0.347477i
$248$	0.220668	+	0.679145i	0.0140124	+	0.0431257i
$249$	3.77708	+	2.74421i	0.239362	+	0.173907i
$250$		0			0
$251$	1.87041	−	5.75652i	0.118059	−	0.363348i	−0.874514	−	0.485001i	$-0.838819\pi$
$251$	1.87041	−	5.75652i	0.118059	−	0.363348i	0.992573	+	0.121653i	$0.0388194\pi$
$252$	41.8187			2.63433
$253$	4.46916	−	4.06749i	0.280974	−	0.255721i
$254$	−0.875381			−0.0549263
$255$		0			0
$256$	−11.7048	+	8.50402i	−0.731548	+	0.531501i
$257$	2.47369	+	1.79724i	0.154305	+	0.112109i	0.662259	−	0.749275i	$-0.269598\pi$
$257$	2.47369	+	1.79724i	0.154305	+	0.112109i	−0.507954	+	0.861384i	$0.669598\pi$
$258$	−0.544792	−	1.67670i	−0.0339172	−	0.104387i
$259$	3.48670	+	10.7310i	0.216653	+	0.666789i
$260$		0			0
$261$	19.8182	−	14.3988i	1.22672	−	0.891263i
$262$	−0.795885	+	2.44948i	−0.0491699	+	0.151330i
$263$	−18.1365			−1.11835			−0.559174	−	0.829050i	$-0.688882\pi$
$263$	−18.1365			−1.11835			−0.559174	+	0.829050i	$0.688882\pi$
$264$	2.26185	+	5.00803i	0.139207	+	0.308223i
$265$		0			0
$266$	0.738498	−	2.27286i	0.0452802	−	0.139358i
$267$	16.6778	−	12.1171i	1.02066	−	0.741555i
$268$	13.0466	+	9.47888i	0.796945	+	0.579015i
$269$	5.38987	+	16.5883i	0.328626	+	1.01141i	0.969777	+	0.243993i	$0.0784574\pi$
$269$	5.38987	+	16.5883i	0.328626	+	1.01141i	−0.641151	+	0.767415i	$0.721543\pi$
$270$		0			0
$271$	5.70006	+	4.14134i	0.346254	+	0.251568i	0.747296	−	0.664492i	$-0.231352\pi$
$271$	5.70006	+	4.14134i	0.346254	+	0.251568i	−0.401042	+	0.916060i	$0.631352\pi$
$272$	17.0784	−	12.4082i	1.03553	−	0.752355i
$273$	3.93782	−	12.1194i	0.238328	−	0.733497i
$274$	0.582227			0.0351736
$275$		0			0
$276$	10.7748			0.648567
$277$	5.72446	−	17.6181i	0.343949	−	1.05857i	−0.618195	−	0.786025i	$-0.712136\pi$
$277$	5.72446	−	17.6181i	0.343949	−	1.05857i	0.962144	−	0.272542i	$-0.0878643\pi$
$278$	−0.307979	+	0.223760i	−0.0184714	+	0.0134202i
$279$	−6.15828	−	4.47425i	−0.368687	−	0.267866i
$280$		0			0
$281$	6.49461	+	19.9884i	0.387436	+	1.19241i	0.934698	+	0.355444i	$0.115670\pi$
$281$	6.49461	+	19.9884i	0.387436	+	1.19241i	−0.547262	+	0.836962i	$0.684330\pi$
$282$	−2.36665	−	1.71947i	−0.140932	−	0.102393i
$283$	1.31449	−	0.955030i	0.0781381	−	0.0567706i	−0.548030	−	0.836458i	$-0.684622\pi$
$283$	1.31449	−	0.955030i	0.0781381	−	0.0567706i	0.626169	+	0.779688i	$0.284622\pi$
$284$	−5.20991	+	16.0345i	−0.309151	+	0.951470i
$285$		0			0
$286$	0.549446	−	0.0607183i	0.0324894	−	0.00359035i
$287$	22.8708			1.35002
$288$	−3.01821	+	9.28911i	−0.177850	+	0.547366i
$289$	−10.1483	+	7.37316i	−0.596957	+	0.433715i
$290$		0			0
$291$	−8.59170	−	26.4425i	−0.503654	−	1.55009i
$292$	5.22738	+	16.0882i	0.305910	+	0.941493i
$293$	−10.1991	−	7.41008i	−0.595838	−	0.432901i	0.248561	−	0.968616i	$-0.420042\pi$
$293$	−10.1991	−	7.41008i	−0.595838	−	0.432901i	−0.844399	+	0.535715i	$0.820042\pi$
$294$	1.93354	−	1.40480i	0.112766	−	0.0819295i
$295$		0			0
$296$	−1.75401			−0.101950
$297$	−25.0771	−	14.3002i	−1.45512	−	0.829782i
$298$	2.47423			0.143328
$299$	0.673179	−	2.07183i	0.0389309	−	0.119817i
$300$		0			0
$301$	12.2317	+	8.88687i	0.705025	+	0.512230i
$302$	0.0626267	+	0.192745i	0.00360376	+	0.0110912i
$303$	−2.41928	−	7.44578i	−0.138984	−	0.427749i
$304$	−15.0900	−	10.9635i	−0.865469	−	0.628800i
$305$		0			0
$306$	1.38501	−	4.26262i	0.0791757	−	0.243678i
$307$	−22.6055			−1.29017			−0.645083	−	0.764112i	$-0.723177\pi$
$307$	−22.6055			−1.29017			−0.645083	+	0.764112i	$0.723177\pi$
$308$	−20.3688	−	11.6153i	−1.16062	−	0.661843i
$309$	19.7231			1.12201
$310$		0			0
$311$	15.0909	−	10.9642i	0.855729	−	0.621723i	−0.0709908	−	0.997477i	$-0.522616\pi$
$311$	15.0909	−	10.9642i	0.855729	−	0.621723i	0.926720	+	0.375754i	$0.122616\pi$
$312$	1.60262	+	1.16437i	0.0907305	+	0.0659196i
$313$	5.40298	+	16.6286i	0.305394	+	0.939907i	0.979530	+	0.201299i	$0.0645163\pi$
$313$	5.40298	+	16.6286i	0.305394	+	0.939907i	−0.674136	+	0.738608i	$0.735484\pi$
$314$	−0.144612	−	0.445069i	−0.00816091	−	0.0251167i
$315$		0			0
$316$	0.631307	−	0.458671i	0.0355138	−	0.0258023i
$317$	−3.45627	+	10.6373i	−0.194123	+	0.597450i	0.805862	+	0.592103i	$0.201702\pi$
$317$	−3.45627	+	10.6373i	−0.194123	+	0.597450i	−0.999986	+	0.00534745i	$0.998298\pi$
$318$	4.49987			0.252340
$319$	−13.6523	+	1.50869i	−0.764380	+	0.0844703i
$320$		0			0
$321$	−12.9748	+	39.9322i	−0.724181	+	2.22880i
$322$	0.733507	−	0.532924i	0.0408767	−	0.0296987i
$323$	21.1188	+	15.3437i	1.17508	+	0.853745i
$324$	−5.04510	−	15.5272i	−0.280283	−	0.862624i
$325$		0			0
$326$	0.767994	+	0.557980i	0.0425353	+	0.0309037i
$327$	−29.8358	+	21.6770i	−1.64992	+	1.19874i
$328$	−1.09866	+	3.38132i	−0.0606632	+	0.186702i
$329$	25.0875			1.38312
$330$		0			0
$331$	−25.7621			−1.41602			−0.708008	−	0.706205i	$-0.750406\pi$
$331$	−25.7621			−1.41602			−0.708008	+	0.706205i	$0.750406\pi$
$332$	0.956988	−	2.94531i	0.0525215	−	0.161645i
$333$	15.1264	−	10.9900i	0.828920	−	0.602246i
$334$	−2.21518	−	1.60942i	−0.121209	−	0.0880637i
$335$		0			0
$336$	−12.7914	−	39.3679i	−0.697828	−	2.14769i
$337$	−9.30216	−	6.75842i	−0.506721	−	0.368154i	0.304857	−	0.952398i	$-0.401391\pi$
$337$	−9.30216	−	6.75842i	−0.506721	−	0.368154i	−0.811578	+	0.584244i	$0.801391\pi$
$338$	−1.30492	+	0.948077i	−0.0709780	+	0.0515686i
$339$	−3.29269	+	10.1339i	−0.178834	+	0.550395i
$340$		0			0
$341$	1.75680	+	3.88978i	0.0951359	+	0.210643i
$342$	−3.96015			−0.214141
$343$	1.38771	−	4.27093i	0.0749293	−	0.230609i
$344$	−1.90146	+	1.38149i	−0.102520	+	0.0744850i
$345$		0			0
$346$	−0.0100870	−	0.0310447i	−0.000542282	−	0.00166897i
$347$	0.267572	+	0.823501i	0.0143640	+	0.0442079i	0.957982	−	0.286830i	$-0.0926014\pi$
$347$	0.267572	+	0.823501i	0.0143640	+	0.0442079i	−0.943618	+	0.331037i	$0.892601\pi$
$348$	−19.8132	−	14.3951i	−1.06210	−	0.771660i
$349$	−14.3937	+	10.4576i	−0.770476	+	0.559784i	−0.902106	−	0.431515i	$-0.857979\pi$
