LMFDB - Embedded newform 1183.2.e.j.508.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, 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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.4
Character	$\chi$	$=$	1183.508
Dual form			1183.2.e.j.170.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.672613 - 1.16500i) q^{2} +(-1.02505 + 1.77544i) q^{3} +(0.0951832 - 0.164862i) q^{4} +(-1.78389 - 3.08979i) q^{5} +2.75785 q^{6} +(2.62255 + 0.349630i) q^{7} -2.94654 q^{8} +(-0.601462 - 1.04176i) q^{9} +O(q^{10})$	\(q+(-0.672613 - 1.16500i) q^{2} +(-1.02505 + 1.77544i) q^{3} +(0.0951832 - 0.164862i) q^{4} +(-1.78389 - 3.08979i) q^{5} +2.75785 q^{6} +(2.62255 + 0.349630i) q^{7} -2.94654 q^{8} +(-0.601462 - 1.04176i) q^{9} +(-2.39973 + 4.15646i) q^{10} +(-0.639336 + 1.10736i) q^{11} +(0.195135 + 0.337984i) q^{12} +(-1.35664 - 3.29043i) q^{14} +7.31431 q^{15} +(1.79151 + 3.10299i) q^{16} +(-3.86960 + 6.70234i) q^{17} +(-0.809103 + 1.40141i) q^{18} +(0.471939 + 0.817422i) q^{19} -0.679185 q^{20} +(-3.30899 + 4.29779i) q^{21} +1.72010 q^{22} +(-0.823637 - 1.42658i) q^{23} +(3.02035 - 5.23141i) q^{24} +(-3.86451 + 6.69354i) q^{25} -3.68419 q^{27} +(0.307263 - 0.399080i) q^{28} +4.04484 q^{29} +(-4.91970 - 8.52117i) q^{30} +(2.57610 - 4.46193i) q^{31} +(-0.536547 + 0.929326i) q^{32} +(-1.31071 - 2.27021i) q^{33} +10.4110 q^{34} +(-3.59805 - 8.72681i) q^{35} -0.228996 q^{36} +(0.528041 + 0.914594i) q^{37} +(0.634865 - 1.09962i) q^{38} +(5.25629 + 9.10417i) q^{40} +4.19882 q^{41} +(7.23260 + 0.964227i) q^{42} +3.83065 q^{43} +(0.121708 + 0.210805i) q^{44} +(-2.14588 + 3.71678i) q^{45} +(-1.10798 + 1.91908i) q^{46} +(0.447109 + 0.774415i) q^{47} -7.34558 q^{48} +(6.75552 + 1.83384i) q^{49} +10.3973 q^{50} +(-7.93308 - 13.7405i) q^{51} +(0.0399961 - 0.0692754i) q^{53} +(2.47804 + 4.29208i) q^{54} +4.56202 q^{55} +(-7.72744 - 1.03020i) q^{56} -1.93505 q^{57} +(-2.72061 - 4.71224i) q^{58} +(-5.59237 + 9.68627i) q^{59} +(0.696200 - 1.20585i) q^{60} +(3.81196 + 6.60251i) q^{61} -6.93087 q^{62} +(-1.21313 - 2.94236i) q^{63} +8.60961 q^{64} +(-1.76319 + 3.05394i) q^{66} +(-3.16052 + 5.47418i) q^{67} +(0.736641 + 1.27590i) q^{68} +3.37708 q^{69} +(-7.74664 + 10.0615i) q^{70} +11.4240 q^{71} +(1.77223 + 3.06959i) q^{72} +(-0.380253 + 0.658617i) q^{73} +(0.710335 - 1.23034i) q^{74} +(-7.92265 - 13.7224i) q^{75} +0.179683 q^{76} +(-2.06386 + 2.68058i) q^{77} +(1.42765 + 2.47277i) q^{79} +(6.39172 - 11.0708i) q^{80} +(5.58087 - 9.66636i) q^{81} +(-2.82418 - 4.89163i) q^{82} -2.32483 q^{83} +(0.393583 + 0.954606i) q^{84} +27.6117 q^{85} +(-2.57654 - 4.46270i) q^{86} +(-4.14617 + 7.18137i) q^{87} +(1.88383 - 3.26289i) q^{88} +(3.78813 + 6.56124i) q^{89} +5.77339 q^{90} -0.313586 q^{92} +(5.28127 + 9.14742i) q^{93} +(0.601462 - 1.04176i) q^{94} +(1.68377 - 2.91638i) q^{95} +(-1.09998 - 1.90522i) q^{96} -0.478557 q^{97} +(-2.40742 - 9.10365i) q^{98} +1.53815 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9	$ 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) $ 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9 - 24 * q^10 + 2 * q^12 + 8 * q^14 - 16 * q^16 - 34 * q^17 + 60 * q^22 - 6 * q^23 + 10 * q^25 + 24 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^35 - 52 * q^36 - 38 * q^38 - 2 * q^40 + 32 * q^42 + 44 * q^43 - 76 * q^48 + 12 * q^49 - 8 * q^51 - 16 * q^53 + 60 * q^55 + 54 * q^56 + 10 * q^61 + 164 * q^62 - 4 * q^64 - 68 * q^66 - 22 * q^68 + 28 * q^69 - 66 * q^74 - 2 * q^75 + 38 * q^77 - 70 * q^79 + 28 * q^81 - 10 * q^82 + 20 * q^87 + 28 * q^88 - 132 * q^92 + 2 * q^94 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.672613	−	1.16500i	−0.475609	−	0.823779i	0.524000	−	0.851718i	$-0.324439\pi$
$2$	−0.672613	−	1.16500i	−0.475609	−	0.823779i	−0.999610	+	0.0279386i	$0.991106\pi$
$3$	−1.02505	+	1.77544i	−0.591814	+	1.02505i	0.402174	+	0.915563i	$0.368255\pi$
$3$	−1.02505	+	1.77544i	−0.591814	+	1.02505i	−0.993988	+	0.109489i	$0.965079\pi$
$4$	0.0951832	−	0.164862i	0.0475916	−	0.0824311i
$5$	−1.78389	−	3.08979i	−0.797779	−	1.38179i	−0.921059	−	0.389422i	$-0.872675\pi$
$5$	−1.78389	−	3.08979i	−0.797779	−	1.38179i	0.123280	−	0.992372i	$-0.460659\pi$
$6$	2.75785			1.12589
$7$	2.62255	+	0.349630i	0.991230	+	0.132148i
$7$	2.62255	+	0.349630i	0.991230	+	0.132148i
$8$	−2.94654			−1.04176
$9$	−0.601462	−	1.04176i	−0.200487	−	0.347254i
$10$	−2.39973	+	4.15646i	−0.758862	+	1.31439i
$11$	−0.639336	+	1.10736i	−0.192767	+	0.333882i	−0.946166	−	0.323681i	$-0.895080\pi$
$11$	−0.639336	+	1.10736i	−0.192767	+	0.333882i	0.753399	+	0.657563i	$0.228413\pi$
$12$	0.195135	+	0.337984i	0.0563307	+	0.0975677i
$13$		0			0
$13$		0			0
$14$	−1.35664	−	3.29043i	−0.362578	−	0.879406i
$15$	7.31431			1.88855
$16$	1.79151	+	3.10299i	0.447878	+	0.775748i
$17$	−3.86960	+	6.70234i	−0.938515	+	1.62556i	−0.170273	+	0.985397i	$0.554465\pi$
$17$	−3.86960	+	6.70234i	−0.938515	+	1.62556i	−0.768242	+	0.640159i	$0.778868\pi$
$18$	−0.809103	+	1.40141i	−0.190707	+	0.330315i
$19$	0.471939	+	0.817422i	0.108270	+	0.187530i	0.915070	−	0.403296i	$-0.132135\pi$
$19$	0.471939	+	0.817422i	0.108270	+	0.187530i	−0.806799	+	0.590826i	$0.798802\pi$
$20$	−0.679185			−0.151870
$21$	−3.30899	+	4.29779i	−0.722082	+	0.937855i
$22$	1.72010			0.366727
$23$	−0.823637	−	1.42658i	−0.171740	−	0.297463i	0.767288	−	0.641303i	$-0.221606\pi$
$23$	−0.823637	−	1.42658i	−0.171740	−	0.297463i	−0.939028	+	0.343840i	$0.888272\pi$
$24$	3.02035	−	5.23141i	0.616527	−	1.06786i
$25$	−3.86451	+	6.69354i	−0.772903	+	1.33871i
$26$		0			0
$27$	−3.68419			−0.709023
$28$	0.307263	−	0.399080i	0.0580673	−	0.0754190i
$29$	4.04484			0.751107			0.375554	−	0.926801i	$-0.377453\pi$
$29$	4.04484			0.751107			0.375554	+	0.926801i	$0.377453\pi$
$30$	−4.91970	−	8.52117i	−0.898210	−	1.55575i
$31$	2.57610	−	4.46193i	0.462681	−	0.801387i	−0.536413	−	0.843956i	$-0.680221\pi$
$31$	2.57610	−	4.46193i	0.462681	−	0.801387i	0.999094	+	0.0425691i	$0.0135543\pi$
$32$	−0.536547	+	0.929326i	−0.0948490	+	0.164283i
$33$	−1.31071	−	2.27021i	−0.228164	−	0.395192i
$34$	10.4110			1.78547
$35$	−3.59805	−	8.72681i	−0.608182	−	1.47510i
$36$	−0.228996			−0.0381661
$37$	0.528041	+	0.914594i	0.0868094	+	0.150358i	0.906161	−	0.422933i	$-0.139000\pi$
$37$	0.528041	+	0.914594i	0.0868094	+	0.150358i	−0.819351	+	0.573292i	$0.805666\pi$
$38$	0.634865	−	1.09962i	0.102989	−	0.178382i
$39$		0			0
$40$	5.25629	+	9.10417i	0.831093	+	1.43950i
$41$	4.19882			0.655746			0.327873	−	0.944722i	$-0.393668\pi$
$41$	4.19882			0.655746			0.327873	+	0.944722i	$0.393668\pi$
$42$	7.23260	+	0.964227i	1.11601	+	0.148784i
$43$	3.83065			0.584168			0.292084	−	0.956393i	$-0.405651\pi$
$43$	3.83065			0.584168			0.292084	+	0.956393i	$0.405651\pi$
$44$	0.121708	+	0.210805i	0.0183482	+	0.0317800i
$45$	−2.14588	+	3.71678i	−0.319889	+	0.554064i
$46$	−1.10798	+	1.91908i	−0.163363	+	0.282952i
$47$	0.447109	+	0.774415i	0.0652175	+	0.112960i	0.896790	−	0.442456i	$-0.145893\pi$
$47$	0.447109	+	0.774415i	0.0652175	+	0.112960i	−0.831573	+	0.555416i	$0.812559\pi$
$48$	−7.34558			−1.06024
$49$	6.75552	+	1.83384i	0.965074	+	0.261977i
$50$	10.3973			1.47040
$51$	−7.93308	−	13.7405i	−1.11085	−	1.92405i
$52$		0			0
$53$	0.0399961	−	0.0692754i	0.00549389	−	0.00951570i	−0.863265	−	0.504750i	$-0.831585\pi$
$53$	0.0399961	−	0.0692754i	0.00549389	−	0.00951570i	0.868759	+	0.495235i	$0.164918\pi$
$54$	2.47804	+	4.29208i	0.337218	+	0.584079i
$55$	4.56202			0.615142
$56$	−7.72744	−	1.03020i	−1.03262	−	0.137666i
$57$	−1.93505			−0.256303
$58$	−2.72061	−	4.71224i	−0.357234	−	0.618747i
$59$	−5.59237	+	9.68627i	−0.728064	+	1.26104i	0.229636	+	0.973277i	$0.426246\pi$
$59$	−5.59237	+	9.68627i	−0.728064	+	1.26104i	−0.957700	+	0.287768i	$0.907087\pi$
$60$	0.696200	−	1.20585i	0.0898790	−	0.155675i
$61$	3.81196	+	6.60251i	0.488072	+	0.845365i	0.999906	−	0.0137195i	$-0.00436719\pi$
$61$	3.81196	+	6.60251i	0.488072	+	0.845365i	−0.511834	+	0.859084i	$0.671034\pi$
$62$	−6.93087			−0.880221
$63$	−1.21313	−	2.94236i	−0.152840	−	0.370703i
$64$	8.60961			1.07620
$65$		0			0
$66$	−1.76319	+	3.05394i	−0.217034	+	0.375914i
$67$	−3.16052	+	5.47418i	−0.386119	+	0.668777i	−0.991924	−	0.126836i	$-0.959518\pi$
$67$	−3.16052	+	5.47418i	−0.386119	+	0.668777i	0.605805	+	0.795613i	$0.292851\pi$
$68$	0.736641	+	1.27590i	0.0893309	+	0.154726i
$69$	3.37708			0.406553
$70$	−7.74664	+	10.0615i	−0.925900	+	1.20258i
$71$	11.4240			1.35578			0.677889	−	0.735165i	$-0.262895\pi$
