LMFDB - Embedded newform 925.2.t.b.843.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(82,925)] 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("925.82"); 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([3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.t (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			843.10
Character	$\chi$	$=$	925.843
Dual form			925.2.t.b.282.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.183474 + 0.317786i) q^{2} +(0.0494608 + 0.184590i) q^{3} +(0.932675 - 1.61544i) q^{4} +(-0.0495854 + 0.0495854i) q^{6} +(-0.511509 - 1.90898i) q^{7} +1.41838 q^{8} +(2.56645 - 1.48174i) q^{9} -3.45234i q^{11} +(0.344325 + 0.0922616i) q^{12} +(1.54894 - 2.68284i) q^{13} +(0.512798 - 0.512798i) q^{14} +(-1.60511 - 2.78014i) q^{16} +(-6.45506 + 3.72683i) q^{17} +(0.941752 + 0.543721i) q^{18} +(-7.19086 + 1.92679i) q^{19} +(0.327079 - 0.188839i) q^{21} +(1.09710 - 0.633414i) q^{22} -1.31718 q^{23} +(0.0701542 + 0.261819i) q^{24} +1.13676 q^{26} +(0.805841 + 0.805841i) q^{27} +(-3.56091 - 0.954144i) q^{28} +(-2.20635 + 2.20635i) q^{29} +(4.00610 + 4.00610i) q^{31} +(2.00737 - 3.47687i) q^{32} +(0.637268 - 0.170755i) q^{33} +(-2.36867 - 1.36755i) q^{34} -5.52793i q^{36} +(5.20549 - 3.14689i) q^{37} +(-1.93164 - 1.93164i) q^{38} +(0.571837 + 0.153223i) q^{39} +(-5.80754 - 3.35298i) q^{41} +(0.120021 + 0.0692941i) q^{42} +12.5857 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} +(-2.88931 - 5.00443i) q^{52} +(1.22993 - 4.59015i) q^{53} +(-0.108234 + 0.403936i) q^{54} +(-0.725515 - 2.70766i) q^{56} +(-0.711331 - 1.23206i) q^{57} +(-1.10595 - 0.296339i) q^{58} +(-1.37883 + 5.14585i) q^{59} +(9.38781 - 2.51546i) q^{61} +(-0.538068 + 2.00810i) q^{62} +(-4.14137 - 4.14137i) q^{63} -4.94725 q^{64} +(0.171186 + 0.171186i) q^{66} +(-4.77781 + 1.28021i) q^{67} +13.9037i q^{68} +(-0.0651488 - 0.243139i) q^{69} +(2.33213 - 4.03937i) q^{71} +(3.64020 - 2.10167i) q^{72} +(6.43715 - 6.43715i) q^{73} +(1.95511 + 1.07686i) q^{74} +(-3.59413 + 13.4135i) q^{76} +(-6.59044 + 1.76590i) q^{77} +(0.0562249 + 0.209834i) q^{78} +(-8.42204 + 2.25668i) q^{79} +(4.33633 - 7.51074i) q^{81} -2.46074i q^{82} +(-3.51999 + 13.1368i) q^{83} -0.704502i q^{84} +(2.30915 + 3.99956i) q^{86} +(-0.516397 - 0.298142i) q^{87} -4.89673i q^{88} +(14.7909 + 3.96321i) q^{89} +(-5.91378 - 1.58459i) q^{91} +(-1.22850 + 2.12783i) q^{92} +(-0.541342 + 0.937632i) q^{93} +(0.980175 + 0.262637i) q^{94} +(0.741082 + 0.198572i) q^{96} +4.35591i q^{97} +(0.983280 + 0.567697i) q^{98} +(-5.11547 - 8.86025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{2} + 8 q^{3} - 30 q^{4} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) $ 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Character values

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

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.183474	+	0.317786i	0.129736	+	0.224709i	0.923574	−	0.383420i	$-0.125254\pi$
$2$	0.183474	+	0.317786i	0.129736	+	0.224709i	−0.793839	+	0.608129i	$0.791920\pi$
$3$	0.0494608	+	0.184590i	0.0285562	+	0.106573i	0.978733	−	0.205138i	$-0.0657644\pi$
$3$	0.0494608	+	0.184590i	0.0285562	+	0.106573i	−0.950177	+	0.311711i	$0.899098\pi$
$4$	0.932675	−	1.61544i	0.466337	−	0.807720i
$5$		0			0
$5$		0			0
$6$	−0.0495854	+	0.0495854i	−0.0202431	+	0.0202431i
$7$	−0.511509	−	1.90898i	−0.193332	−	0.721526i	−0.992692	−	0.120674i	$-0.961495\pi$
$7$	−0.511509	−	1.90898i	−0.193332	−	0.721526i	0.799360	−	0.600853i	$-0.205172\pi$
$8$	1.41838			0.501473
$9$	2.56645	−	1.48174i	0.855483	−	0.493913i
$10$		0			0
$11$		−	3.45234i		−	1.04092i	−0.853886	−	0.520460i	$-0.825761\pi$
$11$		−	3.45234i		−	1.04092i	0.853886	−	0.520460i	$-0.174239\pi$
$12$	0.344325	+	0.0922616i	0.0993981	+	0.0266336i
$13$	1.54894	−	2.68284i	0.429598	−	0.744086i	−0.567239	−	0.823553i	$-0.691989\pi$
$13$	1.54894	−	2.68284i	0.429598	−	0.744086i	0.996837	+	0.0794671i	$0.0253219\pi$
$14$	0.512798	−	0.512798i	0.137051	−	0.137051i
$15$		0			0
$16$	−1.60511	−	2.78014i	−0.401278	−	0.695035i
$17$	−6.45506	+	3.72683i	−1.56558	+	0.903889i	−0.568907	+	0.822402i	$0.692634\pi$
$17$	−6.45506	+	3.72683i	−1.56558	+	0.903889i	−0.996674	+	0.0814869i	$0.974033\pi$
$18$	0.941752	+	0.543721i	0.221973	+	0.128156i
$19$	−7.19086	+	1.92679i	−1.64970	+	0.442035i	−0.959528	−	0.281614i	$-0.909130\pi$
$19$	−7.19086	+	1.92679i	−1.64970	+	0.442035i	−0.690169	+	0.723648i	$0.742464\pi$
$20$		0			0
$21$	0.327079	−	0.188839i	0.0713745	−	0.0412081i
$22$	1.09710	−	0.633414i	0.233904	−	0.135044i
$23$	−1.31718			−0.274651			−0.137326	−	0.990526i	$-0.543851\pi$
$23$	−1.31718			−0.274651			−0.137326	+	0.990526i	$0.543851\pi$
$24$	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
$28$	−3.56091	−	0.954144i	−0.672949	−	0.180316i
$29$	−2.20635	+	2.20635i	−0.409708	+	0.409708i	−0.881637	−	0.471929i	$-0.843558\pi$
$29$	−2.20635	+	2.20635i	−0.409708	+	0.409708i	0.471929	+	0.881637i	$0.343558\pi$
$30$		0			0
$31$	4.00610	+	4.00610i	0.719518	+	0.719518i	0.968506	−	0.248989i	$-0.0800982\pi$
$31$	4.00610	+	4.00610i	0.719518	+	0.719518i	−0.248989	+	0.968506i	$0.580098\pi$
$32$	2.00737	−	3.47687i	0.354857	−	0.614630i
$33$	0.637268	−	0.170755i	0.110934	−	0.0297247i
$34$	−2.36867	−	1.36755i	−0.406223	−	0.234533i
$35$		0			0
$36$		−	5.52793i		−	0.921321i
$37$	5.20549	−	3.14689i	0.855777	−	0.517345i
$37$	5.20549	−	3.14689i	0.855777	−	0.517345i
$38$	−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	−0.0275253	−	0.999621i	$-0.508763\pi$
$41$	−5.80754	−	3.35298i	−0.906985	−	0.523648i	−0.879460	+	0.475973i	$0.842096\pi$
$42$	0.120021	+	0.0692941i	0.0185196	+	0.0106923i
$43$	12.5857			1.91930			0.959652	−	0.281191i	$-0.0907296\pi$
$43$	12.5857			1.91930			0.959652	+	0.281191i	$0.0907296\pi$
$44$	−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
$52$	−2.88931	−	5.00443i	−0.400675	−	0.693990i
$53$	1.22993	−	4.59015i	0.168943	−	0.630506i	−0.828561	−	0.559899i	$-0.810840\pi$
$53$	1.22993	−	4.59015i	0.168943	−	0.630506i	0.997504	−	0.0706065i	$-0.0224934\pi$
$54$	−0.108234	+	0.403936i	−0.0147288	+	0.0549687i
$55$		0			0
$56$	−0.725515	−	2.70766i	−0.0969510	−	0.361826i
$57$	−0.711331	−	1.23206i	−0.0942181	−	0.163191i
$58$	−1.10595	−	0.296339i	−0.145219	−	0.0389112i
$59$	−1.37883	+	5.14585i	−0.179508	+	0.669933i	0.816232	+	0.577725i	$0.196059\pi$
$59$	−1.37883	+	5.14585i	−0.179508	+	0.669933i	−0.995740	+	0.0922082i	$0.970607\pi$
$60$		0			0
$61$	9.38781	−	2.51546i	1.20199	−	0.322071i	0.398373	−	0.917223i	$-0.369575\pi$
$61$	9.38781	−	2.51546i	1.20199	−	0.322071i	0.803613	+	0.595152i	$0.202908\pi$
$62$	−0.538068	+	2.00810i	−0.0683348	+	0.255029i
$63$	−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
$67$	−4.77781	+	1.28021i	−0.583703	+	0.156403i	−0.538574	−	0.842578i	$-0.681037\pi$
$67$	−4.77781	+	1.28021i	−0.583703	+	0.156403i	−0.0451292	+	0.998981i	$0.514370\pi$
$68$			13.9037i			1.68607i
$69$	−0.0651488	−	0.243139i	−0.00784300	−	0.0292705i
$70$		0			0
$71$	2.33213	−	4.03937i	0.276773	−	0.479385i	−0.693808	−	0.720160i	$-0.744068\pi$
$71$	2.33213	−	4.03937i	0.276773	−	0.479385i	0.970581	+	0.240775i	$0.0774016\pi$
$72$	3.64020	−	2.10167i	0.429002	−	0.247684i
$73$	6.43715	−	6.43715i	0.753412	−	0.753412i	−0.221702	−	0.975114i	$-0.571161\pi$