$349$	−14.3937	+	10.4576i	−0.770476	+	0.559784i	0.131630	+	0.991299i	$0.457979\pi$
$350$		0			0
$351$	−10.4067			−0.555466
$352$	4.05018	−	3.68616i	0.215875	−	0.196473i
$353$	−1.11550			−0.0593723			−0.0296862	−	0.999559i	$-0.509451\pi$
$353$	−1.11550			−0.0593723			−0.0296862	+	0.999559i	$0.509451\pi$
$354$	0.516559	−	1.58981i	0.0274548	−	0.0844972i
$355$		0			0
$356$	−11.0628	−	8.03757i	−0.586325	−	0.425990i
$357$	17.9019	+	55.0963i	0.947467	+	2.91600i
$358$	−0.731701	−	2.25194i	−0.0386716	−	0.119019i
$359$	−1.22945	−	0.893247i	−0.0648878	−	0.0471438i	0.554869	−	0.831938i	$-0.312769\pi$
$359$	−1.22945	−	0.893247i	−0.0648878	−	0.0471438i	−0.619756	+	0.784794i	$0.712769\pi$
$360$		0			0
$361$	1.25614	−	3.86601i	0.0661127	−	0.203474i
$362$	2.41801			0.127088
$363$	16.7250	+	28.2667i	0.877832	+	1.48362i
$364$	−8.45278			−0.443046
$365$		0			0
$366$	−4.87645	+	3.54295i	−0.254896	+	0.185193i
$367$	−8.59670	−	6.24587i	−0.448744	−	0.326032i	0.340356	−	0.940297i	$-0.389453\pi$
$367$	−8.59670	−	6.24587i	−0.448744	−	0.326032i	−0.789100	+	0.614265i	$0.789453\pi$
$368$	−2.18672	−	6.73003i	−0.113991	−	0.350827i
$369$	−11.7114	−	36.0439i	−0.609670	−	1.87637i
$370$		0			0
$371$	−31.2204	+	22.6830i	−1.62088	+	1.17764i
$372$	−2.35166	+	7.23765i	−0.121928	+	0.375255i
$373$	27.9435			1.44686			0.723429	−	0.690399i	$-0.242565\pi$
$373$	27.9435			1.44686			0.723429	+	0.690399i	$0.242565\pi$
$374$	−1.85856	+	1.69152i	−0.0961038	+	0.0874664i
$375$		0			0
$376$	−1.20515	+	3.70906i	−0.0621507	+	0.191280i
$377$	−4.00584	+	2.91041i	−0.206311	+	0.149894i
$378$	−3.50403	−	2.54582i	−0.180228	−	0.130943i
$379$	5.76969	+	17.7573i	0.296369	+	0.912130i	0.982758	+	0.184896i	$0.0591948\pi$
$379$	5.76969	+	17.7573i	0.296369	+	0.912130i	−0.686389	+	0.727235i	$0.740805\pi$
$380$		0			0
$381$	−15.1686	−	11.0206i	−0.777111	−	0.564605i
$382$	2.34238	−	1.70184i	0.119847	−	0.0870736i
$383$	−6.69393	+	20.6018i	−0.342044	+	1.05270i	0.621104	+	0.783729i	$0.286685\pi$
$383$	−6.69393	+	20.6018i	−0.342044	+	1.05270i	−0.963147	+	0.268974i	$0.913315\pi$
$384$	12.9978			0.663290
$385$		0			0
$386$	1.18667			0.0603998
$387$	7.74208	−	23.8277i	0.393552	−	1.21123i
$388$	−14.9204	+	10.8403i	−0.757468	+	0.550333i
$389$	30.3224	+	22.0305i	1.53740	+	1.11699i	0.951937	+	0.306294i	$0.0990892\pi$
$389$	30.3224	+	22.0305i	1.53740	+	1.11699i	0.585468	+	0.810696i	$0.300911\pi$
$390$		0			0
$391$	3.06036	+	9.41883i	0.154769	+	0.476331i
$392$	−2.57771	−	1.87282i	−0.130194	−	0.0945916i
$393$	−44.6289	+	32.4248i	−2.25123	+	1.63562i
$394$	−0.112111	+	0.345042i	−0.00564806	+	0.0173829i
$395$		0			0
$396$	−7.87531	+	38.0487i	−0.395749	+	1.91202i
$397$	−18.3084			−0.918873			−0.459437	−	0.888211i	$-0.651949\pi$
$397$	−18.3084			−0.918873			−0.459437	+	0.888211i	$0.651949\pi$
$398$	0.378109	−	1.16370i	0.0189529	−	0.0583309i
$399$	41.4110	−	30.0868i	2.07314	−	1.50623i
$400$		0			0
$401$	4.04434	+	12.4472i	0.201965	+	0.621583i	0.999824	+	0.0187401i	$0.00596551\pi$
$401$	4.04434	+	12.4472i	0.201965	+	0.621583i	−0.797860	+	0.602843i	$0.794034\pi$
$402$	−1.04729	−	3.22323i	−0.0522341	−	0.160760i
$403$	1.24477	+	0.904376i	0.0620063	+	0.0450502i
$404$	−4.20133	+	3.05245i	−0.209024	+	0.151865i
$405$		0			0
$406$	−2.06079			−0.102275
$407$	−10.4202	+	1.15151i	−0.516509	+	0.0570785i
$408$	−9.00566			−0.445846
$409$	6.57096	−	20.2233i	0.324913	−	0.999980i	−0.646567	−	0.762857i	$-0.723796\pi$
$409$	6.57096	−	20.2233i	0.324913	−	0.999980i	0.971480	−	0.237122i	$-0.0762042\pi$
$410$		0			0
$411$	10.0888	+	7.32997i	0.497646	+	0.361561i
$412$	−4.04281	−	12.4425i	−0.199175	−	0.612998i
$413$	4.42998	+	13.6341i	0.217985	+	0.670889i
$414$	−1.21548	−	0.883101i	−0.0597378	−	0.0434021i
$415$		0			0
$416$	0.610069	−	1.87760i	0.0299111	−	0.0920568i
$417$	−8.15371			−0.399289
$418$	1.92889	+	1.09995i	0.0943450	+	0.0538002i
$419$	−37.5627			−1.83506			−0.917528	−	0.397670i	$-0.869819\pi$
$419$	−37.5627			−1.83506			−0.917528	+	0.397670i	$0.869819\pi$
$420$		0			0
$421$	7.41340	−	5.38615i	0.361307	−	0.262505i	−0.392290	−	0.919842i	$-0.628317\pi$
$421$	7.41340	−	5.38615i	0.361307	−	0.262505i	0.753597	+	0.657337i	$0.228317\pi$
$422$	1.21906	+	0.885700i	0.0593430	+	0.0431152i
$423$	−12.8465	−	39.5375i	−0.624619	−	1.92238i
$424$	−1.85380	−	5.70542i	−0.0900286	−	0.277079i
$425$		0			0
$426$	2.86650	−	2.08263i	0.138882	−	0.100904i
$427$	15.9739	−	49.1626i	0.773030	−	2.37914i
$428$	27.8512			1.34624
$429$	10.2852	+	5.86514i	0.496575	+	0.283172i
$430$		0			0
$431$	8.63312	−	26.5700i	0.415843	−	1.27983i	−0.495653	−	0.868521i	$-0.665071\pi$
$431$	8.63312	−	26.5700i	0.415843	−	1.27983i	0.911495	−	0.411311i	$-0.134929\pi$
$432$	−27.3484	+	19.8697i	−1.31580	+	0.955984i
$433$	−16.4642	−	11.9620i	−0.791221	−	0.574856i	0.117105	−	0.993120i	$-0.462639\pi$
$433$	−16.4642	−	11.9620i	−0.791221	−	0.574856i	−0.908325	+	0.418264i	$0.862639\pi$
$434$	0.197884	+	0.609025i	0.00949875	+	0.0292342i
$435$		0			0
$436$	19.7908	+	14.3789i	0.947808	+	0.688623i
$437$	7.07930	−	5.14341i	0.338649	−	0.246043i
$438$	1.09858	−	3.38108i	0.0524921	−	0.161554i
$439$	−5.87262			−0.280285			−0.140142	−	0.990131i	$-0.544756\pi$
$439$	−5.87262			−0.280285			−0.140142	+	0.990131i	$0.544756\pi$
$440$		0			0
$441$	33.9643			1.61735
$442$	−0.279951	+	0.861599i	−0.0133159	+	0.0409821i
$443$	−29.2219	+	21.2309i	−1.38837	+	1.00871i	−0.392332	+	0.919824i	$0.628332\pi$
$443$	−29.2219	+	21.2309i	−1.38837	+	1.00871i	−0.996042	+	0.0888891i	$0.971668\pi$
$444$	−15.1225	−	10.9872i	−0.717684	−	0.521428i
$445$		0			0
$446$	0.346717	+	1.06709i	0.0164175	+	0.0505280i
$447$	42.8735	+	31.1494i	2.02784	+	1.47332i
$448$	−21.7668	+	15.8145i	−1.02839	+	0.747167i
$449$	2.11744	−	6.51680i	0.0999281	−	0.307547i	−0.888579	−	0.458724i	$-0.848306\pi$
