LMFDB - Embedded newform 91.2.f.c.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(22,91)]

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([0, 4]))

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

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

chi := DirichletCharacter("91.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.f (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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			29.1
Root			$-1.11000 - 1.92258i$ of defining polynomial
Character	$\chi$	$=$	91.29
Dual form			91.2.f.c.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11000 - 1.92258i) q^{2} +(-0.274776 - 0.475925i) q^{3} +(-1.46422 + 2.53610i) q^{4} -4.22001 q^{5} +(-0.610004 + 1.05656i) q^{6} +(0.500000 - 0.866025i) q^{7} +2.06113 q^{8} +(1.34900 - 2.33653i) q^{9} +O(q^{10})$	\(q+(-1.11000 - 1.92258i) q^{2} +(-0.274776 - 0.475925i) q^{3} +(-1.46422 + 2.53610i) q^{4} -4.22001 q^{5} +(-0.610004 + 1.05656i) q^{6} +(0.500000 - 0.866025i) q^{7} +2.06113 q^{8} +(1.34900 - 2.33653i) q^{9} +(4.68423 + 8.11332i) q^{10} +(0.274776 + 0.475925i) q^{11} +1.60932 q^{12} +(-2.95900 - 2.06017i) q^{13} -2.22001 q^{14} +(1.15956 + 2.00841i) q^{15} +(0.640570 + 1.10950i) q^{16} +(1.18944 - 2.06017i) q^{17} -5.98957 q^{18} +(1.80534 - 3.12694i) q^{19} +(6.17901 - 10.7024i) q^{20} -0.549551 q^{21} +(0.610004 - 1.05656i) q^{22} +(-2.90945 - 5.03931i) q^{23} +(-0.566349 - 0.980945i) q^{24} +12.8085 q^{25} +(-0.676353 + 7.97573i) q^{26} -3.13134 q^{27} +(1.46422 + 2.53610i) q^{28} +(1.79945 + 3.11673i) q^{29} +(2.57422 - 4.45868i) q^{30} -5.14844 q^{31} +(3.48320 - 6.03308i) q^{32} +(0.151003 - 0.261545i) q^{33} -5.28114 q^{34} +(-2.11000 + 3.65463i) q^{35} +(3.95045 + 6.84238i) q^{36} +(0.164772 + 0.285393i) q^{37} -8.01574 q^{38} +(-0.167428 + 1.97435i) q^{39} -8.69799 q^{40} +(3.14579 + 5.44866i) q^{41} +(0.610004 + 1.05656i) q^{42} +(-1.61000 + 2.78861i) q^{43} -1.60932 q^{44} +(-5.69278 + 9.86018i) q^{45} +(-6.45900 + 11.1873i) q^{46} +8.20957 q^{47} +(0.352026 - 0.609727i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-14.2174 - 24.6253i) q^{50} -1.30732 q^{51} +(9.55742 - 4.48778i) q^{52} +2.65866 q^{53} +(3.47580 + 6.02026i) q^{54} +(-1.15956 - 2.00841i) q^{55} +(1.03057 - 1.78499i) q^{56} -1.98426 q^{57} +(3.99478 - 6.91917i) q^{58} +(0.903765 - 1.56537i) q^{59} -6.79136 q^{60} +(-0.304662 + 0.527691i) q^{61} +(5.71479 + 9.89831i) q^{62} +(-1.34900 - 2.33653i) q^{63} -12.9032 q^{64} +(12.4870 + 8.69395i) q^{65} -0.670457 q^{66} +(-5.18490 - 8.98052i) q^{67} +(3.48320 + 6.03308i) q^{68} +(-1.59889 + 2.76936i) q^{69} +9.36845 q^{70} +(5.59889 - 9.69756i) q^{71} +(2.78046 - 4.81590i) q^{72} +4.90621 q^{73} +(0.365794 - 0.633574i) q^{74} +(-3.51945 - 6.09587i) q^{75} +(5.28682 + 9.15705i) q^{76} +0.549551 q^{77} +(3.98169 - 1.86964i) q^{78} -14.0171 q^{79} +(-2.70321 - 4.68210i) q^{80} +(-3.18657 - 5.51931i) q^{81} +(6.98367 - 12.0961i) q^{82} -5.73159 q^{83} +(0.804662 - 1.39372i) q^{84} +(-5.01945 + 8.69395i) q^{85} +7.14844 q^{86} +(0.988887 - 1.71280i) q^{87} +(0.566349 + 0.980945i) q^{88} +(3.73378 + 6.46709i) q^{89} +25.2760 q^{90} +(-3.26366 + 1.53248i) q^{91} +17.0403 q^{92} +(1.41467 + 2.45027i) q^{93} +(-9.11266 - 15.7836i) q^{94} +(-7.61856 + 13.1957i) q^{95} -3.82840 q^{96} +(3.42035 - 5.92422i) q^{97} +(-1.11000 + 1.92258i) q^{98} +1.48269 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9	\( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 3 q^{15} - 19 q^{16} + 4 q^{17} - 6 q^{18} - q^{19} + 2 q^{20} - 2 q^{21} - 5 q^{22} + 2 q^{23} + 3 q^{24} + 10 q^{25} + 12 q^{26} - 52 q^{27} + 5 q^{28} - q^{29} + 4 q^{30} - 8 q^{31} + 33 q^{32} + 19 q^{33} + 6 q^{34} - 7 q^{35} + 34 q^{36} + 10 q^{37} - 46 q^{38} + 20 q^{39} - 34 q^{40} + 22 q^{41} - 5 q^{42} - 3 q^{43} - 24 q^{44} + 11 q^{45} - 24 q^{46} + 4 q^{47} - 11 q^{48} - 4 q^{49} - 43 q^{50} + 14 q^{51} + 65 q^{52} + 4 q^{53} - 5 q^{54} + 3 q^{55} - 6 q^{56} - 34 q^{57} + 11 q^{58} + 8 q^{59} - 22 q^{60} - 8 q^{61} + 5 q^{62} + 7 q^{63} + 28 q^{64} + 7 q^{65} + 12 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 22 q^{70} + 14 q^{71} - 5 q^{72} - 16 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} + 2 q^{77} - q^{78} - 52 q^{79} - 7 q^{80} - 24 q^{81} + 14 q^{82} + 12 q^{84} - 5 q^{85} + 24 q^{86} - 13 q^{87} - 3 q^{88} + q^{89} + 52 q^{90} - 4 q^{91} + 24 q^{92} + 7 q^{93} - 33 q^{94} - 21 q^{95} - 116 q^{96} - 3 q^{97} + q^{98} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9 + 11 * q^10 + q^11 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 3 * q^15 - 19 * q^16 + 4 * q^17 - 6 * q^18 - q^19 + 2 * q^20 - 2 * q^21 - 5 * q^22 + 2 * q^23 + 3 * q^24 + 10 * q^25 + 12 * q^26 - 52 * q^27 + 5 * q^28 - q^29 + 4 * q^30 - 8 * q^31 + 33 * q^32 + 19 * q^33 + 6 * q^34 - 7 * q^35 + 34 * q^36 + 10 * q^37 - 46 * q^38 + 20 * q^39 - 34 * q^40 + 22 * q^41 - 5 * q^42 - 3 * q^43 - 24 * q^44 + 11 * q^45 - 24 * q^46 + 4 * q^47 - 11 * q^48 - 4 * q^49 - 43 * q^50 + 14 * q^51 + 65 * q^52 + 4 * q^53 - 5 * q^54 + 3 * q^55 - 6 * q^56 - 34 * q^57 + 11 * q^58 + 8 * q^59 - 22 * q^60 - 8 * q^61 + 5 * q^62 + 7 * q^63 + 28 * q^64 + 7 * q^65 + 12 * q^66 + 6 * q^67 + 33 * q^68 + 18 * q^69 + 22 * q^70 + 14 * q^71 - 5 * q^72 - 16 * q^73 - 20 * q^74 + 7 * q^75 - 32 * q^76 + 2 * q^77 - q^78 - 52 * q^79 - 7 * q^80 - 24 * q^81 + 14 * q^82 + 12 * q^84 - 5 * q^85 + 24 * q^86 - 13 * q^87 - 3 * q^88 + q^89 + 52 * q^90 - 4 * q^91 + 24 * q^92 + 7 * q^93 - 33 * q^94 - 21 * q^95 - 116 * q^96 - 3 * q^97 + q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.11000	−	1.92258i	−0.784891	−	1.35947i	−0.929064	−	0.369919i	$-0.879385\pi$
$2$	−1.11000	−	1.92258i	−0.784891	−	1.35947i	0.144173	−	0.989553i	$-0.453948\pi$
$3$	−0.274776	−	0.475925i	−0.158642	−	0.274776i	0.775737	−	0.631056i	$-0.217378\pi$
$3$	−0.274776	−	0.475925i	−0.158642	−	0.274776i	−0.934379	+	0.356280i	$0.884045\pi$
$4$	−1.46422	+	2.53610i	−0.732109	+	1.26805i
$5$	−4.22001			−1.88724			−0.943622	−	0.331024i	$-0.892606\pi$
$5$	−4.22001			−1.88724			−0.943622	+	0.331024i	$0.892606\pi$
$6$	−0.610004	+	1.05656i	−0.249033	+	0.431338i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	2.06113			0.728720
$9$	1.34900	−	2.33653i	0.449666	−	0.778844i
$10$	4.68423	+	8.11332i	1.48128	+	2.56566i
$11$	0.274776	+	0.475925i	0.0828480	+	0.143497i	0.904472	−	0.426533i	$-0.140265\pi$
$11$	0.274776	+	0.475925i	0.0828480	+	0.143497i	−0.821624	+	0.570030i	$0.806932\pi$
$12$	1.60932			0.464572
$13$	−2.95900	−	2.06017i	−0.820679	−	0.571389i
$13$	−2.95900	−	2.06017i	−0.820679	−	0.571389i
$14$	−2.22001			−0.593322
$15$	1.15956	+	2.00841i	0.299396	+	0.518569i
$16$	0.640570	+	1.10950i	0.160142	+	0.277375i
$17$	1.18944	−	2.06017i	0.288482	−	0.499665i	−0.684966	−	0.728575i	$-0.740183\pi$
$17$	1.18944	−	2.06017i	0.288482	−	0.499665i	0.973448	+	0.228910i	$0.0735161\pi$
$18$	−5.98957			−1.41175
$19$	1.80534	−	3.12694i	0.414174	−	0.717370i	−0.581168	−	0.813784i	$-0.697404\pi$
$19$	1.80534	−	3.12694i	0.414174	−	0.717370i	0.995341	+	0.0964139i	$0.0307372\pi$
$20$	6.17901	−	10.7024i	1.38167	−	2.39312i
$21$	−0.549551			−0.119922
$22$	0.610004	−	1.05656i	0.130053	−	0.225259i
$23$	−2.90945	−	5.03931i	−0.606662	−	1.05077i	−0.991786	−	0.127905i	$-0.959175\pi$
$23$	−2.90945	−	5.03931i	−0.606662	−	1.05077i	0.385124	−	0.922865i	$-0.374159\pi$
$24$	−0.566349	−	0.980945i	−0.115605	−	0.200235i
$25$	12.8085			2.56169
$26$	−0.676353	+	7.97573i	−0.132644	+	1.56417i
$27$	−3.13134			−0.602626
$28$	1.46422	+	2.53610i	0.276711	+	0.479278i
$29$	1.79945	+	3.11673i	0.334149	+	0.578762i	0.983321	−	0.181879i	$-0.0582179\pi$
$29$	1.79945	+	3.11673i	0.334149	+	0.578762i	−0.649172	+	0.760641i	$0.724885\pi$
$30$	2.57422	−	4.45868i	0.469986	−	0.814040i
$31$	−5.14844			−0.924688			−0.462344	−	0.886701i	$-0.652991\pi$
$31$	−5.14844			−0.924688			−0.462344	+	0.886701i	$0.652991\pi$
$32$	3.48320	−	6.03308i	0.615749	−	1.06651i
$33$	0.151003	−	0.261545i	0.0262863	−	0.0455292i
$34$	−5.28114			−0.905708
$35$	−2.11000	+	3.65463i	−0.356656	+	0.617746i
$36$	3.95045	+	6.84238i	0.658408	+	1.14040i
$37$	0.164772	+	0.285393i	0.0270883	+	0.0469183i	0.879252	−	0.476357i	$-0.158043\pi$
$37$	0.164772	+	0.285393i	0.0270883	+	0.0469183i	−0.852163	+	0.523276i	$0.824710\pi$
$38$	−8.01574			−1.30033
$39$	−0.167428	+	1.97435i	−0.0268099	+	0.316149i
$40$	−8.69799			−1.37527
$41$	3.14579	+	5.44866i	0.491289	+	0.850938i	0.999950	−	0.0100292i	$-0.00319244\pi$
$41$	3.14579	+	5.44866i	0.491289	+	0.850938i	−0.508660	+	0.860967i	$0.669859\pi$
$42$	0.610004	+	1.05656i	0.0941256	+	0.163030i
$43$	−1.61000	+	2.78861i	−0.245523	+	0.425259i	−0.962279	−	0.272066i	$-0.912293\pi$
$43$	−1.61000	+	2.78861i	−0.245523	+	0.425259i	0.716755	+	0.697325i	$0.245626\pi$
$44$	−1.60932			−0.242615
$45$	−5.69278	+	9.86018i	−0.848629	+	1.46987i
$46$	−6.45900	+	11.1873i	−0.952328	+	1.64948i
$47$	8.20957			1.19749			0.598745	−	0.800940i	$-0.295666\pi$
$47$	8.20957			1.19749			0.598745	+	0.800940i	$0.295666\pi$