$73$	6.43715	−	6.43715i	0.753412	−	0.753412i	0.975114	+	0.221702i	$0.0711613\pi$
$74$	1.95511	+	1.07686i	0.227276	+	0.125182i
$75$		0			0
$76$	−3.59413	+	13.4135i	−0.412275	+	1.53863i
$77$	−6.59044	+	1.76590i	−0.751051	+	0.201243i
$78$	0.0562249	+	0.209834i	0.00636622	+	0.0237591i
$79$	−8.42204	+	2.25668i	−0.947554	+	0.253896i	−0.699324	−	0.714805i	$-0.746515\pi$
$79$	−8.42204	+	2.25668i	−0.947554	+	0.253896i	−0.248230	+	0.968701i	$0.579849\pi$
$80$		0			0
$81$	4.33633	−	7.51074i	0.481814	−	0.834527i
$82$		−	2.46074i		−	0.271743i
$83$	−3.51999	+	13.1368i	−0.386369	+	1.44195i	0.449629	+	0.893215i	$0.351556\pi$
$83$	−3.51999	+	13.1368i	−0.386369	+	1.44195i	−0.835998	+	0.548733i	$0.815111\pi$
$84$		−	0.704502i		−	0.0768675i
$85$		0			0
$86$	2.30915	+	3.99956i	0.249002	+	0.431284i
$87$	−0.516397	−	0.298142i	−0.0553636	−	0.0319642i
$88$		−	4.89673i		−	0.521993i
$89$	14.7909	+	3.96321i	1.56783	+	0.420100i	0.935133	−	0.354297i	$-0.115280\pi$
$89$	14.7909	+	3.96321i	1.56783	+	0.420100i	0.632701	+	0.774397i	$0.281946\pi$
$90$		0			0
$91$	−5.91378	−	1.58459i	−0.619933	−	0.166110i
$92$	−1.22850	+	2.12783i	−0.128080	+	0.221841i
$93$	−0.541342	+	0.937632i	−0.0561346	+	0.0972279i
$94$	0.980175	+	0.262637i	0.101097	+	0.0270890i
$95$		0			0
$96$	0.741082	+	0.198572i	0.0756364	+	0.0202667i
$97$			4.35591i			0.442276i	0.975243	+	0.221138i	$0.0709770\pi$
$97$			4.35591i			0.442276i	−0.975243	+	0.221138i	$0.929023\pi$
$98$	0.983280	+	0.567697i	0.0993263	+	0.0573461i
$99$	−5.11547	−	8.86025i	−0.514124	−	0.890489i
$100$		0			0
$101$		−	0.191058i		−	0.0190110i	−0.999955	−	0.00950548i	$-0.996974\pi$
$101$		−	0.191058i		−	0.0190110i	0.999955	−	0.00950548i	$-0.00302573\pi$
$102$	0.135280	−	0.504873i	0.0133947	−	0.0499898i
$103$		−	2.11028i		−	0.207932i	−0.994581	−	0.103966i	$-0.966847\pi$
$103$		−	2.11028i		−	0.207932i	0.994581	−	0.103966i	$-0.0331532\pi$
$104$	2.19698	−	3.80529i	0.215432	−	0.373139i
$105$		0			0
$106$	1.68434	−	0.451319i	0.163598	−	0.0438359i
$107$	2.54999	+	9.51668i	0.246517	+	0.920012i	0.972615	+	0.232422i	$0.0746650\pi$
$107$	2.54999	+	9.51668i	0.246517	+	0.920012i	−0.726099	+	0.687591i	$0.758668\pi$
$108$	2.05338	−	0.550200i	0.197586	−	0.0529431i
$109$	4.09076	−	15.2669i	0.391824	−	1.46231i	−0.435300	−	0.900286i	$-0.643358\pi$
$109$	4.09076	−	15.2669i	0.391824	−	1.46231i	0.827123	−	0.562020i	$-0.189976\pi$
$110$		0			0
$111$	0.838351	+	0.805234i	0.0795728	+	0.0764295i
$112$	−4.48619	+	4.48619i	−0.423906	+	0.423906i
$113$	5.40479	−	3.12046i	0.508440	−	0.293548i	−0.223752	−	0.974646i	$-0.571831\pi$
$113$	5.40479	−	3.12046i	0.508440	−	0.293548i	0.732192	+	0.681098i	$0.238497\pi$
$114$	0.261021	−	0.452102i	0.0244469	−	0.0423432i
$115$		0			0
$116$	1.50642	+	5.62203i	0.139867	+	0.521992i
$117$		−	9.18050i		−	0.848737i
$118$	−1.88826	+	0.505957i	−0.173828	+	0.0465771i
$119$	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
$123$	0.331682	−	1.23786i	0.0299068	−	0.111614i
$124$	10.2080	−	2.73523i	0.916707	−	0.245631i
$125$		0			0
$126$	0.556237	−	2.07590i	0.0495535	−	0.184936i
$127$	3.86342	+	1.03520i	0.342823	+	0.0918592i	0.426123	−	0.904665i	$-0.359879\pi$
$127$	3.86342	+	1.03520i	0.342823	+	0.0918592i	−0.0832996	+	0.996525i	$0.526546\pi$
$128$	−4.92244	−	8.52591i	−0.435086	−	0.753591i
$129$	0.622499	+	2.32320i	0.0548080	+	0.204546i
$130$		0			0
$131$	0.918927	−	3.42948i	0.0802870	−	0.299635i	−0.914093	−	0.405505i	$-0.867096\pi$
$131$	0.918927	−	3.42948i	0.0802870	−	0.299635i	0.994380	+	0.105869i	$0.0337625\pi$
$132$	0.318519	−	1.18873i	0.0277235	−	0.103465i
$133$	7.35638	+	12.7416i	0.637879	+	1.10484i
$134$	−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	$-0.0797216\pi$
$139$	3.18045	+	5.50870i	0.269762	+	0.467241i	−0.699038	+	0.715084i	$0.746388\pi$
$140$		0			0
$141$	0.457669	+	0.264235i	0.0385427	+	0.0222526i
$142$	1.71154			0.143629
$143$	−9.26208	−	5.34746i	−0.774534	−	0.447177i
$144$	−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
$148$	−0.228577	−	11.3442i	−0.0187889	−	0.932485i
$149$			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	0.488675	−	0.872466i	$-0.337480\pi$
$151$	−0.277285	−	0.160091i	−0.0225651	−	0.0130280i	−0.511240	+	0.859438i	$0.670814\pi$
$152$	−10.1994	+	2.73291i	−0.827279	+	0.221669i
$153$	−11.0444	+	19.1294i	−0.892885	+	1.54652i
$154$	−1.77035	−	1.77035i	−0.142659	−	0.142659i
$155$		0			0
$156$	0.780862	−	0.780862i	0.0625190	−	0.0625190i
$157$	1.13930	+	0.305275i	0.0909263	+	0.0243636i	0.303995	−	0.952674i	$-0.401679\pi$
$157$	1.13930	+	0.305275i	0.0909263	+	0.0243636i	−0.213069	+	0.977037i	$0.568346\pi$
$158$	−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
$162$	3.18241			0.250034
$163$	−7.96311	+	4.59750i	−0.623719	+	0.360104i	−0.778315	−	0.627873i	$-0.783926\pi$
$163$	−7.96311	+	4.59750i	−0.623719	+	0.360104i	0.154597	+	0.987978i	$0.450592\pi$
$164$	−10.8331	+	6.25449i	−0.845922	+	0.488393i
$165$		0			0
$166$	−4.82051	+	1.29165i	−0.374144	+	0.100252i
$167$	18.8329	+	10.8732i	1.45733	+	0.841392i	0.998879	−	0.0473268i	$-0.0150702\pi$
$167$	18.8329	+	10.8732i	1.45733	+	0.841392i	0.458454	+	0.888718i	$0.348404\pi$
$168$	0.463922	−	0.267846i	0.0357924	−	0.0206647i
$169$	1.70158	+	2.94722i	0.130891	+	0.226709i
$170$		0			0
$171$	−15.6000	+	15.6000i	−1.19296	+	1.19296i
$172$	11.7384	−	20.3315i	0.895043	−	1.55026i
$173$	−3.34723	−	0.896886i	−0.254485	−	0.0681890i	0.129321	−	0.991603i	$-0.458720\pi$
$173$	−3.34723	−	0.896886i	−0.254485	−	0.0681890i	−0.383806	+	0.923414i	$0.625387\pi$
$174$		−	0.218805i		−	0.0165876i
$175$		0			0
$176$	−9.59798	+	5.54140i	−0.723475	+	0.417699i
$177$	−1.01807			−0.0765229
$178$	1.45429	+	5.42749i	0.109004	+	0.406807i
$179$	10.5340	−	10.5340i	0.787350	−	0.787350i	−0.193709	−	0.981059i	$-0.562052\pi$
$179$	10.5340	−	10.5340i	0.787350	−	0.787350i	0.981059	+	0.193709i	$0.0620517\pi$
$180$		0			0
$181$	−0.0475195	+	0.0823062i	−0.00353210	+	0.00611777i	−0.867786	−	0.496938i	$-0.834458\pi$
$181$	−0.0475195	+	0.0823062i	−0.00353210	+	0.00611777i	0.864254	+	0.503056i	$0.167791\pi$
$182$	−0.581462	−	2.17005i	−0.0431009	−	0.160855i
$183$	0.928657	+	1.60848i	0.0686483	+	0.118902i
$184$	−1.86827			−0.137730
$185$		0			0
$186$	−0.397288			−0.0291306
$187$	12.8663	+	22.2851i	0.940876	+	1.62964i
$188$	−1.33510	−	4.98265i	−0.0973719	−	0.363397i
$189$	1.12614	−	1.95053i	0.0819145	−	0.141880i
$190$		0			0
$191$	6.76075	−	6.76075i	0.489190	−	0.489190i	−0.418860	−	0.908051i	$-0.637570\pi$
$191$	6.76075	−	6.76075i	0.489190	−	0.489190i	0.908051	+	0.418860i	$0.137570\pi$
$192$	−0.244695	−	0.913214i	−0.0176593	−	0.0659056i
$193$	0.988625			0.0711628			0.0355814	−	0.999367i	$-0.488672\pi$
$193$	0.988625			0.0711628			0.0355814	+	0.999367i	$0.488672\pi$
$194$	−1.38425	+	0.799195i	−0.0993831	+	0.0573789i
$195$		0			0
$196$		−	5.77169i		−	0.412263i
$197$	−7.91972	−	2.12208i	−0.564257	−	0.151192i	−0.0345956	−	0.999401i	$-0.511014\pi$
$197$	−7.91972	−	2.12208i	−0.564257	−	0.151192i	−0.529661	+	0.848209i	$0.677681\pi$
$198$	1.87711	−	3.25125i	0.133400	−	0.231056i
$199$	−0.311060	+	0.311060i	−0.0220505	+	0.0220505i	−0.718046	−	0.695996i	$-0.754963\pi$
$199$	−0.311060	+	0.311060i	−0.0220505	+	0.0220505i	0.695996	+	0.718046i	$0.254963\pi$
$200$		0			0
$201$	−0.472629	−	0.818617i	−0.0333367	−	0.0577408i