$449$	2.11744	−	6.51680i	0.0999281	−	0.307547i	0.988507	+	0.151177i	$0.0483065\pi$
$450$		0			0
$451$	−4.30703	+	20.8089i	−0.202810	+	0.979855i
$452$	7.06796			0.332449
$453$	−1.34138	+	4.12833i	−0.0630233	+	0.193966i
$454$	2.33674	−	1.69774i	0.109668	−	0.0796788i
$455$		0			0
$456$	2.45889	+	7.56770i	0.115148	+	0.354390i
$457$	−6.58590	−	20.2693i	−0.308075	−	0.948158i	−0.978512	−	0.206191i	$-0.933893\pi$
$457$	−6.58590	−	20.2693i	−0.308075	−	0.948158i	0.670437	−	0.741967i	$-0.266107\pi$
$458$	0.903634	+	0.656528i	0.0422240	+	0.0306776i
$459$	38.2747	−	27.8082i	1.78651	−	1.29797i
$460$		0			0
$461$	−29.0126			−1.35125			−0.675626	−	0.737244i	$-0.736127\pi$
$461$	−29.0126			−1.35125			−0.675626	+	0.737244i	$0.736127\pi$
$462$	2.02832	+	4.49097i	0.0943661	+	0.208939i
$463$	−17.8392			−0.829057			−0.414528	−	0.910036i	$-0.636053\pi$
$463$	−17.8392			−0.829057			−0.414528	+	0.910036i	$0.636053\pi$
$464$	−4.97028	+	15.2969i	−0.230739	+	0.710143i
$465$		0			0
$466$	2.87129	+	2.08612i	0.133010	+	0.0966374i
$467$	−1.23677	−	3.80640i	−0.0572311	−	0.176139i	0.918354	−	0.395759i	$-0.129518\pi$
$467$	−1.23677	−	3.80640i	−0.0572311	−	0.176139i	−0.975586	+	0.219620i	$0.929518\pi$
$468$	4.32840	+	13.3214i	0.200080	+	0.615784i
$469$	23.5139	+	17.0838i	1.08577	+	0.788858i
$470$		0			0
$471$	3.09738	−	9.53275i	0.142720	−	0.439246i
$472$	−2.22853			−0.102577
$473$	−10.3892	+	9.45545i	−0.477695	+	0.434762i
$474$	−0.163994			−0.00753252
$475$		0			0
$476$	31.0885	−	22.5871i	1.42494	−	1.03528i
$477$	51.7350	+	37.5877i	2.36878	+	1.72102i
$478$	−0.0235662	−	0.0725292i	−0.00107789	−	0.00331741i
$479$	−0.372018	−	1.14495i	−0.0169979	−	0.0523143i	0.942198	−	0.335057i	$-0.108756\pi$
$479$	−0.372018	−	1.14495i	−0.0169979	−	0.0523143i	−0.959196	+	0.282743i	$0.908756\pi$
$480$		0			0
$481$	−3.05748	+	2.22139i	−0.139409	+	0.101287i
$482$	−0.945992	+	2.91146i	−0.0430888	+	0.132614i
$483$	19.4195			0.883617
$484$	14.4040	−	16.3451i	0.654729	−	0.742961i
$485$		0			0
$486$	0.0645818	−	0.198762i	0.00292949	−	0.00901605i
$487$	34.1902	−	24.8406i	1.54930	−	1.12564i	0.605159	−	0.796105i	$-0.293109\pi$
$487$	34.1902	−	24.8406i	1.54930	−	1.12564i	0.944145	−	0.329531i	$-0.106891\pi$
$488$	6.50108	+	4.72331i	0.294290	+	0.213814i
$489$	6.28309	+	19.3374i	0.284131	+	0.874466i
$490$		0			0
$491$	−14.7908	−	10.7462i	−0.667500	−	0.484967i	0.201687	−	0.979450i	$-0.435358\pi$
$491$	−14.7908	−	10.7462i	−0.667500	−	0.484967i	−0.869188	+	0.494483i	$0.835358\pi$
$492$	−30.6530	+	22.2707i	−1.38194	+	1.00404i
$493$	6.95602	−	21.4084i	0.313283	−	0.964187i
$494$	0.800462			0.0360145
$495$		0			0
$496$	4.99796			0.224415
$497$	−9.38985	+	28.8990i	−0.421192	+	1.29630i
$498$	−0.526536	+	0.382551i	−0.0235947	+	0.0171425i
$499$	−18.3522	−	13.3336i	−0.821557	−	0.596896i	0.0956011	−	0.995420i	$-0.469523\pi$
$499$	−18.3522	−	13.3336i	−0.821557	−	0.596896i	−0.917158	+	0.398524i	$0.869523\pi$
$500$		0			0
$501$	−18.1228	−	55.7762i	−0.809666	−	2.49190i
$502$	0.682627	+	0.495958i	0.0304671	+	0.0221357i
$503$	26.1108	−	18.9706i	1.16422	−	0.845859i	0.173919	−	0.984760i	$-0.444357\pi$
$503$	26.1108	−	18.9706i	1.16422	−	0.845859i	0.990306	+	0.138901i	$0.0443570\pi$
$504$	−3.62060	+	11.1431i	−0.161274	+	0.496352i
$505$		0			0
$506$	0.346746	+	0.767741i	0.0154148	+	0.0341303i
$507$	−34.5474			−1.53430
$508$	−3.84323	+	11.8282i	−0.170516	+	0.524794i
$509$	−17.8771	+	12.9885i	−0.792390	+	0.575705i	−0.908672	−	0.417512i	$-0.862902\pi$
$509$	−17.8771	+	12.9885i	−0.792390	+	0.575705i	0.116282	+	0.993216i	$0.462902\pi$
$510$		0			0
$511$	9.42134	+	28.9959i	0.416776	+	1.28270i
$512$	−3.31365	−	10.1984i	−0.146444	−	0.450709i
$513$	−33.8184	−	24.5705i	−1.49312	−	1.08481i
$514$	−0.344841	+	0.250541i	−0.0152103	+	0.0110509i
$515$		0			0
$516$	−25.0475			−1.10266
$517$	−4.72449	+	22.8259i	−0.207783	+	1.00388i
$518$	−1.57291			−0.0691098
$519$	0.216050	−	0.664934i	0.00948355	−	0.0291874i
$520$		0			0
$521$	13.7909	+	10.0196i	0.604189	+	0.438969i	0.847363	−	0.531014i	$-0.178189\pi$
$521$	13.7909	+	10.0196i	0.604189	+	0.438969i	−0.243175	+	0.969983i	$0.578189\pi$
$522$	1.05527	+	3.24778i	0.0461878	+	0.142151i
$523$	−6.17828	−	19.0148i	−0.270157	−	0.831459i	−0.990460	−	0.137799i	$-0.955997\pi$
$523$	−6.17828	−	19.0148i	−0.270157	−	0.831459i	0.720303	−	0.693660i	$-0.244003\pi$
$524$	29.6035	+	21.5082i	1.29323	+	0.939589i
$525$		0			0
$526$	0.781285	−	2.40455i	0.0340657	−	0.104843i
$527$	−6.99476			−0.304697
$528$	38.2277	−	4.22448i	1.66365	−	0.183847i
$529$	−19.6802			−0.855661
$530$		0			0
$531$	19.2186	−	13.9632i	0.834018	−	0.605949i
$532$	−27.4689	−	19.9573i	−1.19093	−	0.865260i
$533$	2.36721	+	7.28553i	0.102535	+	0.315571i
$534$	0.888045	+	2.73312i	0.0384295	+	0.118274i
$535$		0			0
$536$	−3.65531	+	2.65574i	−0.157885	+	0.114710i
$537$	15.6720	−	48.2334i	0.676297	−	2.08143i
$538$	−2.43147			−0.104828
$539$	−16.5431	−	9.43371i	−0.712563	−	0.406338i
$540$		0			0
$541$	−2.28788	+	7.04138i	−0.0983638	+	0.302733i	−0.988116	−	0.153712i	$-0.950877\pi$
$541$	−2.28788	+	7.04138i	−0.0983638	+	0.302733i	0.889752	+	0.456444i	$0.150877\pi$
$542$	−0.794606	+	0.577315i	−0.0341313	+	0.0247978i
$543$	41.8992	+	30.4416i	1.79807	+	1.30637i
$544$	2.77345	+	8.53582i	0.118911	+	0.365970i
$545$		0			0
$546$	1.43716	+	1.04415i	0.0615046	+	0.0446857i
$547$	−15.8598	+	11.5228i	−0.678115	+	0.492679i	−0.872732	−	0.488200i	$-0.837654\pi$
$547$	−15.8598	+	11.5228i	−0.678115	+	0.492679i	0.194617	+	0.980879i	$0.437654\pi$
$548$	2.55618	−	7.86712i	0.109195	−	0.336067i
$549$	−85.6591			−3.65584
$550$		0			0
$551$	−19.8893			−0.847314
$552$	−0.932866	+	2.87107i	−0.0397054	+	0.122201i
$553$	1.13781	−	0.826665i	0.0483845	−	0.0351534i
$554$	2.08921	+	1.51790i	0.0887620	+	0.0644894i
$555$		0			0
$556$	1.67133	+	5.14384i	0.0708804	+	0.218147i
$557$	13.6773	+	9.93712i	0.579524	+	0.421049i	0.838553	−	0.544821i	$-0.183402\pi$
