LMFDB - Embedded newform 185.2.v.a.104.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(4,185)] 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("185.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$185 = 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	185.v (of order $18$ , degree $6$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.16
Character	$\chi$	$=$	185.104
Dual form			185.2.v.a.169.16

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.37842 - 0.865673i) q^{2} +(0.221617 - 0.608888i) q^{3} +(3.37539 - 2.83229i) q^{4} +(-1.92975 + 1.12963i) q^{5} -1.64004i q^{6} +(-2.50527 + 0.441747i) q^{7} +(3.04520 - 5.27443i) q^{8} +(1.97650 + 1.65848i) q^{9} +(-3.61185 + 4.35727i) q^{10} +(0.365052 - 0.632288i) q^{11} +(-0.976503 - 2.68292i) q^{12} +(0.0470110 - 0.0394470i) q^{13} +(-5.57618 + 3.21941i) q^{14} +(0.260156 + 1.42535i) q^{15} +(1.14653 - 6.50231i) q^{16} +(-1.80272 - 1.51266i) q^{17} +(6.13665 + 2.23356i) q^{18} +(-2.86878 + 7.88190i) q^{19} +(-3.31420 + 9.27857i) q^{20} +(-0.286237 + 1.62333i) q^{21} +(0.320890 - 1.81986i) q^{22} +(-2.46523 - 4.26990i) q^{23} +(-2.53667 - 3.02309i) q^{24} +(2.44785 - 4.35982i) q^{25} +(0.0776637 - 0.134518i) q^{26} +(3.13132 - 1.80787i) q^{27} +(-7.20512 + 8.58673i) q^{28} +(3.57068 + 2.06153i) q^{29} +(1.85264 + 3.16486i) q^{30} -5.93871i q^{31} +(-0.786771 - 4.46200i) q^{32} +(-0.304091 - 0.362401i) q^{33} +(-5.59709 - 2.03717i) q^{34} +(4.33553 - 3.68250i) q^{35} +11.3688 q^{36} +(3.40102 - 5.04312i) q^{37} +21.2299i q^{38} +(-0.0136003 - 0.0373666i) q^{39} +(0.0817255 + 13.6183i) q^{40} +(4.14060 - 3.47438i) q^{41} +(0.724482 + 4.10874i) q^{42} -9.60540 q^{43} +(-0.558631 - 3.16815i) q^{44} +(-5.68763 - 0.967726i) q^{45} +(-9.55969 - 8.02153i) q^{46} +(-6.53846 + 3.77498i) q^{47} +(-3.70509 - 2.13913i) q^{48} +(-0.496600 + 0.180748i) q^{49} +(2.04783 - 12.4885i) q^{50} +(-1.32055 + 0.762423i) q^{51} +(0.0469555 - 0.266298i) q^{52} +(4.23503 + 0.746750i) q^{53} +(5.88256 - 7.01057i) q^{54} +(0.00979708 + 1.63253i) q^{55} +(-5.29908 + 14.5591i) q^{56} +(4.16342 + 3.49353i) q^{57} +(10.2772 + 1.81215i) q^{58} +(11.4401 + 2.01720i) q^{59} +(4.91512 + 4.07427i) q^{60} +(-5.27915 - 6.29144i) q^{61} +(-5.14098 - 14.1247i) q^{62} +(-5.68431 - 3.28184i) q^{63} +(0.868712 + 1.50465i) q^{64} +(-0.0461588 + 0.129228i) q^{65} +(-1.03698 - 0.598699i) q^{66} +(2.44898 - 0.431821i) q^{67} -10.3692 q^{68} +(-3.14623 + 0.554765i) q^{69} +(7.12386 - 12.5117i) q^{70} +(-0.992473 - 0.361230i) q^{71} +(14.7664 - 5.37453i) q^{72} +3.31788i q^{73} +(3.72334 - 14.9388i) q^{74} +(-2.11216 - 2.45668i) q^{75} +(12.6406 + 34.7297i) q^{76} +(-0.635242 + 1.74531i) q^{77} +(-0.0646945 - 0.0770999i) q^{78} +(-2.87364 + 0.506700i) q^{79} +(5.13272 + 13.8430i) q^{80} +(0.937275 + 5.31555i) q^{81} +(6.84041 - 11.8479i) q^{82} +(10.8097 - 12.8824i) q^{83} +(3.63158 + 6.29008i) q^{84} +(5.18755 + 0.882639i) q^{85} +(-22.8457 + 8.31514i) q^{86} +(2.04657 - 1.71727i) q^{87} +(-2.22331 - 3.85088i) q^{88} +(-11.6491 - 2.05406i) q^{89} +(-14.3653 + 2.62197i) q^{90} +(-0.100350 + 0.119592i) q^{91} +(-20.4147 - 7.43035i) q^{92} +(-3.61601 - 1.31612i) q^{93} +(-12.2833 + 14.6387i) q^{94} +(-3.36765 - 18.4507i) q^{95} +(-2.89122 - 0.509800i) q^{96} +(9.44467 + 16.3586i) q^{97} +(-1.02465 + 0.859787i) q^{98} +(1.77016 - 0.644287i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$96 q - 12 q^{4} - 12 q^{5} - 6 q^{9} - 3 q^{10} - 30 q^{11} - 36 q^{14} - 21 q^{15} - 18 q^{19} - 39 q^{20} - 24 q^{21} + 96 q^{24} + 36 q^{25} + 48 q^{26} - 18 q^{29} - 30 q^{30} - 54 q^{34} + 6 q^{35}+ \cdots - 24 q^{99}+O(q^{100})$ 96 * q - 12 * q^4 - 12 * q^5 - 6 * q^9 - 3 * q^10 - 30 * q^11 - 36 * q^14 - 21 * q^15 - 18 * q^19 - 39 * q^20 - 24 * q^21 + 96 * q^24 + 36 * q^25 + 48 * q^26 - 18 * q^29 - 30 * q^30 - 54 * q^34 + 6 * q^35 + 24 * q^36 - 36 * q^39 - 63 * q^40 + 72 * q^41 - 84 * q^44 - 36 * q^45 - 18 * q^46 - 6 * q^49 - 27 * q^50 - 18 * q^51 + 24 * q^54 + 6 * q^55 + 90 * q^56 + 18 * q^59 + 108 * q^60 - 144 * q^61 + 66 * q^64 + 27 * q^65 - 36 * q^66 - 6 * q^69 - 66 * q^70 - 30 * q^71 - 6 * q^74 + 96 * q^75 - 54 * q^76 + 60 * q^79 - 18 * q^81 + 48 * q^84 + 21 * q^85 - 72 * q^86 + 108 * q^89 + 165 * q^90 - 54 * q^91 + 6 * q^94 + 57 * q^95 + 24 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$ .

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	2.37842	−	0.865673i	1.68180	−	0.612123i	0.688241	−	0.725482i	$-0.258383\pi$
$2$	2.37842	−	0.865673i	1.68180	−	0.612123i	0.993554	+	0.113359i	$0.0361609\pi$
$3$	0.221617	−	0.608888i	0.127951	−	0.351542i	−0.859132	−	0.511754i	$-0.828996\pi$
$3$	0.221617	−	0.608888i	0.127951	−	0.351542i	0.987083	+	0.160213i	$0.0512180\pi$
$4$	3.37539	−	2.83229i	1.68770	−	1.41615i
$5$	−1.92975	+	1.12963i	−0.863009	+	0.505188i
$5$	−1.92975	+	1.12963i	−0.863009	+	0.505188i
$6$		−	1.64004i		−	0.669543i
$7$	−2.50527	+	0.441747i	−0.946904	+	0.166965i	−0.625716	−	0.780051i	$-0.715193\pi$
$7$	−2.50527	+	0.441747i	−0.946904	+	0.166965i	−0.321188	+	0.947016i	$0.604082\pi$
$8$	3.04520	−	5.27443i	1.07664	−	1.86479i
$9$	1.97650	+	1.65848i	0.658834	+	0.552828i
$10$	−3.61185	+	4.35727i	−1.14217	+	1.37789i
$11$	0.365052	−	0.632288i	0.110067	−	0.190642i	−0.805730	−	0.592283i	$-0.798227\pi$
$11$	0.365052	−	0.632288i	0.110067	−	0.190642i	0.915797	+	0.401641i	$0.131560\pi$
$12$	−0.976503	−	2.68292i	−0.281892	−	0.774492i
$13$	0.0470110	−	0.0394470i	0.0130385	−	0.0109406i	−0.636245	−	0.771487i	$-0.719513\pi$
$13$	0.0470110	−	0.0394470i	0.0130385	−	0.0109406i	0.649284	+	0.760546i	$0.275069\pi$
$14$	−5.57618	+	3.21941i	−1.49030	+	0.860423i
$15$	0.260156	+	1.42535i	0.0671720	+	0.368023i
$16$	1.14653	−	6.50231i	0.286633	−	1.62558i
$17$	−1.80272	−	1.51266i	−0.437224	−	0.366874i	0.397446	−	0.917626i	$-0.369897\pi$
$17$	−1.80272	−	1.51266i	−0.437224	−	0.366874i	−0.834669	+	0.550752i	$0.814341\pi$
$18$	6.13665	+	2.23356i	1.44642	+	0.526455i
$19$	−2.86878	+	7.88190i	−0.658142	+	1.80823i	−0.0729517	+	0.997335i	$0.523242\pi$
$19$	−2.86878	+	7.88190i	−0.658142	+	1.80823i	−0.585191	+	0.810896i	$0.698980\pi$
$20$	−3.31420	+	9.27857i	−0.741078	+	2.07475i
$21$	−0.286237	+	1.62333i	−0.0624620	+	0.354240i
$22$	0.320890	−	1.81986i	0.0684141	−	0.387995i
$23$	−2.46523	−	4.26990i	−0.514036	−	0.890336i	−0.999867	−	0.0162839i	$-0.994816\pi$
$23$	−2.46523	−	4.26990i	−0.514036	−	0.890336i	0.485831	−	0.874053i	$-0.338517\pi$
$24$	−2.53667	−	3.02309i	−0.517796	−	0.617085i
$25$	2.44785	−	4.35982i	0.489570	−	0.871964i
$26$	0.0776637	−	0.134518i	0.0152311	−	0.0263811i
$27$	3.13132	−	1.80787i	0.602623	−	0.347925i
$28$	−7.20512	+	8.58673i	−1.36164	+	1.62274i
$29$	3.57068	+	2.06153i	0.663059	+	0.382817i	0.793441	−	0.608647i	$-0.208287\pi$
$29$	3.57068	+	2.06153i	0.663059	+	0.382817i	−0.130383	+	0.991464i	$0.541621\pi$
$30$	1.85264	+	3.16486i	0.338245	+	0.577822i
$31$		−	5.93871i		−	1.06662i	−0.845919	−	0.533312i	$-0.820947\pi$
$31$		−	5.93871i		−	1.06662i	0.845919	−	0.533312i	$-0.179053\pi$
$32$	−0.786771	−	4.46200i	−0.139083	−	0.788778i
$33$	−0.304091	−	0.362401i	−0.0529354	−	0.0630860i
$34$	−5.59709	−	2.03717i	−0.959893	−	0.349372i
$35$	4.33553	−	3.68250i	0.732838	−	0.622457i
$36$	11.3688			1.89480
$37$	3.40102	−	5.04312i	0.559124	−	0.829084i
$37$	3.40102	−	5.04312i	0.559124	−	0.829084i
$38$			21.2299i			3.44394i
$39$	−0.0136003	−	0.0373666i	−0.00217780	−	0.00598344i
$40$	0.0817255	+	13.6183i	0.0129219	+	2.15324i
$41$	4.14060	−	3.47438i	0.646653	−	0.542607i	−0.259400	−	0.965770i	$-0.583525\pi$
$41$	4.14060	−	3.47438i	0.646653	−	0.542607i	0.906053	+	0.423163i	$0.139080\pi$
$42$	0.724482	+	4.10874i	0.111790	+	0.633993i
$43$	−9.60540			−1.46481			−0.732405	−	0.680869i	$-0.761602\pi$
$43$	−9.60540			−1.46481			−0.732405	+	0.680869i	$0.761602\pi$
$44$	−0.558631	−	3.16815i	−0.0842167	−	0.477617i
$45$	−5.68763	−	0.967726i	−0.847862	−	0.144260i
$46$	−9.55969	−	8.02153i	−1.40950	−	1.18271i
$47$	−6.53846	+	3.77498i	−0.953733	+	0.550638i	−0.894239	−	0.447591i	$-0.852282\pi$
$47$	−6.53846	+	3.77498i	−0.953733	+	0.550638i	−0.0594943	+	0.998229i	$0.518949\pi$
$48$	−3.70509	−	2.13913i	−0.534783	−	0.308757i
$49$	−0.496600	+	0.180748i	−0.0709428	+	0.0258211i
$50$	2.04783	−	12.4885i	0.289607	−	1.76614i
$51$	−1.32055	+	0.762423i	−0.184915	+	0.106761i
$52$	0.0469555	−	0.266298i	0.00651156	−	0.0369289i
$53$	4.23503	+	0.746750i	0.581726	+	0.102574i	0.456764	−	0.889588i	$-0.349008\pi$
$53$	4.23503	+	0.746750i	0.581726	+	0.102574i	0.124961	+	0.992162i	$0.460119\pi$
$54$	5.88256	−	7.01057i	0.800516	−	0.954017i
$55$	0.00979708	+	1.63253i	0.00132104	+	0.220130i
$56$	−5.29908	+	14.5591i	−0.708119	+	1.94554i
$57$	4.16342	+	3.49353i	0.551459	+	0.462729i
$58$	10.2772	+	1.81215i	1.34946	+	0.237946i
$59$	11.4401	+	2.01720i	1.48938	+	0.262618i	0.858319	−	0.513117i	$-0.171509\pi$
$59$	11.4401	+	2.01720i	1.48938	+	0.262618i	0.631059	+	0.775735i	$0.282620\pi$
$60$	4.91512	+	4.07427i	0.634540	+	0.525986i