$202$	0.0607155	−	0.0350541i	0.00427192	−	0.00246640i
$203$	5.34044	+	3.08330i	0.374825	+	0.216405i
$204$	−2.56648	+	0.687687i	−0.179690	+	0.0481477i
$205$		0			0
$206$	0.670616	−	0.387180i	0.0467240	−	0.0269761i
$207$	−3.38048	+	1.95172i	−0.234960	+	0.135654i
$208$	−9.94489			−0.689554
$209$	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
$213$	0.860977	+	0.230698i	0.0589932	+	0.0158072i
$214$	−2.55641	+	2.55641i	−0.174753	+	0.174753i
$215$		0			0
$216$	1.14299	+	1.14299i	0.0777706	+	0.0777706i
$217$	5.59841	−	9.69673i	0.380045	−	0.658257i
$218$	5.60216	−	1.50109i	0.379426	−	0.101667i
$219$	1.50662	+	0.869849i	0.101808	+	0.0587789i
$220$		0			0
$221$			23.0905i			1.55324i
$222$	−0.102077	+	0.414156i	−0.00685094	+	0.0277963i
$223$	−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
$227$	−17.3295	−	10.0052i	−1.15020	−	0.664066i	−0.201261	−	0.979538i	$-0.564504\pi$
$227$	−17.3295	−	10.0052i	−1.15020	−	0.664066i	−0.948935	+	0.315471i	$0.897837\pi$
$228$	−2.65376			−0.175750
$229$	3.19465	+	1.84443i	0.211108	+	0.121883i	0.601826	−	0.798627i	$-0.294440\pi$
$229$	3.19465	+	1.84443i	0.211108	+	0.121883i	−0.390718	+	0.920510i	$0.627773\pi$
$230$		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	−0.948071	−	0.318060i	$-0.896969\pi$
$233$	−9.61670	+	9.61670i	−0.630011	+	0.630011i	0.318060	+	0.948071i	$0.396969\pi$
$234$	2.91743	−	1.68438i	0.190719	−	0.110111i
$235$		0			0
$236$	7.02682	+	7.02682i	0.457407	+	0.457407i
$237$	−0.833121	−	1.44301i	−0.0541171	−	0.0937335i
$238$	−1.39903	+	5.22125i	−0.0906856	+	0.338443i
$239$	−3.51998	+	13.1367i	−0.227689	+	0.849745i	0.753621	+	0.657309i	$0.228305\pi$
$239$	−3.51998	+	13.1367i	−0.227689	+	0.849745i	−0.981310	+	0.192436i	$0.938361\pi$
$240$		0			0
$241$	6.11044	+	22.8045i	0.393608	+	1.46897i	0.824138	+	0.566389i	$0.191660\pi$
$241$	6.11044	+	22.8045i	0.393608	+	1.46897i	−0.430530	+	0.902576i	$0.641673\pi$
$242$	−0.168548	−	0.291935i	−0.0108347	−	0.0187663i
$243$	4.90329	+	1.31383i	0.314546	+	0.0842823i
$244$	4.69221	−	17.5115i	0.300388	−	1.12106i
$245$		0			0
$246$	0.454228	−	0.121710i	0.0289605	−	0.00775995i
$247$	−5.96894	+	22.2764i	−0.379795	+	1.41741i
$248$	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	0.719669	−	0.694317i	$-0.244293\pi$
$251$	0.401654	+	0.401654i	0.0253522	+	0.0253522i	−0.694317	+	0.719669i	$0.744293\pi$
$252$	−10.5527	+	2.82759i	−0.664757	+	0.178121i
$253$			4.54736i			0.285890i
$254$	0.379864	+	1.41767i	0.0238348	+	0.0889527i
$255$		0			0
$256$	−3.14098	+	5.44033i	−0.196311	+	0.340021i
$257$	−14.1687	+	8.18028i	−0.883817	+	0.510272i	−0.871915	−	0.489657i	$-0.837122\pi$
$257$	−14.1687	+	8.18028i	−0.883817	+	0.510272i	−0.0119019	+	0.999929i	$0.503789\pi$
$258$	−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
$262$	1.25844	−	0.337198i	0.0777467	−	0.0208322i
$263$	4.59860	+	17.1622i	0.283562	+	1.05827i	0.949884	+	0.312603i	$0.101201\pi$
$263$	4.59860	+	17.1622i	0.283562	+	1.05827i	−0.666322	+	0.745664i	$0.732132\pi$
$264$	0.903888	−	0.242196i	0.0556305	−	0.0149061i
$265$		0			0
$266$	−2.69941	+	4.67551i	−0.165511	+	0.286674i
$267$			2.92628i			0.179085i
$268$	−2.38804	+	8.91229i	−0.145873	+	0.544405i
$269$		−	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	−0.999809	−	0.0195654i	$-0.993772\pi$
$271$	−8.50840	−	14.7370i	−0.516848	−	0.895208i	0.482960	−	0.875642i	$-0.339562\pi$
$272$	20.7222	+	11.9640i	1.25647	+	0.725422i
$273$		−	1.17000i		−	0.0708117i
$274$	0.812229	+	0.217636i	0.0490686	+	0.0131479i
$275$		0			0
$276$	−0.453539	−	0.121525i	−0.0272998	−	0.00731497i
$277$	−0.776108	+	1.34426i	−0.0466318	+	0.0807686i	−0.888399	−	0.459072i	$-0.848182\pi$
$277$	−0.776108	+	1.34426i	−0.0466318	+	0.0807686i	0.841767	+	0.539840i	$0.181515\pi$
$278$	−1.16706	+	2.02140i	−0.0699954	+	0.121236i
$279$	16.2175	+	4.34546i	0.970914	+	0.260156i
$280$		0			0
$281$	9.62089	+	2.57791i	0.573934	+	0.153785i	0.534100	−	0.845421i	$-0.320650\pi$
$281$	9.62089	+	2.57791i	0.573934	+	0.153785i	0.0398338	+	0.999206i	$0.487317\pi$
$282$			0.193921i			0.0115478i
$283$	−21.5075	−	12.4174i	−1.27849	−	0.738137i	−0.301919	−	0.953333i	$-0.597627\pi$
$283$	−21.5075	−	12.4174i	−1.27849	−	0.738137i	−0.976571	+	0.215197i	$0.930961\pi$
$284$	−4.35024	−	7.53484i	−0.258139	−	0.447110i
$285$		0			0
$286$		−	3.92448i		−	0.232059i
$287$	−3.43016	+	12.8015i	−0.202476	+	0.755652i
$288$		−	11.8976i		−	0.701074i
$289$	19.2785	−	33.3914i	1.13403	−	1.96420i
$290$		0			0
$291$	−0.804058	+	0.215447i	−0.0471347	+	0.0126297i
$292$	−4.39507	−	16.4026i	−0.257202	−	0.959890i
$293$	6.40278	−	1.71562i	0.374054	−	0.100227i	−0.0668940	−	0.997760i	$-0.521309\pi$
$293$	6.40278	−	1.71562i	0.374054	−	0.100227i	0.440948	+	0.897533i	$0.354642\pi$
$294$	−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
$298$	−5.72645	+	3.30617i	−0.331724	+	0.191521i
$299$	−2.04023	+	3.53379i	−0.117990	+	0.204364i
$300$		0			0
$301$	−6.43771	−	24.0259i	−0.371063	−	1.38483i
$302$		−	0.117490i		−	0.00676077i
$303$	0.0352674	−	0.00944986i	0.00202606	−	0.000542881i
$304$	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	0.384661	−	0.923058i	$-0.374318\pi$
$307$	−9.43347	−	9.43347i	−0.538396	−	0.538396i	−0.923058	+	0.384661i	$0.874318\pi$
$308$	−3.29403	+	12.2935i	−0.187695	+	0.700486i
$309$	0.389536	−	0.104376i	0.0221599	−	0.00593773i
$310$		0			0
$311$	−2.04001	+	7.61341i	−0.115678	+	0.431717i	−0.999337	−	0.0364152i	$-0.988406\pi$
$311$	−2.04001	+	7.61341i	−0.115678	+	0.431717i	0.883659	+	0.468132i	$0.155073\pi$
$312$	0.811083	+	0.217329i	0.0459185	+	0.0123038i
$313$	1.15066	+	1.99301i	0.0650393	+	0.112651i	0.896711	−	0.442616i	$-0.145949\pi$
$313$	1.15066	+	1.99301i	0.0650393	+	0.112651i	−0.831672	+	0.555267i	$0.812616\pi$
$314$	0.112020	+	0.418065i	0.00632166	+	0.0235927i
$315$		0			0
$316$	−4.20950	+	15.7101i	−0.236803	+	0.883759i
$317$	2.10279	−	7.84772i	0.118104	−	0.440772i	−0.881396	−	0.472378i	$-0.843396\pi$
$317$	2.10279	−	7.84772i	0.118104	−	0.440772i	0.999500	+	0.0316064i	$0.0100623\pi$
$318$	0.166618	+	0.288591i	0.00934347	+	0.0161834i
$319$	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
$327$	3.02046			0.167032
$328$	−8.23730	−	4.75581i	−0.454829	−	0.262596i
$329$	−4.73308	−	2.73265i	−0.260943	−	0.150656i
$330$		0			0
$331$	−23.6164	−	6.32799i	−1.29807	−	0.347818i	−0.457352	−	0.889285i	$-0.651202\pi$
$331$	−23.6164	−	6.32799i	−1.29807	−	0.347818i	−0.840722	+	0.541468i	$0.817869\pi$
$332$	17.9387	+	17.9387i	0.984512	+	0.984512i
$333$	8.69676	−	15.7895i	0.476579	−	0.865259i
$334$			7.97977i			0.436634i
$335$		0			0
$336$	−1.05000	−	0.606217i	−0.0572821	−	0.0330718i
$337$	18.7623	−	5.02735i	1.02205	−	0.273857i	0.291394	−	0.956603i	$-0.405881\pi$
$337$	18.7623	−	5.02735i	1.02205	−	0.273857i	0.730656	+	0.682746i	$0.239214\pi$
$338$	−0.624391	+	1.08148i	−0.0339624	+	0.0588245i
$339$	0.843331	+	0.843331i	0.0458035	+	0.0458035i
$340$		0			0
$341$	13.8304	−	13.8304i	0.748960	−	0.748960i
$342$	−7.81964	−	2.09527i	−0.422838	−	0.113299i
$343$	−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
$347$	−3.39588			−0.182300			−0.0911501	−	0.995837i	$-0.529054\pi$
$347$	−3.39588			−0.182300			−0.0911501	+	0.995837i	$0.529054\pi$
$348$	−0.963262	+	0.556139i	−0.0516363	+	0.0298122i
$349$	0.334598	−	0.193180i	0.0179106	−	0.0103407i	−0.491018	−	0.871149i	$-0.663375\pi$
