LMFDB - Embedded newform 91.2.g.b.9.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(9,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("91.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.g (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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.6
Root			$-0.181721 + 0.314749i$ of defining polynomial
Character	$\chi$	$=$	91.9
Dual form			91.2.g.b.81.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19402 + 2.06810i) q^{2} -2.75148 q^{3} +(-1.85136 + 3.20665i) q^{4} +(-0.491140 + 0.850679i) q^{5} +(-3.28532 - 5.69033i) q^{6} +(2.60682 + 0.452230i) q^{7} -4.06616 q^{8} +4.57063 q^{9} +O(q^{10})$	\(q+(1.19402 + 2.06810i) q^{2} -2.75148 q^{3} +(-1.85136 + 3.20665i) q^{4} +(-0.491140 + 0.850679i) q^{5} +(-3.28532 - 5.69033i) q^{6} +(2.60682 + 0.452230i) q^{7} -4.06616 q^{8} +4.57063 q^{9} -2.34572 q^{10} -0.587802 q^{11} +(5.09398 - 8.82303i) q^{12} +(2.39227 + 2.69760i) q^{13} +(2.17733 + 5.93113i) q^{14} +(1.35136 - 2.34063i) q^{15} +(-1.15235 - 1.99593i) q^{16} +(3.22710 - 5.58950i) q^{17} +(5.45742 + 9.45253i) q^{18} -3.82689 q^{19} +(-1.81855 - 3.14983i) q^{20} +(-7.17260 - 1.24430i) q^{21} +(-0.701847 - 1.21563i) q^{22} +(-4.13001 - 7.15338i) q^{23} +11.1880 q^{24} +(2.01756 + 3.49452i) q^{25} +(-2.72249 + 8.16844i) q^{26} -4.32156 q^{27} +(-6.27630 + 7.52191i) q^{28} +(1.98009 - 3.42962i) q^{29} +6.45420 q^{30} +(1.49436 + 2.58831i) q^{31} +(-1.31430 + 2.27644i) q^{32} +1.61733 q^{33} +15.4129 q^{34} +(-1.66501 + 1.99546i) q^{35} +(-8.46189 + 14.6564i) q^{36} +(-0.877941 - 1.52064i) q^{37} +(-4.56938 - 7.91440i) q^{38} +(-6.58228 - 7.42239i) q^{39} +(1.99705 - 3.45900i) q^{40} +(-1.83584 + 3.17977i) q^{41} +(-5.99088 - 16.3194i) q^{42} +(-3.19042 - 5.52598i) q^{43} +(1.08823 - 1.88488i) q^{44} +(-2.24482 + 3.88814i) q^{45} +(9.86261 - 17.0825i) q^{46} +(2.17030 - 3.75906i) q^{47} +(3.17067 + 5.49176i) q^{48} +(6.59098 + 2.35776i) q^{49} +(-4.81802 + 8.34505i) q^{50} +(-8.87930 + 15.3794i) q^{51} +(-13.0792 + 2.67695i) q^{52} +(-0.212770 - 0.368529i) q^{53} +(-5.16002 - 8.93742i) q^{54} +(0.288693 - 0.500031i) q^{55} +(-10.5997 - 1.83884i) q^{56} +10.5296 q^{57} +9.45706 q^{58} +(-3.00431 + 5.20362i) q^{59} +(5.00371 + 8.66669i) q^{60} +2.20674 q^{61} +(-3.56859 + 6.18097i) q^{62} +(11.9148 + 2.06698i) q^{63} -10.8866 q^{64} +(-3.46973 + 0.710156i) q^{65} +(1.93112 + 3.34479i) q^{66} +7.01303 q^{67} +(11.9491 + 20.6964i) q^{68} +(11.3636 + 19.6824i) q^{69} +(-6.11486 - 1.06080i) q^{70} +(-1.80127 - 3.11988i) q^{71} -18.5849 q^{72} +(-2.46714 - 4.27321i) q^{73} +(2.09656 - 3.63134i) q^{74} +(-5.55128 - 9.61510i) q^{75} +(7.08496 - 12.2715i) q^{76} +(-1.53229 - 0.265822i) q^{77} +(7.49088 - 22.4753i) q^{78} +(-1.39270 + 2.41223i) q^{79} +2.26386 q^{80} -1.82122 q^{81} -8.76812 q^{82} -2.86819 q^{83} +(17.2691 - 20.6964i) q^{84} +(3.16992 + 5.49045i) q^{85} +(7.61885 - 13.1962i) q^{86} +(-5.44818 + 9.43652i) q^{87} +2.39010 q^{88} +(1.04656 + 1.81269i) q^{89} -10.7214 q^{90} +(5.01627 + 8.11400i) q^{91} +30.5845 q^{92} +(-4.11170 - 7.12167i) q^{93} +10.3655 q^{94} +(1.87954 - 3.25546i) q^{95} +(3.61628 - 6.26357i) q^{96} +(-3.84852 - 6.66584i) q^{97} +(2.99367 + 16.4460i) q^{98} -2.68663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9} - 8 q^{10} - 8 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} + 8 q^{16} + 5 q^{17} + 3 q^{18} + 2 q^{19} - q^{20} - 9 q^{21} - 5 q^{22} - q^{23} + 22 q^{24} + 7 q^{25} + 5 q^{26} - 8 q^{27} - 7 q^{28} + 3 q^{29} + 10 q^{30} + 16 q^{31} + 8 q^{32} - 32 q^{33} + 32 q^{34} + 8 q^{35} - 21 q^{36} - 13 q^{37} - 17 q^{38} - 23 q^{39} - 5 q^{40} - 8 q^{41} + 2 q^{42} - 11 q^{43} + 21 q^{44} - 7 q^{45} + 16 q^{46} - q^{47} + 21 q^{48} - 3 q^{49} + 6 q^{50} - 20 q^{51} - 25 q^{52} - 2 q^{53} - 18 q^{54} + 9 q^{55} - 18 q^{56} + 42 q^{57} + 16 q^{58} + 13 q^{59} + 20 q^{60} + 10 q^{61} + 5 q^{62} + 32 q^{63} - 30 q^{64} + 19 q^{65} + 18 q^{66} + 22 q^{67} + 29 q^{68} + 23 q^{69} - 39 q^{70} + 6 q^{71} - 50 q^{72} - 30 q^{73} - 3 q^{74} - 3 q^{75} - 9 q^{76} + 11 q^{77} + 16 q^{78} + 7 q^{79} + 14 q^{80} + 12 q^{81} - 2 q^{82} - 54 q^{83} + 5 q^{84} - q^{85} - 7 q^{86} + 16 q^{87} + 4 q^{89} - 16 q^{90} - 20 q^{91} + 54 q^{92} - 7 q^{93} - 90 q^{94} - 6 q^{95} + 19 q^{96} - 35 q^{97} + 62 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9 - 8 * q^10 - 8 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 + 8 * q^16 + 5 * q^17 + 3 * q^18 + 2 * q^19 - q^20 - 9 * q^21 - 5 * q^22 - q^23 + 22 * q^24 + 7 * q^25 + 5 * q^26 - 8 * q^27 - 7 * q^28 + 3 * q^29 + 10 * q^30 + 16 * q^31 + 8 * q^32 - 32 * q^33 + 32 * q^34 + 8 * q^35 - 21 * q^36 - 13 * q^37 - 17 * q^38 - 23 * q^39 - 5 * q^40 - 8 * q^41 + 2 * q^42 - 11 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 - 25 * q^52 - 2 * q^53 - 18 * q^54 + 9 * q^55 - 18 * q^56 + 42 * q^57 + 16 * q^58 + 13 * q^59 + 20 * q^60 + 10 * q^61 + 5 * q^62 + 32 * q^63 - 30 * q^64 + 19 * q^65 + 18 * q^66 + 22 * q^67 + 29 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 - 50 * q^72 - 30 * q^73 - 3 * q^74 - 3 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 + 14 * q^80 + 12 * q^81 - 2 * q^82 - 54 * q^83 + 5 * q^84 - q^85 - 7 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 - 20 * q^91 + 54 * q^92 - 7 * q^93 - 90 * q^94 - 6 * q^95 + 19 * q^96 - 35 * q^97 + 62 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.19402	+	2.06810i	0.844299	+	1.46237i	0.886229	+	0.463248i	$0.153316\pi$
$2$	1.19402	+	2.06810i	0.844299	+	1.46237i	−0.0419302	+	0.999121i	$0.513351\pi$
$3$	−2.75148			−1.58857			−0.794283	−	0.607548i	$-0.792153\pi$
$3$	−2.75148			−1.58857			−0.794283	+	0.607548i	$0.792153\pi$
$4$	−1.85136	+	3.20665i	−0.925680	+	1.60333i
$5$	−0.491140	+	0.850679i	−0.219644	+	0.380435i	−0.954699	−	0.297572i	$-0.903823\pi$
$5$	−0.491140	+	0.850679i	−0.219644	+	0.380435i	0.735055	+	0.678008i	$0.237156\pi$
$6$	−3.28532	−	5.69033i	−1.34122	−	2.32307i
$7$	2.60682	+	0.452230i	0.985284	+	0.170927i
$7$	2.60682	+	0.452230i	0.985284	+	0.170927i
$8$	−4.06616			−1.43761
$9$	4.57063			1.52354
$10$	−2.34572			−0.741782
$11$	−0.587802			−0.177229			−0.0886146	−	0.996066i	$-0.528244\pi$
$11$	−0.587802			−0.177229			−0.0886146	+	0.996066i	$0.528244\pi$
$12$	5.09398	−	8.82303i	1.47051	−	2.54699i
$13$	2.39227	+	2.69760i	0.663496	+	0.748179i
$13$	2.39227	+	2.69760i	0.663496	+	0.748179i
$14$	2.17733	+	5.93113i	0.581916	+	1.58516i
$15$	1.35136	−	2.34063i	0.348920	−	0.604347i
$16$	−1.15235	−	1.99593i	−0.288088	−	0.498983i
$17$	3.22710	−	5.58950i	0.782687	−	1.35565i	−0.147685	−	0.989035i	$-0.547182\pi$
$17$	3.22710	−	5.58950i	0.782687	−	1.35565i	0.930371	−	0.366619i	$-0.119485\pi$
$18$	5.45742	+	9.45253i	1.28633	+	2.22798i
$19$	−3.82689			−0.877950			−0.438975	−	0.898499i	$-0.644658\pi$
$19$	−3.82689			−0.877950			−0.438975	+	0.898499i	$0.644658\pi$
$20$	−1.81855	−	3.14983i	−0.406641	−	0.704323i
$21$	−7.17260	−	1.24430i	−1.56519	−	0.271528i
$22$	−0.701847	−	1.21563i	−0.149634	−	0.259174i
$23$	−4.13001	−	7.15338i	−0.861166	−	1.49158i	−0.870805	−	0.491629i	$-0.836402\pi$
$23$	−4.13001	−	7.15338i	−0.861166	−	1.49158i	0.00963902	−	0.999954i	$-0.496932\pi$
$24$	11.1880			2.28373
$25$	2.01756	+	3.49452i	0.403513	+	0.698904i
$26$	−2.72249	+	8.16844i	−0.533925	+	1.60196i
$27$	−4.32156			−0.831685
$28$	−6.27630	+	7.52191i	−1.18611	+	1.42151i
$29$	1.98009	−	3.42962i	0.367694	−	0.636864i	−0.621511	−	0.783406i	$-0.713481\pi$
$29$	1.98009	−	3.42962i	0.367694	−	0.636864i	0.989205	+	0.146541i	$0.0468141\pi$
$30$	6.45420			1.17837
$31$	1.49436	+	2.58831i	0.268395	+	0.464874i	0.968448	−	0.249218i	$-0.0801734\pi$
$31$	1.49436	+	2.58831i	0.268395	+	0.464874i	−0.700053	+	0.714091i	$0.746840\pi$
$32$	−1.31430	+	2.27644i	−0.232338	+	0.402421i
$33$	1.61733			0.281540
$34$	15.4129			2.64329
$35$	−1.66501	+	1.99546i	−0.281439	+	0.337294i
$36$	−8.46189	+	14.6564i	−1.41031	+	2.44274i
$37$	−0.877941	−	1.52064i	−0.144333	−	0.249991i	0.784791	−	0.619760i	$-0.212770\pi$
$37$	−0.877941	−	1.52064i	−0.144333	−	0.249991i	−0.929124	+	0.369769i	$0.879437\pi$
$38$	−4.56938	−	7.91440i	−0.741252	−	1.28389i
$39$	−6.58228	−	7.42239i	−1.05401	−	1.18853i
$40$	1.99705	−	3.45900i	0.315762	−	0.546916i
$41$	−1.83584	+	3.17977i	−0.286710	+	0.496597i	−0.973023	−	0.230710i	$-0.925895\pi$
$41$	−1.83584	+	3.17977i	−0.286710	+	0.496597i	0.686312	+	0.727307i	$0.259228\pi$
$42$	−5.99088	−	16.3194i	−0.924412	−	2.51813i
$43$	−3.19042	−	5.52598i	−0.486535	−	0.842703i	0.513345	−	0.858182i	$-0.328406\pi$
$43$	−3.19042	−	5.52598i	−0.486535	−	0.842703i	−0.999880	+	0.0154788i	$0.995073\pi$
$44$	1.08823	−	1.88488i	0.164058	−	0.284156i
$45$	−2.24482	+	3.88814i	−0.334638	+	0.579610i
$46$	9.86261	−	17.0825i	1.45416	−	2.51868i
$47$	2.17030	−	3.75906i	0.316570	−	0.548316i	−0.663200	−	0.748442i	$-0.730802\pi$
$47$	2.17030	−	3.75906i	0.316570	−	0.548316i	0.979770	+	0.200127i	$0.0641353\pi$
$48$	3.17067	+	5.49176i	0.457647	+	0.792668i
$49$	6.59098	+	2.35776i	0.941568	+	0.336823i
$50$	−4.81802	+	8.34505i	−0.681370	+	1.18017i
$51$	−8.87930	+	15.3794i	−1.24335	+	2.15355i
