LMFDB - Embedded newform 154.2.i.a.87.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(87,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("154.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.22969619113$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			87.8
Root			$0.601150 + 2.24352i$ of defining polynomial
Character	$\chi$	$=$	154.87
Dual form			154.2.i.a.131.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(2.24749 + 1.29759i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.06486 + 1.76950i) q^{5} +2.59518 q^{6} +(0.649221 - 2.56486i) q^{7} -1.00000i q^{8} +(1.86747 + 3.23456i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(2.24749 + 1.29759i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.06486 + 1.76950i) q^{5} +2.59518 q^{6} +(0.649221 - 2.56486i) q^{7} -1.00000i q^{8} +(1.86747 + 3.23456i) q^{9} +(-1.76950 + 3.06486i) q^{10} +(3.22122 - 0.789769i) q^{11} +(2.24749 - 1.29759i) q^{12} -5.01680 q^{13} +(-0.720188 - 2.54585i) q^{14} -9.18432 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.94681 + 3.37197i) q^{17} +(3.23456 + 1.86747i) q^{18} +(-2.32819 - 4.03254i) q^{19} +3.53900i q^{20} +(4.78725 - 4.92208i) q^{21} +(2.39477 - 2.29457i) q^{22} +(0.779812 + 1.35067i) q^{23} +(1.29759 - 2.24749i) q^{24} +(3.76225 - 6.51641i) q^{25} +(-4.34467 + 2.50840i) q^{26} +1.90732i q^{27} +(-1.89662 - 1.84467i) q^{28} +0.100205i q^{29} +(-7.95386 + 4.59216i) q^{30} +(-0.242252 - 0.139864i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(8.26446 + 2.40482i) q^{33} +3.89362i q^{34} +(2.54874 + 9.00974i) q^{35} +3.73495 q^{36} +(-0.352715 - 0.610920i) q^{37} +(-4.03254 - 2.32819i) q^{38} +(-11.2752 - 6.50974i) q^{39} +(1.76950 + 3.06486i) q^{40} +2.94809 q^{41} +(1.68484 - 6.65627i) q^{42} +9.03556i q^{43} +(0.926651 - 3.18454i) q^{44} +(-11.4471 - 6.60898i) q^{45} +(1.35067 + 0.779812i) q^{46} +(5.68935 - 3.28475i) q^{47} -2.59518i q^{48} +(-6.15702 - 3.33032i) q^{49} -7.52450i q^{50} +(-8.75087 + 5.05232i) q^{51} +(-2.50840 + 4.34467i) q^{52} +(-2.77029 + 4.79828i) q^{53} +(0.953659 + 1.65179i) q^{54} +(-8.47510 + 8.12048i) q^{55} +(-2.56486 - 0.649221i) q^{56} -12.0841i q^{57} +(0.0501023 + 0.0867797i) q^{58} +(12.5871 + 7.26719i) q^{59} +(-4.59216 + 7.95386i) q^{60} +(5.56360 + 9.63644i) q^{61} -0.279729 q^{62} +(9.50860 - 2.68987i) q^{63} -1.00000 q^{64} +(15.3758 - 8.87721i) q^{65} +(8.35964 - 2.04959i) q^{66} +(-1.99196 + 3.45017i) q^{67} +(1.94681 + 3.37197i) q^{68} +4.04750i q^{69} +(6.71215 + 6.52829i) q^{70} -8.45381 q^{71} +(3.23456 - 1.86747i) q^{72} +(1.94885 - 3.37552i) q^{73} +(-0.610920 - 0.352715i) q^{74} +(16.9112 - 9.76370i) q^{75} -4.65637 q^{76} +(0.0656384 - 8.77472i) q^{77} -13.0195 q^{78} +(6.66824 - 3.84991i) q^{79} +(3.06486 + 1.76950i) q^{80} +(3.12751 - 5.41700i) q^{81} +(2.55312 - 1.47405i) q^{82} +2.87320 q^{83} +(-1.86902 - 6.60692i) q^{84} -13.7795i q^{85} +(4.51778 + 7.82503i) q^{86} +(-0.130024 + 0.225209i) q^{87} +(-0.789769 - 3.22122i) q^{88} +(-5.15200 + 2.97451i) q^{89} -13.2180 q^{90} +(-3.25701 + 12.8674i) q^{91} +1.55962 q^{92} +(-0.362973 - 0.628687i) q^{93} +(3.28475 - 5.68935i) q^{94} +(14.2711 + 8.23945i) q^{95} +(-1.29759 - 2.24749i) q^{96} -16.7587i q^{97} +(-6.99730 + 0.194366i) q^{98} +(8.57010 + 8.94436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 - 12 * q^5 + 16 * q^9	$ 16 q + 8 q^{4} - 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} - 36 q^{26} - 12 q^{31} - 24 q^{33} + 32 q^{36} - 16 q^{37} + 12 q^{38} + 12 q^{42} - 8 q^{44} - 108 q^{45} + 24 q^{47} + 8 q^{49} - 28 q^{53} - 4 q^{56} - 12 q^{58} + 60 q^{59} - 4 q^{60} - 16 q^{64} + 48 q^{66} + 12 q^{67} + 60 q^{70} + 8 q^{71} + 60 q^{75} + 44 q^{77} - 16 q^{78} + 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} + 96 q^{89} - 36 q^{91} + 32 q^{92} - 44 q^{93} + 56 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 - 12 * q^5 + 16 * q^9 + 8 * q^11 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^22 + 16 * q^23 - 36 * q^26 - 12 * q^31 - 24 * q^33 + 32 * q^36 - 16 * q^37 + 12 * q^38 + 12 * q^42 - 8 * q^44 - 108 * q^45 + 24 * q^47 + 8 * q^49 - 28 * q^53 - 4 * q^56 - 12 * q^58 + 60 * q^59 - 4 * q^60 - 16 * q^64 + 48 * q^66 + 12 * q^67 + 60 * q^70 + 8 * q^71 + 60 * q^75 + 44 * q^77 - 16 * q^78 + 12 * q^80 - 8 * q^81 + 20 * q^86 - 4 * q^88 + 96 * q^89 - 36 * q^91 + 32 * q^92 - 44 * q^93 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	2.24749	+	1.29759i	1.29759	+	0.749163i	0.979987	−	0.199061i	$-0.0637892\pi$
$3$	2.24749	+	1.29759i	1.29759	+	0.749163i	0.317602	+	0.948224i	$0.397123\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−3.06486	+	1.76950i	−1.37065	+	0.791344i	−0.991010	−	0.133791i	$-0.957285\pi$
$5$	−3.06486	+	1.76950i	−1.37065	+	0.791344i	−0.379638	+	0.925135i	$0.623951\pi$
$6$	2.59518			1.05948
$7$	0.649221	−	2.56486i	0.245383	−	0.969426i
$7$	0.649221	−	2.56486i	0.245383	−	0.969426i
$8$		−	1.00000i		−	0.353553i
$9$	1.86747	+	3.23456i	0.622491	+	1.07819i
$10$	−1.76950	+	3.06486i	−0.559564	+	0.969194i
$11$	3.22122	−	0.789769i	0.971235	−	0.238124i
$11$	3.22122	−	0.789769i	0.971235	−	0.238124i
$12$	2.24749	−	1.29759i	0.648794	−	0.374582i
$13$	−5.01680			−1.39141			−0.695704	−	0.718328i	$-0.744908\pi$
$13$	−5.01680			−1.39141			−0.695704	+	0.718328i	$0.744908\pi$
$14$	−0.720188	−	2.54585i	−0.192478	−	0.680406i
$15$	−9.18432			−2.37138
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.94681	+	3.37197i	−0.472171	+	0.817824i	−0.999493	−	0.0318416i	$-0.989863\pi$
$17$	−1.94681	+	3.37197i	−0.472171	+	0.817824i	0.527322	+	0.849665i	$0.323196\pi$
$18$	3.23456	+	1.86747i	0.762393	+	0.440168i
$19$	−2.32819	−	4.03254i	−0.534123	−	0.925128i	−0.999205	−	0.0398605i	$-0.987309\pi$
$19$	−2.32819	−	4.03254i	−0.534123	−	0.925128i	0.465082	−	0.885267i	$-0.346025\pi$
$20$			3.53900i			0.791344i
$21$	4.78725	−	4.92208i	1.04466	−	1.07409i
$22$	2.39477	−	2.29457i	0.510568	−	0.489204i
$23$	0.779812	+	1.35067i	0.162602	+	0.281635i	0.935801	−	0.352528i	$-0.114678\pi$
$23$	0.779812	+	1.35067i	0.162602	+	0.281635i	−0.773199	+	0.634163i	$0.781345\pi$
$24$	1.29759	−	2.24749i	0.264869	−	0.458767i
$25$	3.76225	−	6.51641i	0.752450	−	1.30328i
$26$	−4.34467	+	2.50840i	−0.852060	+	0.491937i
$27$			1.90732i			0.367064i
$28$	−1.89662	−	1.84467i	−0.358428	−	0.348610i
$29$			0.100205i			0.0186075i	0.999957	+	0.00930376i	$0.00296152\pi$
$29$			0.100205i			0.0186075i	−0.999957	+	0.00930376i	$0.997038\pi$
$30$	−7.95386	+	4.59216i	−1.45217	+	0.838410i
$31$	−0.242252	−	0.139864i	−0.0435098	−	0.0251204i	0.478087	−	0.878312i	$-0.341330\pi$
$31$	−0.242252	−	0.139864i	−0.0435098	−	0.0251204i	−0.521597	+	0.853192i	$0.674664\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	8.26446	+	2.40482i	1.43866	+	0.418626i
$34$			3.89362i			0.667750i
$35$	2.54874	+	9.00974i	0.430816	+	1.52292i
$36$	3.73495			0.622491
$37$	−0.352715	−	0.610920i	−0.0579860	−	0.100435i	0.835575	−	0.549376i	$-0.185135\pi$
$37$	−0.352715	−	0.610920i	−0.0579860	−	0.100435i	−0.893561	+	0.448941i	$0.851801\pi$
$38$	−4.03254	−	2.32819i	−0.654164	−	0.377682i
$39$	−11.2752	−	6.50974i	−1.80548	−	1.04239i
$40$	1.76950	+	3.06486i	0.279782	+	0.484597i
$41$	2.94809			0.460415			0.230207	−	0.973142i	$-0.426060\pi$
$41$	2.94809			0.460415			0.230207	+	0.973142i	$0.426060\pi$
$42$	1.68484	−	6.65627i	0.259977	−	1.02708i
$43$			9.03556i			1.37791i	0.724804	+	0.688955i	$0.241930\pi$
$43$			9.03556i			1.37791i	−0.724804	+	0.688955i	$0.758070\pi$
$44$	0.926651	−	3.18454i	0.139698	−	0.480088i
$45$	−11.4471	−	6.60898i	−1.70643	−	0.985209i
$46$	1.35067	+	0.779812i	0.199146	+	0.114977i
$47$	5.68935	−	3.28475i	0.829876	−	0.479129i	−0.0239340	−	0.999714i	$-0.507619\pi$
$47$	5.68935	−	3.28475i	0.829876	−	0.479129i	0.853810	+	0.520584i	$0.174286\pi$
$48$		−	2.59518i		−	0.374582i
$49$	−6.15702	−	3.33032i	−0.879575	−	0.475761i
$50$		−	7.52450i		−	1.06412i
$51$	−8.75087	+	5.05232i	−1.22537	+	0.707466i
$52$	−2.50840	+	4.34467i	−0.347852	+	0.602498i
$53$	−2.77029	+	4.79828i	−0.380529	+	0.659095i	−0.991138	−	0.132837i	$-0.957591\pi$
$53$	−2.77029	+	4.79828i	−0.380529	+	0.659095i	0.610609	+	0.791932i	$0.290925\pi$
$54$	0.953659	+	1.65179i	0.129777	+	0.224780i
$55$	−8.47510	+	8.12048i	−1.14278	+	1.09496i
$56$	−2.56486	−	0.649221i	−0.342744	−	0.0867558i
$57$		−	12.0841i		−	1.60058i
$58$	0.0501023	+	0.0867797i	0.00657875	+	0.0113947i
$59$	12.5871	+	7.26719i	1.63871	+	0.946108i	0.981279	+	0.192589i	$0.0616884\pi$
$59$	12.5871	+	7.26719i	1.63871	+	0.946108i	0.657427	+	0.753518i	$0.271645\pi$
$60$	−4.59216	+	7.95386i	−0.592846	+	1.02684i
$61$	5.56360	+	9.63644i	0.712346	+	1.23382i	0.963974	+	0.265996i	$0.0857006\pi$
$61$	5.56360	+	9.63644i	0.712346	+	1.23382i	−0.251628	+	0.967824i	$0.580966\pi$
$62$	−0.279729			−0.0355256
$63$	9.50860	−	2.68987i	1.19797	−	0.338891i
$64$	−1.00000			−0.125000
$65$	15.3758	−	8.87721i	1.90713	−	1.10108i
$66$	8.35964	−	2.04959i	1.02900	−	0.252287i
