LMFDB - Embedded newform 1710.2.p.c.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(37,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1710.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.p (of order $4$, degree $2$, 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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 $ x^20 + 108x^16 + 1318x^12 + 4652x^8 + 5057x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.7
Root			$0.922947 - 0.922947i$ of defining polynomial
Character	$\chi$	$=$	1710.37
Dual form			1710.2.p.c.1063.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.42113 + 1.72638i) q^{5} +(3.40461 + 3.40461i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.42113 + 1.72638i) q^{5} +(3.40461 + 3.40461i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.215841 + 2.22563i) q^{10} -3.94163 q^{11} +(-4.03748 - 4.03748i) q^{13} +4.81484 q^{14} -1.00000 q^{16} +(3.90683 + 3.90683i) q^{17} +(3.49740 + 2.60158i) q^{19} +(1.72638 + 1.42113i) q^{20} +(-2.78715 + 2.78715i) q^{22} +(-0.537022 + 0.537022i) q^{23} +(-0.960761 - 4.90683i) q^{25} -5.70985 q^{26} +(3.40461 - 3.40461i) q^{28} -6.28455 q^{29} +7.00112i q^{31} +(-0.707107 + 0.707107i) q^{32} +5.52509 q^{34} +(-10.7160 + 1.03924i) q^{35} +(-1.05593 + 1.05593i) q^{37} +(4.31263 - 0.633437i) q^{38} +(2.22563 - 0.215841i) q^{40} +3.03704i q^{41} +(-5.70094 + 5.70094i) q^{43} +3.94163i q^{44} +0.759463i q^{46} +(2.04815 + 2.04815i) q^{47} +16.1827i q^{49} +(-4.14901 - 2.79029i) q^{50} +(-4.03748 + 4.03748i) q^{52} +(-4.39576 - 4.39576i) q^{53} +(5.60158 - 6.80474i) q^{55} -4.81484i q^{56} +(-4.44385 + 4.44385i) q^{58} +2.32680 q^{59} -9.32341 q^{61} +(4.95054 + 4.95054i) q^{62} +1.00000i q^{64} +(12.7080 - 1.23242i) q^{65} +(-7.35838 + 7.35838i) q^{67} +(3.90683 - 3.90683i) q^{68} +(-6.84253 + 8.31224i) q^{70} +9.62969i q^{71} +(4.47808 - 4.47808i) q^{73} +1.49331i q^{74} +(2.60158 - 3.49740i) q^{76} +(-13.4197 - 13.4197i) q^{77} +0.991285 q^{79} +(1.42113 - 1.72638i) q^{80} +(2.14751 + 2.14751i) q^{82} +(-6.64529 + 6.64529i) q^{83} +(-12.2968 + 1.19254i) q^{85} +8.06235i q^{86} +(2.78715 + 2.78715i) q^{88} -7.09242 q^{89} -27.4920i q^{91} +(0.537022 + 0.537022i) q^{92} +2.89652 q^{94} +(-9.46158 + 2.34063i) q^{95} +(7.11482 - 7.11482i) q^{97} +(11.4429 + 11.4429i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 12 q^{5} - 4 q^{7}+O(q^{10}) $ 20 * q - 12 * q^5 - 4 * q^7	$ 20 q - 12 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} + 12 q^{17} + 4 q^{23} - 28 q^{25} - 24 q^{26} - 4 q^{28} - 4 q^{35} + 12 q^{38} - 12 q^{43} + 44 q^{47} + 64 q^{55} - 8 q^{58} + 24 q^{62} + 12 q^{68} - 4 q^{73} + 4 q^{76} - 88 q^{77} + 12 q^{80} - 8 q^{82} - 76 q^{83} - 12 q^{85} - 4 q^{92} + 24 q^{95}+O(q^{100}) $ 20 * q - 12 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 + 12 * q^17 + 4 * q^23 - 28 * q^25 - 24 * q^26 - 4 * q^28 - 4 * q^35 + 12 * q^38 - 12 * q^43 + 44 * q^47 + 64 * q^55 - 8 * q^58 + 24 * q^62 + 12 * q^68 - 4 * q^73 + 4 * q^76 - 88 * q^77 + 12 * q^80 - 8 * q^82 - 76 * q^83 - 12 * q^85 - 4 * q^92 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−1.42113	+	1.72638i	−0.635550	+	0.772060i
$5$	−1.42113	+	1.72638i	−0.635550	+	0.772060i
$6$		0			0
$7$	3.40461	+	3.40461i	1.28682	+	1.28682i	0.936707	+	0.350114i	$0.113857\pi$
$7$	3.40461	+	3.40461i	1.28682	+	1.28682i	0.350114	+	0.936707i	$0.386143\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	0.215841	+	2.22563i	0.0682548	+	0.703805i
$11$	−3.94163			−1.18845			−0.594223	−	0.804300i	$-0.702540\pi$
$11$	−3.94163			−1.18845			−0.594223	+	0.804300i	$0.702540\pi$
$12$		0			0
$13$	−4.03748	−	4.03748i	−1.11979	−	1.11979i	−0.991771	−	0.128023i	$-0.959137\pi$
$13$	−4.03748	−	4.03748i	−1.11979	−	1.11979i	−0.128023	−	0.991771i	$-0.540863\pi$
$14$	4.81484			1.28682
$15$		0			0
$16$	−1.00000			−0.250000
$17$	3.90683	+	3.90683i	0.947544	+	0.947544i	0.998691	−	0.0511467i	$-0.0162876\pi$
$17$	3.90683	+	3.90683i	0.947544	+	0.947544i	−0.0511467	+	0.998691i	$0.516288\pi$
$18$		0			0
$19$	3.49740	+	2.60158i	0.802358	+	0.596844i
$19$	3.49740	+	2.60158i	0.802358	+	0.596844i
$20$	1.72638	+	1.42113i	0.386030	+	0.317775i
$21$		0			0
$22$	−2.78715	+	2.78715i	−0.594223	+	0.594223i
$23$	−0.537022	+	0.537022i	−0.111977	+	0.111977i	−0.760875	−	0.648898i	$-0.775230\pi$
$23$	−0.537022	+	0.537022i	−0.111977	+	0.111977i	0.648898	+	0.760875i	$0.275230\pi$
$24$		0			0
$25$	−0.960761	−	4.90683i	−0.192152	−	0.981365i
$26$	−5.70985			−1.11979
$27$		0			0
$28$	3.40461	−	3.40461i	0.643411	−	0.643411i
$29$	−6.28455			−1.16701			−0.583506	−	0.812109i	$-0.698319\pi$
$29$	−6.28455			−1.16701			−0.583506	+	0.812109i	$0.698319\pi$
$30$		0			0
$31$			7.00112i			1.25744i	0.777633	+	0.628719i	$0.216420\pi$
$31$			7.00112i			1.25744i	−0.777633	+	0.628719i	$0.783580\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	5.52509			0.947544
$35$	−10.7160	+	1.03924i	−1.81134	+	0.175663i
$36$		0			0
$37$	−1.05593	+	1.05593i	−0.173594	+	0.173594i	−0.788556	−	0.614963i	$-0.789171\pi$
$37$	−1.05593	+	1.05593i	−0.173594	+	0.173594i	0.614963	+	0.788556i	$0.289171\pi$
$38$	4.31263	−	0.633437i	0.699601	−	0.102757i
$39$		0			0
$40$	2.22563	−	0.215841i	0.351902	−	0.0341274i
$41$			3.03704i			0.474306i	0.971472	+	0.237153i	$0.0762142\pi$
$41$			3.03704i			0.474306i	−0.971472	+	0.237153i	$0.923786\pi$
$42$		0			0
$43$	−5.70094	+	5.70094i	−0.869386	+	0.869386i	−0.992404	−	0.123018i	$-0.960743\pi$
$43$	−5.70094	+	5.70094i	−0.869386	+	0.869386i	0.123018	+	0.992404i	$0.460743\pi$
$44$			3.94163i			0.594223i
$45$		0			0
$46$			0.759463i			0.111977i
$47$	2.04815	+	2.04815i	0.298753	+	0.298753i	0.840525	−	0.541772i	$-0.182246\pi$
$47$	2.04815	+	2.04815i	0.298753	+	0.298753i	−0.541772	+	0.840525i	$0.682246\pi$
$48$		0			0
$49$			16.1827i			2.31182i
$50$	−4.14901	−	2.79029i	−0.586759	−	0.394606i
$51$		0			0
$52$	−4.03748	+	4.03748i	−0.559897	+	0.559897i
$53$	−4.39576	−	4.39576i	−0.603804	−	0.603804i	0.337516	−	0.941320i	$-0.390413\pi$
$53$	−4.39576	−	4.39576i	−0.603804	−	0.603804i	−0.941320	+	0.337516i	$0.890413\pi$
$54$		0			0
$55$	5.60158	−	6.80474i	0.755317	−	0.917551i
$56$		−	4.81484i		−	0.643411i
$57$		0			0
$58$	−4.44385	+	4.44385i	−0.583506	+	0.583506i
$59$	2.32680			0.302923			0.151462	−	0.988463i	$-0.451602\pi$
$59$	2.32680			0.302923			0.151462	+	0.988463i	$0.451602\pi$
$60$		0			0
$61$	−9.32341			−1.19374			−0.596870	−	0.802338i	$-0.703589\pi$
$61$	−9.32341			−1.19374			−0.596870	+	0.802338i	$0.703589\pi$
$62$	4.95054	+	4.95054i	0.628719	+	0.628719i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	12.7080	−	1.23242i	1.57623	−	0.152863i
$66$		0			0
$67$	−7.35838	+	7.35838i	−0.898969	+	0.898969i	−0.995345	−	0.0963756i	$-0.969275\pi$
$67$	−7.35838	+	7.35838i	−0.898969	+	0.898969i	0.0963756	+	0.995345i	$0.469275\pi$
$68$	3.90683	−	3.90683i	0.473772	−	0.473772i
$69$		0			0
$70$	−6.84253	+	8.31224i	−0.817839	+	0.993503i
$71$			9.62969i			1.14283i	0.820660	+	0.571417i	$0.193606\pi$