$52$	−13.0792	+	2.67695i	−1.81376	+	0.371226i
$53$	−0.212770	−	0.368529i	−0.0292263	−	0.0506214i	0.851042	−	0.525097i	$-0.175971\pi$
$53$	−0.212770	−	0.368529i	−0.0292263	−	0.0506214i	−0.880269	+	0.474476i	$0.842638\pi$
$54$	−5.16002	−	8.93742i	−0.702190	−	1.21623i
$55$	0.288693	−	0.500031i	0.0389274	−	0.0674242i
$56$	−10.5997	−	1.83884i	−1.41645	−	0.245725i
$57$	10.5296			1.39468
$58$	9.45706			1.24177
$59$	−3.00431	+	5.20362i	−0.391128	+	0.677454i	−0.992599	−	0.121441i	$-0.961248\pi$
$59$	−3.00431	+	5.20362i	−0.391128	+	0.677454i	0.601470	+	0.798895i	$0.294582\pi$
$60$	5.00371	+	8.66669i	0.645977	+	1.11886i
$61$	2.20674			0.282544			0.141272	−	0.989971i	$-0.454881\pi$
$61$	2.20674			0.282544			0.141272	+	0.989971i	$0.454881\pi$
$62$	−3.56859	+	6.18097i	−0.453211	+	0.784985i
$63$	11.9148	+	2.06698i	1.50112	+	0.260414i
$64$	−10.8866			−1.36083
$65$	−3.46973	+	0.710156i	−0.430367	+	0.0880841i
$66$	1.93112	+	3.34479i	0.237704	+	0.411716i
$67$	7.01303			0.856778			0.428389	−	0.903594i	$-0.359081\pi$
$67$	7.01303			0.856778			0.428389	+	0.903594i	$0.359081\pi$
$68$	11.9491	+	20.6964i	1.44904	+	2.50980i
$69$	11.3636	+	19.6824i	1.36802	+	2.36948i
$70$	−6.11486	−	1.06080i	−0.730866	−	0.126790i
$71$	−1.80127	−	3.11988i	−0.213771	−	0.370262i	0.739121	−	0.673573i	$-0.235241\pi$
$71$	−1.80127	−	3.11988i	−0.213771	−	0.370262i	−0.952892	+	0.303311i	$0.901908\pi$
$72$	−18.5849			−2.19026
$73$	−2.46714	−	4.27321i	−0.288756	−	0.500141i	0.684757	−	0.728772i	$-0.259908\pi$
$73$	−2.46714	−	4.27321i	−0.288756	−	0.500141i	−0.973513	+	0.228631i	$0.926575\pi$
$74$	2.09656	−	3.63134i	0.243720	−	0.422135i
$75$	−5.55128	−	9.61510i	−0.641007	−	1.11026i
$76$	7.08496	−	12.2715i	0.812701	−	1.40764i
$77$	−1.53229	−	0.265822i	−0.174621	−	0.0302932i
$78$	7.49088	−	22.4753i	0.848175	−	2.54483i
$79$	−1.39270	+	2.41223i	−0.156691	+	0.271397i	−0.933674	−	0.358125i	$-0.883416\pi$
$79$	−1.39270	+	2.41223i	−0.156691	+	0.271397i	0.776982	+	0.629522i	$0.216749\pi$
$80$	2.26386			0.253108
$81$	−1.82122			−0.202357
$82$	−8.76812			−0.968277
$83$	−2.86819			−0.314825			−0.157412	−	0.987533i	$-0.550315\pi$
$83$	−2.86819			−0.314825			−0.157412	+	0.987533i	$0.550315\pi$
$84$	17.2691	−	20.6964i	1.88421	−	2.25816i
$85$	3.16992	+	5.49045i	0.343826	+	0.595523i
$86$	7.61885	−	13.1962i	0.821562	−	1.42299i
$87$	−5.44818	+	9.43652i	−0.584106	+	1.01170i
$88$	2.39010			0.254786
$89$	1.04656	+	1.81269i	0.110935	+	0.192145i	0.916147	−	0.400842i	$-0.131282\pi$
$89$	1.04656	+	1.81269i	0.110935	+	0.192145i	−0.805213	+	0.592986i	$0.797949\pi$
$90$	−10.7214			−1.13014
$91$	5.01627	+	8.11400i	0.525848	+	0.850578i
$92$	30.5845			3.18866
$93$	−4.11170	−	7.12167i	−0.426363	−	0.738483i
$94$	10.3655			1.06912
$95$	1.87954	−	3.25546i	0.192837	−	0.334003i
$96$	3.61628	−	6.26357i	0.369085	−	0.639273i
$97$	−3.84852	−	6.66584i	−0.390758	−	0.676813i	0.601791	−	0.798653i	$-0.294454\pi$
$97$	−3.84852	−	6.66584i	−0.390758	−	0.676813i	−0.992550	+	0.121840i	$0.961120\pi$
$98$	2.99367	+	16.4460i	0.302406	+	1.66130i
$99$	−2.68663			−0.270016
$100$	−14.9409			−1.49409
$101$	−2.63732			−0.262423			−0.131212	−	0.991354i	$-0.541887\pi$
$101$	−2.63732			−0.262423			−0.131212	+	0.991354i	$0.541887\pi$
$102$	−42.4082			−4.19903
$103$	5.43095	−	9.40669i	0.535128	−	0.926868i	−0.464029	−	0.885820i	$-0.653597\pi$
$103$	5.43095	−	9.40669i	0.535128	−	0.926868i	0.999157	−	0.0410486i	$-0.0130699\pi$
$104$	−9.72736	−	10.9689i	−0.953846	−	1.07559i
$105$	4.58125	−	5.49045i	0.447084	−	0.535813i
$106$	0.508103	−	0.880061i	0.0493514	−	0.0854791i
$107$	7.99024	+	13.8395i	0.772446	+	1.33792i	0.936219	+	0.351418i	$0.114300\pi$
$107$	7.99024	+	13.8395i	0.772446	+	1.33792i	−0.163773	+	0.986498i	$0.552366\pi$
$108$	8.00077	−	13.8577i	0.769874	−	1.33346i
$109$	−4.61738	−	7.99754i	−0.442265	−	0.766026i	0.555592	−	0.831455i	$-0.312492\pi$
$109$	−4.61738	−	7.99754i	−0.442265	−	0.766026i	−0.997857	+	0.0654294i	$0.979158\pi$
$110$	1.37882			0.131465
$111$	2.41564	+	4.18400i	0.229282	+	0.397128i
$112$	−2.10135	−	5.72416i	−0.198559	−	0.540882i
$113$	−5.09012	−	8.81635i	−0.478838	−	0.829372i	0.520867	−	0.853638i	$-0.325609\pi$
$113$	−5.09012	−	8.81635i	−0.478838	−	0.829372i	−0.999706	+	0.0242655i	$0.992275\pi$
$114$	12.5726	+	21.7763i	1.17753	+	2.03954i
$115$	8.11364			0.756601
$116$	7.33173	+	12.6989i	0.680734	+	1.17907i
$117$	10.9342	+	12.3297i	1.01087	+	1.13988i
$118$	−14.3488			−1.32092
$119$	10.9402	−	13.1114i	1.00289	−	1.20192i
$120$	−5.49485	+	9.51736i	−0.501609	+	0.868813i
$121$	−10.6545			−0.968590
$122$	2.63489	+	4.56376i	0.238552	+	0.413184i
$123$	5.05128	−	8.74908i	0.455459	−	0.788878i
$124$	−11.0664			−0.993792
$125$	−8.87502			−0.793806
$126$	9.95178	+	27.1090i	0.886575	+	2.41506i
$127$	−2.12513	+	3.68083i	−0.188575	+	0.326621i	−0.944775	−	0.327719i	$-0.893720\pi$
$127$	−2.12513	+	3.68083i	−0.188575	+	0.326621i	0.756201	+	0.654340i	$0.227053\pi$
$128$	−10.3702	−	17.9617i	−0.916606	−	1.58761i
$129$	8.77838	+	15.2046i	0.772893	+	1.33869i
$130$	−5.61160	−	6.32781i	−0.492170	−	0.554986i
$131$	1.08478	−	1.87890i	0.0947779	−	0.164160i	−0.814738	−	0.579829i	$-0.803119\pi$
$131$	1.08478	−	1.87890i	0.0947779	−	0.164160i	0.909516	+	0.415669i	$0.136453\pi$
$132$	−2.99425	+	5.18620i	−0.260616	+	0.451401i
$133$	−9.97601	−	1.73063i	−0.865030	−	0.150065i
$134$	8.37369	+	14.5037i	0.723376	+	1.25292i
$135$	2.12249	−	3.67626i	0.182675	−	0.316402i
$136$	−13.1219	+	22.7278i	−1.12519	+	1.94889i
$137$	−4.18158	+	7.24271i	−0.357257	+	0.618787i	−0.987501	−	0.157610i	$-0.949621\pi$
$137$	−4.18158	+	7.24271i	−0.357257	+	0.618787i	0.630245	+	0.776396i	$0.282955\pi$
$138$	−27.1367	+	47.0022i	−2.31003	+	4.00110i
$139$	0.288457	+	0.499622i	0.0244666	+	0.0423774i	0.877999	−	0.478662i	$-0.158878\pi$
$139$	0.288457	+	0.499622i	0.0244666	+	0.0423774i	−0.853533	+	0.521039i	$0.825545\pi$
$140$	−3.31619	−	9.03343i	−0.280269	−	0.763464i
$141$	−5.97152	+	10.3430i	−0.502893	+	0.871036i
$142$	4.30149	−	7.45040i	0.360973	−	0.625224i
$143$	−1.40618	−	1.58566i	−0.117591	−	0.132599i
$144$	−5.26698	−	9.12267i	−0.438915	−	0.760223i
$145$	1.94500	+	3.36885i	0.161524	+	0.279767i
$146$	5.89161	−	10.2046i	0.487593	−	0.844537i
$147$	−18.1349	−	6.48732i	−1.49574	−	0.535065i
$148$	6.50154			0.534423
$149$	2.80662			0.229928			0.114964	−	0.993370i	$-0.463325\pi$
$149$	2.80662			0.229928			0.114964	+	0.993370i	$0.463325\pi$
$150$	13.2567	−	22.9612i	1.08240	−	1.87478i
$151$	11.5054	+	19.9280i	0.936300	+	1.62172i	0.772300	+	0.635258i	$0.219106\pi$
$151$	11.5054	+	19.9280i	0.936300	+	1.62172i	0.164000	+	0.986460i	$0.447560\pi$
$152$	15.5608			1.26215
$153$	14.7499	−	25.5476i	1.19246	−	2.06540i
$154$	−1.27984	−	3.48633i	−0.103132	−	0.280937i
$155$	−2.93576			−0.235806
$156$	35.9872	−	7.36556i	2.88128	−	0.589717i
$157$	−11.2880	−	19.5513i	−0.900879	−	1.56037i	−0.826356	−	0.563148i	$-0.809590\pi$
$157$	−11.2880	−	19.5513i	−0.900879	−	1.56037i	−0.0745227	−	0.997219i	$-0.523743\pi$
$158$	−6.65165			−0.529177
$159$	0.585433	+	1.01400i	0.0464278	+	0.0804154i
$160$	−1.29101	−	2.23610i	−0.102064	−	0.176779i
$161$	−7.53119	−	20.5153i	−0.593541	−	1.61683i
$162$	−2.17457	−	3.76646i	−0.170850	−	0.295921i
$163$	8.17714			0.640483			0.320242	−	0.947336i	$-0.396236\pi$
$163$	8.17714			0.640483			0.320242	+	0.947336i	$0.396236\pi$
$164$	−6.79761	−	11.7738i	−0.530804	−	0.919380i
$165$	−0.794333	+	1.37583i	−0.0618388	+	0.107108i
$166$	−3.42467	−	5.93170i	−0.265806	−	0.460389i
$167$	1.16386	−	2.01586i	0.0900619	−	0.155992i	−0.817475	−	0.575964i	$-0.804627\pi$
$167$	1.16386	−	2.01586i	0.0900619	−	0.155992i	0.907537	+	0.419972i	$0.137960\pi$
$168$	29.1649	+	5.05953i	2.25012	+	0.390351i
$169$	−1.55408	+	12.9068i	−0.119545	+	0.992829i
$170$	−7.56988	+	13.1114i	−0.580583	+	1.00560i
$171$	−17.4913			−1.33760
$172$	23.6265			1.80150
$173$	−8.13372			−0.618396			−0.309198	−	0.950998i	$-0.600061\pi$
$173$	−8.13372			−0.618396			−0.309198	+	0.950998i	$0.600061\pi$
$174$	−26.0209			−1.97264
$175$	3.67909	+	10.0220i	0.278113	+	0.757590i
$176$	0.677355	+	1.17321i	0.0510576	+	0.0884343i
$177$	8.26630	−	14.3177i	0.621333	−	1.07618i
$178$	−2.49922	+	4.32877i	−0.187324	+	0.324455i
$179$	−20.9925			−1.56906			−0.784528	−	0.620093i	$-0.787095\pi$
$179$	−20.9925			−1.56906			−0.784528	+	0.620093i	$0.787095\pi$
$180$	−8.31194	−	14.3967i	−0.619536	−	1.07307i
$181$	−1.60807			−0.119527			−0.0597635	−	0.998213i	$-0.519035\pi$
$181$	−1.60807			−0.119527			−0.0597635	+	0.998213i	$0.519035\pi$
$182$	−10.7910	+	20.0624i	−0.799885	+	1.48713i
$183$	−6.07180			−0.448841
$184$	16.7933	+	29.0868i	1.23802	+	2.14431i
$185$	1.72477			0.126807
$186$	9.81889	−	17.0068i	0.719956	−	1.24700i
$187$	−1.89690	+	3.28552i	−0.138715	+	0.240261i
$188$	8.03601	+	13.9188i	0.586086	+	1.01513i
$189$	−11.2655	−	1.95434i	−0.819445	−	0.142157i
$190$	8.97683			0.651247
$191$	−11.5622			−0.836614			−0.418307	−	0.908306i	$-0.637376\pi$
$191$	−11.5622			−0.836614			−0.418307	+	0.908306i	$0.637376\pi$
$192$	29.9543			2.16176
$193$	23.5788			1.69724			0.848621	−	0.529001i	$-0.177433\pi$
$193$	23.5788			1.69724			0.848621	+	0.529001i	$0.177433\pi$