$67$	−1.99196	+	3.45017i	−0.243356	+	0.421506i	−0.961668	−	0.274216i	$-0.911582\pi$
$67$	−1.99196	+	3.45017i	−0.243356	+	0.421506i	0.718312	+	0.695721i	$0.244915\pi$
$68$	1.94681	+	3.37197i	0.236085	+	0.408912i
$69$			4.04750i			0.487262i
$70$	6.71215	+	6.52829i	0.802255	+	0.780280i
$71$	−8.45381			−1.00328			−0.501641	−	0.865076i	$-0.667270\pi$
$71$	−8.45381			−1.00328			−0.501641	+	0.865076i	$0.667270\pi$
$72$	3.23456	−	1.86747i	0.381196	−	0.220084i
$73$	1.94885	−	3.37552i	0.228096	−	0.395074i	−0.729148	−	0.684356i	$-0.760083\pi$
$73$	1.94885	−	3.37552i	0.228096	−	0.395074i	0.957244	+	0.289282i	$0.0934166\pi$
$74$	−0.610920	−	0.352715i	−0.0710180	−	0.0410023i
$75$	16.9112	−	9.76370i	1.95274	−	1.12742i
$76$	−4.65637			−0.534123
$77$	0.0656384	−	8.77472i	0.00748019	−	0.999972i
$78$	−13.0195			−1.47417
$79$	6.66824	−	3.84991i	0.750236	−	0.433149i	−0.0755434	−	0.997143i	$-0.524069\pi$
$79$	6.66824	−	3.84991i	0.750236	−	0.433149i	0.825779	+	0.563994i	$0.190736\pi$
$80$	3.06486	+	1.76950i	0.342662	+	0.197836i
$81$	3.12751	−	5.41700i	0.347501	−	0.601889i
$82$	2.55312	−	1.47405i	0.281945	−	0.162781i
$83$	2.87320			0.315375			0.157687	−	0.987489i	$-0.449596\pi$
$83$	2.87320			0.315375			0.157687	+	0.987489i	$0.449596\pi$
$84$	−1.86902	−	6.60692i	−0.203926	−	0.720874i
$85$		−	13.7795i		−	1.49460i
$86$	4.51778	+	7.82503i	0.487165	+	0.843794i
$87$	−0.130024	+	0.225209i	−0.0139401	+	0.0241449i
$88$	−0.789769	−	3.22122i	−0.0841896	−	0.343383i
$89$	−5.15200	+	2.97451i	−0.546111	+	0.315297i	−0.747552	−	0.664203i	$-0.768771\pi$
$89$	−5.15200	+	2.97451i	−0.546111	+	0.315297i	0.201441	+	0.979501i	$0.435438\pi$
$90$	−13.2180			−1.39330
$91$	−3.25701	+	12.8674i	−0.341428	+	1.34887i
$92$	1.55962			0.162602
$93$	−0.362973	−	0.628687i	−0.0376385	−	0.0651919i
$94$	3.28475	−	5.68935i	0.338796	−	0.586811i
$95$	14.2711	+	8.23945i	1.46419	+	0.845349i
$96$	−1.29759	−	2.24749i	−0.132435	−	0.229383i
$97$		−	16.7587i		−	1.70159i	−0.525502	−	0.850793i	$-0.676122\pi$
$97$		−	16.7587i		−	1.70159i	0.525502	−	0.850793i	$-0.323878\pi$
$98$	−6.99730	+	0.194366i	−0.706834	+	0.0196339i
$99$	8.57010	+	8.94436i	0.861327	+	0.898942i
$100$	−3.76225	−	6.51641i	−0.376225	−	0.651641i
$101$	0.701452	−	1.21495i	0.0697971	−	0.120892i	−0.829015	−	0.559227i	$-0.811098\pi$
$101$	0.701452	−	1.21495i	0.0697971	−	0.120892i	0.898812	+	0.438335i	$0.144431\pi$
$102$	−5.05232	+	8.75087i	−0.500254	+	0.866465i
$103$	1.78653	−	1.03145i	0.176032	−	0.101632i	−0.409395	−	0.912357i	$-0.634260\pi$
$103$	1.78653	−	1.03145i	0.176032	−	0.101632i	0.585427	+	0.810725i	$0.300927\pi$
$104$			5.01680i			0.491937i
$105$	−5.96266	+	23.5565i	−0.581896	+	2.29888i
$106$			5.54058i			0.538149i
$107$	−10.6222	+	6.13274i	−1.02689	+	0.592875i	−0.916092	−	0.400968i	$-0.868674\pi$
$107$	−10.6222	+	6.13274i	−1.02689	+	0.592875i	−0.110797	+	0.993843i	$0.535340\pi$
$108$	1.65179	+	0.953659i	0.158943	+	0.0917659i
$109$	5.82394	+	3.36245i	0.557832	+	0.322065i	0.752275	−	0.658849i	$-0.228957\pi$
$109$	5.82394	+	3.36245i	0.557832	+	0.322065i	−0.194443	+	0.980914i	$0.562290\pi$
$110$	−3.27941	+	11.2701i	−0.312680	+	1.07456i
$111$		−	1.83072i		−	0.173764i
$112$	−2.54585	+	0.720188i	−0.240560	+	0.0680514i
$113$	−11.9900			−1.12792			−0.563960	−	0.825802i	$-0.690723\pi$
$113$	−11.9900			−1.12792			−0.563960	+	0.825802i	$0.690723\pi$
$114$	−6.04206	−	10.4652i	−0.565891	−	0.980152i
$115$	−4.78003	−	2.75975i	−0.445740	−	0.257348i
$116$	0.0867797	+	0.0501023i	0.00805729	+	0.00465188i
$117$	−9.36873	−	16.2271i	−0.866140	−	1.50020i
$118$	14.5344			1.33800
$119$	7.38473	+	7.18245i	0.676957	+	0.658415i
$120$			9.18432i			0.838410i
$121$	9.75253	−	5.08804i	0.886594	−	0.462549i
$122$	9.63644	+	5.56360i	0.872442	+	0.503705i
$123$	6.62581	+	3.82541i	0.597429	+	0.344926i
$124$	−0.242252	+	0.139864i	−0.0217549	+	0.0125602i
$125$			8.93419i			0.799098i
$126$	6.88975	−	7.08379i	0.613788	−	0.631074i
$127$		−	13.2199i		−	1.17308i	−0.809922	−	0.586538i	$-0.800491\pi$
$127$		−	13.2199i		−	1.17308i	0.809922	−	0.586538i	$-0.199509\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−11.7244	+	20.3073i	−1.03228	+	1.78796i
$130$	8.87721	−	15.3758i	0.778583	−	1.34855i
$131$	−8.24931	−	14.2882i	−0.720746	−	1.24837i	−0.960701	−	0.277584i	$-0.910466\pi$
$131$	−8.24931	−	14.2882i	−0.720746	−	1.24837i	0.239956	−	0.970784i	$-0.422867\pi$
$132$	6.21487	−	5.95482i	0.540935	−	0.518300i
$133$	−11.8544	+	3.35347i	−1.02791	+	0.290782i
$134$			3.98392i			0.344158i
$135$	−3.37500	−	5.84566i	−0.290473	−	0.503115i
$136$	3.37197	+	1.94681i	0.289144	+	0.166938i
$137$	−3.32187	+	5.75365i	−0.283807	+	0.491568i	−0.972319	−	0.233657i	$-0.924931\pi$
$137$	−3.32187	+	5.75365i	−0.283807	+	0.491568i	0.688512	+	0.725225i	$0.258264\pi$
$138$	2.02375	+	3.50524i	0.172273	+	0.298386i
$139$	−14.3533			−1.21743			−0.608716	−	0.793388i	$-0.708315\pi$
$139$	−14.3533			−1.21743			−0.608716	+	0.793388i	$0.708315\pi$
$140$	9.07703	+	2.29759i	0.767149	+	0.194182i
$141$	17.0490			1.43578
$142$	−7.32121	+	4.22690i	−0.614383	+	0.354714i
$143$	−16.1602	+	3.96211i	−1.35138	+	0.331328i
$144$	1.86747	−	3.23456i	0.155623	−	0.269547i
$145$	−0.177312	−	0.307113i	−0.0147249	−	0.0255044i
$146$		−	3.89771i		−	0.322577i
$147$	−9.51645	−	15.4742i	−0.784904	−	1.27629i
$148$	−0.705430			−0.0579860
$149$	−2.30871	+	1.33294i	−0.189137	+	0.109198i	−0.591579	−	0.806247i	$-0.701495\pi$
$149$	−2.30871	+	1.33294i	−0.189137	+	0.109198i	0.402441	+	0.915446i	$0.368162\pi$
$150$	9.76370	−	16.9112i	0.797203	−	1.38080i
$151$	−8.99830	−	5.19517i	−0.732271	−	0.422777i	0.0869812	−	0.996210i	$-0.472278\pi$
$151$	−8.99830	−	5.19517i	−0.732271	−	0.422777i	−0.819253	+	0.573433i	$0.805611\pi$
$152$	−4.03254	+	2.32819i	−0.327082	+	0.188841i
$153$	−14.5425			−1.17569
$154$	−4.33051	−	7.63195i	−0.348963	−	0.615000i
$155$	0.989959			0.0795154
$156$	−11.2752	+	6.50974i	−0.902738	+	0.521196i
$157$	7.25273	+	4.18736i	0.578831	+	0.334188i	0.760669	−	0.649140i	$-0.224871\pi$
$157$	7.25273	+	4.18736i	0.578831	+	0.334188i	−0.181838	+	0.983329i	$0.558205\pi$
$158$	3.84991	−	6.66824i	0.306282	−	0.530497i
$159$	−12.4524	+	7.18940i	−0.987540	+	0.570156i
$160$	3.53900			0.279782
$161$	3.97056	−	1.12322i	0.312924	−	0.0885223i
$162$		−	6.25501i		−	0.491440i
$163$	−1.53254	−	2.65444i	−0.120038	−	0.207911i	0.799745	−	0.600340i	$-0.204968\pi$
$163$	−1.53254	−	2.65444i	−0.120038	−	0.207911i	−0.919782	+	0.392429i	$0.871635\pi$
$164$	1.47405	−	2.55312i	0.115104	−	0.199365i
$165$	−29.5847	+	7.25349i	−2.30317	+	0.564684i
$166$	2.48826	−	1.43660i	0.193127	−	0.111502i
$167$	10.0731			0.779482			0.389741	−	0.920925i	$-0.372565\pi$
$167$	10.0731			0.779482			0.389741	+	0.920925i	$0.372565\pi$
$168$	−4.92208	−	4.78725i	−0.379746	−	0.369345i
$169$	12.1682			0.936018
$170$	−6.88975	−	11.9334i	−0.528420	−	0.915250i
$171$	8.69566	−	15.0613i	0.664973	−	1.15177i
$172$	7.82503	+	4.51778i	0.596653	+	0.344478i
$173$	−0.0383013	−	0.0663398i	−0.00291200	−	0.00504372i	0.864566	−	0.502520i	$-0.167594\pi$
$173$	−0.0383013	−	0.0663398i	−0.00291200	−	0.00504372i	−0.867478	+	0.497476i	$0.834260\pi$
$174$			0.260049i			0.0197142i
$175$	−14.2711	−	13.8802i	−1.07880	−	1.04925i
$176$	−2.29457	−	2.39477i	−0.172960	−	0.180513i
$177$	18.8596	+	32.6659i	1.41758	+	2.45532i
$178$	−2.97451	+	5.15200i	−0.222949	+	0.386159i
$179$	4.48746	−	7.77250i	0.335408	−	0.580944i	−0.648155	−	0.761509i	$-0.724459\pi$
$179$	4.48746	−	7.77250i	0.335408	−	0.580944i	0.983563	+	0.180564i	$0.0577924\pi$
$180$	−11.4471	+	6.60898i	−0.853216	+	0.492604i
$181$		−	15.1450i		−	1.12572i	−0.826554	−	0.562858i	$-0.809702\pi$
$181$		−	15.1450i		−	1.12572i	0.826554	−	0.562858i	$-0.190298\pi$
$182$	3.61304	+	12.7720i	0.267816	+	0.946723i
$183$			28.8771i			2.13465i
$184$	1.35067	−	0.779812i	0.0995730	−	0.0574885i
$185$	2.16204	+	1.24826i	0.158957	+	0.0917736i
$186$	−0.628687	−	0.362973i	−0.0460976	−	0.0266145i
$187$	−3.60803	+	12.3994i	−0.263845	+	0.906734i
$188$		−	6.56949i		−	0.479129i
$189$	4.89201	+	1.23827i	0.355841	+	0.0900710i
$190$	16.4789			1.19550
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$	−2.24749	−	1.29759i	−0.162199	−	0.0936454i
$193$	12.8415	+	7.41403i	0.924350	+	0.533674i	0.885020	−	0.465552i	$-0.154144\pi$
$193$	12.8415	+	7.41403i	0.924350	+	0.533674i	0.0393299	+	0.999226i	$0.487478\pi$
$194$	−8.37933	−	14.5134i	−0.601601	−	1.04200i
$195$	46.0759			3.29956
$196$	−5.96266	+	3.66698i	−0.425904	+	0.261927i
$197$			14.4745i			1.03126i	0.856811	+	0.515631i	$0.172443\pi$
$197$			14.4745i			1.03126i	−0.856811	+	0.515631i	$0.827557\pi$
$198$	11.8941	+	3.46099i	0.845277	+	0.245962i
$199$	−9.72188	−	5.61293i	−0.689166	−	0.397890i	0.114133	−	0.993465i	$-0.463591\pi$
$199$	−9.72188	−	5.61293i	−0.689166	−	0.397890i	−0.803300	+	0.595575i	$0.796924\pi$
$200$	−6.51641	−	3.76225i	−0.460779	−	0.266031i
$201$	−8.95381	+	5.16948i	−0.631553	+	0.364627i
$202$		−	1.40290i		−	0.0987080i
$203$	0.257011	+	0.0650550i	0.0180386	+	0.00456596i
$204$			10.1046i			0.707466i