$48$	0.352026	−	0.609727i	0.0508106	−	0.0880065i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−14.2174	−	24.6253i	−2.01065	−	3.48255i
$51$	−1.30732			−0.183061
$52$	9.55742	−	4.48778i	1.32538	−	0.622343i
$53$	2.65866			0.365196			0.182598	−	0.983188i	$-0.441549\pi$
$53$	2.65866			0.365196			0.182598	+	0.983188i	$0.441549\pi$
$54$	3.47580	+	6.02026i	0.472996	+	0.819254i
$55$	−1.15956	−	2.00841i	−0.156354	−	0.270814i
$56$	1.03057	−	1.78499i	0.137715	−	0.238530i
$57$	−1.98426			−0.262821
$58$	3.99478	−	6.91917i	0.524541	−	0.908531i
$59$	0.903765	−	1.56537i	0.117660	−	0.203793i	−0.801180	−	0.598424i	$-0.795794\pi$
$59$	0.903765	−	1.56537i	0.117660	−	0.203793i	0.918840	+	0.394630i	$0.129127\pi$
$60$	−6.79136			−0.876761
$61$	−0.304662	+	0.527691i	−0.0390080	+	0.0675639i	−0.884870	−	0.465838i	$-0.845753\pi$
$61$	−0.304662	+	0.527691i	−0.0390080	+	0.0675639i	0.845862	+	0.533401i	$0.179086\pi$
$62$	5.71479	+	9.89831i	0.725779	+	1.25709i
$63$	−1.34900	−	2.33653i	−0.169958	−	0.294375i
$64$	−12.9032			−1.61290
$65$	12.4870	+	8.69395i	1.54882	+	1.07835i
$66$	−0.670457			−0.0825275
$67$	−5.18490	−	8.98052i	−0.633437	−	1.09714i	−0.986844	−	0.161675i	$-0.948310\pi$
$67$	−5.18490	−	8.98052i	−0.633437	−	1.09714i	0.353407	−	0.935470i	$-0.385023\pi$
$68$	3.48320	+	6.03308i	0.422400	+	0.731619i
$69$	−1.59889	+	2.76936i	−0.192484	+	0.333392i
$70$	9.36845			1.11974
$71$	5.59889	−	9.69756i	0.664466	−	1.15089i	−0.314964	−	0.949104i	$-0.601992\pi$
$71$	5.59889	−	9.69756i	0.664466	−	1.15089i	0.979430	−	0.201785i	$-0.0646743\pi$
$72$	2.78046	−	4.81590i	0.327680	−	0.567559i
$73$	4.90621			0.574228			0.287114	−	0.957896i	$-0.407304\pi$
$73$	4.90621			0.574228			0.287114	+	0.957896i	$0.407304\pi$
$74$	0.365794	−	0.633574i	0.0425227	−	0.0736515i
$75$	−3.51945	−	6.09587i	−0.406391	−	0.703891i
$76$	5.28682	+	9.15705i	0.606440	+	1.05039i
$77$	0.549551			0.0626272
$78$	3.98169	−	1.86964i	0.450838	−	0.211695i
$79$	−14.0171			−1.57705			−0.788524	−	0.615004i	$-0.789154\pi$
$79$	−14.0171			−1.57705			−0.788524	+	0.615004i	$0.789154\pi$
$80$	−2.70321	−	4.68210i	−0.302228	−	0.523474i
$81$	−3.18657	−	5.51931i	−0.354064	−	0.613257i
$82$	6.98367	−	12.0961i	0.771217	−	1.33579i
$83$	−5.73159			−0.629124			−0.314562	−	0.949237i	$-0.601858\pi$
$83$	−5.73159			−0.629124			−0.314562	+	0.949237i	$0.601858\pi$
$84$	0.804662	−	1.39372i	0.0877959	−	0.152067i
$85$	−5.01945	+	8.69395i	−0.544436	+	0.942991i
$86$	7.14844			0.770836
$87$	0.988887	−	1.71280i	0.106020	−	0.183632i
$88$	0.566349	+	0.980945i	0.0603730	+	0.104569i
$89$	3.73378	+	6.46709i	0.395779	+	0.685510i	0.993200	−	0.116418i	$-0.0371411\pi$
$89$	3.73378	+	6.46709i	0.395779	+	0.685510i	−0.597421	+	0.801928i	$0.703808\pi$
$90$	25.2760			2.66433
$91$	−3.26366	+	1.53248i	−0.342125	+	0.160648i
$92$	17.0403			1.77657
$93$	1.41467	+	2.45027i	0.146694	+	0.254082i
$94$	−9.11266	−	15.7836i	−0.939899	−	1.62795i
$95$	−7.61856	+	13.1957i	−0.781647	+	1.35385i
$96$	−3.82840			−0.390734
$97$	3.42035	−	5.92422i	0.347284	−	0.601514i	−0.638482	−	0.769637i	$-0.720437\pi$
$97$	3.42035	−	5.92422i	0.347284	−	0.601514i	0.985766	+	0.168123i	$0.0537706\pi$
$98$	−1.11000	+	1.92258i	−0.112127	+	0.194210i
$99$	1.48269			0.149015
$100$	−18.7544	+	32.4835i	−1.87544	+	3.24835i
$101$	−2.87956	−	4.98755i	−0.286527	−	0.496280i	0.686451	−	0.727176i	$-0.259168\pi$
$101$	−2.87956	−	4.98755i	−0.286527	−	0.496280i	−0.972978	+	0.230896i	$0.925834\pi$
$102$	1.45113	+	2.51343i	0.143683	+	0.248866i
$103$	0.571776			0.0563388			0.0281694	−	0.999603i	$-0.491032\pi$
$103$	0.571776			0.0563388			0.0281694	+	0.999603i	$0.491032\pi$
$104$	−6.09889	−	4.24629i	−0.598045	−	0.416383i
$105$	2.31911			0.226322
$106$	−2.95113	−	5.11150i	−0.286639	−	0.496473i
$107$	−2.03578	−	3.52608i	−0.196807	−	0.340879i	0.750685	−	0.660661i	$-0.229724\pi$
$107$	−2.03578	−	3.52608i	−0.196807	−	0.340879i	−0.947491	+	0.319782i	$0.896390\pi$
$108$	4.58496	−	7.94138i	0.441188	−	0.764160i
$109$	15.3087			1.46631			0.733153	−	0.680064i	$-0.238048\pi$
$109$	15.3087			1.46631			0.733153	+	0.680064i	$0.238048\pi$
$110$	−2.57422	+	4.45868i	−0.245442	+	0.425119i
$111$	0.0905505	−	0.156838i	0.00859467	−	0.0148864i
$112$	1.28114			0.121056
$113$	−6.08846	+	10.5455i	−0.572754	+	0.992039i	0.423528	+	0.905883i	$0.360792\pi$
$113$	−6.08846	+	10.5455i	−0.572754	+	0.992039i	−0.996282	+	0.0861558i	$0.972542\pi$
$114$	2.20253	+	3.81490i	0.206286	+	0.357298i
$115$	12.2779	+	21.2659i	1.14492	+	1.98306i
$116$	−10.5391			−0.978533
$117$	−8.80534	+	4.13463i	−0.814054	+	0.382247i
$118$	−4.01273			−0.369402
$119$	−1.18944	−	2.06017i	−0.109036	−	0.188856i
$120$	2.39000	+	4.13959i	0.218176	+	0.377892i
$121$	5.34900	−	9.26473i	0.486272	−	0.842249i
$122$	1.35271			0.122468
$123$	1.72877	−	2.99432i	0.155878	−	0.269989i
$124$	7.53844	−	13.0570i	0.676972	−	1.17255i
$125$	−32.9518			−2.94730
$126$	−2.99478	+	5.18712i	−0.266797	+	0.462105i
$127$	−0.980336	−	1.69799i	−0.0869907	−	0.150672i	0.819247	−	0.573441i	$-0.194392\pi$
$127$	−0.980336	−	1.69799i	−0.0869907	−	0.150672i	−0.906238	+	0.422768i	$0.861058\pi$
$128$	7.35619	+	12.7413i	0.650201	+	1.12618i
$129$	1.76956			0.155801
$130$	2.85421	−	33.6576i	0.250331	−	2.95197i
$131$	−6.50021			−0.567926			−0.283963	−	0.958835i	$-0.591649\pi$
$131$	−6.50021			−0.567926			−0.283963	+	0.958835i	$0.591649\pi$
$132$	0.442203	+	0.765918i	0.0384888	+	0.0666646i
$133$	−1.80534	−	3.12694i	−0.156543	−	0.271140i
$134$	−11.5105	+	19.9368i	−0.994358	+	1.72228i
$135$	13.2143			1.13730
$136$	2.45160	−	4.24629i	0.210223	−	0.364116i
$137$	7.62878	−	13.2134i	0.651770	−	1.12890i	−0.330923	−	0.943658i	$-0.607360\pi$
$137$	7.62878	−	13.2134i	0.651770	−	1.12890i	0.982693	−	0.185242i	$-0.0593068\pi$
$138$	7.09910			0.604316
$139$	8.74801	−	15.1520i	0.741997	−	1.28518i	−0.209588	−	0.977790i	$-0.567212\pi$
$139$	8.74801	−	15.1520i	0.741997	−	1.28518i	0.951585	−	0.307386i	$-0.0994544\pi$
$140$	−6.17901	−	10.7024i	−0.522222	−	0.904514i
$141$	−2.25579	−	3.90714i	−0.189972	−	0.329041i
$142$	−24.8592			−2.08613
$143$	0.167428	−	1.97435i	0.0140010	−	0.165103i
$144$	3.45651			0.288042
$145$	−7.59367	−	13.1526i	−0.630620	−	1.09227i
$146$	−5.44591	−	9.43260i	−0.450707	−	0.780647i
$147$	−0.274776	+	0.475925i	−0.0226631	+	0.0392537i
$148$	−0.965046			−0.0793263
$149$	−2.27743	+	3.94463i	−0.186574	+	0.323156i	−0.944106	−	0.329642i	$-0.893072\pi$
$149$	−2.27743	+	3.94463i	−0.186574	+	0.323156i	0.757531	+	0.652799i	$0.226405\pi$
$150$	−7.81321	+	13.5329i	−0.637946	+	1.10496i
$151$	−6.32912			−0.515057			−0.257528	−	0.966271i	$-0.582908\pi$
$151$	−6.32912			−0.515057			−0.257528	+	0.966271i	$0.582908\pi$
$152$	3.72105	−	6.44504i	0.301817	−	0.522762i
$153$	−3.20911	−	5.55833i	−0.259441	−	0.449365i
$154$	−0.610004	−	1.05656i	−0.0491555	−	0.0851398i
$155$	21.7265			1.74511
$156$	−4.76199	−	3.31549i	−0.381265	−	0.265451i
$157$	16.3100			1.30168			0.650841	−	0.759214i	$-0.274416\pi$
$157$	16.3100			1.30168			0.650841	+	0.759214i	$0.274416\pi$
$158$	15.5590	+	26.9490i	1.23781	+	2.14395i
$159$	−0.730536	−	1.26533i	−0.0579353	−	0.100347i
$160$	−14.6991	+	25.4597i	−1.16207	+	2.01276i
$161$	−5.81890			−0.458593
$162$	−7.07422	+	12.2529i	−0.555803	+	0.962680i
$163$	−11.7999	+	20.4381i	−0.924241	+	1.60083i	−0.131463	+	0.991321i	$0.541967\pi$
$163$	−11.7999	+	20.4381i	−0.924241	+	1.60083i	−0.792778	+	0.609511i	$0.791366\pi$
$164$	−18.4245			−1.43871
$165$	−0.637235	+	1.10372i	−0.0496087	+	0.0859247i
$166$	6.36209	+	11.0195i	0.493794	+	0.855276i
$167$	8.91513	+	15.4415i	0.689874	+	1.19490i	0.971878	+	0.235483i	$0.0756673\pi$
$167$	8.91513	+	15.4415i	0.689874	+	1.19490i	−0.282005	+	0.959413i	$0.590999\pi$
$168$	−1.13270			−0.0873895
$169$	4.51137	+	12.1921i	0.347028	+	0.937855i
$170$	22.2865			1.70929
$171$	−4.87080	−	8.43647i	−0.372479	−	0.645153i
$172$	−4.71479	−	8.16626i	−0.359499	−	0.622671i
$173$	3.78568	−	6.55699i	0.287820	−	0.498518i	−0.685469	−	0.728101i	$-0.740403\pi$
$173$	3.78568	−	6.55699i	0.287820	−	0.498518i	0.973289	+	0.229583i	$0.0737363\pi$
$174$	−4.39068			−0.332856
$175$	6.40423	−	11.0925i	0.484115	−	0.838511i
$176$	−0.352026	+	0.609727i	−0.0265350	+	0.0459599i
$177$	−0.993330			−0.0746632
$178$	8.28901	−	14.3570i	0.621288	−	1.07610i
$179$	11.4017	+	19.7483i	0.852201	+	1.47606i	0.879218	+	0.476420i	$0.158066\pi$
$179$	11.4017	+	19.7483i	0.852201	+	1.47606i	−0.0270166	+	0.999635i	$0.508601\pi$
$180$	−16.6709	−	28.8749i	−1.24258	−	2.15221i
$181$	13.9294			1.03536			0.517681	−	0.855574i	$-0.326795\pi$
$181$	13.9294			1.03536			0.517681	+	0.855574i	$0.326795\pi$
$182$	6.56900	+	4.57360i	0.486927	+	0.339018i
$183$	0.334855			0.0247532
$184$	−5.99676	−	10.3867i	−0.442087	−	0.765717i
$185$	−0.695338	−	1.20436i	−0.0511222	−	0.0885463i
$186$	3.14057	−	5.43963i	0.230278	−	0.398853i
$187$	1.30732			0.0956006
$188$	−12.0206	+	20.8203i	−0.876692	+	1.51848i
$189$	−1.56567	+	2.71182i	−0.113886	+	0.197256i
$190$	33.8265			2.45403
$191$	6.33591	−	10.9741i	0.458450	−	0.794059i	−0.540429	−	0.841390i	$-0.681738\pi$
$191$	6.33591	−	10.9741i	0.458450	−	0.794059i	0.998879	+	0.0473305i	$0.0150714\pi$
