LMFDB - Embedded newform 275.2.z.c.174.5

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			174.5
Character	$\chi$	$=$	275.174
Dual form			275.2.z.c.49.5

$q$-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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.132580	+	0.0430779i	0.0937484	+	0.0304607i	0.355516	−	0.934670i	$-0.384305\pi$
$2$	0.132580	+	0.0430779i	0.0937484	+	0.0304607i	−0.261767	+	0.965131i	$0.584305\pi$
$3$	−1.75502	−	2.41558i	−1.01326	−	1.39463i	−0.916822	−	0.399296i	$-0.869255\pi$
$3$	−1.75502	−	2.41558i	−1.01326	−	1.39463i	−0.0964394	−	0.995339i	$-0.530745\pi$
$4$	−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	−0.200698	−	0.979653i	$-0.564321\pi$
$7$	2.09815	−	2.88786i	0.793026	−	1.09151i	0.993725	−	0.111854i	$-0.0356789\pi$
$8$	−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	0.147053	−	0.989129i	$-0.453021\pi$
$13$	−1.13710	−	0.369466i	−0.315375	−	0.102471i	−0.462427	+	0.886657i	$0.653021\pi$
$14$	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	−0.859269	−	0.511524i	$-0.829081\pi$
$17$	−5.16941	+	1.67964i	−1.25377	+	0.407373i	−0.394496	+	0.918897i	$0.629081\pi$
$18$	−0.484679	+	0.667104i	−0.114240	+	0.157238i
$19$	3.88538	−	2.82290i	0.891368	−	0.647617i	−0.0448661	−	0.998993i	$-0.514286\pi$
$19$	3.88538	−	2.82290i	0.891368	−	0.647617i	0.936234	+	0.351376i	$0.114286\pi$
$20$		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	$-0.939164\pi$
$23$		−	1.82203i		−	0.379920i	0.981792	−	0.189960i	$-0.0608358\pi$
$24$	−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	0.231515	−	0.972831i	$-0.425632\pi$
$29$	−3.35044	−	2.43424i	−0.622161	−	0.452026i	−0.853676	+	0.520805i	$0.825632\pi$
$30$		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	$0.0631320\pi$
$32$			1.65122i			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	−0.628509	−	0.777802i	$-0.716335\pi$
$37$	1.85794	−	2.55724i	0.305444	−	0.420408i	0.933954	+	0.357394i	$0.116335\pi$
$38$	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	−0.104170	−	0.994559i	$-0.533219\pi$
$41$	5.18347	−	3.76601i	0.809522	−	0.588152i	0.913692	+	0.406408i	$0.133219\pi$
$42$	−1.41306	−	0.459131i	−0.218040	−	0.0708454i
$43$			4.23557i			0.645919i	0.946413	+	0.322959i	$0.104678\pi$
$43$			4.23557i			0.645919i	−0.946413	+	0.322959i	$0.895322\pi$
$44$	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	0.393368	−	0.919381i	$-0.371310\pi$
$47$	−4.13103	−	5.68588i	−0.602573	−	0.829371i	−0.995941	+	0.0900107i	$0.971310\pi$
$48$	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	−0.499164	−	0.866508i	$-0.666359\pi$
$53$	−10.2818	−	3.34076i	−1.41232	−	0.458889i	−0.913152	+	0.407618i	$0.866359\pi$
$54$	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	0.355848	−	0.934544i	$-0.384192\pi$
$59$	−3.24907	−	2.36059i	−0.422993	−	0.307323i	−0.778841	+	0.627221i	$0.784192\pi$
$60$		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	$-0.477686\pi$
$62$	0.105446	−	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	$-0.834298\pi$
$67$		−	8.14233i		−	0.994744i	0.867537	−	0.497372i	$-0.165702\pi$
$68$	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	0.976898	+	0.213707i	$0.0685538\pi$
$71$	2.63051	+	8.09589i	0.312185	+	0.960806i	−0.664713	+	0.747099i	$0.731446\pi$
$72$	3.12167	−	1.01429i	0.367892	−	0.119535i
$73$	−5.02032	+	6.90988i	−0.587584	+	0.808740i	−0.994501	−	0.104725i	$-0.966604\pi$
$73$	−5.02032	+	6.90988i	−0.587584	+	0.808740i	0.406917	+	0.913465i	$0.366604\pi$