$194$	9.19041	−	15.9183i	0.659833	−	1.14286i
$195$	9.54689	−	1.95398i	0.683667	−	0.139927i
$196$	−19.7628	+	16.7699i	−1.41163	+	1.19785i
$197$	0.735472	−	1.27387i	0.0524002	−	0.0907598i	−0.838636	−	0.544693i	$-0.816646\pi$
$197$	0.735472	−	1.27387i	0.0524002	−	0.0907598i	0.891036	+	0.453933i	$0.149980\pi$
$198$	−3.20788	−	5.55622i	−0.227974	−	0.394863i
$199$	−4.69700	+	8.13543i	−0.332961	+	0.576706i	−0.983091	−	0.183117i	$-0.941381\pi$
$199$	−4.69700	+	8.13543i	−0.332961	+	0.576706i	0.650130	+	0.759823i	$0.274714\pi$
$200$	−8.20374	−	14.2093i	−0.580092	−	1.00475i
$201$	−19.2962			−1.36105
$202$	−3.14901	−	5.45425i	−0.221564	−	0.383760i
$203$	6.71271	−	8.04493i	0.471140	−	0.564643i
$204$	−32.8776	−	56.9456i	−2.30189	−	3.98699i
$205$	−1.80331	−	3.12343i	−0.125949	−	0.218150i
$206$	25.9386			1.80723
$207$	−18.8767	−	32.6955i	−1.31202	−	2.27249i
$208$	2.62749	−	7.88340i	0.182183	−	0.546615i
$209$	2.24946			0.155598
$210$	16.8249	+	2.91878i	1.16103	+	0.201415i
$211$	4.47109	−	7.74416i	0.307803	−	0.533130i	−0.670079	−	0.742290i	$-0.733740\pi$
$211$	4.47109	−	7.74416i	0.307803	−	0.533130i	0.977881	+	0.209160i	$0.0670730\pi$
$212$	1.57566			0.108217
$213$	4.95615	+	8.58430i	0.339589	+	0.588186i
$214$	−19.0810	+	33.0493i	−1.30435	+	2.25920i
$215$	6.26778			0.427459
$216$	17.5722			1.19563
$217$	2.72501	+	7.42303i	0.184986	+	0.503908i
$218$	11.0265	−	19.0984i	0.746808	−	1.29351i
$219$	6.78827	+	11.7576i	0.458709	+	0.794507i
$220$	1.06895	+	1.85148i	0.0720686	+	0.124827i
$221$	22.7983	−	4.66618i	1.53358	−	0.313881i
$222$	−5.76863	+	9.99156i	−0.387165	+	0.670589i
$223$	−10.9098	+	18.8963i	−0.730574	+	1.26539i	0.226064	+	0.974112i	$0.427414\pi$
$223$	−10.9098	+	18.8963i	−0.730574	+	1.26539i	−0.956638	+	0.291279i	$0.905919\pi$
$224$	−4.45562	+	5.33989i	−0.297704	+	0.356786i
$225$	9.22154	+	15.9722i	0.614769	+	1.06481i
$226$	12.1554	−	21.0538i	0.808565	−	1.40048i
$227$	9.27627	−	16.0670i	0.615687	−	1.06640i	−0.374576	−	0.927196i	$-0.622212\pi$
$227$	9.27627	−	16.0670i	0.615687	−	1.06640i	0.990263	−	0.139206i	$-0.0444549\pi$
$228$	−19.4941	+	33.7648i	−1.29103	+	2.23613i
$229$	−9.67525	+	16.7580i	−0.639359	+	1.10740i	0.346215	+	0.938155i	$0.387467\pi$
$229$	−9.67525	+	16.7580i	−0.639359	+	1.10740i	−0.985574	+	0.169247i	$0.945867\pi$
$230$	9.68784	+	16.7798i	0.638797	+	1.10643i
$231$	4.21607	+	0.731403i	0.277397	+	0.0481228i
$232$	−8.05137	+	13.9454i	−0.528599	+	0.915560i
$233$	−8.08170	+	13.9979i	−0.529450	+	0.917034i	0.469960	+	0.882688i	$0.344268\pi$
$233$	−8.08170	+	13.9979i	−0.529450	+	0.917034i	−0.999410	+	0.0343462i	$0.989065\pi$
$234$	−12.4435	+	37.3349i	−0.813458	+	2.44066i
$235$	2.13184	+	3.69245i	0.139066	+	0.240869i
$236$	−11.1241	−	19.2676i	−0.724119	−	1.25421i
$237$	3.83199	−	6.63720i	0.248915	−	0.431133i
$238$	40.1785	+	6.97016i	2.60439	+	0.451808i
$239$	16.1037			1.04166			0.520831	−	0.853660i	$-0.325622\pi$
$239$	16.1037			1.04166			0.520831	+	0.853660i	$0.325622\pi$
$240$	−6.22897			−0.402079
$241$	2.00300	−	3.46930i	0.129025	−	0.223477i	−0.794274	−	0.607559i	$-0.792149\pi$
$241$	2.00300	−	3.46930i	0.129025	−	0.223477i	0.923299	+	0.384082i	$0.125482\pi$
$242$	−12.7217	−	22.0346i	−0.817779	−	1.41643i
$243$	17.9757			1.15314
$244$	−4.08548	+	7.07625i	−0.261546	+	0.453011i
$245$	−5.24279	+	4.44882i	−0.334949	+	0.284225i
$246$	24.1253			1.53817
$247$	−9.15497	−	10.3234i	−0.582517	−	0.656864i
$248$	−6.07631	−	10.5245i	−0.385846	−	0.668305i
$249$	7.89176			0.500120
$250$	−10.5969	−	18.3544i	−0.670209	−	1.16084i
$251$	−1.62344	−	2.81188i	−0.102471	−	0.177484i	0.810231	−	0.586110i	$-0.199341\pi$
$251$	−1.62344	−	2.81188i	−0.102471	−	0.177484i	−0.912702	+	0.408626i	$0.866008\pi$
$252$	−28.6867	+	34.3799i	−1.80709	+	2.16573i
$253$	2.42763	+	4.20477i	0.152624	+	0.264352i
$254$	−10.1498			−0.636853
$255$	−8.72195	−	15.1069i	−0.546190	−	0.946029i
$256$	13.8778	−	24.0371i	0.867365	−	1.50232i
$257$	13.4462	+	23.2895i	0.838751	+	1.45276i	0.890940	+	0.454122i	$0.150047\pi$
$257$	13.4462	+	23.2895i	0.838751	+	1.45276i	−0.0521891	+	0.998637i	$0.516620\pi$
$258$	−20.9631	+	36.3092i	−1.30511	+	2.26051i
$259$	−1.60095	−	4.36106i	−0.0994784	−	0.270983i
$260$	4.14650	−	12.4410i	0.257155	−	0.771556i
$261$	9.05027	−	15.6755i	0.560198	−	0.970291i
$262$	5.18100			0.320084
$263$	−3.80706			−0.234753			−0.117377	−	0.993087i	$-0.537448\pi$
$263$	−3.80706			−0.234753			−0.117377	+	0.993087i	$0.537448\pi$
$264$	−6.57631			−0.404744
$265$	0.418000			0.0256775
$266$	−8.33241	−	22.6978i	−0.510893	−	1.39169i
$267$	−2.87958	−	4.98757i	−0.176227	−	0.305235i
$268$	−12.9836	+	22.4883i	−0.793102	+	1.37369i
$269$	11.9190	−	20.6444i	0.726716	−	1.25871i	−0.231548	−	0.972824i	$-0.574379\pi$
$269$	11.9190	−	20.6444i	0.726716	−	1.25871i	0.958264	−	0.285886i	$-0.0922878\pi$
$270$	10.1372			0.616929
$271$	−4.95068	−	8.57482i	−0.300732	−	0.520883i	0.675570	−	0.737296i	$-0.263898\pi$
$271$	−4.95068	−	8.57482i	−0.300732	−	0.520883i	−0.976302	+	0.216413i	$0.930564\pi$
$272$	−14.8750			−0.901931
$273$	−13.8022	−	22.3255i	−0.835345	−	1.35120i
$274$	−19.9715			−1.20653
$275$	−1.18593	−	2.05409i	−0.0715142	−	0.123866i
$276$	−84.1526			−5.06539
$277$	−5.89289	+	10.2068i	−0.354069	+	0.613266i	−0.986958	−	0.160977i	$-0.948536\pi$
$277$	−5.89289	+	10.2068i	−0.354069	+	0.613266i	0.632889	+	0.774243i	$0.281869\pi$
$278$	−0.688846	+	1.19312i	−0.0413142	+	0.0715584i
$279$	6.83017	+	11.8302i	0.408912	+	0.708256i
$280$	6.77022	−	8.11385i	0.404598	−	0.484895i
$281$	12.9976			0.775372			0.387686	−	0.921791i	$-0.373274\pi$
$281$	12.9976			0.775372			0.387686	+	0.921791i	$0.373274\pi$
$282$	−28.5204			−1.69837
$283$	−16.8050			−0.998952			−0.499476	−	0.866328i	$-0.666474\pi$
$283$	−16.8050			−0.998952			−0.499476	+	0.866328i	$0.666474\pi$
$284$	13.3392			0.791534
$285$	−5.17151	+	8.95733i	−0.306334	+	0.530586i
$286$	1.60029	−	4.80143i	0.0946270	−	0.283914i
$287$	−6.22369	+	7.45886i	−0.367373	+	0.440283i
$288$	−6.00719	+	10.4048i	−0.353977	+	0.613107i
$289$	−12.3283	−	21.3533i	−0.725197	−	1.25608i
$290$	−4.64474	+	8.04493i	−0.272749	+	0.472414i
$291$	10.5891	+	18.3409i	0.620746	+	1.07516i
$292$	18.2702			1.06918
$293$	7.04782	+	12.2072i	0.411738	+	0.713151i	0.995080	−	0.0990757i	$-0.0315886\pi$
$293$	7.04782	+	12.2072i	0.411738	+	0.713151i	−0.583342	+	0.812227i	$0.698255\pi$
$294$	−8.23701	−	45.2508i	−0.480392	−	2.63908i
$295$	−2.95108	−	5.11141i	−0.171818	−	0.297598i
$296$	3.56985	+	6.18316i	0.207493	+	0.359389i
$297$	2.54022			0.147399
$298$	3.35116	+	5.80438i	0.194128	+	0.336239i
$299$	9.41686	−	28.2539i	0.544591	−	1.63397i
$300$	41.1097			2.37347
$301$	−5.81784	−	15.8480i	−0.335335	−	0.913464i
$302$	−27.4754	+	47.5888i	−1.58103	+	2.73843i
$303$	7.25654			0.416877
$304$	4.40993	+	7.63822i	0.252927	+	0.438082i
$305$	−1.08382	+	1.87723i	−0.0620593	+	0.107490i
$306$	70.4466			4.02716
$307$	15.8786			0.906240			0.453120	−	0.891450i	$-0.350311\pi$
$307$	15.8786			0.906240			0.453120	+	0.891450i	$0.350311\pi$
$308$	3.68922	−	4.42140i	0.210213	−	0.251932i
$309$	−14.9431	+	25.8823i	−0.850086	+	1.47239i
$310$	−3.50535	−	6.07145i	−0.199091	−	0.344835i
$311$	14.3017	+	24.7713i	0.810975	+	1.40465i	0.912183	+	0.409784i	$0.134396\pi$
$311$	14.3017	+	24.7713i	0.810975	+	1.40465i	−0.101208	+	0.994865i	$0.532271\pi$
$312$	26.7646	+	30.1806i	1.51525	+	1.70864i
$313$	9.28962	−	16.0901i	0.525080	−	0.909465i	−0.474493	−	0.880259i	$-0.657369\pi$
$313$	9.28962	−	16.0901i	0.525080	−	0.909465i	0.999573	−	0.0292063i	$-0.00929798\pi$
$314$	26.9561	−	46.6893i	1.52122	−	2.63483i
$315$	−7.61017	+	9.12050i	−0.428784	+	0.513882i
$316$	−5.15679	−	8.93182i	−0.290092	−	0.502454i
$317$	−15.3223	+	26.5389i	−0.860584	+	1.49057i	0.0107826	+	0.999942i	$0.496568\pi$
$317$	−15.3223	+	26.5389i	−0.860584	+	1.49057i	−0.871366	+	0.490633i	$0.836766\pi$
$318$	−1.39804	+	2.42147i	−0.0783979	+	0.135789i
$319$	−1.16390	+	2.01594i	−0.0651660	+	0.112871i
$320$	5.34685	−	9.26102i	0.298898	−	0.517707i
$321$	−21.9850	−	38.0791i	−1.22708	−	2.12537i
$322$	33.4352	−	40.0709i	1.86327	−	2.23306i
$323$	−12.3498	+	21.3904i	−0.687160	+	1.19020i
$324$	3.37173	−	5.84001i	0.187318	−	0.324445i
$325$	−4.60026	+	13.8024i	−0.255177	+	0.765620i
$326$	9.76366	+	16.9112i	0.540759	+	0.936622i
$327$	12.7046	+	22.0051i	0.702568	+	1.21688i
$328$	7.46483	−	12.9295i	0.412177	−	0.713911i
$329$	7.35752	−	8.81772i	0.405633	−	0.486136i
$330$	−3.79379			−0.208842
$331$	27.2277			1.49657			0.748284	−	0.663378i	$-0.230878\pi$
$331$	27.2277			1.49657			0.748284	+	0.663378i	$0.230878\pi$
$332$	5.31005	−	9.19728i	0.291427	−	0.504766i
$333$	−4.01275	−	6.95028i	−0.219897	−	0.380873i
$334$	5.55867			0.304157
$335$	−3.44438	+	5.96584i	−0.188187	+	0.325949i
$336$	5.78182	+	15.7499i	0.315424	+	0.859227i
$337$	−12.3160			−0.670898			−0.335449	−	0.942058i	$-0.608888\pi$
$337$	−12.3160			−0.670898			−0.335449	+	0.942058i	$0.608888\pi$
$338$	−28.5481	+	12.1969i	−1.55281	+	0.663426i
$339$	14.0054	+	24.2580i	0.760666	+	1.31751i
$340$	−23.4746			−1.27309
$341$	−0.878389	−	1.52141i	−0.0475674	−	0.0823892i
$342$	−20.8850	−	36.1738i	−1.12933	−	1.95606i
$343$	16.1152	+	9.12688i	0.870140	+	0.492805i
