LMFDB - Embedded newform 275.2.z.c.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(49,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([5, 4]))

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

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

chi := DirichletCharacter("275.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	275.49
Dual form			275.2.z.c.174.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.132580 - 0.0430779i) q^{2} +(-1.75502 + 2.41558i) q^{3} +(-1.60231 + 1.16415i) q^{4} +(-0.128623 + 0.395861i) q^{6} +(2.09815 + 2.88786i) q^{7} +(-0.326164 + 0.448926i) q^{8} +(-1.82787 - 5.62561i) q^{9} +(-2.45284 - 2.23239i) q^{11} -5.91361i q^{12} +(-1.13710 + 0.369466i) q^{13} +(0.402576 + 0.292489i) q^{14} +(1.20015 - 3.69369i) q^{16} +(-5.16941 - 1.67964i) q^{17} +(-0.484679 - 0.667104i) q^{18} +(3.88538 + 2.82290i) q^{19} -10.6581 q^{21} +(-0.421365 - 0.190307i) q^{22} +1.82203i q^{23} +(-0.511992 - 1.57575i) q^{24} +(-0.134841 + 0.0979678i) q^{26} +(8.27800 + 2.68969i) q^{27} +(-6.72378 - 2.18469i) q^{28} +(-3.35044 + 2.43424i) q^{29} +(0.397668 + 1.22390i) q^{31} -1.65122i q^{32} +(9.69730 - 2.00714i) q^{33} -0.757717 q^{34} +(9.47786 + 6.88607i) q^{36} +(1.85794 + 2.55724i) q^{37} +(0.636730 + 0.206886i) q^{38} +(1.10316 - 3.39517i) q^{39} +(5.18347 + 3.76601i) q^{41} +(-1.41306 + 0.459131i) q^{42} -4.23557i q^{43} +(6.52905 + 0.721514i) q^{44} +(0.0784894 + 0.241566i) q^{46} +(-4.13103 + 5.68588i) q^{47} +(6.81611 + 9.38157i) q^{48} +(-1.77436 + 5.46092i) q^{49} +(13.1297 - 9.53930i) q^{51} +(1.39187 - 1.91575i) q^{52} +(-10.2818 + 3.34076i) q^{53} +1.21337 q^{54} -1.98078 q^{56} +(-13.6379 + 4.43121i) q^{57} +(-0.339340 + 0.467062i) q^{58} +(-3.24907 + 2.36059i) q^{59} +(-4.47500 + 13.7726i) q^{61} +(0.105446 + 0.145134i) q^{62} +(12.4108 - 17.0820i) q^{63} +(2.32918 + 7.16847i) q^{64} +(1.19921 - 0.683847i) q^{66} +8.14233i q^{67} +(10.2384 - 3.32664i) q^{68} +(-4.40126 - 3.19770i) q^{69} +(2.63051 - 8.09589i) q^{71} +(3.12167 + 1.01429i) q^{72} +(-5.02032 - 6.90988i) q^{73} +(0.356488 + 0.259003i) q^{74} -9.51187 q^{76} +(1.30039 - 11.7673i) q^{77} -0.497655i q^{78} +(-0.121752 - 0.374714i) q^{79} +(-6.66892 + 4.84526i) q^{81} +(0.849457 + 0.276005i) q^{82} +(1.48710 + 0.483189i) q^{83} +(17.0777 - 12.4077i) q^{84} +(-0.182460 - 0.561553i) q^{86} -12.3654i q^{87} +(1.80221 - 0.373020i) q^{88} +6.90425 q^{89} +(-3.45277 - 2.50858i) q^{91} +(-2.12112 - 2.91946i) q^{92} +(-3.65434 - 1.18737i) q^{93} +(-0.302757 + 0.931792i) q^{94} +(3.98865 + 2.89792i) q^{96} +(8.85604 - 2.87750i) q^{97} +0.800446i q^{98} +(-8.07507 + 17.8793i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9} - 10 q^{11} - 6 q^{14} - 8 q^{16} + 26 q^{19} + 20 q^{21} + 86 q^{24} - 68 q^{26} + 22 q^{29} - 20 q^{31} - 40 q^{34} + 6 q^{36} - 6 q^{39} + 50 q^{41} + 2 q^{44} + 80 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) $ 32 * q + 4 * q^4 - 6 * q^6 - 16 * q^9 - 10 * q^11 - 6 * q^14 - 8 * q^16 + 26 * q^19 + 20 * q^21 + 86 * q^24 - 68 * q^26 + 22 * q^29 - 20 * q^31 - 40 * q^34 + 6 * q^36 - 6 * q^39 + 50 * q^41 + 2 * q^44 + 80 * q^46 - 32 * q^49 + 70 * q^51 - 120 * q^54 - 40 * q^56 - 28 * q^59 + 32 * q^61 - 80 * q^64 - 110 * q^66 - 70 * q^69 - 92 * q^71 + 14 * q^74 - 124 * q^76 + 78 * q^79 - 86 * q^81 + 108 * q^84 + 4 * q^86 + 44 * q^89 - 68 * q^91 + 80 * q^94 + 216 * q^96 + 20 * q^99

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	0.132580	−	0.0430779i	0.0937484	−	0.0304607i	−0.261767	−	0.965131i	$-0.584305\pi$
$2$	0.132580	−	0.0430779i	0.0937484	−	0.0304607i	0.355516	+	0.934670i	$0.384305\pi$
$3$	−1.75502	+	2.41558i	−1.01326	+	1.39463i	−0.0964394	+	0.995339i	$0.530745\pi$
$3$	−1.75502	+	2.41558i	−1.01326	+	1.39463i	−0.916822	+	0.399296i	$0.869255\pi$
$4$	−1.60231	+	1.16415i	−0.801156	+	0.582074i
$5$		0			0
$5$		0			0
$6$	−0.128623	+	0.395861i	−0.0525101	+	0.161609i
$7$	2.09815	+	2.88786i	0.793026	+	1.09151i	0.993725	+	0.111854i	$0.0356789\pi$
$7$	2.09815	+	2.88786i	0.793026	+	1.09151i	−0.200698	+	0.979653i	$0.564321\pi$
$8$	−0.326164	+	0.448926i	−0.115316	+	0.158719i
$9$	−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
$12$		−	5.91361i		−	1.70711i
$13$	−1.13710	+	0.369466i	−0.315375	+	0.102471i	−0.462427	−	0.886657i	$-0.653021\pi$
$13$	−1.13710	+	0.369466i	−0.315375	+	0.102471i	0.147053	+	0.989129i	$0.453021\pi$
$14$	0.402576	+	0.292489i	0.107593	+	0.0781709i
$15$		0			0
$16$	1.20015	−	3.69369i	0.300038	−	0.923423i
$17$	−5.16941	−	1.67964i	−1.25377	−	0.407373i	−0.394496	−	0.918897i	$-0.629081\pi$
$17$	−5.16941	−	1.67964i	−1.25377	−	0.407373i	−0.859269	+	0.511524i	$0.829081\pi$
$18$	−0.484679	−	0.667104i	−0.114240	−	0.157238i
$19$	3.88538	+	2.82290i	0.891368	+	0.647617i	0.936234	−	0.351376i	$-0.114286\pi$
$19$	3.88538	+	2.82290i	0.891368	+	0.647617i	−0.0448661	+	0.998993i	$0.514286\pi$
$20$		0			0
$21$	−10.6581			−2.32580
$22$	−0.421365	−	0.190307i	−0.0898354	−	0.0405737i
$23$			1.82203i			0.379920i	0.981792	+	0.189960i	$0.0608358\pi$
$23$			1.82203i			0.379920i	−0.981792	+	0.189960i	$0.939164\pi$
$24$	−0.511992	−	1.57575i	−0.104510	−	0.321649i
$25$		0			0
$26$	−0.134841	+	0.0979678i	−0.0264445	+	0.0192131i
$27$	8.27800	+	2.68969i	1.59310	+	0.517630i
$28$	−6.72378	−	2.18469i	−1.27068	−	0.412868i
$29$	−3.35044	+	2.43424i	−0.622161	+	0.452026i	−0.853676	−	0.520805i	$-0.825632\pi$
$29$	−3.35044	+	2.43424i	−0.622161	+	0.452026i	0.231515	+	0.972831i	$0.425632\pi$
$30$		0			0
$31$	0.397668	+	1.22390i	0.0714233	+	0.219818i	0.980396	−	0.197037i	$-0.0631320\pi$
$31$	0.397668	+	1.22390i	0.0714233	+	0.219818i	−0.908973	+	0.416856i	$0.863132\pi$
$32$		−	1.65122i		−	0.291897i
$33$	9.69730	−	2.00714i	1.68808	−	0.349399i
$34$	−0.757717			−0.129947
$35$		0			0
$36$	9.47786	+	6.88607i	1.57964	+	1.14768i
$37$	1.85794	+	2.55724i	0.305444	+	0.420408i	0.933954	−	0.357394i	$-0.116335\pi$
$37$	1.85794	+	2.55724i	0.305444	+	0.420408i	−0.628509	+	0.777802i	$0.716335\pi$
$38$	0.636730	+	0.206886i	0.103291	+	0.0335614i
$39$	1.10316	−	3.39517i	0.176647	−	0.543663i
$40$		0			0
$41$	5.18347	+	3.76601i	0.809522	+	0.588152i	0.913692	−	0.406408i	$-0.133219\pi$
$41$	5.18347	+	3.76601i	0.809522	+	0.588152i	−0.104170	+	0.994559i	$0.533219\pi$
$42$	−1.41306	+	0.459131i	−0.218040	+	0.0708454i
$43$		−	4.23557i		−	0.645919i	−0.946413	−	0.322959i	$-0.895322\pi$
$43$		−	4.23557i		−	0.645919i	0.946413	−	0.322959i	$-0.104678\pi$
$44$	6.52905	+	0.721514i	0.984291	+	0.108772i
$45$		0			0
$46$	0.0784894	+	0.241566i	0.0115726	+	0.0356169i
$47$	−4.13103	+	5.68588i	−0.602573	+	0.829371i	−0.995941	−	0.0900107i	$-0.971310\pi$
$47$	−4.13103	+	5.68588i	−0.602573	+	0.829371i	0.393368	+	0.919381i	$0.371310\pi$
$48$	6.81611	+	9.38157i	0.983821	+	1.35411i
$49$	−1.77436	+	5.46092i	−0.253480	+	0.780131i
$50$		0			0
$51$	13.1297	−	9.53930i	1.83853	−	1.33577i
$52$	1.39187	−	1.91575i	0.193018	−	0.265667i
$53$	−10.2818	+	3.34076i	−1.41232	+	0.458889i	−0.913152	−	0.407618i	$-0.866359\pi$
$53$	−10.2818	+	3.34076i	−1.41232	+	0.458889i	−0.499164	+	0.866508i	$0.666359\pi$
$54$	1.21337			0.165118
$55$		0			0
$56$	−1.98078			−0.264692
$57$	−13.6379	+	4.43121i	−1.80638	+	0.586928i
$58$	−0.339340	+	0.467062i	−0.0445575	+	0.0613282i
$59$	−3.24907	+	2.36059i	−0.422993	+	0.307323i	−0.778841	−	0.627221i	$-0.784192\pi$
$59$	−3.24907	+	2.36059i	−0.422993	+	0.307323i	0.355848	+	0.934544i	$0.384192\pi$
$60$		0			0
$61$	−4.47500	+	13.7726i	−0.572964	+	1.76340i	0.0700436	+	0.997544i	$0.477686\pi$
$61$	−4.47500	+	13.7726i	−0.572964	+	1.76340i	−0.643008	+	0.765859i	$0.722314\pi$
$62$	0.105446	+	0.145134i	0.0133916	+	0.0184320i
$63$	12.4108	−	17.0820i	1.56361	−	2.15213i
$64$	2.32918	+	7.16847i	0.291147	+	0.896058i
$65$		0			0
$66$	1.19921	−	0.683847i	0.147612	−	0.0841758i
$67$			8.14233i			0.994744i	0.867537	+	0.497372i	$0.165702\pi$
$67$			8.14233i			0.994744i	−0.867537	+	0.497372i	$0.834298\pi$
$68$	10.2384	−	3.32664i	1.24158	−	0.403415i
$69$	−4.40126	−	3.19770i	−0.529850	−	0.384958i
$70$		0			0
$71$	2.63051	−	8.09589i	0.312185	−	0.960806i	−0.664713	−	0.747099i	$-0.731446\pi$