$71$	11.4240			1.35578			0.677889	+	0.735165i	$0.262895\pi$
$72$	1.77223	+	3.06959i	0.208859	+	0.361755i
$73$	−0.380253	+	0.658617i	−0.0445052	+	0.0770853i	−0.887420	−	0.460962i	$-0.847504\pi$
$73$	−0.380253	+	0.658617i	−0.0445052	+	0.0770853i	0.842915	+	0.538047i	$0.180838\pi$
$74$	0.710335	−	1.23034i	0.0825747	−	0.143024i
$75$	−7.92265	−	13.7224i	−0.914829	−	1.58453i
$76$	0.179683			0.0206110
$77$	−2.06386	+	2.68058i	−0.235198	+	0.305481i
$78$		0			0
$79$	1.42765	+	2.47277i	0.160624	+	0.278208i	0.935093	−	0.354404i	$-0.115316\pi$
$79$	1.42765	+	2.47277i	0.160624	+	0.278208i	−0.774469	+	0.632612i	$0.781983\pi$
$80$	6.39172	−	11.0708i	0.714616	−	1.23775i
$81$	5.58087	−	9.66636i	0.620097	−	1.07404i
$82$	−2.82418	−	4.89163i	−0.311879	−	0.540190i
$83$	−2.32483			−0.255183			−0.127591	−	0.991827i	$-0.540725\pi$
$83$	−2.32483			−0.255183			−0.127591	+	0.991827i	$0.540725\pi$
$84$	0.393583	+	0.954606i	0.0429434	+	0.104156i
$85$	27.6117			2.99491
$86$	−2.57654	−	4.46270i	−0.277836	−	0.481226i
$87$	−4.14617	+	7.18137i	−0.444516	+	0.769924i
$88$	1.88383	−	3.26289i	0.200817	−	0.347825i
$89$	3.78813	+	6.56124i	0.401541	+	0.695490i	0.993912	−	0.110176i	$-0.0351414\pi$
$89$	3.78813	+	6.56124i	0.401541	+	0.695490i	−0.592371	+	0.805665i	$0.701808\pi$
$90$	5.77339			0.608569
$91$		0			0
$92$	−0.313586			−0.0326936
$93$	5.28127	+	9.14742i	0.547642	+	0.948544i
$94$	0.601462	−	1.04176i	0.0620361	−	0.107450i
$95$	1.68377	−	2.91638i	0.172751	−	0.299214i
$96$	−1.09998	−	1.90522i	−0.112266	−	0.194450i
$97$	−0.478557			−0.0485901			−0.0242951	−	0.999705i	$-0.507734\pi$
$97$	−0.478557			−0.0485901			−0.0242951	+	0.999705i	$0.507734\pi$
$98$	−2.40742	−	9.10365i	−0.243187	−	0.919607i
$99$	1.53815			0.154589
$100$	0.735674	+	1.27422i	0.0735674	+	0.127422i
$101$	−1.43918	+	2.49273i	−0.143204	+	0.248036i	−0.928701	−	0.370829i	$-0.879074\pi$
$101$	−1.43918	+	2.49273i	−0.143204	+	0.248036i	0.785498	+	0.618865i	$0.212407\pi$
$102$	−10.6718	+	18.4841i	−1.05666	+	1.83020i
$103$	5.66755	+	9.81649i	0.558441	+	0.967248i	0.997627	+	0.0688516i	$0.0219335\pi$
$103$	5.66755	+	9.81649i	0.558441	+	0.967248i	−0.439186	+	0.898396i	$0.644733\pi$
$104$		0			0
$105$	19.1821	+	2.55730i	1.87198	+	0.249567i
$106$	−0.107608			−0.0104518
$107$	3.28603	+	5.69157i	0.317673	+	0.550225i	0.980002	−	0.198988i	$-0.0637653\pi$
$107$	3.28603	+	5.69157i	0.317673	+	0.550225i	−0.662329	+	0.749213i	$0.730432\pi$
$108$	−0.350673	+	0.607384i	−0.0337435	+	0.0584455i
$109$	−2.91957	+	5.05684i	−0.279644	+	0.484358i	−0.971296	−	0.237873i	$-0.923550\pi$
$109$	−2.91957	+	5.05684i	−0.279644	+	0.484358i	0.691652	+	0.722231i	$0.256883\pi$
$110$	−3.06847	−	5.31475i	−0.292567	−	0.506741i
$111$	−2.16508			−0.205500
$112$	3.61343	+	8.76412i	0.341437	+	0.828131i
$113$	6.53233			0.614510			0.307255	−	0.951627i	$-0.400590\pi$
$113$	6.53233			0.614510			0.307255	+	0.951627i	$0.400590\pi$
$114$	1.30154	+	2.25433i	0.121900	+	0.211137i
$115$	−2.93855	+	5.08973i	−0.274022	+	0.474619i
$116$	0.385001	−	0.666841i	0.0357464	−	0.0619146i
$117$		0			0
$118$	15.0460			1.38510
$119$	−12.4915	+	16.2243i	−1.14510	+	1.48728i
$120$	−21.5519			−1.96741
$121$	4.68250	+	8.11033i	0.425682	+	0.737302i
$122$	5.12795	−	8.88187i	0.464263	−	0.804127i
$123$	−4.30401	+	7.45477i	−0.388080	+	0.672174i
$124$	−0.490402	−	0.849402i	−0.0440394	−	0.0762786i
$125$	9.73656			0.870865
$126$	−2.61188	+	3.39237i	−0.232685	+	0.302216i
$127$	14.7164			1.30586			0.652932	−	0.757416i	$-0.273539\pi$
$127$	14.7164			1.30586			0.652932	+	0.757416i	$0.273539\pi$
$128$	−4.71784	−	8.17154i	−0.417002	−	0.722269i
$129$	−3.92661	+	6.80109i	−0.345719	+	0.598802i
$130$		0			0
$131$	−5.59335	−	9.68796i	−0.488693	−	0.846441i	0.511222	−	0.859448i	$-0.329193\pi$
$131$	−5.59335	−	9.68796i	−0.488693	−	0.846441i	−0.999915	+	0.0130074i	$0.995860\pi$
$132$	−0.499028			−0.0434349
$133$	0.951888	+	2.30873i	0.0825391	+	0.200193i
$134$	8.50322			0.734566
$135$	6.57219	+	11.3834i	0.565644	+	0.979724i
$136$	11.4019	−	19.7487i	0.977706	−	1.69344i
$137$	8.81541	−	15.2687i	0.753151	−	1.30450i	−0.193137	−	0.981172i	$-0.561866\pi$
$137$	8.81541	−	15.2687i	0.753151	−	1.30450i	0.946288	−	0.323324i	$-0.104800\pi$
$138$	−2.27147	−	3.93430i	−0.193360	−	0.334910i
$139$	−5.85710			−0.496793			−0.248396	−	0.968658i	$-0.579904\pi$
$139$	−5.85710			−0.496793			−0.248396	+	0.968658i	$0.579904\pi$
$140$	−1.78119	−	0.237463i	−0.150538	−	0.0200693i
$141$	−1.83324			−0.154386
$142$	−7.68392	−	13.3089i	−0.644820	−	1.11686i
$143$		0			0
$144$	2.15506	−	3.73267i	0.179588	−	0.311055i
$145$	−7.21554	−	12.4977i	−0.599218	−	1.03788i
$146$	1.02305			0.0846684
$147$	−10.1806	+	10.1142i	−0.839685	+	0.834209i
$148$	0.201043			0.0165256
$149$	5.23948	+	9.07505i	0.429235	+	0.743457i	0.996805	−	0.0798677i	$-0.0254498\pi$
$149$	5.23948	+	9.07505i	0.429235	+	0.743457i	−0.567570	+	0.823325i	$0.692116\pi$
$150$	−10.6578	+	18.4598i	−0.870203	+	1.50724i
$151$	2.35703	−	4.08249i	0.191812	−	0.332229i	−0.754039	−	0.656830i	$-0.771897\pi$
$151$	2.35703	−	4.08249i	0.191812	−	0.332229i	0.945851	+	0.324602i	$0.105230\pi$
$152$	−1.39059	−	2.40857i	−0.112791	−	0.195361i
$153$	9.30967			0.752642
$154$	4.51105	+	0.601399i	0.363511	+	0.0484621i
$155$	−18.3819			−1.47647
$156$		0			0
$157$	−4.50105	+	7.79604i	−0.359223	+	0.622192i	−0.987831	−	0.155530i	$-0.950291\pi$
$157$	−4.50105	+	7.79604i	−0.359223	+	0.622192i	0.628608	+	0.777722i	$0.283625\pi$
$158$	1.92052	−	3.32643i	0.152788	−	0.264637i
$159$	0.0819962	+	0.142022i	0.00650272	+	0.0112630i
$160$	3.82856			0.302674
$161$	−1.66125	−	4.02925i	−0.130925	−	0.317549i
$162$	−15.0151			−1.17970
$163$	−6.01619	−	10.4203i	−0.471224	−	0.816185i	0.528234	−	0.849099i	$-0.322854\pi$
$163$	−6.01619	−	10.4203i	−0.471224	−	0.816185i	−0.999458	+	0.0329144i	$0.989521\pi$
$164$	0.399657	−	0.692227i	0.0312080	−	0.0540538i
$165$	−4.67630	+	8.09959i	−0.364050	+	0.630553i
$166$	1.56371	+	2.70842i	0.121367	+	0.210214i
$167$	−19.4220			−1.50292			−0.751459	−	0.659780i	$-0.770650\pi$
$167$	−19.4220			−1.50292			−0.751459	+	0.659780i	$0.770650\pi$
$168$	9.75008	−	12.6636i	0.752235	−	0.977019i
$169$		0			0
$170$	−18.5720	−	32.1677i	−1.42441	−	2.46715i
$171$	0.567707	−	0.983297i	0.0434136	−	0.0751946i
$172$	0.364613	−	0.631528i	0.0278015	−	0.0481536i
$173$	−7.18976	−	12.4530i	−0.546627	−	0.946786i	−0.998503	−	0.0547049i	$-0.982578\pi$
$173$	−7.18976	−	12.4530i	−0.546627	−	0.946786i	0.451875	−	0.892081i	$-0.350755\pi$
$174$	11.1551			0.845663
$175$	−12.4751	+	16.2030i	−0.943031	+	1.22483i
$176$	−4.58152			−0.345345
$177$	−11.4649	−	19.8578i	−0.861757	−	1.49261i
$178$	5.09589	−	8.82635i	0.381953	−	0.661563i
$179$	−2.71303	+	4.69911i	−0.202781	+	0.351228i	−0.949424	−	0.313998i	$-0.898331\pi$
$179$	−2.71303	+	4.69911i	−0.202781	+	0.351228i	0.746642	+	0.665226i	$0.231665\pi$
$180$	0.408504	+	0.707550i	0.0304481	+	0.0527376i
$181$	15.4902			1.15138			0.575688	−	0.817669i	$-0.304734\pi$
$181$	15.4902			1.15138			0.575688	+	0.817669i	$0.304734\pi$
$182$		0			0
$183$	−15.6298			−1.15539
$184$	2.42688	+	4.20348i	0.178912	+	0.309885i
$185$	1.88393	−	3.26307i	0.138509	−	0.239905i
$186$	7.10450	−	12.3054i	0.520927	−	0.902272i
$187$	−4.94795	−	8.57010i	−0.361830	−	0.626707i
$188$	0.170229			0.0124152
$189$	−9.66197	−	1.28810i	−0.702805	−	0.0936957i
$190$	−4.53011			−0.328649
$191$	−2.37311	−	4.11035i	−0.171712	−	0.297414i	0.767306	−	0.641281i	$-0.221597\pi$
$191$	−2.37311	−	4.11035i	−0.171712	−	0.297414i	−0.939019	+	0.343866i	$0.888263\pi$
$192$	−8.82529	+	15.2859i	−0.636911	+	1.10316i
$193$	10.5196	−	18.2204i	0.757215	−	1.31154i	−0.187050	−	0.982350i	$-0.559893\pi$
$193$	10.5196	−	18.2204i	0.757215	−	1.31154i	0.944266	−	0.329185i	$-0.106774\pi$
$194$	0.321884	+	0.557519i	0.0231099	+	0.0400276i
$195$		0			0
$196$	0.945343	−	0.939178i	0.0675245	−	0.0670842i
$197$	−5.81209			−0.414094			−0.207047	−	0.978331i	$-0.566385\pi$
$197$	−5.81209			−0.414094			−0.207047	+	0.978331i	$0.566385\pi$
$198$	−1.03458	−	1.79194i	−0.0735242	−	0.127348i
$199$	−5.30909	+	9.19562i	−0.376352	+	0.651860i	−0.990528	−	0.137309i	$-0.956155\pi$
$199$	−5.30909	+	9.19562i	−0.376352	+	0.651860i	0.614177	+	0.789168i	$0.289488\pi$
$200$	11.3869	−	19.7228i	0.805178	−	1.39461i
$201$	−6.47939	−	11.2226i	−0.457021	−	0.791583i
$202$	3.87204			0.272436
$203$	10.6078	+	1.41420i	0.744520	+	0.0992571i
$204$	−3.02038			−0.211469
$205$	−7.49023	−	12.9735i	−0.523140	−	0.906106i
$206$	7.62414	−	13.2054i	0.531199	−	0.920064i