$557$	13.6773	+	9.93712i	0.579524	+	0.421049i	−0.259028	+	0.965870i	$0.583402\pi$
$558$	0.858484	−	0.623725i	0.0363425	−	0.0264044i
$559$	−1.56490	+	4.81627i	−0.0661882	+	0.203706i
$560$		0			0
$561$	−53.5006	+	5.91225i	−2.25880	+	0.249616i
$562$	−2.92984			−0.123588
$563$	−5.90264	+	18.1665i	−0.248767	+	0.765625i	0.746227	+	0.665691i	$0.231863\pi$
$563$	−5.90264	+	18.1665i	−0.248767	+	0.765625i	−0.994994	+	0.0999340i	$0.968137\pi$
$564$	−33.6241	+	24.4293i	−1.41583	+	1.02866i
$565$		0			0
$566$	0.0699928	+	0.215416i	0.00294202	+	0.00905460i
$567$	−9.09282	−	27.9848i	−0.381862	−	1.17525i
$568$	−3.82150	−	2.77648i	−0.160346	−	0.116499i
$569$	14.3191	−	10.4034i	0.600286	−	0.436133i	−0.245694	−	0.969347i	$-0.579016\pi$
$569$	14.3191	−	10.4034i	0.600286	−	0.436133i	0.845980	+	0.533214i	$0.179016\pi$
$570$		0			0
$571$	−5.15632			−0.215785			−0.107893	−	0.994163i	$-0.534410\pi$
$571$	−5.15632			−0.215785			−0.107893	+	0.994163i	$0.534410\pi$
$572$	1.59183	−	7.69075i	0.0665577	−	0.321567i
$573$	62.0141			2.59068
$574$	−0.985225	+	3.03221i	−0.0411225	+	0.126562i
$575$		0			0
$576$	36.0696	+	26.2061i	1.50290	+	1.09192i
$577$	−6.23309	−	19.1835i	−0.259487	−	0.798619i	−0.992912	−	0.118849i	$-0.962080\pi$
$577$	−6.23309	−	19.1835i	−0.259487	−	0.798619i	0.733425	−	0.679770i	$-0.237920\pi$
$578$	−0.540368	−	1.66308i	−0.0224763	−	0.0691751i
$579$	20.5626	+	14.9396i	0.854552	+	0.620868i
$580$		0			0
$581$	1.72478	−	5.30834i	0.0715561	−	0.220227i
$582$	3.87587			0.160660
$583$	−14.7587	−	32.6776i	−0.611241	−	1.35337i
$584$	−4.73947			−0.196121
$585$		0			0
$586$	1.42179	−	1.03299i	0.0587334	−	0.0426723i
$587$	28.6541	+	20.8185i	1.18268	+	0.859270i	0.992472	−	0.122474i	$-0.0390827\pi$
$587$	28.6541	+	20.8185i	1.18268	+	0.859270i	0.190211	+	0.981743i	$0.439083\pi$
$588$	−10.4929	−	32.2938i	−0.432719	−	1.33177i
$589$	1.90984	+	5.87789i	0.0786936	+	0.242194i
$590$		0			0
$591$	−6.28657	+	4.56746i	−0.258595	+	0.187880i
$592$	−3.79359	+	11.6755i	−0.155916	+	0.479859i
$593$	38.2459			1.57057			0.785285	−	0.619134i	$-0.212516\pi$
$593$	38.2459			1.57057			0.785285	+	0.619134i	$0.212516\pi$
$594$	2.97620	−	2.70871i	0.122115	−	0.111140i
$595$		0			0
$596$	10.8627	−	33.4321i	0.444955	−	1.36943i
$597$	21.2023	−	15.4044i	0.867752	−	0.630459i
$598$	0.245685	+	0.178500i	0.0100468	+	0.00729943i
$599$	7.32601	+	22.5471i	0.299333	+	0.921251i	0.981732	+	0.190271i	$0.0609368\pi$
$599$	7.32601	+	22.5471i	0.299333	+	0.921251i	−0.682399	+	0.730980i	$0.739063\pi$
$600$		0			0
$601$	−7.93032	−	5.76172i	−0.323485	−	0.235025i	0.414176	−	0.910197i	$-0.364070\pi$
$601$	−7.93032	−	5.76172i	−0.323485	−	0.235025i	−0.737661	+	0.675171i	$0.764070\pi$
$602$	−1.70514	+	1.23886i	−0.0694963	+	0.0504920i
$603$	14.8831	−	45.8056i	0.606088	−	1.86535i
$604$	2.87935			0.117159
$605$		0			0
$606$	1.09138			0.0443343
$607$	−0.652640	+	2.00862i	−0.0264898	+	0.0815273i	−0.963427	−	0.267969i	$-0.913647\pi$
$607$	−0.652640	+	2.00862i	−0.0264898	+	0.0815273i	0.936938	+	0.349497i	$0.113647\pi$
$608$	6.41562	−	4.66122i	0.260188	−	0.189037i
$609$	−35.7094	−	25.9444i	−1.44702	−	1.05132i
$610$		0			0
$611$	2.59666	+	7.99168i	0.105049	+	0.323309i
$612$	−51.5163	−	37.4288i	−2.08242	−	1.51297i
$613$	−2.29338	+	1.66624i	−0.0926286	+	0.0672986i	−0.633136	−	0.774041i	$-0.718232\pi$
$613$	−2.29338	+	1.66624i	−0.0926286	+	0.0672986i	0.540507	+	0.841340i	$0.318232\pi$
$614$	0.973800	−	2.99705i	0.0392994	−	0.120951i
$615$		0			0
$616$	4.85853	−	4.42186i	0.195756	−	0.178162i
$617$	43.2099			1.73957			0.869783	−	0.493434i	$-0.164259\pi$
$617$	43.2099			1.73957			0.869783	+	0.493434i	$0.164259\pi$
$618$	−0.849631	+	2.61489i	−0.0341772	+	0.105187i
$619$	37.9078	−	27.5416i	1.52364	−	1.10699i	0.563998	−	0.825776i	$-0.309262\pi$
$619$	37.9078	−	27.5416i	1.52364	−	1.10699i	0.959645	−	0.281216i	$-0.0907376\pi$
$620$		0			0
$621$	−4.90070	−	15.0828i	−0.196658	−	0.605252i
$622$	0.803551	+	2.47308i	0.0322195	+	0.0991613i
$623$	−19.9385	−	14.4862i	−0.798818	−	0.580376i
$624$	11.2168	−	8.14946i	0.449030	−	0.326239i
$625$		0			0
$626$	−2.43738			−0.0974173
$627$	19.5760	+	43.3437i	0.781789	+	1.73098i
$628$	−6.64872			−0.265313
$629$	5.30922	−	16.3401i	0.211693	−	0.651523i
$630$		0			0
$631$	−4.16305	−	3.02463i	−0.165728	−	0.120409i	0.501830	−	0.864966i	$-0.332660\pi$
$631$	−4.16305	−	3.02463i	−0.165728	−	0.120409i	−0.667558	+	0.744558i	$0.732660\pi$
$632$	0.0675605	+	0.207930i	0.00268741	+	0.00827101i
$633$	9.97335	+	30.6948i	0.396405	+	1.22001i
$634$	−1.26141	−	0.916466i	−0.0500969	−	0.0363975i
$635$		0			0
$636$	19.7560	−	60.8027i	0.783376	−	2.41098i
$637$	−6.86517			−0.272008
$638$	0.388089	−	1.87501i	0.0153646	−	0.0742324i
$639$	50.3526			1.99192
$640$		0			0
$641$	−13.4838	+	9.79658i	−0.532580	+	0.386942i	−0.821322	−	0.570465i	$-0.806763\pi$
$641$	−13.4838	+	9.79658i	−0.532580	+	0.386942i	0.288742	+	0.957407i	$0.406763\pi$
$642$	−4.73530	−	3.44040i	−0.186887	−	0.135782i
$643$	−11.0614	−	34.0436i	−0.436220	−	1.34255i	−0.891831	−	0.452368i	$-0.850579\pi$
$643$	−11.0614	−	34.0436i	−0.436220	−	1.34255i	0.455611	−	0.890179i	$-0.349421\pi$
$644$	−3.98058	−	12.2510i	−0.156857	−	0.482755i
$645$		0			0
$646$	−2.94402	+	2.13896i	−0.115831	+	0.0841561i
$647$	−9.84530	+	30.3007i	−0.387059	+	1.19124i	0.547917	+	0.836533i	$0.315421\pi$
$647$	−9.84530	+	30.3007i	−0.387059	+	1.19124i	−0.934976	+	0.354712i	$0.884579\pi$
$648$	4.57421			0.179692
$649$	−13.2392	+	1.46304i	−0.519685	+	0.0574295i
$650$		0			0
$651$	−4.23840	+	13.0445i	−0.166116	+	0.511253i
$652$	10.9113	−	7.92749i	0.427318	−	0.310465i
$653$	1.63887	+	1.19071i	0.0641340	+	0.0465961i	0.619390	−	0.785083i	$-0.287380\pi$
$653$	1.63887	+	1.19071i	0.0641340	+	0.0465961i	−0.555256	+	0.831679i	$0.687380\pi$
$654$	−1.58867	−	4.88944i	−0.0621221	−	0.191192i
