LMFDB - Embedded newform 1183.2.e.l.170.16

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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.16
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.l.508.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.514418 - 0.890998i) q^{2} +(-1.33163 - 2.30645i) q^{3} +(0.470749 + 0.815361i) q^{4} +(-0.745563 + 1.29135i) q^{5} -2.74006 q^{6} +(-1.93668 - 1.80257i) q^{7} +3.02632 q^{8} +(-2.04647 + 3.54460i) q^{9} +O(q^{10})$	\(q+(0.514418 - 0.890998i) q^{2} +(-1.33163 - 2.30645i) q^{3} +(0.470749 + 0.815361i) q^{4} +(-0.745563 + 1.29135i) q^{5} -2.74006 q^{6} +(-1.93668 - 1.80257i) q^{7} +3.02632 q^{8} +(-2.04647 + 3.54460i) q^{9} +(0.767061 + 1.32859i) q^{10} +(-2.02066 - 3.49989i) q^{11} +(1.25373 - 2.17152i) q^{12} +(-2.60235 + 0.798305i) q^{14} +3.97125 q^{15} +(0.615293 - 1.06572i) q^{16} +(-1.84438 - 3.19455i) q^{17} +(2.10549 + 3.64681i) q^{18} +(2.64218 - 4.57640i) q^{19} -1.40389 q^{20} +(-1.57860 + 6.86722i) q^{21} -4.15786 q^{22} +(-3.63585 + 6.29747i) q^{23} +(-4.02993 - 6.98005i) q^{24} +(1.38827 + 2.40456i) q^{25} +2.91081 q^{27} +(0.558054 - 2.42765i) q^{28} -7.56677 q^{29} +(2.04288 - 3.53838i) q^{30} +(0.838616 + 1.45253i) q^{31} +(2.39328 + 4.14528i) q^{32} +(-5.38154 + 9.32111i) q^{33} -3.79512 q^{34} +(3.77167 - 1.15701i) q^{35} -3.85350 q^{36} +(-3.51064 + 6.08060i) q^{37} +(-2.71837 - 4.70836i) q^{38} +(-2.25631 + 3.90804i) q^{40} +0.409255 q^{41} +(5.30662 + 4.93914i) q^{42} -6.43516 q^{43} +(1.90245 - 3.29514i) q^{44} +(-3.05155 - 5.28544i) q^{45} +(3.74069 + 6.47906i) q^{46} +(-2.56942 + 4.45036i) q^{47} -3.27737 q^{48} +(0.501479 + 6.98201i) q^{49} +2.85661 q^{50} +(-4.91205 + 8.50792i) q^{51} +(0.790945 + 1.36996i) q^{53} +(1.49737 - 2.59352i) q^{54} +6.02612 q^{55} +(-5.86102 - 5.45515i) q^{56} -14.0736 q^{57} +(-3.89248 + 6.74198i) q^{58} +(-3.82320 - 6.62197i) q^{59} +(1.86946 + 3.23800i) q^{60} +(-5.64467 + 9.77685i) q^{61} +1.72560 q^{62} +(10.3528 - 3.17585i) q^{63} +7.38576 q^{64} +(5.53672 + 9.58989i) q^{66} +(-6.57883 - 11.3949i) q^{67} +(1.73648 - 3.00766i) q^{68} +19.3664 q^{69} +(0.909322 - 3.95574i) q^{70} +8.71275 q^{71} +(-6.19328 + 10.7271i) q^{72} +(-7.59569 - 13.1561i) q^{73} +(3.61187 + 6.25594i) q^{74} +(3.69733 - 6.40396i) q^{75} +4.97522 q^{76} +(-2.39542 + 10.4206i) q^{77} +(0.376918 - 0.652842i) q^{79} +(0.917480 + 1.58912i) q^{80} +(2.26331 + 3.92016i) q^{81} +(0.210528 - 0.364645i) q^{82} -3.96146 q^{83} +(-6.34238 + 1.94561i) q^{84} +5.50039 q^{85} +(-3.31036 + 5.73372i) q^{86} +(10.0761 + 17.4524i) q^{87} +(-6.11516 - 10.5918i) q^{88} +(1.84657 - 3.19835i) q^{89} -6.27909 q^{90} -6.84629 q^{92} +(2.23345 - 3.86845i) q^{93} +(2.64351 + 4.57869i) q^{94} +(3.93983 + 6.82398i) q^{95} +(6.37393 - 11.0400i) q^{96} +8.43912 q^{97} +(6.47893 + 3.14486i) q^{98} +16.5409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9}+O(q^{10}) $ 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 2 q^{14} + 10 q^{15} - 17 q^{16} + 5 q^{17} - 24 q^{19} + 68 q^{20} - q^{21} - 28 q^{22} - 11 q^{23} - 32 q^{24} - 33 q^{25} - 42 q^{27} - 15 q^{28} + 8 q^{29} + 22 q^{30} - 40 q^{31} + 6 q^{32} - 24 q^{33} + 72 q^{34} + 44 q^{35} - 30 q^{36} + 4 q^{37} + 29 q^{38} + 4 q^{40} + 98 q^{41} - 9 q^{42} + 26 q^{43} - 10 q^{44} - 58 q^{45} + 10 q^{46} - 62 q^{47} + 178 q^{48} + 31 q^{49} - 46 q^{50} + 21 q^{51} + 18 q^{53} - 12 q^{54} - 28 q^{55} - 56 q^{56} - 26 q^{57} - 56 q^{58} - 79 q^{59} - 22 q^{60} - 13 q^{61} + 24 q^{62} + 22 q^{63} + 36 q^{64} + 38 q^{66} + 2 q^{67} + 12 q^{68} - 56 q^{69} + 85 q^{70} - 38 q^{71} - 81 q^{72} - 17 q^{73} - 17 q^{74} - 24 q^{75} + 116 q^{76} - 30 q^{77} + 9 q^{79} - 63 q^{80} - 16 q^{81} + 22 q^{82} + 162 q^{83} + 203 q^{84} - 68 q^{85} - 22 q^{86} - 70 q^{87} + 33 q^{88} - 72 q^{89} + 2 q^{90} - 8 q^{92} - 19 q^{93} + 30 q^{94} - 13 q^{95} - 11 q^{96} + 90 q^{97} + 81 q^{98} - 78 q^{99}+O(q^{100}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9 - 5 * q^10 + q^11 - 5 * q^12 - 2 * q^14 + 10 * q^15 - 17 * q^16 + 5 * q^17 - 24 * q^19 + 68 * q^20 - q^21 - 28 * q^22 - 11 * q^23 - 32 * q^24 - 33 * q^25 - 42 * q^27 - 15 * q^28 + 8 * q^29 + 22 * q^30 - 40 * q^31 + 6 * q^32 - 24 * q^33 + 72 * q^34 + 44 * q^35 - 30 * q^36 + 4 * q^37 + 29 * q^38 + 4 * q^40 + 98 * q^41 - 9 * q^42 + 26 * q^43 - 10 * q^44 - 58 * q^45 + 10 * q^46 - 62 * q^47 + 178 * q^48 + 31 * q^49 - 46 * q^50 + 21 * q^51 + 18 * q^53 - 12 * q^54 - 28 * q^55 - 56 * q^56 - 26 * q^57 - 56 * q^58 - 79 * q^59 - 22 * q^60 - 13 * q^61 + 24 * q^62 + 22 * q^63 + 36 * q^64 + 38 * q^66 + 2 * q^67 + 12 * q^68 - 56 * q^69 + 85 * q^70 - 38 * q^71 - 81 * q^72 - 17 * q^73 - 17 * q^74 - 24 * q^75 + 116 * q^76 - 30 * q^77 + 9 * q^79 - 63 * q^80 - 16 * q^81 + 22 * q^82 + 162 * q^83 + 203 * q^84 - 68 * q^85 - 22 * q^86 - 70 * q^87 + 33 * q^88 - 72 * q^89 + 2 * q^90 - 8 * q^92 - 19 * q^93 + 30 * q^94 - 13 * q^95 - 11 * q^96 + 90 * q^97 + 81 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.514418	−	0.890998i	0.363748	−	0.630030i	−0.624826	−	0.780764i	$-0.714830\pi$
$2$	0.514418	−	0.890998i	0.363748	−	0.630030i	0.988574	+	0.150733i	$0.0481635\pi$
$3$	−1.33163	−	2.30645i	−0.768817	−	1.33163i	−0.938205	−	0.346080i	$-0.887513\pi$
$3$	−1.33163	−	2.30645i	−0.768817	−	1.33163i	0.169388	−	0.985549i	$-0.445821\pi$
$4$	0.470749	+	0.815361i	0.235374	+	0.407680i
$5$	−0.745563	+	1.29135i	−0.333426	+	0.577510i	−0.983181	−	0.182633i	$-0.941538\pi$
$5$	−0.745563	+	1.29135i	−0.333426	+	0.577510i	0.649755	+	0.760143i	$0.274871\pi$
$6$	−2.74006			−1.11862
$7$	−1.93668	−	1.80257i	−0.731997	−	0.681308i
$7$	−1.93668	−	1.80257i	−0.731997	−	0.681308i
$8$	3.02632			1.06996
$9$	−2.04647	+	3.54460i	−0.682158	+	1.18153i
$10$	0.767061	+	1.32859i	0.242566	+	0.420137i
$11$	−2.02066	−	3.49989i	−0.609252	−	1.05526i	−0.991364	−	0.131140i	$-0.958136\pi$
$11$	−2.02066	−	3.49989i	−0.609252	−	1.05526i	0.382112	−	0.924116i	$-0.375197\pi$
$12$	1.25373	−	2.17152i	0.361920	−	0.626863i
$13$		0			0
$13$		0			0
$14$	−2.60235	+	0.798305i	−0.695507	+	0.213356i
$15$	3.97125			1.02537
$16$	0.615293	−	1.06572i	0.153823	−	0.266430i
$17$	−1.84438	−	3.19455i	−0.447327	−	0.774793i	0.550884	−	0.834582i	$-0.314291\pi$
$17$	−1.84438	−	3.19455i	−0.447327	−	0.774793i	−0.998211	+	0.0597888i	$0.980957\pi$
$18$	2.10549	+	3.64681i	0.496268	+	0.859561i
$19$	2.64218	−	4.57640i	0.606159	−	1.04990i	−0.385708	−	0.922621i	$-0.626043\pi$
$19$	2.64218	−	4.57640i	0.606159	−	1.04990i	0.991867	−	0.127277i	$-0.0406237\pi$
$20$	−1.40389			−0.313920
$21$	−1.57860	+	6.86722i	−0.344478	+	1.49855i
$22$	−4.15786			−0.886458
$23$	−3.63585	+	6.29747i	−0.758127	+	1.31311i	0.185678	+	0.982611i	$0.440552\pi$
$23$	−3.63585	+	6.29747i	−0.758127	+	1.31311i	−0.943805	+	0.330503i	$0.892781\pi$
$24$	−4.02993	−	6.98005i	−0.822607	−	1.42480i
$25$	1.38827	+	2.40456i	0.277654	+	0.480912i
$26$		0			0
$27$	2.91081			0.560185
$28$	0.558054	−	2.42765i	0.105462	−	0.458783i
$29$	−7.56677			−1.40511			−0.702557	−	0.711627i	$-0.747959\pi$
$29$	−7.56677			−1.40511			−0.702557	+	0.711627i	$0.747959\pi$
$30$	2.04288	−	3.53838i	0.372978	−	0.646016i
$31$	0.838616	+	1.45253i	0.150620	+	0.260881i	0.931456	−	0.363855i	$-0.118540\pi$
$31$	0.838616	+	1.45253i	0.150620	+	0.260881i	−0.780836	+	0.624737i	$0.785206\pi$
$32$	2.39328	+	4.14528i	0.423076	+	0.732790i
$33$	−5.38154	+	9.32111i	−0.936807	+	1.62260i
$34$	−3.79512			−0.650858
$35$	3.77167	−	1.15701i	0.637529	−	0.195570i
$36$	−3.85350			−0.642250
$37$	−3.51064	+	6.08060i	−0.577145	+	0.999645i	0.418659	+	0.908143i	$0.362500\pi$
$37$	−3.51064	+	6.08060i	−0.577145	+	0.999645i	−0.995805	+	0.0915020i	$0.970833\pi$
$38$	−2.71837	−	4.70836i	−0.440978	−	0.763797i
$39$		0			0
$40$	−2.25631	+	3.90804i	−0.356754	+	0.617916i
$41$	0.409255			0.0639148			0.0319574	−	0.999489i	$-0.489826\pi$
$41$	0.409255			0.0639148			0.0319574	+	0.999489i	$0.489826\pi$
$42$	5.30662	+	4.93914i	0.818829	+	0.762126i
$43$	−6.43516			−0.981353			−0.490677	−	0.871342i	$-0.663250\pi$
$43$	−6.43516			−0.981353			−0.490677	+	0.871342i	$0.663250\pi$
$44$	1.90245	−	3.29514i	0.286805	−	0.496760i
$45$	−3.05155	−	5.28544i	−0.454898	−	0.787907i
$46$	3.74069	+	6.47906i	0.551535	+	0.955286i
$47$	−2.56942	+	4.45036i	−0.374788	+	0.649152i	−0.990295	−	0.138979i	$-0.955618\pi$
$47$	−2.56942	+	4.45036i	−0.374788	+	0.649152i	0.615507	+	0.788131i	$0.288951\pi$
$48$	−3.27737			−0.473048
$49$	0.501479	+	6.98201i	0.0716398	+	0.997431i
$50$	2.85661			0.403985
$51$	−4.91205	+	8.50792i	−0.687825	+	1.19135i
$52$		0			0
$53$	0.790945	+	1.36996i	0.108645	+	0.188178i	0.915221	−	0.402951i	$-0.132016\pi$