$349$	0.334598	−	0.193180i	0.0179106	−	0.0103407i	0.508929	+	0.860809i	$0.330042\pi$
$350$		0			0
$351$	3.41014	−	0.913745i	0.182020	−	0.0487721i
$352$	−12.0033	−	6.93013i	−0.639780	−	0.369377i
$353$	−3.67390	+	2.12113i	−0.195542	+	0.112896i	−0.594574	−	0.804041i	$-0.702679\pi$
$353$	−3.67390	+	2.12113i	−0.195542	+	0.112896i	0.399032	+	0.916937i	$0.369346\pi$
$354$	−0.186789	−	0.323529i	−0.00992774	−	0.0171954i
$355$		0			0
$356$	20.1974	−	20.1974i	1.07046	−	1.07046i
$357$	−1.40754	+	2.43793i	−0.0744950	+	0.129029i
$358$	5.28028	+	1.41485i	0.279072	+	0.0747770i
$359$			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
$362$	−0.0348743			−0.00183296
$363$	−0.0454372	−	0.169574i	−0.00238484	−	0.00890033i
$364$	−8.07545	+	8.07545i	−0.423268	+	0.423268i
$365$		0			0
$366$	−0.340768	+	0.590228i	−0.0178122	+	0.0308517i
$367$	−3.44218	−	12.8464i	−0.179680	−	0.670576i	−0.995707	−	0.0925616i	$-0.970494\pi$
$367$	−3.44218	−	12.8464i	−0.179680	−	0.670576i	0.816027	−	0.578014i	$-0.196172\pi$
$368$	2.11423	+	3.66195i	0.110212	+	0.190892i
$369$	−19.8730			−1.03455
$370$		0			0
$371$	−9.39162			−0.487588
$372$	1.00979	+	1.74901i	0.0523553	+	0.0906820i
$373$	5.10346	+	19.0464i	0.264247	+	0.986183i	0.962710	+	0.270536i	$0.0872011\pi$
$373$	5.10346	+	19.0464i	0.264247	+	0.986183i	−0.698463	+	0.715646i	$0.746132\pi$
$374$	−4.72125	+	8.17745i	−0.244130	+	0.422846i
$375$		0			0
$376$	2.77354	−	2.77354i	0.143034	−	0.143034i
$377$	2.50178	+	9.33677i	0.128848	+	0.480868i
$378$	0.826467			0.0425089
$379$	−9.48304	+	5.47504i	−0.487111	+	0.281234i	−0.723375	−	0.690455i	$-0.757410\pi$
$379$	−9.48304	+	5.47504i	−0.487111	+	0.281234i	0.236264	+	0.971689i	$0.424077\pi$
$380$		0			0
$381$			0.764351i			0.0391589i
$382$	3.38889	+	0.908050i	0.173391	+	0.0464599i
$383$	−8.51460	+	14.7477i	−0.435076	+	0.753574i	−0.997302	−	0.0734101i	$-0.976612\pi$
$383$	−8.51460	+	14.7477i	−0.435076	+	0.753574i	0.562226	+	0.826984i	$0.309945\pi$
$384$	1.33033	−	1.33033i	0.0678882	−	0.0678882i
$385$		0			0
$386$	0.181387	+	0.314171i	0.00923234	+	0.0159909i
$387$	32.3006	−	18.6488i	1.64193	−	0.947970i
$388$	7.03671	+	4.06265i	0.357235	+	0.206250i
$389$	−12.4581	+	3.33813i	−0.631649	+	0.169250i	−0.560418	−	0.828210i	$-0.689359\pi$
$389$	−12.4581	+	3.33813i	−0.631649	+	0.169250i	−0.0712310	+	0.997460i	$0.522693\pi$
$390$		0			0
$391$	8.50248	−	4.90891i	0.429989	−	0.248254i
$392$	3.80072	−	2.19435i	0.191965	−	0.110831i
$393$	0.678499			0.0342258
$394$	−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	$0.0309923\pi$
$397$	21.7674	+	21.7674i	1.09248	+	1.09248i	0.0972114	+	0.995264i	$0.469008\pi$
$398$	−0.155922	−	0.0417791i	−0.00781566	−	0.00209420i
$399$	−1.98813	+	1.98813i	−0.0995308	+	0.0995308i
$400$		0			0
$401$	−0.609043	−	0.609043i	−0.0304142	−	0.0304142i	0.691736	−	0.722150i	$-0.256846\pi$
$401$	−0.609043	−	0.609043i	−0.0304142	−	0.0304142i	−0.722150	+	0.691736i	$0.756846\pi$
$402$	0.173430	−	0.300389i	0.00864990	−	0.0149821i
$403$	16.9529	−	4.54253i	0.844486	−	0.226279i
$404$	−0.308642	−	0.178195i	−0.0153555	−	0.00886552i
$405$		0			0
$406$			2.26282i			0.112302i
$407$	−10.8641	−	17.9711i	−0.538514	−	0.890795i
$408$	−1.42860	−	1.42860i	−0.0707264	−	0.0707264i
$409$	−27.7946	−	7.44753i	−1.37435	−	0.368257i	−0.505286	−	0.862952i	$-0.668613\pi$
$409$	−27.7946	−	7.44753i	−1.37435	−	0.368257i	−0.869067	+	0.494695i	$0.835280\pi$
$410$		0			0
$411$	0.379251	+	0.218960i	0.0187071	+	0.0108005i
$412$	−3.40902	−	1.96820i	−0.167951	−	0.0969663i
$413$	10.5286			0.518079
$414$	−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	$-0.683577\pi$
$419$	−1.88268	+	1.08696i	−0.0919747	+	0.0531016i	0.453307	+	0.891354i	$0.350244\pi$
$420$		0			0
$421$	16.3854	+	16.3854i	0.798575	+	0.798575i	0.982871	−	0.184296i	$-0.0590004\pi$
$421$	16.3854	+	16.3854i	0.798575	+	0.798575i	−0.184296	+	0.982871i	$0.559000\pi$
$422$	0.222083	+	0.384659i	0.0108108	+	0.0187249i
$423$	2.12107	−	7.91593i	0.103130	−	0.384886i
$424$	1.74450	−	6.51058i	0.0847206	−	0.316182i
$425$		0			0
$426$	0.0846541	+	0.315933i	0.00410150	+	0.0153070i
$427$	−9.60390	−	16.6345i	−0.464766	−	0.804997i
$428$	17.7519	+	4.75662i	0.858072	+	0.229920i
$429$	0.528979	−	1.97418i	0.0255394	−	0.0953142i
$430$		0			0
$431$	−6.06172	+	1.62423i	−0.291983	+	0.0782366i	−0.401837	−	0.915711i	$-0.631628\pi$
$431$	−6.06172	+	1.62423i	−0.291983	+	0.0782366i	0.109854	+	0.993948i	$0.464962\pi$
$432$	0.946883	−	3.53382i	0.0455570	−	0.170021i
$433$	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
$437$	9.47167	−	2.53793i	0.453091	−	0.121405i
$438$			0.638378i			0.0305029i
$439$	7.05673	+	26.3361i	0.336799	+	1.25695i	0.901905	+	0.431934i	$0.142169\pi$
$439$	7.05673	+	26.3361i	0.336799	+	1.25695i	−0.565106	+	0.825018i	$0.691165\pi$
$440$		0			0
$441$	4.58474	−	7.94100i	0.218321	−	0.378143i
$442$	−7.33784	+	4.23650i	−0.349025	+	0.201510i
$443$	14.0595	−	14.0595i	0.667985	−	0.667985i	−0.289264	−	0.957249i	$-0.593411\pi$
$443$	14.0595	−	14.0595i	0.667985	−	0.667985i	0.957249	+	0.289264i	$0.0934107\pi$
$444$	2.08272	−	0.603285i	0.0988414	−	0.0286306i
$445$		0			0
$446$	1.86259	−	6.95128i	0.0881962	−	0.329153i
$447$	−3.32628	+	0.891275i	−0.157328	+	0.0421559i
$448$	2.53057	+	9.44420i	0.119558	+	0.446197i
$449$	−12.8304	+	3.43788i	−0.605502	+	0.162244i	−0.548528	−	0.836132i	$-0.684812\pi$
$449$	−12.8304	+	3.43788i	−0.605502	+	0.162244i	−0.0569734	+	0.998376i	$0.518145\pi$
$450$		0			0
$451$	−11.5756	+	20.0496i	−0.545076	+	0.944099i
$452$		−	11.6415i		−	0.547570i
$453$	0.0158364	−	0.0591023i	0.000744059	−	0.00277687i
$454$		−	7.34274i		−	0.344612i
$455$		0			0
$456$	−1.00894	−	1.74753i	−0.0472479	−	0.0818357i
$457$	−13.0505	−	7.53471i	−0.610477	−	0.352459i	0.162675	−	0.986680i	$-0.447988\pi$
$457$	−13.0505	−	7.53471i	−0.610477	−	0.352459i	−0.773152	+	0.634221i	$0.781321\pi$
$458$			1.35362i			0.0632504i
$459$	−8.20498	−	2.19852i	−0.382976	−	0.102618i
$460$		0			0
$461$	12.5579	+	3.36489i	0.584882	+	0.156719i	0.539113	−	0.842233i	$-0.318760\pi$
$461$	12.5579	+	3.36489i	0.584882	+	0.156719i	0.0457688	+	0.998952i	$0.485426\pi$
$462$	0.239227	−	0.414353i	0.0111298	−	0.0192774i
$463$	−13.9799	+	24.2140i	−0.649703	+	1.12532i	0.333491	+	0.942753i	$0.391773\pi$
$463$	−13.9799	+	24.2140i	−0.649703	+	1.12532i	−0.983194	+	0.182565i	$0.941560\pi$
$464$	9.67539	+	2.59251i	0.449169	+	0.120354i
$465$		0			0
$466$	−4.82046	−	1.29164i	−0.223304	−	0.0598340i
$467$		−	1.30129i		−	0.0602165i	−0.999547	−	0.0301083i	$-0.990415\pi$
$467$		−	1.30129i		−	0.0602165i	0.999547	−	0.0301083i	$-0.00958521\pi$
$468$	−14.8305	−	8.56242i	−0.685542	−	0.395798i
$469$	4.88779	+	8.46590i	0.225697	+	0.390919i
$470$		0			0
$471$			0.225403i			0.0103860i
$472$	−1.95570	+	7.29877i	−0.0900184	+	0.335953i
$473$		−	43.4502i		−	1.99784i
$474$	0.305712	−	0.529508i	0.0140418	−	0.0243211i
$475$		0			0
$476$	26.5418	−	7.11186i	1.21654	−	0.325972i
$477$	−3.64486	−	13.6028i	−0.166887	−	0.622830i
$478$	−4.82050	+	1.29165i	−0.220484	+	0.0590786i
$479$	−1.00395	+	3.74678i	−0.0458715	+	0.171195i	−0.985061	−	0.172203i	$-0.944911\pi$
$479$	−1.00395	+	3.74678i	−0.0458715	+	0.171195i	0.939190	+	0.343398i	$0.111578\pi$
$480$		0			0
$481$	−0.379608	−	18.8398i	−0.0173087	−	0.859022i