$71$			9.62969i			1.14283i	−0.820660	+	0.571417i	$0.806394\pi$
$72$		0			0
$73$	4.47808	−	4.47808i	0.524119	−	0.524119i	−0.394694	−	0.918813i	$-0.629149\pi$
$73$	4.47808	−	4.47808i	0.524119	−	0.524119i	0.918813	+	0.394694i	$0.129149\pi$
$74$			1.49331i			0.173594i
$75$		0			0
$76$	2.60158	−	3.49740i	0.298422	−	0.401179i
$77$	−13.4197	−	13.4197i	−1.52932	−	1.52932i
$78$		0			0
$79$	0.991285			0.111528			0.0557642	−	0.998444i	$-0.482241\pi$
$79$	0.991285			0.111528			0.0557642	+	0.998444i	$0.482241\pi$
$80$	1.42113	−	1.72638i	0.158888	−	0.193015i
$81$		0			0
$82$	2.14751	+	2.14751i	0.237153	+	0.237153i
$83$	−6.64529	+	6.64529i	−0.729416	+	0.729416i	−0.970503	−	0.241088i	$-0.922496\pi$
$83$	−6.64529	+	6.64529i	−0.729416	+	0.729416i	0.241088	+	0.970503i	$0.422496\pi$
$84$		0			0
$85$	−12.2968	+	1.19254i	−1.33377	+	0.129349i
$86$			8.06235i			0.869386i
$87$		0			0
$88$	2.78715	+	2.78715i	0.297112	+	0.297112i
$89$	−7.09242			−0.751795			−0.375897	−	0.926661i	$-0.622666\pi$
$89$	−7.09242			−0.751795			−0.375897	+	0.926661i	$0.622666\pi$
$90$		0			0
$91$		−	27.4920i		−	2.88195i
$92$	0.537022	+	0.537022i	0.0559884	+	0.0559884i
$93$		0			0
$94$	2.89652			0.298753
$95$	−9.46158	+	2.34063i	−0.970737	+	0.240144i
$96$		0			0
$97$	7.11482	−	7.11482i	0.722401	−	0.722401i	−0.246693	−	0.969094i	$-0.579344\pi$
$97$	7.11482	−	7.11482i	0.722401	−	0.722401i	0.969094	+	0.246693i	$0.0793439\pi$
$98$	11.4429	+	11.4429i	1.15591	+	1.15591i
$99$		0			0
$100$	−4.90683	+	0.960761i	−0.490683	+	0.0960761i
$101$	8.97139			0.892686			0.446343	−	0.894862i	$-0.352726\pi$
$101$	8.97139			0.892686			0.446343	+	0.894862i	$0.352726\pi$
$102$		0			0
$103$	−0.231982	−	0.231982i	−0.0228578	−	0.0228578i	0.695585	−	0.718443i	$-0.255145\pi$
$103$	−0.231982	−	0.231982i	−0.0228578	−	0.0228578i	−0.718443	+	0.695585i	$0.755145\pi$
$104$			5.70985i			0.559897i
$105$		0			0
$106$	−6.21654			−0.603804
$107$	11.8222	−	11.8222i	1.14290	−	1.14290i	0.154981	−	0.987917i	$-0.450468\pi$
$107$	11.8222	−	11.8222i	1.14290	−	1.14290i	0.987917	−	0.154981i	$-0.0495316\pi$
$108$		0			0
$109$	11.4774			1.09934			0.549670	−	0.835382i	$-0.314754\pi$
$109$	11.4774			1.09934			0.549670	+	0.835382i	$0.314754\pi$
$110$	−0.850764	−	8.77260i	−0.0811172	−	0.836434i
$111$		0			0
$112$	−3.40461	−	3.40461i	−0.321705	−	0.321705i
$113$	11.2993	+	11.2993i	1.06294	+	1.06294i	0.997881	+	0.0650630i	$0.0207248\pi$
$113$	11.2993	+	11.2993i	1.06294	+	1.06294i	0.0650630	+	0.997881i	$0.479275\pi$
$114$		0			0
$115$	−0.163923	−	1.69028i	−0.0152859	−	0.157620i
$116$			6.28455i			0.583506i
$117$		0			0
$118$	1.64529	−	1.64529i	0.151462	−	0.151462i
$119$			26.6024i			2.43864i
$120$		0			0
$121$	4.53645			0.412404
$122$	−6.59265	+	6.59265i	−0.596870	+	0.596870i
$123$		0			0
$124$	7.00112			0.628719
$125$	9.83640	+	5.31462i	0.879795	+	0.475354i
$126$		0			0
$127$	−2.01606	+	2.01606i	−0.178896	+	0.178896i	−0.790875	−	0.611978i	$-0.790374\pi$
$127$	−2.01606	+	2.01606i	−0.178896	+	0.178896i	0.611978	+	0.790875i	$0.290374\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	8.11446	−	9.85736i	0.711685	−	0.864548i
$131$	10.6608			0.931438			0.465719	−	0.884933i	$-0.345796\pi$
$131$	10.6608			0.931438			0.465719	+	0.884933i	$0.345796\pi$
$132$		0			0
$133$	3.04990	+	20.7646i	0.264460	+	1.80052i
$134$			10.4063i			0.898969i
$135$		0			0
$136$		−	5.52509i		−	0.473772i
$137$	−1.03924	−	1.03924i	−0.0887882	−	0.0887882i	0.661318	−	0.750106i	$-0.269998\pi$
$137$	−1.03924	−	1.03924i	−0.0887882	−	0.0887882i	−0.750106	+	0.661318i	$0.769998\pi$
$138$		0			0
$139$			8.61936i			0.731084i	0.930795	+	0.365542i	$0.119116\pi$
$139$			8.61936i			0.731084i	−0.930795	+	0.365542i	$0.880884\pi$
$140$	1.03924	+	10.7160i	0.0878317	+	0.905671i
$141$		0			0
$142$	6.80922	+	6.80922i	0.571417	+	0.571417i
$143$	15.9142	+	15.9142i	1.33082	+	1.33082i
$144$		0			0
$145$	8.93118	−	10.8495i	0.741694	−	0.901002i
$146$		−	6.33296i		−	0.524119i
$147$		0			0
$148$	1.05593	+	1.05593i	0.0867968	+	0.0867968i
$149$		−	4.87509i		−	0.399383i	−0.979859	−	0.199691i	$-0.936006\pi$
$149$		−	4.87509i		−	0.399383i	0.979859	−	0.199691i	$-0.0639940\pi$
$150$		0			0
$151$		−	10.0048i		−	0.814177i	−0.913389	−	0.407089i	$-0.866544\pi$
$151$		−	10.0048i		−	0.814177i	0.913389	−	0.407089i	$-0.133456\pi$
$152$	−0.633437	−	4.31263i	−0.0513785	−	0.349800i
$153$		0			0
$154$	−18.9783			−1.52932
$155$	−12.0866	−	9.94952i	−0.970817	−	0.799165i
$156$		0			0
$157$	−7.71934	−	7.71934i	−0.616070	−	0.616070i	0.328451	−	0.944521i	$-0.393473\pi$
$157$	−7.71934	−	7.71934i	−0.616070	−	0.616070i	−0.944521	+	0.328451i	$0.893473\pi$
$158$	0.700945	−	0.700945i	0.0557642	−	0.0557642i
$159$		0			0
$160$	−0.215841	−	2.22563i	−0.0170637	−	0.175951i
$161$	−3.65670			−0.288188
$162$		0			0
$163$	−2.46610	+	2.46610i	−0.193160	+	0.193160i	−0.797060	−	0.603900i	$-0.793613\pi$
$163$	−2.46610	+	2.46610i	−0.193160	+	0.193160i	0.603900	+	0.797060i	$0.293613\pi$
$164$	3.03704			0.237153
$165$		0			0
$166$			9.39786i			0.729416i
$167$	12.6049	−	12.6049i	0.975397	−	0.975397i	−0.0243076	−	0.999705i	$-0.507738\pi$
$167$	12.6049	−	12.6049i	0.975397	−	0.975397i	0.999705	+	0.0243076i	$0.00773810\pi$
$168$		0			0
$169$			19.6024i			1.50788i
$170$	−7.85188	+	9.53839i	−0.602212	+	0.731561i
$171$		0			0
$172$	5.70094	+	5.70094i	0.434693	+	0.434693i
$173$	10.8629	+	10.8629i	0.825892	+	0.825892i	0.986946	−	0.161054i	$-0.0514893\pi$
$173$	10.8629	+	10.8629i	0.825892	+	0.825892i	−0.161054	+	0.986946i	$0.551489\pi$
$174$		0			0
$175$	13.4348	−	19.9768i	1.01558	−	1.51011i
$176$	3.94163			0.297112
$177$		0			0
$178$	−5.01510	+	5.01510i	−0.375897	+	0.375897i
$179$	12.4563			0.931024			0.465512	−	0.885042i	$-0.345870\pi$
$179$	12.4563			0.931024			0.465512	+	0.885042i	$0.345870\pi$
$180$		0			0
$181$		−	11.5778i		−	0.860572i	−0.902693	−	0.430286i	$-0.858413\pi$
$181$		−	11.5778i		−	0.860572i	0.902693	−	0.430286i	$-0.141587\pi$
$182$	−19.4398	−	19.4398i	−1.44097	−	1.44097i
$183$		0			0
$184$	0.759463			0.0559884
$185$	−0.322317	−	3.32355i	−0.0236972	−	0.244352i
$186$		0			0
$187$	−15.3993	−	15.3993i	−1.12611	−	1.12611i
$188$	2.04815	−	2.04815i	0.149377	−	0.149377i
$189$		0			0
$190$	−5.03527	+	8.34542i	−0.365297	+	0.605441i
$191$	−7.59311			−0.549418			−0.274709	−	0.961527i	$-0.588582\pi$
$191$	−7.59311			−0.549418			−0.274709	+	0.961527i	$0.588582\pi$
$192$		0			0
$193$	−9.61547	−	9.61547i	−0.692137	−	0.692137i	0.270565	−	0.962702i	$-0.412789\pi$
$193$	−9.61547	−	9.61547i	−0.692137	−	0.692137i	−0.962702	+	0.270565i	$0.912789\pi$
$194$		−	10.0619i		−	0.722401i
$195$		0			0
$196$	16.1827			1.15591
$197$	9.66171	+	9.66171i	0.688368	+	0.688368i	0.961871	−	0.273503i	$-0.0881824\pi$
$197$	9.66171	+	9.66171i	0.688368	+	0.688368i	−0.273503	+	0.961871i	$0.588182\pi$
$198$		0			0
$199$		−	23.6158i		−	1.67408i	−0.547142	−	0.837040i	$-0.684284\pi$
$199$		−	23.6158i		−	1.67408i	0.547142	−	0.837040i	$-0.315716\pi$
$200$	−2.79029	+	4.14901i	−0.197303	+	0.293379i
$201$		0			0
$202$	6.34373	−	6.34373i	0.446343	−	0.446343i