$655$		0			0
$656$	20.1314	+	14.6263i	0.786001	+	0.571063i
$657$	40.8727	−	29.6958i	1.59460	−	1.15854i
$658$	−1.08072	+	3.32611i	−0.0421308	+	0.129665i
$659$	−14.3580			−0.559308			−0.279654	−	0.960101i	$-0.590220\pi$
$659$	−14.3580			−0.559308			−0.279654	+	0.960101i	$0.590220\pi$
$660$		0			0
$661$	28.0721			1.09188			0.545938	−	0.837825i	$-0.316173\pi$
$661$	28.0721			1.09188			0.545938	+	0.837825i	$0.316173\pi$
$662$	1.10978	−	3.41555i	0.0431328	−	0.132749i
$663$	−15.6981	+	11.4053i	−0.609664	+	0.442947i
$664$	0.701956	+	0.510001i	0.0272412	+	0.0197919i
$665$		0			0
$666$	0.805438	+	2.47888i	0.0312101	+	0.0960548i
$667$	−6.10461	−	4.43526i	−0.236371	−	0.171734i
$668$	−31.4721	+	22.8658i	−1.21769	+	0.884706i
$669$	−7.42620	+	22.8555i	−0.287113	+	0.883644i
$670$		0			0
$671$	41.7223	+	23.7921i	1.61067	+	0.918485i
$672$	17.5989			0.678893
$673$	12.1235	−	37.3122i	0.467326	−	1.43828i	−0.388708	−	0.921361i	$-0.627079\pi$
$673$	12.1235	−	37.3122i	0.467326	−	1.43828i	0.856034	−	0.516919i	$-0.172921\pi$
$674$	1.29675	−	0.942144i	0.0499490	−	0.0362900i
$675$		0			0
$676$	7.08148	+	21.7946i	0.272365	+	0.838252i
$677$	−15.2609	−	46.9682i	−0.586524	−	1.80513i	−0.593063	−	0.805156i	$-0.702082\pi$
$677$	−15.2609	−	46.9682i	−0.586524	−	1.80513i	0.00653953	−	0.999979i	$-0.497918\pi$
$678$	−1.20171	−	0.873091i	−0.0461513	−	0.0335309i
$679$	−26.8911	+	19.5375i	−1.03199	+	0.749782i
$680$		0			0
$681$	61.8647			2.37066
$682$	−0.591387	+	0.0653531i	−0.0226454	+	0.00250250i
$683$	29.7973			1.14016			0.570081	−	0.821589i	$-0.306912\pi$
$683$	29.7973			1.14016			0.570081	+	0.821589i	$0.306912\pi$
$684$	−17.3865	+	53.5101i	−0.664788	+	2.04601i
$685$		0			0
$686$	0.506462	+	0.367966i	0.0193368	+	0.0140490i
$687$	7.39279	+	22.7527i	0.282052	+	0.868068i
$688$	5.08334	+	15.6449i	0.193800	+	0.596456i
$689$	−10.4571	−	7.59756i	−0.398386	−	0.289444i
$690$		0			0
$691$	9.94364	−	30.6034i	0.378274	−	1.16421i	−0.562970	−	0.826478i	$-0.690341\pi$
$691$	9.94364	−	30.6034i	0.378274	−	1.16421i	0.941243	−	0.337729i	$-0.109659\pi$
$692$	−0.463765			−0.0176297
$693$	−14.1937	+	68.5754i	−0.539175	+	2.60497i
$694$	−0.120706			−0.00458195
$695$		0			0
$696$	5.55115	−	4.03314i	0.210416	−	0.152876i
$697$	−28.1744	−	20.4699i	−1.06718	−	0.775353i
$698$	−0.766424	−	2.35881i	−0.0290096	−	0.0892823i
$699$	23.4905	+	72.2964i	0.888494	+	2.73450i
$700$		0			0
$701$	−10.8560	+	7.88737i	−0.410027	+	0.297902i	−0.773613	−	0.633659i	$-0.781552\pi$
$701$	−10.8560	+	7.88737i	−0.410027	+	0.297902i	0.363586	+	0.931561i	$0.381552\pi$
$702$	0.448297	−	1.37972i	0.0169199	−	0.0520741i
$703$	−15.1807			−0.572549
$704$	−10.2897	−	22.7827i	−0.387808	−	0.858657i
$705$		0			0
$706$	0.0480537	−	0.147894i	0.00180852	−	0.00556606i
$707$	−7.57209	+	5.50144i	−0.284778	+	0.206903i
$708$	−19.2138	−	13.9596i	−0.722097	−	0.524634i
$709$	−6.97855	−	21.4778i	−0.262085	−	0.806615i	−0.992351	−	0.123451i	$-0.960604\pi$
$709$	−6.97855	−	21.4778i	−0.262085	−	0.806615i	0.730266	−	0.683163i	$-0.239396\pi$
$710$		0			0
$711$	−1.88545	−	1.36986i	−0.0707097	−	0.0513736i
$712$	3.09950	−	2.25192i	0.116159	−	0.0843942i
$713$	−0.724565	+	2.22998i	−0.0271352	+	0.0835134i
$714$	−8.07585			−0.302231
$715$		0			0
$716$	−33.6409			−1.25722
$717$	0.504754	−	1.55347i	0.0188504	−	0.0580155i
$718$	0.171389	−	0.124521i	0.00639618	−	0.00464710i
$719$	21.5922	+	15.6876i	0.805253	+	0.585050i	0.912450	−	0.409187i	$-0.134188\pi$
$719$	21.5922	+	15.6876i	0.805253	+	0.585050i	−0.107198	+	0.994238i	$0.534188\pi$
$720$		0			0
$721$	−7.28639	−	22.4252i	−0.271359	−	0.835158i
$722$	0.458444	+	0.333079i	0.0170615	+	0.0123959i
$723$	−53.0461	+	38.5403i	−1.97281	+	1.43333i
$724$	10.6159	−	32.6724i	0.394537	−	1.21426i
$725$		0			0
$726$	−4.46808	+	0.999728i	−0.165826	+	0.0371034i
$727$	10.6151			0.393693			0.196846	−	0.980434i	$-0.436930\pi$
$727$	10.6151			0.393693			0.196846	+	0.980434i	$0.436930\pi$
$728$	0.731829	−	2.25234i	0.0271234	−	0.0834772i
$729$	23.6282	−	17.1669i	0.875118	−	0.635810i
$730$		0			0
$731$	−7.11424	−	21.8954i	−0.263130	−	0.809830i
$732$	26.4634	+	81.4460i	0.978115	+	3.01033i
$733$	−10.3886	−	7.54772i	−0.383710	−	0.278782i	0.379163	−	0.925330i	$-0.376212\pi$
$733$	−10.3886	−	7.54772i	−0.383710	−	0.278782i	−0.762873	+	0.646548i	$0.776212\pi$
$734$	1.19841	−	0.870694i	0.0442340	−	0.0321379i
$735$		0			0
$736$	3.00857			0.110897
$737$	−19.9719	+	18.1769i	−0.735673	+	0.669553i
$738$	5.28322			0.194478
$739$	10.4930	−	32.2942i	0.385992	−	1.18796i	−0.549766	−	0.835318i	$-0.685283\pi$
$739$	10.4930	−	32.2942i	0.385992	−	1.18796i	0.935758	−	0.352642i	$-0.114717\pi$
$740$		0			0
$741$	13.8704	+	10.0774i	0.509542	+	0.370204i
$742$	−1.66240	−	5.11635i	−0.0610287	−	0.187827i
$743$	−14.2470	−	43.8477i	−0.522672	−	1.60862i	−0.768875	−	0.639399i	$-0.779183\pi$
$743$	−14.2470	−	43.8477i	−0.522672	−	1.60862i	0.246203	−	0.969218i	$-0.420817\pi$
$744$	−1.72495	−	1.25325i	−0.0632398	−	0.0459464i
$745$		0			0
$746$	−1.20375	+	3.70475i	−0.0440723	+	0.135641i
$747$	−9.24906			−0.338406
$748$	14.6963	+	32.5394i	0.537349	+	1.18976i
$749$	50.1963			1.83413
$750$		0			0
$751$	−33.8831	+	24.6175i	−1.23641	+	0.898306i	−0.997354	−	0.0726986i	$-0.976839\pi$
$751$	−33.8831	+	24.6175i	−1.23641	+	0.898306i	−0.239059	+	0.971005i	$0.576839\pi$
$752$	22.0827	+	16.0440i	0.805273	+	0.585065i
$753$	5.58469	+	17.1879i	0.203517	+	0.626362i
$754$	−0.213300	−	0.656470i	−0.00776793	−	0.0239072i
$755$		0			0
$756$	−49.7834	+	36.1697i	−1.81060	+	1.31548i
$757$	−7.19323	+	22.1385i	−0.261442	+	0.804637i	0.731049	+	0.682325i	$0.239031\pi$
$757$	−7.19323	+	22.1385i	−0.261442	+	0.804637i	−0.992492	+	0.122312i	$0.960969\pi$
$758$	−2.60281			−0.0945384
$759$	−3.65708	+	17.6688i	−0.132744	+	0.641337i
$760$		0			0
$761$	6.47737	−	19.9353i	0.234805	−	0.722654i	−0.762343	−	0.647174i	$-0.775951\pi$