$74$	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	−0.957672	−	0.287862i	$-0.907056\pi$
$79$	−0.121752	+	0.374714i	−0.0136982	+	0.0421586i	0.943974	+	0.330020i	$0.107056\pi$
$80$		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	−0.226262	−	0.974067i	$-0.572650\pi$
$83$	1.48710	−	0.483189i	0.163231	−	0.0530369i	0.389492	+	0.921030i	$0.372650\pi$
$84$	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	0.721905	−	0.691993i	$-0.243267\pi$
$97$	8.85604	+	2.87750i	0.899195	+	0.292166i	0.177290	+	0.984159i	$0.443267\pi$
$98$		−	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	−0.983241	−	0.182309i	$-0.941643\pi$
$101$	−0.810256	+	2.49371i	−0.0806235	+	0.248134i	0.902618	+	0.430443i	$0.141643\pi$
$102$	1.32981	+	1.83032i	0.131671	+	0.181229i
$103$	3.88267	−	5.34404i	0.382571	−	0.526564i	−0.573692	−	0.819071i	$-0.694490\pi$
$103$	3.88267	−	5.34404i	0.382571	−	0.526564i	0.956263	+	0.292507i	$0.0944895\pi$
$104$	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	−0.992920	−	0.118785i	$-0.962100\pi$
$107$	−8.26556	−	11.3766i	−0.799062	−	1.09981i	0.193858	−	0.981030i	$-0.437900\pi$
$108$	−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	0.896201	−	0.443648i	$-0.146316\pi$
$113$	2.09760	+	2.88710i	0.197326	+	0.271596i	−0.698875	+	0.715243i	$0.746316\pi$
$114$	−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	−0.0318100	−	0.999494i	$-0.510127\pi$
$127$	5.97215	−	1.94047i	0.529943	−	0.172189i	0.561753	+	0.827305i	$0.310127\pi$
$128$	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	−0.473741	−	0.880664i	$-0.657097\pi$
$137$	−3.97216	+	1.29063i	−0.339364	+	0.110266i	0.134377	+	0.990930i	$0.457097\pi$
$138$	−0.721271	+	0.234355i	−0.0613987	+	0.0199496i
$139$	−2.20927	−	1.60513i	−0.187388	−	0.136145i	0.490136	−	0.871646i	$-0.336947\pi$
$139$	−2.20927	−	1.60513i	−0.187388	−	0.136145i	−0.677524	+	0.735501i	$0.736947\pi$
$140$		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	0.877675	+	0.479256i	$0.159094\pi$
$149$	5.48466	+	16.8800i	0.449321	+	1.38287i	−0.428354	+	0.903611i	$0.640906\pi$
$150$		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	$0.281160\pi$
$152$	−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	0.880464	−	0.474113i	$-0.157231\pi$
$157$	1.97318	+	2.71585i	0.157477	+	0.216749i	−0.722987	+	0.690862i	$0.757231\pi$
$158$	−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	0.551461	−	0.834201i	$-0.314071\pi$
$163$	6.47640	+	2.10431i	0.507271	+	0.164822i	−0.0441897	+	0.999023i	$0.514071\pi$
$164$	−12.6897			−0.990901
$165$		0			0
$166$	0.217975			0.0169182
$167$	18.6804	+	6.06962i	1.44553	+	0.469681i	0.923616	−	0.383318i	$-0.125219\pi$
$167$	18.6804	+	6.06962i	1.44553	+	0.469681i	0.521913	+	0.852999i	$0.325219\pi$
$168$	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	0.803753	−	0.594963i	$-0.202833\pi$
$173$	−0.137634	−	0.189438i	−0.0104642	−	0.0144027i	−0.814217	+	0.580561i	$0.802833\pi$
$174$	−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	0.0593679	−	0.998236i	$-0.481091\pi$
$179$	13.7416	−	9.98383i	1.02709	−	0.746227i	0.967725	+	0.252010i	$0.0810915\pi$
$180$		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	$-0.322992\pi$
$182$	−0.565834	+	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	−0.220070	−	0.975484i	$-0.570629\pi$
$191$	−16.8029	−	12.2080i	−1.21582	−	0.883342i	−0.995746	+	0.0921420i	$0.970629\pi$
$192$	−21.4037	+	6.95450i	−1.54468	+	0.501898i
$193$	8.09586	−	2.63050i	0.582752	−	0.189348i	−0.00278083	−	0.999996i	$-0.500885\pi$