$61$	−5.27915	−	6.29144i	−0.675926	−	0.805537i	0.313652	−	0.949538i	$-0.398448\pi$
$61$	−5.27915	−	6.29144i	−0.675926	−	0.805537i	−0.989578	+	0.144001i	$0.954003\pi$
$62$	−5.14098	−	14.1247i	−0.652905	−	1.79384i
$63$	−5.68431	−	3.28184i	−0.716155	−	0.413473i
$64$	0.868712	+	1.50465i	0.108589	+	0.188082i
$65$	−0.0461588	+	0.129228i	−0.00572529	+	0.0160288i
$66$	−1.03698	−	0.598699i	−0.127643	−	0.0736947i
$67$	2.44898	−	0.431821i	0.299190	−	0.0527553i	−0.0220380	−	0.999757i	$-0.507015\pi$
$67$	2.44898	−	0.431821i	0.299190	−	0.0527553i	0.321228	+	0.947002i	$0.395904\pi$
$68$	−10.3692			−1.25745
$69$	−3.14623	+	0.554765i	−0.378762	+	0.0667859i
$70$	7.12386	−	12.5117i	0.851464	−	1.49543i
$71$	−0.992473	−	0.361230i	−0.117785	−	0.0428702i	0.282455	−	0.959280i	$-0.408851\pi$
$71$	−0.992473	−	0.361230i	−0.117785	−	0.0428702i	−0.400240	+	0.916410i	$0.631073\pi$
$72$	14.7664	−	5.37453i	1.74024	−	0.633394i
$73$			3.31788i			0.388329i	0.980969	+	0.194164i	$0.0621995\pi$
$73$			3.31788i			0.388329i	−0.980969	+	0.194164i	$0.937800\pi$
$74$	3.72334	−	14.9388i	0.432829	−	1.73660i
$75$	−2.11216	−	2.45668i	−0.243891	−	0.283673i
$76$	12.6406	+	34.7297i	1.44997	+	3.98377i
$77$	−0.635242	+	1.74531i	−0.0723926	+	0.198897i
$78$	−0.0646945	−	0.0770999i	−0.00732521	−	0.00872985i
$79$	−2.87364	+	0.506700i	−0.323310	+	0.0570082i	−0.332948	−	0.942945i	$-0.608043\pi$
$79$	−2.87364	+	0.506700i	−0.323310	+	0.0570082i	0.00963785	+	0.999954i	$0.496932\pi$
$80$	5.13272	+	13.8430i	0.573855	+	1.54769i
$81$	0.937275	+	5.31555i	0.104142	+	0.590617i
$82$	6.84041	−	11.8479i	0.755397	−	1.30839i
$83$	10.8097	−	12.8824i	1.18651	−	1.41403i	0.298380	−	0.954447i	$-0.403554\pi$
$83$	10.8097	−	12.8824i	1.18651	−	1.41403i	0.888134	−	0.459585i	$-0.152002\pi$
$84$	3.63158	+	6.29008i	0.396238	+	0.686304i
$85$	5.18755	+	0.882639i	0.562668	+	0.0957356i
$86$	−22.8457	+	8.31514i	−2.46351	+	0.896645i
$87$	2.04657	−	1.71727i	0.219415	−	0.184111i
$88$	−2.22331	−	3.85088i	−0.237005	−	0.410505i
$89$	−11.6491	−	2.05406i	−1.23481	−	0.217730i	−0.482118	−	0.876106i	$-0.660132\pi$
$89$	−11.6491	−	2.05406i	−1.23481	−	0.217730i	−0.752688	+	0.658377i	$0.771243\pi$
$90$	−14.3653	+	2.62197i	−1.51424	+	0.276380i
$91$	−0.100350	+	0.119592i	−0.0105195	+	0.0125367i
$92$	−20.4147	−	7.43035i	−2.12838	−	0.774668i
$93$	−3.61601	−	1.31612i	−0.374963	−	0.136475i
$94$	−12.2833	+	14.6387i	−1.26693	+	1.50986i
$95$	−3.36765	−	18.4507i	−0.345514	−	1.89301i
$96$	−2.89122	−	0.509800i	−0.295084	−	0.0520313i
$97$	9.44467	+	16.3586i	0.958961	+	1.66097i	0.725032	+	0.688715i	$0.241825\pi$
$97$	9.44467	+	16.3586i	0.958961	+	1.66097i	0.233928	+	0.972254i	$0.424842\pi$
$98$	−1.02465	+	0.859787i	−0.103506	+	0.0868516i
$99$	1.77016	−	0.644287i	0.177908	−	0.0647533i
$100$	−4.08582	−	21.6491i	−0.408582	−	2.16491i
$101$	−2.42576	−	4.20154i	−0.241372	−	0.418068i	0.719733	−	0.694251i	$-0.244264\pi$
$101$	−2.42576	−	4.20154i	−0.241372	−	0.418068i	−0.961105	+	0.276182i	$0.910931\pi$
$102$	−2.48082	+	2.95653i	−0.245638	+	0.292740i
$103$	−7.30758	+	12.6571i	−0.720038	+	1.24714i	0.240946	+	0.970538i	$0.422542\pi$
$103$	−7.30758	+	12.6571i	−0.720038	+	1.24714i	−0.960984	+	0.276603i	$0.910791\pi$
$104$	−0.0649025	−	0.368080i	−0.00636421	−	0.0360932i
$105$	−1.28140	−	3.45596i	−0.125052	−	0.337267i
$106$	10.7191	−	1.89007i	1.04113	−	0.183580i
$107$	−2.73794	−	3.26295i	−0.264686	−	0.315441i	0.617289	−	0.786737i	$-0.288231\pi$
$107$	−2.73794	−	3.26295i	−0.264686	−	0.315441i	−0.881975	+	0.471295i	$0.843787\pi$
$108$	5.44903	−	14.9711i	0.524333	−	1.44059i
$109$	−0.621605	−	1.70785i	−0.0595390	−	0.163582i	0.906357	−	0.422513i	$-0.138852\pi$
$109$	−0.621605	−	1.70785i	−0.0595390	−	0.163582i	−0.965896	+	0.258931i	$0.916630\pi$
$110$	1.43654	+	3.87436i	0.136969	+	0.369406i
$111$	−2.31697	−	3.18848i	−0.219917	−	0.302637i
$112$			16.7965i			1.58712i
$113$	9.44085	−	3.43619i	0.888120	−	0.323249i	0.142638	−	0.989775i	$-0.454441\pi$
$113$	9.44085	−	3.43619i	0.888120	−	0.323249i	0.745482	+	0.666526i	$0.232219\pi$
$114$	12.9266	+	4.70490i	1.21069	+	0.440655i
$115$	9.58070	+	5.45503i	0.893405	+	0.508684i
$116$	17.8913	−	3.15472i	1.66117	−	0.292908i
$117$	0.158340			0.0146385
$118$	28.9556	−	5.10566i	2.66558	−	0.470014i
$119$	5.18451	+	2.99328i	0.475264	+	0.274394i
$120$	8.31012	+	2.96828i	0.758607	+	0.270966i
$121$	5.23347	+	9.06464i	0.475770	+	0.824059i
$122$	−18.0024	−	10.3937i	−1.62986	−	0.940998i
$123$	−1.19788	−	3.29115i	−0.108009	−	0.296753i
$124$	−16.8201	−	20.0455i	−1.51049	−	1.80014i
$125$	0.201272	+	11.1785i	0.0180023	+	0.999838i
$126$	−16.3607	−	2.88482i	−1.45752	−	0.257001i
$127$	−11.1568	−	1.96724i	−0.990005	−	0.174565i	−0.344884	−	0.938645i	$-0.612082\pi$
$127$	−11.1568	−	1.96724i	−0.990005	−	0.174565i	−0.645121	+	0.764081i	$0.723193\pi$
$128$	10.3103	+	8.65140i	0.911314	+	0.764683i
$129$	−2.12872	+	5.84862i	−0.187424	+	0.514942i
$130$	0.00208430	+	0.347317i	0.000182805	+	0.0304617i
$131$	8.62869	−	10.2833i	0.753892	−	0.898454i	−0.243553	−	0.969888i	$-0.578313\pi$
$131$	8.62869	−	10.2833i	0.753892	−	0.898454i	0.997445	+	0.0714338i	$0.0227575\pi$
$132$	−2.05285	−	0.361973i	−0.178678	−	0.0315057i
$133$	3.70526	−	21.0136i	0.321287	−	1.82211i
$134$	5.45088	−	3.14706i	0.470884	−	0.271865i
$135$	−4.00043	+	7.02598i	−0.344302	+	0.604700i
$136$	−13.4681	+	4.90197i	−1.15488	+	0.420341i
$137$	13.0697	+	7.54578i	1.11662	+	0.644680i	0.940535	−	0.339696i	$-0.110324\pi$
$137$	13.0697	+	7.54578i	1.11662	+	0.644680i	0.176083	+	0.984375i	$0.443657\pi$
$138$	−7.00281	+	4.04307i	−0.596118	+	0.344169i
$139$	0.888556	+	0.745587i	0.0753663	+	0.0632399i	0.679693	−	0.733497i	$-0.262113\pi$
$139$	0.888556	+	0.745587i	0.0753663	+	0.0632399i	−0.604326	+	0.796737i	$0.706558\pi$
$140$	4.20420	−	24.7094i	0.355319	−	2.08832i
$141$	0.849507	+	4.81779i	0.0715414	+	0.405731i
$142$	−2.67322			−0.224332
$143$	−0.00778037	−	0.0441247i	−0.000650627	−	0.00368989i
$144$	13.0501	−	10.9503i	1.08751	−	0.912527i
$145$	−9.21929	+	0.0553265i	−0.765621	+	0.00459461i
$146$	2.87220	+	7.89131i	0.237705	+	0.653089i
$147$			0.342431i			0.0282432i
$148$	−2.80383	−	26.6552i	−0.230473	−	2.19104i
$149$	14.0146			1.14812			0.574062	−	0.818812i	$-0.305367\pi$
$149$	14.0146			1.14812			0.574062	+	0.818812i	$0.305367\pi$
$150$	−7.15027	−	4.01457i	−0.583817	−	0.327788i
$151$	−6.92787	−	2.52154i	−0.563782	−	0.205200i	0.0443774	−	0.999015i	$-0.485870\pi$
$151$	−6.92787	−	2.52154i	−0.563782	−	0.205200i	−0.608159	+	0.793815i	$0.708092\pi$
$152$	32.8366	+	39.1331i	2.66340	+	3.17411i
$153$	−1.05436	−	5.97956i	−0.0852397	−	0.483418i
$154$			4.70100i			0.378817i
$155$	6.70857	+	11.4602i	0.538845	+	0.920506i
$156$	−0.151739	−	0.0876068i	−0.0121489	−	0.00701416i
$157$	3.23240	−	3.85223i	0.257974	−	0.307441i	−0.621476	−	0.783434i	$-0.713467\pi$
$157$	3.23240	−	3.85223i	0.257974	−	0.307441i	0.879449	+	0.475992i	$0.157911\pi$
$158$	−6.39608	+	3.69278i	−0.508845	+	0.293782i
$159$	1.39324	−	2.41317i	0.110491	−	0.191376i
$160$	6.55870	+	7.72177i	0.518511	+	0.610459i
$161$	8.06229	+	9.60826i	0.635397	+	0.757237i
$162$	6.83076	+	11.8312i	0.536675	+	0.929549i
$163$	−1.45432	+	8.24786i	−0.113911	+	0.646022i	0.873372	+	0.487053i	$0.161928\pi$
$163$	−1.45432	+	8.24786i	−0.113911	+	0.646022i	−0.987284	+	0.158969i	$0.949183\pi$
$164$	4.13571	−	23.4548i	0.322945	−	1.83151i
$165$	0.996200	+	0.355832i	0.0775541	+	0.0277014i
$166$	14.5579	−	39.9975i	1.12991	−	3.10441i
$167$	−20.7929	−	7.56800i	−1.60900	−	0.585629i	−0.627760	−	0.778407i	$-0.716028\pi$
$167$	−20.7929	−	7.56800i	−1.60900	−	0.585629i	−0.981243	+	0.192777i	$0.938250\pi$
$168$	7.69049	+	6.45309i	0.593335	+	0.497867i
$169$	−2.25677	+	12.7988i	−0.173598	+	0.984522i
$170$	13.1022	−	2.39144i	1.00490	−	0.183415i
$171$	−18.7421	+	10.8208i	−1.43325	+	0.827485i
$172$	−32.4220	+	27.2053i	−2.47215	+	2.07438i
$173$	5.36123	+	14.7299i	0.407607	+	1.11989i	0.958445	+	0.285278i	$0.0920859\pi$
$173$	5.36123	+	14.7299i	0.407607	+	1.11989i	−0.550838	+	0.834612i	$0.685692\pi$
$174$	3.38099	−	5.85605i	0.256313	−	0.443946i
$175$	−4.20659	+	12.0039i	−0.317989	+	0.907407i
$176$	−3.69279	−	3.09862i	−0.278354	−	0.233567i
$177$	3.76358	−	6.51871i	0.282888	−	0.489976i
$178$	−29.4847	+	5.19894i	−2.20997	+	0.389677i
$179$		−	8.29223i		−	0.619791i	−0.950771	−	0.309895i	$-0.899706\pi$
$179$		−	8.29223i		−	0.619791i	0.950771	−	0.309895i	$-0.100294\pi$
$180$	−21.9389	+	12.8426i	−1.63523	+	0.957228i
$181$	−6.11096	+	5.12771i	−0.454224	+	0.381139i	−0.841001	−	0.541034i	$-0.818033\pi$
$181$	−6.11096	+	5.12771i	−0.454224	+	0.381139i	0.386776	+	0.922174i	$0.373589\pi$
$182$	−0.135146	+	0.371311i	−0.0100177	+	0.0275234i
$183$	−5.00074	+	1.82012i	−0.369665	+	0.134547i
$184$	−30.0284			−2.21372
$185$	−0.866214	+	13.5739i	−0.0636853	+	0.997970i
$186$	−9.73971			−0.714150
$187$	−1.61452	+	0.587638i	−0.118066	+	0.0429723i
$188$	−11.3780	+	31.2609i	−0.829828	+	2.27993i
$189$	−7.04619	+	5.91246i	−0.512535	+	0.430068i