$192$	3.54548	+	6.14096i	0.255873	+	0.443185i
$193$	2.07746	+	3.59827i	0.149539	+	0.259009i	0.931057	−	0.364873i	$-0.118888\pi$
$193$	2.07746	+	3.59827i	0.149539	+	0.259009i	−0.781518	+	0.623882i	$0.785554\pi$
$194$	−15.1864			−1.09032
$195$	0.706545	−	8.33177i	0.0505968	−	0.596650i
$196$	2.92843			0.209174
$197$	3.42510	+	5.93245i	0.244028	+	0.422669i	0.961858	−	0.273549i	$-0.0881977\pi$
$197$	3.42510	+	5.93245i	0.244028	+	0.422669i	−0.717830	+	0.696219i	$0.754864\pi$
$198$	−1.64579	−	2.85059i	−0.116961	−	0.202582i
$199$	0.406794	−	0.704587i	0.0288368	−	0.0499469i	−0.851247	−	0.524766i	$-0.824153\pi$
$199$	0.406794	−	0.704587i	0.0288368	−	0.0499469i	0.880084	+	0.474819i	$0.157486\pi$
$200$	26.3999			1.86676
$201$	−2.84937	+	4.93525i	−0.200979	+	0.348106i
$202$	−6.39265	+	11.0724i	−0.449785	+	0.779051i
$203$	3.59889			0.252593
$204$	1.91420	−	3.31549i	0.134021	−	0.232131i
$205$	−13.2752	−	22.9934i	−0.927183	−	1.60593i
$206$	−0.634674	−	1.09929i	−0.0442198	−	0.0765910i
$207$	−15.6994			−1.09118
$208$	0.390315	−	4.60270i	0.0270635	−	0.319140i
$209$	1.98426			0.137254
$210$	−2.57422	−	4.45868i	−0.177638	−	0.307678i
$211$	6.98670	+	12.1013i	0.480984	+	0.833089i	0.999762	−	0.0218200i	$-0.00694608\pi$
$211$	6.98670	+	12.1013i	0.480984	+	0.833089i	−0.518778	+	0.854909i	$0.673613\pi$
$212$	−3.89286	+	6.74264i	−0.267363	+	0.463086i
$213$	−6.15375			−0.421648
$214$	−4.51945	+	7.82792i	−0.308943	+	0.535106i
$215$	6.79423	−	11.7679i	0.463363	−	0.802568i
$216$	−6.45410			−0.439146
$217$	−2.57422	+	4.45868i	−0.174750	+	0.302675i
$218$	−16.9927	−	29.4322i	−1.15089	−	1.99340i
$219$	−1.34811	−	2.33499i	−0.0910966	−	0.157784i
$220$	6.79136			0.457874
$221$	−7.76387	+	3.64560i	−0.522255	+	0.245229i
$222$	−0.402045			−0.0269835
$223$	6.76700	+	11.7208i	0.453152	+	0.784882i	0.998580	−	0.0532758i	$-0.0169662\pi$
$223$	6.76700	+	11.7208i	0.453152	+	0.784882i	−0.545428	+	0.838158i	$0.683633\pi$
$224$	−3.48320	−	6.03308i	−0.232731	−	0.403102i
$225$	17.2786	−	29.9274i	1.15191	−	1.99516i
$226$	27.0328			1.79820
$227$	2.68376	−	4.64840i	0.178127	−	0.308525i	−0.763112	−	0.646266i	$-0.776329\pi$
$227$	2.68376	−	4.64840i	0.178127	−	0.308525i	0.941239	+	0.337741i	$0.109663\pi$
$228$	2.90538	−	5.03227i	0.192414	−	0.333270i
$229$	3.09910			0.204794			0.102397	−	0.994744i	$-0.467349\pi$
$229$	3.09910			0.204794			0.102397	+	0.994744i	$0.467349\pi$
$230$	27.2570	−	47.2106i	1.79728	−	3.11297i
$231$	−0.151003	−	0.261545i	−0.00993528	−	0.0172084i
$232$	3.70890	+	6.42399i	0.243501	+	0.421756i
$233$	−20.3712			−1.33456			−0.667280	−	0.744807i	$-0.732541\pi$
$233$	−20.3712			−1.33456			−0.667280	+	0.744807i	$0.732541\pi$
$234$	17.7231	+	12.3395i	1.15860	+	0.806661i
$235$	−34.6445			−2.25996
$236$	2.64662	+	4.58407i	0.172280	+	0.298398i
$237$	3.85156	+	6.67109i	0.250186	+	0.433334i
$238$	−2.64057	+	4.57360i	−0.171163	+	0.296463i
$239$	−1.29157			−0.0835449			−0.0417725	−	0.999127i	$-0.513300\pi$
$239$	−1.29157			−0.0835449			−0.0417725	+	0.999127i	$0.513300\pi$
$240$	−1.48555	+	2.57305i	−0.0958920	+	0.166090i
$241$	−1.06635	+	1.84697i	−0.0686896	+	0.118974i	−0.898325	−	0.439332i	$-0.855215\pi$
$241$	−1.06635	+	1.84697i	−0.0686896	+	0.118974i	0.829635	+	0.558306i	$0.188548\pi$
$242$	−23.7496			−1.52668
$243$	−6.44819	+	11.1686i	−0.413652	+	0.716466i
$244$	−0.892184	−	1.54531i	−0.0571162	−	0.0989282i
$245$	2.11000	+	3.65463i	0.134803	+	0.233486i
$246$	−7.67577			−0.489389
$247$	−11.7841	+	5.53331i	−0.749801	+	0.352076i
$248$	−10.6116			−0.673839
$249$	1.57490	+	2.72781i	0.0998053	+	0.172868i
$250$	36.5766	+	63.3525i	2.31331	+	4.00677i
$251$	15.3856	−	26.6486i	0.971128	−	1.68204i	0.278964	−	0.960302i	$-0.410009\pi$
$251$	15.3856	−	26.6486i	0.971128	−	1.68204i	0.692164	−	0.721741i	$-0.256658\pi$
$252$	7.90090			0.497710
$253$	1.59889	−	2.76936i	0.100521	−	0.174108i
$254$	−2.17635	+	3.76955i	−0.136557	+	0.236523i
$255$	5.51689			0.345481
$256$	3.42761	−	5.93679i	0.214225	−	0.371049i
$257$	0.736805	+	1.27618i	0.0459607	+	0.0796062i	0.888091	−	0.459669i	$-0.152032\pi$
$257$	0.736805	+	1.27618i	0.0459607	+	0.0796062i	−0.842130	+	0.539275i	$0.818698\pi$
$258$	−1.96422	−	3.40212i	−0.122287	−	0.211807i
$259$	0.329543			0.0204768
$260$	−40.3324	+	18.9385i	−2.50131	+	1.17451i
$261$	9.70979			0.601021
$262$	7.21526	+	12.4972i	0.445760	+	0.772079i
$263$	−3.33847	−	5.78240i	−0.205859	−	0.356558i	0.744547	−	0.667570i	$-0.232665\pi$
$263$	−3.33847	−	5.78240i	−0.205859	−	0.356558i	−0.950406	+	0.311012i	$0.899332\pi$
$264$	0.311238	−	0.539079i	0.0191553	−	0.0331780i
$265$	−11.2196			−0.689214
$266$	−4.00787	+	6.94184i	−0.245738	+	0.425631i
$267$	2.05190	−	3.55400i	0.125574	−	0.217501i
$268$	30.3673			1.85498
$269$	−3.78786	+	6.56077i	−0.230950	+	0.400017i	−0.958088	−	0.286474i	$-0.907517\pi$
$269$	−3.78786	+	6.56077i	−0.230950	+	0.400017i	0.727138	+	0.686492i	$0.240850\pi$
$270$	−14.6679	−	25.4055i	−0.892660	−	1.54613i
$271$	−10.2840	−	17.8124i	−0.624709	−	1.08203i	−0.988597	−	0.150585i	$-0.951884\pi$
$271$	−10.2840	−	17.8124i	−0.624709	−	1.08203i	0.363888	−	0.931443i	$-0.381449\pi$
$272$	3.04768			0.184793
$273$	1.62612	+	1.13217i	0.0984174	+	0.0685221i
$274$	−33.8719			−2.04628
$275$	3.51945	+	6.09587i	0.212231	+	0.367595i
$276$	−4.68225	−	8.10989i	−0.281838	−	0.488158i
$277$	−2.85271	+	4.94103i	−0.171402	+	0.296878i	−0.938910	−	0.344162i	$-0.888163\pi$
$277$	−2.85271	+	4.94103i	−0.171402	+	0.296878i	0.767508	+	0.641039i	$0.221497\pi$
$278$	−38.8413			−2.32955
$279$	−6.94523	+	12.0295i	−0.415800	+	0.720187i
$280$	−4.34900	+	7.53268i	−0.259902	+	0.450164i
$281$	−6.37315			−0.380190			−0.190095	−	0.981766i	$-0.560880\pi$
$281$	−6.37315			−0.380190			−0.190095	+	0.981766i	$0.560880\pi$
$282$	−5.00787	+	8.67389i	−0.298214	+	0.516523i
$283$	−13.5097	−	23.3995i	−0.803068	−	1.39096i	−0.917587	−	0.397534i	$-0.869866\pi$
$283$	−13.5097	−	23.3995i	−0.803068	−	1.39096i	0.114519	−	0.993421i	$-0.463467\pi$
$284$	16.3960	+	28.3987i	0.972923	+	1.68515i
$285$	8.37357			0.496008
$286$	−3.98169	+	1.86964i	−0.235443	+	0.110554i
$287$	6.29157			0.371380
$288$	−9.39766	−	16.2772i	−0.553762	−	0.959144i
$289$	5.67046	+	9.82152i	0.333556	+	0.577736i
$290$	−16.8580	+	29.1989i	−0.989937	+	1.71462i
$291$	−3.75932			−0.220375
$292$	−7.18376	+	12.4426i	−0.420398	+	0.728150i
$293$	2.43736	−	4.22163i	0.142392	−	0.246630i	−0.786005	−	0.618220i	$-0.787854\pi$
$293$	2.43736	−	4.22163i	0.142392	−	0.246630i	0.928397	+	0.371590i	$0.121187\pi$
$294$	1.22001			0.0711523
$295$	−3.81389	+	6.60586i	−0.222053	+	0.384608i
$296$	0.339616	+	0.588232i	0.0197398	+	0.0341903i
$297$	−0.860415	−	1.49028i	−0.0499264	−	0.0864750i
$298$	10.1118			0.585763
$299$	−1.77280	+	20.9053i	−0.102524	+	1.20899i
$300$	20.6130			1.19009
$301$	1.61000	+	2.78861i	0.0927991	+	0.160733i
$302$	7.02535	+	12.1683i	0.404263	+	0.700205i
$303$	−1.58247	+	2.74091i	−0.0909104	+	0.157461i
$304$	4.62579			0.265307
$305$	1.28568	−	2.22686i	0.0736177	−	0.127510i
$306$	−7.12424	+	12.3395i	−0.407266	+	0.705405i
$307$	16.1760			0.923212			0.461606	−	0.887085i	$-0.347273\pi$
$307$	16.1760			0.923212			0.461606	+	0.887085i	$0.347273\pi$
$308$	−0.804662	+	1.39372i	−0.0458499	+	0.0794143i
$309$	−0.157110	−	0.272123i	−0.00893769	−	0.0154805i
$310$	−24.1165	−	41.7709i	−1.36972	−	2.37243i
$311$	−1.30806			−0.0741735			−0.0370868	−	0.999312i	$-0.511808\pi$
$311$	−1.30806			−0.0741735			−0.0370868	+	0.999312i	$0.511808\pi$
$312$	−0.345090	+	4.06939i	−0.0195369	+	0.230384i
$313$	13.1978			0.745983			0.372991	−	0.927835i	$-0.378332\pi$
$313$	13.1978			0.745983			0.372991	+	0.927835i	$0.378332\pi$
$314$	−18.1042	−	31.3574i	−1.02168	−	1.76960i
$315$	5.69278	+	9.86018i	0.320752	+	0.555558i
$316$	20.5241	−	35.5488i	1.15457	−	1.99977i
$317$	−8.07552			−0.453566			−0.226783	−	0.973945i	$-0.572821\pi$
$317$	−8.07552			−0.453566			−0.226783	+	0.973945i	$0.572821\pi$
$318$	−1.62180	+	2.80903i	−0.0909458	+	0.157523i
$319$	−0.988887	+	1.71280i	−0.0553671	+	0.0958986i
$320$	54.4516			3.04394
$321$	−1.11877	+	1.93776i	−0.0624435	+	0.108155i
$322$	6.45900	+	11.1873i	0.359946	+	0.623445i
$323$	−4.29470	−	7.43863i	−0.238963	−	0.413897i
$324$	18.6634			1.03685
$325$	−37.9003	−	26.3877i	−2.10233	−	1.46372i
$326$	52.3918			2.90171
$327$	−4.20645	−	7.28579i	−0.232617	−	0.402905i
$328$	6.48388	+	11.2304i	0.358012	+	0.620096i
$329$	4.10479	−	7.10970i	0.226304	−	0.391970i
$330$	2.82933			0.155750
$331$	7.47256	−	12.9429i	0.410729	−	0.711403i	−0.584241	−	0.811580i	$-0.698608\pi$
$331$	7.47256	−	12.9429i	0.410729	−	0.711403i	0.994970	+	0.100177i	$0.0319409\pi$
$332$	8.39229	−	14.5359i	0.460587	−	0.797760i
$333$	0.889106			0.0487227
$334$	19.7917	−	34.2802i	1.08295	−	1.87573i
$335$	21.8803	+	37.8979i	1.19545	+	2.07058i
$336$	−0.352026	−	0.609727i	−0.0192046	−	0.0332633i
$337$	−17.1695			−0.935282			−0.467641	−	0.883918i	$-0.654896\pi$
$337$	−17.1695			−0.935282			−0.467641	+	0.883918i	$0.654896\pi$
$338$	18.4327	−	22.2068i	1.00261	−	1.20789i
$339$	6.69184			0.363451
$340$	−14.6991	−	25.4597i	−0.797173	−	1.38074i