$207$	−0.990773	+	1.71607i	−0.0688635	+	0.119275i
$208$		0			0
$209$	−1.20691			−0.0834837
$210$	−9.92290	−	24.0673i	−0.684745	−	1.66080i
$211$	−4.66549			−0.321186			−0.160593	−	0.987021i	$-0.551341\pi$
$211$	−4.66549			−0.321186			−0.160593	+	0.987021i	$0.551341\pi$
$212$	−0.00761392	−	0.0131877i	−0.000522926	−	0.000905735i
$213$	−11.7102	+	20.2826i	−0.802368	+	1.38974i
$214$	4.42046	−	7.65645i	0.302176	−	0.523384i
$215$	−6.83344	−	11.8359i	−0.466037	−	0.807200i
$216$	10.8556			0.738631
$217$	8.31596	−	10.8010i	0.564524	−	0.733216i
$218$	7.85497			0.532005
$219$	−0.779558	−	1.35023i	−0.0526776	−	0.0912403i
$220$	0.434227	−	0.752104i	0.0292756	−	0.0507068i
$221$		0			0
$222$	1.45626	+	2.52232i	0.0977377	+	0.169287i
$223$	−24.2254			−1.62225			−0.811126	−	0.584871i	$-0.801145\pi$
$223$	−24.2254			−1.62225			−0.811126	+	0.584871i	$0.801145\pi$
$224$	−1.73204	+	2.24961i	−0.115727	+	0.150308i
$225$	9.29744			0.619829
$226$	−4.39373	−	7.61017i	−0.292267	−	0.506221i
$227$	−7.68764	+	13.3154i	−0.510247	+	0.883773i	0.489683	+	0.871901i	$0.337113\pi$
$227$	−7.68764	+	13.3154i	−0.510247	+	0.883773i	−0.999930	+	0.0118726i	$0.996221\pi$
$228$	−0.184184	+	0.319016i	−0.0121979	+	0.0211274i
$229$	−8.17573	−	14.1608i	−0.540268	−	0.935771i	−0.998888	−	0.0471389i	$-0.984990\pi$
$229$	−8.17573	−	14.1608i	−0.540268	−	0.935771i	0.458621	−	0.888632i	$-0.348344\pi$
$230$	7.90604			0.521309
$231$	−2.64366	−	6.41199i	−0.173940	−	0.421878i
$232$	−11.9183			−0.782473
$233$	14.5554	+	25.2106i	0.953554	+	1.65160i	0.737643	+	0.675191i	$0.235939\pi$
$233$	14.5554	+	25.2106i	0.953554	+	1.65160i	0.215911	+	0.976413i	$0.430728\pi$
$234$		0			0
$235$	1.59518	−	2.76294i	0.104058	−	0.180234i
$236$	1.06460	+	1.84394i	0.0692995	+	0.120030i
$237$	−5.85368			−0.380237
$238$	27.3033	+	3.63998i	1.76981	+	0.235945i
$239$	8.65409			0.559787			0.279893	−	0.960031i	$-0.409701\pi$
$239$	8.65409			0.559787			0.279893	+	0.960031i	$0.409701\pi$
$240$	13.1037	+	22.6963i	0.845840	+	1.46504i
$241$	−9.09909	+	15.7601i	−0.586124	+	1.01520i	0.408611	+	0.912709i	$0.366013\pi$
$241$	−9.09909	+	15.7601i	−0.586124	+	1.01520i	−0.994734	+	0.102487i	$0.967320\pi$
$242$	6.29902	−	10.9102i	0.404916	−	0.701336i
$243$	5.91508	+	10.2452i	0.379453	+	0.657231i
$244$	1.45134			0.0929124
$245$	−6.38491	−	24.1445i	−0.407917	−	1.54253i
$246$	11.5797			0.738297
$247$		0			0
$248$	−7.59057	+	13.1473i	−0.482002	+	0.834851i
$249$	2.38307	−	4.12759i	0.151021	−	0.261576i
$250$	−6.54894	−	11.3431i	−0.414191	−	0.717400i
$251$	15.8720			1.00183			0.500915	−	0.865497i	$-0.332997\pi$
$251$	15.8720			1.00183			0.500915	+	0.865497i	$0.332997\pi$
$252$	−0.600554	−	0.0800639i	−0.0378313	−	0.00504355i
$253$	2.10632			0.132423
$254$	−9.89841	−	17.1446i	−0.621082	−	1.07574i
$255$	−28.3034	+	49.0230i	−1.77243	+	3.06994i
$256$	2.26304	−	3.91971i	0.141440	−	0.244982i
$257$	12.1634	+	21.0676i	0.758730	+	1.31416i	0.943499	+	0.331376i	$0.107513\pi$
$257$	12.1634	+	21.0676i	0.758730	+	1.31416i	−0.184769	+	0.982782i	$0.559154\pi$
$258$	10.5644			0.657708
$259$	1.06504	+	2.58319i	0.0661786	+	0.160511i
$260$		0			0
$261$	−2.43282	−	4.21376i	−0.150588	−	0.260825i
$262$	−7.52432	+	13.0325i	−0.464854	+	0.805150i
$263$	−7.71727	+	13.3667i	−0.475867	+	0.824226i	−0.999618	−	0.0276456i	$-0.991199\pi$
$263$	−7.71727	+	13.3667i	−0.475867	+	0.824226i	0.523751	+	0.851872i	$0.324532\pi$
$264$	3.86204	+	6.68925i	0.237692	+	0.411695i
$265$	−0.285395			−0.0175317
$266$	2.04942	−	2.66183i	0.125658	−	0.163207i
$267$	−15.5321			−0.950550
$268$	0.601656	+	1.04210i	0.0367520	+	0.0636563i
$269$	6.52035	−	11.2936i	0.397553	−	0.688582i	−0.595870	−	0.803081i	$-0.703193\pi$
$269$	6.52035	−	11.2936i	0.397553	−	0.688582i	0.993423	+	0.114499i	$0.0365261\pi$
$270$	8.84108	−	15.3132i	0.538051	−	0.931931i
$271$	13.4853	+	23.3572i	0.819174	+	1.41885i	0.906291	+	0.422654i	$0.138901\pi$
$271$	13.4853	+	23.3572i	0.819174	+	1.41885i	−0.0871168	+	0.996198i	$0.527765\pi$
$272$	−27.7298			−1.68136
$273$		0			0
$274$	−23.7174			−1.43282
$275$	−4.94145	−	8.55884i	−0.297980	−	0.516117i
$276$	0.321442	−	0.556753i	0.0193485	−	0.0335126i
$277$	−6.35073	+	10.9998i	−0.381578	+	0.660913i	−0.991288	−	0.131712i	$-0.957953\pi$
$277$	−6.35073	+	10.9998i	−0.381578	+	0.660913i	0.609710	+	0.792625i	$0.291286\pi$
$278$	3.93956	+	6.82352i	0.236279	+	0.409248i
$279$	−6.19770			−0.371047
$280$	10.6018	+	25.7139i	0.633579	+	1.53670i
$281$	−26.7216			−1.59408			−0.797038	−	0.603930i	$-0.793601\pi$
$281$	−26.7216			−1.59408			−0.797038	+	0.603930i	$0.793601\pi$
$282$	1.23306	+	2.13572i	0.0734276	+	0.127180i
$283$	−7.37113	+	12.7672i	−0.438168	+	0.758929i	−0.997548	−	0.0699819i	$-0.977706\pi$
$283$	−7.37113	+	12.7672i	−0.438168	+	0.758929i	0.559380	+	0.828911i	$0.311039\pi$
$284$	1.08737	−	1.88338i	0.0645236	−	0.111758i
$285$	3.45191	+	5.97888i	0.204473	+	0.354158i
$286$		0			0
$287$	11.0116	+	1.46803i	0.649995	+	0.0866553i
$288$	1.29085			0.0760641
$289$	−21.4476	−	37.1483i	−1.26162	−	2.18519i
$290$	−9.70653	+	16.8122i	−0.569987	+	0.987247i
$291$	0.490546	−	0.849651i	0.0287563	−	0.0498074i
$292$	0.0723874	+	0.125379i	0.00423615	+	0.00733723i
$293$	11.5831			0.676689			0.338345	−	0.941022i	$-0.390133\pi$
$293$	11.5831			0.676689			0.338345	+	0.941022i	$0.390133\pi$
$294$	18.6307	+	5.05747i	1.08657	+	0.294957i
$295$	39.9046			2.32334
$296$	−1.55589	−	2.69489i	−0.0904344	−	0.156637i
$297$	2.35544	−	4.07974i	0.136676	−	0.236730i
$298$	7.04829	−	12.2080i	0.408297	−	0.707190i
$299$		0			0
$300$	−3.01641			−0.174153
$301$	10.0461	+	1.33931i	0.579045	+	0.0771964i
$302$	−6.34147			−0.364911
$303$	−2.95047	−	5.11036i	−0.169500	−	0.293582i
$304$	−1.69097	+	2.92885i	−0.0969838	+	0.167981i
$305$	13.6002	−	23.5563i	0.778746	−	1.34883i
$306$	−6.26180	−	10.8458i	−0.357963	−	0.620011i
$307$	−29.3335			−1.67415			−0.837076	−	0.547086i	$-0.815737\pi$
$307$	−29.3335			−1.67415			−0.837076	+	0.547086i	$0.815737\pi$
$308$	0.245482	+	0.595398i	0.0139876	+	0.0339260i
$309$	−23.2381			−1.32197
$310$	12.3639	+	21.4149i	0.702222	+	1.21628i
$311$	0.0753271	−	0.130470i	0.00427141	−	0.00739830i	−0.863882	−	0.503695i	$-0.831974\pi$
$311$	0.0753271	−	0.130470i	0.00427141	−	0.00739830i	0.868153	+	0.496296i	$0.165307\pi$
$312$		0			0
$313$	5.26057	+	9.11157i	0.297345	+	0.515016i	0.975528	−	0.219877i	$-0.0705656\pi$
$313$	5.26057	+	9.11157i	0.297345	+	0.515016i	−0.678183	+	0.734893i	$0.737232\pi$
$314$	12.1099			0.683399
$315$	−6.92718	+	8.99716i	−0.390302	+	0.506933i
$316$	0.543555			0.0305773
$317$	−0.753380	−	1.30489i	−0.0423140	−	0.0732901i	0.844093	−	0.536197i	$-0.180140\pi$
$317$	−0.753380	−	1.30489i	−0.0423140	−	0.0732901i	−0.886407	+	0.462907i	$0.846806\pi$
$318$	0.110303	−	0.191051i	0.00618551	−	0.0107136i
$319$	−2.58601	+	4.47910i	−0.144789	+	0.250782i
$320$	−15.3586	−	26.6018i	−0.858571	−	1.48709i
$321$	−13.4734			−0.752012
$322$	−3.57669	+	4.64549i	−0.199321	+	0.258883i
$323$	−7.30486			−0.406453
$324$	−1.06241	−	1.84015i	−0.0590228	−	0.102231i
$325$		0			0
$326$	−8.09314	+	14.0177i	−0.448237	+	0.776370i
$327$	−5.98542	−	10.3671i	−0.330995	−	0.573299i
$328$	−12.3720			−0.683129
$329$	0.901805	+	2.18726i	0.0497181	+	0.120588i
$330$	12.5814			0.692582
$331$	−12.6254	−	21.8679i	−0.693957	−	1.20197i	−0.970531	−	0.240976i	$-0.922533\pi$
$331$	−12.6254	−	21.8679i	−0.693957	−	1.20197i	0.276574	−	0.960993i	$-0.410801\pi$
$332$	−0.221284	+	0.383276i	−0.0121446	+	0.0210350i
$333$	0.635193	−	1.10019i	0.0348084	−	0.0602899i
$334$	13.0635	+	22.6266i	0.714802	+	1.23807i
$335$	22.5520			1.23215
$336$	−19.2641	−	2.56823i	−1.05094	−	0.140109i
$337$	−32.1811			−1.75302			−0.876509	−	0.481386i	$-0.840134\pi$
$337$	−32.1811			−1.75302			−0.876509	+	0.481386i	$0.840134\pi$
$338$		0			0
$339$	−6.69598	+	11.5978i	−0.363676	+	0.629905i
$340$	2.62817	−	4.55213i	0.142533	−	0.246874i
$341$	3.29398	+	5.70535i	0.178379	+	0.308962i
$342$	−1.52739			−0.0825917
$343$	17.0755	+	7.17127i	0.921991	+	0.387212i
$344$	−11.2871			−0.608562
$345$	−6.02434	−	10.4345i	−0.324340	−	0.561773i
$346$	−9.67185	+	16.7521i	−0.519962	+	0.900600i
$347$	−12.3819	+	21.4461i	−0.664695	+	1.15128i	0.314673	+	0.949200i	$0.398105\pi$
$347$	−12.3819	+	21.4461i	−0.664695	+	1.15128i	−0.979368	+	0.202085i	$0.935228\pi$
$348$	0.789291	+	1.36709i	0.0423104	+	0.0732838i
$349$	−11.5556			−0.618559			−0.309280	−	0.950971i	$-0.600088\pi$
$349$	−11.5556			−0.618559			−0.309280	+	0.950971i	$0.600088\pi$
$350$	27.2674	+	3.63520i	1.45750	+	0.194310i