$53$	0.790945	+	1.36996i	0.108645	+	0.188178i	−0.806577	+	0.591129i	$0.798682\pi$
$54$	1.49737	−	2.59352i	0.203766	−	0.352934i
$55$	6.02612			0.812562
$56$	−5.86102	−	5.45515i	−0.783211	−	0.728975i
$57$	−14.0736			−1.86410
$58$	−3.89248	+	6.74198i	−0.511108	+	0.885265i
$59$	−3.82320	−	6.62197i	−0.497738	−	0.862108i	0.502259	−	0.864718i	$-0.332503\pi$
$59$	−3.82320	−	6.62197i	−0.497738	−	0.862108i	−0.999997	+	0.00260987i	$0.999169\pi$
$60$	1.86946	+	3.23800i	0.241347	+	0.418025i
$61$	−5.64467	+	9.77685i	−0.722726	+	1.25180i	0.237178	+	0.971466i	$0.423778\pi$
$61$	−5.64467	+	9.77685i	−0.722726	+	1.25180i	−0.959903	+	0.280331i	$0.909556\pi$
$62$	1.72560			0.219151
$63$	10.3528	−	3.17585i	1.30433	−	0.400119i
$64$	7.38576			0.923220
$65$		0			0
$66$	5.53672	+	9.58989i	0.681524	+	1.18043i
$67$	−6.57883	−	11.3949i	−0.803732	−	1.39210i	−0.917144	−	0.398557i	$-0.869511\pi$
$67$	−6.57883	−	11.3949i	−0.803732	−	1.39210i	0.113412	−	0.993548i	$-0.463822\pi$
$68$	1.73648	−	3.00766i	0.210579	−	0.364733i
$69$	19.3664			2.33144
$70$	0.909322	−	3.95574i	0.108685	−	0.472801i
$71$	8.71275			1.03401			0.517007	−	0.855981i	$-0.327046\pi$
$71$	8.71275			1.03401			0.517007	+	0.855981i	$0.327046\pi$
$72$	−6.19328	+	10.7271i	−0.729885	+	1.26420i
$73$	−7.59569	−	13.1561i	−0.889008	−	1.53981i	−0.841049	−	0.540958i	$-0.818062\pi$
$73$	−7.59569	−	13.1561i	−0.889008	−	1.53981i	−0.0479588	−	0.998849i	$-0.515272\pi$
$74$	3.61187	+	6.25594i	0.419871	+	0.727238i
$75$	3.69733	−	6.40396i	0.426931	−	0.739466i
$76$	4.97522			0.570697
$77$	−2.39542	+	10.4206i	−0.272983	+	1.18753i
$78$		0			0
$79$	0.376918	−	0.652842i	0.0424066	−	0.0734505i	−0.844043	−	0.536275i	$-0.819831\pi$
$79$	0.376918	−	0.652842i	0.0424066	−	0.0734505i	0.886450	+	0.462825i	$0.153164\pi$
$80$	0.917480	+	1.58912i	0.102577	+	0.177669i
$81$	2.26331	+	3.92016i	0.251479	+	0.435574i
$82$	0.210528	−	0.364645i	0.0232489	−	0.0402683i
$83$	−3.96146			−0.434827			−0.217413	−	0.976080i	$-0.569762\pi$
$83$	−3.96146			−0.434827			−0.217413	+	0.976080i	$0.569762\pi$
$84$	−6.34238	+	1.94561i	−0.692011	+	0.212283i
$85$	5.50039			0.596601
$86$	−3.31036	+	5.73372i	−0.356966	+	0.618282i
$87$	10.0761	+	17.4524i	1.08028	+	1.87109i
$88$	−6.11516	−	10.5918i	−0.651878	−	1.12909i
$89$	1.84657	−	3.19835i	0.195736	−	0.339024i	−0.751406	−	0.659840i	$-0.770624\pi$
$89$	1.84657	−	3.19835i	0.195736	−	0.339024i	0.947141	+	0.320816i	$0.103957\pi$
$90$	−6.27909			−0.661874
$91$		0			0
$92$	−6.84629			−0.713775
$93$	2.23345	−	3.86845i	0.231598	−	0.401140i
$94$	2.64351	+	4.57869i	0.272657	+	0.472256i
$95$	3.93983	+	6.82398i	0.404218	+	0.700126i
$96$	6.37393	−	11.0400i	0.650536	−	1.12676i
$97$	8.43912			0.856863			0.428432	−	0.903574i	$-0.359066\pi$
$97$	8.43912			0.856863			0.428432	+	0.903574i	$0.359066\pi$
$98$	6.47893	+	3.14486i	0.654471	+	0.317678i
$99$	16.5409			1.66243
$100$	−1.30706	+	2.26389i	−0.130706	+	0.226389i
$101$	−4.23795	−	7.34035i	−0.421692	−	0.730392i	0.574413	−	0.818566i	$-0.305230\pi$
$101$	−4.23795	−	7.34035i	−0.421692	−	0.730392i	−0.996105	+	0.0881733i	$0.971897\pi$
$102$	5.05369	+	8.75325i	0.500390	+	0.866701i
$103$	7.95466	−	13.7779i	0.783796	−	1.35757i	−0.145920	−	0.989296i	$-0.546614\pi$
$103$	7.95466	−	13.7779i	0.783796	−	1.35757i	0.929716	−	0.368277i	$-0.120052\pi$
$104$		0			0
$105$	−7.69106	−	7.15847i	−0.750570	−	0.698595i
$106$	1.62750			0.158077
$107$	−3.57356	+	6.18958i	−0.345469	+	0.598369i	−0.985439	−	0.170031i	$-0.945613\pi$
$107$	−3.57356	+	6.18958i	−0.345469	+	0.598369i	0.639970	+	0.768400i	$0.278947\pi$
$108$	1.37026	+	2.37336i	0.131853	+	0.228376i
$109$	0.556225	+	0.963411i	0.0532767	+	0.0922780i	0.891434	−	0.453151i	$-0.149700\pi$
$109$	0.556225	+	0.963411i	0.0532767	+	0.0922780i	−0.838157	+	0.545429i	$0.816367\pi$
$110$	3.09994	−	5.36926i	0.295568	−	0.511939i
$111$	18.6995			1.77488
$112$	−3.11266	+	0.954851i	−0.294119	+	0.0902249i
$113$	−13.0433			−1.22701			−0.613504	−	0.789692i	$-0.710240\pi$
$113$	−13.0433			−1.22701			−0.613504	+	0.789692i	$0.710240\pi$
$114$	−7.23973	+	12.5396i	−0.678063	+	1.17444i
$115$	−5.42151	−	9.39032i	−0.505558	−	0.875652i
$116$	−3.56205	−	6.16965i	−0.330728	−	0.572838i
$117$		0			0
$118$	−7.86688			−0.724205
$119$	−2.18644	+	9.51145i	−0.200430	+	0.871914i
$120$	12.0183			1.09711
$121$	−2.66614	+	4.61790i	−0.242377	+	0.419809i
$122$	5.80744	+	10.0588i	0.525780	+	0.910678i
$123$	−0.544975	−	0.943925i	−0.0491388	−	0.0851109i
$124$	−0.789555	+	1.36755i	−0.0709041	+	0.122810i
$125$	−11.5958			−1.03716
$126$	2.49597	−	10.8580i	0.222359	−	0.967307i
$127$	11.4482			1.01587			0.507933	−	0.861396i	$-0.330410\pi$
$127$	11.4482			1.01587			0.507933	+	0.861396i	$0.330410\pi$
$128$	−0.987197	+	1.70988i	−0.0872567	+	0.151133i
$129$	8.56925	+	14.8424i	0.754481	+	1.30680i
$130$		0			0
$131$	−0.894228	+	1.54885i	−0.0781290	+	0.135323i	−0.902443	−	0.430810i	$-0.858228\pi$
$131$	−0.894228	+	1.54885i	−0.0781290	+	0.135323i	0.824314	+	0.566133i	$0.191561\pi$
$132$	−10.1334			−0.882001
$133$	−13.3664	+	4.10031i	−1.15901	+	0.355542i
$134$	−13.5371			−1.16942
$135$	−2.17019	+	3.75888i	−0.186780	+	0.323513i
$136$	−5.58167	−	9.66773i	−0.478624	−	0.829001i
$137$	−3.17735	−	5.50333i	−0.271459	−	0.470181i	0.697776	−	0.716316i	$-0.254173\pi$
$137$	−3.17735	−	5.50333i	−0.271459	−	0.470181i	−0.969236	+	0.246134i	$0.920840\pi$
$138$	9.96243	−	17.2554i	0.848058	−	1.46888i
$139$	10.6138			0.900250			0.450125	−	0.892966i	$-0.351380\pi$
$139$	10.6138			0.900250			0.450125	+	0.892966i	$0.351380\pi$
$140$	2.71889	+	2.53061i	0.229788	+	0.213876i
$141$	13.6861			1.15257
$142$	4.48199	−	7.76304i	0.376121	−	0.651460i
$143$		0			0
$144$	2.51836	+	4.36194i	0.209864	+	0.363495i
$145$	5.64150	−	9.77137i	0.468501	−	0.811468i
$146$	−15.6294			−1.29350
$147$	15.4359	−	10.4541i	1.27313	−	0.862239i
$148$	−6.61052			−0.543381
$149$	−2.40270	+	4.16160i	−0.196837	+	0.340931i	−0.947501	−	0.319752i	$-0.896400\pi$
$149$	−2.40270	+	4.16160i	−0.196837	+	0.340931i	0.750664	+	0.660684i	$0.229734\pi$
$150$	−3.80394	−	6.58862i	−0.310591	−	0.537959i
$151$	−2.06539	−	3.57735i	−0.168079	−	0.291121i	0.769666	−	0.638447i	$-0.220423\pi$
$151$	−2.06539	−	3.57735i	−0.168079	−	0.291121i	−0.937744	+	0.347326i	$0.887090\pi$
$152$	7.99609	−	13.8496i	0.648568	−	1.12335i
$153$	15.0979			1.22059
$154$	8.05245	+	7.49483i	0.648885	+	0.603950i
$155$	−2.50096			−0.200882
$156$		0			0
$157$	−2.97959	−	5.16081i	−0.237797	−	0.411877i	0.722285	−	0.691596i	$-0.243092\pi$
$157$	−2.97959	−	5.16081i	−0.237797	−	0.411877i	−0.960082	+	0.279719i	$0.909759\pi$
$158$	−0.387787	−	0.671667i	−0.0308507	−	0.0534349i
$159$	2.10649	−	3.64855i	0.167056	−	0.289349i
$160$	−7.13737			−0.564258
$161$	18.3931	−	5.64234i	1.44958	−	0.444678i
$162$	4.65714			0.365900
$163$	4.43410	−	7.68008i	0.347305	−	0.601551i	−0.638464	−	0.769651i	$-0.720430\pi$
$163$	4.43410	−	7.68008i	0.347305	−	0.601551i	0.985770	+	0.168101i	$0.0537634\pi$
$164$	0.192656	+	0.333690i	0.0150439	+	0.0260568i
$165$	−8.02456	−	13.8989i	−0.624711	−	1.08203i
$166$	−2.03785	+	3.52965i	−0.158167	+	0.273954i
$167$	−11.9219			−0.922547			−0.461274	−	0.887258i	$-0.652607\pi$
$167$	−11.9219			−0.922547			−0.461274	+	0.887258i	$0.652607\pi$
$168$	−4.77733	+	20.7824i	−0.368579	+	1.60340i
$169$		0			0
$170$	2.82950	−	4.90084i	0.217013	−	0.375877i
$171$	10.8143	+	18.7310i	0.826992	+	1.43239i
$172$	−3.02935	−	5.24698i	−0.230985	−	0.400079i
$173$	4.41559	−	7.64803i	0.335711	−	0.581469i	−0.647910	−	0.761717i	$-0.724357\pi$
$173$	4.41559	−	7.64803i	0.335711	−	0.581469i	0.983621	+	0.180248i	$0.0576900\pi$
$174$	20.7334			1.57179
$175$	1.64574	−	7.15932i	0.124406	−	0.541194i
$176$	−4.97320			−0.374869
$177$	−10.1822	+	17.6360i	−0.765339	+	1.32561i
$178$	−1.89981	−	3.29057i	−0.142397	−	0.246639i
$179$	9.05271	+	15.6798i	0.676632	+	1.17196i	0.975989	+	0.217819i	$0.0698943\pi$
$179$	9.05271	+	15.6798i	0.676632	+	1.17196i	−0.299358	+	0.954141i	$0.596772\pi$
$180$	2.87303	−	4.97623i	0.214143	−	0.370906i
$181$	−21.3354			−1.58585			−0.792923	−	0.609322i	$-0.791442\pi$
$181$	−21.3354			−1.58585			−0.792923	+	0.609322i	$0.791442\pi$
$182$		0			0
$183$	30.0664			2.22257
$184$	−11.0032	+	19.0582i	−0.811169	+	1.40499i
$185$	−5.23480	−	9.06695i	−0.384870	−	0.666615i
$186$	−2.29785	−	3.98000i	−0.168487	−	0.291828i
$187$	−7.45372	+	12.9102i	−0.545070	+	0.944089i
$188$	−4.83820			−0.352862
$189$	−5.63731	−	5.24693i	−0.410054	−	0.381658i
$190$	8.10687			0.588134
$191$	8.11444	−	14.0546i	0.587140	−	1.01696i	−0.407465	−	0.913221i	$-0.633587\pi$
$191$	8.11444	−	14.0546i	0.587140	−	1.01696i	0.994605	−	0.103736i	$-0.0330797\pi$