$203$	−21.3964	−	21.3964i	−1.50173	−	1.50173i
$204$		0			0
$205$	−5.24308	−	4.31604i	−0.366192	−	0.301445i
$206$	−0.328072			−0.0228578
$207$		0			0
$208$	4.03748	+	4.03748i	0.279949	+	0.279949i
$209$	−13.7854	−	10.2545i	−0.953559	−	0.709316i
$210$		0			0
$211$			16.4846i			1.13485i	0.823427	+	0.567423i	$0.192059\pi$
$211$			16.4846i			1.13485i	−0.823427	+	0.567423i	$0.807941\pi$
$212$	−4.39576	+	4.39576i	−0.301902	+	0.301902i
$213$		0			0
$214$		−	16.7192i		−	1.14290i
$215$	−1.74018	−	17.9438i	−0.118680	−	1.22376i
$216$		0			0
$217$	−23.8361	+	23.8361i	−1.61810	+	1.61810i
$218$	8.11578	−	8.11578i	0.549670	−	0.549670i
$219$		0			0
$220$	−6.80474	−	5.60158i	−0.458776	−	0.377659i
$221$		−	31.5474i		−	2.12211i
$222$		0			0
$223$	−4.91506	−	4.91506i	−0.329137	−	0.329137i	0.523122	−	0.852258i	$-0.324767\pi$
$223$	−4.91506	−	4.91506i	−0.329137	−	0.329137i	−0.852258	+	0.523122i	$0.824767\pi$
$224$	−4.81484			−0.321705
$225$		0			0
$226$	15.9796			1.06294
$227$	−13.9125	+	13.9125i	−0.923408	+	0.923408i	−0.997269	−	0.0738603i	$-0.976468\pi$
$227$	−13.9125	+	13.9125i	−0.923408	+	0.923408i	0.0738603	+	0.997269i	$0.476468\pi$
$228$		0			0
$229$		−	16.4303i		−	1.08574i	−0.839816	−	0.542872i	$-0.817337\pi$
$229$		−	16.4303i		−	1.08574i	0.839816	−	0.542872i	$-0.182663\pi$
$230$	−1.31112	−	1.07930i	−0.0864527	−	0.0711668i
$231$		0			0
$232$	4.44385	+	4.44385i	0.291753	+	0.291753i
$233$	−0.870707	+	0.870707i	−0.0570419	+	0.0570419i	−0.735052	−	0.678010i	$-0.762842\pi$
$233$	−0.870707	+	0.870707i	−0.0570419	+	0.0570419i	0.678010	+	0.735052i	$0.262842\pi$
$234$		0			0
$235$	−6.44657	+	0.625186i	−0.420528	+	0.0407827i
$236$		−	2.32680i		−	0.151462i
$237$		0			0
$238$	18.8108	+	18.8108i	1.21932	+	1.21932i
$239$		−	8.48625i		−	0.548930i	−0.961597	−	0.274465i	$-0.911499\pi$
$239$		−	8.48625i		−	0.548930i	0.961597	−	0.274465i	$-0.0885007\pi$
$240$		0			0
$241$		−	2.53645i		−	0.163387i	−0.996657	−	0.0816937i	$-0.973967\pi$
$241$		−	2.53645i		−	0.163387i	0.996657	−	0.0816937i	$-0.0260329\pi$
$242$	3.20775	−	3.20775i	0.206202	−	0.206202i
$243$		0			0
$244$			9.32341i			0.596870i
$245$	−27.9375	−	22.9978i	−1.78486	−	1.46928i
$246$		0			0
$247$	−3.61683	−	24.6245i	−0.230133	−	1.56682i
$248$	4.95054	−	4.95054i	0.314360	−	0.314360i
$249$		0			0
$250$	10.7134	−	3.19739i	0.677574	−	0.202221i
$251$	15.7046			0.991268			0.495634	−	0.868531i	$-0.334936\pi$
$251$	15.7046			0.991268			0.495634	+	0.868531i	$0.334936\pi$
$252$		0			0
$253$	2.11674	−	2.11674i	0.133078	−	0.133078i
$254$			2.85114i			0.178896i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−9.53833	+	9.53833i	−0.594985	+	0.594985i	−0.938974	−	0.343989i	$-0.888222\pi$
$257$	−9.53833	+	9.53833i	−0.594985	+	0.594985i	0.343989	+	0.938974i	$0.388222\pi$
$258$		0			0
$259$	−7.19005			−0.446768
$260$	−1.23242	−	12.7080i	−0.0764313	−	0.788117i
$261$		0			0
$262$	7.53832	−	7.53832i	0.465719	−	0.465719i
$263$	1.34136	−	1.34136i	0.0827120	−	0.0827120i	−0.664540	−	0.747252i	$-0.731373\pi$
$263$	1.34136	−	1.34136i	0.0827120	−	0.0827120i	0.747252	+	0.664540i	$0.231373\pi$
$264$		0			0
$265$	13.8357	−	1.34178i	0.849921	−	0.0824251i
$266$	16.8394	+	12.5262i	1.03249	+	0.768031i
$267$		0			0
$268$	7.35838	+	7.35838i	0.449485	+	0.449485i
$269$	1.78351			0.108742			0.0543712	−	0.998521i	$-0.482685\pi$
$269$	1.78351			0.108742			0.0543712	+	0.998521i	$0.482685\pi$
$270$		0			0
$271$	30.0221			1.82371			0.911857	−	0.410507i	$-0.134648\pi$
$271$	30.0221			1.82371			0.911857	+	0.410507i	$0.134648\pi$
$272$	−3.90683	−	3.90683i	−0.236886	−	0.236886i
$273$		0			0
$274$	−1.46971			−0.0887882
$275$	3.78697	+	19.3409i	0.228363	+	1.16630i
$276$		0			0
$277$	14.5286	+	14.5286i	0.872936	+	0.872936i	0.992791	−	0.119855i	$-0.0382430\pi$
$277$	14.5286	+	14.5286i	0.872936	+	0.872936i	−0.119855	+	0.992791i	$0.538243\pi$
$278$	6.09481	+	6.09481i	0.365542	+	0.365542i
$279$		0			0
$280$	8.31224	+	6.84253i	0.496751	+	0.408920i
$281$		−	12.3316i		−	0.735640i	−0.929897	−	0.367820i	$-0.880104\pi$
$281$		−	12.3316i		−	0.735640i	0.929897	−	0.367820i	$-0.119896\pi$
$282$		0			0
$283$	−6.86004	+	6.86004i	−0.407787	+	0.407787i	−0.880966	−	0.473179i	$-0.843106\pi$
$283$	−6.86004	+	6.86004i	−0.407787	+	0.407787i	0.473179	+	0.880966i	$0.343106\pi$
$284$	9.62969			0.571417
$285$		0			0
$286$	22.5061			1.33082
$287$	−10.3399	+	10.3399i	−0.610347	+	0.610347i
$288$		0			0
$289$			13.5266i			0.795681i
$290$	−1.35646	−	13.9871i	−0.0796541	−	0.821348i
$291$		0			0
$292$	−4.47808	−	4.47808i	−0.262060	−	0.262060i
$293$	−18.7006	−	18.7006i	−1.09250	−	1.09250i	−0.995261	−	0.0972386i	$-0.968999\pi$
$293$	−18.7006	−	18.7006i	−1.09250	−	1.09250i	−0.0972386	−	0.995261i	$-0.531001\pi$
$294$		0			0
$295$	−3.30669	+	4.01693i	−0.192523	+	0.233875i
$296$	1.49331			0.0867968
$297$		0			0
$298$	−3.44721	−	3.44721i	−0.199691	−	0.199691i
$299$	4.33642			0.250782
$300$		0			0
$301$	−38.8190			−2.23749
$302$	−7.07444	−	7.07444i	−0.407089	−	0.407089i
$303$		0			0
$304$	−3.49740	−	2.60158i	−0.200589	−	0.149211i
$305$	13.2498	−	16.0957i	0.758682	−	0.921639i
$306$		0			0
$307$	−12.1946	+	12.1946i	−0.695981	+	0.695981i	−0.963541	−	0.267560i	$-0.913783\pi$
$307$	−12.1946	+	12.1946i	−0.695981	+	0.695981i	0.267560	+	0.963541i	$0.413783\pi$
$308$	−13.4197	+	13.4197i	−0.764659	+	0.764659i
$309$		0			0
$310$	−15.5819	+	1.51113i	−0.884991	+	0.0858262i
$311$	3.15000			0.178620			0.0893102	−	0.996004i	$-0.471534\pi$
$311$	3.15000			0.178620			0.0893102	+	0.996004i	$0.471534\pi$
$312$		0			0
$313$	−0.351586	+	0.351586i	−0.0198728	+	0.0198728i	−0.716973	−	0.697101i	$-0.754473\pi$
$313$	−0.351586	+	0.351586i	−0.0198728	+	0.0198728i	0.697101	+	0.716973i	$0.254473\pi$
$314$	−10.9168			−0.616070
$315$		0			0
$316$		−	0.991285i		−	0.0557642i
$317$	−6.49068	+	6.49068i	−0.364553	+	0.364553i	−0.865486	−	0.500933i	$-0.832990\pi$
$317$	−6.49068	+	6.49068i	−0.364553	+	0.364553i	0.500933	+	0.865486i	$0.332990\pi$
$318$		0			0
$319$	24.7714			1.38693
$320$	−1.72638	−	1.42113i	−0.0965075	−	0.0794438i
$321$		0			0
$322$	−2.58567	+	2.58567i	−0.144094	+	0.144094i
$323$	3.49979	+	23.8276i	0.194734	+	1.32581i
$324$		0			0
$325$	−15.9321	+	23.6902i	−0.883756	+	1.31410i
$326$			3.48759i			0.193160i
$327$		0			0
$328$	2.14751	−	2.14751i	0.118576	−	0.118576i
$329$			13.9463i			0.768883i
$330$		0			0
$331$		−	27.0350i		−	1.48598i	−0.669304	−	0.742988i	$-0.733408\pi$
$331$		−	27.0350i		−	1.48598i	0.669304	−	0.742988i	$-0.266592\pi$
$332$	6.64529	+	6.64529i	0.364708	+	0.364708i
$333$		0			0
$334$		−	17.8260i		−	0.975397i
$335$	−2.24611	−	23.1606i	−0.122718	−	1.26540i
$336$		0			0
$337$	−24.0565	+	24.0565i	−1.31044	+	1.31044i	−0.389349	+	0.921090i	$0.627300\pi$
$337$	−24.0565	+	24.0565i	−1.31044	+	1.31044i	−0.921090	+	0.389349i	$0.872700\pi$
$338$	13.8610	+	13.8610i	0.753939	+	0.753939i
$339$		0			0
$340$	1.19254	+	12.2968i	0.0646745	+	0.666886i
$341$		−	27.5958i		−	1.49440i
$342$		0			0
$343$	−31.2636	+	31.2636i	−1.68807	+	1.68807i
$344$	8.06235			0.434693