$351$		0			0
$352$	−0.686067	−	1.18830i	−0.0365675	−	0.0633368i
$353$	10.0442	−	17.3971i	0.534599	−	0.925953i	−0.464583	−	0.885529i	$-0.653796\pi$
$353$	10.0442	−	17.3971i	0.534599	−	0.925953i	0.999183	−	0.0404237i	$-0.0128708\pi$
$354$	−15.4229	+	26.7133i	−0.819719	+	1.41980i
$355$	−20.3791	−	35.2977i	−1.08161	−	1.87340i
$356$	1.44227			0.0764399
$357$	−16.0008	−	38.8087i	−0.846852	−	2.05398i
$358$	7.29928			0.385779
$359$	7.52551	+	13.0346i	0.397181	+	0.687938i	0.993377	−	0.114901i	$-0.0366551\pi$
$359$	7.52551	+	13.0346i	0.397181	+	0.687938i	−0.596196	+	0.802839i	$0.703322\pi$
$360$	6.32292	−	10.9516i	0.333247	−	0.577201i
$361$	9.05455	−	15.6829i	0.476555	−	0.825418i
$362$	−10.4189	−	18.0461i	−0.547606	−	0.948481i
$363$	−19.1992			−1.00770
$364$		0			0
$365$	2.71331			0.142021
$366$	10.5128	+	18.2087i	0.549514	+	0.951787i
$367$	−4.50178	+	7.79731i	−0.234991	+	0.407016i	−0.959270	−	0.282491i	$-0.908839\pi$
$367$	−4.50178	+	7.79731i	−0.234991	+	0.407016i	0.724279	+	0.689507i	$0.242173\pi$
$368$	2.95112	−	5.11148i	0.153838	−	0.266454i
$369$	−2.52543	−	4.37418i	−0.131469	−	0.227711i
$370$	−5.06863			−0.263506
$371$	0.129113	−	0.167694i	0.00670319	−	0.00870624i
$372$	2.01075			0.104253
$373$	8.06953	+	13.9768i	0.417824	+	0.723693i	0.995720	−	0.0924174i	$-0.0294594\pi$
$373$	8.06953	+	13.9768i	0.417824	+	0.723693i	−0.577896	+	0.816110i	$0.696126\pi$
$374$	−6.65611	+	11.5287i	−0.344179	+	0.596136i
$375$	−9.98048	+	17.2867i	−0.515390	+	0.892681i
$376$	−1.31742	−	2.28184i	−0.0679409	−	0.117677i
$377$		0			0
$378$	4.99813	+	12.1226i	0.257076	+	0.623519i
$379$	15.6655			0.804685			0.402342	−	0.915489i	$-0.368196\pi$
$379$	15.6655			0.804685			0.402342	+	0.915489i	$0.368196\pi$
$380$	−0.320534	−	0.555181i	−0.0164430	−	0.0284802i
$381$	−15.0850	+	26.1280i	−0.772829	+	1.33858i
$382$	−3.19237	+	5.52935i	−0.163336	+	0.282906i
$383$	12.3164	+	21.3327i	0.629339	+	1.09005i	0.987685	+	0.156459i	$0.0500078\pi$
$383$	12.3164	+	21.3327i	0.629339	+	1.09005i	−0.358345	+	0.933589i	$0.616659\pi$
$384$	19.3441			0.987151
$385$	11.9641	+	1.59502i	0.609747	+	0.0812896i
$386$	−28.3024			−1.44055
$387$	−2.30399	−	3.99062i	−0.117118	−	0.202855i
$388$	−0.0455506	+	0.0788960i	−0.00231248	+	0.00400534i
$389$	9.42834	−	16.3304i	0.478036	−	0.827982i	−0.521647	−	0.853161i	$-0.674682\pi$
$389$	9.42834	−	16.3304i	0.478036	−	0.827982i	0.999683	+	0.0251791i	$0.00801560\pi$
$390$		0			0
$391$	12.7486			0.644724
$392$	−19.9054	−	5.40348i	−1.00537	−	0.272917i
$393$	22.9339			1.15686
$394$	3.90929	+	6.77108i	0.196947	+	0.341122i
$395$	5.09355	−	8.82229i	0.256284	−	0.443897i
$396$	0.146406	−	0.253582i	0.00735716	−	0.0127430i
$397$	7.25149	+	12.5600i	0.363942	+	0.630366i	0.988606	−	0.150528i	$-0.0480973\pi$
$397$	7.25149	+	12.5600i	0.363942	+	0.630366i	−0.624664	+	0.780894i	$0.714764\pi$
$398$	14.2839			0.715985
$399$	−5.07476	−	0.676550i	−0.254056	−	0.0338699i
$400$	−27.6933			−1.38467
$401$	10.4945	+	18.1770i	0.524069	+	0.907714i	0.999607	+	0.0280189i	$0.00891986\pi$
$401$	10.4945	+	18.1770i	0.524069	+	0.907714i	−0.475539	+	0.879695i	$0.657747\pi$
$402$	−8.71624	+	15.0970i	−0.434727	+	0.752968i
$403$		0			0
$404$	0.273971	+	0.474532i	0.0136306	+	0.0236089i
$405$	−39.8226			−1.97880
$406$	−5.48739	−	13.3093i	−0.272335	−	0.660528i
$407$	−1.35038			−0.0669360
$408$	23.3751	+	40.4869i	1.15724	+	2.00440i
$409$	−10.7138	+	18.5568i	−0.529763	+	0.917576i	0.469635	+	0.882861i	$0.344386\pi$
$409$	−10.7138	+	18.5568i	−0.529763	+	0.917576i	−0.999397	+	0.0347148i	$0.988948\pi$
$410$	−10.0761	+	17.4522i	−0.497621	+	0.861905i
$411$	18.0725	+	31.3025i	0.891451	+	1.54404i
$412$	2.15782			0.106308
$413$	−18.0529	+	23.4474i	−0.888323	+	1.15377i
$414$	2.66563			0.131009
$415$	4.14723	+	7.18321i	0.203580	+	0.352610i
$416$		0			0
$417$	6.00383	−	10.3989i	0.294009	−	0.509238i
$418$	0.811784	+	1.40605i	0.0397056	+	0.0687722i
$419$	7.96406			0.389070			0.194535	−	0.980896i	$-0.437680\pi$
$419$	7.96406			0.389070			0.194535	+	0.980896i	$0.437680\pi$
$420$	2.24742	−	2.91900i	0.109663	−	0.142432i
$421$	−2.81786			−0.137334			−0.0686670	−	0.997640i	$-0.521875\pi$
$421$	−2.81786			−0.137334			−0.0686670	+	0.997640i	$0.521875\pi$
$422$	3.13807	+	5.43530i	0.152759	+	0.264586i
$423$	0.537838	−	0.931562i	0.0261506	−	0.0452941i
$424$	−0.117850	+	0.204122i	−0.00572331	+	0.00991306i
$425$	−29.9082	−	51.8026i	−1.45076	−	2.51279i
$426$	31.5057			1.52645
$427$	7.68862	+	18.6482i	0.372078	+	0.902448i
$428$	1.25110			0.0604742
$429$		0			0
$430$	−9.19253	+	15.9219i	−0.443303	+	0.767823i
$431$	−2.86813	+	4.96775i	−0.138153	+	0.239288i	−0.926797	−	0.375561i	$-0.877450\pi$
$431$	−2.86813	+	4.96775i	−0.138153	+	0.239288i	0.788645	+	0.614849i	$0.210783\pi$
$432$	−6.60028	−	11.4320i	−0.317556	−	0.550023i
$433$	−24.5257			−1.17863			−0.589314	−	0.807904i	$-0.700602\pi$
$433$	−24.5257			−1.17863			−0.589314	+	0.807904i	$0.700602\pi$
$434$	−18.1765	−	2.42324i	−0.872502	−	0.116319i
$435$	29.5852			1.41850
$436$	0.555788	+	0.962653i	0.0266174	+	0.0461027i
$437$	0.777413	−	1.34652i	0.0371887	−	0.0644128i
$438$	−1.04868	+	1.81637i	−0.0501079	+	0.0867895i
$439$	−18.3211	−	31.7332i	−0.874420	−	1.51454i	−0.857379	−	0.514686i	$-0.827909\pi$
$439$	−18.3211	−	31.7332i	−0.874420	−	1.51454i	−0.0170416	−	0.999855i	$-0.505425\pi$
$440$	−13.4422			−0.640830
$441$	−2.15276	−	8.14063i	−0.102512	−	0.387649i
$442$		0			0
$443$	−13.5467	−	23.4635i	−0.643622	−	1.11479i	−0.984618	−	0.174721i	$-0.944098\pi$
$443$	−13.5467	−	23.4635i	−0.643622	−	1.11479i	0.340996	−	0.940065i	$-0.389236\pi$
$444$	−0.206079	+	0.356939i	−0.00978008	+	0.0169396i
$445$	13.5152	−	23.4090i	0.640682	−	1.10969i
$446$	16.2943	+	28.2226i	0.771558	+	1.33638i
$447$	−21.4830			−1.01611
$448$	22.5791	+	3.01018i	1.06676	+	0.142217i
$449$	−27.4324			−1.29461			−0.647307	−	0.762229i	$-0.724105\pi$
$449$	−27.4324			−1.29461			−0.647307	+	0.762229i	$0.724105\pi$
$450$	−6.25358	−	10.8315i	−0.294796	−	0.510602i
$451$	−2.68446	+	4.64962i	−0.126406	+	0.218942i
$452$	0.621768	−	1.07693i	0.0292455	−	0.0506547i
$453$	4.83215	+	8.36953i	0.227034	+	0.393235i
$454$	20.6832			0.970712
$455$		0			0
$456$	5.70169			0.267006
$457$	19.8320	+	34.3500i	0.927700	+	1.60682i	0.787161	+	0.616748i	$0.211550\pi$
$457$	19.8320	+	34.3500i	0.927700	+	1.60682i	0.140539	+	0.990075i	$0.455116\pi$
$458$	−10.9982	+	19.0495i	−0.513913	+	0.890123i
$459$	14.2563	−	24.6927i	0.665429	−	1.15256i
$460$	0.559402	+	0.968913i	0.0260823	+	0.0451758i
$461$	−4.89580			−0.228020			−0.114010	−	0.993480i	$-0.536370\pi$
$461$	−4.89580			−0.228020			−0.114010	+	0.993480i	$0.536370\pi$
$462$	−5.69181	+	7.39265i	−0.264807	+	0.343937i
$463$	−4.71193			−0.218982			−0.109491	−	0.993988i	$-0.534922\pi$
$463$	−4.71193			−0.218982			−0.109491	+	0.993988i	$0.534922\pi$
$464$	7.24638	+	12.5511i	0.336405	+	0.582670i
$465$	18.8424	−	32.6360i	0.873794	−	1.51346i
$466$	19.5803	−	33.9140i	0.907038	−	1.57104i
$467$	−16.0081	−	27.7268i	−0.740765	−	1.28304i	−0.952147	−	0.305639i	$-0.901130\pi$
$467$	−16.0081	−	27.7268i	−0.740765	−	1.28304i	0.211383	−	0.977403i	$-0.432203\pi$
$468$		0			0
$469$	−10.2025	+	13.2513i	−0.471110	+	0.611887i
$470$	−4.29176			−0.197964
$471$	−9.22761	−	15.9827i	−0.425186	−	0.736444i
$472$	16.4781	−	28.5410i	0.758467	−	1.31370i
$473$	−2.44907	+	4.24191i	−0.112608	+	0.195043i
$474$	3.93726	+	6.81953i	0.180844	+	0.313232i
$475$	−7.29526			−0.334730
$476$	1.48578	+	3.60366i	0.0681008	+	0.165174i
$477$	−0.0962247			−0.00440582
$478$	−5.82086	−	10.0820i	−0.266240	−	0.461141i
$479$	9.01224	−	15.6097i	0.411780	−	0.713224i	−0.583305	−	0.812254i	$-0.698241\pi$
$479$	9.01224	−	15.6097i	0.411780	−	0.713224i	0.995084	+	0.0990298i	$0.0315739\pi$
$480$	−3.92447	+	6.79738i	−0.179127	+	0.310257i
$481$		0			0
$482$	24.4807			1.11506
$483$	8.85657	+	1.18073i	0.402988	+	0.0537250i
$484$	1.78278			0.0810355
$485$	0.853693	+	1.47864i	0.0387642	+	0.0671416i
$486$	7.95712	−	13.7821i	0.360942	−	0.625170i
$487$	−8.80020	+	15.2424i	−0.398775	+	0.690699i	−0.993575	−	0.113175i	$-0.963898\pi$
$487$	−8.80020	+	15.2424i	−0.398775	+	0.690699i	0.594800	+	0.803874i	$0.297231\pi$
$488$	−11.2321	−	19.4545i	−0.508453	−	0.880666i
$489$	24.6676			1.11551
$490$	−23.8337	+	23.6783i	−1.07670	+	1.06968i
$491$	3.86360			0.174362			0.0871810	−	0.996192i	$-0.472214\pi$
$491$	3.86360			0.174362			0.0871810	+	0.996192i	$0.472214\pi$
$492$	0.819339	+	1.41914i	0.0369387	+	0.0639796i