$193$	8.09586	−	2.63050i	0.582752	−	0.189348i	0.585533	+	0.810648i	$0.300885\pi$
$194$	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	$-0.970447\pi$
$197$		−	2.60251i		−	0.185421i	0.995693	−	0.0927106i	$-0.0295531\pi$
$198$	−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	−0.767799	−	0.640690i	$-0.778648\pi$
$211$	3.34024	−	10.2802i	0.229952	−	0.707718i	0.997751	−	0.0670281i	$-0.0213517\pi$
$212$	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	0.937487	−	0.348020i	$-0.113146\pi$
$223$	4.73085	+	6.51146i	0.316801	+	0.436040i	−0.620686	+	0.784059i	$0.713146\pi$
$224$	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	0.183257	+	0.983065i	$0.441336\pi$
$227$	−12.1786	+	16.7624i	−0.808323	+	1.11256i	−0.991580	+	0.129496i	$0.958664\pi$
$228$	16.6935	+	22.9767i	1.10556	+	1.52167i
$229$	−2.47597	+	7.62024i	−0.163616	+	0.503560i	−0.998932	−	0.0462117i	$-0.985285\pi$
$229$	−2.47597	+	7.62024i	−0.163616	+	0.503560i	0.835315	+	0.549771i	$0.185285\pi$
$230$		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	0.963661	−	0.267129i	$-0.0860750\pi$
$233$	24.2133	+	7.86737i	1.58626	+	0.515408i	0.622603	+	0.782538i	$0.286075\pi$
$234$	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	−0.573379	−	0.819290i	$-0.694368\pi$
$239$	0.442580	−	0.321553i	0.0286281	−	0.0207995i	0.602007	+	0.798491i	$0.294368\pi$
$240$		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	−0.874514	−	0.485001i	$-0.838819\pi$
$251$	1.87041	−	5.75652i	0.118059	−	0.363348i	0.992573	+	0.121653i	$0.0388194\pi$
$252$		−	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	−0.749275	−	0.662259i	$-0.769598\pi$
$257$	1.79724	−	2.47369i	0.112109	−	0.154305i	0.861384	+	0.507954i	$0.169598\pi$
$258$	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	$-0.811118\pi$
$263$		−	18.1365i		−	1.11835i	0.829050	−	0.559174i	$-0.188882\pi$
$264$	−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	−0.969777	−	0.243993i	$-0.921543\pi$
$269$	−5.38987	−	16.5883i	−0.328626	−	1.01141i	0.641151	−	0.767415i	$-0.278457\pi$
$270$		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	$0.631352\pi$
$272$	−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	−0.272542	−	0.962144i	$-0.587864\pi$
$277$	−17.6181	−	5.72446i	−1.05857	−	0.343949i	−0.786025	+	0.618195i	$0.787864\pi$
$278$	−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	0.934698	+	0.355444i	$0.115670\pi$
$281$	6.49461	+	19.9884i	0.387436	+	1.19241i	−0.547262	+	0.836962i	$0.684330\pi$
$282$	−1.71947	+	2.36665i	−0.102393	+	0.140932i
$283$	0.955030	+	1.31449i	0.0567706	+	0.0781381i	0.836458	−	0.548030i	$-0.184622\pi$
$283$	0.955030	+	1.31449i	0.0567706	+	0.0781381i	−0.779688	+	0.626169i	$0.784622\pi$
$284$	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	−0.535715	−	0.844399i	$-0.679958\pi$
$293$	7.41008	−	10.1991i	0.432901	−	0.595838i	0.968616	+	0.248561i	$0.0799578\pi$
$294$	−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	$0.223177\pi$
$307$			22.6055i			1.29017i	−0.764112	+	0.645083i	$0.776823\pi$
$308$	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	−0.0709908	−	0.997477i	$-0.522616\pi$
$311$	15.0909	−	10.9642i	0.855729	−	0.621723i	0.926720	+	0.375754i	$0.122616\pi$
$312$	1.16437	−	1.60262i	0.0659196	−	0.0907305i
$313$	−16.6286	+	5.40298i	−0.939907	+	0.305394i	−0.738608	−	0.674136i	$-0.764516\pi$
$313$	−16.6286	+	5.40298i	−0.939907	+	0.305394i	−0.201299	+	0.979530i	$0.564516\pi$