$482$	−6.12584	+	6.12584i	−0.279024	+	0.279024i
$483$	−0.430822	+	0.248735i	−0.0196031	+	0.0113179i
$484$	−0.856803	+	1.48403i	−0.0389456	+	0.0674558i
$485$		0			0
$486$	0.482107	+	1.79925i	0.0218688	+	0.0816156i
$487$			17.7036i			0.802228i	0.916028	+	0.401114i	$0.131377\pi$
$487$			17.7036i			0.802228i	−0.916028	+	0.401114i	$0.868623\pi$
$488$	13.3155	−	3.56787i	0.602764	−	0.161510i
$489$	−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
$493$	6.01942	−	22.4648i	0.271101	−	1.01176i
$494$	−8.17427	+	2.19029i	−0.367778	+	0.0985458i
$495$		0			0
$496$	4.70727	−	17.5678i	0.211363	−	0.788817i
$497$	−8.90398	−	2.38581i	−0.399398	−	0.107018i
$498$	−0.476852	−	0.825932i	−0.0213682	−	0.0370109i
$499$	−7.95975	−	29.7062i	−0.356327	−	1.32983i	−0.878806	−	0.477179i	$-0.841659\pi$
$499$	−7.95975	−	29.7062i	−0.356327	−	1.32983i	0.522479	−	0.852652i	$-0.325007\pi$
$500$		0			0
$501$	−1.07559	+	4.01416i	−0.0480539	+	0.179340i
$502$	−0.0539470	+	0.201333i	−0.00240777	+	0.00898593i
$503$	10.1676	+	17.6108i	0.453351	+	0.785227i	0.998592	−	0.0530522i	$-0.0168950\pi$
$503$	10.1676	+	17.6108i	0.453351	+	0.785227i	−0.545240	+	0.838280i	$0.683562\pi$
$504$	−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	$-0.222811\pi$
$509$	−3.95875	−	6.85676i	−0.175469	−	0.303921i	−0.940323	+	0.340282i	$0.889477\pi$
$510$		0			0
$511$	−15.5811	−	8.99573i	−0.689265	−	0.397948i
$512$	−21.9949			−0.972046
$513$	−7.34738	−	4.24201i	−0.324395	−	0.187289i
$514$	−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
$518$	1.05565	−	4.28308i	0.0463825	−	0.188188i
$519$		−	0.662225i		−	0.0290685i
$520$		0			0
$521$	−22.5608	−	13.0255i	−0.988406	−	0.570657i	−0.0836089	−	0.996499i	$-0.526645\pi$
$521$	−22.5608	−	13.0255i	−0.988406	−	0.570657i	−0.904798	+	0.425842i	$0.859978\pi$
$522$	−3.27747	+	0.878195i	−0.143451	+	0.0384376i
$523$	1.66547	−	2.88468i	0.0728259	−	0.126138i	−0.827313	−	0.561741i	$-0.810132\pi$
$523$	1.66547	−	2.88468i	0.0728259	−	0.126138i	0.900139	+	0.435603i	$0.143465\pi$
$524$	−4.68306	−	4.68306i	−0.204581	−	0.204581i
$525$		0			0
$526$	−4.61019	+	4.61019i	−0.201014	+	0.201014i
$527$	−40.7897	−	10.9296i	−1.77683	−	0.476099i
$528$	−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
$532$	27.4445			1.18987
$533$	−17.9910	+	10.3871i	−0.779278	+	0.449917i
$534$	−0.929930	+	0.536896i	−0.0402420	+	0.0232337i
$535$		0			0
$536$	−6.77676	+	1.81583i	−0.292711	+	0.0784318i
$537$	2.46550	+	1.42346i	0.106394	+	0.0614267i
$538$	7.38736	−	4.26509i	0.318492	−	0.183881i
$539$	−5.34104	−	9.25096i	−0.230055	−	0.398467i
$540$		0			0
$541$	−6.36223	+	6.36223i	−0.273534	+	0.273534i	−0.830521	−	0.556987i	$-0.811957\pi$
$541$	−6.36223	+	6.36223i	−0.273534	+	0.273534i	0.556987	+	0.830521i	$0.311957\pi$
$542$	3.12214	−	5.40770i	0.134107	−	0.232281i
$543$	−0.0175433	−	0.00470071i	−0.000752854	−	0.000201727i
$544$			29.9245i			1.28300i
$545$		0			0
$546$	0.371810	−	0.214664i	0.0159120	−	0.00918679i
$547$	−10.6102			−0.453658			−0.226829	−	0.973935i	$-0.572836\pi$
$547$	−10.6102			−0.453658			−0.226829	+	0.973935i	$0.572836\pi$
$548$	−1.10634	−	4.12891i	−0.0472604	−	0.176378i
$549$	20.3661	−	20.3661i	0.869203	−	0.869203i
$550$		0			0
$551$	11.6144	−	20.1167i	0.494789	−	0.857000i
$552$	−0.0924058	−	0.344863i	−0.00393305	−	0.0146784i
$553$	8.61591	+	14.9232i	0.366386	+	0.634598i
$554$	−0.569582			−0.0241992
$555$		0			0
$556$	11.8653			0.503200
$557$	18.0586	+	31.2784i	0.765166	+	1.32531i	0.940159	+	0.340737i	$0.110677\pi$
$557$	18.0586	+	31.2784i	0.765166	+	1.32531i	−0.174992	+	0.984570i	$0.555990\pi$
$558$	1.59455	+	5.95096i	0.0675029	+	0.251924i
$559$	19.4945	−	33.7655i	0.824529	−	1.42813i
$560$		0			0
$561$	−3.47722	+	3.47722i	−0.146809	+	0.146809i
$562$	0.945957	+	3.53036i	0.0399028	+	0.148919i
$563$	−28.0509			−1.18220			−0.591102	−	0.806597i	$-0.701307\pi$
$563$	−28.0509			−1.18220			−0.591102	+	0.806597i	$0.701307\pi$
$564$	0.853712	−	0.492891i	0.0359478	−	0.0207545i
$565$		0			0
$566$		−	9.11305i		−	0.383050i
$567$	−16.5559	−	4.43614i	−0.695283	−	0.186301i
$568$	3.30785	−	5.72936i	0.138794	−	0.240399i
$569$	1.69141	−	1.69141i	0.0709076	−	0.0709076i	−0.670764	−	0.741671i	$-0.734033\pi$
$569$	1.69141	−	1.69141i	0.0709076	−	0.0709076i	0.741671	+	0.670764i	$0.234033\pi$
$570$		0			0
$571$	4.18372	+	7.24641i	0.175083	+	0.303253i	0.940190	−	0.340650i	$-0.110647\pi$
$571$	4.18372	+	7.24641i	0.175083	+	0.303253i	−0.765107	+	0.643903i	$0.777314\pi$
$572$	−17.2770	+	9.97489i	−0.722388	+	0.417071i
$573$	1.58236	+	0.913575i	0.0661040	+	0.0381651i
$574$	−4.69750	+	1.25869i	−0.196070	+	0.0525367i
$575$		0			0
$576$	−12.6969	+	7.33054i	−0.529037	+	0.305439i
$577$	17.7050	−	10.2220i	0.737067	−	0.425546i	−0.0839349	−	0.996471i	$-0.526749\pi$
$577$	17.7050	−	10.2220i	0.737067	−	0.425546i	0.821002	+	0.570925i	$0.193415\pi$
$578$	14.1484			0.588496
$579$	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
$583$	−15.8468	−	4.24613i	−0.656306	−	0.175857i
$584$	9.13033	−	9.13033i	0.377816	−	0.377816i
$585$		0			0
$586$	1.71994	+	1.71994i	0.0710501	+	0.0710501i
$587$	19.7052	−	34.1304i	0.813320	−	1.40871i	−0.0972074	−	0.995264i	$-0.530991\pi$
$587$	19.7052	−	34.1304i	0.813320	−	1.40871i	0.910528	−	0.413448i	$-0.135676\pi$
$588$	1.06540	−	0.285472i	0.0439362	−	0.0117727i
$589$	−36.5262	−	21.0884i	−1.50504	−	0.868934i
$590$		0			0
$591$		−	1.56686i		−	0.0644521i
$592$	−17.1042	−	9.42087i	−0.702977	−	0.387195i
$593$	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
$597$	−0.0728039	−	0.0420333i	−0.00297966	−	0.00172031i
$598$	−1.49732			−0.0612299
$599$	20.3437	+	11.7455i	0.831222	+	0.479906i	0.854271	−	0.519828i	$-0.174004\pi$
$599$	20.3437	+	11.7455i	0.831222	+	0.479906i	−0.0230489	+	0.999734i	$0.507337\pi$
$600$		0			0
$601$	−5.10765	−	8.84671i	−0.208345	−	0.360865i	0.742848	−	0.669460i	$-0.233474\pi$
$601$	−5.10765	−	8.84671i	−0.208345	−	0.360865i	−0.951193	+	0.308595i	$0.900141\pi$
$602$	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
$607$	−0.780718	−	1.35224i	−0.0316884	−	0.0548859i	0.849746	−	0.527192i	$-0.176755\pi$
$607$	−0.780718	−	1.35224i	−0.0316884	−	0.0548859i	−0.881435	+	0.472306i	$0.843422\pi$
$608$	−7.73555	+	28.8695i	−0.313718	+	1.17081i
$609$	−0.305005	+	1.13829i	−0.0123594	+	0.0461260i
$610$		0			0
$611$	−2.21726	−	8.27492i	−0.0897007	−	0.334768i
$612$	20.6016	+	35.6831i	0.832772	+	1.44240i
$613$	−1.48419	−	0.397688i	−0.0599460	−	0.0160625i	0.228721	−	0.973492i	$-0.426546\pi$
$613$	−1.48419	−	0.397688i	−0.0599460	−	0.0160625i	−0.288667	+	0.957429i	$0.593212\pi$
$614$	1.26703	−	4.72862i	0.0511331	−	0.190831i
$615$		0			0
$616$	−9.34776	+	2.50472i	−0.376632	+	0.100918i
$617$	1.04297	−	3.89243i	0.0419886	−	0.156703i	−0.941749	−	0.336318i	$-0.890818\pi$
$617$	1.04297	−	3.89243i	0.0419886	−	0.156703i	0.983737	+	0.179614i	$0.0574850\pi$
$618$	0.104639	+	0.104639i	0.00420919	+	0.00420919i
$619$	24.1544			0.970846			0.485423	−	0.874279i	$-0.338666\pi$
$619$	24.1544			0.970846			0.485423	+	0.874279i	$0.338666\pi$
$620$		0			0
$621$	−1.06144	−	1.06144i	−0.0425941	−	0.0425941i
$622$	−2.79372	+	0.748575i	−0.112018	+	0.0300151i
$623$		−	30.2628i		−	1.21245i
$624$	−0.491882	−	1.83573i	−0.0196910	−	0.0734880i
$625$		0			0
$626$	−0.422233	+	0.731329i	−0.0168758	+	0.0292298i