$493$	−15.6519	+	27.1099i	−0.704926	+	1.22097i
$494$		0			0
$495$	−2.74388	−	4.75254i	−0.123328	−	0.213611i
$496$	18.4605			0.828899
$497$	29.9599	+	3.99416i	1.34389	+	0.179163i
$498$	−6.41153			−0.287308
$499$	6.32363	+	10.9528i	0.283084	+	0.490317i	0.972143	−	0.234389i	$-0.0753090\pi$
$499$	6.32363	+	10.9528i	0.283084	+	0.490317i	−0.689058	+	0.724706i	$0.741976\pi$
$500$	0.926757	−	1.60519i	0.0414458	−	0.0717863i
$501$	19.9085	−	34.4826i	0.889448	−	1.54057i
$502$	−10.6757	−	18.4908i	−0.476480	−	0.825287i
$503$	22.0360			0.982537			0.491268	−	0.871008i	$-0.336533\pi$
$503$	22.0360			0.982537			0.491268	+	0.871008i	$0.336533\pi$
$504$	3.57454	+	8.66978i	0.159223	+	0.386183i
$505$	10.2693			0.456980
$506$	−1.41674	−	2.45387i	−0.0629818	−	0.109088i
$507$		0			0
$508$	1.40075	−	2.42617i	0.0621482	−	0.107644i
$509$	7.83509	+	13.5708i	0.347284	+	0.601514i	0.985766	−	0.168123i	$-0.0537706\pi$
$509$	7.83509	+	13.5708i	0.347284	+	0.601514i	−0.638482	+	0.769637i	$0.720437\pi$
$510$	76.1491			3.37194
$511$	−1.22750	+	1.59431i	−0.0543016	+	0.0705280i
$512$	−24.9600			−1.10309
$513$	−1.73871	−	3.01154i	−0.0767661	−	0.132963i
$514$	16.3625	−	28.3406i	0.721718	−	1.25005i
$515$	20.2206	−	35.0230i	0.891025	−	1.54330i
$516$	0.747495	+	1.29470i	0.0329066	+	0.0569959i
$517$	−1.14341			−0.0502871
$518$	2.29305	−	2.97826i	0.100751	−	0.130857i
$519$	29.4795			1.29401
$520$		0			0
$521$	12.6207	−	21.8598i	0.552925	−	0.957694i	−0.445137	−	0.895463i	$-0.646845\pi$
$521$	12.6207	−	21.8598i	0.552925	−	0.957694i	0.998062	−	0.0622317i	$-0.0198218\pi$
$522$	−3.27269	+	5.66846i	−0.143242	+	0.248102i
$523$	6.62383	+	11.4728i	0.289640	+	0.501671i	0.973724	−	0.227733i	$-0.0731312\pi$
$523$	6.62383	+	11.4728i	0.289640	+	0.501671i	−0.684084	+	0.729403i	$0.739798\pi$
$524$	−2.12957			−0.0930307
$525$	−15.9798	−	38.7578i	−0.697414	−	1.69153i
$526$	20.7629			0.905307
$527$	19.9369	+	34.5318i	0.868466	+	1.50423i
$528$	4.69629	−	8.13422i	0.204380	−	0.353996i
$529$	10.1432	−	17.5686i	0.441011	−	0.763853i
$530$	0.191960	+	0.332485i	0.00833822	+	0.0144422i
$531$	13.4544			0.583871
$532$	0.471226	+	0.0628224i	0.0204303	+	0.00272370i
$533$		0			0
$534$	10.4471	+	18.0949i	0.452091	+	0.783044i
$535$	11.7238	−	20.3063i	0.506865	−	0.877916i
$536$	9.31258	−	16.1299i	0.402242	−	0.696704i
$537$	−5.56200	−	9.63366i	−0.240018	−	0.415723i
$538$	−17.5427			−0.756320
$539$	−6.34977	+	6.30837i	−0.273504	+	0.271721i
$540$	2.50225			0.107680
$541$	−7.20170	−	12.4737i	−0.309625	−	0.536287i	0.668655	−	0.743573i	$-0.266870\pi$
$541$	−7.20170	−	12.4737i	−0.309625	−	0.536287i	−0.978280	+	0.207286i	$0.933537\pi$
$542$	18.1408	−	31.4208i	0.779214	−	1.34964i
$543$	−15.8782	+	27.5019i	−0.681401	+	1.18022i
$544$	−4.15244	−	7.19224i	−0.178034	−	0.308365i
$545$	20.8328			0.892377
$546$		0			0
$547$	2.00679			0.0858042			0.0429021	−	0.999079i	$-0.486340\pi$
$547$	2.00679			0.0858042			0.0429021	+	0.999079i	$0.486340\pi$
$548$	−1.67816	−	2.90665i	−0.0716873	−	0.124166i
$549$	4.58550	−	7.94232i	0.195704	−	0.338970i
$550$	−6.64736	+	11.5136i	−0.283445	+	0.490940i
$551$	1.90892	+	3.30634i	0.0813226	+	0.140855i
$552$	−9.95071			−0.423530
$553$	2.87954	+	6.98411i	0.122450	+	0.296994i
$554$	17.0863			0.725928
$555$	3.86226	+	6.68962i	0.163944	+	0.283959i
$556$	−0.557497	+	0.965614i	−0.0236432	+	0.0409512i
$557$	−4.28958	+	7.42977i	−0.181755	+	0.314810i	−0.942478	−	0.334267i	$-0.891511\pi$
$557$	−4.28958	+	7.42977i	−0.181755	+	0.314810i	0.760723	+	0.649077i	$0.224845\pi$
$558$	4.16865	+	7.22032i	0.176473	+	0.305661i
$559$		0			0
$560$	20.6333	−	26.7989i	0.871915	−	1.13246i
$561$	20.2876			0.856543
$562$	17.9733	+	31.1306i	0.758157	+	1.31317i
$563$	6.38718	−	11.0629i	0.269188	−	0.466247i	−0.699465	−	0.714667i	$-0.746578\pi$
$563$	6.38718	−	11.0629i	0.269188	−	0.466247i	0.968652	+	0.248421i	$0.0799115\pi$
$564$	−0.174493	+	0.302231i	−0.00734750	+	0.0127262i
$565$	−11.6530	−	20.1835i	−0.490243	−	0.849126i
$566$	19.8317			0.833587
$567$	18.0158	−	23.3992i	0.756591	−	0.982676i
$568$	−33.6612			−1.41239
$569$	2.89558	+	5.01530i	0.121389	+	0.210252i	0.920316	−	0.391176i	$-0.127932\pi$
$569$	2.89558	+	5.01530i	0.121389	+	0.210252i	−0.798927	+	0.601429i	$0.794598\pi$
$570$	4.64360	−	8.04295i	0.194499	−	0.336882i
$571$	22.0666	−	38.2204i	0.923458	−	1.59948i	0.129435	−	0.991588i	$-0.458684\pi$
$571$	22.0666	−	38.2204i	0.923458	−	1.59948i	0.794023	−	0.607888i	$-0.207983\pi$
$572$		0			0
$573$	9.73025			0.406487
$574$	−5.69630	−	13.8160i	−0.237759	−	0.576667i
$575$	12.7318			0.530954
$576$	−5.17835	−	8.96917i	−0.215765	−	0.373715i
$577$	5.96649	−	10.3343i	0.248388	−	0.430221i	−0.714691	−	0.699441i	$-0.753432\pi$
$577$	5.96649	−	10.3343i	0.248388	−	0.430221i	0.963079	+	0.269220i	$0.0867658\pi$
$578$	−28.8518	+	49.9729i	−1.20008	+	2.07860i
$579$	21.5662	+	37.3538i	0.896261	+	1.55237i
$580$	−2.74719			−0.114071
$581$	−6.09697	−	0.812829i	−0.252945	−	0.0337218i
$582$	−1.31979			−0.0547071
$583$	0.0511420	+	0.0885805i	0.00211808	+	0.00366863i
$584$	1.12043	−	1.94064i	0.0463637	−	0.0803043i
$585$		0			0
$586$	−7.79091	−	13.4943i	−0.321840	−	0.557443i
$587$	−20.3516			−0.840000			−0.420000	−	0.907524i	$-0.637970\pi$
$587$	−20.3516			−0.840000			−0.420000	+	0.907524i	$0.637970\pi$
$588$	0.698431	+	2.64111i	0.0288028	+	0.108917i
$589$	4.86304			0.200378
$590$	−26.8404	−	46.4889i	−1.10500	−	1.91392i
$591$	5.95769	−	10.3190i	0.245067	−	0.424468i
$592$	−1.89199	+	3.27701i	−0.0777601	+	0.134684i
$593$	9.09000	+	15.7443i	0.373282	+	0.646543i	0.990068	−	0.140588i	$-0.0448991\pi$
$593$	9.09000	+	15.7443i	0.373282	+	0.646543i	−0.616787	+	0.787130i	$0.711566\pi$
$594$	−6.33719			−0.260018
$595$	72.4131	+	9.65388i	2.96865	+	0.395770i
$596$	1.99484			0.0817120
$597$	−10.8842	−	18.8520i	−0.445460	−	0.771560i
$598$		0			0
$599$	19.1341	−	33.1412i	0.781797	−	1.35411i	−0.149096	−	0.988823i	$-0.547636\pi$
$599$	19.1341	−	33.1412i	0.781797	−	1.35411i	0.930894	−	0.365290i	$-0.119030\pi$
$600$	23.3444	+	40.4337i	0.953031	+	1.65070i
$601$	−26.8719			−1.09613			−0.548064	−	0.836436i	$-0.684635\pi$
$601$	−26.8719			−1.09613			−0.548064	+	0.836436i	$0.684635\pi$
$602$	−5.19681	−	12.6045i	−0.211806	−	0.513721i
$603$	7.60372			0.309648
$604$	−0.448699	−	0.777170i	−0.0182573	−	0.0316226i
$605$	16.7061	−	28.9358i	0.679200	−	1.17641i
$606$	−3.96904	+	6.87459i	−0.161231	+	0.279261i
$607$	4.70105	+	8.14245i	0.190810	+	0.330492i	0.945519	−	0.325568i	$-0.105555\pi$
$607$	4.70105	+	8.14245i	0.190810	+	0.330492i	−0.754709	+	0.656059i	$0.772222\pi$
$608$	−1.01287			−0.0410773
$609$	−13.3843	+	17.3839i	−0.542361	+	0.704430i
$610$	−36.5908			−1.48152
$611$		0			0
$612$	0.886124	−	1.53481i	0.0358194	−	0.0620411i
$613$	−6.64469	+	11.5089i	−0.268376	+	0.464842i	−0.968443	−	0.249236i	$-0.919820\pi$
$613$	−6.64469	+	11.5089i	−0.268376	+	0.464842i	0.700066	+	0.714078i	$0.253154\pi$
$614$	19.7301	+	34.1735i	0.796242	+	1.37913i
$615$	30.7115			1.23841
$616$	6.08123	−	7.89843i	0.245020	−	0.318237i
$617$	−11.2261			−0.451947			−0.225973	−	0.974133i	$-0.572556\pi$
$617$	−11.2261			−0.451947			−0.225973	+	0.974133i	$0.572556\pi$
$618$	15.6303	+	27.0724i	0.628742	+	1.08901i
$619$	4.64253	−	8.04109i	0.186599	−	0.323199i	−0.757515	−	0.652817i	$-0.773587\pi$
$619$	4.64253	−	8.04109i	0.186599	−	0.323199i	0.944114	+	0.329619i	$0.106920\pi$
$620$	−1.74965	+	3.03048i	−0.0702675	+	0.121707i
$621$	3.03444	+	5.25580i	0.121768	+	0.210908i
$622$	−0.202664			−0.00812608
$623$	7.64055	+	18.5316i	0.306112	+	0.742453i
$624$		0			0
$625$	1.95363	+	3.38379i	0.0781452	+	0.135351i
$626$	7.07665	−	12.2571i	0.282840	−	0.489893i
$627$	1.23715	−	2.14280i	0.0494068	−	0.0855752i
$628$	0.856848	+	1.48410i	0.0341920	+	0.0592222i
$629$	−8.17322			−0.325888
$630$	15.1410	+	2.01855i	0.603232	+	0.0804210i
$631$	−10.4026			−0.414122			−0.207061	−	0.978328i	$-0.566390\pi$
$631$	−10.4026			−0.414122			−0.207061	+	0.978328i	$0.566390\pi$
$632$	−4.20664	−	7.28611i	−0.167331	−	0.289826i
$633$	4.78237	−	8.28331i	0.190082	−	0.329232i
$634$	−1.01347	+	1.75538i	−0.0402499	+	0.0697149i
$635$	−26.2523	−	45.4704i	−1.04179	−	1.80444i
$636$	0.0312187			0.00123790
$637$		0			0
$638$	6.95754			0.275452
$639$	−6.87109	−	11.9011i	−0.271816	−	0.470800i
$640$	−16.8322	+	29.1542i	−0.665351	+	1.15242i
$641$	−7.42955	+	12.8684i	−0.293449	+	0.508269i	−0.974623	−	0.223853i	$-0.928137\pi$
$641$	−7.42955	+	12.8684i	−0.293449	+	0.508269i	0.681174	+	0.732122i	$0.261470\pi$
$642$	9.06239	+	15.6965i	0.357664	+	0.619492i