$344$	12.9728	+	22.4695i	0.699445	+	1.21148i
$345$	−22.3245			−1.20191
$346$	−9.71182	−	16.8214i	−0.522111	−	0.904322i
$347$	−3.07253	+	5.32177i	−0.164942	+	0.285688i	−0.936635	−	0.350308i	$-0.886077\pi$
$347$	−3.07253	+	5.32177i	−0.164942	+	0.285688i	0.771693	+	0.635996i	$0.219410\pi$
$348$	−20.1731	−	34.9408i	−1.08139	−	1.87302i
$349$	−6.51563	+	11.2854i	−0.348774	+	0.604094i	−0.986032	−	0.166557i	$-0.946735\pi$
$349$	−6.51563	+	11.2854i	−0.348774	+	0.604094i	0.637258	+	0.770650i	$0.280068\pi$
$350$	−16.3336	+	19.5752i	−0.873065	+	1.04634i
$351$	−10.3383	−	11.6578i	−0.551820	−	0.622249i
$352$	0.772550	−	1.33810i	0.0411771	−	0.0713208i
$353$	31.6665			1.68544			0.842718	−	0.538356i	$-0.180954\pi$
$353$	31.6665			1.68544			0.842718	+	0.538356i	$0.180954\pi$
$354$	39.4805			2.09836
$355$	3.53870			0.187814
$356$	−7.75021			−0.410761
$357$	−30.1017	+	36.0758i	−1.59315	+	1.90933i
$358$	−25.0655	−	43.4147i	−1.32475	−	2.29454i
$359$	−9.96610	+	17.2618i	−0.525991	+	0.911043i	0.473551	+	0.880767i	$0.342972\pi$
$359$	−9.96610	+	17.2618i	−0.525991	+	0.911043i	−0.999542	+	0.0302764i	$0.990361\pi$
$360$	9.12780	−	15.8098i	0.481077	−	0.833251i
$361$	−4.35488			−0.229204
$362$	−1.92007	−	3.32566i	−0.100917	−	0.174793i
$363$	29.3156			1.53867
$364$	−35.3057	+	1.06350i	−1.85052	+	0.0557426i
$365$	4.84684			0.253695
$366$	−7.24984	−	12.5571i	−0.378955	−	0.656370i
$367$	19.7190			1.02932			0.514662	−	0.857393i	$-0.327918\pi$
$367$	19.7190			1.02932			0.514662	+	0.857393i	$0.327918\pi$
$368$	−9.51844	+	16.4864i	−0.496183	+	0.859414i
$369$	−8.39096	+	14.5336i	−0.436816	+	0.756588i
$370$	2.05940	+	3.56699i	0.107063	+	0.185439i
$371$	−0.387993	−	1.05691i	−0.0201436	−	0.0548719i
$372$	30.4490			1.57870
$373$	17.5469			0.908544			0.454272	−	0.890863i	$-0.349899\pi$
$373$	17.5469			0.908544			0.454272	+	0.890863i	$0.349899\pi$
$374$	−9.05972			−0.468467
$375$	24.4194			1.26101
$376$	−8.82478	+	15.2850i	−0.455103	+	0.788262i
$377$	13.9887	−	2.86308i	0.720452	−	0.147456i
$378$	−9.40946	−	25.6317i	−0.483971	−	1.31835i
$379$	5.85068	−	10.1337i	0.300529	−	0.520532i	−0.675727	−	0.737152i	$-0.736170\pi$
$379$	5.85068	−	10.1337i	0.300529	−	0.520532i	0.976256	+	0.216620i	$0.0695034\pi$
$380$	6.95942	+	12.0541i	0.357010	+	0.618360i
$381$	5.84725	−	10.1277i	0.299563	−	0.518859i
$382$	−13.8055	−	23.9119i	−0.706352	−	1.22344i
$383$	−21.5288			−1.10007			−0.550036	−	0.835141i	$-0.685386\pi$
$383$	−21.5288			−1.10007			−0.550036	+	0.835141i	$0.685386\pi$
$384$	28.5334	+	49.4213i	1.45609	+	2.52202i
$385$	0.978699	−	1.17293i	0.0498791	−	0.0597783i
$386$	28.1536	+	48.7634i	1.43298	+	2.48199i
$387$	−14.5823	−	25.2572i	−0.741258	−	1.28390i
$388$	28.5000			1.44687
$389$	−13.2455	−	22.9419i	−0.671574	−	1.16320i	−0.977458	−	0.211131i	$-0.932285\pi$
$389$	−13.2455	−	22.9419i	−0.671574	−	1.16320i	0.305884	−	0.952069i	$-0.401048\pi$
$390$	15.4402	+	17.4108i	0.781845	+	0.881632i
$391$	−53.3118			−2.69609
$392$	−26.8000	−	9.58703i	−1.35360	−	0.484218i
$393$	−2.98476	+	5.16975i	−0.150561	+	0.260779i
$394$	3.51267			0.176966
$395$	−1.36802	−	2.36949i	−0.0688327	−	0.119222i
$396$	4.97392	−	8.61508i	0.249949	−	0.432924i
$397$	−33.7989			−1.69632			−0.848160	−	0.529740i	$-0.822289\pi$
$397$	−33.7989			−1.69632			−0.848160	+	0.529740i	$0.822289\pi$
$398$	−22.4332			−1.12447
$399$	27.4488	+	4.76180i	1.37416	+	0.238388i
$400$	4.64989	−	8.05384i	0.232494	−	0.402692i
$401$	−10.8059	−	18.7164i	−0.539623	−	0.934655i	−0.998924	−	0.0463741i	$-0.985233\pi$
$401$	−10.8059	−	18.7164i	−0.539623	−	0.934655i	0.459301	−	0.888281i	$-0.348100\pi$
$402$	−23.0400	−	39.9065i	−1.14913	−	1.99035i
$403$	−3.40730	+	10.2231i	−0.169730	+	0.509250i
$404$	4.88264	−	8.45697i	0.242920	−	0.420750i
$405$	0.894473	−	1.54927i	0.0444467	−	0.0769839i
$406$	24.6528	+	4.27676i	1.22350	+	0.212252i
$407$	0.516056	+	0.893835i	0.0255799	+	0.0443058i
$408$	36.1047	−	62.5351i	1.78745	−	3.09595i
$409$	−3.87109	+	6.70492i	−0.191413	+	0.331537i	−0.945719	−	0.324986i	$-0.894640\pi$
$409$	−3.87109	+	6.70492i	−0.191413	+	0.331537i	0.754306	+	0.656523i	$0.227974\pi$
$410$	4.30637	−	7.45886i	0.212677	−	0.368367i
$411$	11.5055	−	19.9282i	0.567526	−	0.982984i
$412$	20.1093	+	34.8303i	0.990714	+	1.71597i
$413$	−10.1849	+	12.2062i	−0.501167	+	0.600630i
$414$	45.0783	−	78.0780i	2.21548	−	3.83732i
$415$	1.40868	−	2.43991i	0.0691495	−	0.119770i
$416$	−9.28509	+	1.90040i	−0.455239	+	0.0931746i
$417$	−0.793683	−	1.37470i	−0.0388668	−	0.0673193i
$418$	2.68589	+	4.65211i	0.131371	+	0.227542i
$419$	4.05097	−	7.01649i	0.197903	−	0.342778i	−0.749945	−	0.661500i	$-0.769920\pi$
$419$	4.05097	−	7.01649i	0.197903	−	0.342778i	0.947848	+	0.318722i	$0.103254\pi$
$420$	9.12443	+	24.8553i	0.445226	+	1.21281i
$421$	−32.1124			−1.56506			−0.782530	−	0.622612i	$-0.786071\pi$
$421$	−32.1124			−1.56506			−0.782530	+	0.622612i	$0.786071\pi$
$422$	21.3543			1.03951
$423$	9.91963	−	17.1813i	0.482309	−	0.835384i
$424$	0.865159	+	1.49850i	0.0420158	+	0.0727735i
$425$	26.0435			1.26330
$426$	−11.8355	+	20.4996i	−0.573430	+	0.993210i
$427$	5.75257	+	0.997954i	0.278386	+	0.0482944i
$428$	−59.1713			−2.86015
$429$	3.86908	+	4.36290i	0.186801	+	0.210643i
$430$	7.48384	+	12.9624i	0.360903	+	0.625102i
$431$	−29.5281			−1.42232			−0.711159	−	0.703031i	$-0.751829\pi$
$431$	−29.5281			−1.42232			−0.711159	+	0.703031i	$0.751829\pi$
$432$	4.97996	+	8.62554i	0.239598	+	0.414997i
$433$	−11.0455	−	19.1314i	−0.530813	−	0.919395i	−0.999353	−	0.0359531i	$-0.988553\pi$
$433$	−11.0455	−	19.1314i	−0.530813	−	0.919395i	0.468540	−	0.883442i	$-0.344780\pi$
$434$	−12.0979	+	14.4988i	−0.580716	+	0.695967i
$435$	−5.35164	−	9.26931i	−0.256591	−	0.444429i
$436$	34.1938			1.63758
$437$	15.8051	+	27.3752i	0.756060	+	1.30953i
$438$	−16.2106	+	28.0777i	−0.774575	+	1.34160i
$439$	3.17790	+	5.50428i	0.151673	+	0.262705i	0.931843	−	0.362863i	$-0.118201\pi$
$439$	3.17790	+	5.50428i	0.151673	+	0.262705i	−0.780170	+	0.625568i	$0.784867\pi$
$440$	−1.17387	+	2.03321i	−0.0559622	+	0.0969294i
$441$	30.1249	+	10.7764i	1.43452	+	0.513164i
$442$	36.8718	+	41.5777i	1.75381	+	1.97765i
$443$	6.78135	−	11.7456i	0.322192	−	0.558052i	−0.658748	−	0.752363i	$-0.728914\pi$
$443$	6.78135	−	11.7456i	0.322192	−	0.558052i	0.980940	+	0.194311i	$0.0622472\pi$
$444$	−17.8889			−0.848967
$445$	−2.05602			−0.0974648
$446$	−52.1060			−2.46729
$447$	−7.72237			−0.365255
$448$	−28.3794	−	4.92325i	−1.34080	−	0.232602i
$449$	−10.9559	−	18.9762i	−0.517041	−	0.895541i	−0.999804	−	0.0197900i	$-0.993700\pi$
$449$	−10.9559	−	18.9762i	−0.517041	−	0.895541i	0.482763	−	0.875751i	$-0.339633\pi$
$450$	−22.0214	+	38.1421i	−1.03810	+	1.79804i
$451$	1.07911	−	1.86908i	0.0508134	−	0.0880115i
$452$	37.6946			1.77300
$453$	−31.6570	−	54.8315i	−1.48737	−	2.57621i
$454$	44.3041			2.07930
$455$	−9.36610	+	0.282132i	−0.439090	+	0.0132265i
$456$	−42.8151			−2.00500
$457$	−7.60732	−	13.1763i	−0.355855	−	0.616359i	0.631409	−	0.775450i	$-0.282477\pi$
$457$	−7.60732	−	13.1763i	−0.355855	−	0.616359i	−0.987264	+	0.159091i	$0.949144\pi$
$458$	−46.2097			−2.15924
$459$	−13.9461	+	24.1554i	−0.650949	+	1.12748i
$460$	−15.0213	+	26.0176i	−0.700371	+	1.21308i
$461$	8.10813	+	14.0437i	0.377633	+	0.654080i	0.990717	−	0.135937i	$-0.0434046\pi$
$461$	8.10813	+	14.0437i	0.377633	+	0.654080i	−0.613084	+	0.790018i	$0.710071\pi$
$462$	3.52145	+	9.59257i	0.163833	+	0.446287i
$463$	−1.44769			−0.0672799			−0.0336400	−	0.999434i	$-0.510710\pi$
$463$	−1.44769			−0.0672799			−0.0336400	+	0.999434i	$0.510710\pi$
$464$	−9.12705			−0.423713
$465$	8.07768			0.374593
$466$	−38.5988			−1.78805
$467$	−7.00337	+	12.1302i	−0.324078	+	0.561319i	−0.981325	−	0.192356i	$-0.938387\pi$
$467$	−7.00337	+	12.1302i	−0.324078	+	0.561319i	0.657248	+	0.753675i	$0.271721\pi$
$468$	−59.7803	+	12.2353i	−2.76334	+	0.565579i
$469$	18.2817	+	3.17150i	0.844169	+	0.146446i
$470$	−5.09091	+	8.81772i	−0.234826	+	0.406731i
$471$	31.0586	+	53.7951i	1.43111	+	2.47875i
$472$	12.2160	−	21.1588i	0.562288	−	0.973912i
$473$	1.87534	+	3.24818i	0.0862282	+	0.149352i
$474$	18.3019			0.840633
$475$	−7.72100	−	13.3732i	−0.354264	−	0.613603i
$476$	21.7895	+	59.3553i	0.998719	+	2.72055i
$477$	−0.972495	−	1.68441i	−0.0445275	−	0.0771239i
$478$	19.2281	+	33.3041i	0.879474	+	1.52329i
$479$	−30.0243			−1.37185			−0.685923	−	0.727674i	$-0.740601\pi$
$479$	−30.0243			−1.37185			−0.685923	+	0.727674i	$0.740601\pi$
$480$	3.55219	+	6.15258i	0.162135	+	0.280826i
$481$	2.00180	−	6.00611i	0.0912742	−	0.273855i
$482$	9.56649			0.435742
$483$	20.7219	+	56.4473i	0.942880	+	2.56844i
$484$	19.7253	−	34.1652i	0.896605	−	1.55296i
$485$	7.56065			0.343312
$486$	21.4633	+	37.1756i	0.973597	+	1.68632i
$487$	14.2452	−	24.6733i	0.645510	−	1.11806i	−0.338674	−	0.940904i	$-0.609978\pi$
$487$	14.2452	−	24.6733i	0.645510	−	1.11806i	0.984184	−	0.177152i	$-0.0566884\pi$
$488$	−8.97297			−0.406187
$489$	−22.4992			−1.01745
$490$	−15.4606	−	5.53064i	−0.698438	−	0.249849i
$491$	14.2339	−	24.6538i	0.642365	−	1.11261i	−0.342539	−	0.939504i	$-0.611287\pi$
$491$	14.2339	−	24.6538i	0.642365	−	1.11261i	0.984903	−	0.173105i	$-0.0553799\pi$