$71$	2.63051	−	8.09589i	0.312185	−	0.960806i	0.976898	−	0.213707i	$-0.0685538\pi$
$72$	3.12167	+	1.01429i	0.367892	+	0.119535i
$73$	−5.02032	−	6.90988i	−0.587584	−	0.808740i	0.406917	−	0.913465i	$-0.366604\pi$
$73$	−5.02032	−	6.90988i	−0.587584	−	0.808740i	−0.994501	+	0.104725i	$0.966604\pi$
$74$	0.356488	+	0.259003i	0.0414408	+	0.0301085i
$75$		0			0
$76$	−9.51187			−1.09109
$77$	1.30039	−	11.7673i	0.148193	−	1.34101i
$78$		−	0.497655i		−	0.0563483i
$79$	−0.121752	−	0.374714i	−0.0136982	−	0.0421586i	0.943974	−	0.330020i	$-0.107056\pi$
$79$	−0.121752	−	0.374714i	−0.0136982	−	0.0421586i	−0.957672	+	0.287862i	$0.907056\pi$
$80$		0			0
$81$	−6.66892	+	4.84526i	−0.740992	+	0.538362i
$82$	0.849457	+	0.276005i	0.0938069	+	0.0304797i
$83$	1.48710	+	0.483189i	0.163231	+	0.0530369i	0.389492	−	0.921030i	$-0.372650\pi$
$83$	1.48710	+	0.483189i	0.163231	+	0.0530369i	−0.226262	+	0.974067i	$0.572650\pi$
$84$	17.0777	−	12.4077i	1.86333	−	1.35379i
$85$		0			0
$86$	−0.182460	−	0.561553i	−0.0196751	−	0.0605538i
$87$		−	12.3654i		−	1.32571i
$88$	1.80221	−	0.373020i	0.192116	−	0.0397641i
$89$	6.90425			0.731849			0.365925	−	0.930645i	$-0.380753\pi$
$89$	6.90425			0.731849			0.365925	+	0.930645i	$0.380753\pi$
$90$		0			0
$91$	−3.45277	−	2.50858i	−0.361949	−	0.262971i
$92$	−2.12112	−	2.91946i	−0.221142	−	0.304375i
$93$	−3.65434	−	1.18737i	−0.378937	−	0.123124i
$94$	−0.302757	+	0.931792i	−0.0312270	+	0.0961070i
$95$		0			0
$96$	3.98865	+	2.89792i	0.407089	+	0.295768i
$97$	8.85604	−	2.87750i	0.899195	−	0.292166i	0.177290	−	0.984159i	$-0.443267\pi$
$97$	8.85604	−	2.87750i	0.899195	−	0.292166i	0.721905	+	0.691993i	$0.243267\pi$
$98$			0.800446i			0.0808572i
$99$	−8.07507	+	17.8793i	−0.811575	+	1.79693i
$100$		0			0
$101$	−0.810256	−	2.49371i	−0.0806235	−	0.248134i	0.902618	−	0.430443i	$-0.141643\pi$
$101$	−0.810256	−	2.49371i	−0.0806235	−	0.248134i	−0.983241	+	0.182309i	$0.941643\pi$
$102$	1.32981	−	1.83032i	0.131671	−	0.181229i
$103$	3.88267	+	5.34404i	0.382571	+	0.526564i	0.956263	−	0.292507i	$-0.0944895\pi$
$103$	3.88267	+	5.34404i	0.382571	+	0.526564i	−0.573692	+	0.819071i	$0.694490\pi$
$104$	0.205018	−	0.630980i	0.0201037	−	0.0618727i
$105$		0			0
$106$	−1.21925	+	0.885839i	−0.118424	+	0.0860403i
$107$	−8.26556	+	11.3766i	−0.799062	+	1.09981i	0.193858	+	0.981030i	$0.437900\pi$
$107$	−8.26556	+	11.3766i	−0.799062	+	1.09981i	−0.992920	+	0.118785i	$0.962100\pi$
$108$	−16.3951	+	5.32710i	−1.57762	+	0.512601i
$109$	−12.3514			−1.18305			−0.591525	−	0.806286i	$-0.701474\pi$
$109$	−12.3514			−1.18305			−0.591525	+	0.806286i	$0.701474\pi$
$110$		0			0
$111$	−9.43795			−0.895810
$112$	13.1850	−	4.28405i	1.24586	−	0.404805i
$113$	2.09760	−	2.88710i	0.197326	−	0.271596i	−0.698875	−	0.715243i	$-0.746316\pi$
$113$	2.09760	−	2.88710i	0.197326	−	0.271596i	0.896201	+	0.443648i	$0.146316\pi$
$114$	−1.61722	+	1.17498i	−0.151467	+	0.110047i
$115$		0			0
$116$	2.53464	−	7.80081i	0.235335	−	0.724287i
$117$	4.15694	+	5.72154i	0.384309	+	0.528956i
$118$	−0.329074	+	0.452931i	−0.0302937	+	0.0416957i
$119$	−5.99563	−	18.4526i	−0.549618	−	1.69155i
$120$		0			0
$121$	1.03287	+	10.9514i	0.0938974	+	0.995582i
$122$			2.01875i			0.182769i
$123$	−18.1942	+	5.91165i	−1.64051	+	0.533035i
$124$	−2.06199	−	1.49812i	−0.185172	−	0.134535i
$125$		0			0
$126$	0.909570	−	2.79937i	0.0810309	−	0.249388i
$127$	5.97215	+	1.94047i	0.529943	+	0.172189i	0.561753	−	0.827305i	$-0.310127\pi$
$127$	5.97215	+	1.94047i	0.529943	+	0.172189i	−0.0318100	+	0.999494i	$0.510127\pi$
$128$	2.55873	+	3.52179i	0.226162	+	0.311285i
$129$	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	$0.201033\pi$
$132$	−13.2015	+	14.5052i	−1.14904	+	1.26251i
$133$			17.1433i			1.48651i
$134$	0.350755	+	1.07951i	0.0303006	+	0.0932557i
$135$		0			0
$136$	2.44011	−	1.77284i	0.209238	−	0.152020i
$137$	−3.97216	−	1.29063i	−0.339364	−	0.110266i	0.134377	−	0.990930i	$-0.457097\pi$
$137$	−3.97216	−	1.29063i	−0.339364	−	0.110266i	−0.473741	+	0.880664i	$0.657097\pi$
$138$	−0.721271	−	0.234355i	−0.0613987	−	0.0199496i
$139$	−2.20927	+	1.60513i	−0.187388	+	0.136145i	−0.677524	−	0.735501i	$-0.736947\pi$
$139$	−2.20927	+	1.60513i	−0.187388	+	0.136145i	0.490136	+	0.871646i	$0.336947\pi$
$140$		0			0
$141$	−6.48464	−	19.9577i	−0.546105	−	1.68074i
$142$		−	1.18667i		−	0.0995834i
$143$	3.61392	+	1.63221i	0.302211	+	0.136492i
$144$	−22.9730			−1.91442
$145$		0			0
$146$	−0.963258	−	0.699848i	−0.0797198	−	0.0579199i
$147$	−10.0772	−	13.8701i	−0.831156	−	1.14399i
$148$	−5.95401	−	1.93458i	−0.489417	−	0.159021i
$149$	5.48466	−	16.8800i	0.449321	−	1.38287i	−0.428354	−	0.903611i	$-0.640906\pi$
$149$	5.48466	−	16.8800i	0.449321	−	1.38287i	0.877675	−	0.479256i	$-0.159094\pi$
$150$		0			0
$151$	1.17615	+	0.854522i	0.0957136	+	0.0695400i	0.634613	−	0.772830i	$-0.281160\pi$
$151$	1.17615	+	0.854522i	0.0957136	+	0.0695400i	−0.538899	+	0.842370i	$0.681160\pi$
$152$	−2.53455	+	0.823524i	−0.205579	+	0.0667966i
$153$			32.1512i			2.59927i
$154$	−0.334507	−	1.61614i	−0.0269554	−	0.130232i
$155$		0			0
$156$	2.18488	+	6.72437i	0.174930	+	0.538380i
$157$	1.97318	−	2.71585i	0.157477	−	0.216749i	−0.722987	−	0.690862i	$-0.757231\pi$
$157$	1.97318	−	2.71585i	0.157477	−	0.216749i	0.880464	+	0.474113i	$0.157231\pi$
$158$	−0.0322838	−	0.0444348i	−0.00256836	−	0.00353504i
$159$	9.97492	−	30.6996i	0.791062	−	2.43464i
$160$		0			0
$161$	−5.26177	+	3.82290i	−0.414685	+	0.301287i
$162$	−0.675444	+	0.929669i	−0.0530679	+	0.0730417i
$163$	6.47640	−	2.10431i	0.507271	−	0.164822i	−0.0441897	−	0.999023i	$-0.514071\pi$
$163$	6.47640	−	2.10431i	0.507271	−	0.164822i	0.551461	+	0.834201i	$0.314071\pi$
$164$	−12.6897			−0.990901
$165$		0			0
$166$	0.217975			0.0169182
$167$	18.6804	−	6.06962i	1.44553	−	0.469681i	0.521913	−	0.852999i	$-0.325219\pi$
$167$	18.6804	−	6.06962i	1.44553	−	0.469681i	0.923616	+	0.383318i	$0.125219\pi$
$168$	3.47630	−	4.78472i	0.268203	−	0.369149i
$169$	−9.36073	+	6.80097i	−0.720056	+	0.523152i
$170$		0			0
$171$	8.77853	−	27.0175i	0.671311	−	2.06608i
$172$	4.93083	+	6.78671i	0.375972	+	0.517482i
$173$	−0.137634	+	0.189438i	−0.0104642	+	0.0144027i	−0.814217	−	0.580561i	$-0.802833\pi$
$173$	−0.137634	+	0.189438i	−0.0104642	+	0.0144027i	0.803753	+	0.594963i	$0.202833\pi$
$174$	−0.532675	−	1.63941i	−0.0403820	−	0.124283i
$175$		0			0
$176$	−11.1895	+	6.38084i	−0.843444	+	0.480974i
$177$		−	11.9913i		−	0.901319i
$178$	0.915367	−	0.297421i	0.0686097	−	0.0222926i
$179$	13.7416	+	9.98383i	1.02709	+	0.746227i	0.967725	−	0.252010i	$-0.0810915\pi$
$179$	13.7416	+	9.98383i	1.02709	+	0.746227i	0.0593679	+	0.998236i	$0.481091\pi$
$180$		0			0
$181$	−5.36003	+	16.4965i	−0.398408	+	1.22617i	0.527867	+	0.849327i	$0.322992\pi$
$181$	−5.36003	+	16.4965i	−0.398408	+	1.22617i	−0.926275	+	0.376847i	$0.877008\pi$
$182$	−0.565834	−	0.183851i	−0.0419424	−	0.0136279i
$183$	−25.4151	−	34.9809i	−1.87874	−	2.58586i
$184$	−0.817958	−	0.594282i	−0.0603007	−	0.0438110i
$185$		0			0
$186$	−0.535642			−0.0392752
$187$	8.93012	+	15.6600i	0.653035	+	1.14517i
$188$		−	13.9197i		−	1.01520i
$189$	9.60107	+	29.5490i	0.698375	+	2.14938i
$190$		0			0
$191$	−16.8029	+	12.2080i	−1.21582	+	0.883342i	−0.995746	−	0.0921420i	$-0.970629\pi$
$191$	−16.8029	+	12.2080i	−1.21582	+	0.883342i	−0.220070	+	0.975484i	$0.570629\pi$
$192$	−21.4037	−	6.95450i	−1.54468	−	0.501898i
$193$	8.09586	+	2.63050i	0.582752	+	0.189348i	0.585533	−	0.810648i	$-0.300885\pi$
$193$	8.09586	+	2.63050i	0.582752	+	0.189348i	−0.00278083	+	0.999996i	$0.500885\pi$
$194$	1.05018	−	0.763000i	0.0753985	−	0.0547802i
$195$		0			0
$196$	−3.51424	−	10.8157i	−0.251017	−	0.772551i
$197$			2.60251i			0.185421i	0.995693	+	0.0927106i	$0.0295531\pi$
$197$			2.60251i			0.185421i	−0.995693	+	0.0927106i	$0.970447\pi$
$198$	−0.300394	+	2.71829i	−0.0213481	+	0.193181i
$199$	8.77731			0.622207			0.311104	−	0.950376i	$-0.399301\pi$
$199$	8.77731			0.622207			0.311104	+	0.950376i	$0.399301\pi$
$200$		0			0
$201$	−19.6684	−	14.2900i	−1.38730	−	1.00794i
$202$	−0.214848	−	0.295713i	−0.0151167	−	0.0208063i
$203$	−14.0594	−	4.56819i	−0.986780	−	0.320624i
