LMFDB - Embedded newform 925.2.y.b.393.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			393.8
Character	$\chi$	$=$	925.393
Dual form			925.2.y.b.732.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.317786 - 0.183474i) q^{2} +(0.184590 + 0.0494608i) q^{3} +(-0.932675 - 1.61544i) q^{4} +(-0.0495854 - 0.0495854i) q^{6} +(1.90898 + 0.511509i) q^{7} +1.41838i q^{8} +(-2.56645 - 1.48174i) q^{9} +3.45234i q^{11} +(-0.0922616 - 0.344325i) q^{12} +(-2.68284 + 1.54894i) q^{13} +(-0.512798 - 0.512798i) q^{14} +(-1.60511 + 2.78014i) q^{16} +(-3.72683 + 6.45506i) q^{17} +(0.543721 + 0.941752i) q^{18} +(7.19086 + 1.92679i) q^{19} +(0.327079 + 0.188839i) q^{21} +(0.633414 - 1.09710i) q^{22} -1.31718i q^{23} +(-0.0701542 + 0.261819i) q^{24} +1.13676 q^{26} +(-0.805841 - 0.805841i) q^{27} +(-0.954144 - 3.56091i) q^{28} +(2.20635 + 2.20635i) q^{29} +(4.00610 - 4.00610i) q^{31} +(3.47687 - 2.00737i) q^{32} +(-0.170755 + 0.637268i) q^{33} +(2.36867 - 1.36755i) q^{34} +5.52793i q^{36} +(3.14689 - 5.20549i) q^{37} +(-1.93164 - 1.93164i) q^{38} +(-0.571837 + 0.153223i) q^{39} +(-5.80754 + 3.35298i) q^{41} +(-0.0692941 - 0.120021i) q^{42} +12.5857i q^{43} +(5.57705 - 3.21991i) q^{44} +(-0.241668 + 0.418582i) q^{46} +(1.95542 - 1.95542i) q^{47} +(-0.433796 + 0.433796i) q^{48} +(-2.67962 - 1.54708i) q^{49} +(-1.00721 + 1.00721i) q^{51} +(5.00443 + 2.88931i) q^{52} +(-4.59015 + 1.22993i) q^{53} +(0.108234 + 0.403936i) q^{54} +(-0.725515 + 2.70766i) q^{56} +(1.23206 + 0.711331i) q^{57} +(-0.296339 - 1.10595i) q^{58} +(1.37883 + 5.14585i) q^{59} +(9.38781 + 2.51546i) q^{61} +(-2.00810 + 0.538068i) q^{62} +(-4.14137 - 4.14137i) q^{63} +4.94725 q^{64} +(0.171186 - 0.171186i) q^{66} +(-1.28021 + 4.77781i) q^{67} +13.9037 q^{68} +(0.0651488 - 0.243139i) q^{69} +(2.33213 + 4.03937i) q^{71} +(2.10167 - 3.64020i) q^{72} +(-6.43715 + 6.43715i) q^{73} +(-1.95511 + 1.07686i) q^{74} +(-3.59413 - 13.4135i) q^{76} +(-1.76590 + 6.59044i) q^{77} +(0.209834 + 0.0562249i) q^{78} +(8.42204 + 2.25668i) q^{79} +(4.33633 + 7.51074i) q^{81} +2.46074 q^{82} +(13.1368 - 3.51999i) q^{83} -0.704502i q^{84} +(2.30915 - 3.99956i) q^{86} +(0.298142 + 0.516397i) q^{87} -4.89673 q^{88} +(-14.7909 + 3.96321i) q^{89} +(-5.91378 + 1.58459i) q^{91} +(-2.12783 + 1.22850i) q^{92} +(0.937632 - 0.541342i) q^{93} +(-0.980175 + 0.262637i) q^{94} +(0.741082 - 0.198572i) q^{96} -4.35591 q^{97} +(0.567697 + 0.983280i) q^{98} +(5.11547 - 8.86025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.317786	−	0.183474i	−0.224709	−	0.129736i	0.383420	−	0.923574i	$-0.374746\pi$
$2$	−0.317786	−	0.183474i	−0.224709	−	0.129736i	−0.608129	+	0.793839i	$0.708080\pi$
$3$	0.184590	+	0.0494608i	0.106573	+	0.0285562i	0.311711	−	0.950177i	$-0.399098\pi$
$3$	0.184590	+	0.0494608i	0.106573	+	0.0285562i	−0.205138	+	0.978733i	$0.565764\pi$
$4$	−0.932675	−	1.61544i	−0.466337	−	0.807720i
$5$		0			0
$5$		0			0
$6$	−0.0495854	−	0.0495854i	−0.0202431	−	0.0202431i
$7$	1.90898	+	0.511509i	0.721526	+	0.193332i	0.600853	−	0.799360i	$-0.294828\pi$
$7$	1.90898	+	0.511509i	0.721526	+	0.193332i	0.120674	+	0.992692i	$0.461495\pi$
$8$			1.41838i			0.501473i
$9$	−2.56645	−	1.48174i	−0.855483	−	0.493913i
$10$		0			0
$11$			3.45234i			1.04092i	0.853886	+	0.520460i	$0.174239\pi$
$11$			3.45234i			1.04092i	−0.853886	+	0.520460i	$0.825761\pi$
$12$	−0.0922616	−	0.344325i	−0.0266336	−	0.0993981i
$13$	−2.68284	+	1.54894i	−0.744086	+	0.429598i	−0.823553	−	0.567239i	$-0.808011\pi$
$13$	−2.68284	+	1.54894i	−0.744086	+	0.429598i	0.0794671	+	0.996837i	$0.474678\pi$
$14$	−0.512798	−	0.512798i	−0.137051	−	0.137051i
$15$		0			0
$16$	−1.60511	+	2.78014i	−0.401278	+	0.695035i
$17$	−3.72683	+	6.45506i	−0.903889	+	1.56558i	−0.0814869	+	0.996674i	$0.525967\pi$
$17$	−3.72683	+	6.45506i	−0.903889	+	1.56558i	−0.822402	+	0.568907i	$0.807366\pi$
$18$	0.543721	+	0.941752i	0.128156	+	0.221973i
$19$	7.19086	+	1.92679i	1.64970	+	0.442035i	0.959528	−	0.281614i	$-0.0908696\pi$
$19$	7.19086	+	1.92679i	1.64970	+	0.442035i	0.690169	+	0.723648i	$0.257536\pi$
$20$		0			0
$21$	0.327079	+	0.188839i	0.0713745	+	0.0412081i
$22$	0.633414	−	1.09710i	0.135044	−	0.233904i
$23$		−	1.31718i		−	0.274651i	−0.990526	−	0.137326i	$-0.956149\pi$
$23$		−	1.31718i		−	0.274651i	0.990526	−	0.137326i	$-0.0438507\pi$
$24$	−0.0701542	+	0.261819i	−0.0143202	+	0.0534436i
$25$		0			0
$26$	1.13676			0.222937
$27$	−0.805841	−	0.805841i	−0.155084	−	0.155084i
$28$	−0.954144	−	3.56091i	−0.180316	−	0.672949i
$29$	2.20635	+	2.20635i	0.409708	+	0.409708i	0.881637	−	0.471929i	$-0.156442\pi$
$29$	2.20635	+	2.20635i	0.409708	+	0.409708i	−0.471929	+	0.881637i	$0.656442\pi$
$30$		0			0
$31$	4.00610	−	4.00610i	0.719518	−	0.719518i	−0.248989	−	0.968506i	$-0.580098\pi$
$31$	4.00610	−	4.00610i	0.719518	−	0.719518i	0.968506	+	0.248989i	$0.0800982\pi$
$32$	3.47687	−	2.00737i	0.614630	−	0.354857i
$33$	−0.170755	+	0.637268i	−0.0297247	+	0.110934i
$34$	2.36867	−	1.36755i	0.406223	−	0.234533i
$35$		0			0
$36$			5.52793i			0.921321i
$37$	3.14689	−	5.20549i	0.517345	−	0.855777i
$37$	3.14689	−	5.20549i	0.517345	−	0.855777i
$38$	−1.93164	−	1.93164i	−0.313353	−	0.313353i
$39$	−0.571837	+	0.153223i	−0.0915673	+	0.0245354i
$40$		0			0
$41$	−5.80754	+	3.35298i	−0.906985	+	0.523648i	−0.879460	−	0.475973i	$-0.842096\pi$
$41$	−5.80754	+	3.35298i	−0.906985	+	0.523648i	−0.0275253	+	0.999621i	$0.508763\pi$
$42$	−0.0692941	−	0.120021i	−0.0106923	−	0.0185196i
$43$			12.5857i			1.91930i	0.281191	+	0.959652i	$0.409270\pi$
$43$			12.5857i			1.91930i	−0.281191	+	0.959652i	$0.590730\pi$
$44$	5.57705	−	3.21991i	0.840772	−	0.485420i
$45$		0			0
$46$	−0.241668	+	0.418582i	−0.0356320	+	0.0617165i
$47$	1.95542	−	1.95542i	0.285228	−	0.285228i	−0.549962	−	0.835190i	$-0.685358\pi$
$47$	1.95542	−	1.95542i	0.285228	−	0.285228i	0.835190	+	0.549962i	$0.185358\pi$
$48$	−0.433796	+	0.433796i	−0.0626131	+	0.0626131i
$49$	−2.67962	−	1.54708i	−0.382803	−	0.221011i
$50$		0			0
$51$	−1.00721	+	1.00721i	−0.141037	+	0.141037i
$52$	5.00443	+	2.88931i	0.693990	+	0.400675i
$53$	−4.59015	+	1.22993i	−0.630506	+	0.168943i	−0.559899	−	0.828561i	$-0.689160\pi$
$53$	−4.59015	+	1.22993i	−0.630506	+	0.168943i	−0.0706065	+	0.997504i	$0.522493\pi$
$54$	0.108234	+	0.403936i	0.0147288	+	0.0549687i
$55$		0			0
$56$	−0.725515	+	2.70766i	−0.0969510	+	0.361826i
$57$	1.23206	+	0.711331i	0.163191	+	0.0942181i
$58$	−0.296339	−	1.10595i	−0.0389112	−	0.145219i
$59$	1.37883	+	5.14585i	0.179508	+	0.669933i	0.995740	+	0.0922082i	$0.0293925\pi$
$59$	1.37883	+	5.14585i	0.179508	+	0.669933i	−0.816232	+	0.577725i	$0.803941\pi$
$60$		0			0
$61$	9.38781	+	2.51546i	1.20199	+	0.322071i	0.803613	−	0.595152i	$-0.202908\pi$
$61$	9.38781	+	2.51546i	1.20199	+	0.322071i	0.398373	+	0.917223i	$0.369575\pi$
$62$	−2.00810	+	0.538068i	−0.255029	+	0.0683348i
$63$	−4.14137	−	4.14137i	−0.521764	−	0.521764i
$64$	4.94725			0.618407
$65$		0			0
$66$	0.171186	−	0.171186i	0.0210715	−	0.0210715i
$67$	−1.28021	+	4.77781i	−0.156403	+	0.583703i	0.842578	+	0.538574i	$0.181037\pi$
$67$	−1.28021	+	4.77781i	−0.156403	+	0.583703i	−0.998981	+	0.0451292i	$0.985630\pi$
$68$	13.9037			1.68607
$69$	0.0651488	−	0.243139i	0.00784300	−	0.0292705i
$70$		0			0
$71$	2.33213	+	4.03937i	0.276773	+	0.479385i	0.970581	−	0.240775i	$-0.0774016\pi$
$71$	2.33213	+	4.03937i	0.276773	+	0.479385i	−0.693808	+	0.720160i	$0.744068\pi$
$72$	2.10167	−	3.64020i	0.247684	−	0.429002i
$73$	−6.43715	+	6.43715i	−0.753412	+	0.753412i	−0.975114	−	0.221702i	$-0.928839\pi$
$73$	−6.43715	+	6.43715i	−0.753412	+	0.753412i	0.221702	+	0.975114i	$0.428839\pi$
$74$	−1.95511	+	1.07686i	−0.227276	+	0.125182i
$75$		0			0
$76$	−3.59413	−	13.4135i	−0.412275	−	1.53863i
$77$	−1.76590	+	6.59044i	−0.201243	+	0.751051i
$78$	0.209834	+	0.0562249i	0.0237591	+	0.00636622i
$79$	8.42204	+	2.25668i	0.947554	+	0.253896i	0.699324	−	0.714805i	$-0.253485\pi$
$79$	8.42204	+	2.25668i	0.947554	+	0.253896i	0.248230	+	0.968701i	$0.420151\pi$
$80$		0			0
$81$	4.33633	+	7.51074i	0.481814	+	0.834527i
$82$	2.46074			0.271743