$192$	−9.83510	−	17.0349i	−0.709787	−	1.22939i
$193$	−1.02587	−	1.77685i	−0.0738434	−	0.127901i	0.826739	−	0.562585i	$-0.190193\pi$
$193$	−1.02587	−	1.77685i	−0.0738434	−	0.127901i	−0.900583	+	0.434685i	$0.856860\pi$
$194$	4.34123	−	7.51924i	0.311682	−	0.539850i
$195$		0			0
$196$	−5.45679	+	3.69566i	−0.389771	+	0.263976i
$197$	2.49922			0.178062			0.0890309	−	0.996029i	$-0.471623\pi$
$197$	2.49922			0.178062			0.0890309	+	0.996029i	$0.471623\pi$
$198$	8.50895	−	14.7379i	0.604704	−	1.04738i
$199$	7.87329	+	13.6369i	0.558123	+	0.966697i	0.997653	+	0.0684695i	$0.0218116\pi$
$199$	7.87329	+	13.6369i	0.558123	+	0.966697i	−0.439530	+	0.898228i	$0.644855\pi$
$200$	4.20135	+	7.27696i	0.297080	+	0.514558i
$201$	−17.5211	+	30.3475i	−1.23585	+	2.14055i
$202$	−8.72032			−0.613559
$203$	14.6544	+	13.6396i	1.02854	+	0.957315i
$204$	−9.24937			−0.647585
$205$	−0.305125	+	0.528492i	−0.0213109	+	0.0369115i
$206$	−8.18403	−	14.1752i	−0.570209	−	0.987630i
$207$	−14.8813	−	25.7752i	−1.03432	−	1.79150i
$208$		0			0
$209$	−21.3558			−1.47721
$210$	−10.3346	+	3.17027i	−0.713155	+	0.218770i
$211$	7.75205			0.533673			0.266837	−	0.963742i	$-0.414022\pi$
$211$	7.75205			0.533673			0.266837	+	0.963742i	$0.414022\pi$
$212$	−0.744673	+	1.28981i	−0.0511443	+	0.0885846i
$213$	−11.6022	−	20.0955i	−0.794967	−	1.37692i
$214$	3.67660	+	6.36806i	0.251327	+	0.435312i
$215$	4.79782	−	8.31006i	0.327208	−	0.566742i
$216$	8.80902			0.599378
$217$	0.994147	−	4.32475i	0.0674871	−	0.293583i
$218$	1.14453			0.0775173
$219$	−20.2293	+	35.0382i	−1.36697	+	2.36766i
$220$	2.83679	+	4.91346i	0.191256	+	0.331266i
$221$		0			0
$222$	9.61934	−	16.6612i	0.645608	−	1.11823i
$223$	−4.75374			−0.318334			−0.159167	−	0.987252i	$-0.550881\pi$
$223$	−4.75374			−0.318334			−0.159167	+	0.987252i	$0.550881\pi$
$224$	2.83714	−	12.3422i	0.189565	−	0.824645i
$225$	−11.3643			−0.757617
$226$	−6.70969	+	11.6215i	−0.446322	+	0.773052i
$227$	−6.29498	−	10.9032i	−0.417813	−	0.723673i	0.577906	−	0.816103i	$-0.303870\pi$
$227$	−6.29498	−	10.9032i	−0.417813	−	0.723673i	−0.995719	+	0.0924301i	$0.970537\pi$
$228$	−6.62515	−	11.4751i	−0.438761	−	0.759957i
$229$	2.62874	−	4.55311i	0.173712	−	0.300878i	−0.766003	−	0.642837i	$-0.777757\pi$
$229$	2.62874	−	4.55311i	0.173712	−	0.300878i	0.939715	+	0.341959i	$0.111090\pi$
$230$	−11.1557			−0.735583
$231$	27.2243	−	8.35141i	1.79123	−	0.549483i
$232$	−22.8995			−1.50342
$233$	4.22816	−	7.32340i	0.276996	−	0.479772i	−0.693641	−	0.720321i	$-0.743994\pi$
$233$	4.22816	−	7.32340i	0.276996	−	0.479772i	0.970637	+	0.240550i	$0.0773277\pi$
$234$		0			0
$235$	−3.83133	−	6.63605i	−0.249928	−	0.432888i
$236$	3.59953	−	6.23457i	0.234310	−	0.405836i
$237$	−2.00766			−0.130412
$238$	7.34994	+	6.84097i	0.476426	+	0.443434i
$239$	−6.55677			−0.424122			−0.212061	−	0.977256i	$-0.568018\pi$
$239$	−6.55677			−0.424122			−0.212061	+	0.977256i	$0.568018\pi$
$240$	2.44349	−	4.23224i	0.157726	−	0.273190i
$241$	−5.79652	−	10.0399i	−0.373387	−	0.646725i	0.616698	−	0.787200i	$-0.288470\pi$
$241$	−5.79652	−	10.0399i	−0.373387	−	0.646725i	−0.990084	+	0.140476i	$0.955137\pi$
$242$	2.74302	+	4.75106i	0.176328	+	0.305409i
$243$	10.3940	−	18.0029i	0.666774	−	1.15489i
$244$	−10.6289			−0.680445
$245$	−9.39013	−	4.55794i	−0.599913	−	0.291196i
$246$	−1.12138			−0.0714966
$247$		0			0
$248$	2.53792	+	4.39580i	0.161158	+	0.279134i
$249$	5.27520	+	9.13691i	0.334302	+	0.579028i
$250$	−5.96509	+	10.3318i	−0.377265	+	0.653443i
$251$	−19.3214			−1.21956			−0.609778	−	0.792572i	$-0.708741\pi$
$251$	−19.3214			−1.21956			−0.609778	+	0.792572i	$0.708741\pi$
$252$	7.46301	+	6.94621i	0.470125	+	0.437570i
$253$	29.3873			1.84756
$254$	5.88918	−	10.2004i	0.369520	−	0.640027i
$255$	−7.32449	−	12.6864i	−0.458677	−	0.794452i
$256$	8.40142	+	14.5517i	0.525089	+	0.909481i
$257$	8.65652	−	14.9935i	0.539979	−	0.935271i	−0.458925	−	0.888475i	$-0.651765\pi$
$257$	8.65652	−	14.9935i	0.539979	−	0.935271i	0.998904	−	0.0467965i	$-0.0149012\pi$
$258$	17.6327			1.09776
$259$	17.7597	−	5.44803i	1.10353	−	0.338524i
$260$		0			0
$261$	15.4852	−	26.8212i	0.958510	−	1.66019i
$262$	0.920013	+	1.59351i	0.0568386	+	0.0984473i
$263$	−12.6968	−	21.9916i	−0.782921	−	1.35606i	−0.930233	−	0.366969i	$-0.880395\pi$
$263$	−12.6968	−	21.9916i	−0.782921	−	1.35606i	0.147312	−	0.989090i	$-0.452938\pi$
$264$	−16.2863	+	28.2086i	−1.00235	+	1.73612i
$265$	−2.35880			−0.144900
$266$	−3.22253	+	14.0187i	−0.197586	+	0.859539i
$267$	−9.83577			−0.601939
$268$	6.19395	−	10.7282i	0.378356	−	0.655332i
$269$	−5.84420	−	10.1225i	−0.356327	−	0.617177i	0.631017	−	0.775769i	$-0.282638\pi$
$269$	−5.84420	−	10.1225i	−0.356327	−	0.617177i	−0.987344	+	0.158592i	$0.949305\pi$
$270$	2.23277	+	3.86727i	0.135882	+	0.235354i
$271$	−1.70695	+	2.95653i	−0.103690	+	0.179596i	−0.913202	−	0.407507i	$-0.866398\pi$
$271$	−1.70695	+	2.95653i	−0.103690	+	0.179596i	0.809512	+	0.587103i	$0.199732\pi$
$272$	−4.53933			−0.275237
$273$		0			0
$274$	−6.53794			−0.394971
$275$	5.61046	−	9.71759i	0.338323	−	0.585993i
$276$	9.11672	+	15.7906i	0.548762	+	0.950483i
$277$	−0.957821	−	1.65899i	−0.0575499	−	0.0996793i	0.835815	−	0.549011i	$-0.184995\pi$
$277$	−0.957821	−	1.65899i	−0.0575499	−	0.0996793i	−0.893365	+	0.449332i	$0.851662\pi$
$278$	5.45992	−	9.45686i	0.327464	−	0.567185i
$279$	−6.86483			−0.410986
$280$	11.4143	−	3.50148i	0.682134	−	0.209254i
$281$	−14.8090			−0.883432			−0.441716	−	0.897155i	$-0.645630\pi$
$281$	−14.8090			−0.883432			−0.441716	+	0.897155i	$0.645630\pi$
$282$	7.04035	−	12.1942i	0.419247	−	0.726157i
$283$	−16.7797	−	29.0633i	−0.997449	−	1.72763i	−0.560548	−	0.828122i	$-0.689409\pi$
$283$	−16.7797	−	29.0633i	−0.997449	−	1.72763i	−0.436901	−	0.899510i	$-0.643924\pi$
$284$	4.10152	+	7.10404i	0.243380	+	0.421547i
$285$	10.4928	−	18.1740i	0.621539	−	1.07654i
$286$		0			0
$287$	−0.792596	−	0.737710i	−0.0467855	−	0.0435457i
$288$	−19.5912			−1.15442
$289$	1.69655	−	2.93852i	0.0997972	−	0.172854i
$290$	−5.80418	−	10.0531i	−0.340833	−	0.590340i
$291$	−11.2378	−	19.4644i	−0.658771	−	1.14102i
$292$	7.15132	−	12.3865i	0.418500	−	0.724863i
$293$	5.03064			0.293893			0.146946	−	0.989144i	$-0.453056\pi$
$293$	5.03064			0.293893			0.146946	+	0.989144i	$0.453056\pi$
$294$	−1.37408	−	19.1311i	−0.0801380	−	1.11575i
$295$	11.4017			0.663835
$296$	−10.6243	+	18.4018i	−0.617525	+	1.06959i
$297$	−5.88175	−	10.1875i	−0.341294	−	0.591139i
$298$	2.47198	+	4.28160i	0.143198	+	0.248026i
$299$		0			0
$300$	6.96205			0.401954
$301$	12.4629	+	11.5998i	0.718348	+	0.668603i
$302$	−4.24989			−0.244553
$303$	−11.2868	+	19.5493i	−0.648408	+	1.12308i
$304$	−3.25144	−	5.63166i	−0.186483	−	0.322998i
$305$	−8.41691	−	14.5785i	−0.481951	−	0.834763i
$306$	7.76661	−	13.4522i	0.443988	−	0.769009i
$307$	14.1518			0.807688			0.403844	−	0.914828i	$-0.367674\pi$
$307$	14.1518			0.807688			0.403844	+	0.914828i	$0.367674\pi$
$308$	−9.62415	+	2.95234i	−0.548387	+	0.168225i
$309$	−42.3706			−2.41038
$310$	−1.28654	+	2.22835i	−0.0730706	+	0.126562i
$311$	4.34767	+	7.53038i	0.246534	+	0.427009i	0.962562	−	0.271063i	$-0.0873751\pi$
$311$	4.34767	+	7.53038i	0.246534	+	0.427009i	−0.716028	+	0.698072i	$0.754042\pi$
$312$		0			0
$313$	−10.4388	+	18.0806i	−0.590038	+	1.02198i	0.404188	+	0.914676i	$0.367554\pi$
$313$	−10.4388	+	18.0806i	−0.590038	+	1.02198i	−0.994227	+	0.107300i	$0.965779\pi$
$314$	−6.13102			−0.345994
$315$	−3.61749	+	15.7369i	−0.203823	+	0.886671i
$316$	0.709736			0.0399258
$317$	−8.74509	+	15.1469i	−0.491173	+	0.850737i	−0.999948	−	0.0101626i	$-0.996765\pi$
$317$	−8.74509	+	15.1469i	−0.491173	+	0.850737i	0.508775	+	0.860899i	$0.330098\pi$
$318$	−2.16723	−	3.75376i	−0.121532	−	0.210500i
$319$	15.2899	+	26.4829i	0.856069	+	1.48276i
$320$	−5.50655	+	9.53762i	−0.307825	+	0.533169i
$321$	19.0346			1.06241
$322$	4.43444	−	19.2907i	0.247122	−	1.07503i
$323$	−19.4927			−1.08460
$324$	−2.13090	+	3.69082i	−0.118383	+	0.205046i
$325$		0			0
$326$	−4.56196	−	7.90154i	−0.252663	−	0.437626i
$327$	1.48137	−	2.56581i	0.0819201	−	0.141890i
$328$	1.23853			0.0683866
$329$	12.9982	−	3.98738i	0.716616	−	0.219832i
$330$	−16.5119			−0.908950
$331$	−2.28944	+	3.96542i	−0.125839	+	0.217959i	−0.922061	−	0.387046i	$-0.873496\pi$
$331$	−2.28944	+	3.96542i	−0.125839	+	0.217959i	0.796222	+	0.605005i	$0.206829\pi$
$332$	−1.86485	−	3.23002i	−0.102347	−	0.177270i
$333$	−14.3689	−	24.8876i	−0.787409	−	1.36383i
$334$	−6.13286	+	10.6224i	−0.335575	+	0.581233i
$335$	19.6197			1.07194
$336$	6.34723	+	5.90769i	0.346270	+	0.322291i
$337$	23.5671			1.28378			0.641891	−	0.766796i	$-0.278150\pi$
$337$	23.5671			1.28378			0.641891	+	0.766796i	$0.278150\pi$