$341$	−1.41467	−	2.45027i	−0.0766085	−	0.132690i
$342$	−10.8132	+	18.7290i	−0.584712	+	1.01275i
$343$	−1.00000			−0.0539949
$344$	−3.31843	+	5.74769i	−0.178918	+	0.309895i
$345$	6.74733	−	11.6867i	0.363264	−	0.629192i
$346$	−16.8085			−0.903629
$347$	1.96922	−	3.41079i	0.105713	−	0.183101i	−0.808316	−	0.588749i	$-0.799621\pi$
$347$	1.96922	−	3.41079i	0.105713	−	0.183101i	0.914029	+	0.405648i	$0.132954\pi$
$348$	2.89589	+	5.01583i	0.155236	+	0.268877i
$349$	−8.58883	−	14.8763i	−0.459750	−	0.796310i	0.539198	−	0.842179i	$-0.318728\pi$
$349$	−8.58883	−	14.8763i	−0.459750	−	0.796310i	−0.998947	+	0.0458695i	$0.985394\pi$
$350$	−28.4349			−1.51991
$351$	9.26563	+	6.45110i	0.494563	+	0.344334i
$352$	3.82840			0.204054
$353$	9.09821	+	15.7586i	0.484249	+	0.838744i	0.999836	−	0.0180932i	$-0.00575957\pi$
$353$	9.09821	+	15.7586i	0.484249	+	0.838744i	−0.515587	+	0.856837i	$0.672426\pi$
$354$	1.10260	+	1.90976i	0.0586025	+	0.101503i
$355$	−23.6274	+	40.9238i	−1.25401	+	2.17201i
$356$	−21.8682			−1.15901
$357$	−0.653659	+	1.13217i	−0.0345953	+	0.0599208i
$358$	25.3118	−	43.8413i	1.33777	−	2.31709i
$359$	16.3126			0.860948			0.430474	−	0.902603i	$-0.358346\pi$
$359$	16.3126			0.860948			0.430474	+	0.902603i	$0.358346\pi$
$360$	−11.7336	+	20.3231i	−0.618413	+	1.07112i
$361$	2.98148	+	5.16408i	0.156920	+	0.271794i
$362$	−15.4617	−	26.7804i	−0.812647	−	1.40755i
$363$	−5.87909			−0.308572
$364$	0.892184	−	10.5209i	0.0467631	−	0.551443i
$365$	−20.7042			−1.08371
$366$	−0.371690	−	0.643787i	−0.0194286	−	0.0336513i
$367$	18.0982	+	31.3469i	0.944716	+	1.63630i	0.756319	+	0.654203i	$0.226996\pi$
$367$	18.0982	+	31.3469i	0.944716	+	1.63630i	0.188398	+	0.982093i	$0.439671\pi$
$368$	3.72741	−	6.45607i	0.194305	−	0.336546i
$369$	16.9746			0.883664
$370$	−1.54366	+	2.67369i	−0.0802508	+	0.138998i
$371$	1.32933	−	2.30247i	0.0690155	−	0.119538i
$372$	−8.28551			−0.429584
$373$	−4.89892	+	8.48518i	−0.253657	+	0.439346i	−0.964530	−	0.263974i	$-0.914967\pi$
$373$	−4.89892	+	8.48518i	−0.253657	+	0.439346i	0.710873	+	0.703320i	$0.248300\pi$
$374$	−1.45113	−	2.51343i	−0.0750361	−	0.129966i
$375$	9.05435	+	15.6826i	0.467564	+	0.809845i
$376$	16.9210			0.872635
$377$	1.09645	−	12.9296i	0.0564699	−	0.665907i
$378$	6.95160			0.357552
$379$	−6.53275	−	11.3151i	−0.335565	−	0.581216i	0.648028	−	0.761616i	$-0.275594\pi$
$379$	−6.53275	−	11.3151i	−0.335565	−	0.581216i	−0.983593	+	0.180401i	$0.942261\pi$
$380$	−22.3104	−	38.6428i	−1.14450	−	1.98233i
$381$	−0.538745	+	0.933133i	−0.0276007	+	0.0478058i
$382$	−28.1315			−1.43933
$383$	−13.8965	+	24.0694i	−0.710076	+	1.22989i	0.254753	+	0.967006i	$0.418006\pi$
$383$	−13.8965	+	24.0694i	−0.710076	+	1.22989i	−0.964828	+	0.262881i	$0.915327\pi$
$384$	4.04260	−	7.00199i	0.206298	−	0.357319i
$385$	−2.31911			−0.118193
$386$	4.61198	−	7.98818i	0.234744	−	0.406588i
$387$	4.34378	+	7.52365i	0.220807	+	0.382449i
$388$	10.0163	+	17.3487i	0.508499	+	0.880747i
$389$	13.7047			0.694854			0.347427	−	0.937707i	$-0.387055\pi$
$389$	13.7047			0.694854			0.347427	+	0.937707i	$0.387055\pi$
$390$	−16.8028	+	7.88990i	−0.850842	+	0.399521i
$391$	−13.8425			−0.700044
$392$	−1.03057	−	1.78499i	−0.0520514	−	0.0901557i
$393$	1.78610	+	3.09361i	0.0900968	+	0.156052i
$394$	7.60375	−	13.1701i	0.383071	−	0.663499i
$395$	59.1523			2.97627
$396$	−2.17097	+	3.76024i	−0.109096	+	0.188959i
$397$	−3.95597	+	6.85194i	−0.198545	+	0.343889i	−0.948057	−	0.318101i	$-0.896955\pi$
$397$	−3.95597	+	6.85194i	−0.198545	+	0.343889i	0.749512	+	0.661991i	$0.230288\pi$
$398$	−1.80617			−0.0905351
$399$	−0.992128	+	1.71842i	−0.0496685	+	0.0860284i
$400$	8.20472	+	14.2110i	0.410236	+	0.710549i
$401$	8.27212	+	14.3277i	0.413090	+	0.715493i	0.995226	−	0.0975987i	$-0.0311162\pi$
$401$	8.27212	+	14.3277i	0.413090	+	0.715493i	−0.582136	+	0.813092i	$0.697783\pi$
$402$	12.6512			0.630987
$403$	15.2342	+	10.6067i	0.758872	+	0.528357i
$404$	16.8652			0.839076
$405$	13.4474	+	23.2915i	0.668205	+	1.15737i
$406$	−3.99478	−	6.91917i	−0.198258	−	0.343393i
$407$	−0.0905505	+	0.156838i	−0.00448842	+	0.00777417i
$408$	−2.69456			−0.133400
$409$	−12.8909	+	22.3278i	−0.637416	+	1.10404i	0.348582	+	0.937278i	$0.386663\pi$
$409$	−12.8909	+	22.3278i	−0.637416	+	1.10404i	−0.985998	+	0.166758i	$0.946670\pi$
$410$	−29.4711	+	51.0455i	−1.45548	+	2.52096i
$411$	−8.38481			−0.413592
$412$	−0.837205	+	1.45008i	−0.0412461	+	0.0714404i
$413$	−0.903765	−	1.56537i	−0.0444713	−	0.0770266i
$414$	17.4263	+	30.1833i	0.856458	+	1.48343i
$415$	24.1873			1.18731
$416$	−22.7360	+	10.6759i	−1.11472	+	0.523429i
$417$	−9.61496			−0.470847
$418$	−2.20253	−	3.81490i	−0.107729	−	0.186593i
$419$	−11.8436	−	20.5137i	−0.578596	−	1.00216i	−0.995641	−	0.0932720i	$-0.970267\pi$
$419$	−11.8436	−	20.5137i	−0.578596	−	1.00216i	0.417044	−	0.908886i	$-0.363066\pi$
$420$	−3.39568	+	5.88149i	−0.165692	+	0.286987i
$421$	−20.8246			−1.01493			−0.507465	−	0.861672i	$-0.669417\pi$
$421$	−20.8246			−1.01493			−0.507465	+	0.861672i	$0.669417\pi$
$422$	15.5105	−	26.8650i	0.755041	−	1.30777i
$423$	11.0747	−	19.1819i	0.538470	−	0.932657i
$424$	5.47986			0.266125
$425$	15.2349	−	26.3877i	0.739002	−	1.27999i
$426$	6.83069	+	11.8311i	0.330948	+	0.573219i
$427$	0.304662	+	0.527691i	0.0147436	+	0.0255367i
$428$	11.9233			0.576335
$429$	−0.985647	+	0.462820i	−0.0475875	+	0.0223451i
$430$	−30.1665			−1.45476
$431$	−9.97521	−	17.2776i	−0.480489	−	0.832232i	0.519260	−	0.854616i	$-0.326208\pi$
$431$	−9.97521	−	17.2776i	−0.480489	−	0.832232i	−0.999749	+	0.0223845i	$0.992874\pi$
$432$	−2.00584	−	3.47422i	−0.0965061	−	0.167153i
$433$	−0.00834083	+	0.0144467i	−0.000400835	+	0.000694266i	−0.866226	−	0.499653i	$-0.833461\pi$
$433$	−0.00834083	+	0.0144467i	−0.000400835	+	0.000694266i	0.865825	+	0.500347i	$0.166794\pi$
$434$	11.4296			0.548638
$435$	−4.17311	+	7.22804i	−0.200085	+	0.346558i
$436$	−22.4152	+	38.8243i	−1.07349	+	1.85935i
$437$	−21.0102			−1.00505
$438$	−2.99281	+	5.18369i	−0.143002	+	0.247686i
$439$	−6.74801	−	11.6879i	−0.322065	−	0.557833i	0.658849	−	0.752275i	$-0.271044\pi$
$439$	−6.74801	−	11.6879i	−0.322065	−	0.557833i	−0.980914	+	0.194442i	$0.937710\pi$
$440$	−2.39000	−	4.13959i	−0.113939	−	0.197347i
$441$	−2.69799			−0.128476
$442$	15.6269	+	10.8801i	0.743296	+	0.517512i
$443$	−15.0110			−0.713196			−0.356598	−	0.934258i	$-0.616063\pi$
$443$	−15.0110			−0.713196			−0.356598	+	0.934258i	$0.616063\pi$
$444$	0.265171	+	0.459290i	0.0125845	+	0.0217969i
$445$	−15.7566	−	27.2912i	−0.746933	−	1.29373i
$446$	15.0228	−	26.0202i	0.711350	−	1.23209i
$447$	2.50313			0.118394
$448$	−6.45160	+	11.1745i	−0.304809	+	0.527945i
$449$	11.8918	−	20.5972i	0.561210	−	0.972044i	−0.436181	−	0.899859i	$-0.643669\pi$
$449$	11.8918	−	20.5972i	0.561210	−	0.972044i	0.997391	−	0.0721852i	$-0.0229973\pi$
$450$	−76.7172			−3.61648
$451$	−1.72877	+	2.99432i	−0.0814046	+	0.140997i
$452$	−17.8297	−	30.8819i	−0.838636	−	1.45256i
$453$	1.73909	+	3.01219i	0.0817095	+	0.141525i
$454$	−11.9159			−0.559242
$455$	13.7727	−	6.46709i	0.645673	−	0.303182i
$456$	−4.08981			−0.191523
$457$	−9.06567	−	15.7022i	−0.424074	−	0.734518i	0.572259	−	0.820073i	$-0.306067\pi$
$457$	−9.06567	−	15.7022i	−0.424074	−	0.734518i	−0.996333	+	0.0855548i	$0.972734\pi$
$458$	−3.44002	−	5.95828i	−0.160741	−	0.278412i
$459$	−3.72455	+	6.45110i	−0.173847	+	0.301112i
$460$	−71.9101			−3.35282
$461$	3.03980	−	5.26508i	0.141577	−	0.245219i	−0.786513	−	0.617573i	$-0.788116\pi$
$461$	3.03980	−	5.26508i	0.141577	−	0.245219i	0.928091	+	0.372354i	$0.121449\pi$
$462$	−0.335228	+	0.580633i	−0.0155962	+	0.0270135i
$463$	5.19289			0.241334			0.120667	−	0.992693i	$-0.461497\pi$
$463$	5.19289			0.241334			0.120667	+	0.992693i	$0.461497\pi$
$464$	−2.30534	+	3.99297i	−0.107023	+	0.185369i
$465$	−5.96990	−	10.3402i	−0.276848	−	0.479514i
$466$	22.6121	+	39.1653i	1.04748	+	1.81430i
$467$	−8.69968			−0.402573			−0.201287	−	0.979532i	$-0.564512\pi$
$467$	−8.69968			−0.402573			−0.201287	+	0.979532i	$0.564512\pi$
$468$	2.40711	−	28.3852i	0.111268	−	1.31211i
$469$	−10.3698			−0.478833
$470$	38.4555	+	66.6069i	1.77382	+	3.07235i
$471$	−4.48160	−	7.76236i	−0.206501	−	0.357671i
$472$	1.86278	−	3.22643i	0.0857413	−	0.148508i
$473$	−1.76956			−0.0813644
$474$	8.55049	−	14.8099i	0.392737	−	0.680240i
$475$	23.1237	−	40.0513i	1.06099	−	1.83768i
$476$	6.96640			0.319305
$477$	3.58653	−	6.21205i	0.164216	−	0.284430i
$478$	1.43365	+	2.48316i	0.0655737	+	0.113577i
$479$	−12.1094	−	20.9741i	−0.553294	−	0.958332i	−0.998034	−	0.0626730i	$-0.980037\pi$
$479$	−12.1094	−	20.9741i	−0.553294	−	0.958332i	0.444741	−	0.895659i	$-0.353296\pi$
$480$	16.1559			0.737411
$481$	0.100399	−	1.18394i	0.00457782	−	0.0539828i
$482$	4.73461			0.215655
$483$	1.59889	+	2.76936i	0.0727521	+	0.126010i
$484$	15.6642	+	27.1312i	0.712009	+	1.23323i
$485$	−14.4339	+	25.0003i	−0.655410	+	1.13520i
$486$	28.6301			1.29869
$487$	−0.886967	+	1.53627i	−0.0401923	+	0.0696151i	−0.885422	−	0.464788i	$-0.846130\pi$
$487$	−0.886967	+	1.53627i	−0.0401923	+	0.0696151i	0.845229	+	0.534404i	$0.179464\pi$
$488$	−0.627949	+	1.08764i	−0.0284259	+	0.0492351i