$205$	−9.03550	+	5.21665i	−0.631066	+	0.364346i
$206$	1.03145	−	1.78653i	0.0718647	−	0.124473i
$207$	−2.91256	+	5.04469i	−0.202437	+	0.350630i
$208$	2.50840	+	4.34467i	0.173926	+	0.301249i
$209$	−10.6844	−	11.1510i	−0.739054	−	0.771329i
$210$	6.61444	+	23.3819i	0.456440	+	1.61350i
$211$		−	6.44038i		−	0.443374i	−0.975118	−	0.221687i	$-0.928844\pi$
$211$		−	6.44038i		−	0.443374i	0.975118	−	0.221687i	$-0.0711563\pi$
$212$	2.77029	+	4.79828i	0.190264	+	0.329548i
$213$	−18.9999	−	10.9696i	−1.30185	−	0.751622i
$214$	−6.13274	+	10.6222i	−0.419226	+	0.726120i
$215$	−15.9884	−	27.6927i	−1.09040	−	1.88863i
$216$	1.90732			0.129777
$217$	−0.516008	+	0.530540i	−0.0350289	+	0.0360154i
$218$	6.72491			0.455468
$219$	8.76006	−	5.05762i	0.591950	−	0.341763i
$220$	2.79499	+	11.3999i	0.188438	+	0.768580i
$221$	9.76675	−	16.9165i	0.656983	−	1.13793i
$222$	−0.915358	−	1.58545i	−0.0614348	−	0.106408i
$223$		−	4.01793i		−	0.269061i	−0.990909	−	0.134530i	$-0.957047\pi$
$223$		−	4.01793i		−	0.269061i	0.990909	−	0.134530i	$-0.0429526\pi$
$224$	−1.84467	+	1.89662i	−0.123252	+	0.126724i
$225$	28.1036			1.87357
$226$	−10.3836	+	5.99498i	−0.690707	+	0.398780i
$227$	−6.36466	+	11.0239i	−0.422437	+	0.731682i	−0.996177	−	0.0873549i	$-0.972159\pi$
$227$	−6.36466	+	11.0239i	−0.422437	+	0.731682i	0.573740	+	0.819037i	$0.305492\pi$
$228$	−10.4652	−	6.04206i	−0.693072	−	0.400145i
$229$	−5.20780	+	3.00672i	−0.344141	+	0.198690i	−0.662102	−	0.749414i	$-0.730335\pi$
$229$	−5.20780	+	3.00672i	−0.344141	+	0.198690i	0.317961	+	0.948104i	$0.397002\pi$
$230$	−5.51950			−0.363945
$231$	11.5335	−	19.6359i	0.758849	−	1.29195i
$232$	0.100205			0.00657875
$233$	−5.60053	+	3.23347i	−0.366903	+	0.211832i	−0.672105	−	0.740456i	$-0.734609\pi$
$233$	−5.60053	+	3.23347i	−0.366903	+	0.211832i	0.305202	+	0.952288i	$0.401276\pi$
$234$	−16.2271	−	9.36873i	−1.06080	−	0.612453i
$235$	−11.6247	+	20.1346i	−0.758312	+	1.31343i
$236$	12.5871	−	7.26719i	0.819353	−	0.473054i
$237$	19.9824			1.29800
$238$	9.98659	+	2.52782i	0.647335	+	0.163854i
$239$			15.5775i			1.00762i	0.863813	+	0.503812i	$0.168070\pi$
$239$			15.5775i			1.00762i	−0.863813	+	0.503812i	$0.831930\pi$
$240$	4.59216	+	7.95386i	0.296423	+	0.513419i
$241$	11.7381	−	20.3310i	0.756119	−	1.30964i	−0.188697	−	0.982035i	$-0.560427\pi$
$241$	11.7381	−	20.3310i	0.756119	−	1.30964i	0.944816	−	0.327601i	$-0.106240\pi$
$242$	5.90192	−	9.28264i	0.379390	−	0.596710i
$243$	19.0134	−	10.9774i	1.21971	−	0.704201i
$244$	11.1272			0.712346
$245$	24.7634	−	0.687860i	1.58208	−	0.0439457i
$246$	7.65083			0.487799
$247$	11.6800	+	20.2304i	0.743183	+	1.28723i
$248$	−0.139864	+	0.242252i	−0.00888140	+	0.0153830i
$249$	6.45748	+	3.72823i	0.409226	+	0.236267i
$250$	4.46709	+	7.73723i	0.282524	+	0.489345i
$251$			18.2818i			1.15394i	0.816766	+	0.576968i	$0.195764\pi$
$251$			18.2818i			1.15394i	−0.816766	+	0.576968i	$0.804236\pi$
$252$	2.42481	−	9.57962i	0.152748	−	0.603459i
$253$	3.57867	+	3.73495i	0.224989	+	0.234814i
$254$	−6.60994	−	11.4488i	−0.414745	−	0.718359i
$255$	17.8801	−	30.9693i	1.11970	−	1.93937i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.33087	+	4.80983i	−0.519666	+	0.300029i	−0.736798	−	0.676113i	$-0.763663\pi$
$257$	−8.33087	+	4.80983i	−0.519666	+	0.300029i	0.217132	+	0.976142i	$0.430330\pi$
$258$			23.4489i			1.45986i
$259$	−1.79591	+	0.508042i	−0.111593	+	0.0315682i
$260$		−	17.7544i		−	1.10108i
$261$	−0.324118	+	0.187129i	−0.0200624	+	0.0115830i
$262$	−14.2882	−	8.24931i	−0.882729	−	0.509644i
$263$	−0.501139	−	0.289333i	−0.0309016	−	0.0178410i	0.484470	−	0.874808i	$-0.339013\pi$
$263$	−0.501139	−	0.289333i	−0.0309016	−	0.0178410i	−0.515371	+	0.856967i	$0.672346\pi$
$264$	2.40482	−	8.26446i	0.148007	−	0.508642i
$265$		−	19.6081i		−	1.20452i
$266$	−8.58949	+	8.83139i	−0.526655	+	0.541487i
$267$	−15.4388			−0.944837
$268$	1.99196	+	3.45017i	0.121678	+	0.210753i
$269$	19.1302	+	11.0448i	1.16639	+	0.673413i	0.952826	−	0.303517i	$-0.0981608\pi$
$269$	19.1302	+	11.0448i	1.16639	+	0.673413i	0.213560	+	0.976930i	$0.431494\pi$
$270$	−5.84566	−	3.37500i	−0.355756	−	0.205396i
$271$	−2.13111	−	3.69119i	−0.129456	−	0.224224i	0.794010	−	0.607905i	$-0.207990\pi$
$271$	−2.13111	−	3.69119i	−0.129456	−	0.224224i	−0.923466	+	0.383681i	$0.874656\pi$
$272$	3.89362			0.236085
$273$	−24.0167	+	24.6931i	−1.45356	+	1.49449i
$274$			6.64374i			0.401363i
$275$	6.97258	−	23.9621i	0.420462	−	1.44497i
$276$	3.50524	+	2.02375i	0.210991	+	0.121815i
$277$	15.9048	+	9.18263i	0.955626	+	0.551731i	0.894824	−	0.446419i	$-0.147301\pi$
$277$	15.9048	+	9.18263i	0.955626	+	0.551731i	0.0608016	+	0.998150i	$0.480634\pi$
$278$	−12.4303	+	7.17666i	−0.745522	+	0.430427i
$279$		−	1.04477i		−	0.0625489i
$280$	9.00974	−	2.54874i	0.538435	−	0.152317i
$281$			3.72890i			0.222448i	0.993795	+	0.111224i	$0.0354771\pi$
$281$			3.72890i			0.222448i	−0.993795	+	0.111224i	$0.964523\pi$
$282$	14.7649	−	8.52450i	0.879235	−	0.507626i
$283$	−6.36576	+	11.0258i	−0.378405	+	0.655417i	−0.990830	−	0.135111i	$-0.956861\pi$
$283$	−6.36576	+	11.0258i	−0.378405	+	0.655417i	0.612425	+	0.790529i	$0.290194\pi$
$284$	−4.22690	+	7.32121i	−0.250821	+	0.434434i
$285$	21.3828	+	37.0361i	1.26661	+	2.19383i
$286$	−12.0141	+	11.5114i	−0.710408	+	0.680683i
$287$	1.91397	−	7.56145i	0.112978	−	0.446338i
$288$		−	3.73495i		−	0.220084i
$289$	0.919861	+	1.59325i	0.0541094	+	0.0937203i
$290$	−0.307113	−	0.177312i	−0.0180343	−	0.0104121i
$291$	21.7459	−	37.6649i	1.27476	−	2.20796i
$292$	−1.94885	−	3.37552i	−0.114048	−	0.197537i
$293$	−26.2251			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$293$	−26.2251			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$294$	−15.9786	−	8.64278i	−0.931889	−	0.504057i
$295$	−51.4371			−2.99478
$296$	−0.610920	+	0.352715i	−0.0355090	+	0.0205011i
$297$	1.50634	+	6.14389i	0.0874067	+	0.356505i
$298$	−1.33294	+	2.30871i	−0.0772149	+	0.133740i
$299$	−3.91216	−	6.77605i	−0.226246	−	0.391869i
$300$		−	19.5274i		−	1.12742i
$301$	23.1750	+	5.86608i	1.33578	+	0.338115i
$302$	−10.3903			−0.597897
$303$	3.15301	−	1.82039i	0.181136	−	0.104579i
$304$	−2.32819	+	4.03254i	−0.133531	+	0.231282i
$305$	−34.1033	−	19.6896i	−1.95275	−	1.12742i
$306$	−12.5941	+	7.27123i	−0.719959	+	0.415669i
$307$	25.5942			1.46074			0.730369	−	0.683053i	$-0.239348\pi$
$307$	25.5942			1.46074			0.730369	+	0.683053i	$0.239348\pi$
$308$	−7.56631	−	4.44420i	−0.431131	−	0.253232i
$309$	5.35360			0.304556
$310$	0.857330	−	0.494980i	0.0486931	−	0.0281129i
$311$	−1.65385	−	0.954850i	−0.0937811	−	0.0541446i	0.452376	−	0.891827i	$-0.350577\pi$
$311$	−1.65385	−	0.954850i	−0.0937811	−	0.0541446i	−0.546157	+	0.837683i	$0.683910\pi$
$312$	−6.50974	+	11.2752i	−0.368541	+	0.638332i
$313$	−26.3707	+	15.2251i	−1.49056	+	0.860576i	−0.999942	−	0.0107985i	$-0.996563\pi$
$313$	−26.3707	+	15.2251i	−1.49056	+	0.860576i	−0.490619	+	0.871374i	$0.663229\pi$
$314$	8.37473			0.472613
$315$	−24.3828	+	25.0695i	−1.37382	+	1.41251i
$316$		−	7.69982i		−	0.433149i
$317$	−17.1971	−	29.7862i	−0.965885	−	1.67296i	−0.707220	−	0.706994i	$-0.750051\pi$
$317$	−17.1971	−	29.7862i	−0.965885	−	1.67296i	−0.258665	−	0.965967i	$-0.583283\pi$
$318$	−7.18940	+	12.4524i	−0.403161	+	0.698296i
$319$	0.0791385	+	0.322781i	0.00443090	+	0.0180723i
$320$	3.06486	−	1.76950i	0.171331	−	0.0989180i
$321$	−31.8311			−1.77664
$322$	2.87699	−	2.95802i	0.160329	−	0.164844i
$323$	18.1302			1.00879
$324$	−3.12751	−	5.41700i	−0.173750	−	0.300944i
$325$	−18.8744	+	32.6915i	−1.04697	+	1.81340i
$326$	−2.65444	−	1.53254i	−0.147016	−	0.0848795i
$327$	8.72616	+	15.1142i	0.482558	+	0.835815i
$328$		−	2.94809i		−	0.162781i
$329$	−4.73127	−	16.7249i	−0.260843	−	0.922074i
$330$	−21.9944	+	21.0741i	−1.21075	+	1.16009i
$331$	−7.75642	−	13.4345i	−0.426332	−	0.738428i	0.570212	−	0.821497i	$-0.306861\pi$
$331$	−7.75642	−	13.4345i	−0.426332	−	0.738428i	−0.996544	+	0.0830696i	$0.973528\pi$
$332$	1.43660	−	2.48826i	0.0788436	−	0.136561i
$333$	1.31737	−	2.28175i	0.0721915	−	0.125039i
$334$	8.72358	−	5.03656i	0.477333	−	0.275588i
$335$		−	14.0991i		−	0.770314i
$336$	−6.65627	−	1.68484i	−0.363129	−	0.0919158i
$337$		−	7.70882i		−	0.419926i	−0.977709	−	0.209963i	$-0.932666\pi$
$337$		−	7.70882i		−	0.419926i	0.977709	−	0.209963i	$-0.0673344\pi$
$338$	10.5380	−	6.08412i	0.573192	−	0.330933i
$339$	−26.9473	−	15.5580i	−1.46358	−	0.844997i
$340$	−11.9334	−	6.88975i	−0.647180	−	0.373649i
$341$	−0.890808	−	0.259211i	−0.0482400	−	0.0140371i
$342$		−	17.3913i		−	0.940415i
$343$	−12.5391	+	13.6298i	−0.677047	+	0.735940i
$344$	9.03556			0.487165
$345$	−7.16204	−	12.4050i	−0.385591	−	0.667864i
$346$	−0.0663398	−	0.0383013i	−0.00356645	−	0.00205909i
$347$	−18.8285	−	10.8706i	−1.01077	−	0.583567i	−0.0993513	−	0.995052i	$-0.531677\pi$
$347$	−18.8285	−	10.8706i	−1.01077	−	0.583567i	−0.911416	+	0.411485i	$0.865010\pi$
$348$	0.130024	+	0.225209i	0.00697004	+	0.0120725i
$349$	13.4565			0.720307			0.360154	−	0.932893i	$-0.382724\pi$