$83$	13.1368	−	3.51999i	1.44195	−	0.386369i	0.548733	−	0.835998i	$-0.315111\pi$
$83$	13.1368	−	3.51999i	1.44195	−	0.386369i	0.893215	+	0.449629i	$0.148444\pi$
$84$		−	0.704502i		−	0.0768675i
$85$		0			0
$86$	2.30915	−	3.99956i	0.249002	−	0.431284i
$87$	0.298142	+	0.516397i	0.0319642	+	0.0553636i
$88$	−4.89673			−0.521993
$89$	−14.7909	+	3.96321i	−1.56783	+	0.420100i	−0.935133	−	0.354297i	$-0.884720\pi$
$89$	−14.7909	+	3.96321i	−1.56783	+	0.420100i	−0.632701	+	0.774397i	$0.718054\pi$
$90$		0			0
$91$	−5.91378	+	1.58459i	−0.619933	+	0.166110i
$92$	−2.12783	+	1.22850i	−0.221841	+	0.128080i
$93$	0.937632	−	0.541342i	0.0972279	−	0.0561346i
$94$	−0.980175	+	0.262637i	−0.101097	+	0.0270890i
$95$		0			0
$96$	0.741082	−	0.198572i	0.0756364	−	0.0202667i
$97$	−4.35591			−0.442276			−0.221138	−	0.975243i	$-0.570977\pi$
$97$	−4.35591			−0.442276			−0.221138	+	0.975243i	$0.570977\pi$
$98$	0.567697	+	0.983280i	0.0573461	+	0.0993263i
$99$	5.11547	−	8.86025i	0.514124	−	0.890489i
$100$		0			0
$101$			0.191058i			0.0190110i	0.999955	+	0.00950548i	$0.00302573\pi$
$101$			0.191058i			0.0190110i	−0.999955	+	0.00950548i	$0.996974\pi$
$102$	0.504873	−	0.135280i	0.0499898	−	0.0133947i
$103$	−2.11028			−0.207932			−0.103966	−	0.994581i	$-0.533153\pi$
$103$	−2.11028			−0.207932			−0.103966	+	0.994581i	$0.533153\pi$
$104$	−2.19698	−	3.80529i	−0.215432	−	0.373139i
$105$		0			0
$106$	1.68434	+	0.451319i	0.163598	+	0.0438359i
$107$	−9.51668	−	2.54999i	−0.920012	−	0.246517i	−0.232422	−	0.972615i	$-0.574665\pi$
$107$	−9.51668	−	2.54999i	−0.920012	−	0.246517i	−0.687591	+	0.726099i	$0.741332\pi$
$108$	−0.550200	+	2.05338i	−0.0529431	+	0.197586i
$109$	−4.09076	−	15.2669i	−0.391824	−	1.46231i	−0.827123	−	0.562020i	$-0.810024\pi$
$109$	−4.09076	−	15.2669i	−0.391824	−	1.46231i	0.435300	−	0.900286i	$-0.356642\pi$
$110$		0			0
$111$	0.838351	−	0.805234i	0.0795728	−	0.0764295i
$112$	−4.48619	+	4.48619i	−0.423906	+	0.423906i
$113$	−3.12046	+	5.40479i	−0.293548	+	0.508440i	−0.974646	−	0.223752i	$-0.928169\pi$
$113$	−3.12046	+	5.40479i	−0.293548	+	0.508440i	0.681098	+	0.732192i	$0.261503\pi$
$114$	−0.261021	−	0.452102i	−0.0244469	−	0.0423432i
$115$		0			0
$116$	1.50642	−	5.62203i	0.139867	−	0.521992i
$117$	9.18050			0.848737
$118$	0.505957	−	1.88826i	0.0465771	−	0.173828i
$119$	−10.4163	+	10.4163i	−0.954857	+	0.954857i
$120$		0			0
$121$	−0.918652			−0.0835138
$122$	−2.52179	−	2.52179i	−0.228312	−	0.228312i
$123$	−1.23786	+	0.331682i	−0.111614	+	0.0299068i
$124$	−10.2080	−	2.73523i	−0.916707	−	0.245631i
$125$		0			0
$126$	0.556237	+	2.07590i	0.0495535	+	0.184936i
$127$	−1.03520	−	3.86342i	−0.0918592	−	0.342823i	0.904665	−	0.426123i	$-0.140121\pi$
$127$	−1.03520	−	3.86342i	−0.0918592	−	0.342823i	−0.996525	+	0.0832996i	$0.973454\pi$
$128$	−8.52591	−	4.92244i	−0.753591	−	0.435086i
$129$	−0.622499	+	2.32320i	−0.0548080	+	0.204546i
$130$		0			0
$131$	0.918927	+	3.42948i	0.0802870	+	0.299635i	0.994380	−	0.105869i	$-0.0337625\pi$
$131$	0.918927	+	3.42948i	0.0802870	+	0.299635i	−0.914093	+	0.405505i	$0.867096\pi$
$132$	1.18873	−	0.318519i	0.103465	−	0.0277235i
$133$	12.7416	+	7.35638i	1.10484	+	0.637879i
$134$	1.28344	−	1.28344i	0.110872	−	0.110872i
$135$		0			0
$136$	−9.15573	−	5.28606i	−0.785097	−	0.453276i
$137$	1.62038	−	1.62038i	0.138438	−	0.138438i	−0.634492	−	0.772930i	$-0.718790\pi$
$137$	1.62038	−	1.62038i	0.138438	−	0.138438i	0.772930	+	0.634492i	$0.218790\pi$
$138$	−0.0653130	+	0.0653130i	−0.00555981	+	0.00555981i
$139$	−3.18045	+	5.50870i	−0.269762	+	0.467241i	−0.968800	−	0.247843i	$-0.920278\pi$
$139$	−3.18045	+	5.50870i	−0.269762	+	0.467241i	0.699038	+	0.715084i	$0.253612\pi$
$140$		0			0
$141$	0.457669	−	0.264235i	0.0385427	−	0.0222526i
$142$		−	1.71154i		−	0.143629i
$143$	−5.34746	−	9.26208i	−0.447177	−	0.774534i
$144$	8.23889	−	4.75672i	0.686574	−	0.396394i
$145$		0			0
$146$	3.22669	−	0.864588i	0.267042	−	0.0715538i
$147$	−0.418112	−	0.418112i	−0.0344853	−	0.0344853i
$148$	−11.3442	−	0.228577i	−0.932485	−	0.0187889i
$149$			18.0198i			1.47624i	0.674668	+	0.738121i	$0.264287\pi$
$149$			18.0198i			1.47624i	−0.674668	+	0.738121i	$0.735713\pi$
$150$		0			0
$151$	−0.277285	+	0.160091i	−0.0225651	+	0.0130280i	−0.511240	−	0.859438i	$-0.670814\pi$
$151$	−0.277285	+	0.160091i	−0.0225651	+	0.0130280i	0.488675	+	0.872466i	$0.337480\pi$
$152$	−2.73291	+	10.1994i	−0.221669	+	0.827279i
$153$	19.1294	−	11.0444i	1.54652	−	0.892885i
$154$	1.77035	−	1.77035i	0.142659	−	0.142659i
$155$		0			0
$156$	0.780862	+	0.780862i	0.0625190	+	0.0625190i
$157$	−0.305275	−	1.13930i	−0.0243636	−	0.0909263i	0.952674	−	0.303995i	$-0.0983207\pi$
$157$	−0.305275	−	1.13930i	−0.0243636	−	0.0909263i	−0.977037	+	0.213069i	$0.931654\pi$
$158$	−2.26236	−	2.26236i	−0.179984	−	0.179984i
$159$	−0.908129			−0.0720194
$160$		0			0
$161$	0.673751	−	2.51447i	0.0530990	−	0.198168i
$162$		−	3.18241i		−	0.250034i
$163$	4.59750	−	7.96311i	0.360104	−	0.623719i	−0.627873	−	0.778315i	$-0.716074\pi$
$163$	4.59750	−	7.96311i	0.360104	−	0.623719i	0.987978	+	0.154597i	$0.0494078\pi$
$164$	10.8331	+	6.25449i	0.845922	+	0.488393i
$165$		0			0
$166$	−4.82051	−	1.29165i	−0.374144	−	0.100252i
$167$	−10.8732	−	18.8329i	−0.841392	−	1.45733i	−0.888718	−	0.458454i	$-0.848404\pi$
$167$	−10.8732	−	18.8329i	−0.841392	−	1.45733i	0.0473268	−	0.998879i	$-0.484930\pi$
$168$	−0.267846	+	0.463922i	−0.0206647	+	0.0357924i
$169$	−1.70158	+	2.94722i	−0.130891	+	0.226709i
$170$		0			0
$171$	−15.6000	−	15.6000i	−1.19296	−	1.19296i
$172$	20.3315	−	11.7384i	1.55026	−	0.895043i
$173$	−0.896886	−	3.34723i	−0.0681890	−	0.254485i	0.923414	−	0.383806i	$-0.125387\pi$
$173$	−0.896886	−	3.34723i	−0.0681890	−	0.254485i	−0.991603	+	0.129321i	$0.958720\pi$
$174$		−	0.218805i		−	0.0165876i
$175$		0			0
$176$	−9.59798	−	5.54140i	−0.723475	−	0.417699i
$177$			1.01807i			0.0765229i
$178$	5.42749	+	1.45429i	0.406807	+	0.109004i
$179$	−10.5340	−	10.5340i	−0.787350	−	0.787350i	0.193709	−	0.981059i	$-0.437948\pi$
$179$	−10.5340	−	10.5340i	−0.787350	−	0.787350i	−0.981059	+	0.193709i	$0.937948\pi$
$180$		0			0
$181$	−0.0475195	−	0.0823062i	−0.00353210	−	0.00611777i	0.864254	−	0.503056i	$-0.167791\pi$
$181$	−0.0475195	−	0.0823062i	−0.00353210	−	0.00611777i	−0.867786	+	0.496938i	$0.834458\pi$
$182$	2.17005	+	0.581462i	0.160855	+	0.0431009i
$183$	1.60848	+	0.928657i	0.118902	+	0.0686483i
$184$	1.86827			0.137730
$185$		0			0
$186$	−0.397288			−0.0291306
$187$	−22.2851	−	12.8663i	−1.62964	−	0.940876i
$188$	−4.98265	−	1.33510i	−0.363397	−	0.0973719i
$189$	−1.12614	−	1.95053i	−0.0819145	−	0.141880i
$190$		0			0
$191$	6.76075	+	6.76075i	0.489190	+	0.489190i	0.908051	−	0.418860i	$-0.137570\pi$
$191$	6.76075	+	6.76075i	0.489190	+	0.489190i	−0.418860	+	0.908051i	$0.637570\pi$
$192$	0.913214	+	0.244695i	0.0659056	+	0.0176593i
$193$			0.988625i			0.0711628i	0.999367	+	0.0355814i	$0.0113283\pi$
$193$			0.988625i			0.0711628i	−0.999367	+	0.0355814i	$0.988672\pi$
$194$	1.38425	+	0.799195i	0.0993831	+	0.0573789i
$195$		0			0
$196$			5.77169i			0.412263i
$197$	2.12208	+	7.91972i	0.151192	+	0.564257i	0.999401	+	0.0345956i	$0.0110143\pi$
$197$	2.12208	+	7.91972i	0.151192	+	0.564257i	−0.848209	+	0.529661i	$0.822319\pi$
$198$	−3.25125	+	1.87711i	−0.231056	+	0.133400i
$199$	0.311060	+	0.311060i	0.0220505	+	0.0220505i	0.718046	−	0.695996i	$-0.245037\pi$
$199$	0.311060	+	0.311060i	0.0220505	+	0.0220505i	−0.695996	+	0.718046i	$0.745037\pi$
$200$		0			0
$201$	−0.472629	+	0.818617i	−0.0333367	+	0.0577408i
$202$	0.0350541	−	0.0607155i	0.00246640	−	0.00427192i
$203$	3.08330	+	5.34044i	0.216405	+	0.374825i
$204$	2.56648	+	0.687687i	0.179690	+	0.0481477i
$205$		0			0
$206$	0.670616	+	0.387180i	0.0467240	+	0.0269761i
$207$	−1.95172	+	3.38048i	−0.135654	+	0.234960i
$208$		−	9.94489i		−	0.689554i
$209$	−6.65192	+	24.8253i	−0.460123	+	1.71720i
$210$		0			0
$211$	1.21043			0.0833298			0.0416649	−	0.999132i	$-0.486734\pi$
$211$	1.21043			0.0833298			0.0416649	+	0.999132i	$0.486734\pi$
$212$	6.26799	+	6.26799i	0.430487	+	0.430487i
$213$	0.230698	+	0.860977i	0.0158072	+	0.0589932i