$643$	2.29722			0.0905935			0.0452968	−	0.998974i	$-0.485577\pi$
$643$	2.29722			0.0905935			0.0452968	+	0.998974i	$0.485577\pi$
$644$	−0.822394	−	0.109639i	−0.0324069	−	0.00432038i
$645$	28.0185			1.10323
$646$	4.91334	+	8.51016i	0.193313	+	0.334828i
$647$	−3.99932	+	6.92703i	−0.157230	+	0.272330i	−0.933869	−	0.357616i	$-0.883590\pi$
$647$	−3.99932	+	6.92703i	−0.157230	+	0.272330i	0.776639	+	0.629946i	$0.216923\pi$
$648$	−16.4443	+	28.4823i	−0.645991	+	1.11889i
$649$	−7.15081	−	12.3856i	−0.280694	−	0.486176i
$650$		0			0
$651$	10.6522	+	25.8360i	0.417491	+	1.01259i
$652$	−2.29056			−0.0897053
$653$	−1.99222	−	3.45062i	−0.0779615	−	0.135033i	0.824409	−	0.565995i	$-0.191508\pi$
$653$	−1.99222	−	3.45062i	−0.0779615	−	0.135033i	−0.902370	+	0.430962i	$0.858174\pi$
$654$	−8.05175	+	13.9460i	−0.314848	+	0.545333i
$655$	−19.9558	+	34.5645i	−0.779738	+	1.35055i
$656$	7.52225	+	13.0289i	0.293695	+	0.508694i
$657$	0.914831			0.0356910
$658$	1.94159	−	2.52178i	0.0756912	−	0.0983094i
$659$	−27.5003			−1.07126			−0.535629	−	0.844453i	$-0.679925\pi$
$659$	−27.5003			−1.07126			−0.535629	+	0.844453i	$0.679925\pi$
$660$	0.890211	+	1.54189i	0.0346514	+	0.0600180i
$661$	3.49310	−	6.05023i	0.135866	−	0.235327i	−0.790062	−	0.613027i	$-0.789952\pi$
$661$	3.49310	−	6.05023i	0.135866	−	0.235327i	0.925928	+	0.377700i	$0.123285\pi$
$662$	−16.9841	+	29.4173i	−0.660105	+	1.14333i
$663$		0			0
$664$	6.85019			0.265839
$665$	5.43543	−	7.05965i	0.210777	−	0.273762i
$666$	−1.70896			−0.0662207
$667$	−3.33148	−	5.77029i	−0.128995	−	0.223427i
$668$	−1.84865	+	3.20195i	−0.0715263	+	0.123887i
$669$	24.8323	−	43.0108i	0.960071	−	1.66289i
$670$	−15.1688	−	26.2731i	−0.586022	−	1.01502i
$671$	−9.74849			−0.376336
$672$	−2.21862	−	5.38110i	−0.0855852	−	0.207581i
$673$	5.45566			0.210300			0.105150	−	0.994456i	$-0.466468\pi$
$673$	5.45566			0.210300			0.105150	+	0.994456i	$0.466468\pi$
$674$	21.6455	+	37.4910i	0.833752	+	1.44410i
$675$	14.2376	−	24.6603i	0.548006	−	0.949174i
$676$		0			0
$677$	−16.8961	−	29.2649i	−0.649371	−	1.12474i	−0.983273	−	0.182135i	$-0.941699\pi$
$677$	−16.8961	−	29.2649i	−0.649371	−	1.12474i	0.333903	−	0.942607i	$-0.391634\pi$
$678$	18.0152			0.691870
$679$	−1.25504	−	0.167318i	−0.0481640	−	0.00642107i
$680$	−81.3590			−3.11997
$681$	−15.7605	−	27.2979i	−0.603942	−	1.04606i
$682$	4.43115	−	7.67498i	0.169678	−	0.293890i
$683$	6.14942	−	10.6511i	0.235301	−	0.407553i	−0.724059	−	0.689738i	$-0.757726\pi$
$683$	6.14942	−	10.6511i	0.235301	−	0.407553i	0.959360	+	0.282185i	$0.0910591\pi$
$684$	−0.108072	−	0.187187i	−0.00413225	−	0.00715726i
$685$	−62.9028			−2.40339
$686$	−3.13068	−	24.7165i	−0.119530	−	0.943679i
$687$	33.5222			1.27895
$688$	6.86265	+	11.8865i	0.261636	+	0.453167i
$689$		0			0
$690$	−8.10410	+	14.0367i	−0.308518	+	0.534369i
$691$	−5.54483	−	9.60393i	−0.210935	−	0.365351i	0.741072	−	0.671425i	$-0.234318\pi$
$691$	−5.54483	−	9.60393i	−0.210935	−	0.365351i	−0.952008	+	0.306075i	$0.900984\pi$
$692$	−2.73738			−0.104059
$693$	4.03386	+	0.537781i	0.153234	+	0.0204286i
$694$	33.3129			1.26454
$695$	10.4484	+	18.0972i	0.396331	+	0.686465i
$696$	12.2168	−	21.1602i	0.463078	−	0.802075i
$697$	−16.2478	+	28.1419i	−0.615428	+	1.06595i
$698$	7.77247	+	13.4623i	0.294193	+	0.509556i
$699$	−59.6800			−2.25731
$700$	1.48383	+	3.59893i	0.0560836	+	0.136027i
$701$	−10.6470			−0.402133			−0.201066	−	0.979578i	$-0.564441\pi$
$701$	−10.6470			−0.402133			−0.201066	+	0.979578i	$0.564441\pi$
$702$		0			0
$703$	−0.498406	+	0.863265i	−0.0187977	+	0.0325587i
$704$	−5.50443	+	9.53396i	−0.207456	+	0.359325i
$705$	3.27029	+	5.66431i	0.123166	+	0.213330i
$706$	−27.0235			−1.01704
$707$	−4.64585	+	6.03413i	−0.174725	+	0.226937i
$708$	−4.36508			−0.164050
$709$	−20.3535	−	35.2532i	−0.764391	−	1.32396i	−0.940568	−	0.339605i	$-0.889707\pi$
$709$	−20.3535	−	35.2532i	−0.764391	−	1.32396i	0.176178	−	0.984358i	$-0.443627\pi$
$710$	−27.4145	+	47.4833i	−1.02885	+	1.78202i
$711$	1.71736	−	2.97455i	0.0644060	−	0.111554i
$712$	−11.1619	−	19.3329i	−0.418309	−	0.724532i
$713$	−8.48708			−0.317844
$714$	−34.4498	+	44.7442i	−1.28925	+	1.67451i
$715$		0			0
$716$	0.516470	+	0.894552i	0.0193014	+	0.0334310i
$717$	−8.87089	+	15.3648i	−0.331290	+	0.573810i
$718$	10.1235	−	17.5344i	0.377806	−	0.654380i
$719$	4.88769	+	8.46572i	0.182280	+	0.315718i	0.942657	−	0.333764i	$-0.108319\pi$
$719$	4.88769	+	8.46572i	0.182280	+	0.315718i	−0.760377	+	0.649482i	$0.774986\pi$
$720$	−15.3775			−0.573086
$721$	11.4313	+	27.7258i	0.425724	+	1.03256i
$722$	−24.3608			−0.906616
$723$	−18.6541	−	32.3098i	−0.693752	−	1.20161i
$724$	1.47441	−	2.55375i	0.0547959	−	0.0949092i
$725$	−15.6313	+	27.0743i	−0.580533	+	1.00551i
$726$	12.9136	+	22.3671i	0.479270	+	0.830120i
$727$	12.2091			0.452811			0.226406	−	0.974033i	$-0.427303\pi$
$727$	12.2091			0.452811			0.226406	+	0.974033i	$0.427303\pi$
$728$		0			0
$729$	9.23219			0.341933
$730$	−1.82501	−	3.16101i	−0.0675467	−	0.116994i
$731$	−14.8231	+	25.6743i	−0.548251	+	0.949598i
$732$	−1.48770	+	2.57677i	−0.0549869	+	0.0952400i
$733$	11.1577	+	19.3256i	0.412118	+	0.713809i	0.995121	−	0.0986608i	$-0.0314559\pi$
$733$	11.1577	+	19.3256i	0.412118	+	0.713809i	−0.583003	+	0.812470i	$0.698123\pi$
$734$	12.1118			0.447055
$735$	49.4120	+	13.4133i	1.82259	+	0.494757i
$736$	1.76768			0.0651576
$737$	−4.04126	−	6.99968i	−0.148862	−	0.257836i
$738$	−3.39728	+	5.88426i	−0.125056	+	0.216603i
$739$	−21.1865	+	36.6960i	−0.779357	+	1.34989i	0.152956	+	0.988233i	$0.451121\pi$
$739$	−21.1865	+	36.6960i	−0.779357	+	1.34989i	−0.932313	+	0.361653i	$0.882213\pi$
$740$	−0.358637	−	0.621178i	−0.0131838	−	0.0228350i
$741$		0			0
$742$	−0.282206	−	0.0376229i	−0.0103601	−	0.00138118i
$743$	30.9801			1.13655			0.568276	−	0.822838i	$-0.307611\pi$
$743$	30.9801			1.13655			0.568276	+	0.822838i	$0.307611\pi$
$744$	−15.5615	−	26.9532i	−0.570511	−	0.988153i
$745$	18.6933	−	32.3778i	0.684870	−	1.18623i
$746$	10.8553	−	18.8020i	0.397442	−	0.688390i
$747$	1.39830	+	2.42192i	0.0511609	+	0.0886133i
$748$	−1.88385			−0.0688802
$749$	6.62783	+	16.0753i	0.242176	+	0.587379i
$750$	26.8520			0.980497
$751$	−11.2830	−	19.5427i	−0.411722	−	0.713123i	0.583356	−	0.812216i	$-0.301739\pi$
$751$	−11.2830	−	19.5427i	−0.411722	−	0.713123i	−0.995078	+	0.0990930i	$0.968406\pi$
$752$	−1.60200	+	2.77475i	−0.0584190	+	0.101185i
$753$	−16.2696	+	28.1798i	−0.592897	+	1.02693i
$754$		0			0
$755$	−16.8187			−0.612095
$756$	−1.13202	+	1.47029i	−0.0411710	+	0.0534738i
$757$	32.2808			1.17327			0.586633	−	0.809853i	$-0.300453\pi$
$757$	32.2808			1.17327			0.586633	+	0.809853i	$0.300453\pi$
$758$	−10.5368	−	18.2504i	−0.382716	−	0.662883i
$759$	−2.15909	+	3.73966i	−0.0783701	+	0.135741i
$760$	−4.96130	+	8.59323i	−0.179965	+	0.311709i
$761$	14.8758	+	25.7657i	0.539249	+	0.934006i	0.998945	+	0.0459296i	$0.0146250\pi$
$761$	14.8758	+	25.7657i	0.539249	+	0.934006i	−0.459696	+	0.888076i	$0.652042\pi$
$762$	40.5855			1.47026
$763$	−9.42474	+	12.2411i	−0.341198	+	0.443156i
$764$	−0.903521			−0.0326883
$765$	−16.6074	−	28.7649i	−0.600442	−	1.04000i
$766$	16.5684	−	28.6972i	0.598639	−	1.03687i
$767$		0			0
$768$	4.63947	+	8.03581i	0.167413	+	0.289967i
$769$	41.8105			1.50773			0.753863	−	0.657032i	$-0.228188\pi$
$769$	41.8105			1.50773			0.753863	+	0.657032i	$0.228188\pi$
$770$	−6.18902	−	15.0110i	−0.223037	−	0.540959i
$771$	−49.8723			−1.79611
$772$	−2.00257	−	3.46856i	−0.0720742	−	0.124836i
$773$	20.7168	−	35.8826i	0.745132	−	1.29061i	−0.205001	−	0.978762i	$-0.565720\pi$
$773$	20.7168	−	35.8826i	0.745132	−	1.29061i	0.950133	−	0.311845i	$-0.100947\pi$
$774$	−3.09938	+	5.36829i	−0.111405	+	0.192959i
$775$	19.9107	+	34.4864i	0.715215	+	1.23879i
$776$	1.41009			0.0506192
$777$	−5.67802	−	0.756975i	−0.203698	−	0.0271563i
$778$	−25.3665			−0.909433
$779$	1.98159	+	3.43221i	0.0709978	+	0.122972i
$780$		0			0
$781$	−7.30376	+	12.6505i	−0.261349	+	0.452670i
$782$	−8.57486	−	14.8521i	−0.306637	−	0.531110i
$783$	−14.9020			−0.532552
$784$	6.41221	+	24.2477i	0.229007	+	0.865989i
$785$	32.1175			1.14632
$786$	−15.4256	−	26.7180i	−0.550214	−	0.952998i
$787$	−11.9313	+	20.6657i	−0.425306	+	0.736651i	−0.996449	−	0.0841992i	$-0.973167\pi$
$787$	−11.9313	+	20.6657i	−0.425306	+	0.736651i	0.571143	+	0.820851i	$0.306500\pi$
$788$	−0.553213	+	0.958193i	−0.0197074	+	0.0341342i
$789$	−15.8212	−	27.4031i	−0.563250	−	0.975577i
$790$	−13.7040			−0.487565
$791$	17.1314	+	2.28390i	0.609121	+	0.0812061i