$349$	13.4565			0.720307			0.360154	+	0.932893i	$0.382724\pi$
$350$	−19.2993	−	4.88506i	−1.03159	−	0.261118i
$351$		−	9.56862i		−	0.510735i
$352$	−3.18454	−	0.926651i	−0.169737	−	0.0493907i
$353$	5.80903	+	3.35384i	0.309183	+	0.178507i	0.646561	−	0.762862i	$-0.276207\pi$
$353$	5.80903	+	3.35384i	0.309183	+	0.178507i	−0.337378	+	0.941369i	$0.609540\pi$
$354$	32.6659	+	18.8596i	1.73617	+	1.00238i
$355$	25.9098	−	14.9590i	1.37515	−	0.793941i
$356$			5.94902i			0.315297i
$357$	7.27724	+	25.7248i	0.385152	+	1.36150i
$358$		−	8.97491i		−	0.474339i
$359$	26.8869	−	15.5232i	1.41904	−	0.819282i	0.422823	−	0.906212i	$-0.361039\pi$
$359$	26.8869	−	15.5232i	1.41904	−	0.819282i	0.996214	+	0.0869306i	$0.0277058\pi$
$360$	−6.60898	+	11.4471i	−0.348324	+	0.603315i
$361$	−1.34091	+	2.32253i	−0.0705744	+	0.122238i
$362$	−7.57248	−	13.1159i	−0.398001	−	0.689358i
$363$	28.5209	+	1.21946i	1.49696	+	0.0640050i
$364$	9.51498	+	9.25435i	0.498720	+	0.485060i
$365$			13.7940i			0.722010i
$366$	14.4385	+	25.0083i	0.754714	+	1.30720i
$367$	25.6770	+	14.8246i	1.34033	+	0.773838i	0.986855	−	0.161608i	$-0.0516679\pi$
$367$	25.6770	+	14.8246i	1.34033	+	0.773838i	0.353471	+	0.935445i	$0.385001\pi$
$368$	0.779812	−	1.35067i	0.0406505	−	0.0704087i
$369$	5.50549	+	9.53578i	0.286604	+	0.496413i
$370$	2.49651			0.129788
$371$	10.5084	+	10.2206i	0.545569	+	0.530625i
$372$	−0.725946			−0.0376385
$373$	−7.60418	+	4.39027i	−0.393729	+	0.227320i	−0.683775	−	0.729693i	$-0.739663\pi$
$373$	−7.60418	+	4.39027i	−0.393729	+	0.227320i	0.290045	+	0.957013i	$0.406330\pi$
$374$	3.07506	+	12.5422i	0.159008	+	0.648542i
$375$	−11.5929	+	20.0795i	−0.598655	+	1.03690i
$376$	−3.28475	−	5.68935i	−0.169398	−	0.293406i
$377$		−	0.502706i		−	0.0258907i
$378$	4.85574	−	1.37363i	0.249752	−	0.0706518i
$379$	30.8135			1.58278			0.791391	−	0.611311i	$-0.209358\pi$
$379$	30.8135			1.58278			0.791391	+	0.611311i	$0.209358\pi$
$380$	14.2711	−	8.23945i	0.732094	−	0.422675i
$381$	17.1540	−	29.7116i	0.878825	−	1.52217i
$382$	−5.19615	−	3.00000i	−0.265858	−	0.153493i
$383$	4.58545	−	2.64741i	0.234305	−	0.135276i	−0.378251	−	0.925703i	$-0.623474\pi$
$383$	4.58545	−	2.64741i	0.234305	−	0.135276i	0.612557	+	0.790427i	$0.290141\pi$
$384$	−2.59518			−0.132435
$385$	15.3257	+	27.0094i	0.781069	+	1.37653i
$386$	14.8281			0.754729
$387$	−29.2261	+	16.8737i	−1.48564	+	0.857737i
$388$	−14.5134	−	8.37933i	−0.736808	−	0.425396i
$389$	−0.430119	+	0.744987i	−0.0218079	+	0.0377724i	−0.876723	−	0.480995i	$-0.840276\pi$
$389$	−0.430119	+	0.744987i	−0.0218079	+	0.0377724i	0.854916	+	0.518767i	$0.173609\pi$
$390$	39.9029	−	23.0379i	2.02056	−	1.16657i
$391$	−6.07258			−0.307104
$392$	−3.33032	+	6.15702i	−0.168207	+	0.310977i
$393$		−	42.8168i		−	2.15982i
$394$	7.23723	+	12.5353i	0.364606	+	0.631517i
$395$	−13.6248	+	23.5989i	−0.685539	+	1.18739i
$396$	12.0311	−	2.94974i	0.604585	−	0.148230i
$397$	10.6931	−	6.17367i	0.536672	−	0.309847i	−0.207057	−	0.978329i	$-0.566389\pi$
$397$	10.6931	−	6.17367i	0.536672	−	0.309847i	0.743729	+	0.668481i	$0.233055\pi$
$398$	−11.2259			−0.562702
$399$	−30.9941	−	7.84527i	−1.55165	−	0.392755i
$400$	−7.52450			−0.376225
$401$	−16.8626	−	29.2069i	−0.842078	−	1.45852i	−0.888134	−	0.459584i	$-0.847999\pi$
$401$	−16.8626	−	29.2069i	−0.842078	−	1.45852i	0.0460561	−	0.998939i	$-0.485335\pi$
$402$	−5.16948	+	8.95381i	−0.257830	+	0.446575i
$403$	1.21533	+	0.701671i	0.0605399	+	0.0349527i
$404$	−0.701452	−	1.21495i	−0.0348985	−	0.0604461i
$405$			22.1365i			1.09997i
$406$	0.255105	−	0.0721662i	0.0126607	−	0.00358155i
$407$	−1.61866	−	1.68935i	−0.0802339	−	0.0837377i
$408$	5.05232	+	8.75087i	0.250127	+	0.433233i
$409$	19.1846	−	33.2287i	0.948616	−	1.64305i	0.200273	−	0.979740i	$-0.435817\pi$
$409$	19.1846	−	33.2287i	0.948616	−	1.64305i	0.748343	−	0.663312i	$-0.230850\pi$
$410$	−5.21665	+	9.03550i	−0.257632	+	0.446231i
$411$	−14.9317	+	8.62085i	−0.736529	+	0.425235i
$412$		−	2.06291i		−	0.101632i
$413$	26.8112	−	27.5663i	1.31929	−	1.35645i
$414$			5.82511i			0.286289i
$415$	−8.80595	+	5.08412i	−0.432267	+	0.249570i
$416$	4.34467	+	2.50840i	0.213015	+	0.122984i
$417$	−32.2589	−	18.6247i	−1.57973	−	0.912056i
$418$	−14.8284	−	4.31483i	−0.725282	−	0.211045i
$419$			33.5023i			1.63670i	0.574723	+	0.818348i	$0.305110\pi$
$419$			33.5023i			1.63670i	−0.574723	+	0.818348i	$0.694890\pi$
$420$	17.4192	+	16.9421i	0.849970	+	0.826688i
$421$	−23.0155			−1.12171			−0.560853	−	0.827915i	$-0.689527\pi$
$421$	−23.0155			−1.12171			−0.560853	+	0.827915i	$0.689527\pi$
$422$	−3.22019	−	5.57753i	−0.156756	−	0.271510i
$423$	21.2494	+	12.2683i	1.03318	+	0.596508i
$424$	4.79828	+	2.77029i	0.233025	+	0.134537i
$425$	14.6488	+	25.3724i	0.710570	+	1.23074i
$426$	−21.9391			−1.06295
$427$	28.3281	−	8.01368i	1.37089	−	0.387809i
$428$			12.2655i			0.592875i
$429$	−41.4611	−	12.0645i	−2.00176	−	0.582480i
$430$	−27.6927	−	15.9884i	−1.33546	−	0.771030i
$431$	23.2425	+	13.4191i	1.11955	+	0.646373i	0.941286	−	0.337609i	$-0.109618\pi$
$431$	23.2425	+	13.4191i	1.11955	+	0.646373i	0.178265	+	0.983983i	$0.442952\pi$
$432$	1.65179	−	0.953659i	0.0794716	−	0.0458829i
$433$			30.6912i			1.47493i	0.675387	+	0.737463i	$0.263976\pi$
$433$			30.6912i			1.47493i	−0.675387	+	0.737463i	$0.736024\pi$
$434$	−0.181606	+	0.717465i	−0.00871736	+	0.0344394i
$435$		−	0.920312i		−	0.0441256i
$436$	5.82394	−	3.36245i	0.278916	−	0.161032i
$437$	3.63110	−	6.28924i	0.173699	−	0.300855i
$438$	5.05762	−	8.76006i	0.241663	−	0.418572i
$439$	8.42258	+	14.5883i	0.401988	+	0.696263i	0.993966	−	0.109691i	$-0.0349861\pi$
$439$	8.42258	+	14.5883i	0.401988	+	0.696263i	−0.591978	+	0.805954i	$0.701653\pi$
$440$	8.12048	+	8.47510i	0.387129	+	0.404035i
$441$	−0.725946	−	26.1345i	−0.0345688	−	1.24450i
$442$		−	19.5335i		−	0.929114i
$443$	0.395295	+	0.684671i	0.0187810	+	0.0325297i	0.875263	−	0.483647i	$-0.160688\pi$
$443$	0.395295	+	0.684671i	0.0187810	+	0.0325297i	−0.856482	+	0.516177i	$0.827355\pi$
$444$	−1.58545	−	0.915358i	−0.0752419	−	0.0434410i
$445$	10.5268	−	18.2329i	0.499017	−	0.864323i
$446$	−2.00897	−	3.47963i	−0.0951273	−	0.164765i
$447$	−6.91841			−0.327230
$448$	−0.649221	+	2.56486i	−0.0306728	+	0.121178i
$449$	15.9734			0.753833			0.376917	−	0.926247i	$-0.376984\pi$
$449$	15.9734			0.753833			0.376917	+	0.926247i	$0.376984\pi$
$450$	24.3384	−	14.0518i	1.14732	−	0.662408i
$451$	9.49646	−	2.32831i	0.447171	−	0.109636i
$452$	−5.99498	+	10.3836i	−0.281980	+	0.488404i
$453$	−13.4824	−	23.3522i	−0.633458	−	1.09718i
$454$			12.7293i			0.597416i
$455$	−12.7865	−	45.2000i	−0.599442	−	2.11901i
$456$	−12.0841			−0.565891
$457$	−30.2530	+	17.4666i	−1.41517	+	0.817052i	−0.995870	−	0.0907937i	$-0.971060\pi$
$457$	−30.2530	+	17.4666i	−1.41517	+	0.817052i	−0.419305	+	0.907845i	$0.637726\pi$
$458$	−3.00672	+	5.20780i	−0.140495	+	0.243344i
$459$	−6.43143	−	3.71319i	−0.300193	−	0.173317i
$460$	−4.78003	+	2.75975i	−0.222870	+	0.128674i
$461$	20.8346			0.970364			0.485182	−	0.874413i	$-0.338753\pi$
$461$	20.8346			0.970364			0.485182	+	0.874413i	$0.338753\pi$
$462$	0.170343	−	22.7720i	0.00792509	−	1.05945i
$463$	13.1724			0.612172			0.306086	−	0.952004i	$-0.400981\pi$
$463$	13.1724			0.612172			0.306086	+	0.952004i	$0.400981\pi$
$464$	0.0867797	−	0.0501023i	0.00402865	−	0.00232594i
$465$	2.22492	+	1.28456i	0.103178	+	0.0595700i
$466$	−3.23347	+	5.60053i	−0.149788	+	0.259440i
$467$	−14.5651	+	8.40919i	−0.673995	+	0.389131i	−0.797589	−	0.603202i	$-0.793891\pi$
$467$	−14.5651	+	8.40919i	−0.673995	+	0.389131i	0.123594	+	0.992333i	$0.460558\pi$
$468$	−18.7375			−0.866140
$469$	7.55599	+	7.34902i	0.348903	+	0.339346i
$470$			23.2494i			1.07241i
$471$	10.8670	+	18.8221i	0.500723	+	0.867277i
$472$	7.26719	−	12.5871i	0.334500	−	0.579370i
$473$	7.13600	+	29.1055i	0.328114	+	1.33827i
$474$	17.3053	−	9.99120i	0.794857	−	0.458911i
$475$	−35.0369			−1.60760
$476$	9.91256	−	2.80414i	0.454341	−	0.128528i
$477$	−20.6938			−0.947503
$478$	7.78874	+	13.4905i	0.356249	+	0.617041i
$479$	11.4291	−	19.7957i	0.522208	−	0.904491i	−0.477458	−	0.878654i	$-0.658442\pi$
$479$	11.4291	−	19.7957i	0.522208	−	0.904491i	0.999666	−	0.0258361i	$-0.00822481\pi$
$480$	7.95386	+	4.59216i	0.363042	+	0.209603i
$481$	1.76950	+	3.06486i	0.0806822	+	0.139746i
$482$		−	23.4762i		−	1.06931i
$483$	10.3813	+	2.62772i	0.472364	+	0.119566i
$484$	0.469894	−	10.9900i	0.0213588	−	0.499544i
$485$	29.6544	+	51.3630i	1.34654	+	2.33227i
$486$	10.9774	−	19.0134i	0.497945	−	0.862467i
$487$	−15.6314	+	27.0744i	−0.708327	+	1.22686i	0.257150	+	0.966371i	$0.417217\pi$
$487$	−15.6314	+	27.0744i	−0.708327	+	1.22686i	−0.965477	+	0.260487i	$0.916117\pi$
$488$	9.63644	−	5.56360i	0.436221	−	0.251852i
$489$		−	7.95442i		−	0.359711i
$490$	21.1018	−	12.9774i	0.953283	−	0.586260i
$491$		−	22.4979i		−	1.01532i	−0.861558	−	0.507659i	$-0.830511\pi$
$491$		−	22.4979i		−	1.01532i	0.861558	−	0.507659i	$-0.169489\pi$
$492$	6.62581	−	3.82541i	0.298715	−	0.172463i
$493$	−0.337887	−	0.195079i	−0.0152177	−	0.00878593i