$214$	2.55641	+	2.55641i	0.174753	+	0.174753i
$215$		0			0
$216$	1.14299	−	1.14299i	0.0777706	−	0.0777706i
$217$	9.69673	−	5.59841i	0.658257	−	0.380045i
$218$	−1.50109	+	5.60216i	−0.101667	+	0.379426i
$219$	−1.50662	+	0.869849i	−0.101808	+	0.0587789i
$220$		0			0
$221$		−	23.0905i		−	1.55324i
$222$	−0.414156	+	0.102077i	−0.0277963	+	0.00685094i
$223$	−13.8676	−	13.8676i	−0.928645	−	0.928645i	0.0689736	−	0.997618i	$-0.478028\pi$
$223$	−13.8676	−	13.8676i	−0.928645	−	0.928645i	−0.997618	+	0.0689736i	$0.978028\pi$
$224$	7.66406	−	2.05358i	0.512077	−	0.137211i
$225$		0			0
$226$	1.98328	−	1.14504i	0.131926	−	0.0761672i
$227$	10.0052	+	17.3295i	0.664066	+	1.15020i	0.979538	+	0.201261i	$0.0645040\pi$
$227$	10.0052	+	17.3295i	0.664066	+	1.15020i	−0.315471	+	0.948935i	$0.602163\pi$
$228$		−	2.65376i		−	0.175750i
$229$	−3.19465	+	1.84443i	−0.211108	+	0.121883i	−0.601826	−	0.798627i	$-0.705560\pi$
$229$	−3.19465	+	1.84443i	−0.211108	+	0.121883i	0.390718	+	0.920510i	$0.372227\pi$
$230$		0			0
$231$	−0.651937	+	1.12919i	−0.0428943	+	0.0742951i
$232$	−3.12944	+	3.12944i	−0.205458	+	0.205458i
$233$	9.61670	−	9.61670i	0.630011	−	0.630011i	−0.318060	−	0.948071i	$-0.603031\pi$
$233$	9.61670	−	9.61670i	0.630011	−	0.630011i	0.948071	+	0.318060i	$0.103031\pi$
$234$	−2.91743	−	1.68438i	−0.190719	−	0.110111i
$235$		0			0
$236$	7.02682	−	7.02682i	0.457407	−	0.457407i
$237$	1.44301	+	0.833121i	0.0937335	+	0.0541171i
$238$	5.22125	−	1.39903i	0.338443	−	0.0906856i
$239$	3.51998	+	13.1367i	0.227689	+	0.849745i	0.981310	+	0.192436i	$0.0616388\pi$
$239$	3.51998	+	13.1367i	0.227689	+	0.849745i	−0.753621	+	0.657309i	$0.771695\pi$
$240$		0			0
$241$	6.11044	−	22.8045i	0.393608	−	1.46897i	−0.430530	−	0.902576i	$-0.641673\pi$
$241$	6.11044	−	22.8045i	0.393608	−	1.46897i	0.824138	−	0.566389i	$-0.191660\pi$
$242$	0.291935	+	0.168548i	0.0187663	+	0.0108347i
$243$	1.31383	+	4.90329i	0.0842823	+	0.314546i
$244$	−4.69221	−	17.5115i	−0.300388	−	1.12106i
$245$		0			0
$246$	0.454228	+	0.121710i	0.0289605	+	0.00775995i
$247$	−22.2764	+	5.96894i	−1.41741	+	0.379795i
$248$	5.68218	+	5.68218i	0.360819	+	0.360819i
$249$	2.59902			0.164706
$250$		0			0
$251$	0.401654	−	0.401654i	0.0253522	−	0.0253522i	−0.694317	−	0.719669i	$-0.744293\pi$
$251$	0.401654	−	0.401654i	0.0253522	−	0.0253522i	0.719669	+	0.694317i	$0.244293\pi$
$252$	−2.82759	+	10.5527i	−0.178121	+	0.664757i
$253$	4.54736			0.285890
$254$	−0.379864	+	1.41767i	−0.0238348	+	0.0889527i
$255$		0			0
$256$	−3.14098	−	5.44033i	−0.196311	−	0.340021i
$257$	−8.18028	+	14.1687i	−0.510272	+	0.883817i	0.489657	+	0.871915i	$0.337122\pi$
$257$	−8.18028	+	14.1687i	−0.510272	+	0.883817i	−0.999929	+	0.0119019i	$0.996211\pi$
$258$	0.624067	−	0.624067i	0.0388527	−	0.0388527i
$259$	8.66999	−	8.32751i	0.538727	−	0.517446i
$260$		0			0
$261$	−2.39324	−	8.93171i	−0.148138	−	0.552859i
$262$	0.337198	−	1.25844i	0.0208322	−	0.0777467i
$263$	17.1622	+	4.59860i	1.05827	+	0.283562i	0.745664	−	0.666322i	$-0.232132\pi$
$263$	17.1622	+	4.59860i	1.05827	+	0.283562i	0.312603	+	0.949884i	$0.398799\pi$
$264$	−0.903888	−	0.242196i	−0.0556305	−	0.0149061i
$265$		0			0
$266$	−2.69941	−	4.67551i	−0.165511	−	0.286674i
$267$	−2.92628			−0.179085
$268$	8.91229	−	2.38804i	0.544405	−	0.145873i
$269$		−	23.2463i		−	1.41735i	−0.705533	−	0.708677i	$-0.749292\pi$
$269$		−	23.2463i		−	1.41735i	0.705533	−	0.708677i	$-0.250708\pi$
$270$		0			0
$271$	−8.50840	+	14.7370i	−0.516848	+	0.895208i	0.482960	+	0.875642i	$0.339562\pi$
$271$	−8.50840	+	14.7370i	−0.516848	+	0.895208i	−0.999809	+	0.0195654i	$0.993772\pi$
$272$	−11.9640	−	20.7222i	−0.725422	−	1.25647i
$273$	−1.17000			−0.0708117
$274$	−0.812229	+	0.217636i	−0.0490686	+	0.0131479i
$275$		0			0
$276$	−0.453539	+	0.121525i	−0.0272998	+	0.00731497i
$277$	−1.34426	+	0.776108i	−0.0807686	+	0.0466318i	−0.539840	−	0.841767i	$-0.681515\pi$
$277$	−1.34426	+	0.776108i	−0.0807686	+	0.0466318i	0.459072	+	0.888399i	$0.348182\pi$
$278$	2.02140	−	1.16706i	0.121236	−	0.0699954i
$279$	−16.2175	+	4.34546i	−0.970914	+	0.260156i
$280$		0			0
$281$	9.62089	−	2.57791i	0.573934	−	0.153785i	0.0398338	−	0.999206i	$-0.487317\pi$
$281$	9.62089	−	2.57791i	0.573934	−	0.153785i	0.534100	+	0.845421i	$0.320650\pi$
$282$	−0.193921			−0.0115478
$283$	−12.4174	−	21.5075i	−0.738137	−	1.27849i	−0.953333	−	0.301919i	$-0.902373\pi$
$283$	−12.4174	−	21.5075i	−0.738137	−	1.27849i	0.215197	−	0.976571i	$-0.430961\pi$
$284$	4.35024	−	7.53484i	0.258139	−	0.447110i
$285$		0			0
$286$			3.92448i			0.232059i
$287$	−12.8015	+	3.43016i	−0.755652	+	0.202476i
$288$	−11.8976			−0.701074
$289$	−19.2785	−	33.3914i	−1.13403	−	1.96420i
$290$		0			0
$291$	−0.804058	−	0.215447i	−0.0471347	−	0.0126297i
$292$	16.4026	+	4.39507i	0.959890	+	0.257202i
$293$	−1.71562	+	6.40278i	−0.100227	+	0.374054i	−0.997760	−	0.0668940i	$-0.978691\pi$
$293$	−1.71562	+	6.40278i	−0.100227	+	0.374054i	0.897533	+	0.440948i	$0.145358\pi$
$294$	0.0561575	+	0.209583i	0.00327517	+	0.0122231i
$295$		0			0
$296$	7.38336	+	4.46348i	0.429149	+	0.259435i
$297$	2.78204	−	2.78204i	0.161430	−	0.161430i
$298$	3.30617	−	5.72645i	0.191521	−	0.331724i
$299$	2.04023	+	3.53379i	0.117990	+	0.204364i
$300$		0			0
$301$	−6.43771	+	24.0259i	−0.371063	+	1.38483i
$302$	0.117490			0.00676077
$303$	−0.00944986	+	0.0352674i	−0.000542881	+	0.00202606i
$304$	−16.8989	+	16.8989i	−0.969217	+	0.969217i
$305$		0			0
$306$	−8.10542			−0.463356
$307$	9.43347	+	9.43347i	0.538396	+	0.538396i	0.923058	−	0.384661i	$-0.125682\pi$
$307$	9.43347	+	9.43347i	0.538396	+	0.538396i	−0.384661	+	0.923058i	$0.625682\pi$
$308$	12.2935	−	3.29403i	0.700486	−	0.187695i
$309$	−0.389536	−	0.104376i	−0.0221599	−	0.00593773i
$310$		0			0
$311$	−2.04001	−	7.61341i	−0.115678	−	0.431717i	0.883659	−	0.468132i	$-0.155073\pi$
$311$	−2.04001	−	7.61341i	−0.115678	−	0.431717i	−0.999337	+	0.0364152i	$0.988406\pi$
$312$	−0.217329	−	0.811083i	−0.0123038	−	0.0459185i
$313$	1.99301	+	1.15066i	0.112651	+	0.0650393i	0.555267	−	0.831672i	$-0.312616\pi$
$313$	1.99301	+	1.15066i	0.112651	+	0.0650393i	−0.442616	+	0.896711i	$0.645949\pi$
$314$	−0.112020	+	0.418065i	−0.00632166	+	0.0235927i
$315$		0			0
$316$	−4.20950	−	15.7101i	−0.236803	−	0.883759i
$317$	7.84772	−	2.10279i	0.440772	−	0.118104i	−0.0316064	−	0.999500i	$-0.510062\pi$
$317$	7.84772	−	2.10279i	0.440772	−	0.118104i	0.472378	+	0.881396i	$0.343396\pi$
$318$	0.288591	+	0.166618i	0.0161834	+	0.00934347i
$319$	−7.61706	+	7.61706i	−0.426473	+	0.426473i
$320$		0			0
$321$	−1.63056	−	0.941405i	−0.0910091	−	0.0525441i
$322$	−0.675448	+	0.675448i	−0.0376413	+	0.0376413i
$323$	−39.2366	+	39.2366i	−2.18318	+	2.18318i
$324$	8.08877	−	14.0102i	0.449376	−	0.778342i
$325$		0			0
$326$	−2.92204	+	1.68704i	−0.161837	+	0.0934366i
$327$		−	3.02046i		−	0.167032i
$328$	−4.75581	−	8.23730i	−0.262596	−	0.454829i
$329$	4.73308	−	2.73265i	0.260943	−	0.150656i
$330$		0			0
$331$	−23.6164	+	6.32799i	−1.29807	+	0.347818i	−0.840722	−	0.541468i	$-0.817869\pi$
$331$	−23.6164	+	6.32799i	−1.29807	+	0.347818i	−0.457352	+	0.889285i	$0.651202\pi$
$332$	−17.9387	−	17.9387i	−0.984512	−	0.984512i
$333$	−15.7895	+	8.69676i	−0.865259	+	0.476579i
$334$			7.97977i			0.436634i
$335$		0			0
$336$	−1.05000	+	0.606217i	−0.0572821	+	0.0330718i
$337$	5.02735	−	18.7623i	0.273857	−	1.02205i	−0.682746	−	0.730656i	$-0.739214\pi$
$337$	5.02735	−	18.7623i	0.273857	−	1.02205i	0.956603	−	0.291394i	$-0.0941190\pi$
$338$	1.08148	−	0.624391i	0.0588245	−	0.0339624i
$339$	−0.843331	+	0.843331i	−0.0458035	+	0.0458035i
$340$		0			0
$341$	13.8304	+	13.8304i	0.748960	+	0.748960i
$342$	2.09527	+	7.81964i	0.113299	+	0.422838i
$343$	−14.1063	−	14.1063i	−0.761667	−	0.761667i
$344$	−17.8513			−0.962479
$345$		0			0
$346$	−0.329110	+	1.22826i	−0.0176931	+	0.0660315i
$347$			3.39588i			0.182300i	0.995837	+	0.0911501i	$0.0290543\pi$
$347$			3.39588i			0.182300i	−0.995837	+	0.0911501i	$0.970946\pi$
$348$	0.556139	−	0.963262i	0.0298122	−	0.0516363i
$349$	−0.334598	−	0.193180i	−0.0179106	−	0.0103407i	0.491018	−	0.871149i	$-0.336625\pi$