$314$	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	0.592103	−	0.805862i	$-0.298298\pi$
$317$	10.6373	+	3.45627i	0.597450	+	0.194123i	0.00534745	+	0.999986i	$0.498298\pi$
$318$			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	−0.952398	−	0.304857i	$-0.901391\pi$
$337$	−6.75842	+	9.30216i	−0.368154	+	0.506721i	0.584244	+	0.811578i	$0.301391\pi$
$338$	−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	−0.286830	−	0.957982i	$-0.592601\pi$
$347$	0.823501	−	0.267572i	0.0442079	−	0.0143640i	0.331037	+	0.943618i	$0.392601\pi$
$348$	14.3951	−	19.8132i	0.771660	−	1.06210i
$349$	14.3937	−	10.4576i	0.770476	−	0.559784i	−0.131630	−	0.991299i	$-0.542021\pi$
$349$	14.3937	−	10.4576i	0.770476	−	0.559784i	0.902106	+	0.431515i	$0.142021\pi$
$350$		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	$-0.990549\pi$
$353$		−	1.11550i		−	0.0593723i	0.999559	−	0.0296862i	$-0.00945079\pi$
$354$	−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	0.619756	−	0.784794i	$-0.287231\pi$
$359$	1.22945	+	0.893247i	0.0648878	+	0.0471438i	−0.554869	+	0.831938i	$0.687231\pi$
$360$		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	−0.940297	−	0.340356i	$-0.889453\pi$
$367$	−6.24587	+	8.59670i	−0.326032	+	0.448744i	0.614265	+	0.789100i	$0.289453\pi$
$368$	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	$0.257435\pi$
$373$			27.9435i			1.44686i	−0.690399	+	0.723429i	$0.742565\pi$
$374$	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	−0.982758	−	0.184896i	$-0.940805\pi$
$379$	−5.76969	−	17.7573i	−0.296369	−	0.912130i	0.686389	−	0.727235i	$-0.259195\pi$
$380$		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	−0.268974	−	0.963147i	$-0.586685\pi$
$383$	−20.6018	−	6.69393i	−1.05270	−	0.342044i	−0.783729	+	0.621104i	$0.786685\pi$
$384$	−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	−0.951937	−	0.306294i	$-0.900911\pi$
$389$	−30.3224	−	22.0305i	−1.53740	−	1.11699i	−0.585468	−	0.810696i	$-0.699089\pi$
$390$		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	$0.151949\pi$
$397$			18.3084i			0.918873i	−0.888211	+	0.459437i	$0.848051\pi$
$398$	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	0.999824	+	0.0187401i	$0.00596551\pi$
$401$	4.04434	+	12.4472i	0.201965	+	0.621583i	−0.797860	+	0.602843i	$0.794034\pi$
$402$	−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	0.646567	+	0.762857i	$0.276204\pi$
$409$	−6.57096	+	20.2233i	−0.324913	+	0.999980i	−0.971480	+	0.237122i	$0.923796\pi$
$410$		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	−0.392290	−	0.919842i	$-0.628317\pi$
$421$	7.41340	−	5.38615i	0.361307	−	0.262505i	0.753597	+	0.657337i	$0.228317\pi$
$422$	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	−0.495653	−	0.868521i	$-0.665071\pi$
$431$	8.63312	−	26.5700i	0.415843	−	1.27983i	0.911495	−	0.411311i	$-0.134929\pi$
$432$	19.8697	+	27.3484i	0.955984	+	1.31580i
$433$	11.9620	−	16.4642i	0.574856	−	0.791221i	−0.418264	−	0.908325i	$-0.637361\pi$
$433$	11.9620	−	16.4642i	0.574856	−	0.791221i	0.993120	+	0.117105i	$0.0373613\pi$
$434$	−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	−0.919824	−	0.392332i	$-0.871668\pi$
$443$	−21.2309	−	29.2219i	−1.00871	−	1.38837i	−0.0888891	−	0.996042i	$-0.528332\pi$
$444$	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	−0.988507	−	0.151177i	$-0.951694\pi$
$449$	−2.11744	+	6.51680i	−0.0999281	+	0.307547i	0.888579	+	0.458724i	$0.151694\pi$
$450$		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	−0.741967	−	0.670437i	$-0.766107\pi$