$494$	20.2304	+	11.6800i	0.910210	+	0.525510i
$495$	−42.0932	−	12.2484i	−1.89195	−	0.550526i
$496$			0.279729i			0.0125602i
$497$	−5.48839	+	21.6828i	−0.246188	+	0.972609i
$498$	7.45646			0.334132
$499$	15.9548	+	27.6346i	0.714236	+	1.23709i	0.963253	+	0.268595i	$0.0865592\pi$
$499$	15.9548	+	27.6346i	0.714236	+	1.23709i	−0.249017	+	0.968499i	$0.580107\pi$
$500$	7.73723	+	4.46709i	0.346020	+	0.199774i
$501$	22.6392	+	13.0708i	1.01145	+	0.583959i
$502$	9.14090	+	15.8325i	0.407978	+	0.706639i
$503$	−30.2687			−1.34962			−0.674808	−	0.737994i	$-0.735773\pi$
$503$	−30.2687			−1.34962			−0.674808	+	0.737994i	$0.735773\pi$
$504$	−2.68987	−	9.50860i	−0.119816	−	0.423547i
$505$			4.96487i			0.220934i
$506$	4.96669	+	1.44523i	0.220796	+	0.0642481i
$507$	27.3480	+	15.7894i	1.21457	+	0.701231i
$508$	−11.4488	−	6.60994i	−0.507956	−	0.293269i
$509$	−19.9655	+	11.5271i	−0.884957	+	0.510930i	−0.872290	−	0.488989i	$-0.837366\pi$
$509$	−19.9655	+	11.5271i	−0.884957	+	0.510930i	−0.0126676	+	0.999920i	$0.504032\pi$
$510$		−	35.7603i		−	1.58349i
$511$	−7.39249	−	7.19000i	−0.327025	−	0.318067i
$512$			1.00000i			0.0441942i
$513$	7.69133	−	4.44059i	0.339581	−	0.196057i
$514$	−4.80983	+	8.33087i	−0.212153	+	0.367459i
$515$	−3.65031	+	6.32252i	−0.160852	+	0.278603i
$516$	11.7244	+	20.3073i	0.516140	+	0.893980i
$517$	15.7325	−	15.0742i	0.691912	−	0.662961i
$518$	−1.30129	+	1.33793i	−0.0571753	+	0.0587855i
$519$		−	0.198797i		−	0.00872624i
$520$	−8.87721	−	15.3758i	−0.389291	−	0.674273i
$521$	−6.91351	−	3.99152i	−0.302886	−	0.174872i	0.340852	−	0.940117i	$-0.389284\pi$
$521$	−6.91351	−	3.99152i	−0.302886	−	0.174872i	−0.643739	+	0.765245i	$0.722618\pi$
$522$	−0.187129	+	0.324118i	−0.00819043	+	0.0141862i
$523$	−2.79140	−	4.83485i	−0.122059	−	0.211413i	0.798520	−	0.601968i	$-0.205617\pi$
$523$	−2.79140	−	4.83485i	−0.122059	−	0.211413i	−0.920580	+	0.390555i	$0.872283\pi$
$524$	−16.4986			−0.720746
$525$	−14.0634	−	49.7138i	−0.613778	−	2.16969i
$526$	−0.578666			−0.0252310
$527$	0.943238	−	0.544579i	0.0410881	−	0.0237222i
$528$	−2.04959	−	8.35964i	−0.0891970	−	0.363807i
$529$	10.2838	−	17.8120i	0.447121	−	0.774437i
$530$	−9.80405	−	16.9811i	−0.425861	−	0.737612i
$531$			54.2851i			2.35577i
$532$	−3.02302	+	11.9430i	−0.131064	+	0.517793i
$533$	−14.7900			−0.640625
$534$	−13.3704	+	7.71938i	−0.578592	+	0.334050i
$535$	21.7038	−	37.5920i	0.938335	−	1.62524i
$536$	3.45017	+	1.99196i	0.149025	+	0.0860395i
$537$	20.1710	−	11.6457i	0.870444	−	0.502551i
$538$	22.0896			0.952350
$539$	−22.4633	−	5.86509i	−0.967564	−	0.252627i
$540$	−6.74999			−0.290473
$541$	−11.6066	+	6.70108i	−0.499007	+	0.288102i	−0.728304	−	0.685255i	$-0.759691\pi$
$541$	−11.6066	+	6.70108i	−0.499007	+	0.288102i	0.229296	+	0.973357i	$0.426358\pi$
$542$	−3.69119	−	2.13111i	−0.158550	−	0.0915390i
$543$	19.6519	−	34.0381i	0.843345	−	1.46072i
$544$	3.37197	−	1.94681i	0.144572	−	0.0834688i
$545$	−23.7994			−1.01946
$546$	−8.45252	+	33.3931i	−0.361735	+	1.42909i
$547$			24.5161i			1.04823i	0.851647	+	0.524116i	$0.175604\pi$
$547$			24.5161i			1.04823i	−0.851647	+	0.524116i	$0.824396\pi$
$548$	3.32187	+	5.75365i	0.141903	+	0.245784i
$549$	−20.7798	+	35.9916i	−0.886858	+	1.53608i
$550$	−5.94261	−	24.2381i	−0.253394	−	1.03351i
$551$	0.404079	−	0.233295i	0.0172143	−	0.00993870i
$552$	4.04750			0.172273
$553$	−5.54532	−	19.6026i	−0.235811	−	0.833585i
$554$	18.3653			0.780265
$555$	3.23945	+	5.61089i	0.137507	+	0.238169i
$556$	−7.17666	+	12.4303i	−0.304358	+	0.527164i
$557$	−3.12772	−	1.80579i	−0.132526	−	0.0765137i	0.432271	−	0.901744i	$-0.357712\pi$
$557$	−3.12772	−	1.80579i	−0.132526	−	0.0765137i	−0.564797	+	0.825230i	$0.691046\pi$
$558$	−0.522386	−	0.904799i	−0.0221144	−	0.0383032i
$559$		−	45.3296i		−	1.91724i
$560$	6.52829	−	6.71215i	0.275871	−	0.283640i
$561$	−24.1983	+	23.1858i	−1.02165	+	0.978905i
$562$	1.86445	+	3.22933i	0.0786472	+	0.136221i
$563$	−2.92902	+	5.07320i	−0.123443	+	0.213810i	−0.921123	−	0.389271i	$-0.872727\pi$
$563$	−2.92902	+	5.07320i	−0.123443	+	0.213810i	0.797680	+	0.603081i	$0.206060\pi$
$564$	8.52450	−	14.7649i	0.358946	−	0.621713i
$565$	36.7476	−	21.2162i	1.54598	−	0.892573i
$566$			12.7315i			0.535146i
$567$	−11.8634	−	11.5384i	−0.498216	−	0.484569i
$568$			8.45381i			0.354714i
$569$	29.9772	−	17.3073i	1.25671	−	0.725561i	0.284275	−	0.958743i	$-0.408247\pi$
$569$	29.9772	−	17.3073i	1.25671	−	0.725561i	0.972433	+	0.233182i	$0.0749137\pi$
$570$	37.0361	+	21.3828i	1.55127	+	0.895628i
$571$	6.89907	+	3.98318i	0.288717	+	0.166691i	0.637363	−	0.770564i	$-0.280025\pi$
$571$	6.89907	+	3.98318i	0.288717	+	0.166691i	−0.348646	+	0.937254i	$0.613358\pi$
$572$	−4.64882	+	15.9762i	−0.194377	+	0.667999i
$573$		−	15.5711i		−	0.650491i
$574$	−2.12318	−	7.50539i	−0.0886199	−	0.313269i
$575$	11.7354			0.489399
$576$	−1.86747	−	3.23456i	−0.0778114	−	0.134773i
$577$	15.9144	+	9.18819i	0.662525	+	0.382509i	0.793239	−	0.608911i	$-0.208393\pi$
$577$	15.9144	+	9.18819i	0.662525	+	0.382509i	−0.130713	+	0.991420i	$0.541727\pi$
$578$	1.59325	+	0.919861i	0.0662703	+	0.0382612i
$579$	19.2407	+	33.3259i	0.799618	+	1.38498i
$580$	−0.354624			−0.0147249
$581$	1.86534	−	7.36936i	0.0773874	−	0.305732i
$582$		−	43.4917i		−	1.80279i
$583$	−5.13418	+	17.6442i	−0.212636	+	0.730749i
$584$	−3.37552	−	1.94885i	−0.139680	−	0.0806442i
$585$	57.4277	+	33.1559i	2.37434	+	1.37083i
$586$	−22.7116	+	13.1126i	−0.938209	+	0.541675i
$587$		−	17.2267i		−	0.711021i	−0.934672	−	0.355511i	$-0.884307\pi$
$587$		−	17.2267i		−	0.711021i	0.934672	−	0.355511i	$-0.115693\pi$
$588$	−18.1592	+	0.504414i	−0.748874	+	0.0208017i
$589$			1.30252i			0.0536695i
$590$	−44.5459	+	25.7186i	−1.83392	+	1.05882i
$591$	−18.7819	+	32.5312i	−0.772584	+	1.33816i
$592$	−0.352715	+	0.610920i	−0.0144965	+	0.0251087i
$593$	−20.6214	−	35.7172i	−0.846817	−	1.46673i	−0.884033	−	0.467424i	$-0.845182\pi$
$593$	−20.6214	−	35.7172i	−0.846817	−	1.46673i	0.0372161	−	0.999307i	$-0.488151\pi$
$594$	4.37648	+	4.56760i	0.179569	+	0.187411i
$595$	−35.3425	−	8.94595i	−1.44890	−	0.366748i
$596$			2.66587i			0.109198i
$597$	−14.5666	−	25.2300i	−0.596169	−	1.03260i
$598$	−6.77605	−	3.91216i	−0.277093	−	0.159980i
$599$	−4.97720	+	8.62076i	−0.203363	+	0.352235i	−0.949610	−	0.313434i	$-0.898520\pi$
$599$	−4.97720	+	8.62076i	−0.203363	+	0.352235i	0.746247	+	0.665669i	$0.231854\pi$
$600$	−9.76370	−	16.9112i	−0.398602	−	0.690398i
$601$	−4.76767			−0.194477			−0.0972386	−	0.995261i	$-0.531001\pi$
$601$	−4.76767			−0.194477			−0.0972386	+	0.995261i	$0.531001\pi$
$602$	23.0031	−	6.50731i	0.937538	−	0.265218i
$603$	−14.8797			−0.605949
$604$	−8.99830	+	5.19517i	−0.366136	+	0.211389i
$605$	−20.8869	+	32.8512i	−0.849172	+	1.33559i
$606$	1.82039	−	3.15301i	0.0739484	−	0.128082i
$607$	2.27672	+	3.94340i	0.0924094	+	0.160058i	0.908524	−	0.417832i	$-0.137210\pi$
$607$	2.27672	+	3.94340i	0.0924094	+	0.160058i	−0.816115	+	0.577889i	$0.803876\pi$
$608$			4.65637i			0.188841i
$609$	0.493215	+	0.479705i	0.0199861	+	0.0194386i
$610$	−39.3791			−1.59441
$611$	−28.5423	+	16.4789i	−1.15470	+	0.666665i
$612$	−7.27123	+	12.5941i	−0.293922	+	0.509088i
$613$	−1.25482	−	0.724472i	−0.0506818	−	0.0292611i	0.474445	−	0.880285i	$-0.342649\pi$
$613$	−1.25482	−	0.724472i	−0.0506818	−	0.0292611i	−0.525127	+	0.851024i	$0.675982\pi$
$614$	22.1652	−	12.7971i	0.894515	−	0.516449i
$615$	−27.0762			−1.09182
$616$	−8.77472	−	0.0656384i	−0.353543	−	0.00264465i
$617$	−2.96752			−0.119468			−0.0597340	−	0.998214i	$-0.519025\pi$
$617$	−2.96752			−0.119468			−0.0597340	+	0.998214i	$0.519025\pi$
$618$	4.63636	−	2.67680i	0.186502	−	0.107677i
$619$	−10.0004	−	5.77375i	−0.401951	−	0.232067i	0.285374	−	0.958416i	$-0.407882\pi$
$619$	−10.0004	−	5.77375i	−0.401951	−	0.232067i	−0.687326	+	0.726349i	$0.741215\pi$
$620$	0.494980	−	0.857330i	0.0198789	−	0.0344312i
$621$	−2.57616	+	1.48735i	−0.103378	+	0.0596853i
$622$	−1.90970			−0.0765720
$623$	4.28442	+	15.1453i	0.171651	+	0.606783i
$624$			13.0195i			0.521196i
$625$	3.00222	+	5.19999i	0.120089	+	0.208000i
$626$	−15.2251	+	26.3707i	−0.608519	+	1.05399i
$627$	−9.54366	−	38.9256i	−0.381137	−	1.55454i
$628$	7.25273	−	4.18736i	0.289415	−	0.167094i
$629$	2.74668			0.109517
$630$	−8.58138	+	33.9022i	−0.341891	+	1.35070i
$631$	−27.5215			−1.09562			−0.547808	−	0.836604i	$-0.684537\pi$
$631$	−27.5215			−1.09562			−0.547808	+	0.836604i	$0.684537\pi$
$632$	−3.84991	−	6.66824i	−0.153141	−	0.265248i
$633$	8.35696	−	14.4747i	0.332159	−	0.575317i
$634$	−29.7862	−	17.1971i	−1.18296	−	0.682983i
$635$	23.3926	+	40.5171i	0.928306	+	1.60787i
$636$			14.3788i			0.570156i
$637$	30.8885	+	16.7076i	1.22385	+	0.661978i
$638$	0.229926	+	0.239967i	0.00910288	+	0.00950040i
$639$	−15.7873	−	27.3443i	−0.624535	−	1.08173i
$640$	1.76950	−	3.06486i	0.0699456	−	0.121149i
$641$	−16.8273	+	29.1458i	−0.664639	+	1.15119i	0.314744	+	0.949177i	$0.398081\pi$
$641$	−16.8273	+	29.1458i	−0.664639	+	1.15119i	−0.979383	+	0.202013i	$0.935252\pi$