$190$	−23.9820	−	40.9683i	−1.73984	−	2.97215i
$191$		−	8.60962i		−	0.622970i	−0.950251	−	0.311485i	$-0.899174\pi$
$191$		−	8.60962i		−	0.622970i	0.950251	−	0.311485i	$-0.100826\pi$
$192$	1.10869	−	0.195491i	0.0800126	−	0.0141084i
$193$	−4.92928	+	8.53776i	−0.354817	+	0.614562i	−0.987087	−	0.160187i	$-0.948790\pi$
$193$	−4.92928	+	8.53776i	−0.354817	+	0.614562i	0.632269	+	0.774749i	$0.282124\pi$
$194$	36.6246	+	30.7317i	2.62949	+	2.20641i
$195$	0.0684558	+	0.0567447i	0.00490222	+	0.00406357i
$196$	−1.16429	+	2.01661i	−0.0831636	+	0.144044i
$197$	5.57724	+	15.3233i	0.397362	+	1.09174i	0.963564	+	0.267476i	$0.0861897\pi$
$197$	5.57724	+	15.3233i	0.397362	+	1.09174i	−0.566203	+	0.824266i	$0.691588\pi$
$198$	3.65245	−	3.06477i	0.259568	−	0.217804i
$199$	−9.49813	+	5.48375i	−0.673305	+	0.388733i	−0.797328	−	0.603547i	$-0.793754\pi$
$199$	−9.49813	+	5.48375i	−0.673305	+	0.388733i	0.124023	+	0.992279i	$0.460420\pi$
$200$	−15.5414	−	26.1875i	−1.09894	−	1.85174i
$201$	0.279805	−	1.58685i	0.0197359	−	0.111928i
$202$	−9.40662	−	7.89309i	−0.661848	−	0.555356i
$203$	−9.85621	−	3.58737i	−0.691770	−	0.251784i
$204$	−2.29799	+	6.31367i	−0.160891	+	0.442045i
$205$	−4.06554	+	11.3820i	−0.283950	+	0.794956i
$206$	−6.42357	+	36.4299i	−0.447551	+	2.53819i
$207$	2.20903	−	12.5280i	0.153538	−	0.870757i
$208$	−0.202597	−	0.350908i	−0.0140475	−	0.0243311i
$209$	3.93638	+	4.69119i	0.272285	+	0.324496i
$210$	−6.03945	−	7.11044i	−0.416761	−	0.490667i
$211$	−1.20965	+	2.09517i	−0.0832754	+	0.144237i	−0.904655	−	0.426145i	$-0.859871\pi$
$211$	−1.20965	+	2.09517i	−0.0832754	+	0.144237i	0.821380	+	0.570382i	$0.193205\pi$
$212$	16.4099	−	9.47426i	1.12704	−	0.650695i
$213$	−0.439898	+	0.524250i	−0.0301413	+	0.0359210i
$214$	−9.33661	−	5.39049i	−0.638237	−	0.368487i
$215$	18.5360	−	10.8506i	1.26414	−	0.740005i
$216$		−	22.0213i		−	1.49836i
$217$	2.62341	+	14.8781i	0.178088	+	1.00999i
$218$	−2.95687	−	3.52386i	−0.200265	−	0.238666i
$219$	2.02022	+	0.735300i	0.136514	+	0.0496869i
$220$	4.65687	+	5.48268i	0.313966	+	0.369642i
$221$	−0.144418			−0.00971458
$222$	−8.27092	−	5.57780i	−0.555108	−	0.374357i
$223$		−	0.908810i		−	0.0608584i	−0.999537	−	0.0304292i	$-0.990313\pi$
$223$		−	0.908810i		−	0.0608584i	0.999537	−	0.0304292i	$-0.00968741\pi$
$224$	3.94215	+	10.8310i	0.263396	+	0.723675i
$225$	12.0689	−	4.55748i	0.804591	−	0.303832i
$226$	19.4797	−	16.3454i	1.29577	−	1.08728i
$227$	1.35539	+	7.68680i	0.0899604	+	0.510191i	0.996176	+	0.0873739i	$0.0278475\pi$
$227$	1.35539	+	7.68680i	0.0899604	+	0.510191i	−0.906215	+	0.422817i	$0.861041\pi$
$228$	23.9479			1.58599
$229$	1.06291	+	6.02806i	0.0702390	+	0.398345i	0.999576	+	0.0291129i	$0.00926824\pi$
$229$	1.06291	+	6.02806i	0.0702390	+	0.398345i	−0.929337	+	0.369232i	$0.879621\pi$
$230$	27.5092	+	4.68057i	1.81390	+	0.308628i
$231$	0.921920	+	0.773583i	0.0606579	+	0.0508980i
$232$	21.7468	−	12.5555i	1.42775	−	0.824312i
$233$	−20.5034	−	11.8376i	−1.34322	−	0.775509i	−0.355943	−	0.934508i	$-0.615840\pi$
$233$	−20.5034	−	11.8376i	−1.34322	−	0.775509i	−0.987279	+	0.158998i	$0.949174\pi$
$234$	0.376598	−	0.137070i	0.0246190	−	0.00896057i
$235$	8.35323	−	14.6708i	0.544905	−	0.957020i
$236$	44.3282	−	25.5929i	2.88552	−	1.66596i
$237$	−0.328324	+	1.86202i	−0.0213269	+	0.120951i
$238$	14.9221	+	2.63118i	0.967259	+	0.170554i
$239$	−2.96276	+	3.53088i	−0.191645	+	0.228393i	−0.853307	−	0.521408i	$-0.825407\pi$
$239$	−2.96276	+	3.53088i	−0.191645	+	0.228393i	0.661662	+	0.749802i	$0.269851\pi$
$240$	9.56632	−	0.0574090i	0.617503	−	0.00370574i
$241$	2.79355	−	7.67521i	0.179948	−	0.494404i	−0.816620	−	0.577175i	$-0.804155\pi$
$241$	2.79355	−	7.67521i	0.179948	−	0.494404i	0.996569	+	0.0827714i	$0.0263771\pi$
$242$	20.2944	+	17.0290i	1.30457	+	1.09467i
$243$	14.1267	+	2.49092i	0.906229	+	0.159793i
$244$	−35.6384	−	6.28401i	−2.28151	−	0.402293i
$245$	0.754134	−	0.909774i	0.0481798	−	0.0581233i
$246$	−5.69811	−	6.79075i	−0.363298	−	0.432962i
$247$	0.176053	+	0.483701i	0.0112020	+	0.0307771i
$248$	−31.3233	−	18.0845i	−1.98903	−	1.14837i
$249$	−5.44836	−	9.43684i	−0.345276	−	0.598036i
$250$	10.1557	+	26.4130i	0.642300	+	1.67050i
$251$	0.114911	+	0.0663437i	0.00725310	+	0.00418758i	0.503622	−	0.863924i	$-0.332000\pi$
$251$	0.114911	+	0.0663437i	0.00725310	+	0.00418758i	−0.496369	+	0.868112i	$0.665334\pi$
$252$	−28.4819	+	5.02212i	−1.79419	+	0.316364i
$253$	−3.59974			−0.226314
$254$	−28.2385	+	4.97921i	−1.77184	+	0.312423i
$255$	1.68708	−	2.96303i	0.105649	−	0.185552i
$256$	28.7463	+	10.4628i	1.79664	+	0.653925i
$257$	22.6464	−	8.24263i	1.41265	−	0.514161i	0.480741	−	0.876863i	$-0.340368\pi$
$257$	22.6464	−	8.24263i	1.41265	−	0.514161i	0.931905	+	0.362702i	$0.118146\pi$
$258$			15.7532i			0.980753i
$259$	−6.29269	+	14.1368i	−0.391008	+	0.878417i
$260$	0.210207	+	0.566930i	0.0130365	+	0.0351595i
$261$	3.63844	+	9.99654i	0.225214	+	0.618770i
$262$	11.6207	−	31.9275i	0.717928	−	1.97249i
$263$	−7.38282	−	8.79851i	−0.455244	−	0.542539i	0.488783	−	0.872405i	$-0.337441\pi$
$263$	−7.38282	−	8.79851i	−0.455244	−	0.542539i	−0.944028	+	0.329866i	$0.892996\pi$
$264$	−2.83748	+	0.500324i	−0.174635	+	0.0307928i
$265$	−9.01609	+	3.34300i	−0.553854	+	0.205359i
$266$	−9.37823	−	53.1866i	−0.575016	−	3.26108i
$267$	−3.83234	+	6.63781i	−0.234535	+	0.406227i
$268$	7.04322	−	8.39378i	0.430233	−	0.512732i
$269$	−10.8335	−	18.7642i	−0.660531	−	1.14407i	−0.980476	−	0.196637i	$-0.936998\pi$
$269$	−10.8335	−	18.7642i	−0.660531	−	1.14407i	0.319946	−	0.947436i	$-0.396335\pi$
$270$	−3.43248	+	20.1738i	−0.208894	+	1.22774i
$271$	19.2100	−	6.99188i	1.16693	−	0.424727i	0.315360	−	0.948972i	$-0.397875\pi$
$271$	19.2100	−	6.99188i	1.16693	−	0.424727i	0.851567	+	0.524246i	$0.175653\pi$
$272$	−11.9027	+	9.98752i	−0.721705	+	0.605582i
$273$	0.0505791	+	0.0876056i	0.00306119	+	0.00530213i
$274$	37.6173	+	6.63295i	2.27255	+	0.400711i
$275$	−1.86307	−	3.13930i	−0.112347	−	0.189307i
$276$	−9.04851	+	10.7836i	−0.544656	+	0.649096i
$277$	−16.4905	−	6.00205i	−0.990818	−	0.360628i	−0.204781	−	0.978808i	$-0.565648\pi$
$277$	−16.4905	−	6.00205i	−0.990818	−	0.360628i	−0.786037	+	0.618179i	$0.787871\pi$
$278$	2.75879	+	1.00412i	0.165461	+	0.0602230i
$279$	9.84925	−	11.7379i	0.589659	−	0.702728i
$280$	−6.22058	−	34.0814i	−0.371751	−	2.03675i
$281$	−18.4116	−	3.24645i	−1.09834	−	0.193667i	−0.405029	−	0.914304i	$-0.632738\pi$
$281$	−18.4116	−	3.24645i	−1.09834	−	0.193667i	−0.693313	+	0.720637i	$0.743850\pi$
$282$	6.19112	+	10.7233i	0.368676	+	0.638565i
$283$	0.986040	−	0.827386i	0.0586140	−	0.0491830i	−0.613010	−	0.790075i	$-0.710041\pi$
$283$	0.986040	−	0.827386i	0.0586140	−	0.0491830i	0.671624	+	0.740892i	$0.265597\pi$
$284$	−4.37309	+	1.59168i	−0.259495	+	0.0944486i
$285$	−11.9808	−	2.03848i	−0.709679	−	0.120749i
$286$	−0.0567025	−	0.0982117i	−0.00335289	−	0.00580738i
$287$	−8.83854	+	10.5334i	−0.521723	+	0.621765i
$288$	5.84509	−	10.1240i	0.344426	−	0.596563i
$289$	−1.99037	−	11.2879i	−0.117080	−	0.663996i
$290$	−21.8794	+	8.11249i	−1.28480	+	0.476382i
$291$	12.0537	−	2.12539i	0.706600	−	0.124593i
$292$	9.39720	+	11.1992i	0.549930	+	0.655381i
$293$	−2.70235	+	7.42465i	−0.157873	+	0.433753i	−0.993260	−	0.115910i	$-0.963022\pi$
$293$	−2.70235	+	7.42465i	−0.157873	+	0.433753i	0.835387	+	0.549663i	$0.185244\pi$
$294$	0.296433	+	0.814443i	0.0172883	+	0.0474993i
$295$	−24.3553	+	9.03048i	−1.41802	+	0.525775i
$296$	−16.2429	−	33.2957i	−0.944097	−	1.93527i
$297$		−	2.63986i		−	0.153180i
$298$	33.3327	−	12.1321i	1.93091	−	0.702793i
$299$	−0.284328	−	0.103487i	−0.0164431	−	0.00598480i
$300$	−14.0874	−	2.31001i	−0.813335	−	0.133368i
$301$	24.0641	−	4.24316i	1.38703	−	0.244572i
$302$	−18.6602			−1.07377
$303$	−3.09585	+	0.545883i	−0.177852	+	0.0313601i
$304$	47.9614	+	27.6905i	2.75077	+	1.58816i
$305$	17.2945	+	6.17739i	0.990278	+	0.353716i
$306$	−7.68404	−	13.3092i	−0.439267	−	0.760834i
$307$	2.47826	+	1.43082i	0.141442	+	0.0816615i	0.569051	−	0.822302i	$-0.307311\pi$
$307$	2.47826	+	1.43082i	0.141442	+	0.0816615i	−0.427609	+	0.903964i	$0.640644\pi$
$308$	2.79904	+	7.69031i	0.159490	+	0.438196i
$309$	6.08728	+	7.25453i	0.346293	+	0.412696i
$310$	25.8766	+	21.4497i	1.46969	+	1.21826i
$311$	−7.78197	−	1.37217i	−0.441275	−	0.0778087i	−0.0514036	−	0.998678i	$-0.516369\pi$
$311$	−7.78197	−	1.37217i	−0.441275	−	0.0778087i	−0.389872	+	0.920869i	$0.627481\pi$
$312$	−0.238503	−	0.0420546i	−0.0135026	−	0.00238087i
$313$	−10.1816	−	8.54341i	−0.575500	−	0.482902i	0.307966	−	0.951398i	$-0.400352\pi$
$313$	−10.1816	−	8.54341i	−0.575500	−	0.482902i	−0.883466	+	0.468495i	$0.844796\pi$
$314$	4.35323	−	11.9604i	0.245667	−	0.674965i
$315$	14.6766	−	0.0880763i	0.826930	−	0.00496254i
$316$	−8.26454	+	9.84930i	−0.464917	+	0.554066i
$317$	10.9968	+	1.93903i	0.617641	+	0.108907i	0.473710	−	0.880681i	$-0.342914\pi$
$317$	10.9968	+	1.93903i	0.617641	+	0.108907i	0.143931	+	0.989588i	$0.454026\pi$
$318$	1.22470	−	6.94561i	0.0686777	−	0.389490i