$492$	18.7035	+	32.3954i	0.843218	+	1.46050i
$493$	−12.7799	−	22.1354i	−0.575578	−	0.996930i
$494$	10.4187	−	31.2598i	0.468759	−	1.40644i
$495$	1.31951	−	2.28546i	0.0593076	−	0.102724i
$496$	3.44406	−	5.96528i	0.154643	−	0.267849i
$497$	−3.28467	−	8.94755i	−0.147337	−	0.401353i
$498$	9.42290	+	16.3209i	0.422250	+	0.731359i
$499$	13.1164	−	22.7183i	0.587172	−	1.01701i	−0.407429	−	0.913237i	$-0.633575\pi$
$499$	13.1164	−	22.7183i	0.587172	−	1.01701i	0.994601	−	0.103775i	$-0.0330921\pi$
$500$	16.4309	−	28.4591i	0.734811	−	1.27273i
$501$	−3.20233	+	5.54659i	−0.143069	+	0.247803i
$502$	3.87684	−	6.71488i	0.173032	−	0.299700i
$503$	−4.26588	−	7.38872i	−0.190206	−	0.329447i	0.755112	−	0.655595i	$-0.227582\pi$
$503$	−4.26588	−	7.38872i	−0.190206	−	0.329447i	−0.945318	+	0.326149i	$0.894249\pi$
$504$	−48.4475	−	8.40466i	−2.15802	−	0.374373i
$505$	1.29529	−	2.24352i	0.0576398	−	0.0998351i
$506$	−5.79726	+	10.0412i	−0.257720	+	0.446384i
$507$	4.27602	−	35.5127i	0.189905	−	1.57717i
$508$	−7.86876	−	13.6291i	−0.349120	−	0.604693i
$509$	6.51298	+	11.2808i	0.288683	+	0.500014i	0.973496	−	0.228706i	$-0.0734493\pi$
$509$	6.51298	+	11.2808i	0.288683	+	0.500014i	−0.684813	+	0.728719i	$0.740116\pi$
$510$	20.8283	−	36.0758i	0.922295	−	1.59746i
$511$	−4.49890	−	12.2552i	−0.199020	−	0.542137i
$512$	24.8008			1.09605
$513$	16.5382			0.730177
$514$	−32.1100	+	55.6162i	−1.41631	+	2.45312i
$515$	5.33472	+	9.24000i	0.235076	+	0.407163i
$516$	−65.0078			−2.86181
$517$	−1.27571	+	2.20959i	−0.0561055	+	0.0971775i
$518$	7.10753	−	8.51811i	0.312287	−	0.374264i
$519$	22.3798			0.982363
$520$	14.1085	−	2.88761i	0.618698	−	0.126630i
$521$	−2.23285	−	3.86741i	−0.0978230	−	0.169434i	0.812960	−	0.582319i	$-0.197855\pi$
$521$	−2.23285	−	3.86741i	−0.0978230	−	0.169434i	−0.910783	+	0.412885i	$0.864521\pi$
$522$	43.2248			1.89190
$523$	1.45406	+	2.51850i	0.0635815	+	0.110126i	0.896064	−	0.443925i	$-0.146414\pi$
$523$	1.45406	+	2.51850i	0.0635815	+	0.110126i	−0.832482	+	0.554051i	$0.813081\pi$
$524$	4.01665	+	6.95704i	0.175468	+	0.303920i
$525$	−10.1229	−	27.5752i	−0.441801	−	1.20348i
$526$	−4.54570	−	7.87339i	−0.198202	−	0.343296i
$527$	19.2898			0.840277
$528$	−1.86373	−	3.22807i	−0.0811084	−	0.140484i
$529$	−22.6139	+	39.1684i	−0.983213	+	1.70297i
$530$	0.499100	+	0.864466i	0.0216795	+	0.0375500i
$531$	−13.7316	+	23.7838i	−0.595901	+	1.03213i
$532$	24.0187	−	28.7855i	1.04134	−	1.24801i
$533$	−12.9696	+	2.65451i	−0.561775	+	0.114980i
$534$	6.87654	−	11.9105i	0.297577	−	0.515418i
$535$	−15.6973			−0.678654
$536$	−28.5161			−1.23171
$537$	57.7605			2.49255
$538$	56.9262			2.45426
$539$	−3.87419	−	1.38590i	−0.166873	−	0.0596948i
$540$	7.85899	+	13.6122i	0.338197	+	0.585775i
$541$	9.23193	−	15.9902i	0.396912	−	0.687471i	−0.596431	−	0.802664i	$-0.703415\pi$
$541$	9.23193	−	15.9902i	0.396912	−	0.687471i	0.993343	+	0.115193i	$0.0367486\pi$
$542$	11.8224	−	20.4770i	0.507815	−	0.879562i
$543$	4.42458			0.189877
$544$	8.48277	+	14.6926i	0.363696	+	0.629940i
$545$	9.07112			0.388564
$546$	29.6913	−	55.2013i	1.27067	−	2.36240i
$547$	34.9817			1.49571			0.747856	−	0.663861i	$-0.231083\pi$
$547$	34.9817			1.49571			0.747856	+	0.663861i	$0.231083\pi$
$548$	−15.4832	−	26.8177i	−0.661411	−	1.14560i
$549$	10.0862			0.430469
$550$	2.83204	−	4.90524i	0.120759	−	0.209160i
$551$	−7.57760	+	13.1248i	−0.322817	+	0.559135i
$552$	−46.2063	−	80.0317i	−1.96667	−	3.40638i
$553$	−4.72140	+	5.65842i	−0.200774	+	0.240621i
$554$	−28.1449			−1.19576
$555$	−4.74566			−0.201442
$556$	−2.13615			−0.0905930
$557$	0.0531413			0.00225167			0.00112583	−	0.999999i	$-0.499642\pi$
$557$	0.0531413			0.00225167			0.00112583	+	0.999999i	$0.499642\pi$
$558$	−16.3107	+	28.2510i	−0.690487	+	1.19596i
$559$	7.27451	−	21.8261i	0.307679	−	0.923146i
$560$	5.90148	+	1.02379i	0.249383	+	0.0432629i
$561$	5.21927	−	9.04004i	0.220358	−	0.381671i
$562$	15.5194	+	26.8804i	0.654646	+	1.13388i
$563$	−3.99253	+	6.91527i	−0.168265	+	0.291444i	−0.937810	−	0.347149i	$-0.887150\pi$
$563$	−3.99253	+	6.91527i	−0.168265	+	0.291444i	0.769545	+	0.638593i	$0.220483\pi$
$564$	−22.1109	−	38.2972i	−0.931037	−	1.61260i
$565$	9.99985			0.420697
$566$	−20.0655	−	34.7544i	−0.843414	−	1.46084i
$567$	−4.74758	−	0.823608i	−0.199380	−	0.0345883i
$568$	7.32424	+	12.6860i	0.307318	+	0.532291i
$569$	13.3621	+	23.1438i	0.560167	+	0.970237i	0.997481	+	0.0709285i	$0.0225962\pi$
$569$	13.3621	+	23.1438i	0.560167	+	0.970237i	−0.437315	+	0.899308i	$0.644070\pi$
$570$	−24.6995			−1.03455
$571$	−6.74647	−	11.6852i	−0.282331	−	0.489012i	0.689627	−	0.724164i	$-0.257774\pi$
$571$	−6.74647	−	11.6852i	−0.282331	−	0.489012i	−0.971958	+	0.235153i	$0.924441\pi$
$572$	7.68799	−	1.57352i	0.321451	−	0.0657920i
$573$	31.8132			1.32902
$574$	−22.8569	−	3.96520i	−0.954028	−	0.165504i
$575$	16.6651	−	28.8648i	0.694982	−	1.20374i
$576$	−49.7587			−2.07328
$577$	−6.00662	−	10.4038i	−0.250059	−	0.433115i	0.713483	−	0.700673i	$-0.247117\pi$
$577$	−6.00662	−	10.4038i	−0.250059	−	0.433115i	−0.963542	+	0.267558i	$0.913783\pi$
$578$	29.4406	−	50.9925i	1.22457	−	2.12101i
$579$	−64.8767			−2.69618
$580$	−14.4036			−0.598078
$581$	−7.47684	−	1.29708i	−0.310192	−	0.0538119i
$582$	−25.2872	+	43.7988i	−1.04819	+	1.81552i
$583$	0.125067	+	0.216622i	0.00517974	+	0.00897158i
$584$	10.0318	+	17.3756i	0.415118	+	0.719005i
$585$	−15.8589	+	3.24586i	−0.655683	+	0.134200i
$586$	−16.8305	+	29.1512i	−0.695260	+	1.20422i
$587$	−5.21177	+	9.02705i	−0.215113	+	0.372586i	−0.953307	−	0.302002i	$-0.902345\pi$
$587$	−5.21177	+	9.02705i	−0.215113	+	0.372586i	0.738195	+	0.674588i	$0.235679\pi$
$588$	54.3769	−	46.1420i	2.24246	−	1.90286i
$589$	−5.71876	−	9.90518i	−0.235637	−	0.408136i
$590$	7.04728	−	12.2062i	0.290132	−	0.502523i
$591$	−2.02364	+	3.50504i	−0.0832412	+	0.144178i
$592$	−2.02339	+	3.50462i	−0.0831610	+	0.144039i
$593$	11.1751	−	19.3558i	0.458905	−	0.794847i	−0.539998	−	0.841666i	$-0.681575\pi$
$593$	11.1751	−	19.3558i	0.458905	−	0.794847i	0.998903	+	0.0468194i	$0.0149085\pi$
$594$	3.03307	+	5.25344i	0.124449	+	0.215551i
$595$	5.78044	+	15.7461i	0.236975	+	0.645528i
$596$	−5.19607	+	8.99986i	−0.212839	+	0.368649i
$597$	12.9237	−	22.3845i	0.528931	−	0.916135i
$598$	69.6759	−	14.2607i	2.84926	−	0.583163i
$599$	−0.579463	−	1.00366i	−0.0236762	−	0.0410084i	0.853945	−	0.520364i	$-0.174204\pi$
$599$	−0.579463	−	1.00366i	−0.0236762	−	0.0410084i	−0.877621	+	0.479356i	$0.840870\pi$
$600$	22.5724	+	39.0966i	0.921515	+	1.59611i
$601$	−21.0907	+	36.5301i	−0.860306	+	1.49009i	0.0113271	+	0.999936i	$0.496394\pi$
$601$	−21.0907	+	36.5301i	−0.860306	+	1.49009i	−0.871633	+	0.490158i	$0.836939\pi$
$602$	25.8287	−	30.9547i	1.05270	−	1.26162i
$603$	32.0540			1.30534
$604$	−85.2029			−3.46686
$605$	5.23284	−	9.06355i	0.212745	−	0.368486i
$606$	8.66444	+	15.0072i	0.351969	+	0.609628i
$607$	−18.1569			−0.736965			−0.368482	−	0.929635i	$-0.620123\pi$
$607$	−18.1569			−0.736965			−0.368482	+	0.929635i	$0.620123\pi$
$608$	5.02970	−	8.71169i	0.203981	−	0.353306i
$609$	−18.4699	+	22.1354i	−0.748437	+	0.896974i
$610$	−5.17640			−0.209586
$611$	15.3324	−	3.13811i	0.620282	−	0.126954i
$612$	54.6147	+	94.5955i	2.20767	+	3.82380i
$613$	−0.902645			−0.0364575			−0.0182288	−	0.999834i	$-0.505803\pi$
$613$	−0.902645			−0.0364575			−0.0182288	+	0.999834i	$0.505803\pi$
$614$	18.9594	+	32.8386i	0.765137	+	1.32526i
$615$	4.96177	+	8.59404i	0.200078	+	0.346545i
$616$	6.23055	+	1.08087i	0.251036	+	0.0435497i
$617$	13.0218	+	22.5544i	0.524238	+	0.908008i	0.999602	+	0.0282180i	$0.00898327\pi$
$617$	13.0218	+	22.5544i	0.524238	+	0.908008i	−0.475363	+	0.879790i	$0.657683\pi$
$618$	−71.3696			−2.87091
$619$	−13.4171	−	23.2390i	−0.539277	−	0.934056i	−0.998943	−	0.0459638i	$-0.985364\pi$
$619$	−13.4171	−	23.2390i	−0.539277	−	0.934056i	0.459666	−	0.888092i	$-0.347969\pi$
$620$	5.43515	−	9.41396i	0.218281	−	0.378074i
$621$	17.8481	+	30.9138i	0.716218	+	1.24053i
$622$	−34.1530	+	59.1547i	−1.36941	+	2.37189i
$623$	1.90843	+	5.19863i	0.0764596	+	0.208279i
$624$	−7.22948	+	21.6910i	−0.289411	+	0.868335i
$625$	−5.72894	+	9.92281i	−0.229158	+	0.396912i
$626$	44.3679			1.77330
$627$	−6.18933			−0.247178
$628$	83.5925			3.33570
$629$	−11.3328			−0.451869
$630$	−27.9488	−	4.84855i	−1.11351	−	0.193171i
$631$	16.8061	+	29.1089i	0.669039	+	1.15881i	0.978173	+	0.207791i	$0.0666273\pi$
$631$	16.8061	+	29.1089i	0.669039	+	1.15881i	−0.309135	+	0.951018i	$0.600039\pi$
$632$	5.66296	−	9.80853i	0.225260	−	0.390162i
$633$	−12.3021	+	21.3079i	−0.488965	+	0.846913i
$634$	−73.1802			−2.90636
$635$	−2.08747	−	3.61561i	−0.0828388	−	0.143481i
$636$	−4.33539			−0.171909
$637$	9.40711	+	23.4202i	0.372723	+	0.927942i
$638$	−5.55889			−0.220078
$639$	−8.23293	−	14.2598i	−0.325690	−	0.564111i
$640$	20.3729			0.805310
$641$	−10.5921	+	18.3460i	−0.418361	+	0.724622i	−0.995775	−	0.0918294i	$-0.970729\pi$
$641$	−10.5921	+	18.3460i	−0.418361	+	0.724622i	0.577414	+	0.816452i	$0.304062\pi$
$642$	52.5010	−	90.9343i	2.07205	−	3.58889i
$643$	−0.330770	−	0.572910i	−0.0130443	−	0.0225933i	0.859430	−	0.511254i	$-0.170819\pi$
$643$	−0.330770	−	0.572910i	−0.0130443	−	0.0225933i	−0.872474	+	0.488661i	$0.837486\pi$