$457$	−20.2693	+	6.58590i	−0.948158	+	0.308075i	−0.206191	+	0.978512i	$0.566107\pi$
$458$	−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	$-0.863947\pi$
$463$		−	17.8392i		−	0.829057i	0.910036	−	0.414528i	$-0.136053\pi$
$464$	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	−0.395759	−	0.918354i	$-0.629518\pi$
$467$	−3.80640	+	1.23677i	−0.176139	+	0.0572311i	0.219620	+	0.975586i	$0.429518\pi$
$468$	−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	0.959196	−	0.282743i	$-0.0912443\pi$
$479$	0.372018	+	1.14495i	0.0169979	+	0.0523143i	−0.942198	+	0.335057i	$0.891244\pi$
$480$		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	−0.796105	−	0.605159i	$-0.793109\pi$
$487$	−24.8406	−	34.1902i	−1.12564	−	1.54930i	−0.329531	−	0.944145i	$-0.606891\pi$
$488$	−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	0.201687	−	0.979450i	$-0.435358\pi$
$491$	−14.7908	−	10.7462i	−0.667500	−	0.484967i	−0.869188	+	0.494483i	$0.835358\pi$
$492$	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	0.917158	−	0.398524i	$-0.130477\pi$
$499$	18.3522	+	13.3336i	0.821557	+	0.596896i	−0.0956011	+	0.995420i	$0.530477\pi$
$500$		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	0.984760	+	0.173919i	$0.0556430\pi$
$503$	18.9706	+	26.1108i	0.845859	+	1.16422i	−0.138901	+	0.990306i	$0.544357\pi$
$504$	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	−0.116282	−	0.993216i	$-0.537098\pi$
$509$	17.8771	−	12.9885i	0.792390	−	0.575705i	0.908672	+	0.417512i	$0.137098\pi$
$510$		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	0.847363	−	0.531014i	$-0.178189\pi$
$521$	13.7909	+	10.0196i	0.604189	+	0.438969i	−0.243175	+	0.969983i	$0.578189\pi$
$522$	3.24778	−	1.05527i	0.142151	−	0.0461878i
$523$	19.0148	−	6.17828i	0.831459	−	0.270157i	0.137799	−	0.990460i	$-0.455997\pi$
$523$	19.0148	−	6.17828i	0.831459	−	0.270157i	0.693660	+	0.720303i	$0.255997\pi$
$524$	−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	−0.988116	−	0.153712i	$-0.950877\pi$
$541$	−2.28788	+	7.04138i	−0.0983638	+	0.302733i	0.889752	+	0.456444i	$0.150877\pi$
$542$	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	0.980879	−	0.194617i	$-0.0623464\pi$
$547$	11.5228	+	15.8598i	0.492679	+	0.678115i	−0.488200	+	0.872732i	$0.662346\pi$
$548$	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	−0.544821	−	0.838553i	$-0.683402\pi$
$557$	9.93712	−	13.6773i	0.421049	−	0.579524i	0.965870	+	0.259028i	$0.0834023\pi$
$558$	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	−0.0999340	−	0.994994i	$-0.531863\pi$
$563$	−18.1665	−	5.90264i	−0.765625	−	0.248767i	−0.665691	+	0.746227i	$0.731863\pi$
$564$	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	−0.845980	−	0.533214i	$-0.820984\pi$
$569$	−14.3191	+	10.4034i	−0.600286	+	0.436133i	0.245694	+	0.969347i	$0.420984\pi$
$570$		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	−0.679770	−	0.733425i	$-0.737920\pi$
$577$	−19.1835	+	6.23309i	−0.798619	+	0.259487i	−0.118849	+	0.992912i	$0.537920\pi$
$578$	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	−0.122474	−	0.992472i	$-0.539083\pi$
$587$	20.8185	−	28.6541i	0.859270	−	1.18268i	0.981743	−	0.190211i	$-0.0609173\pi$
$588$	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	$0.287484\pi$
$593$			38.2459i			1.57057i	−0.619134	+	0.785285i	$0.712516\pi$
$594$	−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	−0.981732	−	0.190271i	$-0.939063\pi$
$599$	−7.32601	−	22.5471i	−0.299333	−	0.921251i	0.682399	−	0.730980i	$-0.260937\pi$