$319$	2.60697	−	1.50513i	0.145962	−	0.0842712i
$320$	−3.37610	−	1.92227i	−0.188730	−	0.107458i
$321$	−2.59354	+	0.943973i	−0.144758	+	0.0526874i
$322$	27.4931	+	15.8732i	1.53213	+	0.884576i
$323$	17.0942	−	9.86936i	0.951148	−	0.549146i
$324$	18.2189	+	15.2874i	1.01216	+	0.849302i
$325$	−0.0569056	−	0.301520i	−0.00315655	−	0.0167253i
$326$	3.68097	+	20.8758i	0.203870	+	1.15621i
$327$	−1.17765			−0.0651239
$328$	−5.71643	−	32.4195i	−0.315637	−	1.79007i
$329$	14.7130	−	12.3457i	0.811156	−	0.680641i
$330$	2.67741	−	0.0160676i	0.147387	−	0.000884491i
$331$	8.96472	+	24.6304i	0.492746	+	1.35381i	0.898158	+	0.439674i	$0.144906\pi$
$331$	8.96472	+	24.6304i	0.492746	+	1.35381i	−0.405412	+	0.914134i	$0.632872\pi$
$332$		−	74.0994i		−	4.06673i
$333$	15.0860	−	4.32722i	0.826710	−	0.237130i
$334$	−56.0056			−3.06449
$335$	−4.23811	+	3.59975i	−0.231553	+	0.196676i
$336$	10.2272	+	3.72240i	0.557940	+	0.203074i
$337$	−14.9267	−	17.7890i	−0.813111	−	0.969027i	0.186800	−	0.982398i	$-0.440188\pi$
$337$	−14.9267	−	17.7890i	−0.813111	−	0.969027i	−0.999911	+	0.0133705i	$0.995744\pi$
$338$	5.71202	+	32.3945i	0.310693	+	1.76203i
$339$		−	6.50994i		−	0.353571i
$340$	20.0099	−	11.7134i	1.08519	−	0.635247i
$341$	−3.75497	−	2.16793i	−0.203343	−	0.117400i
$342$	−35.2094	+	41.9609i	−1.90390	+	2.26899i
$343$	16.5860	−	9.57591i	0.895558	−	0.517051i
$344$	−29.2503	+	50.6630i	−1.57707	+	2.73157i
$345$	5.44475	−	4.62465i	0.293135	−	0.248983i
$346$	25.5025	+	30.3927i	1.37102	+	1.63392i
$347$	1.74086	+	3.01526i	0.0934544	+	0.161868i	0.908963	−	0.416878i	$-0.136876\pi$
$347$	1.74086	+	3.01526i	0.0934544	+	0.161868i	−0.815508	+	0.578746i	$0.803542\pi$
$348$	2.04415	−	11.5929i	0.109578	−	0.621447i
$349$	3.16448	−	17.9466i	0.169391	−	0.960662i	−0.775031	−	0.631924i	$-0.782266\pi$
$349$	3.16448	−	17.9466i	0.169391	−	0.960662i	0.944421	−	0.328738i	$-0.106623\pi$
$350$	0.386390	+	32.1917i	0.0206534	+	1.72072i
$351$	0.0758917	−	0.208511i	0.00405080	−	0.0111295i
$352$	−3.10848	−	1.13139i	−0.165683	−	0.0603035i
$353$	−10.8847	−	9.13332i	−0.579332	−	0.486117i	0.305396	−	0.952226i	$-0.401211\pi$
$353$	−10.8847	−	9.13332i	−0.579332	−	0.486117i	−0.884728	+	0.466108i	$0.845656\pi$
$354$	3.30829	−	18.7623i	0.175834	−	0.997203i
$355$	2.32328	−	0.424048i	0.123307	−	0.0225061i
$356$	−45.1381	+	26.0605i	−2.39231	+	1.38120i
$357$	2.97155	−	2.49343i	0.157271	−	0.131966i
$358$	−7.17837	−	19.7224i	−0.379388	−	1.04236i
$359$	4.01244	−	6.94975i	0.211768	−	0.366794i	−0.740500	−	0.672057i	$-0.765411\pi$
$359$	4.01244	−	6.94975i	0.211768	−	0.366794i	0.952268	+	0.305263i	$0.0987444\pi$
$360$	−22.4242	+	27.0521i	−1.18186	+	1.42577i
$361$	−39.3396	−	33.0098i	−2.07050	−	1.73736i
$362$	−10.0955	+	17.4859i	−0.530608	+	0.919040i
$363$	6.67918	−	1.17772i	0.350566	−	0.0618143i
$364$			0.687891i			0.0360553i
$365$	−3.74799	−	6.40267i	−0.196179	−	0.335131i
$366$	−10.3182	+	8.65801i	−0.539342	+	0.452561i
$367$	2.11078	−	5.79933i	0.110182	−	0.302723i	−0.872331	−	0.488915i	$-0.837393\pi$
$367$	2.11078	−	5.79933i	0.110182	−	0.302723i	0.982513	+	0.186193i	$0.0596149\pi$
$368$	−30.5907	+	11.1341i	−1.59465	+	0.580405i
$369$	13.9461			0.726005
$370$	9.69031	+	33.0342i	0.503775	+	1.71736i
$371$	−10.9398			−0.567965
$372$	−15.9331	+	5.79917i	−0.826092	+	0.300673i
$373$	−6.82936	+	18.7635i	−0.353611	+	0.971538i	0.627589	+	0.778545i	$0.284042\pi$
$373$	−6.82936	+	18.7635i	−0.353611	+	0.971538i	−0.981200	+	0.192994i	$0.938180\pi$
$374$	−3.33131	+	2.79530i	−0.172258	+	0.144541i
$375$	6.85108	+	2.35480i	0.353788	+	0.121601i
$376$			45.9822i			2.37135i
$377$	0.249183	−	0.0439376i	0.0128336	−	0.00226290i
$378$	−11.6405	+	20.1620i	−0.598724	+	1.03702i
$379$	−17.6823	−	14.8372i	−0.908280	−	0.762137i	0.0635112	−	0.997981i	$-0.479770\pi$
$379$	−17.6823	−	14.8372i	−0.908280	−	0.762137i	−0.971791	+	0.235844i	$0.924215\pi$
$380$	−63.6250	−	52.7403i	−3.26389	−	2.70552i
$381$	−3.67037	+	6.35726i	−0.188039	+	0.325692i
$382$	−7.45312	−	20.4773i	−0.381335	−	1.04771i
$383$	10.2155	−	8.57182i	0.521988	−	0.438000i	−0.343336	−	0.939213i	$-0.611557\pi$
$383$	10.2155	−	8.57182i	0.521988	−	0.438000i	0.865324	+	0.501213i	$0.167113\pi$
$384$	7.55268	−	4.36054i	0.385421	−	0.222523i
$385$	−0.745710	−	4.08561i	−0.0380049	−	0.208222i
$386$	−4.33297	+	24.5735i	−0.220543	+	1.25076i
$387$	−18.9851	−	15.9304i	−0.965067	−	0.809787i
$388$	78.2119	+	28.4668i	3.97061	+	1.44518i
$389$	12.2727	−	33.7189i	0.622249	−	1.70962i	−0.0791653	−	0.996862i	$-0.525226\pi$
$389$	12.2727	−	33.7189i	0.622249	−	1.70962i	0.701414	−	0.712754i	$-0.252552\pi$
$390$	0.211939	+	0.0757022i	0.0107319	+	0.00383333i
$391$	−2.01480	+	11.4265i	−0.101893	+	0.577862i
$392$	−0.558903	+	3.16969i	−0.0282288	+	0.160094i
$393$	−4.34910	−	7.53286i	−0.219383	−	0.379982i
$394$	26.5300	+	31.6172i	1.33656	+	1.59285i
$395$	4.97301	−	4.22397i	0.250219	−	0.212531i
$396$	4.15019	−	7.18834i	0.208555	−	0.361228i
$397$	11.4920	−	6.63492i	0.576768	−	0.332997i	−0.183080	−	0.983098i	$-0.558607\pi$
$397$	11.4920	−	6.63492i	0.576768	−	0.332997i	0.759848	+	0.650101i	$0.225273\pi$
$398$	−17.8434	+	21.2649i	−0.894408	+	1.06591i
$399$	−11.9738	−	6.91306i	−0.599438	−	0.346086i
$400$	−25.5424	−	20.9154i	−1.27712	−	1.04577i
$401$			22.3241i			1.11481i	0.830241	+	0.557405i	$0.188203\pi$
$401$			22.3241i			1.11481i	−0.830241	+	0.557405i	$0.811797\pi$
$402$	−0.708203	−	4.01642i	−0.0353219	−	0.200321i
$403$	−0.234264	−	0.279185i	−0.0116695	−	0.0139072i
$404$	−20.0878	−	7.31138i	−0.999408	−	0.363755i
$405$	−7.81333	−	9.19889i	−0.388248	−	0.457097i
$406$	−26.5477			−1.31754
$407$	−1.94716	−	3.99142i	−0.0965171	−	0.197847i
$408$			9.28690i			0.459770i
$409$	−2.17202	−	5.96758i	−0.107400	−	0.295078i	0.874338	−	0.485317i	$-0.161296\pi$
$409$	−2.17202	−	5.96758i	−0.107400	−	0.295078i	−0.981738	+	0.190239i	$0.939074\pi$
$410$	0.183580	+	30.5907i	0.00906635	+	1.51077i
$411$	7.49100	−	6.28570i	0.369504	−	0.310051i
$412$	11.1826	+	63.4199i	0.550929	+	3.12447i
$413$	−29.5517			−1.45415
$414$	−5.59118	−	31.7092i	−0.274791	−	1.55842i
$415$	−6.30744	+	37.0708i	−0.309620	+	1.81974i
$416$	−0.212999	−	0.178728i	−0.0104431	−	0.00876284i
$417$	0.650898	−	0.375796i	0.0318746	−	0.0184028i
$418$	13.4234	+	7.75000i	0.656559	+	0.379065i
$419$	5.56603	−	2.02587i	0.271918	−	0.0989702i	−0.202462	−	0.979290i	$-0.564894\pi$
$419$	5.56603	−	2.02587i	0.271918	−	0.0989702i	0.474380	+	0.880320i	$0.342672\pi$
$420$	−14.1135	−	8.03591i	−0.688669	−	0.392112i
$421$	23.5266	−	13.5831i	1.14662	−	0.661999i	0.198556	−	0.980090i	$-0.436375\pi$
$421$	23.5266	−	13.5831i	1.14662	−	0.661999i	0.948060	+	0.318090i	$0.103042\pi$
$422$	−1.06331	+	6.03034i	−0.0517612	+	0.293552i
$423$	−19.1840	−	3.38266i	−0.932760	−	0.164471i
$424$	16.8352	−	20.0634i	0.817588	−	0.974363i
$425$	−11.0077	+	4.15676i	−0.533953	+	0.201633i
$426$	−0.592432	+	1.62769i	−0.0287034	+	0.0788620i
$427$	16.0049	+	13.4297i	0.774533	+	0.649910i
$428$	−18.4832	−	3.25909i	−0.893421	−	0.157534i
$429$	−0.0285913	−	0.00504141i	−0.00138040	−	0.000243402i
$430$	34.6933	−	41.8534i	1.67306	−	2.01835i
$431$	18.1122	+	21.5852i	0.872432	+	1.03972i	0.998859	+	0.0477478i	$0.0152044\pi$
$431$	18.1122	+	21.5852i	0.872432	+	1.03972i	−0.126428	+	0.991976i	$0.540351\pi$
$432$	−8.16516	−	22.4336i	−0.392846	−	1.07934i
$433$	6.36189	+	3.67304i	0.305733	+	0.176515i	0.645015	−	0.764170i	$-0.276851\pi$
$433$	6.36189	+	3.67304i	0.305733	+	0.176515i	−0.339283	+	0.940685i	$0.610184\pi$
$434$	19.1191	+	33.1153i	0.917747	+	1.58958i
$435$	−2.00947	+	5.62578i	−0.0963465	+	0.269736i
$436$	−6.93527	−	4.00408i	−0.332139	−	0.191761i
$437$	40.7271	−	7.18129i	1.94824	−	0.343528i
$438$	5.44145			0.260003
$439$	−5.54693	+	0.978074i	−0.264741	+	0.0466809i	−0.304443	−	0.952531i	$-0.598470\pi$
$439$	−5.54693	+	0.978074i	−0.264741	+	0.0466809i	0.0397021	+	0.999212i	$0.487359\pi$
$440$	8.64051	+	4.91970i	0.411920	+	0.234538i
$441$	−1.28130	−	0.466354i	−0.0610142	−	0.0222073i
$442$	−0.343485	+	0.125018i	−0.0163379	+	0.00594652i
$443$			13.8500i			0.658034i	0.944324	+	0.329017i	$0.106717\pi$
$443$			13.8500i			0.658034i	−0.944324	+	0.329017i	$0.893283\pi$
$444$	−16.8514	−	4.20003i	−0.799732	−	0.199325i
$445$	24.8002	−	9.19546i	1.17564	−	0.435907i
$446$	−0.786732	−	2.16153i	−0.0372528	−	0.102351i
$447$	3.10588	−	8.53334i	0.146903	−	0.403613i
$448$	−2.84104	−	3.38582i	−0.134226	−	0.159965i
$449$	−37.7913	+	6.66363i	−1.78348	+	0.314476i	−0.965429	−	0.260666i	$-0.916058\pi$
$449$	−37.7913	+	6.66363i	−1.78348	+	0.314476i	−0.818054	+	0.575142i	$0.804947\pi$
$450$	24.7595	−	21.2873i	1.16718	−	1.00349i
$451$	−0.685274	−	3.88638i	−0.0322683	−	0.183002i
$452$	22.1343	−	38.3377i	1.04111	−	1.80325i
$453$	−3.07067	+	3.65948i	−0.144273	+	0.171937i
$454$	9.87794	+	17.1091i	0.463595	+	0.802969i
$455$	0.0585543	−	0.344142i	0.00274507	−	0.0161336i
$456$	31.1048	−	11.3212i	1.45662	−	0.530165i
$457$	−10.0016	+	8.39233i	−0.467855	+	0.392577i	−0.846011	−	0.533165i	$-0.821003\pi$