$338$		0			0
$339$	17.3688	+	30.0836i	0.943344	+	1.63392i
$340$	2.58930	+	4.48481i	0.140425	+	0.243223i
$341$	3.38912	−	5.87013i	0.183531	−	0.317885i
$342$	22.2523			1.20327
$343$	11.6144	−	14.4259i	0.627117	−	0.778925i
$344$	−19.4748			−1.05001
$345$	−14.4389	+	25.0089i	−0.777363	+	1.34643i
$346$	−4.54292	−	7.86857i	−0.244229	−	0.423017i
$347$	−13.4942	−	23.3727i	−0.724408	−	1.25471i	−0.959217	−	0.282669i	$-0.908780\pi$
$347$	−13.4942	−	23.3727i	−0.724408	−	1.25471i	0.234810	−	0.972041i	$-0.424553\pi$
$348$	−9.48666	+	16.4314i	−0.508538	+	0.880814i
$349$	24.7255			1.32352			0.661762	−	0.749714i	$-0.269809\pi$
$349$	24.7255			1.32352			0.661762	+	0.749714i	$0.269809\pi$
$350$	−5.53234	−	5.14924i	−0.295716	−	0.275238i
$351$		0			0
$352$	9.67202	−	16.7524i	0.515520	−	0.892908i
$353$	−0.722951	−	1.25219i	−0.0384788	−	0.0666473i	0.846145	−	0.532953i	$-0.178918\pi$
$353$	−0.722951	−	1.25219i	−0.0384788	−	0.0666473i	−0.884623	+	0.466306i	$0.845585\pi$
$354$	10.4758	+	18.1446i	0.556781	+	0.964373i
$355$	−6.49590	+	11.2512i	−0.344767	+	0.597154i
$356$	3.47708			0.184285
$357$	24.8492	−	7.62283i	1.31516	−	0.403443i
$358$	18.6275			0.984494
$359$	8.27465	−	14.3321i	0.436719	−	0.756420i	−0.560715	−	0.828009i	$-0.689474\pi$
$359$	8.27465	−	14.3321i	0.436719	−	0.756420i	0.997434	+	0.0715889i	$0.0228070\pi$
$360$	−9.23496	−	15.9954i	−0.486725	−	0.843033i
$361$	−4.46228	−	7.72890i	−0.234857	−	0.406784i
$362$	−10.9753	+	19.0098i	−0.576848	+	0.999131i
$363$	14.2013			0.745373
$364$		0			0
$365$	22.6523			1.18567
$366$	15.4667	−	26.7891i	0.808458	−	1.40029i
$367$	16.3799	+	28.3708i	0.855023	+	1.48094i	0.876624	+	0.481176i	$0.159790\pi$
$367$	16.3799	+	28.3708i	0.855023	+	1.48094i	−0.0216008	+	0.999767i	$0.506876\pi$
$368$	4.47423	+	7.74959i	0.233235	+	0.403975i
$369$	−0.837529	+	1.45064i	−0.0436000	+	0.0755175i
$370$	−10.7715			−0.559984
$371$	0.937635	−	4.07891i	0.0486796	−	0.211766i
$372$	4.20558			0.218049
$373$	−8.01284	+	13.8786i	−0.414889	+	0.718609i	−0.995417	−	0.0956314i	$-0.969513\pi$
$373$	−8.01284	+	13.8786i	−0.414889	+	0.718609i	0.580528	+	0.814241i	$0.302846\pi$
$374$	7.66865	+	13.2825i	0.396536	+	0.686821i
$375$	15.4413	+	26.7451i	0.797386	+	1.38111i
$376$	−7.77588	+	13.4682i	−0.401010	+	0.694570i
$377$		0			0
$378$	−7.57494	+	2.32371i	−0.389613	+	0.119519i
$379$	4.97761			0.255682			0.127841	−	0.991795i	$-0.459195\pi$
$379$	4.97761			0.255682			0.127841	+	0.991795i	$0.459195\pi$
$380$	−3.70934	+	6.42477i	−0.190285	+	0.329584i
$381$	−15.2448	−	26.4048i	−0.781015	−	1.35276i
$382$	−8.34842	−	14.4599i	−0.427143	−	0.739833i
$383$	−11.1258	+	19.2704i	−0.568501	+	0.984672i	0.428214	+	0.903677i	$0.359143\pi$
$383$	−11.1258	+	19.2704i	−0.568501	+	0.984672i	−0.996715	+	0.0809945i	$0.974190\pi$
$384$	5.25832			0.268338
$385$	−11.6707	−	10.8625i	−0.594793	−	0.553605i
$386$	−2.11089			−0.107442
$387$	13.1694	−	22.8101i	0.669438	−	1.15950i
$388$	3.97271	+	6.88093i	0.201684	+	0.349326i
$389$	−0.509272	−	0.882086i	−0.0258211	−	0.0447235i	0.852826	−	0.522195i	$-0.174887\pi$
$389$	−0.509272	−	0.882086i	−0.0258211	−	0.0447235i	−0.878647	+	0.477472i	$0.841553\pi$
$390$		0			0
$391$	26.8235			1.35652
$392$	1.51763	+	21.1298i	0.0766521	+	1.06722i
$393$	4.76312			0.240268
$394$	1.28564	−	2.22680i	0.0647697	−	0.112184i
$395$	0.562033	+	0.973469i	0.0282789	+	0.0489806i
$396$	7.78662	+	13.4868i	0.391292	+	0.677738i
$397$	−10.7037	+	18.5394i	−0.537205	+	0.930467i	0.461848	+	0.886959i	$0.347187\pi$
$397$	−10.7037	+	18.5394i	−0.537205	+	0.930467i	−0.999053	+	0.0435075i	$0.986147\pi$
$398$	16.2006			0.812065
$399$	27.2562	+	25.3687i	1.36452	+	1.27003i
$400$	3.41678			0.170839
$401$	−0.802610	+	1.39016i	−0.0400804	+	0.0694214i	−0.885370	−	0.464888i	$-0.846095\pi$
$401$	−0.802610	+	1.39016i	−0.0400804	+	0.0694214i	0.845289	+	0.534309i	$0.179428\pi$
$402$	18.0264	+	31.2226i	0.899073	+	1.55724i
$403$		0			0
$404$	3.99002	−	6.91093i	0.198511	−	0.343831i
$405$	−6.74975			−0.335398
$406$	19.6914	−	6.04060i	0.977267	−	0.299790i
$407$	28.3752			1.40651
$408$	−14.8654	+	25.7477i	−0.735948	+	1.27470i
$409$	17.8585	+	30.9319i	0.883047	+	1.52948i	0.847936	+	0.530099i	$0.177845\pi$
$409$	17.8585	+	30.9319i	0.883047	+	1.52948i	0.0351113	+	0.999383i	$0.488821\pi$
$410$	0.313923	+	0.543731i	0.0155036	+	0.0268530i
$411$	−8.46211	+	14.6568i	−0.417405	+	0.722966i
$412$	14.9786			0.737942
$413$	−4.53225	+	19.7162i	−0.223018	+	0.970173i
$414$	−30.6209			−1.50494
$415$	2.95352	−	5.11564i	0.144982	−	0.251117i
$416$		0			0
$417$	−14.1336	−	24.4802i	−0.692127	−	1.19880i
$418$	−10.9858	+	19.0280i	−0.537334	+	0.930690i
$419$	12.3317			0.602443			0.301221	−	0.953554i	$-0.402606\pi$
$419$	12.3317			0.602443			0.301221	+	0.953554i	$0.402606\pi$
$420$	2.21618	−	9.64083i	0.108138	−	0.470424i
$421$	12.8739			0.627436			0.313718	−	0.949516i	$-0.398425\pi$
$421$	12.8739			0.627436			0.313718	+	0.949516i	$0.398425\pi$
$422$	3.98779	−	6.90706i	0.194123	−	0.336230i
$423$	−10.5165	−	18.2151i	−0.511330	−	0.885649i
$424$	2.39365	+	4.14592i	0.116246	+	0.201344i
$425$	5.12099	−	8.86982i	0.248405	−	0.430249i
$426$	−23.8734			−1.15667
$427$	28.5554	−	8.75975i	1.38189	−	0.423914i
$428$	−6.72899			−0.325258
$429$		0			0
$430$	−4.93617	−	8.54969i	−0.238043	−	0.412303i
$431$	8.31088	+	14.3949i	0.400321	+	0.693376i	0.993765	−	0.111499i	$-0.0355653\pi$
$431$	8.31088	+	14.3949i	0.400321	+	0.693376i	−0.593444	+	0.804876i	$0.702232\pi$
$432$	1.79100	−	3.10210i	0.0861695	−	0.149250i
$433$	7.34167			0.352818			0.176409	−	0.984317i	$-0.443552\pi$
$433$	7.34167			0.352818			0.176409	+	0.984317i	$0.443552\pi$
$434$	−3.34193	−	3.11051i	−0.160418	−	0.149309i
$435$	−30.0496			−1.44077
$436$	−0.523685	+	0.907049i	−0.0250800	+	0.0434398i
$437$	19.2132	+	33.2782i	0.919090	+	1.59191i
$438$	20.8126	+	36.0485i	0.994465	+	1.72246i
$439$	0.855908	−	1.48248i	0.0408503	−	0.0707547i	−0.844877	−	0.534960i	$-0.820327\pi$
$439$	0.855908	−	1.48248i	0.0408503	−	0.0707547i	0.885728	+	0.464205i	$0.153660\pi$
$440$	18.2369			0.869412
$441$	−25.7747	−	12.5110i	−1.22737	−	0.595761i
$442$		0			0
$443$	−3.60251	+	6.23972i	−0.171160	+	0.296458i	−0.938826	−	0.344392i	$-0.888085\pi$
$443$	−3.60251	+	6.23972i	−0.171160	+	0.296458i	0.767666	+	0.640851i	$0.221418\pi$
$444$	8.80276	+	15.2468i	0.417760	+	0.723582i
$445$	2.75346	+	4.76914i	0.130527	+	0.226079i
$446$	−2.44541	+	4.23557i	−0.115793	+	0.200560i
$447$	12.7980			0.605326
$448$	−14.3039	−	13.3134i	−0.675794	−	0.628997i
$449$	−7.17254			−0.338493			−0.169247	−	0.985574i	$-0.554133\pi$
$449$	−7.17254			−0.338493			−0.169247	+	0.985574i	$0.554133\pi$
$450$	−5.84597	+	10.1255i	−0.275582	+	0.477322i
$451$	−0.826965	−	1.43235i	−0.0389403	−	0.0674465i
$452$	−6.14010	−	10.6350i	−0.288806	−	0.500227i
$453$	−5.50066	+	9.52742i	−0.258444	+	0.447637i
$454$	−12.9530			−0.607915
$455$		0			0
$456$	−42.5913			−1.99452
$457$	18.0487	−	31.2612i	0.844282	−	1.46234i	−0.0419612	−	0.999119i	$-0.513361\pi$
$457$	18.0487	−	31.2612i	0.844282	−	1.46234i	0.886243	−	0.463220i	$-0.153306\pi$
$458$	−2.70454	−	4.68440i	−0.126375	−	0.218888i
$459$	−5.36862	−	9.29873i	−0.250586	−	0.434027i
$460$	5.10434	−	8.84097i	0.237991	−	0.412212i
$461$	21.0255			0.979257			0.489628	−	0.871931i	$-0.337132\pi$
$461$	21.0255			0.979257			0.489628	+	0.871931i	$0.337132\pi$
$462$	6.56357	−	28.5529i	0.305365	−	1.32840i
$463$	−25.7348			−1.19600			−0.597999	−	0.801497i	$-0.704037\pi$
$463$	−25.7348			−1.19600			−0.597999	+	0.801497i	$0.704037\pi$
$464$	−4.65579	+	8.06406i	−0.216139	+	0.374365i
$465$	3.33036	+	5.76835i	0.154442	+	0.267501i
$466$	−4.35009	−	7.53457i	−0.201514	−	0.349032i
$467$	−13.3702	+	23.1578i	−0.618697	+	1.07162i	0.371026	+	0.928622i	$0.379006\pi$
$467$	−13.3702	+	23.1578i	−0.618697	+	1.07162i	−0.989724	+	0.142993i	$0.954327\pi$
$468$		0			0
$469$	−7.79895	+	33.9270i	−0.360122	+	1.56661i
$470$	−7.88361			−0.363644
$471$	−7.93543	+	13.7446i	−0.365645	+	0.633316i
$472$	−11.5702	−	20.0402i	−0.532562	−	0.922425i
$473$	13.0033	+	22.5224i	0.597892	+	1.03558i
$474$	−1.03278	+	1.78882i	−0.0474370	+	0.0821634i
$475$	14.6723			0.673211
$476$	−8.78453	+	2.69477i	−0.402638	+	0.123515i
$477$	−6.47460			−0.296451
$478$	−3.37292	+	5.84207i	−0.154274	+	0.267210i
$479$	−15.5003	−	26.8474i	−0.708228	−	1.22669i	−0.965514	−	0.260352i	$-0.916162\pi$
$479$	−15.5003	−	26.8474i	−0.708228	−	1.22669i	0.257286	−	0.966335i	$-0.417172\pi$
$480$	9.50433	+	16.4620i	0.433811	+	0.751383i
$481$		0			0
$482$	−11.9273			−0.543275
$483$	−37.5066	−	34.9093i	−1.70661	−	1.58843i
$484$	−5.02034			−0.228197
$485$	−6.29190	+	10.8979i	−0.285700	+	0.494847i