$345$		0			0
$346$	15.3625			0.825892
$347$	−8.63756	−	8.63756i	−0.463689	−	0.463689i	0.436174	−	0.899862i	$-0.356333\pi$
$347$	−8.63756	−	8.63756i	−0.463689	−	0.463689i	−0.899862	+	0.436174i	$0.856333\pi$
$348$		0			0
$349$		−	5.73255i		−	0.306856i	−0.988160	−	0.153428i	$-0.950969\pi$
$349$		−	5.73255i		−	0.306856i	0.988160	−	0.153428i	$-0.0490313\pi$
$350$	−4.62591	−	23.6256i	−0.247266	−	1.26284i
$351$		0			0
$352$	2.78715	−	2.78715i	0.148556	−	0.148556i
$353$	1.17731	−	1.17731i	0.0626617	−	0.0626617i	−0.675082	−	0.737743i	$-0.735892\pi$
$353$	1.17731	−	1.17731i	0.0626617	−	0.0626617i	0.737743	+	0.675082i	$0.235892\pi$
$354$		0			0
$355$	−16.6245	−	13.6851i	−0.882336	−	0.726328i
$356$			7.09242i			0.375897i
$357$		0			0
$358$	8.80790	−	8.80790i	0.465512	−	0.465512i
$359$		−	30.2918i		−	1.59874i	−0.600838	−	0.799371i	$-0.705166\pi$
$359$		−	30.2918i		−	1.59874i	0.600838	−	0.799371i	$-0.294834\pi$
$360$		0			0
$361$	5.46355	+	18.1975i	0.287555	+	0.957764i
$362$	−8.18675	−	8.18675i	−0.430286	−	0.430286i
$363$		0			0
$364$	−27.4920			−1.44097
$365$	1.36691	+	14.0948i	0.0715473	+	0.737755i
$366$		0			0
$367$	21.4259	+	21.4259i	1.11842	+	1.11842i	0.991973	+	0.126452i	$0.0403590\pi$
$367$	21.4259	+	21.4259i	1.11842	+	1.11842i	0.126452	+	0.991973i	$0.459641\pi$
$368$	0.537022	−	0.537022i	0.0279942	−	0.0279942i
$369$		0			0
$370$	−2.57802	−	2.12219i	−0.134025	−	0.110327i
$371$		−	29.9317i		−	1.55398i
$372$		0			0
$373$	8.80310	+	8.80310i	0.455807	+	0.455807i	0.897276	−	0.441469i	$-0.145543\pi$
$373$	8.80310	+	8.80310i	0.455807	+	0.455807i	−0.441469	+	0.897276i	$0.645543\pi$
$374$	−21.7778			−1.12611
$375$		0			0
$376$		−	2.89652i		−	0.149377i
$377$	25.3737	+	25.3737i	1.30681	+	1.30681i
$378$		0			0
$379$	25.6560			1.31786			0.658929	−	0.752205i	$-0.271010\pi$
$379$	25.6560			1.31786			0.658929	+	0.752205i	$0.271010\pi$
$380$	2.34063	+	9.46158i	0.120072	+	0.485369i
$381$		0			0
$382$	−5.36914	+	5.36914i	−0.274709	+	0.274709i
$383$	−8.22807	−	8.22807i	−0.420435	−	0.420435i	0.464919	−	0.885353i	$-0.346084\pi$
$383$	−8.22807	−	8.22807i	−0.420435	−	0.420435i	−0.885353	+	0.464919i	$0.846084\pi$
$384$		0			0
$385$	42.2387	−	4.09629i	2.15268	−	0.208767i
$386$	−13.5983			−0.692137
$387$		0			0
$388$	−7.11482	−	7.11482i	−0.361200	−	0.361200i
$389$			32.4669i			1.64614i	0.567940	+	0.823070i	$0.307740\pi$
$389$			32.4669i			1.64614i	−0.567940	+	0.823070i	$0.692260\pi$
$390$		0			0
$391$	−4.19610			−0.212206
$392$	11.4429	−	11.4429i	0.577954	−	0.577954i
$393$		0			0
$394$	13.6637			0.688368
$395$	−1.40875	+	1.71133i	−0.0708818	+	0.0861065i
$396$		0			0
$397$	19.6595	+	19.6595i	0.986681	+	0.986681i	0.999912	−	0.0132315i	$-0.00421184\pi$
$397$	19.6595	+	19.6595i	0.986681	+	0.986681i	−0.0132315	+	0.999912i	$0.504212\pi$
$398$	−16.6989	−	16.6989i	−0.837040	−	0.837040i
$399$		0			0
$400$	0.960761	+	4.90683i	0.0480381	+	0.245341i
$401$			7.83053i			0.391038i	0.980700	+	0.195519i	$0.0626391\pi$
$401$			7.83053i			0.391038i	−0.980700	+	0.195519i	$0.937361\pi$
$402$		0			0
$403$	28.2668	−	28.2668i	1.40807	−	1.40807i
$404$		−	8.97139i		−	0.446343i
$405$		0			0
$406$	−30.2591			−1.50173
$407$	4.16208	−	4.16208i	0.206307	−	0.206307i
$408$		0			0
$409$	−29.4446			−1.45594			−0.727970	−	0.685609i	$-0.759536\pi$
$409$	−29.4446			−1.45594			−0.727970	+	0.685609i	$0.759536\pi$
$410$	−6.75931	+	0.655516i	−0.333819	+	0.0323736i
$411$		0			0
$412$	−0.231982	+	0.231982i	−0.0114289	+	0.0114289i
$413$	7.92183	+	7.92183i	0.389808	+	0.389808i
$414$		0			0
$415$	−2.02844	−	20.9161i	−0.0995723	−	1.02673i
$416$	5.70985			0.279949
$417$		0			0
$418$	−16.9988	+	2.49677i	−0.831438	+	0.122121i
$419$			1.77581i			0.0867538i	0.999059	+	0.0433769i	$0.0138116\pi$
$419$			1.77581i			0.0867538i	−0.999059	+	0.0433769i	$0.986188\pi$
$420$		0			0
$421$		−	18.2662i		−	0.890238i	−0.895471	−	0.445119i	$-0.853161\pi$
$421$		−	18.2662i		−	0.890238i	0.895471	−	0.445119i	$-0.146839\pi$
$422$	11.6564	+	11.6564i	0.567423	+	0.567423i
$423$		0			0
$424$			6.21654i			0.301902i
$425$	15.4166	−	22.9236i	0.747814	−	1.11196i
$426$		0			0
$427$	−31.7426	−	31.7426i	−1.53613	−	1.53613i
$428$	−11.8222	−	11.8222i	−0.571449	−	0.571449i
$429$		0			0
$430$	−13.9187	−	11.4577i	−0.671218	−	0.552538i
$431$			23.1683i			1.11598i	0.829849	+	0.557988i	$0.188427\pi$
$431$			23.1683i			1.11598i	−0.829849	+	0.557988i	$0.811573\pi$
$432$		0			0
$433$	17.1100	+	17.1100i	0.822256	+	0.822256i	0.986431	−	0.164175i	$-0.0524963\pi$
$433$	17.1100	+	17.1100i	0.822256	+	0.822256i	−0.164175	+	0.986431i	$0.552496\pi$
$434$			33.7093i			1.61810i
$435$		0			0
$436$		−	11.4774i		−	0.549670i
$437$	−3.27528	+	0.481072i	−0.156678	+	0.0230128i
$438$		0			0
$439$	13.6373			0.650872			0.325436	−	0.945564i	$-0.394489\pi$
$439$	13.6373			0.650872			0.325436	+	0.945564i	$0.394489\pi$
$440$	−8.77260	+	0.850764i	−0.418217	+	0.0405586i
$441$		0			0
$442$	−22.3074	−	22.3074i	−1.06105	−	1.06105i
$443$	0.0905461	−	0.0905461i	0.00430198	−	0.00430198i	−0.704953	−	0.709254i	$-0.749032\pi$
$443$	0.0905461	−	0.0905461i	0.00430198	−	0.00430198i	0.709254	+	0.704953i	$0.249032\pi$
$444$		0			0
$445$	10.0793	−	12.2442i	0.477803	−	0.580431i
$446$	−6.95094			−0.329137
$447$		0			0
$448$	−3.40461	+	3.40461i	−0.160853	+	0.160853i
$449$	−1.35350			−0.0638754			−0.0319377	−	0.999490i	$-0.510168\pi$
$449$	−1.35350			−0.0638754			−0.0319377	+	0.999490i	$0.510168\pi$
$450$		0			0
$451$		−	11.9709i		−	0.563687i
$452$	11.2993	−	11.2993i	0.531472	−	0.531472i
$453$		0			0
$454$			19.6753i			0.923408i
$455$	47.4617	+	39.0699i	2.22504	+	1.83162i
$456$		0			0
$457$	11.4431	+	11.4431i	0.535286	+	0.535286i	0.922141	−	0.386855i	$-0.126438\pi$
$457$	11.4431	+	11.4431i	0.535286	+	0.535286i	−0.386855	+	0.922141i	$0.626438\pi$
$458$	−11.6180	−	11.6180i	−0.542872	−	0.542872i
$459$		0			0
$460$	−1.69028	+	0.163923i	−0.0788098	+	0.00764295i
$461$	32.5009			1.51372			0.756859	−	0.653578i	$-0.226733\pi$
$461$	32.5009			1.51372			0.756859	+	0.653578i	$0.226733\pi$
$462$		0			0
$463$	10.2521	−	10.2521i	0.476455	−	0.476455i	−0.427541	−	0.903996i	$-0.640620\pi$
$463$	10.2521	−	10.2521i	0.476455	−	0.476455i	0.903996	+	0.427541i	$0.140620\pi$
$464$	6.28455			0.291753
$465$		0			0
$466$			1.23137i			0.0570419i
$467$	12.5702	+	12.5702i	0.581682	+	0.581682i	0.935365	−	0.353684i	$-0.115071\pi$
$467$	12.5702	+	12.5702i	0.581682	+	0.581682i	−0.353684	+	0.935365i	$0.615071\pi$
$468$		0			0
$469$	−50.1048			−2.31363
$470$	−4.11634	+	5.00048i	−0.189872	+	0.230655i
$471$		0			0
$472$	−1.64529	−	1.64529i	−0.0757308	−	0.0757308i
$473$	22.4710	−	22.4710i	1.03322	−	1.03322i
$474$		0			0
$475$	9.40534	−	19.6606i	0.431547	−	0.902091i
$476$	26.6024			1.21932
$477$		0			0
$478$	−6.00068	−	6.00068i	−0.274465	−	0.274465i
$479$		−	34.8202i		−	1.59098i	−0.605969	−	0.795488i	$-0.707214\pi$
$479$		−	34.8202i		−	1.59098i	0.605969	−	0.795488i	$-0.292786\pi$
$480$		0			0
$481$	8.52657			0.388778
$482$	−1.79354	−	1.79354i	−0.0816937	−	0.0816937i
$483$		0			0