$457$	−10.0016	+	8.39233i	−0.467855	+	0.392577i	0.378157	+	0.925742i	$0.376558\pi$
$458$	7.74637	+	13.4171i	0.361964	+	0.626940i
$459$	−8.37958	−	1.47755i	−0.391125	−	0.0689660i
$460$	47.7888	−	8.72248i	2.22817	−	0.406688i
$461$	−4.60445	+	5.48737i	−0.214450	+	0.255572i	−0.862536	−	0.505995i	$-0.831125\pi$
$461$	−4.60445	+	5.48737i	−0.214450	+	0.255572i	0.648086	+	0.761567i	$0.275570\pi$
$462$	2.86238	+	1.04182i	0.133170	+	0.0484699i
$463$	20.4806	+	7.45434i	0.951816	+	0.346433i	0.770821	−	0.637051i	$-0.219846\pi$
$463$	20.4806	+	7.45434i	0.951816	+	0.346433i	0.180995	+	0.983484i	$0.442068\pi$
$464$	17.4986	−	20.8541i	0.812353	−	0.968125i
$465$	8.46472	−	1.54499i	0.392542	−	0.0716473i
$466$	−59.0131	−	10.4056i	−2.73373	−	0.482031i
$467$	−15.1836	−	26.2988i	−0.702613	−	1.21696i	−0.967546	−	0.252694i	$-0.918683\pi$
$467$	−15.1836	−	26.2988i	−0.702613	−	1.21696i	0.264933	−	0.964267i	$-0.414650\pi$
$468$	0.534458	−	0.448464i	0.0247053	−	0.0207302i
$469$	−5.94460	+	2.16366i	−0.274496	+	0.0999084i
$470$	7.16731	−	42.1246i	0.330604	−	1.94306i
$471$	−1.62922	−	2.82189i	−0.0750705	−	0.130026i
$472$	45.4770	−	54.1974i	2.09325	−	2.49464i
$473$	−3.50647	+	6.07338i	−0.161228	+	0.279254i
$474$	0.831008	+	4.71288i	0.0381695	+	0.216470i
$475$	27.3413	+	31.8011i	1.25451	+	1.45913i
$476$	25.9776	−	4.58055i	1.19068	−	0.209949i
$477$	7.13207	+	8.49967i	0.326555	+	0.389173i
$478$	−3.99009	+	10.9627i	−0.182502	+	0.501421i
$479$	1.61694	+	4.44252i	0.0738801	+	0.202984i	0.971136	−	0.238528i	$-0.0766647\pi$
$479$	1.61694	+	4.44252i	0.0738801	+	0.202984i	−0.897256	+	0.441511i	$0.854443\pi$
$480$	6.15521	−	2.28224i	0.280946	−	0.104169i
$481$	−0.0390505	−	0.371242i	−0.00178055	−	0.0169272i
$482$		−	20.6732i		−	0.941637i
$483$	7.63710	−	2.77968i	0.347500	−	0.126480i
$484$	43.3387	+	15.7740i	1.96994	+	0.717000i
$485$	−36.7051	−	20.8990i	−1.66669	−	0.948976i
$486$	35.7555	−	6.30467i	1.62190	−	0.285985i
$487$	−25.1735			−1.14072			−0.570360	−	0.821395i	$-0.693196\pi$
$487$	−25.1735			−1.14072			−0.570360	+	0.821395i	$0.693196\pi$
$488$	−49.2598	+	8.68584i	−2.22989	+	0.393189i
$489$	4.69972	+	2.71339i	0.212529	+	0.122704i
$490$	1.00608	−	2.81666i	0.0454500	−	0.127244i
$491$	3.38199	+	5.85777i	0.152627	+	0.264358i	0.932192	−	0.361963i	$-0.117893\pi$
$491$	3.38199	+	5.85777i	0.152627	+	0.264358i	−0.779565	+	0.626321i	$0.784560\pi$
$492$	−13.3648	−	7.71617i	−0.602531	−	0.347872i
$493$	−3.31853	−	9.11759i	−0.149459	−	0.410636i
$494$	0.837454	+	0.998038i	0.0376788	+	0.0449039i
$495$	−2.68816	+	3.24295i	−0.120824	+	0.145760i
$496$	−38.6153	−	6.80892i	−1.73388	−	0.305730i
$497$	2.64599	+	0.466559i	0.118689	+	0.0209280i
$498$	−21.1277	−	17.7282i	−0.946755	−	0.794422i
$499$	1.91540	−	5.26252i	0.0857450	−	0.235583i	−0.889408	−	0.457114i	$-0.848883\pi$
$499$	1.91540	−	5.26252i	0.0857450	−	0.235583i	0.975153	+	0.221531i	$0.0711055\pi$
$500$	32.3402	+	37.1619i	1.44630	+	1.66193i
$501$	−9.21613	+	10.9834i	−0.411746	+	0.490700i
$502$	0.330738	+	0.0583179i	0.0147615	+	0.00260286i
$503$	−1.75193	+	9.93566i	−0.0781145	+	0.443009i	0.920517	+	0.390703i	$0.127768\pi$
$503$	−1.75193	+	9.93566i	−0.0781145	+	0.443009i	−0.998631	+	0.0523059i	$0.983343\pi$
$504$	−34.6196	+	19.9877i	−1.54208	+	0.890321i
$505$	9.42730	+	5.36768i	0.419509	+	0.238859i
$506$	−8.56169	+	3.11620i	−0.380614	+	0.138532i
$507$	7.29289	+	4.21055i	0.323889	+	0.186997i
$508$	−43.2303	+	24.9590i	−1.91804	+	1.10738i
$509$	2.70961	+	2.27364i	0.120102	+	0.100777i	0.700860	−	0.713299i	$-0.252800\pi$
$509$	2.70961	+	2.27364i	0.120102	+	0.100777i	−0.580759	+	0.814076i	$0.697244\pi$
$510$	1.44756	−	8.50777i	0.0640991	−	0.376731i
$511$	−1.46566	−	8.31220i	−0.0648372	−	0.367710i
$512$	50.5097			2.23223
$513$	5.26638	+	29.8671i	0.232516	+	1.31867i
$514$	46.7273	−	39.2088i	2.06105	−	1.72943i
$515$	−0.196117	−	32.6799i	−0.00864197	−	1.44005i
$516$	9.37970	+	25.7705i	0.412918	+	1.13448i
$517$			5.51225i			0.242429i
$518$	−2.72880	+	39.0706i	−0.119897	+	1.71666i
$519$	10.1570			0.445842
$520$	0.541042	+	0.636986i	0.0237262	+	0.0279337i
$521$	16.2453	+	5.91282i	0.711721	+	0.259045i	0.672407	−	0.740181i	$-0.265260\pi$
$521$	16.2453	+	5.91282i	0.711721	+	0.259045i	0.0393143	+	0.999227i	$0.487483\pi$
$522$	17.3075	+	20.6262i	0.757528	+	0.902786i
$523$	−2.68149	−	15.2075i	−0.117253	−	0.664977i	−0.985610	−	0.169036i	$-0.945934\pi$
$523$	−2.68149	−	15.2075i	−0.117253	−	0.664977i	0.868356	−	0.495941i	$-0.165177\pi$
$524$		−	59.1490i		−	2.58394i
$525$	6.37676	+	5.22161i	0.278305	+	0.227890i
$526$	−25.1761	−	14.5354i	−1.09773	−	0.633774i
$527$	−8.98325	+	10.7058i	−0.391317	+	0.466353i
$528$	−2.70510	+	1.56179i	−0.117724	+	0.0679681i
$529$	−0.654715	+	1.13400i	−0.0284659	+	0.0493044i
$530$	−18.5501	+	15.7560i	−0.805764	+	0.684398i
$531$	19.2660	+	22.9603i	0.836071	+	0.996391i
$532$	−47.0098	−	81.4234i	−2.03813	−	3.53015i
$533$	0.0576004	−	0.326668i	0.00249495	−	0.0141496i
$534$	−3.36873	+	19.1050i	−0.145779	+	0.826756i
$535$	8.96947	+	3.20379i	0.387784	+	0.138512i
$536$	5.18000	−	14.2319i	0.223742	−	0.614726i
$537$	−5.04904	−	1.83770i	−0.217882	−	0.0793027i
$538$	−42.0103	−	35.2508i	−1.81119	−	1.51977i
$539$	−0.0670001	+	0.379976i	−0.00288590	+	0.0163667i
$540$	6.39660	+	35.0458i	0.275266	+	1.50813i
$541$	−5.64201	+	3.25742i	−0.242569	+	0.140047i	−0.616357	−	0.787467i	$-0.711392\pi$
$541$	−5.64201	+	3.25742i	−0.242569	+	0.140047i	0.373788	+	0.927514i	$0.378059\pi$
$542$	39.6368	−	33.2592i	1.70255	−	1.42861i
$543$	1.76791	+	4.85728i	0.0758681	+	0.208446i
$544$	−5.33116	+	9.23385i	−0.228572	+	0.395898i
$545$	3.12878	+	2.59352i	0.134022	+	0.111094i
$546$	0.196136	+	0.164578i	0.00839385	+	0.00704328i
$547$	−14.9199	+	25.8420i	−0.637929	+	1.10493i	0.347957	+	0.937510i	$0.386875\pi$
$547$	−14.9199	+	25.8420i	−0.637929	+	1.10493i	−0.985886	+	0.167415i	$0.946458\pi$
$548$	65.4871	−	11.5472i	2.79747	−	0.493270i
$549$		−	21.1904i		−	0.904386i
$550$	−7.14877	−	5.85377i	−0.304825	−	0.249606i
$551$	−26.4923	+	22.2297i	−1.12861	+	0.947016i
$552$	−6.65481	+	18.2840i	−0.283248	+	0.778217i
$553$	6.97542	−	2.53884i	0.296625	−	0.107963i
$554$	−44.4171			−1.88710
$555$	8.07299	+	3.53563i	0.342680	+	0.150079i
$556$	5.11094			0.216752
$557$	−18.1705	+	6.61350i	−0.769907	+	0.280223i	−0.696957	−	0.717112i	$-0.745463\pi$
$557$	−18.1705	+	6.61350i	−0.769907	+	0.280223i	−0.0729494	+	0.997336i	$0.523241\pi$
$558$	13.2645	−	36.4438i	0.561529	−	1.54279i
$559$	−0.451560	+	0.378904i	−0.0190990	+	0.0160259i
$560$	−18.9739	−	32.4131i	−0.801795	−	1.36970i
$561$			1.11329i			0.0470033i
$562$	−46.6007	+	8.21697i	−1.96573	+	0.346612i
$563$	−5.19532	+	8.99856i	−0.218957	+	0.379244i	−0.954489	−	0.298245i	$-0.903599\pi$
$563$	−5.19532	+	8.99856i	−0.218957	+	0.379244i	0.735533	+	0.677489i	$0.236932\pi$
$564$	16.5128	+	13.8559i	0.695315	+	0.583438i
$565$	−14.3368	+	17.2957i	−0.603154	+	0.727635i
$566$	1.62897	−	2.82146i	0.0684707	−	0.118595i
$567$	−4.69626	−	12.9029i	−0.197224	−	0.541869i
$568$	−4.92756	+	4.13471i	−0.206756	+	0.173489i
$569$	−19.6108	+	11.3223i	−0.822126	+	0.474655i	−0.851149	−	0.524924i	$-0.824094\pi$
$569$	−19.6108	+	11.3223i	−0.822126	+	0.474655i	0.0290232	+	0.999579i	$0.490760\pi$
$570$	−30.2599	+	5.52308i	−1.26745	+	0.231336i
$571$	6.73350	−	38.1876i	0.281788	−	1.59810i	−0.434748	−	0.900552i	$-0.643163\pi$
$571$	6.73350	−	38.1876i	0.281788	−	1.59810i	0.716537	−	0.697549i	$-0.245726\pi$
$572$	−0.151236	−	0.126902i	−0.00632348	−	0.00530603i
$573$	−5.24230	−	1.90804i	−0.219000	−	0.0797095i
$574$	−11.9033	+	32.7040i	−0.496834	+	1.36504i
$575$	−24.6505	+	0.295874i	−1.02800	+	0.0123388i
$576$	−0.778430	+	4.41470i	−0.0324346	+	0.183946i
$577$	2.75757	−	15.6390i	0.114799	−	0.651059i	−0.872050	−	0.489417i	$-0.837210\pi$
$577$	2.75757	−	15.6390i	0.114799	−	0.651059i	0.986849	−	0.161642i	$-0.0516791\pi$
$578$	−14.5056	−	25.1244i	−0.603353	−	1.04504i
$579$	4.10613	+	4.89349i	0.170645	+	0.203367i
$580$	−30.9620	+	26.2985i	−1.28563	+	1.09198i
$581$	−21.3903	+	37.0492i	−0.887421	+	1.53706i
$582$	26.8288	−	15.4896i	1.11209	−	0.642065i
$583$	2.01816	−	2.40515i	0.0835838	−	0.0996113i
$584$	17.4999	+	10.1036i	0.724153	+	0.418090i
$585$	−0.305555	+	0.178866i	−0.0126332	+	0.00739519i
$586$			19.9983i			0.826121i
$587$	−1.28044	−	7.26173i	−0.0528494	−	0.299724i	0.946914	−	0.321488i	$-0.104183\pi$
$587$	−1.28044	−	7.26173i	−0.0528494	−	0.299724i	−0.999763	+	0.0217640i	$0.993072\pi$
$588$	0.969863	+	1.15584i	0.0399965	+	0.0476659i
$589$	46.8083	+	17.0368i	1.92870	+	0.701990i
$590$	−50.1096	+	42.5619i	−2.06298	+	1.75225i
$591$	10.5662			0.434636
$592$	−28.8926	−	27.8966i	−1.18748	−	1.14654i
$593$		−	19.4144i		−	0.797252i	−0.917114	−	0.398626i	$-0.869487\pi$
$593$		−	19.4144i		−	0.797252i	0.917114	−	0.398626i	$-0.130513\pi$
$594$	−2.28526	−	6.27869i	−0.0937652	−	0.257618i
$595$	−13.3861	+	0.0803322i	−0.548777	+	0.00329330i
$596$	47.3049	−	39.6935i	1.93768	−	1.62591i