$204$	−9.93275	+	30.5699i	−0.695432	+	2.14032i
$205$		0			0
$206$	0.744976	+	0.541256i	0.0519049	+	0.0377111i
$207$	10.2500	−	3.33044i	0.712427	−	0.231482i
$208$			4.64351i			0.321970i
$209$	−3.22843	−	15.5978i	−0.223315	−	1.07892i
$210$		0			0
$211$	3.34024	+	10.2802i	0.229952	+	0.707718i	0.997751	+	0.0670281i	$0.0213517\pi$
$211$	3.34024	+	10.2802i	0.229952	+	0.707718i	−0.767799	+	0.640690i	$0.778648\pi$
$212$	12.5855	−	17.3225i	0.864378	−	1.18971i
$213$	14.9397	+	20.5627i	1.02365	+	1.40893i
$214$	−0.605771	+	1.86437i	−0.0414097	+	0.127446i
$215$		0			0
$216$	−3.90746	+	2.83893i	−0.265869	+	0.193165i
$217$	−2.70007	+	3.71633i	−0.183293	+	0.252281i
$218$	−1.63755	+	0.532073i	−0.110909	+	0.0360366i
$219$	25.5021			1.72327
$220$		0			0
$221$	6.49870			0.437150
$222$	−1.25129	+	0.406567i	−0.0839808	+	0.0272870i
$223$	4.73085	−	6.51146i	0.316801	−	0.436040i	−0.620686	−	0.784059i	$-0.713146\pi$
$223$	4.73085	−	6.51146i	0.316801	−	0.436040i	0.937487	+	0.348020i	$0.113146\pi$
$224$	4.76848	−	3.46450i	0.318607	−	0.231482i
$225$		0			0
$226$	0.153730	−	0.473133i	0.0102260	−	0.0314724i
$227$	−12.1786	−	16.7624i	−0.808323	−	1.11256i	−0.991580	−	0.129496i	$-0.958664\pi$
$227$	−12.1786	−	16.7624i	−0.808323	−	1.11256i	0.183257	−	0.983065i	$-0.441336\pi$
$228$	16.6935	−	22.9767i	1.10556	−	1.52167i
$229$	−2.47597	−	7.62024i	−0.163616	−	0.503560i	0.835315	−	0.549771i	$-0.185285\pi$
$229$	−2.47597	−	7.62024i	−0.163616	−	0.503560i	−0.998932	+	0.0462117i	$0.985285\pi$
$230$		0			0
$231$	26.1427	+	23.7931i	1.72007	+	1.56547i
$232$		−	2.29806i		−	0.150875i
$233$	24.2133	−	7.86737i	1.58626	−	0.515408i	0.622603	−	0.782538i	$-0.286075\pi$
$233$	24.2133	−	7.86737i	1.58626	−	0.515408i	0.963661	+	0.267129i	$0.0860750\pi$
$234$	0.797601	+	0.579491i	0.0521408	+	0.0378825i
$235$		0			0
$236$	2.45795	−	7.56480i	0.159999	−	0.492427i
$237$	1.11883	+	0.363529i	0.0726756	+	0.0236137i
$238$	−1.58980	−	2.18818i	−0.103052	−	0.141838i
$239$	0.442580	+	0.321553i	0.0286281	+	0.0207995i	0.602007	−	0.798491i	$-0.294368\pi$
$239$	0.442580	+	0.321553i	0.0286281	+	0.0207995i	−0.573379	+	0.819290i	$0.694368\pi$
$240$		0			0
$241$	21.9600			1.41457			0.707285	−	0.706929i	$-0.249920\pi$
$241$	21.9600			1.41457			0.707285	+	0.706929i	$0.249920\pi$
$242$	0.608702	+	1.40745i	0.0391289	+	0.0904740i
$243$			1.49919i			0.0961728i
$244$	−8.86303	−	27.2776i	−0.567397	−	1.74627i
$245$		0			0
$246$	−2.15753	+	1.56754i	−0.137559	+	0.0999424i
$247$	−5.46103	−	1.77440i	−0.347477	−	0.112902i
$248$	−0.679145	−	0.220668i	−0.0431257	−	0.0140124i
$249$	−3.77708	+	2.74421i	−0.239362	+	0.173907i
$250$		0			0
$251$	1.87041	+	5.75652i	0.118059	+	0.363348i	0.992573	−	0.121653i	$-0.0388194\pi$
$251$	1.87041	+	5.75652i	0.118059	+	0.363348i	−0.874514	+	0.485001i	$0.838819\pi$
$252$			41.8187i			2.63433i
$253$	4.06749	−	4.46916i	0.255721	−	0.280974i
$254$	0.875381			0.0549263
$255$		0			0
$256$	−11.7048	−	8.50402i	−0.731548	−	0.531501i
$257$	1.79724	+	2.47369i	0.112109	+	0.154305i	0.861384	−	0.507954i	$-0.169598\pi$
$257$	1.79724	+	2.47369i	0.112109	+	0.154305i	−0.749275	+	0.662259i	$0.769598\pi$
$258$	1.67670	+	0.544792i	0.104387	+	0.0339172i
$259$	−3.48670	+	10.7310i	−0.216653	+	0.666789i
$260$		0			0
$261$	19.8182	+	14.3988i	1.22672	+	0.891263i
$262$	2.44948	−	0.795885i	0.151330	−	0.0491699i
$263$			18.1365i			1.11835i	0.829050	+	0.559174i	$0.188882\pi$
$263$			18.1365i			1.11835i	−0.829050	+	0.559174i	$0.811118\pi$
$264$	−2.26185	+	5.00803i	−0.139207	+	0.308223i
$265$		0			0
$266$	0.738498	+	2.27286i	0.0452802	+	0.139358i
$267$	−12.1171	+	16.6778i	−0.741555	+	1.02066i
$268$	−9.47888	−	13.0466i	−0.579015	−	0.796945i
$269$	−5.38987	+	16.5883i	−0.328626	+	1.01141i	0.641151	+	0.767415i	$0.278457\pi$
$269$	−5.38987	+	16.5883i	−0.328626	+	1.01141i	−0.969777	+	0.243993i	$0.921543\pi$
$270$		0			0
$271$	5.70006	−	4.14134i	0.346254	−	0.251568i	−0.401042	−	0.916060i	$-0.631352\pi$
$271$	5.70006	−	4.14134i	0.346254	−	0.251568i	0.747296	+	0.664492i	$0.231352\pi$
$272$	−12.4082	+	17.0784i	−0.752355	+	1.03553i
$273$	12.1194	−	3.93782i	0.733497	−	0.238328i
$274$	−0.582227			−0.0351736
$275$		0			0
$276$	10.7748			0.648567
$277$	−17.6181	+	5.72446i	−1.05857	+	0.343949i	−0.786025	−	0.618195i	$-0.787864\pi$
$277$	−17.6181	+	5.72446i	−1.05857	+	0.343949i	−0.272542	+	0.962144i	$0.587864\pi$
$278$	−0.223760	+	0.307979i	−0.0134202	+	0.0184714i
$279$	6.15828	−	4.47425i	0.368687	−	0.267866i
$280$		0			0
$281$	6.49461	−	19.9884i	0.387436	−	1.19241i	−0.547262	−	0.836962i	$-0.684330\pi$
$281$	6.49461	−	19.9884i	0.387436	−	1.19241i	0.934698	−	0.355444i	$-0.115670\pi$
$282$	−1.71947	−	2.36665i	−0.102393	−	0.140932i
$283$	0.955030	−	1.31449i	0.0567706	−	0.0781381i	−0.779688	−	0.626169i	$-0.784622\pi$
$283$	0.955030	−	1.31449i	0.0567706	−	0.0781381i	0.836458	+	0.548030i	$0.184622\pi$
$284$	5.20991	+	16.0345i	0.309151	+	0.951470i
$285$		0			0
$286$	0.549446	+	0.0607183i	0.0324894	+	0.00359035i
$287$			22.8708i			1.35002i
$288$	−9.28911	+	3.01821i	−0.547366	+	0.177850i
$289$	10.1483	+	7.37316i	0.596957	+	0.433715i
$290$		0			0
$291$	−8.59170	+	26.4425i	−0.503654	+	1.55009i
$292$	16.0882	+	5.22738i	0.941493	+	0.305910i
$293$	7.41008	+	10.1991i	0.432901	+	0.595838i	0.968616	−	0.248561i	$-0.0799578\pi$
$293$	7.41008	+	10.1991i	0.432901	+	0.595838i	−0.535715	+	0.844399i	$0.679958\pi$
$294$	−1.93354	−	1.40480i	−0.112766	−	0.0819295i
$295$		0			0
$296$	−1.75401			−0.101950
$297$	−14.3002	−	25.0771i	−0.829782	−	1.45512i
$298$		−	2.47423i		−	0.143328i
$299$	−0.673179	−	2.07183i	−0.0389309	−	0.119817i
$300$		0			0
$301$	12.2317	−	8.88687i	0.705025	−	0.512230i
$302$	0.192745	+	0.0626267i	0.0110912	+	0.00360376i
$303$	7.44578	+	2.41928i	0.427749	+	0.138984i
$304$	15.0900	−	10.9635i	0.865469	−	0.628800i
$305$		0			0
$306$	1.38501	+	4.26262i	0.0791757	+	0.243678i
$307$		−	22.6055i		−	1.29017i	−0.764112	−	0.645083i	$-0.776823\pi$
$307$		−	22.6055i		−	1.29017i	0.764112	−	0.645083i	$-0.223177\pi$
$308$	11.6153	+	20.3688i	0.661843	+	1.16062i
$309$	−19.7231			−1.12201
$310$		0			0
$311$	15.0909	+	10.9642i	0.855729	+	0.621723i	0.926720	−	0.375754i	$-0.122616\pi$
$311$	15.0909	+	10.9642i	0.855729	+	0.621723i	−0.0709908	+	0.997477i	$0.522616\pi$
$312$	1.16437	+	1.60262i	0.0659196	+	0.0907305i
$313$	−16.6286	−	5.40298i	−0.939907	−	0.305394i	−0.201299	−	0.979530i	$-0.564516\pi$
$313$	−16.6286	−	5.40298i	−0.939907	−	0.305394i	−0.738608	+	0.674136i	$0.764516\pi$
$314$	0.144612	−	0.445069i	0.00816091	−	0.0251167i
$315$		0			0
$316$	0.631307	+	0.458671i	0.0355138	+	0.0258023i
$317$	10.6373	−	3.45627i	0.597450	−	0.194123i	0.00534745	−	0.999986i	$-0.498298\pi$
$317$	10.6373	−	3.45627i	0.597450	−	0.194123i	0.592103	+	0.805862i	$0.298298\pi$
$318$		−	4.49987i		−	0.252340i
$319$	13.6523	+	1.50869i	0.764380	+	0.0844703i
$320$		0			0
$321$	−12.9748	−	39.9322i	−0.724181	−	2.22880i
$322$	−0.532924	+	0.733507i	−0.0296987	+	0.0408767i
$323$	−15.3437	−	21.1188i	−0.853745	−	1.17508i
$324$	5.04510	−	15.5272i	0.280283	−	0.862624i
$325$		0			0
$326$	0.767994	−	0.557980i	0.0425353	−	0.0309037i
$327$	21.6770	−	29.8358i	1.19874	−	1.64992i
$328$	−3.38132	+	1.09866i	−0.186702	+	0.0606632i
$329$	−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	$0.750406\pi$
$332$	−2.94531	+	0.956988i	−0.161645	+	0.0525215i
$333$	10.9900	−	15.1264i	0.602246	−	0.828920i
$334$	2.21518	−	1.60942i	0.121209	−	0.0880637i
$335$		0			0
$336$	−12.7914	+	39.3679i	−0.697828	+	2.14769i
$337$	−6.75842	−	9.30216i	−0.368154	−	0.506721i	0.584244	−	0.811578i	$-0.301391\pi$
$337$	−6.75842	−	9.30216i	−0.368154	−	0.506721i	−0.952398	+	0.304857i	$0.901391\pi$
$338$	−0.948077	+	1.30492i	−0.0515686	+	0.0709780i
$339$	3.29269	+	10.1339i	0.178834	+	0.550395i
$340$		0			0
$341$	1.75680	−	3.88978i	0.0951359	−	0.210643i
$342$		−	3.96015i		−	0.214141i
$343$	4.27093	−	1.38771i	0.230609	−	0.0749293i
$344$	1.90146	+	1.38149i	0.102520	+	0.0744850i
$345$		0			0
$346$	−0.0100870	+	0.0310447i	−0.000542282	+	0.00166897i
$347$	0.823501	+	0.267572i	0.0442079	+	0.0143640i	0.331037	−	0.943618i	$-0.392601\pi$