$792$	−4.53221			−0.161045
$793$		0			0
$794$	9.75490	−	16.8960i	0.346188	−	0.599616i
$795$	0.292544	−	0.506701i	0.0103755	−	0.0179708i
$796$	1.01067	+	1.75054i	0.0358223	+	0.0620461i
$797$	50.8231			1.80025			0.900123	−	0.435636i	$-0.143476\pi$
$797$	50.8231			1.80025			0.900123	+	0.435636i	$0.143476\pi$
$798$	2.62517	+	6.36715i	0.0929299	+	0.225395i
$799$	−6.92052			−0.244830
$800$	−4.14699	−	7.18279i	−0.146618	−	0.253950i
$801$	4.55683	−	7.89267i	0.161008	−	0.278874i
$802$	14.1174	−	24.4521i	0.498504	−	0.863434i
$803$	−0.486219	−	0.842156i	−0.0171583	−	0.0297190i
$804$	−2.46691			−0.0870014
$805$	−9.48602	+	12.3206i	−0.334338	+	0.434246i
$806$		0			0
$807$	13.3674	+	23.1530i	0.470555	+	0.815025i
$808$	4.24060	−	7.34493i	0.149184	−	0.258394i
$809$	−2.20588	+	3.82070i	−0.0775547	+	0.134329i	−0.902194	−	0.431330i	$-0.858045\pi$
$809$	−2.20588	+	3.82070i	−0.0775547	+	0.134329i	0.824640	+	0.565658i	$0.191378\pi$
$810$	26.7852	+	46.3933i	0.941136	+	1.63010i
$811$	17.6493			0.619750			0.309875	−	0.950777i	$-0.399713\pi$
$811$	17.6493			0.619750			0.309875	+	0.950777i	$0.399713\pi$
$812$	1.24283	−	1.61421i	0.0436148	−	0.0566478i
$813$	−55.2926			−1.93920
$814$	0.908285	+	1.57320i	0.0318354	+	0.0551405i
$815$	−21.4644	+	37.1775i	−0.751866	+	1.30227i
$816$	28.4244	−	49.2326i	0.995054	−	1.72348i
$817$	1.80783	+	3.13126i	0.0632480	+	0.109549i
$818$	28.8249			1.00784
$819$		0			0
$820$	−2.85178			−0.0995884
$821$	−1.78022	−	3.08342i	−0.0621299	−	0.107612i	0.833287	−	0.552840i	$-0.186456\pi$
$821$	−1.78022	−	3.08342i	−0.0621299	−	0.107612i	−0.895417	+	0.445228i	$0.853123\pi$
$822$	24.3116	−	42.1089i	0.847964	−	1.46872i
$823$	−10.9332	+	18.9369i	−0.381109	+	0.660100i	−0.991221	−	0.132215i	$-0.957791\pi$
$823$	−10.9332	+	18.9369i	−0.381109	+	0.660100i	0.610112	+	0.792315i	$0.291124\pi$
$824$	−16.6997	−	28.9247i	−0.581760	−	1.00764i
$825$	20.2610			0.705396
$826$	39.4589	+	5.26053i	1.37295	+	0.183037i
$827$	−18.1361			−0.630653			−0.315327	−	0.948983i	$-0.602114\pi$
$827$	−18.1361			−0.630653			−0.315327	+	0.948983i	$0.602114\pi$
$828$	0.188610	+	0.326682i	0.00655465	+	0.0113530i
$829$	−15.4497	+	26.7596i	−0.536590	+	0.929401i	0.462495	+	0.886622i	$0.346954\pi$
$829$	−15.4497	+	26.7596i	−0.536590	+	0.929401i	−0.999085	+	0.0427787i	$0.986379\pi$
$830$	5.57896	−	9.66305i	0.193649	−	0.335409i
$831$	−13.0196	−	22.5507i	−0.451646	−	0.782275i
$832$		0			0
$833$	−38.4322	+	38.1816i	−1.33160	+	1.32291i
$834$	−16.1530			−0.559333
$835$	34.6466	+	60.0097i	1.19900	+	2.07672i
$836$	−0.114878	+	0.198974i	−0.00397313	+	0.00688165i
$837$	−9.49084	+	16.4386i	−0.328051	+	0.568202i
$838$	−5.35673	−	9.27813i	−0.185045	−	0.320508i
$839$	15.3959			0.531526			0.265763	−	0.964038i	$-0.414376\pi$
$839$	15.3959			0.531526			0.265763	+	0.964038i	$0.414376\pi$
$840$	−56.5209	−	7.53518i	−1.95016	−	0.259989i
$841$	−12.6393			−0.435838
$842$	1.89533	+	3.28280i	0.0653173	+	0.113133i
$843$	27.3910	−	47.4426i	0.943396	−	1.63401i
$844$	−0.444076	+	0.769163i	−0.0152857	+	0.0264757i
$845$		0			0
$846$	−1.44703			−0.0497498
$847$	9.44447	+	22.9069i	0.324516	+	0.787089i
$848$	0.286615			0.00984239
$849$	−15.1116	−	26.1740i	−0.518628	−	0.898290i
$850$	−40.2333	+	69.6862i	−1.37999	+	2.39022i
$851$	0.869829	−	1.50659i	0.0298173	−	0.0516451i
$852$	2.22922	+	3.86113i	0.0763719	+	0.132280i
$853$	23.7772			0.814116			0.407058	−	0.913402i	$-0.366555\pi$
$853$	23.7772			0.814116			0.407058	+	0.913402i	$0.366555\pi$
$854$	16.5537	−	21.5002i	0.566455	−	0.735723i
$855$	−4.05090			−0.138538
$856$	−9.68242	−	16.7704i	−0.330938	−	0.573202i
$857$	15.0525	−	26.0717i	0.514184	−	0.890592i	−0.485681	−	0.874136i	$-0.661428\pi$
$857$	15.0525	−	26.0717i	0.514184	−	0.890592i	0.999865	−	0.0164561i	$-0.00523837\pi$
$858$		0			0
$859$	7.56717	+	13.1067i	0.258188	+	0.447195i	0.965757	−	0.259450i	$-0.0835411\pi$
$859$	7.56717	+	13.1067i	0.258188	+	0.447195i	−0.707568	+	0.706645i	$0.750208\pi$
$860$	−2.60172			−0.0887178
$861$	−13.8939	+	18.0457i	−0.473502	+	0.614995i
$862$	7.71657			0.262827
$863$	−9.13287	−	15.8186i	−0.310886	−	0.538471i	0.667668	−	0.744459i	$-0.267293\pi$
$863$	−9.13287	−	15.8186i	−0.310886	−	0.538471i	−0.978555	+	0.205988i	$0.933959\pi$
$864$	1.97674	−	3.42382i	0.0672501	−	0.116481i
$865$	−25.6514	+	44.4296i	−0.872175	+	1.51065i
$866$	16.4963	+	28.5724i	0.560566	+	0.970929i
$867$	87.9395			2.98658
$868$	−0.989128	−	2.39906i	−0.0335732	−	0.0814293i
$869$	−3.65100			−0.123852
$870$	−19.8994	−	34.4668i	−0.674653	−	1.16853i
$871$		0			0
$872$	8.60263	−	14.9002i	0.291322	−	0.504584i
$873$	0.287834	+	0.498543i	0.00974171	+	0.0168731i
$874$	−2.09159			−0.0707492
$875$	25.5346	+	3.40419i	0.863227	+	0.115083i
$876$	−0.296803			−0.0100281
$877$	−3.49820	−	6.05906i	−0.118126	−	0.204600i	0.800899	−	0.598799i	$-0.204355\pi$
$877$	−3.49820	−	6.05906i	−0.118126	−	0.204600i	−0.919025	+	0.394199i	$0.871022\pi$
$878$	−24.6461	+	42.6883i	−0.831765	+	1.44066i
$879$	−11.8732	+	20.5650i	−0.400474	+	0.693641i
$880$	8.17292	+	14.1559i	0.275509	+	0.477195i
$881$	25.7746			0.868368			0.434184	−	0.900824i	$-0.357037\pi$
$881$	25.7746			0.868368			0.434184	+	0.900824i	$0.357037\pi$
$882$	−8.03587	+	7.98346i	−0.270582	+	0.268817i
$883$	16.4526			0.553674			0.276837	−	0.960917i	$-0.410714\pi$
$883$	16.4526			0.553674			0.276837	+	0.960917i	$0.410714\pi$
$884$		0			0
$885$	−40.9043	+	70.8484i	−1.37498	+	2.38154i
$886$	−18.2233	+	31.5637i	−0.612225	+	1.06040i
$887$	−27.6227	−	47.8440i	−0.927481	−	1.60644i	−0.787522	−	0.616286i	$-0.788636\pi$
$887$	−27.6227	−	47.8440i	−0.927481	−	1.60644i	−0.139958	−	0.990157i	$-0.544697\pi$
$888$	6.37948			0.214081
$889$	38.5943	+	5.14527i	1.29441	+	0.172567i
$890$	−36.3620			−1.21886
$891$	7.13611	+	12.3601i	0.239069	+	0.414079i
$892$	−2.30585	+	3.99385i	−0.0772056	+	0.133724i
$893$	−0.422016	+	0.730953i	−0.0141222	+	0.0244604i
$894$	14.4497	+	25.0277i	0.483271	+	0.837050i
$895$	19.3590			0.647099
$896$	−9.51575	−	23.0798i	−0.317899	−	0.771041i
$897$		0			0
$898$	18.4514	+	31.9587i	0.615731	+	1.06648i
$899$	10.4199	−	18.0478i	0.347523	−	0.601927i
$900$	0.884960	−	1.53280i	0.0294987	−	0.0510932i
$901$	0.309538	+	0.536136i	0.0103122	+	0.0178613i
$902$	7.22241			0.240480
$903$	−12.6756	+	16.4633i	−0.421817	+	0.547865i
$904$	−19.2478			−0.640171
$905$	−27.6328	−	47.8614i	−0.918544	−	1.59097i
$906$	6.50034	−	11.2589i	0.215959	−	0.374052i
$907$	−23.9212	+	41.4327i	−0.794290	+	1.37575i	0.128998	+	0.991645i	$0.458824\pi$
$907$	−23.9212	+	41.4327i	−0.794290	+	1.37575i	−0.923289	+	0.384107i	$0.874510\pi$
$908$	1.46347	+	2.53480i	0.0485669	+	0.0841204i
$909$	3.46245			0.114842
$910$		0			0
$911$	−23.0711			−0.764380			−0.382190	−	0.924084i	$-0.624830\pi$
$911$	−23.0711			−0.764380			−0.382190	+	0.924084i	$0.624830\pi$
$912$	−3.46666	−	6.00444i	−0.114793	−	0.198827i
$913$	1.48635	−	2.57443i	0.0491909	−	0.0852011i
$914$	26.6785	−	46.2085i	0.882445	−	1.52844i
$915$	27.8819	+	48.2928i	0.921746	+	1.59651i
$916$	−3.11277			−0.102849
$917$	−11.2816	−	27.3627i	−0.372552	−	0.903597i
$918$	−38.3560			−1.26594
$919$	21.7184	+	37.6174i	0.716424	+	1.24088i	0.962408	+	0.271609i	$0.0875557\pi$
$919$	21.7184	+	37.6174i	0.716424	+	1.24088i	−0.245984	+	0.969274i	$0.579111\pi$
$920$	8.65856	−	14.9971i	0.285464	−	0.494439i
$921$	30.0684	−	52.0799i	0.990787	−	1.71609i
$922$	3.29298	+	5.70360i	0.108448	+	0.187838i
$923$		0			0
$924$	−1.30873	−	0.174475i	−0.0430539	−	0.00573981i
$925$	−8.16249			−0.268381
$926$	3.16931	+	5.48940i	0.104150	+	0.180393i
$927$	6.81764	−	11.8085i	0.223921	−	0.387842i
$928$	−2.17024	+	3.75897i	−0.0712418	+	0.123394i
$929$	6.39095	+	11.0695i	0.209680	+	0.363177i	0.951614	−	0.307296i	$-0.0994243\pi$
$929$	6.39095	+	11.0695i	0.209680	+	0.363177i	−0.741933	+	0.670474i	$0.766091\pi$
$930$	−50.6945			−1.66234
$931$	1.68917	+	6.38757i	0.0553603	+	0.209344i
$932$	5.54171			0.181525
$933$	0.154428	+	0.267478i	0.00505576	+	0.00875683i
$934$	−21.5345	+	37.2988i	−0.704629	+	1.22045i
$935$	−17.6532	+	30.5762i	−0.577320	+	0.999948i
$936$		0			0
$937$	16.2533			0.530971			0.265486	−	0.964115i	$-0.414468\pi$
$937$	16.2533			0.530971			0.265486	+	0.964115i	$0.414468\pi$
$938$	22.3001	+	2.97298i	0.728124	+	0.0970712i
$939$	−21.5694			−0.703891
$940$	−0.303669	−	0.525971i	−0.00990460	−	0.0171553i
$941$	22.5744	−	39.1000i	0.735905	−	1.27462i	−0.218420	−	0.975855i	$-0.570090\pi$
$941$	22.5744	−	39.1000i	0.735905	−	1.27462i	0.954325	−	0.298770i	$-0.0965762\pi$