$486$	−10.6937	−	18.5220i	−0.485076	−	0.840176i
$487$	−4.30696	−	7.45988i	−0.195167	−	0.338039i	0.751788	−	0.659405i	$-0.229192\pi$
$487$	−4.30696	−	7.45988i	−0.195167	−	0.338039i	−0.946955	+	0.321365i	$0.895858\pi$
$488$	−17.0826	+	29.5879i	−0.773291	+	1.33938i
$489$	−23.6183			−1.06806
$490$	−8.89156	+	6.02189i	−0.401680	+	0.272041i
$491$	−0.762083			−0.0343923			−0.0171962	−	0.999852i	$-0.505474\pi$
$491$	−0.762083			−0.0343923			−0.0171962	+	0.999852i	$0.505474\pi$
$492$	0.513093	−	0.888703i	0.0231320	−	0.0400658i
$493$	13.9560	+	24.1725i	0.628546	+	1.08867i
$494$		0			0
$495$	−12.3323	+	21.3602i	−0.554296	+	0.960068i
$496$	2.06398			0.0926754
$497$	−16.8738	−	15.7053i	−0.756895	−	0.704481i
$498$	10.8546			0.486407
$499$	15.7076	−	27.2064i	0.703169	−	1.21792i	−0.264179	−	0.964474i	$-0.585101\pi$
$499$	15.7076	−	27.2064i	0.703169	−	1.21792i	0.967348	−	0.253451i	$-0.0815657\pi$
$500$	−5.45871	−	9.45477i	−0.244121	−	0.422830i
$501$	15.8756	+	27.4973i	0.709270	+	1.22849i
$502$	−9.93927	+	17.2153i	−0.443611	+	0.768357i
$503$	−32.0350			−1.42837			−0.714185	−	0.699957i	$-0.753202\pi$
$503$	−32.0350			−1.42837			−0.714185	+	0.699957i	$0.753202\pi$
$504$	31.3307	−	9.61112i	1.39558	−	0.428113i
$505$	12.6386			0.562412
$506$	15.1173	−	26.1840i	0.672047	−	1.16402i
$507$		0			0
$508$	5.38924	+	9.33445i	0.239109	+	0.414149i
$509$	−5.28329	+	9.15092i	−0.234178	+	0.405607i	−0.959033	−	0.283293i	$-0.908573\pi$
$509$	−5.28329	+	9.15092i	−0.234178	+	0.405607i	0.724856	+	0.688901i	$0.241906\pi$
$510$	−15.0714			−0.667372
$511$	−9.00440	+	39.1710i	−0.398331	+	1.73282i
$512$	13.3386			0.589487
$513$	7.69089	−	13.3210i	0.339561	−	0.588137i
$514$	−8.90614	−	15.4259i	−0.392833	−	0.680407i
$515$	11.8614	+	20.5445i	0.522675	+	0.905300i
$516$	−8.06793	+	13.9741i	−0.355171	+	0.615174i
$517$	20.7677			0.913362
$518$	4.28173	−	18.6264i	0.188128	−	0.818398i
$519$	−23.5197			−1.03240
$520$		0			0
$521$	−10.3947	−	18.0041i	−0.455398	−	0.788773i	0.543313	−	0.839530i	$-0.317170\pi$
$521$	−10.3947	−	18.0041i	−0.455398	−	0.788773i	−0.998711	+	0.0507575i	$0.983836\pi$
$522$	−15.9317	−	27.5946i	−0.697313	−	1.20778i
$523$	3.03097	−	5.24979i	0.132535	−	0.229557i	−0.792118	−	0.610368i	$-0.791022\pi$
$523$	3.03097	−	5.24979i	0.132535	−	0.229557i	0.924653	+	0.380811i	$0.124355\pi$
$524$	−1.68383			−0.0735583
$525$	−18.7041	+	5.73774i	−0.816316	+	0.250416i
$526$	−26.1259			−1.13915
$527$	3.09345	−	5.35801i	0.134753	−	0.233399i
$528$	6.62246	+	11.4704i	0.288205	+	0.499187i
$529$	−14.9388	−	25.8747i	−0.649513	−	1.12499i
$530$	−1.21341	+	2.10168i	−0.0527070	+	0.0912912i
$531$	31.2963			1.35814
$532$	−9.63542	−	8.96819i	−0.417749	−	0.388820i
$533$		0			0
$534$	−5.05970	+	8.76365i	−0.218954	+	0.379240i
$535$	−5.32862	−	9.22944i	−0.230376	−	0.399023i
$536$	−19.9096	−	34.4845i	−0.859965	−	1.48950i
$537$	24.1097	−	41.7593i	1.04041	−	1.80205i
$538$	−12.0254			−0.518454
$539$	23.4229	−	15.8634i	1.00890	−	0.683285i
$540$	−4.08646			−0.175853
$541$	16.5689	−	28.6982i	0.712353	−	1.23383i	−0.251618	−	0.967827i	$-0.580963\pi$
$541$	16.5689	−	28.6982i	0.712353	−	1.23383i	0.963972	−	0.266005i	$-0.0857039\pi$
$542$	1.75617	+	3.04178i	0.0754342	+	0.130656i
$543$	28.4108	+	49.2089i	1.21922	+	2.11176i
$544$	8.82822	−	15.2909i	0.378507	−	0.655593i
$545$	−1.65880			−0.0710554
$546$		0			0
$547$	23.8568			1.02004			0.510021	−	0.860162i	$-0.329637\pi$
$547$	23.8568			1.02004			0.510021	+	0.860162i	$0.329637\pi$
$548$	2.99147	−	5.18137i	0.127789	−	0.221337i
$549$	−23.1033	−	40.0162i	−0.986027	−	1.70785i
$550$	−5.77224	−	9.99781i	−0.246129	−	0.426308i
$551$	−19.9928	+	34.6286i	−0.851723	+	1.47523i
$552$	58.6089			2.49456
$553$	−1.90676	+	0.584925i	−0.0810839	+	0.0248736i
$554$	−1.97088			−0.0837347
$555$	−13.9416	+	24.1476i	−0.591790	+	1.02501i
$556$	4.99643	+	8.65407i	0.211896	+	0.367014i
$557$	−16.8012	−	29.1005i	−0.711888	−	1.23303i	−0.964147	−	0.265367i	$-0.914507\pi$
$557$	−16.8012	−	29.1005i	−0.711888	−	1.23303i	0.252259	−	0.967660i	$-0.418827\pi$
$558$	−3.53139	+	6.11654i	−0.149496	+	0.258934i
$559$		0			0
$560$	1.08764	−	4.73145i	0.0459610	−	0.199940i
$561$	39.7024			1.67624
$562$	−7.61802	+	13.1948i	−0.321347	+	0.556589i
$563$	−15.8125	−	27.3881i	−0.666418	−	1.15427i	−0.978899	−	0.204345i	$-0.934493\pi$
$563$	−15.8125	−	27.3881i	−0.666418	−	1.15427i	0.312481	−	0.949924i	$-0.398840\pi$
$564$	6.44269	+	11.1591i	0.271286	+	0.469882i
$565$	9.72457	−	16.8435i	0.409116	−	0.708610i
$566$	−34.5271			−1.45128
$567$	2.68306	−	11.6719i	0.112678	−	0.490173i
$568$	26.3675			1.10636
$569$	−8.40268	+	14.5539i	−0.352259	+	0.610130i	−0.986645	−	0.162886i	$-0.947920\pi$
$569$	−8.40268	+	14.5539i	−0.352259	+	0.610130i	0.634386	+	0.773016i	$0.281253\pi$
$570$	−10.7954	−	18.6981i	−0.452167	−	0.783177i
$571$	−7.03033	−	12.1769i	−0.294210	−	0.509587i	0.680591	−	0.732664i	$-0.261723\pi$
$571$	−7.03033	−	12.1769i	−0.294210	−	0.509587i	−0.974801	+	0.223077i	$0.928390\pi$
$572$		0			0
$573$	−43.2217			−1.80561
$574$	−1.06502	+	0.326710i	−0.0444532	+	0.0136366i
$575$	−20.1902			−0.841989
$576$	−15.1148	+	26.1795i	−0.629782	+	1.09081i
$577$	7.10639	+	12.3086i	0.295843	+	0.512415i	0.975181	−	0.221411i	$-0.0710662\pi$
$577$	7.10639	+	12.3086i	0.295843	+	0.512415i	−0.679338	+	0.733826i	$0.737733\pi$
$578$	−1.74547	−	3.02325i	−0.0726021	−	0.125751i
$579$	−2.73215	+	4.73222i	−0.113544	+	0.196664i
$580$	10.6229			0.441093
$581$	7.67209	+	7.14081i	0.318292	+	0.296251i
$582$	−23.1237			−0.958507
$583$	3.19646	−	5.53644i	0.132384	−	0.229296i
$584$	−22.9870	−	39.8146i	−0.951207	−	1.64754i
$585$		0			0
$586$	2.58785	−	4.48228i	0.106903	−	0.185161i
$587$	−17.9188			−0.739590			−0.369795	−	0.929113i	$-0.620572\pi$
$587$	−17.9188			−0.739590			−0.369795	+	0.929113i	$0.620572\pi$
$588$	15.7903	+	7.66456i	0.651180	+	0.316081i
$589$	8.86312			0.365198
$590$	5.86526	−	10.1589i	0.241469	−	0.418236i
$591$	−3.32803	−	5.76432i	−0.136897	−	0.237112i
$592$	4.32015	+	7.48271i	0.177557	+	0.307538i
$593$	2.65203	−	4.59345i	0.108906	−	0.188630i	−0.806421	−	0.591341i	$-0.798599\pi$
$593$	2.65203	−	4.59345i	0.108906	−	0.188630i	0.915327	+	0.402711i	$0.131932\pi$
$594$	−12.1027			−0.496580
$595$	−10.6525	−	9.91485i	−0.436711	−	0.406469i
$596$	−4.52427			−0.185321
$597$	20.9686	−	36.3187i	0.858188	−	1.48643i
$598$		0			0
$599$	9.96219	+	17.2550i	0.407044	+	0.705021i	0.994557	−	0.104194i	$-0.0332262\pi$
$599$	9.96219	+	17.2550i	0.407044	+	0.705021i	−0.587513	+	0.809215i	$0.699893\pi$
$600$	11.1893	−	19.3804i	0.456801	−	0.791202i
$601$	3.44445			0.140502			0.0702509	−	0.997529i	$-0.477620\pi$
$601$	3.44445			0.140502			0.0702509	+	0.997529i	$0.477620\pi$
$602$	16.7465	−	5.13723i	0.682538	−	0.209378i
$603$	53.8536			2.19309
$604$	1.94456	−	3.36807i	0.0791229	−	0.137045i
$605$	−3.97555	−	6.88586i	−0.161629	−	0.279950i
$606$	11.6122	+	20.1130i	0.471715	+	0.817034i
$607$	−11.6226	+	20.1309i	−0.471745	+	0.817087i	−0.999477	−	0.0323240i	$-0.989709\pi$
$607$	−11.6226	+	20.1309i	−0.471745	+	0.817087i	0.527732	+	0.849411i	$0.323042\pi$
$608$	25.2940			1.02581
$609$	11.9449	−	51.9627i	0.484031	−	2.10563i
$610$	−17.3192			−0.701235
$611$		0			0
$612$	7.10731	+	12.3102i	0.287296	+	0.497611i
$613$	−4.23118	−	7.32862i	−0.170896	−	0.296000i	0.767838	−	0.640645i	$-0.221333\pi$
$613$	−4.23118	−	7.32862i	−0.170896	−	0.296000i	−0.938733	+	0.344645i	$0.887999\pi$
$614$	7.27996	−	12.6093i	0.293795	−	0.508868i
$615$	1.62525			0.0655366
$616$	−7.24929	+	31.5359i	−0.292082	+	1.27062i
$617$	−14.9847			−0.603262			−0.301631	−	0.953425i	$-0.597531\pi$
$617$	−14.9847			−0.603262			−0.301631	+	0.953425i	$0.597531\pi$
$618$	−21.7962	+	37.7521i	−0.876772	+	1.51861i
$619$	15.8131	+	27.3890i	0.635580	+	1.10086i	0.986392	+	0.164411i	$0.0525724\pi$
$619$	15.8131	+	27.3890i	0.635580	+	1.10086i	−0.350812	+	0.936446i	$0.614094\pi$
$620$	−1.17733	−	2.03919i	−0.0472825	−	0.0818958i
$621$	−10.5833	+	18.3307i	−0.424691	+	0.735587i
$622$	8.94607			0.358705
$623$	−9.34146	+	2.86562i	−0.374258	+	0.114809i
$624$		0			0
$625$	1.70404	−	2.95148i	0.0681616	−	0.118059i
$626$	10.7398	+	18.6020i	0.429251	+	0.743484i
$627$	28.4381	+	49.2562i	1.13571	+	1.96710i
$628$	2.80528	−	4.85889i	0.111943	−	0.193891i
$629$	25.8998			1.03269
$630$	12.1606	+	11.3185i	0.484490	+	0.450940i
$631$	−26.9817			−1.07412			−0.537062	−	0.843543i	$-0.680466\pi$
$631$	−26.9817			−1.07412			−0.537062	+	0.843543i	$0.680466\pi$
$632$	1.14067	−	1.97571i	0.0453736	−	0.0785894i
$633$	−10.3229	−	17.8797i	−0.410297	−	0.710655i
$634$	8.99726	+	15.5837i	0.357327	+	0.618908i
$635$	−8.53538	+	14.7837i	−0.338716	+	0.586674i
$636$	3.96651			0.157283