$642$	−27.5666	+	15.9156i	−1.08797	+	0.628137i
$643$			5.95261i			0.234748i	0.993088	+	0.117374i	$0.0374476\pi$
$643$			5.95261i			0.234748i	−0.993088	+	0.117374i	$0.962552\pi$
$644$	1.01254	−	4.00022i	0.0398997	−	0.157631i
$645$		−	82.9855i		−	3.26755i
$646$	15.7012	−	9.06508i	0.617754	−	0.356661i
$647$	10.1963	+	5.88686i	0.400860	+	0.231437i	0.686855	−	0.726795i	$-0.258991\pi$
$647$	10.1963	+	5.88686i	0.400860	+	0.231437i	−0.285995	+	0.958231i	$0.592324\pi$
$648$	−5.41700	−	3.12751i	−0.212800	−	0.122860i
$649$	46.2854	+	13.4683i	1.81686	+	0.528677i
$650$			37.7489i			1.48063i
$651$	−1.84815	+	0.522818i	−0.0724345	+	0.0204908i
$652$	−3.06508			−0.120038
$653$	−14.4335	−	24.9996i	−0.564827	−	0.978309i	−0.997066	−	0.0765498i	$-0.975610\pi$
$653$	−14.4335	−	24.9996i	−0.564827	−	0.978309i	0.432239	−	0.901759i	$-0.357724\pi$
$654$	15.1142	+	8.72616i	0.591010	+	0.341220i
$655$	50.5660	+	29.1943i	1.97578	+	1.14071i
$656$	−1.47405	−	2.55312i	−0.0575519	−	0.0996827i
$657$	14.5577			0.567952
$658$	−12.4599	−	12.1186i	−0.485736	−	0.472431i
$659$		−	44.6812i		−	1.74053i	−0.492581	−	0.870266i	$-0.663947\pi$
$659$		−	44.6812i		−	1.74053i	0.492581	−	0.870266i	$-0.336053\pi$
$660$	−8.51066	+	29.2479i	−0.331277	+	1.13847i
$661$	−34.3242	−	19.8171i	−1.33505	−	0.770794i	−0.348985	−	0.937128i	$-0.613474\pi$
$661$	−34.3242	−	19.8171i	−1.33505	−	0.770794i	−0.986069	+	0.166334i	$0.946807\pi$
$662$	−13.4345	−	7.75642i	−0.522147	−	0.301462i
$663$	43.9013	−	25.3464i	1.70499	−	0.984374i
$664$		−	2.87320i		−	0.111502i
$665$	30.3982	−	31.2543i	1.17879	−	1.21199i
$666$		−	2.63474i		−	0.102094i
$667$	−0.135344	+	0.0781407i	−0.00524053	+	0.00302562i
$668$	5.03656	−	8.72358i	0.194870	−	0.337525i
$669$	5.21362	−	9.03026i	0.201570	−	0.349130i
$670$	−7.04953	−	12.2101i	−0.272347	−	0.471719i
$671$	25.5321	+	26.6471i	0.985657	+	1.02870i
$672$	−6.60692	+	1.86902i	−0.254868	+	0.0720989i
$673$			2.71886i			0.104804i	0.998626	+	0.0524022i	$0.0166878\pi$
$673$			2.71886i			0.104804i	−0.998626	+	0.0524022i	$0.983312\pi$
$674$	−3.85441	−	6.67604i	−0.148466	−	0.257151i
$675$	12.4289	+	7.17580i	0.478387	+	0.276197i
$676$	6.08412	−	10.5380i	0.234005	−	0.405308i
$677$	3.02973	+	5.24764i	0.116442	+	0.201683i	0.918355	−	0.395757i	$-0.129518\pi$
$677$	3.02973	+	5.24764i	0.116442	+	0.201683i	−0.801913	+	0.597440i	$0.796184\pi$
$678$	−31.1161			−1.19501
$679$	−42.9837	−	10.8801i	−1.64956	−	0.417539i
$680$	−13.7795			−0.528420
$681$	−28.6090	+	16.5174i	−1.09630	+	0.632949i
$682$	−0.901068	+	0.220921i	−0.0345037	+	0.00845950i
$683$	3.01704	−	5.22567i	0.115444	−	0.199955i	−0.802513	−	0.596634i	$-0.796504\pi$
$683$	3.01704	−	5.22567i	0.115444	−	0.199955i	0.917957	+	0.396680i	$0.129838\pi$
$684$	−8.69566	−	15.0613i	−0.332487	−	0.575884i
$685$		−	23.5122i		−	0.898354i
$686$	−4.04428	+	18.0733i	−0.154411	+	0.690041i
$687$	−15.6060			−0.595405
$688$	7.82503	−	4.51778i	0.298326	−	0.172239i
$689$	13.8980	−	24.0720i	0.529471	−	0.917071i
$690$	−12.4050	−	7.16204i	−0.472251	−	0.272654i
$691$	−17.1519	+	9.90263i	−0.652487	+	0.376714i	−0.789409	−	0.613868i	$-0.789613\pi$
$691$	−17.1519	+	9.90263i	−0.652487	+	0.376714i	0.136921	+	0.990582i	$0.456279\pi$
$692$	−0.0766026			−0.00291200
$693$	28.5049	−	16.1742i	1.08281	−	0.614409i
$694$	−21.7413			−0.825288
$695$	43.9909	−	25.3982i	1.66867	−	0.963407i
$696$	0.225209	+	0.130024i	0.00853652	+	0.00492856i
$697$	−5.73938	+	9.94090i	−0.217394	+	0.376538i
$698$	11.6536	−	6.72823i	0.441096	−	0.254667i
$699$	−16.7828			−0.634786
$700$	−19.1562	+	5.41905i	−0.724037	+	0.204821i
$701$			26.0155i			0.982591i	0.870993	+	0.491296i	$0.163476\pi$
$701$			26.0155i			0.982591i	−0.870993	+	0.491296i	$0.836524\pi$
$702$	−4.78431	−	8.28667i	−0.180572	−	0.312760i
$703$	−1.64237	+	2.84467i	−0.0619433	+	0.107289i
$704$	−3.22122	+	0.789769i	−0.121404	+	0.0297655i
$705$	−52.2528	+	30.1682i	−1.96795	+	1.13620i
$706$	6.70769			0.252447
$707$	−2.66078	−	2.58790i	−0.100069	−	0.0973280i
$708$	37.7193			1.41758
$709$	12.4458	+	21.5568i	0.467413	+	0.809583i	0.999307	−	0.0372278i	$-0.0118527\pi$
$709$	12.4458	+	21.5568i	0.467413	+	0.809583i	−0.531894	+	0.846811i	$0.678519\pi$
$710$	14.9590	−	25.9098i	0.561401	−	0.972376i
$711$	24.9055	+	14.3792i	0.934030	+	0.539263i
$712$	2.97451	+	5.15200i	0.111474	+	0.193079i
$713$		−	0.436271i		−	0.0163385i
$714$	19.1647	+	18.6397i	0.717221	+	0.697575i
$715$	42.5178	−	40.7388i	1.59008	−	1.52354i
$716$	−4.48746	−	7.77250i	−0.167704	−	0.290472i
$717$	−20.2132	+	35.0102i	−0.754875	+	1.30748i
$718$	15.5232	−	26.8869i	0.579320	−	1.00341i
$719$	−11.5156	+	6.64851i	−0.429458	+	0.247948i	−0.699116	−	0.715009i	$-0.746423\pi$
$719$	−11.5156	+	6.64851i	−0.429458	+	0.247948i	0.269658	+	0.962956i	$0.413089\pi$
$720$			13.2180i			0.492604i
$721$	−1.48568	−	5.25184i	−0.0553296	−	0.195589i
$722$			2.68183i			0.0998073i
$723$	52.7626	−	30.4625i	1.96226	−	1.13291i
$724$	−13.1159	−	7.57248i	−0.487449	−	0.281429i
$725$	0.652974	+	0.376995i	0.0242508	+	0.0140012i
$726$	25.3095	−	13.2044i	0.939325	−	0.490060i
$727$			5.67083i			0.210319i	0.994455	+	0.105160i	$0.0335354\pi$
$727$			5.67083i			0.210319i	−0.994455	+	0.105160i	$0.966465\pi$
$728$	12.8674	+	3.25701i	0.476897	+	0.120713i
$729$	38.2116			1.41525
$730$	6.89699	+	11.9459i	0.255269	+	0.442139i
$731$	−30.4677	−	17.5905i	−1.12689	−	0.650609i
$732$	25.0083	+	14.4385i	0.924332	+	0.533663i
$733$	−20.6879	−	35.8326i	−0.764127	−	1.32351i	−0.940707	−	0.339220i	$-0.889837\pi$
$733$	−20.6879	−	35.8326i	−0.764127	−	1.32351i	0.176580	−	0.984286i	$-0.443496\pi$
$734$	29.6492			1.09437
$735$	56.5481	+	30.5868i	2.08581	+	1.12821i
$736$		−	1.55962i		−	0.0574885i
$737$	−3.69170	+	12.6870i	−0.135985	+	0.467330i
$738$	9.53578	+	5.50549i	0.351017	+	0.202660i
$739$	−35.9749	−	20.7701i	−1.32336	−	0.764042i	−0.339097	−	0.940752i	$-0.610121\pi$
$739$	−35.9749	−	20.7701i	−1.32336	−	0.764042i	−0.984263	+	0.176710i	$0.943455\pi$
$740$	2.16204	−	1.24826i	0.0794783	−	0.0458868i
$741$			60.6236i			2.22706i
$742$	14.2108	+	3.59706i	0.521696	+	0.132052i
$743$			39.7404i			1.45793i	0.684549	+	0.728967i	$0.259999\pi$
$743$			39.7404i			1.45793i	−0.684549	+	0.728967i	$0.740001\pi$
$744$	−0.628687	+	0.362973i	−0.0230488	+	0.0133072i
$745$	4.71725	−	8.17053i	0.172827	−	0.299345i
$746$	−4.39027	+	7.60418i	−0.160739	+	0.278409i
$747$	5.36562	+	9.29353i	0.196318	+	0.340033i
$748$	8.93419	+	9.32434i	0.326666	+	0.340932i
$749$	8.83346	+	31.2260i	0.322768	+	1.14097i
$750$			23.1858i			0.846626i
$751$	−2.68263	−	4.64645i	−0.0978905	−	0.169551i	0.812921	−	0.582374i	$-0.197876\pi$
$751$	−2.68263	−	4.64645i	−0.0978905	−	0.169551i	−0.910811	+	0.412823i	$0.864543\pi$
$752$	−5.68935	−	3.28475i	−0.207469	−	0.119782i
$753$	−23.7223	+	41.0882i	−0.864487	+	1.49734i
$754$	−0.251353	−	0.435356i	−0.00915374	−	0.0158547i
$755$	36.7714			1.33825
$756$	3.51838	−	3.61747i	0.127962	−	0.131566i
$757$	25.8962			0.941215			0.470607	−	0.882343i	$-0.344035\pi$
$757$	25.8962			0.941215			0.470607	+	0.882343i	$0.344035\pi$
$758$	26.6852	−	15.4067i	0.969251	−	0.559598i
$759$	3.19659	+	13.0379i	0.116029	+	0.473245i
$760$	8.23945	−	14.2711i	0.298876	−	0.517669i
$761$	7.61030	+	13.1814i	0.275873	+	0.477827i	0.970355	−	0.241684i	$-0.0776996\pi$
$761$	7.61030	+	13.1814i	0.275873	+	0.477827i	−0.694482	+	0.719510i	$0.744366\pi$
$762$		−	34.3080i		−	1.24285i
$763$	12.4053	−	12.7546i	0.449100	−	0.461748i
$764$	−6.00000			−0.217072
$765$	44.5706	−	25.7329i	1.61145	−	0.930374i
$766$	2.64741	−	4.58545i	0.0956548	−	0.165679i
$767$	−63.1471	−	36.4580i	−2.28011	−	1.31642i
$768$	−2.24749	+	1.29759i	−0.0810993	+	0.0468227i
$769$	−22.5146			−0.811898			−0.405949	−	0.913896i	$-0.633059\pi$
$769$	−22.5146			−0.811898			−0.405949	+	0.913896i	$0.633059\pi$
$770$	26.7771	+	15.7280i	0.964981	+	0.566799i
$771$	−24.9647			−0.899083
$772$	12.8415	−	7.41403i	0.462175	−	0.266837i
$773$	24.2776	+	14.0167i	0.873204	+	0.504144i	0.868412	−	0.495844i	$-0.165141\pi$
$773$	24.2776	+	14.0167i	0.873204	+	0.504144i	0.00479213	+	0.999989i	$0.498475\pi$
$774$	−16.8737	+	29.2261i	−0.606512	+	1.05051i
$775$	−1.82283	+	1.05241i	−0.0654778	+	0.0378036i
$776$	−16.7587			−0.601601
$777$	−4.69553	−	1.18854i	−0.168451	−	0.0426386i
$778$			0.860237i			0.0308410i
$779$	−6.86371	−	11.8883i	−0.245918	−	0.425943i
$780$	23.0379	−	39.9029i	0.824891	−	1.42875i
$781$	−27.2316	+	6.67655i	−0.974423	+	0.238906i
$782$	−5.25901	+	3.03629i	−0.188062	+	0.108578i
$783$	−0.191122			−0.00683014
$784$	0.194366	+	6.99730i	0.00694163	+	0.249904i
$785$	−29.6381			−1.05783
$786$	−21.4084	−	37.0805i	−0.763613	−	1.32262i
$787$	6.37160	−	11.0359i	0.227123	−	0.393388i	−0.729831	−	0.683627i	$-0.760401\pi$
$787$	6.37160	−	11.0359i	0.227123	−	0.393388i	0.956954	+	0.290239i	$0.0937347\pi$
$788$	12.5353	+	7.23723i	0.446550	+	0.257816i
$789$	−0.750870	−	1.30054i	−0.0267317	−	0.0463006i
$790$			27.2496i			0.969499i
$791$	−7.78414	+	30.7526i	−0.276772	+	1.09344i
$792$	8.94436	−	8.57010i	0.317824	−	0.304525i