$347$	0.823501	+	0.267572i	0.0442079	+	0.0143640i	−0.286830	+	0.957982i	$0.592601\pi$
$348$	14.3951	+	19.8132i	0.771660	+	1.06210i
$349$	14.3937	+	10.4576i	0.770476	+	0.559784i	0.902106	−	0.431515i	$-0.142021\pi$
$349$	14.3937	+	10.4576i	0.770476	+	0.559784i	−0.131630	+	0.991299i	$0.542021\pi$
$350$		0			0
$351$	−10.4067			−0.555466
$352$	−3.68616	+	4.05018i	−0.196473	+	0.215875i
$353$			1.11550i			0.0593723i	0.999559	+	0.0296862i	$0.00945079\pi$
$353$			1.11550i			0.0593723i	−0.999559	+	0.0296862i	$0.990549\pi$
$354$	−0.516559	−	1.58981i	−0.0274548	−	0.0844972i
$355$		0			0
$356$	−11.0628	+	8.03757i	−0.586325	+	0.425990i
$357$	55.0963	+	17.9019i	2.91600	+	0.947467i
$358$	2.25194	+	0.731701i	0.119019	+	0.0386716i
$359$	1.22945	−	0.893247i	0.0648878	−	0.0471438i	−0.554869	−	0.831938i	$-0.687231\pi$
$359$	1.22945	−	0.893247i	0.0648878	−	0.0471438i	0.619756	+	0.784794i	$0.287231\pi$
$360$		0			0
$361$	1.25614	+	3.86601i	0.0661127	+	0.203474i
$362$			2.41801i			0.127088i
$363$	−28.2667	−	16.7250i	−1.48362	−	0.877832i
$364$	8.45278			0.443046
$365$		0			0
$366$	−4.87645	−	3.54295i	−0.254896	−	0.185193i
$367$	−6.24587	−	8.59670i	−0.326032	−	0.448744i	0.614265	−	0.789100i	$-0.289453\pi$
$367$	−6.24587	−	8.59670i	−0.326032	−	0.448744i	−0.940297	+	0.340356i	$0.889453\pi$
$368$	6.73003	+	2.18672i	0.350827	+	0.113991i
$369$	11.7114	−	36.0439i	0.609670	−	1.87637i
$370$		0			0
$371$	−31.2204	−	22.6830i	−1.62088	−	1.17764i
$372$	7.23765	−	2.35166i	0.375255	−	0.121928i
$373$		−	27.9435i		−	1.44686i	−0.690399	−	0.723429i	$-0.742565\pi$
$373$		−	27.9435i		−	1.44686i	0.690399	−	0.723429i	$-0.257435\pi$
$374$	1.85856	+	1.69152i	0.0961038	+	0.0874664i
$375$		0			0
$376$	−1.20515	−	3.70906i	−0.0621507	−	0.191280i
$377$	2.91041	−	4.00584i	0.149894	−	0.206311i
$378$	2.54582	+	3.50403i	0.130943	+	0.180228i
$379$	−5.76969	+	17.7573i	−0.296369	+	0.912130i	0.686389	+	0.727235i	$0.259195\pi$
$379$	−5.76969	+	17.7573i	−0.296369	+	0.912130i	−0.982758	+	0.184896i	$0.940805\pi$
$380$		0			0
$381$	−15.1686	+	11.0206i	−0.777111	+	0.564605i
$382$	−1.70184	+	2.34238i	−0.0870736	+	0.119847i
$383$	−20.6018	+	6.69393i	−1.05270	+	0.342044i	−0.783729	−	0.621104i	$-0.786685\pi$
$383$	−20.6018	+	6.69393i	−1.05270	+	0.342044i	−0.268974	+	0.963147i	$0.586685\pi$
$384$	−12.9978			−0.663290
$385$		0			0
$386$	1.18667			0.0603998
$387$	−23.8277	+	7.74208i	−1.21123	+	0.393552i
$388$	−10.8403	+	14.9204i	−0.550333	+	0.757468i
$389$	−30.3224	+	22.0305i	−1.53740	+	1.11699i	−0.585468	+	0.810696i	$0.699089\pi$
$389$	−30.3224	+	22.0305i	−1.53740	+	1.11699i	−0.951937	+	0.306294i	$0.900911\pi$
$390$		0			0
$391$	3.06036	−	9.41883i	0.154769	−	0.476331i
$392$	−1.87282	−	2.57771i	−0.0945916	−	0.130194i
$393$	−32.4248	+	44.6289i	−1.63562	+	2.25123i
$394$	0.112111	+	0.345042i	0.00564806	+	0.0173829i
$395$		0			0
$396$	−7.87531	−	38.0487i	−0.395749	−	1.91202i
$397$		−	18.3084i		−	0.918873i	−0.888211	−	0.459437i	$-0.848051\pi$
$397$		−	18.3084i		−	0.918873i	0.888211	−	0.459437i	$-0.151949\pi$
$398$	1.16370	−	0.378109i	0.0583309	−	0.0189529i
$399$	−41.4110	−	30.0868i	−2.07314	−	1.50623i
$400$		0			0
$401$	4.04434	−	12.4472i	0.201965	−	0.621583i	−0.797860	−	0.602843i	$-0.794034\pi$
$401$	4.04434	−	12.4472i	0.201965	−	0.621583i	0.999824	−	0.0187401i	$-0.00596551\pi$
$402$	−3.22323	−	1.04729i	−0.160760	−	0.0522341i
$403$	−0.904376	−	1.24477i	−0.0450502	−	0.0620063i
$404$	4.20133	+	3.05245i	0.209024	+	0.151865i
$405$		0			0
$406$	−2.06079			−0.102275
$407$	1.15151	−	10.4202i	0.0570785	−	0.516509i
$408$			9.00566i			0.445846i
$409$	−6.57096	−	20.2233i	−0.324913	−	0.999980i	−0.971480	−	0.237122i	$-0.923796\pi$
$409$	−6.57096	−	20.2233i	−0.324913	−	0.999980i	0.646567	−	0.762857i	$-0.276204\pi$
$410$		0			0
$411$	10.0888	−	7.32997i	0.497646	−	0.361561i
$412$	−12.4425	−	4.04281i	−0.612998	−	0.199175i
$413$	−13.6341	−	4.42998i	−0.670889	−	0.217985i
$414$	1.21548	−	0.883101i	0.0597378	−	0.0434021i
$415$		0			0
$416$	0.610069	+	1.87760i	0.0299111	+	0.0920568i
$417$		−	8.15371i		−	0.399289i
$418$	−1.09995	−	1.92889i	−0.0538002	−	0.0943450i
$419$	37.5627			1.83506			0.917528	−	0.397670i	$-0.130181\pi$
$419$	37.5627			1.83506			0.917528	+	0.397670i	$0.130181\pi$
$420$		0			0
$421$	7.41340	+	5.38615i	0.361307	+	0.262505i	0.753597	−	0.657337i	$-0.228317\pi$
$421$	7.41340	+	5.38615i	0.361307	+	0.262505i	−0.392290	+	0.919842i	$0.628317\pi$
$422$	0.885700	+	1.21906i	0.0431152	+	0.0593430i
$423$	39.5375	+	12.8465i	1.92238	+	0.624619i
$424$	1.85380	−	5.70542i	0.0900286	−	0.277079i
$425$		0			0
$426$	2.86650	+	2.08263i	0.138882	+	0.100904i
$427$	−49.1626	+	15.9739i	−2.37914	+	0.773030i
$428$		−	27.8512i		−	1.34624i
$429$	−10.2852	+	5.86514i	−0.496575	+	0.283172i
$430$		0			0
$431$	8.63312	+	26.5700i	0.415843	+	1.27983i	0.911495	+	0.411311i	$0.134929\pi$
$431$	8.63312	+	26.5700i	0.415843	+	1.27983i	−0.495653	+	0.868521i	$0.665071\pi$
$432$	19.8697	−	27.3484i	0.955984	−	1.31580i
$433$	11.9620	+	16.4642i	0.574856	+	0.791221i	0.993120	−	0.117105i	$-0.0373613\pi$
$433$	11.9620	+	16.4642i	0.574856	+	0.791221i	−0.418264	+	0.908325i	$0.637361\pi$
$434$	−0.197884	+	0.609025i	−0.00949875	+	0.0292342i
$435$		0			0
$436$	19.7908	−	14.3789i	0.947808	−	0.688623i
$437$	−5.14341	+	7.07930i	−0.246043	+	0.338649i
$438$	3.38108	−	1.09858i	0.161554	−	0.0524921i
$439$	5.87262			0.280285			0.140142	−	0.990131i	$-0.455244\pi$
$439$	5.87262			0.280285			0.140142	+	0.990131i	$0.455244\pi$
$440$		0			0
$441$	33.9643			1.61735
$442$	0.861599	−	0.279951i	0.0409821	−	0.0133159i
$443$	−21.2309	+	29.2219i	−1.00871	+	1.38837i	−0.0888891	+	0.996042i	$0.528332\pi$
$443$	−21.2309	+	29.2219i	−1.00871	+	1.38837i	−0.919824	+	0.392332i	$0.871668\pi$
$444$	15.1225	−	10.9872i	0.717684	−	0.521428i
$445$		0			0
$446$	0.346717	−	1.06709i	0.0164175	−	0.0505280i
$447$	31.1494	+	42.8735i	1.47332	+	2.02784i
$448$	−15.8145	+	21.7668i	−0.747167	+	1.02839i
$449$	−2.11744	−	6.51680i	−0.0999281	−	0.307547i	0.888579	−	0.458724i	$-0.151694\pi$
$449$	−2.11744	−	6.51680i	−0.0999281	−	0.307547i	−0.988507	+	0.151177i	$0.951694\pi$
$450$		0			0
$451$	−4.30703	−	20.8089i	−0.202810	−	0.979855i
$452$			7.06796i			0.332449i
$453$	−4.12833	+	1.34138i	−0.193966	+	0.0630233i
$454$	−2.33674	−	1.69774i	−0.109668	−	0.0796788i
$455$		0			0
$456$	2.45889	−	7.56770i	0.115148	−	0.354390i
$457$	−20.2693	−	6.58590i	−0.948158	−	0.308075i	−0.206191	−	0.978512i	$-0.566107\pi$
$457$	−20.2693	−	6.58590i	−0.948158	−	0.308075i	−0.741967	+	0.670437i	$0.766107\pi$
$458$	−0.656528	−	0.903634i	−0.0306776	−	0.0422240i
$459$	−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	$0.736127\pi$
$462$	4.49097	+	2.02832i	0.208939	+	0.0943661i
$463$			17.8392i			0.829057i	0.910036	+	0.414528i	$0.136053\pi$
$463$			17.8392i			0.829057i	−0.910036	+	0.414528i	$0.863947\pi$
$464$	4.97028	+	15.2969i	0.230739	+	0.710143i
$465$		0			0
$466$	2.87129	−	2.08612i	0.133010	−	0.0966374i
$467$	−3.80640	−	1.23677i	−0.176139	−	0.0572311i	0.219620	−	0.975586i	$-0.429518\pi$
$467$	−3.80640	−	1.23677i	−0.176139	−	0.0572311i	−0.395759	+	0.918354i	$0.629518\pi$
$468$	−13.3214	−	4.32840i	−0.615784	−	0.200080i
$469$	−23.5139	+	17.0838i	−1.08577	+	0.788858i
$470$		0			0
$471$	3.09738	+	9.53275i	0.142720	+	0.439246i
$472$		−	2.22853i		−	0.102577i
$473$	−9.45545	+	10.3892i	−0.434762	+	0.477695i
$474$	0.163994			0.00753252
$475$		0			0
$476$	31.0885	+	22.5871i	1.42494	+	1.03528i
$477$	37.5877	+	51.7350i	1.72102	+	2.36878i
$478$	0.0725292	+	0.0235662i	0.00331741	+	0.00107789i
$479$	0.372018	−	1.14495i	0.0169979	−	0.0523143i	−0.942198	−	0.335057i	$-0.891244\pi$
$479$	0.372018	−	1.14495i	0.0169979	−	0.0523143i	0.959196	+	0.282743i	$0.0912443\pi$
$480$		0			0
$481$	−3.05748	−	2.22139i	−0.139409	−	0.101287i
$482$	2.91146	−	0.945992i	0.132614	−	0.0430888i
$483$		−	19.4195i		−	0.883617i
$484$	−14.4040	−	16.3451i	−0.654729	−	0.742961i
$485$		0			0
$486$	0.0645818	+	0.198762i	0.00292949	+	0.00901605i
$487$	−24.8406	+	34.1902i	−1.12564	+	1.54930i	−0.329531	+	0.944145i	$0.606891\pi$