$600$		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	$0.764070\pi$
$602$	1.23886	+	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	0.349497	−	0.936938i	$-0.386353\pi$
$607$	2.00862	+	0.652640i	0.0815273	+	0.0264898i	−0.267969	+	0.963427i	$0.586353\pi$
$608$	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	0.774041	−	0.633136i	$-0.218232\pi$
$613$	−1.66624	−	2.29338i	−0.0672986	−	0.0926286i	−0.841340	+	0.540507i	$0.818232\pi$
$614$	−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	$-0.664259\pi$
$617$		−	43.2099i		−	1.73957i	0.493434	−	0.869783i	$-0.335741\pi$
$618$	−2.61489	−	0.849631i	−0.105187	−	0.0341772i
$619$	−37.9078	+	27.5416i	−1.52364	+	1.10699i	−0.563998	+	0.825776i	$0.690738\pi$
$619$	−37.9078	+	27.5416i	−1.52364	+	1.10699i	−0.959645	+	0.281216i	$0.909262\pi$
$620$		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	0.501830	−	0.864966i	$-0.332660\pi$
$631$	−4.16305	−	3.02463i	−0.165728	−	0.120409i	−0.667558	+	0.744558i	$0.732660\pi$
$632$	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	−0.821322	−	0.570465i	$-0.806763\pi$
$641$	−13.4838	+	9.79658i	−0.532580	+	0.386942i	0.288742	+	0.957407i	$0.406763\pi$
$642$	−3.44040	+	4.73530i	−0.135782	+	0.186887i
$643$	34.0436	−	11.0614i	1.34255	−	0.436220i	0.452368	−	0.891831i	$-0.350579\pi$
$643$	34.0436	−	11.0614i	1.34255	−	0.436220i	0.890179	+	0.455611i	$0.150579\pi$
$644$	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	0.836533	−	0.547917i	$-0.184579\pi$
$647$	30.3007	+	9.84530i	1.19124	+	0.387059i	0.354712	+	0.934976i	$0.384579\pi$
$648$			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	−0.831679	−	0.555256i	$-0.812620\pi$
$653$	−1.19071	+	1.63887i	−0.0465961	+	0.0641340i	0.785083	+	0.619390i	$0.212620\pi$
$654$	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	0.921361	−	0.388708i	$-0.127079\pi$
$673$	37.3122	+	12.1235i	1.43828	+	0.467326i	0.516919	+	0.856034i	$0.327079\pi$
$674$	−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	−0.999979	−	0.00653953i	$-0.997918\pi$
$677$	−46.9682	+	15.2609i	−1.80513	+	0.586524i	−0.805156	+	0.593063i	$0.797918\pi$
$678$	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	$0.193088\pi$
$683$			29.7973i			1.14016i	−0.821589	+	0.570081i	$0.806912\pi$
$684$	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	−0.562970	−	0.826478i	$-0.690341\pi$
$691$	9.94364	−	30.6034i	0.378274	−	1.16421i	0.941243	−	0.337729i	$-0.109659\pi$
$692$			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	−0.773613	−	0.633659i	$-0.781552\pi$
$701$	−10.8560	+	7.88737i	−0.410027	+	0.297902i	0.363586	+	0.931561i	$0.381552\pi$
$702$	−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	0.992351	+	0.123451i	$0.0393963\pi$
$709$	6.97855	+	21.4778i	0.262085	+	0.806615i	−0.730266	+	0.683163i	$0.760604\pi$
$710$		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	0.107198	−	0.994238i	$-0.465812\pi$
$719$	−21.5922	−	15.6876i	−0.805253	−	0.585050i	−0.912450	+	0.409187i	$0.865812\pi$
$720$		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	$-0.936930\pi$
$727$		−	10.6151i		−	0.393693i	0.980434	−	0.196846i	$-0.0630700\pi$
$728$	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	−0.646548	−	0.762873i	$-0.723788\pi$
$733$	7.54772	−	10.3886i	0.278782	−	0.383710i	0.925330	+	0.379163i	$0.123788\pi$
$734$	−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	0.549766	+	0.835318i	$0.314717\pi$
$739$	−10.4930	+	32.2942i	−0.385992	+	1.18796i	−0.935758	+	0.352642i	$0.885283\pi$