$793$	−27.9114	−	48.3440i	−0.991165	−	1.71675i
$794$	6.17367	−	10.6931i	0.219095	−	0.379484i
$795$	25.4432	−	44.0690i	0.902379	−	1.56297i
$796$	−9.72188	+	5.61293i	−0.344583	+	0.198945i
$797$			5.63488i			0.199598i	0.995008	+	0.0997989i	$0.0318199\pi$
$797$			5.63488i			0.199598i	−0.995008	+	0.0997989i	$0.968180\pi$
$798$	−30.7643	+	8.70284i	−1.08904	+	0.308077i
$799$			25.5791i			0.904923i
$800$	−6.51641	+	3.76225i	−0.230390	+	0.133016i
$801$	−19.2425	−	11.1096i	−0.679899	−	0.392540i
$802$	−29.2069	−	16.8626i	−1.03133	−	0.595439i
$803$	3.61182	−	12.4124i	0.127458	−	0.438025i
$804$			10.3390i			0.364627i
$805$	−10.1817	+	10.4684i	−0.358857	+	0.368963i
$806$	1.40334			0.0494306
$807$	28.6632	+	49.6462i	1.00899	+	1.74763i
$808$	−1.21495	−	0.701452i	−0.0427418	−	0.0246770i
$809$	14.7572	+	8.52007i	0.518835	+	0.299550i	0.736458	−	0.676483i	$-0.236497\pi$
$809$	14.7572	+	8.52007i	0.518835	+	0.299550i	−0.217623	+	0.976033i	$0.569830\pi$
$810$	11.0682	+	19.1707i	0.388898	+	0.673591i
$811$	−0.332109			−0.0116619			−0.00583097	−	0.999983i	$-0.501856\pi$
$811$	−0.332109			−0.0116619			−0.00583097	+	0.999983i	$0.501856\pi$
$812$	0.184845	−	0.190050i	0.00648678	−	0.00666946i
$813$		−	11.0612i		−	0.387934i
$814$	−2.24647	−	0.653687i	−0.0787388	−	0.0229117i
$815$	9.39404	+	5.42365i	0.329059	+	0.189982i
$816$	8.75087	+	5.05232i	0.306342	+	0.176867i
$817$	36.4363	−	21.0365i	1.27474	−	0.735973i
$818$		−	38.3692i		−	1.34155i
$819$	−47.7027	+	13.4945i	−1.66687	+	0.471536i
$820$			10.4333i			0.364346i
$821$	1.97706	−	1.14146i	0.0690000	−	0.0398372i	−0.465103	−	0.885257i	$-0.653983\pi$
$821$	1.97706	−	1.14146i	0.0690000	−	0.0398372i	0.534103	+	0.845419i	$0.320649\pi$
$822$	−8.62085	+	14.9317i	−0.300687	+	0.520804i
$823$	−5.04228	+	8.73348i	−0.175763	+	0.304430i	−0.940425	−	0.340001i	$-0.889572\pi$
$823$	−5.04228	+	8.73348i	−0.175763	+	0.304430i	0.764662	+	0.644431i	$0.222906\pi$
$824$	−1.03145	−	1.78653i	−0.0359324	−	0.0622367i
$825$	46.7637	−	44.8070i	1.62810	−	1.55998i
$826$	9.43603	−	37.2787i	0.328321	−	1.29709i
$827$			10.9337i			0.380204i	0.981764	+	0.190102i	$0.0608818\pi$
$827$			10.9337i			0.380204i	−0.981764	+	0.190102i	$0.939118\pi$
$828$	2.91256	+	5.04469i	0.101218	+	0.175315i
$829$	−10.0682	−	5.81287i	−0.349683	−	0.201889i	0.314863	−	0.949137i	$-0.398041\pi$
$829$	−10.0682	−	5.81287i	−0.349683	−	0.201889i	−0.664545	+	0.747248i	$0.731375\pi$
$830$	−5.08412	+	8.80595i	−0.176472	+	0.305659i
$831$	23.8306	+	41.2757i	0.826673	+	1.43184i
$832$	5.01680			0.173926
$833$	23.2163	−	14.2778i	0.804398	−	0.494697i
$834$	−37.2494			−1.28984
$835$	−30.8727	+	17.8244i	−1.06839	+	0.616838i
$836$	−14.9992	+	3.67746i	−0.518759	+	0.127188i
$837$	0.266766	−	0.462052i	0.00922078	−	0.0159709i
$838$	16.7512	+	29.0139i	0.578659	+	1.00227i
$839$			23.4571i			0.809828i	0.914355	+	0.404914i	$0.132699\pi$
$839$			23.4571i			0.809828i	−0.914355	+	0.404914i	$0.867301\pi$
$840$	23.5565	+	5.96266i	0.812777	+	0.205731i
$841$	28.9900			0.999654
$842$	−19.9320	+	11.5077i	−0.686902	+	0.396583i
$843$	−4.83858	+	8.38067i	−0.166650	+	0.288646i
$844$	−5.57753	−	3.22019i	−0.191986	−	0.110843i
$845$	−37.2940	+	21.5317i	−1.28295	+	0.740712i
$846$	24.5367			0.843589
$847$	−6.71856	−	28.3171i	−0.230853	−	0.972989i
$848$	5.54058			0.190264
$849$	−28.6140	+	16.5203i	−0.982029	+	0.566975i
$850$	25.3724	+	14.6488i	0.870266	+	0.502449i
$851$	0.550102	−	0.952805i	0.0188573	−	0.0326617i
$852$	−18.9999	+	10.9696i	−0.650924	+	0.375811i
$853$	−38.5870			−1.32119			−0.660597	−	0.750741i	$-0.729697\pi$
$853$	−38.5870			−1.32119			−0.660597	+	0.750741i	$0.729697\pi$
$854$	20.5260	−	21.1041i	0.702387	−	0.722168i
$855$			61.5478i			2.10489i
$856$	6.13274	+	10.6222i	0.209613	+	0.363060i
$857$	−21.3007	+	36.8938i	−0.727617	+	1.26027i	0.230271	+	0.973126i	$0.426039\pi$
$857$	−21.3007	+	36.8938i	−0.727617	+	1.26027i	−0.957888	+	0.287142i	$0.907295\pi$
$858$	−41.9386	+	10.2824i	−1.43176	+	0.351035i
$859$	10.7344	−	6.19752i	0.366254	−	0.211457i	−0.305567	−	0.952171i	$-0.598846\pi$
$859$	10.7344	−	6.19752i	0.366254	−	0.211457i	0.671821	+	0.740714i	$0.265513\pi$
$860$	−31.9768			−1.09040
$861$	14.1133	−	14.5107i	0.480979	−	0.494525i
$862$	26.8381			0.914110
$863$	19.6374	+	34.0130i	0.668465	+	1.15781i	0.978333	+	0.207036i	$0.0663816\pi$
$863$	19.6374	+	34.0130i	0.668465	+	1.15781i	−0.309869	+	0.950779i	$0.600285\pi$
$864$	0.953659	−	1.65179i	0.0324441	−	0.0561949i
$865$	0.234776	+	0.135548i	0.00798264	+	0.00460878i
$866$	15.3456	+	26.5794i	0.521465	+	0.903204i
$867$			4.77440i			0.162147i
$868$	0.201457	+	0.712146i	0.00683791	+	0.0241718i
$869$	18.4393	−	17.6678i	0.625512	−	0.599338i
$870$	−0.460156	−	0.797013i	−0.0156007	−	0.0270213i
$871$	9.99325	−	17.3088i	0.338608	−	0.586487i
$872$	3.36245	−	5.82394i	0.113867	−	0.197223i
$873$	54.2069	−	31.2964i	1.83463	−	1.05922i
$874$		−	7.26219i		−	0.245647i
$875$	22.9149	+	5.80026i	0.774666	+	0.196085i
$876$		−	10.1152i		−	0.341763i
$877$	39.9403	−	23.0595i	1.34869	−	0.778665i	0.360624	−	0.932711i	$-0.382564\pi$
$877$	39.9403	−	23.0595i	1.34869	−	0.778665i	0.988064	+	0.154046i	$0.0492304\pi$
$878$	14.5883	+	8.42258i	0.492332	+	0.284248i
$879$	−58.9407	−	34.0294i	−1.98802	−	1.14778i
$880$	11.2701	+	3.27941i	0.379915	+	0.110549i
$881$		−	14.9583i		−	0.503957i	−0.967733	−	0.251978i	$-0.918919\pi$
$881$		−	14.9583i		−	0.503957i	0.967733	−	0.251978i	$-0.0810812\pi$
$882$	−13.6960	−	22.2702i	−0.461167	−	0.749877i
$883$	−8.42386			−0.283485			−0.141743	−	0.989904i	$-0.545271\pi$
$883$	−8.42386			−0.283485			−0.141743	+	0.989904i	$0.545271\pi$
$884$	−9.76675	−	16.9165i	−0.328491	−	0.568964i
$885$	−115.604	−	66.7442i	−3.88600	−	2.24358i
$886$	0.684671	+	0.395295i	0.0230020	+	0.0132802i
$887$	−5.66022	−	9.80379i	−0.190052	−	0.329179i	0.755216	−	0.655477i	$-0.227532\pi$
$887$	−5.66022	−	9.80379i	−0.190052	−	0.329179i	−0.945267	+	0.326298i	$0.894199\pi$
$888$	−1.83072			−0.0614348
$889$	−33.9072	−	8.58263i	−1.13721	−	0.287852i
$890$		−	21.0536i		−	0.705717i
$891$	5.79621	−	19.9194i	0.194180	−	0.667324i
$892$	−3.47963	−	2.00897i	−0.116507	−	0.0672652i
$893$	−26.4917	−	15.2950i	−0.886512	−	0.511828i
$894$	−5.99152	+	3.45920i	−0.200386	+	0.115693i
$895$			31.7622i			1.06169i
$896$	0.720188	+	2.54585i	0.0240598	+	0.0850507i
$897$		−	20.3055i		−	0.677980i
$898$	13.8334	−	7.98672i	0.461627	−	0.266520i
$899$	0.0140151	−	0.0242748i	0.000467428	−	0.000809609i
$900$	14.0518	−	24.3384i	0.468393	−	0.811281i
$901$	−10.7865	−	18.6827i	−0.359349	−	0.622411i
$902$	7.06002	−	6.76461i	0.235073	−	0.225237i
$903$	44.4737	+	43.2555i	1.47999	+	1.43945i
$904$			11.9900i			0.398780i
$905$	26.7990	+	46.4172i	0.890828	+	1.54296i
$906$	−23.3522	−	13.4824i	−0.775825	−	0.447923i
$907$	−27.4033	+	47.4638i	−0.909910	+	1.57601i	−0.0957232	+	0.995408i	$0.530516\pi$
$907$	−27.4033	+	47.4638i	−0.909910	+	1.57601i	−0.814187	+	0.580603i	$0.802817\pi$
$908$	6.36466	+	11.0239i	0.211219	+	0.365841i
$909$	5.23977			0.173792
$910$	−33.6735	−	32.7511i	−1.11626	−	1.08569i
$911$	46.5914			1.54364			0.771820	−	0.635841i	$-0.219347\pi$
$911$	46.5914			1.54364			0.771820	+	0.635841i	$0.219347\pi$
$912$	−10.4652	+	6.04206i	−0.346536	+	0.200073i
$913$	9.25521	−	2.26916i	0.306303	−	0.0750983i
$914$	−17.4666	+	30.2530i	−0.577743	+	1.00068i
$915$	−51.0979	−	88.5042i	−1.68924	−	2.92586i
$916$			6.01345i			0.198690i
$917$	−42.0029	+	11.8821i	−1.38706	+	0.392382i
$918$	−7.42637			−0.245107
$919$	47.0315	−	27.1536i	1.55142	−	0.895716i	0.553399	−	0.832916i	$-0.313331\pi$
$919$	47.0315	−	27.1536i	1.55142	−	0.895716i	0.998026	−	0.0627991i	$-0.0200028\pi$
$920$	−2.75975	+	4.78003i	−0.0909863	+	0.157593i
$921$	57.5227	+	33.2107i	1.89544	+	1.09433i
$922$	18.0433	−	10.4173i	0.594224	−	0.343076i
$923$	42.4110			1.39598
$924$	−11.2385	−	19.8063i	−0.369718	−	0.651578i
$925$	−5.30800			−0.174526
$926$	11.4076	−	6.58618i	0.374877	−	0.216435i
$927$	6.67259	+	3.85242i	0.219157	+	0.126530i
$928$	0.0501023	−	0.0867797i	0.00164469	−	0.00284868i
$929$	−18.6550	+	10.7704i	−0.612049	+	0.353367i	−0.773767	−	0.633470i	$-0.781630\pi$
$929$	−18.6550	+	10.7704i	−0.612049	+	0.353367i	0.161718	+	0.986837i	$0.448297\pi$
$930$	2.56912			0.0842447
$931$	0.905040	+	32.5821i	0.0296615	+	1.06783i
$932$			6.46694i			0.211832i
$933$	−2.47801	−	4.29203i	−0.0811262	−	0.140515i
$934$	−8.40919	+	14.5651i	−0.275157	+	0.476586i
$935$	−10.8826	−	44.3868i	−0.355900	−	1.45161i
$936$	−16.2271	+	9.36873i	−0.530400	+	0.306227i
$937$	15.2663			0.498729			0.249364	−	0.968410i	$-0.419778\pi$
$937$	15.2663			0.498729			0.249364	+	0.968410i	$0.419778\pi$
$938$	10.2182	+	2.58644i	0.333636	+	0.0844504i
$939$	−79.0239			−2.57885
$940$	11.6247	+	20.1346i	0.379156	+	0.656717i
$941$	18.0945	−	31.3405i	0.589863	−	1.02167i	−0.404387	−	0.914588i	$-0.632515\pi$
$941$	18.0945	−	31.3405i	0.589863	−	1.02167i	0.994250	−	0.107085i	$-0.0341516\pi$
$942$	18.8221	+	10.8670i	0.613258	+	0.354064i