$484$		−	4.53645i		−	0.206202i
$485$	2.17176	+	22.3940i	0.0986147	+	1.01686i
$486$		0			0
$487$	19.1447	−	19.1447i	0.867529	−	0.867529i	−0.124669	−	0.992198i	$-0.539787\pi$
$487$	19.1447	−	19.1447i	0.867529	−	0.867529i	0.992198	+	0.124669i	$0.0397869\pi$
$488$	6.59265	+	6.59265i	0.298435	+	0.298435i
$489$		0			0
$490$	−36.0167	+	3.49289i	−1.62707	+	0.157793i
$491$	5.10573			0.230418			0.115209	−	0.993341i	$-0.463246\pi$
$491$	5.10573			0.230418			0.115209	+	0.993341i	$0.463246\pi$
$492$		0			0
$493$	−24.5526	−	24.5526i	−1.10580	−	1.10580i
$494$	−19.9696	−	14.8546i	−0.898475	−	0.668342i
$495$		0			0
$496$		−	7.00112i		−	0.314360i
$497$	−32.7853	+	32.7853i	−1.47062	+	1.47062i
$498$		0			0
$499$		−	14.3736i		−	0.643450i	−0.946833	−	0.321725i	$-0.895737\pi$
$499$		−	14.3736i		−	0.643450i	0.946833	−	0.321725i	$-0.104263\pi$
$500$	5.31462	−	9.83640i	0.237677	−	0.439897i
$501$		0			0
$502$	11.1049	−	11.1049i	0.495634	−	0.495634i
$503$	−5.66795	+	5.66795i	−0.252721	+	0.252721i	−0.822085	−	0.569364i	$-0.807189\pi$
$503$	−5.66795	+	5.66795i	−0.252721	+	0.252721i	0.569364	+	0.822085i	$0.307189\pi$
$504$		0			0
$505$	−12.7495	+	15.4880i	−0.567347	+	0.689207i
$506$		−	2.99352i		−	0.133078i
$507$		0			0
$508$	2.01606	+	2.01606i	0.0894481	+	0.0894481i
$509$	−38.1688			−1.69180			−0.845900	−	0.533341i	$-0.820936\pi$
$509$	−38.1688			−1.69180			−0.845900	+	0.533341i	$0.820936\pi$
$510$		0			0
$511$	30.4922			1.34890
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			13.4892i			0.594985i
$515$	0.730165	−	0.0708112i	0.0321749	−	0.00312031i
$516$		0			0
$517$	−8.07304	−	8.07304i	−0.355052	−	0.355052i
$518$	−5.08413	+	5.08413i	−0.223384	+	0.223384i
$519$		0			0
$520$	−9.85736	−	8.11446i	−0.432274	−	0.355843i
$521$		−	18.9469i		−	0.830078i	−0.909804	−	0.415039i	$-0.863768\pi$
$521$		−	18.9469i		−	0.830078i	0.909804	−	0.415039i	$-0.136232\pi$
$522$		0			0
$523$	−2.96461	−	2.96461i	−0.129633	−	0.129633i	0.639313	−	0.768946i	$-0.279219\pi$
$523$	−2.96461	−	2.96461i	−0.129633	−	0.129633i	−0.768946	+	0.639313i	$0.779219\pi$
$524$		−	10.6608i		−	0.465719i
$525$		0			0
$526$		−	1.89697i		−	0.0827120i
$527$	−27.3522	+	27.3522i	−1.19148	+	1.19148i
$528$		0			0
$529$			22.4232i			0.974922i
$530$	8.83454	−	10.7321i	0.383748	−	0.466173i
$531$		0			0
$532$	20.7646	−	3.04990i	0.900261	−	0.132230i
$533$	12.2620	−	12.2620i	0.531125	−	0.531125i
$534$		0			0
$535$	3.60867	+	37.2106i	0.156017	+	1.60875i
$536$	10.4063			0.449485
$537$		0			0
$538$	1.26113	−	1.26113i	0.0543712	−	0.0543712i
$539$		−	63.7863i		−	2.74747i
$540$		0			0
$541$	32.1389			1.38176			0.690879	−	0.722970i	$-0.257224\pi$
$541$	32.1389			1.38176			0.690879	+	0.722970i	$0.257224\pi$
$542$	21.2289	−	21.2289i	0.911857	−	0.911857i
$543$		0			0
$544$	−5.52509			−0.236886
$545$	−16.3110	+	19.8144i	−0.698685	+	0.848756i
$546$		0			0
$547$	2.88206	−	2.88206i	0.123228	−	0.123228i	−0.642803	−	0.766031i	$-0.722229\pi$
$547$	2.88206	−	2.88206i	0.123228	−	0.123228i	0.766031	+	0.642803i	$0.222229\pi$
$548$	−1.03924	+	1.03924i	−0.0443941	+	0.0443941i
$549$		0			0
$550$	16.3539	+	10.9983i	0.697331	+	0.468969i
$551$	−21.9796	−	16.3498i	−0.936361	−	0.696523i
$552$		0			0
$553$	3.37494	+	3.37494i	0.143517	+	0.143517i
$554$	20.5465			0.872936
$555$		0			0
$556$	8.61936			0.365542
$557$	−11.6948	−	11.6948i	−0.495523	−	0.495523i	0.414518	−	0.910041i	$-0.363950\pi$
$557$	−11.6948	−	11.6948i	−0.495523	−	0.495523i	−0.910041	+	0.414518i	$0.863950\pi$
$558$		0			0
$559$	46.0349			1.94707
$560$	10.7160	−	1.03924i	0.452835	−	0.0439159i
$561$		0			0
$562$	−8.71974	−	8.71974i	−0.367820	−	0.367820i
$563$	15.5373	+	15.5373i	0.654819	+	0.654819i	0.954149	−	0.299331i	$-0.0967634\pi$
$563$	15.5373	+	15.5373i	0.654819	+	0.654819i	−0.299331	+	0.954149i	$0.596763\pi$
$564$		0			0
$565$	−35.5645	+	3.44904i	−1.49621	+	0.145102i
$566$			9.70157i			0.407787i
$567$		0			0
$568$	6.80922	−	6.80922i	0.285708	−	0.285708i
$569$	−13.6985			−0.574272			−0.287136	−	0.957890i	$-0.592703\pi$
$569$	−13.6985			−0.574272			−0.287136	+	0.957890i	$0.592703\pi$
$570$		0			0
$571$	17.7058			0.740964			0.370482	−	0.928840i	$-0.379193\pi$
$571$	17.7058			0.740964			0.370482	+	0.928840i	$0.379193\pi$
$572$	15.9142	−	15.9142i	0.665408	−	0.665408i
$573$		0			0
$574$			14.6229i			0.610347i
$575$	3.15102	+	2.11912i	0.131407	+	0.0883735i
$576$		0			0
$577$	−23.4215	−	23.4215i	−0.975050	−	0.975050i	0.0246459	−	0.999696i	$-0.492154\pi$
$577$	−23.4215	−	23.4215i	−0.975050	−	0.975050i	−0.999696	+	0.0246459i	$0.992154\pi$
$578$	9.56473	+	9.56473i	0.397840	+	0.397840i
$579$		0			0
$580$	−10.8495	−	8.93118i	−0.450501	−	0.370847i
$581$	−45.2492			−1.87726
$582$		0			0
$583$	17.3265	+	17.3265i	0.717589	+	0.717589i
$584$	−6.33296			−0.262060
$585$		0			0
$586$	−26.4466			−1.09250
$587$	19.2886	+	19.2886i	0.796126	+	0.796126i	0.982482	−	0.186356i	$-0.0596679\pi$
$587$	19.2886	+	19.2886i	0.796126	+	0.796126i	−0.186356	+	0.982482i	$0.559668\pi$
$588$		0			0
$589$	−18.2140	+	24.4857i	−0.750494	+	1.00891i
$590$	0.502217	+	5.17858i	0.0206760	+	0.213199i
$591$		0			0
$592$	1.05593	−	1.05593i	0.0433984	−	0.0433984i
$593$	−25.4634	+	25.4634i	−1.04566	+	1.04566i	−0.0467490	+	0.998907i	$0.514886\pi$
$593$	−25.4634	+	25.4634i	−1.04566	+	1.04566i	−0.998907	+	0.0467490i	$0.985114\pi$
$594$		0			0
$595$	−45.9258	−	37.8056i	−1.88278	−	1.54988i
$596$	−4.87509			−0.199691
$597$		0			0
$598$	3.06631	−	3.06631i	0.125391	−	0.125391i
$599$	44.5540			1.82043			0.910213	−	0.414140i	$-0.135918\pi$
$599$	44.5540			1.82043			0.910213	+	0.414140i	$0.135918\pi$
$600$		0			0
$601$			21.3945i			0.872700i	0.899777	+	0.436350i	$0.143729\pi$
$601$			21.3945i			0.872700i	−0.899777	+	0.436350i	$0.856271\pi$
$602$	−27.4492	+	27.4492i	−1.11874	+	1.11874i
$603$		0			0
$604$	−10.0048			−0.407089
$605$	−6.44689	+	7.83162i	−0.262104	+	0.318401i
$606$		0			0
$607$	−3.46614	+	3.46614i	−0.140686	+	0.140686i	−0.773942	−	0.633256i	$-0.781718\pi$
$607$	−3.46614	+	3.46614i	−0.140686	+	0.140686i	0.633256	+	0.773942i	$0.281718\pi$
$608$	−4.31263	+	0.633437i	−0.174900	+	0.0256893i
$609$		0			0
$610$	−2.01237	−	20.7504i	−0.0814785	−	0.840160i
$611$		−	16.5387i		−	0.669084i
$612$		0			0
$613$	6.23977	−	6.23977i	0.252022	−	0.252022i	−0.569777	−	0.821799i	$-0.692970\pi$
$613$	6.23977	−	6.23977i	0.252022	−	0.252022i	0.821799	+	0.569777i	$0.192970\pi$
$614$			17.2457i			0.695981i
$615$		0			0
$616$			18.9783i			0.764659i
$617$	9.37481	+	9.37481i	0.377416	+	0.377416i	0.870169	−	0.492753i	$-0.164009\pi$
$617$	9.37481	+	9.37481i	0.377416	+	0.377416i	−0.492753	+	0.870169i	$0.664009\pi$
$618$		0			0
$619$			35.9982i			1.44689i	0.690383	+	0.723444i	$0.257442\pi$
$619$			35.9982i			1.44689i	−0.690383	+	0.723444i	$0.742558\pi$
$620$	−9.94952	+	12.0866i	−0.399582	+	0.485409i
$621$		0			0
$622$	2.22739	−	2.22739i	0.0893102	−	0.0893102i
$623$	−24.1469	−	24.1469i	−0.967426	−	0.967426i
$624$		0			0
$625$	−23.1539	+	9.42858i	−0.926155	+	0.377143i
$626$			0.497217i			0.0198728i
$627$		0			0