$740$		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	0.639399	−	0.768875i	$-0.279183\pi$
$743$	43.8477	−	14.2470i	1.60862	−	0.522672i	0.969218	+	0.246203i	$0.0791830\pi$
$744$	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	−0.997354	−	0.0726986i	$-0.976839\pi$
$751$	−33.8831	+	24.6175i	−1.23641	+	0.898306i	−0.239059	+	0.971005i	$0.576839\pi$
$752$	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	0.682325	−	0.731049i	$-0.260969\pi$
$757$	22.1385	+	7.19323i	0.804637	+	0.261442i	0.122312	+	0.992492i	$0.460969\pi$
$758$		−	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	−0.762343	−	0.647174i	$-0.775951\pi$
$761$	6.47737	−	19.9353i	0.234805	−	0.722654i	0.997147	−	0.0754807i	$-0.0240491\pi$
$762$	−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	0.974760	−	0.223254i	$-0.0716681\pi$
$773$	12.8231	+	17.6495i	0.461215	+	0.634808i	−0.513545	+	0.858063i	$0.671668\pi$
$774$	−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	0.123259	−	0.992374i	$-0.460665\pi$
$787$	22.6190	−	7.34937i	0.806281	−	0.261977i	0.683022	+	0.730398i	$0.260665\pi$
$788$	−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	−0.841197	−	0.540729i	$-0.818149\pi$
$797$	−33.9877	+	11.0433i	−1.20391	+	0.391173i	−0.362711	+	0.931902i	$0.618149\pi$
$798$	−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	0.874618	+	0.484812i	$0.161112\pi$
$809$	12.8563	+	39.5676i	0.452003	+	1.39112i	−0.422616	+	0.906309i	$0.638888\pi$
$810$		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	$0.439541\pi$
$812$	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	−0.00765641	−	0.999971i	$-0.502437\pi$
$821$	−27.5371	−	20.0069i	−0.961051	−	0.698244i	−0.953395	+	0.301726i	$0.902437\pi$
$822$	1.02182	+	1.40642i	0.0356401	+	0.0490544i
$823$	5.26935	+	1.71212i	0.183678	+	0.0596806i	0.399412	−	0.916772i	$-0.369214\pi$
$823$	5.26935	+	1.71212i	0.183678	+	0.0596806i	−0.215734	+	0.976452i	$0.569214\pi$
$824$	−3.66547			−0.127693
$825$		0			0
$826$	−1.99845			−0.0695348
$827$	24.4148	+	7.93284i	0.848984	+	0.275852i	0.701021	−	0.713141i	$-0.252728\pi$
$827$	24.4148	+	7.93284i	0.848984	+	0.275852i	0.147964	+	0.988993i	$0.452728\pi$
$828$	−12.5466	−	17.2690i	−0.436026	−	0.600138i
$829$	33.7819	+	24.5440i	1.17329	+	0.852449i	0.991400	−	0.130869i	$-0.0417768\pi$
$829$	33.7819	+	24.5440i	1.17329	+	0.852449i	0.181895	+	0.983318i	$0.441777\pi$
$830$		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	−0.435256	−	0.900307i	$-0.643342\pi$
$839$	8.29817	−	6.02897i	0.286485	−	0.208143i	0.721741	+	0.692163i	$0.243342\pi$
$840$		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	−0.738357	−	0.674410i	$-0.764398\pi$
$853$	−27.4331	+	8.91356i	−0.939292	+	0.305195i	−0.200935	+	0.979605i	$0.564398\pi$
$854$	−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	$0.115397\pi$
$857$			20.7640i			0.709283i	−0.935002	+	0.354642i	$0.884603\pi$
$858$	−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	−0.843899	−	0.536503i	$-0.819745\pi$
$863$	−35.5836	+	11.5618i	−1.21128	+	0.393568i	−0.367380	+	0.930071i	$0.619745\pi$
$864$	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	0.897365	+	0.441289i	$0.145479\pi$
$877$	30.7915	+	42.3808i	1.03975	+	1.43110i	0.142389	+	0.989811i	$0.454521\pi$
$878$	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	0.978210	−	0.207618i	$-0.0665710\pi$
$883$	14.2179	+	19.5693i	0.478470	+	0.658558i	−0.499740	+	0.866176i	$0.666571\pi$