$597$	1.23404	+	6.99859i	0.0505059	+	0.286433i
$598$	−0.765836			−0.0313174
$599$	3.65586	+	20.7334i	0.149374	+	0.847144i	0.963750	+	0.266806i	$0.0859684\pi$
$599$	3.65586	+	20.7334i	0.149374	+	0.847144i	−0.814376	+	0.580338i	$0.802920\pi$
$600$	−19.3895	+	3.65937i	−0.791574	+	0.149393i
$601$	0.811332	+	0.680788i	0.0330949	+	0.0277699i	0.659185	−	0.751981i	$-0.270901\pi$
$601$	0.811332	+	0.680788i	0.0330949	+	0.0277699i	−0.626090	+	0.779751i	$0.715346\pi$
$602$	53.5614	−	30.9237i	2.18300	−	1.26036i
$603$	5.55658	+	3.20809i	0.226281	+	0.130644i
$604$	−30.5260	+	11.1106i	−1.24209	+	0.452082i
$605$	−20.3390	−	11.5806i	−0.826899	−	0.470817i
$606$	−6.89068	+	3.97834i	−0.279915	+	0.161609i
$607$	−5.34525	+	30.3144i	−0.216957	+	1.23043i	0.660521	+	0.750808i	$0.270336\pi$
$607$	−5.34525	+	30.3144i	−0.216957	+	1.23043i	−0.877478	+	0.479617i	$0.840776\pi$
$608$	37.4261	+	6.59923i	1.51783	+	0.267634i
$609$	−4.36861	+	5.20631i	−0.177025	+	0.210970i
$610$	46.4811	−	0.278940i	1.88196	−	0.0112940i
$611$	−0.158468	+	0.435388i	−0.00641095	+	0.0176139i
$612$	−20.4947	−	17.1971i	−0.828449	−	0.695152i
$613$	−23.9478	−	4.22264i	−0.967243	−	0.170551i	−0.332354	−	0.943155i	$-0.607843\pi$
$613$	−23.9478	−	4.22264i	−0.967243	−	0.170551i	−0.634889	+	0.772604i	$0.718954\pi$
$614$	7.13297	+	1.25773i	0.287863	+	0.0507580i
$615$	6.02940	+	4.99791i	0.243129	+	0.201535i
$616$	7.27110	+	8.66536i	0.292961	+	0.349137i
$617$	8.54280	+	23.4712i	0.343920	+	0.944913i	0.984245	+	0.176809i	$0.0565775\pi$
$617$	8.54280	+	23.4712i	0.343920	+	0.944913i	−0.640325	+	0.768104i	$0.721200\pi$
$618$	20.7581	+	11.9847i	0.835015	+	0.482096i
$619$	−10.4311	−	18.0671i	−0.419260	−	0.726179i	0.576606	−	0.817023i	$-0.304377\pi$
$619$	−10.4311	−	18.0671i	−0.419260	−	0.726179i	−0.995865	+	0.0908438i	$0.971044\pi$
$620$	55.1027	+	19.6821i	2.21298	+	0.790451i
$621$	−15.4388	−	8.91362i	−0.619540	−	0.357691i
$622$	−19.6966	+	3.47305i	−0.789763	+	0.139257i
$623$	30.0916			1.20560
$624$	−0.258562	+	0.0455915i	−0.0103508	+	0.00182512i
$625$	−13.0161	−	21.3444i	−0.520642	−	0.853775i
$626$	−31.6120	−	11.5058i	−1.26347	−	0.459865i
$627$	3.72878	−	1.35716i	0.148913	−	0.0541999i
$628$		−	22.1579i		−	0.884196i
$629$	−13.7596	+	3.94675i	−0.548632	+	0.157367i
$630$	34.8307	−	12.9146i	1.38769	−	0.514529i
$631$	−2.06178	−	5.66468i	−0.0820780	−	0.225508i	0.891864	−	0.452303i	$-0.149397\pi$
$631$	−2.06178	−	5.66468i	−0.0820780	−	0.225508i	−0.973942	+	0.226795i	$0.927175\pi$
$632$	−6.07824	+	16.6998i	−0.241779	+	0.664283i
$633$	1.00764	+	1.20086i	0.0400503	+	0.0477300i
$634$	27.8335	−	4.90780i	1.10541	−	0.194914i
$635$	23.7520	−	8.80681i	0.942571	−	0.349488i
$636$	−2.13205	−	12.0914i	−0.0845412	−	0.479457i
$637$	−0.0162157	+	0.0280865i	−0.000642491	+	0.00111283i
$638$	4.89750	−	5.83661i	0.193894	−	0.231074i
$639$	−1.36253	−	2.35997i	−0.0539009	−	0.0933590i
$640$	−29.6693	−	5.04810i	−1.17278	−	0.199544i
$641$	32.4069	−	11.7952i	1.28000	−	0.465881i	0.389565	−	0.920999i	$-0.372625\pi$
$641$	32.4069	−	11.7952i	1.28000	−	0.465881i	0.890431	+	0.455118i	$0.150403\pi$
$642$	−5.35136	+	4.49032i	−0.211201	+	0.177219i
$643$	17.0065	+	29.4562i	0.670673	+	1.16164i	0.977714	+	0.209943i	$0.0673278\pi$
$643$	17.0065	+	29.4562i	0.670673	+	1.16164i	−0.307041	+	0.951696i	$0.599339\pi$
$644$	54.4268	+	9.59691i	2.14472	+	0.378171i
$645$	−2.49890	−	13.6910i	−0.0983943	−	0.539084i
$646$	32.1136	−	38.2715i	1.26349	−	1.50577i
$647$	−21.8014	−	7.93506i	−0.857102	−	0.311960i	−0.124169	−	0.992261i	$-0.539627\pi$
$647$	−21.8014	−	7.93506i	−0.857102	−	0.311960i	−0.732932	+	0.680302i	$0.761849\pi$
$648$	30.8907	+	11.2433i	1.21350	+	0.441678i
$649$	5.45169	−	6.49707i	0.213998	−	0.255032i
$650$	−0.396363	−	0.667879i	−0.0155466	−	0.0261964i
$651$	9.64048	+	1.69988i	0.377840	+	0.0666234i
$652$	18.4514	+	31.9588i	0.722614	+	1.25160i
$653$	21.7973	−	18.2901i	0.852996	−	0.715748i	−0.107452	−	0.994210i	$-0.534269\pi$
$653$	21.7973	−	18.2901i	0.852996	−	0.715748i	0.960447	+	0.278462i	$0.0898246\pi$
$654$	−2.80093	+	1.01946i	−0.109525	+	0.0398639i
$655$	−5.03485	+	29.5914i	−0.196728	+	1.15623i
$656$	−17.8441	−	30.9070i	−0.696697	−	1.20671i
$657$	−5.50265	+	6.55780i	−0.214679	+	0.255844i
$658$	24.3064	−	42.0999i	0.947563	−	1.64123i
$659$	5.95064	+	33.7477i	0.231804	+	1.31463i	0.849241	+	0.528005i	$0.177060\pi$
$659$	5.95064	+	33.7477i	0.231804	+	1.31463i	−0.617437	+	0.786620i	$0.711829\pi$
$660$	4.37038	−	1.62046i	0.170117	−	0.0630762i
$661$	21.5455	−	3.79905i	0.838022	−	0.147766i	0.261865	−	0.965105i	$-0.415663\pi$
$661$	21.5455	−	3.79905i	0.838022	−	0.147766i	0.576157	+	0.817339i	$0.304551\pi$
$662$	42.6437	+	50.8208i	1.65739	+	1.97521i
$663$	−0.0320054	+	0.0879341i	−0.00124299	+	0.00341508i
$664$	−35.0301	−	96.2443i	−1.35943	−	3.73501i
$665$	16.5874	+	44.7365i	0.643234	+	1.73481i
$666$	32.1350	−	23.3515i	1.24520	−	0.904853i
$667$		−	20.3286i		−	0.787127i
$668$	−91.6190	+	33.3466i	−3.54484	+	1.29022i
$669$	−0.553363	−	0.201408i	−0.0213943	−	0.00778688i
$670$	−6.96378	+	12.2305i	−0.269034	+	0.472507i
$671$	−5.90517	+	1.04124i	−0.227966	+	0.0401966i
$672$	7.46850			0.288104
$673$	30.7810	−	5.42753i	1.18652	−	0.209216i	0.454657	−	0.890666i	$-0.349762\pi$
$673$	30.7810	−	5.42753i	1.18652	−	0.209216i	0.731864	+	0.681451i	$0.238651\pi$
$674$	−50.9014	−	29.3880i	−1.96065	−	1.13198i
$675$	−0.216978	−	18.0774i	−0.00835150	−	0.695799i
$676$	28.6324	+	49.5928i	1.10125	+	1.90741i
$677$	−10.8844	−	6.28409i	−0.418320	−	0.241517i	0.276038	−	0.961147i	$-0.410978\pi$
$677$	−10.8844	−	6.28409i	−0.418320	−	0.241517i	−0.694358	+	0.719629i	$0.744312\pi$
$678$	−5.63548	−	15.4834i	−0.216429	−	0.594635i
$679$	−30.8878	−	36.8107i	−1.18537	−	1.41267i
$680$	20.4525	−	24.6736i	0.784318	−	0.946188i
$681$	4.98078	+	0.878246i	0.190864	+	0.0336544i
$682$	−10.8076	−	1.90567i	−0.413845	−	0.0729721i
$683$	15.4028	+	12.9245i	0.589372	+	0.494542i	0.888010	−	0.459825i	$-0.152088\pi$
$683$	15.4028	+	12.9245i	0.589372	+	0.494542i	−0.298638	+	0.954367i	$0.596532\pi$
$684$	−32.6145	+	89.6075i	−1.24705	+	3.42623i
$685$	−33.7452	+	0.202510i	−1.28934	+	0.00773751i
$686$	31.1588	−	37.1336i	1.18965	−	1.41777i
$687$	3.90597	+	0.688728i	0.149022	+	0.0262766i
$688$	−11.0129	+	62.4573i	−0.419863	+	2.38116i
$689$	0.228550	−	0.131953i	0.00870707	−	0.00502703i
$690$	8.94645	−	15.7127i	0.340586	−	0.598173i
$691$	−35.8617	+	13.0526i	−1.36424	+	0.496543i	−0.917363	−	0.398051i	$-0.869687\pi$
$691$	−35.8617	+	13.0526i	−1.36424	+	0.496543i	−0.446878	+	0.894595i	$0.647464\pi$
$692$	59.8155	+	34.5345i	2.27384	+	1.31280i
$693$	−4.15013	+	2.39608i	−0.157650	+	0.0910195i
$694$	6.75073	+	5.66454i	0.256254	+	0.215023i
$695$	−2.55693	−	0.435051i	−0.0969899	−	0.0165024i
$696$	−2.82545	−	16.0239i	−0.107098	−	0.607385i
$697$	−12.7199			−0.481800
$698$	−8.00948	−	45.4240i	−0.303163	−	1.71932i
$699$	−11.7517	+	9.86085i	−0.444490	+	0.372971i
$700$	19.7995	+	52.4320i	0.748352	+	1.98175i
$701$	−14.3463	−	39.4162i	−0.541853	−	1.48873i	−0.844462	−	0.535615i	$-0.820080\pi$
$701$	−14.3463	−	39.4162i	−0.541853	−	1.48873i	0.302609	−	0.953115i	$-0.402142\pi$
$702$		−	0.561623i		−	0.0211971i
$703$	29.9926	+	41.2740i	1.13119	+	1.55668i
$704$	1.26850			0.0478084
$705$	−7.08168	−	8.33749i	−0.266712	−	0.314008i
$706$	−33.7947	−	12.3003i	−1.27188	−	0.462927i
$707$	7.93320	+	9.45442i	0.298359	+	0.355570i
$708$	−5.75933	−	32.6628i	−0.216449	−	1.22754i
$709$			26.7287i			1.00382i	0.864921	+	0.501908i	$0.167369\pi$
$709$			26.7287i			1.00382i	−0.864921	+	0.501908i	$0.832631\pi$
$710$	5.15864	−	3.01976i	0.193600	−	0.113330i
$711$	−6.52011	−	3.76439i	−0.244523	−	0.141176i
$712$	−46.3079	+	55.1876i	−1.73546	+	2.06824i
$713$	−25.3577	+	14.6403i	−0.949654	+	0.548283i
$714$	4.90910	−	8.50280i	0.183718	−	0.318209i
$715$	0.0648589	+	0.0763605i	0.00242559	+	0.00285572i
$716$	−23.4860	−	27.9895i	−0.877714	−	1.04602i
$717$	1.49331	+	2.58649i	0.0557687	+	0.0965943i
$718$	3.52705	−	20.0029i	0.131628	−	0.746500i
$719$	3.46717	−	19.6633i	0.129303	−	0.733316i	−0.849355	−	0.527822i	$-0.823009\pi$
$719$	3.46717	−	19.6633i	0.129303	−	0.733316i	0.978658	−	0.205494i	$-0.0658802\pi$
$720$	−12.8135	+	35.8732i	−0.477531	+	1.33692i
$721$	12.7162	−	34.9376i	0.473578	−	1.30114i
$722$	−122.142	−	44.4559i	−4.54564	−	1.65448i
$723$	−4.05425	−	3.40192i	−0.150779	−	0.126519i
$724$	−6.10374	+	34.6160i	−0.226844	+	1.28649i
$725$	17.7284	−	10.5212i	0.658417	−	0.390748i
$726$	14.8664	−	8.58310i	0.551743	−	0.318549i
$727$	2.04384	−	1.71498i	0.0758017	−	0.0636052i	−0.604100	−	0.796909i	$-0.706467\pi$
$727$	2.04384	−	1.71498i	0.0758017	−	0.0636052i	0.679901	+	0.733304i	$0.262023\pi$
$728$	0.325197	+	0.893471i	0.0120526	+	0.0331142i
$729$	−3.44891	+	5.97369i	−0.127738	+	0.221248i
$730$	−14.4569	−	11.9837i	−0.535075	−	0.443536i
$731$	17.3158	+	14.5297i	0.640449	+	0.537401i
$732$	−11.7243	+	20.3072i	−0.433344	+	0.750574i
$733$	2.72457	−	0.480416i	0.100634	−	0.0177446i	−0.123104	−	0.992394i	$-0.539285\pi$