$761$	6.47737	−	19.9353i	0.234805	−	0.722654i	0.997147	−	0.0754807i	$-0.0240491\pi$
$762$	2.11455	−	1.53631i	0.0766021	−	0.0556547i
$763$	35.6691	+	25.9151i	1.29131	+	0.938190i
$764$	−12.7116	−	39.1221i	−0.459888	−	1.41539i
$765$		0			0
$766$	−2.44303	−	1.77497i	−0.0882703	−	0.0641321i
$767$	−3.88465	+	2.82236i	−0.140266	+	0.101910i
$768$	13.3491	−	41.0842i	0.481693	−	1.48250i
$769$	24.9924			0.901249			0.450624	−	0.892714i	$-0.351201\pi$
$769$	24.9924			0.901249			0.450624	+	0.892714i	$0.351201\pi$
$770$		0			0
$771$	−9.12960			−0.328795
$772$	5.20989	−	16.0344i	0.187508	−	0.577090i
$773$	17.6495	−	12.8231i	0.634808	−	0.461215i	−0.223254	−	0.974760i	$-0.571668\pi$
$773$	17.6495	−	12.8231i	0.634808	−	0.461215i	0.858063	+	0.513545i	$0.171668\pi$
$774$	2.82557	+	2.05289i	0.101563	+	0.0737898i
$775$		0			0
$776$	−1.59674	−	4.91425i	−0.0573195	−	0.176411i
$777$	−27.2554	−	19.8022i	−0.977783	−	0.710401i
$778$	−4.22703	+	3.07112i	−0.151546	+	0.110105i
$779$	−9.50871	+	29.2648i	−0.340685	+	1.04852i
$780$		0			0
$781$	−24.5254	−	13.9856i	−0.877589	−	0.500445i
$782$	−1.38058			−0.0493696
$783$	−11.1390	+	34.2823i	−0.398075	+	1.22515i
$784$	−18.0414	+	13.1079i	−0.644337	+	0.468138i
$785$		0			0
$786$	−2.37637	−	7.31371i	−0.0847623	−	0.260871i
$787$	7.34937	+	22.6190i	0.261977	+	0.806281i	0.992374	+	0.123259i	$0.0393347\pi$
$787$	7.34937	+	22.6190i	0.261977	+	0.806281i	−0.730398	+	0.683022i	$0.760665\pi$
$788$	4.17003	+	3.02971i	0.148551	+	0.107929i
$789$	43.8103	−	31.8300i	1.55969	−	1.13318i
$790$		0			0
$791$	12.7386			0.452933
$792$	−9.45668	−	5.39267i	−0.336029	−	0.191620i
$793$	17.3142			0.614845
$794$	0.788689	−	2.42733i	0.0279895	−	0.0861429i
$795$		0			0
$796$	−14.0640	−	10.2181i	−0.498485	−	0.362171i
$797$	−11.0433	−	33.9877i	−0.391173	−	1.20391i	−0.931902	−	0.362711i	$-0.881851\pi$
$797$	−11.0433	−	33.9877i	−0.391173	−	1.20391i	0.540729	−	0.841197i	$-0.318149\pi$
$798$	2.20502	+	6.78636i	0.0780569	+	0.240234i
$799$	−30.9052	−	22.4540i	−1.09335	−	0.794364i
$800$		0			0
$801$	−12.6201	+	38.8406i	−0.445909	+	1.37237i
$802$	−1.82447			−0.0644244
$803$	−28.1561	+	3.11149i	−0.993609	+	0.109802i
$804$	−48.1506			−1.69814
$805$		0			0
$806$	−0.173524	+	0.126073i	−0.00611214	+	0.00444073i
$807$	−42.1325	−	30.6111i	−1.48313	−	1.07756i
$808$	−0.449614	−	1.38377i	−0.0158174	−	0.0486809i
$809$	−12.8563	−	39.5676i	−0.452003	−	1.39112i	−0.874618	−	0.484812i	$-0.838888\pi$
$809$	−12.8563	−	39.5676i	−0.452003	−	1.39112i	0.422616	−	0.906309i	$-0.361112\pi$
$810$		0			0
$811$	−19.5592	+	14.2106i	−0.686815	+	0.499001i	−0.875612	−	0.483016i	$-0.839541\pi$
$811$	−19.5592	+	14.2106i	−0.686815	+	0.499001i	0.188796	+	0.982016i	$0.439541\pi$
$812$	−9.04761	+	27.8457i	−0.317509	+	0.977192i
$813$	−21.0371			−0.737802
$814$	0.296211	−	1.43111i	0.0103822	−	0.0501605i
$815$		0			0
$816$	−19.4776	+	59.9458i	−0.681851	+	2.09852i
$817$	−16.4568	+	11.9566i	−0.575751	+	0.418308i
$818$	2.39815	+	1.74236i	0.0838494	+	0.0609202i
$819$	7.80109	+	24.0093i	0.272592	+	0.838953i
$820$		0			0
$821$	−27.5371	−	20.0069i	−0.961051	−	0.698244i	−0.00765641	−	0.999971i	$-0.502437\pi$
$821$	−27.5371	−	20.0069i	−0.961051	−	0.698244i	−0.953395	+	0.301726i	$0.902437\pi$
$822$	−1.40642	+	1.02182i	−0.0490544	+	0.0356401i
$823$	1.71212	−	5.26935i	0.0596806	−	0.183678i	−0.916772	−	0.399412i	$-0.869214\pi$
$823$	1.71212	−	5.26935i	0.0596806	−	0.183678i	0.976452	+	0.215734i	$0.0692144\pi$
$824$	3.66547			0.127693
$825$		0			0
$826$	−1.99845			−0.0695348
$827$	−7.93284	+	24.4148i	−0.275852	+	0.848984i	0.713141	+	0.701021i	$0.247272\pi$
$827$	−7.93284	+	24.4148i	−0.275852	+	0.848984i	−0.988993	+	0.147964i	$0.952728\pi$
$828$	−17.2690	+	12.5466i	−0.600138	+	0.436026i
$829$	−33.7819	−	24.5440i	−1.17329	−	0.852449i	−0.181895	−	0.983318i	$-0.558223\pi$
$829$	−33.7819	−	24.5440i	−1.17329	−	0.852449i	−0.991400	+	0.130869i	$0.958223\pi$
$830$		0			0
$831$	17.0922	+	52.6043i	0.592921	+	1.82482i
$832$	−7.29071	−	5.29701i	−0.252760	−	0.183641i
$833$	25.2494	−	18.3448i	0.874840	−	0.635609i
$834$	0.351245	−	1.08102i	0.0121626	−	0.0374327i
$835$		0			0
$836$	23.3311	−	21.2342i	0.806923	−	0.734400i
$837$	11.2010			0.387164
$838$	1.61812	−	4.98007i	0.0558971	−	0.172034i
$839$	−8.29817	+	6.02897i	−0.286485	+	0.208143i	−0.721741	−	0.692163i	$-0.756658\pi$
$839$	−8.29817	+	6.02897i	−0.286485	+	0.208143i	0.435256	+	0.900307i	$0.356658\pi$
$840$		0			0
$841$	−3.66156	−	11.2691i	−0.126261	−	0.388590i
$842$	0.394743	+	1.21489i	0.0136037	+	0.0418680i
$843$	−50.7682	−	36.8853i	−1.74855	−	1.27040i
$844$	17.3198	−	12.5836i	0.596172	−	0.433144i
$845$		0			0
$846$	5.79530			0.199246
$847$	25.9605	−	29.4590i	0.892012	−	1.01222i
$848$	−41.9873			−1.44185
$849$	−1.49915	+	4.61390i	−0.0514506	+	0.158349i
$850$		0			0
$851$	−4.65938	−	3.38524i	−0.159721	−	0.116044i
$852$	−15.5558	−	47.8760i	−0.532935	−	1.64020i
$853$	8.91356	+	27.4331i	0.305195	+	0.939292i	0.979605	+	0.200935i	$0.0643981\pi$
$853$	8.91356	+	27.4331i	0.305195	+	0.939292i	−0.674410	+	0.738357i	$0.735602\pi$
$854$	5.82986	+	4.23564i	0.199494	+	0.144941i
$855$		0			0
$856$	−2.41131	+	7.42126i	−0.0824170	+	0.253653i
$857$	−20.7640			−0.709283			−0.354642	−	0.935002i	$-0.615397\pi$
$857$	−20.7640			−0.709283			−0.354642	+	0.935002i	$0.615397\pi$
$858$	−1.22067	+	1.11096i	−0.0416729	+	0.0379275i
$859$	12.1297			0.413859			0.206929	−	0.978356i	$-0.433653\pi$
$859$	12.1297			0.413859			0.206929	+	0.978356i	$0.433653\pi$
$860$		0			0
$861$	−55.2461	+	40.1386i	−1.88278	+	1.36792i
$862$	3.15076	+	2.28916i	0.107315	+	0.0779692i
$863$	11.5618	+	35.5836i	0.393568	+	1.21128i	0.930071	+	0.367380i	$0.119745\pi$
$863$	11.5618	+	35.5836i	0.393568	+	1.21128i	−0.536503	+	0.843899i	$0.680255\pi$
$864$	−4.44126	−	13.6688i	−0.151095	−	0.465022i
$865$		0			0