$637$		0			0
$638$	31.4616			1.24557
$639$	−17.8304	+	30.8832i	−0.705361	+	1.22172i
$640$	−1.47204	−	2.54964i	−0.0581873	−	0.100783i
$641$	17.5165	+	30.3395i	0.691861	+	1.19834i	0.971227	+	0.238154i	$0.0765422\pi$
$641$	17.5165	+	30.3395i	0.691861	+	1.19834i	−0.279367	+	0.960184i	$0.590124\pi$
$642$	9.79174	−	16.9598i	0.386449	−	0.669349i
$643$	−38.2944			−1.51019			−0.755093	−	0.655618i	$-0.772408\pi$
$643$	−38.2944			−1.51019			−0.755093	+	0.655618i	$0.772408\pi$
$644$	13.2591	+	12.3409i	0.522481	+	0.486300i
$645$	−25.5557			−1.00625
$646$	−10.0274	+	17.3680i	−0.394523	+	0.683334i
$647$	7.43216	+	12.8729i	0.292188	+	0.506085i	0.974327	−	0.225138i	$-0.0722832\pi$
$647$	7.43216	+	12.8729i	0.292188	+	0.506085i	−0.682138	+	0.731223i	$0.738950\pi$
$648$	6.84949	+	11.8637i	0.269073	+	0.466048i
$649$	−15.4508	+	26.7615i	−0.606496	+	1.05048i
$650$		0			0
$651$	−11.2986	+	3.46601i	−0.442829	+	0.135844i
$652$	8.34939			0.326987
$653$	13.1693	−	22.8099i	0.515354	−	0.892620i	−0.484487	−	0.874799i	$-0.660994\pi$
$653$	13.1693	−	22.8099i	0.515354	−	0.892620i	0.999841	−	0.0178215i	$-0.00567306\pi$
$654$	−1.52409	−	2.63980i	−0.0595966	−	0.103224i
$655$	−1.33341	−	2.30953i	−0.0521005	−	0.0902407i
$656$	0.251812	−	0.436151i	0.00983159	−	0.0170288i
$657$	62.1775			2.42578
$658$	3.13378	−	13.6326i	0.122167	−	0.531453i
$659$	3.18074			0.123904			0.0619521	−	0.998079i	$-0.480267\pi$
$659$	3.18074			0.123904			0.0619521	+	0.998079i	$0.480267\pi$
$660$	7.55510	−	13.0858i	0.294082	−	0.509365i
$661$	−0.545429	−	0.944712i	−0.0212147	−	0.0367450i	0.855223	−	0.518260i	$-0.173420\pi$
$661$	−0.545429	−	0.944712i	−0.0212147	−	0.0367450i	−0.876438	+	0.481515i	$0.840087\pi$
$662$	2.35545	+	4.07977i	0.0915473	+	0.158565i
$663$		0			0
$664$	−11.9886			−0.465249
$665$	4.67051	−	20.3177i	0.181115	−	0.787887i
$666$	−29.5664			−1.14567
$667$	27.5116	−	47.6516i	1.06526	−	1.84508i
$668$	−5.61224	−	9.72068i	−0.217144	−	0.376104i
$669$	6.33022	+	10.9643i	0.244740	+	0.423903i
$670$	10.0927	−	17.4811i	0.389916	−	0.675355i
$671$	45.6239			1.76129
$672$	−32.2446	+	9.89146i	−1.24386	+	0.381571i
$673$	−3.63442			−0.140096			−0.0700482	−	0.997544i	$-0.522315\pi$
$673$	−3.63442			−0.140096			−0.0700482	+	0.997544i	$0.522315\pi$
$674$	12.1233	−	20.9982i	0.466973	−	0.808822i
$675$	4.04099	+	6.99920i	0.155538	+	0.269399i
$676$		0			0
$677$	2.09468	−	3.62810i	0.0805052	−	0.139439i	−0.822962	−	0.568097i	$-0.807680\pi$
$677$	2.09468	−	3.62810i	0.0805052	−	0.139439i	0.903467	+	0.428658i	$0.141013\pi$
$678$	35.7393			1.37256
$679$	−16.3439	−	15.2121i	−0.627221	−	0.583787i
$680$	16.6459			0.638342
$681$	−16.7652	+	29.0381i	−0.642443	+	1.11274i
$682$	−3.48685	−	6.03939i	−0.133518	−	0.231260i
$683$	−18.7579	−	32.4896i	−0.717750	−	1.24318i	−0.961889	−	0.273439i	$-0.911839\pi$
$683$	−18.7579	−	32.4896i	−0.717750	−	1.24318i	0.244140	−	0.969740i	$-0.421494\pi$
$684$	−10.1817	+	17.6352i	−0.389306	+	0.674297i
$685$	9.47565			0.362046
$686$	−6.87880	−	17.7693i	−0.262634	−	0.678435i
$687$	−14.0020			−0.534211
$688$	−3.95951	+	6.85808i	−0.150955	+	0.261462i
$689$		0			0
$690$	14.8552	+	25.7300i	0.565529	+	0.979525i
$691$	−7.56277	+	13.0991i	−0.287701	+	0.498313i	−0.973261	−	0.229704i	$-0.926224\pi$
$691$	−7.56277	+	13.0991i	−0.287701	+	0.498313i	0.685559	+	0.728017i	$0.259558\pi$
$692$	8.31454			0.316071
$693$	−32.0345	−	29.8162i	−1.21689	−	1.13262i
$694$	−27.7667			−1.05401
$695$	−7.91324	+	13.7061i	−0.300166	+	0.519903i
$696$	30.4936	+	52.8165i	1.15586	+	2.00200i
$697$	−0.754819	−	1.30739i	−0.0285908	−	0.0495208i
$698$	12.7192	−	22.0303i	0.481430	−	0.833861i
$699$	−22.5214			−0.851837
$700$	6.61216	−	2.02837i	0.249916	−	0.0766652i
$701$	−38.7255			−1.46264			−0.731320	−	0.682034i	$-0.761096\pi$
$701$	−38.7255			−1.46264			−0.731320	+	0.682034i	$0.761096\pi$
$702$		0			0
$703$	18.5515	+	32.1322i	0.699684	+	1.21189i
$704$	−14.9241	−	25.8493i	−0.562474	−	0.974233i
$705$	−10.2038	+	17.6735i	−0.384298	+	0.665623i
$706$	−1.48760			−0.0559864
$707$	−5.02393	+	21.8551i	−0.188944	+	0.821947i
$708$	−19.1730			−0.720565
$709$	−2.21513	+	3.83671i	−0.0831908	+	0.144091i	−0.904619	−	0.426222i	$-0.859844\pi$
$709$	−2.21513	+	3.83671i	−0.0831908	+	0.144091i	0.821428	+	0.570312i	$0.193178\pi$
$710$	6.68322	+	11.5757i	0.250817	+	0.434427i
$711$	1.54271	+	2.67205i	0.0578561	+	0.100210i
$712$	5.58830	−	9.67921i	0.209430	−	0.362744i
$713$	−12.1963			−0.456756
$714$	5.99096	−	26.0619i	0.224206	−	0.975342i
$715$		0			0
$716$	−8.52311	+	14.7625i	−0.318523	+	0.551699i
$717$	8.73119	+	15.1229i	0.326072	+	0.564774i
$718$	−8.51325	−	14.7454i	−0.317712	−	0.550293i
$719$	17.2330	−	29.8484i	0.642681	−	1.11316i	−0.342151	−	0.939645i	$-0.611155\pi$
$719$	17.2330	−	29.8484i	0.642681	−	1.11316i	0.984832	−	0.173511i	$-0.0555113\pi$
$720$	−7.51040			−0.279896
$721$	−40.2412	+	12.3445i	−1.49866	+	0.459734i
$722$	−9.18191			−0.341715
$723$	−15.4376	+	26.7388i	−0.574132	+	0.994425i
$724$	−10.0436	−	17.3960i	−0.373267	−	0.646518i
$725$	−10.5047	−	18.1947i	−0.390136	−	0.675736i
$726$	7.30538	−	12.6533i	0.271128	−	0.469608i
$727$	0.889602			0.0329935			0.0164968	−	0.999864i	$-0.494749\pi$
$727$	0.889602			0.0329935			0.0164968	+	0.999864i	$0.494749\pi$
$728$		0			0
$729$	−41.7839			−1.54755
$730$	11.6527	−	20.1831i	0.431287	−	0.747010i
$731$	11.8689	+	20.5575i	0.438986	+	0.760346i
$732$	14.1537	+	24.5150i	0.523137	+	0.906100i
$733$	−2.79094	+	4.83404i	−0.103086	+	0.178550i	−0.912954	−	0.408061i	$-0.866205\pi$
$733$	−2.79094	+	4.83404i	−0.103086	+	0.178550i	0.809869	+	0.586611i	$0.199538\pi$
$734$	33.7044			1.24405
$735$	1.99150	+	27.7273i	0.0734576	+	1.02274i
$736$	−34.8064			−1.28298
$737$	−26.5872	+	46.0503i	−0.979351	+	1.69629i
$738$	0.861680	+	1.49247i	0.0317189	+	0.0549387i
$739$	12.6439	+	21.8998i	0.465112	+	0.805598i	0.999207	−	0.0398267i	$-0.0126806\pi$
$739$	12.6439	+	21.8998i	0.465112	+	0.805598i	−0.534094	+	0.845425i	$0.679347\pi$
$740$	4.92856	−	8.53651i	0.181177	−	0.313808i
$741$		0			0
$742$	−3.15196	−	2.93369i	−0.115712	−	0.107699i
$743$	12.7921			0.469298			0.234649	−	0.972080i	$-0.424606\pi$
$743$	12.7921			0.469298			0.234649	+	0.972080i	$0.424606\pi$
$744$	6.75913	−	11.7072i	0.247802	−	0.429205i
$745$	−3.58273	−	6.20547i	−0.131261	−	0.227351i
$746$	8.24389	+	14.2788i	0.301830	+	0.522786i
$747$	8.10703	−	14.0418i	0.296621	−	0.513762i
$748$	−14.0353			−0.513182
$749$	18.0780	−	5.54566i	0.660556	−	0.202634i
$750$	31.7731			1.16019
$751$	−18.0839	+	31.3222i	−0.659890	+	1.14296i	0.320754	+	0.947163i	$0.396064\pi$
$751$	−18.0839	+	31.3222i	−0.659890	+	1.14296i	−0.980644	+	0.195800i	$0.937270\pi$
$752$	3.16189	+	5.47656i	0.115302	+	0.199710i
$753$	25.7290	+	44.5638i	0.937615	+	1.62400i
$754$		0			0
$755$	6.15950			0.224167
$756$	1.62439	−	7.06643i	0.0590784	−	0.257004i
$757$	27.7793			1.00966			0.504828	−	0.863220i	$-0.331556\pi$
$757$	27.7793			1.00966			0.504828	+	0.863220i	$0.331556\pi$
$758$	2.56057	−	4.43503i	0.0930040	−	0.161088i
$759$	−39.1330	−	67.7803i	−1.42044	−	2.46027i
$760$	11.9232	+	20.6515i	0.432499	+	0.749110i
$761$	7.85382	−	13.6032i	0.284701	−	0.493116i	−0.687836	−	0.725866i	$-0.741439\pi$
$761$	7.85382	−	13.6032i	0.284701	−	0.493116i	0.972537	+	0.232750i	$0.0747724\pi$
$762$	−31.3688			−1.13637
$763$	0.659384	−	2.86846i	0.0238713	−	0.103845i
$764$	15.2795			0.552791
$765$	−11.2564	+	19.4967i	−0.406977	+	0.704904i
$766$	11.4466	+	19.8261i	0.413582	+	0.716345i
$767$		0			0
$768$	22.3752	−	38.7549i	0.807394	−	1.39845i
$769$	−23.0847			−0.832455			−0.416228	−	0.909260i	$-0.636648\pi$
$769$	−23.0847			−0.832455			−0.416228	+	0.909260i	$0.636648\pi$
$770$	−15.6821	+	4.81068i	−0.565143	+	0.173365i
$771$	−46.1091			−1.66058
$772$	0.965850	−	1.67290i	0.0347617	−	0.0602090i
$773$	12.8693	+	22.2903i	0.462876	+	0.801725i	0.999103	−	0.0423492i	$-0.0134842\pi$
$773$	12.8693	+	22.2903i	0.462876	+	0.801725i	−0.536227	+	0.844074i	$0.680151\pi$
$774$	−13.5491	−	23.4678i	−0.487014	−	0.843533i
$775$	−2.32846	+	4.03300i	−0.0836406	+	0.144870i
$776$	25.5395			0.916813
$777$	−36.2150	−	33.7071i	−1.29920	−	1.20924i
$778$	−1.04791			−0.0375696
$779$	1.08133	−	1.87291i	0.0387425	−	0.0671040i
$780$		0			0
$781$	−17.6055	−	30.4937i	−0.629975	−	1.09115i
$782$	13.7985	−	23.8997i	0.493433	−	0.854650i
$783$	−22.0254			−0.787124
$784$	7.74942	+	3.76155i	0.276765	+	0.134341i
$785$	8.88589			0.317151
$786$	2.45023	−	4.24393i	0.0873969	−	0.151376i
$787$	−2.23959	−	3.87909i	−0.0798328	−	0.138274i	0.823345	−	0.567541i	$-0.192105\pi$
$787$	−2.23959	−	3.87909i	−0.0798328	−	0.138274i	−0.903178	+	0.429267i	$0.858772\pi$
$788$	1.17650	+	2.03776i	0.0419112	+	0.0725924i
