LMFDB - Embedded newform 91.2.f.c.22.1

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			22.1
Root			$-1.11000 + 1.92258i$ of defining polynomial
Character	$\chi$	$=$	91.22
Dual form			91.2.f.c.29.1

$q$-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 $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.11000	+	1.92258i	−0.784891	+	1.35947i	0.144173	+	0.989553i	$0.453948\pi$
$2$	−1.11000	+	1.92258i	−0.784891	+	1.35947i	−0.929064	+	0.369919i	$0.879385\pi$
$3$	−0.274776	+	0.475925i	−0.158642	+	0.274776i	−0.934379	−	0.356280i	$-0.884045\pi$
$3$	−0.274776	+	0.475925i	−0.158642	+	0.274776i	0.775737	+	0.631056i	$0.217378\pi$
$4$	−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	−0.821624	−	0.570030i	$-0.806932\pi$
$11$	0.274776	−	0.475925i	0.0828480	−	0.143497i	0.904472	+	0.426533i	$0.140265\pi$
$12$	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	0.973448	−	0.228910i	$-0.0735161\pi$
$17$	1.18944	+	2.06017i	0.288482	+	0.499665i	−0.684966	+	0.728575i	$0.740183\pi$
$18$	−5.98957			−1.41175
$19$	1.80534	+	3.12694i	0.414174	+	0.717370i	0.995341	−	0.0964139i	$-0.0307372\pi$
$19$	1.80534	+	3.12694i	0.414174	+	0.717370i	−0.581168	+	0.813784i	$0.697404\pi$
$20$	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	0.385124	+	0.922865i	$0.374159\pi$
$23$	−2.90945	+	5.03931i	−0.606662	+	1.05077i	−0.991786	+	0.127905i	$0.959175\pi$
$24$	−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	−0.649172	−	0.760641i	$-0.724885\pi$
$29$	1.79945	−	3.11673i	0.334149	−	0.578762i	0.983321	+	0.181879i	$0.0582179\pi$
$30$	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	−0.852163	−	0.523276i	$-0.824710\pi$
$37$	0.164772	−	0.285393i	0.0270883	−	0.0469183i	0.879252	+	0.476357i	$0.158043\pi$
$38$	−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	−0.508660	−	0.860967i	$-0.669859\pi$
$41$	3.14579	−	5.44866i	0.491289	−	0.850938i	0.999950	+	0.0100292i	$0.00319244\pi$
$42$	0.610004	−	1.05656i	0.0941256	−	0.163030i
$43$	−1.61000	−	2.78861i	−0.245523	−	0.425259i	0.716755	−	0.697325i	$-0.245626\pi$
$43$	−1.61000	−	2.78861i	−0.245523	−	0.425259i	−0.962279	+	0.272066i	$0.912293\pi$
$44$	−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	0.918840	−	0.394630i	$-0.129127\pi$
$59$	0.903765	+	1.56537i	0.117660	+	0.203793i	−0.801180	+	0.598424i	$0.795794\pi$
$60$	−6.79136			−0.876761
$61$	−0.304662	−	0.527691i	−0.0390080	−	0.0675639i	0.845862	−	0.533401i	$-0.179086\pi$
$61$	−0.304662	−	0.527691i	−0.0390080	−	0.0675639i	−0.884870	+	0.465838i	$0.845753\pi$
$62$	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	0.353407	+	0.935470i	$0.385023\pi$
$67$	−5.18490	+	8.98052i	−0.633437	+	1.09714i	−0.986844	+	0.161675i	$0.948310\pi$
$68$	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	0.979430	+	0.201785i	$0.0646743\pi$
$71$	5.59889	+	9.69756i	0.664466	+	1.15089i	−0.314964	+	0.949104i	$0.601992\pi$
$72$	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	−0.597421	−	0.801928i	$-0.703808\pi$
$89$	3.73378	−	6.46709i	0.395779	−	0.685510i	0.993200	+	0.116418i	$0.0371411\pi$
$90$	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	0.985766	−	0.168123i	$-0.0537706\pi$
$97$	3.42035	+	5.92422i	0.347284	+	0.601514i	−0.638482	+	0.769637i	$0.720437\pi$
$98$	−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	−0.972978	−	0.230896i	$-0.925834\pi$
$101$	−2.87956	+	4.98755i	−0.286527	+	0.496280i	0.686451	+	0.727176i	$0.259168\pi$
$102$	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	−0.947491	−	0.319782i	$-0.896390\pi$