$628$	−7.71934	+	7.71934i	−0.308035	+	0.308035i
$629$	−8.25066			−0.328975
$630$		0			0
$631$	−4.26094			−0.169626			−0.0848128	−	0.996397i	$-0.527029\pi$
$631$	−4.26094			−0.169626			−0.0848128	+	0.996397i	$0.527029\pi$
$632$	−0.700945	−	0.700945i	−0.0278821	−	0.0278821i
$633$		0			0
$634$			9.17921i			0.364553i
$635$	−0.615391	−	6.34556i	−0.0244210	−	0.251816i
$636$		0			0
$637$	65.3373	−	65.3373i	2.58876	−	2.58876i
$638$	17.5160	−	17.5160i	0.693465	−	0.693465i
$639$		0			0
$640$	−2.22563	+	0.215841i	−0.0879756	+	0.00853185i
$641$		−	23.3013i		−	0.920345i	−0.887829	−	0.460173i	$-0.847787\pi$
$641$		−	23.3013i		−	0.920345i	0.887829	−	0.460173i	$-0.152213\pi$
$642$		0			0
$643$	−25.8173	+	25.8173i	−1.01814	+	1.01814i	−0.0183043	+	0.999832i	$0.505827\pi$
$643$	−25.8173	+	25.8173i	−1.01814	+	1.01814i	−0.999832	+	0.0183043i	$0.994173\pi$
$644$			3.65670i			0.144094i
$645$		0			0
$646$	19.3234	+	14.3740i	0.760269	+	0.565536i
$647$	−17.2171	−	17.2171i	−0.676875	−	0.676875i	0.282417	−	0.959292i	$-0.408864\pi$
$647$	−17.2171	−	17.2171i	−0.676875	−	0.676875i	−0.959292	+	0.282417i	$0.908864\pi$
$648$		0			0
$649$	−9.17137			−0.360008
$650$	5.48581	+	28.0173i	0.215171	+	1.09893i
$651$		0			0
$652$	2.46610	+	2.46610i	0.0965799	+	0.0965799i
$653$	−8.16718	+	8.16718i	−0.319606	+	0.319606i	−0.848616	−	0.529010i	$-0.822564\pi$
$653$	−8.16718	+	8.16718i	−0.319606	+	0.319606i	0.529010	+	0.848616i	$0.322564\pi$
$654$		0			0
$655$	−15.1504	+	18.4046i	−0.591975	+	0.719126i
$656$		−	3.03704i		−	0.118576i
$657$		0			0
$658$	9.86151	+	9.86151i	0.384442	+	0.384442i
$659$	49.4565			1.92655			0.963275	−	0.268517i	$-0.0865335\pi$
$659$	49.4565			1.92655			0.963275	+	0.268517i	$0.0865335\pi$
$660$		0			0
$661$			42.8869i			1.66811i	0.551683	+	0.834054i	$0.313986\pi$
$661$			42.8869i			1.66811i	−0.551683	+	0.834054i	$0.686014\pi$
$662$	−19.1166	−	19.1166i	−0.742988	−	0.742988i
$663$		0			0
$664$	9.39786			0.364708
$665$	−40.1819	−	24.2440i	−1.55819	−	0.940143i
$666$		0			0
$667$	3.37494	−	3.37494i	0.130678	−	0.130678i
$668$	−12.6049	−	12.6049i	−0.487698	−	0.487698i
$669$		0			0
$670$	−17.9652	−	14.7888i	−0.694058	−	0.571340i
$671$	36.7494			1.41870
$672$		0			0
$673$	−18.4285	−	18.4285i	−0.710368	−	0.710368i	0.256244	−	0.966612i	$-0.417515\pi$
$673$	−18.4285	−	18.4285i	−0.710368	−	0.710368i	−0.966612	+	0.256244i	$0.917515\pi$
$674$			34.0210i			1.31044i
$675$		0			0
$676$	19.6024			0.753939
$677$	−16.5124	+	16.5124i	−0.634623	+	0.634623i	−0.949224	−	0.314601i	$-0.898129\pi$
$677$	−16.5124	+	16.5124i	−0.634623	+	0.634623i	0.314601	+	0.949224i	$0.398129\pi$
$678$		0			0
$679$	48.4464			1.85920
$680$	9.53839	+	7.85188i	0.365780	+	0.301106i
$681$		0			0
$682$	−19.5132	−	19.5132i	−0.747199	−	0.747199i
$683$	0.431737	+	0.431737i	0.0165200	+	0.0165200i	0.715319	−	0.698799i	$-0.246282\pi$
$683$	0.431737	+	0.431737i	0.0165200	+	0.0165200i	−0.698799	+	0.715319i	$0.746282\pi$
$684$		0			0
$685$	3.27102	−	0.317222i	0.124979	−	0.0121204i
$686$			44.2133i			1.68807i
$687$		0			0
$688$	5.70094	−	5.70094i	0.217346	−	0.217346i
$689$			35.4956i			1.35227i
$690$		0			0
$691$	9.51319			0.361899			0.180949	−	0.983492i	$-0.442083\pi$
$691$	9.51319			0.361899			0.180949	+	0.983492i	$0.442083\pi$
$692$	10.8629	−	10.8629i	0.412946	−	0.412946i
$693$		0			0
$694$	−12.2154			−0.463689
$695$	−14.8803	−	12.2493i	−0.564441	−	0.464641i
$696$		0			0
$697$	−11.8652	+	11.8652i	−0.449426	+	0.449426i
$698$	−4.05352	−	4.05352i	−0.153428	−	0.153428i
$699$		0			0
$700$	−19.9768	−	13.4348i	−0.755053	−	0.507788i
$701$	−30.1150			−1.13743			−0.568715	−	0.822535i	$-0.692559\pi$
$701$	−30.1150			−1.13743			−0.568715	+	0.822535i	$0.692559\pi$
$702$		0			0
$703$	−6.44008	+	0.945917i	−0.242892	+	0.0356759i
$704$		−	3.94163i		−	0.148556i
$705$		0			0
$706$		−	1.66496i		−	0.0626617i
$707$	30.5441	+	30.5441i	1.14873	+	1.14873i
$708$		0			0
$709$			15.3806i			0.577632i	0.957385	+	0.288816i	$0.0932616\pi$
$709$			15.3806i			0.577632i	−0.957385	+	0.288816i	$0.906738\pi$
$710$	−21.4321	+	2.07848i	−0.804332	+	0.0780039i
$711$		0			0
$712$	5.01510	+	5.01510i	0.187949	+	0.187949i
$713$	−3.75975	−	3.75975i	−0.140804	−	0.140804i
$714$		0			0
$715$	−50.0902	+	4.85774i	−1.87327	+	0.181669i
$716$		−	12.4563i		−	0.465512i
$717$		0			0
$718$	−21.4196	−	21.4196i	−0.799371	−	0.799371i
$719$			8.69928i			0.324428i	0.986756	+	0.162214i	$0.0518636\pi$
$719$			8.69928i			0.324428i	−0.986756	+	0.162214i	$0.948136\pi$
$720$		0			0
$721$		−	1.57961i		−	0.0588279i
$722$	16.7309	+	9.00427i	0.622660	+	0.335104i
$723$		0			0
$724$	−11.5778			−0.430286
$725$	6.03795	+	30.8372i	0.224244	+	1.14526i
$726$		0			0
$727$	−8.12640	−	8.12640i	−0.301391	−	0.301391i	0.540167	−	0.841558i	$-0.318361\pi$
$727$	−8.12640	−	8.12640i	−0.301391	−	0.301391i	−0.841558	+	0.540167i	$0.818361\pi$
$728$	−19.4398	+	19.4398i	−0.720487	+	0.720487i
$729$		0			0
$730$	10.9331	+	8.99997i	0.404651	+	0.333104i
$731$	−44.5452			−1.64756
$732$		0			0
$733$	3.98915	−	3.98915i	0.147343	−	0.147343i	−0.629587	−	0.776930i	$-0.716776\pi$
$733$	3.98915	−	3.98915i	0.147343	−	0.147343i	0.776930	+	0.629587i	$0.216776\pi$
$734$	30.3008			1.11842
$735$		0			0
$736$		−	0.759463i		−	0.0279942i
$737$	29.0040	−	29.0040i	1.06838	−	1.06838i
$738$		0			0
$739$			10.1757i			0.374317i	0.982330	+	0.187159i	$0.0599279\pi$
$739$			10.1757i			0.374317i	−0.982330	+	0.187159i	$0.940072\pi$
$740$	−3.32355	+	0.322317i	−0.122176	+	0.0118486i
$741$		0			0
$742$	−21.1649	−	21.1649i	−0.776988	−	0.776988i
$743$	−12.6705	−	12.6705i	−0.464836	−	0.464836i	0.435401	−	0.900237i	$-0.356607\pi$
$743$	−12.6705	−	12.6705i	−0.464836	−	0.464836i	−0.900237	+	0.435401i	$0.856607\pi$
$744$		0			0
$745$	8.41625	+	6.92815i	0.308347	+	0.253828i
$746$	12.4495			0.455807
$747$		0			0
$748$	−15.3993	+	15.3993i	−0.563053	+	0.563053i
$749$	80.5001			2.94141
$750$		0			0
$751$		−	23.7459i		−	0.866500i	−0.901274	−	0.433250i	$-0.857367\pi$
$751$		−	23.7459i		−	0.866500i	0.901274	−	0.433250i	$-0.142633\pi$
$752$	−2.04815	−	2.04815i	−0.0746883	−	0.0746883i
$753$		0			0
$754$	35.8839			1.30681
$755$	17.2720	+	14.2181i	0.628593	+	0.517450i
$756$		0			0
$757$	33.7824	+	33.7824i	1.22784	+	1.22784i	0.964779	+	0.263062i	$0.0847322\pi$
$757$	33.7824	+	33.7824i	1.22784	+	1.22784i	0.263062	+	0.964779i	$0.415268\pi$
$758$	18.1415	−	18.1415i	0.658929	−	0.658929i
$759$		0			0
$760$	8.34542	+	5.03527i	0.302720	+	0.182648i
$761$	20.8359			0.755301			0.377650	−	0.925948i	$-0.376732\pi$
$761$	20.8359			0.755301			0.377650	+	0.925948i	$0.376732\pi$
$762$		0			0
$763$	39.0762	+	39.0762i	1.41465	+	1.41465i
$764$			7.59311i			0.274709i
$765$		0			0
$766$	−11.6363			−0.420435
$767$	−9.39439	−	9.39439i	−0.339212	−	0.339212i
$768$		0			0
$769$		−	45.2621i		−	1.63219i	−0.577916	−	0.816096i	$-0.696134\pi$
$769$		−	45.2621i		−	1.63219i	0.577916	−	0.816096i	$-0.303866\pi$
$770$	26.9707	−	32.7638i	0.971958	−	1.18072i
$771$		0			0
$772$	−9.61547	+	9.61547i	−0.346068	+	0.346068i