$627$	−4.25350	+	2.45576i	−0.169868	+	0.0980735i
$628$	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	0.824279	+	0.566184i	$0.191581\pi$
$631$	−4.33716	+	16.1865i	−0.172660	+	0.644374i	−0.996938	+	0.0781902i	$0.975086\pi$
$632$	−11.9457	+	3.20083i	−0.475173	+	0.127322i
$633$	0.0598690	+	0.223434i	0.00237958	+	0.00888071i
$634$	2.87970	−	0.771614i	0.114368	−	0.0306447i
$635$		0			0
$636$	0.846989	−	1.46703i	0.0335853	−	0.0581715i
$637$		−	9.58532i		−	0.379784i
$638$	−1.02306	+	3.81812i	−0.0405035	+	0.151161i
$639$		−	13.8224i		−	0.546808i
$640$		0			0
$641$	−13.1598	−	22.7934i	−0.519779	−	0.900283i	−0.999736	−	0.0229913i	$-0.992681\pi$
$641$	−13.1598	−	22.7934i	−0.519779	−	0.900283i	0.479957	−	0.877292i	$-0.340652\pi$
$642$	−0.598330	−	0.345446i	−0.0236142	−	0.0136337i
$643$		−	34.2404i		−	1.35031i	−0.737675	−	0.675155i	$-0.764077\pi$
$643$		−	34.2404i		−	1.35031i	0.737675	−	0.675155i	$-0.235923\pi$
$644$	4.69037	+	1.25678i	0.184826	+	0.0495241i
$645$		0			0
$646$	19.6677	+	5.26995i	0.773817	+	0.207344i
$647$	−16.4706	+	28.5278i	−0.647524	+	1.12155i	0.336188	+	0.941795i	$0.390862\pi$
$647$	−16.4706	+	28.5278i	−0.647524	+	1.12155i	−0.983712	+	0.179750i	$0.942471\pi$
$648$	6.15056	−	10.6531i	0.241617	−	0.418493i
$649$	17.7652	+	4.76018i	0.697346	+	0.186853i
$650$		0			0
$651$	2.06682	+	0.553803i	0.0810051	+	0.0217053i
$652$			17.1519i			0.671720i
$653$	18.9744	+	10.9549i	0.742526	+	0.428698i	0.822987	−	0.568060i	$-0.192306\pi$
$653$	18.9744	+	10.9549i	0.742526	+	0.428698i	−0.0804608	+	0.996758i	$0.525639\pi$
$654$	0.554174	+	0.959858i	0.0216699	+	0.0375334i
$655$		0			0
$656$			21.5277i			0.840515i
$657$	6.98244	−	26.0588i	0.272411	−	1.01665i
$658$		−	2.00548i		−	0.0781816i
$659$	−4.76225	+	8.24846i	−0.185511	+	0.321314i	−0.943749	−	0.330664i	$-0.892727\pi$
$659$	−4.76225	+	8.24846i	−0.185511	+	0.321314i	0.758238	+	0.651978i	$0.226061\pi$
$660$		0			0
$661$	4.49979	−	1.20572i	0.175022	−	0.0468969i	−0.170244	−	0.985402i	$-0.554456\pi$
$661$	4.49979	−	1.20572i	0.175022	−	0.0468969i	0.345265	+	0.938505i	$0.387789\pi$
$662$	−2.32204	−	8.66598i	−0.0902487	−	0.336813i
$663$	−4.26228	+	1.14207i	−0.165533	+	0.0443545i
$664$	−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
$668$	35.1299	−	20.2823i	1.35922	−	0.784745i
$669$	1.87392	−	3.24573i	0.0724501	−	0.125487i
$670$		0			0
$671$	−8.68421	−	32.4099i	−0.335250	−	1.25117i
$672$		−	1.51628i		−	0.0584919i
$673$	14.3592	−	3.84754i	0.553507	−	0.148312i	0.0287852	−	0.999586i	$-0.490836\pi$
$673$	14.3592	−	3.84754i	0.553507	−	0.148312i	0.524722	+	0.851274i	$0.324169\pi$
$674$	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	0.556184	−	0.831059i	$-0.312265\pi$
$677$	−7.15203	−	7.15203i	−0.274875	−	0.274875i	−0.831059	+	0.556184i	$0.812265\pi$
$678$	−0.113270	+	0.422728i	−0.00435009	+	0.0162348i
$679$	8.31534	−	2.22809i	0.319113	−	0.0855062i
$680$		0			0
$681$	0.989727	−	3.69371i	0.0379264	−	0.141543i
$682$	6.93264	+	1.85759i	0.265464	+	0.0711310i
$683$	8.68491	+	15.0427i	0.332319	+	0.575593i	0.982966	−	0.183787i	$-0.0588357\pi$
$683$	8.68491	+	15.0427i	0.332319	+	0.575593i	−0.650647	+	0.759380i	$0.725502\pi$
$684$	10.6511	+	39.7505i	0.407256	+	1.51990i
$685$		0			0
$686$	1.89464	−	7.07091i	0.0723378	−	0.269969i
$687$	−0.182454	+	0.680927i	−0.00696105	+	0.0259790i
$688$	−20.2015	−	34.9900i	−0.770175	−	1.33398i
$689$	−10.4096	−	10.4096i	−0.396573	−	0.396573i
$690$		0			0
$691$	0.688714	−	0.397629i	0.0261999	−	0.0151265i	−0.486843	−	0.873490i	$-0.661852\pi$
$691$	0.688714	−	0.397629i	0.0261999	−	0.0151265i	0.513043	+	0.858363i	$0.328518\pi$
$692$	−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
$697$	49.9840			1.89328
$698$	0.122780	+	0.0708869i	0.00464728	+	0.00268311i
$699$	−2.25080	−	1.29950i	−0.0851329	−	0.0491515i
$700$		0			0
$701$	−7.03789	−	1.88580i	−0.265817	−	0.0712255i	0.123449	−	0.992351i	$-0.460605\pi$
$701$	−7.03789	−	1.88580i	−0.265817	−	0.0712255i	−0.389266	+	0.921125i	$0.627271\pi$
$702$	0.916047	+	0.916047i	0.0345740	+	0.0345740i
$703$	−31.3686	+	32.6587i	−1.18309	+	1.23175i
$704$			17.0796i			0.643712i
$705$		0			0
$706$	−1.34813	−	0.778343i	−0.0507375	−	0.0292933i
$707$	−0.364725	+	0.0977278i	−0.0137169	+	0.00367543i
$708$	−0.949529	+	1.64463i	−0.0356855	+	0.0618091i
$709$	−0.492179	−	0.492179i	−0.0184842	−	0.0184842i	0.697804	−	0.716288i	$-0.254161\pi$
$709$	−0.492179	−	0.492179i	−0.0184842	−	0.0184842i	−0.716288	+	0.697804i	$0.754161\pi$
$710$		0			0
$711$	−18.2709	+	18.2709i	−0.685213	+	0.685213i
$712$	20.9791	+	5.62134i	0.786227	+	0.210669i
$713$	−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
$717$	−2.59901			−0.0970620
$718$	−5.99734	+	3.46257i	−0.223819	+	0.129222i
$719$	−10.8743	+	6.27829i	−0.405543	+	0.234141i	−0.688873	−	0.724882i	$-0.741894\pi$
$719$	−10.8743	+	6.27829i	−0.405543	+	0.234141i	0.283330	+	0.959023i	$0.408561\pi$
$720$		0			0
$721$	−4.02847	+	1.07943i	−0.150028	+	0.0401999i
$722$	11.5741	+	6.68230i	0.430742	+	0.248689i
$723$	−3.90725	+	2.25585i	−0.145312	+	0.0838961i
$724$	0.0886405	+	0.153530i	0.00329430	+	0.00570589i
$725$		0			0
$726$	0.0455517	−	0.0455517i	0.00169058	−	0.00169058i
$727$	−0.227219	+	0.393556i	−0.00842710	+	0.0145962i	−0.870208	−	0.492684i	$-0.836016\pi$
$727$	−0.227219	+	0.393556i	−0.00842710	+	0.0145962i	0.861781	+	0.507280i	$0.169349\pi$
$728$	−8.38799	−	2.24756i	−0.310880	−	0.0832999i
$729$		−	25.0479i		−	0.927699i
$730$		0			0
$731$	−81.2415	+	46.9048i	−3.00483	+	1.73484i
$732$	3.46454			0.128053
$733$	−0.0722495	−	0.269639i	−0.00266859	−	0.00995933i	0.964579	−	0.263795i	$-0.0849743\pi$
$733$	−0.0722495	−	0.269639i	−0.00266859	−	0.00995933i	−0.967247	+	0.253836i	$0.918308\pi$
$734$	3.45085	−	3.45085i	0.127373	−	0.127373i
$735$		0			0
$736$	−2.64408	+	4.57967i	−0.0974619	+	0.168809i
$737$	4.41972	+	16.4946i	0.162803	+	0.607588i
$738$	−3.64617	−	6.31536i	−0.134218	−	0.232472i
$739$	20.7632			0.763786			0.381893	−	0.924207i	$-0.375272\pi$
$739$	20.7632			0.763786			0.381893	+	0.924207i	$0.375272\pi$
$740$		0			0
$741$	−4.40723			−0.161904
$742$	−1.72312	−	2.98452i	−0.0632576	−	0.109565i
$743$	−4.93760	−	18.4274i	−0.181143	−	0.676035i	−0.995423	−	0.0955632i	$-0.969535\pi$
$743$	−4.93760	−	18.4274i	−0.181143	−	0.676035i	0.814280	−	0.580472i	$-0.197132\pi$
$744$	−0.767829	+	1.32992i	−0.0281500	+	0.0487572i
$745$		0			0
$746$	−5.11631	+	5.11631i	−0.187322	+	0.187322i
$747$	10.4314	+	38.9306i	0.381665	+	1.42439i
$748$	48.0002			1.75506
$749$	16.8628	−	9.73574i	0.616153	−	0.355736i
$750$		0			0
$751$			32.9736i			1.20322i	0.798788	+	0.601612i	$0.205475\pi$
$751$			32.9736i			1.20322i	−0.798788	+	0.601612i	$0.794525\pi$
$752$	−8.57503	−	2.29767i	−0.312699	−	0.0837875i
$753$	−0.0542752	+	0.0940075i	−0.00197790	+	0.00342582i
$754$	−2.50808	+	2.50808i	−0.0913390	+	0.0913390i
$755$		0			0
$756$	−2.10064	−	3.63842i	−0.0763996	−	0.132328i
$757$	44.1108	−	25.4674i	1.60323	−	0.925628i	0.612399	−	0.790549i	$-0.290205\pi$
$757$	44.1108	−	25.4674i	1.60323	−	0.925628i	0.990835	−	0.135079i	$-0.0431287\pi$
$758$	−3.47978	−	2.00905i	−0.126391	−	0.0729720i
$759$	−0.839398	+	0.224916i	−0.0304682	+	0.00816393i
$760$		0			0
$761$	3.27486	−	1.89074i	0.118714	−	0.0685394i	−0.439467	−	0.898259i	$-0.644833\pi$
$761$	3.27486	−	1.89074i	0.118714	−	0.0685394i	0.558181	+	0.829719i	$0.311499\pi$