$942$	−12.4132	+	21.5003i	−0.404445	+	0.700519i
$943$	−3.45831	−	5.98997i	−0.112618	−	0.195060i
$944$	−40.0752			−1.30434
$945$	13.2559	+	32.1512i	0.431215	+	1.04588i
$946$	6.58911			0.214230
$947$	9.92787	+	17.1956i	0.322612	+	0.558781i	0.981026	−	0.193875i	$-0.0621057\pi$
$947$	9.92787	+	17.1956i	0.322612	+	0.558781i	−0.658414	+	0.752656i	$0.728772\pi$
$948$	−0.557172	+	0.965050i	−0.0180961	+	0.0313434i
$949$		0			0
$950$	4.90689	+	8.49898i	0.159200	+	0.275743i
$951$	3.08901			0.100168
$952$	36.8068	−	47.8055i	1.19292	−	1.54938i
$953$	15.7287			0.509501			0.254751	−	0.967007i	$-0.418007\pi$
$953$	15.7287			0.509501			0.254751	+	0.967007i	$0.418007\pi$
$954$	0.0647220	+	0.112102i	0.00209545	+	0.00362943i
$955$	−8.46673	+	14.6648i	−0.273977	+	0.474542i
$956$	0.823724	−	1.42673i	0.0266412	−	0.0461438i
$957$	−5.30159	−	9.18262i	−0.171376	−	0.296832i
$958$	−24.2470			−0.783385
$959$	28.4572	−	36.9609i	0.918932	−	1.19353i
$960$	62.9734			2.03246
$961$	2.22744	+	3.85804i	0.0718529	+	0.124453i
$962$		0			0
$963$	3.95285	−	6.84653i	0.127379	−	0.220626i
$964$	1.73216	+	3.00019i	0.0557891	+	0.0966296i
$965$	−75.0629			−2.41636
$966$	−4.58149	−	11.1121i	−0.147407	−	0.357525i
$967$	−52.1912			−1.67835			−0.839177	−	0.543858i	$-0.816963\pi$
$967$	−52.1912			−1.67835			−0.839177	+	0.543858i	$0.816963\pi$
$968$	−13.7972	−	23.8974i	−0.443458	−	0.768091i
$969$	7.48786	−	12.9693i	0.240545	−	0.416635i
$970$	1.14841	−	1.98910i	0.0368732	−	0.0638663i
$971$	11.2292	+	19.4495i	0.360362	+	0.624165i	0.988020	−	0.154324i	$-0.0493198\pi$
$971$	11.2292	+	19.4495i	0.360362	+	0.624165i	−0.627658	+	0.778489i	$0.715987\pi$
$972$	2.25207			0.0722350
$973$	−15.3605	−	2.04782i	−0.492436	−	0.0656500i
$974$	23.6765			0.758645
$975$		0			0
$976$	−13.6584	+	23.6570i	−0.437193	+	0.757241i
$977$	20.5172	−	35.5369i	0.656405	−	1.13693i	−0.325135	−	0.945668i	$-0.605410\pi$
$977$	20.5172	−	35.5369i	0.656405	−	1.13693i	0.981540	−	0.191259i	$-0.0612570\pi$
$978$	−16.5918	−	28.7378i	−0.530546	−	0.918933i
$979$	−9.68755			−0.309616
$980$	−4.58825	−	1.24552i	−0.146566	−	0.0397866i
$981$	7.02404			0.224260
$982$	−2.59871	−	4.50110i	−0.0829282	−	0.143636i
$983$	13.4164	−	23.2379i	0.427916	−	0.741173i	−0.568772	−	0.822496i	$-0.692581\pi$
$983$	13.4164	−	23.2379i	0.427916	−	0.741173i	0.996688	+	0.0813229i	$0.0259145\pi$
$984$	12.6819	−	21.9658i	0.404285	−	0.700243i
$985$	10.3681	+	17.9581i	0.330356	+	0.572193i
$986$	42.1107			1.34108
$987$	−4.80775	−	0.640954i	−0.153032	−	0.0204018i
$988$		0			0
$989$	−3.15506	−	5.46473i	−0.100325	−	0.173768i
$990$	−3.69114	+	6.39324i	−0.117312	+	0.203191i
$991$	−5.18755	+	8.98510i	−0.164788	+	0.285421i	−0.936580	−	0.350454i	$-0.886027\pi$
$991$	−5.18755	+	8.98510i	−0.164788	+	0.285421i	0.771792	+	0.635875i	$0.219361\pi$
$992$	2.76439	+	4.78807i	0.0877696	+	0.152021i
$993$	51.7669			1.64277
$994$	−15.4983	−	37.5899i	−0.491575	−	1.19228i
$995$	37.8833			1.20098
$996$	−0.453656	−	0.785755i	−0.0143746	−	0.0248976i
$997$	26.9549	−	46.6872i	0.853669	−	1.47860i	−0.0242056	−	0.999707i	$-0.507706\pi$
$997$	26.9549	−	46.6872i	0.853669	−	1.47860i	0.877874	−	0.478891i	$-0.158961\pi$
$998$	8.50671	−	14.7341i	0.269275	−	0.466398i
$999$	−1.94540	−	3.36954i	−0.0615499	−	0.106607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.j.508.4		24
7.2	even	3	inner	1183.2.e.j.170.4		24
7.3	odd	6		8281.2.a.co.1.9		12
7.4	even	3		8281.2.a.cp.1.9		12
13.6	odd	12		91.2.u.b.88.5	yes	12
13.11	odd	12		91.2.k.b.4.5	✓	12
13.12	even	2	inner	1183.2.e.j.508.9		24
39.11	even	12		819.2.bm.f.550.2		12
39.32	even	12		819.2.do.e.361.2		12
91.6	even	12		637.2.u.g.361.5		12
91.11	odd	12		637.2.q.g.589.2		12
91.19	even	12		637.2.k.i.569.2		12
91.24	even	12		637.2.q.i.589.2		12
91.25	even	6		8281.2.a.cp.1.4		12
91.32	odd	12		637.2.q.g.491.2		12
91.37	odd	12		91.2.u.b.30.5	yes	12
91.38	odd	6		8281.2.a.co.1.4		12
91.45	even	12		637.2.q.i.491.2		12
91.51	even	6	inner	1183.2.e.j.170.9		24
91.58	odd	12		91.2.k.b.23.2	yes	12
91.76	even	12		637.2.k.i.459.5		12
91.89	even	12		637.2.u.g.30.5		12
273.128	even	12		819.2.do.e.667.2		12
273.149	even	12		819.2.bm.f.478.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.5	✓	12	13.11	odd	12
91.2.k.b.23.2	yes	12	91.58	odd	12
91.2.u.b.30.5	yes	12	91.37	odd	12
91.2.u.b.88.5	yes	12	13.6	odd	12
637.2.k.i.459.5		12	91.76	even	12
637.2.k.i.569.2		12	91.19	even	12
637.2.q.g.491.2		12	91.32	odd	12
637.2.q.g.589.2		12	91.11	odd	12
637.2.q.i.491.2		12	91.45	even	12
637.2.q.i.589.2		12	91.24	even	12
637.2.u.g.30.5		12	91.89	even	12
637.2.u.g.361.5		12	91.6	even	12
819.2.bm.f.478.5		12	273.149	even	12
819.2.bm.f.550.2		12	39.11	even	12
819.2.do.e.361.2		12	39.32	even	12
819.2.do.e.667.2		12	273.128	even	12
1183.2.e.j.170.4		24	7.2	even	3	inner
1183.2.e.j.170.9		24	91.51	even	6	inner
1183.2.e.j.508.4		24	1.1	even	1	trivial
1183.2.e.j.508.9		24	13.12	even	2	inner
8281.2.a.co.1.4		12	91.38	odd	6
8281.2.a.co.1.9		12	7.3	odd	6
8281.2.a.cp.1.4		12	91.25	even	6
8281.2.a.cp.1.9		12	7.4	even	3

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.672613 - 1.16500i) q^{2} +(-1.02505 + 1.77544i) q^{3} +(0.0951832 - 0.164862i) q^{4} +(-1.78389 - 3.08979i) q^{5} +2.75785 q^{6} +(2.62255 + 0.349630i) q^{7} -2.94654 q^{8} +(-0.601462 - 1.04176i) q^{9} +O(q^{10})\)	\(q+(-0.672613 - 1.16500i) q^{2} +(-1.02505 + 1.77544i) q^{3} +(0.0951832 - 0.164862i) q^{4} +(-1.78389 - 3.08979i) q^{5} +2.75785 q^{6} +(2.62255 + 0.349630i) q^{7} -2.94654 q^{8} +(-0.601462 - 1.04176i) q^{9} +(-2.39973 + 4.15646i) q^{10} +(-0.639336 + 1.10736i) q^{11} +(0.195135 + 0.337984i) q^{12} +(-1.35664 - 3.29043i) q^{14} +7.31431 q^{15} +(1.79151 + 3.10299i) q^{16} +(-3.86960 + 6.70234i) q^{17} +(-0.809103 + 1.40141i) q^{18} +(0.471939 + 0.817422i) q^{19} -0.679185 q^{20} +(-3.30899 + 4.29779i) q^{21} +1.72010 q^{22} +(-0.823637 - 1.42658i) q^{23} +(3.02035 - 5.23141i) q^{24} +(-3.86451 + 6.69354i) q^{25} -3.68419 q^{27} +(0.307263 - 0.399080i) q^{28} +4.04484 q^{29} +(-4.91970 - 8.52117i) q^{30} +(2.57610 - 4.46193i) q^{31} +(-0.536547 + 0.929326i) q^{32} +(-1.31071 - 2.27021i) q^{33} +10.4110 q^{34} +(-3.59805 - 8.72681i) q^{35} -0.228996 q^{36} +(0.528041 + 0.914594i) q^{37} +(0.634865 - 1.09962i) q^{38} +(5.25629 + 9.10417i) q^{40} +4.19882 q^{41} +(7.23260 + 0.964227i) q^{42} +3.83065 q^{43} +(0.121708 + 0.210805i) q^{44} +(-2.14588 + 3.71678i) q^{45} +(-1.10798 + 1.91908i) q^{46} +(0.447109 + 0.774415i) q^{47} -7.34558 q^{48} +(6.75552 + 1.83384i) q^{49} +10.3973 q^{50} +(-7.93308 - 13.7405i) q^{51} +(0.0399961 - 0.0692754i) q^{53} +(2.47804 + 4.29208i) q^{54} +4.56202 q^{55} +(-7.72744 - 1.03020i) q^{56} -1.93505 q^{57} +(-2.72061 - 4.71224i) q^{58} +(-5.59237 + 9.68627i) q^{59} +(0.696200 - 1.20585i) q^{60} +(3.81196 + 6.60251i) q^{61} -6.93087 q^{62} +(-1.21313 - 2.94236i) q^{63} +8.60961 q^{64} +(-1.76319 + 3.05394i) q^{66} +(-3.16052 + 5.47418i) q^{67} +(0.736641 + 1.27590i) q^{68} +3.37708 q^{69} +(-7.74664 + 10.0615i) q^{70} +11.4240 q^{71} +(1.77223 + 3.06959i) q^{72} +(-0.380253 + 0.658617i) q^{73} +(0.710335 - 1.23034i) q^{74} +(-7.92265 - 13.7224i) q^{75} +0.179683 q^{76} +(-2.06386 + 2.68058i) q^{77} +(1.42765 + 2.47277i) q^{79} +(6.39172 - 11.0708i) q^{80} +(5.58087 - 9.66636i) q^{81} +(-2.82418 - 4.89163i) q^{82} -2.32483 q^{83} +(0.393583 + 0.954606i) q^{84} +27.6117 q^{85} +(-2.57654 - 4.46270i) q^{86} +(-4.14617 + 7.18137i) q^{87} +(1.88383 - 3.26289i) q^{88} +(3.78813 + 6.56124i) q^{89} +5.77339 q^{90} -0.313586 q^{92} +(5.28127 + 9.14742i) q^{93} +(0.601462 - 1.04176i) q^{94} +(1.68377 - 2.91638i) q^{95} +(-1.09998 - 1.90522i) q^{96} -0.478557 q^{97} +(-2.40742 - 9.10365i) q^{98} +1.53815 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9	\( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) \) 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9 - 24 * q^10 + 2 * q^12 + 8 * q^14 - 16 * q^16 - 34 * q^17 + 60 * q^22 - 6 * q^23 + 10 * q^25 + 24 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^35 - 52 * q^36 - 38 * q^38 - 2 * q^40 + 32 * q^42 + 44 * q^43 - 76 * q^48 + 12 * q^49 - 8 * q^51 - 16 * q^53 + 60 * q^55 + 54 * q^56 + 10 * q^61 + 164 * q^62 - 4 * q^64 - 68 * q^66 - 22 * q^68 + 28 * q^69 - 66 * q^74 - 2 * q^75 + 38 * q^77 - 70 * q^79 + 28 * q^81 - 10 * q^82 + 20 * q^87 + 28 * q^88 - 132 * q^92 + 2 * q^94 - 4 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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