$487$	−24.8406	+	34.1902i	−1.12564	+	1.54930i	−0.796105	+	0.605159i	$0.793109\pi$
$488$	−4.72331	−	6.50108i	−0.213814	−	0.294290i
$489$	−6.28309	+	19.3374i	−0.284131	+	0.874466i
$490$		0			0
$491$	−14.7908	+	10.7462i	−0.667500	+	0.484967i	−0.869188	−	0.494483i	$-0.835358\pi$
$491$	−14.7908	+	10.7462i	−0.667500	+	0.484967i	0.201687	+	0.979450i	$0.435358\pi$
$492$	22.2707	−	30.6530i	1.00404	−	1.38194i
$493$	21.4084	−	6.95602i	0.964187	−	0.313283i
$494$	−0.800462			−0.0360145
$495$		0			0
$496$	4.99796			0.224415
$497$	28.8990	−	9.38985i	1.29630	−	0.421192i
$498$	−0.382551	+	0.526536i	−0.0171425	+	0.0235947i
$499$	18.3522	−	13.3336i	0.821557	−	0.596896i	−0.0956011	−	0.995420i	$-0.530477\pi$
$499$	18.3522	−	13.3336i	0.821557	−	0.596896i	0.917158	+	0.398524i	$0.130477\pi$
$500$		0			0
$501$	−18.1228	+	55.7762i	−0.809666	+	2.49190i
$502$	0.495958	+	0.682627i	0.0221357	+	0.0304671i
$503$	18.9706	−	26.1108i	0.845859	−	1.16422i	−0.138901	−	0.990306i	$-0.544357\pi$
$503$	18.9706	−	26.1108i	0.845859	−	1.16422i	0.984760	−	0.173919i	$-0.0556430\pi$
$504$	3.62060	+	11.1431i	0.161274	+	0.496352i
$505$		0			0
$506$	0.346746	−	0.767741i	0.0154148	−	0.0341303i
$507$		−	34.5474i		−	1.53430i
$508$	−11.8282	+	3.84323i	−0.524794	+	0.170516i
$509$	17.8771	+	12.9885i	0.792390	+	0.575705i	0.908672	−	0.417512i	$-0.137098\pi$
$509$	17.8771	+	12.9885i	0.792390	+	0.575705i	−0.116282	+	0.993216i	$0.537098\pi$
$510$		0			0
$511$	9.42134	−	28.9959i	0.416776	−	1.28270i
$512$	−10.1984	−	3.31365i	−0.450709	−	0.146444i
$513$	24.5705	+	33.8184i	1.08481	+	1.49312i
$514$	0.344841	+	0.250541i	0.0152103	+	0.0110509i
$515$		0			0
$516$	−25.0475			−1.10266
$517$	22.8259	−	4.72449i	1.00388	−	0.207783i
$518$			1.57291i			0.0691098i
$519$	−0.216050	−	0.664934i	−0.00948355	−	0.0291874i
$520$		0			0
$521$	13.7909	−	10.0196i	0.604189	−	0.438969i	−0.243175	−	0.969983i	$-0.578189\pi$
$521$	13.7909	−	10.0196i	0.604189	−	0.438969i	0.847363	+	0.531014i	$0.178189\pi$
$522$	3.24778	+	1.05527i	0.142151	+	0.0461878i
$523$	19.0148	+	6.17828i	0.831459	+	0.270157i	0.693660	−	0.720303i	$-0.255997\pi$
$523$	19.0148	+	6.17828i	0.831459	+	0.270157i	0.137799	+	0.990460i	$0.455997\pi$
$524$	−29.6035	+	21.5082i	−1.29323	+	0.939589i
$525$		0			0
$526$	0.781285	+	2.40455i	0.0340657	+	0.104843i
$527$		−	6.99476i		−	0.304697i
$528$	4.22448	−	38.2277i	0.183847	−	1.66365i
$529$	19.6802			0.855661
$530$		0			0
$531$	19.2186	+	13.9632i	0.834018	+	0.605949i
$532$	−19.9573	−	27.4689i	−0.865260	−	1.19093i
$533$	−7.28553	−	2.36721i	−0.315571	−	0.102535i
$534$	−0.888045	+	2.73312i	−0.0384295	+	0.118274i
$535$		0			0
$536$	−3.65531	−	2.65574i	−0.157885	−	0.114710i
$537$	−48.2334	+	15.6720i	−2.08143	+	0.676297i
$538$			2.43147i			0.104828i
$539$	16.5431	−	9.43371i	0.712563	−	0.406338i
$540$		0			0
$541$	−2.28788	−	7.04138i	−0.0983638	−	0.302733i	0.889752	−	0.456444i	$-0.150877\pi$
$541$	−2.28788	−	7.04138i	−0.0983638	−	0.302733i	−0.988116	+	0.153712i	$0.950877\pi$
$542$	0.577315	−	0.794606i	0.0247978	−	0.0341313i
$543$	−30.4416	−	41.8992i	−1.30637	−	1.79807i
$544$	−2.77345	+	8.53582i	−0.118911	+	0.365970i
$545$		0			0
$546$	1.43716	−	1.04415i	0.0615046	−	0.0446857i
$547$	11.5228	−	15.8598i	0.492679	−	0.678115i	−0.488200	−	0.872732i	$-0.662346\pi$
$547$	11.5228	−	15.8598i	0.492679	−	0.678115i	0.980879	+	0.194617i	$0.0623464\pi$
$548$	7.86712	−	2.55618i	0.336067	−	0.109195i
$549$	85.6591			3.65584
$550$		0			0
$551$	−19.8893			−0.847314
$552$	2.87107	−	0.932866i	0.122201	−	0.0397054i
$553$	0.826665	−	1.13781i	0.0351534	−	0.0483845i
$554$	−2.08921	+	1.51790i	−0.0887620	+	0.0644894i
$555$		0			0
$556$	1.67133	−	5.14384i	0.0708804	−	0.218147i
$557$	9.93712	+	13.6773i	0.421049	+	0.579524i	0.965870	−	0.259028i	$-0.0834023\pi$
$557$	9.93712	+	13.6773i	0.421049	+	0.579524i	−0.544821	+	0.838553i	$0.683402\pi$
$558$	0.623725	−	0.858484i	0.0264044	−	0.0363425i
$559$	1.56490	+	4.81627i	0.0661882	+	0.203706i
$560$		0			0
$561$	−53.5006	−	5.91225i	−2.25880	−	0.249616i
$562$		−	2.92984i		−	0.123588i
$563$	−18.1665	+	5.90264i	−0.765625	+	0.248767i	−0.665691	−	0.746227i	$-0.731863\pi$
$563$	−18.1665	+	5.90264i	−0.765625	+	0.248767i	−0.0999340	+	0.994994i	$0.531863\pi$
$564$	33.6241	+	24.4293i	1.41583	+	1.02866i
$565$		0			0
$566$	0.0699928	−	0.215416i	0.00294202	−	0.00905460i
$567$	−27.9848	−	9.09282i	−1.17525	−	0.381862i
$568$	2.77648	+	3.82150i	0.116499	+	0.160346i
$569$	−14.3191	−	10.4034i	−0.600286	−	0.436133i	0.245694	−	0.969347i	$-0.420984\pi$
$569$	−14.3191	−	10.4034i	−0.600286	−	0.436133i	−0.845980	+	0.533214i	$0.820984\pi$
$570$		0			0
$571$	−5.15632			−0.215785			−0.107893	−	0.994163i	$-0.534410\pi$
$571$	−5.15632			−0.215785			−0.107893	+	0.994163i	$0.534410\pi$
$572$	−7.69075	+	1.59183i	−0.321567	+	0.0665577i
$573$		−	62.0141i		−	2.59068i
$574$	0.985225	+	3.03221i	0.0411225	+	0.126562i
$575$		0			0
$576$	36.0696	−	26.2061i	1.50290	−	1.09192i
$577$	−19.1835	−	6.23309i	−0.798619	−	0.259487i	−0.118849	−	0.992912i	$-0.537920\pi$
$577$	−19.1835	−	6.23309i	−0.798619	−	0.259487i	−0.679770	+	0.733425i	$0.737920\pi$
$578$	1.66308	+	0.540368i	0.0691751	+	0.0224763i
$579$	−20.5626	+	14.9396i	−0.854552	+	0.620868i
$580$		0			0
$581$	1.72478	+	5.30834i	0.0715561	+	0.220227i
$582$			3.87587i			0.160660i
$583$	32.6776	+	14.7587i	1.35337	+	0.611241i
$584$	4.73947			0.196121
$585$		0			0
$586$	1.42179	+	1.03299i	0.0587334	+	0.0426723i
$587$	20.8185	+	28.6541i	0.859270	+	1.18268i	0.981743	+	0.190211i	$0.0609173\pi$
$587$	20.8185	+	28.6541i	0.859270	+	1.18268i	−0.122474	+	0.992472i	$0.539083\pi$
$588$	32.2938	+	10.4929i	1.33177	+	0.432719i
$589$	−1.90984	+	5.87789i	−0.0786936	+	0.242194i
$590$		0			0
$591$	−6.28657	−	4.56746i	−0.258595	−	0.187880i
$592$	11.6755	−	3.79359i	0.479859	−	0.155916i
$593$		−	38.2459i		−	1.57057i	−0.619134	−	0.785285i	$-0.712516\pi$
$593$		−	38.2459i		−	1.57057i	0.619134	−	0.785285i	$-0.287484\pi$
$594$	−2.97620	−	2.70871i	−0.122115	−	0.111140i
$595$		0			0
$596$	10.8627	+	33.4321i	0.444955	+	1.36943i
$597$	−15.4044	+	21.2023i	−0.630459	+	0.867752i
$598$	−0.178500	−	0.245685i	−0.00729943	−	0.0100468i
$599$	−7.32601	+	22.5471i	−0.299333	+	0.921251i	0.682399	+	0.730980i	$0.260937\pi$
$599$	−7.32601	+	22.5471i	−0.299333	+	0.921251i	−0.981732	+	0.190271i	$0.939063\pi$
$600$		0			0
$601$	−7.93032	+	5.76172i	−0.323485	+	0.235025i	−0.737661	−	0.675171i	$-0.764070\pi$
$601$	−7.93032	+	5.76172i	−0.323485	+	0.235025i	0.414176	+	0.910197i	$0.364070\pi$
$602$	1.23886	−	1.70514i	0.0504920	−	0.0694963i
$603$	45.8056	−	14.8831i	1.86535	−	0.606088i
$604$	−2.87935			−0.117159
$605$		0			0
$606$	1.09138			0.0443343
$607$	2.00862	−	0.652640i	0.0815273	−	0.0264898i	−0.267969	−	0.963427i	$-0.586353\pi$
$607$	2.00862	−	0.652640i	0.0815273	−	0.0264898i	0.349497	+	0.936938i	$0.386353\pi$
$608$	4.66122	−	6.41562i	0.189037	−	0.260188i
$609$	35.7094	−	25.9444i	1.44702	−	1.05132i
$610$		0			0
$611$	2.59666	−	7.99168i	0.105049	−	0.323309i
$612$	−37.4288	−	51.5163i	−1.51297	−	2.08242i
$613$	−1.66624	+	2.29338i	−0.0672986	+	0.0926286i	−0.841340	−	0.540507i	$-0.818232\pi$
$613$	−1.66624	+	2.29338i	−0.0672986	+	0.0926286i	0.774041	+	0.633136i	$0.218232\pi$
$614$	−0.973800	−	2.99705i	−0.0392994	−	0.120951i
$615$		0			0
$616$	4.85853	+	4.42186i	0.195756	+	0.178162i
$617$			43.2099i			1.73957i	0.493434	+	0.869783i	$0.335741\pi$
$617$			43.2099i			1.73957i	−0.493434	+	0.869783i	$0.664259\pi$
$618$	−2.61489	+	0.849631i	−0.105187	+	0.0341772i
$619$	−37.9078	−	27.5416i	−1.52364	−	1.10699i	−0.959645	−	0.281216i	$-0.909262\pi$
$619$	−37.9078	−	27.5416i	−1.52364	−	1.10699i	−0.563998	−	0.825776i	$-0.690738\pi$
$620$		0			0
$621$	−4.90070	+	15.0828i	−0.196658	+	0.605252i
$622$	2.47308	+	0.803551i	0.0991613	+	0.0322195i
$623$	14.4862	+	19.9385i	0.580376	+	0.798818i
$624$	−11.2168	−	8.14946i	−0.449030	−	0.326239i
$625$		0			0
$626$	−2.43738			−0.0974173
$627$	43.3437	+	19.5760i	1.73098	+	0.781789i
$628$			6.64872i			0.265313i
$629$	−5.30922	−	16.3401i	−0.211693	−	0.651523i
$630$		0			0
$631$	−4.16305	+	3.02463i	−0.165728	+	0.120409i	−0.667558	−	0.744558i	$-0.732660\pi$