$762$	−0.242900	+	0.140238i	−0.00879934	+	0.00508030i
$763$	−31.2367			−1.13084
$764$	−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
$768$	−1.15959	−	0.310710i	−0.0418430	−	0.0112118i
$769$	1.69910	−	1.69910i	0.0612712	−	0.0612712i	−0.675807	−	0.737078i	$-0.736205\pi$
$769$	1.69910	−	1.69910i	0.0612712	−	0.0612712i	0.737078	+	0.675807i	$0.236205\pi$
$770$		0			0
$771$	−2.21079	−	2.21079i	−0.0796197	−	0.0796197i
$772$	0.922066	−	1.59706i	0.0331859	−	0.0574796i
$773$	−29.0946	+	7.79586i	−1.04646	+	0.280398i	−0.740787	−	0.671740i	$-0.765547\pi$
$773$	−29.0946	+	7.79586i	−1.04646	+	0.280398i	−0.305671	+	0.952137i	$0.598881\pi$
$774$	11.8526	+	6.84312i	0.426034	+	0.245971i
$775$		0			0
$776$			6.17834i			0.221789i
$777$	1.10835	−	2.01228i	0.0397619	−	0.0721901i
$778$	−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
$782$	3.11997	+	1.80131i	0.111570	+	0.0644148i
$783$	−3.55593			−0.127079
$784$	−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
$792$	−7.25568	−	12.5672i	−0.257819	−	0.446556i
$793$	7.79257	−	29.0823i	0.276722	−	1.03274i
$794$	−2.92363	+	10.9111i	−0.103756	+	0.387221i
$795$		0			0
$796$	0.212381	+	0.792617i	0.00752765	+	0.0280936i
$797$	18.7203	+	32.4245i	0.663106	+	1.14853i	0.979795	+	0.200004i	$0.0640955\pi$
$797$	18.7203	+	32.4245i	0.663106	+	1.14853i	−0.316689	+	0.948529i	$0.602571\pi$
$798$	−0.996568	−	0.267030i	−0.0352781	−	0.00945274i
$799$	−5.33484	+	19.9099i	−0.188733	+	0.704362i
$800$		0			0
$801$	43.8326	−	11.7449i	1.54875	−	0.414986i
$802$	0.0818019	−	0.305289i	0.00288853	−	0.0107801i
$803$	−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
$807$	4.29104	−	1.14978i	0.151052	−	0.0404742i
$808$		−	0.270993i		−	0.00953349i
$809$	−11.2061	−	41.8217i	−0.393985	−	1.47037i	−0.823502	−	0.567313i	$-0.807983\pi$
$809$	−11.2061	−	41.8217i	−0.393985	−	1.47037i	0.429517	−	0.903059i	$-0.358684\pi$
$810$		0			0
$811$	6.94395	−	12.0273i	0.243835	−	0.422335i	−0.717968	−	0.696076i	$-0.754928\pi$
$811$	6.94395	−	12.0273i	0.243835	−	0.422335i	0.961803	+	0.273741i	$0.0882611\pi$
$812$	9.96178	−	5.75144i	0.349590	−	0.201836i
$813$	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
$817$	−90.5021	+	24.2500i	−3.16627	+	0.848399i
$818$	−2.73285	−	10.1991i	−0.0955520	−	0.356605i
$819$	−17.5254	+	4.69591i	−0.612386	+	0.164088i
$820$		0			0
$821$	−5.62408	+	9.74120i	−0.196282	+	0.339970i	−0.947320	−	0.320289i	$-0.896220\pi$
$821$	−5.62408	+	9.74120i	−0.196282	+	0.339970i	0.751038	+	0.660259i	$0.229553\pi$
$822$			0.160694i			0.00560485i
$823$	−8.48178	+	31.6544i	−0.295656	+	1.10340i	0.645038	+	0.764150i	$0.276841\pi$
$823$	−8.48178	+	31.6544i	−0.295656	+	1.10340i	−0.940695	+	0.339254i	$0.889825\pi$
$824$		−	2.99317i		−	0.104272i
$825$		0			0
$826$	1.93172	+	3.34584i	0.0672132	+	0.116417i
$827$	−28.5291	−	16.4713i	−0.992054	−	0.572763i	−0.0861665	−	0.996281i	$-0.527462\pi$
$827$	−28.5291	−	16.4713i	−0.992054	−	0.572763i	−0.905888	+	0.423518i	$0.860795\pi$
$828$			7.28128i			0.253042i
$829$	−4.10251	−	1.09926i	−0.142486	−	0.0381790i	0.186871	−	0.982384i	$-0.440165\pi$
$829$	−4.10251	−	1.09926i	−0.142486	−	0.0381790i	−0.329357	+	0.944205i	$0.606832\pi$
$830$		0			0
$831$	−0.286524	−	0.0767738i	−0.00993940	−	0.00266325i
$832$	−7.66299	+	13.2727i	−0.265666	+	0.460148i
$833$	−11.5314	+	19.9730i	−0.399539	+	0.692023i
$834$	−0.430854	−	0.115447i	−0.0149193	−	0.00399761i
$835$		0			0
$836$	46.3079	+	12.4082i	1.60159	+	0.429145i
$837$			6.45657i			0.223172i
$838$	−0.690843	−	0.398859i	−0.0238648	−	0.0137783i
$839$	1.39115	+	2.40954i	0.0480278	+	0.0831865i	0.889040	−	0.457830i	$-0.151373\pi$
$839$	1.39115	+	2.40954i	0.0480278	+	0.0831865i	−0.841012	+	0.541016i	$0.818040\pi$
$840$		0			0
$841$			19.2641i			0.664278i
$842$	−2.20076	+	8.21333i	−0.0758431	+	0.283050i
$843$			1.90343i			0.0655575i
$844$	1.12894	−	1.95538i	0.0388598	−	0.0673071i
$845$		0			0
$846$	2.90473	−	0.778320i	0.0998667	−	0.0267592i
$847$	0.469899	+	1.75369i	0.0161459	+	0.0602574i
$848$	−14.7354	+	3.94835i	−0.506017	+	0.135587i
$849$	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
$853$	18.5940	−	10.7353i	0.636648	−	0.367569i	−0.146674	−	0.989185i	$-0.546857\pi$
$853$	18.5940	−	10.7353i	0.636648	−	0.367569i	0.783322	+	0.621616i	$0.213524\pi$
$854$	3.52413	−	6.10397i	0.120593	−	0.208874i
$855$		0			0
$856$	3.61685	+	13.4983i	0.123621	+	0.461362i
$857$		−	19.7692i		−	0.675302i	−0.941271	−	0.337651i	$-0.890368\pi$
$857$		−	19.7692i		−	0.675302i	0.941271	−	0.337651i	$-0.109632\pi$
$858$	0.724420	−	0.194108i	0.0247313	−	0.00662673i
$859$	−14.4663	−	14.4663i	−0.493582	−	0.493582i	0.415851	−	0.909433i	$-0.363484\pi$
$859$	−14.4663	−	14.4663i	−0.493582	−	0.493582i	−0.909433	+	0.415851i	$0.863484\pi$
$860$		0			0
$861$	−2.53270			−0.0863141
$862$	−1.62833	−	1.62833i	−0.0554610	−	0.0554610i
$863$	−13.9291	+	51.9841i	−0.474152	+	1.76956i	0.150450	+	0.988618i	$0.451928\pi$
$863$	−13.9291	+	51.9841i	−0.474152	+	1.76956i	−0.624603	+	0.780943i	$0.714739\pi$
$864$	4.41943	−	1.18418i	0.150352	−	0.0402867i
$865$		0			0
$866$	−1.68355	+	6.28310i	−0.0572094	+	0.213509i
$867$	7.11724	+	1.90706i	0.241714	+	0.0647672i
$868$	−10.4430	−	18.0878i	−0.354458	−	0.613939i
$869$	7.79082	+	29.0758i	0.264286	+	0.986327i
$870$		0			0
$871$	−3.96594	+	14.8011i	−0.134381	+	0.501515i
$872$	5.80225	−	21.6543i	0.196489	−	0.733307i
$873$	6.45432	+	11.1792i	0.218446	+	0.378359i
$874$	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	0.999737	+	0.0229301i	$0.00729951\pi$
$881$	45.1002	+	26.0386i	1.51946	+	0.877263i	0.519727	+	0.854333i	$0.326034\pi$
$882$	3.36472			0.113296
$883$	27.5003	+	15.8773i	0.925459	+	0.534314i	0.885372	−	0.464882i	$-0.153903\pi$
$883$	27.5003	+	15.8773i	0.925459	+	0.534314i	0.0400864	+	0.999196i	$0.487237\pi$
$884$	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	0.833655	−	0.552285i	$-0.186244\pi$
$887$	8.37990	+	8.37990i	0.281370	+	0.281370i	−0.552285	+	0.833655i	$0.686244\pi$
$888$	1.18910	+	1.14213i	0.0399036	+	0.0383273i
$889$		−	7.90470i		−	0.265115i
$890$		0			0
$891$	−25.9296	−	14.9705i	−0.868675	−	0.501530i
$892$	−35.3363	+	9.46833i	−1.18315	+	0.317023i
$893$	−10.2935	+	17.8289i	−0.344459	+	0.596620i
$894$	−0.893520	−	0.893520i	−0.0298838	−	0.0298838i
$895$		0			0
$896$	−13.7579	+	13.7579i	−0.459620	+	0.459620i
$897$	−0.753214	−	0.201823i	−0.0251491	−	0.00673868i
$898$	−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
$902$	−8.49531			−0.282863
$903$	4.11652	−	2.37668i	0.136989	−	0.0790908i
$904$	7.66605	−	4.42600i	0.254969	−	0.147207i
$905$		0			0
$906$	0.0216874	−	0.00581113i	0.000720517	−	0.000193062i
$907$	−42.9187	−	24.7791i	−1.42509	−	0.822777i	−0.428364	−	0.903606i	$-0.640910\pi$
$907$	−42.9187	−	24.7791i	−1.42509	−	0.822777i	−0.996728	+	0.0808295i	$0.974243\pi$
$908$	−32.3255	+	18.6631i	−1.07276	+	0.619358i
$909$	−0.283098	−	0.490340i	−0.00938977	−	0.0162636i
$910$		0			0
$911$	−31.0017	+	31.0017i	−1.02713	+	1.02713i	−0.0275118	+	0.999621i	$0.508758\pi$
$911$	−31.0017	+	31.0017i	−1.02713	+	1.02713i	−0.999621	+	0.0275118i	$0.991242\pi$
$912$	−2.28353	+	3.95520i	−0.0756154	+	0.130970i
$913$	45.3526	+	12.1522i	1.50095	+	0.402179i
$914$		−	5.52969i		−	0.182906i
$915$		0			0
$916$	5.95913	−	3.44051i	0.196895	−	0.113678i