$644$	79.7282	+	13.8312i	3.14173	+	0.545027i
$645$	−17.2457			−0.679047
$646$	−58.9834			−2.32067
$647$	−40.0323			−1.57383			−0.786916	−	0.617060i	$-0.788324\pi$
$647$	−40.0323			−1.57383			−0.786916	+	0.617060i	$0.788324\pi$
$648$	7.40537			0.290910
$649$	1.76594	−	3.05870i	0.0693193	−	0.120065i
$650$	−34.0376	+	6.96654i	−1.33506	+	0.273250i
$651$	−7.49781	−	20.4243i	−0.293862	−	0.800492i
$652$	−15.1388	+	26.2212i	−0.592883	+	1.02690i
$653$	−6.35602	−	11.0089i	−0.248730	−	0.430813i	0.714444	−	0.699693i	$-0.246680\pi$
$653$	−6.35602	−	11.0089i	−0.248730	−	0.430813i	−0.963174	+	0.268880i	$0.913347\pi$
$654$	−30.3391	+	52.5489i	−1.18635	+	2.05482i
$655$	1.06556	+	1.84560i	0.0416349	+	0.0721138i
$656$	8.46215			0.330391
$657$	−11.2764	−	19.5313i	−0.439933	−	0.761987i
$658$	27.0209	+	4.68759i	1.05339	+	0.182741i
$659$	7.09522	+	12.2893i	0.276391	+	0.478723i	0.970485	−	0.241161i	$-0.0775283\pi$
$659$	7.09522	+	12.2893i	0.276391	+	0.478723i	−0.694094	+	0.719884i	$0.744195\pi$
$660$	−2.94119	−	5.09430i	−0.114486	−	0.198295i
$661$	50.1780			1.95170			0.975848	−	0.218449i	$-0.0700996\pi$
$661$	50.1780			1.95170			0.975848	+	0.218449i	$0.0700996\pi$
$662$	32.5104	+	56.3096i	1.26355	+	2.18853i
$663$	−62.7291	+	12.8389i	−2.43620	+	0.498621i
$664$	11.6625			0.452594
$665$	6.37183	−	7.63640i	0.247089	−	0.296127i
$666$	9.58259	−	16.5975i	0.371318	−	0.643141i
$667$	−32.7112			−1.26658
$668$	4.30944	+	7.46417i	0.166737	+	0.288797i
$669$	30.0181	−	51.9928i	1.16057	−	2.01016i
$670$	−16.4506			−0.635542
$671$	−1.29713			−0.0500751
$672$	12.2595	−	14.6926i	0.472922	−	0.566779i
$673$	0.937137	−	1.62317i	0.0361240	−	0.0625685i	−0.847398	−	0.530958i	$-0.821832\pi$
$673$	0.937137	−	1.62317i	0.0361240	−	0.0625685i	0.883522	+	0.468389i	$0.155166\pi$
$674$	−14.7056	−	25.4708i	−0.566438	−	0.981100i
$675$	−8.71902	−	15.1018i	−0.335595	−	0.581268i
$676$	−38.5104	−	28.8785i	−1.48117	−	1.11071i
$677$	1.00439	−	1.73966i	0.0386020	−	0.0668607i	−0.846079	−	0.533058i	$-0.821043\pi$
$677$	1.00439	−	1.73966i	0.0386020	−	0.0668607i	0.884681	+	0.466197i	$0.154376\pi$
$678$	−33.4453	+	57.9290i	−1.28446	+	2.22475i
$679$	−7.01790	−	19.1170i	−0.269322	−	0.733644i
$680$	−12.8894	−	22.3251i	−0.494286	−	0.856128i
$681$	−25.5234	+	44.2079i	−0.978061	+	1.69405i
$682$	2.09762	−	3.63319i	0.0803222	−	0.139122i
$683$	7.05061	−	12.2120i	0.269784	−	0.467280i	−0.699022	−	0.715100i	$-0.746381\pi$
$683$	7.05061	−	12.2120i	0.269784	−	0.467280i	0.968806	+	0.247820i	$0.0797143\pi$
$684$	32.3828	−	56.0886i	1.23819	−	2.14460i
$685$	−4.10748	−	7.11437i	−0.156939	−	0.271826i
$686$	0.366563	+	44.2255i	0.0139955	+	1.68854i
$687$	26.6212	−	46.1094i	1.01566	−	1.75918i
$688$	−7.35298	+	12.7357i	−0.280330	+	0.485546i
$689$	0.485139	−	1.45559i	0.0184823	−	0.0554536i
$690$	−26.6559	−	46.1693i	−1.01477	−	1.75764i
$691$	17.8460	+	30.9102i	0.678895	+	1.17588i	0.975314	+	0.220822i	$0.0708741\pi$
$691$	17.8460	+	30.9102i	0.678895	+	1.17588i	−0.296419	+	0.955058i	$0.595793\pi$
$692$	15.0585	−	26.0820i	0.572437	−	0.991489i
$693$	−7.00355	−	1.21497i	−0.266043	−	0.0461530i
$694$	−14.6746			−0.557041
$695$	−0.566691			−0.0214958
$696$	22.1532	−	38.3704i	0.839714	−	1.45443i
$697$	11.8489	+	20.5229i	0.448809	+	0.777360i
$698$	−31.1191			−1.17788
$699$	22.2366	−	38.5150i	0.841066	−	1.45677i
$700$	−38.9483	−	6.75674i	−1.47211	−	0.255381i
$701$	−6.15865			−0.232609			−0.116305	−	0.993214i	$-0.537105\pi$
$701$	−6.15865			−0.232609			−0.116305	+	0.993214i	$0.537105\pi$
$702$	11.7654	−	35.3004i	0.444057	−	1.33233i
$703$	3.35979	+	5.81932i	0.126717	+	0.219480i
$704$	6.39918			0.241178
$705$	−5.86571	−	10.1597i	−0.220915	−	0.382637i
$706$	37.8103	+	65.4894i	1.42301	+	2.46473i
$707$	−6.87501	−	1.19268i	−0.258561	−	0.0448552i
$708$	30.6078	+	53.0143i	1.15031	+	1.99240i
$709$	34.0371			1.27829			0.639144	−	0.769087i	$-0.279289\pi$
$709$	34.0371			1.27829			0.639144	+	0.769087i	$0.279289\pi$
$710$	4.22527	+	7.31838i	0.158571	+	0.274654i
$711$	−6.36553	+	11.0254i	−0.238726	+	0.413486i
$712$	−4.25547	−	7.37069i	−0.159480	−	0.276228i
$713$	12.3434	−	21.3794i	0.462265	−	0.800667i
$714$	−110.550	−	19.1782i	−4.13724	−	0.717727i
$715$	2.03952	−	0.417432i	0.0762736	−	0.0156111i
$716$	38.8648	−	67.3158i	1.45244	−	2.51571i
$717$	−44.3090			−1.65475
$718$	−47.5989			−1.77637
$719$	−22.9648			−0.856444			−0.428222	−	0.903674i	$-0.640860\pi$
$719$	−22.9648			−0.856444			−0.428222	+	0.903674i	$0.640860\pi$
$720$	10.3473			0.385621
$721$	18.4115	−	22.0655i	0.685679	−	0.821761i
$722$	−5.19981	−	9.00633i	−0.193517	−	0.335181i
$723$	−5.51122	+	9.54571i	−0.204964	+	0.355009i
$724$	2.97712	−	5.15653i	0.110644	−	0.191641i
$725$	15.9798			0.593476
$726$	35.0034	+	60.6276i	1.29910	+	2.25010i
$727$	1.06558			0.0395203			0.0197601	−	0.999805i	$-0.493710\pi$
$727$	1.06558			0.0395203			0.0197601	+	0.999805i	$0.493710\pi$
$728$	−20.3970	−	32.9928i	−0.755963	−	1.22280i
$729$	−43.9962			−1.62949
$730$	5.78721	+	10.0237i	0.214194	+	0.370996i
$731$	−41.1833			−1.52322
$732$	11.2411	−	19.4702i	0.415483	−	0.719637i
$733$	13.1689	−	22.8092i	0.486404	−	0.842476i	−0.513474	−	0.858105i	$-0.671642\pi$
$733$	13.1689	−	22.8092i	0.486404	−	0.842476i	0.999878	+	0.0156289i	$0.00497504\pi$
$734$	23.5448	+	40.7809i	0.869056	+	1.50525i
$735$	14.4254	−	12.2408i	0.532090	−	0.451510i
$736$	21.7123			0.800326
$737$	−4.12228			−0.151846
$738$	−40.0759			−1.47521
$739$	34.2149			1.25862			0.629308	−	0.777156i	$-0.283338\pi$
$739$	34.2149			1.25862			0.629308	+	0.777156i	$0.283338\pi$
$740$	−3.19317	+	5.53073i	−0.117383	+	0.203314i
$741$	25.1897	+	28.4047i	0.925366	+	1.04347i
$742$	1.72252	−	2.06438i	0.0632358	−	0.0757857i
$743$	−11.2391	+	19.4667i	−0.412322	+	0.714163i	−0.995143	−	0.0984379i	$-0.968615\pi$
$743$	−11.2391	+	19.4667i	−0.412322	+	0.714163i	0.582821	+	0.812600i	$0.301949\pi$
$744$	16.7188	+	28.9579i	0.612942	+	1.06165i
$745$	−1.37845	+	2.38754i	−0.0505023	+	0.0874726i
$746$	20.9513	+	36.2888i	0.767083	+	1.32863i
$747$	−13.1094			−0.479649
$748$	−7.02368	−	12.1654i	−0.256811	−	0.444810i
$749$	14.5705	+	39.6905i	0.532393	+	1.45026i
$750$	29.1573	+	50.5018i	1.06467	+	1.84407i
$751$	21.2712	+	36.8428i	0.776197	+	1.34441i	0.934119	+	0.356961i	$0.116187\pi$
$751$	21.2712	+	36.8428i	0.776197	+	1.34441i	−0.157923	+	0.987451i	$0.550480\pi$
$752$	−10.0038			−0.364801
$753$	4.46686	+	7.73683i	0.162781	+	0.281946i
$754$	22.6239	+	25.5114i	0.823912	+	0.929069i
$755$	−22.6031			−0.822612
$756$	27.1234	−	32.5064i	0.986469	−	1.18225i
$757$	5.61902	−	9.73243i	0.204227	−	0.353731i	−0.745659	−	0.666327i	$-0.767865\pi$
$757$	5.61902	−	9.73243i	0.204227	−	0.353731i	0.949886	+	0.312596i	$0.101199\pi$
$758$	27.9433			1.01495
$759$	−6.67956	−	11.5693i	−0.242453	−	0.419941i
$760$	−7.64252	+	13.2372i	−0.277223	+	0.480165i
$761$	12.8084			0.464306			0.232153	−	0.972679i	$-0.425423\pi$
$761$	12.8084			0.464306			0.232153	+	0.972679i	$0.425423\pi$
$762$	27.9269			1.01168
$763$	−8.41994	−	22.9362i	−0.304822	−	0.830347i
$764$	21.4059	−	37.0760i	0.774437	−	1.34136i
$765$	14.4885	+	25.0948i	0.523833	+	0.907306i
$766$	−25.7058	−	44.5238i	−0.928789	−	1.60871i
$767$	−21.2244	+	4.34404i	−0.766369	+	0.156854i
$768$	−38.1846	+	66.1377i	−1.37787	+	2.38654i
$769$	25.6759	−	44.4719i	0.925895	−	1.60370i	0.135780	−	0.990739i	$-0.456646\pi$
$769$	25.6759	−	44.4719i	0.925895	−	1.60370i	0.790115	−	0.612958i	$-0.210021\pi$
$770$	3.59433	+	0.623543i	0.129531	+	0.0224709i
$771$	−36.9969	−	64.0805i	−1.33241	−	2.30780i
$772$	−43.6529	+	75.6091i	−1.57110	+	2.72123i
$773$	−10.0023	+	17.3245i	−0.359759	+	0.623120i	−0.987920	−	0.154963i	$-0.950474\pi$
$773$	−10.0023	+	17.3245i	−0.359759	+	0.623120i	0.628162	+	0.778083i	$0.283808\pi$
$774$	34.8230	−	60.3151i	1.25169	−	2.16798i
$775$	−6.02993	+	10.4441i	−0.216602	+	0.375165i
$776$	15.6487	+	27.1044i	0.561756	+	0.972990i
$777$	4.40499	+	11.9993i	0.158028	+	0.430474i
$778$	31.6308	−	54.7861i	1.13402	−	1.96418i
$779$	7.02558	−	12.1687i	0.251717	−	0.435987i
$780$	−11.4090	+	34.2311i	−0.408508	+	1.22567i
$781$	1.05879	+	1.83388i	0.0378864	+	0.0656212i
$782$	−63.6552	−	110.254i	−2.27631	−	3.94268i
$783$	−8.55708	+	14.8213i	−0.305805	+	0.529670i
$784$	−2.88920	−	15.8721i	−0.103186	−	0.566861i
$785$	22.1759			0.791492
$786$	−14.2554			−0.508474
$787$	−14.6596	+	25.3911i	−0.522558	+	0.905096i	0.477098	+	0.878850i	$0.341689\pi$
$787$	−14.6596	+	25.3911i	−0.522558	+	0.905096i	−0.999656	+	0.0262462i	$0.991645\pi$
$788$	2.72325	+	4.71680i	0.0970117	+	0.168029i
$789$	10.4750			0.372921
$790$	3.26689	−	5.65842i	0.116231	−	0.201318i
$791$	−9.28199	−	25.2845i	−0.330030	−	0.899013i
$792$	10.9243			0.388177
$793$	5.27912	+	5.95291i	0.187467	+	0.211394i
$794$	−40.3566	−	69.8996i	−1.43220	−	2.48064i
$795$	−1.15012			−0.0407905
$796$	−17.3917	−	30.1232i	−0.616431	−	1.06769i
$797$	−1.55050	−	2.68554i	−0.0549215	−	0.0951269i	0.837258	−	0.546809i	$-0.184158\pi$
$797$	−1.55050	−	2.68554i	−0.0549215	−	0.0951269i	−0.892179	+	0.451682i	$0.850824\pi$
$798$	22.9264	+	62.4525i	0.811588	+	2.21079i
$799$	−14.0075	−	24.2618i	−0.495551	−	0.858319i