$943$	2.29896	+	3.98191i	0.0748644	+	0.129669i
$944$		−	14.5344i		−	0.473054i
$945$	−17.1844	+	4.86127i	−0.559010	+	0.158137i
$946$	20.7327	+	21.6381i	0.674079	+	0.703516i
$947$	−19.9609	−	34.5733i	−0.648641	−	1.12348i	−0.983448	−	0.181193i	$-0.942004\pi$
$947$	−19.9609	−	34.5733i	−0.648641	−	1.12348i	0.334806	−	0.942287i	$-0.391329\pi$
$948$	9.99120	−	17.3053i	0.324499	−	0.562049i
$949$	−9.77701	+	16.9343i	−0.317375	+	0.549710i
$950$	−30.3428	+	17.5184i	−0.984451	+	0.568373i
$951$		−	89.2590i		−	2.89442i
$952$	7.18245	−	7.38473i	0.232785	−	0.239341i
$953$			8.97831i			0.290836i	0.989370	+	0.145418i	$0.0464527\pi$
$953$			8.97831i			0.290836i	−0.989370	+	0.145418i	$0.953547\pi$
$954$	−17.9213	+	10.3469i	−0.580225	+	0.334993i
$955$	18.3892	+	10.6170i	0.595059	+	0.343558i
$956$	13.4905	+	7.78874i	0.436314	+	0.251906i
$957$	−0.240974	+	0.828136i	−0.00778959	+	0.0267699i
$958$		−	22.8582i		−	0.738513i
$959$	12.6007	+	12.2555i	0.406897	+	0.395752i
$960$	9.18432			0.296423
$961$	−15.4609	−	26.7790i	−0.498738	−	0.863839i
$962$	3.06486	+	1.76950i	0.0988151	+	0.0570509i
$963$	−39.6734	−	22.9055i	−1.27846	−	0.738119i
$964$	−11.7381	−	20.3310i	−0.378059	−	0.654818i
$965$	−52.4765			−1.68928
$966$	10.3043	−	2.91496i	0.331536	−	0.0937874i
$967$			51.5738i			1.65850i	0.558877	+	0.829251i	$0.311232\pi$
$967$			51.5738i			1.65850i	−0.558877	+	0.829251i	$0.688768\pi$
$968$	−5.08804	−	9.75253i	−0.163536	−	0.313458i
$969$	40.7473	+	23.5255i	1.30899	+	0.755748i
$970$	51.3630	+	29.6544i	1.64917	+	0.952147i
$971$	−29.0721	+	16.7848i	−0.932967	+	0.538649i	−0.887749	−	0.460328i	$-0.847732\pi$
$971$	−29.0721	+	16.7848i	−0.932967	+	0.538649i	−0.0452186	+	0.998977i	$0.514398\pi$
$972$		−	21.9548i		−	0.704201i
$973$	−9.31848	+	36.8143i	−0.298737	+	1.18021i
$974$			31.2628i			1.00173i
$975$	−84.8402	+	48.9825i	−2.71706	+	1.56870i
$976$	5.56360	−	9.63644i	0.178087	−	0.308455i
$977$	0.576295	−	0.998172i	0.0184373	−	0.0319344i	−0.856660	−	0.515882i	$-0.827464\pi$
$977$	0.576295	−	0.998172i	0.0184373	−	0.0319344i	0.875097	+	0.483948i	$0.160798\pi$
$978$	−3.97721	−	6.88873i	−0.127177	−	0.220277i
$979$	−14.2466	+	13.6504i	−0.455322	+	0.436270i
$980$	11.7860	−	21.7897i	0.376490	−	0.696046i
$981$			25.1172i			0.801929i
$982$	−11.2490	−	19.4838i	−0.358969	−	0.621753i
$983$	−14.3846	−	8.30496i	−0.458798	−	0.264887i	0.252741	−	0.967534i	$-0.418668\pi$
$983$	−14.3846	−	8.30496i	−0.458798	−	0.264887i	−0.711539	+	0.702647i	$0.752001\pi$
$984$	3.82541	−	6.62581i	0.121950	−	0.211223i
$985$	−25.6125	−	44.3622i	−0.816083	−	1.41350i
$986$	−0.390159			−0.0124252
$987$	11.0686	−	43.7283i	0.352316	−	1.39189i
$988$	23.3601			0.743183
$989$	−12.2041	+	7.04604i	−0.388068	+	0.224051i
$990$	−42.5780	+	10.4391i	−1.35322	+	0.331777i
$991$	9.24571	−	16.0140i	0.293700	−	0.508703i	−0.680982	−	0.732300i	$-0.738447\pi$
$991$	9.24571	−	16.0140i	0.293700	−	0.508703i	0.974682	+	0.223598i	$0.0717801\pi$
$992$	0.139864	+	0.242252i	0.00444070	+	0.00769151i
$993$		−	40.2586i		−	1.27757i
$994$	6.08833	+	21.5221i	0.193110	+	0.682639i
$995$	39.7283			1.25947
$996$	6.45748	−	3.72823i	0.204613	−	0.118134i
$997$	−10.5865	+	18.3363i	−0.335277	+	0.580717i	−0.983538	−	0.180701i	$-0.942163\pi$
$997$	−10.5865	+	18.3363i	−0.335277	+	0.580717i	0.648261	+	0.761418i	$0.275497\pi$
$998$	27.6346	+	15.9548i	0.874757	+	0.505041i
$999$	1.16522	−	0.672739i	0.0368659	−	0.0212845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.i.a.87.8	yes	16
3.2	odd	2		1386.2.bk.c.703.4		16
4.3	odd	2		1232.2.bn.b.241.1		16
7.2	even	3		1078.2.i.c.901.1		16
7.3	odd	6		1078.2.c.b.1077.15		16
7.4	even	3		1078.2.c.b.1077.10		16
7.5	odd	6	inner	154.2.i.a.131.4	yes	16
7.6	odd	2		1078.2.i.c.1011.5		16
11.10	odd	2	inner	154.2.i.a.87.4	✓	16
21.5	even	6		1386.2.bk.c.901.8		16
28.19	even	6		1232.2.bn.b.593.2		16
33.32	even	2		1386.2.bk.c.703.8		16
44.43	even	2		1232.2.bn.b.241.2		16
77.10	even	6		1078.2.c.b.1077.7		16
77.32	odd	6		1078.2.c.b.1077.2		16
77.54	even	6	inner	154.2.i.a.131.8	yes	16
77.65	odd	6		1078.2.i.c.901.5		16
77.76	even	2		1078.2.i.c.1011.1		16
231.131	odd	6		1386.2.bk.c.901.4		16
308.131	odd	6		1232.2.bn.b.593.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.4	✓	16	11.10	odd	2	inner
154.2.i.a.87.8	yes	16	1.1	even	1	trivial
154.2.i.a.131.4	yes	16	7.5	odd	6	inner
154.2.i.a.131.8	yes	16	77.54	even	6	inner
1078.2.c.b.1077.2		16	77.32	odd	6
1078.2.c.b.1077.7		16	77.10	even	6
1078.2.c.b.1077.10		16	7.4	even	3
1078.2.c.b.1077.15		16	7.3	odd	6
1078.2.i.c.901.1		16	7.2	even	3
1078.2.i.c.901.5		16	77.65	odd	6
1078.2.i.c.1011.1		16	77.76	even	2
1078.2.i.c.1011.5		16	7.6	odd	2
1232.2.bn.b.241.1		16	4.3	odd	2
1232.2.bn.b.241.2		16	44.43	even	2
1232.2.bn.b.593.1		16	308.131	odd	6
1232.2.bn.b.593.2		16	28.19	even	6
1386.2.bk.c.703.4		16	3.2	odd	2
1386.2.bk.c.703.8		16	33.32	even	2
1386.2.bk.c.901.4		16	231.131	odd	6
1386.2.bk.c.901.8		16	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(2.24749 + 1.29759i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.06486 + 1.76950i) q^{5} +2.59518 q^{6} +(0.649221 - 2.56486i) q^{7} -1.00000i q^{8} +(1.86747 + 3.23456i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(2.24749 + 1.29759i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.06486 + 1.76950i) q^{5} +2.59518 q^{6} +(0.649221 - 2.56486i) q^{7} -1.00000i q^{8} +(1.86747 + 3.23456i) q^{9} +(-1.76950 + 3.06486i) q^{10} +(3.22122 - 0.789769i) q^{11} +(2.24749 - 1.29759i) q^{12} -5.01680 q^{13} +(-0.720188 - 2.54585i) q^{14} -9.18432 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.94681 + 3.37197i) q^{17} +(3.23456 + 1.86747i) q^{18} +(-2.32819 - 4.03254i) q^{19} +3.53900i q^{20} +(4.78725 - 4.92208i) q^{21} +(2.39477 - 2.29457i) q^{22} +(0.779812 + 1.35067i) q^{23} +(1.29759 - 2.24749i) q^{24} +(3.76225 - 6.51641i) q^{25} +(-4.34467 + 2.50840i) q^{26} +1.90732i q^{27} +(-1.89662 - 1.84467i) q^{28} +0.100205i q^{29} +(-7.95386 + 4.59216i) q^{30} +(-0.242252 - 0.139864i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(8.26446 + 2.40482i) q^{33} +3.89362i q^{34} +(2.54874 + 9.00974i) q^{35} +3.73495 q^{36} +(-0.352715 - 0.610920i) q^{37} +(-4.03254 - 2.32819i) q^{38} +(-11.2752 - 6.50974i) q^{39} +(1.76950 + 3.06486i) q^{40} +2.94809 q^{41} +(1.68484 - 6.65627i) q^{42} +9.03556i q^{43} +(0.926651 - 3.18454i) q^{44} +(-11.4471 - 6.60898i) q^{45} +(1.35067 + 0.779812i) q^{46} +(5.68935 - 3.28475i) q^{47} -2.59518i q^{48} +(-6.15702 - 3.33032i) q^{49} -7.52450i q^{50} +(-8.75087 + 5.05232i) q^{51} +(-2.50840 + 4.34467i) q^{52} +(-2.77029 + 4.79828i) q^{53} +(0.953659 + 1.65179i) q^{54} +(-8.47510 + 8.12048i) q^{55} +(-2.56486 - 0.649221i) q^{56} -12.0841i q^{57} +(0.0501023 + 0.0867797i) q^{58} +(12.5871 + 7.26719i) q^{59} +(-4.59216 + 7.95386i) q^{60} +(5.56360 + 9.63644i) q^{61} -0.279729 q^{62} +(9.50860 - 2.68987i) q^{63} -1.00000 q^{64} +(15.3758 - 8.87721i) q^{65} +(8.35964 - 2.04959i) q^{66} +(-1.99196 + 3.45017i) q^{67} +(1.94681 + 3.37197i) q^{68} +4.04750i q^{69} +(6.71215 + 6.52829i) q^{70} -8.45381 q^{71} +(3.23456 - 1.86747i) q^{72} +(1.94885 - 3.37552i) q^{73} +(-0.610920 - 0.352715i) q^{74} +(16.9112 - 9.76370i) q^{75} -4.65637 q^{76} +(0.0656384 - 8.77472i) q^{77} -13.0195 q^{78} +(6.66824 - 3.84991i) q^{79} +(3.06486 + 1.76950i) q^{80} +(3.12751 - 5.41700i) q^{81} +(2.55312 - 1.47405i) q^{82} +2.87320 q^{83} +(-1.86902 - 6.60692i) q^{84} -13.7795i q^{85} +(4.51778 + 7.82503i) q^{86} +(-0.130024 + 0.225209i) q^{87} +(-0.789769 - 3.22122i) q^{88} +(-5.15200 + 2.97451i) q^{89} -13.2180 q^{90} +(-3.25701 + 12.8674i) q^{91} +1.55962 q^{92} +(-0.362973 - 0.628687i) q^{93} +(3.28475 - 5.68935i) q^{94} +(14.2711 + 8.23945i) q^{95} +(-1.29759 - 2.24749i) q^{96} -16.7587i q^{97} +(-6.99730 + 0.194366i) q^{98} +(8.57010 + 8.94436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 - 12 * q^5 + 16 * q^9	\( 16 q + 8 q^{4} - 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} - 36 q^{26} - 12 q^{31} - 24 q^{33} + 32 q^{36} - 16 q^{37} + 12 q^{38} + 12 q^{42} - 8 q^{44} - 108 q^{45} + 24 q^{47} + 8 q^{49} - 28 q^{53} - 4 q^{56} - 12 q^{58} + 60 q^{59} - 4 q^{60} - 16 q^{64} + 48 q^{66} + 12 q^{67} + 60 q^{70} + 8 q^{71} + 60 q^{75} + 44 q^{77} - 16 q^{78} + 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} + 96 q^{89} - 36 q^{91} + 32 q^{92} - 44 q^{93} + 56 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 - 12 * q^5 + 16 * q^9 + 8 * q^11 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^22 + 16 * q^23 - 36 * q^26 - 12 * q^31 - 24 * q^33 + 32 * q^36 - 16 * q^37 + 12 * q^38 + 12 * q^42 - 8 * q^44 - 108 * q^45 + 24 * q^47 + 8 * q^49 - 28 * q^53 - 4 * q^56 - 12 * q^58 + 60 * q^59 - 4 * q^60 - 16 * q^64 + 48 * q^66 + 12 * q^67 + 60 * q^70 + 8 * q^71 + 60 * q^75 + 44 * q^77 - 16 * q^78 + 12 * q^80 - 8 * q^81 + 20 * q^86 - 4 * q^88 + 96 * q^89 - 36 * q^91 + 32 * q^92 - 44 * q^93 + 56 * q^99

Introduction

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