$631$	−4.16305	+	3.02463i	−0.165728	+	0.120409i	0.501830	+	0.864966i	$0.332660\pi$
$632$	0.207930	+	0.0675605i	0.00827101	+	0.00268741i
$633$	−30.6948	−	9.97335i	−1.22001	−	0.396405i
$634$	1.26141	−	0.916466i	0.0500969	−	0.0363975i
$635$		0			0
$636$	19.7560	+	60.8027i	0.783376	+	2.41098i
$637$		−	6.86517i		−	0.272008i
$638$	1.87501	−	0.388089i	0.0742324	−	0.0153646i
$639$	−50.3526			−1.99192
$640$		0			0
$641$	−13.4838	−	9.79658i	−0.532580	−	0.386942i	0.288742	−	0.957407i	$-0.406763\pi$
$641$	−13.4838	−	9.79658i	−0.532580	−	0.386942i	−0.821322	+	0.570465i	$0.806763\pi$
$642$	−3.44040	−	4.73530i	−0.135782	−	0.186887i
$643$	34.0436	+	11.0614i	1.34255	+	0.436220i	0.890179	−	0.455611i	$-0.150579\pi$
$643$	34.0436	+	11.0614i	1.34255	+	0.436220i	0.452368	+	0.891831i	$0.350579\pi$
$644$	3.98058	−	12.2510i	0.156857	−	0.482755i
$645$		0			0
$646$	−2.94402	−	2.13896i	−0.115831	−	0.0841561i
$647$	30.3007	−	9.84530i	1.19124	−	0.387059i	0.354712	−	0.934976i	$-0.384579\pi$
$647$	30.3007	−	9.84530i	1.19124	−	0.387059i	0.836533	+	0.547917i	$0.184579\pi$
$648$		−	4.57421i		−	0.179692i
$649$	13.2392	+	1.46304i	0.519685	+	0.0574295i
$650$		0			0
$651$	−4.23840	−	13.0445i	−0.166116	−	0.511253i
$652$	−7.92749	+	10.9113i	−0.310465	+	0.427318i
$653$	−1.19071	−	1.63887i	−0.0465961	−	0.0641340i	0.785083	−	0.619390i	$-0.212620\pi$
$653$	−1.19071	−	1.63887i	−0.0465961	−	0.0641340i	−0.831679	+	0.555256i	$0.812620\pi$
$654$	1.58867	−	4.88944i	0.0621221	−	0.191192i
$655$		0			0
$656$	20.1314	−	14.6263i	0.786001	−	0.571063i
$657$	−29.6958	+	40.8727i	−1.15854	+	1.59460i
$658$	−3.32611	+	1.08072i	−0.129665	+	0.0421308i
$659$	14.3580			0.559308			0.279654	−	0.960101i	$-0.409780\pi$
$659$	14.3580			0.559308			0.279654	+	0.960101i	$0.409780\pi$
$660$		0			0
$661$	28.0721			1.09188			0.545938	−	0.837825i	$-0.316173\pi$
$661$	28.0721			1.09188			0.545938	+	0.837825i	$0.316173\pi$
$662$	−3.41555	+	1.10978i	−0.132749	+	0.0431328i
$663$	−11.4053	+	15.6981i	−0.442947	+	0.609664i
$664$	−0.701956	+	0.510001i	−0.0272412	+	0.0197919i
$665$		0			0
$666$	0.805438	−	2.47888i	0.0312101	−	0.0960548i
$667$	−4.43526	−	6.10461i	−0.171734	−	0.236371i
$668$	−22.8658	+	31.4721i	−0.884706	+	1.21769i
$669$	7.42620	+	22.8555i	0.287113	+	0.883644i
$670$		0			0
$671$	41.7223	−	23.7921i	1.61067	−	0.918485i
$672$			17.5989i			0.678893i
$673$	37.3122	−	12.1235i	1.43828	−	0.467326i	0.516919	−	0.856034i	$-0.327079\pi$
$673$	37.3122	−	12.1235i	1.43828	−	0.467326i	0.921361	+	0.388708i	$0.127079\pi$
$674$	−1.29675	−	0.942144i	−0.0499490	−	0.0362900i
$675$		0			0
$676$	7.08148	−	21.7946i	0.272365	−	0.838252i
$677$	−46.9682	−	15.2609i	−1.80513	−	0.586524i	−0.805156	−	0.593063i	$-0.797918\pi$
$677$	−46.9682	−	15.2609i	−1.80513	−	0.586524i	−0.999979	+	0.00653953i	$0.997918\pi$
$678$	0.873091	+	1.20171i	0.0335309	+	0.0461513i
$679$	26.8911	+	19.5375i	1.03199	+	0.749782i
$680$		0			0
$681$	61.8647			2.37066
$682$	0.0653531	−	0.591387i	0.00250250	−	0.0226454i
$683$		−	29.7973i		−	1.14016i	−0.821589	−	0.570081i	$-0.806912\pi$
$683$		−	29.7973i		−	1.14016i	0.821589	−	0.570081i	$-0.193088\pi$
$684$	17.3865	+	53.5101i	0.664788	+	2.04601i
$685$		0			0
$686$	0.506462	−	0.367966i	0.0193368	−	0.0140490i
$687$	22.7527	+	7.39279i	0.868068	+	0.282052i
$688$	−15.6449	−	5.08334i	−0.596456	−	0.193800i
$689$	10.4571	−	7.59756i	0.398386	−	0.289444i
$690$		0			0
$691$	9.94364	+	30.6034i	0.378274	+	1.16421i	0.941243	+	0.337729i	$0.109659\pi$
$691$	9.94364	+	30.6034i	0.378274	+	1.16421i	−0.562970	+	0.826478i	$0.690341\pi$
$692$		−	0.463765i		−	0.0176297i
$693$	−68.5754	+	14.1937i	−2.60497	+	0.539175i
$694$	0.120706			0.00458195
$695$		0			0
$696$	5.55115	+	4.03314i	0.210416	+	0.152876i
$697$	−20.4699	−	28.1744i	−0.775353	−	1.06718i
$698$	2.35881	+	0.766424i	0.0892823	+	0.0290096i
$699$	−23.4905	+	72.2964i	−0.888494	+	2.73450i
$700$		0			0
$701$	−10.8560	−	7.88737i	−0.410027	−	0.297902i	0.363586	−	0.931561i	$-0.381552\pi$
$701$	−10.8560	−	7.88737i	−0.410027	−	0.297902i	−0.773613	+	0.633659i	$0.781552\pi$
$702$	−1.37972	+	0.448297i	−0.0520741	+	0.0169199i
$703$			15.1807i			0.572549i
$704$	10.2897	−	22.7827i	0.387808	−	0.858657i
$705$		0			0
$706$	0.0480537	+	0.147894i	0.00180852	+	0.00556606i
$707$	5.50144	−	7.57209i	0.206903	−	0.284778i
$708$	13.9596	+	19.2138i	0.524634	+	0.722097i
$709$	6.97855	−	21.4778i	0.262085	−	0.806615i	−0.730266	−	0.683163i	$-0.760604\pi$
$709$	6.97855	−	21.4778i	0.262085	−	0.806615i	0.992351	−	0.123451i	$-0.0393963\pi$
$710$		0			0
$711$	−1.88545	+	1.36986i	−0.0707097	+	0.0513736i
$712$	−2.25192	+	3.09950i	−0.0843942	+	0.116159i
$713$	−2.22998	+	0.724565i	−0.0835134	+	0.0271352i
$714$	8.07585			0.302231
$715$		0			0
$716$	−33.6409			−1.25722
$717$	−1.55347	+	0.504754i	−0.0580155	+	0.0188504i
$718$	0.124521	−	0.171389i	0.00464710	−	0.00639618i
$719$	−21.5922	+	15.6876i	−0.805253	+	0.585050i	−0.912450	−	0.409187i	$-0.865812\pi$
$719$	−21.5922	+	15.6876i	−0.805253	+	0.585050i	0.107198	+	0.994238i	$0.465812\pi$
$720$		0			0
$721$	−7.28639	+	22.4252i	−0.271359	+	0.835158i
$722$	0.333079	+	0.458444i	0.0123959	+	0.0170615i
$723$	−38.5403	+	53.0461i	−1.43333	+	1.97281i
$724$	−10.6159	−	32.6724i	−0.394537	−	1.21426i
$725$		0			0
$726$	−4.46808	−	0.999728i	−0.165826	−	0.0371034i
$727$			10.6151i			0.393693i	0.980434	+	0.196846i	$0.0630700\pi$
$727$			10.6151i			0.393693i	−0.980434	+	0.196846i	$0.936930\pi$
$728$	2.25234	−	0.731829i	0.0834772	−	0.0271234i
$729$	−23.6282	−	17.1669i	−0.875118	−	0.635810i
$730$		0			0
$731$	−7.11424	+	21.8954i	−0.263130	+	0.809830i
$732$	81.4460	+	26.4634i	3.01033	+	0.978115i
$733$	7.54772	+	10.3886i	0.278782	+	0.383710i	0.925330	−	0.379163i	$-0.123788\pi$
$733$	7.54772	+	10.3886i	0.278782	+	0.383710i	−0.646548	+	0.762873i	$0.723788\pi$
$734$	−1.19841	−	0.870694i	−0.0442340	−	0.0321379i
$735$		0			0
$736$	3.00857			0.110897
$737$	18.1769	−	19.9719i	0.669553	−	0.735673i
$738$		−	5.28322i		−	0.194478i
$739$	−10.4930	−	32.2942i	−0.385992	−	1.18796i	−0.935758	−	0.352642i	$-0.885283\pi$
$739$	−10.4930	−	32.2942i	−0.385992	−	1.18796i	0.549766	−	0.835318i	$-0.314717\pi$
$740$		0			0
$741$	13.8704	−	10.0774i	0.509542	−	0.370204i
$742$	−5.11635	−	1.66240i	−0.187827	−	0.0610287i
$743$	43.8477	+	14.2470i	1.60862	+	0.522672i	0.969218	−	0.246203i	$-0.0791830\pi$
$743$	43.8477	+	14.2470i	1.60862	+	0.522672i	0.639399	+	0.768875i	$0.279183\pi$
$744$	1.72495	−	1.25325i	0.0632398	−	0.0459464i
$745$		0			0
$746$	−1.20375	−	3.70475i	−0.0440723	−	0.135641i
$747$		−	9.24906i		−	0.338406i
$748$	−32.5394	−	14.6963i	−1.18976	−	0.537349i
$749$	−50.1963			−1.83413
$750$		0			0
$751$	−33.8831	−	24.6175i	−1.23641	−	0.898306i	−0.239059	−	0.971005i	$-0.576839\pi$
$751$	−33.8831	−	24.6175i	−1.23641	−	0.898306i	−0.997354	+	0.0726986i	$0.976839\pi$
$752$	16.0440	+	22.0827i	0.585065	+	0.805273i
$753$	−17.1879	−	5.58469i	−0.626362	−	0.203517i
$754$	0.213300	−	0.656470i	0.00776793	−	0.0239072i
$755$		0			0
$756$	−49.7834	−	36.1697i	−1.81060	−	1.31548i
$757$	22.1385	−	7.19323i	0.804637	−	0.261442i	0.122312	−	0.992492i	$-0.460969\pi$
$757$	22.1385	−	7.19323i	0.804637	−	0.261442i	0.682325	+	0.731049i	$0.260969\pi$
$758$			2.60281i			0.0945384i
$759$	3.65708	+	17.6688i	0.132744	+	0.641337i
$760$		0			0
$761$	6.47737	+	19.9353i	0.234805	+	0.722654i	0.997147	+	0.0754807i	$0.0240491\pi$
$761$	6.47737	+	19.9353i	0.234805	+	0.722654i	−0.762343	+	0.647174i	$0.775951\pi$
$762$	−1.53631	+	2.11455i	−0.0556547	+	0.0766021i
$763$	−25.9151	−	35.6691i	−0.938190	−	1.29131i
$764$	12.7116	−	39.1221i	0.459888	−	1.41539i
$765$		0			0
$766$	−2.44303	+	1.77497i	−0.0882703	+	0.0641321i
$767$	2.82236	−	3.88465i	0.101910	−	0.140266i
$768$	41.0842	−	13.3491i	1.48250	−	0.481693i
$769$	−24.9924			−0.901249			−0.450624	−	0.892714i	$-0.648799\pi$
$769$	−24.9924			−0.901249			−0.450624	+	0.892714i	$0.648799\pi$
$770$		0			0
$771$	−9.12960			−0.328795
$772$	−16.0344	+	5.20989i	−0.577090	+	0.187508i
$773$	12.8231	−	17.6495i	0.461215	−	0.634808i	−0.513545	−	0.858063i	$-0.671668\pi$
$773$	12.8231	−	17.6495i	0.461215	−	0.634808i	0.974760	+	0.223254i	$0.0716681\pi$