$789$	−33.8150	+	58.5693i	−1.20385	+	2.08512i
$790$	1.15648			0.0411457
$791$	25.2607	+	23.5114i	0.898166	+	0.835969i
$792$	50.0581			1.77874
$793$		0			0
$794$	11.0124	+	19.0740i	0.390815	+	0.676911i
$795$	3.14104	+	5.44045i	0.111401	+	0.192953i
$796$	−7.41269	+	12.8391i	−0.262736	+	0.455072i
$797$	−20.6676			−0.732083			−0.366042	−	0.930598i	$-0.619287\pi$
$797$	−20.6676			−0.732083			−0.366042	+	0.930598i	$0.619287\pi$
$798$	36.6245	−	11.2351i	1.29650	−	0.397717i
$799$	18.9559			0.670611
$800$	−6.64505	+	11.5096i	−0.234938	+	0.406925i
$801$	7.55790	+	13.0907i	0.267045	+	0.462536i
$802$	0.825754	+	1.43025i	0.0291584	+	0.0505038i
$803$	−30.6966	+	53.1681i	−1.08326	+	1.87626i
$804$	−32.9922			−1.16355
$805$	−6.42699	+	27.9587i	−0.226521	+	0.985416i
$806$		0			0
$807$	−15.5646	+	26.9587i	−0.547901	+	0.948992i
$808$	−12.8254	−	22.2142i	−0.451196	−	0.781494i
$809$	23.7441	+	41.1259i	0.834797	+	1.44591i	0.894196	+	0.447676i	$0.147748\pi$
$809$	23.7441	+	41.1259i	0.834797	+	1.44591i	−0.0593986	+	0.998234i	$0.518918\pi$
$810$	−3.47219	+	6.01401i	−0.122000	+	0.211311i
$811$	−26.3338			−0.924704			−0.462352	−	0.886697i	$-0.652994\pi$
$811$	−26.3338			−0.924704			−0.462352	+	0.886697i	$0.652994\pi$
$812$	−4.22267	+	18.3695i	−0.148187	+	0.644643i
$813$	9.09212			0.318875
$814$	14.5967	−	25.2823i	0.511615	−	0.886143i
$815$	6.61180	+	11.4520i	0.231601	+	0.401145i
$816$	6.04471	+	10.4697i	0.211607	+	0.366514i
$817$	−17.0029	+	29.4499i	−0.594856	+	1.03032i
$818$	36.7470			1.28483
$819$		0			0
$820$	−0.574549			−0.0200641
$821$	−5.25414	+	9.10043i	−0.183371	+	0.317607i	−0.943026	−	0.332718i	$-0.892034\pi$
$821$	−5.25414	+	9.10043i	−0.183371	+	0.317607i	0.759656	+	0.650326i	$0.225368\pi$
$822$	8.70611	+	15.0794i	0.303661	+	0.525956i
$823$	6.16752	+	10.6825i	0.214986	+	0.372367i	0.953268	−	0.302125i	$-0.0976960\pi$
$823$	6.16752	+	10.6825i	0.214986	+	0.372367i	−0.738282	+	0.674492i	$0.764363\pi$
$824$	24.0733	−	41.6962i	0.838634	−	1.45256i
$825$	−29.8842			−1.04043
$826$	15.2357	+	14.1806i	0.530116	+	0.493407i
$827$	−29.2074			−1.01564			−0.507820	−	0.861463i	$-0.669548\pi$
$827$	−29.2074			−1.01564			−0.507820	+	0.861463i	$0.669548\pi$
$828$	14.0107	−	24.2673i	0.486907	−	0.843348i
$829$	−4.23610	−	7.33714i	−0.147126	−	0.254830i	0.783038	−	0.621974i	$-0.213669\pi$
$829$	−4.23610	−	7.33714i	−0.147126	−	0.254830i	−0.930164	+	0.367144i	$0.880336\pi$
$830$	−3.03868	−	5.26315i	−0.105474	−	0.182687i
$831$	−2.55093	+	4.41833i	−0.0884906	+	0.153270i
$832$		0			0
$833$	21.3795	−	14.4795i	0.740756	−	0.501684i
$834$	−29.0824			−1.00704
$835$	8.88855	−	15.3954i	0.307601	−	0.532781i
$836$	−10.0532	−	17.4127i	−0.347698	−	0.602231i
$837$	2.44105	+	4.22802i	0.0843750	+	0.146142i
$838$	6.34364	−	10.9875i	0.219138	−	0.379557i
$839$	−32.3795			−1.11786			−0.558932	−	0.829213i	$-0.688789\pi$
$839$	−32.3795			−1.11786			−0.558932	+	0.829213i	$0.688789\pi$
$840$	−23.2756	−	21.6638i	−0.803084	−	0.747472i
$841$	28.2561			0.974347
$842$	6.62257	−	11.4706i	0.228229	−	0.395304i
$843$	19.7201	+	34.1563i	0.679197	+	1.17640i
$844$	3.64927	+	6.32072i	0.125613	+	0.217568i
$845$		0			0
$846$	−21.6395			−0.743981
$847$	13.4876	−	4.13749i	0.463438	−	0.142166i
$848$	1.94665			0.0668483
$849$	−44.6886	+	77.4030i	−1.53371	+	2.65646i
$850$	−5.26866	−	9.12558i	−0.180714	−	0.313005i
$851$	−25.5283	−	44.2163i	−0.875099	−	1.51572i
$852$	10.9234	−	18.9199i	0.374230	−	0.648185i
$853$	−39.8315			−1.36381			−0.681903	−	0.731443i	$-0.738847\pi$
$853$	−39.8315			−1.36381			−0.681903	+	0.731443i	$0.738847\pi$
$854$	6.88449	−	29.9490i	0.235582	−	1.02483i
$855$	−32.2510			−1.10296
$856$	−10.8147	+	18.7316i	−0.369639	+	0.640234i
$857$	−1.30280	−	2.25652i	−0.0445028	−	0.0770811i	0.842916	−	0.538045i	$-0.180837\pi$
$857$	−1.30280	−	2.25652i	−0.0445028	−	0.0770811i	−0.887419	+	0.460964i	$0.847504\pi$
$858$		0			0
$859$	23.2583	−	40.2845i	0.793562	−	1.37449i	−0.130186	−	0.991490i	$-0.541557\pi$
$859$	23.2583	−	40.2845i	0.793562	−	1.37449i	0.923748	−	0.383000i	$-0.125109\pi$
$860$	9.03427			0.308066
$861$	−0.646047	+	2.81044i	−0.0220172	+	0.0957795i
$862$	17.1011			0.582464
$863$	−7.05102	+	12.2127i	−0.240019	+	0.415726i	−0.960720	−	0.277521i	$-0.910487\pi$
$863$	−7.05102	+	12.2127i	−0.240019	+	0.415726i	0.720700	+	0.693247i	$0.243820\pi$
$864$	6.96638	+	12.0661i	0.237001	+	0.410498i
$865$	6.58420	+	11.4042i	0.223870	+	0.387754i
$866$	3.77669	−	6.54141i	0.128337	−	0.222286i
$867$	−9.03672			−0.306903
$868$	3.99422	−	1.22528i	0.135573	−	0.0415887i
$869$	−3.04650			−0.103345
$870$	−15.4580	+	26.7741i	−0.524077	+	0.907727i
$871$		0			0
$872$	1.68331	+	2.91559i	0.0570042	+	0.0987342i
$873$	−17.2705	+	29.9133i	−0.584516	+	1.01241i
$874$	39.5344			1.33727
$875$	22.4574	+	20.9023i	0.759198	+	0.706625i
$876$	−38.0917			−1.28700
$877$	5.30523	−	9.18893i	0.179145	−	0.310288i	−0.762443	−	0.647055i	$-0.776000\pi$
$877$	5.30523	−	9.18893i	0.179145	−	0.310288i	0.941588	+	0.336767i	$0.109334\pi$
$878$	−0.880589	−	1.52522i	−0.0297184	−	0.0514738i
$879$	−6.69894	−	11.6029i	−0.225950	−	0.391356i
$880$	3.70783	−	6.42215i	0.124991	−	0.216491i
$881$	33.4123			1.12569			0.562844	−	0.826563i	$-0.309707\pi$
$881$	33.4123			1.12569			0.562844	+	0.826563i	$0.309707\pi$
$882$	−24.4062	+	16.5293i	−0.821800	+	0.556571i
$883$	12.9066			0.434341			0.217170	−	0.976134i	$-0.430317\pi$
$883$	12.9066			0.434341			0.217170	+	0.976134i	$0.430317\pi$
$884$		0			0
$885$	−15.1829	−	26.2975i	−0.510367	−	0.883982i
$886$	3.70639	+	6.41965i	0.124518	+	0.215672i
$887$	8.75988	−	15.1726i	0.294128	−	0.509445i	−0.680654	−	0.732605i	$-0.738304\pi$
$887$	8.75988	−	15.1726i	0.294128	−	0.509445i	0.974782	+	0.223161i	$0.0716375\pi$
$888$	56.5906			1.89905
$889$	−22.1716	−	20.6363i	−0.743612	−	0.692118i
$890$	5.66572			0.189915
$891$	9.14675	−	15.8426i	0.306428	−	0.530749i
$892$	−2.23782	−	3.87601i	−0.0749276	−	0.129778i
$893$	13.5778	+	23.5174i	0.454362	+	0.786979i
$894$	6.58353	−	11.4030i	0.220186	−	0.381374i
$895$	−26.9975			−0.902426
$896$	4.99406	−	1.53199i	0.166840	−	0.0511803i
$897$		0			0
$898$	−3.68968	+	6.39072i	−0.123126	+	0.213261i
$899$	−6.34562	−	10.9909i	−0.211638	−	0.366568i
$900$	−5.34971	−	9.26597i	−0.178324	−	0.308866i
$901$	2.91760	−	5.05343i	0.0971994	−	0.168354i
$902$	−1.70162			−0.0566578
$903$	10.1585	−	44.1917i	0.338054	−	1.47061i
$904$	−39.4731			−1.31285
$905$	15.9069	−	27.5515i	0.528762	−	0.915842i
$906$	5.65927	+	9.80215i	0.188017	+	0.325655i
$907$	−9.60387	−	16.6344i	−0.318891	−	0.552336i	0.661366	−	0.750063i	$-0.269977\pi$
$907$	−9.60387	−	16.6344i	−0.318891	−	0.552336i	−0.980257	+	0.197728i	$0.936644\pi$
$908$	5.92671	−	10.2654i	0.196685	−	0.340668i
$909$	34.6915			1.15064
$910$		0			0
$911$	5.98108			0.198162			0.0990811	−	0.995079i	$-0.468410\pi$
$911$	5.98108			0.198162			0.0990811	+	0.995079i	$0.468410\pi$
$912$	−8.65942	+	14.9986i	−0.286742	+	0.496652i
$913$	8.00477	+	13.8647i	0.264919	+	0.458853i
$914$	−18.5691	−	32.1627i	−0.614212	−	1.06385i
$915$	−22.4164	+	38.8264i	−0.741064	+	1.28356i
$916$	4.94991			0.163549
$917$	4.52374	−	1.38772i	0.149387	−	0.0458265i
$918$	−11.0469			−0.364601
$919$	23.0421	−	39.9101i	0.760090	−	1.31651i	−0.182714	−	0.983166i	$-0.558488\pi$
$919$	23.0421	−	39.9101i	0.760090	−	1.31651i	0.942804	−	0.333348i	$-0.108178\pi$
$920$	−16.4072	−	28.4181i	−0.540929	−	0.936917i
$921$	−18.8450	−	32.6405i	−0.620964	−	1.07554i
$922$	10.8159	−	18.7337i	0.356203	−	0.616961i
$923$		0			0
$924$	19.6252	+	18.2662i	0.645622	+	0.600914i
$925$	−19.4949			−0.640988
$926$	−13.2384	+	22.9296i	−0.435042	+	0.753515i
$927$	32.5580	+	56.3921i	1.06935	+	1.85216i
$928$	−18.1094	−	31.3664i	−0.594471	−	1.02965i
$929$	2.11345	−	3.66060i	0.0693401	−	0.120101i	−0.829271	−	0.558847i	$-0.811244\pi$
$929$	2.11345	−	3.66060i	0.0693401	−	0.120101i	0.898611	+	0.438746i	$0.144577\pi$
$930$	6.85278			0.224712
$931$	33.2775	+	16.1528i	1.09063	+	0.529387i
$932$	7.96161			0.260791
$933$	11.5790	−	20.0554i	0.379078	−	0.656583i
$934$	13.7557	+	23.8256i	0.450100	+	0.779596i
$935$	−11.1144	−	19.2508i	−0.363481	−	0.629567i
$936$		0			0
$937$	45.0155			1.47059			0.735296	−	0.677746i	$-0.237043\pi$
$937$	45.0155			1.47059			0.735296	+	0.677746i	$0.237043\pi$
$938$	26.2170	+	24.4015i	0.856015	+	0.796738i
$939$	55.6027			1.81452
$940$	3.60718	−	6.24783i	0.117653	−	0.203782i
$941$	−10.4884	−	18.1664i	−0.341911	−	0.592207i	0.642876	−	0.765970i	$-0.277741\pi$
$941$	−10.4884	−	18.1664i	−0.341911	−	0.592207i	−0.984788	+	0.173762i	$0.944408\pi$
$942$	8.16425	+	14.1409i	0.266006	+	0.460735i
$943$	−1.48799	+	2.57727i	−0.0484555	+	0.0839275i