$866$	2.29517	−	1.66754i	0.0779929	−	0.0566652i
$867$	11.5739	−	35.6209i	0.393071	−	1.20975i
$868$	9.09800			0.308806
$869$	0.537869	+	1.19091i	0.0182460	+	0.0403989i
$870$		0			0
$871$	−3.00831	+	9.25864i	−0.101933	+	0.313717i
$872$	−5.54487	+	4.02859i	−0.187773	+	0.136425i
$873$	44.5609	+	32.3754i	1.50816	+	1.09574i
$874$	0.376953	+	1.16014i	0.0127506	+	0.0392424i
$875$		0			0
$876$	−40.8623	−	29.6882i	−1.38061	−	1.00307i
$877$	−42.3808	+	30.7915i	−1.43110	+	1.03975i	−0.441289	+	0.897365i	$0.645479\pi$
$877$	−42.3808	+	30.7915i	−1.43110	+	1.03975i	−0.989811	+	0.142389i	$0.954521\pi$
$878$	0.252980	−	0.778593i	0.00853767	−	0.0262762i
$879$	37.6416			1.26962
$880$		0			0
$881$	11.0403			0.371956			0.185978	−	0.982554i	$-0.440455\pi$
$881$	11.0403			0.371956			0.185978	+	0.982554i	$0.440455\pi$
$882$	−1.46311	+	4.50299i	−0.0492655	+	0.151624i
$883$	19.5693	−	14.2179i	0.658558	−	0.478470i	−0.207618	−	0.978210i	$-0.566571\pi$
$883$	19.5693	−	14.2179i	0.658558	−	0.478470i	0.866176	+	0.499740i	$0.166571\pi$
$884$	10.4129	+	7.56545i	0.350225	+	0.254453i
$885$		0			0
$886$	−1.55599	−	4.78883i	−0.0522744	−	0.160884i
$887$	14.1020	+	10.2457i	0.473497	+	0.344016i	0.798803	−	0.601593i	$-0.205467\pi$
$887$	14.1020	+	10.2457i	0.473497	+	0.344016i	−0.325305	+	0.945609i	$0.605467\pi$
$888$	4.23694	−	3.07832i	0.142183	−	0.103302i
$889$	−6.92668	+	21.3181i	−0.232313	+	0.714987i
$890$		0			0
$891$	27.1743	−	3.00299i	0.910374	−	0.100604i
$892$	15.9408			0.533738
$893$	−10.4303	+	32.1013i	−0.349038	+	1.07423i
$894$	−5.97669	+	4.34232i	−0.199891	+	0.145229i
$895$		0			0
$896$	−4.80182	−	14.7785i	−0.160418	−	0.493714i
$897$	2.00999	+	6.18611i	0.0671116	+	0.206548i
$898$	0.772785	+	0.561461i	0.0257882	+	0.0187362i
$899$	4.31162	−	3.13257i	0.143801	−	0.104477i
$900$		0			0
$901$	58.7622			1.95765
$902$	−2.57332	−	1.46743i	−0.0856821	−	0.0488602i
$903$	−45.1433			−1.50228
$904$	−0.611934	+	1.88334i	−0.0203526	+	0.0626389i
$905$		0			0
$906$	−0.489551	−	0.355680i	−0.0162643	−	0.0118167i
$907$	4.00901	+	12.3385i	0.133117	+	0.409692i	0.995292	−	0.0969182i	$-0.0308985\pi$
$907$	4.00901	+	12.3385i	0.133117	+	0.409692i	−0.862176	+	0.506610i	$0.830899\pi$
$908$	−12.6809	−	39.0279i	−0.420832	−	1.29519i
$909$	12.5476	+	9.11637i	0.416178	+	0.302371i
$910$		0			0
$911$	−6.28687	+	19.3490i	−0.208293	+	0.641061i	0.791269	+	0.611468i	$0.209421\pi$
$911$	−6.28687	+	19.3490i	−0.208293	+	0.641061i	−0.999562	+	0.0295922i	$0.990579\pi$
$912$	55.6922			1.84415
$913$	4.50498	+	2.56896i	0.149093	+	0.0850202i
$914$	2.97102			0.0982725
$915$		0			0
$916$	12.8384	−	9.32761i	0.424191	−	0.308193i
$917$	53.3545	+	38.7643i	1.76192	+	1.28011i
$918$	2.03802	+	6.27238i	0.0672647	+	0.207019i
$919$	2.73013	+	8.40248i	0.0900587	+	0.277172i	0.985934	−	0.167133i	$-0.0534508\pi$
$919$	2.73013	+	8.40248i	0.0900587	+	0.277172i	−0.895876	+	0.444305i	$0.853451\pi$
$920$		0			0
$921$	54.6054	−	39.6732i	1.79931	−	1.30728i
$922$	1.24980	−	3.84650i	0.0411601	−	0.126678i
$923$	−10.1777			−0.335004
$924$	69.5875	−	7.69000i	2.28926	−	0.252982i
$925$		0			0
$926$	0.768475	−	2.36512i	0.0252537	−	0.0777228i
$927$	−31.6106	+	22.9664i	−1.03823	+	0.754317i
$928$	−5.53230	−	4.01945i	−0.181607	−	0.131945i
$929$	4.77831	+	14.7061i	0.156771	+	0.482492i	0.998336	−	0.0576639i	$-0.0183652\pi$
$929$	4.77831	+	14.7061i	0.156771	+	0.482492i	−0.841565	+	0.540156i	$0.818365\pi$
$930$		0			0
$931$	−22.3097	−	16.2089i	−0.731170	−	0.531226i
$932$	40.7938	−	29.6384i	1.33625	−	0.970839i
$933$	−17.2109	+	52.9698i	−0.563461	+	1.73415i
$934$	0.557931			0.0182561
$935$		0			0
$936$	−3.92439			−0.128273
$937$	−12.8694	+	39.6078i	−0.420424	+	1.29393i	0.486885	+	0.873466i	$0.338133\pi$
$937$	−12.8694	+	39.6078i	−0.420424	+	1.29393i	−0.907309	+	0.420465i	$0.861867\pi$
$938$	−3.27791	+	2.38154i	−0.107028	+	0.0777601i
$939$	−42.2349	−	30.6855i	−1.37828	−	1.00138i
$940$		0			0
$941$	14.6364	+	45.0462i	0.477133	+	1.46847i	0.843059	+	0.537821i	$0.180753\pi$
$941$	14.6364	+	45.0462i	0.477133	+	1.46847i	−0.365925	+	0.930644i	$0.619247\pi$
$942$	1.13043	+	0.821303i	0.0368313	+	0.0267595i
$943$	−9.44445	+	6.86179i	−0.307553	+	0.223451i
$944$	−4.81991	+	14.8341i	−0.156875	+	0.482810i
$945$		0			0
$946$	−0.806061	−	1.78472i	−0.0262073	−	0.0580263i
$947$	−41.5599			−1.35052			−0.675258	−	0.737581i	$-0.735968\pi$
$947$	−41.5599			−1.35052			−0.675258	+	0.737581i	$0.735968\pi$
$948$	−0.719993	+	2.21591i	−0.0233843	+	0.0719695i
$949$	−8.26156	+	6.00238i	−0.268182	+	0.194845i
$950$		0			0
$951$	−10.3198	−	31.7611i	−0.334642	−	1.02992i
$952$	3.32699	+	10.2394i	0.107829	+	0.331862i
$953$	22.7788	+	16.5498i	0.737877	+	0.536099i	0.892046	−	0.451946i	$-0.149270\pi$
$953$	22.7788	+	16.5498i	0.737877	+	0.536099i	−0.154169	+	0.988045i	$0.549270\pi$
$954$	−7.21202	+	5.23984i	−0.233498	+	0.169646i
$955$		0			0
$956$	−1.08349			−0.0350425
$957$	30.3303	−	27.6044i	0.980440	−	0.892322i
$958$	0.167824			0.00542215
$959$	4.60702	−	14.1790i	0.148769	−	0.457862i
$960$		0			0
$961$	23.7397	+	17.2479i	0.765798	+	0.556385i
$962$	−0.162802	−	0.501055i	−0.00524896	−	0.0161546i
$963$	−25.7039	−	79.1085i	−0.828297	−	2.54924i
$964$	35.1868	+	25.5647i	1.13329	+	0.823384i
$965$		0			0
$966$	−0.836551	+	2.57464i	−0.0269156	+	0.0828377i
$967$	53.8069			1.73031			0.865157	−	0.501502i	$-0.167219\pi$
$967$	53.8069			1.73031			0.865157	+	0.501502i	$0.167219\pi$
$968$	3.10827	+	5.25326i	0.0999036	+	0.168846i
$969$	−77.9425			−2.50387
$970$		0			0
$971$	9.60235	−	6.97651i	0.308154	−	0.223887i	−0.422950	−	0.906153i	$-0.639005\pi$
$971$	9.60235	−	6.97651i	0.308154	−	0.223887i	0.731104	+	0.682266i	$0.239005\pi$
$972$	−2.40216	−	1.74527i	−0.0770494	−	0.0559797i
$973$	3.01226	+	9.27077i	0.0965685	+	0.297207i
$974$	1.82053	+	5.60302i	0.0583336	+	0.179532i
$975$		0			0
$976$	45.5011	−	33.0585i	1.45646	−	1.05818i