$349$	−0.334598	−	0.193180i	−0.0179106	−	0.0103407i	−0.508929	+	0.860809i	$0.669958\pi$
$350$		0			0
$351$	3.41014	+	0.913745i	0.182020	+	0.0487721i
$352$	6.93013	+	12.0033i	0.369377	+	0.639780i
$353$	2.12113	−	3.67390i	0.112896	−	0.195542i	−0.804041	−	0.594574i	$-0.797321\pi$
$353$	2.12113	−	3.67390i	0.112896	−	0.195542i	0.916937	+	0.399032i	$0.130654\pi$
$354$	0.186789	−	0.323529i	0.00992774	−	0.0171954i
$355$		0			0
$356$	20.1974	+	20.1974i	1.07046	+	1.07046i
$357$	−2.43793	+	1.40754i	−0.129029	+	0.0744950i
$358$	1.41485	+	5.28028i	0.0747770	+	0.279072i
$359$			18.8723i			0.996040i	0.867166	+	0.498020i	$0.165939\pi$
$359$			18.8723i			0.996040i	−0.867166	+	0.498020i	$0.834061\pi$
$360$		0			0
$361$	31.5415	+	18.2105i	1.66008	+	0.958447i
$362$			0.0348743i			0.00183296i
$363$	−0.169574	−	0.0454372i	−0.00890033	−	0.00238484i
$364$	8.07545	+	8.07545i	0.423268	+	0.423268i
$365$		0			0
$366$	−0.340768	−	0.590228i	−0.0178122	−	0.0308517i
$367$	12.8464	+	3.44218i	0.670576	+	0.179680i	0.578014	−	0.816027i	$-0.303828\pi$
$367$	12.8464	+	3.44218i	0.670576	+	0.179680i	0.0925616	+	0.995707i	$0.470494\pi$
$368$	3.66195	+	2.11423i	0.190892	+	0.110212i
$369$	19.8730			1.03455
$370$		0			0
$371$	−9.39162			−0.487588
$372$	−1.74901	−	1.00979i	−0.0906820	−	0.0523553i
$373$	19.0464	+	5.10346i	0.986183	+	0.264247i	0.715646	−	0.698463i	$-0.246132\pi$
$373$	19.0464	+	5.10346i	0.986183	+	0.264247i	0.270536	+	0.962710i	$0.412799\pi$
$374$	4.72125	+	8.17745i	0.244130	+	0.422846i
$375$		0			0
$376$	2.77354	+	2.77354i	0.143034	+	0.143034i
$377$	−9.33677	−	2.50178i	−0.480868	−	0.128848i
$378$			0.826467i			0.0425089i
$379$	9.48304	+	5.47504i	0.487111	+	0.281234i	0.723375	−	0.690455i	$-0.242590\pi$
$379$	9.48304	+	5.47504i	0.487111	+	0.281234i	−0.236264	+	0.971689i	$0.575923\pi$
$380$		0			0
$381$		−	0.764351i		−	0.0391589i
$382$	−0.908050	−	3.38889i	−0.0464599	−	0.173391i
$383$	14.7477	−	8.51460i	0.753574	−	0.435076i	−0.0734101	−	0.997302i	$-0.523388\pi$
$383$	14.7477	−	8.51460i	0.753574	−	0.435076i	0.826984	+	0.562226i	$0.190055\pi$
$384$	−1.33033	−	1.33033i	−0.0678882	−	0.0678882i
$385$		0			0
$386$	0.181387	−	0.314171i	0.00923234	−	0.0159909i
$387$	18.6488	−	32.3006i	0.947970	−	1.64193i
$388$	4.06265	+	7.03671i	0.206250	+	0.357235i
$389$	12.4581	+	3.33813i	0.631649	+	0.169250i	0.560418	−	0.828210i	$-0.310641\pi$
$389$	12.4581	+	3.33813i	0.631649	+	0.169250i	0.0712310	+	0.997460i	$0.477307\pi$
$390$		0			0
$391$	8.50248	+	4.90891i	0.429989	+	0.248254i
$392$	2.19435	−	3.80072i	0.110831	−	0.191965i
$393$			0.678499i			0.0342258i
$394$	0.778693	−	2.90612i	0.0392300	−	0.146408i
$395$		0			0
$396$	−19.0843			−0.959021
$397$	−21.7674	−	21.7674i	−1.09248	−	1.09248i	−0.995264	−	0.0972114i	$-0.969008\pi$
$397$	−21.7674	−	21.7674i	−1.09248	−	1.09248i	−0.0972114	−	0.995264i	$-0.530992\pi$
$398$	−0.0417791	−	0.155922i	−0.00209420	−	0.00781566i
$399$	1.98813	+	1.98813i	0.0995308	+	0.0995308i
$400$		0			0
$401$	−0.609043	+	0.609043i	−0.0304142	+	0.0304142i	−0.722150	−	0.691736i	$-0.756846\pi$
$401$	−0.609043	+	0.609043i	−0.0304142	+	0.0304142i	0.691736	+	0.722150i	$0.256846\pi$
$402$	0.300389	−	0.173430i	0.0149821	−	0.00864990i
$403$	−4.54253	+	16.9529i	−0.226279	+	0.844486i
$404$	0.308642	−	0.178195i	0.0153555	−	0.00886552i
$405$		0			0
$406$		−	2.26282i		−	0.112302i
$407$	17.9711	+	10.8641i	0.890795	+	0.538514i
$408$	−1.42860	−	1.42860i	−0.0707264	−	0.0707264i
$409$	27.7946	−	7.44753i	1.37435	−	0.368257i	0.505286	−	0.862952i	$-0.331387\pi$
$409$	27.7946	−	7.44753i	1.37435	−	0.368257i	0.869067	+	0.494695i	$0.164720\pi$
$410$		0			0
$411$	0.379251	−	0.218960i	0.0187071	−	0.0108005i
$412$	1.96820	+	3.40902i	0.0969663	+	0.167951i
$413$			10.5286i			0.518079i
$414$	1.24046	−	0.716179i	0.0609652	−	0.0351983i
$415$		0			0
$416$	−6.21859	+	10.7709i	−0.304892	+	0.528088i
$417$	−0.859544	+	0.859544i	−0.0420920	+	0.0420920i
$418$	6.66868	−	6.66868i	0.326176	−	0.326176i
$419$	1.88268	+	1.08696i	0.0919747	+	0.0531016i	0.545282	−	0.838253i	$-0.316423\pi$
$419$	1.88268	+	1.08696i	0.0919747	+	0.0531016i	−0.453307	+	0.891354i	$0.649756\pi$
$420$		0			0
$421$	16.3854	−	16.3854i	0.798575	−	0.798575i	−0.184296	−	0.982871i	$-0.559000\pi$
$421$	16.3854	−	16.3854i	0.798575	−	0.798575i	0.982871	+	0.184296i	$0.0590004\pi$
$422$	−0.384659	−	0.222083i	−0.0187249	−	0.0108108i
$423$	−7.91593	+	2.12107i	−0.384886	+	0.103130i
$424$	−1.74450	−	6.51058i	−0.0847206	−	0.316182i
$425$		0			0
$426$	0.0846541	−	0.315933i	0.00410150	−	0.0153070i
$427$	16.6345	+	9.60390i	0.804997	+	0.464766i
$428$	4.75662	+	17.7519i	0.229920	+	0.858072i
$429$	−0.528979	−	1.97418i	−0.0255394	−	0.0953142i
$430$		0			0
$431$	−6.06172	−	1.62423i	−0.291983	−	0.0782366i	0.109854	−	0.993948i	$-0.464962\pi$
$431$	−6.06172	−	1.62423i	−0.291983	−	0.0782366i	−0.401837	+	0.915711i	$0.631628\pi$
$432$	3.53382	−	0.946883i	0.170021	−	0.0455570i
$433$	12.5346	+	12.5346i	0.602376	+	0.602376i	0.940942	−	0.338567i	$-0.109942\pi$
$433$	12.5346	+	12.5346i	0.602376	+	0.602376i	−0.338567	+	0.940942i	$0.609942\pi$
$434$	−4.10864			−0.197221
$435$		0			0
$436$	−20.8474	+	20.8474i	−0.998412	+	0.998412i
$437$	2.53793	−	9.47167i	0.121405	−	0.453091i
$438$	0.638378			0.0305029
$439$	−7.05673	+	26.3361i	−0.336799	+	1.25695i	0.565106	+	0.825018i	$0.308835\pi$
$439$	−7.05673	+	26.3361i	−0.336799	+	1.25695i	−0.901905	+	0.431934i	$0.857831\pi$
$440$		0			0
$441$	4.58474	+	7.94100i	0.218321	+	0.378143i
$442$	−4.23650	+	7.33784i	−0.201510	+	0.349025i
$443$	−14.0595	+	14.0595i	−0.667985	+	0.667985i	−0.957249	−	0.289264i	$-0.906589\pi$
$443$	−14.0595	+	14.0595i	−0.667985	+	0.667985i	0.289264	+	0.957249i	$0.406589\pi$
$444$	−2.08272	−	0.603285i	−0.0988414	−	0.0286306i
$445$		0			0
$446$	1.86259	+	6.95128i	0.0881962	+	0.329153i
$447$	−0.891275	+	3.32628i	−0.0421559	+	0.157328i
$448$	9.44420	+	2.53057i	0.446197	+	0.119558i
$449$	12.8304	+	3.43788i	0.605502	+	0.162244i	0.548528	−	0.836132i	$-0.315188\pi$
$449$	12.8304	+	3.43788i	0.605502	+	0.162244i	0.0569734	+	0.998376i	$0.481855\pi$
$450$		0			0
$451$	−11.5756	−	20.0496i	−0.545076	−	0.944099i
$452$	11.6415			0.547570
$453$	−0.0591023	+	0.0158364i	−0.00277687	+	0.000744059i
$454$		−	7.34274i		−	0.344612i
$455$		0			0
$456$	−1.00894	+	1.74753i	−0.0472479	+	0.0818357i
$457$	7.53471	+	13.0505i	0.352459	+	0.610477i	0.986680	−	0.162675i	$-0.0520123\pi$
$457$	7.53471	+	13.0505i	0.352459	+	0.610477i	−0.634221	+	0.773152i	$0.718679\pi$
$458$	1.35362			0.0632504
$459$	8.20498	−	2.19852i	0.382976	−	0.102618i
$460$		0			0
$461$	12.5579	−	3.36489i	0.584882	−	0.156719i	0.0457688	−	0.998952i	$-0.485426\pi$
$461$	12.5579	−	3.36489i	0.584882	−	0.156719i	0.539113	+	0.842233i	$0.318760\pi$
$462$	0.414353	−	0.239227i	0.0192774	−	0.0111298i
$463$	24.2140	−	13.9799i	1.12532	−	0.649703i	0.182565	−	0.983194i	$-0.441560\pi$
$463$	24.2140	−	13.9799i	1.12532	−	0.649703i	0.942753	+	0.333491i	$0.108227\pi$
$464$	−9.67539	+	2.59251i	−0.449169	+	0.120354i
$465$		0			0
$466$	−4.82046	+	1.29164i	−0.223304	+	0.0598340i
$467$	1.30129			0.0602165			0.0301083	−	0.999547i	$-0.490415\pi$
$467$	1.30129			0.0602165			0.0301083	+	0.999547i	$0.490415\pi$
$468$	−8.56242	−	14.8305i	−0.395798	−	0.685542i
$469$	−4.88779	+	8.46590i	−0.225697	+	0.390919i
$470$		0			0
$471$		−	0.225403i		−	0.0103860i
$472$	−7.29877	+	1.95570i	−0.335953	+	0.0900184i
$473$	−43.4502			−1.99784
$474$	−0.305712	−	0.529508i	−0.0140418	−	0.0243211i
$475$		0			0
$476$	26.5418	+	7.11186i	1.21654	+	0.325972i
$477$	13.6028	+	3.64486i	0.622830	+	0.166887i
$478$	1.29165	−	4.82050i	0.0590786	−	0.220484i
$479$	1.00395	+	3.74678i	0.0458715	+	0.171195i	0.985061	−	0.172203i	$-0.0550887\pi$
$479$	1.00395	+	3.74678i	0.0458715	+	0.171195i	−0.939190	+	0.343398i	$0.888422\pi$
$480$		0			0
$481$	−0.379608	+	18.8398i	−0.0173087	+	0.859022i
$482$	−6.12584	+	6.12584i	−0.279024	+	0.279024i
$483$	0.248735	−	0.430822i	0.0113179	−	0.0196031i
$484$	0.856803	+	1.48403i	0.0389456	+	0.0674558i
$485$		0			0
$486$	0.482107	−	1.79925i	0.0218688	−	0.0816156i