$774$	−2.82557	+	2.05289i	−0.101563	+	0.0737898i
$775$		0			0
$776$	−1.59674	+	4.91425i	−0.0573195	+	0.176411i
$777$	−19.8022	−	27.2554i	−0.710401	−	0.977783i
$778$	−3.07112	+	4.22703i	−0.110105	+	0.151546i
$779$	9.50871	+	29.2648i	0.340685	+	1.04852i
$780$		0			0
$781$	−24.5254	+	13.9856i	−0.877589	+	0.500445i
$782$		−	1.38058i		−	0.0493696i
$783$	−34.2823	+	11.1390i	−1.22515	+	0.398075i
$784$	18.0414	+	13.1079i	0.644337	+	0.468138i
$785$		0			0
$786$	−2.37637	+	7.31371i	−0.0847623	+	0.260871i
$787$	22.6190	+	7.34937i	0.806281	+	0.261977i	0.683022	−	0.730398i	$-0.260665\pi$
$787$	22.6190	+	7.34937i	0.806281	+	0.261977i	0.123259	+	0.992374i	$0.460665\pi$
$788$	−3.02971	−	4.17003i	−0.107929	−	0.148551i
$789$	−43.8103	−	31.8300i	−1.55969	−	1.13318i
$790$		0			0
$791$	12.7386			0.452933
$792$	−5.39267	−	9.45668i	−0.191620	−	0.336029i
$793$		−	17.3142i		−	0.614845i
$794$	−0.788689	−	2.42733i	−0.0279895	−	0.0861429i
$795$		0			0
$796$	−14.0640	+	10.2181i	−0.498485	+	0.362171i
$797$	−33.9877	−	11.0433i	−1.20391	−	0.391173i	−0.362711	−	0.931902i	$-0.618149\pi$
$797$	−33.9877	−	11.0433i	−1.20391	−	0.391173i	−0.841197	+	0.540729i	$0.818149\pi$
$798$	−6.78636	−	2.20502i	−0.240234	−	0.0780569i
$799$	30.9052	−	22.4540i	1.09335	−	0.794364i
$800$		0			0
$801$	−12.6201	−	38.8406i	−0.445909	−	1.37237i
$802$		−	1.82447i		−	0.0644244i
$803$	−3.11149	+	28.1561i	−0.109802	+	0.993609i
$804$	48.1506			1.69814
$805$		0			0
$806$	−0.173524	−	0.126073i	−0.00611214	−	0.00444073i
$807$	−30.6111	−	42.1325i	−1.07756	−	1.48313i
$808$	1.38377	+	0.449614i	0.0486809	+	0.0158174i
$809$	12.8563	−	39.5676i	0.452003	−	1.39112i	−0.422616	−	0.906309i	$-0.638888\pi$
$809$	12.8563	−	39.5676i	0.452003	−	1.39112i	0.874618	−	0.484812i	$-0.161112\pi$
$810$		0			0
$811$	−19.5592	−	14.2106i	−0.686815	−	0.499001i	0.188796	−	0.982016i	$-0.439541\pi$
$811$	−19.5592	−	14.2106i	−0.686815	−	0.499001i	−0.875612	+	0.483016i	$0.839541\pi$
$812$	27.8457	−	9.04761i	0.977192	−	0.317509i
$813$			21.0371i			0.737802i
$814$	−0.296211	−	1.43111i	−0.0103822	−	0.0501605i
$815$		0			0
$816$	−19.4776	−	59.9458i	−0.681851	−	2.09852i
$817$	11.9566	−	16.4568i	0.418308	−	0.575751i
$818$	−1.74236	−	2.39815i	−0.0609202	−	0.0838494i
$819$	−7.80109	+	24.0093i	−0.272592	+	0.838953i
$820$		0			0
$821$	−27.5371	+	20.0069i	−0.961051	+	0.698244i	−0.953395	−	0.301726i	$-0.902437\pi$
$821$	−27.5371	+	20.0069i	−0.961051	+	0.698244i	−0.00765641	+	0.999971i	$0.502437\pi$
$822$	1.02182	−	1.40642i	0.0356401	−	0.0490544i
$823$	5.26935	−	1.71212i	0.183678	−	0.0596806i	−0.215734	−	0.976452i	$-0.569214\pi$
$823$	5.26935	−	1.71212i	0.183678	−	0.0596806i	0.399412	+	0.916772i	$0.369214\pi$
$824$	−3.66547			−0.127693
$825$		0			0
$826$	−1.99845			−0.0695348
$827$	24.4148	−	7.93284i	0.848984	−	0.275852i	0.147964	−	0.988993i	$-0.452728\pi$
$827$	24.4148	−	7.93284i	0.848984	−	0.275852i	0.701021	+	0.713141i	$0.252728\pi$
$828$	−12.5466	+	17.2690i	−0.436026	+	0.600138i
$829$	33.7819	−	24.5440i	1.17329	−	0.852449i	0.181895	−	0.983318i	$-0.441777\pi$
$829$	33.7819	−	24.5440i	1.17329	−	0.852449i	0.991400	+	0.130869i	$0.0417768\pi$
$830$		0			0
$831$	17.0922	−	52.6043i	0.592921	−	1.82482i
$832$	−5.29701	−	7.29071i	−0.183641	−	0.252760i
$833$	18.3448	−	25.2494i	0.635609	−	0.874840i
$834$	−0.351245	−	1.08102i	−0.0121626	−	0.0374327i
$835$		0			0
$836$	23.3311	+	21.2342i	0.806923	+	0.734400i
$837$			11.2010i			0.387164i
$838$	4.98007	−	1.61812i	0.172034	−	0.0558971i
$839$	8.29817	+	6.02897i	0.286485	+	0.208143i	0.721741	−	0.692163i	$-0.243342\pi$
$839$	8.29817	+	6.02897i	0.286485	+	0.208143i	−0.435256	+	0.900307i	$0.643342\pi$
$840$		0			0
$841$	−3.66156	+	11.2691i	−0.126261	+	0.388590i
$842$	1.21489	+	0.394743i	0.0418680	+	0.0136037i
$843$	36.8853	+	50.7682i	1.27040	+	1.74855i
$844$	−17.3198	−	12.5836i	−0.596172	−	0.433144i
$845$		0			0
$846$	5.79530			0.199246
$847$	−29.4590	+	25.9605i	−1.01222	+	0.892012i
$848$			41.9873i			1.44185i
$849$	1.49915	+	4.61390i	0.0514506	+	0.158349i
$850$		0			0
$851$	−4.65938	+	3.38524i	−0.159721	+	0.116044i
$852$	−47.8760	−	15.5558i	−1.64020	−	0.532935i
$853$	−27.4331	−	8.91356i	−0.939292	−	0.305195i	−0.200935	−	0.979605i	$-0.564398\pi$
$853$	−27.4331	−	8.91356i	−0.939292	−	0.305195i	−0.738357	+	0.674410i	$0.764398\pi$
$854$	−5.82986	+	4.23564i	−0.199494	+	0.144941i
$855$		0			0
$856$	−2.41131	−	7.42126i	−0.0824170	−	0.253653i
$857$		−	20.7640i		−	0.709283i	−0.935002	−	0.354642i	$-0.884603\pi$
$857$		−	20.7640i		−	0.709283i	0.935002	−	0.354642i	$-0.115397\pi$
$858$	−1.11096	+	1.22067i	−0.0379275	+	0.0416729i
$859$	−12.1297			−0.413859			−0.206929	−	0.978356i	$-0.566347\pi$
$859$	−12.1297			−0.413859			−0.206929	+	0.978356i	$0.566347\pi$
$860$		0			0
$861$	−55.2461	−	40.1386i	−1.88278	−	1.36792i
$862$	2.28916	+	3.15076i	0.0779692	+	0.107315i
$863$	−35.5836	−	11.5618i	−1.21128	−	0.393568i	−0.367380	−	0.930071i	$-0.619745\pi$
$863$	−35.5836	−	11.5618i	−1.21128	−	0.393568i	−0.843899	+	0.536503i	$0.819745\pi$
$864$	4.44126	−	13.6688i	0.151095	−	0.465022i
$865$		0			0
$866$	2.29517	+	1.66754i	0.0779929	+	0.0566652i
$867$	−35.6209	+	11.5739i	−1.20975	+	0.393071i
$868$		−	9.09800i		−	0.308806i
$869$	−0.537869	+	1.19091i	−0.0182460	+	0.0403989i
$870$		0			0
$871$	−3.00831	−	9.25864i	−0.101933	−	0.313717i
$872$	4.02859	−	5.54487i	0.136425	−	0.187773i
$873$	−32.3754	−	44.5609i	−1.09574	−	1.50816i
$874$	−0.376953	+	1.16014i	−0.0127506	+	0.0392424i
$875$		0			0
$876$	−40.8623	+	29.6882i	−1.38061	+	1.00307i
$877$	30.7915	−	42.3808i	1.03975	−	1.43110i	0.142389	−	0.989811i	$-0.454521\pi$
$877$	30.7915	−	42.3808i	1.03975	−	1.43110i	0.897365	−	0.441289i	$-0.145479\pi$
$878$	0.778593	−	0.252980i	0.0262762	−	0.00853767i
$879$	−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	$0.440455\pi$
$882$	4.50299	−	1.46311i	0.151624	−	0.0492655i
$883$	14.2179	−	19.5693i	0.478470	−	0.658558i	−0.499740	−	0.866176i	$-0.666571\pi$
$883$	14.2179	−	19.5693i	0.478470	−	0.658558i	0.978210	+	0.207618i	$0.0665710\pi$
$884$	−10.4129	+	7.56545i	−0.350225	+	0.254453i
$885$		0			0
$886$	−1.55599	+	4.78883i	−0.0522744	+	0.160884i
$887$	10.2457	+	14.1020i	0.344016	+	0.473497i	0.945609	−	0.325305i	$-0.105467\pi$
$887$	10.2457	+	14.1020i	0.344016	+	0.473497i	−0.601593	+	0.798803i	$0.705467\pi$
$888$	3.07832	−	4.23694i	0.103302	−	0.142183i
$889$	6.92668	+	21.3181i	0.232313	+	0.714987i
$890$		0			0
$891$	27.1743	+	3.00299i	0.910374	+	0.100604i
$892$			15.9408i			0.533738i
$893$	−32.1013	+	10.4303i	−1.07423	+	0.349038i
$894$	5.97669	+	4.34232i	0.199891	+	0.145229i
$895$		0			0
$896$	−4.80182	+	14.7785i	−0.160418	+	0.493714i
$897$	6.18611	+	2.00999i	0.206548	+	0.0671116i
$898$	−0.561461	−	0.772785i	−0.0187362	−	0.0257882i
$899$	−4.31162	−	3.13257i	−0.143801	−	0.104477i
$900$		0			0
$901$	58.7622			1.95765
$902$	−1.46743	−	2.57332i	−0.0488602	−	0.0856821i
$903$			45.1433i			1.50228i
$904$	0.611934	+	1.88334i	0.0203526	+	0.0626389i
$905$		0			0
$906$	−0.489551	+	0.355680i	−0.0162643	+	0.0118167i
$907$	12.3385	+	4.00901i	0.409692	+	0.133117i	0.506610	−	0.862176i	$-0.330899\pi$
$907$	12.3385	+	4.00901i	0.409692	+	0.133117i	−0.0969182	+	0.995292i	$0.530899\pi$
$908$	39.0279	+	12.6809i	1.29519	+	0.420832i
$909$	−12.5476	+	9.11637i	−0.416178	+	0.302371i
$910$		0			0
$911$	−6.28687	−	19.3490i	−0.208293	−	0.641061i	−0.999562	−	0.0295922i	$-0.990579\pi$
$911$	−6.28687	−	19.3490i	−0.208293	−	0.641061i	0.791269	−	0.611468i	$-0.209421\pi$
$912$			55.6922i			1.84415i
$913$	−2.56896	−	4.50498i	−0.0850202	−	0.149093i
$914$	−2.97102			−0.0982725
$915$		0			0
$916$	12.8384	+	9.32761i	0.424191	+	0.308193i
$917$	38.7643	+	53.3545i	1.28011	+	1.76192i
$918$	−6.27238	−	2.03802i	−0.207019	−	0.0672647i
$919$	−2.73013	+	8.40248i	−0.0900587	+	0.277172i	−0.985934	−	0.167133i	$-0.946549\pi$
$919$	−2.73013	+	8.40248i	−0.0900587	+	0.277172i	0.895876	+	0.444305i	$0.146549\pi$
$920$		0			0
$921$	54.6054	+	39.6732i	1.79931	+	1.30728i
$922$	−3.84650	+	1.24980i	−0.126678	+	0.0411601i
$923$			10.1777i			0.335004i