$884$	−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	−0.601593	−	0.798803i	$-0.705467\pi$
$887$	10.2457	−	14.1020i	0.344016	−	0.473497i	0.945609	+	0.325305i	$0.105467\pi$
$888$	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	−0.0969182	−	0.995292i	$-0.530899\pi$
$907$	12.3385	−	4.00901i	0.409692	−	0.133117i	0.506610	+	0.862176i	$0.330899\pi$
$908$	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	0.791269	+	0.611468i	$0.209421\pi$
$911$	−6.28687	+	19.3490i	−0.208293	+	0.641061i	−0.999562	+	0.0295922i	$0.990579\pi$
$912$		−	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	0.895876	−	0.444305i	$-0.146549\pi$
$919$	−2.73013	−	8.40248i	−0.0900587	−	0.277172i	−0.985934	+	0.167133i	$0.946549\pi$
$920$		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	0.841565	−	0.540156i	$-0.181635\pi$
$929$	−4.77831	−	14.7061i	−0.156771	−	0.482492i	−0.998336	+	0.0576639i	$0.981635\pi$
$930$		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	0.873466	−	0.486885i	$-0.161867\pi$
$937$	39.6078	+	12.8694i	1.29393	+	0.420424i	0.420465	+	0.907309i	$0.361867\pi$
$938$	−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	0.843059	+	0.537821i	$0.180753\pi$
$941$	14.6364	+	45.0462i	0.477133	+	1.46847i	−0.365925	+	0.930644i	$0.619247\pi$
$942$	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	$0.235968\pi$
$947$			41.5599i			1.35052i	−0.737581	+	0.675258i	$0.764032\pi$
$948$	−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	−0.988045	−	0.154169i	$-0.950730\pi$
$953$	−16.5498	+	22.7788i	−0.536099	+	0.737877i	0.451946	+	0.892046i	$0.350730\pi$
$954$	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	$-0.667219\pi$
$967$		−	53.8069i		−	1.73031i	0.501502	−	0.865157i	$-0.332781\pi$
$968$	−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	−0.422950	−	0.906153i	$-0.639005\pi$
$971$	9.60235	−	6.97651i	0.308154	−	0.223887i	0.731104	+	0.682266i	$0.239005\pi$
$972$	−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	−0.270673	−	0.962671i	$-0.587246\pi$
$977$	−32.9916	−	10.7196i	−1.05550	−	0.342951i	−0.784823	+	0.619720i	$0.787246\pi$
$978$		−	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	0.194446	−	0.980913i	$-0.437709\pi$
$983$	33.4617	−	46.0561i	1.06726	−	1.46896i	0.872817	−	0.488048i	$-0.162291\pi$
$984$	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	−0.523651	−	0.851933i	$-0.675430\pi$
$997$	14.1584	−	19.4874i	0.448402	−	0.617173i	0.972053	+	0.234760i	$0.0754304\pi$
$998$	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.174.5		32
5.2	odd	4		275.2.h.c.251.3	yes	16
5.3	odd	4		275.2.h.e.251.2	yes	16
5.4	even	2	inner	275.2.z.c.174.4		32
11.5	even	5	inner	275.2.z.c.49.4		32
55.7	even	20		3025.2.a.bm.1.4		8
55.18	even	20		3025.2.a.bj.1.5		8
55.27	odd	20		275.2.h.c.126.3	✓	16
55.37	odd	20		3025.2.a.bi.1.5		8
55.38	odd	20		275.2.h.e.126.2	yes	16
55.48	odd	20		3025.2.a.bn.1.4		8
55.49	even	10	inner	275.2.z.c.49.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.h.c.126.3	✓	16	55.27	odd	20
275.2.h.c.251.3	yes	16	5.2	odd	4
275.2.h.e.126.2	yes	16	55.38	odd	20
275.2.h.e.251.2	yes	16	5.3	odd	4
275.2.z.c.49.4		32	11.5	even	5	inner
275.2.z.c.49.5		32	55.49	even	10	inner
275.2.z.c.174.4		32	5.4	even	2	inner
275.2.z.c.174.5		32	1.1	even	1	trivial
3025.2.a.bi.1.5		8	55.37	odd	20
3025.2.a.bj.1.5		8	55.18	even	20
3025.2.a.bm.1.4		8	55.7	even	20
3025.2.a.bn.1.4		8	55.48	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

Modular forms

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