$487$	−17.7036			−0.802228			−0.401114	−	0.916028i	$-0.631377\pi$
$487$	−17.7036			−0.802228			−0.401114	+	0.916028i	$0.631377\pi$
$488$	−3.56787	+	13.3155i	−0.161510	+	0.602764i
$489$	1.24252	−	1.24252i	0.0561885	−	0.0561885i
$490$		0			0
$491$	28.1151			1.26882			0.634408	−	0.772998i	$-0.281244\pi$
$491$	28.1151			1.26882			0.634408	+	0.772998i	$0.281244\pi$
$492$	1.69033	+	1.69033i	0.0762059	+	0.0762059i
$493$	−22.4648	+	6.01942i	−1.01176	+	0.271101i
$494$	8.17427	+	2.19029i	0.367778	+	0.0985458i
$495$		0			0
$496$	4.70727	+	17.5678i	0.211363	+	0.788817i
$497$	2.38581	+	8.90398i	0.107018	+	0.399398i
$498$	−0.825932	−	0.476852i	−0.0370109	−	0.0213682i
$499$	7.95975	−	29.7062i	0.356327	−	1.32983i	−0.522479	−	0.852652i	$-0.674993\pi$
$499$	7.95975	−	29.7062i	0.356327	−	1.32983i	0.878806	−	0.477179i	$-0.158341\pi$
$500$		0			0
$501$	−1.07559	−	4.01416i	−0.0480539	−	0.179340i
$502$	−0.201333	+	0.0539470i	−0.00898593	+	0.00240777i
$503$	17.6108	+	10.1676i	0.785227	+	0.453351i	0.838280	−	0.545240i	$-0.183562\pi$
$503$	17.6108	+	10.1676i	0.785227	+	0.453351i	−0.0530522	+	0.998592i	$0.516895\pi$
$504$	5.87404	−	5.87404i	0.261651	−	0.261651i
$505$		0			0
$506$	−1.44509	−	0.834321i	−0.0642419	−	0.0370901i
$507$	−0.459867	+	0.459867i	−0.0204234	+	0.0204234i
$508$	−5.27562	+	5.27562i	−0.234068	+	0.234068i
$509$	3.95875	−	6.85676i	0.175469	−	0.303921i	−0.764855	−	0.644203i	$-0.777189\pi$
$509$	3.95875	−	6.85676i	0.175469	−	0.303921i	0.940323	+	0.340282i	$0.110523\pi$
$510$		0			0
$511$	−15.5811	+	8.99573i	−0.689265	+	0.397948i
$512$			21.9949i			0.972046i
$513$	−4.24201	−	7.34738i	−0.187289	−	0.324395i
$514$	5.19916	−	3.00173i	0.229325	−	0.132401i
$515$		0			0
$516$	4.33358	−	1.16118i	0.190775	−	0.0511180i
$517$	6.75079	+	6.75079i	0.296899	+	0.296899i
$518$	−4.28308	+	1.05565i	−0.188188	+	0.0463825i
$519$		−	0.662225i		−	0.0290685i
$520$		0			0
$521$	−22.5608	+	13.0255i	−0.988406	+	0.570657i	−0.904798	−	0.425842i	$-0.859978\pi$
$521$	−22.5608	+	13.0255i	−0.988406	+	0.570657i	−0.0836089	+	0.996499i	$0.526645\pi$
$522$	−0.878195	+	3.27747i	−0.0384376	+	0.143451i
$523$	−2.88468	+	1.66547i	−0.126138	+	0.0728259i	−0.561741	−	0.827313i	$-0.689868\pi$
$523$	−2.88468	+	1.66547i	−0.126138	+	0.0728259i	0.435603	+	0.900139i	$0.356535\pi$
$524$	4.68306	−	4.68306i	0.204581	−	0.204581i
$525$		0			0
$526$	−4.61019	−	4.61019i	−0.201014	−	0.201014i
$527$	10.9296	+	40.7897i	0.476099	+	1.77683i
$528$	−1.49761	−	1.49761i	−0.0651752	−	0.0651752i
$529$	21.2650			0.924567
$530$		0			0
$531$	4.08613	−	15.2496i	0.177323	−	0.661777i
$532$		−	27.4445i		−	1.18987i
$533$	10.3871	−	17.9910i	0.449917	−	0.779278i
$534$	0.929930	+	0.536896i	0.0402420	+	0.0232337i
$535$		0			0
$536$	−6.77676	−	1.81583i	−0.292711	−	0.0784318i
$537$	−1.42346	−	2.46550i	−0.0614267	−	0.106394i
$538$	−4.26509	+	7.38736i	−0.183881	+	0.318492i
$539$	5.34104	−	9.25096i	0.230055	−	0.398467i
$540$		0			0
$541$	−6.36223	−	6.36223i	−0.273534	−	0.273534i	0.556987	−	0.830521i	$-0.311957\pi$
$541$	−6.36223	−	6.36223i	−0.273534	−	0.273534i	−0.830521	+	0.556987i	$0.811957\pi$
$542$	5.40770	−	3.12214i	0.232281	−	0.134107i
$543$	−0.00470071	−	0.0175433i	−0.000201727	−	0.000752854i
$544$			29.9245i			1.28300i
$545$		0			0
$546$	0.371810	+	0.214664i	0.0159120	+	0.00918679i
$547$			10.6102i			0.453658i	0.973935	+	0.226829i	$0.0728359\pi$
$547$			10.6102i			0.453658i	−0.973935	+	0.226829i	$0.927164\pi$
$548$	−4.12891	−	1.10634i	−0.176378	−	0.0472604i
$549$	−20.3661	−	20.3661i	−0.869203	−	0.869203i
$550$		0			0
$551$	11.6144	+	20.1167i	0.494789	+	0.857000i
$552$	0.344863	+	0.0924058i	0.0146784	+	0.00393305i
$553$	14.9232	+	8.61591i	0.634598	+	0.366386i
$554$	0.569582			0.0241992
$555$		0			0
$556$	11.8653			0.503200
$557$	−31.2784	−	18.0586i	−1.32531	−	0.765166i	−0.340737	−	0.940159i	$-0.610677\pi$
$557$	−31.2784	−	18.0586i	−1.32531	−	0.765166i	−0.984570	+	0.174992i	$0.944010\pi$
$558$	5.95096	+	1.59455i	0.251924	+	0.0675029i
$559$	−19.4945	−	33.7655i	−0.824529	−	1.42813i
$560$		0			0
$561$	−3.47722	−	3.47722i	−0.146809	−	0.146809i
$562$	−3.53036	−	0.945957i	−0.148919	−	0.0399028i
$563$		−	28.0509i		−	1.18220i	−0.806597	−	0.591102i	$-0.798693\pi$
$563$		−	28.0509i		−	1.18220i	0.806597	−	0.591102i	$-0.201307\pi$
$564$	−0.853712	−	0.492891i	−0.0359478	−	0.0207545i
$565$		0			0
$566$			9.11305i			0.383050i
$567$	4.43614	+	16.5559i	0.186301	+	0.695283i
$568$	−5.72936	+	3.30785i	−0.240399	+	0.138794i
$569$	−1.69141	−	1.69141i	−0.0709076	−	0.0709076i	0.670764	−	0.741671i	$-0.265967\pi$
$569$	−1.69141	−	1.69141i	−0.0709076	−	0.0709076i	−0.741671	+	0.670764i	$0.765967\pi$
$570$		0			0
$571$	4.18372	−	7.24641i	0.175083	−	0.303253i	−0.765107	−	0.643903i	$-0.777314\pi$
$571$	4.18372	−	7.24641i	0.175083	−	0.303253i	0.940190	+	0.340650i	$0.110647\pi$
$572$	−9.97489	+	17.2770i	−0.417071	+	0.722388i
$573$	0.913575	+	1.58236i	0.0381651	+	0.0661040i
$574$	4.69750	+	1.25869i	0.196070	+	0.0525367i
$575$		0			0
$576$	−12.6969	−	7.33054i	−0.529037	−	0.305439i
$577$	10.2220	−	17.7050i	0.425546	−	0.737067i	−0.570925	−	0.821002i	$-0.693415\pi$
$577$	10.2220	−	17.7050i	0.425546	−	0.737067i	0.996471	+	0.0839349i	$0.0267488\pi$
$578$			14.1484i			0.588496i
$579$	−0.0488982	+	0.182490i	−0.00203214	+	0.00758404i
$580$		0			0
$581$	26.8783			1.11510
$582$	0.215989	+	0.215989i	0.00895305	+	0.00895305i
$583$	−4.24613	−	15.8468i	−0.175857	−	0.656306i
$584$	−9.13033	−	9.13033i	−0.377816	−	0.377816i
$585$		0			0
$586$	1.71994	−	1.71994i	0.0710501	−	0.0710501i
$587$	34.1304	−	19.7052i	1.40871	−	0.813320i	0.413448	−	0.910528i	$-0.364324\pi$
$587$	34.1304	−	19.7052i	1.40871	−	0.813320i	0.995264	+	0.0972074i	$0.0309910\pi$
$588$	−0.285472	+	1.06540i	−0.0117727	+	0.0439362i
$589$	36.5262	−	21.0884i	1.50504	−	0.868934i
$590$		0			0
$591$			1.56686i			0.0644521i
$592$	9.42087	+	17.1042i	0.387195	+	0.702977i
$593$	29.8968	+	29.8968i	1.22771	+	1.22771i	0.964827	+	0.262886i	$0.0846742\pi$
$593$	29.8968	+	29.8968i	1.22771	+	1.22771i	0.262886	+	0.964827i	$0.415326\pi$
$594$	−1.39452	+	0.373661i	−0.0572180	+	0.0153315i
$595$		0			0
$596$	29.1100	−	16.8066i	1.19239	−	0.688427i
$597$	0.0420333	+	0.0728039i	0.00172031	+	0.00297966i
$598$		−	1.49732i		−	0.0612299i
$599$	−20.3437	+	11.7455i	−0.831222	+	0.479906i	−0.854271	−	0.519828i	$-0.825996\pi$
$599$	−20.3437	+	11.7455i	−0.831222	+	0.479906i	0.0230489	+	0.999734i	$0.492663\pi$
$600$		0			0
$601$	−5.10765	+	8.84671i	−0.208345	+	0.360865i	−0.951193	−	0.308595i	$-0.900141\pi$
$601$	−5.10765	+	8.84671i	−0.208345	+	0.360865i	0.742848	+	0.669460i	$0.233474\pi$
$602$	6.45393	−	6.45393i	0.263042	−	0.263042i
$603$	10.3651	−	10.3651i	0.422098	−	0.422098i
$604$	0.517233	+	0.298625i	0.0210459	+	0.0121509i
$605$		0			0
$606$	0.00947367	−	0.00947367i	0.000384842	−	0.000384842i
$607$	1.35224	+	0.780718i	0.0548859	+	0.0316884i	0.527192	−	0.849746i	$-0.323245\pi$
$607$	1.35224	+	0.780718i	0.0548859	+	0.0316884i	−0.472306	+	0.881435i	$0.656578\pi$
$608$	28.8695	−	7.73555i	1.17081	−	0.313718i
$609$	0.305005	+	1.13829i	0.0123594	+	0.0461260i
$610$		0			0
$611$	−2.21726	+	8.27492i	−0.0897007	+	0.334768i
$612$	−35.6831	−	20.6016i	−1.44240	−	0.832772i
$613$	−0.397688	−	1.48419i	−0.0160625	−	0.0599460i	0.957429	−	0.288667i	$-0.0932122\pi$
$613$	−0.397688	−	1.48419i	−0.0160625	−	0.0599460i	−0.973492	+	0.228721i	$0.926546\pi$
$614$	−1.26703	−	4.72862i	−0.0511331	−	0.190831i
$615$		0			0
$616$	−9.34776	−	2.50472i	−0.376632	−	0.100918i
$617$	3.89243	−	1.04297i	0.156703	−	0.0419886i	−0.179614	−	0.983737i	$-0.557485\pi$
$617$	3.89243	−	1.04297i	0.156703	−	0.0419886i	0.336318	+	0.941749i	$0.390818\pi$
$618$	0.104639	+	0.104639i	0.00420919	+	0.00420919i
$619$	−24.1544			−0.970846			−0.485423	−	0.874279i	$-0.661334\pi$
$619$	−24.1544			−0.970846			−0.485423	+	0.874279i	$0.661334\pi$
$620$		0			0
$621$	−1.06144	+	1.06144i	−0.0425941	+	0.0425941i
$622$	−0.748575	+	2.79372i	−0.0300151	+	0.112018i
$623$	−30.2628			−1.21245
$624$	0.491882	−	1.83573i	0.0196910	−	0.0734880i
$625$		0			0