$924$	−69.5875	−	7.69000i	−2.28926	−	0.252982i
$925$		0			0
$926$	0.768475	+	2.36512i	0.0252537	+	0.0777228i
$927$	22.9664	−	31.6106i	0.754317	−	1.03823i
$928$	4.01945	+	5.53230i	0.131945	+	0.181607i
$929$	−4.77831	+	14.7061i	−0.156771	+	0.482492i	−0.998336	−	0.0576639i	$-0.981635\pi$
$929$	−4.77831	+	14.7061i	−0.156771	+	0.482492i	0.841565	+	0.540156i	$0.181635\pi$
$930$		0			0
$931$	−22.3097	+	16.2089i	−0.731170	+	0.531226i
$932$	−29.6384	+	40.7938i	−0.970839	+	1.33625i
$933$	−52.9698	+	17.2109i	−1.73415	+	0.563461i
$934$	−0.557931			−0.0182561
$935$		0			0
$936$	−3.92439			−0.128273
$937$	39.6078	−	12.8694i	1.29393	−	0.420424i	0.420465	−	0.907309i	$-0.361867\pi$
$937$	39.6078	−	12.8694i	1.29393	−	0.420424i	0.873466	+	0.486885i	$0.161867\pi$
$938$	−2.38154	+	3.27791i	−0.0777601	+	0.107028i
$939$	42.2349	−	30.6855i	1.37828	−	1.00138i
$940$		0			0
$941$	14.6364	−	45.0462i	0.477133	−	1.46847i	−0.365925	−	0.930644i	$-0.619247\pi$
$941$	14.6364	−	45.0462i	0.477133	−	1.46847i	0.843059	−	0.537821i	$-0.180753\pi$
$942$	0.821303	+	1.13043i	0.0267595	+	0.0368313i
$943$	−6.86179	+	9.44445i	−0.223451	+	0.307553i
$944$	4.81991	+	14.8341i	0.156875	+	0.482810i
$945$		0			0
$946$	−0.806061	+	1.78472i	−0.0262073	+	0.0580263i
$947$		−	41.5599i		−	1.35052i	−0.737581	−	0.675258i	$-0.764032\pi$
$947$		−	41.5599i		−	1.35052i	0.737581	−	0.675258i	$-0.235968\pi$
$948$	−2.21591	+	0.719993i	−0.0719695	+	0.0233843i
$949$	8.26156	+	6.00238i	0.268182	+	0.194845i
$950$		0			0
$951$	−10.3198	+	31.7611i	−0.334642	+	1.02992i
$952$	10.2394	+	3.32699i	0.331862	+	0.107829i
$953$	−16.5498	−	22.7788i	−0.536099	−	0.737877i	0.451946	−	0.892046i	$-0.350730\pi$
$953$	−16.5498	−	22.7788i	−0.536099	−	0.737877i	−0.988045	+	0.154169i	$0.950730\pi$
$954$	7.21202	+	5.23984i	0.233498	+	0.169646i
$955$		0			0
$956$	−1.08349			−0.0350425
$957$	−27.6044	+	30.3303i	−0.892322	+	0.980440i
$958$		−	0.167824i		−	0.00542215i
$959$	−4.60702	−	14.1790i	−0.148769	−	0.457862i
$960$		0			0
$961$	23.7397	−	17.2479i	0.765798	−	0.556385i
$962$	−0.501055	−	0.162802i	−0.0161546	−	0.00524896i
$963$	79.1085	+	25.7039i	2.54924	+	0.828297i
$964$	−35.1868	+	25.5647i	−1.13329	+	0.823384i
$965$		0			0
$966$	−0.836551	−	2.57464i	−0.0269156	−	0.0828377i
$967$			53.8069i			1.73031i	0.501502	+	0.865157i	$0.332781\pi$
$967$			53.8069i			1.73031i	−0.501502	+	0.865157i	$0.667219\pi$
$968$	−5.25326	−	3.10827i	−0.168846	−	0.0999036i
$969$	77.9425			2.50387
$970$		0			0
$971$	9.60235	+	6.97651i	0.308154	+	0.223887i	0.731104	−	0.682266i	$-0.239005\pi$
$971$	9.60235	+	6.97651i	0.308154	+	0.223887i	−0.422950	+	0.906153i	$0.639005\pi$
$972$	−1.74527	−	2.40216i	−0.0559797	−	0.0770494i
$973$	−9.27077	−	3.01226i	−0.297207	−	0.0965685i
$974$	−1.82053	+	5.60302i	−0.0583336	+	0.179532i
$975$		0			0
$976$	45.5011	+	33.0585i	1.45646	+	1.05818i
$977$	−32.9916	+	10.7196i	−1.05550	+	0.342951i	−0.784823	−	0.619720i	$-0.787246\pi$
$977$	−32.9916	+	10.7196i	−1.05550	+	0.342951i	−0.270673	+	0.962671i	$0.587246\pi$
$978$			2.83442i			0.0906346i
$979$	−16.9350	−	15.4130i	−0.541246	−	0.492601i
$980$		0			0
$981$	22.5768	+	69.4842i	0.720821	+	2.21846i
$982$	−1.49805	+	2.06189i	−0.0478047	+	0.0657975i
$983$	33.4617	+	46.0561i	1.06726	+	1.46896i	0.872817	+	0.488048i	$0.162291\pi$
$983$	33.4617	+	46.0561i	1.06726	+	1.46896i	0.194446	+	0.980913i	$0.437709\pi$
$984$	3.28039	−	10.0960i	0.104575	−	0.321849i
$985$		0			0
$986$	2.53868	−	1.84446i	0.0808482	−	0.0587396i
$987$	44.0291	−	60.6009i	1.40146	−	1.92895i
$988$	10.8159	−	3.51431i	0.344101	−	0.111805i
$989$	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	$0.303487\pi$
$992$	2.02092	−	0.656637i	0.0641643	−	0.0208482i
$993$	45.2131	−	62.2305i	1.43479	−	1.97482i
$994$	3.42694	−	2.48982i	0.108696	−	0.0789722i
$995$		0			0
$996$	2.85739	−	8.79415i	0.0905399	−	0.278653i
$997$	14.1584	+	19.4874i	0.448402	+	0.617173i	0.972053	−	0.234760i	$-0.0754304\pi$
$997$	14.1584	+	19.4874i	0.448402	+	0.617173i	−0.523651	+	0.851933i	$0.675430\pi$
$998$	1.85875	−	2.55835i	0.0588378	−	0.0809833i
$999$	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.z.c.49.5		32
5.2	odd	4		275.2.h.e.126.2	yes	16
5.3	odd	4		275.2.h.c.126.3	✓	16
5.4	even	2	inner	275.2.z.c.49.4		32
11.9	even	5	inner	275.2.z.c.174.4		32
55.3	odd	20		3025.2.a.bi.1.5		8
55.8	even	20		3025.2.a.bm.1.4		8
55.9	even	10	inner	275.2.z.c.174.5		32
55.42	odd	20		275.2.h.e.251.2	yes	16
55.47	odd	20		3025.2.a.bn.1.4		8
55.52	even	20		3025.2.a.bj.1.5		8
55.53	odd	20		275.2.h.c.251.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.h.c.126.3	✓	16	5.3	odd	4
275.2.h.c.251.3	yes	16	55.53	odd	20
275.2.h.e.126.2	yes	16	5.2	odd	4
275.2.h.e.251.2	yes	16	55.42	odd	20
275.2.z.c.49.4		32	5.4	even	2	inner
275.2.z.c.49.5		32	1.1	even	1	trivial
275.2.z.c.174.4		32	11.9	even	5	inner
275.2.z.c.174.5		32	55.9	even	10	inner
3025.2.a.bi.1.5		8	55.3	odd	20
3025.2.a.bj.1.5		8	55.52	even	20
3025.2.a.bm.1.4		8	55.8	even	20
3025.2.a.bn.1.4		8	55.47	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.132580 - 0.0430779i) q^{2} +(-1.75502 + 2.41558i) q^{3} +(-1.60231 + 1.16415i) q^{4} +(-0.128623 + 0.395861i) q^{6} +(2.09815 + 2.88786i) q^{7} +(-0.326164 + 0.448926i) q^{8} +(-1.82787 - 5.62561i) q^{9} +(-2.45284 - 2.23239i) q^{11} -5.91361i q^{12} +(-1.13710 + 0.369466i) q^{13} +(0.402576 + 0.292489i) q^{14} +(1.20015 - 3.69369i) q^{16} +(-5.16941 - 1.67964i) q^{17} +(-0.484679 - 0.667104i) q^{18} +(3.88538 + 2.82290i) q^{19} -10.6581 q^{21} +(-0.421365 - 0.190307i) q^{22} +1.82203i q^{23} +(-0.511992 - 1.57575i) q^{24} +(-0.134841 + 0.0979678i) q^{26} +(8.27800 + 2.68969i) q^{27} +(-6.72378 - 2.18469i) q^{28} +(-3.35044 + 2.43424i) q^{29} +(0.397668 + 1.22390i) q^{31} -1.65122i q^{32} +(9.69730 - 2.00714i) q^{33} -0.757717 q^{34} +(9.47786 + 6.88607i) q^{36} +(1.85794 + 2.55724i) q^{37} +(0.636730 + 0.206886i) q^{38} +(1.10316 - 3.39517i) q^{39} +(5.18347 + 3.76601i) q^{41} +(-1.41306 + 0.459131i) q^{42} -4.23557i q^{43} +(6.52905 + 0.721514i) q^{44} +(0.0784894 + 0.241566i) q^{46} +(-4.13103 + 5.68588i) q^{47} +(6.81611 + 9.38157i) q^{48} +(-1.77436 + 5.46092i) q^{49} +(13.1297 - 9.53930i) q^{51} +(1.39187 - 1.91575i) q^{52} +(-10.2818 + 3.34076i) q^{53} +1.21337 q^{54} -1.98078 q^{56} +(-13.6379 + 4.43121i) q^{57} +(-0.339340 + 0.467062i) q^{58} +(-3.24907 + 2.36059i) q^{59} +(-4.47500 + 13.7726i) q^{61} +(0.105446 + 0.145134i) q^{62} +(12.4108 - 17.0820i) q^{63} +(2.32918 + 7.16847i) q^{64} +(1.19921 - 0.683847i) q^{66} +8.14233i q^{67} +(10.2384 - 3.32664i) q^{68} +(-4.40126 - 3.19770i) q^{69} +(2.63051 - 8.09589i) q^{71} +(3.12167 + 1.01429i) q^{72} +(-5.02032 - 6.90988i) q^{73} +(0.356488 + 0.259003i) q^{74} -9.51187 q^{76} +(1.30039 - 11.7673i) q^{77} -0.497655i q^{78} +(-0.121752 - 0.374714i) q^{79} +(-6.66892 + 4.84526i) q^{81} +(0.849457 + 0.276005i) q^{82} +(1.48710 + 0.483189i) q^{83} +(17.0777 - 12.4077i) q^{84} +(-0.182460 - 0.561553i) q^{86} -12.3654i q^{87} +(1.80221 - 0.373020i) q^{88} +6.90425 q^{89} +(-3.45277 - 2.50858i) q^{91} +(-2.12112 - 2.91946i) q^{92} +(-3.65434 - 1.18737i) q^{93} +(-0.302757 + 0.931792i) q^{94} +(3.98865 + 2.89792i) q^{96} +(8.85604 - 2.87750i) q^{97} +0.800446i q^{98} +(-8.07507 + 17.8793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4} - 6 q^{6} - 16 q^{9} - 10 q^{11} - 6 q^{14} - 8 q^{16} + 26 q^{19} + 20 q^{21} + 86 q^{24} - 68 q^{26} + 22 q^{29} - 20 q^{31} - 40 q^{34} + 6 q^{36} - 6 q^{39} + 50 q^{41} + 2 q^{44} + 80 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) \) 32 * q + 4 * q^4 - 6 * q^6 - 16 * q^9 - 10 * q^11 - 6 * q^14 - 8 * q^16 + 26 * q^19 + 20 * q^21 + 86 * q^24 - 68 * q^26 + 22 * q^29 - 20 * q^31 - 40 * q^34 + 6 * q^36 - 6 * q^39 + 50 * q^41 + 2 * q^44 + 80 * q^46 - 32 * q^49 + 70 * q^51 - 120 * q^54 - 40 * q^56 - 28 * q^59 + 32 * q^61 - 80 * q^64 - 110 * q^66 - 70 * q^69 - 92 * q^71 + 14 * q^74 - 124 * q^76 + 78 * q^79 - 86 * q^81 + 108 * q^84 + 4 * q^86 + 44 * q^89 - 68 * q^91 + 80 * q^94 + 216 * q^96 + 20 * q^99

Introduction

L-functions

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