$917$	−7.01685			−0.231717
$918$	−0.806741	−	3.01080i	−0.0266264	−	0.0993712i
$919$	−25.3860	+	25.3860i	−0.837407	+	0.837407i	−0.988517	−	0.151110i	$-0.951715\pi$
$919$	−25.3860	+	25.3860i	−0.837407	+	0.837407i	0.151110	+	0.988517i	$0.451715\pi$
$920$		0			0
$921$	1.27474	−	2.20791i	0.0420041	−	0.0727532i
$922$	1.23474	+	4.60811i	0.0406639	+	0.151760i
$923$	−7.22466	−	12.5135i	−0.237802	−	0.411886i
$924$	−2.43218			−0.0800129
$925$		0			0
$926$	−10.2598			−0.337158
$927$	−3.12688	−	5.41591i	−0.102700	−	0.177882i
$928$	3.24222	+	12.1001i	0.106431	+	0.397207i
$929$	−9.74401	+	16.8771i	−0.319691	+	0.553720i	−0.980423	−	0.196901i	$-0.936912\pi$
$929$	−9.74401	+	16.8771i	−0.319691	+	0.553720i	0.660733	+	0.750621i	$0.270246\pi$
$930$		0			0
$931$	−16.2879	+	16.2879i	−0.533814	+	0.533814i
$932$	6.56595	+	24.5044i	0.215075	+	0.802670i
$933$	−1.50626			−0.0493127
$934$	0.413532	−	0.238753i	0.0135312	−	0.00781223i
$935$		0			0
$936$		−	13.0214i		−	0.425619i
$937$	−41.8686	−	11.2187i	−1.36779	−	0.366498i	−0.501118	−	0.865379i	$-0.667078\pi$
$937$	−41.8686	−	11.2187i	−1.36779	−	0.366498i	−0.866670	+	0.498881i	$0.833744\pi$
$938$	−1.79356	+	3.10654i	−0.0585619	+	0.101432i
$939$	−0.310977	+	0.310977i	−0.0101483	+	0.0101483i
$940$		0			0
$941$	−1.14543	−	1.98394i	−0.0373398	−	0.0646745i	0.846752	−	0.531989i	$-0.178555\pi$
$941$	−1.14543	−	1.98394i	−0.0373398	−	0.0646745i	−0.884091	+	0.467314i	$0.845222\pi$
$942$	−0.0716300	+	0.0413556i	−0.00233383	+	0.00134744i
$943$	7.64958	+	4.41649i	0.249105	+	0.143821i
$944$	16.5194	−	4.42635i	0.537659	−	0.144065i
$945$		0			0
$946$	13.8078	−	7.97197i	0.448932	−	0.259191i
$947$	52.1263	−	30.0952i	1.69388	−	0.977961i	0.742545	−	0.669796i	$-0.233618\pi$
$947$	52.1263	−	30.0952i	1.69388	−	0.977961i	0.951333	−	0.308165i	$-0.0997149\pi$
$948$	−3.10813			−0.100947
$949$	−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
$953$	−16.8063	−	4.50324i	−0.544410	−	0.145874i	−0.0238757	−	0.999715i	$-0.507601\pi$
$953$	−16.8063	−	4.50324i	−0.544410	−	0.145874i	−0.520534	+	0.853841i	$0.674267\pi$
$954$	3.65405	−	3.65405i	0.118304	−	0.118304i
$955$		0			0
$956$	17.9386	+	17.9386i	0.580177	+	0.580177i
$957$	−1.02929	+	1.78278i	−0.0332722	+	0.0576291i
$958$	−1.37487	+	0.368395i	−0.0444201	+	0.0119023i
$959$	−3.92210	−	2.26443i	−0.126651	−	0.0731221i
$960$		0			0
$961$			1.09774i			0.0354111i
$962$	5.91738	−	3.57725i	0.190784	−	0.115335i
$963$	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
$967$	−41.2531	−	23.8175i	−1.32661	−	0.765918i	−0.341836	−	0.939760i	$-0.611049\pi$
$967$	−41.2531	−	23.8175i	−1.32661	−	0.765918i	−0.984774	+	0.173841i	$0.944382\pi$
$968$	−1.30300			−0.0418799
$969$	9.18337	+	5.30202i	0.295012	+	0.170325i
$970$		0			0
$971$	17.9256	+	31.0481i	0.575261	+	0.996382i	0.996013	+	0.0892060i	$0.0284329\pi$
$971$	17.9256	+	31.0481i	0.575261	+	0.996382i	−0.420752	+	0.907176i	$0.638234\pi$
$972$	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
$977$	9.90840	+	17.1619i	0.316998	+	0.549056i	0.979860	−	0.199685i	$-0.0639919\pi$
$977$	9.90840	+	17.1619i	0.316998	+	0.549056i	−0.662862	+	0.748741i	$0.730659\pi$
$978$	0.166885	−	0.622823i	0.00533639	−	0.0199157i
$979$	13.6824	−	51.0633i	0.437290	−	1.63199i
$980$		0			0
$981$	−12.1229	−	45.2432i	−0.387054	−	1.44450i
$982$	5.15838	+	8.93458i	0.164611	+	0.285114i
$983$	−48.9652	−	13.1202i	−1.56175	−	0.418469i	−0.628532	−	0.777784i	$-0.716344\pi$
$983$	−48.9652	−	13.1202i	−1.56175	−	0.418469i	−0.933216	+	0.359315i	$0.883010\pi$
$984$	0.470452	−	1.75575i	0.0149975	−	0.0559713i
$985$		0			0
$986$	8.24339	−	2.20881i	0.262523	−	0.0703429i
$987$	0.270318	−	1.00884i	0.00860430	−	0.0321117i
$988$	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	0.977519	−	0.210846i	$-0.0676220\pi$
$991$	24.1350	+	24.1350i	0.766673	+	0.766673i	−0.210846	+	0.977519i	$0.567622\pi$
$992$	21.9705	−	5.88697i	0.697563	−	0.186911i
$993$		−	4.67234i		−	0.148272i
$994$	−0.875468	−	3.26729i	−0.0277682	−	0.103632i
$995$		0			0
$996$	−2.42404	+	4.19856i	−0.0768086	+	0.133036i
$997$	45.2668	−	26.1348i	1.43361	−	0.827697i	0.436219	−	0.899840i	$-0.356317\pi$
$997$	45.2668	−	26.1348i	1.43361	−	0.827697i	0.997394	+	0.0721432i	$0.0229839\pi$
$998$	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.t.b.843.10		68
5.2	odd	4		925.2.y.b.732.8		68
5.3	odd	4		185.2.u.a.177.10	yes	68
5.4	even	2		185.2.p.a.103.8	yes	68
37.23	odd	12		925.2.y.b.393.8		68
185.23	even	12		185.2.p.a.97.8	✓	68
185.97	even	12	inner	925.2.t.b.282.10		68
185.134	odd	12		185.2.u.a.23.10	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.8	✓	68	185.23	even	12
185.2.p.a.103.8	yes	68	5.4	even	2
185.2.u.a.23.10	yes	68	185.134	odd	12
185.2.u.a.177.10	yes	68	5.3	odd	4
925.2.t.b.282.10		68	185.97	even	12	inner
925.2.t.b.843.10		68	1.1	even	1	trivial
925.2.y.b.393.8		68	37.23	odd	12
925.2.y.b.732.8		68	5.2	odd	4

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.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.183474 + 0.317786i) q^{2} +(0.0494608 + 0.184590i) q^{3} +(0.932675 - 1.61544i) q^{4} +(-0.0495854 + 0.0495854i) q^{6} +(-0.511509 - 1.90898i) q^{7} +1.41838 q^{8} +(2.56645 - 1.48174i) q^{9} -3.45234i q^{11} +(0.344325 + 0.0922616i) q^{12} +(1.54894 - 2.68284i) q^{13} +(0.512798 - 0.512798i) q^{14} +(-1.60511 - 2.78014i) q^{16} +(-6.45506 + 3.72683i) q^{17} +(0.941752 + 0.543721i) q^{18} +(-7.19086 + 1.92679i) q^{19} +(0.327079 - 0.188839i) q^{21} +(1.09710 - 0.633414i) q^{22} -1.31718 q^{23} +(0.0701542 + 0.261819i) q^{24} +1.13676 q^{26} +(0.805841 + 0.805841i) q^{27} +(-3.56091 - 0.954144i) q^{28} +(-2.20635 + 2.20635i) q^{29} +(4.00610 + 4.00610i) q^{31} +(2.00737 - 3.47687i) q^{32} +(0.637268 - 0.170755i) q^{33} +(-2.36867 - 1.36755i) q^{34} -5.52793i q^{36} +(5.20549 - 3.14689i) q^{37} +(-1.93164 - 1.93164i) q^{38} +(0.571837 + 0.153223i) q^{39} +(-5.80754 - 3.35298i) q^{41} +(0.120021 + 0.0692941i) q^{42} +12.5857 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} +(-2.88931 - 5.00443i) q^{52} +(1.22993 - 4.59015i) q^{53} +(-0.108234 + 0.403936i) q^{54} +(-0.725515 - 2.70766i) q^{56} +(-0.711331 - 1.23206i) q^{57} +(-1.10595 - 0.296339i) q^{58} +(-1.37883 + 5.14585i) q^{59} +(9.38781 - 2.51546i) q^{61} +(-0.538068 + 2.00810i) q^{62} +(-4.14137 - 4.14137i) q^{63} -4.94725 q^{64} +(0.171186 + 0.171186i) q^{66} +(-4.77781 + 1.28021i) q^{67} +13.9037i q^{68} +(-0.0651488 - 0.243139i) q^{69} +(2.33213 - 4.03937i) q^{71} +(3.64020 - 2.10167i) q^{72} +(6.43715 - 6.43715i) q^{73} +(1.95511 + 1.07686i) q^{74} +(-3.59413 + 13.4135i) q^{76} +(-6.59044 + 1.76590i) q^{77} +(0.0562249 + 0.209834i) q^{78} +(-8.42204 + 2.25668i) q^{79} +(4.33633 - 7.51074i) q^{81} -2.46074i q^{82} +(-3.51999 + 13.1368i) q^{83} -0.704502i q^{84} +(2.30915 + 3.99956i) q^{86} +(-0.516397 - 0.298142i) q^{87} -4.89673i q^{88} +(14.7909 + 3.96321i) q^{89} +(-5.91378 - 1.58459i) q^{91} +(-1.22850 + 2.12783i) q^{92} +(-0.541342 + 0.937632i) q^{93} +(0.980175 + 0.262637i) q^{94} +(0.741082 + 0.198572i) q^{96} +4.35591i q^{97} +(0.983280 + 0.567697i) q^{98} +(-5.11547 - 8.86025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 8 q^{3} - 30 q^{4} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) \) 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more