$800$	−10.6068			−0.375005
$801$	4.78343	+	8.28514i	0.169014	+	0.292741i
$802$	25.8050	−	44.6956i	0.911206	−	1.57826i
$803$	1.45019	+	2.51180i	0.0511761	+	0.0886395i
$804$	35.7242	−	61.8762i	1.25990	−	2.18220i
$805$	21.1508	+	3.66923i	0.745467	+	0.129323i
$806$	−25.2108	+	5.15995i	−0.888013	+	0.181751i
$807$	−32.7950	+	56.8025i	−1.15444	+	1.99954i
$808$	10.7238			0.377261
$809$	7.99003			0.280914			0.140457	−	0.990087i	$-0.455143\pi$
$809$	7.99003			0.280914			0.140457	+	0.990087i	$0.455143\pi$
$810$	4.27207			0.150105
$811$	−48.2554			−1.69448			−0.847239	−	0.531213i	$-0.821737\pi$
$811$	−48.2554			−1.69448			−0.847239	+	0.531213i	$0.821737\pi$
$812$	13.3696	+	36.4194i	0.469182	+	1.27807i
$813$	13.6217	+	23.5934i	0.477733	+	0.827458i
$814$	−1.23236	+	2.13451i	−0.0431942	+	0.0748146i
$815$	−4.01612	+	6.95612i	−0.140679	+	0.243662i
$816$	40.9283			1.43278
$817$	12.2094	+	21.1473i	0.427153	+	0.739851i
$818$	−18.4886			−0.646439
$819$	22.9275	+	37.0861i	0.801153	+	1.29589i
$820$	13.3543			0.466353
$821$	13.7760	+	23.8607i	0.480785	+	0.832743i	0.999757	−	0.0220477i	$-0.00701856\pi$
$821$	13.7760	+	23.8607i	0.480785	+	0.832743i	−0.518972	+	0.854791i	$0.673685\pi$
$822$	54.9513			1.91665
$823$	−10.2137	+	17.6907i	−0.356028	+	0.616659i	−0.987293	−	0.158908i	$-0.949203\pi$
$823$	−10.2137	+	17.6907i	−0.356028	+	0.616659i	0.631265	+	0.775567i	$0.282536\pi$
$824$	−22.0831	+	38.2491i	−0.769303	+	1.33247i
$825$	3.26306	+	5.65178i	0.113605	+	0.196770i
$826$	−37.4047	−	6.48896i	−1.30148	−	0.225780i
$827$	−27.7142			−0.963719			−0.481859	−	0.876249i	$-0.660038\pi$
$827$	−27.7142			−0.963719			−0.481859	+	0.876249i	$0.660038\pi$
$828$	139.791			4.85806
$829$	9.25664			0.321496			0.160748	−	0.986995i	$-0.448609\pi$
$829$	9.25664			0.321496			0.160748	+	0.986995i	$0.448609\pi$
$830$	6.72797			0.233531
$831$	16.2142	−	28.0837i	0.562463	−	0.974214i
$832$	−26.0437	−	29.3677i	−0.902904	−	1.01814i
$833$	34.4484	−	29.2315i	1.19357	−	1.01281i
$834$	1.89535	−	3.28283i	0.0656304	−	0.113675i
$835$	1.14323	+	1.98014i	0.0395632	+	0.0685255i
$836$	−4.16456	+	7.21323i	−0.144034	+	0.249475i
$837$	−6.45797	−	11.1855i	−0.223220	−	0.386628i
$838$	19.3477			0.668357
$839$	15.1870	+	26.3046i	0.524312	+	0.908135i	0.999599	+	0.0283045i	$0.00901080\pi$
$839$	15.1870	+	26.3046i	0.524312	+	0.908135i	−0.475287	+	0.879831i	$0.657656\pi$
$840$	−18.6281	+	22.3251i	−0.642731	+	0.770288i
$841$	6.65848	+	11.5328i	0.229603	+	0.397683i
$842$	−38.3428	−	66.4116i	−1.32138	−	2.28869i
$843$	−35.7626			−1.23173
$844$	16.5552	+	28.6745i	0.569854	+	0.987016i
$845$	−10.2163	−	7.66106i	−0.351450	−	0.263548i
$846$	47.3769			1.62885
$847$	−27.7743	−	4.81827i	−0.954336	−	0.165558i
$848$	−0.490373	+	0.849350i	−0.0168395	+	0.0291668i
$849$	46.2385			1.58690
$850$	31.0964	+	53.8606i	1.06660	+	1.84740i
$851$	−7.25180	+	12.5605i	−0.248589	+	0.430568i
$852$	−36.7025			−1.25741
$853$	−5.30773			−0.181733			−0.0908666	−	0.995863i	$-0.528964\pi$
$853$	−5.30773			−0.181733			−0.0908666	+	0.995863i	$0.528964\pi$
$854$	4.80481	+	13.0885i	0.164417	+	0.447878i
$855$	8.59069	−	14.8795i	0.293795	−	0.508868i
$856$	−32.4896	−	56.2737i	−1.11047	−	1.92340i
$857$	8.31857	+	14.4082i	0.284157	+	0.492175i	0.972404	−	0.233302i	$-0.0749529\pi$
$857$	8.31857	+	14.4082i	0.284157	+	0.492175i	−0.688247	+	0.725476i	$0.741620\pi$
$858$	−4.40316	+	13.2110i	−0.150321	+	0.451017i
$859$	5.29426	−	9.16993i	0.180638	−	0.312874i	−0.761460	−	0.648212i	$-0.775517\pi$
$859$	5.29426	−	9.16993i	0.180638	−	0.312874i	0.942098	+	0.335338i	$0.108850\pi$
$860$	−11.6039	+	20.0986i	−0.395690	+	0.685356i
$861$	17.1243	−	20.5229i	0.583596	−	0.699418i
$862$	−35.2571	−	61.0671i	−1.20086	−	2.07995i
$863$	28.0316	−	48.5522i	0.954207	−	1.65273i	0.218033	−	0.975941i	$-0.430036\pi$
$863$	28.0316	−	48.5522i	0.954207	−	1.65273i	0.736173	−	0.676793i	$-0.236631\pi$
$864$	5.67984	−	9.83777i	0.193232	−	0.334688i
$865$	3.99480	−	6.91919i	0.135827	−	0.235260i
$866$	26.3771	−	45.6864i	0.896329	−	1.55249i
$867$	33.9212	+	58.7532i	1.15202	+	1.99536i
$868$	−28.8481	−	5.00455i	−0.979167	−	0.169866i
$869$	0.818634	−	1.41792i	0.0277703	−	0.0480995i
$870$	12.7799	−	22.1354i	0.433279	−	0.750462i
$871$	16.7771	+	18.9183i	0.568469	+	0.641024i
$872$	18.7750	+	32.5193i	0.635803	+	1.10124i
$873$	−17.5902	−	30.4671i	−0.595337	−	1.03115i
$874$	−37.7432	+	65.3731i	−1.27668	+	2.21128i
$875$	−23.1355	−	4.01355i	−0.782124	−	0.135683i
$876$	−50.2702			−1.69847
$877$	−3.66051			−0.123607			−0.0618033	−	0.998088i	$-0.519685\pi$
$877$	−3.66051			−0.123607			−0.0618033	+	0.998088i	$0.519685\pi$
$878$	−7.58894	+	13.1444i	−0.256114	+	0.443603i
$879$	−19.3919	−	33.5878i	−0.654073	−	1.13289i
$880$	−1.33071			−0.0448581
$881$	−5.11493	+	8.85932i	−0.172326	+	0.298478i	−0.939233	−	0.343281i	$-0.888462\pi$
$881$	−5.11493	+	8.85932i	−0.172326	+	0.298478i	0.766906	+	0.641759i	$0.221795\pi$
$882$	13.6829	+	75.1687i	0.460729	+	2.53106i
$883$	−3.98979			−0.134267			−0.0671335	−	0.997744i	$-0.521385\pi$
$883$	−3.98979			−0.134267			−0.0671335	+	0.997744i	$0.521385\pi$
$884$	−27.2451	+	81.7451i	−0.916353	+	2.74938i
$885$	8.11982	+	14.0639i	0.272945	+	0.472754i
$886$	32.3882			1.08810
$887$	7.11039	+	12.3155i	0.238743	+	0.413516i	0.960354	−	0.278784i	$-0.0899312\pi$
$887$	7.11039	+	12.3155i	0.238743	+	0.413516i	−0.721611	+	0.692299i	$0.756598\pi$
$888$	−9.82237	−	17.0128i	−0.329617	−	0.570913i
$889$	−7.20440	+	8.63420i	−0.241628	+	0.289582i
$890$	−2.45493	−	4.25206i	−0.0822894	−	0.142529i
$891$	1.07052			0.0358636
$892$	−40.3960	−	69.9678i	−1.35256	−	2.34270i
$893$	−8.30550	+	14.3855i	−0.277933	+	0.481394i
$894$	−9.22065	−	15.9706i	−0.308385	−	0.534138i
$895$	10.3103	−	17.8579i	0.344635	−	0.596924i
$896$	−18.9104	−	51.5127i	−0.631753	−	1.72092i
$897$	−25.9103	+	77.7400i	−0.865119	+	2.59566i
$898$	26.1631	−	45.3158i	0.873074	−	1.51221i
$899$	11.8359			0.394749
$900$	−68.2896			−2.27632
$901$	−2.74652			−0.0915000
$902$	5.15392			0.171607
$903$	16.0077	+	43.6054i	0.532701	+	1.45110i
$904$	20.6973	+	35.8487i	0.688381	+	1.19231i
$905$	0.789789	−	1.36795i	0.0262535	−	0.0454723i
$906$	75.5980	−	130.940i	2.51158	−	4.35018i
$907$	43.4253			1.44191			0.720956	−	0.692981i	$-0.243703\pi$
$907$	43.4253			1.44191			0.720956	+	0.692981i	$0.243703\pi$
$908$	34.3474	+	59.4915i	1.13986	+	1.97429i
$909$	−12.0542			−0.399814
$910$	−11.7668	−	19.0332i	−0.390065	−	0.630944i
$911$	24.8617			0.823706			0.411853	−	0.911250i	$-0.364882\pi$
$911$	24.8617			0.823706			0.411853	+	0.911250i	$0.364882\pi$
$912$	−12.1338	−	21.0164i	−0.401791	−	0.695923i
$913$	1.68593			0.0557961
$914$	18.1666	−	31.4654i	0.600896	−	1.04078i
$915$	2.98210	−	5.16516i	0.0985853	−	0.170755i
$916$	−35.8248	−	62.0503i	−1.18368	−	2.05020i
$917$	3.67752	−	4.40737i	0.121443	−	0.145544i
$918$	−66.6076			−2.19838
$919$	−1.66327			−0.0548664			−0.0274332	−	0.999624i	$-0.508733\pi$
$919$	−1.66327			−0.0548664			−0.0274332	+	0.999624i	$0.508733\pi$
$920$	−32.9914			−1.08769
$921$	−43.6896			−1.43962
$922$	−19.3625	+	33.5369i	−0.637671	+	1.10448i
$923$	4.10708	−	12.3227i	0.135186	−	0.405607i
$924$	−10.1508	+	12.1654i	−0.333937	+	0.400211i
$925$	3.54260	−	6.13597i	0.116480	−	0.201749i
$926$	−1.72857	−	2.99397i	−0.0568044	−	0.0983880i
$927$	24.8229	−	42.9945i	0.815291	−	1.41212i
$928$	5.20488	+	9.01512i	0.170859	+	0.295936i
$929$	9.49521			0.311528			0.155764	−	0.987794i	$-0.450216\pi$
$929$	9.49521			0.311528			0.155764	+	0.987794i	$0.450216\pi$
$930$	9.64490	+	16.7055i	0.316269	+	0.547793i
$931$	−25.2230	−	9.02289i	−0.826649	−	0.295713i
$932$	−29.9243	−	51.8304i	−0.980202	−	1.69776i
$933$	−39.3508	−	68.1576i	−1.28829	−	2.23138i
$934$	−33.4486			−1.09447
$935$	−1.86328	−	3.22730i	−0.0609359	−	0.105544i
$936$	−44.4602	−	50.1347i	−1.45323	−	1.63870i
$937$	−6.41678			−0.209627			−0.104813	−	0.994492i	$-0.533425\pi$
$937$	−6.41678			−0.209627			−0.104813	+	0.994492i	$0.533425\pi$
$938$	15.2697	+	41.5952i	0.498573	+	1.35813i
$939$	−25.5602	+	44.2715i	−0.834125	+	1.44475i
$940$	−15.7872			−0.514922
$941$	25.7593	+	44.6164i	0.839730	+	1.45445i	0.890121	+	0.455725i	$0.150620\pi$
$941$	25.7593	+	44.6164i	0.839730	+	1.45445i	−0.0503911	+	0.998730i	$0.516047\pi$
$942$	−74.1691	+	128.465i	−2.41656	+	4.18561i
$943$	30.3282			0.987621
$944$	13.8481			0.450717
$945$	7.19546	−	8.62348i	0.234068	−	0.280522i
$946$	−4.47838	+	7.75678i	−0.145605	+	0.252195i
$947$	4.20109	+	7.27651i	0.136517	+	0.236455i	0.926176	−	0.377091i	$-0.123076\pi$
$947$	4.20109	+	7.27651i	0.136517	+	0.236455i	−0.789659	+	0.613546i	$0.789742\pi$
$948$	14.1888	+	24.5757i	0.460831	+	0.798182i
$949$	5.62534	−	16.8780i	0.182606	−	0.547883i
$950$	18.4380	−	31.9356i	0.598209	−	1.03613i
$951$	42.1589	−	73.0213i	1.36709	−	2.36788i
$952$	−44.4846	+	53.3131i	−1.44175	+	1.72789i
$953$	18.0455	+	31.2558i	0.584552	+	1.01247i	0.994931	+	0.100559i	$0.0320631\pi$
$953$	18.0455	+	31.2558i	0.584552	+	1.01247i	−0.410379	+	0.911915i	$0.634604\pi$
$954$	2.32235	−	4.02244i	0.0751890	−	0.130231i
$955$	5.67867	−	9.83575i	0.183758	−	0.318277i
$956$	−29.8138	+	51.6390i	−0.964246	+	1.67012i
$957$	3.20245	−	5.54681i	0.103521	−	0.179303i