$107$	−2.03578	+	3.52608i	−0.196807	+	0.340879i	0.750685	+	0.660661i	$0.229724\pi$
$108$	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	−0.996282	−	0.0861558i	$-0.972542\pi$
$113$	−6.08846	−	10.5455i	−0.572754	−	0.992039i	0.423528	−	0.905883i	$-0.360792\pi$
$114$	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	−0.906238	−	0.422768i	$-0.861058\pi$
$127$	−0.980336	+	1.69799i	−0.0869907	+	0.150672i	0.819247	+	0.573441i	$0.194392\pi$
$128$	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	0.982693	+	0.185242i	$0.0593068\pi$
$137$	7.62878	+	13.2134i	0.651770	+	1.12890i	−0.330923	+	0.943658i	$0.607360\pi$
$138$	7.09910			0.604316
$139$	8.74801	+	15.1520i	0.741997	+	1.28518i	0.951585	+	0.307386i	$0.0994544\pi$
$139$	8.74801	+	15.1520i	0.741997	+	1.28518i	−0.209588	+	0.977790i	$0.567212\pi$
$140$	−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	0.757531	−	0.652799i	$-0.226405\pi$
$149$	−2.27743	−	3.94463i	−0.186574	−	0.323156i	−0.944106	+	0.329642i	$0.893072\pi$
$150$	−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	−0.792778	−	0.609511i	$-0.791366\pi$
$163$	−11.7999	−	20.4381i	−0.924241	−	1.60083i	−0.131463	−	0.991321i	$-0.541967\pi$
$164$	−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	−0.282005	−	0.959413i	$-0.590999\pi$
$167$	8.91513	−	15.4415i	0.689874	−	1.19490i	0.971878	−	0.235483i	$-0.0756673\pi$
$168$	−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	0.973289	−	0.229583i	$-0.0737363\pi$
$173$	3.78568	+	6.55699i	0.287820	+	0.498518i	−0.685469	+	0.728101i	$0.740403\pi$
$174$	−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	−0.0270166	−	0.999635i	$-0.508601\pi$
$179$	11.4017	−	19.7483i	0.852201	−	1.47606i	0.879218	−	0.476420i	$-0.158066\pi$
$180$	−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	0.998879	−	0.0473305i	$-0.0150714\pi$
$191$	6.33591	+	10.9741i	0.458450	+	0.794059i	−0.540429	+	0.841390i	$0.681738\pi$
$192$	3.54548	−	6.14096i	0.255873	−	0.443185i
$193$	2.07746	−	3.59827i	0.149539	−	0.259009i	−0.781518	−	0.623882i	$-0.785554\pi$
$193$	2.07746	−	3.59827i	0.149539	−	0.259009i	0.931057	+	0.364873i	$0.118888\pi$
$194$	−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	−0.717830	−	0.696219i	$-0.754864\pi$
$197$	3.42510	−	5.93245i	0.244028	−	0.422669i	0.961858	+	0.273549i	$0.0881977\pi$
$198$	−1.64579	+	2.85059i	−0.116961	+	0.202582i
$199$	0.406794	+	0.704587i	0.0288368	+	0.0499469i	0.880084	−	0.474819i	$-0.157486\pi$
$199$	0.406794	+	0.704587i	0.0288368	+	0.0499469i	−0.851247	+	0.524766i	$0.824153\pi$
$200$	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	−0.518778	−	0.854909i	$-0.673613\pi$
$211$	6.98670	−	12.1013i	0.480984	−	0.833089i	0.999762	+	0.0218200i	$0.00694608\pi$
$212$	−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	−0.545428	−	0.838158i	$-0.683633\pi$
$223$	6.76700	−	11.7208i	0.453152	−	0.784882i	0.998580	+	0.0532758i	$0.0169662\pi$
$224$	−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	0.941239	−	0.337741i	$-0.109663\pi$
$227$	2.68376	+	4.64840i	0.178127	+	0.308525i	−0.763112	+	0.646266i	$0.776329\pi$
$228$	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	0.829635	−	0.558306i	$-0.188548\pi$
$241$	−1.06635	−	1.84697i	−0.0686896	−	0.118974i	−0.898325	+	0.439332i	$0.855215\pi$
$242$	−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	0.692164	+	0.721741i	$0.256658\pi$
$251$	15.3856	+	26.6486i	0.971128	+	1.68204i	0.278964	+	0.960302i	$0.410009\pi$
$252$	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	−0.842130	−	0.539275i	$-0.818698\pi$