$733$	2.72457	−	0.480416i	0.100634	−	0.0177446i	0.223739	+	0.974649i	$0.428174\pi$
$734$		−	15.6205i		−	0.576563i
$735$	−0.386822	−	0.660805i	−0.0142681	−	0.0243741i
$736$	−17.1127	+	14.3593i	−0.630784	+	0.529291i
$737$	0.620968	−	1.70610i	0.0228736	−	0.0628448i
$738$	33.1697	−	12.0728i	1.22099	−	0.444405i
$739$	10.7848			0.396724			0.198362	−	0.980129i	$-0.436438\pi$
$739$	10.7848			0.396724			0.198362	+	0.980129i	$0.436438\pi$
$740$	35.5213	+	48.2705i	1.30579	+	1.77446i
$741$	0.333536			0.0122527
$742$	−26.0193	+	9.47027i	−0.955200	+	0.347664i
$743$	−3.04728	+	8.37232i	−0.111794	+	0.307151i	−0.982955	−	0.183846i	$-0.941145\pi$
$743$	−3.04728	+	8.37232i	−0.111794	+	0.307151i	0.871161	+	0.490997i	$0.163367\pi$
$744$	−17.9532	+	15.0646i	−0.658198	+	0.552293i
$745$	−27.0447	+	15.8314i	−0.990841	+	0.580018i
$746$			50.5395i			1.85038i
$747$	42.7306	−	7.53456i	1.56343	−	0.275675i
$748$	−3.78528	+	6.55630i	−0.138404	+	0.239722i
$749$	8.30068	+	6.96510i	0.303300	+	0.254499i
$750$	18.3332	−	0.330093i	0.669434	−	0.0120533i
$751$	20.4223	−	35.3724i	0.745219	−	1.29076i	−0.204873	−	0.978789i	$-0.565678\pi$
$751$	20.4223	−	35.3724i	0.745219	−	1.29076i	0.950092	−	0.311969i	$-0.100988\pi$
$752$	17.0495	+	46.8432i	0.621733	+	1.70820i
$753$	0.0658621	−	0.0552648i	0.00240015	−	0.00201396i
$754$	0.554625	−	0.320213i	0.0201982	−	0.0116615i
$755$	16.2175	−	2.96003i	0.590214	−	0.107727i
$756$	−7.03786	+	39.9137i	−0.255965	+	1.45165i
$757$	11.5293	+	9.67421i	0.419039	+	0.351615i	0.827797	−	0.561027i	$-0.189594\pi$
$757$	11.5293	+	9.67421i	0.419039	+	0.351615i	−0.408759	+	0.912643i	$0.634038\pi$
$758$	−54.9001	−	19.9820i	−1.99406	−	0.725779i
$759$	−0.797765	+	2.19184i	−0.0289570	+	0.0795588i
$760$	−107.572	−	38.4236i	−3.90206	−	1.39377i
$761$	7.37397	−	41.8198i	0.267306	−	1.51597i	−0.495081	−	0.868847i	$-0.664862\pi$
$761$	7.37397	−	41.8198i	0.267306	−	1.51597i	0.762387	−	0.647121i	$-0.224027\pi$
$762$	−3.22635	+	18.2976i	−0.116878	+	0.662851i
$763$	2.31173	+	4.00403i	0.0836901	+	0.144955i
$764$	−24.3849	−	29.0608i	−0.882216	−	1.05138i
$765$	8.78936	+	10.3480i	0.317780	+	0.374132i
$766$	16.8763	−	29.2307i	0.609767	−	1.05615i
$767$	0.617385	−	0.356447i	0.0222925	−	0.0128706i
$768$	12.7413	−	15.1845i	0.459764	−	0.547925i
$769$	15.9071	+	9.18396i	0.573624	+	0.331182i	0.758596	−	0.651562i	$-0.225886\pi$
$769$	15.9071	+	9.18396i	0.573624	+	0.331182i	−0.184971	+	0.982744i	$0.559219\pi$
$770$	−5.31041	−	9.07174i	−0.191374	−	0.326923i
$771$		−	15.6159i		−	0.562391i
$772$	7.54317	+	42.7794i	0.271485	+	1.53967i
$773$	13.2119	+	15.7453i	0.475199	+	0.566320i	0.949389	−	0.314102i	$-0.101703\pi$
$773$	13.2119	+	15.7453i	0.475199	+	0.566320i	−0.474190	+	0.880423i	$0.657259\pi$
$774$	−58.9450	−	21.4542i	−2.11873	−	0.771156i
$775$	−25.8917	−	14.5371i	−0.930057	−	0.522187i
$776$	115.043			4.12982
$777$	7.21315	+	6.96450i	0.258770	+	0.249850i
$778$		−	90.8217i		−	3.25612i
$779$	15.5062	+	42.6030i	0.555568	+	1.52641i
$780$	0.391783	−	0.00235115i	0.0140281	−	8.41847e-5i
$781$	−0.590705	+	0.495661i	−0.0211371	+	0.0177361i
$782$	5.09957	+	28.9211i	0.182360	+	1.03422i
$783$	14.9079			0.532766
$784$	0.605909	+	3.43628i	0.0216396	+	0.122724i
$785$	−1.88611	+	11.0853i	−0.0673182	+	0.395650i
$786$	−16.8650	−	14.1514i	−0.601553	−	0.504763i
$787$	36.9329	−	21.3232i	1.31652	−	0.760091i	0.333350	−	0.942803i	$-0.391821\pi$
$787$	36.9329	−	21.3232i	1.31652	−	0.760091i	0.983167	+	0.182712i	$0.0584875\pi$
$788$	62.2255	+	35.9259i	2.21669	+	1.27981i
$789$	−6.99347	+	2.54541i	−0.248974	+	0.0906191i
$790$	8.17133	−	14.3514i	0.290723	−	0.510599i
$791$	−22.1340	+	12.7791i	−0.786993	+	0.454371i
$792$	1.99225	−	11.2986i	0.0707914	−	0.401478i
$793$	−0.496357	−	0.0875211i	−0.0176261	−	0.00310796i
$794$	21.5891	−	25.7289i	0.766170	−	0.913086i
$795$	0.0373912	+	6.23066i	0.00132613	+	0.220979i
$796$	−16.5283	+	45.4113i	−0.585832	+	1.60956i
$797$	15.6865	+	13.1626i	0.555646	+	0.466242i	0.876848	−	0.480769i	$-0.159642\pi$
$797$	15.6865	+	13.1626i	0.555646	+	0.466242i	−0.321202	+	0.947011i	$0.604087\pi$
$798$	−34.4631	−	6.07677i	−1.21998	−	0.215115i
$799$	17.4973	+	3.08524i	0.619009	+	0.109148i
$800$	−21.3794	−	7.49213i	−0.755876	−	0.264887i
$801$	−19.6179	−	23.3797i	−0.693166	−	0.826083i
$802$	19.3253	+	53.0959i	0.682402	+	1.87488i
$803$	2.09786	+	1.21120i	0.0740317	+	0.0427422i
$804$	−3.54997	−	6.14874i	−0.125198	−	0.216849i
$805$	−26.4120	−	9.43408i	−0.930901	−	0.332507i
$806$	−0.798860	−	0.461222i	−0.0281387	−	0.0162459i
$807$	−13.8262	+	2.43793i	−0.486705	+	0.0858192i
$808$	−29.5476			−1.03948
$809$	−36.3180	+	6.40385i	−1.27687	+	0.225147i	−0.770652	−	0.637256i	$-0.780069\pi$
$809$	−36.3180	+	6.40385i	−1.27687	+	0.225147i	−0.506222	+	0.862403i	$0.668958\pi$
$810$	−26.5466	−	15.1150i	−0.932753	−	0.531087i
$811$	1.50134	+	0.546444i	0.0527193	+	0.0191882i	0.368245	−	0.929729i	$-0.379959\pi$
$811$	1.50134	+	0.546444i	0.0527193	+	0.0191882i	−0.315526	+	0.948917i	$0.602181\pi$
$812$	−43.4290	+	15.8069i	−1.52406	+	0.554712i
$813$		−	13.2463i		−	0.464568i
$814$	−8.08642	−	7.80766i	−0.283429	−	0.273658i
$815$	−6.51060	−	17.5591i	−0.228056	−	0.615070i
$816$	3.44345	+	9.46079i	0.120545	+	0.331194i
$817$	27.5557	−	75.7088i	0.964053	−	2.64872i
$818$	−10.3319	−	12.3131i	−0.361248	−	0.430519i
$819$	−0.396684	+	0.0699460i	−0.0138612	+	0.00244411i
$820$	18.5145	+	49.9336i	0.646553	+	1.74376i
$821$	5.74522	+	32.5828i	0.200510	+	1.13715i	0.904351	+	0.426789i	$0.140355\pi$
$821$	5.74522	+	32.5828i	0.200510	+	1.13715i	−0.703841	+	0.710357i	$0.748533\pi$
$822$	12.3754	−	21.4348i	0.431641	−	0.747624i
$823$	−16.1524	+	19.2497i	−0.563039	+	0.671003i	−0.970187	−	0.242359i	$-0.922079\pi$
$823$	−16.1524	+	19.2497i	−0.563039	+	0.671003i	0.407148	+	0.913362i	$0.366523\pi$
$824$	44.5060	+	77.0867i	1.55044	+	2.68544i
$825$	−2.32437	+	0.438677i	−0.0809243	+	0.0152728i
$826$	−70.2864	+	25.5821i	−2.44558	+	0.890117i
$827$	−4.14180	+	3.47538i	−0.144024	+	0.120851i	−0.711953	−	0.702227i	$-0.752189\pi$
$827$	−4.14180	+	3.47538i	−0.144024	+	0.120851i	0.567929	+	0.823078i	$0.307745\pi$
$828$	−28.0266	−	48.5436i	−0.973993	−	1.68701i
$829$	−19.1941	−	3.38444i	−0.666640	−	0.117547i	−0.169920	−	0.985458i	$-0.554351\pi$
$829$	−19.1941	−	3.38444i	−0.666640	−	0.117547i	−0.496719	+	0.867911i	$0.665462\pi$
$830$	17.0895	+	93.6301i	0.593185	+	3.24995i
$831$	−7.30916	+	8.71071i	−0.253552	+	0.302171i
$832$	0.100193	+	0.0364673i	0.00347357	+	0.00126428i
$833$	1.16864	+	0.425350i	0.0404910	+	0.0147375i
$834$	1.22279	−	1.45727i	0.0423418	−	0.0504610i
$835$	48.6741	−	8.88406i	1.68444	−	0.307446i
$836$	26.5736	+	4.68565i	0.919068	+	0.162057i
$837$	−10.7364	−	18.5960i	−0.371104	−	0.642772i
$838$	11.4846	−	9.63672i	0.396729	−	0.332895i
$839$	−0.106901	+	0.0389088i	−0.00369064	+	0.00134328i	−0.343865	−	0.939019i	$-0.611736\pi$
$839$	−0.106901	+	0.0389088i	−0.00369064	+	0.00134328i	0.340174	+	0.940362i	$0.389514\pi$
$840$	−22.1303	−	3.76539i	−0.763570	−	0.129918i
$841$	−6.00016	−	10.3926i	−0.206902	−	0.358365i
$842$	44.1976	−	52.6726i	1.52315	−	1.81522i
$843$	−6.05704	+	10.4911i	−0.208616	+	0.361333i
$844$	1.85109	+	10.4981i	0.0637173	+	0.361359i
$845$	−10.1030	−	27.2478i	−0.347552	−	0.937352i
$846$	−48.5559	+	8.56172i	−1.66939	+	0.294358i
$847$	−17.1156	−	20.3975i	−0.588098	−	0.700867i
$848$	9.71119	−	26.6813i	0.333484	−	0.916239i
$849$	−0.285262	−	0.783751i	−0.00979017	−	0.0268983i
$850$	−22.5825	+	19.4156i	−0.774575	+	0.665950i
$851$	−29.9179	−	2.08955i	−1.02557	−	0.0716289i
$852$			3.01547i			0.103308i
$853$	−31.8107	+	11.5781i	−1.08918	+	0.396428i	−0.823316	−	0.567584i	$-0.807878\pi$
$853$	−31.8107	+	11.5781i	−1.08918	+	0.396428i	−0.265861	+	0.964011i	$0.585656\pi$
$854$	49.6922	+	18.0865i	1.70043	+	0.618906i
$855$	23.9441	−	42.0531i	0.818870	−	1.43819i
$856$	−25.5478	+	4.50476i	−0.873204	+	0.153969i
$857$	−42.2128			−1.44196			−0.720980	−	0.692956i	$-0.756308\pi$
$857$	−42.2128			−1.44196			−0.720980	+	0.692956i	$0.756308\pi$
$858$	−0.0723662	+	0.0127601i	−0.00247054	+	0.000435623i
$859$	25.6416	+	14.8042i	0.874881	+	0.505113i	0.868967	−	0.494870i	$-0.164784\pi$
$859$	25.6416	+	14.8042i	0.874881	+	0.505113i	0.00591380	+	0.999983i	$0.498118\pi$
$860$	31.8342	−	89.1243i	1.08554	−	3.03911i
$861$	4.45487	+	7.71606i	0.151821	+	0.262962i
$862$	61.7640	+	35.6595i	2.10369	+	1.21457i
$863$	6.20387	+	17.0450i	0.211182	+	0.580218i	0.999380	−	0.0352036i	$-0.0112080\pi$
$863$	6.20387	+	17.0450i	0.211182	+	0.580218i	−0.788198	+	0.615422i	$0.788986\pi$
$864$	−10.5303	−	12.5496i	−0.358250	−	0.426945i
$865$	−26.9852	−	22.3687i	−0.917523	−	0.760557i
$866$	18.3109	+	3.22870i	0.622229	+	0.109716i
$867$	−7.31419	−	1.28969i	−0.248403	−	0.0438001i
$868$	50.9941	+	42.7891i	1.73085	+	1.45236i
$869$	−0.728646	+	2.00194i	−0.0247176	+	0.0679111i
$870$	0.0907375	+	15.1200i	0.00307629	+	0.512616i
$871$	0.0980950	−	0.116905i	0.00332382	−	0.00396118i
$872$	−10.9008	−	1.92211i	−0.369148	−	0.0650908i