$626$	−0.422233	−	0.731329i	−0.0168758	−	0.0292298i
$627$	−2.45576	+	4.25350i	−0.0980735	+	0.169868i
$628$	−1.55575	+	1.55575i	−0.0620813	+	0.0620813i
$629$	21.8738	+	39.7133i	0.872166	+	1.58347i
$630$		0			0
$631$	−4.33716	−	16.1865i	−0.172660	−	0.644374i	−0.996938	−	0.0781902i	$-0.975086\pi$
$631$	−4.33716	−	16.1865i	−0.172660	−	0.644374i	0.824279	−	0.566184i	$-0.191581\pi$
$632$	−3.20083	+	11.9457i	−0.127322	+	0.475173i
$633$	0.223434	+	0.0598690i	0.00888071	+	0.00237958i
$634$	−2.87970	−	0.771614i	−0.114368	−	0.0306447i
$635$		0			0
$636$	0.846989	+	1.46703i	0.0335853	+	0.0581715i
$637$	9.58532			0.379784
$638$	3.81812	−	1.02306i	0.151161	−	0.0405035i
$639$		−	13.8224i		−	0.546808i
$640$		0			0
$641$	−13.1598	+	22.7934i	−0.519779	+	0.900283i	0.479957	+	0.877292i	$0.340652\pi$
$641$	−13.1598	+	22.7934i	−0.519779	+	0.900283i	−0.999736	+	0.0229913i	$0.992681\pi$
$642$	0.345446	+	0.598330i	0.0136337	+	0.0236142i
$643$	−34.2404			−1.35031			−0.675155	−	0.737675i	$-0.735923\pi$
$643$	−34.2404			−1.35031			−0.675155	+	0.737675i	$0.735923\pi$
$644$	−4.69037	+	1.25678i	−0.184826	+	0.0495241i
$645$		0			0
$646$	19.6677	−	5.26995i	0.773817	−	0.207344i
$647$	−28.5278	+	16.4706i	−1.12155	+	0.647524i	−0.941795	−	0.336188i	$-0.890862\pi$
$647$	−28.5278	+	16.4706i	−1.12155	+	0.647524i	−0.179750	+	0.983712i	$0.557529\pi$
$648$	−10.6531	+	6.15056i	−0.418493	+	0.241617i
$649$	−17.7652	+	4.76018i	−0.697346	+	0.186853i
$650$		0			0
$651$	2.06682	−	0.553803i	0.0810051	−	0.0217053i
$652$	−17.1519			−0.671720
$653$	10.9549	+	18.9744i	0.428698	+	0.742526i	0.996758	−	0.0804608i	$-0.0256392\pi$
$653$	10.9549	+	18.9744i	0.428698	+	0.742526i	−0.568060	+	0.822987i	$0.692306\pi$
$654$	−0.554174	+	0.959858i	−0.0216699	+	0.0375334i
$655$		0			0
$656$		−	21.5277i		−	0.840515i
$657$	26.0588	−	6.98244i	1.01665	−	0.272411i
$658$	−2.00548			−0.0781816
$659$	4.76225	+	8.24846i	0.185511	+	0.321314i	0.943749	−	0.330664i	$-0.107273\pi$
$659$	4.76225	+	8.24846i	0.185511	+	0.321314i	−0.758238	+	0.651978i	$0.773939\pi$
$660$		0			0
$661$	4.49979	+	1.20572i	0.175022	+	0.0468969i	0.345265	−	0.938505i	$-0.387789\pi$
$661$	4.49979	+	1.20572i	0.175022	+	0.0468969i	−0.170244	+	0.985402i	$0.554456\pi$
$662$	8.66598	+	2.32204i	0.336813	+	0.0902487i
$663$	1.14207	−	4.26228i	0.0443545	−	0.165533i
$664$	4.99268	+	18.6329i	0.193754	+	0.723098i
$665$		0			0
$666$	6.61331	+	0.133253i	0.256260	+	0.00516346i
$667$	2.90616	−	2.90616i	0.112527	−	0.112527i
$668$	−20.2823	+	35.1299i	−0.784745	+	1.35922i
$669$	−1.87392	−	3.24573i	−0.0724501	−	0.125487i
$670$		0			0
$671$	−8.68421	+	32.4099i	−0.335250	+	1.25117i
$672$	1.51628			0.0584919
$673$	−3.84754	+	14.3592i	−0.148312	+	0.553507i	0.851274	+	0.524722i	$0.175831\pi$
$673$	−3.84754	+	14.3592i	−0.148312	+	0.553507i	−0.999586	+	0.0287852i	$0.990836\pi$
$674$	−5.04002	+	5.04002i	−0.194134	+	0.194134i
$675$		0			0
$676$	6.34808			0.244157
$677$	7.15203	+	7.15203i	0.274875	+	0.274875i	0.831059	−	0.556184i	$-0.187735\pi$
$677$	7.15203	+	7.15203i	0.274875	+	0.274875i	−0.556184	+	0.831059i	$0.687735\pi$
$678$	0.422728	−	0.113270i	0.0162348	−	0.00435009i
$679$	−8.31534	−	2.22809i	−0.319113	−	0.0855062i
$680$		0			0
$681$	0.989727	+	3.69371i	0.0379264	+	0.141543i
$682$	−1.85759	−	6.93264i	−0.0711310	−	0.265464i
$683$	15.0427	+	8.68491i	0.575593	+	0.332319i	0.759380	−	0.650647i	$-0.225502\pi$
$683$	15.0427	+	8.68491i	0.575593	+	0.332319i	−0.183787	+	0.982966i	$0.558836\pi$
$684$	−10.6511	+	39.7505i	−0.407256	+	1.51990i
$685$		0			0
$686$	1.89464	+	7.07091i	0.0723378	+	0.269969i
$687$	−0.680927	+	0.182454i	−0.0259790	+	0.00696105i
$688$	−34.9900	−	20.2015i	−1.33398	−	0.770175i
$689$	10.4096	−	10.4096i	0.396573	−	0.396573i
$690$		0			0
$691$	0.688714	+	0.397629i	0.0261999	+	0.0151265i	0.513043	−	0.858363i	$-0.328518\pi$
$691$	0.688714	+	0.397629i	0.0261999	+	0.0151265i	−0.486843	+	0.873490i	$0.661852\pi$
$692$	−4.57074	+	4.57074i	−0.173753	+	0.173753i
$693$	14.2974	−	14.2974i	0.543114	−	0.543114i
$694$	0.623054	−	1.07916i	0.0236508	−	0.0409644i
$695$		0			0
$696$	−0.732448	+	0.422879i	−0.0277634	+	0.0160292i
$697$		−	49.9840i		−	1.89328i
$698$	0.0708869	+	0.122780i	0.00268311	+	0.00464728i
$699$	2.25080	−	1.29950i	0.0851329	−	0.0491515i
$700$		0			0
$701$	−7.03789	+	1.88580i	−0.265817	+	0.0712255i	−0.389266	−	0.921125i	$-0.627271\pi$
$701$	−7.03789	+	1.88580i	−0.265817	+	0.0712255i	0.123449	+	0.992351i	$0.460605\pi$
$702$	−0.916047	−	0.916047i	−0.0345740	−	0.0345740i
$703$	32.6587	−	31.3686i	1.23175	−	1.18309i
$704$			17.0796i			0.643712i
$705$		0			0
$706$	−1.34813	+	0.778343i	−0.0507375	+	0.0292933i
$707$	−0.0977278	+	0.364725i	−0.00367543	+	0.0137169i
$708$	1.64463	−	0.949529i	0.0618091	−	0.0356855i
$709$	0.492179	−	0.492179i	0.0184842	−	0.0184842i	−0.697804	−	0.716288i	$-0.745839\pi$
$709$	0.492179	−	0.492179i	0.0184842	−	0.0184842i	0.716288	+	0.697804i	$0.245839\pi$
$710$		0			0
$711$	−18.2709	−	18.2709i	−0.685213	−	0.685213i
$712$	−5.62134	−	20.9791i	−0.210669	−	0.786227i
$713$	−5.27677	−	5.27677i	−0.197617	−	0.197617i
$714$	1.03299			0.0386586
$715$		0			0
$716$	−7.19227	+	26.8419i	−0.268788	+	1.00313i
$717$			2.59901i			0.0970620i
$718$	3.46257	−	5.99734i	0.129222	−	0.223819i
$719$	10.8743	+	6.27829i	0.405543	+	0.234141i	0.688873	−	0.724882i	$-0.258106\pi$
$719$	10.8743	+	6.27829i	0.405543	+	0.234141i	−0.283330	+	0.959023i	$0.591439\pi$
$720$		0			0
$721$	−4.02847	−	1.07943i	−0.150028	−	0.0401999i
$722$	−6.68230	−	11.5741i	−0.248689	−	0.430742i
$723$	2.25585	−	3.90725i	0.0838961	−	0.145312i
$724$	−0.0886405	+	0.153530i	−0.00329430	+	0.00570589i
$725$		0			0
$726$	0.0455517	+	0.0455517i	0.00169058	+	0.00169058i
$727$	−0.393556	+	0.227219i	−0.0145962	+	0.00842710i	−0.507280	−	0.861781i	$-0.669349\pi$
$727$	−0.393556	+	0.227219i	−0.0145962	+	0.00842710i	0.492684	+	0.870208i	$0.336016\pi$
$728$	−2.24756	−	8.38799i	−0.0832999	−	0.310880i
$729$		−	25.0479i		−	0.927699i
$730$		0			0
$731$	−81.2415	−	46.9048i	−3.00483	−	1.73484i
$732$		−	3.46454i		−	0.128053i
$733$	−0.269639	−	0.0722495i	−0.00995933	−	0.00266859i	0.253836	−	0.967247i	$-0.418308\pi$
$733$	−0.269639	−	0.0722495i	−0.00995933	−	0.00266859i	−0.263795	+	0.964579i	$0.584974\pi$
$734$	−3.45085	−	3.45085i	−0.127373	−	0.127373i
$735$		0			0
$736$	−2.64408	−	4.57967i	−0.0974619	−	0.168809i
$737$	−16.4946	−	4.41972i	−0.607588	−	0.162803i
$738$	−6.31536	−	3.64617i	−0.232472	−	0.134218i
$739$	−20.7632			−0.763786			−0.381893	−	0.924207i	$-0.624728\pi$
$739$	−20.7632			−0.763786			−0.381893	+	0.924207i	$0.624728\pi$
$740$		0			0
$741$	−4.40723			−0.161904
$742$	2.98452	+	1.72312i	0.109565	+	0.0632576i
$743$	−18.4274	−	4.93760i	−0.676035	−	0.181143i	−0.0955632	−	0.995423i	$-0.530465\pi$
$743$	−18.4274	−	4.93760i	−0.676035	−	0.181143i	−0.580472	+	0.814280i	$0.697132\pi$
$744$	0.767829	+	1.32992i	0.0281500	+	0.0487572i
$745$		0			0
$746$	−5.11631	−	5.11631i	−0.187322	−	0.187322i
$747$	−38.9306	−	10.4314i	−1.42439	−	0.381665i
$748$			48.0002i			1.75506i
$749$	−16.8628	−	9.73574i	−0.616153	−	0.355736i
$750$		0			0
$751$		−	32.9736i		−	1.20322i	−0.798788	−	0.601612i	$-0.794525\pi$
$751$		−	32.9736i		−	1.20322i	0.798788	−	0.601612i	$-0.205475\pi$
$752$	2.29767	+	8.57503i	0.0837875	+	0.312699i
$753$	0.0940075	−	0.0542752i	0.00342582	−	0.00197790i
$754$	2.50808	+	2.50808i	0.0913390	+	0.0913390i
$755$		0			0
$756$	−2.10064	+	3.63842i	−0.0763996	+	0.132328i
$757$	25.4674	−	44.1108i	0.925628	−	1.60323i	0.135079	−	0.990835i	$-0.456871\pi$
$757$	25.4674	−	44.1108i	0.925628	−	1.60323i	0.790549	−	0.612399i	$-0.209795\pi$
$758$	−2.00905	−	3.47978i	−0.0729720	−	0.126391i
$759$	0.839398	+	0.224916i	0.0304682	+	0.00816393i
$760$		0			0
$761$	3.27486	+	1.89074i	0.118714	+	0.0685394i	0.558181	−	0.829719i	$-0.311499\pi$
$761$	3.27486	+	1.89074i	0.118714	+	0.0685394i	−0.439467	+	0.898259i	$0.644833\pi$
$762$	−0.140238	+	0.242900i	−0.00508030	+	0.00879934i
$763$		−	31.2367i		−	1.13084i
$764$	4.61600	−	17.2272i	0.167001	−	0.623257i
$765$		0			0
$766$	−6.24883			−0.225779
$767$	−11.6698	−	11.6698i	−0.421371	−	0.421371i