$944$	−9.40956			−0.306255
$945$	10.9786	−	3.36783i	0.357134	−	0.109556i
$946$	26.7565			0.869928
$947$	28.2064	−	48.8549i	0.916584	−	1.58757i	0.112019	−	0.993706i	$-0.464268\pi$
$947$	28.2064	−	48.8549i	0.916584	−	1.58757i	0.804565	−	0.593864i	$-0.202398\pi$
$948$	−0.945105	−	1.63697i	−0.0306956	−	0.0531663i
$949$		0			0
$950$	7.54768	−	13.0730i	0.244879	−	0.424143i
$951$	46.5809			1.51049
$952$	−6.61685	+	28.7847i	−0.214453	+	0.932917i
$953$	−46.8932			−1.51902			−0.759510	−	0.650495i	$-0.774561\pi$
$953$	−46.8932			−1.51902			−0.759510	+	0.650495i	$0.774561\pi$
$954$	−3.33065	+	5.76885i	−0.107834	+	0.186773i
$955$	12.0997	+	20.9572i	0.391536	+	0.678159i
$956$	−3.08659	−	5.34613i	−0.0998275	−	0.172906i
$957$	40.7209	−	70.5307i	1.31632	−	2.27993i
$958$	−31.8946			−1.03047
$959$	−3.76662	+	16.3856i	−0.121631	+	0.529119i
$960$	29.3307			0.946645
$961$	14.0934	−	24.4106i	0.454627	−	0.787438i
$962$		0			0
$963$	−14.6264	−	25.3336i	−0.471328	−	0.816365i
$964$	5.45741	−	9.45251i	0.175771	−	0.304445i
$965$	3.05939			0.0984852
$966$	−50.3982	+	15.4603i	−1.62153	+	0.497427i
$967$	44.8315			1.44168			0.720842	−	0.693100i	$-0.243755\pi$
$967$	44.8315			1.44168			0.720842	+	0.693100i	$0.243755\pi$
$968$	−8.06860	+	13.9752i	−0.259334	+	0.449181i
$969$	25.9571	+	44.9590i	0.833862	+	1.44429i
$970$	6.47333	+	11.2121i	0.207846	+	0.360000i
$971$	6.07720	−	10.5260i	0.195027	−	0.337796i	−0.751883	−	0.659297i	$-0.770854\pi$
$971$	6.07720	−	10.5260i	0.195027	−	0.337796i	0.946909	+	0.321501i	$0.104187\pi$
$972$	19.5718			0.627767
$973$	−20.5555	−	19.1321i	−0.658980	−	0.613347i
$974$	−8.86231			−0.283967
$975$		0			0
$976$	6.94626	+	12.0313i	0.222344	+	0.385111i
$977$	13.9808	+	24.2155i	0.447286	+	0.774723i	0.998208	−	0.0598342i	$-0.0190572\pi$
$977$	13.9808	+	24.2155i	0.447286	+	0.774723i	−0.550922	+	0.834557i	$0.685724\pi$
$978$	−12.1497	+	21.0439i	−0.388504	+	0.672908i
$979$	−14.9251			−0.477010
$980$	−0.704022	−	9.80199i	−0.0224892	−	0.313113i
$981$	−4.55320			−0.145373
$982$	−0.392029	+	0.679014i	−0.0125102	+	0.0216682i
$983$	−25.0128	−	43.3234i	−0.797784	−	1.38180i	−0.921056	−	0.389430i	$-0.872672\pi$
$983$	−25.0128	−	43.3234i	−0.797784	−	1.38180i	0.123272	−	0.992373i	$-0.460661\pi$
$984$	−1.64927	−	2.85662i	−0.0525768	−	0.0910656i
$985$	−1.86332	+	3.22737i	−0.0593704	+	0.102833i
$986$	28.7168			0.914530
$987$	−26.5055	−	24.6701i	−0.843681	−	0.785257i
$988$		0			0
$989$	23.3973	−	40.5253i	0.743990	−	1.28863i
$990$	12.6879	+	21.9761i	0.403248	+	0.698446i
$991$	7.02915	+	12.1748i	0.223288	+	0.386747i	0.955805	−	0.294003i	$-0.0949876\pi$
$991$	7.02915	+	12.1748i	0.223288	+	0.386747i	−0.732516	+	0.680749i	$0.761654\pi$
$992$	−4.01409	+	6.95261i	−0.127447	+	0.220745i
$993$	12.1947			0.386988
$994$	−22.6736	+	6.95544i	−0.719164	+	0.220613i
$995$	−23.4801			−0.744370
$996$	−4.96659	+	8.60238i	−0.157372	+	0.272577i
$997$	3.73683	+	6.47237i	0.118346	+	0.204982i	0.919113	−	0.393995i	$-0.128907\pi$
$997$	3.73683	+	6.47237i	0.118346	+	0.204982i	−0.800766	+	0.598977i	$0.795574\pi$
$998$	−16.1605	−	27.9909i	−0.511553	−	0.886036i
$999$	−10.2188	+	17.6995i	−0.323308	+	0.559986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.l.170.16	yes	48
7.2	even	3		8281.2.a.cu.1.9		24
7.4	even	3	inner	1183.2.e.l.508.16	yes	48
7.5	odd	6		8281.2.a.ct.1.9		24
13.12	even	2		1183.2.e.k.170.9	✓	48
91.12	odd	6		8281.2.a.cw.1.16		24
91.25	even	6		1183.2.e.k.508.9	yes	48
91.51	even	6		8281.2.a.cv.1.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.9	✓	48	13.12	even	2
1183.2.e.k.508.9	yes	48	91.25	even	6
1183.2.e.l.170.16	yes	48	1.1	even	1	trivial
1183.2.e.l.508.16	yes	48	7.4	even	3	inner
8281.2.a.ct.1.9		24	7.5	odd	6
8281.2.a.cu.1.9		24	7.2	even	3
8281.2.a.cv.1.16		24	91.51	even	6
8281.2.a.cw.1.16		24	91.12	odd	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.514418 - 0.890998i) q^{2} +(-1.33163 - 2.30645i) q^{3} +(0.470749 + 0.815361i) q^{4} +(-0.745563 + 1.29135i) q^{5} -2.74006 q^{6} +(-1.93668 - 1.80257i) q^{7} +3.02632 q^{8} +(-2.04647 + 3.54460i) q^{9} +O(q^{10})\)	\(q+(0.514418 - 0.890998i) q^{2} +(-1.33163 - 2.30645i) q^{3} +(0.470749 + 0.815361i) q^{4} +(-0.745563 + 1.29135i) q^{5} -2.74006 q^{6} +(-1.93668 - 1.80257i) q^{7} +3.02632 q^{8} +(-2.04647 + 3.54460i) q^{9} +(0.767061 + 1.32859i) q^{10} +(-2.02066 - 3.49989i) q^{11} +(1.25373 - 2.17152i) q^{12} +(-2.60235 + 0.798305i) q^{14} +3.97125 q^{15} +(0.615293 - 1.06572i) q^{16} +(-1.84438 - 3.19455i) q^{17} +(2.10549 + 3.64681i) q^{18} +(2.64218 - 4.57640i) q^{19} -1.40389 q^{20} +(-1.57860 + 6.86722i) q^{21} -4.15786 q^{22} +(-3.63585 + 6.29747i) q^{23} +(-4.02993 - 6.98005i) q^{24} +(1.38827 + 2.40456i) q^{25} +2.91081 q^{27} +(0.558054 - 2.42765i) q^{28} -7.56677 q^{29} +(2.04288 - 3.53838i) q^{30} +(0.838616 + 1.45253i) q^{31} +(2.39328 + 4.14528i) q^{32} +(-5.38154 + 9.32111i) q^{33} -3.79512 q^{34} +(3.77167 - 1.15701i) q^{35} -3.85350 q^{36} +(-3.51064 + 6.08060i) q^{37} +(-2.71837 - 4.70836i) q^{38} +(-2.25631 + 3.90804i) q^{40} +0.409255 q^{41} +(5.30662 + 4.93914i) q^{42} -6.43516 q^{43} +(1.90245 - 3.29514i) q^{44} +(-3.05155 - 5.28544i) q^{45} +(3.74069 + 6.47906i) q^{46} +(-2.56942 + 4.45036i) q^{47} -3.27737 q^{48} +(0.501479 + 6.98201i) q^{49} +2.85661 q^{50} +(-4.91205 + 8.50792i) q^{51} +(0.790945 + 1.36996i) q^{53} +(1.49737 - 2.59352i) q^{54} +6.02612 q^{55} +(-5.86102 - 5.45515i) q^{56} -14.0736 q^{57} +(-3.89248 + 6.74198i) q^{58} +(-3.82320 - 6.62197i) q^{59} +(1.86946 + 3.23800i) q^{60} +(-5.64467 + 9.77685i) q^{61} +1.72560 q^{62} +(10.3528 - 3.17585i) q^{63} +7.38576 q^{64} +(5.53672 + 9.58989i) q^{66} +(-6.57883 - 11.3949i) q^{67} +(1.73648 - 3.00766i) q^{68} +19.3664 q^{69} +(0.909322 - 3.95574i) q^{70} +8.71275 q^{71} +(-6.19328 + 10.7271i) q^{72} +(-7.59569 - 13.1561i) q^{73} +(3.61187 + 6.25594i) q^{74} +(3.69733 - 6.40396i) q^{75} +4.97522 q^{76} +(-2.39542 + 10.4206i) q^{77} +(0.376918 - 0.652842i) q^{79} +(0.917480 + 1.58912i) q^{80} +(2.26331 + 3.92016i) q^{81} +(0.210528 - 0.364645i) q^{82} -3.96146 q^{83} +(-6.34238 + 1.94561i) q^{84} +5.50039 q^{85} +(-3.31036 + 5.73372i) q^{86} +(10.0761 + 17.4524i) q^{87} +(-6.11516 - 10.5918i) q^{88} +(1.84657 - 3.19835i) q^{89} -6.27909 q^{90} -6.84629 q^{92} +(2.23345 - 3.86845i) q^{93} +(2.64351 + 4.57869i) q^{94} +(3.93983 + 6.82398i) q^{95} +(6.37393 - 11.0400i) q^{96} +8.43912 q^{97} +(6.47893 + 3.14486i) q^{98} +16.5409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9}+O(q^{10}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 2 q^{14} + 10 q^{15} - 17 q^{16} + 5 q^{17} - 24 q^{19} + 68 q^{20} - q^{21} - 28 q^{22} - 11 q^{23} - 32 q^{24} - 33 q^{25} - 42 q^{27} - 15 q^{28} + 8 q^{29} + 22 q^{30} - 40 q^{31} + 6 q^{32} - 24 q^{33} + 72 q^{34} + 44 q^{35} - 30 q^{36} + 4 q^{37} + 29 q^{38} + 4 q^{40} + 98 q^{41} - 9 q^{42} + 26 q^{43} - 10 q^{44} - 58 q^{45} + 10 q^{46} - 62 q^{47} + 178 q^{48} + 31 q^{49} - 46 q^{50} + 21 q^{51} + 18 q^{53} - 12 q^{54} - 28 q^{55} - 56 q^{56} - 26 q^{57} - 56 q^{58} - 79 q^{59} - 22 q^{60} - 13 q^{61} + 24 q^{62} + 22 q^{63} + 36 q^{64} + 38 q^{66} + 2 q^{67} + 12 q^{68} - 56 q^{69} + 85 q^{70} - 38 q^{71} - 81 q^{72} - 17 q^{73} - 17 q^{74} - 24 q^{75} + 116 q^{76} - 30 q^{77} + 9 q^{79} - 63 q^{80} - 16 q^{81} + 22 q^{82} + 162 q^{83} + 203 q^{84} - 68 q^{85} - 22 q^{86} - 70 q^{87} + 33 q^{88} - 72 q^{89} + 2 q^{90} - 8 q^{92} - 19 q^{93} + 30 q^{94} - 13 q^{95} - 11 q^{96} + 90 q^{97} + 81 q^{98} - 78 q^{99}+O(q^{100}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9 - 5 * q^10 + q^11 - 5 * q^12 - 2 * q^14 + 10 * q^15 - 17 * q^16 + 5 * q^17 - 24 * q^19 + 68 * q^20 - q^21 - 28 * q^22 - 11 * q^23 - 32 * q^24 - 33 * q^25 - 42 * q^27 - 15 * q^28 + 8 * q^29 + 22 * q^30 - 40 * q^31 + 6 * q^32 - 24 * q^33 + 72 * q^34 + 44 * q^35 - 30 * q^36 + 4 * q^37 + 29 * q^38 + 4 * q^40 + 98 * q^41 - 9 * q^42 + 26 * q^43 - 10 * q^44 - 58 * q^45 + 10 * q^46 - 62 * q^47 + 178 * q^48 + 31 * q^49 - 46 * q^50 + 21 * q^51 + 18 * q^53 - 12 * q^54 - 28 * q^55 - 56 * q^56 - 26 * q^57 - 56 * q^58 - 79 * q^59 - 22 * q^60 - 13 * q^61 + 24 * q^62 + 22 * q^63 + 36 * q^64 + 38 * q^66 + 2 * q^67 + 12 * q^68 - 56 * q^69 + 85 * q^70 - 38 * q^71 - 81 * q^72 - 17 * q^73 - 17 * q^74 - 24 * q^75 + 116 * q^76 - 30 * q^77 + 9 * q^79 - 63 * q^80 - 16 * q^81 + 22 * q^82 + 162 * q^83 + 203 * q^84 - 68 * q^85 - 22 * q^86 - 70 * q^87 + 33 * q^88 - 72 * q^89 + 2 * q^90 - 8 * q^92 - 19 * q^93 + 30 * q^94 - 13 * q^95 - 11 * q^96 + 90 * q^97 + 81 * q^98 - 78 * q^99

Introduction

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