$977$	10.7196	−	32.9916i	0.342951	−	1.05550i	−0.619720	−	0.784823i	$-0.712754\pi$
$977$	10.7196	−	32.9916i	0.342951	−	1.05550i	0.962671	−	0.270673i	$-0.0872461\pi$
$978$	−2.83442			−0.0906346
$979$	16.9350	−	15.4130i	0.541246	−	0.492601i
$980$		0			0
$981$	22.5768	−	69.4842i	0.720821	−	2.21846i
$982$	2.06189	−	1.49805i	0.0657975	−	0.0478047i
$983$	−46.0561	−	33.4617i	−1.46896	−	1.06726i	−0.980913	−	0.194446i	$-0.937709\pi$
$983$	−46.0561	−	33.4617i	−1.46896	−	1.06726i	−0.488048	−	0.872817i	$-0.662291\pi$
$984$	−3.28039	−	10.0960i	−0.104575	−	0.321849i
$985$		0			0
$986$	2.53868	+	1.84446i	0.0808482	+	0.0587396i
$987$	−60.6009	+	44.0291i	−1.92895	+	1.40146i
$988$	3.51431	−	10.8159i	0.111805	−	0.344101i
$989$	−7.71735			−0.245397
$990$		0			0
$991$	36.4470			1.15778			0.578889	−	0.815407i	$-0.303487\pi$
$991$	36.4470			1.15778			0.578889	+	0.815407i	$0.303487\pi$
$992$	−0.656637	+	2.02092i	−0.0208482	+	0.0641643i
$993$	62.2305	−	45.2131i	1.97482	−	1.43479i
$994$	−3.42694	−	2.48982i	−0.108696	−	0.0789722i
$995$		0			0
$996$	2.85739	+	8.79415i	0.0905399	+	0.278653i
$997$	19.4874	+	14.1584i	0.617173	+	0.448402i	0.851933	−	0.523651i	$-0.175430\pi$
$997$	19.4874	+	14.1584i	0.617173	+	0.448402i	−0.234760	+	0.972053i	$0.575430\pi$
$998$	2.55835	−	1.85875i	0.0809833	−	0.0588378i
$999$	−8.50189	+	26.1661i	−0.268988	+	0.827860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.h.c.251.3	yes	16
5.2	odd	4		275.2.z.c.174.4		32
5.3	odd	4		275.2.z.c.174.5		32
5.4	even	2		275.2.h.e.251.2	yes	16
11.4	even	5		3025.2.a.bi.1.5		8
11.5	even	5	inner	275.2.h.c.126.3	✓	16
11.7	odd	10		3025.2.a.bm.1.4		8
55.4	even	10		3025.2.a.bn.1.4		8
55.27	odd	20		275.2.z.c.49.5		32
55.29	odd	10		3025.2.a.bj.1.5		8
55.38	odd	20		275.2.z.c.49.4		32
55.49	even	10		275.2.h.e.126.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.h.c.126.3	✓	16	11.5	even	5	inner
275.2.h.c.251.3	yes	16	1.1	even	1	trivial
275.2.h.e.126.2	yes	16	55.49	even	10
275.2.h.e.251.2	yes	16	5.4	even	2
275.2.z.c.49.4		32	55.38	odd	20
275.2.z.c.49.5		32	55.27	odd	20
275.2.z.c.174.4		32	5.2	odd	4
275.2.z.c.174.5		32	5.3	odd	4
3025.2.a.bi.1.5		8	11.4	even	5
3025.2.a.bj.1.5		8	55.29	odd	10
3025.2.a.bm.1.4		8	11.7	odd	10
3025.2.a.bn.1.4		8	55.4	even	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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0430779 + 0.132580i) q^{2} +(-2.41558 + 1.75502i) q^{3} +(1.60231 + 1.16415i) q^{4} +(-0.128623 - 0.395861i) q^{6} +(2.88786 + 2.09815i) q^{7} +(-0.448926 + 0.326164i) q^{8} +(1.82787 - 5.62561i) q^{9} +(-2.45284 + 2.23239i) q^{11} -5.91361 q^{12} +(-0.369466 + 1.13710i) q^{13} +(-0.402576 + 0.292489i) q^{14} +(1.20015 + 3.69369i) q^{16} +(-1.67964 - 5.16941i) q^{17} +(0.667104 + 0.484679i) q^{18} +(-3.88538 + 2.82290i) q^{19} -10.6581 q^{21} +(-0.190307 - 0.421365i) q^{22} -1.82203 q^{23} +(0.511992 - 1.57575i) q^{24} +(-0.134841 - 0.0979678i) q^{26} +(2.68969 + 8.27800i) q^{27} +(2.18469 + 6.72378i) q^{28} +(3.35044 + 2.43424i) q^{29} +(0.397668 - 1.22390i) q^{31} -1.65122 q^{32} +(2.00714 - 9.69730i) q^{33} +0.757717 q^{34} +(9.47786 - 6.88607i) q^{36} +(2.55724 + 1.85794i) q^{37} +(-0.206886 - 0.636730i) q^{38} +(-1.10316 - 3.39517i) q^{39} +(5.18347 - 3.76601i) q^{41} +(0.459131 - 1.41306i) q^{42} +4.23557 q^{43} +(-6.52905 + 0.721514i) q^{44} +(0.0784894 - 0.241566i) q^{46} +(5.68588 - 4.13103i) q^{47} +(-9.38157 - 6.81611i) q^{48} +(1.77436 + 5.46092i) q^{49} +(13.1297 + 9.53930i) q^{51} +(-1.91575 + 1.39187i) q^{52} +(-3.34076 + 10.2818i) q^{53} -1.21337 q^{54} -1.98078 q^{56} +(4.43121 - 13.6379i) q^{57} +(-0.467062 + 0.339340i) q^{58} +(3.24907 + 2.36059i) q^{59} +(-4.47500 - 13.7726i) q^{61} +(0.145134 + 0.105446i) q^{62} +(17.0820 - 12.4108i) q^{63} +(-2.32918 + 7.16847i) q^{64} +(1.19921 + 0.683847i) q^{66} +8.14233 q^{67} +(3.32664 - 10.2384i) q^{68} +(4.40126 - 3.19770i) q^{69} +(2.63051 + 8.09589i) q^{71} +(1.01429 + 3.12167i) q^{72} +(6.90988 + 5.02032i) q^{73} +(-0.356488 + 0.259003i) q^{74} -9.51187 q^{76} +(-11.7673 + 1.30039i) q^{77} +0.497655 q^{78} +(0.121752 - 0.374714i) q^{79} +(-6.66892 - 4.84526i) q^{81} +(0.276005 + 0.849457i) q^{82} +(-0.483189 - 1.48710i) q^{83} +(-17.0777 - 12.4077i) q^{84} +(-0.182460 + 0.561553i) q^{86} -12.3654 q^{87} +(0.373020 - 1.80221i) q^{88} -6.90425 q^{89} +(-3.45277 + 2.50858i) q^{91} +(-2.91946 - 2.12112i) q^{92} +(1.18737 + 3.65434i) q^{93} +(0.302757 + 0.931792i) q^{94} +(3.98865 - 2.89792i) q^{96} +(-2.87750 + 8.85604i) q^{97} -0.800446 q^{98} +(8.07507 + 17.8793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} + 16 q^{8} + 8 q^{9} - 5 q^{11} - 6 q^{12} + 7 q^{13} + 3 q^{14} - 4 q^{16} + 12 q^{17} + 16 q^{18} - 13 q^{19} + 10 q^{21} + 28 q^{22} - 4 q^{23} - 43 q^{24}+ \cdots - 10 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 - 2 * q^4 - 3 * q^6 + 4 * q^7 + 16 * q^8 + 8 * q^9 - 5 * q^11 - 6 * q^12 + 7 * q^13 + 3 * q^14 - 4 * q^16 + 12 * q^17 + 16 * q^18 - 13 * q^19 + 10 * q^21 + 28 * q^22 - 4 * q^23 - 43 * q^24 - 34 * q^26 - 11 * q^27 + 47 * q^28 - 11 * q^29 - 10 * q^31 - 58 * q^32 - 34 * q^33 + 20 * q^34 + 3 * q^36 - 4 * q^37 - 36 * q^38 + 3 * q^39 + 25 * q^41 + 13 * q^42 - 28 * q^43 - q^44 + 40 * q^46 + 8 * q^47 - 106 * q^48 + 16 * q^49 + 35 * q^51 + 39 * q^52 - 22 * q^53 + 60 * q^54 - 20 * q^56 + 29 * q^57 + 6 * q^58 + 14 * q^59 + 16 * q^61 - 10 * q^62 + 73 * q^63 + 40 * q^64 - 55 * q^66 - 14 * q^67 + 83 * q^68 + 35 * q^69 - 46 * q^71 + 28 * q^72 + 7 * q^73 - 7 * q^74 - 62 * q^76 - 51 * q^77 + 34 * q^78 - 39 * q^79 - 43 * q^81 - 51 * q^82 + 28 * q^83 - 54 * q^84 + 2 * q^86 - 50 * q^87 - 76 * q^88 - 22 * q^89 - 34 * q^91 + 4 * q^92 + 3 * q^93 - 40 * q^94 + 108 * q^96 - 39 * q^97 - 52 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

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