$257$	0.736805	−	1.27618i	0.0459607	−	0.0796062i	0.888091	+	0.459669i	$0.152032\pi$
$258$	−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	−0.950406	−	0.311012i	$-0.899332\pi$
$263$	−3.33847	+	5.78240i	−0.205859	+	0.356558i	0.744547	+	0.667570i	$0.232665\pi$
$264$	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	0.727138	−	0.686492i	$-0.240850\pi$
$269$	−3.78786	−	6.56077i	−0.230950	−	0.400017i	−0.958088	+	0.286474i	$0.907517\pi$
$270$	−14.6679	+	25.4055i	−0.892660	+	1.54613i
$271$	−10.2840	+	17.8124i	−0.624709	+	1.08203i	0.363888	+	0.931443i	$0.381449\pi$
$271$	−10.2840	+	17.8124i	−0.624709	+	1.08203i	−0.988597	+	0.150585i	$0.951884\pi$
$272$	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	0.767508	−	0.641039i	$-0.221497\pi$
$277$	−2.85271	−	4.94103i	−0.171402	−	0.296878i	−0.938910	+	0.344162i	$0.888163\pi$
$278$	−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	0.114519	+	0.993421i	$0.463467\pi$
$283$	−13.5097	+	23.3995i	−0.803068	+	1.39096i	−0.917587	+	0.397534i	$0.869866\pi$
$284$	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	0.928397	−	0.371590i	$-0.121187\pi$
$293$	2.43736	+	4.22163i	0.142392	+	0.246630i	−0.786005	+	0.618220i	$0.787854\pi$
$294$	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	0.994970	−	0.100177i	$-0.0319409\pi$
$331$	7.47256	+	12.9429i	0.410729	+	0.711403i	−0.584241	+	0.811580i	$0.698608\pi$
$332$	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	0.914029	−	0.405648i	$-0.132954\pi$
$347$	1.96922	+	3.41079i	0.105713	+	0.183101i	−0.808316	+	0.588749i	$0.799621\pi$
$348$	2.89589	−	5.01583i	0.155236	−	0.268877i
$349$	−8.58883	+	14.8763i	−0.459750	+	0.796310i	−0.998947	−	0.0458695i	$-0.985394\pi$
$349$	−8.58883	+	14.8763i	−0.459750	+	0.796310i	0.539198	+	0.842179i	$0.318728\pi$
$350$	−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	−0.515587	−	0.856837i	$-0.672426\pi$
$353$	9.09821	−	15.7586i	0.484249	−	0.838744i	0.999836	+	0.0180932i	$0.00575957\pi$
$354$	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	0.188398	−	0.982093i	$-0.439671\pi$
$367$	18.0982	−	31.3469i	0.944716	−	1.63630i	0.756319	−	0.654203i	$-0.226996\pi$
$368$	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	0.710873	−	0.703320i	$-0.248300\pi$
$373$	−4.89892	−	8.48518i	−0.253657	−	0.439346i	−0.964530	+	0.263974i	$0.914967\pi$
$374$	−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	−0.983593	−	0.180401i	$-0.942261\pi$
$379$	−6.53275	+	11.3151i	−0.335565	+	0.581216i	0.648028	+	0.761616i	$0.275594\pi$
$380$	−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	−0.964828	−	0.262881i	$-0.915327\pi$
$383$	−13.8965	−	24.0694i	−0.710076	−	1.22989i	0.254753	−	0.967006i	$-0.418006\pi$
$384$	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	0.749512	−	0.661991i	$-0.230288\pi$
$397$	−3.95597	−	6.85194i	−0.198545	−	0.343889i	−0.948057	+	0.318101i	$0.896955\pi$
$398$	−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	−0.582136	−	0.813092i	$-0.697783\pi$
$401$	8.27212	−	14.3277i	0.413090	−	0.715493i	0.995226	+	0.0975987i	$0.0311162\pi$
$402$	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	−0.985998	−	0.166758i	$-0.946670\pi$
$409$	−12.8909	−	22.3278i	−0.637416	−	1.10404i	0.348582	−	0.937278i	$-0.386663\pi$
$410$	−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	0.417044	+	0.908886i	$0.363066\pi$
$419$	−11.8436	+	20.5137i	−0.578596	+	1.00216i	−0.995641	+	0.0932720i	$0.970267\pi$