$768$	−0.310710	−	1.15959i	−0.0112118	−	0.0418430i
$769$	−1.69910	−	1.69910i	−0.0612712	−	0.0612712i	0.675807	−	0.737078i	$-0.263795\pi$
$769$	−1.69910	−	1.69910i	−0.0612712	−	0.0612712i	−0.737078	+	0.675807i	$0.763795\pi$
$770$		0			0
$771$	−2.21079	+	2.21079i	−0.0796197	+	0.0796197i
$772$	1.59706	−	0.922066i	0.0574796	−	0.0331859i
$773$	7.79586	−	29.0946i	0.280398	−	1.04646i	−0.671740	−	0.740787i	$-0.734453\pi$
$773$	7.79586	−	29.0946i	0.280398	−	1.04646i	0.952137	−	0.305671i	$-0.0988807\pi$
$774$	−11.8526	+	6.84312i	−0.426034	+	0.245971i
$775$		0			0
$776$		−	6.17834i		−	0.221789i
$777$	2.01228	−	1.10835i	0.0721901	−	0.0397619i
$778$	−3.34654	−	3.34654i	−0.119979	−	0.119979i
$779$	−48.2217	+	12.9210i	−1.72772	+	0.462941i
$780$		0			0
$781$	−13.9453	+	8.05131i	−0.499001	+	0.288099i
$782$	−1.80131	−	3.11997i	−0.0644148	−	0.111570i
$783$		−	3.55593i		−	0.127079i
$784$	8.60219	−	4.96648i	0.307221	−	0.177374i
$785$		0			0
$786$	0.124487	−	0.215618i	0.00444030	−	0.00769082i
$787$	15.3527	−	15.3527i	0.547265	−	0.547265i	−0.378384	−	0.925649i	$-0.623520\pi$
$787$	15.3527	−	15.3527i	0.547265	−	0.547265i	0.925649	+	0.378384i	$0.123520\pi$
$788$	10.8146	−	10.8146i	0.385255	−	0.385255i
$789$	2.94052	+	1.69771i	0.104685	+	0.0604402i
$790$		0			0
$791$	−8.72149	+	8.72149i	−0.310101	+	0.310101i
$792$	12.5672	+	7.25568i	0.446556	+	0.257819i
$793$	−29.0823	+	7.79257i	−1.03274	+	0.276722i
$794$	2.92363	+	10.9111i	0.103756	+	0.387221i
$795$		0			0
$796$	0.212381	−	0.792617i	0.00752765	−	0.0280936i
$797$	−32.4245	−	18.7203i	−1.14853	−	0.663106i	−0.200004	−	0.979795i	$-0.564096\pi$
$797$	−32.4245	−	18.7203i	−1.14853	−	0.663106i	−0.948529	+	0.316689i	$0.897429\pi$
$798$	−0.267030	−	0.996568i	−0.00945274	−	0.0352781i
$799$	5.33484	+	19.9099i	0.188733	+	0.704362i
$800$		0			0
$801$	43.8326	+	11.7449i	1.54875	+	0.414986i
$802$	0.305289	−	0.0818019i	0.0107801	−	0.00288853i
$803$	−22.2232	−	22.2232i	−0.784241	−	0.784241i
$804$	1.76324			0.0621845
$805$		0			0
$806$	4.55397	−	4.55397i	0.160407	−	0.160407i
$807$	1.14978	−	4.29104i	0.0404742	−	0.151052i
$808$	−0.270993			−0.00953349
$809$	11.2061	−	41.8217i	0.393985	−	1.47037i	−0.429517	−	0.903059i	$-0.641316\pi$
$809$	11.2061	−	41.8217i	0.393985	−	1.47037i	0.823502	−	0.567313i	$-0.192017\pi$
$810$		0			0
$811$	6.94395	+	12.0273i	0.243835	+	0.422335i	0.961803	−	0.273741i	$-0.0882611\pi$
$811$	6.94395	+	12.0273i	0.243835	+	0.422335i	−0.717968	+	0.696076i	$0.754928\pi$
$812$	5.75144	−	9.96178i	0.201836	−	0.349590i
$813$	−2.29947	+	2.29947i	−0.0806459	+	0.0806459i
$814$	−3.71769	−	6.74969i	−0.130305	−	0.236577i
$815$		0			0
$816$	−1.18349	−	4.41686i	−0.0414306	−	0.154621i
$817$	−24.2500	+	90.5021i	−0.848399	+	3.16627i
$818$	−10.1991	−	2.73285i	−0.356605	−	0.0955520i
$819$	17.5254	+	4.69591i	0.612386	+	0.164088i
$820$		0			0
$821$	−5.62408	−	9.74120i	−0.196282	−	0.339970i	0.751038	−	0.660259i	$-0.229553\pi$
$821$	−5.62408	−	9.74120i	−0.196282	−	0.339970i	−0.947320	+	0.320289i	$0.896220\pi$
$822$	−0.160694			−0.00560485
$823$	31.6544	−	8.48178i	1.10340	−	0.295656i	0.339254	−	0.940695i	$-0.389825\pi$
$823$	31.6544	−	8.48178i	1.10340	−	0.295656i	0.764150	+	0.645038i	$0.223159\pi$
$824$		−	2.99317i		−	0.104272i
$825$		0			0
$826$	1.93172	−	3.34584i	0.0672132	−	0.116417i
$827$	16.4713	+	28.5291i	0.572763	+	0.992054i	0.996281	+	0.0861665i	$0.0274617\pi$
$827$	16.4713	+	28.5291i	0.572763	+	0.992054i	−0.423518	+	0.905888i	$0.639205\pi$
$828$	7.28128			0.253042
$829$	4.10251	−	1.09926i	0.142486	−	0.0381790i	−0.186871	−	0.982384i	$-0.559835\pi$
$829$	4.10251	−	1.09926i	0.142486	−	0.0381790i	0.329357	+	0.944205i	$0.393168\pi$
$830$		0			0
$831$	−0.286524	+	0.0767738i	−0.00993940	+	0.00266325i
$832$	−13.2727	+	7.66299i	−0.460148	+	0.265666i
$833$	19.9730	−	11.5314i	0.692023	−	0.399539i
$834$	0.430854	−	0.115447i	0.0149193	−	0.00399761i
$835$		0			0
$836$	46.3079	−	12.4082i	1.60159	−	0.429145i
$837$	−6.45657			−0.223172
$838$	−0.398859	−	0.690843i	−0.0137783	−	0.0238648i
$839$	−1.39115	+	2.40954i	−0.0480278	+	0.0831865i	−0.889040	−	0.457830i	$-0.848627\pi$
$839$	−1.39115	+	2.40954i	−0.0480278	+	0.0831865i	0.841012	+	0.541016i	$0.181960\pi$
$840$		0			0
$841$		−	19.2641i		−	0.664278i
$842$	−8.21333	+	2.20076i	−0.283050	+	0.0758431i
$843$	1.90343			0.0655575
$844$	−1.12894	−	1.95538i	−0.0388598	−	0.0673071i
$845$		0			0
$846$	2.90473	+	0.778320i	0.0998667	+	0.0267592i
$847$	−1.75369	−	0.469899i	−0.0602574	−	0.0161459i
$848$	3.94835	−	14.7354i	0.135587	−	0.506017i
$849$	−1.22835	−	4.58425i	−0.0421567	−	0.157331i
$850$		0			0
$851$	−6.85658	−	4.14502i	−0.235040	−	0.142089i
$852$	1.17569	−	1.17569i	0.0402785	−	0.0402785i
$853$	−10.7353	+	18.5940i	−0.367569	+	0.636648i	−0.989185	−	0.146674i	$-0.953143\pi$
$853$	−10.7353	+	18.5940i	−0.367569	+	0.636648i	0.621616	+	0.783322i	$0.286476\pi$
$854$	−3.52413	−	6.10397i	−0.120593	−	0.208874i
$855$		0			0
$856$	3.61685	−	13.4983i	0.123621	−	0.461362i
$857$	19.7692			0.675302			0.337651	−	0.941271i	$-0.390368\pi$
$857$	19.7692			0.675302			0.337651	+	0.941271i	$0.390368\pi$
$858$	−0.194108	+	0.724420i	−0.00662673	+	0.0247313i
$859$	14.4663	−	14.4663i	0.493582	−	0.493582i	−0.415851	−	0.909433i	$-0.636516\pi$
$859$	14.4663	−	14.4663i	0.493582	−	0.493582i	0.909433	+	0.415851i	$0.136516\pi$
$860$		0			0
$861$	−2.53270			−0.0863141
$862$	1.62833	+	1.62833i	0.0554610	+	0.0554610i
$863$	51.9841	−	13.9291i	1.76956	−	0.474152i	0.780943	−	0.624603i	$-0.214739\pi$
$863$	51.9841	−	13.9291i	1.76956	−	0.474152i	0.988618	+	0.150450i	$0.0480724\pi$
$864$	−4.41943	−	1.18418i	−0.150352	−	0.0402867i
$865$		0			0
$866$	−1.68355	−	6.28310i	−0.0572094	−	0.213509i
$867$	−1.90706	−	7.11724i	−0.0647672	−	0.241714i
$868$	−18.0878	−	10.4430i	−0.613939	−	0.354458i
$869$	−7.79082	+	29.0758i	−0.264286	+	0.986327i
$870$		0			0
$871$	−3.96594	−	14.8011i	−0.134381	−	0.501515i
$872$	21.6543	−	5.80225i	0.733307	−	0.196489i
$873$	11.1792	+	6.45432i	0.378359	+	0.218446i
$874$	−2.54432	+	2.54432i	−0.0860629	+	0.0860629i
$875$		0			0
$876$	2.81038	+	1.62257i	0.0949538	+	0.0548216i
$877$	−12.5701	+	12.5701i	−0.424462	+	0.424462i	−0.886737	−	0.462275i	$-0.847033\pi$
$877$	−12.5701	+	12.5701i	−0.424462	+	0.424462i	0.462275	+	0.886737i	$0.347033\pi$
$878$	7.07451	−	7.07451i	0.238753	−	0.238753i
$879$	−0.633372	+	1.09703i	−0.0213631	+	0.0370020i
$880$		0			0
$881$	45.1002	−	26.0386i	1.51946	−	0.877263i	0.519727	−	0.854333i	$-0.326034\pi$
$881$	45.1002	−	26.0386i	1.51946	−	0.877263i	0.999737	−	0.0229301i	$-0.00729951\pi$
$882$		−	3.36472i		−	0.113296i
$883$	15.8773	+	27.5003i	0.534314	+	0.925459i	0.999196	+	0.0400864i	$0.0127633\pi$
$883$	15.8773	+	27.5003i	0.534314	+	0.925459i	−0.464882	+	0.885372i	$0.653903\pi$
$884$	−37.3013	+	21.5359i	−1.25458	+	0.724332i
$885$		0			0
$886$	7.04744	−	1.88835i	0.236763	−	0.0634405i
$887$	−8.37990	−	8.37990i	−0.281370	−	0.281370i	0.552285	−	0.833655i	$-0.313756\pi$
$887$	−8.37990	−	8.37990i	−0.281370	−	0.281370i	−0.833655	+	0.552285i	$0.813756\pi$
$888$	1.14213	+	1.18910i	0.0383273	+	0.0399036i
$889$		−	7.90470i		−	0.265115i
$890$		0			0
$891$	−25.9296	+	14.9705i	−0.868675	+	0.501530i
$892$	−9.46833	+	35.3363i	−0.317023	+	1.18315i
$893$	17.8289	−	10.2935i	0.596620	−	0.344459i
$894$	0.893520	−	0.893520i	0.0298838	−	0.0298838i
$895$		0			0
$896$	−13.7579	−	13.7579i	−0.459620	−	0.459620i
$897$	0.201823	+	0.753214i	0.00673868	+	0.0251491i
$898$	−3.44654	−	3.44654i	−0.115013	−	0.115013i
$899$	17.6777			0.589585
$900$		0			0
$901$	9.16745	−	34.2134i	0.305412	−	1.13981i
$902$			8.49531i			0.282863i
$903$	−2.37668	+	4.11652i	−0.0790908	+	0.136989i
$904$	−7.66605	−	4.42600i	−0.254969	−	0.147207i
$905$		0			0
$906$	0.0216874	+	0.00581113i	0.000720517	+	0.000193062i
$907$	24.7791	+	42.9187i	0.822777	+	1.42509i	0.903606	+	0.428364i	$0.140910\pi$
$907$	24.7791	+	42.9187i	0.822777	+	1.42509i	−0.0808295	+	0.996728i	$0.525757\pi$
$908$	18.6631	−	32.3255i	0.619358	−	1.07276i
$909$	0.283098	−	0.490340i	0.00938977	−	0.0162636i
$910$		0			0