$773$	14.8984	+	14.8984i	0.535857	+	0.535857i	0.922309	−	0.386452i	$-0.126300\pi$
$773$	14.8984	+	14.8984i	0.535857	+	0.535857i	−0.386452	+	0.922309i	$0.626300\pi$
$774$		0			0
$775$	34.3533	−	6.72640i	1.23401	−	0.241620i
$776$	−10.0619			−0.361200
$777$		0			0
$778$	22.9576	+	22.9576i	0.823070	+	0.823070i
$779$	−7.90110	+	10.6217i	−0.283086	+	0.380563i
$780$		0			0
$781$		−	37.9567i		−	1.35820i
$782$	−2.96709	+	2.96709i	−0.106103	+	0.106103i
$783$		0			0
$784$		−	16.1827i		−	0.577954i
$785$	24.2967	−	2.35629i	0.867186	−	0.0840995i
$786$		0			0
$787$	−11.1825	+	11.1825i	−0.398613	+	0.398613i	−0.877744	−	0.479131i	$-0.840952\pi$
$787$	−11.1825	+	11.1825i	−0.398613	+	0.398613i	0.479131	+	0.877744i	$0.340952\pi$
$788$	9.66171	−	9.66171i	0.344184	−	0.344184i
$789$		0			0
$790$	0.213960	+	2.20623i	0.00761234	+	0.0784942i
$791$			76.9391i			2.73564i
$792$		0			0
$793$	37.6430	+	37.6430i	1.33674	+	1.33674i
$794$	27.8027			0.986681
$795$		0			0
$796$	−23.6158			−0.837040
$797$	10.8613	−	10.8613i	0.384727	−	0.384727i	−0.488075	−	0.872802i	$-0.662301\pi$
$797$	10.8613	−	10.8613i	0.384727	−	0.384727i	0.872802	+	0.488075i	$0.162301\pi$
$798$		0			0
$799$			16.0035i			0.566163i
$800$	4.14901	+	2.79029i	0.146690	+	0.0986516i
$801$		0			0
$802$	5.53702	+	5.53702i	0.195519	+	0.195519i
$803$	−17.6509	+	17.6509i	−0.622887	+	0.622887i
$804$		0			0
$805$	5.19665	−	6.31284i	0.183158	−	0.222498i
$806$		−	39.9754i		−	1.40807i
$807$		0			0
$808$	−6.34373	−	6.34373i	−0.223172	−	0.223172i
$809$			3.35669i			0.118015i	0.998258	+	0.0590074i	$0.0187936\pi$
$809$			3.35669i			0.118015i	−0.998258	+	0.0590074i	$0.981206\pi$
$810$		0			0
$811$			29.8224i			1.04721i	0.851962	+	0.523604i	$0.175413\pi$
$811$			29.8224i			1.04721i	−0.851962	+	0.523604i	$0.824587\pi$
$812$	−21.3964	+	21.3964i	−0.750867	+	0.750867i
$813$		0			0
$814$		−	5.88607i		−	0.206307i
$815$	−0.752764	−	7.76207i	−0.0263682	−	0.271894i
$816$		0			0
$817$	−34.7699	+	5.10699i	−1.21645	+	0.178671i
$818$	−20.8205	+	20.8205i	−0.727970	+	0.727970i
$819$		0			0
$820$	−4.31604	+	5.24308i	−0.150723	+	0.183096i
$821$	−4.78881			−0.167131			−0.0835654	−	0.996502i	$-0.526631\pi$
$821$	−4.78881			−0.167131			−0.0835654	+	0.996502i	$0.526631\pi$
$822$		0			0
$823$	34.2808	−	34.2808i	1.19495	−	1.19495i	0.219295	−	0.975659i	$-0.429624\pi$
$823$	34.2808	−	34.2808i	1.19495	−	1.19495i	0.975659	−	0.219295i	$-0.0703758\pi$
$824$			0.328072i			0.0114289i
$825$		0			0
$826$	11.2032			0.389808
$827$	31.0384	−	31.0384i	1.07931	−	1.07931i	0.0827407	−	0.996571i	$-0.473633\pi$
$827$	31.0384	−	31.0384i	1.07931	−	1.07931i	0.996571	−	0.0827407i	$-0.0263673\pi$
$828$		0			0
$829$	46.7381			1.62328			0.811641	−	0.584156i	$-0.198574\pi$
$829$	46.7381			1.62328			0.811641	+	0.584156i	$0.198574\pi$
$830$	−16.2243	−	13.3556i	−0.563152	−	0.463580i
$831$		0			0
$832$	4.03748	−	4.03748i	0.139974	−	0.139974i
$833$	−63.2231	+	63.2231i	−2.19055	+	2.19055i
$834$		0			0
$835$	3.84758	+	39.6741i	0.133151	+	1.37298i
$836$	−10.2545	+	13.7854i	−0.354658	+	0.476779i
$837$		0			0
$838$	1.25568	+	1.25568i	0.0433769	+	0.0433769i
$839$	0.139898			0.00482982			0.00241491	−	0.999997i	$-0.499231\pi$
$839$	0.139898			0.00482982			0.00241491	+	0.999997i	$0.499231\pi$
$840$		0			0
$841$	10.4956			0.361916
$842$	−12.9161	−	12.9161i	−0.445119	−	0.445119i
$843$		0			0
$844$	16.4846			0.567423
$845$	−33.8412	−	27.8577i	−1.16417	−	0.958332i
$846$		0			0
$847$	15.4448	+	15.4448i	0.530690	+	0.530690i
$848$	4.39576	+	4.39576i	0.150951	+	0.150951i
$849$		0			0
$850$	−5.30829	−	27.1106i	−0.182073	−	0.929887i
$851$		−	1.13411i		−	0.0388769i
$852$		0			0
$853$	6.40830	−	6.40830i	0.219416	−	0.219416i	−0.588836	−	0.808252i	$-0.700414\pi$
$853$	6.40830	−	6.40830i	0.219416	−	0.219416i	0.808252	+	0.588836i	$0.200414\pi$
$854$	−44.8908			−1.53613
$855$		0			0
$856$	−16.7192			−0.571449
$857$	27.2039	−	27.2039i	0.929268	−	0.929268i	−0.0683904	−	0.997659i	$-0.521786\pi$
$857$	27.2039	−	27.2039i	0.929268	−	0.929268i	0.997659	+	0.0683904i	$0.0217863\pi$
$858$		0			0
$859$		−	41.5961i		−	1.41924i	−0.704585	−	0.709620i	$-0.748867\pi$
$859$		−	41.5961i		−	1.41924i	0.704585	−	0.709620i	$-0.251133\pi$
$860$	−17.9438	+	1.74018i	−0.611878	+	0.0593398i
$861$		0			0
$862$	16.3824	+	16.3824i	0.557988	+	0.557988i
$863$	−33.1532	−	33.1532i	−1.12855	−	1.12855i	−0.990414	−	0.138134i	$-0.955890\pi$
$863$	−33.1532	−	33.1532i	−1.12855	−	1.12855i	−0.138134	−	0.990414i	$-0.544110\pi$
$864$		0			0
$865$	−34.1911	+	3.31585i	−1.16253	+	0.112742i
$866$	24.1972			0.822256
$867$		0			0
$868$	23.8361	+	23.8361i	0.809049	+	0.809049i
$869$	−3.90728			−0.132545
$870$		0			0
$871$	59.4186			2.01332
$872$	−8.11578	−	8.11578i	−0.274835	−	0.274835i
$873$		0			0
$874$	−1.97580	+	2.65614i	−0.0668326	+	0.0898454i
$875$	15.3949	+	51.5833i	0.520443	+	1.74383i
$876$		0			0
$877$	−9.83547	+	9.83547i	−0.332120	+	0.332120i	−0.853391	−	0.521271i	$-0.825458\pi$
$877$	−9.83547	+	9.83547i	−0.332120	+	0.332120i	0.521271	+	0.853391i	$0.325458\pi$
$878$	9.64302	−	9.64302i	0.325436	−	0.325436i
$879$		0			0
$880$	−5.60158	+	6.80474i	−0.188829	+	0.229388i
$881$	−36.2626			−1.22172			−0.610859	−	0.791739i	$-0.709176\pi$
$881$	−36.2626			−1.22172			−0.610859	+	0.791739i	$0.709176\pi$
$882$		0			0
$883$	−12.5406	+	12.5406i	−0.422026	+	0.422026i	−0.885901	−	0.463875i	$-0.846459\pi$
$883$	−12.5406	+	12.5406i	−0.422026	+	0.422026i	0.463875	+	0.885901i	$0.346459\pi$
$884$	−31.5474			−1.06105
$885$		0			0
$886$		−	0.128052i		−	0.00430198i
$887$	−27.4178	+	27.4178i	−0.920598	+	0.920598i	−0.997072	−	0.0764734i	$-0.975634\pi$
$887$	−27.4178	+	27.4178i	−0.920598	+	0.920598i	0.0764734	+	0.997072i	$0.475634\pi$
$888$		0			0
$889$	−13.7278			−0.460415
$890$	−1.53083	−	15.7851i	−0.0513136	−	0.529117i
$891$		0			0
$892$	−4.91506	+	4.91506i	−0.164568	+	0.164568i
$893$	1.83476	+	12.4916i	0.0613979	+	0.418016i
$894$		0			0
$895$	−17.7020	+	21.5042i	−0.591713	+	0.718806i
$896$			4.81484i			0.160853i
$897$		0			0
$898$	−0.957066	+	0.957066i	−0.0319377	+	0.0319377i
$899$		−	43.9989i		−	1.46744i
$900$		0			0
$901$		−	34.3469i		−	1.14426i
$902$	−8.46469	−	8.46469i	−0.281843	−	0.281843i
$903$		0			0
$904$		−	15.9796i		−	0.531472i
$905$	19.9877	+	16.4536i	0.664413	+	0.546937i
$906$		0			0
$907$	−24.2538	+	24.2538i	−0.805333	+	0.805333i	−0.983924	−	0.178590i	$-0.942846\pi$
$907$	−24.2538	+	24.2538i	−0.805333	+	0.805333i	0.178590	+	0.983924i	$0.442846\pi$
$908$	13.9125	+	13.9125i	0.461704	+	0.461704i
$909$		0			0
$910$	61.1870	−	5.93390i	2.02833	−	0.196707i
$911$			22.2288i			0.736474i	0.929732	+	0.368237i	$0.120039\pi$
$911$			22.2288i			0.736474i	−0.929732	+	0.368237i	$0.879961\pi$
$912$		0			0
$913$	26.1933	−	26.1933i	0.866871	−	0.866871i
$914$	16.1830			0.535286
$915$		0			0
$916$	−16.4303			−0.542872
$917$	36.2958	+	36.2958i	1.19859	+	1.19859i
$918$		0			0
$919$			17.3806i			0.573334i	0.958030	+	0.286667i	$0.0925474\pi$
$919$			17.3806i			0.573334i	−0.958030	+	0.286667i	$0.907453\pi$
$920$	−1.07930	+	1.31112i	−0.0355834	+	0.0432264i