$420$	−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	−0.999749	−	0.0223845i	$-0.992874\pi$
$431$	−9.97521	+	17.2776i	−0.480489	+	0.832232i	0.519260	+	0.854616i	$0.326208\pi$
$432$	−2.00584	+	3.47422i	−0.0965061	+	0.167153i
$433$	−0.00834083	−	0.0144467i	−0.000400835	−	0.000694266i	0.865825	−	0.500347i	$-0.166794\pi$
$433$	−0.00834083	−	0.0144467i	−0.000400835	−	0.000694266i	−0.866226	+	0.499653i	$0.833461\pi$
$434$	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	−0.980914	−	0.194442i	$-0.937710\pi$
$439$	−6.74801	+	11.6879i	−0.322065	+	0.557833i	0.658849	+	0.752275i	$0.271044\pi$
$440$	−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	0.997391	+	0.0721852i	$0.0229973\pi$
$449$	11.8918	+	20.5972i	0.561210	+	0.972044i	−0.436181	+	0.899859i	$0.643669\pi$
$450$	−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	−0.996333	−	0.0855548i	$-0.972734\pi$
$457$	−9.06567	+	15.7022i	−0.424074	+	0.734518i	0.572259	+	0.820073i	$0.306067\pi$
$458$	−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	0.928091	−	0.372354i	$-0.121449\pi$
$461$	3.03980	+	5.26508i	0.141577	+	0.245219i	−0.786513	+	0.617573i	$0.788116\pi$
$462$	−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	0.444741	+	0.895659i	$0.353296\pi$
$479$	−12.1094	+	20.9741i	−0.553294	+	0.958332i	−0.998034	+	0.0626730i	$0.980037\pi$
$480$	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	0.845229	−	0.534404i	$-0.179464\pi$
$487$	−0.886967	−	1.53627i	−0.0401923	−	0.0696151i	−0.885422	+	0.464788i	$0.846130\pi$
$488$	−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	−0.780627	−	0.624997i	$-0.785100\pi$
$491$	3.34483	−	5.79342i	0.150950	−	0.261453i	0.931577	+	0.363544i	$0.118433\pi$
$492$	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	−0.952975	−	0.303049i	$-0.901995\pi$
$503$	−16.5726	−	28.7046i	−0.738936	−	1.27987i	0.214039	−	0.976825i	$-0.431338\pi$
$504$	−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	−0.377778	−	0.925896i	$-0.623312\pi$
$509$	13.8290	−	23.9526i	0.612961	−	1.06168i	0.990739	−	0.135783i	$-0.0433549\pi$
$510$	−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	−0.826933	−	0.562301i	$-0.809916\pi$
$523$	1.68089	−	2.91139i	0.0735002	−	0.127306i	0.900433	+	0.434995i	$0.143250\pi$
$524$	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	0.362409	+	0.932019i	$0.381954\pi$
$557$	−14.7729	+	25.5874i	−0.625948	+	1.08417i	−0.988357	+	0.152154i	$0.951379\pi$
$558$	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	0.789804	−	0.613360i	$-0.210182\pi$
$563$	−3.23368	−	5.60090i	−0.136283	−	0.236050i	−0.926087	+	0.377310i	$0.876849\pi$
$564$	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	−0.998675	−	0.0514697i	$-0.983609\pi$
$569$	−10.8478	+	18.7889i	−0.454763	+	0.787673i	0.543911	+	0.839143i	$0.316943\pi$
$570$	−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	−0.932135	−	0.362110i	$-0.882056\pi$
$587$	−3.69407	+	6.39832i	−0.152471	+	0.264087i	0.779664	+	0.626198i	$0.215390\pi$
$588$	−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	0.235070	−	0.971978i	$-0.424468\pi$
$601$	23.5174	−	40.7333i	0.959293	−	1.66154i	0.724223	−	0.689566i	$-0.242199\pi$
$602$	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	0.995922	+	0.0902211i	$0.0287574\pi$
$607$	14.1935	+	24.5838i	0.576095	+	0.997825i	−0.419827	+	0.907604i	$0.637909\pi$
$608$	−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	0.238878	−	0.971050i	$-0.423220\pi$
$613$	23.7782	−	41.1851i	0.960393	−	1.66345i	0.721514	−	0.692399i	$-0.243446\pi$