$958$	−35.8496	−	62.0933i	−1.15825	−	2.00614i
$959$	−14.1760	+	16.9894i	−0.457766	+	0.548616i
$960$	−14.7117	+	25.4815i	−0.474820	+	0.822412i
$961$	11.0338	−	19.1111i	0.355928	−	0.616486i
$962$	14.8114	−	3.03148i	0.477540	−	0.0977390i
$963$	36.5205	+	63.2553i	1.17686	+	2.03837i
$964$	7.41656	+	12.8459i	0.238871	+	0.413737i
$965$	−11.5805	+	20.0580i	−0.372790	+	0.645691i
$966$	−91.9963	+	110.254i	−2.95993	+	3.54737i
$967$	3.18338			0.102371			0.0511853	−	0.998689i	$-0.483700\pi$
$967$	3.18338			0.102371			0.0511853	+	0.998689i	$0.483700\pi$
$968$	43.3229			1.39245
$969$	33.9801	−	58.8553i	1.09160	−	1.89070i
$970$	9.02756	+	15.6362i	0.289857	+	0.502048i
$971$	37.7476			1.21138			0.605690	−	0.795701i	$-0.292897\pi$
$971$	37.7476			1.21138			0.605690	+	0.795701i	$0.292897\pi$
$972$	−33.2795	+	57.6419i	−1.06744	+	1.84886i
$973$	0.526010	+	1.43287i	0.0168631	+	0.0459358i
$974$	68.0359			2.18001
$975$	12.6575	−	37.9771i	0.405365	−	1.21624i
$976$	−2.54294	−	4.40451i	−0.0813977	−	0.140985i
$977$	−21.3076			−0.681692			−0.340846	−	0.940119i	$-0.610713\pi$
$977$	−21.3076			−0.681692			−0.340846	+	0.940119i	$0.610713\pi$
$978$	−26.8645	−	46.5307i	−0.859032	−	1.48789i
$979$	−0.615168	−	1.06550i	−0.0196609	−	0.0340536i
$980$	−4.55951	−	25.0482i	−0.145648	−	0.800134i
$981$	−21.1044	−	36.5538i	−0.673810	−	1.16707i
$982$	67.9819			2.16939
$983$	11.0158	+	19.0799i	0.351350	+	0.608556i	0.986486	−	0.163844i	$-0.0523895\pi$
$983$	11.0158	+	19.0799i	0.351350	+	0.608556i	−0.635136	+	0.772400i	$0.719056\pi$
$984$	−20.5393	+	35.5752i	−0.654770	+	1.13409i
$985$	0.722439	+	1.25130i	0.0230188	+	0.0398698i
$986$	30.5189	−	52.8603i	0.971919	−	1.68341i
$987$	−20.2441	+	24.2618i	−0.644376	+	0.772260i
$988$	50.0528	−	10.2444i	1.59239	−	0.325918i
$989$	−26.3529	+	45.6446i	−0.837975	+	1.45141i
$990$	6.30208			0.200293
$991$	−22.0259			−0.699676			−0.349838	−	0.936810i	$-0.613763\pi$
$991$	−22.0259			−0.699676			−0.349838	+	0.936810i	$0.613763\pi$
$992$	−7.85617			−0.249434
$993$	−74.9164			−2.37740
$994$	14.5825	−	17.4766i	0.462528	−	0.554323i
$995$	−4.61376	−	7.99127i	−0.146266	−	0.253340i
$996$	−14.6105	+	25.3061i	−0.462951	+	0.801855i
$997$	−5.04102	+	8.73130i	−0.159651	+	0.276523i	−0.934743	−	0.355325i	$-0.884370\pi$
$997$	−5.04102	+	8.73130i	−0.159651	+	0.276523i	0.775092	+	0.631848i	$0.217703\pi$
$998$	62.6450			1.98299
$999$	3.79408	+	6.57153i	0.120039	+	0.207914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.g.b.9.6	✓	12
3.2	odd	2		819.2.n.d.100.1		12
7.2	even	3		637.2.f.k.295.6		12
7.3	odd	6		637.2.h.l.165.1		12
7.4	even	3		91.2.h.b.74.1	yes	12
7.5	odd	6		637.2.f.j.295.6		12
7.6	odd	2		637.2.g.l.373.6		12
13.3	even	3		91.2.h.b.16.1	yes	12
13.4	even	6		1183.2.e.g.170.1		12
13.9	even	3		1183.2.e.h.170.6		12
21.11	odd	6		819.2.s.d.802.6		12
39.29	odd	6		819.2.s.d.289.6		12
91.3	odd	6		637.2.g.l.263.6		12
91.4	even	6		1183.2.e.g.508.1		12
91.9	even	3		8281.2.a.bz.1.1		6
91.16	even	3		637.2.f.k.393.6		12
91.30	even	6		8281.2.a.ce.1.6		6
91.55	odd	6		637.2.h.l.471.1		12
91.61	odd	6		8281.2.a.ca.1.1		6
91.68	odd	6		637.2.f.j.393.6		12
91.74	even	3		1183.2.e.h.508.6		12
91.81	even	3	inner	91.2.g.b.81.6	yes	12
91.82	odd	6		8281.2.a.cf.1.6		6
273.263	odd	6		819.2.n.d.172.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.6	✓	12	1.1	even	1	trivial
91.2.g.b.81.6	yes	12	91.81	even	3	inner
91.2.h.b.16.1	yes	12	13.3	even	3
91.2.h.b.74.1	yes	12	7.4	even	3
637.2.f.j.295.6		12	7.5	odd	6
637.2.f.j.393.6		12	91.68	odd	6
637.2.f.k.295.6		12	7.2	even	3
637.2.f.k.393.6		12	91.16	even	3
637.2.g.l.263.6		12	91.3	odd	6
637.2.g.l.373.6		12	7.6	odd	2
637.2.h.l.165.1		12	7.3	odd	6
637.2.h.l.471.1		12	91.55	odd	6
819.2.n.d.100.1		12	3.2	odd	2
819.2.n.d.172.1		12	273.263	odd	6
819.2.s.d.289.6		12	39.29	odd	6
819.2.s.d.802.6		12	21.11	odd	6
1183.2.e.g.170.1		12	13.4	even	6
1183.2.e.g.508.1		12	91.4	even	6
1183.2.e.h.170.6		12	13.9	even	3
1183.2.e.h.508.6		12	91.74	even	3
8281.2.a.bz.1.1		6	91.9	even	3
8281.2.a.ca.1.1		6	91.61	odd	6
8281.2.a.ce.1.6		6	91.30	even	6
8281.2.a.cf.1.6		6	91.82	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19402 + 2.06810i) q^{2} -2.75148 q^{3} +(-1.85136 + 3.20665i) q^{4} +(-0.491140 + 0.850679i) q^{5} +(-3.28532 - 5.69033i) q^{6} +(2.60682 + 0.452230i) q^{7} -4.06616 q^{8} +4.57063 q^{9} +O(q^{10})\)	\(q+(1.19402 + 2.06810i) q^{2} -2.75148 q^{3} +(-1.85136 + 3.20665i) q^{4} +(-0.491140 + 0.850679i) q^{5} +(-3.28532 - 5.69033i) q^{6} +(2.60682 + 0.452230i) q^{7} -4.06616 q^{8} +4.57063 q^{9} -2.34572 q^{10} -0.587802 q^{11} +(5.09398 - 8.82303i) q^{12} +(2.39227 + 2.69760i) q^{13} +(2.17733 + 5.93113i) q^{14} +(1.35136 - 2.34063i) q^{15} +(-1.15235 - 1.99593i) q^{16} +(3.22710 - 5.58950i) q^{17} +(5.45742 + 9.45253i) q^{18} -3.82689 q^{19} +(-1.81855 - 3.14983i) q^{20} +(-7.17260 - 1.24430i) q^{21} +(-0.701847 - 1.21563i) q^{22} +(-4.13001 - 7.15338i) q^{23} +11.1880 q^{24} +(2.01756 + 3.49452i) q^{25} +(-2.72249 + 8.16844i) q^{26} -4.32156 q^{27} +(-6.27630 + 7.52191i) q^{28} +(1.98009 - 3.42962i) q^{29} +6.45420 q^{30} +(1.49436 + 2.58831i) q^{31} +(-1.31430 + 2.27644i) q^{32} +1.61733 q^{33} +15.4129 q^{34} +(-1.66501 + 1.99546i) q^{35} +(-8.46189 + 14.6564i) q^{36} +(-0.877941 - 1.52064i) q^{37} +(-4.56938 - 7.91440i) q^{38} +(-6.58228 - 7.42239i) q^{39} +(1.99705 - 3.45900i) q^{40} +(-1.83584 + 3.17977i) q^{41} +(-5.99088 - 16.3194i) q^{42} +(-3.19042 - 5.52598i) q^{43} +(1.08823 - 1.88488i) q^{44} +(-2.24482 + 3.88814i) q^{45} +(9.86261 - 17.0825i) q^{46} +(2.17030 - 3.75906i) q^{47} +(3.17067 + 5.49176i) q^{48} +(6.59098 + 2.35776i) q^{49} +(-4.81802 + 8.34505i) q^{50} +(-8.87930 + 15.3794i) q^{51} +(-13.0792 + 2.67695i) q^{52} +(-0.212770 - 0.368529i) q^{53} +(-5.16002 - 8.93742i) q^{54} +(0.288693 - 0.500031i) q^{55} +(-10.5997 - 1.83884i) q^{56} +10.5296 q^{57} +9.45706 q^{58} +(-3.00431 + 5.20362i) q^{59} +(5.00371 + 8.66669i) q^{60} +2.20674 q^{61} +(-3.56859 + 6.18097i) q^{62} +(11.9148 + 2.06698i) q^{63} -10.8866 q^{64} +(-3.46973 + 0.710156i) q^{65} +(1.93112 + 3.34479i) q^{66} +7.01303 q^{67} +(11.9491 + 20.6964i) q^{68} +(11.3636 + 19.6824i) q^{69} +(-6.11486 - 1.06080i) q^{70} +(-1.80127 - 3.11988i) q^{71} -18.5849 q^{72} +(-2.46714 - 4.27321i) q^{73} +(2.09656 - 3.63134i) q^{74} +(-5.55128 - 9.61510i) q^{75} +(7.08496 - 12.2715i) q^{76} +(-1.53229 - 0.265822i) q^{77} +(7.49088 - 22.4753i) q^{78} +(-1.39270 + 2.41223i) q^{79} +2.26386 q^{80} -1.82122 q^{81} -8.76812 q^{82} -2.86819 q^{83} +(17.2691 - 20.6964i) q^{84} +(3.16992 + 5.49045i) q^{85} +(7.61885 - 13.1962i) q^{86} +(-5.44818 + 9.43652i) q^{87} +2.39010 q^{88} +(1.04656 + 1.81269i) q^{89} -10.7214 q^{90} +(5.01627 + 8.11400i) q^{91} +30.5845 q^{92} +(-4.11170 - 7.12167i) q^{93} +10.3655 q^{94} +(1.87954 - 3.25546i) q^{95} +(3.61628 - 6.26357i) q^{96} +(-3.84852 - 6.66584i) q^{97} +(2.99367 + 16.4460i) q^{98} -2.68663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9} - 8 q^{10} - 8 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} + 8 q^{16} + 5 q^{17} + 3 q^{18} + 2 q^{19} - q^{20} - 9 q^{21} - 5 q^{22} - q^{23} + 22 q^{24} + 7 q^{25} + 5 q^{26} - 8 q^{27} - 7 q^{28} + 3 q^{29} + 10 q^{30} + 16 q^{31} + 8 q^{32} - 32 q^{33} + 32 q^{34} + 8 q^{35} - 21 q^{36} - 13 q^{37} - 17 q^{38} - 23 q^{39} - 5 q^{40} - 8 q^{41} + 2 q^{42} - 11 q^{43} + 21 q^{44} - 7 q^{45} + 16 q^{46} - q^{47} + 21 q^{48} - 3 q^{49} + 6 q^{50} - 20 q^{51} - 25 q^{52} - 2 q^{53} - 18 q^{54} + 9 q^{55} - 18 q^{56} + 42 q^{57} + 16 q^{58} + 13 q^{59} + 20 q^{60} + 10 q^{61} + 5 q^{62} + 32 q^{63} - 30 q^{64} + 19 q^{65} + 18 q^{66} + 22 q^{67} + 29 q^{68} + 23 q^{69} - 39 q^{70} + 6 q^{71} - 50 q^{72} - 30 q^{73} - 3 q^{74} - 3 q^{75} - 9 q^{76} + 11 q^{77} + 16 q^{78} + 7 q^{79} + 14 q^{80} + 12 q^{81} - 2 q^{82} - 54 q^{83} + 5 q^{84} - q^{85} - 7 q^{86} + 16 q^{87} + 4 q^{89} - 16 q^{90} - 20 q^{91} + 54 q^{92} - 7 q^{93} - 90 q^{94} - 6 q^{95} + 19 q^{96} - 35 q^{97} + 62 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9 - 8 * q^10 - 8 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 + 8 * q^16 + 5 * q^17 + 3 * q^18 + 2 * q^19 - q^20 - 9 * q^21 - 5 * q^22 - q^23 + 22 * q^24 + 7 * q^25 + 5 * q^26 - 8 * q^27 - 7 * q^28 + 3 * q^29 + 10 * q^30 + 16 * q^31 + 8 * q^32 - 32 * q^33 + 32 * q^34 + 8 * q^35 - 21 * q^36 - 13 * q^37 - 17 * q^38 - 23 * q^39 - 5 * q^40 - 8 * q^41 + 2 * q^42 - 11 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 - 25 * q^52 - 2 * q^53 - 18 * q^54 + 9 * q^55 - 18 * q^56 + 42 * q^57 + 16 * q^58 + 13 * q^59 + 20 * q^60 + 10 * q^61 + 5 * q^62 + 32 * q^63 - 30 * q^64 + 19 * q^65 + 18 * q^66 + 22 * q^67 + 29 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 - 50 * q^72 - 30 * q^73 - 3 * q^74 - 3 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 + 14 * q^80 + 12 * q^81 - 2 * q^82 - 54 * q^83 + 5 * q^84 - q^85 - 7 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 - 20 * q^91 + 54 * q^92 - 7 * q^93 - 90 * q^94 - 6 * q^95 + 19 * q^96 - 35 * q^97 + 62 * q^98 - 20 * q^99

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