$873$	−8.46312	+	47.9967i	−0.286433	+	1.62444i
$874$	90.6495	−	52.3365i	3.06626	−	1.77031i
$875$	−5.44232	−	27.9163i	−0.183984	−	0.943745i
$876$	8.90161	−	3.23992i	0.300758	−	0.109467i
$877$	25.5661	+	14.7606i	0.863307	+	0.498430i	0.865118	−	0.501568i	$-0.167243\pi$
$877$	25.5661	+	14.7606i	0.863307	+	0.498430i	−0.00181136	+	0.999998i	$0.500577\pi$
$878$	−12.3462	+	7.12810i	−0.416665	+	0.240562i
$879$	3.92189	+	3.29086i	0.132282	+	0.110998i
$880$	10.6265	+	1.80805i	0.358218	+	0.0609492i
$881$	1.09145	+	6.18991i	0.0367718	+	0.208543i	0.997658	−	0.0684004i	$-0.0217896\pi$
$881$	1.09145	+	6.18991i	0.0367718	+	0.208543i	−0.960886	+	0.276944i	$0.910678\pi$
$882$	−3.45117			−0.116207
$883$	9.55471	+	54.1874i	0.321541	+	1.82355i	0.532941	+	0.846153i	$0.321087\pi$
$883$	9.55471	+	54.1874i	0.321541	+	1.82355i	−0.211399	+	0.977400i	$0.567802\pi$
$884$	−0.487466	+	0.409032i	−0.0163953	+	0.0137572i
$885$	0.101005	+	16.8309i	0.00339525	+	0.565766i
$886$	11.9896	+	32.9411i	0.402798	+	1.10668i
$887$			21.2474i			0.713418i	0.934216	+	0.356709i	$0.116101\pi$
$887$			21.2474i			0.713418i	−0.934216	+	0.356709i	$0.883899\pi$
$888$	−23.8731	+	2.51118i	−0.801128	+	0.0842697i
$889$	28.8198			0.966585
$890$	51.0250	−	43.3395i	1.71036	−	1.45274i
$891$	3.70311	+	1.34782i	0.124059	+	0.0451537i
$892$	−2.57401	−	3.06759i	−0.0861843	−	0.102710i
$893$	−10.9966	−	62.3651i	−0.367989	−	2.08697i
$894$		−	22.9845i		−	0.768718i
$895$	9.36720	+	16.0019i	0.313111	+	0.534885i
$896$	−29.6519	−	17.1196i	−0.990602	−	0.571924i
$897$	−0.126024	+	0.150189i	−0.00420781	+	0.00501468i
$898$	−84.1150	+	48.5638i	−2.80695	+	1.62060i
$899$	12.2428	−	21.2052i	0.408322	−	0.707234i
$900$	27.8291	−	49.5658i	0.927635	−	1.65219i
$901$	−6.50499	−	7.75234i	−0.216712	−	0.258268i
$902$	−4.99420	−	8.65021i	−0.166289	−	0.288021i
$903$	2.74942	−	15.5927i	0.0914949	−	0.518894i
$904$	10.6253	−	60.2590i	0.353392	−	2.00418i
$905$	6.00018	−	16.7983i	0.199453	−	0.558395i
$906$	−4.13542	+	11.3620i	−0.137390	+	0.377476i
$907$	0.270402	+	0.0984185i	0.00897857	+	0.00326793i	0.346506	−	0.938048i	$-0.387368\pi$
$907$	0.270402	+	0.0984185i	0.00897857	+	0.00326793i	−0.337527	+	0.941316i	$0.609590\pi$
$908$	26.3462	+	22.1071i	0.874330	+	0.733650i
$909$	2.17366	−	12.3274i	0.0720957	−	0.408875i
$910$	−0.158648	−	0.869202i	−0.00525912	−	0.0288138i
$911$	7.09183	−	4.09447i	0.234963	−	0.135656i	−0.377897	−	0.925848i	$-0.623353\pi$
$911$	7.09183	−	4.09447i	0.234963	−	0.135656i	0.612859	+	0.790192i	$0.290019\pi$
$912$	27.4895	−	23.0664i	0.910268	−	0.763806i
$913$	−4.19933	−	11.5376i	−0.138978	−	0.381838i
$914$	−16.5229	+	28.6186i	−0.546531	+	0.946619i
$915$	7.59409	−	9.16138i	0.251053	−	0.302866i
$916$	20.6609	+	17.3366i	0.682657	+	0.572817i
$917$	−17.0746	+	29.5741i	−0.563853	+	0.976623i
$918$	−21.2092	+	3.73976i	−0.700009	+	0.123430i
$919$			52.4386i			1.72979i	0.501953	+	0.864895i	$0.332615\pi$
$919$			52.4386i			1.72979i	−0.501953	+	0.864895i	$0.667385\pi$
$920$	57.9473	−	33.9212i	1.91046	−	1.11835i
$921$	1.42044	−	1.19189i	0.0468050	−	0.0392741i
$922$	−6.20103	+	17.0372i	−0.204220	+	0.561090i
$923$	−0.0609066	+	0.0221682i	−0.00200477	+	0.000729675i
$924$	5.30285			0.174451
$925$	−13.6619	−	27.1726i	−0.449202	−	0.893430i
$926$	55.1645			1.81282
$927$	−35.4351	+	12.8973i	−1.16384	+	0.423603i
$928$	6.38926	−	17.5543i	0.209738	−	0.576249i
$929$	31.8458	−	26.7218i	1.04483	−	0.876714i	0.0522868	−	0.998632i	$-0.483349\pi$
$929$	31.8458	−	26.7218i	1.04483	−	0.876714i	0.992540	+	0.121918i	$0.0389046\pi$
$930$	18.7952	−	11.0023i	0.616318	−	0.360780i
$931$		−	4.43267i		−	0.145275i
$932$	−102.735	+	18.1149i	−3.36518	+	0.593373i
$933$	−2.56012	+	4.43425i	−0.0838145	+	0.145171i
$934$	−58.8790	−	49.4054i	−1.92658	−	1.61659i
$935$	2.45180	−	2.95781i	0.0801826	−	0.0967308i
$936$	0.482175	−	0.835151i	0.0157604	−	0.0272978i
$937$	−2.40430	−	6.60577i	−0.0785452	−	0.215801i	0.894205	−	0.447658i	$-0.147742\pi$
$937$	−2.40430	−	6.60577i	−0.0785452	−	0.215801i	−0.972750	+	0.231857i	$0.925520\pi$
$938$	−12.2657	+	10.2922i	−0.400490	+	0.336051i
$939$	−7.45841	+	4.30611i	−0.243396	+	0.140525i
$940$	−13.3567	−	73.1786i	−0.435646	−	2.38682i
$941$	−5.49830	+	31.1824i	−0.179239	+	1.01652i	0.753897	+	0.656993i	$0.228172\pi$
$941$	−5.49830	+	31.1824i	−0.179239	+	1.01652i	−0.933136	+	0.359524i	$0.882939\pi$
$942$	−6.31780	−	5.30127i	−0.205845	−	0.172725i
$943$	−25.0428	−	9.11483i	−0.815506	−	0.296820i
$944$	26.2330	−	72.0745i	0.853810	−	2.34582i
$945$	6.91845	−	19.3692i	0.225057	−	0.630079i
$946$	−3.08228	+	17.4805i	−0.100214	+	0.568340i
$947$	4.29057	−	24.3330i	0.139425	−	0.790718i	−0.832251	−	0.554399i	$-0.812948\pi$
$947$	4.29057	−	24.3330i	0.139425	−	0.790718i	0.971676	−	0.236318i	$-0.0759409\pi$
$948$	4.16556	+	7.21495i	0.135291	+	0.234331i
$949$	0.130880	+	0.155977i	0.00424856	+	0.00506323i
$950$	92.5584	+	51.9675i	3.00299	+	1.68605i
$951$	3.61773	−	6.26609i	0.117313	−	0.203192i
$952$	31.5757	−	18.2302i	1.02337	−	0.590846i
$953$	20.4996	−	24.4305i	0.664048	−	0.791381i	−0.323913	−	0.946087i	$-0.604998\pi$
$953$	20.4996	−	24.4305i	0.664048	−	0.791381i	0.987961	+	0.154705i	$0.0494429\pi$
$954$	24.3210	+	14.0417i	0.787421	+	0.454618i
$955$	9.72573	+	16.6144i	0.314717	+	0.537629i
$956$			20.3095i			0.656856i
$957$	−0.338709	−	1.92091i	−0.0109489	−	0.0620943i
$958$	7.69154	+	9.16642i	0.248502	+	0.296154i
$959$	−36.0764	−	13.1307i	−1.16497	−	0.424014i
$960$	−1.91865	+	1.62966i	−0.0619242	+	0.0525971i
$961$	−4.26826			−0.137686
$962$	−0.414253	−	0.849164i	−0.0133561	−	0.0273781i
$963$		−	10.9900i		−	0.354149i
$964$	−12.3091	−	33.8190i	−0.396450	−	1.08924i
$965$	−0.132290	−	22.0440i	−0.00425855	−	0.709622i
$966$	15.7579	−	13.2225i	0.507003	−	0.425426i
$967$	5.13745	+	29.1359i	0.165209	+	0.936948i	0.948848	+	0.315732i	$0.102250\pi$
$967$	5.13745	+	29.1359i	0.165209	+	0.936948i	−0.783639	+	0.621216i	$0.786639\pi$
$968$	63.7478			2.04893
$969$	−2.22096	−	12.5957i	−0.0713475	−	0.404632i
$970$	−105.392	−	17.9320i	−3.38393	−	0.575761i
$971$	−7.37611	−	6.18929i	−0.236711	−	0.198624i	0.516714	−	0.856158i	$-0.327155\pi$
$971$	−7.37611	−	6.18929i	−0.236711	−	0.198624i	−0.753425	+	0.657534i	$0.771600\pi$
$972$	54.7382	−	31.6031i	1.75573	−	1.01367i
$973$	−2.55544	−	1.47538i	−0.0819235	−	0.0472986i
$974$	−59.8731	+	21.7920i	−1.91846	+	0.698262i
$975$	−0.196203	−	0.0321728i	−0.00628353	−	0.00103036i
$976$	−46.9616	+	27.1133i	−1.50321	+	0.867876i
$977$	4.12229	−	23.3787i	0.131884	−	0.747949i	−0.845096	−	0.534615i	$-0.820457\pi$
$977$	4.12229	−	23.3787i	0.131884	−	0.747949i	0.976979	−	0.213334i	$-0.0684323\pi$
$978$	13.5268	+	2.38514i	0.432540	+	0.0762684i
$979$	−5.55129	+	6.61577i	−0.177420	+	0.211441i
$980$	−0.0312466	−	5.20677i	−0.000998138	−	0.166324i
$981$	1.60383	−	4.40648i	0.0512063	−	0.140688i
$982$	13.1147	+	11.0045i	0.418507	+	0.351169i
$983$	−0.771655	−	0.136064i	−0.0246120	−	0.00433975i	0.161329	−	0.986901i	$-0.448422\pi$
$983$	−0.771655	−	0.136064i	−0.0246120	−	0.00433975i	−0.185941	+	0.982561i	$0.559533\pi$
$984$	−21.0067	−	3.70405i	−0.669669	−	0.118081i
$985$	−28.0724	−	23.2699i	−0.894462	−	0.741441i
$986$	−15.7857	−	18.8127i	−0.502720	−	0.599118i
$987$	−4.25649	−	11.6946i	−0.135486	−	0.372244i
$988$	1.96423	+	1.13405i	0.0624904	+	0.0360789i
$989$	23.6795	+	41.0141i	0.752965	+	1.30417i
$990$	−3.58623	+	10.0402i	−0.113978	+	0.319097i
$991$	1.22110	+	0.705004i	0.0387896	+	0.0223952i	0.519269	−	0.854611i	$-0.326204\pi$
$991$	1.22110	+	0.705004i	0.0387896	+	0.0223952i	−0.480480	+	0.877006i	$0.659537\pi$
$992$	−26.4985	+	4.67240i	−0.841329	+	0.148349i
$993$	16.9839			0.538967
$994$	6.69715	−	1.18089i	0.212421	−	0.0374555i
$995$	12.1344	−	21.3117i	0.384685	−	0.675625i
$996$	−45.1182	−	16.4217i	−1.42963	−	0.520341i
$997$	42.6240	−	15.5139i	1.34992	−	0.491329i	0.436995	−	0.899464i	$-0.356043\pi$
$997$	42.6240	−	15.5139i	1.34992	−	0.491329i	0.912922	+	0.408135i	$0.133821\pi$
$998$		−	14.1746i		−	0.448688i
$999$	1.53237	−	21.9402i	0.0484819	−	0.694158i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.v.a.104.16	yes	96
5.2	odd	4		925.2.bb.e.326.16		96
5.3	odd	4		925.2.bb.e.326.1		96
5.4	even	2	inner	185.2.v.a.104.1	✓	96
37.21	even	18	inner	185.2.v.a.169.1	yes	96
185.58	odd	36		925.2.bb.e.576.1		96
185.132	odd	36		925.2.bb.e.576.16		96
185.169	even	18	inner	185.2.v.a.169.16	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.104.1	✓	96	5.4	even	2	inner
185.2.v.a.104.16	yes	96	1.1	even	1	trivial
185.2.v.a.169.1	yes	96	37.21	even	18	inner
185.2.v.a.169.16	yes	96	185.169	even	18	inner
925.2.bb.e.326.1		96	5.3	odd	4
925.2.bb.e.326.16		96	5.2	odd	4
925.2.bb.e.576.1		96	185.58	odd	36
925.2.bb.e.576.16		96	185.132	odd	36

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

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	185.2.v.a.104.16

Level	$185$
Weight	$2$
Character	185.104
Analytic conductor	$1.477$
Analytic rank	$0$
Dimension	$96$
Inner twists	$4$