$489$	12.9693			0.586493
$490$	4.68423	−	8.11332i	0.211612	−	0.366522i
$491$	3.34483	+	5.79342i	0.150950	+	0.261453i	0.931577	−	0.363544i	$-0.118433\pi$
$491$	3.34483	+	5.79342i	0.150950	+	0.261453i	−0.780627	+	0.624997i	$0.785100\pi$
$492$	5.06259	+	8.76867i	0.228239	+	0.395322i
$493$	8.56134			0.385584
$494$	23.7186	+	16.5138i	1.06715	+	0.742992i
$495$	−6.25694			−0.281229
$496$	−3.29794	−	5.71220i	−0.148082	−	0.256485i
$497$	−5.59889	−	9.69756i	−0.251145	−	0.434995i
$498$	3.49629	−	6.05575i	0.156673	−	0.271365i
$499$	24.6387			1.10298			0.551491	−	0.834181i	$-0.314059\pi$
$499$	24.6387			1.10298			0.551491	+	0.834181i	$0.314059\pi$
$500$	48.2486	−	83.5690i	2.15774	−	3.73732i
$501$	4.89932	−	8.48588i	0.218886	−	0.379121i
$502$	−68.3121			−3.04892
$503$	−16.5726	+	28.7046i	−0.738936	+	1.27987i	0.214039	+	0.976825i	$0.431338\pi$
$503$	−16.5726	+	28.7046i	−0.738936	+	1.27987i	−0.952975	+	0.303049i	$0.901995\pi$
$504$	−2.78046	−	4.81590i	−0.123852	−	0.214517i
$505$	12.1518	+	21.0475i	0.540747	+	0.936601i
$506$	−7.09910			−0.315594
$507$	4.56292	−	5.49717i	0.202646	−	0.244138i
$508$	5.74170			0.254747
$509$	13.8290	+	23.9526i	0.612961	+	1.06168i	0.990739	+	0.135783i	$0.0433549\pi$
$509$	13.8290	+	23.9526i	0.612961	+	1.06168i	−0.377778	+	0.925896i	$0.623312\pi$
$510$	−6.12377	−	10.6067i	−0.271165	−	0.469672i
$511$	2.45310	−	4.24890i	0.108519	−	0.187960i
$512$	14.2061			0.627828
$513$	−5.65314	+	9.79152i	−0.249592	+	0.432306i
$514$	1.63571	−	2.83314i	0.0721482	−	0.124964i
$515$	−2.41290			−0.106325
$516$	−2.59102	+	4.48778i	−0.114063	+	0.197563i
$517$	2.25579	+	3.90714i	0.0992096	+	0.171836i
$518$	−0.365794	−	0.633574i	−0.0160721	−	0.0278377i
$519$	−4.16085			−0.182641
$520$	25.7374	+	17.9194i	1.12866	+	0.785817i
$521$	1.42217			0.0623062			0.0311531	−	0.999515i	$-0.490082\pi$
$521$	1.42217			0.0623062			0.0311531	+	0.999515i	$0.490082\pi$
$522$	−10.7779	−	18.6679i	−0.471736	−	0.817070i
$523$	1.68089	+	2.91139i	0.0735002	+	0.127306i	0.900433	−	0.434995i	$-0.143250\pi$
$523$	1.68089	+	2.91139i	0.0735002	+	0.127306i	−0.826933	+	0.562301i	$0.809916\pi$
$524$	9.51772	−	16.4852i	0.415784	−	0.720158i
$525$	−7.03891			−0.307203
$526$	−7.41143	+	12.8370i	−0.323154	+	0.559718i
$527$	−6.12377	+	10.6067i	−0.266756	+	0.462034i
$528$	0.386913			0.0168382
$529$	−5.42979	+	9.40468i	−0.236078	+	0.408899i
$530$	12.4538	+	21.5706i	0.540958	+	0.936966i
$531$	−2.43835	−	4.22335i	−0.105815	−	0.183278i
$532$	10.5736			0.458426
$533$	1.91681	−	22.6035i	0.0830260	−	0.979065i
$534$	−9.11047			−0.394249
$535$	8.59102	+	14.8801i	0.371422	+	0.643322i
$536$	−10.6868	−	18.5100i	−0.461598	−	0.799512i
$537$	6.26580	−	10.8527i	0.270389	−	0.468328i
$538$	16.8182			0.725083
$539$	0.274776	−	0.475925i	0.0118354	−	0.0204996i
$540$	−19.3486	+	33.5127i	−0.832630	+	1.44216i
$541$	7.76289			0.333753			0.166876	−	0.985978i	$-0.446632\pi$
$541$	7.76289			0.333753			0.166876	+	0.985978i	$0.446632\pi$
$542$	−22.8306	+	39.5437i	−0.980657	+	1.69855i
$543$	−3.82745	−	6.62934i	−0.164252	−	0.284492i
$544$	−8.28613	−	14.3520i	−0.355265	−	0.615337i
$545$	−64.6027			−2.76728
$546$	0.371690	−	4.38307i	0.0159069	−	0.187578i
$547$	−6.19247			−0.264771			−0.132385	−	0.991198i	$-0.542264\pi$
$547$	−6.19247			−0.264771			−0.132385	+	0.991198i	$0.542264\pi$
$548$	22.3404	+	38.6947i	0.954334	+	1.65295i
$549$	0.821977	+	1.42371i	0.0350811	+	0.0607623i
$550$	7.81321	−	13.5329i	0.333157	−	0.577044i
$551$	12.9945			0.553582
$552$	−3.29553	+	5.70802i	−0.140267	+	0.242949i
$553$	−7.00855	+	12.1392i	−0.298034	+	0.516210i
$554$	12.6661			0.538129
$555$	−0.382124	+	0.661858i	−0.0162202	+	0.0280943i
$556$	25.6180	+	44.3717i	1.08644	+	1.88178i
$557$	−14.7729	−	25.5874i	−0.625948	−	1.08417i	−0.988357	−	0.152154i	$-0.951379\pi$
$557$	−14.7729	−	25.5874i	−0.625948	−	1.08417i	0.362409	−	0.932019i	$-0.381954\pi$
$558$	30.8369			1.30543
$559$	10.5090	−	4.93461i	0.444484	−	0.208712i
$560$	−5.40642			−0.228463
$561$	−0.359219	−	0.622186i	−0.0151662	−	0.0262687i
$562$	7.07422	+	12.2529i	0.298408	+	0.516858i
$563$	−3.23368	+	5.60090i	−0.136283	+	0.236050i	−0.926087	−	0.377310i	$-0.876849\pi$
$563$	−3.23368	+	5.60090i	−0.136283	+	0.236050i	0.789804	+	0.613360i	$0.210182\pi$
$564$	13.2119			0.556320
$565$	25.6933	−	44.5022i	1.08093	−	1.87222i
$566$	−29.9916	+	51.9470i	−1.26064	+	2.18350i
$567$	−6.37315			−0.267647
$568$	11.5401	−	19.9880i	0.484210	−	0.838676i
$569$	−10.8478	−	18.7889i	−0.454763	−	0.787673i	0.543911	−	0.839143i	$-0.316943\pi$
$569$	−10.8478	−	18.7889i	−0.454763	−	0.787673i	−0.998675	+	0.0514697i	$0.983609\pi$
$570$	−9.29470	−	16.0989i	−0.389312	−	0.674308i
$571$	−16.6418			−0.696436			−0.348218	−	0.937414i	$-0.613213\pi$
$571$	−16.6418			−0.696436			−0.348218	+	0.937414i	$0.613213\pi$
$572$	4.76199	+	3.31549i	0.199109	+	0.138628i
$573$	−6.96381			−0.290917
$574$	−6.98367	−	12.0961i	−0.291493	−	0.504880i
$575$	−37.2656	−	64.5459i	−1.55408	−	2.69175i
$576$	−17.4064	+	30.1487i	−0.725265	+	1.25620i
$577$	−2.64240			−0.110005			−0.0550024	−	0.998486i	$-0.517517\pi$
$577$	−2.64240			−0.110005			−0.0550024	+	0.998486i	$0.517517\pi$
$578$	12.5885	−	21.8038i	0.523611	−	0.906921i
$579$	1.14167	−	1.97743i	0.0474462	−	0.0821793i
$580$	44.4752			1.84673
$581$	−2.86579	+	4.96370i	−0.118893	+	0.205929i
$582$	4.17286	+	7.22760i	0.172970	+	0.299594i
$583$	0.730536	+	1.26533i	0.0302557	+	0.0524044i
$584$	10.1123			0.418452
$585$	37.1586	−	17.4482i	1.53632	−	0.721393i
$586$	−10.8219			−0.447049
$587$	−3.69407	−	6.39832i	−0.152471	−	0.264087i	0.779664	−	0.626198i	$-0.215390\pi$
$587$	−3.69407	−	6.39832i	−0.152471	−	0.264087i	−0.932135	+	0.362110i	$0.882056\pi$
$588$	−0.804662	−	1.39372i	−0.0331837	−	0.0574759i
$589$	−9.29470	+	16.0989i	−0.382981	+	0.663343i
$590$	16.9337			0.697151
$591$	1.88227	−	3.26018i	0.0774261	−	0.134106i
$592$	−0.211096	+	0.365628i	−0.00867597	+	0.0150272i
$593$	46.9030			1.92607			0.963037	−	0.269370i	$-0.0868153\pi$
$593$	46.9030			1.92607			0.963037	+	0.269370i	$0.0868153\pi$
$594$	−1.91013	+	3.30844i	−0.0783735	+	0.135747i
$595$	5.01945	+	8.69395i	0.205778	+	0.356417i
$596$	−6.66931	−	11.5516i	−0.273186	−	0.473171i
$597$	−0.447108			−0.0182989
$598$	42.1600	−	19.7966i	1.72405	−	0.809544i
$599$	1.62290			0.0663098			0.0331549	−	0.999450i	$-0.489445\pi$
$599$	1.62290			0.0663098			0.0331549	+	0.999450i	$0.489445\pi$
$600$	−7.25406	−	12.5644i	−0.296146	−	0.512939i
$601$	23.5174	+	40.7333i	0.959293	+	1.66154i	0.724223	+	0.689566i	$0.242199\pi$
$601$	23.5174	+	40.7333i	0.959293	+	1.66154i	0.235070	+	0.971978i	$0.424468\pi$
$602$	3.57422	−	6.19073i	0.145674	−	0.252315i
$603$	−27.9777			−1.13934
$604$	9.26721	−	16.0513i	0.377077	−	0.653117i
$605$	−22.5728	+	39.0973i	−0.917715	+	1.58953i
$606$	7.02618			0.285419
$607$	14.1935	−	24.5838i	0.576095	−	0.997825i	−0.419827	−	0.907604i	$-0.637909\pi$
$607$	14.1935	−	24.5838i	0.576095	−	0.997825i	0.995922	−	0.0902211i	$-0.0287574\pi$
$608$	−12.5767	−	21.7836i	−0.510054	−	0.883440i
$609$	−0.988887	−	1.71280i	−0.0400717	−	0.0694063i
$610$	−5.70843			−0.231127
$611$	−24.2921	−	16.9131i	−0.982755	−	0.684233i
$612$	18.7953			0.759756
$613$	23.7782	+	41.1851i	0.960393	+	1.66345i	0.721514	+	0.692399i	$0.243446\pi$
$613$	23.7782	+	41.1851i	0.960393	+	1.66345i	0.238878	+	0.971050i	$0.423220\pi$
$614$	−17.9554	−	31.0997i	−0.724621	−	1.25508i
$615$	−7.29543	+	12.6360i	−0.294180	+	0.509535i
$616$	1.13270			0.0456377
$617$	8.24338	−	14.2780i	0.331866	−	0.574809i	−0.651012	−	0.759068i	$-0.725655\pi$
$617$	8.24338	−	14.2780i	0.331866	−	0.574809i	0.982878	+	0.184259i	$0.0589885\pi$
$618$	−0.348786	+	0.604115i	−0.0140302	+	0.0243011i
$619$	−31.9412			−1.28382			−0.641912	−	0.766778i	$-0.721859\pi$
$619$	−31.9412			−1.28382			−0.641912	+	0.766778i	$0.721859\pi$
$620$	−31.8123	+	55.1005i	−1.27761	+	2.21289i
$621$	9.11047	+	15.7798i	0.365591	+	0.633222i
$622$	1.45196	+	2.51486i	0.0582182	+	0.100837i
$623$	7.46755			0.299181
$624$	−2.29779	+	1.07895i	−0.0919851	+	0.0431925i
$625$	75.0145			3.00058
$626$	−14.6496	−	25.3738i	−0.585515	−	1.01414i
$627$	−0.545225	−	0.944357i	−0.0217742	−	0.0377140i
$628$	−23.8814	+	41.3639i	−0.952973	+	1.65060i
$629$	0.783945			0.0312579
$630$	12.6380	−	21.8897i	0.503510	−	0.872105i
$631$	−6.59577	+	11.4242i	−0.262573	+	0.454790i	−0.966925	−	0.255061i	$-0.917905\pi$
$631$	−6.59577	+	11.4242i	−0.262573	+	0.454790i	0.704352	+	0.709851i	$0.251238\pi$
$632$	−28.8911			−1.14923
$633$	3.83955	−	6.65029i	0.152608	−	0.264325i
$634$	8.96386	+	15.5259i	0.356000	+	0.616610i
$635$	4.13702	+	7.16554i	0.164173	+	0.284356i
$636$	4.27865			0.169660
$637$	−0.304662	+	3.59266i	−0.0120712	+	0.142346i
$638$	4.39068			0.173829
$639$	−15.1058	−	26.1640i	−0.597575	−	1.03503i
$640$	−31.0432	−	53.7684i	−1.22709	−	2.12538i
$641$	23.5814	−	40.8441i	0.931408	−	1.61325i	0.150490	−	0.988612i	$-0.451915\pi$
$641$	23.5814	−	40.8441i	0.931408	−	1.61325i	0.780918	−	0.624634i	$-0.214752\pi$
$642$	4.96734			0.196045
$643$	1.40679	−	2.43664i	0.0554785	−	0.0960916i	−0.836952	−	0.547276i	$-0.815665\pi$