$614$	−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	0.982878	−	0.184259i	$-0.0589885\pi$
$617$	8.24338	+	14.2780i	0.331866	+	0.574809i	−0.651012	+	0.759068i	$0.725655\pi$
$618$	−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	0.704352	−	0.709851i	$-0.251238\pi$
$631$	−6.59577	−	11.4242i	−0.262573	−	0.454790i	−0.966925	+	0.255061i	$0.917905\pi$
$632$	−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	0.780918	+	0.624634i	$0.214752\pi$
$641$	23.5814	+	40.8441i	0.931408	+	1.61325i	0.150490	+	0.988612i	$0.451915\pi$
$642$	4.96734			0.196045
$643$	1.40679	+	2.43664i	0.0554785	+	0.0960916i	0.892431	−	0.451184i	$-0.148998\pi$
$643$	1.40679	+	2.43664i	0.0554785	+	0.0960916i	−0.836952	+	0.547276i	$0.815665\pi$
$644$	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	0.489268	+	0.872134i	$0.337264\pi$
$647$	−12.9891	+	22.4979i	−0.510656	+	0.884482i	−0.999924	+	0.0123485i	$0.996069\pi$
$648$	−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	−0.474353	−	0.880335i	$-0.657318\pi$
$653$	13.4213	−	23.2464i	0.525216	−	0.909700i	0.999569	−	0.0293654i	$-0.00934865\pi$
$654$	−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	0.673562	−	0.739131i	$-0.264764\pi$
$659$	−7.78666	−	13.4869i	−0.303325	−	0.525375i	−0.976887	+	0.213756i	$0.931430\pi$
$660$	−1.86610	+	3.23218i	−0.0726379	+	0.125812i
$661$	−16.6902	+	28.9083i	−0.649174	+	1.12440i	0.334146	+	0.942521i	$0.391552\pi$
$661$	−16.6902	+	28.9083i	−0.649174	+	1.12440i	−0.983320	+	0.181881i	$0.941781\pi$
$662$	−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	−0.874139	−	0.485675i	$-0.838574\pi$
$673$	−0.427076	+	0.739717i	−0.0164626	+	0.0285140i	0.857677	+	0.514189i	$0.171907\pi$
$674$	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	0.903146	+	0.429334i	$0.141252\pi$
$683$	21.5186	+	37.2714i	0.823387	+	1.42615i	−0.0797583	+	0.996814i	$0.525415\pi$
$684$	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	−0.508837	−	0.860863i	$-0.669925\pi$
$691$	12.9098	−	22.3604i	0.491110	−	0.850628i	0.999948	+	0.0102348i	$0.00325788\pi$
$692$	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	0.995963	−	0.0897702i	$-0.0286133\pi$
$709$	11.1897	+	19.3811i	0.420238	+	0.727874i	−0.575725	+	0.817644i	$0.695280\pi$
$710$	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	0.996337	−	0.0855115i	$-0.0272524\pi$
$719$	11.3723	+	19.6973i	0.424113	+	0.734586i	−0.572224	+	0.820098i	$0.693919\pi$
$720$	−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	0.00618065	+	0.999981i	$0.498033\pi$
$739$	−23.4581	+	40.6305i	−0.862919	+	1.49462i	−0.869099	+	0.494638i	$0.835301\pi$
$740$	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	−0.959727	−	0.280936i	$-0.909355\pi$
$743$	−6.44831	+	11.1688i	−0.236566	+	0.409744i	0.723161	+	0.690680i	$0.242688\pi$
$744$	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	−0.0633855	−	0.997989i	$-0.520190\pi$
$751$	22.8166	−	39.5196i	0.832591	−	1.44209i	0.895977	−	0.444101i	$-0.146477\pi$
$752$	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	−0.277303	−	0.960782i	$-0.589441\pi$
$757$	19.0782	−	33.0445i	0.693410	−	1.20102i	0.970714	−	0.240239i	$-0.0772260\pi$
$758$	−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	−0.935040	−	0.354542i	$-0.884637\pi$
$761$	−21.3672	−	37.0092i	−0.774562	−	1.34158i	0.160478	−	0.987039i	$-0.448696\pi$
$762$	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	−0.992419	−

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

Introduction

L-functions

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