$911$	−31.0017	−	31.0017i	−1.02713	−	1.02713i	−0.999621	−	0.0275118i	$-0.991242\pi$
$911$	−31.0017	−	31.0017i	−1.02713	−	1.02713i	−0.0275118	−	0.999621i	$-0.508758\pi$
$912$	−3.95520	+	2.28353i	−0.130970	+	0.0756154i
$913$	12.1522	+	45.3526i	0.402179	+	1.50095i
$914$		−	5.52969i		−	0.182906i
$915$		0			0
$916$	5.95913	+	3.44051i	0.196895	+	0.113678i
$917$			7.01685i			0.231717i
$918$	−3.01080	−	0.806741i	−0.0993712	−	0.0266264i
$919$	25.3860	+	25.3860i	0.837407	+	0.837407i	0.988517	−	0.151110i	$-0.0482847\pi$
$919$	25.3860	+	25.3860i	0.837407	+	0.837407i	−0.151110	+	0.988517i	$0.548285\pi$
$920$		0			0
$921$	1.27474	+	2.20791i	0.0420041	+	0.0727532i
$922$	−4.60811	−	1.23474i	−0.151760	−	0.0406639i
$923$	−12.5135	−	7.22466i	−0.411886	−	0.237802i
$924$	2.43218			0.0800129
$925$		0			0
$926$	−10.2598			−0.337158
$927$	5.41591	+	3.12688i	0.177882	+	0.102700i
$928$	12.1001	+	3.24222i	0.397207	+	0.106431i
$929$	9.74401	+	16.8771i	0.319691	+	0.553720i	0.980423	−	0.196901i	$-0.0630877\pi$
$929$	9.74401	+	16.8771i	0.319691	+	0.553720i	−0.660733	+	0.750621i	$0.729754\pi$
$930$		0			0
$931$	−16.2879	−	16.2879i	−0.533814	−	0.533814i
$932$	−24.5044	−	6.56595i	−0.802670	−	0.215075i
$933$		−	1.50626i		−	0.0493127i
$934$	−0.413532	−	0.238753i	−0.0135312	−	0.00781223i
$935$		0			0
$936$			13.0214i			0.425619i
$937$	11.2187	+	41.8686i	0.366498	+	1.36779i	0.865379	+	0.501118i	$0.167078\pi$
$937$	11.2187	+	41.8686i	0.366498	+	1.36779i	−0.498881	+	0.866670i	$0.666256\pi$
$938$	3.10654	−	1.79356i	0.101432	−	0.0585619i
$939$	0.310977	+	0.310977i	0.0101483	+	0.0101483i
$940$		0			0
$941$	−1.14543	+	1.98394i	−0.0373398	+	0.0646745i	−0.884091	−	0.467314i	$-0.845222\pi$
$941$	−1.14543	+	1.98394i	−0.0373398	+	0.0646745i	0.846752	+	0.531989i	$0.178555\pi$
$942$	−0.0413556	+	0.0716300i	−0.00134744	+	0.00233383i
$943$	4.41649	+	7.64958i	0.143821	+	0.249105i
$944$	−16.5194	−	4.42635i	−0.537659	−	0.144065i
$945$		0			0
$946$	13.8078	+	7.97197i	0.448932	+	0.259191i
$947$	30.0952	−	52.1263i	0.977961	−	1.69388i	0.308165	−	0.951333i	$-0.400285\pi$
$947$	30.0952	−	52.1263i	0.977961	−	1.69388i	0.669796	−	0.742545i	$-0.266382\pi$
$948$		−	3.10813i		−	0.100947i
$949$	7.29910	−	27.2406i	0.236939	−	0.884268i
$950$		0			0
$951$	1.55262			0.0503471
$952$	−14.7742	−	14.7742i	−0.478835	−	0.478835i
$953$	−4.50324	−	16.8063i	−0.145874	−	0.544410i	−0.999715	−	0.0238757i	$-0.992399\pi$
$953$	−4.50324	−	16.8063i	−0.145874	−	0.544410i	0.853841	−	0.520534i	$-0.174267\pi$
$954$	−3.65405	−	3.65405i	−0.118304	−	0.118304i
$955$		0			0
$956$	17.9386	−	17.9386i	0.580177	−	0.580177i
$957$	−1.78278	+	1.02929i	−0.0576291	+	0.0332722i
$958$	0.368395	−	1.37487i	0.0119023	−	0.0444201i
$959$	3.92210	−	2.26443i	0.126651	−	0.0731221i
$960$		0			0
$961$		−	1.09774i		−	0.0354111i
$962$	3.57725	−	5.91738i	0.115335	−	0.190784i
$963$	20.6457	+	20.6457i	0.665297	+	0.665297i
$964$	−42.5383	+	11.3981i	−1.37007	+	0.367108i
$965$		0			0
$966$	−0.158089	+	0.0912729i	−0.00508644	+	0.00293666i
$967$	23.8175	+	41.2531i	0.765918	+	1.32661i	0.939760	+	0.341836i	$0.111049\pi$
$967$	23.8175	+	41.2531i	0.765918	+	1.32661i	−0.173841	+	0.984774i	$0.555618\pi$
$968$		−	1.30300i		−	0.0418799i
$969$	−9.18337	+	5.30202i	−0.295012	+	0.170325i
$970$		0			0
$971$	17.9256	−	31.0481i	0.575261	−	0.996382i	−0.420752	−	0.907176i	$-0.638234\pi$
$971$	17.9256	−	31.0481i	0.575261	−	0.996382i	0.996013	−	0.0892060i	$-0.0284329\pi$
$972$	6.69559	−	6.69559i	0.214761	−	0.214761i
$973$	−8.88915	+	8.88915i	−0.284973	+	0.284973i
$974$	5.62597	+	3.24815i	0.180268	+	0.104078i
$975$		0			0
$976$	−22.0618	+	22.0618i	−0.706182	+	0.706182i
$977$	−17.1619	−	9.90840i	−0.549056	−	0.316998i	0.199685	−	0.979860i	$-0.436008\pi$
$977$	−17.1619	−	9.90840i	−0.549056	−	0.316998i	−0.748741	+	0.662862i	$0.769341\pi$
$978$	−0.622823	+	0.166885i	−0.0199157	+	0.00533639i
$979$	−13.6824	−	51.0633i	−0.437290	−	1.63199i
$980$		0			0
$981$	−12.1229	+	45.2432i	−0.387054	+	1.44450i
$982$	−8.93458	−	5.15838i	−0.285114	−	0.164611i
$983$	−13.1202	−	48.9652i	−0.418469	−	1.56175i	−0.777784	−	0.628532i	$-0.783656\pi$
$983$	−13.1202	−	48.9652i	−0.418469	−	1.56175i	0.359315	−	0.933216i	$-0.383010\pi$
$984$	−0.470452	−	1.75575i	−0.0149975	−	0.0559713i
$985$		0			0
$986$	8.24339	+	2.20881i	0.262523	+	0.0703429i
$987$	1.00884	−	0.270318i	0.0321117	−	0.00860430i
$988$	30.4191	+	30.4191i	0.967761	+	0.967761i
$989$	16.5777			0.527139
$990$		0			0
$991$	24.1350	−	24.1350i	0.766673	−	0.766673i	−0.210846	−	0.977519i	$-0.567622\pi$
$991$	24.1350	−	24.1350i	0.766673	−	0.766673i	0.977519	+	0.210846i	$0.0676220\pi$
$992$	5.88697	−	21.9705i	0.186911	−	0.697563i
$993$	−4.67234			−0.148272
$994$	0.875468	−	3.26729i	0.0277682	−	0.103632i
$995$		0			0
$996$	−2.42404	−	4.19856i	−0.0768086	−	0.133036i
$997$	26.1348	−	45.2668i	0.827697	−	1.43361i	−0.0721432	−	0.997394i	$-0.522984\pi$
$997$	26.1348	−	45.2668i	0.827697	−	1.43361i	0.899840	−	0.436219i	$-0.143683\pi$
$998$	−7.97980	+	7.97980i	−0.252596	+	0.252596i
$999$	−6.73069	+	1.65891i	−0.212950	+	0.0524855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.b.393.8		68
5.2	odd	4		925.2.t.b.282.10		68
5.3	odd	4		185.2.p.a.97.8	✓	68
5.4	even	2		185.2.u.a.23.10	yes	68
37.29	odd	12		925.2.t.b.843.10		68
185.29	odd	12		185.2.p.a.103.8	yes	68
185.103	even	12		185.2.u.a.177.10	yes	68
185.177	even	12	inner	925.2.y.b.732.8		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.8	✓	68	5.3	odd	4
185.2.p.a.103.8	yes	68	185.29	odd	12
185.2.u.a.23.10	yes	68	5.4	even	2
185.2.u.a.177.10	yes	68	185.103	even	12
925.2.t.b.282.10		68	5.2	odd	4
925.2.t.b.843.10		68	37.29	odd	12
925.2.y.b.393.8		68	1.1	even	1	trivial
925.2.y.b.732.8		68	185.177	even	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.317786 - 0.183474i) q^{2} +(0.184590 + 0.0494608i) q^{3} +(-0.932675 - 1.61544i) q^{4} +(-0.0495854 - 0.0495854i) q^{6} +(1.90898 + 0.511509i) q^{7} +1.41838i q^{8} +(-2.56645 - 1.48174i) q^{9} +3.45234i q^{11} +(-0.0922616 - 0.344325i) q^{12} +(-2.68284 + 1.54894i) q^{13} +(-0.512798 - 0.512798i) q^{14} +(-1.60511 + 2.78014i) q^{16} +(-3.72683 + 6.45506i) q^{17} +(0.543721 + 0.941752i) q^{18} +(7.19086 + 1.92679i) q^{19} +(0.327079 + 0.188839i) q^{21} +(0.633414 - 1.09710i) q^{22} -1.31718i q^{23} +(-0.0701542 + 0.261819i) q^{24} +1.13676 q^{26} +(-0.805841 - 0.805841i) q^{27} +(-0.954144 - 3.56091i) q^{28} +(2.20635 + 2.20635i) q^{29} +(4.00610 - 4.00610i) q^{31} +(3.47687 - 2.00737i) q^{32} +(-0.170755 + 0.637268i) q^{33} +(2.36867 - 1.36755i) q^{34} +5.52793i q^{36} +(3.14689 - 5.20549i) q^{37} +(-1.93164 - 1.93164i) q^{38} +(-0.571837 + 0.153223i) q^{39} +(-5.80754 + 3.35298i) q^{41} +(-0.0692941 - 0.120021i) q^{42} +12.5857i q^{43} +(5.57705 - 3.21991i) q^{44} +(-0.241668 + 0.418582i) q^{46} +(1.95542 - 1.95542i) q^{47} +(-0.433796 + 0.433796i) q^{48} +(-2.67962 - 1.54708i) q^{49} +(-1.00721 + 1.00721i) q^{51} +(5.00443 + 2.88931i) q^{52} +(-4.59015 + 1.22993i) q^{53} +(0.108234 + 0.403936i) q^{54} +(-0.725515 + 2.70766i) q^{56} +(1.23206 + 0.711331i) q^{57} +(-0.296339 - 1.10595i) q^{58} +(1.37883 + 5.14585i) q^{59} +(9.38781 + 2.51546i) q^{61} +(-2.00810 + 0.538068i) q^{62} +(-4.14137 - 4.14137i) q^{63} +4.94725 q^{64} +(0.171186 - 0.171186i) q^{66} +(-1.28021 + 4.77781i) q^{67} +13.9037 q^{68} +(0.0651488 - 0.243139i) q^{69} +(2.33213 + 4.03937i) q^{71} +(2.10167 - 3.64020i) q^{72} +(-6.43715 + 6.43715i) q^{73} +(-1.95511 + 1.07686i) q^{74} +(-3.59413 - 13.4135i) q^{76} +(-1.76590 + 6.59044i) q^{77} +(0.209834 + 0.0562249i) q^{78} +(8.42204 + 2.25668i) q^{79} +(4.33633 + 7.51074i) q^{81} +2.46074 q^{82} +(13.1368 - 3.51999i) q^{83} -0.704502i q^{84} +(2.30915 - 3.99956i) q^{86} +(0.298142 + 0.516397i) q^{87} -4.89673 q^{88} +(-14.7909 + 3.96321i) q^{89} +(-5.91378 + 1.58459i) q^{91} +(-2.12783 + 1.22850i) q^{92} +(0.937632 - 0.541342i) q^{93} +(-0.980175 + 0.262637i) q^{94} +(0.741082 - 0.198572i) q^{96} -4.35591 q^{97} +(0.567697 + 0.983280i) q^{98} +(5.11547 - 8.86025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more