$643$	1.40679	−	2.43664i	0.0554785	−	0.0960916i	0.892431	+	0.451184i	$0.148998\pi$
$644$	8.52013	−	14.7573i	0.335740	−	0.581519i
$645$	−7.46755			−0.294035
$646$	−9.53426	+	16.5138i	−0.375121	+	0.649728i
$647$	−12.9891	−	22.4979i	−0.510656	−	0.884482i	−0.999924	−	0.0123485i	$-0.996069\pi$
$647$	−12.9891	−	22.4979i	−0.510656	−	0.884482i	0.489268	−	0.872134i	$-0.337264\pi$
$648$	−6.56795	−	11.3760i	−0.258014	−	0.446893i
$649$	0.993330			0.0389916
$650$	−8.66304	+	102.157i	−0.339792	+	4.00692i
$651$	2.82933			0.110890
$652$	−34.5553	−	59.8515i	−1.35329	−	2.34397i
$653$	13.4213	+	23.2464i	0.525216	+	0.909700i	0.999569	+	0.0293654i	$0.00934865\pi$
$653$	13.4213	+	23.2464i	0.525216	+	0.909700i	−0.474353	+	0.880335i	$0.657318\pi$
$654$	−9.33835	+	16.1745i	−0.365158	+	0.632473i
$655$	27.4309			1.07182
$656$	−4.03019	+	6.98050i	−0.157353	+	0.272543i
$657$	6.61846	−	11.4635i	0.258211	−	0.447234i
$658$	−18.2253			−0.710497
$659$	−7.78666	+	13.4869i	−0.303325	+	0.525375i	−0.976887	−	0.213756i	$-0.931430\pi$
$659$	−7.78666	+	13.4869i	−0.303325	+	0.525375i	0.673562	+	0.739131i	$0.264764\pi$
$660$	−1.86610	−	3.23218i	−0.0726379	−	0.125812i
$661$	−16.6902	−	28.9083i	−0.649174	−	1.12440i	−0.983320	−	0.181881i	$-0.941781\pi$
$661$	−16.6902	−	28.9083i	−0.649174	−	1.12440i	0.334146	−	0.942521i	$-0.391552\pi$
$662$	−33.1783			−1.28951
$663$	3.86836	+	2.69330i	0.150234	+	0.104599i
$664$	−11.8136			−0.458455
$665$	7.61856	+	13.1957i	0.295435	+	0.511708i
$666$	−0.986911	−	1.70938i	−0.0382420	−	0.0662371i
$667$	10.4708	−	18.1359i	0.405431	−	0.702227i
$668$	−52.2148			−2.02025
$669$	3.71881	−	6.44117i	0.143778	−	0.249030i
$670$	48.5745	−	84.1335i	1.87660	−	3.25036i
$671$	−0.334855			−0.0129269
$672$	−1.91420	+	3.31549i	−0.0738418	+	0.127898i
$673$	−0.427076	−	0.739717i	−0.0164626	−	0.0285140i	0.857677	−	0.514189i	$-0.171907\pi$
$673$	−0.427076	−	0.739717i	−0.0164626	−	0.0285140i	−0.874139	+	0.485675i	$0.838574\pi$
$674$	19.0582	+	33.0098i	0.734095	+	1.27149i
$675$	−40.1076			−1.54374
$676$	−37.5260	−	6.41062i	−1.44331	−	0.246562i
$677$	−24.5449			−0.943339			−0.471669	−	0.881775i	$-0.656348\pi$
$677$	−24.5449			−0.943339			−0.471669	+	0.881775i	$0.656348\pi$
$678$	−7.42797	−	12.8656i	−0.285269	−	0.494101i
$679$	−3.42035	−	5.92422i	−0.131261	−	0.227351i
$680$	−10.3458	+	17.9194i	−0.396742	+	0.687177i
$681$	−2.94972			−0.113034
$682$	−3.14057	+	5.43963i	−0.120259	+	0.208294i
$683$	21.5186	−	37.2714i	0.823387	−	1.42615i	−0.0797583	−	0.996814i	$-0.525415\pi$
$683$	21.5186	−	37.2714i	0.823387	−	1.42615i	0.903146	−	0.429334i	$-0.141252\pi$
$684$	28.5276			1.09078
$685$	−32.1935	+	55.7608i	−1.23005	+	2.13051i
$686$	1.11000	+	1.92258i	0.0423801	+	0.0734046i
$687$	−0.851558	−	1.47494i	−0.0324889	−	0.0562725i
$688$	−4.12528			−0.157275
$689$	−7.86699	−	5.47731i	−0.299708	−	0.208669i
$690$	−29.9583			−1.14049
$691$	12.9098	+	22.3604i	0.491110	+	0.850628i	0.999948	−	0.0102348i	$-0.00325788\pi$
$691$	12.9098	+	22.3604i	0.491110	+	0.850628i	−0.508837	+	0.860863i	$0.669925\pi$
$692$	11.0861	+	19.2017i	0.421431	+	0.729939i
$693$	0.741343	−	1.28404i	0.0281613	−	0.0487768i
$694$	−8.74338			−0.331894
$695$	−36.9167	+	63.9416i	−1.40033	+	2.42544i
$696$	2.03823	−	3.53031i	0.0772588	−	0.133816i
$697$	14.9669			0.566913
$698$	−19.0673	+	33.0255i	−0.721707	+	1.25003i
$699$	5.59750	+	9.69515i	0.211717	+	0.366704i
$700$	18.7544	+	32.4835i	0.708849	+	1.22776i
$701$	16.3178			0.616313			0.308156	−	0.951336i	$-0.400288\pi$
$701$	16.3178			0.616313			0.308156	+	0.951336i	$0.400288\pi$
$702$	2.11789	−	24.9747i	0.0799346	−	0.942609i
$703$	1.18988			0.0448770
$704$	−3.54548	−	6.14096i	−0.133625	−	0.231446i
$705$	9.51945	+	16.4882i	0.358523	+	0.620981i
$706$	20.1981	−	34.9841i	0.760166	−	1.31665i
$707$	−5.75913			−0.216594
$708$	1.45445	−	2.51918i	0.0546616	−	0.0946767i
$709$	11.1897	−	19.3811i	0.420238	−	0.727874i	−0.575725	−	0.817644i	$-0.695280\pi$
$709$	11.1897	−	19.3811i	0.420238	−	0.727874i	0.995963	+	0.0897702i	$0.0286133\pi$
$710$	104.906			3.93705
$711$	−18.9090	+	32.7514i	−0.709144	+	1.22827i
$712$	7.69581	+	13.3295i	0.288413	+	0.499545i
$713$	14.9791	+	25.9446i	0.560973	+	0.971634i
$714$	2.90226			0.108614
$715$	−0.706545	+	8.33177i	−0.0264233	+	0.311590i
$716$	−66.7781			−2.49561
$717$	0.354893	+	0.614692i	0.0132537	+	0.0229561i
$718$	−18.1071	−	31.3624i	−0.675750	−	1.17043i
$719$	11.3723	−	19.6973i	0.424113	−	0.734586i	−0.572224	−	0.820098i	$-0.693919\pi$
$719$	11.3723	−	19.6973i	0.424113	−	0.734586i	0.996337	+	0.0855115i	$0.0272524\pi$
$720$	−14.5865			−0.543606
$721$	0.285888	−	0.495173i	0.0106470	−	0.0184412i
$722$	6.61892	−	11.4643i	0.246331	−	0.426657i
$723$	1.17203			0.0435881
$724$	−20.3956	+	35.3263i	−0.757997	+	1.31289i
$725$	23.0481	+	39.9205i	0.855986	+	1.48261i
$726$	6.52582	+	11.3030i	0.242196	+	0.419495i
$727$	18.7274			0.694561			0.347280	−	0.937761i	$-0.387105\pi$
$727$	18.7274			0.694561			0.347280	+	0.937761i	$0.387105\pi$
$728$	−6.72684	+	3.15865i	−0.249313	+	0.117067i
$729$	−12.0322			−0.445638
$730$	22.9818	+	39.8056i	0.850594	+	1.47327i
$731$	3.83001	+	6.63377i	0.141658	+	0.245359i
$732$	−0.490300	+	0.849225i	−0.0181220	+	0.0313883i
$733$	−1.69268			−0.0625206			−0.0312603	−	0.999511i	$-0.509952\pi$
$733$	−1.69268			−0.0625206			−0.0312603	+	0.999511i	$0.509952\pi$
$734$	40.1781	−	69.5904i	1.48300	−	2.56863i
$735$	1.15956	−	2.00841i	0.0427708	−	0.0740813i
$736$	−40.5368			−1.49421
$737$	2.84937	−	4.93525i	0.104958	−	0.181792i
$738$	−18.8419	−	32.6351i	−0.693580	−	1.20132i
$739$	−23.4581	−	40.6305i	−0.862919	−	1.49462i	−0.869099	−	0.494638i	$-0.835301\pi$
$739$	−23.4581	−	40.6305i	−0.862919	−	1.49462i	0.00618065	−	0.999981i	$-0.498033\pi$
$740$	4.07250			0.149708
$741$	5.87141	+	4.08791i	0.215692	+	0.150173i
$742$	−5.90226			−0.216679
$743$	−6.44831	−	11.1688i	−0.236566	−	0.409744i	0.723161	−	0.690680i	$-0.242688\pi$
$743$	−6.44831	−	11.1688i	−0.236566	−	0.409744i	−0.959727	+	0.280936i	$0.909355\pi$
$744$	2.91581	+	5.05034i	0.106899	+	0.185154i
$745$	9.61078	−	16.6464i	0.352112	−	0.609875i
$746$	21.7513			0.796371
$747$	−7.73189	+	13.3920i	−0.282895	+	0.489989i
$748$	−1.91420	+	3.31549i	−0.0699900	+	0.121226i
$749$	−4.07157			−0.148772
$750$	20.1007	−	34.8155i	0.733974	−	1.27128i
$751$	22.8166	+	39.5196i	0.832591	+	1.44209i	0.895977	+	0.444101i	$0.146477\pi$
$751$	22.8166	+	39.5196i	0.832591	+	1.44209i	−0.0633855	+	0.997989i	$0.520190\pi$
$752$	5.25881	+	9.10852i	0.191769	+	0.332154i
$753$	−16.9103			−0.616245
$754$	−26.0753	+	12.2439i	−0.949605	+	0.445896i
$755$	26.7089			0.972038
$756$	−4.58496	−	7.94138i	−0.166753	−	0.288825i
$757$	19.0782	+	33.0445i	0.693410	+	1.20102i	0.970714	+	0.240239i	$0.0772260\pi$
$757$	19.0782	+	33.0445i	0.693410	+	1.20102i	−0.277303	+	0.960782i	$0.589441\pi$
$758$	−14.5028	+	25.1195i	−0.526764	+	0.912382i
$759$	−1.75735			−0.0637876
$760$	−15.7028	+	27.1981i	−0.569602	+	0.986580i
$761$	−21.3672	+	37.0092i	−0.774562	+	1.34158i	0.160478	+	0.987039i	$0.448696\pi$
$761$	−21.3672	+	37.0092i	−0.774562	+	1.34158i	−0.935040	+	0.354542i	$0.884637\pi$
$762$	2.39203			0.0866543
$763$	7.65434	−	13.2577i	0.277106	−	0.479961i
$764$	18.5543	+	32.1370i	0.671271	+	1.16267i
$765$	13.5425	+	23.4562i	0.489628	+	0.848061i
$766$	61.7005			2.22933
$767$	−5.89917	+	2.77001i	−0.213007	+	0.100019i
$768$	−3.76729			−0.135940
$769$	−10.8088	−	18.7215i	−0.389777	−	0.675113i	0.602643	−	0.798011i	$-0.294114\pi$
$769$	−10.8088	−	18.7215i	−0.389777	−	0.675113i	−0.992419	+	0.122898i	$0.960781\pi$
$770$	2.57422	+	4.45868i	0.0927685	+	0.160680i
$771$	0.404912	−	0.701329i	0.0145826	−	0.0252577i
$772$	−12.1674			−0.437915
$773$	−5.00056	+	8.66123i	−0.179858	+	0.311523i	−0.941832	−	0.336085i	$-0.890897\pi$
$773$	−5.00056	+	8.66123i	−0.179858	+	0.311523i	0.761974	+	0.647608i	$0.224230\pi$
$774$	9.64323	−	16.7026i	0.346619	−	0.600361i
$775$	−65.9436			−2.36877
$776$	7.04980	−	12.2106i	0.253073	−	0.438335i
$777$	−0.0905505	−	0.156838i	−0.00324848	−	0.00562653i
$778$	−15.2122	−	26.3484i	−0.545385	−	0.944634i
$779$	22.7169			0.813917
$780$	20.0956	+	13.9914i	0.719540	+	0.500972i
$781$	6.15375			0.220199
$782$	15.3652	+	26.6133i	0.549459	+	0.951691i
$783$	−5.63467	−	9.75954i	−0.201367	−	0.348778i
$784$	0.640570	−	1.10950i	0.0228775	−	0.0396250i
$785$	−68.8285			−2.45659
$786$	3.96515	−	6.86785i	0.141432	−	0.244968i
$787$	−20.8939	+	36.1893i	−0.744787	+	1.29001i	0.205507	+	0.978656i	$0.434116\pi$
$787$	−20.8939	+	36.1893i	−0.744787	+	1.29001i	−0.950294	+	0.311353i	$0.899218\pi$
$788$	−20.0604			−0.714621
$789$	−1.83466	+	3.17772i	−0.0653156	+	0.113130i
$790$	−65.6593	−	113.725i	−2.33605	−	4.04616i
$791$	6.08846	+	10.5455i	0.216481	+	0.374955i
$792$	3.05601			0.108591
$793$	1.98863	−	0.933780i	0.0706183	−	0.0331595i
$794$	17.5646			0.623343
$795$	3.08287	+	5.33968i	0.109338	+	0.189379i
$796$	1.19127	+	2.06334i	0.0422234	+	0.0731331i
$797$	11.3856	−	19.7204i	0.403297	−	0.698531i	−0.590825	−	0.806800i	$-0.701197\pi$
$797$	11.3856	−	19.7204i	0.403297	−	0.698531i	0.994122	+	0.108269i	$0.0345308\pi$
$798$	4.40506			0.155937