$921$		0			0
$922$	22.9816	−	22.9816i	0.756859	−	0.756859i
$923$	38.8796	−	38.8796i	1.27974	−	1.27974i
$924$		0			0
$925$	6.19575	+	4.16676i	0.203715	+	0.137002i
$926$		−	14.4986i		−	0.476455i
$927$		0			0
$928$	4.44385	−	4.44385i	0.145876	−	0.145876i
$929$			54.5348i			1.78923i	0.446840	+	0.894614i	$0.352549\pi$
$929$			54.5348i			1.78923i	−0.446840	+	0.894614i	$0.647451\pi$
$930$		0			0
$931$	−42.1006	+	56.5974i	−1.37979	+	1.85490i
$932$	0.870707	+	0.870707i	0.0285210	+	0.0285210i
$933$		0			0
$934$	17.7770			0.581682
$935$	48.4693	−	4.70054i	1.58512	−	0.153724i
$936$		0			0
$937$	8.93268	+	8.93268i	0.291818	+	0.291818i	0.837798	−	0.545980i	$-0.183843\pi$
$937$	8.93268	+	8.93268i	0.291818	+	0.291818i	−0.545980	+	0.837798i	$0.683843\pi$
$938$	−35.4295	+	35.4295i	−1.15681	+	1.15681i
$939$		0			0
$940$	0.625186	+	6.44657i	0.0203913	+	0.210264i
$941$		−	49.0347i		−	1.59849i	−0.601008	−	0.799243i	$-0.705234\pi$
$941$		−	49.0347i		−	1.59849i	0.601008	−	0.799243i	$-0.294766\pi$
$942$		0			0
$943$	−1.63096	−	1.63096i	−0.0531112	−	0.0531112i
$944$	−2.32680			−0.0757308
$945$		0			0
$946$		−	31.7788i		−	1.03322i
$947$	−6.55014	−	6.55014i	−0.212851	−	0.212851i	0.592626	−	0.805477i	$-0.298091\pi$
$947$	−6.55014	−	6.55014i	−0.212851	−	0.212851i	−0.805477	+	0.592626i	$0.798091\pi$
$948$		0			0
$949$	−36.1603			−1.17381
$950$	−7.25157	−	20.5527i	−0.235272	−	0.666819i
$951$		0			0
$952$	18.8108	−	18.8108i	0.609660	−	0.609660i
$953$	4.38061	+	4.38061i	0.141902	+	0.141902i	0.774489	−	0.632587i	$-0.218007\pi$
$953$	4.38061	+	4.38061i	0.141902	+	0.141902i	−0.632587	+	0.774489i	$0.718007\pi$
$954$		0			0
$955$	10.7908	−	13.1086i	0.349183	−	0.424184i
$956$	−8.48625			−0.274465
$957$		0			0
$958$	−24.6216	−	24.6216i	−0.795488	−	0.795488i
$959$		−	7.07640i		−	0.228509i
$960$		0			0
$961$	−18.0157			−0.581150
$962$	6.02920	−	6.02920i	0.194389	−	0.194389i
$963$		0			0
$964$	−2.53645			−0.0816937
$965$	30.2648	−	2.93507i	0.974258	−	0.0944833i
$966$		0			0
$967$	22.3225	+	22.3225i	0.717843	+	0.717843i	0.968163	−	0.250320i	$-0.0805358\pi$
$967$	22.3225	+	22.3225i	0.717843	+	0.717843i	−0.250320	+	0.968163i	$0.580536\pi$
$968$	−3.20775	−	3.20775i	−0.103101	−	0.103101i
$969$		0			0
$970$	17.3706	+	14.2993i	0.557737	+	0.459122i
$971$		−	19.2624i		−	0.618159i	−0.951036	−	0.309079i	$-0.899979\pi$
$971$		−	19.2624i		−	0.618159i	0.951036	−	0.309079i	$-0.100021\pi$
$972$		0			0
$973$	−29.3455	+	29.3455i	−0.940775	+	0.940775i
$974$		−	27.0747i		−	0.867529i
$975$		0			0
$976$	9.32341			0.298435
$977$	−36.7340	+	36.7340i	−1.17523	+	1.17523i	−0.194280	+	0.980946i	$0.562237\pi$
$977$	−36.7340	+	36.7340i	−1.17523	+	1.17523i	−0.980946	+	0.194280i	$0.937763\pi$
$978$		0			0
$979$	27.9557			0.893468
$980$	−22.9978	+	27.9375i	−0.734638	+	0.892430i
$981$		0			0
$982$	3.61029	−	3.61029i	0.115209	−	0.115209i
$983$	−34.6585	−	34.6585i	−1.10543	−	1.10543i	−0.993743	−	0.111692i	$-0.964373\pi$
$983$	−34.6585	−	34.6585i	−1.10543	−	1.10543i	−0.111692	−	0.993743i	$-0.535627\pi$
$984$		0			0
$985$	−30.4103	+	2.94918i	−0.968954	+	0.0939688i
$986$	−34.7227			−1.10580
$987$		0			0
$988$	−24.6245	+	3.61683i	−0.783409	+	0.115067i
$989$		−	6.12306i		−	0.194702i
$990$		0			0
$991$			8.29436i			0.263479i	0.991284	+	0.131740i	$0.0420562\pi$
$991$			8.29436i			0.263479i	−0.991284	+	0.131740i	$0.957944\pi$
$992$	−4.95054	−	4.95054i	−0.157180	−	0.157180i
$993$		0			0
$994$			46.3654i			1.47062i
$995$	40.7698	+	33.5612i	1.29249	+	1.06396i
$996$		0			0
$997$	−41.2771	−	41.2771i	−1.30726	−	1.30726i	−0.923386	−	0.383873i	$-0.874590\pi$
$997$	−41.2771	−	41.2771i	−1.30726	−	1.30726i	−0.383873	−	0.923386i	$-0.625410\pi$
$998$	−10.1637	−	10.1637i	−0.321725	−	0.321725i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.p.c.37.7		20
3.2	odd	2		570.2.m.b.37.4	✓	20
5.3	odd	4	inner	1710.2.p.c.1063.2		20
15.8	even	4		570.2.m.b.493.9	yes	20
19.18	odd	2	inner	1710.2.p.c.37.2		20
57.56	even	2		570.2.m.b.37.9	yes	20
95.18	even	4	inner	1710.2.p.c.1063.7		20
285.113	odd	4		570.2.m.b.493.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.b.37.4	✓	20	3.2	odd	2
570.2.m.b.37.9	yes	20	57.56	even	2
570.2.m.b.493.4	yes	20	285.113	odd	4
570.2.m.b.493.9	yes	20	15.8	even	4
1710.2.p.c.37.2		20	19.18	odd	2	inner
1710.2.p.c.37.7		20	1.1	even	1	trivial
1710.2.p.c.1063.2		20	5.3	odd	4	inner
1710.2.p.c.1063.7		20	95.18	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.42113 + 1.72638i) q^{5} +(3.40461 + 3.40461i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.42113 + 1.72638i) q^{5} +(3.40461 + 3.40461i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.215841 + 2.22563i) q^{10} -3.94163 q^{11} +(-4.03748 - 4.03748i) q^{13} +4.81484 q^{14} -1.00000 q^{16} +(3.90683 + 3.90683i) q^{17} +(3.49740 + 2.60158i) q^{19} +(1.72638 + 1.42113i) q^{20} +(-2.78715 + 2.78715i) q^{22} +(-0.537022 + 0.537022i) q^{23} +(-0.960761 - 4.90683i) q^{25} -5.70985 q^{26} +(3.40461 - 3.40461i) q^{28} -6.28455 q^{29} +7.00112i q^{31} +(-0.707107 + 0.707107i) q^{32} +5.52509 q^{34} +(-10.7160 + 1.03924i) q^{35} +(-1.05593 + 1.05593i) q^{37} +(4.31263 - 0.633437i) q^{38} +(2.22563 - 0.215841i) q^{40} +3.03704i q^{41} +(-5.70094 + 5.70094i) q^{43} +3.94163i q^{44} +0.759463i q^{46} +(2.04815 + 2.04815i) q^{47} +16.1827i q^{49} +(-4.14901 - 2.79029i) q^{50} +(-4.03748 + 4.03748i) q^{52} +(-4.39576 - 4.39576i) q^{53} +(5.60158 - 6.80474i) q^{55} -4.81484i q^{56} +(-4.44385 + 4.44385i) q^{58} +2.32680 q^{59} -9.32341 q^{61} +(4.95054 + 4.95054i) q^{62} +1.00000i q^{64} +(12.7080 - 1.23242i) q^{65} +(-7.35838 + 7.35838i) q^{67} +(3.90683 - 3.90683i) q^{68} +(-6.84253 + 8.31224i) q^{70} +9.62969i q^{71} +(4.47808 - 4.47808i) q^{73} +1.49331i q^{74} +(2.60158 - 3.49740i) q^{76} +(-13.4197 - 13.4197i) q^{77} +0.991285 q^{79} +(1.42113 - 1.72638i) q^{80} +(2.14751 + 2.14751i) q^{82} +(-6.64529 + 6.64529i) q^{83} +(-12.2968 + 1.19254i) q^{85} +8.06235i q^{86} +(2.78715 + 2.78715i) q^{88} -7.09242 q^{89} -27.4920i q^{91} +(0.537022 + 0.537022i) q^{92} +2.89652 q^{94} +(-9.46158 + 2.34063i) q^{95} +(7.11482 - 7.11482i) q^{97} +(11.4429 + 11.4429i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 12 q^{5} - 4 q^{7}+O(q^{10}) \) 20 * q - 12 * q^5 - 4 * q^7	\( 20 q - 12 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} + 12 q^{17} + 4 q^{23} - 28 q^{25} - 24 q^{26} - 4 q^{28} - 4 q^{35} + 12 q^{38} - 12 q^{43} + 44 q^{47} + 64 q^{55} - 8 q^{58} + 24 q^{62} + 12 q^{68} - 4 q^{73} + 4 q^{76} - 88 q^{77} + 12 q^{80} - 8 q^{82} - 76 q^{83} - 12 q^{85} - 4 q^{92} + 24 q^{95}+O(q^{100}) \) 20 * q - 12 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 + 12 * q^17 + 4 * q^23 - 28 * q^25 - 24 * q^26 - 4 * q^28 - 4 * q^35 + 12 * q^38 - 12 * q^43 + 44 * q^47 + 64 * q^55 - 8 * q^58 + 24 * q^62 + 12 * q^68 - 4 * q^73 + 4 * q^76 - 88 * q^77 + 12 * q^80 - 8 * q^82 - 76 * q^83 - 12 * q^85 - 4 * q^92 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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