$799$	9.76481	−	16.9131i	0.345454	−	0.598344i
$800$	44.6145	−	77.2745i	1.57736	−	2.73207i
$801$	20.1474			0.711874
$802$	18.3642	−	31.8077i	0.648461	−	1.12317i
$803$	1.34811	+	2.33499i	0.0475736	+	0.0824000i
$804$	−8.34419	−	14.4526i	−0.294277	−	0.509703i
$805$	24.5558			0.865478
$806$	3.48216	−	41.0626i	0.122654	−	1.44637i
$807$	4.16325			0.146553
$808$	−5.93516	−	10.2800i	−0.208798	−	0.361649i
$809$	18.7851	+	32.5367i	0.660449	+	1.14393i	0.980498	+	0.196530i	$0.0629672\pi$
$809$	18.7851	+	32.5367i	0.660449	+	1.14393i	−0.320049	+	0.947401i	$0.603699\pi$
$810$	29.8533	−	51.7074i	1.04894	−	1.81681i
$811$	11.5936			0.407106			0.203553	−	0.979064i	$-0.434751\pi$
$811$	11.5936			0.407106			0.203553	+	0.979064i	$0.434751\pi$
$812$	−5.26956	+	9.12714i	−0.184925	+	0.320300i
$813$	−5.65159	+	9.78884i	−0.198210	+	0.343309i
$814$	0.402045			0.0140917
$815$	49.7957	−	86.2487i	1.74427	−	3.02116i
$816$	−0.837429	−	1.45047i	−0.0293159	−	0.0507766i
$817$	5.81321	+	10.0688i	0.203379	+	0.352262i
$818$	57.2359			2.00121
$819$	−0.821977	+	9.69296i	−0.0287222	+	0.338700i
$820$	77.7514			2.71520
$821$	−15.5121	−	26.8678i	−0.541378	−	0.937693i	−0.998825	−	0.0484569i	$-0.984570\pi$
$821$	−15.5121	−	26.8678i	−0.541378	−	0.937693i	0.457448	−	0.889237i	$-0.348764\pi$
$822$	9.30717	+	16.1205i	0.324625	+	0.562267i
$823$	−14.5387	+	25.1818i	−0.506789	+	0.877784i	0.493180	+	0.869927i	$0.335834\pi$
$823$	−14.5387	+	25.1818i	−0.506789	+	0.877784i	−0.999969	+	0.00785682i	$0.997499\pi$
$824$	1.17851			0.0410552
$825$	1.93412	−	3.34999i	0.0673374	−	0.116632i
$826$	−2.00636	+	3.47512i	−0.0698103	+	0.120915i
$827$	14.8920			0.517846			0.258923	−	0.965898i	$-0.416632\pi$
$827$	14.8920			0.517846			0.258923	+	0.965898i	$0.416632\pi$
$828$	22.9873	−	39.8151i	0.798863	−	1.38367i
$829$	2.18594	+	3.78617i	0.0759210	+	0.131499i	0.901486	−	0.432807i	$-0.142477\pi$
$829$	2.18594	+	3.78617i	0.0759210	+	0.131499i	−0.825565	+	0.564306i	$0.809144\pi$
$830$	−26.8481	−	46.5022i	−0.931909	−	1.61411i
$831$	3.13541			0.108766
$832$	38.1806	+	26.5828i	1.32367	+	0.921593i
$833$	−2.37888			−0.0824234
$834$	10.6726	+	18.4856i	0.369563	+	0.640103i
$835$	−37.6219	−	65.1631i	−1.30196	−	2.25506i
$836$	−2.90538	+	5.03227i	−0.100485	+	0.174045i
$837$	16.1215			0.557241
$838$	−26.2928	+	45.5405i	−0.908270	+	1.57317i
$839$	−11.4109	+	19.7643i	−0.393948	+	0.682338i	−0.992966	−	0.118397i	$-0.962224\pi$
$839$	−11.4109	+	19.7643i	−0.393948	+	0.682338i	0.599018	+	0.800735i	$0.295558\pi$
$840$	4.77999			0.164925
$841$	8.02399	−	13.8980i	0.276689	−	0.479240i
$842$	23.1154	+	40.0371i	0.796610	+	1.37977i
$843$	1.75119	+	3.03314i	0.0603140	+	0.104467i
$844$	−40.9202			−1.40853
$845$	−19.0380	−	51.4508i	−0.654928	−	1.76996i
$846$	−49.1718			−1.69056
$847$	−5.34900	−	9.26473i	−0.183794	−	0.318340i
$848$	1.70306	+	2.94979i	0.0584833	+	0.101296i
$849$	−7.42427	+	12.8592i	−0.254800	+	0.441327i
$850$	−67.6433			−2.32015
$851$	0.958790	−	1.66067i	0.0328669	−	0.0569271i
$852$	9.01043	−	15.6065i	0.308692	−	0.534671i
$853$	23.3549			0.799656			0.399828	−	0.916590i	$-0.369070\pi$
$853$	23.3549			0.799656			0.399828	+	0.916590i	$0.369070\pi$
$854$	0.676353	−	1.17148i	0.0231443	−	0.0400871i
$855$	20.5548	+	35.6020i	0.702960	+	1.21756i
$856$	−4.19602	−	7.26771i	−0.143417	−	0.248405i
$857$	−43.5306			−1.48698			−0.743488	−	0.668750i	$-0.766830\pi$
$857$	−43.5306			−1.48698			−0.743488	+	0.668750i	$0.766830\pi$
$858$	1.98388	+	1.38126i	0.0677286	+	0.0471553i
$859$	20.5113			0.699838			0.349919	−	0.936780i	$-0.386209\pi$
$859$	20.5113			0.699838			0.349919	+	0.936780i	$0.386209\pi$
$860$	19.8965	+	34.4617i	0.678464	+	1.17513i
$861$	−1.72877	−	2.99432i	−0.0589163	−	0.102046i
$862$	−22.1451	+	38.3564i	−0.754263	+	1.30642i
$863$	−50.6678			−1.72475			−0.862376	−	0.506268i	$-0.831025\pi$
$863$	−50.6678			−1.72475			−0.862376	+	0.506268i	$0.831025\pi$
$864$	−10.9071	+	18.8916i	−0.371067	+	0.642706i
$865$	−15.9756	+	27.6705i	−0.543186	+	0.940826i
$866$	0.0370334			0.00125845
$867$	3.11621	−	5.39743i	0.105832	−	0.183306i
$868$	−7.53844	−	13.0570i	−0.255871	−	0.443182i
$869$	−3.85156	−	6.67109i	−0.130655	−	0.226301i
$870$	18.5287			0.628181
$871$	−3.15929	+	37.2552i	−0.107048	+	1.26234i
$872$	31.5532			1.06853
$873$	−9.22809	−	15.9835i	−0.312323	−	0.540960i
$874$	23.3214	+	40.3939i	0.788858	+	1.36634i
$875$	−16.4759	+	28.5371i	−0.556987	+	0.964730i
$876$	7.89568			0.266770
$877$	23.5180	−	40.7344i	0.794148	−	1.37550i	−0.129231	−	0.991615i	$-0.541251\pi$
$877$	23.5180	−	40.7344i	0.794148	−	1.37550i	0.923379	−	0.383890i	$-0.125416\pi$
$878$	−14.9806	+	25.9472i	−0.505572	+	0.875677i
$879$	−2.67891			−0.0903573
$880$	1.48555	−	2.57305i	0.0500780	−	0.0867376i
$881$	8.05674	+	13.9547i	0.271439	+	0.470145i	0.969230	−	0.246155i	$-0.0791673\pi$
$881$	8.05674	+	13.9547i	0.271439	+	0.470145i	−0.697792	+	0.716301i	$0.745834\pi$
$882$	2.99478	+	5.18712i	0.100840	+	0.174659i
$883$	42.0733			1.41588			0.707940	−	0.706273i	$-0.249625\pi$
$883$	42.0733			1.41588			0.707940	+	0.706273i	$0.249625\pi$
$884$	2.12240	−	25.0279i	0.0713841	−	0.841779i
$885$	4.19186			0.140908
$886$	16.6623	+	28.8600i	0.559782	+	0.969570i
$887$	20.8814	+	36.1676i	0.701128	+	1.21439i	0.968071	+	0.250678i	$0.0806534\pi$
$887$	20.8814	+	36.1676i	0.701128	+	1.21439i	−0.266942	+	0.963713i	$0.586013\pi$
$888$	0.186636	−	0.323264i	0.00626311	−	0.0108480i
$889$	−1.96067			−0.0657588
$890$	−34.9797	+	60.5866i	−1.17252	+	2.03087i
$891$	1.75119	−	3.03314i	0.0586669	−	0.101614i
$892$	−39.6334			−1.32703
$893$	14.8211	−	25.6709i	0.495969	−	0.859043i
$894$	−2.77848	−	4.81248i	−0.0929264	−	0.160953i
$895$	−48.1151	−	83.3379i	−1.60831	−	2.78568i
$896$	14.7124			0.491506
$897$	10.4365	−	4.90055i	0.348464	−	0.163625i
$898$	−52.7999			−1.76195
$899$	−9.26434	−	16.0463i	−0.308983	−	0.535174i
$900$	50.5992	+	87.6404i	1.68664	+	2.92135i
$901$	3.16233	−	5.47731i	0.105352	−	0.182476i
$902$	7.67577			0.255575
$903$	0.884779	−	1.53248i	0.0294436	−	0.0509978i
$904$	−12.5491	+	21.7357i	−0.417377	+	0.722919i
$905$	−58.7821			−1.95398
$906$	3.86079	−	6.68708i	0.128266	−	0.222163i
$907$	7.71125	+	13.3563i	0.256048	+	0.443488i	0.965180	−	0.261588i	$-0.0842463\pi$
$907$	7.71125	+	13.3563i	0.256048	+	0.443488i	−0.709132	+	0.705076i	$0.750913\pi$
$908$	7.85921	+	13.6125i	0.260817	+	0.451748i
$909$	−15.5381			−0.515366
$910$	−27.7213	−	19.3006i	−0.918951	−	0.639810i
$911$	37.5462			1.24396			0.621981	−	0.783033i	$-0.286328\pi$
$911$	37.5462			1.24396			0.621981	+	0.783033i	$0.286328\pi$
$912$	−1.27105	−	2.20153i	−0.0420888	−	0.0729000i
$913$	−1.57490	−	2.72781i	−0.0521216	−	0.0902773i
$914$	−20.1259	+	34.8590i	−0.665704	+	1.15303i
$915$	−1.41309			−0.0467153
$916$	−4.53776	+	7.85963i	−0.149932	+	0.259689i
$917$	−3.25011	+	5.62935i	−0.107328	+	0.185897i
$918$	16.5370			0.545804
$919$	4.73732	−	8.20528i	0.156270	−	0.270667i	−0.777251	−	0.629191i	$-0.783386\pi$
$919$	4.73732	−	8.20528i	0.156270	−	0.270667i	0.933521	+	0.358524i	$0.116720\pi$
$920$	25.3064	+	43.8319i	0.834326	+	1.44510i
$921$	−4.44476	−	7.69856i	−0.146460	−	0.253676i
$922$	−13.4967			−0.444492
$923$	−36.5458	+	17.1604i	−1.20292	+	0.564842i
$924$	0.884406			0.0290948
$925$	2.11047	+	3.65545i	0.0693919	+	0.120190i
$926$	−5.76413	−	9.98377i	−0.189421	−	0.328087i
$927$	0.771324	−	1.33597i	0.0253336	−	0.0438791i
$928$	25.0713			0.823007
$929$	−17.9220	+	31.0418i	−0.588001	+	1.01845i	0.406493	+	0.913654i	$0.366751\pi$
$929$	−17.9220	+	31.0418i	−0.588001	+	1.01845i	−0.994494	+	0.104793i	$0.966582\pi$
$930$	−13.2532	+	22.9553i	−0.434591	+	0.752733i
$931$	−3.61068			−0.118335
$932$	29.8278	−	51.6633i	0.977043	−	1.69229i
$933$	0.359424	+	0.622541i	0.0117670	+	0.0203811i
$934$	9.65668	+	16.7259i	0.315976	+	0.547287i
$935$	−5.51689			−0.180422
$936$	−18.1490	+	8.52202i	−0.593218	+	0.278551i
$937$	−31.3709			−1.02484			−0.512422	−	0.858734i	$-0.671252\pi$
$937$	−31.3709			−1.02484			−0.512422	+	0.858734i	$0.671252\pi$
$938$	11.5105	+	19.9368i	0.375832	+	0.650960i
$939$	−3.62643	−	6.28116i	−0.118344	−	0.204978i
$940$	50.7270	−	87.8618i	1.65453	−	2.86574i
$941$	44.7844			1.45993			0.729964	−	0.683486i	$-0.239537\pi$
$941$	44.7844			1.45993			0.729964	+	0.683486i	$0.239537\pi$
$942$	−9.94919	+	17.2325i	−0.324162	+	0.561465i
$943$	18.3050	−	31.7052i	0.596093	−	1.03246i
$944$	2.31570			0.0753695
$945$	6.60714	−	11.4439i	0.214930	−	0.372270i
$946$	1.96422	+	3.40212i	0.0638622	+	0.110613i
$947$	17.5337	+	30.3692i	0.569768	+	0.986868i	0.996588	+	0.0825312i	$0.0263004\pi$
$947$	17.5337	+	30.3692i	0.569768	+	0.986868i	−0.426820	+	0.904337i	$0.640366\pi$
$948$	−22.5581			−0.732652
$949$	−14.5175	−	10.1076i	−0.471257	−	0.328108i
$950$	−102.669			−3.33104
$951$	2.21896	+	3.84334i	0.0719546	+	0.124629i
$952$	−2.45160	−	4.24629i	−0.0794567	−	0.137623i
$953$	−29.4852	+	51.0699i	−0.955120	+	1.65432i	−0.221027	+	0.975268i	$0.570941\pi$
$953$	−29.4852	+	51.0699i	−0.955120	+	1.65432i	−0.734093	+	0.679048i	$0.762393\pi$
$954$	−15.9242			−0.515567
$955$	−26.7376	+	46.3108i	−0.865208	+	1.49858i
$956$	1.89114	−	3.27556i	0.0611640	−	0.105939i
$957$	1.08689			0.0351341
$958$	−26.8830	+	46.5627i	−0.868550	+	1.50437i
$959$	−7.62878	−	13.2134i	−0.246346	−	0.426684i
$960$	−14.9620	−	25.9149i	−0.482895	−	0.836399i
$961$	−4.49354			−0.144953
$962$	−2.38766	+	1.12115i	−0.0769812	+	0.0361472i
$963$	−10.9851			−0.353989
$964$	−3.12273	−	5.40873i	−0.100576	−	0.174204i
$965$	−8.76690	−	15.1847i	−0.282217	−	0.488813i
$966$	3.54955	−	6.14800i	0.114205	−	0.197809i
$967$	30.3671			0.976540			0.488270	−	0.872693i	$-0.337628\pi$
$967$	30.3671			0.976540			0.488270	+	0.872693i	$0.337628\pi$
$968$	11.0250	−	19.0958i	0.354357	−	0.613764i
$969$	−2.36016	+	4.08791i	−0.0758191	+	0.131323i
$970$	64.0868			2.05770
$971$	24.7588	−	42.8834i	0.794546	−	1.37619i	−0.128581	−	0.991699i	$-0.541042\pi$
$971$	24.7588	−	42.8834i	0.794546	−	1.37619i	0.923127	−	0.384495i	$-0.125625\pi$
$972$	−18.8831	−	32.7065i	−0.605676	−	1.04906i
$973$	−8.74801	−	15.1520i	−0.280448	−	0.485751i
$974$	3.93815			0.126186
$975$	−2.14449	+	25.2884i	−0.0686786	+	0.809876i
$976$	−0.780630			−0.0249874
$977$	5.43356	+	9.41120i	0.173835	+	0.301091i	0.939757	−	0.341842i	$-0.111051\pi$
$977$	5.43356	+	9.41120i	0.173835	+	0.301091i	−0.765923	+	0.642933i	$0.777717\pi$
$978$	−14.3960	−	24.9346i	−0.460333	−	0.797320i
$979$	−2.05190	+	3.55400i	−0.0655790	+	0.113586i
$980$	−12.3580			−0.394762
$981$	20.6514	−	35.7692i	0.659347	−	1.14202i
$982$	7.42555	−	12.8614i	0.236959	−	0.410425i
$983$	2.34833			0.0749001			0.0374501	−	0.999299i	$-0.488076\pi$
$983$	2.34833			0.0749001			0.0374501	+	0.999299i	$0.488076\pi$
$984$	3.56322	−	6.17169i	0.113591	−	0.196746i
$985$	−14.4539	−	25.0350i	−0.460541	−	0.797680i
$986$	−9.50312	−	16.4599i	−0.302641	−	0.524190i
$987$	−4.51158			−0.143605
$988$	3.22139	−	37.9875i	0.102486	−	1.20854i
$989$	18.7369			0.595799
$990$	6.94523	+	12.0295i	0.220734	+	0.382322i
$991$	−12.2408	−	21.2016i	−0.388841	−	0.673492i	0.603453	−	0.797398i	$-0.293791\pi$
$991$	−12.2408	−	21.2016i	−0.388841	−	0.673492i	−0.992294	+	0.123907i	$0.960458\pi$
$992$	−17.9331	+	31.0610i	−0.569375	+	0.986187i
$993$	−8.21311			−0.260635
$994$	−12.4296	+	21.5287i	−0.394242	+	0.682848i
$995$	−1.71667	+	2.97336i	−0.0544222	+	0.0942620i
$996$	−9.22399			−0.292273
$997$	3.31171	−	5.73604i	0.104883	−	0.181662i	−0.808808	−	0.588073i	$-0.799887\pi$
$997$	3.31171	−	5.73604i	0.104883	−	0.181662i	0.913690	+	0.406411i	$0.133220\pi$
$998$	−27.3491	−	47.3700i	−0.865720	−	1.49947i
$999$	−0.515956	−	0.893662i	−0.0163241	−	0.0282742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.f.c.29.1	yes	8
3.2	odd	2		819.2.o.h.757.4		8
4.3	odd	2		1456.2.s.q.1121.2		8
7.2	even	3		637.2.g.k.263.1		8
7.3	odd	6		637.2.h.i.471.4		8
7.4	even	3		637.2.h.h.471.4		8
7.5	odd	6		637.2.g.j.263.1		8
7.6	odd	2		637.2.f.i.393.1		8
13.2	odd	12		1183.2.c.g.337.2		8
13.3	even	3		1183.2.a.k.1.4		4
13.9	even	3	inner	91.2.f.c.22.1	✓	8
13.10	even	6		1183.2.a.l.1.1		4
13.11	odd	12		1183.2.c.g.337.7		8
39.35	odd	6		819.2.o.h.568.4		8
52.35	odd	6		1456.2.s.q.113.2		8
91.9	even	3		637.2.h.h.165.4		8
91.48	odd	6		637.2.f.i.295.1		8
91.55	odd	6		8281.2.a.bp.1.4		4
91.61	odd	6		637.2.h.i.165.4		8
91.62	odd	6		8281.2.a.bt.1.1		4
91.74	even	3		637.2.g.k.373.1		8
91.87	odd	6		637.2.g.j.373.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.1	✓	8	13.9	even	3	inner
91.2.f.c.29.1	yes	8	1.1	even	1	trivial
637.2.f.i.295.1		8	91.48	odd	6
637.2.f.i.393.1		8	7.6	odd	2
637.2.g.j.263.1		8	7.5	odd	6
637.2.g.j.373.1		8	91.87	odd	6
637.2.g.k.263.1		8	7.2	even	3
637.2.g.k.373.1		8	91.74	even	3
637.2.h.h.165.4		8	91.9	even	3
637.2.h.h.471.4		8	7.4	even	3
637.2.h.i.165.4		8	91.61	odd	6
637.2.h.i.471.4		8	7.3	odd	6
819.2.o.h.568.4		8	39.35	odd	6
819.2.o.h.757.4		8	3.2	odd	2
1183.2.a.k.1.4		4	13.3	even	3
1183.2.a.l.1.1		4	13.10	even	6
1183.2.c.g.337.2		8	13.2	odd	12
1183.2.c.g.337.7		8	13.11	odd	12
1456.2.s.q.113.2		8	52.35	odd	6
1456.2.s.q.1121.2		8	4.3	odd	2
8281.2.a.bp.1.4		4	91.55	odd	6
8281.2.a.bt.1.1		4	91.62	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11000 - 1.92258i) q^{2} +(-0.274776 - 0.475925i) q^{3} +(-1.46422 + 2.53610i) q^{4} -4.22001 q^{5} +(-0.610004 + 1.05656i) q^{6} +(0.500000 - 0.866025i) q^{7} +2.06113 q^{8} +(1.34900 - 2.33653i) q^{9} +O(q^{10})\)	\(q+(-1.11000 - 1.92258i) q^{2} +(-0.274776 - 0.475925i) q^{3} +(-1.46422 + 2.53610i) q^{4} -4.22001 q^{5} +(-0.610004 + 1.05656i) q^{6} +(0.500000 - 0.866025i) q^{7} +2.06113 q^{8} +(1.34900 - 2.33653i) q^{9} +(4.68423 + 8.11332i) q^{10} +(0.274776 + 0.475925i) q^{11} +1.60932 q^{12} +(-2.95900 - 2.06017i) q^{13} -2.22001 q^{14} +(1.15956 + 2.00841i) q^{15} +(0.640570 + 1.10950i) q^{16} +(1.18944 - 2.06017i) q^{17} -5.98957 q^{18} +(1.80534 - 3.12694i) q^{19} +(6.17901 - 10.7024i) q^{20} -0.549551 q^{21} +(0.610004 - 1.05656i) q^{22} +(-2.90945 - 5.03931i) q^{23} +(-0.566349 - 0.980945i) q^{24} +12.8085 q^{25} +(-0.676353 + 7.97573i) q^{26} -3.13134 q^{27} +(1.46422 + 2.53610i) q^{28} +(1.79945 + 3.11673i) q^{29} +(2.57422 - 4.45868i) q^{30} -5.14844 q^{31} +(3.48320 - 6.03308i) q^{32} +(0.151003 - 0.261545i) q^{33} -5.28114 q^{34} +(-2.11000 + 3.65463i) q^{35} +(3.95045 + 6.84238i) q^{36} +(0.164772 + 0.285393i) q^{37} -8.01574 q^{38} +(-0.167428 + 1.97435i) q^{39} -8.69799 q^{40} +(3.14579 + 5.44866i) q^{41} +(0.610004 + 1.05656i) q^{42} +(-1.61000 + 2.78861i) q^{43} -1.60932 q^{44} +(-5.69278 + 9.86018i) q^{45} +(-6.45900 + 11.1873i) q^{46} +8.20957 q^{47} +(0.352026 - 0.609727i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-14.2174 - 24.6253i) q^{50} -1.30732 q^{51} +(9.55742 - 4.48778i) q^{52} +2.65866 q^{53} +(3.47580 + 6.02026i) q^{54} +(-1.15956 - 2.00841i) q^{55} +(1.03057 - 1.78499i) q^{56} -1.98426 q^{57} +(3.99478 - 6.91917i) q^{58} +(0.903765 - 1.56537i) q^{59} -6.79136 q^{60} +(-0.304662 + 0.527691i) q^{61} +(5.71479 + 9.89831i) q^{62} +(-1.34900 - 2.33653i) q^{63} -12.9032 q^{64} +(12.4870 + 8.69395i) q^{65} -0.670457 q^{66} +(-5.18490 - 8.98052i) q^{67} +(3.48320 + 6.03308i) q^{68} +(-1.59889 + 2.76936i) q^{69} +9.36845 q^{70} +(5.59889 - 9.69756i) q^{71} +(2.78046 - 4.81590i) q^{72} +4.90621 q^{73} +(0.365794 - 0.633574i) q^{74} +(-3.51945 - 6.09587i) q^{75} +(5.28682 + 9.15705i) q^{76} +0.549551 q^{77} +(3.98169 - 1.86964i) q^{78} -14.0171 q^{79} +(-2.70321 - 4.68210i) q^{80} +(-3.18657 - 5.51931i) q^{81} +(6.98367 - 12.0961i) q^{82} -5.73159 q^{83} +(0.804662 - 1.39372i) q^{84} +(-5.01945 + 8.69395i) q^{85} +7.14844 q^{86} +(0.988887 - 1.71280i) q^{87} +(0.566349 + 0.980945i) q^{88} +(3.73378 + 6.46709i) q^{89} +25.2760 q^{90} +(-3.26366 + 1.53248i) q^{91} +17.0403 q^{92} +(1.41467 + 2.45027i) q^{93} +(-9.11266 - 15.7836i) q^{94} +(-7.61856 + 13.1957i) q^{95} -3.82840 q^{96} +(3.42035 - 5.92422i) q^{97} +(-1.11000 + 1.92258i) q^{98} +1.48269 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9	\( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 3 q^{15} - 19 q^{16} + 4 q^{17} - 6 q^{18} - q^{19} + 2 q^{20} - 2 q^{21} - 5 q^{22} + 2 q^{23} + 3 q^{24} + 10 q^{25} + 12 q^{26} - 52 q^{27} + 5 q^{28} - q^{29} + 4 q^{30} - 8 q^{31} + 33 q^{32} + 19 q^{33} + 6 q^{34} - 7 q^{35} + 34 q^{36} + 10 q^{37} - 46 q^{38} + 20 q^{39} - 34 q^{40} + 22 q^{41} - 5 q^{42} - 3 q^{43} - 24 q^{44} + 11 q^{45} - 24 q^{46} + 4 q^{47} - 11 q^{48} - 4 q^{49} - 43 q^{50} + 14 q^{51} + 65 q^{52} + 4 q^{53} - 5 q^{54} + 3 q^{55} - 6 q^{56} - 34 q^{57} + 11 q^{58} + 8 q^{59} - 22 q^{60} - 8 q^{61} + 5 q^{62} + 7 q^{63} + 28 q^{64} + 7 q^{65} + 12 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 22 q^{70} + 14 q^{71} - 5 q^{72} - 16 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} + 2 q^{77} - q^{78} - 52 q^{79} - 7 q^{80} - 24 q^{81} + 14 q^{82} + 12 q^{84} - 5 q^{85} + 24 q^{86} - 13 q^{87} - 3 q^{88} + q^{89} + 52 q^{90} - 4 q^{91} + 24 q^{92} + 7 q^{93} - 33 q^{94} - 21 q^{95} - 116 q^{96} - 3 q^{97} + q^{98} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9 + 11 * q^10 + q^11 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 3 * q^15 - 19 * q^16 + 4 * q^17 - 6 * q^18 - q^19 + 2 * q^20 - 2 * q^21 - 5 * q^22 + 2 * q^23 + 3 * q^24 + 10 * q^25 + 12 * q^26 - 52 * q^27 + 5 * q^28 - q^29 + 4 * q^30 - 8 * q^31 + 33 * q^32 + 19 * q^33 + 6 * q^34 - 7 * q^35 + 34 * q^36 + 10 * q^37 - 46 * q^38 + 20 * q^39 - 34 * q^40 + 22 * q^41 - 5 * q^42 - 3 * q^43 - 24 * q^44 + 11 * q^45 - 24 * q^46 + 4 * q^47 - 11 * q^48 - 4 * q^49 - 43 * q^50 + 14 * q^51 + 65 * q^52 + 4 * q^53 - 5 * q^54 + 3 * q^55 - 6 * q^56 - 34 * q^57 + 11 * q^58 + 8 * q^59 - 22 * q^60 - 8 * q^61 + 5 * q^62 + 7 * q^63 + 28 * q^64 + 7 * q^65 + 12 * q^66 + 6 * q^67 + 33 * q^68 + 18 * q^69 + 22 * q^70 + 14 * q^71 - 5 * q^72 - 16 * q^73 - 20 * q^74 + 7 * q^75 - 32 * q^76 + 2 * q^77 - q^78 - 52 * q^79 - 7 * q^80 - 24 * q^81 + 14 * q^82 + 12 * q^84 - 5 * q^85 + 24 * q^86 - 13 * q^87 - 3 * q^88 + q^89 + 52 * q^90 - 4 * q^91 + 24 * q^92 + 7 * q^93 - 33 * q^94 - 21 * q^95 - 116 * q^96 - 3 * q^97 + q^98 + 46 * q^99

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